TSTP Solution File: SYN076-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN076-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 23:53:34 EDT 2022
% Result : Unsatisfiable 27.28s 17.52s
% Output : Proof 30.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : SYN076-1 : TPTP v8.1.0. Released v1.0.0.
% 0.02/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.30 % Computer : n005.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Mon Sep 5 01:36:33 EDT 2022
% 0.10/0.30 % CPUTime :
% 0.10/0.30 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.10/0.30 Usage: tptp [options] [-file:]file
% 0.10/0.30 -h, -? prints this message.
% 0.10/0.30 -smt2 print SMT-LIB2 benchmark.
% 0.10/0.30 -m, -model generate model.
% 0.10/0.30 -p, -proof generate proof.
% 0.10/0.30 -c, -core generate unsat core of named formulas.
% 0.10/0.30 -st, -statistics display statistics.
% 0.10/0.30 -t:timeout set timeout (in second).
% 0.10/0.30 -smt2status display status in smt2 format instead of SZS.
% 0.10/0.30 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.10/0.30 -<param>:<value> configuration parameter and value.
% 0.10/0.30 -o:<output-file> file to place output in.
% 27.28/17.52 % SZS status Unsatisfiable
% 27.28/17.52 % SZS output start Proof
% 27.28/17.52 tff(c1_type, type, (
% 27.28/17.52 c1: $i)).
% 27.28/17.52 tff(c2_type, type, (
% 27.28/17.52 c2: $i)).
% 27.28/17.52 tff(f2_type, type, (
% 27.28/17.52 f2: $i > $i)).
% 27.28/17.52 tff(c4_type, type, (
% 27.28/17.52 c4: $i)).
% 27.28/17.52 tff(f4_type, type, (
% 27.28/17.52 f4: $i > $i)).
% 27.28/17.52 tff(big_f_type, type, (
% 27.28/17.52 big_f: ( $i * $i ) > $o)).
% 27.28/17.52 tff(f6_type, type, (
% 27.28/17.52 f6: ( $i * $i ) > $i)).
% 27.28/17.52 tff(f7_type, type, (
% 27.28/17.52 f7: $i > $i)).
% 27.28/17.52 tff(f9_type, type, (
% 27.28/17.52 f9: ( $i * $i ) > $i)).
% 27.28/17.52 tff(f10_type, type, (
% 27.28/17.52 f10: $i > $i)).
% 27.28/17.52 tff(f8_type, type, (
% 27.28/17.52 f8: $i > $i)).
% 27.28/17.52 tff(f3_type, type, (
% 27.28/17.52 f3: ( $i * $i ) > $i)).
% 27.28/17.52 tff(c3_type, type, (
% 27.28/17.52 c3: $i)).
% 27.28/17.52 tff(f1_type, type, (
% 27.28/17.52 f1: ( $i * $i ) > $i)).
% 27.28/17.52 tff(f5_type, type, (
% 27.28/17.52 f5: $i > $i)).
% 27.28/17.52 tff(1,plain,
% 27.28/17.52 ((c1 = c2) <=> (c2 = c1)),
% 27.28/17.52 inference(commutativity,[status(thm)],[])).
% 27.28/17.52 tff(2,assumption,(~big_f(c2, c1)), introduced(assumption)).
% 27.28/17.52 tff(3,assumption,(~(f10(c1) = c1)), introduced(assumption)).
% 27.28/17.52 tff(4,plain,
% 27.28/17.52 (![X1: $i] : ((X1 = c1) | (X1 = c2)) <=> ![X1: $i] : ((X1 = c1) | (X1 = c2))),
% 27.28/17.52 inference(rewrite,[status(thm)],[])).
% 27.28/17.52 tff(5,plain,
% 27.28/17.52 (^[X1: $i] : rewrite(((X1 = c2) | (X1 = c1)) <=> ((X1 = c1) | (X1 = c2)))),
% 27.28/17.52 inference(bind,[status(th)],[])).
% 27.28/17.52 tff(6,plain,
% 27.28/17.52 (![X1: $i] : ((X1 = c2) | (X1 = c1)) <=> ![X1: $i] : ((X1 = c1) | (X1 = c2))),
% 27.28/17.52 inference(quant_intro,[status(thm)],[5])).
% 27.28/17.52 tff(7,axiom,(![X1: $i] : ((X1 = c2) | (X1 = c1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_2')).
% 27.28/17.52 tff(8,plain,
% 27.28/17.52 (![X1: $i] : ((X1 = c1) | (X1 = c2))),
% 27.28/17.52 inference(modus_ponens,[status(thm)],[7, 6])).
% 27.28/17.52 tff(9,plain,
% 27.28/17.52 (![X1: $i] : ((X1 = c1) | (X1 = c2))),
% 27.28/17.52 inference(modus_ponens,[status(thm)],[8, 4])).
% 27.28/17.52 tff(10,plain,(
% 27.28/17.52 ![X1: $i] : ((X1 = c1) | (X1 = c2))),
% 27.28/17.52 inference(skolemize,[status(sab)],[9])).
% 27.28/17.52 tff(11,plain,
% 27.28/17.52 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f10(c1) = c1) | (f10(c1) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f10(c1) = c1) | (f10(c1) = c2))),
% 27.28/17.52 inference(rewrite,[status(thm)],[])).
% 27.28/17.52 tff(12,plain,
% 27.28/17.52 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f10(c1) = c1) | (f10(c1) = c2))),
% 27.28/17.52 inference(quant_inst,[status(thm)],[])).
% 27.28/17.52 tff(13,plain,
% 27.28/17.52 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f10(c1) = c1) | (f10(c1) = c2)),
% 27.28/17.52 inference(modus_ponens,[status(thm)],[12, 11])).
% 27.28/17.52 tff(14,plain,
% 27.28/17.52 ((f10(c1) = c1) | (f10(c1) = c2)),
% 27.28/17.52 inference(unit_resolution,[status(thm)],[13, 10])).
% 27.28/17.52 tff(15,plain,
% 27.28/17.52 (f10(c1) = c2),
% 27.28/17.52 inference(unit_resolution,[status(thm)],[14, 3])).
% 27.28/17.52 tff(16,assumption,(f10(c1) = c2), introduced(assumption)).
% 27.28/17.52 tff(17,assumption,(~(f7(c2) = c2)), introduced(assumption)).
% 27.28/17.52 tff(18,plain,
% 27.28/17.52 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f7(c2) = c1) | (f7(c2) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f7(c2) = c1) | (f7(c2) = c2))),
% 27.28/17.52 inference(rewrite,[status(thm)],[])).
% 27.28/17.52 tff(19,plain,
% 27.28/17.52 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f7(c2) = c1) | (f7(c2) = c2))),
% 27.28/17.52 inference(quant_inst,[status(thm)],[])).
% 27.28/17.52 tff(20,plain,
% 27.28/17.52 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f7(c2) = c1) | (f7(c2) = c2)),
% 27.28/17.52 inference(modus_ponens,[status(thm)],[19, 18])).
% 27.28/17.52 tff(21,plain,
% 27.28/17.52 ((f7(c2) = c1) | (f7(c2) = c2)),
% 27.28/17.52 inference(unit_resolution,[status(thm)],[20, 10])).
% 27.28/17.52 tff(22,plain,
% 27.28/17.52 (f7(c2) = c1),
% 27.28/17.52 inference(unit_resolution,[status(thm)],[21, 17])).
% 27.28/17.52 tff(23,plain,
% 27.28/17.52 (f10(f7(c2)) = f10(c1)),
% 27.28/17.52 inference(monotonicity,[status(thm)],[22])).
% 27.28/17.52 tff(24,plain,
% 27.28/17.52 (f10(f7(c2)) = c2),
% 27.28/17.52 inference(transitivity,[status(thm)],[23, 16])).
% 27.28/17.52 tff(25,plain,
% 27.28/17.52 (big_f(f7(c2), f10(f7(c2))) <=> big_f(c1, c2)),
% 27.28/17.52 inference(monotonicity,[status(thm)],[22, 24])).
% 27.28/17.52 tff(26,plain,
% 27.28/17.52 (big_f(c1, c2) <=> big_f(f7(c2), f10(f7(c2)))),
% 27.28/17.52 inference(symmetry,[status(thm)],[25])).
% 27.28/17.52 tff(27,assumption,(~big_f(c1, c2)), introduced(assumption)).
% 27.28/17.52 tff(28,assumption,(~(f6(c1, c1) = c1)), introduced(assumption)).
% 27.28/17.52 tff(29,assumption,(f6(c1, f6(c1, c2)) = c1), introduced(assumption)).
% 27.28/17.52 tff(30,plain,
% 27.28/17.52 ((c1 = f6(c1, c2)) <=> (f6(c1, c2) = c1)),
% 27.28/17.52 inference(commutativity,[status(thm)],[])).
% 27.28/17.52 tff(31,plain,
% 27.28/17.52 ((f6(c1, f6(c1, c2)) = f6(c1, c2)) <=> (c1 = f6(c1, c2))),
% 27.28/17.52 inference(monotonicity,[status(thm)],[29])).
% 27.34/17.52 tff(32,plain,
% 27.34/17.52 ((f6(c1, f6(c1, c2)) = f6(c1, c2)) <=> (f6(c1, c2) = c1)),
% 27.34/17.52 inference(transitivity,[status(thm)],[31, 30])).
% 27.34/17.52 tff(33,plain,
% 27.34/17.52 ((~(f6(c1, f6(c1, c2)) = f6(c1, c2))) <=> (~(f6(c1, c2) = c1))),
% 27.34/17.52 inference(monotonicity,[status(thm)],[32])).
% 27.34/17.52 tff(34,assumption,(~(f6(c1, f6(c1, c2)) = f6(c1, c2))), introduced(assumption)).
% 27.34/17.52 tff(35,plain,
% 27.34/17.52 (~(f6(c1, c2) = c1)),
% 27.34/17.52 inference(modus_ponens,[status(thm)],[34, 33])).
% 27.34/17.52 tff(36,assumption,(f6(c1, c2) = c2), introduced(assumption)).
% 27.34/17.52 tff(37,plain,
% 27.34/17.52 ((f6(c1, f6(c1, c2)) = f6(c1, c2)) <=> (f6(c1, f6(c1, c2)) = c2)),
% 27.34/17.52 inference(monotonicity,[status(thm)],[36])).
% 27.34/17.52 tff(38,plain,
% 27.34/17.52 ((f6(c1, f6(c1, c2)) = c2) <=> (f6(c1, f6(c1, c2)) = f6(c1, c2))),
% 27.34/17.52 inference(symmetry,[status(thm)],[37])).
% 27.34/17.52 tff(39,plain,
% 27.34/17.52 (f6(c1, f6(c1, c2)) = f6(c1, c2)),
% 27.34/17.52 inference(monotonicity,[status(thm)],[36])).
% 27.34/17.52 tff(40,plain,
% 27.34/17.52 (f6(c1, f6(c1, c2)) = c2),
% 27.34/17.52 inference(transitivity,[status(thm)],[39, 36])).
% 27.34/17.52 tff(41,plain,
% 27.34/17.52 (f6(c1, f6(c1, c2)) = f6(c1, c2)),
% 27.34/17.52 inference(modus_ponens,[status(thm)],[40, 38])).
% 27.34/17.52 tff(42,plain,
% 27.34/17.52 ($false),
% 27.34/17.52 inference(unit_resolution,[status(thm)],[34, 41])).
% 27.34/17.52 tff(43,plain,((~(f6(c1, c2) = c2)) | (f6(c1, f6(c1, c2)) = f6(c1, c2))), inference(lemma,lemma(discharge,[]))).
% 27.34/17.52 tff(44,plain,
% 27.34/17.52 (~(f6(c1, c2) = c2)),
% 27.34/17.52 inference(unit_resolution,[status(thm)],[43, 34])).
% 27.34/17.52 tff(45,plain,
% 27.34/17.52 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f6(c1, c2) = c1) | (f6(c1, c2) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f6(c1, c2) = c1) | (f6(c1, c2) = c2))),
% 27.34/17.52 inference(rewrite,[status(thm)],[])).
% 27.34/17.52 tff(46,plain,
% 27.34/17.52 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f6(c1, c2) = c1) | (f6(c1, c2) = c2))),
% 27.34/17.52 inference(quant_inst,[status(thm)],[])).
% 27.34/17.52 tff(47,plain,
% 27.34/17.52 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f6(c1, c2) = c1) | (f6(c1, c2) = c2)),
% 27.34/17.52 inference(modus_ponens,[status(thm)],[46, 45])).
% 27.34/17.52 tff(48,plain,
% 27.34/17.52 ((f6(c1, c2) = c1) | (f6(c1, c2) = c2)),
% 27.34/17.52 inference(unit_resolution,[status(thm)],[47, 10])).
% 27.34/17.52 tff(49,plain,
% 27.34/17.52 (f6(c1, c2) = c1),
% 27.34/17.52 inference(unit_resolution,[status(thm)],[48, 44])).
% 27.34/17.52 tff(50,plain,
% 27.34/17.52 ($false),
% 27.34/17.52 inference(unit_resolution,[status(thm)],[49, 35])).
% 27.34/17.52 tff(51,plain,((f6(c1, f6(c1, c2)) = f6(c1, c2)) | (~(f6(c1, f6(c1, c2)) = c1))), inference(lemma,lemma(discharge,[]))).
% 27.34/17.52 tff(52,plain,
% 27.34/17.52 (f6(c1, f6(c1, c2)) = f6(c1, c2)),
% 27.34/17.52 inference(unit_resolution,[status(thm)],[51, 29])).
% 27.34/17.52 tff(53,plain,
% 27.34/17.52 (c1 = f6(c1, f6(c1, c2))),
% 27.34/17.52 inference(symmetry,[status(thm)],[29])).
% 27.34/17.52 tff(54,plain,
% 27.34/17.52 (c1 = f6(c1, c2)),
% 27.34/17.52 inference(transitivity,[status(thm)],[53, 52])).
% 27.34/17.52 tff(55,plain,
% 27.34/17.52 (f6(c1, c1) = f6(c1, f6(c1, c2))),
% 27.34/17.52 inference(monotonicity,[status(thm)],[54])).
% 27.34/17.52 tff(56,plain,
% 27.34/17.52 (f6(c1, c1) = c1),
% 27.34/17.52 inference(transitivity,[status(thm)],[55, 29])).
% 27.34/17.52 tff(57,plain,
% 27.34/17.52 ($false),
% 27.34/17.52 inference(unit_resolution,[status(thm)],[28, 56])).
% 27.34/17.52 tff(58,plain,((~(f6(c1, f6(c1, c2)) = c1)) | (f6(c1, c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 27.34/17.52 tff(59,plain,
% 27.34/17.52 (~(f6(c1, f6(c1, c2)) = c1)),
% 27.34/17.52 inference(unit_resolution,[status(thm)],[58, 28])).
% 27.34/17.52 tff(60,plain,
% 27.34/17.52 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f6(c1, f6(c1, c2)) = c1) | (f6(c1, f6(c1, c2)) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f6(c1, f6(c1, c2)) = c1) | (f6(c1, f6(c1, c2)) = c2))),
% 27.34/17.52 inference(rewrite,[status(thm)],[])).
% 27.34/17.52 tff(61,plain,
% 27.34/17.52 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f6(c1, f6(c1, c2)) = c1) | (f6(c1, f6(c1, c2)) = c2))),
% 27.34/17.52 inference(quant_inst,[status(thm)],[])).
% 27.34/17.52 tff(62,plain,
% 27.34/17.52 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f6(c1, f6(c1, c2)) = c1) | (f6(c1, f6(c1, c2)) = c2)),
% 27.34/17.52 inference(modus_ponens,[status(thm)],[61, 60])).
% 27.34/17.52 tff(63,plain,
% 27.34/17.52 ((f6(c1, f6(c1, c2)) = c1) | (f6(c1, f6(c1, c2)) = c2)),
% 27.34/17.52 inference(unit_resolution,[status(thm)],[62, 10])).
% 27.34/17.52 tff(64,plain,
% 27.34/17.52 (f6(c1, f6(c1, c2)) = c2),
% 27.34/17.52 inference(unit_resolution,[status(thm)],[63, 59])).
% 27.34/17.52 tff(65,assumption,(~big_f(f7(c1), f6(c1, c1))), introduced(assumption)).
% 27.34/17.52 tff(66,assumption,(~big_f(c1, c1)), introduced(assumption)).
% 27.34/17.52 tff(67,assumption,(c3 = c2), introduced(assumption)).
% 27.34/17.52 tff(68,plain,
% 27.34/17.52 ((c3 = c1) <=> (c1 = c3)),
% 27.34/17.52 inference(commutativity,[status(thm)],[])).
% 27.34/17.52 tff(69,plain,
% 27.34/17.52 (c2 = c3),
% 27.34/17.52 inference(symmetry,[status(thm)],[67])).
% 27.34/17.52 tff(70,plain,
% 27.34/17.52 ((c2 = c1) <=> (c3 = c1)),
% 27.34/17.52 inference(monotonicity,[status(thm)],[69])).
% 27.34/17.52 tff(71,plain,
% 27.34/17.52 ((c2 = c1) <=> (c1 = c3)),
% 27.34/17.52 inference(transitivity,[status(thm)],[70, 68])).
% 27.34/17.52 tff(72,plain,
% 27.34/17.52 ((~(c2 = c1)) <=> (~(c1 = c3))),
% 27.34/17.52 inference(monotonicity,[status(thm)],[71])).
% 27.34/17.52 tff(73,plain,
% 27.34/17.52 ((~(c2 = c1)) <=> (~(c2 = c1))),
% 27.34/17.52 inference(rewrite,[status(thm)],[])).
% 27.34/17.52 tff(74,axiom,(~(c2 = c1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_1')).
% 27.34/17.52 tff(75,plain,
% 27.34/17.52 (~(c2 = c1)),
% 27.34/17.52 inference(modus_ponens,[status(thm)],[74, 73])).
% 27.34/17.52 tff(76,plain,
% 27.34/17.52 (~(c1 = c3)),
% 27.34/17.52 inference(modus_ponens,[status(thm)],[75, 72])).
% 27.34/17.52 tff(77,assumption,(f7(c2) = c2), introduced(assumption)).
% 27.34/17.52 tff(78,plain,
% 27.34/17.52 ((c3 = c2) <=> (c2 = c3)),
% 27.34/17.52 inference(commutativity,[status(thm)],[])).
% 27.34/17.52 tff(79,assumption,(f4(c4) = c2), introduced(assumption)).
% 27.34/17.52 tff(80,plain,
% 27.34/17.52 (f7(f4(c4)) = f7(c2)),
% 27.34/17.52 inference(monotonicity,[status(thm)],[79])).
% 27.34/17.52 tff(81,plain,
% 27.34/17.52 (f7(c2) = f7(f4(c4))),
% 27.34/17.52 inference(symmetry,[status(thm)],[80])).
% 27.34/17.52 tff(82,plain,
% 27.34/17.52 (c2 = f7(c2)),
% 27.34/17.52 inference(symmetry,[status(thm)],[77])).
% 27.34/17.52 tff(83,plain,
% 27.34/17.52 (c2 = f7(f4(c4))),
% 27.34/17.52 inference(transitivity,[status(thm)],[82, 81])).
% 27.34/17.52 tff(84,plain,
% 27.34/17.52 (f6(c2, c2) = f6(c2, f7(f4(c4)))),
% 27.34/17.52 inference(monotonicity,[status(thm)],[83])).
% 27.34/17.52 tff(85,plain,
% 27.34/17.52 (f6(c2, f7(f4(c4))) = f6(c2, c2)),
% 27.34/17.52 inference(symmetry,[status(thm)],[84])).
% 27.34/17.52 tff(86,plain,
% 27.34/17.52 ((f6(c2, f7(f4(c4))) = c2) <=> (f6(c2, c2) = c2)),
% 27.34/17.52 inference(monotonicity,[status(thm)],[85])).
% 27.34/17.52 tff(87,plain,
% 27.34/17.52 ((f6(c2, c2) = c2) <=> (f6(c2, f7(f4(c4))) = c2)),
% 27.34/17.52 inference(symmetry,[status(thm)],[86])).
% 27.34/17.52 tff(88,plain,
% 27.34/17.52 ((~(f6(c2, c2) = c2)) <=> (~(f6(c2, f7(f4(c4))) = c2))),
% 27.34/17.52 inference(monotonicity,[status(thm)],[87])).
% 27.34/17.52 tff(89,assumption,(~(f10(c2) = c2)), introduced(assumption)).
% 27.34/17.52 tff(90,plain,
% 27.34/17.52 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f10(c2) = c1) | (f10(c2) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f10(c2) = c1) | (f10(c2) = c2))),
% 27.34/17.52 inference(rewrite,[status(thm)],[])).
% 27.34/17.52 tff(91,plain,
% 27.34/17.52 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f10(c2) = c1) | (f10(c2) = c2))),
% 27.34/17.52 inference(quant_inst,[status(thm)],[])).
% 27.34/17.52 tff(92,plain,
% 27.34/17.52 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f10(c2) = c1) | (f10(c2) = c2)),
% 27.34/17.52 inference(modus_ponens,[status(thm)],[91, 90])).
% 27.34/17.52 tff(93,plain,
% 27.34/17.52 ((f10(c2) = c1) | (f10(c2) = c2)),
% 27.34/17.52 inference(unit_resolution,[status(thm)],[92, 10])).
% 27.34/17.52 tff(94,plain,
% 27.34/17.52 (f10(c2) = c1),
% 27.34/17.52 inference(unit_resolution,[status(thm)],[93, 89])).
% 27.34/17.52 tff(95,plain,
% 27.34/17.52 (f10(f7(c2)) = f10(c2)),
% 27.34/17.52 inference(monotonicity,[status(thm)],[77])).
% 27.34/17.52 tff(96,plain,
% 27.34/17.52 (f10(c2) = f10(f7(c2))),
% 27.34/17.52 inference(symmetry,[status(thm)],[95])).
% 27.34/17.52 tff(97,plain,
% 27.34/17.52 (big_f(c2, f10(c2)) <=> big_f(c2, f10(f7(c2)))),
% 27.34/17.52 inference(monotonicity,[status(thm)],[96])).
% 27.34/17.52 tff(98,plain,
% 27.34/17.52 (big_f(c2, f10(f7(c2))) <=> big_f(c2, f10(c2))),
% 27.34/17.52 inference(symmetry,[status(thm)],[97])).
% 27.34/17.52 tff(99,plain,
% 27.34/17.52 (c1 = f10(c2)),
% 27.34/17.52 inference(symmetry,[status(thm)],[94])).
% 27.34/17.52 tff(100,plain,
% 27.34/17.52 (c1 = f10(f7(c2))),
% 27.34/17.52 inference(transitivity,[status(thm)],[99, 96])).
% 27.34/17.52 tff(101,plain,
% 27.34/17.52 (big_f(c2, c1) <=> big_f(c2, f10(f7(c2)))),
% 27.34/17.52 inference(monotonicity,[status(thm)],[100])).
% 27.34/17.52 tff(102,plain,
% 27.34/17.52 (big_f(c2, c1) <=> big_f(c2, f10(c2))),
% 27.34/17.52 inference(transitivity,[status(thm)],[101, 98])).
% 27.34/17.52 tff(103,plain,
% 27.34/17.52 ((~big_f(c2, c1)) <=> (~big_f(c2, f10(c2)))),
% 27.34/17.52 inference(monotonicity,[status(thm)],[102])).
% 27.34/17.52 tff(104,plain,
% 27.34/17.52 (~big_f(c2, f10(c2))),
% 27.34/17.52 inference(modus_ponens,[status(thm)],[2, 103])).
% 27.34/17.52 tff(105,plain,
% 27.34/17.52 ((f8(f7(f4(c4))) = c2) <=> (c2 = f8(f7(f4(c4))))),
% 27.34/17.52 inference(commutativity,[status(thm)],[])).
% 27.34/17.52 tff(106,plain,
% 27.34/17.52 ((c2 = f8(f7(f4(c4)))) <=> (f8(f7(f4(c4))) = c2)),
% 27.34/17.52 inference(symmetry,[status(thm)],[105])).
% 27.34/17.52 tff(107,plain,
% 27.34/17.52 (f8(f7(f4(c4))) = f8(f7(c2))),
% 27.34/17.52 inference(monotonicity,[status(thm)],[80])).
% 27.34/17.52 tff(108,plain,
% 27.34/17.52 (f8(f7(c2)) = f8(f7(f4(c4)))),
% 27.34/17.52 inference(symmetry,[status(thm)],[107])).
% 27.34/17.53 tff(109,plain,
% 27.34/17.53 ((c2 = f8(f7(c2))) <=> (c2 = f8(f7(f4(c4))))),
% 27.34/17.53 inference(monotonicity,[status(thm)],[108])).
% 27.34/17.53 tff(110,plain,
% 27.34/17.53 (f8(c2) = f8(f7(c2))),
% 27.34/17.53 inference(monotonicity,[status(thm)],[82])).
% 27.34/17.53 tff(111,plain,
% 27.34/17.53 ((c2 = f8(c2)) <=> (c2 = f8(f7(c2)))),
% 27.34/17.53 inference(monotonicity,[status(thm)],[110])).
% 27.34/17.53 tff(112,plain,
% 27.34/17.53 ((c2 = f8(c2)) <=> (f8(f7(f4(c4))) = c2)),
% 27.34/17.53 inference(transitivity,[status(thm)],[111, 109, 106])).
% 27.34/17.53 tff(113,plain,
% 27.34/17.53 ((~(c2 = f8(c2))) <=> (~(f8(f7(f4(c4))) = c2))),
% 27.34/17.53 inference(monotonicity,[status(thm)],[112])).
% 27.34/17.53 tff(114,assumption,(~(f6(c1, c2) = c2)), introduced(assumption)).
% 27.34/17.53 tff(115,assumption,(~(f7(c1) = c1)), introduced(assumption)).
% 27.34/17.53 tff(116,plain,
% 27.34/17.53 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f7(c1) = c1) | (f7(c1) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f7(c1) = c1) | (f7(c1) = c2))),
% 27.34/17.53 inference(rewrite,[status(thm)],[])).
% 27.34/17.53 tff(117,plain,
% 27.34/17.53 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f7(c1) = c1) | (f7(c1) = c2))),
% 27.34/17.53 inference(quant_inst,[status(thm)],[])).
% 27.34/17.53 tff(118,plain,
% 27.34/17.53 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f7(c1) = c1) | (f7(c1) = c2)),
% 27.34/17.53 inference(modus_ponens,[status(thm)],[117, 116])).
% 27.34/17.53 tff(119,plain,
% 27.34/17.53 ((f7(c1) = c1) | (f7(c1) = c2)),
% 27.34/17.53 inference(unit_resolution,[status(thm)],[118, 10])).
% 27.34/17.53 tff(120,plain,
% 27.34/17.53 (f7(c1) = c2),
% 27.34/17.53 inference(unit_resolution,[status(thm)],[119, 115])).
% 27.34/17.53 tff(121,assumption,(~big_f(c2, c2)), introduced(assumption)).
% 27.34/17.53 tff(122,assumption,(f10(c2) = c2), introduced(assumption)).
% 27.34/17.53 tff(123,plain,
% 27.34/17.53 (big_f(f7(c2), f7(c2)) <=> big_f(c1, c1)),
% 27.34/17.53 inference(monotonicity,[status(thm)],[22, 22])).
% 27.34/17.53 tff(124,plain,
% 27.34/17.53 ((~big_f(f7(c2), f7(c2))) <=> (~big_f(c1, c1))),
% 27.34/17.53 inference(monotonicity,[status(thm)],[123])).
% 27.34/17.53 tff(125,plain,
% 27.34/17.53 (c1 = f7(c2)),
% 27.34/17.53 inference(symmetry,[status(thm)],[22])).
% 27.34/17.53 tff(126,plain,
% 27.34/17.53 (big_f(c1, c2) <=> big_f(f7(c2), c2)),
% 27.34/17.53 inference(monotonicity,[status(thm)],[125])).
% 27.34/17.53 tff(127,plain,
% 27.34/17.53 ((c2 = c3) <=> (c3 = c2)),
% 27.34/17.53 inference(symmetry,[status(thm)],[78])).
% 27.34/17.53 tff(128,plain,
% 27.34/17.53 ((c1 = f5(c1)) <=> (f5(c1) = c1)),
% 27.34/17.53 inference(commutativity,[status(thm)],[])).
% 27.34/17.53 tff(129,plain,
% 27.34/17.53 (big_f(f9(c2, c2), f10(c2)) <=> big_f(f9(c2, c2), c2)),
% 27.34/17.53 inference(monotonicity,[status(thm)],[122])).
% 27.34/17.53 tff(130,plain,
% 27.34/17.53 (big_f(f9(c2, c2), c2) <=> big_f(f9(c2, c2), f10(c2))),
% 27.34/17.53 inference(symmetry,[status(thm)],[129])).
% 27.34/17.53 tff(131,assumption,(~(f9(f10(c2), f4(c4)) = c2)), introduced(assumption)).
% 27.34/17.53 tff(132,plain,
% 27.34/17.53 (f9(f10(c2), f4(c4)) = f9(c2, c2)),
% 27.34/17.53 inference(monotonicity,[status(thm)],[122, 79])).
% 27.34/17.53 tff(133,plain,
% 27.34/17.53 ((f9(f10(c2), f4(c4)) = c2) <=> (f9(c2, c2) = c2)),
% 27.34/17.53 inference(monotonicity,[status(thm)],[132])).
% 27.34/17.53 tff(134,plain,
% 27.34/17.53 ((f9(c2, c2) = c2) <=> (f9(f10(c2), f4(c4)) = c2)),
% 27.34/17.53 inference(symmetry,[status(thm)],[133])).
% 27.34/17.53 tff(135,plain,
% 27.34/17.53 (f9(f10(c2), f10(c2)) = f9(c2, c2)),
% 27.34/17.53 inference(monotonicity,[status(thm)],[122, 122])).
% 27.34/17.53 tff(136,plain,
% 27.34/17.53 ((f9(f10(c2), f10(c2)) = f10(c2)) <=> (f9(c2, c2) = c2)),
% 27.34/17.53 inference(monotonicity,[status(thm)],[135, 122])).
% 27.34/17.53 tff(137,plain,
% 27.34/17.53 ((f9(f10(c2), f10(c2)) = f10(c2)) <=> (f9(f10(c2), f4(c4)) = c2)),
% 27.34/17.53 inference(transitivity,[status(thm)],[136, 134])).
% 27.34/17.53 tff(138,assumption,(f9(f10(c2), f10(c2)) = f10(c2)), introduced(assumption)).
% 27.34/17.53 tff(139,plain,
% 27.34/17.53 (f9(f10(c2), f4(c4)) = c2),
% 27.34/17.53 inference(modus_ponens,[status(thm)],[138, 137])).
% 27.34/17.53 tff(140,plain,
% 27.34/17.53 ($false),
% 27.34/17.53 inference(unit_resolution,[status(thm)],[131, 139])).
% 27.34/17.53 tff(141,plain,((f9(f10(c2), f4(c4)) = c2) | (~(f9(f10(c2), f10(c2)) = f10(c2))) | (~(f4(c4) = c2)) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.34/17.53 tff(142,plain,
% 27.34/17.53 (~(f9(f10(c2), f10(c2)) = f10(c2))),
% 27.34/17.53 inference(unit_resolution,[status(thm)],[141, 131, 79, 122])).
% 27.34/17.53 tff(143,plain,
% 27.34/17.53 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f9(f10(c2), f4(c4)) = c1) | (f9(f10(c2), f4(c4)) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f9(f10(c2), f4(c4)) = c1) | (f9(f10(c2), f4(c4)) = c2))),
% 27.34/17.53 inference(rewrite,[status(thm)],[])).
% 27.34/17.53 tff(144,plain,
% 27.34/17.53 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f9(f10(c2), f4(c4)) = c1) | (f9(f10(c2), f4(c4)) = c2))),
% 27.34/17.53 inference(quant_inst,[status(thm)],[])).
% 27.34/17.53 tff(145,plain,
% 27.34/17.53 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f9(f10(c2), f4(c4)) = c1) | (f9(f10(c2), f4(c4)) = c2)),
% 27.34/17.53 inference(modus_ponens,[status(thm)],[144, 143])).
% 27.34/17.53 tff(146,plain,
% 27.34/17.53 ((f9(f10(c2), f4(c4)) = c1) | (f9(f10(c2), f4(c4)) = c2)),
% 27.34/17.53 inference(unit_resolution,[status(thm)],[145, 10])).
% 27.34/17.53 tff(147,plain,
% 27.34/17.53 (f9(f10(c2), f4(c4)) = c1),
% 27.34/17.53 inference(unit_resolution,[status(thm)],[146, 131])).
% 27.34/17.53 tff(148,assumption,(f9(f10(c2), f4(c4)) = c1), introduced(assumption)).
% 27.34/17.53 tff(149,plain,
% 27.34/17.53 (c1 = f9(f10(c2), f4(c4))),
% 27.34/17.53 inference(symmetry,[status(thm)],[148])).
% 27.34/17.53 tff(150,plain,
% 27.34/17.53 (c1 = f9(c2, c2)),
% 27.34/17.53 inference(transitivity,[status(thm)],[149, 132])).
% 27.34/17.53 tff(151,plain,
% 27.34/17.53 (f5(c1) = f5(f9(c2, c2))),
% 27.34/17.53 inference(monotonicity,[status(thm)],[150])).
% 27.34/17.53 tff(152,plain,
% 27.34/17.53 (f5(f9(c2, c2)) = f5(c1)),
% 27.34/17.53 inference(symmetry,[status(thm)],[151])).
% 27.34/17.53 tff(153,plain,
% 27.34/17.53 ((c2 = f5(f9(c2, c2))) <=> (c2 = f5(c1))),
% 27.34/17.53 inference(monotonicity,[status(thm)],[152])).
% 27.34/17.53 tff(154,plain,
% 27.34/17.53 ((c2 = f5(c1)) <=> (c2 = f5(f9(c2, c2)))),
% 27.34/17.53 inference(symmetry,[status(thm)],[153])).
% 27.34/17.53 tff(155,plain,
% 27.34/17.53 ((f5(c1) = c2) <=> (c2 = f5(c1))),
% 27.34/17.53 inference(commutativity,[status(thm)],[])).
% 27.34/17.53 tff(156,plain,
% 27.34/17.53 ((f5(c1) = c2) <=> (c2 = f5(f9(c2, c2)))),
% 27.34/17.53 inference(transitivity,[status(thm)],[155, 154])).
% 27.34/17.53 tff(157,plain,
% 27.34/17.53 ((~(f5(c1) = c2)) <=> (~(c2 = f5(f9(c2, c2))))),
% 27.34/17.53 inference(monotonicity,[status(thm)],[156])).
% 27.34/17.53 tff(158,assumption,(~(f9(f10(c2), f10(c2)) = f10(c2))), introduced(assumption)).
% 27.34/17.53 tff(159,plain,
% 27.34/17.53 ((c4 = c2) <=> (c2 = c4)),
% 27.34/17.53 inference(commutativity,[status(thm)],[])).
% 27.34/17.53 tff(160,plain,
% 27.34/17.53 (f9(c2, c2) = f9(f10(c2), f4(c4))),
% 27.34/17.53 inference(symmetry,[status(thm)],[132])).
% 27.34/17.53 tff(161,plain,
% 27.34/17.53 (f9(c2, c2) = c1),
% 27.34/17.53 inference(transitivity,[status(thm)],[160, 148])).
% 27.34/17.53 tff(162,plain,
% 27.34/17.53 (f5(f9(c2, c2)) = f5(c1)),
% 27.34/17.53 inference(monotonicity,[status(thm)],[161])).
% 27.34/17.53 tff(163,plain,
% 27.34/17.53 ((c2 = f5(f9(c2, c2))) <=> (c2 = f5(c1))),
% 27.34/17.53 inference(monotonicity,[status(thm)],[162])).
% 27.34/17.53 tff(164,plain,
% 27.34/17.53 ((c2 = f5(c1)) <=> (c2 = f5(f9(c2, c2)))),
% 27.34/17.53 inference(symmetry,[status(thm)],[163])).
% 27.34/17.53 tff(165,plain,
% 27.34/17.53 ((f5(c1) = c2) <=> (c2 = f5(f9(c2, c2)))),
% 27.34/17.53 inference(transitivity,[status(thm)],[155, 164])).
% 27.34/17.53 tff(166,plain,
% 27.34/17.53 ((~(f5(c1) = c2)) <=> (~(c2 = f5(f9(c2, c2))))),
% 27.34/17.53 inference(monotonicity,[status(thm)],[165])).
% 27.34/17.53 tff(167,plain,
% 27.34/17.53 ((c2 = f9(c2, c2)) <=> (f9(c2, c2) = c2)),
% 27.34/17.53 inference(commutativity,[status(thm)],[])).
% 27.34/17.53 tff(168,assumption,(~(c1 = c3)), introduced(assumption)).
% 27.34/17.53 tff(169,plain,
% 27.34/17.53 ((f9(c2, c2) = f5(f9(c2, c2))) <=> (c1 = f5(c1))),
% 27.34/17.53 inference(monotonicity,[status(thm)],[161, 162])).
% 27.34/17.53 tff(170,plain,
% 27.34/17.53 ((f9(c2, c2) = f5(f9(c2, c2))) <=> (f5(c1) = c1)),
% 27.34/17.53 inference(transitivity,[status(thm)],[169, 128])).
% 27.34/17.53 tff(171,plain,
% 27.34/17.53 ((f5(c1) = c1) <=> (f9(c2, c2) = f5(f9(c2, c2)))),
% 27.34/17.53 inference(symmetry,[status(thm)],[170])).
% 27.34/17.53 tff(172,assumption,(c3 = c1), introduced(assumption)).
% 27.34/17.53 tff(173,plain,
% 27.34/17.53 (c1 = c3),
% 27.34/17.53 inference(modus_ponens,[status(thm)],[172, 68])).
% 27.34/17.53 tff(174,plain,
% 27.34/17.53 ($false),
% 27.34/17.53 inference(unit_resolution,[status(thm)],[168, 173])).
% 27.34/17.53 tff(175,plain,((~(c3 = c1)) | (c1 = c3)), inference(lemma,lemma(discharge,[]))).
% 27.34/17.53 tff(176,plain,
% 27.34/17.53 (~(c3 = c1)),
% 27.34/17.53 inference(unit_resolution,[status(thm)],[175, 168])).
% 27.34/17.53 tff(177,plain,
% 27.34/17.53 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((c3 = c1) | (c3 = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (c3 = c1) | (c3 = c2))),
% 27.34/17.53 inference(rewrite,[status(thm)],[])).
% 27.34/17.53 tff(178,plain,
% 27.34/17.53 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((c3 = c1) | (c3 = c2))),
% 27.34/17.53 inference(quant_inst,[status(thm)],[])).
% 27.34/17.53 tff(179,plain,
% 27.34/17.53 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (c3 = c1) | (c3 = c2)),
% 27.34/17.53 inference(modus_ponens,[status(thm)],[178, 177])).
% 27.34/17.53 tff(180,plain,
% 27.34/17.53 ((c3 = c1) | (c3 = c2)),
% 27.34/17.53 inference(unit_resolution,[status(thm)],[179, 10])).
% 27.34/17.53 tff(181,plain,
% 27.34/17.53 (c3 = c2),
% 27.34/17.53 inference(unit_resolution,[status(thm)],[180, 176])).
% 27.34/17.53 tff(182,plain,
% 27.34/17.53 ((c2 = c1) <=> (c2 = f9(c2, c2))),
% 27.34/17.53 inference(monotonicity,[status(thm)],[150])).
% 27.34/17.53 tff(183,plain,
% 27.34/17.53 ((c2 = c1) <=> (f9(c2, c2) = c2)),
% 27.34/17.53 inference(transitivity,[status(thm)],[182, 167])).
% 27.34/17.53 tff(184,plain,
% 27.34/17.53 ((~(c2 = c1)) <=> (~(f9(c2, c2) = c2))),
% 27.34/17.53 inference(monotonicity,[status(thm)],[183])).
% 27.34/17.53 tff(185,plain,
% 27.34/17.53 (~(f9(c2, c2) = c2)),
% 27.34/17.53 inference(modus_ponens,[status(thm)],[75, 184])).
% 27.34/17.53 tff(186,assumption,(f5(c1) = c2), introduced(assumption)).
% 27.34/17.53 tff(187,plain,
% 27.34/17.53 (f5(f9(c2, c2)) = c2),
% 27.34/17.53 inference(transitivity,[status(thm)],[162, 186])).
% 27.34/17.53 tff(188,plain,
% 27.34/17.53 ((f9(c2, c2) = f5(f9(c2, c2))) <=> (f9(c2, c2) = c2)),
% 27.34/17.53 inference(monotonicity,[status(thm)],[187])).
% 27.34/17.53 tff(189,plain,
% 27.34/17.53 ((f9(c2, c2) = c2) <=> (f9(c2, c2) = f5(f9(c2, c2)))),
% 27.34/17.53 inference(symmetry,[status(thm)],[188])).
% 27.34/17.53 tff(190,plain,
% 27.34/17.53 ((~(f9(c2, c2) = c2)) <=> (~(f9(c2, c2) = f5(f9(c2, c2))))),
% 27.34/17.53 inference(monotonicity,[status(thm)],[189])).
% 27.34/17.53 tff(191,plain,
% 27.34/17.53 (~(f9(c2, c2) = f5(f9(c2, c2)))),
% 27.34/17.53 inference(modus_ponens,[status(thm)],[185, 190])).
% 27.34/17.53 tff(192,plain,
% 27.34/17.53 ((f5(c1) = c1) <=> (c1 = f5(c1))),
% 27.34/17.53 inference(symmetry,[status(thm)],[128])).
% 27.34/17.53 tff(193,plain,
% 27.34/17.53 ((f5(f9(c2, c2)) = f9(c2, c2)) <=> (f9(c2, c2) = f5(f9(c2, c2)))),
% 27.34/17.53 inference(commutativity,[status(thm)],[])).
% 27.34/17.53 tff(194,plain,
% 27.34/17.53 (f5(c1) = f5(f9(c2, c2))),
% 27.34/17.53 inference(symmetry,[status(thm)],[162])).
% 27.34/17.53 tff(195,plain,
% 27.34/17.53 ((f5(c1) = c1) <=> (f5(f9(c2, c2)) = f9(c2, c2))),
% 27.34/17.53 inference(monotonicity,[status(thm)],[194, 150])).
% 27.34/17.53 tff(196,plain,
% 27.34/17.53 ((f5(c1) = c1) <=> (f9(c2, c2) = f5(f9(c2, c2)))),
% 27.34/17.53 inference(transitivity,[status(thm)],[195, 193])).
% 27.34/17.53 tff(197,plain,
% 27.34/17.53 ((f9(c2, c2) = f5(f9(c2, c2))) <=> (f5(c1) = c1)),
% 27.34/17.53 inference(symmetry,[status(thm)],[196])).
% 27.34/17.53 tff(198,plain,
% 27.34/17.53 ((f9(c2, c2) = c2) <=> (c1 = f5(c1))),
% 27.34/17.53 inference(transitivity,[status(thm)],[189, 197, 192])).
% 27.34/17.53 tff(199,plain,
% 27.34/17.53 ((~(f9(c2, c2) = c2)) <=> (~(c1 = f5(c1)))),
% 27.34/17.53 inference(monotonicity,[status(thm)],[198])).
% 27.34/17.53 tff(200,plain,
% 27.34/17.53 (~(c1 = f5(c1))),
% 27.34/17.53 inference(modus_ponens,[status(thm)],[185, 199])).
% 27.34/17.53 tff(201,plain,
% 27.34/17.53 (f9(f10(c2), f10(c2)) = c1),
% 27.34/17.53 inference(transitivity,[status(thm)],[135, 160, 148])).
% 27.34/17.53 tff(202,plain,
% 27.34/17.53 (f10(f9(f10(c2), f10(c2))) = f10(c1)),
% 27.34/17.53 inference(monotonicity,[status(thm)],[201])).
% 27.34/17.53 tff(203,plain,
% 27.34/17.53 (f9(c2, c2) = f9(f10(c2), f10(c2))),
% 27.34/17.53 inference(symmetry,[status(thm)],[135])).
% 27.34/17.53 tff(204,plain,
% 27.34/17.53 (f10(f9(c2, c2)) = f10(f9(f10(c2), f10(c2)))),
% 27.34/17.53 inference(monotonicity,[status(thm)],[203])).
% 27.34/17.53 tff(205,plain,
% 27.34/17.53 (f10(f9(c2, c2)) = c2),
% 27.34/17.53 inference(transitivity,[status(thm)],[204, 202, 15])).
% 27.34/17.53 tff(206,plain,
% 27.34/17.53 (big_f(c2, f10(f9(c2, c2))) <=> big_f(c2, c2)),
% 27.34/17.53 inference(monotonicity,[status(thm)],[205])).
% 27.34/17.53 tff(207,plain,
% 27.34/17.53 (big_f(c2, c2) <=> big_f(c2, f10(f9(c2, c2)))),
% 27.34/17.53 inference(symmetry,[status(thm)],[206])).
% 27.34/17.53 tff(208,plain,
% 27.34/17.53 ((c2 = f8(c3)) <=> (f8(c3) = c2)),
% 27.34/17.53 inference(commutativity,[status(thm)],[])).
% 27.34/17.53 tff(209,plain,
% 27.34/17.53 ((f8(c3) = c2) <=> (c2 = f8(c3))),
% 27.34/17.53 inference(symmetry,[status(thm)],[208])).
% 27.34/17.53 tff(210,plain,
% 27.34/17.53 ((f8(f9(f10(c2), f10(c2))) = c2) <=> (c2 = f8(f9(f10(c2), f10(c2))))),
% 27.34/17.53 inference(commutativity,[status(thm)],[])).
% 27.34/17.53 tff(211,plain,
% 27.34/17.53 ((c1 = c3) <=> (f9(f10(c2), f4(c4)) = c3)),
% 27.34/17.53 inference(monotonicity,[status(thm)],[149])).
% 27.34/17.53 tff(212,plain,
% 27.34/17.53 ((f9(f10(c2), f4(c4)) = c3) <=> (c1 = c3)),
% 27.34/17.53 inference(symmetry,[status(thm)],[211])).
% 27.34/17.53 tff(213,plain,
% 27.34/17.53 ((f9(c2, c2) = c3) <=> (f9(f10(c2), f4(c4)) = c3)),
% 27.34/17.53 inference(monotonicity,[status(thm)],[160])).
% 27.34/17.53 tff(214,plain,
% 27.34/17.53 ((f9(c2, c2) = c3) <=> (c1 = c3)),
% 27.34/17.53 inference(transitivity,[status(thm)],[213, 212])).
% 27.34/17.53 tff(215,plain,
% 27.34/17.53 ((~(f9(c2, c2) = c3)) <=> (~(c1 = c3))),
% 27.34/17.53 inference(monotonicity,[status(thm)],[214])).
% 27.34/17.53 tff(216,plain,
% 27.34/17.53 (c2 = f10(c2)),
% 27.34/17.53 inference(symmetry,[status(thm)],[122])).
% 27.34/17.53 tff(217,plain,
% 27.34/17.53 (big_f(f9(c2, c2), c2) <=> big_f(f9(c2, c2), f10(c2))),
% 27.34/17.53 inference(monotonicity,[status(thm)],[216])).
% 27.34/17.53 tff(218,plain,
% 27.34/17.53 (big_f(f9(c2, c2), f10(c2)) <=> big_f(f9(c2, c2), c2)),
% 27.34/17.53 inference(symmetry,[status(thm)],[217])).
% 27.34/17.53 tff(219,plain,
% 27.34/17.53 (f7(f10(c1)) = f7(c2)),
% 27.34/17.53 inference(monotonicity,[status(thm)],[15])).
% 27.34/17.53 tff(220,plain,
% 27.34/17.53 ((f7(f10(c1)) = f10(c1)) <=> (f7(c2) = c2)),
% 27.34/17.53 inference(monotonicity,[status(thm)],[219, 15])).
% 27.34/17.53 tff(221,plain,
% 27.34/17.53 ((f7(c2) = c2) <=> (f7(f10(c1)) = f10(c1))),
% 27.34/17.53 inference(symmetry,[status(thm)],[220])).
% 27.34/17.53 tff(222,plain,
% 27.34/17.53 ((~(f7(c2) = c2)) <=> (~(f7(f10(c1)) = f10(c1)))),
% 27.34/17.53 inference(monotonicity,[status(thm)],[221])).
% 27.34/17.53 tff(223,plain,
% 27.34/17.53 (~(f7(f10(c1)) = f10(c1))),
% 27.34/17.53 inference(modus_ponens,[status(thm)],[17, 222])).
% 27.34/17.53 tff(224,plain,
% 27.34/17.53 ((~(f5(c1) = c1)) <=> (~(f9(c2, c2) = f5(f9(c2, c2))))),
% 27.34/17.53 inference(monotonicity,[status(thm)],[196])).
% 27.34/17.53 tff(225,plain,
% 27.34/17.53 (c1 = f9(f10(c2), f10(c2))),
% 27.34/17.53 inference(transitivity,[status(thm)],[149, 132, 203])).
% 27.34/17.53 tff(226,plain,
% 27.34/17.53 (f10(c1) = f10(f9(f10(c2), f10(c2)))),
% 27.34/17.53 inference(symmetry,[status(thm)],[202])).
% 27.34/17.53 tff(227,plain,
% 27.34/17.53 ((f10(c1) = c1) <=> (f10(f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))),
% 27.34/17.53 inference(monotonicity,[status(thm)],[226, 225])).
% 27.34/17.53 tff(228,plain,
% 27.34/17.53 ((~(f10(c1) = c1)) <=> (~(f10(f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2))))),
% 27.34/17.53 inference(monotonicity,[status(thm)],[227])).
% 27.34/17.53 tff(229,plain,
% 27.34/17.53 (~(f10(f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))),
% 27.34/17.53 inference(modus_ponens,[status(thm)],[3, 228])).
% 27.34/17.53 tff(230,assumption,(f5(c1) = c1), introduced(assumption)).
% 27.34/17.53 tff(231,assumption,(~(f10(f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))), introduced(assumption)).
% 27.34/17.53 tff(232,plain,
% 27.34/17.53 (f7(f10(c1)) = f7(c2)),
% 27.34/17.53 inference(monotonicity,[status(thm)],[16])).
% 27.34/17.53 tff(233,plain,
% 27.34/17.53 ((f7(f10(c1)) = f10(c1)) <=> (f7(c2) = c2)),
% 27.34/17.53 inference(monotonicity,[status(thm)],[232, 16])).
% 27.34/17.53 tff(234,plain,
% 27.34/17.53 ((f7(c2) = c2) <=> (f7(f10(c1)) = f10(c1))),
% 27.34/17.53 inference(symmetry,[status(thm)],[233])).
% 27.34/17.53 tff(235,plain,
% 27.34/17.53 ((~(f7(c2) = c2)) <=> (~(f7(f10(c1)) = f10(c1)))),
% 27.34/17.53 inference(monotonicity,[status(thm)],[234])).
% 27.34/17.53 tff(236,plain,
% 27.34/17.53 (~(f7(f10(c1)) = f10(c1))),
% 27.34/17.53 inference(modus_ponens,[status(thm)],[17, 235])).
% 27.34/17.53 tff(237,plain,
% 27.34/17.53 (f5(f9(c2, c2)) = f9(c2, c2)),
% 27.34/17.53 inference(transitivity,[status(thm)],[162, 230, 149, 132])).
% 27.34/17.53 tff(238,plain,
% 27.34/17.53 ((c2 = f5(f9(c2, c2))) <=> (c2 = f9(c2, c2))),
% 27.34/17.53 inference(monotonicity,[status(thm)],[237])).
% 27.34/17.53 tff(239,plain,
% 27.34/17.53 ((c2 = f5(f9(c2, c2))) <=> (f9(c2, c2) = c2)),
% 27.34/17.53 inference(transitivity,[status(thm)],[238, 167])).
% 27.34/17.53 tff(240,plain,
% 27.34/17.53 ((f9(c2, c2) = c2) <=> (c2 = f5(f9(c2, c2)))),
% 27.34/17.53 inference(symmetry,[status(thm)],[239])).
% 27.34/17.53 tff(241,plain,
% 27.34/17.53 ((~(f9(c2, c2) = c2)) <=> (~(c2 = f5(f9(c2, c2))))),
% 27.34/17.53 inference(monotonicity,[status(thm)],[240])).
% 27.34/17.53 tff(242,plain,
% 27.34/17.53 (~(c2 = f5(f9(c2, c2)))),
% 27.34/17.53 inference(modus_ponens,[status(thm)],[185, 241])).
% 27.34/17.53 tff(243,plain,
% 27.34/17.53 (f7(f9(c2, c2)) = f7(c1)),
% 27.34/17.53 inference(monotonicity,[status(thm)],[161])).
% 27.34/17.53 tff(244,plain,
% 27.34/17.53 (f7(f9(c2, c2)) = c2),
% 27.34/17.53 inference(transitivity,[status(thm)],[243, 120])).
% 27.34/17.53 tff(245,plain,
% 27.34/17.53 (big_f(f7(f9(c2, c2)), c2) <=> big_f(c2, c2)),
% 27.34/17.53 inference(monotonicity,[status(thm)],[244])).
% 27.34/17.53 tff(246,plain,
% 27.34/17.53 (big_f(c2, c2) <=> big_f(f7(f9(c2, c2)), c2)),
% 27.34/17.53 inference(symmetry,[status(thm)],[245])).
% 27.34/17.53 tff(247,plain,
% 27.34/17.53 (big_f(f7(c1), c1) <=> big_f(c2, c1)),
% 27.34/17.53 inference(monotonicity,[status(thm)],[120])).
% 27.34/17.53 tff(248,plain,
% 27.34/17.53 ((f10(f10(c2)) = f10(c2)) <=> (f10(f10(c2)) = c2)),
% 27.34/17.53 inference(monotonicity,[status(thm)],[122])).
% 27.34/17.53 tff(249,plain,
% 27.34/17.53 ((f10(f10(c2)) = c2) <=> (f10(f10(c2)) = f10(c2))),
% 27.34/17.53 inference(symmetry,[status(thm)],[248])).
% 27.34/17.53 tff(250,plain,
% 27.34/17.53 (f10(f10(c2)) = f10(c2)),
% 27.34/17.53 inference(monotonicity,[status(thm)],[122])).
% 27.34/17.53 tff(251,plain,
% 27.34/17.53 (f10(f10(c2)) = c2),
% 27.34/17.53 inference(transitivity,[status(thm)],[250, 122])).
% 27.34/17.53 tff(252,plain,
% 27.34/17.53 (f10(f10(c2)) = f10(c2)),
% 27.34/17.53 inference(modus_ponens,[status(thm)],[251, 249])).
% 27.34/17.53 tff(253,plain,
% 27.34/17.53 (big_f(f9(f10(c2), f10(c2)), f10(f10(c2))) <=> big_f(f9(c2, c2), f10(c2))),
% 27.34/17.53 inference(monotonicity,[status(thm)],[135, 250])).
% 27.34/17.53 tff(254,plain,
% 27.34/17.53 (big_f(f9(c2, c2), f10(c2)) <=> big_f(f9(f10(c2), f10(c2)), f10(f10(c2)))),
% 27.34/17.53 inference(symmetry,[status(thm)],[253])).
% 27.34/17.53 tff(255,plain,
% 27.34/17.53 ((~big_f(f9(c2, c2), f10(c2))) <=> (~big_f(f9(f10(c2), f10(c2)), f10(f10(c2))))),
% 27.34/17.53 inference(monotonicity,[status(thm)],[254])).
% 27.34/17.53 tff(256,assumption,(~big_f(f9(c2, c2), f10(c2))), introduced(assumption)).
% 27.34/17.53 tff(257,plain,
% 27.34/17.53 (~big_f(f9(f10(c2), f10(c2)), f10(f10(c2)))),
% 27.34/17.53 inference(modus_ponens,[status(thm)],[256, 255])).
% 27.34/17.53 tff(258,plain,
% 27.34/17.53 (^[X9: $i, X4: $i, X7: $i, X5: $i] : refl(((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4)))) <=> ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4)))))),
% 27.34/17.53 inference(bind,[status(th)],[])).
% 27.34/17.53 tff(259,plain,
% 27.34/17.53 (![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4)))) <=> ![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))),
% 27.34/17.53 inference(quant_intro,[status(thm)],[258])).
% 27.34/17.53 tff(260,plain,
% 27.34/17.53 (![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4)))) <=> ![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))),
% 27.34/17.53 inference(rewrite,[status(thm)],[])).
% 27.34/17.53 tff(261,plain,
% 27.34/17.53 (^[X9: $i, X4: $i, X7: $i, X5: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((big_f(f7(X4), X5) | (~(X5 = f5(X4)))) <=> (big_f(f7(X4), X5) | (~(X5 = f5(X4))))), (((big_f(f7(X4), X5) | (~(X5 = f5(X4)))) | (f7(X4) = X4)) <=> ((big_f(f7(X4), X5) | (~(X5 = f5(X4)))) | (f7(X4) = X4)))), rewrite(((big_f(f7(X4), X5) | (~(X5 = f5(X4)))) | (f7(X4) = X4)) <=> ((f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))), (((big_f(f7(X4), X5) | (~(X5 = f5(X4)))) | (f7(X4) = X4)) <=> ((f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4)))))), ((((big_f(f7(X4), X5) | (~(X5 = f5(X4)))) | (f7(X4) = X4)) | big_f(f9(X7, X9), f10(X7))) <=> (((f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4)))) | big_f(f9(X7, X9), f10(X7))))), rewrite((((f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4)))) | big_f(f9(X7, X9), f10(X7))) <=> (big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))), ((((big_f(f7(X4), X5) | (~(X5 = f5(X4)))) | (f7(X4) = X4)) | big_f(f9(X7, X9), f10(X7))) <=> (big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4)))))), (((((big_f(f7(X4), X5) | (~(X5 = f5(X4)))) | (f7(X4) = X4)) | big_f(f9(X7, X9), f10(X7))) | (f9(X7, X9) = X9)) <=> ((big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4)))) | (f9(X7, X9) = X9)))), rewrite(((big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4)))) | (f9(X7, X9) = X9)) <=> ((f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))), (((((big_f(f7(X4), X5) | (~(X5 = f5(X4)))) | (f7(X4) = X4)) | big_f(f9(X7, X9), f10(X7))) | (f9(X7, X9) = X9)) <=> ((f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4)))))), ((((((big_f(f7(X4), X5) | (~(X5 = f5(X4)))) | (f7(X4) = X4)) | big_f(f9(X7, X9), f10(X7))) | (f9(X7, X9) = X9)) | (~(f10(X7) = X7))) <=> (((f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4)))) | (~(f10(X7) = X7))))), rewrite((((f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4)))) | (~(f10(X7) = X7))) <=> ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))), ((((((big_f(f7(X4), X5) | (~(X5 = f5(X4)))) | (f7(X4) = X4)) | big_f(f9(X7, X9), f10(X7))) | (f9(X7, X9) = X9)) | (~(f10(X7) = X7))) <=> ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))))),
% 27.34/17.53 inference(bind,[status(th)],[])).
% 27.34/17.53 tff(262,plain,
% 27.34/17.53 (![X9: $i, X4: $i, X7: $i, X5: $i] : (((((big_f(f7(X4), X5) | (~(X5 = f5(X4)))) | (f7(X4) = X4)) | big_f(f9(X7, X9), f10(X7))) | (f9(X7, X9) = X9)) | (~(f10(X7) = X7))) <=> ![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))),
% 27.34/17.53 inference(quant_intro,[status(thm)],[261])).
% 27.34/17.53 tff(263,axiom,(![X9: $i, X4: $i, X7: $i, X5: $i] : (((((big_f(f7(X4), X5) | (~(X5 = f5(X4)))) | (f7(X4) = X4)) | big_f(f9(X7, X9), f10(X7))) | (f9(X7, X9) = X9)) | (~(f10(X7) = X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_25')).
% 27.34/17.53 tff(264,plain,
% 27.34/17.53 (![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))),
% 27.34/17.53 inference(modus_ponens,[status(thm)],[263, 262])).
% 27.34/17.53 tff(265,plain,
% 27.34/17.53 (![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))),
% 27.34/17.53 inference(modus_ponens,[status(thm)],[264, 260])).
% 27.34/17.53 tff(266,plain,(
% 27.34/17.53 ![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))),
% 27.34/17.53 inference(skolemize,[status(sab)],[265])).
% 27.34/17.53 tff(267,plain,
% 27.34/17.53 (![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))),
% 27.34/17.53 inference(modus_ponens,[status(thm)],[266, 259])).
% 27.34/17.53 tff(268,plain,
% 27.34/17.53 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (f9(f10(c2), f10(c2)) = f10(c2)) | big_f(f9(f10(c2), f10(c2)), f10(f10(c2))) | (~(f10(f10(c2)) = f10(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (f9(f10(c2), f10(c2)) = f10(c2)) | big_f(f9(f10(c2), f10(c2)), f10(f10(c2))) | (~(f10(f10(c2)) = f10(c2))))),
% 27.34/17.53 inference(rewrite,[status(thm)],[])).
% 27.34/17.53 tff(269,plain,
% 27.34/17.53 (((~(f10(f10(c2)) = f10(c2))) | (f9(f10(c2), f10(c2)) = f10(c2)) | big_f(f9(f10(c2), f10(c2)), f10(f10(c2))) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)) | $false) <=> ((f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (f9(f10(c2), f10(c2)) = f10(c2)) | big_f(f9(f10(c2), f10(c2)), f10(f10(c2))) | (~(f10(f10(c2)) = f10(c2))))),
% 27.34/17.53 inference(rewrite,[status(thm)],[])).
% 27.34/17.53 tff(270,plain,
% 27.34/17.53 ((~$true) <=> $false),
% 27.34/17.53 inference(rewrite,[status(thm)],[])).
% 27.34/17.53 tff(271,plain,
% 27.34/17.53 ((f5(c1) = f5(c1)) <=> $true),
% 27.34/17.53 inference(rewrite,[status(thm)],[])).
% 27.34/17.53 tff(272,plain,
% 27.34/17.53 ((~(f5(c1) = f5(c1))) <=> (~$true)),
% 27.34/17.53 inference(monotonicity,[status(thm)],[271])).
% 27.34/17.53 tff(273,plain,
% 27.34/17.53 ((~(f5(c1) = f5(c1))) <=> $false),
% 27.34/17.53 inference(transitivity,[status(thm)],[272, 270])).
% 27.34/17.53 tff(274,plain,
% 27.34/17.53 (((~(f10(f10(c2)) = f10(c2))) | (f9(f10(c2), f10(c2)) = f10(c2)) | big_f(f9(f10(c2), f10(c2)), f10(f10(c2))) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (~(f5(c1) = f5(c1)))) <=> ((~(f10(f10(c2)) = f10(c2))) | (f9(f10(c2), f10(c2)) = f10(c2)) | big_f(f9(f10(c2), f10(c2)), f10(f10(c2))) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)) | $false)),
% 27.34/17.53 inference(monotonicity,[status(thm)],[273])).
% 27.34/17.53 tff(275,plain,
% 27.34/17.53 (((~(f10(f10(c2)) = f10(c2))) | (f9(f10(c2), f10(c2)) = f10(c2)) | big_f(f9(f10(c2), f10(c2)), f10(f10(c2))) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (~(f5(c1) = f5(c1)))) <=> ((f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (f9(f10(c2), f10(c2)) = f10(c2)) | big_f(f9(f10(c2), f10(c2)), f10(f10(c2))) | (~(f10(f10(c2)) = f10(c2))))),
% 27.34/17.53 inference(transitivity,[status(thm)],[274, 269])).
% 27.34/17.53 tff(276,plain,
% 27.34/17.53 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(f10(c2)) = f10(c2))) | (f9(f10(c2), f10(c2)) = f10(c2)) | big_f(f9(f10(c2), f10(c2)), f10(f10(c2))) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (~(f5(c1) = f5(c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (f9(f10(c2), f10(c2)) = f10(c2)) | big_f(f9(f10(c2), f10(c2)), f10(f10(c2))) | (~(f10(f10(c2)) = f10(c2)))))),
% 27.34/17.53 inference(monotonicity,[status(thm)],[275])).
% 27.34/17.53 tff(277,plain,
% 27.34/17.53 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(f10(c2)) = f10(c2))) | (f9(f10(c2), f10(c2)) = f10(c2)) | big_f(f9(f10(c2), f10(c2)), f10(f10(c2))) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (~(f5(c1) = f5(c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (f9(f10(c2), f10(c2)) = f10(c2)) | big_f(f9(f10(c2), f10(c2)), f10(f10(c2))) | (~(f10(f10(c2)) = f10(c2))))),
% 27.34/17.53 inference(transitivity,[status(thm)],[276, 268])).
% 27.34/17.53 tff(278,plain,
% 27.34/17.53 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(f10(c2)) = f10(c2))) | (f9(f10(c2), f10(c2)) = f10(c2)) | big_f(f9(f10(c2), f10(c2)), f10(f10(c2))) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (~(f5(c1) = f5(c1))))),
% 27.34/17.53 inference(quant_inst,[status(thm)],[])).
% 27.34/17.53 tff(279,plain,
% 27.34/17.53 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (f9(f10(c2), f10(c2)) = f10(c2)) | big_f(f9(f10(c2), f10(c2)), f10(f10(c2))) | (~(f10(f10(c2)) = f10(c2)))),
% 27.34/17.53 inference(modus_ponens,[status(thm)],[278, 277])).
% 27.34/17.53 tff(280,plain,
% 27.34/17.53 ((f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (f9(f10(c2), f10(c2)) = f10(c2)) | big_f(f9(f10(c2), f10(c2)), f10(f10(c2))) | (~(f10(f10(c2)) = f10(c2)))),
% 27.34/17.53 inference(unit_resolution,[status(thm)],[279, 267])).
% 27.34/17.53 tff(281,plain,
% 27.34/17.53 (big_f(f7(c1), f5(c1))),
% 27.34/17.53 inference(unit_resolution,[status(thm)],[280, 257, 252, 115, 158])).
% 27.34/17.53 tff(282,plain,
% 27.34/17.53 (big_f(f7(c1), f5(c1)) <=> big_f(f7(c1), c1)),
% 27.34/17.53 inference(monotonicity,[status(thm)],[230])).
% 27.34/17.53 tff(283,plain,
% 27.34/17.53 (big_f(f7(c1), c1) <=> big_f(f7(c1), f5(c1))),
% 27.34/17.53 inference(symmetry,[status(thm)],[282])).
% 27.34/17.53 tff(284,plain,
% 27.34/17.53 ((~big_f(f7(c1), c1)) <=> (~big_f(f7(c1), f5(c1)))),
% 27.34/17.53 inference(monotonicity,[status(thm)],[283])).
% 27.34/17.53 tff(285,assumption,(~big_f(f7(c1), c1)), introduced(assumption)).
% 27.34/17.53 tff(286,plain,
% 27.34/17.53 (~big_f(f7(c1), f5(c1))),
% 27.34/17.53 inference(modus_ponens,[status(thm)],[285, 284])).
% 27.34/17.53 tff(287,assumption,(big_f(f7(c1), f5(c1))), introduced(assumption)).
% 27.34/17.53 tff(288,plain,
% 27.34/17.53 ($false),
% 27.34/17.53 inference(unit_resolution,[status(thm)],[287, 286])).
% 27.34/17.53 tff(289,plain,((~(f5(c1) = c1)) | (~big_f(f7(c1), f5(c1))) | big_f(f7(c1), c1)), inference(lemma,lemma(discharge,[]))).
% 27.34/17.53 tff(290,plain,
% 27.34/17.53 (big_f(f7(c1), c1)),
% 27.34/17.53 inference(unit_resolution,[status(thm)],[289, 281, 230])).
% 27.34/17.53 tff(291,plain,
% 27.34/17.53 (big_f(c2, c1)),
% 27.34/17.53 inference(modus_ponens,[status(thm)],[290, 247])).
% 27.34/17.53 tff(292,assumption,(f7(c2) = c1), introduced(assumption)).
% 27.34/17.53 tff(293,plain,
% 27.34/17.53 (c2 = f10(c1)),
% 27.34/17.53 inference(symmetry,[status(thm)],[16])).
% 27.34/17.53 tff(294,plain,
% 27.34/17.53 (f5(c2) = f5(f10(c1))),
% 27.34/17.53 inference(monotonicity,[status(thm)],[293])).
% 27.34/17.53 tff(295,plain,
% 27.34/17.53 (f5(f10(c1)) = f5(c2)),
% 27.34/17.53 inference(symmetry,[status(thm)],[294])).
% 27.34/17.53 tff(296,plain,
% 27.34/17.53 (big_f(f7(f10(c1)), f5(f10(c1))) <=> big_f(f7(c2), f5(c2))),
% 27.34/17.53 inference(monotonicity,[status(thm)],[232, 295])).
% 27.34/17.53 tff(297,assumption,(~(f7(f10(c1)) = f10(c1))), introduced(assumption)).
% 27.34/17.53 tff(298,plain,
% 27.34/17.53 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(f10(c1)) = f10(c1)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | big_f(f7(f10(c1)), f5(f10(c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(f10(c1)) = f10(c1)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | big_f(f7(f10(c1)), f5(f10(c1))))),
% 27.34/17.54 inference(rewrite,[status(thm)],[])).
% 27.34/17.54 tff(299,plain,
% 27.34/17.54 (((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), f5(f10(c1))) | $false) <=> ((~(f10(c2) = c2)) | (f7(f10(c1)) = f10(c1)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | big_f(f7(f10(c1)), f5(f10(c1))))),
% 27.34/17.54 inference(rewrite,[status(thm)],[])).
% 27.34/17.54 tff(300,plain,
% 27.34/17.54 ((f5(f10(c1)) = f5(f10(c1))) <=> $true),
% 27.34/17.54 inference(rewrite,[status(thm)],[])).
% 27.34/17.54 tff(301,plain,
% 27.34/17.54 ((~(f5(f10(c1)) = f5(f10(c1)))) <=> (~$true)),
% 27.34/17.54 inference(monotonicity,[status(thm)],[300])).
% 27.34/17.54 tff(302,plain,
% 27.34/17.54 ((~(f5(f10(c1)) = f5(f10(c1)))) <=> $false),
% 27.34/17.54 inference(transitivity,[status(thm)],[301, 270])).
% 27.34/17.54 tff(303,plain,
% 27.34/17.54 (((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), f5(f10(c1))) | (~(f5(f10(c1)) = f5(f10(c1))))) <=> ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), f5(f10(c1))) | $false)),
% 27.34/17.54 inference(monotonicity,[status(thm)],[302])).
% 27.34/17.54 tff(304,plain,
% 27.34/17.54 (((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), f5(f10(c1))) | (~(f5(f10(c1)) = f5(f10(c1))))) <=> ((~(f10(c2) = c2)) | (f7(f10(c1)) = f10(c1)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | big_f(f7(f10(c1)), f5(f10(c1))))),
% 27.34/17.54 inference(transitivity,[status(thm)],[303, 299])).
% 27.34/17.54 tff(305,plain,
% 27.34/17.54 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), f5(f10(c1))) | (~(f5(f10(c1)) = f5(f10(c1)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(f10(c1)) = f10(c1)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | big_f(f7(f10(c1)), f5(f10(c1)))))),
% 27.34/17.54 inference(monotonicity,[status(thm)],[304])).
% 27.34/17.54 tff(306,plain,
% 27.34/17.54 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), f5(f10(c1))) | (~(f5(f10(c1)) = f5(f10(c1)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(f10(c1)) = f10(c1)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | big_f(f7(f10(c1)), f5(f10(c1))))),
% 27.34/17.54 inference(transitivity,[status(thm)],[305, 298])).
% 27.34/17.54 tff(307,plain,
% 27.34/17.54 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), f5(f10(c1))) | (~(f5(f10(c1)) = f5(f10(c1)))))),
% 27.34/17.54 inference(quant_inst,[status(thm)],[])).
% 27.34/17.54 tff(308,plain,
% 27.34/17.54 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(f10(c1)) = f10(c1)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | big_f(f7(f10(c1)), f5(f10(c1)))),
% 27.34/17.54 inference(modus_ponens,[status(thm)],[307, 306])).
% 27.34/17.54 tff(309,plain,
% 27.34/17.54 ((~(f10(c2) = c2)) | (f7(f10(c1)) = f10(c1)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | big_f(f7(f10(c1)), f5(f10(c1)))),
% 27.34/17.54 inference(unit_resolution,[status(thm)],[308, 267])).
% 27.34/17.54 tff(310,plain,
% 27.34/17.54 (big_f(f7(f10(c1)), f5(f10(c1)))),
% 27.34/17.54 inference(unit_resolution,[status(thm)],[309, 256, 122, 297, 185])).
% 27.34/17.54 tff(311,plain,
% 27.34/17.54 (big_f(f7(c2), f5(c2))),
% 27.34/17.54 inference(modus_ponens,[status(thm)],[310, 296])).
% 27.34/17.54 tff(312,assumption,(f5(f10(c1)) = c2), introduced(assumption)).
% 27.34/17.54 tff(313,plain,
% 27.34/17.54 (f5(c2) = f10(c2)),
% 27.34/17.54 inference(transitivity,[status(thm)],[294, 312, 216])).
% 27.34/17.54 tff(314,plain,
% 27.34/17.54 (f7(c2) = f9(c2, c2)),
% 27.34/17.54 inference(transitivity,[status(thm)],[292, 149, 132])).
% 27.34/17.54 tff(315,plain,
% 27.34/17.54 (big_f(f7(c2), f5(c2)) <=> big_f(f9(c2, c2), f10(c2))),
% 27.34/17.54 inference(monotonicity,[status(thm)],[314, 313])).
% 27.34/17.54 tff(316,plain,
% 27.34/17.54 (big_f(f9(c2, c2), f10(c2)) <=> big_f(f7(c2), f5(c2))),
% 27.34/17.54 inference(symmetry,[status(thm)],[315])).
% 27.34/17.54 tff(317,plain,
% 27.34/17.54 ((~big_f(f9(c2, c2), f10(c2))) <=> (~big_f(f7(c2), f5(c2)))),
% 27.34/17.54 inference(monotonicity,[status(thm)],[316])).
% 27.34/17.54 tff(318,plain,
% 27.34/17.54 (~big_f(f7(c2), f5(c2))),
% 27.34/17.54 inference(modus_ponens,[status(thm)],[256, 317])).
% 27.34/17.54 tff(319,assumption,(big_f(f7(c2), f5(c2))), introduced(assumption)).
% 27.34/17.54 tff(320,plain,
% 27.34/17.54 ($false),
% 27.34/17.54 inference(unit_resolution,[status(thm)],[319, 318])).
% 27.34/17.54 tff(321,plain,((~(f5(f10(c1)) = c2)) | (~big_f(f7(c2), f5(c2))) | big_f(f9(c2, c2), f10(c2)) | (~(f10(c2) = c2)) | (~(f10(c1) = c2)) | (~(f7(c2) = c1)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.34/17.54 tff(322,plain,
% 27.34/17.54 (~(f5(f10(c1)) = c2)),
% 27.34/17.54 inference(unit_resolution,[status(thm)],[321, 311, 256, 122, 16, 292, 148, 79])).
% 27.34/17.54 tff(323,plain,
% 27.34/17.54 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f5(f10(c1)) = c1) | (f5(f10(c1)) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f5(f10(c1)) = c1) | (f5(f10(c1)) = c2))),
% 27.34/17.54 inference(rewrite,[status(thm)],[])).
% 27.34/17.54 tff(324,plain,
% 27.34/17.54 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f5(f10(c1)) = c1) | (f5(f10(c1)) = c2))),
% 27.34/17.54 inference(quant_inst,[status(thm)],[])).
% 27.34/17.54 tff(325,plain,
% 27.34/17.54 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f5(f10(c1)) = c1) | (f5(f10(c1)) = c2)),
% 27.34/17.54 inference(modus_ponens,[status(thm)],[324, 323])).
% 27.34/17.54 tff(326,plain,
% 27.34/17.54 ((f5(f10(c1)) = c1) | (f5(f10(c1)) = c2)),
% 27.34/17.54 inference(unit_resolution,[status(thm)],[325, 10])).
% 27.34/17.54 tff(327,plain,
% 27.34/17.54 (f5(f10(c1)) = c1),
% 27.34/17.54 inference(unit_resolution,[status(thm)],[326, 322])).
% 27.34/17.54 tff(328,assumption,(f5(f10(c1)) = c1), introduced(assumption)).
% 27.34/17.54 tff(329,plain,
% 27.34/17.54 (f5(c2) = c1),
% 27.34/17.54 inference(transitivity,[status(thm)],[294, 328])).
% 27.34/17.54 tff(330,plain,
% 27.34/17.54 (big_f(f7(c2), f5(c2)) <=> big_f(f7(c2), c1)),
% 27.34/17.54 inference(monotonicity,[status(thm)],[329])).
% 27.34/17.54 tff(331,plain,
% 27.34/17.54 (big_f(f7(c2), c1) <=> big_f(f7(c2), f5(c2))),
% 27.34/17.54 inference(symmetry,[status(thm)],[330])).
% 27.34/17.54 tff(332,plain,
% 27.34/17.54 ((~big_f(f7(c2), c1)) <=> (~big_f(f7(c2), f5(c2)))),
% 27.34/17.54 inference(monotonicity,[status(thm)],[331])).
% 27.34/17.54 tff(333,assumption,(~big_f(f7(c2), c1)), introduced(assumption)).
% 27.34/17.54 tff(334,plain,
% 27.34/17.54 (~big_f(f7(c2), f5(c2))),
% 27.34/17.54 inference(modus_ponens,[status(thm)],[333, 332])).
% 27.34/17.54 tff(335,plain,
% 27.34/17.54 ($false),
% 27.34/17.54 inference(unit_resolution,[status(thm)],[319, 334])).
% 27.34/17.54 tff(336,plain,((~(f5(f10(c1)) = c1)) | (~big_f(f7(c2), f5(c2))) | big_f(f7(c2), c1) | (~(f10(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.34/17.54 tff(337,plain,
% 27.34/17.54 (big_f(f7(c2), c1)),
% 27.34/17.54 inference(unit_resolution,[status(thm)],[336, 327, 311, 16])).
% 27.34/17.54 tff(338,assumption,(big_f(f7(c2), c1)), introduced(assumption)).
% 27.34/17.54 tff(339,plain,
% 27.34/17.54 ((f9(f10(c2), f4(c4)) = c3) <=> (f9(c2, c2) = c3)),
% 27.34/17.54 inference(symmetry,[status(thm)],[213])).
% 27.34/17.54 tff(340,plain,
% 27.34/17.54 ((c3 = c1) <=> (f9(c2, c2) = c3)),
% 27.34/17.54 inference(transitivity,[status(thm)],[68, 211, 339])).
% 27.34/17.54 tff(341,plain,
% 27.34/17.54 ((~(c3 = c1)) <=> (~(f9(c2, c2) = c3))),
% 27.34/17.54 inference(monotonicity,[status(thm)],[340])).
% 27.34/17.54 tff(342,plain,
% 27.34/17.54 (c1 = f7(c2)),
% 27.34/17.54 inference(symmetry,[status(thm)],[292])).
% 27.34/17.54 tff(343,plain,
% 27.34/17.54 (f9(c2, c2) = f7(c2)),
% 27.34/17.54 inference(transitivity,[status(thm)],[160, 148, 342])).
% 27.34/17.54 tff(344,plain,
% 27.34/17.54 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f7(c2), c1)),
% 27.34/17.54 inference(monotonicity,[status(thm)],[343, 161])).
% 27.34/17.54 tff(345,plain,
% 27.34/17.54 (big_f(f7(c2), c1) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 27.34/17.54 inference(symmetry,[status(thm)],[344])).
% 27.34/17.54 tff(346,plain,
% 27.34/17.54 (big_f(f9(c2, c2), f9(c2, c2))),
% 27.34/17.54 inference(modus_ponens,[status(thm)],[338, 345])).
% 27.34/17.54 tff(347,assumption,(f7(c1) = c2), introduced(assumption)).
% 27.34/17.54 tff(348,assumption,(big_f(c2, c1)), introduced(assumption)).
% 27.34/17.54 tff(349,plain,
% 27.34/17.54 (f1(c2, f9(c2, c2)) = f1(c2, c1)),
% 27.34/17.54 inference(monotonicity,[status(thm)],[161])).
% 27.34/17.54 tff(350,plain,
% 27.34/17.54 (big_f(c2, f1(c2, f9(c2, c2))) <=> big_f(c2, f1(c2, c1))),
% 27.34/17.54 inference(monotonicity,[status(thm)],[349])).
% 27.34/17.54 tff(351,plain,
% 27.34/17.54 (big_f(c2, f1(c2, c1)) <=> big_f(c2, f1(c2, f9(c2, c2)))),
% 27.34/17.54 inference(symmetry,[status(thm)],[350])).
% 27.34/17.54 tff(352,plain,
% 27.34/17.54 (f7(f7(c2)) = f7(c1)),
% 27.34/17.54 inference(monotonicity,[status(thm)],[292])).
% 27.34/17.54 tff(353,plain,
% 27.34/17.54 (f7(c1) = f7(f7(c2))),
% 27.34/17.54 inference(symmetry,[status(thm)],[352])).
% 27.34/17.54 tff(354,plain,
% 27.34/17.54 (c2 = f7(c1)),
% 27.34/17.54 inference(symmetry,[status(thm)],[347])).
% 27.34/17.54 tff(355,plain,
% 27.34/17.54 (c2 = f7(f7(c2))),
% 27.34/17.54 inference(transitivity,[status(thm)],[354, 353])).
% 27.34/17.54 tff(356,plain,
% 27.34/17.54 (f1(c2, c1) = f1(f7(f7(c2)), c1)),
% 27.34/17.54 inference(monotonicity,[status(thm)],[355])).
% 27.34/17.54 tff(357,plain,
% 27.34/17.54 (f1(f7(f7(c2)), c1) = f1(c2, c1)),
% 27.34/17.54 inference(symmetry,[status(thm)],[356])).
% 27.34/17.54 tff(358,plain,
% 27.34/17.54 ((f9(c2, c2) = c4) <=> (f9(f10(c2), f4(c4)) = c4)),
% 27.34/17.54 inference(monotonicity,[status(thm)],[160])).
% 27.34/17.54 tff(359,plain,
% 27.34/17.54 ((f9(f10(c2), f4(c4)) = c4) <=> (f9(c2, c2) = c4)),
% 27.34/17.54 inference(symmetry,[status(thm)],[358])).
% 27.34/17.54 tff(360,plain,
% 27.34/17.54 ((f9(f10(c2), f4(c4)) = c4) <=> (c1 = c4)),
% 27.34/17.54 inference(monotonicity,[status(thm)],[148])).
% 27.34/17.54 tff(361,plain,
% 27.34/17.54 ((c1 = c4) <=> (f9(f10(c2), f4(c4)) = c4)),
% 27.34/17.54 inference(symmetry,[status(thm)],[360])).
% 27.34/17.54 tff(362,plain,
% 27.34/17.54 ((c1 = c4) <=> (f9(c2, c2) = c4)),
% 27.34/17.54 inference(transitivity,[status(thm)],[361, 359])).
% 27.34/17.54 tff(363,plain,
% 27.34/17.54 (f7(f7(c2)) = c2),
% 27.34/17.54 inference(transitivity,[status(thm)],[352, 347])).
% 27.34/17.54 tff(364,plain,
% 27.34/17.54 ((f7(f7(c2)) = c3) <=> (c2 = c3)),
% 27.34/17.54 inference(monotonicity,[status(thm)],[363])).
% 27.34/17.54 tff(365,plain,
% 27.34/17.54 ((c2 = c3) <=> (f7(f7(c2)) = c3)),
% 27.34/17.54 inference(symmetry,[status(thm)],[364])).
% 27.34/17.54 tff(366,plain,
% 27.34/17.54 (c3 = f9(c2, c2)),
% 27.34/17.54 inference(transitivity,[status(thm)],[172, 149, 132])).
% 27.34/17.54 tff(367,plain,
% 27.34/17.54 ((c2 = c3) <=> (c2 = f9(c2, c2))),
% 27.34/17.54 inference(monotonicity,[status(thm)],[366])).
% 27.34/17.54 tff(368,plain,
% 27.34/17.54 ((c2 = c3) <=> (f9(c2, c2) = c2)),
% 27.34/17.54 inference(transitivity,[status(thm)],[367, 167])).
% 27.34/17.54 tff(369,plain,
% 27.34/17.54 ((f9(c2, c2) = c2) <=> (c2 = c3)),
% 27.34/17.54 inference(symmetry,[status(thm)],[368])).
% 27.34/17.54 tff(370,plain,
% 27.34/17.54 ((f9(c2, c2) = c2) <=> (f7(f7(c2)) = c3)),
% 27.34/17.54 inference(transitivity,[status(thm)],[369, 365])).
% 27.34/17.54 tff(371,plain,
% 27.34/17.54 ((~(f9(c2, c2) = c2)) <=> (~(f7(f7(c2)) = c3))),
% 27.34/17.54 inference(monotonicity,[status(thm)],[370])).
% 27.34/17.54 tff(372,plain,
% 27.34/17.54 (~(f7(f7(c2)) = c3)),
% 27.34/17.54 inference(modus_ponens,[status(thm)],[185, 371])).
% 27.34/17.54 tff(373,plain,
% 27.34/17.54 ((~(f9(c2, c2) = c2)) <=> (~(c2 = c3))),
% 27.34/17.54 inference(monotonicity,[status(thm)],[369])).
% 27.34/17.54 tff(374,plain,
% 27.34/17.54 (~(c2 = c3)),
% 27.34/17.54 inference(modus_ponens,[status(thm)],[185, 373])).
% 27.34/17.54 tff(375,plain,
% 27.34/17.54 (big_f(f4(c4), c4) <=> big_f(c2, c4)),
% 27.34/17.54 inference(monotonicity,[status(thm)],[79])).
% 27.34/17.54 tff(376,plain,
% 27.34/17.54 (big_f(c2, c4) <=> big_f(f4(c4), c4)),
% 27.34/17.54 inference(symmetry,[status(thm)],[375])).
% 27.34/17.54 tff(377,assumption,(~(c2 = c3)), introduced(assumption)).
% 27.34/17.54 tff(378,assumption,(~(f7(f7(c2)) = c3)), introduced(assumption)).
% 27.34/17.54 tff(379,assumption,(~big_f(f4(c4), c4)), introduced(assumption)).
% 27.34/17.54 tff(380,assumption,(~(f1(f7(f7(c2)), c1) = c1)), introduced(assumption)).
% 27.34/17.54 tff(381,plain,
% 27.34/17.54 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f1(f7(f7(c2)), c1) = c1) | (f1(f7(f7(c2)), c1) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f1(f7(f7(c2)), c1) = c1) | (f1(f7(f7(c2)), c1) = c2))),
% 27.34/17.54 inference(rewrite,[status(thm)],[])).
% 27.34/17.54 tff(382,plain,
% 27.34/17.54 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f1(f7(f7(c2)), c1) = c1) | (f1(f7(f7(c2)), c1) = c2))),
% 27.34/17.54 inference(quant_inst,[status(thm)],[])).
% 27.34/17.54 tff(383,plain,
% 27.34/17.54 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f1(f7(f7(c2)), c1) = c1) | (f1(f7(f7(c2)), c1) = c2)),
% 27.34/17.54 inference(modus_ponens,[status(thm)],[382, 381])).
% 27.34/17.54 tff(384,plain,
% 27.34/17.54 ((f1(f7(f7(c2)), c1) = c1) | (f1(f7(f7(c2)), c1) = c2)),
% 27.34/17.54 inference(unit_resolution,[status(thm)],[383, 10])).
% 27.34/17.54 tff(385,plain,
% 27.34/17.54 (f1(f7(f7(c2)), c1) = c2),
% 27.34/17.54 inference(unit_resolution,[status(thm)],[384, 380])).
% 27.34/17.54 tff(386,plain,
% 27.34/17.54 (c2 = f1(f7(f7(c2)), c1)),
% 27.34/17.54 inference(symmetry,[status(thm)],[385])).
% 27.34/17.54 tff(387,plain,
% 27.34/17.54 (c2 = f1(c2, c1)),
% 27.34/17.54 inference(transitivity,[status(thm)],[386, 357])).
% 27.34/17.54 tff(388,plain,
% 27.34/17.54 (big_f(c2, c2) <=> big_f(c2, f1(c2, c1))),
% 27.34/17.54 inference(monotonicity,[status(thm)],[387])).
% 27.34/17.54 tff(389,plain,
% 27.34/17.54 (big_f(c2, f1(c2, c1)) <=> big_f(c2, c2)),
% 27.34/17.54 inference(symmetry,[status(thm)],[388])).
% 27.34/17.54 tff(390,plain,
% 27.34/17.54 (big_f(f7(c1), f1(f7(f7(c2)), c1)) <=> big_f(c2, f1(c2, c1))),
% 27.34/17.54 inference(monotonicity,[status(thm)],[347, 357])).
% 27.34/17.54 tff(391,plain,
% 27.34/17.54 (big_f(f7(f7(c2)), f1(f7(f7(c2)), c1)) <=> big_f(f7(c1), f1(f7(f7(c2)), c1))),
% 27.34/17.54 inference(monotonicity,[status(thm)],[352])).
% 27.34/17.54 tff(392,plain,
% 27.34/17.54 (big_f(f7(f7(c2)), f1(f7(f7(c2)), c1)) <=> big_f(c2, f1(c2, c1))),
% 27.34/17.54 inference(transitivity,[status(thm)],[391, 390])).
% 27.34/17.54 tff(393,plain,
% 27.34/17.54 (^[X11: $i, X3: $i, X10: $i, X2: $i] : refl(((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2)))) <=> ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2)))))),
% 27.34/17.54 inference(bind,[status(th)],[])).
% 27.34/17.54 tff(394,plain,
% 27.34/17.54 (![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2)))) <=> ![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))),
% 27.34/17.54 inference(quant_intro,[status(thm)],[393])).
% 27.34/17.54 tff(395,plain,
% 27.34/17.54 (![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2)))) <=> ![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))),
% 27.34/17.54 inference(rewrite,[status(thm)],[])).
% 27.34/17.54 tff(396,plain,
% 27.34/17.54 (^[X11: $i, X3: $i, X10: $i, X2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((big_f(X10, f1(X10, X11)) | (f1(X10, X11) = X11)) <=> ((f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))), (((big_f(X10, f1(X10, X11)) | (f1(X10, X11) = X11)) | (X10 = c3)) <=> (((f1(X10, X11) = X11) | big_f(X10, f1(X10, X11))) | (X10 = c3)))), rewrite((((f1(X10, X11) = X11) | big_f(X10, f1(X10, X11))) | (X10 = c3)) <=> ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))), (((big_f(X10, f1(X10, X11)) | (f1(X10, X11) = X11)) | (X10 = c3)) <=> ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11))))), ((((big_f(X10, f1(X10, X11)) | (f1(X10, X11) = X11)) | (X10 = c3)) | big_f(X3, X2)) <=> (((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11))) | big_f(X3, X2)))), rewrite((((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11))) | big_f(X3, X2)) <=> ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | big_f(X3, X2))), ((((big_f(X10, f1(X10, X11)) | (f1(X10, X11) = X11)) | (X10 = c3)) | big_f(X3, X2)) <=> ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | big_f(X3, X2)))), (((((big_f(X10, f1(X10, X11)) | (f1(X10, X11) = X11)) | (X10 = c3)) | big_f(X3, X2)) | (~(X3 = f4(X2)))) <=> (((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | big_f(X3, X2)) | (~(X3 = f4(X2)))))), rewrite((((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | big_f(X3, X2)) | (~(X3 = f4(X2)))) <=> ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | big_f(X3, X2) | (~(X3 = f4(X2))))), (((((big_f(X10, f1(X10, X11)) | (f1(X10, X11) = X11)) | (X10 = c3)) | big_f(X3, X2)) | (~(X3 = f4(X2)))) <=> ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | big_f(X3, X2) | (~(X3 = f4(X2)))))), ((((((big_f(X10, f1(X10, X11)) | (f1(X10, X11) = X11)) | (X10 = c3)) | big_f(X3, X2)) | (~(X3 = f4(X2)))) | (~(X2 = c4))) <=> (((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | big_f(X3, X2) | (~(X3 = f4(X2)))) | (~(X2 = c4))))), rewrite((((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | big_f(X3, X2) | (~(X3 = f4(X2)))) | (~(X2 = c4))) <=> ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))), ((((((big_f(X10, f1(X10, X11)) | (f1(X10, X11) = X11)) | (X10 = c3)) | big_f(X3, X2)) | (~(X3 = f4(X2)))) | (~(X2 = c4))) <=> ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))))),
% 27.34/17.54 inference(bind,[status(th)],[])).
% 27.34/17.54 tff(397,plain,
% 27.34/17.54 (![X11: $i, X3: $i, X10: $i, X2: $i] : (((((big_f(X10, f1(X10, X11)) | (f1(X10, X11) = X11)) | (X10 = c3)) | big_f(X3, X2)) | (~(X3 = f4(X2)))) | (~(X2 = c4))) <=> ![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))),
% 27.34/17.54 inference(quant_intro,[status(thm)],[396])).
% 27.34/17.54 tff(398,axiom,(![X11: $i, X3: $i, X10: $i, X2: $i] : (((((big_f(X10, f1(X10, X11)) | (f1(X10, X11) = X11)) | (X10 = c3)) | big_f(X3, X2)) | (~(X3 = f4(X2)))) | (~(X2 = c4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_6')).
% 27.34/17.54 tff(399,plain,
% 27.34/17.54 (![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))),
% 27.34/17.54 inference(modus_ponens,[status(thm)],[398, 397])).
% 27.34/17.54 tff(400,plain,
% 27.34/17.54 (![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))),
% 27.34/17.54 inference(modus_ponens,[status(thm)],[399, 395])).
% 27.34/17.54 tff(401,plain,(
% 27.34/17.54 ![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))),
% 27.34/17.54 inference(skolemize,[status(sab)],[400])).
% 27.34/17.54 tff(402,plain,
% 27.34/17.54 (![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))),
% 27.34/17.54 inference(modus_ponens,[status(thm)],[401, 394])).
% 27.34/17.54 tff(403,plain,
% 27.34/17.54 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (big_f(f4(c4), c4) | (f7(f7(c2)) = c3) | (f1(f7(f7(c2)), c1) = c1) | big_f(f7(f7(c2)), f1(f7(f7(c2)), c1)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | big_f(f4(c4), c4) | (f7(f7(c2)) = c3) | (f1(f7(f7(c2)), c1) = c1) | big_f(f7(f7(c2)), f1(f7(f7(c2)), c1)))),
% 27.34/17.54 inference(rewrite,[status(thm)],[])).
% 27.34/17.54 tff(404,plain,
% 27.34/17.54 (((f7(f7(c2)) = c3) | (f1(f7(f7(c2)), c1) = c1) | big_f(f7(f7(c2)), f1(f7(f7(c2)), c1)) | $false | big_f(f4(c4), c4) | $false) <=> (big_f(f4(c4), c4) | (f7(f7(c2)) = c3) | (f1(f7(f7(c2)), c1) = c1) | big_f(f7(f7(c2)), f1(f7(f7(c2)), c1)))),
% 27.34/17.54 inference(rewrite,[status(thm)],[])).
% 27.34/17.54 tff(405,plain,
% 27.34/17.54 ((f4(c4) = f4(c4)) <=> $true),
% 27.34/17.54 inference(rewrite,[status(thm)],[])).
% 27.34/17.54 tff(406,plain,
% 27.34/17.54 ((~(f4(c4) = f4(c4))) <=> (~$true)),
% 27.34/17.54 inference(monotonicity,[status(thm)],[405])).
% 27.34/17.54 tff(407,plain,
% 27.34/17.54 ((~(f4(c4) = f4(c4))) <=> $false),
% 27.34/17.54 inference(transitivity,[status(thm)],[406, 270])).
% 27.34/17.54 tff(408,plain,
% 27.34/17.54 ((c4 = c4) <=> $true),
% 27.34/17.54 inference(rewrite,[status(thm)],[])).
% 27.34/17.54 tff(409,plain,
% 27.34/17.54 ((~(c4 = c4)) <=> (~$true)),
% 27.34/17.54 inference(monotonicity,[status(thm)],[408])).
% 27.34/17.54 tff(410,plain,
% 27.34/17.54 ((~(c4 = c4)) <=> $false),
% 27.34/17.54 inference(transitivity,[status(thm)],[409, 270])).
% 27.34/17.54 tff(411,plain,
% 27.34/17.54 (((f7(f7(c2)) = c3) | (f1(f7(f7(c2)), c1) = c1) | big_f(f7(f7(c2)), f1(f7(f7(c2)), c1)) | (~(c4 = c4)) | big_f(f4(c4), c4) | (~(f4(c4) = f4(c4)))) <=> ((f7(f7(c2)) = c3) | (f1(f7(f7(c2)), c1) = c1) | big_f(f7(f7(c2)), f1(f7(f7(c2)), c1)) | $false | big_f(f4(c4), c4) | $false)),
% 27.34/17.54 inference(monotonicity,[status(thm)],[410, 407])).
% 27.34/17.54 tff(412,plain,
% 27.34/17.54 (((f7(f7(c2)) = c3) | (f1(f7(f7(c2)), c1) = c1) | big_f(f7(f7(c2)), f1(f7(f7(c2)), c1)) | (~(c4 = c4)) | big_f(f4(c4), c4) | (~(f4(c4) = f4(c4)))) <=> (big_f(f4(c4), c4) | (f7(f7(c2)) = c3) | (f1(f7(f7(c2)), c1) = c1) | big_f(f7(f7(c2)), f1(f7(f7(c2)), c1)))),
% 27.34/17.54 inference(transitivity,[status(thm)],[411, 404])).
% 27.34/17.54 tff(413,plain,
% 27.34/17.54 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f7(f7(c2)) = c3) | (f1(f7(f7(c2)), c1) = c1) | big_f(f7(f7(c2)), f1(f7(f7(c2)), c1)) | (~(c4 = c4)) | big_f(f4(c4), c4) | (~(f4(c4) = f4(c4))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (big_f(f4(c4), c4) | (f7(f7(c2)) = c3) | (f1(f7(f7(c2)), c1) = c1) | big_f(f7(f7(c2)), f1(f7(f7(c2)), c1))))),
% 27.34/17.54 inference(monotonicity,[status(thm)],[412])).
% 27.34/17.54 tff(414,plain,
% 27.34/17.54 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f7(f7(c2)) = c3) | (f1(f7(f7(c2)), c1) = c1) | big_f(f7(f7(c2)), f1(f7(f7(c2)), c1)) | (~(c4 = c4)) | big_f(f4(c4), c4) | (~(f4(c4) = f4(c4))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | big_f(f4(c4), c4) | (f7(f7(c2)) = c3) | (f1(f7(f7(c2)), c1) = c1) | big_f(f7(f7(c2)), f1(f7(f7(c2)), c1)))),
% 27.34/17.54 inference(transitivity,[status(thm)],[413, 403])).
% 27.34/17.54 tff(415,plain,
% 27.34/17.54 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f7(f7(c2)) = c3) | (f1(f7(f7(c2)), c1) = c1) | big_f(f7(f7(c2)), f1(f7(f7(c2)), c1)) | (~(c4 = c4)) | big_f(f4(c4), c4) | (~(f4(c4) = f4(c4))))),
% 27.34/17.54 inference(quant_inst,[status(thm)],[])).
% 27.34/17.54 tff(416,plain,
% 27.34/17.54 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | big_f(f4(c4), c4) | (f7(f7(c2)) = c3) | (f1(f7(f7(c2)), c1) = c1) | big_f(f7(f7(c2)), f1(f7(f7(c2)), c1))),
% 27.34/17.54 inference(modus_ponens,[status(thm)],[415, 414])).
% 27.34/17.54 tff(417,plain,
% 27.34/17.54 (big_f(f4(c4), c4) | (f7(f7(c2)) = c3) | (f1(f7(f7(c2)), c1) = c1) | big_f(f7(f7(c2)), f1(f7(f7(c2)), c1))),
% 27.34/17.54 inference(unit_resolution,[status(thm)],[416, 402])).
% 27.34/17.54 tff(418,plain,
% 27.34/17.54 (big_f(f7(f7(c2)), f1(f7(f7(c2)), c1))),
% 27.34/17.54 inference(unit_resolution,[status(thm)],[417, 380, 379, 378])).
% 27.34/17.54 tff(419,plain,
% 27.34/17.54 (big_f(c2, f1(c2, c1))),
% 27.34/17.54 inference(modus_ponens,[status(thm)],[418, 392])).
% 27.34/17.54 tff(420,plain,
% 27.34/17.54 (big_f(c2, c2)),
% 27.34/17.54 inference(modus_ponens,[status(thm)],[419, 389])).
% 27.34/17.54 tff(421,plain,
% 27.34/17.54 ($false),
% 27.34/17.54 inference(unit_resolution,[status(thm)],[121, 420])).
% 27.34/17.54 tff(422,plain,((f1(f7(f7(c2)), c1) = c1) | big_f(c2, c2) | (~(f7(c1) = c2)) | (~(f7(c2) = c1)) | big_f(f4(c4), c4) | (f7(f7(c2)) = c3)), inference(lemma,lemma(discharge,[]))).
% 27.34/17.54 tff(423,plain,
% 27.34/17.54 (f1(f7(f7(c2)), c1) = c1),
% 27.34/17.54 inference(unit_resolution,[status(thm)],[422, 379, 347, 292, 121, 378])).
% 27.34/17.54 tff(424,plain,
% 27.34/17.54 (f1(c2, f9(c2, c2)) = c1),
% 27.34/17.54 inference(transitivity,[status(thm)],[349, 356, 423])).
% 27.34/17.54 tff(425,plain,
% 27.34/17.54 (big_f(c2, f1(c2, f9(c2, c2))) <=> big_f(c2, c1)),
% 27.34/17.54 inference(monotonicity,[status(thm)],[424])).
% 27.34/17.54 tff(426,plain,
% 27.34/17.54 (big_f(c2, c1) <=> big_f(c2, f1(c2, f9(c2, c2)))),
% 27.34/17.54 inference(symmetry,[status(thm)],[425])).
% 27.34/17.54 tff(427,plain,
% 27.34/17.54 (big_f(c2, f1(c2, f9(c2, c2)))),
% 27.34/17.54 inference(modus_ponens,[status(thm)],[348, 426])).
% 27.34/17.54 tff(428,plain,
% 27.34/17.54 (f1(c2, f9(c2, c2)) = f9(c2, c2)),
% 27.34/17.54 inference(transitivity,[status(thm)],[349, 356, 423, 149, 132])).
% 27.34/17.54 tff(429,assumption,(big_f(c2, f1(c2, f9(c2, c2)))), introduced(assumption)).
% 27.34/17.54 tff(430,assumption,(f1(c2, f9(c2, c2)) = f9(c2, c2)), introduced(assumption)).
% 27.34/17.54 tff(431,assumption,(c4 = c2), introduced(assumption)).
% 27.34/17.54 tff(432,plain,
% 27.34/17.54 (c2 = c4),
% 27.34/17.54 inference(modus_ponens,[status(thm)],[431, 159])).
% 27.34/17.54 tff(433,plain,
% 27.34/17.54 (c2 = c4),
% 27.34/17.54 inference(symmetry,[status(thm)],[431])).
% 27.34/17.54 tff(434,plain,
% 27.34/17.54 (f4(c2) = f4(c4)),
% 27.34/17.54 inference(monotonicity,[status(thm)],[433])).
% 27.34/17.54 tff(435,plain,
% 27.34/17.54 (f4(c4) = f4(c2)),
% 27.34/17.54 inference(symmetry,[status(thm)],[434])).
% 27.34/17.54 tff(436,plain,
% 27.34/17.54 (c2 = f4(c4)),
% 27.34/17.54 inference(symmetry,[status(thm)],[79])).
% 27.34/17.54 tff(437,plain,
% 27.34/17.54 (c2 = f4(c2)),
% 27.34/17.54 inference(transitivity,[status(thm)],[436, 435])).
% 27.34/17.54 tff(438,plain,
% 27.34/17.54 (^[X11: $i, X3: $i, X10: $i, X2: $i] : refl(((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))) <=> ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))))),
% 27.34/17.54 inference(bind,[status(th)],[])).
% 27.34/17.54 tff(439,plain,
% 27.34/17.54 (![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))) <=> ![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))),
% 27.34/17.54 inference(quant_intro,[status(thm)],[438])).
% 27.34/17.54 tff(440,plain,
% 27.34/17.54 (![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))) <=> ![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))),
% 27.34/17.54 inference(rewrite,[status(thm)],[])).
% 27.34/17.54 tff(441,plain,
% 27.34/17.54 (^[X11: $i, X3: $i, X10: $i, X2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~big_f(X10, f1(X10, X11))) | (~(f1(X10, X11) = X11))) <=> ((~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))), ((((~big_f(X10, f1(X10, X11))) | (~(f1(X10, X11) = X11))) | (X10 = c3)) <=> (((~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))) | (X10 = c3)))), rewrite((((~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))) | (X10 = c3)) <=> ((X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))), ((((~big_f(X10, f1(X10, X11))) | (~(f1(X10, X11) = X11))) | (X10 = c3)) <=> ((X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))))), (((((~big_f(X10, f1(X10, X11))) | (~(f1(X10, X11) = X11))) | (X10 = c3)) | big_f(X3, X2)) <=> (((X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))) | big_f(X3, X2)))), rewrite((((X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))) | big_f(X3, X2)) <=> ((X10 = c3) | big_f(X3, X2) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))), (((((~big_f(X10, f1(X10, X11))) | (~(f1(X10, X11) = X11))) | (X10 = c3)) | big_f(X3, X2)) <=> ((X10 = c3) | big_f(X3, X2) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))))), ((((((~big_f(X10, f1(X10, X11))) | (~(f1(X10, X11) = X11))) | (X10 = c3)) | big_f(X3, X2)) | (~(X3 = f4(X2)))) <=> (((X10 = c3) | big_f(X3, X2) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))) | (~(X3 = f4(X2)))))), rewrite((((X10 = c3) | big_f(X3, X2) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))) | (~(X3 = f4(X2)))) <=> ((X10 = c3) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))), ((((((~big_f(X10, f1(X10, X11))) | (~(f1(X10, X11) = X11))) | (X10 = c3)) | big_f(X3, X2)) | (~(X3 = f4(X2)))) <=> ((X10 = c3) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))))), (((((((~big_f(X10, f1(X10, X11))) | (~(f1(X10, X11) = X11))) | (X10 = c3)) | big_f(X3, X2)) | (~(X3 = f4(X2)))) | (~(X2 = c4))) <=> (((X10 = c3) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))) | (~(X2 = c4))))), rewrite((((X10 = c3) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))) | (~(X2 = c4))) <=> ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))), (((((((~big_f(X10, f1(X10, X11))) | (~(f1(X10, X11) = X11))) | (X10 = c3)) | big_f(X3, X2)) | (~(X3 = f4(X2)))) | (~(X2 = c4))) <=> ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))))),
% 27.34/17.55 inference(bind,[status(th)],[])).
% 27.34/17.55 tff(442,plain,
% 27.34/17.55 (![X11: $i, X3: $i, X10: $i, X2: $i] : ((((((~big_f(X10, f1(X10, X11))) | (~(f1(X10, X11) = X11))) | (X10 = c3)) | big_f(X3, X2)) | (~(X3 = f4(X2)))) | (~(X2 = c4))) <=> ![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))),
% 27.34/17.55 inference(quant_intro,[status(thm)],[441])).
% 27.34/17.55 tff(443,axiom,(![X11: $i, X3: $i, X10: $i, X2: $i] : ((((((~big_f(X10, f1(X10, X11))) | (~(f1(X10, X11) = X11))) | (X10 = c3)) | big_f(X3, X2)) | (~(X3 = f4(X2)))) | (~(X2 = c4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_10')).
% 27.34/17.55 tff(444,plain,
% 27.34/17.55 (![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))),
% 27.34/17.55 inference(modus_ponens,[status(thm)],[443, 442])).
% 27.34/17.55 tff(445,plain,
% 27.34/17.55 (![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))),
% 27.34/17.55 inference(modus_ponens,[status(thm)],[444, 440])).
% 27.34/17.55 tff(446,plain,(
% 27.34/17.55 ![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))),
% 27.34/17.55 inference(skolemize,[status(sab)],[445])).
% 27.34/17.55 tff(447,plain,
% 27.34/17.55 (![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))),
% 27.34/17.55 inference(modus_ponens,[status(thm)],[446, 439])).
% 27.34/17.55 tff(448,plain,
% 27.34/17.55 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (~(f1(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(c2, f1(c2, f9(c2, c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (~(f1(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(c2, f1(c2, f9(c2, c2)))))),
% 27.34/17.55 inference(rewrite,[status(thm)],[])).
% 27.34/17.55 tff(449,plain,
% 27.34/17.55 (((c2 = c3) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))) | (~(f1(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(c2, f1(c2, f9(c2, c2))))) <=> ((c2 = c3) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (~(f1(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(c2, f1(c2, f9(c2, c2)))))),
% 27.34/17.55 inference(rewrite,[status(thm)],[])).
% 27.34/17.55 tff(450,plain,
% 27.34/17.55 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))) | (~(f1(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(c2, f1(c2, f9(c2, c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (~(f1(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(c2, f1(c2, f9(c2, c2))))))),
% 27.34/17.55 inference(monotonicity,[status(thm)],[449])).
% 27.34/17.55 tff(451,plain,
% 27.34/17.55 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))) | (~(f1(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(c2, f1(c2, f9(c2, c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (~(f1(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(c2, f1(c2, f9(c2, c2)))))),
% 27.34/17.55 inference(transitivity,[status(thm)],[450, 448])).
% 27.34/17.55 tff(452,plain,
% 27.34/17.55 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))) | (~(f1(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(c2, f1(c2, f9(c2, c2)))))),
% 27.34/17.55 inference(quant_inst,[status(thm)],[])).
% 27.34/17.55 tff(453,plain,
% 27.34/17.55 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (~(f1(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(c2, f1(c2, f9(c2, c2))))),
% 27.34/17.55 inference(modus_ponens,[status(thm)],[452, 451])).
% 27.34/17.55 tff(454,plain,
% 27.34/17.55 ((~(c2 = c4)) | (~(c2 = f4(c2))) | (~(f1(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(c2, f1(c2, f9(c2, c2))))),
% 27.34/17.55 inference(unit_resolution,[status(thm)],[453, 447, 121, 377])).
% 27.34/17.55 tff(455,plain,
% 27.34/17.55 ($false),
% 27.34/17.55 inference(unit_resolution,[status(thm)],[454, 437, 432, 430, 429])).
% 27.34/17.55 tff(456,plain,((~(c4 = c2)) | (~(f1(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(c2, f1(c2, f9(c2, c2)))) | big_f(c2, c2) | (c2 = c3) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.34/17.55 tff(457,plain,
% 27.34/17.55 (~(c4 = c2)),
% 27.34/17.55 inference(unit_resolution,[status(thm)],[456, 428, 427, 121, 377, 79])).
% 27.34/17.55 tff(458,plain,
% 27.34/17.55 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((c4 = c1) | (c4 = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (c4 = c1) | (c4 = c2))),
% 27.34/17.55 inference(rewrite,[status(thm)],[])).
% 27.34/17.55 tff(459,plain,
% 27.34/17.55 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((c4 = c1) | (c4 = c2))),
% 27.34/17.55 inference(quant_inst,[status(thm)],[])).
% 27.34/17.55 tff(460,plain,
% 27.34/17.55 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (c4 = c1) | (c4 = c2)),
% 27.34/17.55 inference(modus_ponens,[status(thm)],[459, 458])).
% 27.34/17.55 tff(461,plain,
% 27.34/17.55 ((c4 = c1) | (c4 = c2)),
% 27.34/17.55 inference(unit_resolution,[status(thm)],[460, 10])).
% 27.34/17.55 tff(462,plain,
% 27.34/17.55 (c4 = c1),
% 27.34/17.55 inference(unit_resolution,[status(thm)],[461, 457])).
% 27.34/17.55 tff(463,plain,
% 27.34/17.55 (big_f(c2, c4) <=> big_f(c2, c1)),
% 27.34/17.55 inference(monotonicity,[status(thm)],[462])).
% 27.34/17.55 tff(464,plain,
% 27.34/17.55 (big_f(c2, c1) <=> big_f(c2, c4)),
% 27.34/17.55 inference(symmetry,[status(thm)],[463])).
% 27.34/17.55 tff(465,plain,
% 27.34/17.55 (big_f(c2, c1) <=> big_f(f4(c4), c4)),
% 27.34/17.55 inference(transitivity,[status(thm)],[464, 376])).
% 27.34/17.55 tff(466,plain,
% 27.34/17.55 (big_f(f4(c4), c4)),
% 27.34/17.55 inference(modus_ponens,[status(thm)],[348, 465])).
% 27.34/17.55 tff(467,plain,
% 27.34/17.55 ($false),
% 27.34/17.55 inference(unit_resolution,[status(thm)],[379, 466])).
% 27.34/17.55 tff(468,plain,(big_f(f4(c4), c4) | (~big_f(c2, c1)) | (~(f4(c4) = c2)) | big_f(c2, c2) | (c2 = c3) | (~(f7(c1) = c2)) | (~(f7(c2) = c1)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f10(c2) = c2)) | (f7(f7(c2)) = c3)), inference(lemma,lemma(discharge,[]))).
% 27.34/17.55 tff(469,plain,
% 27.34/17.55 (big_f(f4(c4), c4)),
% 27.34/17.55 inference(unit_resolution,[status(thm)],[468, 374, 79, 121, 348, 347, 292, 148, 122, 372])).
% 27.34/17.55 tff(470,plain,
% 27.34/17.55 (big_f(f4(c4), c4) <=> big_f(c2, c2)),
% 27.34/17.55 inference(monotonicity,[status(thm)],[79, 431])).
% 27.34/17.55 tff(471,plain,
% 27.34/17.55 (big_f(c2, c2) <=> big_f(f4(c4), c4)),
% 27.34/17.55 inference(symmetry,[status(thm)],[470])).
% 27.34/17.55 tff(472,plain,
% 27.34/17.55 ((~big_f(c2, c2)) <=> (~big_f(f4(c4), c4))),
% 27.34/17.55 inference(monotonicity,[status(thm)],[471])).
% 27.34/17.55 tff(473,plain,
% 27.34/17.55 (~big_f(f4(c4), c4)),
% 27.34/17.55 inference(modus_ponens,[status(thm)],[121, 472])).
% 27.34/17.55 tff(474,assumption,(big_f(f4(c4), c4)), introduced(assumption)).
% 27.34/17.55 tff(475,plain,
% 27.34/17.55 ($false),
% 27.34/17.55 inference(unit_resolution,[status(thm)],[474, 473])).
% 27.34/17.55 tff(476,plain,((~(f4(c4) = c2)) | (~big_f(f4(c4), c4)) | big_f(c2, c2) | (~(c4 = c2))), inference(lemma,lemma(discharge,[]))).
% 27.34/17.55 tff(477,plain,
% 27.34/17.55 (~(c4 = c2)),
% 27.34/17.55 inference(unit_resolution,[status(thm)],[476, 469, 79, 121])).
% 27.34/17.55 tff(478,plain,
% 27.34/17.55 (c4 = c1),
% 27.34/17.55 inference(unit_resolution,[status(thm)],[461, 477])).
% 27.34/17.55 tff(479,plain,
% 27.34/17.55 ((c4 = c1) <=> (c1 = c4)),
% 27.34/17.55 inference(commutativity,[status(thm)],[])).
% 27.34/17.55 tff(480,assumption,(c4 = c1), introduced(assumption)).
% 27.34/17.55 tff(481,plain,
% 27.34/17.55 (c1 = c4),
% 27.34/17.55 inference(modus_ponens,[status(thm)],[480, 479])).
% 27.34/17.55 tff(482,assumption,(~(c1 = c4)), introduced(assumption)).
% 27.34/17.55 tff(483,plain,
% 27.34/17.55 ($false),
% 27.34/17.55 inference(unit_resolution,[status(thm)],[482, 481])).
% 27.34/17.55 tff(484,plain,((~(c4 = c1)) | (c1 = c4)), inference(lemma,lemma(discharge,[]))).
% 27.36/17.55 tff(485,plain,
% 27.36/17.55 (c1 = c4),
% 27.36/17.55 inference(unit_resolution,[status(thm)],[484, 478])).
% 27.36/17.55 tff(486,plain,
% 27.36/17.55 (f9(c2, c2) = c4),
% 27.36/17.55 inference(modus_ponens,[status(thm)],[485, 362])).
% 27.36/17.55 tff(487,assumption,(big_f(f9(c2, c2), f9(c2, c2))), introduced(assumption)).
% 27.36/17.55 tff(488,plain,
% 27.36/17.55 (f4(f9(c2, c2)) = f4(c1)),
% 27.36/17.55 inference(monotonicity,[status(thm)],[161])).
% 27.36/17.55 tff(489,plain,
% 27.36/17.55 ((f9(c2, c2) = f4(f9(c2, c2))) <=> (c1 = f4(c1))),
% 27.36/17.55 inference(monotonicity,[status(thm)],[161, 488])).
% 27.36/17.55 tff(490,plain,
% 27.36/17.55 ((c1 = f4(c1)) <=> (f9(c2, c2) = f4(f9(c2, c2)))),
% 27.36/17.55 inference(symmetry,[status(thm)],[489])).
% 27.36/17.55 tff(491,plain,
% 27.36/17.55 (c1 = c4),
% 27.36/17.55 inference(symmetry,[status(thm)],[478])).
% 27.36/17.55 tff(492,plain,
% 27.36/17.55 (f4(c1) = f4(c4)),
% 27.36/17.55 inference(monotonicity,[status(thm)],[491])).
% 27.36/17.55 tff(493,plain,
% 27.36/17.55 (f4(c1) = c2),
% 27.36/17.55 inference(transitivity,[status(thm)],[492, 79])).
% 27.36/17.55 tff(494,plain,
% 27.36/17.55 ((c1 = f4(c1)) <=> (f9(c2, c2) = c2)),
% 27.36/17.55 inference(monotonicity,[status(thm)],[150, 493])).
% 27.36/17.55 tff(495,plain,
% 27.36/17.55 ((f9(c2, c2) = c2) <=> (c1 = f4(c1))),
% 27.36/17.55 inference(symmetry,[status(thm)],[494])).
% 27.36/17.55 tff(496,plain,
% 27.36/17.55 ((f9(c2, c2) = c2) <=> (f9(c2, c2) = f4(f9(c2, c2)))),
% 27.36/17.55 inference(transitivity,[status(thm)],[495, 490])).
% 27.36/17.55 tff(497,plain,
% 27.36/17.55 ((~(f9(c2, c2) = c2)) <=> (~(f9(c2, c2) = f4(f9(c2, c2))))),
% 27.36/17.55 inference(monotonicity,[status(thm)],[496])).
% 27.36/17.55 tff(498,plain,
% 27.36/17.55 (~(f9(c2, c2) = f4(f9(c2, c2)))),
% 27.36/17.55 inference(modus_ponens,[status(thm)],[185, 497])).
% 27.36/17.55 tff(499,assumption,(f1(f7(f7(c2)), c1) = c2), introduced(assumption)).
% 27.36/17.55 tff(500,plain,
% 27.36/17.55 (f1(c2, c1) = c2),
% 27.36/17.55 inference(transitivity,[status(thm)],[356, 499])).
% 27.36/17.55 tff(501,plain,
% 27.36/17.55 (big_f(c2, f1(c2, c1)) <=> big_f(c2, c2)),
% 27.36/17.55 inference(monotonicity,[status(thm)],[500])).
% 27.36/17.55 tff(502,plain,
% 27.36/17.55 (big_f(c2, c2) <=> big_f(c2, f1(c2, c1))),
% 27.36/17.55 inference(symmetry,[status(thm)],[501])).
% 27.36/17.55 tff(503,plain,
% 27.36/17.55 (big_f(c2, c2) <=> big_f(c2, f1(c2, f9(c2, c2)))),
% 27.36/17.55 inference(transitivity,[status(thm)],[502, 351])).
% 27.36/17.55 tff(504,plain,
% 27.36/17.55 ((~big_f(c2, c2)) <=> (~big_f(c2, f1(c2, f9(c2, c2))))),
% 27.36/17.55 inference(monotonicity,[status(thm)],[503])).
% 27.36/17.55 tff(505,plain,
% 27.36/17.55 (~big_f(c2, f1(c2, f9(c2, c2)))),
% 27.36/17.55 inference(modus_ponens,[status(thm)],[121, 504])).
% 27.36/17.55 tff(506,plain,
% 27.36/17.55 ((f1(c2, f9(c2, c2)) = f9(c2, c2)) <=> (f1(c2, c1) = c1)),
% 27.36/17.55 inference(monotonicity,[status(thm)],[349, 161])).
% 27.36/17.55 tff(507,plain,
% 27.36/17.55 ((f1(c2, c1) = c1) <=> (f1(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.36/17.55 inference(symmetry,[status(thm)],[506])).
% 27.36/17.55 tff(508,plain,
% 27.36/17.55 ((f1(c2, c1) = c1) <=> (c2 = f9(c2, c2))),
% 27.36/17.55 inference(monotonicity,[status(thm)],[500, 150])).
% 27.36/17.55 tff(509,plain,
% 27.36/17.55 ((f1(c2, c1) = c1) <=> (f9(c2, c2) = c2)),
% 27.36/17.55 inference(transitivity,[status(thm)],[508, 167])).
% 27.36/17.55 tff(510,plain,
% 27.36/17.55 ((f9(c2, c2) = c2) <=> (f1(c2, c1) = c1)),
% 27.36/17.55 inference(symmetry,[status(thm)],[509])).
% 27.36/17.55 tff(511,plain,
% 27.36/17.55 ((f9(c2, c2) = c2) <=> (f1(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.36/17.55 inference(transitivity,[status(thm)],[510, 507])).
% 27.36/17.55 tff(512,plain,
% 27.36/17.55 ((~(f9(c2, c2) = c2)) <=> (~(f1(c2, f9(c2, c2)) = f9(c2, c2)))),
% 27.36/17.55 inference(monotonicity,[status(thm)],[511])).
% 27.36/17.55 tff(513,plain,
% 27.36/17.55 (~(f1(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.36/17.55 inference(modus_ponens,[status(thm)],[185, 512])).
% 27.36/17.55 tff(514,assumption,(f9(c2, c2) = c4), introduced(assumption)).
% 27.36/17.55 tff(515,assumption,(~(f9(c2, c2) = f4(f9(c2, c2)))), introduced(assumption)).
% 27.36/17.55 tff(516,plain,
% 27.36/17.55 (^[X11: $i, X3: $i, X10: $i, X2: $i] : refl(((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2))) <=> ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2))))),
% 27.36/17.55 inference(bind,[status(th)],[])).
% 27.36/17.55 tff(517,plain,
% 27.36/17.55 (![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2))) <=> ![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))),
% 27.36/17.55 inference(quant_intro,[status(thm)],[516])).
% 27.36/17.55 tff(518,plain,
% 27.36/17.55 (![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2))) <=> ![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))),
% 27.36/17.55 inference(rewrite,[status(thm)],[])).
% 27.36/17.55 tff(519,plain,
% 27.36/17.55 (^[X11: $i, X3: $i, X10: $i, X2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((big_f(X10, f1(X10, X11)) | (f1(X10, X11) = X11)) <=> ((f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))), (((big_f(X10, f1(X10, X11)) | (f1(X10, X11) = X11)) | (X10 = c3)) <=> (((f1(X10, X11) = X11) | big_f(X10, f1(X10, X11))) | (X10 = c3)))), rewrite((((f1(X10, X11) = X11) | big_f(X10, f1(X10, X11))) | (X10 = c3)) <=> ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))), (((big_f(X10, f1(X10, X11)) | (f1(X10, X11) = X11)) | (X10 = c3)) <=> ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11))))), ((((big_f(X10, f1(X10, X11)) | (f1(X10, X11) = X11)) | (X10 = c3)) | (~big_f(X3, X2))) <=> (((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11))) | (~big_f(X3, X2))))), rewrite((((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11))) | (~big_f(X3, X2))) <=> ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~big_f(X3, X2)))), ((((big_f(X10, f1(X10, X11)) | (f1(X10, X11) = X11)) | (X10 = c3)) | (~big_f(X3, X2))) <=> ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~big_f(X3, X2))))), (((((big_f(X10, f1(X10, X11)) | (f1(X10, X11) = X11)) | (X10 = c3)) | (~big_f(X3, X2))) | (X3 = f4(X2))) <=> (((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~big_f(X3, X2))) | (X3 = f4(X2))))), rewrite((((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~big_f(X3, X2))) | (X3 = f4(X2))) <=> ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (X3 = f4(X2)) | (~big_f(X3, X2)))), (((((big_f(X10, f1(X10, X11)) | (f1(X10, X11) = X11)) | (X10 = c3)) | (~big_f(X3, X2))) | (X3 = f4(X2))) <=> ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (X3 = f4(X2)) | (~big_f(X3, X2))))), ((((((big_f(X10, f1(X10, X11)) | (f1(X10, X11) = X11)) | (X10 = c3)) | (~big_f(X3, X2))) | (X3 = f4(X2))) | (~(X2 = c4))) <=> (((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (X3 = f4(X2)) | (~big_f(X3, X2))) | (~(X2 = c4))))), rewrite((((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (X3 = f4(X2)) | (~big_f(X3, X2))) | (~(X2 = c4))) <=> ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))), ((((((big_f(X10, f1(X10, X11)) | (f1(X10, X11) = X11)) | (X10 = c3)) | (~big_f(X3, X2))) | (X3 = f4(X2))) | (~(X2 = c4))) <=> ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))))),
% 27.36/17.55 inference(bind,[status(th)],[])).
% 27.36/17.55 tff(520,plain,
% 27.36/17.55 (![X11: $i, X3: $i, X10: $i, X2: $i] : (((((big_f(X10, f1(X10, X11)) | (f1(X10, X11) = X11)) | (X10 = c3)) | (~big_f(X3, X2))) | (X3 = f4(X2))) | (~(X2 = c4))) <=> ![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))),
% 27.36/17.55 inference(quant_intro,[status(thm)],[519])).
% 27.36/17.55 tff(521,axiom,(![X11: $i, X3: $i, X10: $i, X2: $i] : (((((big_f(X10, f1(X10, X11)) | (f1(X10, X11) = X11)) | (X10 = c3)) | (~big_f(X3, X2))) | (X3 = f4(X2))) | (~(X2 = c4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_5')).
% 27.36/17.55 tff(522,plain,
% 27.36/17.55 (![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))),
% 27.36/17.55 inference(modus_ponens,[status(thm)],[521, 520])).
% 27.36/17.55 tff(523,plain,
% 27.36/17.55 (![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))),
% 27.36/17.55 inference(modus_ponens,[status(thm)],[522, 518])).
% 27.36/17.55 tff(524,plain,(
% 27.36/17.55 ![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))),
% 27.36/17.55 inference(skolemize,[status(sab)],[523])).
% 27.36/17.55 tff(525,plain,
% 27.36/17.55 (![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))),
% 27.36/17.55 inference(modus_ponens,[status(thm)],[524, 517])).
% 27.36/17.55 tff(526,plain,
% 27.36/17.55 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c2 = c3) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)) | (f1(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(c2, f1(c2, f9(c2, c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (c2 = c3) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)) | (f1(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(c2, f1(c2, f9(c2, c2))))),
% 27.36/17.55 inference(rewrite,[status(thm)],[])).
% 27.36/17.55 tff(527,plain,
% 27.36/17.55 (((c2 = c3) | (f1(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(c2, f1(c2, f9(c2, c2))) | (~(f9(c2, c2) = c4)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2)))) <=> ((c2 = c3) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)) | (f1(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(c2, f1(c2, f9(c2, c2))))),
% 27.36/17.55 inference(rewrite,[status(thm)],[])).
% 27.36/17.55 tff(528,plain,
% 27.36/17.55 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c2 = c3) | (f1(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(c2, f1(c2, f9(c2, c2))) | (~(f9(c2, c2) = c4)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c2 = c3) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)) | (f1(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(c2, f1(c2, f9(c2, c2)))))),
% 27.36/17.55 inference(monotonicity,[status(thm)],[527])).
% 27.36/17.55 tff(529,plain,
% 27.36/17.55 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c2 = c3) | (f1(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(c2, f1(c2, f9(c2, c2))) | (~(f9(c2, c2) = c4)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (c2 = c3) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)) | (f1(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(c2, f1(c2, f9(c2, c2))))),
% 27.36/17.55 inference(transitivity,[status(thm)],[528, 526])).
% 27.36/17.55 tff(530,plain,
% 27.36/17.55 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c2 = c3) | (f1(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(c2, f1(c2, f9(c2, c2))) | (~(f9(c2, c2) = c4)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))))),
% 27.36/17.55 inference(quant_inst,[status(thm)],[])).
% 27.36/17.55 tff(531,plain,
% 27.36/17.55 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (c2 = c3) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)) | (f1(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(c2, f1(c2, f9(c2, c2)))),
% 27.36/17.55 inference(modus_ponens,[status(thm)],[530, 529])).
% 27.36/17.55 tff(532,plain,
% 27.36/17.55 ($false),
% 27.36/17.55 inference(unit_resolution,[status(thm)],[531, 525, 377, 515, 487, 514, 513, 505])).
% 27.36/17.55 tff(533,plain,((~(f1(f7(f7(c2)), c1) = c2)) | (c2 = c3) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)) | big_f(c2, c2) | (~(f7(c1) = c2)) | (~(f7(c2) = c1)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.36/17.55 tff(534,plain,
% 27.36/17.55 (~(f1(f7(f7(c2)), c1) = c2)),
% 27.36/17.55 inference(unit_resolution,[status(thm)],[533, 374, 498, 487, 486, 121, 347, 292, 148, 79, 122])).
% 27.36/17.55 tff(535,plain,
% 27.36/17.55 (f1(f7(f7(c2)), c1) = c1),
% 27.36/17.55 inference(unit_resolution,[status(thm)],[384, 534])).
% 27.36/17.55 tff(536,plain,
% 27.36/17.55 (c1 = f1(f7(f7(c2)), c1)),
% 27.36/17.55 inference(symmetry,[status(thm)],[535])).
% 27.36/17.55 tff(537,plain,
% 27.36/17.55 (c1 = f1(c2, c1)),
% 27.36/17.55 inference(transitivity,[status(thm)],[536, 357])).
% 27.36/17.55 tff(538,plain,
% 27.36/17.55 (big_f(c2, c1) <=> big_f(c2, f1(c2, c1))),
% 27.36/17.55 inference(monotonicity,[status(thm)],[537])).
% 27.36/17.55 tff(539,plain,
% 27.36/17.55 (big_f(c2, c1) <=> big_f(c2, f1(c2, f9(c2, c2)))),
% 27.36/17.55 inference(transitivity,[status(thm)],[538, 351])).
% 27.36/17.55 tff(540,plain,
% 27.36/17.55 (big_f(c2, f1(c2, f9(c2, c2)))),
% 27.36/17.55 inference(modus_ponens,[status(thm)],[348, 539])).
% 27.36/17.55 tff(541,plain,
% 27.36/17.55 ((f1(f7(f7(c2)), c1) = c1) <=> (f1(c2, c1) = c1)),
% 27.36/17.55 inference(monotonicity,[status(thm)],[357])).
% 27.36/17.55 tff(542,plain,
% 27.36/17.55 ((f1(f7(f7(c2)), c1) = c1) <=> (f1(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.36/17.55 inference(transitivity,[status(thm)],[541, 507])).
% 27.36/17.55 tff(543,plain,
% 27.36/17.55 (f1(c2, f9(c2, c2)) = f9(c2, c2)),
% 27.36/17.55 inference(modus_ponens,[status(thm)],[535, 542])).
% 27.36/17.55 tff(544,plain,
% 27.36/17.55 (^[X11: $i, X3: $i, X10: $i, X2: $i] : refl(((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))) <=> ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))))),
% 27.36/17.55 inference(bind,[status(th)],[])).
% 27.36/17.55 tff(545,plain,
% 27.36/17.55 (![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))) <=> ![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))),
% 27.36/17.55 inference(quant_intro,[status(thm)],[544])).
% 27.36/17.55 tff(546,plain,
% 27.36/17.55 (![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))) <=> ![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))),
% 27.36/17.55 inference(rewrite,[status(thm)],[])).
% 27.36/17.55 tff(547,plain,
% 27.36/17.55 (^[X11: $i, X3: $i, X10: $i, X2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~big_f(X10, f1(X10, X11))) | (~(f1(X10, X11) = X11))) <=> ((~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))), ((((~big_f(X10, f1(X10, X11))) | (~(f1(X10, X11) = X11))) | (X10 = c3)) <=> (((~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))) | (X10 = c3)))), rewrite((((~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))) | (X10 = c3)) <=> ((X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))), ((((~big_f(X10, f1(X10, X11))) | (~(f1(X10, X11) = X11))) | (X10 = c3)) <=> ((X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))))), (((((~big_f(X10, f1(X10, X11))) | (~(f1(X10, X11) = X11))) | (X10 = c3)) | (~big_f(X3, X2))) <=> (((X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))) | (~big_f(X3, X2))))), rewrite((((X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))) | (~big_f(X3, X2))) <=> ((X10 = c3) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))), (((((~big_f(X10, f1(X10, X11))) | (~(f1(X10, X11) = X11))) | (X10 = c3)) | (~big_f(X3, X2))) <=> ((X10 = c3) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))))), ((((((~big_f(X10, f1(X10, X11))) | (~(f1(X10, X11) = X11))) | (X10 = c3)) | (~big_f(X3, X2))) | (X3 = f4(X2))) <=> (((X10 = c3) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))) | (X3 = f4(X2))))), rewrite((((X10 = c3) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))) | (X3 = f4(X2))) <=> ((X10 = c3) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))), ((((((~big_f(X10, f1(X10, X11))) | (~(f1(X10, X11) = X11))) | (X10 = c3)) | (~big_f(X3, X2))) | (X3 = f4(X2))) <=> ((X10 = c3) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))))), (((((((~big_f(X10, f1(X10, X11))) | (~(f1(X10, X11) = X11))) | (X10 = c3)) | (~big_f(X3, X2))) | (X3 = f4(X2))) | (~(X2 = c4))) <=> (((X10 = c3) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))) | (~(X2 = c4))))), rewrite((((X10 = c3) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))) | (~(X2 = c4))) <=> ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))), (((((((~big_f(X10, f1(X10, X11))) | (~(f1(X10, X11) = X11))) | (X10 = c3)) | (~big_f(X3, X2))) | (X3 = f4(X2))) | (~(X2 = c4))) <=> ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))))),
% 27.36/17.56 inference(bind,[status(th)],[])).
% 27.36/17.56 tff(548,plain,
% 27.36/17.56 (![X11: $i, X3: $i, X10: $i, X2: $i] : ((((((~big_f(X10, f1(X10, X11))) | (~(f1(X10, X11) = X11))) | (X10 = c3)) | (~big_f(X3, X2))) | (X3 = f4(X2))) | (~(X2 = c4))) <=> ![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))),
% 27.36/17.56 inference(quant_intro,[status(thm)],[547])).
% 27.36/17.56 tff(549,axiom,(![X11: $i, X3: $i, X10: $i, X2: $i] : ((((((~big_f(X10, f1(X10, X11))) | (~(f1(X10, X11) = X11))) | (X10 = c3)) | (~big_f(X3, X2))) | (X3 = f4(X2))) | (~(X2 = c4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_9')).
% 27.36/17.56 tff(550,plain,
% 27.36/17.56 (![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))),
% 27.36/17.56 inference(modus_ponens,[status(thm)],[549, 548])).
% 27.36/17.56 tff(551,plain,
% 27.36/17.56 (![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))),
% 27.36/17.56 inference(modus_ponens,[status(thm)],[550, 546])).
% 27.36/17.56 tff(552,plain,(
% 27.36/17.56 ![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))),
% 27.36/17.56 inference(skolemize,[status(sab)],[551])).
% 27.36/17.56 tff(553,plain,
% 27.36/17.56 (![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))),
% 27.36/17.56 inference(modus_ponens,[status(thm)],[552, 545])).
% 27.36/17.56 tff(554,plain,
% 27.36/17.56 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)) | (~(f1(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(c2, f1(c2, f9(c2, c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)) | (~(f1(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(c2, f1(c2, f9(c2, c2)))))),
% 27.36/17.56 inference(rewrite,[status(thm)],[])).
% 27.36/17.56 tff(555,plain,
% 27.36/17.56 (((c2 = c3) | (~(f9(c2, c2) = c4)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f1(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(c2, f1(c2, f9(c2, c2))))) <=> ((c2 = c3) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)) | (~(f1(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(c2, f1(c2, f9(c2, c2)))))),
% 27.36/17.56 inference(rewrite,[status(thm)],[])).
% 27.36/17.56 tff(556,plain,
% 27.36/17.56 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f9(c2, c2) = c4)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f1(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(c2, f1(c2, f9(c2, c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)) | (~(f1(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(c2, f1(c2, f9(c2, c2))))))),
% 27.36/17.56 inference(monotonicity,[status(thm)],[555])).
% 27.36/17.56 tff(557,plain,
% 27.36/17.56 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f9(c2, c2) = c4)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f1(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(c2, f1(c2, f9(c2, c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)) | (~(f1(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(c2, f1(c2, f9(c2, c2)))))),
% 27.36/17.56 inference(transitivity,[status(thm)],[556, 554])).
% 27.36/17.56 tff(558,plain,
% 27.36/17.56 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f9(c2, c2) = c4)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f1(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(c2, f1(c2, f9(c2, c2)))))),
% 27.36/17.56 inference(quant_inst,[status(thm)],[])).
% 27.36/17.56 tff(559,plain,
% 27.36/17.56 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)) | (~(f1(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(c2, f1(c2, f9(c2, c2))))),
% 27.36/17.56 inference(modus_ponens,[status(thm)],[558, 557])).
% 27.36/17.56 tff(560,plain,
% 27.36/17.56 ($false),
% 27.36/17.56 inference(unit_resolution,[status(thm)],[559, 553, 374, 498, 487, 486, 543, 540])).
% 27.36/17.56 tff(561,plain,((~(c3 = c1)) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~big_f(c2, c1)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f7(c1) = c2)) | (~(f7(c2) = c1)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 27.36/17.56 tff(562,plain,
% 27.36/17.56 (~(c3 = c1)),
% 27.36/17.56 inference(unit_resolution,[status(thm)],[561, 121, 348, 148, 79, 122, 347, 292, 346])).
% 27.36/17.56 tff(563,plain,
% 27.36/17.56 (~(f9(c2, c2) = c3)),
% 27.36/17.56 inference(modus_ponens,[status(thm)],[562, 341])).
% 27.36/17.56 tff(564,plain,
% 27.36/17.56 (c1 = c4),
% 27.36/17.56 inference(unit_resolution,[status(thm)],[484, 480])).
% 27.36/17.56 tff(565,plain,
% 27.36/17.56 (f9(c2, c2) = c4),
% 27.36/17.56 inference(modus_ponens,[status(thm)],[564, 362])).
% 27.36/17.56 tff(566,assumption,(~(f9(c2, c2) = c3)), introduced(assumption)).
% 27.36/17.56 tff(567,plain,
% 27.36/17.56 (c1 = c4),
% 27.36/17.56 inference(symmetry,[status(thm)],[480])).
% 27.36/17.56 tff(568,plain,
% 27.36/17.56 (f4(c1) = f4(c4)),
% 27.36/17.56 inference(monotonicity,[status(thm)],[567])).
% 27.36/17.56 tff(569,plain,
% 27.36/17.56 (f4(c1) = c2),
% 27.36/17.56 inference(transitivity,[status(thm)],[568, 79])).
% 27.36/17.56 tff(570,plain,
% 27.36/17.56 ((c1 = f4(c1)) <=> (f9(c2, c2) = c2)),
% 27.36/17.56 inference(monotonicity,[status(thm)],[150, 569])).
% 27.36/17.56 tff(571,plain,
% 27.36/17.56 ((f9(c2, c2) = c2) <=> (c1 = f4(c1))),
% 27.36/17.56 inference(symmetry,[status(thm)],[570])).
% 27.36/17.56 tff(572,plain,
% 27.36/17.56 ((f9(c2, c2) = c2) <=> (f9(c2, c2) = f4(f9(c2, c2)))),
% 27.36/17.56 inference(transitivity,[status(thm)],[571, 490])).
% 27.36/17.56 tff(573,plain,
% 27.36/17.56 ((~(f9(c2, c2) = c2)) <=> (~(f9(c2, c2) = f4(f9(c2, c2))))),
% 27.36/17.56 inference(monotonicity,[status(thm)],[572])).
% 27.36/17.56 tff(574,plain,
% 27.36/17.56 (~(f9(c2, c2) = f4(f9(c2, c2)))),
% 27.36/17.56 inference(modus_ponens,[status(thm)],[185, 573])).
% 27.36/17.56 tff(575,assumption,(f1(c1, c1) = c2), introduced(assumption)).
% 27.36/17.56 tff(576,plain,
% 27.36/17.56 (f1(f9(c2, c2), f9(c2, c2)) = f1(c1, c1)),
% 27.36/17.56 inference(monotonicity,[status(thm)],[161, 161])).
% 27.36/17.56 tff(577,plain,
% 27.36/17.56 (f1(f9(c2, c2), f9(c2, c2)) = c2),
% 27.36/17.56 inference(transitivity,[status(thm)],[576, 575])).
% 27.36/17.56 tff(578,plain,
% 27.36/17.56 ((f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) <=> (c2 = f9(c2, c2))),
% 27.36/17.56 inference(monotonicity,[status(thm)],[577])).
% 27.36/17.56 tff(579,plain,
% 27.36/17.56 ((f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) <=> (f9(c2, c2) = c2)),
% 27.36/17.56 inference(transitivity,[status(thm)],[578, 167])).
% 27.36/17.56 tff(580,plain,
% 27.36/17.56 ((f9(c2, c2) = c2) <=> (f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))),
% 27.36/17.56 inference(symmetry,[status(thm)],[579])).
% 27.36/17.56 tff(581,plain,
% 27.36/17.56 ((~(f9(c2, c2) = c2)) <=> (~(f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)))),
% 27.36/17.56 inference(monotonicity,[status(thm)],[580])).
% 27.36/17.56 tff(582,plain,
% 27.36/17.56 (~(f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))),
% 27.36/17.56 inference(modus_ponens,[status(thm)],[185, 581])).
% 27.36/17.56 tff(583,plain,
% 27.36/17.56 (f1(f9(c2, c2), f9(c2, c2)) = f10(c2)),
% 27.36/17.56 inference(transitivity,[status(thm)],[576, 575, 216])).
% 27.36/17.56 tff(584,plain,
% 27.36/17.56 (big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2))) <=> big_f(f9(c2, c2), f10(c2))),
% 27.36/17.56 inference(monotonicity,[status(thm)],[583])).
% 27.36/17.56 tff(585,plain,
% 27.36/17.56 (big_f(f9(c2, c2), f10(c2)) <=> big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2)))),
% 27.36/17.56 inference(symmetry,[status(thm)],[584])).
% 27.36/17.56 tff(586,plain,
% 27.36/17.56 ((~big_f(f9(c2, c2), f10(c2))) <=> (~big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2))))),
% 27.36/17.56 inference(monotonicity,[status(thm)],[585])).
% 27.36/17.56 tff(587,plain,
% 27.36/17.56 (~big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2)))),
% 27.36/17.56 inference(modus_ponens,[status(thm)],[256, 586])).
% 27.36/17.56 tff(588,plain,
% 27.36/17.56 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((f9(c2, c2) = c3) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)) | (f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (f9(c2, c2) = c3) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)) | (f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2))))),
% 27.36/17.56 inference(rewrite,[status(thm)],[])).
% 27.36/17.56 tff(589,plain,
% 27.36/17.56 (((f9(c2, c2) = c3) | (f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2)))) <=> ((f9(c2, c2) = c3) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)) | (f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2))))),
% 27.36/17.56 inference(rewrite,[status(thm)],[])).
% 27.36/17.56 tff(590,plain,
% 27.36/17.56 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((f9(c2, c2) = c3) | (f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((f9(c2, c2) = c3) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)) | (f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2)))))),
% 27.36/17.56 inference(monotonicity,[status(thm)],[589])).
% 27.36/17.56 tff(591,plain,
% 27.36/17.56 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((f9(c2, c2) = c3) | (f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (f9(c2, c2) = c3) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)) | (f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2))))),
% 27.36/17.56 inference(transitivity,[status(thm)],[590, 588])).
% 27.36/17.56 tff(592,plain,
% 27.36/17.56 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((f9(c2, c2) = c3) | (f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))))),
% 27.36/17.56 inference(quant_inst,[status(thm)],[])).
% 27.36/17.56 tff(593,plain,
% 27.36/17.56 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (f9(c2, c2) = c3) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)) | (f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2)))),
% 27.36/17.56 inference(modus_ponens,[status(thm)],[592, 591])).
% 27.36/17.56 tff(594,plain,
% 27.36/17.56 ((f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2)))),
% 27.36/17.56 inference(unit_resolution,[status(thm)],[593, 525, 566, 515, 487, 514])).
% 27.36/17.56 tff(595,plain,
% 27.36/17.56 ($false),
% 27.36/17.56 inference(unit_resolution,[status(thm)],[594, 587, 582])).
% 27.36/17.56 tff(596,plain,((~(f1(c1, c1) = c2)) | (f9(c2, c2) = c3) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)) | big_f(f9(c2, c2), f10(c2)) | (~(f10(c2) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.36/17.56 tff(597,plain,
% 27.36/17.56 (~(f1(c1, c1) = c2)),
% 27.36/17.56 inference(unit_resolution,[status(thm)],[596, 574, 566, 346, 565, 256, 122, 148, 79])).
% 27.36/17.56 tff(598,plain,
% 27.36/17.56 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f1(c1, c1) = c1) | (f1(c1, c1) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f1(c1, c1) = c1) | (f1(c1, c1) = c2))),
% 27.36/17.56 inference(rewrite,[status(thm)],[])).
% 27.36/17.56 tff(599,plain,
% 27.36/17.56 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f1(c1, c1) = c1) | (f1(c1, c1) = c2))),
% 27.36/17.56 inference(quant_inst,[status(thm)],[])).
% 27.36/17.56 tff(600,plain,
% 27.36/17.56 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f1(c1, c1) = c1) | (f1(c1, c1) = c2)),
% 27.36/17.56 inference(modus_ponens,[status(thm)],[599, 598])).
% 27.36/17.56 tff(601,plain,
% 27.36/17.56 ((f1(c1, c1) = c1) | (f1(c1, c1) = c2)),
% 27.36/17.56 inference(unit_resolution,[status(thm)],[600, 10])).
% 27.36/17.56 tff(602,plain,
% 27.36/17.56 (f1(c1, c1) = c1),
% 27.36/17.56 inference(unit_resolution,[status(thm)],[601, 597])).
% 27.36/17.56 tff(603,plain,
% 27.36/17.56 (f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)),
% 27.36/17.56 inference(transitivity,[status(thm)],[576, 602, 149, 132])).
% 27.36/17.56 tff(604,plain,
% 27.36/17.56 (f1(f9(c2, c2), f9(c2, c2)) = c1),
% 27.36/17.56 inference(transitivity,[status(thm)],[576, 602])).
% 27.36/17.56 tff(605,plain,
% 27.36/17.56 (big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2))) <=> big_f(f7(c2), c1)),
% 27.36/17.56 inference(monotonicity,[status(thm)],[343, 604])).
% 27.36/17.56 tff(606,plain,
% 27.36/17.56 (big_f(f7(c2), c1) <=> big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2)))),
% 27.36/17.56 inference(symmetry,[status(thm)],[605])).
% 27.36/17.56 tff(607,plain,
% 27.36/17.56 (big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2)))),
% 27.36/17.56 inference(modus_ponens,[status(thm)],[338, 606])).
% 27.36/17.56 tff(608,plain,
% 27.36/17.56 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f9(c2, c2) = c3) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)) | (~(f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (f9(c2, c2) = c3) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)) | (~(f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2)))))),
% 27.36/17.56 inference(rewrite,[status(thm)],[])).
% 27.36/17.56 tff(609,plain,
% 27.36/17.56 (((f9(c2, c2) = c3) | (~(f9(c2, c2) = c4)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2))))) <=> ((f9(c2, c2) = c3) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)) | (~(f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2)))))),
% 27.36/17.56 inference(rewrite,[status(thm)],[])).
% 27.36/17.56 tff(610,plain,
% 27.36/17.56 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f9(c2, c2) = c3) | (~(f9(c2, c2) = c4)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f9(c2, c2) = c3) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)) | (~(f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2))))))),
% 27.36/17.56 inference(monotonicity,[status(thm)],[609])).
% 27.36/17.56 tff(611,plain,
% 27.36/17.56 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f9(c2, c2) = c3) | (~(f9(c2, c2) = c4)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (f9(c2, c2) = c3) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)) | (~(f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2)))))),
% 27.36/17.56 inference(transitivity,[status(thm)],[610, 608])).
% 27.36/17.56 tff(612,plain,
% 27.36/17.56 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f9(c2, c2) = c3) | (~(f9(c2, c2) = c4)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2)))))),
% 27.36/17.56 inference(quant_inst,[status(thm)],[])).
% 27.36/17.56 tff(613,plain,
% 27.36/17.56 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (f9(c2, c2) = c3) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)) | (~(f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2))))),
% 27.36/17.56 inference(modus_ponens,[status(thm)],[612, 611])).
% 27.36/17.56 tff(614,plain,
% 27.36/17.56 ((~(f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2))))),
% 27.36/17.56 inference(unit_resolution,[status(thm)],[613, 553, 566, 574, 346, 565])).
% 27.36/17.56 tff(615,plain,
% 27.36/17.56 ($false),
% 27.36/17.56 inference(unit_resolution,[status(thm)],[614, 607, 603])).
% 27.36/17.56 tff(616,plain,((~(c4 = c1)) | (f9(c2, c2) = c3) | (~big_f(f7(c2), c1)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f7(c2) = c1)) | big_f(f9(c2, c2), f10(c2))), inference(lemma,lemma(discharge,[]))).
% 27.36/17.56 tff(617,plain,
% 27.36/17.56 (~(c4 = c1)),
% 27.36/17.56 inference(unit_resolution,[status(thm)],[616, 563, 338, 148, 79, 122, 292, 256])).
% 27.36/17.56 tff(618,plain,
% 27.36/17.56 (c4 = c2),
% 27.36/17.56 inference(unit_resolution,[status(thm)],[461, 617])).
% 27.36/17.56 tff(619,plain,
% 27.36/17.56 (c2 = c4),
% 27.36/17.56 inference(symmetry,[status(thm)],[618])).
% 27.36/17.56 tff(620,plain,
% 27.36/17.56 (f4(c2) = f4(c4)),
% 27.36/17.56 inference(monotonicity,[status(thm)],[619])).
% 27.36/17.56 tff(621,plain,
% 27.36/17.56 (f4(c4) = f4(c2)),
% 27.36/17.56 inference(symmetry,[status(thm)],[620])).
% 27.36/17.56 tff(622,plain,
% 27.36/17.56 (c2 = f4(c2)),
% 27.36/17.56 inference(transitivity,[status(thm)],[436, 621])).
% 27.36/17.56 tff(623,plain,
% 27.36/17.56 (c2 = c4),
% 27.36/17.56 inference(modus_ponens,[status(thm)],[618, 159])).
% 27.36/17.56 tff(624,assumption,(f1(c1, c1) = c1), introduced(assumption)).
% 27.36/17.56 tff(625,plain,
% 27.36/17.56 (f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)),
% 27.36/17.56 inference(transitivity,[status(thm)],[576, 624, 149, 132])).
% 27.36/17.56 tff(626,plain,
% 27.36/17.56 (f1(f9(c2, c2), f9(c2, c2)) = c1),
% 27.36/17.56 inference(transitivity,[status(thm)],[576, 624])).
% 27.36/17.57 tff(627,plain,
% 27.36/17.57 (big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2))) <=> big_f(f7(c2), c1)),
% 27.36/17.57 inference(monotonicity,[status(thm)],[343, 626])).
% 27.36/17.57 tff(628,plain,
% 27.36/17.57 (big_f(f7(c2), c1) <=> big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2)))),
% 27.36/17.57 inference(symmetry,[status(thm)],[627])).
% 27.36/17.57 tff(629,plain,
% 27.36/17.57 (big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2)))),
% 27.36/17.57 inference(modus_ponens,[status(thm)],[338, 628])).
% 27.36/17.57 tff(630,assumption,(c2 = f4(c2)), introduced(assumption)).
% 27.36/17.57 tff(631,assumption,(c2 = c4), introduced(assumption)).
% 27.36/17.57 tff(632,plain,
% 27.36/17.57 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (f9(c2, c2) = c3) | (~(f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (f9(c2, c2) = c3) | (~(f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2)))))),
% 27.36/17.57 inference(rewrite,[status(thm)],[])).
% 27.36/17.57 tff(633,plain,
% 27.36/17.57 (((f9(c2, c2) = c3) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))) | (~(f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2))))) <=> ((~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (f9(c2, c2) = c3) | (~(f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2)))))),
% 27.36/17.57 inference(rewrite,[status(thm)],[])).
% 27.36/17.57 tff(634,plain,
% 27.36/17.57 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f9(c2, c2) = c3) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))) | (~(f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (f9(c2, c2) = c3) | (~(f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2))))))),
% 27.36/17.57 inference(monotonicity,[status(thm)],[633])).
% 27.36/17.57 tff(635,plain,
% 27.36/17.57 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f9(c2, c2) = c3) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))) | (~(f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (f9(c2, c2) = c3) | (~(f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2)))))),
% 27.36/17.57 inference(transitivity,[status(thm)],[634, 632])).
% 27.36/17.57 tff(636,plain,
% 27.36/17.57 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f9(c2, c2) = c3) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))) | (~(f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2)))))),
% 27.36/17.57 inference(quant_inst,[status(thm)],[])).
% 27.36/17.57 tff(637,plain,
% 27.36/17.57 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (f9(c2, c2) = c3) | (~(f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2))))),
% 27.36/17.57 inference(modus_ponens,[status(thm)],[636, 635])).
% 27.36/17.57 tff(638,plain,
% 27.36/17.57 ((~(f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2))))),
% 27.36/17.57 inference(unit_resolution,[status(thm)],[637, 447, 631, 630, 121, 566])).
% 27.36/17.57 tff(639,plain,
% 27.36/17.57 ($false),
% 27.36/17.57 inference(unit_resolution,[status(thm)],[638, 629, 625])).
% 27.36/17.57 tff(640,plain,((~(f1(c1, c1) = c1)) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (f9(c2, c2) = c3) | (~big_f(f7(c2), c1)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f7(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 27.36/17.57 tff(641,plain,
% 27.36/17.57 (~(f1(c1, c1) = c1)),
% 27.36/17.57 inference(unit_resolution,[status(thm)],[640, 623, 622, 121, 563, 338, 148, 79, 122, 292])).
% 27.36/17.57 tff(642,plain,
% 27.36/17.57 (f1(c1, c1) = c2),
% 27.36/17.57 inference(unit_resolution,[status(thm)],[601, 641])).
% 27.36/17.57 tff(643,plain,
% 27.36/17.57 (f1(c1, c1) = f10(c2)),
% 27.36/17.57 inference(transitivity,[status(thm)],[642, 216])).
% 27.36/17.57 tff(644,plain,
% 27.36/17.57 (big_f(c1, f1(c1, c1)) <=> big_f(f9(c2, c2), f10(c2))),
% 27.36/17.57 inference(monotonicity,[status(thm)],[150, 643])).
% 27.36/17.57 tff(645,plain,
% 27.36/17.57 (big_f(f9(c2, c2), f10(c2)) <=> big_f(c1, f1(c1, c1))),
% 27.36/17.57 inference(symmetry,[status(thm)],[644])).
% 27.36/17.57 tff(646,plain,
% 27.36/17.57 ((~big_f(f9(c2, c2), f10(c2))) <=> (~big_f(c1, f1(c1, c1)))),
% 27.36/17.57 inference(monotonicity,[status(thm)],[645])).
% 27.36/17.57 tff(647,plain,
% 27.36/17.57 (~big_f(c1, f1(c1, c1))),
% 27.36/17.57 inference(modus_ponens,[status(thm)],[256, 646])).
% 27.36/17.57 tff(648,plain,
% 27.36/17.57 ((~(c3 = c1)) <=> (~(c1 = c3))),
% 27.36/17.57 inference(monotonicity,[status(thm)],[68])).
% 27.36/17.57 tff(649,plain,
% 27.36/17.57 (~(c1 = c3)),
% 27.36/17.57 inference(modus_ponens,[status(thm)],[562, 648])).
% 27.36/17.57 tff(650,plain,
% 27.36/17.57 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f1(c1, c1) = c1) | (c1 = c3) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | big_f(c1, f1(c1, c1)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (f1(c1, c1) = c1) | (c1 = c3) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | big_f(c1, f1(c1, c1)))),
% 27.36/17.57 inference(rewrite,[status(thm)],[])).
% 27.36/17.57 tff(651,plain,
% 27.36/17.57 (((c1 = c3) | (f1(c1, c1) = c1) | big_f(c1, f1(c1, c1)) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2)))) <=> ((f1(c1, c1) = c1) | (c1 = c3) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | big_f(c1, f1(c1, c1)))),
% 27.36/17.57 inference(rewrite,[status(thm)],[])).
% 27.36/17.57 tff(652,plain,
% 27.36/17.57 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c1 = c3) | (f1(c1, c1) = c1) | big_f(c1, f1(c1, c1)) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f1(c1, c1) = c1) | (c1 = c3) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | big_f(c1, f1(c1, c1))))),
% 27.36/17.57 inference(monotonicity,[status(thm)],[651])).
% 27.36/17.57 tff(653,plain,
% 27.36/17.57 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c1 = c3) | (f1(c1, c1) = c1) | big_f(c1, f1(c1, c1)) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (f1(c1, c1) = c1) | (c1 = c3) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | big_f(c1, f1(c1, c1)))),
% 27.36/17.57 inference(transitivity,[status(thm)],[652, 650])).
% 27.36/17.57 tff(654,plain,
% 27.36/17.57 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c1 = c3) | (f1(c1, c1) = c1) | big_f(c1, f1(c1, c1)) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))))),
% 27.36/17.57 inference(quant_inst,[status(thm)],[])).
% 27.36/17.57 tff(655,plain,
% 27.36/17.57 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (f1(c1, c1) = c1) | (c1 = c3) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | big_f(c1, f1(c1, c1))),
% 27.36/17.57 inference(modus_ponens,[status(thm)],[654, 653])).
% 27.36/17.57 tff(656,plain,
% 27.36/17.57 ((f1(c1, c1) = c1) | (c1 = c3) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | big_f(c1, f1(c1, c1))),
% 27.36/17.57 inference(unit_resolution,[status(thm)],[655, 402])).
% 27.36/17.57 tff(657,plain,
% 27.36/17.57 (big_f(c1, f1(c1, c1))),
% 27.36/17.57 inference(unit_resolution,[status(thm)],[656, 641, 649, 121, 622, 623])).
% 27.36/17.57 tff(658,plain,
% 27.36/17.57 ($false),
% 27.36/17.57 inference(unit_resolution,[status(thm)],[657, 647])).
% 27.36/17.57 tff(659,plain,(big_f(c2, c2) | big_f(f9(c2, c2), f10(c2)) | (~(f10(c2) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~big_f(f7(c2), c1)) | (~(f7(c2) = c1)) | (~big_f(c2, c1)) | (~(f7(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.36/17.57 tff(660,plain,
% 27.36/17.57 (big_f(c2, c2)),
% 27.36/17.57 inference(unit_resolution,[status(thm)],[659, 256, 122, 148, 79, 337, 292, 291, 120])).
% 27.36/17.57 tff(661,plain,
% 27.36/17.57 (big_f(f7(f9(c2, c2)), c2)),
% 27.36/17.57 inference(modus_ponens,[status(thm)],[660, 246])).
% 27.36/17.57 tff(662,plain,
% 27.36/17.57 ((f7(f9(c2, c2)) = f9(c2, c2)) <=> (c2 = f9(c2, c2))),
% 27.36/17.57 inference(monotonicity,[status(thm)],[244])).
% 27.36/17.57 tff(663,plain,
% 27.36/17.57 ((f7(f9(c2, c2)) = f9(c2, c2)) <=> (f9(c2, c2) = c2)),
% 27.36/17.57 inference(transitivity,[status(thm)],[662, 167])).
% 27.36/17.57 tff(664,plain,
% 27.36/17.57 ((f9(c2, c2) = c2) <=> (f7(f9(c2, c2)) = f9(c2, c2))),
% 27.36/17.57 inference(symmetry,[status(thm)],[663])).
% 27.36/17.57 tff(665,plain,
% 27.36/17.57 ((~(f9(c2, c2) = c2)) <=> (~(f7(f9(c2, c2)) = f9(c2, c2)))),
% 27.36/17.57 inference(monotonicity,[status(thm)],[664])).
% 27.36/17.57 tff(666,plain,
% 27.36/17.57 (~(f7(f9(c2, c2)) = f9(c2, c2))),
% 27.36/17.57 inference(modus_ponens,[status(thm)],[185, 665])).
% 27.36/17.57 tff(667,plain,
% 27.36/17.57 (^[X9: $i, X4: $i, X7: $i, X5: $i] : refl(((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5))) <=> ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5))))),
% 27.36/17.57 inference(bind,[status(th)],[])).
% 27.36/17.57 tff(668,plain,
% 27.36/17.57 (![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5))) <=> ![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))),
% 27.36/17.57 inference(quant_intro,[status(thm)],[667])).
% 27.36/17.57 tff(669,plain,
% 27.36/17.57 (![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5))) <=> ![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))),
% 27.36/17.57 inference(rewrite,[status(thm)],[])).
% 27.36/17.57 tff(670,plain,
% 27.36/17.57 (^[X9: $i, X4: $i, X7: $i, X5: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_f(f7(X4), X5)) | (X5 = f5(X4))) | (f7(X4) = X4)) <=> ((f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))), (((((~big_f(f7(X4), X5)) | (X5 = f5(X4))) | (f7(X4) = X4)) | big_f(f9(X7, X9), f10(X7))) <=> (((f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5))) | big_f(f9(X7, X9), f10(X7))))), rewrite((((f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5))) | big_f(f9(X7, X9), f10(X7))) <=> (big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))), (((((~big_f(f7(X4), X5)) | (X5 = f5(X4))) | (f7(X4) = X4)) | big_f(f9(X7, X9), f10(X7))) <=> (big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5))))), ((((((~big_f(f7(X4), X5)) | (X5 = f5(X4))) | (f7(X4) = X4)) | big_f(f9(X7, X9), f10(X7))) | (f9(X7, X9) = X9)) <=> ((big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5))) | (f9(X7, X9) = X9)))), rewrite(((big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5))) | (f9(X7, X9) = X9)) <=> ((f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))), ((((((~big_f(f7(X4), X5)) | (X5 = f5(X4))) | (f7(X4) = X4)) | big_f(f9(X7, X9), f10(X7))) | (f9(X7, X9) = X9)) <=> ((f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5))))), (((((((~big_f(f7(X4), X5)) | (X5 = f5(X4))) | (f7(X4) = X4)) | big_f(f9(X7, X9), f10(X7))) | (f9(X7, X9) = X9)) | (~(f10(X7) = X7))) <=> (((f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5))) | (~(f10(X7) = X7))))), rewrite((((f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5))) | (~(f10(X7) = X7))) <=> ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))), (((((((~big_f(f7(X4), X5)) | (X5 = f5(X4))) | (f7(X4) = X4)) | big_f(f9(X7, X9), f10(X7))) | (f9(X7, X9) = X9)) | (~(f10(X7) = X7))) <=> ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))))),
% 27.36/17.57 inference(bind,[status(th)],[])).
% 27.36/17.57 tff(671,plain,
% 27.36/17.57 (![X9: $i, X4: $i, X7: $i, X5: $i] : ((((((~big_f(f7(X4), X5)) | (X5 = f5(X4))) | (f7(X4) = X4)) | big_f(f9(X7, X9), f10(X7))) | (f9(X7, X9) = X9)) | (~(f10(X7) = X7))) <=> ![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))),
% 27.36/17.57 inference(quant_intro,[status(thm)],[670])).
% 27.36/17.57 tff(672,axiom,(![X9: $i, X4: $i, X7: $i, X5: $i] : ((((((~big_f(f7(X4), X5)) | (X5 = f5(X4))) | (f7(X4) = X4)) | big_f(f9(X7, X9), f10(X7))) | (f9(X7, X9) = X9)) | (~(f10(X7) = X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_21')).
% 27.36/17.57 tff(673,plain,
% 27.36/17.57 (![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))),
% 27.36/17.57 inference(modus_ponens,[status(thm)],[672, 671])).
% 27.36/17.57 tff(674,plain,
% 27.36/17.57 (![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))),
% 27.36/17.57 inference(modus_ponens,[status(thm)],[673, 669])).
% 27.36/17.57 tff(675,plain,(
% 27.36/17.57 ![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))),
% 27.36/17.57 inference(skolemize,[status(sab)],[674])).
% 27.36/17.57 tff(676,plain,
% 27.36/17.57 (![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))),
% 27.36/17.57 inference(modus_ponens,[status(thm)],[675, 668])).
% 27.36/17.57 tff(677,plain,
% 27.36/17.57 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (~big_f(f7(f9(c2, c2)), c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~(f10(c2) = c2)) | (~big_f(f7(f9(c2, c2)), c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2))))),
% 27.36/17.57 inference(rewrite,[status(thm)],[])).
% 27.36/17.57 tff(678,plain,
% 27.36/17.57 (((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), c2))) <=> ((~(f10(c2) = c2)) | (~big_f(f7(f9(c2, c2)), c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2))))),
% 27.36/17.57 inference(rewrite,[status(thm)],[])).
% 27.36/17.57 tff(679,plain,
% 27.36/17.57 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (~big_f(f7(f9(c2, c2)), c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2)))))),
% 27.36/17.57 inference(monotonicity,[status(thm)],[678])).
% 27.36/17.57 tff(680,plain,
% 27.36/17.57 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~(f10(c2) = c2)) | (~big_f(f7(f9(c2, c2)), c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2))))),
% 27.36/17.57 inference(transitivity,[status(thm)],[679, 677])).
% 27.36/17.57 tff(681,plain,
% 27.36/17.57 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), c2)))),
% 27.36/17.57 inference(quant_inst,[status(thm)],[])).
% 27.36/17.57 tff(682,plain,
% 27.36/17.57 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~(f10(c2) = c2)) | (~big_f(f7(f9(c2, c2)), c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2)))),
% 27.36/17.57 inference(modus_ponens,[status(thm)],[681, 680])).
% 27.36/17.57 tff(683,plain,
% 27.36/17.57 ((~big_f(f7(f9(c2, c2)), c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2)))),
% 27.36/17.57 inference(unit_resolution,[status(thm)],[682, 676, 122, 185, 256])).
% 27.36/17.57 tff(684,plain,
% 27.36/17.57 ($false),
% 27.36/17.57 inference(unit_resolution,[status(thm)],[683, 666, 661, 242])).
% 27.36/17.57 tff(685,plain,(big_f(f9(c2, c2), f10(c2)) | (~(f10(c2) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f5(c1) = c1)) | (~(f7(c2) = c1)) | (f7(c1) = c1) | (f9(f10(c2), f10(c2)) = f10(c2)) | (~(f10(c1) = c2)) | (f7(f10(c1)) = f10(c1))), inference(lemma,lemma(discharge,[]))).
% 27.36/17.57 tff(686,plain,
% 27.36/17.57 (big_f(f9(c2, c2), f10(c2))),
% 27.36/17.57 inference(unit_resolution,[status(thm)],[685, 230, 148, 79, 122, 22, 115, 158, 16, 236])).
% 27.36/17.57 tff(687,plain,
% 27.36/17.57 (f10(f9(f10(c2), f10(c2))) = f10(c2)),
% 27.36/17.57 inference(transitivity,[status(thm)],[202, 16, 216])).
% 27.36/17.57 tff(688,plain,
% 27.36/17.57 (big_f(f9(f10(c2), f10(c2)), f10(f9(f10(c2), f10(c2)))) <=> big_f(f9(c2, c2), f10(c2))),
% 27.36/17.57 inference(monotonicity,[status(thm)],[135, 687])).
% 27.36/17.57 tff(689,plain,
% 27.36/17.57 (big_f(f9(c2, c2), f10(c2)) <=> big_f(f9(f10(c2), f10(c2)), f10(f9(f10(c2), f10(c2))))),
% 27.36/17.57 inference(symmetry,[status(thm)],[688])).
% 27.36/17.57 tff(690,assumption,(big_f(f9(c2, c2), f10(c2))), introduced(assumption)).
% 27.36/17.57 tff(691,plain,
% 27.36/17.57 (big_f(f9(f10(c2), f10(c2)), f10(f9(f10(c2), f10(c2))))),
% 27.36/17.57 inference(modus_ponens,[status(thm)],[690, 689])).
% 27.36/17.57 tff(692,plain,
% 27.36/17.57 (c1 = f5(c1)),
% 27.36/17.57 inference(modus_ponens,[status(thm)],[230, 192])).
% 27.36/17.57 tff(693,plain,
% 27.36/17.57 (big_f(c2, c1) <=> big_f(f7(c1), c1)),
% 27.36/17.57 inference(symmetry,[status(thm)],[247])).
% 27.36/17.57 tff(694,plain,
% 27.36/17.57 ((~big_f(c2, c1)) <=> (~big_f(f7(c1), c1))),
% 27.36/17.57 inference(monotonicity,[status(thm)],[693])).
% 27.36/17.57 tff(695,plain,
% 27.36/17.57 (~big_f(f7(c1), c1)),
% 27.36/17.57 inference(modus_ponens,[status(thm)],[2, 694])).
% 27.36/17.57 tff(696,plain,
% 27.36/17.57 (^[X4: $i, X7: $i, X5: $i, X8: $i] : refl(((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5)) <=> ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5)))),
% 27.36/17.57 inference(bind,[status(th)],[])).
% 27.36/17.57 tff(697,plain,
% 27.36/17.57 (![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5)) <=> ![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))),
% 27.36/17.57 inference(quant_intro,[status(thm)],[696])).
% 27.36/17.57 tff(698,plain,
% 27.36/17.57 (![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5)) <=> ![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))),
% 27.36/17.57 inference(rewrite,[status(thm)],[])).
% 27.36/17.57 tff(699,plain,
% 27.36/17.57 (^[X4: $i, X7: $i, X5: $i, X8: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((big_f(f7(X4), X5) | (~(X5 = f5(X4)))) <=> ((~(X5 = f5(X4))) | big_f(f7(X4), X5))), (((big_f(f7(X4), X5) | (~(X5 = f5(X4)))) | (f7(X4) = X4)) <=> (((~(X5 = f5(X4))) | big_f(f7(X4), X5)) | (f7(X4) = X4)))), rewrite((((~(X5 = f5(X4))) | big_f(f7(X4), X5)) | (f7(X4) = X4)) <=> ((~(X5 = f5(X4))) | (f7(X4) = X4) | big_f(f7(X4), X5))), (((big_f(f7(X4), X5) | (~(X5 = f5(X4)))) | (f7(X4) = X4)) <=> ((~(X5 = f5(X4))) | (f7(X4) = X4) | big_f(f7(X4), X5)))), ((((big_f(f7(X4), X5) | (~(X5 = f5(X4)))) | (f7(X4) = X4)) | (~big_f(X8, f10(X7)))) <=> (((~(X5 = f5(X4))) | (f7(X4) = X4) | big_f(f7(X4), X5)) | (~big_f(X8, f10(X7)))))), rewrite((((~(X5 = f5(X4))) | (f7(X4) = X4) | big_f(f7(X4), X5)) | (~big_f(X8, f10(X7)))) <=> ((~(X5 = f5(X4))) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))), ((((big_f(f7(X4), X5) | (~(X5 = f5(X4)))) | (f7(X4) = X4)) | (~big_f(X8, f10(X7)))) <=> ((~(X5 = f5(X4))) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5)))), (((((big_f(f7(X4), X5) | (~(X5 = f5(X4)))) | (f7(X4) = X4)) | (~big_f(X8, f10(X7)))) | (X8 = f8(X7))) <=> (((~(X5 = f5(X4))) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5)) | (X8 = f8(X7))))), rewrite((((~(X5 = f5(X4))) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5)) | (X8 = f8(X7))) <=> ((~(X5 = f5(X4))) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))), (((((big_f(f7(X4), X5) | (~(X5 = f5(X4)))) | (f7(X4) = X4)) | (~big_f(X8, f10(X7)))) | (X8 = f8(X7))) <=> ((~(X5 = f5(X4))) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5)))), ((((((big_f(f7(X4), X5) | (~(X5 = f5(X4)))) | (f7(X4) = X4)) | (~big_f(X8, f10(X7)))) | (X8 = f8(X7))) | (f10(X7) = X7)) <=> (((~(X5 = f5(X4))) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5)) | (f10(X7) = X7)))), rewrite((((~(X5 = f5(X4))) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5)) | (f10(X7) = X7)) <=> ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))), ((((((big_f(f7(X4), X5) | (~(X5 = f5(X4)))) | (f7(X4) = X4)) | (~big_f(X8, f10(X7)))) | (X8 = f8(X7))) | (f10(X7) = X7)) <=> ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))))),
% 27.36/17.57 inference(bind,[status(th)],[])).
% 27.36/17.57 tff(700,plain,
% 27.36/17.57 (![X4: $i, X7: $i, X5: $i, X8: $i] : (((((big_f(f7(X4), X5) | (~(X5 = f5(X4)))) | (f7(X4) = X4)) | (~big_f(X8, f10(X7)))) | (X8 = f8(X7))) | (f10(X7) = X7)) <=> ![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))),
% 27.36/17.57 inference(quant_intro,[status(thm)],[699])).
% 27.36/17.57 tff(701,axiom,(![X4: $i, X7: $i, X5: $i, X8: $i] : (((((big_f(f7(X4), X5) | (~(X5 = f5(X4)))) | (f7(X4) = X4)) | (~big_f(X8, f10(X7)))) | (X8 = f8(X7))) | (f10(X7) = X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_23')).
% 27.36/17.57 tff(702,plain,
% 27.36/17.57 (![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))),
% 27.36/17.57 inference(modus_ponens,[status(thm)],[701, 700])).
% 27.36/17.57 tff(703,plain,
% 27.36/17.57 (![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))),
% 27.36/17.57 inference(modus_ponens,[status(thm)],[702, 698])).
% 27.36/17.57 tff(704,plain,(
% 27.36/17.57 ![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))),
% 27.36/17.58 inference(skolemize,[status(sab)],[703])).
% 27.36/17.58 tff(705,plain,
% 27.36/17.58 (![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))),
% 27.36/17.58 inference(modus_ponens,[status(thm)],[704, 697])).
% 27.36/17.58 tff(706,plain,
% 27.36/17.58 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f7(c1) = c1) | (f9(f10(c2), f10(c2)) = f8(f9(f10(c2), f10(c2)))) | big_f(f7(c1), c1) | (~(c1 = f5(c1))) | (~big_f(f9(f10(c2), f10(c2)), f10(f9(f10(c2), f10(c2))))) | (f10(f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f7(c1) = c1) | (f9(f10(c2), f10(c2)) = f8(f9(f10(c2), f10(c2)))) | big_f(f7(c1), c1) | (~(c1 = f5(c1))) | (~big_f(f9(f10(c2), f10(c2)), f10(f9(f10(c2), f10(c2))))) | (f10(f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2))))),
% 27.36/17.58 inference(rewrite,[status(thm)],[])).
% 27.36/17.58 tff(707,plain,
% 27.36/17.58 (((~(c1 = f5(c1))) | (f10(f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2))) | (f9(f10(c2), f10(c2)) = f8(f9(f10(c2), f10(c2)))) | (~big_f(f9(f10(c2), f10(c2)), f10(f9(f10(c2), f10(c2))))) | (f7(c1) = c1) | big_f(f7(c1), c1)) <=> ((f7(c1) = c1) | (f9(f10(c2), f10(c2)) = f8(f9(f10(c2), f10(c2)))) | big_f(f7(c1), c1) | (~(c1 = f5(c1))) | (~big_f(f9(f10(c2), f10(c2)), f10(f9(f10(c2), f10(c2))))) | (f10(f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2))))),
% 27.36/17.58 inference(rewrite,[status(thm)],[])).
% 27.36/17.58 tff(708,plain,
% 27.36/17.58 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c1 = f5(c1))) | (f10(f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2))) | (f9(f10(c2), f10(c2)) = f8(f9(f10(c2), f10(c2)))) | (~big_f(f9(f10(c2), f10(c2)), f10(f9(f10(c2), f10(c2))))) | (f7(c1) = c1) | big_f(f7(c1), c1))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f7(c1) = c1) | (f9(f10(c2), f10(c2)) = f8(f9(f10(c2), f10(c2)))) | big_f(f7(c1), c1) | (~(c1 = f5(c1))) | (~big_f(f9(f10(c2), f10(c2)), f10(f9(f10(c2), f10(c2))))) | (f10(f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))))),
% 27.36/17.58 inference(monotonicity,[status(thm)],[707])).
% 27.36/17.58 tff(709,plain,
% 27.36/17.58 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c1 = f5(c1))) | (f10(f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2))) | (f9(f10(c2), f10(c2)) = f8(f9(f10(c2), f10(c2)))) | (~big_f(f9(f10(c2), f10(c2)), f10(f9(f10(c2), f10(c2))))) | (f7(c1) = c1) | big_f(f7(c1), c1))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f7(c1) = c1) | (f9(f10(c2), f10(c2)) = f8(f9(f10(c2), f10(c2)))) | big_f(f7(c1), c1) | (~(c1 = f5(c1))) | (~big_f(f9(f10(c2), f10(c2)), f10(f9(f10(c2), f10(c2))))) | (f10(f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2))))),
% 27.36/17.58 inference(transitivity,[status(thm)],[708, 706])).
% 27.36/17.58 tff(710,plain,
% 27.36/17.58 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c1 = f5(c1))) | (f10(f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2))) | (f9(f10(c2), f10(c2)) = f8(f9(f10(c2), f10(c2)))) | (~big_f(f9(f10(c2), f10(c2)), f10(f9(f10(c2), f10(c2))))) | (f7(c1) = c1) | big_f(f7(c1), c1))),
% 27.36/17.58 inference(quant_inst,[status(thm)],[])).
% 27.36/17.58 tff(711,plain,
% 27.36/17.58 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f7(c1) = c1) | (f9(f10(c2), f10(c2)) = f8(f9(f10(c2), f10(c2)))) | big_f(f7(c1), c1) | (~(c1 = f5(c1))) | (~big_f(f9(f10(c2), f10(c2)), f10(f9(f10(c2), f10(c2))))) | (f10(f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))),
% 27.36/17.58 inference(modus_ponens,[status(thm)],[710, 709])).
% 27.36/17.58 tff(712,plain,
% 27.36/17.58 ((f7(c1) = c1) | (f9(f10(c2), f10(c2)) = f8(f9(f10(c2), f10(c2)))) | big_f(f7(c1), c1) | (~(c1 = f5(c1))) | (~big_f(f9(f10(c2), f10(c2)), f10(f9(f10(c2), f10(c2))))) | (f10(f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))),
% 27.36/17.58 inference(unit_resolution,[status(thm)],[711, 705])).
% 27.36/17.58 tff(713,plain,
% 27.36/17.58 (f9(f10(c2), f10(c2)) = f8(f9(f10(c2), f10(c2)))),
% 27.36/17.58 inference(unit_resolution,[status(thm)],[712, 695, 115, 231, 692, 691])).
% 27.36/17.58 tff(714,plain,
% 27.36/17.58 (f8(f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2))),
% 27.36/17.58 inference(symmetry,[status(thm)],[713])).
% 27.36/17.58 tff(715,plain,
% 27.36/17.58 (f8(f9(c2, c2)) = f8(f9(f10(c2), f10(c2)))),
% 27.36/17.58 inference(monotonicity,[status(thm)],[203])).
% 27.36/17.58 tff(716,plain,
% 27.36/17.58 (big_f(f7(f9(c2, c2)), f9(c2, c2)) <=> big_f(c2, c1)),
% 27.36/17.58 inference(monotonicity,[status(thm)],[244, 161])).
% 27.36/17.58 tff(717,plain,
% 27.36/17.58 (big_f(c2, c1) <=> big_f(f7(f9(c2, c2)), f9(c2, c2))),
% 27.36/17.58 inference(symmetry,[status(thm)],[716])).
% 27.36/17.58 tff(718,plain,
% 27.36/17.58 ((~big_f(c2, c1)) <=> (~big_f(f7(f9(c2, c2)), f9(c2, c2)))),
% 27.36/17.58 inference(monotonicity,[status(thm)],[717])).
% 27.36/17.58 tff(719,plain,
% 27.36/17.58 (~big_f(f7(f9(c2, c2)), f9(c2, c2))),
% 27.36/17.58 inference(modus_ponens,[status(thm)],[2, 718])).
% 27.36/17.58 tff(720,plain,
% 27.36/17.58 (f10(f9(c2, c2)) = f10(c2)),
% 27.36/17.58 inference(transitivity,[status(thm)],[204, 202, 16, 216])).
% 27.36/17.58 tff(721,plain,
% 27.36/17.58 (big_f(f9(c2, f9(f10(c2), f10(c2))), f10(f9(c2, c2))) <=> big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2))),
% 27.36/17.58 inference(monotonicity,[status(thm)],[720])).
% 27.36/17.58 tff(722,plain,
% 27.36/17.58 (big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2)) <=> big_f(f9(c2, f9(f10(c2), f10(c2))), f10(f9(c2, c2)))),
% 27.36/17.58 inference(symmetry,[status(thm)],[721])).
% 27.36/17.58 tff(723,plain,
% 27.36/17.58 (f9(c2, c1) = f9(c2, f9(f10(c2), f10(c2)))),
% 27.36/17.58 inference(monotonicity,[status(thm)],[225])).
% 27.36/17.58 tff(724,plain,
% 27.36/17.58 (big_f(f9(c2, c1), f10(c2)) <=> big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2))),
% 27.36/17.58 inference(monotonicity,[status(thm)],[723])).
% 27.36/17.58 tff(725,plain,
% 27.36/17.58 (big_f(f9(c2, c1), f10(c2)) <=> big_f(f9(c2, f9(f10(c2), f10(c2))), f10(f9(c2, c2)))),
% 27.36/17.58 inference(transitivity,[status(thm)],[724, 722])).
% 27.36/17.58 tff(726,plain,
% 27.36/17.58 (big_f(f7(c1), f5(c1)) <=> big_f(c2, c1)),
% 27.36/17.58 inference(monotonicity,[status(thm)],[120, 230])).
% 27.36/17.58 tff(727,plain,
% 27.36/17.58 (big_f(c2, c1) <=> big_f(f7(c1), f5(c1))),
% 27.36/17.58 inference(symmetry,[status(thm)],[726])).
% 27.36/17.58 tff(728,plain,
% 27.36/17.58 ((~big_f(c2, c1)) <=> (~big_f(f7(c1), f5(c1)))),
% 27.36/17.58 inference(monotonicity,[status(thm)],[727])).
% 27.36/17.58 tff(729,plain,
% 27.36/17.58 (~big_f(f7(c1), f5(c1))),
% 27.36/17.58 inference(modus_ponens,[status(thm)],[2, 728])).
% 27.36/17.58 tff(730,assumption,(~big_f(f7(c1), f5(c1))), introduced(assumption)).
% 27.36/17.58 tff(731,assumption,(~big_f(f9(c2, c1), f10(c2))), introduced(assumption)).
% 27.36/17.58 tff(732,plain,
% 27.36/17.58 (f9(c2, f9(f10(c2), f10(c2))) = f9(c2, c1)),
% 27.36/17.58 inference(monotonicity,[status(thm)],[201])).
% 27.36/17.58 tff(733,plain,
% 27.36/17.58 (f9(c2, c1) = f9(c2, f9(f10(c2), f10(c2)))),
% 27.36/17.58 inference(symmetry,[status(thm)],[732])).
% 27.36/17.58 tff(734,plain,
% 27.36/17.58 (big_f(f9(c2, c1), f10(c2)) <=> big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2))),
% 27.36/17.58 inference(monotonicity,[status(thm)],[733])).
% 27.36/17.58 tff(735,plain,
% 27.36/17.58 (big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2)) <=> big_f(f9(c2, c1), f10(c2))),
% 27.36/17.58 inference(symmetry,[status(thm)],[734])).
% 27.36/17.58 tff(736,assumption,(f9(c2, c1) = c1), introduced(assumption)).
% 27.36/17.58 tff(737,plain,
% 27.36/17.58 (f9(c2, f9(f10(c2), f10(c2))) = f9(c2, c2)),
% 27.36/17.58 inference(transitivity,[status(thm)],[732, 736, 149, 132])).
% 27.36/17.58 tff(738,plain,
% 27.36/17.58 (big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2)) <=> big_f(f9(c2, c2), f10(c2))),
% 27.36/17.58 inference(monotonicity,[status(thm)],[737])).
% 27.36/17.58 tff(739,plain,
% 27.36/17.58 (big_f(f9(c2, c2), f10(c2)) <=> big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2))),
% 27.36/17.58 inference(symmetry,[status(thm)],[738])).
% 27.36/17.58 tff(740,plain,
% 27.36/17.58 (big_f(f9(c2, c2), f10(c2)) <=> big_f(f9(c2, c1), f10(c2))),
% 27.36/17.58 inference(transitivity,[status(thm)],[739, 735])).
% 27.36/17.58 tff(741,plain,
% 27.36/17.58 (big_f(f9(c2, c1), f10(c2))),
% 27.36/17.58 inference(modus_ponens,[status(thm)],[690, 740])).
% 27.36/17.58 tff(742,plain,
% 27.36/17.58 ($false),
% 27.36/17.58 inference(unit_resolution,[status(thm)],[731, 741])).
% 27.36/17.58 tff(743,plain,((~(f9(c2, c1) = c1)) | big_f(f9(c2, c1), f10(c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.36/17.58 tff(744,plain,
% 27.36/17.58 (~(f9(c2, c1) = c1)),
% 27.36/17.58 inference(unit_resolution,[status(thm)],[743, 731, 690, 148, 79, 122])).
% 27.36/17.58 tff(745,plain,
% 27.36/17.58 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((f7(c1) = c1) | (~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | big_f(f7(c1), f5(c1)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | big_f(f7(c1), f5(c1)))),
% 27.36/17.58 inference(rewrite,[status(thm)],[])).
% 27.36/17.58 tff(746,plain,
% 27.36/17.58 (((~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)) | $false) <=> ((f7(c1) = c1) | (~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | big_f(f7(c1), f5(c1)))),
% 27.36/17.58 inference(rewrite,[status(thm)],[])).
% 27.36/17.58 tff(747,plain,
% 27.36/17.58 (((~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (~(f5(c1) = f5(c1)))) <=> ((~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)) | $false)),
% 27.36/17.58 inference(monotonicity,[status(thm)],[273])).
% 27.36/17.58 tff(748,plain,
% 27.36/17.58 (((~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (~(f5(c1) = f5(c1)))) <=> ((f7(c1) = c1) | (~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | big_f(f7(c1), f5(c1)))),
% 27.36/17.58 inference(transitivity,[status(thm)],[747, 746])).
% 27.36/17.58 tff(749,plain,
% 27.36/17.58 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (~(f5(c1) = f5(c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((f7(c1) = c1) | (~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | big_f(f7(c1), f5(c1))))),
% 27.36/17.58 inference(monotonicity,[status(thm)],[748])).
% 27.36/17.58 tff(750,plain,
% 27.36/17.58 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (~(f5(c1) = f5(c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | big_f(f7(c1), f5(c1)))),
% 27.36/17.58 inference(transitivity,[status(thm)],[749, 745])).
% 27.36/17.58 tff(751,plain,
% 27.36/17.58 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (~(f5(c1) = f5(c1))))),
% 27.36/17.58 inference(quant_inst,[status(thm)],[])).
% 27.36/17.58 tff(752,plain,
% 27.36/17.58 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | big_f(f7(c1), f5(c1))),
% 27.36/17.58 inference(modus_ponens,[status(thm)],[751, 750])).
% 27.36/17.58 tff(753,plain,
% 27.36/17.58 ((f7(c1) = c1) | (~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | big_f(f7(c1), f5(c1))),
% 27.36/17.58 inference(unit_resolution,[status(thm)],[752, 267])).
% 27.36/17.58 tff(754,plain,
% 27.36/17.58 ($false),
% 27.36/17.58 inference(unit_resolution,[status(thm)],[753, 744, 731, 122, 730, 115])).
% 27.36/17.58 tff(755,plain,(big_f(f9(c2, c1), f10(c2)) | (~(f10(c2) = c2)) | big_f(f7(c1), f5(c1)) | (f7(c1) = c1) | (~big_f(f9(c2, c2), f10(c2))) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.36/17.58 tff(756,plain,
% 27.36/17.58 (big_f(f9(c2, c1), f10(c2))),
% 27.36/17.58 inference(unit_resolution,[status(thm)],[755, 729, 122, 115, 690, 148, 79])).
% 27.36/17.58 tff(757,plain,
% 27.36/17.58 (big_f(f9(c2, f9(f10(c2), f10(c2))), f10(f9(c2, c2)))),
% 27.36/17.58 inference(modus_ponens,[status(thm)],[756, 725])).
% 27.36/17.58 tff(758,assumption,(f10(f9(c2, c2)) = f9(c2, c2)), introduced(assumption)).
% 27.36/17.58 tff(759,plain,
% 27.36/17.58 (f9(c2, c2) = f10(f9(c2, c2))),
% 27.36/17.58 inference(symmetry,[status(thm)],[758])).
% 27.36/17.58 tff(760,plain,
% 27.36/17.58 (f9(c2, c2) = c2),
% 27.36/17.58 inference(transitivity,[status(thm)],[759, 204, 202, 16])).
% 27.36/17.58 tff(761,plain,
% 27.36/17.58 ($false),
% 27.36/17.58 inference(unit_resolution,[status(thm)],[185, 760])).
% 27.36/17.58 tff(762,plain,((~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f10(c1) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.36/17.58 tff(763,plain,
% 27.36/17.58 (~(f10(f9(c2, c2)) = f9(c2, c2))),
% 27.36/17.58 inference(unit_resolution,[status(thm)],[762, 16, 148, 79, 122])).
% 27.36/17.58 tff(764,plain,
% 27.36/17.58 (f9(c2, c2) = f5(f9(c2, c2))),
% 27.36/17.58 inference(modus_ponens,[status(thm)],[230, 171])).
% 27.36/17.58 tff(765,plain,
% 27.36/17.58 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f7(f9(c2, c2)) = f9(c2, c2)) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(f9(c2, c2)))) | (~(f9(c2, c2) = f5(f9(c2, c2)))) | big_f(f7(f9(c2, c2)), f9(c2, c2)) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, f9(f10(c2), f10(c2))) = f8(f9(c2, c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(f9(c2, c2)))) | (~(f9(c2, c2) = f5(f9(c2, c2)))) | big_f(f7(f9(c2, c2)), f9(c2, c2)) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, f9(f10(c2), f10(c2))) = f8(f9(c2, c2))))),
% 27.36/17.58 inference(rewrite,[status(thm)],[])).
% 27.36/17.58 tff(766,plain,
% 27.36/17.58 (((~(f9(c2, c2) = f5(f9(c2, c2)))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, f9(f10(c2), f10(c2))) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(f9(c2, c2)))) | (f7(f9(c2, c2)) = f9(c2, c2)) | big_f(f7(f9(c2, c2)), f9(c2, c2))) <=> ((f7(f9(c2, c2)) = f9(c2, c2)) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(f9(c2, c2)))) | (~(f9(c2, c2) = f5(f9(c2, c2)))) | big_f(f7(f9(c2, c2)), f9(c2, c2)) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, f9(f10(c2), f10(c2))) = f8(f9(c2, c2))))),
% 27.36/17.58 inference(rewrite,[status(thm)],[])).
% 27.36/17.58 tff(767,plain,
% 27.36/17.58 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(f9(c2, c2) = f5(f9(c2, c2)))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, f9(f10(c2), f10(c2))) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(f9(c2, c2)))) | (f7(f9(c2, c2)) = f9(c2, c2)) | big_f(f7(f9(c2, c2)), f9(c2, c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f7(f9(c2, c2)) = f9(c2, c2)) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(f9(c2, c2)))) | (~(f9(c2, c2) = f5(f9(c2, c2)))) | big_f(f7(f9(c2, c2)), f9(c2, c2)) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, f9(f10(c2), f10(c2))) = f8(f9(c2, c2)))))),
% 27.36/17.58 inference(monotonicity,[status(thm)],[766])).
% 27.36/17.58 tff(768,plain,
% 27.36/17.58 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(f9(c2, c2) = f5(f9(c2, c2)))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, f9(f10(c2), f10(c2))) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(f9(c2, c2)))) | (f7(f9(c2, c2)) = f9(c2, c2)) | big_f(f7(f9(c2, c2)), f9(c2, c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(f9(c2, c2)))) | (~(f9(c2, c2) = f5(f9(c2, c2)))) | big_f(f7(f9(c2, c2)), f9(c2, c2)) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, f9(f10(c2), f10(c2))) = f8(f9(c2, c2))))),
% 27.36/17.58 inference(transitivity,[status(thm)],[767, 765])).
% 27.36/17.58 tff(769,plain,
% 27.36/17.58 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(f9(c2, c2) = f5(f9(c2, c2)))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, f9(f10(c2), f10(c2))) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(f9(c2, c2)))) | (f7(f9(c2, c2)) = f9(c2, c2)) | big_f(f7(f9(c2, c2)), f9(c2, c2)))),
% 27.36/17.58 inference(quant_inst,[status(thm)],[])).
% 27.36/17.58 tff(770,plain,
% 27.36/17.58 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(f9(c2, c2)))) | (~(f9(c2, c2) = f5(f9(c2, c2)))) | big_f(f7(f9(c2, c2)), f9(c2, c2)) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, f9(f10(c2), f10(c2))) = f8(f9(c2, c2)))),
% 27.36/17.58 inference(modus_ponens,[status(thm)],[769, 768])).
% 27.36/17.58 tff(771,plain,
% 27.36/17.58 (f9(c2, f9(f10(c2), f10(c2))) = f8(f9(c2, c2))),
% 27.36/17.58 inference(unit_resolution,[status(thm)],[770, 705, 764, 763, 757, 666, 719])).
% 27.36/17.58 tff(772,plain,
% 27.36/17.58 (f9(c2, f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2))),
% 27.36/17.58 inference(transitivity,[status(thm)],[771, 715, 714])).
% 27.36/17.58 tff(773,plain,
% 27.36/17.58 (big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2))),
% 27.36/17.58 inference(modus_ponens,[status(thm)],[756, 724])).
% 27.36/17.58 tff(774,plain,
% 27.36/17.58 (^[X9: $i, X4: $i, X7: $i, X5: $i] : refl(((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4)))) <=> ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4)))))),
% 27.36/17.58 inference(bind,[status(th)],[])).
% 27.36/17.58 tff(775,plain,
% 27.36/17.58 (![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4)))) <=> ![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))),
% 27.36/17.58 inference(quant_intro,[status(thm)],[774])).
% 27.36/17.58 tff(776,plain,
% 27.36/17.58 (![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4)))) <=> ![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))),
% 27.36/17.58 inference(rewrite,[status(thm)],[])).
% 27.36/17.58 tff(777,plain,
% 27.36/17.58 (^[X9: $i, X4: $i, X7: $i, X5: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((big_f(f7(X4), X5) | (~(X5 = f5(X4)))) <=> (big_f(f7(X4), X5) | (~(X5 = f5(X4))))), (((big_f(f7(X4), X5) | (~(X5 = f5(X4)))) | (f7(X4) = X4)) <=> ((big_f(f7(X4), X5) | (~(X5 = f5(X4)))) | (f7(X4) = X4)))), rewrite(((big_f(f7(X4), X5) | (~(X5 = f5(X4)))) | (f7(X4) = X4)) <=> ((f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))), (((big_f(f7(X4), X5) | (~(X5 = f5(X4)))) | (f7(X4) = X4)) <=> ((f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4)))))), ((((big_f(f7(X4), X5) | (~(X5 = f5(X4)))) | (f7(X4) = X4)) | (~big_f(f9(X7, X9), f10(X7)))) <=> (((f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4)))) | (~big_f(f9(X7, X9), f10(X7)))))), rewrite((((f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4)))) | (~big_f(f9(X7, X9), f10(X7)))) <=> ((f7(X4) = X4) | big_f(f7(X4), X5) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))), ((((big_f(f7(X4), X5) | (~(X5 = f5(X4)))) | (f7(X4) = X4)) | (~big_f(f9(X7, X9), f10(X7)))) <=> ((f7(X4) = X4) | big_f(f7(X4), X5) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4)))))), (((((big_f(f7(X4), X5) | (~(X5 = f5(X4)))) | (f7(X4) = X4)) | (~big_f(f9(X7, X9), f10(X7)))) | (~(f9(X7, X9) = X9))) <=> (((f7(X4) = X4) | big_f(f7(X4), X5) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4)))) | (~(f9(X7, X9) = X9))))), rewrite((((f7(X4) = X4) | big_f(f7(X4), X5) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4)))) | (~(f9(X7, X9) = X9))) <=> ((f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))), (((((big_f(f7(X4), X5) | (~(X5 = f5(X4)))) | (f7(X4) = X4)) | (~big_f(f9(X7, X9), f10(X7)))) | (~(f9(X7, X9) = X9))) <=> ((f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4)))))), ((((((big_f(f7(X4), X5) | (~(X5 = f5(X4)))) | (f7(X4) = X4)) | (~big_f(f9(X7, X9), f10(X7)))) | (~(f9(X7, X9) = X9))) | (~(f10(X7) = X7))) <=> (((f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4)))) | (~(f10(X7) = X7))))), rewrite((((f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4)))) | (~(f10(X7) = X7))) <=> ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))), ((((((big_f(f7(X4), X5) | (~(X5 = f5(X4)))) | (f7(X4) = X4)) | (~big_f(f9(X7, X9), f10(X7)))) | (~(f9(X7, X9) = X9))) | (~(f10(X7) = X7))) <=> ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))))),
% 27.36/17.58 inference(bind,[status(th)],[])).
% 27.36/17.58 tff(778,plain,
% 27.36/17.58 (![X9: $i, X4: $i, X7: $i, X5: $i] : (((((big_f(f7(X4), X5) | (~(X5 = f5(X4)))) | (f7(X4) = X4)) | (~big_f(f9(X7, X9), f10(X7)))) | (~(f9(X7, X9) = X9))) | (~(f10(X7) = X7))) <=> ![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))),
% 27.36/17.58 inference(quant_intro,[status(thm)],[777])).
% 27.36/17.58 tff(779,axiom,(![X9: $i, X4: $i, X7: $i, X5: $i] : (((((big_f(f7(X4), X5) | (~(X5 = f5(X4)))) | (f7(X4) = X4)) | (~big_f(f9(X7, X9), f10(X7)))) | (~(f9(X7, X9) = X9))) | (~(f10(X7) = X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_26')).
% 27.36/17.58 tff(780,plain,
% 27.36/17.58 (![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))),
% 27.36/17.58 inference(modus_ponens,[status(thm)],[779, 778])).
% 27.36/17.58 tff(781,plain,
% 27.36/17.58 (![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))),
% 27.36/17.58 inference(modus_ponens,[status(thm)],[780, 776])).
% 27.36/17.58 tff(782,plain,(
% 27.36/17.58 ![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))),
% 27.36/17.58 inference(skolemize,[status(sab)],[781])).
% 27.36/17.58 tff(783,plain,
% 27.36/17.58 (![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))),
% 27.36/17.58 inference(modus_ponens,[status(thm)],[782, 775])).
% 27.36/17.58 tff(784,plain,
% 27.36/17.58 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((f7(c1) = c1) | (~(f10(c2) = c2)) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2))) | (~(f9(c2, f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))) | big_f(f7(c1), c1) | (~(c1 = f5(c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2))) | (~(f9(c2, f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))) | big_f(f7(c1), c1) | (~(c1 = f5(c1))))),
% 27.36/17.58 inference(rewrite,[status(thm)],[])).
% 27.36/17.58 tff(785,plain,
% 27.36/17.58 (((~(f10(c2) = c2)) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(f9(c2, f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2))) | (~(c1 = f5(c1)))) <=> ((f7(c1) = c1) | (~(f10(c2) = c2)) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2))) | (~(f9(c2, f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))) | big_f(f7(c1), c1) | (~(c1 = f5(c1))))),
% 27.36/17.59 inference(rewrite,[status(thm)],[])).
% 27.36/17.59 tff(786,plain,
% 27.36/17.59 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(f9(c2, f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2))) | (~(c1 = f5(c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((f7(c1) = c1) | (~(f10(c2) = c2)) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2))) | (~(f9(c2, f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))) | big_f(f7(c1), c1) | (~(c1 = f5(c1)))))),
% 27.36/17.59 inference(monotonicity,[status(thm)],[785])).
% 27.36/17.59 tff(787,plain,
% 27.36/17.59 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(f9(c2, f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2))) | (~(c1 = f5(c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2))) | (~(f9(c2, f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))) | big_f(f7(c1), c1) | (~(c1 = f5(c1))))),
% 27.36/17.59 inference(transitivity,[status(thm)],[786, 784])).
% 27.36/17.59 tff(788,plain,
% 27.36/17.59 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(f9(c2, f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2))) | (~(c1 = f5(c1))))),
% 27.36/17.59 inference(quant_inst,[status(thm)],[])).
% 27.36/17.59 tff(789,plain,
% 27.36/17.59 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2))) | (~(f9(c2, f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))) | big_f(f7(c1), c1) | (~(c1 = f5(c1)))),
% 27.36/17.59 inference(modus_ponens,[status(thm)],[788, 787])).
% 27.36/17.59 tff(790,plain,
% 27.36/17.59 ((f7(c1) = c1) | (~(f10(c2) = c2)) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2))) | (~(f9(c2, f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))) | big_f(f7(c1), c1) | (~(c1 = f5(c1)))),
% 27.36/17.59 inference(unit_resolution,[status(thm)],[789, 783])).
% 27.36/17.59 tff(791,plain,
% 27.36/17.59 (~(f9(c2, f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))),
% 27.36/17.59 inference(unit_resolution,[status(thm)],[790, 773, 122, 115, 692, 695])).
% 27.36/17.59 tff(792,plain,
% 27.36/17.59 ($false),
% 27.36/17.59 inference(unit_resolution,[status(thm)],[791, 772])).
% 27.36/17.59 tff(793,plain,(big_f(c2, c1) | (~(f10(c2) = c2)) | (f7(c1) = c1) | (~(f10(c1) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f10(f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2))) | (~(f5(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 27.36/17.59 tff(794,plain,
% 27.36/17.59 (big_f(c2, c1)),
% 27.36/17.59 inference(unit_resolution,[status(thm)],[793, 686, 115, 16, 148, 79, 122, 231, 230])).
% 27.36/17.59 tff(795,plain,
% 27.36/17.59 (big_f(f7(c2), f9(c2, c2)) <=> big_f(f7(c2), c1)),
% 27.36/17.59 inference(monotonicity,[status(thm)],[161])).
% 27.36/17.59 tff(796,plain,
% 27.36/17.59 (big_f(f7(c2), c1) <=> big_f(f7(c2), f9(c2, c2))),
% 27.36/17.59 inference(symmetry,[status(thm)],[795])).
% 27.36/17.59 tff(797,plain,
% 27.36/17.59 ((~(c4 = c2)) <=> (~(c2 = c4))),
% 27.36/17.59 inference(monotonicity,[status(thm)],[159])).
% 27.36/17.59 tff(798,plain,
% 27.36/17.59 (f4(c2) = c2),
% 27.36/17.59 inference(transitivity,[status(thm)],[434, 79])).
% 27.36/17.59 tff(799,plain,
% 27.36/17.59 ((f9(f10(c2), f4(c4)) = f4(c2)) <=> (f9(c2, c2) = c2)),
% 27.36/17.59 inference(monotonicity,[status(thm)],[132, 798])).
% 27.36/17.59 tff(800,plain,
% 27.36/17.59 ((f9(c2, c2) = c2) <=> (f9(f10(c2), f4(c4)) = f4(c2))),
% 27.36/17.59 inference(symmetry,[status(thm)],[799])).
% 27.36/17.59 tff(801,plain,
% 27.36/17.59 ((~(f9(c2, c2) = c2)) <=> (~(f9(f10(c2), f4(c4)) = f4(c2)))),
% 27.36/17.59 inference(monotonicity,[status(thm)],[800])).
% 27.36/17.59 tff(802,plain,
% 27.36/17.59 (~(f9(f10(c2), f4(c4)) = f4(c2))),
% 27.36/17.59 inference(modus_ponens,[status(thm)],[185, 801])).
% 27.36/17.59 tff(803,plain,
% 27.36/17.59 (~big_f(f4(c4), c4)),
% 27.36/17.59 inference(unit_resolution,[status(thm)],[476, 431, 79, 121])).
% 27.36/17.59 tff(804,plain,
% 27.36/17.59 (f7(f7(c2)) = c3),
% 27.36/17.59 inference(unit_resolution,[status(thm)],[468, 377, 79, 348, 121, 347, 292, 148, 122, 379])).
% 27.36/17.59 tff(805,plain,
% 27.36/17.59 (c2 = c3),
% 27.36/17.59 inference(modus_ponens,[status(thm)],[804, 364])).
% 27.36/17.59 tff(806,plain,
% 27.36/17.59 ($false),
% 27.36/17.59 inference(unit_resolution,[status(thm)],[377, 805])).
% 27.36/17.59 tff(807,plain,((c2 = c3) | (~(f7(c1) = c2)) | (~(f7(c2) = c1)) | (~(f4(c4) = c2)) | (~big_f(c2, c1)) | big_f(c2, c2) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f10(c2) = c2)) | big_f(f4(c4), c4)), inference(lemma,lemma(discharge,[]))).
% 27.36/17.59 tff(808,plain,
% 27.36/17.59 (c2 = c3),
% 27.36/17.59 inference(unit_resolution,[status(thm)],[807, 803, 292, 79, 348, 121, 148, 122, 347])).
% 27.36/17.59 tff(809,plain,
% 27.36/17.59 (c3 = c2),
% 27.36/17.59 inference(symmetry,[status(thm)],[808])).
% 27.36/17.59 tff(810,plain,
% 27.36/17.59 ((f9(f10(c2), f4(c4)) = c3) <=> (f9(c2, c2) = c2)),
% 27.36/17.59 inference(monotonicity,[status(thm)],[132, 809])).
% 27.36/17.59 tff(811,plain,
% 27.36/17.59 ((f9(c2, c2) = c2) <=> (f9(f10(c2), f4(c4)) = c3)),
% 27.36/17.59 inference(symmetry,[status(thm)],[810])).
% 27.36/17.59 tff(812,plain,
% 27.36/17.59 ((~(f9(c2, c2) = c2)) <=> (~(f9(f10(c2), f4(c4)) = c3))),
% 27.36/17.59 inference(monotonicity,[status(thm)],[811])).
% 27.36/17.59 tff(813,plain,
% 27.36/17.59 (~(f9(f10(c2), f4(c4)) = c3)),
% 27.36/17.59 inference(modus_ponens,[status(thm)],[185, 812])).
% 27.36/17.59 tff(814,assumption,(~(f9(f10(c2), f4(c4)) = f4(c2))), introduced(assumption)).
% 27.36/17.59 tff(815,assumption,(~(f9(f10(c2), f4(c4)) = c3)), introduced(assumption)).
% 27.36/17.59 tff(816,plain,
% 27.36/17.59 (big_f(f9(f10(c2), f4(c4)), c2) <=> big_f(f9(c2, c2), f10(c2))),
% 27.36/17.59 inference(monotonicity,[status(thm)],[132, 216])).
% 27.36/17.59 tff(817,plain,
% 27.36/17.59 (big_f(f9(c2, c2), f10(c2)) <=> big_f(f9(f10(c2), f4(c4)), c2)),
% 27.36/17.59 inference(symmetry,[status(thm)],[816])).
% 27.36/17.59 tff(818,plain,
% 27.36/17.59 (big_f(f9(f10(c2), f4(c4)), c2)),
% 27.36/17.59 inference(modus_ponens,[status(thm)],[690, 817])).
% 27.36/17.59 tff(819,plain,
% 27.36/17.59 (f1(f9(f10(c2), f4(c4)), c2) = f1(c1, c2)),
% 27.36/17.59 inference(monotonicity,[status(thm)],[148])).
% 27.36/17.59 tff(820,plain,
% 27.36/17.59 (f1(c1, c2) = f1(f9(f10(c2), f4(c4)), c2)),
% 27.36/17.59 inference(symmetry,[status(thm)],[819])).
% 27.36/17.59 tff(821,plain,
% 27.36/17.59 ((f1(c1, c2) = c2) <=> (f1(f9(f10(c2), f4(c4)), c2) = c2)),
% 27.36/17.59 inference(monotonicity,[status(thm)],[820])).
% 27.36/17.59 tff(822,assumption,(f1(c1, c2) = c2), introduced(assumption)).
% 27.36/17.59 tff(823,plain,
% 27.36/17.59 (f1(f9(f10(c2), f4(c4)), c2) = c2),
% 27.36/17.59 inference(modus_ponens,[status(thm)],[822, 821])).
% 27.36/17.59 tff(824,plain,
% 27.36/17.59 (f1(f9(f10(c2), f4(c4)), c2) = f10(c2)),
% 27.36/17.59 inference(transitivity,[status(thm)],[819, 822, 216])).
% 27.36/17.59 tff(825,plain,
% 27.36/17.59 (big_f(f9(f10(c2), f4(c4)), f1(f9(f10(c2), f4(c4)), c2)) <=> big_f(f9(c2, c2), f10(c2))),
% 27.36/17.59 inference(monotonicity,[status(thm)],[132, 824])).
% 27.36/17.59 tff(826,plain,
% 27.36/17.59 (big_f(f9(c2, c2), f10(c2)) <=> big_f(f9(f10(c2), f4(c4)), f1(f9(f10(c2), f4(c4)), c2))),
% 27.36/17.59 inference(symmetry,[status(thm)],[825])).
% 27.36/17.59 tff(827,plain,
% 27.36/17.59 (big_f(f9(f10(c2), f4(c4)), f1(f9(f10(c2), f4(c4)), c2))),
% 27.36/17.59 inference(modus_ponens,[status(thm)],[690, 826])).
% 27.36/17.59 tff(828,plain,
% 27.36/17.59 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((~(c2 = c4)) | (~big_f(f9(f10(c2), f4(c4)), f1(f9(f10(c2), f4(c4)), c2))) | (f9(f10(c2), f4(c4)) = f4(c2)) | (~big_f(f9(f10(c2), f4(c4)), c2)) | (f9(f10(c2), f4(c4)) = c3) | (~(f1(f9(f10(c2), f4(c4)), c2) = c2)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (~(c2 = c4)) | (~big_f(f9(f10(c2), f4(c4)), f1(f9(f10(c2), f4(c4)), c2))) | (f9(f10(c2), f4(c4)) = f4(c2)) | (~big_f(f9(f10(c2), f4(c4)), c2)) | (f9(f10(c2), f4(c4)) = c3) | (~(f1(f9(f10(c2), f4(c4)), c2) = c2)))),
% 27.36/17.59 inference(rewrite,[status(thm)],[])).
% 27.36/17.59 tff(829,plain,
% 27.36/17.59 (((f9(f10(c2), f4(c4)) = c3) | (~(c2 = c4)) | (f9(f10(c2), f4(c4)) = f4(c2)) | (~big_f(f9(f10(c2), f4(c4)), c2)) | (~(f1(f9(f10(c2), f4(c4)), c2) = c2)) | (~big_f(f9(f10(c2), f4(c4)), f1(f9(f10(c2), f4(c4)), c2)))) <=> ((~(c2 = c4)) | (~big_f(f9(f10(c2), f4(c4)), f1(f9(f10(c2), f4(c4)), c2))) | (f9(f10(c2), f4(c4)) = f4(c2)) | (~big_f(f9(f10(c2), f4(c4)), c2)) | (f9(f10(c2), f4(c4)) = c3) | (~(f1(f9(f10(c2), f4(c4)), c2) = c2)))),
% 27.36/17.59 inference(rewrite,[status(thm)],[])).
% 27.36/17.59 tff(830,plain,
% 27.36/17.59 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f9(f10(c2), f4(c4)) = c3) | (~(c2 = c4)) | (f9(f10(c2), f4(c4)) = f4(c2)) | (~big_f(f9(f10(c2), f4(c4)), c2)) | (~(f1(f9(f10(c2), f4(c4)), c2) = c2)) | (~big_f(f9(f10(c2), f4(c4)), f1(f9(f10(c2), f4(c4)), c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((~(c2 = c4)) | (~big_f(f9(f10(c2), f4(c4)), f1(f9(f10(c2), f4(c4)), c2))) | (f9(f10(c2), f4(c4)) = f4(c2)) | (~big_f(f9(f10(c2), f4(c4)), c2)) | (f9(f10(c2), f4(c4)) = c3) | (~(f1(f9(f10(c2), f4(c4)), c2) = c2))))),
% 27.36/17.59 inference(monotonicity,[status(thm)],[829])).
% 27.36/17.59 tff(831,plain,
% 27.36/17.59 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f9(f10(c2), f4(c4)) = c3) | (~(c2 = c4)) | (f9(f10(c2), f4(c4)) = f4(c2)) | (~big_f(f9(f10(c2), f4(c4)), c2)) | (~(f1(f9(f10(c2), f4(c4)), c2) = c2)) | (~big_f(f9(f10(c2), f4(c4)), f1(f9(f10(c2), f4(c4)), c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (~(c2 = c4)) | (~big_f(f9(f10(c2), f4(c4)), f1(f9(f10(c2), f4(c4)), c2))) | (f9(f10(c2), f4(c4)) = f4(c2)) | (~big_f(f9(f10(c2), f4(c4)), c2)) | (f9(f10(c2), f4(c4)) = c3) | (~(f1(f9(f10(c2), f4(c4)), c2) = c2)))),
% 27.36/17.59 inference(transitivity,[status(thm)],[830, 828])).
% 27.36/17.59 tff(832,plain,
% 27.36/17.59 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f9(f10(c2), f4(c4)) = c3) | (~(c2 = c4)) | (f9(f10(c2), f4(c4)) = f4(c2)) | (~big_f(f9(f10(c2), f4(c4)), c2)) | (~(f1(f9(f10(c2), f4(c4)), c2) = c2)) | (~big_f(f9(f10(c2), f4(c4)), f1(f9(f10(c2), f4(c4)), c2))))),
% 27.36/17.59 inference(quant_inst,[status(thm)],[])).
% 27.36/17.59 tff(833,plain,
% 27.36/17.59 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (~(c2 = c4)) | (~big_f(f9(f10(c2), f4(c4)), f1(f9(f10(c2), f4(c4)), c2))) | (f9(f10(c2), f4(c4)) = f4(c2)) | (~big_f(f9(f10(c2), f4(c4)), c2)) | (f9(f10(c2), f4(c4)) = c3) | (~(f1(f9(f10(c2), f4(c4)), c2) = c2))),
% 27.36/17.59 inference(modus_ponens,[status(thm)],[832, 831])).
% 27.36/17.59 tff(834,plain,
% 27.36/17.59 ((~(c2 = c4)) | (~big_f(f9(f10(c2), f4(c4)), f1(f9(f10(c2), f4(c4)), c2))) | (f9(f10(c2), f4(c4)) = f4(c2)) | (~big_f(f9(f10(c2), f4(c4)), c2)) | (f9(f10(c2), f4(c4)) = c3) | (~(f1(f9(f10(c2), f4(c4)), c2) = c2))),
% 27.36/17.59 inference(unit_resolution,[status(thm)],[833, 553])).
% 27.36/17.59 tff(835,plain,
% 27.36/17.59 ($false),
% 27.36/17.59 inference(unit_resolution,[status(thm)],[834, 827, 823, 631, 818, 815, 814])).
% 27.36/17.59 tff(836,plain,((~(f1(c1, c2) = c2)) | (~(c2 = c4)) | (f9(f10(c2), f4(c4)) = c3) | (f9(f10(c2), f4(c4)) = f4(c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f10(c2) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.36/17.59 tff(837,plain,
% 27.36/17.59 (~(f1(c1, c2) = c2)),
% 27.36/17.59 inference(unit_resolution,[status(thm)],[836, 432, 813, 802, 690, 122, 148, 79])).
% 27.36/17.59 tff(838,plain,
% 27.36/17.59 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f1(c1, c2) = c1) | (f1(c1, c2) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f1(c1, c2) = c1) | (f1(c1, c2) = c2))),
% 27.36/17.59 inference(rewrite,[status(thm)],[])).
% 27.36/17.59 tff(839,plain,
% 27.36/17.59 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f1(c1, c2) = c1) | (f1(c1, c2) = c2))),
% 27.36/17.59 inference(quant_inst,[status(thm)],[])).
% 27.36/17.59 tff(840,plain,
% 27.36/17.59 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f1(c1, c2) = c1) | (f1(c1, c2) = c2)),
% 27.36/17.59 inference(modus_ponens,[status(thm)],[839, 838])).
% 27.36/17.59 tff(841,plain,
% 27.36/17.59 ((f1(c1, c2) = c1) | (f1(c1, c2) = c2)),
% 27.36/17.59 inference(unit_resolution,[status(thm)],[840, 10])).
% 27.36/17.59 tff(842,plain,
% 27.36/17.59 (f1(c1, c2) = c1),
% 27.36/17.59 inference(unit_resolution,[status(thm)],[841, 837])).
% 27.36/17.59 tff(843,plain,
% 27.36/17.59 (f1(f9(c2, c2), c2) = f1(f9(f10(c2), f4(c4)), c2)),
% 27.36/17.59 inference(monotonicity,[status(thm)],[160])).
% 27.36/17.59 tff(844,plain,
% 27.36/17.59 (f1(f9(c2, c2), c2) = f9(c2, c2)),
% 27.36/17.59 inference(transitivity,[status(thm)],[843, 819, 842, 149, 132])).
% 27.36/17.59 tff(845,plain,
% 27.36/17.59 ((f1(f9(c2, c2), c2) = c2) <=> (f9(c2, c2) = c2)),
% 27.36/17.59 inference(monotonicity,[status(thm)],[844])).
% 27.36/17.59 tff(846,plain,
% 27.36/17.59 ((f9(c2, c2) = c2) <=> (f1(f9(c2, c2), c2) = c2)),
% 27.36/17.59 inference(symmetry,[status(thm)],[845])).
% 27.36/17.59 tff(847,plain,
% 27.36/17.59 ((~(f9(c2, c2) = c2)) <=> (~(f1(f9(c2, c2), c2) = c2))),
% 27.36/17.59 inference(monotonicity,[status(thm)],[846])).
% 27.36/17.59 tff(848,plain,
% 27.36/17.59 (~(f1(f9(c2, c2), c2) = c2)),
% 27.36/17.59 inference(modus_ponens,[status(thm)],[185, 847])).
% 27.36/17.59 tff(849,plain,
% 27.36/17.59 (f1(f9(c2, c2), c2) = c1),
% 27.36/17.59 inference(transitivity,[status(thm)],[843, 819, 842])).
% 27.36/17.59 tff(850,plain,
% 27.36/17.59 (big_f(f9(c2, c2), f1(f9(c2, c2), c2)) <=> big_f(f7(c2), c1)),
% 27.36/17.59 inference(monotonicity,[status(thm)],[343, 849])).
% 27.36/17.59 tff(851,plain,
% 27.36/17.59 (big_f(f7(c2), c1) <=> big_f(f9(c2, c2), f1(f9(c2, c2), c2))),
% 27.36/17.59 inference(symmetry,[status(thm)],[850])).
% 27.36/17.59 tff(852,plain,
% 27.36/17.59 ((~big_f(f7(c2), c1)) <=> (~big_f(f9(c2, c2), f1(f9(c2, c2), c2)))),
% 27.36/17.59 inference(monotonicity,[status(thm)],[851])).
% 27.36/17.59 tff(853,plain,
% 27.36/17.59 (~big_f(f9(c2, c2), f1(f9(c2, c2), c2))),
% 27.36/17.59 inference(modus_ponens,[status(thm)],[333, 852])).
% 27.36/17.59 tff(854,plain,
% 27.36/17.59 ((f9(c2, c2) = c2) <=> (f9(c2, c2) = c3)),
% 27.36/17.59 inference(transitivity,[status(thm)],[811, 339])).
% 27.36/17.59 tff(855,plain,
% 27.36/17.59 ((~(f9(c2, c2) = c2)) <=> (~(f9(c2, c2) = c3))),
% 27.36/17.59 inference(monotonicity,[status(thm)],[854])).
% 27.36/17.59 tff(856,plain,
% 27.36/17.59 (~(f9(c2, c2) = c3)),
% 27.36/17.59 inference(modus_ponens,[status(thm)],[185, 855])).
% 27.36/17.59 tff(857,plain,
% 27.36/17.59 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (f9(c2, c2) = c3) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (f9(c2, c2) = c3) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2)))),
% 27.36/17.59 inference(rewrite,[status(thm)],[])).
% 27.36/17.59 tff(858,plain,
% 27.36/17.59 (((f9(c2, c2) = c3) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2)) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2)))) <=> ((~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (f9(c2, c2) = c3) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2)))),
% 27.36/17.59 inference(rewrite,[status(thm)],[])).
% 27.36/17.59 tff(859,plain,
% 27.36/17.59 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f9(c2, c2) = c3) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2)) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (f9(c2, c2) = c3) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2))))),
% 27.36/17.59 inference(monotonicity,[status(thm)],[858])).
% 27.36/17.59 tff(860,plain,
% 27.36/17.59 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f9(c2, c2) = c3) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2)) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (f9(c2, c2) = c3) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2)))),
% 27.36/17.59 inference(transitivity,[status(thm)],[859, 857])).
% 27.36/17.59 tff(861,plain,
% 27.36/17.59 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f9(c2, c2) = c3) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2)) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))))),
% 27.36/17.59 inference(quant_inst,[status(thm)],[])).
% 27.36/17.59 tff(862,plain,
% 27.36/17.59 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (f9(c2, c2) = c3) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2))),
% 27.36/17.59 inference(modus_ponens,[status(thm)],[861, 860])).
% 27.36/17.59 tff(863,plain,
% 27.36/17.59 ((f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2))),
% 27.36/17.59 inference(unit_resolution,[status(thm)],[862, 402, 432, 437, 121, 856])).
% 27.36/17.59 tff(864,plain,
% 27.36/17.59 ($false),
% 27.36/17.59 inference(unit_resolution,[status(thm)],[863, 853, 848])).
% 27.36/17.59 tff(865,plain,((~(c4 = c2)) | big_f(c2, c2) | big_f(f7(c2), c1) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f7(c2) = c1)) | (~big_f(f9(c2, c2), f10(c2))) | (~big_f(c2, c1)) | (~(f7(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.36/17.59 tff(866,plain,
% 27.36/17.59 (~(c4 = c2)),
% 27.36/17.59 inference(unit_resolution,[status(thm)],[865, 333, 121, 148, 79, 122, 292, 690, 348, 347])).
% 27.36/17.59 tff(867,plain,
% 27.36/17.59 (~(c2 = c4)),
% 27.36/17.59 inference(modus_ponens,[status(thm)],[866, 797])).
% 27.36/17.59 tff(868,plain,
% 27.36/17.59 ((f7(c1) = c4) <=> (c2 = c4)),
% 27.36/17.59 inference(monotonicity,[status(thm)],[347])).
% 27.36/17.59 tff(869,plain,
% 27.36/17.59 ((c2 = c4) <=> (f7(c1) = c4)),
% 27.36/17.59 inference(symmetry,[status(thm)],[868])).
% 27.36/17.59 tff(870,plain,
% 27.36/17.59 ((c4 = c2) <=> (f7(c1) = c4)),
% 27.36/17.59 inference(transitivity,[status(thm)],[159, 869])).
% 27.36/17.59 tff(871,plain,
% 27.36/17.59 ((~(c4 = c2)) <=> (~(f7(c1) = c4))),
% 27.36/17.59 inference(monotonicity,[status(thm)],[870])).
% 27.36/17.59 tff(872,plain,
% 27.36/17.59 (~(f7(c1) = c4)),
% 27.36/17.59 inference(modus_ponens,[status(thm)],[866, 871])).
% 27.36/17.59 tff(873,assumption,(~(c2 = c4)), introduced(assumption)).
% 27.36/17.59 tff(874,assumption,(f1(f7(f7(c2)), c1) = c1), introduced(assumption)).
% 27.36/17.59 tff(875,plain,
% 27.36/17.59 (c1 = f1(f7(f7(c2)), c1)),
% 27.36/17.59 inference(symmetry,[status(thm)],[874])).
% 27.36/17.59 tff(876,plain,
% 27.36/17.59 (c1 = f1(c2, c1)),
% 27.36/17.59 inference(transitivity,[status(thm)],[875, 357])).
% 27.36/17.59 tff(877,plain,
% 27.36/17.59 (big_f(c2, c1) <=> big_f(c2, f1(c2, c1))),
% 27.36/17.59 inference(monotonicity,[status(thm)],[876])).
% 27.36/17.59 tff(878,plain,
% 27.36/17.59 (big_f(c2, c1) <=> big_f(c2, f1(c2, f9(c2, c2)))),
% 27.36/17.59 inference(transitivity,[status(thm)],[877, 351])).
% 27.36/17.59 tff(879,plain,
% 27.36/17.59 (big_f(c2, f1(c2, f9(c2, c2)))),
% 27.36/17.59 inference(modus_ponens,[status(thm)],[348, 878])).
% 27.36/17.59 tff(880,plain,
% 27.36/17.59 (f1(c2, f9(c2, c2)) = f9(c2, c2)),
% 27.36/17.59 inference(modus_ponens,[status(thm)],[874, 542])).
% 27.36/17.59 tff(881,assumption,(f3(f7(c1), c1) = c2), introduced(assumption)).
% 27.36/17.59 tff(882,plain,
% 27.36/17.59 (f10(c1) = f7(c1)),
% 27.36/17.59 inference(transitivity,[status(thm)],[16, 354])).
% 27.36/17.59 tff(883,plain,
% 27.36/17.59 (f3(f10(c1), c1) = f3(f7(c1), c1)),
% 27.36/17.59 inference(monotonicity,[status(thm)],[882])).
% 27.36/17.59 tff(884,plain,
% 27.36/17.59 (f3(c2, f9(c2, c2)) = f3(f10(c1), c1)),
% 27.36/17.59 inference(monotonicity,[status(thm)],[293, 161])).
% 27.36/17.59 tff(885,plain,
% 27.36/17.59 (f3(c2, f9(c2, c2)) = c2),
% 27.36/17.59 inference(transitivity,[status(thm)],[884, 883, 881])).
% 27.36/17.59 tff(886,plain,
% 27.36/17.59 ((f3(c2, f9(c2, c2)) = f9(c2, c2)) <=> (c2 = f9(c2, c2))),
% 27.36/17.59 inference(monotonicity,[status(thm)],[885])).
% 27.36/17.59 tff(887,plain,
% 27.36/17.59 ((f3(c2, f9(c2, c2)) = f9(c2, c2)) <=> (f9(c2, c2) = c2)),
% 27.36/17.59 inference(transitivity,[status(thm)],[886, 167])).
% 27.36/17.59 tff(888,plain,
% 27.36/17.59 ((f9(c2, c2) = c2) <=> (f3(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.36/17.60 inference(symmetry,[status(thm)],[887])).
% 27.36/17.60 tff(889,plain,
% 27.36/17.60 ((~(f9(c2, c2) = c2)) <=> (~(f3(c2, f9(c2, c2)) = f9(c2, c2)))),
% 27.36/17.60 inference(monotonicity,[status(thm)],[888])).
% 27.36/17.60 tff(890,plain,
% 27.36/17.60 (~(f3(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.36/17.60 inference(modus_ponens,[status(thm)],[185, 889])).
% 27.36/17.60 tff(891,plain,
% 27.36/17.60 (big_f(f3(c2, f9(c2, c2)), c2) <=> big_f(c2, c2)),
% 27.36/17.60 inference(monotonicity,[status(thm)],[885])).
% 27.36/17.60 tff(892,plain,
% 27.36/17.60 (big_f(c2, c2) <=> big_f(f3(c2, f9(c2, c2)), c2)),
% 27.36/17.60 inference(symmetry,[status(thm)],[891])).
% 27.36/17.60 tff(893,plain,
% 27.36/17.60 ((~big_f(c2, c2)) <=> (~big_f(f3(c2, f9(c2, c2)), c2))),
% 27.36/17.60 inference(monotonicity,[status(thm)],[892])).
% 27.36/17.60 tff(894,plain,
% 27.36/17.60 (~big_f(f3(c2, f9(c2, c2)), c2)),
% 27.36/17.60 inference(modus_ponens,[status(thm)],[121, 893])).
% 27.36/17.60 tff(895,plain,
% 27.36/17.60 (^[X11: $i, X13: $i, X10: $i, X2: $i] : refl(((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))) <=> ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))))),
% 27.36/17.60 inference(bind,[status(th)],[])).
% 27.36/17.60 tff(896,plain,
% 27.36/17.60 (![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))) <=> ![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))),
% 27.36/17.60 inference(quant_intro,[status(thm)],[895])).
% 27.36/17.60 tff(897,plain,
% 27.36/17.60 (![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))) <=> ![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))),
% 27.36/17.60 inference(rewrite,[status(thm)],[])).
% 27.36/17.60 tff(898,plain,
% 27.36/17.60 (^[X11: $i, X13: $i, X10: $i, X2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~big_f(X10, f1(X10, X11))) | (~(f1(X10, X11) = X11))) <=> ((~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))), ((((~big_f(X10, f1(X10, X11))) | (~(f1(X10, X11) = X11))) | (X10 = c3)) <=> (((~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))) | (X10 = c3)))), rewrite((((~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))) | (X10 = c3)) <=> ((X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))), ((((~big_f(X10, f1(X10, X11))) | (~(f1(X10, X11) = X11))) | (X10 = c3)) <=> ((X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))))), (((((~big_f(X10, f1(X10, X11))) | (~(f1(X10, X11) = X11))) | (X10 = c3)) | big_f(f3(X2, X13), X2)) <=> (((X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))) | big_f(f3(X2, X13), X2)))), rewrite((((X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))) | big_f(f3(X2, X13), X2)) <=> (big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))), (((((~big_f(X10, f1(X10, X11))) | (~(f1(X10, X11) = X11))) | (X10 = c3)) | big_f(f3(X2, X13), X2)) <=> (big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))))), ((((((~big_f(X10, f1(X10, X11))) | (~(f1(X10, X11) = X11))) | (X10 = c3)) | big_f(f3(X2, X13), X2)) | (f3(X2, X13) = X13)) <=> ((big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))) | (f3(X2, X13) = X13)))), rewrite(((big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))) | (f3(X2, X13) = X13)) <=> ((f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))), ((((((~big_f(X10, f1(X10, X11))) | (~(f1(X10, X11) = X11))) | (X10 = c3)) | big_f(f3(X2, X13), X2)) | (f3(X2, X13) = X13)) <=> ((f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))))), (((((((~big_f(X10, f1(X10, X11))) | (~(f1(X10, X11) = X11))) | (X10 = c3)) | big_f(f3(X2, X13), X2)) | (f3(X2, X13) = X13)) | (X2 = c4)) <=> (((f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))) | (X2 = c4)))), rewrite((((f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))) | (X2 = c4)) <=> ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))), (((((((~big_f(X10, f1(X10, X11))) | (~(f1(X10, X11) = X11))) | (X10 = c3)) | big_f(f3(X2, X13), X2)) | (f3(X2, X13) = X13)) | (X2 = c4)) <=> ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))))),
% 27.36/17.60 inference(bind,[status(th)],[])).
% 27.36/17.60 tff(899,plain,
% 27.36/17.60 (![X11: $i, X13: $i, X10: $i, X2: $i] : ((((((~big_f(X10, f1(X10, X11))) | (~(f1(X10, X11) = X11))) | (X10 = c3)) | big_f(f3(X2, X13), X2)) | (f3(X2, X13) = X13)) | (X2 = c4)) <=> ![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))),
% 27.36/17.60 inference(quant_intro,[status(thm)],[898])).
% 27.36/17.60 tff(900,axiom,(![X11: $i, X13: $i, X10: $i, X2: $i] : ((((((~big_f(X10, f1(X10, X11))) | (~(f1(X10, X11) = X11))) | (X10 = c3)) | big_f(f3(X2, X13), X2)) | (f3(X2, X13) = X13)) | (X2 = c4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_7')).
% 27.36/17.60 tff(901,plain,
% 27.36/17.60 (![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))),
% 27.36/17.60 inference(modus_ponens,[status(thm)],[900, 899])).
% 27.36/17.60 tff(902,plain,
% 27.36/17.60 (![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))),
% 27.36/17.60 inference(modus_ponens,[status(thm)],[901, 897])).
% 27.36/17.60 tff(903,plain,(
% 27.36/17.60 ![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))),
% 27.36/17.60 inference(skolemize,[status(sab)],[902])).
% 27.36/17.60 tff(904,plain,
% 27.36/17.60 (![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))),
% 27.36/17.60 inference(modus_ponens,[status(thm)],[903, 896])).
% 27.36/17.60 tff(905,plain,
% 27.36/17.60 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (c2 = c4) | (~(f1(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(c2, f1(c2, f9(c2, c2)))) | (f3(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f3(c2, f9(c2, c2)), c2))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (c2 = c4) | (~(f1(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(c2, f1(c2, f9(c2, c2)))) | (f3(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f3(c2, f9(c2, c2)), c2))),
% 27.36/17.60 inference(rewrite,[status(thm)],[])).
% 27.36/17.60 tff(906,plain,
% 27.36/17.60 (((c2 = c4) | (f3(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f3(c2, f9(c2, c2)), c2) | (c2 = c3) | (~(f1(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(c2, f1(c2, f9(c2, c2))))) <=> ((c2 = c3) | (c2 = c4) | (~(f1(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(c2, f1(c2, f9(c2, c2)))) | (f3(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f3(c2, f9(c2, c2)), c2))),
% 27.36/17.60 inference(rewrite,[status(thm)],[])).
% 27.36/17.60 tff(907,plain,
% 27.36/17.60 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (f3(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f3(c2, f9(c2, c2)), c2) | (c2 = c3) | (~(f1(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(c2, f1(c2, f9(c2, c2)))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (c2 = c4) | (~(f1(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(c2, f1(c2, f9(c2, c2)))) | (f3(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f3(c2, f9(c2, c2)), c2)))),
% 27.36/17.60 inference(monotonicity,[status(thm)],[906])).
% 27.36/17.60 tff(908,plain,
% 27.36/17.60 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (f3(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f3(c2, f9(c2, c2)), c2) | (c2 = c3) | (~(f1(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(c2, f1(c2, f9(c2, c2)))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (c2 = c4) | (~(f1(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(c2, f1(c2, f9(c2, c2)))) | (f3(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f3(c2, f9(c2, c2)), c2))),
% 27.36/17.60 inference(transitivity,[status(thm)],[907, 905])).
% 27.36/17.60 tff(909,plain,
% 27.36/17.60 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (f3(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f3(c2, f9(c2, c2)), c2) | (c2 = c3) | (~(f1(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(c2, f1(c2, f9(c2, c2)))))),
% 27.36/17.60 inference(quant_inst,[status(thm)],[])).
% 27.36/17.60 tff(910,plain,
% 27.36/17.60 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (c2 = c4) | (~(f1(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(c2, f1(c2, f9(c2, c2)))) | (f3(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f3(c2, f9(c2, c2)), c2)),
% 27.36/17.60 inference(modus_ponens,[status(thm)],[909, 908])).
% 27.36/17.60 tff(911,plain,
% 27.36/17.60 ((f3(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f3(c2, f9(c2, c2)), c2)),
% 27.36/17.60 inference(unit_resolution,[status(thm)],[910, 904, 873, 377, 430, 429])).
% 27.36/17.60 tff(912,plain,
% 27.36/17.60 ($false),
% 27.36/17.60 inference(unit_resolution,[status(thm)],[911, 894, 890])).
% 27.36/17.60 tff(913,plain,((~(f3(f7(c1), c1) = c2)) | (c2 = c4) | (c2 = c3) | (~(f1(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(c2, f1(c2, f9(c2, c2)))) | big_f(c2, c2) | (~(f10(c1) = c2)) | (~(f7(c1) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.36/17.60 tff(914,plain,
% 27.36/17.60 (~(f3(f7(c1), c1) = c2)),
% 27.36/17.60 inference(unit_resolution,[status(thm)],[913, 880, 377, 873, 879, 121, 16, 347, 148, 79, 122])).
% 27.36/17.60 tff(915,plain,
% 27.36/17.60 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f3(f7(c1), c1) = c1) | (f3(f7(c1), c1) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f3(f7(c1), c1) = c1) | (f3(f7(c1), c1) = c2))),
% 27.36/17.60 inference(rewrite,[status(thm)],[])).
% 27.36/17.60 tff(916,plain,
% 27.36/17.60 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f3(f7(c1), c1) = c1) | (f3(f7(c1), c1) = c2))),
% 27.36/17.60 inference(quant_inst,[status(thm)],[])).
% 27.36/17.60 tff(917,plain,
% 27.36/17.60 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f3(f7(c1), c1) = c1) | (f3(f7(c1), c1) = c2)),
% 27.36/17.60 inference(modus_ponens,[status(thm)],[916, 915])).
% 27.36/17.60 tff(918,plain,
% 27.36/17.60 ((f3(f7(c1), c1) = c1) | (f3(f7(c1), c1) = c2)),
% 27.36/17.60 inference(unit_resolution,[status(thm)],[917, 10])).
% 27.36/17.60 tff(919,plain,
% 27.36/17.60 (f3(f7(c1), c1) = c1),
% 27.36/17.60 inference(unit_resolution,[status(thm)],[918, 914])).
% 27.36/17.60 tff(920,plain,
% 27.36/17.60 (f3(c2, f9(c2, c2)) = f9(c2, c2)),
% 27.36/17.60 inference(transitivity,[status(thm)],[884, 883, 919, 149, 132])).
% 27.36/17.60 tff(921,plain,
% 27.36/17.60 (big_f(f3(c2, f9(c2, c2)), c2) <=> big_f(f9(c2, c2), f10(c2))),
% 27.36/17.60 inference(monotonicity,[status(thm)],[920, 216])).
% 27.36/17.60 tff(922,plain,
% 27.36/17.60 (big_f(f9(c2, c2), f10(c2)) <=> big_f(f3(c2, f9(c2, c2)), c2)),
% 27.36/17.60 inference(symmetry,[status(thm)],[921])).
% 27.36/17.60 tff(923,plain,
% 27.36/17.60 (big_f(f3(c2, f9(c2, c2)), c2)),
% 27.36/17.60 inference(modus_ponens,[status(thm)],[690, 922])).
% 27.36/17.60 tff(924,plain,
% 27.36/17.60 (^[X11: $i, X13: $i, X10: $i, X2: $i] : refl(((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))) <=> ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))))),
% 27.36/17.60 inference(bind,[status(th)],[])).
% 27.36/17.60 tff(925,plain,
% 27.36/17.60 (![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))) <=> ![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))),
% 27.36/17.60 inference(quant_intro,[status(thm)],[924])).
% 27.36/17.60 tff(926,plain,
% 27.36/17.60 (![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))) <=> ![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))),
% 27.36/17.60 inference(rewrite,[status(thm)],[])).
% 27.36/17.60 tff(927,plain,
% 27.36/17.60 (^[X11: $i, X13: $i, X10: $i, X2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~big_f(X10, f1(X10, X11))) | (~(f1(X10, X11) = X11))) <=> ((~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))), ((((~big_f(X10, f1(X10, X11))) | (~(f1(X10, X11) = X11))) | (X10 = c3)) <=> (((~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))) | (X10 = c3)))), rewrite((((~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))) | (X10 = c3)) <=> ((X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))), ((((~big_f(X10, f1(X10, X11))) | (~(f1(X10, X11) = X11))) | (X10 = c3)) <=> ((X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))))), (((((~big_f(X10, f1(X10, X11))) | (~(f1(X10, X11) = X11))) | (X10 = c3)) | (~big_f(f3(X2, X13), X2))) <=> (((X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))) | (~big_f(f3(X2, X13), X2))))), rewrite((((X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))) | (~big_f(f3(X2, X13), X2))) <=> ((X10 = c3) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))), (((((~big_f(X10, f1(X10, X11))) | (~(f1(X10, X11) = X11))) | (X10 = c3)) | (~big_f(f3(X2, X13), X2))) <=> ((X10 = c3) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))))), ((((((~big_f(X10, f1(X10, X11))) | (~(f1(X10, X11) = X11))) | (X10 = c3)) | (~big_f(f3(X2, X13), X2))) | (~(f3(X2, X13) = X13))) <=> (((X10 = c3) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))) | (~(f3(X2, X13) = X13))))), rewrite((((X10 = c3) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))) | (~(f3(X2, X13) = X13))) <=> ((X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))), ((((((~big_f(X10, f1(X10, X11))) | (~(f1(X10, X11) = X11))) | (X10 = c3)) | (~big_f(f3(X2, X13), X2))) | (~(f3(X2, X13) = X13))) <=> ((X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))))), (((((((~big_f(X10, f1(X10, X11))) | (~(f1(X10, X11) = X11))) | (X10 = c3)) | (~big_f(f3(X2, X13), X2))) | (~(f3(X2, X13) = X13))) | (X2 = c4)) <=> (((X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))) | (X2 = c4)))), rewrite((((X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11)))) | (X2 = c4)) <=> ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))), (((((((~big_f(X10, f1(X10, X11))) | (~(f1(X10, X11) = X11))) | (X10 = c3)) | (~big_f(f3(X2, X13), X2))) | (~(f3(X2, X13) = X13))) | (X2 = c4)) <=> ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))))),
% 27.36/17.60 inference(bind,[status(th)],[])).
% 27.36/17.60 tff(928,plain,
% 27.36/17.60 (![X11: $i, X13: $i, X10: $i, X2: $i] : ((((((~big_f(X10, f1(X10, X11))) | (~(f1(X10, X11) = X11))) | (X10 = c3)) | (~big_f(f3(X2, X13), X2))) | (~(f3(X2, X13) = X13))) | (X2 = c4)) <=> ![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))),
% 27.36/17.60 inference(quant_intro,[status(thm)],[927])).
% 27.36/17.60 tff(929,axiom,(![X11: $i, X13: $i, X10: $i, X2: $i] : ((((((~big_f(X10, f1(X10, X11))) | (~(f1(X10, X11) = X11))) | (X10 = c3)) | (~big_f(f3(X2, X13), X2))) | (~(f3(X2, X13) = X13))) | (X2 = c4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_8')).
% 27.36/17.60 tff(930,plain,
% 27.36/17.60 (![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))),
% 27.36/17.60 inference(modus_ponens,[status(thm)],[929, 928])).
% 27.36/17.60 tff(931,plain,
% 27.36/17.60 (![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))),
% 27.36/17.60 inference(modus_ponens,[status(thm)],[930, 926])).
% 27.36/17.60 tff(932,plain,(
% 27.36/17.60 ![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))),
% 27.36/17.60 inference(skolemize,[status(sab)],[931])).
% 27.36/17.60 tff(933,plain,
% 27.36/17.60 (![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))),
% 27.36/17.60 inference(modus_ponens,[status(thm)],[932, 925])).
% 27.36/17.60 tff(934,plain,
% 27.36/17.60 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (c2 = c4) | (~(f1(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(c2, f1(c2, f9(c2, c2)))) | (~(f3(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(c2, f9(c2, c2)), c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (c2 = c4) | (~(f1(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(c2, f1(c2, f9(c2, c2)))) | (~(f3(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(c2, f9(c2, c2)), c2)))),
% 27.36/17.60 inference(rewrite,[status(thm)],[])).
% 27.36/17.60 tff(935,plain,
% 27.36/17.60 (((c2 = c4) | (c2 = c3) | (~(f3(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(c2, f9(c2, c2)), c2)) | (~(f1(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(c2, f1(c2, f9(c2, c2))))) <=> ((c2 = c3) | (c2 = c4) | (~(f1(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(c2, f1(c2, f9(c2, c2)))) | (~(f3(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(c2, f9(c2, c2)), c2)))),
% 27.36/17.60 inference(rewrite,[status(thm)],[])).
% 27.36/17.60 tff(936,plain,
% 27.36/17.60 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (c2 = c3) | (~(f3(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(c2, f9(c2, c2)), c2)) | (~(f1(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(c2, f1(c2, f9(c2, c2)))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (c2 = c4) | (~(f1(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(c2, f1(c2, f9(c2, c2)))) | (~(f3(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(c2, f9(c2, c2)), c2))))),
% 27.36/17.60 inference(monotonicity,[status(thm)],[935])).
% 27.36/17.60 tff(937,plain,
% 27.36/17.60 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (c2 = c3) | (~(f3(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(c2, f9(c2, c2)), c2)) | (~(f1(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(c2, f1(c2, f9(c2, c2)))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (c2 = c4) | (~(f1(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(c2, f1(c2, f9(c2, c2)))) | (~(f3(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(c2, f9(c2, c2)), c2)))),
% 27.36/17.60 inference(transitivity,[status(thm)],[936, 934])).
% 27.36/17.60 tff(938,plain,
% 27.36/17.60 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (c2 = c3) | (~(f3(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(c2, f9(c2, c2)), c2)) | (~(f1(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(c2, f1(c2, f9(c2, c2)))))),
% 27.36/17.60 inference(quant_inst,[status(thm)],[])).
% 27.36/17.60 tff(939,plain,
% 27.36/17.60 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (c2 = c4) | (~(f1(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(c2, f1(c2, f9(c2, c2)))) | (~(f3(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(c2, f9(c2, c2)), c2))),
% 27.36/17.60 inference(modus_ponens,[status(thm)],[938, 937])).
% 27.36/17.60 tff(940,plain,
% 27.36/17.60 ((~(f3(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(c2, f9(c2, c2)), c2))),
% 27.36/17.60 inference(unit_resolution,[status(thm)],[939, 933, 873, 377, 880, 879])).
% 27.36/17.60 tff(941,plain,
% 27.36/17.60 ($false),
% 27.36/17.60 inference(unit_resolution,[status(thm)],[940, 923, 920])).
% 27.36/17.60 tff(942,plain,((~(f1(f7(f7(c2)), c1) = c1)) | (c2 = c4) | (c2 = c3) | (~big_f(f9(c2, c2), f10(c2))) | (~(f10(c2) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c1) = c2)) | (~(f7(c1) = c2)) | big_f(c2, c2) | (~big_f(c2, c1)) | (~(f7(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 27.36/17.60 tff(943,plain,
% 27.36/17.60 (~(f1(f7(f7(c2)), c1) = c1)),
% 27.36/17.60 inference(unit_resolution,[status(thm)],[942, 377, 873, 690, 122, 148, 79, 16, 347, 121, 348, 292])).
% 27.36/17.60 tff(944,plain,
% 27.36/17.60 (f1(f7(f7(c2)), c1) = c2),
% 27.36/17.60 inference(unit_resolution,[status(thm)],[384, 943])).
% 27.36/17.60 tff(945,plain,
% 27.36/17.60 (f1(c2, c1) = c2),
% 27.36/17.60 inference(transitivity,[status(thm)],[356, 944])).
% 27.36/17.60 tff(946,plain,
% 27.36/17.60 (big_f(c2, f1(c2, c1)) <=> big_f(c2, c2)),
% 27.36/17.60 inference(monotonicity,[status(thm)],[945])).
% 27.36/17.60 tff(947,plain,
% 27.36/17.60 (big_f(c2, c2) <=> big_f(c2, f1(c2, c1))),
% 27.36/17.60 inference(symmetry,[status(thm)],[946])).
% 27.36/17.60 tff(948,plain,
% 27.36/17.60 (big_f(c2, c2) <=> big_f(c2, f1(c2, f9(c2, c2)))),
% 27.36/17.60 inference(transitivity,[status(thm)],[947, 351])).
% 27.36/17.60 tff(949,plain,
% 27.36/17.60 ((~big_f(c2, c2)) <=> (~big_f(c2, f1(c2, f9(c2, c2))))),
% 27.36/17.60 inference(monotonicity,[status(thm)],[948])).
% 27.36/17.60 tff(950,plain,
% 27.36/17.60 (~big_f(c2, f1(c2, f9(c2, c2)))),
% 27.36/17.60 inference(modus_ponens,[status(thm)],[121, 949])).
% 27.36/17.60 tff(951,plain,
% 27.36/17.60 ((~(f1(f7(f7(c2)), c1) = c1)) <=> (~(f1(c2, f9(c2, c2)) = f9(c2, c2)))),
% 27.36/17.60 inference(monotonicity,[status(thm)],[542])).
% 27.36/17.60 tff(952,plain,
% 27.36/17.60 (~(f1(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.36/17.60 inference(modus_ponens,[status(thm)],[943, 951])).
% 27.36/17.60 tff(953,assumption,(f3(f7(c1), c1) = c1), introduced(assumption)).
% 27.36/17.60 tff(954,plain,
% 27.36/17.60 (f3(c2, f9(c2, c2)) = f9(c2, c2)),
% 27.36/17.60 inference(transitivity,[status(thm)],[884, 883, 953, 149, 132])).
% 27.36/17.60 tff(955,plain,
% 27.36/17.60 (big_f(f3(c2, f9(c2, c2)), c2) <=> big_f(f9(c2, c2), f10(c2))),
% 27.36/17.60 inference(monotonicity,[status(thm)],[954, 216])).
% 27.36/17.60 tff(956,plain,
% 27.36/17.60 (big_f(f9(c2, c2), f10(c2)) <=> big_f(f3(c2, f9(c2, c2)), c2)),
% 27.36/17.60 inference(symmetry,[status(thm)],[955])).
% 27.36/17.60 tff(957,plain,
% 27.36/17.60 (big_f(f3(c2, f9(c2, c2)), c2)),
% 27.36/17.60 inference(modus_ponens,[status(thm)],[690, 956])).
% 27.36/17.60 tff(958,assumption,(~big_f(c2, f1(c2, f9(c2, c2)))), introduced(assumption)).
% 27.36/17.60 tff(959,assumption,(~(f1(c2, f9(c2, c2)) = f9(c2, c2))), introduced(assumption)).
% 27.36/17.60 tff(960,plain,
% 27.36/17.60 (^[X11: $i, X13: $i, X10: $i, X2: $i] : refl(((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2))) <=> ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2))))),
% 27.36/17.60 inference(bind,[status(th)],[])).
% 27.36/17.60 tff(961,plain,
% 27.36/17.60 (![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2))) <=> ![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))),
% 27.36/17.60 inference(quant_intro,[status(thm)],[960])).
% 27.36/17.60 tff(962,plain,
% 27.36/17.60 (![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2))) <=> ![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))),
% 27.36/17.60 inference(rewrite,[status(thm)],[])).
% 27.36/17.60 tff(963,plain,
% 27.36/17.60 (^[X11: $i, X13: $i, X10: $i, X2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((big_f(X10, f1(X10, X11)) | (f1(X10, X11) = X11)) <=> ((f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))), (((big_f(X10, f1(X10, X11)) | (f1(X10, X11) = X11)) | (X10 = c3)) <=> (((f1(X10, X11) = X11) | big_f(X10, f1(X10, X11))) | (X10 = c3)))), rewrite((((f1(X10, X11) = X11) | big_f(X10, f1(X10, X11))) | (X10 = c3)) <=> ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))), (((big_f(X10, f1(X10, X11)) | (f1(X10, X11) = X11)) | (X10 = c3)) <=> ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11))))), ((((big_f(X10, f1(X10, X11)) | (f1(X10, X11) = X11)) | (X10 = c3)) | (~big_f(f3(X2, X13), X2))) <=> (((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11))) | (~big_f(f3(X2, X13), X2))))), rewrite((((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11))) | (~big_f(f3(X2, X13), X2))) <=> ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~big_f(f3(X2, X13), X2)))), ((((big_f(X10, f1(X10, X11)) | (f1(X10, X11) = X11)) | (X10 = c3)) | (~big_f(f3(X2, X13), X2))) <=> ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~big_f(f3(X2, X13), X2))))), (((((big_f(X10, f1(X10, X11)) | (f1(X10, X11) = X11)) | (X10 = c3)) | (~big_f(f3(X2, X13), X2))) | (~(f3(X2, X13) = X13))) <=> (((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~big_f(f3(X2, X13), X2))) | (~(f3(X2, X13) = X13))))), rewrite((((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~big_f(f3(X2, X13), X2))) | (~(f3(X2, X13) = X13))) <=> ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))), (((((big_f(X10, f1(X10, X11)) | (f1(X10, X11) = X11)) | (X10 = c3)) | (~big_f(f3(X2, X13), X2))) | (~(f3(X2, X13) = X13))) <=> ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2))))), ((((((big_f(X10, f1(X10, X11)) | (f1(X10, X11) = X11)) | (X10 = c3)) | (~big_f(f3(X2, X13), X2))) | (~(f3(X2, X13) = X13))) | (X2 = c4)) <=> (((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2))) | (X2 = c4)))), rewrite((((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2))) | (X2 = c4)) <=> ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))), ((((((big_f(X10, f1(X10, X11)) | (f1(X10, X11) = X11)) | (X10 = c3)) | (~big_f(f3(X2, X13), X2))) | (~(f3(X2, X13) = X13))) | (X2 = c4)) <=> ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))))),
% 27.36/17.60 inference(bind,[status(th)],[])).
% 27.36/17.60 tff(964,plain,
% 27.36/17.60 (![X11: $i, X13: $i, X10: $i, X2: $i] : (((((big_f(X10, f1(X10, X11)) | (f1(X10, X11) = X11)) | (X10 = c3)) | (~big_f(f3(X2, X13), X2))) | (~(f3(X2, X13) = X13))) | (X2 = c4)) <=> ![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))),
% 27.36/17.60 inference(quant_intro,[status(thm)],[963])).
% 27.36/17.60 tff(965,axiom,(![X11: $i, X13: $i, X10: $i, X2: $i] : (((((big_f(X10, f1(X10, X11)) | (f1(X10, X11) = X11)) | (X10 = c3)) | (~big_f(f3(X2, X13), X2))) | (~(f3(X2, X13) = X13))) | (X2 = c4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_4')).
% 27.36/17.61 tff(966,plain,
% 27.36/17.61 (![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))),
% 27.36/17.61 inference(modus_ponens,[status(thm)],[965, 964])).
% 27.36/17.61 tff(967,plain,
% 27.36/17.61 (![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))),
% 27.36/17.61 inference(modus_ponens,[status(thm)],[966, 962])).
% 27.36/17.61 tff(968,plain,(
% 27.36/17.61 ![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))),
% 27.36/17.61 inference(skolemize,[status(sab)],[967])).
% 27.36/17.61 tff(969,plain,
% 27.36/17.61 (![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))),
% 27.36/17.61 inference(modus_ponens,[status(thm)],[968, 961])).
% 27.36/17.61 tff(970,plain,
% 27.36/17.61 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c3) | (c2 = c4) | (f1(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(c2, f1(c2, f9(c2, c2))) | (~(f3(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(c2, f9(c2, c2)), c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c2 = c3) | (c2 = c4) | (f1(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(c2, f1(c2, f9(c2, c2))) | (~(f3(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(c2, f9(c2, c2)), c2)))),
% 27.36/17.61 inference(rewrite,[status(thm)],[])).
% 27.36/17.61 tff(971,plain,
% 27.36/17.61 (((c2 = c4) | (c2 = c3) | (f1(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(c2, f1(c2, f9(c2, c2))) | (~(f3(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(c2, f9(c2, c2)), c2))) <=> ((c2 = c3) | (c2 = c4) | (f1(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(c2, f1(c2, f9(c2, c2))) | (~(f3(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(c2, f9(c2, c2)), c2)))),
% 27.36/17.61 inference(rewrite,[status(thm)],[])).
% 27.36/17.61 tff(972,plain,
% 27.36/17.61 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c4) | (c2 = c3) | (f1(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(c2, f1(c2, f9(c2, c2))) | (~(f3(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(c2, f9(c2, c2)), c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c3) | (c2 = c4) | (f1(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(c2, f1(c2, f9(c2, c2))) | (~(f3(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(c2, f9(c2, c2)), c2))))),
% 27.36/17.61 inference(monotonicity,[status(thm)],[971])).
% 27.36/17.61 tff(973,plain,
% 27.36/17.61 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c4) | (c2 = c3) | (f1(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(c2, f1(c2, f9(c2, c2))) | (~(f3(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(c2, f9(c2, c2)), c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c2 = c3) | (c2 = c4) | (f1(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(c2, f1(c2, f9(c2, c2))) | (~(f3(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(c2, f9(c2, c2)), c2)))),
% 27.36/17.61 inference(transitivity,[status(thm)],[972, 970])).
% 27.36/17.61 tff(974,plain,
% 27.36/17.61 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c4) | (c2 = c3) | (f1(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(c2, f1(c2, f9(c2, c2))) | (~(f3(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(c2, f9(c2, c2)), c2)))),
% 27.36/17.61 inference(quant_inst,[status(thm)],[])).
% 27.36/17.61 tff(975,plain,
% 27.36/17.61 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c2 = c3) | (c2 = c4) | (f1(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(c2, f1(c2, f9(c2, c2))) | (~(f3(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(c2, f9(c2, c2)), c2))),
% 27.36/17.61 inference(modus_ponens,[status(thm)],[974, 973])).
% 27.36/17.61 tff(976,plain,
% 27.36/17.61 ((~(f3(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(c2, f9(c2, c2)), c2))),
% 27.36/17.61 inference(unit_resolution,[status(thm)],[975, 969, 873, 377, 959, 958])).
% 27.36/17.61 tff(977,plain,
% 27.36/17.61 ($false),
% 27.36/17.61 inference(unit_resolution,[status(thm)],[976, 957, 954])).
% 27.36/17.61 tff(978,plain,((~(f3(f7(c1), c1) = c1)) | (c2 = c4) | (c2 = c3) | (f1(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(c2, f1(c2, f9(c2, c2))) | (~big_f(f9(c2, c2), f10(c2))) | (~(f10(c2) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c1) = c2)) | (~(f7(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.36/17.61 tff(979,plain,
% 27.36/17.61 (~(f3(f7(c1), c1) = c1)),
% 27.36/17.61 inference(unit_resolution,[status(thm)],[978, 377, 873, 952, 950, 690, 122, 148, 79, 16, 347])).
% 27.36/17.61 tff(980,plain,
% 27.36/17.61 (f3(f7(c1), c1) = c2),
% 27.36/17.61 inference(unit_resolution,[status(thm)],[918, 979])).
% 27.36/17.61 tff(981,plain,
% 27.36/17.61 (f3(f10(c1), c1) = c2),
% 27.36/17.61 inference(transitivity,[status(thm)],[883, 980])).
% 27.36/17.61 tff(982,plain,
% 27.36/17.61 (big_f(f3(f10(c1), c1), f10(c1)) <=> big_f(c2, c2)),
% 27.36/17.61 inference(monotonicity,[status(thm)],[981, 16])).
% 27.36/17.61 tff(983,plain,
% 27.36/17.61 (big_f(c2, c2) <=> big_f(f3(f10(c1), c1), f10(c1))),
% 27.36/17.61 inference(symmetry,[status(thm)],[982])).
% 27.36/17.61 tff(984,plain,
% 27.36/17.61 ((~big_f(c2, c2)) <=> (~big_f(f3(f10(c1), c1), f10(c1)))),
% 27.36/17.61 inference(monotonicity,[status(thm)],[983])).
% 27.36/17.61 tff(985,plain,
% 27.36/17.61 (~big_f(f3(f10(c1), c1), f10(c1))),
% 27.36/17.61 inference(modus_ponens,[status(thm)],[121, 984])).
% 27.36/17.61 tff(986,plain,
% 27.36/17.61 (f7(c1) = f10(c1)),
% 27.36/17.61 inference(transitivity,[status(thm)],[347, 293])).
% 27.36/17.61 tff(987,plain,
% 27.36/17.61 (f3(f7(c1), c1) = f3(f10(c1), c1)),
% 27.36/17.61 inference(symmetry,[status(thm)],[883])).
% 27.36/17.61 tff(988,plain,
% 27.36/17.61 (big_f(f3(f7(c1), c1), f7(c1)) <=> big_f(f3(f10(c1), c1), f10(c1))),
% 27.36/17.61 inference(monotonicity,[status(thm)],[987, 986])).
% 27.36/17.61 tff(989,plain,
% 27.36/17.61 (f1(f7(c1), c1) = f1(c2, c1)),
% 27.36/17.61 inference(monotonicity,[status(thm)],[347])).
% 27.36/17.61 tff(990,plain,
% 27.36/17.61 (big_f(f7(c1), f1(f7(c1), c1)) <=> big_f(c2, f1(c2, c1))),
% 27.36/17.61 inference(monotonicity,[status(thm)],[347, 989])).
% 27.36/17.61 tff(991,plain,
% 27.36/17.61 (big_f(c2, f1(c2, c1)) <=> big_f(f7(c1), f1(f7(c1), c1))),
% 27.36/17.61 inference(symmetry,[status(thm)],[990])).
% 27.36/17.61 tff(992,plain,
% 27.36/17.61 (big_f(c2, c2) <=> big_f(f7(c1), f1(f7(c1), c1))),
% 27.36/17.61 inference(transitivity,[status(thm)],[947, 991])).
% 27.36/17.61 tff(993,plain,
% 27.36/17.61 ((~big_f(c2, c2)) <=> (~big_f(f7(c1), f1(f7(c1), c1)))),
% 27.36/17.61 inference(monotonicity,[status(thm)],[992])).
% 27.36/17.61 tff(994,plain,
% 27.36/17.61 (~big_f(f7(c1), f1(f7(c1), c1))),
% 27.36/17.61 inference(modus_ponens,[status(thm)],[121, 993])).
% 27.36/17.61 tff(995,plain,
% 27.36/17.61 ((f1(f7(c1), c1) = c1) <=> (f1(c2, c1) = c1)),
% 27.36/17.61 inference(monotonicity,[status(thm)],[989])).
% 27.36/17.61 tff(996,plain,
% 27.36/17.61 ((f1(c2, c1) = c1) <=> (f1(f7(c1), c1) = c1)),
% 27.36/17.61 inference(symmetry,[status(thm)],[995])).
% 27.36/17.61 tff(997,plain,
% 27.36/17.61 ((f1(f7(f7(c2)), c1) = c1) <=> (f1(f7(c1), c1) = c1)),
% 27.36/17.61 inference(transitivity,[status(thm)],[541, 996])).
% 27.36/17.61 tff(998,plain,
% 27.36/17.61 ((~(f1(f7(f7(c2)), c1) = c1)) <=> (~(f1(f7(c1), c1) = c1))),
% 27.36/17.61 inference(monotonicity,[status(thm)],[997])).
% 27.36/17.61 tff(999,plain,
% 27.36/17.61 (~(f1(f7(c1), c1) = c1)),
% 27.36/17.61 inference(modus_ponens,[status(thm)],[943, 998])).
% 27.36/17.61 tff(1000,assumption,(~(f7(c1) = c4)), introduced(assumption)).
% 27.36/17.61 tff(1001,plain,
% 27.36/17.61 ((f7(c1) = c3) <=> (c2 = c3)),
% 27.36/17.61 inference(monotonicity,[status(thm)],[347])).
% 27.36/17.61 tff(1002,plain,
% 27.36/17.61 ((c2 = c3) <=> (f7(c1) = c3)),
% 27.36/17.61 inference(symmetry,[status(thm)],[1001])).
% 27.36/17.61 tff(1003,plain,
% 27.36/17.61 ((~(c2 = c3)) <=> (~(f7(c1) = c3))),
% 27.36/17.61 inference(monotonicity,[status(thm)],[1002])).
% 27.36/17.61 tff(1004,plain,
% 27.36/17.61 (~(f7(c1) = c3)),
% 27.36/17.61 inference(modus_ponens,[status(thm)],[377, 1003])).
% 27.36/17.61 tff(1005,plain,
% 27.36/17.61 (^[X11: $i, X13: $i, X10: $i, X2: $i] : refl(((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11))) <=> ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11))))),
% 27.36/17.61 inference(bind,[status(th)],[])).
% 27.36/17.61 tff(1006,plain,
% 27.36/17.61 (![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11))) <=> ![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))),
% 27.36/17.61 inference(quant_intro,[status(thm)],[1005])).
% 27.36/17.61 tff(1007,plain,
% 27.36/17.61 (![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11))) <=> ![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))),
% 27.36/17.61 inference(rewrite,[status(thm)],[])).
% 27.36/17.61 tff(1008,plain,
% 27.36/17.61 (^[X11: $i, X13: $i, X10: $i, X2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((big_f(X10, f1(X10, X11)) | (f1(X10, X11) = X11)) <=> ((f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))), (((big_f(X10, f1(X10, X11)) | (f1(X10, X11) = X11)) | (X10 = c3)) <=> (((f1(X10, X11) = X11) | big_f(X10, f1(X10, X11))) | (X10 = c3)))), rewrite((((f1(X10, X11) = X11) | big_f(X10, f1(X10, X11))) | (X10 = c3)) <=> ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))), (((big_f(X10, f1(X10, X11)) | (f1(X10, X11) = X11)) | (X10 = c3)) <=> ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11))))), ((((big_f(X10, f1(X10, X11)) | (f1(X10, X11) = X11)) | (X10 = c3)) | big_f(f3(X2, X13), X2)) <=> (((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11))) | big_f(f3(X2, X13), X2)))), rewrite((((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11))) | big_f(f3(X2, X13), X2)) <=> (big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))), ((((big_f(X10, f1(X10, X11)) | (f1(X10, X11) = X11)) | (X10 = c3)) | big_f(f3(X2, X13), X2)) <=> (big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11))))), (((((big_f(X10, f1(X10, X11)) | (f1(X10, X11) = X11)) | (X10 = c3)) | big_f(f3(X2, X13), X2)) | (f3(X2, X13) = X13)) <=> ((big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11))) | (f3(X2, X13) = X13)))), rewrite(((big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11))) | (f3(X2, X13) = X13)) <=> ((f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))), (((((big_f(X10, f1(X10, X11)) | (f1(X10, X11) = X11)) | (X10 = c3)) | big_f(f3(X2, X13), X2)) | (f3(X2, X13) = X13)) <=> ((f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11))))), ((((((big_f(X10, f1(X10, X11)) | (f1(X10, X11) = X11)) | (X10 = c3)) | big_f(f3(X2, X13), X2)) | (f3(X2, X13) = X13)) | (X2 = c4)) <=> (((f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11))) | (X2 = c4)))), rewrite((((f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11))) | (X2 = c4)) <=> ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))), ((((((big_f(X10, f1(X10, X11)) | (f1(X10, X11) = X11)) | (X10 = c3)) | big_f(f3(X2, X13), X2)) | (f3(X2, X13) = X13)) | (X2 = c4)) <=> ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))))),
% 27.36/17.61 inference(bind,[status(th)],[])).
% 27.36/17.61 tff(1009,plain,
% 27.36/17.61 (![X11: $i, X13: $i, X10: $i, X2: $i] : (((((big_f(X10, f1(X10, X11)) | (f1(X10, X11) = X11)) | (X10 = c3)) | big_f(f3(X2, X13), X2)) | (f3(X2, X13) = X13)) | (X2 = c4)) <=> ![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))),
% 27.36/17.61 inference(quant_intro,[status(thm)],[1008])).
% 27.36/17.61 tff(1010,axiom,(![X11: $i, X13: $i, X10: $i, X2: $i] : (((((big_f(X10, f1(X10, X11)) | (f1(X10, X11) = X11)) | (X10 = c3)) | big_f(f3(X2, X13), X2)) | (f3(X2, X13) = X13)) | (X2 = c4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_3')).
% 27.36/17.61 tff(1011,plain,
% 27.36/17.61 (![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))),
% 27.36/17.61 inference(modus_ponens,[status(thm)],[1010, 1009])).
% 27.36/17.61 tff(1012,plain,
% 27.36/17.61 (![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))),
% 27.36/17.61 inference(modus_ponens,[status(thm)],[1011, 1007])).
% 27.36/17.61 tff(1013,plain,(
% 27.36/17.61 ![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))),
% 27.36/17.61 inference(skolemize,[status(sab)],[1012])).
% 27.36/17.61 tff(1014,plain,
% 27.36/17.61 (![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))),
% 27.36/17.61 inference(modus_ponens,[status(thm)],[1013, 1006])).
% 27.36/17.61 tff(1015,plain,
% 27.36/17.61 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f7(c1) = c3) | (f7(c1) = c4) | (f3(f7(c1), c1) = c1) | big_f(f3(f7(c1), c1), f7(c1)) | (f1(f7(c1), c1) = c1) | big_f(f7(c1), f1(f7(c1), c1)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (f7(c1) = c3) | (f7(c1) = c4) | (f3(f7(c1), c1) = c1) | big_f(f3(f7(c1), c1), f7(c1)) | (f1(f7(c1), c1) = c1) | big_f(f7(c1), f1(f7(c1), c1)))),
% 27.36/17.61 inference(rewrite,[status(thm)],[])).
% 27.36/17.61 tff(1016,plain,
% 27.36/17.61 (((f7(c1) = c4) | (f3(f7(c1), c1) = c1) | big_f(f3(f7(c1), c1), f7(c1)) | (f7(c1) = c3) | (f1(f7(c1), c1) = c1) | big_f(f7(c1), f1(f7(c1), c1))) <=> ((f7(c1) = c3) | (f7(c1) = c4) | (f3(f7(c1), c1) = c1) | big_f(f3(f7(c1), c1), f7(c1)) | (f1(f7(c1), c1) = c1) | big_f(f7(c1), f1(f7(c1), c1)))),
% 27.36/17.61 inference(rewrite,[status(thm)],[])).
% 27.36/17.61 tff(1017,plain,
% 27.36/17.61 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f7(c1) = c4) | (f3(f7(c1), c1) = c1) | big_f(f3(f7(c1), c1), f7(c1)) | (f7(c1) = c3) | (f1(f7(c1), c1) = c1) | big_f(f7(c1), f1(f7(c1), c1)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f7(c1) = c3) | (f7(c1) = c4) | (f3(f7(c1), c1) = c1) | big_f(f3(f7(c1), c1), f7(c1)) | (f1(f7(c1), c1) = c1) | big_f(f7(c1), f1(f7(c1), c1))))),
% 27.36/17.61 inference(monotonicity,[status(thm)],[1016])).
% 27.36/17.61 tff(1018,plain,
% 27.36/17.61 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f7(c1) = c4) | (f3(f7(c1), c1) = c1) | big_f(f3(f7(c1), c1), f7(c1)) | (f7(c1) = c3) | (f1(f7(c1), c1) = c1) | big_f(f7(c1), f1(f7(c1), c1)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (f7(c1) = c3) | (f7(c1) = c4) | (f3(f7(c1), c1) = c1) | big_f(f3(f7(c1), c1), f7(c1)) | (f1(f7(c1), c1) = c1) | big_f(f7(c1), f1(f7(c1), c1)))),
% 27.36/17.61 inference(transitivity,[status(thm)],[1017, 1015])).
% 27.36/17.61 tff(1019,plain,
% 27.36/17.61 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f7(c1) = c4) | (f3(f7(c1), c1) = c1) | big_f(f3(f7(c1), c1), f7(c1)) | (f7(c1) = c3) | (f1(f7(c1), c1) = c1) | big_f(f7(c1), f1(f7(c1), c1)))),
% 27.36/17.61 inference(quant_inst,[status(thm)],[])).
% 27.36/17.61 tff(1020,plain,
% 27.36/17.61 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (f7(c1) = c3) | (f7(c1) = c4) | (f3(f7(c1), c1) = c1) | big_f(f3(f7(c1), c1), f7(c1)) | (f1(f7(c1), c1) = c1) | big_f(f7(c1), f1(f7(c1), c1))),
% 27.36/17.61 inference(modus_ponens,[status(thm)],[1019, 1018])).
% 27.36/17.61 tff(1021,plain,
% 27.36/17.61 ((f7(c1) = c3) | (f7(c1) = c4) | (f3(f7(c1), c1) = c1) | big_f(f3(f7(c1), c1), f7(c1)) | (f1(f7(c1), c1) = c1) | big_f(f7(c1), f1(f7(c1), c1))),
% 27.36/17.61 inference(unit_resolution,[status(thm)],[1020, 1014])).
% 27.36/17.61 tff(1022,plain,
% 27.36/17.61 (big_f(f3(f7(c1), c1), f7(c1))),
% 27.36/17.61 inference(unit_resolution,[status(thm)],[1021, 979, 1004, 1000, 999, 994])).
% 27.36/17.61 tff(1023,plain,
% 27.36/17.61 (big_f(f3(f10(c1), c1), f10(c1))),
% 27.36/17.61 inference(modus_ponens,[status(thm)],[1022, 988])).
% 27.36/17.61 tff(1024,plain,
% 27.36/17.61 ($false),
% 27.36/17.61 inference(unit_resolution,[status(thm)],[1023, 985])).
% 27.36/17.61 tff(1025,plain,((c2 = c3) | big_f(c2, c2) | (~(f10(c1) = c2)) | (~(f7(c1) = c2)) | (f7(c1) = c4) | (c2 = c4) | (~big_f(f9(c2, c2), f10(c2))) | (~(f10(c2) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f7(c2) = c1)) | (~big_f(c2, c1))), inference(lemma,lemma(discharge,[]))).
% 27.36/17.61 tff(1026,plain,
% 27.36/17.61 (c2 = c3),
% 27.36/17.61 inference(unit_resolution,[status(thm)],[1025, 872, 16, 347, 121, 867, 690, 122, 148, 79, 292, 348])).
% 27.36/17.61 tff(1027,plain,
% 27.36/17.61 (c3 = c2),
% 27.36/17.61 inference(symmetry,[status(thm)],[1026])).
% 27.36/17.61 tff(1028,plain,
% 27.36/17.61 ((f9(f10(c2), f4(c4)) = c3) <=> (f9(c2, c2) = c2)),
% 27.36/17.61 inference(monotonicity,[status(thm)],[132, 1027])).
% 27.36/17.61 tff(1029,plain,
% 27.36/17.61 ((f9(c2, c2) = c2) <=> (f9(f10(c2), f4(c4)) = c3)),
% 27.36/17.61 inference(symmetry,[status(thm)],[1028])).
% 27.36/17.61 tff(1030,plain,
% 27.36/17.61 ((f9(c2, c2) = c2) <=> (c1 = c3)),
% 27.36/17.61 inference(transitivity,[status(thm)],[1029, 212])).
% 27.36/17.61 tff(1031,plain,
% 27.36/17.61 ((~(f9(c2, c2) = c2)) <=> (~(c1 = c3))),
% 27.36/17.61 inference(monotonicity,[status(thm)],[1030])).
% 27.36/17.61 tff(1032,plain,
% 27.36/17.61 (~(c1 = c3)),
% 27.36/17.61 inference(modus_ponens,[status(thm)],[185, 1031])).
% 27.36/17.61 tff(1033,plain,
% 27.36/17.61 ((f10(c1) = c4) <=> (c2 = c4)),
% 27.36/17.61 inference(monotonicity,[status(thm)],[16])).
% 27.36/17.61 tff(1034,plain,
% 27.36/17.61 ((c2 = c4) <=> (f10(c1) = c4)),
% 27.36/17.61 inference(symmetry,[status(thm)],[1033])).
% 27.36/17.61 tff(1035,plain,
% 27.36/17.61 ((c4 = c2) <=> (f10(c1) = c4)),
% 27.36/17.61 inference(transitivity,[status(thm)],[159, 1034])).
% 27.36/17.61 tff(1036,plain,
% 27.36/17.61 ((~(c4 = c2)) <=> (~(f10(c1) = c4))),
% 27.36/17.61 inference(monotonicity,[status(thm)],[1035])).
% 27.36/17.61 tff(1037,plain,
% 27.36/17.61 (~(f10(c1) = c4)),
% 27.36/17.61 inference(modus_ponens,[status(thm)],[866, 1036])).
% 27.36/17.61 tff(1038,plain,
% 27.36/17.61 ((f9(c2, c2) = c2) <=> (f9(c2, c2) = c3)),
% 27.36/17.61 inference(transitivity,[status(thm)],[1029, 339])).
% 27.36/17.61 tff(1039,plain,
% 27.36/17.61 ((~(f9(c2, c2) = c2)) <=> (~(f9(c2, c2) = c3))),
% 27.36/17.61 inference(monotonicity,[status(thm)],[1038])).
% 27.36/17.61 tff(1040,plain,
% 27.36/17.61 (~(f9(c2, c2) = c3)),
% 27.36/17.61 inference(modus_ponens,[status(thm)],[185, 1039])).
% 27.36/17.61 tff(1041,plain,
% 27.36/17.61 (f3(f10(c1), c1) = c2),
% 27.36/17.61 inference(transitivity,[status(thm)],[883, 881])).
% 27.36/17.61 tff(1042,plain,
% 27.36/17.61 (big_f(f3(f10(c1), c1), f10(c1)) <=> big_f(c2, c2)),
% 27.36/17.61 inference(monotonicity,[status(thm)],[1041, 16])).
% 27.36/17.61 tff(1043,plain,
% 27.36/17.61 (big_f(c2, c2) <=> big_f(f3(f10(c1), c1), f10(c1))),
% 27.36/17.61 inference(symmetry,[status(thm)],[1042])).
% 27.36/17.61 tff(1044,plain,
% 27.36/17.61 ((~big_f(c2, c2)) <=> (~big_f(f3(f10(c1), c1), f10(c1)))),
% 27.36/17.61 inference(monotonicity,[status(thm)],[1043])).
% 27.36/17.61 tff(1045,plain,
% 27.36/17.61 (~big_f(f3(f10(c1), c1), f10(c1))),
% 27.36/17.61 inference(modus_ponens,[status(thm)],[121, 1044])).
% 27.36/17.61 tff(1046,assumption,(~(f10(c1) = c4)), introduced(assumption)).
% 27.36/17.61 tff(1047,plain,
% 27.36/17.61 ((f3(f10(c1), c1) = c1) <=> (c2 = f9(c2, c2))),
% 27.36/17.61 inference(monotonicity,[status(thm)],[1041, 150])).
% 27.36/17.61 tff(1048,plain,
% 27.36/17.61 ((f3(f10(c1), c1) = c1) <=> (f9(c2, c2) = c2)),
% 27.36/17.61 inference(transitivity,[status(thm)],[1047, 167])).
% 27.36/17.61 tff(1049,plain,
% 27.36/17.61 ((f9(c2, c2) = c2) <=> (f3(f10(c1), c1) = c1)),
% 27.36/17.61 inference(symmetry,[status(thm)],[1048])).
% 27.36/17.61 tff(1050,plain,
% 27.36/17.61 ((~(f9(c2, c2) = c2)) <=> (~(f3(f10(c1), c1) = c1))),
% 27.36/17.61 inference(monotonicity,[status(thm)],[1049])).
% 27.36/17.61 tff(1051,plain,
% 27.36/17.61 (~(f3(f10(c1), c1) = c1)),
% 27.36/17.61 inference(modus_ponens,[status(thm)],[185, 1050])).
% 27.36/17.61 tff(1052,assumption,(~(f1(c1, c2) = c2)), introduced(assumption)).
% 27.36/17.62 tff(1053,plain,
% 27.36/17.62 (f1(c1, c2) = c1),
% 27.36/17.62 inference(unit_resolution,[status(thm)],[841, 1052])).
% 27.36/17.62 tff(1054,plain,
% 27.36/17.62 (f1(f9(f10(c2), f4(c4)), c2) = c1),
% 27.36/17.62 inference(transitivity,[status(thm)],[819, 1053])).
% 27.36/17.62 tff(1055,plain,
% 27.36/17.62 (f9(f10(c2), f4(c4)) = f7(c2)),
% 27.36/17.62 inference(transitivity,[status(thm)],[148, 342])).
% 27.36/17.62 tff(1056,plain,
% 27.36/17.62 (big_f(f9(f10(c2), f4(c4)), f1(f9(f10(c2), f4(c4)), c2)) <=> big_f(f7(c2), c1)),
% 27.36/17.62 inference(monotonicity,[status(thm)],[1055, 1054])).
% 27.36/17.62 tff(1057,plain,
% 27.36/17.62 (big_f(f7(c2), c1) <=> big_f(f9(f10(c2), f4(c4)), f1(f9(f10(c2), f4(c4)), c2))),
% 27.36/17.62 inference(symmetry,[status(thm)],[1056])).
% 27.36/17.62 tff(1058,plain,
% 27.36/17.62 ((~big_f(f7(c2), c1)) <=> (~big_f(f9(f10(c2), f4(c4)), f1(f9(f10(c2), f4(c4)), c2)))),
% 27.36/17.62 inference(monotonicity,[status(thm)],[1057])).
% 27.36/17.62 tff(1059,plain,
% 27.36/17.62 (~big_f(f9(f10(c2), f4(c4)), f1(f9(f10(c2), f4(c4)), c2))),
% 27.36/17.62 inference(modus_ponens,[status(thm)],[333, 1058])).
% 27.36/17.62 tff(1060,plain,
% 27.36/17.62 (big_f(c1, f1(c1, c2)) <=> big_f(f9(f10(c2), f4(c4)), f1(f9(f10(c2), f4(c4)), c2))),
% 27.36/17.62 inference(monotonicity,[status(thm)],[149, 820])).
% 27.36/17.62 tff(1061,assumption,(~big_f(f3(f10(c1), c1), f10(c1))), introduced(assumption)).
% 27.36/17.62 tff(1062,assumption,(~(f3(f10(c1), c1) = c1)), introduced(assumption)).
% 27.36/17.62 tff(1063,plain,
% 27.36/17.62 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f1(c1, c2) = c2) | (c1 = c3) | big_f(c1, f1(c1, c2)) | (f10(c1) = c4) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (f1(c1, c2) = c2) | (c1 = c3) | big_f(c1, f1(c1, c2)) | (f10(c1) = c4) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1)))),
% 27.36/17.62 inference(rewrite,[status(thm)],[])).
% 27.36/17.62 tff(1064,plain,
% 27.36/17.62 (((f10(c1) = c4) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1)) | (c1 = c3) | (f1(c1, c2) = c2) | big_f(c1, f1(c1, c2))) <=> ((f1(c1, c2) = c2) | (c1 = c3) | big_f(c1, f1(c1, c2)) | (f10(c1) = c4) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1)))),
% 27.36/17.62 inference(rewrite,[status(thm)],[])).
% 27.36/17.62 tff(1065,plain,
% 27.36/17.62 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f10(c1) = c4) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1)) | (c1 = c3) | (f1(c1, c2) = c2) | big_f(c1, f1(c1, c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f1(c1, c2) = c2) | (c1 = c3) | big_f(c1, f1(c1, c2)) | (f10(c1) = c4) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1))))),
% 27.36/17.62 inference(monotonicity,[status(thm)],[1064])).
% 27.36/17.62 tff(1066,plain,
% 27.36/17.62 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f10(c1) = c4) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1)) | (c1 = c3) | (f1(c1, c2) = c2) | big_f(c1, f1(c1, c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (f1(c1, c2) = c2) | (c1 = c3) | big_f(c1, f1(c1, c2)) | (f10(c1) = c4) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1)))),
% 27.36/17.62 inference(transitivity,[status(thm)],[1065, 1063])).
% 27.36/17.62 tff(1067,plain,
% 27.36/17.62 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f10(c1) = c4) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1)) | (c1 = c3) | (f1(c1, c2) = c2) | big_f(c1, f1(c1, c2)))),
% 27.36/17.62 inference(quant_inst,[status(thm)],[])).
% 27.36/17.62 tff(1068,plain,
% 27.36/17.62 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (f1(c1, c2) = c2) | (c1 = c3) | big_f(c1, f1(c1, c2)) | (f10(c1) = c4) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1))),
% 27.36/17.62 inference(modus_ponens,[status(thm)],[1067, 1066])).
% 27.36/17.62 tff(1069,plain,
% 27.36/17.62 ((f1(c1, c2) = c2) | (c1 = c3) | big_f(c1, f1(c1, c2)) | (f10(c1) = c4) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1))),
% 27.36/17.62 inference(unit_resolution,[status(thm)],[1068, 1014])).
% 27.36/17.62 tff(1070,plain,
% 27.36/17.62 (big_f(c1, f1(c1, c2))),
% 27.36/17.62 inference(unit_resolution,[status(thm)],[1069, 1052, 1046, 168, 1062, 1061])).
% 27.36/17.62 tff(1071,plain,
% 27.36/17.62 (big_f(f9(f10(c2), f4(c4)), f1(f9(f10(c2), f4(c4)), c2))),
% 27.36/17.62 inference(modus_ponens,[status(thm)],[1070, 1060])).
% 27.36/17.62 tff(1072,plain,
% 27.36/17.62 ($false),
% 27.36/17.62 inference(unit_resolution,[status(thm)],[1071, 1059])).
% 27.36/17.62 tff(1073,plain,((f1(c1, c2) = c2) | big_f(f7(c2), c1) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f7(c2) = c1)) | (f10(c1) = c4) | (c1 = c3) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1))), inference(lemma,lemma(discharge,[]))).
% 27.36/17.62 tff(1074,plain,
% 27.36/17.62 (f1(c1, c2) = c2),
% 27.36/17.62 inference(unit_resolution,[status(thm)],[1073, 1051, 148, 292, 1046, 168, 333, 1045])).
% 27.36/17.62 tff(1075,plain,
% 27.36/17.62 (f1(f9(c2, c2), c2) = c2),
% 27.36/17.62 inference(transitivity,[status(thm)],[843, 819, 1074])).
% 27.36/17.62 tff(1076,plain,
% 27.36/17.62 (f1(f9(c2, c2), c2) = f10(c2)),
% 27.36/17.62 inference(transitivity,[status(thm)],[843, 819, 1074, 216])).
% 27.36/17.62 tff(1077,plain,
% 27.36/17.62 (big_f(f9(c2, c2), f1(f9(c2, c2), c2)) <=> big_f(f9(c2, c2), f10(c2))),
% 27.36/17.62 inference(monotonicity,[status(thm)],[1076])).
% 27.36/17.62 tff(1078,plain,
% 27.36/17.62 (big_f(f9(c2, c2), f10(c2)) <=> big_f(f9(c2, c2), f1(f9(c2, c2), c2))),
% 27.36/17.62 inference(symmetry,[status(thm)],[1077])).
% 27.36/17.62 tff(1079,plain,
% 27.36/17.62 (big_f(f9(c2, c2), f1(f9(c2, c2), c2))),
% 27.36/17.62 inference(modus_ponens,[status(thm)],[690, 1078])).
% 27.36/17.62 tff(1080,plain,
% 27.36/17.62 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (f9(c2, c2) = c3) | (~(f1(f9(c2, c2), c2) = c2)) | (~big_f(f9(c2, c2), f1(f9(c2, c2), c2))) | (f3(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f3(c2, f9(c2, c2)), c2))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c4) | (f9(c2, c2) = c3) | (~(f1(f9(c2, c2), c2) = c2)) | (~big_f(f9(c2, c2), f1(f9(c2, c2), c2))) | (f3(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f3(c2, f9(c2, c2)), c2))),
% 27.36/17.62 inference(rewrite,[status(thm)],[])).
% 27.36/17.62 tff(1081,plain,
% 27.36/17.62 (((c2 = c4) | (f3(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f3(c2, f9(c2, c2)), c2) | (f9(c2, c2) = c3) | (~(f1(f9(c2, c2), c2) = c2)) | (~big_f(f9(c2, c2), f1(f9(c2, c2), c2)))) <=> ((c2 = c4) | (f9(c2, c2) = c3) | (~(f1(f9(c2, c2), c2) = c2)) | (~big_f(f9(c2, c2), f1(f9(c2, c2), c2))) | (f3(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f3(c2, f9(c2, c2)), c2))),
% 27.36/17.62 inference(rewrite,[status(thm)],[])).
% 27.36/17.62 tff(1082,plain,
% 27.36/17.62 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (f3(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f3(c2, f9(c2, c2)), c2) | (f9(c2, c2) = c3) | (~(f1(f9(c2, c2), c2) = c2)) | (~big_f(f9(c2, c2), f1(f9(c2, c2), c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (f9(c2, c2) = c3) | (~(f1(f9(c2, c2), c2) = c2)) | (~big_f(f9(c2, c2), f1(f9(c2, c2), c2))) | (f3(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f3(c2, f9(c2, c2)), c2)))),
% 27.36/17.62 inference(monotonicity,[status(thm)],[1081])).
% 27.36/17.62 tff(1083,plain,
% 27.36/17.62 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (f3(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f3(c2, f9(c2, c2)), c2) | (f9(c2, c2) = c3) | (~(f1(f9(c2, c2), c2) = c2)) | (~big_f(f9(c2, c2), f1(f9(c2, c2), c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c4) | (f9(c2, c2) = c3) | (~(f1(f9(c2, c2), c2) = c2)) | (~big_f(f9(c2, c2), f1(f9(c2, c2), c2))) | (f3(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f3(c2, f9(c2, c2)), c2))),
% 27.36/17.62 inference(transitivity,[status(thm)],[1082, 1080])).
% 27.36/17.62 tff(1084,plain,
% 27.36/17.62 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (f3(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f3(c2, f9(c2, c2)), c2) | (f9(c2, c2) = c3) | (~(f1(f9(c2, c2), c2) = c2)) | (~big_f(f9(c2, c2), f1(f9(c2, c2), c2))))),
% 27.36/17.62 inference(quant_inst,[status(thm)],[])).
% 27.36/17.62 tff(1085,plain,
% 27.36/17.62 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c4) | (f9(c2, c2) = c3) | (~(f1(f9(c2, c2), c2) = c2)) | (~big_f(f9(c2, c2), f1(f9(c2, c2), c2))) | (f3(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f3(c2, f9(c2, c2)), c2)),
% 27.36/17.62 inference(modus_ponens,[status(thm)],[1084, 1083])).
% 27.36/17.62 tff(1086,plain,
% 27.36/17.62 ((~(f1(f9(c2, c2), c2) = c2)) | (~big_f(f9(c2, c2), f1(f9(c2, c2), c2)))),
% 27.36/17.62 inference(unit_resolution,[status(thm)],[1085, 904, 873, 566, 890, 894])).
% 27.36/17.62 tff(1087,plain,
% 27.36/17.62 ($false),
% 27.36/17.62 inference(unit_resolution,[status(thm)],[1086, 1079, 1075])).
% 27.36/17.62 tff(1088,plain,((~(f3(f7(c1), c1) = c2)) | (c2 = c4) | (f9(c2, c2) = c3) | (~big_f(f9(c2, c2), f10(c2))) | (~(f10(c2) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f7(c2) = c1)) | (f10(c1) = c4) | (c1 = c3) | big_f(f7(c2), c1) | big_f(c2, c2) | (~(f10(c1) = c2)) | (~(f7(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.36/17.62 tff(1089,plain,
% 27.36/17.62 (~(f3(f7(c1), c1) = c2)),
% 27.36/17.62 inference(unit_resolution,[status(thm)],[1088, 867, 1040, 690, 122, 148, 79, 292, 1037, 1032, 333, 121, 16, 347])).
% 27.36/17.62 tff(1090,plain,
% 27.36/17.62 (f3(f7(c1), c1) = c1),
% 27.36/17.62 inference(unit_resolution,[status(thm)],[918, 1089])).
% 27.36/17.62 tff(1091,plain,
% 27.36/17.62 (f3(c2, f9(c2, c2)) = f9(c2, c2)),
% 27.36/17.62 inference(transitivity,[status(thm)],[884, 883, 1090, 149, 132])).
% 27.36/17.62 tff(1092,plain,
% 27.36/17.62 (big_f(f3(c2, f9(c2, c2)), c2) <=> big_f(f9(c2, c2), f10(c2))),
% 27.36/17.62 inference(monotonicity,[status(thm)],[1091, 216])).
% 27.36/17.62 tff(1093,plain,
% 27.36/17.62 (big_f(f9(c2, c2), f10(c2)) <=> big_f(f3(c2, f9(c2, c2)), c2)),
% 27.36/17.62 inference(symmetry,[status(thm)],[1092])).
% 27.36/17.62 tff(1094,plain,
% 27.36/17.62 (big_f(f3(c2, f9(c2, c2)), c2)),
% 27.36/17.62 inference(modus_ponens,[status(thm)],[690, 1093])).
% 27.36/17.62 tff(1095,assumption,(f1(c1, c2) = c1), introduced(assumption)).
% 27.36/17.62 tff(1096,plain,
% 27.36/17.62 (f1(f9(c2, c2), c2) = f9(c2, c2)),
% 27.36/17.62 inference(transitivity,[status(thm)],[843, 819, 1095, 149, 132])).
% 27.36/17.62 tff(1097,plain,
% 27.36/17.62 ((f1(f9(c2, c2), c2) = c2) <=> (f9(c2, c2) = c2)),
% 27.36/17.62 inference(monotonicity,[status(thm)],[1096])).
% 27.36/17.62 tff(1098,plain,
% 27.36/17.62 ((f9(c2, c2) = c2) <=> (f1(f9(c2, c2), c2) = c2)),
% 27.36/17.62 inference(symmetry,[status(thm)],[1097])).
% 27.36/17.62 tff(1099,plain,
% 27.36/17.62 ((~(f9(c2, c2) = c2)) <=> (~(f1(f9(c2, c2), c2) = c2))),
% 27.36/17.62 inference(monotonicity,[status(thm)],[1098])).
% 27.36/17.62 tff(1100,plain,
% 27.36/17.62 (~(f1(f9(c2, c2), c2) = c2)),
% 27.36/17.62 inference(modus_ponens,[status(thm)],[185, 1099])).
% 27.36/17.62 tff(1101,plain,
% 27.36/17.62 (f1(f9(c2, c2), c2) = c1),
% 27.36/17.62 inference(transitivity,[status(thm)],[843, 819, 1095])).
% 27.36/17.62 tff(1102,plain,
% 27.36/17.62 (big_f(f9(c2, c2), f1(f9(c2, c2), c2)) <=> big_f(f7(c2), c1)),
% 27.36/17.62 inference(monotonicity,[status(thm)],[343, 1101])).
% 27.36/17.62 tff(1103,plain,
% 27.36/17.62 (big_f(f7(c2), c1) <=> big_f(f9(c2, c2), f1(f9(c2, c2), c2))),
% 27.36/17.62 inference(symmetry,[status(thm)],[1102])).
% 27.36/17.62 tff(1104,plain,
% 27.36/17.62 ((~big_f(f7(c2), c1)) <=> (~big_f(f9(c2, c2), f1(f9(c2, c2), c2)))),
% 27.36/17.62 inference(monotonicity,[status(thm)],[1103])).
% 27.36/17.62 tff(1105,plain,
% 27.36/17.62 (~big_f(f9(c2, c2), f1(f9(c2, c2), c2))),
% 27.36/17.62 inference(modus_ponens,[status(thm)],[333, 1104])).
% 27.36/17.62 tff(1106,assumption,(big_f(f3(c2, f9(c2, c2)), c2)), introduced(assumption)).
% 27.36/17.62 tff(1107,assumption,(f3(c2, f9(c2, c2)) = f9(c2, c2)), introduced(assumption)).
% 27.36/17.62 tff(1108,plain,
% 27.36/17.62 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c4) | (f9(c2, c2) = c3) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2)) | (~(f3(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(c2, f9(c2, c2)), c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c2 = c4) | (f9(c2, c2) = c3) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2)) | (~(f3(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(c2, f9(c2, c2)), c2)))),
% 27.36/17.62 inference(rewrite,[status(thm)],[])).
% 27.36/17.62 tff(1109,plain,
% 27.36/17.62 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c4) | (f9(c2, c2) = c3) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2)) | (~(f3(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(c2, f9(c2, c2)), c2)))),
% 27.36/17.62 inference(quant_inst,[status(thm)],[])).
% 27.36/17.62 tff(1110,plain,
% 27.36/17.62 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c2 = c4) | (f9(c2, c2) = c3) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2)) | (~(f3(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(c2, f9(c2, c2)), c2))),
% 27.36/17.62 inference(modus_ponens,[status(thm)],[1109, 1108])).
% 27.36/17.62 tff(1111,plain,
% 27.36/17.62 ((f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2))),
% 27.36/17.62 inference(unit_resolution,[status(thm)],[1110, 969, 873, 566, 1107, 1106])).
% 27.36/17.62 tff(1112,plain,
% 27.36/17.62 ($false),
% 27.36/17.62 inference(unit_resolution,[status(thm)],[1111, 1105, 1100])).
% 27.36/17.62 tff(1113,plain,((~(f1(c1, c2) = c1)) | (c2 = c4) | (f9(c2, c2) = c3) | (~(f3(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(c2, f9(c2, c2)), c2)) | big_f(f7(c2), c1) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f7(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 27.36/17.62 tff(1114,plain,
% 27.36/17.62 (~(f1(c1, c2) = c1)),
% 27.36/17.62 inference(unit_resolution,[status(thm)],[1113, 867, 1040, 1091, 1094, 333, 148, 79, 122, 292])).
% 27.36/17.62 tff(1115,plain,
% 27.36/17.62 (f1(c1, c2) = c2),
% 27.36/17.62 inference(unit_resolution,[status(thm)],[841, 1114])).
% 27.36/17.62 tff(1116,plain,
% 27.36/17.62 (f1(f9(c2, c2), c2) = c2),
% 27.36/17.62 inference(transitivity,[status(thm)],[843, 819, 1115])).
% 27.36/17.62 tff(1117,plain,
% 27.36/17.62 (f1(f9(c2, c2), c2) = f10(c2)),
% 27.36/17.62 inference(transitivity,[status(thm)],[843, 819, 1115, 216])).
% 27.36/17.62 tff(1118,plain,
% 27.36/17.62 (big_f(f9(c2, c2), f1(f9(c2, c2), c2)) <=> big_f(f9(c2, c2), f10(c2))),
% 27.36/17.62 inference(monotonicity,[status(thm)],[1117])).
% 27.36/17.62 tff(1119,plain,
% 27.36/17.62 (big_f(f9(c2, c2), f10(c2)) <=> big_f(f9(c2, c2), f1(f9(c2, c2), c2))),
% 27.36/17.62 inference(symmetry,[status(thm)],[1118])).
% 27.36/17.62 tff(1120,plain,
% 27.36/17.62 (big_f(f9(c2, c2), f1(f9(c2, c2), c2))),
% 27.36/17.62 inference(modus_ponens,[status(thm)],[690, 1119])).
% 27.36/17.62 tff(1121,plain,
% 27.36/17.62 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (f9(c2, c2) = c3) | (~(f1(f9(c2, c2), c2) = c2)) | (~big_f(f9(c2, c2), f1(f9(c2, c2), c2))) | (~(f3(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(c2, f9(c2, c2)), c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c4) | (f9(c2, c2) = c3) | (~(f1(f9(c2, c2), c2) = c2)) | (~big_f(f9(c2, c2), f1(f9(c2, c2), c2))) | (~(f3(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(c2, f9(c2, c2)), c2)))),
% 27.36/17.62 inference(rewrite,[status(thm)],[])).
% 27.36/17.62 tff(1122,plain,
% 27.36/17.62 (((c2 = c4) | (f9(c2, c2) = c3) | (~(f3(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(c2, f9(c2, c2)), c2)) | (~(f1(f9(c2, c2), c2) = c2)) | (~big_f(f9(c2, c2), f1(f9(c2, c2), c2)))) <=> ((c2 = c4) | (f9(c2, c2) = c3) | (~(f1(f9(c2, c2), c2) = c2)) | (~big_f(f9(c2, c2), f1(f9(c2, c2), c2))) | (~(f3(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(c2, f9(c2, c2)), c2)))),
% 27.44/17.62 inference(rewrite,[status(thm)],[])).
% 27.44/17.62 tff(1123,plain,
% 27.44/17.62 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (f9(c2, c2) = c3) | (~(f3(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(c2, f9(c2, c2)), c2)) | (~(f1(f9(c2, c2), c2) = c2)) | (~big_f(f9(c2, c2), f1(f9(c2, c2), c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (f9(c2, c2) = c3) | (~(f1(f9(c2, c2), c2) = c2)) | (~big_f(f9(c2, c2), f1(f9(c2, c2), c2))) | (~(f3(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(c2, f9(c2, c2)), c2))))),
% 27.44/17.62 inference(monotonicity,[status(thm)],[1122])).
% 27.44/17.62 tff(1124,plain,
% 27.44/17.62 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (f9(c2, c2) = c3) | (~(f3(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(c2, f9(c2, c2)), c2)) | (~(f1(f9(c2, c2), c2) = c2)) | (~big_f(f9(c2, c2), f1(f9(c2, c2), c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c4) | (f9(c2, c2) = c3) | (~(f1(f9(c2, c2), c2) = c2)) | (~big_f(f9(c2, c2), f1(f9(c2, c2), c2))) | (~(f3(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(c2, f9(c2, c2)), c2)))),
% 27.44/17.62 inference(transitivity,[status(thm)],[1123, 1121])).
% 27.44/17.62 tff(1125,plain,
% 27.44/17.62 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (f9(c2, c2) = c3) | (~(f3(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(c2, f9(c2, c2)), c2)) | (~(f1(f9(c2, c2), c2) = c2)) | (~big_f(f9(c2, c2), f1(f9(c2, c2), c2))))),
% 27.44/17.62 inference(quant_inst,[status(thm)],[])).
% 27.44/17.62 tff(1126,plain,
% 27.44/17.62 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c4) | (f9(c2, c2) = c3) | (~(f1(f9(c2, c2), c2) = c2)) | (~big_f(f9(c2, c2), f1(f9(c2, c2), c2))) | (~(f3(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(c2, f9(c2, c2)), c2))),
% 27.44/17.62 inference(modus_ponens,[status(thm)],[1125, 1124])).
% 27.44/17.62 tff(1127,plain,
% 27.44/17.62 ((~(f1(f9(c2, c2), c2) = c2)) | (~big_f(f9(c2, c2), f1(f9(c2, c2), c2)))),
% 27.44/17.62 inference(unit_resolution,[status(thm)],[1126, 933, 867, 1040, 1091, 1094])).
% 27.44/17.62 tff(1128,plain,
% 27.44/17.62 ($false),
% 27.44/17.62 inference(unit_resolution,[status(thm)],[1127, 1120, 1116])).
% 27.44/17.62 tff(1129,plain,(big_f(f7(c2), c1) | (~big_f(f9(c2, c2), f10(c2))) | (~(f10(c2) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f7(c2) = c1)) | (~(f10(c1) = c2)) | (~(f7(c1) = c2)) | big_f(c2, c2) | (~big_f(c2, c1))), inference(lemma,lemma(discharge,[]))).
% 27.44/17.62 tff(1130,plain,
% 27.44/17.62 (big_f(f7(c2), c1)),
% 27.44/17.62 inference(unit_resolution,[status(thm)],[1129, 121, 122, 148, 79, 22, 16, 347, 690, 348])).
% 27.44/17.62 tff(1131,plain,
% 27.44/17.62 (big_f(f7(c2), f9(c2, c2))),
% 27.44/17.62 inference(modus_ponens,[status(thm)],[1130, 796])).
% 27.44/17.62 tff(1132,plain,
% 27.44/17.62 ((f9(c2, c1) = c1) <=> (f9(c2, f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))),
% 27.44/17.62 inference(monotonicity,[status(thm)],[723, 225])).
% 27.44/17.62 tff(1133,plain,
% 27.44/17.62 ((f9(c2, f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2))) <=> (f9(c2, c1) = c1)),
% 27.44/17.62 inference(symmetry,[status(thm)],[1132])).
% 27.44/17.62 tff(1134,plain,
% 27.44/17.62 (f9(c2, f9(c2, c2)) = f9(c2, f9(f10(c2), f10(c2)))),
% 27.44/17.62 inference(monotonicity,[status(thm)],[203])).
% 27.44/17.62 tff(1135,plain,
% 27.44/17.62 ((f9(c2, f9(c2, c2)) = f9(c2, c2)) <=> (f9(c2, f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))),
% 27.44/17.62 inference(monotonicity,[status(thm)],[1134, 203])).
% 27.44/17.62 tff(1136,plain,
% 27.44/17.62 ((f9(c2, f9(c2, c2)) = f9(c2, c2)) <=> (f9(c2, c1) = c1)),
% 27.44/17.63 inference(transitivity,[status(thm)],[1135, 1133])).
% 27.44/17.63 tff(1137,assumption,(f9(c2, f9(c2, c2)) = f9(c2, c2)), introduced(assumption)).
% 27.44/17.63 tff(1138,plain,
% 27.44/17.63 (f9(c2, c1) = c1),
% 27.44/17.63 inference(modus_ponens,[status(thm)],[1137, 1136])).
% 27.44/17.63 tff(1139,assumption,(~(f9(c2, c1) = c1)), introduced(assumption)).
% 27.44/17.63 tff(1140,plain,
% 27.44/17.63 ($false),
% 27.44/17.63 inference(unit_resolution,[status(thm)],[1139, 1138])).
% 27.44/17.63 tff(1141,plain,((~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (f9(c2, c1) = c1) | (~(f10(c2) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.44/17.63 tff(1142,plain,
% 27.44/17.63 (~(f9(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.44/17.63 inference(unit_resolution,[status(thm)],[1141, 744, 122, 148, 79])).
% 27.44/17.63 tff(1143,plain,
% 27.44/17.63 (big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2)) <=> big_f(f9(c2, c1), f10(c2))),
% 27.44/17.63 inference(symmetry,[status(thm)],[724])).
% 27.44/17.63 tff(1144,plain,
% 27.44/17.63 (big_f(f9(c2, f9(c2, c2)), f10(c2)) <=> big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2))),
% 27.44/17.63 inference(monotonicity,[status(thm)],[1134])).
% 27.44/17.63 tff(1145,plain,
% 27.44/17.63 (big_f(f9(c2, f9(c2, c2)), f10(c2)) <=> big_f(f9(c2, c1), f10(c2))),
% 27.44/17.63 inference(transitivity,[status(thm)],[1144, 1143])).
% 27.44/17.63 tff(1146,assumption,(big_f(f9(c2, f9(c2, c2)), f10(c2))), introduced(assumption)).
% 27.44/17.63 tff(1147,plain,
% 27.44/17.63 (big_f(f9(c2, c1), f10(c2))),
% 27.44/17.63 inference(modus_ponens,[status(thm)],[1146, 1145])).
% 27.44/17.63 tff(1148,plain,
% 27.44/17.63 ($false),
% 27.44/17.63 inference(unit_resolution,[status(thm)],[731, 1147])).
% 27.44/17.63 tff(1149,plain,((~big_f(f9(c2, f9(c2, c2)), f10(c2))) | big_f(f9(c2, c1), f10(c2)) | (~(f10(c2) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.44/17.63 tff(1150,plain,
% 27.44/17.63 (~big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 27.44/17.63 inference(unit_resolution,[status(thm)],[1149, 731, 122, 148, 79])).
% 27.44/17.63 tff(1151,plain,
% 27.44/17.63 (f7(c2) = f9(c2, c2)),
% 27.44/17.63 inference(transitivity,[status(thm)],[22, 149, 132])).
% 27.44/17.63 tff(1152,plain,
% 27.44/17.63 (big_f(f7(c2), c2) <=> big_f(f9(c2, c2), f10(c2))),
% 27.44/17.63 inference(monotonicity,[status(thm)],[1151, 216])).
% 27.44/17.63 tff(1153,plain,
% 27.44/17.63 (big_f(f9(c2, c2), f10(c2)) <=> big_f(f7(c2), c2)),
% 27.44/17.63 inference(symmetry,[status(thm)],[1152])).
% 27.44/17.63 tff(1154,plain,
% 27.44/17.63 (big_f(f7(c2), c2)),
% 27.44/17.63 inference(modus_ponens,[status(thm)],[690, 1153])).
% 27.44/17.63 tff(1155,plain,
% 27.44/17.63 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)))),
% 27.44/17.63 inference(rewrite,[status(thm)],[])).
% 27.44/17.63 tff(1156,plain,
% 27.44/17.63 (((~(f10(c2) = c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2))) <=> ((~(f10(c2) = c2)) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)))),
% 27.44/17.63 inference(rewrite,[status(thm)],[])).
% 27.44/17.63 tff(1157,plain,
% 27.44/17.63 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2))))),
% 27.44/17.63 inference(monotonicity,[status(thm)],[1156])).
% 27.44/17.63 tff(1158,plain,
% 27.44/17.63 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)))),
% 27.44/17.63 inference(transitivity,[status(thm)],[1157, 1155])).
% 27.44/17.63 tff(1159,plain,
% 27.44/17.63 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)))),
% 27.44/17.63 inference(quant_inst,[status(thm)],[])).
% 27.44/17.63 tff(1160,plain,
% 27.44/17.63 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.44/17.63 inference(modus_ponens,[status(thm)],[1159, 1158])).
% 27.44/17.63 tff(1161,plain,
% 27.44/17.63 (c2 = f5(c2)),
% 27.44/17.63 inference(unit_resolution,[status(thm)],[1160, 676, 122, 17, 1154, 1150, 1142])).
% 27.44/17.63 tff(1162,plain,
% 27.44/17.63 (f5(c2) = c2),
% 27.44/17.63 inference(symmetry,[status(thm)],[1161])).
% 27.44/17.63 tff(1163,assumption,(big_f(f7(c2), f9(c2, c2))), introduced(assumption)).
% 27.44/17.63 tff(1164,plain,
% 27.44/17.63 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | (~big_f(f7(c2), f9(c2, c2))) | (f9(c2, c2) = f5(c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | (~big_f(f7(c2), f9(c2, c2))) | (f9(c2, c2) = f5(c2)))),
% 27.44/17.63 inference(rewrite,[status(thm)],[])).
% 27.44/17.63 tff(1165,plain,
% 27.44/17.63 (((~(f10(c2) = c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f7(c2) = c2) | (f9(c2, c2) = f5(c2)) | (~big_f(f7(c2), f9(c2, c2)))) <=> ((~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | (~big_f(f7(c2), f9(c2, c2))) | (f9(c2, c2) = f5(c2)))),
% 27.44/17.63 inference(rewrite,[status(thm)],[])).
% 27.44/17.63 tff(1166,plain,
% 27.44/17.63 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f7(c2) = c2) | (f9(c2, c2) = f5(c2)) | (~big_f(f7(c2), f9(c2, c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | (~big_f(f7(c2), f9(c2, c2))) | (f9(c2, c2) = f5(c2))))),
% 27.44/17.63 inference(monotonicity,[status(thm)],[1165])).
% 27.44/17.63 tff(1167,plain,
% 27.44/17.63 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f7(c2) = c2) | (f9(c2, c2) = f5(c2)) | (~big_f(f7(c2), f9(c2, c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | (~big_f(f7(c2), f9(c2, c2))) | (f9(c2, c2) = f5(c2)))),
% 27.44/17.63 inference(transitivity,[status(thm)],[1166, 1164])).
% 27.44/17.63 tff(1168,plain,
% 27.44/17.63 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f7(c2) = c2) | (f9(c2, c2) = f5(c2)) | (~big_f(f7(c2), f9(c2, c2))))),
% 27.44/17.63 inference(quant_inst,[status(thm)],[])).
% 27.44/17.63 tff(1169,plain,
% 27.44/17.63 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | (~big_f(f7(c2), f9(c2, c2))) | (f9(c2, c2) = f5(c2))),
% 27.44/17.63 inference(modus_ponens,[status(thm)],[1168, 1167])).
% 27.44/17.63 tff(1170,plain,
% 27.44/17.63 (f9(c2, c2) = f5(c2)),
% 27.44/17.63 inference(unit_resolution,[status(thm)],[1169, 676, 122, 17, 1150, 1142, 1163])).
% 27.44/17.63 tff(1171,plain,
% 27.44/17.63 (f9(c2, c2) = c2),
% 27.44/17.63 inference(transitivity,[status(thm)],[1170, 1162])).
% 27.44/17.63 tff(1172,plain,
% 27.44/17.63 ($false),
% 27.44/17.63 inference(unit_resolution,[status(thm)],[185, 1171])).
% 27.44/17.63 tff(1173,plain,(big_f(f9(c2, c1), f10(c2)) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~big_f(f7(c2), f9(c2, c2))) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~big_f(f9(c2, c2), f10(c2)))), inference(lemma,lemma(discharge,[]))).
% 27.44/17.63 tff(1174,plain,
% 27.44/17.63 (big_f(f9(c2, c1), f10(c2))),
% 27.44/17.63 inference(unit_resolution,[status(thm)],[1173, 1131, 17, 122, 148, 79, 690])).
% 27.44/17.63 tff(1175,plain,
% 27.44/17.63 (big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2))),
% 27.44/17.63 inference(modus_ponens,[status(thm)],[1174, 724])).
% 27.44/17.63 tff(1176,plain,
% 27.44/17.63 ((~(f9(c2, f9(c2, c2)) = f9(c2, c2))) <=> (~(f9(c2, c1) = c1))),
% 27.44/17.63 inference(monotonicity,[status(thm)],[1136])).
% 27.44/17.63 tff(1177,plain,
% 27.44/17.63 (big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2)) <=> big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 27.44/17.63 inference(symmetry,[status(thm)],[1144])).
% 27.44/17.63 tff(1178,plain,
% 27.44/17.63 (big_f(f9(c2, c1), f10(c2)) <=> big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 27.44/17.63 inference(transitivity,[status(thm)],[724, 1177])).
% 27.44/17.63 tff(1179,plain,
% 27.44/17.63 (big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 27.44/17.63 inference(modus_ponens,[status(thm)],[1174, 1178])).
% 27.44/17.63 tff(1180,assumption,(big_f(f7(c2), c2)), introduced(assumption)).
% 27.44/17.63 tff(1181,plain,
% 27.44/17.63 (^[X9: $i, X4: $i, X7: $i, X5: $i] : refl(((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7)))) <=> ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7)))))),
% 27.44/17.63 inference(bind,[status(th)],[])).
% 27.44/17.63 tff(1182,plain,
% 27.44/17.63 (![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7)))) <=> ![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))),
% 27.44/17.63 inference(quant_intro,[status(thm)],[1181])).
% 27.44/17.63 tff(1183,plain,
% 27.44/17.63 (![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7)))) <=> ![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))),
% 27.44/17.63 inference(rewrite,[status(thm)],[])).
% 27.44/17.63 tff(1184,plain,
% 27.44/17.63 (^[X9: $i, X4: $i, X7: $i, X5: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_f(f7(X4), X5)) | (X5 = f5(X4))) | (f7(X4) = X4)) <=> ((f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))), (((((~big_f(f7(X4), X5)) | (X5 = f5(X4))) | (f7(X4) = X4)) | (~big_f(f9(X7, X9), f10(X7)))) <=> (((f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5))) | (~big_f(f9(X7, X9), f10(X7)))))), rewrite((((f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5))) | (~big_f(f9(X7, X9), f10(X7)))) <=> ((f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~big_f(f9(X7, X9), f10(X7))))), (((((~big_f(f7(X4), X5)) | (X5 = f5(X4))) | (f7(X4) = X4)) | (~big_f(f9(X7, X9), f10(X7)))) <=> ((f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~big_f(f9(X7, X9), f10(X7)))))), ((((((~big_f(f7(X4), X5)) | (X5 = f5(X4))) | (f7(X4) = X4)) | (~big_f(f9(X7, X9), f10(X7)))) | (~(f9(X7, X9) = X9))) <=> (((f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~big_f(f9(X7, X9), f10(X7)))) | (~(f9(X7, X9) = X9))))), rewrite((((f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~big_f(f9(X7, X9), f10(X7)))) | (~(f9(X7, X9) = X9))) <=> ((f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))), ((((((~big_f(f7(X4), X5)) | (X5 = f5(X4))) | (f7(X4) = X4)) | (~big_f(f9(X7, X9), f10(X7)))) | (~(f9(X7, X9) = X9))) <=> ((f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7)))))), (((((((~big_f(f7(X4), X5)) | (X5 = f5(X4))) | (f7(X4) = X4)) | (~big_f(f9(X7, X9), f10(X7)))) | (~(f9(X7, X9) = X9))) | (~(f10(X7) = X7))) <=> (((f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7)))) | (~(f10(X7) = X7))))), rewrite((((f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7)))) | (~(f10(X7) = X7))) <=> ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))), (((((((~big_f(f7(X4), X5)) | (X5 = f5(X4))) | (f7(X4) = X4)) | (~big_f(f9(X7, X9), f10(X7)))) | (~(f9(X7, X9) = X9))) | (~(f10(X7) = X7))) <=> ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))))),
% 27.44/17.63 inference(bind,[status(th)],[])).
% 27.44/17.63 tff(1185,plain,
% 27.44/17.63 (![X9: $i, X4: $i, X7: $i, X5: $i] : ((((((~big_f(f7(X4), X5)) | (X5 = f5(X4))) | (f7(X4) = X4)) | (~big_f(f9(X7, X9), f10(X7)))) | (~(f9(X7, X9) = X9))) | (~(f10(X7) = X7))) <=> ![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))),
% 27.44/17.63 inference(quant_intro,[status(thm)],[1184])).
% 27.44/17.63 tff(1186,axiom,(![X9: $i, X4: $i, X7: $i, X5: $i] : ((((((~big_f(f7(X4), X5)) | (X5 = f5(X4))) | (f7(X4) = X4)) | (~big_f(f9(X7, X9), f10(X7)))) | (~(f9(X7, X9) = X9))) | (~(f10(X7) = X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_22')).
% 27.44/17.63 tff(1187,plain,
% 27.44/17.63 (![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))),
% 27.44/17.63 inference(modus_ponens,[status(thm)],[1186, 1185])).
% 27.44/17.63 tff(1188,plain,
% 27.44/17.63 (![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))),
% 27.44/17.63 inference(modus_ponens,[status(thm)],[1187, 1183])).
% 27.44/17.63 tff(1189,plain,(
% 27.44/17.63 ![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))),
% 27.44/17.63 inference(skolemize,[status(sab)],[1188])).
% 27.44/17.63 tff(1190,plain,
% 27.44/17.63 (![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))),
% 27.44/17.63 inference(modus_ponens,[status(thm)],[1189, 1182])).
% 27.44/17.63 tff(1191,plain,
% 27.44/17.63 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))))),
% 27.44/17.63 inference(rewrite,[status(thm)],[])).
% 27.44/17.63 tff(1192,plain,
% 27.44/17.63 (((~(f10(c2) = c2)) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2)))) <=> ((~(f10(c2) = c2)) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))))),
% 27.44/17.63 inference(rewrite,[status(thm)],[])).
% 27.44/17.63 tff(1193,plain,
% 27.44/17.63 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2)))))),
% 27.44/17.63 inference(monotonicity,[status(thm)],[1192])).
% 27.44/17.63 tff(1194,plain,
% 27.44/17.63 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))))),
% 27.44/17.63 inference(transitivity,[status(thm)],[1193, 1191])).
% 27.44/17.63 tff(1195,plain,
% 27.44/17.63 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))))),
% 27.44/17.63 inference(quant_inst,[status(thm)],[])).
% 27.44/17.63 tff(1196,plain,
% 27.44/17.63 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2)))),
% 27.44/17.63 inference(modus_ponens,[status(thm)],[1195, 1194])).
% 27.44/17.63 tff(1197,plain,
% 27.44/17.63 ((c2 = f5(c2)) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2)))),
% 27.44/17.63 inference(unit_resolution,[status(thm)],[1196, 1190, 122, 17, 1180, 1146])).
% 27.44/17.63 tff(1198,plain,
% 27.44/17.63 (c2 = f5(c2)),
% 27.44/17.63 inference(unit_resolution,[status(thm)],[1197, 1137])).
% 27.44/17.63 tff(1199,plain,
% 27.44/17.63 (f5(c2) = c2),
% 27.44/17.63 inference(symmetry,[status(thm)],[1198])).
% 27.44/17.63 tff(1200,plain,
% 27.44/17.63 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f9(c2, c2))) | (f9(c2, c2) = f5(c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f9(c2, c2))) | (f9(c2, c2) = f5(c2)))),
% 27.44/17.63 inference(rewrite,[status(thm)],[])).
% 27.44/17.63 tff(1201,plain,
% 27.44/17.63 (((~(f10(c2) = c2)) | (f7(c2) = c2) | (f9(c2, c2) = f5(c2)) | (~big_f(f7(c2), f9(c2, c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2)))) <=> ((~(f10(c2) = c2)) | (f7(c2) = c2) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f9(c2, c2))) | (f9(c2, c2) = f5(c2)))),
% 27.44/17.63 inference(rewrite,[status(thm)],[])).
% 27.44/17.63 tff(1202,plain,
% 27.44/17.63 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (f9(c2, c2) = f5(c2)) | (~big_f(f7(c2), f9(c2, c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f9(c2, c2))) | (f9(c2, c2) = f5(c2))))),
% 27.44/17.63 inference(monotonicity,[status(thm)],[1201])).
% 27.44/17.63 tff(1203,plain,
% 27.44/17.63 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (f9(c2, c2) = f5(c2)) | (~big_f(f7(c2), f9(c2, c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f9(c2, c2))) | (f9(c2, c2) = f5(c2)))),
% 27.44/17.63 inference(transitivity,[status(thm)],[1202, 1200])).
% 27.44/17.63 tff(1204,plain,
% 27.44/17.63 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (f9(c2, c2) = f5(c2)) | (~big_f(f7(c2), f9(c2, c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))))),
% 27.44/17.63 inference(quant_inst,[status(thm)],[])).
% 27.44/17.63 tff(1205,plain,
% 27.44/17.63 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f9(c2, c2))) | (f9(c2, c2) = f5(c2))),
% 27.44/17.63 inference(modus_ponens,[status(thm)],[1204, 1203])).
% 27.44/17.63 tff(1206,plain,
% 27.44/17.63 ((~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (f9(c2, c2) = f5(c2))),
% 27.44/17.63 inference(unit_resolution,[status(thm)],[1205, 1190, 122, 17, 1146, 1163])).
% 27.44/17.63 tff(1207,plain,
% 27.44/17.63 (f9(c2, c2) = f5(c2)),
% 27.44/17.63 inference(unit_resolution,[status(thm)],[1206, 1137])).
% 27.44/17.63 tff(1208,plain,
% 27.44/17.63 (f9(c2, c2) = c2),
% 27.44/17.63 inference(transitivity,[status(thm)],[1207, 1199])).
% 27.44/17.63 tff(1209,assumption,(~(f9(c2, c2) = c2)), introduced(assumption)).
% 27.44/17.63 tff(1210,plain,
% 27.44/17.63 ($false),
% 27.44/17.63 inference(unit_resolution,[status(thm)],[1209, 1208])).
% 27.44/17.63 tff(1211,plain,((~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (f9(c2, c2) = c2) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~big_f(f7(c2), f9(c2, c2))) | (~big_f(f7(c2), c2))), inference(lemma,lemma(discharge,[]))).
% 27.44/17.63 tff(1212,plain,
% 27.44/17.63 (~(f9(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.44/17.63 inference(unit_resolution,[status(thm)],[1211, 1179, 122, 17, 185, 1131, 1154])).
% 27.44/17.63 tff(1213,plain,
% 27.44/17.63 (~(f9(c2, c1) = c1)),
% 27.44/17.63 inference(modus_ponens,[status(thm)],[1212, 1176])).
% 27.44/17.63 tff(1214,plain,
% 27.44/17.63 (f9(c2, c2) = f7(c2)),
% 27.44/17.63 inference(transitivity,[status(thm)],[160, 148, 125])).
% 27.44/17.63 tff(1215,plain,
% 27.44/17.63 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f7(c2), c1)),
% 27.44/17.63 inference(monotonicity,[status(thm)],[1214, 161])).
% 27.44/17.63 tff(1216,plain,
% 27.44/17.63 (big_f(f7(c2), c1) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 27.44/17.63 inference(symmetry,[status(thm)],[1215])).
% 27.44/17.63 tff(1217,plain,
% 27.44/17.63 (big_f(f9(c2, c2), f9(c2, c2))),
% 27.44/17.63 inference(modus_ponens,[status(thm)],[1130, 1216])).
% 27.44/17.63 tff(1218,plain,
% 27.44/17.63 (~(c3 = c1)),
% 27.44/17.63 inference(unit_resolution,[status(thm)],[561, 1217, 348, 148, 79, 122, 347, 22, 121])).
% 27.44/17.64 tff(1219,plain,
% 27.44/17.64 (c3 = c2),
% 27.44/17.64 inference(unit_resolution,[status(thm)],[180, 1218])).
% 27.44/17.64 tff(1220,plain,
% 27.44/17.64 ((f2(c2) = c1) <=> (c1 = f2(c2))),
% 27.44/17.64 inference(commutativity,[status(thm)],[])).
% 27.44/17.64 tff(1221,plain,
% 27.44/17.64 (f2(c3) = f2(c2)),
% 27.44/17.64 inference(monotonicity,[status(thm)],[67])).
% 27.44/17.64 tff(1222,plain,
% 27.44/17.64 ((f2(c3) = c1) <=> (f2(c2) = c1)),
% 27.44/17.64 inference(monotonicity,[status(thm)],[1221])).
% 27.44/17.64 tff(1223,plain,
% 27.44/17.64 ((f2(c3) = c1) <=> (c1 = f2(c2))),
% 27.44/17.64 inference(transitivity,[status(thm)],[1222, 1220])).
% 27.44/17.64 tff(1224,plain,
% 27.44/17.64 ((c1 = f2(c2)) <=> (f2(c3) = c1)),
% 27.44/17.64 inference(symmetry,[status(thm)],[1223])).
% 27.44/17.64 tff(1225,plain,
% 27.44/17.64 ((f9(c2, c2) = f2(c2)) <=> (c1 = f2(c2))),
% 27.44/17.64 inference(monotonicity,[status(thm)],[161])).
% 27.44/17.64 tff(1226,plain,
% 27.44/17.64 ((f9(c2, c2) = f2(c2)) <=> (f2(c3) = c1)),
% 27.44/17.64 inference(transitivity,[status(thm)],[1225, 1224])).
% 27.44/17.64 tff(1227,assumption,(f9(c2, c2) = f2(c2)), introduced(assumption)).
% 27.44/17.64 tff(1228,plain,
% 27.44/17.64 (f2(c3) = c1),
% 27.44/17.64 inference(modus_ponens,[status(thm)],[1227, 1226])).
% 27.44/17.64 tff(1229,assumption,(big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2))), introduced(assumption)).
% 27.44/17.64 tff(1230,assumption,(f9(f10(c2), f2(c3)) = c2), introduced(assumption)).
% 27.44/17.64 tff(1231,plain,
% 27.44/17.64 (f2(c2) = f2(c3)),
% 27.44/17.64 inference(symmetry,[status(thm)],[1221])).
% 27.44/17.64 tff(1232,plain,
% 27.44/17.64 (f9(f10(c2), f10(c2)) = f2(c3)),
% 27.44/17.64 inference(transitivity,[status(thm)],[135, 1227, 1231])).
% 27.44/17.64 tff(1233,plain,
% 27.44/17.64 (f9(c2, f9(f10(c2), f10(c2))) = f9(f10(c2), f2(c3))),
% 27.44/17.64 inference(monotonicity,[status(thm)],[216, 1232])).
% 27.44/17.64 tff(1234,plain,
% 27.44/17.64 (f9(c2, f9(f10(c2), f10(c2))) = c2),
% 27.44/17.64 inference(transitivity,[status(thm)],[1233, 1230])).
% 27.44/17.64 tff(1235,plain,
% 27.44/17.64 (big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2)) <=> big_f(c2, c2)),
% 27.44/17.64 inference(monotonicity,[status(thm)],[1234, 122])).
% 27.44/17.64 tff(1236,plain,
% 27.44/17.64 (big_f(c2, c2) <=> big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2))),
% 27.44/17.64 inference(symmetry,[status(thm)],[1235])).
% 27.44/17.64 tff(1237,plain,
% 27.44/17.64 ((~big_f(c2, c2)) <=> (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2)))),
% 27.44/17.64 inference(monotonicity,[status(thm)],[1236])).
% 27.44/17.64 tff(1238,plain,
% 27.44/17.64 (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2))),
% 27.44/17.64 inference(modus_ponens,[status(thm)],[121, 1237])).
% 27.44/17.64 tff(1239,plain,
% 27.44/17.64 ($false),
% 27.44/17.64 inference(unit_resolution,[status(thm)],[1229, 1238])).
% 27.44/17.64 tff(1240,plain,((~(f9(f10(c2), f2(c3)) = c2)) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2))) | big_f(c2, c2) | (~(f10(c2) = c2)) | (~(f9(c2, c2) = f2(c2))) | (~(c3 = c2))), inference(lemma,lemma(discharge,[]))).
% 27.44/17.64 tff(1241,plain,
% 27.44/17.64 (~(f9(f10(c2), f2(c3)) = c2)),
% 27.44/17.64 inference(unit_resolution,[status(thm)],[1240, 1227, 121, 122, 1229, 67])).
% 27.44/17.64 tff(1242,plain,
% 27.44/17.64 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f9(f10(c2), f2(c3)) = c1) | (f9(f10(c2), f2(c3)) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f9(f10(c2), f2(c3)) = c1) | (f9(f10(c2), f2(c3)) = c2))),
% 27.44/17.64 inference(rewrite,[status(thm)],[])).
% 27.44/17.64 tff(1243,plain,
% 27.44/17.64 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f9(f10(c2), f2(c3)) = c1) | (f9(f10(c2), f2(c3)) = c2))),
% 27.44/17.64 inference(quant_inst,[status(thm)],[])).
% 27.44/17.64 tff(1244,plain,
% 27.44/17.64 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f9(f10(c2), f2(c3)) = c1) | (f9(f10(c2), f2(c3)) = c2)),
% 27.44/17.64 inference(modus_ponens,[status(thm)],[1243, 1242])).
% 27.44/17.64 tff(1245,plain,
% 27.44/17.64 ((f9(f10(c2), f2(c3)) = c1) | (f9(f10(c2), f2(c3)) = c2)),
% 27.44/17.64 inference(unit_resolution,[status(thm)],[1244, 10])).
% 27.44/17.64 tff(1246,plain,
% 27.44/17.64 (f9(f10(c2), f2(c3)) = c1),
% 27.44/17.64 inference(unit_resolution,[status(thm)],[1245, 1241])).
% 27.44/17.64 tff(1247,assumption,(f2(c3) = c1), introduced(assumption)).
% 27.44/17.64 tff(1248,plain,
% 27.44/17.64 (f9(f10(c2), f2(c3)) = f9(c2, c1)),
% 27.44/17.64 inference(monotonicity,[status(thm)],[122, 1247])).
% 27.44/17.64 tff(1249,plain,
% 27.44/17.64 (f9(c2, c1) = f9(f10(c2), f2(c3))),
% 27.44/17.64 inference(symmetry,[status(thm)],[1248])).
% 27.44/17.64 tff(1250,plain,
% 27.44/17.64 ((f9(c2, c1) = c1) <=> (f9(f10(c2), f2(c3)) = c1)),
% 27.44/17.64 inference(monotonicity,[status(thm)],[1249])).
% 27.44/17.64 tff(1251,plain,
% 27.44/17.64 ((f9(f10(c2), f2(c3)) = c1) <=> (f9(c2, c1) = c1)),
% 27.44/17.64 inference(symmetry,[status(thm)],[1250])).
% 27.44/17.64 tff(1252,assumption,(f9(f10(c2), f2(c3)) = c1), introduced(assumption)).
% 27.44/17.64 tff(1253,plain,
% 27.44/17.64 (f9(c2, c1) = c1),
% 27.44/17.64 inference(modus_ponens,[status(thm)],[1252, 1251])).
% 27.44/17.64 tff(1254,plain,
% 27.44/17.64 ($false),
% 27.44/17.64 inference(unit_resolution,[status(thm)],[1139, 1253])).
% 27.44/17.64 tff(1255,plain,((~(f9(f10(c2), f2(c3)) = c1)) | (f9(c2, c1) = c1) | (~(f2(c3) = c1)) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.44/17.64 tff(1256,plain,
% 27.44/17.64 (~(f2(c3) = c1)),
% 27.44/17.64 inference(unit_resolution,[status(thm)],[1255, 1246, 122, 1139])).
% 27.44/17.64 tff(1257,plain,
% 27.44/17.64 ($false),
% 27.44/17.64 inference(unit_resolution,[status(thm)],[1256, 1228])).
% 27.44/17.64 tff(1258,plain,((~(f9(c2, c2) = f2(c2))) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(c3 = c2)) | (f9(c2, c1) = c1) | big_f(c2, c2) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2)))), inference(lemma,lemma(discharge,[]))).
% 27.44/17.64 tff(1259,plain,
% 27.44/17.64 (~(f9(c2, c2) = f2(c2))),
% 27.44/17.64 inference(unit_resolution,[status(thm)],[1258, 1219, 79, 122, 148, 1213, 121, 1175])).
% 27.44/17.64 tff(1260,plain,
% 27.44/17.64 (c2 = c3),
% 27.44/17.64 inference(modus_ponens,[status(thm)],[1219, 78])).
% 27.44/17.64 tff(1261,plain,
% 27.44/17.64 (c2 = c3),
% 27.44/17.64 inference(symmetry,[status(thm)],[1219])).
% 27.44/17.64 tff(1262,plain,
% 27.44/17.64 (f2(c2) = f2(c3)),
% 27.44/17.64 inference(monotonicity,[status(thm)],[1261])).
% 27.44/17.64 tff(1263,plain,
% 27.44/17.64 (f2(c3) = f2(c2)),
% 27.44/17.64 inference(symmetry,[status(thm)],[1262])).
% 27.44/17.64 tff(1264,plain,
% 27.44/17.64 ((f2(c3) = c1) <=> (f2(c2) = c1)),
% 27.44/17.64 inference(monotonicity,[status(thm)],[1263])).
% 27.44/17.64 tff(1265,plain,
% 27.44/17.64 ((f2(c3) = c1) <=> (c1 = f2(c2))),
% 27.44/17.64 inference(transitivity,[status(thm)],[1264, 1220])).
% 27.44/17.64 tff(1266,plain,
% 27.44/17.64 ((c1 = f2(c2)) <=> (f2(c3) = c1)),
% 27.44/17.64 inference(symmetry,[status(thm)],[1265])).
% 27.44/17.64 tff(1267,plain,
% 27.44/17.64 ((f9(c2, c2) = f2(c2)) <=> (f2(c3) = c1)),
% 27.44/17.64 inference(transitivity,[status(thm)],[1225, 1266])).
% 27.44/17.64 tff(1268,plain,
% 27.44/17.64 ((~(f9(c2, c2) = f2(c2))) <=> (~(f2(c3) = c1))),
% 27.44/17.64 inference(monotonicity,[status(thm)],[1267])).
% 27.44/17.64 tff(1269,plain,
% 27.44/17.64 (~(f2(c3) = c1)),
% 27.44/17.64 inference(modus_ponens,[status(thm)],[1259, 1268])).
% 27.44/17.64 tff(1270,plain,
% 27.44/17.64 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f2(c3) = c1) | (f2(c3) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f2(c3) = c1) | (f2(c3) = c2))),
% 27.44/17.64 inference(rewrite,[status(thm)],[])).
% 27.44/17.64 tff(1271,plain,
% 27.44/17.64 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f2(c3) = c1) | (f2(c3) = c2))),
% 27.44/17.64 inference(quant_inst,[status(thm)],[])).
% 27.44/17.64 tff(1272,plain,
% 27.44/17.64 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f2(c3) = c1) | (f2(c3) = c2)),
% 27.44/17.64 inference(modus_ponens,[status(thm)],[1271, 1270])).
% 27.44/17.64 tff(1273,plain,
% 27.44/17.64 ((f2(c3) = c1) | (f2(c3) = c2)),
% 27.44/17.64 inference(unit_resolution,[status(thm)],[1272, 10])).
% 27.44/17.64 tff(1274,plain,
% 27.44/17.64 (f2(c3) = c2),
% 27.44/17.64 inference(unit_resolution,[status(thm)],[1273, 1269])).
% 27.44/17.64 tff(1275,plain,
% 27.44/17.64 (big_f(c3, f2(c3)) <=> big_f(c2, c2)),
% 27.44/17.64 inference(monotonicity,[status(thm)],[1219, 1274])).
% 27.44/17.64 tff(1276,plain,
% 27.44/17.64 (big_f(c2, c2) <=> big_f(c3, f2(c3))),
% 27.44/17.64 inference(symmetry,[status(thm)],[1275])).
% 27.44/17.64 tff(1277,plain,
% 27.44/17.64 ((~big_f(c2, c2)) <=> (~big_f(c3, f2(c3)))),
% 27.44/17.64 inference(monotonicity,[status(thm)],[1276])).
% 27.44/17.64 tff(1278,plain,
% 27.44/17.64 (~big_f(c3, f2(c3))),
% 27.44/17.64 inference(modus_ponens,[status(thm)],[121, 1277])).
% 27.44/17.64 tff(1279,plain,
% 27.44/17.64 ((f5(c2) = c2) <=> (c2 = f5(c2))),
% 27.44/17.64 inference(commutativity,[status(thm)],[])).
% 27.44/17.64 tff(1280,plain,
% 27.44/17.64 ((c2 = f5(c2)) <=> (f5(c2) = c2)),
% 27.44/17.64 inference(symmetry,[status(thm)],[1279])).
% 27.44/17.64 tff(1281,plain,
% 27.44/17.64 ((~(c2 = f5(c2))) <=> (~(f5(c2) = c2))),
% 27.44/17.64 inference(monotonicity,[status(thm)],[1280])).
% 27.44/17.64 tff(1282,plain,
% 27.44/17.64 (f10(c2) = f10(f10(c2))),
% 27.44/17.64 inference(symmetry,[status(thm)],[250])).
% 27.44/17.64 tff(1283,plain,
% 27.44/17.64 (f9(c2, c2) = f9(f10(c2), f10(c2))),
% 27.44/17.64 inference(monotonicity,[status(thm)],[216, 216])).
% 27.44/17.64 tff(1284,plain,
% 27.44/17.64 (big_f(f9(c2, c2), f10(c2)) <=> big_f(f9(f10(c2), f10(c2)), f10(f10(c2)))),
% 27.44/17.64 inference(monotonicity,[status(thm)],[1283, 1282])).
% 27.44/17.64 tff(1285,plain,
% 27.44/17.64 (big_f(f9(f10(c2), f10(c2)), f10(f10(c2))) <=> big_f(f9(c2, c2), f10(c2))),
% 27.44/17.64 inference(symmetry,[status(thm)],[1284])).
% 27.44/17.64 tff(1286,assumption,(~big_f(c3, f2(c3))), introduced(assumption)).
% 27.44/17.64 tff(1287,plain,
% 27.44/17.64 (big_f(c3, c2) <=> big_f(c2, c2)),
% 27.44/17.64 inference(monotonicity,[status(thm)],[67])).
% 27.44/17.64 tff(1288,plain,
% 27.44/17.64 (big_f(c2, c2) <=> big_f(c3, c2)),
% 27.44/17.64 inference(symmetry,[status(thm)],[1287])).
% 27.44/17.64 tff(1289,plain,
% 27.44/17.64 (~(c4 = c1)),
% 27.44/17.64 inference(unit_resolution,[status(thm)],[484, 482])).
% 27.44/17.64 tff(1290,plain,
% 27.44/17.64 (c4 = c2),
% 27.44/17.64 inference(unit_resolution,[status(thm)],[461, 1289])).
% 27.44/17.64 tff(1291,plain,
% 27.44/17.64 (^[X12: $i, X3: $i, X10: $i, X2: $i] : refl(((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12)) <=> ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12)))),
% 27.44/17.64 inference(bind,[status(th)],[])).
% 27.44/17.64 tff(1292,plain,
% 27.44/17.64 (![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12)) <=> ![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))),
% 27.44/17.64 inference(quant_intro,[status(thm)],[1291])).
% 27.44/17.64 tff(1293,plain,
% 27.44/17.64 (![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12)) <=> ![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))),
% 27.44/17.64 inference(rewrite,[status(thm)],[])).
% 27.44/17.64 tff(1294,plain,
% 27.44/17.64 (^[X12: $i, X3: $i, X10: $i, X2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((big_f(X10, X12) | (~(X12 = f2(X10)))) <=> ((~(X12 = f2(X10))) | big_f(X10, X12))), (((big_f(X10, X12) | (~(X12 = f2(X10)))) | (~(X10 = c3))) <=> (((~(X12 = f2(X10))) | big_f(X10, X12)) | (~(X10 = c3))))), rewrite((((~(X12 = f2(X10))) | big_f(X10, X12)) | (~(X10 = c3))) <=> ((~(X10 = c3)) | (~(X12 = f2(X10))) | big_f(X10, X12))), (((big_f(X10, X12) | (~(X12 = f2(X10)))) | (~(X10 = c3))) <=> ((~(X10 = c3)) | (~(X12 = f2(X10))) | big_f(X10, X12)))), ((((big_f(X10, X12) | (~(X12 = f2(X10)))) | (~(X10 = c3))) | big_f(X3, X2)) <=> (((~(X10 = c3)) | (~(X12 = f2(X10))) | big_f(X10, X12)) | big_f(X3, X2)))), rewrite((((~(X10 = c3)) | (~(X12 = f2(X10))) | big_f(X10, X12)) | big_f(X3, X2)) <=> ((~(X10 = c3)) | (~(X12 = f2(X10))) | big_f(X3, X2) | big_f(X10, X12))), ((((big_f(X10, X12) | (~(X12 = f2(X10)))) | (~(X10 = c3))) | big_f(X3, X2)) <=> ((~(X10 = c3)) | (~(X12 = f2(X10))) | big_f(X3, X2) | big_f(X10, X12)))), (((((big_f(X10, X12) | (~(X12 = f2(X10)))) | (~(X10 = c3))) | big_f(X3, X2)) | (~(X3 = f4(X2)))) <=> (((~(X10 = c3)) | (~(X12 = f2(X10))) | big_f(X3, X2) | big_f(X10, X12)) | (~(X3 = f4(X2)))))), rewrite((((~(X10 = c3)) | (~(X12 = f2(X10))) | big_f(X3, X2) | big_f(X10, X12)) | (~(X3 = f4(X2)))) <=> ((~(X10 = c3)) | (~(X12 = f2(X10))) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))), (((((big_f(X10, X12) | (~(X12 = f2(X10)))) | (~(X10 = c3))) | big_f(X3, X2)) | (~(X3 = f4(X2)))) <=> ((~(X10 = c3)) | (~(X12 = f2(X10))) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12)))), ((((((big_f(X10, X12) | (~(X12 = f2(X10)))) | (~(X10 = c3))) | big_f(X3, X2)) | (~(X3 = f4(X2)))) | (~(X2 = c4))) <=> (((~(X10 = c3)) | (~(X12 = f2(X10))) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12)) | (~(X2 = c4))))), rewrite((((~(X10 = c3)) | (~(X12 = f2(X10))) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12)) | (~(X2 = c4))) <=> ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))), ((((((big_f(X10, X12) | (~(X12 = f2(X10)))) | (~(X10 = c3))) | big_f(X3, X2)) | (~(X3 = f4(X2)))) | (~(X2 = c4))) <=> ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))))),
% 27.44/17.64 inference(bind,[status(th)],[])).
% 27.44/17.64 tff(1295,plain,
% 27.44/17.64 (![X12: $i, X3: $i, X10: $i, X2: $i] : (((((big_f(X10, X12) | (~(X12 = f2(X10)))) | (~(X10 = c3))) | big_f(X3, X2)) | (~(X3 = f4(X2)))) | (~(X2 = c4))) <=> ![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))),
% 27.44/17.64 inference(quant_intro,[status(thm)],[1294])).
% 27.44/17.64 tff(1296,axiom,(![X12: $i, X3: $i, X10: $i, X2: $i] : (((((big_f(X10, X12) | (~(X12 = f2(X10)))) | (~(X10 = c3))) | big_f(X3, X2)) | (~(X3 = f4(X2)))) | (~(X2 = c4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_18')).
% 27.44/17.64 tff(1297,plain,
% 27.44/17.64 (![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))),
% 27.44/17.64 inference(modus_ponens,[status(thm)],[1296, 1295])).
% 27.44/17.64 tff(1298,plain,
% 27.44/17.64 (![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))),
% 27.44/17.64 inference(modus_ponens,[status(thm)],[1297, 1293])).
% 27.44/17.64 tff(1299,plain,(
% 27.44/17.64 ![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))),
% 27.44/17.64 inference(skolemize,[status(sab)],[1298])).
% 27.44/17.64 tff(1300,plain,
% 27.44/17.64 (![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))),
% 27.44/17.64 inference(modus_ponens,[status(thm)],[1299, 1292])).
% 27.44/17.64 tff(1301,plain,
% 27.44/17.64 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))) | (big_f(f4(c4), c4) | big_f(c3, f2(c3)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))) | big_f(f4(c4), c4) | big_f(c3, f2(c3)))),
% 27.44/17.64 inference(rewrite,[status(thm)],[])).
% 27.44/17.64 tff(1302,plain,
% 27.44/17.64 (($false | $false | $false | big_f(f4(c4), c4) | $false | big_f(c3, f2(c3))) <=> (big_f(f4(c4), c4) | big_f(c3, f2(c3)))),
% 27.44/17.64 inference(rewrite,[status(thm)],[])).
% 27.44/17.64 tff(1303,plain,
% 27.44/17.64 ((f2(c3) = f2(c3)) <=> $true),
% 27.44/17.64 inference(rewrite,[status(thm)],[])).
% 27.44/17.64 tff(1304,plain,
% 27.44/17.64 ((~(f2(c3) = f2(c3))) <=> (~$true)),
% 27.44/17.64 inference(monotonicity,[status(thm)],[1303])).
% 27.44/17.64 tff(1305,plain,
% 27.44/17.64 ((~(f2(c3) = f2(c3))) <=> $false),
% 27.44/17.64 inference(transitivity,[status(thm)],[1304, 270])).
% 27.44/17.64 tff(1306,plain,
% 27.44/17.64 ((c3 = c3) <=> $true),
% 27.44/17.64 inference(rewrite,[status(thm)],[])).
% 27.44/17.64 tff(1307,plain,
% 27.44/17.64 ((~(c3 = c3)) <=> (~$true)),
% 27.44/17.64 inference(monotonicity,[status(thm)],[1306])).
% 27.44/17.64 tff(1308,plain,
% 27.44/17.64 ((~(c3 = c3)) <=> $false),
% 27.44/17.64 inference(transitivity,[status(thm)],[1307, 270])).
% 27.44/17.64 tff(1309,plain,
% 27.44/17.64 (((~(c3 = c3)) | (~(f2(c3) = f2(c3))) | (~(c4 = c4)) | big_f(f4(c4), c4) | (~(f4(c4) = f4(c4))) | big_f(c3, f2(c3))) <=> ($false | $false | $false | big_f(f4(c4), c4) | $false | big_f(c3, f2(c3)))),
% 27.44/17.64 inference(monotonicity,[status(thm)],[1308, 1305, 410, 407])).
% 27.44/17.64 tff(1310,plain,
% 27.44/17.64 (((~(c3 = c3)) | (~(f2(c3) = f2(c3))) | (~(c4 = c4)) | big_f(f4(c4), c4) | (~(f4(c4) = f4(c4))) | big_f(c3, f2(c3))) <=> (big_f(f4(c4), c4) | big_f(c3, f2(c3)))),
% 27.44/17.64 inference(transitivity,[status(thm)],[1309, 1302])).
% 27.44/17.64 tff(1311,plain,
% 27.44/17.64 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))) | ((~(c3 = c3)) | (~(f2(c3) = f2(c3))) | (~(c4 = c4)) | big_f(f4(c4), c4) | (~(f4(c4) = f4(c4))) | big_f(c3, f2(c3)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))) | (big_f(f4(c4), c4) | big_f(c3, f2(c3))))),
% 27.44/17.64 inference(monotonicity,[status(thm)],[1310])).
% 27.44/17.64 tff(1312,plain,
% 27.44/17.64 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))) | ((~(c3 = c3)) | (~(f2(c3) = f2(c3))) | (~(c4 = c4)) | big_f(f4(c4), c4) | (~(f4(c4) = f4(c4))) | big_f(c3, f2(c3)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))) | big_f(f4(c4), c4) | big_f(c3, f2(c3)))),
% 27.44/17.64 inference(transitivity,[status(thm)],[1311, 1301])).
% 27.44/17.64 tff(1313,plain,
% 27.44/17.64 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))) | ((~(c3 = c3)) | (~(f2(c3) = f2(c3))) | (~(c4 = c4)) | big_f(f4(c4), c4) | (~(f4(c4) = f4(c4))) | big_f(c3, f2(c3)))),
% 27.44/17.64 inference(quant_inst,[status(thm)],[])).
% 27.44/17.64 tff(1314,plain,
% 27.44/17.64 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))) | big_f(f4(c4), c4) | big_f(c3, f2(c3))),
% 27.44/17.64 inference(modus_ponens,[status(thm)],[1313, 1312])).
% 27.44/17.64 tff(1315,plain,
% 27.44/17.64 (big_f(f4(c4), c4) | big_f(c3, f2(c3))),
% 27.44/17.64 inference(unit_resolution,[status(thm)],[1314, 1300])).
% 27.44/17.64 tff(1316,plain,
% 27.44/17.64 (big_f(f4(c4), c4)),
% 27.44/17.64 inference(unit_resolution,[status(thm)],[1315, 1286])).
% 27.44/17.64 tff(1317,plain,
% 27.44/17.64 (big_f(c2, c2)),
% 27.44/17.64 inference(unit_resolution,[status(thm)],[476, 1316, 1290, 79])).
% 27.44/17.64 tff(1318,plain,
% 27.44/17.64 (big_f(c3, c2)),
% 27.44/17.64 inference(modus_ponens,[status(thm)],[1317, 1288])).
% 27.44/17.64 tff(1319,assumption,(f2(c3) = c2), introduced(assumption)).
% 27.44/17.64 tff(1320,plain,
% 27.44/17.64 (big_f(c3, f2(c3)) <=> big_f(c3, c2)),
% 27.44/17.64 inference(monotonicity,[status(thm)],[1319])).
% 27.44/17.64 tff(1321,plain,
% 27.44/17.64 (big_f(c3, c2) <=> big_f(c3, f2(c3))),
% 27.44/17.64 inference(symmetry,[status(thm)],[1320])).
% 27.44/17.64 tff(1322,assumption,(big_f(c3, c2)), introduced(assumption)).
% 27.44/17.64 tff(1323,plain,
% 27.44/17.64 (big_f(c3, f2(c3))),
% 27.44/17.64 inference(modus_ponens,[status(thm)],[1322, 1321])).
% 27.44/17.64 tff(1324,plain,
% 27.44/17.64 ($false),
% 27.44/17.64 inference(unit_resolution,[status(thm)],[1286, 1323])).
% 27.44/17.64 tff(1325,plain,((~big_f(c3, c2)) | big_f(c3, f2(c3)) | (~(f2(c3) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.44/17.64 tff(1326,plain,
% 27.44/17.64 (~(f2(c3) = c2)),
% 27.44/17.64 inference(unit_resolution,[status(thm)],[1325, 1318, 1286])).
% 27.44/17.64 tff(1327,plain,
% 27.44/17.64 (f2(c3) = c1),
% 27.44/17.64 inference(unit_resolution,[status(thm)],[1273, 1326])).
% 27.44/17.64 tff(1328,plain,
% 27.44/17.64 (f2(c2) = c1),
% 27.44/17.64 inference(transitivity,[status(thm)],[1231, 1327])).
% 27.44/17.64 tff(1329,plain,
% 27.44/17.64 (big_f(f2(c2), c2) <=> big_f(c1, c2)),
% 27.44/17.64 inference(monotonicity,[status(thm)],[1328])).
% 27.44/17.64 tff(1330,plain,
% 27.44/17.64 ((~big_f(f2(c2), c2)) <=> (~big_f(c1, c2))),
% 27.44/17.64 inference(monotonicity,[status(thm)],[1329])).
% 27.44/17.64 tff(1331,plain,
% 27.44/17.64 ((c2 = f2(c2)) <=> (c2 = c1)),
% 27.44/17.64 inference(monotonicity,[status(thm)],[1328])).
% 27.44/17.64 tff(1332,plain,
% 27.44/17.64 ((c2 = c1) <=> (c2 = f2(c2))),
% 27.44/17.64 inference(symmetry,[status(thm)],[1331])).
% 27.44/17.64 tff(1333,plain,
% 27.44/17.64 ((~(c2 = c1)) <=> (~(c2 = f2(c2)))),
% 27.44/17.64 inference(monotonicity,[status(thm)],[1332])).
% 27.44/17.64 tff(1334,plain,
% 27.44/17.64 (~(c2 = f2(c2))),
% 27.44/17.64 inference(modus_ponens,[status(thm)],[75, 1333])).
% 27.44/17.64 tff(1335,plain,
% 27.44/17.64 (c2 = c3),
% 27.44/17.64 inference(modus_ponens,[status(thm)],[67, 78])).
% 27.44/17.64 tff(1336,assumption,(big_f(f2(c2), c2)), introduced(assumption)).
% 27.44/17.64 tff(1337,plain,
% 27.44/17.64 ((f2(c2) = c2) <=> (c2 = f2(c2))),
% 27.44/17.64 inference(commutativity,[status(thm)],[])).
% 27.44/17.64 tff(1338,plain,
% 27.44/17.64 ((f2(c2) = f4(c2)) <=> (f2(c2) = c2)),
% 27.44/17.64 inference(monotonicity,[status(thm)],[798])).
% 27.44/17.64 tff(1339,plain,
% 27.44/17.64 ((f2(c2) = f4(c2)) <=> (c2 = f2(c2))),
% 27.44/17.64 inference(transitivity,[status(thm)],[1338, 1337])).
% 27.44/17.64 tff(1340,plain,
% 27.44/17.64 ((c2 = f2(c2)) <=> (f2(c2) = f4(c2))),
% 27.44/17.64 inference(symmetry,[status(thm)],[1339])).
% 27.44/17.64 tff(1341,plain,
% 27.44/17.64 ((~(c2 = f2(c2))) <=> (~(f2(c2) = f4(c2)))),
% 27.44/17.64 inference(monotonicity,[status(thm)],[1340])).
% 27.44/17.64 tff(1342,assumption,(~(c2 = f2(c2))), introduced(assumption)).
% 27.44/17.64 tff(1343,plain,
% 27.44/17.64 (~(f2(c2) = f4(c2))),
% 27.44/17.64 inference(modus_ponens,[status(thm)],[1342, 1341])).
% 27.44/17.64 tff(1344,assumption,(c2 = c3), introduced(assumption)).
% 27.44/17.64 tff(1345,assumption,(big_f(c2, c2)), introduced(assumption)).
% 27.44/17.64 tff(1346,plain,
% 27.44/17.64 (^[X12: $i, X3: $i, X10: $i, X2: $i] : refl(((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12))) <=> ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12))))),
% 27.44/17.64 inference(bind,[status(th)],[])).
% 27.44/17.64 tff(1347,plain,
% 27.44/17.64 (![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12))) <=> ![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))),
% 27.44/17.64 inference(quant_intro,[status(thm)],[1346])).
% 27.44/17.64 tff(1348,plain,
% 27.44/17.64 (![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12))) <=> ![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))),
% 27.44/17.64 inference(rewrite,[status(thm)],[])).
% 27.44/17.64 tff(1349,plain,
% 27.44/17.64 (^[X12: $i, X3: $i, X10: $i, X2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_f(X10, X12)) | (X12 = f2(X10))) | (~(X10 = c3))) <=> ((~(X10 = c3)) | (X12 = f2(X10)) | (~big_f(X10, X12)))), (((((~big_f(X10, X12)) | (X12 = f2(X10))) | (~(X10 = c3))) | (~big_f(X3, X2))) <=> (((~(X10 = c3)) | (X12 = f2(X10)) | (~big_f(X10, X12))) | (~big_f(X3, X2))))), rewrite((((~(X10 = c3)) | (X12 = f2(X10)) | (~big_f(X10, X12))) | (~big_f(X3, X2))) <=> ((~(X10 = c3)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))), (((((~big_f(X10, X12)) | (X12 = f2(X10))) | (~(X10 = c3))) | (~big_f(X3, X2))) <=> ((~(X10 = c3)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12))))), ((((((~big_f(X10, X12)) | (X12 = f2(X10))) | (~(X10 = c3))) | (~big_f(X3, X2))) | (X3 = f4(X2))) <=> (((~(X10 = c3)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12))) | (X3 = f4(X2))))), rewrite((((~(X10 = c3)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12))) | (X3 = f4(X2))) <=> ((~(X10 = c3)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))), ((((((~big_f(X10, X12)) | (X12 = f2(X10))) | (~(X10 = c3))) | (~big_f(X3, X2))) | (X3 = f4(X2))) <=> ((~(X10 = c3)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12))))), (((((((~big_f(X10, X12)) | (X12 = f2(X10))) | (~(X10 = c3))) | (~big_f(X3, X2))) | (X3 = f4(X2))) | (~(X2 = c4))) <=> (((~(X10 = c3)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12))) | (~(X2 = c4))))), rewrite((((~(X10 = c3)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12))) | (~(X2 = c4))) <=> ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))), (((((((~big_f(X10, X12)) | (X12 = f2(X10))) | (~(X10 = c3))) | (~big_f(X3, X2))) | (X3 = f4(X2))) | (~(X2 = c4))) <=> ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))))),
% 27.44/17.64 inference(bind,[status(th)],[])).
% 27.44/17.64 tff(1350,plain,
% 27.44/17.64 (![X12: $i, X3: $i, X10: $i, X2: $i] : ((((((~big_f(X10, X12)) | (X12 = f2(X10))) | (~(X10 = c3))) | (~big_f(X3, X2))) | (X3 = f4(X2))) | (~(X2 = c4))) <=> ![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))),
% 27.44/17.64 inference(quant_intro,[status(thm)],[1349])).
% 27.44/17.64 tff(1351,axiom,(![X12: $i, X3: $i, X10: $i, X2: $i] : ((((((~big_f(X10, X12)) | (X12 = f2(X10))) | (~(X10 = c3))) | (~big_f(X3, X2))) | (X3 = f4(X2))) | (~(X2 = c4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_13')).
% 27.44/17.64 tff(1352,plain,
% 27.44/17.64 (![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))),
% 27.44/17.64 inference(modus_ponens,[status(thm)],[1351, 1350])).
% 27.44/17.64 tff(1353,plain,
% 27.44/17.64 (![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))),
% 27.44/17.64 inference(modus_ponens,[status(thm)],[1352, 1348])).
% 27.44/17.64 tff(1354,plain,(
% 27.44/17.64 ![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))),
% 27.44/17.64 inference(skolemize,[status(sab)],[1353])).
% 27.44/17.64 tff(1355,plain,
% 27.44/17.64 (![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))),
% 27.44/17.64 inference(modus_ponens,[status(thm)],[1354, 1347])).
% 27.44/17.64 tff(1356,plain,
% 27.44/17.64 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c2 = c4)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (~big_f(f2(c2), c2)) | (f2(c2) = f4(c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (~(c2 = c4)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (~big_f(f2(c2), c2)) | (f2(c2) = f4(c2)))),
% 27.44/17.64 inference(rewrite,[status(thm)],[])).
% 27.44/17.64 tff(1357,plain,
% 27.44/17.64 (((~(c2 = c3)) | (~(c2 = c4)) | (f2(c2) = f4(c2)) | (~big_f(f2(c2), c2)) | (c2 = f2(c2)) | (~big_f(c2, c2))) <=> ((~(c2 = c3)) | (~(c2 = c4)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (~big_f(f2(c2), c2)) | (f2(c2) = f4(c2)))),
% 27.44/17.64 inference(rewrite,[status(thm)],[])).
% 27.44/17.64 tff(1358,plain,
% 27.44/17.64 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c2 = c4)) | (f2(c2) = f4(c2)) | (~big_f(f2(c2), c2)) | (c2 = f2(c2)) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c2 = c4)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (~big_f(f2(c2), c2)) | (f2(c2) = f4(c2))))),
% 27.44/17.64 inference(monotonicity,[status(thm)],[1357])).
% 27.44/17.64 tff(1359,plain,
% 27.44/17.64 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c2 = c4)) | (f2(c2) = f4(c2)) | (~big_f(f2(c2), c2)) | (c2 = f2(c2)) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (~(c2 = c4)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (~big_f(f2(c2), c2)) | (f2(c2) = f4(c2)))),
% 27.44/17.64 inference(transitivity,[status(thm)],[1358, 1356])).
% 27.44/17.64 tff(1360,plain,
% 27.44/17.64 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c2 = c4)) | (f2(c2) = f4(c2)) | (~big_f(f2(c2), c2)) | (c2 = f2(c2)) | (~big_f(c2, c2)))),
% 27.44/17.64 inference(quant_inst,[status(thm)],[])).
% 27.44/17.64 tff(1361,plain,
% 27.44/17.64 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (~(c2 = c4)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (~big_f(f2(c2), c2)) | (f2(c2) = f4(c2))),
% 27.44/17.64 inference(modus_ponens,[status(thm)],[1360, 1359])).
% 27.44/17.64 tff(1362,plain,
% 27.44/17.64 ((~big_f(f2(c2), c2)) | (f2(c2) = f4(c2))),
% 27.44/17.64 inference(unit_resolution,[status(thm)],[1361, 1355, 432, 1345, 1344, 1342])).
% 27.44/17.64 tff(1363,plain,
% 27.44/17.64 ($false),
% 27.44/17.64 inference(unit_resolution,[status(thm)],[1362, 1343, 1336])).
% 27.44/17.64 tff(1364,plain,((~big_f(f2(c2), c2)) | (~big_f(c2, c2)) | (~(c2 = c3)) | (c2 = f2(c2)) | (~(f4(c4) = c2)) | (~(c4 = c2))), inference(lemma,lemma(discharge,[]))).
% 27.44/17.64 tff(1365,plain,
% 27.44/17.64 (~big_f(f2(c2), c2)),
% 27.44/17.64 inference(unit_resolution,[status(thm)],[1364, 1335, 1317, 1334, 79, 1290])).
% 27.44/17.64 tff(1366,plain,
% 27.44/17.64 (~big_f(c1, c2)),
% 27.44/17.64 inference(modus_ponens,[status(thm)],[1365, 1330])).
% 27.44/17.64 tff(1367,plain,
% 27.44/17.64 (c1 = f2(c3)),
% 27.44/17.64 inference(symmetry,[status(thm)],[1247])).
% 27.44/17.64 tff(1368,plain,
% 27.44/17.64 (f2(c2) = c1),
% 27.44/17.64 inference(transitivity,[status(thm)],[1231, 1247])).
% 27.44/17.64 tff(1369,plain,
% 27.44/17.64 (f3(f2(c2), f2(c2)) = f3(c1, c1)),
% 27.44/17.64 inference(monotonicity,[status(thm)],[1368, 1368])).
% 27.44/17.64 tff(1370,plain,
% 27.44/17.64 ((f3(f2(c2), f2(c2)) = f2(c2)) <=> (f3(c1, c1) = c1)),
% 27.44/17.64 inference(monotonicity,[status(thm)],[1369, 1368])).
% 27.44/17.64 tff(1371,plain,
% 27.44/17.64 ((~(f3(f2(c2), f2(c2)) = f2(c2))) <=> (~(f3(c1, c1) = c1))),
% 27.44/17.64 inference(monotonicity,[status(thm)],[1370])).
% 27.44/17.64 tff(1372,plain,
% 27.44/17.64 (big_f(c2, f2(c2)) <=> big_f(c3, f2(c3))),
% 27.44/17.64 inference(monotonicity,[status(thm)],[69, 1231])).
% 27.44/17.64 tff(1373,plain,
% 27.44/17.64 (big_f(c3, f2(c3)) <=> big_f(c2, f2(c2))),
% 27.44/17.64 inference(symmetry,[status(thm)],[1372])).
% 27.44/17.64 tff(1374,plain,
% 27.44/17.64 ((~big_f(c3, f2(c3))) <=> (~big_f(c2, f2(c2)))),
% 27.44/17.64 inference(monotonicity,[status(thm)],[1373])).
% 27.44/17.64 tff(1375,plain,
% 27.44/17.64 (~big_f(c2, f2(c2))),
% 27.44/17.64 inference(modus_ponens,[status(thm)],[1286, 1374])).
% 27.44/17.64 tff(1376,plain,
% 27.44/17.64 ((f2(c2) = c4) <=> (f2(c2) = c2)),
% 27.44/17.64 inference(monotonicity,[status(thm)],[431])).
% 27.44/17.65 tff(1377,plain,
% 27.44/17.65 ((f2(c2) = c4) <=> (c2 = f2(c2))),
% 27.44/17.65 inference(transitivity,[status(thm)],[1376, 1337])).
% 27.44/17.65 tff(1378,plain,
% 27.44/17.65 ((c2 = f2(c2)) <=> (f2(c2) = c4)),
% 27.44/17.65 inference(symmetry,[status(thm)],[1377])).
% 27.44/17.65 tff(1379,plain,
% 27.44/17.65 ((~(c2 = f2(c2))) <=> (~(f2(c2) = c4))),
% 27.44/17.65 inference(monotonicity,[status(thm)],[1378])).
% 27.44/17.65 tff(1380,plain,
% 27.44/17.65 ((c2 = f2(c2)) <=> (c2 = c1)),
% 27.44/17.65 inference(monotonicity,[status(thm)],[1368])).
% 27.44/17.65 tff(1381,plain,
% 27.44/17.65 ((c2 = c1) <=> (c2 = f2(c2))),
% 27.44/17.65 inference(symmetry,[status(thm)],[1380])).
% 27.44/17.65 tff(1382,plain,
% 27.44/17.65 ((~(c2 = c1)) <=> (~(c2 = f2(c2)))),
% 27.44/17.65 inference(monotonicity,[status(thm)],[1381])).
% 27.44/17.65 tff(1383,plain,
% 27.44/17.65 (~(c2 = f2(c2))),
% 27.44/17.65 inference(modus_ponens,[status(thm)],[75, 1382])).
% 27.44/17.65 tff(1384,plain,
% 27.44/17.65 (~(f2(c2) = c4)),
% 27.44/17.65 inference(modus_ponens,[status(thm)],[1383, 1379])).
% 27.44/17.65 tff(1385,plain,
% 27.44/17.65 (big_f(f3(f2(c2), f2(c2)), f2(c2)) <=> big_f(f3(c1, c1), c1)),
% 27.44/17.65 inference(monotonicity,[status(thm)],[1369, 1368])).
% 27.44/17.65 tff(1386,plain,
% 27.44/17.65 (big_f(f3(c1, c1), c1) <=> big_f(f3(f2(c2), f2(c2)), f2(c2))),
% 27.44/17.65 inference(symmetry,[status(thm)],[1385])).
% 27.44/17.65 tff(1387,assumption,(big_f(f3(c1, c1), c1)), introduced(assumption)).
% 27.44/17.65 tff(1388,plain,
% 27.44/17.65 (big_f(f3(f2(c2), f2(c2)), f2(c2))),
% 27.44/17.65 inference(modus_ponens,[status(thm)],[1387, 1386])).
% 27.44/17.65 tff(1389,plain,
% 27.44/17.65 (^[X12: $i, X13: $i, X10: $i, X2: $i] : refl(((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12)) <=> ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12)))),
% 27.44/17.65 inference(bind,[status(th)],[])).
% 27.44/17.65 tff(1390,plain,
% 27.44/17.65 (![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12)) <=> ![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))),
% 27.44/17.65 inference(quant_intro,[status(thm)],[1389])).
% 27.44/17.65 tff(1391,plain,
% 27.44/17.65 (![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12)) <=> ![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))),
% 27.44/17.65 inference(rewrite,[status(thm)],[])).
% 27.44/17.65 tff(1392,plain,
% 27.44/17.65 (^[X12: $i, X13: $i, X10: $i, X2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((big_f(X10, X12) | (~(X12 = f2(X10)))) <=> ((~(X12 = f2(X10))) | big_f(X10, X12))), (((big_f(X10, X12) | (~(X12 = f2(X10)))) | (~(X10 = c3))) <=> (((~(X12 = f2(X10))) | big_f(X10, X12)) | (~(X10 = c3))))), rewrite((((~(X12 = f2(X10))) | big_f(X10, X12)) | (~(X10 = c3))) <=> ((~(X10 = c3)) | (~(X12 = f2(X10))) | big_f(X10, X12))), (((big_f(X10, X12) | (~(X12 = f2(X10)))) | (~(X10 = c3))) <=> ((~(X10 = c3)) | (~(X12 = f2(X10))) | big_f(X10, X12)))), ((((big_f(X10, X12) | (~(X12 = f2(X10)))) | (~(X10 = c3))) | (~big_f(f3(X2, X13), X2))) <=> (((~(X10 = c3)) | (~(X12 = f2(X10))) | big_f(X10, X12)) | (~big_f(f3(X2, X13), X2))))), rewrite((((~(X10 = c3)) | (~(X12 = f2(X10))) | big_f(X10, X12)) | (~big_f(f3(X2, X13), X2))) <=> ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))), ((((big_f(X10, X12) | (~(X12 = f2(X10)))) | (~(X10 = c3))) | (~big_f(f3(X2, X13), X2))) <=> ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12)))), (((((big_f(X10, X12) | (~(X12 = f2(X10)))) | (~(X10 = c3))) | (~big_f(f3(X2, X13), X2))) | (~(f3(X2, X13) = X13))) <=> (((~(X10 = c3)) | (~(X12 = f2(X10))) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12)) | (~(f3(X2, X13) = X13))))), rewrite((((~(X10 = c3)) | (~(X12 = f2(X10))) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12)) | (~(f3(X2, X13) = X13))) <=> ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))), (((((big_f(X10, X12) | (~(X12 = f2(X10)))) | (~(X10 = c3))) | (~big_f(f3(X2, X13), X2))) | (~(f3(X2, X13) = X13))) <=> ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12)))), ((((((big_f(X10, X12) | (~(X12 = f2(X10)))) | (~(X10 = c3))) | (~big_f(f3(X2, X13), X2))) | (~(f3(X2, X13) = X13))) | (X2 = c4)) <=> (((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12)) | (X2 = c4)))), rewrite((((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12)) | (X2 = c4)) <=> ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))), ((((((big_f(X10, X12) | (~(X12 = f2(X10)))) | (~(X10 = c3))) | (~big_f(f3(X2, X13), X2))) | (~(f3(X2, X13) = X13))) | (X2 = c4)) <=> ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))))),
% 27.44/17.65 inference(bind,[status(th)],[])).
% 27.44/17.65 tff(1393,plain,
% 27.44/17.65 (![X12: $i, X13: $i, X10: $i, X2: $i] : (((((big_f(X10, X12) | (~(X12 = f2(X10)))) | (~(X10 = c3))) | (~big_f(f3(X2, X13), X2))) | (~(f3(X2, X13) = X13))) | (X2 = c4)) <=> ![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))),
% 27.44/17.65 inference(quant_intro,[status(thm)],[1392])).
% 27.44/17.65 tff(1394,axiom,(![X12: $i, X13: $i, X10: $i, X2: $i] : (((((big_f(X10, X12) | (~(X12 = f2(X10)))) | (~(X10 = c3))) | (~big_f(f3(X2, X13), X2))) | (~(f3(X2, X13) = X13))) | (X2 = c4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_16')).
% 27.44/17.65 tff(1395,plain,
% 27.44/17.65 (![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))),
% 27.44/17.65 inference(modus_ponens,[status(thm)],[1394, 1393])).
% 27.44/17.65 tff(1396,plain,
% 27.44/17.65 (![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))),
% 27.44/17.65 inference(modus_ponens,[status(thm)],[1395, 1391])).
% 27.44/17.65 tff(1397,plain,(
% 27.44/17.65 ![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))),
% 27.44/17.65 inference(skolemize,[status(sab)],[1396])).
% 27.44/17.65 tff(1398,plain,
% 27.44/17.65 (![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))),
% 27.44/17.65 inference(modus_ponens,[status(thm)],[1397, 1390])).
% 27.44/17.65 tff(1399,plain,
% 27.44/17.65 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (f2(c2) = c4) | big_f(c2, f2(c2)) | (~big_f(f3(f2(c2), f2(c2)), f2(c2))) | (~(f3(f2(c2), f2(c2)) = f2(c2))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (~(c2 = c3)) | (f2(c2) = c4) | big_f(c2, f2(c2)) | (~big_f(f3(f2(c2), f2(c2)), f2(c2))) | (~(f3(f2(c2), f2(c2)) = f2(c2))))),
% 27.44/17.65 inference(rewrite,[status(thm)],[])).
% 27.44/17.65 tff(1400,plain,
% 27.44/17.65 (((~(c2 = c3)) | $false | (f2(c2) = c4) | (~(f3(f2(c2), f2(c2)) = f2(c2))) | (~big_f(f3(f2(c2), f2(c2)), f2(c2))) | big_f(c2, f2(c2))) <=> ((~(c2 = c3)) | (f2(c2) = c4) | big_f(c2, f2(c2)) | (~big_f(f3(f2(c2), f2(c2)), f2(c2))) | (~(f3(f2(c2), f2(c2)) = f2(c2))))),
% 27.44/17.65 inference(rewrite,[status(thm)],[])).
% 27.44/17.65 tff(1401,plain,
% 27.44/17.65 ((f2(c2) = f2(c2)) <=> $true),
% 27.44/17.65 inference(rewrite,[status(thm)],[])).
% 27.44/17.65 tff(1402,plain,
% 27.44/17.65 ((~(f2(c2) = f2(c2))) <=> (~$true)),
% 27.44/17.65 inference(monotonicity,[status(thm)],[1401])).
% 27.44/17.65 tff(1403,plain,
% 27.44/17.65 ((~(f2(c2) = f2(c2))) <=> $false),
% 27.44/17.65 inference(transitivity,[status(thm)],[1402, 270])).
% 27.44/17.65 tff(1404,plain,
% 27.44/17.65 (((~(c2 = c3)) | (~(f2(c2) = f2(c2))) | (f2(c2) = c4) | (~(f3(f2(c2), f2(c2)) = f2(c2))) | (~big_f(f3(f2(c2), f2(c2)), f2(c2))) | big_f(c2, f2(c2))) <=> ((~(c2 = c3)) | $false | (f2(c2) = c4) | (~(f3(f2(c2), f2(c2)) = f2(c2))) | (~big_f(f3(f2(c2), f2(c2)), f2(c2))) | big_f(c2, f2(c2)))),
% 27.44/17.65 inference(monotonicity,[status(thm)],[1403])).
% 27.44/17.65 tff(1405,plain,
% 27.44/17.65 (((~(c2 = c3)) | (~(f2(c2) = f2(c2))) | (f2(c2) = c4) | (~(f3(f2(c2), f2(c2)) = f2(c2))) | (~big_f(f3(f2(c2), f2(c2)), f2(c2))) | big_f(c2, f2(c2))) <=> ((~(c2 = c3)) | (f2(c2) = c4) | big_f(c2, f2(c2)) | (~big_f(f3(f2(c2), f2(c2)), f2(c2))) | (~(f3(f2(c2), f2(c2)) = f2(c2))))),
% 27.44/17.65 inference(transitivity,[status(thm)],[1404, 1400])).
% 27.44/17.65 tff(1406,plain,
% 27.44/17.65 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(f2(c2) = f2(c2))) | (f2(c2) = c4) | (~(f3(f2(c2), f2(c2)) = f2(c2))) | (~big_f(f3(f2(c2), f2(c2)), f2(c2))) | big_f(c2, f2(c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (f2(c2) = c4) | big_f(c2, f2(c2)) | (~big_f(f3(f2(c2), f2(c2)), f2(c2))) | (~(f3(f2(c2), f2(c2)) = f2(c2)))))),
% 27.44/17.65 inference(monotonicity,[status(thm)],[1405])).
% 27.44/17.65 tff(1407,plain,
% 27.44/17.65 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(f2(c2) = f2(c2))) | (f2(c2) = c4) | (~(f3(f2(c2), f2(c2)) = f2(c2))) | (~big_f(f3(f2(c2), f2(c2)), f2(c2))) | big_f(c2, f2(c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (~(c2 = c3)) | (f2(c2) = c4) | big_f(c2, f2(c2)) | (~big_f(f3(f2(c2), f2(c2)), f2(c2))) | (~(f3(f2(c2), f2(c2)) = f2(c2))))),
% 27.44/17.65 inference(transitivity,[status(thm)],[1406, 1399])).
% 27.44/17.65 tff(1408,plain,
% 27.44/17.65 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(f2(c2) = f2(c2))) | (f2(c2) = c4) | (~(f3(f2(c2), f2(c2)) = f2(c2))) | (~big_f(f3(f2(c2), f2(c2)), f2(c2))) | big_f(c2, f2(c2)))),
% 27.44/17.65 inference(quant_inst,[status(thm)],[])).
% 27.44/17.65 tff(1409,plain,
% 27.44/17.65 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (~(c2 = c3)) | (f2(c2) = c4) | big_f(c2, f2(c2)) | (~big_f(f3(f2(c2), f2(c2)), f2(c2))) | (~(f3(f2(c2), f2(c2)) = f2(c2)))),
% 27.44/17.65 inference(modus_ponens,[status(thm)],[1408, 1407])).
% 27.44/17.65 tff(1410,plain,
% 27.44/17.65 ((f2(c2) = c4) | big_f(c2, f2(c2)) | (~big_f(f3(f2(c2), f2(c2)), f2(c2))) | (~(f3(f2(c2), f2(c2)) = f2(c2)))),
% 27.44/17.65 inference(unit_resolution,[status(thm)],[1409, 1398, 1335])).
% 27.44/17.65 tff(1411,plain,
% 27.44/17.65 (~(f3(f2(c2), f2(c2)) = f2(c2))),
% 27.44/17.65 inference(unit_resolution,[status(thm)],[1410, 1388, 1384, 1375])).
% 27.44/17.65 tff(1412,plain,
% 27.44/17.65 (~(f3(c1, c1) = c1)),
% 27.44/17.65 inference(modus_ponens,[status(thm)],[1411, 1371])).
% 27.44/17.65 tff(1413,plain,
% 27.44/17.65 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f3(c1, c1) = c1) | (f3(c1, c1) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f3(c1, c1) = c1) | (f3(c1, c1) = c2))),
% 27.44/17.65 inference(rewrite,[status(thm)],[])).
% 27.44/17.65 tff(1414,plain,
% 27.44/17.65 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f3(c1, c1) = c1) | (f3(c1, c1) = c2))),
% 27.44/17.65 inference(quant_inst,[status(thm)],[])).
% 27.44/17.65 tff(1415,plain,
% 27.44/17.65 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f3(c1, c1) = c1) | (f3(c1, c1) = c2)),
% 27.44/17.65 inference(modus_ponens,[status(thm)],[1414, 1413])).
% 27.44/17.65 tff(1416,plain,
% 27.44/17.65 ((f3(c1, c1) = c1) | (f3(c1, c1) = c2)),
% 27.44/17.65 inference(unit_resolution,[status(thm)],[1415, 10])).
% 27.44/17.65 tff(1417,plain,
% 27.44/17.65 (f3(c1, c1) = c2),
% 27.44/17.65 inference(unit_resolution,[status(thm)],[1416, 1412])).
% 27.44/17.65 tff(1418,plain,
% 27.44/17.65 (f3(c1, c1) = c3),
% 27.44/17.65 inference(transitivity,[status(thm)],[1417, 69])).
% 27.44/17.65 tff(1419,plain,
% 27.44/17.65 (big_f(f3(c1, c1), c1) <=> big_f(c3, f2(c3))),
% 27.44/17.65 inference(monotonicity,[status(thm)],[1418, 1367])).
% 27.44/17.65 tff(1420,plain,
% 27.44/17.65 (big_f(c3, f2(c3)) <=> big_f(f3(c1, c1), c1)),
% 27.44/17.65 inference(symmetry,[status(thm)],[1419])).
% 27.44/17.65 tff(1421,plain,
% 27.44/17.65 ((~big_f(c3, f2(c3))) <=> (~big_f(f3(c1, c1), c1))),
% 27.44/17.65 inference(monotonicity,[status(thm)],[1420])).
% 27.44/17.65 tff(1422,plain,
% 27.44/17.65 (~big_f(f3(c1, c1), c1)),
% 27.44/17.65 inference(modus_ponens,[status(thm)],[1286, 1421])).
% 27.44/17.65 tff(1423,plain,
% 27.44/17.65 ($false),
% 27.44/17.65 inference(unit_resolution,[status(thm)],[1387, 1422])).
% 27.44/17.65 tff(1424,plain,((~big_f(f3(c1, c1), c1)) | big_f(c3, f2(c3)) | (~(f2(c3) = c1)) | (~(c3 = c2)) | (~(c4 = c2))), inference(lemma,lemma(discharge,[]))).
% 27.44/17.65 tff(1425,plain,
% 27.44/17.65 (~big_f(f3(c1, c1), c1)),
% 27.44/17.65 inference(unit_resolution,[status(thm)],[1424, 1327, 1286, 67, 1290])).
% 27.44/17.65 tff(1426,plain,
% 27.44/17.65 (f2(c2) = f2(c3)),
% 27.44/17.65 inference(monotonicity,[status(thm)],[69])).
% 27.44/17.65 tff(1427,plain,
% 27.44/17.65 (f2(c2) = c1),
% 27.44/17.65 inference(transitivity,[status(thm)],[1426, 1247])).
% 27.44/17.65 tff(1428,plain,
% 27.44/17.65 (big_f(f7(c2), f2(c2)) <=> big_f(f7(c2), c1)),
% 27.44/17.65 inference(monotonicity,[status(thm)],[1427])).
% 27.44/17.65 tff(1429,plain,
% 27.44/17.65 (big_f(f7(c2), c1) <=> big_f(f7(c2), f2(c2))),
% 27.44/17.65 inference(symmetry,[status(thm)],[1428])).
% 27.44/17.65 tff(1430,assumption,(~big_f(f3(c1, c1), c1)), introduced(assumption)).
% 27.44/17.65 tff(1431,assumption,(~(f3(c1, c1) = c1)), introduced(assumption)).
% 27.44/17.65 tff(1432,plain,
% 27.44/17.65 ((c2 = f2(c2)) <=> (c2 = f2(c3))),
% 27.44/17.65 inference(monotonicity,[status(thm)],[1426])).
% 27.44/17.65 tff(1433,plain,
% 27.44/17.65 ((c2 = f2(c3)) <=> (c2 = f2(c2))),
% 27.44/17.65 inference(symmetry,[status(thm)],[1432])).
% 27.44/17.65 tff(1434,plain,
% 27.44/17.65 ((f2(c3) = c2) <=> (c2 = f2(c3))),
% 27.44/17.65 inference(commutativity,[status(thm)],[])).
% 27.44/17.65 tff(1435,plain,
% 27.44/17.65 ((f2(c3) = c2) <=> (c2 = f2(c2))),
% 27.44/17.65 inference(transitivity,[status(thm)],[1434, 1433])).
% 27.44/17.65 tff(1436,plain,
% 27.44/17.65 ((c1 = f2(c3)) <=> (f2(c3) = c1)),
% 27.44/17.65 inference(commutativity,[status(thm)],[])).
% 27.44/17.65 tff(1437,plain,
% 27.44/17.65 ((c1 = f2(c2)) <=> (c1 = f2(c3))),
% 27.44/17.65 inference(monotonicity,[status(thm)],[1426])).
% 27.44/17.65 tff(1438,plain,
% 27.44/17.65 ((c1 = f2(c2)) <=> (f2(c3) = c1)),
% 27.44/17.65 inference(transitivity,[status(thm)],[1437, 1436])).
% 27.44/17.65 tff(1439,plain,
% 27.44/17.65 ((~(c1 = f2(c2))) <=> (~(f2(c3) = c1))),
% 27.44/17.65 inference(monotonicity,[status(thm)],[1438])).
% 27.44/17.65 tff(1440,plain,
% 27.44/17.65 (f3(c1, c1) = c2),
% 27.44/17.65 inference(unit_resolution,[status(thm)],[1416, 1431])).
% 27.44/17.65 tff(1441,assumption,(f3(c1, c1) = c2), introduced(assumption)).
% 27.44/17.65 tff(1442,plain,
% 27.44/17.65 (c2 = f3(c1, c1)),
% 27.44/17.65 inference(symmetry,[status(thm)],[1441])).
% 27.44/17.65 tff(1443,plain,
% 27.44/17.65 (big_f(c2, c1) <=> big_f(f3(c1, c1), c1)),
% 27.44/17.65 inference(monotonicity,[status(thm)],[1442])).
% 27.44/17.65 tff(1444,plain,
% 27.44/17.65 (big_f(f3(c1, c1), c1) <=> big_f(c2, c1)),
% 27.44/17.65 inference(symmetry,[status(thm)],[1443])).
% 27.44/17.65 tff(1445,plain,
% 27.44/17.65 ((~big_f(f3(c1, c1), c1)) <=> (~big_f(c2, c1))),
% 27.44/17.65 inference(monotonicity,[status(thm)],[1444])).
% 27.44/17.65 tff(1446,plain,
% 27.44/17.65 (~big_f(c2, c1)),
% 27.44/17.65 inference(modus_ponens,[status(thm)],[1430, 1445])).
% 27.44/17.65 tff(1447,plain,
% 27.44/17.65 ($false),
% 27.44/17.65 inference(unit_resolution,[status(thm)],[348, 1446])).
% 27.44/17.65 tff(1448,plain,((~big_f(c2, c1)) | big_f(f3(c1, c1), c1) | (~(f3(c1, c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.44/17.65 tff(1449,plain,
% 27.44/17.65 (~big_f(c2, c1)),
% 27.44/17.65 inference(unit_resolution,[status(thm)],[1448, 1440, 1430])).
% 27.44/17.65 tff(1450,plain,
% 27.44/17.65 (^[X12: $i, X13: $i, X10: $i, X2: $i] : refl(((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12)) <=> ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12)))),
% 27.44/17.65 inference(bind,[status(th)],[])).
% 27.44/17.65 tff(1451,plain,
% 27.44/17.65 (![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12)) <=> ![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))),
% 27.44/17.65 inference(quant_intro,[status(thm)],[1450])).
% 27.44/17.65 tff(1452,plain,
% 27.44/17.65 (![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12)) <=> ![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))),
% 27.44/17.65 inference(rewrite,[status(thm)],[])).
% 27.44/17.65 tff(1453,plain,
% 27.44/17.65 (^[X12: $i, X13: $i, X10: $i, X2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((big_f(X10, X12) | (~(X12 = f2(X10)))) <=> ((~(X12 = f2(X10))) | big_f(X10, X12))), (((big_f(X10, X12) | (~(X12 = f2(X10)))) | (~(X10 = c3))) <=> (((~(X12 = f2(X10))) | big_f(X10, X12)) | (~(X10 = c3))))), rewrite((((~(X12 = f2(X10))) | big_f(X10, X12)) | (~(X10 = c3))) <=> ((~(X10 = c3)) | (~(X12 = f2(X10))) | big_f(X10, X12))), (((big_f(X10, X12) | (~(X12 = f2(X10)))) | (~(X10 = c3))) <=> ((~(X10 = c3)) | (~(X12 = f2(X10))) | big_f(X10, X12)))), ((((big_f(X10, X12) | (~(X12 = f2(X10)))) | (~(X10 = c3))) | big_f(f3(X2, X13), X2)) <=> (((~(X10 = c3)) | (~(X12 = f2(X10))) | big_f(X10, X12)) | big_f(f3(X2, X13), X2)))), rewrite((((~(X10 = c3)) | (~(X12 = f2(X10))) | big_f(X10, X12)) | big_f(f3(X2, X13), X2)) <=> ((~(X10 = c3)) | (~(X12 = f2(X10))) | big_f(f3(X2, X13), X2) | big_f(X10, X12))), ((((big_f(X10, X12) | (~(X12 = f2(X10)))) | (~(X10 = c3))) | big_f(f3(X2, X13), X2)) <=> ((~(X10 = c3)) | (~(X12 = f2(X10))) | big_f(f3(X2, X13), X2) | big_f(X10, X12)))), (((((big_f(X10, X12) | (~(X12 = f2(X10)))) | (~(X10 = c3))) | big_f(f3(X2, X13), X2)) | (f3(X2, X13) = X13)) <=> (((~(X10 = c3)) | (~(X12 = f2(X10))) | big_f(f3(X2, X13), X2) | big_f(X10, X12)) | (f3(X2, X13) = X13)))), rewrite((((~(X10 = c3)) | (~(X12 = f2(X10))) | big_f(f3(X2, X13), X2) | big_f(X10, X12)) | (f3(X2, X13) = X13)) <=> ((~(X10 = c3)) | (~(X12 = f2(X10))) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))), (((((big_f(X10, X12) | (~(X12 = f2(X10)))) | (~(X10 = c3))) | big_f(f3(X2, X13), X2)) | (f3(X2, X13) = X13)) <=> ((~(X10 = c3)) | (~(X12 = f2(X10))) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12)))), ((((((big_f(X10, X12) | (~(X12 = f2(X10)))) | (~(X10 = c3))) | big_f(f3(X2, X13), X2)) | (f3(X2, X13) = X13)) | (X2 = c4)) <=> (((~(X10 = c3)) | (~(X12 = f2(X10))) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12)) | (X2 = c4)))), rewrite((((~(X10 = c3)) | (~(X12 = f2(X10))) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12)) | (X2 = c4)) <=> ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))), ((((((big_f(X10, X12) | (~(X12 = f2(X10)))) | (~(X10 = c3))) | big_f(f3(X2, X13), X2)) | (f3(X2, X13) = X13)) | (X2 = c4)) <=> ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))))),
% 27.44/17.65 inference(bind,[status(th)],[])).
% 27.44/17.65 tff(1454,plain,
% 27.44/17.65 (![X12: $i, X13: $i, X10: $i, X2: $i] : (((((big_f(X10, X12) | (~(X12 = f2(X10)))) | (~(X10 = c3))) | big_f(f3(X2, X13), X2)) | (f3(X2, X13) = X13)) | (X2 = c4)) <=> ![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))),
% 27.44/17.65 inference(quant_intro,[status(thm)],[1453])).
% 27.44/17.65 tff(1455,axiom,(![X12: $i, X13: $i, X10: $i, X2: $i] : (((((big_f(X10, X12) | (~(X12 = f2(X10)))) | (~(X10 = c3))) | big_f(f3(X2, X13), X2)) | (f3(X2, X13) = X13)) | (X2 = c4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_15')).
% 27.44/17.65 tff(1456,plain,
% 27.44/17.65 (![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))),
% 27.44/17.65 inference(modus_ponens,[status(thm)],[1455, 1454])).
% 27.44/17.65 tff(1457,plain,
% 27.44/17.65 (![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))),
% 27.44/17.65 inference(modus_ponens,[status(thm)],[1456, 1452])).
% 27.44/17.65 tff(1458,plain,(
% 27.44/17.65 ![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))),
% 27.44/17.65 inference(skolemize,[status(sab)],[1457])).
% 27.44/17.65 tff(1459,plain,
% 27.44/17.65 (![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))),
% 27.44/17.65 inference(modus_ponens,[status(thm)],[1458, 1451])).
% 27.44/17.65 tff(1460,plain,
% 27.44/17.65 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (big_f(f3(c1, c1), c1) | (f3(c1, c1) = c1) | (~(c2 = c3)) | (c1 = c4) | big_f(c2, c1) | (~(c1 = f2(c2))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | big_f(f3(c1, c1), c1) | (f3(c1, c1) = c1) | (~(c2 = c3)) | (c1 = c4) | big_f(c2, c1) | (~(c1 = f2(c2))))),
% 27.44/17.65 inference(rewrite,[status(thm)],[])).
% 27.44/17.65 tff(1461,plain,
% 27.44/17.65 (((~(c2 = c3)) | (~(c1 = f2(c2))) | (c1 = c4) | (f3(c1, c1) = c1) | big_f(f3(c1, c1), c1) | big_f(c2, c1)) <=> (big_f(f3(c1, c1), c1) | (f3(c1, c1) = c1) | (~(c2 = c3)) | (c1 = c4) | big_f(c2, c1) | (~(c1 = f2(c2))))),
% 27.44/17.65 inference(rewrite,[status(thm)],[])).
% 27.44/17.65 tff(1462,plain,
% 27.44/17.65 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c1 = f2(c2))) | (c1 = c4) | (f3(c1, c1) = c1) | big_f(f3(c1, c1), c1) | big_f(c2, c1))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (big_f(f3(c1, c1), c1) | (f3(c1, c1) = c1) | (~(c2 = c3)) | (c1 = c4) | big_f(c2, c1) | (~(c1 = f2(c2)))))),
% 27.44/17.65 inference(monotonicity,[status(thm)],[1461])).
% 27.44/17.65 tff(1463,plain,
% 27.44/17.65 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c1 = f2(c2))) | (c1 = c4) | (f3(c1, c1) = c1) | big_f(f3(c1, c1), c1) | big_f(c2, c1))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | big_f(f3(c1, c1), c1) | (f3(c1, c1) = c1) | (~(c2 = c3)) | (c1 = c4) | big_f(c2, c1) | (~(c1 = f2(c2))))),
% 27.44/17.65 inference(transitivity,[status(thm)],[1462, 1460])).
% 27.44/17.65 tff(1464,plain,
% 27.44/17.65 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c1 = f2(c2))) | (c1 = c4) | (f3(c1, c1) = c1) | big_f(f3(c1, c1), c1) | big_f(c2, c1))),
% 27.44/17.65 inference(quant_inst,[status(thm)],[])).
% 27.44/17.65 tff(1465,plain,
% 27.44/17.65 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | big_f(f3(c1, c1), c1) | (f3(c1, c1) = c1) | (~(c2 = c3)) | (c1 = c4) | big_f(c2, c1) | (~(c1 = f2(c2)))),
% 27.44/17.65 inference(modus_ponens,[status(thm)],[1464, 1463])).
% 27.44/17.65 tff(1466,plain,
% 27.44/17.65 ((c1 = c4) | (~(c1 = f2(c2)))),
% 27.44/17.65 inference(unit_resolution,[status(thm)],[1465, 1459, 1430, 1431, 1335, 1449])).
% 27.44/17.65 tff(1467,plain,
% 27.44/17.65 (~(c1 = f2(c2))),
% 27.44/17.65 inference(unit_resolution,[status(thm)],[1466, 482])).
% 27.44/17.65 tff(1468,plain,
% 27.44/17.65 (~(f2(c3) = c1)),
% 27.44/17.65 inference(modus_ponens,[status(thm)],[1467, 1439])).
% 27.44/17.65 tff(1469,plain,
% 27.44/17.65 (f2(c3) = c2),
% 27.44/17.65 inference(unit_resolution,[status(thm)],[1273, 1468])).
% 27.44/17.65 tff(1470,plain,
% 27.44/17.65 (c2 = f2(c2)),
% 27.44/17.65 inference(modus_ponens,[status(thm)],[1469, 1435])).
% 27.44/17.65 tff(1471,plain,
% 27.44/17.65 (big_f(c3, f2(c3)) <=> big_f(c2, c2)),
% 27.44/17.65 inference(monotonicity,[status(thm)],[67, 1469])).
% 27.44/17.65 tff(1472,plain,
% 27.44/17.65 ((~big_f(c3, f2(c3))) <=> (~big_f(c2, c2))),
% 27.44/17.65 inference(monotonicity,[status(thm)],[1471])).
% 27.44/17.65 tff(1473,plain,
% 27.44/17.65 (~big_f(c2, c2)),
% 27.44/17.65 inference(modus_ponens,[status(thm)],[1286, 1472])).
% 27.44/17.65 tff(1474,plain,
% 27.44/17.65 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (big_f(f3(c1, c1), c1) | (f3(c1, c1) = c1) | (~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (c1 = c4))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | big_f(f3(c1, c1), c1) | (f3(c1, c1) = c1) | (~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (c1 = c4))),
% 27.44/17.65 inference(rewrite,[status(thm)],[])).
% 27.44/17.65 tff(1475,plain,
% 27.44/17.65 (((~(c2 = c3)) | (~(c2 = f2(c2))) | (c1 = c4) | (f3(c1, c1) = c1) | big_f(f3(c1, c1), c1) | big_f(c2, c2)) <=> (big_f(f3(c1, c1), c1) | (f3(c1, c1) = c1) | (~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (c1 = c4))),
% 27.44/17.65 inference(rewrite,[status(thm)],[])).
% 27.44/17.65 tff(1476,plain,
% 27.44/17.65 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | (c1 = c4) | (f3(c1, c1) = c1) | big_f(f3(c1, c1), c1) | big_f(c2, c2))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (big_f(f3(c1, c1), c1) | (f3(c1, c1) = c1) | (~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (c1 = c4)))),
% 27.44/17.65 inference(monotonicity,[status(thm)],[1475])).
% 27.44/17.65 tff(1477,plain,
% 27.44/17.65 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | (c1 = c4) | (f3(c1, c1) = c1) | big_f(f3(c1, c1), c1) | big_f(c2, c2))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | big_f(f3(c1, c1), c1) | (f3(c1, c1) = c1) | (~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (c1 = c4))),
% 27.44/17.65 inference(transitivity,[status(thm)],[1476, 1474])).
% 27.44/17.65 tff(1478,plain,
% 27.44/17.65 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | (c1 = c4) | (f3(c1, c1) = c1) | big_f(f3(c1, c1), c1) | big_f(c2, c2))),
% 27.44/17.65 inference(quant_inst,[status(thm)],[])).
% 27.44/17.65 tff(1479,plain,
% 27.44/17.65 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | big_f(f3(c1, c1), c1) | (f3(c1, c1) = c1) | (~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (c1 = c4)),
% 27.44/17.65 inference(modus_ponens,[status(thm)],[1478, 1477])).
% 27.44/17.65 tff(1480,plain,
% 27.44/17.65 (big_f(f3(c1, c1), c1) | (f3(c1, c1) = c1) | (~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (c1 = c4)),
% 27.44/17.65 inference(unit_resolution,[status(thm)],[1479, 1459])).
% 27.44/17.65 tff(1481,plain,
% 27.44/17.65 ($false),
% 27.44/17.65 inference(unit_resolution,[status(thm)],[1480, 1473, 1470, 1431, 1430, 482, 1335])).
% 27.44/17.65 tff(1482,plain,((c1 = c4) | (f3(c1, c1) = c1) | big_f(f3(c1, c1), c1) | big_f(c3, f2(c3)) | (~(c3 = c2))), inference(lemma,lemma(discharge,[]))).
% 27.44/17.65 tff(1483,plain,
% 27.44/17.65 (f3(c1, c1) = c1),
% 27.44/17.65 inference(unit_resolution,[status(thm)],[1482, 1430, 482, 1286, 67])).
% 27.44/17.65 tff(1484,plain,
% 27.44/17.65 (f3(c1, c1) = f7(c2)),
% 27.44/17.65 inference(transitivity,[status(thm)],[1483, 342])).
% 27.44/17.65 tff(1485,plain,
% 27.44/17.65 (big_f(f3(c1, c1), c1) <=> big_f(f7(c2), c1)),
% 27.44/17.65 inference(monotonicity,[status(thm)],[1484])).
% 27.44/17.65 tff(1486,plain,
% 27.44/17.65 (big_f(f3(c1, c1), c1) <=> big_f(f7(c2), f2(c2))),
% 27.44/17.65 inference(transitivity,[status(thm)],[1485, 1429])).
% 27.44/17.65 tff(1487,plain,
% 27.44/17.65 ((~big_f(f3(c1, c1), c1)) <=> (~big_f(f7(c2), f2(c2)))),
% 27.44/17.65 inference(monotonicity,[status(thm)],[1486])).
% 27.44/17.65 tff(1488,plain,
% 27.44/17.65 (~big_f(f7(c2), f2(c2))),
% 27.44/17.65 inference(modus_ponens,[status(thm)],[1430, 1487])).
% 27.44/17.65 tff(1489,assumption,(big_f(f7(c2), f2(c2))), introduced(assumption)).
% 27.44/17.65 tff(1490,plain,
% 27.44/17.65 ($false),
% 27.44/17.65 inference(unit_resolution,[status(thm)],[1489, 1488])).
% 27.44/17.65 tff(1491,plain,(big_f(f3(c1, c1), c1) | (~big_f(f7(c2), f2(c2))) | (~(f2(c3) = c1)) | (~(c3 = c2)) | (~(f7(c2) = c1)) | (c1 = c4) | big_f(c3, f2(c3))), inference(lemma,lemma(discharge,[]))).
% 27.44/17.65 tff(1492,plain,
% 27.44/17.65 (~big_f(f7(c2), f2(c2))),
% 27.44/17.65 inference(unit_resolution,[status(thm)],[1491, 22, 1327, 67, 1425, 482, 1286])).
% 27.44/17.65 tff(1493,plain,
% 27.44/17.65 (f4(c4) = f10(c2)),
% 27.44/17.65 inference(transitivity,[status(thm)],[79, 216])).
% 27.44/17.65 tff(1494,plain,
% 27.44/17.65 (f9(f10(c2), f4(c4)) = f9(f10(c2), f10(c2))),
% 27.44/17.66 inference(monotonicity,[status(thm)],[1493])).
% 27.44/17.66 tff(1495,plain,
% 27.44/17.66 (f9(f10(c2), f10(c2)) = f9(f10(c2), f4(c4))),
% 27.44/17.66 inference(symmetry,[status(thm)],[1494])).
% 27.44/17.66 tff(1496,plain,
% 27.44/17.66 ((f9(f10(c2), f10(c2)) = f10(c2)) <=> (f9(f10(c2), f4(c4)) = c2)),
% 27.44/17.66 inference(monotonicity,[status(thm)],[1495, 122])).
% 27.44/17.66 tff(1497,plain,
% 27.44/17.66 ((f9(f10(c2), f4(c4)) = c2) <=> (f9(f10(c2), f10(c2)) = f10(c2))),
% 27.44/17.66 inference(symmetry,[status(thm)],[1496])).
% 27.44/17.66 tff(1498,assumption,(f9(f10(c2), f4(c4)) = c2), introduced(assumption)).
% 27.44/17.66 tff(1499,plain,
% 27.44/17.66 (f9(f10(c2), f10(c2)) = f10(c2)),
% 27.44/17.66 inference(modus_ponens,[status(thm)],[1498, 1497])).
% 27.44/17.66 tff(1500,plain,
% 27.44/17.66 ($false),
% 27.44/17.66 inference(unit_resolution,[status(thm)],[158, 1499])).
% 27.44/17.66 tff(1501,plain,((~(f9(f10(c2), f4(c4)) = c2)) | (f9(f10(c2), f10(c2)) = f10(c2)) | (~(f10(c2) = c2)) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.44/17.66 tff(1502,plain,
% 27.44/17.66 (~(f9(f10(c2), f4(c4)) = c2)),
% 27.44/17.66 inference(unit_resolution,[status(thm)],[1501, 158, 122, 79])).
% 27.44/17.66 tff(1503,plain,
% 27.44/17.66 (f9(f10(c2), f4(c4)) = c1),
% 27.44/17.66 inference(unit_resolution,[status(thm)],[146, 1502])).
% 27.44/17.66 tff(1504,plain,
% 27.44/17.66 (f10(c2) = f4(c4)),
% 27.44/17.66 inference(transitivity,[status(thm)],[122, 436])).
% 27.44/17.66 tff(1505,plain,
% 27.44/17.66 (f9(f10(c2), f10(c2)) = f9(f10(c2), f4(c4))),
% 27.44/17.66 inference(monotonicity,[status(thm)],[1504])).
% 27.44/17.66 tff(1506,plain,
% 27.44/17.66 (f9(f10(c2), f10(c2)) = c1),
% 27.44/17.66 inference(transitivity,[status(thm)],[1505, 1503])).
% 27.44/17.66 tff(1507,plain,
% 27.44/17.66 (big_f(f9(f10(c2), f10(c2)), f10(f10(c2))) <=> big_f(c1, c2)),
% 27.44/17.66 inference(monotonicity,[status(thm)],[1506, 251])).
% 27.44/17.66 tff(1508,plain,
% 27.44/17.66 (big_f(c1, c2) <=> big_f(f9(f10(c2), f10(c2)), f10(f10(c2)))),
% 27.44/17.66 inference(symmetry,[status(thm)],[1507])).
% 27.44/17.66 tff(1509,plain,
% 27.44/17.66 ((~big_f(c1, c2)) <=> (~big_f(f9(f10(c2), f10(c2)), f10(f10(c2))))),
% 27.44/17.66 inference(monotonicity,[status(thm)],[1508])).
% 27.44/17.66 tff(1510,plain,
% 27.44/17.66 (~big_f(f9(f10(c2), f10(c2)), f10(f10(c2)))),
% 27.44/17.66 inference(modus_ponens,[status(thm)],[27, 1509])).
% 27.44/17.66 tff(1511,plain,
% 27.44/17.66 ((~big_f(c1, c2)) <=> (~big_f(f7(c2), c2))),
% 27.44/17.66 inference(monotonicity,[status(thm)],[126])).
% 27.44/17.66 tff(1512,plain,
% 27.44/17.66 (~big_f(f7(c2), c2)),
% 27.44/17.66 inference(modus_ponens,[status(thm)],[27, 1511])).
% 27.44/17.66 tff(1513,assumption,(~big_f(f7(c2), f2(c2))), introduced(assumption)).
% 27.44/17.66 tff(1514,plain,
% 27.44/17.66 ((~big_f(f9(f10(c2), f10(c2)), f10(f10(c2)))) <=> (~big_f(f9(c2, c2), f10(c2)))),
% 27.44/17.66 inference(monotonicity,[status(thm)],[1285])).
% 27.44/17.66 tff(1515,assumption,(~big_f(f9(f10(c2), f10(c2)), f10(f10(c2)))), introduced(assumption)).
% 27.44/17.66 tff(1516,plain,
% 27.44/17.66 (~big_f(f9(c2, c2), f10(c2))),
% 27.44/17.66 inference(modus_ponens,[status(thm)],[1515, 1514])).
% 27.44/17.66 tff(1517,plain,
% 27.44/17.66 ((f9(c2, c2) = c2) <=> (f9(f10(c2), f10(c2)) = f10(c2))),
% 27.44/17.66 inference(monotonicity,[status(thm)],[1283, 216])).
% 27.44/17.66 tff(1518,plain,
% 27.44/17.66 ((f9(f10(c2), f10(c2)) = f10(c2)) <=> (f9(c2, c2) = c2)),
% 27.44/17.66 inference(symmetry,[status(thm)],[1517])).
% 27.44/17.66 tff(1519,plain,
% 27.44/17.66 ((~(f9(f10(c2), f10(c2)) = f10(c2))) <=> (~(f9(c2, c2) = c2))),
% 27.44/17.66 inference(monotonicity,[status(thm)],[1518])).
% 27.44/17.66 tff(1520,plain,
% 27.44/17.66 (~(f9(c2, c2) = c2)),
% 27.44/17.66 inference(modus_ponens,[status(thm)],[158, 1519])).
% 27.44/17.66 tff(1521,assumption,(~big_f(f7(c2), c2)), introduced(assumption)).
% 27.44/17.66 tff(1522,plain,
% 27.44/17.66 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)))),
% 27.44/17.66 inference(rewrite,[status(thm)],[])).
% 27.44/17.66 tff(1523,plain,
% 27.44/17.66 (((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(c2 = f5(c2)))) <=> ((~(f10(c2) = c2)) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)))),
% 27.44/17.66 inference(rewrite,[status(thm)],[])).
% 27.44/17.66 tff(1524,plain,
% 27.44/17.66 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(c2 = f5(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2))))),
% 27.44/17.66 inference(monotonicity,[status(thm)],[1523])).
% 27.44/17.66 tff(1525,plain,
% 27.44/17.66 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(c2 = f5(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)))),
% 27.44/17.66 inference(transitivity,[status(thm)],[1524, 1522])).
% 27.44/17.66 tff(1526,plain,
% 27.44/17.66 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(c2 = f5(c2))))),
% 27.44/17.66 inference(quant_inst,[status(thm)],[])).
% 27.44/17.66 tff(1527,plain,
% 27.44/17.66 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2))),
% 27.44/17.66 inference(modus_ponens,[status(thm)],[1526, 1525])).
% 27.44/17.66 tff(1528,plain,
% 27.44/17.66 ((~(c2 = f5(c2))) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2))),
% 27.44/17.66 inference(unit_resolution,[status(thm)],[1527, 267, 122, 17, 1521])).
% 27.44/17.66 tff(1529,plain,
% 27.44/17.66 (~(c2 = f5(c2))),
% 27.44/17.66 inference(unit_resolution,[status(thm)],[1528, 1520, 1516])).
% 27.44/17.66 tff(1530,plain,
% 27.44/17.66 (~(f5(c2) = c2)),
% 27.44/17.66 inference(modus_ponens,[status(thm)],[1529, 1281])).
% 27.44/17.66 tff(1531,plain,
% 27.44/17.66 ((c1 = f5(c2)) <=> (f5(c2) = c1)),
% 27.44/17.66 inference(commutativity,[status(thm)],[])).
% 27.44/17.66 tff(1532,plain,
% 27.44/17.66 ((f2(c2) = f5(c2)) <=> (c1 = f5(c2))),
% 27.44/17.66 inference(monotonicity,[status(thm)],[1368])).
% 27.44/17.66 tff(1533,plain,
% 27.44/17.66 ((f2(c2) = f5(c2)) <=> (f5(c2) = c1)),
% 27.44/17.66 inference(transitivity,[status(thm)],[1532, 1531])).
% 27.44/17.66 tff(1534,plain,
% 27.44/17.66 ((~(f2(c2) = f5(c2))) <=> (~(f5(c2) = c1))),
% 27.44/17.66 inference(monotonicity,[status(thm)],[1533])).
% 27.44/17.66 tff(1535,plain,
% 27.44/17.66 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f7(c2), f2(c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f2(c2) = f5(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f7(c2), f2(c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f2(c2) = f5(c2))))),
% 27.44/17.66 inference(rewrite,[status(thm)],[])).
% 27.44/17.66 tff(1536,plain,
% 27.44/17.66 (((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), f2(c2)) | (~(f2(c2) = f5(c2)))) <=> ((~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f7(c2), f2(c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f2(c2) = f5(c2))))),
% 27.44/17.66 inference(rewrite,[status(thm)],[])).
% 27.44/17.66 tff(1537,plain,
% 27.44/17.66 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), f2(c2)) | (~(f2(c2) = f5(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f7(c2), f2(c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f2(c2) = f5(c2)))))),
% 27.44/17.66 inference(monotonicity,[status(thm)],[1536])).
% 27.44/17.66 tff(1538,plain,
% 27.44/17.66 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), f2(c2)) | (~(f2(c2) = f5(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f7(c2), f2(c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f2(c2) = f5(c2))))),
% 27.44/17.66 inference(transitivity,[status(thm)],[1537, 1535])).
% 27.44/17.66 tff(1539,plain,
% 27.44/17.66 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), f2(c2)) | (~(f2(c2) = f5(c2))))),
% 27.44/17.66 inference(quant_inst,[status(thm)],[])).
% 27.44/17.66 tff(1540,plain,
% 27.44/17.66 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f7(c2), f2(c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f2(c2) = f5(c2)))),
% 27.44/17.66 inference(modus_ponens,[status(thm)],[1539, 1538])).
% 27.44/17.66 tff(1541,plain,
% 27.44/17.66 (big_f(f7(c2), f2(c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f2(c2) = f5(c2)))),
% 27.44/17.66 inference(unit_resolution,[status(thm)],[1540, 267, 122, 17])).
% 27.44/17.66 tff(1542,plain,
% 27.44/17.66 (~(f2(c2) = f5(c2))),
% 27.44/17.66 inference(unit_resolution,[status(thm)],[1541, 1520, 1516, 1513])).
% 27.44/17.66 tff(1543,plain,
% 27.44/17.66 (~(f5(c2) = c1)),
% 27.44/17.66 inference(modus_ponens,[status(thm)],[1542, 1534])).
% 27.44/17.66 tff(1544,plain,
% 27.44/17.66 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f5(c2) = c1) | (f5(c2) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f5(c2) = c1) | (f5(c2) = c2))),
% 27.44/17.66 inference(rewrite,[status(thm)],[])).
% 27.44/17.66 tff(1545,plain,
% 27.44/17.66 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f5(c2) = c1) | (f5(c2) = c2))),
% 27.44/17.66 inference(quant_inst,[status(thm)],[])).
% 27.44/17.66 tff(1546,plain,
% 27.44/17.66 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f5(c2) = c1) | (f5(c2) = c2)),
% 27.44/17.66 inference(modus_ponens,[status(thm)],[1545, 1544])).
% 27.44/17.66 tff(1547,plain,
% 27.44/17.66 ((f5(c2) = c1) | (f5(c2) = c2)),
% 27.44/17.66 inference(unit_resolution,[status(thm)],[1546, 10])).
% 27.44/17.66 tff(1548,plain,
% 27.44/17.66 ($false),
% 27.44/17.66 inference(unit_resolution,[status(thm)],[1547, 1543, 1530])).
% 27.44/17.66 tff(1549,plain,(big_f(f7(c2), f2(c2)) | (~(f2(c3) = c1)) | (~(c3 = c2)) | (~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f7(c2), c2) | big_f(f9(f10(c2), f10(c2)), f10(f10(c2))) | (f9(f10(c2), f10(c2)) = f10(c2))), inference(lemma,lemma(discharge,[]))).
% 27.44/17.66 tff(1550,plain,
% 27.44/17.66 (big_f(f9(f10(c2), f10(c2)), f10(f10(c2)))),
% 27.44/17.66 inference(unit_resolution,[status(thm)],[1549, 158, 67, 122, 1513, 17, 1512, 1247])).
% 27.44/17.66 tff(1551,plain,
% 27.44/17.66 ($false),
% 27.44/17.66 inference(unit_resolution,[status(thm)],[1550, 1510])).
% 27.44/17.66 tff(1552,plain,((f9(f10(c2), f10(c2)) = f10(c2)) | big_f(c1, c2) | (~(f10(c2) = c2)) | (~(f4(c4) = c2)) | (~(c3 = c2)) | big_f(f7(c2), f2(c2)) | (f7(c2) = c2) | (~(f2(c3) = c1))), inference(lemma,lemma(discharge,[]))).
% 27.44/17.66 tff(1553,plain,
% 27.44/17.66 (f9(f10(c2), f10(c2)) = f10(c2)),
% 27.44/17.66 inference(unit_resolution,[status(thm)],[1552, 1492, 122, 79, 67, 1366, 17, 1327])).
% 27.44/17.66 tff(1554,plain,
% 27.44/17.66 (f9(f10(c2), f10(c2)) = c2),
% 27.44/17.66 inference(transitivity,[status(thm)],[1553, 122])).
% 27.44/17.66 tff(1555,plain,
% 27.44/17.66 (big_f(f9(f10(c2), f10(c2)), f10(f10(c2))) <=> big_f(c2, c2)),
% 27.44/17.66 inference(monotonicity,[status(thm)],[1554, 251])).
% 27.44/17.66 tff(1556,plain,
% 27.44/17.66 (big_f(c2, c2) <=> big_f(f9(f10(c2), f10(c2)), f10(f10(c2)))),
% 27.44/17.66 inference(symmetry,[status(thm)],[1555])).
% 27.44/17.66 tff(1557,plain,
% 27.44/17.66 (big_f(c2, c2) <=> big_f(f9(c2, c2), f10(c2))),
% 27.44/17.66 inference(transitivity,[status(thm)],[1556, 1285])).
% 27.44/17.66 tff(1558,plain,
% 27.44/17.66 (big_f(f9(c2, c2), f10(c2))),
% 27.44/17.66 inference(modus_ponens,[status(thm)],[1317, 1557])).
% 27.44/17.66 tff(1559,plain,
% 27.44/17.66 (f9(c2, c2) = c2),
% 27.44/17.66 inference(modus_ponens,[status(thm)],[1553, 1518])).
% 27.44/17.66 tff(1560,plain,
% 27.44/17.66 (~big_f(f7(c2), c2)),
% 27.44/17.66 inference(modus_ponens,[status(thm)],[1366, 1511])).
% 27.44/17.66 tff(1561,plain,
% 27.44/17.66 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))),
% 27.44/17.66 inference(rewrite,[status(thm)],[])).
% 27.44/17.66 tff(1562,plain,
% 27.44/17.66 (((~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(c2 = f5(c2)))) <=> ((~(f10(c2) = c2)) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))),
% 27.44/17.66 inference(rewrite,[status(thm)],[])).
% 27.44/17.66 tff(1563,plain,
% 27.44/17.66 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(c2 = f5(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2)))))),
% 27.44/17.66 inference(monotonicity,[status(thm)],[1562])).
% 27.44/17.66 tff(1564,plain,
% 27.44/17.66 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(c2 = f5(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))),
% 27.44/17.66 inference(transitivity,[status(thm)],[1563, 1561])).
% 27.44/17.66 tff(1565,plain,
% 27.44/17.66 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(c2 = f5(c2))))),
% 27.44/17.66 inference(quant_inst,[status(thm)],[])).
% 27.44/17.66 tff(1566,plain,
% 27.44/17.66 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2)))),
% 27.44/17.66 inference(modus_ponens,[status(thm)],[1565, 1564])).
% 27.44/17.66 tff(1567,plain,
% 27.44/17.66 (~(c2 = f5(c2))),
% 27.44/17.66 inference(unit_resolution,[status(thm)],[1566, 783, 122, 17, 1560, 1559, 1558])).
% 27.44/17.66 tff(1568,plain,
% 27.44/17.66 (~(f5(c2) = c2)),
% 27.44/17.66 inference(modus_ponens,[status(thm)],[1567, 1281])).
% 27.44/17.66 tff(1569,assumption,(f5(c2) = c1), introduced(assumption)).
% 27.44/17.66 tff(1570,plain,
% 27.44/17.66 (c1 = f5(c2)),
% 27.44/17.66 inference(symmetry,[status(thm)],[1569])).
% 27.44/17.66 tff(1571,plain,
% 27.44/17.66 (f2(c2) = f5(c2)),
% 27.44/17.66 inference(transitivity,[status(thm)],[1231, 1247, 1570])).
% 27.44/17.66 tff(1572,assumption,(f9(c2, c2) = c2), introduced(assumption)).
% 27.44/17.66 tff(1573,plain,
% 27.44/17.66 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f7(c2), f2(c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f2(c2) = f5(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f7(c2), f2(c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f2(c2) = f5(c2))))),
% 27.44/17.66 inference(rewrite,[status(thm)],[])).
% 27.44/17.66 tff(1574,plain,
% 27.44/17.66 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f7(c2), f2(c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f2(c2) = f5(c2))))),
% 27.44/17.66 inference(quant_inst,[status(thm)],[])).
% 27.44/17.66 tff(1575,plain,
% 27.44/17.66 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f7(c2), f2(c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f2(c2) = f5(c2)))),
% 27.44/17.66 inference(modus_ponens,[status(thm)],[1574, 1573])).
% 27.44/17.66 tff(1576,plain,
% 27.44/17.66 ($false),
% 27.44/17.66 inference(unit_resolution,[status(thm)],[1575, 783, 122, 17, 1513, 1572, 690, 1571])).
% 27.44/17.66 tff(1577,plain,(big_f(f7(c2), f2(c2)) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f5(c2) = c1)) | (~(f2(c3) = c1)) | (~(c3 = c2))), inference(lemma,lemma(discharge,[]))).
% 27.44/17.66 tff(1578,plain,
% 27.44/17.66 (~(f5(c2) = c1)),
% 27.44/17.66 inference(unit_resolution,[status(thm)],[1577, 1559, 17, 1492, 1558, 122, 1327, 67])).
% 27.44/17.66 tff(1579,plain,
% 27.44/17.66 (f5(c2) = c2),
% 27.44/17.66 inference(unit_resolution,[status(thm)],[1547, 1578])).
% 27.44/17.66 tff(1580,plain,
% 27.44/17.66 ($false),
% 27.44/17.66 inference(unit_resolution,[status(thm)],[1579, 1568])).
% 27.44/17.66 tff(1581,plain,((f7(c2) = c2) | (~(f10(c2) = c2)) | (~(c3 = c2)) | (~(f4(c4) = c2)) | (c1 = c4) | big_f(c3, f2(c3))), inference(lemma,lemma(discharge,[]))).
% 27.44/17.66 tff(1582,plain,
% 27.44/17.66 (c1 = c4),
% 27.44/17.66 inference(unit_resolution,[status(thm)],[1581, 1278, 122, 79, 17, 1219])).
% 27.44/17.66 tff(1583,plain,
% 27.44/17.66 (f9(c2, c2) = c4),
% 27.44/17.66 inference(modus_ponens,[status(thm)],[1582, 362])).
% 27.44/17.66 tff(1584,plain,
% 27.44/17.66 (f4(c1) = f4(c4)),
% 27.44/17.66 inference(monotonicity,[status(thm)],[1582])).
% 27.44/17.66 tff(1585,plain,
% 27.44/17.66 (f4(c1) = c2),
% 27.44/17.66 inference(transitivity,[status(thm)],[1584, 79])).
% 27.44/17.66 tff(1586,plain,
% 27.44/17.66 ((c1 = f4(c1)) <=> (f9(c2, c2) = c2)),
% 27.44/17.66 inference(monotonicity,[status(thm)],[150, 1585])).
% 27.44/17.66 tff(1587,plain,
% 27.44/17.66 ((f9(c2, c2) = c2) <=> (c1 = f4(c1))),
% 27.44/17.66 inference(symmetry,[status(thm)],[1586])).
% 27.44/17.66 tff(1588,plain,
% 27.44/17.66 ((f9(c2, c2) = c2) <=> (f9(c2, c2) = f4(f9(c2, c2)))),
% 27.44/17.66 inference(transitivity,[status(thm)],[1587, 490])).
% 27.44/17.66 tff(1589,plain,
% 27.44/17.66 ((~(f9(c2, c2) = c2)) <=> (~(f9(c2, c2) = f4(f9(c2, c2))))),
% 27.44/17.66 inference(monotonicity,[status(thm)],[1588])).
% 27.44/17.66 tff(1590,plain,
% 27.44/17.66 (~(f9(c2, c2) = f4(f9(c2, c2)))),
% 27.44/17.66 inference(modus_ponens,[status(thm)],[185, 1589])).
% 27.44/17.66 tff(1591,plain,
% 27.44/17.66 (big_f(c2, f9(c2, c2)) <=> big_f(c2, c1)),
% 27.44/17.66 inference(monotonicity,[status(thm)],[161])).
% 27.44/17.66 tff(1592,plain,
% 27.44/17.66 (big_f(c2, c1) <=> big_f(c2, f9(c2, c2))),
% 27.44/17.66 inference(symmetry,[status(thm)],[1591])).
% 27.44/17.66 tff(1593,plain,
% 27.44/17.66 (big_f(c2, f9(c2, c2))),
% 27.44/17.66 inference(modus_ponens,[status(thm)],[348, 1592])).
% 27.44/17.66 tff(1594,plain,
% 27.44/17.66 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2))) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2))) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)))),
% 27.44/17.67 inference(rewrite,[status(thm)],[])).
% 27.44/17.67 tff(1595,plain,
% 27.44/17.67 (((~(c2 = c3)) | (~(f9(c2, c2) = c4)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2)))) <=> ((~(c2 = c3)) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2))) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)))),
% 27.44/17.67 inference(rewrite,[status(thm)],[])).
% 27.44/17.67 tff(1596,plain,
% 27.44/17.67 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(f9(c2, c2) = c4)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2))) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4))))),
% 27.44/17.67 inference(monotonicity,[status(thm)],[1595])).
% 27.44/17.67 tff(1597,plain,
% 27.44/17.67 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(f9(c2, c2) = c4)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2))) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)))),
% 27.44/17.67 inference(transitivity,[status(thm)],[1596, 1594])).
% 27.44/17.67 tff(1598,plain,
% 27.44/17.67 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(f9(c2, c2) = c4)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2))))),
% 27.44/17.67 inference(quant_inst,[status(thm)],[])).
% 27.44/17.67 tff(1599,plain,
% 27.44/17.67 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2))) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4))),
% 27.44/17.67 inference(modus_ponens,[status(thm)],[1598, 1597])).
% 27.44/17.67 tff(1600,plain,
% 27.44/17.67 ((~(c2 = c3)) | (f9(c2, c2) = f2(c2)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~(f9(c2, c2) = c4))),
% 27.44/17.67 inference(unit_resolution,[status(thm)],[1599, 1355, 1217, 1593])).
% 27.44/17.67 tff(1601,plain,
% 27.44/17.67 ($false),
% 27.44/17.67 inference(unit_resolution,[status(thm)],[1600, 1590, 1583, 1260, 1259])).
% 27.44/17.67 tff(1602,plain,(big_f(c2, c2) | (~(f4(c4) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~big_f(f9(c2, c2), f10(c2))) | (~big_f(c2, c1)) | (~(f7(c1) = c2)) | (~(f10(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.44/17.67 tff(1603,plain,
% 27.44/17.67 (big_f(c2, c2)),
% 27.44/17.67 inference(unit_resolution,[status(thm)],[1602, 686, 148, 122, 17, 79, 794, 120, 16])).
% 27.44/17.67 tff(1604,plain,
% 27.44/17.67 (f9(c2, c2) = c2),
% 27.44/17.67 inference(modus_ponens,[status(thm)],[1498, 133])).
% 27.44/17.67 tff(1605,plain,
% 27.44/17.67 ($false),
% 27.44/17.67 inference(unit_resolution,[status(thm)],[1209, 1604])).
% 27.44/17.67 tff(1606,plain,((~(f9(f10(c2), f4(c4)) = c2)) | (f9(c2, c2) = c2) | (~(f4(c4) = c2)) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.44/17.67 tff(1607,plain,
% 27.44/17.67 (~(f9(f10(c2), f4(c4)) = c2)),
% 27.44/17.67 inference(unit_resolution,[status(thm)],[1606, 1209, 79, 122])).
% 27.44/17.67 tff(1608,plain,
% 27.44/17.67 (f9(f10(c2), f4(c4)) = c1),
% 27.44/17.67 inference(unit_resolution,[status(thm)],[146, 1607])).
% 27.44/17.67 tff(1609,plain,
% 27.44/17.67 (f9(f10(c2), f10(c2)) = c1),
% 27.44/17.67 inference(transitivity,[status(thm)],[135, 160, 1608])).
% 27.44/17.67 tff(1610,plain,
% 27.44/17.67 (f10(f9(f10(c2), f10(c2))) = f10(c1)),
% 27.44/17.67 inference(monotonicity,[status(thm)],[1609])).
% 27.44/17.67 tff(1611,plain,
% 27.44/17.67 (f10(f9(c2, c2)) = f10(c2)),
% 27.44/17.67 inference(transitivity,[status(thm)],[204, 1610, 16, 216])).
% 27.44/17.67 tff(1612,plain,
% 27.44/17.67 (big_f(f9(c2, c2), f10(f9(c2, c2))) <=> big_f(f9(c2, c2), f10(c2))),
% 27.44/17.67 inference(monotonicity,[status(thm)],[1611])).
% 27.44/17.67 tff(1613,plain,
% 27.44/17.67 (big_f(f9(c2, c2), f10(c2)) <=> big_f(f9(c2, c2), f10(f9(c2, c2)))),
% 27.44/17.67 inference(symmetry,[status(thm)],[1612])).
% 27.44/17.67 tff(1614,plain,
% 27.44/17.67 (c1 = f9(f10(c2), f4(c4))),
% 27.44/17.67 inference(symmetry,[status(thm)],[1608])).
% 27.44/17.67 tff(1615,plain,
% 27.44/17.67 (f9(c2, c2) = c1),
% 27.44/17.67 inference(transitivity,[status(thm)],[160, 1608])).
% 27.44/17.67 tff(1616,plain,
% 27.44/17.67 (f5(f9(c2, c2)) = f5(c1)),
% 27.44/17.67 inference(monotonicity,[status(thm)],[1615])).
% 27.44/17.67 tff(1617,plain,
% 27.44/17.67 (f5(f9(c2, c2)) = f9(c2, c2)),
% 27.44/17.67 inference(transitivity,[status(thm)],[1616, 230, 1614, 132])).
% 27.44/17.67 tff(1618,plain,
% 27.44/17.67 ((c2 = f5(f9(c2, c2))) <=> (c2 = f9(c2, c2))),
% 27.44/17.67 inference(monotonicity,[status(thm)],[1617])).
% 27.44/17.67 tff(1619,plain,
% 27.44/17.67 ((c2 = f5(f9(c2, c2))) <=> (f9(c2, c2) = c2)),
% 27.44/17.67 inference(transitivity,[status(thm)],[1618, 167])).
% 27.44/17.67 tff(1620,plain,
% 27.44/17.67 ((f9(c2, c2) = c2) <=> (c2 = f5(f9(c2, c2)))),
% 27.44/17.67 inference(symmetry,[status(thm)],[1619])).
% 27.44/17.67 tff(1621,plain,
% 27.44/17.67 ((~(f9(c2, c2) = c2)) <=> (~(c2 = f5(f9(c2, c2))))),
% 27.44/17.67 inference(monotonicity,[status(thm)],[1620])).
% 27.44/17.67 tff(1622,plain,
% 27.44/17.67 (~(c2 = f5(f9(c2, c2)))),
% 27.44/17.67 inference(modus_ponens,[status(thm)],[1209, 1621])).
% 27.44/17.67 tff(1623,plain,
% 27.44/17.67 (f7(f9(c2, c2)) = f7(c1)),
% 27.44/17.67 inference(monotonicity,[status(thm)],[1615])).
% 27.44/17.67 tff(1624,plain,
% 27.44/17.67 (f7(f9(c2, c2)) = c2),
% 27.44/17.67 inference(transitivity,[status(thm)],[1623, 347])).
% 27.44/17.67 tff(1625,plain,
% 27.44/17.67 ((f7(f9(c2, c2)) = f9(c2, c2)) <=> (c2 = f9(c2, c2))),
% 27.44/17.67 inference(monotonicity,[status(thm)],[1624])).
% 27.44/17.67 tff(1626,plain,
% 27.44/17.67 ((f7(f9(c2, c2)) = f9(c2, c2)) <=> (f9(c2, c2) = c2)),
% 27.44/17.67 inference(transitivity,[status(thm)],[1625, 167])).
% 27.44/17.67 tff(1627,plain,
% 27.44/17.67 ((f9(c2, c2) = c2) <=> (f7(f9(c2, c2)) = f9(c2, c2))),
% 27.44/17.67 inference(symmetry,[status(thm)],[1626])).
% 27.44/17.67 tff(1628,plain,
% 27.44/17.67 ((~(f9(c2, c2) = c2)) <=> (~(f7(f9(c2, c2)) = f9(c2, c2)))),
% 27.44/17.67 inference(monotonicity,[status(thm)],[1627])).
% 27.44/17.67 tff(1629,plain,
% 27.44/17.67 (~(f7(f9(c2, c2)) = f9(c2, c2))),
% 27.44/17.67 inference(modus_ponens,[status(thm)],[1209, 1628])).
% 27.44/17.67 tff(1630,plain,
% 27.44/17.67 (big_f(f7(f9(c2, c2)), c2) <=> big_f(c2, c2)),
% 27.44/17.67 inference(monotonicity,[status(thm)],[1624])).
% 27.44/17.67 tff(1631,plain,
% 27.44/17.67 (big_f(c2, c2) <=> big_f(f7(f9(c2, c2)), c2)),
% 27.44/17.67 inference(symmetry,[status(thm)],[1630])).
% 27.44/17.67 tff(1632,plain,
% 27.44/17.67 (big_f(f7(f9(c2, c2)), c2)),
% 27.44/17.67 inference(modus_ponens,[status(thm)],[1345, 1631])).
% 27.44/17.67 tff(1633,plain,
% 27.44/17.67 ((~big_f(f7(f9(c2, c2)), c2)) | big_f(f9(c2, c2), f10(c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2)))),
% 27.44/17.67 inference(unit_resolution,[status(thm)],[682, 676, 122, 1209])).
% 27.44/17.67 tff(1634,plain,
% 27.44/17.67 (big_f(f9(c2, c2), f10(c2))),
% 27.44/17.67 inference(unit_resolution,[status(thm)],[1633, 1632, 1629, 1622])).
% 27.44/17.67 tff(1635,plain,
% 27.44/17.67 (big_f(f9(c2, c2), f10(f9(c2, c2)))),
% 27.44/17.67 inference(modus_ponens,[status(thm)],[1634, 1613])).
% 27.44/17.67 tff(1636,plain,
% 27.44/17.67 (f10(f9(c2, c2)) = c2),
% 27.44/17.67 inference(transitivity,[status(thm)],[204, 1610, 16])).
% 27.44/17.67 tff(1637,plain,
% 27.44/17.67 ((f10(f9(c2, c2)) = f9(c2, c2)) <=> (c2 = f9(c2, c2))),
% 27.44/17.67 inference(monotonicity,[status(thm)],[1636])).
% 27.44/17.67 tff(1638,plain,
% 27.44/17.67 ((f10(f9(c2, c2)) = f9(c2, c2)) <=> (f9(c2, c2) = c2)),
% 27.44/17.67 inference(transitivity,[status(thm)],[1637, 167])).
% 27.44/17.67 tff(1639,plain,
% 27.44/17.67 ((f9(c2, c2) = c2) <=> (f10(f9(c2, c2)) = f9(c2, c2))),
% 27.44/17.67 inference(symmetry,[status(thm)],[1638])).
% 27.44/17.67 tff(1640,plain,
% 27.44/17.67 ((~(f9(c2, c2) = c2)) <=> (~(f10(f9(c2, c2)) = f9(c2, c2)))),
% 27.44/17.67 inference(monotonicity,[status(thm)],[1639])).
% 27.44/17.67 tff(1641,plain,
% 27.44/17.67 (~(f10(f9(c2, c2)) = f9(c2, c2))),
% 27.44/17.67 inference(modus_ponens,[status(thm)],[1209, 1640])).
% 27.44/17.67 tff(1642,assumption,(c2 = f8(c1)), introduced(assumption)).
% 27.44/17.67 tff(1643,plain,
% 27.44/17.67 (f8(c1) = c2),
% 27.44/17.67 inference(symmetry,[status(thm)],[1642])).
% 27.44/17.67 tff(1644,plain,
% 27.44/17.67 (f8(f9(f10(c2), f10(c2))) = f8(c1)),
% 27.44/17.67 inference(monotonicity,[status(thm)],[1609])).
% 27.44/17.67 tff(1645,plain,
% 27.44/17.67 (f8(f9(c2, c2)) = c2),
% 27.44/17.67 inference(transitivity,[status(thm)],[715, 1644, 1643])).
% 27.44/17.67 tff(1646,plain,
% 27.44/17.67 ((f9(c2, c2) = f8(f9(c2, c2))) <=> (f9(c2, c2) = c2)),
% 27.44/17.67 inference(monotonicity,[status(thm)],[1645])).
% 27.44/17.67 tff(1647,plain,
% 27.44/17.67 ((f9(c2, c2) = c2) <=> (f9(c2, c2) = f8(f9(c2, c2)))),
% 27.44/17.67 inference(symmetry,[status(thm)],[1646])).
% 27.44/17.67 tff(1648,plain,
% 27.44/17.67 ((~(f9(c2, c2) = c2)) <=> (~(f9(c2, c2) = f8(f9(c2, c2))))),
% 27.44/17.67 inference(monotonicity,[status(thm)],[1647])).
% 27.44/17.67 tff(1649,plain,
% 27.44/17.67 (~(f9(c2, c2) = f8(f9(c2, c2)))),
% 27.44/17.67 inference(modus_ponens,[status(thm)],[1209, 1648])).
% 27.44/17.67 tff(1650,plain,
% 27.44/17.67 (^[X4: $i, X7: $i, X5: $i, X8: $i] : refl(((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5))) <=> ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5))))),
% 27.44/17.67 inference(bind,[status(th)],[])).
% 27.44/17.67 tff(1651,plain,
% 27.44/17.67 (![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5))) <=> ![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))),
% 27.44/17.67 inference(quant_intro,[status(thm)],[1650])).
% 27.44/17.67 tff(1652,plain,
% 27.44/17.67 (![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5))) <=> ![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))),
% 27.44/17.67 inference(rewrite,[status(thm)],[])).
% 27.44/17.67 tff(1653,plain,
% 27.44/17.67 (^[X4: $i, X7: $i, X5: $i, X8: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_f(f7(X4), X5)) | (X5 = f5(X4))) | (f7(X4) = X4)) <=> ((f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))), (((((~big_f(f7(X4), X5)) | (X5 = f5(X4))) | (f7(X4) = X4)) | (~big_f(X8, f10(X7)))) <=> (((f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5))) | (~big_f(X8, f10(X7)))))), rewrite((((f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5))) | (~big_f(X8, f10(X7)))) <=> ((~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))), (((((~big_f(f7(X4), X5)) | (X5 = f5(X4))) | (f7(X4) = X4)) | (~big_f(X8, f10(X7)))) <=> ((~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5))))), ((((((~big_f(f7(X4), X5)) | (X5 = f5(X4))) | (f7(X4) = X4)) | (~big_f(X8, f10(X7)))) | (X8 = f8(X7))) <=> (((~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5))) | (X8 = f8(X7))))), rewrite((((~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5))) | (X8 = f8(X7))) <=> ((X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))), ((((((~big_f(f7(X4), X5)) | (X5 = f5(X4))) | (f7(X4) = X4)) | (~big_f(X8, f10(X7)))) | (X8 = f8(X7))) <=> ((X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5))))), (((((((~big_f(f7(X4), X5)) | (X5 = f5(X4))) | (f7(X4) = X4)) | (~big_f(X8, f10(X7)))) | (X8 = f8(X7))) | (f10(X7) = X7)) <=> (((X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5))) | (f10(X7) = X7)))), rewrite((((X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5))) | (f10(X7) = X7)) <=> ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))), (((((((~big_f(f7(X4), X5)) | (X5 = f5(X4))) | (f7(X4) = X4)) | (~big_f(X8, f10(X7)))) | (X8 = f8(X7))) | (f10(X7) = X7)) <=> ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))))),
% 27.44/17.67 inference(bind,[status(th)],[])).
% 27.44/17.67 tff(1654,plain,
% 27.44/17.67 (![X4: $i, X7: $i, X5: $i, X8: $i] : ((((((~big_f(f7(X4), X5)) | (X5 = f5(X4))) | (f7(X4) = X4)) | (~big_f(X8, f10(X7)))) | (X8 = f8(X7))) | (f10(X7) = X7)) <=> ![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))),
% 27.48/17.67 inference(quant_intro,[status(thm)],[1653])).
% 27.48/17.67 tff(1655,axiom,(![X4: $i, X7: $i, X5: $i, X8: $i] : ((((((~big_f(f7(X4), X5)) | (X5 = f5(X4))) | (f7(X4) = X4)) | (~big_f(X8, f10(X7)))) | (X8 = f8(X7))) | (f10(X7) = X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_19')).
% 27.48/17.67 tff(1656,plain,
% 27.48/17.67 (![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))),
% 27.48/17.67 inference(modus_ponens,[status(thm)],[1655, 1654])).
% 27.48/17.67 tff(1657,plain,
% 27.48/17.67 (![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))),
% 27.48/17.67 inference(modus_ponens,[status(thm)],[1656, 1652])).
% 27.48/17.67 tff(1658,plain,(
% 27.48/17.67 ![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))),
% 27.48/17.67 inference(skolemize,[status(sab)],[1657])).
% 27.48/17.67 tff(1659,plain,
% 27.48/17.67 (![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))),
% 27.48/17.67 inference(modus_ponens,[status(thm)],[1658, 1651])).
% 27.48/17.67 tff(1660,plain,
% 27.48/17.67 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~big_f(f7(f9(c2, c2)), c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~big_f(f7(f9(c2, c2)), c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))))),
% 27.48/17.67 inference(rewrite,[status(thm)],[])).
% 27.48/17.67 tff(1661,plain,
% 27.48/17.67 (((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), c2))) <=> ((~big_f(f7(f9(c2, c2)), c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))))),
% 27.48/17.67 inference(rewrite,[status(thm)],[])).
% 27.48/17.67 tff(1662,plain,
% 27.48/17.67 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~big_f(f7(f9(c2, c2)), c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2))))))),
% 27.48/17.67 inference(monotonicity,[status(thm)],[1661])).
% 27.48/17.67 tff(1663,plain,
% 27.48/17.67 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~big_f(f7(f9(c2, c2)), c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))))),
% 27.48/17.67 inference(transitivity,[status(thm)],[1662, 1660])).
% 27.48/17.67 tff(1664,plain,
% 27.48/17.67 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), c2)))),
% 27.48/17.67 inference(quant_inst,[status(thm)],[])).
% 27.48/17.67 tff(1665,plain,
% 27.48/17.67 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~big_f(f7(f9(c2, c2)), c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2))))),
% 27.48/17.67 inference(modus_ponens,[status(thm)],[1664, 1663])).
% 27.48/17.67 tff(1666,plain,
% 27.48/17.67 ((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2))))),
% 27.48/17.67 inference(unit_resolution,[status(thm)],[1665, 1659, 1632, 1629, 1622])).
% 27.48/17.67 tff(1667,plain,
% 27.48/17.67 ($false),
% 27.48/17.67 inference(unit_resolution,[status(thm)],[1666, 1649, 1641, 1635])).
% 27.48/17.67 tff(1668,plain,((f9(c2, c2) = c2) | (~(c2 = f8(c1))) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f10(c1) = c2)) | (~(f7(c1) = c2)) | (~big_f(c2, c2)) | (~(f5(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 27.48/17.67 tff(1669,plain,
% 27.48/17.67 (~(c2 = f8(c1))),
% 27.48/17.67 inference(unit_resolution,[status(thm)],[1668, 1603, 79, 122, 185, 16, 120, 230])).
% 27.48/17.67 tff(1670,plain,
% 27.48/17.67 ((f8(c1) = c2) <=> (c2 = f8(c1))),
% 27.48/17.67 inference(commutativity,[status(thm)],[])).
% 27.48/17.67 tff(1671,assumption,(f8(c1) = c2), introduced(assumption)).
% 27.48/17.67 tff(1672,plain,
% 27.48/17.67 (c2 = f8(c1)),
% 27.48/17.67 inference(modus_ponens,[status(thm)],[1671, 1670])).
% 27.48/17.67 tff(1673,assumption,(~(c2 = f8(c1))), introduced(assumption)).
% 27.48/17.67 tff(1674,plain,
% 27.48/17.67 ($false),
% 27.48/17.67 inference(unit_resolution,[status(thm)],[1673, 1672])).
% 27.48/17.67 tff(1675,plain,((~(f8(c1) = c2)) | (c2 = f8(c1))), inference(lemma,lemma(discharge,[]))).
% 27.48/17.67 tff(1676,plain,
% 27.48/17.67 (~(f8(c1) = c2)),
% 27.48/17.67 inference(unit_resolution,[status(thm)],[1675, 1669])).
% 27.48/17.67 tff(1677,plain,
% 27.48/17.67 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f8(c1) = c1) | (f8(c1) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f8(c1) = c1) | (f8(c1) = c2))),
% 27.48/17.67 inference(rewrite,[status(thm)],[])).
% 27.48/17.67 tff(1678,plain,
% 27.48/17.67 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f8(c1) = c1) | (f8(c1) = c2))),
% 27.48/17.67 inference(quant_inst,[status(thm)],[])).
% 27.48/17.67 tff(1679,plain,
% 27.48/17.67 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f8(c1) = c1) | (f8(c1) = c2)),
% 27.48/17.67 inference(modus_ponens,[status(thm)],[1678, 1677])).
% 27.48/17.67 tff(1680,plain,
% 27.48/17.67 ((f8(c1) = c1) | (f8(c1) = c2)),
% 27.48/17.67 inference(unit_resolution,[status(thm)],[1679, 10])).
% 27.48/17.67 tff(1681,plain,
% 27.48/17.67 (f8(c1) = c1),
% 27.48/17.67 inference(unit_resolution,[status(thm)],[1680, 1676])).
% 27.48/17.67 tff(1682,plain,
% 27.48/17.67 (f8(f9(f10(c2), f10(c2))) = f8(c1)),
% 27.48/17.67 inference(monotonicity,[status(thm)],[201])).
% 27.48/17.67 tff(1683,plain,
% 27.48/17.67 (f8(f9(c2, c2)) = f9(c2, c2)),
% 27.48/17.67 inference(transitivity,[status(thm)],[715, 1682, 1681, 149, 132])).
% 27.48/17.67 tff(1684,plain,
% 27.48/17.67 ((c2 = f8(f9(c2, c2))) <=> (c2 = f9(c2, c2))),
% 27.48/17.67 inference(monotonicity,[status(thm)],[1683])).
% 27.48/17.67 tff(1685,plain,
% 27.48/17.67 ((c2 = f8(f9(c2, c2))) <=> (f9(c2, c2) = c2)),
% 27.48/17.67 inference(transitivity,[status(thm)],[1684, 167])).
% 27.48/17.67 tff(1686,plain,
% 27.48/17.67 ((f9(c2, c2) = c2) <=> (c2 = f8(f9(c2, c2)))),
% 27.48/17.67 inference(symmetry,[status(thm)],[1685])).
% 27.48/17.67 tff(1687,plain,
% 27.48/17.67 ((~(f9(c2, c2) = c2)) <=> (~(c2 = f8(f9(c2, c2))))),
% 27.48/17.67 inference(monotonicity,[status(thm)],[1686])).
% 27.48/17.67 tff(1688,plain,
% 27.48/17.67 (~(c2 = f8(f9(c2, c2)))),
% 27.48/17.67 inference(modus_ponens,[status(thm)],[185, 1687])).
% 27.48/17.67 tff(1689,plain,
% 27.48/17.67 (f10(f9(c2, c2)) = c2),
% 27.48/17.67 inference(transitivity,[status(thm)],[204, 202, 16])).
% 27.48/17.67 tff(1690,plain,
% 27.48/17.67 (big_f(c2, f10(f9(c2, c2))) <=> big_f(c2, c2)),
% 27.48/17.67 inference(monotonicity,[status(thm)],[1689])).
% 27.48/17.67 tff(1691,plain,
% 27.48/17.67 (big_f(c2, c2) <=> big_f(c2, f10(f9(c2, c2)))),
% 27.48/17.67 inference(symmetry,[status(thm)],[1690])).
% 27.48/17.67 tff(1692,plain,
% 27.48/17.67 (big_f(c2, f10(f9(c2, c2)))),
% 27.48/17.67 inference(modus_ponens,[status(thm)],[1603, 1691])).
% 27.48/17.67 tff(1693,plain,
% 27.48/17.67 (big_f(f7(f9(c2, c2)), c2)),
% 27.48/17.67 inference(modus_ponens,[status(thm)],[1603, 246])).
% 27.48/17.67 tff(1694,plain,
% 27.48/17.67 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~big_f(f7(f9(c2, c2)), c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2))) | (~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~big_f(f7(f9(c2, c2)), c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2))) | (~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)))),
% 27.48/17.67 inference(rewrite,[status(thm)],[])).
% 27.48/17.67 tff(1695,plain,
% 27.48/17.67 (((f10(f9(c2, c2)) = f9(c2, c2)) | (c2 = f8(f9(c2, c2))) | (~big_f(c2, f10(f9(c2, c2)))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), c2))) <=> ((~big_f(f7(f9(c2, c2)), c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2))) | (~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)))),
% 27.48/17.67 inference(rewrite,[status(thm)],[])).
% 27.48/17.67 tff(1696,plain,
% 27.48/17.67 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (c2 = f8(f9(c2, c2))) | (~big_f(c2, f10(f9(c2, c2)))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~big_f(f7(f9(c2, c2)), c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2))) | (~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2))))),
% 27.48/17.67 inference(monotonicity,[status(thm)],[1695])).
% 27.48/17.67 tff(1697,plain,
% 27.48/17.67 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (c2 = f8(f9(c2, c2))) | (~big_f(c2, f10(f9(c2, c2)))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~big_f(f7(f9(c2, c2)), c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2))) | (~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)))),
% 27.48/17.67 inference(transitivity,[status(thm)],[1696, 1694])).
% 27.48/17.67 tff(1698,plain,
% 27.48/17.67 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (c2 = f8(f9(c2, c2))) | (~big_f(c2, f10(f9(c2, c2)))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), c2)))),
% 27.48/17.67 inference(quant_inst,[status(thm)],[])).
% 27.48/17.67 tff(1699,plain,
% 27.48/17.67 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~big_f(f7(f9(c2, c2)), c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2))) | (~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2))),
% 27.48/17.67 inference(modus_ponens,[status(thm)],[1698, 1697])).
% 27.48/17.67 tff(1700,plain,
% 27.48/17.67 ((~big_f(f7(f9(c2, c2)), c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2))) | (~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2)))),
% 27.48/17.67 inference(unit_resolution,[status(thm)],[1699, 1659, 763])).
% 27.48/17.67 tff(1701,plain,
% 27.48/17.67 ($false),
% 27.48/17.67 inference(unit_resolution,[status(thm)],[1700, 666, 1693, 242, 1692, 1688])).
% 27.48/17.67 tff(1702,plain,((~(f5(c1) = c1)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f10(c1) = c2)) | (f7(c2) = c2) | (f7(c1) = c1) | (f10(f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2))) | (f9(f10(c2), f10(c2)) = f10(c2))), inference(lemma,lemma(discharge,[]))).
% 27.48/17.67 tff(1703,plain,
% 27.48/17.67 (~(f5(c1) = c1)),
% 27.48/17.67 inference(unit_resolution,[status(thm)],[1702, 17, 79, 122, 15, 148, 115, 229, 158])).
% 27.48/17.68 tff(1704,plain,
% 27.48/17.68 (~(f9(c2, c2) = f5(f9(c2, c2)))),
% 27.48/17.68 inference(modus_ponens,[status(thm)],[1703, 224])).
% 27.48/17.68 tff(1705,plain,
% 27.48/17.68 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f5(c1) = c1) | (f5(c1) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f5(c1) = c1) | (f5(c1) = c2))),
% 27.48/17.68 inference(rewrite,[status(thm)],[])).
% 27.48/17.68 tff(1706,plain,
% 27.48/17.68 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f5(c1) = c1) | (f5(c1) = c2))),
% 27.48/17.68 inference(quant_inst,[status(thm)],[])).
% 27.48/17.68 tff(1707,plain,
% 27.48/17.68 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f5(c1) = c1) | (f5(c1) = c2)),
% 27.48/17.68 inference(modus_ponens,[status(thm)],[1706, 1705])).
% 27.48/17.68 tff(1708,plain,
% 27.48/17.68 ((f5(c1) = c1) | (f5(c1) = c2)),
% 27.48/17.68 inference(unit_resolution,[status(thm)],[1707, 10])).
% 27.48/17.68 tff(1709,plain,
% 27.48/17.68 (f5(c1) = c2),
% 27.48/17.68 inference(unit_resolution,[status(thm)],[1708, 1703])).
% 27.48/17.68 tff(1710,plain,
% 27.48/17.68 (big_f(f7(c1), f5(c1)) <=> big_f(c2, c2)),
% 27.48/17.68 inference(monotonicity,[status(thm)],[347, 186])).
% 27.48/17.68 tff(1711,plain,
% 27.48/17.68 (big_f(c2, c2) <=> big_f(f7(c1), f5(c1))),
% 27.48/17.68 inference(symmetry,[status(thm)],[1710])).
% 27.48/17.68 tff(1712,plain,
% 27.48/17.68 ((~big_f(c2, c2)) <=> (~big_f(f7(c1), f5(c1)))),
% 27.48/17.68 inference(monotonicity,[status(thm)],[1711])).
% 27.48/17.68 tff(1713,plain,
% 27.48/17.68 (~big_f(f7(c1), f5(c1))),
% 27.48/17.68 inference(modus_ponens,[status(thm)],[121, 1712])).
% 27.48/17.68 tff(1714,plain,
% 27.48/17.68 ($false),
% 27.48/17.68 inference(unit_resolution,[status(thm)],[287, 1713])).
% 27.48/17.68 tff(1715,plain,((~(f5(c1) = c2)) | (~big_f(f7(c1), f5(c1))) | big_f(c2, c2) | (~(f7(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.48/17.68 tff(1716,plain,
% 27.48/17.68 (~big_f(f7(c1), f5(c1))),
% 27.48/17.68 inference(unit_resolution,[status(thm)],[1715, 121, 120, 186])).
% 27.48/17.68 tff(1717,plain,
% 27.48/17.68 (big_f(f9(f10(c2), f10(c2)), f10(f10(c2)))),
% 27.48/17.68 inference(unit_resolution,[status(thm)],[280, 1716, 252, 115, 158])).
% 27.48/17.68 tff(1718,plain,
% 27.48/17.68 (big_f(f9(c2, c2), f10(c2))),
% 27.48/17.68 inference(modus_ponens,[status(thm)],[1717, 253])).
% 27.48/17.68 tff(1719,plain,
% 27.48/17.68 (big_f(f9(c2, c1), f10(c2))),
% 27.48/17.68 inference(unit_resolution,[status(thm)],[755, 1718, 122, 115, 1716, 148, 79])).
% 27.48/17.68 tff(1720,plain,
% 27.48/17.68 (big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2))),
% 27.48/17.68 inference(modus_ponens,[status(thm)],[1719, 724])).
% 27.48/17.68 tff(1721,plain,
% 27.48/17.68 (~(f10(f9(c2, c2)) = f9(c2, c2))),
% 27.48/17.68 inference(unit_resolution,[status(thm)],[762, 15, 148, 79, 122])).
% 27.48/17.68 tff(1722,plain,
% 27.48/17.68 ((f9(c2, f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2))) <=> (f9(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.48/17.68 inference(symmetry,[status(thm)],[1135])).
% 27.48/17.68 tff(1723,plain,
% 27.48/17.68 (big_f(f7(c1), c2) <=> big_f(c2, c2)),
% 27.48/17.68 inference(monotonicity,[status(thm)],[120])).
% 27.48/17.68 tff(1724,plain,
% 27.48/17.68 (big_f(c2, c2) <=> big_f(f7(c1), c2)),
% 27.48/17.68 inference(symmetry,[status(thm)],[1723])).
% 27.48/17.68 tff(1725,plain,
% 27.48/17.68 ((~big_f(c2, c2)) <=> (~big_f(f7(c1), c2))),
% 27.48/17.68 inference(monotonicity,[status(thm)],[1724])).
% 27.48/17.68 tff(1726,plain,
% 27.48/17.68 (~big_f(f7(c1), c2)),
% 27.48/17.68 inference(modus_ponens,[status(thm)],[121, 1725])).
% 27.48/17.68 tff(1727,plain,
% 27.48/17.68 (c2 = f5(c1)),
% 27.48/17.68 inference(modus_ponens,[status(thm)],[186, 155])).
% 27.48/17.68 tff(1728,plain,
% 27.48/17.68 (big_f(c2, f10(c1)) <=> big_f(c2, f10(f9(f10(c2), f10(c2))))),
% 27.48/17.68 inference(monotonicity,[status(thm)],[226])).
% 27.48/17.68 tff(1729,plain,
% 27.48/17.68 (big_f(c2, f10(f9(f10(c2), f10(c2)))) <=> big_f(c2, f10(c1))),
% 27.48/17.68 inference(symmetry,[status(thm)],[1728])).
% 27.48/17.68 tff(1730,plain,
% 27.48/17.68 (f10(f9(f10(c2), f10(c2))) = c2),
% 27.48/17.68 inference(transitivity,[status(thm)],[202, 15])).
% 27.48/17.68 tff(1731,plain,
% 27.48/17.68 (big_f(c2, f10(f9(f10(c2), f10(c2)))) <=> big_f(c2, c2)),
% 27.48/17.68 inference(monotonicity,[status(thm)],[1730])).
% 27.48/17.68 tff(1732,plain,
% 27.48/17.68 (big_f(c2, c2) <=> big_f(c2, f10(f9(f10(c2), f10(c2))))),
% 27.48/17.68 inference(symmetry,[status(thm)],[1731])).
% 27.48/17.68 tff(1733,plain,
% 27.48/17.68 (big_f(c2, c2) <=> big_f(c2, f10(c1))),
% 27.48/17.68 inference(transitivity,[status(thm)],[1732, 1729])).
% 27.48/17.68 tff(1734,plain,
% 27.48/17.68 ((~big_f(c2, c2)) <=> (~big_f(c2, f10(c1)))),
% 27.48/17.68 inference(monotonicity,[status(thm)],[1733])).
% 27.48/17.68 tff(1735,plain,
% 27.48/17.68 (~big_f(c2, f10(c1))),
% 27.48/17.68 inference(modus_ponens,[status(thm)],[121, 1734])).
% 27.48/17.68 tff(1736,plain,
% 27.48/17.68 (^[X4: $i, X7: $i, X5: $i, X8: $i] : refl(((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7)))) <=> ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7)))))),
% 27.48/17.68 inference(bind,[status(th)],[])).
% 27.48/17.68 tff(1737,plain,
% 27.48/17.68 (![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7)))) <=> ![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))),
% 27.48/17.68 inference(quant_intro,[status(thm)],[1736])).
% 27.48/17.68 tff(1738,plain,
% 27.48/17.68 (![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7)))) <=> ![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))),
% 27.48/17.68 inference(rewrite,[status(thm)],[])).
% 27.48/17.68 tff(1739,plain,
% 27.48/17.68 (^[X4: $i, X7: $i, X5: $i, X8: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((big_f(f7(X4), X5) | (~(X5 = f5(X4)))) <=> ((~(X5 = f5(X4))) | big_f(f7(X4), X5))), (((big_f(f7(X4), X5) | (~(X5 = f5(X4)))) | (f7(X4) = X4)) <=> (((~(X5 = f5(X4))) | big_f(f7(X4), X5)) | (f7(X4) = X4)))), rewrite((((~(X5 = f5(X4))) | big_f(f7(X4), X5)) | (f7(X4) = X4)) <=> ((~(X5 = f5(X4))) | (f7(X4) = X4) | big_f(f7(X4), X5))), (((big_f(f7(X4), X5) | (~(X5 = f5(X4)))) | (f7(X4) = X4)) <=> ((~(X5 = f5(X4))) | (f7(X4) = X4) | big_f(f7(X4), X5)))), ((((big_f(f7(X4), X5) | (~(X5 = f5(X4)))) | (f7(X4) = X4)) | big_f(X8, f10(X7))) <=> (((~(X5 = f5(X4))) | (f7(X4) = X4) | big_f(f7(X4), X5)) | big_f(X8, f10(X7))))), rewrite((((~(X5 = f5(X4))) | (f7(X4) = X4) | big_f(f7(X4), X5)) | big_f(X8, f10(X7))) <=> ((~(X5 = f5(X4))) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5))), ((((big_f(f7(X4), X5) | (~(X5 = f5(X4)))) | (f7(X4) = X4)) | big_f(X8, f10(X7))) <=> ((~(X5 = f5(X4))) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5)))), (((((big_f(f7(X4), X5) | (~(X5 = f5(X4)))) | (f7(X4) = X4)) | big_f(X8, f10(X7))) | (~(X8 = f8(X7)))) <=> (((~(X5 = f5(X4))) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5)) | (~(X8 = f8(X7)))))), rewrite((((~(X5 = f5(X4))) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5)) | (~(X8 = f8(X7)))) <=> ((~(X5 = f5(X4))) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))), (((((big_f(f7(X4), X5) | (~(X5 = f5(X4)))) | (f7(X4) = X4)) | big_f(X8, f10(X7))) | (~(X8 = f8(X7)))) <=> ((~(X5 = f5(X4))) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7)))))), ((((((big_f(f7(X4), X5) | (~(X5 = f5(X4)))) | (f7(X4) = X4)) | big_f(X8, f10(X7))) | (~(X8 = f8(X7)))) | (f10(X7) = X7)) <=> (((~(X5 = f5(X4))) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7)))) | (f10(X7) = X7)))), rewrite((((~(X5 = f5(X4))) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7)))) | (f10(X7) = X7)) <=> ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))), ((((((big_f(f7(X4), X5) | (~(X5 = f5(X4)))) | (f7(X4) = X4)) | big_f(X8, f10(X7))) | (~(X8 = f8(X7)))) | (f10(X7) = X7)) <=> ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))))),
% 27.48/17.68 inference(bind,[status(th)],[])).
% 27.48/17.68 tff(1740,plain,
% 27.48/17.68 (![X4: $i, X7: $i, X5: $i, X8: $i] : (((((big_f(f7(X4), X5) | (~(X5 = f5(X4)))) | (f7(X4) = X4)) | big_f(X8, f10(X7))) | (~(X8 = f8(X7)))) | (f10(X7) = X7)) <=> ![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))),
% 27.48/17.68 inference(quant_intro,[status(thm)],[1739])).
% 27.48/17.68 tff(1741,axiom,(![X4: $i, X7: $i, X5: $i, X8: $i] : (((((big_f(f7(X4), X5) | (~(X5 = f5(X4)))) | (f7(X4) = X4)) | big_f(X8, f10(X7))) | (~(X8 = f8(X7)))) | (f10(X7) = X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_24')).
% 27.48/17.68 tff(1742,plain,
% 27.48/17.68 (![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))),
% 27.48/17.68 inference(modus_ponens,[status(thm)],[1741, 1740])).
% 27.48/17.68 tff(1743,plain,
% 27.48/17.68 (![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))),
% 27.48/17.68 inference(modus_ponens,[status(thm)],[1742, 1738])).
% 27.48/17.68 tff(1744,plain,(
% 27.48/17.68 ![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))),
% 27.48/17.68 inference(skolemize,[status(sab)],[1743])).
% 27.48/17.68 tff(1745,plain,
% 27.48/17.68 (![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))),
% 27.48/17.68 inference(modus_ponens,[status(thm)],[1744, 1737])).
% 27.48/17.68 tff(1746,plain,
% 27.48/17.68 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))))),
% 27.48/17.68 inference(rewrite,[status(thm)],[])).
% 27.48/17.68 tff(1747,plain,
% 27.48/17.68 (((~(c2 = f5(c1))) | (f10(c1) = c1) | big_f(c2, f10(c1)) | (f7(c1) = c1) | big_f(f7(c1), c2) | (~(c2 = f8(c1)))) <=> ((~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))))),
% 27.48/17.68 inference(rewrite,[status(thm)],[])).
% 27.48/17.68 tff(1748,plain,
% 27.48/17.68 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c2 = f5(c1))) | (f10(c1) = c1) | big_f(c2, f10(c1)) | (f7(c1) = c1) | big_f(f7(c1), c2) | (~(c2 = f8(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1)))))),
% 27.48/17.68 inference(monotonicity,[status(thm)],[1747])).
% 27.48/17.68 tff(1749,plain,
% 27.48/17.68 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c2 = f5(c1))) | (f10(c1) = c1) | big_f(c2, f10(c1)) | (f7(c1) = c1) | big_f(f7(c1), c2) | (~(c2 = f8(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))))),
% 27.48/17.68 inference(transitivity,[status(thm)],[1748, 1746])).
% 27.48/17.68 tff(1750,plain,
% 27.48/17.68 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c2 = f5(c1))) | (f10(c1) = c1) | big_f(c2, f10(c1)) | (f7(c1) = c1) | big_f(f7(c1), c2) | (~(c2 = f8(c1))))),
% 27.48/17.68 inference(quant_inst,[status(thm)],[])).
% 27.48/17.68 tff(1751,plain,
% 27.48/17.68 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1)))),
% 27.48/17.68 inference(modus_ponens,[status(thm)],[1750, 1749])).
% 27.48/17.68 tff(1752,plain,
% 27.48/17.68 ((~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1)))),
% 27.48/17.68 inference(unit_resolution,[status(thm)],[1751, 1745])).
% 27.48/17.68 tff(1753,plain,
% 27.48/17.68 (~(c2 = f8(c1))),
% 27.48/17.68 inference(unit_resolution,[status(thm)],[1752, 1735, 115, 1727, 3, 1726])).
% 27.48/17.68 tff(1754,plain,
% 27.48/17.68 (~(f8(c1) = c2)),
% 27.48/17.68 inference(unit_resolution,[status(thm)],[1675, 1753])).
% 27.48/17.68 tff(1755,plain,
% 27.48/17.68 (f8(c1) = c1),
% 27.48/17.68 inference(unit_resolution,[status(thm)],[1680, 1754])).
% 27.48/17.68 tff(1756,plain,
% 27.48/17.68 (f8(f9(c2, c2)) = f9(f10(c2), f10(c2))),
% 27.48/17.68 inference(transitivity,[status(thm)],[715, 1682, 1755, 149, 132, 203])).
% 27.48/17.68 tff(1757,plain,
% 27.48/17.68 ((f9(c2, f9(f10(c2), f10(c2))) = f8(f9(c2, c2))) <=> (f9(c2, f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))),
% 27.48/17.68 inference(monotonicity,[status(thm)],[1756])).
% 27.48/17.68 tff(1758,plain,
% 27.48/17.68 ((f9(c2, f9(f10(c2), f10(c2))) = f8(f9(c2, c2))) <=> (f9(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.48/17.68 inference(transitivity,[status(thm)],[1757, 1722])).
% 27.48/17.68 tff(1759,plain,
% 27.48/17.68 ((~big_f(c2, c2)) <=> (~big_f(f7(f9(c2, c2)), c2))),
% 27.48/17.68 inference(monotonicity,[status(thm)],[246])).
% 27.48/17.68 tff(1760,plain,
% 27.48/17.68 (~big_f(f7(f9(c2, c2)), c2)),
% 27.48/17.68 inference(modus_ponens,[status(thm)],[121, 1759])).
% 27.48/17.68 tff(1761,plain,
% 27.48/17.68 (c2 = f5(c1)),
% 27.48/17.68 inference(symmetry,[status(thm)],[186])).
% 27.48/17.68 tff(1762,plain,
% 27.48/17.68 (c2 = f5(f9(c2, c2))),
% 27.48/17.68 inference(transitivity,[status(thm)],[1761, 194])).
% 27.48/17.68 tff(1763,plain,
% 27.48/17.68 (f10(f9(c2, c2)) = f10(c2)),
% 27.48/17.68 inference(transitivity,[status(thm)],[204, 202, 15, 216])).
% 27.48/17.68 tff(1764,plain,
% 27.48/17.68 (big_f(f9(c2, f9(f10(c2), f10(c2))), f10(f9(c2, c2))) <=> big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2))),
% 27.48/17.68 inference(monotonicity,[status(thm)],[1763])).
% 27.48/17.68 tff(1765,plain,
% 27.48/17.68 (big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2)) <=> big_f(f9(c2, f9(f10(c2), f10(c2))), f10(f9(c2, c2)))),
% 27.48/17.68 inference(symmetry,[status(thm)],[1764])).
% 27.48/17.68 tff(1766,plain,
% 27.48/17.68 (big_f(f9(c2, f9(f10(c2), f10(c2))), f10(f9(c2, c2)))),
% 27.48/17.68 inference(modus_ponens,[status(thm)],[1229, 1765])).
% 27.48/17.68 tff(1767,assumption,(~(f10(f9(c2, c2)) = f9(c2, c2))), introduced(assumption)).
% 27.48/17.68 tff(1768,plain,
% 27.48/17.68 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (big_f(f7(f9(c2, c2)), c2) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(f9(c2, c2)))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~(c2 = f5(f9(c2, c2)))) | (f9(c2, f9(f10(c2), f10(c2))) = f8(f9(c2, c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | big_f(f7(f9(c2, c2)), c2) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(f9(c2, c2)))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~(c2 = f5(f9(c2, c2)))) | (f9(c2, f9(f10(c2), f10(c2))) = f8(f9(c2, c2))))),
% 27.48/17.68 inference(rewrite,[status(thm)],[])).
% 27.48/17.68 tff(1769,plain,
% 27.48/17.68 (((~(c2 = f5(f9(c2, c2)))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, f9(f10(c2), f10(c2))) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(f9(c2, c2)))) | (f7(f9(c2, c2)) = f9(c2, c2)) | big_f(f7(f9(c2, c2)), c2)) <=> (big_f(f7(f9(c2, c2)), c2) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(f9(c2, c2)))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~(c2 = f5(f9(c2, c2)))) | (f9(c2, f9(f10(c2), f10(c2))) = f8(f9(c2, c2))))),
% 27.48/17.68 inference(rewrite,[status(thm)],[])).
% 27.48/17.68 tff(1770,plain,
% 27.48/17.68 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c2 = f5(f9(c2, c2)))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, f9(f10(c2), f10(c2))) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(f9(c2, c2)))) | (f7(f9(c2, c2)) = f9(c2, c2)) | big_f(f7(f9(c2, c2)), c2))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (big_f(f7(f9(c2, c2)), c2) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(f9(c2, c2)))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~(c2 = f5(f9(c2, c2)))) | (f9(c2, f9(f10(c2), f10(c2))) = f8(f9(c2, c2)))))),
% 27.48/17.68 inference(monotonicity,[status(thm)],[1769])).
% 27.48/17.68 tff(1771,plain,
% 27.48/17.68 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c2 = f5(f9(c2, c2)))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, f9(f10(c2), f10(c2))) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(f9(c2, c2)))) | (f7(f9(c2, c2)) = f9(c2, c2)) | big_f(f7(f9(c2, c2)), c2))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | big_f(f7(f9(c2, c2)), c2) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(f9(c2, c2)))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~(c2 = f5(f9(c2, c2)))) | (f9(c2, f9(f10(c2), f10(c2))) = f8(f9(c2, c2))))),
% 27.48/17.68 inference(transitivity,[status(thm)],[1770, 1768])).
% 27.48/17.68 tff(1772,plain,
% 27.48/17.68 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c2 = f5(f9(c2, c2)))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, f9(f10(c2), f10(c2))) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(f9(c2, c2)))) | (f7(f9(c2, c2)) = f9(c2, c2)) | big_f(f7(f9(c2, c2)), c2))),
% 27.48/17.68 inference(quant_inst,[status(thm)],[])).
% 27.48/17.68 tff(1773,plain,
% 27.48/17.68 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | big_f(f7(f9(c2, c2)), c2) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(f9(c2, c2)))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~(c2 = f5(f9(c2, c2)))) | (f9(c2, f9(f10(c2), f10(c2))) = f8(f9(c2, c2)))),
% 27.48/17.68 inference(modus_ponens,[status(thm)],[1772, 1771])).
% 27.48/17.68 tff(1774,plain,
% 27.48/17.68 (big_f(f7(f9(c2, c2)), c2) | (f7(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, f9(f10(c2), f10(c2))) = f8(f9(c2, c2)))),
% 27.48/17.68 inference(unit_resolution,[status(thm)],[1773, 705, 1767, 1766, 1762])).
% 27.48/17.68 tff(1775,plain,
% 27.48/17.68 (f9(c2, f9(f10(c2), f10(c2))) = f8(f9(c2, c2))),
% 27.48/17.68 inference(unit_resolution,[status(thm)],[1774, 666, 1760])).
% 27.48/17.68 tff(1776,plain,
% 27.48/17.68 (f9(c2, f9(c2, c2)) = f9(c2, c2)),
% 27.48/17.68 inference(modus_ponens,[status(thm)],[1775, 1758])).
% 27.48/17.68 tff(1777,plain,
% 27.48/17.68 (big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 27.48/17.68 inference(modus_ponens,[status(thm)],[1229, 1177])).
% 27.48/17.68 tff(1778,plain,
% 27.48/17.68 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | big_f(f7(f9(c2, c2)), c2) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~(c2 = f5(f9(c2, c2)))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | big_f(f7(f9(c2, c2)), c2) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~(c2 = f5(f9(c2, c2)))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))))),
% 27.48/17.68 inference(rewrite,[status(thm)],[])).
% 27.48/17.68 tff(1779,plain,
% 27.48/17.68 (((~(f10(c2) = c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | big_f(f7(f9(c2, c2)), c2) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(c2 = f5(f9(c2, c2))))) <=> ((~(f10(c2) = c2)) | big_f(f7(f9(c2, c2)), c2) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~(c2 = f5(f9(c2, c2)))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))))),
% 27.48/17.68 inference(rewrite,[status(thm)],[])).
% 27.48/17.68 tff(1780,plain,
% 27.48/17.68 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | big_f(f7(f9(c2, c2)), c2) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(c2 = f5(f9(c2, c2)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | big_f(f7(f9(c2, c2)), c2) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~(c2 = f5(f9(c2, c2)))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2)))))),
% 27.48/17.68 inference(monotonicity,[status(thm)],[1779])).
% 27.48/17.68 tff(1781,plain,
% 27.48/17.68 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | big_f(f7(f9(c2, c2)), c2) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(c2 = f5(f9(c2, c2)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | big_f(f7(f9(c2, c2)), c2) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~(c2 = f5(f9(c2, c2)))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))))),
% 27.48/17.68 inference(transitivity,[status(thm)],[1780, 1778])).
% 27.48/17.68 tff(1782,plain,
% 27.48/17.68 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | big_f(f7(f9(c2, c2)), c2) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(c2 = f5(f9(c2, c2)))))),
% 27.48/17.68 inference(quant_inst,[status(thm)],[])).
% 27.48/17.68 tff(1783,plain,
% 27.48/17.68 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | big_f(f7(f9(c2, c2)), c2) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~(c2 = f5(f9(c2, c2)))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2)))),
% 27.48/17.68 inference(modus_ponens,[status(thm)],[1782, 1781])).
% 27.48/17.68 tff(1784,plain,
% 27.48/17.68 (big_f(f7(f9(c2, c2)), c2) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2)))),
% 27.48/17.68 inference(unit_resolution,[status(thm)],[1783, 783, 122, 1777, 1762])).
% 27.48/17.68 tff(1785,plain,
% 27.48/17.68 (~(f9(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.48/17.68 inference(unit_resolution,[status(thm)],[1784, 1760, 666])).
% 27.48/17.68 tff(1786,plain,
% 27.48/17.68 ($false),
% 27.48/17.68 inference(unit_resolution,[status(thm)],[1785, 1776])).
% 27.48/17.68 tff(1787,plain,((f10(f9(c2, c2)) = f9(c2, c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | big_f(c2, c2) | (f7(c1) = c1) | (f10(c1) = c1) | (~(f5(c1) = c2)) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2)))), inference(lemma,lemma(discharge,[]))).
% 27.48/17.68 tff(1788,plain,
% 27.48/17.68 (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2))),
% 27.48/17.68 inference(unit_resolution,[status(thm)],[1787, 121, 79, 122, 1721, 115, 3, 186, 148])).
% 27.48/17.68 tff(1789,plain,
% 27.48/17.68 ($false),
% 27.48/17.68 inference(unit_resolution,[status(thm)],[1788, 1720])).
% 27.48/17.68 tff(1790,plain,(big_f(c2, c2) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (f7(c1) = c1) | (f9(f10(c2), f10(c2)) = f10(c2)) | (f10(c1) = c1) | (~(f5(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.48/17.68 tff(1791,plain,
% 27.48/17.68 (big_f(c2, c2)),
% 27.48/17.68 inference(unit_resolution,[status(thm)],[1790, 1709, 79, 122, 115, 158, 3, 148])).
% 27.48/17.68 tff(1792,assumption,(~(f9(c2, c2) = f5(f9(c2, c2)))), introduced(assumption)).
% 27.48/17.68 tff(1793,plain,
% 27.48/17.68 (f7(f9(c2, c2)) = c2),
% 27.48/17.68 inference(transitivity,[status(thm)],[243, 347])).
% 27.48/17.68 tff(1794,plain,
% 27.48/17.68 ((f7(f9(c2, c2)) = f9(c2, c2)) <=> (c2 = f9(c2, c2))),
% 27.48/17.68 inference(monotonicity,[status(thm)],[1793])).
% 27.48/17.68 tff(1795,plain,
% 27.48/17.68 ((f7(f9(c2, c2)) = f9(c2, c2)) <=> (f9(c2, c2) = c2)),
% 27.48/17.68 inference(transitivity,[status(thm)],[1794, 167])).
% 27.48/17.68 tff(1796,plain,
% 27.48/17.68 ((f9(c2, c2) = c2) <=> (f7(f9(c2, c2)) = f9(c2, c2))),
% 27.48/17.68 inference(symmetry,[status(thm)],[1795])).
% 27.48/17.68 tff(1797,plain,
% 27.48/17.68 ((~(f9(c2, c2) = c2)) <=> (~(f7(f9(c2, c2)) = f9(c2, c2)))),
% 27.48/17.68 inference(monotonicity,[status(thm)],[1796])).
% 27.48/17.68 tff(1798,plain,
% 27.48/17.68 (~(f7(f9(c2, c2)) = f9(c2, c2))),
% 27.48/17.68 inference(modus_ponens,[status(thm)],[185, 1797])).
% 27.48/17.68 tff(1799,plain,
% 27.48/17.68 (big_f(f7(f9(c2, c2)), f9(c2, c2)) <=> big_f(c2, c1)),
% 27.48/17.68 inference(monotonicity,[status(thm)],[1793, 161])).
% 27.48/17.68 tff(1800,plain,
% 27.48/17.68 (big_f(c2, c1) <=> big_f(f7(f9(c2, c2)), f9(c2, c2))),
% 27.48/17.68 inference(symmetry,[status(thm)],[1799])).
% 27.48/17.68 tff(1801,plain,
% 27.48/17.68 (big_f(f7(f9(c2, c2)), f9(c2, c2))),
% 27.48/17.68 inference(modus_ponens,[status(thm)],[348, 1800])).
% 27.48/17.68 tff(1802,plain,
% 27.48/17.68 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = f5(f9(c2, c2))) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~big_f(f7(f9(c2, c2)), f9(c2, c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~(f10(c2) = c2)) | (f9(c2, c2) = f5(f9(c2, c2))) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~big_f(f7(f9(c2, c2)), f9(c2, c2))))),
% 27.48/17.69 inference(rewrite,[status(thm)],[])).
% 27.48/17.69 tff(1803,plain,
% 27.48/17.69 (((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f9(c2, c2)))) <=> ((~(f10(c2) = c2)) | (f9(c2, c2) = f5(f9(c2, c2))) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~big_f(f7(f9(c2, c2)), f9(c2, c2))))),
% 27.48/17.69 inference(rewrite,[status(thm)],[])).
% 27.48/17.69 tff(1804,plain,
% 27.48/17.69 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f9(c2, c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = f5(f9(c2, c2))) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~big_f(f7(f9(c2, c2)), f9(c2, c2)))))),
% 27.48/17.69 inference(monotonicity,[status(thm)],[1803])).
% 27.48/17.69 tff(1805,plain,
% 27.48/17.69 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f9(c2, c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~(f10(c2) = c2)) | (f9(c2, c2) = f5(f9(c2, c2))) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~big_f(f7(f9(c2, c2)), f9(c2, c2))))),
% 27.48/17.69 inference(transitivity,[status(thm)],[1804, 1802])).
% 27.48/17.69 tff(1806,plain,
% 27.48/17.69 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f9(c2, c2))))),
% 27.48/17.69 inference(quant_inst,[status(thm)],[])).
% 27.48/17.69 tff(1807,plain,
% 27.48/17.69 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~(f10(c2) = c2)) | (f9(c2, c2) = f5(f9(c2, c2))) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~big_f(f7(f9(c2, c2)), f9(c2, c2)))),
% 27.48/17.69 inference(modus_ponens,[status(thm)],[1806, 1805])).
% 27.48/17.69 tff(1808,plain,
% 27.48/17.69 ((f7(f9(c2, c2)) = f9(c2, c2)) | (~big_f(f7(f9(c2, c2)), f9(c2, c2)))),
% 27.48/17.69 inference(unit_resolution,[status(thm)],[1807, 676, 122, 185, 256, 1792])).
% 27.48/17.69 tff(1809,plain,
% 27.48/17.69 ($false),
% 27.48/17.69 inference(unit_resolution,[status(thm)],[1808, 1801, 1798])).
% 27.48/17.69 tff(1810,plain,((~big_f(c2, c1)) | (~(f10(c2) = c2)) | big_f(f9(c2, c2), f10(c2)) | (f9(c2, c2) = f5(f9(c2, c2))) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f7(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.48/17.69 tff(1811,plain,
% 27.48/17.69 (~big_f(c2, c1)),
% 27.48/17.69 inference(unit_resolution,[status(thm)],[1810, 256, 122, 1792, 148, 79, 347])).
% 27.48/17.69 tff(1812,plain,
% 27.48/17.69 ((c1 = c4) <=> (f9(f10(c2), f4(c4)) = c4)),
% 27.48/17.69 inference(monotonicity,[status(thm)],[149])).
% 27.48/17.69 tff(1813,plain,
% 27.48/17.69 ((c4 = c1) <=> (f9(c2, c2) = c4)),
% 27.48/17.69 inference(transitivity,[status(thm)],[479, 1812, 359])).
% 27.48/17.69 tff(1814,plain,
% 27.48/17.69 ((~(c4 = c1)) <=> (~(f9(c2, c2) = c4))),
% 27.48/17.69 inference(monotonicity,[status(thm)],[1813])).
% 27.48/17.69 tff(1815,plain,
% 27.48/17.69 (f9(c2, c2) = c3),
% 27.48/17.69 inference(unit_resolution,[status(thm)],[616, 480, 256, 148, 79, 122, 292, 338])).
% 27.48/17.69 tff(1816,plain,
% 27.48/17.69 (c3 = c2),
% 27.48/17.69 inference(symmetry,[status(thm)],[1344])).
% 27.48/17.69 tff(1817,plain,
% 27.48/17.69 ((f9(f10(c2), f4(c4)) = c3) <=> (f9(c2, c2) = c2)),
% 27.48/17.69 inference(monotonicity,[status(thm)],[132, 1816])).
% 27.48/17.69 tff(1818,plain,
% 27.48/17.69 ((f9(c2, c2) = c2) <=> (f9(f10(c2), f4(c4)) = c3)),
% 27.48/17.69 inference(symmetry,[status(thm)],[1817])).
% 27.48/17.69 tff(1819,plain,
% 27.48/17.69 ((f9(c2, c2) = c2) <=> (f9(c2, c2) = c3)),
% 27.48/17.69 inference(transitivity,[status(thm)],[1818, 339])).
% 27.48/17.69 tff(1820,plain,
% 27.48/17.69 ((~(f9(c2, c2) = c2)) <=> (~(f9(c2, c2) = c3))),
% 27.48/17.69 inference(monotonicity,[status(thm)],[1819])).
% 27.48/17.69 tff(1821,plain,
% 27.48/17.69 (~(f9(c2, c2) = c3)),
% 27.48/17.69 inference(modus_ponens,[status(thm)],[1209, 1820])).
% 27.48/17.69 tff(1822,assumption,(f9(c2, c2) = c3), introduced(assumption)).
% 27.48/17.69 tff(1823,plain,
% 27.48/17.69 ($false),
% 27.48/17.69 inference(unit_resolution,[status(thm)],[1822, 1821])).
% 27.48/17.69 tff(1824,plain,((~(c2 = c3)) | (~(f9(c2, c2) = c3)) | (f9(c2, c2) = c2) | (~(f4(c4) = c2)) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.48/17.69 tff(1825,plain,
% 27.48/17.69 (~(c2 = c3)),
% 27.48/17.69 inference(unit_resolution,[status(thm)],[1824, 1815, 185, 79, 122])).
% 27.48/17.69 tff(1826,plain,
% 27.48/17.69 (big_f(f7(f9(c2, c2)), f1(c2, c2)) <=> big_f(c2, f1(c2, c2))),
% 27.48/17.69 inference(monotonicity,[status(thm)],[1793])).
% 27.48/17.69 tff(1827,plain,
% 27.48/17.69 (big_f(c2, f1(c2, c2)) <=> big_f(f7(f9(c2, c2)), f1(c2, c2))),
% 27.48/17.69 inference(symmetry,[status(thm)],[1826])).
% 27.48/17.69 tff(1828,assumption,(~(f1(c2, c2) = c2)), introduced(assumption)).
% 27.48/17.69 tff(1829,plain,
% 27.48/17.69 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)))),
% 27.48/17.69 inference(rewrite,[status(thm)],[])).
% 27.48/17.69 tff(1830,plain,
% 27.48/17.69 (((c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f9(c2, c2) = c4)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2)))) <=> ((c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)))),
% 27.48/17.69 inference(rewrite,[status(thm)],[])).
% 27.48/17.69 tff(1831,plain,
% 27.48/17.69 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f9(c2, c2) = c4)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4))))),
% 27.48/17.69 inference(monotonicity,[status(thm)],[1830])).
% 27.48/17.69 tff(1832,plain,
% 27.48/17.69 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f9(c2, c2) = c4)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)))),
% 27.48/17.69 inference(transitivity,[status(thm)],[1831, 1829])).
% 27.48/17.69 tff(1833,plain,
% 27.48/17.69 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f9(c2, c2) = c4)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))))),
% 27.48/17.69 inference(quant_inst,[status(thm)],[])).
% 27.48/17.69 tff(1834,plain,
% 27.48/17.69 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4))),
% 27.48/17.69 inference(modus_ponens,[status(thm)],[1833, 1832])).
% 27.48/17.69 tff(1835,plain,
% 27.48/17.69 (big_f(c2, f1(c2, c2))),
% 27.48/17.69 inference(unit_resolution,[status(thm)],[1834, 525, 377, 1828, 515, 487, 514])).
% 27.48/17.69 tff(1836,plain,
% 27.48/17.69 (big_f(f7(f9(c2, c2)), f1(c2, c2))),
% 27.48/17.69 inference(modus_ponens,[status(thm)],[1835, 1827])).
% 27.48/17.69 tff(1837,plain,
% 27.48/17.69 ((f1(c2, c2) = f5(f9(c2, c2))) <=> (f1(c2, c2) = c2)),
% 27.48/17.69 inference(monotonicity,[status(thm)],[187])).
% 27.48/17.69 tff(1838,plain,
% 27.48/17.69 ((f1(c2, c2) = c2) <=> (f1(c2, c2) = f5(f9(c2, c2)))),
% 27.48/17.69 inference(symmetry,[status(thm)],[1837])).
% 27.48/17.69 tff(1839,plain,
% 27.48/17.69 ((~(f1(c2, c2) = c2)) <=> (~(f1(c2, c2) = f5(f9(c2, c2))))),
% 27.48/17.69 inference(monotonicity,[status(thm)],[1838])).
% 27.48/17.69 tff(1840,plain,
% 27.48/17.69 (~(f1(c2, c2) = f5(f9(c2, c2)))),
% 27.48/17.69 inference(modus_ponens,[status(thm)],[1828, 1839])).
% 27.48/17.69 tff(1841,plain,
% 27.48/17.69 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (f1(c2, c2) = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f1(c2, c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (f1(c2, c2) = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f1(c2, c2))))),
% 27.48/17.69 inference(rewrite,[status(thm)],[])).
% 27.48/17.69 tff(1842,plain,
% 27.48/17.69 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (f1(c2, c2) = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f1(c2, c2))))),
% 27.48/17.69 inference(quant_inst,[status(thm)],[])).
% 27.48/17.69 tff(1843,plain,
% 27.48/17.69 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (f1(c2, c2) = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f1(c2, c2)))),
% 27.48/17.69 inference(modus_ponens,[status(thm)],[1842, 1841])).
% 27.48/17.69 tff(1844,plain,
% 27.48/17.69 ((f7(f9(c2, c2)) = f9(c2, c2)) | (f1(c2, c2) = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f1(c2, c2)))),
% 27.48/17.69 inference(unit_resolution,[status(thm)],[1843, 676, 122, 185, 256])).
% 27.48/17.69 tff(1845,plain,
% 27.48/17.69 ($false),
% 27.48/17.69 inference(unit_resolution,[status(thm)],[1844, 1798, 1840, 1836])).
% 27.48/17.69 tff(1846,plain,((f1(c2, c2) = c2) | (~(f10(c2) = c2)) | big_f(f9(c2, c2), f10(c2)) | (~(f7(c1) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f5(c1) = c2)) | (c2 = c3) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4))), inference(lemma,lemma(discharge,[]))).
% 27.48/17.69 tff(1847,plain,
% 27.48/17.69 (f1(c2, c2) = c2),
% 27.48/17.69 inference(unit_resolution,[status(thm)],[1846, 1825, 256, 347, 148, 79, 186, 122, 574, 346, 565])).
% 27.48/17.69 tff(1848,plain,
% 27.48/17.69 (big_f(c2, f1(c2, c2)) <=> big_f(c2, c2)),
% 27.48/17.69 inference(monotonicity,[status(thm)],[1847])).
% 27.48/17.69 tff(1849,plain,
% 27.48/17.69 (big_f(c2, c2) <=> big_f(c2, f1(c2, c2))),
% 27.48/17.69 inference(symmetry,[status(thm)],[1848])).
% 27.48/17.69 tff(1850,plain,
% 27.48/17.69 (big_f(c2, f1(c2, c2))),
% 27.48/17.69 inference(modus_ponens,[status(thm)],[1345, 1849])).
% 27.48/17.69 tff(1851,plain,
% 27.48/17.69 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)))),
% 27.48/17.69 inference(rewrite,[status(thm)],[])).
% 27.48/17.69 tff(1852,plain,
% 27.48/17.69 (((c2 = c3) | (~(f9(c2, c2) = c4)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2)))) <=> ((c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)))),
% 27.48/17.69 inference(rewrite,[status(thm)],[])).
% 27.48/17.69 tff(1853,plain,
% 27.48/17.69 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f9(c2, c2) = c4)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4))))),
% 27.48/17.69 inference(monotonicity,[status(thm)],[1852])).
% 27.48/17.69 tff(1854,plain,
% 27.48/17.69 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f9(c2, c2) = c4)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)))),
% 27.48/17.69 inference(transitivity,[status(thm)],[1853, 1851])).
% 27.48/17.69 tff(1855,plain,
% 27.48/17.69 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f9(c2, c2) = c4)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))),
% 27.48/17.69 inference(quant_inst,[status(thm)],[])).
% 27.48/17.69 tff(1856,plain,
% 27.48/17.69 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4))),
% 27.48/17.69 inference(modus_ponens,[status(thm)],[1855, 1854])).
% 27.48/17.69 tff(1857,plain,
% 27.48/17.69 ($false),
% 27.48/17.69 inference(unit_resolution,[status(thm)],[1856, 553, 1825, 1847, 1850, 574, 346, 565])).
% 27.48/17.69 tff(1858,plain,((~(c4 = c1)) | (~big_f(c2, c2)) | big_f(f9(c2, c2), f10(c2)) | (~(f7(c1) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f5(c1) = c2)) | (~(f10(c2) = c2)) | (~(f7(c2) = c1)) | (~big_f(f7(c2), c1))), inference(lemma,lemma(discharge,[]))).
% 27.48/17.69 tff(1859,plain,
% 27.48/17.69 (~(c4 = c1)),
% 27.48/17.69 inference(unit_resolution,[status(thm)],[1858, 256, 1345, 347, 148, 79, 186, 122, 292, 338])).
% 27.48/17.69 tff(1860,plain,
% 27.48/17.69 (~(f9(c2, c2) = c4)),
% 27.48/17.69 inference(modus_ponens,[status(thm)],[1859, 1814])).
% 27.48/17.70 tff(1861,assumption,(~(f9(c2, c2) = c4)), introduced(assumption)).
% 27.48/17.70 tff(1862,assumption,(~big_f(c2, f1(c2, c2))), introduced(assumption)).
% 27.48/17.70 tff(1863,plain,
% 27.48/17.70 (f3(f9(c2, c2), f9(c2, c2)) = f3(c1, c1)),
% 27.48/17.70 inference(monotonicity,[status(thm)],[161, 161])).
% 27.48/17.70 tff(1864,plain,
% 27.48/17.70 (f3(f9(c2, c2), f9(c2, c2)) = c2),
% 27.48/17.70 inference(transitivity,[status(thm)],[1863, 1441])).
% 27.48/17.70 tff(1865,plain,
% 27.48/17.70 ((f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) <=> (c2 = f9(c2, c2))),
% 27.48/17.70 inference(monotonicity,[status(thm)],[1864])).
% 27.48/17.70 tff(1866,plain,
% 27.48/17.70 ((f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) <=> (f9(c2, c2) = c2)),
% 27.48/17.70 inference(transitivity,[status(thm)],[1865, 167])).
% 27.48/17.70 tff(1867,plain,
% 27.48/17.70 ((f9(c2, c2) = c2) <=> (f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))),
% 27.48/17.70 inference(symmetry,[status(thm)],[1866])).
% 27.48/17.70 tff(1868,plain,
% 27.48/17.70 ((~(f9(c2, c2) = c2)) <=> (~(f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)))),
% 27.48/17.70 inference(monotonicity,[status(thm)],[1867])).
% 27.48/17.70 tff(1869,plain,
% 27.48/17.70 (~(f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))),
% 27.48/17.70 inference(modus_ponens,[status(thm)],[185, 1868])).
% 27.48/17.70 tff(1870,plain,
% 27.48/17.70 (big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2)) <=> big_f(c2, c1)),
% 27.48/17.70 inference(monotonicity,[status(thm)],[1864, 161])).
% 27.48/17.70 tff(1871,plain,
% 27.48/17.70 (big_f(c2, c1) <=> big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))),
% 27.48/17.70 inference(symmetry,[status(thm)],[1870])).
% 27.48/17.70 tff(1872,plain,
% 27.48/17.70 ((~big_f(c2, c1)) <=> (~big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2)))),
% 27.48/17.70 inference(monotonicity,[status(thm)],[1871])).
% 27.48/17.70 tff(1873,plain,
% 27.48/17.70 (~big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))),
% 27.48/17.70 inference(modus_ponens,[status(thm)],[2, 1872])).
% 27.48/17.70 tff(1874,plain,
% 27.48/17.70 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (f9(c2, c2) = c4) | (f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (f9(c2, c2) = c4) | (f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2)))),
% 27.48/17.70 inference(rewrite,[status(thm)],[])).
% 27.48/17.70 tff(1875,plain,
% 27.48/17.70 (((f9(c2, c2) = c4) | (f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2)) | (c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2))) <=> ((c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (f9(c2, c2) = c4) | (f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2)))),
% 27.48/17.70 inference(rewrite,[status(thm)],[])).
% 27.48/17.70 tff(1876,plain,
% 27.48/17.70 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f9(c2, c2) = c4) | (f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2)) | (c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (f9(c2, c2) = c4) | (f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))))),
% 27.48/17.70 inference(monotonicity,[status(thm)],[1875])).
% 27.48/17.70 tff(1877,plain,
% 27.48/17.70 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f9(c2, c2) = c4) | (f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2)) | (c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (f9(c2, c2) = c4) | (f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2)))),
% 27.48/17.70 inference(transitivity,[status(thm)],[1876, 1874])).
% 27.48/17.70 tff(1878,plain,
% 27.48/17.70 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f9(c2, c2) = c4) | (f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2)) | (c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)))),
% 27.48/17.70 inference(quant_inst,[status(thm)],[])).
% 27.48/17.70 tff(1879,plain,
% 27.48/17.70 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (f9(c2, c2) = c4) | (f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))),
% 27.48/17.70 inference(modus_ponens,[status(thm)],[1878, 1877])).
% 27.48/17.70 tff(1880,plain,
% 27.48/17.70 ((f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))),
% 27.48/17.70 inference(unit_resolution,[status(thm)],[1879, 1014, 377, 1828, 1862, 1861])).
% 27.48/17.70 tff(1881,plain,
% 27.48/17.70 ($false),
% 27.48/17.70 inference(unit_resolution,[status(thm)],[1880, 1873, 1869])).
% 27.48/17.70 tff(1882,plain,((~(f3(c1, c1) = c2)) | (c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (f9(c2, c2) = c4) | big_f(c2, c1) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.48/17.70 tff(1883,plain,
% 27.48/17.70 (~(f3(c1, c1) = c2)),
% 27.48/17.70 inference(unit_resolution,[status(thm)],[1882, 1862, 1828, 377, 1861, 2, 148, 79, 122])).
% 27.48/17.70 tff(1884,plain,
% 27.48/17.70 (f3(c1, c1) = c1),
% 27.48/17.70 inference(unit_resolution,[status(thm)],[1416, 1883])).
% 27.48/17.70 tff(1885,plain,
% 27.48/17.70 (f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)),
% 27.48/17.70 inference(transitivity,[status(thm)],[1863, 1884, 149, 132])).
% 27.48/17.70 tff(1886,plain,
% 27.48/17.70 (f3(f9(c2, c2), f9(c2, c2)) = f7(c2)),
% 27.48/17.70 inference(transitivity,[status(thm)],[1863, 1884, 342])).
% 27.48/17.70 tff(1887,plain,
% 27.48/17.70 (big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2)) <=> big_f(f7(c2), c1)),
% 27.48/17.70 inference(monotonicity,[status(thm)],[1886, 161])).
% 27.48/17.70 tff(1888,plain,
% 27.48/17.70 (big_f(f7(c2), c1) <=> big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))),
% 27.48/17.70 inference(symmetry,[status(thm)],[1887])).
% 27.48/17.70 tff(1889,plain,
% 27.48/17.70 (big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))),
% 27.48/17.70 inference(modus_ponens,[status(thm)],[338, 1888])).
% 27.48/17.70 tff(1890,plain,
% 27.48/17.70 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))))),
% 27.48/17.70 inference(rewrite,[status(thm)],[])).
% 27.48/17.70 tff(1891,plain,
% 27.48/17.70 (((f9(c2, c2) = c4) | (c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2)))) <=> ((c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))))),
% 27.48/17.70 inference(rewrite,[status(thm)],[])).
% 27.48/17.70 tff(1892,plain,
% 27.48/17.70 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((f9(c2, c2) = c4) | (c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2)))))),
% 27.48/17.70 inference(monotonicity,[status(thm)],[1891])).
% 27.48/17.70 tff(1893,plain,
% 27.48/17.70 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((f9(c2, c2) = c4) | (c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))))),
% 27.48/17.70 inference(transitivity,[status(thm)],[1892, 1890])).
% 27.48/17.70 tff(1894,plain,
% 27.48/17.70 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((f9(c2, c2) = c4) | (c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))))),
% 27.48/17.70 inference(quant_inst,[status(thm)],[])).
% 27.48/17.70 tff(1895,plain,
% 27.48/17.70 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2)))),
% 27.48/17.70 inference(modus_ponens,[status(thm)],[1894, 1893])).
% 27.48/17.70 tff(1896,plain,
% 27.48/17.70 ((~(f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2)))),
% 27.48/17.70 inference(unit_resolution,[status(thm)],[1895, 969, 377, 1828, 1862, 1861])).
% 27.48/17.70 tff(1897,plain,
% 27.48/17.70 ($false),
% 27.48/17.70 inference(unit_resolution,[status(thm)],[1896, 1889, 1885])).
% 27.48/17.70 tff(1898,plain,(big_f(c2, f1(c2, c2)) | (c2 = c3) | (f1(c2, c2) = c2) | (f9(c2, c2) = c4) | (~big_f(f7(c2), c1)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f7(c2) = c1)) | big_f(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 27.48/17.70 tff(1899,plain,
% 27.48/17.70 (big_f(c2, f1(c2, c2))),
% 27.48/17.70 inference(unit_resolution,[status(thm)],[1898, 1828, 377, 1861, 338, 148, 79, 122, 292, 2])).
% 27.48/17.70 tff(1900,plain,
% 27.48/17.70 (big_f(f7(f9(c2, c2)), f1(c2, c2))),
% 27.48/17.70 inference(modus_ponens,[status(thm)],[1899, 1827])).
% 27.48/17.70 tff(1901,plain,
% 27.48/17.70 ($false),
% 27.48/17.70 inference(unit_resolution,[status(thm)],[1844, 1798, 1840, 1900])).
% 27.48/17.70 tff(1902,plain,((f1(c2, c2) = c2) | (~(f10(c2) = c2)) | big_f(f9(c2, c2), f10(c2)) | (~(f7(c1) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f5(c1) = c2)) | (c2 = c3) | (f9(c2, c2) = c4) | (~big_f(f7(c2), c1)) | (~(f7(c2) = c1)) | big_f(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 27.48/17.70 tff(1903,plain,
% 27.48/17.70 (f1(c2, c2) = c2),
% 27.48/17.70 inference(unit_resolution,[status(thm)],[1902, 2, 256, 347, 148, 79, 186, 377, 1860, 338, 292, 122])).
% 27.48/17.70 tff(1904,plain,
% 27.48/17.70 (big_f(c2, f1(c2, c2)) <=> big_f(c2, c2)),
% 27.48/17.70 inference(monotonicity,[status(thm)],[1903])).
% 27.48/17.70 tff(1905,plain,
% 27.48/17.70 (big_f(c2, c2) <=> big_f(c2, f1(c2, c2))),
% 27.48/17.70 inference(symmetry,[status(thm)],[1904])).
% 27.48/17.70 tff(1906,plain,
% 27.48/17.70 (big_f(c2, f1(c2, c2))),
% 27.48/17.70 inference(modus_ponens,[status(thm)],[1345, 1905])).
% 27.48/17.70 tff(1907,assumption,(big_f(c2, f1(c2, c2))), introduced(assumption)).
% 27.48/17.70 tff(1908,assumption,(f1(c2, c2) = c2), introduced(assumption)).
% 27.48/17.70 tff(1909,plain,
% 27.48/17.70 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f9(c2, c2) = c4) | (f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f9(c2, c2) = c4) | (f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2)))),
% 27.48/17.70 inference(rewrite,[status(thm)],[])).
% 27.48/17.70 tff(1910,plain,
% 27.48/17.70 (((f9(c2, c2) = c4) | (f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2)) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2)))) <=> ((c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f9(c2, c2) = c4) | (f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2)))),
% 27.48/17.70 inference(rewrite,[status(thm)],[])).
% 27.48/17.70 tff(1911,plain,
% 27.48/17.70 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f9(c2, c2) = c4) | (f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2)) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f9(c2, c2) = c4) | (f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))))),
% 27.48/17.70 inference(monotonicity,[status(thm)],[1910])).
% 27.48/17.70 tff(1912,plain,
% 27.48/17.70 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f9(c2, c2) = c4) | (f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2)) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f9(c2, c2) = c4) | (f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2)))),
% 27.48/17.70 inference(transitivity,[status(thm)],[1911, 1909])).
% 27.48/17.70 tff(1913,plain,
% 27.48/17.70 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f9(c2, c2) = c4) | (f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2)) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))),
% 27.48/17.70 inference(quant_inst,[status(thm)],[])).
% 27.48/17.70 tff(1914,plain,
% 27.48/17.70 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f9(c2, c2) = c4) | (f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))),
% 27.48/17.70 inference(modus_ponens,[status(thm)],[1913, 1912])).
% 27.48/17.70 tff(1915,plain,
% 27.48/17.70 ((f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))),
% 27.48/17.70 inference(unit_resolution,[status(thm)],[1914, 904, 377, 1908, 1907, 1861])).
% 27.48/17.70 tff(1916,plain,
% 27.48/17.70 ($false),
% 27.48/17.70 inference(unit_resolution,[status(thm)],[1915, 1873, 1869])).
% 27.48/17.70 tff(1917,plain,((~(f3(c1, c1) = c2)) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f9(c2, c2) = c4) | big_f(c2, c1) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.48/17.70 tff(1918,plain,
% 27.48/17.70 (~(f3(c1, c1) = c2)),
% 27.48/17.70 inference(unit_resolution,[status(thm)],[1917, 1903, 377, 1906, 1860, 2, 148, 79, 122])).
% 27.48/17.70 tff(1919,plain,
% 27.48/17.70 (f3(c1, c1) = c1),
% 27.48/17.70 inference(unit_resolution,[status(thm)],[1416, 1918])).
% 27.48/17.70 tff(1920,plain,
% 27.48/17.70 (f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)),
% 27.48/17.70 inference(transitivity,[status(thm)],[1863, 1919, 149, 132])).
% 27.48/17.70 tff(1921,plain,
% 27.48/17.70 (f3(f9(c2, c2), f9(c2, c2)) = f7(c2)),
% 27.48/17.70 inference(transitivity,[status(thm)],[1863, 1919, 342])).
% 27.48/17.70 tff(1922,plain,
% 27.48/17.70 (big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2)) <=> big_f(f7(c2), c1)),
% 27.48/17.70 inference(monotonicity,[status(thm)],[1921, 161])).
% 27.48/17.70 tff(1923,plain,
% 27.48/17.70 (big_f(f7(c2), c1) <=> big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))),
% 27.48/17.70 inference(symmetry,[status(thm)],[1922])).
% 27.48/17.70 tff(1924,plain,
% 27.48/17.70 (big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))),
% 27.48/17.70 inference(modus_ponens,[status(thm)],[338, 1923])).
% 27.48/17.70 tff(1925,plain,
% 27.48/17.70 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))))),
% 27.48/17.70 inference(rewrite,[status(thm)],[])).
% 27.48/17.70 tff(1926,plain,
% 27.48/17.70 (((f9(c2, c2) = c4) | (c2 = c3) | (~(f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2)))) <=> ((c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))))),
% 27.48/17.70 inference(rewrite,[status(thm)],[])).
% 27.48/17.70 tff(1927,plain,
% 27.48/17.70 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f9(c2, c2) = c4) | (c2 = c3) | (~(f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2)))))),
% 27.48/17.70 inference(monotonicity,[status(thm)],[1926])).
% 27.48/17.70 tff(1928,plain,
% 27.48/17.70 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f9(c2, c2) = c4) | (c2 = c3) | (~(f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))))),
% 27.48/17.70 inference(transitivity,[status(thm)],[1927, 1925])).
% 27.48/17.70 tff(1929,plain,
% 27.48/17.70 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f9(c2, c2) = c4) | (c2 = c3) | (~(f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))),
% 27.48/17.70 inference(quant_inst,[status(thm)],[])).
% 27.48/17.70 tff(1930,plain,
% 27.48/17.70 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2)))),
% 27.48/17.71 inference(modus_ponens,[status(thm)],[1929, 1928])).
% 27.48/17.71 tff(1931,plain,
% 27.48/17.71 ((~(f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2)))),
% 27.48/17.71 inference(unit_resolution,[status(thm)],[1930, 933, 377, 1903, 1906, 1860])).
% 27.48/17.71 tff(1932,plain,
% 27.48/17.71 ($false),
% 27.48/17.71 inference(unit_resolution,[status(thm)],[1931, 1924, 1920])).
% 27.48/17.71 tff(1933,plain,(big_f(c2, c1) | (c2 = c3) | (~big_f(f7(c2), c1)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f7(c2) = c1)) | (~big_f(c2, c2)) | big_f(f9(c2, c2), f10(c2)) | (~(f7(c1) = c2)) | (~(f5(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.48/17.71 tff(1934,plain,
% 27.48/17.71 (c2 = c3),
% 27.48/17.71 inference(unit_resolution,[status(thm)],[1933, 1811, 337, 148, 79, 122, 292, 1345, 256, 347, 186])).
% 27.48/17.71 tff(1935,plain,
% 27.48/17.71 (~(f9(c2, c2) = c3)),
% 27.48/17.71 inference(unit_resolution,[status(thm)],[1824, 1934, 185, 79, 122])).
% 27.48/17.71 tff(1936,plain,
% 27.48/17.71 (~(c4 = c1)),
% 27.48/17.71 inference(unit_resolution,[status(thm)],[1858, 256, 1345, 347, 148, 79, 186, 122, 292, 337])).
% 27.48/17.71 tff(1937,plain,
% 27.48/17.71 (~(f9(c2, c2) = c4)),
% 27.48/17.71 inference(modus_ponens,[status(thm)],[1936, 1814])).
% 27.48/17.71 tff(1938,assumption,(f3(c1, c1) = c1), introduced(assumption)).
% 27.48/17.71 tff(1939,plain,
% 27.48/17.71 (f3(f9(c2, c2), f9(c2, c2)) = f7(c2)),
% 27.48/17.71 inference(transitivity,[status(thm)],[1863, 1938, 342])).
% 27.48/17.71 tff(1940,plain,
% 27.48/17.71 (big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2)) <=> big_f(f7(c2), c1)),
% 27.48/17.71 inference(monotonicity,[status(thm)],[1939, 161])).
% 27.48/17.71 tff(1941,plain,
% 27.48/17.71 (big_f(f7(c2), c1) <=> big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))),
% 27.48/17.71 inference(symmetry,[status(thm)],[1940])).
% 27.48/17.71 tff(1942,plain,
% 27.48/17.71 (big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))),
% 27.48/17.71 inference(modus_ponens,[status(thm)],[338, 1941])).
% 27.48/17.71 tff(1943,plain,
% 27.48/17.71 (f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)),
% 27.48/17.71 inference(transitivity,[status(thm)],[1863, 1938, 149, 132])).
% 27.48/17.71 tff(1944,plain,
% 27.48/17.71 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((f9(c2, c2) = c3) | (f9(c2, c2) = c4) | (f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2))) | (~(f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (f9(c2, c2) = c3) | (f9(c2, c2) = c4) | (f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2))) | (~(f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))))),
% 27.48/17.71 inference(rewrite,[status(thm)],[])).
% 27.48/17.71 tff(1945,plain,
% 27.48/17.71 (((f9(c2, c2) = c4) | (f9(c2, c2) = c3) | (f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2))) | (~(f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2)))) <=> ((f9(c2, c2) = c3) | (f9(c2, c2) = c4) | (f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2))) | (~(f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))))),
% 27.48/17.71 inference(rewrite,[status(thm)],[])).
% 27.48/17.71 tff(1946,plain,
% 27.48/17.71 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((f9(c2, c2) = c4) | (f9(c2, c2) = c3) | (f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2))) | (~(f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((f9(c2, c2) = c3) | (f9(c2, c2) = c4) | (f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2))) | (~(f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2)))))),
% 27.48/17.71 inference(monotonicity,[status(thm)],[1945])).
% 27.48/17.71 tff(1947,plain,
% 27.48/17.71 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((f9(c2, c2) = c4) | (f9(c2, c2) = c3) | (f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2))) | (~(f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (f9(c2, c2) = c3) | (f9(c2, c2) = c4) | (f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2))) | (~(f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))))),
% 27.48/17.71 inference(transitivity,[status(thm)],[1946, 1944])).
% 27.48/17.71 tff(1948,plain,
% 27.48/17.71 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((f9(c2, c2) = c4) | (f9(c2, c2) = c3) | (f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2))) | (~(f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))))),
% 27.48/17.71 inference(quant_inst,[status(thm)],[])).
% 27.48/17.71 tff(1949,plain,
% 27.48/17.71 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (f9(c2, c2) = c3) | (f9(c2, c2) = c4) | (f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2))) | (~(f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2)))),
% 27.48/17.71 inference(modus_ponens,[status(thm)],[1948, 1947])).
% 27.48/17.71 tff(1950,plain,
% 27.48/17.71 ((f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2))) | (~(f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2)))),
% 27.48/17.71 inference(unit_resolution,[status(thm)],[1949, 969, 1861, 566])).
% 27.48/17.71 tff(1951,plain,
% 27.48/17.71 ($false),
% 27.48/17.71 inference(unit_resolution,[status(thm)],[1950, 587, 582, 1943, 1942])).
% 27.48/17.71 tff(1952,plain,((~(f1(c1, c1) = c2)) | (f9(c2, c2) = c4) | (f9(c2, c2) = c3) | (~big_f(f7(c2), c1)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f7(c2) = c1)) | (~(f3(c1, c1) = c1)) | big_f(f9(c2, c2), f10(c2))), inference(lemma,lemma(discharge,[]))).
% 27.48/17.71 tff(1953,plain,
% 27.48/17.71 (~(f1(c1, c1) = c2)),
% 27.48/17.71 inference(unit_resolution,[status(thm)],[1952, 1938, 566, 338, 148, 79, 122, 292, 1861, 256])).
% 27.48/17.71 tff(1954,plain,
% 27.48/17.71 (f1(c1, c1) = c1),
% 27.48/17.71 inference(unit_resolution,[status(thm)],[601, 1953])).
% 27.48/17.71 tff(1955,plain,
% 27.48/17.71 (f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)),
% 27.48/17.71 inference(transitivity,[status(thm)],[576, 1954, 149, 132])).
% 27.48/17.71 tff(1956,plain,
% 27.48/17.71 (f1(f9(c2, c2), f9(c2, c2)) = c1),
% 27.48/17.71 inference(transitivity,[status(thm)],[576, 1954])).
% 27.48/17.71 tff(1957,plain,
% 27.48/17.71 (big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2))) <=> big_f(f7(c2), c1)),
% 27.48/17.71 inference(monotonicity,[status(thm)],[343, 1956])).
% 27.48/17.71 tff(1958,plain,
% 27.48/17.71 (big_f(f7(c2), c1) <=> big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2)))),
% 27.48/17.71 inference(symmetry,[status(thm)],[1957])).
% 27.48/17.71 tff(1959,plain,
% 27.48/17.71 (big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2)))),
% 27.48/17.71 inference(modus_ponens,[status(thm)],[338, 1958])).
% 27.48/17.71 tff(1960,plain,
% 27.48/17.71 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f9(c2, c2) = c3) | (f9(c2, c2) = c4) | (~(f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2)))) | (~(f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (f9(c2, c2) = c3) | (f9(c2, c2) = c4) | (~(f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2)))) | (~(f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))))),
% 27.48/17.71 inference(rewrite,[status(thm)],[])).
% 27.48/17.71 tff(1961,plain,
% 27.48/17.71 (((f9(c2, c2) = c4) | (f9(c2, c2) = c3) | (~(f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))) | (~(f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2))))) <=> ((f9(c2, c2) = c3) | (f9(c2, c2) = c4) | (~(f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2)))) | (~(f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))))),
% 27.48/17.71 inference(rewrite,[status(thm)],[])).
% 27.48/17.71 tff(1962,plain,
% 27.48/17.71 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f9(c2, c2) = c4) | (f9(c2, c2) = c3) | (~(f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))) | (~(f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2)))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f9(c2, c2) = c3) | (f9(c2, c2) = c4) | (~(f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2)))) | (~(f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2)))))),
% 27.48/17.71 inference(monotonicity,[status(thm)],[1961])).
% 27.48/17.71 tff(1963,plain,
% 27.48/17.71 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f9(c2, c2) = c4) | (f9(c2, c2) = c3) | (~(f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))) | (~(f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2)))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (f9(c2, c2) = c3) | (f9(c2, c2) = c4) | (~(f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2)))) | (~(f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))))),
% 27.48/17.71 inference(transitivity,[status(thm)],[1962, 1960])).
% 27.48/17.71 tff(1964,plain,
% 27.48/17.71 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f9(c2, c2) = c4) | (f9(c2, c2) = c3) | (~(f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))) | (~(f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2)))))),
% 27.48/17.71 inference(quant_inst,[status(thm)],[])).
% 27.48/17.71 tff(1965,plain,
% 27.48/17.71 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (f9(c2, c2) = c3) | (f9(c2, c2) = c4) | (~(f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2)))) | (~(f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2)))),
% 27.48/17.71 inference(modus_ponens,[status(thm)],[1964, 1963])).
% 27.48/17.71 tff(1966,plain,
% 27.48/17.71 ((~(f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2)))) | (~(f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2)))),
% 27.48/17.71 inference(unit_resolution,[status(thm)],[1965, 933, 1861, 566])).
% 27.48/17.71 tff(1967,plain,
% 27.48/17.71 ($false),
% 27.48/17.71 inference(unit_resolution,[status(thm)],[1966, 1959, 1955, 1943, 1942])).
% 27.48/17.71 tff(1968,plain,((~(f3(c1, c1) = c1)) | (f9(c2, c2) = c4) | (f9(c2, c2) = c3) | (~big_f(f7(c2), c1)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f7(c2) = c1)) | big_f(f9(c2, c2), f10(c2))), inference(lemma,lemma(discharge,[]))).
% 27.48/17.71 tff(1969,plain,
% 27.48/17.71 (~(f3(c1, c1) = c1)),
% 27.48/17.71 inference(unit_resolution,[status(thm)],[1968, 1937, 1935, 337, 148, 79, 122, 292, 256])).
% 27.48/17.71 tff(1970,plain,
% 27.48/17.71 (f3(c1, c1) = c2),
% 27.48/17.71 inference(unit_resolution,[status(thm)],[1416, 1969])).
% 27.48/17.71 tff(1971,plain,
% 27.48/17.71 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f9(c2, c2) = c3) | (f9(c2, c2) = c4) | (~(f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2)))) | (f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (f9(c2, c2) = c3) | (f9(c2, c2) = c4) | (~(f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2)))) | (f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2)))),
% 27.48/17.71 inference(rewrite,[status(thm)],[])).
% 27.48/17.71 tff(1972,plain,
% 27.48/17.71 (((f9(c2, c2) = c4) | (f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2)) | (f9(c2, c2) = c3) | (~(f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2))))) <=> ((f9(c2, c2) = c3) | (f9(c2, c2) = c4) | (~(f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2)))) | (f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2)))),
% 27.48/17.71 inference(rewrite,[status(thm)],[])).
% 27.48/17.71 tff(1973,plain,
% 27.48/17.71 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f9(c2, c2) = c4) | (f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2)) | (f9(c2, c2) = c3) | (~(f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2)))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f9(c2, c2) = c3) | (f9(c2, c2) = c4) | (~(f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2)))) | (f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))))),
% 27.48/17.71 inference(monotonicity,[status(thm)],[1972])).
% 27.48/17.71 tff(1974,plain,
% 27.48/17.71 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f9(c2, c2) = c4) | (f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2)) | (f9(c2, c2) = c3) | (~(f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2)))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (f9(c2, c2) = c3) | (f9(c2, c2) = c4) | (~(f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2)))) | (f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2)))),
% 27.48/17.71 inference(transitivity,[status(thm)],[1973, 1971])).
% 27.48/17.71 tff(1975,plain,
% 27.48/17.71 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f9(c2, c2) = c4) | (f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2)) | (f9(c2, c2) = c3) | (~(f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2)))))),
% 27.48/17.71 inference(quant_inst,[status(thm)],[])).
% 27.48/17.71 tff(1976,plain,
% 27.48/17.71 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (f9(c2, c2) = c3) | (f9(c2, c2) = c4) | (~(f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2)))) | (f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))),
% 27.48/17.72 inference(modus_ponens,[status(thm)],[1975, 1974])).
% 27.48/17.72 tff(1977,plain,
% 27.48/17.72 ((~(f1(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, c2), f1(f9(c2, c2), f9(c2, c2)))) | (f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))),
% 27.48/17.72 inference(unit_resolution,[status(thm)],[1976, 904, 1861, 566])).
% 27.48/17.72 tff(1978,plain,
% 27.48/17.72 ($false),
% 27.48/17.72 inference(unit_resolution,[status(thm)],[1977, 629, 625, 1869, 1873])).
% 27.48/17.72 tff(1979,plain,((~(f1(c1, c1) = c1)) | (f9(c2, c2) = c4) | (f9(c2, c2) = c3) | big_f(c2, c1) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f3(c1, c1) = c2)) | (~big_f(f7(c2), c1)) | (~(f7(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 27.48/17.72 tff(1980,plain,
% 27.48/17.72 (~(f1(c1, c1) = c1)),
% 27.48/17.72 inference(unit_resolution,[status(thm)],[1979, 1937, 1935, 1811, 148, 79, 122, 1970, 337, 292])).
% 27.48/17.72 tff(1981,plain,
% 27.48/17.72 (f1(c1, c1) = c2),
% 27.48/17.72 inference(unit_resolution,[status(thm)],[601, 1980])).
% 27.48/17.72 tff(1982,plain,
% 27.48/17.72 (f1(c1, c1) = f10(c2)),
% 27.48/17.72 inference(transitivity,[status(thm)],[1981, 216])).
% 27.48/17.72 tff(1983,plain,
% 27.48/17.72 (big_f(c1, f1(c1, c1)) <=> big_f(f9(c2, c2), f10(c2))),
% 27.48/17.72 inference(monotonicity,[status(thm)],[150, 1982])).
% 27.48/17.72 tff(1984,plain,
% 27.48/17.72 (big_f(f9(c2, c2), f10(c2)) <=> big_f(c1, f1(c1, c1))),
% 27.48/17.72 inference(symmetry,[status(thm)],[1983])).
% 27.48/17.72 tff(1985,plain,
% 27.48/17.72 ((~big_f(f9(c2, c2), f10(c2))) <=> (~big_f(c1, f1(c1, c1)))),
% 27.48/17.72 inference(monotonicity,[status(thm)],[1984])).
% 27.48/17.72 tff(1986,plain,
% 27.48/17.72 (~big_f(c1, f1(c1, c1))),
% 27.48/17.72 inference(modus_ponens,[status(thm)],[256, 1985])).
% 27.48/17.72 tff(1987,plain,
% 27.48/17.72 (c2 = f3(c1, c1)),
% 27.48/17.72 inference(symmetry,[status(thm)],[1970])).
% 27.48/17.72 tff(1988,plain,
% 27.48/17.72 (big_f(c2, c1) <=> big_f(f3(c1, c1), c1)),
% 27.48/17.72 inference(monotonicity,[status(thm)],[1987])).
% 27.48/17.72 tff(1989,plain,
% 27.48/17.72 ((~big_f(c2, c1)) <=> (~big_f(f3(c1, c1), c1))),
% 27.48/17.72 inference(monotonicity,[status(thm)],[1988])).
% 27.48/17.72 tff(1990,plain,
% 27.48/17.72 (~big_f(f3(c1, c1), c1)),
% 27.48/17.72 inference(modus_ponens,[status(thm)],[1811, 1989])).
% 27.48/17.72 tff(1991,plain,
% 27.48/17.72 (c3 = c2),
% 27.48/17.72 inference(symmetry,[status(thm)],[1934])).
% 27.48/17.72 tff(1992,plain,
% 27.48/17.72 ((f9(f10(c2), f4(c4)) = c3) <=> (f9(c2, c2) = c2)),
% 27.48/17.72 inference(monotonicity,[status(thm)],[132, 1991])).
% 27.48/17.72 tff(1993,plain,
% 27.48/17.72 ((f9(c2, c2) = c2) <=> (f9(f10(c2), f4(c4)) = c3)),
% 27.48/17.72 inference(symmetry,[status(thm)],[1992])).
% 27.48/17.72 tff(1994,plain,
% 27.48/17.72 ((f9(c2, c2) = c2) <=> (c1 = c3)),
% 27.48/17.72 inference(transitivity,[status(thm)],[1993, 212])).
% 27.48/17.72 tff(1995,plain,
% 27.48/17.72 ((~(f9(c2, c2) = c2)) <=> (~(c1 = c3))),
% 27.48/17.72 inference(monotonicity,[status(thm)],[1994])).
% 27.48/17.72 tff(1996,plain,
% 27.48/17.72 (~(c1 = c3)),
% 27.48/17.72 inference(modus_ponens,[status(thm)],[185, 1995])).
% 27.48/17.72 tff(1997,plain,
% 27.48/17.72 ((~(c4 = c1)) <=> (~(c1 = c4))),
% 27.48/17.72 inference(monotonicity,[status(thm)],[479])).
% 27.48/17.72 tff(1998,plain,
% 27.48/17.72 (~(c1 = c4)),
% 27.48/17.72 inference(modus_ponens,[status(thm)],[1936, 1997])).
% 27.48/17.72 tff(1999,plain,
% 27.48/17.72 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (big_f(f3(c1, c1), c1) | (f1(c1, c1) = c1) | (c1 = c3) | (f3(c1, c1) = c1) | (c1 = c4) | big_f(c1, f1(c1, c1)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | big_f(f3(c1, c1), c1) | (f1(c1, c1) = c1) | (c1 = c3) | (f3(c1, c1) = c1) | (c1 = c4) | big_f(c1, f1(c1, c1)))),
% 27.48/17.72 inference(rewrite,[status(thm)],[])).
% 27.48/17.72 tff(2000,plain,
% 27.48/17.72 (((c1 = c4) | (f3(c1, c1) = c1) | big_f(f3(c1, c1), c1) | (c1 = c3) | (f1(c1, c1) = c1) | big_f(c1, f1(c1, c1))) <=> (big_f(f3(c1, c1), c1) | (f1(c1, c1) = c1) | (c1 = c3) | (f3(c1, c1) = c1) | (c1 = c4) | big_f(c1, f1(c1, c1)))),
% 27.48/17.72 inference(rewrite,[status(thm)],[])).
% 27.48/17.72 tff(2001,plain,
% 27.48/17.72 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c1 = c4) | (f3(c1, c1) = c1) | big_f(f3(c1, c1), c1) | (c1 = c3) | (f1(c1, c1) = c1) | big_f(c1, f1(c1, c1)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (big_f(f3(c1, c1), c1) | (f1(c1, c1) = c1) | (c1 = c3) | (f3(c1, c1) = c1) | (c1 = c4) | big_f(c1, f1(c1, c1))))),
% 27.48/17.72 inference(monotonicity,[status(thm)],[2000])).
% 27.48/17.72 tff(2002,plain,
% 27.48/17.72 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c1 = c4) | (f3(c1, c1) = c1) | big_f(f3(c1, c1), c1) | (c1 = c3) | (f1(c1, c1) = c1) | big_f(c1, f1(c1, c1)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | big_f(f3(c1, c1), c1) | (f1(c1, c1) = c1) | (c1 = c3) | (f3(c1, c1) = c1) | (c1 = c4) | big_f(c1, f1(c1, c1)))),
% 27.48/17.72 inference(transitivity,[status(thm)],[2001, 1999])).
% 27.48/17.72 tff(2003,plain,
% 27.48/17.72 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c1 = c4) | (f3(c1, c1) = c1) | big_f(f3(c1, c1), c1) | (c1 = c3) | (f1(c1, c1) = c1) | big_f(c1, f1(c1, c1)))),
% 27.48/17.72 inference(quant_inst,[status(thm)],[])).
% 27.48/17.72 tff(2004,plain,
% 27.48/17.72 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | big_f(f3(c1, c1), c1) | (f1(c1, c1) = c1) | (c1 = c3) | (f3(c1, c1) = c1) | (c1 = c4) | big_f(c1, f1(c1, c1))),
% 27.48/17.72 inference(modus_ponens,[status(thm)],[2003, 2002])).
% 27.48/17.72 tff(2005,plain,
% 27.48/17.72 (big_f(f3(c1, c1), c1) | (f1(c1, c1) = c1) | (c1 = c3) | (f3(c1, c1) = c1) | (c1 = c4) | big_f(c1, f1(c1, c1))),
% 27.48/17.72 inference(unit_resolution,[status(thm)],[2004, 1014])).
% 27.48/17.72 tff(2006,plain,
% 27.48/17.72 (big_f(c1, f1(c1, c1))),
% 27.48/17.72 inference(unit_resolution,[status(thm)],[2005, 1980, 1998, 1996, 1969, 1990])).
% 27.48/17.72 tff(2007,plain,
% 27.48/17.72 ($false),
% 27.48/17.72 inference(unit_resolution,[status(thm)],[2006, 1986])).
% 27.48/17.72 tff(2008,plain,(big_f(f9(c2, c2), f10(c2)) | (~(f10(c2) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f7(c2) = c1)) | (~big_f(c2, c2)) | (~(f7(c1) = c2)) | (~(f5(c1) = c2)) | (f9(c2, c2) = f5(f9(c2, c2))) | (~(f10(c1) = c2)) | (f7(f10(c1)) = f10(c1))), inference(lemma,lemma(discharge,[]))).
% 27.48/17.72 tff(2009,plain,
% 27.48/17.72 (big_f(f9(c2, c2), f10(c2))),
% 27.48/17.72 inference(unit_resolution,[status(thm)],[2008, 22, 148, 79, 122, 1791, 120, 1709, 1704, 15, 223])).
% 27.48/17.72 tff(2010,plain,
% 27.48/17.72 (big_f(f9(c2, c2), c2)),
% 27.48/17.72 inference(modus_ponens,[status(thm)],[2009, 218])).
% 27.48/17.72 tff(2011,plain,
% 27.48/17.72 (big_f(c2, f10(f9(c2, c2)))),
% 27.48/17.72 inference(modus_ponens,[status(thm)],[1791, 207])).
% 27.48/17.72 tff(2012,plain,
% 27.48/17.72 (big_f(f9(c2, c2), f10(f9(c2, c2))) <=> big_f(f9(c2, c2), f10(c2))),
% 27.48/17.72 inference(monotonicity,[status(thm)],[1763])).
% 27.48/17.72 tff(2013,plain,
% 27.48/17.72 (big_f(f9(c2, c2), f10(c2)) <=> big_f(f9(c2, c2), f10(f9(c2, c2)))),
% 27.48/17.72 inference(symmetry,[status(thm)],[2012])).
% 27.48/17.72 tff(2014,plain,
% 27.48/17.72 (big_f(f9(c2, c2), f10(f9(c2, c2)))),
% 27.48/17.72 inference(modus_ponens,[status(thm)],[2009, 2013])).
% 27.48/17.72 tff(2015,plain,
% 27.48/17.72 ((~big_f(c2, c1)) <=> (~big_f(c2, f9(c2, c2)))),
% 27.48/17.72 inference(monotonicity,[status(thm)],[1592])).
% 27.48/17.72 tff(2016,assumption,(big_f(c2, f10(f9(c2, c2)))), introduced(assumption)).
% 27.48/17.72 tff(2017,plain,
% 27.48/17.72 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f9(c2, c2) = f5(f9(c2, c2))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~big_f(f7(f9(c2, c2)), f9(c2, c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f9(c2, c2) = f5(f9(c2, c2))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~big_f(f7(f9(c2, c2)), f9(c2, c2))))),
% 27.48/17.72 inference(rewrite,[status(thm)],[])).
% 27.48/17.72 tff(2018,plain,
% 27.48/17.72 (((f10(f9(c2, c2)) = f9(c2, c2)) | (c2 = f8(f9(c2, c2))) | (~big_f(c2, f10(f9(c2, c2)))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f9(c2, c2)))) <=> ((f9(c2, c2) = f5(f9(c2, c2))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~big_f(f7(f9(c2, c2)), f9(c2, c2))))),
% 27.48/17.72 inference(rewrite,[status(thm)],[])).
% 27.48/17.72 tff(2019,plain,
% 27.48/17.72 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (c2 = f8(f9(c2, c2))) | (~big_f(c2, f10(f9(c2, c2)))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f9(c2, c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f9(c2, c2) = f5(f9(c2, c2))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~big_f(f7(f9(c2, c2)), f9(c2, c2)))))),
% 27.48/17.72 inference(monotonicity,[status(thm)],[2018])).
% 27.48/17.72 tff(2020,plain,
% 27.48/17.72 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (c2 = f8(f9(c2, c2))) | (~big_f(c2, f10(f9(c2, c2)))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f9(c2, c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f9(c2, c2) = f5(f9(c2, c2))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~big_f(f7(f9(c2, c2)), f9(c2, c2))))),
% 27.48/17.72 inference(transitivity,[status(thm)],[2019, 2017])).
% 27.48/17.72 tff(2021,plain,
% 27.48/17.72 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (c2 = f8(f9(c2, c2))) | (~big_f(c2, f10(f9(c2, c2)))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f9(c2, c2))))),
% 27.48/17.72 inference(quant_inst,[status(thm)],[])).
% 27.48/17.72 tff(2022,plain,
% 27.48/17.72 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f9(c2, c2) = f5(f9(c2, c2))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~big_f(f7(f9(c2, c2)), f9(c2, c2)))),
% 27.48/17.72 inference(modus_ponens,[status(thm)],[2021, 2020])).
% 27.48/17.72 tff(2023,plain,
% 27.48/17.72 ((f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f8(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f9(c2, c2)))),
% 27.48/17.72 inference(unit_resolution,[status(thm)],[2022, 1659, 1792, 1767, 2016])).
% 27.48/17.72 tff(2024,plain,
% 27.48/17.72 (c2 = f8(f9(c2, c2))),
% 27.48/17.72 inference(unit_resolution,[status(thm)],[2023, 1798, 1801])).
% 27.48/17.72 tff(2025,plain,
% 27.48/17.72 (f8(f9(c2, c2)) = c2),
% 27.48/17.72 inference(symmetry,[status(thm)],[2024])).
% 27.48/17.72 tff(2026,assumption,(big_f(f9(c2, c2), f10(f9(c2, c2)))), introduced(assumption)).
% 27.48/17.72 tff(2027,plain,
% 27.48/17.72 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f9(c2, c2) = f5(f9(c2, c2))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (~big_f(f7(f9(c2, c2)), f9(c2, c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f9(c2, c2) = f5(f9(c2, c2))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (~big_f(f7(f9(c2, c2)), f9(c2, c2))))),
% 27.48/17.72 inference(rewrite,[status(thm)],[])).
% 27.48/17.72 tff(2028,plain,
% 27.48/17.72 (((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f9(c2, c2)))) <=> ((f9(c2, c2) = f5(f9(c2, c2))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (~big_f(f7(f9(c2, c2)), f9(c2, c2))))),
% 27.48/17.72 inference(rewrite,[status(thm)],[])).
% 27.48/17.72 tff(2029,plain,
% 27.48/17.72 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f9(c2, c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f9(c2, c2) = f5(f9(c2, c2))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (~big_f(f7(f9(c2, c2)), f9(c2, c2)))))),
% 27.48/17.72 inference(monotonicity,[status(thm)],[2028])).
% 27.48/17.72 tff(2030,plain,
% 27.48/17.72 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f9(c2, c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f9(c2, c2) = f5(f9(c2, c2))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (~big_f(f7(f9(c2, c2)), f9(c2, c2))))),
% 27.48/17.72 inference(transitivity,[status(thm)],[2029, 2027])).
% 27.48/17.72 tff(2031,plain,
% 27.48/17.72 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f9(c2, c2))))),
% 27.48/17.72 inference(quant_inst,[status(thm)],[])).
% 27.48/17.72 tff(2032,plain,
% 27.48/17.72 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f9(c2, c2) = f5(f9(c2, c2))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (~big_f(f7(f9(c2, c2)), f9(c2, c2)))),
% 27.48/17.72 inference(modus_ponens,[status(thm)],[2031, 2030])).
% 27.48/17.72 tff(2033,plain,
% 27.48/17.72 ((f7(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f9(c2, c2)))),
% 27.48/17.72 inference(unit_resolution,[status(thm)],[2032, 1659, 1792, 1767, 2026])).
% 27.48/17.72 tff(2034,plain,
% 27.48/17.72 (f9(c2, c2) = f8(f9(c2, c2))),
% 27.48/17.72 inference(unit_resolution,[status(thm)],[2033, 1798, 1801])).
% 27.48/17.72 tff(2035,plain,
% 27.48/17.72 (f9(c2, c2) = c2),
% 27.48/17.72 inference(transitivity,[status(thm)],[2034, 2025])).
% 27.48/17.72 tff(2036,plain,
% 27.48/17.72 ($false),
% 27.48/17.72 inference(unit_resolution,[status(thm)],[185, 2035])).
% 27.48/17.72 tff(2037,plain,((~big_f(c2, c1)) | (f9(c2, c2) = f5(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (~big_f(c2, f10(f9(c2, c2)))) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f7(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.48/17.73 tff(2038,plain,
% 27.48/17.73 (~big_f(c2, c1)),
% 27.48/17.73 inference(unit_resolution,[status(thm)],[2037, 1704, 1721, 2014, 2011, 148, 79, 122, 120])).
% 27.48/17.73 tff(2039,plain,
% 27.48/17.73 (~big_f(c2, f9(c2, c2))),
% 27.48/17.73 inference(modus_ponens,[status(thm)],[2038, 2015])).
% 27.48/17.73 tff(2040,assumption,(~big_f(c2, f9(c2, c2))), introduced(assumption)).
% 27.48/17.73 tff(2041,assumption,(big_f(f9(c2, c2), c2)), introduced(assumption)).
% 27.48/17.73 tff(2042,plain,
% 27.48/17.73 ((f9(c2, c2) = f4(c2)) <=> (f9(f10(c2), f4(c4)) = f4(c2))),
% 27.48/17.73 inference(monotonicity,[status(thm)],[160])).
% 27.48/17.73 tff(2043,plain,
% 27.48/17.73 ((f9(f10(c2), f4(c4)) = f4(c2)) <=> (f9(c2, c2) = f4(c2))),
% 27.48/17.73 inference(symmetry,[status(thm)],[2042])).
% 27.48/17.73 tff(2044,plain,
% 27.48/17.73 ((f9(c2, c2) = c2) <=> (f9(c2, c2) = f4(c2))),
% 27.48/17.73 inference(transitivity,[status(thm)],[800, 2043])).
% 27.48/17.73 tff(2045,plain,
% 27.48/17.73 ((~(f9(c2, c2) = c2)) <=> (~(f9(c2, c2) = f4(c2)))),
% 27.48/17.73 inference(monotonicity,[status(thm)],[2044])).
% 27.48/17.73 tff(2046,plain,
% 27.48/17.73 (~(f9(c2, c2) = f4(c2))),
% 27.48/17.73 inference(modus_ponens,[status(thm)],[185, 2045])).
% 27.48/17.73 tff(2047,assumption,(~(f9(c2, c2) = f4(c2))), introduced(assumption)).
% 27.48/17.73 tff(2048,plain,
% 27.48/17.73 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c2 = c3) | (~(c2 = c4)) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f4(c2)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (c2 = c3) | (~(c2 = c4)) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f4(c2)))),
% 27.48/17.73 inference(rewrite,[status(thm)],[])).
% 27.48/17.73 tff(2049,plain,
% 27.48/17.73 (((c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(c2 = c4)) | (f9(c2, c2) = f4(c2)) | (~big_f(f9(c2, c2), c2))) <=> ((c2 = c3) | (~(c2 = c4)) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f4(c2)))),
% 27.48/17.73 inference(rewrite,[status(thm)],[])).
% 27.48/17.73 tff(2050,plain,
% 27.48/17.73 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(c2 = c4)) | (f9(c2, c2) = f4(c2)) | (~big_f(f9(c2, c2), c2)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c2 = c3) | (~(c2 = c4)) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f4(c2))))),
% 27.48/17.73 inference(monotonicity,[status(thm)],[2049])).
% 27.48/17.73 tff(2051,plain,
% 27.48/17.73 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(c2 = c4)) | (f9(c2, c2) = f4(c2)) | (~big_f(f9(c2, c2), c2)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (c2 = c3) | (~(c2 = c4)) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f4(c2)))),
% 27.48/17.73 inference(transitivity,[status(thm)],[2050, 2048])).
% 27.48/17.73 tff(2052,plain,
% 27.48/17.73 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(c2 = c4)) | (f9(c2, c2) = f4(c2)) | (~big_f(f9(c2, c2), c2)))),
% 27.48/17.73 inference(quant_inst,[status(thm)],[])).
% 27.48/17.73 tff(2053,plain,
% 27.48/17.73 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (c2 = c3) | (~(c2 = c4)) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f4(c2))),
% 27.48/17.73 inference(modus_ponens,[status(thm)],[2052, 2051])).
% 27.48/17.73 tff(2054,plain,
% 27.48/17.73 (big_f(c2, f1(c2, c2))),
% 27.48/17.73 inference(unit_resolution,[status(thm)],[2053, 525, 631, 377, 1828, 2041, 2047])).
% 27.48/17.73 tff(2055,plain,
% 27.48/17.73 (big_f(f7(f9(c2, c2)), f1(c2, c2))),
% 27.48/17.73 inference(modus_ponens,[status(thm)],[2054, 1827])).
% 27.48/17.73 tff(2056,plain,
% 27.48/17.73 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(f9(c2, c2)) = f9(c2, c2)) | (~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f1(c2, c2) = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f1(c2, c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f1(c2, c2) = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f1(c2, c2))))),
% 27.48/17.73 inference(rewrite,[status(thm)],[])).
% 27.48/17.73 tff(2057,plain,
% 27.48/17.73 (((f10(f9(c2, c2)) = f9(c2, c2)) | (c2 = f8(f9(c2, c2))) | (~big_f(c2, f10(f9(c2, c2)))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (f1(c2, c2) = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f1(c2, c2)))) <=> ((f7(f9(c2, c2)) = f9(c2, c2)) | (~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f1(c2, c2) = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f1(c2, c2))))),
% 27.48/17.73 inference(rewrite,[status(thm)],[])).
% 27.48/17.73 tff(2058,plain,
% 27.48/17.73 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (c2 = f8(f9(c2, c2))) | (~big_f(c2, f10(f9(c2, c2)))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (f1(c2, c2) = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f1(c2, c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(f9(c2, c2)) = f9(c2, c2)) | (~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f1(c2, c2) = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f1(c2, c2)))))),
% 27.48/17.73 inference(monotonicity,[status(thm)],[2057])).
% 27.48/17.73 tff(2059,plain,
% 27.48/17.73 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (c2 = f8(f9(c2, c2))) | (~big_f(c2, f10(f9(c2, c2)))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (f1(c2, c2) = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f1(c2, c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f1(c2, c2) = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f1(c2, c2))))),
% 27.48/17.73 inference(transitivity,[status(thm)],[2058, 2056])).
% 27.48/17.73 tff(2060,plain,
% 27.48/17.73 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (c2 = f8(f9(c2, c2))) | (~big_f(c2, f10(f9(c2, c2)))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (f1(c2, c2) = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f1(c2, c2))))),
% 27.48/17.73 inference(quant_inst,[status(thm)],[])).
% 27.48/17.73 tff(2061,plain,
% 27.48/17.73 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f1(c2, c2) = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f1(c2, c2)))),
% 27.48/17.73 inference(modus_ponens,[status(thm)],[2060, 2059])).
% 27.48/17.73 tff(2062,plain,
% 27.48/17.73 ((f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f8(f9(c2, c2))) | (f1(c2, c2) = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f1(c2, c2)))),
% 27.48/17.73 inference(unit_resolution,[status(thm)],[2061, 1659, 1767, 2016])).
% 27.48/17.73 tff(2063,plain,
% 27.48/17.73 (c2 = f8(f9(c2, c2))),
% 27.48/17.73 inference(unit_resolution,[status(thm)],[2062, 1798, 1840, 2055])).
% 27.48/17.73 tff(2064,plain,
% 27.48/17.73 (f8(f9(c2, c2)) = c2),
% 27.48/17.73 inference(symmetry,[status(thm)],[2063])).
% 27.48/17.73 tff(2065,plain,
% 27.48/17.73 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(f9(c2, c2)) = f9(c2, c2)) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (f1(c2, c2) = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f1(c2, c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (f1(c2, c2) = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f1(c2, c2))))),
% 27.48/17.73 inference(rewrite,[status(thm)],[])).
% 27.48/17.73 tff(2066,plain,
% 27.48/17.73 (((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (f1(c2, c2) = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f1(c2, c2)))) <=> ((f7(f9(c2, c2)) = f9(c2, c2)) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (f1(c2, c2) = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f1(c2, c2))))),
% 27.48/17.73 inference(rewrite,[status(thm)],[])).
% 27.48/17.73 tff(2067,plain,
% 27.48/17.73 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (f1(c2, c2) = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f1(c2, c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(f9(c2, c2)) = f9(c2, c2)) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (f1(c2, c2) = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f1(c2, c2)))))),
% 27.48/17.73 inference(monotonicity,[status(thm)],[2066])).
% 27.48/17.73 tff(2068,plain,
% 27.48/17.73 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (f1(c2, c2) = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f1(c2, c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (f1(c2, c2) = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f1(c2, c2))))),
% 27.48/17.73 inference(transitivity,[status(thm)],[2067, 2065])).
% 27.48/17.73 tff(2069,plain,
% 27.48/17.73 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (f1(c2, c2) = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f1(c2, c2))))),
% 27.48/17.73 inference(quant_inst,[status(thm)],[])).
% 27.48/17.73 tff(2070,plain,
% 27.48/17.73 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (f1(c2, c2) = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f1(c2, c2)))),
% 27.48/17.73 inference(modus_ponens,[status(thm)],[2069, 2068])).
% 27.48/17.73 tff(2071,plain,
% 27.48/17.73 ((f7(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (f1(c2, c2) = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f1(c2, c2)))),
% 27.48/17.73 inference(unit_resolution,[status(thm)],[2070, 1659, 1767, 2026])).
% 27.48/17.73 tff(2072,plain,
% 27.48/17.73 (f9(c2, c2) = f8(f9(c2, c2))),
% 27.48/17.73 inference(unit_resolution,[status(thm)],[2071, 1798, 1840, 2055])).
% 27.48/17.73 tff(2073,plain,
% 27.48/17.73 (f9(c2, c2) = c2),
% 27.48/17.73 inference(transitivity,[status(thm)],[2072, 2064])).
% 27.48/17.73 tff(2074,plain,
% 27.48/17.73 ($false),
% 27.48/17.73 inference(unit_resolution,[status(thm)],[185, 2073])).
% 27.48/17.73 tff(2075,plain,((f1(c2, c2) = c2) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (~big_f(c2, f10(f9(c2, c2)))) | (~(f7(c1) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f5(c1) = c2)) | (~(c2 = c4)) | (c2 = c3) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f4(c2))), inference(lemma,lemma(discharge,[]))).
% 27.48/17.73 tff(2076,plain,
% 27.48/17.73 (f1(c2, c2) = c2),
% 27.48/17.73 inference(unit_resolution,[status(thm)],[2075, 377, 2026, 2016, 347, 148, 79, 122, 186, 631, 1767, 2041, 2047])).
% 27.48/17.73 tff(2077,plain,
% 27.48/17.73 (big_f(c2, f1(c2, c2)) <=> big_f(c2, c2)),
% 27.48/17.73 inference(monotonicity,[status(thm)],[2076])).
% 27.48/17.73 tff(2078,plain,
% 27.48/17.73 (big_f(c2, c2) <=> big_f(c2, f1(c2, c2))),
% 27.48/17.73 inference(symmetry,[status(thm)],[2077])).
% 27.48/17.73 tff(2079,plain,
% 27.48/17.73 (big_f(c2, f1(c2, c2))),
% 27.48/17.73 inference(modus_ponens,[status(thm)],[1345, 2078])).
% 27.48/17.73 tff(2080,plain,
% 27.48/17.73 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c2 = c4)) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f4(c2)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(c2 = c4)) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f4(c2)))),
% 27.48/17.73 inference(rewrite,[status(thm)],[])).
% 27.48/17.73 tff(2081,plain,
% 27.48/17.73 (((c2 = c3) | (~(c2 = c4)) | (f9(c2, c2) = f4(c2)) | (~big_f(f9(c2, c2), c2)) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2)))) <=> ((c2 = c3) | (~(c2 = c4)) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f4(c2)))),
% 27.48/17.73 inference(rewrite,[status(thm)],[])).
% 27.48/17.73 tff(2082,plain,
% 27.48/17.73 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c2 = c4)) | (f9(c2, c2) = f4(c2)) | (~big_f(f9(c2, c2), c2)) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c2 = c4)) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f4(c2))))),
% 27.48/17.73 inference(monotonicity,[status(thm)],[2081])).
% 27.48/17.73 tff(2083,plain,
% 27.48/17.73 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c2 = c4)) | (f9(c2, c2) = f4(c2)) | (~big_f(f9(c2, c2), c2)) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(c2 = c4)) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f4(c2)))),
% 27.48/17.73 inference(transitivity,[status(thm)],[2082, 2080])).
% 27.48/17.73 tff(2084,plain,
% 27.48/17.73 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c2 = c4)) | (f9(c2, c2) = f4(c2)) | (~big_f(f9(c2, c2), c2)) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))),
% 27.48/17.73 inference(quant_inst,[status(thm)],[])).
% 27.48/17.73 tff(2085,plain,
% 27.48/17.73 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(c2 = c4)) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f4(c2))),
% 27.48/17.73 inference(modus_ponens,[status(thm)],[2084, 2083])).
% 27.48/17.73 tff(2086,plain,
% 27.48/17.73 ($false),
% 27.48/17.73 inference(unit_resolution,[status(thm)],[2085, 553, 631, 377, 2076, 2079, 2041, 2047])).
% 27.48/17.73 tff(2087,plain,((c2 = c3) | (~(c2 = c4)) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f4(c2)) | (~big_f(c2, c2)) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (~big_f(c2, f10(f9(c2, c2)))) | (~(f7(c1) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f5(c1) = c2)) | (f10(f9(c2, c2)) = f9(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 27.48/17.73 tff(2088,plain,
% 27.48/17.73 ($false),
% 27.48/17.73 inference(unit_resolution,[status(thm)],[2087, 2046, 432, 2041, 377, 1345, 2026, 2016, 347, 148, 79, 122, 186, 1767])).
% 27.48/17.73 tff(2089,plain,((~(c4 = c2)) | (~big_f(f9(c2, c2), c2)) | (c2 = c3) | (~big_f(c2, c2)) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (~big_f(c2, f10(f9(c2, c2)))) | (~(f7(c1) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f5(c1) = c2)) | (f10(f9(c2, c2)) = f9(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 27.48/17.73 tff(2090,plain,
% 27.48/17.73 (~(c4 = c2)),
% 27.48/17.73 inference(unit_resolution,[status(thm)],[2089, 377, 2041, 1345, 2026, 2016, 347, 148, 79, 122, 186, 1767])).
% 27.48/17.73 tff(2091,plain,
% 27.48/17.73 (c4 = c1),
% 27.48/17.73 inference(unit_resolution,[status(thm)],[461, 2090])).
% 27.48/17.73 tff(2092,plain,
% 27.48/17.73 (c1 = c4),
% 27.48/17.73 inference(unit_resolution,[status(thm)],[484, 2091])).
% 27.48/17.73 tff(2093,plain,
% 27.48/17.73 (f9(c2, c2) = c4),
% 27.48/17.73 inference(modus_ponens,[status(thm)],[2092, 362])).
% 27.48/17.73 tff(2094,plain,
% 27.48/17.73 (f4(c1) = f4(f9(c2, c2))),
% 27.48/17.73 inference(symmetry,[status(thm)],[488])).
% 27.48/17.73 tff(2095,plain,
% 27.48/17.73 (c1 = c4),
% 27.48/17.73 inference(symmetry,[status(thm)],[2091])).
% 27.48/17.73 tff(2096,plain,
% 27.48/17.73 (f4(c1) = f4(c4)),
% 27.48/17.73 inference(monotonicity,[status(thm)],[2095])).
% 27.48/17.73 tff(2097,plain,
% 27.48/17.73 (f4(c4) = f4(c1)),
% 27.48/17.73 inference(symmetry,[status(thm)],[2096])).
% 27.48/17.73 tff(2098,plain,
% 27.48/17.73 (c2 = f4(f9(c2, c2))),
% 27.48/17.73 inference(transitivity,[status(thm)],[436, 2097, 2094])).
% 27.48/17.73 tff(2099,assumption,(c2 = f4(f9(c2, c2))), introduced(assumption)).
% 27.48/17.73 tff(2100,plain,
% 27.48/17.73 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | big_f(c2, f9(c2, c2)) | (~(f9(c2, c2) = c4)) | (~(c2 = f4(f9(c2, c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | big_f(c2, f9(c2, c2)) | (~(f9(c2, c2) = c4)) | (~(c2 = f4(f9(c2, c2)))))),
% 27.48/17.73 inference(rewrite,[status(thm)],[])).
% 27.48/17.73 tff(2101,plain,
% 27.48/17.73 (((c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f9(c2, c2) = c4)) | big_f(c2, f9(c2, c2)) | (~(c2 = f4(f9(c2, c2))))) <=> ((c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | big_f(c2, f9(c2, c2)) | (~(f9(c2, c2) = c4)) | (~(c2 = f4(f9(c2, c2)))))),
% 27.48/17.73 inference(rewrite,[status(thm)],[])).
% 27.48/17.73 tff(2102,plain,
% 27.48/17.73 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f9(c2, c2) = c4)) | big_f(c2, f9(c2, c2)) | (~(c2 = f4(f9(c2, c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | big_f(c2, f9(c2, c2)) | (~(f9(c2, c2) = c4)) | (~(c2 = f4(f9(c2, c2))))))),
% 27.48/17.73 inference(monotonicity,[status(thm)],[2101])).
% 27.48/17.73 tff(2103,plain,
% 27.48/17.73 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f9(c2, c2) = c4)) | big_f(c2, f9(c2, c2)) | (~(c2 = f4(f9(c2, c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | big_f(c2, f9(c2, c2)) | (~(f9(c2, c2) = c4)) | (~(c2 = f4(f9(c2, c2)))))),
% 27.48/17.74 inference(transitivity,[status(thm)],[2102, 2100])).
% 27.48/17.74 tff(2104,plain,
% 27.48/17.74 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f9(c2, c2) = c4)) | big_f(c2, f9(c2, c2)) | (~(c2 = f4(f9(c2, c2)))))),
% 27.48/17.74 inference(quant_inst,[status(thm)],[])).
% 27.48/17.74 tff(2105,plain,
% 27.48/17.74 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | big_f(c2, f9(c2, c2)) | (~(f9(c2, c2) = c4)) | (~(c2 = f4(f9(c2, c2))))),
% 27.48/17.74 inference(modus_ponens,[status(thm)],[2104, 2103])).
% 27.48/17.74 tff(2106,plain,
% 27.48/17.74 (big_f(c2, f1(c2, c2))),
% 27.48/17.74 inference(unit_resolution,[status(thm)],[2105, 402, 377, 1828, 514, 2040, 2099])).
% 27.48/17.74 tff(2107,plain,
% 27.48/17.74 (big_f(f7(f9(c2, c2)), f1(c2, c2))),
% 27.48/17.74 inference(modus_ponens,[status(thm)],[2106, 1827])).
% 27.48/17.74 tff(2108,plain,
% 27.48/17.74 (c2 = f8(f9(c2, c2))),
% 27.48/17.74 inference(unit_resolution,[status(thm)],[2062, 1798, 1840, 2107])).
% 27.48/17.74 tff(2109,plain,
% 27.48/17.74 (f8(f9(c2, c2)) = c2),
% 27.48/17.74 inference(symmetry,[status(thm)],[2108])).
% 27.48/17.74 tff(2110,plain,
% 27.48/17.74 (f9(c2, c2) = f8(f9(c2, c2))),
% 27.48/17.74 inference(unit_resolution,[status(thm)],[2071, 1798, 1840, 2107])).
% 27.48/17.74 tff(2111,plain,
% 27.48/17.74 (f9(c2, c2) = c2),
% 27.48/17.74 inference(transitivity,[status(thm)],[2110, 2109])).
% 27.48/17.74 tff(2112,plain,
% 27.48/17.74 ($false),
% 27.48/17.74 inference(unit_resolution,[status(thm)],[185, 2111])).
% 27.48/17.74 tff(2113,plain,((f1(c2, c2) = c2) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (~big_f(c2, f10(f9(c2, c2)))) | (~(f7(c1) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f5(c1) = c2)) | (c2 = c3) | (~(f9(c2, c2) = c4)) | big_f(c2, f9(c2, c2)) | (~(c2 = f4(f9(c2, c2))))), inference(lemma,lemma(discharge,[]))).
% 27.48/17.74 tff(2114,plain,
% 27.48/17.74 (f1(c2, c2) = c2),
% 27.48/17.74 inference(unit_resolution,[status(thm)],[2113, 2040, 2026, 2016, 347, 148, 79, 122, 186, 377, 514, 1767, 2099])).
% 27.48/17.74 tff(2115,plain,
% 27.48/17.74 (big_f(c2, f1(c2, c2)) <=> big_f(c2, c2)),
% 27.48/17.74 inference(monotonicity,[status(thm)],[2114])).
% 27.48/17.74 tff(2116,plain,
% 27.48/17.74 (big_f(c2, c2) <=> big_f(c2, f1(c2, c2))),
% 27.48/17.74 inference(symmetry,[status(thm)],[2115])).
% 27.48/17.74 tff(2117,plain,
% 27.48/17.74 (big_f(c2, f1(c2, c2))),
% 27.48/17.74 inference(modus_ponens,[status(thm)],[1345, 2116])).
% 27.48/17.74 tff(2118,plain,
% 27.48/17.74 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | big_f(c2, f9(c2, c2)) | (~(f9(c2, c2) = c4)) | (~(c2 = f4(f9(c2, c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | big_f(c2, f9(c2, c2)) | (~(f9(c2, c2) = c4)) | (~(c2 = f4(f9(c2, c2)))))),
% 27.48/17.74 inference(rewrite,[status(thm)],[])).
% 27.48/17.74 tff(2119,plain,
% 27.48/17.74 (((c2 = c3) | (~(f9(c2, c2) = c4)) | big_f(c2, f9(c2, c2)) | (~(c2 = f4(f9(c2, c2)))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2)))) <=> ((c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | big_f(c2, f9(c2, c2)) | (~(f9(c2, c2) = c4)) | (~(c2 = f4(f9(c2, c2)))))),
% 27.48/17.74 inference(rewrite,[status(thm)],[])).
% 27.48/17.74 tff(2120,plain,
% 27.48/17.74 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f9(c2, c2) = c4)) | big_f(c2, f9(c2, c2)) | (~(c2 = f4(f9(c2, c2)))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | big_f(c2, f9(c2, c2)) | (~(f9(c2, c2) = c4)) | (~(c2 = f4(f9(c2, c2))))))),
% 27.48/17.74 inference(monotonicity,[status(thm)],[2119])).
% 27.48/17.74 tff(2121,plain,
% 27.48/17.74 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f9(c2, c2) = c4)) | big_f(c2, f9(c2, c2)) | (~(c2 = f4(f9(c2, c2)))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | big_f(c2, f9(c2, c2)) | (~(f9(c2, c2) = c4)) | (~(c2 = f4(f9(c2, c2)))))),
% 27.48/17.74 inference(transitivity,[status(thm)],[2120, 2118])).
% 27.48/17.74 tff(2122,plain,
% 27.48/17.74 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f9(c2, c2) = c4)) | big_f(c2, f9(c2, c2)) | (~(c2 = f4(f9(c2, c2)))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))),
% 27.48/17.74 inference(quant_inst,[status(thm)],[])).
% 27.48/17.74 tff(2123,plain,
% 27.48/17.74 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | big_f(c2, f9(c2, c2)) | (~(f9(c2, c2) = c4)) | (~(c2 = f4(f9(c2, c2))))),
% 27.48/17.74 inference(modus_ponens,[status(thm)],[2122, 2121])).
% 27.48/17.74 tff(2124,plain,
% 27.48/17.74 ($false),
% 27.48/17.74 inference(unit_resolution,[status(thm)],[2123, 447, 377, 2114, 2117, 514, 2040, 2099])).
% 27.48/17.74 tff(2125,plain,(big_f(c2, f9(c2, c2)) | (c2 = c3) | (~(f9(c2, c2) = c4)) | (~(c2 = f4(f9(c2, c2)))) | (~big_f(c2, c2)) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (~big_f(c2, f10(f9(c2, c2)))) | (~(f7(c1) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f5(c1) = c2)) | (f10(f9(c2, c2)) = f9(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 27.48/17.74 tff(2126,plain,
% 27.48/17.74 ($false),
% 27.48/17.74 inference(unit_resolution,[status(thm)],[2125, 2098, 2093, 2040, 377, 1345, 2026, 2016, 347, 148, 79, 122, 186, 1767])).
% 27.48/17.74 tff(2127,plain,((c2 = c3) | big_f(c2, f9(c2, c2)) | (~big_f(c2, c2)) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (~big_f(c2, f10(f9(c2, c2)))) | (~(f7(c1) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f5(c1) = c2)) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~big_f(f9(c2, c2), c2))), inference(lemma,lemma(discharge,[]))).
% 27.48/17.74 tff(2128,plain,
% 27.48/17.74 (c2 = c3),
% 27.48/17.74 inference(unit_resolution,[status(thm)],[2127, 2039, 1791, 2014, 2011, 120, 148, 79, 122, 1709, 1721, 2010])).
% 27.48/17.74 tff(2129,plain,
% 27.48/17.74 (~(f9(c2, c2) = c3)),
% 27.48/17.74 inference(unit_resolution,[status(thm)],[1824, 2128, 185, 79, 122])).
% 27.48/17.74 tff(2130,plain,
% 27.48/17.74 (~(c1 = c3)),
% 27.48/17.74 inference(modus_ponens,[status(thm)],[2129, 215])).
% 27.48/17.74 tff(2131,plain,
% 27.48/17.74 ((~big_f(f7(c2), f9(c2, c2))) <=> (~big_f(f7(c2), c1))),
% 27.48/17.74 inference(monotonicity,[status(thm)],[795])).
% 27.48/17.74 tff(2132,plain,
% 27.48/17.74 (big_f(f7(c2), c2)),
% 27.48/17.74 inference(modus_ponens,[status(thm)],[2009, 1153])).
% 27.48/17.74 tff(2133,plain,
% 27.48/17.74 (f8(f9(f10(c2), f10(c2))) = f8(f9(c2, c2))),
% 27.48/17.74 inference(monotonicity,[status(thm)],[135])).
% 27.48/17.74 tff(2134,plain,
% 27.48/17.74 (f8(f9(c2, c2)) = f8(f9(f10(c2), f10(c2)))),
% 27.48/17.74 inference(symmetry,[status(thm)],[2133])).
% 27.48/17.74 tff(2135,plain,
% 27.48/17.74 ((c2 = f8(f9(c2, c2))) <=> (c2 = f8(f9(f10(c2), f10(c2))))),
% 27.48/17.74 inference(monotonicity,[status(thm)],[2134])).
% 27.48/17.74 tff(2136,plain,
% 27.48/17.74 ((c2 = f8(f9(f10(c2), f10(c2)))) <=> (c2 = f8(f9(c2, c2)))),
% 27.48/17.74 inference(symmetry,[status(thm)],[2135])).
% 27.48/17.74 tff(2137,assumption,(~(f9(c2, c2) = f8(f9(c2, c2)))), introduced(assumption)).
% 27.48/17.74 tff(2138,plain,
% 27.48/17.74 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))))),
% 27.48/17.74 inference(rewrite,[status(thm)],[])).
% 27.48/17.74 tff(2139,plain,
% 27.48/17.74 (((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2))) <=> ((f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))))),
% 27.48/17.74 inference(rewrite,[status(thm)],[])).
% 27.48/17.74 tff(2140,plain,
% 27.48/17.74 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2))))))),
% 27.48/17.74 inference(monotonicity,[status(thm)],[2139])).
% 27.48/17.74 tff(2141,plain,
% 27.48/17.74 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))))),
% 27.48/17.74 inference(transitivity,[status(thm)],[2140, 2138])).
% 27.48/17.74 tff(2142,plain,
% 27.48/17.74 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)))),
% 27.48/17.74 inference(quant_inst,[status(thm)],[])).
% 27.48/17.74 tff(2143,plain,
% 27.48/17.74 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2))))),
% 27.48/17.74 inference(modus_ponens,[status(thm)],[2142, 2141])).
% 27.48/17.74 tff(2144,plain,
% 27.48/17.74 ((c2 = f5(c2)) | (f9(c2, c2) = f8(f9(c2, c2)))),
% 27.48/17.74 inference(unit_resolution,[status(thm)],[2143, 1659, 17, 1180, 1767, 2026])).
% 27.48/17.74 tff(2145,plain,
% 27.48/17.74 (c2 = f5(c2)),
% 27.48/17.74 inference(unit_resolution,[status(thm)],[2144, 2137])).
% 27.48/17.74 tff(2146,plain,
% 27.48/17.74 (f5(c2) = c2),
% 27.48/17.74 inference(symmetry,[status(thm)],[2145])).
% 27.48/17.74 tff(2147,plain,
% 27.48/17.74 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(c2) = c2) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (~big_f(f7(c2), f9(c2, c2))) | (f9(c2, c2) = f5(c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c2) = c2) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (~big_f(f7(c2), f9(c2, c2))) | (f9(c2, c2) = f5(c2)))),
% 27.48/17.74 inference(rewrite,[status(thm)],[])).
% 27.48/17.74 tff(2148,plain,
% 27.48/17.74 (((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (f7(c2) = c2) | (f9(c2, c2) = f5(c2)) | (~big_f(f7(c2), f9(c2, c2)))) <=> ((f7(c2) = c2) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (~big_f(f7(c2), f9(c2, c2))) | (f9(c2, c2) = f5(c2)))),
% 27.48/17.74 inference(rewrite,[status(thm)],[])).
% 27.48/17.74 tff(2149,plain,
% 27.48/17.74 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (f7(c2) = c2) | (f9(c2, c2) = f5(c2)) | (~big_f(f7(c2), f9(c2, c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(c2) = c2) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (~big_f(f7(c2), f9(c2, c2))) | (f9(c2, c2) = f5(c2))))),
% 27.48/17.74 inference(monotonicity,[status(thm)],[2148])).
% 27.48/17.74 tff(2150,plain,
% 27.48/17.74 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (f7(c2) = c2) | (f9(c2, c2) = f5(c2)) | (~big_f(f7(c2), f9(c2, c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c2) = c2) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (~big_f(f7(c2), f9(c2, c2))) | (f9(c2, c2) = f5(c2)))),
% 27.48/17.74 inference(transitivity,[status(thm)],[2149, 2147])).
% 27.48/17.74 tff(2151,plain,
% 27.48/17.74 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (f7(c2) = c2) | (f9(c2, c2) = f5(c2)) | (~big_f(f7(c2), f9(c2, c2))))),
% 27.48/17.74 inference(quant_inst,[status(thm)],[])).
% 27.48/17.74 tff(2152,plain,
% 27.48/17.74 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c2) = c2) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (~big_f(f7(c2), f9(c2, c2))) | (f9(c2, c2) = f5(c2))),
% 27.48/17.74 inference(modus_ponens,[status(thm)],[2151, 2150])).
% 27.48/17.74 tff(2153,plain,
% 27.48/17.74 ((f9(c2, c2) = f8(f9(c2, c2))) | (f9(c2, c2) = f5(c2))),
% 27.48/17.74 inference(unit_resolution,[status(thm)],[2152, 1659, 17, 1767, 2026, 1163])).
% 27.48/17.74 tff(2154,plain,
% 27.48/17.74 (f9(c2, c2) = f5(c2)),
% 27.48/17.74 inference(unit_resolution,[status(thm)],[2153, 2137])).
% 27.48/17.74 tff(2155,plain,
% 27.48/17.74 (f9(c2, c2) = c2),
% 27.48/17.74 inference(transitivity,[status(thm)],[2154, 2146])).
% 27.48/17.74 tff(2156,plain,
% 27.48/17.74 ($false),
% 27.48/17.74 inference(unit_resolution,[status(thm)],[1209, 2155])).
% 27.48/17.74 tff(2157,plain,((f9(c2, c2) = f8(f9(c2, c2))) | (f9(c2, c2) = c2) | (f7(c2) = c2) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (~big_f(f7(c2), f9(c2, c2))) | (~big_f(f7(c2), c2))), inference(lemma,lemma(discharge,[]))).
% 27.48/17.74 tff(2158,plain,
% 27.48/17.74 (f9(c2, c2) = f8(f9(c2, c2))),
% 27.48/17.74 inference(unit_resolution,[status(thm)],[2157, 1163, 17, 1767, 2026, 1209, 1180])).
% 27.48/17.74 tff(2159,plain,
% 27.48/17.74 (f8(f9(c2, c2)) = f9(c2, c2)),
% 27.48/17.74 inference(symmetry,[status(thm)],[2158])).
% 27.48/17.74 tff(2160,plain,
% 27.48/17.74 (f8(f9(f10(c2), f10(c2))) = f9(c2, c2)),
% 27.48/17.74 inference(transitivity,[status(thm)],[2133, 2159])).
% 27.48/17.74 tff(2161,plain,
% 27.48/17.74 ((c2 = f8(f9(f10(c2), f10(c2)))) <=> (c2 = f9(c2, c2))),
% 27.48/17.74 inference(monotonicity,[status(thm)],[2160])).
% 27.48/17.74 tff(2162,plain,
% 27.48/17.74 ((c2 = f8(f9(f10(c2), f10(c2)))) <=> (f9(c2, c2) = c2)),
% 27.48/17.74 inference(transitivity,[status(thm)],[2161, 167])).
% 27.48/17.74 tff(2163,plain,
% 27.48/17.74 ((f9(c2, c2) = c2) <=> (c2 = f8(f9(f10(c2), f10(c2))))),
% 27.48/17.74 inference(symmetry,[status(thm)],[2162])).
% 27.48/17.74 tff(2164,plain,
% 27.48/17.74 ((f9(c2, c2) = c2) <=> (c2 = f8(f9(c2, c2)))),
% 27.48/17.74 inference(transitivity,[status(thm)],[2163, 2136])).
% 27.48/17.74 tff(2165,plain,
% 27.56/17.74 ((~(f9(c2, c2) = c2)) <=> (~(c2 = f8(f9(c2, c2))))),
% 27.56/17.74 inference(monotonicity,[status(thm)],[2164])).
% 27.56/17.74 tff(2166,plain,
% 27.56/17.74 (~(c2 = f8(f9(c2, c2)))),
% 27.56/17.74 inference(modus_ponens,[status(thm)],[1209, 2165])).
% 27.56/17.74 tff(2167,plain,
% 27.56/17.74 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)))),
% 27.56/17.74 inference(rewrite,[status(thm)],[])).
% 27.56/17.74 tff(2168,plain,
% 27.56/17.74 (((f10(f9(c2, c2)) = f9(c2, c2)) | (c2 = f8(f9(c2, c2))) | (~big_f(c2, f10(f9(c2, c2)))) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2))) <=> ((f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)))),
% 27.56/17.74 inference(rewrite,[status(thm)],[])).
% 27.56/17.74 tff(2169,plain,
% 27.56/17.74 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (c2 = f8(f9(c2, c2))) | (~big_f(c2, f10(f9(c2, c2)))) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2))))),
% 27.56/17.74 inference(monotonicity,[status(thm)],[2168])).
% 27.56/17.74 tff(2170,plain,
% 27.56/17.74 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (c2 = f8(f9(c2, c2))) | (~big_f(c2, f10(f9(c2, c2)))) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)))),
% 27.56/17.74 inference(transitivity,[status(thm)],[2169, 2167])).
% 27.56/17.74 tff(2171,plain,
% 27.56/17.74 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (c2 = f8(f9(c2, c2))) | (~big_f(c2, f10(f9(c2, c2)))) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)))),
% 27.56/17.74 inference(quant_inst,[status(thm)],[])).
% 27.56/17.74 tff(2172,plain,
% 27.56/17.74 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2))),
% 27.56/17.74 inference(modus_ponens,[status(thm)],[2171, 2170])).
% 27.56/17.74 tff(2173,plain,
% 27.56/17.74 ((c2 = f5(c2)) | (~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2)))),
% 27.56/17.74 inference(unit_resolution,[status(thm)],[2172, 1659, 17, 1180, 1767])).
% 27.56/17.74 tff(2174,plain,
% 27.56/17.74 (c2 = f5(c2)),
% 27.56/17.74 inference(unit_resolution,[status(thm)],[2173, 2166, 2016])).
% 27.56/17.74 tff(2175,plain,
% 27.56/17.74 (f5(c2) = c2),
% 27.56/17.74 inference(symmetry,[status(thm)],[2174])).
% 27.56/17.74 tff(2176,plain,
% 27.56/17.74 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(c2) = c2) | (~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~big_f(f7(c2), f9(c2, c2))) | (f9(c2, c2) = f5(c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c2) = c2) | (~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~big_f(f7(c2), f9(c2, c2))) | (f9(c2, c2) = f5(c2)))),
% 27.56/17.75 inference(rewrite,[status(thm)],[])).
% 27.56/17.75 tff(2177,plain,
% 27.56/17.75 (((f10(f9(c2, c2)) = f9(c2, c2)) | (c2 = f8(f9(c2, c2))) | (~big_f(c2, f10(f9(c2, c2)))) | (f7(c2) = c2) | (f9(c2, c2) = f5(c2)) | (~big_f(f7(c2), f9(c2, c2)))) <=> ((f7(c2) = c2) | (~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~big_f(f7(c2), f9(c2, c2))) | (f9(c2, c2) = f5(c2)))),
% 27.56/17.75 inference(rewrite,[status(thm)],[])).
% 27.56/17.75 tff(2178,plain,
% 27.56/17.75 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (c2 = f8(f9(c2, c2))) | (~big_f(c2, f10(f9(c2, c2)))) | (f7(c2) = c2) | (f9(c2, c2) = f5(c2)) | (~big_f(f7(c2), f9(c2, c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(c2) = c2) | (~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~big_f(f7(c2), f9(c2, c2))) | (f9(c2, c2) = f5(c2))))),
% 27.56/17.75 inference(monotonicity,[status(thm)],[2177])).
% 27.56/17.75 tff(2179,plain,
% 27.56/17.75 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (c2 = f8(f9(c2, c2))) | (~big_f(c2, f10(f9(c2, c2)))) | (f7(c2) = c2) | (f9(c2, c2) = f5(c2)) | (~big_f(f7(c2), f9(c2, c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c2) = c2) | (~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~big_f(f7(c2), f9(c2, c2))) | (f9(c2, c2) = f5(c2)))),
% 27.56/17.75 inference(transitivity,[status(thm)],[2178, 2176])).
% 27.56/17.75 tff(2180,plain,
% 27.56/17.75 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (c2 = f8(f9(c2, c2))) | (~big_f(c2, f10(f9(c2, c2)))) | (f7(c2) = c2) | (f9(c2, c2) = f5(c2)) | (~big_f(f7(c2), f9(c2, c2))))),
% 27.56/17.75 inference(quant_inst,[status(thm)],[])).
% 27.56/17.75 tff(2181,plain,
% 27.56/17.75 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c2) = c2) | (~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~big_f(f7(c2), f9(c2, c2))) | (f9(c2, c2) = f5(c2))),
% 27.56/17.75 inference(modus_ponens,[status(thm)],[2180, 2179])).
% 27.56/17.75 tff(2182,plain,
% 27.56/17.75 ((c2 = f8(f9(c2, c2))) | (f9(c2, c2) = f5(c2))),
% 27.56/17.75 inference(unit_resolution,[status(thm)],[2181, 1659, 17, 1767, 1163, 2016])).
% 27.56/17.75 tff(2183,plain,
% 27.56/17.75 (f9(c2, c2) = f5(c2)),
% 27.56/17.75 inference(unit_resolution,[status(thm)],[2182, 2166])).
% 27.56/17.75 tff(2184,plain,
% 27.56/17.75 (f9(c2, c2) = c2),
% 27.56/17.75 inference(transitivity,[status(thm)],[2183, 2175])).
% 27.56/17.75 tff(2185,plain,
% 27.56/17.75 ($false),
% 27.56/17.75 inference(unit_resolution,[status(thm)],[1209, 2184])).
% 27.56/17.75 tff(2186,plain,((~big_f(f7(c2), f9(c2, c2))) | (f9(c2, c2) = c2) | (f7(c2) = c2) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~big_f(c2, f10(f9(c2, c2)))) | (~big_f(f7(c2), c2)) | (~(f10(c2) = c2)) | (~big_f(f9(c2, c2), f10(f9(c2, c2))))), inference(lemma,lemma(discharge,[]))).
% 27.56/17.75 tff(2187,plain,
% 27.56/17.75 (~big_f(f7(c2), f9(c2, c2))),
% 27.56/17.75 inference(unit_resolution,[status(thm)],[2186, 17, 185, 1721, 2011, 2132, 122, 2014])).
% 27.56/17.75 tff(2188,plain,
% 27.56/17.75 (~big_f(f7(c2), c1)),
% 27.56/17.75 inference(modus_ponens,[status(thm)],[2187, 2131])).
% 27.56/17.75 tff(2189,plain,
% 27.56/17.75 ((~(f9(c2, c2) = c3)) <=> (~(f9(f10(c2), f4(c4)) = c3))),
% 27.56/17.75 inference(monotonicity,[status(thm)],[213])).
% 27.56/17.75 tff(2190,plain,
% 27.56/17.75 (big_f(f9(c2, c2), c2)),
% 27.56/17.75 inference(modus_ponens,[status(thm)],[690, 218])).
% 27.56/17.75 tff(2191,plain,
% 27.56/17.75 (c2 = c3),
% 27.56/17.75 inference(unit_resolution,[status(thm)],[2087, 432, 2190, 2046, 1345, 2026, 2016, 347, 148, 79, 122, 186, 1767])).
% 27.56/17.75 tff(2192,plain,
% 27.56/17.75 (~(f9(c2, c2) = c3)),
% 27.56/17.75 inference(unit_resolution,[status(thm)],[1824, 2191, 185, 79, 122])).
% 27.56/17.75 tff(2193,plain,
% 27.56/17.75 (~(f9(f10(c2), f4(c4)) = c3)),
% 27.56/17.75 inference(modus_ponens,[status(thm)],[2192, 2189])).
% 27.56/17.75 tff(2194,plain,
% 27.56/17.75 (~(f1(c1, c2) = c2)),
% 27.56/17.75 inference(unit_resolution,[status(thm)],[836, 2193, 690, 802, 432, 122, 148, 79])).
% 27.56/17.75 tff(2195,plain,
% 27.56/17.75 (f1(c1, c2) = c1),
% 27.56/17.75 inference(unit_resolution,[status(thm)],[841, 2194])).
% 27.56/17.75 tff(2196,plain,
% 27.56/17.75 (f1(f9(c2, c2), c2) = f9(c2, c2)),
% 27.56/17.75 inference(transitivity,[status(thm)],[843, 819, 2195, 149, 132])).
% 27.56/17.75 tff(2197,plain,
% 27.56/17.75 ((f1(f9(c2, c2), c2) = c2) <=> (f9(c2, c2) = c2)),
% 27.56/17.75 inference(monotonicity,[status(thm)],[2196])).
% 27.56/17.75 tff(2198,plain,
% 27.56/17.75 ((f9(c2, c2) = c2) <=> (f1(f9(c2, c2), c2) = c2)),
% 27.56/17.75 inference(symmetry,[status(thm)],[2197])).
% 27.56/17.75 tff(2199,plain,
% 27.56/17.75 ((~(f9(c2, c2) = c2)) <=> (~(f1(f9(c2, c2), c2) = c2))),
% 27.56/17.75 inference(monotonicity,[status(thm)],[2198])).
% 27.56/17.75 tff(2200,plain,
% 27.56/17.75 (~(f1(f9(c2, c2), c2) = c2)),
% 27.56/17.75 inference(modus_ponens,[status(thm)],[185, 2199])).
% 27.56/17.75 tff(2201,plain,
% 27.56/17.75 (f1(f9(c2, c2), c2) = c1),
% 27.56/17.75 inference(transitivity,[status(thm)],[843, 819, 2195])).
% 27.56/17.75 tff(2202,plain,
% 27.56/17.75 (big_f(f9(c2, c2), f1(f9(c2, c2), c2)) <=> big_f(f7(c2), c1)),
% 27.56/17.75 inference(monotonicity,[status(thm)],[343, 2201])).
% 27.56/17.75 tff(2203,plain,
% 27.56/17.75 (big_f(f7(c2), c1) <=> big_f(f9(c2, c2), f1(f9(c2, c2), c2))),
% 27.56/17.75 inference(symmetry,[status(thm)],[2202])).
% 27.56/17.75 tff(2204,plain,
% 27.56/17.75 ((~big_f(f7(c2), c1)) <=> (~big_f(f9(c2, c2), f1(f9(c2, c2), c2)))),
% 27.56/17.75 inference(monotonicity,[status(thm)],[2203])).
% 27.56/17.75 tff(2205,plain,
% 27.56/17.75 (~big_f(f9(c2, c2), f1(f9(c2, c2), c2))),
% 27.56/17.75 inference(modus_ponens,[status(thm)],[333, 2204])).
% 27.56/17.75 tff(2206,plain,
% 27.56/17.75 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((~(c2 = c4)) | (f9(c2, c2) = c3) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f4(c2)) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (~(c2 = c4)) | (f9(c2, c2) = c3) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f4(c2)) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2)))),
% 27.56/17.75 inference(rewrite,[status(thm)],[])).
% 27.56/17.75 tff(2207,plain,
% 27.56/17.75 (((f9(c2, c2) = c3) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2)) | (~(c2 = c4)) | (f9(c2, c2) = f4(c2)) | (~big_f(f9(c2, c2), c2))) <=> ((~(c2 = c4)) | (f9(c2, c2) = c3) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f4(c2)) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2)))),
% 27.56/17.75 inference(rewrite,[status(thm)],[])).
% 27.56/17.75 tff(2208,plain,
% 27.56/17.75 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((f9(c2, c2) = c3) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2)) | (~(c2 = c4)) | (f9(c2, c2) = f4(c2)) | (~big_f(f9(c2, c2), c2)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((~(c2 = c4)) | (f9(c2, c2) = c3) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f4(c2)) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2))))),
% 27.56/17.75 inference(monotonicity,[status(thm)],[2207])).
% 27.56/17.75 tff(2209,plain,
% 27.56/17.75 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((f9(c2, c2) = c3) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2)) | (~(c2 = c4)) | (f9(c2, c2) = f4(c2)) | (~big_f(f9(c2, c2), c2)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (~(c2 = c4)) | (f9(c2, c2) = c3) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f4(c2)) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2)))),
% 27.56/17.75 inference(transitivity,[status(thm)],[2208, 2206])).
% 27.56/17.75 tff(2210,plain,
% 27.56/17.75 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((f9(c2, c2) = c3) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2)) | (~(c2 = c4)) | (f9(c2, c2) = f4(c2)) | (~big_f(f9(c2, c2), c2)))),
% 27.56/17.75 inference(quant_inst,[status(thm)],[])).
% 27.56/17.75 tff(2211,plain,
% 27.56/17.75 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (~(c2 = c4)) | (f9(c2, c2) = c3) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f4(c2)) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2))),
% 27.56/17.75 inference(modus_ponens,[status(thm)],[2210, 2209])).
% 27.56/17.75 tff(2212,plain,
% 27.56/17.75 ((f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2))),
% 27.56/17.75 inference(unit_resolution,[status(thm)],[2211, 525, 432, 2192, 2190, 2046])).
% 27.56/17.75 tff(2213,plain,
% 27.56/17.75 ($false),
% 27.56/17.75 inference(unit_resolution,[status(thm)],[2212, 2205, 2200])).
% 27.56/17.75 tff(2214,plain,((~(c4 = c2)) | big_f(f7(c2), c1) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f7(c2) = c1)) | (~big_f(f9(c2, c2), f10(c2))) | (~big_f(c2, c2)) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (~big_f(c2, f10(f9(c2, c2)))) | (~(f7(c1) = c2)) | (~(f5(c1) = c2)) | (f10(f9(c2, c2)) = f9(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 27.56/17.75 tff(2215,plain,
% 27.56/17.75 (~(c4 = c2)),
% 27.56/17.75 inference(unit_resolution,[status(thm)],[2214, 2188, 148, 79, 122, 22, 2009, 1791, 2014, 2011, 120, 1709, 1721])).
% 27.56/17.75 tff(2216,plain,
% 27.56/17.75 (c4 = c1),
% 27.56/17.75 inference(unit_resolution,[status(thm)],[461, 2215])).
% 27.56/17.75 tff(2217,plain,
% 27.56/17.75 (big_f(c2, c4) <=> big_f(c2, c1)),
% 27.56/17.75 inference(monotonicity,[status(thm)],[480])).
% 27.56/17.75 tff(2218,plain,
% 27.56/17.75 (big_f(f4(c4), c4) <=> big_f(c2, c1)),
% 27.56/17.75 inference(transitivity,[status(thm)],[375, 2217])).
% 27.56/17.75 tff(2219,plain,
% 27.56/17.75 (big_f(c2, c1)),
% 27.56/17.75 inference(modus_ponens,[status(thm)],[474, 2218])).
% 27.56/17.75 tff(2220,plain,
% 27.56/17.75 ($false),
% 27.56/17.75 inference(unit_resolution,[status(thm)],[2, 2219])).
% 27.56/17.75 tff(2221,plain,((~big_f(f4(c4), c4)) | big_f(c2, c1) | (~(c4 = c1)) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.56/17.75 tff(2222,plain,
% 27.56/17.75 (~big_f(f4(c4), c4)),
% 27.56/17.75 inference(unit_resolution,[status(thm)],[2221, 2216, 2038, 79])).
% 27.56/17.75 tff(2223,plain,
% 27.56/17.75 (c1 = c4),
% 27.56/17.75 inference(symmetry,[status(thm)],[2216])).
% 27.56/17.75 tff(2224,plain,
% 27.56/17.75 (f4(c1) = f4(c4)),
% 27.56/17.75 inference(monotonicity,[status(thm)],[2223])).
% 27.56/17.75 tff(2225,plain,
% 27.56/17.75 (f4(c4) = f4(c1)),
% 27.56/17.75 inference(symmetry,[status(thm)],[2224])).
% 27.56/17.75 tff(2226,plain,
% 27.56/17.75 (c2 = f4(f9(c2, c2))),
% 27.56/17.75 inference(transitivity,[status(thm)],[436, 2225, 2094])).
% 27.56/17.75 tff(2227,plain,
% 27.56/17.75 (c1 = c4),
% 27.56/17.75 inference(unit_resolution,[status(thm)],[484, 2216])).
% 27.56/17.75 tff(2228,plain,
% 27.56/17.75 (f9(c2, c2) = c4),
% 27.56/17.75 inference(modus_ponens,[status(thm)],[2227, 362])).
% 27.56/17.75 tff(2229,plain,
% 27.56/17.75 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f9(c2, c2) = c3) | big_f(c2, f9(c2, c2)) | (~(f9(c2, c2) = c4)) | (~(c2 = f4(f9(c2, c2)))) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (f9(c2, c2) = c3) | big_f(c2, f9(c2, c2)) | (~(f9(c2, c2) = c4)) | (~(c2 = f4(f9(c2, c2)))) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2)))),
% 27.56/17.75 inference(rewrite,[status(thm)],[])).
% 27.56/17.75 tff(2230,plain,
% 27.56/17.75 (((f9(c2, c2) = c3) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2)) | (~(f9(c2, c2) = c4)) | big_f(c2, f9(c2, c2)) | (~(c2 = f4(f9(c2, c2))))) <=> ((f9(c2, c2) = c3) | big_f(c2, f9(c2, c2)) | (~(f9(c2, c2) = c4)) | (~(c2 = f4(f9(c2, c2)))) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2)))),
% 27.56/17.75 inference(rewrite,[status(thm)],[])).
% 27.56/17.75 tff(2231,plain,
% 27.56/17.75 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f9(c2, c2) = c3) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2)) | (~(f9(c2, c2) = c4)) | big_f(c2, f9(c2, c2)) | (~(c2 = f4(f9(c2, c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f9(c2, c2) = c3) | big_f(c2, f9(c2, c2)) | (~(f9(c2, c2) = c4)) | (~(c2 = f4(f9(c2, c2)))) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2))))),
% 27.56/17.75 inference(monotonicity,[status(thm)],[2230])).
% 27.56/17.75 tff(2232,plain,
% 27.56/17.75 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f9(c2, c2) = c3) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2)) | (~(f9(c2, c2) = c4)) | big_f(c2, f9(c2, c2)) | (~(c2 = f4(f9(c2, c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (f9(c2, c2) = c3) | big_f(c2, f9(c2, c2)) | (~(f9(c2, c2) = c4)) | (~(c2 = f4(f9(c2, c2)))) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2)))),
% 27.56/17.75 inference(transitivity,[status(thm)],[2231, 2229])).
% 27.56/17.75 tff(2233,plain,
% 27.56/17.75 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f9(c2, c2) = c3) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2)) | (~(f9(c2, c2) = c4)) | big_f(c2, f9(c2, c2)) | (~(c2 = f4(f9(c2, c2)))))),
% 27.56/17.75 inference(quant_inst,[status(thm)],[])).
% 27.56/17.75 tff(2234,plain,
% 27.56/17.75 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (f9(c2, c2) = c3) | big_f(c2, f9(c2, c2)) | (~(f9(c2, c2) = c4)) | (~(c2 = f4(f9(c2, c2)))) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2))),
% 27.56/17.75 inference(modus_ponens,[status(thm)],[2233, 2232])).
% 27.56/17.75 tff(2235,plain,
% 27.56/17.75 ((f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2))),
% 27.56/17.75 inference(unit_resolution,[status(thm)],[2234, 402, 514, 566, 2040, 2099])).
% 27.56/17.75 tff(2236,plain,
% 27.56/17.75 ($false),
% 27.56/17.75 inference(unit_resolution,[status(thm)],[2235, 1105, 1100])).
% 27.56/17.75 tff(2237,plain,((~(f1(c1, c2) = c1)) | (~(f9(c2, c2) = c4)) | (f9(c2, c2) = c3) | big_f(c2, f9(c2, c2)) | (~(c2 = f4(f9(c2, c2)))) | big_f(f7(c2), c1) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f7(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 27.56/17.75 tff(2238,plain,
% 27.56/17.75 (~(f1(c1, c2) = c1)),
% 27.56/17.75 inference(unit_resolution,[status(thm)],[2237, 2228, 2129, 2039, 2226, 2188, 148, 79, 122, 22])).
% 27.56/17.75 tff(2239,plain,
% 27.56/17.75 (f1(c1, c2) = c2),
% 27.56/17.75 inference(unit_resolution,[status(thm)],[841, 2238])).
% 27.56/17.75 tff(2240,plain,
% 27.56/17.75 (f1(c1, f1(c1, c2)) = f1(f9(f10(c2), f4(c4)), c2)),
% 27.56/17.75 inference(monotonicity,[status(thm)],[149, 2239])).
% 27.56/17.75 tff(2241,plain,
% 27.56/17.75 (f1(c1, f1(c1, c2)) = f1(c1, c2)),
% 27.56/17.75 inference(transitivity,[status(thm)],[2240, 819])).
% 27.56/17.75 tff(2242,plain,
% 27.56/17.75 (f1(c1, f1(c1, c2)) = f10(c2)),
% 27.56/17.75 inference(transitivity,[status(thm)],[2240, 819, 2239, 216])).
% 27.56/17.75 tff(2243,plain,
% 27.56/17.75 (big_f(c1, f1(c1, f1(c1, c2))) <=> big_f(f9(c2, c2), f10(c2))),
% 27.56/17.75 inference(monotonicity,[status(thm)],[150, 2242])).
% 27.56/17.75 tff(2244,plain,
% 27.56/17.75 (big_f(f9(c2, c2), f10(c2)) <=> big_f(c1, f1(c1, f1(c1, c2)))),
% 27.56/17.75 inference(symmetry,[status(thm)],[2243])).
% 27.56/17.75 tff(2245,plain,
% 27.56/17.75 (big_f(c1, f1(c1, f1(c1, c2)))),
% 27.56/17.75 inference(modus_ponens,[status(thm)],[2009, 2244])).
% 27.56/17.75 tff(2246,plain,
% 27.56/17.75 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | big_f(f4(c4), c4) | (~(f1(c1, f1(c1, c2)) = f1(c1, c2))) | (~big_f(c1, f1(c1, f1(c1, c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | big_f(f4(c4), c4) | (~(f1(c1, f1(c1, c2)) = f1(c1, c2))) | (~big_f(c1, f1(c1, f1(c1, c2)))))),
% 27.56/17.76 inference(rewrite,[status(thm)],[])).
% 27.56/17.76 tff(2247,plain,
% 27.56/17.76 (((c1 = c3) | $false | big_f(f4(c4), c4) | $false | (~(f1(c1, f1(c1, c2)) = f1(c1, c2))) | (~big_f(c1, f1(c1, f1(c1, c2))))) <=> ((c1 = c3) | big_f(f4(c4), c4) | (~(f1(c1, f1(c1, c2)) = f1(c1, c2))) | (~big_f(c1, f1(c1, f1(c1, c2)))))),
% 27.56/17.76 inference(rewrite,[status(thm)],[])).
% 27.56/17.76 tff(2248,plain,
% 27.56/17.76 (((c1 = c3) | (~(c4 = c4)) | big_f(f4(c4), c4) | (~(f4(c4) = f4(c4))) | (~(f1(c1, f1(c1, c2)) = f1(c1, c2))) | (~big_f(c1, f1(c1, f1(c1, c2))))) <=> ((c1 = c3) | $false | big_f(f4(c4), c4) | $false | (~(f1(c1, f1(c1, c2)) = f1(c1, c2))) | (~big_f(c1, f1(c1, f1(c1, c2)))))),
% 27.56/17.76 inference(monotonicity,[status(thm)],[410, 407])).
% 27.56/17.76 tff(2249,plain,
% 27.56/17.76 (((c1 = c3) | (~(c4 = c4)) | big_f(f4(c4), c4) | (~(f4(c4) = f4(c4))) | (~(f1(c1, f1(c1, c2)) = f1(c1, c2))) | (~big_f(c1, f1(c1, f1(c1, c2))))) <=> ((c1 = c3) | big_f(f4(c4), c4) | (~(f1(c1, f1(c1, c2)) = f1(c1, c2))) | (~big_f(c1, f1(c1, f1(c1, c2)))))),
% 27.56/17.76 inference(transitivity,[status(thm)],[2248, 2247])).
% 27.56/17.76 tff(2250,plain,
% 27.56/17.76 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~(c4 = c4)) | big_f(f4(c4), c4) | (~(f4(c4) = f4(c4))) | (~(f1(c1, f1(c1, c2)) = f1(c1, c2))) | (~big_f(c1, f1(c1, f1(c1, c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | big_f(f4(c4), c4) | (~(f1(c1, f1(c1, c2)) = f1(c1, c2))) | (~big_f(c1, f1(c1, f1(c1, c2))))))),
% 27.56/17.76 inference(monotonicity,[status(thm)],[2249])).
% 27.56/17.76 tff(2251,plain,
% 27.56/17.76 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~(c4 = c4)) | big_f(f4(c4), c4) | (~(f4(c4) = f4(c4))) | (~(f1(c1, f1(c1, c2)) = f1(c1, c2))) | (~big_f(c1, f1(c1, f1(c1, c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | big_f(f4(c4), c4) | (~(f1(c1, f1(c1, c2)) = f1(c1, c2))) | (~big_f(c1, f1(c1, f1(c1, c2)))))),
% 27.56/17.76 inference(transitivity,[status(thm)],[2250, 2246])).
% 27.56/17.76 tff(2252,plain,
% 27.56/17.76 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~(c4 = c4)) | big_f(f4(c4), c4) | (~(f4(c4) = f4(c4))) | (~(f1(c1, f1(c1, c2)) = f1(c1, c2))) | (~big_f(c1, f1(c1, f1(c1, c2)))))),
% 27.56/17.76 inference(quant_inst,[status(thm)],[])).
% 27.56/17.76 tff(2253,plain,
% 27.56/17.76 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | big_f(f4(c4), c4) | (~(f1(c1, f1(c1, c2)) = f1(c1, c2))) | (~big_f(c1, f1(c1, f1(c1, c2))))),
% 27.56/17.76 inference(modus_ponens,[status(thm)],[2252, 2251])).
% 27.56/17.76 tff(2254,plain,
% 27.56/17.76 ((c1 = c3) | big_f(f4(c4), c4) | (~(f1(c1, f1(c1, c2)) = f1(c1, c2))) | (~big_f(c1, f1(c1, f1(c1, c2))))),
% 27.56/17.76 inference(unit_resolution,[status(thm)],[2253, 447])).
% 27.56/17.76 tff(2255,plain,
% 27.56/17.76 ($false),
% 27.56/17.76 inference(unit_resolution,[status(thm)],[2254, 2245, 2241, 2222, 2130])).
% 27.56/17.76 tff(2256,plain,((f7(c2) = c2) | (~(f10(c2) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (f7(c1) = c1) | (f9(f10(c2), f10(c2)) = f10(c2)) | (f10(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 27.56/17.76 tff(2257,plain,
% 27.56/17.76 (f7(c2) = c2),
% 27.56/17.76 inference(unit_resolution,[status(thm)],[2256, 115, 148, 79, 122, 158, 3])).
% 27.56/17.76 tff(2258,plain,
% 27.56/17.76 (f6(c2, c2) = f6(f7(c2), f5(c1))),
% 27.56/17.76 inference(monotonicity,[status(thm)],[82, 1761])).
% 27.56/17.76 tff(2259,plain,
% 27.56/17.76 (f6(f7(c2), f5(c1)) = f6(c2, c2)),
% 27.56/17.76 inference(symmetry,[status(thm)],[2258])).
% 27.56/17.76 tff(2260,plain,
% 27.56/17.76 ((f6(f7(c2), f5(c1)) = c2) <=> (f6(c2, c2) = c2)),
% 27.56/17.76 inference(monotonicity,[status(thm)],[2259])).
% 27.56/17.76 tff(2261,plain,
% 27.56/17.76 ((~(f5(c1) = c1)) <=> (~(c1 = f5(c1)))),
% 27.56/17.76 inference(monotonicity,[status(thm)],[192])).
% 27.56/17.76 tff(2262,plain,
% 27.56/17.76 (big_f(f7(c2), c1) <=> big_f(c2, c1)),
% 27.56/17.76 inference(monotonicity,[status(thm)],[77])).
% 27.56/17.76 tff(2263,plain,
% 27.56/17.76 ((~big_f(f7(c2), c1)) <=> (~big_f(c2, c1))),
% 27.56/17.76 inference(monotonicity,[status(thm)],[2262])).
% 27.56/17.76 tff(2264,plain,
% 27.56/17.76 (~big_f(c2, c1)),
% 27.56/17.76 inference(modus_ponens,[status(thm)],[333, 2263])).
% 27.56/17.76 tff(2265,plain,
% 27.56/17.76 (f2(c3) = f2(c2)),
% 27.56/17.76 inference(symmetry,[status(thm)],[1426])).
% 27.56/17.76 tff(2266,plain,
% 27.56/17.76 (c3 = f7(c2)),
% 27.56/17.76 inference(transitivity,[status(thm)],[67, 82])).
% 27.56/17.76 tff(2267,plain,
% 27.56/17.76 (big_f(c3, f2(c3)) <=> big_f(f7(c2), f2(c2))),
% 27.56/17.76 inference(monotonicity,[status(thm)],[2266, 2265])).
% 27.56/17.76 tff(2268,plain,
% 27.56/17.76 (big_f(f7(c2), f2(c2)) <=> big_f(c3, f2(c3))),
% 27.56/17.76 inference(symmetry,[status(thm)],[2267])).
% 27.56/17.76 tff(2269,plain,
% 27.56/17.76 (big_f(f7(c2), f2(c2)) <=> big_f(c2, c1)),
% 27.56/17.76 inference(monotonicity,[status(thm)],[77, 1427])).
% 27.56/17.76 tff(2270,plain,
% 27.56/17.76 (big_f(c2, c1) <=> big_f(f7(c2), f2(c2))),
% 27.56/17.76 inference(symmetry,[status(thm)],[2269])).
% 27.56/17.76 tff(2271,plain,
% 27.56/17.76 (big_f(f7(c2), c1) <=> big_f(c3, f2(c3))),
% 27.56/17.76 inference(transitivity,[status(thm)],[2262, 2270, 2268])).
% 27.56/17.76 tff(2272,plain,
% 27.56/17.76 ((~big_f(f7(c2), c1)) <=> (~big_f(c3, f2(c3)))),
% 27.56/17.76 inference(monotonicity,[status(thm)],[2271])).
% 27.56/17.76 tff(2273,plain,
% 27.56/17.76 (~big_f(c3, f2(c3))),
% 27.56/17.76 inference(modus_ponens,[status(thm)],[333, 2272])).
% 27.56/17.76 tff(2274,assumption,(big_f(c3, f2(c3))), introduced(assumption)).
% 27.56/17.76 tff(2275,plain,
% 27.56/17.76 ($false),
% 27.56/17.76 inference(unit_resolution,[status(thm)],[2274, 2273])).
% 27.56/17.76 tff(2276,plain,((~big_f(c3, f2(c3))) | big_f(f7(c2), c1) | (~(f2(c3) = c1)) | (~(c3 = c2)) | (~(f7(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.56/17.76 tff(2277,plain,
% 27.56/17.76 (~big_f(c3, f2(c3))),
% 27.56/17.76 inference(unit_resolution,[status(thm)],[2276, 1247, 333, 67, 77])).
% 27.56/17.76 tff(2278,plain,
% 27.56/17.76 (big_f(c2, c1) <=> big_f(f7(c2), c1)),
% 27.56/17.76 inference(symmetry,[status(thm)],[2262])).
% 27.56/17.76 tff(2279,plain,
% 27.56/17.76 ((~(c1 = f5(c1))) <=> (~(f5(c1) = c1))),
% 27.56/17.76 inference(monotonicity,[status(thm)],[128])).
% 27.56/17.76 tff(2280,plain,
% 27.56/17.76 (big_f(c2, c2)),
% 27.56/17.76 inference(unit_resolution,[status(thm)],[476, 1316, 431, 79])).
% 27.56/17.76 tff(2281,plain,
% 27.56/17.76 (big_f(c3, c2)),
% 27.56/17.76 inference(modus_ponens,[status(thm)],[2280, 1288])).
% 27.56/17.76 tff(2282,plain,
% 27.56/17.76 (~(f2(c3) = c2)),
% 27.56/17.76 inference(unit_resolution,[status(thm)],[1325, 2281, 1286])).
% 27.56/17.76 tff(2283,plain,
% 27.56/17.76 (f2(c3) = c1),
% 27.56/17.76 inference(unit_resolution,[status(thm)],[1273, 2282])).
% 27.56/17.76 tff(2284,plain,
% 27.56/17.76 (f2(c2) = c1),
% 27.56/17.76 inference(transitivity,[status(thm)],[1231, 2283])).
% 27.56/17.76 tff(2285,plain,
% 27.56/17.76 ((c2 = f2(c2)) <=> (c2 = c1)),
% 27.56/17.76 inference(monotonicity,[status(thm)],[2284])).
% 27.56/17.76 tff(2286,plain,
% 27.56/17.76 ((c2 = c1) <=> (c2 = f2(c2))),
% 27.56/17.76 inference(symmetry,[status(thm)],[2285])).
% 27.56/17.76 tff(2287,plain,
% 27.56/17.76 ((~(c2 = c1)) <=> (~(c2 = f2(c2)))),
% 27.56/17.76 inference(monotonicity,[status(thm)],[2286])).
% 27.56/17.76 tff(2288,plain,
% 27.56/17.76 (~(c2 = f2(c2))),
% 27.56/17.76 inference(modus_ponens,[status(thm)],[75, 2287])).
% 27.56/17.76 tff(2289,plain,
% 27.56/17.76 (f4(c2) = f10(c2)),
% 27.56/17.76 inference(transitivity,[status(thm)],[434, 79, 216])).
% 27.56/17.76 tff(2290,plain,
% 27.56/17.76 ((f9(f10(c2), f10(c2)) = f4(c2)) <=> (f9(f10(c2), f10(c2)) = f10(c2))),
% 27.56/17.76 inference(monotonicity,[status(thm)],[2289])).
% 27.56/17.76 tff(2291,plain,
% 27.56/17.76 ((f9(f10(c2), f10(c2)) = f10(c2)) <=> (f9(f10(c2), f10(c2)) = f4(c2))),
% 27.56/17.76 inference(symmetry,[status(thm)],[2290])).
% 27.56/17.76 tff(2292,plain,
% 27.56/17.76 ((~(f9(f10(c2), f10(c2)) = f10(c2))) <=> (~(f9(f10(c2), f10(c2)) = f4(c2)))),
% 27.56/17.76 inference(monotonicity,[status(thm)],[2291])).
% 27.56/17.76 tff(2293,plain,
% 27.56/17.76 (~(f9(f10(c2), f10(c2)) = f4(c2))),
% 27.56/17.76 inference(modus_ponens,[status(thm)],[158, 2292])).
% 27.56/17.76 tff(2294,plain,
% 27.56/17.76 (c2 = f10(f10(c2))),
% 27.56/17.76 inference(transitivity,[status(thm)],[216, 1282])).
% 27.56/17.76 tff(2295,plain,
% 27.56/17.76 (big_f(f9(f10(c2), f10(c2)), c2) <=> big_f(f9(f10(c2), f10(c2)), f10(f10(c2)))),
% 27.56/17.76 inference(monotonicity,[status(thm)],[2294])).
% 27.56/17.76 tff(2296,plain,
% 27.56/17.76 (big_f(f9(f10(c2), f10(c2)), f10(f10(c2))) <=> big_f(f9(f10(c2), f10(c2)), c2)),
% 27.56/17.76 inference(symmetry,[status(thm)],[2295])).
% 27.56/17.76 tff(2297,plain,
% 27.56/17.76 (big_f(f9(f10(c2), f10(c2)), f10(f10(c2)))),
% 27.56/17.76 inference(unit_resolution,[status(thm)],[280, 158, 115, 252, 730])).
% 27.56/17.76 tff(2298,plain,
% 27.56/17.76 (big_f(f9(f10(c2), f10(c2)), c2)),
% 27.56/17.76 inference(modus_ponens,[status(thm)],[2297, 2296])).
% 27.56/17.76 tff(2299,plain,
% 27.56/17.76 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c2 = c4)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (f9(f10(c2), f10(c2)) = f4(c2)) | (~big_f(f9(f10(c2), f10(c2)), c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (~(c2 = c4)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (f9(f10(c2), f10(c2)) = f4(c2)) | (~big_f(f9(f10(c2), f10(c2)), c2)))),
% 27.56/17.76 inference(rewrite,[status(thm)],[])).
% 27.56/17.76 tff(2300,plain,
% 27.56/17.76 (((~(c2 = c3)) | (~(c2 = c4)) | (f9(f10(c2), f10(c2)) = f4(c2)) | (~big_f(f9(f10(c2), f10(c2)), c2)) | (c2 = f2(c2)) | (~big_f(c2, c2))) <=> ((~(c2 = c3)) | (~(c2 = c4)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (f9(f10(c2), f10(c2)) = f4(c2)) | (~big_f(f9(f10(c2), f10(c2)), c2)))),
% 27.56/17.76 inference(rewrite,[status(thm)],[])).
% 27.56/17.76 tff(2301,plain,
% 27.56/17.76 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c2 = c4)) | (f9(f10(c2), f10(c2)) = f4(c2)) | (~big_f(f9(f10(c2), f10(c2)), c2)) | (c2 = f2(c2)) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c2 = c4)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (f9(f10(c2), f10(c2)) = f4(c2)) | (~big_f(f9(f10(c2), f10(c2)), c2))))),
% 27.56/17.76 inference(monotonicity,[status(thm)],[2300])).
% 27.56/17.76 tff(2302,plain,
% 27.56/17.76 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c2 = c4)) | (f9(f10(c2), f10(c2)) = f4(c2)) | (~big_f(f9(f10(c2), f10(c2)), c2)) | (c2 = f2(c2)) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (~(c2 = c4)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (f9(f10(c2), f10(c2)) = f4(c2)) | (~big_f(f9(f10(c2), f10(c2)), c2)))),
% 27.56/17.76 inference(transitivity,[status(thm)],[2301, 2299])).
% 27.56/17.76 tff(2303,plain,
% 27.56/17.76 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c2 = c4)) | (f9(f10(c2), f10(c2)) = f4(c2)) | (~big_f(f9(f10(c2), f10(c2)), c2)) | (c2 = f2(c2)) | (~big_f(c2, c2)))),
% 27.56/17.76 inference(quant_inst,[status(thm)],[])).
% 27.56/17.76 tff(2304,plain,
% 27.56/17.76 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (~(c2 = c4)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (f9(f10(c2), f10(c2)) = f4(c2)) | (~big_f(f9(f10(c2), f10(c2)), c2))),
% 27.56/17.76 inference(modus_ponens,[status(thm)],[2303, 2302])).
% 27.56/17.76 tff(2305,plain,
% 27.56/17.76 ((f9(f10(c2), f10(c2)) = f4(c2)) | (~big_f(f9(f10(c2), f10(c2)), c2))),
% 27.56/17.76 inference(unit_resolution,[status(thm)],[2304, 1355, 432, 1345, 1344, 1342])).
% 27.56/17.76 tff(2306,plain,
% 27.56/17.76 ($false),
% 27.56/17.76 inference(unit_resolution,[status(thm)],[2305, 2298, 2293])).
% 27.56/17.76 tff(2307,plain,((f9(f10(c2), f10(c2)) = f10(c2)) | (~big_f(c2, c2)) | (~(c2 = c3)) | (c2 = f2(c2)) | (~(f10(c2) = c2)) | (~(f4(c4) = c2)) | (~(c4 = c2)) | (f7(c1) = c1) | big_f(f7(c1), f5(c1))), inference(lemma,lemma(discharge,[]))).
% 27.56/17.76 tff(2308,plain,
% 27.56/17.76 (f9(f10(c2), f10(c2)) = f10(c2)),
% 27.56/17.76 inference(unit_resolution,[status(thm)],[2307, 115, 1335, 2288, 122, 79, 431, 2280, 730])).
% 27.56/17.76 tff(2309,plain,
% 27.56/17.76 (f9(c2, f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2))),
% 27.56/17.76 inference(monotonicity,[status(thm)],[216, 2308])).
% 27.56/17.76 tff(2310,plain,
% 27.56/17.76 (c1 = f2(c3)),
% 27.56/17.76 inference(symmetry,[status(thm)],[2283])).
% 27.56/17.76 tff(2311,plain,
% 27.56/17.76 (f7(c1) = c3),
% 27.56/17.76 inference(transitivity,[status(thm)],[120, 69])).
% 27.56/17.76 tff(2312,plain,
% 27.56/17.76 (big_f(f7(c1), c1) <=> big_f(c3, f2(c3))),
% 27.56/17.76 inference(monotonicity,[status(thm)],[2311, 2310])).
% 27.56/17.76 tff(2313,plain,
% 27.56/17.76 (big_f(c3, f2(c3)) <=> big_f(f7(c1), c1)),
% 27.56/17.76 inference(symmetry,[status(thm)],[2312])).
% 27.56/17.76 tff(2314,plain,
% 27.56/17.76 ((~big_f(c3, f2(c3))) <=> (~big_f(f7(c1), c1))),
% 27.56/17.76 inference(monotonicity,[status(thm)],[2313])).
% 27.56/17.76 tff(2315,plain,
% 27.56/17.76 (~big_f(f7(c1), c1)),
% 27.56/17.76 inference(modus_ponens,[status(thm)],[1286, 2314])).
% 27.56/17.76 tff(2316,plain,
% 27.56/17.76 (f9(c2, f9(f10(c2), f10(c2))) = c2),
% 27.56/17.76 inference(transitivity,[status(thm)],[2309, 2308, 122])).
% 27.56/17.76 tff(2317,plain,
% 27.56/17.76 (big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2)) <=> big_f(c2, c2)),
% 27.56/17.76 inference(monotonicity,[status(thm)],[2316, 122])).
% 27.56/17.76 tff(2318,plain,
% 27.56/17.76 (big_f(c2, c2) <=> big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2))),
% 27.56/17.76 inference(symmetry,[status(thm)],[2317])).
% 27.56/17.76 tff(2319,plain,
% 27.56/17.76 (big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2))),
% 27.56/17.76 inference(modus_ponens,[status(thm)],[2280, 2318])).
% 27.56/17.76 tff(2320,plain,
% 27.56/17.76 (~(c1 = f5(c1))),
% 27.56/17.76 inference(unit_resolution,[status(thm)],[790, 2319, 122, 115, 2315, 2309])).
% 27.56/17.76 tff(2321,plain,
% 27.56/17.76 (~(f5(c1) = c1)),
% 27.56/17.76 inference(modus_ponens,[status(thm)],[2320, 2279])).
% 27.56/17.76 tff(2322,plain,
% 27.56/17.76 (f5(c1) = c2),
% 27.56/17.76 inference(unit_resolution,[status(thm)],[1708, 2321])).
% 27.56/17.76 tff(2323,plain,
% 27.56/17.76 (big_f(f7(c1), f5(c1)) <=> big_f(c2, c2)),
% 27.56/17.76 inference(monotonicity,[status(thm)],[120, 2322])).
% 27.56/17.76 tff(2324,plain,
% 27.56/17.76 (big_f(c2, c2) <=> big_f(f7(c1), f5(c1))),
% 27.56/17.76 inference(symmetry,[status(thm)],[2323])).
% 27.56/17.76 tff(2325,plain,
% 27.56/17.76 (big_f(f7(c1), f5(c1))),
% 27.56/17.76 inference(modus_ponens,[status(thm)],[2280, 2324])).
% 27.56/17.76 tff(2326,plain,
% 27.56/17.76 ($false),
% 27.56/17.76 inference(unit_resolution,[status(thm)],[730, 2325])).
% 27.56/17.76 tff(2327,plain,((f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (~(f10(c2) = c2)) | (~(f4(c4) = c2)) | (~(c4 = c2)) | big_f(c3, f2(c3)) | (~(c3 = c2))), inference(lemma,lemma(discharge,[]))).
% 27.56/17.76 tff(2328,plain,
% 27.56/17.76 (~(c4 = c2)),
% 27.56/17.76 inference(unit_resolution,[status(thm)],[2327, 1286, 122, 79, 115, 730, 67])).
% 27.56/17.76 tff(2329,plain,
% 27.56/17.76 (c4 = c1),
% 27.56/17.76 inference(unit_resolution,[status(thm)],[461, 2328])).
% 27.56/17.76 tff(2330,plain,
% 27.56/17.76 (c4 = f2(c2)),
% 27.56/17.76 inference(transitivity,[status(thm)],[2329, 1367, 2265])).
% 27.56/17.76 tff(2331,plain,
% 27.56/17.76 (big_f(c2, c4) <=> big_f(f7(c2), f2(c2))),
% 27.56/17.76 inference(monotonicity,[status(thm)],[82, 2330])).
% 27.56/17.76 tff(2332,plain,
% 27.56/17.76 (big_f(c2, c4) <=> big_f(f7(c2), c1)),
% 27.56/17.76 inference(transitivity,[status(thm)],[2331, 2269, 2278])).
% 27.56/17.76 tff(2333,plain,
% 27.56/17.76 (big_f(c2, c4)),
% 27.56/17.76 inference(modus_ponens,[status(thm)],[1316, 375])).
% 27.56/17.76 tff(2334,plain,
% 27.56/17.76 (big_f(f7(c2), c1)),
% 27.56/17.76 inference(modus_ponens,[status(thm)],[2333, 2332])).
% 27.56/17.76 tff(2335,plain,
% 27.56/17.76 ($false),
% 27.56/17.76 inference(unit_resolution,[status(thm)],[333, 2334])).
% 27.56/17.76 tff(2336,plain,(big_f(c3, f2(c3)) | big_f(f7(c2), c1) | (~(f2(c3) = c1)) | (~(c3 = c2)) | (~(f7(c2) = c2)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (f7(c1) = c1) | big_f(f7(c1), f5(c1))), inference(lemma,lemma(discharge,[]))).
% 27.56/17.76 tff(2337,plain,
% 27.56/17.76 (big_f(f7(c1), f5(c1))),
% 27.56/17.76 inference(unit_resolution,[status(thm)],[2336, 2277, 1247, 67, 77, 79, 122, 115, 333])).
% 27.56/17.76 tff(2338,plain,
% 27.56/17.76 (f5(c1) = f2(c3)),
% 27.56/17.76 inference(transitivity,[status(thm)],[230, 1367])).
% 27.56/17.76 tff(2339,plain,
% 27.56/17.76 (f7(c1) = c3),
% 27.56/17.76 inference(transitivity,[status(thm)],[347, 69])).
% 27.56/17.76 tff(2340,plain,
% 27.56/17.76 (big_f(f7(c1), f5(c1)) <=> big_f(c3, f2(c3))),
% 27.56/17.76 inference(monotonicity,[status(thm)],[2339, 2338])).
% 27.56/17.76 tff(2341,plain,
% 27.56/17.76 (big_f(c3, f2(c3)) <=> big_f(f7(c1), f5(c1))),
% 27.56/17.76 inference(symmetry,[status(thm)],[2340])).
% 27.56/17.76 tff(2342,plain,
% 27.56/17.76 ((~big_f(c3, f2(c3))) <=> (~big_f(f7(c1), f5(c1)))),
% 27.56/17.76 inference(monotonicity,[status(thm)],[2341])).
% 27.56/17.76 tff(2343,plain,
% 27.56/17.76 (~big_f(f7(c1), f5(c1))),
% 27.56/17.76 inference(modus_ponens,[status(thm)],[1286, 2342])).
% 27.56/17.76 tff(2344,plain,
% 27.56/17.76 ($false),
% 27.56/17.76 inference(unit_resolution,[status(thm)],[287, 2343])).
% 27.56/17.76 tff(2345,plain,((~(f5(c1) = c1)) | (~big_f(f7(c1), f5(c1))) | big_f(c3, f2(c3)) | (~(f2(c3) = c1)) | (~(c3 = c2)) | (~(f7(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.56/17.76 tff(2346,plain,
% 27.56/17.76 (~(f5(c1) = c1)),
% 27.56/17.76 inference(unit_resolution,[status(thm)],[2345, 2337, 1247, 120, 67, 2277])).
% 27.56/17.76 tff(2347,plain,
% 27.56/17.76 (f5(c1) = c2),
% 27.56/17.76 inference(unit_resolution,[status(thm)],[1708, 2346])).
% 27.56/17.76 tff(2348,plain,
% 27.56/17.76 (big_f(f7(c1), f5(c1)) <=> big_f(c2, c2)),
% 27.56/17.76 inference(monotonicity,[status(thm)],[120, 2347])).
% 27.56/17.76 tff(2349,plain,
% 27.56/17.76 (big_f(c2, c2)),
% 27.56/17.76 inference(modus_ponens,[status(thm)],[2337, 2348])).
% 27.56/17.76 tff(2350,plain,
% 27.56/17.76 (big_f(f7(c2), c1) <=> big_f(f7(c2), f2(c2))),
% 27.56/17.76 inference(transitivity,[status(thm)],[2262, 2270])).
% 27.56/17.76 tff(2351,plain,
% 27.56/17.76 ((~big_f(f7(c2), c1)) <=> (~big_f(f7(c2), f2(c2)))),
% 27.56/17.76 inference(monotonicity,[status(thm)],[2350])).
% 27.56/17.76 tff(2352,plain,
% 27.56/17.76 (~big_f(f7(c2), f2(c2))),
% 27.56/17.76 inference(modus_ponens,[status(thm)],[333, 2351])).
% 27.56/17.76 tff(2353,plain,
% 27.56/17.76 (f9(c2, c2) = c2),
% 27.56/17.76 inference(transitivity,[status(thm)],[1283, 138, 122])).
% 27.56/17.76 tff(2354,plain,
% 27.56/17.76 (big_f(f9(c2, c2), f10(c2)) <=> big_f(c2, c2)),
% 27.56/17.76 inference(monotonicity,[status(thm)],[2353, 122])).
% 27.56/17.76 tff(2355,plain,
% 27.56/17.76 (big_f(c2, c2) <=> big_f(f9(c2, c2), f10(c2))),
% 27.56/17.76 inference(symmetry,[status(thm)],[2354])).
% 27.56/17.76 tff(2356,plain,
% 27.56/17.76 (big_f(f9(c2, c2), f10(c2))),
% 27.56/17.76 inference(modus_ponens,[status(thm)],[1345, 2355])).
% 27.56/17.76 tff(2357,plain,
% 27.56/17.76 (f9(f10(c2), f10(c2)) = f9(c2, c2)),
% 27.56/17.76 inference(symmetry,[status(thm)],[1283])).
% 27.56/17.76 tff(2358,plain,
% 27.56/17.76 ((f9(f10(c2), f10(c2)) = f10(c2)) <=> (f9(c2, c2) = c2)),
% 27.56/17.76 inference(monotonicity,[status(thm)],[2357, 122])).
% 27.56/17.76 tff(2359,plain,
% 27.56/17.76 (f9(c2, c2) = c2),
% 27.56/17.76 inference(modus_ponens,[status(thm)],[138, 2358])).
% 27.56/17.76 tff(2360,plain,
% 27.56/17.76 (f6(c2, c2) = f6(f7(c2), c3)),
% 27.56/17.76 inference(monotonicity,[status(thm)],[82, 69])).
% 27.56/17.76 tff(2361,plain,
% 27.56/17.76 (f6(f7(c2), c3) = f6(c2, c2)),
% 27.56/17.76 inference(symmetry,[status(thm)],[2360])).
% 27.56/17.76 tff(2362,assumption,(f6(f7(c2), c3) = c2), introduced(assumption)).
% 27.56/17.76 tff(2363,plain,
% 27.56/17.76 (f6(c2, c2) = c2),
% 27.56/17.76 inference(transitivity,[status(thm)],[2360, 2362])).
% 27.56/17.76 tff(2364,plain,
% 27.56/17.76 (big_f(f7(c2), f6(c2, c2)) <=> big_f(c2, c2)),
% 27.56/17.76 inference(monotonicity,[status(thm)],[77, 2363])).
% 27.56/17.76 tff(2365,plain,
% 27.56/17.76 (big_f(c2, c2) <=> big_f(f7(c2), f6(c2, c2))),
% 27.56/17.76 inference(symmetry,[status(thm)],[2364])).
% 27.56/17.76 tff(2366,plain,
% 27.56/17.76 (big_f(f7(c2), f6(c2, c2))),
% 27.56/17.76 inference(modus_ponens,[status(thm)],[1345, 2365])).
% 27.56/17.76 tff(2367,plain,
% 27.56/17.76 ((f6(f7(c2), c3) = c2) <=> (f6(c2, c2) = c2)),
% 27.56/17.76 inference(monotonicity,[status(thm)],[2361])).
% 27.56/17.76 tff(2368,plain,
% 27.56/17.76 (f6(c2, c2) = c2),
% 27.56/17.76 inference(modus_ponens,[status(thm)],[2362, 2367])).
% 27.56/17.76 tff(2369,plain,
% 27.56/17.76 (^[X9: $i, X6: $i, X4: $i, X7: $i] : refl(((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))) <=> ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))))),
% 27.56/17.76 inference(bind,[status(th)],[])).
% 27.56/17.76 tff(2370,plain,
% 27.56/17.76 (![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))) <=> ![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))),
% 27.56/17.76 inference(quant_intro,[status(thm)],[2369])).
% 27.56/17.76 tff(2371,plain,
% 27.56/17.76 (![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))) <=> ![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))),
% 27.56/17.76 inference(rewrite,[status(thm)],[])).
% 27.56/17.76 tff(2372,plain,
% 27.56/17.76 (^[X9: $i, X6: $i, X4: $i, X7: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~big_f(f7(X4), f6(X4, X6))) | (~(f6(X4, X6) = X6))) <=> ((~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))), ((((~big_f(f7(X4), f6(X4, X6))) | (~(f6(X4, X6) = X6))) | (~(f7(X4) = X4))) <=> (((~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))) | (~(f7(X4) = X4))))), rewrite((((~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))) | (~(f7(X4) = X4))) <=> ((~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))), ((((~big_f(f7(X4), f6(X4, X6))) | (~(f6(X4, X6) = X6))) | (~(f7(X4) = X4))) <=> ((~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))))), (((((~big_f(f7(X4), f6(X4, X6))) | (~(f6(X4, X6) = X6))) | (~(f7(X4) = X4))) | (~big_f(f9(X7, X9), f10(X7)))) <=> (((~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))) | (~big_f(f9(X7, X9), f10(X7)))))), rewrite((((~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))) | (~big_f(f9(X7, X9), f10(X7)))) <=> ((~(f7(X4) = X4)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))), (((((~big_f(f7(X4), f6(X4, X6))) | (~(f6(X4, X6) = X6))) | (~(f7(X4) = X4))) | (~big_f(f9(X7, X9), f10(X7)))) <=> ((~(f7(X4) = X4)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))))), ((((((~big_f(f7(X4), f6(X4, X6))) | (~(f6(X4, X6) = X6))) | (~(f7(X4) = X4))) | (~big_f(f9(X7, X9), f10(X7)))) | (~(f9(X7, X9) = X9))) <=> (((~(f7(X4) = X4)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))) | (~(f9(X7, X9) = X9))))), rewrite((((~(f7(X4) = X4)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))) | (~(f9(X7, X9) = X9))) <=> ((~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))), ((((((~big_f(f7(X4), f6(X4, X6))) | (~(f6(X4, X6) = X6))) | (~(f7(X4) = X4))) | (~big_f(f9(X7, X9), f10(X7)))) | (~(f9(X7, X9) = X9))) <=> ((~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))))), (((((((~big_f(f7(X4), f6(X4, X6))) | (~(f6(X4, X6) = X6))) | (~(f7(X4) = X4))) | (~big_f(f9(X7, X9), f10(X7)))) | (~(f9(X7, X9) = X9))) | (~(f10(X7) = X7))) <=> (((~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))) | (~(f10(X7) = X7))))), rewrite((((~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))) | (~(f10(X7) = X7))) <=> ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))), (((((((~big_f(f7(X4), f6(X4, X6))) | (~(f6(X4, X6) = X6))) | (~(f7(X4) = X4))) | (~big_f(f9(X7, X9), f10(X7)))) | (~(f9(X7, X9) = X9))) | (~(f10(X7) = X7))) <=> ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))))),
% 27.56/17.76 inference(bind,[status(th)],[])).
% 27.56/17.76 tff(2373,plain,
% 27.56/17.76 (![X9: $i, X6: $i, X4: $i, X7: $i] : ((((((~big_f(f7(X4), f6(X4, X6))) | (~(f6(X4, X6) = X6))) | (~(f7(X4) = X4))) | (~big_f(f9(X7, X9), f10(X7)))) | (~(f9(X7, X9) = X9))) | (~(f10(X7) = X7))) <=> ![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))),
% 27.56/17.76 inference(quant_intro,[status(thm)],[2372])).
% 27.56/17.76 tff(2374,axiom,(![X9: $i, X6: $i, X4: $i, X7: $i] : ((((((~big_f(f7(X4), f6(X4, X6))) | (~(f6(X4, X6) = X6))) | (~(f7(X4) = X4))) | (~big_f(f9(X7, X9), f10(X7)))) | (~(f9(X7, X9) = X9))) | (~(f10(X7) = X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_34')).
% 27.56/17.76 tff(2375,plain,
% 27.56/17.76 (![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))),
% 27.56/17.76 inference(modus_ponens,[status(thm)],[2374, 2373])).
% 27.56/17.76 tff(2376,plain,
% 27.56/17.76 (![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))),
% 27.56/17.76 inference(modus_ponens,[status(thm)],[2375, 2371])).
% 27.56/17.76 tff(2377,plain,(
% 27.56/17.76 ![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))),
% 27.56/17.76 inference(skolemize,[status(sab)],[2376])).
% 27.56/17.76 tff(2378,plain,
% 27.56/17.76 (![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))),
% 27.56/17.76 inference(modus_ponens,[status(thm)],[2377, 2370])).
% 27.56/17.76 tff(2379,plain,
% 27.56/17.76 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))),
% 27.56/17.76 inference(rewrite,[status(thm)],[])).
% 27.56/17.76 tff(2380,plain,
% 27.56/17.76 (((~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2)))) <=> ((~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))),
% 27.56/17.76 inference(rewrite,[status(thm)],[])).
% 27.56/17.76 tff(2381,plain,
% 27.56/17.76 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2)))))),
% 27.56/17.76 inference(monotonicity,[status(thm)],[2380])).
% 27.56/17.76 tff(2382,plain,
% 27.56/17.76 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))),
% 27.56/17.76 inference(transitivity,[status(thm)],[2381, 2379])).
% 27.56/17.76 tff(2383,plain,
% 27.56/17.76 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))),
% 27.56/17.76 inference(quant_inst,[status(thm)],[])).
% 27.56/17.76 tff(2384,plain,
% 27.56/17.76 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2)))),
% 27.56/17.76 inference(modus_ponens,[status(thm)],[2383, 2382])).
% 27.56/17.76 tff(2385,plain,
% 27.56/17.76 ($false),
% 27.56/17.76 inference(unit_resolution,[status(thm)],[2384, 2378, 122, 77, 2368, 2366, 1572, 690])).
% 27.56/17.76 tff(2386,plain,((~(f6(f7(c2), c3) = c2)) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~big_f(c2, c2)) | (~(c3 = c2))), inference(lemma,lemma(discharge,[]))).
% 27.56/17.76 tff(2387,plain,
% 27.56/17.76 (~(f6(f7(c2), c3) = c2)),
% 27.56/17.76 inference(unit_resolution,[status(thm)],[2386, 2359, 77, 122, 2356, 1345, 67])).
% 27.56/17.76 tff(2388,plain,
% 27.56/17.76 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f6(f7(c2), c3) = c1) | (f6(f7(c2), c3) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f6(f7(c2), c3) = c1) | (f6(f7(c2), c3) = c2))),
% 27.56/17.76 inference(rewrite,[status(thm)],[])).
% 27.56/17.76 tff(2389,plain,
% 27.56/17.76 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f6(f7(c2), c3) = c1) | (f6(f7(c2), c3) = c2))),
% 27.56/17.76 inference(quant_inst,[status(thm)],[])).
% 27.56/17.76 tff(2390,plain,
% 27.56/17.76 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f6(f7(c2), c3) = c1) | (f6(f7(c2), c3) = c2)),
% 27.56/17.76 inference(modus_ponens,[status(thm)],[2389, 2388])).
% 27.56/17.76 tff(2391,plain,
% 27.56/17.76 ((f6(f7(c2), c3) = c1) | (f6(f7(c2), c3) = c2)),
% 27.56/17.76 inference(unit_resolution,[status(thm)],[2390, 10])).
% 27.56/17.76 tff(2392,plain,
% 27.56/17.76 (f6(f7(c2), c3) = c1),
% 27.56/17.76 inference(unit_resolution,[status(thm)],[2391, 2387])).
% 27.56/17.76 tff(2393,plain,
% 27.56/17.76 (c1 = f6(f7(c2), c3)),
% 27.56/17.76 inference(symmetry,[status(thm)],[2392])).
% 27.56/17.76 tff(2394,plain,
% 27.56/17.76 (f2(c2) = f6(c2, c2)),
% 27.56/17.76 inference(transitivity,[status(thm)],[1231, 1247, 2393, 2361])).
% 27.56/17.76 tff(2395,plain,
% 27.56/17.76 (big_f(f7(c2), f2(c2)) <=> big_f(f7(c2), f6(c2, c2))),
% 27.56/17.76 inference(monotonicity,[status(thm)],[2394])).
% 27.56/17.76 tff(2396,plain,
% 27.56/17.76 ((~big_f(f7(c2), f2(c2))) <=> (~big_f(f7(c2), f6(c2, c2)))),
% 27.56/17.76 inference(monotonicity,[status(thm)],[2395])).
% 27.56/17.76 tff(2397,plain,
% 27.56/17.76 (~big_f(f7(c2), f6(c2, c2))),
% 27.56/17.76 inference(modus_ponens,[status(thm)],[1513, 2396])).
% 27.56/17.76 tff(2398,plain,
% 27.56/17.76 ((~(f6(f7(c2), c3) = c2)) <=> (~(f6(c2, c2) = c2))),
% 27.56/17.76 inference(monotonicity,[status(thm)],[2367])).
% 27.56/17.76 tff(2399,plain,
% 27.56/17.76 (~(f6(c2, c2) = c2)),
% 27.56/17.76 inference(modus_ponens,[status(thm)],[2387, 2398])).
% 27.56/17.76 tff(2400,plain,
% 27.56/17.76 (^[X9: $i, X6: $i, X4: $i, X7: $i] : refl(((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7)))) <=> ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7)))))),
% 27.56/17.76 inference(bind,[status(th)],[])).
% 27.56/17.76 tff(2401,plain,
% 27.56/17.76 (![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7)))) <=> ![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))),
% 27.56/17.76 inference(quant_intro,[status(thm)],[2400])).
% 27.56/17.76 tff(2402,plain,
% 27.56/17.76 (![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7)))) <=> ![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))),
% 27.56/17.76 inference(rewrite,[status(thm)],[])).
% 27.56/17.76 tff(2403,plain,
% 27.56/17.76 (^[X9: $i, X6: $i, X4: $i, X7: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((big_f(f7(X4), f6(X4, X6)) | (f6(X4, X6) = X6)) <=> ((f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))), (((big_f(f7(X4), f6(X4, X6)) | (f6(X4, X6) = X6)) | (~(f7(X4) = X4))) <=> (((f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6))) | (~(f7(X4) = X4))))), rewrite((((f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6))) | (~(f7(X4) = X4))) <=> ((~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))), (((big_f(f7(X4), f6(X4, X6)) | (f6(X4, X6) = X6)) | (~(f7(X4) = X4))) <=> ((~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6))))), ((((big_f(f7(X4), f6(X4, X6)) | (f6(X4, X6) = X6)) | (~(f7(X4) = X4))) | (~big_f(f9(X7, X9), f10(X7)))) <=> (((~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6))) | (~big_f(f9(X7, X9), f10(X7)))))), rewrite((((~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6))) | (~big_f(f9(X7, X9), f10(X7)))) <=> ((~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~big_f(f9(X7, X9), f10(X7))))), ((((big_f(f7(X4), f6(X4, X6)) | (f6(X4, X6) = X6)) | (~(f7(X4) = X4))) | (~big_f(f9(X7, X9), f10(X7)))) <=> ((~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~big_f(f9(X7, X9), f10(X7)))))), (((((big_f(f7(X4), f6(X4, X6)) | (f6(X4, X6) = X6)) | (~(f7(X4) = X4))) | (~big_f(f9(X7, X9), f10(X7)))) | (~(f9(X7, X9) = X9))) <=> (((~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~big_f(f9(X7, X9), f10(X7)))) | (~(f9(X7, X9) = X9))))), rewrite((((~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~big_f(f9(X7, X9), f10(X7)))) | (~(f9(X7, X9) = X9))) <=> ((~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))), (((((big_f(f7(X4), f6(X4, X6)) | (f6(X4, X6) = X6)) | (~(f7(X4) = X4))) | (~big_f(f9(X7, X9), f10(X7)))) | (~(f9(X7, X9) = X9))) <=> ((~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7)))))), ((((((big_f(f7(X4), f6(X4, X6)) | (f6(X4, X6) = X6)) | (~(f7(X4) = X4))) | (~big_f(f9(X7, X9), f10(X7)))) | (~(f9(X7, X9) = X9))) | (~(f10(X7) = X7))) <=> (((~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7)))) | (~(f10(X7) = X7))))), rewrite((((~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7)))) | (~(f10(X7) = X7))) <=> ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))), ((((((big_f(f7(X4), f6(X4, X6)) | (f6(X4, X6) = X6)) | (~(f7(X4) = X4))) | (~big_f(f9(X7, X9), f10(X7)))) | (~(f9(X7, X9) = X9))) | (~(f10(X7) = X7))) <=> ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))))),
% 27.56/17.77 inference(bind,[status(th)],[])).
% 27.56/17.77 tff(2404,plain,
% 27.56/17.77 (![X9: $i, X6: $i, X4: $i, X7: $i] : (((((big_f(f7(X4), f6(X4, X6)) | (f6(X4, X6) = X6)) | (~(f7(X4) = X4))) | (~big_f(f9(X7, X9), f10(X7)))) | (~(f9(X7, X9) = X9))) | (~(f10(X7) = X7))) <=> ![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))),
% 27.56/17.77 inference(quant_intro,[status(thm)],[2403])).
% 27.56/17.77 tff(2405,axiom,(![X9: $i, X6: $i, X4: $i, X7: $i] : (((((big_f(f7(X4), f6(X4, X6)) | (f6(X4, X6) = X6)) | (~(f7(X4) = X4))) | (~big_f(f9(X7, X9), f10(X7)))) | (~(f9(X7, X9) = X9))) | (~(f10(X7) = X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_30')).
% 27.56/17.77 tff(2406,plain,
% 27.56/17.77 (![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))),
% 27.56/17.77 inference(modus_ponens,[status(thm)],[2405, 2404])).
% 27.56/17.77 tff(2407,plain,
% 27.56/17.77 (![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))),
% 27.56/17.77 inference(modus_ponens,[status(thm)],[2406, 2402])).
% 27.56/17.77 tff(2408,plain,(
% 27.56/17.77 ![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))),
% 27.56/17.77 inference(skolemize,[status(sab)],[2407])).
% 27.56/17.77 tff(2409,plain,
% 27.56/17.77 (![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))),
% 27.56/17.77 inference(modus_ponens,[status(thm)],[2408, 2401])).
% 27.56/17.77 tff(2410,plain,
% 27.56/17.77 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))),
% 27.56/17.77 inference(rewrite,[status(thm)],[])).
% 27.56/17.77 tff(2411,plain,
% 27.56/17.77 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))),
% 27.56/17.77 inference(quant_inst,[status(thm)],[])).
% 27.56/17.77 tff(2412,plain,
% 27.56/17.77 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2)))),
% 27.56/17.77 inference(modus_ponens,[status(thm)],[2411, 2410])).
% 27.56/17.77 tff(2413,plain,
% 27.56/17.77 ($false),
% 27.56/17.77 inference(unit_resolution,[status(thm)],[2412, 2409, 122, 77, 2399, 2397, 2359, 2356])).
% 27.56/17.77 tff(2414,plain,((~(f9(f10(c2), f10(c2)) = f10(c2))) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | big_f(f7(c2), f2(c2)) | (~(f2(c3) = c1)) | (~(c3 = c2)) | (~big_f(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 27.56/17.77 tff(2415,plain,
% 27.56/17.77 (~(f9(f10(c2), f10(c2)) = f10(c2))),
% 27.56/17.77 inference(unit_resolution,[status(thm)],[2414, 2352, 77, 122, 1247, 67, 2349])).
% 27.56/17.77 tff(2416,plain,
% 27.56/17.77 (c1 = f2(c3)),
% 27.56/17.77 inference(symmetry,[status(thm)],[1327])).
% 27.56/17.77 tff(2417,plain,
% 27.56/17.77 (f9(f10(c2), f10(c2)) = c1),
% 27.56/17.77 inference(transitivity,[status(thm)],[1495, 1503])).
% 27.56/17.77 tff(2418,plain,
% 27.56/17.77 (f3(f9(f10(c2), f10(c2)), f9(f10(c2), f10(c2))) = f3(c1, c1)),
% 27.56/17.77 inference(monotonicity,[status(thm)],[2417, 2417])).
% 27.56/17.77 tff(2419,plain,
% 27.56/17.77 ((f3(f9(f10(c2), f10(c2)), f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2))) <=> (f3(c1, c1) = c1)),
% 27.56/17.77 inference(monotonicity,[status(thm)],[2418, 2417])).
% 27.56/17.77 tff(2420,plain,
% 27.56/17.77 ((~(f3(f9(f10(c2), f10(c2)), f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))) <=> (~(f3(c1, c1) = c1))),
% 27.56/17.77 inference(monotonicity,[status(thm)],[2419])).
% 27.56/17.77 tff(2421,plain,
% 27.56/17.77 (f9(f10(c2), f10(c2)) = f2(c3)),
% 27.56/17.77 inference(transitivity,[status(thm)],[1495, 1503, 2416])).
% 27.56/17.77 tff(2422,plain,
% 27.56/17.77 (big_f(c2, f9(f10(c2), f10(c2))) <=> big_f(c3, f2(c3))),
% 27.56/17.77 inference(monotonicity,[status(thm)],[69, 2421])).
% 27.56/17.77 tff(2423,plain,
% 27.56/17.77 (big_f(c3, f2(c3)) <=> big_f(c2, f9(f10(c2), f10(c2)))),
% 27.56/17.77 inference(symmetry,[status(thm)],[2422])).
% 27.56/17.77 tff(2424,plain,
% 27.56/17.77 ((~big_f(c3, f2(c3))) <=> (~big_f(c2, f9(f10(c2), f10(c2))))),
% 27.56/17.77 inference(monotonicity,[status(thm)],[2423])).
% 27.56/17.77 tff(2425,plain,
% 27.56/17.77 (~big_f(c2, f9(f10(c2), f10(c2)))),
% 27.56/17.77 inference(modus_ponens,[status(thm)],[1286, 2424])).
% 27.56/17.77 tff(2426,plain,
% 27.56/17.77 (big_f(f3(f9(f10(c2), f10(c2)), f9(f10(c2), f10(c2))), f9(f10(c2), f10(c2))) <=> big_f(f3(c1, c1), c1)),
% 27.56/17.77 inference(monotonicity,[status(thm)],[2418, 2417])).
% 27.56/17.77 tff(2427,plain,
% 27.56/17.77 (big_f(f3(c1, c1), c1) <=> big_f(f3(f9(f10(c2), f10(c2)), f9(f10(c2), f10(c2))), f9(f10(c2), f10(c2)))),
% 27.56/17.77 inference(symmetry,[status(thm)],[2426])).
% 27.56/17.77 tff(2428,plain,
% 27.56/17.77 (c2 = c4),
% 27.56/17.77 inference(symmetry,[status(thm)],[1290])).
% 27.56/17.77 tff(2429,plain,
% 27.56/17.77 (f4(c2) = f4(c4)),
% 27.56/17.77 inference(monotonicity,[status(thm)],[2428])).
% 27.56/17.77 tff(2430,plain,
% 27.56/17.77 (f4(c4) = f4(c2)),
% 27.56/17.77 inference(symmetry,[status(thm)],[2429])).
% 27.56/17.77 tff(2431,plain,
% 27.56/17.77 ((f9(f10(c2), f4(c4)) = f4(c4)) <=> (f9(f10(c2), f4(c4)) = f4(c2))),
% 27.56/17.77 inference(monotonicity,[status(thm)],[2430])).
% 27.56/17.77 tff(2432,plain,
% 27.56/17.77 ((f9(f10(c2), f4(c4)) = f4(c2)) <=> (f9(f10(c2), f4(c4)) = f4(c4))),
% 27.56/17.77 inference(symmetry,[status(thm)],[2431])).
% 27.56/17.77 tff(2433,plain,
% 27.56/17.77 (f4(c2) = c2),
% 27.56/17.77 inference(transitivity,[status(thm)],[2429, 79])).
% 27.56/17.77 tff(2434,plain,
% 27.56/17.77 ((f9(f10(c2), f4(c4)) = f4(c2)) <=> (f9(f10(c2), f4(c4)) = c2)),
% 27.56/17.77 inference(monotonicity,[status(thm)],[2433])).
% 27.56/17.77 tff(2435,plain,
% 27.56/17.77 ((f9(f10(c2), f4(c4)) = c2) <=> (f9(f10(c2), f4(c4)) = f4(c2))),
% 27.56/17.77 inference(symmetry,[status(thm)],[2434])).
% 27.56/17.77 tff(2436,plain,
% 27.56/17.77 ((f9(f10(c2), f4(c4)) = c2) <=> (f9(f10(c2), f4(c4)) = f4(c4))),
% 27.56/17.77 inference(transitivity,[status(thm)],[2435, 2432])).
% 27.56/17.77 tff(2437,plain,
% 27.56/17.77 ((~(f9(f10(c2), f4(c4)) = c2)) <=> (~(f9(f10(c2), f4(c4)) = f4(c4)))),
% 27.56/17.77 inference(monotonicity,[status(thm)],[2436])).
% 27.56/17.77 tff(2438,plain,
% 27.56/17.77 (~(f9(f10(c2), f4(c4)) = f4(c4))),
% 27.56/17.77 inference(modus_ponens,[status(thm)],[1502, 2437])).
% 27.56/17.77 tff(2439,plain,
% 27.56/17.77 (big_f(f9(f10(c2), f4(c4)), f10(f10(c2))) <=> big_f(f9(f10(c2), f4(c4)), c2)),
% 27.56/17.77 inference(monotonicity,[status(thm)],[251])).
% 27.56/17.77 tff(2440,plain,
% 27.56/17.77 (big_f(f9(f10(c2), f4(c4)), c2) <=> big_f(f9(f10(c2), f4(c4)), f10(f10(c2)))),
% 27.56/17.77 inference(symmetry,[status(thm)],[2439])).
% 27.56/17.77 tff(2441,plain,
% 27.56/17.77 (big_f(f9(f10(c2), f10(c2)), f10(f10(c2))) <=> big_f(f9(f10(c2), f4(c4)), c2)),
% 27.56/17.77 inference(monotonicity,[status(thm)],[1495, 251])).
% 27.56/17.77 tff(2442,plain,
% 27.56/17.77 (c1 = f9(f10(c2), f4(c4))),
% 27.56/17.77 inference(symmetry,[status(thm)],[1503])).
% 27.56/17.77 tff(2443,plain,
% 27.56/17.77 (c1 = f9(f10(c2), f10(c2))),
% 27.56/17.77 inference(transitivity,[status(thm)],[2442, 1494])).
% 27.56/17.77 tff(2444,plain,
% 27.56/17.77 (big_f(c1, c2) <=> big_f(f9(f10(c2), f10(c2)), f10(f10(c2)))),
% 27.56/17.77 inference(monotonicity,[status(thm)],[2443, 2294])).
% 27.56/17.77 tff(2445,plain,
% 27.56/17.77 (big_f(c1, c2) <=> big_f(f9(f10(c2), f4(c4)), f10(f10(c2)))),
% 27.56/17.77 inference(transitivity,[status(thm)],[2444, 2441, 2440])).
% 27.56/17.77 tff(2446,plain,
% 27.56/17.77 ((~big_f(c1, c2)) <=> (~big_f(f9(f10(c2), f4(c4)), f10(f10(c2))))),
% 27.56/17.77 inference(monotonicity,[status(thm)],[2445])).
% 27.56/17.77 tff(2447,plain,
% 27.56/17.77 (f2(c2) = c1),
% 27.56/17.77 inference(transitivity,[status(thm)],[1426, 1327])).
% 27.56/17.77 tff(2448,plain,
% 27.56/17.77 (big_f(f2(c2), c2) <=> big_f(c1, c2)),
% 27.56/17.77 inference(monotonicity,[status(thm)],[2447])).
% 27.56/17.77 tff(2449,plain,
% 27.56/17.77 ((~big_f(f2(c2), c2)) <=> (~big_f(c1, c2))),
% 27.56/17.77 inference(monotonicity,[status(thm)],[2448])).
% 27.56/17.77 tff(2450,plain,
% 27.56/17.77 ((c2 = f2(c2)) <=> (c2 = c1)),
% 27.56/17.77 inference(monotonicity,[status(thm)],[2447])).
% 27.56/17.77 tff(2451,plain,
% 27.56/17.77 ((c2 = c1) <=> (c2 = f2(c2))),
% 27.56/17.77 inference(symmetry,[status(thm)],[2450])).
% 27.56/17.77 tff(2452,plain,
% 27.56/17.77 ((~(c2 = c1)) <=> (~(c2 = f2(c2)))),
% 27.56/17.77 inference(monotonicity,[status(thm)],[2451])).
% 27.56/17.77 tff(2453,plain,
% 27.56/17.77 (~(c2 = f2(c2))),
% 27.56/17.77 inference(modus_ponens,[status(thm)],[75, 2452])).
% 27.56/17.77 tff(2454,plain,
% 27.56/17.77 (~big_f(f2(c2), c2)),
% 27.56/17.77 inference(unit_resolution,[status(thm)],[1364, 1335, 1317, 2453, 79, 1290])).
% 27.56/17.77 tff(2455,plain,
% 27.56/17.77 (~big_f(c1, c2)),
% 27.56/17.77 inference(modus_ponens,[status(thm)],[2454, 2449])).
% 27.56/17.77 tff(2456,plain,
% 27.56/17.77 (~big_f(f9(f10(c2), f4(c4)), f10(f10(c2)))),
% 27.56/17.77 inference(modus_ponens,[status(thm)],[2455, 2446])).
% 27.56/17.77 tff(2457,plain,
% 27.56/17.77 ((~big_f(c1, c2)) <=> (~big_f(f9(f10(c2), f10(c2)), f10(f10(c2))))),
% 27.56/17.77 inference(monotonicity,[status(thm)],[2444])).
% 27.56/17.77 tff(2458,plain,
% 27.56/17.77 (~big_f(f9(f10(c2), f10(c2)), f10(f10(c2)))),
% 27.56/17.77 inference(modus_ponens,[status(thm)],[2455, 2457])).
% 27.56/17.77 tff(2459,plain,
% 27.56/17.77 (f5(f9(f10(c2), f10(c2))) = f5(c1)),
% 27.56/17.77 inference(monotonicity,[status(thm)],[2417])).
% 27.56/17.77 tff(2460,plain,
% 27.56/17.77 (f5(f9(f10(c2), f10(c2))) = c2),
% 27.56/17.77 inference(transitivity,[status(thm)],[2459, 186])).
% 27.56/17.77 tff(2461,plain,
% 27.56/17.77 ((f6(c2, c2) = f5(f9(f10(c2), f10(c2)))) <=> (f6(c2, c2) = c2)),
% 27.56/17.77 inference(monotonicity,[status(thm)],[2460])).
% 27.56/17.77 tff(2462,plain,
% 27.56/17.77 (f7(f9(f10(c2), f10(c2))) = f7(c1)),
% 27.56/17.77 inference(monotonicity,[status(thm)],[2417])).
% 27.56/17.77 tff(2463,plain,
% 27.56/17.77 (f7(f9(f10(c2), f10(c2))) = f7(c2)),
% 27.56/17.77 inference(transitivity,[status(thm)],[2462, 347, 82])).
% 27.56/17.77 tff(2464,plain,
% 27.56/17.77 (big_f(f7(f9(f10(c2), f10(c2))), f6(c2, c2)) <=> big_f(f7(c2), f6(c2, c2))),
% 27.56/17.77 inference(monotonicity,[status(thm)],[2463])).
% 27.56/17.77 tff(2465,plain,
% 27.56/17.77 (big_f(f7(c2), f6(c2, c2)) <=> big_f(f7(f9(f10(c2), f10(c2))), f6(c2, c2))),
% 27.56/17.77 inference(symmetry,[status(thm)],[2464])).
% 27.56/17.77 tff(2466,plain,
% 27.56/17.77 (f6(f7(c2), c3) = f6(c2, c2)),
% 27.56/17.77 inference(monotonicity,[status(thm)],[77, 67])).
% 27.56/17.77 tff(2467,plain,
% 27.56/17.77 (f7(f7(c2)) = f7(c2)),
% 27.56/17.77 inference(monotonicity,[status(thm)],[77])).
% 27.58/17.77 tff(2468,plain,
% 27.58/17.77 (big_f(f7(f7(c2)), f6(f7(c2), c3)) <=> big_f(f7(c2), f6(c2, c2))),
% 27.58/17.77 inference(monotonicity,[status(thm)],[2467, 2466])).
% 27.58/17.77 tff(2469,assumption,(~(f9(f10(c2), f4(c4)) = f4(c4))), introduced(assumption)).
% 27.58/17.77 tff(2470,assumption,(~big_f(f9(f10(c2), f4(c4)), f10(f10(c2)))), introduced(assumption)).
% 27.58/17.77 tff(2471,assumption,(f10(f10(c2)) = f10(c2)), introduced(assumption)).
% 27.58/17.77 tff(2472,assumption,(~big_f(f7(f7(c2)), f6(f7(c2), c3))), introduced(assumption)).
% 27.58/17.77 tff(2473,plain,
% 27.58/17.77 (big_f(f7(c2), f6(c2, c2)) <=> big_f(f7(f7(c2)), f6(f7(c2), c3))),
% 27.58/17.77 inference(symmetry,[status(thm)],[2468])).
% 27.58/17.77 tff(2474,plain,
% 27.58/17.77 (f7(f4(c4)) = c2),
% 27.58/17.77 inference(transitivity,[status(thm)],[80, 77])).
% 27.58/17.77 tff(2475,plain,
% 27.58/17.77 (f6(c2, f7(f4(c4))) = f6(c2, c2)),
% 27.58/17.77 inference(monotonicity,[status(thm)],[2474])).
% 27.58/17.77 tff(2476,plain,
% 27.58/17.77 (big_f(f7(c2), f6(c2, f7(f4(c4)))) <=> big_f(f7(c2), f6(c2, c2))),
% 27.58/17.77 inference(monotonicity,[status(thm)],[2475])).
% 27.58/17.77 tff(2477,plain,
% 27.58/17.77 (big_f(f7(c2), f6(c2, f7(f4(c4)))) <=> big_f(f7(f7(c2)), f6(f7(c2), c3))),
% 27.58/17.77 inference(transitivity,[status(thm)],[2476, 2473])).
% 27.58/17.77 tff(2478,assumption,(big_f(f7(c2), f6(c2, f7(f4(c4))))), introduced(assumption)).
% 27.58/17.77 tff(2479,plain,
% 27.58/17.77 (big_f(f7(f7(c2)), f6(f7(c2), c3))),
% 27.58/17.77 inference(modus_ponens,[status(thm)],[2478, 2477])).
% 27.58/17.77 tff(2480,plain,
% 27.58/17.77 ($false),
% 27.58/17.77 inference(unit_resolution,[status(thm)],[2472, 2479])).
% 27.58/17.77 tff(2481,plain,((~big_f(f7(c2), f6(c2, f7(f4(c4))))) | big_f(f7(f7(c2)), f6(f7(c2), c3)) | (~(f7(c2) = c2)) | (~(f4(c4) = c2)) | (~(c3 = c2))), inference(lemma,lemma(discharge,[]))).
% 27.58/17.77 tff(2482,plain,
% 27.58/17.77 (~big_f(f7(c2), f6(c2, f7(f4(c4))))),
% 27.58/17.77 inference(unit_resolution,[status(thm)],[2481, 2472, 77, 79, 67])).
% 27.58/17.77 tff(2483,plain,
% 27.58/17.77 (^[X9: $i, X6: $i, X4: $i, X7: $i] : refl(((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6))) <=> ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6))))),
% 27.58/17.77 inference(bind,[status(th)],[])).
% 27.58/17.77 tff(2484,plain,
% 27.58/17.77 (![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6))) <=> ![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))),
% 27.58/17.77 inference(quant_intro,[status(thm)],[2483])).
% 27.58/17.77 tff(2485,plain,
% 27.58/17.77 (![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6))) <=> ![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))),
% 27.58/17.77 inference(rewrite,[status(thm)],[])).
% 27.58/17.77 tff(2486,plain,
% 27.58/17.77 (^[X9: $i, X6: $i, X4: $i, X7: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((big_f(f7(X4), f6(X4, X6)) | (f6(X4, X6) = X6)) <=> ((f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))), (((big_f(f7(X4), f6(X4, X6)) | (f6(X4, X6) = X6)) | (~(f7(X4) = X4))) <=> (((f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6))) | (~(f7(X4) = X4))))), rewrite((((f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6))) | (~(f7(X4) = X4))) <=> ((~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))), (((big_f(f7(X4), f6(X4, X6)) | (f6(X4, X6) = X6)) | (~(f7(X4) = X4))) <=> ((~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6))))), ((((big_f(f7(X4), f6(X4, X6)) | (f6(X4, X6) = X6)) | (~(f7(X4) = X4))) | big_f(f9(X7, X9), f10(X7))) <=> (((~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6))) | big_f(f9(X7, X9), f10(X7))))), rewrite((((~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6))) | big_f(f9(X7, X9), f10(X7))) <=> (big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))), ((((big_f(f7(X4), f6(X4, X6)) | (f6(X4, X6) = X6)) | (~(f7(X4) = X4))) | big_f(f9(X7, X9), f10(X7))) <=> (big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6))))), (((((big_f(f7(X4), f6(X4, X6)) | (f6(X4, X6) = X6)) | (~(f7(X4) = X4))) | big_f(f9(X7, X9), f10(X7))) | (f9(X7, X9) = X9)) <=> ((big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6))) | (f9(X7, X9) = X9)))), rewrite(((big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6))) | (f9(X7, X9) = X9)) <=> ((f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))), (((((big_f(f7(X4), f6(X4, X6)) | (f6(X4, X6) = X6)) | (~(f7(X4) = X4))) | big_f(f9(X7, X9), f10(X7))) | (f9(X7, X9) = X9)) <=> ((f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6))))), ((((((big_f(f7(X4), f6(X4, X6)) | (f6(X4, X6) = X6)) | (~(f7(X4) = X4))) | big_f(f9(X7, X9), f10(X7))) | (f9(X7, X9) = X9)) | (~(f10(X7) = X7))) <=> (((f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6))) | (~(f10(X7) = X7))))), rewrite((((f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6))) | (~(f10(X7) = X7))) <=> ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))), ((((((big_f(f7(X4), f6(X4, X6)) | (f6(X4, X6) = X6)) | (~(f7(X4) = X4))) | big_f(f9(X7, X9), f10(X7))) | (f9(X7, X9) = X9)) | (~(f10(X7) = X7))) <=> ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))))),
% 27.58/17.77 inference(bind,[status(th)],[])).
% 27.58/17.77 tff(2487,plain,
% 27.58/17.77 (![X9: $i, X6: $i, X4: $i, X7: $i] : (((((big_f(f7(X4), f6(X4, X6)) | (f6(X4, X6) = X6)) | (~(f7(X4) = X4))) | big_f(f9(X7, X9), f10(X7))) | (f9(X7, X9) = X9)) | (~(f10(X7) = X7))) <=> ![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))),
% 27.58/17.77 inference(quant_intro,[status(thm)],[2486])).
% 27.58/17.77 tff(2488,axiom,(![X9: $i, X6: $i, X4: $i, X7: $i] : (((((big_f(f7(X4), f6(X4, X6)) | (f6(X4, X6) = X6)) | (~(f7(X4) = X4))) | big_f(f9(X7, X9), f10(X7))) | (f9(X7, X9) = X9)) | (~(f10(X7) = X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_29')).
% 27.58/17.77 tff(2489,plain,
% 27.58/17.77 (![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))),
% 27.58/17.77 inference(modus_ponens,[status(thm)],[2488, 2487])).
% 27.58/17.77 tff(2490,plain,
% 27.58/17.77 (![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))),
% 27.58/17.77 inference(modus_ponens,[status(thm)],[2489, 2485])).
% 27.58/17.77 tff(2491,plain,(
% 27.58/17.77 ![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))),
% 27.58/17.77 inference(skolemize,[status(sab)],[2490])).
% 27.58/17.77 tff(2492,plain,
% 27.58/17.77 (![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))),
% 27.58/17.77 inference(modus_ponens,[status(thm)],[2491, 2484])).
% 27.58/17.77 tff(2493,plain,
% 27.58/17.77 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f7(c2) = c2)) | (~(f10(f10(c2)) = f10(c2))) | (f6(c2, f7(f4(c4))) = f7(f4(c4))) | big_f(f7(c2), f6(c2, f7(f4(c4)))) | big_f(f9(f10(c2), f4(c4)), f10(f10(c2))) | (f9(f10(c2), f4(c4)) = f4(c4)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c2) = c2)) | (~(f10(f10(c2)) = f10(c2))) | (f6(c2, f7(f4(c4))) = f7(f4(c4))) | big_f(f7(c2), f6(c2, f7(f4(c4)))) | big_f(f9(f10(c2), f4(c4)), f10(f10(c2))) | (f9(f10(c2), f4(c4)) = f4(c4)))),
% 27.58/17.77 inference(rewrite,[status(thm)],[])).
% 27.58/17.77 tff(2494,plain,
% 27.58/17.77 (((~(f10(f10(c2)) = f10(c2))) | (f9(f10(c2), f4(c4)) = f4(c4)) | big_f(f9(f10(c2), f4(c4)), f10(f10(c2))) | (~(f7(c2) = c2)) | (f6(c2, f7(f4(c4))) = f7(f4(c4))) | big_f(f7(c2), f6(c2, f7(f4(c4))))) <=> ((~(f7(c2) = c2)) | (~(f10(f10(c2)) = f10(c2))) | (f6(c2, f7(f4(c4))) = f7(f4(c4))) | big_f(f7(c2), f6(c2, f7(f4(c4)))) | big_f(f9(f10(c2), f4(c4)), f10(f10(c2))) | (f9(f10(c2), f4(c4)) = f4(c4)))),
% 27.58/17.77 inference(rewrite,[status(thm)],[])).
% 27.58/17.77 tff(2495,plain,
% 27.58/17.77 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(f10(c2)) = f10(c2))) | (f9(f10(c2), f4(c4)) = f4(c4)) | big_f(f9(f10(c2), f4(c4)), f10(f10(c2))) | (~(f7(c2) = c2)) | (f6(c2, f7(f4(c4))) = f7(f4(c4))) | big_f(f7(c2), f6(c2, f7(f4(c4)))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f7(c2) = c2)) | (~(f10(f10(c2)) = f10(c2))) | (f6(c2, f7(f4(c4))) = f7(f4(c4))) | big_f(f7(c2), f6(c2, f7(f4(c4)))) | big_f(f9(f10(c2), f4(c4)), f10(f10(c2))) | (f9(f10(c2), f4(c4)) = f4(c4))))),
% 27.58/17.77 inference(monotonicity,[status(thm)],[2494])).
% 27.58/17.77 tff(2496,plain,
% 27.58/17.77 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(f10(c2)) = f10(c2))) | (f9(f10(c2), f4(c4)) = f4(c4)) | big_f(f9(f10(c2), f4(c4)), f10(f10(c2))) | (~(f7(c2) = c2)) | (f6(c2, f7(f4(c4))) = f7(f4(c4))) | big_f(f7(c2), f6(c2, f7(f4(c4)))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c2) = c2)) | (~(f10(f10(c2)) = f10(c2))) | (f6(c2, f7(f4(c4))) = f7(f4(c4))) | big_f(f7(c2), f6(c2, f7(f4(c4)))) | big_f(f9(f10(c2), f4(c4)), f10(f10(c2))) | (f9(f10(c2), f4(c4)) = f4(c4)))),
% 27.58/17.77 inference(transitivity,[status(thm)],[2495, 2493])).
% 27.58/17.77 tff(2497,plain,
% 27.58/17.77 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(f10(c2)) = f10(c2))) | (f9(f10(c2), f4(c4)) = f4(c4)) | big_f(f9(f10(c2), f4(c4)), f10(f10(c2))) | (~(f7(c2) = c2)) | (f6(c2, f7(f4(c4))) = f7(f4(c4))) | big_f(f7(c2), f6(c2, f7(f4(c4)))))),
% 27.58/17.77 inference(quant_inst,[status(thm)],[])).
% 27.58/17.77 tff(2498,plain,
% 27.58/17.77 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c2) = c2)) | (~(f10(f10(c2)) = f10(c2))) | (f6(c2, f7(f4(c4))) = f7(f4(c4))) | big_f(f7(c2), f6(c2, f7(f4(c4)))) | big_f(f9(f10(c2), f4(c4)), f10(f10(c2))) | (f9(f10(c2), f4(c4)) = f4(c4))),
% 27.58/17.77 inference(modus_ponens,[status(thm)],[2497, 2496])).
% 27.58/17.77 tff(2499,plain,
% 27.58/17.77 ((~(f7(c2) = c2)) | (~(f10(f10(c2)) = f10(c2))) | (f6(c2, f7(f4(c4))) = f7(f4(c4))) | big_f(f7(c2), f6(c2, f7(f4(c4)))) | big_f(f9(f10(c2), f4(c4)), f10(f10(c2))) | (f9(f10(c2), f4(c4)) = f4(c4))),
% 27.58/17.77 inference(unit_resolution,[status(thm)],[2498, 2492])).
% 27.58/17.77 tff(2500,plain,
% 27.58/17.77 (f6(c2, f7(f4(c4))) = f7(f4(c4))),
% 27.58/17.77 inference(unit_resolution,[status(thm)],[2499, 2482, 2470, 2471, 77, 2469])).
% 27.58/17.77 tff(2501,plain,
% 27.58/17.77 (f6(c2, c2) = c2),
% 27.58/17.77 inference(transitivity,[status(thm)],[84, 2500, 80, 77])).
% 27.58/17.77 tff(2502,plain,
% 27.58/17.77 (big_f(f7(c2), f6(c2, c2)) <=> big_f(c2, c2)),
% 27.58/17.77 inference(monotonicity,[status(thm)],[77, 2501])).
% 27.58/17.77 tff(2503,plain,
% 27.58/17.77 (big_f(c2, c2) <=> big_f(f7(c2), f6(c2, c2))),
% 27.58/17.77 inference(symmetry,[status(thm)],[2502])).
% 27.58/17.77 tff(2504,plain,
% 27.58/17.77 (big_f(f7(c2), f6(c2, c2))),
% 27.58/17.77 inference(modus_ponens,[status(thm)],[1345, 2503])).
% 27.58/17.77 tff(2505,plain,
% 27.58/17.77 ((~big_f(f7(f7(c2)), f6(f7(c2), c3))) <=> (~big_f(f7(c2), f6(c2, c2)))),
% 27.58/17.77 inference(monotonicity,[status(thm)],[2468])).
% 27.58/17.77 tff(2506,plain,
% 27.58/17.77 (~big_f(f7(c2), f6(c2, c2))),
% 27.58/17.77 inference(modus_ponens,[status(thm)],[2472, 2505])).
% 27.58/17.77 tff(2507,plain,
% 27.58/17.77 ($false),
% 27.58/17.77 inference(unit_resolution,[status(thm)],[2506, 2504])).
% 27.58/17.77 tff(2508,plain,(big_f(f7(f7(c2)), f6(f7(c2), c3)) | (~big_f(c2, c2)) | (~(f7(c2) = c2)) | (~(f4(c4) = c2)) | (~(c3 = c2)) | big_f(f9(f10(c2), f4(c4)), f10(f10(c2))) | (~(f10(f10(c2)) = f10(c2))) | (f9(f10(c2), f4(c4)) = f4(c4))), inference(lemma,lemma(discharge,[]))).
% 27.58/17.77 tff(2509,plain,
% 27.58/17.77 (big_f(f7(f7(c2)), f6(f7(c2), c3))),
% 27.58/17.77 inference(unit_resolution,[status(thm)],[2508, 77, 1345, 79, 67, 2470, 252, 2469])).
% 27.58/17.77 tff(2510,plain,
% 27.58/17.77 (big_f(f7(c2), f6(c2, c2))),
% 27.58/17.77 inference(modus_ponens,[status(thm)],[2509, 2468])).
% 27.58/17.77 tff(2511,plain,
% 27.58/17.77 (big_f(f7(f9(f10(c2), f10(c2))), f6(c2, c2))),
% 27.58/17.77 inference(modus_ponens,[status(thm)],[2510, 2465])).
% 27.58/17.77 tff(2512,plain,
% 27.58/17.77 ((f10(c2) = f9(f10(c2), f10(c2))) <=> (f9(f10(c2), f10(c2)) = f10(c2))),
% 27.58/17.77 inference(commutativity,[status(thm)],[])).
% 27.58/17.77 tff(2513,plain,
% 27.58/17.77 (f7(f9(f10(c2), f10(c2))) = f10(c2)),
% 27.58/17.77 inference(transitivity,[status(thm)],[2462, 347, 216])).
% 27.58/17.77 tff(2514,plain,
% 27.58/17.77 ((f7(f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2))) <=> (f10(c2) = f9(f10(c2), f10(c2)))),
% 27.58/17.77 inference(monotonicity,[status(thm)],[2513])).
% 27.58/17.77 tff(2515,plain,
% 27.58/17.77 ((f7(f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2))) <=> (f9(f10(c2), f10(c2)) = f10(c2))),
% 27.58/17.77 inference(transitivity,[status(thm)],[2514, 2512])).
% 27.58/17.77 tff(2516,plain,
% 27.58/17.77 ((f9(f10(c2), f10(c2)) = f10(c2)) <=> (f7(f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))),
% 27.58/17.77 inference(symmetry,[status(thm)],[2515])).
% 27.58/17.77 tff(2517,plain,
% 27.58/17.77 ((~(f9(f10(c2), f10(c2)) = f10(c2))) <=> (~(f7(f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2))))),
% 27.58/17.77 inference(monotonicity,[status(thm)],[2516])).
% 27.58/17.77 tff(2518,plain,
% 27.58/17.77 (~(f7(f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))),
% 27.58/17.77 inference(modus_ponens,[status(thm)],[158, 2517])).
% 27.58/17.77 tff(2519,plain,
% 27.58/17.77 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2))) | (f6(c2, c2) = f5(f9(f10(c2), f10(c2)))) | (~big_f(f7(f9(f10(c2), f10(c2))), f6(c2, c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2))) | (f6(c2, c2) = f5(f9(f10(c2), f10(c2)))) | (~big_f(f7(f9(f10(c2), f10(c2))), f6(c2, c2))))),
% 27.58/17.77 inference(rewrite,[status(thm)],[])).
% 27.58/17.77 tff(2520,plain,
% 27.58/17.77 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2))) | (f6(c2, c2) = f5(f9(f10(c2), f10(c2)))) | (~big_f(f7(f9(f10(c2), f10(c2))), f6(c2, c2))))),
% 27.58/17.77 inference(quant_inst,[status(thm)],[])).
% 27.58/17.77 tff(2521,plain,
% 27.58/17.77 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2))) | (f6(c2, c2) = f5(f9(f10(c2), f10(c2)))) | (~big_f(f7(f9(f10(c2), f10(c2))), f6(c2, c2)))),
% 27.58/17.77 inference(modus_ponens,[status(thm)],[2520, 2519])).
% 27.58/17.77 tff(2522,plain,
% 27.58/17.77 ((f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2))) | (f6(c2, c2) = f5(f9(f10(c2), f10(c2)))) | (~big_f(f7(f9(f10(c2), f10(c2))), f6(c2, c2)))),
% 27.58/17.77 inference(unit_resolution,[status(thm)],[2521, 676, 122])).
% 27.58/17.77 tff(2523,plain,
% 27.58/17.77 (f6(c2, c2) = f5(f9(f10(c2), f10(c2)))),
% 27.58/17.77 inference(unit_resolution,[status(thm)],[2522, 1516, 2518, 1520, 2511])).
% 27.58/17.77 tff(2524,plain,
% 27.58/17.77 (f6(c2, c2) = c2),
% 27.58/17.77 inference(modus_ponens,[status(thm)],[2523, 2461])).
% 27.58/17.77 tff(2525,plain,
% 27.58/17.77 (^[X9: $i, X6: $i, X4: $i, X7: $i] : refl(((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))) <=> ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))))),
% 27.58/17.77 inference(bind,[status(th)],[])).
% 27.58/17.77 tff(2526,plain,
% 27.58/17.77 (![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))) <=> ![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))),
% 27.58/17.77 inference(quant_intro,[status(thm)],[2525])).
% 27.58/17.77 tff(2527,plain,
% 27.58/17.77 (![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))) <=> ![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))),
% 27.58/17.77 inference(rewrite,[status(thm)],[])).
% 27.58/17.77 tff(2528,plain,
% 27.58/17.77 (^[X9: $i, X6: $i, X4: $i, X7: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~big_f(f7(X4), f6(X4, X6))) | (~(f6(X4, X6) = X6))) <=> ((~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))), ((((~big_f(f7(X4), f6(X4, X6))) | (~(f6(X4, X6) = X6))) | (~(f7(X4) = X4))) <=> (((~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))) | (~(f7(X4) = X4))))), rewrite((((~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))) | (~(f7(X4) = X4))) <=> ((~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))), ((((~big_f(f7(X4), f6(X4, X6))) | (~(f6(X4, X6) = X6))) | (~(f7(X4) = X4))) <=> ((~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))))), (((((~big_f(f7(X4), f6(X4, X6))) | (~(f6(X4, X6) = X6))) | (~(f7(X4) = X4))) | big_f(f9(X7, X9), f10(X7))) <=> (((~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))) | big_f(f9(X7, X9), f10(X7))))), rewrite((((~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))) | big_f(f9(X7, X9), f10(X7))) <=> (big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))), (((((~big_f(f7(X4), f6(X4, X6))) | (~(f6(X4, X6) = X6))) | (~(f7(X4) = X4))) | big_f(f9(X7, X9), f10(X7))) <=> (big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))))), ((((((~big_f(f7(X4), f6(X4, X6))) | (~(f6(X4, X6) = X6))) | (~(f7(X4) = X4))) | big_f(f9(X7, X9), f10(X7))) | (f9(X7, X9) = X9)) <=> ((big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))) | (f9(X7, X9) = X9)))), rewrite(((big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))) | (f9(X7, X9) = X9)) <=> ((f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))), ((((((~big_f(f7(X4), f6(X4, X6))) | (~(f6(X4, X6) = X6))) | (~(f7(X4) = X4))) | big_f(f9(X7, X9), f10(X7))) | (f9(X7, X9) = X9)) <=> ((f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))))), (((((((~big_f(f7(X4), f6(X4, X6))) | (~(f6(X4, X6) = X6))) | (~(f7(X4) = X4))) | big_f(f9(X7, X9), f10(X7))) | (f9(X7, X9) = X9)) | (~(f10(X7) = X7))) <=> (((f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))) | (~(f10(X7) = X7))))), rewrite((((f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))) | (~(f10(X7) = X7))) <=> ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))), (((((((~big_f(f7(X4), f6(X4, X6))) | (~(f6(X4, X6) = X6))) | (~(f7(X4) = X4))) | big_f(f9(X7, X9), f10(X7))) | (f9(X7, X9) = X9)) | (~(f10(X7) = X7))) <=> ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))))),
% 27.58/17.78 inference(bind,[status(th)],[])).
% 27.58/17.78 tff(2529,plain,
% 27.58/17.78 (![X9: $i, X6: $i, X4: $i, X7: $i] : ((((((~big_f(f7(X4), f6(X4, X6))) | (~(f6(X4, X6) = X6))) | (~(f7(X4) = X4))) | big_f(f9(X7, X9), f10(X7))) | (f9(X7, X9) = X9)) | (~(f10(X7) = X7))) <=> ![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))),
% 27.58/17.78 inference(quant_intro,[status(thm)],[2528])).
% 27.58/17.78 tff(2530,axiom,(![X9: $i, X6: $i, X4: $i, X7: $i] : ((((((~big_f(f7(X4), f6(X4, X6))) | (~(f6(X4, X6) = X6))) | (~(f7(X4) = X4))) | big_f(f9(X7, X9), f10(X7))) | (f9(X7, X9) = X9)) | (~(f10(X7) = X7)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_33')).
% 27.58/17.78 tff(2531,plain,
% 27.58/17.78 (![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))),
% 27.58/17.78 inference(modus_ponens,[status(thm)],[2530, 2529])).
% 27.58/17.78 tff(2532,plain,
% 27.58/17.78 (![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))),
% 27.58/17.78 inference(modus_ponens,[status(thm)],[2531, 2527])).
% 27.58/17.78 tff(2533,plain,(
% 27.58/17.78 ![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))),
% 27.58/17.78 inference(skolemize,[status(sab)],[2532])).
% 27.58/17.78 tff(2534,plain,
% 27.58/17.78 (![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))),
% 27.58/17.78 inference(modus_ponens,[status(thm)],[2533, 2526])).
% 27.58/17.78 tff(2535,plain,
% 27.58/17.78 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)))),
% 27.58/17.78 inference(rewrite,[status(thm)],[])).
% 27.58/17.78 tff(2536,plain,
% 27.58/17.78 (((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2)))) <=> ((~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)))),
% 27.58/17.78 inference(rewrite,[status(thm)],[])).
% 27.58/17.78 tff(2537,plain,
% 27.58/17.78 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2))))),
% 27.58/17.78 inference(monotonicity,[status(thm)],[2536])).
% 27.58/17.78 tff(2538,plain,
% 27.58/17.78 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)))),
% 27.58/17.78 inference(transitivity,[status(thm)],[2537, 2535])).
% 27.58/17.78 tff(2539,plain,
% 27.58/17.78 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))),
% 27.58/17.78 inference(quant_inst,[status(thm)],[])).
% 27.58/17.78 tff(2540,plain,
% 27.58/17.78 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2))),
% 27.58/17.78 inference(modus_ponens,[status(thm)],[2539, 2538])).
% 27.58/17.78 tff(2541,plain,
% 27.58/17.78 ((~(f6(c2, c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2))),
% 27.58/17.78 inference(unit_resolution,[status(thm)],[2540, 2534, 122, 77, 2510])).
% 27.58/17.78 tff(2542,plain,
% 27.58/17.78 (~(f6(c2, c2) = c2)),
% 27.58/17.78 inference(unit_resolution,[status(thm)],[2541, 1520, 1516])).
% 27.58/17.78 tff(2543,plain,
% 27.58/17.78 ($false),
% 27.58/17.78 inference(unit_resolution,[status(thm)],[2542, 2524])).
% 27.58/17.78 tff(2544,plain,((~(f7(c2) = c2)) | (~(f5(c1) = c2)) | (~(f10(c2) = c2)) | (~(f4(c4) = c2)) | (~(f7(c1) = c2)) | (f9(f10(c2), f10(c2)) = f10(c2)) | big_f(f9(f10(c2), f10(c2)), f10(f10(c2))) | (~(c3 = c2)) | (~big_f(c2, c2)) | big_f(f9(f10(c2), f4(c4)), f10(f10(c2))) | (f9(f10(c2), f4(c4)) = f4(c4))), inference(lemma,lemma(discharge,[]))).
% 27.58/17.78 tff(2545,plain,
% 27.58/17.78 (~(f7(c2) = c2)),
% 27.58/17.78 inference(unit_resolution,[status(thm)],[2544, 158, 122, 79, 347, 186, 2458, 67, 1317, 2456, 2438])).
% 27.58/17.78 tff(2546,plain,
% 27.58/17.78 (f7(c2) = c1),
% 27.58/17.78 inference(unit_resolution,[status(thm)],[21, 2545])).
% 27.58/17.78 tff(2547,plain,
% 27.58/17.78 (f7(c2) = f9(f10(c2), f10(c2))),
% 27.58/17.78 inference(transitivity,[status(thm)],[2546, 2442, 1494])).
% 27.58/17.78 tff(2548,plain,
% 27.58/17.78 (big_f(f7(c2), c2) <=> big_f(f9(f10(c2), f10(c2)), f10(f10(c2)))),
% 27.58/17.78 inference(monotonicity,[status(thm)],[2547, 2294])).
% 27.58/17.78 tff(2549,plain,
% 27.58/17.78 (big_f(f9(f10(c2), f10(c2)), f10(f10(c2))) <=> big_f(f7(c2), c2)),
% 27.58/17.78 inference(symmetry,[status(thm)],[2548])).
% 27.58/17.78 tff(2550,plain,
% 27.58/17.78 ((~big_f(f9(f10(c2), f10(c2)), f10(f10(c2)))) <=> (~big_f(f7(c2), c2))),
% 27.58/17.78 inference(monotonicity,[status(thm)],[2549])).
% 27.58/17.78 tff(2551,plain,
% 27.58/17.78 (~big_f(f7(c2), c2)),
% 27.58/17.78 inference(modus_ponens,[status(thm)],[2458, 2550])).
% 27.58/17.78 tff(2552,plain,
% 27.58/17.78 (big_f(f7(c2), f2(c2))),
% 27.58/17.78 inference(unit_resolution,[status(thm)],[1549, 2551, 67, 122, 158, 2545, 2458, 1327])).
% 27.58/17.78 tff(2553,plain,
% 27.58/17.78 (big_f(f3(c1, c1), c1)),
% 27.58/17.78 inference(unit_resolution,[status(thm)],[1491, 2552, 1327, 67, 2546, 482, 1286])).
% 27.58/17.78 tff(2554,plain,
% 27.58/17.78 (big_f(f3(f9(f10(c2), f10(c2)), f9(f10(c2), f10(c2))), f9(f10(c2), f10(c2)))),
% 27.58/17.78 inference(modus_ponens,[status(thm)],[2553, 2427])).
% 27.58/17.78 tff(2555,plain,
% 27.58/17.78 (c4 = f10(c2)),
% 27.58/17.78 inference(transitivity,[status(thm)],[1290, 216])).
% 27.58/17.78 tff(2556,plain,
% 27.58/17.78 ((f9(f10(c2), f10(c2)) = c4) <=> (f9(f10(c2), f10(c2)) = f10(c2))),
% 27.58/17.78 inference(monotonicity,[status(thm)],[2555])).
% 27.58/17.78 tff(2557,plain,
% 27.58/17.78 ((f9(f10(c2), f10(c2)) = f10(c2)) <=> (f9(f10(c2), f10(c2)) = c4)),
% 27.58/17.78 inference(symmetry,[status(thm)],[2556])).
% 27.58/17.78 tff(2558,plain,
% 27.58/17.78 ((~(f9(f10(c2), f10(c2)) = f10(c2))) <=> (~(f9(f10(c2), f10(c2)) = c4))),
% 27.58/17.78 inference(monotonicity,[status(thm)],[2557])).
% 27.58/17.78 tff(2559,plain,
% 27.58/17.78 (~(f9(f10(c2), f10(c2)) = c4)),
% 27.58/17.78 inference(modus_ponens,[status(thm)],[158, 2558])).
% 27.58/17.78 tff(2560,plain,
% 27.58/17.78 (f9(f10(c2), f10(c2)) = f2(c2)),
% 27.58/17.78 inference(transitivity,[status(thm)],[1495, 1503, 2416, 2265])).
% 27.58/17.78 tff(2561,plain,
% 27.58/17.78 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(f9(f10(c2), f10(c2)) = f2(c2))) | big_f(c2, f9(f10(c2), f10(c2))) | (~(f3(f9(f10(c2), f10(c2)), f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))) | (f9(f10(c2), f10(c2)) = c4) | (~big_f(f3(f9(f10(c2), f10(c2)), f9(f10(c2), f10(c2))), f9(f10(c2), f10(c2)))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (~(c2 = c3)) | (~(f9(f10(c2), f10(c2)) = f2(c2))) | big_f(c2, f9(f10(c2), f10(c2))) | (~(f3(f9(f10(c2), f10(c2)), f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))) | (f9(f10(c2), f10(c2)) = c4) | (~big_f(f3(f9(f10(c2), f10(c2)), f9(f10(c2), f10(c2))), f9(f10(c2), f10(c2)))))),
% 27.58/17.78 inference(rewrite,[status(thm)],[])).
% 27.58/17.78 tff(2562,plain,
% 27.58/17.78 (((~(c2 = c3)) | (~(f9(f10(c2), f10(c2)) = f2(c2))) | (f9(f10(c2), f10(c2)) = c4) | (~(f3(f9(f10(c2), f10(c2)), f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))) | (~big_f(f3(f9(f10(c2), f10(c2)), f9(f10(c2), f10(c2))), f9(f10(c2), f10(c2)))) | big_f(c2, f9(f10(c2), f10(c2)))) <=> ((~(c2 = c3)) | (~(f9(f10(c2), f10(c2)) = f2(c2))) | big_f(c2, f9(f10(c2), f10(c2))) | (~(f3(f9(f10(c2), f10(c2)), f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))) | (f9(f10(c2), f10(c2)) = c4) | (~big_f(f3(f9(f10(c2), f10(c2)), f9(f10(c2), f10(c2))), f9(f10(c2), f10(c2)))))),
% 27.58/17.78 inference(rewrite,[status(thm)],[])).
% 27.58/17.78 tff(2563,plain,
% 27.58/17.78 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(f9(f10(c2), f10(c2)) = f2(c2))) | (f9(f10(c2), f10(c2)) = c4) | (~(f3(f9(f10(c2), f10(c2)), f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))) | (~big_f(f3(f9(f10(c2), f10(c2)), f9(f10(c2), f10(c2))), f9(f10(c2), f10(c2)))) | big_f(c2, f9(f10(c2), f10(c2))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(f9(f10(c2), f10(c2)) = f2(c2))) | big_f(c2, f9(f10(c2), f10(c2))) | (~(f3(f9(f10(c2), f10(c2)), f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))) | (f9(f10(c2), f10(c2)) = c4) | (~big_f(f3(f9(f10(c2), f10(c2)), f9(f10(c2), f10(c2))), f9(f10(c2), f10(c2))))))),
% 27.58/17.78 inference(monotonicity,[status(thm)],[2562])).
% 27.58/17.78 tff(2564,plain,
% 27.58/17.78 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(f9(f10(c2), f10(c2)) = f2(c2))) | (f9(f10(c2), f10(c2)) = c4) | (~(f3(f9(f10(c2), f10(c2)), f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))) | (~big_f(f3(f9(f10(c2), f10(c2)), f9(f10(c2), f10(c2))), f9(f10(c2), f10(c2)))) | big_f(c2, f9(f10(c2), f10(c2))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (~(c2 = c3)) | (~(f9(f10(c2), f10(c2)) = f2(c2))) | big_f(c2, f9(f10(c2), f10(c2))) | (~(f3(f9(f10(c2), f10(c2)), f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))) | (f9(f10(c2), f10(c2)) = c4) | (~big_f(f3(f9(f10(c2), f10(c2)), f9(f10(c2), f10(c2))), f9(f10(c2), f10(c2)))))),
% 27.58/17.78 inference(transitivity,[status(thm)],[2563, 2561])).
% 27.58/17.78 tff(2565,plain,
% 27.58/17.78 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(f9(f10(c2), f10(c2)) = f2(c2))) | (f9(f10(c2), f10(c2)) = c4) | (~(f3(f9(f10(c2), f10(c2)), f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))) | (~big_f(f3(f9(f10(c2), f10(c2)), f9(f10(c2), f10(c2))), f9(f10(c2), f10(c2)))) | big_f(c2, f9(f10(c2), f10(c2))))),
% 27.58/17.78 inference(quant_inst,[status(thm)],[])).
% 27.58/17.78 tff(2566,plain,
% 27.58/17.78 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (~(c2 = c3)) | (~(f9(f10(c2), f10(c2)) = f2(c2))) | big_f(c2, f9(f10(c2), f10(c2))) | (~(f3(f9(f10(c2), f10(c2)), f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))) | (f9(f10(c2), f10(c2)) = c4) | (~big_f(f3(f9(f10(c2), f10(c2)), f9(f10(c2), f10(c2))), f9(f10(c2), f10(c2))))),
% 27.58/17.78 inference(modus_ponens,[status(thm)],[2565, 2564])).
% 27.58/17.78 tff(2567,plain,
% 27.58/17.78 (big_f(c2, f9(f10(c2), f10(c2))) | (~(f3(f9(f10(c2), f10(c2)), f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))) | (f9(f10(c2), f10(c2)) = c4) | (~big_f(f3(f9(f10(c2), f10(c2)), f9(f10(c2), f10(c2))), f9(f10(c2), f10(c2))))),
% 27.58/17.78 inference(unit_resolution,[status(thm)],[2566, 1398, 1335, 2560])).
% 27.58/17.78 tff(2568,plain,
% 27.58/17.78 (~(f3(f9(f10(c2), f10(c2)), f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))),
% 27.58/17.78 inference(unit_resolution,[status(thm)],[2567, 2559, 2554, 2425])).
% 27.58/17.78 tff(2569,plain,
% 27.58/17.78 (~(f3(c1, c1) = c1)),
% 27.58/17.78 inference(modus_ponens,[status(thm)],[2568, 2420])).
% 27.58/17.78 tff(2570,plain,
% 27.58/17.78 (f3(c1, c1) = c2),
% 27.58/17.78 inference(unit_resolution,[status(thm)],[1416, 2569])).
% 27.58/17.78 tff(2571,plain,
% 27.58/17.78 (f3(c1, c1) = c3),
% 27.58/17.78 inference(transitivity,[status(thm)],[2570, 69])).
% 27.58/17.78 tff(2572,plain,
% 27.58/17.78 (big_f(f3(c1, c1), c1) <=> big_f(c3, f2(c3))),
% 27.58/17.78 inference(monotonicity,[status(thm)],[2571, 2416])).
% 27.58/17.78 tff(2573,plain,
% 27.58/17.78 (big_f(c3, f2(c3)) <=> big_f(f3(c1, c1), c1)),
% 27.58/17.78 inference(symmetry,[status(thm)],[2572])).
% 27.58/17.78 tff(2574,plain,
% 27.58/17.78 ((~big_f(c3, f2(c3))) <=> (~big_f(f3(c1, c1), c1))),
% 27.58/17.78 inference(monotonicity,[status(thm)],[2573])).
% 27.58/17.78 tff(2575,plain,
% 27.58/17.78 (~big_f(f3(c1, c1), c1)),
% 27.58/17.78 inference(modus_ponens,[status(thm)],[1286, 2574])).
% 27.58/17.78 tff(2576,plain,
% 27.58/17.78 ($false),
% 27.58/17.78 inference(unit_resolution,[status(thm)],[2553, 2575])).
% 27.58/17.78 tff(2577,plain,((f9(f10(c2), f10(c2)) = f10(c2)) | big_f(c3, f2(c3)) | (~(c3 = c2)) | (~(f10(c2) = c2)) | (~(f4(c4) = c2)) | (c1 = c4) | (~(f7(c1) = c2)) | (~(f5(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.58/17.78 tff(2578,plain,
% 27.58/17.78 (c1 = c4),
% 27.58/17.78 inference(unit_resolution,[status(thm)],[2577, 2415, 120, 122, 79, 67, 2347, 2277])).
% 27.58/17.78 tff(2579,plain,
% 27.58/17.78 (c4 = c1),
% 27.58/17.78 inference(symmetry,[status(thm)],[2578])).
% 27.58/17.78 tff(2580,plain,
% 27.58/17.78 (c4 = f2(c2)),
% 27.58/17.78 inference(transitivity,[status(thm)],[2579, 1367, 2265])).
% 27.58/17.78 tff(2581,plain,
% 27.58/17.78 (big_f(c2, c4) <=> big_f(f7(c2), f2(c2))),
% 27.58/17.78 inference(monotonicity,[status(thm)],[82, 2580])).
% 27.58/17.78 tff(2582,plain,
% 27.58/17.78 (big_f(f7(c2), f2(c2)) <=> big_f(c2, c4)),
% 27.58/17.78 inference(symmetry,[status(thm)],[2581])).
% 27.58/17.78 tff(2583,plain,
% 27.58/17.78 ((~big_f(f7(c2), f2(c2))) <=> (~big_f(c2, c4))),
% 27.58/17.78 inference(monotonicity,[status(thm)],[2582])).
% 27.58/17.78 tff(2584,plain,
% 27.58/17.78 (~big_f(c2, c4)),
% 27.58/17.78 inference(modus_ponens,[status(thm)],[2352, 2583])).
% 27.58/17.78 tff(2585,plain,
% 27.58/17.78 (big_f(f4(c4), c4)),
% 27.58/17.78 inference(unit_resolution,[status(thm)],[1315, 2277])).
% 27.58/17.78 tff(2586,plain,
% 27.58/17.78 (big_f(c2, c4)),
% 27.58/17.78 inference(modus_ponens,[status(thm)],[2585, 375])).
% 27.58/17.78 tff(2587,plain,
% 27.58/17.78 ($false),
% 27.58/17.78 inference(unit_resolution,[status(thm)],[2586, 2584])).
% 27.58/17.78 tff(2588,plain,((~(f2(c3) = c1)) | (~(c3 = c2)) | (~(f7(c2) = c2)) | (~(f10(c2) = c2)) | (~(f4(c4) = c2)) | big_f(f7(c2), c1) | (f7(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 27.58/17.78 tff(2589,plain,
% 27.58/17.78 (~(f2(c3) = c1)),
% 27.58/17.78 inference(unit_resolution,[status(thm)],[2588, 333, 77, 122, 79, 67, 115])).
% 27.58/17.78 tff(2590,plain,
% 27.58/17.78 (f2(c3) = c2),
% 27.58/17.78 inference(unit_resolution,[status(thm)],[1273, 2589])).
% 27.58/17.78 tff(2591,plain,
% 27.58/17.78 (f2(c2) = c2),
% 27.58/17.78 inference(transitivity,[status(thm)],[1426, 1319])).
% 27.58/17.78 tff(2592,plain,
% 27.58/17.78 (big_f(f7(c2), f2(c2)) <=> big_f(c2, c2)),
% 27.58/17.78 inference(monotonicity,[status(thm)],[77, 2591])).
% 27.58/17.78 tff(2593,plain,
% 27.58/17.78 (big_f(c3, f2(c3)) <=> big_f(c2, c2)),
% 27.58/17.78 inference(transitivity,[status(thm)],[2267, 2592])).
% 27.58/17.78 tff(2594,plain,
% 27.58/17.78 (~(c4 = c2)),
% 27.58/17.78 inference(unit_resolution,[status(thm)],[476, 1316, 79, 121])).
% 27.58/17.78 tff(2595,plain,
% 27.58/17.78 (c4 = c1),
% 27.58/17.78 inference(unit_resolution,[status(thm)],[461, 2594])).
% 27.58/17.78 tff(2596,plain,
% 27.58/17.78 (big_f(c2, c4) <=> big_f(c2, c1)),
% 27.58/17.78 inference(monotonicity,[status(thm)],[2595])).
% 27.58/17.78 tff(2597,plain,
% 27.58/17.78 (big_f(c2, c1) <=> big_f(c2, c4)),
% 27.58/17.78 inference(symmetry,[status(thm)],[2596])).
% 27.58/17.78 tff(2598,plain,
% 27.58/17.78 ((~big_f(c2, c1)) <=> (~big_f(c2, c4))),
% 27.58/17.78 inference(monotonicity,[status(thm)],[2597])).
% 27.58/17.78 tff(2599,plain,
% 27.58/17.78 (~big_f(c2, c4)),
% 27.58/17.78 inference(modus_ponens,[status(thm)],[2, 2598])).
% 27.58/17.78 tff(2600,plain,
% 27.58/17.78 (c2 = f2(c3)),
% 27.58/17.78 inference(modus_ponens,[status(thm)],[1319, 1434])).
% 27.58/17.78 tff(2601,plain,
% 27.58/17.78 ((f4(c4) = c2) <=> (c2 = f4(c4))),
% 27.58/17.78 inference(commutativity,[status(thm)],[])).
% 27.58/17.78 tff(2602,plain,
% 27.58/17.78 (c2 = f4(c4)),
% 27.58/17.78 inference(modus_ponens,[status(thm)],[79, 2601])).
% 27.58/17.78 tff(2603,plain,
% 27.58/17.78 (~big_f(c3, c2)),
% 27.58/17.78 inference(unit_resolution,[status(thm)],[1325, 1286, 1319])).
% 27.58/17.78 tff(2604,plain,
% 27.58/17.78 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))) | ((~(c2 = f2(c3))) | big_f(c2, c4) | (~(c2 = f4(c4))) | big_f(c3, c2))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))) | (~(c2 = f2(c3))) | big_f(c2, c4) | (~(c2 = f4(c4))) | big_f(c3, c2))),
% 27.58/17.78 inference(rewrite,[status(thm)],[])).
% 27.58/17.78 tff(2605,plain,
% 27.58/17.78 (($false | (~(c2 = f2(c3))) | $false | big_f(c2, c4) | (~(c2 = f4(c4))) | big_f(c3, c2)) <=> ((~(c2 = f2(c3))) | big_f(c2, c4) | (~(c2 = f4(c4))) | big_f(c3, c2))),
% 27.58/17.78 inference(rewrite,[status(thm)],[])).
% 27.58/17.78 tff(2606,plain,
% 27.58/17.78 (((~(c3 = c3)) | (~(c2 = f2(c3))) | (~(c4 = c4)) | big_f(c2, c4) | (~(c2 = f4(c4))) | big_f(c3, c2)) <=> ($false | (~(c2 = f2(c3))) | $false | big_f(c2, c4) | (~(c2 = f4(c4))) | big_f(c3, c2))),
% 27.58/17.78 inference(monotonicity,[status(thm)],[1308, 410])).
% 27.58/17.78 tff(2607,plain,
% 27.58/17.78 (((~(c3 = c3)) | (~(c2 = f2(c3))) | (~(c4 = c4)) | big_f(c2, c4) | (~(c2 = f4(c4))) | big_f(c3, c2)) <=> ((~(c2 = f2(c3))) | big_f(c2, c4) | (~(c2 = f4(c4))) | big_f(c3, c2))),
% 27.58/17.78 inference(transitivity,[status(thm)],[2606, 2605])).
% 27.58/17.78 tff(2608,plain,
% 27.58/17.78 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))) | ((~(c3 = c3)) | (~(c2 = f2(c3))) | (~(c4 = c4)) | big_f(c2, c4) | (~(c2 = f4(c4))) | big_f(c3, c2))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))) | ((~(c2 = f2(c3))) | big_f(c2, c4) | (~(c2 = f4(c4))) | big_f(c3, c2)))),
% 27.58/17.78 inference(monotonicity,[status(thm)],[2607])).
% 27.58/17.78 tff(2609,plain,
% 27.58/17.78 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))) | ((~(c3 = c3)) | (~(c2 = f2(c3))) | (~(c4 = c4)) | big_f(c2, c4) | (~(c2 = f4(c4))) | big_f(c3, c2))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))) | (~(c2 = f2(c3))) | big_f(c2, c4) | (~(c2 = f4(c4))) | big_f(c3, c2))),
% 27.58/17.78 inference(transitivity,[status(thm)],[2608, 2604])).
% 27.58/17.78 tff(2610,plain,
% 27.58/17.78 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))) | ((~(c3 = c3)) | (~(c2 = f2(c3))) | (~(c4 = c4)) | big_f(c2, c4) | (~(c2 = f4(c4))) | big_f(c3, c2))),
% 27.58/17.78 inference(quant_inst,[status(thm)],[])).
% 27.58/17.78 tff(2611,plain,
% 27.58/17.78 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))) | (~(c2 = f2(c3))) | big_f(c2, c4) | (~(c2 = f4(c4))) | big_f(c3, c2)),
% 27.58/17.78 inference(modus_ponens,[status(thm)],[2610, 2609])).
% 27.58/17.78 tff(2612,plain,
% 27.58/17.78 ((~(c2 = f2(c3))) | big_f(c2, c4) | (~(c2 = f4(c4))) | big_f(c3, c2)),
% 27.58/17.78 inference(unit_resolution,[status(thm)],[2611, 1300])).
% 27.58/17.78 tff(2613,plain,
% 27.58/17.78 (big_f(c2, c4)),
% 27.58/17.78 inference(unit_resolution,[status(thm)],[2612, 2603, 2602, 2600])).
% 27.58/17.78 tff(2614,plain,
% 27.58/17.78 ($false),
% 27.58/17.78 inference(unit_resolution,[status(thm)],[2613, 2599])).
% 27.58/17.78 tff(2615,plain,(big_f(c3, f2(c3)) | big_f(c2, c1) | (~(f4(c4) = c2)) | big_f(c2, c2) | (~(f2(c3) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.58/17.78 tff(2616,plain,
% 27.58/17.78 (big_f(c3, f2(c3))),
% 27.58/17.78 inference(unit_resolution,[status(thm)],[2615, 121, 79, 2, 1319])).
% 27.58/17.78 tff(2617,plain,
% 27.58/17.78 (big_f(c2, c2)),
% 27.58/17.78 inference(modus_ponens,[status(thm)],[2616, 2593])).
% 27.58/17.78 tff(2618,plain,
% 27.58/17.78 ($false),
% 27.58/17.78 inference(unit_resolution,[status(thm)],[121, 2617])).
% 27.58/17.78 tff(2619,plain,(big_f(c2, c2) | (~(f2(c3) = c2)) | (~(c3 = c2)) | (~(f7(c2) = c2)) | (~(f4(c4) = c2)) | big_f(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 27.58/17.78 tff(2620,plain,
% 27.58/17.78 (big_f(c2, c2)),
% 27.58/17.78 inference(unit_resolution,[status(thm)],[2619, 2590, 67, 77, 79, 2264])).
% 27.58/17.78 tff(2621,assumption,(~big_f(f7(c2), f6(c2, c2))), introduced(assumption)).
% 27.58/17.78 tff(2622,assumption,(f6(c2, c2) = c2), introduced(assumption)).
% 27.58/17.78 tff(2623,plain,
% 27.58/17.78 (big_f(f7(c2), f6(c2, c2)) <=> big_f(c2, c2)),
% 27.58/17.78 inference(monotonicity,[status(thm)],[77, 2622])).
% 27.58/17.78 tff(2624,plain,
% 27.58/17.78 (big_f(c2, c2) <=> big_f(f7(c2), f6(c2, c2))),
% 27.58/17.78 inference(symmetry,[status(thm)],[2623])).
% 27.58/17.78 tff(2625,plain,
% 27.58/17.78 (big_f(f7(c2), f6(c2, c2))),
% 27.58/17.78 inference(modus_ponens,[status(thm)],[1345, 2624])).
% 27.58/17.78 tff(2626,plain,
% 27.58/17.78 ($false),
% 27.58/17.78 inference(unit_resolution,[status(thm)],[2621, 2625])).
% 27.58/17.78 tff(2627,plain,((~(f6(c2, c2) = c2)) | big_f(f7(c2), f6(c2, c2)) | (~big_f(c2, c2)) | (~(f7(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.58/17.78 tff(2628,plain,
% 27.58/17.78 (~(f6(c2, c2) = c2)),
% 27.58/17.78 inference(unit_resolution,[status(thm)],[2627, 2621, 1345, 77])).
% 27.58/17.78 tff(2629,plain,
% 27.58/17.78 (f9(c2, c2) = f9(f10(c2), f4(c4))),
% 27.58/17.78 inference(monotonicity,[status(thm)],[216, 436])).
% 27.58/17.78 tff(2630,plain,
% 27.58/17.78 (f9(c2, c2) = c2),
% 27.58/17.78 inference(transitivity,[status(thm)],[2629, 1498])).
% 27.58/17.78 tff(2631,plain,
% 27.58/17.78 (big_f(f9(c2, c2), f10(c2)) <=> big_f(c2, c2)),
% 27.58/17.78 inference(monotonicity,[status(thm)],[2630, 122])).
% 27.58/17.78 tff(2632,plain,
% 27.58/17.78 (big_f(c2, c2) <=> big_f(f9(c2, c2), f10(c2))),
% 27.58/17.78 inference(symmetry,[status(thm)],[2631])).
% 27.58/17.78 tff(2633,plain,
% 27.58/17.78 (big_f(f9(c2, c2), f10(c2))),
% 27.58/17.78 inference(modus_ponens,[status(thm)],[1345, 2632])).
% 27.58/17.78 tff(2634,plain,
% 27.58/17.78 (f9(f10(c2), f4(c4)) = f9(c2, c2)),
% 27.58/17.78 inference(symmetry,[status(thm)],[2629])).
% 27.58/17.78 tff(2635,plain,
% 27.58/17.78 ((f9(f10(c2), f4(c4)) = c2) <=> (f9(c2, c2) = c2)),
% 27.58/17.78 inference(monotonicity,[status(thm)],[2634])).
% 27.58/17.78 tff(2636,plain,
% 27.58/17.78 (f9(c2, c2) = c2),
% 27.58/17.78 inference(modus_ponens,[status(thm)],[1498, 2635])).
% 27.58/17.78 tff(2637,assumption,(~(f6(c2, c2) = c2)), introduced(assumption)).
% 27.58/17.78 tff(2638,plain,
% 27.58/17.78 ($false),
% 27.58/17.78 inference(unit_resolution,[status(thm)],[2412, 2409, 122, 77, 2637, 2621, 2636, 2633])).
% 27.58/17.78 tff(2639,plain,((~(f9(f10(c2), f4(c4)) = c2)) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (~big_f(c2, c2)) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.58/17.78 tff(2640,plain,
% 27.58/17.78 (~(f9(f10(c2), f4(c4)) = c2)),
% 27.58/17.78 inference(unit_resolution,[status(thm)],[2639, 2628, 77, 122, 2621, 1345, 79])).
% 27.58/17.78 tff(2641,plain,
% 27.58/17.78 (f9(f10(c2), f4(c4)) = c1),
% 27.58/17.78 inference(unit_resolution,[status(thm)],[146, 2640])).
% 27.58/17.78 tff(2642,plain,
% 27.58/17.78 ((f10(f9(c2, c2)) = f9(c2, c2)) <=> (c2 = f9(c2, c2))),
% 27.58/17.78 inference(monotonicity,[status(thm)],[1689])).
% 27.58/17.78 tff(2643,plain,
% 27.58/17.78 ((f10(f9(c2, c2)) = f9(c2, c2)) <=> (f9(c2, c2) = c2)),
% 27.58/17.78 inference(transitivity,[status(thm)],[2642, 167])).
% 27.58/17.78 tff(2644,plain,
% 27.58/17.78 ((f9(c2, c2) = c2) <=> (f10(f9(c2, c2)) = f9(c2, c2))),
% 27.58/17.78 inference(symmetry,[status(thm)],[2643])).
% 27.58/17.78 tff(2645,plain,
% 27.58/17.78 ((~(f9(c2, c2) = c2)) <=> (~(f10(f9(c2, c2)) = f9(c2, c2)))),
% 27.58/17.78 inference(monotonicity,[status(thm)],[2644])).
% 27.58/17.78 tff(2646,plain,
% 27.58/17.78 ((f9(c2, c2) = c2) <=> (c1 = c2)),
% 27.58/17.78 inference(monotonicity,[status(thm)],[161])).
% 27.58/17.78 tff(2647,plain,
% 27.58/17.78 ((f9(c2, c2) = c2) <=> (c2 = c1)),
% 27.58/17.78 inference(transitivity,[status(thm)],[2646, 1])).
% 27.58/17.78 tff(2648,plain,
% 27.58/17.78 ((c2 = c1) <=> (f9(c2, c2) = c2)),
% 27.58/17.78 inference(symmetry,[status(thm)],[2647])).
% 27.58/17.78 tff(2649,plain,
% 27.58/17.78 ((~(c2 = c1)) <=> (~(f9(c2, c2) = c2))),
% 27.58/17.78 inference(monotonicity,[status(thm)],[2648])).
% 27.58/17.78 tff(2650,plain,
% 27.58/17.78 (~(f9(c2, c2) = c2)),
% 27.58/17.78 inference(modus_ponens,[status(thm)],[75, 2649])).
% 27.58/17.78 tff(2651,plain,
% 27.58/17.78 (~(f10(f9(c2, c2)) = f9(c2, c2))),
% 27.58/17.78 inference(modus_ponens,[status(thm)],[2650, 2645])).
% 27.58/17.78 tff(2652,plain,
% 27.58/17.78 (big_f(c2, f10(f9(c2, c2)))),
% 27.58/17.79 inference(modus_ponens,[status(thm)],[1345, 1691])).
% 27.58/17.79 tff(2653,plain,
% 27.58/17.79 (^[X6: $i, X4: $i, X7: $i, X8: $i] : refl(((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6))) <=> ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6))))),
% 27.58/17.79 inference(bind,[status(th)],[])).
% 27.58/17.79 tff(2654,plain,
% 27.58/17.79 (![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6))) <=> ![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))),
% 27.58/17.79 inference(quant_intro,[status(thm)],[2653])).
% 27.58/17.79 tff(2655,plain,
% 27.58/17.79 (![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6))) <=> ![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))),
% 27.58/17.79 inference(rewrite,[status(thm)],[])).
% 27.58/17.79 tff(2656,plain,
% 27.58/17.79 (^[X6: $i, X4: $i, X7: $i, X8: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((big_f(f7(X4), f6(X4, X6)) | (f6(X4, X6) = X6)) <=> ((f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))), (((big_f(f7(X4), f6(X4, X6)) | (f6(X4, X6) = X6)) | (~(f7(X4) = X4))) <=> (((f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6))) | (~(f7(X4) = X4))))), rewrite((((f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6))) | (~(f7(X4) = X4))) <=> ((~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))), (((big_f(f7(X4), f6(X4, X6)) | (f6(X4, X6) = X6)) | (~(f7(X4) = X4))) <=> ((~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6))))), ((((big_f(f7(X4), f6(X4, X6)) | (f6(X4, X6) = X6)) | (~(f7(X4) = X4))) | (~big_f(X8, f10(X7)))) <=> (((~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6))) | (~big_f(X8, f10(X7)))))), rewrite((((~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6))) | (~big_f(X8, f10(X7)))) <=> ((~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))), ((((big_f(f7(X4), f6(X4, X6)) | (f6(X4, X6) = X6)) | (~(f7(X4) = X4))) | (~big_f(X8, f10(X7)))) <=> ((~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6))))), (((((big_f(f7(X4), f6(X4, X6)) | (f6(X4, X6) = X6)) | (~(f7(X4) = X4))) | (~big_f(X8, f10(X7)))) | (X8 = f8(X7))) <=> (((~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6))) | (X8 = f8(X7))))), rewrite((((~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6))) | (X8 = f8(X7))) <=> ((X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))), (((((big_f(f7(X4), f6(X4, X6)) | (f6(X4, X6) = X6)) | (~(f7(X4) = X4))) | (~big_f(X8, f10(X7)))) | (X8 = f8(X7))) <=> ((X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6))))), ((((((big_f(f7(X4), f6(X4, X6)) | (f6(X4, X6) = X6)) | (~(f7(X4) = X4))) | (~big_f(X8, f10(X7)))) | (X8 = f8(X7))) | (f10(X7) = X7)) <=> (((X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6))) | (f10(X7) = X7)))), rewrite((((X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6))) | (f10(X7) = X7)) <=> ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))), ((((((big_f(f7(X4), f6(X4, X6)) | (f6(X4, X6) = X6)) | (~(f7(X4) = X4))) | (~big_f(X8, f10(X7)))) | (X8 = f8(X7))) | (f10(X7) = X7)) <=> ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))))),
% 27.58/17.79 inference(bind,[status(th)],[])).
% 27.58/17.79 tff(2657,plain,
% 27.58/17.79 (![X6: $i, X4: $i, X7: $i, X8: $i] : (((((big_f(f7(X4), f6(X4, X6)) | (f6(X4, X6) = X6)) | (~(f7(X4) = X4))) | (~big_f(X8, f10(X7)))) | (X8 = f8(X7))) | (f10(X7) = X7)) <=> ![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))),
% 27.58/17.79 inference(quant_intro,[status(thm)],[2656])).
% 27.58/17.79 tff(2658,axiom,(![X6: $i, X4: $i, X7: $i, X8: $i] : (((((big_f(f7(X4), f6(X4, X6)) | (f6(X4, X6) = X6)) | (~(f7(X4) = X4))) | (~big_f(X8, f10(X7)))) | (X8 = f8(X7))) | (f10(X7) = X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_27')).
% 27.58/17.79 tff(2659,plain,
% 27.58/17.79 (![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))),
% 27.58/17.79 inference(modus_ponens,[status(thm)],[2658, 2657])).
% 27.58/17.79 tff(2660,plain,
% 27.58/17.79 (![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))),
% 27.58/17.79 inference(modus_ponens,[status(thm)],[2659, 2655])).
% 27.58/17.79 tff(2661,plain,(
% 27.58/17.79 ![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))),
% 27.58/17.79 inference(skolemize,[status(sab)],[2660])).
% 27.58/17.79 tff(2662,plain,
% 27.58/17.79 (![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))),
% 27.58/17.79 inference(modus_ponens,[status(thm)],[2661, 2654])).
% 27.58/17.79 tff(2663,plain,
% 27.58/17.79 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)))),
% 27.58/17.79 inference(rewrite,[status(thm)],[])).
% 27.58/17.79 tff(2664,plain,
% 27.58/17.79 (((f10(f9(c2, c2)) = f9(c2, c2)) | (c2 = f8(f9(c2, c2))) | (~big_f(c2, f10(f9(c2, c2)))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2))) <=> ((~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)))),
% 27.58/17.79 inference(rewrite,[status(thm)],[])).
% 27.58/17.79 tff(2665,plain,
% 27.58/17.79 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (c2 = f8(f9(c2, c2))) | (~big_f(c2, f10(f9(c2, c2)))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2))))),
% 27.58/17.79 inference(monotonicity,[status(thm)],[2664])).
% 27.58/17.79 tff(2666,plain,
% 27.58/17.79 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (c2 = f8(f9(c2, c2))) | (~big_f(c2, f10(f9(c2, c2)))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)))),
% 27.58/17.79 inference(transitivity,[status(thm)],[2665, 2663])).
% 27.58/17.79 tff(2667,plain,
% 27.58/17.79 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (c2 = f8(f9(c2, c2))) | (~big_f(c2, f10(f9(c2, c2)))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)))),
% 27.58/17.79 inference(quant_inst,[status(thm)],[])).
% 27.58/17.79 tff(2668,plain,
% 27.58/17.79 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2))),
% 27.58/17.79 inference(modus_ponens,[status(thm)],[2667, 2666])).
% 27.58/17.79 tff(2669,plain,
% 27.58/17.79 ((~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2))),
% 27.58/17.79 inference(unit_resolution,[status(thm)],[2668, 2662, 77, 2637, 2621])).
% 27.58/17.79 tff(2670,plain,
% 27.58/17.79 (c2 = f8(f9(c2, c2))),
% 27.58/17.79 inference(unit_resolution,[status(thm)],[2669, 2652, 2651])).
% 27.58/17.79 tff(2671,plain,
% 27.58/17.79 (f8(f9(c2, c2)) = c2),
% 27.58/17.79 inference(symmetry,[status(thm)],[2670])).
% 27.58/17.79 tff(2672,plain,
% 27.58/17.79 (big_f(f9(c2, c2), f10(f9(c2, c2))) <=> big_f(f9(c2, c2), f10(c2))),
% 27.58/17.79 inference(monotonicity,[status(thm)],[720])).
% 27.58/17.79 tff(2673,plain,
% 27.58/17.79 (big_f(f9(c2, c2), f10(c2)) <=> big_f(f9(c2, c2), f10(f9(c2, c2)))),
% 27.58/17.79 inference(symmetry,[status(thm)],[2672])).
% 27.58/17.79 tff(2674,plain,
% 27.58/17.79 (big_f(f9(c2, c2), f10(f9(c2, c2)))),
% 27.58/17.79 inference(modus_ponens,[status(thm)],[690, 2673])).
% 27.58/17.79 tff(2675,plain,
% 27.58/17.79 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))))),
% 27.58/17.79 inference(rewrite,[status(thm)],[])).
% 27.58/17.79 tff(2676,plain,
% 27.58/17.79 (((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2))) <=> ((~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))))),
% 27.58/17.79 inference(rewrite,[status(thm)],[])).
% 27.58/17.79 tff(2677,plain,
% 27.58/17.79 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2))))))),
% 27.58/17.79 inference(monotonicity,[status(thm)],[2676])).
% 27.58/17.79 tff(2678,plain,
% 27.58/17.79 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))))),
% 27.58/17.79 inference(transitivity,[status(thm)],[2677, 2675])).
% 27.58/17.79 tff(2679,plain,
% 27.58/17.79 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)))),
% 27.58/17.79 inference(quant_inst,[status(thm)],[])).
% 27.58/17.79 tff(2680,plain,
% 27.58/17.79 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2))))),
% 27.58/17.79 inference(modus_ponens,[status(thm)],[2679, 2678])).
% 27.58/17.79 tff(2681,plain,
% 27.58/17.79 ((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2))))),
% 27.58/17.79 inference(unit_resolution,[status(thm)],[2680, 2662, 77, 2637, 2621])).
% 27.58/17.79 tff(2682,plain,
% 27.58/17.79 (f9(c2, c2) = f8(f9(c2, c2))),
% 27.58/17.79 inference(unit_resolution,[status(thm)],[2681, 2651, 2674])).
% 27.58/17.79 tff(2683,plain,
% 27.58/17.79 (f9(c2, c2) = c2),
% 27.58/17.79 inference(transitivity,[status(thm)],[2682, 2671])).
% 27.58/17.79 tff(2684,plain,
% 27.58/17.79 ($false),
% 27.58/17.79 inference(unit_resolution,[status(thm)],[2650, 2683])).
% 27.58/17.79 tff(2685,plain,((f6(c2, c2) = c2) | (~(f7(c2) = c2)) | big_f(f7(c2), f6(c2, c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f10(c2) = c2)) | (~(f10(c1) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~big_f(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 27.58/17.79 tff(2686,plain,
% 27.58/17.79 (~big_f(f9(c2, c2), f10(c2))),
% 27.58/17.79 inference(unit_resolution,[status(thm)],[2685, 2641, 2621, 77, 122, 16, 2628, 79, 1345])).
% 27.58/17.79 tff(2687,plain,
% 27.58/17.79 (f9(c2, c2) = c1),
% 27.58/17.79 inference(transitivity,[status(thm)],[160, 2641])).
% 27.58/17.79 tff(2688,plain,
% 27.58/17.79 ((f9(c2, c2) = c2) <=> (c1 = c2)),
% 27.58/17.79 inference(monotonicity,[status(thm)],[2687])).
% 27.58/17.79 tff(2689,plain,
% 27.58/17.79 ((f9(c2, c2) = c2) <=> (c2 = c1)),
% 27.58/17.79 inference(transitivity,[status(thm)],[2688, 1])).
% 27.58/17.79 tff(2690,plain,
% 27.58/17.79 ((c2 = c1) <=> (f9(c2, c2) = c2)),
% 27.58/17.79 inference(symmetry,[status(thm)],[2689])).
% 27.58/17.79 tff(2691,plain,
% 27.58/17.79 ((~(c2 = c1)) <=> (~(f9(c2, c2) = c2))),
% 27.58/17.79 inference(monotonicity,[status(thm)],[2690])).
% 27.58/17.79 tff(2692,plain,
% 27.58/17.79 (~(f9(c2, c2) = c2)),
% 27.58/17.79 inference(modus_ponens,[status(thm)],[75, 2691])).
% 27.58/17.79 tff(2693,plain,
% 27.58/17.79 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)))),
% 27.58/17.79 inference(rewrite,[status(thm)],[])).
% 27.58/17.79 tff(2694,plain,
% 27.58/17.79 (((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2))) <=> ((~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)))),
% 27.58/17.79 inference(rewrite,[status(thm)],[])).
% 27.58/17.79 tff(2695,plain,
% 27.58/17.79 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2))))),
% 27.58/17.79 inference(monotonicity,[status(thm)],[2694])).
% 27.58/17.79 tff(2696,plain,
% 27.58/17.79 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)))),
% 27.58/17.79 inference(transitivity,[status(thm)],[2695, 2693])).
% 27.58/17.79 tff(2697,plain,
% 27.58/17.79 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)))),
% 27.58/17.79 inference(quant_inst,[status(thm)],[])).
% 27.58/17.79 tff(2698,plain,
% 27.58/17.79 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2))),
% 27.58/17.79 inference(modus_ponens,[status(thm)],[2697, 2696])).
% 27.58/17.79 tff(2699,plain,
% 27.58/17.79 ($false),
% 27.58/17.79 inference(unit_resolution,[status(thm)],[2698, 2492, 122, 77, 2628, 2621, 2692, 2686])).
% 27.58/17.79 tff(2700,plain,(big_f(f7(c2), f6(c2, c2)) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~(f4(c4) = c2)) | (~(f10(c1) = c2)) | (~big_f(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 27.58/17.79 tff(2701,plain,
% 27.58/17.79 (big_f(f7(c2), f6(c2, c2))),
% 27.58/17.79 inference(unit_resolution,[status(thm)],[2700, 2620, 77, 79, 15, 122])).
% 27.58/17.79 tff(2702,assumption,(f6(f7(c2), c3) = c1), introduced(assumption)).
% 27.58/17.79 tff(2703,plain,
% 27.58/17.79 (c1 = f6(f7(c2), c3)),
% 27.58/17.79 inference(symmetry,[status(thm)],[2702])).
% 27.58/17.79 tff(2704,plain,
% 27.58/17.79 (c1 = f6(c2, c2)),
% 27.58/17.79 inference(transitivity,[status(thm)],[2703, 2466])).
% 27.58/17.79 tff(2705,plain,
% 27.58/17.79 (big_f(c2, c1) <=> big_f(f7(c2), f6(c2, c2))),
% 27.58/17.79 inference(monotonicity,[status(thm)],[82, 2704])).
% 27.58/17.79 tff(2706,plain,
% 27.58/17.79 (big_f(f7(c2), f6(c2, c2)) <=> big_f(c2, c1)),
% 27.58/17.79 inference(symmetry,[status(thm)],[2705])).
% 27.58/17.79 tff(2707,assumption,(big_f(f7(c2), f6(c2, c2))), introduced(assumption)).
% 27.58/17.79 tff(2708,plain,
% 27.58/17.79 (big_f(c2, c1)),
% 27.58/17.79 inference(modus_ponens,[status(thm)],[2707, 2706])).
% 27.58/17.79 tff(2709,plain,
% 27.58/17.79 ($false),
% 27.58/17.79 inference(unit_resolution,[status(thm)],[2, 2708])).
% 27.58/17.79 tff(2710,plain,((~(f6(f7(c2), c3) = c1)) | big_f(c2, c1) | (~big_f(f7(c2), f6(c2, c2))) | (~(c3 = c2)) | (~(f7(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.58/17.79 tff(2711,plain,
% 27.58/17.79 (~(f6(f7(c2), c3) = c1)),
% 27.58/17.79 inference(unit_resolution,[status(thm)],[2710, 2264, 2701, 67, 77])).
% 27.58/17.79 tff(2712,plain,
% 27.58/17.79 (f6(f7(c2), c3) = c2),
% 27.58/17.79 inference(unit_resolution,[status(thm)],[2391, 2711])).
% 27.58/17.79 tff(2713,plain,
% 27.58/17.79 ((f6(f7(c2), c3) = c2) <=> (f6(c2, c2) = c2)),
% 27.58/17.79 inference(monotonicity,[status(thm)],[2466])).
% 27.58/17.79 tff(2714,plain,
% 27.58/17.79 (f6(c2, c2) = c2),
% 27.58/17.79 inference(modus_ponens,[status(thm)],[2362, 2713])).
% 27.58/17.79 tff(2715,plain,
% 27.58/17.79 ($false),
% 27.58/17.79 inference(unit_resolution,[status(thm)],[2637, 2714])).
% 27.58/17.79 tff(2716,plain,((~(f6(f7(c2), c3) = c2)) | (f6(c2, c2) = c2) | (~(c3 = c2)) | (~(f7(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.58/17.79 tff(2717,plain,
% 27.58/17.79 (f6(c2, c2) = c2),
% 27.58/17.79 inference(unit_resolution,[status(thm)],[2716, 2712, 67, 77])).
% 27.58/17.79 tff(2718,plain,
% 27.58/17.79 (big_f(c2, f10(c1)) <=> big_f(c2, c2)),
% 27.58/17.79 inference(monotonicity,[status(thm)],[15])).
% 27.58/17.79 tff(2719,plain,
% 27.58/17.79 (big_f(c2, c2) <=> big_f(c2, f10(c1))),
% 27.58/17.79 inference(symmetry,[status(thm)],[2718])).
% 27.58/17.79 tff(2720,plain,
% 27.58/17.79 (big_f(c2, f10(c1))),
% 27.58/17.79 inference(modus_ponens,[status(thm)],[2620, 2719])).
% 27.58/17.79 tff(2721,plain,
% 27.58/17.79 (^[X6: $i, X4: $i, X7: $i, X8: $i] : refl(((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))) <=> ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))))),
% 27.58/17.79 inference(bind,[status(th)],[])).
% 27.58/17.79 tff(2722,plain,
% 27.58/17.79 (![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))) <=> ![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))),
% 27.58/17.79 inference(quant_intro,[status(thm)],[2721])).
% 27.58/17.79 tff(2723,plain,
% 27.58/17.79 (![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))) <=> ![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))),
% 27.58/17.79 inference(rewrite,[status(thm)],[])).
% 27.58/17.79 tff(2724,plain,
% 27.58/17.79 (^[X6: $i, X4: $i, X7: $i, X8: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~big_f(f7(X4), f6(X4, X6))) | (~(f6(X4, X6) = X6))) <=> ((~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))), ((((~big_f(f7(X4), f6(X4, X6))) | (~(f6(X4, X6) = X6))) | (~(f7(X4) = X4))) <=> (((~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))) | (~(f7(X4) = X4))))), rewrite((((~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))) | (~(f7(X4) = X4))) <=> ((~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))), ((((~big_f(f7(X4), f6(X4, X6))) | (~(f6(X4, X6) = X6))) | (~(f7(X4) = X4))) <=> ((~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))))), (((((~big_f(f7(X4), f6(X4, X6))) | (~(f6(X4, X6) = X6))) | (~(f7(X4) = X4))) | (~big_f(X8, f10(X7)))) <=> (((~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))) | (~big_f(X8, f10(X7)))))), rewrite((((~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))) | (~big_f(X8, f10(X7)))) <=> ((~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))), (((((~big_f(f7(X4), f6(X4, X6))) | (~(f6(X4, X6) = X6))) | (~(f7(X4) = X4))) | (~big_f(X8, f10(X7)))) <=> ((~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))))), ((((((~big_f(f7(X4), f6(X4, X6))) | (~(f6(X4, X6) = X6))) | (~(f7(X4) = X4))) | (~big_f(X8, f10(X7)))) | (X8 = f8(X7))) <=> (((~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))) | (X8 = f8(X7))))), rewrite((((~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))) | (X8 = f8(X7))) <=> ((X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))), ((((((~big_f(f7(X4), f6(X4, X6))) | (~(f6(X4, X6) = X6))) | (~(f7(X4) = X4))) | (~big_f(X8, f10(X7)))) | (X8 = f8(X7))) <=> ((X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))))), (((((((~big_f(f7(X4), f6(X4, X6))) | (~(f6(X4, X6) = X6))) | (~(f7(X4) = X4))) | (~big_f(X8, f10(X7)))) | (X8 = f8(X7))) | (f10(X7) = X7)) <=> (((X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))) | (f10(X7) = X7)))), rewrite((((X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))) | (f10(X7) = X7)) <=> ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))), (((((((~big_f(f7(X4), f6(X4, X6))) | (~(f6(X4, X6) = X6))) | (~(f7(X4) = X4))) | (~big_f(X8, f10(X7)))) | (X8 = f8(X7))) | (f10(X7) = X7)) <=> ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))))),
% 27.58/17.79 inference(bind,[status(th)],[])).
% 27.58/17.79 tff(2725,plain,
% 27.58/17.79 (![X6: $i, X4: $i, X7: $i, X8: $i] : ((((((~big_f(f7(X4), f6(X4, X6))) | (~(f6(X4, X6) = X6))) | (~(f7(X4) = X4))) | (~big_f(X8, f10(X7)))) | (X8 = f8(X7))) | (f10(X7) = X7)) <=> ![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))),
% 27.58/17.79 inference(quant_intro,[status(thm)],[2724])).
% 27.58/17.79 tff(2726,axiom,(![X6: $i, X4: $i, X7: $i, X8: $i] : ((((((~big_f(f7(X4), f6(X4, X6))) | (~(f6(X4, X6) = X6))) | (~(f7(X4) = X4))) | (~big_f(X8, f10(X7)))) | (X8 = f8(X7))) | (f10(X7) = X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_31')).
% 27.58/17.79 tff(2727,plain,
% 27.58/17.79 (![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))),
% 27.58/17.79 inference(modus_ponens,[status(thm)],[2726, 2725])).
% 27.58/17.79 tff(2728,plain,
% 27.58/17.79 (![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))),
% 27.58/17.80 inference(modus_ponens,[status(thm)],[2727, 2723])).
% 27.58/17.80 tff(2729,plain,(
% 27.58/17.80 ![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))),
% 27.58/17.80 inference(skolemize,[status(sab)],[2728])).
% 27.58/17.80 tff(2730,plain,
% 27.58/17.80 (![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))),
% 27.58/17.80 inference(modus_ponens,[status(thm)],[2729, 2722])).
% 27.58/17.80 tff(2731,plain,
% 27.58/17.80 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (c2 = f8(c1)) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~big_f(c2, f10(c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (c2 = f8(c1)) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~big_f(c2, f10(c1))))),
% 27.58/17.80 inference(rewrite,[status(thm)],[])).
% 27.58/17.80 tff(2732,plain,
% 27.58/17.80 (((f10(c1) = c1) | (c2 = f8(c1)) | (~big_f(c2, f10(c1))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2)))) <=> ((f10(c1) = c1) | (c2 = f8(c1)) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~big_f(c2, f10(c1))))),
% 27.58/17.80 inference(rewrite,[status(thm)],[])).
% 27.58/17.80 tff(2733,plain,
% 27.58/17.80 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (c2 = f8(c1)) | (~big_f(c2, f10(c1))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (c2 = f8(c1)) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~big_f(c2, f10(c1)))))),
% 27.58/17.80 inference(monotonicity,[status(thm)],[2732])).
% 27.58/17.80 tff(2734,plain,
% 27.58/17.80 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (c2 = f8(c1)) | (~big_f(c2, f10(c1))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (c2 = f8(c1)) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~big_f(c2, f10(c1))))),
% 27.58/17.80 inference(transitivity,[status(thm)],[2733, 2731])).
% 27.58/17.80 tff(2735,plain,
% 27.58/17.80 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (c2 = f8(c1)) | (~big_f(c2, f10(c1))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))),
% 27.58/17.80 inference(quant_inst,[status(thm)],[])).
% 27.58/17.80 tff(2736,plain,
% 27.58/17.80 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (c2 = f8(c1)) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~big_f(c2, f10(c1)))),
% 27.58/17.80 inference(modus_ponens,[status(thm)],[2735, 2734])).
% 27.58/17.80 tff(2737,plain,
% 27.58/17.80 ((c2 = f8(c1)) | (~(f6(c2, c2) = c2))),
% 27.58/17.80 inference(unit_resolution,[status(thm)],[2736, 2730, 2720, 3, 77, 2701])).
% 27.58/17.80 tff(2738,plain,
% 27.58/17.80 (c2 = f8(c1)),
% 27.58/17.80 inference(unit_resolution,[status(thm)],[2737, 2717])).
% 27.58/17.80 tff(2739,plain,
% 27.58/17.80 (f8(c1) = c2),
% 27.58/17.80 inference(symmetry,[status(thm)],[2738])).
% 27.58/17.80 tff(2740,plain,
% 27.58/17.80 ((f9(c2, c2) = f8(c1)) <=> (f9(c2, c2) = c2)),
% 27.58/17.80 inference(monotonicity,[status(thm)],[2739])).
% 27.58/17.80 tff(2741,plain,
% 27.58/17.80 ((f9(c2, c2) = c2) <=> (f9(c2, c2) = f8(c1))),
% 27.58/17.80 inference(symmetry,[status(thm)],[2740])).
% 27.58/17.80 tff(2742,plain,
% 27.58/17.80 ((~(f9(c2, c2) = c2)) <=> (~(f9(c2, c2) = f8(c1)))),
% 27.58/17.80 inference(monotonicity,[status(thm)],[2741])).
% 27.58/17.80 tff(2743,plain,
% 27.58/17.80 ($false),
% 27.58/17.80 inference(unit_resolution,[status(thm)],[2540, 2534, 122, 77, 2622, 2707, 1209, 256])).
% 27.58/17.80 tff(2744,plain,((f9(c2, c2) = c2) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | big_f(f9(c2, c2), f10(c2))), inference(lemma,lemma(discharge,[]))).
% 27.58/17.80 tff(2745,plain,
% 27.58/17.80 (f9(c2, c2) = c2),
% 27.58/17.80 inference(unit_resolution,[status(thm)],[2744, 256, 77, 2622, 2707, 122])).
% 27.58/17.80 tff(2746,plain,
% 27.58/17.80 (big_f(f9(c2, c2), f10(c2)) <=> big_f(c2, c2)),
% 27.58/17.80 inference(monotonicity,[status(thm)],[2745, 122])).
% 27.58/17.80 tff(2747,plain,
% 27.58/17.80 (big_f(c2, c2) <=> big_f(f9(c2, c2), f10(c2))),
% 27.58/17.80 inference(symmetry,[status(thm)],[2746])).
% 27.58/17.80 tff(2748,plain,
% 27.58/17.80 (big_f(f9(c2, c2), f10(c2))),
% 27.58/17.80 inference(modus_ponens,[status(thm)],[1345, 2747])).
% 27.58/17.80 tff(2749,plain,
% 27.58/17.80 ($false),
% 27.58/17.80 inference(unit_resolution,[status(thm)],[256, 2748])).
% 27.58/17.80 tff(2750,plain,(big_f(f9(c2, c2), f10(c2)) | (~big_f(c2, c2)) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2)))), inference(lemma,lemma(discharge,[]))).
% 27.58/17.80 tff(2751,plain,
% 27.58/17.80 (big_f(f9(c2, c2), f10(c2))),
% 27.58/17.80 inference(unit_resolution,[status(thm)],[2750, 2620, 122, 77, 2717, 2701])).
% 27.58/17.80 tff(2752,plain,
% 27.58/17.80 (~(f9(c2, c2) = c2)),
% 27.58/17.80 inference(unit_resolution,[status(thm)],[2386, 2751, 77, 122, 2712, 2620, 67])).
% 27.58/17.80 tff(2753,plain,
% 27.58/17.80 (~(f9(c2, c2) = f8(c1))),
% 27.58/17.80 inference(modus_ponens,[status(thm)],[2752, 2742])).
% 27.58/17.80 tff(2754,plain,
% 27.58/17.80 (f10(c1) = f10(c2)),
% 27.58/17.80 inference(transitivity,[status(thm)],[15, 216])).
% 27.58/17.80 tff(2755,plain,
% 27.58/17.80 (big_f(f9(c2, c2), f10(c1)) <=> big_f(f9(c2, c2), f10(c2))),
% 27.58/17.80 inference(monotonicity,[status(thm)],[2754])).
% 27.58/17.80 tff(2756,plain,
% 27.58/17.80 (big_f(f9(c2, c2), f10(c2)) <=> big_f(f9(c2, c2), f10(c1))),
% 27.58/17.80 inference(symmetry,[status(thm)],[2755])).
% 27.58/17.80 tff(2757,plain,
% 27.58/17.80 (big_f(f9(c2, c2), f10(c1))),
% 27.58/17.80 inference(modus_ponens,[status(thm)],[2751, 2756])).
% 27.58/17.80 tff(2758,plain,
% 27.58/17.80 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (f9(c2, c2) = f8(c1)) | (~big_f(f9(c2, c2), f10(c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (f9(c2, c2) = f8(c1)) | (~big_f(f9(c2, c2), f10(c1))))),
% 27.58/17.80 inference(rewrite,[status(thm)],[])).
% 27.58/17.80 tff(2759,plain,
% 27.58/17.80 (((f10(c1) = c1) | (f9(c2, c2) = f8(c1)) | (~big_f(f9(c2, c2), f10(c1))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2)))) <=> ((f10(c1) = c1) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (f9(c2, c2) = f8(c1)) | (~big_f(f9(c2, c2), f10(c1))))),
% 27.58/17.80 inference(rewrite,[status(thm)],[])).
% 27.58/17.80 tff(2760,plain,
% 27.58/17.80 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (f9(c2, c2) = f8(c1)) | (~big_f(f9(c2, c2), f10(c1))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (f9(c2, c2) = f8(c1)) | (~big_f(f9(c2, c2), f10(c1)))))),
% 27.58/17.80 inference(monotonicity,[status(thm)],[2759])).
% 27.58/17.80 tff(2761,plain,
% 27.58/17.80 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (f9(c2, c2) = f8(c1)) | (~big_f(f9(c2, c2), f10(c1))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (f9(c2, c2) = f8(c1)) | (~big_f(f9(c2, c2), f10(c1))))),
% 27.58/17.80 inference(transitivity,[status(thm)],[2760, 2758])).
% 27.58/17.80 tff(2762,plain,
% 27.58/17.80 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (f9(c2, c2) = f8(c1)) | (~big_f(f9(c2, c2), f10(c1))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))),
% 27.58/17.80 inference(quant_inst,[status(thm)],[])).
% 27.58/17.80 tff(2763,plain,
% 27.58/17.80 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (f9(c2, c2) = f8(c1)) | (~big_f(f9(c2, c2), f10(c1)))),
% 27.58/17.80 inference(modus_ponens,[status(thm)],[2762, 2761])).
% 27.58/17.80 tff(2764,plain,
% 27.58/17.80 ((f9(c2, c2) = f8(c1)) | (~big_f(f9(c2, c2), f10(c1)))),
% 27.58/17.80 inference(unit_resolution,[status(thm)],[2763, 2730, 3, 77, 2717, 2701])).
% 27.58/17.80 tff(2765,plain,
% 27.58/17.80 ($false),
% 27.58/17.80 inference(unit_resolution,[status(thm)],[2764, 2757, 2753])).
% 27.58/17.80 tff(2766,plain,(big_f(f7(c2), c1) | (f10(c1) = c1) | (~(f7(c2) = c2)) | (~(f10(c2) = c2)) | (~(c3 = c2)) | (~(f4(c4) = c2)) | (f7(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 27.58/17.80 tff(2767,plain,
% 27.58/17.80 (big_f(f7(c2), c1)),
% 27.58/17.80 inference(unit_resolution,[status(thm)],[2766, 3, 77, 122, 67, 79, 115])).
% 27.58/17.80 tff(2768,plain,
% 27.58/17.80 (big_f(c2, c1)),
% 27.58/17.80 inference(modus_ponens,[status(thm)],[2767, 2262])).
% 27.58/17.80 tff(2769,plain,
% 27.58/17.80 (big_f(f7(c1), f5(c1)) <=> big_f(c2, c1)),
% 27.58/17.80 inference(monotonicity,[status(thm)],[347, 230])).
% 27.58/17.80 tff(2770,plain,
% 27.58/17.80 (big_f(c2, c1) <=> big_f(f7(c1), f5(c1))),
% 27.58/17.80 inference(symmetry,[status(thm)],[2769])).
% 27.58/17.80 tff(2771,plain,
% 27.58/17.80 (big_f(f7(c1), f5(c1))),
% 27.58/17.80 inference(modus_ponens,[status(thm)],[348, 2770])).
% 27.58/17.80 tff(2772,plain,
% 27.58/17.80 ($false),
% 27.58/17.80 inference(unit_resolution,[status(thm)],[730, 2771])).
% 27.58/17.80 tff(2773,plain,((~(f5(c1) = c1)) | big_f(f7(c1), f5(c1)) | (~big_f(c2, c1)) | (~(f7(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.58/17.80 tff(2774,plain,
% 27.58/17.80 (~(f5(c1) = c1)),
% 27.58/17.80 inference(unit_resolution,[status(thm)],[2773, 730, 2768, 120])).
% 27.58/17.80 tff(2775,plain,
% 27.58/17.80 (~(c1 = f5(c1))),
% 27.58/17.80 inference(modus_ponens,[status(thm)],[2774, 2261])).
% 27.58/17.80 tff(2776,plain,
% 27.58/17.80 (big_f(f7(c2), c1) <=> big_f(f7(c1), c1)),
% 27.58/17.80 inference(transitivity,[status(thm)],[2262, 693])).
% 27.58/17.80 tff(2777,plain,
% 27.58/17.80 (big_f(f7(c1), c1)),
% 27.58/17.80 inference(modus_ponens,[status(thm)],[2767, 2776])).
% 27.58/17.80 tff(2778,plain,
% 27.58/17.80 (c2 = f7(c1)),
% 27.58/17.80 inference(symmetry,[status(thm)],[120])).
% 27.58/17.80 tff(2779,plain,
% 27.58/17.80 (f3(c2, c1) = f3(f7(c1), c1)),
% 27.58/17.80 inference(monotonicity,[status(thm)],[2778])).
% 27.58/17.80 tff(2780,plain,
% 27.58/17.80 ((f3(c2, c1) = c1) <=> (f3(f7(c1), c1) = c1)),
% 27.58/17.80 inference(monotonicity,[status(thm)],[2779])).
% 27.58/17.80 tff(2781,plain,
% 27.58/17.80 ((f3(f7(c1), c1) = c1) <=> (f3(c2, c1) = c1)),
% 27.58/17.80 inference(symmetry,[status(thm)],[2780])).
% 27.58/17.80 tff(2782,plain,
% 27.58/17.80 ((c2 = f8(c1)) <=> (f8(c1) = c2)),
% 27.58/17.80 inference(symmetry,[status(thm)],[1670])).
% 27.58/17.80 tff(2783,plain,
% 27.58/17.80 ((~(c2 = f8(c1))) <=> (~(f8(c1) = c2))),
% 27.58/17.80 inference(monotonicity,[status(thm)],[2782])).
% 27.58/17.80 tff(2784,plain,
% 27.58/17.80 ((~big_f(c2, c2)) <=> (~big_f(c2, f10(c1)))),
% 27.58/17.80 inference(monotonicity,[status(thm)],[2719])).
% 27.58/17.80 tff(2785,plain,
% 27.58/17.80 (~big_f(c2, f10(c1))),
% 27.58/17.80 inference(modus_ponens,[status(thm)],[121, 2784])).
% 27.58/17.80 tff(2786,plain,
% 27.58/17.80 (^[X4: $i, X7: $i, X5: $i, X8: $i] : refl(((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7)))) <=> ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7)))))),
% 27.58/17.80 inference(bind,[status(th)],[])).
% 27.58/17.80 tff(2787,plain,
% 27.58/17.80 (![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7)))) <=> ![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))),
% 27.58/17.80 inference(quant_intro,[status(thm)],[2786])).
% 27.58/17.80 tff(2788,plain,
% 27.58/17.80 (![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7)))) <=> ![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))),
% 27.58/17.80 inference(rewrite,[status(thm)],[])).
% 27.58/17.80 tff(2789,plain,
% 27.58/17.80 (^[X4: $i, X7: $i, X5: $i, X8: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_f(f7(X4), X5)) | (X5 = f5(X4))) | (f7(X4) = X4)) <=> ((f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))), (((((~big_f(f7(X4), X5)) | (X5 = f5(X4))) | (f7(X4) = X4)) | big_f(X8, f10(X7))) <=> (((f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5))) | big_f(X8, f10(X7))))), rewrite((((f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5))) | big_f(X8, f10(X7))) <=> (big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))), (((((~big_f(f7(X4), X5)) | (X5 = f5(X4))) | (f7(X4) = X4)) | big_f(X8, f10(X7))) <=> (big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5))))), ((((((~big_f(f7(X4), X5)) | (X5 = f5(X4))) | (f7(X4) = X4)) | big_f(X8, f10(X7))) | (~(X8 = f8(X7)))) <=> ((big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5))) | (~(X8 = f8(X7)))))), rewrite(((big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5))) | (~(X8 = f8(X7)))) <=> (big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))), ((((((~big_f(f7(X4), X5)) | (X5 = f5(X4))) | (f7(X4) = X4)) | big_f(X8, f10(X7))) | (~(X8 = f8(X7)))) <=> (big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7)))))), (((((((~big_f(f7(X4), X5)) | (X5 = f5(X4))) | (f7(X4) = X4)) | big_f(X8, f10(X7))) | (~(X8 = f8(X7)))) | (f10(X7) = X7)) <=> ((big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7)))) | (f10(X7) = X7)))), rewrite(((big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7)))) | (f10(X7) = X7)) <=> ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))), (((((((~big_f(f7(X4), X5)) | (X5 = f5(X4))) | (f7(X4) = X4)) | big_f(X8, f10(X7))) | (~(X8 = f8(X7)))) | (f10(X7) = X7)) <=> ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))))),
% 27.58/17.80 inference(bind,[status(th)],[])).
% 27.58/17.80 tff(2790,plain,
% 27.58/17.80 (![X4: $i, X7: $i, X5: $i, X8: $i] : ((((((~big_f(f7(X4), X5)) | (X5 = f5(X4))) | (f7(X4) = X4)) | big_f(X8, f10(X7))) | (~(X8 = f8(X7)))) | (f10(X7) = X7)) <=> ![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))),
% 27.58/17.80 inference(quant_intro,[status(thm)],[2789])).
% 27.58/17.80 tff(2791,axiom,(![X4: $i, X7: $i, X5: $i, X8: $i] : ((((((~big_f(f7(X4), X5)) | (X5 = f5(X4))) | (f7(X4) = X4)) | big_f(X8, f10(X7))) | (~(X8 = f8(X7)))) | (f10(X7) = X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_20')).
% 27.58/17.80 tff(2792,plain,
% 27.58/17.80 (![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))),
% 27.58/17.80 inference(modus_ponens,[status(thm)],[2791, 2790])).
% 27.58/17.80 tff(2793,plain,
% 27.58/17.80 (![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))),
% 27.58/17.80 inference(modus_ponens,[status(thm)],[2792, 2788])).
% 27.58/17.80 tff(2794,plain,(
% 27.58/17.80 ![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))),
% 27.58/17.80 inference(skolemize,[status(sab)],[2793])).
% 27.58/17.80 tff(2795,plain,
% 27.58/17.80 (![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))),
% 27.58/17.80 inference(modus_ponens,[status(thm)],[2794, 2787])).
% 27.58/17.80 tff(2796,plain,
% 27.58/17.80 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f7(c1) = c1) | big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | (f7(c1) = c1) | big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)))),
% 27.58/17.80 inference(rewrite,[status(thm)],[])).
% 27.58/17.80 tff(2797,plain,
% 27.58/17.80 (((f10(c1) = c1) | big_f(c2, f10(c1)) | (f7(c1) = c1) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)) | (~(c2 = f8(c1)))) <=> ((f7(c1) = c1) | big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)))),
% 27.58/17.80 inference(rewrite,[status(thm)],[])).
% 27.58/17.80 tff(2798,plain,
% 27.58/17.80 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | big_f(c2, f10(c1)) | (f7(c1) = c1) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)) | (~(c2 = f8(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f7(c1) = c1) | big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (c1 = f5(c1)) | (~big_f(f7(c1), c1))))),
% 27.58/17.80 inference(monotonicity,[status(thm)],[2797])).
% 27.58/17.80 tff(2799,plain,
% 27.58/17.80 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | big_f(c2, f10(c1)) | (f7(c1) = c1) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)) | (~(c2 = f8(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | (f7(c1) = c1) | big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)))),
% 27.58/17.80 inference(transitivity,[status(thm)],[2798, 2796])).
% 27.58/17.80 tff(2800,plain,
% 27.58/17.80 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | big_f(c2, f10(c1)) | (f7(c1) = c1) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)) | (~(c2 = f8(c1))))),
% 27.58/17.80 inference(quant_inst,[status(thm)],[])).
% 27.58/17.80 tff(2801,plain,
% 27.58/17.80 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | (f7(c1) = c1) | big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (c1 = f5(c1)) | (~big_f(f7(c1), c1))),
% 27.58/17.80 inference(modus_ponens,[status(thm)],[2800, 2799])).
% 27.58/17.80 tff(2802,plain,
% 27.58/17.80 ((~(c2 = f8(c1))) | (c1 = f5(c1))),
% 27.58/17.80 inference(unit_resolution,[status(thm)],[2801, 2795, 115, 2785, 3, 2777])).
% 27.58/17.80 tff(2803,plain,
% 27.58/17.80 (~(c2 = f8(c1))),
% 27.58/17.80 inference(unit_resolution,[status(thm)],[2802, 2775])).
% 27.58/17.80 tff(2804,plain,
% 27.58/17.80 (~(f8(c1) = c2)),
% 27.58/17.80 inference(modus_ponens,[status(thm)],[2803, 2783])).
% 27.58/17.80 tff(2805,plain,
% 27.58/17.80 (f8(c1) = c1),
% 27.58/17.80 inference(unit_resolution,[status(thm)],[1680, 2804])).
% 27.58/17.80 tff(2806,plain,
% 27.58/17.80 ((f3(f7(c1), c1) = f8(c1)) <=> (f3(f7(c1), c1) = c1)),
% 27.58/17.80 inference(monotonicity,[status(thm)],[2805])).
% 27.58/17.80 tff(2807,plain,
% 27.58/17.80 ((f3(f7(c1), c1) = f8(c1)) <=> (f3(c2, c1) = c1)),
% 27.58/17.80 inference(transitivity,[status(thm)],[2806, 2781])).
% 27.58/17.80 tff(2808,plain,
% 27.58/17.80 (f10(c1) = f7(c1)),
% 27.58/17.80 inference(transitivity,[status(thm)],[15, 2778])).
% 27.58/17.80 tff(2809,plain,
% 27.58/17.80 (big_f(f3(f7(c1), c1), f10(c1)) <=> big_f(f3(f7(c1), c1), f7(c1))),
% 27.58/17.80 inference(monotonicity,[status(thm)],[2808])).
% 27.58/17.80 tff(2810,plain,
% 27.58/17.80 (big_f(f3(f7(c1), c1), f7(c1)) <=> big_f(f3(f7(c1), c1), f10(c1))),
% 27.58/17.80 inference(symmetry,[status(thm)],[2809])).
% 27.58/17.80 tff(2811,plain,
% 27.58/17.80 ((f7(c1) = c4) <=> (c2 = c4)),
% 27.58/17.80 inference(monotonicity,[status(thm)],[120])).
% 27.58/17.80 tff(2812,plain,
% 27.58/17.80 ((c2 = c4) <=> (f7(c1) = c4)),
% 27.58/17.80 inference(symmetry,[status(thm)],[2811])).
% 27.58/17.80 tff(2813,plain,
% 27.58/17.80 (big_f(c2, c2) <=> big_f(f7(c2), f2(c2))),
% 27.58/17.80 inference(symmetry,[status(thm)],[2592])).
% 27.58/17.80 tff(2814,plain,
% 27.58/17.80 (big_f(c2, c2) <=> big_f(c3, f2(c3))),
% 27.58/17.80 inference(transitivity,[status(thm)],[2813, 2268])).
% 27.58/17.80 tff(2815,plain,
% 27.58/17.80 ((~big_f(c2, c2)) <=> (~big_f(c3, f2(c3)))),
% 27.58/17.80 inference(monotonicity,[status(thm)],[2814])).
% 27.58/17.80 tff(2816,plain,
% 27.58/17.80 (~big_f(c3, f2(c3))),
% 27.58/17.80 inference(modus_ponens,[status(thm)],[121, 2815])).
% 27.58/17.80 tff(2817,plain,
% 27.58/17.80 (~(c4 = c2)),
% 27.58/17.80 inference(unit_resolution,[status(thm)],[2327, 2816, 122, 79, 115, 730, 67])).
% 27.58/17.80 tff(2818,plain,
% 27.58/17.80 (c4 = c1),
% 27.58/17.80 inference(unit_resolution,[status(thm)],[461, 2817])).
% 27.58/17.80 tff(2819,plain,
% 27.58/17.80 ((c2 = c4) <=> (c2 = c1)),
% 27.58/17.80 inference(monotonicity,[status(thm)],[2818])).
% 27.58/17.80 tff(2820,plain,
% 27.58/17.80 ((c2 = c1) <=> (c2 = c4)),
% 27.58/17.80 inference(symmetry,[status(thm)],[2819])).
% 27.58/17.80 tff(2821,plain,
% 27.58/17.80 ((c2 = c1) <=> (f7(c1) = c4)),
% 27.58/17.80 inference(transitivity,[status(thm)],[2820, 2812])).
% 27.58/17.80 tff(2822,plain,
% 27.58/17.80 ((~(c2 = c1)) <=> (~(f7(c1) = c4))),
% 27.58/17.80 inference(monotonicity,[status(thm)],[2821])).
% 27.58/17.80 tff(2823,plain,
% 27.58/17.80 (~(f7(c1) = c4)),
% 27.58/17.80 inference(modus_ponens,[status(thm)],[75, 2822])).
% 27.58/17.80 tff(2824,plain,
% 27.58/17.80 (f10(c3) = f10(c2)),
% 27.58/17.80 inference(monotonicity,[status(thm)],[67])).
% 27.58/17.80 tff(2825,plain,
% 27.58/17.80 ((f10(c3) = c3) <=> (f10(c2) = c2)),
% 27.58/17.80 inference(monotonicity,[status(thm)],[2824, 67])).
% 27.58/17.80 tff(2826,plain,
% 27.58/17.80 ((f10(c2) = c2) <=> (f10(c3) = c3)),
% 27.58/17.80 inference(symmetry,[status(thm)],[2825])).
% 27.58/17.80 tff(2827,plain,
% 27.58/17.80 (f10(c3) = c3),
% 27.58/17.80 inference(modus_ponens,[status(thm)],[122, 2826])).
% 27.58/17.80 tff(2828,assumption,(~(f10(c3) = c3)), introduced(assumption)).
% 27.58/17.80 tff(2829,plain,
% 27.58/17.80 ($false),
% 27.58/17.80 inference(unit_resolution,[status(thm)],[2828, 2827])).
% 27.58/17.80 tff(2830,plain,((~(f10(c2) = c2)) | (f10(c3) = c3) | (~(c3 = c2))), inference(lemma,lemma(discharge,[]))).
% 27.58/17.80 tff(2831,plain,
% 27.58/17.80 (f10(c3) = c3),
% 27.58/17.80 inference(unit_resolution,[status(thm)],[2830, 67, 122])).
% 27.58/17.80 tff(2832,plain,
% 27.58/17.80 (f10(c3) = c2),
% 27.58/17.80 inference(transitivity,[status(thm)],[2831, 67])).
% 27.58/17.80 tff(2833,plain,
% 27.58/17.80 (big_f(f8(c1), f10(c3)) <=> big_f(c1, c2)),
% 27.58/17.80 inference(monotonicity,[status(thm)],[2805, 2832])).
% 27.58/17.80 tff(2834,plain,
% 27.58/17.80 (c3 = f10(c3)),
% 27.58/17.80 inference(symmetry,[status(thm)],[2831])).
% 27.58/17.80 tff(2835,plain,
% 27.58/17.80 (f10(c1) = f10(c3)),
% 27.58/17.80 inference(transitivity,[status(thm)],[15, 69, 2834])).
% 27.58/17.80 tff(2836,plain,
% 27.58/17.80 (big_f(f8(c1), f10(c1)) <=> big_f(f8(c1), f10(c3))),
% 27.58/17.80 inference(monotonicity,[status(thm)],[2835])).
% 27.58/17.80 tff(2837,plain,
% 27.58/17.80 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f7(c1) = c1) | (f10(c1) = c1) | big_f(f7(c1), f5(c1)) | big_f(f8(c1), f10(c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(c1) = c1) | (f10(c1) = c1) | big_f(f7(c1), f5(c1)) | big_f(f8(c1), f10(c1)))),
% 27.58/17.80 inference(rewrite,[status(thm)],[])).
% 27.58/17.80 tff(2838,plain,
% 27.58/17.80 (($false | (f10(c1) = c1) | big_f(f8(c1), f10(c1)) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)) | $false) <=> ((f7(c1) = c1) | (f10(c1) = c1) | big_f(f7(c1), f5(c1)) | big_f(f8(c1), f10(c1)))),
% 27.58/17.80 inference(rewrite,[status(thm)],[])).
% 27.58/17.80 tff(2839,plain,
% 27.58/17.80 ((f8(c1) = f8(c1)) <=> $true),
% 27.58/17.80 inference(rewrite,[status(thm)],[])).
% 27.58/17.80 tff(2840,plain,
% 27.58/17.80 ((~(f8(c1) = f8(c1))) <=> (~$true)),
% 27.58/17.80 inference(monotonicity,[status(thm)],[2839])).
% 27.58/17.80 tff(2841,plain,
% 27.58/17.80 ((~(f8(c1) = f8(c1))) <=> $false),
% 27.58/17.80 inference(transitivity,[status(thm)],[2840, 270])).
% 27.58/17.80 tff(2842,plain,
% 27.58/17.80 (((~(f5(c1) = f5(c1))) | (f10(c1) = c1) | big_f(f8(c1), f10(c1)) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (~(f8(c1) = f8(c1)))) <=> ($false | (f10(c1) = c1) | big_f(f8(c1), f10(c1)) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)) | $false)),
% 27.58/17.80 inference(monotonicity,[status(thm)],[273, 2841])).
% 27.58/17.80 tff(2843,plain,
% 27.58/17.80 (((~(f5(c1) = f5(c1))) | (f10(c1) = c1) | big_f(f8(c1), f10(c1)) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (~(f8(c1) = f8(c1)))) <=> ((f7(c1) = c1) | (f10(c1) = c1) | big_f(f7(c1), f5(c1)) | big_f(f8(c1), f10(c1)))),
% 27.58/17.80 inference(transitivity,[status(thm)],[2842, 2838])).
% 27.58/17.80 tff(2844,plain,
% 27.58/17.80 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(f5(c1) = f5(c1))) | (f10(c1) = c1) | big_f(f8(c1), f10(c1)) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (~(f8(c1) = f8(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f7(c1) = c1) | (f10(c1) = c1) | big_f(f7(c1), f5(c1)) | big_f(f8(c1), f10(c1))))),
% 27.58/17.80 inference(monotonicity,[status(thm)],[2843])).
% 27.58/17.80 tff(2845,plain,
% 27.58/17.80 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(f5(c1) = f5(c1))) | (f10(c1) = c1) | big_f(f8(c1), f10(c1)) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (~(f8(c1) = f8(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(c1) = c1) | (f10(c1) = c1) | big_f(f7(c1), f5(c1)) | big_f(f8(c1), f10(c1)))),
% 27.58/17.80 inference(transitivity,[status(thm)],[2844, 2837])).
% 27.58/17.80 tff(2846,plain,
% 27.58/17.80 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(f5(c1) = f5(c1))) | (f10(c1) = c1) | big_f(f8(c1), f10(c1)) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (~(f8(c1) = f8(c1))))),
% 27.58/17.80 inference(quant_inst,[status(thm)],[])).
% 27.58/17.80 tff(2847,plain,
% 27.58/17.80 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(c1) = c1) | (f10(c1) = c1) | big_f(f7(c1), f5(c1)) | big_f(f8(c1), f10(c1))),
% 27.58/17.80 inference(modus_ponens,[status(thm)],[2846, 2845])).
% 27.58/17.80 tff(2848,plain,
% 27.58/17.80 ((f7(c1) = c1) | (f10(c1) = c1) | big_f(f7(c1), f5(c1)) | big_f(f8(c1), f10(c1))),
% 27.58/17.80 inference(unit_resolution,[status(thm)],[2847, 1745])).
% 27.58/17.80 tff(2849,plain,
% 27.58/17.80 (big_f(f8(c1), f10(c1))),
% 27.58/17.80 inference(unit_resolution,[status(thm)],[2848, 730, 115, 3])).
% 27.58/17.80 tff(2850,plain,
% 27.58/17.80 (big_f(f8(c1), f10(c3))),
% 27.58/17.80 inference(modus_ponens,[status(thm)],[2849, 2836])).
% 27.58/17.80 tff(2851,plain,
% 27.58/17.80 (big_f(c1, c2)),
% 27.58/17.80 inference(modus_ponens,[status(thm)],[2850, 2833])).
% 27.58/17.80 tff(2852,plain,
% 27.58/17.80 (c2 = f2(c2)),
% 27.58/17.80 inference(modus_ponens,[status(thm)],[1319, 1435])).
% 27.58/17.80 tff(2853,assumption,(c2 = f2(c2)), introduced(assumption)).
% 27.58/17.80 tff(2854,assumption,(~big_f(f3(f7(c1), c1), f7(c1))), introduced(assumption)).
% 27.58/17.80 tff(2855,plain,
% 27.58/17.80 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (f7(c1) = c4) | (f3(f7(c1), c1) = c1) | big_f(f3(f7(c1), c1), f7(c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (f7(c1) = c4) | (f3(f7(c1), c1) = c1) | big_f(f3(f7(c1), c1), f7(c1)))),
% 27.58/17.81 inference(rewrite,[status(thm)],[])).
% 27.58/17.81 tff(2856,plain,
% 27.58/17.81 (((~(c2 = c3)) | (~(c2 = f2(c2))) | (f7(c1) = c4) | (f3(f7(c1), c1) = c1) | big_f(f3(f7(c1), c1), f7(c1)) | big_f(c2, c2)) <=> ((~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (f7(c1) = c4) | (f3(f7(c1), c1) = c1) | big_f(f3(f7(c1), c1), f7(c1)))),
% 27.58/17.81 inference(rewrite,[status(thm)],[])).
% 27.58/17.81 tff(2857,plain,
% 27.58/17.81 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | (f7(c1) = c4) | (f3(f7(c1), c1) = c1) | big_f(f3(f7(c1), c1), f7(c1)) | big_f(c2, c2))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (f7(c1) = c4) | (f3(f7(c1), c1) = c1) | big_f(f3(f7(c1), c1), f7(c1))))),
% 27.58/17.81 inference(monotonicity,[status(thm)],[2856])).
% 27.58/17.81 tff(2858,plain,
% 27.58/17.81 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | (f7(c1) = c4) | (f3(f7(c1), c1) = c1) | big_f(f3(f7(c1), c1), f7(c1)) | big_f(c2, c2))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (f7(c1) = c4) | (f3(f7(c1), c1) = c1) | big_f(f3(f7(c1), c1), f7(c1)))),
% 27.58/17.81 inference(transitivity,[status(thm)],[2857, 2855])).
% 27.58/17.81 tff(2859,plain,
% 27.58/17.81 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | (f7(c1) = c4) | (f3(f7(c1), c1) = c1) | big_f(f3(f7(c1), c1), f7(c1)) | big_f(c2, c2))),
% 27.58/17.81 inference(quant_inst,[status(thm)],[])).
% 27.58/17.81 tff(2860,plain,
% 27.58/17.81 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (f7(c1) = c4) | (f3(f7(c1), c1) = c1) | big_f(f3(f7(c1), c1), f7(c1))),
% 27.58/17.81 inference(modus_ponens,[status(thm)],[2859, 2858])).
% 27.58/17.81 tff(2861,plain,
% 27.58/17.81 ((~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (f7(c1) = c4) | (f3(f7(c1), c1) = c1) | big_f(f3(f7(c1), c1), f7(c1))),
% 27.58/17.81 inference(unit_resolution,[status(thm)],[2860, 1459])).
% 27.58/17.81 tff(2862,plain,
% 27.58/17.81 (f3(f7(c1), c1) = c1),
% 27.58/17.81 inference(unit_resolution,[status(thm)],[2861, 2854, 1344, 2853, 121, 1000])).
% 27.58/17.81 tff(2863,plain,
% 27.58/17.81 (big_f(f3(f7(c1), c1), f7(c1)) <=> big_f(c1, c2)),
% 27.58/17.81 inference(monotonicity,[status(thm)],[2862, 347])).
% 27.58/17.81 tff(2864,plain,
% 27.58/17.81 (big_f(c1, c2) <=> big_f(f3(f7(c1), c1), f7(c1))),
% 27.58/17.81 inference(symmetry,[status(thm)],[2863])).
% 27.58/17.81 tff(2865,assumption,(big_f(c1, c2)), introduced(assumption)).
% 27.58/17.81 tff(2866,plain,
% 27.58/17.81 (big_f(f3(f7(c1), c1), f7(c1))),
% 27.58/17.81 inference(modus_ponens,[status(thm)],[2865, 2864])).
% 27.58/17.81 tff(2867,plain,
% 27.58/17.81 ($false),
% 27.58/17.81 inference(unit_resolution,[status(thm)],[2854, 2866])).
% 27.58/17.81 tff(2868,plain,(big_f(f3(f7(c1), c1), f7(c1)) | (~big_f(c1, c2)) | (~(f7(c1) = c2)) | (~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (f7(c1) = c4)), inference(lemma,lemma(discharge,[]))).
% 27.58/17.81 tff(2869,plain,
% 27.58/17.81 (big_f(f3(f7(c1), c1), f7(c1))),
% 27.58/17.81 inference(unit_resolution,[status(thm)],[2868, 2852, 120, 1335, 2851, 121, 2823])).
% 27.58/17.81 tff(2870,plain,
% 27.58/17.81 (big_f(f3(f7(c1), c1), f10(c1))),
% 27.58/17.81 inference(modus_ponens,[status(thm)],[2869, 2810])).
% 27.58/17.81 tff(2871,plain,
% 27.58/17.81 (f5(c1) = c2),
% 27.58/17.81 inference(unit_resolution,[status(thm)],[1708, 2774])).
% 27.58/17.81 tff(2872,plain,
% 27.58/17.81 (c2 = f5(c1)),
% 27.58/17.81 inference(modus_ponens,[status(thm)],[2871, 155])).
% 27.58/17.81 tff(2873,plain,
% 27.58/17.81 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (f10(c1) = c1) | (f3(f7(c1), c1) = f8(c1)) | (~big_f(f3(f7(c1), c1), f10(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (f10(c1) = c1) | (f3(f7(c1), c1) = f8(c1)) | (~big_f(f3(f7(c1), c1), f10(c1))))),
% 27.58/17.81 inference(rewrite,[status(thm)],[])).
% 27.58/17.81 tff(2874,plain,
% 27.58/17.81 (((~(c2 = f5(c1))) | (f10(c1) = c1) | (f3(f7(c1), c1) = f8(c1)) | (~big_f(f3(f7(c1), c1), f10(c1))) | (f7(c1) = c1) | big_f(f7(c1), c2)) <=> ((~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (f10(c1) = c1) | (f3(f7(c1), c1) = f8(c1)) | (~big_f(f3(f7(c1), c1), f10(c1))))),
% 27.58/17.81 inference(rewrite,[status(thm)],[])).
% 27.58/17.81 tff(2875,plain,
% 27.58/17.81 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c2 = f5(c1))) | (f10(c1) = c1) | (f3(f7(c1), c1) = f8(c1)) | (~big_f(f3(f7(c1), c1), f10(c1))) | (f7(c1) = c1) | big_f(f7(c1), c2))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (f10(c1) = c1) | (f3(f7(c1), c1) = f8(c1)) | (~big_f(f3(f7(c1), c1), f10(c1)))))),
% 27.58/17.81 inference(monotonicity,[status(thm)],[2874])).
% 27.58/17.81 tff(2876,plain,
% 27.58/17.81 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c2 = f5(c1))) | (f10(c1) = c1) | (f3(f7(c1), c1) = f8(c1)) | (~big_f(f3(f7(c1), c1), f10(c1))) | (f7(c1) = c1) | big_f(f7(c1), c2))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (f10(c1) = c1) | (f3(f7(c1), c1) = f8(c1)) | (~big_f(f3(f7(c1), c1), f10(c1))))),
% 27.58/17.81 inference(transitivity,[status(thm)],[2875, 2873])).
% 27.58/17.81 tff(2877,plain,
% 27.58/17.81 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c2 = f5(c1))) | (f10(c1) = c1) | (f3(f7(c1), c1) = f8(c1)) | (~big_f(f3(f7(c1), c1), f10(c1))) | (f7(c1) = c1) | big_f(f7(c1), c2))),
% 27.58/17.81 inference(quant_inst,[status(thm)],[])).
% 27.58/17.81 tff(2878,plain,
% 27.58/17.81 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (f10(c1) = c1) | (f3(f7(c1), c1) = f8(c1)) | (~big_f(f3(f7(c1), c1), f10(c1)))),
% 27.58/17.81 inference(modus_ponens,[status(thm)],[2877, 2876])).
% 27.58/17.81 tff(2879,plain,
% 27.58/17.81 ((f3(f7(c1), c1) = f8(c1)) | (~big_f(f3(f7(c1), c1), f10(c1)))),
% 27.58/17.81 inference(unit_resolution,[status(thm)],[2878, 705, 2872, 1726, 115, 3])).
% 27.58/17.81 tff(2880,plain,
% 27.58/17.81 (f3(f7(c1), c1) = f8(c1)),
% 27.58/17.81 inference(unit_resolution,[status(thm)],[2879, 2870])).
% 27.58/17.81 tff(2881,plain,
% 27.58/17.81 (f3(c2, c1) = c1),
% 27.58/17.81 inference(modus_ponens,[status(thm)],[2880, 2807])).
% 27.58/17.81 tff(2882,plain,
% 27.58/17.81 (big_f(f3(c2, c1), c2) <=> big_f(f3(f7(c1), c1), f7(c1))),
% 27.58/17.81 inference(monotonicity,[status(thm)],[2779, 2778])).
% 27.58/17.81 tff(2883,plain,
% 27.58/17.81 (big_f(f3(f7(c1), c1), f7(c1)) <=> big_f(f3(c2, c1), c2)),
% 27.58/17.81 inference(symmetry,[status(thm)],[2882])).
% 27.58/17.81 tff(2884,plain,
% 27.58/17.81 (big_f(f3(c2, c1), c2)),
% 27.58/17.81 inference(modus_ponens,[status(thm)],[2869, 2883])).
% 27.58/17.81 tff(2885,plain,
% 27.58/17.81 ((~(c2 = c1)) <=> (~(c2 = c4))),
% 27.58/17.81 inference(monotonicity,[status(thm)],[2820])).
% 27.58/17.81 tff(2886,plain,
% 27.58/17.81 (~(c2 = c4)),
% 27.58/17.81 inference(modus_ponens,[status(thm)],[75, 2885])).
% 27.58/17.81 tff(2887,plain,
% 27.58/17.81 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (c2 = c4) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (c2 = c4) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)))),
% 27.58/17.81 inference(rewrite,[status(thm)],[])).
% 27.58/17.81 tff(2888,plain,
% 27.58/17.81 (((~(c2 = c3)) | (~(c2 = f2(c2))) | (c2 = c4) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)) | big_f(c2, c2)) <=> ((~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (c2 = c4) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)))),
% 27.58/17.81 inference(rewrite,[status(thm)],[])).
% 27.58/17.81 tff(2889,plain,
% 27.58/17.81 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | (c2 = c4) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)) | big_f(c2, c2))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (c2 = c4) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2))))),
% 27.58/17.81 inference(monotonicity,[status(thm)],[2888])).
% 27.58/17.81 tff(2890,plain,
% 27.58/17.81 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | (c2 = c4) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)) | big_f(c2, c2))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (c2 = c4) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)))),
% 27.58/17.81 inference(transitivity,[status(thm)],[2889, 2887])).
% 27.58/17.81 tff(2891,plain,
% 27.58/17.81 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | (c2 = c4) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)) | big_f(c2, c2))),
% 27.58/17.81 inference(quant_inst,[status(thm)],[])).
% 27.58/17.81 tff(2892,plain,
% 27.58/17.81 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (c2 = c4) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2))),
% 27.58/17.81 inference(modus_ponens,[status(thm)],[2891, 2890])).
% 27.58/17.81 tff(2893,plain,
% 27.58/17.81 ((~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2))),
% 27.58/17.81 inference(unit_resolution,[status(thm)],[2892, 1398, 2886, 121, 1335, 2852])).
% 27.58/17.81 tff(2894,plain,
% 27.58/17.81 (~(f3(c2, c1) = c1)),
% 27.58/17.81 inference(unit_resolution,[status(thm)],[2893, 2884])).
% 27.58/17.81 tff(2895,plain,
% 27.58/17.81 ($false),
% 27.58/17.81 inference(unit_resolution,[status(thm)],[2894, 2881])).
% 27.58/17.81 tff(2896,plain,((~(f2(c3) = c2)) | big_f(c2, c2) | (f7(c1) = c1) | (f10(c1) = c1) | (~(f10(c2) = c2)) | (~(f4(c4) = c2)) | big_f(f7(c1), f5(c1)) | (~(c3 = c2)) | (~(f7(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.58/17.81 tff(2897,plain,
% 27.58/17.81 (~(f2(c3) = c2)),
% 27.58/17.81 inference(unit_resolution,[status(thm)],[2896, 730, 115, 3, 122, 79, 121, 67, 77])).
% 27.58/17.81 tff(2898,plain,
% 27.58/17.81 (f2(c3) = c1),
% 27.58/17.81 inference(unit_resolution,[status(thm)],[1273, 2897])).
% 27.58/17.81 tff(2899,plain,
% 27.58/17.81 (f9(c2, c1) = f9(f10(c2), f2(c3))),
% 27.58/17.81 inference(monotonicity,[status(thm)],[216, 1367])).
% 27.58/17.81 tff(2900,plain,
% 27.58/17.81 (f9(c2, c1) = c1),
% 27.58/17.81 inference(transitivity,[status(thm)],[2899, 1252])).
% 27.58/17.81 tff(2901,plain,
% 27.58/17.81 (big_f(f9(c2, c1), f10(c2)) <=> big_f(c1, c2)),
% 27.58/17.81 inference(monotonicity,[status(thm)],[2900, 122])).
% 27.58/17.81 tff(2902,plain,
% 27.58/17.81 (big_f(c1, c2) <=> big_f(f9(c2, c1), f10(c2))),
% 27.58/17.81 inference(symmetry,[status(thm)],[2901])).
% 27.58/17.81 tff(2903,plain,
% 27.58/17.81 (big_f(f9(c2, c1), f10(c2))),
% 27.58/17.81 inference(modus_ponens,[status(thm)],[2865, 2902])).
% 27.58/17.81 tff(2904,plain,
% 27.58/17.81 ((f9(c2, c1) = c1) <=> (f9(f10(c2), f2(c3)) = c1)),
% 27.58/17.81 inference(monotonicity,[status(thm)],[2899])).
% 27.58/17.81 tff(2905,plain,
% 27.58/17.81 ((f9(f10(c2), f2(c3)) = c1) <=> (f9(c2, c1) = c1)),
% 27.58/17.81 inference(symmetry,[status(thm)],[2904])).
% 27.58/17.81 tff(2906,plain,
% 27.58/17.81 (f9(c2, c1) = c1),
% 27.58/17.81 inference(modus_ponens,[status(thm)],[1252, 2905])).
% 27.58/17.81 tff(2907,assumption,(~big_f(f7(c1), c2)), introduced(assumption)).
% 27.58/17.81 tff(2908,assumption,(c2 = f5(c1)), introduced(assumption)).
% 27.58/17.81 tff(2909,plain,
% 27.58/17.81 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))))),
% 27.58/17.81 inference(rewrite,[status(thm)],[])).
% 27.58/17.81 tff(2910,plain,
% 27.58/17.81 (((~(f10(c2) = c2)) | (f7(c1) = c1) | big_f(f7(c1), c2) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))) | (~(c2 = f5(c1)))) <=> ((~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))))),
% 27.58/17.81 inference(rewrite,[status(thm)],[])).
% 27.58/17.81 tff(2911,plain,
% 27.58/17.81 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c1) = c1) | big_f(f7(c1), c2) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))) | (~(c2 = f5(c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2)))))),
% 27.58/17.81 inference(monotonicity,[status(thm)],[2910])).
% 27.58/17.81 tff(2912,plain,
% 27.58/17.81 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c1) = c1) | big_f(f7(c1), c2) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))) | (~(c2 = f5(c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))))),
% 27.58/17.81 inference(transitivity,[status(thm)],[2911, 2909])).
% 27.58/17.81 tff(2913,plain,
% 27.58/17.81 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c1) = c1) | big_f(f7(c1), c2) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))) | (~(c2 = f5(c1))))),
% 27.58/17.81 inference(quant_inst,[status(thm)],[])).
% 27.58/17.81 tff(2914,plain,
% 27.58/17.81 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2)))),
% 27.58/17.81 inference(modus_ponens,[status(thm)],[2913, 2912])).
% 27.58/17.81 tff(2915,plain,
% 27.58/17.81 ($false),
% 27.58/17.81 inference(unit_resolution,[status(thm)],[2914, 783, 2908, 2907, 115, 122, 2906, 2903])).
% 27.58/17.81 tff(2916,plain,((~(f9(f10(c2), f2(c3)) = c1)) | (~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (~big_f(c1, c2)) | (~(f2(c3) = c1))), inference(lemma,lemma(discharge,[]))).
% 27.58/17.81 tff(2917,plain,
% 27.58/17.81 (~(f9(f10(c2), f2(c3)) = c1)),
% 27.58/17.81 inference(unit_resolution,[status(thm)],[2916, 2872, 1726, 115, 122, 2851, 2898])).
% 27.58/17.81 tff(2918,plain,
% 27.58/17.81 (f9(f10(c2), f2(c3)) = c2),
% 27.58/17.81 inference(unit_resolution,[status(thm)],[1245, 2917])).
% 27.58/17.81 tff(2919,plain,
% 27.58/17.81 (c1 = f2(c3)),
% 27.58/17.81 inference(symmetry,[status(thm)],[2898])).
% 27.58/17.81 tff(2920,plain,
% 27.58/17.81 (f9(c2, c1) = f9(f10(c2), f2(c3))),
% 27.58/17.81 inference(monotonicity,[status(thm)],[216, 2919])).
% 27.58/17.81 tff(2921,plain,
% 27.58/17.81 (f9(c2, c1) = c2),
% 27.58/17.81 inference(transitivity,[status(thm)],[2920, 2918])).
% 27.58/17.81 tff(2922,plain,
% 27.58/17.81 (big_f(f9(c2, c1), f10(c2)) <=> big_f(c2, c2)),
% 27.58/17.81 inference(monotonicity,[status(thm)],[2921, 122])).
% 27.58/17.81 tff(2923,plain,
% 27.58/17.81 (big_f(c2, c2) <=> big_f(f9(c2, c1), f10(c2))),
% 27.58/17.81 inference(symmetry,[status(thm)],[2922])).
% 27.58/17.81 tff(2924,plain,
% 27.58/17.81 ((~big_f(c2, c2)) <=> (~big_f(f9(c2, c1), f10(c2)))),
% 27.58/17.81 inference(monotonicity,[status(thm)],[2923])).
% 27.58/17.81 tff(2925,plain,
% 27.58/17.81 (~big_f(f9(c2, c1), f10(c2))),
% 27.58/17.81 inference(modus_ponens,[status(thm)],[121, 2924])).
% 27.58/17.81 tff(2926,plain,
% 27.58/17.81 (f9(f10(c2), f2(c3)) = f9(c2, c1)),
% 27.58/17.81 inference(symmetry,[status(thm)],[2920])).
% 27.58/17.81 tff(2927,plain,
% 27.58/17.81 ((f9(f10(c2), f2(c3)) = c1) <=> (f9(c2, c1) = c1)),
% 27.58/17.81 inference(monotonicity,[status(thm)],[2926])).
% 27.58/17.81 tff(2928,plain,
% 27.58/17.81 ((~(f9(f10(c2), f2(c3)) = c1)) <=> (~(f9(c2, c1) = c1))),
% 27.58/17.81 inference(monotonicity,[status(thm)],[2927])).
% 27.58/17.81 tff(2929,plain,
% 27.58/17.81 (~(f9(c2, c1) = c1)),
% 27.58/17.81 inference(modus_ponens,[status(thm)],[2917, 2928])).
% 27.58/17.81 tff(2930,plain,
% 27.58/17.81 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(c1) = c1) | (~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)))),
% 27.58/17.81 inference(rewrite,[status(thm)],[])).
% 27.58/17.81 tff(2931,plain,
% 27.58/17.81 (((~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (f7(c1) = c1) | (c1 = f5(c1)) | (~big_f(f7(c1), c1))) <=> ((f7(c1) = c1) | (~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)))),
% 27.58/17.81 inference(rewrite,[status(thm)],[])).
% 27.58/17.81 tff(2932,plain,
% 27.58/17.81 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (f7(c1) = c1) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(c1) = c1) | (~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (c1 = f5(c1)) | (~big_f(f7(c1), c1))))),
% 27.58/17.81 inference(monotonicity,[status(thm)],[2931])).
% 27.58/17.81 tff(2933,plain,
% 27.58/17.81 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (f7(c1) = c1) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)))),
% 27.58/17.81 inference(transitivity,[status(thm)],[2932, 2930])).
% 27.58/17.81 tff(2934,plain,
% 27.58/17.81 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (f7(c1) = c1) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)))),
% 27.58/17.81 inference(quant_inst,[status(thm)],[])).
% 27.58/17.81 tff(2935,plain,
% 27.58/17.81 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (c1 = f5(c1)) | (~big_f(f7(c1), c1))),
% 27.58/17.81 inference(modus_ponens,[status(thm)],[2934, 2933])).
% 27.58/17.81 tff(2936,plain,
% 27.58/17.81 ($false),
% 27.58/17.81 inference(unit_resolution,[status(thm)],[2935, 676, 115, 122, 2929, 2925, 2777, 2775])).
% 27.58/17.81 tff(2937,plain,(big_f(f7(c1), f5(c1)) | (f7(c1) = c1) | (~(f10(c2) = c2)) | big_f(c2, c2) | (f10(c1) = c1) | (~(f4(c4) = c2)) | (~(c3 = c2)) | (~(f7(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.58/17.81 tff(2938,plain,
% 27.58/17.81 (big_f(f7(c1), f5(c1))),
% 27.58/17.81 inference(unit_resolution,[status(thm)],[2937, 121, 122, 115, 3, 79, 67, 77])).
% 27.58/17.81 tff(2939,plain,
% 27.58/17.81 (~(f5(c1) = c2)),
% 27.58/17.81 inference(unit_resolution,[status(thm)],[1715, 2938, 121, 120])).
% 27.58/17.81 tff(2940,plain,
% 27.58/17.81 (f5(c1) = c1),
% 27.58/17.81 inference(unit_resolution,[status(thm)],[1708, 2939])).
% 27.58/17.81 tff(2941,plain,
% 27.58/17.81 (c1 = f5(c1)),
% 27.58/17.81 inference(symmetry,[status(thm)],[230])).
% 27.58/17.81 tff(2942,plain,
% 27.58/17.81 (f6(c2, c1) = f6(f7(c2), f5(c1))),
% 27.58/17.81 inference(monotonicity,[status(thm)],[82, 2941])).
% 27.58/17.81 tff(2943,plain,
% 27.58/17.81 (f6(f7(c2), f5(c1)) = f6(c2, c1)),
% 27.58/17.81 inference(symmetry,[status(thm)],[2942])).
% 27.58/17.81 tff(2944,plain,
% 27.58/17.81 ((f6(f7(c2), f5(c1)) = c1) <=> (f6(c2, c1) = c1)),
% 27.58/17.81 inference(monotonicity,[status(thm)],[2943])).
% 27.58/17.81 tff(2945,plain,
% 27.58/17.81 ((~(f6(f7(c2), f5(c1)) = c1)) <=> (~(f6(c2, c1) = c1))),
% 27.58/17.81 inference(monotonicity,[status(thm)],[2944])).
% 27.58/17.81 tff(2946,assumption,(~big_f(c2, f10(c1))), introduced(assumption)).
% 27.58/17.81 tff(2947,assumption,(f6(f7(c2), f5(c1)) = c1), introduced(assumption)).
% 27.58/17.81 tff(2948,plain,
% 27.58/17.81 (f6(c2, c1) = c1),
% 27.58/17.81 inference(transitivity,[status(thm)],[2942, 2947])).
% 27.58/17.81 tff(2949,plain,
% 27.58/17.81 (f6(c2, f6(c2, c1)) = f6(c2, c1)),
% 27.58/17.81 inference(monotonicity,[status(thm)],[2948])).
% 27.58/17.81 tff(2950,plain,
% 27.58/17.81 (f6(c2, f6(c2, c1)) = c1),
% 27.58/17.81 inference(transitivity,[status(thm)],[2949, 2942, 2947])).
% 27.58/17.81 tff(2951,plain,
% 27.58/17.81 (big_f(f7(c2), f6(c2, f6(c2, c1))) <=> big_f(c2, c1)),
% 27.58/17.81 inference(monotonicity,[status(thm)],[77, 2950])).
% 27.58/17.81 tff(2952,plain,
% 27.58/17.81 (big_f(c2, c1) <=> big_f(f7(c2), f6(c2, f6(c2, c1)))),
% 27.58/17.81 inference(symmetry,[status(thm)],[2951])).
% 27.58/17.81 tff(2953,plain,
% 27.58/17.81 (big_f(f7(c2), f6(c2, f6(c2, c1)))),
% 27.58/17.81 inference(modus_ponens,[status(thm)],[348, 2952])).
% 27.58/17.81 tff(2954,plain,
% 27.58/17.81 (^[X6: $i, X4: $i, X7: $i, X8: $i] : refl(((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))) <=> ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))))),
% 27.58/17.81 inference(bind,[status(th)],[])).
% 27.58/17.81 tff(2955,plain,
% 27.58/17.81 (![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))) <=> ![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))),
% 27.58/17.81 inference(quant_intro,[status(thm)],[2954])).
% 27.58/17.81 tff(2956,plain,
% 27.58/17.81 (![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))) <=> ![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))),
% 27.58/17.81 inference(rewrite,[status(thm)],[])).
% 27.58/17.81 tff(2957,plain,
% 27.58/17.81 (^[X6: $i, X4: $i, X7: $i, X8: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~big_f(f7(X4), f6(X4, X6))) | (~(f6(X4, X6) = X6))) <=> ((~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))), ((((~big_f(f7(X4), f6(X4, X6))) | (~(f6(X4, X6) = X6))) | (~(f7(X4) = X4))) <=> (((~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))) | (~(f7(X4) = X4))))), rewrite((((~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))) | (~(f7(X4) = X4))) <=> ((~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))), ((((~big_f(f7(X4), f6(X4, X6))) | (~(f6(X4, X6) = X6))) | (~(f7(X4) = X4))) <=> ((~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))))), (((((~big_f(f7(X4), f6(X4, X6))) | (~(f6(X4, X6) = X6))) | (~(f7(X4) = X4))) | big_f(X8, f10(X7))) <=> (((~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))) | big_f(X8, f10(X7))))), rewrite((((~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))) | big_f(X8, f10(X7))) <=> (big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))), (((((~big_f(f7(X4), f6(X4, X6))) | (~(f6(X4, X6) = X6))) | (~(f7(X4) = X4))) | big_f(X8, f10(X7))) <=> (big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))))), ((((((~big_f(f7(X4), f6(X4, X6))) | (~(f6(X4, X6) = X6))) | (~(f7(X4) = X4))) | big_f(X8, f10(X7))) | (~(X8 = f8(X7)))) <=> ((big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))) | (~(X8 = f8(X7)))))), rewrite(((big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))) | (~(X8 = f8(X7)))) <=> (big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))), ((((((~big_f(f7(X4), f6(X4, X6))) | (~(f6(X4, X6) = X6))) | (~(f7(X4) = X4))) | big_f(X8, f10(X7))) | (~(X8 = f8(X7)))) <=> (big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))))), (((((((~big_f(f7(X4), f6(X4, X6))) | (~(f6(X4, X6) = X6))) | (~(f7(X4) = X4))) | big_f(X8, f10(X7))) | (~(X8 = f8(X7)))) | (f10(X7) = X7)) <=> ((big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))) | (f10(X7) = X7)))), rewrite(((big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6)))) | (f10(X7) = X7)) <=> ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))), (((((((~big_f(f7(X4), f6(X4, X6))) | (~(f6(X4, X6) = X6))) | (~(f7(X4) = X4))) | big_f(X8, f10(X7))) | (~(X8 = f8(X7)))) | (f10(X7) = X7)) <=> ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))))),
% 27.58/17.82 inference(bind,[status(th)],[])).
% 27.58/17.82 tff(2958,plain,
% 27.58/17.82 (![X6: $i, X4: $i, X7: $i, X8: $i] : ((((((~big_f(f7(X4), f6(X4, X6))) | (~(f6(X4, X6) = X6))) | (~(f7(X4) = X4))) | big_f(X8, f10(X7))) | (~(X8 = f8(X7)))) | (f10(X7) = X7)) <=> ![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))),
% 27.58/17.82 inference(quant_intro,[status(thm)],[2957])).
% 27.58/17.82 tff(2959,axiom,(![X6: $i, X4: $i, X7: $i, X8: $i] : ((((((~big_f(f7(X4), f6(X4, X6))) | (~(f6(X4, X6) = X6))) | (~(f7(X4) = X4))) | big_f(X8, f10(X7))) | (~(X8 = f8(X7)))) | (f10(X7) = X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_32')).
% 27.58/17.82 tff(2960,plain,
% 27.58/17.82 (![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))),
% 27.58/17.82 inference(modus_ponens,[status(thm)],[2959, 2958])).
% 27.58/17.82 tff(2961,plain,
% 27.58/17.82 (![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))),
% 27.58/17.82 inference(modus_ponens,[status(thm)],[2960, 2956])).
% 27.58/17.82 tff(2962,plain,(
% 27.58/17.82 ![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))),
% 27.58/17.82 inference(skolemize,[status(sab)],[2961])).
% 27.58/17.82 tff(2963,plain,
% 27.58/17.82 (![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))),
% 27.58/17.82 inference(modus_ponens,[status(thm)],[2962, 2955])).
% 27.58/17.82 tff(2964,plain,
% 27.58/17.82 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (~(f7(c2) = c2)) | (~big_f(f7(c2), f6(c2, f6(c2, c1)))) | (~(f6(c2, f6(c2, c1)) = f6(c2, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (~(f7(c2) = c2)) | (~big_f(f7(c2), f6(c2, f6(c2, c1)))) | (~(f6(c2, f6(c2, c1)) = f6(c2, c1))))),
% 27.58/17.82 inference(rewrite,[status(thm)],[])).
% 27.58/17.82 tff(2965,plain,
% 27.58/17.82 (((f10(c1) = c1) | big_f(c2, f10(c1)) | (~(f7(c2) = c2)) | (~(c2 = f8(c1))) | (~(f6(c2, f6(c2, c1)) = f6(c2, c1))) | (~big_f(f7(c2), f6(c2, f6(c2, c1))))) <=> (big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (~(f7(c2) = c2)) | (~big_f(f7(c2), f6(c2, f6(c2, c1)))) | (~(f6(c2, f6(c2, c1)) = f6(c2, c1))))),
% 27.58/17.82 inference(rewrite,[status(thm)],[])).
% 27.58/17.82 tff(2966,plain,
% 27.58/17.82 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | big_f(c2, f10(c1)) | (~(f7(c2) = c2)) | (~(c2 = f8(c1))) | (~(f6(c2, f6(c2, c1)) = f6(c2, c1))) | (~big_f(f7(c2), f6(c2, f6(c2, c1)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (~(f7(c2) = c2)) | (~big_f(f7(c2), f6(c2, f6(c2, c1)))) | (~(f6(c2, f6(c2, c1)) = f6(c2, c1)))))),
% 27.58/17.82 inference(monotonicity,[status(thm)],[2965])).
% 27.58/17.82 tff(2967,plain,
% 27.58/17.82 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | big_f(c2, f10(c1)) | (~(f7(c2) = c2)) | (~(c2 = f8(c1))) | (~(f6(c2, f6(c2, c1)) = f6(c2, c1))) | (~big_f(f7(c2), f6(c2, f6(c2, c1)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (~(f7(c2) = c2)) | (~big_f(f7(c2), f6(c2, f6(c2, c1)))) | (~(f6(c2, f6(c2, c1)) = f6(c2, c1))))),
% 27.58/17.82 inference(transitivity,[status(thm)],[2966, 2964])).
% 27.58/17.82 tff(2968,plain,
% 27.58/17.82 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | big_f(c2, f10(c1)) | (~(f7(c2) = c2)) | (~(c2 = f8(c1))) | (~(f6(c2, f6(c2, c1)) = f6(c2, c1))) | (~big_f(f7(c2), f6(c2, f6(c2, c1)))))),
% 27.58/17.82 inference(quant_inst,[status(thm)],[])).
% 27.58/17.82 tff(2969,plain,
% 27.58/17.82 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (~(f7(c2) = c2)) | (~big_f(f7(c2), f6(c2, f6(c2, c1)))) | (~(f6(c2, f6(c2, c1)) = f6(c2, c1)))),
% 27.58/17.82 inference(modus_ponens,[status(thm)],[2968, 2967])).
% 27.58/17.82 tff(2970,plain,
% 27.58/17.82 (big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (~(f7(c2) = c2)) | (~big_f(f7(c2), f6(c2, f6(c2, c1)))) | (~(f6(c2, f6(c2, c1)) = f6(c2, c1)))),
% 27.58/17.82 inference(unit_resolution,[status(thm)],[2969, 2963])).
% 27.58/17.82 tff(2971,plain,
% 27.58/17.82 ($false),
% 27.58/17.82 inference(unit_resolution,[status(thm)],[2970, 2953, 2949, 77, 3, 2946, 1642])).
% 27.58/17.82 tff(2972,plain,((~(f6(f7(c2), f5(c1)) = c1)) | (~(f7(c2) = c2)) | (f10(c1) = c1) | big_f(c2, f10(c1)) | (~(c2 = f8(c1))) | (~big_f(c2, c1)) | (~(f5(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 27.58/17.82 tff(2973,plain,
% 27.58/17.82 (~(f6(f7(c2), f5(c1)) = c1)),
% 27.58/17.82 inference(unit_resolution,[status(thm)],[2972, 1642, 3, 2785, 77, 348, 230])).
% 27.58/17.82 tff(2974,plain,
% 27.58/17.82 (~(f6(c2, c1) = c1)),
% 27.58/17.82 inference(modus_ponens,[status(thm)],[2973, 2945])).
% 27.58/17.82 tff(2975,plain,
% 27.58/17.82 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f6(f7(c2), f5(c1)) = c1) | (f6(f7(c2), f5(c1)) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f6(f7(c2), f5(c1)) = c1) | (f6(f7(c2), f5(c1)) = c2))),
% 27.58/17.82 inference(rewrite,[status(thm)],[])).
% 27.58/17.82 tff(2976,plain,
% 27.58/17.82 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f6(f7(c2), f5(c1)) = c1) | (f6(f7(c2), f5(c1)) = c2))),
% 27.58/17.82 inference(quant_inst,[status(thm)],[])).
% 27.58/17.82 tff(2977,plain,
% 27.58/17.82 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f6(f7(c2), f5(c1)) = c1) | (f6(f7(c2), f5(c1)) = c2)),
% 27.58/17.82 inference(modus_ponens,[status(thm)],[2976, 2975])).
% 27.58/17.82 tff(2978,plain,
% 27.58/17.82 ((f6(f7(c2), f5(c1)) = c1) | (f6(f7(c2), f5(c1)) = c2)),
% 27.58/17.82 inference(unit_resolution,[status(thm)],[2977, 10])).
% 27.58/17.82 tff(2979,plain,
% 27.58/17.82 (f6(f7(c2), f5(c1)) = c2),
% 27.58/17.82 inference(unit_resolution,[status(thm)],[2978, 2973])).
% 27.58/17.82 tff(2980,plain,
% 27.58/17.82 (f6(c2, c1) = c2),
% 27.58/17.82 inference(transitivity,[status(thm)],[2942, 2979])).
% 27.58/17.82 tff(2981,plain,
% 27.58/17.82 (big_f(f7(c2), f6(c2, c1)) <=> big_f(c2, c2)),
% 27.58/17.82 inference(monotonicity,[status(thm)],[77, 2980])).
% 27.58/17.82 tff(2982,plain,
% 27.58/17.82 (big_f(c2, c2) <=> big_f(f7(c2), f6(c2, c1))),
% 27.58/17.82 inference(symmetry,[status(thm)],[2981])).
% 27.58/17.82 tff(2983,plain,
% 27.58/17.82 ((~big_f(c2, c2)) <=> (~big_f(f7(c2), f6(c2, c1)))),
% 27.58/17.82 inference(monotonicity,[status(thm)],[2982])).
% 27.58/17.82 tff(2984,plain,
% 27.58/17.82 (~big_f(f7(c2), f6(c2, c1))),
% 27.58/17.82 inference(modus_ponens,[status(thm)],[121, 2983])).
% 27.58/17.82 tff(2985,plain,
% 27.58/17.82 (^[X6: $i, X4: $i, X7: $i, X8: $i] : refl(((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7)))) <=> ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7)))))),
% 27.58/17.82 inference(bind,[status(th)],[])).
% 27.58/17.82 tff(2986,plain,
% 27.58/17.82 (![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7)))) <=> ![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))),
% 27.58/17.82 inference(quant_intro,[status(thm)],[2985])).
% 27.58/17.82 tff(2987,plain,
% 27.58/17.82 (![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7)))) <=> ![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))),
% 27.58/17.82 inference(rewrite,[status(thm)],[])).
% 27.58/17.82 tff(2988,plain,
% 27.58/17.82 (^[X6: $i, X4: $i, X7: $i, X8: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((big_f(f7(X4), f6(X4, X6)) | (f6(X4, X6) = X6)) <=> ((f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))), (((big_f(f7(X4), f6(X4, X6)) | (f6(X4, X6) = X6)) | (~(f7(X4) = X4))) <=> (((f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6))) | (~(f7(X4) = X4))))), rewrite((((f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6))) | (~(f7(X4) = X4))) <=> ((~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))), (((big_f(f7(X4), f6(X4, X6)) | (f6(X4, X6) = X6)) | (~(f7(X4) = X4))) <=> ((~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6))))), ((((big_f(f7(X4), f6(X4, X6)) | (f6(X4, X6) = X6)) | (~(f7(X4) = X4))) | big_f(X8, f10(X7))) <=> (((~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6))) | big_f(X8, f10(X7))))), rewrite((((~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6))) | big_f(X8, f10(X7))) <=> (big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))), ((((big_f(f7(X4), f6(X4, X6)) | (f6(X4, X6) = X6)) | (~(f7(X4) = X4))) | big_f(X8, f10(X7))) <=> (big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6))))), (((((big_f(f7(X4), f6(X4, X6)) | (f6(X4, X6) = X6)) | (~(f7(X4) = X4))) | big_f(X8, f10(X7))) | (~(X8 = f8(X7)))) <=> ((big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6))) | (~(X8 = f8(X7)))))), rewrite(((big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6))) | (~(X8 = f8(X7)))) <=> (big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))), (((((big_f(f7(X4), f6(X4, X6)) | (f6(X4, X6) = X6)) | (~(f7(X4) = X4))) | big_f(X8, f10(X7))) | (~(X8 = f8(X7)))) <=> (big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7)))))), ((((((big_f(f7(X4), f6(X4, X6)) | (f6(X4, X6) = X6)) | (~(f7(X4) = X4))) | big_f(X8, f10(X7))) | (~(X8 = f8(X7)))) | (f10(X7) = X7)) <=> ((big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7)))) | (f10(X7) = X7)))), rewrite(((big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7)))) | (f10(X7) = X7)) <=> ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))), ((((((big_f(f7(X4), f6(X4, X6)) | (f6(X4, X6) = X6)) | (~(f7(X4) = X4))) | big_f(X8, f10(X7))) | (~(X8 = f8(X7)))) | (f10(X7) = X7)) <=> ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))))),
% 27.58/17.82 inference(bind,[status(th)],[])).
% 27.58/17.82 tff(2989,plain,
% 27.58/17.82 (![X6: $i, X4: $i, X7: $i, X8: $i] : (((((big_f(f7(X4), f6(X4, X6)) | (f6(X4, X6) = X6)) | (~(f7(X4) = X4))) | big_f(X8, f10(X7))) | (~(X8 = f8(X7)))) | (f10(X7) = X7)) <=> ![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))),
% 27.58/17.82 inference(quant_intro,[status(thm)],[2988])).
% 27.58/17.82 tff(2990,axiom,(![X6: $i, X4: $i, X7: $i, X8: $i] : (((((big_f(f7(X4), f6(X4, X6)) | (f6(X4, X6) = X6)) | (~(f7(X4) = X4))) | big_f(X8, f10(X7))) | (~(X8 = f8(X7)))) | (f10(X7) = X7))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_28')).
% 27.58/17.82 tff(2991,plain,
% 27.58/17.82 (![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))),
% 27.58/17.82 inference(modus_ponens,[status(thm)],[2990, 2989])).
% 27.58/17.82 tff(2992,plain,
% 27.58/17.82 (![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))),
% 27.58/17.82 inference(modus_ponens,[status(thm)],[2991, 2987])).
% 27.58/17.82 tff(2993,plain,(
% 27.58/17.82 ![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))),
% 27.58/17.82 inference(skolemize,[status(sab)],[2992])).
% 27.58/17.82 tff(2994,plain,
% 27.58/17.82 (![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))),
% 27.58/17.82 inference(modus_ponens,[status(thm)],[2993, 2986])).
% 27.58/17.82 tff(2995,plain,
% 27.58/17.82 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)))),
% 27.58/17.82 inference(rewrite,[status(thm)],[])).
% 27.58/17.82 tff(2996,plain,
% 27.58/17.82 (((f10(c1) = c1) | big_f(c2, f10(c1)) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (~(c2 = f8(c1)))) <=> (big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)))),
% 27.58/17.82 inference(rewrite,[status(thm)],[])).
% 27.58/17.82 tff(2997,plain,
% 27.58/17.82 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | big_f(c2, f10(c1)) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (~(c2 = f8(c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1))))),
% 27.58/17.82 inference(monotonicity,[status(thm)],[2996])).
% 27.58/17.82 tff(2998,plain,
% 27.58/17.82 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | big_f(c2, f10(c1)) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (~(c2 = f8(c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)))),
% 27.58/17.82 inference(transitivity,[status(thm)],[2997, 2995])).
% 27.58/17.82 tff(2999,plain,
% 27.58/17.82 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | big_f(c2, f10(c1)) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (~(c2 = f8(c1))))),
% 27.58/17.82 inference(quant_inst,[status(thm)],[])).
% 27.58/17.82 tff(3000,plain,
% 27.58/17.82 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1))),
% 27.58/17.82 inference(modus_ponens,[status(thm)],[2999, 2998])).
% 27.58/17.82 tff(3001,plain,
% 27.58/17.82 (big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1))),
% 27.58/17.82 inference(unit_resolution,[status(thm)],[3000, 2994])).
% 27.58/17.82 tff(3002,plain,
% 27.58/17.82 ($false),
% 27.58/17.82 inference(unit_resolution,[status(thm)],[3001, 2984, 2974, 77, 2785, 3, 1642])).
% 27.58/17.82 tff(3003,plain,((~(c2 = f8(c1))) | (~(f7(c2) = c2)) | (f10(c1) = c1) | big_f(c2, c2) | (~(f5(c1) = c1)) | (~big_f(c2, c1))), inference(lemma,lemma(discharge,[]))).
% 27.58/17.82 tff(3004,plain,
% 27.58/17.82 (~(c2 = f8(c1))),
% 27.58/17.82 inference(unit_resolution,[status(thm)],[3003, 230, 3, 121, 77, 348])).
% 27.58/17.82 tff(3005,plain,
% 27.58/17.82 (~(f8(c1) = c2)),
% 27.58/17.82 inference(modus_ponens,[status(thm)],[3004, 2783])).
% 27.58/17.82 tff(3006,plain,
% 27.58/17.82 (f8(c1) = c1),
% 27.58/17.82 inference(unit_resolution,[status(thm)],[1680, 3005])).
% 27.58/17.82 tff(3007,assumption,(f10(c3) = c3), introduced(assumption)).
% 27.58/17.82 tff(3008,plain,
% 27.58/17.82 (c3 = f10(c3)),
% 27.58/17.82 inference(symmetry,[status(thm)],[3007])).
% 27.58/17.82 tff(3009,plain,
% 27.58/17.82 (f10(c1) = f10(c3)),
% 27.58/17.82 inference(transitivity,[status(thm)],[15, 69, 3008])).
% 27.58/17.82 tff(3010,plain,
% 27.58/17.82 (big_f(f8(c1), f10(c1)) <=> big_f(f8(c1), f10(c3))),
% 27.58/17.82 inference(monotonicity,[status(thm)],[3009])).
% 27.58/17.82 tff(3011,plain,
% 27.58/17.82 (big_f(f8(c1), f10(c3)) <=> big_f(f8(c1), f10(c1))),
% 27.58/17.82 inference(symmetry,[status(thm)],[3010])).
% 27.58/17.82 tff(3012,plain,
% 27.58/17.82 (f10(c3) = c2),
% 27.58/17.82 inference(transitivity,[status(thm)],[3007, 67])).
% 27.58/17.82 tff(3013,plain,
% 27.58/17.82 (big_f(f8(c1), f10(c3)) <=> big_f(c1, c2)),
% 27.58/17.82 inference(monotonicity,[status(thm)],[3006, 3012])).
% 27.58/17.82 tff(3014,plain,
% 27.58/17.82 (big_f(c1, c2) <=> big_f(f8(c1), f10(c3))),
% 27.58/17.82 inference(symmetry,[status(thm)],[3013])).
% 27.58/17.82 tff(3015,plain,
% 27.58/17.82 (big_f(c1, c2) <=> big_f(f8(c1), f10(c1))),
% 27.58/17.82 inference(transitivity,[status(thm)],[3014, 3011])).
% 27.58/17.82 tff(3016,plain,
% 27.58/17.82 ((~big_f(c1, c2)) <=> (~big_f(f8(c1), f10(c1)))),
% 27.58/17.82 inference(monotonicity,[status(thm)],[3015])).
% 27.58/17.82 tff(3017,plain,
% 27.58/17.82 (~big_f(f8(c1), f10(c1))),
% 27.58/17.82 inference(modus_ponens,[status(thm)],[27, 3016])).
% 27.58/17.82 tff(3018,assumption,(f8(c1) = c1), introduced(assumption)).
% 27.58/17.82 tff(3019,plain,
% 27.58/17.82 (big_f(f8(c1), f10(c1)) <=> big_f(c1, f10(c1))),
% 27.58/17.82 inference(monotonicity,[status(thm)],[3018])).
% 27.58/17.82 tff(3020,plain,
% 27.58/17.82 ((~big_f(f8(c1), f10(c1))) <=> (~big_f(c1, f10(c1)))),
% 27.58/17.82 inference(monotonicity,[status(thm)],[3019])).
% 27.58/17.82 tff(3021,assumption,(~big_f(f8(c1), f10(c1))), introduced(assumption)).
% 27.58/17.82 tff(3022,plain,
% 27.58/17.82 (~big_f(c1, f10(c1))),
% 27.64/17.82 inference(modus_ponens,[status(thm)],[3021, 3020])).
% 27.64/17.82 tff(3023,assumption,(big_f(c1, f10(c1))), introduced(assumption)).
% 27.64/17.82 tff(3024,plain,
% 27.64/17.82 ($false),
% 27.64/17.82 inference(unit_resolution,[status(thm)],[3023, 3022])).
% 27.64/17.82 tff(3025,plain,(big_f(f8(c1), f10(c1)) | (~big_f(c1, f10(c1))) | (~(f8(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 27.64/17.82 tff(3026,plain,
% 27.64/17.82 (~big_f(c1, f10(c1))),
% 27.64/17.82 inference(unit_resolution,[status(thm)],[3025, 3017, 3006])).
% 27.64/17.82 tff(3027,plain,
% 27.64/17.82 ((c1 = f8(c1)) <=> (f8(c1) = c1)),
% 27.64/17.82 inference(commutativity,[status(thm)],[])).
% 27.64/17.82 tff(3028,plain,
% 27.64/17.82 ((f8(c1) = c1) <=> (c1 = f8(c1))),
% 27.64/17.82 inference(symmetry,[status(thm)],[3027])).
% 27.64/17.82 tff(3029,plain,
% 27.64/17.82 (c1 = f8(c1)),
% 27.64/17.82 inference(modus_ponens,[status(thm)],[3006, 3028])).
% 27.64/17.82 tff(3030,assumption,(~big_f(c1, f10(c1))), introduced(assumption)).
% 27.64/17.82 tff(3031,assumption,(c1 = f8(c1)), introduced(assumption)).
% 27.64/17.82 tff(3032,assumption,(f6(f7(c2), f5(c1)) = c2), introduced(assumption)).
% 27.64/17.82 tff(3033,plain,
% 27.64/17.82 (f6(c2, c1) = c2),
% 27.64/17.82 inference(transitivity,[status(thm)],[2942, 3032])).
% 27.64/17.82 tff(3034,plain,
% 27.64/17.82 (big_f(f7(c2), f6(c2, c1)) <=> big_f(c2, c2)),
% 27.64/17.82 inference(monotonicity,[status(thm)],[77, 3033])).
% 27.64/17.82 tff(3035,plain,
% 27.64/17.82 (big_f(c2, c2) <=> big_f(f7(c2), f6(c2, c1))),
% 27.64/17.82 inference(symmetry,[status(thm)],[3034])).
% 27.64/17.82 tff(3036,plain,
% 27.64/17.82 ((~big_f(c2, c2)) <=> (~big_f(f7(c2), f6(c2, c1)))),
% 27.64/17.82 inference(monotonicity,[status(thm)],[3035])).
% 27.64/17.82 tff(3037,plain,
% 27.64/17.82 (~big_f(f7(c2), f6(c2, c1))),
% 27.64/17.82 inference(modus_ponens,[status(thm)],[121, 3036])).
% 27.64/17.82 tff(3038,plain,
% 27.64/17.82 ((f6(c2, c1) = c1) <=> (c2 = c1)),
% 27.64/17.82 inference(monotonicity,[status(thm)],[3033])).
% 27.64/17.82 tff(3039,plain,
% 27.64/17.82 ((c2 = c1) <=> (f6(c2, c1) = c1)),
% 27.64/17.82 inference(symmetry,[status(thm)],[3038])).
% 27.64/17.82 tff(3040,plain,
% 27.64/17.82 ((~(c2 = c1)) <=> (~(f6(c2, c1) = c1))),
% 27.64/17.82 inference(monotonicity,[status(thm)],[3039])).
% 27.64/17.82 tff(3041,plain,
% 27.64/17.82 (~(f6(c2, c1) = c1)),
% 27.64/17.82 inference(modus_ponens,[status(thm)],[75, 3040])).
% 27.64/17.82 tff(3042,plain,
% 27.64/17.82 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (f10(c1) = c1) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)))),
% 27.64/17.82 inference(rewrite,[status(thm)],[])).
% 27.64/17.82 tff(3043,plain,
% 27.64/17.82 (((f10(c1) = c1) | big_f(c1, f10(c1)) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (~(c1 = f8(c1)))) <=> ((f10(c1) = c1) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)))),
% 27.64/17.82 inference(rewrite,[status(thm)],[])).
% 27.64/17.82 tff(3044,plain,
% 27.64/17.82 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | big_f(c1, f10(c1)) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (~(c1 = f8(c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (~(c1 = f8(c1))) | big_f(c1, f10(c1))))),
% 27.64/17.82 inference(monotonicity,[status(thm)],[3043])).
% 27.64/17.82 tff(3045,plain,
% 27.64/17.82 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | big_f(c1, f10(c1)) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (~(c1 = f8(c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (f10(c1) = c1) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)))),
% 27.64/17.82 inference(transitivity,[status(thm)],[3044, 3042])).
% 27.64/17.82 tff(3046,plain,
% 27.64/17.82 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | big_f(c1, f10(c1)) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (~(c1 = f8(c1))))),
% 27.64/17.82 inference(quant_inst,[status(thm)],[])).
% 27.64/17.82 tff(3047,plain,
% 27.64/17.82 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (f10(c1) = c1) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (~(c1 = f8(c1))) | big_f(c1, f10(c1))),
% 27.64/17.82 inference(modus_ponens,[status(thm)],[3046, 3045])).
% 27.64/17.82 tff(3048,plain,
% 27.64/17.82 ($false),
% 27.64/17.82 inference(unit_resolution,[status(thm)],[3047, 2994, 3, 77, 3041, 3037, 3031, 3030])).
% 27.64/17.82 tff(3049,plain,((~(f6(f7(c2), f5(c1)) = c2)) | (f10(c1) = c1) | (~(f7(c2) = c2)) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | big_f(c2, c2) | (~(f5(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 27.64/17.82 tff(3050,plain,
% 27.64/17.82 (~(f6(f7(c2), f5(c1)) = c2)),
% 27.64/17.82 inference(unit_resolution,[status(thm)],[3049, 3029, 77, 3, 3026, 121, 230])).
% 27.64/17.82 tff(3051,plain,
% 27.64/17.82 (f6(f7(c2), f5(c1)) = c1),
% 27.64/17.82 inference(unit_resolution,[status(thm)],[2978, 3050])).
% 27.64/17.82 tff(3052,plain,
% 27.64/17.82 (f6(c2, c1) = c1),
% 27.64/17.82 inference(transitivity,[status(thm)],[2942, 3051])).
% 27.64/17.82 tff(3053,plain,
% 27.64/17.82 (big_f(f7(c2), f6(c2, c1)) <=> big_f(c2, c1)),
% 27.64/17.82 inference(monotonicity,[status(thm)],[77, 3052])).
% 27.64/17.82 tff(3054,plain,
% 27.64/17.82 (big_f(c2, c1) <=> big_f(f7(c2), f6(c2, c1))),
% 27.64/17.82 inference(symmetry,[status(thm)],[3053])).
% 27.64/17.82 tff(3055,plain,
% 27.64/17.82 (big_f(f7(c2), f6(c2, c1))),
% 27.64/17.82 inference(modus_ponens,[status(thm)],[348, 3054])).
% 27.64/17.82 tff(3056,plain,
% 27.64/17.82 ((f6(c2, c1) = c1) <=> (f6(f7(c2), f5(c1)) = c1)),
% 27.64/17.82 inference(monotonicity,[status(thm)],[2942])).
% 27.64/17.82 tff(3057,plain,
% 27.64/17.82 ((f6(f7(c2), f5(c1)) = c1) <=> (f6(c2, c1) = c1)),
% 27.64/17.82 inference(symmetry,[status(thm)],[3056])).
% 27.64/17.82 tff(3058,plain,
% 27.64/17.82 (f6(c2, c1) = c1),
% 27.64/17.82 inference(modus_ponens,[status(thm)],[3051, 3057])).
% 27.64/17.82 tff(3059,plain,
% 27.64/17.82 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (~(f7(c2) = c2)) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(f7(c2) = c2)) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1))))),
% 27.64/17.82 inference(rewrite,[status(thm)],[])).
% 27.64/17.82 tff(3060,plain,
% 27.64/17.82 (((f10(c1) = c1) | big_f(c1, f10(c1)) | (~(f7(c2) = c2)) | (~(c1 = f8(c1))) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1)))) <=> ((f10(c1) = c1) | (~(f7(c2) = c2)) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1))))),
% 27.64/17.82 inference(rewrite,[status(thm)],[])).
% 27.64/17.82 tff(3061,plain,
% 27.64/17.82 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | big_f(c1, f10(c1)) | (~(f7(c2) = c2)) | (~(c1 = f8(c1))) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (~(f7(c2) = c2)) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1)))))),
% 27.64/17.82 inference(monotonicity,[status(thm)],[3060])).
% 27.64/17.82 tff(3062,plain,
% 27.64/17.82 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | big_f(c1, f10(c1)) | (~(f7(c2) = c2)) | (~(c1 = f8(c1))) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(f7(c2) = c2)) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1))))),
% 27.64/17.83 inference(transitivity,[status(thm)],[3061, 3059])).
% 27.64/17.83 tff(3063,plain,
% 27.64/17.83 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | big_f(c1, f10(c1)) | (~(f7(c2) = c2)) | (~(c1 = f8(c1))) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1))))),
% 27.64/17.83 inference(quant_inst,[status(thm)],[])).
% 27.64/17.83 tff(3064,plain,
% 27.64/17.83 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(f7(c2) = c2)) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1)))),
% 27.64/17.83 inference(modus_ponens,[status(thm)],[3063, 3062])).
% 27.64/17.83 tff(3065,plain,
% 27.64/17.83 ($false),
% 27.64/17.83 inference(unit_resolution,[status(thm)],[3064, 2963, 3, 77, 3058, 3055, 3029, 3026])).
% 27.64/17.83 tff(3066,plain,((~(f5(c1) = c1)) | (f10(c1) = c1) | (~(f7(c2) = c2)) | (~big_f(c2, c1)) | big_f(c2, c2) | big_f(c1, c2) | (~(f10(c3) = c3)) | (~(c3 = c2))), inference(lemma,lemma(discharge,[]))).
% 27.64/17.83 tff(3067,plain,
% 27.64/17.83 (big_f(c1, c2)),
% 27.64/17.83 inference(unit_resolution,[status(thm)],[3066, 2940, 77, 2768, 121, 3, 2831, 67])).
% 27.64/17.83 tff(3068,plain,
% 27.64/17.83 (~(c2 = f8(c1))),
% 27.64/17.83 inference(unit_resolution,[status(thm)],[3003, 2940, 3, 121, 77, 2768])).
% 27.64/17.83 tff(3069,plain,
% 27.64/17.83 (~(f8(c1) = c2)),
% 27.64/17.83 inference(modus_ponens,[status(thm)],[3068, 2783])).
% 27.64/17.83 tff(3070,plain,
% 27.64/17.83 (f8(c1) = c1),
% 27.64/17.83 inference(unit_resolution,[status(thm)],[1680, 3069])).
% 27.64/17.83 tff(3071,plain,
% 27.64/17.83 ((f9(c2, c1) = f8(c1)) <=> (f9(c2, c1) = c1)),
% 27.64/17.83 inference(monotonicity,[status(thm)],[3018])).
% 27.64/17.83 tff(3072,plain,
% 27.64/17.83 ((f9(c2, c1) = c1) <=> (f9(c2, c1) = f8(c1))),
% 27.64/17.83 inference(symmetry,[status(thm)],[3071])).
% 27.64/17.83 tff(3073,plain,
% 27.64/17.83 ((~(f9(c2, c1) = c1)) <=> (~(f9(c2, c1) = f8(c1)))),
% 27.64/17.83 inference(monotonicity,[status(thm)],[3072])).
% 27.64/17.83 tff(3074,plain,
% 27.64/17.83 (big_f(f7(c2), f6(c2, c1)) <=> big_f(c2, c1)),
% 27.64/17.83 inference(monotonicity,[status(thm)],[77, 2948])).
% 27.64/17.83 tff(3075,plain,
% 27.64/17.83 (big_f(c2, c1) <=> big_f(f7(c2), f6(c2, c1))),
% 27.64/17.83 inference(symmetry,[status(thm)],[3074])).
% 27.64/17.83 tff(3076,plain,
% 27.64/17.83 (big_f(f7(c2), f6(c2, c1))),
% 27.64/17.83 inference(modus_ponens,[status(thm)],[348, 3075])).
% 27.64/17.83 tff(3077,plain,
% 27.64/17.83 (f6(c2, c1) = c1),
% 27.64/17.83 inference(modus_ponens,[status(thm)],[2947, 3057])).
% 27.64/17.83 tff(3078,assumption,(big_f(f7(c2), f6(c2, c1))), introduced(assumption)).
% 27.64/17.83 tff(3079,assumption,(f6(c2, c1) = c1), introduced(assumption)).
% 27.64/17.83 tff(3080,plain,
% 27.64/17.83 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1))))),
% 27.64/17.83 inference(rewrite,[status(thm)],[])).
% 27.64/17.83 tff(3081,plain,
% 27.64/17.83 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1))))),
% 27.64/17.83 inference(quant_inst,[status(thm)],[])).
% 27.64/17.83 tff(3082,plain,
% 27.64/17.83 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1)))),
% 27.64/17.83 inference(modus_ponens,[status(thm)],[3081, 3080])).
% 27.64/17.83 tff(3083,plain,
% 27.64/17.83 ($false),
% 27.64/17.83 inference(unit_resolution,[status(thm)],[3082, 2534, 122, 1139, 731, 77, 3079, 3078])).
% 27.64/17.83 tff(3084,plain,((f9(c2, c1) = c1) | (~(f10(c2) = c2)) | big_f(f9(c2, c1), f10(c2)) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1)))), inference(lemma,lemma(discharge,[]))).
% 27.64/17.83 tff(3085,plain,
% 27.64/17.83 (f9(c2, c1) = c1),
% 27.64/17.83 inference(unit_resolution,[status(thm)],[3084, 731, 122, 77, 3079, 3078])).
% 27.64/17.83 tff(3086,plain,
% 27.64/17.83 (big_f(f9(c2, c1), f10(c2)) <=> big_f(c1, c2)),
% 27.64/17.83 inference(monotonicity,[status(thm)],[3085, 122])).
% 27.64/17.83 tff(3087,plain,
% 27.64/17.83 (big_f(c1, c2) <=> big_f(f9(c2, c1), f10(c2))),
% 27.64/17.83 inference(symmetry,[status(thm)],[3086])).
% 27.64/17.83 tff(3088,plain,
% 27.64/17.83 (big_f(f9(c2, c1), f10(c2))),
% 27.64/17.83 inference(modus_ponens,[status(thm)],[2865, 3087])).
% 27.64/17.83 tff(3089,plain,
% 27.64/17.83 ($false),
% 27.64/17.83 inference(unit_resolution,[status(thm)],[731, 3088])).
% 27.64/17.83 tff(3090,plain,(big_f(f9(c2, c1), f10(c2)) | (~big_f(c1, c2)) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1)))), inference(lemma,lemma(discharge,[]))).
% 27.64/17.83 tff(3091,plain,
% 27.64/17.83 (big_f(f9(c2, c1), f10(c2))),
% 27.64/17.83 inference(unit_resolution,[status(thm)],[3090, 3077, 122, 77, 2865, 3076])).
% 27.64/17.83 tff(3092,plain,
% 27.64/17.83 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))) | (~big_f(f7(c2), f6(c2, c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))) | (~big_f(f7(c2), f6(c2, c1))))),
% 27.64/17.83 inference(rewrite,[status(thm)],[])).
% 27.64/17.83 tff(3093,plain,
% 27.64/17.83 (((~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1)))) <=> ((~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))) | (~big_f(f7(c2), f6(c2, c1))))),
% 27.64/17.83 inference(rewrite,[status(thm)],[])).
% 27.64/17.83 tff(3094,plain,
% 27.64/17.83 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))) | (~big_f(f7(c2), f6(c2, c1)))))),
% 27.64/17.83 inference(monotonicity,[status(thm)],[3093])).
% 27.64/17.83 tff(3095,plain,
% 27.64/17.83 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))) | (~big_f(f7(c2), f6(c2, c1))))),
% 27.64/17.83 inference(transitivity,[status(thm)],[3094, 3092])).
% 27.64/17.83 tff(3096,plain,
% 27.64/17.83 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1))))),
% 27.64/17.83 inference(quant_inst,[status(thm)],[])).
% 27.64/17.83 tff(3097,plain,
% 27.64/17.83 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))) | (~big_f(f7(c2), f6(c2, c1)))),
% 27.64/17.83 inference(modus_ponens,[status(thm)],[3096, 3095])).
% 27.64/17.83 tff(3098,plain,
% 27.64/17.83 (~(f9(c2, c1) = c1)),
% 27.64/17.83 inference(unit_resolution,[status(thm)],[3097, 2378, 122, 3091, 77, 3077, 3076])).
% 27.64/17.83 tff(3099,plain,
% 27.64/17.83 (~(f9(c2, c1) = f8(c1))),
% 27.64/17.83 inference(modus_ponens,[status(thm)],[3098, 3073])).
% 27.64/17.83 tff(3100,plain,
% 27.64/17.83 (big_f(f9(c2, c1), f10(c1)) <=> big_f(f9(c2, c1), f10(c2))),
% 27.64/17.83 inference(monotonicity,[status(thm)],[2754])).
% 27.64/17.83 tff(3101,plain,
% 27.64/17.83 (big_f(f9(c2, c1), f10(c2)) <=> big_f(f9(c2, c1), f10(c1))),
% 27.64/17.83 inference(symmetry,[status(thm)],[3100])).
% 27.64/17.83 tff(3102,plain,
% 27.64/17.83 (big_f(f9(c2, c1), f10(c1))),
% 27.64/17.83 inference(modus_ponens,[status(thm)],[3091, 3101])).
% 27.64/17.83 tff(3103,plain,
% 27.64/17.83 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1))) | (f9(c2, c1) = f8(c1)) | (~big_f(f9(c2, c1), f10(c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1))) | (f9(c2, c1) = f8(c1)) | (~big_f(f9(c2, c1), f10(c1))))),
% 27.64/17.83 inference(rewrite,[status(thm)],[])).
% 27.64/17.83 tff(3104,plain,
% 27.64/17.83 (((f10(c1) = c1) | (f9(c2, c1) = f8(c1)) | (~big_f(f9(c2, c1), f10(c1))) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1)))) <=> ((f10(c1) = c1) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1))) | (f9(c2, c1) = f8(c1)) | (~big_f(f9(c2, c1), f10(c1))))),
% 27.64/17.83 inference(rewrite,[status(thm)],[])).
% 27.64/17.83 tff(3105,plain,
% 27.64/17.83 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (f9(c2, c1) = f8(c1)) | (~big_f(f9(c2, c1), f10(c1))) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1))) | (f9(c2, c1) = f8(c1)) | (~big_f(f9(c2, c1), f10(c1)))))),
% 27.64/17.83 inference(monotonicity,[status(thm)],[3104])).
% 27.64/17.83 tff(3106,plain,
% 27.64/17.83 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (f9(c2, c1) = f8(c1)) | (~big_f(f9(c2, c1), f10(c1))) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1))) | (f9(c2, c1) = f8(c1)) | (~big_f(f9(c2, c1), f10(c1))))),
% 27.64/17.83 inference(transitivity,[status(thm)],[3105, 3103])).
% 27.64/17.83 tff(3107,plain,
% 27.64/17.83 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (f9(c2, c1) = f8(c1)) | (~big_f(f9(c2, c1), f10(c1))) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1))))),
% 27.64/17.83 inference(quant_inst,[status(thm)],[])).
% 27.64/17.83 tff(3108,plain,
% 27.64/17.83 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1))) | (f9(c2, c1) = f8(c1)) | (~big_f(f9(c2, c1), f10(c1)))),
% 27.64/17.83 inference(modus_ponens,[status(thm)],[3107, 3106])).
% 27.64/17.83 tff(3109,plain,
% 27.64/17.83 ((f9(c2, c1) = f8(c1)) | (~big_f(f9(c2, c1), f10(c1)))),
% 27.64/17.83 inference(unit_resolution,[status(thm)],[3108, 2730, 3, 77, 3077, 3076])).
% 27.64/17.83 tff(3110,plain,
% 27.64/17.83 ($false),
% 27.64/17.83 inference(unit_resolution,[status(thm)],[3109, 3102, 3099])).
% 27.64/17.83 tff(3111,plain,((~(f6(f7(c2), f5(c1)) = c1)) | (f10(c1) = c1) | (~(f7(c2) = c2)) | (~(f10(c2) = c2)) | (~(f8(c1) = c1)) | (~big_f(c1, c2)) | (~big_f(c2, c1)) | (~(f5(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 27.64/17.83 tff(3112,plain,
% 27.64/17.83 (~(f6(f7(c2), f5(c1)) = c1)),
% 27.64/17.83 inference(unit_resolution,[status(thm)],[3111, 3070, 77, 122, 3, 3067, 2768, 2940])).
% 27.64/17.83 tff(3113,plain,
% 27.64/17.83 (f6(f7(c2), f5(c1)) = c2),
% 27.64/17.83 inference(unit_resolution,[status(thm)],[2978, 3112])).
% 27.64/17.83 tff(3114,plain,
% 27.64/17.83 (c1 = f5(c1)),
% 27.64/17.83 inference(symmetry,[status(thm)],[2940])).
% 27.64/17.83 tff(3115,plain,
% 27.64/17.83 (f6(c2, c1) = f6(f7(c2), f5(c1))),
% 27.64/17.83 inference(monotonicity,[status(thm)],[82, 3114])).
% 27.64/17.83 tff(3116,plain,
% 27.64/17.83 (f6(c2, c1) = c2),
% 27.64/17.83 inference(transitivity,[status(thm)],[3115, 3113])).
% 27.64/17.83 tff(3117,plain,
% 27.64/17.83 (big_f(f7(c2), f6(c2, c1)) <=> big_f(c2, c2)),
% 27.64/17.83 inference(monotonicity,[status(thm)],[77, 3116])).
% 27.64/17.83 tff(3118,plain,
% 27.64/17.83 (big_f(c2, c2) <=> big_f(f7(c2), f6(c2, c1))),
% 27.64/17.83 inference(symmetry,[status(thm)],[3117])).
% 27.64/17.83 tff(3119,plain,
% 27.64/17.83 ((~big_f(c2, c2)) <=> (~big_f(f7(c2), f6(c2, c1)))),
% 27.64/17.83 inference(monotonicity,[status(thm)],[3118])).
% 27.64/17.83 tff(3120,plain,
% 27.64/17.83 (~big_f(f7(c2), f6(c2, c1))),
% 27.64/17.83 inference(modus_ponens,[status(thm)],[121, 3119])).
% 27.64/17.83 tff(3121,plain,
% 27.64/17.83 (f6(f7(c2), f5(c1)) = f6(c2, c1)),
% 27.64/17.83 inference(symmetry,[status(thm)],[3115])).
% 27.64/17.83 tff(3122,plain,
% 27.64/17.83 ((f6(f7(c2), f5(c1)) = c1) <=> (f6(c2, c1) = c1)),
% 27.64/17.83 inference(monotonicity,[status(thm)],[3121])).
% 27.64/17.83 tff(3123,plain,
% 27.64/17.83 ((~(f6(f7(c2), f5(c1)) = c1)) <=> (~(f6(c2, c1) = c1))),
% 27.64/17.83 inference(monotonicity,[status(thm)],[3122])).
% 27.64/17.83 tff(3124,plain,
% 27.64/17.83 (~(f6(c2, c1) = c1)),
% 27.64/17.83 inference(modus_ponens,[status(thm)],[3112, 3123])).
% 27.64/17.83 tff(3125,plain,
% 27.64/17.83 (f3(c2, c1) = f3(f7(c1), c1)),
% 27.64/17.83 inference(monotonicity,[status(thm)],[354])).
% 27.64/17.83 tff(3126,plain,
% 27.64/17.83 ((f3(c2, c1) = c1) <=> (f3(f7(c1), c1) = c1)),
% 27.64/17.83 inference(monotonicity,[status(thm)],[3125])).
% 27.64/17.83 tff(3127,plain,
% 27.64/17.83 ((f3(f7(c1), c1) = c1) <=> (f3(c2, c1) = c1)),
% 27.64/17.83 inference(symmetry,[status(thm)],[3126])).
% 27.64/17.83 tff(3128,plain,
% 27.64/17.83 ((f3(f7(c1), c1) = f8(c1)) <=> (f3(f7(c1), c1) = c1)),
% 27.64/17.83 inference(monotonicity,[status(thm)],[3018])).
% 27.64/17.83 tff(3129,plain,
% 27.64/17.83 ((f3(f7(c1), c1) = f8(c1)) <=> (f3(c2, c1) = c1)),
% 27.64/17.83 inference(transitivity,[status(thm)],[3128, 3127])).
% 27.64/17.83 tff(3130,plain,
% 27.64/17.83 (f10(c1) = f7(c1)),
% 27.64/17.83 inference(transitivity,[status(thm)],[15, 354])).
% 27.64/17.83 tff(3131,plain,
% 27.64/17.83 (big_f(f3(f7(c1), c1), f10(c1)) <=> big_f(f3(f7(c1), c1), f7(c1))),
% 27.64/17.83 inference(monotonicity,[status(thm)],[3130])).
% 27.64/17.83 tff(3132,plain,
% 27.64/17.83 (big_f(f3(f7(c1), c1), f7(c1)) <=> big_f(f3(f7(c1), c1), f10(c1))),
% 27.64/17.83 inference(symmetry,[status(thm)],[3131])).
% 27.64/17.83 tff(3133,plain,
% 27.64/17.83 (big_f(f4(c4), c4)),
% 27.64/17.83 inference(unit_resolution,[status(thm)],[1315, 2816])).
% 27.64/17.83 tff(3134,plain,
% 27.64/17.83 (~(c4 = c2)),
% 27.64/17.83 inference(unit_resolution,[status(thm)],[476, 3133, 79, 121])).
% 27.64/17.83 tff(3135,plain,
% 27.64/17.83 (c4 = c1),
% 27.64/17.83 inference(unit_resolution,[status(thm)],[461, 3134])).
% 27.64/17.83 tff(3136,plain,
% 27.64/17.83 ((c2 = c4) <=> (c2 = c1)),
% 27.64/17.83 inference(monotonicity,[status(thm)],[3135])).
% 27.64/17.83 tff(3137,plain,
% 27.64/17.83 ((c2 = c1) <=> (c2 = c4)),
% 27.64/17.83 inference(symmetry,[status(thm)],[3136])).
% 27.64/17.83 tff(3138,plain,
% 27.64/17.83 ((c2 = c1) <=> (f7(c1) = c4)),
% 27.64/17.83 inference(transitivity,[status(thm)],[3137, 869])).
% 27.64/17.83 tff(3139,plain,
% 27.64/17.83 ((~(c2 = c1)) <=> (~(f7(c1) = c4))),
% 27.64/17.83 inference(monotonicity,[status(thm)],[3138])).
% 27.64/17.83 tff(3140,plain,
% 27.64/17.83 (~(f7(c1) = c4)),
% 27.64/17.83 inference(modus_ponens,[status(thm)],[75, 3139])).
% 27.64/17.83 tff(3141,plain,
% 27.64/17.83 (f8(f3(f7(c1), c1)) = f8(c1)),
% 27.64/17.83 inference(monotonicity,[status(thm)],[2862])).
% 27.64/17.83 tff(3142,plain,
% 27.64/17.83 (f8(c1) = f8(f3(f7(c1), c1))),
% 27.64/17.83 inference(symmetry,[status(thm)],[3141])).
% 27.64/17.83 tff(3143,plain,
% 27.64/17.83 (c1 = f8(c1)),
% 27.64/17.83 inference(symmetry,[status(thm)],[3018])).
% 27.64/17.83 tff(3144,plain,
% 27.64/17.83 (f3(f7(c1), c1) = f8(f3(f7(c1), c1))),
% 27.64/17.83 inference(transitivity,[status(thm)],[2862, 3143, 3142])).
% 27.64/17.83 tff(3145,plain,
% 27.64/17.83 (f6(c2, f3(f7(c1), c1)) = f6(c2, c1)),
% 27.64/17.83 inference(monotonicity,[status(thm)],[2862])).
% 27.64/17.83 tff(3146,plain,
% 27.64/17.83 (f6(c2, f3(f7(c1), c1)) = c2),
% 27.64/17.83 inference(transitivity,[status(thm)],[3145, 2942, 3032])).
% 27.64/17.83 tff(3147,plain,
% 27.64/17.83 (big_f(f7(c2), f6(c2, f3(f7(c1), c1))) <=> big_f(c2, c2)),
% 27.64/17.83 inference(monotonicity,[status(thm)],[77, 3146])).
% 27.64/17.83 tff(3148,plain,
% 27.64/17.83 (big_f(c2, c2) <=> big_f(f7(c2), f6(c2, f3(f7(c1), c1)))),
% 27.64/17.83 inference(symmetry,[status(thm)],[3147])).
% 27.64/17.83 tff(3149,plain,
% 27.64/17.83 ((~big_f(c2, c2)) <=> (~big_f(f7(c2), f6(c2, f3(f7(c1), c1))))),
% 27.64/17.83 inference(monotonicity,[status(thm)],[3148])).
% 27.64/17.83 tff(3150,plain,
% 27.64/17.83 (~big_f(f7(c2), f6(c2, f3(f7(c1), c1)))),
% 27.64/17.83 inference(modus_ponens,[status(thm)],[121, 3149])).
% 27.64/17.83 tff(3151,plain,
% 27.64/17.83 ((f6(c2, f3(f7(c1), c1)) = f3(f7(c1), c1)) <=> (c2 = c1)),
% 27.64/17.83 inference(monotonicity,[status(thm)],[3146, 2862])).
% 27.64/17.83 tff(3152,plain,
% 27.64/17.83 ((c2 = c1) <=> (f6(c2, f3(f7(c1), c1)) = f3(f7(c1), c1))),
% 27.64/17.83 inference(symmetry,[status(thm)],[3151])).
% 27.64/17.83 tff(3153,plain,
% 27.64/17.83 ((~(c2 = c1)) <=> (~(f6(c2, f3(f7(c1), c1)) = f3(f7(c1), c1)))),
% 27.64/17.83 inference(monotonicity,[status(thm)],[3152])).
% 27.64/17.83 tff(3154,plain,
% 27.64/17.83 (~(f6(c2, f3(f7(c1), c1)) = f3(f7(c1), c1))),
% 27.64/17.83 inference(modus_ponens,[status(thm)],[75, 3153])).
% 27.64/17.83 tff(3155,plain,
% 27.64/17.83 (f10(f3(f7(c1), c1)) = f10(c1)),
% 27.64/17.83 inference(monotonicity,[status(thm)],[2862])).
% 27.64/17.83 tff(3156,plain,
% 27.64/17.83 (f10(f3(f7(c1), c1)) = c2),
% 27.64/17.83 inference(transitivity,[status(thm)],[3155, 16])).
% 27.64/17.83 tff(3157,plain,
% 27.64/17.83 ((f10(f3(f7(c1), c1)) = f3(f7(c1), c1)) <=> (c2 = c1)),
% 27.64/17.83 inference(monotonicity,[status(thm)],[3156, 2862])).
% 27.64/17.83 tff(3158,plain,
% 27.64/17.83 ((c2 = c1) <=> (f10(f3(f7(c1), c1)) = f3(f7(c1), c1))),
% 27.64/17.83 inference(symmetry,[status(thm)],[3157])).
% 27.64/17.83 tff(3159,plain,
% 27.64/17.83 ((~(c2 = c1)) <=> (~(f10(f3(f7(c1), c1)) = f3(f7(c1), c1)))),
% 27.64/17.83 inference(monotonicity,[status(thm)],[3158])).
% 27.64/17.83 tff(3160,plain,
% 27.64/17.83 (~(f10(f3(f7(c1), c1)) = f3(f7(c1), c1))),
% 27.64/17.83 inference(modus_ponens,[status(thm)],[75, 3159])).
% 27.64/17.83 tff(3161,plain,
% 27.64/17.83 (f10(f3(f7(c1), c1)) = f7(c1)),
% 27.64/17.83 inference(transitivity,[status(thm)],[3155, 16, 354])).
% 27.64/17.83 tff(3162,plain,
% 27.64/17.83 (big_f(f3(f7(c1), c1), f10(f3(f7(c1), c1))) <=> big_f(f3(f7(c1), c1), f7(c1))),
% 27.64/17.83 inference(monotonicity,[status(thm)],[3161])).
% 27.64/17.83 tff(3163,plain,
% 27.64/17.83 (big_f(f3(f7(c1), c1), f7(c1)) <=> big_f(f3(f7(c1), c1), f10(f3(f7(c1), c1)))),
% 27.64/17.83 inference(symmetry,[status(thm)],[3162])).
% 27.64/17.83 tff(3164,plain,
% 27.64/17.83 ((~big_f(f3(f7(c1), c1), f7(c1))) <=> (~big_f(f3(f7(c1), c1), f10(f3(f7(c1), c1))))),
% 27.64/17.83 inference(monotonicity,[status(thm)],[3163])).
% 27.64/17.83 tff(3165,plain,
% 27.64/17.83 (~big_f(f3(f7(c1), c1), f10(f3(f7(c1), c1)))),
% 27.64/17.83 inference(modus_ponens,[status(thm)],[2854, 3164])).
% 27.64/17.83 tff(3166,plain,
% 27.64/17.83 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((~(f7(c2) = c2)) | (f10(f3(f7(c1), c1)) = f3(f7(c1), c1)) | big_f(f3(f7(c1), c1), f10(f3(f7(c1), c1))) | (f6(c2, f3(f7(c1), c1)) = f3(f7(c1), c1)) | big_f(f7(c2), f6(c2, f3(f7(c1), c1))) | (~(f3(f7(c1), c1) = f8(f3(f7(c1), c1)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (~(f7(c2) = c2)) | (f10(f3(f7(c1), c1)) = f3(f7(c1), c1)) | big_f(f3(f7(c1), c1), f10(f3(f7(c1), c1))) | (f6(c2, f3(f7(c1), c1)) = f3(f7(c1), c1)) | big_f(f7(c2), f6(c2, f3(f7(c1), c1))) | (~(f3(f7(c1), c1) = f8(f3(f7(c1), c1)))))),
% 27.64/17.84 inference(rewrite,[status(thm)],[])).
% 27.64/17.84 tff(3167,plain,
% 27.64/17.84 (((f10(f3(f7(c1), c1)) = f3(f7(c1), c1)) | big_f(f3(f7(c1), c1), f10(f3(f7(c1), c1))) | (~(f7(c2) = c2)) | (f6(c2, f3(f7(c1), c1)) = f3(f7(c1), c1)) | big_f(f7(c2), f6(c2, f3(f7(c1), c1))) | (~(f3(f7(c1), c1) = f8(f3(f7(c1), c1))))) <=> ((~(f7(c2) = c2)) | (f10(f3(f7(c1), c1)) = f3(f7(c1), c1)) | big_f(f3(f7(c1), c1), f10(f3(f7(c1), c1))) | (f6(c2, f3(f7(c1), c1)) = f3(f7(c1), c1)) | big_f(f7(c2), f6(c2, f3(f7(c1), c1))) | (~(f3(f7(c1), c1) = f8(f3(f7(c1), c1)))))),
% 27.64/17.84 inference(rewrite,[status(thm)],[])).
% 27.64/17.84 tff(3168,plain,
% 27.64/17.84 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(f3(f7(c1), c1)) = f3(f7(c1), c1)) | big_f(f3(f7(c1), c1), f10(f3(f7(c1), c1))) | (~(f7(c2) = c2)) | (f6(c2, f3(f7(c1), c1)) = f3(f7(c1), c1)) | big_f(f7(c2), f6(c2, f3(f7(c1), c1))) | (~(f3(f7(c1), c1) = f8(f3(f7(c1), c1)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((~(f7(c2) = c2)) | (f10(f3(f7(c1), c1)) = f3(f7(c1), c1)) | big_f(f3(f7(c1), c1), f10(f3(f7(c1), c1))) | (f6(c2, f3(f7(c1), c1)) = f3(f7(c1), c1)) | big_f(f7(c2), f6(c2, f3(f7(c1), c1))) | (~(f3(f7(c1), c1) = f8(f3(f7(c1), c1))))))),
% 27.64/17.84 inference(monotonicity,[status(thm)],[3167])).
% 27.64/17.84 tff(3169,plain,
% 27.64/17.84 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(f3(f7(c1), c1)) = f3(f7(c1), c1)) | big_f(f3(f7(c1), c1), f10(f3(f7(c1), c1))) | (~(f7(c2) = c2)) | (f6(c2, f3(f7(c1), c1)) = f3(f7(c1), c1)) | big_f(f7(c2), f6(c2, f3(f7(c1), c1))) | (~(f3(f7(c1), c1) = f8(f3(f7(c1), c1)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (~(f7(c2) = c2)) | (f10(f3(f7(c1), c1)) = f3(f7(c1), c1)) | big_f(f3(f7(c1), c1), f10(f3(f7(c1), c1))) | (f6(c2, f3(f7(c1), c1)) = f3(f7(c1), c1)) | big_f(f7(c2), f6(c2, f3(f7(c1), c1))) | (~(f3(f7(c1), c1) = f8(f3(f7(c1), c1)))))),
% 27.64/17.84 inference(transitivity,[status(thm)],[3168, 3166])).
% 27.64/17.84 tff(3170,plain,
% 27.64/17.84 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(f3(f7(c1), c1)) = f3(f7(c1), c1)) | big_f(f3(f7(c1), c1), f10(f3(f7(c1), c1))) | (~(f7(c2) = c2)) | (f6(c2, f3(f7(c1), c1)) = f3(f7(c1), c1)) | big_f(f7(c2), f6(c2, f3(f7(c1), c1))) | (~(f3(f7(c1), c1) = f8(f3(f7(c1), c1)))))),
% 27.64/17.84 inference(quant_inst,[status(thm)],[])).
% 27.64/17.84 tff(3171,plain,
% 27.64/17.84 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (~(f7(c2) = c2)) | (f10(f3(f7(c1), c1)) = f3(f7(c1), c1)) | big_f(f3(f7(c1), c1), f10(f3(f7(c1), c1))) | (f6(c2, f3(f7(c1), c1)) = f3(f7(c1), c1)) | big_f(f7(c2), f6(c2, f3(f7(c1), c1))) | (~(f3(f7(c1), c1) = f8(f3(f7(c1), c1))))),
% 27.64/17.84 inference(modus_ponens,[status(thm)],[3170, 3169])).
% 27.64/17.84 tff(3172,plain,
% 27.64/17.84 ((f10(f3(f7(c1), c1)) = f3(f7(c1), c1)) | big_f(f3(f7(c1), c1), f10(f3(f7(c1), c1))) | (f6(c2, f3(f7(c1), c1)) = f3(f7(c1), c1)) | big_f(f7(c2), f6(c2, f3(f7(c1), c1))) | (~(f3(f7(c1), c1) = f8(f3(f7(c1), c1))))),
% 27.64/17.84 inference(unit_resolution,[status(thm)],[3171, 2994, 77])).
% 27.64/17.84 tff(3173,plain,
% 27.64/17.84 ($false),
% 27.64/17.84 inference(unit_resolution,[status(thm)],[3172, 3165, 3160, 3154, 3150, 3144])).
% 27.64/17.84 tff(3174,plain,(big_f(f3(f7(c1), c1), f7(c1)) | (~(f7(c2) = c2)) | big_f(c2, c2) | (~(f6(f7(c2), f5(c1)) = c2)) | (~(f5(c1) = c1)) | (~(f7(c1) = c2)) | (~(f10(c1) = c2)) | (~(f8(c1) = c1)) | (~(c2 = c3)) | (~(c2 = f2(c2))) | (f7(c1) = c4)), inference(lemma,lemma(discharge,[]))).
% 27.64/17.84 tff(3175,plain,
% 27.64/17.84 (big_f(f3(f7(c1), c1), f7(c1))),
% 27.64/17.84 inference(unit_resolution,[status(thm)],[3174, 2852, 121, 3032, 230, 347, 15, 3018, 1335, 77, 3140])).
% 27.64/17.84 tff(3176,plain,
% 27.64/17.84 (big_f(f3(f7(c1), c1), f10(c1))),
% 27.64/17.84 inference(modus_ponens,[status(thm)],[3175, 3132])).
% 27.64/17.84 tff(3177,plain,
% 27.64/17.84 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (f3(f7(c1), c1) = f8(c1)) | (~big_f(f3(f7(c1), c1), f10(c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c1) = c1) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (f3(f7(c1), c1) = f8(c1)) | (~big_f(f3(f7(c1), c1), f10(c1))))),
% 27.64/17.84 inference(rewrite,[status(thm)],[])).
% 27.64/17.84 tff(3178,plain,
% 27.64/17.84 (((f10(c1) = c1) | (f3(f7(c1), c1) = f8(c1)) | (~big_f(f3(f7(c1), c1), f10(c1))) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1))) <=> ((f10(c1) = c1) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (f3(f7(c1), c1) = f8(c1)) | (~big_f(f3(f7(c1), c1), f10(c1))))),
% 27.64/17.84 inference(rewrite,[status(thm)],[])).
% 27.64/17.84 tff(3179,plain,
% 27.64/17.84 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (f3(f7(c1), c1) = f8(c1)) | (~big_f(f3(f7(c1), c1), f10(c1))) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (f3(f7(c1), c1) = f8(c1)) | (~big_f(f3(f7(c1), c1), f10(c1)))))),
% 27.64/17.84 inference(monotonicity,[status(thm)],[3178])).
% 27.64/17.84 tff(3180,plain,
% 27.64/17.84 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (f3(f7(c1), c1) = f8(c1)) | (~big_f(f3(f7(c1), c1), f10(c1))) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c1) = c1) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (f3(f7(c1), c1) = f8(c1)) | (~big_f(f3(f7(c1), c1), f10(c1))))),
% 27.64/17.84 inference(transitivity,[status(thm)],[3179, 3177])).
% 27.64/17.84 tff(3181,plain,
% 27.64/17.84 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (f3(f7(c1), c1) = f8(c1)) | (~big_f(f3(f7(c1), c1), f10(c1))) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)))),
% 27.64/17.84 inference(quant_inst,[status(thm)],[])).
% 27.64/17.84 tff(3182,plain,
% 27.64/17.84 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c1) = c1) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (f3(f7(c1), c1) = f8(c1)) | (~big_f(f3(f7(c1), c1), f10(c1)))),
% 27.64/17.84 inference(modus_ponens,[status(thm)],[3181, 3180])).
% 27.64/17.84 tff(3183,plain,
% 27.64/17.84 ((f3(f7(c1), c1) = f8(c1)) | (~big_f(f3(f7(c1), c1), f10(c1)))),
% 27.64/17.84 inference(unit_resolution,[status(thm)],[3182, 2662, 3, 77, 3041, 3037])).
% 27.64/17.84 tff(3184,plain,
% 27.64/17.84 (f3(f7(c1), c1) = f8(c1)),
% 27.64/17.84 inference(unit_resolution,[status(thm)],[3183, 3176])).
% 27.64/17.84 tff(3185,plain,
% 27.64/17.84 (f3(c2, c1) = c1),
% 27.64/17.84 inference(modus_ponens,[status(thm)],[3184, 3129])).
% 27.64/17.84 tff(3186,plain,
% 27.64/17.84 (big_f(f3(c2, c1), c2) <=> big_f(f3(f7(c1), c1), f7(c1))),
% 27.64/17.84 inference(monotonicity,[status(thm)],[3125, 354])).
% 27.64/17.84 tff(3187,plain,
% 27.64/17.84 (big_f(f3(f7(c1), c1), f7(c1)) <=> big_f(f3(c2, c1), c2)),
% 27.64/17.84 inference(symmetry,[status(thm)],[3186])).
% 27.64/17.84 tff(3188,plain,
% 27.64/17.84 (big_f(f3(c2, c1), c2)),
% 27.64/17.84 inference(modus_ponens,[status(thm)],[3175, 3187])).
% 27.64/17.84 tff(3189,plain,
% 27.64/17.84 ((~(c2 = c1)) <=> (~(c2 = c4))),
% 27.64/17.84 inference(monotonicity,[status(thm)],[3137])).
% 27.64/17.84 tff(3190,plain,
% 27.64/17.84 (~(c2 = c4)),
% 27.64/17.84 inference(modus_ponens,[status(thm)],[75, 3189])).
% 27.64/17.84 tff(3191,plain,
% 27.64/17.84 ((~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2))),
% 27.64/17.84 inference(unit_resolution,[status(thm)],[2892, 1398, 3190, 121, 1335, 2852])).
% 27.64/17.84 tff(3192,plain,
% 27.64/17.84 (~(f3(c2, c1) = c1)),
% 27.64/17.84 inference(unit_resolution,[status(thm)],[3191, 3188])).
% 27.64/17.84 tff(3193,plain,
% 27.64/17.84 ($false),
% 27.64/17.84 inference(unit_resolution,[status(thm)],[3192, 3185])).
% 27.64/17.84 tff(3194,plain,((~(f2(c3) = c2)) | (~(f7(c1) = c2)) | (~(f8(c1) = c1)) | big_f(c2, c2) | (f10(c1) = c1) | (~(f7(c2) = c2)) | (~(f6(f7(c2), f5(c1)) = c2)) | (~(f5(c1) = c1)) | (~(f4(c4) = c2)) | (~(c3 = c2))), inference(lemma,lemma(discharge,[]))).
% 27.64/17.84 tff(3195,plain,
% 27.64/17.84 (~(f2(c3) = c2)),
% 27.64/17.84 inference(unit_resolution,[status(thm)],[3194, 3113, 3070, 121, 3, 77, 120, 2940, 79, 67])).
% 27.64/17.84 tff(3196,plain,
% 27.64/17.84 (f2(c3) = c1),
% 27.64/17.84 inference(unit_resolution,[status(thm)],[1273, 3195])).
% 27.64/17.84 tff(3197,assumption,(~big_f(f7(c2), f6(c2, c1))), introduced(assumption)).
% 27.64/17.84 tff(3198,assumption,(~(f6(c2, c1) = c1)), introduced(assumption)).
% 27.64/17.84 tff(3199,plain,
% 27.64/17.84 (f9(c2, c1) = c2),
% 27.64/17.84 inference(transitivity,[status(thm)],[2899, 1230])).
% 27.64/17.84 tff(3200,plain,
% 27.64/17.84 ((f9(c2, c1) = c1) <=> (c2 = c1)),
% 27.64/17.84 inference(monotonicity,[status(thm)],[3199])).
% 27.64/17.84 tff(3201,plain,
% 27.64/17.84 ((c2 = c1) <=> (f9(c2, c1) = c1)),
% 27.64/17.84 inference(symmetry,[status(thm)],[3200])).
% 27.64/17.84 tff(3202,plain,
% 27.64/17.84 ((~(c2 = c1)) <=> (~(f9(c2, c1) = c1))),
% 27.64/17.84 inference(monotonicity,[status(thm)],[3201])).
% 27.64/17.84 tff(3203,plain,
% 27.64/17.84 (~(f9(c2, c1) = c1)),
% 27.64/17.84 inference(modus_ponens,[status(thm)],[75, 3202])).
% 27.64/17.84 tff(3204,plain,
% 27.64/17.84 (big_f(f9(c2, c1), f10(c2)) <=> big_f(c2, c2)),
% 27.64/17.84 inference(monotonicity,[status(thm)],[3199, 122])).
% 27.64/17.84 tff(3205,plain,
% 27.64/17.84 (big_f(c2, c2) <=> big_f(f9(c2, c1), f10(c2))),
% 27.64/17.84 inference(symmetry,[status(thm)],[3204])).
% 27.64/17.84 tff(3206,plain,
% 27.64/17.84 ((~big_f(c2, c2)) <=> (~big_f(f9(c2, c1), f10(c2)))),
% 27.64/17.84 inference(monotonicity,[status(thm)],[3205])).
% 27.64/17.84 tff(3207,plain,
% 27.64/17.84 (~big_f(f9(c2, c1), f10(c2))),
% 27.64/17.84 inference(modus_ponens,[status(thm)],[121, 3206])).
% 27.64/17.84 tff(3208,plain,
% 27.64/17.84 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)))),
% 27.64/17.84 inference(rewrite,[status(thm)],[])).
% 27.64/17.84 tff(3209,plain,
% 27.64/17.84 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)))),
% 27.64/17.84 inference(quant_inst,[status(thm)],[])).
% 27.64/17.84 tff(3210,plain,
% 27.64/17.84 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1))),
% 27.64/17.84 inference(modus_ponens,[status(thm)],[3209, 3208])).
% 27.64/17.84 tff(3211,plain,
% 27.64/17.84 ((~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1))),
% 27.64/17.84 inference(unit_resolution,[status(thm)],[3210, 2492])).
% 27.64/17.84 tff(3212,plain,
% 27.64/17.84 ($false),
% 27.64/17.84 inference(unit_resolution,[status(thm)],[3211, 3207, 3203, 122, 3198, 77, 3197])).
% 27.64/17.84 tff(3213,plain,((~(f9(f10(c2), f2(c3)) = c2)) | (~(f10(c2) = c2)) | (f6(c2, c1) = c1) | (~(f7(c2) = c2)) | big_f(f7(c2), f6(c2, c1)) | big_f(c2, c2) | (~(f2(c3) = c1))), inference(lemma,lemma(discharge,[]))).
% 27.64/17.84 tff(3214,plain,
% 27.64/17.84 (~(f9(f10(c2), f2(c3)) = c2)),
% 27.64/17.84 inference(unit_resolution,[status(thm)],[3213, 3124, 122, 77, 3120, 121, 3196])).
% 27.64/17.84 tff(3215,plain,
% 27.64/17.84 (f9(f10(c2), f2(c3)) = c1),
% 27.64/17.84 inference(unit_resolution,[status(thm)],[1245, 3214])).
% 27.64/17.84 tff(3216,plain,
% 27.64/17.84 (c1 = f2(c3)),
% 27.64/17.84 inference(symmetry,[status(thm)],[3196])).
% 27.64/17.84 tff(3217,plain,
% 27.64/17.84 (f9(c2, c1) = f9(f10(c2), f2(c3))),
% 27.64/17.84 inference(monotonicity,[status(thm)],[216, 3216])).
% 27.64/17.84 tff(3218,plain,
% 27.64/17.84 (f9(c2, c1) = c1),
% 27.64/17.84 inference(transitivity,[status(thm)],[3217, 3215])).
% 27.64/17.84 tff(3219,plain,
% 27.64/17.84 (big_f(f9(c2, c1), f10(c2)) <=> big_f(c1, c2)),
% 27.64/17.84 inference(monotonicity,[status(thm)],[3218, 122])).
% 27.64/17.84 tff(3220,plain,
% 27.64/17.84 (big_f(c1, c2) <=> big_f(f9(c2, c1), f10(c2))),
% 27.64/17.84 inference(symmetry,[status(thm)],[3219])).
% 27.64/17.84 tff(3221,plain,
% 27.64/17.84 (big_f(f9(c2, c1), f10(c2))),
% 27.64/17.84 inference(modus_ponens,[status(thm)],[3067, 3220])).
% 27.64/17.84 tff(3222,plain,
% 27.64/17.84 (f9(c2, c1) = c1),
% 27.64/17.84 inference(unit_resolution,[status(thm)],[1255, 3215, 3196, 122])).
% 27.64/17.84 tff(3223,plain,
% 27.64/17.84 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))))),
% 27.64/17.84 inference(rewrite,[status(thm)],[])).
% 27.64/17.84 tff(3224,plain,
% 27.64/17.84 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))))),
% 27.64/17.84 inference(quant_inst,[status(thm)],[])).
% 27.64/17.84 tff(3225,plain,
% 27.64/17.84 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2)))),
% 27.64/17.84 inference(modus_ponens,[status(thm)],[3224, 3223])).
% 27.64/17.84 tff(3226,plain,
% 27.64/17.84 ($false),
% 27.64/17.84 inference(unit_resolution,[status(thm)],[3225, 2409, 122, 3222, 3221, 77, 3124, 3120])).
% 27.64/17.84 tff(3227,plain,(big_f(c2, c2) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (f10(c1) = c1) | (~(f4(c4) = c2)) | (~(c3 = c2)) | (f7(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 27.64/17.84 tff(3228,plain,
% 27.64/17.84 (big_f(c2, c2)),
% 27.64/17.84 inference(unit_resolution,[status(thm)],[3227, 3, 77, 122, 79, 67, 115])).
% 27.64/17.84 tff(3229,plain,
% 27.64/17.84 (f7(c1) = f7(c2)),
% 27.64/17.84 inference(transitivity,[status(thm)],[120, 82])).
% 27.64/17.84 tff(3230,plain,
% 27.64/17.84 (big_f(f7(c1), f6(c2, c2)) <=> big_f(f7(c2), f6(c2, c2))),
% 27.64/17.84 inference(monotonicity,[status(thm)],[3229])).
% 27.64/17.84 tff(3231,plain,
% 27.64/17.84 (big_f(f7(c2), f6(c2, c2)) <=> big_f(f7(c1), f6(c2, c2))),
% 27.64/17.84 inference(symmetry,[status(thm)],[3230])).
% 27.64/17.84 tff(3232,plain,
% 27.64/17.84 (big_f(f7(c2), f6(c2, c2))),
% 27.64/17.84 inference(unit_resolution,[status(thm)],[2700, 1345, 77, 79, 15, 122])).
% 27.64/17.84 tff(3233,plain,
% 27.64/17.84 (big_f(f7(c1), f6(c2, c2))),
% 27.64/17.84 inference(modus_ponens,[status(thm)],[3232, 3231])).
% 27.64/17.84 tff(3234,plain,
% 27.64/17.84 ((f6(c2, c2) = f5(c1)) <=> (f6(c2, c2) = c2)),
% 27.64/17.84 inference(monotonicity,[status(thm)],[186])).
% 27.64/17.84 tff(3235,plain,
% 27.64/17.84 ((f6(c2, c2) = c2) <=> (f6(c2, c2) = f5(c1))),
% 27.64/17.84 inference(symmetry,[status(thm)],[3234])).
% 27.64/17.84 tff(3236,plain,
% 27.64/17.84 (f6(f7(c2), f5(c1)) = f6(c2, c2)),
% 27.64/17.84 inference(monotonicity,[status(thm)],[77, 186])).
% 27.64/17.84 tff(3237,plain,
% 27.64/17.84 ((f6(f7(c2), f5(c1)) = c2) <=> (f6(c2, c2) = c2)),
% 27.64/17.84 inference(monotonicity,[status(thm)],[3236])).
% 27.64/17.84 tff(3238,plain,
% 27.64/17.84 ((f6(f7(c2), f5(c1)) = c2) <=> (f6(c2, c2) = f5(c1))),
% 27.64/17.84 inference(transitivity,[status(thm)],[3237, 3235])).
% 27.64/17.84 tff(3239,plain,
% 27.64/17.84 ((~(f6(f7(c2), f5(c1)) = c2)) <=> (~(f6(c2, c2) = f5(c1)))),
% 27.64/17.84 inference(monotonicity,[status(thm)],[3238])).
% 27.64/17.84 tff(3240,assumption,(~(f6(f7(c2), f5(c1)) = c2)), introduced(assumption)).
% 27.64/17.84 tff(3241,plain,
% 27.64/17.84 (~(f6(c2, c2) = f5(c1))),
% 27.64/17.84 inference(modus_ponens,[status(thm)],[3240, 3239])).
% 27.64/17.84 tff(3242,plain,
% 27.64/17.84 ((c2 = f6(c2, c2)) <=> (f6(c2, c2) = c2)),
% 27.64/17.84 inference(commutativity,[status(thm)],[])).
% 27.64/17.84 tff(3243,plain,
% 27.64/17.84 (f6(f7(c2), f5(c1)) = c1),
% 27.64/17.84 inference(unit_resolution,[status(thm)],[2978, 3240])).
% 27.64/17.84 tff(3244,plain,
% 27.64/17.84 (c1 = f6(f7(c2), f5(c1))),
% 27.64/17.84 inference(symmetry,[status(thm)],[3243])).
% 27.64/17.84 tff(3245,plain,
% 27.64/17.84 (f6(c2, c2) = f6(f7(c2), f5(c1))),
% 27.64/17.84 inference(symmetry,[status(thm)],[3236])).
% 27.64/17.84 tff(3246,plain,
% 27.64/17.84 (f6(c2, c2) = c1),
% 27.64/17.84 inference(transitivity,[status(thm)],[3245, 2947])).
% 27.64/17.84 tff(3247,plain,
% 27.64/17.84 (f8(f6(c2, c2)) = f8(c1)),
% 27.64/17.84 inference(monotonicity,[status(thm)],[3246])).
% 27.64/17.84 tff(3248,plain,
% 27.64/17.84 (f8(f6(c2, c2)) = c2),
% 27.64/17.84 inference(transitivity,[status(thm)],[3247, 1671])).
% 27.64/17.84 tff(3249,plain,
% 27.64/17.84 ((f9(c2, c2) = f8(f6(c2, c2))) <=> (f9(c2, c2) = c2)),
% 27.64/17.84 inference(monotonicity,[status(thm)],[3248])).
% 27.64/17.84 tff(3250,plain,
% 27.64/17.84 ((f9(c2, c2) = f8(f6(c2, c2))) <=> (f9(f10(c2), f4(c4)) = c2)),
% 27.64/17.84 inference(transitivity,[status(thm)],[3249, 134])).
% 27.64/17.84 tff(3251,plain,
% 27.64/17.84 (f10(f6(c2, c2)) = f10(c1)),
% 27.64/17.84 inference(monotonicity,[status(thm)],[3246])).
% 27.64/17.84 tff(3252,plain,
% 27.64/17.84 (f10(f6(c2, c2)) = f10(c2)),
% 27.64/17.84 inference(transitivity,[status(thm)],[3251, 16, 216])).
% 27.64/17.84 tff(3253,plain,
% 27.64/17.84 (big_f(f9(c2, c2), f10(f6(c2, c2))) <=> big_f(f9(c2, c2), f10(c2))),
% 27.64/17.84 inference(monotonicity,[status(thm)],[3252])).
% 27.64/17.84 tff(3254,plain,
% 27.64/17.84 (big_f(f9(c2, c2), f10(c2)) <=> big_f(f9(c2, c2), f10(f6(c2, c2)))),
% 27.64/17.84 inference(symmetry,[status(thm)],[3253])).
% 27.64/17.84 tff(3255,plain,
% 27.64/17.84 (big_f(f7(c2), f6(c2, c2))),
% 27.64/17.84 inference(unit_resolution,[status(thm)],[2700, 1345, 77, 79, 16, 122])).
% 27.64/17.84 tff(3256,plain,
% 27.64/17.84 (f7(f6(c2, c2)) = f7(c1)),
% 27.64/17.84 inference(monotonicity,[status(thm)],[3246])).
% 27.64/17.84 tff(3257,plain,
% 27.64/17.84 (f7(f6(c2, c2)) = f7(c2)),
% 27.64/17.84 inference(transitivity,[status(thm)],[3256, 347, 82])).
% 27.64/17.84 tff(3258,plain,
% 27.64/17.84 (big_f(f7(f6(c2, c2)), f6(c2, c2)) <=> big_f(f7(c2), f6(c2, c2))),
% 27.64/17.84 inference(monotonicity,[status(thm)],[3257])).
% 27.64/17.84 tff(3259,plain,
% 27.64/17.84 (big_f(f7(c2), f6(c2, c2)) <=> big_f(f7(f6(c2, c2)), f6(c2, c2))),
% 27.64/17.84 inference(symmetry,[status(thm)],[3258])).
% 27.64/17.84 tff(3260,plain,
% 27.64/17.84 (big_f(f7(f6(c2, c2)), f6(c2, c2))),
% 27.64/17.84 inference(modus_ponens,[status(thm)],[2707, 3259])).
% 27.64/17.84 tff(3261,plain,
% 27.64/17.84 (f5(f6(c2, c2)) = f5(c1)),
% 27.64/17.84 inference(monotonicity,[status(thm)],[3246])).
% 27.64/17.84 tff(3262,plain,
% 27.64/17.84 (f5(f6(c2, c2)) = c2),
% 27.64/17.84 inference(transitivity,[status(thm)],[3261, 186])).
% 27.64/17.84 tff(3263,plain,
% 27.64/17.84 ((f6(c2, c2) = f5(f6(c2, c2))) <=> (f6(c2, c2) = c2)),
% 27.64/17.84 inference(monotonicity,[status(thm)],[3262])).
% 27.64/17.84 tff(3264,plain,
% 27.64/17.84 ((f6(c2, c2) = c2) <=> (f6(c2, c2) = f5(f6(c2, c2)))),
% 27.64/17.84 inference(symmetry,[status(thm)],[3263])).
% 27.64/17.84 tff(3265,plain,
% 27.64/17.84 ((~(f6(c2, c2) = c2)) <=> (~(f6(c2, c2) = f5(f6(c2, c2))))),
% 27.64/17.84 inference(monotonicity,[status(thm)],[3264])).
% 27.64/17.84 tff(3266,plain,
% 27.64/17.84 ((f6(c2, c2) = c2) <=> (c1 = c2)),
% 27.64/17.84 inference(monotonicity,[status(thm)],[3246])).
% 27.64/17.84 tff(3267,plain,
% 27.64/17.84 ((f6(c2, c2) = c2) <=> (c2 = c1)),
% 27.64/17.84 inference(transitivity,[status(thm)],[3266, 1])).
% 27.64/17.84 tff(3268,plain,
% 27.64/17.84 ((c2 = c1) <=> (f6(c2, c2) = c2)),
% 27.64/17.84 inference(symmetry,[status(thm)],[3267])).
% 27.64/17.84 tff(3269,plain,
% 27.64/17.84 ((~(c2 = c1)) <=> (~(f6(c2, c2) = c2))),
% 27.64/17.84 inference(monotonicity,[status(thm)],[3268])).
% 27.64/17.84 tff(3270,plain,
% 27.64/17.84 (~(f6(c2, c2) = c2)),
% 27.64/17.84 inference(modus_ponens,[status(thm)],[75, 3269])).
% 27.64/17.84 tff(3271,plain,
% 27.64/17.84 (~(f6(c2, c2) = f5(f6(c2, c2)))),
% 27.64/17.84 inference(modus_ponens,[status(thm)],[3270, 3265])).
% 27.64/17.84 tff(3272,plain,
% 27.64/17.84 (f7(f6(c2, c2)) = c2),
% 27.64/17.84 inference(transitivity,[status(thm)],[3256, 347])).
% 27.64/17.84 tff(3273,plain,
% 27.64/17.84 ((f7(f6(c2, c2)) = f6(c2, c2)) <=> (c2 = f6(c2, c2))),
% 27.64/17.84 inference(monotonicity,[status(thm)],[3272])).
% 27.64/17.84 tff(3274,plain,
% 27.64/17.84 ((f7(f6(c2, c2)) = f6(c2, c2)) <=> (f6(c2, c2) = c2)),
% 27.64/17.84 inference(transitivity,[status(thm)],[3273, 3242])).
% 27.64/17.84 tff(3275,plain,
% 27.64/17.84 ((f6(c2, c2) = c2) <=> (f7(f6(c2, c2)) = f6(c2, c2))),
% 27.64/17.84 inference(symmetry,[status(thm)],[3274])).
% 27.64/17.84 tff(3276,plain,
% 27.64/17.84 ((~(f6(c2, c2) = c2)) <=> (~(f7(f6(c2, c2)) = f6(c2, c2)))),
% 27.64/17.84 inference(monotonicity,[status(thm)],[3275])).
% 27.64/17.84 tff(3277,plain,
% 27.64/17.84 (~(f7(f6(c2, c2)) = f6(c2, c2))),
% 27.64/17.84 inference(modus_ponens,[status(thm)],[3270, 3276])).
% 27.64/17.84 tff(3278,plain,
% 27.64/17.84 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f6(c2, c2) = f5(f6(c2, c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f7(f6(c2, c2)), f6(c2, c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f6(c2, c2) = f5(f6(c2, c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f7(f6(c2, c2)), f6(c2, c2))))),
% 27.64/17.84 inference(rewrite,[status(thm)],[])).
% 27.64/17.84 tff(3279,plain,
% 27.64/17.84 (((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f6(c2, c2)) = f6(c2, c2)) | (f6(c2, c2) = f5(f6(c2, c2))) | (~big_f(f7(f6(c2, c2)), f6(c2, c2)))) <=> ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f6(c2, c2) = f5(f6(c2, c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f7(f6(c2, c2)), f6(c2, c2))))),
% 27.64/17.84 inference(rewrite,[status(thm)],[])).
% 27.64/17.84 tff(3280,plain,
% 27.64/17.84 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f6(c2, c2)) = f6(c2, c2)) | (f6(c2, c2) = f5(f6(c2, c2))) | (~big_f(f7(f6(c2, c2)), f6(c2, c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f6(c2, c2) = f5(f6(c2, c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f7(f6(c2, c2)), f6(c2, c2)))))),
% 27.64/17.84 inference(monotonicity,[status(thm)],[3279])).
% 27.64/17.84 tff(3281,plain,
% 27.64/17.84 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f6(c2, c2)) = f6(c2, c2)) | (f6(c2, c2) = f5(f6(c2, c2))) | (~big_f(f7(f6(c2, c2)), f6(c2, c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f6(c2, c2) = f5(f6(c2, c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f7(f6(c2, c2)), f6(c2, c2))))),
% 27.64/17.84 inference(transitivity,[status(thm)],[3280, 3278])).
% 27.64/17.84 tff(3282,plain,
% 27.64/17.84 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f6(c2, c2)) = f6(c2, c2)) | (f6(c2, c2) = f5(f6(c2, c2))) | (~big_f(f7(f6(c2, c2)), f6(c2, c2))))),
% 27.64/17.84 inference(quant_inst,[status(thm)],[])).
% 27.64/17.84 tff(3283,plain,
% 27.64/17.84 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f6(c2, c2) = f5(f6(c2, c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f7(f6(c2, c2)), f6(c2, c2)))),
% 27.64/17.84 inference(modus_ponens,[status(thm)],[3282, 3281])).
% 27.64/17.84 tff(3284,plain,
% 27.64/17.84 ((f6(c2, c2) = f5(f6(c2, c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f7(f6(c2, c2)), f6(c2, c2)))),
% 27.64/17.84 inference(unit_resolution,[status(thm)],[3283, 676, 122, 1209, 256])).
% 27.64/17.85 tff(3285,plain,
% 27.64/17.85 ($false),
% 27.64/17.85 inference(unit_resolution,[status(thm)],[3284, 3277, 3271, 3260])).
% 27.64/17.85 tff(3286,plain,((f9(c2, c2) = c2) | (~(f10(c2) = c2)) | big_f(f9(c2, c2), f10(c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~(f7(c2) = c2)) | (~(f7(c1) = c2)) | (~(f6(f7(c2), f5(c1)) = c1)) | (~(f5(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.64/17.85 tff(3287,plain,
% 27.64/17.85 (f9(c2, c2) = c2),
% 27.64/17.85 inference(unit_resolution,[status(thm)],[3286, 256, 122, 2707, 77, 347, 2947, 186])).
% 27.64/17.85 tff(3288,plain,
% 27.64/17.85 (big_f(f9(c2, c2), f10(c2)) <=> big_f(c2, c2)),
% 27.64/17.85 inference(monotonicity,[status(thm)],[3287, 122])).
% 27.64/17.85 tff(3289,plain,
% 27.64/17.85 (big_f(c2, c2) <=> big_f(f9(c2, c2), f10(c2))),
% 27.64/17.85 inference(symmetry,[status(thm)],[3288])).
% 27.64/17.85 tff(3290,plain,
% 27.64/17.85 (big_f(f9(c2, c2), f10(c2))),
% 27.64/17.85 inference(modus_ponens,[status(thm)],[1345, 3289])).
% 27.64/17.85 tff(3291,plain,
% 27.64/17.85 ($false),
% 27.64/17.85 inference(unit_resolution,[status(thm)],[256, 3290])).
% 27.64/17.85 tff(3292,plain,(big_f(f9(c2, c2), f10(c2)) | (~big_f(c2, c2)) | (~(f10(c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~(f7(c2) = c2)) | (~(f7(c1) = c2)) | (~(f6(f7(c2), f5(c1)) = c1)) | (~(f5(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.64/17.85 tff(3293,plain,
% 27.64/17.85 (big_f(f9(c2, c2), f10(c2))),
% 27.64/17.85 inference(unit_resolution,[status(thm)],[3292, 2947, 122, 3255, 77, 347, 1345, 186])).
% 27.64/17.85 tff(3294,plain,
% 27.64/17.85 (big_f(f9(c2, c2), f10(f6(c2, c2)))),
% 27.64/17.85 inference(modus_ponens,[status(thm)],[3293, 3254])).
% 27.64/17.85 tff(3295,plain,
% 27.64/17.85 (f10(f6(c2, c2)) = c2),
% 27.64/17.85 inference(transitivity,[status(thm)],[3251, 16])).
% 27.64/17.85 tff(3296,plain,
% 27.64/17.85 ((f10(f6(c2, c2)) = f6(c2, c2)) <=> (c2 = f6(c2, c2))),
% 27.64/17.85 inference(monotonicity,[status(thm)],[3295])).
% 27.64/17.85 tff(3297,plain,
% 27.64/17.85 ((f10(f6(c2, c2)) = f6(c2, c2)) <=> (f6(c2, c2) = c2)),
% 27.64/17.85 inference(transitivity,[status(thm)],[3296, 3242])).
% 27.64/17.85 tff(3298,plain,
% 27.64/17.85 ((f6(c2, c2) = c2) <=> (f10(f6(c2, c2)) = f6(c2, c2))),
% 27.64/17.85 inference(symmetry,[status(thm)],[3297])).
% 27.64/17.85 tff(3299,plain,
% 27.64/17.85 ((~(f6(c2, c2) = c2)) <=> (~(f10(f6(c2, c2)) = f6(c2, c2)))),
% 27.64/17.85 inference(monotonicity,[status(thm)],[3298])).
% 27.64/17.85 tff(3300,plain,
% 27.64/17.85 (~(f10(f6(c2, c2)) = f6(c2, c2))),
% 27.64/17.85 inference(modus_ponens,[status(thm)],[3270, 3299])).
% 27.64/17.85 tff(3301,plain,
% 27.64/17.85 (big_f(f7(f6(c2, c2)), f6(c2, c2))),
% 27.64/17.85 inference(modus_ponens,[status(thm)],[3255, 3259])).
% 27.64/17.85 tff(3302,plain,
% 27.64/17.85 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f6(c2, c2)) = f6(c2, c2)) | (f6(c2, c2) = f5(f6(c2, c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f7(f6(c2, c2)), f6(c2, c2))) | (f9(c2, c2) = f8(f6(c2, c2))) | (~big_f(f9(c2, c2), f10(f6(c2, c2)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(f6(c2, c2)) = f6(c2, c2)) | (f6(c2, c2) = f5(f6(c2, c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f7(f6(c2, c2)), f6(c2, c2))) | (f9(c2, c2) = f8(f6(c2, c2))) | (~big_f(f9(c2, c2), f10(f6(c2, c2)))))),
% 27.64/17.85 inference(rewrite,[status(thm)],[])).
% 27.64/17.85 tff(3303,plain,
% 27.64/17.85 (((f10(f6(c2, c2)) = f6(c2, c2)) | (f9(c2, c2) = f8(f6(c2, c2))) | (~big_f(f9(c2, c2), f10(f6(c2, c2)))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (f6(c2, c2) = f5(f6(c2, c2))) | (~big_f(f7(f6(c2, c2)), f6(c2, c2)))) <=> ((f10(f6(c2, c2)) = f6(c2, c2)) | (f6(c2, c2) = f5(f6(c2, c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f7(f6(c2, c2)), f6(c2, c2))) | (f9(c2, c2) = f8(f6(c2, c2))) | (~big_f(f9(c2, c2), f10(f6(c2, c2)))))),
% 27.64/17.85 inference(rewrite,[status(thm)],[])).
% 27.64/17.85 tff(3304,plain,
% 27.64/17.85 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f6(c2, c2)) = f6(c2, c2)) | (f9(c2, c2) = f8(f6(c2, c2))) | (~big_f(f9(c2, c2), f10(f6(c2, c2)))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (f6(c2, c2) = f5(f6(c2, c2))) | (~big_f(f7(f6(c2, c2)), f6(c2, c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f6(c2, c2)) = f6(c2, c2)) | (f6(c2, c2) = f5(f6(c2, c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f7(f6(c2, c2)), f6(c2, c2))) | (f9(c2, c2) = f8(f6(c2, c2))) | (~big_f(f9(c2, c2), f10(f6(c2, c2))))))),
% 27.66/17.85 inference(monotonicity,[status(thm)],[3303])).
% 27.66/17.85 tff(3305,plain,
% 27.66/17.85 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f6(c2, c2)) = f6(c2, c2)) | (f9(c2, c2) = f8(f6(c2, c2))) | (~big_f(f9(c2, c2), f10(f6(c2, c2)))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (f6(c2, c2) = f5(f6(c2, c2))) | (~big_f(f7(f6(c2, c2)), f6(c2, c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(f6(c2, c2)) = f6(c2, c2)) | (f6(c2, c2) = f5(f6(c2, c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f7(f6(c2, c2)), f6(c2, c2))) | (f9(c2, c2) = f8(f6(c2, c2))) | (~big_f(f9(c2, c2), f10(f6(c2, c2)))))),
% 27.66/17.85 inference(transitivity,[status(thm)],[3304, 3302])).
% 27.66/17.85 tff(3306,plain,
% 27.66/17.85 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f6(c2, c2)) = f6(c2, c2)) | (f9(c2, c2) = f8(f6(c2, c2))) | (~big_f(f9(c2, c2), f10(f6(c2, c2)))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (f6(c2, c2) = f5(f6(c2, c2))) | (~big_f(f7(f6(c2, c2)), f6(c2, c2))))),
% 27.66/17.85 inference(quant_inst,[status(thm)],[])).
% 27.66/17.85 tff(3307,plain,
% 27.66/17.85 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(f6(c2, c2)) = f6(c2, c2)) | (f6(c2, c2) = f5(f6(c2, c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f7(f6(c2, c2)), f6(c2, c2))) | (f9(c2, c2) = f8(f6(c2, c2))) | (~big_f(f9(c2, c2), f10(f6(c2, c2))))),
% 27.66/17.85 inference(modus_ponens,[status(thm)],[3306, 3305])).
% 27.66/17.85 tff(3308,plain,
% 27.66/17.85 ((f10(f6(c2, c2)) = f6(c2, c2)) | (f6(c2, c2) = f5(f6(c2, c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f7(f6(c2, c2)), f6(c2, c2))) | (f9(c2, c2) = f8(f6(c2, c2))) | (~big_f(f9(c2, c2), f10(f6(c2, c2))))),
% 27.66/17.85 inference(unit_resolution,[status(thm)],[3307, 1659])).
% 27.66/17.85 tff(3309,plain,
% 27.66/17.85 (f9(c2, c2) = f8(f6(c2, c2))),
% 27.66/17.85 inference(unit_resolution,[status(thm)],[3308, 3271, 3277, 3301, 3300, 3294])).
% 27.66/17.85 tff(3310,plain,
% 27.66/17.85 (f9(f10(c2), f4(c4)) = c2),
% 27.66/17.85 inference(modus_ponens,[status(thm)],[3309, 3250])).
% 27.66/17.85 tff(3311,plain,
% 27.66/17.85 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f6(c2, c2) = f5(f6(c2, c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f7(f6(c2, c2)), f6(c2, c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f6(c2, c2) = f5(f6(c2, c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f7(f6(c2, c2)), f6(c2, c2))))),
% 27.66/17.85 inference(rewrite,[status(thm)],[])).
% 27.66/17.85 tff(3312,plain,
% 27.66/17.85 (((~(f10(c2) = c2)) | (f7(f6(c2, c2)) = f6(c2, c2)) | (f6(c2, c2) = f5(f6(c2, c2))) | (~big_f(f7(f6(c2, c2)), f6(c2, c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2)))) <=> ((~(f10(c2) = c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f6(c2, c2) = f5(f6(c2, c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f7(f6(c2, c2)), f6(c2, c2))))),
% 27.66/17.85 inference(rewrite,[status(thm)],[])).
% 27.66/17.85 tff(3313,plain,
% 27.66/17.85 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(f6(c2, c2)) = f6(c2, c2)) | (f6(c2, c2) = f5(f6(c2, c2))) | (~big_f(f7(f6(c2, c2)), f6(c2, c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f6(c2, c2) = f5(f6(c2, c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f7(f6(c2, c2)), f6(c2, c2)))))),
% 27.66/17.85 inference(monotonicity,[status(thm)],[3312])).
% 27.66/17.85 tff(3314,plain,
% 27.66/17.85 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(f6(c2, c2)) = f6(c2, c2)) | (f6(c2, c2) = f5(f6(c2, c2))) | (~big_f(f7(f6(c2, c2)), f6(c2, c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f6(c2, c2) = f5(f6(c2, c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f7(f6(c2, c2)), f6(c2, c2))))),
% 27.66/17.85 inference(transitivity,[status(thm)],[3313, 3311])).
% 27.66/17.85 tff(3315,plain,
% 27.66/17.85 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(f6(c2, c2)) = f6(c2, c2)) | (f6(c2, c2) = f5(f6(c2, c2))) | (~big_f(f7(f6(c2, c2)), f6(c2, c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))),
% 27.66/17.85 inference(quant_inst,[status(thm)],[])).
% 27.66/17.85 tff(3316,plain,
% 27.66/17.85 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f6(c2, c2) = f5(f6(c2, c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f7(f6(c2, c2)), f6(c2, c2)))),
% 27.66/17.85 inference(modus_ponens,[status(thm)],[3315, 3314])).
% 27.66/17.85 tff(3317,plain,
% 27.66/17.85 ((~(f9(c2, c2) = c2)) | (f6(c2, c2) = f5(f6(c2, c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f7(f6(c2, c2)), f6(c2, c2)))),
% 27.66/17.85 inference(unit_resolution,[status(thm)],[3316, 1190, 122, 3293])).
% 27.66/17.85 tff(3318,plain,
% 27.66/17.85 (~(f9(c2, c2) = c2)),
% 27.66/17.85 inference(unit_resolution,[status(thm)],[3317, 3271, 3277, 3301])).
% 27.66/17.85 tff(3319,plain,
% 27.66/17.85 (~(f9(f10(c2), f4(c4)) = c2)),
% 27.66/17.85 inference(unit_resolution,[status(thm)],[1606, 3318, 79, 122])).
% 27.66/17.85 tff(3320,plain,
% 27.66/17.85 ($false),
% 27.66/17.85 inference(unit_resolution,[status(thm)],[3319, 3310])).
% 27.66/17.85 tff(3321,plain,((~(f6(f7(c2), f5(c1)) = c1)) | (~(f8(c1) = c2)) | (~(f5(c1) = c2)) | (~(f7(c2) = c2)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f7(c1) = c2)) | (~(f10(c1) = c2)) | (~big_f(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 27.66/17.85 tff(3322,plain,
% 27.66/17.85 (~(f8(c1) = c2)),
% 27.66/17.85 inference(unit_resolution,[status(thm)],[3321, 3243, 186, 77, 79, 122, 120, 15, 1345])).
% 27.66/17.85 tff(3323,plain,
% 27.66/17.85 (f8(c1) = c1),
% 27.66/17.85 inference(unit_resolution,[status(thm)],[1680, 3322])).
% 27.66/17.85 tff(3324,plain,
% 27.66/17.85 (f8(c1) = f6(c2, c2)),
% 27.66/17.85 inference(transitivity,[status(thm)],[3323, 3244, 3236])).
% 27.66/17.85 tff(3325,plain,
% 27.66/17.85 ((c2 = f8(c1)) <=> (c2 = f6(c2, c2))),
% 27.66/17.85 inference(monotonicity,[status(thm)],[3324])).
% 27.66/17.85 tff(3326,plain,
% 27.66/17.85 ((c2 = f8(c1)) <=> (f6(c2, c2) = c2)),
% 27.66/17.85 inference(transitivity,[status(thm)],[3325, 3242])).
% 27.66/17.85 tff(3327,plain,
% 27.66/17.85 ((f6(c2, c2) = c2) <=> (c2 = f8(c1))),
% 27.66/17.85 inference(symmetry,[status(thm)],[3326])).
% 27.66/17.85 tff(3328,plain,
% 27.66/17.85 ((~(f6(c2, c2) = c2)) <=> (~(c2 = f8(c1)))),
% 27.66/17.85 inference(monotonicity,[status(thm)],[3327])).
% 27.66/17.85 tff(3329,plain,
% 27.66/17.85 ((~(f6(f7(c2), f5(c1)) = c2)) <=> (~(f6(c2, c2) = c2))),
% 27.66/17.85 inference(monotonicity,[status(thm)],[3237])).
% 27.66/17.85 tff(3330,plain,
% 27.66/17.85 (~(f6(c2, c2) = c2)),
% 27.66/17.85 inference(modus_ponens,[status(thm)],[3240, 3329])).
% 27.66/17.85 tff(3331,plain,
% 27.66/17.85 (~(c2 = f8(c1))),
% 27.66/17.85 inference(modus_ponens,[status(thm)],[3330, 3328])).
% 27.66/17.85 tff(3332,plain,
% 27.66/17.85 (big_f(c2, f10(c1))),
% 27.66/17.85 inference(modus_ponens,[status(thm)],[1345, 2719])).
% 27.66/17.85 tff(3333,plain,
% 27.66/17.85 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(c1) = c1) | (f10(c1) = c1) | (c2 = f8(c1)) | (~big_f(c2, f10(c1))) | (f6(c2, c2) = f5(c1)) | (~big_f(f7(c1), f6(c2, c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c1) = c1) | (f10(c1) = c1) | (c2 = f8(c1)) | (~big_f(c2, f10(c1))) | (f6(c2, c2) = f5(c1)) | (~big_f(f7(c1), f6(c2, c2))))),
% 27.66/17.85 inference(rewrite,[status(thm)],[])).
% 27.66/17.85 tff(3334,plain,
% 27.66/17.85 (((f10(c1) = c1) | (c2 = f8(c1)) | (~big_f(c2, f10(c1))) | (f7(c1) = c1) | (f6(c2, c2) = f5(c1)) | (~big_f(f7(c1), f6(c2, c2)))) <=> ((f7(c1) = c1) | (f10(c1) = c1) | (c2 = f8(c1)) | (~big_f(c2, f10(c1))) | (f6(c2, c2) = f5(c1)) | (~big_f(f7(c1), f6(c2, c2))))),
% 27.66/17.85 inference(rewrite,[status(thm)],[])).
% 27.66/17.85 tff(3335,plain,
% 27.66/17.85 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c1) = c1) | (c2 = f8(c1)) | (~big_f(c2, f10(c1))) | (f7(c1) = c1) | (f6(c2, c2) = f5(c1)) | (~big_f(f7(c1), f6(c2, c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(c1) = c1) | (f10(c1) = c1) | (c2 = f8(c1)) | (~big_f(c2, f10(c1))) | (f6(c2, c2) = f5(c1)) | (~big_f(f7(c1), f6(c2, c2)))))),
% 27.66/17.85 inference(monotonicity,[status(thm)],[3334])).
% 27.66/17.85 tff(3336,plain,
% 27.66/17.85 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c1) = c1) | (c2 = f8(c1)) | (~big_f(c2, f10(c1))) | (f7(c1) = c1) | (f6(c2, c2) = f5(c1)) | (~big_f(f7(c1), f6(c2, c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c1) = c1) | (f10(c1) = c1) | (c2 = f8(c1)) | (~big_f(c2, f10(c1))) | (f6(c2, c2) = f5(c1)) | (~big_f(f7(c1), f6(c2, c2))))),
% 27.66/17.85 inference(transitivity,[status(thm)],[3335, 3333])).
% 27.66/17.85 tff(3337,plain,
% 27.66/17.85 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c1) = c1) | (c2 = f8(c1)) | (~big_f(c2, f10(c1))) | (f7(c1) = c1) | (f6(c2, c2) = f5(c1)) | (~big_f(f7(c1), f6(c2, c2))))),
% 27.66/17.85 inference(quant_inst,[status(thm)],[])).
% 27.66/17.85 tff(3338,plain,
% 27.66/17.85 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c1) = c1) | (f10(c1) = c1) | (c2 = f8(c1)) | (~big_f(c2, f10(c1))) | (f6(c2, c2) = f5(c1)) | (~big_f(f7(c1), f6(c2, c2)))),
% 27.66/17.85 inference(modus_ponens,[status(thm)],[3337, 3336])).
% 27.66/17.85 tff(3339,plain,
% 27.66/17.85 ((c2 = f8(c1)) | (f6(c2, c2) = f5(c1)) | (~big_f(f7(c1), f6(c2, c2)))),
% 27.66/17.85 inference(unit_resolution,[status(thm)],[3338, 1659, 115, 3332, 3])).
% 27.66/17.85 tff(3340,plain,
% 27.66/17.85 ($false),
% 27.66/17.85 inference(unit_resolution,[status(thm)],[3339, 3331, 3241, 3233])).
% 27.66/17.85 tff(3341,plain,((f6(f7(c2), f5(c1)) = c2) | (f7(c1) = c1) | (f10(c1) = c1) | (~(f5(c1) = c2)) | (~(f7(c2) = c2)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~big_f(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 27.66/17.85 tff(3342,plain,
% 27.66/17.85 (f6(f7(c2), f5(c1)) = c2),
% 27.66/17.85 inference(unit_resolution,[status(thm)],[3341, 186, 3, 115, 77, 79, 122, 3228])).
% 27.66/17.85 tff(3343,plain,
% 27.66/17.85 (f6(c2, c2) = c2),
% 27.66/17.85 inference(modus_ponens,[status(thm)],[3342, 2260])).
% 27.66/17.85 tff(3344,plain,
% 27.66/17.85 (big_f(f7(c2), f6(c2, c2))),
% 27.66/17.85 inference(unit_resolution,[status(thm)],[2700, 3228, 77, 79, 15, 122])).
% 27.66/17.85 tff(3345,plain,
% 27.66/17.85 (big_f(c2, f10(c1))),
% 27.66/17.85 inference(modus_ponens,[status(thm)],[3228, 2719])).
% 27.66/17.85 tff(3346,plain,
% 27.66/17.85 ((c2 = f8(c1)) | (~(f6(c2, c2) = c2))),
% 27.66/17.85 inference(unit_resolution,[status(thm)],[2736, 2730, 3345, 3, 77, 3344])).
% 27.66/17.85 tff(3347,plain,
% 27.66/17.85 (c2 = f8(c1)),
% 27.66/17.85 inference(unit_resolution,[status(thm)],[3346, 3343])).
% 27.66/17.85 tff(3348,plain,
% 27.66/17.85 (f8(c1) = c2),
% 27.66/17.85 inference(symmetry,[status(thm)],[3347])).
% 27.66/17.85 tff(3349,plain,
% 27.66/17.85 (big_f(c1, f10(c1)) <=> big_f(c1, c2)),
% 27.66/17.85 inference(monotonicity,[status(thm)],[15])).
% 27.66/17.85 tff(3350,plain,
% 27.66/17.85 (big_f(c1, c2) <=> big_f(c1, f10(c1))),
% 27.66/17.85 inference(symmetry,[status(thm)],[3349])).
% 27.66/17.85 tff(3351,plain,
% 27.66/17.85 ((f6(c2, c2) = c2) <=> (f6(f7(c2), c3) = c2)),
% 27.66/17.85 inference(symmetry,[status(thm)],[2713])).
% 27.66/17.85 tff(3352,plain,
% 27.66/17.85 ((f6(f7(c2), f5(c1)) = c2) <=> (f6(f7(c2), c3) = c2)),
% 27.66/17.85 inference(transitivity,[status(thm)],[2260, 3351])).
% 27.66/17.85 tff(3353,plain,
% 27.66/17.85 (f6(f7(c2), c3) = c2),
% 27.66/17.85 inference(modus_ponens,[status(thm)],[3032, 3352])).
% 27.66/17.85 tff(3354,plain,
% 27.66/17.85 (f6(c2, c2) = c2),
% 27.66/17.85 inference(modus_ponens,[status(thm)],[3032, 2260])).
% 27.66/17.85 tff(3355,plain,
% 27.66/17.85 (big_f(f9(c2, c2), f10(c2))),
% 27.66/17.85 inference(unit_resolution,[status(thm)],[2750, 3354, 122, 77, 1345, 2707])).
% 27.66/17.85 tff(3356,plain,
% 27.66/17.85 (~(f9(c2, c2) = c2)),
% 27.66/17.85 inference(unit_resolution,[status(thm)],[2386, 3355, 77, 122, 3353, 1345, 67])).
% 27.66/17.85 tff(3357,plain,
% 27.66/17.85 (~(f9(f10(c2), f4(c4)) = c2)),
% 27.66/17.85 inference(unit_resolution,[status(thm)],[1606, 3356, 79, 122])).
% 27.66/17.85 tff(3358,plain,
% 27.66/17.85 (f9(f10(c2), f4(c4)) = c1),
% 27.66/17.85 inference(unit_resolution,[status(thm)],[146, 3357])).
% 27.66/17.85 tff(3359,plain,
% 27.66/17.85 (c1 = f9(f10(c2), f4(c4))),
% 27.66/17.85 inference(symmetry,[status(thm)],[3358])).
% 27.66/17.85 tff(3360,plain,
% 27.66/17.85 (c1 = f9(c2, c2)),
% 27.66/17.85 inference(transitivity,[status(thm)],[3359, 132])).
% 27.66/17.85 tff(3361,plain,
% 27.66/17.85 (big_f(c1, c2) <=> big_f(f9(c2, c2), f10(c2))),
% 27.66/17.85 inference(monotonicity,[status(thm)],[3360, 216])).
% 27.66/17.85 tff(3362,plain,
% 27.66/17.85 (big_f(f9(c2, c2), f10(c2)) <=> big_f(c1, c2)),
% 27.66/17.85 inference(symmetry,[status(thm)],[3361])).
% 27.66/17.85 tff(3363,plain,
% 27.66/17.85 (big_f(c1, c2)),
% 27.66/17.85 inference(modus_ponens,[status(thm)],[3355, 3362])).
% 27.66/17.85 tff(3364,plain,
% 27.66/17.85 ($false),
% 27.66/17.85 inference(unit_resolution,[status(thm)],[27, 3363])).
% 27.66/17.85 tff(3365,plain,((~(f6(f7(c2), f5(c1)) = c2)) | big_f(c1, c2) | (~(f10(c2) = c2)) | (~(f4(c4) = c2)) | (~(f7(c2) = c2)) | (~big_f(c2, c2)) | (~(c3 = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~(f5(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.66/17.85 tff(3366,plain,
% 27.66/17.85 (big_f(c1, c2)),
% 27.66/17.85 inference(unit_resolution,[status(thm)],[3365, 3342, 122, 79, 77, 3228, 67, 3344, 186])).
% 27.66/17.85 tff(3367,plain,
% 27.66/17.85 (big_f(c1, f10(c1))),
% 27.66/17.85 inference(modus_ponens,[status(thm)],[3366, 3350])).
% 27.66/17.85 tff(3368,plain,
% 27.66/17.85 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (~(f7(c2) = c2)) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(f7(c2) = c2)) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))),
% 27.66/17.85 inference(rewrite,[status(thm)],[])).
% 27.66/17.85 tff(3369,plain,
% 27.66/17.85 (((f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2)))) <=> ((f10(c1) = c1) | (~(f7(c2) = c2)) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))),
% 27.66/17.85 inference(rewrite,[status(thm)],[])).
% 27.66/17.85 tff(3370,plain,
% 27.66/17.85 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (~(f7(c2) = c2)) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2)))))),
% 27.66/17.85 inference(monotonicity,[status(thm)],[3369])).
% 27.66/17.85 tff(3371,plain,
% 27.66/17.85 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(f7(c2) = c2)) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))),
% 27.66/17.86 inference(transitivity,[status(thm)],[3370, 3368])).
% 27.66/17.86 tff(3372,plain,
% 27.66/17.86 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))),
% 27.66/17.86 inference(quant_inst,[status(thm)],[])).
% 27.66/17.86 tff(3373,plain,
% 27.66/17.86 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(f7(c2) = c2)) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2)))),
% 27.66/17.86 inference(modus_ponens,[status(thm)],[3372, 3371])).
% 27.66/17.86 tff(3374,plain,
% 27.66/17.86 (c1 = f8(c1)),
% 27.66/17.86 inference(unit_resolution,[status(thm)],[3373, 2730, 3, 77, 3367, 3343, 3344])).
% 27.66/17.86 tff(3375,plain,
% 27.66/17.86 (f6(f7(c2), c3) = c2),
% 27.66/17.86 inference(modus_ponens,[status(thm)],[3342, 3352])).
% 27.66/17.86 tff(3376,plain,
% 27.66/17.86 (big_f(f9(c2, c2), f10(c2))),
% 27.66/17.86 inference(unit_resolution,[status(thm)],[2750, 3343, 122, 77, 3228, 3344])).
% 27.66/17.86 tff(3377,plain,
% 27.66/17.86 (~(f9(c2, c2) = c2)),
% 27.66/17.86 inference(unit_resolution,[status(thm)],[2386, 3376, 77, 122, 3375, 3228, 67])).
% 27.66/17.86 tff(3378,plain,
% 27.66/17.86 (~(f9(f10(c2), f4(c4)) = c2)),
% 27.66/17.86 inference(unit_resolution,[status(thm)],[1606, 3377, 79, 122])).
% 27.66/17.86 tff(3379,plain,
% 27.66/17.86 (f9(f10(c2), f4(c4)) = c1),
% 27.66/17.86 inference(unit_resolution,[status(thm)],[146, 3378])).
% 27.66/17.86 tff(3380,plain,
% 27.66/17.86 (f9(c2, c2) = c2),
% 27.66/17.86 inference(transitivity,[status(thm)],[2629, 3379, 3374, 3348])).
% 27.66/17.86 tff(3381,plain,
% 27.66/17.86 ($false),
% 27.66/17.86 inference(unit_resolution,[status(thm)],[3377, 3380])).
% 27.66/17.86 tff(3382,plain,((~(f5(c1) = c2)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~(c3 = c2)) | (f10(c1) = c1) | (f7(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 27.66/17.86 tff(3383,plain,
% 27.66/17.86 (~(f5(c1) = c2)),
% 27.66/17.86 inference(unit_resolution,[status(thm)],[3382, 3, 122, 77, 67, 79, 115])).
% 27.66/17.86 tff(3384,plain,
% 27.66/17.86 (f5(c1) = c1),
% 27.66/17.86 inference(unit_resolution,[status(thm)],[1708, 3383])).
% 27.66/17.86 tff(3385,plain,
% 27.66/17.86 ((~(f5(c1) = c2)) <=> (~(c2 = f5(c1)))),
% 27.66/17.86 inference(monotonicity,[status(thm)],[155])).
% 27.66/17.86 tff(3386,plain,
% 27.66/17.86 (~(c2 = f5(c1))),
% 27.66/17.86 inference(modus_ponens,[status(thm)],[3383, 3385])).
% 27.66/17.86 tff(3387,plain,
% 27.66/17.86 (big_f(f7(c1), c2)),
% 27.66/17.86 inference(modus_ponens,[status(thm)],[3228, 1724])).
% 27.66/17.86 tff(3388,plain,
% 27.66/17.86 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((c2 = f5(c1)) | (f7(c1) = c1) | (f10(c1) = c1) | (c2 = f8(c1)) | (~big_f(f7(c1), c2)) | (~big_f(c2, f10(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (c2 = f5(c1)) | (f7(c1) = c1) | (f10(c1) = c1) | (c2 = f8(c1)) | (~big_f(f7(c1), c2)) | (~big_f(c2, f10(c1))))),
% 27.66/17.86 inference(rewrite,[status(thm)],[])).
% 27.66/17.86 tff(3389,plain,
% 27.66/17.86 (((f10(c1) = c1) | (c2 = f8(c1)) | (~big_f(c2, f10(c1))) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2))) <=> ((c2 = f5(c1)) | (f7(c1) = c1) | (f10(c1) = c1) | (c2 = f8(c1)) | (~big_f(f7(c1), c2)) | (~big_f(c2, f10(c1))))),
% 27.66/17.86 inference(rewrite,[status(thm)],[])).
% 27.66/17.86 tff(3390,plain,
% 27.66/17.86 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c1) = c1) | (c2 = f8(c1)) | (~big_f(c2, f10(c1))) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((c2 = f5(c1)) | (f7(c1) = c1) | (f10(c1) = c1) | (c2 = f8(c1)) | (~big_f(f7(c1), c2)) | (~big_f(c2, f10(c1)))))),
% 27.66/17.86 inference(monotonicity,[status(thm)],[3389])).
% 27.66/17.86 tff(3391,plain,
% 27.66/17.86 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c1) = c1) | (c2 = f8(c1)) | (~big_f(c2, f10(c1))) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (c2 = f5(c1)) | (f7(c1) = c1) | (f10(c1) = c1) | (c2 = f8(c1)) | (~big_f(f7(c1), c2)) | (~big_f(c2, f10(c1))))),
% 27.66/17.86 inference(transitivity,[status(thm)],[3390, 3388])).
% 27.66/17.86 tff(3392,plain,
% 27.66/17.86 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c1) = c1) | (c2 = f8(c1)) | (~big_f(c2, f10(c1))) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)))),
% 27.66/17.86 inference(quant_inst,[status(thm)],[])).
% 27.66/17.86 tff(3393,plain,
% 27.66/17.86 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (c2 = f5(c1)) | (f7(c1) = c1) | (f10(c1) = c1) | (c2 = f8(c1)) | (~big_f(f7(c1), c2)) | (~big_f(c2, f10(c1)))),
% 27.66/17.86 inference(modus_ponens,[status(thm)],[3392, 3391])).
% 27.66/17.86 tff(3394,plain,
% 27.66/17.86 ((c2 = f5(c1)) | (c2 = f8(c1))),
% 27.66/17.86 inference(unit_resolution,[status(thm)],[3393, 1659, 3387, 115, 3345, 3])).
% 27.66/17.86 tff(3395,plain,
% 27.66/17.86 (c2 = f8(c1)),
% 27.66/17.86 inference(unit_resolution,[status(thm)],[3394, 3386])).
% 27.66/17.86 tff(3396,plain,
% 27.66/17.86 (f9(c2, c2) = c2),
% 27.66/17.86 inference(unit_resolution,[status(thm)],[1668, 3395, 79, 122, 15, 120, 3228, 3384])).
% 27.66/17.86 tff(3397,plain,
% 27.66/17.86 (big_f(f9(c2, c2), f10(c2)) <=> big_f(c2, c2)),
% 27.66/17.86 inference(monotonicity,[status(thm)],[3396, 122])).
% 27.66/17.86 tff(3398,plain,
% 27.66/17.86 (big_f(c2, c2) <=> big_f(f9(c2, c2), f10(c2))),
% 27.66/17.86 inference(symmetry,[status(thm)],[3397])).
% 27.66/17.86 tff(3399,plain,
% 27.66/17.86 (big_f(f9(c2, c2), f10(c2))),
% 27.66/17.86 inference(modus_ponens,[status(thm)],[3228, 3398])).
% 27.66/17.86 tff(3400,plain,
% 27.66/17.86 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((c2 = f5(c1)) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (~big_f(f7(c1), c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (c2 = f5(c1)) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (~big_f(f7(c1), c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))),
% 27.66/17.86 inference(rewrite,[status(thm)],[])).
% 27.66/17.86 tff(3401,plain,
% 27.66/17.86 (((~(f10(c2) = c2)) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2)))) <=> ((c2 = f5(c1)) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (~big_f(f7(c1), c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))),
% 27.66/17.86 inference(rewrite,[status(thm)],[])).
% 27.66/17.86 tff(3402,plain,
% 27.66/17.86 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((c2 = f5(c1)) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (~big_f(f7(c1), c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2)))))),
% 27.66/17.86 inference(monotonicity,[status(thm)],[3401])).
% 27.66/17.86 tff(3403,plain,
% 27.66/17.86 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (c2 = f5(c1)) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (~big_f(f7(c1), c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))),
% 27.66/17.86 inference(transitivity,[status(thm)],[3402, 3400])).
% 27.66/17.86 tff(3404,plain,
% 27.66/17.86 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))),
% 27.66/17.86 inference(quant_inst,[status(thm)],[])).
% 27.66/17.86 tff(3405,plain,
% 27.66/17.86 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (c2 = f5(c1)) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (~big_f(f7(c1), c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2)))),
% 27.66/17.86 inference(modus_ponens,[status(thm)],[3404, 3403])).
% 27.66/17.86 tff(3406,plain,
% 27.66/17.86 ($false),
% 27.66/17.86 inference(unit_resolution,[status(thm)],[3405, 1190, 3386, 3387, 115, 122, 3396, 3399])).
% 27.66/17.86 tff(3407,plain,((f10(c1) = c1) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (~(f4(c4) = c2)) | (~(f7(c2) = c2)) | (~(c3 = c2))), inference(lemma,lemma(discharge,[]))).
% 27.66/17.86 tff(3408,plain,
% 27.66/17.86 (~(c3 = c2)),
% 27.66/17.86 inference(unit_resolution,[status(thm)],[3407, 2257, 122, 79, 3, 115])).
% 27.66/17.86 tff(3409,plain,
% 27.66/17.86 (c3 = c1),
% 27.66/17.86 inference(unit_resolution,[status(thm)],[180, 3408])).
% 27.66/17.86 tff(3410,plain,
% 27.66/17.86 (c3 = f9(f10(c2), f10(c2))),
% 27.66/17.86 inference(transitivity,[status(thm)],[3409, 149, 132, 203])).
% 27.66/17.86 tff(3411,plain,
% 27.66/17.86 (f8(c3) = f8(f9(f10(c2), f10(c2)))),
% 27.66/17.86 inference(monotonicity,[status(thm)],[3410])).
% 27.66/17.86 tff(3412,plain,
% 27.66/17.86 ((f8(c3) = c2) <=> (f8(f9(f10(c2), f10(c2))) = c2)),
% 27.66/17.86 inference(monotonicity,[status(thm)],[3411])).
% 27.66/17.86 tff(3413,plain,
% 27.66/17.86 ((f8(c3) = c2) <=> (c2 = f8(f9(f10(c2), f10(c2))))),
% 27.66/17.86 inference(transitivity,[status(thm)],[3412, 210])).
% 27.66/17.86 tff(3414,plain,
% 27.66/17.86 ((c2 = f8(f9(f10(c2), f10(c2)))) <=> (f8(c3) = c2)),
% 27.66/17.86 inference(symmetry,[status(thm)],[3413])).
% 27.66/17.86 tff(3415,plain,
% 27.66/17.86 (f8(c1) = f8(f9(f10(c2), f10(c2)))),
% 27.66/17.86 inference(symmetry,[status(thm)],[1682])).
% 27.66/17.86 tff(3416,plain,
% 27.66/17.86 ((c2 = f8(c1)) <=> (c2 = f8(f9(f10(c2), f10(c2))))),
% 27.66/17.86 inference(monotonicity,[status(thm)],[3415])).
% 27.66/17.86 tff(3417,plain,
% 27.66/17.86 ((c2 = f8(c1)) <=> (c2 = f8(c3))),
% 27.66/17.86 inference(transitivity,[status(thm)],[3416, 3414, 209])).
% 27.66/17.86 tff(3418,plain,
% 27.66/17.86 ((~(c2 = f8(c1))) <=> (~(c2 = f8(c3)))),
% 27.66/17.86 inference(monotonicity,[status(thm)],[3417])).
% 27.66/17.86 tff(3419,plain,
% 27.66/17.86 (big_f(f9(f10(c2), f10(c2)), f10(f10(c2)))),
% 27.66/17.86 inference(unit_resolution,[status(thm)],[280, 729, 252, 115, 158])).
% 27.66/17.86 tff(3420,plain,
% 27.66/17.86 (big_f(f9(c2, c2), f10(c2))),
% 27.66/17.86 inference(modus_ponens,[status(thm)],[3419, 253])).
% 27.66/17.86 tff(3421,plain,
% 27.66/17.86 (~big_f(f9(c2, c2), f10(c2))),
% 27.66/17.86 inference(unit_resolution,[status(thm)],[793, 2, 115, 16, 148, 79, 122, 231, 230])).
% 27.66/17.86 tff(3422,plain,
% 27.66/17.86 ($false),
% 27.66/17.86 inference(unit_resolution,[status(thm)],[3421, 3420])).
% 27.66/17.86 tff(3423,plain,(big_f(c2, c1) | (~(f10(c2) = c2)) | (f7(c1) = c1) | (f9(f10(c2), f10(c2)) = f10(c2)) | (~(f5(c1) = c1)) | (~(f10(c1) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (f10(f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))), inference(lemma,lemma(discharge,[]))).
% 27.66/17.86 tff(3424,plain,
% 27.66/17.86 (big_f(c2, c1)),
% 27.66/17.86 inference(unit_resolution,[status(thm)],[3423, 230, 115, 158, 122, 15, 148, 79, 229])).
% 27.66/17.86 tff(3425,plain,
% 27.66/17.86 (big_f(c1, c2) <=> big_f(f9(c2, c2), f10(c2))),
% 27.66/17.86 inference(monotonicity,[status(thm)],[150, 216])).
% 27.66/17.86 tff(3426,plain,
% 27.66/17.86 (big_f(f9(c2, c2), f10(c2)) <=> big_f(c1, c2)),
% 27.66/17.86 inference(symmetry,[status(thm)],[3425])).
% 27.66/17.86 tff(3427,plain,
% 27.66/17.86 (big_f(c1, f10(c1)) <=> big_f(f9(f10(c2), f10(c2)), f10(f9(f10(c2), f10(c2))))),
% 27.66/17.86 inference(monotonicity,[status(thm)],[225, 226])).
% 27.66/17.86 tff(3428,plain,
% 27.66/17.86 (big_f(f9(f10(c2), f10(c2)), f10(f9(f10(c2), f10(c2)))) <=> big_f(c1, f10(c1))),
% 27.66/17.86 inference(symmetry,[status(thm)],[3427])).
% 27.66/17.86 tff(3429,plain,
% 27.66/17.86 (f10(f9(f10(c2), f10(c2))) = f10(c2)),
% 27.66/17.86 inference(transitivity,[status(thm)],[202, 15, 216])).
% 27.66/17.86 tff(3430,plain,
% 27.66/17.86 (big_f(f9(f10(c2), f10(c2)), f10(f9(f10(c2), f10(c2)))) <=> big_f(f9(c2, c2), f10(c2))),
% 27.66/17.86 inference(monotonicity,[status(thm)],[135, 3429])).
% 27.66/17.86 tff(3431,plain,
% 27.66/17.86 (big_f(f9(c2, c2), f10(c2)) <=> big_f(f9(f10(c2), f10(c2)), f10(f9(f10(c2), f10(c2))))),
% 27.66/17.86 inference(symmetry,[status(thm)],[3430])).
% 27.66/17.86 tff(3432,plain,
% 27.66/17.86 (big_f(f9(c2, c2), f10(c2)) <=> big_f(c1, f10(c1))),
% 27.66/17.86 inference(transitivity,[status(thm)],[3431, 3428])).
% 27.66/17.86 tff(3433,plain,
% 27.66/17.86 ((~big_f(f9(c2, c2), f10(c2))) <=> (~big_f(c1, f10(c1)))),
% 27.66/17.86 inference(monotonicity,[status(thm)],[3432])).
% 27.66/17.86 tff(3434,plain,
% 27.66/17.86 (~big_f(c1, f10(c1))),
% 27.66/17.86 inference(modus_ponens,[status(thm)],[256, 3433])).
% 27.66/17.86 tff(3435,plain,
% 27.66/17.86 (big_f(c1, f10(c1)) <=> big_f(f9(f10(c2), f10(c2)), f10(f10(c2)))),
% 27.66/17.86 inference(transitivity,[status(thm)],[3427, 3430, 254])).
% 27.66/17.86 tff(3436,plain,
% 27.66/17.86 ((~big_f(c1, f10(c1))) <=> (~big_f(f9(f10(c2), f10(c2)), f10(f10(c2))))),
% 27.66/17.86 inference(monotonicity,[status(thm)],[3435])).
% 27.66/17.86 tff(3437,plain,
% 27.66/17.86 (~big_f(f9(f10(c2), f10(c2)), f10(f10(c2)))),
% 27.66/17.86 inference(modus_ponens,[status(thm)],[3030, 3436])).
% 27.66/17.86 tff(3438,plain,
% 27.66/17.86 (big_f(f7(c1), f5(c1))),
% 27.66/17.86 inference(unit_resolution,[status(thm)],[280, 1515, 252, 115, 158])).
% 27.66/17.86 tff(3439,plain,
% 27.66/17.86 (big_f(c2, c2)),
% 27.66/17.86 inference(unit_resolution,[status(thm)],[1715, 3438, 120, 186])).
% 27.66/17.86 tff(3440,plain,
% 27.66/17.86 (f6(f7(c2), f5(c1)) = c2),
% 27.66/17.86 inference(unit_resolution,[status(thm)],[3341, 3439, 115, 3, 186, 79, 122, 77])).
% 27.66/17.86 tff(3441,plain,
% 27.66/17.86 (f6(c2, c2) = c2),
% 27.66/17.86 inference(modus_ponens,[status(thm)],[3440, 3237])).
% 27.66/17.86 tff(3442,plain,
% 27.66/17.86 (big_f(f7(c2), f6(c2, c2))),
% 27.66/17.86 inference(unit_resolution,[status(thm)],[2700, 3439, 77, 79, 15, 122])).
% 27.66/17.86 tff(3443,plain,
% 27.66/17.86 (big_f(c1, f10(c1)) <=> big_f(f9(c2, c2), f10(c2))),
% 27.66/17.86 inference(transitivity,[status(thm)],[3427, 3430])).
% 27.66/17.86 tff(3444,plain,
% 27.66/17.86 ((~big_f(c1, f10(c1))) <=> (~big_f(f9(c2, c2), f10(c2)))),
% 27.66/17.86 inference(monotonicity,[status(thm)],[3443])).
% 27.66/17.86 tff(3445,plain,
% 27.66/17.86 (~big_f(f9(c2, c2), f10(c2))),
% 27.66/17.86 inference(modus_ponens,[status(thm)],[3030, 3444])).
% 27.66/17.86 tff(3446,plain,
% 27.66/17.86 (~(f6(c2, c2) = c2)),
% 27.66/17.86 inference(unit_resolution,[status(thm)],[2750, 3439, 122, 77, 3445, 3442])).
% 27.66/17.86 tff(3447,plain,
% 27.66/17.86 ($false),
% 27.66/17.86 inference(unit_resolution,[status(thm)],[3446, 3441])).
% 27.66/17.86 tff(3448,plain,(big_f(f9(f10(c2), f10(c2)), f10(f10(c2))) | (~(f5(c1) = c2)) | (~(f7(c2) = c2)) | (f7(c1) = c1) | (f10(c1) = c1) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (f9(f10(c2), f10(c2)) = f10(c2)) | big_f(c1, f10(c1)) | (~(f9(f10(c2), f4(c4)) = c1))), inference(lemma,lemma(discharge,[]))).
% 27.66/17.86 tff(3449,plain,
% 27.66/17.86 (big_f(f9(f10(c2), f10(c2)), f10(f10(c2)))),
% 27.66/17.86 inference(unit_resolution,[status(thm)],[3448, 3030, 77, 115, 3, 79, 122, 158, 186, 148])).
% 27.66/17.86 tff(3450,plain,
% 27.66/17.86 ($false),
% 27.66/17.86 inference(unit_resolution,[status(thm)],[3449, 3437])).
% 27.66/17.86 tff(3451,plain,(big_f(c1, f10(c1)) | (~(f10(c2) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f7(c2) = c2)) | (f7(c1) = c1) | (f10(c1) = c1) | (f9(f10(c2), f10(c2)) = f10(c2)) | (~(f5(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.66/17.86 tff(3452,plain,
% 27.66/17.86 (~(f5(c1) = c2)),
% 27.66/17.86 inference(unit_resolution,[status(thm)],[3451, 3434, 148, 79, 122, 115, 3, 158, 2257])).
% 27.66/17.86 tff(3453,plain,
% 27.66/17.86 (f5(c1) = c1),
% 27.66/17.86 inference(unit_resolution,[status(thm)],[1708, 3452])).
% 27.66/17.86 tff(3454,plain,
% 27.66/17.86 (big_f(c2, c1)),
% 27.66/17.86 inference(unit_resolution,[status(thm)],[3423, 3453, 115, 158, 122, 15, 148, 79, 229])).
% 27.66/17.86 tff(3455,plain,
% 27.66/17.86 (~(f7(f9(c2, c2)) = f9(c2, c2))),
% 27.66/17.86 inference(modus_ponens,[status(thm)],[1209, 1797])).
% 27.66/17.86 tff(3456,plain,
% 27.66/17.86 ((f9(c2, c2) = f5(f9(c2, c2))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~big_f(f7(f9(c2, c2)), f9(c2, c2)))),
% 27.66/17.86 inference(unit_resolution,[status(thm)],[1807, 676, 122, 1209, 256])).
% 27.66/17.86 tff(3457,plain,
% 27.66/17.86 (f9(c2, c2) = f5(f9(c2, c2))),
% 27.66/17.86 inference(unit_resolution,[status(thm)],[3456, 3455, 1801])).
% 27.66/17.86 tff(3458,assumption,(f9(c2, c2) = f5(f9(c2, c2))), introduced(assumption)).
% 27.66/17.86 tff(3459,plain,
% 27.66/17.86 (c1 = f5(c1)),
% 27.66/17.86 inference(transitivity,[status(thm)],[149, 132, 3458, 152])).
% 27.66/17.86 tff(3460,plain,
% 27.66/17.86 (f6(c2, c1) = f6(f7(c2), f5(c1))),
% 27.66/17.86 inference(monotonicity,[status(thm)],[82, 3459])).
% 27.66/17.86 tff(3461,plain,
% 27.66/17.86 (f6(c2, f9(c2, c2)) = f6(c2, c1)),
% 27.66/17.86 inference(monotonicity,[status(thm)],[161])).
% 27.66/17.86 tff(3462,plain,
% 27.66/17.86 (f6(c2, f9(c2, c2)) = c2),
% 27.66/17.86 inference(transitivity,[status(thm)],[3461, 3460, 3032])).
% 27.66/17.86 tff(3463,plain,
% 27.66/17.86 ((f6(c2, f9(c2, c2)) = f9(c2, c2)) <=> (c2 = f9(c2, c2))),
% 27.66/17.86 inference(monotonicity,[status(thm)],[3462])).
% 27.66/17.86 tff(3464,plain,
% 27.66/17.86 ((f6(c2, f9(c2, c2)) = f9(c2, c2)) <=> (f9(c2, c2) = c2)),
% 27.66/17.86 inference(transitivity,[status(thm)],[3463, 167])).
% 27.66/17.86 tff(3465,plain,
% 27.66/17.86 ((f9(c2, c2) = c2) <=> (f6(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.66/17.86 inference(symmetry,[status(thm)],[3464])).
% 27.66/17.86 tff(3466,plain,
% 27.66/17.86 ((~(f9(c2, c2) = c2)) <=> (~(f6(c2, f9(c2, c2)) = f9(c2, c2)))),
% 27.66/17.86 inference(monotonicity,[status(thm)],[3465])).
% 27.66/17.86 tff(3467,plain,
% 27.66/17.86 (~(f6(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.66/17.86 inference(modus_ponens,[status(thm)],[1209, 3466])).
% 27.66/17.86 tff(3468,plain,
% 27.66/17.86 (big_f(f7(c2), f6(c2, f9(c2, c2))) <=> big_f(c2, c2)),
% 27.66/17.86 inference(monotonicity,[status(thm)],[77, 3462])).
% 27.66/17.86 tff(3469,plain,
% 27.66/17.86 (big_f(c2, c2) <=> big_f(f7(c2), f6(c2, f9(c2, c2)))),
% 27.66/17.86 inference(symmetry,[status(thm)],[3468])).
% 27.66/17.86 tff(3470,plain,
% 27.66/17.86 ((~big_f(c2, c2)) <=> (~big_f(f7(c2), f6(c2, f9(c2, c2))))),
% 27.66/17.86 inference(monotonicity,[status(thm)],[3469])).
% 27.66/17.86 tff(3471,plain,
% 27.66/17.86 (~big_f(f7(c2), f6(c2, f9(c2, c2)))),
% 27.66/17.86 inference(modus_ponens,[status(thm)],[121, 3470])).
% 27.66/17.86 tff(3472,plain,
% 27.66/17.86 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f6(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f7(c2), f6(c2, f9(c2, c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f6(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f7(c2), f6(c2, f9(c2, c2))))),
% 27.66/17.86 inference(rewrite,[status(thm)],[])).
% 27.66/17.86 tff(3473,plain,
% 27.66/17.86 (((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(c2) = c2)) | (f6(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f7(c2), f6(c2, f9(c2, c2)))) <=> ((~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f6(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f7(c2), f6(c2, f9(c2, c2))))),
% 27.66/17.86 inference(rewrite,[status(thm)],[])).
% 27.66/17.86 tff(3474,plain,
% 27.66/17.86 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(c2) = c2)) | (f6(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f7(c2), f6(c2, f9(c2, c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f6(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f7(c2), f6(c2, f9(c2, c2)))))),
% 27.66/17.86 inference(monotonicity,[status(thm)],[3473])).
% 27.66/17.86 tff(3475,plain,
% 27.66/17.86 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(c2) = c2)) | (f6(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f7(c2), f6(c2, f9(c2, c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f6(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f7(c2), f6(c2, f9(c2, c2))))),
% 27.66/17.87 inference(transitivity,[status(thm)],[3474, 3472])).
% 27.66/17.87 tff(3476,plain,
% 27.66/17.87 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(c2) = c2)) | (f6(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f7(c2), f6(c2, f9(c2, c2))))),
% 27.66/17.87 inference(quant_inst,[status(thm)],[])).
% 27.66/17.87 tff(3477,plain,
% 27.66/17.87 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f6(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f7(c2), f6(c2, f9(c2, c2)))),
% 27.66/17.87 inference(modus_ponens,[status(thm)],[3476, 3475])).
% 27.66/17.87 tff(3478,plain,
% 27.66/17.87 ((f6(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f7(c2), f6(c2, f9(c2, c2)))),
% 27.66/17.87 inference(unit_resolution,[status(thm)],[3477, 2492, 122, 77, 1209, 256])).
% 27.66/17.87 tff(3479,plain,
% 27.66/17.87 ($false),
% 27.66/17.87 inference(unit_resolution,[status(thm)],[3478, 3471, 3467])).
% 27.66/17.87 tff(3480,plain,((~(f6(f7(c2), f5(c1)) = c2)) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | big_f(c2, c2) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f9(c2, c2) = f5(f9(c2, c2)))) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.66/17.87 tff(3481,plain,
% 27.66/17.87 (~(f6(f7(c2), f5(c1)) = c2)),
% 27.66/17.87 inference(unit_resolution,[status(thm)],[3480, 148, 77, 1209, 256, 121, 122, 3457, 79])).
% 27.66/17.87 tff(3482,plain,
% 27.66/17.87 (f6(f7(c2), f5(c1)) = c1),
% 27.66/17.87 inference(unit_resolution,[status(thm)],[2978, 3481])).
% 27.66/17.87 tff(3483,plain,
% 27.66/17.87 (c1 = f5(c1)),
% 27.66/17.87 inference(transitivity,[status(thm)],[149, 132, 3457, 152])).
% 27.66/17.87 tff(3484,plain,
% 27.66/17.87 (f6(c2, c1) = f6(f7(c2), f5(c1))),
% 27.66/17.87 inference(monotonicity,[status(thm)],[82, 3483])).
% 27.66/17.87 tff(3485,plain,
% 27.66/17.87 (f6(c2, f9(c2, c2)) = f9(c2, c2)),
% 27.66/17.87 inference(transitivity,[status(thm)],[3461, 3484, 3482, 149, 132])).
% 27.66/17.87 tff(3486,plain,
% 27.66/17.87 (f6(c2, f9(c2, c2)) = c1),
% 27.66/17.87 inference(transitivity,[status(thm)],[3461, 3484, 3482])).
% 27.66/17.87 tff(3487,plain,
% 27.66/17.87 (big_f(f7(c2), f6(c2, f9(c2, c2))) <=> big_f(c2, c1)),
% 27.66/17.87 inference(monotonicity,[status(thm)],[77, 3486])).
% 27.66/17.87 tff(3488,plain,
% 27.66/17.87 (big_f(c2, c1) <=> big_f(f7(c2), f6(c2, f9(c2, c2)))),
% 27.66/17.87 inference(symmetry,[status(thm)],[3487])).
% 27.66/17.87 tff(3489,plain,
% 27.66/17.87 (big_f(f7(c2), f6(c2, f9(c2, c2)))),
% 27.66/17.87 inference(modus_ponens,[status(thm)],[348, 3488])).
% 27.66/17.87 tff(3490,plain,
% 27.66/17.87 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f6(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f6(c2, f9(c2, c2)))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f6(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f6(c2, f9(c2, c2)))))),
% 27.66/17.87 inference(rewrite,[status(thm)],[])).
% 27.66/17.87 tff(3491,plain,
% 27.66/17.87 (((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(c2) = c2)) | (~(f6(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f6(c2, f9(c2, c2))))) <=> ((~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f6(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f6(c2, f9(c2, c2)))))),
% 27.66/17.87 inference(rewrite,[status(thm)],[])).
% 27.66/17.87 tff(3492,plain,
% 27.66/17.87 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(c2) = c2)) | (~(f6(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f6(c2, f9(c2, c2)))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f6(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f6(c2, f9(c2, c2))))))),
% 27.66/17.87 inference(monotonicity,[status(thm)],[3491])).
% 27.66/17.87 tff(3493,plain,
% 27.66/17.87 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(c2) = c2)) | (~(f6(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f6(c2, f9(c2, c2)))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f6(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f6(c2, f9(c2, c2)))))),
% 27.66/17.87 inference(transitivity,[status(thm)],[3492, 3490])).
% 27.66/17.87 tff(3494,plain,
% 27.66/17.87 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(c2) = c2)) | (~(f6(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f6(c2, f9(c2, c2)))))),
% 27.66/17.87 inference(quant_inst,[status(thm)],[])).
% 27.66/17.87 tff(3495,plain,
% 27.66/17.87 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f6(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f6(c2, f9(c2, c2))))),
% 27.66/17.87 inference(modus_ponens,[status(thm)],[3494, 3493])).
% 27.66/17.87 tff(3496,plain,
% 27.66/17.87 ((~(f6(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f6(c2, f9(c2, c2))))),
% 27.66/17.87 inference(unit_resolution,[status(thm)],[3495, 2534, 122, 77, 1209, 256])).
% 27.66/17.87 tff(3497,plain,
% 27.66/17.87 ($false),
% 27.66/17.87 inference(unit_resolution,[status(thm)],[3496, 3489, 3485])).
% 27.66/17.87 tff(3498,plain,((~(f9(f10(c2), f4(c4)) = c1)) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~big_f(c2, c1)) | (~(f4(c4) = c2)) | big_f(c2, c2) | (~(f7(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.66/17.87 tff(3499,plain,
% 27.66/17.87 (big_f(c2, c2)),
% 27.66/17.87 inference(unit_resolution,[status(thm)],[3498, 3454, 148, 122, 2257, 256, 79, 185, 120])).
% 27.66/17.87 tff(3500,plain,
% 27.66/17.87 (~(c2 = f8(c1))),
% 27.66/17.87 inference(unit_resolution,[status(thm)],[1668, 3499, 79, 122, 185, 15, 120, 3453])).
% 27.66/17.87 tff(3501,plain,
% 27.66/17.87 (~(c2 = f8(c3))),
% 27.66/17.87 inference(modus_ponens,[status(thm)],[3500, 3418])).
% 27.66/17.87 tff(3502,plain,
% 27.66/17.87 ((f10(c3) = c3) <=> (f10(c3) = c1)),
% 27.66/17.87 inference(monotonicity,[status(thm)],[3409])).
% 27.66/17.87 tff(3503,plain,
% 27.66/17.87 ((f10(c3) = c1) <=> (f10(c3) = c3)),
% 27.66/17.87 inference(symmetry,[status(thm)],[3502])).
% 27.66/17.87 tff(3504,plain,
% 27.66/17.87 (f10(c3) = f10(f9(f10(c2), f10(c2)))),
% 27.66/17.87 inference(monotonicity,[status(thm)],[3410])).
% 27.66/17.87 tff(3505,plain,
% 27.66/17.87 (f10(c3) = c2),
% 27.66/17.87 inference(transitivity,[status(thm)],[3504, 202, 15])).
% 27.66/17.87 tff(3506,plain,
% 27.66/17.87 ((f10(c3) = c1) <=> (c2 = f9(c2, c2))),
% 27.66/17.87 inference(monotonicity,[status(thm)],[3505, 150])).
% 27.66/17.87 tff(3507,plain,
% 27.66/17.87 ((f10(c3) = c1) <=> (f9(c2, c2) = c2)),
% 27.66/17.87 inference(transitivity,[status(thm)],[3506, 167])).
% 27.66/17.87 tff(3508,plain,
% 27.66/17.87 ((f9(c2, c2) = c2) <=> (f10(c3) = c1)),
% 27.66/17.87 inference(symmetry,[status(thm)],[3507])).
% 27.66/17.87 tff(3509,plain,
% 27.66/17.87 ((f9(c2, c2) = c2) <=> (f10(c3) = c3)),
% 27.66/17.87 inference(transitivity,[status(thm)],[3508, 3503])).
% 27.66/17.87 tff(3510,plain,
% 27.66/17.87 ((~(f9(c2, c2) = c2)) <=> (~(f10(c3) = c3))),
% 27.66/17.87 inference(monotonicity,[status(thm)],[3509])).
% 27.66/17.87 tff(3511,plain,
% 27.66/17.87 (~(f10(c3) = c3)),
% 27.66/17.87 inference(modus_ponens,[status(thm)],[185, 3510])).
% 27.66/17.87 tff(3512,plain,
% 27.66/17.87 (f5(c1) = f9(c2, c2)),
% 27.66/17.87 inference(transitivity,[status(thm)],[3453, 149, 132])).
% 27.66/17.87 tff(3513,plain,
% 27.66/17.87 ((c2 = f5(c1)) <=> (c2 = f9(c2, c2))),
% 27.66/17.87 inference(monotonicity,[status(thm)],[3512])).
% 27.66/17.87 tff(3514,plain,
% 27.66/17.87 ((c2 = f5(c1)) <=> (f9(c2, c2) = c2)),
% 27.66/17.87 inference(transitivity,[status(thm)],[3513, 167])).
% 27.66/17.87 tff(3515,plain,
% 27.66/17.87 ((f9(c2, c2) = c2) <=> (c2 = f5(c1))),
% 27.66/17.87 inference(symmetry,[status(thm)],[3514])).
% 27.66/17.87 tff(3516,plain,
% 27.66/17.87 ((~(f9(c2, c2) = c2)) <=> (~(c2 = f5(c1)))),
% 27.66/17.87 inference(monotonicity,[status(thm)],[3515])).
% 27.66/17.87 tff(3517,plain,
% 27.66/17.87 (~(c2 = f5(c1))),
% 27.66/17.87 inference(modus_ponens,[status(thm)],[185, 3516])).
% 27.66/17.87 tff(3518,plain,
% 27.66/17.87 (big_f(c2, f10(c3)) <=> big_f(c2, c2)),
% 27.66/17.87 inference(monotonicity,[status(thm)],[3505])).
% 27.66/17.87 tff(3519,plain,
% 27.66/17.87 (big_f(c2, c2) <=> big_f(c2, f10(c3))),
% 27.66/17.87 inference(symmetry,[status(thm)],[3518])).
% 27.66/17.87 tff(3520,plain,
% 27.66/17.87 (big_f(c2, f10(c3))),
% 27.66/17.87 inference(modus_ponens,[status(thm)],[3499, 3519])).
% 27.66/17.87 tff(3521,plain,
% 27.66/17.87 (big_f(f7(c1), c2)),
% 27.66/17.87 inference(modus_ponens,[status(thm)],[3499, 1724])).
% 27.66/17.87 tff(3522,plain,
% 27.66/17.87 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((c2 = f5(c1)) | (f7(c1) = c1) | (f10(c3) = c3) | (~big_f(f7(c1), c2)) | (~big_f(c2, f10(c3))) | (c2 = f8(c3)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (c2 = f5(c1)) | (f7(c1) = c1) | (f10(c3) = c3) | (~big_f(f7(c1), c2)) | (~big_f(c2, f10(c3))) | (c2 = f8(c3)))),
% 27.66/17.87 inference(rewrite,[status(thm)],[])).
% 27.66/17.87 tff(3523,plain,
% 27.66/17.87 (((f10(c3) = c3) | (c2 = f8(c3)) | (~big_f(c2, f10(c3))) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2))) <=> ((c2 = f5(c1)) | (f7(c1) = c1) | (f10(c3) = c3) | (~big_f(f7(c1), c2)) | (~big_f(c2, f10(c3))) | (c2 = f8(c3)))),
% 27.66/17.87 inference(rewrite,[status(thm)],[])).
% 27.66/17.87 tff(3524,plain,
% 27.66/17.87 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c3) = c3) | (c2 = f8(c3)) | (~big_f(c2, f10(c3))) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((c2 = f5(c1)) | (f7(c1) = c1) | (f10(c3) = c3) | (~big_f(f7(c1), c2)) | (~big_f(c2, f10(c3))) | (c2 = f8(c3))))),
% 27.66/17.87 inference(monotonicity,[status(thm)],[3523])).
% 27.66/17.87 tff(3525,plain,
% 27.66/17.87 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c3) = c3) | (c2 = f8(c3)) | (~big_f(c2, f10(c3))) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (c2 = f5(c1)) | (f7(c1) = c1) | (f10(c3) = c3) | (~big_f(f7(c1), c2)) | (~big_f(c2, f10(c3))) | (c2 = f8(c3)))),
% 27.66/17.87 inference(transitivity,[status(thm)],[3524, 3522])).
% 27.66/17.87 tff(3526,plain,
% 27.66/17.87 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c3) = c3) | (c2 = f8(c3)) | (~big_f(c2, f10(c3))) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)))),
% 27.66/17.87 inference(quant_inst,[status(thm)],[])).
% 27.66/17.87 tff(3527,plain,
% 27.66/17.87 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (c2 = f5(c1)) | (f7(c1) = c1) | (f10(c3) = c3) | (~big_f(f7(c1), c2)) | (~big_f(c2, f10(c3))) | (c2 = f8(c3))),
% 27.66/17.87 inference(modus_ponens,[status(thm)],[3526, 3525])).
% 27.66/17.87 tff(3528,plain,
% 27.66/17.87 ((c2 = f5(c1)) | (f7(c1) = c1) | (f10(c3) = c3) | (~big_f(f7(c1), c2)) | (~big_f(c2, f10(c3))) | (c2 = f8(c3))),
% 27.66/17.87 inference(unit_resolution,[status(thm)],[3527, 1659])).
% 27.66/17.87 tff(3529,plain,
% 27.66/17.87 ($false),
% 27.66/17.87 inference(unit_resolution,[status(thm)],[3528, 3521, 3520, 115, 3517, 3511, 3501])).
% 27.66/17.87 tff(3530,plain,(big_f(f9(c2, c2), f10(c2)) | (f7(c1) = c1) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (f9(f10(c2), f10(c2)) = f10(c2)) | (f10(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 27.66/17.87 tff(3531,plain,
% 27.66/17.87 (big_f(f9(c2, c2), f10(c2))),
% 27.66/17.87 inference(unit_resolution,[status(thm)],[3530, 115, 148, 79, 122, 158, 3])).
% 27.66/17.87 tff(3532,plain,
% 27.66/17.87 (big_f(c1, c2)),
% 27.66/17.87 inference(modus_ponens,[status(thm)],[3531, 3426])).
% 27.66/17.87 tff(3533,plain,
% 27.66/17.87 (~(c2 = f8(c1))),
% 27.66/17.87 inference(unit_resolution,[status(thm)],[3003, 121, 3, 77, 230, 348])).
% 27.66/17.87 tff(3534,plain,
% 27.66/17.87 (~(f8(c1) = c2)),
% 27.66/17.87 inference(unit_resolution,[status(thm)],[1675, 3533])).
% 27.66/17.87 tff(3535,plain,
% 27.66/17.87 (f8(c1) = c1),
% 27.66/17.87 inference(unit_resolution,[status(thm)],[1680, 3534])).
% 27.66/17.87 tff(3536,plain,
% 27.66/17.87 (f8(f9(c2, c2)) = f9(f10(c2), f10(c2))),
% 27.66/17.87 inference(transitivity,[status(thm)],[715, 1682, 3535, 149, 132, 203])).
% 27.66/17.87 tff(3537,plain,
% 27.66/17.87 ((f9(c2, f9(f10(c2), f10(c2))) = f8(f9(c2, c2))) <=> (f9(c2, f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))),
% 27.66/17.87 inference(monotonicity,[status(thm)],[3536])).
% 27.66/17.87 tff(3538,plain,
% 27.66/17.87 ((f9(c2, f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2))) <=> (f9(c2, f9(f10(c2), f10(c2))) = f8(f9(c2, c2)))),
% 27.66/17.87 inference(symmetry,[status(thm)],[3537])).
% 27.66/17.87 tff(3539,plain,
% 27.66/17.87 ((~(f9(c2, f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))) <=> (~(f9(c2, f9(f10(c2), f10(c2))) = f8(f9(c2, c2))))),
% 27.66/17.87 inference(monotonicity,[status(thm)],[3538])).
% 27.66/17.87 tff(3540,plain,
% 27.66/17.87 ((~(f9(c2, f9(c2, c2)) = f9(c2, c2))) <=> (~(f9(c2, f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2))))),
% 27.66/17.87 inference(monotonicity,[status(thm)],[1135])).
% 27.66/17.87 tff(3541,plain,
% 27.66/17.87 (~(f6(f7(c2), f5(c1)) = c1)),
% 27.66/17.87 inference(unit_resolution,[status(thm)],[3111, 3535, 3, 122, 77, 2865, 348, 230])).
% 27.66/17.87 tff(3542,plain,
% 27.66/17.87 (f6(f7(c2), f5(c1)) = c2),
% 27.66/17.87 inference(unit_resolution,[status(thm)],[2978, 3541])).
% 27.66/17.87 tff(3543,plain,
% 27.66/17.87 (f6(c2, c1) = c2),
% 27.66/17.87 inference(transitivity,[status(thm)],[2942, 3542])).
% 27.66/17.87 tff(3544,plain,
% 27.66/17.87 ((f6(c2, c1) = c1) <=> (c2 = f9(c2, c2))),
% 27.66/17.87 inference(monotonicity,[status(thm)],[3543, 150])).
% 27.66/17.87 tff(3545,plain,
% 27.66/17.87 ((f6(c2, c1) = c1) <=> (f9(c2, c2) = c2)),
% 27.66/17.87 inference(transitivity,[status(thm)],[3544, 167])).
% 27.66/17.87 tff(3546,plain,
% 27.66/17.87 ((f9(c2, c2) = c2) <=> (f6(c2, c1) = c1)),
% 27.66/17.87 inference(symmetry,[status(thm)],[3545])).
% 27.66/17.87 tff(3547,plain,
% 27.66/17.87 ((~(f9(c2, c2) = c2)) <=> (~(f6(c2, c1) = c1))),
% 27.66/17.87 inference(monotonicity,[status(thm)],[3546])).
% 27.66/17.87 tff(3548,plain,
% 27.66/17.87 (~(f6(c2, c1) = c1)),
% 27.66/17.87 inference(modus_ponens,[status(thm)],[185, 3547])).
% 27.66/17.87 tff(3549,plain,
% 27.66/17.87 (big_f(f7(c2), f6(c2, c1)) <=> big_f(c2, c2)),
% 27.66/17.87 inference(monotonicity,[status(thm)],[77, 3543])).
% 27.66/17.87 tff(3550,plain,
% 27.66/17.87 (big_f(c2, c2) <=> big_f(f7(c2), f6(c2, c1))),
% 27.66/17.87 inference(symmetry,[status(thm)],[3549])).
% 27.66/17.87 tff(3551,plain,
% 27.66/17.87 ((~big_f(c2, c2)) <=> (~big_f(f7(c2), f6(c2, c1)))),
% 27.66/17.87 inference(monotonicity,[status(thm)],[3550])).
% 27.66/17.87 tff(3552,plain,
% 27.66/17.87 (~big_f(f7(c2), f6(c2, c1))),
% 27.66/17.87 inference(modus_ponens,[status(thm)],[121, 3551])).
% 27.66/17.87 tff(3553,plain,
% 27.66/17.87 (f9(c2, f5(c1)) = f9(c2, c1)),
% 27.66/17.87 inference(monotonicity,[status(thm)],[230])).
% 27.66/17.87 tff(3554,plain,
% 27.66/17.87 (f9(c2, c1) = f9(c2, f5(c1))),
% 27.66/17.87 inference(symmetry,[status(thm)],[3553])).
% 27.66/17.87 tff(3555,plain,
% 27.66/17.87 (big_f(f9(c2, c1), f10(c2)) <=> big_f(f9(c2, f5(c1)), f10(c2))),
% 27.66/17.87 inference(monotonicity,[status(thm)],[3554])).
% 27.66/17.87 tff(3556,plain,
% 27.66/17.87 (big_f(f9(c2, f5(c1)), f10(c2)) <=> big_f(f9(c2, c1), f10(c2))),
% 27.66/17.87 inference(symmetry,[status(thm)],[3555])).
% 27.66/17.87 tff(3557,plain,
% 27.66/17.87 (f9(c2, f5(c1)) = c1),
% 27.66/17.87 inference(transitivity,[status(thm)],[3553, 736])).
% 27.66/17.87 tff(3558,plain,
% 27.66/17.87 (big_f(f9(c2, f5(c1)), f10(c2)) <=> big_f(c1, c2)),
% 27.66/17.87 inference(monotonicity,[status(thm)],[3557, 122])).
% 27.66/17.87 tff(3559,plain,
% 27.66/17.87 (big_f(c1, c2) <=> big_f(f9(c2, f5(c1)), f10(c2))),
% 27.66/17.87 inference(symmetry,[status(thm)],[3558])).
% 27.66/17.87 tff(3560,plain,
% 27.66/17.87 (big_f(c1, c2) <=> big_f(f9(c2, c1), f10(c2))),
% 27.66/17.87 inference(transitivity,[status(thm)],[3559, 3556])).
% 27.66/17.87 tff(3561,plain,
% 27.66/17.87 (big_f(f9(c2, c1), f10(c2))),
% 27.66/17.87 inference(modus_ponens,[status(thm)],[2865, 3560])).
% 27.66/17.87 tff(3562,plain,
% 27.66/17.87 ($false),
% 27.66/17.87 inference(unit_resolution,[status(thm)],[3225, 2409, 122, 736, 3561, 77, 3198, 3197])).
% 27.66/17.87 tff(3563,plain,((~(f9(c2, c1) = c1)) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (~big_f(c1, c2)) | (~(f5(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 27.66/17.87 tff(3564,plain,
% 27.66/17.87 (~(f9(c2, c1) = c1)),
% 27.66/17.87 inference(unit_resolution,[status(thm)],[3563, 3552, 77, 122, 3548, 2865, 230])).
% 27.66/17.87 tff(3565,plain,
% 27.66/17.87 (~(f9(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.66/17.87 inference(unit_resolution,[status(thm)],[1141, 3564, 122, 148, 79])).
% 27.66/17.87 tff(3566,plain,
% 27.66/17.87 (~(f9(c2, f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))),
% 27.66/17.87 inference(modus_ponens,[status(thm)],[3565, 3540])).
% 27.66/17.87 tff(3567,plain,
% 27.66/17.87 (~(f9(c2, f9(f10(c2), f10(c2))) = f8(f9(c2, c2)))),
% 27.66/17.87 inference(modus_ponens,[status(thm)],[3566, 3539])).
% 27.66/17.87 tff(3568,plain,
% 27.66/17.87 (f6(c2, f9(c2, c2)) = c2),
% 27.66/17.87 inference(transitivity,[status(thm)],[3461, 2942, 3542])).
% 27.66/17.87 tff(3569,plain,
% 27.66/17.87 ((f6(c2, f9(c2, c2)) = f9(c2, c2)) <=> (c2 = f9(c2, c2))),
% 27.66/17.87 inference(monotonicity,[status(thm)],[3568])).
% 27.66/17.87 tff(3570,plain,
% 27.66/17.87 ((f6(c2, f9(c2, c2)) = f9(c2, c2)) <=> (f9(c2, c2) = c2)),
% 27.66/17.87 inference(transitivity,[status(thm)],[3569, 167])).
% 27.66/17.87 tff(3571,plain,
% 27.66/17.87 ((f9(c2, c2) = c2) <=> (f6(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.66/17.87 inference(symmetry,[status(thm)],[3570])).
% 27.66/17.87 tff(3572,plain,
% 27.66/17.87 ((~(f9(c2, c2) = c2)) <=> (~(f6(c2, f9(c2, c2)) = f9(c2, c2)))),
% 27.66/17.87 inference(monotonicity,[status(thm)],[3571])).
% 27.66/17.87 tff(3573,plain,
% 27.66/17.87 (~(f6(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.66/17.87 inference(modus_ponens,[status(thm)],[185, 3572])).
% 27.66/17.87 tff(3574,plain,
% 27.66/17.87 (big_f(f7(c2), f6(c2, f9(c2, c2))) <=> big_f(c2, c2)),
% 27.66/17.87 inference(monotonicity,[status(thm)],[77, 3568])).
% 27.66/17.87 tff(3575,plain,
% 27.66/17.87 (big_f(c2, c2) <=> big_f(f7(c2), f6(c2, f9(c2, c2)))),
% 27.66/17.87 inference(symmetry,[status(thm)],[3574])).
% 27.66/17.87 tff(3576,plain,
% 27.66/17.87 ((~big_f(c2, c2)) <=> (~big_f(f7(c2), f6(c2, f9(c2, c2))))),
% 27.66/17.87 inference(monotonicity,[status(thm)],[3575])).
% 27.66/17.87 tff(3577,plain,
% 27.66/17.87 (~big_f(f7(c2), f6(c2, f9(c2, c2)))),
% 27.66/17.87 inference(modus_ponens,[status(thm)],[121, 3576])).
% 27.66/17.87 tff(3578,plain,
% 27.66/17.87 (big_f(f9(c2, c1), f10(c2)) <=> big_f(f9(c2, f9(f10(c2), f10(c2))), f10(f9(c2, c2)))),
% 27.66/17.87 inference(transitivity,[status(thm)],[724, 1765])).
% 27.66/17.87 tff(3579,plain,
% 27.66/17.87 (big_f(f9(c2, c1), f10(c2))),
% 27.66/17.87 inference(unit_resolution,[status(thm)],[3211, 3564, 122, 77, 3552, 3548])).
% 27.66/17.87 tff(3580,plain,
% 27.66/17.87 (big_f(f9(c2, f9(f10(c2), f10(c2))), f10(f9(c2, c2)))),
% 27.66/17.87 inference(modus_ponens,[status(thm)],[3579, 3578])).
% 27.66/17.87 tff(3581,plain,
% 27.66/17.87 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f7(c2) = c2)) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(f9(c2, c2)))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f6(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f7(c2), f6(c2, f9(c2, c2))) | (f9(c2, f9(f10(c2), f10(c2))) = f8(f9(c2, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c2) = c2)) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(f9(c2, c2)))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f6(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f7(c2), f6(c2, f9(c2, c2))) | (f9(c2, f9(f10(c2), f10(c2))) = f8(f9(c2, c2))))),
% 27.66/17.87 inference(rewrite,[status(thm)],[])).
% 27.66/17.87 tff(3582,plain,
% 27.66/17.87 (((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, f9(f10(c2), f10(c2))) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(f9(c2, c2)))) | (~(f7(c2) = c2)) | (f6(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f7(c2), f6(c2, f9(c2, c2)))) <=> ((~(f7(c2) = c2)) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(f9(c2, c2)))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f6(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f7(c2), f6(c2, f9(c2, c2))) | (f9(c2, f9(f10(c2), f10(c2))) = f8(f9(c2, c2))))),
% 27.66/17.87 inference(rewrite,[status(thm)],[])).
% 27.66/17.87 tff(3583,plain,
% 27.66/17.87 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, f9(f10(c2), f10(c2))) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(f9(c2, c2)))) | (~(f7(c2) = c2)) | (f6(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f7(c2), f6(c2, f9(c2, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f7(c2) = c2)) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(f9(c2, c2)))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f6(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f7(c2), f6(c2, f9(c2, c2))) | (f9(c2, f9(f10(c2), f10(c2))) = f8(f9(c2, c2)))))),
% 27.66/17.87 inference(monotonicity,[status(thm)],[3582])).
% 27.66/17.87 tff(3584,plain,
% 27.66/17.87 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, f9(f10(c2), f10(c2))) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(f9(c2, c2)))) | (~(f7(c2) = c2)) | (f6(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f7(c2), f6(c2, f9(c2, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c2) = c2)) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(f9(c2, c2)))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f6(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f7(c2), f6(c2, f9(c2, c2))) | (f9(c2, f9(f10(c2), f10(c2))) = f8(f9(c2, c2))))),
% 27.66/17.87 inference(transitivity,[status(thm)],[3583, 3581])).
% 27.66/17.87 tff(3585,plain,
% 27.66/17.87 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, f9(f10(c2), f10(c2))) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(f9(c2, c2)))) | (~(f7(c2) = c2)) | (f6(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f7(c2), f6(c2, f9(c2, c2))))),
% 27.66/17.87 inference(quant_inst,[status(thm)],[])).
% 27.66/17.87 tff(3586,plain,
% 27.66/17.87 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c2) = c2)) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(f9(c2, c2)))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f6(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f7(c2), f6(c2, f9(c2, c2))) | (f9(c2, f9(f10(c2), f10(c2))) = f8(f9(c2, c2)))),
% 27.66/17.87 inference(modus_ponens,[status(thm)],[3585, 3584])).
% 27.66/17.87 tff(3587,plain,
% 27.66/17.87 ((f6(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f7(c2), f6(c2, f9(c2, c2))) | (f9(c2, f9(f10(c2), f10(c2))) = f8(f9(c2, c2)))),
% 27.66/17.87 inference(unit_resolution,[status(thm)],[3586, 2662, 77, 1721, 3580])).
% 27.66/17.87 tff(3588,plain,
% 27.66/17.87 ($false),
% 27.66/17.87 inference(unit_resolution,[status(thm)],[3587, 3577, 3573, 3567])).
% 27.66/17.87 tff(3589,plain,(big_f(c2, c2) | (~(f7(c2) = c2)) | (~(f5(c1) = c1)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~big_f(c1, c2)) | (f10(c1) = c1) | (~big_f(c2, c1))), inference(lemma,lemma(discharge,[]))).
% 27.66/17.87 tff(3590,plain,
% 27.66/17.87 (big_f(c2, c2)),
% 27.66/17.87 inference(unit_resolution,[status(thm)],[3589, 230, 2257, 148, 79, 122, 3532, 3, 3424])).
% 27.66/17.87 tff(3591,plain,
% 27.66/17.87 (~(c2 = f8(c1))),
% 27.66/17.87 inference(unit_resolution,[status(thm)],[1668, 3590, 79, 122, 185, 15, 120, 230])).
% 27.66/17.87 tff(3592,plain,
% 27.66/17.87 (~(c2 = f8(c3))),
% 27.66/17.87 inference(modus_ponens,[status(thm)],[3591, 3418])).
% 27.66/17.87 tff(3593,plain,
% 27.66/17.87 (f5(c1) = f9(c2, c2)),
% 27.66/17.87 inference(transitivity,[status(thm)],[230, 149, 132])).
% 27.66/17.87 tff(3594,plain,
% 27.66/17.87 ((c2 = f5(c1)) <=> (c2 = f9(c2, c2))),
% 27.66/17.87 inference(monotonicity,[status(thm)],[3593])).
% 27.66/17.87 tff(3595,plain,
% 27.66/17.87 ((c2 = f5(c1)) <=> (f9(c2, c2) = c2)),
% 27.66/17.87 inference(transitivity,[status(thm)],[3594, 167])).
% 27.66/17.87 tff(3596,plain,
% 27.66/17.87 ((f9(c2, c2) = c2) <=> (c2 = f5(c1))),
% 27.66/17.87 inference(symmetry,[status(thm)],[3595])).
% 27.66/17.87 tff(3597,plain,
% 27.66/17.87 ((~(f9(c2, c2) = c2)) <=> (~(c2 = f5(c1)))),
% 27.66/17.87 inference(monotonicity,[status(thm)],[3596])).
% 27.66/17.87 tff(3598,plain,
% 27.66/17.87 (~(c2 = f5(c1))),
% 27.66/17.87 inference(modus_ponens,[status(thm)],[185, 3597])).
% 27.66/17.87 tff(3599,plain,
% 27.66/17.87 (big_f(c2, f10(c3))),
% 27.66/17.87 inference(modus_ponens,[status(thm)],[3590, 3519])).
% 27.66/17.88 tff(3600,plain,
% 27.66/17.88 (big_f(f7(c1), c2)),
% 27.66/17.88 inference(modus_ponens,[status(thm)],[3590, 1724])).
% 27.66/17.88 tff(3601,plain,
% 27.66/17.88 ($false),
% 27.66/17.88 inference(unit_resolution,[status(thm)],[3528, 3600, 3599, 115, 3598, 3511, 3592])).
% 27.66/17.88 tff(3602,plain,((~(f5(c1) = c1)) | (f7(c1) = c1) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (f10(c1) = c1) | (f9(f10(c2), f10(c2)) = f10(c2))), inference(lemma,lemma(discharge,[]))).
% 27.66/17.88 tff(3603,plain,
% 27.66/17.88 (~(f5(c1) = c1)),
% 27.66/17.88 inference(unit_resolution,[status(thm)],[3602, 115, 148, 79, 122, 3, 158])).
% 27.66/17.88 tff(3604,plain,
% 27.66/17.88 (f5(c1) = c2),
% 27.66/17.88 inference(unit_resolution,[status(thm)],[1708, 3603])).
% 27.66/17.88 tff(3605,plain,
% 27.66/17.88 (big_f(c2, c2)),
% 27.66/17.88 inference(unit_resolution,[status(thm)],[1790, 3604, 79, 122, 115, 158, 3, 148])).
% 27.66/17.88 tff(3606,plain,
% 27.66/17.88 (big_f(c2, f10(f9(c2, c2)))),
% 27.66/17.88 inference(modus_ponens,[status(thm)],[3605, 207])).
% 27.66/17.88 tff(3607,plain,
% 27.66/17.88 (big_f(f7(c2), f6(c2, c2))),
% 27.66/17.88 inference(unit_resolution,[status(thm)],[2700, 3605, 2257, 79, 15, 122])).
% 27.66/17.88 tff(3608,plain,
% 27.66/17.88 (f6(f7(c2), f5(c1)) = c2),
% 27.66/17.88 inference(unit_resolution,[status(thm)],[3341, 3604, 115, 3, 2257, 79, 122, 3605])).
% 27.66/17.88 tff(3609,plain,
% 27.66/17.88 (c2 = f5(c1)),
% 27.66/17.88 inference(symmetry,[status(thm)],[3604])).
% 27.66/17.88 tff(3610,plain,
% 27.66/17.88 (c2 = f7(c2)),
% 27.66/17.88 inference(symmetry,[status(thm)],[2257])).
% 27.66/17.88 tff(3611,plain,
% 27.66/17.88 (f6(c2, c2) = f6(f7(c2), f5(c1))),
% 27.66/17.88 inference(monotonicity,[status(thm)],[3610, 3609])).
% 27.66/17.88 tff(3612,plain,
% 27.66/17.88 (f6(c2, c2) = c2),
% 27.66/17.88 inference(transitivity,[status(thm)],[3611, 3608])).
% 27.66/17.88 tff(3613,plain,
% 27.66/17.88 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)))),
% 27.66/17.88 inference(rewrite,[status(thm)],[])).
% 27.66/17.88 tff(3614,plain,
% 27.66/17.88 (((f10(f9(c2, c2)) = f9(c2, c2)) | (c2 = f8(f9(c2, c2))) | (~big_f(c2, f10(f9(c2, c2)))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2)))) <=> ((~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)))),
% 27.66/17.88 inference(rewrite,[status(thm)],[])).
% 27.66/17.88 tff(3615,plain,
% 27.66/17.88 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (c2 = f8(f9(c2, c2))) | (~big_f(c2, f10(f9(c2, c2)))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2))))),
% 27.66/17.88 inference(monotonicity,[status(thm)],[3614])).
% 27.66/17.88 tff(3616,plain,
% 27.66/17.88 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (c2 = f8(f9(c2, c2))) | (~big_f(c2, f10(f9(c2, c2)))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)))),
% 27.66/17.88 inference(transitivity,[status(thm)],[3615, 3613])).
% 27.66/17.88 tff(3617,plain,
% 27.66/17.88 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (c2 = f8(f9(c2, c2))) | (~big_f(c2, f10(f9(c2, c2)))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))),
% 27.66/17.88 inference(quant_inst,[status(thm)],[])).
% 27.66/17.88 tff(3618,plain,
% 27.66/17.88 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2))),
% 27.66/17.88 inference(modus_ponens,[status(thm)],[3617, 3616])).
% 27.66/17.88 tff(3619,plain,
% 27.66/17.88 (c2 = f8(f9(c2, c2))),
% 27.66/17.88 inference(unit_resolution,[status(thm)],[3618, 2730, 2257, 3612, 3607, 1721, 3606])).
% 27.66/17.88 tff(3620,plain,
% 27.66/17.88 (f8(f9(c2, c2)) = c2),
% 27.66/17.88 inference(symmetry,[status(thm)],[3619])).
% 27.66/17.88 tff(3621,plain,
% 27.66/17.88 ((~big_f(f9(c2, c2), f10(f9(c2, c2)))) <=> (~big_f(f9(c2, c2), f10(c2)))),
% 27.66/17.88 inference(monotonicity,[status(thm)],[2672])).
% 27.66/17.88 tff(3622,assumption,(~big_f(f9(c2, c2), f10(f9(c2, c2)))), introduced(assumption)).
% 27.66/17.88 tff(3623,plain,
% 27.66/17.88 (~big_f(f9(c2, c2), f10(c2))),
% 27.66/17.88 inference(modus_ponens,[status(thm)],[3622, 3621])).
% 27.66/17.88 tff(3624,plain,
% 27.66/17.88 ($false),
% 27.66/17.88 inference(unit_resolution,[status(thm)],[690, 3623])).
% 27.66/17.88 tff(3625,plain,((~big_f(f9(c2, c2), f10(c2))) | big_f(f9(c2, c2), f10(f9(c2, c2))) | (~(f10(c2) = c2)) | (~(f10(c1) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.66/17.88 tff(3626,plain,
% 27.66/17.88 (big_f(f9(c2, c2), f10(f9(c2, c2)))),
% 27.66/17.88 inference(unit_resolution,[status(thm)],[3625, 3531, 122, 15, 148, 79])).
% 27.66/17.88 tff(3627,plain,
% 27.66/17.88 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))))),
% 27.66/17.88 inference(rewrite,[status(thm)],[])).
% 27.66/17.88 tff(3628,plain,
% 27.66/17.88 (((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2)))) <=> ((~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))))),
% 27.66/17.88 inference(rewrite,[status(thm)],[])).
% 27.66/17.88 tff(3629,plain,
% 27.66/17.88 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2))))))),
% 27.66/17.88 inference(monotonicity,[status(thm)],[3628])).
% 27.66/17.88 tff(3630,plain,
% 27.66/17.88 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))))),
% 27.66/17.88 inference(transitivity,[status(thm)],[3629, 3627])).
% 27.66/17.88 tff(3631,plain,
% 27.66/17.88 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))),
% 27.66/17.88 inference(quant_inst,[status(thm)],[])).
% 27.66/17.88 tff(3632,plain,
% 27.66/17.88 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2))))),
% 27.66/17.88 inference(modus_ponens,[status(thm)],[3631, 3630])).
% 27.66/17.88 tff(3633,plain,
% 27.66/17.88 (f9(c2, c2) = f8(f9(c2, c2))),
% 27.66/17.88 inference(unit_resolution,[status(thm)],[3632, 2730, 2257, 3612, 3607, 1721, 3626])).
% 27.66/17.88 tff(3634,plain,
% 27.66/17.88 (f9(c2, c2) = c2),
% 27.66/17.88 inference(transitivity,[status(thm)],[3633, 3620])).
% 27.66/17.88 tff(3635,plain,
% 27.66/17.88 ($false),
% 27.66/17.88 inference(unit_resolution,[status(thm)],[185, 3634])).
% 27.66/17.88 tff(3636,plain,((f7(c1) = c1) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (f10(c1) = c1) | (f9(f10(c2), f10(c2)) = f10(c2))), inference(lemma,lemma(discharge,[]))).
% 27.66/17.88 tff(3637,plain,
% 27.66/17.88 (f10(c1) = c1),
% 27.66/17.88 inference(unit_resolution,[status(thm)],[3636, 115, 148, 122, 79, 158])).
% 27.66/17.88 tff(3638,plain,
% 27.66/17.88 ((f9(f10(c2), f4(c4)) = c3) <=> (f9(c2, c2) = c3)),
% 27.66/17.88 inference(monotonicity,[status(thm)],[132])).
% 27.66/17.88 tff(3639,plain,
% 27.66/17.88 ((f9(c2, c2) = c3) <=> (f9(f10(c2), f4(c4)) = c3)),
% 27.66/17.88 inference(symmetry,[status(thm)],[3638])).
% 27.66/17.88 tff(3640,plain,
% 27.66/17.88 ((c1 = c3) <=> (f9(c2, c2) = c3)),
% 27.66/17.88 inference(monotonicity,[status(thm)],[150])).
% 27.66/17.88 tff(3641,plain,
% 27.66/17.88 ((c1 = c3) <=> (f9(f10(c2), f4(c4)) = c3)),
% 27.66/17.88 inference(transitivity,[status(thm)],[3640, 3639])).
% 27.66/17.88 tff(3642,plain,
% 27.66/17.88 ((~(c1 = c3)) <=> (~(f9(f10(c2), f4(c4)) = c3))),
% 27.66/17.88 inference(monotonicity,[status(thm)],[3641])).
% 27.66/17.88 tff(3643,plain,
% 27.66/17.88 (~(f9(f10(c2), f4(c4)) = c3)),
% 27.66/17.88 inference(modus_ponens,[status(thm)],[168, 3642])).
% 27.66/17.88 tff(3644,plain,
% 27.66/17.88 ((~(c1 = c3)) <=> (~(f9(c2, c2) = c3))),
% 27.66/17.88 inference(monotonicity,[status(thm)],[3640])).
% 27.66/17.88 tff(3645,plain,
% 27.66/17.88 (~(f9(c2, c2) = c3)),
% 27.66/17.88 inference(modus_ponens,[status(thm)],[168, 3644])).
% 27.66/17.88 tff(3646,plain,
% 27.66/17.88 (f10(f9(c2, c2)) = f10(c1)),
% 27.66/17.88 inference(monotonicity,[status(thm)],[161])).
% 27.66/17.88 tff(3647,plain,
% 27.66/17.88 (f10(f9(c2, c2)) = c1),
% 27.66/17.88 inference(transitivity,[status(thm)],[3646, 3637])).
% 27.66/17.88 tff(3648,plain,
% 27.66/17.88 (f9(f9(c2, c2), f9(c2, c2)) = f9(c1, c1)),
% 27.66/17.88 inference(monotonicity,[status(thm)],[161, 161])).
% 27.66/17.88 tff(3649,plain,
% 27.66/17.88 (big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))) <=> big_f(f9(c1, c1), c1)),
% 27.66/17.88 inference(monotonicity,[status(thm)],[3648, 3647])).
% 27.66/17.88 tff(3650,plain,
% 27.66/17.88 (big_f(f9(c1, c1), c1) <=> big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))),
% 27.66/17.88 inference(symmetry,[status(thm)],[3649])).
% 27.66/17.88 tff(3651,plain,
% 27.66/17.88 (f7(c1) = f7(f9(c2, c2))),
% 27.66/17.88 inference(symmetry,[status(thm)],[243])).
% 27.66/17.88 tff(3652,plain,
% 27.66/17.88 ((f7(c1) = c1) <=> (f7(f9(c2, c2)) = f9(c2, c2))),
% 27.66/17.88 inference(monotonicity,[status(thm)],[3651, 150])).
% 27.66/17.88 tff(3653,plain,
% 27.66/17.88 ((~(f7(c1) = c1)) <=> (~(f7(f9(c2, c2)) = f9(c2, c2)))),
% 27.66/17.88 inference(monotonicity,[status(thm)],[3652])).
% 27.66/17.88 tff(3654,plain,
% 27.66/17.88 (~(f7(f9(c2, c2)) = f9(c2, c2))),
% 27.66/17.88 inference(modus_ponens,[status(thm)],[115, 3653])).
% 27.66/17.88 tff(3655,plain,
% 27.66/17.88 (big_f(f9(f10(c2), f10(c2)), f10(f10(c2))) <=> big_f(f9(c2, c2), c2)),
% 27.66/17.88 inference(monotonicity,[status(thm)],[135, 251])).
% 27.66/17.88 tff(3656,plain,
% 27.66/17.88 (big_f(f9(c2, c2), c2) <=> big_f(f9(f10(c2), f10(c2)), f10(f10(c2)))),
% 27.66/17.88 inference(symmetry,[status(thm)],[3655])).
% 27.66/17.88 tff(3657,plain,
% 27.66/17.88 (big_f(c1, c2) <=> big_f(f9(c2, c2), c2)),
% 27.66/17.88 inference(monotonicity,[status(thm)],[150])).
% 27.66/17.88 tff(3658,plain,
% 27.66/17.88 (big_f(c1, c2) <=> big_f(f9(f10(c2), f10(c2)), f10(f10(c2)))),
% 27.66/17.88 inference(transitivity,[status(thm)],[3657, 3656])).
% 27.66/17.88 tff(3659,plain,
% 27.66/17.88 ((~big_f(c1, c2)) <=> (~big_f(f9(f10(c2), f10(c2)), f10(f10(c2))))),
% 27.66/17.88 inference(monotonicity,[status(thm)],[3658])).
% 27.66/17.88 tff(3660,plain,
% 27.66/17.88 (~big_f(f9(f10(c2), f10(c2)), f10(f10(c2)))),
% 27.66/17.88 inference(modus_ponens,[status(thm)],[27, 3659])).
% 27.66/17.88 tff(3661,plain,
% 27.66/17.88 ((f9(f10(c2), f4(c4)) = f4(c4)) <=> (f9(f10(c2), f4(c4)) = c2)),
% 27.66/17.88 inference(monotonicity,[status(thm)],[79])).
% 27.66/17.88 tff(3662,plain,
% 27.66/17.88 ((f9(f10(c2), f4(c4)) = c2) <=> (f9(f10(c2), f4(c4)) = f4(c4))),
% 27.66/17.88 inference(symmetry,[status(thm)],[3661])).
% 27.66/17.88 tff(3663,plain,
% 27.66/17.88 ((c2 = c1) <=> (f9(f10(c2), f4(c4)) = f4(c4))),
% 27.66/17.88 inference(transitivity,[status(thm)],[183, 134, 3662])).
% 27.66/17.88 tff(3664,plain,
% 27.66/17.88 ((~(c2 = c1)) <=> (~(f9(f10(c2), f4(c4)) = f4(c4)))),
% 27.66/17.88 inference(monotonicity,[status(thm)],[3663])).
% 27.66/17.88 tff(3665,plain,
% 27.66/17.88 (~(f9(f10(c2), f4(c4)) = f4(c4))),
% 27.66/17.88 inference(modus_ponens,[status(thm)],[75, 3664])).
% 27.66/17.88 tff(3666,plain,
% 27.66/17.88 (big_f(f9(f10(c2), f4(c4)), c2) <=> big_f(f9(c2, c2), c2)),
% 27.66/17.88 inference(monotonicity,[status(thm)],[132])).
% 27.66/17.88 tff(3667,plain,
% 27.66/17.88 (big_f(f9(c2, c2), c2) <=> big_f(f9(f10(c2), f4(c4)), c2)),
% 27.66/17.88 inference(symmetry,[status(thm)],[3666])).
% 27.66/17.88 tff(3668,plain,
% 27.66/17.88 (big_f(c1, c2) <=> big_f(f9(f10(c2), f4(c4)), f10(f10(c2)))),
% 27.66/17.88 inference(transitivity,[status(thm)],[3657, 3667, 2440])).
% 27.66/17.88 tff(3669,plain,
% 27.66/17.88 ((~big_f(c1, c2)) <=> (~big_f(f9(f10(c2), f4(c4)), f10(f10(c2))))),
% 27.66/17.88 inference(monotonicity,[status(thm)],[3668])).
% 27.66/17.88 tff(3670,plain,
% 27.66/17.88 (~big_f(f9(f10(c2), f4(c4)), f10(f10(c2)))),
% 27.66/17.88 inference(modus_ponens,[status(thm)],[27, 3669])).
% 27.66/17.88 tff(3671,plain,
% 27.66/17.88 ($false),
% 27.66/17.88 inference(unit_resolution,[status(thm)],[2544, 3660, 3670, 122, 79, 67, 186, 347, 1345, 77, 158, 3665])).
% 27.66/17.88 tff(3672,plain,(big_f(c1, c2) | (~(f10(c2) = c2)) | (~(f4(c4) = c2)) | (~(c3 = c2)) | (~(f5(c1) = c2)) | (~(f7(c1) = c2)) | (~big_f(c2, c2)) | (~(f7(c2) = c2)) | (f9(f10(c2), f10(c2)) = f10(c2)) | (~(f9(f10(c2), f4(c4)) = c1))), inference(lemma,lemma(discharge,[]))).
% 27.66/17.88 tff(3673,plain,
% 27.66/17.88 (~big_f(c2, c2)),
% 27.66/17.88 inference(unit_resolution,[status(thm)],[3672, 27, 79, 67, 186, 120, 122, 77, 158, 148])).
% 27.66/17.88 tff(3674,plain,
% 27.66/17.88 (~big_f(f7(c1), f5(c1))),
% 27.66/17.88 inference(unit_resolution,[status(thm)],[1715, 3673, 186, 120])).
% 27.66/17.88 tff(3675,plain,
% 27.66/17.88 (big_f(f9(f10(c2), f10(c2)), f10(f10(c2)))),
% 27.66/17.88 inference(unit_resolution,[status(thm)],[280, 3674, 252, 115, 158])).
% 27.66/17.88 tff(3676,plain,
% 27.66/17.88 ($false),
% 27.66/17.88 inference(unit_resolution,[status(thm)],[3675, 3660])).
% 27.66/17.88 tff(3677,plain,(big_f(c1, c2) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (f7(c1) = c1) | (f9(f10(c2), f10(c2)) = f10(c2)) | (~(f5(c1) = c2)) | (~(c3 = c2)) | (~(f7(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.66/17.88 tff(3678,plain,
% 27.66/17.88 (big_f(c1, c2)),
% 27.66/17.88 inference(unit_resolution,[status(thm)],[3677, 186, 79, 122, 148, 158, 115, 181, 77])).
% 27.66/17.88 tff(3679,plain,
% 27.66/17.88 (big_f(c1, c2) <=> big_f(f9(c2, c2), f10(c2))),
% 27.66/17.88 inference(transitivity,[status(thm)],[3657, 130])).
% 27.66/17.88 tff(3680,plain,
% 27.66/17.88 (big_f(f9(c2, c2), f10(c2))),
% 27.66/17.88 inference(modus_ponens,[status(thm)],[2865, 3679])).
% 27.66/17.88 tff(3681,plain,
% 27.66/17.88 ($false),
% 27.66/17.88 inference(unit_resolution,[status(thm)],[256, 3680])).
% 27.66/17.88 tff(3682,plain,((~big_f(c1, c2)) | big_f(f9(c2, c2), f10(c2)) | (~(f10(c2) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.66/17.88 tff(3683,plain,
% 27.66/17.88 (big_f(f9(c2, c2), f10(c2))),
% 27.66/17.88 inference(unit_resolution,[status(thm)],[3682, 3678, 122, 148, 79])).
% 27.66/17.88 tff(3684,plain,
% 27.66/17.88 (big_f(f9(c2, c2), c2)),
% 27.66/17.88 inference(modus_ponens,[status(thm)],[690, 129])).
% 27.66/17.88 tff(3685,assumption,(~big_f(f9(c2, c2), c2)), introduced(assumption)).
% 27.66/17.88 tff(3686,plain,
% 27.66/17.88 ($false),
% 27.66/17.88 inference(unit_resolution,[status(thm)],[3685, 3684])).
% 27.66/17.88 tff(3687,plain,((~big_f(f9(c2, c2), f10(c2))) | big_f(f9(c2, c2), c2) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.66/17.88 tff(3688,plain,
% 27.66/17.88 (big_f(f9(c2, c2), c2)),
% 27.66/17.88 inference(unit_resolution,[status(thm)],[3687, 3683, 122])).
% 27.66/17.88 tff(3689,assumption,(~big_f(f9(c2, c2), f9(c2, c2))), introduced(assumption)).
% 27.66/17.88 tff(3690,plain,
% 27.66/17.88 (big_f(f9(c2, c2), c2) <=> big_f(c1, c2)),
% 27.66/17.88 inference(symmetry,[status(thm)],[3657])).
% 27.66/17.88 tff(3691,plain,
% 27.66/17.88 (big_f(c1, c2)),
% 27.66/17.88 inference(modus_ponens,[status(thm)],[2041, 3690])).
% 27.66/17.88 tff(3692,plain,
% 27.66/17.88 (~big_f(f4(c4), c4)),
% 27.66/17.88 inference(unit_resolution,[status(thm)],[2221, 2, 79, 480])).
% 27.66/17.88 tff(3693,plain,
% 27.66/17.88 (f1(c1, f1(c1, c2)) = f1(f9(f10(c2), f4(c4)), c2)),
% 27.66/17.88 inference(monotonicity,[status(thm)],[149, 822])).
% 27.66/17.88 tff(3694,plain,
% 27.66/17.88 (f1(c1, f1(c1, c2)) = f1(c1, c2)),
% 27.66/17.88 inference(transitivity,[status(thm)],[3693, 819])).
% 27.66/17.88 tff(3695,plain,
% 27.66/17.88 (f1(c1, f1(c1, c2)) = c2),
% 27.66/17.88 inference(transitivity,[status(thm)],[3693, 819, 822])).
% 27.66/17.88 tff(3696,plain,
% 27.66/17.88 (big_f(c1, f1(c1, f1(c1, c2))) <=> big_f(f9(c2, c2), c2)),
% 27.66/17.88 inference(monotonicity,[status(thm)],[150, 3695])).
% 27.66/17.88 tff(3697,plain,
% 27.66/17.88 (big_f(f9(c2, c2), c2) <=> big_f(c1, f1(c1, f1(c1, c2)))),
% 27.66/17.88 inference(symmetry,[status(thm)],[3696])).
% 27.66/17.88 tff(3698,plain,
% 27.66/17.88 (big_f(c1, f1(c1, f1(c1, c2)))),
% 27.66/17.88 inference(modus_ponens,[status(thm)],[2041, 3697])).
% 27.66/17.88 tff(3699,plain,
% 27.66/17.88 ($false),
% 27.66/17.88 inference(unit_resolution,[status(thm)],[2254, 3698, 3694, 168, 379])).
% 27.66/17.88 tff(3700,plain,((~(f1(c1, c2) = c2)) | (c1 = c3) | big_f(f4(c4), c4) | (~big_f(f9(c2, c2), c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.66/17.88 tff(3701,plain,
% 27.66/17.88 (~(f1(c1, c2) = c2)),
% 27.66/17.88 inference(unit_resolution,[status(thm)],[3700, 3692, 168, 2041, 148, 79, 122])).
% 27.66/17.88 tff(3702,plain,
% 27.66/17.88 (f1(c1, c2) = c1),
% 27.66/17.88 inference(unit_resolution,[status(thm)],[841, 3701])).
% 27.66/17.88 tff(3703,plain,
% 27.66/17.88 (f1(f9(c2, c2), c2) = f9(c2, c2)),
% 27.66/17.88 inference(transitivity,[status(thm)],[843, 819, 3702, 149, 132])).
% 27.66/17.88 tff(3704,plain,
% 27.66/17.88 ((f1(f9(c2, c2), c2) = c2) <=> (f9(c2, c2) = c2)),
% 27.66/17.88 inference(monotonicity,[status(thm)],[3703])).
% 27.66/17.88 tff(3705,plain,
% 27.66/17.88 ((f9(c2, c2) = c2) <=> (f1(f9(c2, c2), c2) = c2)),
% 27.66/17.88 inference(symmetry,[status(thm)],[3704])).
% 27.66/17.88 tff(3706,plain,
% 27.66/17.88 ((~(f9(c2, c2) = c2)) <=> (~(f1(f9(c2, c2), c2) = c2))),
% 27.66/17.88 inference(monotonicity,[status(thm)],[3705])).
% 27.66/17.88 tff(3707,plain,
% 27.66/17.88 (~(f1(f9(c2, c2), c2) = c2)),
% 27.66/17.88 inference(modus_ponens,[status(thm)],[185, 3706])).
% 27.66/17.88 tff(3708,plain,
% 27.66/17.88 (big_f(f9(c2, c2), f1(f9(c2, c2), c2)) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 27.66/17.88 inference(monotonicity,[status(thm)],[3703])).
% 27.66/17.88 tff(3709,plain,
% 27.66/17.88 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f9(c2, c2), f1(f9(c2, c2), c2))),
% 27.66/17.88 inference(symmetry,[status(thm)],[3708])).
% 27.66/17.88 tff(3710,plain,
% 27.66/17.88 ((~big_f(f9(c2, c2), f9(c2, c2))) <=> (~big_f(f9(c2, c2), f1(f9(c2, c2), c2)))),
% 27.66/17.88 inference(monotonicity,[status(thm)],[3709])).
% 27.66/17.88 tff(3711,plain,
% 27.66/17.88 (~big_f(f9(c2, c2), f1(f9(c2, c2), c2))),
% 27.66/17.88 inference(modus_ponens,[status(thm)],[3689, 3710])).
% 27.66/17.88 tff(3712,plain,
% 27.66/17.88 (f9(c2, c2) = c4),
% 27.66/17.88 inference(transitivity,[status(thm)],[160, 148, 567])).
% 27.66/17.88 tff(3713,plain,
% 27.66/17.88 (f4(f9(c2, c2)) = f4(c4)),
% 27.66/17.88 inference(monotonicity,[status(thm)],[3712])).
% 27.66/17.88 tff(3714,plain,
% 27.66/17.88 (f4(c4) = f4(f9(c2, c2))),
% 27.66/17.88 inference(symmetry,[status(thm)],[3713])).
% 27.66/17.88 tff(3715,plain,
% 27.66/17.88 (c2 = f4(f9(c2, c2))),
% 27.66/17.88 inference(transitivity,[status(thm)],[436, 3714])).
% 27.66/17.88 tff(3716,plain,
% 27.66/17.88 (big_f(c2, c1) <=> big_f(c2, f9(c2, c2))),
% 27.66/17.88 inference(monotonicity,[status(thm)],[150])).
% 27.66/17.88 tff(3717,plain,
% 27.66/17.88 ((~big_f(c2, c1)) <=> (~big_f(c2, f9(c2, c2)))),
% 27.66/17.88 inference(monotonicity,[status(thm)],[3716])).
% 27.66/17.88 tff(3718,plain,
% 27.66/17.88 (~big_f(c2, f9(c2, c2))),
% 27.66/17.88 inference(modus_ponens,[status(thm)],[2, 3717])).
% 27.66/17.88 tff(3719,assumption,(big_f(c2, f9(c2, c2))), introduced(assumption)).
% 27.66/17.88 tff(3720,plain,
% 27.66/17.88 ($false),
% 27.66/17.88 inference(unit_resolution,[status(thm)],[3719, 3718])).
% 27.66/17.88 tff(3721,plain,(big_f(c2, c1) | (~big_f(c2, f9(c2, c2))) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.66/17.88 tff(3722,plain,
% 27.66/17.88 (~big_f(c2, f9(c2, c2))),
% 27.66/17.88 inference(unit_resolution,[status(thm)],[3721, 2, 148, 79, 122])).
% 27.66/17.88 tff(3723,plain,
% 27.66/17.88 ((c1 = c4) <=> (f9(c2, c2) = c4)),
% 27.66/17.88 inference(monotonicity,[status(thm)],[150])).
% 27.66/17.88 tff(3724,plain,
% 27.66/17.88 ((c4 = c1) <=> (f9(c2, c2) = c4)),
% 27.66/17.88 inference(transitivity,[status(thm)],[479, 3723])).
% 27.66/17.88 tff(3725,plain,
% 27.66/17.88 (f9(c2, c2) = c4),
% 27.66/17.88 inference(modus_ponens,[status(thm)],[480, 3724])).
% 27.66/17.88 tff(3726,plain,
% 27.66/17.88 ((f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2))),
% 27.66/17.88 inference(unit_resolution,[status(thm)],[2234, 402, 3725, 566, 3722, 3715])).
% 27.66/17.88 tff(3727,plain,
% 27.66/17.88 ($false),
% 27.66/17.88 inference(unit_resolution,[status(thm)],[3726, 3711, 3707])).
% 27.66/17.88 tff(3728,plain,(big_f(c2, c1) | (f9(c2, c2) = c3) | big_f(f9(c2, c2), f9(c2, c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (c1 = c3) | (~big_f(f9(c2, c2), c2)) | (~(c4 = c1))), inference(lemma,lemma(discharge,[]))).
% 27.66/17.88 tff(3729,plain,
% 27.66/17.88 (~(c4 = c1)),
% 27.66/17.88 inference(unit_resolution,[status(thm)],[3728, 2041, 566, 148, 79, 122, 168, 3689, 2])).
% 27.66/17.88 tff(3730,plain,
% 27.66/17.88 (c4 = c2),
% 27.66/17.88 inference(unit_resolution,[status(thm)],[461, 3729])).
% 27.66/17.88 tff(3731,plain,
% 27.66/17.88 ((f9(f10(c2), f4(c4)) = f4(c2)) <=> (f9(c2, c2) = f4(c2))),
% 27.66/17.88 inference(monotonicity,[status(thm)],[132])).
% 27.66/17.88 tff(3732,plain,
% 27.66/17.88 ((f9(c2, c2) = f4(c2)) <=> (f9(f10(c2), f4(c4)) = f4(c2))),
% 27.66/17.88 inference(symmetry,[status(thm)],[3731])).
% 27.66/17.88 tff(3733,plain,
% 27.66/17.88 ((f9(c2, c2) = f4(c2)) <=> (f9(c2, c2) = c2)),
% 27.66/17.88 inference(monotonicity,[status(thm)],[798])).
% 27.66/17.88 tff(3734,plain,
% 27.66/17.88 ((f9(c2, c2) = c2) <=> (f9(c2, c2) = f4(c2))),
% 27.66/17.88 inference(symmetry,[status(thm)],[3733])).
% 27.66/17.88 tff(3735,plain,
% 27.66/17.88 ((f9(c2, c2) = c2) <=> (f9(f10(c2), f4(c4)) = f4(c2))),
% 27.66/17.88 inference(transitivity,[status(thm)],[3734, 3732])).
% 27.66/17.88 tff(3736,plain,
% 27.66/17.88 ((~(f9(c2, c2) = c2)) <=> (~(f9(f10(c2), f4(c4)) = f4(c2)))),
% 27.66/17.88 inference(monotonicity,[status(thm)],[3735])).
% 27.66/17.88 tff(3737,plain,
% 27.66/17.88 (~(f9(f10(c2), f4(c4)) = f4(c2))),
% 27.66/17.88 inference(modus_ponens,[status(thm)],[185, 3736])).
% 27.66/17.88 tff(3738,plain,
% 27.66/17.88 ((~(f9(c2, c2) = c2)) <=> (~(f9(c2, c2) = f4(c2)))),
% 27.66/17.88 inference(monotonicity,[status(thm)],[3734])).
% 27.66/17.88 tff(3739,plain,
% 27.66/17.88 (~(f9(c2, c2) = f4(c2))),
% 27.66/17.88 inference(modus_ponens,[status(thm)],[185, 3738])).
% 27.66/17.88 tff(3740,plain,
% 27.66/17.88 (~(f1(c1, c2) = c2)),
% 27.66/17.88 inference(unit_resolution,[status(thm)],[836, 3680, 122, 815, 631, 814, 148, 79])).
% 27.66/17.88 tff(3741,plain,
% 27.66/17.88 (f1(c1, c2) = c1),
% 27.66/17.88 inference(unit_resolution,[status(thm)],[841, 3740])).
% 27.66/17.88 tff(3742,plain,
% 27.66/17.88 (f1(f9(c2, c2), c2) = f9(c2, c2)),
% 27.66/17.88 inference(transitivity,[status(thm)],[843, 819, 3741, 149, 132])).
% 27.66/17.88 tff(3743,plain,
% 27.66/17.88 ((f1(f9(c2, c2), c2) = c2) <=> (f9(c2, c2) = c2)),
% 27.66/17.88 inference(monotonicity,[status(thm)],[3742])).
% 27.66/17.88 tff(3744,plain,
% 27.66/17.88 ((f9(c2, c2) = c2) <=> (f1(f9(c2, c2), c2) = c2)),
% 27.66/17.88 inference(symmetry,[status(thm)],[3743])).
% 27.66/17.88 tff(3745,plain,
% 27.66/17.88 ((~(f9(c2, c2) = c2)) <=> (~(f1(f9(c2, c2), c2) = c2))),
% 27.66/17.88 inference(monotonicity,[status(thm)],[3744])).
% 27.66/17.88 tff(3746,plain,
% 27.66/17.88 (~(f1(f9(c2, c2), c2) = c2)),
% 27.66/17.88 inference(modus_ponens,[status(thm)],[185, 3745])).
% 27.66/17.88 tff(3747,plain,
% 27.66/17.88 (big_f(f9(c2, c2), f1(f9(c2, c2), c2)) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 27.66/17.88 inference(monotonicity,[status(thm)],[3742])).
% 27.66/17.88 tff(3748,plain,
% 27.66/17.88 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f9(c2, c2), f1(f9(c2, c2), c2))),
% 27.66/17.88 inference(symmetry,[status(thm)],[3747])).
% 27.66/17.88 tff(3749,plain,
% 27.66/17.88 ((~big_f(f9(c2, c2), f9(c2, c2))) <=> (~big_f(f9(c2, c2), f1(f9(c2, c2), c2)))),
% 27.66/17.88 inference(monotonicity,[status(thm)],[3748])).
% 27.66/17.88 tff(3750,plain,
% 27.66/17.88 (~big_f(f9(c2, c2), f1(f9(c2, c2), c2))),
% 27.66/17.88 inference(modus_ponens,[status(thm)],[3689, 3749])).
% 27.66/17.88 tff(3751,plain,
% 27.66/17.88 (big_f(f9(c2, c2), c2)),
% 27.66/17.88 inference(modus_ponens,[status(thm)],[2865, 3657])).
% 27.66/17.88 tff(3752,plain,
% 27.66/17.88 ((f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2))),
% 27.66/17.88 inference(unit_resolution,[status(thm)],[2211, 525, 631, 566, 3751, 2047])).
% 27.66/17.88 tff(3753,plain,
% 27.66/17.88 ($false),
% 27.66/17.88 inference(unit_resolution,[status(thm)],[3752, 3750, 3746])).
% 27.66/17.88 tff(3754,plain,((~big_f(c1, c2)) | (~(c2 = c4)) | (f9(c2, c2) = c3) | (f9(c2, c2) = f4(c2)) | big_f(f9(c2, c2), f9(c2, c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (f9(f10(c2), f4(c4)) = c3) | (f9(f10(c2), f4(c4)) = f4(c2))), inference(lemma,lemma(discharge,[]))).
% 27.66/17.89 tff(3755,plain,
% 27.66/17.89 ($false),
% 27.66/17.89 inference(unit_resolution,[status(thm)],[3754, 3739, 432, 566, 2865, 3689, 148, 79, 122, 815, 3737])).
% 27.66/17.89 tff(3756,plain,((~(c4 = c2)) | (f9(c2, c2) = c3) | (~big_f(c1, c2)) | big_f(f9(c2, c2), f9(c2, c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (f9(f10(c2), f4(c4)) = c3)), inference(lemma,lemma(discharge,[]))).
% 27.66/17.89 tff(3757,plain,
% 27.66/17.89 (~big_f(c1, c2)),
% 27.66/17.89 inference(unit_resolution,[status(thm)],[3756, 3730, 566, 3689, 148, 79, 122, 815])).
% 27.66/17.89 tff(3758,plain,
% 27.66/17.89 ($false),
% 27.66/17.89 inference(unit_resolution,[status(thm)],[3757, 3691])).
% 27.66/17.89 tff(3759,plain,((~big_f(f9(c2, c2), c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (f9(c2, c2) = c3) | big_f(f9(c2, c2), f9(c2, c2)) | (f9(f10(c2), f4(c4)) = c3) | (c1 = c3) | big_f(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 27.66/17.89 tff(3760,plain,
% 27.66/17.89 (big_f(c2, c1)),
% 27.66/17.89 inference(unit_resolution,[status(thm)],[3759, 3689, 79, 122, 3645, 2041, 3643, 168, 148])).
% 27.66/17.89 tff(3761,assumption,(~(c1 = f5(c1))), introduced(assumption)).
% 27.66/17.89 tff(3762,assumption,(f10(c1) = c1), introduced(assumption)).
% 27.66/17.89 tff(3763,plain,
% 27.66/17.89 (f10(c1) = f9(c2, c2)),
% 27.66/17.89 inference(transitivity,[status(thm)],[3762, 149, 132])).
% 27.66/17.89 tff(3764,assumption,(f9(c1, c2) = c2), introduced(assumption)).
% 27.66/17.89 tff(3765,plain,
% 27.66/17.89 (f9(f9(c2, c2), c2) = f9(c1, c2)),
% 27.66/17.89 inference(monotonicity,[status(thm)],[161])).
% 27.66/17.89 tff(3766,plain,
% 27.66/17.89 (f9(f9(c2, c2), c2) = c2),
% 27.66/17.89 inference(transitivity,[status(thm)],[3765, 3764])).
% 27.66/17.89 tff(3767,plain,
% 27.66/17.89 (big_f(f7(f9(c2, c2)), f9(c2, c2)) <=> big_f(c2, f9(c2, c2))),
% 27.66/17.89 inference(monotonicity,[status(thm)],[1793])).
% 27.66/17.89 tff(3768,plain,
% 27.66/17.89 (big_f(c2, f9(c2, c2)) <=> big_f(f7(f9(c2, c2)), f9(c2, c2))),
% 27.66/17.89 inference(symmetry,[status(thm)],[3767])).
% 27.66/17.89 tff(3769,plain,
% 27.66/17.89 (big_f(f7(f9(c2, c2)), f9(c2, c2))),
% 27.66/17.89 inference(modus_ponens,[status(thm)],[3719, 3768])).
% 27.66/17.89 tff(3770,plain,
% 27.66/17.89 (f10(f9(c2, c2)) = f9(c2, c2)),
% 27.66/17.89 inference(transitivity,[status(thm)],[3646, 3762, 149, 132])).
% 27.66/17.89 tff(3771,plain,
% 27.66/17.89 (big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2))) <=> big_f(c2, f9(c2, c2))),
% 27.66/17.89 inference(monotonicity,[status(thm)],[3766, 3770])).
% 27.66/17.89 tff(3772,plain,
% 27.66/17.89 (big_f(c2, f9(c2, c2)) <=> big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))),
% 27.66/17.89 inference(symmetry,[status(thm)],[3771])).
% 27.66/17.89 tff(3773,plain,
% 27.66/17.89 (big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))),
% 27.66/17.89 inference(modus_ponens,[status(thm)],[3719, 3772])).
% 27.66/17.89 tff(3774,assumption,(~(f7(f9(c2, c2)) = f9(c2, c2))), introduced(assumption)).
% 27.66/17.89 tff(3775,plain,
% 27.66/17.89 (f10(c1) = f10(f9(c2, c2))),
% 27.66/17.89 inference(symmetry,[status(thm)],[3646])).
% 27.66/17.89 tff(3776,plain,
% 27.66/17.89 ((f10(c1) = c1) <=> (f10(f9(c2, c2)) = f9(c2, c2))),
% 27.66/17.89 inference(monotonicity,[status(thm)],[3775, 150])).
% 27.66/17.89 tff(3777,plain,
% 27.66/17.89 (f10(f9(c2, c2)) = f9(c2, c2)),
% 27.66/17.89 inference(modus_ponens,[status(thm)],[3762, 3776])).
% 27.66/17.89 tff(3778,plain,
% 27.66/17.89 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((f9(c2, c2) = f5(f9(c2, c2))) | (~big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f9(c2, c2))) | (~(f9(f9(c2, c2), c2) = c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (f9(c2, c2) = f5(f9(c2, c2))) | (~big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f9(c2, c2))) | (~(f9(f9(c2, c2), c2) = c2)))),
% 27.66/17.89 inference(rewrite,[status(thm)],[])).
% 27.66/17.89 tff(3779,plain,
% 27.66/17.89 (((~(f10(f9(c2, c2)) = f9(c2, c2))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f9(c2, c2))) | (~(f9(f9(c2, c2), c2) = c2)) | (~big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2))))) <=> ((f9(c2, c2) = f5(f9(c2, c2))) | (~big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f9(c2, c2))) | (~(f9(f9(c2, c2), c2) = c2)))),
% 27.66/17.89 inference(rewrite,[status(thm)],[])).
% 27.66/17.89 tff(3780,plain,
% 27.66/17.89 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f9(c2, c2))) | (~(f9(f9(c2, c2), c2) = c2)) | (~big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((f9(c2, c2) = f5(f9(c2, c2))) | (~big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f9(c2, c2))) | (~(f9(f9(c2, c2), c2) = c2))))),
% 27.66/17.89 inference(monotonicity,[status(thm)],[3779])).
% 27.66/17.89 tff(3781,plain,
% 27.66/17.89 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f9(c2, c2))) | (~(f9(f9(c2, c2), c2) = c2)) | (~big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (f9(c2, c2) = f5(f9(c2, c2))) | (~big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f9(c2, c2))) | (~(f9(f9(c2, c2), c2) = c2)))),
% 27.66/17.89 inference(transitivity,[status(thm)],[3780, 3778])).
% 27.66/17.89 tff(3782,plain,
% 27.66/17.89 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f9(c2, c2))) | (~(f9(f9(c2, c2), c2) = c2)) | (~big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))))),
% 27.66/17.89 inference(quant_inst,[status(thm)],[])).
% 27.66/17.89 tff(3783,plain,
% 27.66/17.89 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (f9(c2, c2) = f5(f9(c2, c2))) | (~big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f9(c2, c2))) | (~(f9(f9(c2, c2), c2) = c2))),
% 27.66/17.89 inference(modus_ponens,[status(thm)],[3782, 3781])).
% 27.66/17.89 tff(3784,plain,
% 27.66/17.89 ((~big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))) | (~big_f(f7(f9(c2, c2)), f9(c2, c2))) | (~(f9(f9(c2, c2), c2) = c2))),
% 27.66/17.89 inference(unit_resolution,[status(thm)],[3783, 1190, 1792, 3777, 3774])).
% 27.66/17.89 tff(3785,plain,
% 27.66/17.89 ($false),
% 27.66/17.89 inference(unit_resolution,[status(thm)],[3784, 3773, 3769, 3766])).
% 27.66/17.89 tff(3786,plain,((~(f9(c1, c2) = c2)) | (f9(c2, c2) = f5(f9(c2, c2))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~big_f(c2, f9(c2, c2))) | (~(f10(c1) = c1)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f7(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.66/17.89 tff(3787,plain,
% 27.66/17.89 (~(f9(c1, c2) = c2)),
% 27.66/17.89 inference(unit_resolution,[status(thm)],[3786, 3654, 1792, 3719, 3762, 148, 79, 122, 120])).
% 27.66/17.89 tff(3788,plain,
% 27.66/17.89 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f9(c1, c2) = c1) | (f9(c1, c2) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f9(c1, c2) = c1) | (f9(c1, c2) = c2))),
% 27.66/17.89 inference(rewrite,[status(thm)],[])).
% 27.66/17.89 tff(3789,plain,
% 27.66/17.89 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f9(c1, c2) = c1) | (f9(c1, c2) = c2))),
% 27.66/17.89 inference(quant_inst,[status(thm)],[])).
% 27.66/17.89 tff(3790,plain,
% 27.66/17.89 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f9(c1, c2) = c1) | (f9(c1, c2) = c2)),
% 27.66/17.89 inference(modus_ponens,[status(thm)],[3789, 3788])).
% 27.66/17.89 tff(3791,plain,
% 27.66/17.89 ((f9(c1, c2) = c1) | (f9(c1, c2) = c2)),
% 27.66/17.89 inference(unit_resolution,[status(thm)],[3790, 10])).
% 27.66/17.89 tff(3792,plain,
% 27.66/17.89 (f9(c1, c2) = c1),
% 27.66/17.89 inference(unit_resolution,[status(thm)],[3791, 3787])).
% 27.66/17.89 tff(3793,plain,
% 27.66/17.89 (f9(c1, c2) = f9(c2, c2)),
% 27.66/17.89 inference(transitivity,[status(thm)],[3792, 149, 132])).
% 27.66/17.89 tff(3794,plain,
% 27.66/17.89 (big_f(f9(c1, c2), f10(c1)) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 27.66/17.89 inference(monotonicity,[status(thm)],[3793, 3763])).
% 27.66/17.89 tff(3795,plain,
% 27.66/17.89 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f9(c1, c2), f10(c1))),
% 27.66/17.89 inference(symmetry,[status(thm)],[3794])).
% 27.66/17.89 tff(3796,plain,
% 27.66/17.89 ((~big_f(f9(c2, c2), f9(c2, c2))) <=> (~big_f(f9(c1, c2), f10(c1)))),
% 27.66/17.89 inference(monotonicity,[status(thm)],[3795])).
% 27.66/17.89 tff(3797,plain,
% 27.66/17.89 (~big_f(f9(c1, c2), f10(c1))),
% 27.66/17.89 inference(modus_ponens,[status(thm)],[3689, 3796])).
% 27.66/17.89 tff(3798,plain,
% 27.66/17.89 (big_f(f7(c1), c1) <=> big_f(c2, f9(c2, c2))),
% 27.66/17.89 inference(monotonicity,[status(thm)],[120, 150])).
% 27.66/17.89 tff(3799,plain,
% 27.66/17.89 (big_f(c2, f9(c2, c2)) <=> big_f(f7(c1), c1)),
% 27.66/17.89 inference(symmetry,[status(thm)],[3798])).
% 27.66/17.89 tff(3800,plain,
% 27.66/17.89 (big_f(f7(c1), c1)),
% 27.66/17.89 inference(modus_ponens,[status(thm)],[3719, 3799])).
% 27.66/17.89 tff(3801,plain,
% 27.66/17.89 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(c1) = c1) | (~(f10(c1) = c1)) | (c1 = f5(c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (~big_f(f7(c1), c1)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c1) = c1) | (~(f10(c1) = c1)) | (c1 = f5(c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (~big_f(f7(c1), c1)))),
% 27.66/17.89 inference(rewrite,[status(thm)],[])).
% 27.66/17.89 tff(3802,plain,
% 27.66/17.89 (((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (f7(c1) = c1) | (c1 = f5(c1)) | (~big_f(f7(c1), c1))) <=> ((f7(c1) = c1) | (~(f10(c1) = c1)) | (c1 = f5(c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (~big_f(f7(c1), c1)))),
% 27.66/17.89 inference(rewrite,[status(thm)],[])).
% 27.66/17.89 tff(3803,plain,
% 27.66/17.89 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (f7(c1) = c1) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(c1) = c1) | (~(f10(c1) = c1)) | (c1 = f5(c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (~big_f(f7(c1), c1))))),
% 27.66/17.89 inference(monotonicity,[status(thm)],[3802])).
% 27.66/17.89 tff(3804,plain,
% 27.66/17.89 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (f7(c1) = c1) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c1) = c1) | (~(f10(c1) = c1)) | (c1 = f5(c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (~big_f(f7(c1), c1)))),
% 27.66/17.89 inference(transitivity,[status(thm)],[3803, 3801])).
% 27.66/17.89 tff(3805,plain,
% 27.66/17.89 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (f7(c1) = c1) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)))),
% 27.66/17.89 inference(quant_inst,[status(thm)],[])).
% 27.66/17.89 tff(3806,plain,
% 27.66/17.89 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c1) = c1) | (~(f10(c1) = c1)) | (c1 = f5(c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (~big_f(f7(c1), c1))),
% 27.66/17.89 inference(modus_ponens,[status(thm)],[3805, 3804])).
% 27.66/17.89 tff(3807,plain,
% 27.66/17.89 ((f7(c1) = c1) | (~(f10(c1) = c1)) | (c1 = f5(c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (~big_f(f7(c1), c1))),
% 27.66/17.89 inference(unit_resolution,[status(thm)],[3806, 676])).
% 27.66/17.89 tff(3808,plain,
% 27.66/17.89 (big_f(f9(c1, c2), f10(c1))),
% 27.66/17.89 inference(unit_resolution,[status(thm)],[3807, 3787, 3761, 3762, 115, 3800])).
% 27.66/17.89 tff(3809,plain,
% 27.66/17.89 ($false),
% 27.66/17.89 inference(unit_resolution,[status(thm)],[3808, 3797])).
% 27.66/17.89 tff(3810,plain,((f7(c1) = c1) | big_f(f9(c2, c2), f9(c2, c2)) | (~(f10(c1) = c1)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (c1 = f5(c1)) | (f9(c2, c2) = f5(f9(c2, c2))) | (~big_f(c2, f9(c2, c2)))), inference(lemma,lemma(discharge,[]))).
% 27.66/17.89 tff(3811,plain,
% 27.66/17.89 (~big_f(c2, f9(c2, c2))),
% 27.66/17.89 inference(unit_resolution,[status(thm)],[3810, 3689, 148, 3762, 79, 122, 115, 1792, 3761])).
% 27.66/17.89 tff(3812,plain,
% 27.66/17.89 (big_f(c2, f9(c2, c2))),
% 27.66/17.89 inference(modus_ponens,[status(thm)],[348, 3716])).
% 27.66/17.89 tff(3813,plain,
% 27.66/17.89 ($false),
% 27.66/17.89 inference(unit_resolution,[status(thm)],[2040, 3812])).
% 27.66/17.89 tff(3814,plain,((~big_f(c2, c1)) | big_f(c2, f9(c2, c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.66/17.89 tff(3815,plain,
% 27.66/17.89 ($false),
% 27.66/17.89 inference(unit_resolution,[status(thm)],[3814, 3811, 3760, 148, 79, 122])).
% 27.66/17.89 tff(3816,plain,(big_f(f9(c2, c2), f9(c2, c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f10(c1) = c1)) | (f7(c1) = c1) | (f9(c2, c2) = f5(f9(c2, c2))) | (c1 = f5(c1)) | (~big_f(f9(c2, c2), c2)) | (c1 = c3)), inference(lemma,lemma(discharge,[]))).
% 27.66/17.89 tff(3817,plain,
% 27.66/17.89 (big_f(f9(c2, c2), f9(c2, c2))),
% 27.66/17.89 inference(unit_resolution,[status(thm)],[3816, 191, 79, 122, 3637, 115, 148, 200, 3688, 168])).
% 27.66/17.89 tff(3818,plain,
% 27.66/17.89 (f9(c2, f9(c2, c2)) = f9(c2, c1)),
% 27.66/17.89 inference(monotonicity,[status(thm)],[161])).
% 27.66/17.89 tff(3819,plain,
% 27.66/17.89 (f9(c2, c1) = f9(c2, f9(c2, c2))),
% 27.66/17.89 inference(symmetry,[status(thm)],[3818])).
% 27.66/17.89 tff(3820,plain,
% 27.66/17.89 ((f9(c2, c1) = c1) <=> (f9(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.66/17.89 inference(monotonicity,[status(thm)],[3819, 150])).
% 27.66/17.89 tff(3821,plain,
% 27.66/17.89 ((f9(c2, f9(c2, c2)) = f9(c2, c2)) <=> (f9(c2, c1) = c1)),
% 27.66/17.89 inference(symmetry,[status(thm)],[3820])).
% 27.66/17.89 tff(3822,plain,
% 27.66/17.89 (f9(c2, f9(f10(c2), f10(c2))) = f9(c2, f9(c2, c2))),
% 27.66/17.89 inference(monotonicity,[status(thm)],[135])).
% 27.66/17.89 tff(3823,plain,
% 27.66/17.89 ((f9(c2, f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2))) <=> (f9(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.66/17.89 inference(monotonicity,[status(thm)],[3822, 135])).
% 27.66/17.89 tff(3824,plain,
% 27.66/17.89 ((f9(c2, f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2))) <=> (f9(c2, c1) = c1)),
% 27.66/17.89 inference(transitivity,[status(thm)],[3823, 3821])).
% 27.66/17.89 tff(3825,plain,
% 27.66/17.89 ((~(f9(c2, f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))) <=> (~(f9(c2, c1) = c1))),
% 27.66/17.89 inference(monotonicity,[status(thm)],[3824])).
% 27.66/17.89 tff(3826,plain,
% 27.66/17.89 (big_f(f7(c1), f10(c1)) <=> big_f(f7(c1), c1)),
% 27.66/17.89 inference(monotonicity,[status(thm)],[3762])).
% 27.66/17.89 tff(3827,plain,
% 27.66/17.89 (big_f(f7(c1), c1) <=> big_f(f7(c1), f10(c1))),
% 27.66/17.89 inference(symmetry,[status(thm)],[3826])).
% 27.66/17.89 tff(3828,plain,
% 27.66/17.89 (big_f(c2, c1) <=> big_f(f7(c1), f10(c1))),
% 27.66/17.89 inference(transitivity,[status(thm)],[3716, 3799, 3827])).
% 27.66/17.89 tff(3829,plain,
% 27.66/17.89 ((~big_f(c2, c2)) <=> (~big_f(c3, c2))),
% 27.66/17.89 inference(monotonicity,[status(thm)],[1288])).
% 27.66/17.89 tff(3830,plain,
% 27.66/17.89 (~big_f(c3, c2)),
% 27.66/17.89 inference(modus_ponens,[status(thm)],[121, 3829])).
% 27.66/17.89 tff(3831,plain,
% 27.66/17.89 ((c2 = f2(c3)) <=> (f2(c3) = c2)),
% 27.66/17.89 inference(symmetry,[status(thm)],[1434])).
% 27.66/17.89 tff(3832,plain,
% 27.66/17.89 ((~(c2 = f2(c3))) <=> (~(f2(c3) = c2))),
% 27.66/17.89 inference(monotonicity,[status(thm)],[3831])).
% 27.66/17.89 tff(3833,assumption,(~big_f(c3, c2)), introduced(assumption)).
% 27.66/17.89 tff(3834,plain,
% 27.66/17.89 (big_f(c2, c1) <=> big_f(c2, c4)),
% 27.66/17.89 inference(symmetry,[status(thm)],[2217])).
% 27.66/17.89 tff(3835,plain,
% 27.66/17.89 ((~big_f(c2, c1)) <=> (~big_f(c2, c4))),
% 27.66/17.89 inference(monotonicity,[status(thm)],[3834])).
% 27.66/17.89 tff(3836,plain,
% 27.66/17.89 (~big_f(c2, c4)),
% 27.66/17.89 inference(modus_ponens,[status(thm)],[2, 3835])).
% 27.66/17.89 tff(3837,plain,
% 27.66/17.89 (~(c2 = f2(c3))),
% 27.66/17.89 inference(unit_resolution,[status(thm)],[2612, 3836, 2602, 3833])).
% 27.66/17.89 tff(3838,plain,
% 27.66/17.89 (~(f2(c3) = c2)),
% 27.66/17.89 inference(modus_ponens,[status(thm)],[3837, 3832])).
% 27.66/17.89 tff(3839,plain,
% 27.66/17.89 ((~(f9(c2, c2) = f2(c2))) <=> (~(f2(c3) = c1))),
% 27.66/17.89 inference(monotonicity,[status(thm)],[1226])).
% 27.66/17.89 tff(3840,plain,
% 27.66/17.89 (f4(c4) = f4(c1)),
% 27.66/17.89 inference(symmetry,[status(thm)],[568])).
% 27.66/17.89 tff(3841,plain,
% 27.66/17.89 (c2 = f4(f9(c2, c2))),
% 27.66/17.89 inference(transitivity,[status(thm)],[436, 3840, 2094])).
% 27.66/17.89 tff(3842,plain,
% 27.66/17.89 (~big_f(c2, f9(c2, c2))),
% 27.66/17.89 inference(modus_ponens,[status(thm)],[2, 2015])).
% 27.66/17.89 tff(3843,plain,
% 27.66/17.89 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))) | ((~(c2 = c3)) | big_f(c2, f9(c2, c2)) | (~(f9(c2, c2) = c4)) | (~(c2 = f4(f9(c2, c2)))) | (~(f9(c2, c2) = f2(c2))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))) | (~(c2 = c3)) | big_f(c2, f9(c2, c2)) | (~(f9(c2, c2) = c4)) | (~(c2 = f4(f9(c2, c2)))) | (~(f9(c2, c2) = f2(c2))))),
% 27.66/17.89 inference(rewrite,[status(thm)],[])).
% 27.66/17.89 tff(3844,plain,
% 27.66/17.89 (((~(c2 = c3)) | (~(f9(c2, c2) = f2(c2))) | (~(f9(c2, c2) = c4)) | big_f(c2, f9(c2, c2)) | (~(c2 = f4(f9(c2, c2)))) | big_f(c2, f9(c2, c2))) <=> ((~(c2 = c3)) | big_f(c2, f9(c2, c2)) | (~(f9(c2, c2) = c4)) | (~(c2 = f4(f9(c2, c2)))) | (~(f9(c2, c2) = f2(c2))))),
% 27.66/17.89 inference(rewrite,[status(thm)],[])).
% 27.66/17.89 tff(3845,plain,
% 27.66/17.89 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(f9(c2, c2) = f2(c2))) | (~(f9(c2, c2) = c4)) | big_f(c2, f9(c2, c2)) | (~(c2 = f4(f9(c2, c2)))) | big_f(c2, f9(c2, c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))) | ((~(c2 = c3)) | big_f(c2, f9(c2, c2)) | (~(f9(c2, c2) = c4)) | (~(c2 = f4(f9(c2, c2)))) | (~(f9(c2, c2) = f2(c2)))))),
% 27.66/17.89 inference(monotonicity,[status(thm)],[3844])).
% 27.66/17.89 tff(3846,plain,
% 27.66/17.89 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(f9(c2, c2) = f2(c2))) | (~(f9(c2, c2) = c4)) | big_f(c2, f9(c2, c2)) | (~(c2 = f4(f9(c2, c2)))) | big_f(c2, f9(c2, c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))) | (~(c2 = c3)) | big_f(c2, f9(c2, c2)) | (~(f9(c2, c2) = c4)) | (~(c2 = f4(f9(c2, c2)))) | (~(f9(c2, c2) = f2(c2))))),
% 27.66/17.89 inference(transitivity,[status(thm)],[3845, 3843])).
% 27.66/17.89 tff(3847,plain,
% 27.66/17.89 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(f9(c2, c2) = f2(c2))) | (~(f9(c2, c2) = c4)) | big_f(c2, f9(c2, c2)) | (~(c2 = f4(f9(c2, c2)))) | big_f(c2, f9(c2, c2)))),
% 27.66/17.89 inference(quant_inst,[status(thm)],[])).
% 27.66/17.89 tff(3848,plain,
% 27.66/17.89 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))) | (~(c2 = c3)) | big_f(c2, f9(c2, c2)) | (~(f9(c2, c2) = c4)) | (~(c2 = f4(f9(c2, c2)))) | (~(f9(c2, c2) = f2(c2)))),
% 27.66/17.89 inference(modus_ponens,[status(thm)],[3847, 3846])).
% 27.66/17.89 tff(3849,plain,
% 27.66/17.89 ((~(c2 = c3)) | (~(f9(c2, c2) = c4)) | (~(c2 = f4(f9(c2, c2)))) | (~(f9(c2, c2) = f2(c2)))),
% 27.66/17.89 inference(unit_resolution,[status(thm)],[3848, 1300, 3842])).
% 27.66/17.89 tff(3850,plain,
% 27.66/17.89 (~(f9(c2, c2) = f2(c2))),
% 27.66/17.89 inference(unit_resolution,[status(thm)],[3849, 3841, 1335, 565])).
% 27.66/17.89 tff(3851,plain,
% 27.66/17.89 (~(f2(c3) = c1)),
% 27.66/17.89 inference(modus_ponens,[status(thm)],[3850, 3839])).
% 27.66/17.89 tff(3852,plain,
% 27.66/17.89 ($false),
% 27.66/17.89 inference(unit_resolution,[status(thm)],[1273, 3851, 3838])).
% 27.66/17.90 tff(3853,plain,((~(c4 = c1)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(c3 = c2)) | big_f(c3, c2) | big_f(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 27.66/17.90 tff(3854,plain,
% 27.66/17.90 (~(c4 = c1)),
% 27.66/17.90 inference(unit_resolution,[status(thm)],[3853, 67, 79, 122, 148, 3830, 2])).
% 27.66/17.90 tff(3855,plain,
% 27.66/17.90 (c4 = c2),
% 27.66/17.90 inference(unit_resolution,[status(thm)],[461, 3854])).
% 27.66/17.90 tff(3856,plain,
% 27.66/17.90 (c2 = c4),
% 27.66/17.90 inference(symmetry,[status(thm)],[3855])).
% 27.66/17.90 tff(3857,plain,
% 27.66/17.90 (f4(c2) = f4(c4)),
% 27.66/17.90 inference(monotonicity,[status(thm)],[3856])).
% 27.66/17.90 tff(3858,plain,
% 27.66/17.90 (f4(c4) = f4(c2)),
% 27.66/17.90 inference(symmetry,[status(thm)],[3857])).
% 27.66/17.90 tff(3859,plain,
% 27.66/17.90 (c2 = f4(c2)),
% 27.66/17.90 inference(transitivity,[status(thm)],[436, 3858])).
% 27.66/17.90 tff(3860,plain,
% 27.66/17.90 (c2 = c4),
% 27.66/17.90 inference(modus_ponens,[status(thm)],[3855, 159])).
% 27.66/17.90 tff(3861,plain,
% 27.66/17.90 (big_f(c2, c4) <=> big_f(c2, c2)),
% 27.66/17.90 inference(monotonicity,[status(thm)],[3855])).
% 27.66/17.90 tff(3862,plain,
% 27.66/17.90 (big_f(c2, c2) <=> big_f(c2, c4)),
% 27.66/17.90 inference(symmetry,[status(thm)],[3861])).
% 27.66/17.90 tff(3863,plain,
% 27.66/17.90 ((~big_f(c2, c2)) <=> (~big_f(c2, c4))),
% 27.66/17.90 inference(monotonicity,[status(thm)],[3862])).
% 27.66/17.90 tff(3864,plain,
% 27.66/17.90 (~big_f(c2, c4)),
% 27.66/17.90 inference(modus_ponens,[status(thm)],[121, 3863])).
% 27.66/17.90 tff(3865,assumption,(~big_f(c2, c4)), introduced(assumption)).
% 27.66/17.90 tff(3866,plain,
% 27.66/17.90 (~(c2 = f2(c3))),
% 27.66/17.90 inference(unit_resolution,[status(thm)],[2612, 3830, 2602, 3865])).
% 27.66/17.90 tff(3867,plain,
% 27.66/17.90 (~(f2(c3) = c2)),
% 27.66/17.90 inference(modus_ponens,[status(thm)],[3866, 3832])).
% 27.66/17.90 tff(3868,plain,
% 27.66/17.90 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | big_f(c2, f9(c2, c2)) | (~(f9(c2, c2) = f2(c2))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))) | (~(c2 = c3)) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | big_f(c2, f9(c2, c2)) | (~(f9(c2, c2) = f2(c2))))),
% 27.66/17.90 inference(rewrite,[status(thm)],[])).
% 27.66/17.90 tff(3869,plain,
% 27.66/17.90 (((~(c2 = c3)) | (~(f9(c2, c2) = f2(c2))) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))) | big_f(c2, f9(c2, c2))) <=> ((~(c2 = c3)) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | big_f(c2, f9(c2, c2)) | (~(f9(c2, c2) = f2(c2))))),
% 27.66/17.90 inference(rewrite,[status(thm)],[])).
% 27.66/17.90 tff(3870,plain,
% 27.66/17.90 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(f9(c2, c2) = f2(c2))) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))) | big_f(c2, f9(c2, c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | big_f(c2, f9(c2, c2)) | (~(f9(c2, c2) = f2(c2)))))),
% 27.66/17.90 inference(monotonicity,[status(thm)],[3869])).
% 27.66/17.90 tff(3871,plain,
% 27.66/17.90 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(f9(c2, c2) = f2(c2))) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))) | big_f(c2, f9(c2, c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))) | (~(c2 = c3)) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | big_f(c2, f9(c2, c2)) | (~(f9(c2, c2) = f2(c2))))),
% 27.66/17.90 inference(transitivity,[status(thm)],[3870, 3868])).
% 27.66/17.90 tff(3872,plain,
% 27.66/17.90 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(f9(c2, c2) = f2(c2))) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))) | big_f(c2, f9(c2, c2)))),
% 27.66/17.90 inference(quant_inst,[status(thm)],[])).
% 27.66/17.90 tff(3873,plain,
% 27.66/17.90 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))) | (~(c2 = c3)) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | big_f(c2, f9(c2, c2)) | (~(f9(c2, c2) = f2(c2)))),
% 27.66/17.90 inference(modus_ponens,[status(thm)],[3872, 3871])).
% 27.66/17.90 tff(3874,plain,
% 27.66/17.90 ((~(c2 = c3)) | big_f(c2, f9(c2, c2)) | (~(f9(c2, c2) = f2(c2)))),
% 27.66/17.90 inference(unit_resolution,[status(thm)],[3873, 1300, 631, 630, 121])).
% 27.66/17.90 tff(3875,plain,
% 27.66/17.90 (~(f9(c2, c2) = f2(c2))),
% 27.66/17.90 inference(unit_resolution,[status(thm)],[3874, 1335, 2040])).
% 27.66/17.90 tff(3876,plain,
% 27.66/17.90 (~(f2(c3) = c1)),
% 27.66/17.90 inference(modus_ponens,[status(thm)],[3875, 3839])).
% 27.66/17.90 tff(3877,plain,
% 27.66/17.90 ($false),
% 27.66/17.90 inference(unit_resolution,[status(thm)],[1273, 3876, 3867])).
% 27.66/17.90 tff(3878,plain,((~(c3 = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | big_f(c2, c4) | big_f(c2, f9(c2, c2)) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 27.66/17.90 tff(3879,plain,
% 27.66/17.90 ($false),
% 27.66/17.90 inference(unit_resolution,[status(thm)],[3878, 3864, 3860, 79, 122, 121, 3842, 67, 3859, 148])).
% 27.66/17.90 tff(3880,plain,((~(c3 = c2)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | big_f(c2, c2) | (~(f9(f10(c2), f4(c4)) = c1)) | big_f(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 27.66/17.90 tff(3881,plain,
% 27.66/17.90 (big_f(c2, c1)),
% 27.66/17.90 inference(unit_resolution,[status(thm)],[3880, 121, 122, 67, 148, 79])).
% 27.66/17.90 tff(3882,plain,
% 27.66/17.90 (big_f(f7(c1), f10(c1))),
% 27.66/17.90 inference(modus_ponens,[status(thm)],[3881, 3828])).
% 27.66/17.90 tff(3883,plain,
% 27.66/17.90 ((f10(c1) = f5(c1)) <=> (f9(c2, c2) = f5(f9(c2, c2)))),
% 27.66/17.90 inference(monotonicity,[status(thm)],[3763, 194])).
% 27.66/17.90 tff(3884,plain,
% 27.66/17.90 ((f9(c2, c2) = f5(f9(c2, c2))) <=> (f10(c1) = f5(c1))),
% 27.66/17.90 inference(symmetry,[status(thm)],[3883])).
% 27.66/17.90 tff(3885,plain,
% 27.66/17.90 ((f9(c2, c2) = c2) <=> (f10(c1) = f5(c1))),
% 27.66/17.90 inference(transitivity,[status(thm)],[189, 3884])).
% 27.66/17.90 tff(3886,plain,
% 27.66/17.90 ((~(f9(c2, c2) = c2)) <=> (~(f10(c1) = f5(c1)))),
% 27.66/17.90 inference(monotonicity,[status(thm)],[3885])).
% 27.66/17.90 tff(3887,plain,
% 27.66/17.90 (~(f10(c1) = f5(c1))),
% 27.66/17.90 inference(modus_ponens,[status(thm)],[185, 3886])).
% 27.66/17.90 tff(3888,plain,
% 27.66/17.90 (big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2)) <=> big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 27.66/17.90 inference(monotonicity,[status(thm)],[3822])).
% 27.66/17.90 tff(3889,plain,
% 27.66/17.90 (big_f(f9(c2, f9(c2, c2)), f10(c2)) <=> big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2))),
% 27.66/17.90 inference(symmetry,[status(thm)],[3888])).
% 27.66/17.90 tff(3890,plain,
% 27.66/17.90 (~big_f(f7(c1), f5(c1))),
% 27.66/17.90 inference(unit_resolution,[status(thm)],[1715, 121, 186, 120])).
% 27.66/17.90 tff(3891,plain,
% 27.66/17.90 (big_f(f9(c2, c1), f10(c2))),
% 27.66/17.90 inference(unit_resolution,[status(thm)],[755, 3890, 122, 115, 690, 148, 79])).
% 27.66/17.90 tff(3892,plain,
% 27.66/17.90 (f9(c2, c1) = f9(c2, f9(c2, c2))),
% 27.66/17.90 inference(monotonicity,[status(thm)],[150])).
% 27.66/17.90 tff(3893,plain,
% 27.66/17.90 (big_f(f9(c2, c1), f10(c2)) <=> big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 27.66/17.90 inference(monotonicity,[status(thm)],[3892])).
% 27.66/17.90 tff(3894,assumption,(big_f(f9(c2, c1), f10(c2))), introduced(assumption)).
% 27.66/17.90 tff(3895,plain,
% 27.66/17.90 (big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 27.66/17.90 inference(modus_ponens,[status(thm)],[3894, 3893])).
% 27.66/17.90 tff(3896,assumption,(~big_f(f9(c2, f9(c2, c2)), f10(c2))), introduced(assumption)).
% 27.66/17.90 tff(3897,plain,
% 27.66/17.90 ($false),
% 27.66/17.90 inference(unit_resolution,[status(thm)],[3896, 3895])).
% 27.66/17.90 tff(3898,plain,((~big_f(f9(c2, c1), f10(c2))) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.66/17.90 tff(3899,plain,
% 27.66/17.90 (big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 27.66/17.90 inference(unit_resolution,[status(thm)],[3898, 3891, 148, 79, 122])).
% 27.66/17.90 tff(3900,plain,
% 27.66/17.90 (big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2))),
% 27.66/17.90 inference(modus_ponens,[status(thm)],[3899, 3889])).
% 27.66/17.90 tff(3901,plain,
% 27.66/17.90 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((f7(c1) = c1) | (~(f10(c2) = c2)) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2))) | (~(f9(c2, f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))) | (~big_f(f7(c1), f10(c1))) | (f10(c1) = f5(c1)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2))) | (~(f9(c2, f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))) | (~big_f(f7(c1), f10(c1))) | (f10(c1) = f5(c1)))),
% 27.66/17.90 inference(rewrite,[status(thm)],[])).
% 27.66/17.90 tff(3902,plain,
% 27.66/17.90 (((~(f10(c2) = c2)) | (f7(c1) = c1) | (f10(c1) = f5(c1)) | (~big_f(f7(c1), f10(c1))) | (~(f9(c2, f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2)))) <=> ((f7(c1) = c1) | (~(f10(c2) = c2)) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2))) | (~(f9(c2, f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))) | (~big_f(f7(c1), f10(c1))) | (f10(c1) = f5(c1)))),
% 27.66/17.90 inference(rewrite,[status(thm)],[])).
% 27.66/17.90 tff(3903,plain,
% 27.66/17.90 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c1) = c1) | (f10(c1) = f5(c1)) | (~big_f(f7(c1), f10(c1))) | (~(f9(c2, f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((f7(c1) = c1) | (~(f10(c2) = c2)) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2))) | (~(f9(c2, f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))) | (~big_f(f7(c1), f10(c1))) | (f10(c1) = f5(c1))))),
% 27.66/17.90 inference(monotonicity,[status(thm)],[3902])).
% 27.66/17.90 tff(3904,plain,
% 27.66/17.90 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c1) = c1) | (f10(c1) = f5(c1)) | (~big_f(f7(c1), f10(c1))) | (~(f9(c2, f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2))) | (~(f9(c2, f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))) | (~big_f(f7(c1), f10(c1))) | (f10(c1) = f5(c1)))),
% 27.66/17.90 inference(transitivity,[status(thm)],[3903, 3901])).
% 27.66/17.90 tff(3905,plain,
% 27.66/17.90 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c1) = c1) | (f10(c1) = f5(c1)) | (~big_f(f7(c1), f10(c1))) | (~(f9(c2, f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2))))),
% 27.66/17.90 inference(quant_inst,[status(thm)],[])).
% 27.66/17.90 tff(3906,plain,
% 27.66/17.90 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2))) | (~(f9(c2, f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))) | (~big_f(f7(c1), f10(c1))) | (f10(c1) = f5(c1))),
% 27.66/17.90 inference(modus_ponens,[status(thm)],[3905, 3904])).
% 27.66/17.90 tff(3907,plain,
% 27.66/17.90 ((f7(c1) = c1) | (~(f10(c2) = c2)) | (~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2))) | (~(f9(c2, f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))) | (~big_f(f7(c1), f10(c1))) | (f10(c1) = f5(c1))),
% 27.66/17.90 inference(unit_resolution,[status(thm)],[3906, 1190])).
% 27.66/17.90 tff(3908,plain,
% 27.66/17.90 (~(f9(c2, f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))),
% 27.66/17.90 inference(unit_resolution,[status(thm)],[3907, 3900, 122, 3887, 115, 3882])).
% 27.66/17.90 tff(3909,plain,
% 27.66/17.90 (~(f9(c2, c1) = c1)),
% 27.66/17.90 inference(modus_ponens,[status(thm)],[3908, 3825])).
% 27.66/17.90 tff(3910,plain,
% 27.66/17.90 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f9(c2, c1) = c1) | (f9(c2, c1) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f9(c2, c1) = c1) | (f9(c2, c1) = c2))),
% 27.66/17.90 inference(rewrite,[status(thm)],[])).
% 27.66/17.90 tff(3911,plain,
% 27.66/17.90 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f9(c2, c1) = c1) | (f9(c2, c1) = c2))),
% 27.66/17.90 inference(quant_inst,[status(thm)],[])).
% 27.66/17.90 tff(3912,plain,
% 27.66/17.90 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f9(c2, c1) = c1) | (f9(c2, c1) = c2)),
% 27.66/17.90 inference(modus_ponens,[status(thm)],[3911, 3910])).
% 27.66/17.90 tff(3913,plain,
% 27.66/17.90 ((f9(c2, c1) = c1) | (f9(c2, c1) = c2)),
% 27.66/17.90 inference(unit_resolution,[status(thm)],[3912, 10])).
% 27.66/17.90 tff(3914,plain,
% 27.66/17.90 (f9(c2, c1) = c2),
% 27.66/17.90 inference(unit_resolution,[status(thm)],[3913, 3909])).
% 27.66/17.90 tff(3915,plain,
% 27.66/17.90 (f9(c2, f9(c2, c2)) = c2),
% 27.66/17.90 inference(transitivity,[status(thm)],[3818, 3914])).
% 27.66/17.90 tff(3916,plain,
% 27.66/17.90 (big_f(f9(c2, f9(c2, c2)), f10(c2)) <=> big_f(c2, c2)),
% 27.66/17.90 inference(monotonicity,[status(thm)],[3915, 122])).
% 27.66/17.90 tff(3917,plain,
% 27.66/17.90 (big_f(c2, c2) <=> big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 27.66/17.90 inference(symmetry,[status(thm)],[3916])).
% 27.66/17.90 tff(3918,plain,
% 27.66/17.90 ((~big_f(c2, c2)) <=> (~big_f(f9(c2, f9(c2, c2)), f10(c2)))),
% 27.66/17.90 inference(monotonicity,[status(thm)],[3917])).
% 27.66/17.90 tff(3919,plain,
% 27.66/17.90 (~big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 27.66/17.90 inference(modus_ponens,[status(thm)],[121, 3918])).
% 27.66/17.90 tff(3920,plain,
% 27.66/17.90 ($false),
% 27.66/17.90 inference(unit_resolution,[status(thm)],[3899, 3919])).
% 27.66/17.90 tff(3921,plain,(big_f(c2, c2) | (~(f10(c2) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (f7(c1) = c1) | (~(f10(c1) = c1)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f5(c1) = c2)) | (~(c3 = c2))), inference(lemma,lemma(discharge,[]))).
% 27.66/17.90 tff(3922,plain,
% 27.66/17.90 (big_f(c2, c2)),
% 27.66/17.90 inference(unit_resolution,[status(thm)],[3921, 3683, 148, 79, 122, 3637, 115, 186, 181])).
% 27.66/17.90 tff(3923,assumption,(~(f9(c1, c1) = c4)), introduced(assumption)).
% 27.66/17.90 tff(3924,plain,
% 27.66/17.90 ((f6(f7(c2), c3) = c4) <=> (f6(c2, c2) = c2)),
% 27.66/17.90 inference(monotonicity,[status(thm)],[2466, 431])).
% 27.66/17.90 tff(3925,plain,
% 27.66/17.90 ((f6(c2, c2) = c2) <=> (f6(f7(c2), c3) = c4)),
% 27.66/17.90 inference(symmetry,[status(thm)],[3924])).
% 27.66/17.90 tff(3926,plain,
% 27.66/17.90 ((f6(c2, c2) = f5(f9(c2, c2))) <=> (f6(c2, c2) = c2)),
% 27.66/17.90 inference(monotonicity,[status(thm)],[187])).
% 27.66/17.90 tff(3927,plain,
% 27.66/17.90 ((f6(c2, c2) = f5(f9(c2, c2))) <=> (f6(f7(c2), c3) = c4)),
% 27.66/17.90 inference(transitivity,[status(thm)],[3926, 3925])).
% 27.66/17.90 tff(3928,plain,
% 27.66/17.90 (f7(f9(c2, c2)) = f7(c2)),
% 27.66/17.90 inference(transitivity,[status(thm)],[243, 347, 82])).
% 27.66/17.90 tff(3929,plain,
% 27.66/17.90 (big_f(f7(f9(c2, c2)), f6(c2, c2)) <=> big_f(f7(c2), f6(c2, c2))),
% 27.66/17.90 inference(monotonicity,[status(thm)],[3928])).
% 27.66/17.90 tff(3930,plain,
% 27.66/17.90 (big_f(f7(c2), f6(c2, c2)) <=> big_f(f7(f9(c2, c2)), f6(c2, c2))),
% 27.66/17.90 inference(symmetry,[status(thm)],[3929])).
% 27.66/17.90 tff(3931,plain,
% 27.66/17.90 (big_f(f9(c1, c1), f10(c1)) <=> big_f(f9(c1, c1), c1)),
% 27.66/17.90 inference(monotonicity,[status(thm)],[3762])).
% 27.66/17.90 tff(3932,plain,
% 27.66/17.90 (big_f(f9(c1, c1), c1) <=> big_f(f9(c1, c1), f10(c1))),
% 27.66/17.90 inference(symmetry,[status(thm)],[3931])).
% 27.66/17.90 tff(3933,plain,
% 27.66/17.90 ((f9(c1, c1) = c4) <=> (f9(c1, c1) = c2)),
% 27.66/17.90 inference(monotonicity,[status(thm)],[431])).
% 27.66/17.90 tff(3934,plain,
% 27.66/17.90 ((~(f9(c1, c1) = c4)) <=> (~(f9(c1, c1) = c2))),
% 27.66/17.90 inference(monotonicity,[status(thm)],[3933])).
% 27.66/17.90 tff(3935,plain,
% 27.66/17.90 (~(f9(c1, c1) = c2)),
% 27.66/17.90 inference(modus_ponens,[status(thm)],[3923, 3934])).
% 27.66/17.90 tff(3936,plain,
% 27.66/17.90 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f9(c1, c1) = c1) | (f9(c1, c1) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f9(c1, c1) = c1) | (f9(c1, c1) = c2))),
% 27.66/17.90 inference(rewrite,[status(thm)],[])).
% 27.66/17.90 tff(3937,plain,
% 27.66/17.90 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f9(c1, c1) = c1) | (f9(c1, c1) = c2))),
% 27.66/17.90 inference(quant_inst,[status(thm)],[])).
% 27.66/17.90 tff(3938,plain,
% 27.66/17.90 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f9(c1, c1) = c1) | (f9(c1, c1) = c2)),
% 27.66/17.90 inference(modus_ponens,[status(thm)],[3937, 3936])).
% 27.66/17.90 tff(3939,plain,
% 27.66/17.90 ((f9(c1, c1) = c1) | (f9(c1, c1) = c2)),
% 27.66/17.90 inference(unit_resolution,[status(thm)],[3938, 10])).
% 27.66/17.90 tff(3940,plain,
% 27.66/17.90 (f9(c1, c1) = c1),
% 27.66/17.90 inference(unit_resolution,[status(thm)],[3939, 3935])).
% 27.66/17.90 tff(3941,plain,
% 27.66/17.90 (f9(c1, c1) = f9(c2, c2)),
% 27.66/17.90 inference(transitivity,[status(thm)],[3940, 149, 132])).
% 27.66/17.90 tff(3942,plain,
% 27.66/17.90 (big_f(f9(c1, c1), c1) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 27.66/17.90 inference(monotonicity,[status(thm)],[3941, 150])).
% 27.66/17.90 tff(3943,plain,
% 27.66/17.90 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f9(c1, c1), c1)),
% 27.66/17.90 inference(symmetry,[status(thm)],[3942])).
% 27.66/17.90 tff(3944,plain,
% 27.66/17.90 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f9(c1, c1), f10(c1))),
% 27.66/17.90 inference(transitivity,[status(thm)],[3943, 3932])).
% 27.66/17.90 tff(3945,plain,
% 27.66/17.90 (big_f(f9(c1, c1), f10(c1))),
% 27.66/17.90 inference(modus_ponens,[status(thm)],[487, 3944])).
% 27.66/17.90 tff(3946,plain,
% 27.66/17.90 (f6(c2, f4(c4)) = f6(c2, c2)),
% 27.66/17.90 inference(monotonicity,[status(thm)],[79])).
% 27.66/17.90 tff(3947,plain,
% 27.66/17.90 (big_f(f7(c2), f6(c2, f4(c4))) <=> big_f(f7(c2), f6(c2, c2))),
% 27.66/17.90 inference(monotonicity,[status(thm)],[3946])).
% 27.66/17.90 tff(3948,assumption,(big_f(f9(c1, c1), f10(c1))), introduced(assumption)).
% 27.66/17.90 tff(3949,assumption,(f9(c1, c1) = c1), introduced(assumption)).
% 27.66/17.90 tff(3950,plain,
% 27.66/17.90 ((f6(c2, f4(c4)) = f4(c4)) <=> (f6(c2, c2) = c2)),
% 27.66/17.90 inference(monotonicity,[status(thm)],[3946, 79])).
% 27.66/17.90 tff(3951,plain,
% 27.66/17.90 ((f6(c2, c2) = c2) <=> (f6(c2, f4(c4)) = f4(c4))),
% 27.66/17.90 inference(symmetry,[status(thm)],[3950])).
% 27.66/17.90 tff(3952,plain,
% 27.66/17.90 ((~(f6(c2, c2) = c2)) <=> (~(f6(c2, f4(c4)) = f4(c4)))),
% 27.66/17.90 inference(monotonicity,[status(thm)],[3951])).
% 27.66/17.90 tff(3953,plain,
% 27.66/17.90 (~(f6(c2, c2) = c2)),
% 27.66/17.90 inference(unit_resolution,[status(thm)],[2627, 2621, 77, 1345])).
% 27.66/17.90 tff(3954,plain,
% 27.66/17.90 (~(f6(c2, f4(c4)) = f4(c4))),
% 27.66/17.90 inference(modus_ponens,[status(thm)],[3953, 3952])).
% 27.66/17.90 tff(3955,plain,
% 27.66/17.90 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f7(c2) = c2)) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | big_f(f7(c2), f6(c2, f4(c4))) | (f6(c2, f4(c4)) = f4(c4)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f7(c2) = c2)) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | big_f(f7(c2), f6(c2, f4(c4))) | (f6(c2, f4(c4)) = f4(c4)))),
% 27.66/17.90 inference(rewrite,[status(thm)],[])).
% 27.66/17.90 tff(3956,plain,
% 27.66/17.90 (((~(f10(c1) = c1)) | (~(f7(c2) = c2)) | (f6(c2, f4(c4)) = f4(c4)) | big_f(f7(c2), f6(c2, f4(c4))) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1)))) <=> ((~(f7(c2) = c2)) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | big_f(f7(c2), f6(c2, f4(c4))) | (f6(c2, f4(c4)) = f4(c4)))),
% 27.66/17.90 inference(rewrite,[status(thm)],[])).
% 27.66/17.90 tff(3957,plain,
% 27.66/17.90 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c1) = c1)) | (~(f7(c2) = c2)) | (f6(c2, f4(c4)) = f4(c4)) | big_f(f7(c2), f6(c2, f4(c4))) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f7(c2) = c2)) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | big_f(f7(c2), f6(c2, f4(c4))) | (f6(c2, f4(c4)) = f4(c4))))),
% 27.66/17.90 inference(monotonicity,[status(thm)],[3956])).
% 27.66/17.90 tff(3958,plain,
% 27.66/17.90 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c1) = c1)) | (~(f7(c2) = c2)) | (f6(c2, f4(c4)) = f4(c4)) | big_f(f7(c2), f6(c2, f4(c4))) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f7(c2) = c2)) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | big_f(f7(c2), f6(c2, f4(c4))) | (f6(c2, f4(c4)) = f4(c4)))),
% 27.66/17.90 inference(transitivity,[status(thm)],[3957, 3955])).
% 27.66/17.90 tff(3959,plain,
% 27.66/17.90 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c1) = c1)) | (~(f7(c2) = c2)) | (f6(c2, f4(c4)) = f4(c4)) | big_f(f7(c2), f6(c2, f4(c4))) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))),
% 27.66/17.90 inference(quant_inst,[status(thm)],[])).
% 27.66/17.90 tff(3960,plain,
% 27.66/17.90 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f7(c2) = c2)) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | big_f(f7(c2), f6(c2, f4(c4))) | (f6(c2, f4(c4)) = f4(c4))),
% 27.66/17.90 inference(modus_ponens,[status(thm)],[3959, 3958])).
% 27.66/17.90 tff(3961,plain,
% 27.66/17.90 ((~(f7(c2) = c2)) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | big_f(f7(c2), f6(c2, f4(c4))) | (f6(c2, f4(c4)) = f4(c4))),
% 27.66/17.90 inference(unit_resolution,[status(thm)],[3960, 2409])).
% 27.66/17.90 tff(3962,plain,
% 27.66/17.90 (big_f(f7(c2), f6(c2, f4(c4)))),
% 27.66/17.91 inference(unit_resolution,[status(thm)],[3961, 3954, 77, 3762, 3949, 3948])).
% 27.66/17.91 tff(3963,plain,
% 27.66/17.91 (big_f(f7(c2), f6(c2, c2))),
% 27.66/17.91 inference(modus_ponens,[status(thm)],[3962, 3947])).
% 27.66/17.91 tff(3964,plain,
% 27.66/17.91 ($false),
% 27.66/17.91 inference(unit_resolution,[status(thm)],[2621, 3963])).
% 27.66/17.91 tff(3965,plain,(big_f(f7(c2), f6(c2, c2)) | (~(f4(c4) = c2)) | (~(f7(c2) = c2)) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~big_f(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 27.66/17.91 tff(3966,plain,
% 27.66/17.91 (big_f(f7(c2), f6(c2, c2))),
% 27.66/17.91 inference(unit_resolution,[status(thm)],[3965, 3940, 77, 3762, 79, 3945, 1345])).
% 27.66/17.91 tff(3967,plain,
% 27.66/17.91 (big_f(f7(f9(c2, c2)), f6(c2, c2))),
% 27.66/17.91 inference(modus_ponens,[status(thm)],[3966, 3930])).
% 27.66/17.91 tff(3968,plain,
% 27.66/17.91 (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)),
% 27.66/17.91 inference(transitivity,[status(thm)],[3648, 3940, 149, 132])).
% 27.66/17.91 tff(3969,plain,
% 27.66/17.91 (big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 27.66/17.91 inference(monotonicity,[status(thm)],[3968, 3770])).
% 27.66/17.91 tff(3970,plain,
% 27.66/17.91 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))),
% 27.66/17.91 inference(symmetry,[status(thm)],[3969])).
% 27.66/17.91 tff(3971,plain,
% 27.66/17.91 (big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))),
% 27.66/17.91 inference(modus_ponens,[status(thm)],[487, 3970])).
% 27.66/17.91 tff(3972,plain,
% 27.66/17.91 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((f7(f9(c2, c2)) = f9(c2, c2)) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (f6(c2, c2) = f5(f9(c2, c2))) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))) | (~big_f(f7(f9(c2, c2)), f6(c2, c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (f6(c2, c2) = f5(f9(c2, c2))) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))) | (~big_f(f7(f9(c2, c2)), f6(c2, c2))))),
% 27.66/17.91 inference(rewrite,[status(thm)],[])).
% 27.66/17.91 tff(3973,plain,
% 27.66/17.91 (((~(f10(f9(c2, c2)) = f9(c2, c2))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (f6(c2, c2) = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f6(c2, c2))) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))))) <=> ((f7(f9(c2, c2)) = f9(c2, c2)) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (f6(c2, c2) = f5(f9(c2, c2))) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))) | (~big_f(f7(f9(c2, c2)), f6(c2, c2))))),
% 27.66/17.91 inference(rewrite,[status(thm)],[])).
% 27.66/17.91 tff(3974,plain,
% 27.66/17.91 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (f6(c2, c2) = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f6(c2, c2))) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((f7(f9(c2, c2)) = f9(c2, c2)) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (f6(c2, c2) = f5(f9(c2, c2))) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))) | (~big_f(f7(f9(c2, c2)), f6(c2, c2)))))),
% 27.66/17.91 inference(monotonicity,[status(thm)],[3973])).
% 27.66/17.91 tff(3975,plain,
% 27.66/17.91 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (f6(c2, c2) = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f6(c2, c2))) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (f6(c2, c2) = f5(f9(c2, c2))) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))) | (~big_f(f7(f9(c2, c2)), f6(c2, c2))))),
% 27.66/17.91 inference(transitivity,[status(thm)],[3974, 3972])).
% 27.66/17.91 tff(3976,plain,
% 27.66/17.91 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (f6(c2, c2) = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f6(c2, c2))) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))))),
% 27.66/17.91 inference(quant_inst,[status(thm)],[])).
% 27.66/17.91 tff(3977,plain,
% 27.66/17.91 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (f6(c2, c2) = f5(f9(c2, c2))) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))) | (~big_f(f7(f9(c2, c2)), f6(c2, c2)))),
% 27.66/17.91 inference(modus_ponens,[status(thm)],[3976, 3975])).
% 27.66/17.91 tff(3978,plain,
% 27.66/17.91 ((f6(c2, c2) = f5(f9(c2, c2))) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))) | (~big_f(f7(f9(c2, c2)), f6(c2, c2)))),
% 27.66/17.91 inference(unit_resolution,[status(thm)],[3977, 1190, 3777, 3774])).
% 27.66/17.91 tff(3979,plain,
% 27.66/17.91 (f6(c2, c2) = f5(f9(c2, c2))),
% 27.66/17.91 inference(unit_resolution,[status(thm)],[3978, 3968, 3971, 3967])).
% 27.66/17.91 tff(3980,plain,
% 27.66/17.91 (f6(f7(c2), c3) = c4),
% 27.66/17.91 inference(modus_ponens,[status(thm)],[3979, 3927])).
% 27.66/17.91 tff(3981,plain,
% 27.66/17.91 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))))),
% 27.66/17.91 inference(rewrite,[status(thm)],[])).
% 27.66/17.91 tff(3982,plain,
% 27.66/17.91 (((~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f7(c2) = c2)) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2)))) <=> ((~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))))),
% 27.66/17.91 inference(rewrite,[status(thm)],[])).
% 27.66/17.91 tff(3983,plain,
% 27.66/17.91 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f7(c2) = c2)) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))))))),
% 27.66/17.91 inference(monotonicity,[status(thm)],[3982])).
% 27.66/17.91 tff(3984,plain,
% 27.66/17.91 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f7(c2) = c2)) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))))),
% 27.66/17.91 inference(transitivity,[status(thm)],[3983, 3981])).
% 27.66/17.91 tff(3985,plain,
% 27.66/17.91 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f7(c2) = c2)) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))),
% 27.66/17.91 inference(quant_inst,[status(thm)],[])).
% 27.66/17.91 tff(3986,plain,
% 27.66/17.91 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))))),
% 27.66/17.91 inference(modus_ponens,[status(thm)],[3985, 3984])).
% 27.66/17.91 tff(3987,plain,
% 27.66/17.91 ((~(f6(c2, c2) = c2)) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))))),
% 27.66/17.91 inference(unit_resolution,[status(thm)],[3986, 2378, 77, 3966, 3777])).
% 27.66/17.91 tff(3988,plain,
% 27.66/17.91 (~(f6(c2, c2) = c2)),
% 27.66/17.91 inference(unit_resolution,[status(thm)],[3987, 3968, 3971])).
% 27.66/17.91 tff(3989,plain,
% 27.66/17.91 (~(f6(f7(c2), c3) = c2)),
% 27.66/17.91 inference(unit_resolution,[status(thm)],[2716, 3988, 67, 77])).
% 27.66/17.91 tff(3990,plain,
% 27.66/17.91 ((f6(f7(c2), c3) = c4) <=> (f6(f7(c2), c3) = c2)),
% 27.66/17.91 inference(monotonicity,[status(thm)],[431])).
% 27.66/17.91 tff(3991,assumption,(f6(f7(c2), c3) = c4), introduced(assumption)).
% 27.66/17.91 tff(3992,plain,
% 27.66/17.91 (f6(f7(c2), c3) = c2),
% 27.66/17.91 inference(modus_ponens,[status(thm)],[3991, 3990])).
% 27.66/17.91 tff(3993,assumption,(~(f6(f7(c2), c3) = c2)), introduced(assumption)).
% 27.66/17.91 tff(3994,plain,
% 27.66/17.91 ($false),
% 27.66/17.91 inference(unit_resolution,[status(thm)],[3993, 3992])).
% 27.66/17.91 tff(3995,plain,((~(f6(f7(c2), c3) = c4)) | (f6(f7(c2), c3) = c2) | (~(c4 = c2))), inference(lemma,lemma(discharge,[]))).
% 27.66/17.91 tff(3996,plain,
% 27.66/17.91 (~(f6(f7(c2), c3) = c4)),
% 27.66/17.91 inference(unit_resolution,[status(thm)],[3995, 3989, 431])).
% 27.66/17.91 tff(3997,plain,
% 27.66/17.91 ($false),
% 27.66/17.91 inference(unit_resolution,[status(thm)],[3996, 3980])).
% 27.66/17.91 tff(3998,plain,((~(c4 = c2)) | (~(f5(c1) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(c3 = c2)) | (~(f7(c2) = c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f10(c1) = c1)) | (~(f7(c1) = c2)) | (~big_f(c2, c2)) | (f9(c1, c1) = c4)), inference(lemma,lemma(discharge,[]))).
% 27.66/17.91 tff(3999,plain,
% 27.66/17.91 (~(c4 = c2)),
% 27.66/17.91 inference(unit_resolution,[status(thm)],[3998, 3923, 148, 79, 122, 67, 77, 3774, 487, 3762, 347, 1345, 186])).
% 27.66/17.91 tff(4000,plain,
% 27.66/17.91 (c4 = c1),
% 27.66/17.91 inference(unit_resolution,[status(thm)],[461, 3999])).
% 27.66/17.91 tff(4001,plain,
% 27.66/17.91 ((f9(c1, c1) = c4) <=> (f9(c1, c1) = c1)),
% 27.66/17.91 inference(monotonicity,[status(thm)],[4000])).
% 27.66/17.91 tff(4002,plain,
% 27.66/17.91 ((~(f9(c1, c1) = c4)) <=> (~(f9(c1, c1) = c1))),
% 27.66/17.91 inference(monotonicity,[status(thm)],[4001])).
% 27.66/17.91 tff(4003,plain,
% 27.66/17.91 (~(f9(c1, c1) = c1)),
% 27.66/17.91 inference(modus_ponens,[status(thm)],[3923, 4002])).
% 27.66/17.91 tff(4004,plain,
% 27.66/17.91 (f9(c1, c1) = c2),
% 27.66/17.91 inference(unit_resolution,[status(thm)],[3939, 4003])).
% 27.66/17.91 tff(4005,plain,
% 27.66/17.91 (f9(f9(c2, c2), f9(c2, c2)) = c2),
% 27.66/17.91 inference(transitivity,[status(thm)],[3648, 4004])).
% 27.66/17.91 tff(4006,plain,
% 27.66/17.91 (big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))) <=> big_f(c2, f9(c2, c2))),
% 27.66/17.91 inference(monotonicity,[status(thm)],[4005, 3770])).
% 27.66/17.91 tff(4007,plain,
% 27.66/17.91 (big_f(c2, f9(c2, c2)) <=> big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))),
% 27.66/17.91 inference(symmetry,[status(thm)],[4006])).
% 27.66/17.91 tff(4008,plain,
% 27.66/17.91 ((~big_f(c2, f9(c2, c2))) <=> (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))))),
% 27.66/17.91 inference(monotonicity,[status(thm)],[4007])).
% 27.66/17.91 tff(4009,plain,
% 27.66/17.91 (f4(f9(c2, c2)) = c2),
% 27.66/17.91 inference(transitivity,[status(thm)],[3713, 79])).
% 27.66/17.91 tff(4010,plain,
% 27.66/17.91 ((f9(c2, c2) = f4(f9(c2, c2))) <=> (f9(c2, c2) = c2)),
% 27.66/17.91 inference(monotonicity,[status(thm)],[4009])).
% 27.66/17.91 tff(4011,plain,
% 27.66/17.91 ((f9(c2, c2) = c2) <=> (f9(c2, c2) = f4(f9(c2, c2)))),
% 27.66/17.91 inference(symmetry,[status(thm)],[4010])).
% 27.66/17.91 tff(4012,plain,
% 27.66/17.91 ((~(f9(c2, c2) = c2)) <=> (~(f9(c2, c2) = f4(f9(c2, c2))))),
% 27.66/17.91 inference(monotonicity,[status(thm)],[4011])).
% 27.66/17.91 tff(4013,plain,
% 27.66/17.91 (~(f9(c2, c2) = f4(f9(c2, c2)))),
% 27.66/17.91 inference(modus_ponens,[status(thm)],[185, 4012])).
% 27.66/17.91 tff(4014,plain,
% 27.66/17.91 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)))),
% 27.66/17.91 inference(rewrite,[status(thm)],[])).
% 27.66/17.91 tff(4015,plain,
% 27.66/17.91 (((~(c2 = c3)) | (~(f9(c2, c2) = c4)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (c2 = f2(c2)) | (~big_f(c2, c2))) <=> ((~(c2 = c3)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)))),
% 27.66/17.91 inference(rewrite,[status(thm)],[])).
% 27.66/17.91 tff(4016,plain,
% 27.66/17.91 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(f9(c2, c2) = c4)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (c2 = f2(c2)) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4))))),
% 27.66/17.91 inference(monotonicity,[status(thm)],[4015])).
% 27.66/17.91 tff(4017,plain,
% 27.66/17.91 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(f9(c2, c2) = c4)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (c2 = f2(c2)) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)))),
% 27.66/17.91 inference(transitivity,[status(thm)],[4016, 4014])).
% 27.66/17.91 tff(4018,plain,
% 27.66/17.91 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(f9(c2, c2) = c4)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (c2 = f2(c2)) | (~big_f(c2, c2)))),
% 27.66/17.91 inference(quant_inst,[status(thm)],[])).
% 27.66/17.91 tff(4019,plain,
% 27.66/17.91 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4))),
% 27.66/17.91 inference(modus_ponens,[status(thm)],[4018, 4017])).
% 27.66/17.91 tff(4020,plain,
% 27.66/17.91 ((c2 = f2(c2)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~(f9(c2, c2) = c4))),
% 27.66/17.91 inference(unit_resolution,[status(thm)],[4019, 1355, 1345, 1344, 487])).
% 27.66/17.91 tff(4021,plain,
% 27.66/17.91 (c2 = f2(c2)),
% 27.66/17.91 inference(unit_resolution,[status(thm)],[4020, 4013, 3725])).
% 27.66/17.91 tff(4022,plain,
% 27.66/17.91 (f2(c2) = c2),
% 27.66/17.91 inference(symmetry,[status(thm)],[4021])).
% 27.66/17.91 tff(4023,plain,
% 27.66/17.91 ((f9(c2, c2) = f2(c2)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~(f9(c2, c2) = c4))),
% 27.66/17.91 inference(unit_resolution,[status(thm)],[1599, 1355, 1344, 487, 3719])).
% 27.66/17.91 tff(4024,plain,
% 27.66/17.91 (f9(c2, c2) = f2(c2)),
% 27.66/17.91 inference(unit_resolution,[status(thm)],[4023, 4013, 3725])).
% 27.66/17.91 tff(4025,plain,
% 27.66/17.91 (f9(c2, c2) = c2),
% 27.66/17.91 inference(transitivity,[status(thm)],[4024, 4022])).
% 27.66/17.91 tff(4026,plain,
% 27.66/17.91 ($false),
% 27.66/17.91 inference(unit_resolution,[status(thm)],[185, 4025])).
% 27.66/17.91 tff(4027,plain,((~(c4 = c1)) | (~(c2 = c3)) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~big_f(c2, f9(c2, c2))) | (~big_f(c2, c2)) | (~(f4(c4) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.66/17.91 tff(4028,plain,
% 27.66/17.91 (~big_f(c2, f9(c2, c2))),
% 27.66/17.91 inference(unit_resolution,[status(thm)],[4027, 4000, 1335, 1345, 487, 79, 148, 122])).
% 27.66/17.91 tff(4029,plain,
% 27.66/17.91 (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))),
% 27.66/17.91 inference(modus_ponens,[status(thm)],[4028, 4008])).
% 27.66/17.91 tff(4030,plain,
% 27.66/17.91 ((f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) <=> (c2 = f9(c2, c2))),
% 27.66/17.91 inference(monotonicity,[status(thm)],[4005])).
% 27.66/17.91 tff(4031,plain,
% 27.66/17.91 ((f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) <=> (f9(c2, c2) = c2)),
% 27.66/17.91 inference(transitivity,[status(thm)],[4030, 167])).
% 27.66/17.91 tff(4032,plain,
% 27.66/17.91 ((f9(c2, c2) = c2) <=> (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))),
% 27.66/17.91 inference(symmetry,[status(thm)],[4031])).
% 27.66/17.91 tff(4033,plain,
% 27.66/17.91 ((~(f9(c2, c2) = c2)) <=> (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)))),
% 27.66/17.91 inference(monotonicity,[status(thm)],[4032])).
% 27.66/17.91 tff(4034,plain,
% 27.66/17.91 (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))),
% 27.66/17.91 inference(modus_ponens,[status(thm)],[185, 4033])).
% 27.66/17.91 tff(4035,assumption,(~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))), introduced(assumption)).
% 27.66/17.91 tff(4036,assumption,(~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))), introduced(assumption)).
% 27.66/17.91 tff(4037,plain,
% 27.66/17.91 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))))),
% 27.66/17.92 inference(rewrite,[status(thm)],[])).
% 27.66/17.92 tff(4038,plain,
% 27.66/17.92 (((~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2))) <=> ((~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))))),
% 27.66/17.92 inference(rewrite,[status(thm)],[])).
% 27.66/17.92 tff(4039,plain,
% 27.66/17.92 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))))),
% 27.66/17.92 inference(monotonicity,[status(thm)],[4038])).
% 27.66/17.92 tff(4040,plain,
% 27.66/17.92 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))))),
% 27.66/17.92 inference(transitivity,[status(thm)],[4039, 4037])).
% 27.66/17.92 tff(4041,plain,
% 27.66/17.92 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)))),
% 27.66/17.92 inference(quant_inst,[status(thm)],[])).
% 27.66/17.92 tff(4042,plain,
% 27.66/17.92 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))),
% 27.66/17.92 inference(modus_ponens,[status(thm)],[4041, 4040])).
% 27.66/17.92 tff(4043,plain,
% 27.66/17.92 ($false),
% 27.66/17.92 inference(unit_resolution,[status(thm)],[4042, 2492, 77, 3953, 2621, 758, 4036, 4035])).
% 27.66/17.92 tff(4044,plain,(big_f(f7(c2), f6(c2, c2)) | (~(f7(c2) = c2)) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))) | (~big_f(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 27.66/17.92 tff(4045,plain,
% 27.66/17.92 (big_f(f7(c2), f6(c2, c2))),
% 27.66/17.92 inference(unit_resolution,[status(thm)],[4044, 4034, 3777, 77, 4029, 1345])).
% 27.66/17.92 tff(4046,plain,
% 27.66/17.92 ((f6(c2, c2) = c2) <=> (f6(f7(c2), f5(c1)) = c2)),
% 27.66/17.92 inference(symmetry,[status(thm)],[2260])).
% 27.66/17.92 tff(4047,plain,
% 27.66/17.92 ((~(f6(c2, c2) = c2)) <=> (~(f6(f7(c2), f5(c1)) = c2))),
% 27.66/17.92 inference(monotonicity,[status(thm)],[4046])).
% 27.66/17.92 tff(4048,plain,
% 27.66/17.92 (~(f6(f7(c2), f5(c1)) = c2)),
% 27.66/17.92 inference(modus_ponens,[status(thm)],[2637, 4047])).
% 27.66/17.92 tff(4049,plain,
% 27.66/17.92 (f6(f7(c2), f5(c1)) = c1),
% 27.66/17.92 inference(unit_resolution,[status(thm)],[2978, 4048])).
% 27.66/17.92 tff(4050,plain,
% 27.66/17.92 (f6(c2, c2) = f9(c2, c2)),
% 27.66/17.92 inference(transitivity,[status(thm)],[2258, 4049, 149, 132])).
% 27.66/17.92 tff(4051,plain,
% 27.66/17.92 (big_f(f7(c2), f6(c2, c2)) <=> big_f(c2, f9(c2, c2))),
% 27.66/17.92 inference(monotonicity,[status(thm)],[77, 4050])).
% 27.66/17.92 tff(4052,plain,
% 27.66/17.92 (big_f(c2, f9(c2, c2)) <=> big_f(f7(c2), f6(c2, c2))),
% 27.66/17.92 inference(symmetry,[status(thm)],[4051])).
% 27.66/17.92 tff(4053,plain,
% 27.66/17.92 ((~big_f(c2, f9(c2, c2))) <=> (~big_f(f7(c2), f6(c2, c2)))),
% 27.66/17.92 inference(monotonicity,[status(thm)],[4052])).
% 27.66/17.92 tff(4054,plain,
% 27.66/17.92 (~big_f(f7(c2), f6(c2, c2))),
% 27.66/17.92 inference(modus_ponens,[status(thm)],[2040, 4053])).
% 27.66/17.92 tff(4055,plain,
% 27.66/17.92 ($false),
% 27.66/17.92 inference(unit_resolution,[status(thm)],[2707, 4054])).
% 27.66/17.92 tff(4056,plain,((~(f5(c1) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | big_f(c2, f9(c2, c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 27.66/17.92 tff(4057,plain,
% 27.66/17.92 (f6(c2, c2) = c2),
% 27.66/17.92 inference(unit_resolution,[status(thm)],[4056, 4045, 148, 186, 79, 122, 77, 4028])).
% 27.66/17.92 tff(4058,plain,
% 27.66/17.92 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))))),
% 27.66/17.92 inference(rewrite,[status(thm)],[])).
% 27.66/17.92 tff(4059,plain,
% 27.66/17.92 (((~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2)))) <=> ((~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))))),
% 27.66/17.92 inference(rewrite,[status(thm)],[])).
% 27.66/17.92 tff(4060,plain,
% 27.66/17.92 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))))),
% 27.66/17.92 inference(monotonicity,[status(thm)],[4059])).
% 27.66/17.92 tff(4061,plain,
% 27.66/17.92 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))))),
% 27.66/17.92 inference(transitivity,[status(thm)],[4060, 4058])).
% 27.66/17.92 tff(4062,plain,
% 27.66/17.92 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))),
% 27.66/17.92 inference(quant_inst,[status(thm)],[])).
% 27.66/17.92 tff(4063,plain,
% 27.66/17.92 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))),
% 27.66/17.92 inference(modus_ponens,[status(thm)],[4062, 4061])).
% 27.66/17.92 tff(4064,plain,
% 27.66/17.92 ($false),
% 27.66/17.92 inference(unit_resolution,[status(thm)],[4063, 2534, 77, 4057, 4045, 3777, 4034, 4029])).
% 27.66/17.92 tff(4065,plain,((f9(c1, c1) = c4) | (~(f7(c2) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f5(c1) = c2)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~big_f(c2, c2)) | (~(f10(c1) = c1)) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(c3 = c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~(f7(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.66/17.92 tff(4066,plain,
% 27.66/17.92 (f9(c1, c1) = c4),
% 27.66/17.92 inference(unit_resolution,[status(thm)],[4065, 186, 148, 77, 79, 122, 3922, 3637, 3817, 181, 3654, 120])).
% 27.66/17.92 tff(4067,plain,
% 27.66/17.92 (c2 = c3),
% 27.66/17.92 inference(modus_ponens,[status(thm)],[181, 78])).
% 27.66/17.92 tff(4068,assumption,(f9(c1, c1) = c4), introduced(assumption)).
% 27.66/17.92 tff(4069,plain,
% 27.66/17.92 (f4(f9(c1, c1)) = f4(c4)),
% 27.66/17.92 inference(monotonicity,[status(thm)],[4068])).
% 27.66/17.92 tff(4070,assumption,(~(f9(c1, c1) = c1)), introduced(assumption)).
% 27.66/17.92 tff(4071,plain,
% 27.66/17.92 (f9(c1, c1) = c2),
% 27.66/17.92 inference(unit_resolution,[status(thm)],[3939, 4070])).
% 27.66/17.92 tff(4072,plain,
% 27.66/17.92 (c2 = f9(c1, c1)),
% 27.66/17.92 inference(symmetry,[status(thm)],[4071])).
% 27.66/17.92 tff(4073,plain,
% 27.66/17.92 (f4(c2) = f4(f9(c1, c1))),
% 27.66/17.92 inference(monotonicity,[status(thm)],[4072])).
% 27.66/17.92 tff(4074,plain,
% 27.66/17.92 (f4(c2) = c2),
% 27.66/17.92 inference(transitivity,[status(thm)],[4073, 4069, 79])).
% 27.66/17.92 tff(4075,plain,
% 27.66/17.92 ((f9(c2, c2) = f4(c2)) <=> (f9(c2, c2) = c2)),
% 27.66/17.92 inference(monotonicity,[status(thm)],[4074])).
% 27.66/17.92 tff(4076,plain,
% 27.66/17.92 ((f9(c2, c2) = c2) <=> (f9(c2, c2) = f4(c2))),
% 27.66/17.92 inference(symmetry,[status(thm)],[4075])).
% 27.66/17.92 tff(4077,plain,
% 27.66/17.92 ((~(f9(c2, c2) = c2)) <=> (~(f9(c2, c2) = f4(c2)))),
% 27.66/17.92 inference(monotonicity,[status(thm)],[4076])).
% 27.66/17.92 tff(4078,plain,
% 27.66/17.92 (~(f9(c2, c2) = f4(c2))),
% 27.66/17.92 inference(modus_ponens,[status(thm)],[185, 4077])).
% 27.66/17.92 tff(4079,plain,
% 27.66/17.92 ((f9(c1, c1) = c2) <=> (c4 = c2)),
% 27.66/17.92 inference(monotonicity,[status(thm)],[4068])).
% 27.66/17.92 tff(4080,plain,
% 27.66/17.92 ((f9(c1, c1) = c2) <=> (c2 = c4)),
% 27.66/17.92 inference(transitivity,[status(thm)],[4079, 159])).
% 27.66/17.92 tff(4081,plain,
% 27.66/17.92 (c2 = c4),
% 27.66/17.92 inference(modus_ponens,[status(thm)],[4071, 4080])).
% 27.66/17.92 tff(4082,plain,
% 27.66/17.92 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c2 = c4)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f4(c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (~(c2 = c4)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f4(c2)))),
% 27.66/17.92 inference(rewrite,[status(thm)],[])).
% 27.66/17.92 tff(4083,plain,
% 27.66/17.92 (((~(c2 = c3)) | (~(c2 = c4)) | (f9(c2, c2) = f4(c2)) | (~big_f(f9(c2, c2), c2)) | (c2 = f2(c2)) | (~big_f(c2, c2))) <=> ((~(c2 = c3)) | (~(c2 = c4)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f4(c2)))),
% 27.66/17.92 inference(rewrite,[status(thm)],[])).
% 27.66/17.92 tff(4084,plain,
% 27.66/17.92 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c2 = c4)) | (f9(c2, c2) = f4(c2)) | (~big_f(f9(c2, c2), c2)) | (c2 = f2(c2)) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c2 = c4)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f4(c2))))),
% 27.66/17.92 inference(monotonicity,[status(thm)],[4083])).
% 27.66/17.92 tff(4085,plain,
% 27.66/17.92 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c2 = c4)) | (f9(c2, c2) = f4(c2)) | (~big_f(f9(c2, c2), c2)) | (c2 = f2(c2)) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (~(c2 = c4)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f4(c2)))),
% 27.66/17.92 inference(transitivity,[status(thm)],[4084, 4082])).
% 27.66/17.92 tff(4086,plain,
% 27.66/17.92 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c2 = c4)) | (f9(c2, c2) = f4(c2)) | (~big_f(f9(c2, c2), c2)) | (c2 = f2(c2)) | (~big_f(c2, c2)))),
% 27.66/17.92 inference(quant_inst,[status(thm)],[])).
% 27.66/17.92 tff(4087,plain,
% 27.66/17.92 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (~(c2 = c4)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f4(c2))),
% 27.66/17.92 inference(modus_ponens,[status(thm)],[4086, 4085])).
% 27.66/17.92 tff(4088,plain,
% 27.66/17.92 ((~(c2 = c4)) | (c2 = f2(c2)) | (f9(c2, c2) = f4(c2))),
% 27.66/17.92 inference(unit_resolution,[status(thm)],[4087, 1355, 1345, 1344, 2041])).
% 27.66/17.92 tff(4089,plain,
% 27.66/17.92 (c2 = f2(c2)),
% 27.66/17.92 inference(unit_resolution,[status(thm)],[4088, 4081, 4078])).
% 27.66/17.92 tff(4090,plain,
% 27.66/17.92 (f2(c2) = c2),
% 27.66/17.92 inference(symmetry,[status(thm)],[4089])).
% 27.66/17.92 tff(4091,plain,
% 27.66/17.92 ((f9(c2, c2) = f2(c2)) <=> (f9(c2, c2) = c2)),
% 27.66/17.92 inference(monotonicity,[status(thm)],[4090])).
% 27.66/17.92 tff(4092,plain,
% 27.66/17.92 ((f9(c2, c2) = c2) <=> (f9(c2, c2) = f2(c2))),
% 27.66/17.92 inference(symmetry,[status(thm)],[4091])).
% 27.66/17.92 tff(4093,plain,
% 27.66/17.92 ((~(f9(c2, c2) = c2)) <=> (~(f9(c2, c2) = f2(c2)))),
% 27.66/17.92 inference(monotonicity,[status(thm)],[4092])).
% 27.66/17.92 tff(4094,plain,
% 27.66/17.92 (~(f9(c2, c2) = f2(c2))),
% 27.66/17.92 inference(modus_ponens,[status(thm)],[185, 4093])).
% 27.66/17.92 tff(4095,plain,
% 27.66/17.92 ((f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) <=> (f9(c1, c1) = c1)),
% 27.66/17.92 inference(monotonicity,[status(thm)],[3648, 161])).
% 27.66/17.92 tff(4096,plain,
% 27.66/17.92 ((f9(c1, c1) = c1) <=> (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))),
% 27.66/17.92 inference(symmetry,[status(thm)],[4095])).
% 27.66/17.92 tff(4097,plain,
% 27.66/17.92 ((~(f9(c1, c1) = c1)) <=> (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)))),
% 27.66/17.92 inference(monotonicity,[status(thm)],[4096])).
% 27.66/17.92 tff(4098,plain,
% 27.66/17.92 (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))),
% 27.66/17.92 inference(modus_ponens,[status(thm)],[4070, 4097])).
% 27.74/17.92 tff(4099,plain,
% 27.74/17.92 (f10(f9(c2, c2)) = c1),
% 27.74/17.92 inference(transitivity,[status(thm)],[3646, 3762])).
% 27.74/17.92 tff(4100,plain,
% 27.74/17.92 (big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))) <=> big_f(f9(c1, c1), c1)),
% 27.74/17.92 inference(monotonicity,[status(thm)],[3648, 4099])).
% 27.74/17.92 tff(4101,plain,
% 27.74/17.92 (big_f(f9(c1, c1), c1) <=> big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))),
% 27.74/17.92 inference(symmetry,[status(thm)],[4100])).
% 27.74/17.92 tff(4102,assumption,(f9(c1, c1) = c2), introduced(assumption)).
% 27.74/17.92 tff(4103,plain,
% 27.74/17.92 (big_f(f9(c1, c1), c1) <=> big_f(c2, f9(c2, c2))),
% 27.74/17.92 inference(monotonicity,[status(thm)],[4102, 150])).
% 27.74/17.92 tff(4104,plain,
% 27.74/17.92 (big_f(c2, f9(c2, c2)) <=> big_f(f9(c1, c1), c1)),
% 27.74/17.92 inference(symmetry,[status(thm)],[4103])).
% 27.74/17.92 tff(4105,plain,
% 27.74/17.92 (big_f(c2, c1) <=> big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))),
% 27.74/17.92 inference(transitivity,[status(thm)],[3716, 4104, 4101])).
% 27.74/17.92 tff(4106,plain,
% 27.74/17.92 ((~big_f(c2, c1)) <=> (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))))),
% 27.74/17.92 inference(monotonicity,[status(thm)],[4105])).
% 27.74/17.92 tff(4107,plain,
% 27.74/17.92 (~big_f(c2, c1)),
% 27.74/17.92 inference(unit_resolution,[status(thm)],[3814, 2040, 148, 79, 122])).
% 27.74/17.92 tff(4108,plain,
% 27.74/17.92 (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))),
% 27.74/17.92 inference(modus_ponens,[status(thm)],[4107, 4106])).
% 27.74/17.92 tff(4109,plain,
% 27.74/17.92 (big_f(f7(c2), f6(c2, c2))),
% 27.74/17.92 inference(unit_resolution,[status(thm)],[4044, 4108, 3777, 4036, 77, 1345])).
% 27.74/17.92 tff(4110,plain,
% 27.74/17.92 (f6(c2, c2) = c2),
% 27.74/17.92 inference(unit_resolution,[status(thm)],[4056, 4109, 148, 186, 79, 122, 77, 2040])).
% 27.74/17.92 tff(4111,plain,
% 27.74/17.92 ($false),
% 27.74/17.92 inference(unit_resolution,[status(thm)],[4063, 2534, 77, 4110, 4109, 3777, 4036, 4108])).
% 27.74/17.92 tff(4112,plain,(big_f(c2, f9(c2, c2)) | (~(f7(c2) = c2)) | (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f5(c1) = c2)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~big_f(c2, c2)) | (~(f9(c1, c1) = c2)) | (~(f10(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 27.74/17.92 tff(4113,plain,
% 27.74/17.92 (big_f(c2, f9(c2, c2))),
% 27.74/17.92 inference(unit_resolution,[status(thm)],[4112, 4098, 77, 148, 186, 79, 122, 1345, 4071, 3762])).
% 27.74/17.92 tff(4114,plain,
% 27.74/17.92 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c2 = c4)) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f4(c2)) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (~(c2 = c4)) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f4(c2)) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2))))),
% 27.74/17.92 inference(rewrite,[status(thm)],[])).
% 27.74/17.92 tff(4115,plain,
% 27.74/17.92 (((~(c2 = c3)) | (~(c2 = c4)) | (f9(c2, c2) = f4(c2)) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2)))) <=> ((~(c2 = c3)) | (~(c2 = c4)) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f4(c2)) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2))))),
% 27.74/17.92 inference(rewrite,[status(thm)],[])).
% 27.74/17.92 tff(4116,plain,
% 27.74/17.92 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c2 = c4)) | (f9(c2, c2) = f4(c2)) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c2 = c4)) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f4(c2)) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2)))))),
% 27.74/17.92 inference(monotonicity,[status(thm)],[4115])).
% 27.74/17.92 tff(4117,plain,
% 27.74/17.92 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c2 = c4)) | (f9(c2, c2) = f4(c2)) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (~(c2 = c4)) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f4(c2)) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2))))),
% 27.74/17.92 inference(transitivity,[status(thm)],[4116, 4114])).
% 27.74/17.92 tff(4118,plain,
% 27.74/17.92 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c2 = c4)) | (f9(c2, c2) = f4(c2)) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2))))),
% 27.74/17.92 inference(quant_inst,[status(thm)],[])).
% 27.74/17.92 tff(4119,plain,
% 27.74/17.92 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (~(c2 = c4)) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f4(c2)) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2)))),
% 27.74/17.92 inference(modus_ponens,[status(thm)],[4118, 4117])).
% 27.74/17.92 tff(4120,plain,
% 27.74/17.92 ($false),
% 27.74/17.92 inference(unit_resolution,[status(thm)],[4119, 1355, 4081, 1344, 4113, 4094, 2041, 4078])).
% 27.74/17.93 tff(4121,plain,((f9(c1, c1) = c1) | (~(c2 = c3)) | (~big_f(f9(c2, c2), c2)) | (~(f7(c2) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f5(c1) = c2)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~big_f(c2, c2)) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c4))), inference(lemma,lemma(discharge,[]))).
% 27.74/17.93 tff(4122,plain,
% 27.74/17.93 (f9(c1, c1) = c1),
% 27.74/17.93 inference(unit_resolution,[status(thm)],[4121, 3688, 4067, 77, 148, 186, 79, 122, 3922, 3637, 4066])).
% 27.74/17.93 tff(4123,plain,
% 27.74/17.93 (f9(c1, c1) = f9(c2, c2)),
% 27.74/17.93 inference(transitivity,[status(thm)],[4122, 149, 132])).
% 27.74/17.93 tff(4124,plain,
% 27.74/17.93 (big_f(f9(c1, c1), c1) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 27.74/17.93 inference(monotonicity,[status(thm)],[4123, 150])).
% 27.74/17.93 tff(4125,plain,
% 27.74/17.93 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f9(c1, c1), c1)),
% 27.74/17.93 inference(symmetry,[status(thm)],[4124])).
% 27.74/17.93 tff(4126,plain,
% 27.74/17.93 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))),
% 27.74/17.93 inference(transitivity,[status(thm)],[4125, 3650])).
% 27.74/17.93 tff(4127,plain,
% 27.74/17.93 (big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))),
% 27.74/17.93 inference(modus_ponens,[status(thm)],[3817, 4126])).
% 27.74/17.93 tff(4128,plain,
% 27.74/17.93 (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)),
% 27.74/17.93 inference(modus_ponens,[status(thm)],[4122, 4096])).
% 27.74/17.93 tff(4129,plain,
% 27.74/17.93 (f10(f9(c2, c2)) = f9(c2, c2)),
% 27.74/17.93 inference(modus_ponens,[status(thm)],[3637, 3776])).
% 27.74/17.93 tff(4130,plain,
% 27.74/17.93 (big_f(f9(c1, c1), f10(c1)) <=> big_f(f9(c1, c1), c1)),
% 27.74/17.93 inference(monotonicity,[status(thm)],[3637])).
% 27.74/17.93 tff(4131,plain,
% 27.74/17.93 (big_f(f9(c1, c1), c1) <=> big_f(f9(c1, c1), f10(c1))),
% 27.74/17.93 inference(symmetry,[status(thm)],[4130])).
% 27.74/17.93 tff(4132,plain,
% 27.74/17.93 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f9(c1, c1), f10(c1))),
% 27.74/17.93 inference(transitivity,[status(thm)],[4125, 4131])).
% 27.74/17.93 tff(4133,plain,
% 27.74/17.93 (big_f(f9(c1, c1), f10(c1))),
% 27.74/17.93 inference(modus_ponens,[status(thm)],[3817, 4132])).
% 27.74/17.93 tff(4134,plain,
% 27.74/17.93 (big_f(f7(c2), f6(c2, c2))),
% 27.74/17.93 inference(unit_resolution,[status(thm)],[3965, 4133, 77, 3637, 79, 4122, 3922])).
% 27.74/17.93 tff(4135,plain,
% 27.74/17.93 ((c1 = c4) <=> (c4 = c1)),
% 27.74/17.93 inference(symmetry,[status(thm)],[479])).
% 27.74/17.93 tff(4136,plain,
% 27.74/17.93 ((f9(c2, c2) = c4) <=> (c1 = c4)),
% 27.74/17.93 inference(symmetry,[status(thm)],[3723])).
% 27.74/17.93 tff(4137,plain,
% 27.74/17.93 ((c4 = f9(c2, c2)) <=> (f9(c2, c2) = c4)),
% 27.74/17.93 inference(commutativity,[status(thm)],[])).
% 27.74/17.93 tff(4138,plain,
% 27.74/17.93 ((f9(c1, c1) = c1) <=> (c4 = f9(c2, c2))),
% 27.74/17.93 inference(monotonicity,[status(thm)],[4066, 150])).
% 27.74/17.93 tff(4139,plain,
% 27.74/17.93 ((f9(c1, c1) = c1) <=> (f9(c2, c2) = c4)),
% 27.74/17.93 inference(transitivity,[status(thm)],[4138, 4137])).
% 27.74/17.93 tff(4140,plain,
% 27.74/17.93 ((f9(c1, c1) = c1) <=> (c4 = c1)),
% 27.74/17.93 inference(transitivity,[status(thm)],[4139, 4136, 4135])).
% 27.74/17.93 tff(4141,plain,
% 27.74/17.93 (c4 = c1),
% 27.74/17.93 inference(modus_ponens,[status(thm)],[4122, 4140])).
% 27.74/17.93 tff(4142,plain,
% 27.74/17.93 (~big_f(c2, f9(c2, c2))),
% 27.74/17.93 inference(unit_resolution,[status(thm)],[4027, 4141, 4067, 3922, 3817, 79, 148, 122])).
% 27.74/17.93 tff(4143,plain,
% 27.74/17.93 (f6(c2, c2) = c2),
% 27.74/17.93 inference(unit_resolution,[status(thm)],[4056, 4134, 148, 186, 79, 122, 77, 4142])).
% 27.74/17.93 tff(4144,plain,
% 27.74/17.93 ($false),
% 27.74/17.93 inference(unit_resolution,[status(thm)],[3986, 2378, 77, 4143, 4134, 4129, 4128, 4127])).
% 27.74/17.93 tff(4145,plain,((~(f5(c1) = c2)) | (~(f7(c2) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (f7(c1) = c1) | (c1 = c3) | (f9(f10(c2), f10(c2)) = f10(c2))), inference(lemma,lemma(discharge,[]))).
% 27.74/17.93 tff(4146,plain,
% 27.74/17.93 (~(f5(c1) = c2)),
% 27.74/17.93 inference(unit_resolution,[status(thm)],[4145, 77, 148, 79, 122, 115, 168, 158])).
% 27.74/17.93 tff(4147,plain,
% 27.74/17.93 (f5(c1) = c1),
% 27.74/17.93 inference(unit_resolution,[status(thm)],[1708, 4146])).
% 27.74/17.93 tff(4148,plain,
% 27.74/17.93 (f7(f10(c1)) = f7(f9(c2, c2))),
% 27.74/17.93 inference(monotonicity,[status(thm)],[3763])).
% 27.74/17.93 tff(4149,plain,
% 27.74/17.93 (f7(f10(c1)) = c2),
% 27.74/17.93 inference(transitivity,[status(thm)],[4148, 243, 347])).
% 27.74/17.93 tff(4150,plain,
% 27.74/17.93 (big_f(f7(f10(c1)), c2) <=> big_f(c2, c2)),
% 27.74/17.93 inference(monotonicity,[status(thm)],[4149])).
% 27.74/17.93 tff(4151,plain,
% 27.74/17.93 (big_f(c2, c2) <=> big_f(f7(f10(c1)), c2)),
% 27.74/17.93 inference(symmetry,[status(thm)],[4150])).
% 27.74/17.93 tff(4152,plain,
% 27.74/17.93 (f5(f10(c1)) = f5(c1)),
% 27.74/17.93 inference(monotonicity,[status(thm)],[3762])).
% 27.74/17.93 tff(4153,plain,
% 27.74/17.93 (f7(f10(c1)) = f7(c1)),
% 27.74/17.93 inference(monotonicity,[status(thm)],[3762])).
% 27.74/17.93 tff(4154,plain,
% 27.74/17.93 (big_f(f7(f10(c1)), f5(f10(c1))) <=> big_f(f7(c1), f5(c1))),
% 27.74/17.93 inference(monotonicity,[status(thm)],[4153, 4152])).
% 27.74/17.93 tff(4155,plain,
% 27.74/17.93 (big_f(f7(f10(c1)), f5(f10(c1))) <=> big_f(c2, c1)),
% 27.74/17.93 inference(transitivity,[status(thm)],[4154, 2769])).
% 27.74/17.93 tff(4156,plain,
% 27.74/17.93 (f7(f10(c1)) = c2),
% 27.74/17.93 inference(transitivity,[status(thm)],[4153, 347])).
% 27.74/17.93 tff(4157,plain,
% 27.74/17.93 ((f7(f10(c1)) = f10(c1)) <=> (c2 = c1)),
% 27.74/17.93 inference(monotonicity,[status(thm)],[4156, 3762])).
% 27.74/17.93 tff(4158,plain,
% 27.74/17.93 ((c2 = c1) <=> (f7(f10(c1)) = f10(c1))),
% 27.74/17.93 inference(symmetry,[status(thm)],[4157])).
% 27.74/17.93 tff(4159,plain,
% 27.74/17.93 ((~(c2 = c1)) <=> (~(f7(f10(c1)) = f10(c1)))),
% 27.74/17.93 inference(monotonicity,[status(thm)],[4158])).
% 27.74/17.93 tff(4160,plain,
% 27.74/17.93 (~(f7(f10(c1)) = f10(c1))),
% 27.74/17.93 inference(modus_ponens,[status(thm)],[75, 4159])).
% 27.74/17.93 tff(4161,plain,
% 27.74/17.93 (big_f(f7(f10(c1)), f5(f10(c1)))),
% 27.74/17.93 inference(unit_resolution,[status(thm)],[309, 256, 122, 4160, 1209])).
% 27.74/17.93 tff(4162,plain,
% 27.74/17.93 (big_f(c2, c1)),
% 27.74/17.93 inference(modus_ponens,[status(thm)],[4161, 4155])).
% 27.74/17.93 tff(4163,plain,
% 27.74/17.93 ((~(f9(c2, c2) = c2)) <=> (~(f9(f10(c2), f4(c4)) = c2))),
% 27.74/17.93 inference(monotonicity,[status(thm)],[134])).
% 27.74/17.93 tff(4164,plain,
% 27.74/17.93 (~(f9(f10(c2), f4(c4)) = c2)),
% 27.74/17.93 inference(modus_ponens,[status(thm)],[1209, 4163])).
% 27.74/17.93 tff(4165,plain,
% 27.74/17.93 (~(f9(f10(c2), f4(c4)) = c1)),
% 27.74/17.93 inference(unit_resolution,[status(thm)],[3498, 1209, 77, 122, 256, 348, 79, 121, 347])).
% 27.74/17.93 tff(4166,plain,
% 27.74/17.93 (f9(f10(c2), f4(c4)) = c2),
% 27.74/17.93 inference(unit_resolution,[status(thm)],[146, 4165])).
% 27.74/17.93 tff(4167,plain,
% 27.74/17.93 ($false),
% 27.74/17.93 inference(unit_resolution,[status(thm)],[4166, 4164])).
% 27.74/17.93 tff(4168,plain,((f9(c2, c2) = c2) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | big_f(f9(c2, c2), f10(c2)) | (~big_f(c2, c1)) | big_f(c2, c2) | (~(f7(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.74/17.93 tff(4169,plain,
% 27.74/17.93 (~big_f(c2, c1)),
% 27.74/17.93 inference(unit_resolution,[status(thm)],[4168, 256, 122, 77, 79, 121, 1209, 347])).
% 27.74/17.93 tff(4170,plain,
% 27.74/17.93 ($false),
% 27.74/17.93 inference(unit_resolution,[status(thm)],[4169, 4162])).
% 27.74/17.93 tff(4171,plain,(big_f(f9(c2, c2), f10(c2)) | (~(f5(c1) = c1)) | (~(f7(c1) = c2)) | (~(f10(c1) = c1)) | (~(f10(c2) = c2)) | (f9(c2, c2) = c2) | (~(f7(c2) = c2)) | (~(f4(c4) = c2)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 27.74/17.93 tff(4172,plain,
% 27.74/17.93 (big_f(c2, c2)),
% 27.74/17.93 inference(unit_resolution,[status(thm)],[4171, 256, 122, 185, 3762, 347, 77, 79, 230])).
% 27.74/17.93 tff(4173,plain,
% 27.74/17.93 (big_f(f7(f10(c1)), c2)),
% 27.74/17.93 inference(modus_ponens,[status(thm)],[4172, 4151])).
% 27.74/17.93 tff(4174,plain,
% 27.74/17.93 (f5(f10(c1)) = f5(f9(c2, c2))),
% 27.74/17.93 inference(monotonicity,[status(thm)],[3763])).
% 27.74/17.93 tff(4175,plain,
% 27.74/17.93 (f5(f10(c1)) = f5(c1)),
% 27.74/17.93 inference(transitivity,[status(thm)],[4174, 162])).
% 27.74/17.93 tff(4176,plain,
% 27.74/17.93 ((c2 = f5(f10(c1))) <=> (c2 = f5(c1))),
% 27.74/17.93 inference(monotonicity,[status(thm)],[4175])).
% 27.74/17.93 tff(4177,plain,
% 27.74/17.93 ((c2 = f5(c1)) <=> (c2 = f5(f10(c1)))),
% 27.74/17.93 inference(symmetry,[status(thm)],[4176])).
% 27.74/17.93 tff(4178,plain,
% 27.74/17.93 ((f9(c2, c2) = c2) <=> (c2 = f5(f10(c1)))),
% 27.74/17.93 inference(transitivity,[status(thm)],[3596, 4177])).
% 27.74/17.93 tff(4179,plain,
% 27.74/17.93 ((~(f9(c2, c2) = c2)) <=> (~(c2 = f5(f10(c1))))),
% 27.74/17.93 inference(monotonicity,[status(thm)],[4178])).
% 27.74/17.93 tff(4180,plain,
% 27.74/17.93 (~(c2 = f5(f10(c1)))),
% 27.74/17.93 inference(modus_ponens,[status(thm)],[185, 4179])).
% 27.74/17.93 tff(4181,plain,
% 27.74/17.93 ((f7(f10(c1)) = f10(c1)) <=> (c2 = f9(c2, c2))),
% 27.74/17.93 inference(monotonicity,[status(thm)],[4149, 3763])).
% 27.74/17.93 tff(4182,plain,
% 27.74/17.93 ((f7(f10(c1)) = f10(c1)) <=> (f9(c2, c2) = c2)),
% 27.74/17.93 inference(transitivity,[status(thm)],[4181, 167])).
% 27.74/17.93 tff(4183,plain,
% 27.74/17.93 ((f9(c2, c2) = c2) <=> (f7(f10(c1)) = f10(c1))),
% 27.74/17.93 inference(symmetry,[status(thm)],[4182])).
% 27.74/17.93 tff(4184,plain,
% 27.74/17.93 ((~(f9(c2, c2) = c2)) <=> (~(f7(f10(c1)) = f10(c1)))),
% 27.74/17.93 inference(monotonicity,[status(thm)],[4183])).
% 27.74/17.93 tff(4185,plain,
% 27.74/17.93 (~(f7(f10(c1)) = f10(c1))),
% 27.74/17.93 inference(modus_ponens,[status(thm)],[185, 4184])).
% 27.74/17.93 tff(4186,plain,
% 27.74/17.93 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f7(f10(c1)) = f10(c1)) | (c2 = f5(f10(c1))) | (~big_f(f7(f10(c1)), c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~(f10(c2) = c2)) | (f7(f10(c1)) = f10(c1)) | (c2 = f5(f10(c1))) | (~big_f(f7(f10(c1)), c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)))),
% 27.74/17.93 inference(rewrite,[status(thm)],[])).
% 27.74/17.93 tff(4187,plain,
% 27.74/17.93 (((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f10(c1)) = f10(c1)) | (c2 = f5(f10(c1))) | (~big_f(f7(f10(c1)), c2))) <=> ((~(f10(c2) = c2)) | (f7(f10(c1)) = f10(c1)) | (c2 = f5(f10(c1))) | (~big_f(f7(f10(c1)), c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)))),
% 27.74/17.93 inference(rewrite,[status(thm)],[])).
% 27.74/17.93 tff(4188,plain,
% 27.74/17.93 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f10(c1)) = f10(c1)) | (c2 = f5(f10(c1))) | (~big_f(f7(f10(c1)), c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f7(f10(c1)) = f10(c1)) | (c2 = f5(f10(c1))) | (~big_f(f7(f10(c1)), c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2))))),
% 27.74/17.93 inference(monotonicity,[status(thm)],[4187])).
% 27.74/17.93 tff(4189,plain,
% 27.74/17.93 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f10(c1)) = f10(c1)) | (c2 = f5(f10(c1))) | (~big_f(f7(f10(c1)), c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~(f10(c2) = c2)) | (f7(f10(c1)) = f10(c1)) | (c2 = f5(f10(c1))) | (~big_f(f7(f10(c1)), c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)))),
% 27.74/17.93 inference(transitivity,[status(thm)],[4188, 4186])).
% 27.74/17.93 tff(4190,plain,
% 27.74/17.93 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f10(c1)) = f10(c1)) | (c2 = f5(f10(c1))) | (~big_f(f7(f10(c1)), c2)))),
% 27.74/17.93 inference(quant_inst,[status(thm)],[])).
% 27.74/17.93 tff(4191,plain,
% 27.74/17.93 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~(f10(c2) = c2)) | (f7(f10(c1)) = f10(c1)) | (c2 = f5(f10(c1))) | (~big_f(f7(f10(c1)), c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2))),
% 27.74/17.93 inference(modus_ponens,[status(thm)],[4190, 4189])).
% 27.74/17.93 tff(4192,plain,
% 27.74/17.93 ((~(f10(c2) = c2)) | (f7(f10(c1)) = f10(c1)) | (c2 = f5(f10(c1))) | (~big_f(f7(f10(c1)), c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2))),
% 27.74/17.93 inference(unit_resolution,[status(thm)],[4191, 676])).
% 27.74/17.93 tff(4193,plain,
% 27.74/17.93 (~big_f(f7(f10(c1)), c2)),
% 27.74/17.93 inference(unit_resolution,[status(thm)],[4192, 256, 122, 4185, 185, 4180])).
% 27.74/17.93 tff(4194,plain,
% 27.74/17.93 ($false),
% 27.74/17.93 inference(unit_resolution,[status(thm)],[4193, 4173])).
% 27.74/17.93 tff(4195,plain,(big_f(f9(c2, c2), f10(c2)) | (~(f7(c1) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f10(c1) = c1)) | (~(f7(c2) = c2)) | (~(f5(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 27.74/17.93 tff(4196,plain,
% 27.74/17.93 (big_f(f9(c2, c2), f10(c2))),
% 27.74/17.93 inference(unit_resolution,[status(thm)],[4195, 4147, 148, 79, 122, 3637, 77, 120])).
% 27.74/17.93 tff(4197,plain,
% 27.74/17.93 (big_f(f9(c2, c2), c2)),
% 27.74/17.93 inference(unit_resolution,[status(thm)],[3687, 4196, 122])).
% 27.74/17.93 tff(4198,plain,
% 27.74/17.93 (f9(c2, c2) = f5(f9(c2, c2))),
% 27.74/17.93 inference(modus_ponens,[status(thm)],[4147, 171])).
% 27.74/17.93 tff(4199,plain,
% 27.74/17.93 ((~big_f(c2, f9(c2, c2))) <=> (~big_f(f7(f9(c2, c2)), f9(c2, c2)))),
% 27.74/17.93 inference(monotonicity,[status(thm)],[3768])).
% 27.74/17.93 tff(4200,plain,
% 27.74/17.93 (~big_f(f7(f9(c2, c2)), f9(c2, c2))),
% 27.74/17.93 inference(modus_ponens,[status(thm)],[2040, 4199])).
% 27.74/17.93 tff(4201,assumption,(~big_f(f7(f9(c2, c2)), f9(c2, c2))), introduced(assumption)).
% 27.74/17.93 tff(4202,plain,
% 27.74/17.93 (big_f(f9(c1, c1), c1) <=> big_f(c2, f9(c2, c2))),
% 27.74/17.93 inference(monotonicity,[status(thm)],[4071, 150])).
% 27.74/17.93 tff(4203,plain,
% 27.74/17.93 (big_f(c2, f9(c2, c2)) <=> big_f(f9(c1, c1), c1)),
% 27.74/17.93 inference(symmetry,[status(thm)],[4202])).
% 27.74/17.93 tff(4204,plain,
% 27.74/17.93 (big_f(c2, f9(c2, c2)) <=> big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))),
% 27.74/17.93 inference(transitivity,[status(thm)],[4203, 4101])).
% 27.74/17.93 tff(4205,plain,
% 27.74/17.93 ((~big_f(c2, f9(c2, c2))) <=> (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))))),
% 27.74/17.93 inference(monotonicity,[status(thm)],[4204])).
% 27.74/17.93 tff(4206,plain,
% 27.74/17.93 (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))),
% 27.74/17.93 inference(modus_ponens,[status(thm)],[2040, 4205])).
% 27.74/17.93 tff(4207,plain,
% 27.74/17.93 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((f7(f9(c2, c2)) = f9(c2, c2)) | (~(f9(c2, c2) = f5(f9(c2, c2)))) | big_f(f7(f9(c2, c2)), f9(c2, c2)) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~(f9(c2, c2) = f5(f9(c2, c2)))) | big_f(f7(f9(c2, c2)), f9(c2, c2)) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))))),
% 27.74/17.93 inference(rewrite,[status(thm)],[])).
% 27.74/17.93 tff(4208,plain,
% 27.74/17.93 (((~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))) | (f7(f9(c2, c2)) = f9(c2, c2)) | big_f(f7(f9(c2, c2)), f9(c2, c2)) | (~(f9(c2, c2) = f5(f9(c2, c2))))) <=> ((f7(f9(c2, c2)) = f9(c2, c2)) | (~(f9(c2, c2) = f5(f9(c2, c2)))) | big_f(f7(f9(c2, c2)), f9(c2, c2)) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))))),
% 27.74/17.93 inference(rewrite,[status(thm)],[])).
% 27.74/17.93 tff(4209,plain,
% 27.74/17.93 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))) | (f7(f9(c2, c2)) = f9(c2, c2)) | big_f(f7(f9(c2, c2)), f9(c2, c2)) | (~(f9(c2, c2) = f5(f9(c2, c2)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((f7(f9(c2, c2)) = f9(c2, c2)) | (~(f9(c2, c2) = f5(f9(c2, c2)))) | big_f(f7(f9(c2, c2)), f9(c2, c2)) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))))),
% 27.74/17.93 inference(monotonicity,[status(thm)],[4208])).
% 27.74/17.93 tff(4210,plain,
% 27.74/17.93 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))) | (f7(f9(c2, c2)) = f9(c2, c2)) | big_f(f7(f9(c2, c2)), f9(c2, c2)) | (~(f9(c2, c2) = f5(f9(c2, c2)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~(f9(c2, c2) = f5(f9(c2, c2)))) | big_f(f7(f9(c2, c2)), f9(c2, c2)) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))))),
% 27.74/17.93 inference(transitivity,[status(thm)],[4209, 4207])).
% 27.74/17.93 tff(4211,plain,
% 27.74/17.93 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))) | (f7(f9(c2, c2)) = f9(c2, c2)) | big_f(f7(f9(c2, c2)), f9(c2, c2)) | (~(f9(c2, c2) = f5(f9(c2, c2)))))),
% 27.74/17.93 inference(quant_inst,[status(thm)],[])).
% 27.74/17.93 tff(4212,plain,
% 27.74/17.93 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~(f9(c2, c2) = f5(f9(c2, c2)))) | big_f(f7(f9(c2, c2)), f9(c2, c2)) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))),
% 27.74/17.93 inference(modus_ponens,[status(thm)],[4211, 4210])).
% 27.74/17.93 tff(4213,plain,
% 27.74/17.93 ($false),
% 27.74/17.93 inference(unit_resolution,[status(thm)],[4212, 267, 3458, 3777, 3774, 4098, 4206, 4201])).
% 27.74/17.93 tff(4214,plain,((f9(c1, c1) = c1) | (~(f9(c2, c2) = f5(f9(c2, c2)))) | (f7(f9(c2, c2)) = f9(c2, c2)) | big_f(f7(f9(c2, c2)), f9(c2, c2)) | big_f(c2, f9(c2, c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f10(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 27.74/17.93 tff(4215,plain,
% 27.74/17.93 (f9(c1, c1) = c1),
% 27.74/17.93 inference(unit_resolution,[status(thm)],[4214, 4200, 3774, 3458, 2040, 148, 79, 122, 3762])).
% 27.74/17.93 tff(4216,plain,
% 27.74/17.93 (f9(c1, c1) = f9(c2, c2)),
% 27.74/17.93 inference(transitivity,[status(thm)],[4215, 149, 132])).
% 27.74/17.93 tff(4217,plain,
% 27.74/17.93 (big_f(f9(c1, c1), c1) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 27.74/17.93 inference(monotonicity,[status(thm)],[4216, 150])).
% 27.74/17.93 tff(4218,plain,
% 27.74/17.93 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f9(c1, c1), c1)),
% 27.74/17.93 inference(symmetry,[status(thm)],[4217])).
% 27.74/17.93 tff(4219,plain,
% 27.74/17.93 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))),
% 27.74/17.93 inference(transitivity,[status(thm)],[4218, 4101])).
% 27.74/17.93 tff(4220,plain,
% 27.74/17.93 (big_f(f9(c2, c2), f9(c2, c2))),
% 27.74/17.93 inference(unit_resolution,[status(thm)],[3759, 4107, 79, 122, 3645, 2041, 3643, 168, 148])).
% 27.74/17.93 tff(4221,plain,
% 27.74/17.93 (big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))),
% 27.74/17.93 inference(modus_ponens,[status(thm)],[4220, 4219])).
% 27.74/17.93 tff(4222,plain,
% 27.74/17.93 (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)),
% 27.74/17.93 inference(modus_ponens,[status(thm)],[4215, 4096])).
% 27.74/17.93 tff(4223,plain,
% 27.74/17.93 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((f7(f9(c2, c2)) = f9(c2, c2)) | (~(f9(c2, c2) = f5(f9(c2, c2)))) | big_f(f7(f9(c2, c2)), f9(c2, c2)) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~(f9(c2, c2) = f5(f9(c2, c2)))) | big_f(f7(f9(c2, c2)), f9(c2, c2)) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))))),
% 27.74/17.93 inference(rewrite,[status(thm)],[])).
% 27.74/17.93 tff(4224,plain,
% 27.74/17.93 (((~(f10(f9(c2, c2)) = f9(c2, c2))) | (f7(f9(c2, c2)) = f9(c2, c2)) | big_f(f7(f9(c2, c2)), f9(c2, c2)) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))) | (~(f9(c2, c2) = f5(f9(c2, c2))))) <=> ((f7(f9(c2, c2)) = f9(c2, c2)) | (~(f9(c2, c2) = f5(f9(c2, c2)))) | big_f(f7(f9(c2, c2)), f9(c2, c2)) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))))),
% 27.74/17.93 inference(rewrite,[status(thm)],[])).
% 27.74/17.93 tff(4225,plain,
% 27.74/17.94 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (f7(f9(c2, c2)) = f9(c2, c2)) | big_f(f7(f9(c2, c2)), f9(c2, c2)) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))) | (~(f9(c2, c2) = f5(f9(c2, c2)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((f7(f9(c2, c2)) = f9(c2, c2)) | (~(f9(c2, c2) = f5(f9(c2, c2)))) | big_f(f7(f9(c2, c2)), f9(c2, c2)) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))))))),
% 27.74/17.94 inference(monotonicity,[status(thm)],[4224])).
% 27.74/17.94 tff(4226,plain,
% 27.74/17.94 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (f7(f9(c2, c2)) = f9(c2, c2)) | big_f(f7(f9(c2, c2)), f9(c2, c2)) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))) | (~(f9(c2, c2) = f5(f9(c2, c2)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~(f9(c2, c2) = f5(f9(c2, c2)))) | big_f(f7(f9(c2, c2)), f9(c2, c2)) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))))),
% 27.74/17.94 inference(transitivity,[status(thm)],[4225, 4223])).
% 27.74/17.94 tff(4227,plain,
% 27.74/17.94 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (f7(f9(c2, c2)) = f9(c2, c2)) | big_f(f7(f9(c2, c2)), f9(c2, c2)) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))) | (~(f9(c2, c2) = f5(f9(c2, c2)))))),
% 27.74/17.94 inference(quant_inst,[status(thm)],[])).
% 27.74/17.94 tff(4228,plain,
% 27.74/17.94 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~(f9(c2, c2) = f5(f9(c2, c2)))) | big_f(f7(f9(c2, c2)), f9(c2, c2)) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))))),
% 27.74/17.94 inference(modus_ponens,[status(thm)],[4227, 4226])).
% 27.74/17.94 tff(4229,plain,
% 27.74/17.94 ($false),
% 27.74/17.94 inference(unit_resolution,[status(thm)],[4228, 783, 3458, 3777, 3774, 4222, 4221, 4200])).
% 27.74/17.94 tff(4230,plain,(big_f(c2, f9(c2, c2)) | (~(f9(c2, c2) = f5(f9(c2, c2)))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f10(c1) = c1)) | (~(f7(c1) = c2)) | (~big_f(f9(c2, c2), c2)) | (c1 = c3)), inference(lemma,lemma(discharge,[]))).
% 27.74/17.94 tff(4231,plain,
% 27.74/17.94 (big_f(c2, f9(c2, c2))),
% 27.74/17.94 inference(unit_resolution,[status(thm)],[4230, 4198, 3654, 148, 79, 122, 3637, 120, 4197, 168])).
% 27.74/17.94 tff(4232,plain,
% 27.74/17.94 ((f9(f9(c2, c2), c2) = c2) <=> (f9(c1, c2) = c2)),
% 27.74/17.94 inference(monotonicity,[status(thm)],[3765])).
% 27.74/17.94 tff(4233,plain,
% 27.74/17.94 ((f9(c1, c2) = c2) <=> (f9(f9(c2, c2), c2) = c2)),
% 27.74/17.94 inference(symmetry,[status(thm)],[4232])).
% 27.74/17.94 tff(4234,assumption,(f7(c1) = c1), introduced(assumption)).
% 27.74/17.94 tff(4235,plain,
% 27.74/17.94 ((~(f9(c1, c2) = c2)) <=> (~(f9(f9(c2, c2), c2) = c2))),
% 27.74/17.94 inference(monotonicity,[status(thm)],[4233])).
% 27.74/17.94 tff(4236,assumption,(~(f9(c1, c2) = c2)), introduced(assumption)).
% 27.74/17.94 tff(4237,plain,
% 27.74/17.94 (~(f9(f9(c2, c2), c2) = c2)),
% 27.74/17.94 inference(modus_ponens,[status(thm)],[4236, 4235])).
% 27.74/17.94 tff(4238,plain,
% 27.74/17.94 (big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2))) <=> big_f(f9(c1, c2), f10(c1))),
% 27.74/17.94 inference(monotonicity,[status(thm)],[3765, 3646])).
% 27.74/17.94 tff(4239,plain,
% 27.74/17.94 (big_f(f9(c1, c2), f10(c1)) <=> big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))),
% 27.74/17.94 inference(symmetry,[status(thm)],[4238])).
% 27.74/17.94 tff(4240,plain,
% 27.74/17.94 (f9(c1, c2) = c1),
% 27.74/17.94 inference(unit_resolution,[status(thm)],[3791, 4236])).
% 27.74/17.94 tff(4241,plain,
% 27.74/17.94 (f9(c1, c2) = f9(c2, c2)),
% 27.74/17.94 inference(transitivity,[status(thm)],[4240, 149, 132])).
% 27.74/17.94 tff(4242,plain,
% 27.74/17.94 (big_f(f9(c1, c2), f10(c1)) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 27.74/17.94 inference(monotonicity,[status(thm)],[4241, 3763])).
% 27.74/17.94 tff(4243,plain,
% 27.74/17.94 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f9(c1, c2), f10(c1))),
% 27.74/17.94 inference(symmetry,[status(thm)],[4242])).
% 27.74/17.94 tff(4244,plain,
% 27.74/17.94 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))),
% 27.74/17.94 inference(transitivity,[status(thm)],[4243, 4239])).
% 27.74/17.94 tff(4245,plain,
% 27.74/17.94 ((~big_f(f9(c2, c2), f9(c2, c2))) <=> (~big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2))))),
% 27.74/17.94 inference(monotonicity,[status(thm)],[4244])).
% 27.74/17.94 tff(4246,plain,
% 27.74/17.94 (~big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))),
% 27.74/17.94 inference(modus_ponens,[status(thm)],[3689, 4245])).
% 27.74/17.94 tff(4247,plain,
% 27.74/17.94 (f6(f9(c2, c2), c2) = f6(c1, c2)),
% 27.74/17.94 inference(monotonicity,[status(thm)],[161])).
% 27.74/17.94 tff(4248,plain,
% 27.74/17.94 (f6(c1, c2) = f6(f9(c2, c2), c2)),
% 27.74/17.94 inference(symmetry,[status(thm)],[4247])).
% 27.74/17.94 tff(4249,plain,
% 27.74/17.94 ((f6(c1, c2) = c2) <=> (f6(f9(c2, c2), c2) = c2)),
% 27.74/17.94 inference(monotonicity,[status(thm)],[4248])).
% 27.74/17.94 tff(4250,assumption,(~(f9(f9(c2, c2), c2) = c2)), introduced(assumption)).
% 27.74/17.94 tff(4251,assumption,(~big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))), introduced(assumption)).
% 27.74/17.94 tff(4252,plain,
% 27.74/17.94 ((f6(f9(c2, c2), c2) = c2) <=> (f6(c1, c2) = c2)),
% 27.74/17.94 inference(monotonicity,[status(thm)],[4247])).
% 27.74/17.94 tff(4253,assumption,(f6(f9(c2, c2), c2) = c2), introduced(assumption)).
% 27.74/17.94 tff(4254,plain,
% 27.74/17.94 (f6(c1, c2) = c2),
% 27.74/17.94 inference(modus_ponens,[status(thm)],[4253, 4252])).
% 27.74/17.94 tff(4255,plain,
% 27.74/17.94 ($false),
% 27.74/17.94 inference(unit_resolution,[status(thm)],[114, 4254])).
% 27.74/17.94 tff(4256,plain,((~(f6(f9(c2, c2), c2) = c2)) | (f6(c1, c2) = c2) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.74/17.94 tff(4257,plain,
% 27.74/17.94 (~(f6(f9(c2, c2), c2) = c2)),
% 27.74/17.94 inference(unit_resolution,[status(thm)],[4256, 114, 122, 79, 148])).
% 27.74/17.94 tff(4258,plain,
% 27.74/17.94 (f7(f9(c2, c2)) = f9(c2, c2)),
% 27.74/17.94 inference(modus_ponens,[status(thm)],[4234, 3652])).
% 27.74/17.94 tff(4259,plain,
% 27.74/17.94 (f7(f9(c2, c2)) = c1),
% 27.74/17.94 inference(transitivity,[status(thm)],[243, 4234])).
% 27.74/17.94 tff(4260,plain,
% 27.74/17.94 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)) <=> big_f(c1, f6(c1, c2))),
% 27.74/17.94 inference(monotonicity,[status(thm)],[4259, 4247])).
% 27.74/17.94 tff(4261,plain,
% 27.74/17.94 (big_f(c1, f6(c1, c2)) <=> big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))),
% 27.74/17.94 inference(symmetry,[status(thm)],[4260])).
% 27.74/17.94 tff(4262,plain,
% 27.74/17.94 (f6(c1, c2) = c1),
% 27.74/17.94 inference(unit_resolution,[status(thm)],[48, 114])).
% 27.74/17.94 tff(4263,plain,
% 27.74/17.94 (f6(c1, c2) = f9(c2, c2)),
% 27.74/17.94 inference(transitivity,[status(thm)],[4262, 149, 132])).
% 27.74/17.94 tff(4264,plain,
% 27.74/17.94 (big_f(c1, f6(c1, c2)) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 27.74/17.94 inference(monotonicity,[status(thm)],[150, 4263])).
% 27.74/17.94 tff(4265,plain,
% 27.74/17.94 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(c1, f6(c1, c2))),
% 27.74/17.94 inference(symmetry,[status(thm)],[4264])).
% 27.74/17.94 tff(4266,plain,
% 27.74/17.94 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))),
% 27.74/17.94 inference(transitivity,[status(thm)],[4265, 4261])).
% 27.74/17.94 tff(4267,plain,
% 27.74/17.94 ((~big_f(f9(c2, c2), f9(c2, c2))) <=> (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)))),
% 27.74/17.94 inference(monotonicity,[status(thm)],[4266])).
% 27.74/17.94 tff(4268,plain,
% 27.74/17.94 (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))),
% 27.74/17.94 inference(modus_ponens,[status(thm)],[3689, 4267])).
% 27.74/17.94 tff(4269,plain,
% 27.74/17.94 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)) | (f9(f9(c2, c2), c2) = c2) | big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)) | (f9(f9(c2, c2), c2) = c2) | big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2))))),
% 27.74/17.94 inference(rewrite,[status(thm)],[])).
% 27.74/17.94 tff(4270,plain,
% 27.74/17.94 (((~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), c2) = c2) | big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))) <=> ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)) | (f9(f9(c2, c2), c2) = c2) | big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2))))),
% 27.74/17.94 inference(rewrite,[status(thm)],[])).
% 27.74/17.94 tff(4271,plain,
% 27.74/17.94 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), c2) = c2) | big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)) | (f9(f9(c2, c2), c2) = c2) | big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))))),
% 27.74/17.94 inference(monotonicity,[status(thm)],[4270])).
% 27.74/17.94 tff(4272,plain,
% 27.74/17.94 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), c2) = c2) | big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)) | (f9(f9(c2, c2), c2) = c2) | big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2))))),
% 27.74/17.94 inference(transitivity,[status(thm)],[4271, 4269])).
% 27.74/17.94 tff(4273,plain,
% 27.74/17.94 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), c2) = c2) | big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)))),
% 27.74/17.94 inference(quant_inst,[status(thm)],[])).
% 27.74/17.94 tff(4274,plain,
% 27.74/17.94 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)) | (f9(f9(c2, c2), c2) = c2) | big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))),
% 27.74/17.94 inference(modus_ponens,[status(thm)],[4273, 4272])).
% 27.74/17.94 tff(4275,plain,
% 27.74/17.94 ($false),
% 27.74/17.94 inference(unit_resolution,[status(thm)],[4274, 2492, 758, 4268, 4258, 4257, 4251, 4250])).
% 27.74/17.94 tff(4276,plain,((f6(c1, c2) = c2) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2))) | (f9(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f9(c2, c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f7(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 27.74/17.94 tff(4277,plain,
% 27.74/17.94 (f6(c1, c2) = c2),
% 27.74/17.94 inference(unit_resolution,[status(thm)],[4276, 4246, 3777, 4237, 3689, 148, 79, 122, 4234])).
% 27.74/17.94 tff(4278,plain,
% 27.74/17.94 (f6(f9(c2, c2), c2) = c2),
% 27.74/17.94 inference(modus_ponens,[status(thm)],[4277, 4249])).
% 27.74/17.94 tff(4279,plain,
% 27.74/17.94 (big_f(c1, f6(c1, c2)) <=> big_f(f9(c2, c2), c2)),
% 27.74/17.94 inference(monotonicity,[status(thm)],[150, 4277])).
% 27.74/17.94 tff(4280,plain,
% 27.74/17.94 (big_f(f9(c2, c2), c2) <=> big_f(c1, f6(c1, c2))),
% 27.74/17.94 inference(symmetry,[status(thm)],[4279])).
% 27.74/17.94 tff(4281,plain,
% 27.74/17.94 (big_f(f9(c2, c2), c2) <=> big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))),
% 27.74/17.94 inference(transitivity,[status(thm)],[4280, 4261])).
% 27.74/17.94 tff(4282,plain,
% 27.74/17.94 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))),
% 27.74/17.94 inference(modus_ponens,[status(thm)],[2041, 4281])).
% 27.74/17.94 tff(4283,plain,
% 27.74/17.94 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), c2) = c2)) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))) | (f9(f9(c2, c2), c2) = c2) | big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), c2) = c2)) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))) | (f9(f9(c2, c2), c2) = c2) | big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2))))),
% 27.74/17.94 inference(rewrite,[status(thm)],[])).
% 27.74/17.94 tff(4284,plain,
% 27.74/17.94 (((~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), c2) = c2) | big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), c2) = c2)) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)))) <=> ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), c2) = c2)) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))) | (f9(f9(c2, c2), c2) = c2) | big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2))))),
% 27.74/17.94 inference(rewrite,[status(thm)],[])).
% 27.74/17.94 tff(4285,plain,
% 27.74/17.94 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), c2) = c2) | big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), c2) = c2)) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), c2) = c2)) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))) | (f9(f9(c2, c2), c2) = c2) | big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))))),
% 27.74/17.94 inference(monotonicity,[status(thm)],[4284])).
% 27.74/17.94 tff(4286,plain,
% 27.74/17.94 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), c2) = c2) | big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), c2) = c2)) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), c2) = c2)) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))) | (f9(f9(c2, c2), c2) = c2) | big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2))))),
% 27.74/17.94 inference(transitivity,[status(thm)],[4285, 4283])).
% 27.74/17.94 tff(4287,plain,
% 27.74/17.94 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), c2) = c2) | big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), c2) = c2)) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))))),
% 27.74/17.94 inference(quant_inst,[status(thm)],[])).
% 27.74/17.94 tff(4288,plain,
% 27.74/17.94 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), c2) = c2)) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))) | (f9(f9(c2, c2), c2) = c2) | big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))),
% 27.74/17.94 inference(modus_ponens,[status(thm)],[4287, 4286])).
% 27.74/17.94 tff(4289,plain,
% 27.74/17.94 ($false),
% 27.74/17.94 inference(unit_resolution,[status(thm)],[4288, 2534, 3777, 4282, 4258, 4278, 4246, 4237])).
% 27.74/17.94 tff(4290,plain,((f9(c1, c2) = c2) | (~big_f(f9(c2, c2), c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f7(c1) = c1)) | big_f(f9(c2, c2), f9(c2, c2)) | (~(f10(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 27.74/17.94 tff(4291,plain,
% 27.74/17.94 (f9(c1, c2) = c2),
% 27.74/17.94 inference(unit_resolution,[status(thm)],[4290, 4234, 148, 79, 122, 2041, 3689, 3762])).
% 27.74/17.94 tff(4292,plain,
% 27.74/17.94 (f9(f9(c2, c2), c2) = c2),
% 27.74/17.94 inference(modus_ponens,[status(thm)],[4291, 4233])).
% 27.74/17.94 tff(4293,plain,
% 27.74/17.94 (big_f(f9(c1, c2), f10(c1)) <=> big_f(c2, f9(c2, c2))),
% 27.74/17.94 inference(monotonicity,[status(thm)],[4291, 3763])).
% 27.74/17.94 tff(4294,plain,
% 27.74/17.94 (big_f(c2, f9(c2, c2)) <=> big_f(f9(c1, c2), f10(c1))),
% 27.74/17.94 inference(symmetry,[status(thm)],[4293])).
% 27.74/17.94 tff(4295,plain,
% 27.74/17.94 (big_f(c2, f9(c2, c2)) <=> big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))),
% 27.74/17.94 inference(transitivity,[status(thm)],[4294, 4239])).
% 27.74/17.94 tff(4296,plain,
% 27.74/17.94 (big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))),
% 27.74/17.94 inference(modus_ponens,[status(thm)],[3719, 4295])).
% 27.74/17.94 tff(4297,assumption,(f9(f9(c2, c2), c2) = c2), introduced(assumption)).
% 27.74/17.94 tff(4298,assumption,(big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))), introduced(assumption)).
% 27.74/17.94 tff(4299,plain,
% 27.74/17.94 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)) | (~(f9(f9(c2, c2), c2) = c2)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)) | (~(f9(f9(c2, c2), c2) = c2)))),
% 27.74/17.94 inference(rewrite,[status(thm)],[])).
% 27.74/17.94 tff(4300,plain,
% 27.74/17.94 (((~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)) | (~(f9(f9(c2, c2), c2) = c2)) | (~big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2))))) <=> ((~big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)) | (~(f9(f9(c2, c2), c2) = c2)))),
% 27.74/17.94 inference(rewrite,[status(thm)],[])).
% 27.74/17.94 tff(4301,plain,
% 27.74/17.94 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)) | (~(f9(f9(c2, c2), c2) = c2)) | (~big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)) | (~(f9(f9(c2, c2), c2) = c2))))),
% 27.74/17.95 inference(monotonicity,[status(thm)],[4300])).
% 27.74/17.95 tff(4302,plain,
% 27.74/17.95 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)) | (~(f9(f9(c2, c2), c2) = c2)) | (~big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)) | (~(f9(f9(c2, c2), c2) = c2)))),
% 27.74/17.95 inference(transitivity,[status(thm)],[4301, 4299])).
% 27.74/17.95 tff(4303,plain,
% 27.74/17.95 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)) | (~(f9(f9(c2, c2), c2) = c2)) | (~big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))))),
% 27.74/17.95 inference(quant_inst,[status(thm)],[])).
% 27.74/17.95 tff(4304,plain,
% 27.74/17.95 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)) | (~(f9(f9(c2, c2), c2) = c2))),
% 27.74/17.95 inference(modus_ponens,[status(thm)],[4303, 4302])).
% 27.74/17.95 tff(4305,plain,
% 27.74/17.95 ($false),
% 27.74/17.95 inference(unit_resolution,[status(thm)],[4304, 2409, 758, 4268, 4258, 4257, 4298, 4297])).
% 27.74/17.95 tff(4306,plain,((f6(c1, c2) = c2) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))) | (~(f9(f9(c2, c2), c2) = c2)) | big_f(f9(c2, c2), f9(c2, c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f7(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 27.74/17.95 tff(4307,plain,
% 27.74/17.95 (f6(c1, c2) = c2),
% 27.74/17.95 inference(unit_resolution,[status(thm)],[4306, 4296, 4234, 4292, 3689, 148, 79, 122, 3777])).
% 27.74/17.95 tff(4308,plain,
% 27.74/17.95 (f6(f9(c2, c2), c2) = c2),
% 27.74/17.95 inference(modus_ponens,[status(thm)],[4307, 4249])).
% 27.74/17.95 tff(4309,plain,
% 27.74/17.95 (big_f(c1, f6(c1, c2)) <=> big_f(f9(c2, c2), c2)),
% 27.74/17.95 inference(monotonicity,[status(thm)],[150, 4307])).
% 27.74/17.95 tff(4310,plain,
% 27.74/17.95 (big_f(f9(c2, c2), c2) <=> big_f(c1, f6(c1, c2))),
% 27.74/17.95 inference(symmetry,[status(thm)],[4309])).
% 27.74/17.95 tff(4311,plain,
% 27.74/17.95 (big_f(f9(c2, c2), c2) <=> big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))),
% 27.74/17.95 inference(transitivity,[status(thm)],[4310, 4261])).
% 27.74/17.95 tff(4312,plain,
% 27.74/17.95 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))),
% 27.74/17.95 inference(modus_ponens,[status(thm)],[2041, 4311])).
% 27.74/17.95 tff(4313,plain,
% 27.74/17.95 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), c2) = c2)) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))) | (~(f9(f9(c2, c2), c2) = c2)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), c2) = c2)) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))) | (~(f9(f9(c2, c2), c2) = c2)))),
% 27.74/17.95 inference(rewrite,[status(thm)],[])).
% 27.74/17.95 tff(4314,plain,
% 27.74/17.95 (((~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f9(f9(c2, c2), c2) = c2)) | (~big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))) | (~(f6(f9(c2, c2), c2) = c2)) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)))) <=> ((~big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), c2) = c2)) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))) | (~(f9(f9(c2, c2), c2) = c2)))),
% 27.74/17.95 inference(rewrite,[status(thm)],[])).
% 27.74/17.95 tff(4315,plain,
% 27.74/17.95 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f9(f9(c2, c2), c2) = c2)) | (~big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))) | (~(f6(f9(c2, c2), c2) = c2)) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), c2) = c2)) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))) | (~(f9(f9(c2, c2), c2) = c2))))),
% 27.74/17.95 inference(monotonicity,[status(thm)],[4314])).
% 27.74/17.95 tff(4316,plain,
% 27.74/17.95 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f9(f9(c2, c2), c2) = c2)) | (~big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))) | (~(f6(f9(c2, c2), c2) = c2)) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), c2) = c2)) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))) | (~(f9(f9(c2, c2), c2) = c2)))),
% 27.74/17.95 inference(transitivity,[status(thm)],[4315, 4313])).
% 27.74/17.95 tff(4317,plain,
% 27.74/17.95 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f9(f9(c2, c2), c2) = c2)) | (~big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))) | (~(f6(f9(c2, c2), c2) = c2)) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))))),
% 27.74/17.95 inference(quant_inst,[status(thm)],[])).
% 27.74/17.95 tff(4318,plain,
% 27.74/17.95 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), c2) = c2)) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))) | (~(f9(f9(c2, c2), c2) = c2))),
% 27.74/17.95 inference(modus_ponens,[status(thm)],[4317, 4316])).
% 27.74/17.95 tff(4319,plain,
% 27.74/17.95 ($false),
% 27.74/17.95 inference(unit_resolution,[status(thm)],[4318, 2378, 3777, 4312, 4258, 4308, 4296, 4292])).
% 27.74/17.95 tff(4320,plain,((~(f7(c1) = c1)) | (~big_f(f9(c2, c2), c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | big_f(f9(c2, c2), f9(c2, c2)) | (~big_f(c2, f9(c2, c2))) | (~(f10(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 27.74/17.95 tff(4321,plain,
% 27.74/17.95 (~(f7(c1) = c1)),
% 27.74/17.95 inference(unit_resolution,[status(thm)],[4320, 2041, 148, 79, 122, 3689, 3719, 3762])).
% 27.74/17.95 tff(4322,plain,
% 27.74/17.95 (f7(c1) = c2),
% 27.74/17.95 inference(unit_resolution,[status(thm)],[119, 4321])).
% 27.74/17.95 tff(4323,plain,
% 27.74/17.95 (f7(f9(c2, c2)) = c2),
% 27.74/17.95 inference(transitivity,[status(thm)],[243, 4322])).
% 27.74/17.95 tff(4324,plain,
% 27.74/17.95 (big_f(f7(f9(c2, c2)), c2) <=> big_f(c2, c2)),
% 27.74/17.95 inference(monotonicity,[status(thm)],[4323])).
% 27.74/17.95 tff(4325,plain,
% 27.74/17.95 (big_f(c2, c2) <=> big_f(f7(f9(c2, c2)), c2)),
% 27.74/17.95 inference(symmetry,[status(thm)],[4324])).
% 27.74/17.95 tff(4326,plain,
% 27.74/17.95 (~(c4 = c2)),
% 27.74/17.95 inference(unit_resolution,[status(thm)],[3756, 3691, 566, 3689, 148, 79, 122, 815])).
% 27.74/17.95 tff(4327,plain,
% 27.74/17.95 (c4 = c1),
% 27.74/17.95 inference(unit_resolution,[status(thm)],[461, 4326])).
% 27.74/17.95 tff(4328,plain,
% 27.74/17.95 (c4 = f9(c2, c2)),
% 27.74/17.95 inference(transitivity,[status(thm)],[4327, 149, 132])).
% 27.74/17.95 tff(4329,plain,
% 27.74/17.95 ((c2 = c4) <=> (c2 = f9(c2, c2))),
% 27.74/17.95 inference(monotonicity,[status(thm)],[4328])).
% 27.74/17.95 tff(4330,plain,
% 27.74/17.95 ((c2 = c4) <=> (f9(c2, c2) = c2)),
% 27.74/17.95 inference(transitivity,[status(thm)],[4329, 167])).
% 27.74/17.95 tff(4331,plain,
% 27.74/17.95 ((f9(c2, c2) = c2) <=> (c2 = c4)),
% 27.74/17.95 inference(symmetry,[status(thm)],[4330])).
% 27.74/17.95 tff(4332,plain,
% 27.74/17.95 ((~(f9(c2, c2) = c2)) <=> (~(c2 = c4))),
% 27.74/17.95 inference(monotonicity,[status(thm)],[4331])).
% 27.74/17.95 tff(4333,plain,
% 27.74/17.95 (~(c2 = c4)),
% 27.74/17.95 inference(modus_ponens,[status(thm)],[185, 4332])).
% 27.74/17.95 tff(4334,plain,
% 27.74/17.95 (big_f(f9(c2, c2), f1(f9(c2, c2), c2)) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 27.74/17.95 inference(monotonicity,[status(thm)],[1096])).
% 27.74/17.95 tff(4335,plain,
% 27.74/17.95 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f9(c2, c2), f1(f9(c2, c2), c2))),
% 27.74/17.95 inference(symmetry,[status(thm)],[4334])).
% 27.74/17.95 tff(4336,plain,
% 27.74/17.95 ((~big_f(f9(c2, c2), f9(c2, c2))) <=> (~big_f(f9(c2, c2), f1(f9(c2, c2), c2)))),
% 27.74/17.95 inference(monotonicity,[status(thm)],[4335])).
% 27.74/17.95 tff(4337,plain,
% 27.74/17.95 (~big_f(f9(c2, c2), f1(f9(c2, c2), c2))),
% 27.74/17.95 inference(modus_ponens,[status(thm)],[3689, 4336])).
% 27.74/17.95 tff(4338,assumption,(~(f1(f9(c2, c2), c2) = c2)), introduced(assumption)).
% 27.74/17.95 tff(4339,assumption,(~big_f(f9(c2, c2), f1(f9(c2, c2), c2))), introduced(assumption)).
% 27.74/17.95 tff(4340,plain,
% 27.74/17.95 (f3(c2, f9(c2, c2)) = f3(f7(c1), c1)),
% 27.74/17.95 inference(monotonicity,[status(thm)],[354, 161])).
% 27.74/17.95 tff(4341,plain,
% 27.74/17.95 (f3(c2, f9(c2, c2)) = c2),
% 27.74/17.95 inference(transitivity,[status(thm)],[4340, 881])).
% 27.74/17.95 tff(4342,plain,
% 27.74/17.95 (big_f(f3(c2, f9(c2, c2)), c2) <=> big_f(c2, c2)),
% 27.74/17.95 inference(monotonicity,[status(thm)],[4341])).
% 27.74/17.95 tff(4343,plain,
% 27.74/17.95 (big_f(c2, c2) <=> big_f(f3(c2, f9(c2, c2)), c2)),
% 27.74/17.95 inference(symmetry,[status(thm)],[4342])).
% 27.74/17.95 tff(4344,plain,
% 27.74/17.95 ((~big_f(c2, c2)) <=> (~big_f(f3(c2, f9(c2, c2)), c2))),
% 27.74/17.95 inference(monotonicity,[status(thm)],[4343])).
% 27.74/17.95 tff(4345,plain,
% 27.74/17.95 (~big_f(f3(c2, f9(c2, c2)), c2)),
% 27.74/17.95 inference(modus_ponens,[status(thm)],[121, 4344])).
% 27.74/17.95 tff(4346,plain,
% 27.74/17.95 ((f3(c2, f9(c2, c2)) = f9(c2, c2)) <=> (c2 = f9(c2, c2))),
% 27.74/17.95 inference(monotonicity,[status(thm)],[4341])).
% 27.74/17.95 tff(4347,plain,
% 27.74/17.95 ((f3(c2, f9(c2, c2)) = f9(c2, c2)) <=> (f9(c2, c2) = c2)),
% 27.74/17.95 inference(transitivity,[status(thm)],[4346, 167])).
% 27.74/17.95 tff(4348,plain,
% 27.74/17.95 ((f9(c2, c2) = c2) <=> (f3(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.74/17.95 inference(symmetry,[status(thm)],[4347])).
% 27.74/17.95 tff(4349,plain,
% 27.74/17.95 ((~(f9(c2, c2) = c2)) <=> (~(f3(c2, f9(c2, c2)) = f9(c2, c2)))),
% 27.74/17.95 inference(monotonicity,[status(thm)],[4348])).
% 27.74/17.95 tff(4350,plain,
% 27.74/17.95 (~(f3(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.74/17.95 inference(modus_ponens,[status(thm)],[185, 4349])).
% 27.74/17.95 tff(4351,plain,
% 27.74/17.95 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c2 = c4) | (f9(c2, c2) = c3) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2)) | (f3(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f3(c2, f9(c2, c2)), c2))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (c2 = c4) | (f9(c2, c2) = c3) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2)) | (f3(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f3(c2, f9(c2, c2)), c2))),
% 27.74/17.95 inference(rewrite,[status(thm)],[])).
% 27.74/17.95 tff(4352,plain,
% 27.74/17.95 (((c2 = c4) | (f3(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f3(c2, f9(c2, c2)), c2) | (f9(c2, c2) = c3) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2))) <=> ((c2 = c4) | (f9(c2, c2) = c3) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2)) | (f3(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f3(c2, f9(c2, c2)), c2))),
% 27.74/17.95 inference(rewrite,[status(thm)],[])).
% 27.74/17.95 tff(4353,plain,
% 27.74/17.95 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c2 = c4) | (f3(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f3(c2, f9(c2, c2)), c2) | (f9(c2, c2) = c3) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c2 = c4) | (f9(c2, c2) = c3) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2)) | (f3(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f3(c2, f9(c2, c2)), c2)))),
% 27.74/17.95 inference(monotonicity,[status(thm)],[4352])).
% 27.74/17.95 tff(4354,plain,
% 27.74/17.95 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c2 = c4) | (f3(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f3(c2, f9(c2, c2)), c2) | (f9(c2, c2) = c3) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (c2 = c4) | (f9(c2, c2) = c3) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2)) | (f3(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f3(c2, f9(c2, c2)), c2))),
% 27.74/17.95 inference(transitivity,[status(thm)],[4353, 4351])).
% 27.74/17.95 tff(4355,plain,
% 27.74/17.95 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c2 = c4) | (f3(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f3(c2, f9(c2, c2)), c2) | (f9(c2, c2) = c3) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2)))),
% 27.74/17.95 inference(quant_inst,[status(thm)],[])).
% 27.74/17.95 tff(4356,plain,
% 27.74/17.95 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (c2 = c4) | (f9(c2, c2) = c3) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2)) | (f3(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f3(c2, f9(c2, c2)), c2)),
% 27.74/17.95 inference(modus_ponens,[status(thm)],[4355, 4354])).
% 27.74/17.95 tff(4357,plain,
% 27.74/17.95 ($false),
% 27.74/17.95 inference(unit_resolution,[status(thm)],[4356, 1014, 873, 566, 4350, 4345, 4338, 4339])).
% 27.74/17.95 tff(4358,plain,((~(f3(f7(c1), c1) = c2)) | (c2 = c4) | (f9(c2, c2) = c3) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2)) | big_f(c2, c2) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f7(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.74/17.95 tff(4359,plain,
% 27.74/17.95 (~(f3(f7(c1), c1) = c2)),
% 27.74/17.95 inference(unit_resolution,[status(thm)],[4358, 4338, 566, 873, 4337, 121, 148, 79, 122, 347])).
% 27.74/17.95 tff(4360,plain,
% 27.74/17.95 (f3(f7(c1), c1) = c1),
% 27.74/17.95 inference(unit_resolution,[status(thm)],[918, 4359])).
% 27.74/17.95 tff(4361,plain,
% 27.74/17.95 (f3(c2, f9(c2, c2)) = f9(c2, c2)),
% 27.74/17.95 inference(transitivity,[status(thm)],[4340, 4360, 149, 132])).
% 27.74/17.95 tff(4362,plain,
% 27.74/17.95 (big_f(f3(c2, f9(c2, c2)), c2) <=> big_f(f9(c2, c2), c2)),
% 27.74/17.95 inference(monotonicity,[status(thm)],[4361])).
% 27.74/17.95 tff(4363,plain,
% 27.74/17.95 (big_f(f9(c2, c2), c2) <=> big_f(f3(c2, f9(c2, c2)), c2)),
% 27.74/17.95 inference(symmetry,[status(thm)],[4362])).
% 27.74/17.95 tff(4364,plain,
% 27.74/17.95 (big_f(f3(c2, f9(c2, c2)), c2)),
% 27.74/17.95 inference(modus_ponens,[status(thm)],[2041, 4363])).
% 27.74/17.95 tff(4365,plain,
% 27.74/17.95 (f3(f7(c1), c1) = f3(c2, f9(c2, c2))),
% 27.74/17.95 inference(symmetry,[status(thm)],[4340])).
% 27.74/17.95 tff(4366,plain,
% 27.74/17.95 ((f3(f7(c1), c1) = c1) <=> (f3(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.74/17.95 inference(monotonicity,[status(thm)],[4365, 150])).
% 27.74/17.95 tff(4367,plain,
% 27.74/17.95 (f3(c2, f9(c2, c2)) = f9(c2, c2)),
% 27.74/17.95 inference(modus_ponens,[status(thm)],[4360, 4366])).
% 27.74/17.95 tff(4368,plain,
% 27.74/17.95 ($false),
% 27.74/17.95 inference(unit_resolution,[status(thm)],[1110, 969, 873, 566, 4367, 4364, 4338, 4337])).
% 27.74/17.95 tff(4369,plain,((f1(f9(c2, c2), c2) = c2) | (c2 = c4) | (f9(c2, c2) = c3) | (~big_f(f9(c2, c2), c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f7(c1) = c2)) | big_f(c2, c2) | big_f(f9(c2, c2), f9(c2, c2)) | (~(f1(c1, c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 27.74/17.95 tff(4370,plain,
% 27.74/17.95 (f1(f9(c2, c2), c2) = c2),
% 27.74/17.95 inference(unit_resolution,[status(thm)],[4369, 1095, 566, 2041, 148, 79, 122, 347, 121, 3689, 873])).
% 27.74/17.95 tff(4371,plain,
% 27.74/17.95 (f1(f9(f10(c2), f4(c4)), c2) = f1(f9(c2, c2), c2)),
% 27.74/17.95 inference(symmetry,[status(thm)],[843])).
% 27.74/17.95 tff(4372,plain,
% 27.74/17.95 (c1 = f1(c1, c2)),
% 27.74/17.95 inference(symmetry,[status(thm)],[1095])).
% 27.74/17.95 tff(4373,plain,
% 27.74/17.95 (f9(c2, c2) = c2),
% 27.74/17.95 inference(transitivity,[status(thm)],[160, 148, 4372, 820, 4371, 4370])).
% 27.74/17.95 tff(4374,plain,
% 27.74/17.95 ($false),
% 27.74/17.95 inference(unit_resolution,[status(thm)],[185, 4373])).
% 27.74/17.95 tff(4375,plain,((~(f1(c1, c2) = c1)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (f9(c2, c2) = c3) | (~big_f(f9(c2, c2), c2)) | (~(f7(c1) = c2)) | big_f(c2, c2) | big_f(f9(c2, c2), f9(c2, c2)) | (c2 = c4)), inference(lemma,lemma(discharge,[]))).
% 27.74/17.95 tff(4376,plain,
% 27.74/17.95 (~(f1(c1, c2) = c1)),
% 27.74/17.95 inference(unit_resolution,[status(thm)],[4375, 347, 79, 122, 566, 2041, 148, 121, 3689, 873])).
% 27.74/17.95 tff(4377,plain,
% 27.74/17.95 (f1(c1, c2) = c2),
% 27.74/17.95 inference(unit_resolution,[status(thm)],[841, 4376])).
% 27.74/17.95 tff(4378,plain,
% 27.74/17.95 (f1(f9(c2, c2), c2) = c2),
% 27.74/17.95 inference(transitivity,[status(thm)],[843, 819, 4377])).
% 27.74/17.95 tff(4379,plain,
% 27.74/17.95 (big_f(f9(c2, c2), f1(f9(c2, c2), c2)) <=> big_f(f9(c2, c2), c2)),
% 27.74/17.95 inference(monotonicity,[status(thm)],[4378])).
% 27.74/17.95 tff(4380,plain,
% 27.74/17.95 (big_f(f9(c2, c2), c2) <=> big_f(f9(c2, c2), f1(f9(c2, c2), c2))),
% 27.74/17.95 inference(symmetry,[status(thm)],[4379])).
% 27.74/17.95 tff(4381,plain,
% 27.74/17.95 (big_f(f9(c2, c2), f1(f9(c2, c2), c2))),
% 27.74/17.95 inference(modus_ponens,[status(thm)],[2041, 4380])).
% 27.74/17.95 tff(4382,assumption,(big_f(f9(c2, c2), f1(f9(c2, c2), c2))), introduced(assumption)).
% 27.74/17.95 tff(4383,assumption,(f1(f9(c2, c2), c2) = c2), introduced(assumption)).
% 27.74/17.95 tff(4384,plain,
% 27.74/17.95 (f3(c2, f9(c2, c2)) = f9(c2, c2)),
% 27.74/17.95 inference(transitivity,[status(thm)],[4340, 953, 149, 132])).
% 27.74/17.95 tff(4385,plain,
% 27.74/17.95 (big_f(f3(c2, f9(c2, c2)), c2) <=> big_f(f9(c2, c2), c2)),
% 27.74/17.95 inference(monotonicity,[status(thm)],[4384])).
% 27.74/17.95 tff(4386,plain,
% 27.74/17.95 (big_f(f9(c2, c2), c2) <=> big_f(f3(c2, f9(c2, c2)), c2)),
% 27.74/17.95 inference(symmetry,[status(thm)],[4385])).
% 27.74/17.95 tff(4387,plain,
% 27.74/17.95 (big_f(f3(c2, f9(c2, c2)), c2)),
% 27.74/17.95 inference(modus_ponens,[status(thm)],[2041, 4386])).
% 27.74/17.95 tff(4388,plain,
% 27.74/17.95 (f3(c2, f9(c2, c2)) = f9(c2, c2)),
% 27.74/17.95 inference(modus_ponens,[status(thm)],[953, 4366])).
% 27.74/17.95 tff(4389,plain,
% 27.74/17.95 ($false),
% 27.74/17.95 inference(unit_resolution,[status(thm)],[1126, 933, 873, 566, 4388, 4387, 4383, 4382])).
% 27.74/17.95 tff(4390,plain,((~(f3(f7(c1), c1) = c1)) | (c2 = c4) | (f9(c2, c2) = c3) | (~(f1(f9(c2, c2), c2) = c2)) | (~big_f(f9(c2, c2), f1(f9(c2, c2), c2))) | (~big_f(f9(c2, c2), c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f7(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.74/17.96 tff(4391,plain,
% 27.74/17.96 (~(f3(f7(c1), c1) = c1)),
% 27.74/17.96 inference(unit_resolution,[status(thm)],[4390, 4378, 566, 873, 4381, 2041, 148, 79, 122, 347])).
% 27.74/17.96 tff(4392,plain,
% 27.74/17.96 (f3(f7(c1), c1) = c2),
% 27.74/17.96 inference(unit_resolution,[status(thm)],[918, 4391])).
% 27.74/17.96 tff(4393,plain,
% 27.74/17.96 (f3(c2, f9(c2, c2)) = c2),
% 27.74/17.96 inference(transitivity,[status(thm)],[4340, 4392])).
% 27.74/17.96 tff(4394,plain,
% 27.74/17.96 (big_f(f3(c2, f9(c2, c2)), c2) <=> big_f(c2, c2)),
% 27.74/17.96 inference(monotonicity,[status(thm)],[4393])).
% 27.74/17.96 tff(4395,plain,
% 27.74/17.96 (big_f(c2, c2) <=> big_f(f3(c2, f9(c2, c2)), c2)),
% 27.74/17.96 inference(symmetry,[status(thm)],[4394])).
% 27.74/17.96 tff(4396,plain,
% 27.74/17.96 ((~big_f(c2, c2)) <=> (~big_f(f3(c2, f9(c2, c2)), c2))),
% 27.74/17.96 inference(monotonicity,[status(thm)],[4395])).
% 27.74/17.96 tff(4397,plain,
% 27.74/17.96 (~big_f(f3(c2, f9(c2, c2)), c2)),
% 27.74/17.96 inference(modus_ponens,[status(thm)],[121, 4396])).
% 27.74/17.96 tff(4398,plain,
% 27.74/17.96 ((~(f3(f7(c1), c1) = c1)) <=> (~(f3(c2, f9(c2, c2)) = f9(c2, c2)))),
% 27.74/17.96 inference(monotonicity,[status(thm)],[4366])).
% 27.74/17.96 tff(4399,plain,
% 27.74/17.96 (~(f3(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.74/17.96 inference(modus_ponens,[status(thm)],[4391, 4398])).
% 27.74/17.96 tff(4400,plain,
% 27.74/17.96 ($false),
% 27.74/17.96 inference(unit_resolution,[status(thm)],[1085, 904, 873, 566, 4399, 4397, 4378, 4381])).
% 27.74/17.96 tff(4401,plain,((~(f7(c1) = c2)) | (c2 = c4) | (f9(c2, c2) = c3) | big_f(c2, c2) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~big_f(f9(c2, c2), c2)) | big_f(f9(c2, c2), f9(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 27.74/17.96 tff(4402,plain,
% 27.74/17.96 (big_f(c2, c2)),
% 27.74/17.96 inference(unit_resolution,[status(thm)],[4401, 4322, 566, 4333, 148, 79, 122, 2041, 3689])).
% 27.74/17.96 tff(4403,plain,
% 27.74/17.96 (big_f(f7(f9(c2, c2)), c2)),
% 27.74/17.96 inference(modus_ponens,[status(thm)],[4402, 4325])).
% 27.74/17.96 tff(4404,plain,
% 27.74/17.96 (~(f7(f9(c2, c2)) = f9(c2, c2))),
% 27.74/17.96 inference(modus_ponens,[status(thm)],[4321, 3653])).
% 27.74/17.96 tff(4405,plain,
% 27.74/17.96 (big_f(f7(f9(c2, c2)), c2) <=> big_f(c2, c2)),
% 27.74/17.96 inference(monotonicity,[status(thm)],[1793])).
% 27.74/17.96 tff(4406,plain,
% 27.74/17.96 (big_f(c2, c2) <=> big_f(f7(f9(c2, c2)), c2)),
% 27.74/17.96 inference(symmetry,[status(thm)],[4405])).
% 27.74/17.96 tff(4407,plain,
% 27.74/17.96 (big_f(f7(f9(c2, c2)), c2)),
% 27.74/17.96 inference(modus_ponens,[status(thm)],[1345, 4406])).
% 27.74/17.96 tff(4408,plain,
% 27.74/17.96 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~big_f(f7(f9(c2, c2)), c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2))) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), c2) = c2) | big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~big_f(f7(f9(c2, c2)), c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2))) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), c2) = c2) | big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2))))),
% 27.74/17.96 inference(rewrite,[status(thm)],[])).
% 27.74/17.96 tff(4409,plain,
% 27.74/17.96 (((~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), c2) = c2) | big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), c2))) <=> ((~big_f(f7(f9(c2, c2)), c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2))) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), c2) = c2) | big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2))))),
% 27.74/17.96 inference(rewrite,[status(thm)],[])).
% 27.74/17.96 tff(4410,plain,
% 27.74/17.96 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), c2) = c2) | big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~big_f(f7(f9(c2, c2)), c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2))) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), c2) = c2) | big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))))),
% 27.74/17.96 inference(monotonicity,[status(thm)],[4409])).
% 27.74/17.96 tff(4411,plain,
% 27.74/17.96 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), c2) = c2) | big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~big_f(f7(f9(c2, c2)), c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2))) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), c2) = c2) | big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2))))),
% 27.74/17.96 inference(transitivity,[status(thm)],[4410, 4408])).
% 27.74/17.96 tff(4412,plain,
% 27.74/17.96 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), c2) = c2) | big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), c2)))),
% 27.74/17.96 inference(quant_inst,[status(thm)],[])).
% 27.74/17.96 tff(4413,plain,
% 27.74/17.96 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~big_f(f7(f9(c2, c2)), c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2))) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), c2) = c2) | big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))),
% 27.74/17.96 inference(modus_ponens,[status(thm)],[4412, 4411])).
% 27.74/17.96 tff(4414,plain,
% 27.74/17.96 ((~big_f(f7(f9(c2, c2)), c2)) | (c2 = f5(f9(c2, c2)))),
% 27.74/17.96 inference(unit_resolution,[status(thm)],[4413, 676, 3777, 3774, 4246, 4237])).
% 27.74/17.96 tff(4415,plain,
% 27.74/17.96 ($false),
% 27.74/17.96 inference(unit_resolution,[status(thm)],[4414, 242, 4407])).
% 27.74/17.96 tff(4416,plain,((f9(c1, c2) = c2) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~(f5(c1) = c1)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~big_f(c2, c2)) | (~(f7(c1) = c2)) | big_f(f9(c2, c2), f9(c2, c2)) | (~(f10(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 27.74/17.96 tff(4417,plain,
% 27.74/17.96 (f9(c1, c2) = c2),
% 27.74/17.96 inference(unit_resolution,[status(thm)],[4416, 4404, 230, 148, 79, 122, 4402, 4322, 3689, 3762])).
% 27.74/17.96 tff(4418,plain,
% 27.74/17.96 (f9(f9(c2, c2), c2) = c2),
% 27.74/17.96 inference(modus_ponens,[status(thm)],[4417, 4233])).
% 27.74/17.96 tff(4419,plain,
% 27.74/17.96 (big_f(f9(c1, c2), f10(c1)) <=> big_f(c2, f9(c2, c2))),
% 27.74/17.96 inference(monotonicity,[status(thm)],[4417, 3763])).
% 27.74/17.96 tff(4420,plain,
% 27.74/17.96 (big_f(c2, f9(c2, c2)) <=> big_f(f9(c1, c2), f10(c1))),
% 27.74/17.96 inference(symmetry,[status(thm)],[4419])).
% 27.74/17.96 tff(4421,plain,
% 27.74/17.96 (big_f(c2, f9(c2, c2)) <=> big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))),
% 27.74/17.96 inference(transitivity,[status(thm)],[4420, 4239])).
% 27.74/17.96 tff(4422,plain,
% 27.74/17.96 (big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))),
% 27.74/17.96 inference(modus_ponens,[status(thm)],[3719, 4421])).
% 27.74/17.96 tff(4423,plain,
% 27.74/17.96 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~big_f(f7(f9(c2, c2)), c2)) | (~big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2))) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f9(f9(c2, c2), c2) = c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~big_f(f7(f9(c2, c2)), c2)) | (~big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2))) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f9(f9(c2, c2), c2) = c2)))),
% 27.74/17.96 inference(rewrite,[status(thm)],[])).
% 27.74/17.96 tff(4424,plain,
% 27.74/17.96 (((~(f10(f9(c2, c2)) = f9(c2, c2))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), c2)) | (~(f9(f9(c2, c2), c2) = c2)) | (~big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2))))) <=> ((~big_f(f7(f9(c2, c2)), c2)) | (~big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2))) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f9(f9(c2, c2), c2) = c2)))),
% 27.74/17.96 inference(rewrite,[status(thm)],[])).
% 27.74/17.96 tff(4425,plain,
% 27.74/17.96 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), c2)) | (~(f9(f9(c2, c2), c2) = c2)) | (~big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~big_f(f7(f9(c2, c2)), c2)) | (~big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2))) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f9(f9(c2, c2), c2) = c2))))),
% 27.74/17.96 inference(monotonicity,[status(thm)],[4424])).
% 27.74/17.96 tff(4426,plain,
% 27.74/17.96 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), c2)) | (~(f9(f9(c2, c2), c2) = c2)) | (~big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~big_f(f7(f9(c2, c2)), c2)) | (~big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2))) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f9(f9(c2, c2), c2) = c2)))),
% 27.74/17.96 inference(transitivity,[status(thm)],[4425, 4423])).
% 27.74/17.96 tff(4427,plain,
% 27.74/17.96 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), c2)) | (~(f9(f9(c2, c2), c2) = c2)) | (~big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))))),
% 27.74/17.96 inference(quant_inst,[status(thm)],[])).
% 27.74/17.96 tff(4428,plain,
% 27.74/17.96 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~big_f(f7(f9(c2, c2)), c2)) | (~big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))) | (f7(f9(c2, c2)) = f9(c2, c2)) | (c2 = f5(f9(c2, c2))) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f9(f9(c2, c2), c2) = c2))),
% 27.74/17.96 inference(modus_ponens,[status(thm)],[4427, 4426])).
% 27.74/17.96 tff(4429,plain,
% 27.74/17.96 ((~big_f(f7(f9(c2, c2)), c2)) | (c2 = f5(f9(c2, c2)))),
% 27.74/17.96 inference(unit_resolution,[status(thm)],[4428, 1190, 3777, 4404, 4422, 4418])).
% 27.74/17.96 tff(4430,plain,
% 27.74/17.96 ($false),
% 27.74/17.96 inference(unit_resolution,[status(thm)],[4429, 242, 4403])).
% 27.74/17.96 tff(4431,plain,((~big_f(f9(c2, c2), c2)) | (~(f5(c1) = c1)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~big_f(c2, f9(c2, c2))) | (~(f10(c1) = c1)) | big_f(f9(c2, c2), f9(c2, c2)) | (f9(c2, c2) = c3) | (f9(f10(c2), f4(c4)) = c3)), inference(lemma,lemma(discharge,[]))).
% 27.74/17.96 tff(4432,plain,
% 27.74/17.96 (big_f(f9(c2, c2), f9(c2, c2))),
% 27.74/17.96 inference(unit_resolution,[status(thm)],[4431, 4231, 148, 79, 122, 4147, 3637, 4197, 3645, 3643])).
% 27.74/17.96 tff(4433,plain,
% 27.74/17.96 (big_f(c1, c2)),
% 27.74/17.96 inference(modus_ponens,[status(thm)],[4197, 3690])).
% 27.74/17.96 tff(4434,plain,
% 27.74/17.96 (f10(c1) = f9(c2, c2)),
% 27.74/17.96 inference(transitivity,[status(thm)],[3637, 149, 132])).
% 27.74/17.96 tff(4435,plain,
% 27.74/17.96 (f5(f10(c1)) = f5(f9(c2, c2))),
% 27.74/17.96 inference(monotonicity,[status(thm)],[4434])).
% 27.74/17.96 tff(4436,plain,
% 27.74/17.96 ((f5(f10(c1)) = c1) <=> (f5(f9(c2, c2)) = f9(c2, c2))),
% 27.74/17.96 inference(monotonicity,[status(thm)],[4435, 150])).
% 27.74/17.96 tff(4437,plain,
% 27.74/17.96 ((f5(f10(c1)) = c1) <=> (f9(c2, c2) = f5(f9(c2, c2)))),
% 27.74/17.96 inference(transitivity,[status(thm)],[4436, 193])).
% 27.74/17.96 tff(4438,plain,
% 27.74/17.96 ((f9(c2, c2) = f5(f9(c2, c2))) <=> (f5(f10(c1)) = c1)),
% 27.74/17.96 inference(symmetry,[status(thm)],[4437])).
% 27.74/17.96 tff(4439,plain,
% 27.74/17.96 ((f5(c1) = c1) <=> (f5(f10(c1)) = c1)),
% 27.74/17.96 inference(transitivity,[status(thm)],[171, 4438])).
% 27.74/17.96 tff(4440,plain,
% 27.74/17.96 (f5(f10(c1)) = c1),
% 27.74/17.96 inference(modus_ponens,[status(thm)],[4147, 4439])).
% 27.74/17.96 tff(4441,plain,
% 27.74/17.96 (f6(c2, c1) = f6(c2, f9(c2, c2))),
% 27.74/17.96 inference(monotonicity,[status(thm)],[150])).
% 27.74/17.96 tff(4442,plain,
% 27.74/17.96 (big_f(f7(c2), f6(c2, c1)) <=> big_f(f7(c2), f6(c2, f9(c2, c2)))),
% 27.74/17.96 inference(monotonicity,[status(thm)],[4441])).
% 27.74/17.96 tff(4443,plain,
% 27.74/17.96 (big_f(f7(c2), f6(c2, f9(c2, c2))) <=> big_f(f7(c2), f6(c2, c1))),
% 27.74/17.96 inference(symmetry,[status(thm)],[4442])).
% 27.74/17.96 tff(4444,plain,
% 27.74/17.96 (big_f(c2, f9(c2, c2))),
% 27.74/17.96 inference(unit_resolution,[status(thm)],[3814, 3881, 148, 79, 122])).
% 27.74/17.96 tff(4445,plain,
% 27.74/17.96 (f9(c2, c2) = f5(c1)),
% 27.74/17.96 inference(transitivity,[status(thm)],[160, 148, 2941])).
% 27.74/17.96 tff(4446,plain,
% 27.74/17.96 (f6(c2, f9(c2, c2)) = f6(f7(c2), f5(c1))),
% 27.74/17.96 inference(monotonicity,[status(thm)],[82, 4445])).
% 27.74/17.96 tff(4447,plain,
% 27.74/17.96 (f6(c2, f9(c2, c2)) = f9(c2, c2)),
% 27.74/17.96 inference(transitivity,[status(thm)],[4446, 2947, 149, 132])).
% 27.74/17.96 tff(4448,plain,
% 27.74/17.96 (big_f(f7(c2), f6(c2, f9(c2, c2))) <=> big_f(c2, f9(c2, c2))),
% 27.74/17.96 inference(monotonicity,[status(thm)],[77, 4447])).
% 27.74/17.96 tff(4449,plain,
% 27.74/17.96 (big_f(c2, f9(c2, c2)) <=> big_f(f7(c2), f6(c2, f9(c2, c2)))),
% 27.74/17.96 inference(symmetry,[status(thm)],[4448])).
% 27.74/17.96 tff(4450,plain,
% 27.74/17.96 (big_f(f7(c2), f6(c2, f9(c2, c2)))),
% 27.74/17.96 inference(modus_ponens,[status(thm)],[3719, 4449])).
% 27.74/17.96 tff(4451,plain,
% 27.74/17.96 ((f6(c2, f9(c2, c2)) = f9(c2, c2)) <=> (f6(f7(c2), f5(c1)) = c1)),
% 27.74/17.96 inference(monotonicity,[status(thm)],[4446, 161])).
% 27.74/17.96 tff(4452,plain,
% 27.74/17.96 ((f6(f7(c2), f5(c1)) = c1) <=> (f6(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.74/17.96 inference(symmetry,[status(thm)],[4451])).
% 27.74/17.96 tff(4453,plain,
% 27.74/17.96 (f6(c2, f9(c2, c2)) = f9(c2, c2)),
% 27.74/17.96 inference(modus_ponens,[status(thm)],[2947, 4452])).
% 27.74/17.96 tff(4454,plain,
% 27.74/17.96 (big_f(c2, f9(c2, c2)) <=> big_f(f7(c2), f6(c2, c1))),
% 27.74/17.96 inference(transitivity,[status(thm)],[4449, 4443])).
% 27.74/17.96 tff(4455,plain,
% 27.74/17.96 (big_f(f7(c2), f6(c2, c1))),
% 27.74/17.96 inference(modus_ponens,[status(thm)],[3719, 4454])).
% 27.74/17.96 tff(4456,plain,
% 27.74/17.96 ((f6(c2, c1) = c1) <=> (f6(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.74/17.96 inference(monotonicity,[status(thm)],[4441, 150])).
% 27.74/17.96 tff(4457,plain,
% 27.74/17.96 ((f6(c2, f9(c2, c2)) = f9(c2, c2)) <=> (f6(c2, c1) = c1)),
% 27.74/17.96 inference(symmetry,[status(thm)],[4456])).
% 27.74/17.96 tff(4458,plain,
% 27.74/17.96 ((f6(f7(c2), f5(c1)) = c1) <=> (f6(c2, c1) = c1)),
% 27.74/17.96 inference(transitivity,[status(thm)],[4452, 4457])).
% 27.74/17.96 tff(4459,plain,
% 27.74/17.96 (f6(c2, c1) = c1),
% 27.74/17.96 inference(modus_ponens,[status(thm)],[2947, 4458])).
% 27.74/17.96 tff(4460,plain,
% 27.74/17.96 (big_f(f9(c2, c1), f10(c2))),
% 27.74/17.96 inference(unit_resolution,[status(thm)],[3090, 4459, 122, 4455, 77, 2865])).
% 27.74/17.96 tff(4461,plain,
% 27.74/17.96 (big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 27.74/17.96 inference(unit_resolution,[status(thm)],[3898, 4460, 148, 79, 122])).
% 27.74/17.96 tff(4462,plain,
% 27.74/17.96 (c1 = f5(f10(c1))),
% 27.74/17.96 inference(symmetry,[status(thm)],[328])).
% 27.74/17.96 tff(4463,plain,
% 27.74/17.96 (f9(c2, c2) = f5(f10(c1))),
% 27.74/17.96 inference(transitivity,[status(thm)],[160, 148, 4462])).
% 27.74/17.96 tff(4464,plain,
% 27.74/17.96 (f9(c2, f9(c2, c2)) = f9(c2, f5(f10(c1)))),
% 27.74/17.96 inference(monotonicity,[status(thm)],[4463])).
% 27.74/17.96 tff(4465,plain,
% 27.74/17.96 (f9(c2, f5(f10(c1))) = f9(c2, f9(c2, c2))),
% 27.74/17.96 inference(symmetry,[status(thm)],[4464])).
% 27.74/17.96 tff(4466,plain,
% 27.74/17.96 ((f9(c2, f5(f10(c1))) = c1) <=> (f9(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.74/17.96 inference(monotonicity,[status(thm)],[4465, 150])).
% 27.74/17.96 tff(4467,plain,
% 27.74/17.96 ((f9(c2, f9(c2, c2)) = f9(c2, c2)) <=> (f9(c2, f5(f10(c1))) = c1)),
% 27.74/17.96 inference(symmetry,[status(thm)],[4466])).
% 27.74/17.96 tff(4468,plain,
% 27.74/17.96 ((~(f9(c2, f9(c2, c2)) = f9(c2, c2))) <=> (~(f9(c2, f5(f10(c1))) = c1))),
% 27.74/17.96 inference(monotonicity,[status(thm)],[4467])).
% 27.74/17.96 tff(4469,assumption,(~(f9(c2, f9(c2, c2)) = f9(c2, c2))), introduced(assumption)).
% 27.74/17.96 tff(4470,plain,
% 27.74/17.96 (~(f9(c2, f5(f10(c1))) = c1)),
% 27.74/17.96 inference(modus_ponens,[status(thm)],[4469, 4468])).
% 27.74/17.96 tff(4471,plain,
% 27.74/17.96 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f9(c2, f5(f10(c1))) = c1) | (f9(c2, f5(f10(c1))) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f9(c2, f5(f10(c1))) = c1) | (f9(c2, f5(f10(c1))) = c2))),
% 27.74/17.96 inference(rewrite,[status(thm)],[])).
% 27.74/17.96 tff(4472,plain,
% 27.74/17.96 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f9(c2, f5(f10(c1))) = c1) | (f9(c2, f5(f10(c1))) = c2))),
% 27.74/17.96 inference(quant_inst,[status(thm)],[])).
% 27.74/17.96 tff(4473,plain,
% 27.74/17.96 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f9(c2, f5(f10(c1))) = c1) | (f9(c2, f5(f10(c1))) = c2)),
% 27.74/17.96 inference(modus_ponens,[status(thm)],[4472, 4471])).
% 27.74/17.96 tff(4474,plain,
% 27.74/17.96 ((f9(c2, f5(f10(c1))) = c1) | (f9(c2, f5(f10(c1))) = c2)),
% 27.74/17.96 inference(unit_resolution,[status(thm)],[4473, 10])).
% 27.74/17.96 tff(4475,plain,
% 27.74/17.96 (f9(c2, f5(f10(c1))) = c2),
% 27.74/17.96 inference(unit_resolution,[status(thm)],[4474, 4470])).
% 27.74/17.96 tff(4476,plain,
% 27.74/17.96 (f9(c2, f9(c2, c2)) = c2),
% 27.74/17.96 inference(transitivity,[status(thm)],[4464, 4475])).
% 27.74/17.96 tff(4477,plain,
% 27.74/17.96 (big_f(f9(c2, f9(c2, c2)), f10(c2)) <=> big_f(c2, c2)),
% 27.74/17.96 inference(monotonicity,[status(thm)],[4476, 122])).
% 27.74/17.96 tff(4478,plain,
% 27.74/17.96 (big_f(c2, c2) <=> big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 27.74/17.96 inference(symmetry,[status(thm)],[4477])).
% 27.74/17.96 tff(4479,plain,
% 27.74/17.96 ((~big_f(c2, c2)) <=> (~big_f(f9(c2, f9(c2, c2)), f10(c2)))),
% 27.74/17.96 inference(monotonicity,[status(thm)],[4478])).
% 27.74/17.96 tff(4480,plain,
% 27.74/17.96 (~big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 27.74/17.96 inference(modus_ponens,[status(thm)],[121, 4479])).
% 27.74/17.96 tff(4481,plain,
% 27.74/17.96 ($false),
% 27.74/17.96 inference(unit_resolution,[status(thm)],[1146, 4480])).
% 27.74/17.96 tff(4482,plain,((~(f5(f10(c1)) = c1)) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | big_f(c2, c2) | (~(f10(c2) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 27.74/17.96 tff(4483,plain,
% 27.74/17.96 (f9(c2, f9(c2, c2)) = f9(c2, c2)),
% 27.74/17.96 inference(unit_resolution,[status(thm)],[4482, 4461, 122, 328, 148, 79, 121])).
% 27.74/17.96 tff(4484,plain,
% 27.74/17.96 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~(f6(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f6(c2, f9(c2, c2)))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~(f6(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f6(c2, f9(c2, c2)))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))))),
% 27.74/17.96 inference(rewrite,[status(thm)],[])).
% 27.74/17.96 tff(4485,plain,
% 27.74/17.96 (((~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f6(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f6(c2, f9(c2, c2))))) <=> ((~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~(f6(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f6(c2, f9(c2, c2)))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))))),
% 27.74/17.96 inference(rewrite,[status(thm)],[])).
% 27.74/17.96 tff(4486,plain,
% 27.74/17.96 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f6(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f6(c2, f9(c2, c2)))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~(f6(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f6(c2, f9(c2, c2)))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2)))))),
% 27.74/17.96 inference(monotonicity,[status(thm)],[4485])).
% 27.74/17.96 tff(4487,plain,
% 27.74/17.96 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f6(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f6(c2, f9(c2, c2)))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~(f6(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f6(c2, f9(c2, c2)))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))))),
% 27.74/17.96 inference(transitivity,[status(thm)],[4486, 4484])).
% 27.74/17.96 tff(4488,plain,
% 27.74/17.96 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f6(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f6(c2, f9(c2, c2)))))),
% 27.74/17.97 inference(quant_inst,[status(thm)],[])).
% 27.74/17.97 tff(4489,plain,
% 27.74/17.97 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~(f6(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f6(c2, f9(c2, c2)))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2)))),
% 27.74/17.97 inference(modus_ponens,[status(thm)],[4488, 4487])).
% 27.74/17.97 tff(4490,plain,
% 27.74/17.97 ($false),
% 27.74/17.97 inference(unit_resolution,[status(thm)],[4489, 2378, 122, 77, 4461, 4483, 4453, 4450])).
% 27.74/17.97 tff(4491,plain,((~(f6(f7(c2), f5(c1)) = c1)) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~(f5(f10(c1)) = c1)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | big_f(c2, c2) | (~big_f(c1, c2)) | (~big_f(c2, f9(c2, c2))) | (~(f5(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 27.74/17.97 tff(4492,plain,
% 27.74/17.97 (~(f6(f7(c2), f5(c1)) = c1)),
% 27.74/17.97 inference(unit_resolution,[status(thm)],[4491, 121, 77, 328, 148, 79, 122, 2865, 4444, 230])).
% 27.74/17.97 tff(4493,plain,
% 27.74/17.97 (f6(f7(c2), f5(c1)) = c2),
% 27.74/17.97 inference(unit_resolution,[status(thm)],[2978, 4492])).
% 27.74/17.97 tff(4494,plain,
% 27.74/17.97 (f6(c2, f9(c2, c2)) = c2),
% 27.74/17.97 inference(transitivity,[status(thm)],[4446, 4493])).
% 27.74/17.97 tff(4495,plain,
% 27.74/17.97 (big_f(f7(c2), f6(c2, f9(c2, c2))) <=> big_f(c2, c2)),
% 27.74/17.97 inference(monotonicity,[status(thm)],[77, 4494])).
% 27.74/17.97 tff(4496,plain,
% 27.74/17.97 (big_f(c2, c2) <=> big_f(f7(c2), f6(c2, f9(c2, c2)))),
% 27.74/17.97 inference(symmetry,[status(thm)],[4495])).
% 27.74/17.97 tff(4497,plain,
% 27.74/17.97 (big_f(c2, c2) <=> big_f(f7(c2), f6(c2, c1))),
% 27.74/17.97 inference(transitivity,[status(thm)],[4496, 4443])).
% 27.74/17.97 tff(4498,plain,
% 27.74/17.97 ((~big_f(c2, c2)) <=> (~big_f(f7(c2), f6(c2, c1)))),
% 27.74/17.97 inference(monotonicity,[status(thm)],[4497])).
% 27.74/17.97 tff(4499,plain,
% 27.74/17.97 (~big_f(f7(c2), f6(c2, c1))),
% 27.74/17.97 inference(modus_ponens,[status(thm)],[121, 4498])).
% 27.74/17.97 tff(4500,plain,
% 27.74/17.97 (f6(f7(c2), f5(c1)) = f6(c2, f9(c2, c2))),
% 27.74/17.97 inference(symmetry,[status(thm)],[4446])).
% 27.74/17.97 tff(4501,plain,
% 27.74/17.97 ((f6(f7(c2), f5(c1)) = c1) <=> (f6(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.74/17.97 inference(monotonicity,[status(thm)],[4500, 150])).
% 27.74/17.97 tff(4502,plain,
% 27.74/17.97 ((f6(f7(c2), f5(c1)) = c1) <=> (f6(c2, c1) = c1)),
% 27.74/17.97 inference(transitivity,[status(thm)],[4501, 4457])).
% 27.74/17.97 tff(4503,plain,
% 27.74/17.97 ((~(f6(f7(c2), f5(c1)) = c1)) <=> (~(f6(c2, c1) = c1))),
% 27.74/17.97 inference(monotonicity,[status(thm)],[4502])).
% 27.74/17.97 tff(4504,plain,
% 27.74/17.97 (~(f6(c2, c1) = c1)),
% 27.74/17.97 inference(modus_ponens,[status(thm)],[4492, 4503])).
% 27.74/17.97 tff(4505,plain,
% 27.74/17.97 (~(f9(c2, c1) = c1)),
% 27.74/17.97 inference(unit_resolution,[status(thm)],[3563, 4504, 122, 230, 77, 2865, 4499])).
% 27.74/17.97 tff(4506,plain,
% 27.74/17.97 (~(f9(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.74/17.97 inference(unit_resolution,[status(thm)],[1141, 4505, 122, 79, 148])).
% 27.74/17.97 tff(4507,plain,
% 27.74/17.97 (big_f(f9(c2, c1), f10(c2))),
% 27.74/17.97 inference(unit_resolution,[status(thm)],[3211, 4499, 122, 77, 4504, 4505])).
% 27.74/17.97 tff(4508,plain,
% 27.74/17.97 (big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 27.74/17.97 inference(unit_resolution,[status(thm)],[3898, 4507, 148, 79, 122])).
% 27.74/17.97 tff(4509,plain,
% 27.74/17.97 ($false),
% 27.74/17.97 inference(unit_resolution,[status(thm)],[4482, 4508, 4506, 122, 328, 148, 79, 121])).
% 27.74/17.97 tff(4510,plain,(big_f(c2, c2) | (~(f10(c2) = c2)) | (~(f5(f10(c1)) = c1)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f7(c2) = c2)) | (~(f5(c1) = c1)) | (~big_f(c1, c2)) | (~(c3 = c2))), inference(lemma,lemma(discharge,[]))).
% 27.74/17.97 tff(4511,plain,
% 27.74/17.97 (big_f(c2, c2)),
% 27.74/17.97 inference(unit_resolution,[status(thm)],[4510, 4440, 122, 148, 79, 77, 4147, 4433, 181])).
% 27.74/17.97 tff(4512,plain,
% 27.74/17.97 (~(c4 = c1)),
% 27.74/17.97 inference(unit_resolution,[status(thm)],[4027, 4231, 4067, 4511, 4432, 79, 148, 122])).
% 27.74/17.97 tff(4513,plain,
% 27.74/17.97 (c4 = c2),
% 27.74/17.97 inference(unit_resolution,[status(thm)],[461, 4512])).
% 27.74/17.97 tff(4514,plain,
% 27.74/17.97 (c2 = c4),
% 27.74/17.97 inference(symmetry,[status(thm)],[4513])).
% 27.74/17.97 tff(4515,plain,
% 27.74/17.97 (f4(c2) = f4(c4)),
% 27.74/17.97 inference(monotonicity,[status(thm)],[4514])).
% 27.74/17.97 tff(4516,plain,
% 27.74/17.97 (f4(c2) = c2),
% 27.74/17.97 inference(transitivity,[status(thm)],[4515, 79])).
% 27.74/17.97 tff(4517,plain,
% 27.74/17.97 ((f9(c2, c2) = f4(c2)) <=> (f9(c2, c2) = c2)),
% 27.74/17.97 inference(monotonicity,[status(thm)],[4516])).
% 27.74/17.97 tff(4518,plain,
% 27.74/17.97 ((f9(c2, c2) = c2) <=> (f9(c2, c2) = f4(c2))),
% 27.74/17.97 inference(symmetry,[status(thm)],[4517])).
% 27.74/17.97 tff(4519,plain,
% 27.74/17.97 ((~(f9(c2, c2) = c2)) <=> (~(f9(c2, c2) = f4(c2)))),
% 27.74/17.97 inference(monotonicity,[status(thm)],[4518])).
% 27.74/17.97 tff(4520,plain,
% 27.74/17.97 (~(f9(c2, c2) = f4(c2))),
% 27.74/17.97 inference(modus_ponens,[status(thm)],[185, 4519])).
% 27.74/17.97 tff(4521,plain,
% 27.74/17.97 (c2 = c4),
% 27.74/17.97 inference(modus_ponens,[status(thm)],[4513, 159])).
% 27.74/17.97 tff(4522,plain,
% 27.74/17.97 ((~(c2 = c4)) | (c2 = f2(c2)) | (f9(c2, c2) = f4(c2))),
% 27.74/17.97 inference(unit_resolution,[status(thm)],[4087, 1355, 4511, 4067, 4197])).
% 27.74/17.97 tff(4523,plain,
% 27.74/17.97 (c2 = f2(c2)),
% 27.74/17.97 inference(unit_resolution,[status(thm)],[4522, 4521, 4520])).
% 27.74/17.97 tff(4524,plain,
% 27.74/17.97 (f2(c2) = c2),
% 27.74/17.97 inference(symmetry,[status(thm)],[4523])).
% 27.74/17.97 tff(4525,plain,
% 27.74/17.97 (f9(c2, c2) = f2(c2)),
% 27.74/17.97 inference(unit_resolution,[status(thm)],[4119, 1355, 4521, 4067, 4231, 4197, 4520])).
% 27.74/17.97 tff(4526,plain,
% 27.74/17.97 (f9(c2, c2) = c2),
% 27.74/17.97 inference(transitivity,[status(thm)],[4525, 4524])).
% 27.74/17.97 tff(4527,plain,
% 27.74/17.97 ($false),
% 27.74/17.97 inference(unit_resolution,[status(thm)],[185, 4526])).
% 27.74/17.97 tff(4528,plain,((~(f7(c2) = c2)) | (~(f4(c4) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f10(c2) = c2)) | (c1 = c3) | (f7(c1) = c1) | (f9(f10(c2), f10(c2)) = f10(c2))), inference(lemma,lemma(discharge,[]))).
% 27.74/17.97 tff(4529,plain,
% 27.74/17.97 (~(f7(c2) = c2)),
% 27.74/17.97 inference(unit_resolution,[status(thm)],[4528, 168, 148, 122, 79, 115, 158])).
% 27.74/17.97 tff(4530,plain,
% 27.74/17.97 ((f9(c2, c2) = c3) <=> (f9(c2, c2) = c2)),
% 27.74/17.97 inference(monotonicity,[status(thm)],[67])).
% 27.74/17.97 tff(4531,plain,
% 27.74/17.97 ((f9(c2, c2) = c2) <=> (f9(c2, c2) = c3)),
% 27.74/17.97 inference(symmetry,[status(thm)],[4530])).
% 27.74/17.97 tff(4532,plain,
% 27.74/17.97 ((~(f9(c2, c2) = c2)) <=> (~(f9(c2, c2) = c3))),
% 27.74/17.97 inference(monotonicity,[status(thm)],[4531])).
% 27.74/17.97 tff(4533,plain,
% 27.74/17.97 (~(f9(c2, c2) = c3)),
% 27.74/17.97 inference(modus_ponens,[status(thm)],[185, 4532])).
% 27.74/17.97 tff(4534,plain,
% 27.74/17.97 (big_f(f7(c2), c1) <=> big_f(f7(c2), f9(c2, c2))),
% 27.74/17.97 inference(monotonicity,[status(thm)],[150])).
% 27.74/17.97 tff(4535,plain,
% 27.74/17.97 (big_f(f7(c2), f9(c2, c2)) <=> big_f(f7(c2), c1)),
% 27.74/17.97 inference(symmetry,[status(thm)],[4534])).
% 27.74/17.97 tff(4536,plain,
% 27.74/17.97 (big_f(f7(c2), f9(c2, c2)) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 27.74/17.97 inference(monotonicity,[status(thm)],[1151])).
% 27.74/17.97 tff(4537,plain,
% 27.74/17.97 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f7(c2), f9(c2, c2))),
% 27.74/17.97 inference(symmetry,[status(thm)],[4536])).
% 27.74/17.97 tff(4538,plain,
% 27.74/17.97 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f7(c2), c1)),
% 27.74/17.97 inference(transitivity,[status(thm)],[4537, 4535])).
% 27.74/17.97 tff(4539,plain,
% 27.74/17.97 (big_f(f7(c2), c1)),
% 27.74/17.97 inference(modus_ponens,[status(thm)],[487, 4538])).
% 27.74/17.97 tff(4540,plain,
% 27.74/17.97 ((f9(c2, c2) = c3) <=> (c1 = c3)),
% 27.74/17.97 inference(symmetry,[status(thm)],[3640])).
% 27.74/17.97 tff(4541,plain,
% 27.74/17.97 ((f9(c2, c2) = c2) <=> (c1 = c3)),
% 27.74/17.97 inference(transitivity,[status(thm)],[4531, 4540])).
% 27.74/17.97 tff(4542,plain,
% 27.74/17.97 ((~(f9(c2, c2) = c2)) <=> (~(c1 = c3))),
% 27.74/17.97 inference(monotonicity,[status(thm)],[4541])).
% 27.74/17.97 tff(4543,plain,
% 27.74/17.97 (~(c1 = c3)),
% 27.74/17.97 inference(modus_ponens,[status(thm)],[185, 4542])).
% 27.74/17.97 tff(4544,plain,
% 27.74/17.97 (big_f(f7(c2), f9(c2, c2))),
% 27.74/17.97 inference(modus_ponens,[status(thm)],[487, 4537])).
% 27.74/17.97 tff(4545,plain,
% 27.74/17.97 (~(c4 = c1)),
% 27.74/17.97 inference(unit_resolution,[status(thm)],[616, 256, 148, 292, 79, 122, 566, 338])).
% 27.74/17.97 tff(4546,plain,
% 27.74/17.97 (c4 = c2),
% 27.74/17.97 inference(unit_resolution,[status(thm)],[461, 4545])).
% 27.74/17.97 tff(4547,plain,
% 27.74/17.97 (c2 = c4),
% 27.74/17.97 inference(modus_ponens,[status(thm)],[4546, 159])).
% 27.74/17.97 tff(4548,plain,
% 27.74/17.97 (c2 = c4),
% 27.74/17.97 inference(symmetry,[status(thm)],[4546])).
% 27.74/17.97 tff(4549,plain,
% 27.74/17.97 (f4(c2) = f4(c4)),
% 27.74/17.97 inference(monotonicity,[status(thm)],[4548])).
% 27.74/17.97 tff(4550,plain,
% 27.74/17.97 (f4(c4) = f4(c2)),
% 27.74/17.97 inference(symmetry,[status(thm)],[4549])).
% 27.74/17.97 tff(4551,plain,
% 27.74/17.97 (c2 = f4(c2)),
% 27.74/17.97 inference(transitivity,[status(thm)],[436, 4550])).
% 27.74/17.97 tff(4552,plain,
% 27.74/17.97 (~(f1(c1, c1) = c1)),
% 27.74/17.97 inference(unit_resolution,[status(thm)],[640, 4551, 148, 292, 121, 338, 566, 79, 122, 4547])).
% 27.74/17.97 tff(4553,plain,
% 27.74/17.97 (f1(c1, c1) = c2),
% 27.74/17.97 inference(unit_resolution,[status(thm)],[601, 4552])).
% 27.74/17.97 tff(4554,plain,
% 27.74/17.97 (big_f(c1, f1(c1, c1))),
% 27.74/17.97 inference(unit_resolution,[status(thm)],[656, 4552, 168, 121, 4551, 4547])).
% 27.74/17.97 tff(4555,plain,
% 27.74/17.97 (big_f(c1, f1(c1, c1)) <=> big_f(c1, c2)),
% 27.74/17.97 inference(monotonicity,[status(thm)],[575])).
% 27.74/17.97 tff(4556,plain,
% 27.74/17.97 (big_f(c1, c2) <=> big_f(c1, f1(c1, c1))),
% 27.74/17.97 inference(symmetry,[status(thm)],[4555])).
% 27.74/17.97 tff(4557,plain,
% 27.74/17.97 ((~big_f(c1, c2)) <=> (~big_f(c1, f1(c1, c1)))),
% 27.74/17.97 inference(monotonicity,[status(thm)],[4556])).
% 27.74/17.97 tff(4558,plain,
% 27.74/17.97 (~big_f(c1, f1(c1, c1))),
% 27.74/17.97 inference(modus_ponens,[status(thm)],[27, 4557])).
% 27.74/17.97 tff(4559,assumption,(big_f(c1, f1(c1, c1))), introduced(assumption)).
% 27.74/17.97 tff(4560,plain,
% 27.74/17.97 ($false),
% 27.74/17.97 inference(unit_resolution,[status(thm)],[4559, 4558])).
% 27.74/17.97 tff(4561,plain,((~(f1(c1, c1) = c2)) | (~big_f(c1, f1(c1, c1))) | big_f(c1, c2)), inference(lemma,lemma(discharge,[]))).
% 27.74/17.97 tff(4562,plain,
% 27.74/17.97 (big_f(c1, c2)),
% 27.74/17.97 inference(unit_resolution,[status(thm)],[4561, 4554, 4553])).
% 27.74/17.97 tff(4563,plain,
% 27.74/17.97 (big_f(f9(c2, c2), f10(c2))),
% 27.74/17.97 inference(modus_ponens,[status(thm)],[4562, 3679])).
% 27.74/17.97 tff(4564,plain,
% 27.74/17.97 ($false),
% 27.74/17.97 inference(unit_resolution,[status(thm)],[256, 4563])).
% 27.74/17.97 tff(4565,plain,(big_f(f9(c2, c2), f10(c2)) | (~(f10(c2) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (c1 = c3) | big_f(c2, c2) | (~(f7(c2) = c1)) | (~big_f(f7(c2), c1)) | (f9(c2, c2) = c3)), inference(lemma,lemma(discharge,[]))).
% 27.74/17.97 tff(4566,plain,
% 27.74/17.97 (big_f(f9(c2, c2), f10(c2))),
% 27.74/17.97 inference(unit_resolution,[status(thm)],[4565, 121, 148, 79, 168, 122, 22, 338, 566])).
% 27.74/17.97 tff(4567,plain,
% 27.74/17.97 (big_f(f9(c2, c1), f10(c2))),
% 27.74/17.97 inference(unit_resolution,[status(thm)],[1173, 4566, 148, 17, 1163, 79, 122])).
% 27.74/17.97 tff(4568,plain,
% 27.74/17.97 (big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 27.74/17.97 inference(unit_resolution,[status(thm)],[3898, 4567, 148, 79, 122])).
% 27.74/17.97 tff(4569,plain,
% 27.74/17.97 (big_f(f7(c2), c2) <=> big_f(f9(c2, c2), c2)),
% 27.74/17.97 inference(monotonicity,[status(thm)],[1151])).
% 27.74/17.97 tff(4570,plain,
% 27.74/17.97 (big_f(f9(c2, c2), c2) <=> big_f(f7(c2), c2)),
% 27.74/17.97 inference(symmetry,[status(thm)],[4569])).
% 27.74/17.97 tff(4571,plain,
% 27.74/17.97 (big_f(f9(c2, c2), c2)),
% 27.74/17.97 inference(unit_resolution,[status(thm)],[3687, 4566, 122])).
% 27.74/17.97 tff(4572,plain,
% 27.74/17.97 (big_f(f7(c2), c2)),
% 27.74/17.97 inference(modus_ponens,[status(thm)],[4571, 4570])).
% 27.74/17.97 tff(4573,plain,
% 27.74/17.97 (~(f9(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.74/17.97 inference(unit_resolution,[status(thm)],[1211, 4572, 122, 17, 4568, 1163, 185])).
% 27.74/17.97 tff(4574,plain,
% 27.74/17.97 ((f9(c2, c1) = c1) <=> (f9(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.74/17.97 inference(monotonicity,[status(thm)],[3892, 150])).
% 27.74/17.97 tff(4575,plain,
% 27.74/17.97 ((f9(c2, f9(c2, c2)) = f9(c2, c2)) <=> (f9(c2, c1) = c1)),
% 27.74/17.97 inference(symmetry,[status(thm)],[4574])).
% 27.74/17.97 tff(4576,plain,
% 27.74/17.97 ((~(f9(c2, f9(c2, c2)) = f9(c2, c2))) <=> (~(f9(c2, c1) = c1))),
% 27.74/17.97 inference(monotonicity,[status(thm)],[4575])).
% 27.74/17.97 tff(4577,plain,
% 27.74/17.97 (~(f9(c2, c1) = c1)),
% 27.74/17.97 inference(modus_ponens,[status(thm)],[4469, 4576])).
% 27.74/17.97 tff(4578,plain,
% 27.74/17.97 ($false),
% 27.74/17.97 inference(unit_resolution,[status(thm)],[736, 4577])).
% 27.74/17.97 tff(4579,plain,((~(f9(c2, c1) = c1)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.74/17.97 tff(4580,plain,
% 27.74/17.97 (~(f9(c2, c1) = c1)),
% 27.74/17.97 inference(unit_resolution,[status(thm)],[4579, 4573, 148, 79, 122])).
% 27.74/17.97 tff(4581,plain,
% 27.74/17.97 (f9(c2, c1) = c2),
% 27.74/17.97 inference(unit_resolution,[status(thm)],[3913, 4580])).
% 27.74/17.97 tff(4582,plain,
% 27.74/17.97 (f9(c2, f9(c2, c2)) = c2),
% 27.74/17.97 inference(transitivity,[status(thm)],[3818, 4581])).
% 27.74/17.97 tff(4583,plain,
% 27.74/17.97 (big_f(f9(c2, f9(c2, c2)), f10(c2)) <=> big_f(c2, c2)),
% 27.74/17.97 inference(monotonicity,[status(thm)],[4582, 122])).
% 27.74/17.97 tff(4584,plain,
% 27.74/17.97 (big_f(c2, c2) <=> big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 27.74/17.97 inference(symmetry,[status(thm)],[4583])).
% 27.74/17.97 tff(4585,plain,
% 27.74/17.97 ((~big_f(c2, c2)) <=> (~big_f(f9(c2, f9(c2, c2)), f10(c2)))),
% 27.74/17.97 inference(monotonicity,[status(thm)],[4584])).
% 27.74/17.97 tff(4586,plain,
% 27.74/17.97 (~big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 27.74/17.97 inference(modus_ponens,[status(thm)],[121, 4585])).
% 27.74/17.97 tff(4587,plain,
% 27.74/17.97 ($false),
% 27.74/17.97 inference(unit_resolution,[status(thm)],[4568, 4586])).
% 27.74/17.97 tff(4588,plain,(big_f(c2, c2) | (~(f10(c2) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (f7(c2) = c2) | (~big_f(f7(c2), f9(c2, c2))) | (c1 = c3) | (~big_f(f7(c2), c1)) | (f9(c2, c2) = c3)), inference(lemma,lemma(discharge,[]))).
% 27.74/17.97 tff(4589,plain,
% 27.74/17.97 (big_f(c2, c2)),
% 27.74/17.97 inference(unit_resolution,[status(thm)],[4588, 17, 148, 79, 122, 4544, 4543, 4539, 4533])).
% 27.74/17.97 tff(4590,plain,
% 27.74/17.97 (f7(c3) = f7(c2)),
% 27.74/17.97 inference(monotonicity,[status(thm)],[67])).
% 27.74/17.97 tff(4591,plain,
% 27.74/17.97 (big_f(f7(c3), c2) <=> big_f(f7(c2), c2)),
% 27.74/17.97 inference(monotonicity,[status(thm)],[4590])).
% 27.74/17.97 tff(4592,plain,
% 27.74/17.97 (big_f(f7(c2), c2) <=> big_f(f7(c3), c2)),
% 27.74/17.97 inference(symmetry,[status(thm)],[4591])).
% 27.74/17.97 tff(4593,plain,
% 27.74/17.97 (big_f(f9(c2, c2), c2) <=> big_f(f7(c3), c2)),
% 27.74/17.97 inference(transitivity,[status(thm)],[4570, 4592])).
% 27.74/17.97 tff(4594,plain,
% 27.74/17.97 (f6(f9(c2, c2), f9(c2, c2)) = f6(c1, c1)),
% 27.74/17.97 inference(monotonicity,[status(thm)],[161, 161])).
% 27.74/17.97 tff(4595,plain,
% 27.74/17.97 ((f6(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) <=> (f6(c1, c1) = c1)),
% 27.74/17.97 inference(monotonicity,[status(thm)],[4594, 161])).
% 27.74/17.97 tff(4596,plain,
% 27.74/17.97 ((f6(c1, c1) = c1) <=> (f6(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))),
% 27.74/17.97 inference(symmetry,[status(thm)],[4595])).
% 27.74/17.97 tff(4597,plain,
% 27.74/17.97 (~big_f(f9(c2, c2), f10(c2))),
% 27.74/17.97 inference(unit_resolution,[status(thm)],[3687, 3685, 122])).
% 27.74/17.97 tff(4598,plain,
% 27.74/17.97 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~big_f(f7(c2), f9(c2, c2))) | (f9(c2, c2) = f5(c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~big_f(f7(c2), f9(c2, c2))) | (f9(c2, c2) = f5(c2)))),
% 27.74/17.97 inference(rewrite,[status(thm)],[])).
% 27.74/17.97 tff(4599,plain,
% 27.74/17.97 (((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(c2) = c2) | (f9(c2, c2) = f5(c2)) | (~big_f(f7(c2), f9(c2, c2)))) <=> ((~(f10(c2) = c2)) | (f7(c2) = c2) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~big_f(f7(c2), f9(c2, c2))) | (f9(c2, c2) = f5(c2)))),
% 27.74/17.97 inference(rewrite,[status(thm)],[])).
% 27.74/17.97 tff(4600,plain,
% 27.74/17.97 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(c2) = c2) | (f9(c2, c2) = f5(c2)) | (~big_f(f7(c2), f9(c2, c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~big_f(f7(c2), f9(c2, c2))) | (f9(c2, c2) = f5(c2))))),
% 27.74/17.97 inference(monotonicity,[status(thm)],[4599])).
% 27.74/17.97 tff(4601,plain,
% 27.74/17.97 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(c2) = c2) | (f9(c2, c2) = f5(c2)) | (~big_f(f7(c2), f9(c2, c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~big_f(f7(c2), f9(c2, c2))) | (f9(c2, c2) = f5(c2)))),
% 27.74/17.97 inference(transitivity,[status(thm)],[4600, 4598])).
% 27.74/17.97 tff(4602,plain,
% 27.74/17.97 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(c2) = c2) | (f9(c2, c2) = f5(c2)) | (~big_f(f7(c2), f9(c2, c2))))),
% 27.74/17.97 inference(quant_inst,[status(thm)],[])).
% 27.74/17.97 tff(4603,plain,
% 27.74/17.97 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~big_f(f7(c2), f9(c2, c2))) | (f9(c2, c2) = f5(c2))),
% 27.74/17.97 inference(modus_ponens,[status(thm)],[4602, 4601])).
% 27.74/17.97 tff(4604,plain,
% 27.74/17.97 (big_f(f9(c2, c2), f10(c2)) | (f9(c2, c2) = f5(c2))),
% 27.74/17.97 inference(unit_resolution,[status(thm)],[4603, 676, 122, 17, 185, 4544])).
% 27.74/17.97 tff(4605,plain,
% 27.74/17.97 (f9(c2, c2) = f5(c2)),
% 27.74/17.97 inference(unit_resolution,[status(thm)],[4604, 4597])).
% 27.74/17.97 tff(4606,plain,
% 27.74/17.97 (f5(c2) = f9(c2, c2)),
% 27.74/17.97 inference(symmetry,[status(thm)],[4605])).
% 27.74/17.97 tff(4607,plain,
% 27.74/17.97 (f5(c2) = c1),
% 27.74/17.97 inference(transitivity,[status(thm)],[4606, 160, 148])).
% 27.74/17.97 tff(4608,plain,
% 27.74/17.97 ((f6(c1, c1) = f5(c2)) <=> (f6(c1, c1) = c1)),
% 27.74/17.97 inference(monotonicity,[status(thm)],[4607])).
% 27.74/17.97 tff(4609,plain,
% 27.74/17.97 ((f6(c1, c1) = f5(c2)) <=> (f6(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))),
% 27.74/17.97 inference(transitivity,[status(thm)],[4608, 4596])).
% 27.74/17.97 tff(4610,plain,
% 27.74/17.97 (~(c4 = c1)),
% 27.74/17.97 inference(unit_resolution,[status(thm)],[616, 4597, 148, 292, 79, 122, 566, 338])).
% 27.74/17.97 tff(4611,plain,
% 27.74/17.97 (c4 = c2),
% 27.74/17.97 inference(unit_resolution,[status(thm)],[461, 4610])).
% 27.74/17.97 tff(4612,plain,
% 27.74/17.97 ((f9(f10(c2), f4(c4)) = c4) <=> (f9(c2, c2) = c2)),
% 27.74/17.97 inference(monotonicity,[status(thm)],[132, 431])).
% 27.74/17.97 tff(4613,plain,
% 27.74/17.97 ((f9(c2, c2) = c2) <=> (f9(f10(c2), f4(c4)) = c4)),
% 27.74/17.97 inference(symmetry,[status(thm)],[4612])).
% 27.74/17.97 tff(4614,plain,
% 27.74/17.97 ((f9(c2, c2) = c2) <=> (f9(c2, c2) = c4)),
% 27.74/17.97 inference(transitivity,[status(thm)],[4613, 359])).
% 27.74/17.97 tff(4615,plain,
% 27.74/17.97 ((~(f9(c2, c2) = c2)) <=> (~(f9(c2, c2) = c4))),
% 27.74/17.97 inference(monotonicity,[status(thm)],[4614])).
% 27.74/17.97 tff(4616,plain,
% 27.74/17.97 (~(f9(c2, c2) = c4)),
% 27.74/17.97 inference(modus_ponens,[status(thm)],[1209, 4615])).
% 27.74/17.97 tff(4617,plain,
% 27.74/17.97 ($false),
% 27.74/17.97 inference(unit_resolution,[status(thm)],[514, 4616])).
% 27.74/17.97 tff(4618,plain,((~(c4 = c2)) | (~(f9(c2, c2) = c4)) | (f9(c2, c2) = c2) | (~(f4(c4) = c2)) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.74/17.97 tff(4619,plain,
% 27.74/17.97 (~(f9(c2, c2) = c4)),
% 27.74/17.97 inference(unit_resolution,[status(thm)],[4618, 4611, 122, 79, 185])).
% 27.74/17.97 tff(4620,plain,
% 27.74/17.97 (~(f3(c1, c1) = c1)),
% 27.74/17.97 inference(unit_resolution,[status(thm)],[1968, 4619, 148, 566, 292, 79, 122, 338, 4597])).
% 27.74/17.97 tff(4621,plain,
% 27.74/17.97 (f3(c1, c1) = c2),
% 27.74/17.97 inference(unit_resolution,[status(thm)],[1416, 4620])).
% 27.74/17.97 tff(4622,plain,
% 27.74/17.97 (~(f1(c1, c1) = c1)),
% 27.74/17.97 inference(unit_resolution,[status(thm)],[1979, 2, 148, 566, 4621, 79, 122, 292, 338, 4619])).
% 27.74/17.97 tff(4623,plain,
% 27.74/17.97 ((~(f9(c2, c2) = c4)) <=> (~(c1 = c4))),
% 27.74/17.97 inference(monotonicity,[status(thm)],[4136])).
% 27.74/17.97 tff(4624,plain,
% 27.74/17.97 (~(c1 = c4)),
% 27.74/17.97 inference(modus_ponens,[status(thm)],[4619, 4623])).
% 27.74/17.97 tff(4625,plain,
% 27.74/17.97 (big_f(f3(c1, c1), c1) <=> big_f(c2, f9(c2, c2))),
% 27.74/17.97 inference(monotonicity,[status(thm)],[4621, 150])).
% 27.74/17.97 tff(4626,plain,
% 27.74/17.97 (big_f(c2, f9(c2, c2)) <=> big_f(f3(c1, c1), c1)),
% 27.74/17.97 inference(symmetry,[status(thm)],[4625])).
% 27.74/17.97 tff(4627,plain,
% 27.74/17.97 (big_f(c2, c1) <=> big_f(f3(c1, c1), c1)),
% 27.74/17.97 inference(transitivity,[status(thm)],[3716, 4626])).
% 27.74/17.97 tff(4628,plain,
% 27.74/17.97 ((~big_f(c2, c1)) <=> (~big_f(f3(c1, c1), c1))),
% 27.74/17.97 inference(monotonicity,[status(thm)],[4627])).
% 27.74/17.97 tff(4629,plain,
% 27.74/17.97 (~big_f(f3(c1, c1), c1)),
% 27.74/17.97 inference(modus_ponens,[status(thm)],[2, 4628])).
% 27.74/17.97 tff(4630,plain,
% 27.74/17.97 (f1(c1, c1) = c2),
% 27.74/17.97 inference(unit_resolution,[status(thm)],[601, 4622])).
% 27.74/17.97 tff(4631,plain,
% 27.74/17.97 (big_f(c1, f1(c1, c1)) <=> big_f(f9(c2, c2), c2)),
% 27.74/17.97 inference(monotonicity,[status(thm)],[150, 4630])).
% 27.74/17.97 tff(4632,plain,
% 27.74/17.97 (big_f(f9(c2, c2), c2) <=> big_f(c1, f1(c1, c1))),
% 27.74/17.97 inference(symmetry,[status(thm)],[4631])).
% 27.74/17.97 tff(4633,plain,
% 27.74/17.97 ((~big_f(f9(c2, c2), c2)) <=> (~big_f(c1, f1(c1, c1)))),
% 27.74/17.97 inference(monotonicity,[status(thm)],[4632])).
% 27.74/17.97 tff(4634,plain,
% 27.74/17.97 (~big_f(c1, f1(c1, c1))),
% 27.74/17.97 inference(modus_ponens,[status(thm)],[3685, 4633])).
% 27.74/17.97 tff(4635,plain,
% 27.74/17.97 ($false),
% 27.74/17.97 inference(unit_resolution,[status(thm)],[2005, 4634, 4629, 168, 4620, 4624, 4622])).
% 27.74/17.97 tff(4636,plain,(big_f(c2, c1) | (c1 = c3) | big_f(f9(c2, c2), c2) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (f9(c2, c2) = c3) | (~(f7(c2) = c1)) | (~big_f(f7(c2), c1))), inference(lemma,lemma(discharge,[]))).
% 27.74/17.97 tff(4637,plain,
% 27.74/17.97 (big_f(c2, c1)),
% 27.74/17.97 inference(unit_resolution,[status(thm)],[4636, 3685, 168, 148, 79, 122, 566, 22, 4539])).
% 27.74/17.97 tff(4638,plain,
% 27.74/17.97 (~(f7(c1) = c2)),
% 27.74/17.97 inference(unit_resolution,[status(thm)],[1810, 4637, 122, 1792, 148, 79, 4597])).
% 27.74/17.97 tff(4639,plain,
% 27.74/17.97 (f7(c1) = c1),
% 27.74/17.97 inference(unit_resolution,[status(thm)],[119, 4638])).
% 27.74/17.97 tff(4640,plain,
% 27.74/17.97 (c1 = f7(c1)),
% 27.74/17.97 inference(symmetry,[status(thm)],[4639])).
% 27.74/17.97 tff(4641,plain,
% 27.74/17.97 (f7(c2) = f7(c1)),
% 27.74/17.97 inference(transitivity,[status(thm)],[22, 4640])).
% 27.74/17.97 tff(4642,plain,
% 27.74/17.97 (big_f(f7(c2), f6(c1, c1)) <=> big_f(f7(c1), f6(c1, c1))),
% 27.74/17.97 inference(monotonicity,[status(thm)],[4641])).
% 27.74/17.97 tff(4643,plain,
% 27.74/17.97 (big_f(f7(c1), f6(c1, c1)) <=> big_f(f7(c2), f6(c1, c1))),
% 27.74/17.97 inference(symmetry,[status(thm)],[4642])).
% 27.74/17.97 tff(4644,plain,
% 27.74/17.97 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f6(c1, c1) = c1))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f10(c2) = c2)) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f6(c1, c1) = c1))),
% 27.74/17.97 inference(rewrite,[status(thm)],[])).
% 27.74/17.97 tff(4645,plain,
% 27.74/17.97 (((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1))) <=> ((~(f10(c2) = c2)) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f6(c1, c1) = c1))),
% 27.74/17.97 inference(rewrite,[status(thm)],[])).
% 27.74/17.98 tff(4646,plain,
% 27.74/17.98 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f6(c1, c1) = c1)))),
% 27.74/17.98 inference(monotonicity,[status(thm)],[4645])).
% 27.74/17.98 tff(4647,plain,
% 27.74/17.98 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f10(c2) = c2)) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f6(c1, c1) = c1))),
% 27.74/17.98 inference(transitivity,[status(thm)],[4646, 4644])).
% 27.74/17.98 tff(4648,plain,
% 27.74/17.98 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1)))),
% 27.74/17.98 inference(quant_inst,[status(thm)],[])).
% 27.74/17.98 tff(4649,plain,
% 27.74/17.98 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f10(c2) = c2)) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f6(c1, c1) = c1)),
% 27.74/17.98 inference(modus_ponens,[status(thm)],[4648, 4647])).
% 27.74/17.98 tff(4650,plain,
% 27.74/17.98 ((~(f10(c2) = c2)) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f6(c1, c1) = c1)),
% 27.74/17.98 inference(unit_resolution,[status(thm)],[4649, 2492])).
% 27.74/17.98 tff(4651,plain,
% 27.74/17.98 (f6(c1, c1) = c1),
% 27.74/17.98 inference(unit_resolution,[status(thm)],[4650, 65, 122, 2650, 4234, 256])).
% 27.74/17.98 tff(4652,plain,
% 27.74/17.98 (f6(c1, c1) = f9(c2, c2)),
% 27.74/17.98 inference(transitivity,[status(thm)],[4651, 149, 132])).
% 27.74/17.98 tff(4653,plain,
% 27.74/17.98 (f7(c1) = f9(c2, c2)),
% 27.74/17.98 inference(transitivity,[status(thm)],[4234, 149, 132])).
% 27.74/17.98 tff(4654,plain,
% 27.74/17.98 (big_f(f7(c1), f6(c1, c1)) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 27.74/17.98 inference(monotonicity,[status(thm)],[4653, 4652])).
% 27.74/17.98 tff(4655,plain,
% 27.74/17.98 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f7(c1), f6(c1, c1))),
% 27.74/17.98 inference(symmetry,[status(thm)],[4654])).
% 27.74/17.98 tff(4656,plain,
% 27.74/17.98 (big_f(f7(c1), f6(c1, c1))),
% 27.74/17.98 inference(modus_ponens,[status(thm)],[487, 4655])).
% 27.74/17.98 tff(4657,plain,
% 27.74/17.98 ($false),
% 27.74/17.98 inference(unit_resolution,[status(thm)],[65, 4656])).
% 27.74/17.98 tff(4658,plain,(big_f(f7(c1), f6(c1, c1)) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f7(c1) = c1)) | big_f(f9(c2, c2), f10(c2))), inference(lemma,lemma(discharge,[]))).
% 27.74/17.98 tff(4659,plain,
% 27.74/17.98 (big_f(f7(c1), f6(c1, c1))),
% 27.74/17.98 inference(unit_resolution,[status(thm)],[4658, 4639, 148, 79, 122, 487, 4597])).
% 27.74/17.98 tff(4660,plain,
% 27.74/17.98 (big_f(f7(c2), f6(c1, c1))),
% 27.74/17.98 inference(modus_ponens,[status(thm)],[4659, 4643])).
% 27.74/17.98 tff(4661,plain,
% 27.74/17.98 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))))),
% 27.74/17.98 inference(rewrite,[status(thm)],[])).
% 27.74/17.98 tff(4662,plain,
% 27.74/17.98 (((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(c2) = c2) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1)))) <=> ((~(f10(c2) = c2)) | (f7(c2) = c2) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))))),
% 27.74/17.98 inference(rewrite,[status(thm)],[])).
% 27.74/17.98 tff(4663,plain,
% 27.74/17.98 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(c2) = c2) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1)))))),
% 27.74/17.98 inference(monotonicity,[status(thm)],[4662])).
% 27.74/17.98 tff(4664,plain,
% 27.74/17.98 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(c2) = c2) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))))),
% 27.74/17.98 inference(transitivity,[status(thm)],[4663, 4661])).
% 27.74/17.98 tff(4665,plain,
% 27.74/17.98 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(c2) = c2) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))))),
% 27.74/17.98 inference(quant_inst,[status(thm)],[])).
% 27.74/17.98 tff(4666,plain,
% 27.74/17.98 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1)))),
% 27.74/17.98 inference(modus_ponens,[status(thm)],[4665, 4664])).
% 27.74/17.98 tff(4667,plain,
% 27.74/17.98 ((f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1)))),
% 27.74/17.98 inference(unit_resolution,[status(thm)],[4666, 676, 122, 17, 185, 4597])).
% 27.74/17.98 tff(4668,plain,
% 27.74/17.98 (f6(c1, c1) = f5(c2)),
% 27.74/17.98 inference(unit_resolution,[status(thm)],[4667, 4660])).
% 27.74/17.98 tff(4669,plain,
% 27.74/17.98 (f6(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)),
% 27.74/17.98 inference(modus_ponens,[status(thm)],[4668, 4609])).
% 27.74/17.98 tff(4670,plain,
% 27.74/17.98 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2))) <=> big_f(f7(c1), f6(c1, c1))),
% 27.74/17.98 inference(monotonicity,[status(thm)],[243, 4594])).
% 27.74/17.98 tff(4671,plain,
% 27.74/17.98 (big_f(f7(c1), f6(c1, c1)) <=> big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2)))),
% 27.74/17.98 inference(symmetry,[status(thm)],[4670])).
% 27.74/17.98 tff(4672,plain,
% 27.74/17.98 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2)))),
% 27.74/17.98 inference(modus_ponens,[status(thm)],[4659, 4671])).
% 27.74/17.98 tff(4673,plain,
% 27.74/17.98 (f7(f9(c2, c2)) = f9(c2, c2)),
% 27.74/17.98 inference(modus_ponens,[status(thm)],[4639, 3652])).
% 27.74/17.98 tff(4674,plain,
% 27.74/17.98 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2)))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2)))))),
% 27.74/17.98 inference(rewrite,[status(thm)],[])).
% 27.74/17.98 tff(4675,plain,
% 27.74/17.98 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2)))))),
% 27.74/17.98 inference(quant_inst,[status(thm)],[])).
% 27.74/17.98 tff(4676,plain,
% 27.74/17.98 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2))))),
% 27.74/17.98 inference(modus_ponens,[status(thm)],[4675, 4674])).
% 27.74/17.98 tff(4677,plain,
% 27.74/17.98 ((~(f6(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2))))),
% 27.74/17.98 inference(unit_resolution,[status(thm)],[4676, 2534, 122, 185, 4597, 4673])).
% 27.74/17.98 tff(4678,plain,
% 27.74/17.98 (~(f6(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))),
% 27.74/17.98 inference(unit_resolution,[status(thm)],[4677, 4672])).
% 27.74/17.98 tff(4679,plain,
% 27.74/17.98 ($false),
% 27.74/17.98 inference(unit_resolution,[status(thm)],[4678, 4669])).
% 27.74/17.98 tff(4680,plain,(big_f(f9(c2, c2), c2) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~big_f(f9(c2, c2), f9(c2, c2))) | (f9(c2, c2) = f5(f9(c2, c2))) | (c1 = c3) | (f9(c2, c2) = c3)), inference(lemma,lemma(discharge,[]))).
% 27.74/17.98 tff(4681,plain,
% 27.74/17.98 (big_f(f9(c2, c2), c2)),
% 27.74/17.98 inference(unit_resolution,[status(thm)],[4680, 17, 79, 122, 148, 487, 1792, 4543, 4533])).
% 27.74/17.98 tff(4682,plain,
% 27.74/17.98 (big_f(f7(c3), c2)),
% 27.74/17.98 inference(modus_ponens,[status(thm)],[4681, 4593])).
% 27.74/17.98 tff(4683,plain,
% 27.74/17.98 (big_f(f7(c2), c2)),
% 27.74/17.98 inference(modus_ponens,[status(thm)],[4681, 4570])).
% 27.74/17.98 tff(4684,plain,
% 27.74/17.98 (big_f(f7(c2), f9(c1, c1)) <=> big_f(c1, f9(c1, c1))),
% 27.74/17.98 inference(monotonicity,[status(thm)],[22])).
% 27.74/17.98 tff(4685,plain,
% 27.74/17.98 (big_f(c1, f9(c1, c1)) <=> big_f(f7(c2), f9(c1, c1))),
% 27.74/17.98 inference(symmetry,[status(thm)],[4684])).
% 27.74/17.98 tff(4686,assumption,(~big_f(c1, f9(c1, c1))), introduced(assumption)).
% 27.74/17.98 tff(4687,plain,
% 27.74/17.98 (big_f(c1, f9(c1, c1)) <=> big_f(f9(c2, c2), c2)),
% 27.74/17.98 inference(monotonicity,[status(thm)],[150, 4102])).
% 27.74/17.98 tff(4688,plain,
% 27.74/17.98 (big_f(f9(c2, c2), c2) <=> big_f(c1, f9(c1, c1))),
% 27.74/17.98 inference(symmetry,[status(thm)],[4687])).
% 27.74/17.98 tff(4689,plain,
% 27.74/17.98 (big_f(c1, f9(c1, c1))),
% 27.74/17.98 inference(modus_ponens,[status(thm)],[2041, 4688])).
% 27.74/17.98 tff(4690,plain,
% 27.74/17.98 ($false),
% 27.74/17.98 inference(unit_resolution,[status(thm)],[4686, 4689])).
% 27.74/17.98 tff(4691,plain,((~(f9(c1, c1) = c2)) | big_f(c1, f9(c1, c1)) | (~big_f(f9(c2, c2), c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.74/17.98 tff(4692,plain,
% 27.74/17.98 (~(f9(c1, c1) = c2)),
% 27.74/17.98 inference(unit_resolution,[status(thm)],[4691, 4686, 2041, 148, 79, 122])).
% 27.74/17.98 tff(4693,plain,
% 27.74/17.98 (f9(c1, c1) = c1),
% 27.74/17.98 inference(unit_resolution,[status(thm)],[3939, 4692])).
% 27.74/17.98 tff(4694,plain,
% 27.74/17.98 (f9(c1, c1) = f9(c2, c2)),
% 27.74/17.98 inference(transitivity,[status(thm)],[4693, 149, 132])).
% 27.74/17.98 tff(4695,plain,
% 27.74/17.98 (big_f(c1, f9(c1, c1)) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 27.74/17.98 inference(monotonicity,[status(thm)],[150, 4694])).
% 27.74/17.98 tff(4696,plain,
% 27.74/17.98 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(c1, f9(c1, c1))),
% 27.74/17.98 inference(symmetry,[status(thm)],[4695])).
% 27.74/17.98 tff(4697,plain,
% 27.74/17.98 (big_f(c1, f9(c1, c1))),
% 27.74/17.98 inference(modus_ponens,[status(thm)],[487, 4696])).
% 27.74/17.98 tff(4698,plain,
% 27.74/17.98 ($false),
% 27.74/17.98 inference(unit_resolution,[status(thm)],[4686, 4697])).
% 27.74/17.98 tff(4699,plain,(big_f(c1, f9(c1, c1)) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~big_f(f9(c2, c2), c2))), inference(lemma,lemma(discharge,[]))).
% 27.74/17.98 tff(4700,plain,
% 27.74/17.98 (big_f(c1, f9(c1, c1))),
% 27.74/17.98 inference(unit_resolution,[status(thm)],[4699, 4681, 148, 79, 122, 487])).
% 27.74/17.98 tff(4701,plain,
% 27.74/17.98 (big_f(f7(c2), f9(c1, c1))),
% 27.74/17.98 inference(modus_ponens,[status(thm)],[4700, 4685])).
% 27.74/17.98 tff(4702,plain,
% 27.74/17.98 (f9(c2, c2) = c1),
% 27.74/17.98 inference(transitivity,[status(thm)],[2629, 148])).
% 27.74/17.98 tff(4703,plain,
% 27.74/17.98 (f10(f9(c2, c2)) = f10(c1)),
% 27.74/17.98 inference(monotonicity,[status(thm)],[4702])).
% 27.74/17.98 tff(4704,plain,
% 27.74/17.98 (f10(f9(c2, c2)) = c1),
% 27.74/17.98 inference(transitivity,[status(thm)],[4703, 3762])).
% 27.74/17.98 tff(4705,plain,
% 27.74/17.98 (f9(f9(c2, c2), f9(c2, c2)) = f9(c1, c1)),
% 27.74/17.98 inference(monotonicity,[status(thm)],[4702, 4702])).
% 27.74/17.98 tff(4706,plain,
% 27.74/17.98 (big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))) <=> big_f(f9(c1, c1), c1)),
% 27.74/17.98 inference(monotonicity,[status(thm)],[4705, 4704])).
% 27.74/17.98 tff(4707,plain,
% 27.74/17.98 (big_f(f9(c1, c1), c1) <=> big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))),
% 27.74/17.98 inference(symmetry,[status(thm)],[4706])).
% 27.74/17.98 tff(4708,plain,
% 27.74/17.98 (c1 = f9(c2, c2)),
% 27.74/17.98 inference(transitivity,[status(thm)],[149, 2634])).
% 27.74/17.98 tff(4709,plain,
% 27.74/17.98 (f9(c1, c1) = f9(c2, c2)),
% 27.74/17.98 inference(transitivity,[status(thm)],[3949, 149, 2634])).
% 27.74/17.98 tff(4710,plain,
% 27.74/17.98 (big_f(f9(c1, c1), c1) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 27.74/17.98 inference(monotonicity,[status(thm)],[4709, 4708])).
% 27.74/17.98 tff(4711,plain,
% 27.74/17.98 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f9(c1, c1), c1)),
% 27.74/17.98 inference(symmetry,[status(thm)],[4710])).
% 27.74/17.98 tff(4712,plain,
% 27.74/17.98 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))),
% 27.74/17.98 inference(transitivity,[status(thm)],[4711, 4707])).
% 27.74/17.98 tff(4713,plain,
% 27.74/17.98 (big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))),
% 27.74/17.98 inference(modus_ponens,[status(thm)],[487, 4712])).
% 27.74/17.98 tff(4714,plain,
% 27.74/17.98 ((f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) <=> (f9(c1, c1) = c1)),
% 27.74/17.98 inference(monotonicity,[status(thm)],[4705, 4702])).
% 27.74/17.98 tff(4715,plain,
% 27.74/17.98 ((f9(c1, c1) = c1) <=> (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))),
% 27.74/17.98 inference(symmetry,[status(thm)],[4714])).
% 27.74/17.98 tff(4716,plain,
% 27.74/17.98 (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)),
% 27.74/17.98 inference(modus_ponens,[status(thm)],[3949, 4715])).
% 27.74/17.98 tff(4717,plain,
% 27.74/17.98 (f10(c1) = f10(f9(c2, c2))),
% 27.74/17.98 inference(symmetry,[status(thm)],[4703])).
% 27.74/17.98 tff(4718,plain,
% 27.74/17.98 ((f10(c1) = c1) <=> (f10(f9(c2, c2)) = f9(c2, c2))),
% 27.74/17.98 inference(monotonicity,[status(thm)],[4717, 4708])).
% 27.74/17.98 tff(4719,plain,
% 27.74/17.98 (f10(f9(c2, c2)) = f9(c2, c2)),
% 27.74/17.98 inference(modus_ponens,[status(thm)],[3762, 4718])).
% 27.74/17.98 tff(4720,plain,
% 27.74/17.98 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))))),
% 27.74/17.98 inference(rewrite,[status(thm)],[])).
% 27.74/17.98 tff(4721,plain,
% 27.74/17.98 (((~(f10(f9(c2, c2)) = f9(c2, c2))) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))))) <=> ((f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))))),
% 27.74/17.98 inference(rewrite,[status(thm)],[])).
% 27.74/17.98 tff(4722,plain,
% 27.74/17.98 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))))))),
% 27.74/17.98 inference(monotonicity,[status(thm)],[4721])).
% 27.74/17.98 tff(4723,plain,
% 27.74/17.98 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))))),
% 27.74/17.98 inference(transitivity,[status(thm)],[4722, 4720])).
% 27.74/17.98 tff(4724,plain,
% 27.74/17.98 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))))),
% 27.74/17.98 inference(quant_inst,[status(thm)],[])).
% 27.74/17.98 tff(4725,plain,
% 27.74/17.98 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))))),
% 27.80/17.99 inference(modus_ponens,[status(thm)],[4724, 4723])).
% 27.80/17.99 tff(4726,plain,
% 27.80/17.99 ((c2 = f5(c2)) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))))),
% 27.80/17.99 inference(unit_resolution,[status(thm)],[4725, 1190, 17, 1180, 4719])).
% 27.80/17.99 tff(4727,plain,
% 27.80/17.99 (c2 = f5(c2)),
% 27.80/17.99 inference(unit_resolution,[status(thm)],[4726, 4716, 4713])).
% 27.80/17.99 tff(4728,plain,
% 27.80/17.99 (f5(c2) = c2),
% 27.80/17.99 inference(symmetry,[status(thm)],[4727])).
% 27.80/17.99 tff(4729,assumption,(big_f(f7(c2), f9(c1, c1))), introduced(assumption)).
% 27.80/17.99 tff(4730,plain,
% 27.80/17.99 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((f7(c2) = c2) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(c1, c1) = f5(c2)) | (~big_f(f7(c2), f9(c1, c1))) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (f7(c2) = c2) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(c1, c1) = f5(c2)) | (~big_f(f7(c2), f9(c1, c1))) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))))),
% 27.80/17.99 inference(rewrite,[status(thm)],[])).
% 27.80/17.99 tff(4731,plain,
% 27.80/17.99 (((~(f10(f9(c2, c2)) = f9(c2, c2))) | (f7(c2) = c2) | (f9(c1, c1) = f5(c2)) | (~big_f(f7(c2), f9(c1, c1))) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))))) <=> ((f7(c2) = c2) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(c1, c1) = f5(c2)) | (~big_f(f7(c2), f9(c1, c1))) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))))),
% 27.80/17.99 inference(rewrite,[status(thm)],[])).
% 27.80/17.99 tff(4732,plain,
% 27.80/17.99 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (f7(c2) = c2) | (f9(c1, c1) = f5(c2)) | (~big_f(f7(c2), f9(c1, c1))) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((f7(c2) = c2) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(c1, c1) = f5(c2)) | (~big_f(f7(c2), f9(c1, c1))) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))))))),
% 27.80/17.99 inference(monotonicity,[status(thm)],[4731])).
% 27.80/17.99 tff(4733,plain,
% 27.80/17.99 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (f7(c2) = c2) | (f9(c1, c1) = f5(c2)) | (~big_f(f7(c2), f9(c1, c1))) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (f7(c2) = c2) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(c1, c1) = f5(c2)) | (~big_f(f7(c2), f9(c1, c1))) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))))),
% 27.80/17.99 inference(transitivity,[status(thm)],[4732, 4730])).
% 27.80/17.99 tff(4734,plain,
% 27.80/17.99 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (f7(c2) = c2) | (f9(c1, c1) = f5(c2)) | (~big_f(f7(c2), f9(c1, c1))) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))))),
% 27.80/17.99 inference(quant_inst,[status(thm)],[])).
% 27.80/17.99 tff(4735,plain,
% 27.80/17.99 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (f7(c2) = c2) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(c1, c1) = f5(c2)) | (~big_f(f7(c2), f9(c1, c1))) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))))),
% 27.80/17.99 inference(modus_ponens,[status(thm)],[4734, 4733])).
% 27.80/17.99 tff(4736,plain,
% 27.80/17.99 ((f9(c1, c1) = f5(c2)) | (~big_f(f7(c2), f9(c1, c1))) | (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))))),
% 27.80/17.99 inference(unit_resolution,[status(thm)],[4735, 1190, 17, 4719])).
% 27.80/17.99 tff(4737,plain,
% 27.80/17.99 (f9(c1, c1) = f5(c2)),
% 27.80/17.99 inference(unit_resolution,[status(thm)],[4736, 4716, 4729, 4713])).
% 27.80/17.99 tff(4738,plain,
% 27.80/17.99 (c1 = f9(c1, c1)),
% 27.80/17.99 inference(symmetry,[status(thm)],[3949])).
% 27.80/17.99 tff(4739,plain,
% 27.80/17.99 (f9(c2, c2) = c2),
% 27.80/17.99 inference(transitivity,[status(thm)],[2629, 148, 4738, 4737, 4728])).
% 27.80/17.99 tff(4740,plain,
% 27.80/17.99 ((c2 = c1) <=> (c2 = f9(c2, c2))),
% 27.80/17.99 inference(monotonicity,[status(thm)],[4708])).
% 27.80/17.99 tff(4741,plain,
% 27.80/17.99 ((c2 = c1) <=> (f9(c2, c2) = c2)),
% 27.80/17.99 inference(transitivity,[status(thm)],[4740, 167])).
% 27.80/17.99 tff(4742,plain,
% 27.80/17.99 ((~(c2 = c1)) <=> (~(f9(c2, c2) = c2))),
% 27.80/17.99 inference(monotonicity,[status(thm)],[4741])).
% 27.80/17.99 tff(4743,plain,
% 27.80/17.99 (~(f9(c2, c2) = c2)),
% 27.80/17.99 inference(modus_ponens,[status(thm)],[75, 4742])).
% 27.80/17.99 tff(4744,plain,
% 27.80/17.99 ($false),
% 27.80/17.99 inference(unit_resolution,[status(thm)],[4743, 4739])).
% 27.80/17.99 tff(4745,plain,((~(f9(c1, c1) = c1)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~big_f(f7(c2), f9(c1, c1))) | (f7(c2) = c2) | (~big_f(f7(c2), c2)) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f10(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 27.80/17.99 tff(4746,plain,
% 27.80/17.99 (~(f9(c1, c1) = c1)),
% 27.80/17.99 inference(unit_resolution,[status(thm)],[4745, 4701, 79, 122, 148, 17, 4683, 487, 3762])).
% 27.80/17.99 tff(4747,plain,
% 27.80/17.99 ((f9(c2, c2) = f5(c2)) <=> (c1 = f5(c2))),
% 27.80/17.99 inference(monotonicity,[status(thm)],[161])).
% 27.80/17.99 tff(4748,plain,
% 27.80/17.99 ((f9(c2, c2) = f5(c2)) <=> (f5(c2) = c1)),
% 27.80/17.99 inference(transitivity,[status(thm)],[4747, 1531])).
% 27.80/17.99 tff(4749,plain,
% 27.80/17.99 ((f5(c2) = c1) <=> (f9(c2, c2) = f5(c2))),
% 27.80/17.99 inference(symmetry,[status(thm)],[4748])).
% 27.80/17.99 tff(4750,assumption,(big_f(f7(c3), c2)), introduced(assumption)).
% 27.80/17.99 tff(4751,plain,
% 27.80/17.99 ((f7(c3) = c3) <=> (f7(c2) = c2)),
% 27.80/17.99 inference(monotonicity,[status(thm)],[4590, 67])).
% 27.80/17.99 tff(4752,plain,
% 27.80/17.99 ((f7(c2) = c2) <=> (f7(c3) = c3)),
% 27.80/17.99 inference(symmetry,[status(thm)],[4751])).
% 27.80/17.99 tff(4753,plain,
% 27.80/17.99 ((~(f7(c2) = c2)) <=> (~(f7(c3) = c3))),
% 27.80/17.99 inference(monotonicity,[status(thm)],[4752])).
% 27.80/17.99 tff(4754,plain,
% 27.80/17.99 (~(f7(c3) = c3)),
% 27.80/17.99 inference(modus_ponens,[status(thm)],[17, 4753])).
% 27.80/17.99 tff(4755,plain,
% 27.80/17.99 (big_f(c2, f9(c2, c2)) <=> big_f(f9(c1, c1), f10(c1))),
% 27.80/17.99 inference(transitivity,[status(thm)],[4203, 3932])).
% 27.80/17.99 tff(4756,plain,
% 27.80/17.99 ((~big_f(c2, f9(c2, c2))) <=> (~big_f(f9(c1, c1), f10(c1)))),
% 27.80/17.99 inference(monotonicity,[status(thm)],[4755])).
% 27.80/17.99 tff(4757,plain,
% 27.80/17.99 (~big_f(f9(c1, c1), f10(c1))),
% 27.80/17.99 inference(modus_ponens,[status(thm)],[2040, 4756])).
% 27.80/17.99 tff(4758,plain,
% 27.80/17.99 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((c2 = f5(c3)) | (~big_f(f7(c3), c2)) | (f7(c3) = c3) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (c2 = f5(c3)) | (~big_f(f7(c3), c2)) | (f7(c3) = c3) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)))),
% 27.80/17.99 inference(rewrite,[status(thm)],[])).
% 27.80/17.99 tff(4759,plain,
% 27.80/17.99 (((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(c3) = c3) | (c2 = f5(c3)) | (~big_f(f7(c3), c2))) <=> ((c2 = f5(c3)) | (~big_f(f7(c3), c2)) | (f7(c3) = c3) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)))),
% 27.80/17.99 inference(rewrite,[status(thm)],[])).
% 27.80/17.99 tff(4760,plain,
% 27.80/17.99 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(c3) = c3) | (c2 = f5(c3)) | (~big_f(f7(c3), c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((c2 = f5(c3)) | (~big_f(f7(c3), c2)) | (f7(c3) = c3) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1))))),
% 27.80/17.99 inference(monotonicity,[status(thm)],[4759])).
% 27.80/17.99 tff(4761,plain,
% 27.80/17.99 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(c3) = c3) | (c2 = f5(c3)) | (~big_f(f7(c3), c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (c2 = f5(c3)) | (~big_f(f7(c3), c2)) | (f7(c3) = c3) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)))),
% 27.80/17.99 inference(transitivity,[status(thm)],[4760, 4758])).
% 27.80/17.99 tff(4762,plain,
% 27.80/17.99 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(c3) = c3) | (c2 = f5(c3)) | (~big_f(f7(c3), c2)))),
% 27.80/17.99 inference(quant_inst,[status(thm)],[])).
% 27.80/17.99 tff(4763,plain,
% 27.80/17.99 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (c2 = f5(c3)) | (~big_f(f7(c3), c2)) | (f7(c3) = c3) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1))),
% 27.80/17.99 inference(modus_ponens,[status(thm)],[4762, 4761])).
% 27.80/17.99 tff(4764,plain,
% 27.80/17.99 ((c2 = f5(c3)) | (~big_f(f7(c3), c2)) | (f7(c3) = c3) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1))),
% 27.80/17.99 inference(unit_resolution,[status(thm)],[4763, 676])).
% 27.80/17.99 tff(4765,plain,
% 27.80/17.99 (c2 = f5(c3)),
% 27.80/17.99 inference(unit_resolution,[status(thm)],[4764, 4757, 3762, 4754, 4070, 4750])).
% 27.80/17.99 tff(4766,plain,
% 27.80/17.99 (f5(c3) = c2),
% 27.80/17.99 inference(symmetry,[status(thm)],[4765])).
% 27.80/17.99 tff(4767,plain,
% 27.80/17.99 (f5(c2) = f5(c3)),
% 27.80/17.99 inference(monotonicity,[status(thm)],[69])).
% 27.80/17.99 tff(4768,plain,
% 27.80/17.99 (f5(c2) = c2),
% 27.80/17.99 inference(transitivity,[status(thm)],[4767, 4766])).
% 27.80/17.99 tff(4769,plain,
% 27.80/17.99 ((f5(c2) = c1) <=> (c2 = f9(c2, c2))),
% 27.80/17.99 inference(monotonicity,[status(thm)],[4768, 150])).
% 27.80/17.99 tff(4770,plain,
% 27.80/17.99 ((f5(c2) = c1) <=> (f9(c2, c2) = c2)),
% 27.80/17.99 inference(transitivity,[status(thm)],[4769, 167])).
% 27.80/17.99 tff(4771,plain,
% 27.80/17.99 ((f9(c2, c2) = c2) <=> (f5(c2) = c1)),
% 27.80/17.99 inference(symmetry,[status(thm)],[4770])).
% 27.80/17.99 tff(4772,plain,
% 27.80/17.99 ((f9(c2, c2) = c2) <=> (f9(c2, c2) = f5(c2))),
% 27.80/17.99 inference(transitivity,[status(thm)],[4771, 4749])).
% 27.80/17.99 tff(4773,plain,
% 27.80/17.99 ((~(f9(c2, c2) = c2)) <=> (~(f9(c2, c2) = f5(c2)))),
% 27.80/17.99 inference(monotonicity,[status(thm)],[4772])).
% 27.80/17.99 tff(4774,plain,
% 27.80/17.99 (~(f9(c2, c2) = f5(c2))),
% 27.80/17.99 inference(modus_ponens,[status(thm)],[185, 4773])).
% 27.80/17.99 tff(4775,plain,
% 27.80/17.99 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(c2) = c2) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f9(c2, c2))) | (f9(c2, c2) = f5(c2)) | (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c2) = c2) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f9(c2, c2))) | (f9(c2, c2) = f5(c2)) | (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))))),
% 27.80/17.99 inference(rewrite,[status(thm)],[])).
% 27.80/17.99 tff(4776,plain,
% 27.80/17.99 (((~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))) | (f7(c2) = c2) | (f9(c2, c2) = f5(c2)) | (~big_f(f7(c2), f9(c2, c2)))) <=> ((f7(c2) = c2) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f9(c2, c2))) | (f9(c2, c2) = f5(c2)) | (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))))),
% 27.80/17.99 inference(rewrite,[status(thm)],[])).
% 27.80/17.99 tff(4777,plain,
% 27.80/17.99 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))) | (f7(c2) = c2) | (f9(c2, c2) = f5(c2)) | (~big_f(f7(c2), f9(c2, c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(c2) = c2) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f9(c2, c2))) | (f9(c2, c2) = f5(c2)) | (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))))),
% 27.80/17.99 inference(monotonicity,[status(thm)],[4776])).
% 27.80/17.99 tff(4778,plain,
% 27.80/17.99 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))) | (f7(c2) = c2) | (f9(c2, c2) = f5(c2)) | (~big_f(f7(c2), f9(c2, c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c2) = c2) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f9(c2, c2))) | (f9(c2, c2) = f5(c2)) | (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))))),
% 27.80/17.99 inference(transitivity,[status(thm)],[4777, 4775])).
% 27.80/17.99 tff(4779,plain,
% 27.80/17.99 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(f9(c2, c2)) = f9(c2, c2))) | (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))) | (f7(c2) = c2) | (f9(c2, c2) = f5(c2)) | (~big_f(f7(c2), f9(c2, c2))))),
% 27.80/17.99 inference(quant_inst,[status(thm)],[])).
% 27.80/17.99 tff(4780,plain,
% 27.80/17.99 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c2) = c2) | (~(f10(f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f9(c2, c2))) | (f9(c2, c2) = f5(c2)) | (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))),
% 27.80/17.99 inference(modus_ponens,[status(thm)],[4779, 4778])).
% 27.80/17.99 tff(4781,plain,
% 27.80/17.99 ((f9(c2, c2) = f5(c2)) | (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))),
% 27.80/17.99 inference(unit_resolution,[status(thm)],[4780, 676, 17, 3777, 1163])).
% 27.80/17.99 tff(4782,plain,
% 27.80/17.99 (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)),
% 27.80/17.99 inference(unit_resolution,[status(thm)],[4781, 4774, 4206])).
% 27.80/17.99 tff(4783,plain,
% 27.80/17.99 (f9(c1, c1) = c1),
% 27.80/17.99 inference(modus_ponens,[status(thm)],[4782, 4095])).
% 27.80/17.99 tff(4784,plain,
% 27.80/17.99 ($false),
% 27.80/17.99 inference(unit_resolution,[status(thm)],[4070, 4783])).
% 27.80/17.99 tff(4785,plain,((f9(c1, c1) = c1) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~big_f(f7(c2), f9(c2, c2))) | (~(c3 = c2)) | (~(f10(c1) = c1)) | (~big_f(f7(c3), c2)) | big_f(c2, f9(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 27.80/17.99 tff(4786,plain,
% 27.80/17.99 (big_f(c2, f9(c2, c2))),
% 27.80/17.99 inference(unit_resolution,[status(thm)],[4785, 4746, 79, 122, 17, 4544, 67, 3762, 4682, 148])).
% 27.80/17.99 tff(4787,plain,
% 27.80/17.99 (~(c4 = c1)),
% 27.80/17.99 inference(unit_resolution,[status(thm)],[4027, 4786, 487, 1335, 4589, 79, 148, 122])).
% 27.80/17.99 tff(4788,plain,
% 27.80/17.99 (c4 = c2),
% 27.80/17.99 inference(unit_resolution,[status(thm)],[461, 4787])).
% 27.80/17.99 tff(4789,plain,
% 27.80/17.99 (c2 = c4),
% 27.80/17.99 inference(symmetry,[status(thm)],[4788])).
% 27.80/17.99 tff(4790,plain,
% 27.80/17.99 (f4(c2) = f4(c4)),
% 27.80/17.99 inference(monotonicity,[status(thm)],[4789])).
% 27.80/17.99 tff(4791,plain,
% 27.80/17.99 (f4(c2) = c2),
% 27.80/17.99 inference(transitivity,[status(thm)],[4790, 79])).
% 27.80/17.99 tff(4792,plain,
% 27.80/17.99 ((f9(c2, c2) = f4(c2)) <=> (f9(c2, c2) = c2)),
% 27.80/17.99 inference(monotonicity,[status(thm)],[4791])).
% 27.80/17.99 tff(4793,plain,
% 27.80/17.99 ((f9(c2, c2) = c2) <=> (f9(c2, c2) = f4(c2))),
% 27.80/17.99 inference(symmetry,[status(thm)],[4792])).
% 27.80/17.99 tff(4794,plain,
% 27.80/17.99 ((~(f9(c2, c2) = c2)) <=> (~(f9(c2, c2) = f4(c2)))),
% 27.80/17.99 inference(monotonicity,[status(thm)],[4793])).
% 27.80/17.99 tff(4795,plain,
% 27.80/17.99 (~(f9(c2, c2) = f4(c2))),
% 27.80/17.99 inference(modus_ponens,[status(thm)],[185, 4794])).
% 27.80/17.99 tff(4796,plain,
% 27.80/17.99 (c2 = c4),
% 27.80/17.99 inference(modus_ponens,[status(thm)],[4788, 159])).
% 27.80/17.99 tff(4797,plain,
% 27.80/17.99 ((~(c2 = c4)) | (c2 = f2(c2)) | (f9(c2, c2) = f4(c2))),
% 27.80/17.99 inference(unit_resolution,[status(thm)],[4087, 1355, 4589, 1335, 4681])).
% 27.80/17.99 tff(4798,plain,
% 27.80/17.99 (c2 = f2(c2)),
% 27.80/17.99 inference(unit_resolution,[status(thm)],[4797, 4796, 4795])).
% 27.80/17.99 tff(4799,plain,
% 27.80/17.99 (f2(c2) = c2),
% 27.80/17.99 inference(symmetry,[status(thm)],[4798])).
% 27.80/17.99 tff(4800,plain,
% 27.80/17.99 ((~(c2 = c4)) | (f9(c2, c2) = f4(c2)) | (f9(c2, c2) = f2(c2))),
% 27.80/17.99 inference(unit_resolution,[status(thm)],[4119, 1355, 1335, 4786, 4681])).
% 27.80/17.99 tff(4801,plain,
% 27.80/17.99 (f9(c2, c2) = f2(c2)),
% 27.80/17.99 inference(unit_resolution,[status(thm)],[4800, 4796, 4795])).
% 27.80/17.99 tff(4802,plain,
% 27.80/17.99 (f9(c2, c2) = c2),
% 27.80/17.99 inference(transitivity,[status(thm)],[4801, 4799])).
% 27.80/17.99 tff(4803,plain,
% 27.80/17.99 ($false),
% 27.80/17.99 inference(unit_resolution,[status(thm)],[185, 4802])).
% 27.80/17.99 tff(4804,plain,((f7(c2) = c2) | (~(f4(c4) = c2)) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f10(c2) = c2)) | (~(c3 = c2)) | (~(f10(c1) = c1)) | (f9(c2, c2) = f5(f9(c2, c2)))), inference(lemma,lemma(discharge,[]))).
% 27.80/17.99 tff(4805,plain,
% 27.80/17.99 (~big_f(f9(c2, c2), f9(c2, c2))),
% 27.80/17.99 inference(unit_resolution,[status(thm)],[4804, 191, 79, 148, 122, 181, 3637, 4529])).
% 27.80/17.99 tff(4806,plain,
% 27.80/17.99 (~big_f(f9(c2, c2), c2)),
% 27.80/17.99 inference(unit_resolution,[status(thm)],[3816, 4805, 79, 122, 3637, 115, 148, 200, 191, 168])).
% 27.80/17.99 tff(4807,plain,
% 27.80/17.99 (f7(c2) = c1),
% 27.80/17.99 inference(unit_resolution,[status(thm)],[21, 4529])).
% 27.80/17.99 tff(4808,plain,
% 27.80/17.99 (~big_f(c2, f9(c2, c2))),
% 27.80/17.99 inference(unit_resolution,[status(thm)],[3810, 4805, 148, 3637, 79, 122, 115, 191, 200])).
% 27.80/17.99 tff(4809,plain,
% 27.80/17.99 (~big_f(c2, c1)),
% 27.80/17.99 inference(unit_resolution,[status(thm)],[3814, 4808, 148, 79, 122])).
% 27.80/17.99 tff(4810,plain,
% 27.80/17.99 (~big_f(f7(c2), c1)),
% 27.80/17.99 inference(unit_resolution,[status(thm)],[4636, 4809, 148, 168, 79, 122, 3645, 4807, 4806])).
% 27.80/17.99 tff(4811,plain,
% 27.80/17.99 (~big_f(f9(c2, c2), f10(c2))),
% 27.80/17.99 inference(unit_resolution,[status(thm)],[3687, 4806, 122])).
% 27.80/17.99 tff(4812,plain,
% 27.80/17.99 (f7(c2) = f9(c2, c2)),
% 27.80/17.99 inference(transitivity,[status(thm)],[4807, 149, 132])).
% 27.80/17.99 tff(4813,plain,
% 27.80/17.99 (big_f(f7(c2), c2) <=> big_f(f9(c2, c2), c2)),
% 27.80/17.99 inference(monotonicity,[status(thm)],[4812])).
% 27.80/17.99 tff(4814,plain,
% 27.80/17.99 (big_f(f9(c2, c2), c2) <=> big_f(f7(c2), c2)),
% 27.80/17.99 inference(symmetry,[status(thm)],[4813])).
% 27.80/17.99 tff(4815,plain,
% 27.80/17.99 ((~big_f(f9(c2, c2), c2)) <=> (~big_f(f7(c2), c2))),
% 27.80/17.99 inference(monotonicity,[status(thm)],[4814])).
% 27.80/17.99 tff(4816,plain,
% 27.80/17.99 (~big_f(f7(c2), c2)),
% 27.80/17.99 inference(modus_ponens,[status(thm)],[4806, 4815])).
% 27.80/17.99 tff(4817,plain,
% 27.80/17.99 (~(c2 = f5(c2))),
% 27.80/17.99 inference(unit_resolution,[status(thm)],[1527, 267, 122, 4529, 4816, 185, 4811])).
% 27.80/17.99 tff(4818,plain,
% 27.80/17.99 (~(f5(c2) = c2)),
% 27.80/17.99 inference(modus_ponens,[status(thm)],[4817, 1281])).
% 27.80/17.99 tff(4819,plain,
% 27.80/17.99 (f5(c2) = c1),
% 27.80/17.99 inference(unit_resolution,[status(thm)],[1547, 4818])).
% 27.80/17.99 tff(4820,plain,
% 27.80/17.99 (big_f(f7(c2), f9(c2, c2)) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 27.80/17.99 inference(monotonicity,[status(thm)],[314])).
% 27.80/17.99 tff(4821,plain,
% 27.80/17.99 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f7(c2), f9(c2, c2))),
% 27.80/17.99 inference(symmetry,[status(thm)],[4820])).
% 27.80/17.99 tff(4822,plain,
% 27.80/17.99 (f5(c2) = f9(c2, c2)),
% 27.80/17.99 inference(transitivity,[status(thm)],[1569, 149, 132])).
% 27.80/17.99 tff(4823,plain,
% 27.80/17.99 (big_f(f7(c2), f5(c2)) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 27.80/17.99 inference(monotonicity,[status(thm)],[314, 4822])).
% 27.80/17.99 tff(4824,plain,
% 27.80/17.99 (big_f(f7(c2), f5(c2)) <=> big_f(f7(c2), c1)),
% 27.80/17.99 inference(transitivity,[status(thm)],[4823, 4821, 4535])).
% 27.80/17.99 tff(4825,plain,
% 27.80/17.99 (big_f(f7(c2), c1)),
% 27.80/17.99 inference(modus_ponens,[status(thm)],[319, 4824])).
% 27.80/17.99 tff(4826,plain,
% 27.80/17.99 ($false),
% 27.80/17.99 inference(unit_resolution,[status(thm)],[333, 4825])).
% 27.80/17.99 tff(4827,plain,((~big_f(f7(c2), f5(c2))) | big_f(f7(c2), c1) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f5(c2) = c1)) | (~(f7(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 27.80/17.99 tff(4828,plain,
% 27.80/17.99 (~big_f(f7(c2), f5(c2))),
% 27.80/17.99 inference(unit_resolution,[status(thm)],[4827, 4819, 148, 79, 122, 4810, 4807])).
% 27.80/17.99 tff(4829,assumption,(~big_f(f7(c2), f5(c2))), introduced(assumption)).
% 27.80/18.00 tff(4830,plain,
% 27.80/18.00 (f2(c2) = c2),
% 27.80/18.00 inference(symmetry,[status(thm)],[2853])).
% 27.80/18.00 tff(4831,plain,
% 27.80/18.00 (f2(c3) = c2),
% 27.80/18.00 inference(transitivity,[status(thm)],[1221, 4830])).
% 27.80/18.00 tff(4832,plain,
% 27.80/18.00 ((f9(f10(c2), f2(c3)) = f2(c3)) <=> (f9(f10(c2), f2(c3)) = c2)),
% 27.80/18.00 inference(monotonicity,[status(thm)],[4831])).
% 27.80/18.00 tff(4833,plain,
% 27.80/18.00 ((f9(f10(c2), f2(c3)) = c2) <=> (f9(f10(c2), f2(c3)) = f2(c3))),
% 27.80/18.00 inference(symmetry,[status(thm)],[4832])).
% 27.80/18.00 tff(4834,plain,
% 27.80/18.00 (f9(f10(c2), f2(c3)) = f9(c2, c2)),
% 27.80/18.00 inference(monotonicity,[status(thm)],[122, 4831])).
% 27.80/18.00 tff(4835,plain,
% 27.80/18.00 ((f9(f10(c2), f2(c3)) = c2) <=> (f9(c2, c2) = c2)),
% 27.80/18.00 inference(monotonicity,[status(thm)],[4834])).
% 27.80/18.00 tff(4836,plain,
% 27.80/18.00 ((f9(c2, c2) = c2) <=> (f9(f10(c2), f2(c3)) = c2)),
% 27.80/18.00 inference(symmetry,[status(thm)],[4835])).
% 27.80/18.00 tff(4837,plain,
% 27.80/18.00 ((f9(c2, c2) = c2) <=> (f9(f10(c2), f2(c3)) = f2(c3))),
% 27.80/18.00 inference(transitivity,[status(thm)],[4836, 4833])).
% 27.80/18.00 tff(4838,plain,
% 27.80/18.00 ((~(f9(c2, c2) = c2)) <=> (~(f9(f10(c2), f2(c3)) = f2(c3)))),
% 27.80/18.00 inference(monotonicity,[status(thm)],[4837])).
% 27.80/18.00 tff(4839,plain,
% 27.80/18.00 (~(f9(f10(c2), f2(c3)) = f2(c3))),
% 27.80/18.00 inference(modus_ponens,[status(thm)],[1209, 4838])).
% 27.80/18.00 tff(4840,plain,
% 27.80/18.00 (big_f(f9(f10(c2), f2(c3)), f10(f10(c2))) <=> big_f(f9(f10(c2), f2(c3)), c2)),
% 27.80/18.00 inference(monotonicity,[status(thm)],[251])).
% 27.80/18.00 tff(4841,plain,
% 27.80/18.00 (big_f(f9(f10(c2), f2(c3)), c2) <=> big_f(f9(f10(c2), f2(c3)), f10(f10(c2)))),
% 27.80/18.00 inference(symmetry,[status(thm)],[4840])).
% 27.80/18.00 tff(4842,plain,
% 27.80/18.00 (big_f(f9(f10(c2), f2(c3)), c2) <=> big_f(f9(c2, c2), c2)),
% 27.80/18.00 inference(monotonicity,[status(thm)],[4834])).
% 27.80/18.00 tff(4843,plain,
% 27.80/18.00 (big_f(f9(c2, c2), c2) <=> big_f(f9(f10(c2), f2(c3)), c2)),
% 27.80/18.00 inference(symmetry,[status(thm)],[4842])).
% 27.80/18.00 tff(4844,plain,
% 27.80/18.00 (big_f(f9(c2, c2), c2) <=> big_f(f9(f10(c2), f2(c3)), f10(f10(c2)))),
% 27.80/18.00 inference(transitivity,[status(thm)],[4843, 4841])).
% 27.80/18.00 tff(4845,plain,
% 27.80/18.00 ((~big_f(f9(c2, c2), c2)) <=> (~big_f(f9(f10(c2), f2(c3)), f10(f10(c2))))),
% 27.80/18.00 inference(monotonicity,[status(thm)],[4844])).
% 27.80/18.00 tff(4846,plain,
% 27.80/18.00 (~big_f(f9(f10(c2), f2(c3)), f10(f10(c2)))),
% 27.80/18.00 inference(modus_ponens,[status(thm)],[3685, 4845])).
% 27.80/18.00 tff(4847,plain,
% 27.80/18.00 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((f7(c2) = c2) | big_f(f7(c2), f5(c2)) | big_f(f9(f10(c2), f2(c3)), f10(f10(c2))) | (~(f10(f10(c2)) = f10(c2))) | (f9(f10(c2), f2(c3)) = f2(c3)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (f7(c2) = c2) | big_f(f7(c2), f5(c2)) | big_f(f9(f10(c2), f2(c3)), f10(f10(c2))) | (~(f10(f10(c2)) = f10(c2))) | (f9(f10(c2), f2(c3)) = f2(c3)))),
% 27.80/18.00 inference(rewrite,[status(thm)],[])).
% 27.80/18.00 tff(4848,plain,
% 27.80/18.00 (((~(f10(f10(c2)) = f10(c2))) | (f9(f10(c2), f2(c3)) = f2(c3)) | big_f(f9(f10(c2), f2(c3)), f10(f10(c2))) | (f7(c2) = c2) | big_f(f7(c2), f5(c2)) | $false) <=> ((f7(c2) = c2) | big_f(f7(c2), f5(c2)) | big_f(f9(f10(c2), f2(c3)), f10(f10(c2))) | (~(f10(f10(c2)) = f10(c2))) | (f9(f10(c2), f2(c3)) = f2(c3)))),
% 27.80/18.00 inference(rewrite,[status(thm)],[])).
% 27.80/18.00 tff(4849,plain,
% 27.80/18.00 ((f5(c2) = f5(c2)) <=> $true),
% 27.80/18.00 inference(rewrite,[status(thm)],[])).
% 27.80/18.00 tff(4850,plain,
% 27.80/18.00 ((~(f5(c2) = f5(c2))) <=> (~$true)),
% 27.80/18.00 inference(monotonicity,[status(thm)],[4849])).
% 27.80/18.00 tff(4851,plain,
% 27.80/18.00 ((~(f5(c2) = f5(c2))) <=> $false),
% 27.80/18.00 inference(transitivity,[status(thm)],[4850, 270])).
% 27.80/18.00 tff(4852,plain,
% 27.80/18.00 (((~(f10(f10(c2)) = f10(c2))) | (f9(f10(c2), f2(c3)) = f2(c3)) | big_f(f9(f10(c2), f2(c3)), f10(f10(c2))) | (f7(c2) = c2) | big_f(f7(c2), f5(c2)) | (~(f5(c2) = f5(c2)))) <=> ((~(f10(f10(c2)) = f10(c2))) | (f9(f10(c2), f2(c3)) = f2(c3)) | big_f(f9(f10(c2), f2(c3)), f10(f10(c2))) | (f7(c2) = c2) | big_f(f7(c2), f5(c2)) | $false)),
% 27.80/18.00 inference(monotonicity,[status(thm)],[4851])).
% 27.80/18.00 tff(4853,plain,
% 27.80/18.00 (((~(f10(f10(c2)) = f10(c2))) | (f9(f10(c2), f2(c3)) = f2(c3)) | big_f(f9(f10(c2), f2(c3)), f10(f10(c2))) | (f7(c2) = c2) | big_f(f7(c2), f5(c2)) | (~(f5(c2) = f5(c2)))) <=> ((f7(c2) = c2) | big_f(f7(c2), f5(c2)) | big_f(f9(f10(c2), f2(c3)), f10(f10(c2))) | (~(f10(f10(c2)) = f10(c2))) | (f9(f10(c2), f2(c3)) = f2(c3)))),
% 27.80/18.00 inference(transitivity,[status(thm)],[4852, 4848])).
% 27.80/18.00 tff(4854,plain,
% 27.80/18.00 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(f10(c2)) = f10(c2))) | (f9(f10(c2), f2(c3)) = f2(c3)) | big_f(f9(f10(c2), f2(c3)), f10(f10(c2))) | (f7(c2) = c2) | big_f(f7(c2), f5(c2)) | (~(f5(c2) = f5(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((f7(c2) = c2) | big_f(f7(c2), f5(c2)) | big_f(f9(f10(c2), f2(c3)), f10(f10(c2))) | (~(f10(f10(c2)) = f10(c2))) | (f9(f10(c2), f2(c3)) = f2(c3))))),
% 27.80/18.00 inference(monotonicity,[status(thm)],[4853])).
% 27.80/18.00 tff(4855,plain,
% 27.80/18.00 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(f10(c2)) = f10(c2))) | (f9(f10(c2), f2(c3)) = f2(c3)) | big_f(f9(f10(c2), f2(c3)), f10(f10(c2))) | (f7(c2) = c2) | big_f(f7(c2), f5(c2)) | (~(f5(c2) = f5(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (f7(c2) = c2) | big_f(f7(c2), f5(c2)) | big_f(f9(f10(c2), f2(c3)), f10(f10(c2))) | (~(f10(f10(c2)) = f10(c2))) | (f9(f10(c2), f2(c3)) = f2(c3)))),
% 27.80/18.00 inference(transitivity,[status(thm)],[4854, 4847])).
% 27.80/18.00 tff(4856,plain,
% 27.80/18.00 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(f10(c2)) = f10(c2))) | (f9(f10(c2), f2(c3)) = f2(c3)) | big_f(f9(f10(c2), f2(c3)), f10(f10(c2))) | (f7(c2) = c2) | big_f(f7(c2), f5(c2)) | (~(f5(c2) = f5(c2))))),
% 27.80/18.00 inference(quant_inst,[status(thm)],[])).
% 27.80/18.00 tff(4857,plain,
% 27.80/18.00 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (f7(c2) = c2) | big_f(f7(c2), f5(c2)) | big_f(f9(f10(c2), f2(c3)), f10(f10(c2))) | (~(f10(f10(c2)) = f10(c2))) | (f9(f10(c2), f2(c3)) = f2(c3))),
% 27.80/18.00 inference(modus_ponens,[status(thm)],[4856, 4855])).
% 27.80/18.00 tff(4858,plain,
% 27.80/18.00 ((f7(c2) = c2) | big_f(f7(c2), f5(c2)) | big_f(f9(f10(c2), f2(c3)), f10(f10(c2))) | (~(f10(f10(c2)) = f10(c2))) | (f9(f10(c2), f2(c3)) = f2(c3))),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[4857, 267])).
% 27.80/18.00 tff(4859,plain,
% 27.80/18.00 ($false),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[4858, 4846, 4839, 252, 17, 4829])).
% 27.80/18.00 tff(4860,plain,((~(c2 = f2(c2))) | (f7(c2) = c2) | big_f(f7(c2), f5(c2)) | big_f(f9(c2, c2), c2) | (~(c3 = c2)) | (~(f10(c2) = c2)) | (f9(c2, c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 27.80/18.00 tff(4861,plain,
% 27.80/18.00 (~(c2 = f2(c2))),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[4860, 4828, 4529, 4806, 181, 122, 185])).
% 27.80/18.00 tff(4862,plain,
% 27.80/18.00 ((c2 = f2(c2)) <=> (c2 = f2(c3))),
% 27.80/18.00 inference(monotonicity,[status(thm)],[1231])).
% 27.80/18.00 tff(4863,plain,
% 27.80/18.00 ((c2 = f2(c3)) <=> (c2 = f2(c2))),
% 27.80/18.00 inference(symmetry,[status(thm)],[4862])).
% 27.80/18.00 tff(4864,plain,
% 27.80/18.00 ((f2(c3) = c2) <=> (c2 = f2(c2))),
% 27.80/18.00 inference(transitivity,[status(thm)],[1434, 4863])).
% 27.80/18.00 tff(4865,plain,
% 27.80/18.00 (c2 = f2(c2)),
% 27.80/18.00 inference(modus_ponens,[status(thm)],[1319, 4864])).
% 27.80/18.00 tff(4866,plain,
% 27.80/18.00 ($false),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[1342, 4865])).
% 27.80/18.00 tff(4867,plain,((~(f2(c3) = c2)) | (c2 = f2(c2)) | (~(c3 = c2))), inference(lemma,lemma(discharge,[]))).
% 27.80/18.00 tff(4868,plain,
% 27.80/18.00 (~(f2(c3) = c2)),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[4867, 4861, 181])).
% 27.80/18.00 tff(4869,plain,
% 27.80/18.00 (f2(c3) = c1),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[1273, 4868])).
% 27.80/18.00 tff(4870,plain,
% 27.80/18.00 (c2 = c3),
% 27.80/18.00 inference(symmetry,[status(thm)],[181])).
% 27.80/18.00 tff(4871,plain,
% 27.80/18.00 (f2(c2) = f2(c3)),
% 27.80/18.00 inference(monotonicity,[status(thm)],[4870])).
% 27.80/18.00 tff(4872,plain,
% 27.80/18.00 (f2(c2) = f9(c2, c2)),
% 27.80/18.00 inference(transitivity,[status(thm)],[4871, 4869, 149, 132])).
% 27.80/18.00 tff(4873,plain,
% 27.80/18.00 (big_f(f7(c2), f2(c2)) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 27.80/18.00 inference(monotonicity,[status(thm)],[4812, 4872])).
% 27.80/18.00 tff(4874,plain,
% 27.80/18.00 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f7(c2), f2(c2))),
% 27.80/18.00 inference(symmetry,[status(thm)],[4873])).
% 27.80/18.00 tff(4875,plain,
% 27.80/18.00 ((~big_f(f9(c2, c2), f9(c2, c2))) <=> (~big_f(f7(c2), f2(c2)))),
% 27.80/18.00 inference(monotonicity,[status(thm)],[4874])).
% 27.80/18.00 tff(4876,plain,
% 27.80/18.00 (~big_f(f7(c2), f2(c2))),
% 27.80/18.00 inference(modus_ponens,[status(thm)],[4805, 4875])).
% 27.80/18.00 tff(4877,plain,
% 27.80/18.00 (~big_f(c1, c2)),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[3682, 4811, 122, 148, 79])).
% 27.80/18.00 tff(4878,plain,
% 27.80/18.00 (big_f(f7(c2), f2(c2))),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[1552, 4869, 122, 79, 158, 181, 4529, 4877])).
% 27.80/18.00 tff(4879,plain,
% 27.80/18.00 ($false),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[4878, 4876])).
% 27.80/18.00 tff(4880,plain,((~(f5(c1) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (f9(f10(c2), f10(c2)) = f10(c2)) | (c1 = c3) | (f7(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 27.80/18.00 tff(4881,plain,
% 27.80/18.00 (~(f5(c1) = c2)),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[4880, 168, 79, 122, 158, 148, 115])).
% 27.80/18.00 tff(4882,plain,
% 27.80/18.00 (f5(c1) = c1),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[1708, 4881])).
% 27.80/18.00 tff(4883,plain,
% 27.80/18.00 (f9(c2, c2) = f5(f9(c2, c2))),
% 27.80/18.00 inference(modus_ponens,[status(thm)],[4882, 171])).
% 27.80/18.00 tff(4884,plain,
% 27.80/18.00 (~big_f(f9(c2, c2), f10(c2))),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[3921, 115, 148, 79, 122, 3762, 121, 186, 67])).
% 27.80/18.00 tff(4885,plain,
% 27.80/18.00 ($false),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[1810, 4884, 120, 122, 191, 148, 79, 348])).
% 27.80/18.00 tff(4886,plain,((f7(c1) = c1) | (~(f10(c2) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~big_f(c2, c1)) | (~(f10(c1) = c1)) | big_f(c2, c2) | (~(f5(c1) = c2)) | (~(c3 = c2))), inference(lemma,lemma(discharge,[]))).
% 27.80/18.00 tff(4887,plain,
% 27.80/18.00 (~(f5(c1) = c2)),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[4886, 3881, 148, 79, 115, 3762, 122, 121, 67])).
% 27.80/18.00 tff(4888,plain,
% 27.80/18.00 (f5(c1) = c1),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[1708, 4887])).
% 27.80/18.00 tff(4889,plain,
% 27.80/18.00 (big_f(c1, c1) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 27.80/18.00 inference(monotonicity,[status(thm)],[150, 150])).
% 27.80/18.00 tff(4890,plain,
% 27.80/18.00 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(c1, c1)),
% 27.80/18.00 inference(symmetry,[status(thm)],[4889])).
% 27.80/18.00 tff(4891,plain,
% 27.80/18.00 (big_f(f7(c2), c1) <=> big_f(c1, c1)),
% 27.80/18.00 inference(transitivity,[status(thm)],[4534, 4536, 4890])).
% 27.80/18.00 tff(4892,plain,
% 27.80/18.00 ((~big_f(f7(c2), c1)) <=> (~big_f(c1, c1))),
% 27.80/18.00 inference(monotonicity,[status(thm)],[4891])).
% 27.80/18.00 tff(4893,plain,
% 27.80/18.00 ((~big_f(c1, c2)) <=> (~big_f(f9(c2, c2), f10(c2)))),
% 27.80/18.00 inference(monotonicity,[status(thm)],[3679])).
% 27.80/18.00 tff(4894,plain,
% 27.80/18.00 (~big_f(f9(c2, c2), f10(c2))),
% 27.80/18.00 inference(modus_ponens,[status(thm)],[27, 4893])).
% 27.80/18.00 tff(4895,plain,
% 27.80/18.00 (~big_f(f7(c2), c1)),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[659, 4894, 122, 148, 79, 347, 121, 348, 22])).
% 27.80/18.00 tff(4896,plain,
% 27.80/18.00 (~big_f(c1, c1)),
% 27.80/18.00 inference(modus_ponens,[status(thm)],[4895, 4892])).
% 27.80/18.00 tff(4897,plain,
% 27.80/18.00 ((~big_f(c1, c2)) <=> (~big_f(f9(c2, c2), c2))),
% 27.80/18.00 inference(monotonicity,[status(thm)],[3657])).
% 27.80/18.00 tff(4898,plain,
% 27.80/18.00 (~big_f(f9(c2, c2), c2)),
% 27.80/18.00 inference(modus_ponens,[status(thm)],[27, 4897])).
% 27.80/18.00 tff(4899,plain,
% 27.80/18.00 ((~big_f(f9(c2, c2), c2)) <=> (~big_f(f7(c2), c2))),
% 27.80/18.00 inference(monotonicity,[status(thm)],[4570])).
% 27.80/18.00 tff(4900,plain,
% 27.80/18.00 (~big_f(f7(c2), c2)),
% 27.80/18.00 inference(modus_ponens,[status(thm)],[3685, 4899])).
% 27.80/18.00 tff(4901,plain,
% 27.80/18.00 (~(c2 = f5(c2))),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[1527, 267, 122, 17, 4900, 185, 256])).
% 27.80/18.00 tff(4902,plain,
% 27.80/18.00 (~(f5(c2) = c2)),
% 27.80/18.00 inference(modus_ponens,[status(thm)],[4901, 1281])).
% 27.80/18.00 tff(4903,plain,
% 27.80/18.00 ((~(f9(c2, c2) = f5(c2))) <=> (~(f5(c2) = c1))),
% 27.80/18.00 inference(monotonicity,[status(thm)],[4748])).
% 27.80/18.00 tff(4904,plain,
% 27.80/18.00 ((~big_f(f9(c2, c2), f9(c2, c2))) <=> (~big_f(f7(c2), f9(c2, c2)))),
% 27.80/18.00 inference(monotonicity,[status(thm)],[4537])).
% 27.80/18.00 tff(4905,plain,
% 27.80/18.00 ((~big_f(c1, c1)) <=> (~big_f(f9(c2, c2), f9(c2, c2)))),
% 27.80/18.00 inference(monotonicity,[status(thm)],[4889])).
% 27.80/18.00 tff(4906,plain,
% 27.80/18.00 (~big_f(f9(c2, c2), f9(c2, c2))),
% 27.80/18.00 inference(modus_ponens,[status(thm)],[66, 4905])).
% 27.80/18.00 tff(4907,plain,
% 27.80/18.00 (~big_f(f7(c2), f9(c2, c2))),
% 27.80/18.00 inference(modus_ponens,[status(thm)],[4906, 4904])).
% 27.80/18.00 tff(4908,plain,
% 27.80/18.00 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f9(c2, c2) = f5(c2))) | big_f(f7(c2), f9(c2, c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f9(c2, c2) = f5(c2))) | big_f(f7(c2), f9(c2, c2)))),
% 27.80/18.00 inference(rewrite,[status(thm)],[])).
% 27.80/18.00 tff(4909,plain,
% 27.80/18.00 (((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), f9(c2, c2)) | (~(f9(c2, c2) = f5(c2)))) <=> ((~(f10(c2) = c2)) | (f7(c2) = c2) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f9(c2, c2) = f5(c2))) | big_f(f7(c2), f9(c2, c2)))),
% 27.80/18.00 inference(rewrite,[status(thm)],[])).
% 27.80/18.00 tff(4910,plain,
% 27.80/18.00 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), f9(c2, c2)) | (~(f9(c2, c2) = f5(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f9(c2, c2) = f5(c2))) | big_f(f7(c2), f9(c2, c2))))),
% 27.80/18.00 inference(monotonicity,[status(thm)],[4909])).
% 27.80/18.00 tff(4911,plain,
% 27.80/18.00 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), f9(c2, c2)) | (~(f9(c2, c2) = f5(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f9(c2, c2) = f5(c2))) | big_f(f7(c2), f9(c2, c2)))),
% 27.80/18.00 inference(transitivity,[status(thm)],[4910, 4908])).
% 27.80/18.00 tff(4912,plain,
% 27.80/18.00 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), f9(c2, c2)) | (~(f9(c2, c2) = f5(c2))))),
% 27.80/18.00 inference(quant_inst,[status(thm)],[])).
% 27.80/18.00 tff(4913,plain,
% 27.80/18.00 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f9(c2, c2) = f5(c2))) | big_f(f7(c2), f9(c2, c2))),
% 27.80/18.00 inference(modus_ponens,[status(thm)],[4912, 4911])).
% 27.80/18.00 tff(4914,plain,
% 27.80/18.00 (~(f9(c2, c2) = f5(c2))),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[4913, 267, 122, 17, 185, 256, 4907])).
% 27.80/18.00 tff(4915,plain,
% 27.80/18.00 (~(f5(c2) = c1)),
% 27.80/18.00 inference(modus_ponens,[status(thm)],[4914, 4903])).
% 27.80/18.00 tff(4916,plain,
% 27.80/18.00 ($false),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[1547, 4915, 4902])).
% 27.80/18.00 tff(4917,plain,((f7(c2) = c2) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | big_f(f9(c2, c2), f10(c2)) | big_f(f9(c2, c2), c2) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 27.80/18.00 tff(4918,plain,
% 27.80/18.00 (big_f(c1, c1)),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[4917, 4894, 79, 122, 17, 4898, 148])).
% 27.80/18.00 tff(4919,plain,
% 27.80/18.00 ($false),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[4918, 4896])).
% 27.80/18.00 tff(4920,plain,(big_f(c1, c2) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~(f7(c1) = c2)) | big_f(c2, c2) | (~big_f(c2, c1))), inference(lemma,lemma(discharge,[]))).
% 27.80/18.00 tff(4921,plain,
% 27.80/18.00 (big_f(c1, c2)),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[4920, 121, 79, 122, 17, 120, 148, 3881])).
% 27.80/18.00 tff(4922,plain,
% 27.80/18.00 (big_f(f9(c2, c2), f10(c2))),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[3682, 4921, 122, 148, 79])).
% 27.80/18.00 tff(4923,plain,
% 27.80/18.00 (big_f(f9(c2, c2), c2)),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[3687, 4922, 122])).
% 27.80/18.00 tff(4924,plain,
% 27.80/18.00 (big_f(f9(c2, c2), f9(c2, c2))),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[4431, 4923, 148, 79, 122, 4444, 3762, 4888, 566, 815])).
% 27.80/18.00 tff(4925,plain,
% 27.80/18.00 ($false),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[487, 4906])).
% 27.80/18.00 tff(4926,plain,((~big_f(f9(c2, c2), f9(c2, c2))) | big_f(c1, c1) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.80/18.00 tff(4927,plain,
% 27.80/18.00 (big_f(c1, c1)),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[4926, 4924, 148, 79, 122])).
% 27.80/18.00 tff(4928,plain,
% 27.80/18.00 (big_f(f7(c2), f9(c2, c2)) <=> big_f(c1, c1)),
% 27.80/18.00 inference(transitivity,[status(thm)],[4820, 4890])).
% 27.80/18.00 tff(4929,plain,
% 27.80/18.00 ((~big_f(f7(c2), f9(c2, c2))) <=> (~big_f(c1, c1))),
% 27.80/18.00 inference(monotonicity,[status(thm)],[4928])).
% 27.80/18.00 tff(4930,assumption,(~big_f(f7(c2), f9(c2, c2))), introduced(assumption)).
% 27.80/18.00 tff(4931,plain,
% 27.80/18.00 (~big_f(c1, c1)),
% 27.80/18.00 inference(modus_ponens,[status(thm)],[4930, 4929])).
% 27.80/18.00 tff(4932,assumption,(big_f(c1, c1)), introduced(assumption)).
% 27.80/18.00 tff(4933,plain,
% 27.80/18.00 ($false),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[4932, 4931])).
% 27.80/18.00 tff(4934,plain,(big_f(f7(c2), f9(c2, c2)) | (~big_f(c1, c1)) | (~(f7(c2) = c1)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.80/18.00 tff(4935,plain,
% 27.80/18.00 (big_f(f7(c2), f9(c2, c2))),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[4934, 4927, 22, 148, 79, 122])).
% 27.80/18.00 tff(4936,plain,
% 27.80/18.00 (big_f(f7(c2), c2)),
% 27.80/18.00 inference(modus_ponens,[status(thm)],[4923, 4570])).
% 27.80/18.00 tff(4937,plain,
% 27.80/18.00 (big_f(f9(c2, c1), f10(c2))),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[1173, 4935, 148, 17, 4922, 79, 122])).
% 27.80/18.00 tff(4938,plain,
% 27.80/18.00 (big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[3898, 4937, 148, 79, 122])).
% 27.80/18.00 tff(4939,plain,
% 27.80/18.00 ((f5(f10(c1)) = c1) <=> (f5(f9(c2, c2)) = f9(c2, c2))),
% 27.80/18.00 inference(monotonicity,[status(thm)],[4174, 150])).
% 27.80/18.00 tff(4940,plain,
% 27.80/18.00 ((f5(f10(c1)) = c1) <=> (f9(c2, c2) = f5(f9(c2, c2)))),
% 27.80/18.00 inference(transitivity,[status(thm)],[4939, 193])).
% 27.80/18.00 tff(4941,plain,
% 27.80/18.00 ((f9(c2, c2) = f5(f9(c2, c2))) <=> (f5(f10(c1)) = c1)),
% 27.80/18.00 inference(symmetry,[status(thm)],[4940])).
% 27.80/18.00 tff(4942,plain,
% 27.80/18.00 ((f5(c1) = c1) <=> (f5(f10(c1)) = c1)),
% 27.80/18.00 inference(transitivity,[status(thm)],[171, 4941])).
% 27.80/18.00 tff(4943,plain,
% 27.80/18.00 (f5(f10(c1)) = c1),
% 27.80/18.00 inference(modus_ponens,[status(thm)],[4888, 4942])).
% 27.80/18.00 tff(4944,plain,
% 27.80/18.00 (f9(c2, f9(c2, c2)) = f9(c2, c2)),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[4482, 4938, 122, 121, 148, 79, 4943])).
% 27.80/18.00 tff(4945,plain,
% 27.80/18.00 ($false),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[1211, 4944, 4938, 122, 17, 4936, 4935, 185])).
% 27.80/18.00 tff(4946,plain,(big_f(c2, c2) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c1) = c1)) | (f9(c2, c2) = c3) | (f9(f10(c2), f4(c4)) = c3) | (f7(c1) = c1) | (~(c3 = c2))), inference(lemma,lemma(discharge,[]))).
% 27.80/18.00 tff(4947,plain,
% 27.80/18.00 (big_f(c2, c2)),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[4946, 4529, 122, 148, 79, 3637, 3645, 3643, 115, 181])).
% 27.80/18.00 tff(4948,plain,
% 27.80/18.00 (big_f(f7(f9(c2, c2)), c2)),
% 27.80/18.00 inference(modus_ponens,[status(thm)],[4947, 246])).
% 27.80/18.00 tff(4949,plain,
% 27.80/18.00 (~(c2 = f5(f9(c2, c2)))),
% 27.80/18.00 inference(modus_ponens,[status(thm)],[4881, 166])).
% 27.80/18.00 tff(4950,plain,
% 27.80/18.00 ((~big_f(f7(f9(c2, c2)), c2)) | big_f(f9(c2, c2), f10(c2)) | (c2 = f5(f9(c2, c2)))),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[682, 676, 122, 185, 3654])).
% 27.80/18.00 tff(4951,plain,
% 27.80/18.00 (big_f(f9(c2, c2), f10(c2))),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[4950, 4949, 4948])).
% 27.80/18.00 tff(4952,plain,
% 27.80/18.00 (big_f(f9(c2, c2), c2)),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[3687, 4951, 122])).
% 27.80/18.00 tff(4953,plain,
% 27.80/18.00 (big_f(c2, f9(c2, c2))),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[4230, 4952, 3654, 148, 79, 122, 3637, 120, 4883, 168])).
% 27.80/18.00 tff(4954,plain,
% 27.80/18.00 (big_f(f9(c2, c2), f9(c2, c2))),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[4431, 4953, 148, 79, 122, 4952, 3637, 4882, 3645, 3643])).
% 27.80/18.00 tff(4955,plain,
% 27.80/18.00 (~(c4 = c1)),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[4027, 4954, 4067, 4947, 4953, 79, 148, 122])).
% 27.80/18.00 tff(4956,plain,
% 27.80/18.00 (c4 = c2),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[461, 4955])).
% 27.80/18.00 tff(4957,plain,
% 27.80/18.00 (c2 = c4),
% 27.80/18.00 inference(symmetry,[status(thm)],[4956])).
% 27.80/18.00 tff(4958,plain,
% 27.80/18.00 (f4(c2) = f4(c4)),
% 27.80/18.00 inference(monotonicity,[status(thm)],[4957])).
% 27.80/18.00 tff(4959,plain,
% 27.80/18.00 (f4(c2) = c2),
% 27.80/18.00 inference(transitivity,[status(thm)],[4958, 79])).
% 27.80/18.00 tff(4960,plain,
% 27.80/18.00 ((f9(c2, c2) = f4(c2)) <=> (f9(c2, c2) = c2)),
% 27.80/18.00 inference(monotonicity,[status(thm)],[4959])).
% 27.80/18.00 tff(4961,plain,
% 27.80/18.00 ((f9(c2, c2) = c2) <=> (f9(c2, c2) = f4(c2))),
% 27.80/18.00 inference(symmetry,[status(thm)],[4960])).
% 27.80/18.00 tff(4962,plain,
% 27.80/18.00 ((~(f9(c2, c2) = c2)) <=> (~(f9(c2, c2) = f4(c2)))),
% 27.80/18.00 inference(monotonicity,[status(thm)],[4961])).
% 27.80/18.00 tff(4963,plain,
% 27.80/18.00 (~(f9(c2, c2) = f4(c2))),
% 27.80/18.00 inference(modus_ponens,[status(thm)],[185, 4962])).
% 27.80/18.00 tff(4964,plain,
% 27.80/18.00 (c2 = c4),
% 27.80/18.00 inference(modus_ponens,[status(thm)],[4956, 159])).
% 27.80/18.00 tff(4965,plain,
% 27.80/18.00 (c2 = f2(c2)),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[4087, 1355, 4964, 4947, 4067, 4952, 4963])).
% 27.80/18.00 tff(4966,plain,
% 27.80/18.00 (f2(c2) = c2),
% 27.80/18.00 inference(symmetry,[status(thm)],[4965])).
% 27.80/18.00 tff(4967,plain,
% 27.80/18.00 (f9(c2, c2) = f2(c2)),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[4119, 1355, 4964, 4067, 4953, 4952, 4963])).
% 27.80/18.00 tff(4968,plain,
% 27.80/18.00 (f9(c2, c2) = c2),
% 27.80/18.00 inference(transitivity,[status(thm)],[4967, 4966])).
% 27.80/18.00 tff(4969,plain,
% 27.80/18.00 ($false),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[185, 4968])).
% 27.80/18.00 tff(4970,plain,((c1 = c3) | (~(f4(c4) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f10(c2) = c2)) | (f9(f10(c2), f10(c2)) = f10(c2)) | (f7(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 27.80/18.00 tff(4971,plain,
% 27.80/18.00 (c1 = c3),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[4970, 115, 148, 122, 158, 79])).
% 27.80/18.00 tff(4972,plain,
% 27.80/18.00 (c3 = c1),
% 27.80/18.00 inference(symmetry,[status(thm)],[4971])).
% 27.80/18.00 tff(4973,plain,
% 27.80/18.00 (c3 = f9(c2, c2)),
% 27.80/18.00 inference(transitivity,[status(thm)],[4972, 149, 132])).
% 27.80/18.00 tff(4974,plain,
% 27.80/18.00 ((c2 = c3) <=> (c2 = f9(c2, c2))),
% 27.80/18.00 inference(monotonicity,[status(thm)],[4973])).
% 27.80/18.00 tff(4975,plain,
% 27.80/18.00 ((c2 = c3) <=> (f9(c2, c2) = c2)),
% 27.80/18.00 inference(transitivity,[status(thm)],[4974, 167])).
% 27.80/18.00 tff(4976,plain,
% 27.80/18.00 ((f9(c2, c2) = c2) <=> (c2 = c3)),
% 27.80/18.00 inference(symmetry,[status(thm)],[4975])).
% 27.80/18.00 tff(4977,plain,
% 27.80/18.00 ((~(f9(c2, c2) = c2)) <=> (~(c2 = c3))),
% 27.80/18.00 inference(monotonicity,[status(thm)],[4976])).
% 27.80/18.00 tff(4978,plain,
% 27.80/18.00 (~(c2 = c3)),
% 27.80/18.00 inference(modus_ponens,[status(thm)],[185, 4977])).
% 27.80/18.00 tff(4979,plain,
% 27.80/18.00 (f9(c2, c2) = c3),
% 27.80/18.00 inference(modus_ponens,[status(thm)],[4971, 3640])).
% 27.80/18.00 tff(4980,plain,
% 27.80/18.00 (c2 = f5(f9(c2, c2))),
% 27.80/18.00 inference(modus_ponens,[status(thm)],[186, 165])).
% 27.80/18.00 tff(4981,plain,
% 27.80/18.00 ((~big_f(c2, c2)) <=> (~big_f(f7(f9(c2, c2)), c2))),
% 27.80/18.00 inference(monotonicity,[status(thm)],[4406])).
% 27.80/18.00 tff(4982,plain,
% 27.80/18.00 (~big_f(f7(f9(c2, c2)), c2)),
% 27.80/18.00 inference(modus_ponens,[status(thm)],[121, 4981])).
% 27.80/18.00 tff(4983,assumption,(big_f(f7(f9(c2, c2)), c2)), introduced(assumption)).
% 27.80/18.00 tff(4984,plain,
% 27.80/18.00 ($false),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[4983, 4982])).
% 27.80/18.00 tff(4985,plain,((~big_f(f7(f9(c2, c2)), c2)) | big_f(c2, c2) | (~(f7(c1) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.80/18.00 tff(4986,plain,
% 27.80/18.00 (~big_f(f7(f9(c2, c2)), c2)),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[4985, 121, 120, 148, 79, 122])).
% 27.80/18.00 tff(4987,plain,
% 27.80/18.00 ((c2 = f10(c2)) <=> (f10(c2) = c2)),
% 27.80/18.00 inference(commutativity,[status(thm)],[])).
% 27.80/18.00 tff(4988,plain,
% 27.80/18.00 ((f10(c2) = c2) <=> (c2 = f10(c2))),
% 27.80/18.00 inference(symmetry,[status(thm)],[4987])).
% 27.80/18.00 tff(4989,plain,
% 27.80/18.00 (c2 = f10(c2)),
% 27.80/18.00 inference(modus_ponens,[status(thm)],[122, 4988])).
% 27.80/18.00 tff(4990,plain,
% 27.80/18.00 (~big_f(f7(c1), f5(c1))),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[1715, 186, 120, 121])).
% 27.80/18.00 tff(4991,plain,
% 27.80/18.00 (big_f(f9(f10(c2), f10(c2)), f10(f10(c2))) <=> big_f(f9(c2, c2), f10(c2))),
% 27.80/18.00 inference(transitivity,[status(thm)],[3655, 130])).
% 27.80/18.00 tff(4992,plain,
% 27.80/18.00 (big_f(f9(f10(c2), f10(c2)), f10(f10(c2)))),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[280, 4990, 252, 115, 158])).
% 27.80/18.00 tff(4993,plain,
% 27.80/18.00 (big_f(f9(c2, c2), f10(c2))),
% 27.80/18.00 inference(modus_ponens,[status(thm)],[4992, 4991])).
% 27.80/18.00 tff(4994,plain,
% 27.80/18.00 (big_f(f9(c2, c1), f10(c2))),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[755, 4993, 122, 115, 4990, 148, 79])).
% 27.80/18.00 tff(4995,plain,
% 27.80/18.00 (big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[3898, 4994, 148, 79, 122])).
% 27.80/18.00 tff(4996,plain,
% 27.80/18.00 ((~(big_f(c2, c2) <=> big_f(f9(c2, f9(c2, c2)), f10(c2)))) | big_f(c2, c2) | (~big_f(f9(c2, f9(c2, c2)), f10(c2)))),
% 27.80/18.00 inference(tautology,[status(thm)],[])).
% 27.80/18.00 tff(4997,plain,
% 27.80/18.00 (~(big_f(c2, c2) <=> big_f(f9(c2, f9(c2, c2)), f10(c2)))),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[4996, 4995, 121])).
% 27.80/18.00 tff(4998,assumption,(~(big_f(c2, c2) <=> big_f(f9(c2, f9(c2, c2)), f10(c2)))), introduced(assumption)).
% 27.80/18.00 tff(4999,assumption,(c2 = f10(c2)), introduced(assumption)).
% 27.80/18.00 tff(5000,assumption,(c2 = f9(c2, f9(c2, c2))), introduced(assumption)).
% 27.80/18.00 tff(5001,plain,
% 27.80/18.00 (big_f(c2, c2) <=> big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 27.80/18.00 inference(monotonicity,[status(thm)],[5000, 4999])).
% 27.80/18.00 tff(5002,plain,
% 27.80/18.00 ($false),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[5001, 4998])).
% 27.80/18.00 tff(5003,plain,((~(c2 = f9(c2, f9(c2, c2)))) | (~(c2 = f10(c2))) | (big_f(c2, c2) <=> big_f(f9(c2, f9(c2, c2)), f10(c2)))), inference(lemma,lemma(discharge,[]))).
% 27.80/18.00 tff(5004,plain,
% 27.80/18.00 (~(c2 = f9(c2, f9(c2, c2)))),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[5003, 4997, 4989])).
% 27.80/18.00 tff(5005,plain,
% 27.80/18.00 ((f9(c2, f9(c2, c2)) = c2) <=> (c2 = f9(c2, f9(c2, c2)))),
% 27.80/18.00 inference(commutativity,[status(thm)],[])).
% 27.80/18.00 tff(5006,plain,
% 27.80/18.00 ((f9(c2, c1) = c2) <=> (f9(c2, f9(c2, c2)) = c2)),
% 27.80/18.00 inference(monotonicity,[status(thm)],[3892])).
% 27.80/18.00 tff(5007,plain,
% 27.80/18.00 ((f9(c2, c1) = c2) <=> (c2 = f9(c2, f9(c2, c2)))),
% 27.80/18.00 inference(transitivity,[status(thm)],[5006, 5005])).
% 27.80/18.00 tff(5008,assumption,(f9(c2, c1) = c2), introduced(assumption)).
% 27.80/18.00 tff(5009,plain,
% 27.80/18.00 (c2 = f9(c2, f9(c2, c2))),
% 27.80/18.00 inference(modus_ponens,[status(thm)],[5008, 5007])).
% 27.80/18.00 tff(5010,assumption,(~(c2 = f9(c2, f9(c2, c2)))), introduced(assumption)).
% 27.80/18.00 tff(5011,plain,
% 27.80/18.00 ($false),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[5010, 5009])).
% 27.80/18.00 tff(5012,plain,((~(f9(c2, c1) = c2)) | (c2 = f9(c2, f9(c2, c2))) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.80/18.00 tff(5013,plain,
% 27.80/18.00 (~(f9(c2, c1) = c2)),
% 27.80/18.00 inference(unit_resolution,[status(thm)],[5012, 5004, 148, 79, 122])).
% 27.80/18.01 tff(5014,plain,
% 27.80/18.01 (f9(c2, c1) = c1),
% 27.80/18.01 inference(unit_resolution,[status(thm)],[3913, 5013])).
% 27.80/18.01 tff(5015,plain,
% 27.80/18.01 (f9(c2, f9(c2, c2)) = f9(c2, c2)),
% 27.80/18.01 inference(unit_resolution,[status(thm)],[4579, 5014, 148, 79, 122])).
% 27.80/18.01 tff(5016,plain,
% 27.80/18.01 ($false),
% 27.80/18.01 inference(unit_resolution,[status(thm)],[1783, 783, 122, 4995, 5015, 3654, 4986, 4980])).
% 27.80/18.01 tff(5017,plain,((~(f5(c1) = c2)) | (~(f10(c2) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | big_f(c2, c2) | (f7(c1) = c1) | (f9(f10(c2), f10(c2)) = f10(c2))), inference(lemma,lemma(discharge,[]))).
% 27.80/18.01 tff(5018,plain,
% 27.80/18.01 (~(f5(c1) = c2)),
% 27.80/18.01 inference(unit_resolution,[status(thm)],[5017, 121, 148, 79, 122, 115, 158])).
% 27.80/18.01 tff(5019,plain,
% 27.80/18.01 (f5(c1) = c1),
% 27.80/18.01 inference(unit_resolution,[status(thm)],[1708, 5018])).
% 27.80/18.01 tff(5020,plain,
% 27.80/18.01 (f5(f10(c1)) = c1),
% 27.80/18.01 inference(modus_ponens,[status(thm)],[5019, 4439])).
% 27.80/18.01 tff(5021,plain,
% 27.80/18.01 ((f7(f7(c2)) = c3) <=> (f7(f7(c2)) = c1)),
% 27.80/18.01 inference(monotonicity,[status(thm)],[4972])).
% 27.80/18.01 tff(5022,plain,
% 27.80/18.01 ((f7(f7(c2)) = c1) <=> (f7(f7(c2)) = c3)),
% 27.80/18.01 inference(symmetry,[status(thm)],[5021])).
% 27.80/18.01 tff(5023,plain,
% 27.80/18.01 (f7(f7(c2)) = f7(f9(c2, c2))),
% 27.80/18.01 inference(monotonicity,[status(thm)],[1151])).
% 27.80/18.01 tff(5024,plain,
% 27.80/18.01 (f7(f7(c2)) = c2),
% 27.80/18.01 inference(transitivity,[status(thm)],[5023, 243, 120])).
% 27.80/18.01 tff(5025,plain,
% 27.80/18.01 ((f7(f7(c2)) = c1) <=> (c2 = f9(c2, c2))),
% 27.80/18.01 inference(monotonicity,[status(thm)],[5024, 150])).
% 27.80/18.01 tff(5026,plain,
% 27.80/18.01 ((f7(f7(c2)) = c1) <=> (f9(c2, c2) = c2)),
% 27.80/18.01 inference(transitivity,[status(thm)],[5025, 167])).
% 27.80/18.01 tff(5027,plain,
% 27.80/18.01 ((f9(c2, c2) = c2) <=> (f7(f7(c2)) = c1)),
% 27.80/18.01 inference(symmetry,[status(thm)],[5026])).
% 27.80/18.01 tff(5028,plain,
% 27.80/18.01 ((f9(c2, c2) = c2) <=> (f7(f7(c2)) = c3)),
% 27.80/18.01 inference(transitivity,[status(thm)],[5027, 5022])).
% 27.80/18.01 tff(5029,plain,
% 27.80/18.01 ((~(f9(c2, c2) = c2)) <=> (~(f7(f7(c2)) = c3))),
% 27.80/18.01 inference(monotonicity,[status(thm)],[5028])).
% 27.80/18.01 tff(5030,plain,
% 27.80/18.01 (~(f7(f7(c2)) = c3)),
% 27.80/18.01 inference(modus_ponens,[status(thm)],[185, 5029])).
% 27.80/18.01 tff(5031,plain,
% 27.80/18.01 (big_f(f7(f9(c2, c2)), f9(c2, c2)) <=> big_f(c2, f9(c2, c2))),
% 27.80/18.01 inference(monotonicity,[status(thm)],[244])).
% 27.80/18.01 tff(5032,plain,
% 27.80/18.01 (big_f(c2, f9(c2, c2)) <=> big_f(f7(f9(c2, c2)), f9(c2, c2))),
% 27.80/18.01 inference(symmetry,[status(thm)],[5031])).
% 27.80/18.01 tff(5033,plain,
% 27.80/18.01 (~(c4 = c2)),
% 27.80/18.01 inference(unit_resolution,[status(thm)],[476, 474, 79, 121])).
% 27.80/18.01 tff(5034,plain,
% 27.80/18.01 (~(c4 = c1)),
% 27.80/18.01 inference(unit_resolution,[status(thm)],[2221, 474, 2, 79])).
% 27.80/18.01 tff(5035,plain,
% 27.80/18.01 ($false),
% 27.80/18.01 inference(unit_resolution,[status(thm)],[461, 5034, 5033])).
% 27.80/18.01 tff(5036,plain,((~big_f(f4(c4), c4)) | big_f(c2, c1) | (~(f4(c4) = c2)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 27.80/18.01 tff(5037,plain,
% 27.80/18.01 (~big_f(f4(c4), c4)),
% 27.80/18.01 inference(unit_resolution,[status(thm)],[5036, 4107, 79, 121])).
% 27.80/18.01 tff(5038,plain,
% 27.80/18.01 (f1(f7(f7(c2)), c1) = c1),
% 27.80/18.01 inference(unit_resolution,[status(thm)],[422, 5037, 292, 378, 120, 121])).
% 27.80/18.01 tff(5039,plain,
% 27.80/18.01 (f7(f7(c2)) = f7(f9(c2, c2))),
% 27.80/18.01 inference(monotonicity,[status(thm)],[314])).
% 27.80/18.01 tff(5040,plain,
% 27.80/18.01 (f7(f9(c2, c2)) = f7(f7(c2))),
% 27.80/18.01 inference(symmetry,[status(thm)],[5039])).
% 27.80/18.01 tff(5041,plain,
% 27.80/18.01 (c2 = f7(f7(c2))),
% 27.80/18.01 inference(transitivity,[status(thm)],[2778, 3651, 5040])).
% 27.80/18.01 tff(5042,plain,
% 27.80/18.01 (f1(c2, f9(c2, c2)) = f1(f7(f7(c2)), c1)),
% 27.80/18.01 inference(monotonicity,[status(thm)],[5041, 161])).
% 27.80/18.01 tff(5043,plain,
% 27.80/18.01 (f1(c2, c1) = f1(c2, f9(c2, c2))),
% 27.80/18.01 inference(monotonicity,[status(thm)],[150])).
% 27.80/18.01 tff(5044,plain,
% 27.80/18.01 (f1(c2, c1) = f9(c2, c2)),
% 27.80/18.01 inference(transitivity,[status(thm)],[5043, 5042, 5038, 149, 132])).
% 27.80/18.01 tff(5045,plain,
% 27.80/18.01 (big_f(c2, f1(c2, c1)) <=> big_f(c2, f9(c2, c2))),
% 27.80/18.01 inference(monotonicity,[status(thm)],[5044])).
% 27.80/18.01 tff(5046,plain,
% 27.80/18.01 (f1(c2, f9(c2, c2)) = f1(c2, c1)),
% 27.80/18.01 inference(symmetry,[status(thm)],[5043])).
% 27.80/18.01 tff(5047,plain,
% 27.80/18.01 (big_f(c2, f1(c2, f9(c2, c2))) <=> big_f(c2, f1(c2, c1))),
% 27.80/18.01 inference(monotonicity,[status(thm)],[5046])).
% 27.80/18.01 tff(5048,plain,
% 27.80/18.01 (big_f(c2, f1(c2, f9(c2, c2))) <=> big_f(f7(f9(c2, c2)), f9(c2, c2))),
% 27.80/18.01 inference(transitivity,[status(thm)],[5047, 5045, 5032])).
% 27.80/18.01 tff(5049,plain,
% 27.80/18.01 ((~big_f(c2, f1(c2, f9(c2, c2)))) <=> (~big_f(f7(f9(c2, c2)), f9(c2, c2)))),
% 27.80/18.01 inference(monotonicity,[status(thm)],[5048])).
% 27.80/18.01 tff(5050,plain,
% 27.80/18.01 (big_f(c2, f1(c2, c1)) <=> big_f(c2, f1(c2, f9(c2, c2)))),
% 27.80/18.01 inference(symmetry,[status(thm)],[5047])).
% 27.80/18.01 tff(5051,plain,
% 27.80/18.01 (big_f(c2, f9(c2, c2)) <=> big_f(c2, f1(c2, c1))),
% 27.80/18.01 inference(symmetry,[status(thm)],[5045])).
% 27.80/18.01 tff(5052,plain,
% 27.80/18.01 (big_f(c2, f9(c2, c2)) <=> big_f(c2, f1(c2, f9(c2, c2)))),
% 27.80/18.01 inference(transitivity,[status(thm)],[5051, 5050])).
% 27.80/18.01 tff(5053,plain,
% 27.80/18.01 ((~big_f(c2, f9(c2, c2))) <=> (~big_f(c2, f1(c2, f9(c2, c2))))),
% 27.80/18.01 inference(monotonicity,[status(thm)],[5052])).
% 27.80/18.01 tff(5054,plain,
% 27.80/18.01 (~big_f(c2, f1(c2, f9(c2, c2)))),
% 27.80/18.01 inference(modus_ponens,[status(thm)],[2040, 5053])).
% 27.80/18.01 tff(5055,plain,
% 27.80/18.01 (~big_f(f7(f9(c2, c2)), f9(c2, c2))),
% 27.80/18.01 inference(modus_ponens,[status(thm)],[5054, 5049])).
% 27.80/18.01 tff(5056,plain,
% 27.80/18.01 (big_f(f7(c1), f5(c1)) <=> big_f(c2, f9(c2, c2))),
% 27.80/18.01 inference(monotonicity,[status(thm)],[120, 3593])).
% 27.80/18.01 tff(5057,plain,
% 27.80/18.01 (big_f(c2, f9(c2, c2)) <=> big_f(f7(c1), f5(c1))),
% 27.80/18.01 inference(symmetry,[status(thm)],[5056])).
% 27.80/18.01 tff(5058,plain,
% 27.80/18.01 (big_f(c2, f1(c2, f9(c2, c2))) <=> big_f(f7(c1), f5(c1))),
% 27.80/18.01 inference(transitivity,[status(thm)],[5047, 5045, 5057])).
% 27.80/18.01 tff(5059,plain,
% 27.80/18.01 ((~big_f(c2, f1(c2, f9(c2, c2)))) <=> (~big_f(f7(c1), f5(c1)))),
% 27.80/18.01 inference(monotonicity,[status(thm)],[5058])).
% 27.80/18.01 tff(5060,plain,
% 27.80/18.01 (~big_f(f7(c1), f5(c1))),
% 27.80/18.01 inference(modus_ponens,[status(thm)],[5054, 5059])).
% 27.80/18.01 tff(5061,plain,
% 27.80/18.01 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~(f9(c2, c2) = f5(f9(c2, c2)))) | big_f(f7(f9(c2, c2)), f9(c2, c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~(f9(c2, c2) = f5(f9(c2, c2)))) | big_f(f7(f9(c2, c2)), f9(c2, c2)))),
% 27.80/18.01 inference(rewrite,[status(thm)],[])).
% 27.80/18.01 tff(5062,plain,
% 27.80/18.01 (((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | big_f(f7(f9(c2, c2)), f9(c2, c2)) | (~(f9(c2, c2) = f5(f9(c2, c2))))) <=> ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~(f9(c2, c2) = f5(f9(c2, c2)))) | big_f(f7(f9(c2, c2)), f9(c2, c2)))),
% 27.80/18.01 inference(rewrite,[status(thm)],[])).
% 27.80/18.01 tff(5063,plain,
% 27.80/18.01 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | big_f(f7(f9(c2, c2)), f9(c2, c2)) | (~(f9(c2, c2) = f5(f9(c2, c2)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~(f9(c2, c2) = f5(f9(c2, c2)))) | big_f(f7(f9(c2, c2)), f9(c2, c2))))),
% 27.80/18.01 inference(monotonicity,[status(thm)],[5062])).
% 27.80/18.01 tff(5064,plain,
% 27.80/18.01 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | big_f(f7(f9(c2, c2)), f9(c2, c2)) | (~(f9(c2, c2) = f5(f9(c2, c2)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~(f9(c2, c2) = f5(f9(c2, c2)))) | big_f(f7(f9(c2, c2)), f9(c2, c2)))),
% 27.80/18.01 inference(transitivity,[status(thm)],[5063, 5061])).
% 27.80/18.01 tff(5065,plain,
% 27.80/18.01 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | big_f(f7(f9(c2, c2)), f9(c2, c2)) | (~(f9(c2, c2) = f5(f9(c2, c2)))))),
% 27.80/18.01 inference(quant_inst,[status(thm)],[])).
% 27.80/18.01 tff(5066,plain,
% 27.80/18.01 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~(f9(c2, c2) = f5(f9(c2, c2)))) | big_f(f7(f9(c2, c2)), f9(c2, c2))),
% 27.80/18.01 inference(modus_ponens,[status(thm)],[5065, 5064])).
% 27.80/18.01 tff(5067,plain,
% 27.80/18.01 (big_f(f9(c2, c2), f10(c2))),
% 27.80/18.01 inference(unit_resolution,[status(thm)],[5066, 267, 122, 185, 764, 3654, 5055])).
% 27.80/18.01 tff(5068,plain,
% 27.80/18.01 (big_f(f9(c2, c1), f10(c2))),
% 27.80/18.01 inference(unit_resolution,[status(thm)],[755, 5067, 122, 115, 5060, 148, 79])).
% 27.80/18.01 tff(5069,plain,
% 27.80/18.01 (big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 27.80/18.01 inference(unit_resolution,[status(thm)],[3898, 5068, 148, 79, 122])).
% 27.80/18.01 tff(5070,plain,
% 27.80/18.01 (f9(c2, f9(c2, c2)) = f9(c2, c2)),
% 27.80/18.01 inference(unit_resolution,[status(thm)],[4482, 5069, 122, 121, 148, 79, 328])).
% 27.80/18.01 tff(5071,plain,
% 27.80/18.01 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~(f9(c2, c2) = f5(f9(c2, c2)))) | big_f(f7(f9(c2, c2)), f9(c2, c2)) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~(f9(c2, c2) = f5(f9(c2, c2)))) | big_f(f7(f9(c2, c2)), f9(c2, c2)) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))))),
% 27.80/18.01 inference(rewrite,[status(thm)],[])).
% 27.80/18.01 tff(5072,plain,
% 27.80/18.01 (((~(f10(c2) = c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | big_f(f7(f9(c2, c2)), f9(c2, c2)) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, c2) = f5(f9(c2, c2))))) <=> ((~(f10(c2) = c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~(f9(c2, c2) = f5(f9(c2, c2)))) | big_f(f7(f9(c2, c2)), f9(c2, c2)) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))))),
% 27.80/18.01 inference(rewrite,[status(thm)],[])).
% 27.80/18.01 tff(5073,plain,
% 27.80/18.01 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | big_f(f7(f9(c2, c2)), f9(c2, c2)) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, c2) = f5(f9(c2, c2)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~(f9(c2, c2) = f5(f9(c2, c2)))) | big_f(f7(f9(c2, c2)), f9(c2, c2)) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2)))))),
% 27.80/18.01 inference(monotonicity,[status(thm)],[5072])).
% 27.80/18.01 tff(5074,plain,
% 27.80/18.01 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | big_f(f7(f9(c2, c2)), f9(c2, c2)) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, c2) = f5(f9(c2, c2)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~(f9(c2, c2) = f5(f9(c2, c2)))) | big_f(f7(f9(c2, c2)), f9(c2, c2)) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))))),
% 27.80/18.01 inference(transitivity,[status(thm)],[5073, 5071])).
% 27.80/18.01 tff(5075,plain,
% 27.80/18.01 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | big_f(f7(f9(c2, c2)), f9(c2, c2)) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, c2) = f5(f9(c2, c2)))))),
% 27.80/18.01 inference(quant_inst,[status(thm)],[])).
% 27.80/18.01 tff(5076,plain,
% 27.80/18.01 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~(f9(c2, c2) = f5(f9(c2, c2)))) | big_f(f7(f9(c2, c2)), f9(c2, c2)) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2)))),
% 27.80/18.01 inference(modus_ponens,[status(thm)],[5075, 5074])).
% 27.80/18.01 tff(5077,plain,
% 27.80/18.01 ($false),
% 27.80/18.01 inference(unit_resolution,[status(thm)],[5076, 783, 122, 764, 5069, 5070, 3654, 5055])).
% 27.80/18.01 tff(5078,plain,(big_f(c2, f9(c2, c2)) | (~(f10(c2) = c2)) | big_f(c2, c2) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f5(f10(c1)) = c1)) | (f7(c1) = c1) | (~(f7(c2) = c1)) | (~(f5(c1) = c1)) | (f7(f7(c2)) = c3)), inference(lemma,lemma(discharge,[]))).
% 27.80/18.01 tff(5079,plain,
% 27.80/18.01 (big_f(c2, f9(c2, c2))),
% 27.80/18.01 inference(unit_resolution,[status(thm)],[5078, 121, 122, 148, 79, 5020, 115, 22, 5019, 5030])).
% 27.80/18.01 tff(5080,assumption,(c1 = c3), introduced(assumption)).
% 27.80/18.01 tff(5081,plain,
% 27.80/18.01 (big_f(c2, c1)),
% 27.80/18.01 inference(unit_resolution,[status(thm)],[3721, 3719, 148, 79, 122])).
% 27.80/18.01 tff(5082,plain,
% 27.80/18.01 (big_f(c1, c2)),
% 27.80/18.01 inference(unit_resolution,[status(thm)],[4920, 5081, 79, 122, 17, 347, 148, 121])).
% 27.80/18.01 tff(5083,plain,
% 27.80/18.01 (big_f(f9(c2, c2), f10(c2))),
% 27.80/18.01 inference(unit_resolution,[status(thm)],[3682, 5082, 122, 148, 79])).
% 27.80/18.01 tff(5084,plain,
% 27.80/18.01 (~(f9(c2, c1) = c1)),
% 27.80/18.01 inference(unit_resolution,[status(thm)],[743, 731, 148, 5083, 79, 122])).
% 27.80/18.01 tff(5085,plain,
% 27.80/18.01 (~(f9(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.80/18.01 inference(unit_resolution,[status(thm)],[1141, 5084, 122, 79, 148])).
% 27.80/18.01 tff(5086,plain,
% 27.80/18.01 (~big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 27.80/18.01 inference(unit_resolution,[status(thm)],[1149, 731, 122, 79, 148])).
% 27.80/18.01 tff(5087,plain,
% 27.80/18.01 (big_f(f9(c2, c2), c2)),
% 27.80/18.01 inference(unit_resolution,[status(thm)],[3687, 5083, 122])).
% 27.80/18.01 tff(5088,plain,
% 27.80/18.01 (big_f(f7(c2), c2)),
% 27.80/18.01 inference(modus_ponens,[status(thm)],[5087, 4570])).
% 27.80/18.01 tff(5089,plain,
% 27.80/18.01 (c2 = f5(c2)),
% 27.80/18.01 inference(unit_resolution,[status(thm)],[1160, 676, 122, 17, 5088, 5086, 5085])).
% 27.80/18.01 tff(5090,plain,
% 27.80/18.01 (c3 = c1),
% 27.80/18.01 inference(symmetry,[status(thm)],[5080])).
% 27.80/18.01 tff(5091,plain,
% 27.80/18.01 (c3 = f9(c2, c2)),
% 27.80/18.01 inference(transitivity,[status(thm)],[5090, 149, 132])).
% 27.80/18.01 tff(5092,plain,
% 27.80/18.01 ((c2 = c3) <=> (c2 = f9(c2, c2))),
% 27.80/18.01 inference(monotonicity,[status(thm)],[5091])).
% 27.80/18.01 tff(5093,plain,
% 27.80/18.01 ((c2 = c3) <=> (f9(c2, c2) = c2)),
% 27.80/18.01 inference(transitivity,[status(thm)],[5092, 167])).
% 27.80/18.01 tff(5094,plain,
% 27.80/18.01 ((f9(c2, c2) = c2) <=> (c2 = c3)),
% 27.80/18.01 inference(symmetry,[status(thm)],[5093])).
% 27.80/18.01 tff(5095,plain,
% 27.80/18.01 ((~(f9(c2, c2) = c2)) <=> (~(c2 = c3))),
% 27.80/18.01 inference(monotonicity,[status(thm)],[5094])).
% 27.80/18.01 tff(5096,plain,
% 27.80/18.01 (~(c2 = c3)),
% 27.80/18.01 inference(modus_ponens,[status(thm)],[185, 5095])).
% 27.80/18.01 tff(5097,plain,
% 27.80/18.01 (big_f(f4(c4), c4)),
% 27.80/18.01 inference(unit_resolution,[status(thm)],[807, 5081, 79, 347, 5096, 121, 148, 122, 22])).
% 27.80/18.01 tff(5098,plain,
% 27.80/18.01 (~(c4 = c2)),
% 27.80/18.01 inference(unit_resolution,[status(thm)],[476, 5097, 79, 121])).
% 27.80/18.01 tff(5099,plain,
% 27.80/18.01 (c4 = c1),
% 27.80/18.01 inference(unit_resolution,[status(thm)],[461, 5098])).
% 27.80/18.01 tff(5100,plain,
% 27.80/18.01 (c4 = f9(c2, c2)),
% 27.80/18.01 inference(transitivity,[status(thm)],[5099, 149, 132])).
% 27.80/18.01 tff(5101,plain,
% 27.80/18.01 ((c2 = c4) <=> (c2 = f9(c2, c2))),
% 27.80/18.01 inference(monotonicity,[status(thm)],[5100])).
% 27.80/18.01 tff(5102,plain,
% 27.80/18.01 ((c2 = c4) <=> (f9(c2, c2) = c2)),
% 27.80/18.01 inference(transitivity,[status(thm)],[5101, 167])).
% 27.80/18.01 tff(5103,plain,
% 27.80/18.01 ((f9(c2, c2) = c2) <=> (c2 = c4)),
% 27.80/18.01 inference(symmetry,[status(thm)],[5102])).
% 27.80/18.01 tff(5104,plain,
% 27.80/18.01 ((f9(c2, c2) = c2) <=> (f7(c1) = c4)),
% 27.80/18.01 inference(transitivity,[status(thm)],[5103, 869])).
% 27.80/18.01 tff(5105,plain,
% 27.80/18.01 ((~(f9(c2, c2) = c2)) <=> (~(f7(c1) = c4))),
% 27.80/18.01 inference(monotonicity,[status(thm)],[5104])).
% 27.80/18.01 tff(5106,plain,
% 27.80/18.01 (~(f7(c1) = c4)),
% 27.80/18.01 inference(modus_ponens,[status(thm)],[185, 5105])).
% 27.80/18.01 tff(5107,plain,
% 27.80/18.01 ((~(f9(c2, c2) = c2)) <=> (~(c2 = c4))),
% 27.80/18.01 inference(monotonicity,[status(thm)],[5103])).
% 27.80/18.01 tff(5108,plain,
% 27.80/18.01 (~(c2 = c4)),
% 27.80/18.01 inference(modus_ponens,[status(thm)],[185, 5107])).
% 27.80/18.01 tff(5109,plain,
% 27.80/18.01 ((f5(c2) = c3) <=> (f5(c2) = c1)),
% 27.80/18.01 inference(monotonicity,[status(thm)],[5090])).
% 27.80/18.01 tff(5110,plain,
% 27.80/18.01 ((f5(c2) = c1) <=> (f5(c2) = c3)),
% 27.80/18.01 inference(symmetry,[status(thm)],[5109])).
% 27.80/18.01 tff(5111,plain,
% 27.80/18.01 ((f9(c2, c2) = f5(c2)) <=> (f5(c2) = c3)),
% 27.80/18.01 inference(transitivity,[status(thm)],[4748, 5110])).
% 27.80/18.01 tff(5112,plain,
% 27.80/18.01 ((~(f9(c2, c2) = f5(c2))) <=> (~(f5(c2) = c3))),
% 27.80/18.01 inference(monotonicity,[status(thm)],[5111])).
% 27.80/18.01 tff(5113,plain,
% 27.80/18.01 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | (~(f9(c2, c2) = f5(c2))) | big_f(f7(c2), f9(c2, c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | (~(f9(c2, c2) = f5(c2))) | big_f(f7(c2), f9(c2, c2)))),
% 27.80/18.01 inference(rewrite,[status(thm)],[])).
% 27.80/18.01 tff(5114,plain,
% 27.80/18.01 (((~(f10(c2) = c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), f9(c2, c2)) | (~(f9(c2, c2) = f5(c2)))) <=> ((~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | (~(f9(c2, c2) = f5(c2))) | big_f(f7(c2), f9(c2, c2)))),
% 27.80/18.01 inference(rewrite,[status(thm)],[])).
% 27.80/18.01 tff(5115,plain,
% 27.80/18.01 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), f9(c2, c2)) | (~(f9(c2, c2) = f5(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | (~(f9(c2, c2) = f5(c2))) | big_f(f7(c2), f9(c2, c2))))),
% 27.80/18.01 inference(monotonicity,[status(thm)],[5114])).
% 27.80/18.01 tff(5116,plain,
% 27.80/18.01 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), f9(c2, c2)) | (~(f9(c2, c2) = f5(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | (~(f9(c2, c2) = f5(c2))) | big_f(f7(c2), f9(c2, c2)))),
% 27.80/18.01 inference(transitivity,[status(thm)],[5115, 5113])).
% 27.80/18.01 tff(5117,plain,
% 27.80/18.01 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), f9(c2, c2)) | (~(f9(c2, c2) = f5(c2))))),
% 27.80/18.01 inference(quant_inst,[status(thm)],[])).
% 27.80/18.01 tff(5118,plain,
% 27.80/18.01 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | (~(f9(c2, c2) = f5(c2))) | big_f(f7(c2), f9(c2, c2))),
% 27.80/18.01 inference(modus_ponens,[status(thm)],[5117, 5116])).
% 27.80/18.01 tff(5119,plain,
% 27.80/18.01 (~(f9(c2, c2) = f5(c2))),
% 27.80/18.01 inference(unit_resolution,[status(thm)],[5118, 267, 122, 17, 5086, 5085, 4930])).
% 27.80/18.01 tff(5120,plain,
% 27.80/18.01 (~(f5(c2) = c3)),
% 27.80/18.01 inference(modus_ponens,[status(thm)],[5119, 5112])).
% 27.80/18.01 tff(5121,plain,
% 27.80/18.01 ((f3(c2, f9(c2, c2)) = f9(c2, c2)) <=> (f3(f7(c1), c1) = c1)),
% 27.80/18.01 inference(symmetry,[status(thm)],[4366])).
% 27.80/18.01 tff(5122,plain,
% 27.80/18.01 ((~(f3(c2, f9(c2, c2)) = f9(c2, c2))) <=> (~(f3(f7(c1), c1) = c1))),
% 27.80/18.01 inference(monotonicity,[status(thm)],[5121])).
% 27.80/18.01 tff(5123,plain,
% 27.80/18.01 (big_f(f3(f7(c1), c1), f7(c1)) <=> big_f(f3(c2, f9(c2, c2)), c2)),
% 27.80/18.01 inference(monotonicity,[status(thm)],[4365, 347])).
% 27.80/18.01 tff(5124,assumption,(c2 = f5(c2)), introduced(assumption)).
% 27.80/18.01 tff(5125,plain,
% 27.80/18.01 (f1(c2, f9(c2, c2)) = f1(f5(c2), f5(c1))),
% 27.80/18.01 inference(monotonicity,[status(thm)],[5124, 4445])).
% 27.80/18.01 tff(5126,plain,
% 27.80/18.01 (f1(f5(c2), f5(c1)) = f1(c2, f9(c2, c2))),
% 27.80/18.01 inference(symmetry,[status(thm)],[5125])).
% 27.80/18.01 tff(5127,plain,
% 27.80/18.01 (f1(f5(c2), f5(c1)) = f1(c2, c1)),
% 27.80/18.01 inference(transitivity,[status(thm)],[5126, 5046])).
% 27.80/18.01 tff(5128,plain,
% 27.80/18.01 (f5(c2) = c2),
% 27.80/18.01 inference(symmetry,[status(thm)],[5124])).
% 27.80/18.01 tff(5129,plain,
% 27.80/18.01 (big_f(f5(c2), f1(f5(c2), f5(c1))) <=> big_f(c2, f1(c2, c1))),
% 27.80/18.01 inference(monotonicity,[status(thm)],[5128, 5127])).
% 27.80/18.01 tff(5130,plain,
% 27.80/18.01 (big_f(c2, f1(c2, c1)) <=> big_f(f5(c2), f1(f5(c2), f5(c1)))),
% 27.80/18.01 inference(symmetry,[status(thm)],[5129])).
% 27.80/18.01 tff(5131,assumption,(f1(f5(c2), f5(c1)) = c2), introduced(assumption)).
% 27.80/18.01 tff(5132,plain,
% 27.80/18.01 (f1(c2, c1) = c2),
% 27.80/18.01 inference(transitivity,[status(thm)],[5043, 5125, 5131])).
% 27.80/18.01 tff(5133,plain,
% 27.80/18.01 (big_f(c2, f1(c2, c1)) <=> big_f(c2, c2)),
% 27.80/18.01 inference(monotonicity,[status(thm)],[5132])).
% 27.80/18.01 tff(5134,plain,
% 27.80/18.01 (big_f(c2, c2) <=> big_f(c2, f1(c2, c1))),
% 27.80/18.01 inference(symmetry,[status(thm)],[5133])).
% 27.80/18.01 tff(5135,plain,
% 27.80/18.01 (big_f(c2, c2) <=> big_f(f5(c2), f1(f5(c2), f5(c1)))),
% 27.80/18.01 inference(transitivity,[status(thm)],[5134, 5130])).
% 27.80/18.01 tff(5136,plain,
% 27.80/18.01 ((~big_f(c2, c2)) <=> (~big_f(f5(c2), f1(f5(c2), f5(c1))))),
% 27.80/18.01 inference(monotonicity,[status(thm)],[5135])).
% 27.80/18.01 tff(5137,plain,
% 27.80/18.01 (~big_f(f5(c2), f1(f5(c2), f5(c1)))),
% 27.80/18.01 inference(modus_ponens,[status(thm)],[121, 5136])).
% 27.80/18.01 tff(5138,assumption,(~(f5(c2) = c3)), introduced(assumption)).
% 27.80/18.01 tff(5139,plain,
% 27.80/18.01 ((f1(f5(c2), f5(c1)) = f5(c1)) <=> (f1(f5(c2), f5(c1)) = c1)),
% 27.80/18.01 inference(monotonicity,[status(thm)],[230])).
% 27.80/18.01 tff(5140,plain,
% 27.80/18.01 ((f1(f5(c2), f5(c1)) = c1) <=> (f1(f5(c2), f5(c1)) = f5(c1))),
% 27.80/18.01 inference(symmetry,[status(thm)],[5139])).
% 27.80/18.01 tff(5141,plain,
% 27.80/18.01 ((f1(f5(c2), f5(c1)) = c1) <=> (f1(c2, c1) = c1)),
% 27.80/18.01 inference(monotonicity,[status(thm)],[5127])).
% 27.80/18.02 tff(5142,plain,
% 27.80/18.02 ((f1(c2, c1) = c1) <=> (f1(f5(c2), f5(c1)) = c1)),
% 27.80/18.02 inference(symmetry,[status(thm)],[5141])).
% 27.80/18.02 tff(5143,plain,
% 27.80/18.02 ((f1(c2, c1) = c1) <=> (c2 = f9(c2, c2))),
% 27.80/18.02 inference(monotonicity,[status(thm)],[5132, 150])).
% 27.80/18.02 tff(5144,plain,
% 27.80/18.02 ((f1(c2, c1) = c1) <=> (f9(c2, c2) = c2)),
% 27.80/18.02 inference(transitivity,[status(thm)],[5143, 167])).
% 27.80/18.02 tff(5145,plain,
% 27.80/18.02 ((f9(c2, c2) = c2) <=> (f1(c2, c1) = c1)),
% 27.80/18.02 inference(symmetry,[status(thm)],[5144])).
% 27.80/18.02 tff(5146,plain,
% 27.80/18.02 ((f9(c2, c2) = c2) <=> (f1(f5(c2), f5(c1)) = f5(c1))),
% 27.80/18.02 inference(transitivity,[status(thm)],[5145, 5142, 5140])).
% 27.80/18.02 tff(5147,plain,
% 27.80/18.02 ((~(f9(c2, c2) = c2)) <=> (~(f1(f5(c2), f5(c1)) = f5(c1)))),
% 27.80/18.02 inference(monotonicity,[status(thm)],[5146])).
% 27.80/18.02 tff(5148,plain,
% 27.80/18.02 (~(f1(f5(c2), f5(c1)) = f5(c1))),
% 27.80/18.02 inference(modus_ponens,[status(thm)],[185, 5147])).
% 27.80/18.02 tff(5149,plain,
% 27.80/18.02 (big_f(f3(c2, f9(c2, c2)), c2) <=> big_f(f3(f7(c1), c1), f7(c1))),
% 27.80/18.02 inference(symmetry,[status(thm)],[5123])).
% 27.80/18.02 tff(5150,assumption,(~big_f(f5(c2), f1(f5(c2), f5(c1)))), introduced(assumption)).
% 27.80/18.02 tff(5151,assumption,(~(f1(f5(c2), f5(c1)) = f5(c1))), introduced(assumption)).
% 27.80/18.02 tff(5152,plain,
% 27.80/18.02 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f7(c1) = c4) | (f5(c2) = c3) | (f3(f7(c1), c1) = c1) | big_f(f3(f7(c1), c1), f7(c1)) | (f1(f5(c2), f5(c1)) = f5(c1)) | big_f(f5(c2), f1(f5(c2), f5(c1))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (f7(c1) = c4) | (f5(c2) = c3) | (f3(f7(c1), c1) = c1) | big_f(f3(f7(c1), c1), f7(c1)) | (f1(f5(c2), f5(c1)) = f5(c1)) | big_f(f5(c2), f1(f5(c2), f5(c1))))),
% 27.80/18.02 inference(rewrite,[status(thm)],[])).
% 27.80/18.02 tff(5153,plain,
% 27.80/18.02 (((f7(c1) = c4) | (f3(f7(c1), c1) = c1) | big_f(f3(f7(c1), c1), f7(c1)) | (f5(c2) = c3) | (f1(f5(c2), f5(c1)) = f5(c1)) | big_f(f5(c2), f1(f5(c2), f5(c1)))) <=> ((f7(c1) = c4) | (f5(c2) = c3) | (f3(f7(c1), c1) = c1) | big_f(f3(f7(c1), c1), f7(c1)) | (f1(f5(c2), f5(c1)) = f5(c1)) | big_f(f5(c2), f1(f5(c2), f5(c1))))),
% 27.80/18.02 inference(rewrite,[status(thm)],[])).
% 27.80/18.02 tff(5154,plain,
% 27.80/18.02 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f7(c1) = c4) | (f3(f7(c1), c1) = c1) | big_f(f3(f7(c1), c1), f7(c1)) | (f5(c2) = c3) | (f1(f5(c2), f5(c1)) = f5(c1)) | big_f(f5(c2), f1(f5(c2), f5(c1))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f7(c1) = c4) | (f5(c2) = c3) | (f3(f7(c1), c1) = c1) | big_f(f3(f7(c1), c1), f7(c1)) | (f1(f5(c2), f5(c1)) = f5(c1)) | big_f(f5(c2), f1(f5(c2), f5(c1)))))),
% 27.80/18.02 inference(monotonicity,[status(thm)],[5153])).
% 27.80/18.02 tff(5155,plain,
% 27.80/18.02 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f7(c1) = c4) | (f3(f7(c1), c1) = c1) | big_f(f3(f7(c1), c1), f7(c1)) | (f5(c2) = c3) | (f1(f5(c2), f5(c1)) = f5(c1)) | big_f(f5(c2), f1(f5(c2), f5(c1))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (f7(c1) = c4) | (f5(c2) = c3) | (f3(f7(c1), c1) = c1) | big_f(f3(f7(c1), c1), f7(c1)) | (f1(f5(c2), f5(c1)) = f5(c1)) | big_f(f5(c2), f1(f5(c2), f5(c1))))),
% 27.80/18.02 inference(transitivity,[status(thm)],[5154, 5152])).
% 27.80/18.02 tff(5156,plain,
% 27.80/18.02 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f7(c1) = c4) | (f3(f7(c1), c1) = c1) | big_f(f3(f7(c1), c1), f7(c1)) | (f5(c2) = c3) | (f1(f5(c2), f5(c1)) = f5(c1)) | big_f(f5(c2), f1(f5(c2), f5(c1))))),
% 27.80/18.02 inference(quant_inst,[status(thm)],[])).
% 27.80/18.02 tff(5157,plain,
% 27.80/18.02 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (f7(c1) = c4) | (f5(c2) = c3) | (f3(f7(c1), c1) = c1) | big_f(f3(f7(c1), c1), f7(c1)) | (f1(f5(c2), f5(c1)) = f5(c1)) | big_f(f5(c2), f1(f5(c2), f5(c1)))),
% 27.80/18.02 inference(modus_ponens,[status(thm)],[5156, 5155])).
% 27.80/18.02 tff(5158,plain,
% 27.80/18.02 ((f7(c1) = c4) | (f5(c2) = c3) | (f3(f7(c1), c1) = c1) | big_f(f3(f7(c1), c1), f7(c1)) | (f1(f5(c2), f5(c1)) = f5(c1)) | big_f(f5(c2), f1(f5(c2), f5(c1)))),
% 27.80/18.02 inference(unit_resolution,[status(thm)],[5157, 1014])).
% 27.80/18.02 tff(5159,plain,
% 27.80/18.02 (f3(f7(c1), c1) = c1),
% 27.80/18.02 inference(unit_resolution,[status(thm)],[5158, 2854, 5138, 1000, 5151, 5150])).
% 27.80/18.02 tff(5160,plain,
% 27.80/18.02 (f3(c2, f9(c2, c2)) = f9(c2, c2)),
% 27.80/18.02 inference(transitivity,[status(thm)],[4340, 5159, 149, 132])).
% 27.80/18.02 tff(5161,plain,
% 27.80/18.02 (big_f(f3(c2, f9(c2, c2)), c2) <=> big_f(f9(c2, c2), c2)),
% 27.80/18.02 inference(monotonicity,[status(thm)],[5160])).
% 27.80/18.02 tff(5162,plain,
% 27.80/18.02 (big_f(f9(c2, c2), c2) <=> big_f(f3(c2, f9(c2, c2)), c2)),
% 27.80/18.02 inference(symmetry,[status(thm)],[5161])).
% 27.80/18.02 tff(5163,plain,
% 27.80/18.02 (big_f(f9(c2, c2), c2) <=> big_f(f3(f7(c1), c1), f7(c1))),
% 27.80/18.02 inference(transitivity,[status(thm)],[5162, 5149])).
% 27.80/18.02 tff(5164,plain,
% 27.80/18.02 (big_f(f3(f7(c1), c1), f7(c1))),
% 27.80/18.02 inference(modus_ponens,[status(thm)],[2041, 5163])).
% 27.80/18.02 tff(5165,plain,
% 27.80/18.02 ($false),
% 27.80/18.02 inference(unit_resolution,[status(thm)],[2854, 5164])).
% 27.80/18.02 tff(5166,plain,(big_f(f3(f7(c1), c1), f7(c1)) | (~big_f(f9(c2, c2), c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f7(c1) = c2)) | (f5(c2) = c3) | (f7(c1) = c4) | (f1(f5(c2), f5(c1)) = f5(c1)) | big_f(f5(c2), f1(f5(c2), f5(c1)))), inference(lemma,lemma(discharge,[]))).
% 27.80/18.02 tff(5167,plain,
% 27.80/18.02 (big_f(f3(f7(c1), c1), f7(c1))),
% 27.80/18.02 inference(unit_resolution,[status(thm)],[5166, 5148, 148, 79, 122, 347, 2041, 5138, 1000, 5137])).
% 27.80/18.02 tff(5168,plain,
% 27.80/18.02 (big_f(f3(c2, f9(c2, c2)), c2)),
% 27.80/18.02 inference(modus_ponens,[status(thm)],[5167, 5123])).
% 27.80/18.02 tff(5169,plain,
% 27.80/18.02 (big_f(c2, c2) <=> big_f(c2, f1(c2, f9(c2, c2)))),
% 27.80/18.02 inference(transitivity,[status(thm)],[5134, 5050])).
% 27.80/18.02 tff(5170,plain,
% 27.80/18.02 ((~big_f(c2, c2)) <=> (~big_f(c2, f1(c2, f9(c2, c2))))),
% 27.80/18.02 inference(monotonicity,[status(thm)],[5169])).
% 27.80/18.02 tff(5171,plain,
% 27.80/18.02 (~big_f(c2, f1(c2, f9(c2, c2)))),
% 27.80/18.02 inference(modus_ponens,[status(thm)],[121, 5170])).
% 27.80/18.02 tff(5172,plain,
% 27.80/18.02 ((f1(c2, f9(c2, c2)) = f9(c2, c2)) <=> (f1(c2, c1) = c1)),
% 27.80/18.02 inference(monotonicity,[status(thm)],[5046, 161])).
% 27.80/18.02 tff(5173,plain,
% 27.80/18.02 ((f1(c2, c1) = c1) <=> (f1(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.80/18.02 inference(symmetry,[status(thm)],[5172])).
% 27.80/18.02 tff(5174,plain,
% 27.80/18.02 ((f9(c2, c2) = c2) <=> (f1(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.80/18.02 inference(transitivity,[status(thm)],[5145, 5173])).
% 27.80/18.02 tff(5175,plain,
% 27.80/18.02 ((~(f9(c2, c2) = c2)) <=> (~(f1(c2, f9(c2, c2)) = f9(c2, c2)))),
% 27.80/18.02 inference(monotonicity,[status(thm)],[5174])).
% 27.80/18.02 tff(5176,plain,
% 27.80/18.02 (~(f1(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.80/18.02 inference(modus_ponens,[status(thm)],[185, 5175])).
% 27.80/18.02 tff(5177,plain,
% 27.80/18.02 (~(f3(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.80/18.02 inference(unit_resolution,[status(thm)],[975, 969, 873, 377, 5176, 5171, 5168])).
% 27.80/18.02 tff(5178,plain,
% 27.80/18.02 (~(f3(f7(c1), c1) = c1)),
% 27.80/18.02 inference(modus_ponens,[status(thm)],[5177, 5122])).
% 27.80/18.02 tff(5179,plain,
% 27.80/18.02 (f3(f7(c1), c1) = c2),
% 27.80/18.02 inference(unit_resolution,[status(thm)],[918, 5178])).
% 27.80/18.02 tff(5180,plain,
% 27.80/18.02 (f3(c2, f9(c2, c2)) = c2),
% 27.80/18.02 inference(transitivity,[status(thm)],[4340, 5179])).
% 27.80/18.02 tff(5181,plain,
% 27.80/18.02 (big_f(f3(c2, f9(c2, c2)), c2) <=> big_f(c2, c2)),
% 27.80/18.02 inference(monotonicity,[status(thm)],[5180])).
% 27.80/18.02 tff(5182,plain,
% 27.80/18.02 (big_f(c2, c2) <=> big_f(f3(c2, f9(c2, c2)), c2)),
% 27.80/18.02 inference(symmetry,[status(thm)],[5181])).
% 27.80/18.02 tff(5183,plain,
% 27.80/18.02 ((~big_f(c2, c2)) <=> (~big_f(f3(c2, f9(c2, c2)), c2))),
% 27.80/18.02 inference(monotonicity,[status(thm)],[5182])).
% 27.80/18.02 tff(5184,plain,
% 27.80/18.02 (~big_f(f3(c2, f9(c2, c2)), c2)),
% 27.80/18.02 inference(modus_ponens,[status(thm)],[121, 5183])).
% 27.80/18.02 tff(5185,plain,
% 27.80/18.02 ($false),
% 27.80/18.02 inference(unit_resolution,[status(thm)],[5168, 5184])).
% 27.80/18.02 tff(5186,plain,((~(f1(f5(c2), f5(c1)) = c2)) | big_f(c2, c2) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f7(c1) = c2)) | (c2 = c4) | (c2 = c3) | (~big_f(f9(c2, c2), c2)) | (f5(c2) = c3) | (f7(c1) = c4) | (~(f5(c1) = c1)) | (~(c2 = f5(c2)))), inference(lemma,lemma(discharge,[]))).
% 27.80/18.02 tff(5187,plain,
% 27.80/18.02 (~(f1(f5(c2), f5(c1)) = c2)),
% 27.80/18.02 inference(unit_resolution,[status(thm)],[5186, 5120, 148, 79, 122, 347, 5108, 5096, 5087, 121, 5106, 230, 5089])).
% 27.80/18.02 tff(5188,plain,
% 27.80/18.02 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f1(f5(c2), f5(c1)) = c1) | (f1(f5(c2), f5(c1)) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f1(f5(c2), f5(c1)) = c1) | (f1(f5(c2), f5(c1)) = c2))),
% 27.80/18.02 inference(rewrite,[status(thm)],[])).
% 27.80/18.02 tff(5189,plain,
% 27.80/18.02 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f1(f5(c2), f5(c1)) = c1) | (f1(f5(c2), f5(c1)) = c2))),
% 27.80/18.02 inference(quant_inst,[status(thm)],[])).
% 27.80/18.02 tff(5190,plain,
% 27.80/18.02 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f1(f5(c2), f5(c1)) = c1) | (f1(f5(c2), f5(c1)) = c2)),
% 27.80/18.02 inference(modus_ponens,[status(thm)],[5189, 5188])).
% 27.80/18.02 tff(5191,plain,
% 27.80/18.02 ((f1(f5(c2), f5(c1)) = c1) | (f1(f5(c2), f5(c1)) = c2)),
% 27.80/18.02 inference(unit_resolution,[status(thm)],[5190, 10])).
% 27.80/18.02 tff(5192,plain,
% 27.80/18.02 (f1(f5(c2), f5(c1)) = c1),
% 27.80/18.02 inference(unit_resolution,[status(thm)],[5191, 5187])).
% 27.80/18.02 tff(5193,plain,
% 27.80/18.02 (f1(c2, f9(c2, c2)) = f1(f5(c2), f5(c1))),
% 27.80/18.02 inference(monotonicity,[status(thm)],[5089, 4445])).
% 27.80/18.02 tff(5194,plain,
% 27.80/18.02 (f1(c2, c1) = f9(c2, c2)),
% 27.80/18.02 inference(transitivity,[status(thm)],[5043, 5193, 5192, 149, 132])).
% 27.80/18.02 tff(5195,plain,
% 27.80/18.02 (big_f(c2, f1(c2, c1)) <=> big_f(c2, f9(c2, c2))),
% 27.80/18.02 inference(monotonicity,[status(thm)],[5194])).
% 27.80/18.02 tff(5196,plain,
% 27.80/18.02 (big_f(c2, f9(c2, c2)) <=> big_f(c2, f1(c2, c1))),
% 27.80/18.02 inference(symmetry,[status(thm)],[5195])).
% 27.80/18.02 tff(5197,plain,
% 27.80/18.02 (big_f(c2, f9(c2, c2)) <=> big_f(c2, f1(c2, f9(c2, c2)))),
% 27.80/18.02 inference(transitivity,[status(thm)],[5196, 5050])).
% 27.80/18.02 tff(5198,plain,
% 27.80/18.02 (big_f(c2, f1(c2, f9(c2, c2)))),
% 27.80/18.02 inference(modus_ponens,[status(thm)],[3719, 5197])).
% 27.80/18.02 tff(5199,plain,
% 27.80/18.02 (f1(f5(c2), f5(c1)) = f1(c2, f9(c2, c2))),
% 27.80/18.02 inference(symmetry,[status(thm)],[5193])).
% 27.80/18.02 tff(5200,plain,
% 27.80/18.02 (f1(f5(c2), f5(c1)) = f1(c2, c1)),
% 27.80/18.02 inference(transitivity,[status(thm)],[5199, 5046])).
% 27.80/18.02 tff(5201,plain,
% 27.80/18.02 ((f1(f5(c2), f5(c1)) = c1) <=> (f1(c2, c1) = c1)),
% 27.80/18.02 inference(monotonicity,[status(thm)],[5200])).
% 27.80/18.02 tff(5202,plain,
% 27.80/18.02 ((f1(f5(c2), f5(c1)) = c1) <=> (f1(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.80/18.02 inference(transitivity,[status(thm)],[5201, 5173])).
% 27.80/18.02 tff(5203,plain,
% 27.80/18.02 (f1(c2, f9(c2, c2)) = f9(c2, c2)),
% 27.80/18.02 inference(modus_ponens,[status(thm)],[5192, 5202])).
% 27.80/18.02 tff(5204,plain,
% 27.80/18.02 ($false),
% 27.80/18.02 inference(unit_resolution,[status(thm)],[910, 904, 873, 377, 430, 429, 4350, 4345])).
% 27.80/18.02 tff(5205,plain,((~(f3(f7(c1), c1) = c2)) | (c2 = c4) | (c2 = c3) | (~(f1(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(c2, f1(c2, f9(c2, c2)))) | big_f(c2, c2) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f7(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.80/18.02 tff(5206,plain,
% 27.80/18.02 (~(f3(f7(c1), c1) = c2)),
% 27.80/18.02 inference(unit_resolution,[status(thm)],[5205, 5203, 5096, 5108, 5198, 121, 148, 79, 122, 347])).
% 27.80/18.02 tff(5207,plain,
% 27.80/18.02 (f3(f7(c1), c1) = c1),
% 27.80/18.02 inference(unit_resolution,[status(thm)],[918, 5206])).
% 27.80/18.02 tff(5208,plain,
% 27.80/18.02 (f3(c2, f9(c2, c2)) = f9(c2, c2)),
% 27.80/18.02 inference(transitivity,[status(thm)],[4340, 5207, 149, 132])).
% 27.80/18.02 tff(5209,plain,
% 27.80/18.02 (big_f(f3(c2, f9(c2, c2)), c2) <=> big_f(f9(c2, c2), c2)),
% 27.80/18.02 inference(monotonicity,[status(thm)],[5208])).
% 27.80/18.02 tff(5210,plain,
% 27.80/18.02 (big_f(f9(c2, c2), c2) <=> big_f(f3(c2, f9(c2, c2)), c2)),
% 27.80/18.02 inference(symmetry,[status(thm)],[5209])).
% 27.80/18.02 tff(5211,plain,
% 27.80/18.02 (big_f(f3(c2, f9(c2, c2)), c2)),
% 27.80/18.02 inference(modus_ponens,[status(thm)],[5087, 5210])).
% 27.80/18.02 tff(5212,plain,
% 27.80/18.02 (f3(c2, f9(c2, c2)) = f9(c2, c2)),
% 27.80/18.02 inference(modus_ponens,[status(thm)],[5207, 4366])).
% 27.80/18.02 tff(5213,plain,
% 27.80/18.02 ($false),
% 27.80/18.02 inference(unit_resolution,[status(thm)],[939, 933, 5108, 5096, 5203, 5198, 5212, 5211])).
% 27.80/18.02 tff(5214,plain,(big_f(f9(c2, c1), f10(c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f7(c1) = c2)) | big_f(c2, c2) | (~big_f(c2, f9(c2, c2))) | (~(f5(c1) = c1)) | (~(c1 = c3)) | (f7(c2) = c2) | big_f(f7(c2), f9(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 27.80/18.02 tff(5215,plain,
% 27.80/18.02 (big_f(f9(c2, c1), f10(c2))),
% 27.80/18.02 inference(unit_resolution,[status(thm)],[5214, 4930, 79, 122, 347, 121, 3719, 230, 5080, 17, 148])).
% 27.80/18.02 tff(5216,plain,
% 27.80/18.02 (big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 27.80/18.02 inference(unit_resolution,[status(thm)],[3898, 5215, 148, 79, 122])).
% 27.80/18.02 tff(5217,plain,
% 27.80/18.02 (f9(c2, f9(c2, c2)) = f9(c2, c2)),
% 27.80/18.02 inference(unit_resolution,[status(thm)],[4482, 5216, 122, 121, 148, 79, 328])).
% 27.80/18.02 tff(5218,plain,
% 27.80/18.02 (c2 = f5(c2)),
% 27.80/18.02 inference(unit_resolution,[status(thm)],[1196, 1190, 122, 17, 5088, 5216, 5217])).
% 27.80/18.02 tff(5219,plain,
% 27.80/18.02 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~(f9(c2, c2) = f5(c2))) | big_f(f7(c2), f9(c2, c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~(f9(c2, c2) = f5(c2))) | big_f(f7(c2), f9(c2, c2)))),
% 27.80/18.02 inference(rewrite,[status(thm)],[])).
% 27.80/18.02 tff(5220,plain,
% 27.80/18.02 (((~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f7(c2), f9(c2, c2)) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, c2) = f5(c2)))) <=> ((~(f10(c2) = c2)) | (f7(c2) = c2) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~(f9(c2, c2) = f5(c2))) | big_f(f7(c2), f9(c2, c2)))),
% 27.80/18.02 inference(rewrite,[status(thm)],[])).
% 27.80/18.02 tff(5221,plain,
% 27.80/18.02 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f7(c2), f9(c2, c2)) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, c2) = f5(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~(f9(c2, c2) = f5(c2))) | big_f(f7(c2), f9(c2, c2))))),
% 27.80/18.02 inference(monotonicity,[status(thm)],[5220])).
% 27.80/18.02 tff(5222,plain,
% 27.80/18.02 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f7(c2), f9(c2, c2)) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, c2) = f5(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~(f9(c2, c2) = f5(c2))) | big_f(f7(c2), f9(c2, c2)))),
% 27.80/18.02 inference(transitivity,[status(thm)],[5221, 5219])).
% 27.80/18.02 tff(5223,plain,
% 27.80/18.02 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f7(c2), f9(c2, c2)) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, c2) = f5(c2))))),
% 27.80/18.02 inference(quant_inst,[status(thm)],[])).
% 27.80/18.02 tff(5224,plain,
% 27.80/18.02 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~(f9(c2, c2) = f5(c2))) | big_f(f7(c2), f9(c2, c2))),
% 27.80/18.02 inference(modus_ponens,[status(thm)],[5223, 5222])).
% 27.80/18.02 tff(5225,plain,
% 27.80/18.02 (~(f9(c2, c2) = f5(c2))),
% 27.80/18.02 inference(unit_resolution,[status(thm)],[5224, 783, 122, 17, 5216, 5217, 4930])).
% 27.80/18.02 tff(5226,plain,
% 27.80/18.02 (~(f5(c2) = c3)),
% 27.80/18.02 inference(modus_ponens,[status(thm)],[5225, 5112])).
% 27.80/18.02 tff(5227,plain,
% 27.80/18.02 (~(f1(f5(c2), f5(c1)) = c2)),
% 27.80/18.02 inference(unit_resolution,[status(thm)],[5186, 5226, 148, 79, 122, 347, 5108, 5096, 5087, 121, 5106, 230, 5218])).
% 27.80/18.02 tff(5228,plain,
% 27.80/18.02 (f1(f5(c2), f5(c1)) = c1),
% 27.80/18.02 inference(unit_resolution,[status(thm)],[5191, 5227])).
% 27.80/18.02 tff(5229,plain,
% 27.80/18.02 (f1(c2, f9(c2, c2)) = f1(f5(c2), f5(c1))),
% 27.80/18.02 inference(monotonicity,[status(thm)],[5218, 4445])).
% 27.80/18.02 tff(5230,plain,
% 27.80/18.02 (f1(c2, c1) = f9(c2, c2)),
% 27.80/18.02 inference(transitivity,[status(thm)],[5043, 5229, 5228, 149, 132])).
% 27.80/18.02 tff(5231,plain,
% 27.80/18.02 (big_f(c2, f1(c2, c1)) <=> big_f(c2, f9(c2, c2))),
% 27.80/18.02 inference(monotonicity,[status(thm)],[5230])).
% 27.80/18.02 tff(5232,plain,
% 27.80/18.02 (big_f(c2, f9(c2, c2)) <=> big_f(c2, f1(c2, c1))),
% 27.80/18.02 inference(symmetry,[status(thm)],[5231])).
% 27.80/18.02 tff(5233,plain,
% 27.80/18.02 (big_f(c2, f9(c2, c2)) <=> big_f(c2, f1(c2, f9(c2, c2)))),
% 27.80/18.02 inference(transitivity,[status(thm)],[5232, 5050])).
% 27.80/18.02 tff(5234,plain,
% 27.80/18.02 (big_f(c2, f1(c2, f9(c2, c2)))),
% 27.80/18.02 inference(modus_ponens,[status(thm)],[3719, 5233])).
% 27.80/18.02 tff(5235,plain,
% 27.80/18.02 (f1(f5(c2), f5(c1)) = f1(c2, f9(c2, c2))),
% 27.80/18.02 inference(symmetry,[status(thm)],[5229])).
% 27.80/18.02 tff(5236,plain,
% 27.80/18.02 (f1(f5(c2), f5(c1)) = f1(c2, c1)),
% 27.80/18.02 inference(transitivity,[status(thm)],[5235, 5046])).
% 27.80/18.02 tff(5237,plain,
% 27.80/18.02 ((f1(f5(c2), f5(c1)) = c1) <=> (f1(c2, c1) = c1)),
% 27.80/18.02 inference(monotonicity,[status(thm)],[5236])).
% 27.80/18.02 tff(5238,plain,
% 27.80/18.02 ((f1(f5(c2), f5(c1)) = c1) <=> (f1(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.80/18.02 inference(transitivity,[status(thm)],[5237, 5173])).
% 27.80/18.02 tff(5239,plain,
% 27.80/18.02 (f1(c2, f9(c2, c2)) = f9(c2, c2)),
% 27.80/18.02 inference(modus_ponens,[status(thm)],[5228, 5238])).
% 27.80/18.02 tff(5240,plain,
% 27.80/18.02 (~(f3(f7(c1), c1) = c2)),
% 27.80/18.02 inference(unit_resolution,[status(thm)],[5205, 5239, 5096, 5108, 5234, 121, 148, 79, 122, 347])).
% 27.80/18.02 tff(5241,plain,
% 27.80/18.02 (f3(f7(c1), c1) = c1),
% 27.80/18.02 inference(unit_resolution,[status(thm)],[918, 5240])).
% 27.80/18.02 tff(5242,plain,
% 27.80/18.02 (f3(c2, f9(c2, c2)) = f9(c2, c2)),
% 27.80/18.02 inference(transitivity,[status(thm)],[4340, 5241, 149, 132])).
% 27.80/18.02 tff(5243,plain,
% 27.80/18.02 (big_f(f3(c2, f9(c2, c2)), c2) <=> big_f(f9(c2, c2), c2)),
% 27.80/18.02 inference(monotonicity,[status(thm)],[5242])).
% 27.80/18.02 tff(5244,plain,
% 27.80/18.02 (big_f(f9(c2, c2), c2) <=> big_f(f3(c2, f9(c2, c2)), c2)),
% 27.80/18.02 inference(symmetry,[status(thm)],[5243])).
% 27.80/18.02 tff(5245,plain,
% 27.80/18.02 (big_f(f3(c2, f9(c2, c2)), c2)),
% 27.80/18.02 inference(modus_ponens,[status(thm)],[5087, 5244])).
% 27.80/18.02 tff(5246,plain,
% 27.80/18.02 (f3(c2, f9(c2, c2)) = f9(c2, c2)),
% 27.80/18.02 inference(modus_ponens,[status(thm)],[5241, 4366])).
% 27.80/18.02 tff(5247,plain,
% 27.80/18.02 ($false),
% 27.80/18.02 inference(unit_resolution,[status(thm)],[939, 933, 5108, 5096, 5239, 5234, 5246, 5245])).
% 27.80/18.02 tff(5248,plain,(big_f(f7(c2), f9(c2, c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f7(c1) = c2)) | big_f(c2, c2) | (~big_f(c2, f9(c2, c2))) | (~(f5(c1) = c1)) | (~(c1 = c3)) | (f7(c2) = c2) | (~(f5(f10(c1)) = c1))), inference(lemma,lemma(discharge,[]))).
% 27.80/18.02 tff(5249,plain,
% 27.80/18.02 (big_f(f7(c2), f9(c2, c2))),
% 27.80/18.02 inference(unit_resolution,[status(thm)],[5248, 121, 79, 122, 120, 148, 5079, 5019, 4971, 17, 5020])).
% 27.80/18.02 tff(5250,plain,
% 27.80/18.02 (big_f(c2, c1)),
% 27.80/18.02 inference(unit_resolution,[status(thm)],[3721, 5079, 148, 79, 122])).
% 27.80/18.02 tff(5251,plain,
% 27.80/18.02 (big_f(c1, c2)),
% 27.80/18.02 inference(unit_resolution,[status(thm)],[4920, 5250, 79, 122, 17, 120, 148, 121])).
% 27.80/18.02 tff(5252,plain,
% 27.80/18.02 (big_f(f9(c2, c2), f10(c2))),
% 27.80/18.02 inference(unit_resolution,[status(thm)],[3682, 5251, 122, 148, 79])).
% 27.80/18.02 tff(5253,plain,
% 27.80/18.02 (big_f(f9(c2, c2), c2)),
% 27.80/18.02 inference(unit_resolution,[status(thm)],[3687, 5252, 122])).
% 27.80/18.02 tff(5254,plain,
% 27.80/18.02 (big_f(f7(c2), c2)),
% 27.80/18.02 inference(modus_ponens,[status(thm)],[5253, 4570])).
% 27.80/18.02 tff(5255,plain,
% 27.80/18.02 (big_f(f9(c2, c1), f10(c2))),
% 27.80/18.02 inference(unit_resolution,[status(thm)],[1173, 5249, 148, 17, 5252, 79, 122])).
% 27.80/18.02 tff(5256,plain,
% 27.80/18.02 (big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 27.80/18.02 inference(unit_resolution,[status(thm)],[3898, 5255, 148, 79, 122])).
% 27.80/18.02 tff(5257,plain,
% 27.80/18.02 (f9(c2, f9(c2, c2)) = f9(c2, c2)),
% 27.80/18.02 inference(unit_resolution,[status(thm)],[4482, 5256, 122, 121, 148, 79, 5020])).
% 27.80/18.02 tff(5258,plain,
% 27.80/18.02 ($false),
% 27.80/18.02 inference(unit_resolution,[status(thm)],[1211, 5257, 5256, 122, 17, 5254, 5249, 185])).
% 27.80/18.02 tff(5259,plain,(big_f(c2, c2) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (f7(c1) = c1) | (f9(f10(c2), f10(c2)) = f10(c2))), inference(lemma,lemma(discharge,[]))).
% 27.80/18.02 tff(5260,plain,
% 27.80/18.02 (big_f(c2, c2)),
% 27.80/18.02 inference(unit_resolution,[status(thm)],[5259, 17, 122, 148, 79, 115, 158])).
% 27.80/18.02 tff(5261,plain,
% 27.80/18.02 (big_f(c2, f1(c2, c2)) <=> big_f(c2, c2)),
% 27.80/18.02 inference(monotonicity,[status(thm)],[1908])).
% 27.80/18.02 tff(5262,plain,
% 27.80/18.02 (big_f(c2, c2) <=> big_f(c2, f1(c2, c2))),
% 27.80/18.02 inference(symmetry,[status(thm)],[5261])).
% 27.80/18.02 tff(5263,plain,
% 27.80/18.03 (big_f(c2, f1(c2, c2))),
% 27.80/18.03 inference(modus_ponens,[status(thm)],[1345, 5262])).
% 27.80/18.03 tff(5264,plain,
% 27.80/18.03 ($false),
% 27.80/18.03 inference(unit_resolution,[status(thm)],[2123, 447, 377, 1908, 5263, 514, 2040, 2099])).
% 27.80/18.03 tff(5265,plain,((~(f1(c2, c2) = c2)) | (c2 = c3) | (~(f9(c2, c2) = c4)) | big_f(c2, f9(c2, c2)) | (~(c2 = f4(f9(c2, c2)))) | (~big_f(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 27.80/18.03 tff(5266,plain,
% 27.80/18.03 (~(f1(c2, c2) = c2)),
% 27.80/18.03 inference(unit_resolution,[status(thm)],[5265, 3725, 377, 2040, 3715, 1345])).
% 27.80/18.03 tff(5267,plain,
% 27.80/18.03 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f1(c2, c2) = c1) | (f1(c2, c2) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f1(c2, c2) = c1) | (f1(c2, c2) = c2))),
% 27.80/18.03 inference(rewrite,[status(thm)],[])).
% 27.80/18.03 tff(5268,plain,
% 27.80/18.03 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f1(c2, c2) = c1) | (f1(c2, c2) = c2))),
% 27.80/18.03 inference(quant_inst,[status(thm)],[])).
% 27.80/18.03 tff(5269,plain,
% 27.80/18.03 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f1(c2, c2) = c1) | (f1(c2, c2) = c2)),
% 27.80/18.03 inference(modus_ponens,[status(thm)],[5268, 5267])).
% 27.80/18.03 tff(5270,plain,
% 27.80/18.03 ((f1(c2, c2) = c1) | (f1(c2, c2) = c2)),
% 27.80/18.03 inference(unit_resolution,[status(thm)],[5269, 10])).
% 27.80/18.03 tff(5271,plain,
% 27.80/18.03 (f1(c2, c2) = c1),
% 27.80/18.03 inference(unit_resolution,[status(thm)],[5270, 5266])).
% 27.80/18.03 tff(5272,plain,
% 27.80/18.03 (f1(c2, c2) = f9(c2, c2)),
% 27.80/18.03 inference(transitivity,[status(thm)],[5271, 149, 132])).
% 27.80/18.03 tff(5273,plain,
% 27.80/18.03 (big_f(c2, f1(c2, c2)) <=> big_f(c2, f9(c2, c2))),
% 27.80/18.03 inference(monotonicity,[status(thm)],[5272])).
% 27.80/18.03 tff(5274,plain,
% 27.80/18.03 (big_f(c2, f9(c2, c2)) <=> big_f(c2, f1(c2, c2))),
% 27.80/18.03 inference(symmetry,[status(thm)],[5273])).
% 27.80/18.03 tff(5275,plain,
% 27.80/18.03 ((~big_f(c2, f9(c2, c2))) <=> (~big_f(c2, f1(c2, c2)))),
% 27.80/18.03 inference(monotonicity,[status(thm)],[5274])).
% 27.80/18.03 tff(5276,plain,
% 27.80/18.03 (~big_f(c2, f1(c2, c2))),
% 27.80/18.03 inference(modus_ponens,[status(thm)],[2040, 5275])).
% 27.80/18.03 tff(5277,plain,
% 27.80/18.03 ($false),
% 27.80/18.03 inference(unit_resolution,[status(thm)],[2105, 402, 377, 5266, 5276, 3725, 2040, 3715])).
% 27.80/18.03 tff(5278,plain,((~(c4 = c1)) | (c2 = c3) | big_f(c2, f9(c2, c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~big_f(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 27.80/18.03 tff(5279,plain,
% 27.80/18.03 (~(c4 = c1)),
% 27.80/18.03 inference(unit_resolution,[status(thm)],[5278, 2040, 377, 148, 79, 122, 1345])).
% 27.80/18.03 tff(5280,plain,
% 27.80/18.03 (c4 = c2),
% 27.80/18.03 inference(unit_resolution,[status(thm)],[461, 5279])).
% 27.80/18.03 tff(5281,plain,
% 27.80/18.03 (c2 = c4),
% 27.80/18.03 inference(symmetry,[status(thm)],[5280])).
% 27.80/18.03 tff(5282,plain,
% 27.80/18.03 (f4(c2) = f4(c4)),
% 27.80/18.03 inference(monotonicity,[status(thm)],[5281])).
% 27.80/18.03 tff(5283,plain,
% 27.80/18.03 (f4(c2) = c2),
% 27.80/18.03 inference(transitivity,[status(thm)],[5282, 79])).
% 27.80/18.03 tff(5284,plain,
% 27.80/18.03 ((f9(c2, c2) = f4(c2)) <=> (f9(c2, c2) = c2)),
% 27.80/18.03 inference(monotonicity,[status(thm)],[5283])).
% 27.80/18.03 tff(5285,plain,
% 27.80/18.03 ((f9(c2, c2) = c2) <=> (f9(c2, c2) = f4(c2))),
% 27.80/18.03 inference(symmetry,[status(thm)],[5284])).
% 27.80/18.03 tff(5286,plain,
% 27.80/18.03 ((~(f9(c2, c2) = c2)) <=> (~(f9(c2, c2) = f4(c2)))),
% 27.80/18.03 inference(monotonicity,[status(thm)],[5285])).
% 27.80/18.03 tff(5287,plain,
% 27.80/18.03 (~(f9(c2, c2) = f4(c2))),
% 27.80/18.03 inference(modus_ponens,[status(thm)],[185, 5286])).
% 27.80/18.03 tff(5288,plain,
% 27.80/18.03 (big_f(c1, c1) <=> big_f(f7(c2), c1)),
% 27.80/18.03 inference(transitivity,[status(thm)],[4889, 4537, 4535])).
% 27.80/18.03 tff(5289,plain,
% 27.80/18.03 ($false),
% 27.80/18.03 inference(unit_resolution,[status(thm)],[4917, 4597, 3685, 79, 122, 66, 17, 148])).
% 27.80/18.03 tff(5290,plain,(big_f(f9(c2, c2), c2) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | big_f(c1, c1) | (f7(c2) = c2) | (~(f9(f10(c2), f4(c4)) = c1))), inference(lemma,lemma(discharge,[]))).
% 27.80/18.03 tff(5291,plain,
% 27.80/18.03 (big_f(c1, c1)),
% 27.80/18.03 inference(unit_resolution,[status(thm)],[5290, 3685, 122, 17, 79, 148])).
% 27.80/18.03 tff(5292,plain,
% 27.80/18.03 (big_f(f7(c2), c1)),
% 27.80/18.03 inference(modus_ponens,[status(thm)],[5291, 5288])).
% 27.80/18.03 tff(5293,plain,
% 27.80/18.03 (~big_f(f7(c2), c1)),
% 27.80/18.03 inference(unit_resolution,[status(thm)],[1933, 4597, 148, 377, 79, 122, 22, 1345, 347, 2, 186])).
% 27.80/18.03 tff(5294,plain,
% 27.80/18.03 ($false),
% 27.80/18.03 inference(unit_resolution,[status(thm)],[5293, 5292])).
% 27.80/18.03 tff(5295,plain,(big_f(f9(c2, c2), c2) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (c2 = c3) | (~big_f(c2, c2)) | (~(f7(c1) = c2)) | big_f(c2, c1) | (~(f5(c1) = c2)) | (f7(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 27.80/18.03 tff(5296,plain,
% 27.80/18.03 (big_f(f9(c2, c2), c2)),
% 27.80/18.03 inference(unit_resolution,[status(thm)],[5295, 4107, 79, 122, 377, 1345, 347, 148, 186, 17])).
% 27.80/18.03 tff(5297,plain,
% 27.80/18.03 (c2 = c4),
% 27.80/18.03 inference(modus_ponens,[status(thm)],[5280, 159])).
% 27.80/18.03 tff(5298,plain,
% 27.80/18.03 (f1(c2, c2) = c1),
% 27.80/18.03 inference(unit_resolution,[status(thm)],[5270, 1828])).
% 27.80/18.03 tff(5299,plain,
% 27.80/18.03 (f1(c2, c2) = f9(c2, c2)),
% 27.80/18.03 inference(transitivity,[status(thm)],[5298, 149, 132])).
% 27.80/18.03 tff(5300,plain,
% 27.80/18.03 (big_f(c2, f1(c2, c2)) <=> big_f(c2, f9(c2, c2))),
% 27.80/18.03 inference(monotonicity,[status(thm)],[5299])).
% 27.80/18.03 tff(5301,plain,
% 27.80/18.03 (big_f(c2, f9(c2, c2)) <=> big_f(c2, f1(c2, c2))),
% 27.80/18.03 inference(symmetry,[status(thm)],[5300])).
% 27.80/18.03 tff(5302,plain,
% 27.80/18.03 ((~big_f(c2, f9(c2, c2))) <=> (~big_f(c2, f1(c2, c2)))),
% 27.80/18.03 inference(monotonicity,[status(thm)],[5301])).
% 27.80/18.03 tff(5303,plain,
% 27.80/18.03 (~big_f(c2, f1(c2, c2))),
% 27.80/18.03 inference(modus_ponens,[status(thm)],[2040, 5302])).
% 27.80/18.03 tff(5304,plain,
% 27.80/18.03 ($false),
% 27.80/18.03 inference(unit_resolution,[status(thm)],[2053, 525, 631, 377, 1828, 5303, 2041, 2047])).
% 27.80/18.03 tff(5305,plain,((f1(c2, c2) = c2) | (~(c2 = c4)) | (c2 = c3) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f4(c2)) | big_f(c2, f9(c2, c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.80/18.03 tff(5306,plain,
% 27.80/18.03 (f1(c2, c2) = c2),
% 27.80/18.03 inference(unit_resolution,[status(thm)],[5305, 5297, 377, 5296, 5287, 2040, 148, 79, 122])).
% 27.80/18.03 tff(5307,plain,
% 27.80/18.03 (big_f(c2, f1(c2, c2)) <=> big_f(c2, c2)),
% 27.80/18.03 inference(monotonicity,[status(thm)],[5306])).
% 27.80/18.03 tff(5308,plain,
% 27.80/18.03 (big_f(c2, c2) <=> big_f(c2, f1(c2, c2))),
% 27.80/18.03 inference(symmetry,[status(thm)],[5307])).
% 27.80/18.03 tff(5309,plain,
% 27.80/18.03 (big_f(c2, f1(c2, c2))),
% 27.80/18.03 inference(modus_ponens,[status(thm)],[1345, 5308])).
% 27.80/18.03 tff(5310,plain,
% 27.80/18.03 ($false),
% 27.80/18.03 inference(unit_resolution,[status(thm)],[2085, 553, 5297, 377, 5306, 5309, 5296, 5287])).
% 27.80/18.03 tff(5311,plain,(big_f(c2, f9(c2, c2)) | (c2 = c3) | (~big_f(c2, c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f7(c1) = c2)) | (~(f5(c1) = c2)) | (f7(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 27.80/18.03 tff(5312,plain,
% 27.80/18.03 (big_f(c2, f9(c2, c2))),
% 27.80/18.03 inference(unit_resolution,[status(thm)],[5311, 186, 1345, 148, 79, 122, 120, 377, 17])).
% 27.80/18.03 tff(5313,plain,
% 27.80/18.03 (big_f(c2, c1)),
% 27.80/18.03 inference(unit_resolution,[status(thm)],[3721, 5312, 148, 79, 122])).
% 27.80/18.03 tff(5314,plain,
% 27.80/18.03 (big_f(f9(c2, c2), f10(c2))),
% 27.80/18.03 inference(unit_resolution,[status(thm)],[1810, 5313, 122, 120, 148, 79, 191])).
% 27.80/18.03 tff(5315,plain,
% 27.80/18.03 (big_f(f9(c2, c2), c2)),
% 27.80/18.03 inference(unit_resolution,[status(thm)],[3687, 5314, 122])).
% 27.80/18.03 tff(5316,plain,
% 27.80/18.03 (big_f(f9(c2, c2), f9(c2, c2))),
% 27.80/18.03 inference(unit_resolution,[status(thm)],[3810, 5312, 148, 3762, 79, 122, 115, 191, 200])).
% 27.80/18.03 tff(5317,plain,
% 27.80/18.03 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c2, c2) = c3)) | (c2 = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(f9(c2, c2) = c3)) | (c2 = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)))),
% 27.80/18.03 inference(rewrite,[status(thm)],[])).
% 27.80/18.03 tff(5318,plain,
% 27.80/18.03 (((~(f9(c2, c2) = c3)) | (~(f9(c2, c2) = c4)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (c2 = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), c2))) <=> ((~(f9(c2, c2) = c3)) | (c2 = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)))),
% 27.80/18.03 inference(rewrite,[status(thm)],[])).
% 27.80/18.03 tff(5319,plain,
% 27.80/18.03 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c2, c2) = c3)) | (~(f9(c2, c2) = c4)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (c2 = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c2, c2) = c3)) | (c2 = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4))))),
% 27.80/18.03 inference(monotonicity,[status(thm)],[5318])).
% 27.80/18.03 tff(5320,plain,
% 27.80/18.03 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c2, c2) = c3)) | (~(f9(c2, c2) = c4)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (c2 = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(f9(c2, c2) = c3)) | (c2 = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)))),
% 27.80/18.03 inference(transitivity,[status(thm)],[5319, 5317])).
% 27.80/18.03 tff(5321,plain,
% 27.80/18.03 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c2, c2) = c3)) | (~(f9(c2, c2) = c4)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (c2 = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), c2)))),
% 27.80/18.03 inference(quant_inst,[status(thm)],[])).
% 27.80/18.03 tff(5322,plain,
% 27.80/18.03 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(f9(c2, c2) = c3)) | (c2 = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4))),
% 27.80/18.03 inference(modus_ponens,[status(thm)],[5321, 5320])).
% 27.80/18.03 tff(5323,plain,
% 27.80/18.03 ((c2 = f2(f9(c2, c2))) | (f9(c2, c2) = f4(f9(c2, c2))) | (~(f9(c2, c2) = c4))),
% 27.80/18.03 inference(unit_resolution,[status(thm)],[5322, 1355, 487, 1822, 2041])).
% 27.80/18.03 tff(5324,plain,
% 27.80/18.03 (c2 = f2(f9(c2, c2))),
% 27.80/18.03 inference(unit_resolution,[status(thm)],[5323, 4013, 3725])).
% 27.80/18.03 tff(5325,plain,
% 27.80/18.03 (f2(f9(c2, c2)) = c2),
% 27.80/18.03 inference(symmetry,[status(thm)],[5324])).
% 27.80/18.03 tff(5326,plain,
% 27.80/18.03 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c2, c2) = c3)) | (f9(c2, c2) = f2(f9(c2, c2))) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(f9(c2, c2) = c3)) | (f9(c2, c2) = f2(f9(c2, c2))) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)))),
% 27.80/18.03 inference(rewrite,[status(thm)],[])).
% 27.80/18.03 tff(5327,plain,
% 27.80/18.03 (((~(f9(c2, c2) = c3)) | (~(f9(c2, c2) = c4)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (f9(c2, c2) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2)))) <=> ((~(f9(c2, c2) = c3)) | (f9(c2, c2) = f2(f9(c2, c2))) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)))),
% 27.80/18.03 inference(rewrite,[status(thm)],[])).
% 27.80/18.03 tff(5328,plain,
% 27.80/18.03 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c2, c2) = c3)) | (~(f9(c2, c2) = c4)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (f9(c2, c2) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c2, c2) = c3)) | (f9(c2, c2) = f2(f9(c2, c2))) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4))))),
% 27.80/18.03 inference(monotonicity,[status(thm)],[5327])).
% 27.80/18.03 tff(5329,plain,
% 27.80/18.03 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c2, c2) = c3)) | (~(f9(c2, c2) = c4)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (f9(c2, c2) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(f9(c2, c2) = c3)) | (f9(c2, c2) = f2(f9(c2, c2))) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)))),
% 27.80/18.03 inference(transitivity,[status(thm)],[5328, 5326])).
% 27.80/18.03 tff(5330,plain,
% 27.80/18.03 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c2, c2) = c3)) | (~(f9(c2, c2) = c4)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (f9(c2, c2) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))))),
% 27.80/18.03 inference(quant_inst,[status(thm)],[])).
% 27.80/18.03 tff(5331,plain,
% 27.80/18.03 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(f9(c2, c2) = c3)) | (f9(c2, c2) = f2(f9(c2, c2))) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4))),
% 27.80/18.03 inference(modus_ponens,[status(thm)],[5330, 5329])).
% 27.80/18.03 tff(5332,plain,
% 27.80/18.03 ((f9(c2, c2) = f2(f9(c2, c2))) | (f9(c2, c2) = f4(f9(c2, c2))) | (~(f9(c2, c2) = c4))),
% 27.80/18.03 inference(unit_resolution,[status(thm)],[5331, 1355, 487, 1822])).
% 27.80/18.03 tff(5333,plain,
% 27.80/18.03 (f9(c2, c2) = f2(f9(c2, c2))),
% 27.80/18.03 inference(unit_resolution,[status(thm)],[5332, 4013, 3725])).
% 27.80/18.03 tff(5334,plain,
% 27.80/18.03 (f9(c2, c2) = c2),
% 27.80/18.03 inference(transitivity,[status(thm)],[5333, 5325])).
% 27.80/18.03 tff(5335,plain,
% 27.80/18.03 ($false),
% 27.80/18.03 inference(unit_resolution,[status(thm)],[185, 5334])).
% 27.80/18.03 tff(5336,plain,((~(c4 = c1)) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c3)) | (~big_f(f9(c2, c2), c2)) | (~(f4(c4) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.80/18.03 tff(5337,plain,
% 27.80/18.03 (~(c4 = c1)),
% 27.80/18.03 inference(unit_resolution,[status(thm)],[5336, 5316, 1822, 5315, 79, 148, 122])).
% 27.80/18.03 tff(5338,plain,
% 27.80/18.03 (c4 = c2),
% 27.80/18.03 inference(unit_resolution,[status(thm)],[461, 5337])).
% 27.80/18.03 tff(5339,plain,
% 27.80/18.03 (c2 = c4),
% 27.80/18.03 inference(modus_ponens,[status(thm)],[5338, 159])).
% 27.80/18.03 tff(5340,plain,
% 27.80/18.03 (c2 = c4),
% 27.80/18.03 inference(symmetry,[status(thm)],[5338])).
% 27.80/18.03 tff(5341,plain,
% 27.80/18.03 (f4(c2) = f4(c4)),
% 27.80/18.03 inference(monotonicity,[status(thm)],[5340])).
% 27.80/18.03 tff(5342,plain,
% 27.80/18.03 (f4(c2) = c2),
% 27.80/18.03 inference(transitivity,[status(thm)],[5341, 79])).
% 27.80/18.03 tff(5343,plain,
% 27.80/18.03 ((f9(c2, c2) = f4(c2)) <=> (f9(c2, c2) = c2)),
% 27.80/18.03 inference(monotonicity,[status(thm)],[5342])).
% 27.80/18.03 tff(5344,plain,
% 27.80/18.03 ((f9(c2, c2) = c2) <=> (f9(c2, c2) = f4(c2))),
% 27.80/18.03 inference(symmetry,[status(thm)],[5343])).
% 27.80/18.03 tff(5345,plain,
% 27.80/18.03 ((~(f9(c2, c2) = c2)) <=> (~(f9(c2, c2) = f4(c2)))),
% 27.80/18.03 inference(monotonicity,[status(thm)],[5344])).
% 27.80/18.03 tff(5346,plain,
% 27.80/18.03 (~(f9(c2, c2) = f4(c2))),
% 27.80/18.03 inference(modus_ponens,[status(thm)],[185, 5345])).
% 27.80/18.03 tff(5347,plain,
% 27.80/18.03 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c4)) | (~(f9(c2, c2) = c3)) | (c2 = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f4(c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c4)) | (~(f9(c2, c2) = c3)) | (c2 = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f4(c2)))),
% 27.80/18.03 inference(rewrite,[status(thm)],[])).
% 27.80/18.03 tff(5348,plain,
% 27.80/18.03 (((~(f9(c2, c2) = c3)) | (~(c2 = c4)) | (f9(c2, c2) = f4(c2)) | (~big_f(f9(c2, c2), c2)) | (c2 = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), c2))) <=> ((~(c2 = c4)) | (~(f9(c2, c2) = c3)) | (c2 = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f4(c2)))),
% 27.80/18.03 inference(rewrite,[status(thm)],[])).
% 27.80/18.03 tff(5349,plain,
% 27.80/18.03 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c2, c2) = c3)) | (~(c2 = c4)) | (f9(c2, c2) = f4(c2)) | (~big_f(f9(c2, c2), c2)) | (c2 = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c4)) | (~(f9(c2, c2) = c3)) | (c2 = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f4(c2))))),
% 27.80/18.03 inference(monotonicity,[status(thm)],[5348])).
% 27.80/18.03 tff(5350,plain,
% 27.80/18.03 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c2, c2) = c3)) | (~(c2 = c4)) | (f9(c2, c2) = f4(c2)) | (~big_f(f9(c2, c2), c2)) | (c2 = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c4)) | (~(f9(c2, c2) = c3)) | (c2 = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f4(c2)))),
% 27.80/18.03 inference(transitivity,[status(thm)],[5349, 5347])).
% 27.80/18.03 tff(5351,plain,
% 27.80/18.03 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c2, c2) = c3)) | (~(c2 = c4)) | (f9(c2, c2) = f4(c2)) | (~big_f(f9(c2, c2), c2)) | (c2 = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), c2)))),
% 27.80/18.03 inference(quant_inst,[status(thm)],[])).
% 27.80/18.03 tff(5352,plain,
% 27.80/18.03 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c4)) | (~(f9(c2, c2) = c3)) | (c2 = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f4(c2))),
% 27.80/18.03 inference(modus_ponens,[status(thm)],[5351, 5350])).
% 27.80/18.03 tff(5353,plain,
% 27.80/18.03 ((~(c2 = c4)) | (c2 = f2(f9(c2, c2))) | (f9(c2, c2) = f4(c2))),
% 27.80/18.03 inference(unit_resolution,[status(thm)],[5352, 1355, 1822, 5315])).
% 27.80/18.03 tff(5354,plain,
% 27.80/18.03 (c2 = f2(f9(c2, c2))),
% 27.80/18.03 inference(unit_resolution,[status(thm)],[5353, 5346, 5339])).
% 27.80/18.03 tff(5355,plain,
% 27.80/18.03 (f2(f9(c2, c2)) = c2),
% 27.80/18.03 inference(symmetry,[status(thm)],[5354])).
% 27.80/18.03 tff(5356,plain,
% 27.80/18.03 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c4)) | (~(f9(c2, c2) = c3)) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f4(c2)) | (f9(c2, c2) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c4)) | (~(f9(c2, c2) = c3)) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f4(c2)) | (f9(c2, c2) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))))),
% 27.80/18.03 inference(rewrite,[status(thm)],[])).
% 27.80/18.03 tff(5357,plain,
% 27.80/18.03 (((~(f9(c2, c2) = c3)) | (~(c2 = c4)) | (f9(c2, c2) = f4(c2)) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2)))) <=> ((~(c2 = c4)) | (~(f9(c2, c2) = c3)) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f4(c2)) | (f9(c2, c2) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))))),
% 27.80/18.03 inference(rewrite,[status(thm)],[])).
% 27.80/18.03 tff(5358,plain,
% 27.80/18.03 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c2, c2) = c3)) | (~(c2 = c4)) | (f9(c2, c2) = f4(c2)) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c4)) | (~(f9(c2, c2) = c3)) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f4(c2)) | (f9(c2, c2) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2)))))),
% 27.80/18.04 inference(monotonicity,[status(thm)],[5357])).
% 27.80/18.04 tff(5359,plain,
% 27.80/18.04 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c2, c2) = c3)) | (~(c2 = c4)) | (f9(c2, c2) = f4(c2)) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c4)) | (~(f9(c2, c2) = c3)) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f4(c2)) | (f9(c2, c2) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))))),
% 27.80/18.04 inference(transitivity,[status(thm)],[5358, 5356])).
% 27.80/18.04 tff(5360,plain,
% 27.80/18.04 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c2, c2) = c3)) | (~(c2 = c4)) | (f9(c2, c2) = f4(c2)) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))))),
% 27.80/18.04 inference(quant_inst,[status(thm)],[])).
% 27.80/18.04 tff(5361,plain,
% 27.80/18.04 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c4)) | (~(f9(c2, c2) = c3)) | (~big_f(f9(c2, c2), c2)) | (f9(c2, c2) = f4(c2)) | (f9(c2, c2) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2)))),
% 27.80/18.04 inference(modus_ponens,[status(thm)],[5360, 5359])).
% 27.80/18.04 tff(5362,plain,
% 27.80/18.04 ((~(c2 = c4)) | (f9(c2, c2) = f4(c2)) | (f9(c2, c2) = f2(f9(c2, c2)))),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[5361, 1355, 5316, 1822, 5315])).
% 27.80/18.04 tff(5363,plain,
% 27.80/18.04 (f9(c2, c2) = f2(f9(c2, c2))),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[5362, 5346, 5339])).
% 27.80/18.04 tff(5364,plain,
% 27.80/18.04 (f9(c2, c2) = c2),
% 27.80/18.04 inference(transitivity,[status(thm)],[5363, 5355])).
% 27.80/18.04 tff(5365,plain,
% 27.80/18.04 ($false),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[185, 5364])).
% 27.80/18.04 tff(5366,plain,((~(f5(c1) = c2)) | (~(f9(c2, c2) = c3)) | (~(f4(c4) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f10(c2) = c2)) | (~(f10(c1) = c1)) | (f7(c1) = c1) | (~big_f(c2, c2)) | (c2 = c3) | (f7(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 27.80/18.04 tff(5367,plain,
% 27.80/18.04 (~(f5(c1) = c2)),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[5366, 5260, 79, 148, 122, 3637, 115, 4979, 4978, 17])).
% 27.80/18.04 tff(5368,plain,
% 27.80/18.04 (~(c2 = f5(f9(c2, c2)))),
% 27.80/18.04 inference(modus_ponens,[status(thm)],[5367, 166])).
% 27.80/18.04 tff(5369,plain,
% 27.80/18.04 (big_f(f7(f9(c2, c2)), c2)),
% 27.80/18.04 inference(modus_ponens,[status(thm)],[5260, 246])).
% 27.80/18.04 tff(5370,plain,
% 27.80/18.04 (big_f(f9(c2, c2), f10(c2)) | (c2 = f5(f9(c2, c2)))),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[682, 676, 122, 185, 3654, 5369])).
% 27.80/18.04 tff(5371,plain,
% 27.80/18.04 (big_f(f9(c2, c2), f10(c2))),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[5370, 5368])).
% 27.80/18.04 tff(5372,plain,
% 27.80/18.04 (big_f(f9(c2, c2), c2)),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[3687, 5371, 122])).
% 27.80/18.04 tff(5373,plain,
% 27.80/18.04 (f5(c1) = c1),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[1708, 5367])).
% 27.80/18.04 tff(5374,plain,
% 27.80/18.04 (f1(c2, c2) = c2),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[5305, 5287, 377, 2041, 2040, 5297, 148, 79, 122])).
% 27.80/18.04 tff(5375,plain,
% 27.80/18.04 (big_f(c2, f1(c2, c2)) <=> big_f(c2, c2)),
% 27.80/18.04 inference(monotonicity,[status(thm)],[5374])).
% 27.80/18.04 tff(5376,plain,
% 27.80/18.04 (big_f(c2, c2) <=> big_f(c2, f1(c2, c2))),
% 27.80/18.04 inference(symmetry,[status(thm)],[5375])).
% 27.80/18.04 tff(5377,plain,
% 27.80/18.04 (big_f(c2, f1(c2, c2))),
% 27.80/18.04 inference(modus_ponens,[status(thm)],[1345, 5376])).
% 27.80/18.04 tff(5378,plain,
% 27.80/18.04 ($false),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[2085, 553, 5297, 377, 5374, 5377, 2041, 5287])).
% 27.80/18.04 tff(5379,plain,(big_f(c2, f9(c2, c2)) | (c2 = c3) | (~big_f(f9(c2, c2), c2)) | (~big_f(c2, c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.80/18.04 tff(5380,plain,
% 27.80/18.04 (big_f(c2, f9(c2, c2))),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[5379, 5372, 4978, 5260, 148, 79, 122])).
% 27.80/18.04 tff(5381,assumption,(~(c2 = f5(f9(c2, c2)))), introduced(assumption)).
% 27.80/18.04 tff(5382,plain,
% 27.80/18.04 (f9(f9(c2, c2), c2) = c2),
% 27.80/18.04 inference(modus_ponens,[status(thm)],[3764, 4233])).
% 27.80/18.04 tff(5383,plain,
% 27.80/18.04 (big_f(f9(c1, c2), f10(c1)) <=> big_f(c2, f9(c2, c2))),
% 27.80/18.04 inference(monotonicity,[status(thm)],[3764, 3763])).
% 27.80/18.04 tff(5384,plain,
% 27.80/18.04 (big_f(c2, f9(c2, c2)) <=> big_f(f9(c1, c2), f10(c1))),
% 27.80/18.04 inference(symmetry,[status(thm)],[5383])).
% 27.80/18.04 tff(5385,plain,
% 27.80/18.04 (big_f(c2, f9(c2, c2)) <=> big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))),
% 27.80/18.04 inference(transitivity,[status(thm)],[5384, 4239])).
% 27.80/18.04 tff(5386,plain,
% 27.80/18.04 (big_f(f9(f9(c2, c2), c2), f10(f9(c2, c2)))),
% 27.80/18.04 inference(modus_ponens,[status(thm)],[3719, 5385])).
% 27.80/18.04 tff(5387,plain,
% 27.80/18.04 ($false),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[4428, 1190, 3777, 3774, 5386, 5382, 4983, 5381])).
% 27.80/18.04 tff(5388,plain,((~(f9(c1, c2) = c2)) | (f7(f9(c2, c2)) = f9(c2, c2)) | (~big_f(f7(f9(c2, c2)), c2)) | (c2 = f5(f9(c2, c2))) | (~big_f(c2, f9(c2, c2))) | (~(f10(c1) = c1)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.80/18.04 tff(5389,plain,
% 27.80/18.04 (~(f9(c1, c2) = c2)),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[5388, 5369, 3654, 5368, 5380, 3637, 148, 79, 122])).
% 27.80/18.04 tff(5390,plain,
% 27.80/18.04 (big_f(f9(c2, c2), f9(c2, c2))),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[4416, 5389, 148, 3654, 79, 122, 5260, 120, 5373, 3637])).
% 27.80/18.04 tff(5391,plain,
% 27.80/18.04 (~(c4 = c1)),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[5336, 5390, 4979, 5372, 79, 148, 122])).
% 27.80/18.04 tff(5392,plain,
% 27.80/18.04 (c4 = c2),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[461, 5391])).
% 27.80/18.04 tff(5393,plain,
% 27.80/18.04 (c2 = c4),
% 27.80/18.04 inference(modus_ponens,[status(thm)],[5392, 159])).
% 27.80/18.04 tff(5394,plain,
% 27.80/18.04 (c2 = c4),
% 27.80/18.04 inference(symmetry,[status(thm)],[5392])).
% 27.80/18.04 tff(5395,plain,
% 27.80/18.04 (f4(c2) = f4(c4)),
% 27.80/18.04 inference(monotonicity,[status(thm)],[5394])).
% 27.80/18.04 tff(5396,plain,
% 27.80/18.04 (f4(c2) = c2),
% 27.80/18.04 inference(transitivity,[status(thm)],[5395, 79])).
% 27.80/18.04 tff(5397,plain,
% 27.80/18.04 ((f9(c2, c2) = f4(c2)) <=> (f9(c2, c2) = c2)),
% 27.80/18.04 inference(monotonicity,[status(thm)],[5396])).
% 27.80/18.04 tff(5398,plain,
% 27.80/18.04 ((f9(c2, c2) = c2) <=> (f9(c2, c2) = f4(c2))),
% 27.80/18.04 inference(symmetry,[status(thm)],[5397])).
% 27.80/18.04 tff(5399,plain,
% 27.80/18.04 ((~(f9(c2, c2) = c2)) <=> (~(f9(c2, c2) = f4(c2)))),
% 27.80/18.04 inference(monotonicity,[status(thm)],[5398])).
% 27.80/18.04 tff(5400,plain,
% 27.80/18.04 (~(f9(c2, c2) = f4(c2))),
% 27.80/18.04 inference(modus_ponens,[status(thm)],[185, 5399])).
% 27.80/18.04 tff(5401,plain,
% 27.80/18.04 ((~(c2 = c4)) | (c2 = f2(f9(c2, c2))) | (f9(c2, c2) = f4(c2))),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[5352, 1355, 4979, 5372])).
% 27.80/18.04 tff(5402,plain,
% 27.80/18.04 (c2 = f2(f9(c2, c2))),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[5401, 5400, 5393])).
% 27.80/18.04 tff(5403,plain,
% 27.80/18.04 (f2(f9(c2, c2)) = c2),
% 27.80/18.04 inference(symmetry,[status(thm)],[5402])).
% 27.80/18.04 tff(5404,plain,
% 27.80/18.04 (f9(c2, c2) = f2(f9(c2, c2))),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[5361, 1355, 5393, 5390, 4979, 5372, 5400])).
% 27.80/18.04 tff(5405,plain,
% 27.80/18.04 (f9(c2, c2) = c2),
% 27.80/18.04 inference(transitivity,[status(thm)],[5404, 5403])).
% 27.80/18.04 tff(5406,plain,
% 27.80/18.04 ($false),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[185, 5405])).
% 27.80/18.04 tff(5407,plain,((f7(c2) = c2) | (~(f4(c4) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f10(c2) = c2)) | (f7(c1) = c1) | (f9(f10(c2), f10(c2)) = f10(c2))), inference(lemma,lemma(discharge,[]))).
% 27.80/18.04 tff(5408,plain,
% 27.80/18.04 (f7(c2) = c2),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[5407, 115, 148, 122, 79, 158])).
% 27.80/18.04 tff(5409,plain,
% 27.80/18.04 (big_f(f9(c2, c2), f10(c2))),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[4195, 5019, 148, 79, 122, 3637, 5408, 120])).
% 27.80/18.04 tff(5410,plain,
% 27.80/18.04 (big_f(f9(c2, c2), c2)),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[3687, 5409, 122])).
% 27.80/18.04 tff(5411,plain,
% 27.80/18.04 (big_f(c1, c2)),
% 27.80/18.04 inference(modus_ponens,[status(thm)],[5410, 3690])).
% 27.80/18.04 tff(5412,plain,
% 27.80/18.04 (f7(f7(c2)) = f7(c2)),
% 27.80/18.04 inference(monotonicity,[status(thm)],[5408])).
% 27.80/18.04 tff(5413,plain,
% 27.80/18.04 (f7(f7(c2)) = c2),
% 27.80/18.04 inference(transitivity,[status(thm)],[5412, 5408])).
% 27.80/18.04 tff(5414,plain,
% 27.80/18.04 ((f7(f7(c2)) = c1) <=> (c2 = f9(c2, c2))),
% 27.80/18.04 inference(monotonicity,[status(thm)],[5413, 150])).
% 27.80/18.04 tff(5415,plain,
% 27.80/18.04 ((f7(f7(c2)) = c1) <=> (f9(c2, c2) = c2)),
% 27.80/18.04 inference(transitivity,[status(thm)],[5414, 167])).
% 27.80/18.04 tff(5416,plain,
% 27.80/18.04 ((f9(c2, c2) = c2) <=> (f7(f7(c2)) = c1)),
% 27.80/18.04 inference(symmetry,[status(thm)],[5415])).
% 27.80/18.04 tff(5417,plain,
% 27.80/18.04 ((f9(c2, c2) = c2) <=> (f7(f7(c2)) = c3)),
% 27.80/18.04 inference(transitivity,[status(thm)],[5416, 5022])).
% 27.80/18.04 tff(5418,plain,
% 27.80/18.04 ((~(f9(c2, c2) = c2)) <=> (~(f7(f7(c2)) = c3))),
% 27.80/18.04 inference(monotonicity,[status(thm)],[5417])).
% 27.80/18.04 tff(5419,plain,
% 27.80/18.04 (~(f7(f7(c2)) = c3)),
% 27.80/18.04 inference(modus_ponens,[status(thm)],[185, 5418])).
% 27.80/18.04 tff(5420,plain,
% 27.80/18.04 (f7(c2) = f7(f7(c2))),
% 27.80/18.04 inference(symmetry,[status(thm)],[2467])).
% 27.80/18.04 tff(5421,plain,
% 27.80/18.04 (c2 = f7(f7(c2))),
% 27.80/18.04 inference(transitivity,[status(thm)],[82, 5420])).
% 27.80/18.04 tff(5422,plain,
% 27.80/18.04 (f1(c2, c1) = f1(f7(f7(c2)), c1)),
% 27.80/18.04 inference(monotonicity,[status(thm)],[5421])).
% 27.80/18.04 tff(5423,plain,
% 27.80/18.04 (f1(c2, c1) = c2),
% 27.80/18.04 inference(transitivity,[status(thm)],[5422, 385])).
% 27.80/18.04 tff(5424,plain,
% 27.80/18.04 (big_f(c2, f1(c2, c1)) <=> big_f(c2, c2)),
% 27.80/18.04 inference(monotonicity,[status(thm)],[5423])).
% 27.80/18.04 tff(5425,plain,
% 27.80/18.04 (big_f(c2, c2) <=> big_f(c2, f1(c2, c1))),
% 27.80/18.04 inference(symmetry,[status(thm)],[5424])).
% 27.80/18.04 tff(5426,plain,
% 27.80/18.04 ((~big_f(c2, c2)) <=> (~big_f(c2, f1(c2, c1)))),
% 27.80/18.04 inference(monotonicity,[status(thm)],[5425])).
% 27.80/18.04 tff(5427,plain,
% 27.80/18.04 (~big_f(c2, f1(c2, c1))),
% 27.80/18.04 inference(modus_ponens,[status(thm)],[121, 5426])).
% 27.80/18.04 tff(5428,plain,
% 27.80/18.04 (f1(f7(f7(c2)), c1) = f1(c2, c1)),
% 27.80/18.04 inference(symmetry,[status(thm)],[5422])).
% 27.80/18.04 tff(5429,plain,
% 27.80/18.04 (f7(f7(c2)) = c2),
% 27.80/18.04 inference(transitivity,[status(thm)],[2467, 77])).
% 27.80/18.04 tff(5430,plain,
% 27.80/18.04 (big_f(f7(f7(c2)), f1(f7(f7(c2)), c1)) <=> big_f(c2, f1(c2, c1))),
% 27.80/18.04 inference(monotonicity,[status(thm)],[5429, 5428])).
% 27.80/18.04 tff(5431,plain,
% 27.80/18.04 (big_f(c2, f1(c2, c1))),
% 27.80/18.04 inference(modus_ponens,[status(thm)],[418, 5430])).
% 27.80/18.04 tff(5432,plain,
% 27.80/18.04 ($false),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[5431, 5427])).
% 27.80/18.04 tff(5433,plain,((f1(f7(f7(c2)), c1) = c1) | big_f(c2, c2) | (~(f7(c2) = c2)) | big_f(f4(c4), c4) | (f7(f7(c2)) = c3)), inference(lemma,lemma(discharge,[]))).
% 27.80/18.04 tff(5434,plain,
% 27.80/18.04 (f1(f7(f7(c2)), c1) = c1),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[5433, 5037, 77, 378, 121])).
% 27.80/18.04 tff(5435,plain,
% 27.80/18.04 (f1(c2, f9(c2, c2)) = f1(f7(f7(c2)), c1)),
% 27.80/18.04 inference(monotonicity,[status(thm)],[5421, 161])).
% 27.80/18.04 tff(5436,plain,
% 27.80/18.04 (f1(c2, c1) = f9(c2, c2)),
% 27.80/18.04 inference(transitivity,[status(thm)],[5043, 5435, 5434, 149, 132])).
% 27.80/18.04 tff(5437,plain,
% 27.80/18.04 (big_f(c2, f1(c2, c1)) <=> big_f(c2, f9(c2, c2))),
% 27.80/18.04 inference(monotonicity,[status(thm)],[5436])).
% 27.80/18.04 tff(5438,plain,
% 27.80/18.04 (big_f(c2, f1(c2, f9(c2, c2))) <=> big_f(f7(f9(c2, c2)), f9(c2, c2))),
% 27.80/18.04 inference(transitivity,[status(thm)],[5047, 5437, 5032])).
% 27.80/18.04 tff(5439,plain,
% 27.80/18.04 ((~big_f(c2, f1(c2, f9(c2, c2)))) <=> (~big_f(f7(f9(c2, c2)), f9(c2, c2)))),
% 27.80/18.04 inference(monotonicity,[status(thm)],[5438])).
% 27.80/18.04 tff(5440,plain,
% 27.80/18.04 (big_f(c2, f9(c2, c2)) <=> big_f(c2, f1(c2, c1))),
% 27.80/18.04 inference(symmetry,[status(thm)],[5437])).
% 27.80/18.04 tff(5441,plain,
% 27.80/18.04 (big_f(c2, f9(c2, c2)) <=> big_f(c2, f1(c2, f9(c2, c2)))),
% 27.80/18.04 inference(transitivity,[status(thm)],[5440, 5050])).
% 27.80/18.04 tff(5442,plain,
% 27.80/18.04 ((~big_f(c2, f9(c2, c2))) <=> (~big_f(c2, f1(c2, f9(c2, c2))))),
% 27.80/18.04 inference(monotonicity,[status(thm)],[5441])).
% 27.80/18.04 tff(5443,plain,
% 27.80/18.04 (~big_f(c2, f1(c2, f9(c2, c2)))),
% 27.80/18.04 inference(modus_ponens,[status(thm)],[2040, 5442])).
% 27.80/18.04 tff(5444,plain,
% 27.80/18.04 (~big_f(f7(f9(c2, c2)), f9(c2, c2))),
% 27.80/18.04 inference(modus_ponens,[status(thm)],[5443, 5439])).
% 27.80/18.04 tff(5445,plain,
% 27.80/18.04 (big_f(c2, f1(c2, f9(c2, c2))) <=> big_f(f7(c1), f5(c1))),
% 27.80/18.04 inference(transitivity,[status(thm)],[5047, 5437, 5057])).
% 27.80/18.04 tff(5446,plain,
% 27.80/18.04 ((~big_f(c2, f1(c2, f9(c2, c2)))) <=> (~big_f(f7(c1), f5(c1)))),
% 27.80/18.04 inference(monotonicity,[status(thm)],[5445])).
% 27.80/18.04 tff(5447,plain,
% 27.80/18.04 (~big_f(f7(c1), f5(c1))),
% 27.80/18.04 inference(modus_ponens,[status(thm)],[5443, 5446])).
% 27.80/18.04 tff(5448,plain,
% 27.80/18.04 (big_f(f9(c2, c1), f10(c2))),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[755, 5447, 122, 115, 690, 148, 79])).
% 27.80/18.04 tff(5449,plain,
% 27.80/18.04 (big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[3898, 5448, 148, 79, 122])).
% 27.80/18.04 tff(5450,plain,
% 27.80/18.04 (f9(c2, f9(c2, c2)) = f9(c2, c2)),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[4482, 5449, 122, 121, 148, 79, 328])).
% 27.80/18.04 tff(5451,plain,
% 27.80/18.04 ($false),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[5076, 783, 122, 764, 5449, 5450, 3654, 5444])).
% 27.80/18.04 tff(5452,plain,(big_f(c2, f9(c2, c2)) | (~(f10(c2) = c2)) | big_f(c2, c2) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f5(f10(c1)) = c1)) | (f7(c1) = c1) | (~big_f(f9(c2, c2), f10(c2))) | (~(f7(c2) = c2)) | (~(f5(c1) = c1)) | (f7(f7(c2)) = c3)), inference(lemma,lemma(discharge,[]))).
% 27.80/18.04 tff(5453,plain,
% 27.80/18.04 (big_f(c2, f9(c2, c2))),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[5452, 121, 122, 148, 79, 5020, 115, 5409, 5408, 5019, 5419])).
% 27.80/18.04 tff(5454,plain,
% 27.80/18.04 (~(f6(f7(c2), f5(c1)) = c1)),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[4491, 5453, 5408, 121, 148, 79, 122, 5411, 5020, 5019])).
% 27.80/18.04 tff(5455,plain,
% 27.80/18.04 (f6(f7(c2), f5(c1)) = c2),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[2978, 5454])).
% 27.80/18.04 tff(5456,plain,
% 27.80/18.04 (c1 = f5(c1)),
% 27.80/18.04 inference(symmetry,[status(thm)],[5019])).
% 27.80/18.04 tff(5457,plain,
% 27.80/18.04 (f9(c2, c2) = f5(c1)),
% 27.80/18.04 inference(transitivity,[status(thm)],[160, 148, 5456])).
% 27.80/18.04 tff(5458,plain,
% 27.80/18.04 (c2 = f7(c2)),
% 27.80/18.04 inference(symmetry,[status(thm)],[5408])).
% 27.80/18.04 tff(5459,plain,
% 27.80/18.04 (f6(c2, f9(c2, c2)) = f6(f7(c2), f5(c1))),
% 27.80/18.04 inference(monotonicity,[status(thm)],[5458, 5457])).
% 27.80/18.04 tff(5460,plain,
% 27.80/18.04 (f6(c2, f9(c2, c2)) = c2),
% 27.80/18.04 inference(transitivity,[status(thm)],[5459, 5455])).
% 27.80/18.04 tff(5461,plain,
% 27.80/18.04 ((f6(c2, f9(c2, c2)) = f9(c2, c2)) <=> (c2 = f9(c2, c2))),
% 27.80/18.04 inference(monotonicity,[status(thm)],[5460])).
% 27.80/18.04 tff(5462,plain,
% 27.80/18.04 ((f6(c2, f9(c2, c2)) = f9(c2, c2)) <=> (f9(c2, c2) = c2)),
% 27.80/18.04 inference(transitivity,[status(thm)],[5461, 167])).
% 27.80/18.04 tff(5463,plain,
% 27.80/18.04 ((f9(c2, c2) = c2) <=> (f6(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.80/18.04 inference(symmetry,[status(thm)],[5462])).
% 27.80/18.04 tff(5464,plain,
% 27.80/18.04 ((f9(c2, c2) = c2) <=> (f6(c2, c1) = c1)),
% 27.80/18.04 inference(transitivity,[status(thm)],[5463, 4457])).
% 27.80/18.04 tff(5465,plain,
% 27.80/18.04 ((~(f9(c2, c2) = c2)) <=> (~(f6(c2, c1) = c1))),
% 27.80/18.04 inference(monotonicity,[status(thm)],[5464])).
% 27.80/18.04 tff(5466,plain,
% 27.80/18.04 (~(f6(c2, c1) = c1)),
% 27.80/18.04 inference(modus_ponens,[status(thm)],[185, 5465])).
% 27.80/18.04 tff(5467,plain,
% 27.80/18.04 (big_f(f7(c2), f6(c2, f9(c2, c2))) <=> big_f(c2, c2)),
% 27.80/18.04 inference(monotonicity,[status(thm)],[5408, 5460])).
% 27.80/18.04 tff(5468,plain,
% 27.80/18.04 (big_f(c2, c2) <=> big_f(f7(c2), f6(c2, f9(c2, c2)))),
% 27.80/18.04 inference(symmetry,[status(thm)],[5467])).
% 27.80/18.04 tff(5469,plain,
% 27.80/18.04 (big_f(c2, c2) <=> big_f(f7(c2), f6(c2, c1))),
% 27.80/18.04 inference(transitivity,[status(thm)],[5468, 4443])).
% 27.80/18.04 tff(5470,plain,
% 27.80/18.04 ((~big_f(c2, c2)) <=> (~big_f(f7(c2), f6(c2, c1)))),
% 27.80/18.04 inference(monotonicity,[status(thm)],[5469])).
% 27.80/18.04 tff(5471,plain,
% 27.80/18.04 (~big_f(f7(c2), f6(c2, c1))),
% 27.80/18.04 inference(modus_ponens,[status(thm)],[121, 5470])).
% 27.80/18.04 tff(5472,plain,
% 27.80/18.04 (f9(c2, c1) = c1),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[3211, 731, 122, 3197, 77, 3198])).
% 27.80/18.04 tff(5473,plain,
% 27.80/18.04 ($false),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[743, 5472, 731, 148, 690, 79, 122])).
% 27.80/18.04 tff(5474,plain,(big_f(f9(c2, c1), f10(c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | big_f(f7(c2), f6(c2, c1)) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 27.80/18.04 tff(5475,plain,
% 27.80/18.04 (big_f(f9(c2, c1), f10(c2))),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[5474, 5471, 5408, 79, 122, 5409, 5466, 148])).
% 27.80/18.04 tff(5476,plain,
% 27.80/18.04 (big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[3898, 5475, 148, 79, 122])).
% 27.80/18.04 tff(5477,plain,
% 27.80/18.04 (~(f9(c2, c1) = c1)),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[3563, 5471, 122, 5408, 5019, 5411, 5466])).
% 27.80/18.04 tff(5478,plain,
% 27.80/18.04 (~(f9(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[1141, 5477, 122, 79, 148])).
% 27.80/18.04 tff(5479,plain,
% 27.80/18.04 ($false),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[4482, 5478, 5476, 122, 121, 148, 79, 5020])).
% 27.80/18.04 tff(5480,plain,(big_f(c2, c2) | (~(f10(c2) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (f7(c1) = c1) | (f9(f10(c2), f10(c2)) = f10(c2))), inference(lemma,lemma(discharge,[]))).
% 27.80/18.04 tff(5481,plain,
% 27.80/18.04 (big_f(c2, c2)),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[5480, 115, 148, 79, 122, 158])).
% 27.80/18.04 tff(5482,plain,
% 27.80/18.04 (~big_f(f9(c2, c2), c2)),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[5379, 2040, 377, 1345, 148, 79, 122])).
% 27.80/18.04 tff(5483,plain,
% 27.80/18.04 (~big_f(f9(c2, c2), f10(c2))),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[3687, 5482, 122])).
% 27.80/18.04 tff(5484,plain,
% 27.80/18.04 ($false),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[2698, 2492, 122, 77, 3953, 2621, 1209, 256])).
% 27.80/18.04 tff(5485,plain,(big_f(f7(c2), f6(c2, c2)) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~big_f(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 27.80/18.04 tff(5486,plain,
% 27.80/18.04 (big_f(f7(c2), f6(c2, c2))),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[5485, 5483, 77, 185, 122, 1345])).
% 27.80/18.04 tff(5487,plain,
% 27.80/18.04 (~(f5(c1) = c1)),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[4195, 5483, 148, 79, 122, 3762, 77, 347])).
% 27.80/18.04 tff(5488,plain,
% 27.80/18.04 (f5(c1) = c2),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[1708, 5487])).
% 27.80/18.04 tff(5489,plain,
% 27.80/18.04 (f6(c2, c2) = c2),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[4056, 5486, 148, 5488, 79, 122, 77, 2040])).
% 27.80/18.04 tff(5490,plain,
% 27.80/18.04 ($false),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[2750, 5489, 5486, 122, 5483, 1345, 77])).
% 27.80/18.04 tff(5491,plain,(big_f(c2, f9(c2, c2)) | (~(f10(c2) = c2)) | (~big_f(c2, c2)) | (~(f7(c2) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c1) = c1)) | (~(f7(c1) = c2)) | (c2 = c3)), inference(lemma,lemma(discharge,[]))).
% 27.80/18.04 tff(5492,plain,
% 27.80/18.04 (big_f(c2, f9(c2, c2))),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[5491, 5481, 122, 5408, 148, 79, 3637, 120, 4978])).
% 27.80/18.04 tff(5493,plain,
% 27.80/18.04 (big_f(c2, c1)),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[3721, 5492, 148, 79, 122])).
% 27.80/18.04 tff(5494,plain,
% 27.80/18.04 ((f9(c2, c2) = f5(f9(c2, c2))) <=> (c1 = f5(c1))),
% 27.80/18.04 inference(monotonicity,[status(thm)],[161, 152])).
% 27.80/18.04 tff(5495,plain,
% 27.80/18.04 ((f9(c2, c2) = f5(f9(c2, c2))) <=> (f5(c1) = c1)),
% 27.80/18.04 inference(transitivity,[status(thm)],[5494, 128])).
% 27.80/18.04 tff(5496,plain,
% 27.80/18.04 (f9(c2, c2) = f5(f9(c2, c2))),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[1810, 256, 122, 347, 148, 79, 348])).
% 27.80/18.04 tff(5497,plain,
% 27.80/18.04 (f5(c1) = c1),
% 27.80/18.04 inference(modus_ponens,[status(thm)],[5496, 5495])).
% 27.80/18.04 tff(5498,plain,
% 27.80/18.04 (~(f5(c1) = c1)),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[4195, 256, 148, 79, 122, 3762, 77, 347])).
% 27.80/18.04 tff(5499,plain,
% 27.80/18.04 ($false),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[5498, 5497])).
% 27.80/18.04 tff(5500,plain,(big_f(f9(c2, c2), f10(c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f7(c1) = c2)) | (~big_f(c2, c1)) | (~(f10(c1) = c1)) | (~(f7(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.80/18.04 tff(5501,plain,
% 27.80/18.04 (big_f(f9(c2, c2), f10(c2))),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[5500, 120, 79, 122, 148, 5493, 3637, 5408])).
% 27.80/18.04 tff(5502,plain,
% 27.80/18.04 (big_f(f9(c2, c2), c2)),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[3687, 5501, 122])).
% 27.80/18.04 tff(5503,plain,
% 27.80/18.04 (~(c4 = c1)),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[5336, 487, 1822, 2041, 79, 148, 122])).
% 27.80/18.04 tff(5504,plain,
% 27.80/18.04 (c4 = c2),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[461, 5503])).
% 27.80/18.04 tff(5505,plain,
% 27.80/18.04 (c2 = c4),
% 27.80/18.04 inference(modus_ponens,[status(thm)],[5504, 159])).
% 27.80/18.04 tff(5506,plain,
% 27.80/18.04 (c2 = c4),
% 27.80/18.04 inference(symmetry,[status(thm)],[5504])).
% 27.80/18.04 tff(5507,plain,
% 27.80/18.04 (f4(c2) = f4(c4)),
% 27.80/18.04 inference(monotonicity,[status(thm)],[5506])).
% 27.80/18.04 tff(5508,plain,
% 27.80/18.04 (f4(c2) = c2),
% 27.80/18.04 inference(transitivity,[status(thm)],[5507, 79])).
% 27.80/18.04 tff(5509,plain,
% 27.80/18.04 ((f9(c2, c2) = f4(c2)) <=> (f9(c2, c2) = c2)),
% 27.80/18.04 inference(monotonicity,[status(thm)],[5508])).
% 27.80/18.04 tff(5510,plain,
% 27.80/18.04 ((f9(c2, c2) = c2) <=> (f9(c2, c2) = f4(c2))),
% 27.80/18.04 inference(symmetry,[status(thm)],[5509])).
% 27.80/18.04 tff(5511,plain,
% 27.80/18.04 ((~(f9(c2, c2) = c2)) <=> (~(f9(c2, c2) = f4(c2)))),
% 27.80/18.04 inference(monotonicity,[status(thm)],[5510])).
% 27.80/18.04 tff(5512,plain,
% 27.80/18.04 (~(f9(c2, c2) = f4(c2))),
% 27.80/18.04 inference(modus_ponens,[status(thm)],[185, 5511])).
% 27.80/18.04 tff(5513,plain,
% 27.80/18.04 ((~(c2 = c4)) | (c2 = f2(f9(c2, c2))) | (f9(c2, c2) = f4(c2))),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[5352, 1355, 1822, 2041])).
% 27.80/18.04 tff(5514,plain,
% 27.80/18.04 (c2 = f2(f9(c2, c2))),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[5513, 5512, 5505])).
% 27.80/18.04 tff(5515,plain,
% 27.80/18.04 (f2(f9(c2, c2)) = c2),
% 27.80/18.04 inference(symmetry,[status(thm)],[5514])).
% 27.80/18.04 tff(5516,plain,
% 27.80/18.04 (f9(c2, c2) = f2(f9(c2, c2))),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[5361, 1355, 5505, 487, 1822, 2041, 5512])).
% 27.80/18.04 tff(5517,plain,
% 27.80/18.04 (f9(c2, c2) = c2),
% 27.80/18.04 inference(transitivity,[status(thm)],[5516, 5515])).
% 27.80/18.04 tff(5518,plain,
% 27.80/18.04 ($false),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[185, 5517])).
% 27.80/18.04 tff(5519,plain,((~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c3)) | (~big_f(f9(c2, c2), c2)) | (~(f4(c4) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.80/18.04 tff(5520,plain,
% 27.80/18.04 (~big_f(f9(c2, c2), f9(c2, c2))),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[5519, 4979, 5502, 79, 148, 122])).
% 27.80/18.04 tff(5521,plain,
% 27.80/18.04 ($false),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[3810, 200, 191, 148, 3762, 79, 122, 115, 3719, 3689])).
% 27.80/18.04 tff(5522,plain,((~(f5(c1) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f10(c1) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (f7(c1) = c1) | (~big_f(c2, f9(c2, c2))) | big_f(f9(c2, c2), f9(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 27.80/18.04 tff(5523,plain,
% 27.80/18.04 (~(f5(c1) = c2)),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[5522, 3637, 148, 79, 122, 115, 5492, 5520])).
% 27.80/18.04 tff(5524,plain,
% 27.80/18.04 (~(c2 = f5(f9(c2, c2)))),
% 27.80/18.04 inference(modus_ponens,[status(thm)],[5523, 157])).
% 27.80/18.04 tff(5525,plain,
% 27.80/18.04 (big_f(f7(f9(c2, c2)), c2)),
% 27.80/18.04 inference(modus_ponens,[status(thm)],[5481, 246])).
% 27.80/18.04 tff(5526,plain,
% 27.80/18.04 (f5(c1) = c1),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[1708, 5523])).
% 27.80/18.04 tff(5527,plain,
% 27.80/18.04 (f9(c1, c2) = c2),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[4416, 5526, 148, 3654, 79, 122, 5481, 120, 5520, 3637])).
% 27.80/18.04 tff(5528,plain,
% 27.80/18.04 (c2 = f5(f9(c2, c2))),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[5388, 5527, 5525, 5492, 3654, 3637, 148, 79, 122])).
% 27.80/18.04 tff(5529,plain,
% 27.80/18.04 ($false),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[5528, 5524])).
% 27.80/18.04 tff(5530,plain,((f7(c1) = c1) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (f9(f10(c2), f10(c2)) = f10(c2))), inference(lemma,lemma(discharge,[]))).
% 27.80/18.04 tff(5531,plain,
% 27.80/18.04 (f7(c1) = c1),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[5530, 147, 79, 122, 142])).
% 27.80/18.04 tff(5532,plain,
% 27.80/18.04 (f7(f9(c2, c2)) = f9(c2, c2)),
% 27.80/18.04 inference(transitivity,[status(thm)],[243, 4234, 149, 132])).
% 27.80/18.04 tff(5533,plain,
% 27.80/18.04 (f6(f9(c2, c2), c2) = f9(c2, c2)),
% 27.80/18.04 inference(transitivity,[status(thm)],[4247, 4262, 149, 132])).
% 27.80/18.04 tff(5534,plain,
% 27.80/18.04 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 27.80/18.04 inference(monotonicity,[status(thm)],[5532, 5533])).
% 27.80/18.04 tff(5535,plain,
% 27.80/18.04 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))),
% 27.80/18.04 inference(symmetry,[status(thm)],[5534])).
% 27.80/18.04 tff(5536,plain,
% 27.80/18.04 ((~big_f(f9(c2, c2), f9(c2, c2))) <=> (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)))),
% 27.80/18.04 inference(monotonicity,[status(thm)],[5535])).
% 27.80/18.04 tff(5537,plain,
% 27.80/18.04 (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))),
% 27.80/18.04 inference(modus_ponens,[status(thm)],[3689, 5536])).
% 27.80/18.04 tff(5538,plain,
% 27.80/18.04 (big_f(f7(c2), f9(c2, c2))),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[4934, 5291, 22, 148, 79, 122])).
% 27.80/18.04 tff(5539,plain,
% 27.80/18.04 (f9(c2, c2) = f5(c2)),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[4603, 676, 122, 17, 185, 4597, 5538])).
% 27.80/18.04 tff(5540,plain,
% 27.80/18.04 (f5(c2) = f9(c2, c2)),
% 27.80/18.04 inference(symmetry,[status(thm)],[5539])).
% 27.80/18.04 tff(5541,plain,
% 27.80/18.04 (f5(c2) = c1),
% 27.80/18.04 inference(transitivity,[status(thm)],[5540, 160, 148])).
% 27.80/18.04 tff(5542,plain,
% 27.80/18.04 ((f6(c1, c1) = f5(c2)) <=> (f6(c1, c1) = c1)),
% 27.80/18.04 inference(monotonicity,[status(thm)],[5541])).
% 27.80/18.04 tff(5543,plain,
% 27.80/18.04 ((f6(c1, c1) = f5(c2)) <=> (f6(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))),
% 27.80/18.04 inference(transitivity,[status(thm)],[5542, 4596])).
% 27.80/18.04 tff(5544,plain,
% 27.80/18.04 (c1 = f7(c1)),
% 27.80/18.04 inference(symmetry,[status(thm)],[4234])).
% 27.80/18.04 tff(5545,plain,
% 27.80/18.04 (f7(c2) = f7(c1)),
% 27.80/18.04 inference(transitivity,[status(thm)],[22, 5544])).
% 27.80/18.04 tff(5546,plain,
% 27.80/18.04 (big_f(f7(c2), f6(c1, c1)) <=> big_f(f7(c1), f6(c1, c1))),
% 27.80/18.04 inference(monotonicity,[status(thm)],[5545])).
% 27.80/18.04 tff(5547,plain,
% 27.80/18.04 (big_f(f7(c1), f6(c1, c1)) <=> big_f(f7(c2), f6(c1, c1))),
% 27.80/18.04 inference(symmetry,[status(thm)],[5546])).
% 27.80/18.04 tff(5548,plain,
% 27.80/18.04 (big_f(f9(c2, c2), f9(c2, c2))),
% 27.80/18.04 inference(modus_ponens,[status(thm)],[5291, 4889])).
% 27.80/18.04 tff(5549,plain,
% 27.80/18.04 (big_f(f7(c1), f6(c1, c1))),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[4658, 5548, 148, 79, 122, 4234, 4597])).
% 27.80/18.04 tff(5550,plain,
% 27.80/18.04 (big_f(f7(c2), f6(c1, c1))),
% 27.80/18.04 inference(modus_ponens,[status(thm)],[5549, 5547])).
% 27.80/18.04 tff(5551,plain,
% 27.80/18.04 (f6(c1, c1) = f5(c2)),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[4667, 5550])).
% 27.80/18.04 tff(5552,plain,
% 27.80/18.04 (f6(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)),
% 27.80/18.04 inference(modus_ponens,[status(thm)],[5551, 5543])).
% 27.80/18.04 tff(5553,plain,
% 27.80/18.04 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2)))),
% 27.80/18.04 inference(modus_ponens,[status(thm)],[5549, 4671])).
% 27.80/18.04 tff(5554,plain,
% 27.80/18.04 ((~(f6(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2))))),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[4676, 2534, 122, 185, 4597, 4258])).
% 27.80/18.04 tff(5555,plain,
% 27.80/18.04 (~(f6(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[5554, 5553])).
% 27.80/18.04 tff(5556,plain,
% 27.80/18.04 ($false),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[5555, 5552])).
% 27.80/18.04 tff(5557,plain,(big_f(f9(c2, c2), c2) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~(f7(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 27.80/18.04 tff(5558,plain,
% 27.80/18.04 (f7(c2) = c2),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[5557, 3685, 79, 122, 148, 4234])).
% 27.80/18.04 tff(5559,plain,
% 27.80/18.04 (c2 = f7(c2)),
% 27.80/18.04 inference(symmetry,[status(thm)],[5558])).
% 27.80/18.04 tff(5560,plain,
% 27.80/18.04 (c2 = f7(f4(c4))),
% 27.80/18.04 inference(transitivity,[status(thm)],[5559, 81])).
% 27.80/18.04 tff(5561,plain,
% 27.80/18.04 (f3(c2, c2) = f3(f7(f4(c4)), f4(c4))),
% 27.80/18.04 inference(monotonicity,[status(thm)],[5560, 436])).
% 27.80/18.04 tff(5562,plain,
% 27.80/18.04 (f3(f7(f4(c4)), f4(c4)) = f3(c2, c2)),
% 27.80/18.04 inference(symmetry,[status(thm)],[5561])).
% 27.80/18.04 tff(5563,plain,
% 27.80/18.04 ((f3(f7(f4(c4)), f4(c4)) = c2) <=> (f3(c2, c2) = c2)),
% 27.80/18.04 inference(monotonicity,[status(thm)],[5562])).
% 27.80/18.04 tff(5564,plain,
% 27.80/18.04 ((f3(c2, c2) = c2) <=> (f3(f7(f4(c4)), f4(c4)) = c2)),
% 27.80/18.04 inference(symmetry,[status(thm)],[5563])).
% 27.80/18.04 tff(5565,plain,
% 27.80/18.04 ((c1 = c3) <=> (f9(c2, c2) = c3)),
% 27.80/18.04 inference(monotonicity,[status(thm)],[4708])).
% 27.80/18.04 tff(5566,plain,
% 27.80/18.04 ((c3 = c1) <=> (f9(c2, c2) = c3)),
% 27.80/18.04 inference(transitivity,[status(thm)],[68, 5565])).
% 27.80/18.04 tff(5567,plain,
% 27.80/18.04 (f9(c2, c2) = c3),
% 27.80/18.04 inference(modus_ponens,[status(thm)],[172, 5566])).
% 27.80/18.04 tff(5568,plain,
% 27.80/18.04 (big_f(c1, c1) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 27.80/18.04 inference(monotonicity,[status(thm)],[4708, 4708])).
% 27.80/18.04 tff(5569,plain,
% 27.80/18.04 (~big_f(f9(c2, c2), f9(c2, c2))),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[4926, 66, 148, 79, 122])).
% 27.80/18.04 tff(5570,plain,
% 27.80/18.04 (f10(c1) = f10(f9(c2, c2))),
% 27.80/18.04 inference(monotonicity,[status(thm)],[150])).
% 27.80/18.04 tff(5571,plain,
% 27.80/18.04 (c2 = f10(c1)),
% 27.80/18.04 inference(symmetry,[status(thm)],[15])).
% 27.80/18.04 tff(5572,plain,
% 27.80/18.04 (c2 = f10(f9(c2, c2))),
% 27.80/18.04 inference(transitivity,[status(thm)],[5571, 5570])).
% 27.80/18.04 tff(5573,plain,
% 27.80/18.04 (big_f(c2, c2) <=> big_f(c2, f10(f9(c2, c2)))),
% 27.80/18.04 inference(monotonicity,[status(thm)],[5572])).
% 27.80/18.04 tff(5574,plain,
% 27.80/18.04 ((f6(c1, c2) = c2) <=> (f6(f9(c2, c2), c2) = c2)),
% 27.80/18.04 inference(symmetry,[status(thm)],[4252])).
% 27.80/18.04 tff(5575,plain,
% 27.80/18.04 (big_f(f9(c2, c2), f10(c2)) <=> big_f(c1, c2)),
% 27.80/18.04 inference(transitivity,[status(thm)],[129, 3690])).
% 27.80/18.04 tff(5576,plain,
% 27.80/18.04 ((~big_f(f4(c4), c4)) <=> (~big_f(c2, c4))),
% 27.80/18.04 inference(monotonicity,[status(thm)],[375])).
% 27.80/18.04 tff(5577,plain,
% 27.80/18.04 (~big_f(f4(c4), c4)),
% 27.80/18.04 inference(unit_resolution,[status(thm)],[5036, 2, 79, 121])).
% 27.80/18.04 tff(5578,plain,
% 27.80/18.04 (~big_f(c2, c4)),
% 27.80/18.04 inference(modus_ponens,[status(thm)],[5577, 5576])).
% 27.80/18.04 tff(5579,plain,
% 27.80/18.04 ((c3 = c1) <=> (f9(c2, c2) = c3)),
% 27.80/18.04 inference(transitivity,[status(thm)],[68, 3640])).
% 27.80/18.04 tff(5580,plain,
% 27.80/18.04 (f9(c2, c2) = c3),
% 27.80/18.04 inference(modus_ponens,[status(thm)],[172, 5579])).
% 27.80/18.04 tff(5581,plain,
% 27.80/18.04 (big_f(f9(c2, c2), f10(c2)) <=> big_f(c1, f10(c1))),
% 27.80/18.04 inference(transitivity,[status(thm)],[689, 3428])).
% 27.80/18.04 tff(5582,plain,
% 27.80/18.04 ((~big_f(f9(c2, c2), f10(c2))) <=> (~big_f(c1, f10(c1)))),
% 27.80/18.05 inference(monotonicity,[status(thm)],[5581])).
% 27.80/18.05 tff(5583,plain,
% 27.80/18.05 (~big_f(c1, f10(c1))),
% 27.80/18.05 inference(modus_ponens,[status(thm)],[256, 5582])).
% 27.80/18.05 tff(5584,plain,
% 27.80/18.05 (big_f(c3, f2(c3))),
% 27.80/18.05 inference(unit_resolution,[status(thm)],[1315, 803])).
% 27.80/18.05 tff(5585,plain,
% 27.80/18.05 (c1 = c3),
% 27.80/18.05 inference(symmetry,[status(thm)],[172])).
% 27.80/18.05 tff(5586,plain,
% 27.80/18.05 (f2(c1) = f2(c3)),
% 27.80/18.05 inference(monotonicity,[status(thm)],[5585])).
% 27.80/18.05 tff(5587,plain,
% 27.80/18.05 (f2(c1) = f10(c2)),
% 27.80/18.05 inference(transitivity,[status(thm)],[5586, 1319, 216])).
% 27.80/18.05 tff(5588,plain,
% 27.80/18.05 (big_f(c1, f2(c1)) <=> big_f(f9(c2, c2), f10(c2))),
% 27.80/18.05 inference(monotonicity,[status(thm)],[150, 5587])).
% 27.80/18.05 tff(5589,plain,
% 27.80/18.05 (f2(c3) = f2(c1)),
% 27.80/18.05 inference(symmetry,[status(thm)],[5586])).
% 27.80/18.05 tff(5590,plain,
% 27.80/18.05 (big_f(c3, f2(c3)) <=> big_f(c1, f2(c1))),
% 27.80/18.05 inference(monotonicity,[status(thm)],[172, 5589])).
% 27.80/18.05 tff(5591,plain,
% 27.80/18.05 (big_f(c3, f2(c3)) <=> big_f(c1, f10(c1))),
% 27.80/18.05 inference(transitivity,[status(thm)],[5590, 5588, 689, 3428])).
% 27.80/18.05 tff(5592,plain,
% 27.80/18.05 (big_f(c1, f10(c1))),
% 27.80/18.05 inference(modus_ponens,[status(thm)],[2274, 5591])).
% 27.80/18.05 tff(5593,plain,
% 27.80/18.05 ($false),
% 27.80/18.05 inference(unit_resolution,[status(thm)],[3030, 5592])).
% 27.80/18.05 tff(5594,plain,((~big_f(c3, f2(c3))) | big_f(c1, f10(c1)) | (~(f10(c2) = c2)) | (~(f10(c1) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f2(c3) = c2)) | (~(c3 = c1))), inference(lemma,lemma(discharge,[]))).
% 27.80/18.05 tff(5595,plain,
% 27.80/18.05 (~(f2(c3) = c2)),
% 27.80/18.05 inference(unit_resolution,[status(thm)],[5594, 5584, 122, 16, 148, 79, 172, 5583])).
% 27.80/18.05 tff(5596,plain,
% 27.80/18.05 (f2(c3) = c1),
% 27.80/18.05 inference(unit_resolution,[status(thm)],[1273, 5595])).
% 27.80/18.05 tff(5597,plain,
% 27.80/18.05 (f2(f9(c2, c2)) = f2(c1)),
% 27.80/18.05 inference(monotonicity,[status(thm)],[161])).
% 27.80/18.05 tff(5598,plain,
% 27.80/18.05 (f2(f9(c2, c2)) = c1),
% 27.80/18.05 inference(transitivity,[status(thm)],[5597, 5586, 1247])).
% 27.80/18.05 tff(5599,plain,
% 27.80/18.05 ((f6(c1, c1) = f2(f9(c2, c2))) <=> (f6(c1, c1) = c1)),
% 27.80/18.05 inference(monotonicity,[status(thm)],[5598])).
% 27.80/18.05 tff(5600,plain,
% 27.80/18.05 ((f6(c1, c1) = c1) <=> (f6(c1, c1) = f2(f9(c2, c2)))),
% 27.80/18.05 inference(symmetry,[status(thm)],[5599])).
% 27.80/18.05 tff(5601,plain,
% 27.80/18.05 ((~(f6(c1, c1) = c1)) <=> (~(f6(c1, c1) = f2(f9(c2, c2))))),
% 27.80/18.05 inference(monotonicity,[status(thm)],[5600])).
% 27.80/18.05 tff(5602,plain,
% 27.80/18.05 (~(f6(c1, c1) = f2(f9(c2, c2)))),
% 27.80/18.05 inference(modus_ponens,[status(thm)],[28, 5601])).
% 27.80/18.05 tff(5603,plain,
% 27.80/18.05 (f9(c2, c2) = f7(c1)),
% 27.80/18.05 inference(transitivity,[status(thm)],[160, 148, 5544])).
% 27.80/18.05 tff(5604,plain,
% 27.80/18.05 (big_f(f9(c2, c2), f6(c1, c1)) <=> big_f(f7(c1), f6(c1, c1))),
% 27.80/18.05 inference(monotonicity,[status(thm)],[5603])).
% 27.80/18.05 tff(5605,plain,
% 27.80/18.05 (big_f(f7(c1), f6(c1, c1)) <=> big_f(f9(c2, c2), f6(c1, c1))),
% 27.80/18.05 inference(symmetry,[status(thm)],[5604])).
% 27.80/18.05 tff(5606,plain,
% 27.80/18.05 (big_f(f7(c1), f6(c1, c1))),
% 27.80/18.05 inference(unit_resolution,[status(thm)],[4650, 28, 122, 185, 4234, 256])).
% 27.80/18.05 tff(5607,plain,
% 27.80/18.05 (big_f(f9(c2, c2), f6(c1, c1))),
% 27.80/18.05 inference(modus_ponens,[status(thm)],[5606, 5605])).
% 27.80/18.05 tff(5608,plain,
% 27.80/18.05 ((f9(f10(c2), f4(c4)) = c3) <=> (c1 = c3)),
% 27.80/18.05 inference(monotonicity,[status(thm)],[148])).
% 27.80/18.05 tff(5609,plain,
% 27.80/18.05 ((c1 = c3) <=> (f9(f10(c2), f4(c4)) = c3)),
% 27.80/18.05 inference(symmetry,[status(thm)],[5608])).
% 27.80/18.05 tff(5610,plain,
% 27.80/18.05 ((c1 = c3) <=> (f9(c2, c2) = c3)),
% 27.80/18.05 inference(transitivity,[status(thm)],[5609, 339])).
% 27.80/18.05 tff(5611,plain,
% 27.80/18.05 (c1 = c3),
% 27.80/18.05 inference(unit_resolution,[status(thm)],[175, 172])).
% 27.80/18.05 tff(5612,plain,
% 27.80/18.05 (f9(c2, c2) = c3),
% 27.80/18.05 inference(modus_ponens,[status(thm)],[5611, 5610])).
% 27.80/18.05 tff(5613,plain,
% 27.80/18.05 (^[X12: $i, X3: $i, X10: $i, X2: $i] : refl(((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12))) <=> ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12))))),
% 27.80/18.05 inference(bind,[status(th)],[])).
% 27.80/18.05 tff(5614,plain,
% 27.80/18.05 (![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12))) <=> ![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))),
% 27.80/18.05 inference(quant_intro,[status(thm)],[5613])).
% 27.80/18.05 tff(5615,plain,
% 27.80/18.05 (![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12))) <=> ![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))),
% 27.80/18.05 inference(rewrite,[status(thm)],[])).
% 27.80/18.05 tff(5616,plain,
% 27.80/18.05 (^[X12: $i, X3: $i, X10: $i, X2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_f(X10, X12)) | (X12 = f2(X10))) | (~(X10 = c3))) <=> ((~(X10 = c3)) | (X12 = f2(X10)) | (~big_f(X10, X12)))), (((((~big_f(X10, X12)) | (X12 = f2(X10))) | (~(X10 = c3))) | big_f(X3, X2)) <=> (((~(X10 = c3)) | (X12 = f2(X10)) | (~big_f(X10, X12))) | big_f(X3, X2)))), rewrite((((~(X10 = c3)) | (X12 = f2(X10)) | (~big_f(X10, X12))) | big_f(X3, X2)) <=> ((~(X10 = c3)) | big_f(X3, X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))), (((((~big_f(X10, X12)) | (X12 = f2(X10))) | (~(X10 = c3))) | big_f(X3, X2)) <=> ((~(X10 = c3)) | big_f(X3, X2) | (X12 = f2(X10)) | (~big_f(X10, X12))))), ((((((~big_f(X10, X12)) | (X12 = f2(X10))) | (~(X10 = c3))) | big_f(X3, X2)) | (~(X3 = f4(X2)))) <=> (((~(X10 = c3)) | big_f(X3, X2) | (X12 = f2(X10)) | (~big_f(X10, X12))) | (~(X3 = f4(X2)))))), rewrite((((~(X10 = c3)) | big_f(X3, X2) | (X12 = f2(X10)) | (~big_f(X10, X12))) | (~(X3 = f4(X2)))) <=> ((~(X10 = c3)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))), ((((((~big_f(X10, X12)) | (X12 = f2(X10))) | (~(X10 = c3))) | big_f(X3, X2)) | (~(X3 = f4(X2)))) <=> ((~(X10 = c3)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12))))), (((((((~big_f(X10, X12)) | (X12 = f2(X10))) | (~(X10 = c3))) | big_f(X3, X2)) | (~(X3 = f4(X2)))) | (~(X2 = c4))) <=> (((~(X10 = c3)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12))) | (~(X2 = c4))))), rewrite((((~(X10 = c3)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12))) | (~(X2 = c4))) <=> ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))), (((((((~big_f(X10, X12)) | (X12 = f2(X10))) | (~(X10 = c3))) | big_f(X3, X2)) | (~(X3 = f4(X2)))) | (~(X2 = c4))) <=> ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))))),
% 27.80/18.05 inference(bind,[status(th)],[])).
% 27.80/18.05 tff(5617,plain,
% 27.80/18.05 (![X12: $i, X3: $i, X10: $i, X2: $i] : ((((((~big_f(X10, X12)) | (X12 = f2(X10))) | (~(X10 = c3))) | big_f(X3, X2)) | (~(X3 = f4(X2)))) | (~(X2 = c4))) <=> ![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))),
% 27.80/18.05 inference(quant_intro,[status(thm)],[5616])).
% 27.80/18.05 tff(5618,axiom,(![X12: $i, X3: $i, X10: $i, X2: $i] : ((((((~big_f(X10, X12)) | (X12 = f2(X10))) | (~(X10 = c3))) | big_f(X3, X2)) | (~(X3 = f4(X2)))) | (~(X2 = c4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_14')).
% 27.80/18.05 tff(5619,plain,
% 27.80/18.05 (![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))),
% 27.80/18.05 inference(modus_ponens,[status(thm)],[5618, 5617])).
% 27.80/18.05 tff(5620,plain,
% 27.80/18.05 (![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))),
% 27.80/18.05 inference(modus_ponens,[status(thm)],[5619, 5615])).
% 27.80/18.05 tff(5621,plain,(
% 27.80/18.05 ![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))),
% 27.80/18.05 inference(skolemize,[status(sab)],[5620])).
% 27.80/18.05 tff(5622,plain,
% 27.80/18.05 (![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))),
% 27.80/18.05 inference(modus_ponens,[status(thm)],[5621, 5614])).
% 27.80/18.05 tff(5623,plain,
% 27.80/18.05 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (~(f9(c2, c2) = c3)) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (~(f9(c2, c2) = c3)) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1))))),
% 27.80/18.05 inference(rewrite,[status(thm)],[])).
% 27.80/18.05 tff(5624,plain,
% 27.80/18.05 (((~(f9(c2, c2) = c3)) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1)))) <=> ((~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (~(f9(c2, c2) = c3)) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1))))),
% 27.80/18.05 inference(rewrite,[status(thm)],[])).
% 27.80/18.05 tff(5625,plain,
% 27.80/18.05 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c2, c2) = c3)) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (~(f9(c2, c2) = c3)) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1)))))),
% 27.80/18.05 inference(monotonicity,[status(thm)],[5624])).
% 27.80/18.05 tff(5626,plain,
% 27.80/18.05 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c2, c2) = c3)) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (~(f9(c2, c2) = c3)) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1))))),
% 27.80/18.05 inference(transitivity,[status(thm)],[5625, 5623])).
% 27.80/18.05 tff(5627,plain,
% 27.80/18.05 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c2, c2) = c3)) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1))))),
% 27.80/18.05 inference(quant_inst,[status(thm)],[])).
% 27.80/18.05 tff(5628,plain,
% 27.80/18.05 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (~(f9(c2, c2) = c3)) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1)))),
% 27.80/18.05 inference(modus_ponens,[status(thm)],[5627, 5626])).
% 27.80/18.05 tff(5629,plain,
% 27.80/18.05 ((f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1)))),
% 27.80/18.05 inference(unit_resolution,[status(thm)],[5628, 5622, 631, 630, 121, 5612])).
% 27.80/18.05 tff(5630,plain,
% 27.80/18.05 ($false),
% 27.80/18.05 inference(unit_resolution,[status(thm)],[5629, 5607, 5602])).
% 27.80/18.05 tff(5631,plain,((f6(c1, c1) = c1) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (~(f7(c1) = c1)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f2(c3) = c1)) | (~(c3 = c1)) | big_f(f9(c2, c2), f10(c2))), inference(lemma,lemma(discharge,[]))).
% 27.80/18.05 tff(5632,plain,
% 27.80/18.05 (f6(c1, c1) = c1),
% 27.80/18.05 inference(unit_resolution,[status(thm)],[5631, 432, 437, 121, 4234, 148, 79, 122, 5596, 172, 256])).
% 27.80/18.05 tff(5633,plain,
% 27.80/18.05 (f6(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)),
% 27.80/18.05 inference(transitivity,[status(thm)],[4594, 5632, 149, 132])).
% 27.80/18.05 tff(5634,plain,
% 27.80/18.05 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2))) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 27.80/18.05 inference(monotonicity,[status(thm)],[5532, 5633])).
% 27.80/18.05 tff(5635,plain,
% 27.80/18.05 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2)))),
% 27.80/18.05 inference(symmetry,[status(thm)],[5634])).
% 27.80/18.05 tff(5636,plain,
% 27.80/18.05 (f2(c1) = f9(c2, c2)),
% 27.80/18.05 inference(transitivity,[status(thm)],[5586, 5596, 149, 132])).
% 27.80/18.05 tff(5637,plain,
% 27.80/18.05 (big_f(c1, f2(c1)) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 27.80/18.05 inference(monotonicity,[status(thm)],[150, 5636])).
% 27.80/18.05 tff(5638,plain,
% 27.80/18.05 (big_f(c1, f2(c1))),
% 27.80/18.05 inference(modus_ponens,[status(thm)],[5584, 5590])).
% 27.80/18.05 tff(5639,plain,
% 27.80/18.05 (big_f(f9(c2, c2), f9(c2, c2))),
% 27.80/18.05 inference(modus_ponens,[status(thm)],[5638, 5637])).
% 27.80/18.05 tff(5640,plain,
% 27.80/18.05 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2)))),
% 27.80/18.05 inference(modus_ponens,[status(thm)],[5639, 5635])).
% 27.80/18.05 tff(5641,plain,
% 27.80/18.05 ((~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2))))),
% 27.80/18.05 inference(unit_resolution,[status(thm)],[4676, 2534, 122, 185, 256])).
% 27.80/18.05 tff(5642,plain,
% 27.80/18.05 ($false),
% 27.80/18.05 inference(unit_resolution,[status(thm)],[5641, 5633, 5532, 5640])).
% 27.80/18.05 tff(5643,plain,((~(c4 = c2)) | (~(f10(c2) = c2)) | big_f(f9(c2, c2), f10(c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f7(c1) = c1)) | big_f(c2, c2) | (~(c3 = c1)) | (~(f10(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.80/18.05 tff(5644,plain,
% 27.80/18.05 (~(c4 = c2)),
% 27.80/18.05 inference(unit_resolution,[status(thm)],[5643, 172, 256, 148, 79, 4234, 121, 122, 16])).
% 27.80/18.05 tff(5645,plain,
% 27.80/18.05 (c4 = c1),
% 27.80/18.05 inference(unit_resolution,[status(thm)],[461, 5644])).
% 27.80/18.05 tff(5646,plain,
% 27.80/18.05 (~big_f(f4(c4), c4)),
% 27.80/18.05 inference(unit_resolution,[status(thm)],[2221, 5645, 2, 79])).
% 27.80/18.05 tff(5647,plain,
% 27.80/18.05 (big_f(c3, f2(c3))),
% 27.80/18.05 inference(unit_resolution,[status(thm)],[1315, 5646])).
% 27.80/18.05 tff(5648,plain,
% 27.80/18.05 (~(f2(c3) = c2)),
% 27.80/18.05 inference(unit_resolution,[status(thm)],[5594, 5647, 122, 16, 148, 79, 172, 5583])).
% 27.80/18.05 tff(5649,plain,
% 27.80/18.05 (f2(c3) = c1),
% 27.80/18.05 inference(unit_resolution,[status(thm)],[1273, 5648])).
% 27.80/18.05 tff(5650,plain,
% 27.80/18.05 (c1 = c4),
% 27.80/18.05 inference(symmetry,[status(thm)],[5645])).
% 27.80/18.05 tff(5651,plain,
% 27.80/18.05 (f4(c1) = f4(c4)),
% 27.80/18.05 inference(monotonicity,[status(thm)],[5650])).
% 27.80/18.05 tff(5652,plain,
% 27.80/18.05 (f4(c4) = f4(c1)),
% 27.80/18.05 inference(symmetry,[status(thm)],[5651])).
% 27.80/18.05 tff(5653,plain,
% 27.80/18.05 (c2 = f4(f9(c2, c2))),
% 27.80/18.05 inference(transitivity,[status(thm)],[436, 5652, 2094])).
% 27.80/18.05 tff(5654,plain,
% 27.80/18.05 (c1 = c4),
% 27.80/18.05 inference(unit_resolution,[status(thm)],[484, 5645])).
% 27.80/18.05 tff(5655,plain,
% 27.80/18.05 (f9(c2, c2) = c4),
% 27.80/18.05 inference(modus_ponens,[status(thm)],[5654, 362])).
% 27.80/18.05 tff(5656,plain,
% 27.80/18.05 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c2, c2) = c3)) | big_f(c2, f9(c2, c2)) | (~(f9(c2, c2) = c4)) | (~(c2 = f4(f9(c2, c2)))) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(f9(c2, c2) = c3)) | big_f(c2, f9(c2, c2)) | (~(f9(c2, c2) = c4)) | (~(c2 = f4(f9(c2, c2)))) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1))))),
% 27.80/18.05 inference(rewrite,[status(thm)],[])).
% 27.80/18.05 tff(5657,plain,
% 27.80/18.05 (((~(f9(c2, c2) = c3)) | (~(f9(c2, c2) = c4)) | big_f(c2, f9(c2, c2)) | (~(c2 = f4(f9(c2, c2)))) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1)))) <=> ((~(f9(c2, c2) = c3)) | big_f(c2, f9(c2, c2)) | (~(f9(c2, c2) = c4)) | (~(c2 = f4(f9(c2, c2)))) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1))))),
% 27.80/18.05 inference(rewrite,[status(thm)],[])).
% 27.80/18.05 tff(5658,plain,
% 27.80/18.05 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c2, c2) = c3)) | (~(f9(c2, c2) = c4)) | big_f(c2, f9(c2, c2)) | (~(c2 = f4(f9(c2, c2)))) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c2, c2) = c3)) | big_f(c2, f9(c2, c2)) | (~(f9(c2, c2) = c4)) | (~(c2 = f4(f9(c2, c2)))) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1)))))),
% 27.80/18.05 inference(monotonicity,[status(thm)],[5657])).
% 27.80/18.05 tff(5659,plain,
% 27.80/18.05 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c2, c2) = c3)) | (~(f9(c2, c2) = c4)) | big_f(c2, f9(c2, c2)) | (~(c2 = f4(f9(c2, c2)))) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(f9(c2, c2) = c3)) | big_f(c2, f9(c2, c2)) | (~(f9(c2, c2) = c4)) | (~(c2 = f4(f9(c2, c2)))) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1))))),
% 27.80/18.05 inference(transitivity,[status(thm)],[5658, 5656])).
% 27.80/18.05 tff(5660,plain,
% 27.80/18.05 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c2, c2) = c3)) | (~(f9(c2, c2) = c4)) | big_f(c2, f9(c2, c2)) | (~(c2 = f4(f9(c2, c2)))) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1))))),
% 27.80/18.05 inference(quant_inst,[status(thm)],[])).
% 27.80/18.05 tff(5661,plain,
% 27.80/18.05 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(f9(c2, c2) = c3)) | big_f(c2, f9(c2, c2)) | (~(f9(c2, c2) = c4)) | (~(c2 = f4(f9(c2, c2)))) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1)))),
% 27.80/18.05 inference(modus_ponens,[status(thm)],[5660, 5659])).
% 27.80/18.05 tff(5662,plain,
% 27.80/18.05 ((f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1)))),
% 27.80/18.05 inference(unit_resolution,[status(thm)],[5661, 5622, 514, 5612, 2040, 2099])).
% 27.80/18.05 tff(5663,plain,
% 27.80/18.05 ($false),
% 27.80/18.05 inference(unit_resolution,[status(thm)],[5662, 5607, 5602])).
% 27.80/18.05 tff(5664,plain,((f6(c1, c1) = c1) | (~(f9(c2, c2) = c4)) | big_f(c2, f9(c2, c2)) | (~(c2 = f4(f9(c2, c2)))) | (~(f7(c1) = c1)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f2(c3) = c1)) | (~(c3 = c1)) | big_f(f9(c2, c2), f10(c2))), inference(lemma,lemma(discharge,[]))).
% 27.80/18.05 tff(5665,plain,
% 27.80/18.05 (f6(c1, c1) = c1),
% 27.80/18.05 inference(unit_resolution,[status(thm)],[5664, 5655, 3842, 5653, 4234, 148, 79, 122, 5649, 172, 256])).
% 27.80/18.05 tff(5666,plain,
% 27.80/18.05 (f6(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)),
% 27.80/18.05 inference(transitivity,[status(thm)],[4594, 5665, 149, 132])).
% 27.80/18.05 tff(5667,plain,
% 27.80/18.05 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2))) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 27.80/18.05 inference(monotonicity,[status(thm)],[5532, 5666])).
% 27.80/18.05 tff(5668,plain,
% 27.80/18.05 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2)))),
% 27.80/18.05 inference(symmetry,[status(thm)],[5667])).
% 27.80/18.05 tff(5669,plain,
% 27.80/18.05 (f2(c1) = f9(c2, c2)),
% 27.80/18.05 inference(transitivity,[status(thm)],[5586, 5649, 149, 132])).
% 27.80/18.05 tff(5670,plain,
% 27.80/18.05 (big_f(c1, f2(c1)) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 27.80/18.05 inference(monotonicity,[status(thm)],[150, 5669])).
% 27.80/18.05 tff(5671,plain,
% 27.80/18.05 (big_f(c1, f2(c1))),
% 27.80/18.05 inference(modus_ponens,[status(thm)],[5647, 5590])).
% 27.80/18.05 tff(5672,plain,
% 27.80/18.05 (big_f(f9(c2, c2), f9(c2, c2))),
% 27.80/18.05 inference(modus_ponens,[status(thm)],[5671, 5670])).
% 27.80/18.05 tff(5673,plain,
% 27.80/18.05 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2)))),
% 27.80/18.05 inference(modus_ponens,[status(thm)],[5672, 5668])).
% 27.80/18.05 tff(5674,plain,
% 27.80/18.05 ($false),
% 27.80/18.05 inference(unit_resolution,[status(thm)],[5641, 5666, 5532, 5673])).
% 27.80/18.05 tff(5675,plain,((~(c3 = c1)) | (~(f10(c2) = c2)) | big_f(f9(c2, c2), f10(c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f7(c1) = c1)) | (~(f10(c1) = c2)) | big_f(c2, c1) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 27.80/18.05 tff(5676,plain,
% 27.80/18.05 (big_f(f9(c2, c2), f10(c2))),
% 27.80/18.05 inference(unit_resolution,[status(thm)],[5675, 2, 122, 148, 79, 4234, 16, 172, 121])).
% 27.80/18.05 tff(5677,plain,
% 27.80/18.05 (~big_f(f9(c2, c1), f10(c2))),
% 27.80/18.05 inference(unit_resolution,[status(thm)],[3898, 3896, 148, 79, 122])).
% 27.80/18.05 tff(5678,plain,
% 27.80/18.05 (~(f9(c2, c1) = c1)),
% 27.80/18.05 inference(unit_resolution,[status(thm)],[743, 5677, 690, 148, 79, 122])).
% 27.80/18.05 tff(5679,plain,
% 27.80/18.05 (~(f9(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.80/18.05 inference(unit_resolution,[status(thm)],[1141, 5678, 122, 79, 148])).
% 27.80/18.05 tff(5680,plain,
% 27.80/18.05 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (big_f(c2, c4) | (~(c2 = f4(c4))) | (~(f9(c2, c2) = c3)) | (c2 = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | big_f(c2, c4) | (~(c2 = f4(c4))) | (~(f9(c2, c2) = c3)) | (c2 = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), c2)))),
% 27.80/18.05 inference(rewrite,[status(thm)],[])).
% 27.80/18.05 tff(5681,plain,
% 27.80/18.05 (((~(f9(c2, c2) = c3)) | $false | big_f(c2, c4) | (~(c2 = f4(c4))) | (c2 = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), c2))) <=> (big_f(c2, c4) | (~(c2 = f4(c4))) | (~(f9(c2, c2) = c3)) | (c2 = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), c2)))),
% 27.80/18.05 inference(rewrite,[status(thm)],[])).
% 27.80/18.05 tff(5682,plain,
% 27.80/18.05 (((~(f9(c2, c2) = c3)) | (~(c4 = c4)) | big_f(c2, c4) | (~(c2 = f4(c4))) | (c2 = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), c2))) <=> ((~(f9(c2, c2) = c3)) | $false | big_f(c2, c4) | (~(c2 = f4(c4))) | (c2 = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), c2)))),
% 27.80/18.05 inference(monotonicity,[status(thm)],[410])).
% 27.80/18.05 tff(5683,plain,
% 27.80/18.05 (((~(f9(c2, c2) = c3)) | (~(c4 = c4)) | big_f(c2, c4) | (~(c2 = f4(c4))) | (c2 = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), c2))) <=> (big_f(c2, c4) | (~(c2 = f4(c4))) | (~(f9(c2, c2) = c3)) | (c2 = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), c2)))),
% 27.80/18.05 inference(transitivity,[status(thm)],[5682, 5681])).
% 27.80/18.05 tff(5684,plain,
% 27.80/18.05 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c2, c2) = c3)) | (~(c4 = c4)) | big_f(c2, c4) | (~(c2 = f4(c4))) | (c2 = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (big_f(c2, c4) | (~(c2 = f4(c4))) | (~(f9(c2, c2) = c3)) | (c2 = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), c2))))),
% 27.80/18.05 inference(monotonicity,[status(thm)],[5683])).
% 27.80/18.05 tff(5685,plain,
% 27.80/18.05 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c2, c2) = c3)) | (~(c4 = c4)) | big_f(c2, c4) | (~(c2 = f4(c4))) | (c2 = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | big_f(c2, c4) | (~(c2 = f4(c4))) | (~(f9(c2, c2) = c3)) | (c2 = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), c2)))),
% 27.80/18.05 inference(transitivity,[status(thm)],[5684, 5680])).
% 27.80/18.05 tff(5686,plain,
% 27.80/18.05 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c2, c2) = c3)) | (~(c4 = c4)) | big_f(c2, c4) | (~(c2 = f4(c4))) | (c2 = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), c2)))),
% 27.80/18.05 inference(quant_inst,[status(thm)],[])).
% 27.80/18.05 tff(5687,plain,
% 27.80/18.05 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | big_f(c2, c4) | (~(c2 = f4(c4))) | (~(f9(c2, c2) = c3)) | (c2 = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), c2))),
% 27.80/18.05 inference(modus_ponens,[status(thm)],[5686, 5685])).
% 27.80/18.05 tff(5688,plain,
% 27.80/18.05 (c2 = f2(f9(c2, c2))),
% 27.80/18.05 inference(unit_resolution,[status(thm)],[5687, 5622, 3865, 2602, 1822, 3684])).
% 27.80/18.05 tff(5689,assumption,(c2 = f2(f9(c2, c2))), introduced(assumption)).
% 27.80/18.05 tff(5690,plain,
% 27.80/18.05 (f2(f9(c2, c2)) = c2),
% 27.80/18.05 inference(symmetry,[status(thm)],[5689])).
% 27.80/18.05 tff(5691,plain,
% 27.80/18.05 ((f6(c1, c2) = f2(f9(c2, c2))) <=> (f6(c1, c2) = c2)),
% 27.80/18.05 inference(monotonicity,[status(thm)],[5690])).
% 27.80/18.05 tff(5692,plain,
% 27.80/18.05 ((f6(c1, c2) = c2) <=> (f6(c1, c2) = f2(f9(c2, c2)))),
% 27.80/18.05 inference(symmetry,[status(thm)],[5691])).
% 27.80/18.05 tff(5693,plain,
% 27.80/18.05 ((~(f6(c1, c2) = c2)) <=> (~(f6(c1, c2) = f2(f9(c2, c2))))),
% 27.80/18.05 inference(monotonicity,[status(thm)],[5692])).
% 27.80/18.05 tff(5694,plain,
% 27.80/18.05 (~(f6(c1, c2) = f2(f9(c2, c2)))),
% 27.80/18.05 inference(modus_ponens,[status(thm)],[114, 5693])).
% 27.80/18.06 tff(5695,plain,
% 27.80/18.06 (big_f(f9(c2, c2), f6(c1, c2)) <=> big_f(f7(c1), f6(c1, c2))),
% 27.80/18.06 inference(monotonicity,[status(thm)],[5603])).
% 27.80/18.06 tff(5696,plain,
% 27.80/18.06 (big_f(f7(c1), f6(c1, c2)) <=> big_f(f9(c2, c2), f6(c1, c2))),
% 27.80/18.06 inference(symmetry,[status(thm)],[5695])).
% 27.80/18.06 tff(5697,plain,
% 27.80/18.06 ((~(f6(c1, c2) = c2)) <=> (~(f6(f9(c2, c2), c2) = c2))),
% 27.80/18.06 inference(monotonicity,[status(thm)],[5574])).
% 27.80/18.06 tff(5698,plain,
% 27.80/18.06 (~(f6(f9(c2, c2), c2) = c2)),
% 27.80/18.06 inference(modus_ponens,[status(thm)],[114, 5697])).
% 27.80/18.06 tff(5699,assumption,(~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))), introduced(assumption)).
% 27.80/18.06 tff(5700,assumption,(~(f6(f9(c2, c2), c2) = c2)), introduced(assumption)).
% 27.80/18.06 tff(5701,assumption,(f7(f9(c2, c2)) = f9(c2, c2)), introduced(assumption)).
% 27.80/18.06 tff(5702,plain,
% 27.80/18.06 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f10(c2) = c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)))),
% 27.80/18.06 inference(rewrite,[status(thm)],[])).
% 27.80/18.06 tff(5703,plain,
% 27.80/18.06 (((~(f10(c2) = c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))) <=> ((~(f10(c2) = c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)))),
% 27.80/18.06 inference(rewrite,[status(thm)],[])).
% 27.80/18.06 tff(5704,plain,
% 27.80/18.06 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))))),
% 27.80/18.06 inference(monotonicity,[status(thm)],[5703])).
% 27.80/18.06 tff(5705,plain,
% 27.80/18.06 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f10(c2) = c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)))),
% 27.80/18.06 inference(transitivity,[status(thm)],[5704, 5702])).
% 27.80/18.06 tff(5706,plain,
% 27.80/18.06 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)))),
% 27.87/18.06 inference(quant_inst,[status(thm)],[])).
% 27.87/18.06 tff(5707,plain,
% 27.87/18.06 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f10(c2) = c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))),
% 27.87/18.06 inference(modus_ponens,[status(thm)],[5706, 5705])).
% 27.87/18.06 tff(5708,plain,
% 27.87/18.06 ($false),
% 27.87/18.06 inference(unit_resolution,[status(thm)],[5707, 2492, 122, 3896, 4469, 5701, 5700, 5699])).
% 27.87/18.06 tff(5709,plain,(big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)) | (~(f10(c2) = c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 27.87/18.06 tff(5710,plain,
% 27.87/18.06 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))),
% 27.87/18.06 inference(unit_resolution,[status(thm)],[5709, 5698, 3896, 4469, 5532, 122])).
% 27.87/18.06 tff(5711,plain,
% 27.87/18.06 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)) <=> big_f(f7(c1), f6(c1, c2))),
% 27.87/18.06 inference(monotonicity,[status(thm)],[243, 4247])).
% 27.87/18.06 tff(5712,assumption,(big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))), introduced(assumption)).
% 27.87/18.06 tff(5713,plain,
% 27.87/18.06 (big_f(f7(c1), f6(c1, c2))),
% 27.87/18.06 inference(modus_ponens,[status(thm)],[5712, 5711])).
% 27.87/18.06 tff(5714,assumption,(~big_f(f7(c1), f6(c1, c2))), introduced(assumption)).
% 27.87/18.06 tff(5715,plain,
% 27.87/18.06 ($false),
% 27.87/18.06 inference(unit_resolution,[status(thm)],[5714, 5713])).
% 27.87/18.06 tff(5716,plain,((~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))) | big_f(f7(c1), f6(c1, c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.87/18.06 tff(5717,plain,
% 27.87/18.06 (big_f(f7(c1), f6(c1, c2))),
% 27.87/18.06 inference(unit_resolution,[status(thm)],[5716, 5710, 148, 79, 122])).
% 27.87/18.06 tff(5718,plain,
% 27.87/18.06 (big_f(f9(c2, c2), f6(c1, c2))),
% 27.87/18.06 inference(modus_ponens,[status(thm)],[5717, 5696])).
% 27.87/18.06 tff(5719,plain,
% 27.87/18.06 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (big_f(c2, c4) | (~(c2 = f4(c4))) | (~(f9(c2, c2) = c3)) | (f6(c1, c2) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c2))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | big_f(c2, c4) | (~(c2 = f4(c4))) | (~(f9(c2, c2) = c3)) | (f6(c1, c2) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c2))))),
% 27.87/18.06 inference(rewrite,[status(thm)],[])).
% 27.87/18.06 tff(5720,plain,
% 27.87/18.06 (((~(f9(c2, c2) = c3)) | $false | big_f(c2, c4) | (~(c2 = f4(c4))) | (f6(c1, c2) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c2)))) <=> (big_f(c2, c4) | (~(c2 = f4(c4))) | (~(f9(c2, c2) = c3)) | (f6(c1, c2) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c2))))),
% 27.87/18.06 inference(rewrite,[status(thm)],[])).
% 27.87/18.06 tff(5721,plain,
% 27.87/18.06 (((~(f9(c2, c2) = c3)) | (~(c4 = c4)) | big_f(c2, c4) | (~(c2 = f4(c4))) | (f6(c1, c2) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c2)))) <=> ((~(f9(c2, c2) = c3)) | $false | big_f(c2, c4) | (~(c2 = f4(c4))) | (f6(c1, c2) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c2))))),
% 27.87/18.06 inference(monotonicity,[status(thm)],[410])).
% 27.87/18.06 tff(5722,plain,
% 27.87/18.06 (((~(f9(c2, c2) = c3)) | (~(c4 = c4)) | big_f(c2, c4) | (~(c2 = f4(c4))) | (f6(c1, c2) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c2)))) <=> (big_f(c2, c4) | (~(c2 = f4(c4))) | (~(f9(c2, c2) = c3)) | (f6(c1, c2) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c2))))),
% 27.87/18.06 inference(transitivity,[status(thm)],[5721, 5720])).
% 27.87/18.06 tff(5723,plain,
% 27.87/18.06 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c2, c2) = c3)) | (~(c4 = c4)) | big_f(c2, c4) | (~(c2 = f4(c4))) | (f6(c1, c2) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c2))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (big_f(c2, c4) | (~(c2 = f4(c4))) | (~(f9(c2, c2) = c3)) | (f6(c1, c2) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c2)))))),
% 27.87/18.06 inference(monotonicity,[status(thm)],[5722])).
% 27.87/18.06 tff(5724,plain,
% 27.87/18.06 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c2, c2) = c3)) | (~(c4 = c4)) | big_f(c2, c4) | (~(c2 = f4(c4))) | (f6(c1, c2) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c2))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | big_f(c2, c4) | (~(c2 = f4(c4))) | (~(f9(c2, c2) = c3)) | (f6(c1, c2) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c2))))),
% 27.87/18.06 inference(transitivity,[status(thm)],[5723, 5719])).
% 27.87/18.06 tff(5725,plain,
% 27.87/18.06 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c2, c2) = c3)) | (~(c4 = c4)) | big_f(c2, c4) | (~(c2 = f4(c4))) | (f6(c1, c2) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c2))))),
% 27.87/18.06 inference(quant_inst,[status(thm)],[])).
% 27.87/18.06 tff(5726,plain,
% 27.87/18.06 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | big_f(c2, c4) | (~(c2 = f4(c4))) | (~(f9(c2, c2) = c3)) | (f6(c1, c2) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c2)))),
% 27.87/18.06 inference(modus_ponens,[status(thm)],[5725, 5724])).
% 27.87/18.06 tff(5727,plain,
% 27.87/18.06 ((f6(c1, c2) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c2)))),
% 27.87/18.06 inference(unit_resolution,[status(thm)],[5726, 5622, 3865, 2602, 1822])).
% 27.87/18.06 tff(5728,plain,
% 27.87/18.06 ($false),
% 27.87/18.06 inference(unit_resolution,[status(thm)],[5727, 5718, 5694])).
% 27.87/18.06 tff(5729,plain,((f6(c1, c2) = c2) | big_f(c2, c4) | (~(f9(c2, c2) = c3)) | (~(f7(c1) = c1)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(c2 = f2(f9(c2, c2)))) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 27.87/18.06 tff(5730,plain,
% 27.87/18.06 (f6(c1, c2) = c2),
% 27.87/18.06 inference(unit_resolution,[status(thm)],[5729, 5679, 1822, 4234, 148, 79, 122, 5688, 3896, 3865])).
% 27.87/18.06 tff(5731,plain,
% 27.87/18.06 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)))),
% 27.87/18.06 inference(rewrite,[status(thm)],[])).
% 27.87/18.06 tff(5732,plain,
% 27.87/18.06 (((~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (~(f7(c1) = c1)) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2)))) <=> ((~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)))),
% 27.87/18.06 inference(rewrite,[status(thm)],[])).
% 27.87/18.06 tff(5733,plain,
% 27.87/18.06 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (~(f7(c1) = c1)) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2))))),
% 27.87/18.06 inference(monotonicity,[status(thm)],[5732])).
% 27.87/18.06 tff(5734,plain,
% 27.87/18.06 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (~(f7(c1) = c1)) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)))),
% 27.87/18.06 inference(transitivity,[status(thm)],[5733, 5731])).
% 27.87/18.06 tff(5735,plain,
% 27.87/18.06 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (~(f7(c1) = c1)) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2))))),
% 27.87/18.06 inference(quant_inst,[status(thm)],[])).
% 27.87/18.06 tff(5736,plain,
% 27.87/18.06 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2))),
% 27.87/18.06 inference(modus_ponens,[status(thm)],[5735, 5734])).
% 27.87/18.06 tff(5737,plain,
% 27.87/18.06 ((~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2))),
% 27.87/18.06 inference(unit_resolution,[status(thm)],[5736, 2534])).
% 27.87/18.06 tff(5738,plain,
% 27.87/18.06 (~big_f(f7(c1), f6(c1, c2))),
% 27.87/18.06 inference(unit_resolution,[status(thm)],[5737, 5730, 122, 4234, 5677, 5678])).
% 27.87/18.06 tff(5739,plain,
% 27.87/18.06 (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))),
% 27.87/18.06 inference(unit_resolution,[status(thm)],[5716, 5738, 148, 79, 122])).
% 27.87/18.06 tff(5740,plain,
% 27.87/18.06 (f6(f9(c2, c2), c2) = c2),
% 27.87/18.06 inference(unit_resolution,[status(thm)],[5709, 5739, 3896, 5679, 5532, 122])).
% 27.87/18.06 tff(5741,plain,
% 27.87/18.06 (f6(c1, c2) = f6(f9(c2, c2), c2)),
% 27.87/18.06 inference(monotonicity,[status(thm)],[150])).
% 27.87/18.06 tff(5742,plain,
% 27.87/18.06 (f6(c1, c2) = c2),
% 27.87/18.06 inference(transitivity,[status(thm)],[5741, 5740])).
% 27.87/18.06 tff(5743,plain,
% 27.87/18.06 (big_f(f7(c1), f6(c1, c2)) <=> big_f(f9(c2, c2), c2)),
% 27.87/18.06 inference(monotonicity,[status(thm)],[4653, 5742])).
% 27.87/18.06 tff(5744,plain,
% 27.87/18.06 (big_f(f9(c2, c2), c2) <=> big_f(f7(c1), f6(c1, c2))),
% 27.87/18.06 inference(symmetry,[status(thm)],[5743])).
% 27.87/18.06 tff(5745,plain,
% 27.87/18.06 (big_f(f7(c1), f6(c1, c2))),
% 27.87/18.06 inference(modus_ponens,[status(thm)],[3684, 5744])).
% 27.87/18.06 tff(5746,plain,
% 27.87/18.06 ($false),
% 27.87/18.06 inference(unit_resolution,[status(thm)],[5738, 5745])).
% 27.87/18.06 tff(5747,plain,(big_f(f9(c2, f9(c2, c2)), f10(c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(f9(c2, c2) = c3)) | big_f(c2, c4) | (~big_f(f9(c2, c2), f10(c2)))), inference(lemma,lemma(discharge,[]))).
% 27.87/18.06 tff(5748,plain,
% 27.87/18.06 (big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 27.87/18.06 inference(unit_resolution,[status(thm)],[5747, 5578, 79, 122, 4234, 5580, 148, 5676])).
% 27.87/18.06 tff(5749,plain,
% 27.87/18.06 (big_f(f9(c2, c2), c2)),
% 27.87/18.06 inference(modus_ponens,[status(thm)],[5676, 129])).
% 27.87/18.06 tff(5750,plain,
% 27.87/18.06 (big_f(f9(c2, c2), f10(f9(c2, c2)))),
% 27.87/18.06 inference(unit_resolution,[status(thm)],[3625, 5676, 122, 16, 79, 148])).
% 27.87/18.06 tff(5751,plain,
% 27.87/18.06 (c2 = f2(f9(c2, c2))),
% 27.87/18.06 inference(unit_resolution,[status(thm)],[5687, 5622, 3865, 2602, 1822, 2041])).
% 27.87/18.06 tff(5752,plain,
% 27.87/18.06 (~(f10(f9(c2, c2)) = f9(c2, c2))),
% 27.87/18.06 inference(unit_resolution,[status(thm)],[762, 148, 122, 79, 16])).
% 27.87/18.06 tff(5753,plain,
% 27.87/18.06 (f10(f9(c2, c2)) = f10(c2)),
% 27.87/18.06 inference(transitivity,[status(thm)],[3646, 16, 216])).
% 27.87/18.06 tff(5754,plain,
% 27.87/18.06 (big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2))) <=> big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 27.87/18.06 inference(monotonicity,[status(thm)],[5753])).
% 27.87/18.06 tff(5755,plain,
% 27.87/18.06 (big_f(f9(c2, f9(c2, c2)), f10(c2)) <=> big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))),
% 27.87/18.06 inference(symmetry,[status(thm)],[5754])).
% 27.87/18.07 tff(5756,plain,
% 27.87/18.07 (big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))),
% 27.87/18.07 inference(modus_ponens,[status(thm)],[1146, 5755])).
% 27.87/18.07 tff(5757,plain,
% 27.87/18.07 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)))),
% 27.87/18.07 inference(rewrite,[status(thm)],[])).
% 27.87/18.07 tff(5758,plain,
% 27.87/18.07 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)))),
% 27.87/18.07 inference(quant_inst,[status(thm)],[])).
% 27.87/18.07 tff(5759,plain,
% 27.87/18.07 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))),
% 27.87/18.07 inference(modus_ponens,[status(thm)],[5758, 5757])).
% 27.87/18.07 tff(5760,plain,
% 27.87/18.07 ((f9(c2, c2) = f8(f9(c2, c2))) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))),
% 27.87/18.07 inference(unit_resolution,[status(thm)],[5759, 2662, 1767, 2026, 5701, 5700])).
% 27.87/18.07 tff(5761,plain,
% 27.87/18.07 (f9(c2, c2) = f8(f9(c2, c2))),
% 27.87/18.07 inference(unit_resolution,[status(thm)],[5760, 5699])).
% 27.87/18.07 tff(5762,plain,
% 27.87/18.07 (f8(f9(c2, c2)) = f9(c2, c2)),
% 27.87/18.07 inference(symmetry,[status(thm)],[5761])).
% 27.87/18.07 tff(5763,assumption,(big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))), introduced(assumption)).
% 27.87/18.07 tff(5764,plain,
% 27.87/18.07 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)))),
% 27.87/18.07 inference(rewrite,[status(thm)],[])).
% 27.87/18.07 tff(5765,plain,
% 27.87/18.07 (((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))) <=> ((f10(f9(c2, c2)) = f9(c2, c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)))),
% 27.87/18.07 inference(rewrite,[status(thm)],[])).
% 27.87/18.07 tff(5766,plain,
% 27.87/18.07 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))))),
% 27.87/18.07 inference(monotonicity,[status(thm)],[5765])).
% 27.87/18.07 tff(5767,plain,
% 27.87/18.07 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)))),
% 27.87/18.07 inference(transitivity,[status(thm)],[5766, 5764])).
% 27.87/18.07 tff(5768,plain,
% 27.87/18.07 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)))),
% 27.87/18.07 inference(quant_inst,[status(thm)],[])).
% 27.87/18.07 tff(5769,plain,
% 27.87/18.07 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))),
% 27.87/18.07 inference(modus_ponens,[status(thm)],[5768, 5767])).
% 27.87/18.07 tff(5770,plain,
% 27.87/18.07 ((f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))),
% 27.87/18.07 inference(unit_resolution,[status(thm)],[5769, 2662, 1767, 5701, 5700])).
% 27.87/18.07 tff(5771,plain,
% 27.87/18.07 (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))),
% 27.87/18.07 inference(unit_resolution,[status(thm)],[5770, 5699, 5763])).
% 27.87/18.07 tff(5772,plain,
% 27.87/18.07 (f9(c2, f9(c2, c2)) = f9(c2, c2)),
% 27.87/18.07 inference(transitivity,[status(thm)],[5771, 5762])).
% 27.87/18.07 tff(5773,plain,
% 27.87/18.07 ($false),
% 27.87/18.07 inference(unit_resolution,[status(thm)],[4469, 5772])).
% 27.87/18.07 tff(5774,plain,(big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | (~big_f(f9(c2, c2), f10(f9(c2, c2))))), inference(lemma,lemma(discharge,[]))).
% 27.87/18.07 tff(5775,plain,
% 27.87/18.07 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))),
% 27.87/18.07 inference(unit_resolution,[status(thm)],[5774, 5756, 4469, 5752, 5532, 5698, 2026])).
% 27.87/18.07 tff(5776,plain,
% 27.87/18.07 (big_f(f7(c1), f6(c1, c2))),
% 27.87/18.07 inference(unit_resolution,[status(thm)],[5716, 5775, 148, 79, 122])).
% 27.87/18.07 tff(5777,plain,
% 27.87/18.07 (big_f(f9(c2, c2), f6(c1, c2))),
% 27.87/18.07 inference(modus_ponens,[status(thm)],[5776, 5696])).
% 27.87/18.07 tff(5778,plain,
% 27.87/18.07 ($false),
% 27.87/18.07 inference(unit_resolution,[status(thm)],[5727, 5777, 5694])).
% 27.87/18.07 tff(5779,plain,((f6(c1, c2) = c2) | big_f(c2, c4) | (~(f9(c2, c2) = c3)) | (~(f7(c1) = c1)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(c2 = f2(f9(c2, c2)))) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f10(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.87/18.07 tff(5780,plain,
% 27.87/18.07 (f6(c1, c2) = c2),
% 27.87/18.07 inference(unit_resolution,[status(thm)],[5779, 4469, 1822, 4234, 148, 79, 122, 5751, 3865, 2026, 1146, 16])).
% 27.87/18.07 tff(5781,plain,
% 27.87/18.07 (f6(f9(c2, c2), c2) = c2),
% 27.87/18.07 inference(modus_ponens,[status(thm)],[5780, 5574])).
% 27.87/18.07 tff(5782,plain,
% 27.87/18.07 (big_f(f7(c1), f6(c1, c2)) <=> big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))),
% 27.87/18.07 inference(symmetry,[status(thm)],[5711])).
% 27.87/18.07 tff(5783,plain,
% 27.87/18.07 (big_f(f7(c1), f6(c1, c2)) <=> big_f(f9(c2, c2), c2)),
% 27.87/18.07 inference(monotonicity,[status(thm)],[4653, 5780])).
% 27.87/18.07 tff(5784,plain,
% 27.87/18.07 (big_f(f9(c2, c2), c2) <=> big_f(f7(c1), f6(c1, c2))),
% 27.87/18.07 inference(symmetry,[status(thm)],[5783])).
% 27.87/18.07 tff(5785,plain,
% 27.87/18.07 (big_f(f9(c2, c2), c2) <=> big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))),
% 27.87/18.07 inference(transitivity,[status(thm)],[5784, 5782])).
% 27.87/18.07 tff(5786,plain,
% 27.87/18.07 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))),
% 27.87/18.07 inference(modus_ponens,[status(thm)],[2041, 5785])).
% 27.87/18.07 tff(5787,plain,
% 27.87/18.07 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), c2) = c2)) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), c2) = c2)) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))))),
% 27.87/18.07 inference(rewrite,[status(thm)],[])).
% 27.87/18.07 tff(5788,plain,
% 27.87/18.07 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), c2) = c2)) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))))),
% 27.87/18.07 inference(quant_inst,[status(thm)],[])).
% 27.87/18.07 tff(5789,plain,
% 27.87/18.07 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), c2) = c2)) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)))),
% 27.87/18.07 inference(modus_ponens,[status(thm)],[5788, 5787])).
% 27.87/18.07 tff(5790,plain,
% 27.87/18.07 (f9(c2, c2) = f8(f9(c2, c2))),
% 27.87/18.07 inference(unit_resolution,[status(thm)],[5789, 2730, 5752, 2026, 5786, 5532, 5781])).
% 27.87/18.07 tff(5791,plain,
% 27.87/18.07 (f8(f9(c2, c2)) = f9(c2, c2)),
% 27.87/18.07 inference(symmetry,[status(thm)],[5790])).
% 27.87/18.07 tff(5792,plain,
% 27.87/18.07 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), c2) = c2)) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))) | (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), c2) = c2)) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))) | (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))))),
% 27.87/18.07 inference(rewrite,[status(thm)],[])).
% 27.87/18.07 tff(5793,plain,
% 27.87/18.07 (((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), c2) = c2)) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)))) <=> ((f10(f9(c2, c2)) = f9(c2, c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), c2) = c2)) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))) | (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))))),
% 27.87/18.07 inference(rewrite,[status(thm)],[])).
% 27.87/18.07 tff(5794,plain,
% 27.87/18.07 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), c2) = c2)) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), c2) = c2)) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))) | (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2))))))),
% 27.87/18.07 inference(monotonicity,[status(thm)],[5793])).
% 27.87/18.07 tff(5795,plain,
% 27.87/18.07 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), c2) = c2)) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), c2) = c2)) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))) | (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))))),
% 27.87/18.07 inference(transitivity,[status(thm)],[5794, 5792])).
% 27.87/18.07 tff(5796,plain,
% 27.87/18.07 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), c2) = c2)) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))))),
% 27.87/18.07 inference(quant_inst,[status(thm)],[])).
% 27.87/18.07 tff(5797,plain,
% 27.87/18.07 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), c2) = c2)) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))) | (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2))))),
% 27.87/18.07 inference(modus_ponens,[status(thm)],[5796, 5795])).
% 27.87/18.07 tff(5798,plain,
% 27.87/18.07 (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))),
% 27.87/18.07 inference(unit_resolution,[status(thm)],[5797, 2730, 5752, 5786, 5532, 5781, 5756])).
% 27.87/18.07 tff(5799,plain,
% 27.87/18.07 (f9(c2, f9(c2, c2)) = f9(c2, c2)),
% 27.87/18.07 inference(transitivity,[status(thm)],[5798, 5791])).
% 27.87/18.07 tff(5800,plain,
% 27.87/18.07 ($false),
% 27.87/18.07 inference(unit_resolution,[status(thm)],[4469, 5799])).
% 27.87/18.07 tff(5801,plain,((f9(c2, f9(c2, c2)) = f9(c2, c2)) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (~big_f(f9(c2, c2), c2)) | (~(f7(c1) = c1)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f10(c1) = c2)) | (~(f9(c2, c2) = c3)) | big_f(c2, c4)), inference(lemma,lemma(discharge,[]))).
% 27.87/18.07 tff(5802,plain,
% 27.87/18.07 (f9(c2, f9(c2, c2)) = f9(c2, c2)),
% 27.87/18.07 inference(unit_resolution,[status(thm)],[5801, 5750, 5749, 4234, 148, 79, 122, 5748, 16, 5580, 5578])).
% 27.87/18.07 tff(5803,plain,
% 27.87/18.07 (c2 = f2(f9(c2, c2))),
% 27.87/18.07 inference(unit_resolution,[status(thm)],[5687, 5622, 5578, 2602, 5580, 5749])).
% 27.87/18.07 tff(5804,plain,
% 27.87/18.07 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)))),
% 27.87/18.07 inference(rewrite,[status(thm)],[])).
% 27.87/18.07 tff(5805,plain,
% 27.87/18.07 (((~(f10(c2) = c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2)))) <=> ((~(f10(c2) = c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)))),
% 27.87/18.07 inference(rewrite,[status(thm)],[])).
% 27.87/18.07 tff(5806,plain,
% 27.87/18.07 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))))),
% 27.87/18.07 inference(monotonicity,[status(thm)],[5805])).
% 27.87/18.07 tff(5807,plain,
% 27.87/18.07 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)))),
% 27.87/18.07 inference(transitivity,[status(thm)],[5806, 5804])).
% 27.87/18.07 tff(5808,plain,
% 27.87/18.07 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))))),
% 27.87/18.07 inference(quant_inst,[status(thm)],[])).
% 27.87/18.07 tff(5809,plain,
% 27.87/18.07 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))),
% 27.87/18.07 inference(modus_ponens,[status(thm)],[5808, 5807])).
% 27.87/18.07 tff(5810,plain,
% 27.87/18.07 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))),
% 27.87/18.07 inference(unit_resolution,[status(thm)],[5809, 2409, 122, 1146, 1137, 5532, 5698])).
% 27.87/18.07 tff(5811,plain,
% 27.87/18.07 (big_f(f7(c1), f6(c1, c2))),
% 27.87/18.07 inference(unit_resolution,[status(thm)],[5716, 5810, 148, 79, 122])).
% 27.87/18.08 tff(5812,plain,
% 27.87/18.08 (big_f(f9(c2, c2), f6(c1, c2))),
% 27.87/18.08 inference(modus_ponens,[status(thm)],[5811, 5696])).
% 27.87/18.08 tff(5813,plain,
% 27.87/18.08 ($false),
% 27.87/18.08 inference(unit_resolution,[status(thm)],[5727, 5812, 5694])).
% 27.87/18.08 tff(5814,plain,((f6(c1, c2) = c2) | big_f(c2, c4) | (~(f9(c2, c2) = c3)) | (~(f7(c1) = c1)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(c2 = f2(f9(c2, c2)))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2)))), inference(lemma,lemma(discharge,[]))).
% 27.87/18.08 tff(5815,plain,
% 27.87/18.08 (f6(c1, c2) = c2),
% 27.87/18.08 inference(unit_resolution,[status(thm)],[5814, 5578, 5580, 4234, 148, 79, 122, 5803, 5748, 5802])).
% 27.87/18.08 tff(5816,plain,
% 27.87/18.08 (big_f(f7(c1), f6(c1, c2)) <=> big_f(f9(c2, c2), c2)),
% 27.87/18.08 inference(monotonicity,[status(thm)],[4653, 5815])).
% 27.87/18.08 tff(5817,plain,
% 27.87/18.08 (big_f(f9(c2, c2), c2) <=> big_f(f7(c1), f6(c1, c2))),
% 27.87/18.08 inference(symmetry,[status(thm)],[5816])).
% 27.87/18.08 tff(5818,plain,
% 27.87/18.08 (big_f(f7(c1), f6(c1, c2))),
% 27.87/18.08 inference(modus_ponens,[status(thm)],[5749, 5817])).
% 27.87/18.08 tff(5819,plain,
% 27.87/18.08 (f9(c2, c1) = c1),
% 27.87/18.08 inference(unit_resolution,[status(thm)],[1141, 5802, 122, 79, 148])).
% 27.87/18.08 tff(5820,plain,
% 27.87/18.08 (big_f(f9(c2, c1), f10(c2))),
% 27.87/18.08 inference(unit_resolution,[status(thm)],[1149, 5748, 122, 79, 148])).
% 27.87/18.08 tff(5821,plain,
% 27.87/18.08 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)))),
% 27.87/18.08 inference(rewrite,[status(thm)],[])).
% 27.87/18.08 tff(5822,plain,
% 27.87/18.08 (((~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2)))) <=> ((~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)))),
% 27.87/18.08 inference(rewrite,[status(thm)],[])).
% 27.87/18.08 tff(5823,plain,
% 27.87/18.08 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2))))),
% 27.87/18.08 inference(monotonicity,[status(thm)],[5822])).
% 27.87/18.08 tff(5824,plain,
% 27.87/18.08 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)))),
% 27.87/18.08 inference(transitivity,[status(thm)],[5823, 5821])).
% 27.87/18.08 tff(5825,plain,
% 27.87/18.08 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2))))),
% 27.87/18.08 inference(quant_inst,[status(thm)],[])).
% 27.87/18.08 tff(5826,plain,
% 27.87/18.08 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2))),
% 27.87/18.08 inference(modus_ponens,[status(thm)],[5825, 5824])).
% 27.87/18.08 tff(5827,plain,
% 27.87/18.08 ((~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2))),
% 27.87/18.08 inference(unit_resolution,[status(thm)],[5826, 2378])).
% 27.87/18.08 tff(5828,plain,
% 27.87/18.08 (~big_f(f7(c1), f6(c1, c2))),
% 27.87/18.08 inference(unit_resolution,[status(thm)],[5827, 5815, 122, 4234, 5820, 5819])).
% 27.87/18.08 tff(5829,plain,
% 27.87/18.08 ($false),
% 27.87/18.08 inference(unit_resolution,[status(thm)],[5828, 5818])).
% 27.87/18.08 tff(5830,plain,(big_f(c2, c1) | (~(f7(c1) = c1)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f10(c1) = c2)) | (~(c3 = c1)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 27.87/18.08 tff(5831,plain,
% 27.87/18.08 (big_f(c2, c1)),
% 27.87/18.08 inference(unit_resolution,[status(thm)],[5830, 121, 148, 79, 122, 15, 172, 4234])).
% 27.87/18.08 tff(5832,plain,
% 27.87/18.08 (big_f(c2, f9(c2, c2))),
% 27.87/18.08 inference(modus_ponens,[status(thm)],[5831, 3716])).
% 27.87/18.08 tff(5833,plain,
% 27.87/18.08 (big_f(c2, c1)),
% 27.87/18.08 inference(unit_resolution,[status(thm)],[5830, 121, 148, 79, 122, 16, 172, 4234])).
% 27.87/18.08 tff(5834,plain,
% 27.87/18.08 (big_f(c2, f9(c2, c2))),
% 27.87/18.08 inference(modus_ponens,[status(thm)],[5833, 3716])).
% 27.87/18.08 tff(5835,plain,
% 27.87/18.08 (~(f9(c2, c1) = c1)),
% 27.87/18.08 inference(unit_resolution,[status(thm)],[4579, 4469, 148, 79, 122])).
% 27.87/18.08 tff(5836,plain,
% 27.87/18.08 (f6(f7(c2), c3) = f6(c2, c1)),
% 27.87/18.08 inference(monotonicity,[status(thm)],[77, 172])).
% 27.87/18.08 tff(5837,plain,
% 27.87/18.08 (f6(c2, c1) = f6(f7(c2), c3)),
% 27.87/18.08 inference(symmetry,[status(thm)],[5836])).
% 27.87/18.08 tff(5838,plain,
% 27.87/18.08 ((f6(c2, c1) = c1) <=> (f6(f7(c2), c3) = c1)),
% 27.87/18.08 inference(monotonicity,[status(thm)],[5837])).
% 27.87/18.08 tff(5839,plain,
% 27.87/18.08 ((f6(f7(c2), c3) = c1) <=> (f6(c2, c1) = c1)),
% 27.87/18.08 inference(symmetry,[status(thm)],[5838])).
% 27.87/18.08 tff(5840,plain,
% 27.87/18.08 (big_f(f7(c2), f6(c2, c1))),
% 27.87/18.08 inference(unit_resolution,[status(thm)],[3211, 3198, 122, 77, 1139, 731])).
% 27.87/18.08 tff(5841,plain,
% 27.87/18.08 (f6(c2, c1) = f6(f7(c2), c3)),
% 27.87/18.08 inference(monotonicity,[status(thm)],[82, 5585])).
% 27.87/18.08 tff(5842,plain,
% 27.87/18.08 (f6(c2, c1) = c2),
% 27.87/18.08 inference(transitivity,[status(thm)],[5841, 2362])).
% 27.87/18.08 tff(5843,plain,
% 27.87/18.08 (big_f(f7(c2), f6(c2, c1)) <=> big_f(c2, c2)),
% 27.87/18.08 inference(monotonicity,[status(thm)],[77, 5842])).
% 27.87/18.08 tff(5844,plain,
% 27.87/18.08 (big_f(c2, c2) <=> big_f(f7(c2), f6(c2, c1))),
% 27.87/18.08 inference(symmetry,[status(thm)],[5843])).
% 27.87/18.08 tff(5845,plain,
% 27.87/18.08 ((~big_f(c2, c2)) <=> (~big_f(f7(c2), f6(c2, c1)))),
% 27.87/18.08 inference(monotonicity,[status(thm)],[5844])).
% 27.87/18.08 tff(5846,plain,
% 27.87/18.08 (~big_f(f7(c2), f6(c2, c1))),
% 27.87/18.08 inference(modus_ponens,[status(thm)],[121, 5845])).
% 27.87/18.08 tff(5847,plain,
% 27.87/18.08 ($false),
% 27.87/18.08 inference(unit_resolution,[status(thm)],[3078, 5846])).
% 27.87/18.08 tff(5848,plain,((~(f6(f7(c2), c3) = c2)) | (~big_f(f7(c2), f6(c2, c1))) | big_f(c2, c2) | (~(c3 = c1)) | (~(f7(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.87/18.08 tff(5849,plain,
% 27.87/18.08 (~(f6(f7(c2), c3) = c2)),
% 27.87/18.08 inference(unit_resolution,[status(thm)],[5848, 5840, 121, 172, 77])).
% 27.87/18.08 tff(5850,plain,
% 27.87/18.08 (f6(f7(c2), c3) = c1),
% 27.87/18.08 inference(unit_resolution,[status(thm)],[2391, 5849])).
% 27.87/18.08 tff(5851,plain,
% 27.87/18.08 (f6(c2, c1) = c1),
% 27.87/18.08 inference(modus_ponens,[status(thm)],[5850, 5839])).
% 27.87/18.08 tff(5852,plain,
% 27.87/18.08 ($false),
% 27.87/18.08 inference(unit_resolution,[status(thm)],[3198, 5851])).
% 27.87/18.08 tff(5853,plain,((f6(c2, c1) = c1) | (~(c3 = c1)) | (~(f7(c2) = c2)) | big_f(c2, c2) | (~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2))), inference(lemma,lemma(discharge,[]))).
% 27.87/18.08 tff(5854,plain,
% 27.87/18.08 (f6(c2, c1) = c1),
% 27.87/18.08 inference(unit_resolution,[status(thm)],[5853, 77, 731, 121, 122, 172, 1139])).
% 27.87/18.08 tff(5855,plain,
% 27.87/18.08 (f6(c2, c1) = f9(c2, c2)),
% 27.87/18.08 inference(transitivity,[status(thm)],[5854, 149, 132])).
% 27.87/18.08 tff(5856,plain,
% 27.87/18.08 (big_f(f7(c2), f6(c2, c1)) <=> big_f(c2, f9(c2, c2))),
% 27.87/18.08 inference(monotonicity,[status(thm)],[77, 5855])).
% 27.87/18.08 tff(5857,plain,
% 27.87/18.08 (big_f(c2, f9(c2, c2)) <=> big_f(f7(c2), f6(c2, c1))),
% 27.87/18.08 inference(symmetry,[status(thm)],[5856])).
% 27.87/18.08 tff(5858,plain,
% 27.87/18.08 (big_f(f7(c2), f6(c2, c1))),
% 27.87/18.08 inference(modus_ponens,[status(thm)],[3719, 5857])).
% 27.87/18.08 tff(5859,plain,
% 27.87/18.08 (~big_f(f7(c2), f6(c2, c1))),
% 27.87/18.08 inference(unit_resolution,[status(thm)],[3084, 5854, 122, 77, 731, 1139])).
% 27.87/18.08 tff(5860,plain,
% 27.87/18.08 ($false),
% 27.87/18.08 inference(unit_resolution,[status(thm)],[5859, 5858])).
% 27.87/18.08 tff(5861,plain,((~(f7(c2) = c2)) | (~big_f(c2, f9(c2, c2))) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | big_f(f9(c2, c1), f10(c2)) | (f9(c2, c1) = c1) | big_f(c2, c2) | (~(c3 = c1))), inference(lemma,lemma(discharge,[]))).
% 27.87/18.08 tff(5862,plain,
% 27.87/18.08 (~(f7(c2) = c2)),
% 27.87/18.08 inference(unit_resolution,[status(thm)],[5861, 5835, 148, 79, 122, 5677, 5834, 121, 172])).
% 27.87/18.08 tff(5863,plain,
% 27.87/18.08 (f7(c2) = c1),
% 27.87/18.08 inference(unit_resolution,[status(thm)],[21, 5862])).
% 27.87/18.08 tff(5864,plain,
% 27.87/18.08 (big_f(f7(f10(c1)), c2) <=> big_f(f7(c2), c2)),
% 27.87/18.08 inference(monotonicity,[status(thm)],[232])).
% 27.87/18.08 tff(5865,plain,
% 27.87/18.08 (big_f(f7(f10(c1)), c2) <=> big_f(f9(c2, c2), c2)),
% 27.87/18.08 inference(transitivity,[status(thm)],[5864, 4569])).
% 27.87/18.08 tff(5866,plain,
% 27.87/18.08 ((~big_f(f7(f10(c1)), c2)) <=> (~big_f(f9(c2, c2), c2))),
% 27.87/18.08 inference(monotonicity,[status(thm)],[5865])).
% 27.87/18.08 tff(5867,plain,
% 27.87/18.08 ((c2 = f5(f10(c1))) <=> (c2 = f5(c2))),
% 27.87/18.08 inference(monotonicity,[status(thm)],[295])).
% 27.87/18.08 tff(5868,plain,
% 27.87/18.08 ((c2 = f5(c2)) <=> (c2 = f5(f10(c1)))),
% 27.87/18.08 inference(symmetry,[status(thm)],[5867])).
% 27.87/18.08 tff(5869,plain,
% 27.87/18.08 (big_f(f7(c2), f6(c1, c2)) <=> big_f(f7(c1), f6(c1, c2))),
% 27.87/18.08 inference(monotonicity,[status(thm)],[5545])).
% 27.87/18.08 tff(5870,plain,
% 27.87/18.08 (big_f(f7(c1), f6(c1, c2)) <=> big_f(f7(c2), f6(c1, c2))),
% 27.87/18.08 inference(symmetry,[status(thm)],[5869])).
% 27.87/18.08 tff(5871,plain,
% 27.87/18.08 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))),
% 27.87/18.08 inference(unit_resolution,[status(thm)],[5707, 2492, 122, 3896, 4469, 5532, 5698])).
% 27.87/18.08 tff(5872,plain,
% 27.87/18.08 (big_f(f7(c1), f6(c1, c2))),
% 27.87/18.08 inference(unit_resolution,[status(thm)],[5716, 5871, 148, 79, 122])).
% 27.87/18.08 tff(5873,plain,
% 27.87/18.08 (big_f(f7(c2), f6(c1, c2))),
% 27.87/18.08 inference(modus_ponens,[status(thm)],[5872, 5870])).
% 27.87/18.08 tff(5874,plain,
% 27.87/18.08 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | (~big_f(f7(c2), f6(c1, c2))) | (f6(c1, c2) = f5(c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | (~big_f(f7(c2), f6(c1, c2))) | (f6(c1, c2) = f5(c2)))),
% 27.87/18.08 inference(rewrite,[status(thm)],[])).
% 27.87/18.08 tff(5875,plain,
% 27.87/18.08 (((~(f10(c2) = c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f7(c2) = c2) | (f6(c1, c2) = f5(c2)) | (~big_f(f7(c2), f6(c1, c2)))) <=> ((~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | (~big_f(f7(c2), f6(c1, c2))) | (f6(c1, c2) = f5(c2)))),
% 27.87/18.08 inference(rewrite,[status(thm)],[])).
% 27.87/18.08 tff(5876,plain,
% 27.87/18.08 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f7(c2) = c2) | (f6(c1, c2) = f5(c2)) | (~big_f(f7(c2), f6(c1, c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | (~big_f(f7(c2), f6(c1, c2))) | (f6(c1, c2) = f5(c2))))),
% 27.87/18.08 inference(monotonicity,[status(thm)],[5875])).
% 27.87/18.08 tff(5877,plain,
% 27.87/18.08 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f7(c2) = c2) | (f6(c1, c2) = f5(c2)) | (~big_f(f7(c2), f6(c1, c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | (~big_f(f7(c2), f6(c1, c2))) | (f6(c1, c2) = f5(c2)))),
% 27.87/18.08 inference(transitivity,[status(thm)],[5876, 5874])).
% 27.87/18.08 tff(5878,plain,
% 27.87/18.08 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f7(c2) = c2) | (f6(c1, c2) = f5(c2)) | (~big_f(f7(c2), f6(c1, c2))))),
% 27.87/18.08 inference(quant_inst,[status(thm)],[])).
% 27.87/18.08 tff(5879,plain,
% 27.87/18.08 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | (~big_f(f7(c2), f6(c1, c2))) | (f6(c1, c2) = f5(c2))),
% 27.87/18.08 inference(modus_ponens,[status(thm)],[5878, 5877])).
% 27.87/18.08 tff(5880,plain,
% 27.87/18.08 ((~big_f(f7(c2), f6(c1, c2))) | (f6(c1, c2) = f5(c2))),
% 27.87/18.08 inference(unit_resolution,[status(thm)],[5879, 676, 122, 17, 3896, 4469])).
% 27.87/18.08 tff(5881,plain,
% 27.87/18.08 (f6(c1, c2) = f5(c2)),
% 27.87/18.08 inference(unit_resolution,[status(thm)],[5880, 5873])).
% 27.87/18.08 tff(5882,plain,
% 27.87/18.08 ((f6(c1, c2) = c2) <=> (f5(c2) = c2)),
% 27.87/18.08 inference(monotonicity,[status(thm)],[5881])).
% 27.87/18.08 tff(5883,plain,
% 27.87/18.08 ((f6(c1, c2) = c2) <=> (c2 = f5(c2))),
% 27.87/18.08 inference(transitivity,[status(thm)],[5882, 1279])).
% 27.87/18.08 tff(5884,plain,
% 27.87/18.08 ((f6(c1, c2) = c2) <=> (c2 = f5(f10(c1)))),
% 27.87/18.08 inference(transitivity,[status(thm)],[5883, 5868])).
% 27.87/18.08 tff(5885,plain,
% 27.87/18.08 ((~(f6(c1, c2) = c2)) <=> (~(c2 = f5(f10(c1))))),
% 27.87/18.08 inference(monotonicity,[status(thm)],[5884])).
% 27.87/18.08 tff(5886,plain,
% 27.87/18.08 (~(c2 = f5(f10(c1)))),
% 27.87/18.08 inference(modus_ponens,[status(thm)],[114, 5885])).
% 27.87/18.08 tff(5887,plain,
% 27.87/18.08 (f5(c2) = f6(c1, c2)),
% 27.87/18.08 inference(symmetry,[status(thm)],[5881])).
% 27.87/18.08 tff(5888,plain,
% 27.87/18.08 (big_f(f7(c2), f5(c2)) <=> big_f(f7(c1), f6(c1, c2))),
% 27.87/18.08 inference(monotonicity,[status(thm)],[5545, 5887])).
% 27.87/18.08 tff(5889,plain,
% 27.87/18.08 (big_f(f7(c1), f6(c1, c2)) <=> big_f(f7(c2), f5(c2))),
% 27.87/18.08 inference(symmetry,[status(thm)],[5888])).
% 27.87/18.08 tff(5890,plain,
% 27.87/18.08 (big_f(f7(c2), f5(c2))),
% 27.87/18.08 inference(modus_ponens,[status(thm)],[5872, 5889])).
% 27.87/18.08 tff(5891,plain,
% 27.87/18.08 ((f5(f10(c1)) = c2) <=> (c2 = f5(f10(c1)))),
% 27.87/18.08 inference(commutativity,[status(thm)],[])).
% 27.87/18.08 tff(5892,plain,
% 27.87/18.08 ((c2 = f5(f10(c1))) <=> (f5(f10(c1)) = c2)),
% 27.87/18.08 inference(symmetry,[status(thm)],[5891])).
% 27.87/18.08 tff(5893,plain,
% 27.87/18.08 ((f6(c1, c2) = c2) <=> (f5(f10(c1)) = c2)),
% 27.87/18.08 inference(transitivity,[status(thm)],[5883, 5868, 5892])).
% 27.87/18.08 tff(5894,plain,
% 27.87/18.08 ((~(f6(c1, c2) = c2)) <=> (~(f5(f10(c1)) = c2))),
% 27.87/18.08 inference(monotonicity,[status(thm)],[5893])).
% 27.87/18.08 tff(5895,plain,
% 27.87/18.08 (~(f5(f10(c1)) = c2)),
% 27.87/18.08 inference(modus_ponens,[status(thm)],[114, 5894])).
% 27.87/18.08 tff(5896,plain,
% 27.87/18.08 (f5(f10(c1)) = c1),
% 27.87/18.08 inference(unit_resolution,[status(thm)],[326, 5895])).
% 27.87/18.08 tff(5897,plain,
% 27.87/18.08 (big_f(f7(c2), c1)),
% 27.87/18.08 inference(unit_resolution,[status(thm)],[336, 5896, 16, 5890])).
% 27.87/18.08 tff(5898,plain,
% 27.87/18.08 (big_f(f7(c2), f9(c2, c2))),
% 27.87/18.08 inference(modus_ponens,[status(thm)],[5897, 4534])).
% 27.87/18.08 tff(5899,plain,
% 27.87/18.08 (~big_f(f9(c2, c2), f10(c2))),
% 27.87/18.08 inference(unit_resolution,[status(thm)],[1173, 5898, 5677, 17, 148, 79, 122])).
% 27.87/18.08 tff(5900,plain,
% 27.87/18.08 (~big_f(f7(f10(c1)), c2)),
% 27.87/18.08 inference(unit_resolution,[status(thm)],[4192, 5899, 122, 5886, 2650, 236])).
% 27.87/18.08 tff(5901,plain,
% 27.87/18.08 (~big_f(f9(c2, c2), c2)),
% 27.87/18.08 inference(modus_ponens,[status(thm)],[5900, 5866])).
% 27.87/18.08 tff(5902,plain,
% 27.87/18.08 (f6(c1, c1) = f6(f7(c2), f5(c1))),
% 27.87/18.08 inference(monotonicity,[status(thm)],[125, 2941])).
% 27.87/18.08 tff(5903,plain,
% 27.87/18.08 (f6(f7(c2), f5(c1)) = f6(c1, c1)),
% 27.87/18.08 inference(symmetry,[status(thm)],[5902])).
% 27.87/18.08 tff(5904,plain,
% 27.87/18.08 ((f6(f7(c2), f5(c1)) = c1) <=> (f6(c1, c1) = c1)),
% 27.87/18.08 inference(monotonicity,[status(thm)],[5903])).
% 27.87/18.08 tff(5905,plain,
% 27.87/18.08 ((~(f6(f7(c2), f5(c1)) = c1)) <=> (~(f6(c1, c1) = c1))),
% 27.87/18.08 inference(monotonicity,[status(thm)],[5904])).
% 27.87/18.08 tff(5906,plain,
% 27.87/18.08 (big_f(f7(c2), c1) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 27.87/18.08 inference(monotonicity,[status(thm)],[1151, 150])).
% 27.87/18.08 tff(5907,plain,
% 27.87/18.08 (big_f(f7(f10(c1)), f5(f10(c1)))),
% 27.87/18.08 inference(unit_resolution,[status(thm)],[309, 236, 122, 256, 185])).
% 27.87/18.08 tff(5908,plain,
% 27.87/18.08 (big_f(f7(c2), f5(c2))),
% 27.87/18.08 inference(modus_ponens,[status(thm)],[5907, 296])).
% 27.87/18.08 tff(5909,plain,
% 27.87/18.08 (~(f5(f10(c1)) = c2)),
% 27.87/18.08 inference(unit_resolution,[status(thm)],[321, 5908, 256, 122, 16, 22, 148, 79])).
% 27.87/18.08 tff(5910,plain,
% 27.87/18.08 (f5(f10(c1)) = c1),
% 27.87/18.08 inference(unit_resolution,[status(thm)],[326, 5909])).
% 27.87/18.08 tff(5911,plain,
% 27.87/18.08 (big_f(f7(c2), c1)),
% 27.87/18.08 inference(unit_resolution,[status(thm)],[336, 5910, 5908, 16])).
% 27.87/18.08 tff(5912,plain,
% 27.87/18.08 (big_f(f9(c2, c2), f9(c2, c2))),
% 27.87/18.08 inference(modus_ponens,[status(thm)],[5911, 5906])).
% 27.87/18.08 tff(5913,plain,
% 27.87/18.08 (f6(c1, c1) = f6(f7(c2), f5(c1))),
% 27.87/18.08 inference(monotonicity,[status(thm)],[342, 2941])).
% 27.87/18.08 tff(5914,plain,
% 27.87/18.08 (f6(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)),
% 27.87/18.08 inference(transitivity,[status(thm)],[4594, 5913, 2947, 149, 132])).
% 27.87/18.08 tff(5915,plain,
% 27.87/18.08 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2))) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 27.87/18.08 inference(monotonicity,[status(thm)],[5532, 5914])).
% 27.87/18.08 tff(5916,plain,
% 27.87/18.08 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2)))),
% 27.87/18.08 inference(symmetry,[status(thm)],[5915])).
% 27.87/18.08 tff(5917,plain,
% 27.87/18.08 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2)))),
% 27.87/18.08 inference(modus_ponens,[status(thm)],[487, 5916])).
% 27.87/18.08 tff(5918,plain,
% 27.87/18.08 ($false),
% 27.87/18.08 inference(unit_resolution,[status(thm)],[5641, 5914, 5532, 5917])).
% 27.87/18.08 tff(5919,plain,((~(f6(f7(c2), f5(c1)) = c1)) | (~(f10(c2) = c2)) | big_f(f9(c2, c2), f10(c2)) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f5(c1) = c1)) | (~(f7(c2) = c1)) | (~(f7(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 27.87/18.08 tff(5920,plain,
% 27.87/18.08 (~(f6(f7(c2), f5(c1)) = c1)),
% 27.87/18.08 inference(unit_resolution,[status(thm)],[5919, 5912, 256, 122, 148, 79, 230, 22, 4234])).
% 27.87/18.08 tff(5921,plain,
% 27.87/18.08 (~(f6(c1, c1) = c1)),
% 27.87/18.08 inference(modus_ponens,[status(thm)],[5920, 5905])).
% 27.87/18.08 tff(5922,plain,
% 27.87/18.08 (f6(f7(c2), f5(c1)) = c2),
% 27.87/18.08 inference(unit_resolution,[status(thm)],[2978, 5920])).
% 27.87/18.08 tff(5923,plain,
% 27.87/18.08 (f6(c1, c1) = f10(c2)),
% 27.87/18.08 inference(transitivity,[status(thm)],[5902, 5922, 216])).
% 27.87/18.08 tff(5924,plain,
% 27.87/18.08 (big_f(f7(c1), f6(c1, c1)) <=> big_f(f9(c2, c2), f10(c2))),
% 27.87/18.08 inference(monotonicity,[status(thm)],[4653, 5923])).
% 27.87/18.08 tff(5925,plain,
% 27.87/18.08 (big_f(f9(c2, c2), f10(c2)) <=> big_f(f7(c1), f6(c1, c1))),
% 27.87/18.08 inference(symmetry,[status(thm)],[5924])).
% 27.87/18.08 tff(5926,plain,
% 27.87/18.08 ((~big_f(f9(c2, c2), f10(c2))) <=> (~big_f(f7(c1), f6(c1, c1)))),
% 27.87/18.08 inference(monotonicity,[status(thm)],[5925])).
% 27.87/18.08 tff(5927,plain,
% 27.87/18.08 (~big_f(f7(c1), f6(c1, c1))),
% 27.87/18.08 inference(modus_ponens,[status(thm)],[256, 5926])).
% 27.87/18.08 tff(5928,plain,
% 27.87/18.08 ($false),
% 27.87/18.08 inference(unit_resolution,[status(thm)],[4650, 5927, 5921, 122, 185, 4234, 256])).
% 27.87/18.08 tff(5929,plain,((f7(c2) = c2) | (~(f10(c2) = c2)) | (~(f7(c1) = c1)) | big_f(f9(c2, c2), f10(c2)) | (~(f5(c1) = c1)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.87/18.08 tff(5930,plain,
% 27.87/18.08 (~(f5(c1) = c1)),
% 27.87/18.08 inference(unit_resolution,[status(thm)],[5929, 17, 122, 256, 4234, 148, 79, 16])).
% 27.87/18.08 tff(5931,plain,
% 27.87/18.08 (f5(c1) = c2),
% 27.87/18.08 inference(unit_resolution,[status(thm)],[1708, 5930])).
% 27.87/18.08 tff(5932,plain,
% 27.87/18.08 (big_f(f7(c1), f5(c1)) <=> big_f(c1, f5(c1))),
% 27.87/18.08 inference(monotonicity,[status(thm)],[4234])).
% 27.87/18.08 tff(5933,plain,
% 27.90/18.08 (big_f(c1, f5(c1)) <=> big_f(f7(c1), f5(c1))),
% 27.90/18.08 inference(symmetry,[status(thm)],[5932])).
% 27.90/18.08 tff(5934,plain,
% 27.90/18.08 (big_f(c1, f5(c1)) <=> big_f(f9(c2, c2), c2)),
% 27.90/18.08 inference(monotonicity,[status(thm)],[150, 5931])).
% 27.90/18.08 tff(5935,plain,
% 27.90/18.08 (big_f(f9(c2, c2), c2) <=> big_f(c1, f5(c1))),
% 27.90/18.08 inference(symmetry,[status(thm)],[5934])).
% 27.90/18.08 tff(5936,plain,
% 27.90/18.08 (big_f(f9(c2, c2), c2) <=> big_f(f7(c1), f5(c1))),
% 27.90/18.08 inference(transitivity,[status(thm)],[5935, 5933])).
% 27.90/18.08 tff(5937,plain,
% 27.90/18.08 ((~big_f(f9(c2, c2), c2)) <=> (~big_f(f7(c1), f5(c1)))),
% 27.90/18.08 inference(monotonicity,[status(thm)],[5936])).
% 27.90/18.08 tff(5938,plain,
% 27.90/18.08 (~big_f(f7(c1), f5(c1))),
% 27.90/18.08 inference(modus_ponens,[status(thm)],[3685, 5937])).
% 27.90/18.08 tff(5939,plain,
% 27.90/18.08 (c2 = f5(c1)),
% 27.90/18.08 inference(symmetry,[status(thm)],[5931])).
% 27.90/18.08 tff(5940,plain,
% 27.90/18.08 (f6(c1, c2) = f6(c1, f5(c1))),
% 27.90/18.08 inference(monotonicity,[status(thm)],[5939])).
% 27.90/18.08 tff(5941,plain,
% 27.90/18.08 (f6(c1, f5(c1)) = f6(c1, c2)),
% 27.90/18.08 inference(symmetry,[status(thm)],[5940])).
% 27.90/18.08 tff(5942,plain,
% 27.90/18.08 (f6(c1, f5(c1)) = f6(f7(c2), f5(c1))),
% 27.90/18.08 inference(monotonicity,[status(thm)],[125])).
% 27.90/18.08 tff(5943,plain,
% 27.90/18.08 (f6(f7(c2), f5(c1)) = f6(c1, f5(c1))),
% 27.90/18.08 inference(symmetry,[status(thm)],[5942])).
% 27.90/18.08 tff(5944,plain,
% 27.90/18.08 ((f6(f7(c2), f5(c1)) = c2) <=> (f6(c1, f5(c1)) = f5(c1))),
% 27.90/18.08 inference(monotonicity,[status(thm)],[5943, 5939])).
% 27.90/18.08 tff(5945,plain,
% 27.90/18.08 ((f6(c1, f5(c1)) = f5(c1)) <=> (f6(f7(c2), f5(c1)) = c2)),
% 27.90/18.08 inference(symmetry,[status(thm)],[5944])).
% 27.90/18.08 tff(5946,plain,
% 27.90/18.08 ((f6(c1, f5(c1)) = f5(c1)) <=> (f6(c1, c2) = c2)),
% 27.90/18.08 inference(monotonicity,[status(thm)],[5941, 5931])).
% 27.90/18.08 tff(5947,plain,
% 27.90/18.08 ((f6(c1, c2) = c2) <=> (f6(c1, f5(c1)) = f5(c1))),
% 27.90/18.08 inference(symmetry,[status(thm)],[5946])).
% 27.90/18.08 tff(5948,plain,
% 27.90/18.08 ((f6(c1, c2) = c2) <=> (f6(f7(c2), f5(c1)) = c2)),
% 27.90/18.08 inference(transitivity,[status(thm)],[5947, 5945])).
% 27.90/18.08 tff(5949,plain,
% 27.90/18.08 ((~(f6(c1, c2) = c2)) <=> (~(f6(f7(c2), f5(c1)) = c2))),
% 27.90/18.08 inference(monotonicity,[status(thm)],[5948])).
% 27.90/18.08 tff(5950,plain,
% 27.90/18.08 (~(f6(f7(c2), f5(c1)) = c2)),
% 27.90/18.08 inference(modus_ponens,[status(thm)],[114, 5949])).
% 27.90/18.08 tff(5951,plain,
% 27.90/18.08 (f6(f7(c2), f5(c1)) = c1),
% 27.90/18.08 inference(unit_resolution,[status(thm)],[2978, 5950])).
% 27.90/18.08 tff(5952,plain,
% 27.90/18.08 (c1 = f6(f7(c2), f5(c1))),
% 27.90/18.08 inference(symmetry,[status(thm)],[5951])).
% 27.90/18.08 tff(5953,plain,
% 27.90/18.08 (f9(c2, c2) = f6(c1, c2)),
% 27.90/18.08 inference(transitivity,[status(thm)],[160, 148, 5952, 5943, 5941])).
% 27.90/18.08 tff(5954,plain,
% 27.90/18.08 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f7(c1), f6(c1, c2))),
% 27.90/18.08 inference(monotonicity,[status(thm)],[5603, 5953])).
% 27.90/18.08 tff(5955,plain,
% 27.90/18.08 (big_f(f7(c1), f6(c1, c2)) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 27.90/18.08 inference(symmetry,[status(thm)],[5954])).
% 27.90/18.08 tff(5956,plain,
% 27.90/18.08 (big_f(f9(c2, c2), f9(c2, c2))),
% 27.90/18.08 inference(modus_ponens,[status(thm)],[5872, 5955])).
% 27.90/18.08 tff(5957,plain,
% 27.90/18.08 (big_f(f7(c1), f6(c1, c1))),
% 27.90/18.08 inference(unit_resolution,[status(thm)],[4658, 5956, 148, 79, 122, 4234, 256])).
% 27.90/18.08 tff(5958,plain,
% 27.90/18.08 (f6(c1, c1) = f6(f7(c2), c3)),
% 27.90/18.08 inference(monotonicity,[status(thm)],[342, 5585])).
% 27.90/18.08 tff(5959,plain,
% 27.90/18.08 (f6(c1, c1) = f5(c1)),
% 27.90/18.08 inference(transitivity,[status(thm)],[5958, 2362, 1761])).
% 27.90/18.08 tff(5960,plain,
% 27.90/18.08 (big_f(f7(c1), f6(c1, c1)) <=> big_f(f7(c1), f5(c1))),
% 27.90/18.08 inference(monotonicity,[status(thm)],[5959])).
% 27.90/18.08 tff(5961,plain,
% 27.90/18.08 (big_f(f7(c1), f5(c1)) <=> big_f(f7(c1), f6(c1, c1))),
% 27.90/18.08 inference(symmetry,[status(thm)],[5960])).
% 27.90/18.08 tff(5962,plain,
% 27.90/18.08 ((~big_f(f7(c1), f5(c1))) <=> (~big_f(f7(c1), f6(c1, c1)))),
% 27.90/18.08 inference(monotonicity,[status(thm)],[5961])).
% 27.90/18.08 tff(5963,plain,
% 27.90/18.08 (~big_f(f7(c1), f6(c1, c1))),
% 27.90/18.08 inference(modus_ponens,[status(thm)],[730, 5962])).
% 27.90/18.08 tff(5964,assumption,(big_f(f7(c1), f6(c1, c1))), introduced(assumption)).
% 27.90/18.08 tff(5965,plain,
% 27.90/18.08 ($false),
% 27.90/18.08 inference(unit_resolution,[status(thm)],[5964, 5963])).
% 27.90/18.08 tff(5966,plain,((~(f6(f7(c2), c3) = c2)) | (~big_f(f7(c1), f6(c1, c1))) | big_f(f7(c1), f5(c1)) | (~(f5(c1) = c2)) | (~(c3 = c1)) | (~(f7(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 27.90/18.08 tff(5967,plain,
% 27.90/18.08 (~(f6(f7(c2), c3) = c2)),
% 27.90/18.08 inference(unit_resolution,[status(thm)],[5966, 5957, 172, 5938, 5931, 22])).
% 27.90/18.08 tff(5968,plain,
% 27.90/18.09 (f6(f7(c2), c3) = c1),
% 27.90/18.09 inference(unit_resolution,[status(thm)],[2391, 5967])).
% 27.90/18.09 tff(5969,plain,
% 27.90/18.09 (f6(c1, c1) = f6(f7(c2), c3)),
% 27.90/18.09 inference(monotonicity,[status(thm)],[125, 5585])).
% 27.90/18.09 tff(5970,plain,
% 27.90/18.09 (f6(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)),
% 27.90/18.09 inference(transitivity,[status(thm)],[4594, 5969, 5968, 149, 132])).
% 27.90/18.09 tff(5971,plain,
% 27.90/18.09 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2))) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 27.90/18.09 inference(monotonicity,[status(thm)],[5532, 5970])).
% 27.90/18.09 tff(5972,plain,
% 27.90/18.09 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2)))),
% 27.90/18.09 inference(symmetry,[status(thm)],[5971])).
% 27.90/18.09 tff(5973,plain,
% 27.90/18.09 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2)))),
% 27.90/18.09 inference(modus_ponens,[status(thm)],[5956, 5972])).
% 27.90/18.09 tff(5974,plain,
% 27.90/18.09 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | (~(f6(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2)))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | (~(f6(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2)))))),
% 27.90/18.09 inference(rewrite,[status(thm)],[])).
% 27.90/18.09 tff(5975,plain,
% 27.90/18.09 (((~(f10(c2) = c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2))))) <=> ((~(f10(c2) = c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | (~(f6(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2)))))),
% 27.90/18.09 inference(rewrite,[status(thm)],[])).
% 27.90/18.09 tff(5976,plain,
% 27.90/18.09 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2)))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | (~(f6(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2))))))),
% 27.90/18.09 inference(monotonicity,[status(thm)],[5975])).
% 27.90/18.09 tff(5977,plain,
% 27.90/18.09 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2)))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | (~(f6(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2)))))),
% 27.90/18.09 inference(transitivity,[status(thm)],[5976, 5974])).
% 27.90/18.09 tff(5978,plain,
% 27.90/18.09 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2)))))),
% 27.90/18.09 inference(quant_inst,[status(thm)],[])).
% 27.90/18.09 tff(5979,plain,
% 27.90/18.09 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | (~(f6(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2))))),
% 27.90/18.09 inference(modus_ponens,[status(thm)],[5978, 5977])).
% 27.90/18.09 tff(5980,plain,
% 27.90/18.09 ((~(f6(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2))))),
% 27.90/18.09 inference(unit_resolution,[status(thm)],[5979, 2534, 122, 3896, 4469, 5532])).
% 27.90/18.09 tff(5981,plain,
% 27.90/18.09 ($false),
% 27.90/18.09 inference(unit_resolution,[status(thm)],[5980, 5973, 5970])).
% 27.90/18.09 tff(5982,plain,((f7(c2) = c2) | (~(f10(c2) = c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(c3 = c1)) | (~(f7(c1) = c1)) | big_f(f9(c2, c2), f10(c2)) | (f6(c1, c2) = c2) | big_f(f9(c2, c2), c2) | (~(f10(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.90/18.09 tff(5983,plain,
% 27.90/18.09 (big_f(f9(c2, c2), c2)),
% 27.90/18.09 inference(unit_resolution,[status(thm)],[5982, 5899, 3896, 4469, 148, 79, 172, 4234, 122, 17, 114, 16])).
% 27.90/18.09 tff(5984,plain,
% 27.90/18.09 ($false),
% 27.90/18.09 inference(unit_resolution,[status(thm)],[5983, 5901])).
% 27.90/18.09 tff(5985,plain,((f6(c1, c2) = c2) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f10(c1) = c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | (~(c3 = c1)) | (~(f7(c1) = c1)) | (f7(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 27.90/18.09 tff(5986,plain,
% 27.90/18.09 (f6(c1, c2) = c2),
% 27.90/18.09 inference(unit_resolution,[status(thm)],[5985, 4469, 79, 122, 16, 3896, 148, 172, 4234, 5862])).
% 27.90/18.09 tff(5987,plain,
% 27.90/18.09 (big_f(f7(c1), f6(c1, c2)) <=> big_f(f9(c2, c2), c2)),
% 27.90/18.09 inference(monotonicity,[status(thm)],[4653, 5986])).
% 27.90/18.09 tff(5988,plain,
% 27.90/18.09 (big_f(f7(c1), f6(c1, c2)) <=> big_f(f9(c2, c2), f10(c2))),
% 27.90/18.09 inference(transitivity,[status(thm)],[5987, 130])).
% 27.90/18.09 tff(5989,plain,
% 27.90/18.09 ((~big_f(f7(c1), f6(c1, c2))) <=> (~big_f(f9(c2, c2), f10(c2)))),
% 27.90/18.09 inference(monotonicity,[status(thm)],[5988])).
% 27.90/18.09 tff(5990,plain,
% 27.90/18.09 (~big_f(f7(c1), f6(c1, c2))),
% 27.90/18.09 inference(unit_resolution,[status(thm)],[5737, 5986, 122, 4234, 5677, 5835])).
% 27.90/18.09 tff(5991,plain,
% 27.90/18.09 (~big_f(f9(c2, c2), f10(c2))),
% 27.90/18.09 inference(modus_ponens,[status(thm)],[5990, 5989])).
% 27.90/18.09 tff(5992,plain,
% 27.90/18.09 (~(f5(c1) = c1)),
% 27.90/18.09 inference(unit_resolution,[status(thm)],[5929, 5991, 122, 5862, 4234, 148, 79, 16])).
% 27.90/18.09 tff(5993,plain,
% 27.90/18.09 (f5(c1) = c2),
% 27.90/18.09 inference(unit_resolution,[status(thm)],[1708, 5992])).
% 27.90/18.09 tff(5994,plain,
% 27.90/18.09 (big_f(c1, f5(c1)) <=> big_f(f9(c2, c2), c2)),
% 27.90/18.09 inference(monotonicity,[status(thm)],[150, 5993])).
% 27.90/18.09 tff(5995,plain,
% 27.90/18.09 (big_f(f9(c2, c2), c2) <=> big_f(c1, f5(c1))),
% 27.90/18.09 inference(symmetry,[status(thm)],[5994])).
% 27.90/18.09 tff(5996,plain,
% 27.90/18.09 (big_f(f9(c2, c2), c2) <=> big_f(f7(c1), f5(c1))),
% 27.90/18.09 inference(transitivity,[status(thm)],[5995, 5933])).
% 27.90/18.09 tff(5997,plain,
% 27.90/18.09 ((~big_f(f9(c2, c2), c2)) <=> (~big_f(f7(c1), f5(c1)))),
% 27.90/18.09 inference(monotonicity,[status(thm)],[5996])).
% 27.90/18.09 tff(5998,plain,
% 27.90/18.09 ((~big_f(f7(c1), f6(c1, c2))) <=> (~big_f(f9(c2, c2), c2))),
% 27.90/18.09 inference(monotonicity,[status(thm)],[5987])).
% 27.90/18.09 tff(5999,plain,
% 27.90/18.09 (~big_f(f9(c2, c2), c2)),
% 27.90/18.09 inference(modus_ponens,[status(thm)],[5990, 5998])).
% 27.90/18.09 tff(6000,plain,
% 27.90/18.09 (~big_f(f7(c1), f5(c1))),
% 27.90/18.09 inference(modus_ponens,[status(thm)],[5999, 5997])).
% 27.90/18.09 tff(6001,plain,
% 27.90/18.09 (f7(c2) = f9(c2, c2)),
% 27.90/18.09 inference(transitivity,[status(thm)],[5863, 149, 132])).
% 27.90/18.09 tff(6002,plain,
% 27.90/18.09 (big_f(f7(c2), f9(c2, c2)) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 27.90/18.09 inference(monotonicity,[status(thm)],[6001])).
% 27.90/18.09 tff(6003,plain,
% 27.90/18.09 (big_f(f7(c2), c1) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 27.90/18.09 inference(transitivity,[status(thm)],[4534, 6002])).
% 27.90/18.09 tff(6004,plain,
% 27.90/18.09 (~(f7(f10(c1)) = f10(c1))),
% 27.90/18.09 inference(modus_ponens,[status(thm)],[5862, 235])).
% 27.90/18.09 tff(6005,plain,
% 27.90/18.09 (big_f(f7(f10(c1)), f5(f10(c1)))),
% 27.90/18.09 inference(unit_resolution,[status(thm)],[309, 5991, 122, 6004, 2650])).
% 27.90/18.09 tff(6006,plain,
% 27.90/18.09 (big_f(f7(c2), f5(c2))),
% 27.90/18.09 inference(modus_ponens,[status(thm)],[6005, 296])).
% 27.90/18.09 tff(6007,plain,
% 27.90/18.09 ((c2 = f5(c2)) <=> (f5(f10(c1)) = c2)),
% 27.90/18.09 inference(transitivity,[status(thm)],[5868, 5892])).
% 27.90/18.09 tff(6008,plain,
% 27.90/18.09 ((~(c2 = f5(c2))) <=> (~(f5(f10(c1)) = c2))),
% 27.90/18.09 inference(monotonicity,[status(thm)],[6007])).
% 27.90/18.09 tff(6009,plain,
% 27.90/18.09 (big_f(f7(c2), c2) <=> big_f(f9(c2, c2), c2)),
% 27.90/18.09 inference(monotonicity,[status(thm)],[6001])).
% 27.90/18.09 tff(6010,plain,
% 27.90/18.09 (big_f(f9(c2, c2), c2) <=> big_f(f7(c2), c2)),
% 27.90/18.09 inference(symmetry,[status(thm)],[6009])).
% 27.90/18.09 tff(6011,plain,
% 27.90/18.09 (big_f(f7(c1), f6(c1, c2)) <=> big_f(f7(c2), c2)),
% 27.90/18.09 inference(transitivity,[status(thm)],[5987, 6010])).
% 27.90/18.09 tff(6012,plain,
% 27.90/18.09 ((~big_f(f7(c1), f6(c1, c2))) <=> (~big_f(f7(c2), c2))),
% 27.90/18.09 inference(monotonicity,[status(thm)],[6011])).
% 27.90/18.09 tff(6013,plain,
% 27.90/18.09 (~big_f(f7(c2), c2)),
% 27.90/18.09 inference(modus_ponens,[status(thm)],[5990, 6012])).
% 27.90/18.09 tff(6014,plain,
% 27.90/18.09 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)))),
% 27.90/18.09 inference(rewrite,[status(thm)],[])).
% 27.90/18.09 tff(6015,plain,
% 27.90/18.09 (((~(f10(c2) = c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(c2 = f5(c2)))) <=> ((~(f10(c2) = c2)) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)))),
% 27.90/18.09 inference(rewrite,[status(thm)],[])).
% 27.90/18.09 tff(6016,plain,
% 27.90/18.09 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(c2 = f5(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2))))),
% 27.90/18.09 inference(monotonicity,[status(thm)],[6015])).
% 27.90/18.09 tff(6017,plain,
% 27.90/18.09 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(c2 = f5(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)))),
% 27.90/18.09 inference(transitivity,[status(thm)],[6016, 6014])).
% 27.90/18.09 tff(6018,plain,
% 27.90/18.09 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(c2 = f5(c2))))),
% 27.90/18.09 inference(quant_inst,[status(thm)],[])).
% 27.90/18.09 tff(6019,plain,
% 27.90/18.09 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.90/18.09 inference(modus_ponens,[status(thm)],[6018, 6017])).
% 27.90/18.09 tff(6020,plain,
% 27.90/18.09 (~(c2 = f5(c2))),
% 27.90/18.09 inference(unit_resolution,[status(thm)],[6019, 267, 122, 5862, 6013, 3896, 4469])).
% 27.90/18.09 tff(6021,plain,
% 27.90/18.09 (~(f5(f10(c1)) = c2)),
% 27.90/18.09 inference(modus_ponens,[status(thm)],[6020, 6008])).
% 27.90/18.09 tff(6022,plain,
% 27.90/18.09 (f5(f10(c1)) = c1),
% 27.90/18.09 inference(unit_resolution,[status(thm)],[326, 6021])).
% 27.90/18.09 tff(6023,plain,
% 27.90/18.09 (big_f(f7(c2), c1)),
% 27.90/18.09 inference(unit_resolution,[status(thm)],[336, 6022, 16, 6006])).
% 27.90/18.09 tff(6024,plain,
% 27.90/18.09 (big_f(f9(c2, c2), f9(c2, c2))),
% 27.90/18.09 inference(modus_ponens,[status(thm)],[6023, 6003])).
% 27.90/18.09 tff(6025,plain,
% 27.90/18.09 (big_f(f7(c1), f6(c1, c1))),
% 27.90/18.09 inference(unit_resolution,[status(thm)],[4658, 6024, 148, 79, 122, 4234, 5991])).
% 27.90/18.09 tff(6026,plain,
% 27.90/18.09 (~(f6(f7(c2), c3) = c2)),
% 27.90/18.09 inference(unit_resolution,[status(thm)],[5966, 6025, 172, 6000, 5993, 5863])).
% 27.90/18.09 tff(6027,plain,
% 27.90/18.09 (f6(f7(c2), c3) = c1),
% 27.90/18.09 inference(unit_resolution,[status(thm)],[2391, 6026])).
% 27.90/18.09 tff(6028,plain,
% 27.90/18.09 (c1 = f7(c2)),
% 27.90/18.09 inference(symmetry,[status(thm)],[5863])).
% 27.90/18.09 tff(6029,plain,
% 27.90/18.09 (f6(c1, c1) = f6(f7(c2), c3)),
% 27.90/18.09 inference(monotonicity,[status(thm)],[6028, 5585])).
% 27.90/18.09 tff(6030,plain,
% 27.90/18.09 (f6(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)),
% 27.90/18.09 inference(transitivity,[status(thm)],[4594, 6029, 6027, 149, 132])).
% 27.90/18.09 tff(6031,plain,
% 27.90/18.09 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2))) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 27.90/18.09 inference(monotonicity,[status(thm)],[5532, 6030])).
% 27.90/18.09 tff(6032,plain,
% 27.90/18.09 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2)))),
% 27.90/18.09 inference(symmetry,[status(thm)],[6031])).
% 27.90/18.09 tff(6033,plain,
% 27.90/18.09 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2)))),
% 27.90/18.09 inference(modus_ponens,[status(thm)],[6024, 6032])).
% 27.90/18.09 tff(6034,plain,
% 27.90/18.09 ($false),
% 27.90/18.09 inference(unit_resolution,[status(thm)],[5980, 6033, 6030])).
% 27.90/18.09 tff(6035,plain,((f9(c2, f9(c2, c2)) = f9(c2, c2)) | (~(f10(c2) = c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(c3 = c1)) | (~(f7(c1) = c1)) | (~(f10(c1) = c2)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 27.90/18.09 tff(6036,plain,
% 27.90/18.09 (f9(c2, f9(c2, c2)) = f9(c2, c2)),
% 27.90/18.09 inference(unit_resolution,[status(thm)],[6035, 3896, 122, 148, 79, 172, 4234, 16, 121])).
% 27.90/18.09 tff(6037,plain,
% 27.90/18.09 (f9(c2, c1) = c1),
% 27.90/18.09 inference(unit_resolution,[status(thm)],[1141, 6036, 122, 79, 148])).
% 27.90/18.09 tff(6038,plain,
% 27.90/18.09 (~big_f(f9(c2, c2), f10(c2))),
% 27.90/18.09 inference(unit_resolution,[status(thm)],[743, 6037, 5677, 148, 79, 122])).
% 27.90/18.09 tff(6039,plain,
% 27.90/18.09 (f6(c2, f9(c2, c2)) = c2),
% 27.90/18.09 inference(transitivity,[status(thm)],[3461, 5841, 2362])).
% 27.90/18.09 tff(6040,plain,
% 27.90/18.09 ((f6(c2, f9(c2, c2)) = f9(c2, c2)) <=> (c2 = f9(c2, c2))),
% 27.90/18.09 inference(monotonicity,[status(thm)],[6039])).
% 27.90/18.09 tff(6041,plain,
% 27.90/18.09 ((f6(c2, f9(c2, c2)) = f9(c2, c2)) <=> (f9(c2, c2) = c2)),
% 27.90/18.09 inference(transitivity,[status(thm)],[6040, 167])).
% 27.90/18.09 tff(6042,plain,
% 27.90/18.09 ((f9(c2, c2) = c2) <=> (f6(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.90/18.09 inference(symmetry,[status(thm)],[6041])).
% 27.90/18.09 tff(6043,plain,
% 27.90/18.09 ((~(f9(c2, c2) = c2)) <=> (~(f6(c2, f9(c2, c2)) = f9(c2, c2)))),
% 27.90/18.09 inference(monotonicity,[status(thm)],[6042])).
% 27.90/18.09 tff(6044,plain,
% 27.90/18.09 (~(f6(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.90/18.09 inference(modus_ponens,[status(thm)],[2650, 6043])).
% 27.90/18.09 tff(6045,plain,
% 27.90/18.09 (big_f(f7(c2), f6(c2, f9(c2, c2))) <=> big_f(c2, c2)),
% 27.90/18.09 inference(monotonicity,[status(thm)],[77, 6039])).
% 27.90/18.09 tff(6046,plain,
% 27.90/18.09 (big_f(c2, c2) <=> big_f(f7(c2), f6(c2, f9(c2, c2)))),
% 27.90/18.09 inference(symmetry,[status(thm)],[6045])).
% 27.90/18.09 tff(6047,plain,
% 27.90/18.09 ((~big_f(c2, c2)) <=> (~big_f(f7(c2), f6(c2, f9(c2, c2))))),
% 27.90/18.09 inference(monotonicity,[status(thm)],[6046])).
% 27.90/18.09 tff(6048,plain,
% 27.90/18.09 (~big_f(f7(c2), f6(c2, f9(c2, c2)))),
% 27.90/18.09 inference(modus_ponens,[status(thm)],[121, 6047])).
% 27.90/18.09 tff(6049,plain,
% 27.90/18.09 ((f6(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f7(c2), f6(c2, f9(c2, c2)))),
% 27.90/18.09 inference(unit_resolution,[status(thm)],[3477, 2492, 122, 77, 2650, 256])).
% 27.90/18.09 tff(6050,plain,
% 27.90/18.09 ($false),
% 27.90/18.09 inference(unit_resolution,[status(thm)],[6049, 6048, 6044])).
% 27.90/18.09 tff(6051,plain,((~(f6(f7(c2), c3) = c2)) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | big_f(f9(c2, c2), f10(c2)) | big_f(c2, c2) | (~(c3 = c1)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.90/18.09 tff(6052,plain,
% 27.90/18.09 (~(f6(f7(c2), c3) = c2)),
% 27.90/18.09 inference(unit_resolution,[status(thm)],[6051, 77, 122, 256, 121, 172, 148, 79])).
% 27.90/18.09 tff(6053,plain,
% 27.90/18.09 (f6(f7(c2), c3) = c1),
% 27.90/18.09 inference(unit_resolution,[status(thm)],[2391, 6052])).
% 27.90/18.09 tff(6054,plain,
% 27.90/18.09 (f6(c2, f9(c2, c2)) = f9(c2, c2)),
% 27.90/18.09 inference(transitivity,[status(thm)],[3461, 5841, 6053, 149, 132])).
% 27.90/18.09 tff(6055,plain,
% 27.90/18.09 (big_f(f7(c2), f6(c2, f9(c2, c2))) <=> big_f(c2, f9(c2, c2))),
% 27.90/18.09 inference(monotonicity,[status(thm)],[77, 6054])).
% 27.90/18.09 tff(6056,plain,
% 27.90/18.09 (big_f(c2, f9(c2, c2)) <=> big_f(f7(c2), f6(c2, f9(c2, c2)))),
% 27.90/18.09 inference(symmetry,[status(thm)],[6055])).
% 27.90/18.09 tff(6057,plain,
% 27.90/18.09 (big_f(f7(c2), f6(c2, f9(c2, c2)))),
% 27.90/18.09 inference(modus_ponens,[status(thm)],[3719, 6056])).
% 27.90/18.09 tff(6058,plain,
% 27.90/18.09 ((~(f6(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f6(c2, f9(c2, c2))))),
% 27.90/18.09 inference(unit_resolution,[status(thm)],[3495, 2534, 122, 77, 2650, 256])).
% 27.90/18.09 tff(6059,plain,
% 27.90/18.09 ($false),
% 27.90/18.09 inference(unit_resolution,[status(thm)],[6058, 6057, 6054])).
% 27.90/18.09 tff(6060,plain,((~(f7(c2) = c2)) | (~(f10(c2) = c2)) | big_f(f9(c2, c2), f10(c2)) | (~big_f(c2, f9(c2, c2))) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(c3 = c1)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 27.90/18.09 tff(6061,plain,
% 27.90/18.09 (~(f7(c2) = c2)),
% 27.90/18.09 inference(unit_resolution,[status(thm)],[6060, 6038, 122, 5834, 148, 79, 172, 121])).
% 27.90/18.09 tff(6062,plain,
% 27.90/18.09 (f7(c2) = c1),
% 27.90/18.09 inference(unit_resolution,[status(thm)],[21, 6061])).
% 27.90/18.09 tff(6063,plain,
% 27.90/18.09 (~(f5(c1) = c1)),
% 27.90/18.09 inference(unit_resolution,[status(thm)],[5929, 6061, 122, 6038, 4234, 148, 79, 16])).
% 27.90/18.09 tff(6064,plain,
% 27.90/18.09 (f5(c1) = c2),
% 27.90/18.09 inference(unit_resolution,[status(thm)],[1708, 6063])).
% 27.90/18.09 tff(6065,plain,
% 27.90/18.09 (big_f(c1, f5(c1)) <=> big_f(f9(c2, c2), c2)),
% 27.90/18.09 inference(monotonicity,[status(thm)],[150, 6064])).
% 27.90/18.09 tff(6066,plain,
% 27.90/18.09 (big_f(f9(c2, c2), c2) <=> big_f(c1, f5(c1))),
% 27.90/18.09 inference(symmetry,[status(thm)],[6065])).
% 27.90/18.09 tff(6067,plain,
% 27.90/18.09 (big_f(f9(c2, c2), c2) <=> big_f(f7(c1), f5(c1))),
% 27.90/18.09 inference(transitivity,[status(thm)],[6066, 5933])).
% 27.90/18.09 tff(6068,plain,
% 27.90/18.09 ((~big_f(f9(c2, c2), c2)) <=> (~big_f(f7(c1), f5(c1)))),
% 27.90/18.09 inference(monotonicity,[status(thm)],[6067])).
% 27.90/18.09 tff(6069,plain,
% 27.90/18.09 (big_f(f9(c2, f9(c2, c2)), f10(c2)) <=> big_f(f9(c2, c2), c2)),
% 27.90/18.09 inference(monotonicity,[status(thm)],[6036, 122])).
% 27.90/18.09 tff(6070,plain,
% 27.90/18.09 ((~big_f(f9(c2, f9(c2, c2)), f10(c2))) <=> (~big_f(f9(c2, c2), c2))),
% 27.90/18.09 inference(monotonicity,[status(thm)],[6069])).
% 27.90/18.09 tff(6071,plain,
% 27.90/18.09 (~big_f(f9(c2, c2), c2)),
% 27.90/18.09 inference(modus_ponens,[status(thm)],[3896, 6070])).
% 27.90/18.09 tff(6072,plain,
% 27.90/18.09 (~big_f(f7(c1), f5(c1))),
% 27.90/18.09 inference(modus_ponens,[status(thm)],[6071, 6068])).
% 27.90/18.09 tff(6073,plain,
% 27.90/18.09 (f7(c2) = f9(c2, c2)),
% 27.90/18.09 inference(transitivity,[status(thm)],[6062, 149, 132])).
% 27.90/18.09 tff(6074,plain,
% 27.90/18.09 (big_f(f7(c2), f9(c2, c2)) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 27.90/18.09 inference(monotonicity,[status(thm)],[6073])).
% 27.90/18.09 tff(6075,plain,
% 27.90/18.09 (big_f(f7(c2), c1) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 27.90/18.09 inference(transitivity,[status(thm)],[4534, 6074])).
% 27.90/18.09 tff(6076,plain,
% 27.90/18.09 (~(f7(f10(c1)) = f10(c1))),
% 27.90/18.09 inference(modus_ponens,[status(thm)],[6061, 235])).
% 27.90/18.09 tff(6077,plain,
% 27.90/18.09 (big_f(f7(f10(c1)), f5(f10(c1)))),
% 27.90/18.09 inference(unit_resolution,[status(thm)],[309, 6076, 122, 6038, 2650])).
% 27.90/18.09 tff(6078,plain,
% 27.90/18.09 (big_f(f7(c2), f5(c2))),
% 27.90/18.09 inference(modus_ponens,[status(thm)],[6077, 296])).
% 27.90/18.09 tff(6079,plain,
% 27.90/18.09 (big_f(f7(c2), c2) <=> big_f(f9(c2, c2), c2)),
% 27.90/18.09 inference(monotonicity,[status(thm)],[6073])).
% 27.90/18.09 tff(6080,plain,
% 27.90/18.09 (big_f(f9(c2, c2), c2) <=> big_f(f7(c2), c2)),
% 27.90/18.09 inference(symmetry,[status(thm)],[6079])).
% 27.90/18.09 tff(6081,plain,
% 27.90/18.09 ((~big_f(f9(c2, c2), c2)) <=> (~big_f(f7(c2), c2))),
% 27.90/18.09 inference(monotonicity,[status(thm)],[6080])).
% 27.90/18.09 tff(6082,plain,
% 27.90/18.09 (~big_f(f7(c2), c2)),
% 27.90/18.09 inference(modus_ponens,[status(thm)],[6071, 6081])).
% 27.90/18.09 tff(6083,plain,
% 27.90/18.09 (~(c2 = f5(c2))),
% 27.90/18.09 inference(unit_resolution,[status(thm)],[1527, 267, 122, 6061, 6082, 2650, 6038])).
% 27.90/18.09 tff(6084,plain,
% 27.90/18.09 (~(f5(f10(c1)) = c2)),
% 27.90/18.09 inference(modus_ponens,[status(thm)],[6083, 6008])).
% 27.90/18.09 tff(6085,plain,
% 27.90/18.09 (f5(f10(c1)) = c1),
% 27.90/18.09 inference(unit_resolution,[status(thm)],[326, 6084])).
% 27.90/18.09 tff(6086,plain,
% 27.90/18.09 (big_f(f7(c2), c1)),
% 27.90/18.09 inference(unit_resolution,[status(thm)],[336, 6085, 16, 6078])).
% 27.90/18.09 tff(6087,plain,
% 27.90/18.09 (big_f(f9(c2, c2), f9(c2, c2))),
% 27.90/18.09 inference(modus_ponens,[status(thm)],[6086, 6075])).
% 27.90/18.09 tff(6088,plain,
% 27.90/18.09 (big_f(f7(c1), f6(c1, c1))),
% 27.90/18.09 inference(unit_resolution,[status(thm)],[4658, 6087, 148, 79, 122, 4234, 6038])).
% 27.90/18.09 tff(6089,plain,
% 27.90/18.09 (~(f6(f7(c2), c3) = c2)),
% 27.90/18.09 inference(unit_resolution,[status(thm)],[5966, 6088, 172, 6072, 6064, 6062])).
% 27.90/18.09 tff(6090,plain,
% 27.90/18.09 (f6(f7(c2), c3) = c1),
% 27.90/18.09 inference(unit_resolution,[status(thm)],[2391, 6089])).
% 27.90/18.09 tff(6091,plain,
% 27.90/18.09 (c1 = f7(c2)),
% 27.90/18.09 inference(symmetry,[status(thm)],[6062])).
% 27.90/18.09 tff(6092,plain,
% 27.90/18.09 (f6(c1, c1) = f6(f7(c2), c3)),
% 27.90/18.09 inference(monotonicity,[status(thm)],[6091, 5585])).
% 27.90/18.09 tff(6093,plain,
% 27.90/18.09 (f6(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)),
% 27.90/18.09 inference(transitivity,[status(thm)],[4594, 6092, 6090, 149, 132])).
% 27.90/18.09 tff(6094,plain,
% 27.90/18.09 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2))) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 27.90/18.09 inference(monotonicity,[status(thm)],[5532, 6093])).
% 27.90/18.09 tff(6095,plain,
% 27.90/18.09 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2)))),
% 27.90/18.09 inference(symmetry,[status(thm)],[6094])).
% 27.90/18.09 tff(6096,plain,
% 27.90/18.09 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2)))),
% 27.90/18.09 inference(modus_ponens,[status(thm)],[6087, 6095])).
% 27.90/18.09 tff(6097,plain,
% 27.90/18.09 ((~(f6(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2))))),
% 27.90/18.09 inference(unit_resolution,[status(thm)],[4676, 2534, 122, 2650, 6038, 5532])).
% 27.90/18.09 tff(6098,plain,
% 27.90/18.09 ($false),
% 27.90/18.09 inference(unit_resolution,[status(thm)],[6097, 6096, 6093])).
% 27.90/18.09 tff(6099,plain,(big_f(f9(c2, f9(c2, c2)), f10(c2)) | (~(f10(c2) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(c3 = c1)) | (~(f7(c1) = c1)) | (~(f10(c1) = c2)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 27.90/18.09 tff(6100,plain,
% 27.90/18.09 (big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 27.90/18.09 inference(unit_resolution,[status(thm)],[6099, 121, 148, 79, 172, 4234, 15, 122])).
% 27.90/18.09 tff(6101,plain,
% 27.90/18.09 (~(f5(f10(c1)) = c1)),
% 27.90/18.09 inference(unit_resolution,[status(thm)],[4482, 4469, 121, 122, 148, 79, 6100])).
% 27.90/18.09 tff(6102,plain,
% 27.90/18.09 (f5(f10(c1)) = c2),
% 27.90/18.09 inference(unit_resolution,[status(thm)],[326, 6101])).
% 27.90/18.09 tff(6103,plain,
% 27.90/18.09 (~(f7(c2) = c2)),
% 27.90/18.09 inference(unit_resolution,[status(thm)],[6060, 256, 122, 3719, 148, 79, 172, 121])).
% 27.90/18.09 tff(6104,plain,
% 27.90/18.09 (~(f7(f10(c1)) = f10(c1))),
% 27.90/18.09 inference(modus_ponens,[status(thm)],[6103, 235])).
% 27.90/18.09 tff(6105,plain,
% 27.90/18.09 (big_f(f7(f10(c1)), f5(f10(c1)))),
% 27.90/18.09 inference(unit_resolution,[status(thm)],[309, 6104, 122, 256, 2650])).
% 27.90/18.09 tff(6106,plain,
% 27.90/18.09 (big_f(f7(c2), f5(c2))),
% 27.90/18.09 inference(modus_ponens,[status(thm)],[6105, 296])).
% 27.90/18.09 tff(6107,plain,
% 27.90/18.09 (f7(c2) = c1),
% 27.90/18.09 inference(unit_resolution,[status(thm)],[21, 6103])).
% 27.90/18.09 tff(6108,plain,
% 27.90/18.09 (~big_f(f7(c2), f5(c2))),
% 27.90/18.09 inference(unit_resolution,[status(thm)],[321, 6107, 122, 312, 16, 256, 148, 79])).
% 27.90/18.09 tff(6109,plain,
% 27.90/18.09 ($false),
% 27.90/18.09 inference(unit_resolution,[status(thm)],[6108, 6106])).
% 27.90/18.09 tff(6110,plain,(big_f(f9(c2, c2), f10(c2)) | (~(f10(c1) = c2)) | (~(f10(c2) = c2)) | (~(f5(f10(c1)) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~big_f(c2, f9(c2, c2))) | (~(c3 = c1)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 27.90/18.09 tff(6111,plain,
% 27.90/18.09 (big_f(f9(c2, c2), f10(c2))),
% 27.90/18.09 inference(unit_resolution,[status(thm)],[6110, 6102, 122, 15, 148, 79, 5832, 172, 121])).
% 27.90/18.10 tff(6112,plain,
% 27.90/18.10 (big_f(c1, c2)),
% 27.90/18.10 inference(modus_ponens,[status(thm)],[6111, 5575])).
% 27.90/18.10 tff(6113,plain,
% 27.90/18.10 (big_f(f9(c2, c2), c2)),
% 27.90/18.10 inference(modus_ponens,[status(thm)],[6111, 129])).
% 27.90/18.10 tff(6114,plain,
% 27.90/18.10 (f10(f9(c2, c2)) = f10(c2)),
% 27.90/18.10 inference(transitivity,[status(thm)],[3646, 15, 216])).
% 27.90/18.10 tff(6115,plain,
% 27.90/18.10 (big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2))) <=> big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 27.90/18.10 inference(monotonicity,[status(thm)],[6114])).
% 27.90/18.10 tff(6116,plain,
% 27.90/18.10 (big_f(f9(c2, f9(c2, c2)), f10(c2)) <=> big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))),
% 27.90/18.10 inference(symmetry,[status(thm)],[6115])).
% 27.90/18.10 tff(6117,plain,
% 27.90/18.10 (big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))),
% 27.90/18.10 inference(modus_ponens,[status(thm)],[6100, 6116])).
% 27.90/18.10 tff(6118,plain,
% 27.90/18.10 (~(f5(c1) = c1)),
% 27.90/18.10 inference(unit_resolution,[status(thm)],[3589, 77, 148, 121, 79, 122, 348, 3, 2865])).
% 27.90/18.10 tff(6119,plain,
% 27.90/18.10 (f5(c1) = c2),
% 27.90/18.10 inference(unit_resolution,[status(thm)],[1708, 6118])).
% 27.90/18.10 tff(6120,plain,
% 27.90/18.10 (f9(c2, f5(c1)) = f9(c2, c2)),
% 27.90/18.10 inference(monotonicity,[status(thm)],[6119])).
% 27.90/18.10 tff(6121,plain,
% 27.90/18.10 (big_f(c2, f10(c1)) <=> big_f(c2, c2)),
% 27.90/18.10 inference(monotonicity,[status(thm)],[16])).
% 27.90/18.10 tff(6122,assumption,(big_f(c2, f10(c1))), introduced(assumption)).
% 27.90/18.10 tff(6123,plain,
% 27.90/18.10 (big_f(c2, c2)),
% 27.90/18.10 inference(modus_ponens,[status(thm)],[6122, 6121])).
% 27.90/18.10 tff(6124,plain,
% 27.90/18.10 ($false),
% 27.90/18.10 inference(unit_resolution,[status(thm)],[121, 6123])).
% 27.90/18.10 tff(6125,plain,((~big_f(c2, f10(c1))) | big_f(c2, c2) | (~(f10(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.90/18.10 tff(6126,plain,
% 27.90/18.10 (~big_f(c2, f10(c1))),
% 27.90/18.10 inference(unit_resolution,[status(thm)],[6125, 121, 15])).
% 27.90/18.10 tff(6127,plain,
% 27.90/18.10 (f6(c2, c1) = c1),
% 27.90/18.10 inference(transitivity,[status(thm)],[5841, 2702])).
% 27.90/18.10 tff(6128,plain,
% 27.90/18.10 (f6(c2, f6(c2, c1)) = f6(c2, c1)),
% 27.90/18.10 inference(monotonicity,[status(thm)],[6127])).
% 27.90/18.10 tff(6129,plain,
% 27.90/18.10 (f6(c2, f6(c2, c1)) = f9(c2, c2)),
% 27.90/18.10 inference(transitivity,[status(thm)],[6128, 5841, 2702, 149, 132])).
% 27.90/18.10 tff(6130,plain,
% 27.90/18.10 (big_f(f7(c2), f6(c2, f6(c2, c1))) <=> big_f(c2, f9(c2, c2))),
% 27.90/18.10 inference(monotonicity,[status(thm)],[77, 6129])).
% 27.90/18.10 tff(6131,plain,
% 27.90/18.10 (big_f(c2, f9(c2, c2)) <=> big_f(f7(c2), f6(c2, f6(c2, c1)))),
% 27.90/18.10 inference(symmetry,[status(thm)],[6130])).
% 27.90/18.10 tff(6132,plain,
% 27.90/18.10 (big_f(f7(c2), f6(c2, f6(c2, c1)))),
% 27.90/18.10 inference(modus_ponens,[status(thm)],[3719, 6131])).
% 27.90/18.10 tff(6133,plain,
% 27.90/18.10 (~(c2 = f8(c1))),
% 27.90/18.10 inference(unit_resolution,[status(thm)],[2970, 6132, 6128, 3, 2946, 77])).
% 27.90/18.10 tff(6134,plain,
% 27.90/18.10 (~(f8(c1) = c2)),
% 27.90/18.10 inference(unit_resolution,[status(thm)],[1675, 6133])).
% 27.90/18.10 tff(6135,plain,
% 27.90/18.10 (f8(c1) = c1),
% 27.90/18.10 inference(unit_resolution,[status(thm)],[1680, 6134])).
% 27.90/18.10 tff(6136,plain,
% 27.90/18.10 (f8(f9(c2, c2)) = f8(c1)),
% 27.90/18.10 inference(monotonicity,[status(thm)],[161])).
% 27.90/18.10 tff(6137,plain,
% 27.90/18.10 (f8(f9(c2, c2)) = f9(c2, c2)),
% 27.90/18.10 inference(transitivity,[status(thm)],[6136, 6135, 149, 132])).
% 27.90/18.10 tff(6138,plain,
% 27.90/18.10 ((f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) <=> (f9(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.90/18.10 inference(monotonicity,[status(thm)],[6137])).
% 27.90/18.10 tff(6139,plain,
% 27.90/18.10 ((f9(c2, f9(c2, c2)) = f9(c2, c2)) <=> (f9(c2, f9(c2, c2)) = f8(f9(c2, c2)))),
% 27.90/18.10 inference(symmetry,[status(thm)],[6138])).
% 27.90/18.10 tff(6140,plain,
% 27.90/18.10 ((~(f9(c2, f9(c2, c2)) = f9(c2, c2))) <=> (~(f9(c2, f9(c2, c2)) = f8(f9(c2, c2))))),
% 27.90/18.10 inference(monotonicity,[status(thm)],[6139])).
% 27.90/18.10 tff(6141,plain,
% 27.90/18.10 (~(f9(c2, f9(c2, c2)) = f8(f9(c2, c2)))),
% 27.90/18.10 inference(modus_ponens,[status(thm)],[4469, 6140])).
% 27.90/18.10 tff(6142,plain,
% 27.90/18.10 (f6(c2, f9(c2, c2)) = f9(c2, c2)),
% 27.90/18.10 inference(transitivity,[status(thm)],[3461, 5841, 2702, 149, 132])).
% 27.90/18.10 tff(6143,plain,
% 27.90/18.10 (big_f(f7(c2), f6(c2, f9(c2, c2))) <=> big_f(c2, f9(c2, c2))),
% 27.90/18.10 inference(monotonicity,[status(thm)],[77, 6142])).
% 27.90/18.10 tff(6144,plain,
% 27.90/18.10 (big_f(c2, f9(c2, c2)) <=> big_f(f7(c2), f6(c2, f9(c2, c2)))),
% 27.90/18.10 inference(symmetry,[status(thm)],[6143])).
% 27.90/18.10 tff(6145,plain,
% 27.90/18.10 (big_f(f7(c2), f6(c2, f9(c2, c2)))),
% 27.90/18.10 inference(modus_ponens,[status(thm)],[3719, 6144])).
% 27.90/18.10 tff(6146,plain,
% 27.90/18.10 (~(f10(f9(c2, c2)) = f9(c2, c2))),
% 27.90/18.10 inference(unit_resolution,[status(thm)],[762, 148, 122, 79, 15])).
% 27.90/18.10 tff(6147,plain,
% 27.90/18.10 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(c2) = c2)) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~(f6(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f6(c2, f9(c2, c2)))) | (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c2) = c2)) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~(f6(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f6(c2, f9(c2, c2)))) | (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))))),
% 27.90/18.10 inference(rewrite,[status(thm)],[])).
% 27.90/18.10 tff(6148,plain,
% 27.90/18.10 (((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))) | (~(f7(c2) = c2)) | (~(f6(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f6(c2, f9(c2, c2))))) <=> ((~(f7(c2) = c2)) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~(f6(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f6(c2, f9(c2, c2)))) | (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))))),
% 27.90/18.10 inference(rewrite,[status(thm)],[])).
% 27.90/18.10 tff(6149,plain,
% 27.90/18.10 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))) | (~(f7(c2) = c2)) | (~(f6(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f6(c2, f9(c2, c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(c2) = c2)) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~(f6(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f6(c2, f9(c2, c2)))) | (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2))))))),
% 27.90/18.10 inference(monotonicity,[status(thm)],[6148])).
% 27.90/18.10 tff(6150,plain,
% 27.90/18.10 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))) | (~(f7(c2) = c2)) | (~(f6(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f6(c2, f9(c2, c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c2) = c2)) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~(f6(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f6(c2, f9(c2, c2)))) | (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))))),
% 27.90/18.10 inference(transitivity,[status(thm)],[6149, 6147])).
% 27.90/18.10 tff(6151,plain,
% 27.90/18.10 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))) | (~(f7(c2) = c2)) | (~(f6(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f6(c2, f9(c2, c2)))))),
% 27.90/18.10 inference(quant_inst,[status(thm)],[])).
% 27.90/18.10 tff(6152,plain,
% 27.90/18.10 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c2) = c2)) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~(f6(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f6(c2, f9(c2, c2)))) | (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2))))),
% 27.90/18.10 inference(modus_ponens,[status(thm)],[6151, 6150])).
% 27.90/18.10 tff(6153,plain,
% 27.90/18.10 ((~(f6(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f6(c2, f9(c2, c2)))) | (f9(c2, f9(c2, c2)) = f8(f9(c2, c2)))),
% 27.90/18.10 inference(unit_resolution,[status(thm)],[6152, 2730, 77, 6146, 5763])).
% 27.90/18.10 tff(6154,plain,
% 27.90/18.10 ($false),
% 27.90/18.10 inference(unit_resolution,[status(thm)],[6153, 6145, 6142, 6141])).
% 27.90/18.10 tff(6155,plain,((~(f6(f7(c2), c3) = c1)) | (~(f7(c2) = c2)) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))) | (~big_f(c2, f9(c2, c2))) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(c3 = c1)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | (f10(c1) = c1) | big_f(c2, f10(c1))), inference(lemma,lemma(discharge,[]))).
% 27.90/18.10 tff(6156,plain,
% 27.90/18.10 (~(f6(f7(c2), c3) = c1)),
% 27.90/18.10 inference(unit_resolution,[status(thm)],[6155, 77, 5763, 3812, 148, 79, 122, 172, 4469, 3, 6126])).
% 27.90/18.10 tff(6157,plain,
% 27.90/18.10 (f6(f7(c2), c3) = c2),
% 27.90/18.10 inference(unit_resolution,[status(thm)],[2391, 6156])).
% 27.90/18.10 tff(6158,plain,
% 27.90/18.10 (~big_f(f7(c2), f6(c2, c1))),
% 27.90/18.10 inference(unit_resolution,[status(thm)],[5848, 6157, 172, 121, 77])).
% 27.90/18.10 tff(6159,plain,
% 27.90/18.10 (f10(f9(c2, f5(c1))) = f10(f9(c2, c2))),
% 27.90/18.10 inference(monotonicity,[status(thm)],[6120])).
% 27.90/18.10 tff(6160,plain,
% 27.90/18.10 (f10(f9(c2, f5(c1))) = c2),
% 27.90/18.10 inference(transitivity,[status(thm)],[6159, 3646, 15])).
% 27.90/18.10 tff(6161,plain,
% 27.90/18.10 (big_f(f9(c2, f5(c1)), f10(f9(c2, f5(c1)))) <=> big_f(f9(c2, c2), c2)),
% 27.90/18.10 inference(monotonicity,[status(thm)],[6120, 6160])).
% 27.90/18.10 tff(6162,plain,
% 27.90/18.10 (big_f(f9(c2, c2), c2) <=> big_f(f9(c2, f5(c1)), f10(f9(c2, f5(c1))))),
% 27.90/18.10 inference(symmetry,[status(thm)],[6161])).
% 27.90/18.10 tff(6163,plain,
% 27.90/18.10 (big_f(f9(c2, f5(c1)), f10(f9(c2, f5(c1))))),
% 27.90/18.10 inference(modus_ponens,[status(thm)],[2041, 6162])).
% 27.90/18.10 tff(6164,plain,
% 27.90/18.10 ((f10(f9(c2, f5(c1))) = f9(c2, f5(c1))) <=> (c2 = f9(c2, c2))),
% 27.90/18.10 inference(monotonicity,[status(thm)],[6160, 6120])).
% 27.90/18.10 tff(6165,plain,
% 27.90/18.10 ((f10(f9(c2, f5(c1))) = f9(c2, f5(c1))) <=> (f9(c2, c2) = c2)),
% 27.90/18.10 inference(transitivity,[status(thm)],[6164, 167])).
% 27.90/18.10 tff(6166,plain,
% 27.90/18.10 ((f9(c2, c2) = c2) <=> (f10(f9(c2, f5(c1))) = f9(c2, f5(c1)))),
% 27.90/18.10 inference(symmetry,[status(thm)],[6165])).
% 27.90/18.10 tff(6167,plain,
% 27.90/18.10 ((~(f9(c2, c2) = c2)) <=> (~(f10(f9(c2, f5(c1))) = f9(c2, f5(c1))))),
% 27.90/18.10 inference(monotonicity,[status(thm)],[6166])).
% 27.90/18.10 tff(6168,plain,
% 27.90/18.10 (~(f10(f9(c2, f5(c1))) = f9(c2, f5(c1)))),
% 27.90/18.10 inference(modus_ponens,[status(thm)],[2650, 6167])).
% 27.90/18.10 tff(6169,plain,
% 27.90/18.10 (f6(f7(c2), c3) = f6(c2, c1)),
% 27.90/18.10 inference(symmetry,[status(thm)],[5841])).
% 27.90/18.10 tff(6170,plain,
% 27.90/18.10 ((f6(f7(c2), c3) = c1) <=> (f6(c2, c1) = c1)),
% 27.90/18.10 inference(monotonicity,[status(thm)],[6169])).
% 27.90/18.10 tff(6171,plain,
% 27.90/18.10 ((~(f6(f7(c2), c3) = c1)) <=> (~(f6(c2, c1) = c1))),
% 27.90/18.10 inference(monotonicity,[status(thm)],[6170])).
% 27.90/18.10 tff(6172,plain,
% 27.90/18.10 (~(f6(c2, c1) = c1)),
% 27.90/18.10 inference(modus_ponens,[status(thm)],[6156, 6171])).
% 27.90/18.10 tff(6173,plain,
% 27.90/18.10 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (f10(f9(c2, f5(c1))) = f9(c2, f5(c1))) | (f9(c2, f5(c1)) = f8(f9(c2, f5(c1)))) | (~big_f(f9(c2, f5(c1)), f10(f9(c2, f5(c1))))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (f10(f9(c2, f5(c1))) = f9(c2, f5(c1))) | (f9(c2, f5(c1)) = f8(f9(c2, f5(c1)))) | (~big_f(f9(c2, f5(c1)), f10(f9(c2, f5(c1))))))),
% 27.90/18.10 inference(rewrite,[status(thm)],[])).
% 27.90/18.10 tff(6174,plain,
% 27.90/18.10 (((f10(f9(c2, f5(c1))) = f9(c2, f5(c1))) | (f9(c2, f5(c1)) = f8(f9(c2, f5(c1)))) | (~big_f(f9(c2, f5(c1)), f10(f9(c2, f5(c1))))) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1))) <=> ((~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (f10(f9(c2, f5(c1))) = f9(c2, f5(c1))) | (f9(c2, f5(c1)) = f8(f9(c2, f5(c1)))) | (~big_f(f9(c2, f5(c1)), f10(f9(c2, f5(c1))))))),
% 27.90/18.10 inference(rewrite,[status(thm)],[])).
% 27.90/18.10 tff(6175,plain,
% 27.90/18.10 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f9(c2, f5(c1))) = f9(c2, f5(c1))) | (f9(c2, f5(c1)) = f8(f9(c2, f5(c1)))) | (~big_f(f9(c2, f5(c1)), f10(f9(c2, f5(c1))))) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (f10(f9(c2, f5(c1))) = f9(c2, f5(c1))) | (f9(c2, f5(c1)) = f8(f9(c2, f5(c1)))) | (~big_f(f9(c2, f5(c1)), f10(f9(c2, f5(c1)))))))),
% 27.90/18.10 inference(monotonicity,[status(thm)],[6174])).
% 27.90/18.10 tff(6176,plain,
% 27.90/18.10 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f9(c2, f5(c1))) = f9(c2, f5(c1))) | (f9(c2, f5(c1)) = f8(f9(c2, f5(c1)))) | (~big_f(f9(c2, f5(c1)), f10(f9(c2, f5(c1))))) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (f10(f9(c2, f5(c1))) = f9(c2, f5(c1))) | (f9(c2, f5(c1)) = f8(f9(c2, f5(c1)))) | (~big_f(f9(c2, f5(c1)), f10(f9(c2, f5(c1))))))),
% 27.90/18.10 inference(transitivity,[status(thm)],[6175, 6173])).
% 27.90/18.10 tff(6177,plain,
% 27.90/18.10 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f9(c2, f5(c1))) = f9(c2, f5(c1))) | (f9(c2, f5(c1)) = f8(f9(c2, f5(c1)))) | (~big_f(f9(c2, f5(c1)), f10(f9(c2, f5(c1))))) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)))),
% 27.90/18.10 inference(quant_inst,[status(thm)],[])).
% 27.90/18.10 tff(6178,plain,
% 27.90/18.10 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (f10(f9(c2, f5(c1))) = f9(c2, f5(c1))) | (f9(c2, f5(c1)) = f8(f9(c2, f5(c1)))) | (~big_f(f9(c2, f5(c1)), f10(f9(c2, f5(c1)))))),
% 27.90/18.10 inference(modus_ponens,[status(thm)],[6177, 6176])).
% 27.90/18.10 tff(6179,plain,
% 27.90/18.10 ((~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (f10(f9(c2, f5(c1))) = f9(c2, f5(c1))) | (f9(c2, f5(c1)) = f8(f9(c2, f5(c1)))) | (~big_f(f9(c2, f5(c1)), f10(f9(c2, f5(c1)))))),
% 27.90/18.10 inference(unit_resolution,[status(thm)],[6178, 2662])).
% 27.90/18.10 tff(6180,plain,
% 27.90/18.10 (f9(c2, f5(c1)) = f8(f9(c2, f5(c1)))),
% 27.90/18.10 inference(unit_resolution,[status(thm)],[6179, 6172, 77, 6168, 6163, 6158])).
% 27.90/18.10 tff(6181,plain,
% 27.90/18.10 (f8(f9(c2, f5(c1))) = f9(c2, f5(c1))),
% 27.90/18.10 inference(symmetry,[status(thm)],[6180])).
% 27.90/18.10 tff(6182,plain,
% 27.90/18.10 (f9(c2, c2) = f9(c2, f5(c1))),
% 27.90/18.10 inference(symmetry,[status(thm)],[6120])).
% 27.90/18.10 tff(6183,plain,
% 27.90/18.10 (f8(f9(c2, c2)) = f8(f9(c2, f5(c1)))),
% 27.90/18.10 inference(monotonicity,[status(thm)],[6182])).
% 27.90/18.10 tff(6184,plain,
% 27.90/18.10 (f8(f9(c2, c2)) = f9(c2, c2)),
% 27.90/18.10 inference(transitivity,[status(thm)],[6183, 6181, 6120])).
% 27.90/18.10 tff(6185,plain,
% 27.90/18.10 ((f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) <=> (f9(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.90/18.10 inference(monotonicity,[status(thm)],[6184])).
% 27.90/18.10 tff(6186,plain,
% 27.90/18.10 ((f9(c2, f9(c2, c2)) = f9(c2, c2)) <=> (f9(c2, f9(c2, c2)) = f8(f9(c2, c2)))),
% 27.90/18.10 inference(symmetry,[status(thm)],[6185])).
% 27.90/18.10 tff(6187,plain,
% 27.90/18.10 ((~(f9(c2, f9(c2, c2)) = f9(c2, c2))) <=> (~(f9(c2, f9(c2, c2)) = f8(f9(c2, c2))))),
% 27.90/18.10 inference(monotonicity,[status(thm)],[6186])).
% 27.90/18.10 tff(6188,plain,
% 27.90/18.10 (~(f9(c2, f9(c2, c2)) = f8(f9(c2, c2)))),
% 27.90/18.10 inference(modus_ponens,[status(thm)],[4469, 6187])).
% 27.90/18.10 tff(6189,plain,
% 27.90/18.10 (f6(c2, f9(c2, c2)) = c2),
% 27.90/18.10 inference(transitivity,[status(thm)],[3461, 5841, 6157])).
% 27.90/18.10 tff(6190,plain,
% 27.90/18.10 ((f6(c2, f9(c2, c2)) = f9(c2, c2)) <=> (c2 = f9(c2, c2))),
% 27.90/18.10 inference(monotonicity,[status(thm)],[6189])).
% 27.90/18.10 tff(6191,plain,
% 27.90/18.10 ((f6(c2, f9(c2, c2)) = f9(c2, c2)) <=> (f9(c2, c2) = c2)),
% 27.90/18.10 inference(transitivity,[status(thm)],[6190, 167])).
% 27.90/18.10 tff(6192,plain,
% 27.90/18.10 ((f9(c2, c2) = c2) <=> (f6(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.90/18.10 inference(symmetry,[status(thm)],[6191])).
% 27.90/18.10 tff(6193,plain,
% 27.90/18.10 ((~(f9(c2, c2) = c2)) <=> (~(f6(c2, f9(c2, c2)) = f9(c2, c2)))),
% 27.90/18.10 inference(monotonicity,[status(thm)],[6192])).
% 27.90/18.10 tff(6194,plain,
% 27.90/18.10 (~(f6(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.90/18.10 inference(modus_ponens,[status(thm)],[2650, 6193])).
% 27.90/18.10 tff(6195,plain,
% 27.90/18.10 (big_f(f7(c2), f6(c2, f9(c2, c2))) <=> big_f(c2, c2)),
% 27.90/18.10 inference(monotonicity,[status(thm)],[77, 6189])).
% 27.90/18.10 tff(6196,plain,
% 27.90/18.10 (big_f(c2, c2) <=> big_f(f7(c2), f6(c2, f9(c2, c2)))),
% 27.90/18.10 inference(symmetry,[status(thm)],[6195])).
% 27.90/18.10 tff(6197,plain,
% 27.90/18.10 ((~big_f(c2, c2)) <=> (~big_f(f7(c2), f6(c2, f9(c2, c2))))),
% 27.90/18.10 inference(monotonicity,[status(thm)],[6196])).
% 27.90/18.10 tff(6198,plain,
% 27.90/18.10 (~big_f(f7(c2), f6(c2, f9(c2, c2)))),
% 27.90/18.10 inference(modus_ponens,[status(thm)],[121, 6197])).
% 27.90/18.10 tff(6199,plain,
% 27.90/18.10 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f7(c2) = c2)) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f6(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f7(c2), f6(c2, f9(c2, c2))) | (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c2) = c2)) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f6(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f7(c2), f6(c2, f9(c2, c2))) | (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))))),
% 27.90/18.10 inference(rewrite,[status(thm)],[])).
% 27.90/18.10 tff(6200,plain,
% 27.90/18.10 (((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))) | (~(f7(c2) = c2)) | (f6(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f7(c2), f6(c2, f9(c2, c2)))) <=> ((~(f7(c2) = c2)) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f6(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f7(c2), f6(c2, f9(c2, c2))) | (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))))),
% 27.90/18.10 inference(rewrite,[status(thm)],[])).
% 27.90/18.10 tff(6201,plain,
% 27.90/18.10 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))) | (~(f7(c2) = c2)) | (f6(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f7(c2), f6(c2, f9(c2, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f7(c2) = c2)) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f6(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f7(c2), f6(c2, f9(c2, c2))) | (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2))))))),
% 27.90/18.10 inference(monotonicity,[status(thm)],[6200])).
% 27.90/18.10 tff(6202,plain,
% 27.90/18.10 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))) | (~(f7(c2) = c2)) | (f6(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f7(c2), f6(c2, f9(c2, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c2) = c2)) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f6(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f7(c2), f6(c2, f9(c2, c2))) | (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))))),
% 27.90/18.10 inference(transitivity,[status(thm)],[6201, 6199])).
% 27.90/18.10 tff(6203,plain,
% 27.90/18.10 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))) | (~(f7(c2) = c2)) | (f6(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f7(c2), f6(c2, f9(c2, c2))))),
% 27.90/18.11 inference(quant_inst,[status(thm)],[])).
% 27.90/18.11 tff(6204,plain,
% 27.90/18.11 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c2) = c2)) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f6(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f7(c2), f6(c2, f9(c2, c2))) | (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2))))),
% 27.90/18.11 inference(modus_ponens,[status(thm)],[6203, 6202])).
% 27.90/18.11 tff(6205,plain,
% 27.90/18.11 ((f6(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f7(c2), f6(c2, f9(c2, c2))) | (f9(c2, f9(c2, c2)) = f8(f9(c2, c2)))),
% 27.90/18.11 inference(unit_resolution,[status(thm)],[6204, 2662, 77, 6146, 5763])).
% 27.90/18.11 tff(6206,plain,
% 27.90/18.11 ($false),
% 27.90/18.11 inference(unit_resolution,[status(thm)],[6205, 6198, 6194, 6188])).
% 27.90/18.11 tff(6207,plain,((~(f7(c2) = c2)) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))) | big_f(c2, c2) | (~(c3 = c1)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | (f10(c1) = c1) | (~big_f(f9(c2, c2), c2)) | (~big_f(c2, c1)) | (~big_f(c1, c2))), inference(lemma,lemma(discharge,[]))).
% 27.90/18.11 tff(6208,plain,
% 27.90/18.11 (~(f7(c2) = c2)),
% 27.90/18.11 inference(unit_resolution,[status(thm)],[6207, 4469, 121, 172, 148, 79, 122, 6117, 3, 6113, 5831, 6112])).
% 27.90/18.11 tff(6209,plain,
% 27.90/18.11 (big_f(f9(c2, c2), f10(f9(c2, c2)))),
% 27.90/18.11 inference(unit_resolution,[status(thm)],[3625, 6111, 122, 15, 79, 148])).
% 27.90/18.11 tff(6210,plain,
% 27.90/18.11 (f5(c2) = c2),
% 27.90/18.11 inference(transitivity,[status(thm)],[294, 312])).
% 27.90/18.11 tff(6211,plain,
% 27.90/18.11 ((f6(c1, c2) = f5(c2)) <=> (f6(c1, c2) = c2)),
% 27.90/18.11 inference(monotonicity,[status(thm)],[6210])).
% 27.90/18.11 tff(6212,plain,
% 27.90/18.11 ((f6(c1, c2) = c2) <=> (f6(c1, c2) = f5(c2))),
% 27.90/18.11 inference(symmetry,[status(thm)],[6211])).
% 27.90/18.11 tff(6213,plain,
% 27.90/18.11 ((~(f6(c1, c2) = c2)) <=> (~(f6(c1, c2) = f5(c2)))),
% 27.90/18.11 inference(monotonicity,[status(thm)],[6212])).
% 27.90/18.11 tff(6214,plain,
% 27.90/18.11 (~(f6(c1, c2) = f5(c2))),
% 27.90/18.11 inference(modus_ponens,[status(thm)],[114, 6213])).
% 27.90/18.11 tff(6215,assumption,(big_f(f7(c1), f6(c1, c2))), introduced(assumption)).
% 27.90/18.11 tff(6216,plain,
% 27.90/18.11 (big_f(f7(c2), f6(c1, c2))),
% 27.90/18.11 inference(modus_ponens,[status(thm)],[6215, 5870])).
% 27.90/18.11 tff(6217,plain,
% 27.90/18.11 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(c2) = c2) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (~big_f(f7(c2), f6(c1, c2))) | (f6(c1, c2) = f5(c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c2) = c2) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (~big_f(f7(c2), f6(c1, c2))) | (f6(c1, c2) = f5(c2)))),
% 27.90/18.11 inference(rewrite,[status(thm)],[])).
% 27.90/18.11 tff(6218,plain,
% 27.90/18.11 (((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (f7(c2) = c2) | (f6(c1, c2) = f5(c2)) | (~big_f(f7(c2), f6(c1, c2)))) <=> ((f7(c2) = c2) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (~big_f(f7(c2), f6(c1, c2))) | (f6(c1, c2) = f5(c2)))),
% 27.90/18.11 inference(rewrite,[status(thm)],[])).
% 27.90/18.11 tff(6219,plain,
% 27.90/18.11 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (f7(c2) = c2) | (f6(c1, c2) = f5(c2)) | (~big_f(f7(c2), f6(c1, c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(c2) = c2) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (~big_f(f7(c2), f6(c1, c2))) | (f6(c1, c2) = f5(c2))))),
% 27.90/18.11 inference(monotonicity,[status(thm)],[6218])).
% 27.90/18.11 tff(6220,plain,
% 27.90/18.11 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (f7(c2) = c2) | (f6(c1, c2) = f5(c2)) | (~big_f(f7(c2), f6(c1, c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c2) = c2) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (~big_f(f7(c2), f6(c1, c2))) | (f6(c1, c2) = f5(c2)))),
% 27.90/18.11 inference(transitivity,[status(thm)],[6219, 6217])).
% 27.90/18.11 tff(6221,plain,
% 27.90/18.11 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (f7(c2) = c2) | (f6(c1, c2) = f5(c2)) | (~big_f(f7(c2), f6(c1, c2))))),
% 27.90/18.11 inference(quant_inst,[status(thm)],[])).
% 27.90/18.11 tff(6222,plain,
% 27.90/18.11 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c2) = c2) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (~big_f(f7(c2), f6(c1, c2))) | (f6(c1, c2) = f5(c2))),
% 27.90/18.11 inference(modus_ponens,[status(thm)],[6221, 6220])).
% 27.90/18.11 tff(6223,plain,
% 27.90/18.11 ((f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(f7(c2), f6(c1, c2))) | (f6(c1, c2) = f5(c2))),
% 27.90/18.11 inference(unit_resolution,[status(thm)],[6222, 1659, 17, 1767, 2026])).
% 27.90/18.11 tff(6224,plain,
% 27.90/18.11 (f9(c2, c2) = f8(f9(c2, c2))),
% 27.90/18.11 inference(unit_resolution,[status(thm)],[6223, 6216, 6214])).
% 27.90/18.11 tff(6225,plain,
% 27.90/18.11 (f8(f9(c2, c2)) = f9(c2, c2)),
% 27.90/18.11 inference(symmetry,[status(thm)],[6224])).
% 27.90/18.11 tff(6226,plain,
% 27.90/18.11 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(c2) = c2) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))) | (~big_f(f7(c2), f6(c1, c2))) | (f6(c1, c2) = f5(c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c2) = c2) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))) | (~big_f(f7(c2), f6(c1, c2))) | (f6(c1, c2) = f5(c2)))),
% 27.90/18.11 inference(rewrite,[status(thm)],[])).
% 27.90/18.11 tff(6227,plain,
% 27.90/18.11 (((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))) | (f7(c2) = c2) | (f6(c1, c2) = f5(c2)) | (~big_f(f7(c2), f6(c1, c2)))) <=> ((f7(c2) = c2) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))) | (~big_f(f7(c2), f6(c1, c2))) | (f6(c1, c2) = f5(c2)))),
% 27.90/18.11 inference(rewrite,[status(thm)],[])).
% 27.90/18.11 tff(6228,plain,
% 27.90/18.11 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))) | (f7(c2) = c2) | (f6(c1, c2) = f5(c2)) | (~big_f(f7(c2), f6(c1, c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(c2) = c2) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))) | (~big_f(f7(c2), f6(c1, c2))) | (f6(c1, c2) = f5(c2))))),
% 27.90/18.11 inference(monotonicity,[status(thm)],[6227])).
% 27.90/18.11 tff(6229,plain,
% 27.90/18.11 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))) | (f7(c2) = c2) | (f6(c1, c2) = f5(c2)) | (~big_f(f7(c2), f6(c1, c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c2) = c2) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))) | (~big_f(f7(c2), f6(c1, c2))) | (f6(c1, c2) = f5(c2)))),
% 27.90/18.11 inference(transitivity,[status(thm)],[6228, 6226])).
% 27.90/18.11 tff(6230,plain,
% 27.90/18.11 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))) | (f7(c2) = c2) | (f6(c1, c2) = f5(c2)) | (~big_f(f7(c2), f6(c1, c2))))),
% 27.90/18.11 inference(quant_inst,[status(thm)],[])).
% 27.90/18.11 tff(6231,plain,
% 27.90/18.11 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c2) = c2) | (f10(f9(c2, c2)) = f9(c2, c2)) | (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))) | (~big_f(f7(c2), f6(c1, c2))) | (f6(c1, c2) = f5(c2))),
% 27.90/18.11 inference(modus_ponens,[status(thm)],[6230, 6229])).
% 27.90/18.11 tff(6232,plain,
% 27.90/18.11 ((f9(c2, f9(c2, c2)) = f8(f9(c2, c2))) | (~big_f(f7(c2), f6(c1, c2))) | (f6(c1, c2) = f5(c2))),
% 27.90/18.11 inference(unit_resolution,[status(thm)],[6231, 1659, 17, 1767, 5763])).
% 27.90/18.11 tff(6233,plain,
% 27.90/18.11 (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))),
% 27.90/18.11 inference(unit_resolution,[status(thm)],[6232, 6214, 6216])).
% 27.90/18.11 tff(6234,plain,
% 27.90/18.11 (f9(c2, f9(c2, c2)) = f9(c2, c2)),
% 27.90/18.11 inference(transitivity,[status(thm)],[6233, 6225])).
% 27.90/18.11 tff(6235,plain,
% 27.90/18.11 ($false),
% 27.90/18.11 inference(unit_resolution,[status(thm)],[4469, 6234])).
% 27.90/18.11 tff(6236,plain,((f7(c2) = c2) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (f6(c1, c2) = c2) | (~(f5(f10(c1)) = c2)) | (~(f10(c1) = c2)) | (~big_f(f7(c1), f6(c1, c2))) | (~(f7(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 27.90/18.11 tff(6237,plain,
% 27.90/18.11 (~big_f(f7(c1), f6(c1, c2))),
% 27.90/18.11 inference(unit_resolution,[status(thm)],[6236, 114, 5752, 5763, 2026, 4469, 312, 16, 17, 4234])).
% 27.90/18.11 tff(6238,plain,
% 27.90/18.11 (~(f6(f9(c2, c2), c2) = c2)),
% 27.90/18.11 inference(unit_resolution,[status(thm)],[4256, 114, 148, 79, 122])).
% 27.90/18.11 tff(6239,plain,
% 27.90/18.11 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))),
% 27.90/18.11 inference(unit_resolution,[status(thm)],[5774, 6238, 5763, 5752, 5532, 2026, 4469])).
% 27.90/18.11 tff(6240,plain,
% 27.90/18.11 ($false),
% 27.90/18.11 inference(unit_resolution,[status(thm)],[5716, 6239, 6237, 148, 79, 122])).
% 27.90/18.11 tff(6241,plain,((f6(c1, c2) = c2) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | (~(f5(f10(c1)) = c2)) | (~(f10(c1) = c2)) | (f7(c2) = c2) | (~(f7(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 27.90/18.11 tff(6242,plain,
% 27.90/18.11 (f6(c1, c2) = c2),
% 27.90/18.11 inference(unit_resolution,[status(thm)],[6241, 6209, 79, 122, 6117, 148, 4469, 6102, 15, 6208, 4234])).
% 27.90/18.11 tff(6243,plain,
% 27.90/18.11 (f6(f9(c2, c2), c2) = c2),
% 27.90/18.11 inference(modus_ponens,[status(thm)],[6242, 5574])).
% 27.90/18.11 tff(6244,plain,
% 27.90/18.11 (big_f(f7(c1), f6(c1, c2)) <=> big_f(f9(c2, c2), c2)),
% 27.90/18.11 inference(monotonicity,[status(thm)],[4653, 36])).
% 27.90/18.11 tff(6245,plain,
% 27.90/18.11 (big_f(f9(c2, c2), c2) <=> big_f(f7(c1), f6(c1, c2))),
% 27.90/18.11 inference(symmetry,[status(thm)],[6244])).
% 27.90/18.11 tff(6246,plain,
% 27.90/18.11 (big_f(f7(c1), f6(c1, c2))),
% 27.90/18.11 inference(modus_ponens,[status(thm)],[2041, 6245])).
% 27.90/18.11 tff(6247,plain,
% 27.90/18.11 ($false),
% 27.90/18.11 inference(unit_resolution,[status(thm)],[5714, 6246])).
% 27.90/18.11 tff(6248,plain,(big_f(f7(c1), f6(c1, c2)) | (~big_f(f9(c2, c2), c2)) | (~(f6(c1, c2) = c2)) | (~(f7(c1) = c1)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.90/18.11 tff(6249,plain,
% 27.90/18.11 (big_f(f7(c1), f6(c1, c2))),
% 27.90/18.11 inference(unit_resolution,[status(thm)],[6248, 6113, 6242, 4234, 148, 79, 122])).
% 27.90/18.11 tff(6250,plain,
% 27.90/18.11 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))),
% 27.90/18.11 inference(modus_ponens,[status(thm)],[6249, 5782])).
% 27.90/18.11 tff(6251,plain,
% 27.90/18.11 (f9(c2, c2) = f8(f9(c2, c2))),
% 27.90/18.11 inference(unit_resolution,[status(thm)],[5789, 2730, 6146, 6209, 6250, 5532, 6243])).
% 27.90/18.11 tff(6252,plain,
% 27.90/18.11 (f8(f9(c2, c2)) = f9(c2, c2)),
% 27.90/18.11 inference(symmetry,[status(thm)],[6251])).
% 27.90/18.11 tff(6253,plain,
% 27.90/18.11 (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))),
% 27.90/18.11 inference(unit_resolution,[status(thm)],[5797, 2730, 6146, 6250, 5532, 6243, 6117])).
% 27.90/18.11 tff(6254,plain,
% 27.90/18.11 (f9(c2, f9(c2, c2)) = f9(c2, c2)),
% 27.90/18.11 inference(transitivity,[status(thm)],[6253, 6252])).
% 27.90/18.11 tff(6255,plain,
% 27.90/18.11 ($false),
% 27.90/18.11 inference(unit_resolution,[status(thm)],[4469, 6254])).
% 27.90/18.11 tff(6256,plain,((f9(c2, f9(c2, c2)) = f9(c2, c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f7(c1) = c1)) | big_f(c2, c2) | (~(c3 = c1)) | (f10(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 27.90/18.11 tff(6257,plain,
% 27.90/18.11 (f9(c2, f9(c2, c2)) = f9(c2, c2)),
% 27.90/18.11 inference(unit_resolution,[status(thm)],[6256, 121, 79, 122, 4234, 148, 172, 3])).
% 27.90/18.11 tff(6258,plain,
% 27.90/18.11 (big_f(f9(c2, f9(c2, c2)), f10(c2)) <=> big_f(f9(c2, c2), c2)),
% 27.90/18.11 inference(monotonicity,[status(thm)],[6257, 122])).
% 27.90/18.11 tff(6259,plain,
% 27.90/18.11 (big_f(f9(c2, c2), c2)),
% 27.90/18.11 inference(modus_ponens,[status(thm)],[6100, 6258])).
% 27.90/18.11 tff(6260,plain,
% 27.90/18.11 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (f6(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f7(c2), f6(c2, f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (f6(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f7(c2), f6(c2, f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))))),
% 27.90/18.11 inference(rewrite,[status(thm)],[])).
% 27.90/18.11 tff(6261,plain,
% 27.90/18.11 (((~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (f6(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f7(c2), f6(c2, f9(c2, c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2)))) <=> ((~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (f6(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f7(c2), f6(c2, f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))))),
% 27.90/18.11 inference(rewrite,[status(thm)],[])).
% 27.90/18.11 tff(6262,plain,
% 27.90/18.11 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (f6(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f7(c2), f6(c2, f9(c2, c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (f6(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f7(c2), f6(c2, f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2)))))),
% 27.90/18.11 inference(monotonicity,[status(thm)],[6261])).
% 27.90/18.11 tff(6263,plain,
% 27.90/18.11 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (f6(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f7(c2), f6(c2, f9(c2, c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (f6(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f7(c2), f6(c2, f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))))),
% 27.90/18.11 inference(transitivity,[status(thm)],[6262, 6260])).
% 27.90/18.11 tff(6264,plain,
% 27.90/18.11 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (f6(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f7(c2), f6(c2, f9(c2, c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))))),
% 27.90/18.11 inference(quant_inst,[status(thm)],[])).
% 27.90/18.11 tff(6265,plain,
% 27.90/18.11 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (f6(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f7(c2), f6(c2, f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2)))),
% 27.90/18.11 inference(modus_ponens,[status(thm)],[6264, 6263])).
% 27.90/18.11 tff(6266,plain,
% 27.90/18.11 ((f6(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f7(c2), f6(c2, f9(c2, c2)))),
% 27.90/18.11 inference(unit_resolution,[status(thm)],[6265, 2409, 122, 77, 1146, 1137])).
% 27.90/18.11 tff(6267,plain,
% 27.90/18.11 ($false),
% 27.90/18.11 inference(unit_resolution,[status(thm)],[6266, 6048, 6044])).
% 27.90/18.11 tff(6268,plain,((~(f6(f7(c2), c3) = c2)) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | big_f(c2, c2) | (~(c3 = c1)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.90/18.11 tff(6269,plain,
% 27.90/18.11 (~(f6(f7(c2), c3) = c2)),
% 27.90/18.11 inference(unit_resolution,[status(thm)],[6268, 77, 122, 1146, 1137, 121, 172, 148, 79])).
% 27.90/18.12 tff(6270,plain,
% 27.90/18.12 (f6(f7(c2), c3) = c1),
% 27.90/18.12 inference(unit_resolution,[status(thm)],[2391, 6269])).
% 27.90/18.12 tff(6271,plain,
% 27.90/18.12 (f6(c2, f9(c2, c2)) = f9(c2, c2)),
% 27.90/18.12 inference(transitivity,[status(thm)],[3461, 5841, 6270, 149, 132])).
% 27.90/18.12 tff(6272,plain,
% 27.90/18.12 (big_f(f7(c2), f6(c2, f9(c2, c2))) <=> big_f(c2, f9(c2, c2))),
% 27.90/18.12 inference(monotonicity,[status(thm)],[77, 6271])).
% 27.90/18.12 tff(6273,plain,
% 27.90/18.12 (big_f(c2, f9(c2, c2)) <=> big_f(f7(c2), f6(c2, f9(c2, c2)))),
% 27.90/18.12 inference(symmetry,[status(thm)],[6272])).
% 27.90/18.12 tff(6274,plain,
% 27.90/18.12 (big_f(f7(c2), f6(c2, f9(c2, c2)))),
% 27.90/18.12 inference(modus_ponens,[status(thm)],[3719, 6273])).
% 27.90/18.12 tff(6275,plain,
% 27.90/18.12 ((~(f6(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f6(c2, f9(c2, c2))))),
% 27.90/18.12 inference(unit_resolution,[status(thm)],[4489, 2378, 122, 77, 1146, 1137])).
% 27.90/18.12 tff(6276,plain,
% 27.90/18.12 ($false),
% 27.90/18.12 inference(unit_resolution,[status(thm)],[6275, 6274, 6271])).
% 27.90/18.12 tff(6277,plain,((~(f7(c2) = c2)) | (~(f10(c2) = c2)) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(c2, f9(c2, c2))) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(c3 = c1)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 27.90/18.12 tff(6278,plain,
% 27.90/18.12 (~(f7(c2) = c2)),
% 27.90/18.12 inference(unit_resolution,[status(thm)],[6277, 6100, 122, 6257, 5832, 148, 79, 172, 121])).
% 27.90/18.12 tff(6279,plain,
% 27.90/18.12 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))),
% 27.90/18.12 inference(unit_resolution,[status(thm)],[5809, 2409, 122, 1146, 1137, 5532, 6238])).
% 27.90/18.12 tff(6280,plain,
% 27.90/18.12 (big_f(f7(c1), f6(c1, c2))),
% 27.90/18.12 inference(unit_resolution,[status(thm)],[5716, 6279, 148, 79, 122])).
% 27.90/18.12 tff(6281,plain,
% 27.90/18.12 (big_f(f7(c2), f6(c1, c2))),
% 27.90/18.12 inference(modus_ponens,[status(thm)],[6280, 5870])).
% 27.90/18.12 tff(6282,plain,
% 27.90/18.12 (big_f(f9(c2, f9(c2, c2)), f10(c2)) <=> big_f(f9(c2, c2), c2)),
% 27.90/18.12 inference(monotonicity,[status(thm)],[1137, 122])).
% 27.90/18.12 tff(6283,plain,
% 27.90/18.12 (big_f(f9(c2, c2), c2)),
% 27.90/18.12 inference(modus_ponens,[status(thm)],[1146, 6282])).
% 27.90/18.12 tff(6284,plain,
% 27.90/18.12 (big_f(f7(c2), c2)),
% 27.90/18.12 inference(modus_ponens,[status(thm)],[6283, 4570])).
% 27.90/18.12 tff(6285,plain,
% 27.90/18.12 (c2 = f5(c2)),
% 27.90/18.12 inference(unit_resolution,[status(thm)],[1196, 1190, 122, 17, 6284, 1146, 1137])).
% 27.90/18.12 tff(6286,plain,
% 27.90/18.12 (f5(c2) = c2),
% 27.90/18.12 inference(symmetry,[status(thm)],[6285])).
% 27.90/18.12 tff(6287,plain,
% 27.90/18.12 ((f6(c1, c2) = f5(c2)) <=> (f6(c1, c2) = c2)),
% 27.90/18.12 inference(monotonicity,[status(thm)],[6286])).
% 27.90/18.12 tff(6288,plain,
% 27.90/18.12 ((f6(c1, c2) = c2) <=> (f6(c1, c2) = f5(c2))),
% 27.90/18.12 inference(symmetry,[status(thm)],[6287])).
% 27.90/18.12 tff(6289,plain,
% 27.90/18.12 ((~(f6(c1, c2) = c2)) <=> (~(f6(c1, c2) = f5(c2)))),
% 27.90/18.12 inference(monotonicity,[status(thm)],[6288])).
% 27.90/18.12 tff(6290,plain,
% 27.90/18.12 (~(f6(c1, c2) = f5(c2))),
% 27.90/18.12 inference(modus_ponens,[status(thm)],[114, 6289])).
% 27.90/18.12 tff(6291,plain,
% 27.90/18.12 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f6(c1, c2))) | (f6(c1, c2) = f5(c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f6(c1, c2))) | (f6(c1, c2) = f5(c2)))),
% 27.90/18.12 inference(rewrite,[status(thm)],[])).
% 27.90/18.12 tff(6292,plain,
% 27.90/18.12 (((~(f10(c2) = c2)) | (f7(c2) = c2) | (f6(c1, c2) = f5(c2)) | (~big_f(f7(c2), f6(c1, c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2)))) <=> ((~(f10(c2) = c2)) | (f7(c2) = c2) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f6(c1, c2))) | (f6(c1, c2) = f5(c2)))),
% 27.90/18.12 inference(rewrite,[status(thm)],[])).
% 27.90/18.12 tff(6293,plain,
% 27.90/18.12 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (f6(c1, c2) = f5(c2)) | (~big_f(f7(c2), f6(c1, c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f6(c1, c2))) | (f6(c1, c2) = f5(c2))))),
% 27.90/18.12 inference(monotonicity,[status(thm)],[6292])).
% 27.90/18.12 tff(6294,plain,
% 27.90/18.12 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (f6(c1, c2) = f5(c2)) | (~big_f(f7(c2), f6(c1, c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f6(c1, c2))) | (f6(c1, c2) = f5(c2)))),
% 27.90/18.12 inference(transitivity,[status(thm)],[6293, 6291])).
% 27.90/18.12 tff(6295,plain,
% 27.90/18.12 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (f6(c1, c2) = f5(c2)) | (~big_f(f7(c2), f6(c1, c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))))),
% 27.90/18.12 inference(quant_inst,[status(thm)],[])).
% 27.90/18.12 tff(6296,plain,
% 27.90/18.12 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f6(c1, c2))) | (f6(c1, c2) = f5(c2))),
% 27.90/18.12 inference(modus_ponens,[status(thm)],[6295, 6294])).
% 27.90/18.12 tff(6297,plain,
% 27.90/18.12 ((~big_f(f7(c2), f6(c1, c2))) | (f6(c1, c2) = f5(c2))),
% 27.90/18.12 inference(unit_resolution,[status(thm)],[6296, 1190, 122, 17, 1146, 1137])).
% 27.90/18.12 tff(6298,plain,
% 27.90/18.12 ($false),
% 27.90/18.12 inference(unit_resolution,[status(thm)],[6297, 6290, 6281])).
% 27.90/18.12 tff(6299,plain,((f7(c2) = c2) | (~(f10(c2) = c2)) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (f6(c1, c2) = c2) | (~(f7(c1) = c1)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.90/18.12 tff(6300,plain,
% 27.90/18.12 (f6(c1, c2) = c2),
% 27.90/18.12 inference(unit_resolution,[status(thm)],[6299, 6278, 6100, 6257, 122, 4234, 148, 79])).
% 27.90/18.12 tff(6301,plain,
% 27.90/18.12 (f9(c2, c1) = c1),
% 27.90/18.12 inference(unit_resolution,[status(thm)],[1141, 6257, 122, 79, 148])).
% 27.90/18.12 tff(6302,plain,
% 27.90/18.12 (big_f(f9(c2, c1), f10(c2))),
% 27.90/18.12 inference(unit_resolution,[status(thm)],[1149, 6100, 122, 79, 148])).
% 27.90/18.12 tff(6303,plain,
% 27.90/18.12 (~big_f(f7(c1), f6(c1, c2))),
% 27.90/18.12 inference(unit_resolution,[status(thm)],[5827, 6300, 122, 4234, 6302, 6301])).
% 27.90/18.12 tff(6304,plain,
% 27.90/18.12 ($false),
% 27.90/18.12 inference(unit_resolution,[status(thm)],[6248, 6303, 6300, 6259, 4234, 148, 79, 122])).
% 27.90/18.12 tff(6305,plain,(big_f(c2, c2) | (~(f7(c1) = c1)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(c3 = c1)) | (f10(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 27.90/18.12 tff(6306,plain,
% 27.90/18.12 (big_f(c2, c2)),
% 27.90/18.12 inference(unit_resolution,[status(thm)],[6305, 3, 148, 79, 122, 4234, 172])).
% 27.90/18.12 tff(6307,plain,
% 27.90/18.12 (big_f(c2, f10(f9(c2, c2)))),
% 27.90/18.12 inference(modus_ponens,[status(thm)],[6306, 5573])).
% 27.90/18.12 tff(6308,plain,
% 27.90/18.12 (big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 27.90/18.12 inference(unit_resolution,[status(thm)],[5985, 114, 79, 122, 16, 4469, 148, 172, 4234, 17])).
% 27.90/18.12 tff(6309,plain,
% 27.90/18.12 (big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))),
% 27.90/18.12 inference(modus_ponens,[status(thm)],[6308, 5755])).
% 27.90/18.12 tff(6310,plain,
% 27.90/18.12 (f10(f9(c2, c2)) = c2),
% 27.90/18.12 inference(transitivity,[status(thm)],[3646, 16])).
% 27.90/18.12 tff(6311,plain,
% 27.90/18.12 (big_f(f9(c2, c2), f10(f9(c2, c2))) <=> big_f(f9(c2, c2), c2)),
% 27.90/18.12 inference(monotonicity,[status(thm)],[6310])).
% 27.90/18.12 tff(6312,plain,
% 27.90/18.12 (big_f(f9(c2, c2), c2) <=> big_f(f9(c2, c2), f10(f9(c2, c2)))),
% 27.90/18.12 inference(symmetry,[status(thm)],[6311])).
% 27.90/18.12 tff(6313,plain,
% 27.90/18.12 (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))),
% 27.90/18.12 inference(unit_resolution,[status(thm)],[5716, 5714, 148, 79, 122])).
% 27.90/18.12 tff(6314,plain,
% 27.90/18.12 (~big_f(f9(c2, c2), f10(f9(c2, c2)))),
% 27.90/18.12 inference(unit_resolution,[status(thm)],[5774, 6313, 5763, 5752, 5532, 6238, 4469])).
% 27.90/18.12 tff(6315,plain,
% 27.90/18.12 (~big_f(f9(c2, c2), f10(c2))),
% 27.90/18.12 inference(unit_resolution,[status(thm)],[3625, 6314, 122, 16, 79, 148])).
% 27.90/18.12 tff(6316,plain,
% 27.90/18.12 (~(f5(c1) = c1)),
% 27.90/18.12 inference(unit_resolution,[status(thm)],[5929, 6315, 122, 17, 4234, 148, 79, 16])).
% 27.90/18.12 tff(6317,plain,
% 27.90/18.12 (f5(c1) = c2),
% 27.90/18.12 inference(unit_resolution,[status(thm)],[1708, 6316])).
% 27.90/18.12 tff(6318,plain,
% 27.90/18.12 (f9(c2, f5(c1)) = f9(c2, c2)),
% 27.90/18.12 inference(monotonicity,[status(thm)],[6317])).
% 27.90/18.12 tff(6319,plain,
% 27.90/18.12 (big_f(f9(c2, f5(c1)), f10(c2)) <=> big_f(f9(c2, c2), c2)),
% 27.90/18.12 inference(monotonicity,[status(thm)],[6318, 122])).
% 27.90/18.12 tff(6320,plain,
% 27.90/18.12 (big_f(f9(c2, f5(c1)), f10(c2)) <=> big_f(f9(c2, c2), f10(f9(c2, c2)))),
% 27.90/18.12 inference(transitivity,[status(thm)],[6319, 6312])).
% 27.90/18.12 tff(6321,plain,
% 27.90/18.12 ((f9(c2, f5(c1)) = f5(c1)) <=> (f9(c2, f5(c1)) = c2)),
% 27.90/18.12 inference(monotonicity,[status(thm)],[6317])).
% 27.90/18.12 tff(6322,plain,
% 27.90/18.12 ((f9(c2, f5(c1)) = c2) <=> (f9(c2, f5(c1)) = f5(c1))),
% 27.90/18.12 inference(symmetry,[status(thm)],[6321])).
% 27.90/18.12 tff(6323,plain,
% 27.90/18.12 ((f9(c2, f5(c1)) = c2) <=> (f9(c2, c2) = c2)),
% 27.90/18.12 inference(monotonicity,[status(thm)],[6318])).
% 27.90/18.12 tff(6324,plain,
% 27.90/18.12 ((f9(c2, c2) = c2) <=> (f9(c2, f5(c1)) = c2)),
% 27.90/18.12 inference(symmetry,[status(thm)],[6323])).
% 27.90/18.12 tff(6325,plain,
% 27.90/18.12 ((f9(c2, c2) = c2) <=> (f9(c2, f5(c1)) = f5(c1))),
% 27.90/18.12 inference(transitivity,[status(thm)],[6324, 6322])).
% 27.90/18.12 tff(6326,plain,
% 27.90/18.12 ((~(f9(c2, c2) = c2)) <=> (~(f9(c2, f5(c1)) = f5(c1)))),
% 27.90/18.12 inference(monotonicity,[status(thm)],[6325])).
% 27.90/18.12 tff(6327,plain,
% 27.90/18.12 (~(f9(c2, f5(c1)) = f5(c1))),
% 27.90/18.12 inference(modus_ponens,[status(thm)],[2650, 6326])).
% 27.90/18.12 tff(6328,assumption,(~(f9(c2, f5(c1)) = f5(c1))), introduced(assumption)).
% 27.90/18.12 tff(6329,plain,
% 27.90/18.12 ((f7(f7(c2)) = f7(c2)) <=> (f7(f7(c2)) = c1)),
% 27.90/18.12 inference(monotonicity,[status(thm)],[292])).
% 27.90/18.12 tff(6330,plain,
% 27.90/18.12 ((f7(f7(c2)) = c1) <=> (f7(f7(c2)) = f7(c2))),
% 27.90/18.12 inference(symmetry,[status(thm)],[6329])).
% 27.90/18.12 tff(6331,plain,
% 27.90/18.12 (f7(f7(c2)) = c1),
% 27.90/18.12 inference(transitivity,[status(thm)],[352, 4234])).
% 27.90/18.12 tff(6332,plain,
% 27.90/18.12 (f7(f7(c2)) = f7(c2)),
% 27.90/18.12 inference(modus_ponens,[status(thm)],[6331, 6330])).
% 27.90/18.12 tff(6333,assumption,(~big_f(f9(c2, f5(c1)), f10(c2))), introduced(assumption)).
% 27.90/18.12 tff(6334,plain,
% 27.90/18.12 ((f6(f7(c2), f5(c1)) = f5(c1)) <=> (f6(f7(c2), f5(c1)) = c2)),
% 27.90/18.12 inference(monotonicity,[status(thm)],[186])).
% 27.90/18.12 tff(6335,plain,
% 27.90/18.12 ((f6(f7(c2), f5(c1)) = c2) <=> (f6(f7(c2), f5(c1)) = f5(c1))),
% 27.90/18.12 inference(symmetry,[status(thm)],[6334])).
% 27.90/18.12 tff(6336,plain,
% 27.90/18.12 (f6(f7(c2), f5(c1)) = f6(c1, c2)),
% 27.90/18.12 inference(monotonicity,[status(thm)],[292, 186])).
% 27.90/18.12 tff(6337,plain,
% 27.90/18.12 ((f6(f7(c2), f5(c1)) = c2) <=> (f6(c1, c2) = c2)),
% 27.90/18.12 inference(monotonicity,[status(thm)],[6336])).
% 27.90/18.12 tff(6338,plain,
% 27.90/18.12 ((f6(c1, c2) = c2) <=> (f6(f7(c2), f5(c1)) = c2)),
% 27.90/18.12 inference(symmetry,[status(thm)],[6337])).
% 27.90/18.12 tff(6339,plain,
% 27.90/18.12 ((f6(c1, c2) = c2) <=> (f6(f7(c2), f5(c1)) = f5(c1))),
% 27.90/18.12 inference(transitivity,[status(thm)],[6338, 6335])).
% 27.90/18.12 tff(6340,plain,
% 27.90/18.12 ((~(f6(c1, c2) = c2)) <=> (~(f6(f7(c2), f5(c1)) = f5(c1)))),
% 27.90/18.12 inference(monotonicity,[status(thm)],[6339])).
% 27.90/18.12 tff(6341,plain,
% 27.90/18.12 (~(f6(f7(c2), f5(c1)) = f5(c1))),
% 27.90/18.12 inference(modus_ponens,[status(thm)],[114, 6340])).
% 27.90/18.12 tff(6342,plain,
% 27.90/18.12 (f7(c2) = f7(f10(c1))),
% 27.90/18.12 inference(symmetry,[status(thm)],[232])).
% 27.90/18.12 tff(6343,plain,
% 27.90/18.12 (f7(f7(c2)) = f7(f10(c1))),
% 27.90/18.12 inference(transitivity,[status(thm)],[352, 4234, 342, 6342])).
% 27.90/18.12 tff(6344,plain,
% 27.90/18.12 (big_f(f7(f7(c2)), f6(f7(c2), f5(c1))) <=> big_f(f7(f10(c1)), f6(f7(c2), f5(c1)))),
% 27.90/18.12 inference(monotonicity,[status(thm)],[6343])).
% 27.90/18.12 tff(6345,plain,
% 27.90/18.12 (big_f(f7(f10(c1)), f6(f7(c2), f5(c1))) <=> big_f(f7(f7(c2)), f6(f7(c2), f5(c1)))),
% 27.90/18.12 inference(symmetry,[status(thm)],[6344])).
% 27.90/18.12 tff(6346,plain,
% 27.90/18.12 (f7(f10(c1)) = f7(c1)),
% 27.90/18.12 inference(transitivity,[status(thm)],[232, 292, 5544])).
% 27.90/18.12 tff(6347,plain,
% 27.90/18.12 (big_f(f7(f10(c1)), f6(f7(c2), f5(c1))) <=> big_f(f7(c1), f6(c1, c2))),
% 27.90/18.12 inference(monotonicity,[status(thm)],[6346, 6336])).
% 27.90/18.12 tff(6348,plain,
% 27.90/18.12 (big_f(f7(c1), f6(c1, c2)) <=> big_f(f7(f10(c1)), f6(f7(c2), f5(c1)))),
% 27.90/18.12 inference(symmetry,[status(thm)],[6347])).
% 27.90/18.12 tff(6349,plain,
% 27.90/18.12 (big_f(f7(c1), f6(c1, c2)) <=> big_f(f7(f7(c2)), f6(f7(c2), f5(c1)))),
% 27.90/18.12 inference(transitivity,[status(thm)],[6348, 6345])).
% 27.90/18.12 tff(6350,plain,
% 27.90/18.12 ((~big_f(f7(c1), f6(c1, c2))) <=> (~big_f(f7(f7(c2)), f6(f7(c2), f5(c1))))),
% 27.90/18.12 inference(monotonicity,[status(thm)],[6349])).
% 27.90/18.12 tff(6351,plain,
% 27.90/18.12 (~big_f(f7(f7(c2)), f6(f7(c2), f5(c1)))),
% 27.90/18.12 inference(modus_ponens,[status(thm)],[5714, 6350])).
% 27.90/18.12 tff(6352,plain,
% 27.90/18.12 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (f9(c2, f5(c1)) = f5(c1)) | big_f(f9(c2, f5(c1)), f10(c2)) | (f6(f7(c2), f5(c1)) = f5(c1)) | big_f(f7(f7(c2)), f6(f7(c2), f5(c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (f9(c2, f5(c1)) = f5(c1)) | big_f(f9(c2, f5(c1)), f10(c2)) | (f6(f7(c2), f5(c1)) = f5(c1)) | big_f(f7(f7(c2)), f6(f7(c2), f5(c1))))),
% 27.90/18.12 inference(rewrite,[status(thm)],[])).
% 27.90/18.12 tff(6353,plain,
% 27.90/18.12 (((~(f10(c2) = c2)) | (f9(c2, f5(c1)) = f5(c1)) | big_f(f9(c2, f5(c1)), f10(c2)) | (~(f7(f7(c2)) = f7(c2))) | (f6(f7(c2), f5(c1)) = f5(c1)) | big_f(f7(f7(c2)), f6(f7(c2), f5(c1)))) <=> ((~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (f9(c2, f5(c1)) = f5(c1)) | big_f(f9(c2, f5(c1)), f10(c2)) | (f6(f7(c2), f5(c1)) = f5(c1)) | big_f(f7(f7(c2)), f6(f7(c2), f5(c1))))),
% 27.94/18.12 inference(rewrite,[status(thm)],[])).
% 27.94/18.12 tff(6354,plain,
% 27.94/18.12 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (f9(c2, f5(c1)) = f5(c1)) | big_f(f9(c2, f5(c1)), f10(c2)) | (~(f7(f7(c2)) = f7(c2))) | (f6(f7(c2), f5(c1)) = f5(c1)) | big_f(f7(f7(c2)), f6(f7(c2), f5(c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (f9(c2, f5(c1)) = f5(c1)) | big_f(f9(c2, f5(c1)), f10(c2)) | (f6(f7(c2), f5(c1)) = f5(c1)) | big_f(f7(f7(c2)), f6(f7(c2), f5(c1)))))),
% 27.94/18.12 inference(monotonicity,[status(thm)],[6353])).
% 27.94/18.12 tff(6355,plain,
% 27.94/18.12 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (f9(c2, f5(c1)) = f5(c1)) | big_f(f9(c2, f5(c1)), f10(c2)) | (~(f7(f7(c2)) = f7(c2))) | (f6(f7(c2), f5(c1)) = f5(c1)) | big_f(f7(f7(c2)), f6(f7(c2), f5(c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (f9(c2, f5(c1)) = f5(c1)) | big_f(f9(c2, f5(c1)), f10(c2)) | (f6(f7(c2), f5(c1)) = f5(c1)) | big_f(f7(f7(c2)), f6(f7(c2), f5(c1))))),
% 27.94/18.12 inference(transitivity,[status(thm)],[6354, 6352])).
% 27.94/18.12 tff(6356,plain,
% 27.94/18.12 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (f9(c2, f5(c1)) = f5(c1)) | big_f(f9(c2, f5(c1)), f10(c2)) | (~(f7(f7(c2)) = f7(c2))) | (f6(f7(c2), f5(c1)) = f5(c1)) | big_f(f7(f7(c2)), f6(f7(c2), f5(c1))))),
% 27.94/18.12 inference(quant_inst,[status(thm)],[])).
% 27.94/18.12 tff(6357,plain,
% 27.94/18.12 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (f9(c2, f5(c1)) = f5(c1)) | big_f(f9(c2, f5(c1)), f10(c2)) | (f6(f7(c2), f5(c1)) = f5(c1)) | big_f(f7(f7(c2)), f6(f7(c2), f5(c1)))),
% 27.94/18.12 inference(modus_ponens,[status(thm)],[6356, 6355])).
% 27.94/18.12 tff(6358,plain,
% 27.94/18.12 ((~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (f9(c2, f5(c1)) = f5(c1)) | big_f(f9(c2, f5(c1)), f10(c2)) | (f6(f7(c2), f5(c1)) = f5(c1)) | big_f(f7(f7(c2)), f6(f7(c2), f5(c1)))),
% 27.94/18.12 inference(unit_resolution,[status(thm)],[6357, 2492])).
% 27.94/18.12 tff(6359,plain,
% 27.94/18.12 ($false),
% 27.94/18.12 inference(unit_resolution,[status(thm)],[6358, 6351, 6341, 122, 6333, 6332, 6328])).
% 27.94/18.12 tff(6360,plain,((~(f7(c2) = c1)) | (~(f10(c2) = c2)) | big_f(f9(c2, f5(c1)), f10(c2)) | (f9(c2, f5(c1)) = f5(c1)) | big_f(f7(c1), f6(c1, c2)) | (~(f5(c1) = c2)) | (~(f7(c1) = c1)) | (~(f10(c1) = c2)) | (f6(c1, c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 27.94/18.12 tff(6361,plain,
% 27.94/18.12 (big_f(f9(c2, f5(c1)), f10(c2))),
% 27.94/18.12 inference(unit_resolution,[status(thm)],[6360, 6327, 122, 114, 5714, 22, 4234, 16, 6317])).
% 27.94/18.12 tff(6362,plain,
% 27.94/18.12 (big_f(f9(c2, c2), f10(f9(c2, c2)))),
% 27.94/18.12 inference(modus_ponens,[status(thm)],[6361, 6320])).
% 27.94/18.12 tff(6363,plain,
% 27.94/18.12 ($false),
% 27.94/18.12 inference(unit_resolution,[status(thm)],[6314, 6362])).
% 27.94/18.12 tff(6364,plain,(big_f(f7(c1), f6(c1, c2)) | (~(f10(c1) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (f6(c1, c2) = c2) | (~(f7(c1) = c1)) | (f7(c2) = c2) | (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))) | (f9(c2, f9(c2, c2)) = f9(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 27.94/18.12 tff(6365,plain,
% 27.94/18.12 (big_f(f7(c1), f6(c1, c2))),
% 27.94/18.12 inference(unit_resolution,[status(thm)],[6364, 114, 148, 79, 122, 16, 4234, 17, 6309, 4469])).
% 27.94/18.12 tff(6366,plain,
% 27.94/18.12 (big_f(f7(c2), f6(c1, c2))),
% 27.94/18.12 inference(modus_ponens,[status(thm)],[6365, 5870])).
% 27.94/18.12 tff(6367,plain,
% 27.94/18.12 ((~big_f(f9(c2, c2), c2)) <=> (~big_f(f9(c2, c2), f10(f9(c2, c2))))),
% 27.94/18.12 inference(monotonicity,[status(thm)],[6312])).
% 27.94/18.12 tff(6368,plain,
% 27.94/18.12 (~big_f(f9(c2, c2), f10(f9(c2, c2)))),
% 27.94/18.12 inference(modus_ponens,[status(thm)],[3685, 6367])).
% 27.94/18.12 tff(6369,assumption,(big_f(f7(c2), f6(c1, c2))), introduced(assumption)).
% 27.94/18.12 tff(6370,plain,
% 27.94/18.12 (~(f5(c1) = c1)),
% 27.94/18.12 inference(unit_resolution,[status(thm)],[5929, 256, 122, 17, 4234, 148, 79, 16])).
% 27.94/18.12 tff(6371,plain,
% 27.94/18.12 (f5(c1) = c2),
% 27.94/18.12 inference(unit_resolution,[status(thm)],[1708, 6370])).
% 27.94/18.12 tff(6372,plain,
% 27.94/18.12 (big_f(c1, f5(c1)) <=> big_f(f9(c2, c2), c2)),
% 27.94/18.12 inference(monotonicity,[status(thm)],[150, 6371])).
% 27.94/18.12 tff(6373,plain,
% 27.94/18.12 (big_f(f9(c2, c2), c2) <=> big_f(c1, f5(c1))),
% 27.94/18.12 inference(symmetry,[status(thm)],[6372])).
% 27.94/18.12 tff(6374,plain,
% 27.94/18.12 (big_f(f9(c2, c2), c2) <=> big_f(f7(c1), f5(c1))),
% 27.94/18.12 inference(transitivity,[status(thm)],[6373, 5933])).
% 27.94/18.12 tff(6375,plain,
% 27.94/18.12 ((~big_f(f9(c2, c2), c2)) <=> (~big_f(f7(c1), f5(c1)))),
% 27.94/18.12 inference(monotonicity,[status(thm)],[6374])).
% 27.94/18.12 tff(6376,plain,
% 27.94/18.12 (~big_f(f7(c1), f5(c1))),
% 27.94/18.12 inference(modus_ponens,[status(thm)],[3685, 6375])).
% 27.94/18.12 tff(6377,plain,
% 27.94/18.12 (big_f(f7(c2), c1) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 27.94/18.12 inference(transitivity,[status(thm)],[4534, 4536])).
% 27.94/18.12 tff(6378,plain,
% 27.94/18.12 (big_f(f7(f10(c1)), f5(f10(c1)))),
% 27.94/18.12 inference(unit_resolution,[status(thm)],[309, 256, 122, 236, 2650])).
% 27.94/18.12 tff(6379,plain,
% 27.94/18.12 (big_f(f7(c2), f5(c2))),
% 27.94/18.12 inference(modus_ponens,[status(thm)],[6378, 296])).
% 27.94/18.12 tff(6380,plain,
% 27.94/18.12 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~big_f(f7(c2), f6(c1, c2))) | (f6(c1, c2) = f5(c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~big_f(f7(c2), f6(c1, c2))) | (f6(c1, c2) = f5(c2)))),
% 27.94/18.12 inference(rewrite,[status(thm)],[])).
% 27.94/18.12 tff(6381,plain,
% 27.94/18.12 (((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(c2) = c2) | (f6(c1, c2) = f5(c2)) | (~big_f(f7(c2), f6(c1, c2)))) <=> ((~(f10(c2) = c2)) | (f7(c2) = c2) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~big_f(f7(c2), f6(c1, c2))) | (f6(c1, c2) = f5(c2)))),
% 27.94/18.12 inference(rewrite,[status(thm)],[])).
% 27.94/18.12 tff(6382,plain,
% 27.94/18.12 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(c2) = c2) | (f6(c1, c2) = f5(c2)) | (~big_f(f7(c2), f6(c1, c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~big_f(f7(c2), f6(c1, c2))) | (f6(c1, c2) = f5(c2))))),
% 27.94/18.12 inference(monotonicity,[status(thm)],[6381])).
% 27.94/18.12 tff(6383,plain,
% 27.94/18.12 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(c2) = c2) | (f6(c1, c2) = f5(c2)) | (~big_f(f7(c2), f6(c1, c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~big_f(f7(c2), f6(c1, c2))) | (f6(c1, c2) = f5(c2)))),
% 27.94/18.12 inference(transitivity,[status(thm)],[6382, 6380])).
% 27.94/18.12 tff(6384,plain,
% 27.94/18.12 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(c2) = c2) | (f6(c1, c2) = f5(c2)) | (~big_f(f7(c2), f6(c1, c2))))),
% 27.94/18.13 inference(quant_inst,[status(thm)],[])).
% 27.94/18.13 tff(6385,plain,
% 27.94/18.13 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~big_f(f7(c2), f6(c1, c2))) | (f6(c1, c2) = f5(c2))),
% 27.94/18.13 inference(modus_ponens,[status(thm)],[6384, 6383])).
% 27.94/18.13 tff(6386,plain,
% 27.94/18.13 (big_f(f9(c2, c2), f10(c2)) | (~big_f(f7(c2), f6(c1, c2))) | (f6(c1, c2) = f5(c2))),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[6385, 676, 122, 17, 2650])).
% 27.94/18.13 tff(6387,plain,
% 27.94/18.13 (f6(c1, c2) = f5(c2)),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[6386, 256, 6369])).
% 27.94/18.13 tff(6388,plain,
% 27.94/18.13 ((f6(c1, c2) = c2) <=> (f5(c2) = c2)),
% 27.94/18.13 inference(monotonicity,[status(thm)],[6387])).
% 27.94/18.13 tff(6389,plain,
% 27.94/18.13 ((f6(c1, c2) = c2) <=> (c2 = f5(c2))),
% 27.94/18.13 inference(transitivity,[status(thm)],[6388, 1279])).
% 27.94/18.13 tff(6390,plain,
% 27.94/18.13 ((f6(c1, c2) = c2) <=> (f5(f10(c1)) = c2)),
% 27.94/18.13 inference(transitivity,[status(thm)],[6389, 5868, 5892])).
% 27.94/18.13 tff(6391,plain,
% 27.94/18.13 ((~(f6(c1, c2) = c2)) <=> (~(f5(f10(c1)) = c2))),
% 27.94/18.13 inference(monotonicity,[status(thm)],[6390])).
% 27.94/18.13 tff(6392,plain,
% 27.94/18.13 (~(f5(f10(c1)) = c2)),
% 27.94/18.13 inference(modus_ponens,[status(thm)],[114, 6391])).
% 27.94/18.13 tff(6393,plain,
% 27.94/18.13 (f5(f10(c1)) = c1),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[326, 6392])).
% 27.94/18.13 tff(6394,plain,
% 27.94/18.13 (big_f(f7(c2), c1)),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[336, 6393, 16, 6379])).
% 27.94/18.13 tff(6395,plain,
% 27.94/18.13 (big_f(f9(c2, c2), f9(c2, c2))),
% 27.94/18.13 inference(modus_ponens,[status(thm)],[6394, 6377])).
% 27.94/18.13 tff(6396,plain,
% 27.94/18.13 (big_f(f7(c1), f6(c1, c1))),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[4658, 6395, 148, 79, 122, 4234, 256])).
% 27.94/18.13 tff(6397,plain,
% 27.94/18.13 (~(f6(f7(c2), c3) = c2)),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[5966, 6396, 172, 6371, 6376, 22])).
% 27.94/18.13 tff(6398,plain,
% 27.94/18.13 (f6(f7(c2), c3) = c1),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[2391, 6397])).
% 27.94/18.13 tff(6399,plain,
% 27.94/18.13 (f6(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)),
% 27.94/18.13 inference(transitivity,[status(thm)],[4594, 5969, 6398, 149, 132])).
% 27.94/18.13 tff(6400,plain,
% 27.94/18.13 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2))) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 27.94/18.13 inference(monotonicity,[status(thm)],[5532, 6399])).
% 27.94/18.13 tff(6401,plain,
% 27.94/18.13 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2)))),
% 27.94/18.13 inference(symmetry,[status(thm)],[6400])).
% 27.94/18.13 tff(6402,plain,
% 27.94/18.13 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2)))),
% 27.94/18.13 inference(modus_ponens,[status(thm)],[6395, 6401])).
% 27.94/18.13 tff(6403,plain,
% 27.94/18.13 ((~(f6(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2))))),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[4676, 2534, 122, 2650, 256, 5532])).
% 27.94/18.13 tff(6404,plain,
% 27.94/18.13 ($false),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[6403, 6402, 6399])).
% 27.94/18.13 tff(6405,plain,(big_f(f9(c2, c2), f10(c2)) | (~(f10(c2) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(c3 = c1)) | (~(f7(c1) = c1)) | (~(f10(c1) = c2)) | big_f(f9(c2, c2), c2) | (f6(c1, c2) = c2) | (~big_f(f7(c2), f6(c1, c2))) | (f7(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 27.94/18.13 tff(6406,plain,
% 27.94/18.13 (big_f(f9(c2, c2), f10(c2))),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[6405, 3685, 148, 79, 172, 4234, 16, 122, 114, 6369, 17])).
% 27.94/18.13 tff(6407,plain,
% 27.94/18.13 (big_f(f9(c2, c2), f10(f9(c2, c2)))),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[3625, 6406, 122, 16, 79, 148])).
% 27.94/18.13 tff(6408,plain,
% 27.94/18.13 ($false),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[6407, 6368])).
% 27.94/18.13 tff(6409,plain,(big_f(f9(c2, c2), c2) | (~(f10(c1) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(c3 = c1)) | (~(f7(c1) = c1)) | (f6(c1, c2) = c2) | (~big_f(f7(c2), f6(c1, c2))) | (f7(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 27.94/18.13 tff(6410,plain,
% 27.94/18.13 (big_f(f9(c2, c2), c2)),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[6409, 114, 148, 79, 122, 172, 4234, 16, 6366, 17])).
% 27.94/18.13 tff(6411,plain,
% 27.94/18.13 (big_f(f9(c2, c2), f10(f9(c2, c2)))),
% 27.94/18.13 inference(modus_ponens,[status(thm)],[6410, 6312])).
% 27.94/18.13 tff(6412,plain,
% 27.94/18.13 (~(f5(f10(c1)) = c2)),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[6241, 6411, 79, 122, 17, 114, 4469, 6309, 16, 148, 4234])).
% 27.94/18.13 tff(6413,plain,
% 27.94/18.13 (f5(f10(c1)) = c1),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[326, 6412])).
% 27.94/18.13 tff(6414,plain,
% 27.94/18.13 (f5(c2) = f9(c2, c2)),
% 27.94/18.13 inference(transitivity,[status(thm)],[294, 6413, 149, 132])).
% 27.94/18.13 tff(6415,plain,
% 27.94/18.13 ((c2 = f5(c2)) <=> (c2 = f9(c2, c2))),
% 27.94/18.13 inference(monotonicity,[status(thm)],[6414])).
% 27.94/18.13 tff(6416,plain,
% 27.94/18.13 ((c2 = f5(c2)) <=> (f9(c2, c2) = c2)),
% 27.94/18.13 inference(transitivity,[status(thm)],[6415, 167])).
% 27.94/18.13 tff(6417,plain,
% 27.94/18.13 ((f9(c2, c2) = c2) <=> (c2 = f5(c2))),
% 27.94/18.13 inference(symmetry,[status(thm)],[6416])).
% 27.94/18.13 tff(6418,plain,
% 27.94/18.13 ((~(f9(c2, c2) = c2)) <=> (~(c2 = f5(c2)))),
% 27.94/18.13 inference(monotonicity,[status(thm)],[6417])).
% 27.94/18.13 tff(6419,plain,
% 27.94/18.13 (~(c2 = f5(c2))),
% 27.94/18.13 inference(modus_ponens,[status(thm)],[2650, 6418])).
% 27.94/18.13 tff(6420,plain,
% 27.94/18.13 (big_f(f7(c2), c2)),
% 27.94/18.13 inference(modus_ponens,[status(thm)],[6410, 4570])).
% 27.94/18.13 tff(6421,plain,
% 27.94/18.13 ((c2 = f5(c2)) | (c2 = f8(f9(c2, c2)))),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[2172, 1659, 17, 6420, 5752, 2016])).
% 27.94/18.13 tff(6422,plain,
% 27.94/18.13 (c2 = f8(f9(c2, c2))),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[6421, 6419])).
% 27.94/18.13 tff(6423,plain,
% 27.94/18.13 (f8(f9(c2, c2)) = c2),
% 27.94/18.13 inference(symmetry,[status(thm)],[6422])).
% 27.94/18.13 tff(6424,plain,
% 27.94/18.13 ((c2 = f5(c2)) | (f9(c2, c2) = f8(f9(c2, c2)))),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[2143, 1659, 17, 6420, 5752, 6411])).
% 27.94/18.13 tff(6425,plain,
% 27.94/18.13 (f9(c2, c2) = f8(f9(c2, c2))),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[6424, 6419])).
% 27.94/18.13 tff(6426,plain,
% 27.94/18.13 (f9(c2, c2) = c2),
% 27.94/18.13 inference(transitivity,[status(thm)],[6425, 6423])).
% 27.94/18.13 tff(6427,plain,
% 27.94/18.13 ($false),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[2650, 6426])).
% 27.94/18.13 tff(6428,plain,((f6(c1, c2) = c2) | (f7(c2) = c2) | (~big_f(c2, f10(f9(c2, c2)))) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f10(c1) = c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | (~(f7(c1) = c1)) | (~(c3 = c1))), inference(lemma,lemma(discharge,[]))).
% 27.94/18.13 tff(6429,plain,
% 27.94/18.13 (f6(c1, c2) = c2),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[6428, 17, 2016, 148, 79, 122, 16, 4469, 4234, 172])).
% 27.94/18.13 tff(6430,plain,
% 27.94/18.13 (f6(f9(c2, c2), c2) = c2),
% 27.94/18.13 inference(modus_ponens,[status(thm)],[6429, 5574])).
% 27.94/18.13 tff(6431,plain,
% 27.94/18.13 (big_f(f7(c1), f6(c1, c2)) <=> big_f(f9(c2, c2), c2)),
% 27.94/18.13 inference(monotonicity,[status(thm)],[4653, 6429])).
% 27.94/18.13 tff(6432,plain,
% 27.94/18.13 (big_f(f9(c2, c2), c2) <=> big_f(f7(c1), f6(c1, c2))),
% 27.94/18.13 inference(symmetry,[status(thm)],[6431])).
% 27.94/18.13 tff(6433,plain,
% 27.94/18.13 (big_f(f9(c2, c2), c2) <=> big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))),
% 27.94/18.13 inference(transitivity,[status(thm)],[6432, 5782])).
% 27.94/18.13 tff(6434,plain,
% 27.94/18.13 ((~big_f(f9(c2, c2), c2)) <=> (~big_f(f9(c2, c2), f10(c2)))),
% 27.94/18.13 inference(monotonicity,[status(thm)],[130])).
% 27.94/18.13 tff(6435,plain,
% 27.94/18.13 (~big_f(f9(c2, c2), f10(c2))),
% 27.94/18.13 inference(modus_ponens,[status(thm)],[3685, 6434])).
% 27.94/18.13 tff(6436,plain,
% 27.94/18.13 (~(f5(c1) = c1)),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[5929, 6435, 122, 17, 4234, 148, 79, 16])).
% 27.94/18.13 tff(6437,plain,
% 27.94/18.13 (f5(c1) = c2),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[1708, 6436])).
% 27.94/18.13 tff(6438,plain,
% 27.94/18.13 (big_f(c1, f5(c1)) <=> big_f(f9(c2, c2), c2)),
% 27.94/18.13 inference(monotonicity,[status(thm)],[150, 6437])).
% 27.94/18.13 tff(6439,plain,
% 27.94/18.13 (big_f(f9(c2, c2), c2) <=> big_f(c1, f5(c1))),
% 27.94/18.13 inference(symmetry,[status(thm)],[6438])).
% 27.94/18.13 tff(6440,plain,
% 27.94/18.13 (big_f(f9(c2, c2), c2) <=> big_f(f7(c1), f5(c1))),
% 27.94/18.13 inference(transitivity,[status(thm)],[6439, 5933])).
% 27.94/18.13 tff(6441,plain,
% 27.94/18.13 ((~big_f(f9(c2, c2), c2)) <=> (~big_f(f7(c1), f5(c1)))),
% 27.94/18.13 inference(monotonicity,[status(thm)],[6440])).
% 27.94/18.13 tff(6442,plain,
% 27.94/18.13 (~big_f(f7(c1), f5(c1))),
% 27.94/18.13 inference(modus_ponens,[status(thm)],[3685, 6441])).
% 27.94/18.13 tff(6443,plain,
% 27.94/18.13 (~(c2 = f5(c2))),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[1527, 267, 122, 17, 1521, 2650, 6435])).
% 27.94/18.13 tff(6444,plain,
% 27.94/18.13 (~(f5(f10(c1)) = c2)),
% 27.94/18.13 inference(modus_ponens,[status(thm)],[6443, 6008])).
% 27.94/18.13 tff(6445,plain,
% 27.94/18.13 (f5(f10(c1)) = c1),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[326, 6444])).
% 27.94/18.13 tff(6446,plain,
% 27.94/18.13 (big_f(f7(f10(c1)), f5(f10(c1)))),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[309, 6435, 122, 236, 2650])).
% 27.94/18.13 tff(6447,plain,
% 27.94/18.13 (big_f(f7(c2), f5(c2))),
% 27.94/18.13 inference(modus_ponens,[status(thm)],[6446, 296])).
% 27.94/18.13 tff(6448,plain,
% 27.94/18.13 (big_f(f7(c2), c1)),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[336, 6447, 16, 6445])).
% 27.94/18.13 tff(6449,plain,
% 27.94/18.13 (big_f(f9(c2, c2), f9(c2, c2))),
% 27.94/18.13 inference(modus_ponens,[status(thm)],[6448, 6377])).
% 27.94/18.13 tff(6450,plain,
% 27.94/18.13 (big_f(f7(c1), f6(c1, c1))),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[4658, 6449, 148, 79, 122, 4234, 6435])).
% 27.94/18.13 tff(6451,plain,
% 27.94/18.13 (~(f6(f7(c2), c3) = c2)),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[5966, 6450, 172, 6437, 6442, 22])).
% 27.94/18.13 tff(6452,plain,
% 27.94/18.13 (f6(f7(c2), c3) = c1),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[2391, 6451])).
% 27.94/18.13 tff(6453,plain,
% 27.94/18.13 (f6(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)),
% 27.94/18.13 inference(transitivity,[status(thm)],[4594, 5969, 6452, 149, 132])).
% 27.94/18.13 tff(6454,plain,
% 27.94/18.13 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2))) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 27.94/18.13 inference(monotonicity,[status(thm)],[5532, 6453])).
% 27.94/18.13 tff(6455,plain,
% 27.94/18.13 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2)))),
% 27.94/18.13 inference(symmetry,[status(thm)],[6454])).
% 27.94/18.13 tff(6456,plain,
% 27.94/18.13 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2)))),
% 27.94/18.13 inference(modus_ponens,[status(thm)],[6449, 6455])).
% 27.94/18.13 tff(6457,plain,
% 27.94/18.13 ((~(f6(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2))))),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[4676, 2534, 122, 2650, 6435, 5532])).
% 27.94/18.13 tff(6458,plain,
% 27.94/18.13 ($false),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[6457, 6456, 6453])).
% 27.94/18.13 tff(6459,plain,(big_f(f7(c2), c2) | (~(f10(c2) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(c3 = c1)) | (~(f7(c1) = c1)) | (~(f10(c1) = c2)) | big_f(f9(c2, c2), c2) | (f7(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 27.94/18.13 tff(6460,plain,
% 27.94/18.13 (big_f(f7(c2), c2)),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[6459, 3685, 148, 79, 172, 4234, 16, 122, 17])).
% 27.94/18.13 tff(6461,plain,
% 27.94/18.13 ($false),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[6460, 4900])).
% 27.94/18.13 tff(6462,plain,(big_f(f9(c2, c2), c2) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(c3 = c1)) | (~(f7(c1) = c1)) | (~(f10(c1) = c2)) | (f7(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 27.94/18.13 tff(6463,plain,
% 27.94/18.13 (big_f(f9(c2, c2), c2)),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[6462, 17, 79, 122, 172, 4234, 16, 148])).
% 27.94/18.13 tff(6464,plain,
% 27.94/18.13 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))),
% 27.94/18.13 inference(modus_ponens,[status(thm)],[6463, 6433])).
% 27.94/18.13 tff(6465,plain,
% 27.94/18.13 (big_f(f9(c2, c2), f10(f9(c2, c2)))),
% 27.94/18.13 inference(modus_ponens,[status(thm)],[6463, 6312])).
% 27.94/18.13 tff(6466,plain,
% 27.94/18.13 (f9(c2, c2) = f8(f9(c2, c2))),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[5789, 2730, 5752, 6465, 6464, 5532, 6430])).
% 27.94/18.13 tff(6467,plain,
% 27.94/18.13 (f8(f9(c2, c2)) = f9(c2, c2)),
% 27.94/18.13 inference(symmetry,[status(thm)],[6466])).
% 27.94/18.13 tff(6468,plain,
% 27.94/18.13 (big_f(f7(c1), f6(c1, c2))),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[6248, 6463, 6429, 4234, 148, 79, 122])).
% 27.94/18.13 tff(6469,plain,
% 27.94/18.13 (big_f(f9(c2, c1), f10(c2))),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[5737, 6468, 122, 4234, 6429, 5835])).
% 27.94/18.13 tff(6470,plain,
% 27.94/18.13 (big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[3898, 6469, 148, 79, 122])).
% 27.94/18.13 tff(6471,plain,
% 27.94/18.13 (big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))),
% 27.94/18.13 inference(modus_ponens,[status(thm)],[6470, 5755])).
% 27.94/18.13 tff(6472,plain,
% 27.94/18.13 (f9(c2, f9(c2, c2)) = f8(f9(c2, c2))),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[5797, 2730, 5752, 6464, 5532, 6430, 6471])).
% 27.94/18.13 tff(6473,plain,
% 27.94/18.13 (f9(c2, f9(c2, c2)) = f9(c2, c2)),
% 27.94/18.13 inference(transitivity,[status(thm)],[6472, 6467])).
% 27.94/18.13 tff(6474,plain,
% 27.94/18.13 ($false),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[4469, 6473])).
% 27.94/18.13 tff(6475,plain,((f7(c2) = c2) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | (~(f10(c2) = c2)) | (~(f10(c1) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f7(c1) = c1)) | (~(c3 = c1)) | (~big_f(c2, f10(f9(c2, c2))))), inference(lemma,lemma(discharge,[]))).
% 27.94/18.13 tff(6476,plain,
% 27.94/18.13 (f9(c2, f9(c2, c2)) = f9(c2, c2)),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[6475, 6307, 122, 17, 148, 79, 4234, 172, 15])).
% 27.94/18.13 tff(6477,plain,
% 27.94/18.13 (f9(c2, c1) = c1),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[1141, 6476, 122, 79, 148])).
% 27.94/18.13 tff(6478,plain,
% 27.94/18.13 (big_f(f9(c2, c2), c2)),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[5557, 17, 79, 122, 148, 4234])).
% 27.94/18.13 tff(6479,plain,
% 27.94/18.13 ((~big_f(f9(c2, c2), f10(c2))) <=> (~big_f(f9(c2, c2), c2))),
% 27.94/18.13 inference(monotonicity,[status(thm)],[129])).
% 27.94/18.13 tff(6480,plain,
% 27.94/18.13 (~big_f(f9(c2, c2), c2)),
% 27.94/18.13 inference(modus_ponens,[status(thm)],[256, 6479])).
% 27.94/18.13 tff(6481,plain,
% 27.94/18.13 ($false),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[2041, 6480])).
% 27.94/18.13 tff(6482,plain,(big_f(f9(c2, c2), f10(c2)) | (~big_f(f9(c2, c2), c2)) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.94/18.13 tff(6483,plain,
% 27.94/18.13 (big_f(f9(c2, c2), f10(c2))),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[6482, 6478, 122])).
% 27.94/18.13 tff(6484,plain,
% 27.94/18.13 (~(f9(c2, c1) = c1)),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[743, 731, 148, 690, 79, 122])).
% 27.94/18.13 tff(6485,plain,
% 27.94/18.13 (f9(c2, c1) = c2),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[3913, 6484])).
% 27.94/18.13 tff(6486,plain,
% 27.94/18.13 ((~(big_f(c2, c2) <=> big_f(f9(c2, f9(c2, c2)), f10(c2)))) | (~big_f(c2, c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 27.94/18.13 inference(tautology,[status(thm)],[])).
% 27.94/18.13 tff(6487,plain,
% 27.94/18.13 (~(big_f(c2, c2) <=> big_f(f9(c2, f9(c2, c2)), f10(c2)))),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[6486, 5086, 1345])).
% 27.94/18.13 tff(6488,plain,
% 27.94/18.13 (~(c2 = f9(c2, f9(c2, c2)))),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[5003, 6487, 4989])).
% 27.94/18.13 tff(6489,plain,
% 27.94/18.13 ($false),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[5012, 6488, 6485, 148, 79, 122])).
% 27.94/18.13 tff(6490,plain,(big_f(f9(c2, c1), f10(c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~big_f(c2, c2)) | (~big_f(f9(c2, c2), f10(c2)))), inference(lemma,lemma(discharge,[]))).
% 27.94/18.13 tff(6491,plain,
% 27.94/18.13 (big_f(f9(c2, c1), f10(c2))),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[6490, 6306, 79, 122, 6483, 148])).
% 27.94/18.13 tff(6492,plain,
% 27.94/18.13 (big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[3898, 6491, 148, 79, 122])).
% 27.94/18.13 tff(6493,plain,
% 27.94/18.13 (f6(c1, c2) = c2),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[6299, 6476, 122, 4234, 17, 6492, 148, 79])).
% 27.94/18.13 tff(6494,plain,
% 27.94/18.13 (big_f(f7(c1), f6(c1, c2))),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[6248, 6493, 148, 4234, 6478, 79, 122])).
% 27.94/18.13 tff(6495,plain,
% 27.94/18.13 ($false),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[5827, 6494, 6493, 122, 4234, 6491, 6477])).
% 27.94/18.13 tff(6496,plain,((f10(c1) = c1) | (~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (f7(c2) = c2) | (~(c3 = c1))), inference(lemma,lemma(discharge,[]))).
% 27.94/18.13 tff(6497,plain,
% 27.94/18.13 (f10(c1) = c1),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[6496, 17, 4234, 148, 79, 122, 172])).
% 27.94/18.13 tff(6498,plain,
% 27.94/18.13 (big_f(f9(c2, c2), c2)),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[5290, 17, 122, 66, 79, 148])).
% 27.94/18.13 tff(6499,plain,
% 27.94/18.13 (big_f(f9(c2, c2), f9(c2, c2))),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[4320, 6498, 148, 79, 122, 4234, 3719, 3762])).
% 27.94/18.13 tff(6500,plain,
% 27.94/18.13 (big_f(f7(c2), c1)),
% 27.94/18.13 inference(modus_ponens,[status(thm)],[6499, 4538])).
% 27.94/18.13 tff(6501,plain,
% 27.94/18.13 (big_f(c1, c1)),
% 27.94/18.13 inference(modus_ponens,[status(thm)],[6500, 4891])).
% 27.94/18.13 tff(6502,plain,
% 27.94/18.13 ($false),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[66, 6501])).
% 27.94/18.13 tff(6503,plain,((f7(c2) = c2) | big_f(c1, c1) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~big_f(c2, f9(c2, c2))) | (~(f10(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 27.94/18.13 tff(6504,plain,
% 27.94/18.13 (~big_f(c2, f9(c2, c2))),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[6503, 6497, 148, 79, 122, 4234, 66, 17])).
% 27.94/18.13 tff(6505,plain,
% 27.94/18.13 (~big_f(c2, c1)),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[3814, 6504, 148, 79, 122])).
% 27.94/18.13 tff(6506,plain,
% 27.94/18.13 (~big_f(c2, c2)),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[5379, 6504, 374, 6478, 148, 79, 122])).
% 27.94/18.13 tff(6507,plain,
% 27.94/18.13 (f2(c1) = f2(f9(c2, c2))),
% 27.94/18.13 inference(monotonicity,[status(thm)],[150])).
% 27.94/18.13 tff(6508,plain,
% 27.94/18.13 (f2(f9(c2, c2)) = f2(c1)),
% 27.94/18.13 inference(symmetry,[status(thm)],[6507])).
% 27.94/18.13 tff(6509,plain,
% 27.94/18.13 (~(c3 = c2)),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[3880, 121, 122, 2, 148, 79])).
% 27.94/18.13 tff(6510,plain,
% 27.94/18.13 (c3 = c1),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[180, 6509])).
% 27.94/18.13 tff(6511,plain,
% 27.94/18.13 (c3 = f9(c2, c2)),
% 27.94/18.13 inference(transitivity,[status(thm)],[6510, 149, 132])).
% 27.94/18.13 tff(6512,plain,
% 27.94/18.13 (f2(c3) = f2(f9(c2, c2))),
% 27.94/18.13 inference(monotonicity,[status(thm)],[6511])).
% 27.94/18.13 tff(6513,plain,
% 27.94/18.13 (f2(c3) = f2(c1)),
% 27.94/18.13 inference(transitivity,[status(thm)],[6512, 6508])).
% 27.94/18.13 tff(6514,plain,
% 27.94/18.13 (big_f(c3, f2(c3)) <=> big_f(c1, f2(c1))),
% 27.94/18.13 inference(monotonicity,[status(thm)],[6510, 6513])).
% 27.94/18.13 tff(6515,plain,
% 27.94/18.13 (~big_f(f4(c4), c4)),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[5036, 121, 79, 2])).
% 27.94/18.13 tff(6516,plain,
% 27.94/18.13 (big_f(c3, f2(c3))),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[1315, 6515])).
% 27.94/18.13 tff(6517,plain,
% 27.94/18.13 (big_f(c1, f2(c1))),
% 27.94/18.13 inference(modus_ponens,[status(thm)],[6516, 6514])).
% 27.94/18.13 tff(6518,assumption,(big_f(c2, c4)), introduced(assumption)).
% 27.94/18.13 tff(6519,plain,
% 27.94/18.13 (big_f(f4(c4), c4)),
% 27.94/18.13 inference(modus_ponens,[status(thm)],[6518, 376])).
% 27.94/18.13 tff(6520,plain,
% 27.94/18.13 ($false),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[379, 6519])).
% 27.94/18.13 tff(6521,plain,((~big_f(c2, c4)) | big_f(f4(c4), c4) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.94/18.13 tff(6522,plain,
% 27.94/18.13 (~big_f(c2, c4)),
% 27.94/18.13 inference(unit_resolution,[status(thm)],[6521, 6515, 79])).
% 27.94/18.13 tff(6523,plain,
% 27.94/18.13 (f9(c2, c2) = c3),
% 27.94/18.13 inference(transitivity,[status(thm)],[160, 148, 5585])).
% 27.94/18.13 tff(6524,plain,
% 27.94/18.13 (f2(f9(c2, c2)) = f2(c3)),
% 27.94/18.13 inference(monotonicity,[status(thm)],[6523])).
% 27.94/18.13 tff(6525,plain,
% 27.94/18.13 (f2(c3) = f2(f9(c2, c2))),
% 27.94/18.13 inference(symmetry,[status(thm)],[6524])).
% 27.94/18.13 tff(6526,plain,
% 27.94/18.13 ((c2 = f2(c3)) <=> (c2 = f2(f9(c2, c2)))),
% 27.94/18.13 inference(monotonicity,[status(thm)],[6525])).
% 27.94/18.13 tff(6527,plain,
% 27.94/18.13 ((c2 = f2(f9(c2, c2))) <=> (c2 = f2(c3))),
% 27.94/18.13 inference(symmetry,[status(thm)],[6526])).
% 27.94/18.13 tff(6528,plain,
% 27.94/18.13 ((c2 = f2(f9(c2, c2))) <=> (f2(c3) = c2)),
% 27.94/18.13 inference(transitivity,[status(thm)],[6527, 3831])).
% 27.94/18.13 tff(6529,plain,
% 27.94/18.13 ((~(c2 = f2(f9(c2, c2)))) <=> (~(f2(c3) = c2))),
% 27.94/18.13 inference(monotonicity,[status(thm)],[6528])).
% 27.94/18.13 tff(6530,plain,
% 27.94/18.13 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))) | (big_f(c2, c4) | (~(c2 = f4(c4))) | (~(c2 = f2(f9(c2, c2)))) | (~(f9(c2, c2) = c3)) | big_f(f9(c2, c2), c2))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))) | big_f(c2, c4) | (~(c2 = f4(c4))) | (~(c2 = f2(f9(c2, c2)))) | (~(f9(c2, c2) = c3)) | big_f(f9(c2, c2), c2))),
% 27.94/18.13 inference(rewrite,[status(thm)],[])).
% 27.94/18.13 tff(6531,plain,
% 27.94/18.13 (((~(f9(c2, c2) = c3)) | (~(c2 = f2(f9(c2, c2)))) | $false | big_f(c2, c4) | (~(c2 = f4(c4))) | big_f(f9(c2, c2), c2)) <=> (big_f(c2, c4) | (~(c2 = f4(c4))) | (~(c2 = f2(f9(c2, c2)))) | (~(f9(c2, c2) = c3)) | big_f(f9(c2, c2), c2))),
% 27.94/18.13 inference(rewrite,[status(thm)],[])).
% 27.94/18.13 tff(6532,plain,
% 27.94/18.13 (((~(f9(c2, c2) = c3)) | (~(c2 = f2(f9(c2, c2)))) | (~(c4 = c4)) | big_f(c2, c4) | (~(c2 = f4(c4))) | big_f(f9(c2, c2), c2)) <=> ((~(f9(c2, c2) = c3)) | (~(c2 = f2(f9(c2, c2)))) | $false | big_f(c2, c4) | (~(c2 = f4(c4))) | big_f(f9(c2, c2), c2))),
% 27.94/18.13 inference(monotonicity,[status(thm)],[410])).
% 27.94/18.13 tff(6533,plain,
% 27.94/18.13 (((~(f9(c2, c2) = c3)) | (~(c2 = f2(f9(c2, c2)))) | (~(c4 = c4)) | big_f(c2, c4) | (~(c2 = f4(c4))) | big_f(f9(c2, c2), c2)) <=> (big_f(c2, c4) | (~(c2 = f4(c4))) | (~(c2 = f2(f9(c2, c2)))) | (~(f9(c2, c2) = c3)) | big_f(f9(c2, c2), c2))),
% 27.94/18.13 inference(transitivity,[status(thm)],[6532, 6531])).
% 27.94/18.13 tff(6534,plain,
% 27.94/18.13 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))) | ((~(f9(c2, c2) = c3)) | (~(c2 = f2(f9(c2, c2)))) | (~(c4 = c4)) | big_f(c2, c4) | (~(c2 = f4(c4))) | big_f(f9(c2, c2), c2))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))) | (big_f(c2, c4) | (~(c2 = f4(c4))) | (~(c2 = f2(f9(c2, c2)))) | (~(f9(c2, c2) = c3)) | big_f(f9(c2, c2), c2)))),
% 27.95/18.13 inference(monotonicity,[status(thm)],[6533])).
% 27.95/18.13 tff(6535,plain,
% 27.95/18.13 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))) | ((~(f9(c2, c2) = c3)) | (~(c2 = f2(f9(c2, c2)))) | (~(c4 = c4)) | big_f(c2, c4) | (~(c2 = f4(c4))) | big_f(f9(c2, c2), c2))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))) | big_f(c2, c4) | (~(c2 = f4(c4))) | (~(c2 = f2(f9(c2, c2)))) | (~(f9(c2, c2) = c3)) | big_f(f9(c2, c2), c2))),
% 27.95/18.13 inference(transitivity,[status(thm)],[6534, 6530])).
% 27.95/18.13 tff(6536,plain,
% 27.95/18.13 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))) | ((~(f9(c2, c2) = c3)) | (~(c2 = f2(f9(c2, c2)))) | (~(c4 = c4)) | big_f(c2, c4) | (~(c2 = f4(c4))) | big_f(f9(c2, c2), c2))),
% 27.95/18.13 inference(quant_inst,[status(thm)],[])).
% 27.95/18.13 tff(6537,plain,
% 27.95/18.13 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))) | big_f(c2, c4) | (~(c2 = f4(c4))) | (~(c2 = f2(f9(c2, c2)))) | (~(f9(c2, c2) = c3)) | big_f(f9(c2, c2), c2)),
% 27.95/18.13 inference(modus_ponens,[status(thm)],[6536, 6535])).
% 27.95/18.13 tff(6538,plain,
% 27.95/18.13 (~(c2 = f2(f9(c2, c2)))),
% 27.95/18.13 inference(unit_resolution,[status(thm)],[6537, 1300, 3865, 2602, 5580, 3685])).
% 27.95/18.13 tff(6539,plain,
% 27.95/18.13 (~(f2(c3) = c2)),
% 27.95/18.13 inference(modus_ponens,[status(thm)],[6538, 6529])).
% 27.95/18.13 tff(6540,plain,
% 27.95/18.13 (f2(c3) = c1),
% 27.95/18.13 inference(unit_resolution,[status(thm)],[1273, 6539])).
% 27.95/18.13 tff(6541,plain,
% 27.95/18.13 (f2(f9(c2, c2)) = c1),
% 27.95/18.13 inference(transitivity,[status(thm)],[6524, 6540])).
% 27.95/18.13 tff(6542,plain,
% 27.95/18.13 ((f6(c1, c1) = f2(f9(c2, c2))) <=> (f6(c1, c1) = c1)),
% 27.95/18.13 inference(monotonicity,[status(thm)],[6541])).
% 27.95/18.13 tff(6543,plain,
% 27.95/18.13 ((f6(c1, c1) = f2(f9(c2, c2))) <=> (f6(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))),
% 27.95/18.13 inference(transitivity,[status(thm)],[6542, 4596])).
% 27.95/18.13 tff(6544,plain,
% 27.95/18.13 (f2(c1) = f9(c2, c2)),
% 27.95/18.13 inference(transitivity,[status(thm)],[6507, 6524, 6540, 149, 132])).
% 27.95/18.13 tff(6545,plain,
% 27.95/18.13 (big_f(c1, f2(c1)) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 27.95/18.13 inference(monotonicity,[status(thm)],[150, 6544])).
% 27.95/18.13 tff(6546,assumption,(big_f(c1, f2(c1))), introduced(assumption)).
% 27.95/18.13 tff(6547,plain,
% 27.95/18.13 (big_f(f9(c2, c2), f9(c2, c2))),
% 27.95/18.13 inference(modus_ponens,[status(thm)],[6546, 6545])).
% 27.95/18.13 tff(6548,plain,
% 27.95/18.13 (big_f(f7(c1), f6(c1, c1))),
% 27.95/18.13 inference(unit_resolution,[status(thm)],[4658, 6547, 148, 79, 122, 4234, 4597])).
% 27.95/18.13 tff(6549,plain,
% 27.95/18.13 (big_f(f9(c2, c2), f6(c1, c1))),
% 27.95/18.13 inference(modus_ponens,[status(thm)],[6548, 5605])).
% 27.95/18.13 tff(6550,plain,
% 27.95/18.13 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (big_f(c2, c4) | (~(c2 = f4(c4))) | (~(f9(c2, c2) = c3)) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | big_f(c2, c4) | (~(c2 = f4(c4))) | (~(f9(c2, c2) = c3)) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1))))),
% 27.95/18.13 inference(rewrite,[status(thm)],[])).
% 27.95/18.13 tff(6551,plain,
% 27.95/18.13 (((~(f9(c2, c2) = c3)) | $false | big_f(c2, c4) | (~(c2 = f4(c4))) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1)))) <=> (big_f(c2, c4) | (~(c2 = f4(c4))) | (~(f9(c2, c2) = c3)) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1))))),
% 27.95/18.13 inference(rewrite,[status(thm)],[])).
% 27.95/18.13 tff(6552,plain,
% 27.95/18.13 (((~(f9(c2, c2) = c3)) | (~(c4 = c4)) | big_f(c2, c4) | (~(c2 = f4(c4))) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1)))) <=> ((~(f9(c2, c2) = c3)) | $false | big_f(c2, c4) | (~(c2 = f4(c4))) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1))))),
% 27.95/18.14 inference(monotonicity,[status(thm)],[410])).
% 27.95/18.14 tff(6553,plain,
% 27.95/18.14 (((~(f9(c2, c2) = c3)) | (~(c4 = c4)) | big_f(c2, c4) | (~(c2 = f4(c4))) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1)))) <=> (big_f(c2, c4) | (~(c2 = f4(c4))) | (~(f9(c2, c2) = c3)) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1))))),
% 27.95/18.14 inference(transitivity,[status(thm)],[6552, 6551])).
% 27.95/18.14 tff(6554,plain,
% 27.95/18.14 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c2, c2) = c3)) | (~(c4 = c4)) | big_f(c2, c4) | (~(c2 = f4(c4))) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (big_f(c2, c4) | (~(c2 = f4(c4))) | (~(f9(c2, c2) = c3)) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1)))))),
% 27.95/18.14 inference(monotonicity,[status(thm)],[6553])).
% 27.95/18.14 tff(6555,plain,
% 27.95/18.14 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c2, c2) = c3)) | (~(c4 = c4)) | big_f(c2, c4) | (~(c2 = f4(c4))) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | big_f(c2, c4) | (~(c2 = f4(c4))) | (~(f9(c2, c2) = c3)) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1))))),
% 27.95/18.14 inference(transitivity,[status(thm)],[6554, 6550])).
% 27.95/18.14 tff(6556,plain,
% 27.95/18.14 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c2, c2) = c3)) | (~(c4 = c4)) | big_f(c2, c4) | (~(c2 = f4(c4))) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1))))),
% 27.95/18.14 inference(quant_inst,[status(thm)],[])).
% 27.95/18.14 tff(6557,plain,
% 27.95/18.14 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | big_f(c2, c4) | (~(c2 = f4(c4))) | (~(f9(c2, c2) = c3)) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1)))),
% 27.95/18.14 inference(modus_ponens,[status(thm)],[6556, 6555])).
% 27.95/18.14 tff(6558,plain,
% 27.95/18.14 ((f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1)))),
% 27.95/18.14 inference(unit_resolution,[status(thm)],[6557, 5622, 3865, 2602, 5580])).
% 27.95/18.14 tff(6559,plain,
% 27.95/18.14 (f6(c1, c1) = f2(f9(c2, c2))),
% 27.95/18.14 inference(unit_resolution,[status(thm)],[6558, 6549])).
% 27.95/18.14 tff(6560,plain,
% 27.95/18.14 (f6(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)),
% 27.95/18.14 inference(modus_ponens,[status(thm)],[6559, 6543])).
% 27.95/18.14 tff(6561,plain,
% 27.95/18.14 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2)))),
% 27.95/18.14 inference(modus_ponens,[status(thm)],[6548, 4671])).
% 27.95/18.14 tff(6562,plain,
% 27.95/18.14 (~(f6(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))),
% 27.95/18.14 inference(unit_resolution,[status(thm)],[5554, 6561])).
% 27.95/18.14 tff(6563,plain,
% 27.95/18.14 ($false),
% 27.95/18.14 inference(unit_resolution,[status(thm)],[6562, 6560])).
% 27.95/18.14 tff(6564,plain,(big_f(f9(c2, c2), c2) | (~(c3 = c1)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | big_f(c2, c4) | (~(f7(c1) = c1)) | (~big_f(c1, f2(c1)))), inference(lemma,lemma(discharge,[]))).
% 27.95/18.14 tff(6565,plain,
% 27.95/18.14 (big_f(f9(c2, c2), c2)),
% 27.95/18.14 inference(unit_resolution,[status(thm)],[6564, 6510, 148, 79, 122, 6522, 4234, 6517])).
% 27.95/18.14 tff(6566,plain,
% 27.95/18.14 (f9(c2, c2) = c3),
% 27.95/18.14 inference(modus_ponens,[status(thm)],[6510, 5579])).
% 27.95/18.14 tff(6567,plain,
% 27.95/18.14 (big_f(f9(c2, c2), f10(c2))),
% 27.95/18.14 inference(unit_resolution,[status(thm)],[6482, 6565, 122])).
% 27.95/18.14 tff(6568,plain,
% 27.95/18.14 (big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 27.95/18.14 inference(unit_resolution,[status(thm)],[5747, 6567, 79, 122, 4234, 6566, 148, 6522])).
% 27.95/18.14 tff(6569,plain,
% 27.95/18.14 (~(big_f(c2, c2) <=> big_f(f9(c2, f9(c2, c2)), f10(c2)))),
% 27.95/18.14 inference(unit_resolution,[status(thm)],[4996, 6568, 121])).
% 27.95/18.14 tff(6570,plain,
% 27.95/18.14 (~(c2 = f9(c2, f9(c2, c2)))),
% 27.95/18.14 inference(unit_resolution,[status(thm)],[5003, 6569, 4989])).
% 27.95/18.14 tff(6571,plain,
% 27.95/18.14 (~(f9(c2, c1) = c2)),
% 27.95/18.14 inference(unit_resolution,[status(thm)],[5012, 6570, 148, 79, 122])).
% 27.95/18.14 tff(6572,plain,
% 27.95/18.14 (f9(c2, c1) = c1),
% 27.95/18.14 inference(unit_resolution,[status(thm)],[3913, 6571])).
% 27.95/18.14 tff(6573,plain,
% 27.95/18.14 (f9(c2, f9(c2, c2)) = f9(c2, c2)),
% 27.95/18.14 inference(unit_resolution,[status(thm)],[4579, 6572, 148, 79, 122])).
% 27.95/18.14 tff(6574,plain,
% 27.95/18.14 (c2 = f2(f9(c2, c2))),
% 27.95/18.14 inference(unit_resolution,[status(thm)],[5687, 5622, 6522, 2602, 6566, 6565])).
% 27.95/18.14 tff(6575,plain,
% 27.95/18.14 (f6(c1, c2) = c2),
% 27.95/18.14 inference(unit_resolution,[status(thm)],[5814, 6574, 148, 4234, 6566, 79, 122, 6522, 6568, 6573])).
% 27.95/18.14 tff(6576,plain,
% 27.95/18.14 (big_f(f9(c2, c1), f10(c2))),
% 27.95/18.14 inference(unit_resolution,[status(thm)],[1149, 6568, 122, 79, 148])).
% 27.95/18.14 tff(6577,plain,
% 27.95/18.14 (~big_f(f7(c1), f6(c1, c2))),
% 27.95/18.14 inference(unit_resolution,[status(thm)],[5827, 6575, 122, 4234, 6576, 6572])).
% 27.95/18.14 tff(6578,plain,
% 27.95/18.14 ($false),
% 27.95/18.14 inference(unit_resolution,[status(thm)],[6248, 6577, 6575, 148, 4234, 6565, 79, 122])).
% 27.95/18.14 tff(6579,plain,(big_f(c2, c2) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f7(c1) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | big_f(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 27.95/18.14 tff(6580,plain,
% 27.95/18.14 ($false),
% 27.95/18.14 inference(unit_resolution,[status(thm)],[6579, 6506, 6505, 79, 4234, 122, 148])).
% 27.95/18.14 tff(6581,plain,((f7(c2) = c2) | (~(f4(c4) = c2)) | (~(f7(c1) = c1)) | (~(f10(c2) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | big_f(c1, c1) | (~(c3 = c1))), inference(lemma,lemma(discharge,[]))).
% 27.95/18.14 tff(6582,plain,
% 27.95/18.14 (f7(c2) = c2),
% 27.95/18.14 inference(unit_resolution,[status(thm)],[6581, 66, 4234, 122, 148, 79, 172])).
% 27.95/18.14 tff(6583,plain,
% 27.95/18.14 (big_f(f7(c2), f6(c2, c2))),
% 27.95/18.14 inference(unit_resolution,[status(thm)],[2700, 6306, 79, 6582, 15, 122])).
% 27.95/18.14 tff(6584,plain,
% 27.95/18.14 (c2 = f7(c2)),
% 27.95/18.14 inference(symmetry,[status(thm)],[6582])).
% 27.95/18.14 tff(6585,plain,
% 27.95/18.14 (f6(c2, f9(c2, c2)) = f6(f7(c2), c3)),
% 27.95/18.14 inference(monotonicity,[status(thm)],[6584, 6523])).
% 27.95/18.14 tff(6586,plain,
% 27.95/18.14 (f6(f7(c2), c3) = f6(c2, f9(c2, c2))),
% 27.95/18.14 inference(symmetry,[status(thm)],[6585])).
% 27.95/18.14 tff(6587,plain,
% 27.95/18.14 ((f6(f7(c2), c3) = c1) <=> (f6(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.95/18.14 inference(monotonicity,[status(thm)],[6586, 150])).
% 27.95/18.14 tff(6588,plain,
% 27.95/18.14 ((f6(c2, f9(c2, c2)) = f9(c2, c2)) <=> (f6(f7(c2), c3) = c1)),
% 27.95/18.14 inference(symmetry,[status(thm)],[6587])).
% 27.95/18.14 tff(6589,plain,
% 27.95/18.14 ((~(f6(c2, f9(c2, c2)) = f9(c2, c2))) <=> (~(f6(f7(c2), c3) = c1))),
% 27.95/18.14 inference(monotonicity,[status(thm)],[6588])).
% 27.95/18.14 tff(6590,plain,
% 27.95/18.14 (c2 = f7(f4(c4))),
% 27.95/18.14 inference(transitivity,[status(thm)],[6584, 81])).
% 27.95/18.14 tff(6591,plain,
% 27.95/18.14 (f6(c2, c2) = f6(c2, f7(f4(c4)))),
% 27.95/18.14 inference(monotonicity,[status(thm)],[6590])).
% 27.95/18.14 tff(6592,plain,
% 27.95/18.14 (f6(c2, f7(f4(c4))) = f6(c2, c2)),
% 27.95/18.14 inference(symmetry,[status(thm)],[6591])).
% 27.95/18.14 tff(6593,plain,
% 27.95/18.14 ((f6(c2, f7(f4(c4))) = c2) <=> (f6(c2, c2) = c2)),
% 27.95/18.14 inference(monotonicity,[status(thm)],[6592])).
% 27.95/18.14 tff(6594,plain,
% 27.95/18.14 ((f6(c2, c2) = c2) <=> (f6(c2, f7(f4(c4))) = c2)),
% 27.95/18.14 inference(symmetry,[status(thm)],[6593])).
% 27.95/18.14 tff(6595,plain,
% 27.95/18.14 ((~(f6(c2, c2) = c2)) <=> (~(f6(c2, f7(f4(c4))) = c2))),
% 27.95/18.14 inference(monotonicity,[status(thm)],[6594])).
% 27.95/18.14 tff(6596,plain,
% 27.95/18.14 (~(f6(c2, c2) = c2)),
% 27.95/18.14 inference(unit_resolution,[status(thm)],[2744, 4597, 6582, 2707, 185, 122])).
% 27.95/18.14 tff(6597,plain,
% 27.95/18.14 (~(f6(c2, f7(f4(c4))) = c2)),
% 27.95/18.14 inference(modus_ponens,[status(thm)],[6596, 6595])).
% 27.95/18.14 tff(6598,plain,
% 27.95/18.14 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f6(c2, f7(f4(c4))) = c1) | (f6(c2, f7(f4(c4))) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f6(c2, f7(f4(c4))) = c1) | (f6(c2, f7(f4(c4))) = c2))),
% 27.95/18.14 inference(rewrite,[status(thm)],[])).
% 27.95/18.14 tff(6599,plain,
% 27.95/18.14 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f6(c2, f7(f4(c4))) = c1) | (f6(c2, f7(f4(c4))) = c2))),
% 27.95/18.14 inference(quant_inst,[status(thm)],[])).
% 27.95/18.14 tff(6600,plain,
% 27.95/18.14 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f6(c2, f7(f4(c4))) = c1) | (f6(c2, f7(f4(c4))) = c2)),
% 27.95/18.14 inference(modus_ponens,[status(thm)],[6599, 6598])).
% 27.95/18.14 tff(6601,plain,
% 27.95/18.14 ((f6(c2, f7(f4(c4))) = c1) | (f6(c2, f7(f4(c4))) = c2)),
% 27.95/18.14 inference(unit_resolution,[status(thm)],[6600, 10])).
% 27.95/18.14 tff(6602,plain,
% 27.95/18.14 (f6(c2, f7(f4(c4))) = c1),
% 27.95/18.14 inference(unit_resolution,[status(thm)],[6601, 6597])).
% 27.95/18.14 tff(6603,plain,
% 27.95/18.14 (f6(c2, c2) = f9(c2, c2)),
% 27.95/18.14 inference(transitivity,[status(thm)],[6591, 6602, 149, 132])).
% 27.95/18.14 tff(6604,plain,
% 27.95/18.14 (big_f(f7(c2), f6(c2, c2)) <=> big_f(c2, f9(c2, c2))),
% 27.95/18.14 inference(monotonicity,[status(thm)],[6582, 6603])).
% 27.95/18.14 tff(6605,plain,
% 27.95/18.14 (big_f(c2, f9(c2, c2))),
% 27.95/18.14 inference(modus_ponens,[status(thm)],[2707, 6604])).
% 27.95/18.14 tff(6606,plain,
% 27.95/18.14 ((f6(c2, f9(c2, c2)) = f9(c2, c2)) <=> (f6(c2, c1) = c1)),
% 27.95/18.14 inference(monotonicity,[status(thm)],[3461, 161])).
% 27.95/18.14 tff(6607,plain,
% 27.95/18.14 ((f6(c2, c1) = c1) <=> (f6(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.95/18.14 inference(symmetry,[status(thm)],[6606])).
% 27.95/18.14 tff(6608,plain,
% 27.95/18.14 ((~(f6(c2, c1) = c1)) <=> (~(f6(c2, f9(c2, c2)) = f9(c2, c2)))),
% 27.95/18.14 inference(monotonicity,[status(thm)],[6607])).
% 27.95/18.14 tff(6609,plain,
% 27.95/18.14 (f6(c2, c1) = f9(c2, c2)),
% 27.95/18.14 inference(transitivity,[status(thm)],[3079, 149, 132])).
% 27.95/18.14 tff(6610,plain,
% 27.95/18.14 (big_f(f7(c2), f6(c2, c1)) <=> big_f(c2, f9(c2, c2))),
% 27.95/18.14 inference(monotonicity,[status(thm)],[77, 6609])).
% 27.95/18.14 tff(6611,plain,
% 27.95/18.14 (big_f(c2, f9(c2, c2)) <=> big_f(f7(c2), f6(c2, c1))),
% 27.95/18.14 inference(symmetry,[status(thm)],[6610])).
% 27.95/18.14 tff(6612,plain,
% 27.95/18.14 (big_f(f7(c2), f6(c2, c1))),
% 27.95/18.14 inference(modus_ponens,[status(thm)],[3719, 6611])).
% 27.95/18.14 tff(6613,plain,
% 27.95/18.14 ($false),
% 27.95/18.14 inference(unit_resolution,[status(thm)],[3197, 6612])).
% 27.95/18.14 tff(6614,plain,((~(f6(c2, c1) = c1)) | big_f(f7(c2), f6(c2, c1)) | (~big_f(c2, f9(c2, c2))) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f7(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.95/18.14 tff(6615,plain,
% 27.95/18.14 (~(f6(c2, c1) = c1)),
% 27.95/18.14 inference(unit_resolution,[status(thm)],[6614, 3197, 3719, 148, 79, 122, 77])).
% 27.95/18.14 tff(6616,plain,
% 27.95/18.14 (~(f6(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.95/18.14 inference(modus_ponens,[status(thm)],[6615, 6608])).
% 27.95/18.14 tff(6617,plain,
% 27.95/18.14 (big_f(f7(c2), f6(c2, f9(c2, c2))) <=> big_f(f7(c2), f6(c2, c1))),
% 27.95/18.14 inference(monotonicity,[status(thm)],[3461])).
% 27.95/18.14 tff(6618,plain,
% 27.95/18.14 (big_f(f7(c2), f6(c2, c1)) <=> big_f(f7(c2), f6(c2, f9(c2, c2)))),
% 27.95/18.14 inference(symmetry,[status(thm)],[6617])).
% 27.95/18.14 tff(6619,plain,
% 27.95/18.14 ((~big_f(f7(c2), f6(c2, c1))) <=> (~big_f(f7(c2), f6(c2, f9(c2, c2))))),
% 27.95/18.14 inference(monotonicity,[status(thm)],[6618])).
% 27.95/18.14 tff(6620,plain,
% 27.95/18.14 (~big_f(f7(c2), f6(c2, f9(c2, c2)))),
% 27.95/18.14 inference(modus_ponens,[status(thm)],[3197, 6619])).
% 27.95/18.14 tff(6621,plain,
% 27.95/18.14 ((f6(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f7(c2), f6(c2, f9(c2, c2)))),
% 27.95/18.14 inference(unit_resolution,[status(thm)],[3477, 2492, 122, 77, 185, 256])).
% 27.95/18.14 tff(6622,plain,
% 27.95/18.14 ($false),
% 27.95/18.14 inference(unit_resolution,[status(thm)],[6621, 6620, 6616])).
% 27.95/18.14 tff(6623,plain,(big_f(f7(c2), f6(c2, c1)) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | big_f(f9(c2, c2), f10(c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~big_f(c2, f9(c2, c2)))), inference(lemma,lemma(discharge,[]))).
% 27.95/18.14 tff(6624,plain,
% 27.95/18.14 (big_f(f7(c2), f6(c2, c1))),
% 27.95/18.14 inference(unit_resolution,[status(thm)],[6623, 6605, 148, 4597, 6582, 79, 122])).
% 27.95/18.14 tff(6625,plain,
% 27.95/18.14 (big_f(f7(c2), f6(c2, f9(c2, c2)))),
% 27.95/18.14 inference(modus_ponens,[status(thm)],[6624, 4442])).
% 27.95/18.14 tff(6626,plain,
% 27.95/18.14 (~(f6(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.95/18.14 inference(unit_resolution,[status(thm)],[3495, 2534, 122, 6582, 185, 4597, 6625])).
% 27.95/18.14 tff(6627,plain,
% 27.95/18.14 (~(f6(f7(c2), c3) = c1)),
% 27.95/18.14 inference(modus_ponens,[status(thm)],[6626, 6589])).
% 27.95/18.14 tff(6628,plain,
% 27.95/18.14 (f6(f7(c2), c3) = c2),
% 27.95/18.14 inference(unit_resolution,[status(thm)],[2391, 6627])).
% 27.95/18.14 tff(6629,plain,
% 27.95/18.14 ((f2(c3) = c2) <=> (c2 = f2(f9(c2, c2)))),
% 27.95/18.14 inference(transitivity,[status(thm)],[1434, 6526])).
% 27.95/18.14 tff(6630,plain,
% 27.95/18.14 ((f9(c2, c2) = f2(f9(c2, c2))) <=> (c1 = f2(c1))),
% 27.95/18.14 inference(monotonicity,[status(thm)],[161, 6508])).
% 27.95/18.14 tff(6631,plain,
% 27.95/18.14 ((c1 = f2(c1)) <=> (f9(c2, c2) = f2(f9(c2, c2)))),
% 27.95/18.14 inference(symmetry,[status(thm)],[6630])).
% 27.95/18.14 tff(6632,assumption,(c1 = f2(c1)), introduced(assumption)).
% 27.95/18.14 tff(6633,plain,
% 27.95/18.14 (f9(c2, c2) = f2(f9(c2, c2))),
% 27.95/18.14 inference(modus_ponens,[status(thm)],[6632, 6631])).
% 27.95/18.14 tff(6634,assumption,(f6(c2, f7(f4(c4))) = c1), introduced(assumption)).
% 27.95/18.14 tff(6635,plain,
% 27.95/18.14 (f6(c2, f7(f4(c4))) = f9(c2, c2)),
% 27.95/18.14 inference(transitivity,[status(thm)],[6634, 149, 132])).
% 27.95/18.14 tff(6636,plain,
% 27.95/18.14 ((f6(c2, f7(f4(c4))) = c4) <=> (f9(c2, c2) = c4)),
% 27.95/18.14 inference(monotonicity,[status(thm)],[6635])).
% 27.95/18.14 tff(6637,plain,
% 27.95/18.14 ((f9(c2, c2) = c4) <=> (f6(c2, f7(f4(c4))) = c4)),
% 27.95/18.14 inference(symmetry,[status(thm)],[6636])).
% 27.95/18.14 tff(6638,plain,
% 27.95/18.14 ((~(f9(c2, c2) = c4)) <=> (~(f6(c2, f7(f4(c4))) = c4))),
% 27.95/18.14 inference(monotonicity,[status(thm)],[6637])).
% 27.95/18.14 tff(6639,plain,
% 27.95/18.14 (~(f6(c2, f7(f4(c4))) = c4)),
% 27.95/18.14 inference(modus_ponens,[status(thm)],[1861, 6638])).
% 27.95/18.14 tff(6640,plain,
% 27.95/18.14 (f3(f6(c2, f7(f4(c4))), c2) = f3(c1, c2)),
% 27.95/18.14 inference(monotonicity,[status(thm)],[6634])).
% 27.95/18.14 tff(6641,plain,
% 27.95/18.14 ((f3(f6(c2, f7(f4(c4))), c2) = c2) <=> (f3(c1, c2) = c2)),
% 27.95/18.14 inference(monotonicity,[status(thm)],[6640])).
% 27.95/18.14 tff(6642,plain,
% 27.95/18.14 ((f3(c1, c2) = c2) <=> (f3(f6(c2, f7(f4(c4))), c2) = c2)),
% 27.95/18.14 inference(symmetry,[status(thm)],[6641])).
% 27.95/18.14 tff(6643,plain,
% 27.95/18.14 ((c2 = f3(c1, c2)) <=> (f3(c1, c2) = c2)),
% 27.95/18.14 inference(commutativity,[status(thm)],[])).
% 27.95/18.14 tff(6644,plain,
% 27.95/18.14 (f3(f9(c2, c2), c2) = f3(c1, c2)),
% 27.95/18.14 inference(monotonicity,[status(thm)],[161])).
% 27.95/18.14 tff(6645,plain,
% 27.95/18.14 (big_f(f3(f9(c2, c2), c2), f9(c2, c2)) <=> big_f(f3(c1, c2), c1)),
% 27.95/18.14 inference(monotonicity,[status(thm)],[6644, 161])).
% 27.95/18.14 tff(6646,plain,
% 27.95/18.14 (big_f(f3(c1, c2), c1) <=> big_f(f3(f9(c2, c2), c2), f9(c2, c2))),
% 27.95/18.14 inference(symmetry,[status(thm)],[6645])).
% 27.95/18.14 tff(6647,assumption,(f6(c1, f3(c1, c2)) = c1), introduced(assumption)).
% 27.95/18.14 tff(6648,plain,
% 27.95/18.14 (f6(f9(c2, c2), f3(c1, c2)) = f6(c1, f3(c1, c2))),
% 27.95/18.14 inference(monotonicity,[status(thm)],[161])).
% 27.95/18.14 tff(6649,plain,
% 27.95/18.14 (f6(f9(c2, c2), f3(c1, c2)) = f9(c2, c2)),
% 27.95/18.14 inference(transitivity,[status(thm)],[6648, 6647, 149, 132])).
% 27.95/18.14 tff(6650,plain,
% 27.95/18.14 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(c1, c2))) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 27.95/18.14 inference(monotonicity,[status(thm)],[5532, 6649])).
% 27.95/18.14 tff(6651,plain,
% 27.95/18.14 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(c1, c2)))),
% 27.95/18.14 inference(symmetry,[status(thm)],[6650])).
% 27.95/18.14 tff(6652,plain,
% 27.95/18.14 ((~big_f(f9(c2, c2), f9(c2, c2))) <=> (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(c1, c2))))),
% 27.95/18.14 inference(monotonicity,[status(thm)],[6651])).
% 27.95/18.14 tff(6653,plain,
% 27.95/18.14 (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(c1, c2)))),
% 27.95/18.14 inference(modus_ponens,[status(thm)],[3689, 6652])).
% 27.95/18.14 tff(6654,plain,
% 27.95/18.14 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(c1, c2))) | (f6(f9(c2, c2), f3(c1, c2)) = f3(c1, c2)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(c1, c2))) | (f6(f9(c2, c2), f3(c1, c2)) = f3(c1, c2)))),
% 27.95/18.14 inference(rewrite,[status(thm)],[])).
% 27.95/18.14 tff(6655,plain,
% 27.95/18.14 (((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), f3(c1, c2)) = f3(c1, c2)) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(c1, c2)))) <=> ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(c1, c2))) | (f6(f9(c2, c2), f3(c1, c2)) = f3(c1, c2)))),
% 27.95/18.14 inference(rewrite,[status(thm)],[])).
% 27.95/18.14 tff(6656,plain,
% 27.95/18.14 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), f3(c1, c2)) = f3(c1, c2)) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(c1, c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(c1, c2))) | (f6(f9(c2, c2), f3(c1, c2)) = f3(c1, c2))))),
% 27.95/18.14 inference(monotonicity,[status(thm)],[6655])).
% 27.95/18.14 tff(6657,plain,
% 27.95/18.14 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), f3(c1, c2)) = f3(c1, c2)) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(c1, c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(c1, c2))) | (f6(f9(c2, c2), f3(c1, c2)) = f3(c1, c2)))),
% 27.95/18.14 inference(transitivity,[status(thm)],[6656, 6654])).
% 27.95/18.14 tff(6658,plain,
% 27.95/18.14 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), f3(c1, c2)) = f3(c1, c2)) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(c1, c2))))),
% 27.95/18.14 inference(quant_inst,[status(thm)],[])).
% 27.95/18.14 tff(6659,plain,
% 27.95/18.14 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(c1, c2))) | (f6(f9(c2, c2), f3(c1, c2)) = f3(c1, c2))),
% 27.95/18.14 inference(modus_ponens,[status(thm)],[6658, 6657])).
% 27.95/18.14 tff(6660,plain,
% 27.95/18.14 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(c1, c2))) | (f6(f9(c2, c2), f3(c1, c2)) = f3(c1, c2))),
% 27.95/18.14 inference(unit_resolution,[status(thm)],[6659, 2492, 122, 185, 256, 5532])).
% 27.95/18.14 tff(6661,plain,
% 27.95/18.14 (f6(f9(c2, c2), f3(c1, c2)) = f3(c1, c2)),
% 27.95/18.14 inference(unit_resolution,[status(thm)],[6660, 6653])).
% 27.95/18.14 tff(6662,plain,
% 27.95/18.14 (f3(c1, c2) = f6(f9(c2, c2), f3(c1, c2))),
% 27.95/18.14 inference(symmetry,[status(thm)],[6661])).
% 27.95/18.14 tff(6663,plain,
% 27.95/18.14 (f3(c1, c2) = f9(c2, c2)),
% 27.95/18.14 inference(transitivity,[status(thm)],[6662, 6648, 6647, 149, 132])).
% 27.95/18.14 tff(6664,plain,
% 27.95/18.14 (big_f(f3(c1, c2), c1) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 27.95/18.14 inference(monotonicity,[status(thm)],[6663, 150])).
% 27.95/18.14 tff(6665,plain,
% 27.95/18.14 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f3(c1, c2), c1)),
% 27.95/18.14 inference(symmetry,[status(thm)],[6664])).
% 27.95/18.14 tff(6666,plain,
% 27.95/18.14 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f3(f9(c2, c2), c2), f9(c2, c2))),
% 27.95/18.14 inference(transitivity,[status(thm)],[6665, 6646])).
% 27.95/18.14 tff(6667,plain,
% 27.95/18.14 ((~big_f(f9(c2, c2), f9(c2, c2))) <=> (~big_f(f3(f9(c2, c2), c2), f9(c2, c2)))),
% 27.95/18.14 inference(monotonicity,[status(thm)],[6666])).
% 27.95/18.14 tff(6668,plain,
% 27.95/18.14 (~big_f(f3(f9(c2, c2), c2), f9(c2, c2))),
% 27.95/18.14 inference(modus_ponens,[status(thm)],[3689, 6667])).
% 27.95/18.14 tff(6669,plain,
% 27.95/18.14 ((f3(f9(c2, c2), c2) = c2) <=> (f3(c1, c2) = c2)),
% 27.95/18.14 inference(monotonicity,[status(thm)],[6644])).
% 27.95/18.14 tff(6670,plain,
% 27.95/18.14 ((f3(c1, c2) = c2) <=> (f3(f9(c2, c2), c2) = c2)),
% 27.95/18.14 inference(symmetry,[status(thm)],[6669])).
% 27.95/18.14 tff(6671,plain,
% 27.95/18.14 ((f3(c1, c2) = c2) <=> (f9(c2, c2) = c2)),
% 27.95/18.14 inference(monotonicity,[status(thm)],[6663])).
% 27.95/18.14 tff(6672,plain,
% 27.95/18.14 ((f9(c2, c2) = c2) <=> (f3(c1, c2) = c2)),
% 27.95/18.14 inference(symmetry,[status(thm)],[6671])).
% 27.95/18.15 tff(6673,plain,
% 27.95/18.15 ((f9(c2, c2) = c2) <=> (f3(f9(c2, c2), c2) = c2)),
% 27.95/18.15 inference(transitivity,[status(thm)],[6672, 6670])).
% 27.95/18.15 tff(6674,plain,
% 27.95/18.15 ((~(f9(c2, c2) = c2)) <=> (~(f3(f9(c2, c2), c2) = c2))),
% 27.95/18.15 inference(monotonicity,[status(thm)],[6673])).
% 27.95/18.15 tff(6675,plain,
% 27.95/18.15 (~(f3(f9(c2, c2), c2) = c2)),
% 27.95/18.15 inference(modus_ponens,[status(thm)],[185, 6674])).
% 27.95/18.15 tff(6676,assumption,(f9(c2, c2) = f2(f9(c2, c2))), introduced(assumption)).
% 27.95/18.15 tff(6677,plain,
% 27.95/18.15 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(f9(c2, c2) = c3)) | (f9(c2, c2) = c4) | big_f(f9(c2, c2), f9(c2, c2)) | (~(f9(c2, c2) = f2(f9(c2, c2)))) | (f3(f9(c2, c2), c2) = c2) | big_f(f3(f9(c2, c2), c2), f9(c2, c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (~(f9(c2, c2) = c3)) | (f9(c2, c2) = c4) | big_f(f9(c2, c2), f9(c2, c2)) | (~(f9(c2, c2) = f2(f9(c2, c2)))) | (f3(f9(c2, c2), c2) = c2) | big_f(f3(f9(c2, c2), c2), f9(c2, c2)))),
% 27.95/18.15 inference(rewrite,[status(thm)],[])).
% 27.95/18.15 tff(6678,plain,
% 27.95/18.15 (((~(f9(c2, c2) = c3)) | (~(f9(c2, c2) = f2(f9(c2, c2)))) | (f9(c2, c2) = c4) | (f3(f9(c2, c2), c2) = c2) | big_f(f3(f9(c2, c2), c2), f9(c2, c2)) | big_f(f9(c2, c2), f9(c2, c2))) <=> ((~(f9(c2, c2) = c3)) | (f9(c2, c2) = c4) | big_f(f9(c2, c2), f9(c2, c2)) | (~(f9(c2, c2) = f2(f9(c2, c2)))) | (f3(f9(c2, c2), c2) = c2) | big_f(f3(f9(c2, c2), c2), f9(c2, c2)))),
% 27.95/18.15 inference(rewrite,[status(thm)],[])).
% 27.95/18.15 tff(6679,plain,
% 27.95/18.15 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(f9(c2, c2) = c3)) | (~(f9(c2, c2) = f2(f9(c2, c2)))) | (f9(c2, c2) = c4) | (f3(f9(c2, c2), c2) = c2) | big_f(f3(f9(c2, c2), c2), f9(c2, c2)) | big_f(f9(c2, c2), f9(c2, c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(f9(c2, c2) = c3)) | (f9(c2, c2) = c4) | big_f(f9(c2, c2), f9(c2, c2)) | (~(f9(c2, c2) = f2(f9(c2, c2)))) | (f3(f9(c2, c2), c2) = c2) | big_f(f3(f9(c2, c2), c2), f9(c2, c2))))),
% 27.95/18.15 inference(monotonicity,[status(thm)],[6678])).
% 27.95/18.15 tff(6680,plain,
% 27.95/18.15 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(f9(c2, c2) = c3)) | (~(f9(c2, c2) = f2(f9(c2, c2)))) | (f9(c2, c2) = c4) | (f3(f9(c2, c2), c2) = c2) | big_f(f3(f9(c2, c2), c2), f9(c2, c2)) | big_f(f9(c2, c2), f9(c2, c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (~(f9(c2, c2) = c3)) | (f9(c2, c2) = c4) | big_f(f9(c2, c2), f9(c2, c2)) | (~(f9(c2, c2) = f2(f9(c2, c2)))) | (f3(f9(c2, c2), c2) = c2) | big_f(f3(f9(c2, c2), c2), f9(c2, c2)))),
% 27.95/18.15 inference(transitivity,[status(thm)],[6679, 6677])).
% 27.95/18.15 tff(6681,plain,
% 27.95/18.15 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(f9(c2, c2) = c3)) | (~(f9(c2, c2) = f2(f9(c2, c2)))) | (f9(c2, c2) = c4) | (f3(f9(c2, c2), c2) = c2) | big_f(f3(f9(c2, c2), c2), f9(c2, c2)) | big_f(f9(c2, c2), f9(c2, c2)))),
% 27.95/18.15 inference(quant_inst,[status(thm)],[])).
% 27.95/18.15 tff(6682,plain,
% 27.95/18.15 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (~(f9(c2, c2) = c3)) | (f9(c2, c2) = c4) | big_f(f9(c2, c2), f9(c2, c2)) | (~(f9(c2, c2) = f2(f9(c2, c2)))) | (f3(f9(c2, c2), c2) = c2) | big_f(f3(f9(c2, c2), c2), f9(c2, c2))),
% 27.95/18.15 inference(modus_ponens,[status(thm)],[6681, 6680])).
% 27.95/18.15 tff(6683,plain,
% 27.95/18.15 ((f3(f9(c2, c2), c2) = c2) | big_f(f3(f9(c2, c2), c2), f9(c2, c2))),
% 27.95/18.15 inference(unit_resolution,[status(thm)],[6682, 1459, 3689, 1861, 1822, 6676])).
% 27.95/18.15 tff(6684,plain,
% 27.95/18.15 ($false),
% 27.95/18.15 inference(unit_resolution,[status(thm)],[6683, 6675, 6668])).
% 27.95/18.15 tff(6685,plain,((~(f6(c1, f3(c1, c2)) = c1)) | big_f(f9(c2, c2), f9(c2, c2)) | (f9(c2, c2) = c4) | (~(f9(c2, c2) = c3)) | (~(f9(c2, c2) = f2(f9(c2, c2)))) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | big_f(f9(c2, c2), f10(c2)) | (~(f7(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 27.95/18.15 tff(6686,plain,
% 27.95/18.15 (~(f6(c1, f3(c1, c2)) = c1)),
% 27.95/18.15 inference(unit_resolution,[status(thm)],[6685, 1861, 5569, 1822, 6633, 148, 79, 122, 4597, 4234])).
% 27.95/18.15 tff(6687,plain,
% 27.95/18.15 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f6(c1, f3(c1, c2)) = c1) | (f6(c1, f3(c1, c2)) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f6(c1, f3(c1, c2)) = c1) | (f6(c1, f3(c1, c2)) = c2))),
% 27.95/18.15 inference(rewrite,[status(thm)],[])).
% 27.95/18.15 tff(6688,plain,
% 27.95/18.15 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f6(c1, f3(c1, c2)) = c1) | (f6(c1, f3(c1, c2)) = c2))),
% 27.95/18.15 inference(quant_inst,[status(thm)],[])).
% 27.95/18.15 tff(6689,plain,
% 27.95/18.15 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f6(c1, f3(c1, c2)) = c1) | (f6(c1, f3(c1, c2)) = c2)),
% 27.95/18.15 inference(modus_ponens,[status(thm)],[6688, 6687])).
% 27.95/18.15 tff(6690,plain,
% 27.95/18.15 ((f6(c1, f3(c1, c2)) = c1) | (f6(c1, f3(c1, c2)) = c2)),
% 27.95/18.15 inference(unit_resolution,[status(thm)],[6689, 10])).
% 27.95/18.15 tff(6691,plain,
% 27.95/18.15 (f6(c1, f3(c1, c2)) = c2),
% 27.95/18.15 inference(unit_resolution,[status(thm)],[6690, 6686])).
% 27.95/18.15 tff(6692,plain,
% 27.95/18.15 (f6(f9(c2, c2), f3(c1, c2)) = c2),
% 27.95/18.15 inference(transitivity,[status(thm)],[6648, 6691])).
% 27.95/18.15 tff(6693,plain,
% 27.95/18.15 ((f6(f9(c2, c2), f3(c1, c2)) = f3(c1, c2)) <=> (c2 = f3(c1, c2))),
% 27.95/18.15 inference(monotonicity,[status(thm)],[6692])).
% 27.95/18.15 tff(6694,plain,
% 27.95/18.15 ((f6(f9(c2, c2), f3(c1, c2)) = f3(c1, c2)) <=> (f3(c1, c2) = c2)),
% 27.95/18.15 inference(transitivity,[status(thm)],[6693, 6643])).
% 27.95/18.15 tff(6695,plain,
% 27.95/18.15 ((f6(f9(c2, c2), f3(c1, c2)) = f3(c1, c2)) <=> (f3(f6(c2, f7(f4(c4))), c2) = c2)),
% 27.95/18.15 inference(transitivity,[status(thm)],[6694, 6642])).
% 27.95/18.15 tff(6696,plain,
% 27.95/18.15 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(c1, c2))) <=> big_f(f9(c2, c2), c2)),
% 27.95/18.15 inference(monotonicity,[status(thm)],[5532, 6692])).
% 27.95/18.15 tff(6697,plain,
% 27.95/18.15 (big_f(f9(c2, c2), c2) <=> big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(c1, c2)))),
% 27.95/18.15 inference(symmetry,[status(thm)],[6696])).
% 27.95/18.15 tff(6698,plain,
% 27.95/18.15 ((~big_f(f9(c2, c2), c2)) <=> (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(c1, c2))))),
% 27.95/18.15 inference(monotonicity,[status(thm)],[6697])).
% 27.95/18.15 tff(6699,plain,
% 27.95/18.15 (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(c1, c2)))),
% 27.95/18.15 inference(modus_ponens,[status(thm)],[3685, 6698])).
% 27.95/18.15 tff(6700,plain,
% 27.95/18.15 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(c1, c2))) | (f6(f9(c2, c2), f3(c1, c2)) = f3(c1, c2))),
% 27.95/18.15 inference(unit_resolution,[status(thm)],[6659, 2492, 122, 185, 4597, 5532])).
% 27.95/18.15 tff(6701,plain,
% 27.95/18.15 (f6(f9(c2, c2), f3(c1, c2)) = f3(c1, c2)),
% 27.95/18.15 inference(unit_resolution,[status(thm)],[6700, 6699])).
% 27.95/18.15 tff(6702,plain,
% 27.95/18.15 (f3(f6(c2, f7(f4(c4))), c2) = c2),
% 27.95/18.15 inference(modus_ponens,[status(thm)],[6701, 6695])).
% 27.95/18.15 tff(6703,plain,
% 27.95/18.15 (big_f(f3(f6(c2, f7(f4(c4))), c2), f6(c2, f7(f4(c4)))) <=> big_f(f3(c1, c2), c1)),
% 27.95/18.15 inference(monotonicity,[status(thm)],[6640, 6634])).
% 27.95/18.15 tff(6704,plain,
% 27.95/18.15 (big_f(f3(c1, c2), c1) <=> big_f(f3(f6(c2, f7(f4(c4))), c2), f6(c2, f7(f4(c4))))),
% 27.95/18.15 inference(symmetry,[status(thm)],[6703])).
% 27.95/18.15 tff(6705,plain,
% 27.95/18.15 (f3(c1, c2) = f6(f9(c2, c2), f3(c1, c2))),
% 27.95/18.15 inference(symmetry,[status(thm)],[6701])).
% 27.95/18.15 tff(6706,plain,
% 27.95/18.15 (f3(c1, c2) = c2),
% 27.95/18.15 inference(transitivity,[status(thm)],[6705, 6648, 6691])).
% 27.95/18.15 tff(6707,plain,
% 27.95/18.15 (big_f(f3(c1, c2), c1) <=> big_f(c2, f9(c2, c2))),
% 27.95/18.15 inference(monotonicity,[status(thm)],[6706, 150])).
% 27.95/18.15 tff(6708,plain,
% 27.95/18.15 (big_f(c2, f9(c2, c2)) <=> big_f(f3(c1, c2), c1)),
% 27.95/18.15 inference(symmetry,[status(thm)],[6707])).
% 27.95/18.15 tff(6709,plain,
% 27.95/18.15 (big_f(c2, f9(c2, c2)) <=> big_f(f3(f6(c2, f7(f4(c4))), c2), f6(c2, f7(f4(c4))))),
% 27.95/18.15 inference(transitivity,[status(thm)],[6708, 6704])).
% 27.95/18.15 tff(6710,plain,
% 27.95/18.15 (big_f(f3(f6(c2, f7(f4(c4))), c2), f6(c2, f7(f4(c4))))),
% 27.95/18.15 inference(modus_ponens,[status(thm)],[3719, 6709])).
% 27.95/18.15 tff(6711,plain,
% 27.95/18.15 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(c1 = f2(c1))) | big_f(c1, c1) | (~big_f(f3(f6(c2, f7(f4(c4))), c2), f6(c2, f7(f4(c4))))) | (~(f3(f6(c2, f7(f4(c4))), c2) = c2)) | (f6(c2, f7(f4(c4))) = c4))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (~(c1 = c3)) | (~(c1 = f2(c1))) | big_f(c1, c1) | (~big_f(f3(f6(c2, f7(f4(c4))), c2), f6(c2, f7(f4(c4))))) | (~(f3(f6(c2, f7(f4(c4))), c2) = c2)) | (f6(c2, f7(f4(c4))) = c4))),
% 27.95/18.15 inference(rewrite,[status(thm)],[])).
% 27.95/18.15 tff(6712,plain,
% 27.95/18.15 (((~(c1 = c3)) | (~(c1 = f2(c1))) | (f6(c2, f7(f4(c4))) = c4) | (~(f3(f6(c2, f7(f4(c4))), c2) = c2)) | (~big_f(f3(f6(c2, f7(f4(c4))), c2), f6(c2, f7(f4(c4))))) | big_f(c1, c1)) <=> ((~(c1 = c3)) | (~(c1 = f2(c1))) | big_f(c1, c1) | (~big_f(f3(f6(c2, f7(f4(c4))), c2), f6(c2, f7(f4(c4))))) | (~(f3(f6(c2, f7(f4(c4))), c2) = c2)) | (f6(c2, f7(f4(c4))) = c4))),
% 27.95/18.15 inference(rewrite,[status(thm)],[])).
% 27.95/18.15 tff(6713,plain,
% 27.95/18.15 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(c1 = f2(c1))) | (f6(c2, f7(f4(c4))) = c4) | (~(f3(f6(c2, f7(f4(c4))), c2) = c2)) | (~big_f(f3(f6(c2, f7(f4(c4))), c2), f6(c2, f7(f4(c4))))) | big_f(c1, c1))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(c1 = f2(c1))) | big_f(c1, c1) | (~big_f(f3(f6(c2, f7(f4(c4))), c2), f6(c2, f7(f4(c4))))) | (~(f3(f6(c2, f7(f4(c4))), c2) = c2)) | (f6(c2, f7(f4(c4))) = c4)))),
% 27.95/18.15 inference(monotonicity,[status(thm)],[6712])).
% 27.95/18.15 tff(6714,plain,
% 27.95/18.15 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(c1 = f2(c1))) | (f6(c2, f7(f4(c4))) = c4) | (~(f3(f6(c2, f7(f4(c4))), c2) = c2)) | (~big_f(f3(f6(c2, f7(f4(c4))), c2), f6(c2, f7(f4(c4))))) | big_f(c1, c1))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (~(c1 = c3)) | (~(c1 = f2(c1))) | big_f(c1, c1) | (~big_f(f3(f6(c2, f7(f4(c4))), c2), f6(c2, f7(f4(c4))))) | (~(f3(f6(c2, f7(f4(c4))), c2) = c2)) | (f6(c2, f7(f4(c4))) = c4))),
% 27.95/18.15 inference(transitivity,[status(thm)],[6713, 6711])).
% 27.95/18.15 tff(6715,plain,
% 27.95/18.15 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(c1 = f2(c1))) | (f6(c2, f7(f4(c4))) = c4) | (~(f3(f6(c2, f7(f4(c4))), c2) = c2)) | (~big_f(f3(f6(c2, f7(f4(c4))), c2), f6(c2, f7(f4(c4))))) | big_f(c1, c1))),
% 27.95/18.15 inference(quant_inst,[status(thm)],[])).
% 27.95/18.15 tff(6716,plain,
% 27.95/18.15 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (~(c1 = c3)) | (~(c1 = f2(c1))) | big_f(c1, c1) | (~big_f(f3(f6(c2, f7(f4(c4))), c2), f6(c2, f7(f4(c4))))) | (~(f3(f6(c2, f7(f4(c4))), c2) = c2)) | (f6(c2, f7(f4(c4))) = c4)),
% 27.95/18.15 inference(modus_ponens,[status(thm)],[6715, 6714])).
% 27.95/18.15 tff(6717,plain,
% 27.95/18.15 ((~(c1 = c3)) | (~(c1 = f2(c1))) | big_f(c1, c1) | (~big_f(f3(f6(c2, f7(f4(c4))), c2), f6(c2, f7(f4(c4))))) | (~(f3(f6(c2, f7(f4(c4))), c2) = c2)) | (f6(c2, f7(f4(c4))) = c4)),
% 27.95/18.15 inference(unit_resolution,[status(thm)],[6716, 1398])).
% 27.95/18.15 tff(6718,plain,
% 27.95/18.15 ($false),
% 27.95/18.15 inference(unit_resolution,[status(thm)],[6717, 6710, 6702, 66, 5080, 6632, 6639])).
% 27.95/18.15 tff(6719,plain,((f9(c2, c2) = c4) | big_f(c1, c1) | (~(c1 = c3)) | (~(c1 = f2(c1))) | (~big_f(c2, f9(c2, c2))) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f6(c2, f7(f4(c4))) = c1)) | big_f(f9(c2, c2), c2) | (~(f7(c1) = c1)) | (~(f9(c2, c2) = c3))), inference(lemma,lemma(discharge,[]))).
% 27.95/18.15 tff(6720,plain,
% 27.95/18.15 (f9(c2, c2) = c4),
% 27.95/18.15 inference(unit_resolution,[status(thm)],[6719, 6632, 5080, 66, 3719, 148, 79, 122, 6634, 3685, 4234, 1822])).
% 27.95/18.15 tff(6721,plain,
% 27.95/18.15 (c4 = f9(c2, c2)),
% 27.95/18.15 inference(symmetry,[status(thm)],[6720])).
% 27.95/18.15 tff(6722,plain,
% 27.95/18.15 ((c2 = c4) <=> (c2 = f9(c2, c2))),
% 27.95/18.15 inference(monotonicity,[status(thm)],[6721])).
% 27.95/18.15 tff(6723,plain,
% 27.95/18.15 ((c2 = c4) <=> (f9(c2, c2) = c2)),
% 27.95/18.15 inference(transitivity,[status(thm)],[6722, 167])).
% 27.95/18.15 tff(6724,plain,
% 27.95/18.15 ((f9(c2, c2) = c2) <=> (c2 = c4)),
% 27.95/18.15 inference(symmetry,[status(thm)],[6723])).
% 27.95/18.15 tff(6725,plain,
% 27.95/18.15 ((~(f9(c2, c2) = c2)) <=> (~(c2 = c4))),
% 27.95/18.15 inference(monotonicity,[status(thm)],[6724])).
% 27.95/18.15 tff(6726,plain,
% 27.95/18.15 (~(c2 = c4)),
% 27.95/18.15 inference(modus_ponens,[status(thm)],[185, 6725])).
% 27.95/18.15 tff(6727,assumption,(f3(f6(f7(c2), c3), c2) = c2), introduced(assumption)).
% 27.95/18.15 tff(6728,plain,
% 27.95/18.15 (c2 = f6(f7(c2), c3)),
% 27.95/18.15 inference(symmetry,[status(thm)],[2362])).
% 27.95/18.15 tff(6729,plain,
% 27.95/18.15 (f3(c2, c2) = f3(f6(f7(c2), c3), c2)),
% 27.95/18.15 inference(monotonicity,[status(thm)],[6728])).
% 27.95/18.15 tff(6730,plain,
% 27.95/18.15 (f3(c2, c2) = c2),
% 27.95/18.15 inference(transitivity,[status(thm)],[6729, 6727])).
% 27.95/18.15 tff(6731,plain,
% 27.95/18.15 (big_f(f3(c2, c2), c2) <=> big_f(c2, c2)),
% 27.95/18.15 inference(monotonicity,[status(thm)],[6730])).
% 27.95/18.15 tff(6732,plain,
% 27.95/18.15 (big_f(c2, c2) <=> big_f(f3(c2, c2), c2)),
% 27.95/18.15 inference(symmetry,[status(thm)],[6731])).
% 27.95/18.15 tff(6733,plain,
% 27.95/18.15 (big_f(f3(c2, c2), c2)),
% 27.95/18.15 inference(modus_ponens,[status(thm)],[1345, 6732])).
% 27.95/18.15 tff(6734,plain,
% 27.95/18.15 (f3(f6(f7(c2), c3), c2) = f3(c2, c2)),
% 27.95/18.15 inference(symmetry,[status(thm)],[6729])).
% 27.95/18.15 tff(6735,plain,
% 27.95/18.15 ((f3(f6(f7(c2), c3), c2) = c2) <=> (f3(c2, c2) = c2)),
% 27.95/18.15 inference(monotonicity,[status(thm)],[6734])).
% 27.95/18.15 tff(6736,plain,
% 27.95/18.15 (f3(c2, c2) = c2),
% 27.95/18.15 inference(modus_ponens,[status(thm)],[6727, 6735])).
% 27.95/18.15 tff(6737,plain,
% 27.95/18.15 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~(f9(c2, c2) = c3)) | big_f(f9(c2, c2), f9(c2, c2)) | (~(f9(c2, c2) = f2(f9(c2, c2)))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~(f9(c2, c2) = c3)) | big_f(f9(c2, c2), f9(c2, c2)) | (~(f9(c2, c2) = f2(f9(c2, c2)))))),
% 27.95/18.15 inference(rewrite,[status(thm)],[])).
% 27.95/18.15 tff(6738,plain,
% 27.95/18.15 (((~(f9(c2, c2) = c3)) | (~(f9(c2, c2) = f2(f9(c2, c2)))) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | big_f(f9(c2, c2), f9(c2, c2))) <=> ((c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~(f9(c2, c2) = c3)) | big_f(f9(c2, c2), f9(c2, c2)) | (~(f9(c2, c2) = f2(f9(c2, c2)))))),
% 27.95/18.15 inference(rewrite,[status(thm)],[])).
% 27.95/18.15 tff(6739,plain,
% 27.95/18.15 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(f9(c2, c2) = c3)) | (~(f9(c2, c2) = f2(f9(c2, c2)))) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | big_f(f9(c2, c2), f9(c2, c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~(f9(c2, c2) = c3)) | big_f(f9(c2, c2), f9(c2, c2)) | (~(f9(c2, c2) = f2(f9(c2, c2))))))),
% 27.95/18.15 inference(monotonicity,[status(thm)],[6738])).
% 27.95/18.15 tff(6740,plain,
% 27.95/18.15 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(f9(c2, c2) = c3)) | (~(f9(c2, c2) = f2(f9(c2, c2)))) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | big_f(f9(c2, c2), f9(c2, c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~(f9(c2, c2) = c3)) | big_f(f9(c2, c2), f9(c2, c2)) | (~(f9(c2, c2) = f2(f9(c2, c2)))))),
% 27.95/18.15 inference(transitivity,[status(thm)],[6739, 6737])).
% 27.95/18.15 tff(6741,plain,
% 27.95/18.15 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(f9(c2, c2) = c3)) | (~(f9(c2, c2) = f2(f9(c2, c2)))) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | big_f(f9(c2, c2), f9(c2, c2)))),
% 27.95/18.15 inference(quant_inst,[status(thm)],[])).
% 27.95/18.15 tff(6742,plain,
% 27.95/18.15 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~(f9(c2, c2) = c3)) | big_f(f9(c2, c2), f9(c2, c2)) | (~(f9(c2, c2) = f2(f9(c2, c2))))),
% 27.95/18.15 inference(modus_ponens,[status(thm)],[6741, 6740])).
% 27.95/18.15 tff(6743,plain,
% 27.95/18.15 ($false),
% 27.95/18.15 inference(unit_resolution,[status(thm)],[6742, 1398, 873, 3689, 1822, 6736, 6733, 6676])).
% 27.95/18.15 tff(6744,plain,((~(f3(f6(f7(c2), c3), c2) = c2)) | (c2 = c4) | big_f(f9(c2, c2), f9(c2, c2)) | (~(f9(c2, c2) = c3)) | (~(f9(c2, c2) = f2(f9(c2, c2)))) | (~big_f(c2, c2)) | (~(f6(f7(c2), c3) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.95/18.15 tff(6745,plain,
% 27.95/18.15 (~(f3(f6(f7(c2), c3), c2) = c2)),
% 27.95/18.15 inference(unit_resolution,[status(thm)],[6744, 6726, 5569, 1822, 6633, 1345, 2362])).
% 27.95/18.15 tff(6746,plain,
% 27.95/18.15 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f3(f6(f7(c2), c3), c2) = c1) | (f3(f6(f7(c2), c3), c2) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f3(f6(f7(c2), c3), c2) = c1) | (f3(f6(f7(c2), c3), c2) = c2))),
% 27.95/18.15 inference(rewrite,[status(thm)],[])).
% 27.95/18.15 tff(6747,plain,
% 27.95/18.15 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f3(f6(f7(c2), c3), c2) = c1) | (f3(f6(f7(c2), c3), c2) = c2))),
% 27.95/18.15 inference(quant_inst,[status(thm)],[])).
% 27.95/18.15 tff(6748,plain,
% 27.95/18.15 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f3(f6(f7(c2), c3), c2) = c1) | (f3(f6(f7(c2), c3), c2) = c2)),
% 27.95/18.15 inference(modus_ponens,[status(thm)],[6747, 6746])).
% 27.95/18.15 tff(6749,plain,
% 27.95/18.15 ((f3(f6(f7(c2), c3), c2) = c1) | (f3(f6(f7(c2), c3), c2) = c2)),
% 27.95/18.15 inference(unit_resolution,[status(thm)],[6748, 10])).
% 27.95/18.15 tff(6750,plain,
% 27.95/18.15 (f3(f6(f7(c2), c3), c2) = c1),
% 27.95/18.15 inference(unit_resolution,[status(thm)],[6749, 6745])).
% 27.95/18.15 tff(6751,plain,
% 27.95/18.15 (f3(c2, c2) = f9(c2, c2)),
% 27.95/18.15 inference(transitivity,[status(thm)],[6729, 6750, 149, 132])).
% 27.95/18.15 tff(6752,plain,
% 27.95/18.15 (big_f(f3(c2, c2), c2) <=> big_f(f9(c2, c2), c2)),
% 27.95/18.15 inference(monotonicity,[status(thm)],[6751])).
% 27.95/18.15 tff(6753,plain,
% 27.95/18.15 (big_f(f9(c2, c2), c2) <=> big_f(f3(c2, c2), c2)),
% 27.95/18.15 inference(symmetry,[status(thm)],[6752])).
% 27.95/18.15 tff(6754,plain,
% 27.95/18.15 ((~big_f(f9(c2, c2), c2)) <=> (~big_f(f3(c2, c2), c2))),
% 27.95/18.15 inference(monotonicity,[status(thm)],[6753])).
% 27.95/18.15 tff(6755,plain,
% 27.95/18.15 (~big_f(f3(c2, c2), c2)),
% 27.95/18.15 inference(modus_ponens,[status(thm)],[3685, 6754])).
% 27.95/18.15 tff(6756,plain,
% 27.95/18.15 ((~(f3(f6(f7(c2), c3), c2) = c2)) <=> (~(f3(c2, c2) = c2))),
% 27.95/18.15 inference(monotonicity,[status(thm)],[6735])).
% 27.95/18.15 tff(6757,plain,
% 27.95/18.15 (~(f3(c2, c2) = c2)),
% 27.95/18.15 inference(modus_ponens,[status(thm)],[6745, 6756])).
% 27.95/18.15 tff(6758,plain,
% 27.95/18.15 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(f9(c2, c2) = c3)) | (~(f9(c2, c2) = f2(f9(c2, c2)))) | (c2 = c4) | (f3(c2, c2) = c2) | big_f(f3(c2, c2), c2) | big_f(f9(c2, c2), f9(c2, c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (~(f9(c2, c2) = c3)) | (~(f9(c2, c2) = f2(f9(c2, c2)))) | (c2 = c4) | (f3(c2, c2) = c2) | big_f(f3(c2, c2), c2) | big_f(f9(c2, c2), f9(c2, c2)))),
% 27.95/18.15 inference(rewrite,[status(thm)],[])).
% 27.95/18.15 tff(6759,plain,
% 27.95/18.15 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(f9(c2, c2) = c3)) | (~(f9(c2, c2) = f2(f9(c2, c2)))) | (c2 = c4) | (f3(c2, c2) = c2) | big_f(f3(c2, c2), c2) | big_f(f9(c2, c2), f9(c2, c2)))),
% 27.95/18.16 inference(quant_inst,[status(thm)],[])).
% 27.95/18.16 tff(6760,plain,
% 27.95/18.16 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (~(f9(c2, c2) = c3)) | (~(f9(c2, c2) = f2(f9(c2, c2)))) | (c2 = c4) | (f3(c2, c2) = c2) | big_f(f3(c2, c2), c2) | big_f(f9(c2, c2), f9(c2, c2))),
% 27.95/18.16 inference(modus_ponens,[status(thm)],[6759, 6758])).
% 27.95/18.16 tff(6761,plain,
% 27.95/18.16 ($false),
% 27.95/18.16 inference(unit_resolution,[status(thm)],[6760, 1459, 6726, 5569, 1822, 6757, 6755, 6633])).
% 27.95/18.16 tff(6762,plain,((~(c1 = f2(c1))) | (~(f9(c2, c2) = c3)) | big_f(f9(c2, c2), c2) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f6(f7(c2), c3) = c2)) | (~big_f(c2, c2)) | (~(c1 = c3)) | big_f(c1, c1) | (~big_f(c2, f9(c2, c2))) | (~(f6(c2, f7(f4(c4))) = c1)) | (~(f7(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 27.95/18.16 tff(6763,plain,
% 27.95/18.16 (~(c1 = f2(c1))),
% 27.95/18.16 inference(unit_resolution,[status(thm)],[6762, 3685, 5580, 148, 79, 122, 6628, 1345, 5611, 66, 6605, 6602, 4234])).
% 27.95/18.16 tff(6764,plain,
% 27.95/18.16 ((f2(c1) = c1) <=> (c1 = f2(c1))),
% 27.95/18.16 inference(commutativity,[status(thm)],[])).
% 27.95/18.16 tff(6765,plain,
% 27.95/18.16 (f2(c3) = f2(c1)),
% 27.95/18.16 inference(monotonicity,[status(thm)],[172])).
% 27.95/18.16 tff(6766,plain,
% 27.95/18.16 ((f2(c3) = c1) <=> (f2(c1) = c1)),
% 27.95/18.16 inference(monotonicity,[status(thm)],[6765])).
% 27.95/18.16 tff(6767,plain,
% 27.95/18.16 ((f2(c3) = c1) <=> (c1 = f2(c1))),
% 27.95/18.16 inference(transitivity,[status(thm)],[6766, 6764])).
% 27.95/18.16 tff(6768,plain,
% 27.95/18.16 (c1 = f2(c1)),
% 27.95/18.16 inference(modus_ponens,[status(thm)],[1247, 6767])).
% 27.95/18.16 tff(6769,assumption,(~(c1 = f2(c1))), introduced(assumption)).
% 27.95/18.16 tff(6770,plain,
% 27.95/18.16 ($false),
% 27.95/18.16 inference(unit_resolution,[status(thm)],[6769, 6768])).
% 27.95/18.16 tff(6771,plain,((~(f2(c3) = c1)) | (c1 = f2(c1)) | (~(c3 = c1))), inference(lemma,lemma(discharge,[]))).
% 27.95/18.16 tff(6772,plain,
% 27.95/18.16 (~(f2(c3) = c1)),
% 27.95/18.16 inference(unit_resolution,[status(thm)],[6771, 6763, 172])).
% 27.95/18.16 tff(6773,plain,
% 27.95/18.16 (f2(c3) = c2),
% 27.95/18.16 inference(unit_resolution,[status(thm)],[1273, 6772])).
% 27.95/18.16 tff(6774,plain,
% 27.95/18.16 (c2 = f2(f9(c2, c2))),
% 27.95/18.16 inference(modus_ponens,[status(thm)],[6773, 6629])).
% 27.95/18.16 tff(6775,plain,
% 27.95/18.16 (f6(f9(c2, c2), f3(c1, c2)) = f3(c1, c2)),
% 27.95/18.16 inference(unit_resolution,[status(thm)],[6700, 6653])).
% 27.95/18.16 tff(6776,plain,
% 27.95/18.16 (f3(c1, c2) = f6(f9(c2, c2), f3(c1, c2))),
% 27.95/18.16 inference(symmetry,[status(thm)],[6775])).
% 27.95/18.16 tff(6777,plain,
% 27.95/18.16 (f3(c1, c2) = f9(c2, c2)),
% 27.95/18.16 inference(transitivity,[status(thm)],[6776, 6648, 6647, 149, 132])).
% 27.95/18.16 tff(6778,plain,
% 27.95/18.16 (big_f(f3(c1, c2), c1) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 27.95/18.16 inference(monotonicity,[status(thm)],[6777, 150])).
% 27.95/18.16 tff(6779,plain,
% 27.95/18.16 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f3(c1, c2), c1)),
% 27.95/18.16 inference(symmetry,[status(thm)],[6778])).
% 27.95/18.16 tff(6780,plain,
% 27.95/18.16 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f3(f9(c2, c2), c2), f9(c2, c2))),
% 27.95/18.16 inference(transitivity,[status(thm)],[6779, 6646])).
% 27.95/18.16 tff(6781,plain,
% 27.95/18.16 ((~big_f(f9(c2, c2), f9(c2, c2))) <=> (~big_f(f3(f9(c2, c2), c2), f9(c2, c2)))),
% 27.95/18.16 inference(monotonicity,[status(thm)],[6780])).
% 27.95/18.16 tff(6782,plain,
% 27.95/18.16 (~big_f(f3(f9(c2, c2), c2), f9(c2, c2))),
% 27.95/18.16 inference(modus_ponens,[status(thm)],[3689, 6781])).
% 27.95/18.16 tff(6783,plain,
% 27.95/18.16 ((f3(c1, c2) = c2) <=> (f9(c2, c2) = c2)),
% 27.95/18.16 inference(monotonicity,[status(thm)],[6777])).
% 27.95/18.16 tff(6784,plain,
% 27.95/18.16 ((f9(c2, c2) = c2) <=> (f3(c1, c2) = c2)),
% 27.95/18.16 inference(symmetry,[status(thm)],[6783])).
% 27.95/18.16 tff(6785,plain,
% 27.95/18.16 ((f9(c2, c2) = c2) <=> (f3(f9(c2, c2), c2) = c2)),
% 27.95/18.16 inference(transitivity,[status(thm)],[6784, 6670])).
% 27.95/18.16 tff(6786,plain,
% 27.95/18.16 ((~(f9(c2, c2) = c2)) <=> (~(f3(f9(c2, c2), c2) = c2))),
% 27.95/18.16 inference(monotonicity,[status(thm)],[6785])).
% 27.95/18.16 tff(6787,plain,
% 27.95/18.16 (~(f3(f9(c2, c2), c2) = c2)),
% 27.95/18.16 inference(modus_ponens,[status(thm)],[185, 6786])).
% 27.95/18.16 tff(6788,plain,
% 27.95/18.16 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c2 = f2(f9(c2, c2)))) | (~(f9(c2, c2) = c3)) | big_f(f9(c2, c2), c2) | (f9(c2, c2) = c4) | (f3(f9(c2, c2), c2) = c2) | big_f(f3(f9(c2, c2), c2), f9(c2, c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (~(c2 = f2(f9(c2, c2)))) | (~(f9(c2, c2) = c3)) | big_f(f9(c2, c2), c2) | (f9(c2, c2) = c4) | (f3(f9(c2, c2), c2) = c2) | big_f(f3(f9(c2, c2), c2), f9(c2, c2)))),
% 27.95/18.16 inference(rewrite,[status(thm)],[])).
% 27.95/18.16 tff(6789,plain,
% 27.95/18.16 (((~(f9(c2, c2) = c3)) | (~(c2 = f2(f9(c2, c2)))) | (f9(c2, c2) = c4) | (f3(f9(c2, c2), c2) = c2) | big_f(f3(f9(c2, c2), c2), f9(c2, c2)) | big_f(f9(c2, c2), c2)) <=> ((~(c2 = f2(f9(c2, c2)))) | (~(f9(c2, c2) = c3)) | big_f(f9(c2, c2), c2) | (f9(c2, c2) = c4) | (f3(f9(c2, c2), c2) = c2) | big_f(f3(f9(c2, c2), c2), f9(c2, c2)))),
% 27.95/18.16 inference(rewrite,[status(thm)],[])).
% 27.95/18.16 tff(6790,plain,
% 27.95/18.16 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(f9(c2, c2) = c3)) | (~(c2 = f2(f9(c2, c2)))) | (f9(c2, c2) = c4) | (f3(f9(c2, c2), c2) = c2) | big_f(f3(f9(c2, c2), c2), f9(c2, c2)) | big_f(f9(c2, c2), c2))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c2 = f2(f9(c2, c2)))) | (~(f9(c2, c2) = c3)) | big_f(f9(c2, c2), c2) | (f9(c2, c2) = c4) | (f3(f9(c2, c2), c2) = c2) | big_f(f3(f9(c2, c2), c2), f9(c2, c2))))),
% 27.95/18.16 inference(monotonicity,[status(thm)],[6789])).
% 27.95/18.16 tff(6791,plain,
% 27.95/18.16 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(f9(c2, c2) = c3)) | (~(c2 = f2(f9(c2, c2)))) | (f9(c2, c2) = c4) | (f3(f9(c2, c2), c2) = c2) | big_f(f3(f9(c2, c2), c2), f9(c2, c2)) | big_f(f9(c2, c2), c2))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (~(c2 = f2(f9(c2, c2)))) | (~(f9(c2, c2) = c3)) | big_f(f9(c2, c2), c2) | (f9(c2, c2) = c4) | (f3(f9(c2, c2), c2) = c2) | big_f(f3(f9(c2, c2), c2), f9(c2, c2)))),
% 27.95/18.16 inference(transitivity,[status(thm)],[6790, 6788])).
% 27.95/18.16 tff(6792,plain,
% 27.95/18.16 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(f9(c2, c2) = c3)) | (~(c2 = f2(f9(c2, c2)))) | (f9(c2, c2) = c4) | (f3(f9(c2, c2), c2) = c2) | big_f(f3(f9(c2, c2), c2), f9(c2, c2)) | big_f(f9(c2, c2), c2))),
% 27.95/18.16 inference(quant_inst,[status(thm)],[])).
% 27.95/18.16 tff(6793,plain,
% 27.95/18.16 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (~(c2 = f2(f9(c2, c2)))) | (~(f9(c2, c2) = c3)) | big_f(f9(c2, c2), c2) | (f9(c2, c2) = c4) | (f3(f9(c2, c2), c2) = c2) | big_f(f3(f9(c2, c2), c2), f9(c2, c2))),
% 27.95/18.16 inference(modus_ponens,[status(thm)],[6792, 6791])).
% 27.95/18.16 tff(6794,plain,
% 27.95/18.16 ((f3(f9(c2, c2), c2) = c2) | big_f(f3(f9(c2, c2), c2), f9(c2, c2))),
% 27.95/18.16 inference(unit_resolution,[status(thm)],[6793, 1459, 1861, 1822, 3685, 5689])).
% 27.95/18.16 tff(6795,plain,
% 27.95/18.16 ($false),
% 27.95/18.16 inference(unit_resolution,[status(thm)],[6794, 6787, 6782])).
% 27.95/18.16 tff(6796,plain,((~(f6(c1, f3(c1, c2)) = c1)) | (f9(c2, c2) = c4) | (~(f9(c2, c2) = c3)) | big_f(f9(c2, c2), c2) | (~(c2 = f2(f9(c2, c2)))) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | big_f(f9(c2, c2), f9(c2, c2)) | (~(f7(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 27.95/18.16 tff(6797,plain,
% 27.95/18.16 (~(f6(c1, f3(c1, c2)) = c1)),
% 27.95/18.16 inference(unit_resolution,[status(thm)],[6796, 1861, 1822, 3685, 5689, 148, 79, 122, 3689, 4234])).
% 27.95/18.16 tff(6798,plain,
% 27.95/18.16 (f6(c1, f3(c1, c2)) = c2),
% 27.95/18.16 inference(unit_resolution,[status(thm)],[6690, 6797])).
% 27.95/18.16 tff(6799,plain,
% 27.95/18.16 ((f6(c1, f3(c1, c2)) = f3(c1, c2)) <=> (c2 = f3(c1, c2))),
% 27.95/18.16 inference(monotonicity,[status(thm)],[6798])).
% 27.95/18.16 tff(6800,plain,
% 27.95/18.16 ((f6(c1, f3(c1, c2)) = f3(c1, c2)) <=> (f3(c1, c2) = c2)),
% 27.95/18.16 inference(transitivity,[status(thm)],[6799, 6643])).
% 27.95/18.16 tff(6801,plain,
% 27.95/18.16 ((f6(f9(c2, c2), f3(c1, c2)) = f3(c1, c2)) <=> (f6(c1, f3(c1, c2)) = f3(c1, c2))),
% 27.95/18.16 inference(monotonicity,[status(thm)],[6648])).
% 27.95/18.16 tff(6802,plain,
% 27.95/18.16 ((f6(f9(c2, c2), f3(c1, c2)) = f3(c1, c2)) <=> (f3(f9(c2, c2), c2) = c2)),
% 27.95/18.16 inference(transitivity,[status(thm)],[6801, 6800, 6670])).
% 27.95/18.16 tff(6803,plain,
% 27.95/18.16 (f6(f9(c2, c2), f3(c1, c2)) = c2),
% 27.95/18.16 inference(transitivity,[status(thm)],[6648, 6798])).
% 27.95/18.16 tff(6804,plain,
% 27.95/18.16 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(c1, c2))) <=> big_f(f9(c2, c2), c2)),
% 27.95/18.16 inference(monotonicity,[status(thm)],[5532, 6803])).
% 27.95/18.16 tff(6805,plain,
% 27.95/18.16 (big_f(f9(c2, c2), c2) <=> big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(c1, c2)))),
% 27.95/18.16 inference(symmetry,[status(thm)],[6804])).
% 27.95/18.16 tff(6806,plain,
% 27.95/18.16 ((~big_f(f9(c2, c2), c2)) <=> (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(c1, c2))))),
% 27.95/18.16 inference(monotonicity,[status(thm)],[6805])).
% 27.95/18.16 tff(6807,plain,
% 27.95/18.16 (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(c1, c2)))),
% 27.95/18.16 inference(modus_ponens,[status(thm)],[3685, 6806])).
% 27.95/18.16 tff(6808,plain,
% 27.95/18.16 (f6(f9(c2, c2), f3(c1, c2)) = f3(c1, c2)),
% 27.95/18.16 inference(unit_resolution,[status(thm)],[6700, 6807])).
% 27.95/18.16 tff(6809,plain,
% 27.95/18.16 (f3(f9(c2, c2), c2) = c2),
% 27.95/18.16 inference(modus_ponens,[status(thm)],[6808, 6802])).
% 27.95/18.16 tff(6810,plain,
% 27.95/18.16 (f3(c1, c2) = f6(f9(c2, c2), f3(c1, c2))),
% 27.95/18.16 inference(symmetry,[status(thm)],[6808])).
% 27.95/18.16 tff(6811,plain,
% 27.95/18.16 (f3(c1, c2) = c2),
% 27.95/18.16 inference(transitivity,[status(thm)],[6810, 6648, 6798])).
% 27.95/18.16 tff(6812,plain,
% 27.95/18.16 (big_f(f3(c1, c2), c1) <=> big_f(c2, f9(c2, c2))),
% 27.95/18.16 inference(monotonicity,[status(thm)],[6811, 150])).
% 27.95/18.16 tff(6813,plain,
% 27.95/18.16 (big_f(c2, f9(c2, c2)) <=> big_f(f3(c1, c2), c1)),
% 27.95/18.16 inference(symmetry,[status(thm)],[6812])).
% 27.95/18.16 tff(6814,plain,
% 27.95/18.16 (big_f(c2, f9(c2, c2)) <=> big_f(f3(f9(c2, c2), c2), f9(c2, c2))),
% 27.95/18.16 inference(transitivity,[status(thm)],[6813, 6646])).
% 27.95/18.16 tff(6815,plain,
% 27.95/18.16 (big_f(f3(f9(c2, c2), c2), f9(c2, c2))),
% 27.95/18.16 inference(modus_ponens,[status(thm)],[3719, 6814])).
% 27.95/18.16 tff(6816,plain,
% 27.95/18.16 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c2 = f2(f9(c2, c2)))) | (~(f9(c2, c2) = c3)) | big_f(f9(c2, c2), c2) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), c2) = c2)) | (~big_f(f3(f9(c2, c2), c2), f9(c2, c2))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (~(c2 = f2(f9(c2, c2)))) | (~(f9(c2, c2) = c3)) | big_f(f9(c2, c2), c2) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), c2) = c2)) | (~big_f(f3(f9(c2, c2), c2), f9(c2, c2))))),
% 27.95/18.16 inference(rewrite,[status(thm)],[])).
% 27.95/18.16 tff(6817,plain,
% 27.95/18.16 (((~(f9(c2, c2) = c3)) | (~(c2 = f2(f9(c2, c2)))) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), c2) = c2)) | (~big_f(f3(f9(c2, c2), c2), f9(c2, c2))) | big_f(f9(c2, c2), c2)) <=> ((~(c2 = f2(f9(c2, c2)))) | (~(f9(c2, c2) = c3)) | big_f(f9(c2, c2), c2) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), c2) = c2)) | (~big_f(f3(f9(c2, c2), c2), f9(c2, c2))))),
% 27.95/18.16 inference(rewrite,[status(thm)],[])).
% 27.95/18.16 tff(6818,plain,
% 27.95/18.16 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(f9(c2, c2) = c3)) | (~(c2 = f2(f9(c2, c2)))) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), c2) = c2)) | (~big_f(f3(f9(c2, c2), c2), f9(c2, c2))) | big_f(f9(c2, c2), c2))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c2 = f2(f9(c2, c2)))) | (~(f9(c2, c2) = c3)) | big_f(f9(c2, c2), c2) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), c2) = c2)) | (~big_f(f3(f9(c2, c2), c2), f9(c2, c2)))))),
% 27.95/18.16 inference(monotonicity,[status(thm)],[6817])).
% 27.95/18.16 tff(6819,plain,
% 27.95/18.16 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(f9(c2, c2) = c3)) | (~(c2 = f2(f9(c2, c2)))) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), c2) = c2)) | (~big_f(f3(f9(c2, c2), c2), f9(c2, c2))) | big_f(f9(c2, c2), c2))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (~(c2 = f2(f9(c2, c2)))) | (~(f9(c2, c2) = c3)) | big_f(f9(c2, c2), c2) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), c2) = c2)) | (~big_f(f3(f9(c2, c2), c2), f9(c2, c2))))),
% 27.95/18.16 inference(transitivity,[status(thm)],[6818, 6816])).
% 27.95/18.16 tff(6820,plain,
% 27.95/18.16 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(f9(c2, c2) = c3)) | (~(c2 = f2(f9(c2, c2)))) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), c2) = c2)) | (~big_f(f3(f9(c2, c2), c2), f9(c2, c2))) | big_f(f9(c2, c2), c2))),
% 27.95/18.16 inference(quant_inst,[status(thm)],[])).
% 27.95/18.16 tff(6821,plain,
% 27.95/18.16 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (~(c2 = f2(f9(c2, c2)))) | (~(f9(c2, c2) = c3)) | big_f(f9(c2, c2), c2) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), c2) = c2)) | (~big_f(f3(f9(c2, c2), c2), f9(c2, c2)))),
% 27.95/18.16 inference(modus_ponens,[status(thm)],[6820, 6819])).
% 27.95/18.16 tff(6822,plain,
% 27.95/18.16 ((~(f3(f9(c2, c2), c2) = c2)) | (~big_f(f3(f9(c2, c2), c2), f9(c2, c2)))),
% 27.95/18.16 inference(unit_resolution,[status(thm)],[6821, 1398, 1861, 1822, 3685, 5689])).
% 27.95/18.16 tff(6823,plain,
% 27.95/18.16 ($false),
% 27.95/18.16 inference(unit_resolution,[status(thm)],[6822, 6815, 6809])).
% 27.95/18.16 tff(6824,plain,((f9(c2, c2) = c4) | (~(f9(c2, c2) = c3)) | big_f(f9(c2, c2), c2) | (~(c2 = f2(f9(c2, c2)))) | (~big_f(c2, f9(c2, c2))) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f7(c1) = c1)) | big_f(f9(c2, c2), f9(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 27.95/18.16 tff(6825,plain,
% 27.95/18.16 (f9(c2, c2) = c4),
% 27.95/18.16 inference(unit_resolution,[status(thm)],[6824, 3685, 5580, 6774, 6605, 148, 79, 122, 4234, 5569])).
% 27.95/18.16 tff(6826,plain,
% 27.95/18.16 (c4 = f9(c2, c2)),
% 27.95/18.16 inference(symmetry,[status(thm)],[6825])).
% 27.95/18.16 tff(6827,plain,
% 27.95/18.16 ((c2 = c4) <=> (c2 = f9(c2, c2))),
% 27.95/18.16 inference(monotonicity,[status(thm)],[6826])).
% 27.95/18.16 tff(6828,plain,
% 27.95/18.16 ((c2 = c4) <=> (f9(c2, c2) = c2)),
% 27.95/18.16 inference(transitivity,[status(thm)],[6827, 167])).
% 27.95/18.16 tff(6829,plain,
% 27.95/18.16 ((f9(c2, c2) = c2) <=> (c2 = c4)),
% 27.95/18.16 inference(symmetry,[status(thm)],[6828])).
% 27.95/18.16 tff(6830,plain,
% 27.95/18.16 ((~(f9(c2, c2) = c2)) <=> (~(c2 = c4))),
% 27.95/18.16 inference(monotonicity,[status(thm)],[6829])).
% 27.95/18.16 tff(6831,plain,
% 27.95/18.16 (~(c2 = c4)),
% 27.95/18.16 inference(modus_ponens,[status(thm)],[185, 6830])).
% 27.95/18.16 tff(6832,assumption,(~(f3(f6(f7(c2), c3), c2) = c2)), introduced(assumption)).
% 27.95/18.16 tff(6833,plain,
% 27.95/18.16 (f3(f6(f7(c2), c3), c2) = c1),
% 27.95/18.16 inference(unit_resolution,[status(thm)],[6749, 6832])).
% 27.95/18.16 tff(6834,plain,
% 27.95/18.16 (f3(c2, c2) = f9(c2, c2)),
% 27.95/18.16 inference(transitivity,[status(thm)],[6729, 6833, 149, 132])).
% 27.95/18.16 tff(6835,plain,
% 27.95/18.16 (big_f(f3(c2, c2), c2) <=> big_f(f9(c2, c2), c2)),
% 27.95/18.16 inference(monotonicity,[status(thm)],[6834])).
% 27.95/18.16 tff(6836,plain,
% 27.95/18.16 (big_f(f9(c2, c2), c2) <=> big_f(f3(c2, c2), c2)),
% 27.95/18.16 inference(symmetry,[status(thm)],[6835])).
% 27.95/18.16 tff(6837,plain,
% 27.95/18.16 ((~big_f(f9(c2, c2), c2)) <=> (~big_f(f3(c2, c2), c2))),
% 27.95/18.16 inference(monotonicity,[status(thm)],[6836])).
% 27.95/18.16 tff(6838,plain,
% 27.95/18.16 (~big_f(f3(c2, c2), c2)),
% 27.95/18.16 inference(modus_ponens,[status(thm)],[3685, 6837])).
% 27.95/18.16 tff(6839,plain,
% 27.95/18.16 (~(f3(c2, c2) = c2)),
% 27.95/18.16 inference(modus_ponens,[status(thm)],[6832, 6756])).
% 27.95/18.16 tff(6840,plain,
% 27.95/18.16 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(f9(c2, c2) = c3)) | (~(c2 = f2(f9(c2, c2)))) | (c2 = c4) | (f3(c2, c2) = c2) | big_f(f3(c2, c2), c2) | big_f(f9(c2, c2), c2))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (~(f9(c2, c2) = c3)) | (~(c2 = f2(f9(c2, c2)))) | (c2 = c4) | (f3(c2, c2) = c2) | big_f(f3(c2, c2), c2) | big_f(f9(c2, c2), c2))),
% 27.95/18.16 inference(rewrite,[status(thm)],[])).
% 27.95/18.16 tff(6841,plain,
% 27.95/18.16 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(f9(c2, c2) = c3)) | (~(c2 = f2(f9(c2, c2)))) | (c2 = c4) | (f3(c2, c2) = c2) | big_f(f3(c2, c2), c2) | big_f(f9(c2, c2), c2))),
% 27.95/18.16 inference(quant_inst,[status(thm)],[])).
% 27.95/18.16 tff(6842,plain,
% 27.95/18.16 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (~(f9(c2, c2) = c3)) | (~(c2 = f2(f9(c2, c2)))) | (c2 = c4) | (f3(c2, c2) = c2) | big_f(f3(c2, c2), c2) | big_f(f9(c2, c2), c2)),
% 27.95/18.16 inference(modus_ponens,[status(thm)],[6841, 6840])).
% 27.95/18.16 tff(6843,plain,
% 27.95/18.16 ($false),
% 27.95/18.16 inference(unit_resolution,[status(thm)],[6842, 1459, 873, 1822, 3685, 5689, 6839, 6838])).
% 27.95/18.16 tff(6844,plain,((f3(f6(f7(c2), c3), c2) = c2) | (c2 = c4) | (~(f9(c2, c2) = c3)) | big_f(f9(c2, c2), c2) | (~(c2 = f2(f9(c2, c2)))) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f6(f7(c2), c3) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.95/18.16 tff(6845,plain,
% 27.95/18.16 (f3(f6(f7(c2), c3), c2) = c2),
% 27.95/18.16 inference(unit_resolution,[status(thm)],[6844, 6831, 5580, 3685, 6774, 148, 79, 122, 6628])).
% 27.95/18.16 tff(6846,plain,
% 27.95/18.16 (c2 = f6(f7(c2), c3)),
% 27.95/18.16 inference(symmetry,[status(thm)],[6628])).
% 27.95/18.16 tff(6847,plain,
% 27.95/18.16 (f3(c2, c2) = f3(f6(f7(c2), c3), c2)),
% 27.95/18.16 inference(monotonicity,[status(thm)],[6846])).
% 27.95/18.16 tff(6848,plain,
% 27.95/18.16 (f3(c2, c2) = c2),
% 27.95/18.16 inference(transitivity,[status(thm)],[6847, 6845])).
% 27.95/18.16 tff(6849,plain,
% 27.95/18.16 (big_f(f3(c2, c2), c2) <=> big_f(c2, c2)),
% 27.95/18.16 inference(monotonicity,[status(thm)],[6848])).
% 27.95/18.16 tff(6850,plain,
% 27.95/18.16 (big_f(c2, c2) <=> big_f(f3(c2, c2), c2)),
% 27.95/18.16 inference(symmetry,[status(thm)],[6849])).
% 27.95/18.17 tff(6851,plain,
% 27.95/18.17 (big_f(f3(c2, c2), c2)),
% 27.95/18.17 inference(modus_ponens,[status(thm)],[1345, 6850])).
% 27.95/18.17 tff(6852,plain,
% 27.95/18.17 (f3(f6(f7(c2), c3), c2) = f3(c2, c2)),
% 27.95/18.17 inference(symmetry,[status(thm)],[6847])).
% 27.95/18.17 tff(6853,plain,
% 27.95/18.17 ((f3(f6(f7(c2), c3), c2) = c2) <=> (f3(c2, c2) = c2)),
% 27.95/18.17 inference(monotonicity,[status(thm)],[6852])).
% 27.95/18.17 tff(6854,plain,
% 27.95/18.17 (f3(c2, c2) = c2),
% 27.95/18.17 inference(modus_ponens,[status(thm)],[6845, 6853])).
% 27.95/18.17 tff(6855,plain,
% 27.95/18.17 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((c2 = c4) | (~(c2 = f2(f9(c2, c2)))) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~(f9(c2, c2) = c3)) | big_f(f9(c2, c2), c2))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (c2 = c4) | (~(c2 = f2(f9(c2, c2)))) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~(f9(c2, c2) = c3)) | big_f(f9(c2, c2), c2))),
% 27.95/18.17 inference(rewrite,[status(thm)],[])).
% 27.95/18.17 tff(6856,plain,
% 27.95/18.17 (((~(f9(c2, c2) = c3)) | (~(c2 = f2(f9(c2, c2)))) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | big_f(f9(c2, c2), c2)) <=> ((c2 = c4) | (~(c2 = f2(f9(c2, c2)))) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~(f9(c2, c2) = c3)) | big_f(f9(c2, c2), c2))),
% 27.95/18.17 inference(rewrite,[status(thm)],[])).
% 27.95/18.17 tff(6857,plain,
% 27.95/18.17 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(f9(c2, c2) = c3)) | (~(c2 = f2(f9(c2, c2)))) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | big_f(f9(c2, c2), c2))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((c2 = c4) | (~(c2 = f2(f9(c2, c2)))) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~(f9(c2, c2) = c3)) | big_f(f9(c2, c2), c2)))),
% 27.95/18.17 inference(monotonicity,[status(thm)],[6856])).
% 27.95/18.17 tff(6858,plain,
% 27.95/18.17 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(f9(c2, c2) = c3)) | (~(c2 = f2(f9(c2, c2)))) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | big_f(f9(c2, c2), c2))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (c2 = c4) | (~(c2 = f2(f9(c2, c2)))) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~(f9(c2, c2) = c3)) | big_f(f9(c2, c2), c2))),
% 27.95/18.17 inference(transitivity,[status(thm)],[6857, 6855])).
% 27.95/18.17 tff(6859,plain,
% 27.95/18.17 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(f9(c2, c2) = c3)) | (~(c2 = f2(f9(c2, c2)))) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | big_f(f9(c2, c2), c2))),
% 27.95/18.17 inference(quant_inst,[status(thm)],[])).
% 27.95/18.17 tff(6860,plain,
% 27.95/18.17 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (c2 = c4) | (~(c2 = f2(f9(c2, c2)))) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~(f9(c2, c2) = c3)) | big_f(f9(c2, c2), c2)),
% 27.95/18.17 inference(modus_ponens,[status(thm)],[6859, 6858])).
% 27.95/18.17 tff(6861,plain,
% 27.95/18.17 ($false),
% 27.95/18.17 inference(unit_resolution,[status(thm)],[6860, 1398, 6831, 5580, 3685, 6774, 6854, 6851])).
% 27.95/18.17 tff(6862,plain,(big_f(f9(c2, c2), c2) | (~big_f(c2, c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(c3 = c1)) | big_f(c1, c1) | (~big_f(f7(c2), f6(c2, c2)))), inference(lemma,lemma(discharge,[]))).
% 27.95/18.17 tff(6863,plain,
% 27.95/18.17 (big_f(f9(c2, c2), c2)),
% 27.95/18.17 inference(unit_resolution,[status(thm)],[6862, 6306, 148, 79, 122, 4234, 172, 66, 6583])).
% 27.95/18.17 tff(6864,plain,
% 27.95/18.17 (big_f(f9(c2, c2), f10(c2))),
% 27.95/18.17 inference(unit_resolution,[status(thm)],[6482, 6863, 122])).
% 27.95/18.17 tff(6865,plain,
% 27.95/18.17 (big_f(f9(c2, c2), f10(f9(c2, c2)))),
% 27.95/18.17 inference(unit_resolution,[status(thm)],[3625, 6864, 122, 15, 79, 148])).
% 27.95/18.17 tff(6866,plain,
% 27.95/18.17 (~(f10(f9(c2, c2)) = f9(c2, c2))),
% 27.95/18.17 inference(unit_resolution,[status(thm)],[762, 15, 122, 79, 148])).
% 27.95/18.17 tff(6867,plain,
% 27.95/18.17 ($false),
% 27.95/18.17 inference(unit_resolution,[status(thm)],[5759, 2662, 1767, 2026, 2137, 5537, 5532, 4257])).
% 27.95/18.17 tff(6868,plain,((f6(c1, c2) = c2) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (f9(c2, c2) = f8(f9(c2, c2))) | big_f(f9(c2, c2), f9(c2, c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f7(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 27.95/18.17 tff(6869,plain,
% 27.95/18.17 (f6(c1, c2) = c2),
% 27.95/18.17 inference(unit_resolution,[status(thm)],[6868, 2137, 2026, 1767, 3689, 148, 79, 122, 4234])).
% 27.95/18.17 tff(6870,plain,
% 27.95/18.17 (f6(f9(c2, c2), c2) = c2),
% 27.95/18.17 inference(modus_ponens,[status(thm)],[6869, 4249])).
% 27.95/18.17 tff(6871,plain,
% 27.95/18.17 (f6(f9(c2, c2), c2) = c2),
% 27.95/18.17 inference(transitivity,[status(thm)],[4247, 6869])).
% 27.95/18.17 tff(6872,plain,
% 27.95/18.17 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)) <=> big_f(f9(c2, c2), c2)),
% 27.95/18.17 inference(monotonicity,[status(thm)],[5532, 6871])).
% 27.95/18.17 tff(6873,plain,
% 27.95/18.17 (big_f(f9(c2, c2), c2) <=> big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))),
% 27.95/18.17 inference(symmetry,[status(thm)],[6872])).
% 27.95/18.17 tff(6874,plain,
% 27.95/18.17 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))),
% 27.95/18.17 inference(modus_ponens,[status(thm)],[2041, 6873])).
% 27.95/18.17 tff(6875,plain,
% 27.95/18.17 ($false),
% 27.95/18.17 inference(unit_resolution,[status(thm)],[5789, 2730, 1767, 2026, 2137, 6874, 5532, 6870])).
% 27.95/18.17 tff(6876,plain,((f9(c2, c2) = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (~big_f(f9(c2, c2), c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f7(c1) = c1)) | big_f(f9(c2, c2), f9(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 27.95/18.17 tff(6877,plain,
% 27.95/18.17 (f9(c2, c2) = f8(f9(c2, c2))),
% 27.95/18.17 inference(unit_resolution,[status(thm)],[6876, 6866, 6865, 6863, 148, 79, 122, 4234, 5569])).
% 27.95/18.17 tff(6878,plain,
% 27.95/18.17 (f8(f9(c2, c2)) = f9(c2, c2)),
% 27.95/18.17 inference(symmetry,[status(thm)],[6877])).
% 27.95/18.17 tff(6879,plain,
% 27.95/18.17 ((c2 = f8(f9(c2, c2))) <=> (c2 = f9(c2, c2))),
% 27.95/18.17 inference(monotonicity,[status(thm)],[6878])).
% 27.95/18.17 tff(6880,plain,
% 27.95/18.17 ((c2 = f8(f9(c2, c2))) <=> (f9(c2, c2) = c2)),
% 27.95/18.17 inference(transitivity,[status(thm)],[6879, 167])).
% 27.95/18.17 tff(6881,plain,
% 27.95/18.17 ((f9(c2, c2) = c2) <=> (c2 = f8(f9(c2, c2)))),
% 27.95/18.17 inference(symmetry,[status(thm)],[6880])).
% 27.95/18.17 tff(6882,plain,
% 27.95/18.17 ((~(f9(c2, c2) = c2)) <=> (~(c2 = f8(f9(c2, c2))))),
% 27.95/18.17 inference(monotonicity,[status(thm)],[6881])).
% 27.95/18.17 tff(6883,plain,
% 27.95/18.17 (~(c2 = f8(f9(c2, c2)))),
% 27.95/18.17 inference(modus_ponens,[status(thm)],[185, 6882])).
% 27.95/18.17 tff(6884,plain,
% 27.95/18.17 (f10(f9(c2, c2)) = c2),
% 27.95/18.17 inference(transitivity,[status(thm)],[3646, 15])).
% 27.95/18.17 tff(6885,plain,
% 27.95/18.17 (big_f(c2, f10(f9(c2, c2))) <=> big_f(c2, c2)),
% 27.95/18.17 inference(monotonicity,[status(thm)],[6884])).
% 27.95/18.17 tff(6886,plain,
% 27.95/18.17 (big_f(c2, c2) <=> big_f(c2, f10(f9(c2, c2)))),
% 27.95/18.17 inference(symmetry,[status(thm)],[6885])).
% 27.95/18.17 tff(6887,plain,
% 27.95/18.17 (big_f(c2, f10(f9(c2, c2)))),
% 27.95/18.17 inference(modus_ponens,[status(thm)],[6306, 6886])).
% 27.95/18.17 tff(6888,assumption,(~(c2 = f8(f9(c2, c2)))), introduced(assumption)).
% 27.95/18.17 tff(6889,plain,
% 27.95/18.17 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)))),
% 27.95/18.17 inference(rewrite,[status(thm)],[])).
% 27.95/18.17 tff(6890,plain,
% 27.95/18.17 (((f10(f9(c2, c2)) = f9(c2, c2)) | (c2 = f8(f9(c2, c2))) | (~big_f(c2, f10(f9(c2, c2)))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))) <=> ((~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)))),
% 27.95/18.17 inference(rewrite,[status(thm)],[])).
% 27.95/18.17 tff(6891,plain,
% 27.95/18.17 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (c2 = f8(f9(c2, c2))) | (~big_f(c2, f10(f9(c2, c2)))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))))),
% 27.95/18.17 inference(monotonicity,[status(thm)],[6890])).
% 27.95/18.17 tff(6892,plain,
% 27.95/18.17 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (c2 = f8(f9(c2, c2))) | (~big_f(c2, f10(f9(c2, c2)))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)))),
% 27.95/18.17 inference(transitivity,[status(thm)],[6891, 6889])).
% 27.95/18.17 tff(6893,plain,
% 27.95/18.17 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (c2 = f8(f9(c2, c2))) | (~big_f(c2, f10(f9(c2, c2)))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)))),
% 27.95/18.17 inference(quant_inst,[status(thm)],[])).
% 27.95/18.17 tff(6894,plain,
% 27.95/18.17 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))),
% 27.95/18.17 inference(modus_ponens,[status(thm)],[6893, 6892])).
% 27.95/18.17 tff(6895,plain,
% 27.95/18.17 ($false),
% 27.95/18.17 inference(unit_resolution,[status(thm)],[6894, 2662, 1767, 2016, 6888, 5537, 5532, 4257])).
% 27.95/18.17 tff(6896,plain,((f6(c1, c2) = c2) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | big_f(f9(c2, c2), f9(c2, c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f7(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 27.95/18.17 tff(6897,plain,
% 27.95/18.17 (f6(c1, c2) = c2),
% 27.95/18.17 inference(unit_resolution,[status(thm)],[6896, 6866, 6887, 6883, 5569, 148, 79, 122, 4234])).
% 27.95/18.17 tff(6898,plain,
% 27.95/18.17 (f6(f9(c2, c2), c2) = c2),
% 27.95/18.17 inference(modus_ponens,[status(thm)],[6897, 4249])).
% 27.95/18.17 tff(6899,plain,
% 27.95/18.17 (f6(f9(c2, c2), c2) = c2),
% 27.95/18.17 inference(transitivity,[status(thm)],[4247, 6897])).
% 27.95/18.17 tff(6900,plain,
% 27.95/18.17 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)) <=> big_f(f9(c2, c2), c2)),
% 27.95/18.17 inference(monotonicity,[status(thm)],[5532, 6899])).
% 27.95/18.17 tff(6901,plain,
% 27.95/18.17 (big_f(f9(c2, c2), c2) <=> big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))),
% 27.95/18.17 inference(symmetry,[status(thm)],[6900])).
% 27.95/18.17 tff(6902,plain,
% 27.95/18.17 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))),
% 27.95/18.17 inference(modus_ponens,[status(thm)],[6863, 6901])).
% 27.95/18.17 tff(6903,plain,
% 27.95/18.17 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), c2) = c2)) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), c2) = c2)) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))))),
% 27.95/18.17 inference(rewrite,[status(thm)],[])).
% 27.95/18.17 tff(6904,plain,
% 27.95/18.17 (((f10(f9(c2, c2)) = f9(c2, c2)) | (c2 = f8(f9(c2, c2))) | (~big_f(c2, f10(f9(c2, c2)))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), c2) = c2)) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)))) <=> ((~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), c2) = c2)) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))))),
% 27.95/18.17 inference(rewrite,[status(thm)],[])).
% 27.95/18.17 tff(6905,plain,
% 27.95/18.17 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (c2 = f8(f9(c2, c2))) | (~big_f(c2, f10(f9(c2, c2)))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), c2) = c2)) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), c2) = c2)) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)))))),
% 27.95/18.17 inference(monotonicity,[status(thm)],[6904])).
% 27.95/18.17 tff(6906,plain,
% 27.95/18.17 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (c2 = f8(f9(c2, c2))) | (~big_f(c2, f10(f9(c2, c2)))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), c2) = c2)) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), c2) = c2)) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))))),
% 27.95/18.17 inference(transitivity,[status(thm)],[6905, 6903])).
% 27.95/18.17 tff(6907,plain,
% 27.95/18.17 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f9(c2, c2)) = f9(c2, c2)) | (c2 = f8(f9(c2, c2))) | (~big_f(c2, f10(f9(c2, c2)))) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), c2) = c2)) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))))),
% 27.95/18.17 inference(quant_inst,[status(thm)],[])).
% 27.95/18.17 tff(6908,plain,
% 27.95/18.17 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), c2) = c2)) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)))),
% 27.95/18.17 inference(modus_ponens,[status(thm)],[6907, 6906])).
% 27.95/18.17 tff(6909,plain,
% 27.95/18.17 ($false),
% 27.95/18.17 inference(unit_resolution,[status(thm)],[6908, 2730, 6866, 6887, 6883, 6902, 5532, 6898])).
% 27.95/18.17 tff(6910,plain,((f10(c1) = c1) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(c3 = c1)) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 27.95/18.17 tff(6911,plain,
% 27.95/18.17 (f10(c1) = c1),
% 27.95/18.17 inference(unit_resolution,[status(thm)],[6910, 66, 79, 122, 4234, 172, 148])).
% 27.95/18.17 tff(6912,plain,
% 27.95/18.17 (big_f(f7(c2), f6(c2, c2))),
% 27.95/18.17 inference(unit_resolution,[status(thm)],[5485, 1345, 6582, 185, 122, 4597])).
% 27.95/18.17 tff(6913,plain,
% 27.95/18.17 ($false),
% 27.95/18.17 inference(unit_resolution,[status(thm)],[6862, 6912, 1345, 148, 79, 122, 4234, 172, 66, 3685])).
% 27.95/18.17 tff(6914,plain,((~big_f(c2, c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(c3 = c1)) | big_f(c1, c1) | big_f(f9(c2, c2), c2)), inference(lemma,lemma(discharge,[]))).
% 27.95/18.17 tff(6915,plain,
% 27.95/18.17 (~big_f(c2, c2)),
% 27.95/18.17 inference(unit_resolution,[status(thm)],[6914, 3685, 79, 122, 4234, 172, 66, 148])).
% 27.95/18.17 tff(6916,plain,
% 27.95/18.17 (big_f(c2, c1)),
% 27.95/18.17 inference(unit_resolution,[status(thm)],[6579, 6915, 79, 4234, 122, 148])).
% 27.95/18.17 tff(6917,plain,
% 27.95/18.17 (~big_f(c2, f9(c2, c2))),
% 27.95/18.17 inference(unit_resolution,[status(thm)],[6060, 6915, 122, 4597, 148, 79, 172, 6582])).
% 27.95/18.17 tff(6918,plain,
% 27.95/18.17 ($false),
% 27.95/18.17 inference(unit_resolution,[status(thm)],[3814, 6917, 6916, 148, 79, 122])).
% 27.95/18.17 tff(6919,plain,(big_f(f9(c2, c2), c2) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(c3 = c1)) | (~(f7(c1) = c1)) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 27.95/18.17 tff(6920,plain,
% 27.95/18.17 (big_f(f9(c2, c2), c2)),
% 27.95/18.17 inference(unit_resolution,[status(thm)],[6919, 66, 79, 122, 172, 4234, 148])).
% 27.95/18.17 tff(6921,plain,
% 27.95/18.17 (~big_f(c2, f9(c2, c2))),
% 27.95/18.17 inference(unit_resolution,[status(thm)],[4320, 6920, 148, 79, 122, 4234, 5569, 6911])).
% 27.95/18.17 tff(6922,plain,
% 27.95/18.17 (~big_f(c2, c1)),
% 27.95/18.17 inference(unit_resolution,[status(thm)],[3814, 6921, 148, 79, 122])).
% 27.95/18.17 tff(6923,plain,
% 27.95/18.17 (~big_f(c2, c2)),
% 27.95/18.17 inference(unit_resolution,[status(thm)],[5379, 6921, 374, 6920, 148, 79, 122])).
% 27.95/18.17 tff(6924,plain,
% 27.95/18.17 ($false),
% 27.95/18.17 inference(unit_resolution,[status(thm)],[6579, 6923, 6922, 79, 4234, 122, 148])).
% 27.95/18.17 tff(6925,plain,(big_f(c1, c1) | (~(f4(c4) = c2)) | (~(f7(c1) = c1)) | (~(f10(c2) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(c3 = c1))), inference(lemma,lemma(discharge,[]))).
% 27.95/18.17 tff(6926,plain,
% 27.95/18.17 (big_f(c1, c1)),
% 27.95/18.17 inference(unit_resolution,[status(thm)],[6925, 172, 4234, 122, 148, 79])).
% 27.95/18.17 tff(6927,plain,
% 27.95/18.17 (big_f(f9(c2, c2), f9(c2, c2))),
% 27.95/18.17 inference(modus_ponens,[status(thm)],[6926, 5568])).
% 27.95/18.17 tff(6928,plain,
% 27.95/18.17 (~big_f(f9(c2, c2), c2)),
% 27.95/18.17 inference(unit_resolution,[status(thm)],[5519, 6927, 5567, 79, 148, 122])).
% 27.95/18.17 tff(6929,plain,
% 27.95/18.17 (~big_f(f9(c2, c2), f10(c2))),
% 27.95/18.17 inference(unit_resolution,[status(thm)],[3687, 6928, 122])).
% 27.95/18.17 tff(6930,plain,
% 27.95/18.17 (big_f(f7(c1), f6(c1, c1))),
% 27.95/18.17 inference(unit_resolution,[status(thm)],[4658, 6929, 148, 79, 122, 4234, 6927])).
% 27.95/18.17 tff(6931,assumption,(f6(c1, c2) = c1), introduced(assumption)).
% 27.95/18.17 tff(6932,plain,
% 27.95/18.17 (c1 = f6(c1, c2)),
% 27.95/18.17 inference(symmetry,[status(thm)],[6931])).
% 27.95/18.17 tff(6933,plain,
% 27.95/18.17 (f6(c1, c1) = f6(c1, f6(c1, c2))),
% 27.95/18.17 inference(monotonicity,[status(thm)],[6932])).
% 27.95/18.17 tff(6934,plain,
% 27.95/18.17 (f6(c1, f6(c1, c2)) = f6(c1, c1)),
% 27.95/18.17 inference(symmetry,[status(thm)],[6933])).
% 27.95/18.17 tff(6935,plain,
% 27.95/18.17 ((f6(c1, f6(c1, c2)) = c1) <=> (f6(c1, c1) = c1)),
% 27.95/18.17 inference(monotonicity,[status(thm)],[6934])).
% 27.95/18.17 tff(6936,plain,
% 27.95/18.17 ((f6(c1, c1) = c1) <=> (f6(c1, f6(c1, c2)) = c1)),
% 27.95/18.17 inference(symmetry,[status(thm)],[6935])).
% 27.95/18.17 tff(6937,plain,
% 27.95/18.17 ((~(f6(c1, c1) = c1)) <=> (~(f6(c1, f6(c1, c2)) = c1))),
% 27.95/18.17 inference(monotonicity,[status(thm)],[6936])).
% 27.95/18.17 tff(6938,plain,
% 27.95/18.17 ((~(f6(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) <=> (~(f6(c1, c1) = c1))),
% 27.95/18.17 inference(monotonicity,[status(thm)],[4595])).
% 27.95/18.17 tff(6939,plain,
% 27.95/18.17 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2)))),
% 27.95/18.17 inference(modus_ponens,[status(thm)],[5964, 4671])).
% 27.95/18.17 tff(6940,plain,
% 27.95/18.17 ((~(f6(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2))))),
% 27.95/18.17 inference(unit_resolution,[status(thm)],[4676, 2534, 122, 185, 4597, 5532])).
% 27.95/18.17 tff(6941,plain,
% 27.95/18.17 (~(f6(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))),
% 27.95/18.17 inference(unit_resolution,[status(thm)],[6940, 6939])).
% 27.95/18.17 tff(6942,plain,
% 27.95/18.17 (~(f6(c1, c1) = c1)),
% 27.95/18.17 inference(modus_ponens,[status(thm)],[6941, 6938])).
% 27.95/18.17 tff(6943,plain,
% 27.95/18.17 (~(f6(c1, f6(c1, c2)) = c1)),
% 27.95/18.17 inference(modus_ponens,[status(thm)],[6942, 6937])).
% 27.95/18.17 tff(6944,plain,
% 27.95/18.17 (f6(c1, f6(c1, c2)) = c2),
% 27.95/18.17 inference(unit_resolution,[status(thm)],[63, 6943])).
% 27.95/18.17 tff(6945,plain,
% 27.95/18.17 (f6(c1, c1) = c2),
% 27.95/18.17 inference(transitivity,[status(thm)],[6933, 6944])).
% 27.95/18.17 tff(6946,plain,
% 27.95/18.17 (big_f(f7(c1), f6(c1, c1)) <=> big_f(f9(c2, c2), c2)),
% 27.95/18.17 inference(monotonicity,[status(thm)],[4653, 6945])).
% 27.95/18.17 tff(6947,plain,
% 27.95/18.17 (big_f(f9(c2, c2), c2) <=> big_f(f7(c1), f6(c1, c1))),
% 27.95/18.17 inference(symmetry,[status(thm)],[6946])).
% 27.95/18.17 tff(6948,plain,
% 27.95/18.17 ((~big_f(f9(c2, c2), c2)) <=> (~big_f(f7(c1), f6(c1, c1)))),
% 27.95/18.17 inference(monotonicity,[status(thm)],[6947])).
% 27.95/18.17 tff(6949,plain,
% 27.95/18.17 (~big_f(f7(c1), f6(c1, c1))),
% 27.95/18.17 inference(modus_ponens,[status(thm)],[3685, 6948])).
% 27.95/18.17 tff(6950,plain,
% 27.95/18.17 ($false),
% 27.95/18.17 inference(unit_resolution,[status(thm)],[5964, 6949])).
% 27.95/18.17 tff(6951,plain,((~(f6(c1, c2) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | big_f(f9(c2, c2), c2) | (~(f7(c1) = c1)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.95/18.17 tff(6952,plain,
% 27.95/18.17 (~(f6(c1, c2) = c1)),
% 27.95/18.17 inference(unit_resolution,[status(thm)],[6951, 6930, 6928, 4234, 148, 79, 122])).
% 27.95/18.17 tff(6953,plain,
% 27.95/18.17 (f6(c1, c2) = c2),
% 27.95/18.17 inference(unit_resolution,[status(thm)],[48, 6952])).
% 27.95/18.17 tff(6954,plain,
% 27.95/18.17 (f6(f9(c2, c2), c2) = f6(c1, c2)),
% 27.95/18.17 inference(monotonicity,[status(thm)],[4702])).
% 27.95/18.17 tff(6955,plain,
% 27.95/18.17 ((f3(c1, c2) = f6(c1, f3(c1, c2))) <=> (f6(c1, f3(c1, c2)) = f3(c1, c2))),
% 27.95/18.17 inference(commutativity,[status(thm)],[])).
% 27.95/18.17 tff(6956,plain,
% 27.95/18.17 (f7(c2) = c2),
% 27.95/18.17 inference(unit_resolution,[status(thm)],[5557, 6928, 79, 122, 148, 4234])).
% 27.95/18.17 tff(6957,plain,
% 27.95/18.17 (c2 = f7(c2)),
% 27.95/18.17 inference(symmetry,[status(thm)],[6956])).
% 27.95/18.17 tff(6958,plain,
% 27.95/18.17 (c2 = f7(f4(c4))),
% 27.95/18.17 inference(transitivity,[status(thm)],[6957, 81])).
% 27.95/18.17 tff(6959,plain,
% 27.95/18.17 (f6(c2, c2) = f6(c2, f7(f4(c4)))),
% 27.95/18.17 inference(monotonicity,[status(thm)],[6958])).
% 27.95/18.18 tff(6960,plain,
% 27.95/18.18 (f6(c2, f7(f4(c4))) = f6(c2, c2)),
% 27.95/18.18 inference(symmetry,[status(thm)],[6959])).
% 27.95/18.18 tff(6961,plain,
% 27.95/18.18 ((f6(c2, f7(f4(c4))) = c2) <=> (f6(c2, c2) = c2)),
% 27.95/18.18 inference(monotonicity,[status(thm)],[6960])).
% 27.95/18.18 tff(6962,plain,
% 27.95/18.18 ((f6(c2, c2) = c2) <=> (f6(c2, f7(f4(c4))) = c2)),
% 27.95/18.18 inference(symmetry,[status(thm)],[6961])).
% 27.95/18.18 tff(6963,plain,
% 27.95/18.18 ((~(f6(c2, c2) = c2)) <=> (~(f6(c2, f7(f4(c4))) = c2))),
% 27.95/18.18 inference(monotonicity,[status(thm)],[6962])).
% 27.95/18.18 tff(6964,plain,
% 27.95/18.18 (big_f(c2, c1)),
% 27.95/18.18 inference(unit_resolution,[status(thm)],[6579, 121, 79, 4234, 122, 148])).
% 27.95/18.18 tff(6965,plain,
% 27.95/18.18 (big_f(f9(c2, c2), f9(c2, c2))),
% 27.95/18.18 inference(modus_ponens,[status(thm)],[6926, 4889])).
% 27.95/18.18 tff(6966,plain,
% 27.95/18.18 (~big_f(f9(c2, c2), c2)),
% 27.95/18.18 inference(unit_resolution,[status(thm)],[5519, 6965, 5580, 79, 148, 122])).
% 27.95/18.18 tff(6967,plain,
% 27.95/18.18 (f7(c2) = c2),
% 27.95/18.18 inference(unit_resolution,[status(thm)],[5557, 6966, 79, 122, 148, 4234])).
% 27.95/18.18 tff(6968,plain,
% 27.95/18.18 (~big_f(f9(c2, c2), f10(c2))),
% 27.95/18.18 inference(unit_resolution,[status(thm)],[3687, 6966, 122])).
% 27.95/18.18 tff(6969,plain,
% 27.95/18.18 (~big_f(c2, f9(c2, c2))),
% 27.95/18.18 inference(unit_resolution,[status(thm)],[6060, 121, 122, 6968, 148, 79, 172, 6967])).
% 27.95/18.18 tff(6970,plain,
% 27.95/18.18 ($false),
% 27.95/18.18 inference(unit_resolution,[status(thm)],[3814, 6969, 6964, 148, 79, 122])).
% 27.95/18.18 tff(6971,plain,(big_f(c2, c2) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(c3 = c1)) | (~(f7(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 27.95/18.18 tff(6972,plain,
% 27.95/18.18 (big_f(c2, c2)),
% 27.95/18.18 inference(unit_resolution,[status(thm)],[6971, 172, 79, 122, 148, 4234])).
% 27.95/18.18 tff(6973,plain,
% 27.95/18.18 (big_f(f7(c2), f6(c2, c2))),
% 27.95/18.18 inference(unit_resolution,[status(thm)],[5485, 6972, 6956, 4743, 122, 6929])).
% 27.95/18.18 tff(6974,plain,
% 27.95/18.18 (~(f6(c2, c2) = c2)),
% 27.95/18.18 inference(unit_resolution,[status(thm)],[2744, 6973, 6956, 6929, 4743, 122])).
% 27.95/18.18 tff(6975,plain,
% 27.95/18.18 (~(f6(c2, f7(f4(c4))) = c2)),
% 27.95/18.18 inference(modus_ponens,[status(thm)],[6974, 6963])).
% 27.95/18.18 tff(6976,plain,
% 27.95/18.18 (f6(c2, f7(f4(c4))) = c1),
% 27.95/18.18 inference(unit_resolution,[status(thm)],[6601, 6975])).
% 27.95/18.18 tff(6977,plain,
% 27.95/18.18 (f6(c2, c2) = f9(c2, c2)),
% 27.95/18.18 inference(transitivity,[status(thm)],[6959, 6976, 149, 2634])).
% 27.95/18.18 tff(6978,plain,
% 27.95/18.18 (big_f(f7(c2), f6(c2, c2)) <=> big_f(c2, f9(c2, c2))),
% 27.95/18.18 inference(monotonicity,[status(thm)],[6956, 6977])).
% 27.95/18.18 tff(6979,plain,
% 27.95/18.18 (big_f(c2, f9(c2, c2))),
% 27.95/18.18 inference(modus_ponens,[status(thm)],[6973, 6978])).
% 27.95/18.18 tff(6980,plain,
% 27.95/18.18 (f9(c2, c2) = f7(c1)),
% 27.95/18.18 inference(transitivity,[status(thm)],[2629, 148, 5544])).
% 27.95/18.18 tff(6981,plain,
% 27.95/18.18 (big_f(f9(c2, c2), f6(c1, c1)) <=> big_f(f7(c1), f6(c1, c1))),
% 27.95/18.18 inference(monotonicity,[status(thm)],[6980])).
% 27.95/18.18 tff(6982,plain,
% 27.95/18.18 (big_f(f7(c1), f6(c1, c1)) <=> big_f(f9(c2, c2), f6(c1, c1))),
% 27.95/18.18 inference(symmetry,[status(thm)],[6981])).
% 27.95/18.18 tff(6983,plain,
% 27.95/18.18 (big_f(f9(c2, c2), f6(c1, c1))),
% 27.95/18.18 inference(modus_ponens,[status(thm)],[6930, 6982])).
% 27.95/18.18 tff(6984,plain,
% 27.95/18.18 (f6(f9(c2, c2), f9(c2, c2)) = f6(c1, c1)),
% 27.95/18.18 inference(monotonicity,[status(thm)],[4702, 4702])).
% 27.95/18.18 tff(6985,plain,
% 27.95/18.18 ((f6(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) <=> (f6(c1, c1) = c1)),
% 27.95/18.18 inference(monotonicity,[status(thm)],[6984, 4702])).
% 27.95/18.18 tff(6986,plain,
% 27.95/18.18 ((~(f6(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) <=> (~(f6(c1, c1) = c1))),
% 27.95/18.18 inference(monotonicity,[status(thm)],[6985])).
% 27.95/18.18 tff(6987,plain,
% 27.95/18.18 (f7(f9(c2, c2)) = f7(c1)),
% 27.95/18.18 inference(monotonicity,[status(thm)],[4702])).
% 27.95/18.18 tff(6988,plain,
% 27.95/18.18 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2))) <=> big_f(f7(c1), f6(c1, c1))),
% 27.95/18.18 inference(monotonicity,[status(thm)],[6987, 6984])).
% 27.95/18.18 tff(6989,plain,
% 27.95/18.18 (big_f(f7(c1), f6(c1, c1)) <=> big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2)))),
% 27.95/18.18 inference(symmetry,[status(thm)],[6988])).
% 27.95/18.18 tff(6990,plain,
% 27.95/18.18 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2)))),
% 27.95/18.18 inference(modus_ponens,[status(thm)],[6930, 6989])).
% 27.95/18.18 tff(6991,plain,
% 27.95/18.18 (f7(f9(c2, c2)) = f9(c2, c2)),
% 27.95/18.18 inference(transitivity,[status(thm)],[6987, 4234, 149, 2634])).
% 27.95/18.18 tff(6992,plain,
% 27.95/18.18 ((~(f6(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2))))),
% 27.95/18.18 inference(unit_resolution,[status(thm)],[4676, 2534, 122, 4743, 6929, 6991])).
% 27.95/18.18 tff(6993,plain,
% 27.95/18.18 (~(f6(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))),
% 27.95/18.18 inference(unit_resolution,[status(thm)],[6992, 6990])).
% 27.95/18.18 tff(6994,plain,
% 27.95/18.18 (~(f6(c1, c1) = c1)),
% 27.95/18.18 inference(modus_ponens,[status(thm)],[6993, 6986])).
% 27.95/18.18 tff(6995,assumption,(big_f(f9(c2, c2), f6(c1, c1))), introduced(assumption)).
% 27.95/18.18 tff(6996,plain,
% 27.95/18.18 (f4(f9(c2, c2)) = f4(c4)),
% 27.95/18.18 inference(monotonicity,[status(thm)],[514])).
% 27.95/18.18 tff(6997,plain,
% 27.95/18.18 (f4(f9(c2, c2)) = c2),
% 27.95/18.18 inference(transitivity,[status(thm)],[6996, 79])).
% 27.95/18.18 tff(6998,plain,
% 27.95/18.18 ((f9(c2, c2) = f4(f9(c2, c2))) <=> (f9(c2, c2) = c2)),
% 27.95/18.18 inference(monotonicity,[status(thm)],[6997])).
% 27.95/18.18 tff(6999,plain,
% 27.95/18.18 ((f9(c2, c2) = c2) <=> (f9(c2, c2) = f4(f9(c2, c2)))),
% 27.95/18.18 inference(symmetry,[status(thm)],[6998])).
% 27.95/18.18 tff(7000,plain,
% 27.95/18.18 ((~(f9(c2, c2) = c2)) <=> (~(f9(c2, c2) = f4(f9(c2, c2))))),
% 27.95/18.18 inference(monotonicity,[status(thm)],[6999])).
% 27.95/18.18 tff(7001,plain,
% 27.95/18.18 (~(f9(c2, c2) = f4(f9(c2, c2)))),
% 27.95/18.18 inference(modus_ponens,[status(thm)],[185, 7000])).
% 27.95/18.18 tff(7002,plain,
% 27.95/18.18 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c2, c2) = c3)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(f9(c2, c2) = c3)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1))))),
% 27.95/18.18 inference(rewrite,[status(thm)],[])).
% 27.95/18.18 tff(7003,plain,
% 27.95/18.18 (((~(f9(c2, c2) = c3)) | (~(f9(c2, c2) = c4)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1)))) <=> ((~(f9(c2, c2) = c3)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1))))),
% 27.95/18.18 inference(rewrite,[status(thm)],[])).
% 27.95/18.18 tff(7004,plain,
% 27.95/18.18 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c2, c2) = c3)) | (~(f9(c2, c2) = c4)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c2, c2) = c3)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1)))))),
% 27.95/18.18 inference(monotonicity,[status(thm)],[7003])).
% 27.95/18.18 tff(7005,plain,
% 27.95/18.18 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c2, c2) = c3)) | (~(f9(c2, c2) = c4)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(f9(c2, c2) = c3)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1))))),
% 27.95/18.18 inference(transitivity,[status(thm)],[7004, 7002])).
% 27.95/18.18 tff(7006,plain,
% 27.95/18.18 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c2, c2) = c3)) | (~(f9(c2, c2) = c4)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1))))),
% 27.95/18.18 inference(quant_inst,[status(thm)],[])).
% 27.95/18.18 tff(7007,plain,
% 27.95/18.18 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(f9(c2, c2) = c3)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1)))),
% 27.95/18.18 inference(modus_ponens,[status(thm)],[7006, 7005])).
% 27.95/18.18 tff(7008,plain,
% 27.95/18.18 ((f9(c2, c2) = f4(f9(c2, c2))) | (~(f9(c2, c2) = c4)) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1)))),
% 27.95/18.18 inference(unit_resolution,[status(thm)],[7007, 1355, 487, 1822])).
% 27.95/18.18 tff(7009,plain,
% 27.95/18.18 (f6(c1, c1) = f2(f9(c2, c2))),
% 27.95/18.18 inference(unit_resolution,[status(thm)],[7008, 7001, 6995, 514])).
% 27.95/18.18 tff(7010,plain,
% 27.95/18.18 (f6(c1, c1) = f2(c1)),
% 27.95/18.18 inference(transitivity,[status(thm)],[7009, 6508])).
% 27.95/18.18 tff(7011,plain,
% 27.95/18.18 ((f6(c1, c1) = c1) <=> (f2(c1) = c1)),
% 27.95/18.18 inference(monotonicity,[status(thm)],[7010])).
% 27.95/18.18 tff(7012,plain,
% 27.95/18.18 ((f6(c1, c1) = c1) <=> (c1 = f2(c1))),
% 27.95/18.18 inference(transitivity,[status(thm)],[7011, 6764])).
% 27.95/18.18 tff(7013,plain,
% 27.95/18.18 ((c1 = f2(c1)) <=> (f6(c1, c1) = c1)),
% 27.95/18.18 inference(symmetry,[status(thm)],[7012])).
% 27.95/18.18 tff(7014,plain,
% 27.95/18.18 (f9(c2, c2) = f2(f9(c2, c2))),
% 27.95/18.18 inference(unit_resolution,[status(thm)],[5332, 7001, 514])).
% 27.95/18.18 tff(7015,plain,
% 27.95/18.18 (c1 = f2(c1)),
% 27.95/18.18 inference(modus_ponens,[status(thm)],[7014, 6630])).
% 27.95/18.18 tff(7016,plain,
% 27.95/18.18 (f6(c1, c1) = c1),
% 27.95/18.18 inference(modus_ponens,[status(thm)],[7015, 7013])).
% 27.95/18.18 tff(7017,plain,
% 27.95/18.18 ($false),
% 27.95/18.18 inference(unit_resolution,[status(thm)],[28, 7016])).
% 27.95/18.18 tff(7018,plain,((~(f9(c2, c2) = c4)) | (f6(c1, c1) = c1) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~big_f(f9(c2, c2), f6(c1, c1))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c3))), inference(lemma,lemma(discharge,[]))).
% 27.95/18.18 tff(7019,plain,
% 27.95/18.18 (~(f9(c2, c2) = c4)),
% 27.95/18.18 inference(unit_resolution,[status(thm)],[7018, 6994, 148, 79, 122, 6983, 6927, 5567])).
% 27.95/18.18 tff(7020,plain,
% 27.95/18.18 (~big_f(f9(c2, c2), c2)),
% 27.95/18.18 inference(unit_resolution,[status(thm)],[5519, 487, 1822, 79, 148, 122])).
% 27.95/18.18 tff(7021,assumption,(f6(c1, f3(c1, c2)) = c2), introduced(assumption)).
% 27.95/18.18 tff(7022,plain,
% 27.95/18.18 (~big_f(f9(c2, c2), f10(c2))),
% 27.95/18.18 inference(unit_resolution,[status(thm)],[3687, 7020, 122])).
% 27.95/18.18 tff(7023,plain,
% 27.95/18.18 (big_f(f7(c1), f6(c1, c1))),
% 27.95/18.18 inference(unit_resolution,[status(thm)],[4658, 7022, 148, 79, 122, 4234, 487])).
% 27.95/18.18 tff(7024,plain,
% 27.95/18.18 (big_f(f9(c2, c2), f6(c1, c1))),
% 27.95/18.18 inference(modus_ponens,[status(thm)],[7023, 5605])).
% 27.95/18.18 tff(7025,plain,
% 27.95/18.18 ((f6(c1, f3(c1, c2)) = f3(c1, c2)) <=> (c2 = f3(c1, c2))),
% 27.95/18.18 inference(monotonicity,[status(thm)],[7021])).
% 27.95/18.18 tff(7026,plain,
% 27.95/18.18 ((f6(c1, f3(c1, c2)) = f3(c1, c2)) <=> (f3(c1, c2) = c2)),
% 27.95/18.18 inference(transitivity,[status(thm)],[7025, 6643])).
% 27.95/18.18 tff(7027,plain,
% 27.95/18.18 ((f6(f9(c2, c2), f3(c1, c2)) = f3(c1, c2)) <=> (f3(f9(c2, c2), c2) = c2)),
% 27.95/18.18 inference(transitivity,[status(thm)],[6801, 7026, 6670])).
% 27.95/18.18 tff(7028,plain,
% 27.95/18.18 (f6(f9(c2, c2), f3(c1, c2)) = c2),
% 27.95/18.18 inference(transitivity,[status(thm)],[6648, 7021])).
% 27.95/18.18 tff(7029,plain,
% 27.95/18.18 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(c1, c2))) <=> big_f(f9(c2, c2), c2)),
% 27.95/18.18 inference(monotonicity,[status(thm)],[5532, 7028])).
% 27.95/18.18 tff(7030,plain,
% 27.95/18.18 (big_f(f9(c2, c2), c2) <=> big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(c1, c2)))),
% 27.95/18.18 inference(symmetry,[status(thm)],[7029])).
% 27.95/18.18 tff(7031,plain,
% 27.95/18.18 ((~big_f(f9(c2, c2), c2)) <=> (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(c1, c2))))),
% 27.95/18.18 inference(monotonicity,[status(thm)],[7030])).
% 27.95/18.18 tff(7032,plain,
% 27.95/18.18 (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(c1, c2)))),
% 27.95/18.18 inference(modus_ponens,[status(thm)],[3685, 7031])).
% 27.95/18.18 tff(7033,plain,
% 27.95/18.18 (f6(f9(c2, c2), f3(c1, c2)) = f3(c1, c2)),
% 27.95/18.18 inference(unit_resolution,[status(thm)],[6700, 7032])).
% 27.95/18.18 tff(7034,plain,
% 27.95/18.18 (f3(f9(c2, c2), c2) = c2),
% 27.95/18.18 inference(modus_ponens,[status(thm)],[7033, 7027])).
% 27.95/18.18 tff(7035,plain,
% 27.95/18.18 (f3(c1, c2) = f6(f9(c2, c2), f3(c1, c2))),
% 27.95/18.18 inference(symmetry,[status(thm)],[7033])).
% 27.95/18.18 tff(7036,plain,
% 27.95/18.18 (f3(c1, c2) = c2),
% 27.95/18.18 inference(transitivity,[status(thm)],[7035, 6648, 7021])).
% 27.95/18.18 tff(7037,plain,
% 27.95/18.18 (big_f(f3(c1, c2), c1) <=> big_f(c2, f9(c2, c2))),
% 27.95/18.18 inference(monotonicity,[status(thm)],[7036, 150])).
% 27.95/18.18 tff(7038,plain,
% 27.95/18.18 (big_f(c2, f9(c2, c2)) <=> big_f(f3(c1, c2), c1)),
% 27.95/18.18 inference(symmetry,[status(thm)],[7037])).
% 27.95/18.18 tff(7039,plain,
% 27.95/18.18 (big_f(c2, f9(c2, c2)) <=> big_f(f3(f9(c2, c2), c2), f9(c2, c2))),
% 27.95/18.18 inference(transitivity,[status(thm)],[7038, 6646])).
% 27.95/18.18 tff(7040,plain,
% 27.95/18.18 (big_f(f3(f9(c2, c2), c2), f9(c2, c2))),
% 27.95/18.18 inference(modus_ponens,[status(thm)],[3719, 7039])).
% 27.95/18.18 tff(7041,assumption,(~(f6(c1, c1) = f2(f9(c2, c2)))), introduced(assumption)).
% 27.95/18.18 tff(7042,plain,
% 27.95/18.18 (^[X12: $i, X13: $i, X10: $i, X2: $i] : refl(((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12))) <=> ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12))))),
% 27.95/18.18 inference(bind,[status(th)],[])).
% 27.95/18.18 tff(7043,plain,
% 27.95/18.18 (![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12))) <=> ![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))),
% 27.95/18.18 inference(quant_intro,[status(thm)],[7042])).
% 27.95/18.18 tff(7044,plain,
% 27.95/18.18 (![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12))) <=> ![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))),
% 27.95/18.18 inference(rewrite,[status(thm)],[])).
% 27.95/18.18 tff(7045,plain,
% 27.95/18.18 (^[X12: $i, X13: $i, X10: $i, X2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_f(X10, X12)) | (X12 = f2(X10))) | (~(X10 = c3))) <=> ((~(X10 = c3)) | (X12 = f2(X10)) | (~big_f(X10, X12)))), (((((~big_f(X10, X12)) | (X12 = f2(X10))) | (~(X10 = c3))) | (~big_f(f3(X2, X13), X2))) <=> (((~(X10 = c3)) | (X12 = f2(X10)) | (~big_f(X10, X12))) | (~big_f(f3(X2, X13), X2))))), rewrite((((~(X10 = c3)) | (X12 = f2(X10)) | (~big_f(X10, X12))) | (~big_f(f3(X2, X13), X2))) <=> ((~(X10 = c3)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))), (((((~big_f(X10, X12)) | (X12 = f2(X10))) | (~(X10 = c3))) | (~big_f(f3(X2, X13), X2))) <=> ((~(X10 = c3)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12))))), ((((((~big_f(X10, X12)) | (X12 = f2(X10))) | (~(X10 = c3))) | (~big_f(f3(X2, X13), X2))) | (~(f3(X2, X13) = X13))) <=> (((~(X10 = c3)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12))) | (~(f3(X2, X13) = X13))))), rewrite((((~(X10 = c3)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12))) | (~(f3(X2, X13) = X13))) <=> ((~(X10 = c3)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))), ((((((~big_f(X10, X12)) | (X12 = f2(X10))) | (~(X10 = c3))) | (~big_f(f3(X2, X13), X2))) | (~(f3(X2, X13) = X13))) <=> ((~(X10 = c3)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12))))), (((((((~big_f(X10, X12)) | (X12 = f2(X10))) | (~(X10 = c3))) | (~big_f(f3(X2, X13), X2))) | (~(f3(X2, X13) = X13))) | (X2 = c4)) <=> (((~(X10 = c3)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12))) | (X2 = c4)))), rewrite((((~(X10 = c3)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12))) | (X2 = c4)) <=> ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))), (((((((~big_f(X10, X12)) | (X12 = f2(X10))) | (~(X10 = c3))) | (~big_f(f3(X2, X13), X2))) | (~(f3(X2, X13) = X13))) | (X2 = c4)) <=> ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))))),
% 27.95/18.18 inference(bind,[status(th)],[])).
% 27.95/18.18 tff(7046,plain,
% 27.95/18.18 (![X12: $i, X13: $i, X10: $i, X2: $i] : ((((((~big_f(X10, X12)) | (X12 = f2(X10))) | (~(X10 = c3))) | (~big_f(f3(X2, X13), X2))) | (~(f3(X2, X13) = X13))) | (X2 = c4)) <=> ![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))),
% 27.95/18.18 inference(quant_intro,[status(thm)],[7045])).
% 27.95/18.18 tff(7047,axiom,(![X12: $i, X13: $i, X10: $i, X2: $i] : ((((((~big_f(X10, X12)) | (X12 = f2(X10))) | (~(X10 = c3))) | (~big_f(f3(X2, X13), X2))) | (~(f3(X2, X13) = X13))) | (X2 = c4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_12')).
% 27.95/18.18 tff(7048,plain,
% 27.95/18.18 (![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))),
% 27.95/18.18 inference(modus_ponens,[status(thm)],[7047, 7046])).
% 27.95/18.18 tff(7049,plain,
% 27.95/18.18 (![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))),
% 27.95/18.18 inference(modus_ponens,[status(thm)],[7048, 7044])).
% 27.95/18.18 tff(7050,plain,(
% 27.95/18.18 ![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))),
% 27.95/18.18 inference(skolemize,[status(sab)],[7049])).
% 27.95/18.18 tff(7051,plain,
% 27.95/18.18 (![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))),
% 27.95/18.18 inference(modus_ponens,[status(thm)],[7050, 7043])).
% 27.95/18.18 tff(7052,plain,
% 27.95/18.18 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c2, c2) = c3)) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), c2) = c2)) | (~big_f(f3(f9(c2, c2), c2), f9(c2, c2))) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(f9(c2, c2) = c3)) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), c2) = c2)) | (~big_f(f3(f9(c2, c2), c2), f9(c2, c2))) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1))))),
% 27.95/18.18 inference(rewrite,[status(thm)],[])).
% 27.95/18.18 tff(7053,plain,
% 27.95/18.18 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c2, c2) = c3)) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), c2) = c2)) | (~big_f(f3(f9(c2, c2), c2), f9(c2, c2))) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1))))),
% 27.95/18.18 inference(quant_inst,[status(thm)],[])).
% 27.95/18.18 tff(7054,plain,
% 27.95/18.18 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(f9(c2, c2) = c3)) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), c2) = c2)) | (~big_f(f3(f9(c2, c2), c2), f9(c2, c2))) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1)))),
% 27.95/18.18 inference(modus_ponens,[status(thm)],[7053, 7052])).
% 27.95/18.18 tff(7055,plain,
% 27.95/18.18 ((~(f3(f9(c2, c2), c2) = c2)) | (~big_f(f3(f9(c2, c2), c2), f9(c2, c2)))),
% 27.95/18.18 inference(unit_resolution,[status(thm)],[7054, 7051, 1861, 1822, 6995, 7041])).
% 27.95/18.18 tff(7056,plain,
% 27.95/18.18 ($false),
% 27.95/18.18 inference(unit_resolution,[status(thm)],[7055, 7040, 7034])).
% 27.95/18.18 tff(7057,plain,((~(f6(c1, f3(c1, c2)) = c2)) | (f9(c2, c2) = c4) | (~(f9(c2, c2) = c3)) | (~big_f(f9(c2, c2), f6(c1, c1))) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(c2, f9(c2, c2))) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | big_f(f9(c2, c2), c2) | (~(f7(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 27.95/18.18 tff(7058,plain,
% 27.95/18.18 (f6(c1, c1) = f2(f9(c2, c2))),
% 27.95/18.18 inference(unit_resolution,[status(thm)],[7057, 1861, 1822, 7024, 7021, 3719, 148, 79, 122, 7020, 4234])).
% 27.95/18.18 tff(7059,plain,
% 27.95/18.18 (f6(c1, c1) = f2(c1)),
% 27.95/18.18 inference(transitivity,[status(thm)],[7058, 6508])).
% 27.95/18.18 tff(7060,plain,
% 27.95/18.18 ((f6(c1, c1) = c1) <=> (f2(c1) = c1)),
% 27.95/18.18 inference(monotonicity,[status(thm)],[7059])).
% 27.95/18.18 tff(7061,plain,
% 27.95/18.18 ((f6(c1, c1) = c1) <=> (c1 = f2(c1))),
% 27.95/18.18 inference(transitivity,[status(thm)],[7060, 6764])).
% 27.95/18.18 tff(7062,plain,
% 27.95/18.18 ((c1 = f2(c1)) <=> (f6(c1, c1) = c1)),
% 27.95/18.18 inference(symmetry,[status(thm)],[7061])).
% 27.95/18.18 tff(7063,plain,
% 27.95/18.18 (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(c1, c2)))),
% 27.95/18.18 inference(modus_ponens,[status(thm)],[7020, 7031])).
% 27.95/18.18 tff(7064,plain,
% 27.95/18.18 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(c1, c2))) | (f6(f9(c2, c2), f3(c1, c2)) = f3(c1, c2))),
% 27.95/18.18 inference(unit_resolution,[status(thm)],[6659, 2492, 122, 185, 7022, 5532])).
% 27.95/18.18 tff(7065,plain,
% 27.95/18.18 (f6(f9(c2, c2), f3(c1, c2)) = f3(c1, c2)),
% 27.95/18.18 inference(unit_resolution,[status(thm)],[7064, 7063])).
% 27.95/18.18 tff(7066,plain,
% 27.95/18.18 (f3(c1, c2) = f6(f9(c2, c2), f3(c1, c2))),
% 27.95/18.18 inference(symmetry,[status(thm)],[7065])).
% 27.95/18.18 tff(7067,plain,
% 27.95/18.18 (f3(c1, c2) = c2),
% 27.95/18.18 inference(transitivity,[status(thm)],[7066, 6648, 7021])).
% 27.95/18.18 tff(7068,plain,
% 27.95/18.18 (big_f(f3(c1, c2), c1) <=> big_f(c2, f9(c2, c2))),
% 27.95/18.18 inference(monotonicity,[status(thm)],[7067, 150])).
% 27.95/18.19 tff(7069,plain,
% 27.95/18.19 (big_f(c2, f9(c2, c2)) <=> big_f(f3(c1, c2), c1)),
% 27.95/18.19 inference(symmetry,[status(thm)],[7068])).
% 27.95/18.19 tff(7070,plain,
% 27.95/18.19 (big_f(c2, f9(c2, c2)) <=> big_f(f3(f9(c2, c2), c2), f9(c2, c2))),
% 27.95/18.19 inference(transitivity,[status(thm)],[7069, 6646])).
% 27.95/18.19 tff(7071,plain,
% 27.95/18.19 (big_f(f3(f9(c2, c2), c2), f9(c2, c2))),
% 27.95/18.19 inference(modus_ponens,[status(thm)],[3719, 7070])).
% 27.95/18.19 tff(7072,plain,
% 27.95/18.19 (f3(f9(c2, c2), c2) = c2),
% 27.95/18.19 inference(modus_ponens,[status(thm)],[7065, 7027])).
% 27.95/18.19 tff(7073,plain,
% 27.95/18.19 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c2, c2) = c3)) | (f9(c2, c2) = f2(f9(c2, c2))) | (f9(c2, c2) = c4) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f3(f9(c2, c2), c2) = c2)) | (~big_f(f3(f9(c2, c2), c2), f9(c2, c2))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(f9(c2, c2) = c3)) | (f9(c2, c2) = f2(f9(c2, c2))) | (f9(c2, c2) = c4) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f3(f9(c2, c2), c2) = c2)) | (~big_f(f3(f9(c2, c2), c2), f9(c2, c2))))),
% 27.95/18.19 inference(rewrite,[status(thm)],[])).
% 27.95/18.19 tff(7074,plain,
% 27.95/18.19 (((~(f9(c2, c2) = c3)) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), c2) = c2)) | (~big_f(f3(f9(c2, c2), c2), f9(c2, c2))) | (f9(c2, c2) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2)))) <=> ((~(f9(c2, c2) = c3)) | (f9(c2, c2) = f2(f9(c2, c2))) | (f9(c2, c2) = c4) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f3(f9(c2, c2), c2) = c2)) | (~big_f(f3(f9(c2, c2), c2), f9(c2, c2))))),
% 27.95/18.19 inference(rewrite,[status(thm)],[])).
% 27.95/18.19 tff(7075,plain,
% 27.95/18.19 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c2, c2) = c3)) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), c2) = c2)) | (~big_f(f3(f9(c2, c2), c2), f9(c2, c2))) | (f9(c2, c2) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c2, c2) = c3)) | (f9(c2, c2) = f2(f9(c2, c2))) | (f9(c2, c2) = c4) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f3(f9(c2, c2), c2) = c2)) | (~big_f(f3(f9(c2, c2), c2), f9(c2, c2)))))),
% 27.95/18.19 inference(monotonicity,[status(thm)],[7074])).
% 27.95/18.19 tff(7076,plain,
% 27.95/18.19 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c2, c2) = c3)) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), c2) = c2)) | (~big_f(f3(f9(c2, c2), c2), f9(c2, c2))) | (f9(c2, c2) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(f9(c2, c2) = c3)) | (f9(c2, c2) = f2(f9(c2, c2))) | (f9(c2, c2) = c4) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f3(f9(c2, c2), c2) = c2)) | (~big_f(f3(f9(c2, c2), c2), f9(c2, c2))))),
% 27.95/18.19 inference(transitivity,[status(thm)],[7075, 7073])).
% 27.95/18.19 tff(7077,plain,
% 27.95/18.19 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c2, c2) = c3)) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), c2) = c2)) | (~big_f(f3(f9(c2, c2), c2), f9(c2, c2))) | (f9(c2, c2) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))))),
% 27.95/18.19 inference(quant_inst,[status(thm)],[])).
% 27.95/18.19 tff(7078,plain,
% 27.95/18.19 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(f9(c2, c2) = c3)) | (f9(c2, c2) = f2(f9(c2, c2))) | (f9(c2, c2) = c4) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f3(f9(c2, c2), c2) = c2)) | (~big_f(f3(f9(c2, c2), c2), f9(c2, c2)))),
% 27.95/18.19 inference(modus_ponens,[status(thm)],[7077, 7076])).
% 27.95/18.19 tff(7079,plain,
% 27.95/18.19 ((f9(c2, c2) = f2(f9(c2, c2))) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), c2) = c2)) | (~big_f(f3(f9(c2, c2), c2), f9(c2, c2)))),
% 27.95/18.19 inference(unit_resolution,[status(thm)],[7078, 7051, 487, 1822])).
% 27.95/18.19 tff(7080,plain,
% 27.95/18.19 (f9(c2, c2) = f2(f9(c2, c2))),
% 27.95/18.19 inference(unit_resolution,[status(thm)],[7079, 1861, 7072, 7071])).
% 27.95/18.19 tff(7081,plain,
% 27.95/18.19 (c1 = f2(c1)),
% 27.95/18.19 inference(modus_ponens,[status(thm)],[7080, 6630])).
% 27.95/18.19 tff(7082,plain,
% 27.95/18.19 (f6(c1, c1) = c1),
% 27.95/18.19 inference(modus_ponens,[status(thm)],[7081, 7062])).
% 27.95/18.19 tff(7083,plain,
% 27.95/18.19 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2)))),
% 27.95/18.19 inference(modus_ponens,[status(thm)],[7023, 4671])).
% 27.95/18.19 tff(7084,plain,
% 27.95/18.19 ((~(f6(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2))))),
% 27.95/18.19 inference(unit_resolution,[status(thm)],[4676, 2534, 122, 185, 7022, 5532])).
% 27.95/18.19 tff(7085,plain,
% 27.95/18.19 (~(f6(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))),
% 27.95/18.19 inference(unit_resolution,[status(thm)],[7084, 7083])).
% 27.95/18.19 tff(7086,plain,
% 27.95/18.19 (~(f6(c1, c1) = c1)),
% 27.95/18.19 inference(modus_ponens,[status(thm)],[7085, 6938])).
% 27.95/18.19 tff(7087,plain,
% 27.95/18.19 ($false),
% 27.95/18.19 inference(unit_resolution,[status(thm)],[7086, 7082])).
% 27.95/18.19 tff(7088,plain,((f9(c2, c2) = c4) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c3)) | (~(f6(c1, f3(c1, c2)) = c2)) | (~big_f(c2, f9(c2, c2))) | (~(f7(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 27.95/18.19 tff(7089,plain,
% 27.95/18.19 (~(f6(c1, f3(c1, c2)) = c2)),
% 27.95/18.19 inference(unit_resolution,[status(thm)],[7088, 7019, 79, 122, 6927, 5567, 148, 6979, 4234])).
% 27.95/18.19 tff(7090,plain,
% 27.95/18.19 (f6(c1, f3(c1, c2)) = c1),
% 27.95/18.19 inference(unit_resolution,[status(thm)],[6690, 7089])).
% 27.95/18.19 tff(7091,plain,
% 27.95/18.19 (c1 = f6(c1, f3(c1, c2))),
% 27.95/18.19 inference(symmetry,[status(thm)],[7090])).
% 27.95/18.19 tff(7092,plain,
% 27.95/18.19 ((c1 = f3(c1, f8(c3))) <=> (f3(c1, f8(c3)) = c1)),
% 27.95/18.19 inference(commutativity,[status(thm)],[])).
% 27.95/18.19 tff(7093,plain,
% 27.95/18.19 (c3 = f9(c2, c2)),
% 27.95/18.19 inference(transitivity,[status(thm)],[172, 149, 2634])).
% 27.95/18.19 tff(7094,plain,
% 27.95/18.19 (f8(c3) = f8(f9(c2, c2))),
% 27.95/18.19 inference(monotonicity,[status(thm)],[7093])).
% 27.95/18.19 tff(7095,plain,
% 27.95/18.19 (f8(f9(c2, c2)) = f8(c3)),
% 27.95/18.19 inference(symmetry,[status(thm)],[7094])).
% 27.95/18.19 tff(7096,plain,
% 27.95/18.19 (f8(f9(c2, c2)) = f8(c1)),
% 27.95/18.19 inference(monotonicity,[status(thm)],[4702])).
% 27.95/18.19 tff(7097,plain,
% 27.95/18.19 (f8(c1) = f8(f9(c2, c2))),
% 27.95/18.19 inference(symmetry,[status(thm)],[7096])).
% 27.95/18.19 tff(7098,plain,
% 27.95/18.19 (c2 = f8(c1)),
% 27.95/18.19 inference(symmetry,[status(thm)],[1671])).
% 27.95/18.19 tff(7099,plain,
% 27.95/18.19 (c2 = f8(c3)),
% 27.95/18.19 inference(transitivity,[status(thm)],[7098, 7097, 7095])).
% 27.95/18.19 tff(7100,plain,
% 27.95/18.19 (f3(c1, c2) = f3(c1, f8(c3))),
% 27.95/18.19 inference(monotonicity,[status(thm)],[7099])).
% 27.95/18.19 tff(7101,plain,
% 27.95/18.19 ((f6(c1, f3(c1, c2)) = f3(c1, c2)) <=> (c1 = f3(c1, f8(c3)))),
% 27.95/18.19 inference(monotonicity,[status(thm)],[6647, 7100])).
% 27.95/18.19 tff(7102,plain,
% 27.95/18.19 ((f6(c1, f3(c1, c2)) = f3(c1, c2)) <=> (f3(c1, f8(c3)) = c1)),
% 27.95/18.19 inference(transitivity,[status(thm)],[7101, 7092])).
% 27.95/18.19 tff(7103,plain,
% 27.95/18.19 (f6(f9(c2, c2), f3(c1, c2)) = f6(c1, f3(c1, c2))),
% 27.95/18.19 inference(monotonicity,[status(thm)],[4702])).
% 27.95/18.19 tff(7104,plain,
% 27.95/18.19 ((f6(f9(c2, c2), f3(c1, c2)) = f3(c1, c2)) <=> (f6(c1, f3(c1, c2)) = f3(c1, c2))),
% 27.95/18.19 inference(monotonicity,[status(thm)],[7103])).
% 27.95/18.19 tff(7105,plain,
% 27.95/18.19 ((f6(f9(c2, c2), f3(c1, c2)) = f3(c1, c2)) <=> (f3(c1, f8(c3)) = c1)),
% 27.95/18.19 inference(transitivity,[status(thm)],[7104, 7102])).
% 27.95/18.19 tff(7106,plain,
% 27.95/18.19 ((~(f6(f9(c2, c2), f3(c1, c2)) = f3(c1, c2))) <=> (~(f3(c1, f8(c3)) = c1))),
% 27.95/18.19 inference(monotonicity,[status(thm)],[7105])).
% 27.95/18.19 tff(7107,plain,
% 27.95/18.19 (f6(f9(c2, c2), f3(c1, c2)) = f9(c2, c2)),
% 27.95/18.19 inference(transitivity,[status(thm)],[7103, 6647, 149, 2634])).
% 27.95/18.19 tff(7108,plain,
% 27.95/18.19 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(c1, c2))) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 27.95/18.19 inference(monotonicity,[status(thm)],[6991, 7107])).
% 27.95/18.19 tff(7109,plain,
% 27.95/18.19 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(c1, c2)))),
% 27.95/18.19 inference(symmetry,[status(thm)],[7108])).
% 27.95/18.19 tff(7110,plain,
% 27.95/18.19 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(c1, c2)))),
% 27.95/18.19 inference(modus_ponens,[status(thm)],[6927, 7109])).
% 27.95/18.19 tff(7111,plain,
% 27.95/18.19 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(c1, c2)))) | (~(f6(f9(c2, c2), f3(c1, c2)) = f3(c1, c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(c1, c2)))) | (~(f6(f9(c2, c2), f3(c1, c2)) = f3(c1, c2))))),
% 27.95/18.19 inference(rewrite,[status(thm)],[])).
% 27.95/18.19 tff(7112,plain,
% 27.95/18.19 (((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), f3(c1, c2)) = f3(c1, c2))) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(c1, c2))))) <=> ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(c1, c2)))) | (~(f6(f9(c2, c2), f3(c1, c2)) = f3(c1, c2))))),
% 27.95/18.19 inference(rewrite,[status(thm)],[])).
% 27.95/18.19 tff(7113,plain,
% 27.95/18.19 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), f3(c1, c2)) = f3(c1, c2))) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(c1, c2)))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(c1, c2)))) | (~(f6(f9(c2, c2), f3(c1, c2)) = f3(c1, c2)))))),
% 27.95/18.19 inference(monotonicity,[status(thm)],[7112])).
% 27.95/18.19 tff(7114,plain,
% 27.95/18.19 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), f3(c1, c2)) = f3(c1, c2))) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(c1, c2)))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(c1, c2)))) | (~(f6(f9(c2, c2), f3(c1, c2)) = f3(c1, c2))))),
% 27.95/18.19 inference(transitivity,[status(thm)],[7113, 7111])).
% 27.95/18.19 tff(7115,plain,
% 27.95/18.19 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~(f6(f9(c2, c2), f3(c1, c2)) = f3(c1, c2))) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(c1, c2)))))),
% 27.95/18.19 inference(quant_inst,[status(thm)],[])).
% 27.95/18.19 tff(7116,plain,
% 27.95/18.19 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(c1, c2)))) | (~(f6(f9(c2, c2), f3(c1, c2)) = f3(c1, c2)))),
% 27.95/18.19 inference(modus_ponens,[status(thm)],[7115, 7114])).
% 27.95/18.19 tff(7117,plain,
% 27.95/18.19 ((~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(c1, c2)))) | (~(f6(f9(c2, c2), f3(c1, c2)) = f3(c1, c2)))),
% 27.95/18.19 inference(unit_resolution,[status(thm)],[7116, 2534, 122, 4743, 6929, 6991])).
% 27.95/18.19 tff(7118,plain,
% 27.95/18.19 (~(f6(f9(c2, c2), f3(c1, c2)) = f3(c1, c2))),
% 27.95/18.19 inference(unit_resolution,[status(thm)],[7117, 7110])).
% 27.95/18.19 tff(7119,plain,
% 27.95/18.19 (~(f3(c1, f8(c3)) = c1)),
% 27.95/18.19 inference(modus_ponens,[status(thm)],[7118, 7106])).
% 27.95/18.19 tff(7120,plain,
% 27.95/18.19 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f3(c1, f8(c3)) = c1) | (f3(c1, f8(c3)) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f3(c1, f8(c3)) = c1) | (f3(c1, f8(c3)) = c2))),
% 27.95/18.19 inference(rewrite,[status(thm)],[])).
% 27.95/18.19 tff(7121,plain,
% 27.95/18.19 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f3(c1, f8(c3)) = c1) | (f3(c1, f8(c3)) = c2))),
% 27.95/18.19 inference(quant_inst,[status(thm)],[])).
% 27.95/18.19 tff(7122,plain,
% 27.95/18.19 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f3(c1, f8(c3)) = c1) | (f3(c1, f8(c3)) = c2)),
% 27.95/18.19 inference(modus_ponens,[status(thm)],[7121, 7120])).
% 27.95/18.19 tff(7123,plain,
% 27.95/18.19 ((f3(c1, f8(c3)) = c1) | (f3(c1, f8(c3)) = c2)),
% 27.95/18.19 inference(unit_resolution,[status(thm)],[7122, 10])).
% 27.95/18.19 tff(7124,plain,
% 27.95/18.19 (f3(c1, f8(c3)) = c2),
% 27.95/18.19 inference(unit_resolution,[status(thm)],[7123, 7119])).
% 27.95/18.19 tff(7125,plain,
% 27.95/18.19 (f3(c1, c2) = c2),
% 27.95/18.19 inference(transitivity,[status(thm)],[7100, 7124])).
% 27.95/18.19 tff(7126,plain,
% 27.95/18.19 (f6(c1, f3(c1, c2)) = f6(f9(c2, c2), c2)),
% 27.95/18.19 inference(monotonicity,[status(thm)],[4708, 7125])).
% 27.95/18.19 tff(7127,plain,
% 27.95/18.19 (c1 = f6(c1, f3(c1, c2))),
% 27.95/18.19 inference(symmetry,[status(thm)],[6647])).
% 27.95/18.19 tff(7128,plain,
% 27.95/18.19 (f9(c2, c2) = c2),
% 27.95/18.19 inference(transitivity,[status(thm)],[2629, 148, 7127, 7126, 6954, 6953])).
% 27.95/18.19 tff(7129,plain,
% 27.95/18.19 ($false),
% 27.95/18.19 inference(unit_resolution,[status(thm)],[4743, 7128])).
% 27.95/18.19 tff(7130,plain,((~(f6(c1, f3(c1, c2)) = c1)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f8(c1) = c2)) | (~(c3 = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f7(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 27.95/18.19 tff(7131,plain,
% 27.95/18.19 (~(f8(c1) = c2)),
% 27.95/18.19 inference(unit_resolution,[status(thm)],[7130, 7090, 148, 172, 79, 122, 4234])).
% 27.95/18.19 tff(7132,plain,
% 27.95/18.19 (f8(c1) = c1),
% 27.95/18.19 inference(unit_resolution,[status(thm)],[1680, 7131])).
% 27.95/18.19 tff(7133,plain,
% 27.95/18.19 (f8(c3) = c1),
% 27.95/18.19 inference(transitivity,[status(thm)],[7094, 7096, 7132])).
% 27.95/18.19 tff(7134,plain,
% 27.95/18.19 (f3(c1, f8(c3)) = f3(c1, c1)),
% 27.95/18.19 inference(monotonicity,[status(thm)],[7133])).
% 27.95/18.19 tff(7135,plain,
% 27.95/18.19 (f3(c1, c1) = f3(c1, f8(c3))),
% 27.95/18.19 inference(symmetry,[status(thm)],[7134])).
% 27.95/18.19 tff(7136,plain,
% 27.95/18.19 (f3(c1, c1) = f3(f7(c1), c1)),
% 27.95/18.19 inference(monotonicity,[status(thm)],[5544])).
% 27.95/18.19 tff(7137,plain,
% 27.95/18.19 (f3(f7(c1), c1) = f3(c1, c1)),
% 27.95/18.19 inference(symmetry,[status(thm)],[7136])).
% 27.95/18.19 tff(7138,plain,
% 27.95/18.19 (c2 = f3(f7(c1), c1)),
% 27.95/18.19 inference(symmetry,[status(thm)],[881])).
% 27.95/18.19 tff(7139,plain,
% 27.95/18.19 (c2 = f3(c1, f8(c3))),
% 27.95/18.19 inference(transitivity,[status(thm)],[7138, 7137, 7135])).
% 27.95/18.19 tff(7140,plain,
% 27.95/18.19 (f3(c1, c2) = f3(c1, f3(c1, f8(c3)))),
% 27.95/18.19 inference(monotonicity,[status(thm)],[7139])).
% 27.95/18.19 tff(7141,plain,
% 27.95/18.19 (f3(c1, f3(c1, f8(c3))) = f3(c1, c2)),
% 27.95/18.19 inference(symmetry,[status(thm)],[7140])).
% 27.95/18.19 tff(7142,plain,
% 27.95/18.19 ((f3(c1, f3(c1, f8(c3))) = c1) <=> (f3(c1, c2) = f6(c1, f3(c1, c2)))),
% 27.95/18.19 inference(monotonicity,[status(thm)],[7141, 7091])).
% 27.95/18.19 tff(7143,plain,
% 27.95/18.19 ((f3(c1, f3(c1, f8(c3))) = c1) <=> (f6(c1, f3(c1, c2)) = f3(c1, c2))),
% 27.95/18.19 inference(transitivity,[status(thm)],[7142, 6955])).
% 27.95/18.19 tff(7144,plain,
% 27.95/18.19 ((f6(c1, f3(c1, c2)) = f3(c1, c2)) <=> (f3(c1, f3(c1, f8(c3))) = c1)),
% 27.95/18.19 inference(symmetry,[status(thm)],[7143])).
% 27.95/18.19 tff(7145,plain,
% 27.95/18.19 ((~(f6(c1, f3(c1, c2)) = f3(c1, c2))) <=> (~(f3(c1, f3(c1, f8(c3))) = c1))),
% 27.95/18.19 inference(monotonicity,[status(thm)],[7144])).
% 27.95/18.19 tff(7146,plain,
% 27.95/18.19 ((~(f6(f9(c2, c2), f3(c1, c2)) = f3(c1, c2))) <=> (~(f6(c1, f3(c1, c2)) = f3(c1, c2)))),
% 27.95/18.19 inference(monotonicity,[status(thm)],[7104])).
% 27.95/18.19 tff(7147,plain,
% 27.95/18.19 (f6(f9(c2, c2), f3(c1, c2)) = f9(c2, c2)),
% 27.95/18.19 inference(transitivity,[status(thm)],[7103, 7090, 149, 2634])).
% 27.95/18.19 tff(7148,plain,
% 27.95/18.19 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(c1, c2))) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 27.95/18.19 inference(monotonicity,[status(thm)],[6991, 7147])).
% 27.95/18.19 tff(7149,plain,
% 27.95/18.19 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(c1, c2)))),
% 27.95/18.19 inference(symmetry,[status(thm)],[7148])).
% 27.95/18.19 tff(7150,plain,
% 27.95/18.19 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(c1, c2)))),
% 27.95/18.19 inference(modus_ponens,[status(thm)],[6927, 7149])).
% 27.95/18.19 tff(7151,plain,
% 27.95/18.19 (~(f6(f9(c2, c2), f3(c1, c2)) = f3(c1, c2))),
% 27.95/18.19 inference(unit_resolution,[status(thm)],[7117, 7150])).
% 27.95/18.19 tff(7152,plain,
% 27.95/18.19 (~(f6(c1, f3(c1, c2)) = f3(c1, c2))),
% 27.95/18.19 inference(modus_ponens,[status(thm)],[7151, 7146])).
% 27.95/18.19 tff(7153,plain,
% 27.95/18.19 (~(f3(c1, f3(c1, f8(c3))) = c1)),
% 27.95/18.19 inference(modus_ponens,[status(thm)],[7152, 7145])).
% 27.95/18.19 tff(7154,plain,
% 27.95/18.19 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f3(c1, f3(c1, f8(c3))) = c1) | (f3(c1, f3(c1, f8(c3))) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f3(c1, f3(c1, f8(c3))) = c1) | (f3(c1, f3(c1, f8(c3))) = c2))),
% 27.95/18.19 inference(rewrite,[status(thm)],[])).
% 27.95/18.19 tff(7155,plain,
% 27.95/18.19 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f3(c1, f3(c1, f8(c3))) = c1) | (f3(c1, f3(c1, f8(c3))) = c2))),
% 27.95/18.19 inference(quant_inst,[status(thm)],[])).
% 27.95/18.19 tff(7156,plain,
% 27.95/18.19 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f3(c1, f3(c1, f8(c3))) = c1) | (f3(c1, f3(c1, f8(c3))) = c2)),
% 27.95/18.19 inference(modus_ponens,[status(thm)],[7155, 7154])).
% 27.95/18.19 tff(7157,plain,
% 27.95/18.19 ((f3(c1, f3(c1, f8(c3))) = c1) | (f3(c1, f3(c1, f8(c3))) = c2)),
% 27.95/18.19 inference(unit_resolution,[status(thm)],[7156, 10])).
% 27.95/18.19 tff(7158,plain,
% 27.95/18.19 (f3(c1, f3(c1, f8(c3))) = c2),
% 27.95/18.19 inference(unit_resolution,[status(thm)],[7157, 7153])).
% 27.95/18.19 tff(7159,plain,
% 27.95/18.19 (f3(c1, c2) = c2),
% 27.95/18.19 inference(transitivity,[status(thm)],[7140, 7158])).
% 27.95/18.19 tff(7160,plain,
% 27.95/18.19 (f6(c1, f3(c1, c2)) = f6(f9(c2, c2), c2)),
% 27.95/18.19 inference(monotonicity,[status(thm)],[4708, 7159])).
% 27.95/18.19 tff(7161,plain,
% 27.95/18.19 (f9(c2, c2) = c2),
% 27.95/18.19 inference(transitivity,[status(thm)],[2629, 148, 7091, 7160, 6954, 6953])).
% 27.95/18.19 tff(7162,plain,
% 27.95/18.19 ($false),
% 27.95/18.19 inference(unit_resolution,[status(thm)],[4743, 7161])).
% 27.95/18.19 tff(7163,plain,((~(f3(f7(c1), c1) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f7(c1) = c1)) | (~(c3 = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 27.95/18.19 tff(7164,plain,
% 27.95/18.19 (~(f3(f7(c1), c1) = c2)),
% 27.95/18.19 inference(unit_resolution,[status(thm)],[7163, 172, 4234, 148, 79, 122])).
% 27.95/18.19 tff(7165,plain,
% 27.95/18.19 (f3(f7(c1), c1) = c1),
% 27.95/18.19 inference(unit_resolution,[status(thm)],[918, 7164])).
% 27.95/18.19 tff(7166,plain,
% 27.95/18.19 (f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)),
% 27.95/18.19 inference(transitivity,[status(thm)],[1863, 7136, 7165, 149, 132])).
% 27.95/18.19 tff(7167,plain,
% 27.95/18.19 (big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2)) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 27.95/18.19 inference(monotonicity,[status(thm)],[7166])).
% 27.95/18.19 tff(7168,plain,
% 27.95/18.19 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))),
% 27.95/18.19 inference(symmetry,[status(thm)],[7167])).
% 27.95/18.19 tff(7169,plain,
% 27.95/18.19 (big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))),
% 27.95/18.19 inference(modus_ponens,[status(thm)],[6965, 7168])).
% 27.95/18.19 tff(7170,plain,
% 27.95/18.19 (big_f(f7(c1), f6(c1, c1))),
% 27.95/18.19 inference(unit_resolution,[status(thm)],[4658, 6968, 148, 79, 122, 4234, 6965])).
% 27.95/18.19 tff(7171,plain,
% 27.95/18.19 (big_f(f9(c2, c2), f6(c1, c1))),
% 27.95/18.19 inference(modus_ponens,[status(thm)],[7170, 5605])).
% 27.95/18.19 tff(7172,plain,
% 27.95/18.19 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2)))),
% 27.95/18.19 inference(modus_ponens,[status(thm)],[7170, 4671])).
% 27.95/18.19 tff(7173,plain,
% 27.95/18.19 ((~(f6(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f9(c2, c2))))),
% 27.95/18.19 inference(unit_resolution,[status(thm)],[4676, 2534, 122, 185, 6968, 5532])).
% 27.95/18.19 tff(7174,plain,
% 27.95/18.19 (~(f6(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))),
% 27.95/18.19 inference(unit_resolution,[status(thm)],[7173, 7172])).
% 27.95/18.19 tff(7175,plain,
% 27.95/18.19 (~(f6(c1, c1) = c1)),
% 27.95/18.19 inference(modus_ponens,[status(thm)],[7174, 6938])).
% 27.95/18.19 tff(7176,plain,
% 27.95/18.19 (~(f9(c2, c2) = c4)),
% 27.95/18.19 inference(unit_resolution,[status(thm)],[7018, 7175, 148, 79, 122, 7171, 6965, 5580])).
% 27.95/18.19 tff(7177,plain,
% 27.95/18.19 (~(c1 = c4)),
% 27.95/18.19 inference(modus_ponens,[status(thm)],[7176, 4623])).
% 27.95/18.19 tff(7178,plain,
% 27.95/18.19 ((f3(f7(c1), c1) = c1) <=> (f3(c1, c1) = c1)),
% 27.95/18.19 inference(monotonicity,[status(thm)],[7137])).
% 27.95/18.19 tff(7179,plain,
% 27.95/18.19 (f3(c1, c1) = c1),
% 27.95/18.19 inference(modus_ponens,[status(thm)],[953, 7178])).
% 27.95/18.19 tff(7180,plain,
% 27.95/18.19 (f3(c1, c1) = c1),
% 27.95/18.19 inference(transitivity,[status(thm)],[7136, 953])).
% 27.95/18.19 tff(7181,plain,
% 27.95/18.19 (big_f(f3(c1, c1), c1) <=> big_f(c1, c1)),
% 27.95/18.19 inference(monotonicity,[status(thm)],[7180])).
% 27.95/18.19 tff(7182,plain,
% 27.95/18.19 (big_f(c1, c1) <=> big_f(f3(c1, c1), c1)),
% 27.95/18.19 inference(symmetry,[status(thm)],[7181])).
% 27.95/18.19 tff(7183,plain,
% 27.95/18.19 (big_f(f3(c1, c1), c1)),
% 27.95/18.19 inference(modus_ponens,[status(thm)],[4932, 7182])).
% 27.95/18.19 tff(7184,plain,
% 27.95/18.19 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((c1 = c4) | (~(c1 = c3)) | (c1 = f2(c1)) | (~big_f(f3(c1, c1), c1)) | (~big_f(c1, c1)) | (~(f3(c1, c1) = c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (c1 = c4) | (~(c1 = c3)) | (c1 = f2(c1)) | (~big_f(f3(c1, c1), c1)) | (~big_f(c1, c1)) | (~(f3(c1, c1) = c1)))),
% 27.95/18.19 inference(rewrite,[status(thm)],[])).
% 27.95/18.19 tff(7185,plain,
% 27.95/18.19 (((~(c1 = c3)) | (c1 = c4) | (~(f3(c1, c1) = c1)) | (~big_f(f3(c1, c1), c1)) | (c1 = f2(c1)) | (~big_f(c1, c1))) <=> ((c1 = c4) | (~(c1 = c3)) | (c1 = f2(c1)) | (~big_f(f3(c1, c1), c1)) | (~big_f(c1, c1)) | (~(f3(c1, c1) = c1)))),
% 27.95/18.19 inference(rewrite,[status(thm)],[])).
% 27.95/18.19 tff(7186,plain,
% 27.95/18.19 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c1 = c4) | (~(f3(c1, c1) = c1)) | (~big_f(f3(c1, c1), c1)) | (c1 = f2(c1)) | (~big_f(c1, c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((c1 = c4) | (~(c1 = c3)) | (c1 = f2(c1)) | (~big_f(f3(c1, c1), c1)) | (~big_f(c1, c1)) | (~(f3(c1, c1) = c1))))),
% 27.95/18.19 inference(monotonicity,[status(thm)],[7185])).
% 27.95/18.19 tff(7187,plain,
% 27.95/18.19 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c1 = c4) | (~(f3(c1, c1) = c1)) | (~big_f(f3(c1, c1), c1)) | (c1 = f2(c1)) | (~big_f(c1, c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (c1 = c4) | (~(c1 = c3)) | (c1 = f2(c1)) | (~big_f(f3(c1, c1), c1)) | (~big_f(c1, c1)) | (~(f3(c1, c1) = c1)))),
% 27.95/18.19 inference(transitivity,[status(thm)],[7186, 7184])).
% 27.95/18.19 tff(7188,plain,
% 27.95/18.19 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c1 = c4) | (~(f3(c1, c1) = c1)) | (~big_f(f3(c1, c1), c1)) | (c1 = f2(c1)) | (~big_f(c1, c1)))),
% 27.95/18.19 inference(quant_inst,[status(thm)],[])).
% 27.95/18.19 tff(7189,plain,
% 27.95/18.19 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (c1 = c4) | (~(c1 = c3)) | (c1 = f2(c1)) | (~big_f(f3(c1, c1), c1)) | (~big_f(c1, c1)) | (~(f3(c1, c1) = c1))),
% 27.95/18.20 inference(modus_ponens,[status(thm)],[7188, 7187])).
% 27.95/18.20 tff(7190,plain,
% 27.95/18.20 ($false),
% 27.95/18.20 inference(unit_resolution,[status(thm)],[7189, 7051, 7183, 5080, 7179, 482, 6769, 4932])).
% 27.95/18.20 tff(7191,plain,((~(f3(f7(c1), c1) = c1)) | (~(c1 = c3)) | (c1 = c4) | (c1 = f2(c1)) | (~big_f(c1, c1)) | (~(f7(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 27.95/18.20 tff(7192,plain,
% 27.95/18.20 (c1 = f2(c1)),
% 27.95/18.20 inference(unit_resolution,[status(thm)],[7191, 7165, 4234, 6926, 7177, 5611])).
% 27.95/18.20 tff(7193,plain,
% 27.95/18.20 (f2(c1) = c1),
% 27.95/18.20 inference(symmetry,[status(thm)],[7192])).
% 27.95/18.20 tff(7194,plain,
% 27.95/18.20 (f2(f9(c2, c2)) = c1),
% 27.95/18.20 inference(transitivity,[status(thm)],[5597, 7193])).
% 27.95/18.20 tff(7195,plain,
% 27.95/18.20 ((f6(c1, c1) = f2(f9(c2, c2))) <=> (f6(c1, c1) = c1)),
% 27.95/18.20 inference(monotonicity,[status(thm)],[7194])).
% 27.95/18.20 tff(7196,plain,
% 27.95/18.20 ((f6(c1, c1) = c1) <=> (f6(c1, c1) = f2(f9(c2, c2)))),
% 27.95/18.20 inference(symmetry,[status(thm)],[7195])).
% 27.95/18.20 tff(7197,plain,
% 27.95/18.20 ((~(f6(c1, c1) = c1)) <=> (~(f6(c1, c1) = f2(f9(c2, c2))))),
% 27.95/18.20 inference(monotonicity,[status(thm)],[7196])).
% 27.95/18.20 tff(7198,plain,
% 27.95/18.20 (~(f6(c1, c1) = f2(f9(c2, c2)))),
% 27.95/18.20 inference(modus_ponens,[status(thm)],[7175, 7197])).
% 27.95/18.20 tff(7199,plain,
% 27.95/18.20 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c2, c2) = c3)) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(f9(c2, c2) = c3)) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1))))),
% 27.95/18.20 inference(rewrite,[status(thm)],[])).
% 27.95/18.20 tff(7200,plain,
% 27.95/18.20 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c2, c2) = c3)) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1))))),
% 27.95/18.20 inference(quant_inst,[status(thm)],[])).
% 27.95/18.20 tff(7201,plain,
% 27.95/18.20 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(f9(c2, c2) = c3)) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2))) | (f6(c1, c1) = f2(f9(c2, c2))) | (~big_f(f9(c2, c2), f6(c1, c1)))),
% 27.95/18.20 inference(modus_ponens,[status(thm)],[7200, 7199])).
% 27.95/18.20 tff(7202,plain,
% 27.95/18.20 ((~(f3(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))) | (~big_f(f3(f9(c2, c2), f9(c2, c2)), f9(c2, c2)))),
% 27.95/18.20 inference(unit_resolution,[status(thm)],[7201, 7051, 7176, 5580, 7171, 7198])).
% 27.95/18.20 tff(7203,plain,
% 27.95/18.20 ($false),
% 27.95/18.20 inference(unit_resolution,[status(thm)],[7202, 7169, 7166])).
% 27.95/18.20 tff(7204,plain,((~(c3 = c1)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f7(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 27.95/18.20 tff(7205,plain,
% 27.95/18.20 (~(c3 = c1)),
% 27.95/18.20 inference(unit_resolution,[status(thm)],[7204, 148, 79, 122, 4234])).
% 27.95/18.20 tff(7206,plain,
% 27.95/18.20 (c3 = c2),
% 27.95/18.20 inference(unit_resolution,[status(thm)],[180, 7205])).
% 27.95/18.20 tff(7207,plain,
% 27.95/18.20 (big_f(c2, c2)),
% 27.95/18.20 inference(unit_resolution,[status(thm)],[6579, 2, 79, 4234, 122, 148])).
% 27.95/18.20 tff(7208,plain,
% 27.95/18.20 (big_f(f7(c2), f6(c2, c2))),
% 27.95/18.20 inference(unit_resolution,[status(thm)],[5485, 7207, 77, 185, 122, 256])).
% 27.95/18.20 tff(7209,plain,
% 27.95/18.20 (~(f6(c2, c2) = c2)),
% 27.95/18.20 inference(unit_resolution,[status(thm)],[2744, 7208, 77, 256, 185, 122])).
% 27.95/18.20 tff(7210,plain,
% 27.95/18.20 (~(f6(f7(c2), c3) = c2)),
% 27.95/18.20 inference(unit_resolution,[status(thm)],[2716, 67, 77, 2637])).
% 27.95/18.20 tff(7211,plain,
% 27.95/18.20 (~(f6(f7(c2), c3) = c1)),
% 27.95/18.20 inference(unit_resolution,[status(thm)],[2710, 67, 2707, 77, 2])).
% 27.95/18.20 tff(7212,plain,
% 27.95/18.20 ($false),
% 27.95/18.20 inference(unit_resolution,[status(thm)],[2391, 7211, 7210])).
% 27.95/18.20 tff(7213,plain,((~(c3 = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~(f7(c2) = c2)) | big_f(c2, c1) | (f6(c2, c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 27.95/18.20 tff(7214,plain,
% 27.95/18.20 ($false),
% 27.95/18.20 inference(unit_resolution,[status(thm)],[7213, 7209, 7208, 7206, 77, 2])).
% 27.95/18.20 tff(7215,plain,(big_f(c2, c1) | (~(f7(c2) = c2)) | big_f(f9(c2, c2), f10(c2)) | (~(f10(c2) = c2)) | (~(f4(c4) = c2)) | (~(f7(c1) = c1)) | (~(f9(f10(c2), f4(c4)) = c1))), inference(lemma,lemma(discharge,[]))).
% 27.95/18.20 tff(7216,plain,
% 27.95/18.20 (big_f(c2, c1)),
% 27.95/18.20 inference(unit_resolution,[status(thm)],[7215, 5558, 4597, 122, 79, 4234, 148])).
% 27.95/18.20 tff(7217,plain,
% 27.95/18.20 (big_f(c2, f9(c2, c2))),
% 27.95/18.20 inference(unit_resolution,[status(thm)],[3814, 7216, 148, 79, 122])).
% 27.95/18.20 tff(7218,plain,
% 27.95/18.20 (f9(c2, f5(c1)) = f9(c2, c2)),
% 27.95/18.20 inference(monotonicity,[status(thm)],[186])).
% 27.95/18.20 tff(7219,plain,
% 27.95/18.20 (f9(c2, c2) = f9(c2, f5(c1))),
% 27.95/18.20 inference(symmetry,[status(thm)],[7218])).
% 27.95/18.20 tff(7220,plain,
% 27.95/18.20 (c1 = f9(c2, f5(c1))),
% 27.95/18.20 inference(transitivity,[status(thm)],[149, 132, 7219])).
% 27.95/18.20 tff(7221,plain,
% 27.95/18.20 (f6(c2, c1) = f6(c2, f9(c2, f5(c1)))),
% 27.95/18.20 inference(monotonicity,[status(thm)],[7220])).
% 27.95/18.20 tff(7222,plain,
% 27.95/18.20 (f6(c2, f9(c2, f5(c1))) = f6(c2, c1)),
% 27.95/18.20 inference(symmetry,[status(thm)],[7221])).
% 27.95/18.20 tff(7223,plain,
% 27.95/18.20 ((f6(c2, f9(c2, f5(c1))) = c1) <=> (f6(c2, c1) = c1)),
% 27.95/18.20 inference(monotonicity,[status(thm)],[7222])).
% 27.95/18.20 tff(7224,plain,
% 27.95/18.20 ((f6(c2, c1) = c1) <=> (f6(c2, f9(c2, f5(c1))) = c1)),
% 27.95/18.20 inference(symmetry,[status(thm)],[7223])).
% 27.95/18.20 tff(7225,plain,
% 27.95/18.20 ((f6(c2, f9(c2, c2)) = f9(c2, c2)) <=> (f6(c2, f9(c2, f5(c1))) = c1)),
% 27.95/18.20 inference(transitivity,[status(thm)],[6606, 7224])).
% 27.95/18.20 tff(7226,plain,
% 27.95/18.20 ((~(f6(c2, f9(c2, c2)) = f9(c2, c2))) <=> (~(f6(c2, f9(c2, f5(c1))) = c1))),
% 27.95/18.20 inference(monotonicity,[status(thm)],[7225])).
% 27.95/18.20 tff(7227,plain,
% 27.95/18.20 (big_f(f7(c2), f6(c2, c1))),
% 27.95/18.20 inference(unit_resolution,[status(thm)],[6623, 256, 77, 3719, 148, 79, 122])).
% 27.95/18.20 tff(7228,plain,
% 27.95/18.20 (big_f(f7(c2), f6(c2, f9(c2, c2)))),
% 27.95/18.20 inference(modus_ponens,[status(thm)],[7227, 6618])).
% 27.95/18.20 tff(7229,plain,
% 27.95/18.20 (~(f6(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.95/18.20 inference(unit_resolution,[status(thm)],[3495, 2534, 122, 77, 185, 256, 7228])).
% 27.95/18.20 tff(7230,plain,
% 27.95/18.20 (~(f6(c2, f9(c2, f5(c1))) = c1)),
% 27.95/18.20 inference(modus_ponens,[status(thm)],[7229, 7226])).
% 27.95/18.20 tff(7231,plain,
% 27.95/18.20 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f6(c2, f9(c2, f5(c1))) = c1) | (f6(c2, f9(c2, f5(c1))) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f6(c2, f9(c2, f5(c1))) = c1) | (f6(c2, f9(c2, f5(c1))) = c2))),
% 27.95/18.20 inference(rewrite,[status(thm)],[])).
% 27.95/18.20 tff(7232,plain,
% 27.95/18.20 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f6(c2, f9(c2, f5(c1))) = c1) | (f6(c2, f9(c2, f5(c1))) = c2))),
% 27.95/18.20 inference(quant_inst,[status(thm)],[])).
% 27.95/18.20 tff(7233,plain,
% 27.95/18.20 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f6(c2, f9(c2, f5(c1))) = c1) | (f6(c2, f9(c2, f5(c1))) = c2)),
% 27.95/18.20 inference(modus_ponens,[status(thm)],[7232, 7231])).
% 27.95/18.20 tff(7234,plain,
% 27.95/18.20 ((f6(c2, f9(c2, f5(c1))) = c1) | (f6(c2, f9(c2, f5(c1))) = c2)),
% 27.95/18.20 inference(unit_resolution,[status(thm)],[7233, 10])).
% 27.95/18.20 tff(7235,plain,
% 27.95/18.20 (f6(c2, f9(c2, f5(c1))) = c2),
% 27.95/18.20 inference(unit_resolution,[status(thm)],[7234, 7230])).
% 27.95/18.20 tff(7236,plain,
% 27.95/18.20 (f6(c2, c1) = c2),
% 27.95/18.20 inference(transitivity,[status(thm)],[7221, 7235])).
% 27.95/18.20 tff(7237,plain,
% 27.95/18.20 (big_f(f7(c2), f6(c2, c1)) <=> big_f(c2, c2)),
% 27.95/18.20 inference(monotonicity,[status(thm)],[77, 7236])).
% 27.95/18.20 tff(7238,plain,
% 27.95/18.20 (big_f(c2, c2) <=> big_f(f7(c2), f6(c2, c1))),
% 27.95/18.20 inference(symmetry,[status(thm)],[7237])).
% 27.95/18.20 tff(7239,plain,
% 27.95/18.20 ((~big_f(c2, c2)) <=> (~big_f(f7(c2), f6(c2, c1)))),
% 27.95/18.20 inference(monotonicity,[status(thm)],[7238])).
% 27.95/18.20 tff(7240,plain,
% 27.95/18.20 (~big_f(f7(c2), f6(c2, c1))),
% 27.95/18.20 inference(modus_ponens,[status(thm)],[121, 7239])).
% 27.95/18.20 tff(7241,plain,
% 27.95/18.20 ($false),
% 27.95/18.20 inference(unit_resolution,[status(thm)],[7227, 7240])).
% 27.95/18.20 tff(7242,plain,(big_f(f9(c2, c2), f10(c2)) | big_f(c2, c2) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f5(c1) = c2)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~big_f(c2, f9(c2, c2)))), inference(lemma,lemma(discharge,[]))).
% 27.95/18.20 tff(7243,plain,
% 27.95/18.20 (~(f5(c1) = c2)),
% 27.95/18.20 inference(unit_resolution,[status(thm)],[7242, 121, 148, 3719, 79, 122, 77, 256])).
% 27.95/18.20 tff(7244,plain,
% 27.95/18.20 ((~(f6(c2, f9(c2, c2)) = f9(c2, c2))) <=> (~(f6(c2, c1) = c1))),
% 27.95/18.20 inference(monotonicity,[status(thm)],[4457])).
% 27.95/18.20 tff(7245,plain,
% 27.95/18.20 (big_f(f7(c2), f6(c2, c1))),
% 27.95/18.20 inference(unit_resolution,[status(thm)],[6623, 3719, 148, 256, 77, 79, 122])).
% 27.95/18.20 tff(7246,plain,
% 27.95/18.20 (big_f(f7(c2), f6(c2, f9(c2, c2)))),
% 27.95/18.20 inference(modus_ponens,[status(thm)],[7245, 4442])).
% 27.95/18.20 tff(7247,plain,
% 27.95/18.20 (~(f6(c2, f9(c2, c2)) = f9(c2, c2))),
% 27.95/18.20 inference(unit_resolution,[status(thm)],[3495, 2534, 122, 77, 185, 256, 7246])).
% 27.95/18.20 tff(7248,plain,
% 27.95/18.20 (~(f6(c2, c1) = c1)),
% 27.95/18.20 inference(modus_ponens,[status(thm)],[7247, 7244])).
% 27.95/18.20 tff(7249,plain,
% 27.95/18.20 (f6(f7(c2), f5(c1)) = f6(c2, c1)),
% 27.95/18.20 inference(monotonicity,[status(thm)],[77, 230])).
% 27.95/18.20 tff(7250,plain,
% 27.95/18.20 ((f6(f7(c2), f5(c1)) = c1) <=> (f6(c2, c1) = c1)),
% 27.95/18.20 inference(monotonicity,[status(thm)],[7249])).
% 27.95/18.20 tff(7251,plain,
% 27.95/18.20 ((f6(c2, c1) = c1) <=> (f6(f7(c2), f5(c1)) = c1)),
% 27.95/18.20 inference(symmetry,[status(thm)],[7250])).
% 27.95/18.20 tff(7252,plain,
% 27.95/18.20 ((~(f6(c2, c1) = c1)) <=> (~(f6(f7(c2), f5(c1)) = c1))),
% 27.95/18.20 inference(monotonicity,[status(thm)],[7251])).
% 27.95/18.20 tff(7253,plain,
% 27.95/18.20 (~(f6(f7(c2), f5(c1)) = c1)),
% 27.95/18.20 inference(modus_ponens,[status(thm)],[3198, 7252])).
% 27.95/18.20 tff(7254,plain,
% 27.95/18.20 (~(f6(f7(c2), f5(c1)) = c2)),
% 27.95/18.20 inference(unit_resolution,[status(thm)],[3480, 764, 79, 185, 256, 121, 148, 77, 122])).
% 27.95/18.20 tff(7255,plain,
% 27.95/18.20 ($false),
% 27.95/18.20 inference(unit_resolution,[status(thm)],[2978, 7254, 7253])).
% 27.95/18.20 tff(7256,plain,((~(f5(c1) = c1)) | (~(f4(c4) = c2)) | big_f(f9(c2, c2), f10(c2)) | big_f(c2, c2) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f7(c2) = c2)) | (~(f10(c2) = c2)) | (f6(c2, c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 27.95/18.20 tff(7257,plain,
% 27.95/18.20 (~(f5(c1) = c1)),
% 27.95/18.20 inference(unit_resolution,[status(thm)],[7256, 121, 79, 7248, 148, 77, 122, 256])).
% 27.95/18.20 tff(7258,plain,
% 27.95/18.20 ($false),
% 27.95/18.20 inference(unit_resolution,[status(thm)],[1708, 7257, 7243])).
% 27.95/18.20 tff(7259,plain,(big_f(c2, c2) | (~(f4(c4) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f7(c2) = c2)) | (~(f10(c2) = c2)) | big_f(f9(c2, c2), f10(c2)) | (~big_f(c2, f9(c2, c2)))), inference(lemma,lemma(discharge,[]))).
% 27.95/18.20 tff(7260,plain,
% 27.95/18.20 (big_f(c2, c2)),
% 27.95/18.20 inference(unit_resolution,[status(thm)],[7259, 5558, 148, 79, 122, 4597, 7217])).
% 27.95/18.20 tff(7261,plain,
% 27.95/18.20 ((~big_f(f9(c2, c2), f9(c2, c2))) <=> (~big_f(c1, c1))),
% 27.95/18.20 inference(monotonicity,[status(thm)],[4890])).
% 27.95/18.20 tff(7262,plain,
% 27.95/18.20 (~big_f(c1, c1)),
% 27.95/18.20 inference(modus_ponens,[status(thm)],[3689, 7261])).
% 27.95/18.20 tff(7263,plain,
% 27.95/18.20 (big_f(f7(c2), f6(c2, c2))),
% 27.95/18.20 inference(unit_resolution,[status(thm)],[5485, 7260, 5558, 185, 122, 4597])).
% 27.95/18.20 tff(7264,plain,
% 27.95/18.20 (~(f6(c2, c2) = c2)),
% 27.95/18.20 inference(unit_resolution,[status(thm)],[2744, 7263, 5558, 4597, 185, 122])).
% 27.95/18.20 tff(7265,plain,
% 27.95/18.20 (~(f6(f7(c2), c3) = c2)),
% 27.95/18.20 inference(unit_resolution,[status(thm)],[2716, 7264, 7206, 5558])).
% 27.95/18.20 tff(7266,plain,
% 27.95/18.20 (f6(f7(c2), c3) = c1),
% 27.95/18.20 inference(unit_resolution,[status(thm)],[2391, 7265])).
% 27.95/18.20 tff(7267,plain,
% 27.95/18.20 (c1 = f6(f7(c2), c3)),
% 27.95/18.20 inference(symmetry,[status(thm)],[7266])).
% 27.95/18.20 tff(7268,plain,
% 27.95/18.20 (f9(c2, c2) = f6(f7(c2), c3)),
% 27.95/18.20 inference(transitivity,[status(thm)],[160, 148, 7267])).
% 27.95/18.20 tff(7269,plain,
% 27.95/18.20 (f3(c1, c2) = f3(f6(f7(c2), c3), c2)),
% 27.95/18.20 inference(monotonicity,[status(thm)],[7267])).
% 27.95/18.20 tff(7270,plain,
% 27.95/18.20 (f3(f9(c2, c2), c2) = f3(f6(f7(c2), c3), c2)),
% 27.95/18.20 inference(transitivity,[status(thm)],[6644, 7269])).
% 27.95/18.20 tff(7271,plain,
% 27.95/18.20 (big_f(f3(f9(c2, c2), c2), f9(c2, c2)) <=> big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))),
% 27.95/18.20 inference(monotonicity,[status(thm)],[7270, 7268])).
% 27.95/18.20 tff(7272,plain,
% 27.95/18.20 (big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3)) <=> big_f(f3(f9(c2, c2), c2), f9(c2, c2))),
% 27.95/18.20 inference(symmetry,[status(thm)],[7271])).
% 27.95/18.20 tff(7273,plain,
% 27.95/18.20 (f6(f7(c2), c3) = f9(c2, c2)),
% 27.95/18.20 inference(transitivity,[status(thm)],[7266, 149, 132])).
% 27.95/18.20 tff(7274,plain,
% 27.95/18.20 (f3(f6(f7(c2), c3), c2) = f3(c1, c2)),
% 27.95/18.20 inference(symmetry,[status(thm)],[7269])).
% 27.95/18.20 tff(7275,plain,
% 27.95/18.20 (f6(f9(c2, c2), f3(f6(f7(c2), c3), c2)) = f6(c1, f3(c1, c2))),
% 27.95/18.20 inference(monotonicity,[status(thm)],[161, 7274])).
% 27.95/18.20 tff(7276,plain,
% 27.95/18.20 (f6(f9(c2, c2), f3(f6(f7(c2), c3), c2)) = c2),
% 27.95/18.20 inference(transitivity,[status(thm)],[7275, 7021])).
% 27.95/18.20 tff(7277,plain,
% 27.95/18.20 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(f6(f7(c2), c3), c2))) <=> big_f(f9(c2, c2), c2)),
% 27.95/18.20 inference(monotonicity,[status(thm)],[5532, 7276])).
% 27.95/18.20 tff(7278,plain,
% 27.95/18.20 (big_f(f9(c2, c2), c2) <=> big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(f6(f7(c2), c3), c2)))),
% 27.95/18.20 inference(symmetry,[status(thm)],[7277])).
% 27.95/18.20 tff(7279,plain,
% 27.95/18.20 ((~big_f(f9(c2, c2), c2)) <=> (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(f6(f7(c2), c3), c2))))),
% 27.95/18.20 inference(monotonicity,[status(thm)],[7278])).
% 27.95/18.20 tff(7280,plain,
% 27.95/18.20 (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(f6(f7(c2), c3), c2)))),
% 27.95/18.20 inference(modus_ponens,[status(thm)],[3685, 7279])).
% 27.95/18.20 tff(7281,plain,
% 27.95/18.20 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(f6(f7(c2), c3), c2))) | (f6(f9(c2, c2), f3(f6(f7(c2), c3), c2)) = f3(f6(f7(c2), c3), c2)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(f6(f7(c2), c3), c2))) | (f6(f9(c2, c2), f3(f6(f7(c2), c3), c2)) = f3(f6(f7(c2), c3), c2)))),
% 27.95/18.20 inference(rewrite,[status(thm)],[])).
% 27.95/18.20 tff(7282,plain,
% 27.95/18.20 (((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), f3(f6(f7(c2), c3), c2)) = f3(f6(f7(c2), c3), c2)) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(f6(f7(c2), c3), c2)))) <=> ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(f6(f7(c2), c3), c2))) | (f6(f9(c2, c2), f3(f6(f7(c2), c3), c2)) = f3(f6(f7(c2), c3), c2)))),
% 27.95/18.20 inference(rewrite,[status(thm)],[])).
% 27.95/18.20 tff(7283,plain,
% 27.95/18.20 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), f3(f6(f7(c2), c3), c2)) = f3(f6(f7(c2), c3), c2)) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(f6(f7(c2), c3), c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(f6(f7(c2), c3), c2))) | (f6(f9(c2, c2), f3(f6(f7(c2), c3), c2)) = f3(f6(f7(c2), c3), c2))))),
% 27.95/18.20 inference(monotonicity,[status(thm)],[7282])).
% 27.95/18.20 tff(7284,plain,
% 27.95/18.20 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), f3(f6(f7(c2), c3), c2)) = f3(f6(f7(c2), c3), c2)) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(f6(f7(c2), c3), c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(f6(f7(c2), c3), c2))) | (f6(f9(c2, c2), f3(f6(f7(c2), c3), c2)) = f3(f6(f7(c2), c3), c2)))),
% 27.95/18.20 inference(transitivity,[status(thm)],[7283, 7281])).
% 27.95/18.20 tff(7285,plain,
% 27.95/18.20 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), f3(f6(f7(c2), c3), c2)) = f3(f6(f7(c2), c3), c2)) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(f6(f7(c2), c3), c2))))),
% 27.95/18.20 inference(quant_inst,[status(thm)],[])).
% 27.95/18.20 tff(7286,plain,
% 27.95/18.20 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(f6(f7(c2), c3), c2))) | (f6(f9(c2, c2), f3(f6(f7(c2), c3), c2)) = f3(f6(f7(c2), c3), c2))),
% 27.95/18.20 inference(modus_ponens,[status(thm)],[7285, 7284])).
% 27.95/18.20 tff(7287,plain,
% 27.95/18.20 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(f6(f7(c2), c3), c2))) | (f6(f9(c2, c2), f3(f6(f7(c2), c3), c2)) = f3(f6(f7(c2), c3), c2))),
% 27.95/18.20 inference(unit_resolution,[status(thm)],[7286, 2492, 122, 185, 4597, 5532])).
% 27.95/18.20 tff(7288,plain,
% 27.95/18.20 (f6(f9(c2, c2), f3(f6(f7(c2), c3), c2)) = f3(f6(f7(c2), c3), c2)),
% 27.95/18.20 inference(unit_resolution,[status(thm)],[7287, 7280])).
% 27.95/18.20 tff(7289,plain,
% 27.95/18.20 (f3(f6(f7(c2), c3), c2) = f6(f9(c2, c2), f3(f6(f7(c2), c3), c2))),
% 27.95/18.20 inference(symmetry,[status(thm)],[7288])).
% 27.95/18.20 tff(7290,plain,
% 27.95/18.20 (f3(f6(f7(c2), c3), c2) = c2),
% 27.95/18.20 inference(transitivity,[status(thm)],[7289, 7275, 7021])).
% 27.95/18.20 tff(7291,plain,
% 27.95/18.20 (big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3)) <=> big_f(c2, f9(c2, c2))),
% 27.95/18.20 inference(monotonicity,[status(thm)],[7290, 7273])).
% 27.95/18.20 tff(7292,plain,
% 27.95/18.20 (big_f(c2, f9(c2, c2)) <=> big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))),
% 27.95/18.20 inference(symmetry,[status(thm)],[7291])).
% 27.95/18.20 tff(7293,plain,
% 27.95/18.20 (big_f(c2, f9(c2, c2)) <=> big_f(f3(f9(c2, c2), c2), f9(c2, c2))),
% 27.95/18.20 inference(transitivity,[status(thm)],[7292, 7272])).
% 27.95/18.20 tff(7294,plain,
% 27.95/18.20 (big_f(f3(f9(c2, c2), c2), f9(c2, c2))),
% 27.95/18.20 inference(modus_ponens,[status(thm)],[7217, 7293])).
% 27.95/18.20 tff(7295,plain,
% 27.95/18.20 ((f3(f9(c2, c2), c2) = c2) <=> (f3(f6(f7(c2), c3), c2) = c2)),
% 27.95/18.20 inference(monotonicity,[status(thm)],[7270])).
% 27.95/18.20 tff(7296,plain,
% 27.95/18.20 ((f3(f6(f7(c2), c3), c2) = c2) <=> (f3(f9(c2, c2), c2) = c2)),
% 27.95/18.20 inference(symmetry,[status(thm)],[7295])).
% 27.95/18.20 tff(7297,plain,
% 27.95/18.20 ((c2 = f3(f6(f7(c2), c3), c2)) <=> (f3(f6(f7(c2), c3), c2) = c2)),
% 27.95/18.20 inference(commutativity,[status(thm)],[])).
% 27.95/18.20 tff(7298,plain,
% 27.95/18.20 ((f6(f9(c2, c2), f3(f6(f7(c2), c3), c2)) = f3(f6(f7(c2), c3), c2)) <=> (c2 = f3(f6(f7(c2), c3), c2))),
% 27.95/18.20 inference(monotonicity,[status(thm)],[7276])).
% 27.95/18.20 tff(7299,plain,
% 27.95/18.20 ((f6(f9(c2, c2), f3(f6(f7(c2), c3), c2)) = f3(f6(f7(c2), c3), c2)) <=> (f3(f6(f7(c2), c3), c2) = c2)),
% 27.95/18.20 inference(transitivity,[status(thm)],[7298, 7297])).
% 27.95/18.20 tff(7300,plain,
% 27.95/18.20 ((f6(f9(c2, c2), f3(f6(f7(c2), c3), c2)) = f3(f6(f7(c2), c3), c2)) <=> (f3(f9(c2, c2), c2) = c2)),
% 27.95/18.20 inference(transitivity,[status(thm)],[7299, 7296])).
% 27.95/18.20 tff(7301,plain,
% 27.95/18.20 (f3(f9(c2, c2), c2) = c2),
% 27.95/18.20 inference(modus_ponens,[status(thm)],[7288, 7300])).
% 27.95/18.20 tff(7302,plain,
% 27.95/18.20 (c2 = c3),
% 27.95/18.20 inference(modus_ponens,[status(thm)],[7206, 78])).
% 27.95/18.20 tff(7303,plain,
% 27.95/18.20 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), c2) = c2)) | (~big_f(f3(f9(c2, c2), c2), f9(c2, c2))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), c2) = c2)) | (~big_f(f3(f9(c2, c2), c2), f9(c2, c2))))),
% 27.95/18.21 inference(rewrite,[status(thm)],[])).
% 27.95/18.21 tff(7304,plain,
% 27.95/18.21 (((~(c2 = c3)) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), c2) = c2)) | (~big_f(f3(f9(c2, c2), c2), f9(c2, c2))) | (c2 = f2(c2)) | (~big_f(c2, c2))) <=> ((~(c2 = c3)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), c2) = c2)) | (~big_f(f3(f9(c2, c2), c2), f9(c2, c2))))),
% 27.95/18.21 inference(rewrite,[status(thm)],[])).
% 27.95/18.21 tff(7305,plain,
% 27.95/18.21 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), c2) = c2)) | (~big_f(f3(f9(c2, c2), c2), f9(c2, c2))) | (c2 = f2(c2)) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), c2) = c2)) | (~big_f(f3(f9(c2, c2), c2), f9(c2, c2)))))),
% 27.95/18.21 inference(monotonicity,[status(thm)],[7304])).
% 27.95/18.21 tff(7306,plain,
% 27.95/18.21 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), c2) = c2)) | (~big_f(f3(f9(c2, c2), c2), f9(c2, c2))) | (c2 = f2(c2)) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), c2) = c2)) | (~big_f(f3(f9(c2, c2), c2), f9(c2, c2))))),
% 27.95/18.21 inference(transitivity,[status(thm)],[7305, 7303])).
% 27.95/18.21 tff(7307,plain,
% 27.95/18.21 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), c2) = c2)) | (~big_f(f3(f9(c2, c2), c2), f9(c2, c2))) | (c2 = f2(c2)) | (~big_f(c2, c2)))),
% 27.95/18.21 inference(quant_inst,[status(thm)],[])).
% 27.95/18.21 tff(7308,plain,
% 27.95/18.21 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), c2) = c2)) | (~big_f(f3(f9(c2, c2), c2), f9(c2, c2)))),
% 27.95/18.21 inference(modus_ponens,[status(thm)],[7307, 7306])).
% 27.95/18.21 tff(7309,plain,
% 27.95/18.21 ((c2 = f2(c2)) | (~(f3(f9(c2, c2), c2) = c2)) | (~big_f(f3(f9(c2, c2), c2), f9(c2, c2)))),
% 27.95/18.21 inference(unit_resolution,[status(thm)],[7308, 7051, 7260, 7302, 1861])).
% 27.95/18.21 tff(7310,plain,
% 27.95/18.21 (c2 = f2(c2)),
% 27.95/18.21 inference(unit_resolution,[status(thm)],[7309, 7301, 7294])).
% 27.95/18.21 tff(7311,plain,
% 27.95/18.21 (f2(c2) = c2),
% 27.95/18.21 inference(symmetry,[status(thm)],[7310])).
% 27.95/18.21 tff(7312,plain,
% 27.95/18.21 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2))) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), c2) = c2)) | (~big_f(f3(f9(c2, c2), c2), f9(c2, c2))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2))) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), c2) = c2)) | (~big_f(f3(f9(c2, c2), c2), f9(c2, c2))))),
% 27.95/18.21 inference(rewrite,[status(thm)],[])).
% 27.95/18.21 tff(7313,plain,
% 27.95/18.21 (((~(c2 = c3)) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), c2) = c2)) | (~big_f(f3(f9(c2, c2), c2), f9(c2, c2))) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2)))) <=> ((~(c2 = c3)) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2))) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), c2) = c2)) | (~big_f(f3(f9(c2, c2), c2), f9(c2, c2))))),
% 28.02/18.21 inference(rewrite,[status(thm)],[])).
% 28.02/18.21 tff(7314,plain,
% 28.02/18.21 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), c2) = c2)) | (~big_f(f3(f9(c2, c2), c2), f9(c2, c2))) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2))) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), c2) = c2)) | (~big_f(f3(f9(c2, c2), c2), f9(c2, c2)))))),
% 28.02/18.21 inference(monotonicity,[status(thm)],[7313])).
% 28.02/18.21 tff(7315,plain,
% 28.02/18.21 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), c2) = c2)) | (~big_f(f3(f9(c2, c2), c2), f9(c2, c2))) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2))) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), c2) = c2)) | (~big_f(f3(f9(c2, c2), c2), f9(c2, c2))))),
% 28.02/18.21 inference(transitivity,[status(thm)],[7314, 7312])).
% 28.02/18.21 tff(7316,plain,
% 28.02/18.21 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), c2) = c2)) | (~big_f(f3(f9(c2, c2), c2), f9(c2, c2))) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2))))),
% 28.02/18.21 inference(quant_inst,[status(thm)],[])).
% 28.02/18.21 tff(7317,plain,
% 28.02/18.21 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2))) | (f9(c2, c2) = c4) | (~(f3(f9(c2, c2), c2) = c2)) | (~big_f(f3(f9(c2, c2), c2), f9(c2, c2)))),
% 28.02/18.21 inference(modus_ponens,[status(thm)],[7316, 7315])).
% 28.02/18.21 tff(7318,plain,
% 28.02/18.21 ((f9(c2, c2) = f2(c2)) | (~(f3(f9(c2, c2), c2) = c2)) | (~big_f(f3(f9(c2, c2), c2), f9(c2, c2)))),
% 28.02/18.21 inference(unit_resolution,[status(thm)],[7317, 7051, 7302, 1861, 7217])).
% 28.02/18.21 tff(7319,plain,
% 28.02/18.21 (f9(c2, c2) = f2(c2)),
% 28.02/18.21 inference(unit_resolution,[status(thm)],[7318, 7301, 7294])).
% 28.02/18.21 tff(7320,plain,
% 28.02/18.21 (f9(c2, c2) = c2),
% 28.02/18.21 inference(transitivity,[status(thm)],[7319, 7311])).
% 28.02/18.21 tff(7321,plain,
% 28.02/18.21 ($false),
% 28.02/18.21 inference(unit_resolution,[status(thm)],[185, 7320])).
% 28.02/18.21 tff(7322,plain,((~(f6(c1, f3(c1, c2)) = c2)) | (f9(c2, c2) = c4) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | big_f(f9(c2, c2), c2) | (~(f7(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.02/18.21 tff(7323,plain,
% 28.02/18.21 (~(f6(c1, f3(c1, c2)) = c2)),
% 28.02/18.21 inference(unit_resolution,[status(thm)],[7322, 1861, 148, 79, 122, 3685, 4234])).
% 28.02/18.21 tff(7324,plain,
% 28.02/18.21 (f6(c1, f3(c1, c2)) = c1),
% 28.02/18.21 inference(unit_resolution,[status(thm)],[6690, 7323])).
% 28.02/18.21 tff(7325,plain,
% 28.02/18.21 (f6(f9(c2, c2), f3(f6(f7(c2), c3), c2)) = f9(c2, c2)),
% 28.02/18.21 inference(transitivity,[status(thm)],[7275, 7324, 149, 132])).
% 28.02/18.21 tff(7326,plain,
% 28.02/18.21 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(f6(f7(c2), c3), c2))) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 28.02/18.21 inference(monotonicity,[status(thm)],[5532, 7325])).
% 28.02/18.21 tff(7327,plain,
% 28.02/18.21 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(f6(f7(c2), c3), c2)))),
% 28.02/18.21 inference(symmetry,[status(thm)],[7326])).
% 28.02/18.21 tff(7328,plain,
% 28.02/18.21 ((~big_f(f9(c2, c2), f9(c2, c2))) <=> (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(f6(f7(c2), c3), c2))))),
% 28.02/18.21 inference(monotonicity,[status(thm)],[7327])).
% 28.02/18.21 tff(7329,plain,
% 28.02/18.21 (~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(f6(f7(c2), c3), c2)))),
% 28.02/18.21 inference(modus_ponens,[status(thm)],[3689, 7328])).
% 28.02/18.21 tff(7330,plain,
% 28.02/18.21 (f6(f9(c2, c2), f3(f6(f7(c2), c3), c2)) = f3(f6(f7(c2), c3), c2)),
% 28.02/18.21 inference(unit_resolution,[status(thm)],[7287, 7329])).
% 28.02/18.21 tff(7331,plain,
% 28.02/18.21 (f3(f6(f7(c2), c3), c2) = f6(f9(c2, c2), f3(f6(f7(c2), c3), c2))),
% 28.02/18.21 inference(symmetry,[status(thm)],[7330])).
% 28.02/18.21 tff(7332,plain,
% 28.02/18.21 (f3(f6(f7(c2), c3), c2) = f9(c2, c2)),
% 28.02/18.21 inference(transitivity,[status(thm)],[7331, 7275, 7324, 149, 132])).
% 28.02/18.21 tff(7333,plain,
% 28.02/18.21 (big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3)) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 28.02/18.21 inference(monotonicity,[status(thm)],[7332, 7273])).
% 28.02/18.21 tff(7334,plain,
% 28.02/18.21 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))),
% 28.02/18.21 inference(symmetry,[status(thm)],[7333])).
% 28.02/18.21 tff(7335,plain,
% 28.02/18.21 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f3(f9(c2, c2), c2), f9(c2, c2))),
% 28.02/18.21 inference(transitivity,[status(thm)],[7334, 7272])).
% 28.02/18.21 tff(7336,plain,
% 28.02/18.21 ((~big_f(f9(c2, c2), f9(c2, c2))) <=> (~big_f(f3(f9(c2, c2), c2), f9(c2, c2)))),
% 28.02/18.21 inference(monotonicity,[status(thm)],[7335])).
% 28.02/18.21 tff(7337,plain,
% 28.02/18.21 (~big_f(f3(f9(c2, c2), c2), f9(c2, c2))),
% 28.02/18.21 inference(modus_ponens,[status(thm)],[3689, 7336])).
% 28.02/18.21 tff(7338,plain,
% 28.02/18.21 ((f3(f6(f7(c2), c3), c2) = c2) <=> (f9(c2, c2) = c2)),
% 28.02/18.21 inference(monotonicity,[status(thm)],[7332])).
% 28.02/18.21 tff(7339,plain,
% 28.02/18.21 ((f9(c2, c2) = c2) <=> (f3(f6(f7(c2), c3), c2) = c2)),
% 28.02/18.21 inference(symmetry,[status(thm)],[7338])).
% 28.02/18.21 tff(7340,plain,
% 28.02/18.21 ((f9(c2, c2) = c2) <=> (f3(f9(c2, c2), c2) = c2)),
% 28.02/18.21 inference(transitivity,[status(thm)],[7339, 7296])).
% 28.02/18.21 tff(7341,plain,
% 28.02/18.21 ((~(f9(c2, c2) = c2)) <=> (~(f3(f9(c2, c2), c2) = c2))),
% 28.02/18.21 inference(monotonicity,[status(thm)],[7340])).
% 28.02/18.21 tff(7342,plain,
% 28.02/18.21 (~(f3(f9(c2, c2), c2) = c2)),
% 28.02/18.21 inference(modus_ponens,[status(thm)],[185, 7341])).
% 28.02/18.21 tff(7343,plain,
% 28.02/18.21 (^[X12: $i, X13: $i, X10: $i, X2: $i] : refl(((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12))) <=> ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12))))),
% 28.02/18.21 inference(bind,[status(th)],[])).
% 28.02/18.21 tff(7344,plain,
% 28.02/18.21 (![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12))) <=> ![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))),
% 28.02/18.21 inference(quant_intro,[status(thm)],[7343])).
% 28.02/18.21 tff(7345,plain,
% 28.02/18.21 (![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12))) <=> ![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))),
% 28.02/18.21 inference(rewrite,[status(thm)],[])).
% 28.02/18.21 tff(7346,plain,
% 28.02/18.21 (^[X12: $i, X13: $i, X10: $i, X2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_f(X10, X12)) | (X12 = f2(X10))) | (~(X10 = c3))) <=> ((~(X10 = c3)) | (X12 = f2(X10)) | (~big_f(X10, X12)))), (((((~big_f(X10, X12)) | (X12 = f2(X10))) | (~(X10 = c3))) | big_f(f3(X2, X13), X2)) <=> (((~(X10 = c3)) | (X12 = f2(X10)) | (~big_f(X10, X12))) | big_f(f3(X2, X13), X2)))), rewrite((((~(X10 = c3)) | (X12 = f2(X10)) | (~big_f(X10, X12))) | big_f(f3(X2, X13), X2)) <=> ((~(X10 = c3)) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))), (((((~big_f(X10, X12)) | (X12 = f2(X10))) | (~(X10 = c3))) | big_f(f3(X2, X13), X2)) <=> ((~(X10 = c3)) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12))))), ((((((~big_f(X10, X12)) | (X12 = f2(X10))) | (~(X10 = c3))) | big_f(f3(X2, X13), X2)) | (f3(X2, X13) = X13)) <=> (((~(X10 = c3)) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12))) | (f3(X2, X13) = X13)))), rewrite((((~(X10 = c3)) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12))) | (f3(X2, X13) = X13)) <=> ((~(X10 = c3)) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))), ((((((~big_f(X10, X12)) | (X12 = f2(X10))) | (~(X10 = c3))) | big_f(f3(X2, X13), X2)) | (f3(X2, X13) = X13)) <=> ((~(X10 = c3)) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12))))), (((((((~big_f(X10, X12)) | (X12 = f2(X10))) | (~(X10 = c3))) | big_f(f3(X2, X13), X2)) | (f3(X2, X13) = X13)) | (X2 = c4)) <=> (((~(X10 = c3)) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12))) | (X2 = c4)))), rewrite((((~(X10 = c3)) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12))) | (X2 = c4)) <=> ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))), (((((((~big_f(X10, X12)) | (X12 = f2(X10))) | (~(X10 = c3))) | big_f(f3(X2, X13), X2)) | (f3(X2, X13) = X13)) | (X2 = c4)) <=> ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))))),
% 28.02/18.21 inference(bind,[status(th)],[])).
% 28.02/18.21 tff(7347,plain,
% 28.02/18.21 (![X12: $i, X13: $i, X10: $i, X2: $i] : ((((((~big_f(X10, X12)) | (X12 = f2(X10))) | (~(X10 = c3))) | big_f(f3(X2, X13), X2)) | (f3(X2, X13) = X13)) | (X2 = c4)) <=> ![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))),
% 28.02/18.21 inference(quant_intro,[status(thm)],[7346])).
% 28.02/18.21 tff(7348,axiom,(![X12: $i, X13: $i, X10: $i, X2: $i] : ((((((~big_f(X10, X12)) | (X12 = f2(X10))) | (~(X10 = c3))) | big_f(f3(X2, X13), X2)) | (f3(X2, X13) = X13)) | (X2 = c4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_11')).
% 28.02/18.21 tff(7349,plain,
% 28.02/18.21 (![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))),
% 28.02/18.21 inference(modus_ponens,[status(thm)],[7348, 7347])).
% 28.02/18.21 tff(7350,plain,
% 28.02/18.21 (![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))),
% 28.02/18.21 inference(modus_ponens,[status(thm)],[7349, 7345])).
% 28.02/18.21 tff(7351,plain,(
% 28.02/18.21 ![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))),
% 28.02/18.21 inference(skolemize,[status(sab)],[7350])).
% 28.02/18.21 tff(7352,plain,
% 28.02/18.21 (![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))),
% 28.02/18.21 inference(modus_ponens,[status(thm)],[7351, 7344])).
% 28.02/18.21 tff(7353,plain,
% 28.02/18.21 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (f9(c2, c2) = c4) | (f3(f9(c2, c2), c2) = c2) | big_f(f3(f9(c2, c2), c2), f9(c2, c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (f9(c2, c2) = c4) | (f3(f9(c2, c2), c2) = c2) | big_f(f3(f9(c2, c2), c2), f9(c2, c2)))),
% 28.02/18.21 inference(rewrite,[status(thm)],[])).
% 28.02/18.21 tff(7354,plain,
% 28.02/18.21 (((~(c2 = c3)) | (f9(c2, c2) = c4) | (f3(f9(c2, c2), c2) = c2) | big_f(f3(f9(c2, c2), c2), f9(c2, c2)) | (c2 = f2(c2)) | (~big_f(c2, c2))) <=> ((~(c2 = c3)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (f9(c2, c2) = c4) | (f3(f9(c2, c2), c2) = c2) | big_f(f3(f9(c2, c2), c2), f9(c2, c2)))),
% 28.02/18.21 inference(rewrite,[status(thm)],[])).
% 28.02/18.21 tff(7355,plain,
% 28.02/18.21 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f9(c2, c2) = c4) | (f3(f9(c2, c2), c2) = c2) | big_f(f3(f9(c2, c2), c2), f9(c2, c2)) | (c2 = f2(c2)) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (f9(c2, c2) = c4) | (f3(f9(c2, c2), c2) = c2) | big_f(f3(f9(c2, c2), c2), f9(c2, c2))))),
% 28.02/18.21 inference(monotonicity,[status(thm)],[7354])).
% 28.02/18.21 tff(7356,plain,
% 28.02/18.21 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f9(c2, c2) = c4) | (f3(f9(c2, c2), c2) = c2) | big_f(f3(f9(c2, c2), c2), f9(c2, c2)) | (c2 = f2(c2)) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (f9(c2, c2) = c4) | (f3(f9(c2, c2), c2) = c2) | big_f(f3(f9(c2, c2), c2), f9(c2, c2)))),
% 28.02/18.21 inference(transitivity,[status(thm)],[7355, 7353])).
% 28.02/18.21 tff(7357,plain,
% 28.02/18.21 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f9(c2, c2) = c4) | (f3(f9(c2, c2), c2) = c2) | big_f(f3(f9(c2, c2), c2), f9(c2, c2)) | (c2 = f2(c2)) | (~big_f(c2, c2)))),
% 28.02/18.21 inference(quant_inst,[status(thm)],[])).
% 28.02/18.21 tff(7358,plain,
% 28.02/18.21 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (f9(c2, c2) = c4) | (f3(f9(c2, c2), c2) = c2) | big_f(f3(f9(c2, c2), c2), f9(c2, c2))),
% 28.02/18.21 inference(modus_ponens,[status(thm)],[7357, 7356])).
% 28.02/18.21 tff(7359,plain,
% 28.02/18.21 ((c2 = f2(c2)) | (f3(f9(c2, c2), c2) = c2) | big_f(f3(f9(c2, c2), c2), f9(c2, c2))),
% 28.02/18.21 inference(unit_resolution,[status(thm)],[7358, 7352, 7260, 7302, 1861])).
% 28.02/18.21 tff(7360,plain,
% 28.02/18.21 (c2 = f2(c2)),
% 28.02/18.21 inference(unit_resolution,[status(thm)],[7359, 7342, 7337])).
% 28.02/18.21 tff(7361,plain,
% 28.02/18.21 (f2(c2) = c2),
% 28.02/18.21 inference(symmetry,[status(thm)],[7360])).
% 28.02/18.21 tff(7362,plain,
% 28.02/18.21 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2))) | (f9(c2, c2) = c4) | (f3(f9(c2, c2), c2) = c2) | big_f(f3(f9(c2, c2), c2), f9(c2, c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2))) | (f9(c2, c2) = c4) | (f3(f9(c2, c2), c2) = c2) | big_f(f3(f9(c2, c2), c2), f9(c2, c2)))),
% 28.02/18.21 inference(rewrite,[status(thm)],[])).
% 28.02/18.21 tff(7363,plain,
% 28.02/18.21 (((~(c2 = c3)) | (f9(c2, c2) = c4) | (f3(f9(c2, c2), c2) = c2) | big_f(f3(f9(c2, c2), c2), f9(c2, c2)) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2)))) <=> ((~(c2 = c3)) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2))) | (f9(c2, c2) = c4) | (f3(f9(c2, c2), c2) = c2) | big_f(f3(f9(c2, c2), c2), f9(c2, c2)))),
% 28.02/18.21 inference(rewrite,[status(thm)],[])).
% 28.02/18.21 tff(7364,plain,
% 28.02/18.21 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f9(c2, c2) = c4) | (f3(f9(c2, c2), c2) = c2) | big_f(f3(f9(c2, c2), c2), f9(c2, c2)) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2))) | (f9(c2, c2) = c4) | (f3(f9(c2, c2), c2) = c2) | big_f(f3(f9(c2, c2), c2), f9(c2, c2))))),
% 28.02/18.21 inference(monotonicity,[status(thm)],[7363])).
% 28.02/18.21 tff(7365,plain,
% 28.02/18.21 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f9(c2, c2) = c4) | (f3(f9(c2, c2), c2) = c2) | big_f(f3(f9(c2, c2), c2), f9(c2, c2)) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2))) | (f9(c2, c2) = c4) | (f3(f9(c2, c2), c2) = c2) | big_f(f3(f9(c2, c2), c2), f9(c2, c2)))),
% 28.02/18.22 inference(transitivity,[status(thm)],[7364, 7362])).
% 28.02/18.22 tff(7366,plain,
% 28.02/18.22 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f9(c2, c2) = c4) | (f3(f9(c2, c2), c2) = c2) | big_f(f3(f9(c2, c2), c2), f9(c2, c2)) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2))))),
% 28.02/18.22 inference(quant_inst,[status(thm)],[])).
% 28.02/18.22 tff(7367,plain,
% 28.02/18.22 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2))) | (f9(c2, c2) = c4) | (f3(f9(c2, c2), c2) = c2) | big_f(f3(f9(c2, c2), c2), f9(c2, c2))),
% 28.02/18.22 inference(modus_ponens,[status(thm)],[7366, 7365])).
% 28.02/18.22 tff(7368,plain,
% 28.02/18.22 ((f9(c2, c2) = f2(c2)) | (f3(f9(c2, c2), c2) = c2) | big_f(f3(f9(c2, c2), c2), f9(c2, c2))),
% 28.02/18.22 inference(unit_resolution,[status(thm)],[7367, 7352, 7302, 1861, 7217])).
% 28.02/18.22 tff(7369,plain,
% 28.02/18.22 (f9(c2, c2) = f2(c2)),
% 28.02/18.22 inference(unit_resolution,[status(thm)],[7368, 7342, 7337])).
% 28.02/18.22 tff(7370,plain,
% 28.02/18.22 (f9(c2, c2) = c2),
% 28.02/18.22 inference(transitivity,[status(thm)],[7369, 7361])).
% 28.02/18.22 tff(7371,plain,
% 28.02/18.22 ($false),
% 28.02/18.22 inference(unit_resolution,[status(thm)],[185, 7370])).
% 28.02/18.22 tff(7372,plain,((f9(c2, c2) = c4) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | big_f(f9(c2, c2), f9(c2, c2)) | (~(f7(c1) = c1)) | big_f(f9(c2, c2), c2)), inference(lemma,lemma(discharge,[]))).
% 28.02/18.22 tff(7373,plain,
% 28.02/18.22 (f9(c2, c2) = c4),
% 28.02/18.22 inference(unit_resolution,[status(thm)],[7372, 3685, 79, 122, 3689, 4234, 148])).
% 28.02/18.22 tff(7374,plain,
% 28.02/18.22 (c4 = f9(c2, c2)),
% 28.02/18.22 inference(symmetry,[status(thm)],[7373])).
% 28.02/18.22 tff(7375,plain,
% 28.02/18.22 ((c2 = c4) <=> (c2 = f9(c2, c2))),
% 28.02/18.22 inference(monotonicity,[status(thm)],[7374])).
% 28.02/18.22 tff(7376,plain,
% 28.02/18.22 ((c2 = c4) <=> (f9(c2, c2) = c2)),
% 28.02/18.22 inference(transitivity,[status(thm)],[7375, 167])).
% 28.02/18.22 tff(7377,plain,
% 28.02/18.22 ((f9(c2, c2) = c2) <=> (c2 = c4)),
% 28.02/18.22 inference(symmetry,[status(thm)],[7376])).
% 28.02/18.22 tff(7378,plain,
% 28.02/18.22 ((~(f9(c2, c2) = c2)) <=> (~(c2 = c4))),
% 28.02/18.22 inference(monotonicity,[status(thm)],[7377])).
% 28.02/18.22 tff(7379,plain,
% 28.02/18.22 (~(c2 = c4)),
% 28.02/18.22 inference(modus_ponens,[status(thm)],[185, 7378])).
% 28.02/18.22 tff(7380,plain,
% 28.02/18.22 (c2 = f10(c3)),
% 28.02/18.22 inference(transitivity,[status(thm)],[69, 3008])).
% 28.02/18.22 tff(7381,plain,
% 28.02/18.22 (f3(c2, c2) = f3(f10(c3), c2)),
% 28.02/18.22 inference(monotonicity,[status(thm)],[7380])).
% 28.02/18.22 tff(7382,plain,
% 28.02/18.22 (big_f(f3(c2, c2), c2) <=> big_f(f3(f10(c3), c2), f10(c3))),
% 28.02/18.22 inference(monotonicity,[status(thm)],[7381, 7380])).
% 28.02/18.22 tff(7383,plain,
% 28.02/18.22 (big_f(f3(f10(c3), c2), f10(c3)) <=> big_f(f3(c2, c2), c2)),
% 28.02/18.22 inference(symmetry,[status(thm)],[7382])).
% 28.02/18.22 tff(7384,plain,
% 28.02/18.22 ((~big_f(f3(f10(c3), c2), f10(c3))) <=> (~big_f(f3(c2, c2), c2))),
% 28.02/18.22 inference(monotonicity,[status(thm)],[7383])).
% 28.02/18.22 tff(7385,assumption,(~big_f(f3(f10(c3), c2), f10(c3))), introduced(assumption)).
% 28.02/18.22 tff(7386,plain,
% 28.02/18.22 (~big_f(f3(c2, c2), c2)),
% 28.02/18.22 inference(modus_ponens,[status(thm)],[7385, 7384])).
% 28.02/18.22 tff(7387,assumption,(f3(c2, c2) = c2), introduced(assumption)).
% 28.02/18.22 tff(7388,plain,
% 28.02/18.22 (f3(f10(c3), c2) = f3(c2, c2)),
% 28.02/18.22 inference(monotonicity,[status(thm)],[3012])).
% 28.02/18.22 tff(7389,plain,
% 28.02/18.22 (f3(f10(c3), c2) = c2),
% 28.02/18.22 inference(transitivity,[status(thm)],[7388, 7387])).
% 28.02/18.22 tff(7390,plain,
% 28.02/18.22 (big_f(f3(f10(c3), c2), f10(c3)) <=> big_f(c2, c2)),
% 28.02/18.22 inference(monotonicity,[status(thm)],[7389, 3012])).
% 28.02/18.22 tff(7391,plain,
% 28.02/18.22 (big_f(c2, c2) <=> big_f(f3(f10(c3), c2), f10(c3))),
% 28.02/18.22 inference(symmetry,[status(thm)],[7390])).
% 28.02/18.22 tff(7392,plain,
% 28.02/18.22 (big_f(f3(f10(c3), c2), f10(c3))),
% 28.02/18.22 inference(modus_ponens,[status(thm)],[1345, 7391])).
% 28.02/18.22 tff(7393,plain,
% 28.02/18.22 ($false),
% 28.02/18.22 inference(unit_resolution,[status(thm)],[7385, 7392])).
% 28.02/18.22 tff(7394,plain,((~(f3(c2, c2) = c2)) | big_f(f3(f10(c3), c2), f10(c3)) | (~big_f(c2, c2)) | (~(f10(c3) = c3)) | (~(c3 = c2))), inference(lemma,lemma(discharge,[]))).
% 28.02/18.22 tff(7395,plain,
% 28.02/18.22 (~(f3(c2, c2) = c2)),
% 28.02/18.22 inference(unit_resolution,[status(thm)],[7394, 7385, 1345, 3007, 67])).
% 28.02/18.22 tff(7396,plain,
% 28.02/18.22 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = f2(c2)) | (c2 = c4) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = f2(c2)) | (c2 = c4) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2) | (~big_f(c2, c2)))),
% 28.02/18.22 inference(rewrite,[status(thm)],[])).
% 28.02/18.22 tff(7397,plain,
% 28.02/18.22 (((~(c2 = c3)) | (c2 = c4) | (f3(c2, c2) = c2) | big_f(f3(c2, c2), c2) | (c2 = f2(c2)) | (~big_f(c2, c2))) <=> ((~(c2 = c3)) | (c2 = f2(c2)) | (c2 = c4) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2) | (~big_f(c2, c2)))),
% 28.02/18.22 inference(rewrite,[status(thm)],[])).
% 28.02/18.22 tff(7398,plain,
% 28.02/18.22 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = c4) | (f3(c2, c2) = c2) | big_f(f3(c2, c2), c2) | (c2 = f2(c2)) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = f2(c2)) | (c2 = c4) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2) | (~big_f(c2, c2))))),
% 28.02/18.22 inference(monotonicity,[status(thm)],[7397])).
% 28.02/18.22 tff(7399,plain,
% 28.02/18.22 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = c4) | (f3(c2, c2) = c2) | big_f(f3(c2, c2), c2) | (c2 = f2(c2)) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = f2(c2)) | (c2 = c4) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2) | (~big_f(c2, c2)))),
% 28.02/18.22 inference(transitivity,[status(thm)],[7398, 7396])).
% 28.02/18.22 tff(7400,plain,
% 28.02/18.22 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = c4) | (f3(c2, c2) = c2) | big_f(f3(c2, c2), c2) | (c2 = f2(c2)) | (~big_f(c2, c2)))),
% 28.02/18.22 inference(quant_inst,[status(thm)],[])).
% 28.02/18.22 tff(7401,plain,
% 28.02/18.22 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = f2(c2)) | (c2 = c4) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2) | (~big_f(c2, c2))),
% 28.02/18.22 inference(modus_ponens,[status(thm)],[7400, 7399])).
% 28.02/18.22 tff(7402,plain,
% 28.02/18.22 ((c2 = f2(c2)) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2)),
% 28.02/18.22 inference(unit_resolution,[status(thm)],[7401, 7352, 873, 1345, 1335])).
% 28.02/18.22 tff(7403,plain,
% 28.02/18.22 (c2 = f2(c2)),
% 28.02/18.22 inference(unit_resolution,[status(thm)],[7402, 7395, 7386])).
% 28.02/18.22 tff(7404,plain,
% 28.02/18.22 (f2(c2) = c2),
% 28.02/18.22 inference(symmetry,[status(thm)],[7403])).
% 28.02/18.22 tff(7405,plain,
% 28.02/18.22 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = c4) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = c4) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2))))),
% 28.02/18.22 inference(rewrite,[status(thm)],[])).
% 28.02/18.22 tff(7406,plain,
% 28.02/18.22 (((~(c2 = c3)) | (c2 = c4) | (f3(c2, c2) = c2) | big_f(f3(c2, c2), c2) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2)))) <=> ((~(c2 = c3)) | (c2 = c4) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2))))),
% 28.02/18.22 inference(rewrite,[status(thm)],[])).
% 28.02/18.22 tff(7407,plain,
% 28.02/18.22 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = c4) | (f3(c2, c2) = c2) | big_f(f3(c2, c2), c2) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = c4) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2)))))),
% 28.02/18.22 inference(monotonicity,[status(thm)],[7406])).
% 28.02/18.22 tff(7408,plain,
% 28.02/18.22 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = c4) | (f3(c2, c2) = c2) | big_f(f3(c2, c2), c2) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = c4) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2))))),
% 28.02/18.22 inference(transitivity,[status(thm)],[7407, 7405])).
% 28.02/18.22 tff(7409,plain,
% 28.02/18.22 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = c4) | (f3(c2, c2) = c2) | big_f(f3(c2, c2), c2) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2))))),
% 28.02/18.22 inference(quant_inst,[status(thm)],[])).
% 28.02/18.22 tff(7410,plain,
% 28.02/18.22 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = c4) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2)))),
% 28.02/18.22 inference(modus_ponens,[status(thm)],[7409, 7408])).
% 28.02/18.22 tff(7411,plain,
% 28.02/18.22 (big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2) | (f9(c2, c2) = f2(c2))),
% 28.02/18.22 inference(unit_resolution,[status(thm)],[7410, 7352, 873, 1335, 3719])).
% 28.02/18.22 tff(7412,plain,
% 28.02/18.22 (f9(c2, c2) = f2(c2)),
% 28.02/18.22 inference(unit_resolution,[status(thm)],[7411, 7395, 7386])).
% 28.02/18.22 tff(7413,plain,
% 28.02/18.22 (f9(c2, c2) = c2),
% 28.02/18.22 inference(transitivity,[status(thm)],[7412, 7404])).
% 28.02/18.22 tff(7414,plain,
% 28.02/18.22 ($false),
% 28.02/18.22 inference(unit_resolution,[status(thm)],[1209, 7413])).
% 28.02/18.22 tff(7415,plain,(big_f(f3(f10(c3), c2), f10(c3)) | (f9(c2, c2) = c2) | (c2 = c4) | (~big_f(c2, f9(c2, c2))) | (~big_f(c2, c2)) | (~(f10(c3) = c3)) | (~(c3 = c2))), inference(lemma,lemma(discharge,[]))).
% 28.02/18.22 tff(7416,plain,
% 28.02/18.22 (big_f(f3(f10(c3), c2), f10(c3))),
% 28.02/18.22 inference(unit_resolution,[status(thm)],[7415, 873, 3719, 185, 1345, 2831, 67])).
% 28.02/18.22 tff(7417,assumption,(f3(f10(c2), f1(c1, c2)) = c1), introduced(assumption)).
% 28.02/18.22 tff(7418,plain,
% 28.02/18.22 (c2 = f1(c1, c2)),
% 28.02/18.22 inference(symmetry,[status(thm)],[822])).
% 28.02/18.22 tff(7419,plain,
% 28.02/18.22 (f10(c3) = f10(c2)),
% 28.02/18.22 inference(transitivity,[status(thm)],[2831, 67, 216])).
% 28.02/18.22 tff(7420,plain,
% 28.02/18.22 (f3(f10(c3), c2) = f3(f10(c2), f1(c1, c2))),
% 28.02/18.22 inference(monotonicity,[status(thm)],[7419, 7418])).
% 28.02/18.22 tff(7421,plain,
% 28.02/18.22 (f3(f10(c3), c2) = f9(c2, c2)),
% 28.02/18.22 inference(transitivity,[status(thm)],[7420, 7417, 149, 132])).
% 28.02/18.22 tff(7422,plain,
% 28.02/18.22 (big_f(f3(f10(c3), c2), f10(c3)) <=> big_f(f9(c2, c2), c2)),
% 28.02/18.22 inference(monotonicity,[status(thm)],[7421, 2832])).
% 28.02/18.22 tff(7423,plain,
% 28.02/18.22 (big_f(f9(c2, c2), c2) <=> big_f(f3(f10(c3), c2), f10(c3))),
% 28.02/18.22 inference(symmetry,[status(thm)],[7422])).
% 28.02/18.22 tff(7424,plain,
% 28.02/18.22 ((~big_f(f9(c2, c2), c2)) <=> (~big_f(f3(f10(c3), c2), f10(c3)))),
% 28.02/18.22 inference(monotonicity,[status(thm)],[7423])).
% 28.02/18.22 tff(7425,plain,
% 28.02/18.22 (~big_f(f3(f10(c3), c2), f10(c3))),
% 28.02/18.22 inference(modus_ponens,[status(thm)],[3685, 7424])).
% 28.02/18.22 tff(7426,assumption,(big_f(f3(f10(c3), c2), f10(c3))), introduced(assumption)).
% 28.02/18.22 tff(7427,plain,
% 28.02/18.22 ($false),
% 28.02/18.22 inference(unit_resolution,[status(thm)],[7426, 7425])).
% 28.02/18.22 tff(7428,plain,((~(f3(f10(c2), f1(c1, c2)) = c1)) | (~big_f(f3(f10(c3), c2), f10(c3))) | big_f(f9(c2, c2), c2) | (~(c3 = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f1(c1, c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.02/18.22 tff(7429,plain,
% 28.02/18.22 (~(f3(f10(c2), f1(c1, c2)) = c1)),
% 28.02/18.22 inference(unit_resolution,[status(thm)],[7428, 7416, 67, 3685, 148, 79, 122, 822])).
% 28.02/18.22 tff(7430,plain,
% 28.02/18.22 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f3(f10(c2), f1(c1, c2)) = c1) | (f3(f10(c2), f1(c1, c2)) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f3(f10(c2), f1(c1, c2)) = c1) | (f3(f10(c2), f1(c1, c2)) = c2))),
% 28.02/18.22 inference(rewrite,[status(thm)],[])).
% 28.02/18.22 tff(7431,plain,
% 28.02/18.22 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f3(f10(c2), f1(c1, c2)) = c1) | (f3(f10(c2), f1(c1, c2)) = c2))),
% 28.02/18.22 inference(quant_inst,[status(thm)],[])).
% 28.02/18.22 tff(7432,plain,
% 28.02/18.22 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f3(f10(c2), f1(c1, c2)) = c1) | (f3(f10(c2), f1(c1, c2)) = c2)),
% 28.02/18.22 inference(modus_ponens,[status(thm)],[7431, 7430])).
% 28.02/18.22 tff(7433,plain,
% 28.02/18.22 ((f3(f10(c2), f1(c1, c2)) = c1) | (f3(f10(c2), f1(c1, c2)) = c2)),
% 28.02/18.22 inference(unit_resolution,[status(thm)],[7432, 10])).
% 28.02/18.22 tff(7434,plain,
% 28.02/18.22 (f3(f10(c2), f1(c1, c2)) = c2),
% 28.02/18.22 inference(unit_resolution,[status(thm)],[7433, 7429])).
% 28.02/18.22 tff(7435,plain,
% 28.02/18.22 (f3(c2, c2) = f3(f10(c2), f1(c1, c2))),
% 28.02/18.22 inference(monotonicity,[status(thm)],[216, 7418])).
% 28.02/18.22 tff(7436,plain,
% 28.02/18.22 (f3(c2, c2) = c2),
% 28.02/18.22 inference(transitivity,[status(thm)],[7435, 7434])).
% 28.02/18.22 tff(7437,plain,
% 28.02/18.22 (big_f(f3(c2, c2), c2) <=> big_f(c2, c2)),
% 28.02/18.22 inference(monotonicity,[status(thm)],[7436])).
% 28.02/18.22 tff(7438,plain,
% 28.02/18.22 (big_f(c2, c2) <=> big_f(f3(c2, c2), c2)),
% 28.02/18.22 inference(symmetry,[status(thm)],[7437])).
% 28.02/18.22 tff(7439,plain,
% 28.02/18.22 (big_f(f3(c2, c2), c2)),
% 28.02/18.22 inference(modus_ponens,[status(thm)],[1345, 7438])).
% 28.02/18.22 tff(7440,plain,
% 28.02/18.22 (f3(f7(f4(c4)), f4(c4)) = f3(c2, c2)),
% 28.02/18.22 inference(monotonicity,[status(thm)],[2474, 79])).
% 28.02/18.22 tff(7441,plain,
% 28.02/18.22 (f3(c2, c2) = f3(f7(f4(c4)), f4(c4))),
% 28.02/18.22 inference(symmetry,[status(thm)],[7440])).
% 28.02/18.22 tff(7442,plain,
% 28.02/18.22 (f3(f7(f4(c4)), f4(c4)) = c2),
% 28.02/18.22 inference(transitivity,[status(thm)],[7440, 7435, 7434])).
% 28.02/18.22 tff(7443,plain,
% 28.02/18.22 (f3(c2, f3(f7(f4(c4)), f4(c4))) = f3(c2, c2)),
% 28.02/18.22 inference(monotonicity,[status(thm)],[7442])).
% 28.02/18.22 tff(7444,plain,
% 28.02/18.22 (f3(c2, f3(f7(f4(c4)), f4(c4))) = f3(f7(f4(c4)), f4(c4))),
% 28.02/18.22 inference(transitivity,[status(thm)],[7443, 7441])).
% 28.02/18.22 tff(7445,plain,
% 28.02/18.22 (f3(c2, f3(f7(f4(c4)), f4(c4))) = c2),
% 28.02/18.22 inference(transitivity,[status(thm)],[7443, 7435, 7434])).
% 28.02/18.22 tff(7446,plain,
% 28.02/18.22 (big_f(f3(c2, f3(f7(f4(c4)), f4(c4))), c2) <=> big_f(c2, c2)),
% 28.02/18.22 inference(monotonicity,[status(thm)],[7445])).
% 28.02/18.22 tff(7447,plain,
% 28.02/18.22 (big_f(c2, c2) <=> big_f(f3(c2, f3(f7(f4(c4)), f4(c4))), c2)),
% 28.02/18.22 inference(symmetry,[status(thm)],[7446])).
% 28.02/18.22 tff(7448,plain,
% 28.02/18.22 (big_f(f3(c2, f3(f7(f4(c4)), f4(c4))), c2)),
% 28.02/18.22 inference(modus_ponens,[status(thm)],[1345, 7447])).
% 28.02/18.22 tff(7449,plain,
% 28.02/18.22 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = f2(c2)) | (c2 = c4) | (~big_f(c2, c2)) | (~big_f(f3(c2, f3(f7(f4(c4)), f4(c4))), c2)) | (~(f3(c2, f3(f7(f4(c4)), f4(c4))) = f3(f7(f4(c4)), f4(c4)))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = f2(c2)) | (c2 = c4) | (~big_f(c2, c2)) | (~big_f(f3(c2, f3(f7(f4(c4)), f4(c4))), c2)) | (~(f3(c2, f3(f7(f4(c4)), f4(c4))) = f3(f7(f4(c4)), f4(c4)))))),
% 28.02/18.22 inference(rewrite,[status(thm)],[])).
% 28.02/18.22 tff(7450,plain,
% 28.02/18.22 (((~(c2 = c3)) | (c2 = c4) | (~(f3(c2, f3(f7(f4(c4)), f4(c4))) = f3(f7(f4(c4)), f4(c4)))) | (~big_f(f3(c2, f3(f7(f4(c4)), f4(c4))), c2)) | (c2 = f2(c2)) | (~big_f(c2, c2))) <=> ((~(c2 = c3)) | (c2 = f2(c2)) | (c2 = c4) | (~big_f(c2, c2)) | (~big_f(f3(c2, f3(f7(f4(c4)), f4(c4))), c2)) | (~(f3(c2, f3(f7(f4(c4)), f4(c4))) = f3(f7(f4(c4)), f4(c4)))))),
% 28.02/18.22 inference(rewrite,[status(thm)],[])).
% 28.02/18.22 tff(7451,plain,
% 28.02/18.22 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = c4) | (~(f3(c2, f3(f7(f4(c4)), f4(c4))) = f3(f7(f4(c4)), f4(c4)))) | (~big_f(f3(c2, f3(f7(f4(c4)), f4(c4))), c2)) | (c2 = f2(c2)) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = f2(c2)) | (c2 = c4) | (~big_f(c2, c2)) | (~big_f(f3(c2, f3(f7(f4(c4)), f4(c4))), c2)) | (~(f3(c2, f3(f7(f4(c4)), f4(c4))) = f3(f7(f4(c4)), f4(c4))))))),
% 28.02/18.22 inference(monotonicity,[status(thm)],[7450])).
% 28.02/18.22 tff(7452,plain,
% 28.02/18.22 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = c4) | (~(f3(c2, f3(f7(f4(c4)), f4(c4))) = f3(f7(f4(c4)), f4(c4)))) | (~big_f(f3(c2, f3(f7(f4(c4)), f4(c4))), c2)) | (c2 = f2(c2)) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = f2(c2)) | (c2 = c4) | (~big_f(c2, c2)) | (~big_f(f3(c2, f3(f7(f4(c4)), f4(c4))), c2)) | (~(f3(c2, f3(f7(f4(c4)), f4(c4))) = f3(f7(f4(c4)), f4(c4)))))),
% 28.02/18.22 inference(transitivity,[status(thm)],[7451, 7449])).
% 28.02/18.22 tff(7453,plain,
% 28.02/18.22 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = c4) | (~(f3(c2, f3(f7(f4(c4)), f4(c4))) = f3(f7(f4(c4)), f4(c4)))) | (~big_f(f3(c2, f3(f7(f4(c4)), f4(c4))), c2)) | (c2 = f2(c2)) | (~big_f(c2, c2)))),
% 28.02/18.22 inference(quant_inst,[status(thm)],[])).
% 28.02/18.22 tff(7454,plain,
% 28.02/18.22 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = f2(c2)) | (c2 = c4) | (~big_f(c2, c2)) | (~big_f(f3(c2, f3(f7(f4(c4)), f4(c4))), c2)) | (~(f3(c2, f3(f7(f4(c4)), f4(c4))) = f3(f7(f4(c4)), f4(c4))))),
% 28.02/18.22 inference(modus_ponens,[status(thm)],[7453, 7452])).
% 28.02/18.22 tff(7455,plain,
% 28.02/18.22 ((~(c2 = c3)) | (c2 = f2(c2)) | (c2 = c4) | (~big_f(c2, c2)) | (~big_f(f3(c2, f3(f7(f4(c4)), f4(c4))), c2)) | (~(f3(c2, f3(f7(f4(c4)), f4(c4))) = f3(f7(f4(c4)), f4(c4))))),
% 28.02/18.22 inference(unit_resolution,[status(thm)],[7454, 7051])).
% 28.02/18.22 tff(7456,plain,
% 28.02/18.22 (c2 = f2(c2)),
% 28.02/18.22 inference(unit_resolution,[status(thm)],[7455, 7448, 1335, 1345, 873, 7444])).
% 28.02/18.22 tff(7457,plain,
% 28.02/18.22 (f2(c2) = c2),
% 28.02/18.22 inference(symmetry,[status(thm)],[7456])).
% 28.02/18.22 tff(7458,plain,
% 28.02/18.22 ((f9(c2, c2) = f2(c2)) <=> (f9(c2, c2) = c2)),
% 28.02/18.22 inference(monotonicity,[status(thm)],[7457])).
% 28.02/18.22 tff(7459,plain,
% 28.02/18.22 ((f9(c2, c2) = c2) <=> (f9(c2, c2) = f2(c2))),
% 28.02/18.22 inference(symmetry,[status(thm)],[7458])).
% 28.02/18.22 tff(7460,plain,
% 28.02/18.22 ((~(f9(c2, c2) = c2)) <=> (~(f9(c2, c2) = f2(c2)))),
% 28.02/18.22 inference(monotonicity,[status(thm)],[7459])).
% 28.02/18.22 tff(7461,plain,
% 28.02/18.22 (~(f9(c2, c2) = f2(c2))),
% 28.02/18.22 inference(modus_ponens,[status(thm)],[185, 7460])).
% 28.02/18.22 tff(7462,plain,
% 28.02/18.22 (f3(f10(c2), f1(c1, c2)) = f3(c2, c2)),
% 28.02/18.22 inference(symmetry,[status(thm)],[7435])).
% 28.02/18.22 tff(7463,plain,
% 28.02/18.22 ((f3(f10(c2), f1(c1, c2)) = c2) <=> (f3(c2, c2) = c2)),
% 28.02/18.22 inference(monotonicity,[status(thm)],[7462])).
% 28.02/18.22 tff(7464,plain,
% 28.02/18.22 (f3(c2, c2) = c2),
% 28.02/18.22 inference(modus_ponens,[status(thm)],[7434, 7463])).
% 28.02/18.22 tff(7465,plain,
% 28.02/18.22 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2))))),
% 28.02/18.23 inference(rewrite,[status(thm)],[])).
% 28.02/18.23 tff(7466,plain,
% 28.02/18.23 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2))))),
% 28.02/18.23 inference(quant_inst,[status(thm)],[])).
% 28.02/18.23 tff(7467,plain,
% 28.02/18.23 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (f9(c2, c2) = f2(c2)) | (~big_f(c2, f9(c2, c2)))),
% 28.02/18.23 inference(modus_ponens,[status(thm)],[7466, 7465])).
% 28.02/18.23 tff(7468,plain,
% 28.02/18.23 ((~big_f(f3(c2, c2), c2)) | (f9(c2, c2) = f2(c2))),
% 28.02/18.23 inference(unit_resolution,[status(thm)],[7467, 7051, 873, 1335, 3719, 7464])).
% 28.02/18.23 tff(7469,plain,
% 28.02/18.23 ($false),
% 28.02/18.23 inference(unit_resolution,[status(thm)],[7468, 7461, 7439])).
% 28.02/18.23 tff(7470,plain,((c2 = c4) | (~big_f(c2, f9(c2, c2))) | (~big_f(c2, c2)) | (~(f1(c1, c2) = c2)) | (~(f10(c2) = c2)) | (~(f4(c4) = c2)) | (~(f7(c2) = c2)) | (~(c3 = c2)) | big_f(f9(c2, c2), c2) | (~(f9(f10(c2), f4(c4)) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.02/18.23 tff(7471,plain,
% 28.02/18.23 (~(f1(c1, c2) = c2)),
% 28.02/18.23 inference(unit_resolution,[status(thm)],[7470, 7379, 7206, 5558, 122, 79, 7217, 7260, 3685, 148])).
% 28.02/18.23 tff(7472,plain,
% 28.02/18.23 (f10(c3) = f5(c1)),
% 28.02/18.23 inference(transitivity,[status(thm)],[2831, 67, 1761])).
% 28.02/18.23 tff(7473,plain,
% 28.02/18.23 (f3(f10(c3), c2) = f3(f5(c1), f5(c1))),
% 28.02/18.23 inference(monotonicity,[status(thm)],[7472, 1761])).
% 28.02/18.23 tff(7474,plain,
% 28.02/18.23 ((f3(f10(c3), c2) = c2) <=> (f3(f5(c1), f5(c1)) = c2)),
% 28.02/18.23 inference(monotonicity,[status(thm)],[7473])).
% 28.02/18.23 tff(7475,plain,
% 28.02/18.23 (c2 = f10(c3)),
% 28.02/18.23 inference(transitivity,[status(thm)],[69, 2834])).
% 28.02/18.23 tff(7476,plain,
% 28.02/18.23 (f3(c2, c2) = f3(f10(c3), c2)),
% 28.02/18.23 inference(monotonicity,[status(thm)],[7475])).
% 28.02/18.23 tff(7477,plain,
% 28.02/18.23 ((f3(c2, c2) = c2) <=> (f3(f10(c3), c2) = c2)),
% 28.02/18.23 inference(monotonicity,[status(thm)],[7476])).
% 28.02/18.23 tff(7478,plain,
% 28.02/18.23 ((f3(c2, c2) = c2) <=> (f3(f5(c1), f5(c1)) = c2)),
% 28.02/18.23 inference(transitivity,[status(thm)],[7477, 7474])).
% 28.02/18.23 tff(7479,plain,
% 28.02/18.23 ((~(f3(c2, c2) = c2)) <=> (~(f3(f5(c1), f5(c1)) = c2))),
% 28.02/18.23 inference(monotonicity,[status(thm)],[7478])).
% 28.02/18.23 tff(7480,plain,
% 28.02/18.23 (f1(f9(c2, c2), c2) = f9(c2, c2)),
% 28.02/18.23 inference(transitivity,[status(thm)],[843, 819, 1053, 149, 132])).
% 28.02/18.23 tff(7481,plain,
% 28.02/18.23 (big_f(f9(c2, c2), f1(f9(c2, c2), c2)) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 28.02/18.23 inference(monotonicity,[status(thm)],[7480])).
% 28.02/18.23 tff(7482,plain,
% 28.02/18.23 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f9(c2, c2), f1(f9(c2, c2), c2))),
% 28.02/18.23 inference(symmetry,[status(thm)],[7481])).
% 28.02/18.23 tff(7483,plain,
% 28.02/18.23 ((~big_f(f9(c2, c2), f9(c2, c2))) <=> (~big_f(f9(c2, c2), f1(f9(c2, c2), c2)))),
% 28.02/18.23 inference(monotonicity,[status(thm)],[7482])).
% 28.02/18.23 tff(7484,plain,
% 28.02/18.23 (~big_f(f9(c2, c2), f1(f9(c2, c2), c2))),
% 28.02/18.23 inference(modus_ponens,[status(thm)],[4906, 7483])).
% 28.02/18.23 tff(7485,plain,
% 28.02/18.23 ((f1(f9(c2, c2), c2) = c2) <=> (f9(c2, c2) = c2)),
% 28.02/18.23 inference(monotonicity,[status(thm)],[7480])).
% 28.02/18.23 tff(7486,plain,
% 28.02/18.23 ((f9(c2, c2) = c2) <=> (f1(f9(c2, c2), c2) = c2)),
% 28.02/18.23 inference(symmetry,[status(thm)],[7485])).
% 28.02/18.23 tff(7487,plain,
% 28.02/18.23 ((~(f9(c2, c2) = c2)) <=> (~(f1(f9(c2, c2), c2) = c2))),
% 28.02/18.23 inference(monotonicity,[status(thm)],[7486])).
% 28.02/18.23 tff(7488,plain,
% 28.02/18.23 (~(f1(f9(c2, c2), c2) = c2)),
% 28.02/18.23 inference(modus_ponens,[status(thm)],[185, 7487])).
% 28.02/18.23 tff(7489,plain,
% 28.02/18.23 (big_f(f3(c2, c2), c2) <=> big_f(f3(f10(c3), c2), f10(c3))),
% 28.02/18.23 inference(monotonicity,[status(thm)],[7476, 7475])).
% 28.02/18.23 tff(7490,plain,
% 28.02/18.23 (big_f(f3(f10(c3), c2), f10(c3)) <=> big_f(f3(c2, c2), c2)),
% 28.02/18.23 inference(symmetry,[status(thm)],[7489])).
% 28.02/18.23 tff(7491,plain,
% 28.02/18.23 (big_f(f9(c2, c2), c2) <=> big_f(f9(f10(c2), f4(c4)), f10(f10(c2)))),
% 28.02/18.23 inference(transitivity,[status(thm)],[3667, 2440])).
% 28.02/18.23 tff(7492,plain,
% 28.02/18.23 ((~big_f(f9(c2, c2), c2)) <=> (~big_f(f9(f10(c2), f4(c4)), f10(f10(c2))))),
% 28.02/18.23 inference(monotonicity,[status(thm)],[7491])).
% 28.02/18.23 tff(7493,plain,
% 28.02/18.23 (~big_f(f9(f10(c2), f4(c4)), f10(f10(c2)))),
% 28.02/18.23 inference(modus_ponens,[status(thm)],[3685, 7492])).
% 28.02/18.23 tff(7494,plain,
% 28.02/18.23 (big_f(f7(f7(c2)), f6(f7(c2), c3))),
% 28.02/18.23 inference(unit_resolution,[status(thm)],[2508, 77, 79, 181, 2470, 1345, 252, 3665])).
% 28.02/18.23 tff(7495,plain,
% 28.02/18.23 ((~big_f(f7(c2), f6(c2, c2))) <=> (~big_f(f7(f7(c2)), f6(f7(c2), c3)))),
% 28.02/18.23 inference(monotonicity,[status(thm)],[2473])).
% 28.02/18.23 tff(7496,plain,
% 28.02/18.23 (~big_f(f7(f7(c2)), f6(f7(c2), c3))),
% 28.02/18.23 inference(modus_ponens,[status(thm)],[2621, 7495])).
% 28.02/18.23 tff(7497,assumption,(big_f(f7(f7(c2)), f6(f7(c2), c3))), introduced(assumption)).
% 28.02/18.23 tff(7498,plain,
% 28.02/18.23 ($false),
% 28.02/18.23 inference(unit_resolution,[status(thm)],[7497, 7496])).
% 28.02/18.23 tff(7499,plain,(big_f(f7(c2), f6(c2, c2)) | (~big_f(f7(f7(c2)), f6(f7(c2), c3))) | (~(c3 = c2)) | (~(f7(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.02/18.23 tff(7500,plain,
% 28.02/18.23 (big_f(f7(c2), f6(c2, c2))),
% 28.02/18.23 inference(unit_resolution,[status(thm)],[7499, 7494, 181, 77])).
% 28.02/18.23 tff(7501,plain,
% 28.02/18.23 (~(f6(c2, c2) = c2)),
% 28.02/18.23 inference(unit_resolution,[status(thm)],[2744, 7500, 256, 77, 185, 122])).
% 28.02/18.23 tff(7502,plain,
% 28.02/18.23 (~(f6(f7(c2), c3) = c2)),
% 28.02/18.23 inference(unit_resolution,[status(thm)],[2716, 7501, 181, 77])).
% 28.02/18.23 tff(7503,plain,
% 28.02/18.23 (f6(f7(c2), c3) = c1),
% 28.02/18.23 inference(unit_resolution,[status(thm)],[2391, 7502])).
% 28.02/18.23 tff(7504,plain,
% 28.02/18.23 (c1 = f6(f7(c2), c3)),
% 28.02/18.23 inference(symmetry,[status(thm)],[7503])).
% 28.02/18.23 tff(7505,plain,
% 28.02/18.23 (f3(c1, c2) = f3(f6(f7(c2), c3), c2)),
% 28.02/18.23 inference(monotonicity,[status(thm)],[7504])).
% 28.02/18.23 tff(7506,plain,
% 28.02/18.23 (f3(f6(f7(c2), c3), c2) = f3(c1, c2)),
% 28.02/18.23 inference(symmetry,[status(thm)],[7505])).
% 28.02/18.23 tff(7507,plain,
% 28.02/18.23 (big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3)) <=> big_f(f3(c1, c2), c1)),
% 28.02/18.23 inference(monotonicity,[status(thm)],[7506, 7503])).
% 28.02/18.23 tff(7508,plain,
% 28.02/18.23 (big_f(f3(c1, c2), c1) <=> big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))),
% 28.02/18.23 inference(symmetry,[status(thm)],[7507])).
% 28.02/18.23 tff(7509,plain,
% 28.02/18.23 (~(f6(f7(c2), c3) = c4)),
% 28.02/18.23 inference(unit_resolution,[status(thm)],[3995, 7502, 431])).
% 28.02/18.23 tff(7510,plain,
% 28.02/18.23 (big_f(c2, c1)),
% 28.02/18.23 inference(unit_resolution,[status(thm)],[2710, 7503, 181, 77, 7500])).
% 28.02/18.23 tff(7511,plain,
% 28.02/18.23 (big_f(c2, f9(c2, c2))),
% 28.02/18.23 inference(modus_ponens,[status(thm)],[7510, 3716])).
% 28.02/18.23 tff(7512,plain,
% 28.02/18.23 (f3(c1, c2) = f3(f6(f7(c2), c3), c2)),
% 28.02/18.23 inference(monotonicity,[status(thm)],[2703])).
% 28.02/18.23 tff(7513,plain,
% 28.02/18.23 (f3(c1, c2) = c2),
% 28.02/18.23 inference(transitivity,[status(thm)],[7512, 6727])).
% 28.02/18.23 tff(7514,plain,
% 28.02/18.23 (big_f(f3(c1, c2), c1) <=> big_f(c2, f9(c2, c2))),
% 28.02/18.23 inference(monotonicity,[status(thm)],[7513, 150])).
% 28.02/18.23 tff(7515,plain,
% 28.02/18.23 (big_f(c2, f9(c2, c2)) <=> big_f(f3(c1, c2), c1)),
% 28.02/18.23 inference(symmetry,[status(thm)],[7514])).
% 28.02/18.23 tff(7516,plain,
% 28.02/18.23 (big_f(f3(c1, c2), c1)),
% 28.02/18.23 inference(modus_ponens,[status(thm)],[3719, 7515])).
% 28.02/18.23 tff(7517,plain,
% 28.02/18.23 (f3(f6(f7(c2), c3), c2) = f3(c1, c2)),
% 28.02/18.23 inference(symmetry,[status(thm)],[7512])).
% 28.02/18.23 tff(7518,plain,
% 28.02/18.23 (big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3)) <=> big_f(f3(c1, c2), c1)),
% 28.02/18.23 inference(monotonicity,[status(thm)],[7517, 2702])).
% 28.02/18.23 tff(7519,plain,
% 28.02/18.23 ((~big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))) <=> (~big_f(f3(c1, c2), c1))),
% 28.02/18.23 inference(monotonicity,[status(thm)],[7518])).
% 28.02/18.23 tff(7520,assumption,(~(f6(f7(c2), c3) = c4)), introduced(assumption)).
% 28.02/18.23 tff(7521,plain,
% 28.02/18.23 (big_f(c1, f1(c1, c2)) <=> big_f(c1, c1)),
% 28.02/18.23 inference(monotonicity,[status(thm)],[1053])).
% 28.02/18.23 tff(7522,plain,
% 28.02/18.23 (big_f(c1, c1) <=> big_f(c1, f1(c1, c2))),
% 28.02/18.23 inference(symmetry,[status(thm)],[7521])).
% 28.02/18.23 tff(7523,plain,
% 28.02/18.23 ((~big_f(c1, c1)) <=> (~big_f(c1, f1(c1, c2)))),
% 28.02/18.23 inference(monotonicity,[status(thm)],[7522])).
% 28.02/18.23 tff(7524,plain,
% 28.02/18.23 (~big_f(c1, f1(c1, c2))),
% 28.02/18.23 inference(modus_ponens,[status(thm)],[66, 7523])).
% 28.02/18.23 tff(7525,assumption,(big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))), introduced(assumption)).
% 28.02/18.23 tff(7526,plain,
% 28.02/18.23 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((f1(c1, c2) = c2) | (c1 = c3) | big_f(c1, f1(c1, c2)) | (f6(f7(c2), c3) = c4) | (~big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))) | (~(f3(f6(f7(c2), c3), c2) = c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (f1(c1, c2) = c2) | (c1 = c3) | big_f(c1, f1(c1, c2)) | (f6(f7(c2), c3) = c4) | (~big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))) | (~(f3(f6(f7(c2), c3), c2) = c2)))),
% 28.02/18.23 inference(rewrite,[status(thm)],[])).
% 28.02/18.23 tff(7527,plain,
% 28.02/18.23 (((f6(f7(c2), c3) = c4) | (c1 = c3) | (f1(c1, c2) = c2) | big_f(c1, f1(c1, c2)) | (~(f3(f6(f7(c2), c3), c2) = c2)) | (~big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3)))) <=> ((f1(c1, c2) = c2) | (c1 = c3) | big_f(c1, f1(c1, c2)) | (f6(f7(c2), c3) = c4) | (~big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))) | (~(f3(f6(f7(c2), c3), c2) = c2)))),
% 28.02/18.23 inference(rewrite,[status(thm)],[])).
% 28.02/18.23 tff(7528,plain,
% 28.02/18.23 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((f6(f7(c2), c3) = c4) | (c1 = c3) | (f1(c1, c2) = c2) | big_f(c1, f1(c1, c2)) | (~(f3(f6(f7(c2), c3), c2) = c2)) | (~big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((f1(c1, c2) = c2) | (c1 = c3) | big_f(c1, f1(c1, c2)) | (f6(f7(c2), c3) = c4) | (~big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))) | (~(f3(f6(f7(c2), c3), c2) = c2))))),
% 28.02/18.23 inference(monotonicity,[status(thm)],[7527])).
% 28.02/18.23 tff(7529,plain,
% 28.02/18.23 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((f6(f7(c2), c3) = c4) | (c1 = c3) | (f1(c1, c2) = c2) | big_f(c1, f1(c1, c2)) | (~(f3(f6(f7(c2), c3), c2) = c2)) | (~big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (f1(c1, c2) = c2) | (c1 = c3) | big_f(c1, f1(c1, c2)) | (f6(f7(c2), c3) = c4) | (~big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))) | (~(f3(f6(f7(c2), c3), c2) = c2)))),
% 28.02/18.23 inference(transitivity,[status(thm)],[7528, 7526])).
% 28.02/18.23 tff(7530,plain,
% 28.02/18.23 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((f6(f7(c2), c3) = c4) | (c1 = c3) | (f1(c1, c2) = c2) | big_f(c1, f1(c1, c2)) | (~(f3(f6(f7(c2), c3), c2) = c2)) | (~big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))))),
% 28.02/18.23 inference(quant_inst,[status(thm)],[])).
% 28.02/18.23 tff(7531,plain,
% 28.02/18.23 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (f1(c1, c2) = c2) | (c1 = c3) | big_f(c1, f1(c1, c2)) | (f6(f7(c2), c3) = c4) | (~big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))) | (~(f3(f6(f7(c2), c3), c2) = c2))),
% 28.02/18.23 inference(modus_ponens,[status(thm)],[7530, 7529])).
% 28.02/18.23 tff(7532,plain,
% 28.02/18.23 ((f1(c1, c2) = c2) | (c1 = c3) | big_f(c1, f1(c1, c2)) | (f6(f7(c2), c3) = c4) | (~big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))) | (~(f3(f6(f7(c2), c3), c2) = c2))),
% 28.02/18.23 inference(unit_resolution,[status(thm)],[7531, 969])).
% 28.02/18.23 tff(7533,plain,
% 28.02/18.23 (big_f(c1, f1(c1, c2))),
% 28.02/18.23 inference(unit_resolution,[status(thm)],[7532, 1052, 168, 7520, 7525, 6727])).
% 28.02/18.23 tff(7534,plain,
% 28.02/18.23 ($false),
% 28.02/18.23 inference(unit_resolution,[status(thm)],[7533, 7524])).
% 28.02/18.23 tff(7535,plain,((f1(c1, c2) = c2) | big_f(c1, c1) | (c1 = c3) | (f6(f7(c2), c3) = c4) | (~big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))) | (~(f3(f6(f7(c2), c3), c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.02/18.23 tff(7536,plain,
% 28.02/18.23 (~big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))),
% 28.02/18.23 inference(unit_resolution,[status(thm)],[7535, 6727, 168, 7520, 66, 1052])).
% 28.02/18.23 tff(7537,plain,
% 28.02/18.23 (~big_f(f3(c1, c2), c1)),
% 28.02/18.23 inference(modus_ponens,[status(thm)],[7536, 7519])).
% 28.02/18.23 tff(7538,plain,
% 28.02/18.23 ($false),
% 28.02/18.23 inference(unit_resolution,[status(thm)],[7537, 7516])).
% 28.02/18.23 tff(7539,plain,((~(f3(f6(f7(c2), c3), c2) = c2)) | (~big_f(c2, f9(c2, c2))) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f6(f7(c2), c3) = c1)) | (c1 = c3) | (f6(f7(c2), c3) = c4) | big_f(c1, c1) | (f1(c1, c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 28.02/18.23 tff(7540,plain,
% 28.02/18.23 (~(f3(f6(f7(c2), c3), c2) = c2)),
% 28.02/18.23 inference(unit_resolution,[status(thm)],[7539, 7511, 148, 79, 122, 7503, 168, 7509, 66, 1052])).
% 28.02/18.23 tff(7541,plain,
% 28.02/18.23 (f3(f6(f7(c2), c3), c2) = c1),
% 28.02/18.23 inference(unit_resolution,[status(thm)],[6749, 7540])).
% 28.02/18.23 tff(7542,plain,
% 28.02/18.23 (f3(c1, c2) = f9(c2, c2)),
% 28.02/18.23 inference(transitivity,[status(thm)],[7505, 7541, 149, 132])).
% 28.02/18.23 tff(7543,plain,
% 28.02/18.23 (big_f(f3(c1, c2), c1) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 28.02/18.23 inference(monotonicity,[status(thm)],[7542, 150])).
% 28.02/18.23 tff(7544,plain,
% 28.02/18.23 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f3(c1, c2), c1)),
% 28.02/18.23 inference(symmetry,[status(thm)],[7543])).
% 28.02/18.23 tff(7545,plain,
% 28.02/18.23 (big_f(c1, c1) <=> big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))),
% 28.02/18.23 inference(transitivity,[status(thm)],[4889, 7544, 7508])).
% 28.02/18.23 tff(7546,plain,
% 28.02/18.23 ((~big_f(c1, c1)) <=> (~big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3)))),
% 28.02/18.23 inference(monotonicity,[status(thm)],[7545])).
% 28.02/18.23 tff(7547,plain,
% 28.02/18.23 (~big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))),
% 28.02/18.23 inference(modus_ponens,[status(thm)],[66, 7546])).
% 28.02/18.23 tff(7548,plain,
% 28.02/18.23 ((f3(f6(f7(c2), c3), c2) = c4) <=> (f3(f6(f7(c2), c3), c2) = c2)),
% 28.02/18.23 inference(monotonicity,[status(thm)],[431])).
% 28.02/18.23 tff(7549,plain,
% 28.02/18.23 ((f3(f6(f7(c2), c3), c2) = c2) <=> (f3(f6(f7(c2), c3), c2) = c4)),
% 28.02/18.23 inference(symmetry,[status(thm)],[7548])).
% 28.02/18.23 tff(7550,plain,
% 28.02/18.23 ((~(f3(f6(f7(c2), c3), c2) = c2)) <=> (~(f3(f6(f7(c2), c3), c2) = c4))),
% 28.02/18.23 inference(monotonicity,[status(thm)],[7549])).
% 28.02/18.23 tff(7551,plain,
% 28.02/18.23 (~(f3(f6(f7(c2), c3), c2) = c4)),
% 28.02/18.23 inference(modus_ponens,[status(thm)],[7540, 7550])).
% 28.02/18.23 tff(7552,plain,
% 28.02/18.23 ((f3(f6(f7(c2), c3), c2) = c3) <=> (f3(f6(f7(c2), c3), c2) = c2)),
% 28.02/18.23 inference(monotonicity,[status(thm)],[181])).
% 28.02/18.23 tff(7553,plain,
% 28.02/18.23 ((f3(f6(f7(c2), c3), c2) = c2) <=> (f3(f6(f7(c2), c3), c2) = c3)),
% 28.02/18.23 inference(symmetry,[status(thm)],[7552])).
% 28.02/18.23 tff(7554,plain,
% 28.02/18.23 ((~(f3(f6(f7(c2), c3), c2) = c2)) <=> (~(f3(f6(f7(c2), c3), c2) = c3))),
% 28.02/18.23 inference(monotonicity,[status(thm)],[7553])).
% 28.02/18.23 tff(7555,plain,
% 28.02/18.23 (~(f3(f6(f7(c2), c3), c2) = c3)),
% 28.02/18.23 inference(modus_ponens,[status(thm)],[7540, 7554])).
% 28.02/18.23 tff(7556,assumption,(f3(f6(f7(c2), c3), c2) = c1), introduced(assumption)).
% 28.02/18.23 tff(7557,plain,
% 28.02/18.23 (f3(f6(f7(c2), c3), c2) = f9(c2, c2)),
% 28.02/18.23 inference(transitivity,[status(thm)],[7556, 149, 132])).
% 28.02/18.23 tff(7558,plain,
% 28.02/18.23 (f3(f3(f6(f7(c2), c3), c2), c2) = f3(c1, c2)),
% 28.02/18.23 inference(monotonicity,[status(thm)],[7556])).
% 28.02/18.23 tff(7559,plain,
% 28.02/18.23 (f3(f3(f6(f7(c2), c3), c2), c2) = f9(c2, c2)),
% 28.02/18.23 inference(transitivity,[status(thm)],[7558, 7512, 7556, 149, 132])).
% 28.02/18.23 tff(7560,plain,
% 28.02/18.23 (big_f(f3(f3(f6(f7(c2), c3), c2), c2), f3(f6(f7(c2), c3), c2)) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 28.02/18.23 inference(monotonicity,[status(thm)],[7559, 7557])).
% 28.02/18.23 tff(7561,plain,
% 28.02/18.23 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f3(f3(f6(f7(c2), c3), c2), c2), f3(f6(f7(c2), c3), c2))),
% 28.02/18.23 inference(symmetry,[status(thm)],[7560])).
% 28.02/18.23 tff(7562,plain,
% 28.02/18.23 (f3(c1, c2) = f9(c2, c2)),
% 28.02/18.23 inference(transitivity,[status(thm)],[7512, 7556, 149, 132])).
% 28.02/18.23 tff(7563,plain,
% 28.02/18.23 (big_f(f3(c1, c2), c1) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 28.02/18.23 inference(monotonicity,[status(thm)],[7562, 150])).
% 28.02/18.23 tff(7564,plain,
% 28.02/18.23 (big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3)) <=> big_f(f3(f3(f6(f7(c2), c3), c2), c2), f3(f6(f7(c2), c3), c2))),
% 28.02/18.23 inference(transitivity,[status(thm)],[7518, 7563, 7561])).
% 28.02/18.23 tff(7565,plain,
% 28.02/18.23 ((~big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))) <=> (~big_f(f3(f3(f6(f7(c2), c3), c2), c2), f3(f6(f7(c2), c3), c2)))),
% 28.02/18.23 inference(monotonicity,[status(thm)],[7564])).
% 28.02/18.23 tff(7566,assumption,(~big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))), introduced(assumption)).
% 28.02/18.23 tff(7567,plain,
% 28.02/18.23 (~big_f(f3(f3(f6(f7(c2), c3), c2), c2), f3(f6(f7(c2), c3), c2))),
% 28.02/18.23 inference(modus_ponens,[status(thm)],[7566, 7565])).
% 28.02/18.23 tff(7568,plain,
% 28.02/18.23 (f3(f6(f7(c2), c3), c2) = f9(f10(c2), f4(c4))),
% 28.02/18.23 inference(transitivity,[status(thm)],[7556, 149])).
% 28.02/18.23 tff(7569,plain,
% 28.02/18.23 (f1(f3(f6(f7(c2), c3), c2), c2) = f1(f9(f10(c2), f4(c4)), c2)),
% 28.02/18.23 inference(monotonicity,[status(thm)],[7568])).
% 28.02/18.23 tff(7570,plain,
% 28.02/18.23 (f1(f3(f6(f7(c2), c3), c2), c2) = f9(c2, c2)),
% 28.02/18.23 inference(transitivity,[status(thm)],[7569, 819, 1095, 149, 132])).
% 28.02/18.23 tff(7571,plain,
% 28.02/18.23 ((f1(f3(f6(f7(c2), c3), c2), c2) = c2) <=> (f9(c2, c2) = c2)),
% 28.02/18.23 inference(monotonicity,[status(thm)],[7570])).
% 28.02/18.23 tff(7572,plain,
% 28.02/18.23 ((f9(c2, c2) = c2) <=> (f1(f3(f6(f7(c2), c3), c2), c2) = c2)),
% 28.02/18.23 inference(symmetry,[status(thm)],[7571])).
% 28.02/18.23 tff(7573,plain,
% 28.02/18.23 ((~(f9(c2, c2) = c2)) <=> (~(f1(f3(f6(f7(c2), c3), c2), c2) = c2))),
% 28.02/18.23 inference(monotonicity,[status(thm)],[7572])).
% 28.02/18.23 tff(7574,plain,
% 28.02/18.23 (~(f1(f3(f6(f7(c2), c3), c2), c2) = c2)),
% 28.02/18.23 inference(modus_ponens,[status(thm)],[185, 7573])).
% 28.02/18.23 tff(7575,plain,
% 28.02/18.23 ((f3(f3(f6(f7(c2), c3), c2), c2) = c2) <=> (f9(c2, c2) = c2)),
% 28.02/18.23 inference(monotonicity,[status(thm)],[7559])).
% 28.02/18.23 tff(7576,plain,
% 28.02/18.23 ((f9(c2, c2) = c2) <=> (f3(f3(f6(f7(c2), c3), c2), c2) = c2)),
% 28.02/18.23 inference(symmetry,[status(thm)],[7575])).
% 28.02/18.23 tff(7577,plain,
% 28.02/18.23 ((~(f9(c2, c2) = c2)) <=> (~(f3(f3(f6(f7(c2), c3), c2), c2) = c2))),
% 28.02/18.23 inference(monotonicity,[status(thm)],[7576])).
% 28.02/18.23 tff(7578,plain,
% 28.02/18.23 (~(f3(f3(f6(f7(c2), c3), c2), c2) = c2)),
% 28.02/18.23 inference(modus_ponens,[status(thm)],[185, 7577])).
% 28.02/18.23 tff(7579,assumption,(~(f3(f6(f7(c2), c3), c2) = c4)), introduced(assumption)).
% 28.02/18.23 tff(7580,assumption,(~(f3(f6(f7(c2), c3), c2) = c3)), introduced(assumption)).
% 28.02/18.23 tff(7581,plain,
% 28.02/18.23 (big_f(f3(c1, c2), c1) <=> big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))),
% 28.02/18.23 inference(symmetry,[status(thm)],[7518])).
% 28.02/18.23 tff(7582,plain,
% 28.02/18.23 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f3(c1, c2), c1)),
% 28.02/18.23 inference(symmetry,[status(thm)],[7563])).
% 28.02/18.23 tff(7583,plain,
% 28.02/18.23 (big_f(f3(f6(f7(c2), c3), c2), f1(f3(f6(f7(c2), c3), c2), c2)) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 28.02/18.23 inference(monotonicity,[status(thm)],[7557, 7570])).
% 28.02/18.23 tff(7584,plain,
% 28.02/18.23 (big_f(f3(f6(f7(c2), c3), c2), f1(f3(f6(f7(c2), c3), c2), c2)) <=> big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))),
% 28.02/18.23 inference(transitivity,[status(thm)],[7583, 7582, 7581])).
% 28.02/18.23 tff(7585,assumption,(big_f(f3(f6(f7(c2), c3), c2), f1(f3(f6(f7(c2), c3), c2), c2))), introduced(assumption)).
% 28.02/18.23 tff(7586,plain,
% 28.02/18.23 (big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))),
% 28.02/18.23 inference(modus_ponens,[status(thm)],[7585, 7584])).
% 28.02/18.23 tff(7587,plain,
% 28.02/18.23 ($false),
% 28.02/18.23 inference(unit_resolution,[status(thm)],[7566, 7586])).
% 28.02/18.23 tff(7588,plain,((~big_f(f3(f6(f7(c2), c3), c2), f1(f3(f6(f7(c2), c3), c2), c2))) | big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f3(f6(f7(c2), c3), c2) = c1)) | (~(f6(f7(c2), c3) = c1)) | (~(f1(c1, c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.02/18.23 tff(7589,plain,
% 28.02/18.23 (~big_f(f3(f6(f7(c2), c3), c2), f1(f3(f6(f7(c2), c3), c2), c2))),
% 28.02/18.23 inference(unit_resolution,[status(thm)],[7588, 7566, 148, 79, 122, 7556, 2702, 1095])).
% 28.02/18.23 tff(7590,plain,
% 28.02/18.23 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f1(f3(f6(f7(c2), c3), c2), c2) = c2) | big_f(f3(f6(f7(c2), c3), c2), f1(f3(f6(f7(c2), c3), c2), c2)) | (f3(f6(f7(c2), c3), c2) = c3) | (f3(f6(f7(c2), c3), c2) = c4) | (f3(f3(f6(f7(c2), c3), c2), c2) = c2) | big_f(f3(f3(f6(f7(c2), c3), c2), c2), f3(f6(f7(c2), c3), c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (f1(f3(f6(f7(c2), c3), c2), c2) = c2) | big_f(f3(f6(f7(c2), c3), c2), f1(f3(f6(f7(c2), c3), c2), c2)) | (f3(f6(f7(c2), c3), c2) = c3) | (f3(f6(f7(c2), c3), c2) = c4) | (f3(f3(f6(f7(c2), c3), c2), c2) = c2) | big_f(f3(f3(f6(f7(c2), c3), c2), c2), f3(f6(f7(c2), c3), c2)))),
% 28.02/18.24 inference(rewrite,[status(thm)],[])).
% 28.02/18.24 tff(7591,plain,
% 28.02/18.24 (((f3(f6(f7(c2), c3), c2) = c4) | (f3(f3(f6(f7(c2), c3), c2), c2) = c2) | big_f(f3(f3(f6(f7(c2), c3), c2), c2), f3(f6(f7(c2), c3), c2)) | (f3(f6(f7(c2), c3), c2) = c3) | (f1(f3(f6(f7(c2), c3), c2), c2) = c2) | big_f(f3(f6(f7(c2), c3), c2), f1(f3(f6(f7(c2), c3), c2), c2))) <=> ((f1(f3(f6(f7(c2), c3), c2), c2) = c2) | big_f(f3(f6(f7(c2), c3), c2), f1(f3(f6(f7(c2), c3), c2), c2)) | (f3(f6(f7(c2), c3), c2) = c3) | (f3(f6(f7(c2), c3), c2) = c4) | (f3(f3(f6(f7(c2), c3), c2), c2) = c2) | big_f(f3(f3(f6(f7(c2), c3), c2), c2), f3(f6(f7(c2), c3), c2)))),
% 28.02/18.24 inference(rewrite,[status(thm)],[])).
% 28.02/18.24 tff(7592,plain,
% 28.02/18.24 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f3(f6(f7(c2), c3), c2) = c4) | (f3(f3(f6(f7(c2), c3), c2), c2) = c2) | big_f(f3(f3(f6(f7(c2), c3), c2), c2), f3(f6(f7(c2), c3), c2)) | (f3(f6(f7(c2), c3), c2) = c3) | (f1(f3(f6(f7(c2), c3), c2), c2) = c2) | big_f(f3(f6(f7(c2), c3), c2), f1(f3(f6(f7(c2), c3), c2), c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f1(f3(f6(f7(c2), c3), c2), c2) = c2) | big_f(f3(f6(f7(c2), c3), c2), f1(f3(f6(f7(c2), c3), c2), c2)) | (f3(f6(f7(c2), c3), c2) = c3) | (f3(f6(f7(c2), c3), c2) = c4) | (f3(f3(f6(f7(c2), c3), c2), c2) = c2) | big_f(f3(f3(f6(f7(c2), c3), c2), c2), f3(f6(f7(c2), c3), c2))))),
% 28.02/18.24 inference(monotonicity,[status(thm)],[7591])).
% 28.02/18.24 tff(7593,plain,
% 28.02/18.24 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f3(f6(f7(c2), c3), c2) = c4) | (f3(f3(f6(f7(c2), c3), c2), c2) = c2) | big_f(f3(f3(f6(f7(c2), c3), c2), c2), f3(f6(f7(c2), c3), c2)) | (f3(f6(f7(c2), c3), c2) = c3) | (f1(f3(f6(f7(c2), c3), c2), c2) = c2) | big_f(f3(f6(f7(c2), c3), c2), f1(f3(f6(f7(c2), c3), c2), c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (f1(f3(f6(f7(c2), c3), c2), c2) = c2) | big_f(f3(f6(f7(c2), c3), c2), f1(f3(f6(f7(c2), c3), c2), c2)) | (f3(f6(f7(c2), c3), c2) = c3) | (f3(f6(f7(c2), c3), c2) = c4) | (f3(f3(f6(f7(c2), c3), c2), c2) = c2) | big_f(f3(f3(f6(f7(c2), c3), c2), c2), f3(f6(f7(c2), c3), c2)))),
% 28.02/18.24 inference(transitivity,[status(thm)],[7592, 7590])).
% 28.02/18.24 tff(7594,plain,
% 28.02/18.24 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f3(f6(f7(c2), c3), c2) = c4) | (f3(f3(f6(f7(c2), c3), c2), c2) = c2) | big_f(f3(f3(f6(f7(c2), c3), c2), c2), f3(f6(f7(c2), c3), c2)) | (f3(f6(f7(c2), c3), c2) = c3) | (f1(f3(f6(f7(c2), c3), c2), c2) = c2) | big_f(f3(f6(f7(c2), c3), c2), f1(f3(f6(f7(c2), c3), c2), c2)))),
% 28.02/18.24 inference(quant_inst,[status(thm)],[])).
% 28.02/18.24 tff(7595,plain,
% 28.02/18.24 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (f1(f3(f6(f7(c2), c3), c2), c2) = c2) | big_f(f3(f6(f7(c2), c3), c2), f1(f3(f6(f7(c2), c3), c2), c2)) | (f3(f6(f7(c2), c3), c2) = c3) | (f3(f6(f7(c2), c3), c2) = c4) | (f3(f3(f6(f7(c2), c3), c2), c2) = c2) | big_f(f3(f3(f6(f7(c2), c3), c2), c2), f3(f6(f7(c2), c3), c2))),
% 28.02/18.24 inference(modus_ponens,[status(thm)],[7594, 7593])).
% 28.02/18.24 tff(7596,plain,
% 28.02/18.24 ((f1(f3(f6(f7(c2), c3), c2), c2) = c2) | big_f(f3(f6(f7(c2), c3), c2), f1(f3(f6(f7(c2), c3), c2), c2)) | (f3(f6(f7(c2), c3), c2) = c3) | (f3(f6(f7(c2), c3), c2) = c4) | (f3(f3(f6(f7(c2), c3), c2), c2) = c2) | big_f(f3(f3(f6(f7(c2), c3), c2), c2), f3(f6(f7(c2), c3), c2))),
% 28.02/18.24 inference(unit_resolution,[status(thm)],[7595, 1014])).
% 28.02/18.24 tff(7597,plain,
% 28.02/18.24 (big_f(f3(f3(f6(f7(c2), c3), c2), c2), f3(f6(f7(c2), c3), c2))),
% 28.02/18.24 inference(unit_resolution,[status(thm)],[7596, 7589, 7580, 7579, 7578, 7574])).
% 28.02/18.24 tff(7598,plain,
% 28.02/18.24 ($false),
% 28.02/18.24 inference(unit_resolution,[status(thm)],[7597, 7567])).
% 28.02/18.24 tff(7599,plain,(big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3)) | (~(f3(f6(f7(c2), c3), c2) = c1)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f6(f7(c2), c3) = c1)) | (f3(f6(f7(c2), c3), c2) = c3) | (f3(f6(f7(c2), c3), c2) = c4) | (~(f1(c1, c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.02/18.24 tff(7600,plain,
% 28.02/18.24 (big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))),
% 28.02/18.24 inference(unit_resolution,[status(thm)],[7599, 7541, 148, 79, 122, 7503, 7555, 7551, 1053])).
% 28.02/18.24 tff(7601,plain,
% 28.02/18.24 ($false),
% 28.02/18.24 inference(unit_resolution,[status(thm)],[7600, 7547])).
% 28.02/18.24 tff(7602,plain,((~(f7(c2) = c2)) | big_f(c1, c1) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(c4 = c2)) | (c1 = c3) | (f1(c1, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | big_f(f9(f10(c2), f4(c4)), f10(f10(c2))) | (~big_f(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 28.02/18.24 tff(7603,plain,
% 28.02/18.24 (~(c4 = c2)),
% 28.02/18.24 inference(unit_resolution,[status(thm)],[7602, 1052, 148, 79, 122, 77, 4543, 4597, 1345, 7493, 66])).
% 28.02/18.24 tff(7604,plain,
% 28.02/18.24 (c4 = c1),
% 28.02/18.24 inference(unit_resolution,[status(thm)],[461, 7603])).
% 28.02/18.24 tff(7605,plain,
% 28.02/18.24 (c4 = f9(c2, c2)),
% 28.02/18.24 inference(transitivity,[status(thm)],[7604, 149, 132])).
% 28.02/18.24 tff(7606,plain,
% 28.02/18.24 ((c2 = c4) <=> (c2 = f9(c2, c2))),
% 28.02/18.24 inference(monotonicity,[status(thm)],[7605])).
% 28.02/18.24 tff(7607,plain,
% 28.02/18.24 ((c2 = c4) <=> (f9(c2, c2) = c2)),
% 28.02/18.24 inference(transitivity,[status(thm)],[7606, 167])).
% 28.02/18.24 tff(7608,plain,
% 28.02/18.24 ((f9(c2, c2) = c2) <=> (c2 = c4)),
% 28.02/18.24 inference(symmetry,[status(thm)],[7607])).
% 28.02/18.24 tff(7609,plain,
% 28.02/18.24 ((~(f9(c2, c2) = c2)) <=> (~(c2 = c4))),
% 28.02/18.24 inference(monotonicity,[status(thm)],[7608])).
% 28.02/18.24 tff(7610,plain,
% 28.02/18.24 (~(c2 = c4)),
% 28.02/18.24 inference(modus_ponens,[status(thm)],[185, 7609])).
% 28.02/18.24 tff(7611,plain,
% 28.02/18.24 (big_f(f3(f10(c3), c2), f10(c3))),
% 28.02/18.24 inference(unit_resolution,[status(thm)],[7415, 7610, 185, 3719, 1345, 2831, 67])).
% 28.02/18.24 tff(7612,plain,
% 28.02/18.24 (big_f(f3(c2, c2), c2)),
% 28.02/18.24 inference(modus_ponens,[status(thm)],[7611, 7490])).
% 28.02/18.24 tff(7613,plain,
% 28.02/18.24 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (f9(c2, c2) = c3) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (f9(c2, c2) = c3) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2)))),
% 28.02/18.24 inference(rewrite,[status(thm)],[])).
% 28.02/18.24 tff(7614,plain,
% 28.02/18.24 (((c2 = c4) | (f9(c2, c2) = c3) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2)) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2))) <=> ((c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (f9(c2, c2) = c3) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2)))),
% 28.02/18.24 inference(rewrite,[status(thm)],[])).
% 28.02/18.24 tff(7615,plain,
% 28.02/18.24 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c4) | (f9(c2, c2) = c3) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2)) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (f9(c2, c2) = c3) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2))))),
% 28.02/18.24 inference(monotonicity,[status(thm)],[7614])).
% 28.02/18.24 tff(7616,plain,
% 28.02/18.24 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c4) | (f9(c2, c2) = c3) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2)) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (f9(c2, c2) = c3) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2)))),
% 28.02/18.24 inference(transitivity,[status(thm)],[7615, 7613])).
% 28.02/18.24 tff(7617,plain,
% 28.02/18.24 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c4) | (f9(c2, c2) = c3) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2)) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)))),
% 28.02/18.24 inference(quant_inst,[status(thm)],[])).
% 28.02/18.24 tff(7618,plain,
% 28.02/18.24 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (f9(c2, c2) = c3) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2))),
% 28.02/18.24 inference(modus_ponens,[status(thm)],[7617, 7616])).
% 28.02/18.24 tff(7619,plain,
% 28.02/18.24 ((~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (f1(f9(c2, c2), c2) = c2) | big_f(f9(c2, c2), f1(f9(c2, c2), c2))),
% 28.02/18.24 inference(unit_resolution,[status(thm)],[7618, 969, 7610, 4533])).
% 28.02/18.24 tff(7620,plain,
% 28.02/18.24 (~(f3(c2, c2) = c2)),
% 28.02/18.24 inference(unit_resolution,[status(thm)],[7619, 7612, 7488, 7484])).
% 28.02/18.24 tff(7621,plain,
% 28.02/18.24 (~(f3(f5(c1), f5(c1)) = c2)),
% 28.02/18.24 inference(modus_ponens,[status(thm)],[7620, 7479])).
% 28.02/18.24 tff(7622,plain,
% 28.02/18.24 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f3(f5(c1), f5(c1)) = c1) | (f3(f5(c1), f5(c1)) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f3(f5(c1), f5(c1)) = c1) | (f3(f5(c1), f5(c1)) = c2))),
% 28.02/18.24 inference(rewrite,[status(thm)],[])).
% 28.02/18.24 tff(7623,plain,
% 28.02/18.24 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f3(f5(c1), f5(c1)) = c1) | (f3(f5(c1), f5(c1)) = c2))),
% 28.02/18.24 inference(quant_inst,[status(thm)],[])).
% 28.02/18.24 tff(7624,plain,
% 28.02/18.24 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f3(f5(c1), f5(c1)) = c1) | (f3(f5(c1), f5(c1)) = c2)),
% 28.02/18.24 inference(modus_ponens,[status(thm)],[7623, 7622])).
% 28.02/18.24 tff(7625,plain,
% 28.02/18.24 ((f3(f5(c1), f5(c1)) = c1) | (f3(f5(c1), f5(c1)) = c2)),
% 28.02/18.24 inference(unit_resolution,[status(thm)],[7624, 10])).
% 28.02/18.24 tff(7626,plain,
% 28.02/18.24 (f3(f5(c1), f5(c1)) = c1),
% 28.02/18.24 inference(unit_resolution,[status(thm)],[7625, 7621])).
% 28.02/18.24 tff(7627,plain,
% 28.02/18.24 (f3(f10(c3), c2) = f9(c2, c2)),
% 28.02/18.24 inference(transitivity,[status(thm)],[7473, 7626, 149, 132])).
% 28.02/18.24 tff(7628,plain,
% 28.02/18.24 (big_f(f3(f10(c3), c2), f10(c3)) <=> big_f(f9(c2, c2), c2)),
% 28.02/18.24 inference(monotonicity,[status(thm)],[7627, 2832])).
% 28.02/18.24 tff(7629,plain,
% 28.02/18.24 (big_f(f9(c2, c2), c2) <=> big_f(f3(f10(c3), c2), f10(c3))),
% 28.02/18.24 inference(symmetry,[status(thm)],[7628])).
% 28.02/18.24 tff(7630,plain,
% 28.02/18.24 ((~big_f(f9(c2, c2), c2)) <=> (~big_f(f3(f10(c3), c2), f10(c3)))),
% 28.02/18.24 inference(monotonicity,[status(thm)],[7629])).
% 28.02/18.24 tff(7631,plain,
% 28.02/18.24 (~big_f(f3(f10(c3), c2), f10(c3))),
% 28.02/18.24 inference(modus_ponens,[status(thm)],[3685, 7630])).
% 28.02/18.24 tff(7632,plain,
% 28.02/18.24 ($false),
% 28.02/18.24 inference(unit_resolution,[status(thm)],[7611, 7631])).
% 28.02/18.24 tff(7633,plain,((f1(c1, c2) = c2) | big_f(f9(c2, c2), c2) | (~(c3 = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f5(c1) = c2)) | (~big_f(c2, f9(c2, c2))) | (~big_f(c2, c2)) | (~(f7(c2) = c2)) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 28.02/18.24 tff(7634,plain,
% 28.02/18.24 (~(f5(c1) = c2)),
% 28.02/18.24 inference(unit_resolution,[status(thm)],[7633, 7471, 148, 7206, 79, 122, 7262, 5558, 3685, 7260, 7217])).
% 28.02/18.24 tff(7635,plain,
% 28.02/18.24 (f5(c1) = c1),
% 28.02/18.24 inference(unit_resolution,[status(thm)],[1708, 7634])).
% 28.02/18.24 tff(7636,plain,
% 28.02/18.24 (c1 = f5(c1)),
% 28.02/18.24 inference(symmetry,[status(thm)],[7635])).
% 28.02/18.24 tff(7637,plain,
% 28.02/18.24 (f9(c2, c2) = f5(c1)),
% 28.02/18.24 inference(transitivity,[status(thm)],[160, 148, 7636])).
% 28.02/18.24 tff(7638,plain,
% 28.02/18.24 (f6(c2, f9(c2, c2)) = f6(f7(c2), f5(c1))),
% 28.02/18.24 inference(monotonicity,[status(thm)],[5559, 7637])).
% 28.02/18.24 tff(7639,plain,
% 28.02/18.24 (f6(f7(c2), f5(c1)) = f6(c2, f9(c2, c2))),
% 28.02/18.24 inference(symmetry,[status(thm)],[7638])).
% 28.02/18.24 tff(7640,plain,
% 28.02/18.24 ((f6(f7(c2), f5(c1)) = c1) <=> (f6(c2, f9(c2, c2)) = f9(c2, c2))),
% 28.02/18.24 inference(monotonicity,[status(thm)],[7639, 150])).
% 28.02/18.24 tff(7641,plain,
% 28.02/18.24 ((f6(c2, f9(c2, c2)) = f9(c2, c2)) <=> (f6(f7(c2), f5(c1)) = c1)),
% 28.02/18.24 inference(symmetry,[status(thm)],[7640])).
% 28.02/18.24 tff(7642,plain,
% 28.02/18.24 ((~(f6(c2, f9(c2, c2)) = f9(c2, c2))) <=> (~(f6(f7(c2), f5(c1)) = c1))),
% 28.02/18.24 inference(monotonicity,[status(thm)],[7641])).
% 28.02/18.24 tff(7643,plain,
% 28.02/18.24 (big_f(f7(c2), f6(c2, c1))),
% 28.02/18.24 inference(unit_resolution,[status(thm)],[6623, 7217, 148, 4597, 5558, 79, 122])).
% 28.02/18.24 tff(7644,plain,
% 28.02/18.24 (big_f(f7(c2), f6(c2, f9(c2, c2)))),
% 28.02/18.24 inference(modus_ponens,[status(thm)],[7643, 4442])).
% 28.02/18.24 tff(7645,plain,
% 28.02/18.24 (~(f6(c2, f9(c2, c2)) = f9(c2, c2))),
% 28.02/18.24 inference(unit_resolution,[status(thm)],[3495, 2534, 122, 5558, 185, 4597, 7644])).
% 28.02/18.24 tff(7646,plain,
% 28.02/18.24 (~(f6(f7(c2), f5(c1)) = c1)),
% 28.02/18.24 inference(modus_ponens,[status(thm)],[7645, 7642])).
% 28.02/18.24 tff(7647,plain,
% 28.02/18.24 (f6(f7(c2), f5(c1)) = c2),
% 28.02/18.24 inference(unit_resolution,[status(thm)],[2978, 7646])).
% 28.02/18.24 tff(7648,plain,
% 28.02/18.24 (f3(f6(f7(c2), f5(c1)), c2) = f3(c2, c2)),
% 28.02/18.24 inference(monotonicity,[status(thm)],[7647])).
% 28.02/18.24 tff(7649,plain,
% 28.02/18.24 ((f3(f6(f7(c2), f5(c1)), c2) = c2) <=> (f3(c2, c2) = c2)),
% 28.02/18.24 inference(monotonicity,[status(thm)],[7648])).
% 28.02/18.24 tff(7650,plain,
% 28.02/18.24 ((f3(f6(f7(c2), f5(c1)), c2) = c2) <=> (f3(f7(f4(c4)), f4(c4)) = c2)),
% 28.02/18.24 inference(transitivity,[status(thm)],[7649, 5564])).
% 28.02/18.24 tff(7651,plain,
% 28.02/18.24 ((~(f3(f6(f7(c2), f5(c1)), c2) = c2)) <=> (~(f3(f7(f4(c4)), f4(c4)) = c2))),
% 28.02/18.24 inference(monotonicity,[status(thm)],[7650])).
% 28.02/18.24 tff(7652,plain,
% 28.02/18.24 (f1(f9(c2, c2), c2) = f1(c1, c2)),
% 28.02/18.24 inference(monotonicity,[status(thm)],[161])).
% 28.02/18.24 tff(7653,plain,
% 28.02/18.24 (f1(c1, c2) = f1(f9(c2, c2), c2)),
% 28.02/18.24 inference(symmetry,[status(thm)],[7652])).
% 28.02/18.24 tff(7654,plain,
% 28.02/18.24 (big_f(c1, f1(c1, c2)) <=> big_f(f9(c2, c2), f1(f9(c2, c2), c2))),
% 28.02/18.24 inference(monotonicity,[status(thm)],[150, 7653])).
% 28.02/18.24 tff(7655,plain,
% 28.02/18.24 (big_f(f9(c2, c2), f1(f9(c2, c2), c2)) <=> big_f(c1, f1(c1, c2))),
% 28.02/18.24 inference(symmetry,[status(thm)],[7654])).
% 28.02/18.24 tff(7656,plain,
% 28.02/18.24 (f1(c1, c2) = c1),
% 28.02/18.24 inference(unit_resolution,[status(thm)],[841, 7471])).
% 28.02/18.24 tff(7657,plain,
% 28.02/18.24 (f1(f9(c2, c2), c2) = f9(c2, c2)),
% 28.02/18.24 inference(transitivity,[status(thm)],[7652, 7656, 149, 132])).
% 28.02/18.24 tff(7658,plain,
% 28.02/18.24 (big_f(f9(c2, c2), f1(f9(c2, c2), c2)) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 28.02/18.24 inference(monotonicity,[status(thm)],[7657])).
% 28.02/18.24 tff(7659,plain,
% 28.02/18.24 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f9(c2, c2), f1(f9(c2, c2), c2))),
% 28.02/18.24 inference(symmetry,[status(thm)],[7658])).
% 28.02/18.24 tff(7660,plain,
% 28.02/18.24 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(c1, f1(c1, c2))),
% 28.02/18.24 inference(transitivity,[status(thm)],[7659, 7655])).
% 28.02/18.24 tff(7661,plain,
% 28.02/18.24 ((~big_f(f9(c2, c2), f9(c2, c2))) <=> (~big_f(c1, f1(c1, c2)))),
% 28.02/18.24 inference(monotonicity,[status(thm)],[7660])).
% 28.02/18.24 tff(7662,plain,
% 28.02/18.24 (~big_f(c1, f1(c1, c2))),
% 28.02/18.24 inference(modus_ponens,[status(thm)],[3689, 7661])).
% 28.02/18.24 tff(7663,plain,
% 28.02/18.24 (c4 = c1),
% 28.02/18.24 inference(transitivity,[status(thm)],[7374, 160, 148])).
% 28.02/18.24 tff(7664,plain,
% 28.02/18.24 ((f6(f7(c2), f5(c1)) = c4) <=> (f6(f7(c2), f5(c1)) = c1)),
% 28.02/18.24 inference(monotonicity,[status(thm)],[7663])).
% 28.02/18.24 tff(7665,plain,
% 28.02/18.24 ((f6(f7(c2), f5(c1)) = c1) <=> (f6(f7(c2), f5(c1)) = c4)),
% 28.02/18.24 inference(symmetry,[status(thm)],[7664])).
% 28.02/18.24 tff(7666,plain,
% 28.02/18.24 ((f6(c2, f9(c2, c2)) = f9(c2, c2)) <=> (f6(f7(c2), f5(c1)) = c4)),
% 28.02/18.24 inference(transitivity,[status(thm)],[7641, 7665])).
% 28.02/18.24 tff(7667,plain,
% 28.02/18.24 ((~(f6(c2, f9(c2, c2)) = f9(c2, c2))) <=> (~(f6(f7(c2), f5(c1)) = c4))),
% 28.02/18.24 inference(monotonicity,[status(thm)],[7666])).
% 28.02/18.24 tff(7668,plain,
% 28.02/18.24 (~(f6(f7(c2), f5(c1)) = c4)),
% 28.02/18.24 inference(modus_ponens,[status(thm)],[7645, 7667])).
% 28.02/18.24 tff(7669,plain,
% 28.02/18.24 (~(c1 = c3)),
% 28.02/18.24 inference(modus_ponens,[status(thm)],[7205, 648])).
% 28.02/18.24 tff(7670,plain,
% 28.02/18.24 (f10(c3) = c3),
% 28.02/18.24 inference(unit_resolution,[status(thm)],[2830, 7206, 122])).
% 28.02/18.24 tff(7671,plain,
% 28.02/18.24 (big_f(f3(f10(c3), c2), f10(c3))),
% 28.02/18.24 inference(unit_resolution,[status(thm)],[7415, 7379, 7670, 185, 7217, 7206, 7260])).
% 28.02/18.24 tff(7672,plain,
% 28.02/18.24 (f6(f7(c2), f5(c1)) = f10(c3)),
% 28.02/18.24 inference(transitivity,[status(thm)],[3032, 69, 3008])).
% 28.02/18.24 tff(7673,plain,
% 28.02/18.24 (f3(f6(f7(c2), f5(c1)), c2) = f3(f10(c3), c2)),
% 28.02/18.24 inference(monotonicity,[status(thm)],[7672])).
% 28.02/18.24 tff(7674,plain,
% 28.02/18.24 (big_f(f3(f6(f7(c2), f5(c1)), c2), f6(f7(c2), f5(c1))) <=> big_f(f3(f10(c3), c2), f10(c3))),
% 28.02/18.24 inference(monotonicity,[status(thm)],[7673, 7672])).
% 28.02/18.24 tff(7675,plain,
% 28.02/18.24 ((~big_f(f3(f6(f7(c2), f5(c1)), c2), f6(f7(c2), f5(c1)))) <=> (~big_f(f3(f10(c3), c2), f10(c3)))),
% 28.02/18.24 inference(monotonicity,[status(thm)],[7674])).
% 28.02/18.24 tff(7676,assumption,(~big_f(f3(f6(f7(c2), f5(c1)), c2), f6(f7(c2), f5(c1)))), introduced(assumption)).
% 28.02/18.24 tff(7677,plain,
% 28.02/18.24 (~big_f(f3(f10(c3), c2), f10(c3))),
% 28.02/18.24 inference(modus_ponens,[status(thm)],[7676, 7675])).
% 28.02/18.24 tff(7678,plain,
% 28.02/18.24 ($false),
% 28.02/18.24 inference(unit_resolution,[status(thm)],[7426, 7677])).
% 28.02/18.24 tff(7679,plain,(big_f(f3(f6(f7(c2), f5(c1)), c2), f6(f7(c2), f5(c1))) | (~big_f(f3(f10(c3), c2), f10(c3))) | (~(f10(c3) = c3)) | (~(c3 = c2)) | (~(f6(f7(c2), f5(c1)) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.02/18.24 tff(7680,plain,
% 28.02/18.24 (big_f(f3(f6(f7(c2), f5(c1)), c2), f6(f7(c2), f5(c1)))),
% 28.02/18.24 inference(unit_resolution,[status(thm)],[7679, 7647, 7670, 7206, 7671])).
% 28.02/18.24 tff(7681,plain,
% 28.02/18.24 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((f1(c1, c2) = c2) | (c1 = c3) | big_f(c1, f1(c1, c2)) | (~big_f(f3(f6(f7(c2), f5(c1)), c2), f6(f7(c2), f5(c1)))) | (~(f3(f6(f7(c2), f5(c1)), c2) = c2)) | (f6(f7(c2), f5(c1)) = c4))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (f1(c1, c2) = c2) | (c1 = c3) | big_f(c1, f1(c1, c2)) | (~big_f(f3(f6(f7(c2), f5(c1)), c2), f6(f7(c2), f5(c1)))) | (~(f3(f6(f7(c2), f5(c1)), c2) = c2)) | (f6(f7(c2), f5(c1)) = c4))),
% 28.02/18.24 inference(rewrite,[status(thm)],[])).
% 28.02/18.24 tff(7682,plain,
% 28.02/18.24 (((f6(f7(c2), f5(c1)) = c4) | (c1 = c3) | (f1(c1, c2) = c2) | big_f(c1, f1(c1, c2)) | (~(f3(f6(f7(c2), f5(c1)), c2) = c2)) | (~big_f(f3(f6(f7(c2), f5(c1)), c2), f6(f7(c2), f5(c1))))) <=> ((f1(c1, c2) = c2) | (c1 = c3) | big_f(c1, f1(c1, c2)) | (~big_f(f3(f6(f7(c2), f5(c1)), c2), f6(f7(c2), f5(c1)))) | (~(f3(f6(f7(c2), f5(c1)), c2) = c2)) | (f6(f7(c2), f5(c1)) = c4))),
% 28.02/18.24 inference(rewrite,[status(thm)],[])).
% 28.02/18.24 tff(7683,plain,
% 28.02/18.24 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((f6(f7(c2), f5(c1)) = c4) | (c1 = c3) | (f1(c1, c2) = c2) | big_f(c1, f1(c1, c2)) | (~(f3(f6(f7(c2), f5(c1)), c2) = c2)) | (~big_f(f3(f6(f7(c2), f5(c1)), c2), f6(f7(c2), f5(c1)))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((f1(c1, c2) = c2) | (c1 = c3) | big_f(c1, f1(c1, c2)) | (~big_f(f3(f6(f7(c2), f5(c1)), c2), f6(f7(c2), f5(c1)))) | (~(f3(f6(f7(c2), f5(c1)), c2) = c2)) | (f6(f7(c2), f5(c1)) = c4)))),
% 28.02/18.24 inference(monotonicity,[status(thm)],[7682])).
% 28.02/18.24 tff(7684,plain,
% 28.02/18.24 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((f6(f7(c2), f5(c1)) = c4) | (c1 = c3) | (f1(c1, c2) = c2) | big_f(c1, f1(c1, c2)) | (~(f3(f6(f7(c2), f5(c1)), c2) = c2)) | (~big_f(f3(f6(f7(c2), f5(c1)), c2), f6(f7(c2), f5(c1)))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (f1(c1, c2) = c2) | (c1 = c3) | big_f(c1, f1(c1, c2)) | (~big_f(f3(f6(f7(c2), f5(c1)), c2), f6(f7(c2), f5(c1)))) | (~(f3(f6(f7(c2), f5(c1)), c2) = c2)) | (f6(f7(c2), f5(c1)) = c4))),
% 28.02/18.25 inference(transitivity,[status(thm)],[7683, 7681])).
% 28.02/18.25 tff(7685,plain,
% 28.02/18.25 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((f6(f7(c2), f5(c1)) = c4) | (c1 = c3) | (f1(c1, c2) = c2) | big_f(c1, f1(c1, c2)) | (~(f3(f6(f7(c2), f5(c1)), c2) = c2)) | (~big_f(f3(f6(f7(c2), f5(c1)), c2), f6(f7(c2), f5(c1)))))),
% 28.02/18.25 inference(quant_inst,[status(thm)],[])).
% 28.02/18.25 tff(7686,plain,
% 28.02/18.25 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (f1(c1, c2) = c2) | (c1 = c3) | big_f(c1, f1(c1, c2)) | (~big_f(f3(f6(f7(c2), f5(c1)), c2), f6(f7(c2), f5(c1)))) | (~(f3(f6(f7(c2), f5(c1)), c2) = c2)) | (f6(f7(c2), f5(c1)) = c4)),
% 28.02/18.25 inference(modus_ponens,[status(thm)],[7685, 7684])).
% 28.02/18.25 tff(7687,plain,
% 28.02/18.25 ((f1(c1, c2) = c2) | (c1 = c3) | big_f(c1, f1(c1, c2)) | (~big_f(f3(f6(f7(c2), f5(c1)), c2), f6(f7(c2), f5(c1)))) | (~(f3(f6(f7(c2), f5(c1)), c2) = c2)) | (f6(f7(c2), f5(c1)) = c4)),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[7686, 969])).
% 28.02/18.25 tff(7688,plain,
% 28.02/18.25 (~(f3(f6(f7(c2), f5(c1)), c2) = c2)),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[7687, 7680, 7669, 7668, 7471, 7662])).
% 28.02/18.25 tff(7689,plain,
% 28.02/18.25 (~(f3(f7(f4(c4)), f4(c4)) = c2)),
% 28.02/18.25 inference(modus_ponens,[status(thm)],[7688, 7651])).
% 28.02/18.25 tff(7690,plain,
% 28.02/18.25 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f3(f7(f4(c4)), f4(c4)) = c1) | (f3(f7(f4(c4)), f4(c4)) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f3(f7(f4(c4)), f4(c4)) = c1) | (f3(f7(f4(c4)), f4(c4)) = c2))),
% 28.02/18.25 inference(rewrite,[status(thm)],[])).
% 28.02/18.25 tff(7691,plain,
% 28.02/18.25 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f3(f7(f4(c4)), f4(c4)) = c1) | (f3(f7(f4(c4)), f4(c4)) = c2))),
% 28.02/18.25 inference(quant_inst,[status(thm)],[])).
% 28.02/18.25 tff(7692,plain,
% 28.02/18.25 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f3(f7(f4(c4)), f4(c4)) = c1) | (f3(f7(f4(c4)), f4(c4)) = c2)),
% 28.02/18.25 inference(modus_ponens,[status(thm)],[7691, 7690])).
% 28.02/18.25 tff(7693,plain,
% 28.02/18.25 ((f3(f7(f4(c4)), f4(c4)) = c1) | (f3(f7(f4(c4)), f4(c4)) = c2)),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[7692, 10])).
% 28.02/18.25 tff(7694,plain,
% 28.02/18.25 (f3(f7(f4(c4)), f4(c4)) = c1),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[7693, 7689])).
% 28.02/18.25 tff(7695,plain,
% 28.02/18.25 (f3(c2, c2) = f9(c2, c2)),
% 28.02/18.25 inference(transitivity,[status(thm)],[5561, 7694, 149, 132])).
% 28.02/18.25 tff(7696,plain,
% 28.02/18.25 (big_f(f3(c2, c2), c2) <=> big_f(f9(c2, c2), c2)),
% 28.02/18.25 inference(monotonicity,[status(thm)],[7695])).
% 28.02/18.25 tff(7697,plain,
% 28.02/18.25 (big_f(f9(c2, c2), c2) <=> big_f(f3(c2, c2), c2)),
% 28.02/18.25 inference(symmetry,[status(thm)],[7696])).
% 28.02/18.25 tff(7698,plain,
% 28.02/18.25 ((~big_f(f9(c2, c2), c2)) <=> (~big_f(f3(c2, c2), c2))),
% 28.02/18.25 inference(monotonicity,[status(thm)],[7697])).
% 28.02/18.25 tff(7699,plain,
% 28.02/18.25 (~big_f(f3(c2, c2), c2)),
% 28.02/18.25 inference(modus_ponens,[status(thm)],[3685, 7698])).
% 28.02/18.25 tff(7700,plain,
% 28.02/18.25 (big_f(f3(f6(f7(c2), f5(c1)), c2), f6(f7(c2), f5(c1))) <=> big_f(f3(c2, c2), c2)),
% 28.02/18.25 inference(monotonicity,[status(thm)],[7648, 7647])).
% 28.02/18.25 tff(7701,plain,
% 28.02/18.25 (big_f(f3(c2, c2), c2)),
% 28.02/18.25 inference(modus_ponens,[status(thm)],[7680, 7700])).
% 28.02/18.25 tff(7702,plain,
% 28.02/18.25 ($false),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[7701, 7699])).
% 28.02/18.25 tff(7703,plain,(big_f(f9(c2, c2), c2) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f10(c2) = c2)) | (~(f4(c4) = c2)) | big_f(f9(c2, c2), f9(c2, c2)) | (~(f7(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.02/18.25 tff(7704,plain,
% 28.02/18.25 (big_f(f9(c2, c2), c2)),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[7703, 3689, 122, 79, 148, 4234])).
% 28.02/18.25 tff(7705,plain,
% 28.02/18.25 ((c3 = c1) <=> (f9(f10(c2), f4(c4)) = c3)),
% 28.02/18.25 inference(transitivity,[status(thm)],[68, 3640, 3639])).
% 28.02/18.25 tff(7706,plain,
% 28.02/18.25 ((~(c3 = c1)) <=> (~(f9(f10(c2), f4(c4)) = c3))),
% 28.02/18.25 inference(monotonicity,[status(thm)],[7705])).
% 28.02/18.25 tff(7707,plain,
% 28.02/18.25 (~(f9(f10(c2), f4(c4)) = c3)),
% 28.02/18.25 inference(modus_ponens,[status(thm)],[7205, 7706])).
% 28.02/18.25 tff(7708,plain,
% 28.02/18.25 ((~(c3 = c1)) <=> (~(f9(c2, c2) = c3))),
% 28.02/18.25 inference(monotonicity,[status(thm)],[5579])).
% 28.02/18.25 tff(7709,plain,
% 28.02/18.25 (~(f9(c2, c2) = c3)),
% 28.02/18.25 inference(modus_ponens,[status(thm)],[7205, 7708])).
% 28.02/18.25 tff(7710,plain,
% 28.02/18.25 (big_f(c2, c1)),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[3759, 7704, 79, 122, 7709, 3689, 7707, 7669, 148])).
% 28.02/18.25 tff(7711,plain,
% 28.02/18.25 (big_f(c2, f9(c2, c2))),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[3814, 7710, 148, 79, 122])).
% 28.02/18.25 tff(7712,plain,
% 28.02/18.25 (~(f10(c1) = c1)),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[4320, 7711, 148, 79, 122, 4234, 3689, 7704])).
% 28.02/18.25 tff(7713,plain,
% 28.02/18.25 (f10(c1) = c2),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[14, 7712])).
% 28.02/18.25 tff(7714,plain,
% 28.02/18.25 (big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[5709, 5699, 5700, 4469, 5701, 122])).
% 28.02/18.25 tff(7715,plain,
% 28.02/18.25 (big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))),
% 28.02/18.25 inference(modus_ponens,[status(thm)],[7714, 5755])).
% 28.02/18.25 tff(7716,plain,
% 28.02/18.25 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)))),
% 28.02/18.25 inference(rewrite,[status(thm)],[])).
% 28.02/18.25 tff(7717,plain,
% 28.02/18.25 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)))),
% 28.02/18.25 inference(quant_inst,[status(thm)],[])).
% 28.02/18.25 tff(7718,plain,
% 28.02/18.25 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))),
% 28.02/18.25 inference(modus_ponens,[status(thm)],[7717, 7716])).
% 28.02/18.25 tff(7719,plain,
% 28.02/18.25 (big_f(f9(c2, c2), f10(c2)) | big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[7718, 2492, 122, 2650, 5701, 5700])).
% 28.02/18.25 tff(7720,plain,
% 28.02/18.25 (big_f(f9(c2, c2), f10(c2))),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[7719, 5699])).
% 28.02/18.25 tff(7721,plain,
% 28.02/18.25 (big_f(f9(c2, c2), f10(f9(c2, c2)))),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[3625, 7720, 122, 16, 79, 148])).
% 28.02/18.25 tff(7722,plain,
% 28.02/18.25 (~big_f(f9(c2, f9(c2, c2)), f10(f9(c2, c2)))),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[5774, 7721, 5699, 5752, 5701, 5700, 4469])).
% 28.02/18.25 tff(7723,plain,
% 28.02/18.25 ($false),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[7722, 7715])).
% 28.02/18.25 tff(7724,plain,(big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)) | (~(f10(c2) = c2)) | (~(f10(c1) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f7(f9(c2, c2)) = f9(c2, c2))) | (f6(f9(c2, c2), c2) = c2) | (f9(c2, f9(c2, c2)) = f9(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 28.02/18.25 tff(7725,plain,
% 28.02/18.25 (f9(c2, f9(c2, c2)) = f9(c2, c2)),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[7724, 5537, 148, 7713, 79, 5532, 4257, 122])).
% 28.02/18.25 tff(7726,plain,
% 28.02/18.25 (big_f(f9(c2, c2), f10(c2))),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[6482, 7704, 122])).
% 28.02/18.25 tff(7727,plain,
% 28.02/18.25 (f9(c2, c1) = c1),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[1141, 7725, 122, 79, 148])).
% 28.02/18.25 tff(7728,plain,
% 28.02/18.25 (big_f(f9(c2, c1), f10(c2))),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[743, 7727, 148, 7726, 79, 122])).
% 28.02/18.25 tff(7729,plain,
% 28.02/18.25 (big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[3898, 7728, 148, 79, 122])).
% 28.02/18.25 tff(7730,plain,
% 28.02/18.25 ($false),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[5809, 2409, 122, 7729, 7725, 5537, 5532, 4257])).
% 28.02/18.25 tff(7731,plain,((f6(c1, c2) = c2) | (~(f10(c2) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | big_f(f9(c2, c2), f9(c2, c2)) | (~(f7(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.02/18.25 tff(7732,plain,
% 28.02/18.25 (f6(c1, c2) = c2),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[7731, 3689, 148, 79, 122, 4234])).
% 28.02/18.25 tff(7733,plain,
% 28.02/18.25 (f6(f9(c2, c2), c2) = c2),
% 28.02/18.25 inference(modus_ponens,[status(thm)],[7732, 4249])).
% 28.02/18.25 tff(7734,plain,
% 28.02/18.25 (f6(f9(c2, c2), c2) = c2),
% 28.02/18.25 inference(transitivity,[status(thm)],[4247, 7732])).
% 28.02/18.25 tff(7735,plain,
% 28.02/18.25 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2)) <=> big_f(f9(c2, c2), c2)),
% 28.02/18.25 inference(monotonicity,[status(thm)],[5532, 7734])).
% 28.02/18.25 tff(7736,plain,
% 28.02/18.25 (big_f(f9(c2, c2), c2) <=> big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))),
% 28.02/18.25 inference(symmetry,[status(thm)],[7735])).
% 28.02/18.25 tff(7737,plain,
% 28.02/18.25 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), c2))),
% 28.02/18.25 inference(modus_ponens,[status(thm)],[7704, 7736])).
% 28.02/18.25 tff(7738,plain,
% 28.02/18.25 (f10(f9(c2, c2)) = c2),
% 28.02/18.25 inference(transitivity,[status(thm)],[3646, 7713])).
% 28.02/18.25 tff(7739,plain,
% 28.02/18.25 (big_f(c2, f10(f9(c2, c2))) <=> big_f(c2, c2)),
% 28.02/18.25 inference(monotonicity,[status(thm)],[7738])).
% 28.02/18.25 tff(7740,plain,
% 28.02/18.25 (big_f(c2, c2) <=> big_f(c2, f10(f9(c2, c2)))),
% 28.02/18.25 inference(symmetry,[status(thm)],[7739])).
% 28.02/18.25 tff(7741,plain,
% 28.02/18.25 (big_f(f7(c1), f6(c1, c2))),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[6248, 36, 148, 4234, 2041, 79, 122])).
% 28.02/18.25 tff(7742,plain,
% 28.02/18.25 (big_f(f9(c2, c2), f10(c2))),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[6482, 2041, 122])).
% 28.02/18.25 tff(7743,plain,
% 28.02/18.25 (f9(c2, c1) = c1),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[5737, 731, 122, 4234, 36, 6215])).
% 28.02/18.25 tff(7744,plain,
% 28.02/18.25 ($false),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[743, 7743, 731, 148, 690, 79, 122])).
% 28.02/18.25 tff(7745,plain,(big_f(f9(c2, c1), f10(c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2)))), inference(lemma,lemma(discharge,[]))).
% 28.02/18.25 tff(7746,plain,
% 28.02/18.25 (big_f(f9(c2, c1), f10(c2))),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[7745, 36, 7742, 79, 122, 4234, 148, 7741])).
% 28.02/18.25 tff(7747,plain,
% 28.02/18.25 (~(f9(c2, c1) = c1)),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[5827, 7746, 122, 4234, 7741, 36])).
% 28.02/18.25 tff(7748,plain,
% 28.02/18.25 (f9(c2, c1) = c2),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[3913, 7747])).
% 28.02/18.25 tff(7749,plain,
% 28.02/18.25 (big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[3898, 7746, 148, 79, 122])).
% 28.02/18.25 tff(7750,plain,
% 28.02/18.25 (~(big_f(c2, c2) <=> big_f(f9(c2, f9(c2, c2)), f10(c2)))),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[4996, 7749, 121])).
% 28.02/18.25 tff(7751,plain,
% 28.02/18.25 (~(c2 = f9(c2, f9(c2, c2)))),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[5003, 7750, 4989])).
% 28.02/18.25 tff(7752,plain,
% 28.02/18.25 ($false),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[5012, 7751, 7748, 148, 79, 122])).
% 28.02/18.25 tff(7753,plain,((~(f6(c1, c2) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | big_f(c2, c2) | (~(f7(c1) = c1)) | (~big_f(f9(c2, c2), c2))), inference(lemma,lemma(discharge,[]))).
% 28.02/18.25 tff(7754,plain,
% 28.02/18.25 (big_f(c2, c2)),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[7753, 7732, 79, 122, 148, 4234, 7704])).
% 28.02/18.25 tff(7755,plain,
% 28.02/18.25 (big_f(c2, f10(f9(c2, c2)))),
% 28.02/18.25 inference(modus_ponens,[status(thm)],[7754, 7740])).
% 28.02/18.25 tff(7756,plain,
% 28.02/18.25 (~(f10(f9(c2, c2)) = f9(c2, c2))),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[762, 7713, 122, 79, 148])).
% 28.02/18.25 tff(7757,plain,
% 28.02/18.25 (c2 = f8(f9(c2, c2))),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[6908, 2730, 7756, 7755, 7737, 5532, 7733])).
% 28.02/18.25 tff(7758,plain,
% 28.02/18.25 (f8(f9(c2, c2)) = c2),
% 28.02/18.25 inference(symmetry,[status(thm)],[7757])).
% 28.02/18.25 tff(7759,plain,
% 28.02/18.25 (big_f(f9(c2, c2), f10(f9(c2, c2)))),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[3625, 7713, 122, 7726, 79, 148])).
% 28.02/18.25 tff(7760,plain,
% 28.02/18.25 (f9(c2, c2) = f8(f9(c2, c2))),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[6876, 7759, 7704, 7756, 148, 79, 122, 4234, 3689])).
% 28.02/18.25 tff(7761,plain,
% 28.02/18.25 (f9(c2, c2) = c2),
% 28.02/18.25 inference(transitivity,[status(thm)],[7760, 7758])).
% 28.02/18.25 tff(7762,plain,
% 28.02/18.25 ($false),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[185, 7761])).
% 28.02/18.25 tff(7763,plain,(big_f(f9(c2, c2), f9(c2, c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f7(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.02/18.25 tff(7764,plain,
% 28.02/18.25 (big_f(f9(c2, c2), f9(c2, c2))),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[7763, 147, 79, 122, 5531])).
% 28.02/18.25 tff(7765,plain,
% 28.02/18.25 (~big_f(f9(c2, c2), c2)),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[6482, 256, 122])).
% 28.02/18.25 tff(7766,plain,
% 28.02/18.25 (big_f(f9(c2, c2), f9(c2, c2))),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[7763, 148, 79, 122, 4234])).
% 28.02/18.25 tff(7767,plain,
% 28.02/18.25 (big_f(f7(c1), f6(c1, c1))),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[4658, 256, 148, 79, 122, 4234, 7766])).
% 28.02/18.25 tff(7768,plain,
% 28.02/18.25 (~(f6(c1, c2) = c1)),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[6951, 7767, 7765, 4234, 148, 79, 122])).
% 28.02/18.25 tff(7769,plain,
% 28.02/18.25 (f6(c1, c2) = c2),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[48, 7768])).
% 28.02/18.25 tff(7770,plain,
% 28.02/18.25 (f7(c2) = c2),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[5557, 7765, 79, 122, 148, 4234])).
% 28.02/18.25 tff(7771,plain,
% 28.02/18.25 (big_f(c2, c1)),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[7215, 7770, 256, 122, 79, 4234, 148])).
% 28.02/18.25 tff(7772,plain,
% 28.02/18.25 (big_f(c2, f9(c2, c2))),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[3814, 7771, 148, 79, 122])).
% 28.02/18.25 tff(7773,plain,
% 28.02/18.25 (big_f(c2, c2)),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[7259, 7772, 148, 79, 122, 256, 7770])).
% 28.02/18.25 tff(7774,plain,
% 28.02/18.25 (~(c4 = c1)),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[4027, 7773, 7302, 7766, 7772, 79, 148, 122])).
% 28.02/18.25 tff(7775,plain,
% 28.02/18.25 (c4 = c2),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[461, 7774])).
% 28.02/18.25 tff(7776,plain,
% 28.02/18.25 (~(f9(c2, c2) = c4)),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[4618, 7775, 122, 79, 4743])).
% 28.02/18.25 tff(7777,plain,
% 28.02/18.25 (~(f6(c1, f3(c1, c2)) = c2)),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[7322, 7776, 148, 79, 122, 7765, 4234])).
% 28.02/18.25 tff(7778,plain,
% 28.02/18.25 (f6(c1, f3(c1, c2)) = c1),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[6690, 7777])).
% 28.02/18.25 tff(7779,plain,
% 28.02/18.25 (c1 = f6(c1, f3(c1, c2))),
% 28.02/18.25 inference(symmetry,[status(thm)],[7778])).
% 28.02/18.25 tff(7780,plain,
% 28.02/18.25 (big_f(f7(c2), f6(c2, c2))),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[5485, 7773, 7770, 4743, 122, 256])).
% 28.02/18.25 tff(7781,plain,
% 28.02/18.25 (~(f6(c2, c2) = c2)),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[2744, 7780, 7770, 256, 4743, 122])).
% 28.02/18.25 tff(7782,plain,
% 28.02/18.25 (~(f6(f7(c2), c3) = c2)),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[2716, 7781, 7206, 7770])).
% 28.02/18.25 tff(7783,plain,
% 28.02/18.25 (f6(f7(c2), c3) = c1),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[2391, 7782])).
% 28.02/18.25 tff(7784,plain,
% 28.02/18.25 (c1 = f6(f7(c2), c3)),
% 28.02/18.25 inference(symmetry,[status(thm)],[7783])).
% 28.02/18.25 tff(7785,plain,
% 28.02/18.25 (f3(c1, c2) = f3(f6(f7(c2), c3), c2)),
% 28.02/18.25 inference(monotonicity,[status(thm)],[7784])).
% 28.02/18.25 tff(7786,plain,
% 28.02/18.25 (f3(f6(f7(c2), c3), c2) = f3(c1, c2)),
% 28.02/18.25 inference(symmetry,[status(thm)],[7785])).
% 28.02/18.25 tff(7787,plain,
% 28.02/18.25 ((f3(f6(f7(c2), c3), c2) = c1) <=> (f3(c1, c2) = f6(c1, f3(c1, c2)))),
% 28.02/18.25 inference(monotonicity,[status(thm)],[7786, 7779])).
% 28.02/18.25 tff(7788,plain,
% 28.02/18.25 ((f3(f6(f7(c2), c3), c2) = c1) <=> (f6(c1, f3(c1, c2)) = f3(c1, c2))),
% 28.02/18.25 inference(transitivity,[status(thm)],[7787, 6955])).
% 28.02/18.25 tff(7789,plain,
% 28.02/18.25 ((f6(c1, f3(c1, c2)) = f3(c1, c2)) <=> (f3(f6(f7(c2), c3), c2) = c1)),
% 28.02/18.25 inference(symmetry,[status(thm)],[7788])).
% 28.02/18.25 tff(7790,plain,
% 28.02/18.25 ((f6(f9(c2, c2), f3(c1, c2)) = f3(c1, c2)) <=> (f3(f6(f7(c2), c3), c2) = c1)),
% 28.02/18.25 inference(transitivity,[status(thm)],[7104, 7789])).
% 28.02/18.25 tff(7791,plain,
% 28.02/18.25 ((~(f6(f9(c2, c2), f3(c1, c2)) = f3(c1, c2))) <=> (~(f3(f6(f7(c2), c3), c2) = c1))),
% 28.02/18.25 inference(monotonicity,[status(thm)],[7790])).
% 28.02/18.25 tff(7792,plain,
% 28.02/18.25 (f6(f9(c2, c2), f3(c1, c2)) = f9(c2, c2)),
% 28.02/18.25 inference(transitivity,[status(thm)],[7103, 7778, 149, 2634])).
% 28.02/18.25 tff(7793,plain,
% 28.02/18.25 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(c1, c2))) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 28.02/18.25 inference(monotonicity,[status(thm)],[6991, 7792])).
% 28.02/18.25 tff(7794,plain,
% 28.02/18.25 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(c1, c2)))),
% 28.02/18.25 inference(symmetry,[status(thm)],[7793])).
% 28.02/18.25 tff(7795,plain,
% 28.02/18.25 (big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(c1, c2)))),
% 28.02/18.25 inference(modus_ponens,[status(thm)],[7766, 7794])).
% 28.02/18.25 tff(7796,plain,
% 28.02/18.25 ((~big_f(f7(f9(c2, c2)), f6(f9(c2, c2), f3(c1, c2)))) | (~(f6(f9(c2, c2), f3(c1, c2)) = f3(c1, c2)))),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[7116, 2534, 122, 4743, 256, 6991])).
% 28.02/18.25 tff(7797,plain,
% 28.02/18.25 (~(f6(f9(c2, c2), f3(c1, c2)) = f3(c1, c2))),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[7796, 7795])).
% 28.02/18.25 tff(7798,plain,
% 28.02/18.25 (~(f3(f6(f7(c2), c3), c2) = c1)),
% 28.02/18.25 inference(modus_ponens,[status(thm)],[7797, 7791])).
% 28.02/18.25 tff(7799,plain,
% 28.02/18.25 (f3(f6(f7(c2), c3), c2) = c2),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[6749, 7798])).
% 28.02/18.25 tff(7800,plain,
% 28.02/18.25 (f3(c1, c2) = c2),
% 28.02/18.25 inference(transitivity,[status(thm)],[7785, 7799])).
% 28.02/18.25 tff(7801,plain,
% 28.02/18.25 (f6(c1, f3(c1, c2)) = f6(f9(c2, c2), c2)),
% 28.02/18.25 inference(monotonicity,[status(thm)],[4708, 7800])).
% 28.02/18.25 tff(7802,plain,
% 28.02/18.25 (f9(c2, c2) = c2),
% 28.02/18.25 inference(transitivity,[status(thm)],[2629, 148, 7779, 7801, 6954, 7769])).
% 28.02/18.25 tff(7803,plain,
% 28.02/18.25 ($false),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[4743, 7802])).
% 28.02/18.25 tff(7804,plain,(big_f(f9(c2, c2), f10(c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f7(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.02/18.25 tff(7805,plain,
% 28.02/18.25 (big_f(f9(c2, c2), f10(c2))),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[7804, 147, 79, 122, 5531])).
% 28.02/18.25 tff(7806,plain,
% 28.02/18.25 (big_f(f9(c2, c2), c2)),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[3687, 7805, 122])).
% 28.02/18.25 tff(7807,plain,
% 28.02/18.25 (~(c3 = c1)),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[7204, 147, 79, 122, 5531])).
% 28.02/18.25 tff(7808,plain,
% 28.02/18.25 (c3 = c2),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[180, 7807])).
% 28.02/18.25 tff(7809,plain,
% 28.02/18.25 (c2 = c3),
% 28.02/18.25 inference(modus_ponens,[status(thm)],[7808, 78])).
% 28.02/18.25 tff(7810,plain,
% 28.02/18.25 (big_f(f9(c2, c2), f10(c2))),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[7804, 148, 79, 122, 4234])).
% 28.02/18.25 tff(7811,plain,
% 28.02/18.25 (big_f(c2, f9(c2, c2))),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[3814, 6964, 148, 79, 122])).
% 28.02/18.25 tff(7812,plain,
% 28.02/18.25 (big_f(f9(c2, c2), c2)),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[3687, 7810, 122])).
% 28.02/18.25 tff(7813,plain,
% 28.02/18.25 (~(f6(c1, c2) = c2)),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[7753, 121, 79, 122, 148, 4234, 7812])).
% 28.02/18.25 tff(7814,plain,
% 28.02/18.25 (big_f(c1, c1)),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[4926, 7766, 148, 79, 122])).
% 28.02/18.25 tff(7815,plain,
% 28.02/18.25 (big_f(f7(c2), f9(c2, c2))),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[4934, 22, 148, 7814, 79, 122])).
% 28.02/18.25 tff(7816,plain,
% 28.02/18.25 (big_f(f9(c2, c1), f10(c2))),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[1173, 7815, 148, 17, 7810, 79, 122])).
% 28.02/18.25 tff(7817,plain,
% 28.02/18.25 (big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[3898, 7816, 148, 79, 122])).
% 28.02/18.25 tff(7818,plain,
% 28.02/18.25 (~(f9(c2, f9(c2, c2)) = f9(c2, c2))),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[6299, 7817, 122, 4234, 7813, 17, 148, 79])).
% 28.02/18.25 tff(7819,plain,
% 28.02/18.25 (~(f9(c2, c1) = c1)),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[4579, 7818, 148, 79, 122])).
% 28.02/18.25 tff(7820,plain,
% 28.02/18.25 (~(big_f(c2, c2) <=> big_f(f9(c2, f9(c2, c2)), f10(c2)))),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[4996, 7817, 121])).
% 28.02/18.25 tff(7821,plain,
% 28.02/18.25 (~(c2 = f9(c2, f9(c2, c2)))),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[5003, 7820, 4989])).
% 28.02/18.25 tff(7822,plain,
% 28.02/18.25 (~(f9(c2, c1) = c2)),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[5012, 7821, 148, 79, 122])).
% 28.02/18.25 tff(7823,plain,
% 28.02/18.25 ($false),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[3913, 7822, 7819])).
% 28.02/18.25 tff(7824,plain,((f7(c2) = c2) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f7(c1) = c1)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 28.02/18.25 tff(7825,plain,
% 28.02/18.25 (f7(c2) = c2),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[7824, 121, 79, 122, 4234, 148])).
% 28.02/18.25 tff(7826,plain,
% 28.02/18.25 (big_f(c3, f2(c3)) <=> big_f(c2, c2)),
% 28.02/18.25 inference(monotonicity,[status(thm)],[67, 1319])).
% 28.02/18.25 tff(7827,plain,
% 28.02/18.25 (big_f(c2, c2) <=> big_f(c3, f2(c3))),
% 28.02/18.25 inference(symmetry,[status(thm)],[7826])).
% 28.02/18.25 tff(7828,plain,
% 28.02/18.25 ((~big_f(c2, c2)) <=> (~big_f(c3, f2(c3)))),
% 28.02/18.25 inference(monotonicity,[status(thm)],[7827])).
% 28.02/18.25 tff(7829,plain,
% 28.02/18.25 (~big_f(c3, f2(c3))),
% 28.02/18.25 inference(modus_ponens,[status(thm)],[121, 7828])).
% 28.02/18.25 tff(7830,plain,
% 28.02/18.25 ($false),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[2274, 7829])).
% 28.02/18.25 tff(7831,plain,((~(f2(c3) = c2)) | (~big_f(c3, f2(c3))) | big_f(c2, c2) | (~(c3 = c2))), inference(lemma,lemma(discharge,[]))).
% 28.02/18.25 tff(7832,plain,
% 28.02/18.25 (~(f2(c3) = c2)),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[7831, 5584, 121, 67])).
% 28.02/18.25 tff(7833,plain,
% 28.02/18.25 (f2(c3) = c1),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[1273, 7832])).
% 28.02/18.25 tff(7834,plain,
% 28.02/18.25 (f2(c2) = f9(c2, c2)),
% 28.02/18.25 inference(transitivity,[status(thm)],[1426, 1247, 149, 132])).
% 28.02/18.25 tff(7835,plain,
% 28.02/18.25 ((f6(c2, f9(c2, c2)) = f2(c2)) <=> (f6(c2, f9(c2, c2)) = f9(c2, c2))),
% 28.02/18.25 inference(monotonicity,[status(thm)],[7834])).
% 28.02/18.25 tff(7836,plain,
% 28.02/18.25 ((f6(c2, f9(c2, c2)) = f9(c2, c2)) <=> (f6(c2, f9(c2, c2)) = f2(c2))),
% 28.02/18.25 inference(symmetry,[status(thm)],[7835])).
% 28.02/18.25 tff(7837,plain,
% 28.02/18.25 ((~(f6(c2, f9(c2, c2)) = f9(c2, c2))) <=> (~(f6(c2, f9(c2, c2)) = f2(c2)))),
% 28.02/18.25 inference(monotonicity,[status(thm)],[7836])).
% 28.02/18.25 tff(7838,plain,
% 28.02/18.25 (f6(c2, c1) = c1),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[3211, 3197, 122, 1139, 77, 731])).
% 28.02/18.25 tff(7839,plain,
% 28.02/18.25 (f6(c2, c1) = f9(c2, c2)),
% 28.02/18.25 inference(transitivity,[status(thm)],[7838, 149, 132])).
% 28.02/18.25 tff(7840,plain,
% 28.02/18.25 (big_f(f7(c2), f6(c2, c1)) <=> big_f(c2, f9(c2, c2))),
% 28.02/18.25 inference(monotonicity,[status(thm)],[77, 7839])).
% 28.02/18.25 tff(7841,plain,
% 28.02/18.25 (big_f(c2, f9(c2, c2)) <=> big_f(f7(c2), f6(c2, c1))),
% 28.02/18.25 inference(symmetry,[status(thm)],[7840])).
% 28.02/18.25 tff(7842,plain,
% 28.02/18.25 (big_f(f7(c2), f6(c2, c1))),
% 28.02/18.25 inference(modus_ponens,[status(thm)],[3719, 7841])).
% 28.02/18.25 tff(7843,plain,
% 28.02/18.25 ($false),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[3197, 7842])).
% 28.02/18.25 tff(7844,plain,(big_f(f7(c2), f6(c2, c1)) | (~big_f(c2, f9(c2, c2))) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2))), inference(lemma,lemma(discharge,[]))).
% 28.02/18.25 tff(7845,plain,
% 28.02/18.25 (big_f(f7(c2), f6(c2, c1))),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[7844, 6484, 148, 79, 122, 77, 3719, 731])).
% 28.02/18.25 tff(7846,plain,
% 28.02/18.25 (big_f(f7(c2), f6(c2, f9(c2, c2)))),
% 28.02/18.25 inference(modus_ponens,[status(thm)],[7845, 4442])).
% 28.02/18.25 tff(7847,plain,
% 28.02/18.25 (~(f9(c2, f9(c2, c2)) = f9(c2, c2))),
% 28.02/18.25 inference(unit_resolution,[status(thm)],[1141, 6484, 122, 79, 148])).
% 28.02/18.25 tff(7848,plain,
% 28.02/18.25 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~(f6(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f6(c2, f9(c2, c2)))) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~(f6(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f6(c2, f9(c2, c2)))) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)))),
% 28.02/18.25 inference(rewrite,[status(thm)],[])).
% 28.02/18.25 tff(7849,plain,
% 28.02/18.25 (((~(f10(c2) = c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (~(f7(c2) = c2)) | (~(f6(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f6(c2, f9(c2, c2))))) <=> ((~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~(f6(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f6(c2, f9(c2, c2)))) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)))),
% 28.02/18.25 inference(rewrite,[status(thm)],[])).
% 28.02/18.25 tff(7850,plain,
% 28.02/18.25 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (~(f7(c2) = c2)) | (~(f6(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f6(c2, f9(c2, c2)))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~(f6(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f6(c2, f9(c2, c2)))) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2))))),
% 28.02/18.26 inference(monotonicity,[status(thm)],[7849])).
% 28.02/18.26 tff(7851,plain,
% 28.02/18.26 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (~(f7(c2) = c2)) | (~(f6(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f6(c2, f9(c2, c2)))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~(f6(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f6(c2, f9(c2, c2)))) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)))),
% 28.02/18.26 inference(transitivity,[status(thm)],[7850, 7848])).
% 28.02/18.26 tff(7852,plain,
% 28.02/18.26 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (~(f7(c2) = c2)) | (~(f6(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f6(c2, f9(c2, c2)))))),
% 28.02/18.26 inference(quant_inst,[status(thm)],[])).
% 28.02/18.26 tff(7853,plain,
% 28.02/18.26 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~(f6(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f7(c2), f6(c2, f9(c2, c2)))) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2))),
% 28.02/18.26 inference(modus_ponens,[status(thm)],[7852, 7851])).
% 28.02/18.26 tff(7854,plain,
% 28.02/18.26 (~(f6(c2, f9(c2, c2)) = f9(c2, c2))),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[7853, 2534, 122, 77, 5086, 7847, 7846])).
% 28.02/18.26 tff(7855,plain,
% 28.02/18.26 (~(f6(c2, f9(c2, c2)) = f2(c2))),
% 28.02/18.26 inference(modus_ponens,[status(thm)],[7854, 7837])).
% 28.02/18.26 tff(7856,plain,
% 28.02/18.26 (big_f(c2, f6(c2, f9(c2, c2))) <=> big_f(f7(c2), f6(c2, f9(c2, c2)))),
% 28.02/18.26 inference(monotonicity,[status(thm)],[82])).
% 28.02/18.26 tff(7857,plain,
% 28.02/18.26 (big_f(f7(c2), f6(c2, f9(c2, c2))) <=> big_f(c2, f6(c2, f9(c2, c2)))),
% 28.02/18.26 inference(symmetry,[status(thm)],[7856])).
% 28.02/18.26 tff(7858,plain,
% 28.02/18.26 (big_f(c2, f6(c2, f9(c2, c2)))),
% 28.02/18.26 inference(modus_ponens,[status(thm)],[7846, 7857])).
% 28.02/18.26 tff(7859,plain,
% 28.02/18.26 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (f6(c2, f9(c2, c2)) = f2(c2)) | (~big_f(c2, f6(c2, f9(c2, c2)))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (f6(c2, f9(c2, c2)) = f2(c2)) | (~big_f(c2, f6(c2, f9(c2, c2)))))),
% 28.02/18.26 inference(rewrite,[status(thm)],[])).
% 28.02/18.26 tff(7860,plain,
% 28.02/18.26 (((~(c2 = c3)) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))) | (f6(c2, f9(c2, c2)) = f2(c2)) | (~big_f(c2, f6(c2, f9(c2, c2))))) <=> ((~(c2 = c3)) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (f6(c2, f9(c2, c2)) = f2(c2)) | (~big_f(c2, f6(c2, f9(c2, c2)))))),
% 28.02/18.26 inference(rewrite,[status(thm)],[])).
% 28.02/18.26 tff(7861,plain,
% 28.02/18.26 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))) | (f6(c2, f9(c2, c2)) = f2(c2)) | (~big_f(c2, f6(c2, f9(c2, c2)))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (f6(c2, f9(c2, c2)) = f2(c2)) | (~big_f(c2, f6(c2, f9(c2, c2))))))),
% 28.02/18.26 inference(monotonicity,[status(thm)],[7860])).
% 28.02/18.26 tff(7862,plain,
% 28.02/18.26 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))) | (f6(c2, f9(c2, c2)) = f2(c2)) | (~big_f(c2, f6(c2, f9(c2, c2)))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (f6(c2, f9(c2, c2)) = f2(c2)) | (~big_f(c2, f6(c2, f9(c2, c2)))))),
% 28.02/18.26 inference(transitivity,[status(thm)],[7861, 7859])).
% 28.02/18.26 tff(7863,plain,
% 28.02/18.26 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))) | (f6(c2, f9(c2, c2)) = f2(c2)) | (~big_f(c2, f6(c2, f9(c2, c2)))))),
% 28.02/18.26 inference(quant_inst,[status(thm)],[])).
% 28.02/18.26 tff(7864,plain,
% 28.02/18.26 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (f6(c2, f9(c2, c2)) = f2(c2)) | (~big_f(c2, f6(c2, f9(c2, c2))))),
% 28.02/18.26 inference(modus_ponens,[status(thm)],[7863, 7862])).
% 28.02/18.26 tff(7865,plain,
% 28.02/18.26 ((f6(c2, f9(c2, c2)) = f2(c2)) | (~big_f(c2, f6(c2, f9(c2, c2))))),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[7864, 5622, 631, 630, 121, 1335])).
% 28.02/18.26 tff(7866,plain,
% 28.02/18.26 ($false),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[7865, 7858, 7855])).
% 28.02/18.26 tff(7867,plain,(big_f(f9(c2, c1), f10(c2)) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (~(f7(c2) = c2)) | (~(f2(c3) = c1)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(c3 = c2)) | (~big_f(c2, f9(c2, c2))) | (~big_f(f9(c2, c2), f10(c2)))), inference(lemma,lemma(discharge,[]))).
% 28.02/18.26 tff(7868,plain,
% 28.02/18.26 (big_f(f9(c2, c1), f10(c2))),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[7867, 432, 437, 121, 77, 7833, 148, 79, 122, 67, 3719, 690])).
% 28.02/18.26 tff(7869,plain,
% 28.02/18.26 (big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[3898, 7868, 148, 79, 122])).
% 28.02/18.26 tff(7870,assumption,(~(f6(c2, f9(c2, c2)) = f9(c2, c2))), introduced(assumption)).
% 28.02/18.26 tff(7871,plain,
% 28.02/18.26 (~(f6(c2, f9(c2, c2)) = f2(c2))),
% 28.02/18.26 inference(modus_ponens,[status(thm)],[7870, 7837])).
% 28.02/18.26 tff(7872,plain,
% 28.02/18.26 (~(big_f(c2, c2) <=> big_f(f9(c2, f9(c2, c2)), f10(c2)))),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[4996, 1146, 121])).
% 28.02/18.26 tff(7873,plain,
% 28.02/18.26 (~(c2 = f9(c2, f9(c2, c2)))),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[5003, 7872, 4989])).
% 28.02/18.26 tff(7874,plain,
% 28.02/18.26 (~(f9(c2, c1) = c2)),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[5012, 7873, 148, 79, 122])).
% 28.02/18.26 tff(7875,plain,
% 28.02/18.26 (f9(c2, c1) = c1),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[3913, 7874])).
% 28.02/18.26 tff(7876,plain,
% 28.02/18.26 (f9(c2, f9(c2, c2)) = f9(c2, c2)),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[4579, 7875, 148, 79, 122])).
% 28.02/18.26 tff(7877,assumption,(~big_f(f7(c2), f6(c2, f9(c2, c2)))), introduced(assumption)).
% 28.02/18.26 tff(7878,plain,
% 28.02/18.26 ($false),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[6265, 2409, 122, 77, 1146, 1137, 7870, 7877])).
% 28.02/18.26 tff(7879,plain,(big_f(f7(c2), f6(c2, f9(c2, c2))) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (f6(c2, f9(c2, c2)) = f9(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 28.02/18.26 tff(7880,plain,
% 28.02/18.26 (big_f(f7(c2), f6(c2, f9(c2, c2)))),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[7879, 7870, 77, 1146, 7876, 122])).
% 28.02/18.26 tff(7881,plain,
% 28.02/18.26 (big_f(c2, f6(c2, f9(c2, c2)))),
% 28.02/18.26 inference(modus_ponens,[status(thm)],[7880, 7857])).
% 28.02/18.26 tff(7882,plain,
% 28.02/18.26 ($false),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[7865, 7881, 7871])).
% 28.02/18.26 tff(7883,plain,((f6(c2, f9(c2, c2)) = f9(c2, c2)) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (~(f7(c2) = c2)) | (~(f2(c3) = c1)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(c3 = c2)) | (~big_f(f9(c2, f9(c2, c2)), f10(c2)))), inference(lemma,lemma(discharge,[]))).
% 28.02/18.26 tff(7884,plain,
% 28.02/18.26 (f6(c2, f9(c2, c2)) = f9(c2, c2)),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[7883, 432, 437, 121, 77, 7833, 148, 79, 122, 67, 7869])).
% 28.02/18.26 tff(7885,plain,
% 28.02/18.26 (big_f(f7(c2), f6(c2, f9(c2, c2))) <=> big_f(c2, f9(c2, c2))),
% 28.02/18.26 inference(monotonicity,[status(thm)],[77, 7884])).
% 28.02/18.26 tff(7886,plain,
% 28.02/18.26 (big_f(c2, f9(c2, c2)) <=> big_f(f7(c2), f6(c2, f9(c2, c2)))),
% 28.02/18.26 inference(symmetry,[status(thm)],[7885])).
% 28.02/18.26 tff(7887,plain,
% 28.02/18.26 (big_f(f7(c2), f6(c2, f9(c2, c2)))),
% 28.02/18.26 inference(modus_ponens,[status(thm)],[3719, 7886])).
% 28.02/18.26 tff(7888,plain,
% 28.02/18.26 (~(big_f(c2, c2) <=> big_f(f9(c2, f9(c2, c2)), f10(c2)))),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[4996, 7869, 121])).
% 28.02/18.26 tff(7889,plain,
% 28.02/18.26 (~(c2 = f9(c2, f9(c2, c2)))),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[5003, 7888, 4989])).
% 28.02/18.26 tff(7890,plain,
% 28.02/18.26 (~(f9(c2, c1) = c2)),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[5012, 7889, 148, 79, 122])).
% 28.02/18.26 tff(7891,plain,
% 28.02/18.26 (f9(c2, c1) = c1),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[3913, 7890])).
% 28.02/18.26 tff(7892,plain,
% 28.02/18.26 (f9(c2, f9(c2, c2)) = f9(c2, c2)),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[4579, 7891, 148, 79, 122])).
% 28.02/18.26 tff(7893,plain,
% 28.02/18.26 ($false),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[4489, 2378, 122, 77, 7869, 7892, 7884, 7887])).
% 28.02/18.26 tff(7894,plain,((~(c4 = c2)) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~big_f(c2, f9(c2, c2))) | big_f(c2, c2) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(c3 = c2)) | (~big_f(f9(c2, c2), f10(c2)))), inference(lemma,lemma(discharge,[]))).
% 28.02/18.26 tff(7895,plain,
% 28.02/18.26 (~(c4 = c2)),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[7894, 7825, 122, 7811, 121, 148, 79, 7206, 7810])).
% 28.02/18.26 tff(7896,plain,
% 28.02/18.26 (c4 = c1),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[461, 7895])).
% 28.02/18.26 tff(7897,plain,
% 28.02/18.26 (f9(c2, c2) = c4),
% 28.02/18.26 inference(modus_ponens,[status(thm)],[7896, 3724])).
% 28.02/18.26 tff(7898,plain,
% 28.02/18.26 (c1 = c4),
% 28.02/18.26 inference(symmetry,[status(thm)],[7896])).
% 28.02/18.26 tff(7899,plain,
% 28.02/18.26 (f9(c2, c2) = c4),
% 28.02/18.26 inference(transitivity,[status(thm)],[160, 148, 7898])).
% 28.02/18.26 tff(7900,plain,
% 28.02/18.26 (f4(f9(c2, c2)) = f4(c4)),
% 28.02/18.26 inference(monotonicity,[status(thm)],[7899])).
% 28.02/18.26 tff(7901,plain,
% 28.02/18.26 (f4(f9(c2, c2)) = c2),
% 28.02/18.26 inference(transitivity,[status(thm)],[7900, 79])).
% 28.02/18.26 tff(7902,plain,
% 28.02/18.26 ((f9(c2, c2) = f4(f9(c2, c2))) <=> (f9(c2, c2) = c2)),
% 28.02/18.26 inference(monotonicity,[status(thm)],[7901])).
% 28.02/18.26 tff(7903,plain,
% 28.02/18.26 ((f9(c2, c2) = c2) <=> (f9(c2, c2) = f4(f9(c2, c2)))),
% 28.02/18.26 inference(symmetry,[status(thm)],[7902])).
% 28.02/18.26 tff(7904,plain,
% 28.02/18.26 ((~(f9(c2, c2) = c2)) <=> (~(f9(c2, c2) = f4(f9(c2, c2))))),
% 28.02/18.26 inference(monotonicity,[status(thm)],[7903])).
% 28.02/18.26 tff(7905,plain,
% 28.02/18.26 (~(f9(c2, c2) = f4(f9(c2, c2)))),
% 28.02/18.26 inference(modus_ponens,[status(thm)],[185, 7904])).
% 28.02/18.26 tff(7906,plain,
% 28.02/18.26 ((f9(c2, c2) = f2(c2)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~(f9(c2, c2) = c4))),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[1599, 1355, 7302, 7766, 7811])).
% 28.02/18.26 tff(7907,plain,
% 28.02/18.26 (f9(c2, c2) = f2(c2)),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[7906, 7905, 7897])).
% 28.02/18.26 tff(7908,plain,
% 28.02/18.26 (f2(c2) = f9(c2, c2)),
% 28.02/18.26 inference(symmetry,[status(thm)],[7907])).
% 28.02/18.26 tff(7909,plain,
% 28.02/18.26 ((f6(c2, f9(c2, c2)) = f2(c2)) <=> (f6(c2, f9(c2, c2)) = f9(c2, c2))),
% 28.02/18.26 inference(monotonicity,[status(thm)],[7908])).
% 28.02/18.26 tff(7910,plain,
% 28.02/18.26 ((f6(c2, f9(c2, c2)) = f9(c2, c2)) <=> (f6(c2, f9(c2, c2)) = f2(c2))),
% 28.02/18.26 inference(symmetry,[status(thm)],[7909])).
% 28.02/18.26 tff(7911,plain,
% 28.02/18.26 ((~(f6(c2, f9(c2, c2)) = f9(c2, c2))) <=> (~(f6(c2, f9(c2, c2)) = f2(c2)))),
% 28.02/18.26 inference(monotonicity,[status(thm)],[7910])).
% 28.02/18.26 tff(7912,plain,
% 28.02/18.26 (f9(c2, c2) = f2(c2)),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[4023, 515, 514])).
% 28.02/18.26 tff(7913,plain,
% 28.02/18.26 (f2(c2) = f9(c2, c2)),
% 28.02/18.26 inference(symmetry,[status(thm)],[7912])).
% 28.02/18.26 tff(7914,plain,
% 28.02/18.26 ((f6(c2, f9(c2, c2)) = f2(c2)) <=> (f6(c2, f9(c2, c2)) = f9(c2, c2))),
% 28.02/18.26 inference(monotonicity,[status(thm)],[7913])).
% 28.02/18.26 tff(7915,plain,
% 28.02/18.26 ((f6(c2, f9(c2, c2)) = f9(c2, c2)) <=> (f6(c2, f9(c2, c2)) = f2(c2))),
% 28.02/18.26 inference(symmetry,[status(thm)],[7914])).
% 28.02/18.26 tff(7916,plain,
% 28.02/18.26 ((~(f6(c2, f9(c2, c2)) = f9(c2, c2))) <=> (~(f6(c2, f9(c2, c2)) = f2(c2)))),
% 28.02/18.26 inference(monotonicity,[status(thm)],[7915])).
% 28.02/18.26 tff(7917,plain,
% 28.02/18.26 (~(f9(c2, c1) = c1)),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[743, 5677, 148, 690, 79, 122])).
% 28.02/18.26 tff(7918,plain,
% 28.02/18.26 (big_f(f7(c2), f6(c2, c1))),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[7844, 7917, 148, 79, 122, 77, 3719, 5677])).
% 28.02/18.26 tff(7919,plain,
% 28.02/18.26 (big_f(f7(c2), f6(c2, f9(c2, c2)))),
% 28.02/18.26 inference(modus_ponens,[status(thm)],[7918, 4442])).
% 28.02/18.26 tff(7920,plain,
% 28.02/18.26 (~(f9(c2, f9(c2, c2)) = f9(c2, c2))),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[1141, 7917, 122, 79, 148])).
% 28.02/18.26 tff(7921,plain,
% 28.02/18.26 (~(f6(c2, f9(c2, c2)) = f9(c2, c2))),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[7853, 2534, 122, 77, 3896, 7920, 7919])).
% 28.02/18.26 tff(7922,plain,
% 28.02/18.26 (~(f6(c2, f9(c2, c2)) = f2(c2))),
% 28.02/18.26 inference(modus_ponens,[status(thm)],[7921, 7916])).
% 28.02/18.26 tff(7923,plain,
% 28.02/18.26 (big_f(c2, f6(c2, f9(c2, c2)))),
% 28.02/18.26 inference(modus_ponens,[status(thm)],[7919, 7857])).
% 28.02/18.26 tff(7924,plain,
% 28.02/18.26 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)) | (f6(c2, f9(c2, c2)) = f2(c2)) | (~big_f(c2, f6(c2, f9(c2, c2)))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)) | (f6(c2, f9(c2, c2)) = f2(c2)) | (~big_f(c2, f6(c2, f9(c2, c2)))))),
% 28.02/18.26 inference(rewrite,[status(thm)],[])).
% 28.02/18.26 tff(7925,plain,
% 28.02/18.26 (((~(c2 = c3)) | (~(f9(c2, c2) = c4)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (f6(c2, f9(c2, c2)) = f2(c2)) | (~big_f(c2, f6(c2, f9(c2, c2))))) <=> ((~(c2 = c3)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)) | (f6(c2, f9(c2, c2)) = f2(c2)) | (~big_f(c2, f6(c2, f9(c2, c2)))))),
% 28.02/18.26 inference(rewrite,[status(thm)],[])).
% 28.02/18.26 tff(7926,plain,
% 28.02/18.26 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(f9(c2, c2) = c4)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (f6(c2, f9(c2, c2)) = f2(c2)) | (~big_f(c2, f6(c2, f9(c2, c2)))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)) | (f6(c2, f9(c2, c2)) = f2(c2)) | (~big_f(c2, f6(c2, f9(c2, c2))))))),
% 28.02/18.26 inference(monotonicity,[status(thm)],[7925])).
% 28.02/18.26 tff(7927,plain,
% 28.02/18.26 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(f9(c2, c2) = c4)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (f6(c2, f9(c2, c2)) = f2(c2)) | (~big_f(c2, f6(c2, f9(c2, c2)))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)) | (f6(c2, f9(c2, c2)) = f2(c2)) | (~big_f(c2, f6(c2, f9(c2, c2)))))),
% 28.02/18.26 inference(transitivity,[status(thm)],[7926, 7924])).
% 28.02/18.26 tff(7928,plain,
% 28.02/18.26 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(f9(c2, c2) = c4)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (f6(c2, f9(c2, c2)) = f2(c2)) | (~big_f(c2, f6(c2, f9(c2, c2)))))),
% 28.02/18.26 inference(quant_inst,[status(thm)],[])).
% 28.02/18.26 tff(7929,plain,
% 28.02/18.26 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)) | (f6(c2, f9(c2, c2)) = f2(c2)) | (~big_f(c2, f6(c2, f9(c2, c2))))),
% 28.02/18.26 inference(modus_ponens,[status(thm)],[7928, 7927])).
% 28.02/18.26 tff(7930,plain,
% 28.02/18.26 ((f6(c2, f9(c2, c2)) = f2(c2)) | (~big_f(c2, f6(c2, f9(c2, c2))))),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[7929, 1355, 1344, 515, 487, 514])).
% 28.02/18.26 tff(7931,plain,
% 28.02/18.26 ($false),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[7930, 7923, 7922])).
% 28.02/18.26 tff(7932,plain,(big_f(f9(c2, f9(c2, c2)), f10(c2)) | (~(c2 = c3)) | (f9(c2, c2) = f4(f9(c2, c2))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(c2, c2) = c4)) | (~(f7(c2) = c2)) | (~(f10(c2) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~big_f(c2, f9(c2, c2))) | (~big_f(f9(c2, c2), f10(c2)))), inference(lemma,lemma(discharge,[]))).
% 28.02/18.26 tff(7933,plain,
% 28.02/18.26 (big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[7932, 7905, 7302, 7766, 7897, 7825, 122, 148, 79, 7811, 7810])).
% 28.02/18.26 tff(7934,plain,
% 28.02/18.26 (~(big_f(c2, c2) <=> big_f(f9(c2, f9(c2, c2)), f10(c2)))),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[4996, 7933, 121])).
% 28.02/18.26 tff(7935,plain,
% 28.02/18.26 (~(c2 = f9(c2, f9(c2, c2)))),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[5003, 7934, 4989])).
% 28.02/18.26 tff(7936,plain,
% 28.02/18.26 (~(f9(c2, c1) = c2)),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[5012, 7935, 148, 79, 122])).
% 28.02/18.26 tff(7937,plain,
% 28.02/18.26 (f9(c2, c1) = c1),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[3913, 7936])).
% 28.02/18.26 tff(7938,plain,
% 28.02/18.26 (big_f(c1, c2)),
% 28.02/18.26 inference(modus_ponens,[status(thm)],[7812, 3690])).
% 28.02/18.26 tff(7939,plain,
% 28.02/18.26 (f9(c2, f9(c2, c2)) = f9(c2, c2)),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[4579, 736, 148, 79, 122])).
% 28.02/18.26 tff(7940,plain,
% 28.02/18.26 (f6(c2, f9(c2, c2)) = f9(c2, c2)),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[7879, 7877, 77, 1146, 7939, 122])).
% 28.02/18.26 tff(7941,plain,
% 28.02/18.26 (~(f6(c2, c1) = c1)),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[6614, 3197, 148, 77, 79, 122, 3719])).
% 28.02/18.26 tff(7942,plain,
% 28.02/18.26 (~(f5(c1) = c1)),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[3563, 3197, 122, 77, 2865, 736, 7941])).
% 28.02/18.26 tff(7943,plain,
% 28.02/18.26 (f5(c1) = c2),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[1708, 7942])).
% 28.02/18.26 tff(7944,plain,
% 28.02/18.26 (f9(c2, f5(c1)) = f9(c2, c2)),
% 28.02/18.26 inference(monotonicity,[status(thm)],[7943])).
% 28.02/18.26 tff(7945,plain,
% 28.02/18.26 (f6(c2, f9(c2, f5(c1))) = f6(c2, f9(c2, c2))),
% 28.02/18.26 inference(monotonicity,[status(thm)],[7944])).
% 28.02/18.26 tff(7946,plain,
% 28.02/18.26 (f6(c2, f9(c2, c2)) = f6(c2, f9(c2, f5(c1)))),
% 28.02/18.26 inference(symmetry,[status(thm)],[7945])).
% 28.02/18.26 tff(7947,plain,
% 28.02/18.26 ((f6(c2, f9(c2, c2)) = f9(c2, c2)) <=> (f6(c2, f9(c2, f5(c1))) = c1)),
% 28.02/18.26 inference(monotonicity,[status(thm)],[7946, 161])).
% 28.02/18.26 tff(7948,plain,
% 28.02/18.26 ((f6(c2, f9(c2, f5(c1))) = c1) <=> (f6(c2, f9(c2, c2)) = f9(c2, c2))),
% 28.02/18.26 inference(symmetry,[status(thm)],[7947])).
% 28.02/18.26 tff(7949,plain,
% 28.02/18.26 ((f6(c2, f9(c2, f5(c1))) = c1) <=> (f6(c2, c1) = c1)),
% 28.02/18.26 inference(transitivity,[status(thm)],[7948, 4457])).
% 28.02/18.26 tff(7950,assumption,(f6(c2, f9(c2, c2)) = f9(c2, c2)), introduced(assumption)).
% 28.02/18.26 tff(7951,plain,
% 28.02/18.26 (f6(c2, f9(c2, f5(c1))) = c1),
% 28.02/18.26 inference(modus_ponens,[status(thm)],[7950, 7947])).
% 28.02/18.26 tff(7952,plain,
% 28.02/18.26 (f6(c2, c1) = c1),
% 28.02/18.26 inference(modus_ponens,[status(thm)],[7951, 7949])).
% 28.02/18.26 tff(7953,plain,
% 28.02/18.26 ($false),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[7941, 7952])).
% 28.02/18.26 tff(7954,plain,(big_f(f7(c2), f6(c2, c1)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f6(c2, f9(c2, c2)) = f9(c2, c2))) | (~(f7(c2) = c2)) | (~big_f(c1, c2)) | (~(f9(c2, c1) = c1)) | (~big_f(c2, f9(c2, c2)))), inference(lemma,lemma(discharge,[]))).
% 28.02/18.26 tff(7955,plain,
% 28.02/18.26 (big_f(f7(c2), f6(c2, c1))),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[7954, 7940, 79, 122, 148, 77, 2865, 736, 3719])).
% 28.02/18.26 tff(7956,plain,
% 28.02/18.26 (big_f(f7(c2), f6(c2, f9(c2, c2)))),
% 28.02/18.26 inference(modus_ponens,[status(thm)],[7955, 4442])).
% 28.02/18.26 tff(7957,plain,
% 28.02/18.26 ($false),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[7877, 7956])).
% 28.02/18.26 tff(7958,plain,(big_f(f7(c2), f6(c2, f9(c2, c2))) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~big_f(c1, c2)) | (~(f9(c2, c1) = c1)) | (~big_f(c2, f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2)))), inference(lemma,lemma(discharge,[]))).
% 28.02/18.26 tff(7959,plain,
% 28.02/18.26 (big_f(f7(c2), f6(c2, f9(c2, c2)))),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[7958, 7825, 79, 122, 148, 7938, 7937, 7811, 7933])).
% 28.02/18.26 tff(7960,plain,
% 28.02/18.26 (f9(c2, f9(c2, c2)) = f9(c2, c2)),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[4579, 7937, 148, 79, 122])).
% 28.02/18.26 tff(7961,plain,
% 28.02/18.26 (~(f6(c2, f9(c2, c2)) = f9(c2, c2))),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[4489, 2378, 122, 7825, 7933, 7960, 7959])).
% 28.02/18.26 tff(7962,plain,
% 28.02/18.26 (~(f6(c2, f9(c2, c2)) = f2(c2))),
% 28.02/18.26 inference(modus_ponens,[status(thm)],[7961, 7911])).
% 28.02/18.26 tff(7963,plain,
% 28.02/18.26 (c2 = f7(c2)),
% 28.02/18.26 inference(symmetry,[status(thm)],[7825])).
% 28.02/18.26 tff(7964,plain,
% 28.02/18.26 (big_f(c2, f6(c2, f9(c2, c2))) <=> big_f(f7(c2), f6(c2, f9(c2, c2)))),
% 28.02/18.26 inference(monotonicity,[status(thm)],[7963])).
% 28.02/18.26 tff(7965,plain,
% 28.02/18.26 (big_f(f7(c2), f6(c2, f9(c2, c2))) <=> big_f(c2, f6(c2, f9(c2, c2)))),
% 28.02/18.26 inference(symmetry,[status(thm)],[7964])).
% 28.02/18.26 tff(7966,plain,
% 28.02/18.26 (big_f(c2, f6(c2, f9(c2, c2)))),
% 28.02/18.26 inference(modus_ponens,[status(thm)],[7959, 7965])).
% 28.02/18.26 tff(7967,plain,
% 28.02/18.26 ((f6(c2, f9(c2, c2)) = f2(c2)) | (~big_f(c2, f6(c2, f9(c2, c2))))),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[7929, 1355, 7302, 7905, 7766, 7897])).
% 28.02/18.26 tff(7968,plain,
% 28.02/18.26 ($false),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[7967, 7966, 7962])).
% 28.02/18.26 tff(7969,plain,(big_f(c2, c2) | (~(f10(c2) = c2)) | (~(f4(c4) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f7(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.02/18.26 tff(7970,plain,
% 28.02/18.26 (big_f(c2, c2)),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[7969, 147, 79, 122, 5531])).
% 28.02/18.26 tff(7971,plain,
% 28.02/18.26 (~(c4 = c1)),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[4027, 3719, 1344, 487, 1345, 79, 148, 122])).
% 28.02/18.26 tff(7972,plain,
% 28.02/18.26 (c4 = c2),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[461, 7971])).
% 28.02/18.26 tff(7973,plain,
% 28.02/18.26 (c2 = c4),
% 28.02/18.26 inference(symmetry,[status(thm)],[7972])).
% 28.02/18.26 tff(7974,plain,
% 28.02/18.26 (f4(c2) = f4(c4)),
% 28.02/18.26 inference(monotonicity,[status(thm)],[7973])).
% 28.02/18.26 tff(7975,plain,
% 28.02/18.26 (f4(c2) = c2),
% 28.02/18.26 inference(transitivity,[status(thm)],[7974, 79])).
% 28.02/18.26 tff(7976,plain,
% 28.02/18.26 ((f9(c2, c2) = f4(c2)) <=> (f9(c2, c2) = c2)),
% 28.02/18.26 inference(monotonicity,[status(thm)],[7975])).
% 28.02/18.26 tff(7977,plain,
% 28.02/18.26 ((f9(c2, c2) = c2) <=> (f9(c2, c2) = f4(c2))),
% 28.02/18.26 inference(symmetry,[status(thm)],[7976])).
% 28.02/18.26 tff(7978,plain,
% 28.02/18.26 ((~(f9(c2, c2) = c2)) <=> (~(f9(c2, c2) = f4(c2)))),
% 28.02/18.26 inference(monotonicity,[status(thm)],[7977])).
% 28.02/18.26 tff(7979,plain,
% 28.02/18.26 (~(f9(c2, c2) = f4(c2))),
% 28.02/18.26 inference(modus_ponens,[status(thm)],[185, 7978])).
% 28.02/18.26 tff(7980,plain,
% 28.02/18.26 (c2 = c4),
% 28.02/18.26 inference(modus_ponens,[status(thm)],[7972, 159])).
% 28.02/18.26 tff(7981,plain,
% 28.02/18.26 (c2 = f2(c2)),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[4088, 7980, 7979])).
% 28.02/18.26 tff(7982,plain,
% 28.02/18.26 (f2(c2) = c2),
% 28.02/18.26 inference(symmetry,[status(thm)],[7981])).
% 28.02/18.26 tff(7983,plain,
% 28.02/18.26 (f9(c2, c2) = f2(c2)),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[4119, 1355, 7980, 1344, 3719, 2041, 7979])).
% 28.02/18.26 tff(7984,plain,
% 28.02/18.26 (f9(c2, c2) = c2),
% 28.02/18.26 inference(transitivity,[status(thm)],[7983, 7982])).
% 28.02/18.26 tff(7985,plain,
% 28.02/18.26 ($false),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[185, 7984])).
% 28.02/18.26 tff(7986,plain,((~big_f(c2, f9(c2, c2))) | (~big_f(c2, c2)) | (~(c2 = c3)) | (~big_f(f9(c2, c2), c2)) | (~(f4(c4) = c2)) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.02/18.26 tff(7987,plain,
% 28.02/18.26 (~big_f(c2, f9(c2, c2))),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[7986, 7970, 7809, 7806, 79, 7764, 147, 122])).
% 28.02/18.26 tff(7988,plain,
% 28.02/18.26 (big_f(f9(c2, c2), c2)),
% 28.02/18.26 inference(unit_resolution,[status(thm)],[3687, 690, 122])).
% 28.02/18.26 tff(7989,plain,
% 28.02/18.26 (big_f(f7(c2), c2)),
% 28.02/18.26 inference(modus_ponens,[status(thm)],[7988, 4570])).
% 28.02/18.27 tff(7990,plain,
% 28.02/18.27 (big_f(c1, c1)),
% 28.02/18.27 inference(unit_resolution,[status(thm)],[4926, 487, 148, 79, 122])).
% 28.02/18.27 tff(7991,plain,
% 28.02/18.27 (big_f(f7(c2), f9(c2, c2))),
% 28.02/18.27 inference(unit_resolution,[status(thm)],[4934, 22, 148, 7990, 79, 122])).
% 28.02/18.27 tff(7992,plain,
% 28.02/18.27 (big_f(c2, f10(f9(c2, c2))) <=> big_f(c2, c2)),
% 28.02/18.27 inference(monotonicity,[status(thm)],[6310])).
% 28.02/18.27 tff(7993,plain,
% 28.02/18.27 (big_f(c2, c2) <=> big_f(c2, f10(f9(c2, c2)))),
% 28.02/18.27 inference(symmetry,[status(thm)],[7992])).
% 28.02/18.27 tff(7994,plain,
% 28.02/18.27 (big_f(c2, f10(f9(c2, c2)))),
% 28.02/18.27 inference(modus_ponens,[status(thm)],[1345, 7993])).
% 28.02/18.27 tff(7995,plain,
% 28.02/18.27 (~(f10(f9(c2, c2)) = f9(c2, c2))),
% 28.02/18.27 inference(unit_resolution,[status(thm)],[762, 16, 122, 79, 148])).
% 28.02/18.27 tff(7996,plain,
% 28.02/18.27 (big_f(f9(c2, c2), f10(f9(c2, c2)))),
% 28.02/18.27 inference(unit_resolution,[status(thm)],[3625, 16, 122, 690, 79, 148])).
% 28.02/18.27 tff(7997,plain,
% 28.02/18.27 (~big_f(c2, f10(f9(c2, c2)))),
% 28.02/18.27 inference(unit_resolution,[status(thm)],[2186, 7996, 122, 17, 1163, 7989, 7995, 185])).
% 28.02/18.27 tff(7998,plain,
% 28.02/18.27 ($false),
% 28.02/18.27 inference(unit_resolution,[status(thm)],[7997, 7994])).
% 28.02/18.27 tff(7999,plain,((~(f10(c1) = c2)) | (~big_f(c2, c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~big_f(f7(c2), f9(c2, c2))) | (~big_f(f9(c2, c2), f10(c2)))), inference(lemma,lemma(discharge,[]))).
% 28.02/18.27 tff(8000,plain,
% 28.02/18.27 (~(f10(c1) = c2)),
% 28.02/18.27 inference(unit_resolution,[status(thm)],[7999, 7991, 148, 79, 122, 1345, 17, 690])).
% 28.02/18.27 tff(8001,plain,
% 28.02/18.27 (f10(c1) = c1),
% 28.02/18.27 inference(unit_resolution,[status(thm)],[14, 8000])).
% 28.02/18.27 tff(8002,plain,
% 28.02/18.27 (~big_f(c2, f9(c2, c2))),
% 28.02/18.27 inference(unit_resolution,[status(thm)],[7986, 1345, 1335, 7988, 79, 487, 148, 122])).
% 28.02/18.27 tff(8003,plain,
% 28.02/18.27 (big_f(f7(c3), c2)),
% 28.02/18.27 inference(modus_ponens,[status(thm)],[7988, 4593])).
% 28.02/18.27 tff(8004,plain,
% 28.02/18.27 (big_f(c1, f9(c1, c1))),
% 28.02/18.27 inference(unit_resolution,[status(thm)],[4699, 7988, 148, 79, 122, 487])).
% 28.02/18.27 tff(8005,plain,
% 28.02/18.27 (big_f(f7(c2), f9(c1, c1))),
% 28.02/18.27 inference(modus_ponens,[status(thm)],[8004, 4685])).
% 28.02/18.27 tff(8006,plain,
% 28.02/18.27 (~(f9(c1, c1) = c1)),
% 28.02/18.27 inference(unit_resolution,[status(thm)],[4745, 3762, 79, 122, 17, 4729, 487, 1180, 148])).
% 28.02/18.27 tff(8007,plain,
% 28.02/18.27 ($false),
% 28.02/18.27 inference(unit_resolution,[status(thm)],[4785, 8006, 3762, 79, 122, 67, 17, 7991, 2040, 4750, 148])).
% 28.02/18.27 tff(8008,plain,((~(f10(c1) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(c3 = c2)) | (f7(c2) = c2) | big_f(c2, f9(c2, c2)) | (~big_f(f7(c3), c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~big_f(f7(c2), f9(c1, c1))) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~big_f(f7(c2), c2))), inference(lemma,lemma(discharge,[]))).
% 28.02/18.27 tff(8009,plain,
% 28.02/18.27 ($false),
% 28.02/18.27 inference(unit_resolution,[status(thm)],[8008, 8005, 8003, 122, 67, 8002, 79, 17, 148, 8001, 487, 7989])).
% 28.02/18.27 tff(8010,plain,((f7(c2) = c2) | (~(f10(c2) = c2)) | (~(c3 = c2)) | (~(f4(c4) = c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~big_f(c2, c2)) | (~big_f(f9(c2, c2), f10(c2)))), inference(lemma,lemma(discharge,[]))).
% 28.02/18.27 tff(8011,plain,
% 28.02/18.27 (f7(c2) = c2),
% 28.02/18.27 inference(unit_resolution,[status(thm)],[8010, 7808, 122, 79, 147, 7764, 7970, 7805])).
% 28.02/18.27 tff(8012,plain,
% 28.02/18.27 (f9(c1, c1) = f9(c2, c2)),
% 28.02/18.27 inference(transitivity,[status(thm)],[3949, 149, 132])).
% 28.02/18.27 tff(8013,plain,
% 28.02/18.27 (big_f(f9(c1, c1), c1) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 28.02/18.27 inference(monotonicity,[status(thm)],[8012, 150])).
% 28.02/18.27 tff(8014,plain,
% 28.02/18.27 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f9(c1, c1), c1)),
% 28.02/18.27 inference(symmetry,[status(thm)],[8013])).
% 28.02/18.27 tff(8015,plain,
% 28.02/18.27 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))),
% 28.02/18.27 inference(transitivity,[status(thm)],[8014, 4101])).
% 28.02/18.27 tff(8016,plain,
% 28.02/18.27 (big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))),
% 28.02/18.27 inference(modus_ponens,[status(thm)],[487, 8015])).
% 28.02/18.27 tff(8017,plain,
% 28.02/18.27 (f9(c1, c1) = f9(f9(c2, c2), f9(c2, c2))),
% 28.02/18.27 inference(symmetry,[status(thm)],[3648])).
% 28.02/18.27 tff(8018,plain,
% 28.02/18.27 ((f9(c1, c1) = c1) <=> (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))),
% 28.02/18.27 inference(monotonicity,[status(thm)],[8017, 150])).
% 28.02/18.27 tff(8019,plain,
% 28.02/18.27 (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)),
% 28.02/18.27 inference(modus_ponens,[status(thm)],[3949, 8018])).
% 28.02/18.27 tff(8020,plain,
% 28.02/18.27 (big_f(f9(c1, c1), f10(c1)) <=> big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))),
% 28.02/18.27 inference(monotonicity,[status(thm)],[8017, 3775])).
% 28.02/18.27 tff(8021,plain,
% 28.02/18.27 (big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))) <=> big_f(f9(c1, c1), f10(c1))),
% 28.02/18.27 inference(symmetry,[status(thm)],[8020])).
% 28.02/18.27 tff(8022,plain,
% 28.02/18.27 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f9(c1, c1), f10(c1))),
% 28.02/18.27 inference(transitivity,[status(thm)],[8014, 4101, 8021])).
% 28.02/18.27 tff(8023,plain,
% 28.02/18.27 (big_f(f9(c1, c1), f10(c1))),
% 28.02/18.27 inference(modus_ponens,[status(thm)],[487, 8022])).
% 28.02/18.27 tff(8024,plain,
% 28.02/18.27 (big_f(f7(c2), f6(c2, c2))),
% 28.02/18.27 inference(unit_resolution,[status(thm)],[3965, 8023, 77, 3762, 79, 3949, 1345])).
% 28.02/18.27 tff(8025,plain,
% 28.02/18.27 (f6(c2, c2) = c2),
% 28.02/18.27 inference(unit_resolution,[status(thm)],[7213, 8024, 67, 2, 77])).
% 28.02/18.27 tff(8026,plain,
% 28.02/18.27 ($false),
% 28.02/18.27 inference(unit_resolution,[status(thm)],[3986, 2378, 77, 8025, 8024, 3777, 8019, 8016])).
% 28.02/18.27 tff(8027,plain,((~(f9(c1, c1) = c1)) | (~(f7(c2) = c2)) | (~(c3 = c2)) | big_f(c2, c1) | (~(f10(c1) = c1)) | (~(f4(c4) = c2)) | (~big_f(c2, c2)) | (~big_f(f9(c2, c2), f9(c2, c2))) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.02/18.27 tff(8028,plain,
% 28.02/18.27 (~(f9(c1, c1) = c1)),
% 28.02/18.27 inference(unit_resolution,[status(thm)],[8027, 3762, 67, 4107, 77, 79, 1345, 487, 148, 122])).
% 28.02/18.27 tff(8029,plain,
% 28.02/18.27 (f9(c1, c1) = c2),
% 28.02/18.27 inference(unit_resolution,[status(thm)],[3939, 8028])).
% 28.02/18.27 tff(8030,plain,
% 28.02/18.27 (big_f(f9(c1, c1), c1) <=> big_f(c2, f9(c2, c2))),
% 28.02/18.27 inference(monotonicity,[status(thm)],[8029, 150])).
% 28.02/18.27 tff(8031,plain,
% 28.02/18.27 (big_f(c2, f9(c2, c2)) <=> big_f(f9(c1, c1), c1)),
% 28.02/18.27 inference(symmetry,[status(thm)],[8030])).
% 28.02/18.27 tff(8032,plain,
% 28.02/18.27 (big_f(c2, f9(c2, c2)) <=> big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))),
% 28.02/18.27 inference(transitivity,[status(thm)],[8031, 4101])).
% 28.02/18.27 tff(8033,plain,
% 28.02/18.27 ((~big_f(c2, f9(c2, c2))) <=> (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))))),
% 28.02/18.27 inference(monotonicity,[status(thm)],[8032])).
% 28.02/18.27 tff(8034,plain,
% 28.02/18.27 (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))),
% 28.02/18.27 inference(modus_ponens,[status(thm)],[2040, 8033])).
% 28.02/18.27 tff(8035,plain,
% 28.02/18.27 ((~(f9(c1, c1) = c1)) <=> (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)))),
% 28.02/18.27 inference(monotonicity,[status(thm)],[8018])).
% 28.02/18.27 tff(8036,plain,
% 28.02/18.27 (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))),
% 28.02/18.27 inference(modus_ponens,[status(thm)],[8028, 8035])).
% 28.02/18.27 tff(8037,plain,
% 28.02/18.27 (big_f(f7(c2), f6(c2, c2))),
% 28.02/18.27 inference(unit_resolution,[status(thm)],[4044, 8034, 1345, 8036, 3777, 77])).
% 28.02/18.27 tff(8038,plain,
% 28.02/18.27 (f6(c2, c2) = c2),
% 28.02/18.27 inference(unit_resolution,[status(thm)],[7213, 8037, 67, 4107, 77])).
% 28.02/18.27 tff(8039,plain,
% 28.02/18.27 ($false),
% 28.02/18.27 inference(unit_resolution,[status(thm)],[4063, 2534, 77, 8038, 8037, 3777, 8036, 8034])).
% 28.02/18.27 tff(8040,plain,((~(f10(c1) = c1)) | (~(f7(c2) = c2)) | (~(c3 = c2)) | (~big_f(c2, c2)) | big_f(c2, f9(c2, c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~big_f(f9(c2, c2), f9(c2, c2)))), inference(lemma,lemma(discharge,[]))).
% 28.02/18.27 tff(8041,plain,
% 28.02/18.27 (~(f10(c1) = c1)),
% 28.02/18.27 inference(unit_resolution,[status(thm)],[8040, 8011, 7808, 7970, 7987, 147, 79, 122, 7764])).
% 28.02/18.27 tff(8042,plain,
% 28.02/18.27 (f10(c1) = c2),
% 28.02/18.27 inference(unit_resolution,[status(thm)],[14, 8041])).
% 28.02/18.27 tff(8043,plain,
% 28.02/18.27 (f9(c2, c2) = c1),
% 28.02/18.27 inference(transitivity,[status(thm)],[160, 147])).
% 28.02/18.27 tff(8044,plain,
% 28.02/18.27 (f10(f9(c2, c2)) = f10(c1)),
% 28.02/18.27 inference(monotonicity,[status(thm)],[8043])).
% 28.02/18.27 tff(8045,plain,
% 28.02/18.27 (f10(f9(c2, c2)) = c2),
% 28.02/18.27 inference(transitivity,[status(thm)],[8044, 8042])).
% 28.02/18.27 tff(8046,plain,
% 28.02/18.27 (big_f(c2, f10(f9(c2, c2))) <=> big_f(c2, c2)),
% 28.02/18.27 inference(monotonicity,[status(thm)],[8045])).
% 28.02/18.27 tff(8047,plain,
% 28.02/18.27 (big_f(c2, c2) <=> big_f(c2, f10(f9(c2, c2)))),
% 28.02/18.27 inference(symmetry,[status(thm)],[8046])).
% 28.02/18.27 tff(8048,plain,
% 28.02/18.27 (big_f(c2, f10(f9(c2, c2)))),
% 28.02/18.27 inference(modus_ponens,[status(thm)],[7970, 8047])).
% 28.02/18.27 tff(8049,plain,
% 28.02/18.27 (~(f10(f9(c2, c2)) = f9(c2, c2))),
% 28.02/18.27 inference(unit_resolution,[status(thm)],[762, 8042, 122, 79, 147])).
% 28.02/18.27 tff(8050,plain,
% 28.02/18.27 (big_f(f7(c2), f6(c2, c2))),
% 28.02/18.27 inference(unit_resolution,[status(thm)],[2700, 8042, 79, 8011, 7970, 122])).
% 28.02/18.27 tff(8051,plain,
% 28.02/18.27 (~big_f(c2, c1)),
% 28.02/18.27 inference(unit_resolution,[status(thm)],[3814, 7987, 147, 79, 122])).
% 28.02/18.27 tff(8052,plain,
% 28.02/18.27 (f6(c2, c2) = c2),
% 28.02/18.27 inference(unit_resolution,[status(thm)],[7213, 8050, 7808, 8051, 8011])).
% 28.02/18.27 tff(8053,plain,
% 28.02/18.27 (c2 = f8(f9(c2, c2))),
% 28.02/18.27 inference(unit_resolution,[status(thm)],[3618, 2730, 8011, 8052, 8050, 8049, 8048])).
% 28.02/18.27 tff(8054,plain,
% 28.02/18.27 (f8(f9(c2, c2)) = c2),
% 28.02/18.27 inference(symmetry,[status(thm)],[8053])).
% 28.02/18.27 tff(8055,plain,
% 28.02/18.27 (big_f(f9(c2, c2), f10(f9(c2, c2)))),
% 28.02/18.27 inference(unit_resolution,[status(thm)],[3625, 8042, 122, 7805, 79, 147])).
% 28.02/18.27 tff(8056,plain,
% 28.02/18.27 (f9(c2, c2) = f8(f9(c2, c2))),
% 28.02/18.27 inference(unit_resolution,[status(thm)],[3632, 2730, 8011, 8052, 8050, 8049, 8055])).
% 28.02/18.27 tff(8057,plain,
% 28.02/18.27 (f9(c2, c2) = c2),
% 28.02/18.27 inference(transitivity,[status(thm)],[8056, 8054])).
% 28.02/18.27 tff(8058,plain,
% 28.02/18.27 (c1 = f9(f10(c2), f4(c4))),
% 28.02/18.27 inference(symmetry,[status(thm)],[147])).
% 28.02/18.27 tff(8059,plain,
% 28.02/18.27 (c1 = f9(c2, c2)),
% 28.02/18.27 inference(transitivity,[status(thm)],[8058, 132])).
% 28.02/18.27 tff(8060,plain,
% 28.02/18.27 ((c2 = c1) <=> (c2 = f9(c2, c2))),
% 28.02/18.27 inference(monotonicity,[status(thm)],[8059])).
% 28.02/18.27 tff(8061,plain,
% 28.02/18.27 ((c2 = c1) <=> (f9(c2, c2) = c2)),
% 28.02/18.27 inference(transitivity,[status(thm)],[8060, 167])).
% 28.02/18.27 tff(8062,plain,
% 28.02/18.27 ((~(c2 = c1)) <=> (~(f9(c2, c2) = c2))),
% 28.02/18.27 inference(monotonicity,[status(thm)],[8061])).
% 28.02/18.27 tff(8063,plain,
% 28.02/18.27 (~(f9(c2, c2) = c2)),
% 28.02/18.27 inference(modus_ponens,[status(thm)],[75, 8062])).
% 28.02/18.27 tff(8064,plain,
% 28.02/18.27 ($false),
% 28.02/18.27 inference(unit_resolution,[status(thm)],[8063, 8057])).
% 28.02/18.27 tff(8065,plain,((f9(f10(c2), f4(c4)) = c2) | (~(f4(c4) = c2)) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.02/18.27 tff(8066,plain,
% 28.02/18.27 (f9(f10(c2), f4(c4)) = c2),
% 28.02/18.27 inference(unit_resolution,[status(thm)],[8065, 122, 79])).
% 28.02/18.27 tff(8067,plain,
% 28.02/18.27 (f9(c2, c2) = c2),
% 28.02/18.27 inference(transitivity,[status(thm)],[2629, 8066])).
% 28.02/18.27 tff(8068,plain,
% 28.02/18.27 (big_f(f9(c2, c2), c2) <=> big_f(c2, c2)),
% 28.02/18.27 inference(monotonicity,[status(thm)],[8067])).
% 28.02/18.27 tff(8069,plain,
% 28.02/18.27 (big_f(c2, c2) <=> big_f(f9(c2, c2), c2)),
% 28.02/18.27 inference(symmetry,[status(thm)],[8068])).
% 28.02/18.27 tff(8070,plain,
% 28.02/18.27 (big_f(c2, c2) <=> big_f(f9(c2, c2), f10(c2))),
% 28.02/18.27 inference(transitivity,[status(thm)],[8069, 130])).
% 28.02/18.27 tff(8071,plain,
% 28.02/18.27 (f9(c2, f7(c2)) = f9(c2, c1)),
% 28.02/18.27 inference(monotonicity,[status(thm)],[22])).
% 28.02/18.27 tff(8072,plain,
% 28.02/18.27 ((f9(c2, f7(c2)) = f7(c2)) <=> (f9(c2, c1) = c1)),
% 28.02/18.27 inference(monotonicity,[status(thm)],[8071, 22])).
% 28.02/18.27 tff(8073,plain,
% 28.02/18.27 ((f9(c2, c1) = c1) <=> (f9(c2, f7(c2)) = f7(c2))),
% 28.02/18.27 inference(symmetry,[status(thm)],[8072])).
% 28.02/18.27 tff(8074,plain,
% 28.02/18.27 ((~(f9(c2, c1) = c1)) <=> (~(f9(c2, f7(c2)) = f7(c2)))),
% 28.02/18.27 inference(monotonicity,[status(thm)],[8073])).
% 28.02/18.27 tff(8075,plain,
% 28.02/18.27 (big_f(f7(c2), f7(c2)) <=> big_f(f7(c2), c1)),
% 28.02/18.27 inference(monotonicity,[status(thm)],[22])).
% 28.02/18.27 tff(8076,plain,
% 28.02/18.27 (big_f(f7(c2), c1) <=> big_f(f7(c2), f7(c2))),
% 28.02/18.27 inference(symmetry,[status(thm)],[8075])).
% 28.02/18.27 tff(8077,plain,
% 28.02/18.27 (f7(f7(c2)) = f7(c1)),
% 28.02/18.27 inference(monotonicity,[status(thm)],[22])).
% 28.02/18.27 tff(8078,plain,
% 28.02/18.27 (big_f(f7(f7(c2)), c2) <=> big_f(f7(c1), c2)),
% 28.02/18.27 inference(monotonicity,[status(thm)],[8077])).
% 28.02/18.27 tff(8079,plain,
% 28.02/18.27 (big_f(f7(c1), c2) <=> big_f(f7(f7(c2)), c2)),
% 28.02/18.27 inference(symmetry,[status(thm)],[8078])).
% 28.02/18.27 tff(8080,plain,
% 28.02/18.27 (f9(c2, c2) = c2),
% 28.02/18.27 inference(unit_resolution,[status(thm)],[1606, 8066, 79, 122])).
% 28.02/18.27 tff(8081,plain,
% 28.02/18.27 (f7(f4(c4)) = c1),
% 28.02/18.27 inference(transitivity,[status(thm)],[80, 22])).
% 28.02/18.27 tff(8082,plain,
% 28.02/18.27 (f10(f7(f4(c4))) = f10(c1)),
% 28.02/18.27 inference(monotonicity,[status(thm)],[8081])).
% 28.02/18.27 tff(8083,plain,
% 28.02/18.27 (f10(c1) = f10(f7(f4(c4)))),
% 28.02/18.27 inference(symmetry,[status(thm)],[8082])).
% 28.02/18.27 tff(8084,plain,
% 28.02/18.27 (big_f(c1, f10(c1)) <=> big_f(c1, f10(f7(f4(c4))))),
% 28.02/18.27 inference(monotonicity,[status(thm)],[8083])).
% 28.02/18.27 tff(8085,plain,
% 28.02/18.27 (big_f(c1, f10(f7(f4(c4)))) <=> big_f(c1, f10(c1))),
% 28.02/18.27 inference(symmetry,[status(thm)],[8084])).
% 28.02/18.27 tff(8086,plain,
% 28.02/18.27 (f8(f7(f4(c4))) = f8(c1)),
% 28.02/18.27 inference(monotonicity,[status(thm)],[8081])).
% 28.02/18.27 tff(8087,plain,
% 28.08/18.27 (f8(c1) = f8(f7(f4(c4)))),
% 28.08/18.27 inference(symmetry,[status(thm)],[8086])).
% 28.08/18.27 tff(8088,plain,
% 28.08/18.27 (big_f(f8(c1), f10(c1)) <=> big_f(f8(f7(f4(c4))), f10(f7(f4(c4))))),
% 28.08/18.27 inference(monotonicity,[status(thm)],[8087, 8083])).
% 28.08/18.27 tff(8089,plain,
% 28.08/18.27 (big_f(f8(f7(f4(c4))), f10(f7(f4(c4)))) <=> big_f(f8(c1), f10(c1))),
% 28.08/18.27 inference(symmetry,[status(thm)],[8088])).
% 28.08/18.27 tff(8090,plain,
% 28.08/18.27 (f10(f7(f4(c4))) = f10(c2)),
% 28.08/18.27 inference(transitivity,[status(thm)],[8082, 15, 216])).
% 28.08/18.27 tff(8091,plain,
% 28.08/18.27 (big_f(f8(f7(f4(c4))), f10(f7(f4(c4)))) <=> big_f(f8(f7(f4(c4))), f10(c2))),
% 28.08/18.27 inference(monotonicity,[status(thm)],[8090])).
% 28.08/18.27 tff(8092,plain,
% 28.08/18.27 (big_f(f8(f7(f4(c4))), f10(c2)) <=> big_f(f8(f7(f4(c4))), f10(f7(f4(c4))))),
% 28.08/18.27 inference(symmetry,[status(thm)],[8091])).
% 28.08/18.27 tff(8093,plain,
% 28.08/18.27 (f8(f7(f4(c4))) = f7(c2)),
% 28.08/18.27 inference(transitivity,[status(thm)],[8086, 3018, 125])).
% 28.08/18.27 tff(8094,plain,
% 28.08/18.27 (big_f(f8(f7(f4(c4))), f10(c2)) <=> big_f(f7(c2), c2)),
% 28.08/18.27 inference(monotonicity,[status(thm)],[8093, 122])).
% 28.08/18.27 tff(8095,plain,
% 28.08/18.27 (big_f(f7(c2), c2) <=> big_f(f8(f7(f4(c4))), f10(c2))),
% 28.08/18.27 inference(symmetry,[status(thm)],[8094])).
% 28.08/18.27 tff(8096,plain,
% 28.08/18.27 (big_f(f7(c2), c2) <=> big_f(f8(c1), f10(c1))),
% 28.08/18.27 inference(transitivity,[status(thm)],[8095, 8092, 8089])).
% 28.08/18.27 tff(8097,plain,
% 28.08/18.27 ((~big_f(f7(c2), c2)) <=> (~big_f(f8(c1), f10(c1)))),
% 28.08/18.27 inference(monotonicity,[status(thm)],[8096])).
% 28.08/18.27 tff(8098,plain,
% 28.08/18.27 (~big_f(f8(c1), f10(c1))),
% 28.08/18.27 inference(modus_ponens,[status(thm)],[1521, 8097])).
% 28.08/18.27 tff(8099,plain,
% 28.08/18.27 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | (f7(c2) = c2) | big_f(f8(c1), f10(c1)) | (~(c2 = f5(c2))) | big_f(f7(c2), c2))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c1) = c1) | (f7(c2) = c2) | big_f(f8(c1), f10(c1)) | (~(c2 = f5(c2))) | big_f(f7(c2), c2))),
% 28.08/18.27 inference(rewrite,[status(thm)],[])).
% 28.08/18.27 tff(8100,plain,
% 28.08/18.27 (((~(c2 = f5(c2))) | (f10(c1) = c1) | big_f(f8(c1), f10(c1)) | (f7(c2) = c2) | big_f(f7(c2), c2) | $false) <=> ((f10(c1) = c1) | (f7(c2) = c2) | big_f(f8(c1), f10(c1)) | (~(c2 = f5(c2))) | big_f(f7(c2), c2))),
% 28.08/18.27 inference(rewrite,[status(thm)],[])).
% 28.08/18.27 tff(8101,plain,
% 28.08/18.27 (((~(c2 = f5(c2))) | (f10(c1) = c1) | big_f(f8(c1), f10(c1)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(f8(c1) = f8(c1)))) <=> ((~(c2 = f5(c2))) | (f10(c1) = c1) | big_f(f8(c1), f10(c1)) | (f7(c2) = c2) | big_f(f7(c2), c2) | $false)),
% 28.08/18.27 inference(monotonicity,[status(thm)],[2841])).
% 28.08/18.27 tff(8102,plain,
% 28.08/18.27 (((~(c2 = f5(c2))) | (f10(c1) = c1) | big_f(f8(c1), f10(c1)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(f8(c1) = f8(c1)))) <=> ((f10(c1) = c1) | (f7(c2) = c2) | big_f(f8(c1), f10(c1)) | (~(c2 = f5(c2))) | big_f(f7(c2), c2))),
% 28.08/18.27 inference(transitivity,[status(thm)],[8101, 8100])).
% 28.08/18.27 tff(8103,plain,
% 28.08/18.27 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c2 = f5(c2))) | (f10(c1) = c1) | big_f(f8(c1), f10(c1)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(f8(c1) = f8(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | (f7(c2) = c2) | big_f(f8(c1), f10(c1)) | (~(c2 = f5(c2))) | big_f(f7(c2), c2)))),
% 28.08/18.27 inference(monotonicity,[status(thm)],[8102])).
% 28.08/18.27 tff(8104,plain,
% 28.08/18.27 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c2 = f5(c2))) | (f10(c1) = c1) | big_f(f8(c1), f10(c1)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(f8(c1) = f8(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c1) = c1) | (f7(c2) = c2) | big_f(f8(c1), f10(c1)) | (~(c2 = f5(c2))) | big_f(f7(c2), c2))),
% 28.08/18.27 inference(transitivity,[status(thm)],[8103, 8099])).
% 28.08/18.27 tff(8105,plain,
% 28.08/18.27 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c2 = f5(c2))) | (f10(c1) = c1) | big_f(f8(c1), f10(c1)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(f8(c1) = f8(c1))))),
% 28.08/18.27 inference(quant_inst,[status(thm)],[])).
% 28.08/18.27 tff(8106,plain,
% 28.08/18.27 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c1) = c1) | (f7(c2) = c2) | big_f(f8(c1), f10(c1)) | (~(c2 = f5(c2))) | big_f(f7(c2), c2)),
% 28.08/18.27 inference(modus_ponens,[status(thm)],[8105, 8104])).
% 28.08/18.27 tff(8107,plain,
% 28.08/18.27 ((f10(c1) = c1) | (f7(c2) = c2) | big_f(f8(c1), f10(c1)) | (~(c2 = f5(c2))) | big_f(f7(c2), c2)),
% 28.08/18.27 inference(unit_resolution,[status(thm)],[8106, 1745])).
% 28.08/18.27 tff(8108,plain,
% 28.08/18.27 (~(c2 = f5(c2))),
% 28.08/18.27 inference(unit_resolution,[status(thm)],[8107, 8098, 17, 3, 1521])).
% 28.08/18.27 tff(8109,assumption,(f5(c2) = c2), introduced(assumption)).
% 28.08/18.27 tff(8110,plain,
% 28.08/18.27 (c2 = f5(c2)),
% 28.08/18.27 inference(modus_ponens,[status(thm)],[8109, 1279])).
% 28.08/18.27 tff(8111,assumption,(~(c2 = f5(c2))), introduced(assumption)).
% 28.08/18.27 tff(8112,plain,
% 28.08/18.27 ($false),
% 28.08/18.27 inference(unit_resolution,[status(thm)],[8111, 8110])).
% 28.08/18.27 tff(8113,plain,((~(f5(c2) = c2)) | (c2 = f5(c2))), inference(lemma,lemma(discharge,[]))).
% 28.08/18.27 tff(8114,plain,
% 28.08/18.27 (~(f5(c2) = c2)),
% 28.08/18.27 inference(unit_resolution,[status(thm)],[8113, 8108])).
% 28.08/18.27 tff(8115,plain,
% 28.08/18.27 (c1 = f7(f4(c4))),
% 28.08/18.27 inference(transitivity,[status(thm)],[125, 81])).
% 28.08/18.27 tff(8116,plain,
% 28.08/18.27 ((f10(c1) = c1) <=> (f10(f7(f4(c4))) = f7(f4(c4)))),
% 28.08/18.27 inference(monotonicity,[status(thm)],[8083, 8115])).
% 28.08/18.27 tff(8117,plain,
% 28.08/18.27 ((~(f10(c1) = c1)) <=> (~(f10(f7(f4(c4))) = f7(f4(c4))))),
% 28.08/18.27 inference(monotonicity,[status(thm)],[8116])).
% 28.08/18.27 tff(8118,plain,
% 28.08/18.27 (~(f10(f7(f4(c4))) = f7(f4(c4)))),
% 28.08/18.27 inference(modus_ponens,[status(thm)],[3, 8117])).
% 28.08/18.27 tff(8119,plain,
% 28.08/18.27 (big_f(f7(c2), c2) <=> big_f(f8(f7(f4(c4))), f10(f7(f4(c4))))),
% 28.08/18.27 inference(transitivity,[status(thm)],[8095, 8092])).
% 28.08/18.27 tff(8120,plain,
% 28.08/18.27 ((~big_f(f7(c2), c2)) <=> (~big_f(f8(f7(f4(c4))), f10(f7(f4(c4)))))),
% 28.08/18.27 inference(monotonicity,[status(thm)],[8119])).
% 28.08/18.27 tff(8121,plain,
% 28.08/18.27 (~big_f(f8(f7(f4(c4))), f10(f7(f4(c4))))),
% 28.08/18.27 inference(modus_ponens,[status(thm)],[1521, 8120])).
% 28.08/18.27 tff(8122,plain,
% 28.08/18.27 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f7(c2) = c2) | (f10(f7(f4(c4))) = f7(f4(c4))) | big_f(f8(f7(f4(c4))), f10(f7(f4(c4)))) | (~(c1 = f5(c2))) | big_f(f7(c2), c1))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(c2) = c2) | (f10(f7(f4(c4))) = f7(f4(c4))) | big_f(f8(f7(f4(c4))), f10(f7(f4(c4)))) | (~(c1 = f5(c2))) | big_f(f7(c2), c1))),
% 28.08/18.27 inference(rewrite,[status(thm)],[])).
% 28.08/18.27 tff(8123,plain,
% 28.08/18.27 (((~(c1 = f5(c2))) | (f10(f7(f4(c4))) = f7(f4(c4))) | big_f(f8(f7(f4(c4))), f10(f7(f4(c4)))) | (f7(c2) = c2) | big_f(f7(c2), c1) | $false) <=> ((f7(c2) = c2) | (f10(f7(f4(c4))) = f7(f4(c4))) | big_f(f8(f7(f4(c4))), f10(f7(f4(c4)))) | (~(c1 = f5(c2))) | big_f(f7(c2), c1))),
% 28.08/18.27 inference(rewrite,[status(thm)],[])).
% 28.08/18.27 tff(8124,plain,
% 28.08/18.27 ((f8(f7(f4(c4))) = f8(f7(f4(c4)))) <=> $true),
% 28.08/18.27 inference(rewrite,[status(thm)],[])).
% 28.08/18.27 tff(8125,plain,
% 28.08/18.27 ((~(f8(f7(f4(c4))) = f8(f7(f4(c4))))) <=> (~$true)),
% 28.08/18.27 inference(monotonicity,[status(thm)],[8124])).
% 28.08/18.27 tff(8126,plain,
% 28.08/18.27 ((~(f8(f7(f4(c4))) = f8(f7(f4(c4))))) <=> $false),
% 28.08/18.27 inference(transitivity,[status(thm)],[8125, 270])).
% 28.08/18.27 tff(8127,plain,
% 28.08/18.27 (((~(c1 = f5(c2))) | (f10(f7(f4(c4))) = f7(f4(c4))) | big_f(f8(f7(f4(c4))), f10(f7(f4(c4)))) | (f7(c2) = c2) | big_f(f7(c2), c1) | (~(f8(f7(f4(c4))) = f8(f7(f4(c4)))))) <=> ((~(c1 = f5(c2))) | (f10(f7(f4(c4))) = f7(f4(c4))) | big_f(f8(f7(f4(c4))), f10(f7(f4(c4)))) | (f7(c2) = c2) | big_f(f7(c2), c1) | $false)),
% 28.08/18.27 inference(monotonicity,[status(thm)],[8126])).
% 28.08/18.27 tff(8128,plain,
% 28.08/18.27 (((~(c1 = f5(c2))) | (f10(f7(f4(c4))) = f7(f4(c4))) | big_f(f8(f7(f4(c4))), f10(f7(f4(c4)))) | (f7(c2) = c2) | big_f(f7(c2), c1) | (~(f8(f7(f4(c4))) = f8(f7(f4(c4)))))) <=> ((f7(c2) = c2) | (f10(f7(f4(c4))) = f7(f4(c4))) | big_f(f8(f7(f4(c4))), f10(f7(f4(c4)))) | (~(c1 = f5(c2))) | big_f(f7(c2), c1))),
% 28.08/18.27 inference(transitivity,[status(thm)],[8127, 8123])).
% 28.08/18.27 tff(8129,plain,
% 28.08/18.27 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c1 = f5(c2))) | (f10(f7(f4(c4))) = f7(f4(c4))) | big_f(f8(f7(f4(c4))), f10(f7(f4(c4)))) | (f7(c2) = c2) | big_f(f7(c2), c1) | (~(f8(f7(f4(c4))) = f8(f7(f4(c4))))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f7(c2) = c2) | (f10(f7(f4(c4))) = f7(f4(c4))) | big_f(f8(f7(f4(c4))), f10(f7(f4(c4)))) | (~(c1 = f5(c2))) | big_f(f7(c2), c1)))),
% 28.08/18.27 inference(monotonicity,[status(thm)],[8128])).
% 28.08/18.27 tff(8130,plain,
% 28.08/18.27 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c1 = f5(c2))) | (f10(f7(f4(c4))) = f7(f4(c4))) | big_f(f8(f7(f4(c4))), f10(f7(f4(c4)))) | (f7(c2) = c2) | big_f(f7(c2), c1) | (~(f8(f7(f4(c4))) = f8(f7(f4(c4))))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(c2) = c2) | (f10(f7(f4(c4))) = f7(f4(c4))) | big_f(f8(f7(f4(c4))), f10(f7(f4(c4)))) | (~(c1 = f5(c2))) | big_f(f7(c2), c1))),
% 28.08/18.27 inference(transitivity,[status(thm)],[8129, 8122])).
% 28.08/18.27 tff(8131,plain,
% 28.08/18.27 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c1 = f5(c2))) | (f10(f7(f4(c4))) = f7(f4(c4))) | big_f(f8(f7(f4(c4))), f10(f7(f4(c4)))) | (f7(c2) = c2) | big_f(f7(c2), c1) | (~(f8(f7(f4(c4))) = f8(f7(f4(c4))))))),
% 28.08/18.27 inference(quant_inst,[status(thm)],[])).
% 28.08/18.27 tff(8132,plain,
% 28.08/18.27 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(c2) = c2) | (f10(f7(f4(c4))) = f7(f4(c4))) | big_f(f8(f7(f4(c4))), f10(f7(f4(c4)))) | (~(c1 = f5(c2))) | big_f(f7(c2), c1)),
% 28.08/18.27 inference(modus_ponens,[status(thm)],[8131, 8130])).
% 28.08/18.27 tff(8133,plain,
% 28.08/18.27 ((f7(c2) = c2) | (f10(f7(f4(c4))) = f7(f4(c4))) | big_f(f8(f7(f4(c4))), f10(f7(f4(c4)))) | (~(c1 = f5(c2))) | big_f(f7(c2), c1)),
% 28.08/18.27 inference(unit_resolution,[status(thm)],[8132, 1745])).
% 28.08/18.27 tff(8134,plain,
% 28.08/18.27 (~(c1 = f5(c2))),
% 28.08/18.27 inference(unit_resolution,[status(thm)],[8133, 8121, 17, 333, 8118])).
% 28.08/18.27 tff(8135,plain,
% 28.08/18.27 ((f5(c2) = c1) <=> (c1 = f5(c2))),
% 28.08/18.27 inference(symmetry,[status(thm)],[1531])).
% 28.08/18.27 tff(8136,plain,
% 28.08/18.27 (c1 = f5(c2)),
% 28.08/18.27 inference(modus_ponens,[status(thm)],[1569, 8135])).
% 28.08/18.27 tff(8137,assumption,(~(c1 = f5(c2))), introduced(assumption)).
% 28.08/18.27 tff(8138,plain,
% 28.08/18.27 ($false),
% 28.08/18.27 inference(unit_resolution,[status(thm)],[8137, 8136])).
% 28.08/18.27 tff(8139,plain,((~(f5(c2) = c1)) | (c1 = f5(c2))), inference(lemma,lemma(discharge,[]))).
% 28.08/18.27 tff(8140,plain,
% 28.08/18.27 (~(f5(c2) = c1)),
% 28.08/18.27 inference(unit_resolution,[status(thm)],[8139, 8134])).
% 28.08/18.27 tff(8141,plain,
% 28.08/18.27 ($false),
% 28.08/18.27 inference(unit_resolution,[status(thm)],[1547, 8140, 8114])).
% 28.08/18.27 tff(8142,plain,((~(f8(c1) = c1)) | (f7(c2) = c2) | big_f(f7(c2), c1) | (f10(c1) = c1) | big_f(f7(c2), c2) | (~(f10(c2) = c2)) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.08/18.27 tff(8143,plain,
% 28.08/18.27 (~(f8(c1) = c1)),
% 28.08/18.27 inference(unit_resolution,[status(thm)],[8142, 1521, 333, 3, 17, 122, 79])).
% 28.08/18.27 tff(8144,plain,
% 28.08/18.27 (f8(c1) = c2),
% 28.08/18.27 inference(unit_resolution,[status(thm)],[1680, 8143])).
% 28.08/18.27 tff(8145,plain,
% 28.08/18.27 (f8(f7(f4(c4))) = c2),
% 28.08/18.27 inference(transitivity,[status(thm)],[8086, 8144])).
% 28.08/18.27 tff(8146,plain,
% 28.08/18.27 (big_f(f8(f7(f4(c4))), f10(c2)) <=> big_f(c2, c2)),
% 28.08/18.27 inference(monotonicity,[status(thm)],[8145, 122])).
% 28.08/18.27 tff(8147,plain,
% 28.08/18.27 (big_f(c2, c2) <=> big_f(f8(f7(f4(c4))), f10(c2))),
% 28.08/18.27 inference(symmetry,[status(thm)],[8146])).
% 28.08/18.27 tff(8148,plain,
% 28.08/18.27 (big_f(c2, c2) <=> big_f(f8(c1), f10(c1))),
% 28.08/18.27 inference(transitivity,[status(thm)],[8147, 8092, 8089])).
% 28.08/18.27 tff(8149,plain,
% 28.08/18.27 ((~big_f(c2, c2)) <=> (~big_f(f8(c1), f10(c1)))),
% 28.08/18.27 inference(monotonicity,[status(thm)],[8148])).
% 28.08/18.27 tff(8150,plain,
% 28.08/18.27 (~big_f(f8(c1), f10(c1))),
% 28.08/18.27 inference(modus_ponens,[status(thm)],[121, 8149])).
% 28.08/18.27 tff(8151,plain,
% 28.08/18.27 (~(c2 = f5(c2))),
% 28.08/18.27 inference(unit_resolution,[status(thm)],[8107, 8150, 17, 3, 1521])).
% 28.08/18.27 tff(8152,plain,
% 28.08/18.27 (~(f5(c2) = c2)),
% 28.08/18.27 inference(unit_resolution,[status(thm)],[8113, 8151])).
% 28.08/18.27 tff(8153,plain,
% 28.08/18.27 (big_f(c2, c2) <=> big_f(f8(f7(f4(c4))), f10(f7(f4(c4))))),
% 28.08/18.27 inference(transitivity,[status(thm)],[8147, 8092])).
% 28.08/18.27 tff(8154,plain,
% 28.08/18.27 ((~big_f(c2, c2)) <=> (~big_f(f8(f7(f4(c4))), f10(f7(f4(c4)))))),
% 28.08/18.27 inference(monotonicity,[status(thm)],[8153])).
% 28.08/18.27 tff(8155,plain,
% 28.08/18.27 (~big_f(f8(f7(f4(c4))), f10(f7(f4(c4))))),
% 28.08/18.27 inference(modus_ponens,[status(thm)],[121, 8154])).
% 28.08/18.27 tff(8156,plain,
% 28.08/18.27 (~(c1 = f5(c2))),
% 28.08/18.27 inference(unit_resolution,[status(thm)],[8133, 8155, 17, 333, 8118])).
% 28.08/18.27 tff(8157,plain,
% 28.08/18.27 (~(f5(c2) = c1)),
% 28.08/18.27 inference(unit_resolution,[status(thm)],[8139, 8156])).
% 28.08/18.27 tff(8158,plain,
% 28.08/18.27 ($false),
% 28.08/18.27 inference(unit_resolution,[status(thm)],[1547, 8157, 8152])).
% 28.08/18.27 tff(8159,plain,(big_f(f7(c2), c2) | (f7(c2) = c2) | big_f(f7(c2), c1) | (f10(c1) = c1) | big_f(c2, c2) | (~(f10(c2) = c2)) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.08/18.27 tff(8160,plain,
% 28.08/18.27 (f10(c1) = c1),
% 28.08/18.27 inference(unit_resolution,[status(thm)],[8159, 1521, 17, 333, 121, 122, 79])).
% 28.08/18.27 tff(8161,plain,
% 28.08/18.27 (f10(f7(f4(c4))) = c1),
% 28.08/18.27 inference(transitivity,[status(thm)],[8082, 8160])).
% 28.08/18.27 tff(8162,plain,
% 28.08/18.27 (big_f(c1, f10(f7(f4(c4)))) <=> big_f(f7(c2), c1)),
% 28.08/18.27 inference(monotonicity,[status(thm)],[125, 8161])).
% 28.08/18.27 tff(8163,plain,
% 28.08/18.27 (big_f(f7(c2), c1) <=> big_f(c1, f10(f7(f4(c4))))),
% 28.08/18.27 inference(symmetry,[status(thm)],[8162])).
% 28.08/18.27 tff(8164,plain,
% 28.08/18.27 (big_f(f7(c2), c1) <=> big_f(c1, f10(c1))),
% 28.08/18.27 inference(transitivity,[status(thm)],[8163, 8085])).
% 28.08/18.27 tff(8165,plain,
% 28.08/18.27 ((~big_f(f7(c2), c1)) <=> (~big_f(c1, f10(c1)))),
% 28.08/18.27 inference(monotonicity,[status(thm)],[8164])).
% 28.08/18.27 tff(8166,plain,
% 28.08/18.27 (~big_f(c1, f10(c1))),
% 28.08/18.27 inference(modus_ponens,[status(thm)],[333, 8165])).
% 28.08/18.27 tff(8167,plain,
% 28.08/18.27 (f10(f7(c2)) = f10(f7(f4(c4)))),
% 28.08/18.27 inference(monotonicity,[status(thm)],[81])).
% 28.08/18.27 tff(8168,plain,
% 28.08/18.27 (f10(f7(c2)) = c1),
% 28.08/18.27 inference(transitivity,[status(thm)],[8167, 8082, 3762])).
% 28.08/18.27 tff(8169,assumption,(f9(c1, c2) = c1), introduced(assumption)).
% 28.08/18.27 tff(8170,plain,
% 28.08/18.27 (f9(f7(c2), c2) = f9(c1, c2)),
% 28.08/18.27 inference(monotonicity,[status(thm)],[22])).
% 28.08/18.27 tff(8171,plain,
% 28.08/18.27 (f9(f7(c2), c2) = f7(c2)),
% 28.08/18.27 inference(transitivity,[status(thm)],[8170, 8169, 125])).
% 28.08/18.27 tff(8172,plain,
% 28.08/18.27 (big_f(f9(f7(c2), c2), f10(f7(c2))) <=> big_f(f7(c2), c1)),
% 28.08/18.27 inference(monotonicity,[status(thm)],[8171, 8168])).
% 28.08/18.27 tff(8173,plain,
% 28.08/18.27 (big_f(f7(c2), c1) <=> big_f(f9(f7(c2), c2), f10(f7(c2)))),
% 28.08/18.27 inference(symmetry,[status(thm)],[8172])).
% 28.08/18.27 tff(8174,plain,
% 28.08/18.27 ((~big_f(f7(c2), c1)) <=> (~big_f(f9(f7(c2), c2), f10(f7(c2))))),
% 28.08/18.27 inference(monotonicity,[status(thm)],[8173])).
% 28.08/18.27 tff(8175,plain,
% 28.08/18.27 (~big_f(f9(f7(c2), c2), f10(f7(c2)))),
% 28.08/18.27 inference(modus_ponens,[status(thm)],[333, 8174])).
% 28.08/18.27 tff(8176,plain,
% 28.08/18.27 ((f9(f7(c2), c2) = c2) <=> (f7(c2) = c2)),
% 28.08/18.27 inference(monotonicity,[status(thm)],[8171])).
% 28.08/18.27 tff(8177,plain,
% 28.08/18.27 ((f7(c2) = c2) <=> (f9(f7(c2), c2) = c2)),
% 28.08/18.27 inference(symmetry,[status(thm)],[8176])).
% 28.08/18.27 tff(8178,plain,
% 28.08/18.27 ((~(f7(c2) = c2)) <=> (~(f9(f7(c2), c2) = c2))),
% 28.08/18.27 inference(monotonicity,[status(thm)],[8177])).
% 28.08/18.27 tff(8179,plain,
% 28.08/18.27 (~(f9(f7(c2), c2) = c2)),
% 28.08/18.27 inference(modus_ponens,[status(thm)],[17, 8178])).
% 28.08/18.27 tff(8180,plain,
% 28.08/18.27 ((f10(f7(c2)) = f7(c2)) <=> (f10(f7(f4(c4))) = f7(f4(c4)))),
% 28.08/18.27 inference(monotonicity,[status(thm)],[8167, 81])).
% 28.08/18.27 tff(8181,plain,
% 28.08/18.27 ((f10(f7(f4(c4))) = f7(f4(c4))) <=> (f10(f7(c2)) = f7(c2))),
% 28.08/18.27 inference(symmetry,[status(thm)],[8180])).
% 28.08/18.27 tff(8182,plain,
% 28.08/18.27 ((f10(c1) = c1) <=> (f10(f7(c2)) = f7(c2))),
% 28.08/18.28 inference(transitivity,[status(thm)],[8116, 8181])).
% 28.08/18.28 tff(8183,plain,
% 28.08/18.28 (f10(f7(c2)) = f7(c2)),
% 28.08/18.28 inference(modus_ponens,[status(thm)],[3762, 8182])).
% 28.08/18.28 tff(8184,plain,
% 28.08/18.28 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (~(f10(f7(c2)) = f7(c2))) | big_f(f9(f7(c2), c2), f10(f7(c2))) | (f9(f7(c2), c2) = c2))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (~(f10(f7(c2)) = f7(c2))) | big_f(f9(f7(c2), c2), f10(f7(c2))) | (f9(f7(c2), c2) = c2))),
% 28.08/18.28 inference(rewrite,[status(thm)],[])).
% 28.08/18.28 tff(8185,plain,
% 28.08/18.28 (((~(f10(f7(c2)) = f7(c2))) | (f9(f7(c2), c2) = c2) | big_f(f9(f7(c2), c2), f10(f7(c2))) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(c2 = f5(c2)))) <=> ((f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (~(f10(f7(c2)) = f7(c2))) | big_f(f9(f7(c2), c2), f10(f7(c2))) | (f9(f7(c2), c2) = c2))),
% 28.08/18.28 inference(rewrite,[status(thm)],[])).
% 28.08/18.28 tff(8186,plain,
% 28.08/18.28 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(f7(c2)) = f7(c2))) | (f9(f7(c2), c2) = c2) | big_f(f9(f7(c2), c2), f10(f7(c2))) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(c2 = f5(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (~(f10(f7(c2)) = f7(c2))) | big_f(f9(f7(c2), c2), f10(f7(c2))) | (f9(f7(c2), c2) = c2)))),
% 28.08/18.28 inference(monotonicity,[status(thm)],[8185])).
% 28.08/18.28 tff(8187,plain,
% 28.08/18.28 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(f7(c2)) = f7(c2))) | (f9(f7(c2), c2) = c2) | big_f(f9(f7(c2), c2), f10(f7(c2))) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(c2 = f5(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (~(f10(f7(c2)) = f7(c2))) | big_f(f9(f7(c2), c2), f10(f7(c2))) | (f9(f7(c2), c2) = c2))),
% 28.08/18.28 inference(transitivity,[status(thm)],[8186, 8184])).
% 28.08/18.28 tff(8188,plain,
% 28.08/18.28 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(f7(c2)) = f7(c2))) | (f9(f7(c2), c2) = c2) | big_f(f9(f7(c2), c2), f10(f7(c2))) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(c2 = f5(c2))))),
% 28.08/18.28 inference(quant_inst,[status(thm)],[])).
% 28.08/18.28 tff(8189,plain,
% 28.08/18.28 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (~(f10(f7(c2)) = f7(c2))) | big_f(f9(f7(c2), c2), f10(f7(c2))) | (f9(f7(c2), c2) = c2)),
% 28.08/18.28 inference(modus_ponens,[status(thm)],[8188, 8187])).
% 28.08/18.28 tff(8190,plain,
% 28.08/18.28 (big_f(f9(f7(c2), c2), f10(f7(c2))) | (f9(f7(c2), c2) = c2)),
% 28.08/18.28 inference(unit_resolution,[status(thm)],[8189, 267, 17, 5124, 1521, 8183])).
% 28.08/18.28 tff(8191,plain,
% 28.08/18.28 ($false),
% 28.08/18.28 inference(unit_resolution,[status(thm)],[8190, 8179, 8175])).
% 28.08/18.28 tff(8192,plain,((~(f9(c1, c2) = c1)) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | big_f(f7(c2), c1) | (~(f10(c1) = c1)) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.08/18.28 tff(8193,plain,
% 28.08/18.28 (~(f9(c1, c2) = c1)),
% 28.08/18.28 inference(unit_resolution,[status(thm)],[8192, 5124, 17, 1521, 333, 3762, 79])).
% 28.08/18.28 tff(8194,plain,
% 28.08/18.28 (f9(c1, c2) = c2),
% 28.08/18.28 inference(unit_resolution,[status(thm)],[3791, 8193])).
% 28.08/18.28 tff(8195,plain,
% 28.08/18.28 (big_f(f9(c1, c2), f10(c1)) <=> big_f(c2, c1)),
% 28.08/18.28 inference(monotonicity,[status(thm)],[8194, 3762])).
% 28.08/18.28 tff(8196,plain,
% 28.08/18.28 (big_f(c2, c1) <=> big_f(f9(c1, c2), f10(c1))),
% 28.08/18.28 inference(symmetry,[status(thm)],[8195])).
% 28.08/18.28 tff(8197,plain,
% 28.08/18.28 (big_f(f9(c1, c2), f10(c1))),
% 28.08/18.28 inference(modus_ponens,[status(thm)],[348, 8196])).
% 28.08/18.28 tff(8198,plain,
% 28.08/18.28 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (~(f10(c1) = c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (~(f10(c1) = c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2)))),
% 28.08/18.28 inference(rewrite,[status(thm)],[])).
% 28.08/18.28 tff(8199,plain,
% 28.08/18.28 (((~(f10(c1) = c1)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(f9(c1, c2) = c2)) | (~big_f(f9(c1, c2), f10(c1))) | (~(c2 = f5(c2)))) <=> ((f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (~(f10(c1) = c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2)))),
% 28.08/18.28 inference(rewrite,[status(thm)],[])).
% 28.08/18.28 tff(8200,plain,
% 28.08/18.28 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(f9(c1, c2) = c2)) | (~big_f(f9(c1, c2), f10(c1))) | (~(c2 = f5(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (~(f10(c1) = c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2))))),
% 28.08/18.28 inference(monotonicity,[status(thm)],[8199])).
% 28.08/18.28 tff(8201,plain,
% 28.08/18.28 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(f9(c1, c2) = c2)) | (~big_f(f9(c1, c2), f10(c1))) | (~(c2 = f5(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (~(f10(c1) = c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2)))),
% 28.08/18.28 inference(transitivity,[status(thm)],[8200, 8198])).
% 28.08/18.28 tff(8202,plain,
% 28.08/18.28 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(f9(c1, c2) = c2)) | (~big_f(f9(c1, c2), f10(c1))) | (~(c2 = f5(c2))))),
% 28.08/18.28 inference(quant_inst,[status(thm)],[])).
% 28.08/18.28 tff(8203,plain,
% 28.08/18.28 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (~(f10(c1) = c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2))),
% 28.08/18.28 inference(modus_ponens,[status(thm)],[8202, 8201])).
% 28.08/18.28 tff(8204,plain,
% 28.08/18.28 ((f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (~(f10(c1) = c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2))),
% 28.08/18.28 inference(unit_resolution,[status(thm)],[8203, 783])).
% 28.08/18.28 tff(8205,plain,
% 28.08/18.28 (~big_f(f9(c1, c2), f10(c1))),
% 28.08/18.28 inference(unit_resolution,[status(thm)],[8204, 8194, 17, 1521, 3762, 5124])).
% 28.08/18.28 tff(8206,plain,
% 28.08/18.28 ($false),
% 28.08/18.28 inference(unit_resolution,[status(thm)],[8205, 8197])).
% 28.08/18.28 tff(8207,plain,((~(c2 = f5(c2))) | (~big_f(c2, c1)) | (~(f10(c1) = c1)) | (f7(c2) = c2) | big_f(f7(c2), c2) | big_f(f7(c2), c1) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.08/18.28 tff(8208,plain,
% 28.08/18.28 (~(c2 = f5(c2))),
% 28.08/18.28 inference(unit_resolution,[status(thm)],[8207, 348, 3762, 17, 1521, 333, 79])).
% 28.08/18.28 tff(8209,plain,
% 28.08/18.28 (~(f5(c2) = c2)),
% 28.08/18.28 inference(unit_resolution,[status(thm)],[8113, 8208])).
% 28.08/18.28 tff(8210,plain,
% 28.08/18.28 (f5(c2) = c1),
% 28.08/18.28 inference(unit_resolution,[status(thm)],[1547, 8209])).
% 28.08/18.28 tff(8211,plain,
% 28.08/18.28 ((~big_f(f7(c2), c1)) <=> (~big_f(f7(c2), f7(c2)))),
% 28.08/18.28 inference(monotonicity,[status(thm)],[8076])).
% 28.08/18.28 tff(8212,plain,
% 28.08/18.28 (~big_f(f7(c2), f7(c2))),
% 28.08/18.28 inference(modus_ponens,[status(thm)],[333, 8211])).
% 28.08/18.28 tff(8213,plain,
% 28.08/18.28 (f9(f7(c2), c2) = c2),
% 28.08/18.28 inference(transitivity,[status(thm)],[8170, 3764])).
% 28.08/18.28 tff(8214,plain,
% 28.08/18.28 (big_f(f9(f7(c2), c2), f10(f7(c2))) <=> big_f(c2, c1)),
% 28.08/18.28 inference(monotonicity,[status(thm)],[8213, 8168])).
% 28.08/18.28 tff(8215,plain,
% 28.08/18.28 (big_f(c2, c1) <=> big_f(f9(f7(c2), c2), f10(f7(c2)))),
% 28.08/18.28 inference(symmetry,[status(thm)],[8214])).
% 28.08/18.28 tff(8216,plain,
% 28.08/18.28 (big_f(f9(f7(c2), c2), f10(f7(c2)))),
% 28.08/18.28 inference(modus_ponens,[status(thm)],[348, 8215])).
% 28.08/18.28 tff(8217,plain,
% 28.08/18.28 (f7(c2) = f5(c2)),
% 28.08/18.28 inference(transitivity,[status(thm)],[22, 1570])).
% 28.08/18.28 tff(8218,assumption,(~big_f(f7(c2), f7(c2))), introduced(assumption)).
% 28.08/18.28 tff(8219,plain,
% 28.08/18.28 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((f7(c2) = c2) | (~(f7(c2) = f5(c2))) | big_f(f7(c2), f7(c2)) | (~(f10(f7(c2)) = f7(c2))) | (~(f9(f7(c2), c2) = c2)) | (~big_f(f9(f7(c2), c2), f10(f7(c2)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (f7(c2) = c2) | (~(f7(c2) = f5(c2))) | big_f(f7(c2), f7(c2)) | (~(f10(f7(c2)) = f7(c2))) | (~(f9(f7(c2), c2) = c2)) | (~big_f(f9(f7(c2), c2), f10(f7(c2)))))),
% 28.08/18.28 inference(rewrite,[status(thm)],[])).
% 28.08/18.28 tff(8220,plain,
% 28.08/18.28 (((~(f10(f7(c2)) = f7(c2))) | (f7(c2) = c2) | big_f(f7(c2), f7(c2)) | (~(f9(f7(c2), c2) = c2)) | (~big_f(f9(f7(c2), c2), f10(f7(c2)))) | (~(f7(c2) = f5(c2)))) <=> ((f7(c2) = c2) | (~(f7(c2) = f5(c2))) | big_f(f7(c2), f7(c2)) | (~(f10(f7(c2)) = f7(c2))) | (~(f9(f7(c2), c2) = c2)) | (~big_f(f9(f7(c2), c2), f10(f7(c2)))))),
% 28.08/18.28 inference(rewrite,[status(thm)],[])).
% 28.08/18.28 tff(8221,plain,
% 28.08/18.28 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(f7(c2)) = f7(c2))) | (f7(c2) = c2) | big_f(f7(c2), f7(c2)) | (~(f9(f7(c2), c2) = c2)) | (~big_f(f9(f7(c2), c2), f10(f7(c2)))) | (~(f7(c2) = f5(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((f7(c2) = c2) | (~(f7(c2) = f5(c2))) | big_f(f7(c2), f7(c2)) | (~(f10(f7(c2)) = f7(c2))) | (~(f9(f7(c2), c2) = c2)) | (~big_f(f9(f7(c2), c2), f10(f7(c2))))))),
% 28.08/18.28 inference(monotonicity,[status(thm)],[8220])).
% 28.08/18.28 tff(8222,plain,
% 28.08/18.28 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(f7(c2)) = f7(c2))) | (f7(c2) = c2) | big_f(f7(c2), f7(c2)) | (~(f9(f7(c2), c2) = c2)) | (~big_f(f9(f7(c2), c2), f10(f7(c2)))) | (~(f7(c2) = f5(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (f7(c2) = c2) | (~(f7(c2) = f5(c2))) | big_f(f7(c2), f7(c2)) | (~(f10(f7(c2)) = f7(c2))) | (~(f9(f7(c2), c2) = c2)) | (~big_f(f9(f7(c2), c2), f10(f7(c2)))))),
% 28.08/18.28 inference(transitivity,[status(thm)],[8221, 8219])).
% 28.08/18.28 tff(8223,plain,
% 28.08/18.28 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(f7(c2)) = f7(c2))) | (f7(c2) = c2) | big_f(f7(c2), f7(c2)) | (~(f9(f7(c2), c2) = c2)) | (~big_f(f9(f7(c2), c2), f10(f7(c2)))) | (~(f7(c2) = f5(c2))))),
% 28.08/18.28 inference(quant_inst,[status(thm)],[])).
% 28.08/18.28 tff(8224,plain,
% 28.08/18.28 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (f7(c2) = c2) | (~(f7(c2) = f5(c2))) | big_f(f7(c2), f7(c2)) | (~(f10(f7(c2)) = f7(c2))) | (~(f9(f7(c2), c2) = c2)) | (~big_f(f9(f7(c2), c2), f10(f7(c2))))),
% 28.08/18.28 inference(modus_ponens,[status(thm)],[8223, 8222])).
% 28.08/18.28 tff(8225,plain,
% 28.08/18.28 ((~(f9(f7(c2), c2) = c2)) | (~big_f(f9(f7(c2), c2), f10(f7(c2))))),
% 28.08/18.28 inference(unit_resolution,[status(thm)],[8224, 783, 17, 8183, 8218, 8217])).
% 28.08/18.28 tff(8226,plain,
% 28.08/18.28 ($false),
% 28.08/18.28 inference(unit_resolution,[status(thm)],[8225, 8216, 8213])).
% 28.08/18.28 tff(8227,plain,((~(f9(c1, c2) = c2)) | (f7(c2) = c2) | big_f(f7(c2), f7(c2)) | (~big_f(c2, c1)) | (~(f10(c1) = c1)) | (~(f4(c4) = c2)) | (~(f5(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.08/18.28 tff(8228,plain,
% 28.08/18.28 (~(f9(c1, c2) = c2)),
% 28.08/18.28 inference(unit_resolution,[status(thm)],[8227, 8212, 17, 348, 3762, 79, 8210])).
% 28.08/18.28 tff(8229,plain,
% 28.08/18.28 (f9(c1, c2) = c1),
% 28.08/18.28 inference(unit_resolution,[status(thm)],[3791, 8228])).
% 28.08/18.28 tff(8230,plain,
% 28.08/18.28 (f9(c1, c2) = f7(c2)),
% 28.08/18.28 inference(transitivity,[status(thm)],[8229, 125])).
% 28.08/18.28 tff(8231,plain,
% 28.08/18.28 (big_f(f9(c1, c2), f10(c1)) <=> big_f(f7(c2), c1)),
% 28.08/18.28 inference(monotonicity,[status(thm)],[8230, 3762])).
% 28.08/18.28 tff(8232,plain,
% 28.08/18.28 (big_f(f7(c2), c1) <=> big_f(f9(c1, c2), f10(c1))),
% 28.08/18.28 inference(symmetry,[status(thm)],[8231])).
% 28.08/18.28 tff(8233,plain,
% 28.08/18.28 ((~big_f(f7(c2), c1)) <=> (~big_f(f9(c1, c2), f10(c1)))),
% 28.08/18.28 inference(monotonicity,[status(thm)],[8232])).
% 28.08/18.28 tff(8234,plain,
% 28.08/18.28 (~big_f(f9(c1, c2), f10(c1))),
% 28.08/18.28 inference(modus_ponens,[status(thm)],[333, 8233])).
% 28.08/18.28 tff(8235,plain,
% 28.08/18.28 (c1 = f5(c2)),
% 28.08/18.28 inference(unit_resolution,[status(thm)],[8139, 8210])).
% 28.08/18.28 tff(8236,plain,
% 28.08/18.28 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((f7(c2) = c2) | (~(f10(c1) = c1)) | (~(c1 = f5(c2))) | big_f(f7(c2), c1) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (f7(c2) = c2) | (~(f10(c1) = c1)) | (~(c1 = f5(c2))) | big_f(f7(c2), c1) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)))),
% 28.08/18.28 inference(rewrite,[status(thm)],[])).
% 28.08/18.28 tff(8237,plain,
% 28.08/18.28 (((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (f7(c2) = c2) | big_f(f7(c2), c1) | (~(c1 = f5(c2)))) <=> ((f7(c2) = c2) | (~(f10(c1) = c1)) | (~(c1 = f5(c2))) | big_f(f7(c2), c1) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)))),
% 28.08/18.28 inference(rewrite,[status(thm)],[])).
% 28.08/18.28 tff(8238,plain,
% 28.08/18.28 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (f7(c2) = c2) | big_f(f7(c2), c1) | (~(c1 = f5(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((f7(c2) = c2) | (~(f10(c1) = c1)) | (~(c1 = f5(c2))) | big_f(f7(c2), c1) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1))))),
% 28.08/18.28 inference(monotonicity,[status(thm)],[8237])).
% 28.08/18.28 tff(8239,plain,
% 28.08/18.28 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (f7(c2) = c2) | big_f(f7(c2), c1) | (~(c1 = f5(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (f7(c2) = c2) | (~(f10(c1) = c1)) | (~(c1 = f5(c2))) | big_f(f7(c2), c1) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)))),
% 28.08/18.28 inference(transitivity,[status(thm)],[8238, 8236])).
% 28.08/18.28 tff(8240,plain,
% 28.08/18.28 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (f7(c2) = c2) | big_f(f7(c2), c1) | (~(c1 = f5(c2))))),
% 28.08/18.28 inference(quant_inst,[status(thm)],[])).
% 28.08/18.28 tff(8241,plain,
% 28.08/18.28 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (f7(c2) = c2) | (~(f10(c1) = c1)) | (~(c1 = f5(c2))) | big_f(f7(c2), c1) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1))),
% 28.08/18.28 inference(modus_ponens,[status(thm)],[8240, 8239])).
% 28.08/18.28 tff(8242,plain,
% 28.08/18.28 ((f7(c2) = c2) | (~(f10(c1) = c1)) | (~(c1 = f5(c2))) | big_f(f7(c2), c1) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1))),
% 28.08/18.28 inference(unit_resolution,[status(thm)],[8241, 267])).
% 28.08/18.28 tff(8243,plain,
% 28.08/18.28 (big_f(f9(c1, c2), f10(c1))),
% 28.08/18.28 inference(unit_resolution,[status(thm)],[8242, 8228, 17, 333, 3762, 8235])).
% 28.08/18.28 tff(8244,plain,
% 28.08/18.28 ($false),
% 28.08/18.28 inference(unit_resolution,[status(thm)],[8243, 8234])).
% 28.08/18.28 tff(8245,plain,((~big_f(c2, c1)) | big_f(f7(c2), c1) | (~(f10(c1) = c1)) | (f7(c2) = c2) | (~(f4(c4) = c2)) | big_f(f7(c2), c2)), inference(lemma,lemma(discharge,[]))).
% 28.08/18.28 tff(8246,plain,
% 28.08/18.28 (~big_f(c2, c1)),
% 28.08/18.28 inference(unit_resolution,[status(thm)],[8245, 8160, 333, 17, 79, 1521])).
% 28.08/18.28 tff(8247,plain,
% 28.08/18.28 (~big_f(f4(c4), c4)),
% 28.08/18.28 inference(unit_resolution,[status(thm)],[5036, 8246, 79, 121])).
% 28.08/18.28 tff(8248,plain,
% 28.08/18.28 (big_f(c3, f2(c3))),
% 28.08/18.28 inference(unit_resolution,[status(thm)],[1315, 8247])).
% 28.08/18.28 tff(8249,plain,
% 28.08/18.28 (~(f2(c3) = c2)),
% 28.08/18.28 inference(unit_resolution,[status(thm)],[7831, 2274, 121, 67])).
% 28.08/18.28 tff(8250,plain,
% 28.08/18.28 (f2(c3) = c1),
% 28.08/18.28 inference(unit_resolution,[status(thm)],[1273, 8249])).
% 28.08/18.28 tff(8251,plain,
% 28.08/18.28 (big_f(c3, f2(c3)) <=> big_f(c2, c1)),
% 28.08/18.28 inference(monotonicity,[status(thm)],[67, 8250])).
% 28.08/18.28 tff(8252,plain,
% 28.08/18.28 (big_f(c2, c1) <=> big_f(c3, f2(c3))),
% 28.08/18.28 inference(symmetry,[status(thm)],[8251])).
% 28.08/18.28 tff(8253,plain,
% 28.08/18.28 ((~big_f(c2, c1)) <=> (~big_f(c3, f2(c3)))),
% 28.08/18.28 inference(monotonicity,[status(thm)],[8252])).
% 28.08/18.28 tff(8254,plain,
% 28.08/18.28 (~big_f(c3, f2(c3))),
% 28.08/18.28 inference(modus_ponens,[status(thm)],[2, 8253])).
% 28.08/18.28 tff(8255,plain,
% 28.08/18.28 ($false),
% 28.08/18.28 inference(unit_resolution,[status(thm)],[2274, 8254])).
% 28.08/18.28 tff(8256,plain,((~big_f(c3, f2(c3))) | big_f(c2, c1) | (~(c3 = c2)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 28.08/18.28 tff(8257,plain,
% 28.08/18.28 (~big_f(c3, f2(c3))),
% 28.08/18.28 inference(unit_resolution,[status(thm)],[8256, 2, 121, 67])).
% 28.08/18.28 tff(8258,plain,
% 28.08/18.28 ($false),
% 28.08/18.28 inference(unit_resolution,[status(thm)],[1315, 8257, 5577])).
% 28.08/18.28 tff(8259,plain,(big_f(c2, c1) | big_f(c2, c2) | (~(c3 = c2)) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.08/18.28 tff(8260,plain,
% 28.08/18.28 (~(c3 = c2)),
% 28.08/18.28 inference(unit_resolution,[status(thm)],[8259, 8246, 121, 79])).
% 28.08/18.28 tff(8261,plain,
% 28.08/18.28 (c3 = c1),
% 28.08/18.28 inference(unit_resolution,[status(thm)],[180, 8260])).
% 28.08/18.28 tff(8262,plain,
% 28.08/18.28 (f10(c1) = f2(c3)),
% 28.08/18.28 inference(transitivity,[status(thm)],[3762, 1367])).
% 28.08/18.28 tff(8263,plain,
% 28.08/18.28 (big_f(c1, f10(c1)) <=> big_f(c3, f2(c3))),
% 28.08/18.28 inference(monotonicity,[status(thm)],[5585, 8262])).
% 28.08/18.28 tff(8264,plain,
% 28.08/18.28 (big_f(c3, f2(c3)) <=> big_f(c1, f10(c1))),
% 28.08/18.28 inference(symmetry,[status(thm)],[8263])).
% 28.08/18.28 tff(8265,plain,
% 28.08/18.28 (big_f(c1, f10(c1))),
% 28.08/18.28 inference(modus_ponens,[status(thm)],[2274, 8264])).
% 28.08/18.28 tff(8266,plain,
% 28.08/18.28 ($false),
% 28.08/18.28 inference(unit_resolution,[status(thm)],[3030, 8265])).
% 28.08/18.28 tff(8267,plain,((~(f10(c1) = c1)) | big_f(c1, f10(c1)) | (~big_f(c3, f2(c3))) | (~(f2(c3) = c1)) | (~(c3 = c1))), inference(lemma,lemma(discharge,[]))).
% 28.08/18.28 tff(8268,plain,
% 28.08/18.28 (~(f2(c3) = c1)),
% 28.08/18.28 inference(unit_resolution,[status(thm)],[8267, 8261, 8248, 8160, 8166])).
% 28.08/18.28 tff(8269,plain,
% 28.08/18.28 (f2(c3) = c2),
% 28.08/18.28 inference(unit_resolution,[status(thm)],[1273, 8268])).
% 28.08/18.28 tff(8270,plain,
% 28.08/18.28 (c3 = f7(c2)),
% 28.08/18.28 inference(transitivity,[status(thm)],[8261, 125])).
% 28.08/18.28 tff(8271,plain,
% 28.08/18.28 (big_f(c3, f2(c3)) <=> big_f(f7(c2), c2)),
% 28.08/18.28 inference(monotonicity,[status(thm)],[8270, 8269])).
% 28.08/18.28 tff(8272,plain,
% 28.08/18.28 (big_f(f7(c2), c2) <=> big_f(c3, f2(c3))),
% 28.08/18.28 inference(symmetry,[status(thm)],[8271])).
% 28.08/18.28 tff(8273,plain,
% 28.08/18.28 ((~big_f(f7(c2), c2)) <=> (~big_f(c3, f2(c3)))),
% 28.08/18.28 inference(monotonicity,[status(thm)],[8272])).
% 28.08/18.28 tff(8274,plain,
% 28.08/18.28 (~big_f(c3, f2(c3))),
% 28.08/18.28 inference(modus_ponens,[status(thm)],[1521, 8273])).
% 28.08/18.28 tff(8275,plain,
% 28.08/18.28 ($false),
% 28.08/18.28 inference(unit_resolution,[status(thm)],[8248, 8274])).
% 28.08/18.28 tff(8276,plain,(big_f(f7(c2), c2) | big_f(c2, c2) | (~(f4(c4) = c2)) | big_f(f7(c2), c1) | (f7(c2) = c2) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.08/18.28 tff(8277,plain,
% 28.08/18.28 (big_f(f7(c2), c2)),
% 28.08/18.28 inference(unit_resolution,[status(thm)],[8276, 333, 79, 121, 17, 122])).
% 28.08/18.28 tff(8278,plain,
% 28.08/18.28 (f9(c2, c1) = c2),
% 28.08/18.28 inference(unit_resolution,[status(thm)],[3913, 1139])).
% 28.08/18.28 tff(8279,plain,
% 28.08/18.28 (big_f(f9(c2, c1), f10(c2)) <=> big_f(c2, c2)),
% 28.08/18.28 inference(monotonicity,[status(thm)],[8278, 122])).
% 28.08/18.28 tff(8280,plain,
% 28.08/18.28 (big_f(c2, c2) <=> big_f(f9(c2, c1), f10(c2))),
% 28.08/18.28 inference(symmetry,[status(thm)],[8279])).
% 28.08/18.28 tff(8281,plain,
% 28.08/18.28 ((~big_f(c2, c2)) <=> (~big_f(f9(c2, c1), f10(c2)))),
% 28.08/18.28 inference(monotonicity,[status(thm)],[8280])).
% 28.08/18.28 tff(8282,plain,
% 28.08/18.28 (~big_f(f9(c2, c1), f10(c2))),
% 28.08/18.28 inference(modus_ponens,[status(thm)],[121, 8281])).
% 28.08/18.28 tff(8283,plain,
% 28.08/18.28 (big_f(f7(c2), f6(c1, c2)) <=> big_f(f7(c2), c2)),
% 28.08/18.28 inference(monotonicity,[status(thm)],[36])).
% 28.08/18.28 tff(8284,plain,
% 28.08/18.28 (big_f(f7(c2), c2) <=> big_f(f7(c2), f6(c1, c2))),
% 28.08/18.28 inference(symmetry,[status(thm)],[8283])).
% 28.08/18.28 tff(8285,plain,
% 28.08/18.28 (big_f(f7(c2), f6(c1, c2))),
% 28.08/18.28 inference(modus_ponens,[status(thm)],[1180, 8284])).
% 28.08/18.28 tff(8286,plain,
% 28.08/18.28 (f7(c1) = f7(c2)),
% 28.08/18.28 inference(transitivity,[status(thm)],[4234, 342])).
% 28.08/18.28 tff(8287,plain,
% 28.08/18.28 (big_f(f7(c1), f6(c1, c2)) <=> big_f(f7(c2), f6(c1, c2))),
% 28.08/18.28 inference(monotonicity,[status(thm)],[8286])).
% 28.08/18.28 tff(8288,plain,
% 28.08/18.28 ((~big_f(f7(c1), f6(c1, c2))) <=> (~big_f(f7(c2), f6(c1, c2)))),
% 28.08/18.28 inference(monotonicity,[status(thm)],[8287])).
% 28.08/18.28 tff(8289,plain,
% 28.08/18.28 (~big_f(f7(c1), f6(c1, c2))),
% 28.08/18.28 inference(unit_resolution,[status(thm)],[5737, 36, 122, 4234, 1139, 731])).
% 28.08/18.28 tff(8290,plain,
% 28.08/18.28 (~big_f(f7(c2), f6(c1, c2))),
% 28.08/18.28 inference(modus_ponens,[status(thm)],[8289, 8288])).
% 28.08/18.28 tff(8291,plain,
% 28.08/18.28 ($false),
% 28.08/18.28 inference(unit_resolution,[status(thm)],[8290, 8285])).
% 28.08/18.28 tff(8292,plain,((~(f6(c1, c2) = c2)) | (~big_f(f7(c2), c2)) | (~(f7(c1) = c1)) | (~(f7(c2) = c1)) | (~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2))), inference(lemma,lemma(discharge,[]))).
% 28.08/18.28 tff(8293,plain,
% 28.08/18.28 (~(f6(c1, c2) = c2)),
% 28.08/18.28 inference(unit_resolution,[status(thm)],[8292, 1139, 4234, 22, 122, 1180, 8282])).
% 28.08/18.28 tff(8294,plain,
% 28.08/18.28 (f6(c1, c2) = c1),
% 28.08/18.28 inference(unit_resolution,[status(thm)],[48, 8293])).
% 28.08/18.28 tff(8295,plain,
% 28.08/18.28 (f6(f7(c2), c2) = f6(c1, c2)),
% 28.08/18.28 inference(monotonicity,[status(thm)],[22])).
% 28.08/18.28 tff(8296,plain,
% 28.08/18.28 (f6(f7(c2), c2) = c1),
% 28.08/18.28 inference(transitivity,[status(thm)],[8295, 8294])).
% 28.08/18.28 tff(8297,plain,
% 28.08/18.28 (f7(f7(c2)) = f7(c2)),
% 28.08/18.28 inference(transitivity,[status(thm)],[8077, 4234, 125])).
% 28.08/18.28 tff(8298,plain,
% 28.08/18.28 (big_f(f7(f7(c2)), f6(f7(c2), c2)) <=> big_f(f7(c2), c1)),
% 28.08/18.28 inference(monotonicity,[status(thm)],[8297, 8296])).
% 28.08/18.28 tff(8299,plain,
% 28.08/18.28 (big_f(f7(c2), c1) <=> big_f(f7(f7(c2)), f6(f7(c2), c2))),
% 28.08/18.28 inference(symmetry,[status(thm)],[8298])).
% 28.08/18.28 tff(8300,plain,
% 28.08/18.28 ((~big_f(f7(c2), c1)) <=> (~big_f(f7(f7(c2)), f6(f7(c2), c2)))),
% 28.08/18.28 inference(monotonicity,[status(thm)],[8299])).
% 28.08/18.28 tff(8301,plain,
% 28.08/18.28 (~big_f(f7(f7(c2)), f6(f7(c2), c2))),
% 28.08/18.28 inference(modus_ponens,[status(thm)],[333, 8300])).
% 28.08/18.28 tff(8302,plain,
% 28.08/18.28 (f6(f7(c2), c2) = f7(c2)),
% 28.08/18.28 inference(transitivity,[status(thm)],[8295, 8294, 125])).
% 28.08/18.28 tff(8303,plain,
% 28.08/18.28 ((f6(f7(c2), c2) = c2) <=> (f7(c2) = c2)),
% 28.08/18.28 inference(monotonicity,[status(thm)],[8302])).
% 28.08/18.28 tff(8304,plain,
% 28.08/18.28 ((f7(c2) = c2) <=> (f6(f7(c2), c2) = c2)),
% 28.08/18.28 inference(symmetry,[status(thm)],[8303])).
% 28.08/18.28 tff(8305,plain,
% 28.08/18.28 ((~(f7(c2) = c2)) <=> (~(f6(f7(c2), c2) = c2))),
% 28.08/18.28 inference(monotonicity,[status(thm)],[8304])).
% 28.08/18.28 tff(8306,plain,
% 28.08/18.28 (~(f6(f7(c2), c2) = c2)),
% 28.08/18.28 inference(modus_ponens,[status(thm)],[17, 8305])).
% 28.08/18.29 tff(8307,plain,
% 28.08/18.29 (~(f9(c2, f7(c2)) = f7(c2))),
% 28.08/18.29 inference(modus_ponens,[status(thm)],[1139, 8074])).
% 28.08/18.29 tff(8308,plain,
% 28.08/18.29 (big_f(f9(c2, f7(c2)), f10(c2)) <=> big_f(f9(c2, c1), f10(c2))),
% 28.08/18.29 inference(monotonicity,[status(thm)],[8071])).
% 28.08/18.29 tff(8309,plain,
% 28.08/18.29 (big_f(f9(c2, c1), f10(c2)) <=> big_f(f9(c2, f7(c2)), f10(c2))),
% 28.08/18.29 inference(symmetry,[status(thm)],[8308])).
% 28.08/18.29 tff(8310,plain,
% 28.08/18.29 (big_f(c2, c2) <=> big_f(f9(c2, f7(c2)), f10(c2))),
% 28.08/18.29 inference(transitivity,[status(thm)],[8280, 8309])).
% 28.08/18.29 tff(8311,plain,
% 28.08/18.29 ((~big_f(c2, c2)) <=> (~big_f(f9(c2, f7(c2)), f10(c2)))),
% 28.08/18.29 inference(monotonicity,[status(thm)],[8310])).
% 28.08/18.29 tff(8312,plain,
% 28.08/18.29 (~big_f(f9(c2, f7(c2)), f10(c2))),
% 28.08/18.29 inference(modus_ponens,[status(thm)],[121, 8311])).
% 28.08/18.29 tff(8313,plain,
% 28.08/18.29 (f7(c1) = f7(f7(c2))),
% 28.08/18.29 inference(symmetry,[status(thm)],[8077])).
% 28.08/18.29 tff(8314,plain,
% 28.08/18.29 ((f7(c1) = c1) <=> (f7(f7(c2)) = f7(c2))),
% 28.08/18.29 inference(monotonicity,[status(thm)],[8313, 125])).
% 28.08/18.29 tff(8315,plain,
% 28.08/18.29 (f7(f7(c2)) = f7(c2)),
% 28.08/18.29 inference(modus_ponens,[status(thm)],[4234, 8314])).
% 28.08/18.29 tff(8316,plain,
% 28.08/18.29 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | big_f(f7(f7(c2)), f6(f7(c2), c2)) | (f6(f7(c2), c2) = c2))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | big_f(f7(f7(c2)), f6(f7(c2), c2)) | (f6(f7(c2), c2) = c2))),
% 28.08/18.29 inference(rewrite,[status(thm)],[])).
% 28.08/18.29 tff(8317,plain,
% 28.08/18.29 (((~(f10(c2) = c2)) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (~(f7(f7(c2)) = f7(c2))) | (f6(f7(c2), c2) = c2) | big_f(f7(f7(c2)), f6(f7(c2), c2))) <=> ((~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | big_f(f7(f7(c2)), f6(f7(c2), c2)) | (f6(f7(c2), c2) = c2))),
% 28.08/18.29 inference(rewrite,[status(thm)],[])).
% 28.08/18.29 tff(8318,plain,
% 28.08/18.29 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (~(f7(f7(c2)) = f7(c2))) | (f6(f7(c2), c2) = c2) | big_f(f7(f7(c2)), f6(f7(c2), c2)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | big_f(f7(f7(c2)), f6(f7(c2), c2)) | (f6(f7(c2), c2) = c2)))),
% 28.08/18.29 inference(monotonicity,[status(thm)],[8317])).
% 28.08/18.29 tff(8319,plain,
% 28.08/18.29 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (~(f7(f7(c2)) = f7(c2))) | (f6(f7(c2), c2) = c2) | big_f(f7(f7(c2)), f6(f7(c2), c2)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | big_f(f7(f7(c2)), f6(f7(c2), c2)) | (f6(f7(c2), c2) = c2))),
% 28.08/18.29 inference(transitivity,[status(thm)],[8318, 8316])).
% 28.08/18.29 tff(8320,plain,
% 28.08/18.29 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (~(f7(f7(c2)) = f7(c2))) | (f6(f7(c2), c2) = c2) | big_f(f7(f7(c2)), f6(f7(c2), c2)))),
% 28.08/18.29 inference(quant_inst,[status(thm)],[])).
% 28.08/18.29 tff(8321,plain,
% 28.08/18.29 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | big_f(f7(f7(c2)), f6(f7(c2), c2)) | (f6(f7(c2), c2) = c2)),
% 28.08/18.29 inference(modus_ponens,[status(thm)],[8320, 8319])).
% 28.08/18.29 tff(8322,plain,
% 28.08/18.29 (big_f(f7(f7(c2)), f6(f7(c2), c2)) | (f6(f7(c2), c2) = c2)),
% 28.08/18.29 inference(unit_resolution,[status(thm)],[8321, 2492, 122, 8315, 8312, 8307])).
% 28.08/18.29 tff(8323,plain,
% 28.08/18.29 ($false),
% 28.08/18.29 inference(unit_resolution,[status(thm)],[8322, 8306, 8301])).
% 28.08/18.29 tff(8324,plain,((f9(c2, c1) = c1) | (~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f7(c2), c1) | (~(f7(c1) = c1)) | (~big_f(f7(c2), c2)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 28.08/18.29 tff(8325,plain,
% 28.08/18.29 (f9(c2, c1) = c1),
% 28.08/18.29 inference(unit_resolution,[status(thm)],[8324, 333, 17, 122, 4234, 8277, 121])).
% 28.08/18.29 tff(8326,plain,
% 28.08/18.29 (f9(c2, f7(c2)) = f7(c2)),
% 28.08/18.29 inference(modus_ponens,[status(thm)],[8325, 8073])).
% 28.08/18.29 tff(8327,plain,
% 28.08/18.29 (f9(c2, c1) = f7(c2)),
% 28.08/18.29 inference(transitivity,[status(thm)],[8325, 125])).
% 28.08/18.29 tff(8328,plain,
% 28.08/18.29 (big_f(f9(c2, c1), f10(c2)) <=> big_f(f7(c2), c2)),
% 28.08/18.29 inference(monotonicity,[status(thm)],[8327, 122])).
% 28.08/18.29 tff(8329,plain,
% 28.08/18.29 (big_f(f7(c2), c2) <=> big_f(f9(c2, c1), f10(c2))),
% 28.08/18.29 inference(symmetry,[status(thm)],[8328])).
% 28.08/18.29 tff(8330,plain,
% 28.08/18.29 (big_f(f7(c2), c2) <=> big_f(f9(c2, f7(c2)), f10(c2))),
% 28.08/18.29 inference(transitivity,[status(thm)],[8329, 8309])).
% 28.08/18.29 tff(8331,plain,
% 28.08/18.29 (big_f(f9(c2, f7(c2)), f10(c2))),
% 28.08/18.29 inference(modus_ponens,[status(thm)],[8277, 8330])).
% 28.08/18.29 tff(8332,plain,
% 28.08/18.29 (f6(f7(c2), c2) = c1),
% 28.08/18.29 inference(transitivity,[status(thm)],[8295, 6931])).
% 28.08/18.29 tff(8333,plain,
% 28.08/18.29 (big_f(f7(f7(c2)), f6(f7(c2), c2)) <=> big_f(f7(c2), c1)),
% 28.08/18.29 inference(monotonicity,[status(thm)],[8297, 8332])).
% 28.08/18.29 tff(8334,plain,
% 28.08/18.29 (big_f(f7(c2), c1) <=> big_f(f7(f7(c2)), f6(f7(c2), c2))),
% 28.08/18.29 inference(symmetry,[status(thm)],[8333])).
% 28.08/18.29 tff(8335,plain,
% 28.08/18.29 ((~big_f(f7(c2), c1)) <=> (~big_f(f7(f7(c2)), f6(f7(c2), c2)))),
% 28.08/18.29 inference(monotonicity,[status(thm)],[8334])).
% 28.08/18.29 tff(8336,plain,
% 28.08/18.29 (~big_f(f7(f7(c2)), f6(f7(c2), c2))),
% 28.08/18.29 inference(modus_ponens,[status(thm)],[333, 8335])).
% 28.08/18.29 tff(8337,plain,
% 28.08/18.29 (f6(f7(c2), c2) = f7(c2)),
% 28.08/18.29 inference(transitivity,[status(thm)],[8295, 6931, 125])).
% 28.08/18.29 tff(8338,plain,
% 28.08/18.29 ((f6(f7(c2), c2) = c2) <=> (f7(c2) = c2)),
% 28.08/18.29 inference(monotonicity,[status(thm)],[8337])).
% 28.08/18.29 tff(8339,plain,
% 28.08/18.29 ((f7(c2) = c2) <=> (f6(f7(c2), c2) = c2)),
% 28.08/18.29 inference(symmetry,[status(thm)],[8338])).
% 28.08/18.29 tff(8340,plain,
% 28.08/18.29 ((~(f7(c2) = c2)) <=> (~(f6(f7(c2), c2) = c2))),
% 28.08/18.29 inference(monotonicity,[status(thm)],[8339])).
% 28.08/18.29 tff(8341,plain,
% 28.08/18.29 (~(f6(f7(c2), c2) = c2)),
% 28.08/18.29 inference(modus_ponens,[status(thm)],[17, 8340])).
% 28.08/18.29 tff(8342,assumption,(f9(c2, f7(c2)) = f7(c2)), introduced(assumption)).
% 28.08/18.29 tff(8343,assumption,(big_f(f9(c2, f7(c2)), f10(c2))), introduced(assumption)).
% 28.08/18.29 tff(8344,plain,
% 28.08/18.29 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2))) | big_f(f7(f7(c2)), f6(f7(c2), c2)) | (f6(f7(c2), c2) = c2))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2))) | big_f(f7(f7(c2)), f6(f7(c2), c2)) | (f6(f7(c2), c2) = c2))),
% 28.08/18.29 inference(rewrite,[status(thm)],[])).
% 28.08/18.29 tff(8345,plain,
% 28.08/18.29 (((~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (f6(f7(c2), c2) = c2) | big_f(f7(f7(c2)), f6(f7(c2), c2)) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2)))) <=> ((~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2))) | big_f(f7(f7(c2)), f6(f7(c2), c2)) | (f6(f7(c2), c2) = c2))),
% 28.08/18.29 inference(rewrite,[status(thm)],[])).
% 28.08/18.29 tff(8346,plain,
% 28.08/18.29 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (f6(f7(c2), c2) = c2) | big_f(f7(f7(c2)), f6(f7(c2), c2)) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2))) | big_f(f7(f7(c2)), f6(f7(c2), c2)) | (f6(f7(c2), c2) = c2)))),
% 28.08/18.29 inference(monotonicity,[status(thm)],[8345])).
% 28.08/18.29 tff(8347,plain,
% 28.08/18.29 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (f6(f7(c2), c2) = c2) | big_f(f7(f7(c2)), f6(f7(c2), c2)) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2))) | big_f(f7(f7(c2)), f6(f7(c2), c2)) | (f6(f7(c2), c2) = c2))),
% 28.08/18.29 inference(transitivity,[status(thm)],[8346, 8344])).
% 28.08/18.29 tff(8348,plain,
% 28.08/18.29 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (f6(f7(c2), c2) = c2) | big_f(f7(f7(c2)), f6(f7(c2), c2)) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2))))),
% 28.08/18.29 inference(quant_inst,[status(thm)],[])).
% 28.08/18.29 tff(8349,plain,
% 28.08/18.29 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2))) | big_f(f7(f7(c2)), f6(f7(c2), c2)) | (f6(f7(c2), c2) = c2)),
% 28.08/18.29 inference(modus_ponens,[status(thm)],[8348, 8347])).
% 28.08/18.29 tff(8350,plain,
% 28.08/18.29 (big_f(f7(f7(c2)), f6(f7(c2), c2)) | (f6(f7(c2), c2) = c2)),
% 28.08/18.29 inference(unit_resolution,[status(thm)],[8349, 2409, 122, 8315, 8343, 8342])).
% 28.08/18.29 tff(8351,plain,
% 28.08/18.29 ($false),
% 28.08/18.29 inference(unit_resolution,[status(thm)],[8350, 8341, 8336])).
% 28.08/18.29 tff(8352,plain,((~(f6(c1, c2) = c1)) | (~(f10(c2) = c2)) | (~big_f(f9(c2, f7(c2)), f10(c2))) | (~(f9(c2, f7(c2)) = f7(c2))) | (f7(c2) = c2) | big_f(f7(c2), c1) | (~(f7(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.08/18.29 tff(8353,plain,
% 28.08/18.29 (~(f6(c1, c2) = c1)),
% 28.08/18.29 inference(unit_resolution,[status(thm)],[8352, 8331, 122, 8326, 17, 333, 4234])).
% 28.08/18.29 tff(8354,plain,
% 28.08/18.29 (f6(c1, c2) = c2),
% 28.08/18.29 inference(unit_resolution,[status(thm)],[48, 8353])).
% 28.08/18.29 tff(8355,plain,
% 28.08/18.29 (big_f(f7(c2), f6(c1, c2)) <=> big_f(f7(c2), c2)),
% 28.08/18.29 inference(monotonicity,[status(thm)],[8354])).
% 28.08/18.29 tff(8356,plain,
% 28.08/18.29 (big_f(f7(c2), c2) <=> big_f(f7(c2), f6(c1, c2))),
% 28.08/18.29 inference(symmetry,[status(thm)],[8355])).
% 28.08/18.29 tff(8357,plain,
% 28.08/18.29 (big_f(f7(c2), f6(c1, c2))),
% 28.08/18.29 inference(modus_ponens,[status(thm)],[8277, 8356])).
% 28.08/18.29 tff(8358,plain,
% 28.08/18.29 (f7(c1) = f7(c2)),
% 28.08/18.29 inference(transitivity,[status(thm)],[4234, 125])).
% 28.08/18.29 tff(8359,plain,
% 28.08/18.29 (big_f(f7(c1), f6(c1, c2)) <=> big_f(f7(c2), f6(c1, c2))),
% 28.08/18.29 inference(monotonicity,[status(thm)],[8358])).
% 28.08/18.29 tff(8360,plain,
% 28.08/18.29 ((~big_f(f7(c1), f6(c1, c2))) <=> (~big_f(f7(c2), f6(c1, c2)))),
% 28.08/18.29 inference(monotonicity,[status(thm)],[8359])).
% 28.08/18.29 tff(8361,plain,
% 28.08/18.29 (big_f(f9(c2, c1), f10(c2))),
% 28.08/18.29 inference(modus_ponens,[status(thm)],[8277, 8329])).
% 28.08/18.29 tff(8362,plain,
% 28.08/18.29 (~big_f(f7(c1), f6(c1, c2))),
% 28.08/18.29 inference(unit_resolution,[status(thm)],[5827, 8354, 122, 4234, 8325, 8361])).
% 28.08/18.29 tff(8363,plain,
% 28.08/18.29 (~big_f(f7(c2), f6(c1, c2))),
% 28.08/18.29 inference(modus_ponens,[status(thm)],[8362, 8360])).
% 28.08/18.29 tff(8364,plain,
% 28.08/18.29 ($false),
% 28.08/18.29 inference(unit_resolution,[status(thm)],[8363, 8357])).
% 28.08/18.29 tff(8365,plain,(big_f(f7(c2), c1) | (~(f7(c1) = c1)) | (~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(c2, c2) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.08/18.29 tff(8366,plain,
% 28.08/18.29 (~(f7(c1) = c1)),
% 28.08/18.29 inference(unit_resolution,[status(thm)],[8365, 121, 122, 17, 333, 79])).
% 28.08/18.29 tff(8367,plain,
% 28.08/18.29 (f7(c1) = c2),
% 28.08/18.29 inference(unit_resolution,[status(thm)],[119, 8366])).
% 28.08/18.29 tff(8368,plain,
% 28.08/18.29 (big_f(f7(c2), f7(c2)) <=> big_f(f7(c2), c1)),
% 28.08/18.29 inference(monotonicity,[status(thm)],[292])).
% 28.08/18.29 tff(8369,plain,
% 28.08/18.29 (big_f(f7(c2), c1) <=> big_f(f7(c2), f7(c2))),
% 28.08/18.29 inference(symmetry,[status(thm)],[8368])).
% 28.08/18.29 tff(8370,plain,
% 28.08/18.29 ((~big_f(f7(c2), c1)) <=> (~big_f(f7(c2), f7(c2)))),
% 28.08/18.29 inference(monotonicity,[status(thm)],[8369])).
% 28.08/18.29 tff(8371,plain,
% 28.08/18.29 (~big_f(f7(c2), f7(c2))),
% 28.08/18.29 inference(modus_ponens,[status(thm)],[333, 8370])).
% 28.08/18.29 tff(8372,assumption,(big_f(f7(c2), f7(c2))), introduced(assumption)).
% 28.08/18.29 tff(8373,plain,
% 28.08/18.29 ($false),
% 28.08/18.29 inference(unit_resolution,[status(thm)],[8372, 8371])).
% 28.08/18.29 tff(8374,plain,((~big_f(f7(c2), f7(c2))) | big_f(f7(c2), c1) | (~(f7(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.08/18.29 tff(8375,plain,
% 28.08/18.29 (~big_f(f7(c2), f7(c2))),
% 28.08/18.29 inference(unit_resolution,[status(thm)],[8374, 333, 22])).
% 28.08/18.29 tff(8376,plain,
% 28.08/18.29 (big_f(c2, c2)),
% 28.08/18.29 inference(unit_resolution,[status(thm)],[8276, 1521, 79, 333, 17, 122])).
% 28.08/18.29 tff(8377,plain,
% 28.08/18.29 (big_f(f9(c2, c2), f10(c2))),
% 28.08/18.29 inference(modus_ponens,[status(thm)],[8376, 8070])).
% 28.08/18.29 tff(8378,assumption,(f7(c2) = f5(c2)), introduced(assumption)).
% 28.08/18.29 tff(8379,plain,
% 28.08/18.29 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f7(c2) = f5(c2))) | big_f(f7(c2), f7(c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f7(c2) = f5(c2))) | big_f(f7(c2), f7(c2)))),
% 28.08/18.29 inference(rewrite,[status(thm)],[])).
% 28.08/18.29 tff(8380,plain,
% 28.08/18.29 (((~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f7(c2), f7(c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f7(c2) = f5(c2)))) <=> ((~(f10(c2) = c2)) | (f7(c2) = c2) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f7(c2) = f5(c2))) | big_f(f7(c2), f7(c2)))),
% 28.08/18.29 inference(rewrite,[status(thm)],[])).
% 28.08/18.29 tff(8381,plain,
% 28.08/18.29 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f7(c2), f7(c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f7(c2) = f5(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f7(c2) = f5(c2))) | big_f(f7(c2), f7(c2))))),
% 28.08/18.29 inference(monotonicity,[status(thm)],[8380])).
% 28.08/18.29 tff(8382,plain,
% 28.08/18.29 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f7(c2), f7(c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f7(c2) = f5(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f7(c2) = f5(c2))) | big_f(f7(c2), f7(c2)))),
% 28.08/18.29 inference(transitivity,[status(thm)],[8381, 8379])).
% 28.08/18.29 tff(8383,plain,
% 28.08/18.29 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f7(c2), f7(c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f7(c2) = f5(c2))))),
% 28.08/18.29 inference(quant_inst,[status(thm)],[])).
% 28.08/18.29 tff(8384,plain,
% 28.08/18.29 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f7(c2) = f5(c2))) | big_f(f7(c2), f7(c2))),
% 28.08/18.29 inference(modus_ponens,[status(thm)],[8383, 8382])).
% 28.08/18.29 tff(8385,plain,
% 28.08/18.29 ($false),
% 28.08/18.29 inference(unit_resolution,[status(thm)],[8384, 783, 122, 17, 1572, 690, 8218, 8378])).
% 28.08/18.29 tff(8386,plain,(big_f(f7(c2), f7(c2)) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f7(c2) = f5(c2)))), inference(lemma,lemma(discharge,[]))).
% 28.08/18.29 tff(8387,plain,
% 28.08/18.29 (~(f7(c2) = f5(c2))),
% 28.08/18.29 inference(unit_resolution,[status(thm)],[8386, 8377, 17, 8080, 8375, 122])).
% 28.08/18.29 tff(8388,plain,
% 28.08/18.29 ((f7(c2) = f5(c2)) <=> (c1 = f5(c2))),
% 28.08/18.29 inference(monotonicity,[status(thm)],[292])).
% 28.08/18.29 tff(8389,plain,
% 28.08/18.29 ((f7(c2) = f5(c2)) <=> (f5(c2) = c1)),
% 28.08/18.29 inference(transitivity,[status(thm)],[8388, 1531])).
% 28.08/18.29 tff(8390,plain,
% 28.08/18.29 ((f5(c2) = c1) <=> (f7(c2) = f5(c2))),
% 28.08/18.29 inference(symmetry,[status(thm)],[8389])).
% 28.08/18.29 tff(8391,plain,
% 28.08/18.29 (f7(c2) = f5(c2)),
% 28.08/18.29 inference(modus_ponens,[status(thm)],[1569, 8390])).
% 28.08/18.29 tff(8392,assumption,(~(f7(c2) = f5(c2))), introduced(assumption)).
% 28.08/18.29 tff(8393,plain,
% 28.08/18.29 ($false),
% 28.08/18.29 inference(unit_resolution,[status(thm)],[8392, 8391])).
% 28.08/18.29 tff(8394,plain,((~(f5(c2) = c1)) | (f7(c2) = f5(c2)) | (~(f7(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.08/18.29 tff(8395,plain,
% 28.08/18.29 (~(f5(c2) = c1)),
% 28.08/18.29 inference(unit_resolution,[status(thm)],[8394, 8387, 22])).
% 28.08/18.29 tff(8396,plain,
% 28.08/18.29 ($false),
% 28.08/18.29 inference(unit_resolution,[status(thm)],[1566, 783, 122, 17, 5124, 1521, 1572, 690])).
% 28.08/18.29 tff(8397,plain,(big_f(f7(c2), c2) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~(c2 = f5(c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2)))), inference(lemma,lemma(discharge,[]))).
% 28.08/18.29 tff(8398,plain,
% 28.08/18.29 (~(c2 = f5(c2))),
% 28.08/18.29 inference(unit_resolution,[status(thm)],[8397, 8377, 17, 122, 8080, 1521])).
% 28.08/18.29 tff(8399,plain,
% 28.08/18.29 (~(f5(c2) = c2)),
% 28.08/18.29 inference(unit_resolution,[status(thm)],[8113, 8398])).
% 28.08/18.29 tff(8400,plain,
% 28.08/18.29 ($false),
% 28.08/18.29 inference(unit_resolution,[status(thm)],[1547, 8399, 8395])).
% 28.08/18.29 tff(8401,plain,(big_f(f7(c2), c2) | (f7(c2) = c2) | (~(f10(c2) = c2)) | (~(f4(c4) = c2)) | big_f(f7(c2), c1)), inference(lemma,lemma(discharge,[]))).
% 28.08/18.29 tff(8402,plain,
% 28.08/18.29 (big_f(f7(c2), c2)),
% 28.08/18.29 inference(unit_resolution,[status(thm)],[8401, 333, 122, 79, 17])).
% 28.08/18.29 tff(8403,plain,
% 28.08/18.29 (c2 = f7(f7(c2))),
% 28.08/18.29 inference(transitivity,[status(thm)],[2778, 8313])).
% 28.08/18.29 tff(8404,plain,
% 28.08/18.29 (f1(c2, c1) = f1(f7(f7(c2)), c1)),
% 28.08/18.29 inference(monotonicity,[status(thm)],[8403])).
% 28.08/18.29 tff(8405,plain,
% 28.08/18.29 (f1(f7(f7(c2)), c1) = f1(c2, c1)),
% 28.08/18.29 inference(symmetry,[status(thm)],[8404])).
% 28.08/18.29 tff(8406,plain,
% 28.08/18.29 (f7(f7(c2)) = c2),
% 28.08/18.29 inference(transitivity,[status(thm)],[8077, 120])).
% 28.08/18.29 tff(8407,plain,
% 28.08/18.29 ((f7(f7(c2)) = c3) <=> (c2 = c3)),
% 28.08/18.29 inference(monotonicity,[status(thm)],[8406])).
% 28.08/18.29 tff(8408,plain,
% 28.08/18.29 ((c2 = c3) <=> (f7(f7(c2)) = c3)),
% 28.08/18.29 inference(symmetry,[status(thm)],[8407])).
% 28.08/18.29 tff(8409,plain,
% 28.08/18.29 ((c2 = f7(c2)) <=> (f7(c2) = c2)),
% 28.08/18.29 inference(commutativity,[status(thm)],[])).
% 28.08/18.29 tff(8410,plain,
% 28.08/18.29 (c3 = f7(c2)),
% 28.08/18.29 inference(transitivity,[status(thm)],[172, 125])).
% 28.08/18.29 tff(8411,plain,
% 28.08/18.29 ((c2 = c3) <=> (c2 = f7(c2))),
% 28.08/18.29 inference(monotonicity,[status(thm)],[8410])).
% 28.08/18.29 tff(8412,plain,
% 28.08/18.29 ((c2 = c3) <=> (f7(c2) = c2)),
% 28.08/18.29 inference(transitivity,[status(thm)],[8411, 8409])).
% 28.08/18.29 tff(8413,plain,
% 28.08/18.29 ((f7(c2) = c2) <=> (c2 = c3)),
% 28.08/18.29 inference(symmetry,[status(thm)],[8412])).
% 28.08/18.29 tff(8414,plain,
% 28.08/18.29 ((f7(c2) = c2) <=> (f7(f7(c2)) = c3)),
% 28.08/18.29 inference(transitivity,[status(thm)],[8413, 8408])).
% 28.08/18.29 tff(8415,plain,
% 28.08/18.29 ((~(f7(c2) = c2)) <=> (~(f7(f7(c2)) = c3))),
% 28.08/18.29 inference(monotonicity,[status(thm)],[8414])).
% 28.08/18.29 tff(8416,plain,
% 28.08/18.29 (~(f7(f7(c2)) = c3)),
% 28.08/18.29 inference(modus_ponens,[status(thm)],[17, 8415])).
% 28.08/18.29 tff(8417,plain,
% 28.08/18.29 (f1(f7(f7(c2)), c1) = c1),
% 28.08/18.29 inference(unit_resolution,[status(thm)],[422, 5577, 22, 121, 120, 8416])).
% 28.08/18.29 tff(8418,plain,
% 28.08/18.29 (c1 = f1(f7(f7(c2)), c1)),
% 28.08/18.29 inference(symmetry,[status(thm)],[8417])).
% 28.08/18.29 tff(8419,plain,
% 28.08/18.29 (c1 = f1(c2, c1)),
% 28.08/18.29 inference(transitivity,[status(thm)],[8418, 8405])).
% 28.08/18.29 tff(8420,plain,
% 28.08/18.29 (big_f(c2, c1) <=> big_f(c2, f1(c2, c1))),
% 28.08/18.29 inference(monotonicity,[status(thm)],[8419])).
% 28.08/18.29 tff(8421,plain,
% 28.08/18.29 (big_f(c2, f1(c2, c1)) <=> big_f(c2, c1)),
% 28.08/18.29 inference(symmetry,[status(thm)],[8420])).
% 28.08/18.29 tff(8422,plain,
% 28.08/18.29 (big_f(c2, f1(c2, c1)) <=> big_f(f7(c1), c1)),
% 28.08/18.29 inference(transitivity,[status(thm)],[8421, 693])).
% 28.08/18.29 tff(8423,plain,
% 28.08/18.29 ((~big_f(c2, f1(c2, c1))) <=> (~big_f(f7(c1), c1))),
% 28.08/18.29 inference(monotonicity,[status(thm)],[8422])).
% 28.08/18.29 tff(8424,plain,
% 28.08/18.29 ((~big_f(c2, c1)) <=> (~big_f(c2, f1(c2, c1)))),
% 28.08/18.29 inference(monotonicity,[status(thm)],[8420])).
% 28.08/18.29 tff(8425,plain,
% 28.08/18.29 (~big_f(c2, f1(c2, c1))),
% 28.08/18.29 inference(modus_ponens,[status(thm)],[2, 8424])).
% 28.08/18.29 tff(8426,plain,
% 28.08/18.29 (~big_f(f7(c1), c1)),
% 28.08/18.29 inference(modus_ponens,[status(thm)],[8425, 8423])).
% 28.08/18.29 tff(8427,plain,
% 28.08/18.29 (~(f5(c1) = c2)),
% 28.08/18.29 inference(unit_resolution,[status(thm)],[1715, 287, 121, 347])).
% 28.08/18.29 tff(8428,plain,
% 28.08/18.29 (~(f5(c1) = c1)),
% 28.08/18.29 inference(unit_resolution,[status(thm)],[289, 287, 285])).
% 28.08/18.29 tff(8429,plain,
% 28.08/18.29 ($false),
% 28.08/18.29 inference(unit_resolution,[status(thm)],[1708, 8428, 8427])).
% 28.08/18.29 tff(8430,plain,((~big_f(f7(c1), f5(c1))) | big_f(f7(c1), c1) | big_f(c2, c2) | (~(f7(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.08/18.29 tff(8431,plain,
% 28.08/18.29 (~big_f(f7(c1), f5(c1))),
% 28.08/18.29 inference(unit_resolution,[status(thm)],[8430, 8426, 121, 120])).
% 28.08/18.29 tff(8432,plain,
% 28.08/18.29 ((c2 = f9(c2, c1)) <=> (f9(c2, c1) = c2)),
% 28.08/18.29 inference(commutativity,[status(thm)],[])).
% 28.08/18.29 tff(8433,plain,
% 28.08/18.29 ((f9(c2, c1) = c2) <=> (c2 = f9(c2, c1))),
% 28.08/18.29 inference(symmetry,[status(thm)],[8432])).
% 28.08/18.29 tff(8434,plain,
% 28.08/18.29 (c2 = f9(c2, c1)),
% 28.08/18.29 inference(modus_ponens,[status(thm)],[8278, 8433])).
% 28.08/18.29 tff(8435,plain,
% 28.08/18.29 (big_f(f9(c2, c1), f10(c2))),
% 28.08/18.29 inference(unit_resolution,[status(thm)],[753, 1139, 122, 115, 730])).
% 28.08/18.29 tff(8436,plain,
% 28.08/18.29 ((~(big_f(c2, c2) <=> big_f(f9(c2, c1), f10(c2)))) | big_f(c2, c2) | (~big_f(f9(c2, c1), f10(c2)))),
% 28.08/18.29 inference(tautology,[status(thm)],[])).
% 28.08/18.29 tff(8437,plain,
% 28.08/18.29 (~(big_f(c2, c2) <=> big_f(f9(c2, c1), f10(c2)))),
% 28.08/18.29 inference(unit_resolution,[status(thm)],[8436, 8435, 121])).
% 28.08/18.29 tff(8438,assumption,(~(big_f(c2, c2) <=> big_f(f9(c2, c1), f10(c2)))), introduced(assumption)).
% 28.08/18.29 tff(8439,assumption,(c2 = f9(c2, c1)), introduced(assumption)).
% 28.08/18.29 tff(8440,plain,
% 28.08/18.29 (big_f(c2, c2) <=> big_f(f9(c2, c1), f10(c2))),
% 28.08/18.29 inference(monotonicity,[status(thm)],[8439, 4999])).
% 28.08/18.29 tff(8441,plain,
% 28.08/18.29 ($false),
% 28.08/18.29 inference(unit_resolution,[status(thm)],[8440, 8438])).
% 28.08/18.29 tff(8442,plain,((~(c2 = f9(c2, c1))) | (~(c2 = f10(c2))) | (big_f(c2, c2) <=> big_f(f9(c2, c1), f10(c2)))), inference(lemma,lemma(discharge,[]))).
% 28.08/18.29 tff(8443,plain,
% 28.08/18.29 (~(c2 = f9(c2, c1))),
% 28.08/18.29 inference(unit_resolution,[status(thm)],[8442, 8437, 4989])).
% 28.08/18.29 tff(8444,plain,
% 28.08/18.29 ($false),
% 28.08/18.29 inference(unit_resolution,[status(thm)],[8443, 8434])).
% 28.08/18.29 tff(8445,plain,((f9(c2, c1) = c1) | big_f(c2, c2) | (~(f10(c2) = c2)) | (f7(c1) = c1) | big_f(f7(c1), f5(c1))), inference(lemma,lemma(discharge,[]))).
% 28.08/18.29 tff(8446,plain,
% 28.08/18.29 (f9(c2, c1) = c1),
% 28.08/18.29 inference(unit_resolution,[status(thm)],[8445, 8431, 122, 115, 121])).
% 28.08/18.29 tff(8447,plain,
% 28.08/18.29 (big_f(f7(f7(c2)), f7(c2)) <=> big_f(c2, c1)),
% 28.08/18.29 inference(monotonicity,[status(thm)],[8406, 22])).
% 28.08/18.29 tff(8448,plain,
% 28.08/18.29 (big_f(c2, c1) <=> big_f(f7(f7(c2)), f7(c2))),
% 28.08/18.29 inference(symmetry,[status(thm)],[8447])).
% 28.08/18.30 tff(8449,plain,
% 28.08/18.30 ((~big_f(c2, c1)) <=> (~big_f(f7(f7(c2)), f7(c2)))),
% 28.08/18.30 inference(monotonicity,[status(thm)],[8448])).
% 28.08/18.30 tff(8450,plain,
% 28.08/18.30 (~big_f(f7(f7(c2)), f7(c2))),
% 28.08/18.30 inference(modus_ponens,[status(thm)],[2, 8449])).
% 28.08/18.30 tff(8451,plain,
% 28.08/18.30 (~big_f(c2, f10(c1))),
% 28.08/18.30 inference(unit_resolution,[status(thm)],[6125, 15, 121])).
% 28.08/18.30 tff(8452,assumption,(~big_f(f7(f7(c2)), f7(c2))), introduced(assumption)).
% 28.08/18.30 tff(8453,plain,
% 28.08/18.30 (f9(c2, c1) = f7(c2)),
% 28.08/18.30 inference(transitivity,[status(thm)],[736, 342])).
% 28.08/18.30 tff(8454,plain,
% 28.08/18.30 (big_f(f9(c2, c1), f10(c2)) <=> big_f(f7(c2), c2)),
% 28.08/18.30 inference(monotonicity,[status(thm)],[8453, 122])).
% 28.08/18.30 tff(8455,plain,
% 28.08/18.30 (big_f(f7(c2), c2) <=> big_f(f9(c2, c1), f10(c2))),
% 28.08/18.30 inference(symmetry,[status(thm)],[8454])).
% 28.08/18.30 tff(8456,plain,
% 28.08/18.30 (f9(c2, f7(c2)) = f9(c2, c1)),
% 28.08/18.30 inference(monotonicity,[status(thm)],[292])).
% 28.08/18.30 tff(8457,plain,
% 28.08/18.30 (f9(c2, f7(c2)) = f7(c2)),
% 28.08/18.30 inference(transitivity,[status(thm)],[8456, 736, 342])).
% 28.08/18.30 tff(8458,plain,
% 28.08/18.30 (big_f(f9(c2, f7(c2)), f10(c2)) <=> big_f(f7(c2), c2)),
% 28.08/18.30 inference(monotonicity,[status(thm)],[8457, 122])).
% 28.08/18.30 tff(8459,plain,
% 28.08/18.30 (big_f(f9(c2, f7(c2)), f10(c2)) <=> big_f(f9(c2, c1), f10(c2))),
% 28.08/18.30 inference(transitivity,[status(thm)],[8458, 8455])).
% 28.08/18.30 tff(8460,plain,
% 28.08/18.30 ((~big_f(f9(c2, f7(c2)), f10(c2))) <=> (~big_f(f9(c2, c1), f10(c2)))),
% 28.08/18.30 inference(monotonicity,[status(thm)],[8459])).
% 28.08/18.30 tff(8461,plain,
% 28.08/18.30 ((f7(c1) = c1) <=> (f7(f7(c2)) = f7(c2))),
% 28.08/18.30 inference(monotonicity,[status(thm)],[353, 342])).
% 28.08/18.30 tff(8462,plain,
% 28.08/18.30 ((~(f7(c1) = c1)) <=> (~(f7(f7(c2)) = f7(c2)))),
% 28.08/18.30 inference(monotonicity,[status(thm)],[8461])).
% 28.08/18.30 tff(8463,plain,
% 28.08/18.30 (~(f7(f7(c2)) = f7(c2))),
% 28.08/18.30 inference(modus_ponens,[status(thm)],[115, 8462])).
% 28.08/18.30 tff(8464,plain,
% 28.08/18.30 (f7(f7(c2)) = c2),
% 28.08/18.30 inference(transitivity,[status(thm)],[352, 120])).
% 28.08/18.30 tff(8465,plain,
% 28.08/18.30 (big_f(f7(f7(c2)), c2) <=> big_f(c2, c2)),
% 28.08/18.30 inference(monotonicity,[status(thm)],[8464])).
% 28.08/18.30 tff(8466,plain,
% 28.08/18.30 (big_f(c2, c2) <=> big_f(f7(f7(c2)), c2)),
% 28.08/18.30 inference(symmetry,[status(thm)],[8465])).
% 28.08/18.30 tff(8467,plain,
% 28.08/18.30 ((~big_f(c2, c2)) <=> (~big_f(f7(f7(c2)), c2))),
% 28.08/18.30 inference(monotonicity,[status(thm)],[8466])).
% 28.08/18.30 tff(8468,plain,
% 28.08/18.30 (~big_f(f7(f7(c2)), c2)),
% 28.08/18.30 inference(modus_ponens,[status(thm)],[121, 8467])).
% 28.08/18.30 tff(8469,plain,
% 28.08/18.30 (f5(f7(c2)) = f5(c1)),
% 28.08/18.30 inference(monotonicity,[status(thm)],[292])).
% 28.08/18.30 tff(8470,plain,
% 28.08/18.30 ((f7(c2) = f5(f7(c2))) <=> (c1 = f5(c1))),
% 28.08/18.30 inference(monotonicity,[status(thm)],[292, 8469])).
% 28.08/18.30 tff(8471,plain,
% 28.08/18.30 ((f7(c2) = f5(f7(c2))) <=> (f5(c1) = c1)),
% 28.08/18.30 inference(transitivity,[status(thm)],[8470, 128])).
% 28.08/18.30 tff(8472,plain,
% 28.08/18.30 ((~(f7(c2) = f5(f7(c2)))) <=> (~(f5(c1) = c1))),
% 28.08/18.30 inference(monotonicity,[status(thm)],[8471])).
% 28.08/18.30 tff(8473,assumption,(~(f7(f7(c2)) = f7(c2))), introduced(assumption)).
% 28.08/18.30 tff(8474,plain,
% 28.08/18.30 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2))) | big_f(f7(f7(c2)), f7(c2)) | (~(f7(c2) = f5(f7(c2)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2))) | big_f(f7(f7(c2)), f7(c2)) | (~(f7(c2) = f5(f7(c2)))))),
% 28.08/18.30 inference(rewrite,[status(thm)],[])).
% 28.08/18.30 tff(8475,plain,
% 28.08/18.30 (((~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f7(c2)) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2))) | (~(f7(c2) = f5(f7(c2))))) <=> ((~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2))) | big_f(f7(f7(c2)), f7(c2)) | (~(f7(c2) = f5(f7(c2)))))),
% 28.08/18.30 inference(rewrite,[status(thm)],[])).
% 28.08/18.30 tff(8476,plain,
% 28.08/18.30 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f7(c2)) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2))) | (~(f7(c2) = f5(f7(c2)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2))) | big_f(f7(f7(c2)), f7(c2)) | (~(f7(c2) = f5(f7(c2))))))),
% 28.08/18.30 inference(monotonicity,[status(thm)],[8475])).
% 28.08/18.30 tff(8477,plain,
% 28.08/18.30 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f7(c2)) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2))) | (~(f7(c2) = f5(f7(c2)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2))) | big_f(f7(f7(c2)), f7(c2)) | (~(f7(c2) = f5(f7(c2)))))),
% 28.08/18.30 inference(transitivity,[status(thm)],[8476, 8474])).
% 28.08/18.30 tff(8478,plain,
% 28.08/18.30 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f7(c2)) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2))) | (~(f7(c2) = f5(f7(c2)))))),
% 28.08/18.30 inference(quant_inst,[status(thm)],[])).
% 28.08/18.30 tff(8479,plain,
% 28.08/18.30 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2))) | big_f(f7(f7(c2)), f7(c2)) | (~(f7(c2) = f5(f7(c2))))),
% 28.08/18.30 inference(modus_ponens,[status(thm)],[8478, 8477])).
% 28.08/18.30 tff(8480,plain,
% 28.08/18.30 ((~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2))) | big_f(f7(f7(c2)), f7(c2)) | (~(f7(c2) = f5(f7(c2))))),
% 28.08/18.30 inference(unit_resolution,[status(thm)],[8479, 783, 122, 8473])).
% 28.08/18.30 tff(8481,plain,
% 28.08/18.30 (~(f7(c2) = f5(f7(c2)))),
% 28.08/18.30 inference(unit_resolution,[status(thm)],[8480, 8343, 8452, 8342])).
% 28.08/18.30 tff(8482,plain,
% 28.08/18.30 (~(f5(c1) = c1)),
% 28.08/18.30 inference(modus_ponens,[status(thm)],[8481, 8472])).
% 28.08/18.30 tff(8483,plain,
% 28.08/18.30 ((c2 = f5(c1)) <=> (f5(c1) = c2)),
% 28.08/18.30 inference(symmetry,[status(thm)],[155])).
% 28.08/18.30 tff(8484,plain,
% 28.08/18.30 ((c2 = f5(f7(c2))) <=> (c2 = f5(c1))),
% 28.08/18.30 inference(monotonicity,[status(thm)],[8469])).
% 28.08/18.30 tff(8485,plain,
% 28.08/18.30 ((c2 = f5(f7(c2))) <=> (f5(c1) = c2)),
% 28.08/18.30 inference(transitivity,[status(thm)],[8484, 8483])).
% 28.08/18.30 tff(8486,plain,
% 28.08/18.30 ((~(c2 = f5(f7(c2)))) <=> (~(f5(c1) = c2))),
% 28.08/18.30 inference(monotonicity,[status(thm)],[8485])).
% 28.08/18.30 tff(8487,assumption,(~big_f(f7(f7(c2)), c2)), introduced(assumption)).
% 28.08/18.30 tff(8488,plain,
% 28.08/18.30 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), c2) | (~(c2 = f5(f7(c2)))) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), c2) | (~(c2 = f5(f7(c2)))) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2))))),
% 28.08/18.30 inference(rewrite,[status(thm)],[])).
% 28.08/18.30 tff(8489,plain,
% 28.08/18.30 (((~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), c2) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2))) | (~(c2 = f5(f7(c2))))) <=> ((~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), c2) | (~(c2 = f5(f7(c2)))) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2))))),
% 28.08/18.30 inference(rewrite,[status(thm)],[])).
% 28.08/18.30 tff(8490,plain,
% 28.08/18.30 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), c2) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2))) | (~(c2 = f5(f7(c2)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), c2) | (~(c2 = f5(f7(c2)))) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2)))))),
% 28.08/18.30 inference(monotonicity,[status(thm)],[8489])).
% 28.08/18.30 tff(8491,plain,
% 28.08/18.30 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), c2) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2))) | (~(c2 = f5(f7(c2)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), c2) | (~(c2 = f5(f7(c2)))) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2))))),
% 28.08/18.30 inference(transitivity,[status(thm)],[8490, 8488])).
% 28.08/18.30 tff(8492,plain,
% 28.08/18.30 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), c2) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2))) | (~(c2 = f5(f7(c2)))))),
% 28.08/18.30 inference(quant_inst,[status(thm)],[])).
% 28.08/18.30 tff(8493,plain,
% 28.08/18.30 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), c2) | (~(c2 = f5(f7(c2)))) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2)))),
% 28.08/18.30 inference(modus_ponens,[status(thm)],[8492, 8491])).
% 28.08/18.30 tff(8494,plain,
% 28.08/18.30 (big_f(f7(f7(c2)), c2) | (~(c2 = f5(f7(c2)))) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2)))),
% 28.08/18.30 inference(unit_resolution,[status(thm)],[8493, 783, 122, 8473])).
% 28.08/18.30 tff(8495,plain,
% 28.08/18.30 (~(c2 = f5(f7(c2)))),
% 28.08/18.30 inference(unit_resolution,[status(thm)],[8494, 8343, 8342, 8487])).
% 28.08/18.30 tff(8496,plain,
% 28.08/18.30 (~(f5(c1) = c2)),
% 28.08/18.30 inference(modus_ponens,[status(thm)],[8495, 8486])).
% 28.08/18.30 tff(8497,plain,
% 28.08/18.30 ($false),
% 28.08/18.30 inference(unit_resolution,[status(thm)],[1708, 8496, 8482])).
% 28.08/18.30 tff(8498,plain,((~big_f(f9(c2, f7(c2)), f10(c2))) | (~(f7(c2) = c1)) | (~(f9(c2, f7(c2)) = f7(c2))) | big_f(f7(f7(c2)), c2) | (~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f7(c2))), inference(lemma,lemma(discharge,[]))).
% 28.08/18.30 tff(8499,plain,
% 28.08/18.30 (~big_f(f9(c2, f7(c2)), f10(c2))),
% 28.08/18.30 inference(unit_resolution,[status(thm)],[8498, 8457, 292, 8468, 122, 8463, 8452])).
% 28.08/18.30 tff(8500,plain,
% 28.08/18.30 (~big_f(f9(c2, c1), f10(c2))),
% 28.08/18.30 inference(modus_ponens,[status(thm)],[8499, 8460])).
% 28.08/18.30 tff(8501,plain,
% 28.08/18.30 (c1 = f7(f4(c4))),
% 28.08/18.30 inference(transitivity,[status(thm)],[342, 81])).
% 28.08/18.30 tff(8502,plain,
% 28.08/18.30 (f7(f4(c4)) = c1),
% 28.08/18.30 inference(transitivity,[status(thm)],[80, 292])).
% 28.08/18.30 tff(8503,plain,
% 28.08/18.30 (f10(f7(f4(c4))) = f10(c1)),
% 28.08/18.30 inference(monotonicity,[status(thm)],[8502])).
% 28.08/18.30 tff(8504,plain,
% 28.08/18.30 (f10(c1) = f10(f7(f4(c4)))),
% 28.08/18.30 inference(symmetry,[status(thm)],[8503])).
% 28.08/18.30 tff(8505,plain,
% 28.08/18.30 ((f10(c1) = c1) <=> (f10(f7(f4(c4))) = f7(f4(c4)))),
% 28.08/18.30 inference(monotonicity,[status(thm)],[8504, 8501])).
% 28.08/18.30 tff(8506,plain,
% 28.08/18.30 ((f10(c1) = c1) <=> (f10(f7(c2)) = f7(c2))),
% 28.08/18.30 inference(transitivity,[status(thm)],[8505, 8181])).
% 28.08/18.30 tff(8507,plain,
% 28.08/18.30 ((~(f10(c1) = c1)) <=> (~(f10(f7(c2)) = f7(c2)))),
% 28.08/18.30 inference(monotonicity,[status(thm)],[8506])).
% 28.08/18.30 tff(8508,plain,
% 28.08/18.30 (~(f10(f7(c2)) = f7(c2))),
% 28.08/18.30 inference(modus_ponens,[status(thm)],[3, 8507])).
% 28.08/18.30 tff(8509,plain,
% 28.08/18.30 (big_f(c2, f10(f7(c2))) <=> big_f(c2, f10(f7(f4(c4))))),
% 28.08/18.30 inference(monotonicity,[status(thm)],[8167])).
% 28.08/18.30 tff(8510,plain,
% 28.08/18.30 (big_f(c2, f10(f7(f4(c4)))) <=> big_f(c2, f10(f7(c2)))),
% 28.08/18.30 inference(symmetry,[status(thm)],[8509])).
% 28.08/18.30 tff(8511,plain,
% 28.08/18.30 (f10(f7(f4(c4))) = c2),
% 28.08/18.30 inference(transitivity,[status(thm)],[8503, 15])).
% 28.08/18.30 tff(8512,plain,
% 28.08/18.30 (big_f(c2, f10(f7(f4(c4)))) <=> big_f(c2, c2)),
% 28.08/18.30 inference(monotonicity,[status(thm)],[8511])).
% 28.08/18.30 tff(8513,plain,
% 28.08/18.30 (big_f(c2, c2) <=> big_f(c2, f10(f7(f4(c4))))),
% 28.08/18.30 inference(symmetry,[status(thm)],[8512])).
% 28.08/18.30 tff(8514,plain,
% 28.08/18.30 (big_f(c2, c2) <=> big_f(c2, f10(f7(c2)))),
% 28.08/18.30 inference(transitivity,[status(thm)],[8513, 8510])).
% 28.08/18.30 tff(8515,plain,
% 28.08/18.30 ((~big_f(c2, c2)) <=> (~big_f(c2, f10(f7(c2))))),
% 28.08/18.30 inference(monotonicity,[status(thm)],[8514])).
% 28.08/18.30 tff(8516,plain,
% 28.08/18.30 (~big_f(c2, f10(f7(c2)))),
% 28.08/18.30 inference(modus_ponens,[status(thm)],[121, 8515])).
% 28.08/18.30 tff(8517,plain,
% 28.08/18.30 ((c1 = f8(f7(f4(c4)))) <=> (f8(f7(f4(c4))) = c1)),
% 28.08/18.30 inference(commutativity,[status(thm)],[])).
% 28.08/18.30 tff(8518,plain,
% 28.08/18.30 ((f8(f7(f4(c4))) = c1) <=> (c1 = f8(f7(f4(c4))))),
% 28.08/18.30 inference(symmetry,[status(thm)],[8517])).
% 28.08/18.30 tff(8519,plain,
% 28.08/18.30 (f8(c1) = f8(f7(f4(c4)))),
% 28.08/18.30 inference(monotonicity,[status(thm)],[8501])).
% 28.08/18.30 tff(8520,plain,
% 28.08/18.30 ((f8(c1) = c1) <=> (f8(f7(f4(c4))) = c1)),
% 28.08/18.30 inference(monotonicity,[status(thm)],[8519])).
% 28.08/18.30 tff(8521,plain,
% 28.08/18.30 ((f8(c1) = c1) <=> (c1 = f8(f7(f4(c4))))),
% 28.08/18.30 inference(transitivity,[status(thm)],[8520, 8518])).
% 28.08/18.30 tff(8522,assumption,(~big_f(c2, f10(f7(c2)))), introduced(assumption)).
% 28.08/18.30 tff(8523,assumption,(~(f10(f7(c2)) = f7(c2))), introduced(assumption)).
% 28.08/18.30 tff(8524,plain,
% 28.08/18.30 (f10(f7(c2)) = c2),
% 28.08/18.30 inference(transitivity,[status(thm)],[8167, 8503, 15])).
% 28.08/18.30 tff(8525,plain,
% 28.08/18.30 (big_f(f7(c2), f10(f7(c2))) <=> big_f(f7(c2), c2)),
% 28.08/18.30 inference(monotonicity,[status(thm)],[8524])).
% 28.08/18.30 tff(8526,plain,
% 28.08/18.30 (big_f(f7(c2), c2) <=> big_f(f7(c2), f10(f7(c2)))),
% 28.08/18.30 inference(symmetry,[status(thm)],[8525])).
% 28.08/18.30 tff(8527,plain,
% 28.08/18.30 ((~big_f(f7(c2), c2)) <=> (~big_f(f7(c2), f10(f7(c2))))),
% 28.08/18.30 inference(monotonicity,[status(thm)],[8526])).
% 28.08/18.30 tff(8528,plain,
% 28.08/18.30 ((~big_f(f9(c2, c1), f10(c2))) <=> (~big_f(f7(c2), c2))),
% 28.08/18.30 inference(monotonicity,[status(thm)],[8454])).
% 28.08/18.30 tff(8529,plain,
% 28.08/18.30 (~big_f(f7(c2), c2)),
% 28.08/18.30 inference(modus_ponens,[status(thm)],[731, 8528])).
% 28.08/18.30 tff(8530,plain,
% 28.08/18.30 (~big_f(f7(c2), f10(f7(c2)))),
% 28.08/18.30 inference(modus_ponens,[status(thm)],[8529, 8527])).
% 28.08/18.30 tff(8531,plain,
% 28.08/18.30 (c3 = f7(f4(c4))),
% 28.08/18.30 inference(transitivity,[status(thm)],[172, 342, 81])).
% 28.08/18.30 tff(8532,plain,
% 28.08/18.30 (f8(c3) = f8(f7(f4(c4)))),
% 28.08/18.30 inference(monotonicity,[status(thm)],[8531])).
% 28.08/18.30 tff(8533,plain,
% 28.08/18.30 ((f8(c3) = c2) <=> (f8(f7(f4(c4))) = c2)),
% 28.08/18.30 inference(monotonicity,[status(thm)],[8532])).
% 28.08/18.30 tff(8534,plain,
% 28.08/18.30 ((f8(c3) = c2) <=> (c2 = f8(f7(f4(c4))))),
% 28.08/18.30 inference(transitivity,[status(thm)],[8533, 105])).
% 28.08/18.30 tff(8535,plain,
% 28.08/18.30 ((c2 = f8(f7(f4(c4)))) <=> (f8(c3) = c2)),
% 28.08/18.30 inference(symmetry,[status(thm)],[8534])).
% 28.08/18.30 tff(8536,plain,
% 28.08/18.30 (f8(f7(c2)) = f8(f7(f4(c4)))),
% 28.08/18.30 inference(monotonicity,[status(thm)],[81])).
% 28.08/18.30 tff(8537,plain,
% 28.08/18.30 ((c2 = f8(f7(c2))) <=> (c2 = f8(f7(f4(c4))))),
% 28.08/18.30 inference(monotonicity,[status(thm)],[8536])).
% 28.08/18.30 tff(8538,plain,
% 28.08/18.30 ((c2 = f8(f7(c2))) <=> (f8(c3) = c2)),
% 28.08/18.30 inference(transitivity,[status(thm)],[8537, 8535])).
% 28.08/18.30 tff(8539,plain,
% 28.08/18.30 ((~(c2 = f8(f7(c2)))) <=> (~(f8(c3) = c2))),
% 28.08/18.30 inference(monotonicity,[status(thm)],[8538])).
% 28.08/18.30 tff(8540,assumption,(f7(c2) = f5(f7(c2))), introduced(assumption)).
% 28.08/18.30 tff(8541,plain,
% 28.08/18.30 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f7(f7(c2)) = f7(c2)) | (f10(f7(c2)) = f7(c2)) | big_f(c2, f10(f7(c2))) | (~(c2 = f8(f7(c2)))) | big_f(f7(f7(c2)), f7(c2)) | (~(f7(c2) = f5(f7(c2)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(f7(c2)) = f7(c2)) | (f10(f7(c2)) = f7(c2)) | big_f(c2, f10(f7(c2))) | (~(c2 = f8(f7(c2)))) | big_f(f7(f7(c2)), f7(c2)) | (~(f7(c2) = f5(f7(c2)))))),
% 28.08/18.30 inference(rewrite,[status(thm)],[])).
% 28.08/18.30 tff(8542,plain,
% 28.08/18.30 (((~(f7(c2) = f5(f7(c2)))) | (f10(f7(c2)) = f7(c2)) | big_f(c2, f10(f7(c2))) | (f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f7(c2)) | (~(c2 = f8(f7(c2))))) <=> ((f7(f7(c2)) = f7(c2)) | (f10(f7(c2)) = f7(c2)) | big_f(c2, f10(f7(c2))) | (~(c2 = f8(f7(c2)))) | big_f(f7(f7(c2)), f7(c2)) | (~(f7(c2) = f5(f7(c2)))))),
% 28.08/18.30 inference(rewrite,[status(thm)],[])).
% 28.08/18.30 tff(8543,plain,
% 28.08/18.30 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(f7(c2) = f5(f7(c2)))) | (f10(f7(c2)) = f7(c2)) | big_f(c2, f10(f7(c2))) | (f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f7(c2)) | (~(c2 = f8(f7(c2)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f7(f7(c2)) = f7(c2)) | (f10(f7(c2)) = f7(c2)) | big_f(c2, f10(f7(c2))) | (~(c2 = f8(f7(c2)))) | big_f(f7(f7(c2)), f7(c2)) | (~(f7(c2) = f5(f7(c2))))))),
% 28.08/18.30 inference(monotonicity,[status(thm)],[8542])).
% 28.08/18.30 tff(8544,plain,
% 28.08/18.30 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(f7(c2) = f5(f7(c2)))) | (f10(f7(c2)) = f7(c2)) | big_f(c2, f10(f7(c2))) | (f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f7(c2)) | (~(c2 = f8(f7(c2)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(f7(c2)) = f7(c2)) | (f10(f7(c2)) = f7(c2)) | big_f(c2, f10(f7(c2))) | (~(c2 = f8(f7(c2)))) | big_f(f7(f7(c2)), f7(c2)) | (~(f7(c2) = f5(f7(c2)))))),
% 28.08/18.30 inference(transitivity,[status(thm)],[8543, 8541])).
% 28.08/18.30 tff(8545,plain,
% 28.08/18.30 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(f7(c2) = f5(f7(c2)))) | (f10(f7(c2)) = f7(c2)) | big_f(c2, f10(f7(c2))) | (f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f7(c2)) | (~(c2 = f8(f7(c2)))))),
% 28.08/18.30 inference(quant_inst,[status(thm)],[])).
% 28.08/18.30 tff(8546,plain,
% 28.08/18.30 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(f7(c2)) = f7(c2)) | (f10(f7(c2)) = f7(c2)) | big_f(c2, f10(f7(c2))) | (~(c2 = f8(f7(c2)))) | big_f(f7(f7(c2)), f7(c2)) | (~(f7(c2) = f5(f7(c2))))),
% 28.08/18.30 inference(modus_ponens,[status(thm)],[8545, 8544])).
% 28.08/18.30 tff(8547,plain,
% 28.08/18.30 ((f10(f7(c2)) = f7(c2)) | big_f(c2, f10(f7(c2))) | (~(c2 = f8(f7(c2)))) | (~(f7(c2) = f5(f7(c2))))),
% 28.08/18.30 inference(unit_resolution,[status(thm)],[8546, 1745, 8473, 8452])).
% 28.08/18.30 tff(8548,plain,
% 28.08/18.30 (~(c2 = f8(f7(c2)))),
% 28.08/18.30 inference(unit_resolution,[status(thm)],[8547, 8540, 8522, 8523])).
% 28.08/18.30 tff(8549,plain,
% 28.08/18.30 (~(f8(c3) = c2)),
% 28.08/18.30 inference(modus_ponens,[status(thm)],[8548, 8539])).
% 28.08/18.30 tff(8550,plain,
% 28.08/18.30 ((f8(c3) = c1) <=> (f8(f7(f4(c4))) = c1)),
% 28.08/18.30 inference(monotonicity,[status(thm)],[8532])).
% 28.08/18.30 tff(8551,plain,
% 28.08/18.30 ((f8(f7(f4(c4))) = c1) <=> (f8(c3) = c1)),
% 28.08/18.30 inference(symmetry,[status(thm)],[8550])).
% 28.08/18.30 tff(8552,plain,
% 28.08/18.30 ((f7(c2) = f8(f7(c2))) <=> (c1 = f8(f7(f4(c4))))),
% 28.08/18.30 inference(monotonicity,[status(thm)],[292, 8536])).
% 28.08/18.30 tff(8553,plain,
% 28.08/18.30 ((f7(c2) = f8(f7(c2))) <=> (f8(f7(f4(c4))) = c1)),
% 28.08/18.30 inference(transitivity,[status(thm)],[8552, 8517])).
% 28.08/18.30 tff(8554,plain,
% 28.08/18.30 ((f7(c2) = f8(f7(c2))) <=> (f8(c3) = c1)),
% 28.08/18.30 inference(transitivity,[status(thm)],[8553, 8551])).
% 28.08/18.30 tff(8555,plain,
% 28.08/18.30 ((~(f7(c2) = f8(f7(c2)))) <=> (~(f8(c3) = c1))),
% 28.08/18.30 inference(monotonicity,[status(thm)],[8554])).
% 28.08/18.30 tff(8556,assumption,(~big_f(f7(c2), f10(f7(c2)))), introduced(assumption)).
% 28.08/18.30 tff(8557,plain,
% 28.08/18.30 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f7(f7(c2)) = f7(c2)) | (f10(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f7(c2)) | (~(f7(c2) = f5(f7(c2)))) | big_f(f7(c2), f10(f7(c2))) | (~(f7(c2) = f8(f7(c2)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(f7(c2)) = f7(c2)) | (f10(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f7(c2)) | (~(f7(c2) = f5(f7(c2)))) | big_f(f7(c2), f10(f7(c2))) | (~(f7(c2) = f8(f7(c2)))))),
% 28.08/18.30 inference(rewrite,[status(thm)],[])).
% 28.08/18.30 tff(8558,plain,
% 28.08/18.30 (((~(f7(c2) = f5(f7(c2)))) | (f10(f7(c2)) = f7(c2)) | big_f(f7(c2), f10(f7(c2))) | (f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f7(c2)) | (~(f7(c2) = f8(f7(c2))))) <=> ((f7(f7(c2)) = f7(c2)) | (f10(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f7(c2)) | (~(f7(c2) = f5(f7(c2)))) | big_f(f7(c2), f10(f7(c2))) | (~(f7(c2) = f8(f7(c2)))))),
% 28.08/18.30 inference(rewrite,[status(thm)],[])).
% 28.08/18.30 tff(8559,plain,
% 28.08/18.30 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(f7(c2) = f5(f7(c2)))) | (f10(f7(c2)) = f7(c2)) | big_f(f7(c2), f10(f7(c2))) | (f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f7(c2)) | (~(f7(c2) = f8(f7(c2)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f7(f7(c2)) = f7(c2)) | (f10(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f7(c2)) | (~(f7(c2) = f5(f7(c2)))) | big_f(f7(c2), f10(f7(c2))) | (~(f7(c2) = f8(f7(c2))))))),
% 28.08/18.30 inference(monotonicity,[status(thm)],[8558])).
% 28.08/18.30 tff(8560,plain,
% 28.08/18.30 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(f7(c2) = f5(f7(c2)))) | (f10(f7(c2)) = f7(c2)) | big_f(f7(c2), f10(f7(c2))) | (f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f7(c2)) | (~(f7(c2) = f8(f7(c2)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(f7(c2)) = f7(c2)) | (f10(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f7(c2)) | (~(f7(c2) = f5(f7(c2)))) | big_f(f7(c2), f10(f7(c2))) | (~(f7(c2) = f8(f7(c2)))))),
% 28.08/18.30 inference(transitivity,[status(thm)],[8559, 8557])).
% 28.08/18.30 tff(8561,plain,
% 28.08/18.30 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(f7(c2) = f5(f7(c2)))) | (f10(f7(c2)) = f7(c2)) | big_f(f7(c2), f10(f7(c2))) | (f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f7(c2)) | (~(f7(c2) = f8(f7(c2)))))),
% 28.08/18.30 inference(quant_inst,[status(thm)],[])).
% 28.08/18.30 tff(8562,plain,
% 28.08/18.30 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(f7(c2)) = f7(c2)) | (f10(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f7(c2)) | (~(f7(c2) = f5(f7(c2)))) | big_f(f7(c2), f10(f7(c2))) | (~(f7(c2) = f8(f7(c2))))),
% 28.08/18.30 inference(modus_ponens,[status(thm)],[8561, 8560])).
% 28.08/18.30 tff(8563,plain,
% 28.08/18.30 ((~(f7(c2) = f5(f7(c2)))) | big_f(f7(c2), f10(f7(c2))) | (~(f7(c2) = f8(f7(c2))))),
% 28.08/18.30 inference(unit_resolution,[status(thm)],[8562, 1745, 8473, 8452, 8523])).
% 28.08/18.30 tff(8564,plain,
% 28.08/18.30 (~(f7(c2) = f8(f7(c2)))),
% 28.08/18.30 inference(unit_resolution,[status(thm)],[8563, 8540, 8556])).
% 28.08/18.30 tff(8565,plain,
% 28.08/18.30 (~(f8(c3) = c1)),
% 28.08/18.30 inference(modus_ponens,[status(thm)],[8564, 8555])).
% 28.08/18.30 tff(8566,plain,
% 28.08/18.30 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f8(c3) = c1) | (f8(c3) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f8(c3) = c1) | (f8(c3) = c2))),
% 28.08/18.30 inference(rewrite,[status(thm)],[])).
% 28.08/18.30 tff(8567,plain,
% 28.08/18.30 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f8(c3) = c1) | (f8(c3) = c2))),
% 28.08/18.30 inference(quant_inst,[status(thm)],[])).
% 28.08/18.30 tff(8568,plain,
% 28.08/18.30 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f8(c3) = c1) | (f8(c3) = c2)),
% 28.08/18.30 inference(modus_ponens,[status(thm)],[8567, 8566])).
% 28.08/18.30 tff(8569,plain,
% 28.08/18.31 ((f8(c3) = c1) | (f8(c3) = c2)),
% 28.08/18.31 inference(unit_resolution,[status(thm)],[8568, 10])).
% 28.08/18.31 tff(8570,plain,
% 28.08/18.31 ($false),
% 28.08/18.31 inference(unit_resolution,[status(thm)],[8569, 8565, 8549])).
% 28.08/18.31 tff(8571,plain,((~(f7(c2) = f5(f7(c2)))) | (~(f4(c4) = c2)) | (~(f7(c2) = c1)) | (~(c3 = c1)) | big_f(f7(c2), f10(f7(c2))) | (f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f7(c2)) | (f10(f7(c2)) = f7(c2)) | big_f(c2, f10(f7(c2)))), inference(lemma,lemma(discharge,[]))).
% 28.08/18.31 tff(8572,plain,
% 28.08/18.31 (~(f7(c2) = f5(f7(c2)))),
% 28.08/18.31 inference(unit_resolution,[status(thm)],[8571, 8530, 292, 172, 79, 8463, 8452, 8523, 8522])).
% 28.08/18.31 tff(8573,plain,
% 28.08/18.31 (~(f5(c1) = c1)),
% 28.08/18.31 inference(modus_ponens,[status(thm)],[8572, 8472])).
% 28.08/18.31 tff(8574,plain,
% 28.08/18.31 (f5(c1) = c2),
% 28.08/18.31 inference(unit_resolution,[status(thm)],[1708, 8573])).
% 28.08/18.31 tff(8575,plain,
% 28.08/18.31 (c2 = f5(c1)),
% 28.08/18.31 inference(modus_ponens,[status(thm)],[8574, 155])).
% 28.08/18.31 tff(8576,plain,
% 28.08/18.31 (~(c2 = f8(c1))),
% 28.08/18.31 inference(unit_resolution,[status(thm)],[1752, 8575, 115, 3, 2907, 2946])).
% 28.08/18.31 tff(8577,plain,
% 28.08/18.31 (~(f8(c1) = c2)),
% 28.08/18.31 inference(unit_resolution,[status(thm)],[1675, 8576])).
% 28.08/18.31 tff(8578,plain,
% 28.08/18.31 (f8(c1) = c1),
% 28.08/18.31 inference(unit_resolution,[status(thm)],[1680, 8577])).
% 28.08/18.31 tff(8579,plain,
% 28.08/18.31 (c1 = f8(f7(f4(c4)))),
% 28.08/18.31 inference(modus_ponens,[status(thm)],[8578, 8521])).
% 28.08/18.31 tff(8580,plain,
% 28.08/18.31 ((~(f10(c1) = c1)) <=> (~(f10(f7(f4(c4))) = f7(f4(c4))))),
% 28.08/18.31 inference(monotonicity,[status(thm)],[8505])).
% 28.08/18.31 tff(8581,plain,
% 28.08/18.31 (~(f10(f7(f4(c4))) = f7(f4(c4)))),
% 28.08/18.31 inference(modus_ponens,[status(thm)],[3, 8580])).
% 28.08/18.31 tff(8582,plain,
% 28.08/18.31 (big_f(c1, f10(f7(f4(c4)))) <=> big_f(f7(c2), c2)),
% 28.08/18.31 inference(monotonicity,[status(thm)],[342, 8511])).
% 28.08/18.31 tff(8583,plain,
% 28.08/18.31 (big_f(f7(c2), c2) <=> big_f(c1, f10(f7(f4(c4))))),
% 28.08/18.31 inference(symmetry,[status(thm)],[8582])).
% 28.08/18.31 tff(8584,plain,
% 28.08/18.31 (big_f(f9(c2, c1), f10(c2)) <=> big_f(c1, f10(f7(f4(c4))))),
% 28.08/18.31 inference(transitivity,[status(thm)],[8454, 8583])).
% 28.08/18.31 tff(8585,plain,
% 28.08/18.31 ((~big_f(f9(c2, c1), f10(c2))) <=> (~big_f(c1, f10(f7(f4(c4)))))),
% 28.08/18.31 inference(monotonicity,[status(thm)],[8584])).
% 28.08/18.31 tff(8586,plain,
% 28.08/18.31 (~big_f(c1, f10(f7(f4(c4))))),
% 28.08/18.31 inference(modus_ponens,[status(thm)],[731, 8585])).
% 28.08/18.31 tff(8587,plain,
% 28.08/18.31 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (f10(f7(f4(c4))) = f7(f4(c4))) | big_f(c1, f10(f7(f4(c4)))) | (~(c1 = f8(f7(f4(c4))))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (f10(f7(f4(c4))) = f7(f4(c4))) | big_f(c1, f10(f7(f4(c4)))) | (~(c1 = f8(f7(f4(c4))))))),
% 28.08/18.31 inference(rewrite,[status(thm)],[])).
% 28.08/18.31 tff(8588,plain,
% 28.08/18.31 (((~(c2 = f5(c1))) | (f10(f7(f4(c4))) = f7(f4(c4))) | big_f(c1, f10(f7(f4(c4)))) | (f7(c1) = c1) | big_f(f7(c1), c2) | (~(c1 = f8(f7(f4(c4)))))) <=> ((~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (f10(f7(f4(c4))) = f7(f4(c4))) | big_f(c1, f10(f7(f4(c4)))) | (~(c1 = f8(f7(f4(c4))))))),
% 28.08/18.31 inference(rewrite,[status(thm)],[])).
% 28.08/18.31 tff(8589,plain,
% 28.08/18.31 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c2 = f5(c1))) | (f10(f7(f4(c4))) = f7(f4(c4))) | big_f(c1, f10(f7(f4(c4)))) | (f7(c1) = c1) | big_f(f7(c1), c2) | (~(c1 = f8(f7(f4(c4))))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (f10(f7(f4(c4))) = f7(f4(c4))) | big_f(c1, f10(f7(f4(c4)))) | (~(c1 = f8(f7(f4(c4)))))))),
% 28.08/18.31 inference(monotonicity,[status(thm)],[8588])).
% 28.08/18.31 tff(8590,plain,
% 28.08/18.31 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c2 = f5(c1))) | (f10(f7(f4(c4))) = f7(f4(c4))) | big_f(c1, f10(f7(f4(c4)))) | (f7(c1) = c1) | big_f(f7(c1), c2) | (~(c1 = f8(f7(f4(c4))))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (f10(f7(f4(c4))) = f7(f4(c4))) | big_f(c1, f10(f7(f4(c4)))) | (~(c1 = f8(f7(f4(c4))))))),
% 28.08/18.31 inference(transitivity,[status(thm)],[8589, 8587])).
% 28.08/18.31 tff(8591,plain,
% 28.08/18.31 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c2 = f5(c1))) | (f10(f7(f4(c4))) = f7(f4(c4))) | big_f(c1, f10(f7(f4(c4)))) | (f7(c1) = c1) | big_f(f7(c1), c2) | (~(c1 = f8(f7(f4(c4))))))),
% 28.08/18.31 inference(quant_inst,[status(thm)],[])).
% 28.08/18.31 tff(8592,plain,
% 28.08/18.31 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (f10(f7(f4(c4))) = f7(f4(c4))) | big_f(c1, f10(f7(f4(c4)))) | (~(c1 = f8(f7(f4(c4)))))),
% 28.08/18.31 inference(modus_ponens,[status(thm)],[8591, 8590])).
% 28.08/18.31 tff(8593,plain,
% 28.08/18.31 ((~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (f10(f7(f4(c4))) = f7(f4(c4))) | big_f(c1, f10(f7(f4(c4)))) | (~(c1 = f8(f7(f4(c4)))))),
% 28.08/18.31 inference(unit_resolution,[status(thm)],[8592, 1745])).
% 28.08/18.31 tff(8594,plain,
% 28.08/18.31 (~(c1 = f8(f7(f4(c4))))),
% 28.08/18.31 inference(unit_resolution,[status(thm)],[8593, 8575, 115, 8586, 2907, 8581])).
% 28.08/18.31 tff(8595,plain,
% 28.08/18.31 ($false),
% 28.08/18.31 inference(unit_resolution,[status(thm)],[8594, 8579])).
% 28.08/18.31 tff(8596,plain,(big_f(f9(c2, c1), f10(c2)) | (~(f7(c2) = c1)) | (~(f4(c4) = c2)) | (f7(c1) = c1) | big_f(f7(c1), c2) | (f10(c1) = c1) | big_f(c2, f10(c1)) | (~(c3 = c1)) | big_f(f7(f7(c2)), f7(c2)) | (f10(f7(c2)) = f7(c2)) | big_f(c2, f10(f7(c2))) | (~(f10(c2) = c2)) | (~(f9(c2, c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.08/18.31 tff(8597,plain,
% 28.08/18.31 ($false),
% 28.08/18.31 inference(unit_resolution,[status(thm)],[8596, 8516, 8508, 79, 115, 1726, 8500, 3, 172, 8452, 8451, 292, 122, 736])).
% 28.08/18.31 tff(8598,plain,((f10(c1) = c1) | (~(f4(c4) = c2)) | (f7(c1) = c1) | (~(c3 = c1)) | big_f(f7(f7(c2)), f7(c2)) | (~(f7(c2) = c1)) | (~(f10(c2) = c2)) | (~(f9(c2, c1) = c1)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 28.08/18.31 tff(8599,plain,
% 28.08/18.31 (f10(c1) = c1),
% 28.08/18.31 inference(unit_resolution,[status(thm)],[8598, 8450, 115, 172, 79, 22, 122, 8446, 121])).
% 28.08/18.31 tff(8600,plain,
% 28.08/18.31 (f5(f7(c2)) = f5(c1)),
% 28.08/18.31 inference(monotonicity,[status(thm)],[22])).
% 28.08/18.31 tff(8601,plain,
% 28.08/18.31 ((c2 = f5(f7(c2))) <=> (c2 = f5(c1))),
% 28.08/18.31 inference(monotonicity,[status(thm)],[8600])).
% 28.08/18.31 tff(8602,plain,
% 28.08/18.31 ((c2 = f5(c1)) <=> (c2 = f5(f7(c2)))),
% 28.08/18.31 inference(symmetry,[status(thm)],[8601])).
% 28.08/18.31 tff(8603,plain,
% 28.08/18.31 ((f5(c1) = c2) <=> (c2 = f5(f7(c2)))),
% 28.08/18.31 inference(transitivity,[status(thm)],[155, 8602])).
% 28.08/18.31 tff(8604,plain,
% 28.08/18.31 ((f7(c2) = f5(f7(c2))) <=> (c1 = f5(c1))),
% 28.08/18.31 inference(monotonicity,[status(thm)],[22, 8600])).
% 28.08/18.31 tff(8605,plain,
% 28.08/18.31 ((f7(c2) = f5(f7(c2))) <=> (f5(c1) = c1)),
% 28.08/18.31 inference(transitivity,[status(thm)],[8604, 128])).
% 28.08/18.31 tff(8606,plain,
% 28.08/18.31 ((~(f7(c2) = f5(f7(c2)))) <=> (~(f5(c1) = c1))),
% 28.08/18.31 inference(monotonicity,[status(thm)],[8605])).
% 28.08/18.31 tff(8607,plain,
% 28.08/18.31 (~big_f(c2, c4)),
% 28.08/18.31 inference(unit_resolution,[status(thm)],[6521, 5577, 79])).
% 28.08/18.31 tff(8608,plain,
% 28.08/18.31 (big_f(c3, c2) <=> big_f(f7(c2), c2)),
% 28.08/18.31 inference(monotonicity,[status(thm)],[8410])).
% 28.08/18.31 tff(8609,plain,
% 28.08/18.31 (big_f(f7(c2), c2) <=> big_f(c3, c2)),
% 28.08/18.31 inference(symmetry,[status(thm)],[8608])).
% 28.08/18.31 tff(8610,plain,
% 28.08/18.31 (f9(c2, f7(c2)) = f7(c2)),
% 28.08/18.31 inference(transitivity,[status(thm)],[8071, 8446, 125])).
% 28.08/18.31 tff(8611,plain,
% 28.08/18.31 (big_f(f9(c2, f7(c2)), f10(c2)) <=> big_f(f7(c2), c2)),
% 28.08/18.31 inference(monotonicity,[status(thm)],[8610, 122])).
% 28.08/18.31 tff(8612,plain,
% 28.08/18.31 (big_f(f9(c2, f7(c2)), f10(c2)) <=> big_f(c3, c2)),
% 28.08/18.31 inference(transitivity,[status(thm)],[8611, 8609])).
% 28.08/18.31 tff(8613,plain,
% 28.08/18.31 ((~big_f(f9(c2, f7(c2)), f10(c2))) <=> (~big_f(c3, c2))),
% 28.08/18.31 inference(monotonicity,[status(thm)],[8612])).
% 28.08/18.31 tff(8614,plain,
% 28.08/18.31 ((~(f7(c1) = c1)) <=> (~(f7(f7(c2)) = f7(c2)))),
% 28.08/18.31 inference(monotonicity,[status(thm)],[8314])).
% 28.08/18.31 tff(8615,plain,
% 28.08/18.31 (~(f7(f7(c2)) = f7(c2))),
% 28.08/18.31 inference(modus_ponens,[status(thm)],[115, 8614])).
% 28.08/18.31 tff(8616,plain,
% 28.08/18.31 (big_f(f7(f7(c2)), c2) <=> big_f(c2, c2)),
% 28.08/18.31 inference(monotonicity,[status(thm)],[8406])).
% 28.08/18.31 tff(8617,plain,
% 28.08/18.31 (big_f(c2, c2) <=> big_f(f7(f7(c2)), c2)),
% 28.08/18.31 inference(symmetry,[status(thm)],[8616])).
% 28.08/18.31 tff(8618,plain,
% 28.08/18.31 ((~big_f(c2, c2)) <=> (~big_f(f7(f7(c2)), c2))),
% 28.08/18.31 inference(monotonicity,[status(thm)],[8617])).
% 28.08/18.31 tff(8619,plain,
% 28.08/18.31 (~big_f(f7(f7(c2)), c2)),
% 28.08/18.31 inference(modus_ponens,[status(thm)],[121, 8618])).
% 28.08/18.31 tff(8620,plain,
% 28.08/18.31 (~big_f(f9(c2, f7(c2)), f10(c2))),
% 28.08/18.31 inference(unit_resolution,[status(thm)],[8498, 8610, 22, 8619, 122, 8615, 8450])).
% 28.08/18.31 tff(8621,plain,
% 28.08/18.31 (~big_f(c3, c2)),
% 28.08/18.31 inference(modus_ponens,[status(thm)],[8620, 8613])).
% 28.08/18.31 tff(8622,plain,
% 28.08/18.31 (~(c2 = f2(c3))),
% 28.08/18.31 inference(unit_resolution,[status(thm)],[2612, 8621, 2602, 8607])).
% 28.08/18.31 tff(8623,plain,
% 28.08/18.31 (~(f2(c3) = c2)),
% 28.08/18.31 inference(modus_ponens,[status(thm)],[8622, 3832])).
% 28.08/18.31 tff(8624,plain,
% 28.08/18.31 (f2(c3) = c1),
% 28.08/18.31 inference(unit_resolution,[status(thm)],[1273, 8623])).
% 28.08/18.31 tff(8625,plain,
% 28.08/18.31 (f2(c1) = c1),
% 28.08/18.31 inference(transitivity,[status(thm)],[5586, 8624])).
% 28.08/18.31 tff(8626,plain,
% 28.08/18.31 (big_f(c1, f2(c1)) <=> big_f(f7(c2), c1)),
% 28.08/18.31 inference(monotonicity,[status(thm)],[125, 8625])).
% 28.08/18.31 tff(8627,plain,
% 28.08/18.31 (big_f(c3, f2(c3))),
% 28.08/18.31 inference(unit_resolution,[status(thm)],[1315, 5577])).
% 28.08/18.31 tff(8628,plain,
% 28.08/18.31 (big_f(c1, f2(c1))),
% 28.08/18.31 inference(modus_ponens,[status(thm)],[2274, 5590])).
% 28.08/18.31 tff(8629,assumption,(~big_f(c1, f2(c1))), introduced(assumption)).
% 28.08/18.31 tff(8630,plain,
% 28.08/18.31 ($false),
% 28.08/18.31 inference(unit_resolution,[status(thm)],[8629, 8628])).
% 28.08/18.31 tff(8631,plain,((~big_f(c3, f2(c3))) | big_f(c1, f2(c1)) | (~(c3 = c1))), inference(lemma,lemma(discharge,[]))).
% 28.08/18.31 tff(8632,plain,
% 28.08/18.31 (big_f(c1, f2(c1))),
% 28.08/18.31 inference(unit_resolution,[status(thm)],[8631, 8627, 172])).
% 28.08/18.31 tff(8633,plain,
% 28.08/18.31 (big_f(f7(c2), c1)),
% 28.08/18.31 inference(modus_ponens,[status(thm)],[8632, 8626])).
% 28.08/18.31 tff(8634,plain,
% 28.08/18.31 (f9(f7(c2), f7(c2)) = f9(c1, c1)),
% 28.08/18.31 inference(monotonicity,[status(thm)],[292, 292])).
% 28.08/18.31 tff(8635,plain,
% 28.08/18.31 (f9(f7(c2), f7(c2)) = f7(c2)),
% 28.08/18.31 inference(transitivity,[status(thm)],[8634, 3949, 342])).
% 28.08/18.31 tff(8636,plain,
% 28.08/18.31 (f10(f7(c2)) = c1),
% 28.08/18.31 inference(transitivity,[status(thm)],[8167, 8503, 3762])).
% 28.08/18.31 tff(8637,plain,
% 28.08/18.31 (big_f(f9(f7(c2), f7(c2)), f10(f7(c2))) <=> big_f(f7(c2), c1)),
% 28.08/18.31 inference(monotonicity,[status(thm)],[8635, 8636])).
% 28.08/18.31 tff(8638,plain,
% 28.08/18.31 (big_f(f7(c2), c1) <=> big_f(f9(f7(c2), f7(c2)), f10(f7(c2)))),
% 28.08/18.31 inference(symmetry,[status(thm)],[8637])).
% 28.08/18.31 tff(8639,plain,
% 28.08/18.31 (big_f(f9(f7(c2), f7(c2)), f10(f7(c2)))),
% 28.08/18.31 inference(modus_ponens,[status(thm)],[338, 8638])).
% 28.08/18.31 tff(8640,plain,
% 28.08/18.31 (f10(f7(c2)) = f7(c2)),
% 28.08/18.31 inference(modus_ponens,[status(thm)],[3762, 8506])).
% 28.08/18.31 tff(8641,plain,
% 28.08/18.31 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f7(c2)) | (~(f7(c2) = f5(f7(c2)))) | (~(f9(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f9(f7(c2), f7(c2)), f10(f7(c2)))) | (~(f10(f7(c2)) = f7(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f7(c2)) | (~(f7(c2) = f5(f7(c2)))) | (~(f9(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f9(f7(c2), f7(c2)), f10(f7(c2)))) | (~(f10(f7(c2)) = f7(c2))))),
% 28.08/18.31 inference(rewrite,[status(thm)],[])).
% 28.08/18.31 tff(8642,plain,
% 28.08/18.31 (((~(f10(f7(c2)) = f7(c2))) | (f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f7(c2)) | (~(f9(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f9(f7(c2), f7(c2)), f10(f7(c2)))) | (~(f7(c2) = f5(f7(c2))))) <=> ((f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f7(c2)) | (~(f7(c2) = f5(f7(c2)))) | (~(f9(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f9(f7(c2), f7(c2)), f10(f7(c2)))) | (~(f10(f7(c2)) = f7(c2))))),
% 28.08/18.31 inference(rewrite,[status(thm)],[])).
% 28.08/18.31 tff(8643,plain,
% 28.08/18.31 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(f7(c2)) = f7(c2))) | (f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f7(c2)) | (~(f9(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f9(f7(c2), f7(c2)), f10(f7(c2)))) | (~(f7(c2) = f5(f7(c2)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f7(c2)) | (~(f7(c2) = f5(f7(c2)))) | (~(f9(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f9(f7(c2), f7(c2)), f10(f7(c2)))) | (~(f10(f7(c2)) = f7(c2)))))),
% 28.08/18.31 inference(monotonicity,[status(thm)],[8642])).
% 28.08/18.31 tff(8644,plain,
% 28.08/18.31 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(f7(c2)) = f7(c2))) | (f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f7(c2)) | (~(f9(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f9(f7(c2), f7(c2)), f10(f7(c2)))) | (~(f7(c2) = f5(f7(c2)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f7(c2)) | (~(f7(c2) = f5(f7(c2)))) | (~(f9(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f9(f7(c2), f7(c2)), f10(f7(c2)))) | (~(f10(f7(c2)) = f7(c2))))),
% 28.08/18.31 inference(transitivity,[status(thm)],[8643, 8641])).
% 28.08/18.31 tff(8645,plain,
% 28.08/18.31 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(f7(c2)) = f7(c2))) | (f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f7(c2)) | (~(f9(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f9(f7(c2), f7(c2)), f10(f7(c2)))) | (~(f7(c2) = f5(f7(c2)))))),
% 28.08/18.31 inference(quant_inst,[status(thm)],[])).
% 28.08/18.31 tff(8646,plain,
% 28.08/18.31 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f7(c2)) | (~(f7(c2) = f5(f7(c2)))) | (~(f9(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f9(f7(c2), f7(c2)), f10(f7(c2)))) | (~(f10(f7(c2)) = f7(c2)))),
% 28.08/18.31 inference(modus_ponens,[status(thm)],[8645, 8644])).
% 28.08/18.31 tff(8647,plain,
% 28.08/18.31 ((~(f9(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f9(f7(c2), f7(c2)), f10(f7(c2))))),
% 28.08/18.31 inference(unit_resolution,[status(thm)],[8646, 783, 8473, 8452, 8540, 8640])).
% 28.08/18.31 tff(8648,plain,
% 28.08/18.31 ($false),
% 28.08/18.31 inference(unit_resolution,[status(thm)],[8647, 8639, 8635])).
% 28.08/18.31 tff(8649,plain,((~(f9(c1, c1) = c1)) | (f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f7(c2)) | (~(f7(c2) = f5(f7(c2)))) | (~big_f(f7(c2), c1)) | (~(f10(c1) = c1)) | (~(f7(c2) = c1)) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.08/18.31 tff(8650,plain,
% 28.08/18.31 (~(f9(c1, c1) = c1)),
% 28.08/18.31 inference(unit_resolution,[status(thm)],[8649, 8540, 8452, 8473, 338, 3762, 22, 79])).
% 28.08/18.31 tff(8651,plain,
% 28.08/18.31 (f9(c1, c1) = c2),
% 28.08/18.31 inference(unit_resolution,[status(thm)],[3939, 8650])).
% 28.08/18.31 tff(8652,plain,
% 28.08/18.31 (f9(f7(c2), f7(c2)) = f9(c1, c1)),
% 28.08/18.31 inference(monotonicity,[status(thm)],[22, 22])).
% 28.08/18.31 tff(8653,plain,
% 28.08/18.31 (f9(f7(c2), f7(c2)) = c2),
% 28.08/18.31 inference(transitivity,[status(thm)],[8652, 8651])).
% 28.08/18.31 tff(8654,plain,
% 28.08/18.31 (big_f(f9(f7(c2), f7(c2)), f10(f7(c2))) <=> big_f(c2, c1)),
% 28.08/18.31 inference(monotonicity,[status(thm)],[8653, 8168])).
% 28.08/18.31 tff(8655,plain,
% 28.08/18.31 (big_f(c2, c1) <=> big_f(f9(f7(c2), f7(c2)), f10(f7(c2)))),
% 28.08/18.31 inference(symmetry,[status(thm)],[8654])).
% 28.08/18.31 tff(8656,plain,
% 28.08/18.31 ((~big_f(c2, c1)) <=> (~big_f(f9(f7(c2), f7(c2)), f10(f7(c2))))),
% 28.08/18.31 inference(monotonicity,[status(thm)],[8655])).
% 28.08/18.31 tff(8657,plain,
% 28.08/18.31 (~big_f(f9(f7(c2), f7(c2)), f10(f7(c2)))),
% 28.08/18.31 inference(modus_ponens,[status(thm)],[2, 8656])).
% 28.08/18.31 tff(8658,plain,
% 28.08/18.31 ((f9(f7(c2), f7(c2)) = f7(c2)) <=> (c2 = f7(c2))),
% 28.08/18.31 inference(monotonicity,[status(thm)],[8653])).
% 28.08/18.31 tff(8659,plain,
% 28.08/18.31 ((f9(f7(c2), f7(c2)) = f7(c2)) <=> (f7(c2) = c2)),
% 28.08/18.31 inference(transitivity,[status(thm)],[8658, 8409])).
% 28.08/18.31 tff(8660,plain,
% 28.08/18.31 ((f7(c2) = c2) <=> (f9(f7(c2), f7(c2)) = f7(c2))),
% 28.08/18.31 inference(symmetry,[status(thm)],[8659])).
% 28.08/18.31 tff(8661,plain,
% 28.08/18.31 ((~(f7(c2) = c2)) <=> (~(f9(f7(c2), f7(c2)) = f7(c2)))),
% 28.08/18.31 inference(monotonicity,[status(thm)],[8660])).
% 28.08/18.31 tff(8662,plain,
% 28.08/18.31 (~(f9(f7(c2), f7(c2)) = f7(c2))),
% 28.08/18.31 inference(modus_ponens,[status(thm)],[17, 8661])).
% 28.08/18.31 tff(8663,plain,
% 28.08/18.31 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f7(c2)) | (~(f7(c2) = f5(f7(c2)))) | big_f(f9(f7(c2), f7(c2)), f10(f7(c2))) | (f9(f7(c2), f7(c2)) = f7(c2)) | (~(f10(f7(c2)) = f7(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f7(c2)) | (~(f7(c2) = f5(f7(c2)))) | big_f(f9(f7(c2), f7(c2)), f10(f7(c2))) | (f9(f7(c2), f7(c2)) = f7(c2)) | (~(f10(f7(c2)) = f7(c2))))),
% 28.08/18.31 inference(rewrite,[status(thm)],[])).
% 28.08/18.31 tff(8664,plain,
% 28.08/18.31 (((~(f10(f7(c2)) = f7(c2))) | (f9(f7(c2), f7(c2)) = f7(c2)) | big_f(f9(f7(c2), f7(c2)), f10(f7(c2))) | (f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f7(c2)) | (~(f7(c2) = f5(f7(c2))))) <=> ((f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f7(c2)) | (~(f7(c2) = f5(f7(c2)))) | big_f(f9(f7(c2), f7(c2)), f10(f7(c2))) | (f9(f7(c2), f7(c2)) = f7(c2)) | (~(f10(f7(c2)) = f7(c2))))),
% 28.08/18.31 inference(rewrite,[status(thm)],[])).
% 28.08/18.31 tff(8665,plain,
% 28.08/18.31 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(f7(c2)) = f7(c2))) | (f9(f7(c2), f7(c2)) = f7(c2)) | big_f(f9(f7(c2), f7(c2)), f10(f7(c2))) | (f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f7(c2)) | (~(f7(c2) = f5(f7(c2)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f7(c2)) | (~(f7(c2) = f5(f7(c2)))) | big_f(f9(f7(c2), f7(c2)), f10(f7(c2))) | (f9(f7(c2), f7(c2)) = f7(c2)) | (~(f10(f7(c2)) = f7(c2)))))),
% 28.08/18.31 inference(monotonicity,[status(thm)],[8664])).
% 28.08/18.31 tff(8666,plain,
% 28.08/18.31 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(f7(c2)) = f7(c2))) | (f9(f7(c2), f7(c2)) = f7(c2)) | big_f(f9(f7(c2), f7(c2)), f10(f7(c2))) | (f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f7(c2)) | (~(f7(c2) = f5(f7(c2)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f7(c2)) | (~(f7(c2) = f5(f7(c2)))) | big_f(f9(f7(c2), f7(c2)), f10(f7(c2))) | (f9(f7(c2), f7(c2)) = f7(c2)) | (~(f10(f7(c2)) = f7(c2))))),
% 28.08/18.31 inference(transitivity,[status(thm)],[8665, 8663])).
% 28.08/18.31 tff(8667,plain,
% 28.08/18.31 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(f7(c2)) = f7(c2))) | (f9(f7(c2), f7(c2)) = f7(c2)) | big_f(f9(f7(c2), f7(c2)), f10(f7(c2))) | (f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f7(c2)) | (~(f7(c2) = f5(f7(c2)))))),
% 28.08/18.31 inference(quant_inst,[status(thm)],[])).
% 28.08/18.31 tff(8668,plain,
% 28.08/18.31 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f7(c2)) | (~(f7(c2) = f5(f7(c2)))) | big_f(f9(f7(c2), f7(c2)), f10(f7(c2))) | (f9(f7(c2), f7(c2)) = f7(c2)) | (~(f10(f7(c2)) = f7(c2)))),
% 28.08/18.31 inference(modus_ponens,[status(thm)],[8667, 8666])).
% 28.08/18.31 tff(8669,plain,
% 28.08/18.31 (big_f(f9(f7(c2), f7(c2)), f10(f7(c2))) | (f9(f7(c2), f7(c2)) = f7(c2))),
% 28.08/18.31 inference(unit_resolution,[status(thm)],[8668, 267, 8473, 8452, 8540, 8183])).
% 28.08/18.31 tff(8670,plain,
% 28.08/18.31 ($false),
% 28.08/18.31 inference(unit_resolution,[status(thm)],[8669, 8662, 8657])).
% 28.08/18.31 tff(8671,plain,((~(f7(c2) = f5(f7(c2)))) | (f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f7(c2)) | (f7(c2) = c2) | big_f(c2, c1) | (~(f10(c1) = c1)) | (~(f4(c4) = c2)) | (~big_f(f7(c2), c1))), inference(lemma,lemma(discharge,[]))).
% 28.08/18.31 tff(8672,plain,
% 28.08/18.31 (~(f7(c2) = f5(f7(c2)))),
% 28.08/18.31 inference(unit_resolution,[status(thm)],[8671, 8450, 8615, 17, 2, 8599, 79, 8633])).
% 28.08/18.31 tff(8673,plain,
% 28.08/18.31 (~(f5(c1) = c1)),
% 28.08/18.31 inference(modus_ponens,[status(thm)],[8672, 8606])).
% 28.08/18.31 tff(8674,plain,
% 28.08/18.31 (f5(c1) = c2),
% 28.08/18.31 inference(unit_resolution,[status(thm)],[1708, 8673])).
% 28.08/18.31 tff(8675,plain,
% 28.08/18.31 (c2 = f5(f7(c2))),
% 28.08/18.31 inference(modus_ponens,[status(thm)],[8674, 8603])).
% 28.08/18.31 tff(8676,plain,
% 28.08/18.31 (f9(f7(c2), f7(c2)) = c2),
% 28.08/18.31 inference(transitivity,[status(thm)],[8652, 4102])).
% 28.08/18.31 tff(8677,plain,
% 28.08/18.31 (big_f(f9(f7(c2), f7(c2)), f10(f7(c2))) <=> big_f(c2, c1)),
% 28.08/18.31 inference(monotonicity,[status(thm)],[8676, 8168])).
% 28.08/18.31 tff(8678,plain,
% 28.08/18.31 (big_f(c2, c1) <=> big_f(f9(f7(c2), f7(c2)), f10(f7(c2)))),
% 28.08/18.31 inference(symmetry,[status(thm)],[8677])).
% 28.08/18.31 tff(8679,plain,
% 28.08/18.31 ((~big_f(c2, c1)) <=> (~big_f(f9(f7(c2), f7(c2)), f10(f7(c2))))),
% 28.08/18.31 inference(monotonicity,[status(thm)],[8678])).
% 28.08/18.31 tff(8680,plain,
% 28.08/18.31 (~big_f(f9(f7(c2), f7(c2)), f10(f7(c2)))),
% 28.08/18.31 inference(modus_ponens,[status(thm)],[2, 8679])).
% 28.08/18.31 tff(8681,plain,
% 28.08/18.31 ((f9(f7(c2), f7(c2)) = f7(c2)) <=> (c2 = f7(c2))),
% 28.08/18.31 inference(monotonicity,[status(thm)],[8676])).
% 28.08/18.31 tff(8682,plain,
% 28.08/18.31 ((f9(f7(c2), f7(c2)) = f7(c2)) <=> (f7(c2) = c2)),
% 28.08/18.31 inference(transitivity,[status(thm)],[8681, 8409])).
% 28.08/18.31 tff(8683,plain,
% 28.08/18.31 ((f7(c2) = c2) <=> (f9(f7(c2), f7(c2)) = f7(c2))),
% 28.08/18.31 inference(symmetry,[status(thm)],[8682])).
% 28.08/18.31 tff(8684,plain,
% 28.08/18.31 ((~(f7(c2) = c2)) <=> (~(f9(f7(c2), f7(c2)) = f7(c2)))),
% 28.08/18.31 inference(monotonicity,[status(thm)],[8683])).
% 28.08/18.31 tff(8685,plain,
% 28.08/18.31 (~(f9(f7(c2), f7(c2)) = f7(c2))),
% 28.08/18.31 inference(modus_ponens,[status(thm)],[17, 8684])).
% 28.08/18.31 tff(8686,assumption,(c2 = f5(f7(c2))), introduced(assumption)).
% 28.08/18.31 tff(8687,plain,
% 28.08/18.31 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), c2) | (~(c2 = f5(f7(c2)))) | big_f(f9(f7(c2), f7(c2)), f10(f7(c2))) | (f9(f7(c2), f7(c2)) = f7(c2)) | (~(f10(f7(c2)) = f7(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), c2) | (~(c2 = f5(f7(c2)))) | big_f(f9(f7(c2), f7(c2)), f10(f7(c2))) | (f9(f7(c2), f7(c2)) = f7(c2)) | (~(f10(f7(c2)) = f7(c2))))),
% 28.08/18.31 inference(rewrite,[status(thm)],[])).
% 28.08/18.31 tff(8688,plain,
% 28.08/18.31 (((~(f10(f7(c2)) = f7(c2))) | (f9(f7(c2), f7(c2)) = f7(c2)) | big_f(f9(f7(c2), f7(c2)), f10(f7(c2))) | (f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), c2) | (~(c2 = f5(f7(c2))))) <=> ((f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), c2) | (~(c2 = f5(f7(c2)))) | big_f(f9(f7(c2), f7(c2)), f10(f7(c2))) | (f9(f7(c2), f7(c2)) = f7(c2)) | (~(f10(f7(c2)) = f7(c2))))),
% 28.08/18.31 inference(rewrite,[status(thm)],[])).
% 28.08/18.31 tff(8689,plain,
% 28.08/18.31 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(f7(c2)) = f7(c2))) | (f9(f7(c2), f7(c2)) = f7(c2)) | big_f(f9(f7(c2), f7(c2)), f10(f7(c2))) | (f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), c2) | (~(c2 = f5(f7(c2)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), c2) | (~(c2 = f5(f7(c2)))) | big_f(f9(f7(c2), f7(c2)), f10(f7(c2))) | (f9(f7(c2), f7(c2)) = f7(c2)) | (~(f10(f7(c2)) = f7(c2)))))),
% 28.08/18.31 inference(monotonicity,[status(thm)],[8688])).
% 28.08/18.31 tff(8690,plain,
% 28.08/18.31 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(f7(c2)) = f7(c2))) | (f9(f7(c2), f7(c2)) = f7(c2)) | big_f(f9(f7(c2), f7(c2)), f10(f7(c2))) | (f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), c2) | (~(c2 = f5(f7(c2)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), c2) | (~(c2 = f5(f7(c2)))) | big_f(f9(f7(c2), f7(c2)), f10(f7(c2))) | (f9(f7(c2), f7(c2)) = f7(c2)) | (~(f10(f7(c2)) = f7(c2))))),
% 28.08/18.32 inference(transitivity,[status(thm)],[8689, 8687])).
% 28.08/18.32 tff(8691,plain,
% 28.08/18.32 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(f7(c2)) = f7(c2))) | (f9(f7(c2), f7(c2)) = f7(c2)) | big_f(f9(f7(c2), f7(c2)), f10(f7(c2))) | (f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), c2) | (~(c2 = f5(f7(c2)))))),
% 28.08/18.32 inference(quant_inst,[status(thm)],[])).
% 28.08/18.32 tff(8692,plain,
% 28.08/18.32 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), c2) | (~(c2 = f5(f7(c2)))) | big_f(f9(f7(c2), f7(c2)), f10(f7(c2))) | (f9(f7(c2), f7(c2)) = f7(c2)) | (~(f10(f7(c2)) = f7(c2)))),
% 28.08/18.32 inference(modus_ponens,[status(thm)],[8691, 8690])).
% 28.08/18.32 tff(8693,plain,
% 28.08/18.32 (big_f(f9(f7(c2), f7(c2)), f10(f7(c2))) | (f9(f7(c2), f7(c2)) = f7(c2))),
% 28.08/18.32 inference(unit_resolution,[status(thm)],[8692, 267, 8473, 8487, 8686, 8183])).
% 28.08/18.32 tff(8694,plain,
% 28.08/18.32 ($false),
% 28.08/18.32 inference(unit_resolution,[status(thm)],[8693, 8685, 8680])).
% 28.08/18.32 tff(8695,plain,((~(f9(c1, c1) = c2)) | (f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), c2) | (~(c2 = f5(f7(c2)))) | (f7(c2) = c2) | big_f(c2, c1) | (~(f10(c1) = c1)) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.08/18.32 tff(8696,plain,
% 28.08/18.32 (~(f9(c1, c1) = c2)),
% 28.08/18.32 inference(unit_resolution,[status(thm)],[8695, 8619, 8615, 8675, 17, 2, 8599, 79])).
% 28.08/18.32 tff(8697,plain,
% 28.08/18.32 (f9(c1, c1) = c1),
% 28.08/18.32 inference(unit_resolution,[status(thm)],[3939, 8696])).
% 28.08/18.32 tff(8698,plain,
% 28.08/18.32 (f9(c1, c1) = f7(c2)),
% 28.08/18.32 inference(transitivity,[status(thm)],[8697, 125])).
% 28.08/18.32 tff(8699,plain,
% 28.08/18.32 (big_f(f9(c1, c1), c1) <=> big_f(f7(c2), c1)),
% 28.08/18.32 inference(monotonicity,[status(thm)],[8698])).
% 28.08/18.32 tff(8700,plain,
% 28.08/18.32 (big_f(f7(c2), c1) <=> big_f(f9(c1, c1), c1)),
% 28.08/18.32 inference(symmetry,[status(thm)],[8699])).
% 28.08/18.32 tff(8701,plain,
% 28.08/18.32 (big_f(f9(c1, c1), c1)),
% 28.08/18.32 inference(modus_ponens,[status(thm)],[8633, 8700])).
% 28.08/18.32 tff(8702,plain,
% 28.08/18.32 (c2 = f5(c1)),
% 28.08/18.32 inference(modus_ponens,[status(thm)],[8674, 155])).
% 28.08/18.32 tff(8703,plain,
% 28.08/18.32 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))),
% 28.08/18.32 inference(rewrite,[status(thm)],[])).
% 28.08/18.32 tff(8704,plain,
% 28.08/18.32 (((~(f10(c1) = c1)) | (f7(c1) = c1) | big_f(f7(c1), c2) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(c2 = f5(c1)))) <=> ((~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))),
% 28.08/18.32 inference(rewrite,[status(thm)],[])).
% 28.08/18.32 tff(8705,plain,
% 28.08/18.32 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f7(c1) = c1) | big_f(f7(c1), c2) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(c2 = f5(c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1)))))),
% 28.08/18.32 inference(monotonicity,[status(thm)],[8704])).
% 28.08/18.32 tff(8706,plain,
% 28.08/18.32 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f7(c1) = c1) | big_f(f7(c1), c2) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(c2 = f5(c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))),
% 28.08/18.32 inference(transitivity,[status(thm)],[8705, 8703])).
% 28.08/18.32 tff(8707,plain,
% 28.08/18.32 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f7(c1) = c1) | big_f(f7(c1), c2) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(c2 = f5(c1))))),
% 28.08/18.32 inference(quant_inst,[status(thm)],[])).
% 28.08/18.32 tff(8708,plain,
% 28.08/18.32 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1)))),
% 28.08/18.32 inference(modus_ponens,[status(thm)],[8707, 8706])).
% 28.08/18.32 tff(8709,plain,
% 28.08/18.32 ((~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1)))),
% 28.08/18.32 inference(unit_resolution,[status(thm)],[8708, 783])).
% 28.08/18.32 tff(8710,plain,
% 28.08/18.32 (~big_f(f9(c1, c1), f10(c1))),
% 28.08/18.32 inference(unit_resolution,[status(thm)],[8709, 8697, 115, 1726, 8702, 8599])).
% 28.08/18.32 tff(8711,plain,
% 28.08/18.32 ((~big_f(f9(c1, c1), f10(c1))) <=> (~big_f(f9(c1, c1), c1))),
% 28.08/18.32 inference(monotonicity,[status(thm)],[3931])).
% 28.08/18.32 tff(8712,assumption,(~big_f(f9(c1, c1), f10(c1))), introduced(assumption)).
% 28.08/18.32 tff(8713,plain,
% 28.08/18.32 (~big_f(f9(c1, c1), c1)),
% 28.08/18.32 inference(modus_ponens,[status(thm)],[8712, 8711])).
% 28.08/18.32 tff(8714,assumption,(big_f(f9(c1, c1), c1)), introduced(assumption)).
% 28.08/18.32 tff(8715,plain,
% 28.08/18.32 ($false),
% 28.08/18.32 inference(unit_resolution,[status(thm)],[8714, 8713])).
% 28.08/18.32 tff(8716,plain,(big_f(f9(c1, c1), f10(c1)) | (~big_f(f9(c1, c1), c1)) | (~(f10(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.08/18.32 tff(8717,plain,
% 28.08/18.32 (~big_f(f9(c1, c1), c1)),
% 28.08/18.32 inference(unit_resolution,[status(thm)],[8716, 8710, 8599])).
% 28.08/18.32 tff(8718,plain,
% 28.08/18.32 ($false),
% 28.08/18.32 inference(unit_resolution,[status(thm)],[8717, 8701])).
% 28.08/18.32 tff(8719,plain,(big_f(c2, c1) | (f7(c1) = c1) | (f7(c2) = c2) | (~(f4(c4) = c2)) | (~(c3 = c1)) | (~(f10(c2) = c2)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 28.08/18.32 tff(8720,plain,
% 28.08/18.32 (big_f(c2, c1)),
% 28.08/18.32 inference(unit_resolution,[status(thm)],[8719, 172, 17, 79, 115, 122, 121])).
% 28.08/18.32 tff(8721,plain,
% 28.08/18.32 ((c2 = c4) <=> (c4 = c2)),
% 28.08/18.32 inference(symmetry,[status(thm)],[159])).
% 28.08/18.32 tff(8722,plain,
% 28.08/18.32 ((~(c2 = c4)) <=> (~(c4 = c2))),
% 28.08/18.32 inference(monotonicity,[status(thm)],[8721])).
% 28.08/18.32 tff(8723,plain,
% 28.08/18.32 ((~(f7(c2) = c2)) <=> (~(c2 = c3))),
% 28.08/18.32 inference(monotonicity,[status(thm)],[8413])).
% 28.08/18.32 tff(8724,plain,
% 28.08/18.32 (~(c2 = c3)),
% 28.08/18.32 inference(modus_ponens,[status(thm)],[17, 8723])).
% 28.08/18.32 tff(8725,plain,
% 28.08/18.32 (f1(c2, f7(c2)) = f1(c2, c1)),
% 28.08/18.32 inference(monotonicity,[status(thm)],[292])).
% 28.08/18.32 tff(8726,plain,
% 28.08/18.32 (big_f(c2, f1(c2, f7(c2))) <=> big_f(c2, f1(c2, c1))),
% 28.08/18.32 inference(monotonicity,[status(thm)],[8725])).
% 28.08/18.32 tff(8727,plain,
% 28.08/18.32 (big_f(c2, f1(c2, c1)) <=> big_f(c2, f1(c2, f7(c2)))),
% 28.08/18.32 inference(symmetry,[status(thm)],[8726])).
% 28.08/18.32 tff(8728,plain,
% 28.08/18.32 (c4 = c2),
% 28.08/18.32 inference(symmetry,[status(thm)],[631])).
% 28.08/18.32 tff(8729,plain,
% 28.08/18.32 (big_f(c2, c4) <=> big_f(c2, c2)),
% 28.08/18.32 inference(monotonicity,[status(thm)],[8728])).
% 28.08/18.32 tff(8730,plain,
% 28.08/18.32 (big_f(c2, c2) <=> big_f(c2, c4)),
% 28.08/18.32 inference(symmetry,[status(thm)],[8729])).
% 28.08/18.32 tff(8731,plain,
% 28.08/18.32 (big_f(c2, c2) <=> big_f(f4(c4), c4)),
% 28.08/18.32 inference(transitivity,[status(thm)],[8730, 376])).
% 28.08/18.32 tff(8732,plain,
% 28.08/18.32 ((~big_f(c2, c2)) <=> (~big_f(f4(c4), c4))),
% 28.08/18.32 inference(monotonicity,[status(thm)],[8731])).
% 28.08/18.32 tff(8733,plain,
% 28.08/18.32 (~big_f(f4(c4), c4)),
% 28.08/18.32 inference(modus_ponens,[status(thm)],[121, 8732])).
% 28.08/18.32 tff(8734,plain,
% 28.08/18.32 (f1(f7(f7(c2)), c1) = c1),
% 28.08/18.32 inference(unit_resolution,[status(thm)],[422, 8733, 292, 121, 347, 378])).
% 28.08/18.32 tff(8735,plain,
% 28.08/18.32 (c1 = f1(f7(f7(c2)), c1)),
% 28.08/18.32 inference(symmetry,[status(thm)],[8734])).
% 28.08/18.32 tff(8736,plain,
% 28.08/18.32 (c1 = f1(c2, c1)),
% 28.08/18.32 inference(transitivity,[status(thm)],[8735, 357])).
% 28.08/18.32 tff(8737,plain,
% 28.08/18.32 (big_f(c2, c1) <=> big_f(c2, f1(c2, c1))),
% 28.08/18.32 inference(monotonicity,[status(thm)],[8736])).
% 28.08/18.32 tff(8738,plain,
% 28.08/18.32 (big_f(c2, c1) <=> big_f(c2, f1(c2, f7(c2)))),
% 28.08/18.32 inference(transitivity,[status(thm)],[8737, 8727])).
% 28.08/18.32 tff(8739,plain,
% 28.08/18.32 (big_f(c2, f1(c2, f7(c2)))),
% 28.08/18.32 inference(modus_ponens,[status(thm)],[348, 8738])).
% 28.08/18.32 tff(8740,plain,
% 28.08/18.32 ((f1(c2, f7(c2)) = f7(c2)) <=> (f1(c2, c1) = c1)),
% 28.08/18.32 inference(monotonicity,[status(thm)],[8725, 292])).
% 28.08/18.32 tff(8741,plain,
% 28.08/18.32 ((f1(c2, c1) = c1) <=> (f1(c2, f7(c2)) = f7(c2))),
% 28.08/18.32 inference(symmetry,[status(thm)],[8740])).
% 28.08/18.32 tff(8742,plain,
% 28.08/18.32 ((f1(f7(f7(c2)), c1) = c1) <=> (f1(c2, f7(c2)) = f7(c2))),
% 28.08/18.32 inference(transitivity,[status(thm)],[541, 8741])).
% 28.08/18.32 tff(8743,plain,
% 28.08/18.32 (f1(c2, f7(c2)) = f7(c2)),
% 28.08/18.32 inference(modus_ponens,[status(thm)],[8734, 8742])).
% 28.08/18.32 tff(8744,plain,
% 28.08/18.32 (f4(c2) = f4(c4)),
% 28.08/18.32 inference(monotonicity,[status(thm)],[631])).
% 28.08/18.32 tff(8745,plain,
% 28.08/18.32 (f4(c4) = f4(c2)),
% 28.08/18.32 inference(symmetry,[status(thm)],[8744])).
% 28.08/18.32 tff(8746,plain,
% 28.08/18.32 (c2 = f4(c2)),
% 28.08/18.32 inference(transitivity,[status(thm)],[436, 8745])).
% 28.08/18.32 tff(8747,plain,
% 28.08/18.32 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (~big_f(c2, f1(c2, f7(c2)))) | (~(f1(c2, f7(c2)) = f7(c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (~big_f(c2, f1(c2, f7(c2)))) | (~(f1(c2, f7(c2)) = f7(c2))))),
% 28.08/18.32 inference(rewrite,[status(thm)],[])).
% 28.08/18.32 tff(8748,plain,
% 28.08/18.32 (((c2 = c3) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))) | (~(f1(c2, f7(c2)) = f7(c2))) | (~big_f(c2, f1(c2, f7(c2))))) <=> ((c2 = c3) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (~big_f(c2, f1(c2, f7(c2)))) | (~(f1(c2, f7(c2)) = f7(c2))))),
% 28.08/18.32 inference(rewrite,[status(thm)],[])).
% 28.08/18.32 tff(8749,plain,
% 28.08/18.32 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))) | (~(f1(c2, f7(c2)) = f7(c2))) | (~big_f(c2, f1(c2, f7(c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (~big_f(c2, f1(c2, f7(c2)))) | (~(f1(c2, f7(c2)) = f7(c2)))))),
% 28.08/18.32 inference(monotonicity,[status(thm)],[8748])).
% 28.08/18.32 tff(8750,plain,
% 28.08/18.32 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))) | (~(f1(c2, f7(c2)) = f7(c2))) | (~big_f(c2, f1(c2, f7(c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (~big_f(c2, f1(c2, f7(c2)))) | (~(f1(c2, f7(c2)) = f7(c2))))),
% 28.08/18.32 inference(transitivity,[status(thm)],[8749, 8747])).
% 28.08/18.32 tff(8751,plain,
% 28.08/18.32 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))) | (~(f1(c2, f7(c2)) = f7(c2))) | (~big_f(c2, f1(c2, f7(c2)))))),
% 28.08/18.32 inference(quant_inst,[status(thm)],[])).
% 28.08/18.32 tff(8752,plain,
% 28.08/18.32 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (~big_f(c2, f1(c2, f7(c2)))) | (~(f1(c2, f7(c2)) = f7(c2)))),
% 28.08/18.32 inference(modus_ponens,[status(thm)],[8751, 8750])).
% 28.08/18.32 tff(8753,plain,
% 28.08/18.32 ($false),
% 28.08/18.32 inference(unit_resolution,[status(thm)],[8752, 447, 631, 8746, 121, 377, 8743, 8739])).
% 28.08/18.32 tff(8754,plain,((~(c2 = c4)) | big_f(c2, c2) | (c2 = c3) | (~big_f(c2, c1)) | (~(f7(c2) = c1)) | (~(f7(c1) = c2)) | (f7(f7(c2)) = c3) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.08/18.32 tff(8755,plain,
% 28.08/18.32 (~(c2 = c4)),
% 28.08/18.32 inference(unit_resolution,[status(thm)],[8754, 8724, 121, 8720, 22, 120, 8416, 79])).
% 28.08/18.32 tff(8756,plain,
% 28.08/18.32 (~(c4 = c2)),
% 28.08/18.32 inference(modus_ponens,[status(thm)],[8755, 8722])).
% 28.08/18.32 tff(8757,plain,
% 28.08/18.32 (c4 = c1),
% 28.08/18.32 inference(unit_resolution,[status(thm)],[461, 8756])).
% 28.08/18.32 tff(8758,plain,
% 28.08/18.32 (f4(f7(c2)) = f4(c1)),
% 28.08/18.32 inference(monotonicity,[status(thm)],[22])).
% 28.08/18.32 tff(8759,plain,
% 28.08/18.32 (f4(f7(c2)) = c2),
% 28.08/18.32 inference(transitivity,[status(thm)],[8758, 568, 79])).
% 28.08/18.32 tff(8760,plain,
% 28.08/18.32 ((f7(c2) = f4(f7(c2))) <=> (f7(c2) = c2)),
% 28.08/18.32 inference(monotonicity,[status(thm)],[8759])).
% 28.08/18.32 tff(8761,plain,
% 28.08/18.32 ((f7(c2) = c2) <=> (f7(c2) = f4(f7(c2)))),
% 28.08/18.32 inference(symmetry,[status(thm)],[8760])).
% 28.08/18.32 tff(8762,plain,
% 28.08/18.32 ((~(f7(c2) = c2)) <=> (~(f7(c2) = f4(f7(c2))))),
% 28.08/18.32 inference(monotonicity,[status(thm)],[8761])).
% 28.08/18.32 tff(8763,plain,
% 28.08/18.32 (~(f7(c2) = f4(f7(c2)))),
% 28.08/18.32 inference(modus_ponens,[status(thm)],[17, 8762])).
% 28.08/18.32 tff(8764,plain,
% 28.08/18.32 (f7(c2) = c4),
% 28.08/18.32 inference(transitivity,[status(thm)],[22, 567])).
% 28.08/18.32 tff(8765,plain,
% 28.08/18.32 (big_f(f7(c2), f7(c2))),
% 28.08/18.32 inference(modus_ponens,[status(thm)],[338, 8076])).
% 28.08/18.32 tff(8766,plain,
% 28.08/18.32 (f1(c2, f7(c2)) = f1(c2, c1)),
% 28.08/18.32 inference(monotonicity,[status(thm)],[22])).
% 28.08/18.32 tff(8767,plain,
% 28.08/18.32 (big_f(c2, f1(c2, f7(c2))) <=> big_f(c2, f1(c2, c1))),
% 28.08/18.32 inference(monotonicity,[status(thm)],[8766])).
% 28.08/18.32 tff(8768,plain,
% 28.08/18.32 (big_f(c2, f1(c2, c1)) <=> big_f(c2, f1(c2, f7(c2)))),
% 28.08/18.32 inference(symmetry,[status(thm)],[8767])).
% 28.08/18.32 tff(8769,assumption,(~(f7(c2) = f4(f7(c2)))), introduced(assumption)).
% 28.08/18.32 tff(8770,assumption,(f7(c2) = c4), introduced(assumption)).
% 28.08/18.32 tff(8771,plain,
% 28.08/18.32 (big_f(c2, c1) <=> big_f(c2, f1(c2, f7(c2)))),
% 28.08/18.32 inference(transitivity,[status(thm)],[877, 8727])).
% 28.08/18.32 tff(8772,plain,
% 28.08/18.32 (big_f(c2, f1(c2, f7(c2)))),
% 28.08/18.32 inference(modus_ponens,[status(thm)],[348, 8771])).
% 28.08/18.32 tff(8773,plain,
% 28.08/18.32 (f1(c2, f7(c2)) = f7(c2)),
% 28.08/18.32 inference(modus_ponens,[status(thm)],[874, 8742])).
% 28.08/18.32 tff(8774,plain,
% 28.08/18.32 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~big_f(c2, f1(c2, f7(c2)))) | (~(f1(c2, f7(c2)) = f7(c2))) | (~(f7(c2) = c4)) | (~big_f(f7(c2), f7(c2))) | (f7(c2) = f4(f7(c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~big_f(c2, f1(c2, f7(c2)))) | (~(f1(c2, f7(c2)) = f7(c2))) | (~(f7(c2) = c4)) | (~big_f(f7(c2), f7(c2))) | (f7(c2) = f4(f7(c2))))),
% 28.08/18.32 inference(rewrite,[status(thm)],[])).
% 28.08/18.32 tff(8775,plain,
% 28.08/18.32 (((c2 = c3) | (~(f7(c2) = c4)) | (f7(c2) = f4(f7(c2))) | (~big_f(f7(c2), f7(c2))) | (~(f1(c2, f7(c2)) = f7(c2))) | (~big_f(c2, f1(c2, f7(c2))))) <=> ((c2 = c3) | (~big_f(c2, f1(c2, f7(c2)))) | (~(f1(c2, f7(c2)) = f7(c2))) | (~(f7(c2) = c4)) | (~big_f(f7(c2), f7(c2))) | (f7(c2) = f4(f7(c2))))),
% 28.08/18.32 inference(rewrite,[status(thm)],[])).
% 28.08/18.32 tff(8776,plain,
% 28.08/18.32 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f7(c2) = c4)) | (f7(c2) = f4(f7(c2))) | (~big_f(f7(c2), f7(c2))) | (~(f1(c2, f7(c2)) = f7(c2))) | (~big_f(c2, f1(c2, f7(c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~big_f(c2, f1(c2, f7(c2)))) | (~(f1(c2, f7(c2)) = f7(c2))) | (~(f7(c2) = c4)) | (~big_f(f7(c2), f7(c2))) | (f7(c2) = f4(f7(c2)))))),
% 28.08/18.32 inference(monotonicity,[status(thm)],[8775])).
% 28.08/18.32 tff(8777,plain,
% 28.08/18.32 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f7(c2) = c4)) | (f7(c2) = f4(f7(c2))) | (~big_f(f7(c2), f7(c2))) | (~(f1(c2, f7(c2)) = f7(c2))) | (~big_f(c2, f1(c2, f7(c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~big_f(c2, f1(c2, f7(c2)))) | (~(f1(c2, f7(c2)) = f7(c2))) | (~(f7(c2) = c4)) | (~big_f(f7(c2), f7(c2))) | (f7(c2) = f4(f7(c2))))),
% 28.08/18.32 inference(transitivity,[status(thm)],[8776, 8774])).
% 28.08/18.32 tff(8778,plain,
% 28.08/18.32 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f7(c2) = c4)) | (f7(c2) = f4(f7(c2))) | (~big_f(f7(c2), f7(c2))) | (~(f1(c2, f7(c2)) = f7(c2))) | (~big_f(c2, f1(c2, f7(c2)))))),
% 28.08/18.32 inference(quant_inst,[status(thm)],[])).
% 28.08/18.32 tff(8779,plain,
% 28.08/18.32 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~big_f(c2, f1(c2, f7(c2)))) | (~(f1(c2, f7(c2)) = f7(c2))) | (~(f7(c2) = c4)) | (~big_f(f7(c2), f7(c2))) | (f7(c2) = f4(f7(c2)))),
% 28.08/18.32 inference(modus_ponens,[status(thm)],[8778, 8777])).
% 28.08/18.32 tff(8780,plain,
% 28.08/18.32 ($false),
% 28.08/18.32 inference(unit_resolution,[status(thm)],[8779, 553, 377, 8773, 8772, 8372, 8770, 8769])).
% 28.08/18.32 tff(8781,plain,((~(f1(f7(f7(c2)), c1) = c1)) | (c2 = c3) | (~big_f(f7(c2), f7(c2))) | (~(f7(c2) = c4)) | (f7(c2) = f4(f7(c2))) | (~big_f(c2, c1)) | (~(f7(c2) = c1)) | (~(f7(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.08/18.32 tff(8782,plain,
% 28.08/18.32 (~(f1(f7(f7(c2)), c1) = c1)),
% 28.08/18.32 inference(unit_resolution,[status(thm)],[8781, 8765, 377, 8764, 8763, 348, 22, 347])).
% 28.08/18.32 tff(8783,plain,
% 28.08/18.32 (f1(f7(f7(c2)), c1) = c2),
% 28.08/18.32 inference(unit_resolution,[status(thm)],[384, 8782])).
% 28.08/18.32 tff(8784,plain,
% 28.08/18.32 (c2 = f7(f7(c2))),
% 28.08/18.32 inference(transitivity,[status(thm)],[354, 8313])).
% 28.08/18.32 tff(8785,plain,
% 28.08/18.32 (f1(c2, c1) = f1(f7(f7(c2)), c1)),
% 28.08/18.32 inference(monotonicity,[status(thm)],[8784])).
% 28.08/18.32 tff(8786,plain,
% 28.08/18.32 (f1(c2, c1) = c2),
% 28.08/18.32 inference(transitivity,[status(thm)],[8785, 8783])).
% 28.08/18.32 tff(8787,plain,
% 28.08/18.32 (big_f(c2, f1(c2, c1)) <=> big_f(c2, c2)),
% 28.08/18.32 inference(monotonicity,[status(thm)],[8786])).
% 28.08/18.32 tff(8788,plain,
% 28.08/18.32 (big_f(c2, c2) <=> big_f(c2, f1(c2, c1))),
% 28.08/18.32 inference(symmetry,[status(thm)],[8787])).
% 28.08/18.32 tff(8789,plain,
% 28.08/18.32 (big_f(c2, c2) <=> big_f(c2, f1(c2, f7(c2)))),
% 28.08/18.32 inference(transitivity,[status(thm)],[8788, 8768])).
% 28.08/18.32 tff(8790,plain,
% 28.08/18.32 ((~big_f(c2, c2)) <=> (~big_f(c2, f1(c2, f7(c2))))),
% 28.08/18.32 inference(monotonicity,[status(thm)],[8789])).
% 28.08/18.32 tff(8791,plain,
% 28.08/18.32 (~big_f(c2, f1(c2, f7(c2)))),
% 28.08/18.32 inference(modus_ponens,[status(thm)],[121, 8790])).
% 28.08/18.32 tff(8792,plain,
% 28.08/18.32 ((f1(c2, f7(c2)) = f7(c2)) <=> (f1(c2, c1) = c1)),
% 28.08/18.32 inference(monotonicity,[status(thm)],[8766, 22])).
% 28.08/18.32 tff(8793,plain,
% 28.08/18.32 ((f1(c2, c1) = c1) <=> (f1(c2, f7(c2)) = f7(c2))),
% 28.08/18.32 inference(symmetry,[status(thm)],[8792])).
% 28.08/18.32 tff(8794,plain,
% 28.08/18.32 (f1(f7(f7(c2)), c1) = f1(c2, c1)),
% 28.08/18.32 inference(symmetry,[status(thm)],[8785])).
% 28.08/18.32 tff(8795,plain,
% 28.08/18.32 ((f1(f7(f7(c2)), c1) = c1) <=> (f1(c2, c1) = c1)),
% 28.08/18.32 inference(monotonicity,[status(thm)],[8794])).
% 28.08/18.32 tff(8796,plain,
% 28.08/18.32 ((f1(f7(f7(c2)), c1) = c1) <=> (f1(c2, f7(c2)) = f7(c2))),
% 28.08/18.32 inference(transitivity,[status(thm)],[8795, 8793])).
% 28.08/18.32 tff(8797,plain,
% 28.08/18.32 ((~(f1(f7(f7(c2)), c1) = c1)) <=> (~(f1(c2, f7(c2)) = f7(c2)))),
% 28.08/18.32 inference(monotonicity,[status(thm)],[8796])).
% 28.08/18.32 tff(8798,plain,
% 28.08/18.32 (~(f1(c2, f7(c2)) = f7(c2))),
% 28.08/18.32 inference(modus_ponens,[status(thm)],[8782, 8797])).
% 28.08/18.32 tff(8799,plain,
% 28.08/18.32 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c2 = c3) | (f1(c2, f7(c2)) = f7(c2)) | big_f(c2, f1(c2, f7(c2))) | (~(f7(c2) = c4)) | (~big_f(f7(c2), f7(c2))) | (f7(c2) = f4(f7(c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (c2 = c3) | (f1(c2, f7(c2)) = f7(c2)) | big_f(c2, f1(c2, f7(c2))) | (~(f7(c2) = c4)) | (~big_f(f7(c2), f7(c2))) | (f7(c2) = f4(f7(c2))))),
% 28.08/18.32 inference(rewrite,[status(thm)],[])).
% 28.08/18.32 tff(8800,plain,
% 28.08/18.32 (((c2 = c3) | (f1(c2, f7(c2)) = f7(c2)) | big_f(c2, f1(c2, f7(c2))) | (~(f7(c2) = c4)) | (f7(c2) = f4(f7(c2))) | (~big_f(f7(c2), f7(c2)))) <=> ((c2 = c3) | (f1(c2, f7(c2)) = f7(c2)) | big_f(c2, f1(c2, f7(c2))) | (~(f7(c2) = c4)) | (~big_f(f7(c2), f7(c2))) | (f7(c2) = f4(f7(c2))))),
% 28.08/18.32 inference(rewrite,[status(thm)],[])).
% 28.08/18.32 tff(8801,plain,
% 28.08/18.32 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c2 = c3) | (f1(c2, f7(c2)) = f7(c2)) | big_f(c2, f1(c2, f7(c2))) | (~(f7(c2) = c4)) | (f7(c2) = f4(f7(c2))) | (~big_f(f7(c2), f7(c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c2 = c3) | (f1(c2, f7(c2)) = f7(c2)) | big_f(c2, f1(c2, f7(c2))) | (~(f7(c2) = c4)) | (~big_f(f7(c2), f7(c2))) | (f7(c2) = f4(f7(c2)))))),
% 28.08/18.32 inference(monotonicity,[status(thm)],[8800])).
% 28.08/18.32 tff(8802,plain,
% 28.08/18.32 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c2 = c3) | (f1(c2, f7(c2)) = f7(c2)) | big_f(c2, f1(c2, f7(c2))) | (~(f7(c2) = c4)) | (f7(c2) = f4(f7(c2))) | (~big_f(f7(c2), f7(c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (c2 = c3) | (f1(c2, f7(c2)) = f7(c2)) | big_f(c2, f1(c2, f7(c2))) | (~(f7(c2) = c4)) | (~big_f(f7(c2), f7(c2))) | (f7(c2) = f4(f7(c2))))),
% 28.08/18.32 inference(transitivity,[status(thm)],[8801, 8799])).
% 28.08/18.32 tff(8803,plain,
% 28.08/18.32 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c2 = c3) | (f1(c2, f7(c2)) = f7(c2)) | big_f(c2, f1(c2, f7(c2))) | (~(f7(c2) = c4)) | (f7(c2) = f4(f7(c2))) | (~big_f(f7(c2), f7(c2))))),
% 28.08/18.32 inference(quant_inst,[status(thm)],[])).
% 28.08/18.32 tff(8804,plain,
% 28.08/18.32 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (c2 = c3) | (f1(c2, f7(c2)) = f7(c2)) | big_f(c2, f1(c2, f7(c2))) | (~(f7(c2) = c4)) | (~big_f(f7(c2), f7(c2))) | (f7(c2) = f4(f7(c2)))),
% 28.08/18.32 inference(modus_ponens,[status(thm)],[8803, 8802])).
% 28.08/18.32 tff(8805,plain,
% 28.08/18.32 ($false),
% 28.08/18.32 inference(unit_resolution,[status(thm)],[8804, 525, 377, 8798, 8791, 8765, 8764, 8763])).
% 28.08/18.32 tff(8806,plain,((~big_f(f7(c2), c1)) | (c2 = c3) | big_f(c2, c2) | (~(f7(c1) = c2)) | (~big_f(c2, c1)) | (f7(c2) = c2) | (~(f4(c4) = c2)) | (~(c4 = c1))), inference(lemma,lemma(discharge,[]))).
% 28.08/18.32 tff(8807,plain,
% 28.08/18.32 (~big_f(f7(c2), c1)),
% 28.08/18.32 inference(unit_resolution,[status(thm)],[8806, 8724, 121, 120, 8720, 17, 79, 8757])).
% 28.08/18.32 tff(8808,plain,
% 28.08/18.32 (f7(f7(c2)) = c2),
% 28.08/18.32 inference(transitivity,[status(thm)],[8077, 347])).
% 28.08/18.32 tff(8809,plain,
% 28.08/18.32 ((f7(f7(c2)) = c3) <=> (c2 = c3)),
% 28.08/18.32 inference(monotonicity,[status(thm)],[8808])).
% 28.08/18.33 tff(8810,plain,
% 28.08/18.33 ((c2 = c3) <=> (f7(f7(c2)) = c3)),
% 28.08/18.33 inference(symmetry,[status(thm)],[8809])).
% 28.08/18.33 tff(8811,plain,
% 28.08/18.33 ((f7(c2) = c2) <=> (f7(f7(c2)) = c3)),
% 28.08/18.33 inference(transitivity,[status(thm)],[8413, 8810])).
% 28.08/18.33 tff(8812,plain,
% 28.08/18.33 ((~(f7(c2) = c2)) <=> (~(f7(f7(c2)) = c3))),
% 28.08/18.33 inference(monotonicity,[status(thm)],[8811])).
% 28.08/18.33 tff(8813,plain,
% 28.08/18.33 (~(f7(f7(c2)) = c3)),
% 28.08/18.33 inference(modus_ponens,[status(thm)],[17, 8812])).
% 28.08/18.33 tff(8814,plain,
% 28.08/18.33 (~(c2 = c4)),
% 28.08/18.33 inference(unit_resolution,[status(thm)],[8754, 8724, 121, 348, 22, 347, 8813, 79])).
% 28.08/18.33 tff(8815,plain,
% 28.08/18.33 (~(c4 = c2)),
% 28.08/18.33 inference(modus_ponens,[status(thm)],[8814, 8722])).
% 28.08/18.33 tff(8816,plain,
% 28.08/18.33 (c4 = c1),
% 28.08/18.33 inference(unit_resolution,[status(thm)],[461, 8815])).
% 28.08/18.33 tff(8817,plain,
% 28.08/18.33 (~big_f(f7(c2), c1)),
% 28.08/18.33 inference(unit_resolution,[status(thm)],[8806, 8724, 121, 347, 348, 17, 79, 8816])).
% 28.08/18.33 tff(8818,plain,
% 28.08/18.33 (big_f(f7(c2), c2)),
% 28.08/18.33 inference(unit_resolution,[status(thm)],[8159, 3, 17, 8817, 121, 122, 79])).
% 28.08/18.33 tff(8819,plain,
% 28.08/18.33 ((f9(f10(c2), f4(c4)) = c4) <=> (f9(c2, c2) = c4)),
% 28.08/18.33 inference(monotonicity,[status(thm)],[2634])).
% 28.08/18.33 tff(8820,plain,
% 28.08/18.33 ((f9(c2, c2) = c4) <=> (f9(f10(c2), f4(c4)) = c4)),
% 28.08/18.33 inference(symmetry,[status(thm)],[8819])).
% 28.08/18.33 tff(8821,plain,
% 28.08/18.33 ((f9(c2, c2) = c4) <=> (c2 = c4)),
% 28.08/18.33 inference(monotonicity,[status(thm)],[8067])).
% 28.08/18.33 tff(8822,plain,
% 28.08/18.33 ((c2 = c4) <=> (f9(c2, c2) = c4)),
% 28.08/18.33 inference(symmetry,[status(thm)],[8821])).
% 28.08/18.33 tff(8823,plain,
% 28.08/18.33 ((c2 = c4) <=> (f9(f10(c2), f4(c4)) = c4)),
% 28.08/18.33 inference(transitivity,[status(thm)],[8822, 8820])).
% 28.08/18.33 tff(8824,plain,
% 28.08/18.33 ((~(c2 = c4)) <=> (~(f9(f10(c2), f4(c4)) = c4))),
% 28.08/18.33 inference(monotonicity,[status(thm)],[8823])).
% 28.08/18.33 tff(8825,plain,
% 28.08/18.33 (~(f9(f10(c2), f4(c4)) = c4)),
% 28.08/18.33 inference(modus_ponens,[status(thm)],[8814, 8824])).
% 28.08/18.33 tff(8826,plain,
% 28.08/18.33 ((f10(c3) = c3) <=> (f10(c3) = c1)),
% 28.08/18.33 inference(monotonicity,[status(thm)],[172])).
% 28.08/18.33 tff(8827,plain,
% 28.08/18.33 ((f10(c3) = c1) <=> (f10(c3) = c3)),
% 28.08/18.33 inference(symmetry,[status(thm)],[8826])).
% 28.08/18.33 tff(8828,plain,
% 28.08/18.33 (c3 = f7(f4(c4))),
% 28.08/18.33 inference(transitivity,[status(thm)],[172, 125, 81])).
% 28.08/18.33 tff(8829,plain,
% 28.08/18.33 (f10(c3) = f10(f7(f4(c4)))),
% 28.08/18.33 inference(monotonicity,[status(thm)],[8828])).
% 28.08/18.33 tff(8830,plain,
% 28.08/18.33 ((f10(c3) = c1) <=> (f10(f7(f4(c4))) = f7(f4(c4)))),
% 28.08/18.33 inference(monotonicity,[status(thm)],[8829, 8115])).
% 28.08/18.33 tff(8831,plain,
% 28.08/18.33 ((f10(f7(f4(c4))) = f7(f4(c4))) <=> (f10(c3) = c1)),
% 28.08/18.33 inference(symmetry,[status(thm)],[8830])).
% 28.08/18.33 tff(8832,plain,
% 28.08/18.33 ((f10(c1) = c1) <=> (f10(c3) = c3)),
% 28.08/18.33 inference(transitivity,[status(thm)],[8116, 8831, 8827])).
% 28.08/18.33 tff(8833,plain,
% 28.08/18.33 ((~(f10(c1) = c1)) <=> (~(f10(c3) = c3))),
% 28.08/18.33 inference(monotonicity,[status(thm)],[8832])).
% 28.08/18.33 tff(8834,plain,
% 28.08/18.33 (~(f10(c3) = c3)),
% 28.08/18.33 inference(modus_ponens,[status(thm)],[3, 8833])).
% 28.08/18.33 tff(8835,plain,
% 28.08/18.33 (f3(f9(f10(c2), f4(c4)), c1) = f3(c2, c1)),
% 28.08/18.33 inference(monotonicity,[status(thm)],[1498])).
% 28.08/18.33 tff(8836,plain,
% 28.08/18.33 (big_f(f3(f9(f10(c2), f4(c4)), c1), f9(f10(c2), f4(c4))) <=> big_f(f3(c2, c1), c2)),
% 28.08/18.33 inference(monotonicity,[status(thm)],[8835, 1498])).
% 28.08/18.33 tff(8837,plain,
% 28.08/18.33 (big_f(f3(c2, c1), c2) <=> big_f(f3(f9(f10(c2), f4(c4)), c1), f9(f10(c2), f4(c4)))),
% 28.08/18.33 inference(symmetry,[status(thm)],[8836])).
% 28.08/18.33 tff(8838,plain,
% 28.08/18.33 (f1(c2, f7(c2)) = c2),
% 28.08/18.33 inference(transitivity,[status(thm)],[8766, 8785, 499])).
% 28.08/18.33 tff(8839,plain,
% 28.08/18.33 ((f1(c2, f7(c2)) = f7(c2)) <=> (c2 = f7(c2))),
% 28.08/18.33 inference(monotonicity,[status(thm)],[8838])).
% 28.08/18.33 tff(8840,plain,
% 28.08/18.33 ((f1(c2, f7(c2)) = f7(c2)) <=> (f7(c2) = c2)),
% 28.08/18.33 inference(transitivity,[status(thm)],[8839, 8409])).
% 28.08/18.33 tff(8841,plain,
% 28.08/18.33 ((f7(c2) = c2) <=> (f1(c2, f7(c2)) = f7(c2))),
% 28.08/18.33 inference(symmetry,[status(thm)],[8840])).
% 28.08/18.33 tff(8842,plain,
% 28.08/18.33 ((~(f7(c2) = c2)) <=> (~(f1(c2, f7(c2)) = f7(c2)))),
% 28.08/18.33 inference(monotonicity,[status(thm)],[8841])).
% 28.08/18.33 tff(8843,plain,
% 28.08/18.33 (~(f1(c2, f7(c2)) = f7(c2))),
% 28.08/18.33 inference(modus_ponens,[status(thm)],[17, 8842])).
% 28.08/18.33 tff(8844,plain,
% 28.08/18.33 (big_f(c2, f1(c2, f7(c2))) <=> big_f(c2, c2)),
% 28.08/18.33 inference(monotonicity,[status(thm)],[8838])).
% 28.08/18.33 tff(8845,plain,
% 28.08/18.33 (big_f(c2, c2) <=> big_f(c2, f1(c2, f7(c2)))),
% 28.08/18.33 inference(symmetry,[status(thm)],[8844])).
% 28.08/18.33 tff(8846,plain,
% 28.08/18.33 ((~big_f(c2, c2)) <=> (~big_f(c2, f1(c2, f7(c2))))),
% 28.08/18.33 inference(monotonicity,[status(thm)],[8845])).
% 28.08/18.33 tff(8847,plain,
% 28.08/18.33 (~big_f(c2, f1(c2, f7(c2)))),
% 28.08/18.33 inference(modus_ponens,[status(thm)],[121, 8846])).
% 28.08/18.33 tff(8848,plain,
% 28.08/18.33 (f3(c2, f7(c2)) = f3(c2, c1)),
% 28.08/18.33 inference(monotonicity,[status(thm)],[292])).
% 28.08/18.33 tff(8849,plain,
% 28.08/18.33 (f3(c2, f7(c2)) = f7(c2)),
% 28.08/18.33 inference(transitivity,[status(thm)],[8848, 3125, 953, 342])).
% 28.08/18.33 tff(8850,plain,
% 28.08/18.33 (big_f(f3(c2, f7(c2)), c2) <=> big_f(f7(c2), c2)),
% 28.08/18.33 inference(monotonicity,[status(thm)],[8849])).
% 28.08/18.33 tff(8851,plain,
% 28.08/18.33 (big_f(f7(c2), c2) <=> big_f(f3(c2, f7(c2)), c2)),
% 28.08/18.33 inference(symmetry,[status(thm)],[8850])).
% 28.08/18.33 tff(8852,plain,
% 28.08/18.33 (big_f(f3(c2, f7(c2)), c2)),
% 28.08/18.33 inference(modus_ponens,[status(thm)],[1180, 8851])).
% 28.08/18.33 tff(8853,assumption,(~big_f(c2, f1(c2, f7(c2)))), introduced(assumption)).
% 28.08/18.33 tff(8854,assumption,(~(f1(c2, f7(c2)) = f7(c2))), introduced(assumption)).
% 28.08/18.33 tff(8855,plain,
% 28.08/18.33 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c3) | (c2 = c4) | (f1(c2, f7(c2)) = f7(c2)) | big_f(c2, f1(c2, f7(c2))) | (~(f3(c2, f7(c2)) = f7(c2))) | (~big_f(f3(c2, f7(c2)), c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c2 = c3) | (c2 = c4) | (f1(c2, f7(c2)) = f7(c2)) | big_f(c2, f1(c2, f7(c2))) | (~(f3(c2, f7(c2)) = f7(c2))) | (~big_f(f3(c2, f7(c2)), c2)))),
% 28.08/18.33 inference(rewrite,[status(thm)],[])).
% 28.08/18.33 tff(8856,plain,
% 28.08/18.33 (((c2 = c4) | (c2 = c3) | (f1(c2, f7(c2)) = f7(c2)) | big_f(c2, f1(c2, f7(c2))) | (~(f3(c2, f7(c2)) = f7(c2))) | (~big_f(f3(c2, f7(c2)), c2))) <=> ((c2 = c3) | (c2 = c4) | (f1(c2, f7(c2)) = f7(c2)) | big_f(c2, f1(c2, f7(c2))) | (~(f3(c2, f7(c2)) = f7(c2))) | (~big_f(f3(c2, f7(c2)), c2)))),
% 28.08/18.33 inference(rewrite,[status(thm)],[])).
% 28.08/18.33 tff(8857,plain,
% 28.08/18.33 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c4) | (c2 = c3) | (f1(c2, f7(c2)) = f7(c2)) | big_f(c2, f1(c2, f7(c2))) | (~(f3(c2, f7(c2)) = f7(c2))) | (~big_f(f3(c2, f7(c2)), c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c3) | (c2 = c4) | (f1(c2, f7(c2)) = f7(c2)) | big_f(c2, f1(c2, f7(c2))) | (~(f3(c2, f7(c2)) = f7(c2))) | (~big_f(f3(c2, f7(c2)), c2))))),
% 28.08/18.33 inference(monotonicity,[status(thm)],[8856])).
% 28.08/18.33 tff(8858,plain,
% 28.08/18.33 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c4) | (c2 = c3) | (f1(c2, f7(c2)) = f7(c2)) | big_f(c2, f1(c2, f7(c2))) | (~(f3(c2, f7(c2)) = f7(c2))) | (~big_f(f3(c2, f7(c2)), c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c2 = c3) | (c2 = c4) | (f1(c2, f7(c2)) = f7(c2)) | big_f(c2, f1(c2, f7(c2))) | (~(f3(c2, f7(c2)) = f7(c2))) | (~big_f(f3(c2, f7(c2)), c2)))),
% 28.08/18.33 inference(transitivity,[status(thm)],[8857, 8855])).
% 28.08/18.33 tff(8859,plain,
% 28.08/18.33 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c4) | (c2 = c3) | (f1(c2, f7(c2)) = f7(c2)) | big_f(c2, f1(c2, f7(c2))) | (~(f3(c2, f7(c2)) = f7(c2))) | (~big_f(f3(c2, f7(c2)), c2)))),
% 28.08/18.33 inference(quant_inst,[status(thm)],[])).
% 28.08/18.33 tff(8860,plain,
% 28.08/18.33 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c2 = c3) | (c2 = c4) | (f1(c2, f7(c2)) = f7(c2)) | big_f(c2, f1(c2, f7(c2))) | (~(f3(c2, f7(c2)) = f7(c2))) | (~big_f(f3(c2, f7(c2)), c2))),
% 28.08/18.33 inference(modus_ponens,[status(thm)],[8859, 8858])).
% 28.08/18.33 tff(8861,plain,
% 28.08/18.33 ((~(f3(c2, f7(c2)) = f7(c2))) | (~big_f(f3(c2, f7(c2)), c2))),
% 28.08/18.33 inference(unit_resolution,[status(thm)],[8860, 969, 873, 377, 8854, 8853])).
% 28.08/18.33 tff(8862,plain,
% 28.08/18.33 ($false),
% 28.08/18.33 inference(unit_resolution,[status(thm)],[8861, 8852, 8849])).
% 28.08/18.33 tff(8863,plain,((~(f3(f7(c1), c1) = c1)) | (c2 = c4) | (c2 = c3) | (f1(c2, f7(c2)) = f7(c2)) | big_f(c2, f1(c2, f7(c2))) | (~big_f(f7(c2), c2)) | (~(f7(c2) = c1)) | (~(f7(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.08/18.33 tff(8864,plain,
% 28.08/18.33 ($false),
% 28.08/18.33 inference(unit_resolution,[status(thm)],[8863, 8847, 8843, 377, 953, 873, 1180, 22, 347])).
% 28.08/18.33 tff(8865,plain,((~(f3(f7(c1), c1) = c1)) | (c2 = c3) | (c2 = c4) | (~big_f(f7(c2), c2)) | (~(f7(c1) = c2)) | big_f(c2, c2) | (~(f1(f7(f7(c2)), c1) = c2)) | (f7(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 28.08/18.33 tff(8866,plain,
% 28.08/18.33 (~(f3(f7(c1), c1) = c1)),
% 28.08/18.33 inference(unit_resolution,[status(thm)],[8865, 499, 873, 1180, 347, 121, 8724, 17])).
% 28.08/18.33 tff(8867,plain,
% 28.08/18.33 (f3(f7(c1), c1) = c2),
% 28.08/18.33 inference(unit_resolution,[status(thm)],[918, 8866])).
% 28.08/18.33 tff(8868,plain,
% 28.08/18.33 (f3(c2, c1) = c2),
% 28.08/18.33 inference(transitivity,[status(thm)],[3125, 8867])).
% 28.08/18.33 tff(8869,plain,
% 28.08/18.33 (big_f(f3(c2, c1), c2) <=> big_f(c2, c2)),
% 28.08/18.33 inference(monotonicity,[status(thm)],[8868])).
% 28.08/18.33 tff(8870,plain,
% 28.08/18.33 (big_f(c2, c2) <=> big_f(f3(c2, c1), c2)),
% 28.08/18.33 inference(symmetry,[status(thm)],[8869])).
% 28.08/18.33 tff(8871,plain,
% 28.08/18.33 (big_f(c2, c2) <=> big_f(f3(f9(f10(c2), f4(c4)), c1), f9(f10(c2), f4(c4)))),
% 28.08/18.33 inference(transitivity,[status(thm)],[8870, 8837])).
% 28.08/18.33 tff(8872,plain,
% 28.08/18.33 ((~big_f(c2, c2)) <=> (~big_f(f3(f9(f10(c2), f4(c4)), c1), f9(f10(c2), f4(c4))))),
% 28.08/18.33 inference(monotonicity,[status(thm)],[8871])).
% 28.08/18.33 tff(8873,plain,
% 28.08/18.33 (~big_f(f3(f9(f10(c2), f4(c4)), c1), f9(f10(c2), f4(c4)))),
% 28.08/18.33 inference(modus_ponens,[status(thm)],[121, 8872])).
% 28.08/18.33 tff(8874,assumption,(~(f9(f10(c2), f4(c4)) = c4)), introduced(assumption)).
% 28.08/18.33 tff(8875,plain,
% 28.08/18.33 ((f3(f9(f10(c2), f4(c4)), c1) = c1) <=> (f3(c2, c1) = c1)),
% 28.08/18.33 inference(monotonicity,[status(thm)],[8835])).
% 28.08/18.33 tff(8876,plain,
% 28.08/18.33 ((f3(c2, c1) = c1) <=> (f3(f9(f10(c2), f4(c4)), c1) = c1)),
% 28.08/18.33 inference(symmetry,[status(thm)],[8875])).
% 28.08/18.33 tff(8877,plain,
% 28.08/18.33 ((f3(c2, c1) = c1) <=> (c2 = f7(c2))),
% 28.08/18.33 inference(monotonicity,[status(thm)],[8868, 125])).
% 28.08/18.33 tff(8878,plain,
% 28.08/18.33 ((f3(c2, c1) = c1) <=> (f7(c2) = c2)),
% 28.08/18.33 inference(transitivity,[status(thm)],[8877, 8409])).
% 28.08/18.33 tff(8879,plain,
% 28.08/18.33 ((f7(c2) = c2) <=> (f3(c2, c1) = c1)),
% 28.08/18.33 inference(symmetry,[status(thm)],[8878])).
% 28.08/18.33 tff(8880,plain,
% 28.08/18.33 ((f7(c2) = c2) <=> (f3(f9(f10(c2), f4(c4)), c1) = c1)),
% 28.08/18.33 inference(transitivity,[status(thm)],[8879, 8876])).
% 28.08/18.33 tff(8881,plain,
% 28.08/18.33 ((~(f7(c2) = c2)) <=> (~(f3(f9(f10(c2), f4(c4)), c1) = c1))),
% 28.08/18.33 inference(monotonicity,[status(thm)],[8880])).
% 28.08/18.33 tff(8882,plain,
% 28.08/18.33 (~(f3(f9(f10(c2), f4(c4)), c1) = c1)),
% 28.08/18.33 inference(modus_ponens,[status(thm)],[17, 8881])).
% 28.08/18.33 tff(8883,plain,
% 28.08/18.33 (f10(c3) = f10(c1)),
% 28.08/18.33 inference(transitivity,[status(thm)],[8829, 8082])).
% 28.08/18.33 tff(8884,plain,
% 28.08/18.33 (f1(f10(c3), c1) = f1(f10(c1), c1)),
% 28.08/18.33 inference(monotonicity,[status(thm)],[8883])).
% 28.08/18.33 tff(8885,plain,
% 28.08/18.33 ((f1(f10(c3), c1) = c1) <=> (f1(f10(c1), c1) = c1)),
% 28.08/18.33 inference(monotonicity,[status(thm)],[8884])).
% 28.08/18.33 tff(8886,plain,
% 28.08/18.33 ((f1(f10(c1), c1) = c1) <=> (f1(f10(c3), c1) = c1)),
% 28.08/18.33 inference(symmetry,[status(thm)],[8885])).
% 28.08/18.33 tff(8887,plain,
% 28.08/18.33 (f1(f10(c1), c1) = f1(c2, c1)),
% 28.08/18.33 inference(monotonicity,[status(thm)],[16])).
% 28.08/18.33 tff(8888,plain,
% 28.08/18.33 ((f1(f10(c1), c1) = c1) <=> (f1(c2, c1) = c1)),
% 28.08/18.33 inference(monotonicity,[status(thm)],[8887])).
% 28.08/18.33 tff(8889,plain,
% 28.08/18.33 ((f1(c2, c1) = c1) <=> (f1(f10(c1), c1) = c1)),
% 28.08/18.33 inference(symmetry,[status(thm)],[8888])).
% 28.08/18.33 tff(8890,plain,
% 28.08/18.33 (f1(c2, c1) = c2),
% 28.08/18.33 inference(transitivity,[status(thm)],[8785, 499])).
% 28.08/18.33 tff(8891,plain,
% 28.08/18.33 ((f1(c2, c1) = c1) <=> (c2 = f7(c2))),
% 28.08/18.33 inference(monotonicity,[status(thm)],[8890, 125])).
% 28.08/18.33 tff(8892,plain,
% 28.08/18.33 ((f1(c2, c1) = c1) <=> (f7(c2) = c2)),
% 28.08/18.33 inference(transitivity,[status(thm)],[8891, 8409])).
% 28.08/18.33 tff(8893,plain,
% 28.08/18.33 ((f7(c2) = c2) <=> (f1(c2, c1) = c1)),
% 28.08/18.33 inference(symmetry,[status(thm)],[8892])).
% 28.08/18.33 tff(8894,plain,
% 28.08/18.33 ((f7(c2) = c2) <=> (f1(f10(c3), c1) = c1)),
% 28.08/18.33 inference(transitivity,[status(thm)],[8893, 8889, 8886])).
% 28.08/18.33 tff(8895,plain,
% 28.08/18.33 ((~(f7(c2) = c2)) <=> (~(f1(f10(c3), c1) = c1))),
% 28.08/18.33 inference(monotonicity,[status(thm)],[8894])).
% 28.08/18.33 tff(8896,plain,
% 28.08/18.33 (~(f1(f10(c3), c1) = c1)),
% 28.08/18.33 inference(modus_ponens,[status(thm)],[17, 8895])).
% 28.08/18.33 tff(8897,plain,
% 28.08/18.33 (big_f(f10(c3), f1(f10(c3), c1)) <=> big_f(f10(c1), f1(f10(c1), c1))),
% 28.08/18.33 inference(monotonicity,[status(thm)],[8883, 8884])).
% 28.08/18.33 tff(8898,plain,
% 28.08/18.33 (big_f(f10(c1), f1(f10(c1), c1)) <=> big_f(f10(c3), f1(f10(c3), c1))),
% 28.08/18.33 inference(symmetry,[status(thm)],[8897])).
% 28.08/18.33 tff(8899,plain,
% 28.08/18.33 (big_f(f10(c1), f1(f10(c1), c1)) <=> big_f(c2, f1(c2, c1))),
% 28.08/18.33 inference(monotonicity,[status(thm)],[16, 8887])).
% 28.08/18.33 tff(8900,plain,
% 28.08/18.33 (big_f(c2, f1(c2, c1)) <=> big_f(f10(c1), f1(f10(c1), c1))),
% 28.08/18.33 inference(symmetry,[status(thm)],[8899])).
% 28.08/18.33 tff(8901,plain,
% 28.08/18.33 (big_f(c2, f1(c2, c1)) <=> big_f(c2, c2)),
% 28.08/18.33 inference(monotonicity,[status(thm)],[8890])).
% 28.08/18.33 tff(8902,plain,
% 28.08/18.33 (big_f(c2, c2) <=> big_f(c2, f1(c2, c1))),
% 28.08/18.33 inference(symmetry,[status(thm)],[8901])).
% 28.08/18.33 tff(8903,plain,
% 28.08/18.33 (big_f(c2, c2) <=> big_f(f10(c3), f1(f10(c3), c1))),
% 28.08/18.33 inference(transitivity,[status(thm)],[8902, 8900, 8898])).
% 28.08/18.33 tff(8904,plain,
% 28.08/18.33 ((~big_f(c2, c2)) <=> (~big_f(f10(c3), f1(f10(c3), c1)))),
% 28.08/18.33 inference(monotonicity,[status(thm)],[8903])).
% 28.08/18.33 tff(8905,plain,
% 28.08/18.33 (~big_f(f10(c3), f1(f10(c3), c1))),
% 28.08/18.33 inference(modus_ponens,[status(thm)],[121, 8904])).
% 28.08/18.33 tff(8906,plain,
% 28.08/18.33 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f10(c3) = c3) | (f9(f10(c2), f4(c4)) = c4) | (f3(f9(f10(c2), f4(c4)), c1) = c1) | (f1(f10(c3), c1) = c1) | big_f(f10(c3), f1(f10(c3), c1)) | big_f(f3(f9(f10(c2), f4(c4)), c1), f9(f10(c2), f4(c4))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (f10(c3) = c3) | (f9(f10(c2), f4(c4)) = c4) | (f3(f9(f10(c2), f4(c4)), c1) = c1) | (f1(f10(c3), c1) = c1) | big_f(f10(c3), f1(f10(c3), c1)) | big_f(f3(f9(f10(c2), f4(c4)), c1), f9(f10(c2), f4(c4))))),
% 28.08/18.33 inference(rewrite,[status(thm)],[])).
% 28.08/18.33 tff(8907,plain,
% 28.08/18.33 (((f9(f10(c2), f4(c4)) = c4) | (f3(f9(f10(c2), f4(c4)), c1) = c1) | big_f(f3(f9(f10(c2), f4(c4)), c1), f9(f10(c2), f4(c4))) | (f10(c3) = c3) | (f1(f10(c3), c1) = c1) | big_f(f10(c3), f1(f10(c3), c1))) <=> ((f10(c3) = c3) | (f9(f10(c2), f4(c4)) = c4) | (f3(f9(f10(c2), f4(c4)), c1) = c1) | (f1(f10(c3), c1) = c1) | big_f(f10(c3), f1(f10(c3), c1)) | big_f(f3(f9(f10(c2), f4(c4)), c1), f9(f10(c2), f4(c4))))),
% 28.08/18.33 inference(rewrite,[status(thm)],[])).
% 28.08/18.33 tff(8908,plain,
% 28.08/18.33 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f9(f10(c2), f4(c4)) = c4) | (f3(f9(f10(c2), f4(c4)), c1) = c1) | big_f(f3(f9(f10(c2), f4(c4)), c1), f9(f10(c2), f4(c4))) | (f10(c3) = c3) | (f1(f10(c3), c1) = c1) | big_f(f10(c3), f1(f10(c3), c1)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f10(c3) = c3) | (f9(f10(c2), f4(c4)) = c4) | (f3(f9(f10(c2), f4(c4)), c1) = c1) | (f1(f10(c3), c1) = c1) | big_f(f10(c3), f1(f10(c3), c1)) | big_f(f3(f9(f10(c2), f4(c4)), c1), f9(f10(c2), f4(c4)))))),
% 28.08/18.33 inference(monotonicity,[status(thm)],[8907])).
% 28.08/18.33 tff(8909,plain,
% 28.08/18.33 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f9(f10(c2), f4(c4)) = c4) | (f3(f9(f10(c2), f4(c4)), c1) = c1) | big_f(f3(f9(f10(c2), f4(c4)), c1), f9(f10(c2), f4(c4))) | (f10(c3) = c3) | (f1(f10(c3), c1) = c1) | big_f(f10(c3), f1(f10(c3), c1)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (f10(c3) = c3) | (f9(f10(c2), f4(c4)) = c4) | (f3(f9(f10(c2), f4(c4)), c1) = c1) | (f1(f10(c3), c1) = c1) | big_f(f10(c3), f1(f10(c3), c1)) | big_f(f3(f9(f10(c2), f4(c4)), c1), f9(f10(c2), f4(c4))))),
% 28.08/18.33 inference(transitivity,[status(thm)],[8908, 8906])).
% 28.08/18.33 tff(8910,plain,
% 28.08/18.33 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f9(f10(c2), f4(c4)) = c4) | (f3(f9(f10(c2), f4(c4)), c1) = c1) | big_f(f3(f9(f10(c2), f4(c4)), c1), f9(f10(c2), f4(c4))) | (f10(c3) = c3) | (f1(f10(c3), c1) = c1) | big_f(f10(c3), f1(f10(c3), c1)))),
% 28.08/18.33 inference(quant_inst,[status(thm)],[])).
% 28.08/18.33 tff(8911,plain,
% 28.08/18.33 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (f10(c3) = c3) | (f9(f10(c2), f4(c4)) = c4) | (f3(f9(f10(c2), f4(c4)), c1) = c1) | (f1(f10(c3), c1) = c1) | big_f(f10(c3), f1(f10(c3), c1)) | big_f(f3(f9(f10(c2), f4(c4)), c1), f9(f10(c2), f4(c4)))),
% 28.08/18.33 inference(modus_ponens,[status(thm)],[8910, 8909])).
% 28.08/18.33 tff(8912,plain,
% 28.08/18.33 ((f10(c3) = c3) | (f9(f10(c2), f4(c4)) = c4) | (f3(f9(f10(c2), f4(c4)), c1) = c1) | (f1(f10(c3), c1) = c1) | big_f(f10(c3), f1(f10(c3), c1)) | big_f(f3(f9(f10(c2), f4(c4)), c1), f9(f10(c2), f4(c4)))),
% 28.08/18.33 inference(unit_resolution,[status(thm)],[8911, 1014])).
% 28.08/18.33 tff(8913,plain,
% 28.08/18.33 ($false),
% 28.08/18.33 inference(unit_resolution,[status(thm)],[8912, 8905, 8896, 2828, 8882, 8874, 8873])).
% 28.08/18.33 tff(8914,plain,((~(f1(f7(f7(c2)), c1) = c2)) | (f10(c3) = c3) | (f9(f10(c2), f4(c4)) = c4) | big_f(c2, c2) | (~(f7(c1) = c2)) | (~(f9(f10(c2), f4(c4)) = c2)) | (f7(c2) = c2) | (~(f10(c1) = c2)) | (~(f4(c4) = c2)) | (~(c3 = c1)) | (c2 = c4) | (~big_f(f7(c2), c2))), inference(lemma,lemma(discharge,[]))).
% 28.08/18.33 tff(8915,plain,
% 28.08/18.33 (~(f1(f7(f7(c2)), c1) = c2)),
% 28.08/18.33 inference(unit_resolution,[status(thm)],[8914, 8834, 8825, 121, 347, 8066, 17, 15, 79, 172, 8814, 8818])).
% 28.08/18.33 tff(8916,plain,
% 28.08/18.33 (f1(f7(f7(c2)), c1) = c1),
% 28.08/18.33 inference(unit_resolution,[status(thm)],[384, 8915])).
% 28.08/18.33 tff(8917,plain,
% 28.08/18.33 (f1(c2, f7(c2)) = f7(c2)),
% 28.08/18.33 inference(modus_ponens,[status(thm)],[8916, 8796])).
% 28.08/18.33 tff(8918,plain,
% 28.08/18.33 (c1 = f1(f7(f7(c2)), c1)),
% 28.08/18.33 inference(symmetry,[status(thm)],[8916])).
% 28.08/18.33 tff(8919,plain,
% 28.08/18.33 (c1 = f1(c2, c1)),
% 28.08/18.33 inference(transitivity,[status(thm)],[8918, 8794])).
% 28.08/18.33 tff(8920,plain,
% 28.08/18.33 (big_f(c2, c1) <=> big_f(c2, f1(c2, c1))),
% 28.08/18.33 inference(monotonicity,[status(thm)],[8919])).
% 28.08/18.33 tff(8921,plain,
% 28.08/18.33 (big_f(c2, c1) <=> big_f(c2, f1(c2, f7(c2)))),
% 28.08/18.33 inference(transitivity,[status(thm)],[8920, 8768])).
% 28.08/18.33 tff(8922,plain,
% 28.08/18.33 (big_f(c2, f1(c2, f7(c2)))),
% 28.08/18.33 inference(modus_ponens,[status(thm)],[348, 8921])).
% 28.08/18.33 tff(8923,plain,
% 28.08/18.33 (f3(c2, f7(c2)) = f3(c2, c1)),
% 28.08/18.33 inference(monotonicity,[status(thm)],[22])).
% 28.08/18.33 tff(8924,plain,
% 28.08/18.33 (f3(c2, f7(c2)) = c2),
% 28.08/18.33 inference(transitivity,[status(thm)],[8923, 3125, 881])).
% 28.08/18.33 tff(8925,plain,
% 28.08/18.33 ((f3(c2, f7(c2)) = f7(c2)) <=> (c2 = f7(c2))),
% 28.08/18.33 inference(monotonicity,[status(thm)],[8924])).
% 28.08/18.33 tff(8926,plain,
% 28.08/18.33 ((f3(c2, f7(c2)) = f7(c2)) <=> (f7(c2) = c2)),
% 28.08/18.33 inference(transitivity,[status(thm)],[8925, 8409])).
% 28.08/18.33 tff(8927,plain,
% 28.08/18.33 ((f7(c2) = c2) <=> (f3(c2, f7(c2)) = f7(c2))),
% 28.08/18.33 inference(symmetry,[status(thm)],[8926])).
% 28.08/18.33 tff(8928,plain,
% 28.08/18.33 ((~(f7(c2) = c2)) <=> (~(f3(c2, f7(c2)) = f7(c2)))),
% 28.08/18.33 inference(monotonicity,[status(thm)],[8927])).
% 28.08/18.33 tff(8929,plain,
% 28.08/18.33 (~(f3(c2, f7(c2)) = f7(c2))),
% 28.08/18.33 inference(modus_ponens,[status(thm)],[17, 8928])).
% 28.08/18.33 tff(8930,plain,
% 28.08/18.33 (big_f(f3(c2, f7(c2)), c2) <=> big_f(c2, c2)),
% 28.08/18.33 inference(monotonicity,[status(thm)],[8924])).
% 28.08/18.33 tff(8931,plain,
% 28.08/18.33 (big_f(c2, c2) <=> big_f(f3(c2, f7(c2)), c2)),
% 28.08/18.33 inference(symmetry,[status(thm)],[8930])).
% 28.08/18.33 tff(8932,plain,
% 28.08/18.33 ((~big_f(c2, c2)) <=> (~big_f(f3(c2, f7(c2)), c2))),
% 28.08/18.33 inference(monotonicity,[status(thm)],[8931])).
% 28.08/18.34 tff(8933,plain,
% 28.08/18.34 (~big_f(f3(c2, f7(c2)), c2)),
% 28.08/18.34 inference(modus_ponens,[status(thm)],[121, 8932])).
% 28.08/18.34 tff(8934,assumption,(big_f(c2, f1(c2, f7(c2)))), introduced(assumption)).
% 28.08/18.34 tff(8935,assumption,(f1(c2, f7(c2)) = f7(c2)), introduced(assumption)).
% 28.08/18.34 tff(8936,plain,
% 28.08/18.34 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (c2 = c4) | (~big_f(c2, f1(c2, f7(c2)))) | (~(f1(c2, f7(c2)) = f7(c2))) | (f3(c2, f7(c2)) = f7(c2)) | big_f(f3(c2, f7(c2)), c2))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (c2 = c4) | (~big_f(c2, f1(c2, f7(c2)))) | (~(f1(c2, f7(c2)) = f7(c2))) | (f3(c2, f7(c2)) = f7(c2)) | big_f(f3(c2, f7(c2)), c2))),
% 28.08/18.34 inference(rewrite,[status(thm)],[])).
% 28.08/18.34 tff(8937,plain,
% 28.08/18.34 (((c2 = c4) | (f3(c2, f7(c2)) = f7(c2)) | big_f(f3(c2, f7(c2)), c2) | (c2 = c3) | (~(f1(c2, f7(c2)) = f7(c2))) | (~big_f(c2, f1(c2, f7(c2))))) <=> ((c2 = c3) | (c2 = c4) | (~big_f(c2, f1(c2, f7(c2)))) | (~(f1(c2, f7(c2)) = f7(c2))) | (f3(c2, f7(c2)) = f7(c2)) | big_f(f3(c2, f7(c2)), c2))),
% 28.08/18.34 inference(rewrite,[status(thm)],[])).
% 28.08/18.34 tff(8938,plain,
% 28.08/18.34 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (f3(c2, f7(c2)) = f7(c2)) | big_f(f3(c2, f7(c2)), c2) | (c2 = c3) | (~(f1(c2, f7(c2)) = f7(c2))) | (~big_f(c2, f1(c2, f7(c2)))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (c2 = c4) | (~big_f(c2, f1(c2, f7(c2)))) | (~(f1(c2, f7(c2)) = f7(c2))) | (f3(c2, f7(c2)) = f7(c2)) | big_f(f3(c2, f7(c2)), c2)))),
% 28.08/18.34 inference(monotonicity,[status(thm)],[8937])).
% 28.08/18.34 tff(8939,plain,
% 28.08/18.34 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (f3(c2, f7(c2)) = f7(c2)) | big_f(f3(c2, f7(c2)), c2) | (c2 = c3) | (~(f1(c2, f7(c2)) = f7(c2))) | (~big_f(c2, f1(c2, f7(c2)))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (c2 = c4) | (~big_f(c2, f1(c2, f7(c2)))) | (~(f1(c2, f7(c2)) = f7(c2))) | (f3(c2, f7(c2)) = f7(c2)) | big_f(f3(c2, f7(c2)), c2))),
% 28.08/18.34 inference(transitivity,[status(thm)],[8938, 8936])).
% 28.08/18.34 tff(8940,plain,
% 28.08/18.34 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (f3(c2, f7(c2)) = f7(c2)) | big_f(f3(c2, f7(c2)), c2) | (c2 = c3) | (~(f1(c2, f7(c2)) = f7(c2))) | (~big_f(c2, f1(c2, f7(c2)))))),
% 28.08/18.34 inference(quant_inst,[status(thm)],[])).
% 28.08/18.34 tff(8941,plain,
% 28.08/18.34 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (c2 = c4) | (~big_f(c2, f1(c2, f7(c2)))) | (~(f1(c2, f7(c2)) = f7(c2))) | (f3(c2, f7(c2)) = f7(c2)) | big_f(f3(c2, f7(c2)), c2)),
% 28.08/18.34 inference(modus_ponens,[status(thm)],[8940, 8939])).
% 28.08/18.34 tff(8942,plain,
% 28.08/18.34 ((f3(c2, f7(c2)) = f7(c2)) | big_f(f3(c2, f7(c2)), c2)),
% 28.08/18.34 inference(unit_resolution,[status(thm)],[8941, 904, 873, 377, 8935, 8934])).
% 28.08/18.34 tff(8943,plain,
% 28.08/18.34 ($false),
% 28.08/18.34 inference(unit_resolution,[status(thm)],[8942, 8933, 8929])).
% 28.08/18.34 tff(8944,plain,((~(f3(f7(c1), c1) = c2)) | (c2 = c4) | (c2 = c3) | (~(f1(c2, f7(c2)) = f7(c2))) | (~big_f(c2, f1(c2, f7(c2)))) | big_f(c2, c2) | (~(f7(c1) = c2)) | (f7(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 28.08/18.34 tff(8945,plain,
% 28.08/18.34 (~(f3(f7(c1), c1) = c2)),
% 28.08/18.34 inference(unit_resolution,[status(thm)],[8944, 8922, 8724, 8917, 8814, 121, 347, 17])).
% 28.08/18.34 tff(8946,plain,
% 28.08/18.34 (f3(f7(c1), c1) = c1),
% 28.08/18.34 inference(unit_resolution,[status(thm)],[918, 8945])).
% 28.08/18.34 tff(8947,plain,
% 28.08/18.34 (f3(c2, f7(c2)) = f7(c2)),
% 28.08/18.34 inference(transitivity,[status(thm)],[8923, 3125, 8946, 125])).
% 28.08/18.34 tff(8948,plain,
% 28.08/18.34 (big_f(f3(c2, f7(c2)), c2) <=> big_f(f7(c2), c2)),
% 28.08/18.34 inference(monotonicity,[status(thm)],[8947])).
% 28.08/18.34 tff(8949,plain,
% 28.08/18.34 (big_f(f7(c2), c2) <=> big_f(f3(c2, f7(c2)), c2)),
% 28.08/18.34 inference(symmetry,[status(thm)],[8948])).
% 28.08/18.34 tff(8950,plain,
% 28.08/18.34 (big_f(f3(c2, f7(c2)), c2)),
% 28.08/18.34 inference(modus_ponens,[status(thm)],[8818, 8949])).
% 28.08/18.34 tff(8951,plain,
% 28.08/18.34 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (c2 = c4) | (~big_f(c2, f1(c2, f7(c2)))) | (~(f1(c2, f7(c2)) = f7(c2))) | (~(f3(c2, f7(c2)) = f7(c2))) | (~big_f(f3(c2, f7(c2)), c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (c2 = c4) | (~big_f(c2, f1(c2, f7(c2)))) | (~(f1(c2, f7(c2)) = f7(c2))) | (~(f3(c2, f7(c2)) = f7(c2))) | (~big_f(f3(c2, f7(c2)), c2)))),
% 28.08/18.34 inference(rewrite,[status(thm)],[])).
% 28.08/18.34 tff(8952,plain,
% 28.08/18.34 (((c2 = c4) | (c2 = c3) | (~(f3(c2, f7(c2)) = f7(c2))) | (~big_f(f3(c2, f7(c2)), c2)) | (~(f1(c2, f7(c2)) = f7(c2))) | (~big_f(c2, f1(c2, f7(c2))))) <=> ((c2 = c3) | (c2 = c4) | (~big_f(c2, f1(c2, f7(c2)))) | (~(f1(c2, f7(c2)) = f7(c2))) | (~(f3(c2, f7(c2)) = f7(c2))) | (~big_f(f3(c2, f7(c2)), c2)))),
% 28.08/18.34 inference(rewrite,[status(thm)],[])).
% 28.08/18.34 tff(8953,plain,
% 28.08/18.34 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (c2 = c3) | (~(f3(c2, f7(c2)) = f7(c2))) | (~big_f(f3(c2, f7(c2)), c2)) | (~(f1(c2, f7(c2)) = f7(c2))) | (~big_f(c2, f1(c2, f7(c2)))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (c2 = c4) | (~big_f(c2, f1(c2, f7(c2)))) | (~(f1(c2, f7(c2)) = f7(c2))) | (~(f3(c2, f7(c2)) = f7(c2))) | (~big_f(f3(c2, f7(c2)), c2))))),
% 28.08/18.34 inference(monotonicity,[status(thm)],[8952])).
% 28.08/18.34 tff(8954,plain,
% 28.08/18.34 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (c2 = c3) | (~(f3(c2, f7(c2)) = f7(c2))) | (~big_f(f3(c2, f7(c2)), c2)) | (~(f1(c2, f7(c2)) = f7(c2))) | (~big_f(c2, f1(c2, f7(c2)))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (c2 = c4) | (~big_f(c2, f1(c2, f7(c2)))) | (~(f1(c2, f7(c2)) = f7(c2))) | (~(f3(c2, f7(c2)) = f7(c2))) | (~big_f(f3(c2, f7(c2)), c2)))),
% 28.08/18.34 inference(transitivity,[status(thm)],[8953, 8951])).
% 28.08/18.34 tff(8955,plain,
% 28.08/18.34 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (c2 = c3) | (~(f3(c2, f7(c2)) = f7(c2))) | (~big_f(f3(c2, f7(c2)), c2)) | (~(f1(c2, f7(c2)) = f7(c2))) | (~big_f(c2, f1(c2, f7(c2)))))),
% 28.08/18.34 inference(quant_inst,[status(thm)],[])).
% 28.08/18.34 tff(8956,plain,
% 28.08/18.34 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (c2 = c4) | (~big_f(c2, f1(c2, f7(c2)))) | (~(f1(c2, f7(c2)) = f7(c2))) | (~(f3(c2, f7(c2)) = f7(c2))) | (~big_f(f3(c2, f7(c2)), c2))),
% 28.08/18.34 inference(modus_ponens,[status(thm)],[8955, 8954])).
% 28.08/18.34 tff(8957,plain,
% 28.08/18.34 ((~(f3(c2, f7(c2)) = f7(c2))) | (~big_f(f3(c2, f7(c2)), c2))),
% 28.08/18.34 inference(unit_resolution,[status(thm)],[8956, 933, 8814, 8724, 8917, 8922])).
% 28.08/18.34 tff(8958,plain,
% 28.08/18.34 ($false),
% 28.08/18.34 inference(unit_resolution,[status(thm)],[8957, 8950, 8947])).
% 28.08/18.34 tff(8959,plain,((f10(c1) = c1) | (~(f7(c1) = c2)) | big_f(c2, c2) | (f7(c2) = c2) | (~big_f(c2, c1)) | (~(f4(c4) = c2)) | (~(c3 = c1)) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.08/18.34 tff(8960,plain,
% 28.08/18.34 (f10(c1) = c1),
% 28.08/18.34 inference(unit_resolution,[status(thm)],[8959, 8720, 121, 17, 120, 79, 172, 122])).
% 28.08/18.34 tff(8961,plain,
% 28.08/18.34 (f9(f10(c2), f7(c1)) = f9(c2, c2)),
% 28.08/18.34 inference(monotonicity,[status(thm)],[122, 347])).
% 28.08/18.34 tff(8962,plain,
% 28.08/18.34 (f9(f10(c2), f7(c1)) = c2),
% 28.08/18.34 inference(transitivity,[status(thm)],[8961, 2629, 8066])).
% 28.08/18.34 tff(8963,plain,
% 28.08/18.34 ((f7(f9(f10(c2), f7(c1))) = f9(f10(c2), f7(c1))) <=> (f7(f9(f10(c2), f7(c1))) = c2)),
% 28.08/18.34 inference(monotonicity,[status(thm)],[8962])).
% 28.08/18.34 tff(8964,plain,
% 28.08/18.34 ((f7(f9(f10(c2), f7(c1))) = c2) <=> (f7(f9(f10(c2), f7(c1))) = f9(f10(c2), f7(c1)))),
% 28.08/18.34 inference(symmetry,[status(thm)],[8963])).
% 28.08/18.34 tff(8965,plain,
% 28.08/18.34 (f7(f9(f10(c2), f7(c1))) = f7(c2)),
% 28.08/18.34 inference(monotonicity,[status(thm)],[8962])).
% 28.08/18.34 tff(8966,plain,
% 28.08/18.34 ((f7(f9(f10(c2), f7(c1))) = c2) <=> (f7(c2) = c2)),
% 28.08/18.34 inference(monotonicity,[status(thm)],[8965])).
% 28.08/18.34 tff(8967,plain,
% 28.08/18.34 ((f7(c2) = c2) <=> (f7(f9(f10(c2), f7(c1))) = c2)),
% 28.08/18.34 inference(symmetry,[status(thm)],[8966])).
% 28.08/18.34 tff(8968,plain,
% 28.08/18.34 ((f7(c2) = c2) <=> (f7(f9(f10(c2), f7(c1))) = f9(f10(c2), f7(c1)))),
% 28.08/18.34 inference(transitivity,[status(thm)],[8967, 8964])).
% 28.08/18.34 tff(8969,plain,
% 28.08/18.34 ((~(f7(c2) = c2)) <=> (~(f7(f9(f10(c2), f7(c1))) = f9(f10(c2), f7(c1))))),
% 28.08/18.34 inference(monotonicity,[status(thm)],[8968])).
% 28.08/18.34 tff(8970,plain,
% 28.08/18.34 (~(f7(f9(f10(c2), f7(c1))) = f9(f10(c2), f7(c1)))),
% 28.08/18.34 inference(modus_ponens,[status(thm)],[17, 8969])).
% 28.08/18.34 tff(8971,plain,
% 28.08/18.34 (f5(f9(f10(c2), f7(c1))) = f5(c2)),
% 28.08/18.34 inference(monotonicity,[status(thm)],[8962])).
% 28.08/18.34 tff(8972,plain,
% 28.08/18.34 (big_f(f7(f9(f10(c2), f7(c1))), f5(f9(f10(c2), f7(c1)))) <=> big_f(f7(c2), f5(c2))),
% 28.08/18.34 inference(monotonicity,[status(thm)],[8965, 8971])).
% 28.08/18.34 tff(8973,plain,
% 28.08/18.34 (big_f(f7(c2), f5(c2)) <=> big_f(f7(f9(f10(c2), f7(c1))), f5(f9(f10(c2), f7(c1))))),
% 28.08/18.34 inference(symmetry,[status(thm)],[8972])).
% 28.08/18.34 tff(8974,plain,
% 28.08/18.34 (big_f(f7(c2), f5(c2)) <=> big_f(f7(c2), c1)),
% 28.08/18.34 inference(monotonicity,[status(thm)],[1569])).
% 28.08/18.34 tff(8975,plain,
% 28.08/18.34 (big_f(f7(c2), c1) <=> big_f(f7(c2), f5(c2))),
% 28.08/18.34 inference(symmetry,[status(thm)],[8974])).
% 28.08/18.34 tff(8976,plain,
% 28.08/18.34 (big_f(f7(c2), c1) <=> big_f(f7(f9(f10(c2), f7(c1))), f5(f9(f10(c2), f7(c1))))),
% 28.08/18.34 inference(transitivity,[status(thm)],[8975, 8973])).
% 28.08/18.34 tff(8977,plain,
% 28.08/18.34 ((~big_f(f7(c2), c1)) <=> (~big_f(f7(f9(f10(c2), f7(c1))), f5(f9(f10(c2), f7(c1)))))),
% 28.08/18.34 inference(monotonicity,[status(thm)],[8976])).
% 28.08/18.34 tff(8978,plain,
% 28.08/18.34 (~big_f(f7(f9(f10(c2), f7(c1))), f5(f9(f10(c2), f7(c1))))),
% 28.08/18.34 inference(modus_ponens,[status(thm)],[333, 8977])).
% 28.08/18.34 tff(8979,plain,
% 28.08/18.34 (f9(c1, c2) = f7(c2)),
% 28.08/18.34 inference(transitivity,[status(thm)],[4240, 342])).
% 28.08/18.34 tff(8980,plain,
% 28.08/18.34 (big_f(f9(c1, c2), f10(c1)) <=> big_f(f7(c2), c1)),
% 28.08/18.34 inference(monotonicity,[status(thm)],[8979, 3762])).
% 28.08/18.34 tff(8981,plain,
% 28.08/18.34 (big_f(f7(c2), c1) <=> big_f(f9(c1, c2), f10(c1))),
% 28.08/18.34 inference(symmetry,[status(thm)],[8980])).
% 28.08/18.34 tff(8982,plain,
% 28.08/18.34 ((~big_f(f7(c2), c1)) <=> (~big_f(f9(c1, c2), f10(c1)))),
% 28.08/18.34 inference(monotonicity,[status(thm)],[8981])).
% 28.08/18.34 tff(8983,plain,
% 28.08/18.34 (~big_f(f9(c1, c2), f10(c1))),
% 28.08/18.34 inference(modus_ponens,[status(thm)],[333, 8982])).
% 28.08/18.34 tff(8984,assumption,(~big_f(f7(f9(f10(c2), f7(c1))), f5(f9(f10(c2), f7(c1))))), introduced(assumption)).
% 28.08/18.34 tff(8985,assumption,(~(f7(f9(f10(c2), f7(c1))) = f9(f10(c2), f7(c1)))), introduced(assumption)).
% 28.08/18.34 tff(8986,plain,
% 28.08/18.34 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((f7(f9(f10(c2), f7(c1))) = f9(f10(c2), f7(c1))) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | big_f(f7(f9(f10(c2), f7(c1))), f5(f9(f10(c2), f7(c1)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (f7(f9(f10(c2), f7(c1))) = f9(f10(c2), f7(c1))) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | big_f(f7(f9(f10(c2), f7(c1))), f5(f9(f10(c2), f7(c1)))))),
% 28.08/18.34 inference(rewrite,[status(thm)],[])).
% 28.08/18.34 tff(8987,plain,
% 28.08/18.34 (((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (f7(f9(f10(c2), f7(c1))) = f9(f10(c2), f7(c1))) | big_f(f7(f9(f10(c2), f7(c1))), f5(f9(f10(c2), f7(c1)))) | $false) <=> ((f7(f9(f10(c2), f7(c1))) = f9(f10(c2), f7(c1))) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | big_f(f7(f9(f10(c2), f7(c1))), f5(f9(f10(c2), f7(c1)))))),
% 28.08/18.34 inference(rewrite,[status(thm)],[])).
% 28.08/18.34 tff(8988,plain,
% 28.08/18.34 ((f5(f9(f10(c2), f7(c1))) = f5(f9(f10(c2), f7(c1)))) <=> $true),
% 28.08/18.34 inference(rewrite,[status(thm)],[])).
% 28.08/18.34 tff(8989,plain,
% 28.08/18.34 ((~(f5(f9(f10(c2), f7(c1))) = f5(f9(f10(c2), f7(c1))))) <=> (~$true)),
% 28.08/18.34 inference(monotonicity,[status(thm)],[8988])).
% 28.08/18.34 tff(8990,plain,
% 28.08/18.34 ((~(f5(f9(f10(c2), f7(c1))) = f5(f9(f10(c2), f7(c1))))) <=> $false),
% 28.08/18.34 inference(transitivity,[status(thm)],[8989, 270])).
% 28.08/18.34 tff(8991,plain,
% 28.08/18.34 (((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (f7(f9(f10(c2), f7(c1))) = f9(f10(c2), f7(c1))) | big_f(f7(f9(f10(c2), f7(c1))), f5(f9(f10(c2), f7(c1)))) | (~(f5(f9(f10(c2), f7(c1))) = f5(f9(f10(c2), f7(c1)))))) <=> ((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (f7(f9(f10(c2), f7(c1))) = f9(f10(c2), f7(c1))) | big_f(f7(f9(f10(c2), f7(c1))), f5(f9(f10(c2), f7(c1)))) | $false)),
% 28.08/18.34 inference(monotonicity,[status(thm)],[8990])).
% 28.08/18.34 tff(8992,plain,
% 28.08/18.34 (((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (f7(f9(f10(c2), f7(c1))) = f9(f10(c2), f7(c1))) | big_f(f7(f9(f10(c2), f7(c1))), f5(f9(f10(c2), f7(c1)))) | (~(f5(f9(f10(c2), f7(c1))) = f5(f9(f10(c2), f7(c1)))))) <=> ((f7(f9(f10(c2), f7(c1))) = f9(f10(c2), f7(c1))) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | big_f(f7(f9(f10(c2), f7(c1))), f5(f9(f10(c2), f7(c1)))))),
% 28.08/18.34 inference(transitivity,[status(thm)],[8991, 8987])).
% 28.08/18.34 tff(8993,plain,
% 28.08/18.34 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (f7(f9(f10(c2), f7(c1))) = f9(f10(c2), f7(c1))) | big_f(f7(f9(f10(c2), f7(c1))), f5(f9(f10(c2), f7(c1)))) | (~(f5(f9(f10(c2), f7(c1))) = f5(f9(f10(c2), f7(c1))))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((f7(f9(f10(c2), f7(c1))) = f9(f10(c2), f7(c1))) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | big_f(f7(f9(f10(c2), f7(c1))), f5(f9(f10(c2), f7(c1))))))),
% 28.08/18.34 inference(monotonicity,[status(thm)],[8992])).
% 28.08/18.34 tff(8994,plain,
% 28.08/18.34 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (f7(f9(f10(c2), f7(c1))) = f9(f10(c2), f7(c1))) | big_f(f7(f9(f10(c2), f7(c1))), f5(f9(f10(c2), f7(c1)))) | (~(f5(f9(f10(c2), f7(c1))) = f5(f9(f10(c2), f7(c1))))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (f7(f9(f10(c2), f7(c1))) = f9(f10(c2), f7(c1))) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | big_f(f7(f9(f10(c2), f7(c1))), f5(f9(f10(c2), f7(c1)))))),
% 28.08/18.34 inference(transitivity,[status(thm)],[8993, 8986])).
% 28.08/18.34 tff(8995,plain,
% 28.08/18.34 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (f7(f9(f10(c2), f7(c1))) = f9(f10(c2), f7(c1))) | big_f(f7(f9(f10(c2), f7(c1))), f5(f9(f10(c2), f7(c1)))) | (~(f5(f9(f10(c2), f7(c1))) = f5(f9(f10(c2), f7(c1))))))),
% 28.08/18.34 inference(quant_inst,[status(thm)],[])).
% 28.08/18.34 tff(8996,plain,
% 28.08/18.34 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (f7(f9(f10(c2), f7(c1))) = f9(f10(c2), f7(c1))) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | big_f(f7(f9(f10(c2), f7(c1))), f5(f9(f10(c2), f7(c1))))),
% 28.08/18.34 inference(modus_ponens,[status(thm)],[8995, 8994])).
% 28.08/18.34 tff(8997,plain,
% 28.08/18.34 ((f7(f9(f10(c2), f7(c1))) = f9(f10(c2), f7(c1))) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | big_f(f7(f9(f10(c2), f7(c1))), f5(f9(f10(c2), f7(c1))))),
% 28.08/18.34 inference(unit_resolution,[status(thm)],[8996, 267])).
% 28.08/18.34 tff(8998,plain,
% 28.08/18.34 (big_f(f9(c1, c2), f10(c1))),
% 28.08/18.34 inference(unit_resolution,[status(thm)],[8997, 4236, 8985, 3762, 8984])).
% 28.08/18.34 tff(8999,plain,
% 28.08/18.34 ($false),
% 28.08/18.34 inference(unit_resolution,[status(thm)],[8998, 8983])).
% 28.08/18.34 tff(9000,plain,((f9(c1, c2) = c2) | big_f(f7(c2), c1) | (~(f10(c1) = c1)) | (~(f7(c2) = c1)) | (f7(f9(f10(c2), f7(c1))) = f9(f10(c2), f7(c1))) | big_f(f7(f9(f10(c2), f7(c1))), f5(f9(f10(c2), f7(c1))))), inference(lemma,lemma(discharge,[]))).
% 28.08/18.34 tff(9001,plain,
% 28.08/18.34 (f9(c1, c2) = c2),
% 28.08/18.34 inference(unit_resolution,[status(thm)],[9000, 8978, 3762, 22, 8970, 333])).
% 28.08/18.34 tff(9002,plain,
% 28.08/18.34 (f9(f7(c2), c2) = c2),
% 28.08/18.34 inference(transitivity,[status(thm)],[8170, 9001])).
% 28.08/18.34 tff(9003,plain,
% 28.08/18.34 (big_f(f9(f7(c2), c2), f10(f7(c2))) <=> big_f(c2, c1)),
% 28.08/18.34 inference(monotonicity,[status(thm)],[9002, 8168])).
% 28.08/18.34 tff(9004,plain,
% 28.08/18.34 (big_f(c2, c1) <=> big_f(f9(f7(c2), c2), f10(f7(c2)))),
% 28.08/18.34 inference(symmetry,[status(thm)],[9003])).
% 28.08/18.34 tff(9005,plain,
% 28.08/18.34 (big_f(f9(f7(c2), c2), f10(f7(c2)))),
% 28.08/18.34 inference(modus_ponens,[status(thm)],[348, 9004])).
% 28.08/18.34 tff(9006,plain,
% 28.08/18.34 ((~(f9(f7(c2), c2) = c2)) | (~big_f(f9(f7(c2), c2), f10(f7(c2))))),
% 28.08/18.34 inference(unit_resolution,[status(thm)],[8224, 783, 17, 8183, 8212, 8217])).
% 28.08/18.34 tff(9007,plain,
% 28.08/18.34 ($false),
% 28.08/18.34 inference(unit_resolution,[status(thm)],[9006, 9005, 9002])).
% 28.08/18.34 tff(9008,plain,((~(f5(c2) = c1)) | (f7(c2) = c2) | (~big_f(c2, c1)) | (~(f10(c1) = c1)) | (~(f4(c4) = c2)) | big_f(f7(c2), c1) | (~(f7(c1) = c2)) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.08/18.34 tff(9009,plain,
% 28.08/18.34 (~(f5(c2) = c1)),
% 28.08/18.34 inference(unit_resolution,[status(thm)],[9008, 8720, 17, 8960, 79, 8807, 120, 122])).
% 28.08/18.34 tff(9010,plain,
% 28.08/18.34 (f5(c2) = c2),
% 28.08/18.34 inference(unit_resolution,[status(thm)],[1547, 9009])).
% 28.08/18.34 tff(9011,plain,
% 28.08/18.34 (big_f(f7(c2), f5(c2)) <=> big_f(f7(c2), c2)),
% 28.08/18.34 inference(monotonicity,[status(thm)],[8109])).
% 28.08/18.34 tff(9012,plain,
% 28.08/18.34 (big_f(f7(c2), c2) <=> big_f(f7(c2), f5(c2))),
% 28.08/18.34 inference(symmetry,[status(thm)],[9011])).
% 28.08/18.34 tff(9013,plain,
% 28.08/18.34 (big_f(f7(c2), c2) <=> big_f(f7(f9(f10(c2), f7(c1))), f5(f9(f10(c2), f7(c1))))),
% 28.08/18.34 inference(transitivity,[status(thm)],[9012, 8973])).
% 28.08/18.34 tff(9014,plain,
% 28.08/18.34 ((~big_f(f7(c2), c2)) <=> (~big_f(f7(f9(f10(c2), f7(c1))), f5(f9(f10(c2), f7(c1)))))),
% 28.08/18.34 inference(monotonicity,[status(thm)],[9013])).
% 28.08/18.34 tff(9015,plain,
% 28.08/18.34 (~big_f(f7(f9(f10(c2), f7(c1))), f5(f9(f10(c2), f7(c1))))),
% 28.08/18.34 inference(modus_ponens,[status(thm)],[1521, 9014])).
% 28.08/18.34 tff(9016,plain,
% 28.08/18.34 (f9(c1, c2) = c2),
% 28.08/18.34 inference(unit_resolution,[status(thm)],[9000, 9015, 3762, 22, 8970, 333])).
% 28.08/18.34 tff(9017,plain,
% 28.08/18.34 (big_f(f9(c1, c2), f10(c1)) <=> big_f(c2, c1)),
% 28.08/18.34 inference(monotonicity,[status(thm)],[9016, 3762])).
% 28.08/18.34 tff(9018,plain,
% 28.08/18.34 (big_f(c2, c1) <=> big_f(f9(c1, c2), f10(c1))),
% 28.08/18.34 inference(symmetry,[status(thm)],[9017])).
% 28.08/18.34 tff(9019,plain,
% 28.08/18.34 (big_f(f9(c1, c2), f10(c1))),
% 28.08/18.34 inference(modus_ponens,[status(thm)],[348, 9018])).
% 28.08/18.34 tff(9020,plain,
% 28.08/18.34 (c2 = f5(c2)),
% 28.08/18.34 inference(unit_resolution,[status(thm)],[8113, 8109])).
% 28.08/18.34 tff(9021,plain,
% 28.08/18.34 (~big_f(f9(c1, c2), f10(c1))),
% 28.08/18.34 inference(unit_resolution,[status(thm)],[8204, 9016, 17, 1521, 3762, 9020])).
% 28.08/18.34 tff(9022,plain,
% 28.08/18.34 ($false),
% 28.08/18.34 inference(unit_resolution,[status(thm)],[9021, 9019])).
% 28.08/18.34 tff(9023,plain,((~(f5(c2) = c2)) | (~big_f(c2, c1)) | (~(f10(c1) = c1)) | (f7(c2) = c2) | big_f(f7(c2), c2) | big_f(f7(c2), c1) | (~(f4(c4) = c2)) | (~(f7(c1) = c2)) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.08/18.34 tff(9024,plain,
% 28.08/18.34 (big_f(f7(c2), c2)),
% 28.08/18.34 inference(unit_resolution,[status(thm)],[9023, 9010, 8960, 17, 8720, 8807, 79, 120, 122])).
% 28.08/18.34 tff(9025,plain,
% 28.08/18.34 (f3(c2, f7(c2)) = f7(c2)),
% 28.08/18.34 inference(transitivity,[status(thm)],[8923, 3125, 953, 125])).
% 28.08/18.34 tff(9026,plain,
% 28.08/18.34 (big_f(f3(c2, f7(c2)), c2) <=> big_f(f7(c2), c2)),
% 28.08/18.34 inference(monotonicity,[status(thm)],[9025])).
% 28.08/18.34 tff(9027,plain,
% 28.08/18.34 (big_f(f7(c2), c2) <=> big_f(f3(c2, f7(c2)), c2)),
% 28.08/18.34 inference(symmetry,[status(thm)],[9026])).
% 28.08/18.34 tff(9028,plain,
% 28.08/18.34 (big_f(f3(c2, f7(c2)), c2)),
% 28.08/18.34 inference(modus_ponens,[status(thm)],[1180, 9027])).
% 28.08/18.34 tff(9029,plain,
% 28.08/18.34 (~(f1(f7(f7(c2)), c1) = c2)),
% 28.08/18.34 inference(unit_resolution,[status(thm)],[8865, 953, 873, 1180, 347, 121, 377, 17])).
% 28.08/18.34 tff(9030,plain,
% 28.08/18.34 (f1(f7(f7(c2)), c1) = c1),
% 28.08/18.34 inference(unit_resolution,[status(thm)],[384, 9029])).
% 28.08/18.34 tff(9031,plain,
% 28.08/18.34 (f1(c2, c1) = c1),
% 28.08/18.34 inference(transitivity,[status(thm)],[8785, 9030])).
% 28.08/18.34 tff(9032,plain,
% 28.08/18.34 (big_f(c2, f1(c2, c1)) <=> big_f(c2, c1)),
% 28.08/18.34 inference(monotonicity,[status(thm)],[9031])).
% 28.08/18.34 tff(9033,plain,
% 28.08/18.34 (big_f(c2, c1) <=> big_f(c2, f1(c2, c1))),
% 28.08/18.34 inference(symmetry,[status(thm)],[9032])).
% 28.08/18.34 tff(9034,plain,
% 28.08/18.34 (big_f(c2, c1) <=> big_f(c2, f1(c2, f7(c2)))),
% 28.08/18.34 inference(transitivity,[status(thm)],[9033, 8768])).
% 28.08/18.34 tff(9035,plain,
% 28.08/18.34 (big_f(c2, f1(c2, f7(c2)))),
% 28.08/18.34 inference(modus_ponens,[status(thm)],[348, 9034])).
% 28.08/18.34 tff(9036,plain,
% 28.08/18.34 (f1(c2, f7(c2)) = f7(c2)),
% 28.08/18.34 inference(modus_ponens,[status(thm)],[9030, 8796])).
% 28.08/18.34 tff(9037,plain,
% 28.08/18.34 ((~(f3(c2, f7(c2)) = f7(c2))) | (~big_f(f3(c2, f7(c2)), c2))),
% 28.08/18.34 inference(unit_resolution,[status(thm)],[8956, 933, 873, 377, 9036, 9035])).
% 28.08/18.34 tff(9038,plain,
% 28.08/18.34 ($false),
% 28.08/18.34 inference(unit_resolution,[status(thm)],[9037, 9028, 9025])).
% 28.08/18.34 tff(9039,plain,((~(f3(f7(c1), c1) = c1)) | (c2 = c4) | (c2 = c3) | (~big_f(f7(c2), c2)) | (~(f7(c1) = c2)) | (~big_f(c2, c1)) | big_f(c2, c2) | (f7(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 28.08/18.34 tff(9040,plain,
% 28.08/18.34 (~(f3(f7(c1), c1) = c1)),
% 28.08/18.34 inference(unit_resolution,[status(thm)],[9039, 8755, 8724, 9024, 120, 8720, 121, 17])).
% 28.08/18.34 tff(9041,plain,
% 28.08/18.34 (f3(f7(c1), c1) = c2),
% 28.08/18.34 inference(unit_resolution,[status(thm)],[918, 9040])).
% 28.08/18.34 tff(9042,plain,
% 28.08/18.34 (f3(c2, f7(c2)) = c2),
% 28.08/18.34 inference(transitivity,[status(thm)],[8923, 2779, 9041])).
% 28.08/18.34 tff(9043,plain,
% 28.08/18.34 (big_f(f3(c2, f7(c2)), c2) <=> big_f(c2, c2)),
% 28.08/18.34 inference(monotonicity,[status(thm)],[9042])).
% 28.08/18.34 tff(9044,plain,
% 28.08/18.34 (big_f(c2, c2) <=> big_f(f3(c2, f7(c2)), c2)),
% 28.08/18.34 inference(symmetry,[status(thm)],[9043])).
% 28.08/18.34 tff(9045,plain,
% 28.08/18.34 ((~big_f(c2, c2)) <=> (~big_f(f3(c2, f7(c2)), c2))),
% 28.08/18.34 inference(monotonicity,[status(thm)],[9044])).
% 28.08/18.34 tff(9046,plain,
% 28.08/18.34 (~big_f(f3(c2, f7(c2)), c2)),
% 28.08/18.34 inference(modus_ponens,[status(thm)],[121, 9045])).
% 28.08/18.34 tff(9047,plain,
% 28.08/18.34 ((f3(c2, f7(c2)) = f7(c2)) <=> (c2 = f7(c2))),
% 28.08/18.34 inference(monotonicity,[status(thm)],[9042])).
% 28.08/18.34 tff(9048,plain,
% 28.08/18.34 ((f3(c2, f7(c2)) = f7(c2)) <=> (f7(c2) = c2)),
% 28.08/18.34 inference(transitivity,[status(thm)],[9047, 8409])).
% 28.08/18.34 tff(9049,plain,
% 28.08/18.34 ((f7(c2) = c2) <=> (f3(c2, f7(c2)) = f7(c2))),
% 28.08/18.34 inference(symmetry,[status(thm)],[9048])).
% 28.08/18.34 tff(9050,plain,
% 28.08/18.34 ((~(f7(c2) = c2)) <=> (~(f3(c2, f7(c2)) = f7(c2)))),
% 28.08/18.34 inference(monotonicity,[status(thm)],[9049])).
% 28.08/18.34 tff(9051,plain,
% 28.08/18.34 (~(f3(c2, f7(c2)) = f7(c2))),
% 28.08/18.34 inference(modus_ponens,[status(thm)],[17, 9050])).
% 28.08/18.34 tff(9052,assumption,(~big_f(f3(c2, f7(c2)), c2)), introduced(assumption)).
% 28.08/18.34 tff(9053,assumption,(~(f3(c2, f7(c2)) = f7(c2))), introduced(assumption)).
% 28.08/18.34 tff(9054,plain,
% 28.08/18.34 (f1(c2, c1) = c1),
% 28.08/18.34 inference(transitivity,[status(thm)],[356, 874])).
% 28.08/18.34 tff(9055,plain,
% 28.08/18.34 (big_f(c2, f1(c2, c1)) <=> big_f(c2, c1)),
% 28.08/18.34 inference(monotonicity,[status(thm)],[9054])).
% 28.08/18.34 tff(9056,plain,
% 28.08/18.34 (big_f(c2, c1) <=> big_f(c2, f1(c2, c1))),
% 28.08/18.34 inference(symmetry,[status(thm)],[9055])).
% 28.08/18.34 tff(9057,plain,
% 28.08/18.34 (big_f(c2, c1) <=> big_f(c2, f1(c2, f7(c2)))),
% 28.08/18.34 inference(transitivity,[status(thm)],[9056, 8727])).
% 28.08/18.35 tff(9058,plain,
% 28.08/18.35 (big_f(c2, f1(c2, f7(c2)))),
% 28.08/18.35 inference(modus_ponens,[status(thm)],[348, 9057])).
% 28.08/18.35 tff(9059,plain,
% 28.08/18.35 ($false),
% 28.08/18.35 inference(unit_resolution,[status(thm)],[8941, 904, 873, 377, 8773, 9058, 9053, 9052])).
% 28.08/18.35 tff(9060,plain,((~(f1(f7(f7(c2)), c1) = c1)) | (c2 = c4) | (c2 = c3) | (f3(c2, f7(c2)) = f7(c2)) | big_f(f3(c2, f7(c2)), c2) | (~big_f(c2, c1)) | (~(f7(c1) = c2)) | (~(f7(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.08/18.35 tff(9061,plain,
% 28.08/18.35 (~(f1(f7(f7(c2)), c1) = c1)),
% 28.08/18.35 inference(unit_resolution,[status(thm)],[9060, 8755, 8724, 9051, 9046, 8720, 120, 22])).
% 28.08/18.35 tff(9062,plain,
% 28.08/18.35 (f1(f7(f7(c2)), c1) = c2),
% 28.08/18.35 inference(unit_resolution,[status(thm)],[384, 9061])).
% 28.08/18.35 tff(9063,plain,
% 28.08/18.35 (f1(c2, c1) = c2),
% 28.08/18.35 inference(transitivity,[status(thm)],[8404, 9062])).
% 28.08/18.35 tff(9064,plain,
% 28.08/18.35 (big_f(c2, f1(c2, c1)) <=> big_f(c2, c2)),
% 28.08/18.35 inference(monotonicity,[status(thm)],[9063])).
% 28.08/18.35 tff(9065,plain,
% 28.08/18.35 (big_f(c2, c2) <=> big_f(c2, f1(c2, c1))),
% 28.08/18.35 inference(symmetry,[status(thm)],[9064])).
% 28.08/18.35 tff(9066,plain,
% 28.08/18.35 (big_f(c2, c2) <=> big_f(c2, f1(c2, f7(c2)))),
% 28.08/18.35 inference(transitivity,[status(thm)],[9065, 8768])).
% 28.08/18.35 tff(9067,plain,
% 28.08/18.35 ((~big_f(c2, c2)) <=> (~big_f(c2, f1(c2, f7(c2))))),
% 28.08/18.35 inference(monotonicity,[status(thm)],[9066])).
% 28.08/18.35 tff(9068,plain,
% 28.08/18.35 (~big_f(c2, f1(c2, f7(c2)))),
% 28.08/18.35 inference(modus_ponens,[status(thm)],[121, 9067])).
% 28.08/18.35 tff(9069,plain,
% 28.08/18.35 ((f1(f7(f7(c2)), c1) = c1) <=> (f1(c2, c1) = c1)),
% 28.08/18.35 inference(monotonicity,[status(thm)],[8405])).
% 28.08/18.35 tff(9070,plain,
% 28.08/18.35 ((f1(f7(f7(c2)), c1) = c1) <=> (f1(c2, f7(c2)) = f7(c2))),
% 28.08/18.35 inference(transitivity,[status(thm)],[9069, 8793])).
% 28.08/18.35 tff(9071,plain,
% 28.08/18.35 ((~(f1(f7(f7(c2)), c1) = c1)) <=> (~(f1(c2, f7(c2)) = f7(c2)))),
% 28.08/18.35 inference(monotonicity,[status(thm)],[9070])).
% 28.08/18.35 tff(9072,plain,
% 28.08/18.35 (~(f1(c2, f7(c2)) = f7(c2))),
% 28.08/18.35 inference(modus_ponens,[status(thm)],[9061, 9071])).
% 28.08/18.35 tff(9073,plain,
% 28.08/18.35 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c2 = c3) | (c2 = c4) | (f1(c2, f7(c2)) = f7(c2)) | big_f(c2, f1(c2, f7(c2))) | (f3(c2, f7(c2)) = f7(c2)) | big_f(f3(c2, f7(c2)), c2))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (c2 = c3) | (c2 = c4) | (f1(c2, f7(c2)) = f7(c2)) | big_f(c2, f1(c2, f7(c2))) | (f3(c2, f7(c2)) = f7(c2)) | big_f(f3(c2, f7(c2)), c2))),
% 28.08/18.35 inference(rewrite,[status(thm)],[])).
% 28.08/18.35 tff(9074,plain,
% 28.08/18.35 (((c2 = c4) | (f3(c2, f7(c2)) = f7(c2)) | big_f(f3(c2, f7(c2)), c2) | (c2 = c3) | (f1(c2, f7(c2)) = f7(c2)) | big_f(c2, f1(c2, f7(c2)))) <=> ((c2 = c3) | (c2 = c4) | (f1(c2, f7(c2)) = f7(c2)) | big_f(c2, f1(c2, f7(c2))) | (f3(c2, f7(c2)) = f7(c2)) | big_f(f3(c2, f7(c2)), c2))),
% 28.08/18.35 inference(rewrite,[status(thm)],[])).
% 28.08/18.35 tff(9075,plain,
% 28.08/18.35 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c2 = c4) | (f3(c2, f7(c2)) = f7(c2)) | big_f(f3(c2, f7(c2)), c2) | (c2 = c3) | (f1(c2, f7(c2)) = f7(c2)) | big_f(c2, f1(c2, f7(c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c2 = c3) | (c2 = c4) | (f1(c2, f7(c2)) = f7(c2)) | big_f(c2, f1(c2, f7(c2))) | (f3(c2, f7(c2)) = f7(c2)) | big_f(f3(c2, f7(c2)), c2)))),
% 28.08/18.35 inference(monotonicity,[status(thm)],[9074])).
% 28.08/18.35 tff(9076,plain,
% 28.08/18.35 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c2 = c4) | (f3(c2, f7(c2)) = f7(c2)) | big_f(f3(c2, f7(c2)), c2) | (c2 = c3) | (f1(c2, f7(c2)) = f7(c2)) | big_f(c2, f1(c2, f7(c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (c2 = c3) | (c2 = c4) | (f1(c2, f7(c2)) = f7(c2)) | big_f(c2, f1(c2, f7(c2))) | (f3(c2, f7(c2)) = f7(c2)) | big_f(f3(c2, f7(c2)), c2))),
% 28.08/18.35 inference(transitivity,[status(thm)],[9075, 9073])).
% 28.08/18.35 tff(9077,plain,
% 28.08/18.35 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c2 = c4) | (f3(c2, f7(c2)) = f7(c2)) | big_f(f3(c2, f7(c2)), c2) | (c2 = c3) | (f1(c2, f7(c2)) = f7(c2)) | big_f(c2, f1(c2, f7(c2))))),
% 28.08/18.35 inference(quant_inst,[status(thm)],[])).
% 28.08/18.35 tff(9078,plain,
% 28.08/18.35 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (c2 = c3) | (c2 = c4) | (f1(c2, f7(c2)) = f7(c2)) | big_f(c2, f1(c2, f7(c2))) | (f3(c2, f7(c2)) = f7(c2)) | big_f(f3(c2, f7(c2)), c2)),
% 28.08/18.35 inference(modus_ponens,[status(thm)],[9077, 9076])).
% 28.08/18.35 tff(9079,plain,
% 28.08/18.35 ($false),
% 28.08/18.35 inference(unit_resolution,[status(thm)],[9078, 1014, 8755, 8724, 9072, 9068, 9051, 9046])).
% 28.08/18.35 tff(9080,plain,((~(c3 = c1)) | big_f(c2, c2) | (f7(c2) = c2) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (f7(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 28.08/18.35 tff(9081,plain,
% 28.08/18.35 (~(c3 = c1)),
% 28.08/18.35 inference(unit_resolution,[status(thm)],[9080, 121, 17, 79, 122, 8366])).
% 28.08/18.35 tff(9082,plain,
% 28.08/18.35 (c3 = c2),
% 28.08/18.35 inference(unit_resolution,[status(thm)],[180, 9081])).
% 28.08/18.35 tff(9083,plain,
% 28.08/18.35 ((f7(c2) = c3) <=> (f7(c2) = c2)),
% 28.08/18.35 inference(monotonicity,[status(thm)],[9082])).
% 28.08/18.35 tff(9084,plain,
% 28.08/18.35 ((f7(c2) = c2) <=> (f7(c2) = c3)),
% 28.08/18.35 inference(symmetry,[status(thm)],[9083])).
% 28.08/18.35 tff(9085,plain,
% 28.08/18.35 ((~(f7(c2) = c2)) <=> (~(f7(c2) = c3))),
% 28.08/18.35 inference(monotonicity,[status(thm)],[9084])).
% 28.08/18.35 tff(9086,plain,
% 28.08/18.35 (~(f7(c2) = c3)),
% 28.08/18.35 inference(modus_ponens,[status(thm)],[17, 9085])).
% 28.08/18.35 tff(9087,plain,
% 28.08/18.35 ((c1 = c3) <=> (f7(c2) = c3)),
% 28.08/18.35 inference(monotonicity,[status(thm)],[125])).
% 28.08/18.35 tff(9088,plain,
% 28.08/18.35 ((f7(c2) = c3) <=> (c1 = c3)),
% 28.08/18.35 inference(symmetry,[status(thm)],[9087])).
% 28.08/18.35 tff(9089,plain,
% 28.08/18.35 ((f7(c2) = c2) <=> (c1 = c3)),
% 28.08/18.35 inference(transitivity,[status(thm)],[9084, 9088])).
% 28.08/18.35 tff(9090,plain,
% 28.08/18.35 ((~(f7(c2) = c2)) <=> (~(c1 = c3))),
% 28.08/18.35 inference(monotonicity,[status(thm)],[9089])).
% 28.08/18.35 tff(9091,plain,
% 28.08/18.35 (~(c1 = c3)),
% 28.08/18.35 inference(modus_ponens,[status(thm)],[17, 9090])).
% 28.08/18.35 tff(9092,assumption,(~(f7(c2) = c3)), introduced(assumption)).
% 28.08/18.35 tff(9093,plain,
% 28.08/18.35 (~(c4 = c2)),
% 28.08/18.35 inference(modus_ponens,[status(thm)],[873, 8722])).
% 28.08/18.35 tff(9094,plain,
% 28.08/18.35 (c4 = c1),
% 28.08/18.35 inference(unit_resolution,[status(thm)],[461, 9093])).
% 28.08/18.35 tff(9095,plain,
% 28.08/18.35 (f3(f7(c1), c1) = f3(c2, c1)),
% 28.08/18.35 inference(symmetry,[status(thm)],[3125])).
% 28.08/18.35 tff(9096,plain,
% 28.08/18.35 ((f3(f7(c1), c1) = c4) <=> (f3(c2, c1) = c1)),
% 28.08/18.35 inference(monotonicity,[status(thm)],[9095, 9094])).
% 28.08/18.35 tff(9097,plain,
% 28.08/18.35 ((f3(c2, c1) = c1) <=> (f3(f7(c1), c1) = c4)),
% 28.08/18.35 inference(symmetry,[status(thm)],[9096])).
% 28.08/18.35 tff(9098,plain,
% 28.08/18.35 ((f3(f7(c1), c1) = c1) <=> (f3(c2, c1) = c1)),
% 28.08/18.35 inference(monotonicity,[status(thm)],[9095])).
% 28.08/18.35 tff(9099,plain,
% 28.08/18.35 ((f3(f7(c1), c1) = c1) <=> (f3(f7(c1), c1) = c4)),
% 28.08/18.35 inference(transitivity,[status(thm)],[9098, 9097])).
% 28.08/18.35 tff(9100,plain,
% 28.08/18.35 ((~(f3(f7(c1), c1) = c1)) <=> (~(f3(f7(c1), c1) = c4))),
% 28.08/18.35 inference(monotonicity,[status(thm)],[9099])).
% 28.08/18.35 tff(9101,plain,
% 28.08/18.35 (big_f(f3(c2, f7(c2)), c2) <=> big_f(f3(c2, c1), c2)),
% 28.08/18.35 inference(monotonicity,[status(thm)],[8923])).
% 28.08/18.35 tff(9102,plain,
% 28.08/18.35 (big_f(f3(c2, c1), c2) <=> big_f(f3(c2, f7(c2)), c2)),
% 28.08/18.35 inference(symmetry,[status(thm)],[9101])).
% 28.08/18.35 tff(9103,plain,
% 28.08/18.35 (f3(c2, c1) = f7(c2)),
% 28.08/18.35 inference(transitivity,[status(thm)],[3125, 953, 125])).
% 28.08/18.35 tff(9104,plain,
% 28.08/18.35 (big_f(f3(c2, c1), c2) <=> big_f(f7(c2), c2)),
% 28.08/18.35 inference(monotonicity,[status(thm)],[9103])).
% 28.08/18.35 tff(9105,plain,
% 28.08/18.35 (big_f(f7(c2), c2) <=> big_f(f3(c2, c1), c2)),
% 28.08/18.35 inference(symmetry,[status(thm)],[9104])).
% 28.08/18.35 tff(9106,plain,
% 28.08/18.35 (big_f(f7(c2), c2) <=> big_f(f3(c2, f7(c2)), c2)),
% 28.08/18.35 inference(transitivity,[status(thm)],[9105, 9102])).
% 28.08/18.35 tff(9107,plain,
% 28.08/18.35 (big_f(f3(c2, f7(c2)), c2)),
% 28.08/18.35 inference(modus_ponens,[status(thm)],[1180, 9106])).
% 28.08/18.35 tff(9108,plain,
% 28.08/18.35 ((f3(c2, f7(c2)) = f7(c2)) <=> (f3(c2, c1) = c1)),
% 28.08/18.35 inference(monotonicity,[status(thm)],[8923, 22])).
% 28.08/18.35 tff(9109,plain,
% 28.08/18.35 ((f3(c2, c1) = c1) <=> (f3(c2, f7(c2)) = f7(c2))),
% 28.08/18.35 inference(symmetry,[status(thm)],[9108])).
% 28.08/18.35 tff(9110,plain,
% 28.08/18.35 ((f3(f7(c1), c1) = c1) <=> (f3(c2, f7(c2)) = f7(c2))),
% 28.08/18.35 inference(transitivity,[status(thm)],[9098, 9109])).
% 28.08/18.35 tff(9111,plain,
% 28.08/18.35 (f3(c2, f7(c2)) = f7(c2)),
% 28.08/18.35 inference(modus_ponens,[status(thm)],[953, 9110])).
% 28.08/18.35 tff(9112,plain,
% 28.08/18.35 (f1(f7(c2), c2) = f1(c1, c2)),
% 28.08/18.35 inference(monotonicity,[status(thm)],[22])).
% 28.08/18.35 tff(9113,plain,
% 28.08/18.35 (f1(f7(c2), c2) = c1),
% 28.08/18.35 inference(transitivity,[status(thm)],[9112, 1095])).
% 28.08/18.35 tff(9114,plain,
% 28.08/18.35 (big_f(f7(c2), f1(f7(c2), c2)) <=> big_f(f7(c2), c1)),
% 28.08/18.35 inference(monotonicity,[status(thm)],[9113])).
% 28.08/18.35 tff(9115,plain,
% 28.08/18.35 (big_f(f7(c2), c1) <=> big_f(f7(c2), f1(f7(c2), c2))),
% 28.08/18.35 inference(symmetry,[status(thm)],[9114])).
% 28.08/18.35 tff(9116,plain,
% 28.08/18.35 ((~big_f(f7(c2), c1)) <=> (~big_f(f7(c2), f1(f7(c2), c2)))),
% 28.08/18.35 inference(monotonicity,[status(thm)],[9115])).
% 28.08/18.35 tff(9117,plain,
% 28.08/18.35 (~big_f(f7(c2), f1(f7(c2), c2))),
% 28.08/18.35 inference(modus_ponens,[status(thm)],[333, 9116])).
% 28.08/18.35 tff(9118,plain,
% 28.08/18.35 (f1(f7(c2), c2) = f7(c2)),
% 28.08/18.35 inference(transitivity,[status(thm)],[9112, 1095, 125])).
% 28.08/18.35 tff(9119,plain,
% 28.08/18.35 ((f1(f7(c2), c2) = c2) <=> (f7(c2) = c2)),
% 28.08/18.35 inference(monotonicity,[status(thm)],[9118])).
% 28.08/18.35 tff(9120,plain,
% 28.08/18.35 ((f7(c2) = c2) <=> (f1(f7(c2), c2) = c2)),
% 28.08/18.35 inference(symmetry,[status(thm)],[9119])).
% 28.08/18.35 tff(9121,plain,
% 28.08/18.35 ((~(f7(c2) = c2)) <=> (~(f1(f7(c2), c2) = c2))),
% 28.08/18.35 inference(monotonicity,[status(thm)],[9120])).
% 28.08/18.35 tff(9122,plain,
% 28.08/18.35 (~(f1(f7(c2), c2) = c2)),
% 28.08/18.35 inference(modus_ponens,[status(thm)],[17, 9121])).
% 28.08/18.35 tff(9123,assumption,(big_f(f3(c2, f7(c2)), c2)), introduced(assumption)).
% 28.08/18.35 tff(9124,assumption,(f3(c2, f7(c2)) = f7(c2)), introduced(assumption)).
% 28.08/18.35 tff(9125,plain,
% 28.08/18.35 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c4) | (f7(c2) = c3) | (~(f3(c2, f7(c2)) = f7(c2))) | (~big_f(f3(c2, f7(c2)), c2)) | big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c2 = c4) | (f7(c2) = c3) | (~(f3(c2, f7(c2)) = f7(c2))) | (~big_f(f3(c2, f7(c2)), c2)) | big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2))),
% 28.08/18.35 inference(rewrite,[status(thm)],[])).
% 28.08/18.35 tff(9126,plain,
% 28.08/18.35 (((c2 = c4) | (f7(c2) = c3) | (f1(f7(c2), c2) = c2) | big_f(f7(c2), f1(f7(c2), c2)) | (~(f3(c2, f7(c2)) = f7(c2))) | (~big_f(f3(c2, f7(c2)), c2))) <=> ((c2 = c4) | (f7(c2) = c3) | (~(f3(c2, f7(c2)) = f7(c2))) | (~big_f(f3(c2, f7(c2)), c2)) | big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2))),
% 28.08/18.35 inference(rewrite,[status(thm)],[])).
% 28.08/18.35 tff(9127,plain,
% 28.08/18.35 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c4) | (f7(c2) = c3) | (f1(f7(c2), c2) = c2) | big_f(f7(c2), f1(f7(c2), c2)) | (~(f3(c2, f7(c2)) = f7(c2))) | (~big_f(f3(c2, f7(c2)), c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c4) | (f7(c2) = c3) | (~(f3(c2, f7(c2)) = f7(c2))) | (~big_f(f3(c2, f7(c2)), c2)) | big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2)))),
% 28.08/18.35 inference(monotonicity,[status(thm)],[9126])).
% 28.08/18.35 tff(9128,plain,
% 28.08/18.35 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c4) | (f7(c2) = c3) | (f1(f7(c2), c2) = c2) | big_f(f7(c2), f1(f7(c2), c2)) | (~(f3(c2, f7(c2)) = f7(c2))) | (~big_f(f3(c2, f7(c2)), c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c2 = c4) | (f7(c2) = c3) | (~(f3(c2, f7(c2)) = f7(c2))) | (~big_f(f3(c2, f7(c2)), c2)) | big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2))),
% 28.08/18.35 inference(transitivity,[status(thm)],[9127, 9125])).
% 28.08/18.35 tff(9129,plain,
% 28.08/18.35 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c4) | (f7(c2) = c3) | (f1(f7(c2), c2) = c2) | big_f(f7(c2), f1(f7(c2), c2)) | (~(f3(c2, f7(c2)) = f7(c2))) | (~big_f(f3(c2, f7(c2)), c2)))),
% 28.08/18.35 inference(quant_inst,[status(thm)],[])).
% 28.08/18.35 tff(9130,plain,
% 28.08/18.35 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c2 = c4) | (f7(c2) = c3) | (~(f3(c2, f7(c2)) = f7(c2))) | (~big_f(f3(c2, f7(c2)), c2)) | big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2)),
% 28.08/18.35 inference(modus_ponens,[status(thm)],[9129, 9128])).
% 28.08/18.35 tff(9131,plain,
% 28.08/18.35 (big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2)),
% 28.08/18.35 inference(unit_resolution,[status(thm)],[9130, 969, 873, 9092, 9124, 9123])).
% 28.08/18.35 tff(9132,plain,
% 28.08/18.35 ($false),
% 28.08/18.35 inference(unit_resolution,[status(thm)],[9131, 9122, 9117])).
% 28.08/18.35 tff(9133,plain,((~(f1(c1, c2) = c1)) | (c2 = c4) | (f7(c2) = c3) | (~(f3(c2, f7(c2)) = f7(c2))) | (~big_f(f3(c2, f7(c2)), c2)) | (f7(c2) = c2) | big_f(f7(c2), c1)), inference(lemma,lemma(discharge,[]))).
% 28.08/18.35 tff(9134,plain,
% 28.08/18.35 (~(f1(c1, c2) = c1)),
% 28.08/18.35 inference(unit_resolution,[status(thm)],[9133, 9111, 9092, 873, 9107, 17, 333])).
% 28.08/18.35 tff(9135,plain,
% 28.08/18.35 (f1(c1, c2) = c2),
% 28.08/18.35 inference(unit_resolution,[status(thm)],[841, 9134])).
% 28.08/18.35 tff(9136,plain,
% 28.08/18.35 (f1(f7(c2), c2) = c2),
% 28.08/18.35 inference(transitivity,[status(thm)],[9112, 9135])).
% 28.08/18.35 tff(9137,plain,
% 28.08/18.35 (big_f(f7(c2), f1(f7(c2), c2)) <=> big_f(f7(c2), c2)),
% 28.08/18.35 inference(monotonicity,[status(thm)],[9136])).
% 28.08/18.35 tff(9138,plain,
% 28.08/18.35 (big_f(f7(c2), c2) <=> big_f(f7(c2), f1(f7(c2), c2))),
% 28.08/18.35 inference(symmetry,[status(thm)],[9137])).
% 28.08/18.35 tff(9139,plain,
% 28.08/18.35 (big_f(f7(c2), f1(f7(c2), c2))),
% 28.08/18.35 inference(modus_ponens,[status(thm)],[1180, 9138])).
% 28.08/18.35 tff(9140,plain,
% 28.08/18.35 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (f7(c2) = c3) | (~(f3(c2, f7(c2)) = f7(c2))) | (~big_f(f3(c2, f7(c2)), c2)) | (~big_f(f7(c2), f1(f7(c2), c2))) | (~(f1(f7(c2), c2) = c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c4) | (f7(c2) = c3) | (~(f3(c2, f7(c2)) = f7(c2))) | (~big_f(f3(c2, f7(c2)), c2)) | (~big_f(f7(c2), f1(f7(c2), c2))) | (~(f1(f7(c2), c2) = c2)))),
% 28.08/18.35 inference(rewrite,[status(thm)],[])).
% 28.08/18.35 tff(9141,plain,
% 28.08/18.35 (((c2 = c4) | (f7(c2) = c3) | (~(f3(c2, f7(c2)) = f7(c2))) | (~big_f(f3(c2, f7(c2)), c2)) | (~(f1(f7(c2), c2) = c2)) | (~big_f(f7(c2), f1(f7(c2), c2)))) <=> ((c2 = c4) | (f7(c2) = c3) | (~(f3(c2, f7(c2)) = f7(c2))) | (~big_f(f3(c2, f7(c2)), c2)) | (~big_f(f7(c2), f1(f7(c2), c2))) | (~(f1(f7(c2), c2) = c2)))),
% 28.08/18.35 inference(rewrite,[status(thm)],[])).
% 28.08/18.35 tff(9142,plain,
% 28.08/18.35 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (f7(c2) = c3) | (~(f3(c2, f7(c2)) = f7(c2))) | (~big_f(f3(c2, f7(c2)), c2)) | (~(f1(f7(c2), c2) = c2)) | (~big_f(f7(c2), f1(f7(c2), c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (f7(c2) = c3) | (~(f3(c2, f7(c2)) = f7(c2))) | (~big_f(f3(c2, f7(c2)), c2)) | (~big_f(f7(c2), f1(f7(c2), c2))) | (~(f1(f7(c2), c2) = c2))))),
% 28.08/18.35 inference(monotonicity,[status(thm)],[9141])).
% 28.08/18.35 tff(9143,plain,
% 28.08/18.35 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (f7(c2) = c3) | (~(f3(c2, f7(c2)) = f7(c2))) | (~big_f(f3(c2, f7(c2)), c2)) | (~(f1(f7(c2), c2) = c2)) | (~big_f(f7(c2), f1(f7(c2), c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c4) | (f7(c2) = c3) | (~(f3(c2, f7(c2)) = f7(c2))) | (~big_f(f3(c2, f7(c2)), c2)) | (~big_f(f7(c2), f1(f7(c2), c2))) | (~(f1(f7(c2), c2) = c2)))),
% 28.08/18.35 inference(transitivity,[status(thm)],[9142, 9140])).
% 28.08/18.35 tff(9144,plain,
% 28.08/18.35 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (f7(c2) = c3) | (~(f3(c2, f7(c2)) = f7(c2))) | (~big_f(f3(c2, f7(c2)), c2)) | (~(f1(f7(c2), c2) = c2)) | (~big_f(f7(c2), f1(f7(c2), c2))))),
% 28.08/18.35 inference(quant_inst,[status(thm)],[])).
% 28.08/18.35 tff(9145,plain,
% 28.08/18.35 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c4) | (f7(c2) = c3) | (~(f3(c2, f7(c2)) = f7(c2))) | (~big_f(f3(c2, f7(c2)), c2)) | (~big_f(f7(c2), f1(f7(c2), c2))) | (~(f1(f7(c2), c2) = c2))),
% 28.08/18.35 inference(modus_ponens,[status(thm)],[9144, 9143])).
% 28.08/18.35 tff(9146,plain,
% 28.08/18.35 ((~big_f(f7(c2), f1(f7(c2), c2))) | (~(f1(f7(c2), c2) = c2))),
% 28.08/18.35 inference(unit_resolution,[status(thm)],[9145, 933, 873, 9092, 9111, 9107])).
% 28.08/18.35 tff(9147,plain,
% 28.08/18.35 ($false),
% 28.08/18.35 inference(unit_resolution,[status(thm)],[9146, 9139, 9136])).
% 28.08/18.35 tff(9148,plain,((~(f3(f7(c1), c1) = c1)) | (c2 = c4) | (f7(c2) = c3) | (~big_f(f7(c2), c2)) | (f7(c2) = c2) | big_f(f7(c2), c1) | (~(f7(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.08/18.35 tff(9149,plain,
% 28.08/18.35 (~(f3(f7(c1), c1) = c1)),
% 28.08/18.35 inference(unit_resolution,[status(thm)],[9148, 873, 9092, 1180, 17, 333, 347])).
% 28.08/18.35 tff(9150,plain,
% 28.08/18.35 (~(f3(f7(c1), c1) = c4)),
% 28.08/18.35 inference(modus_ponens,[status(thm)],[9149, 9100])).
% 28.08/18.35 tff(9151,plain,
% 28.08/18.35 (f3(f7(c1), c1) = c2),
% 28.08/18.35 inference(unit_resolution,[status(thm)],[918, 9149])).
% 28.08/18.35 tff(9152,plain,
% 28.08/18.35 (f3(f3(f7(c1), c1), c1) = f3(c2, c1)),
% 28.08/18.35 inference(monotonicity,[status(thm)],[9151])).
% 28.08/18.35 tff(9153,plain,
% 28.08/18.35 (f3(f3(f7(c1), c1), c1) = c2),
% 28.08/18.35 inference(transitivity,[status(thm)],[9152, 3125, 9151])).
% 28.08/18.35 tff(9154,plain,
% 28.08/18.35 ((f3(f3(f7(c1), c1), c1) = c1) <=> (c2 = f7(c2))),
% 28.08/18.35 inference(monotonicity,[status(thm)],[9153, 125])).
% 28.08/18.35 tff(9155,plain,
% 28.08/18.35 ((f3(f3(f7(c1), c1), c1) = c1) <=> (f7(c2) = c2)),
% 28.08/18.35 inference(transitivity,[status(thm)],[9154, 8409])).
% 28.08/18.35 tff(9156,plain,
% 28.08/18.35 ((f7(c2) = c2) <=> (f3(f3(f7(c1), c1), c1) = c1)),
% 28.08/18.35 inference(symmetry,[status(thm)],[9155])).
% 28.08/18.35 tff(9157,plain,
% 28.08/18.35 ((~(f7(c2) = c2)) <=> (~(f3(f3(f7(c1), c1), c1) = c1))),
% 28.08/18.35 inference(monotonicity,[status(thm)],[9156])).
% 28.08/18.35 tff(9158,plain,
% 28.08/18.35 (~(f3(f3(f7(c1), c1), c1) = c1)),
% 28.08/18.35 inference(modus_ponens,[status(thm)],[17, 9157])).
% 28.08/18.35 tff(9159,plain,
% 28.08/18.35 (big_f(f3(f3(f7(c1), c1), c1), f3(f7(c1), c1)) <=> big_f(c2, c2)),
% 28.08/18.35 inference(monotonicity,[status(thm)],[9153, 9151])).
% 28.08/18.35 tff(9160,plain,
% 28.08/18.35 (big_f(c2, c2) <=> big_f(f3(f3(f7(c1), c1), c1), f3(f7(c1), c1))),
% 28.08/18.35 inference(symmetry,[status(thm)],[9159])).
% 28.08/18.35 tff(9161,plain,
% 28.08/18.35 ((~big_f(c2, c2)) <=> (~big_f(f3(f3(f7(c1), c1), c1), f3(f7(c1), c1)))),
% 28.08/18.35 inference(monotonicity,[status(thm)],[9160])).
% 28.08/18.35 tff(9162,plain,
% 28.08/18.35 (~big_f(f3(f3(f7(c1), c1), c1), f3(f7(c1), c1))),
% 28.08/18.35 inference(modus_ponens,[status(thm)],[121, 9161])).
% 28.08/18.35 tff(9163,plain,
% 28.08/18.35 (big_f(f7(c2), f1(c1, c2)) <=> big_f(f7(c2), c1)),
% 28.08/18.35 inference(monotonicity,[status(thm)],[1053])).
% 28.08/18.35 tff(9164,plain,
% 28.08/18.35 (big_f(f7(c2), c1) <=> big_f(f7(c2), f1(c1, c2))),
% 28.08/18.35 inference(symmetry,[status(thm)],[9163])).
% 28.08/18.35 tff(9165,plain,
% 28.08/18.35 ((~big_f(f7(c2), c1)) <=> (~big_f(f7(c2), f1(c1, c2)))),
% 28.08/18.35 inference(monotonicity,[status(thm)],[9164])).
% 28.08/18.35 tff(9166,plain,
% 28.08/18.35 (~big_f(f7(c2), f1(c1, c2))),
% 28.08/18.36 inference(modus_ponens,[status(thm)],[333, 9165])).
% 28.08/18.36 tff(9167,plain,
% 28.08/18.36 (big_f(c1, f1(c1, c2)) <=> big_f(f7(c2), f1(c1, c2))),
% 28.08/18.36 inference(monotonicity,[status(thm)],[342])).
% 28.08/18.36 tff(9168,assumption,(~(f3(f7(c1), c1) = c4)), introduced(assumption)).
% 28.08/18.36 tff(9169,assumption,(~(f3(f3(f7(c1), c1), c1) = c1)), introduced(assumption)).
% 28.08/18.36 tff(9170,assumption,(~big_f(f3(f3(f7(c1), c1), c1), f3(f7(c1), c1))), introduced(assumption)).
% 28.08/18.36 tff(9171,plain,
% 28.08/18.36 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f1(c1, c2) = c2) | (c1 = c3) | big_f(c1, f1(c1, c2)) | (f3(f3(f7(c1), c1), c1) = c1) | big_f(f3(f3(f7(c1), c1), c1), f3(f7(c1), c1)) | (f3(f7(c1), c1) = c4))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (f1(c1, c2) = c2) | (c1 = c3) | big_f(c1, f1(c1, c2)) | (f3(f3(f7(c1), c1), c1) = c1) | big_f(f3(f3(f7(c1), c1), c1), f3(f7(c1), c1)) | (f3(f7(c1), c1) = c4))),
% 28.08/18.36 inference(rewrite,[status(thm)],[])).
% 28.08/18.36 tff(9172,plain,
% 28.08/18.36 (((f3(f7(c1), c1) = c4) | (f3(f3(f7(c1), c1), c1) = c1) | big_f(f3(f3(f7(c1), c1), c1), f3(f7(c1), c1)) | (c1 = c3) | (f1(c1, c2) = c2) | big_f(c1, f1(c1, c2))) <=> ((f1(c1, c2) = c2) | (c1 = c3) | big_f(c1, f1(c1, c2)) | (f3(f3(f7(c1), c1), c1) = c1) | big_f(f3(f3(f7(c1), c1), c1), f3(f7(c1), c1)) | (f3(f7(c1), c1) = c4))),
% 28.08/18.36 inference(rewrite,[status(thm)],[])).
% 28.08/18.36 tff(9173,plain,
% 28.08/18.36 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f3(f7(c1), c1) = c4) | (f3(f3(f7(c1), c1), c1) = c1) | big_f(f3(f3(f7(c1), c1), c1), f3(f7(c1), c1)) | (c1 = c3) | (f1(c1, c2) = c2) | big_f(c1, f1(c1, c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f1(c1, c2) = c2) | (c1 = c3) | big_f(c1, f1(c1, c2)) | (f3(f3(f7(c1), c1), c1) = c1) | big_f(f3(f3(f7(c1), c1), c1), f3(f7(c1), c1)) | (f3(f7(c1), c1) = c4)))),
% 28.08/18.36 inference(monotonicity,[status(thm)],[9172])).
% 28.08/18.36 tff(9174,plain,
% 28.08/18.36 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f3(f7(c1), c1) = c4) | (f3(f3(f7(c1), c1), c1) = c1) | big_f(f3(f3(f7(c1), c1), c1), f3(f7(c1), c1)) | (c1 = c3) | (f1(c1, c2) = c2) | big_f(c1, f1(c1, c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (f1(c1, c2) = c2) | (c1 = c3) | big_f(c1, f1(c1, c2)) | (f3(f3(f7(c1), c1), c1) = c1) | big_f(f3(f3(f7(c1), c1), c1), f3(f7(c1), c1)) | (f3(f7(c1), c1) = c4))),
% 28.08/18.36 inference(transitivity,[status(thm)],[9173, 9171])).
% 28.08/18.36 tff(9175,plain,
% 28.08/18.36 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f3(f7(c1), c1) = c4) | (f3(f3(f7(c1), c1), c1) = c1) | big_f(f3(f3(f7(c1), c1), c1), f3(f7(c1), c1)) | (c1 = c3) | (f1(c1, c2) = c2) | big_f(c1, f1(c1, c2)))),
% 28.08/18.36 inference(quant_inst,[status(thm)],[])).
% 28.08/18.36 tff(9176,plain,
% 28.08/18.36 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (f1(c1, c2) = c2) | (c1 = c3) | big_f(c1, f1(c1, c2)) | (f3(f3(f7(c1), c1), c1) = c1) | big_f(f3(f3(f7(c1), c1), c1), f3(f7(c1), c1)) | (f3(f7(c1), c1) = c4)),
% 28.08/18.36 inference(modus_ponens,[status(thm)],[9175, 9174])).
% 28.08/18.36 tff(9177,plain,
% 28.08/18.36 ((f1(c1, c2) = c2) | (c1 = c3) | big_f(c1, f1(c1, c2)) | (f3(f3(f7(c1), c1), c1) = c1) | big_f(f3(f3(f7(c1), c1), c1), f3(f7(c1), c1)) | (f3(f7(c1), c1) = c4)),
% 28.08/18.36 inference(unit_resolution,[status(thm)],[9176, 1014])).
% 28.08/18.36 tff(9178,plain,
% 28.08/18.36 (big_f(c1, f1(c1, c2))),
% 28.08/18.36 inference(unit_resolution,[status(thm)],[9177, 1052, 168, 9170, 9169, 9168])).
% 28.17/18.36 tff(9179,plain,
% 28.17/18.36 (big_f(f7(c2), f1(c1, c2))),
% 28.17/18.36 inference(modus_ponens,[status(thm)],[9178, 9167])).
% 28.17/18.36 tff(9180,plain,
% 28.17/18.36 ($false),
% 28.17/18.36 inference(unit_resolution,[status(thm)],[9179, 9166])).
% 28.17/18.36 tff(9181,plain,((f1(c1, c2) = c2) | big_f(f7(c2), c1) | (~(f7(c2) = c1)) | (c1 = c3) | big_f(f3(f3(f7(c1), c1), c1), f3(f7(c1), c1)) | (f3(f3(f7(c1), c1), c1) = c1) | (f3(f7(c1), c1) = c4)), inference(lemma,lemma(discharge,[]))).
% 28.17/18.36 tff(9182,plain,
% 28.17/18.36 (f1(c1, c2) = c2),
% 28.17/18.36 inference(unit_resolution,[status(thm)],[9181, 9162, 22, 168, 333, 9158, 9150])).
% 28.17/18.36 tff(9183,plain,
% 28.17/18.36 (f1(f7(c2), c2) = c2),
% 28.17/18.36 inference(transitivity,[status(thm)],[9112, 9182])).
% 28.17/18.36 tff(9184,plain,
% 28.17/18.36 (big_f(f7(c2), f1(f7(c2), c2)) <=> big_f(f7(c2), c2)),
% 28.17/18.36 inference(monotonicity,[status(thm)],[9183])).
% 28.17/18.36 tff(9185,plain,
% 28.17/18.36 (big_f(f7(c2), c2) <=> big_f(f7(c2), f1(f7(c2), c2))),
% 28.17/18.36 inference(symmetry,[status(thm)],[9184])).
% 28.17/18.36 tff(9186,plain,
% 28.17/18.36 (big_f(f7(c2), f1(f7(c2), c2))),
% 28.17/18.36 inference(modus_ponens,[status(thm)],[1180, 9185])).
% 28.17/18.36 tff(9187,plain,
% 28.17/18.36 (f3(c2, c1) = c2),
% 28.17/18.36 inference(transitivity,[status(thm)],[3125, 9151])).
% 28.17/18.36 tff(9188,plain,
% 28.17/18.36 (big_f(f3(c2, c1), c2) <=> big_f(c2, c2)),
% 28.17/18.36 inference(monotonicity,[status(thm)],[9187])).
% 28.17/18.36 tff(9189,plain,
% 28.17/18.36 (big_f(c2, c2) <=> big_f(f3(c2, c1), c2)),
% 28.17/18.36 inference(symmetry,[status(thm)],[9188])).
% 28.17/18.36 tff(9190,plain,
% 28.17/18.36 (big_f(c2, c2) <=> big_f(f3(c2, f7(c2)), c2)),
% 28.17/18.36 inference(transitivity,[status(thm)],[9189, 9102])).
% 28.17/18.36 tff(9191,plain,
% 28.17/18.36 ((~big_f(c2, c2)) <=> (~big_f(f3(c2, f7(c2)), c2))),
% 28.17/18.36 inference(monotonicity,[status(thm)],[9190])).
% 28.17/18.36 tff(9192,plain,
% 28.17/18.36 (~big_f(f3(c2, f7(c2)), c2)),
% 28.17/18.36 inference(modus_ponens,[status(thm)],[121, 9191])).
% 28.17/18.36 tff(9193,plain,
% 28.17/18.36 ((~(f3(f7(c1), c1) = c1)) <=> (~(f3(c2, f7(c2)) = f7(c2)))),
% 28.17/18.36 inference(monotonicity,[status(thm)],[9110])).
% 28.17/18.36 tff(9194,plain,
% 28.17/18.36 (~(f3(c2, f7(c2)) = f7(c2))),
% 28.17/18.36 inference(modus_ponens,[status(thm)],[9149, 9193])).
% 28.17/18.36 tff(9195,plain,
% 28.17/18.36 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (f7(c2) = c3) | (f3(c2, f7(c2)) = f7(c2)) | big_f(f3(c2, f7(c2)), c2) | (~big_f(f7(c2), f1(f7(c2), c2))) | (~(f1(f7(c2), c2) = c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c4) | (f7(c2) = c3) | (f3(c2, f7(c2)) = f7(c2)) | big_f(f3(c2, f7(c2)), c2) | (~big_f(f7(c2), f1(f7(c2), c2))) | (~(f1(f7(c2), c2) = c2)))),
% 28.17/18.36 inference(rewrite,[status(thm)],[])).
% 28.17/18.36 tff(9196,plain,
% 28.17/18.36 (((c2 = c4) | (f3(c2, f7(c2)) = f7(c2)) | big_f(f3(c2, f7(c2)), c2) | (f7(c2) = c3) | (~(f1(f7(c2), c2) = c2)) | (~big_f(f7(c2), f1(f7(c2), c2)))) <=> ((c2 = c4) | (f7(c2) = c3) | (f3(c2, f7(c2)) = f7(c2)) | big_f(f3(c2, f7(c2)), c2) | (~big_f(f7(c2), f1(f7(c2), c2))) | (~(f1(f7(c2), c2) = c2)))),
% 28.17/18.36 inference(rewrite,[status(thm)],[])).
% 28.17/18.36 tff(9197,plain,
% 28.17/18.36 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (f3(c2, f7(c2)) = f7(c2)) | big_f(f3(c2, f7(c2)), c2) | (f7(c2) = c3) | (~(f1(f7(c2), c2) = c2)) | (~big_f(f7(c2), f1(f7(c2), c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (f7(c2) = c3) | (f3(c2, f7(c2)) = f7(c2)) | big_f(f3(c2, f7(c2)), c2) | (~big_f(f7(c2), f1(f7(c2), c2))) | (~(f1(f7(c2), c2) = c2))))),
% 28.17/18.36 inference(monotonicity,[status(thm)],[9196])).
% 28.17/18.36 tff(9198,plain,
% 28.17/18.36 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (f3(c2, f7(c2)) = f7(c2)) | big_f(f3(c2, f7(c2)), c2) | (f7(c2) = c3) | (~(f1(f7(c2), c2) = c2)) | (~big_f(f7(c2), f1(f7(c2), c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c4) | (f7(c2) = c3) | (f3(c2, f7(c2)) = f7(c2)) | big_f(f3(c2, f7(c2)), c2) | (~big_f(f7(c2), f1(f7(c2), c2))) | (~(f1(f7(c2), c2) = c2)))),
% 28.17/18.36 inference(transitivity,[status(thm)],[9197, 9195])).
% 28.17/18.36 tff(9199,plain,
% 28.17/18.36 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (f3(c2, f7(c2)) = f7(c2)) | big_f(f3(c2, f7(c2)), c2) | (f7(c2) = c3) | (~(f1(f7(c2), c2) = c2)) | (~big_f(f7(c2), f1(f7(c2), c2))))),
% 28.17/18.36 inference(quant_inst,[status(thm)],[])).
% 28.17/18.36 tff(9200,plain,
% 28.17/18.36 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c4) | (f7(c2) = c3) | (f3(c2, f7(c2)) = f7(c2)) | big_f(f3(c2, f7(c2)), c2) | (~big_f(f7(c2), f1(f7(c2), c2))) | (~(f1(f7(c2), c2) = c2))),
% 28.17/18.36 inference(modus_ponens,[status(thm)],[9199, 9198])).
% 28.17/18.36 tff(9201,plain,
% 28.17/18.36 ((~big_f(f7(c2), f1(f7(c2), c2))) | (~(f1(f7(c2), c2) = c2))),
% 28.17/18.36 inference(unit_resolution,[status(thm)],[9200, 904, 873, 9092, 9194, 9192])).
% 28.17/18.36 tff(9202,plain,
% 28.17/18.36 ($false),
% 28.17/18.36 inference(unit_resolution,[status(thm)],[9201, 9186, 9183])).
% 28.17/18.36 tff(9203,plain,((c2 = c4) | (f7(c2) = c3) | (~big_f(f7(c2), c2)) | (c1 = c3) | big_f(f7(c2), c1) | big_f(c2, c2) | (~(f7(c1) = c2)) | (f7(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 28.17/18.36 tff(9204,plain,
% 28.17/18.36 (c2 = c4),
% 28.17/18.36 inference(unit_resolution,[status(thm)],[9203, 333, 1180, 168, 9092, 121, 347, 17])).
% 28.17/18.36 tff(9205,plain,
% 28.17/18.36 (c4 = c2),
% 28.17/18.36 inference(symmetry,[status(thm)],[9204])).
% 28.17/18.36 tff(9206,plain,
% 28.17/18.36 (big_f(c2, c4) <=> big_f(c2, c2)),
% 28.17/18.36 inference(monotonicity,[status(thm)],[9205])).
% 28.17/18.36 tff(9207,plain,
% 28.17/18.36 (big_f(c2, c2) <=> big_f(c2, c4)),
% 28.17/18.36 inference(symmetry,[status(thm)],[9206])).
% 28.17/18.36 tff(9208,plain,
% 28.17/18.36 (big_f(c2, c2) <=> big_f(f4(c4), c4)),
% 28.17/18.36 inference(transitivity,[status(thm)],[9207, 376])).
% 28.17/18.36 tff(9209,plain,
% 28.17/18.36 ((~big_f(c2, c2)) <=> (~big_f(f4(c4), c4))),
% 28.17/18.36 inference(monotonicity,[status(thm)],[9208])).
% 28.17/18.36 tff(9210,plain,
% 28.17/18.36 (~big_f(f4(c4), c4)),
% 28.17/18.36 inference(modus_ponens,[status(thm)],[121, 9209])).
% 28.17/18.36 tff(9211,plain,
% 28.17/18.36 (f4(c2) = f4(c4)),
% 28.17/18.36 inference(monotonicity,[status(thm)],[9204])).
% 28.17/18.36 tff(9212,plain,
% 28.17/18.36 (f4(c4) = f4(c2)),
% 28.17/18.36 inference(symmetry,[status(thm)],[9211])).
% 28.17/18.36 tff(9213,plain,
% 28.17/18.36 (c2 = f4(c2)),
% 28.17/18.36 inference(transitivity,[status(thm)],[436, 9212])).
% 28.17/18.36 tff(9214,plain,
% 28.17/18.36 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (f7(c2) = c3) | big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (f7(c2) = c3) | big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2))),
% 28.17/18.36 inference(rewrite,[status(thm)],[])).
% 28.17/18.36 tff(9215,plain,
% 28.17/18.36 (((f7(c2) = c3) | (f1(f7(c2), c2) = c2) | big_f(f7(c2), f1(f7(c2), c2)) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2)))) <=> ((~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (f7(c2) = c3) | big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2))),
% 28.17/18.36 inference(rewrite,[status(thm)],[])).
% 28.17/18.36 tff(9216,plain,
% 28.17/18.36 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f7(c2) = c3) | (f1(f7(c2), c2) = c2) | big_f(f7(c2), f1(f7(c2), c2)) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (f7(c2) = c3) | big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2)))),
% 28.17/18.36 inference(monotonicity,[status(thm)],[9215])).
% 28.17/18.36 tff(9217,plain,
% 28.17/18.36 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f7(c2) = c3) | (f1(f7(c2), c2) = c2) | big_f(f7(c2), f1(f7(c2), c2)) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (f7(c2) = c3) | big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2))),
% 28.17/18.36 inference(transitivity,[status(thm)],[9216, 9214])).
% 28.17/18.36 tff(9218,plain,
% 28.17/18.36 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f7(c2) = c3) | (f1(f7(c2), c2) = c2) | big_f(f7(c2), f1(f7(c2), c2)) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))))),
% 28.17/18.36 inference(quant_inst,[status(thm)],[])).
% 28.17/18.36 tff(9219,plain,
% 28.17/18.36 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (f7(c2) = c3) | big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2)),
% 28.17/18.36 inference(modus_ponens,[status(thm)],[9218, 9217])).
% 28.17/18.36 tff(9220,plain,
% 28.17/18.36 (big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2)),
% 28.17/18.36 inference(unit_resolution,[status(thm)],[9219, 402, 631, 630, 121, 9092])).
% 28.17/18.36 tff(9221,plain,
% 28.17/18.36 ($false),
% 28.17/18.36 inference(unit_resolution,[status(thm)],[9220, 9122, 9117])).
% 28.17/18.36 tff(9222,plain,((~(f1(c1, c2) = c1)) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (f7(c2) = c3) | (f7(c2) = c2) | big_f(f7(c2), c1)), inference(lemma,lemma(discharge,[]))).
% 28.17/18.36 tff(9223,plain,
% 28.17/18.36 (~(f1(c1, c2) = c1)),
% 28.17/18.36 inference(unit_resolution,[status(thm)],[9222, 9204, 9213, 121, 9092, 17, 333])).
% 28.17/18.36 tff(9224,plain,
% 28.17/18.36 (f1(c1, c2) = c2),
% 28.17/18.36 inference(unit_resolution,[status(thm)],[841, 9223])).
% 28.17/18.36 tff(9225,plain,
% 28.17/18.36 (f1(c1, f1(c1, c2)) = f1(c1, c2)),
% 28.17/18.36 inference(monotonicity,[status(thm)],[9224])).
% 28.17/18.36 tff(9226,plain,
% 28.17/18.36 (f1(c1, f1(c1, c2)) = c2),
% 28.17/18.36 inference(transitivity,[status(thm)],[9225, 9224])).
% 28.17/18.36 tff(9227,plain,
% 28.17/18.36 (big_f(c1, f1(c1, f1(c1, c2))) <=> big_f(f7(c2), c2)),
% 28.17/18.36 inference(monotonicity,[status(thm)],[125, 9226])).
% 28.17/18.36 tff(9228,plain,
% 28.17/18.36 (big_f(f7(c2), c2) <=> big_f(c1, f1(c1, f1(c1, c2)))),
% 28.17/18.36 inference(symmetry,[status(thm)],[9227])).
% 28.17/18.36 tff(9229,plain,
% 28.17/18.36 (big_f(c1, f1(c1, f1(c1, c2)))),
% 28.17/18.36 inference(modus_ponens,[status(thm)],[1180, 9228])).
% 28.17/18.36 tff(9230,plain,
% 28.17/18.36 ($false),
% 28.17/18.36 inference(unit_resolution,[status(thm)],[2254, 9229, 9225, 9210, 168])).
% 28.17/18.36 tff(9231,plain,(big_f(f7(c2), c1) | (c1 = c3) | (~big_f(f7(c2), c2)) | big_f(c2, c2) | (f7(c2) = c3) | (f7(c2) = c2) | (~(f4(c4) = c2)) | (~(f7(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.17/18.36 tff(9232,plain,
% 28.17/18.36 ($false),
% 28.17/18.36 inference(unit_resolution,[status(thm)],[9231, 9091, 9086, 333, 121, 8402, 17, 79, 8367])).
% 28.17/18.36 tff(9233,plain,(big_f(c2, c2) | big_f(f7(c2), c1) | (f7(c2) = c2) | (~(f4(c4) = c2)) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.17/18.36 tff(9234,plain,
% 28.17/18.36 (big_f(c2, c2)),
% 28.17/18.36 inference(unit_resolution,[status(thm)],[9233, 333, 17, 79, 122])).
% 28.17/18.36 tff(9235,plain,
% 28.17/18.36 (big_f(f9(c2, c2), f10(c2))),
% 28.17/18.36 inference(modus_ponens,[status(thm)],[9234, 8070])).
% 28.17/18.36 tff(9236,plain,
% 28.17/18.36 (~(f7(c2) = f5(c2))),
% 28.17/18.36 inference(unit_resolution,[status(thm)],[8386, 8375, 17, 1572, 690, 122])).
% 28.17/18.36 tff(9237,plain,
% 28.17/18.36 (~(f5(c2) = c1)),
% 28.17/18.36 inference(unit_resolution,[status(thm)],[8394, 9236, 22])).
% 28.17/18.36 tff(9238,plain,
% 28.17/18.36 (f5(c2) = c2),
% 28.17/18.36 inference(unit_resolution,[status(thm)],[1547, 9237])).
% 28.17/18.36 tff(9239,plain,
% 28.17/18.36 (c2 = f5(c2)),
% 28.17/18.36 inference(unit_resolution,[status(thm)],[8113, 9238])).
% 28.17/18.36 tff(9240,plain,
% 28.17/18.36 (big_f(f7(c2), c2)),
% 28.17/18.36 inference(unit_resolution,[status(thm)],[8397, 9239, 17, 122, 1572, 690])).
% 28.17/18.36 tff(9241,plain,
% 28.17/18.36 (f6(f7(c2), c2) = f6(c1, c2)),
% 28.17/18.36 inference(monotonicity,[status(thm)],[292])).
% 28.17/18.36 tff(9242,plain,
% 28.17/18.36 (f6(f7(c2), c2) = c2),
% 28.17/18.36 inference(transitivity,[status(thm)],[9241, 36])).
% 28.17/18.36 tff(9243,plain,
% 28.17/18.36 (f7(f7(c2)) = f7(c2)),
% 28.17/18.36 inference(transitivity,[status(thm)],[352, 4234, 342])).
% 28.17/18.36 tff(9244,plain,
% 28.17/18.36 (big_f(f7(f7(c2)), f6(f7(c2), c2)) <=> big_f(f7(c2), c2)),
% 28.17/18.36 inference(monotonicity,[status(thm)],[9243, 9242])).
% 28.17/18.36 tff(9245,plain,
% 28.17/18.36 (big_f(f7(c2), c2) <=> big_f(f7(f7(c2)), f6(f7(c2), c2))),
% 28.17/18.36 inference(symmetry,[status(thm)],[9244])).
% 28.17/18.36 tff(9246,plain,
% 28.17/18.36 (big_f(f7(f7(c2)), f6(f7(c2), c2))),
% 28.17/18.36 inference(modus_ponens,[status(thm)],[1180, 9245])).
% 28.17/18.36 tff(9247,plain,
% 28.17/18.36 (f7(f7(c2)) = f7(c2)),
% 28.17/18.36 inference(modus_ponens,[status(thm)],[4234, 8461])).
% 28.17/18.36 tff(9248,plain,
% 28.17/18.36 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), c2))) | (~(f6(f7(c2), c2) = c2)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), c2))) | (~(f6(f7(c2), c2) = c2)))),
% 28.17/18.36 inference(rewrite,[status(thm)],[])).
% 28.17/18.36 tff(9249,plain,
% 28.17/18.36 (((~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f6(f7(c2), c2) = c2)) | (~big_f(f7(f7(c2)), f6(f7(c2), c2)))) <=> ((~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), c2))) | (~(f6(f7(c2), c2) = c2)))),
% 28.17/18.36 inference(rewrite,[status(thm)],[])).
% 28.17/18.36 tff(9250,plain,
% 28.17/18.36 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f6(f7(c2), c2) = c2)) | (~big_f(f7(f7(c2)), f6(f7(c2), c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), c2))) | (~(f6(f7(c2), c2) = c2))))),
% 28.17/18.36 inference(monotonicity,[status(thm)],[9249])).
% 28.17/18.36 tff(9251,plain,
% 28.17/18.36 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f6(f7(c2), c2) = c2)) | (~big_f(f7(f7(c2)), f6(f7(c2), c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), c2))) | (~(f6(f7(c2), c2) = c2)))),
% 28.17/18.36 inference(transitivity,[status(thm)],[9250, 9248])).
% 28.17/18.36 tff(9252,plain,
% 28.17/18.36 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f6(f7(c2), c2) = c2)) | (~big_f(f7(f7(c2)), f6(f7(c2), c2))))),
% 28.17/18.36 inference(quant_inst,[status(thm)],[])).
% 28.17/18.36 tff(9253,plain,
% 28.17/18.36 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), c2))) | (~(f6(f7(c2), c2) = c2))),
% 28.17/18.37 inference(modus_ponens,[status(thm)],[9252, 9251])).
% 28.17/18.37 tff(9254,plain,
% 28.17/18.37 ((~big_f(f7(f7(c2)), f6(f7(c2), c2))) | (~(f6(f7(c2), c2) = c2))),
% 28.17/18.37 inference(unit_resolution,[status(thm)],[9253, 2378, 122, 9247, 1572, 690])).
% 28.17/18.37 tff(9255,plain,
% 28.17/18.37 ($false),
% 28.17/18.37 inference(unit_resolution,[status(thm)],[9254, 9246, 9242])).
% 28.17/18.37 tff(9256,plain,((~(f6(c1, c2) = c2)) | (~(f10(c2) = c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~big_f(f7(c2), c2)) | (~(f7(c2) = c1)) | (~(f7(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.17/18.37 tff(9257,plain,
% 28.17/18.37 (~(f6(c1, c2) = c2)),
% 28.17/18.37 inference(unit_resolution,[status(thm)],[9256, 9240, 1572, 690, 122, 22, 4234])).
% 28.17/18.37 tff(9258,plain,
% 28.17/18.37 (f6(c1, c2) = c1),
% 28.17/18.37 inference(unit_resolution,[status(thm)],[48, 9257])).
% 28.17/18.37 tff(9259,plain,
% 28.17/18.37 (f6(f7(c2), c2) = c1),
% 28.17/18.37 inference(transitivity,[status(thm)],[8295, 9258])).
% 28.17/18.37 tff(9260,plain,
% 28.17/18.37 (big_f(f7(f7(c2)), f6(f7(c2), c2)) <=> big_f(f7(c2), c1)),
% 28.17/18.37 inference(monotonicity,[status(thm)],[8297, 9259])).
% 28.17/18.37 tff(9261,plain,
% 28.17/18.37 (big_f(f7(c2), c1) <=> big_f(f7(f7(c2)), f6(f7(c2), c2))),
% 28.17/18.37 inference(symmetry,[status(thm)],[9260])).
% 28.17/18.37 tff(9262,plain,
% 28.17/18.37 ((~big_f(f7(c2), c1)) <=> (~big_f(f7(f7(c2)), f6(f7(c2), c2)))),
% 28.17/18.37 inference(monotonicity,[status(thm)],[9261])).
% 28.17/18.37 tff(9263,plain,
% 28.17/18.37 (~big_f(f7(f7(c2)), f6(f7(c2), c2))),
% 28.17/18.37 inference(modus_ponens,[status(thm)],[333, 9262])).
% 28.17/18.37 tff(9264,plain,
% 28.17/18.37 (f6(f7(c2), c2) = f7(c2)),
% 28.17/18.37 inference(transitivity,[status(thm)],[8295, 9258, 125])).
% 28.17/18.37 tff(9265,plain,
% 28.17/18.37 ((f6(f7(c2), c2) = c2) <=> (f7(c2) = c2)),
% 28.17/18.37 inference(monotonicity,[status(thm)],[9264])).
% 28.17/18.37 tff(9266,plain,
% 28.17/18.37 ((f7(c2) = c2) <=> (f6(f7(c2), c2) = c2)),
% 28.17/18.37 inference(symmetry,[status(thm)],[9265])).
% 28.17/18.37 tff(9267,plain,
% 28.17/18.37 ((~(f7(c2) = c2)) <=> (~(f6(f7(c2), c2) = c2))),
% 28.17/18.37 inference(monotonicity,[status(thm)],[9266])).
% 28.17/18.37 tff(9268,plain,
% 28.17/18.37 (~(f6(f7(c2), c2) = c2)),
% 28.17/18.37 inference(modus_ponens,[status(thm)],[17, 9267])).
% 28.17/18.37 tff(9269,plain,
% 28.17/18.37 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | big_f(f7(f7(c2)), f6(f7(c2), c2)) | (f6(f7(c2), c2) = c2))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | big_f(f7(f7(c2)), f6(f7(c2), c2)) | (f6(f7(c2), c2) = c2))),
% 28.17/18.37 inference(rewrite,[status(thm)],[])).
% 28.17/18.37 tff(9270,plain,
% 28.17/18.37 (((~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (f6(f7(c2), c2) = c2) | big_f(f7(f7(c2)), f6(f7(c2), c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2)))) <=> ((~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | big_f(f7(f7(c2)), f6(f7(c2), c2)) | (f6(f7(c2), c2) = c2))),
% 28.17/18.37 inference(rewrite,[status(thm)],[])).
% 28.17/18.37 tff(9271,plain,
% 28.17/18.37 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (f6(f7(c2), c2) = c2) | big_f(f7(f7(c2)), f6(f7(c2), c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | big_f(f7(f7(c2)), f6(f7(c2), c2)) | (f6(f7(c2), c2) = c2)))),
% 28.17/18.37 inference(monotonicity,[status(thm)],[9270])).
% 28.17/18.37 tff(9272,plain,
% 28.17/18.37 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (f6(f7(c2), c2) = c2) | big_f(f7(f7(c2)), f6(f7(c2), c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | big_f(f7(f7(c2)), f6(f7(c2), c2)) | (f6(f7(c2), c2) = c2))),
% 28.17/18.37 inference(transitivity,[status(thm)],[9271, 9269])).
% 28.17/18.37 tff(9273,plain,
% 28.17/18.37 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (f6(f7(c2), c2) = c2) | big_f(f7(f7(c2)), f6(f7(c2), c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))),
% 28.17/18.37 inference(quant_inst,[status(thm)],[])).
% 28.17/18.37 tff(9274,plain,
% 28.17/18.37 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | big_f(f7(f7(c2)), f6(f7(c2), c2)) | (f6(f7(c2), c2) = c2)),
% 28.17/18.37 inference(modus_ponens,[status(thm)],[9273, 9272])).
% 28.17/18.37 tff(9275,plain,
% 28.17/18.37 (big_f(f7(f7(c2)), f6(f7(c2), c2)) | (f6(f7(c2), c2) = c2)),
% 28.17/18.37 inference(unit_resolution,[status(thm)],[9274, 2409, 122, 8315, 1572, 690])).
% 28.17/18.37 tff(9276,plain,
% 28.17/18.37 ($false),
% 28.17/18.37 inference(unit_resolution,[status(thm)],[9275, 9268, 9263])).
% 28.17/18.37 tff(9277,plain,(big_f(f7(c2), c1) | (~(f10(c2) = c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f7(c2) = c2) | (~(f7(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.17/18.37 tff(9278,plain,
% 28.17/18.37 (~(f7(c1) = c1)),
% 28.17/18.37 inference(unit_resolution,[status(thm)],[9277, 9235, 8080, 122, 17, 333])).
% 28.17/18.37 tff(9279,plain,
% 28.17/18.37 (f7(c1) = c2),
% 28.17/18.37 inference(unit_resolution,[status(thm)],[119, 9278])).
% 28.17/18.37 tff(9280,plain,
% 28.17/18.37 (big_f(f7(c1), c2) <=> big_f(c2, c2)),
% 28.17/18.37 inference(monotonicity,[status(thm)],[9279])).
% 28.17/18.37 tff(9281,plain,
% 28.17/18.37 (big_f(c2, c2) <=> big_f(f7(c1), c2)),
% 28.17/18.37 inference(symmetry,[status(thm)],[9280])).
% 28.17/18.37 tff(9282,plain,
% 28.17/18.37 (big_f(c2, c2) <=> big_f(f7(f7(c2)), c2)),
% 28.17/18.37 inference(transitivity,[status(thm)],[9281, 8079])).
% 28.17/18.37 tff(9283,plain,
% 28.17/18.37 (big_f(f7(f7(c2)), c2)),
% 28.17/18.37 inference(modus_ponens,[status(thm)],[9234, 9282])).
% 28.17/18.37 tff(9284,plain,
% 28.17/18.37 (~(f7(f7(c2)) = f7(c2))),
% 28.17/18.37 inference(modus_ponens,[status(thm)],[9278, 8614])).
% 28.17/18.37 tff(9285,plain,
% 28.17/18.37 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2)))),
% 28.17/18.37 inference(rewrite,[status(thm)],[])).
% 28.17/18.37 tff(9286,plain,
% 28.17/18.37 (((~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2)))) <=> ((~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2)))),
% 28.17/18.37 inference(rewrite,[status(thm)],[])).
% 28.17/18.37 tff(9287,plain,
% 28.17/18.37 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2))))),
% 28.17/18.37 inference(monotonicity,[status(thm)],[9286])).
% 28.17/18.37 tff(9288,plain,
% 28.17/18.37 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2)))),
% 28.17/18.37 inference(transitivity,[status(thm)],[9287, 9285])).
% 28.17/18.37 tff(9289,plain,
% 28.17/18.37 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))),
% 28.17/18.37 inference(quant_inst,[status(thm)],[])).
% 28.17/18.37 tff(9290,plain,
% 28.17/18.37 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2))),
% 28.17/18.37 inference(modus_ponens,[status(thm)],[9289, 9288])).
% 28.17/18.37 tff(9291,plain,
% 28.17/18.37 (c2 = f5(f7(c2))),
% 28.17/18.37 inference(unit_resolution,[status(thm)],[9290, 1190, 122, 9284, 8080, 9235, 9283])).
% 28.17/18.37 tff(9292,plain,
% 28.17/18.37 (f5(f7(c2)) = c2),
% 28.17/18.37 inference(symmetry,[status(thm)],[9291])).
% 28.17/18.37 tff(9293,plain,
% 28.17/18.37 (big_f(f7(f7(c2)), f7(c2)) <=> big_f(f7(c1), c1)),
% 28.17/18.37 inference(monotonicity,[status(thm)],[8077, 22])).
% 28.17/18.37 tff(9294,plain,
% 28.17/18.37 (big_f(f7(c1), c1) <=> big_f(f7(f7(c2)), f7(c2))),
% 28.17/18.37 inference(symmetry,[status(thm)],[9293])).
% 28.17/18.37 tff(9295,plain,
% 28.17/18.37 (big_f(f7(c1), c1) <=> big_f(c2, c1)),
% 28.17/18.37 inference(monotonicity,[status(thm)],[9279])).
% 28.17/18.37 tff(9296,plain,
% 28.17/18.37 (big_f(c2, c1) <=> big_f(f7(c1), c1)),
% 28.17/18.37 inference(symmetry,[status(thm)],[9295])).
% 28.17/18.37 tff(9297,plain,
% 28.17/18.37 (big_f(c2, c1) <=> big_f(f7(f7(c2)), f7(c2))),
% 28.17/18.37 inference(transitivity,[status(thm)],[9296, 9294])).
% 28.17/18.37 tff(9298,plain,
% 28.17/18.37 (big_f(f9(c2, c2), f10(c2))),
% 28.17/18.37 inference(modus_ponens,[status(thm)],[1345, 8070])).
% 28.17/18.37 tff(9299,plain,
% 28.17/18.37 (~(f7(c2) = f5(c2))),
% 28.17/18.37 inference(unit_resolution,[status(thm)],[8386, 8375, 17, 8080, 9298, 122])).
% 28.17/18.37 tff(9300,plain,
% 28.17/18.37 (c3 = c2),
% 28.17/18.37 inference(modus_ponens,[status(thm)],[1344, 127])).
% 28.17/18.37 tff(9301,plain,
% 28.17/18.37 ((f7(c2) = f4(c2)) <=> (c1 = f4(c2))),
% 28.17/18.37 inference(monotonicity,[status(thm)],[22])).
% 28.17/18.37 tff(9302,plain,
% 28.17/18.37 ((c1 = f4(c2)) <=> (f7(c2) = f4(c2))),
% 28.17/18.37 inference(symmetry,[status(thm)],[9301])).
% 28.17/18.37 tff(9303,plain,
% 28.17/18.37 ((f7(c2) = c3) <=> (f7(c2) = c2)),
% 28.17/18.37 inference(monotonicity,[status(thm)],[67])).
% 28.17/18.37 tff(9304,plain,
% 28.17/18.37 ((f7(c2) = c2) <=> (f7(c2) = c3)),
% 28.17/18.37 inference(symmetry,[status(thm)],[9303])).
% 28.17/18.37 tff(9305,plain,
% 28.17/18.37 ((~(f7(c2) = c2)) <=> (~(f7(c2) = c3))),
% 28.17/18.37 inference(monotonicity,[status(thm)],[9304])).
% 28.17/18.37 tff(9306,plain,
% 28.17/18.37 (~(f7(c2) = c3)),
% 28.17/18.37 inference(modus_ponens,[status(thm)],[17, 9305])).
% 28.17/18.37 tff(9307,plain,
% 28.17/18.37 ((f7(c2) = c2) <=> (c1 = c3)),
% 28.17/18.37 inference(transitivity,[status(thm)],[9304, 9088])).
% 28.17/18.37 tff(9308,plain,
% 28.17/18.37 ((~(f7(c2) = c2)) <=> (~(c1 = c3))),
% 28.17/18.37 inference(monotonicity,[status(thm)],[9307])).
% 28.17/18.37 tff(9309,plain,
% 28.17/18.37 (~(c1 = c3)),
% 28.17/18.37 inference(modus_ponens,[status(thm)],[17, 9308])).
% 28.17/18.37 tff(9310,plain,
% 28.17/18.37 (~big_f(f4(c4), c4)),
% 28.17/18.37 inference(unit_resolution,[status(thm)],[2221, 480, 79, 2])).
% 28.17/18.37 tff(9311,plain,
% 28.17/18.37 (big_f(c2, f7(c2)) <=> big_f(c2, c1)),
% 28.17/18.37 inference(monotonicity,[status(thm)],[22])).
% 28.17/18.37 tff(9312,plain,
% 28.17/18.37 (big_f(c2, c1) <=> big_f(c2, f7(c2))),
% 28.17/18.37 inference(symmetry,[status(thm)],[9311])).
% 28.17/18.37 tff(9313,plain,
% 28.17/18.37 ((~big_f(c2, c1)) <=> (~big_f(c2, f7(c2)))),
% 28.17/18.37 inference(monotonicity,[status(thm)],[9312])).
% 28.17/18.37 tff(9314,plain,
% 28.17/18.37 (~big_f(c2, f7(c2))),
% 28.17/18.37 inference(modus_ponens,[status(thm)],[2, 9313])).
% 28.17/18.37 tff(9315,plain,
% 28.17/18.37 (c2 = f4(c1)),
% 28.17/18.37 inference(transitivity,[status(thm)],[436, 3840])).
% 28.17/18.37 tff(9316,plain,
% 28.17/18.37 (f4(f7(c2)) = f4(c1)),
% 28.17/18.37 inference(monotonicity,[status(thm)],[292])).
% 28.17/18.37 tff(9317,plain,
% 28.17/18.37 ((c2 = f4(f7(c2))) <=> (c2 = f4(c1))),
% 28.17/18.37 inference(monotonicity,[status(thm)],[9316])).
% 28.17/18.37 tff(9318,plain,
% 28.17/18.37 ((~(c2 = f4(f7(c2)))) <=> (~(c2 = f4(c1)))),
% 28.17/18.37 inference(monotonicity,[status(thm)],[9317])).
% 28.17/18.37 tff(9319,assumption,(~(c2 = f4(f7(c2)))), introduced(assumption)).
% 28.17/18.37 tff(9320,plain,
% 28.17/18.37 (~(c2 = f4(c1))),
% 28.17/18.37 inference(modus_ponens,[status(thm)],[9319, 9318])).
% 28.17/18.37 tff(9321,assumption,(c2 = f4(c1)), introduced(assumption)).
% 28.17/18.37 tff(9322,plain,
% 28.17/18.37 ($false),
% 28.17/18.37 inference(unit_resolution,[status(thm)],[9321, 9320])).
% 28.17/18.37 tff(9323,plain,((c2 = f4(f7(c2))) | (~(c2 = f4(c1))) | (~(f7(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.17/18.37 tff(9324,plain,
% 28.17/18.37 (c2 = f4(f7(c2))),
% 28.17/18.37 inference(unit_resolution,[status(thm)],[9323, 9315, 22])).
% 28.17/18.37 tff(9325,plain,
% 28.17/18.37 ((f7(c2) = c4) <=> (f7(f4(c4)) = c4)),
% 28.17/18.37 inference(monotonicity,[status(thm)],[81])).
% 28.17/18.37 tff(9326,plain,
% 28.17/18.37 ((f7(f4(c4)) = c4) <=> (f7(c2) = c4)),
% 28.17/18.37 inference(symmetry,[status(thm)],[9325])).
% 28.17/18.37 tff(9327,plain,
% 28.17/18.37 ((f7(f4(c4)) = c4) <=> (c1 = c4)),
% 28.17/18.37 inference(monotonicity,[status(thm)],[8081])).
% 28.17/18.37 tff(9328,plain,
% 28.17/18.37 ((c1 = c4) <=> (f7(f4(c4)) = c4)),
% 28.17/18.37 inference(symmetry,[status(thm)],[9327])).
% 28.17/18.37 tff(9329,plain,
% 28.17/18.37 ((c1 = c4) <=> (f7(c2) = c4)),
% 28.17/18.37 inference(transitivity,[status(thm)],[9328, 9326])).
% 28.17/18.37 tff(9330,plain,
% 28.17/18.37 (f7(c2) = c4),
% 28.17/18.37 inference(modus_ponens,[status(thm)],[564, 9329])).
% 28.17/18.37 tff(9331,assumption,(~big_f(c2, f7(c2))), introduced(assumption)).
% 28.17/18.37 tff(9332,assumption,(c2 = f4(f7(c2))), introduced(assumption)).
% 28.17/18.37 tff(9333,plain,
% 28.17/18.37 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f7(c2) = c3) | big_f(c2, f7(c2)) | (~(c2 = f4(f7(c2)))) | (~(f7(c2) = c4)) | big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (f7(c2) = c3) | big_f(c2, f7(c2)) | (~(c2 = f4(f7(c2)))) | (~(f7(c2) = c4)) | big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2))),
% 28.17/18.37 inference(rewrite,[status(thm)],[])).
% 28.17/18.37 tff(9334,plain,
% 28.17/18.37 (((f7(c2) = c3) | (f1(f7(c2), c2) = c2) | big_f(f7(c2), f1(f7(c2), c2)) | (~(f7(c2) = c4)) | big_f(c2, f7(c2)) | (~(c2 = f4(f7(c2))))) <=> ((f7(c2) = c3) | big_f(c2, f7(c2)) | (~(c2 = f4(f7(c2)))) | (~(f7(c2) = c4)) | big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2))),
% 28.17/18.37 inference(rewrite,[status(thm)],[])).
% 28.17/18.37 tff(9335,plain,
% 28.17/18.37 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f7(c2) = c3) | (f1(f7(c2), c2) = c2) | big_f(f7(c2), f1(f7(c2), c2)) | (~(f7(c2) = c4)) | big_f(c2, f7(c2)) | (~(c2 = f4(f7(c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f7(c2) = c3) | big_f(c2, f7(c2)) | (~(c2 = f4(f7(c2)))) | (~(f7(c2) = c4)) | big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2)))),
% 28.17/18.37 inference(monotonicity,[status(thm)],[9334])).
% 28.17/18.37 tff(9336,plain,
% 28.17/18.37 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f7(c2) = c3) | (f1(f7(c2), c2) = c2) | big_f(f7(c2), f1(f7(c2), c2)) | (~(f7(c2) = c4)) | big_f(c2, f7(c2)) | (~(c2 = f4(f7(c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (f7(c2) = c3) | big_f(c2, f7(c2)) | (~(c2 = f4(f7(c2)))) | (~(f7(c2) = c4)) | big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2))),
% 28.17/18.37 inference(transitivity,[status(thm)],[9335, 9333])).
% 28.17/18.37 tff(9337,plain,
% 28.17/18.37 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f7(c2) = c3) | (f1(f7(c2), c2) = c2) | big_f(f7(c2), f1(f7(c2), c2)) | (~(f7(c2) = c4)) | big_f(c2, f7(c2)) | (~(c2 = f4(f7(c2)))))),
% 28.17/18.37 inference(quant_inst,[status(thm)],[])).
% 28.17/18.37 tff(9338,plain,
% 28.17/18.37 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (f7(c2) = c3) | big_f(c2, f7(c2)) | (~(c2 = f4(f7(c2)))) | (~(f7(c2) = c4)) | big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2)),
% 28.17/18.37 inference(modus_ponens,[status(thm)],[9337, 9336])).
% 28.17/18.37 tff(9339,plain,
% 28.17/18.37 (big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2)),
% 28.17/18.37 inference(unit_resolution,[status(thm)],[9338, 402, 9092, 8770, 9332, 9331])).
% 28.17/18.37 tff(9340,plain,
% 28.17/18.37 ($false),
% 28.17/18.37 inference(unit_resolution,[status(thm)],[9339, 9122, 9117])).
% 28.17/18.37 tff(9341,plain,((~(f1(c1, c2) = c1)) | (f7(c2) = c3) | (~(f7(c2) = c4)) | (~(c2 = f4(f7(c2)))) | big_f(c2, f7(c2)) | (f7(c2) = c2) | big_f(f7(c2), c1)), inference(lemma,lemma(discharge,[]))).
% 28.17/18.37 tff(9342,plain,
% 28.17/18.37 (~(f1(c1, c2) = c1)),
% 28.17/18.37 inference(unit_resolution,[status(thm)],[9341, 9330, 9092, 9324, 9314, 17, 333])).
% 28.17/18.37 tff(9343,plain,
% 28.17/18.37 (f1(c1, c2) = c2),
% 28.17/18.37 inference(unit_resolution,[status(thm)],[841, 9342])).
% 28.17/18.37 tff(9344,plain,
% 28.17/18.37 (f1(c1, f1(c1, c2)) = f1(c1, c2)),
% 28.17/18.37 inference(monotonicity,[status(thm)],[9343])).
% 28.17/18.37 tff(9345,plain,
% 28.17/18.37 (f1(c1, f1(c1, c2)) = c2),
% 28.17/18.37 inference(transitivity,[status(thm)],[9344, 9343])).
% 28.17/18.37 tff(9346,plain,
% 28.17/18.37 (big_f(c1, f1(c1, f1(c1, c2))) <=> big_f(f7(c2), c2)),
% 28.17/18.37 inference(monotonicity,[status(thm)],[125, 9345])).
% 28.17/18.37 tff(9347,plain,
% 28.17/18.37 (big_f(f7(c2), c2) <=> big_f(c1, f1(c1, f1(c1, c2)))),
% 28.17/18.37 inference(symmetry,[status(thm)],[9346])).
% 28.17/18.37 tff(9348,plain,
% 28.17/18.37 (big_f(c1, f1(c1, f1(c1, c2)))),
% 28.17/18.37 inference(modus_ponens,[status(thm)],[1180, 9347])).
% 28.17/18.37 tff(9349,plain,
% 28.17/18.37 ($false),
% 28.17/18.37 inference(unit_resolution,[status(thm)],[2254, 9348, 9344, 168, 9310])).
% 28.17/18.37 tff(9350,plain,((~(c4 = c1)) | (c1 = c3) | (~big_f(f7(c2), c2)) | (f7(c2) = c3) | (f7(c2) = c2) | big_f(f7(c2), c1) | (~(f4(c4) = c2)) | big_f(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 28.17/18.37 tff(9351,plain,
% 28.17/18.37 (~(c4 = c1)),
% 28.17/18.37 inference(unit_resolution,[status(thm)],[9350, 9309, 1180, 9306, 17, 333, 79, 2])).
% 28.17/18.37 tff(9352,plain,
% 28.17/18.37 (c4 = c2),
% 28.17/18.37 inference(unit_resolution,[status(thm)],[461, 9351])).
% 28.17/18.37 tff(9353,plain,
% 28.17/18.37 (c2 = c4),
% 28.17/18.37 inference(symmetry,[status(thm)],[9352])).
% 28.17/18.37 tff(9354,plain,
% 28.17/18.37 (f4(c2) = f4(c4)),
% 28.17/18.37 inference(monotonicity,[status(thm)],[9353])).
% 28.17/18.37 tff(9355,plain,
% 28.17/18.37 (f4(c2) = c2),
% 28.17/18.37 inference(transitivity,[status(thm)],[9354, 79])).
% 28.17/18.37 tff(9356,plain,
% 28.17/18.37 ((c1 = f4(c2)) <=> (f7(c2) = c2)),
% 28.17/18.37 inference(monotonicity,[status(thm)],[125, 9355])).
% 28.17/18.37 tff(9357,plain,
% 28.17/18.37 ((f7(c2) = c2) <=> (c1 = f4(c2))),
% 28.17/18.37 inference(symmetry,[status(thm)],[9356])).
% 28.17/18.37 tff(9358,plain,
% 28.17/18.37 ((f7(c2) = c2) <=> (f7(c2) = f4(c2))),
% 28.17/18.37 inference(transitivity,[status(thm)],[9357, 9302])).
% 28.17/18.37 tff(9359,plain,
% 28.17/18.37 ((~(f7(c2) = c2)) <=> (~(f7(c2) = f4(c2)))),
% 28.17/18.37 inference(monotonicity,[status(thm)],[9358])).
% 28.17/18.37 tff(9360,plain,
% 28.17/18.37 (~(f7(c2) = f4(c2))),
% 28.17/18.37 inference(modus_ponens,[status(thm)],[17, 9359])).
% 28.17/18.37 tff(9361,plain,
% 28.17/18.37 (c2 = c4),
% 28.17/18.37 inference(modus_ponens,[status(thm)],[9352, 159])).
% 28.17/18.37 tff(9362,plain,
% 28.17/18.37 (f1(f7(c2), c2) = f1(c1, c2)),
% 28.17/18.37 inference(monotonicity,[status(thm)],[292])).
% 28.17/18.37 tff(9363,plain,
% 28.17/18.37 (f1(f7(c2), c2) = c2),
% 28.17/18.37 inference(transitivity,[status(thm)],[9362, 822])).
% 28.17/18.37 tff(9364,plain,
% 28.17/18.37 (big_f(f7(c2), f1(f7(c2), c2)) <=> big_f(f7(c2), c2)),
% 28.17/18.37 inference(monotonicity,[status(thm)],[9363])).
% 28.17/18.37 tff(9365,plain,
% 28.17/18.37 (big_f(f7(c2), c2) <=> big_f(f7(c2), f1(f7(c2), c2))),
% 28.17/18.37 inference(symmetry,[status(thm)],[9364])).
% 28.17/18.37 tff(9366,plain,
% 28.17/18.37 (big_f(f7(c2), f1(f7(c2), c2))),
% 28.17/18.37 inference(modus_ponens,[status(thm)],[1180, 9365])).
% 28.17/18.37 tff(9367,assumption,(~(f7(c2) = f4(c2))), introduced(assumption)).
% 28.17/18.37 tff(9368,plain,
% 28.17/18.37 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((~(c2 = c4)) | (f7(c2) = c3) | (~big_f(f7(c2), c2)) | (f7(c2) = f4(c2)) | (~big_f(f7(c2), f1(f7(c2), c2))) | (~(f1(f7(c2), c2) = c2)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (~(c2 = c4)) | (f7(c2) = c3) | (~big_f(f7(c2), c2)) | (f7(c2) = f4(c2)) | (~big_f(f7(c2), f1(f7(c2), c2))) | (~(f1(f7(c2), c2) = c2)))),
% 28.17/18.37 inference(rewrite,[status(thm)],[])).
% 28.17/18.37 tff(9369,plain,
% 28.17/18.37 (((f7(c2) = c3) | (~(c2 = c4)) | (f7(c2) = f4(c2)) | (~big_f(f7(c2), c2)) | (~(f1(f7(c2), c2) = c2)) | (~big_f(f7(c2), f1(f7(c2), c2)))) <=> ((~(c2 = c4)) | (f7(c2) = c3) | (~big_f(f7(c2), c2)) | (f7(c2) = f4(c2)) | (~big_f(f7(c2), f1(f7(c2), c2))) | (~(f1(f7(c2), c2) = c2)))),
% 28.17/18.37 inference(rewrite,[status(thm)],[])).
% 28.17/18.37 tff(9370,plain,
% 28.17/18.37 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c2) = c3) | (~(c2 = c4)) | (f7(c2) = f4(c2)) | (~big_f(f7(c2), c2)) | (~(f1(f7(c2), c2) = c2)) | (~big_f(f7(c2), f1(f7(c2), c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((~(c2 = c4)) | (f7(c2) = c3) | (~big_f(f7(c2), c2)) | (f7(c2) = f4(c2)) | (~big_f(f7(c2), f1(f7(c2), c2))) | (~(f1(f7(c2), c2) = c2))))),
% 28.17/18.37 inference(monotonicity,[status(thm)],[9369])).
% 28.17/18.37 tff(9371,plain,
% 28.17/18.37 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c2) = c3) | (~(c2 = c4)) | (f7(c2) = f4(c2)) | (~big_f(f7(c2), c2)) | (~(f1(f7(c2), c2) = c2)) | (~big_f(f7(c2), f1(f7(c2), c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (~(c2 = c4)) | (f7(c2) = c3) | (~big_f(f7(c2), c2)) | (f7(c2) = f4(c2)) | (~big_f(f7(c2), f1(f7(c2), c2))) | (~(f1(f7(c2), c2) = c2)))),
% 28.17/18.37 inference(transitivity,[status(thm)],[9370, 9368])).
% 28.17/18.37 tff(9372,plain,
% 28.17/18.37 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c2) = c3) | (~(c2 = c4)) | (f7(c2) = f4(c2)) | (~big_f(f7(c2), c2)) | (~(f1(f7(c2), c2) = c2)) | (~big_f(f7(c2), f1(f7(c2), c2))))),
% 28.17/18.37 inference(quant_inst,[status(thm)],[])).
% 28.17/18.37 tff(9373,plain,
% 28.17/18.37 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (~(c2 = c4)) | (f7(c2) = c3) | (~big_f(f7(c2), c2)) | (f7(c2) = f4(c2)) | (~big_f(f7(c2), f1(f7(c2), c2))) | (~(f1(f7(c2), c2) = c2))),
% 28.17/18.37 inference(modus_ponens,[status(thm)],[9372, 9371])).
% 28.17/18.37 tff(9374,plain,
% 28.17/18.37 ((~big_f(f7(c2), f1(f7(c2), c2))) | (~(f1(f7(c2), c2) = c2))),
% 28.17/18.37 inference(unit_resolution,[status(thm)],[9373, 553, 631, 9092, 1180, 9367])).
% 28.17/18.37 tff(9375,plain,
% 28.17/18.37 ($false),
% 28.17/18.37 inference(unit_resolution,[status(thm)],[9374, 9366, 9363])).
% 28.17/18.37 tff(9376,plain,((~(f1(c1, c2) = c2)) | (~(c2 = c4)) | (f7(c2) = c3) | (~big_f(f7(c2), c2)) | (f7(c2) = f4(c2)) | (~(f7(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.17/18.37 tff(9377,plain,
% 28.17/18.37 (~(f1(c1, c2) = c2)),
% 28.17/18.37 inference(unit_resolution,[status(thm)],[9376, 9361, 9306, 1180, 9360, 22])).
% 28.17/18.37 tff(9378,plain,
% 28.17/18.37 (f1(c1, c2) = c1),
% 28.17/18.37 inference(unit_resolution,[status(thm)],[841, 9377])).
% 28.17/18.37 tff(9379,plain,
% 28.17/18.37 (f1(f7(c2), c2) = c1),
% 28.17/18.37 inference(transitivity,[status(thm)],[9112, 9378])).
% 28.17/18.38 tff(9380,plain,
% 28.17/18.38 (big_f(f7(c2), f1(f7(c2), c2)) <=> big_f(f7(c2), c1)),
% 28.17/18.38 inference(monotonicity,[status(thm)],[9379])).
% 28.17/18.38 tff(9381,plain,
% 28.17/18.38 (big_f(f7(c2), c1) <=> big_f(f7(c2), f1(f7(c2), c2))),
% 28.17/18.38 inference(symmetry,[status(thm)],[9380])).
% 28.17/18.38 tff(9382,plain,
% 28.17/18.38 ((~big_f(f7(c2), c1)) <=> (~big_f(f7(c2), f1(f7(c2), c2)))),
% 28.17/18.38 inference(monotonicity,[status(thm)],[9381])).
% 28.17/18.38 tff(9383,plain,
% 28.17/18.38 (~big_f(f7(c2), f1(f7(c2), c2))),
% 28.17/18.38 inference(modus_ponens,[status(thm)],[333, 9382])).
% 28.17/18.38 tff(9384,plain,
% 28.17/18.38 (f1(f7(c2), c2) = f7(c2)),
% 28.17/18.38 inference(transitivity,[status(thm)],[9112, 9378, 125])).
% 28.17/18.38 tff(9385,plain,
% 28.17/18.38 ((f1(f7(c2), c2) = c2) <=> (f7(c2) = c2)),
% 28.17/18.38 inference(monotonicity,[status(thm)],[9384])).
% 28.17/18.38 tff(9386,plain,
% 28.17/18.38 ((f7(c2) = c2) <=> (f1(f7(c2), c2) = c2)),
% 28.17/18.38 inference(symmetry,[status(thm)],[9385])).
% 28.17/18.38 tff(9387,plain,
% 28.17/18.38 ((~(f7(c2) = c2)) <=> (~(f1(f7(c2), c2) = c2))),
% 28.17/18.38 inference(monotonicity,[status(thm)],[9386])).
% 28.17/18.38 tff(9388,plain,
% 28.17/18.38 (~(f1(f7(c2), c2) = c2)),
% 28.17/18.38 inference(modus_ponens,[status(thm)],[17, 9387])).
% 28.17/18.38 tff(9389,plain,
% 28.17/18.38 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((~(c2 = c4)) | (f7(c2) = c3) | (~big_f(f7(c2), c2)) | (f7(c2) = f4(c2)) | big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (~(c2 = c4)) | (f7(c2) = c3) | (~big_f(f7(c2), c2)) | (f7(c2) = f4(c2)) | big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2))),
% 28.17/18.38 inference(rewrite,[status(thm)],[])).
% 28.17/18.38 tff(9390,plain,
% 28.17/18.38 (((f7(c2) = c3) | (f1(f7(c2), c2) = c2) | big_f(f7(c2), f1(f7(c2), c2)) | (~(c2 = c4)) | (f7(c2) = f4(c2)) | (~big_f(f7(c2), c2))) <=> ((~(c2 = c4)) | (f7(c2) = c3) | (~big_f(f7(c2), c2)) | (f7(c2) = f4(c2)) | big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2))),
% 28.17/18.38 inference(rewrite,[status(thm)],[])).
% 28.17/18.38 tff(9391,plain,
% 28.17/18.38 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((f7(c2) = c3) | (f1(f7(c2), c2) = c2) | big_f(f7(c2), f1(f7(c2), c2)) | (~(c2 = c4)) | (f7(c2) = f4(c2)) | (~big_f(f7(c2), c2)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((~(c2 = c4)) | (f7(c2) = c3) | (~big_f(f7(c2), c2)) | (f7(c2) = f4(c2)) | big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2)))),
% 28.17/18.38 inference(monotonicity,[status(thm)],[9390])).
% 28.17/18.38 tff(9392,plain,
% 28.17/18.38 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((f7(c2) = c3) | (f1(f7(c2), c2) = c2) | big_f(f7(c2), f1(f7(c2), c2)) | (~(c2 = c4)) | (f7(c2) = f4(c2)) | (~big_f(f7(c2), c2)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (~(c2 = c4)) | (f7(c2) = c3) | (~big_f(f7(c2), c2)) | (f7(c2) = f4(c2)) | big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2))),
% 28.17/18.38 inference(transitivity,[status(thm)],[9391, 9389])).
% 28.17/18.38 tff(9393,plain,
% 28.17/18.38 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((f7(c2) = c3) | (f1(f7(c2), c2) = c2) | big_f(f7(c2), f1(f7(c2), c2)) | (~(c2 = c4)) | (f7(c2) = f4(c2)) | (~big_f(f7(c2), c2)))),
% 28.17/18.38 inference(quant_inst,[status(thm)],[])).
% 28.17/18.38 tff(9394,plain,
% 28.17/18.38 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (~(c2 = c4)) | (f7(c2) = c3) | (~big_f(f7(c2), c2)) | (f7(c2) = f4(c2)) | big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2)),
% 28.17/18.38 inference(modus_ponens,[status(thm)],[9393, 9392])).
% 28.17/18.38 tff(9395,plain,
% 28.17/18.38 (big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2)),
% 28.17/18.38 inference(unit_resolution,[status(thm)],[9394, 525, 9361, 9306, 1180, 9360])).
% 28.17/18.38 tff(9396,plain,
% 28.17/18.38 ($false),
% 28.17/18.38 inference(unit_resolution,[status(thm)],[9395, 9388, 9383])).
% 28.17/18.38 tff(9397,plain,((~(c3 = c2)) | (~big_f(f7(c2), c2)) | (f7(c2) = c2) | big_f(f7(c2), c1) | (~(f4(c4) = c2)) | big_f(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 28.17/18.38 tff(9398,plain,
% 28.17/18.38 (~big_f(f7(c2), c2)),
% 28.17/18.38 inference(unit_resolution,[status(thm)],[9397, 9300, 17, 333, 79, 2])).
% 28.17/18.38 tff(9399,plain,
% 28.17/18.38 ((f7(c2) = f5(c2)) <=> (c1 = f5(c2))),
% 28.17/18.38 inference(monotonicity,[status(thm)],[22])).
% 28.17/18.38 tff(9400,plain,
% 28.17/18.38 ((f7(c2) = f5(c2)) <=> (f5(c2) = c1)),
% 28.17/18.38 inference(transitivity,[status(thm)],[9399, 1531])).
% 28.17/18.38 tff(9401,plain,
% 28.17/18.38 ((~(f7(c2) = f5(c2))) <=> (~(f5(c2) = c1))),
% 28.17/18.38 inference(monotonicity,[status(thm)],[9400])).
% 28.17/18.38 tff(9402,plain,
% 28.17/18.38 (~(f7(c2) = f5(c2))),
% 28.17/18.38 inference(unit_resolution,[status(thm)],[8386, 8375, 17, 8080, 690, 122])).
% 28.17/18.38 tff(9403,plain,
% 28.17/18.38 (~(f5(c2) = c1)),
% 28.17/18.38 inference(modus_ponens,[status(thm)],[9402, 9401])).
% 28.17/18.38 tff(9404,plain,
% 28.17/18.38 (f5(c2) = c2),
% 28.17/18.38 inference(unit_resolution,[status(thm)],[1547, 9403])).
% 28.17/18.38 tff(9405,plain,
% 28.17/18.38 (c2 = f5(c2)),
% 28.17/18.38 inference(unit_resolution,[status(thm)],[8113, 9404])).
% 28.17/18.38 tff(9406,plain,
% 28.17/18.38 ($false),
% 28.17/18.38 inference(unit_resolution,[status(thm)],[8397, 9405, 9398, 17, 122, 8080, 690])).
% 28.17/18.38 tff(9407,plain,((~(c2 = c3)) | (f7(c2) = c2) | (~(f10(c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | big_f(f7(c2), c1) | (~(f4(c4) = c2)) | big_f(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 28.17/18.38 tff(9408,plain,
% 28.17/18.38 (~(c2 = c3)),
% 28.17/18.38 inference(unit_resolution,[status(thm)],[9407, 2, 122, 9298, 333, 79, 17])).
% 28.17/18.38 tff(9409,plain,
% 28.17/18.38 (c2 = f4(f7(c2))),
% 28.17/18.38 inference(unit_resolution,[status(thm)],[9323, 9315, 292])).
% 28.17/18.38 tff(9410,plain,
% 28.17/18.38 ((f7(f4(c4)) = c4) <=> (c1 = c4)),
% 28.17/18.38 inference(monotonicity,[status(thm)],[8502])).
% 28.17/18.38 tff(9411,plain,
% 28.17/18.38 ((c1 = c4) <=> (f7(f4(c4)) = c4)),
% 28.17/18.38 inference(symmetry,[status(thm)],[9410])).
% 28.17/18.38 tff(9412,plain,
% 28.17/18.38 ((c1 = c4) <=> (f7(c2) = c4)),
% 28.17/18.38 inference(transitivity,[status(thm)],[9411, 9326])).
% 28.17/18.38 tff(9413,plain,
% 28.17/18.38 (f7(c2) = c4),
% 28.17/18.38 inference(modus_ponens,[status(thm)],[564, 9412])).
% 28.17/18.38 tff(9414,plain,
% 28.17/18.38 (big_f(c2, f1(c2, c2)) <=> big_f(c2, c1)),
% 28.17/18.38 inference(monotonicity,[status(thm)],[5298])).
% 28.17/18.38 tff(9415,plain,
% 28.17/18.38 (big_f(c2, c1) <=> big_f(c2, f1(c2, c2))),
% 28.17/18.38 inference(symmetry,[status(thm)],[9414])).
% 28.17/18.38 tff(9416,plain,
% 28.17/18.38 ((~big_f(c2, c1)) <=> (~big_f(c2, f1(c2, c2)))),
% 28.17/18.38 inference(monotonicity,[status(thm)],[9415])).
% 28.17/18.38 tff(9417,plain,
% 28.17/18.38 (~big_f(c2, f1(c2, c2))),
% 28.17/18.38 inference(modus_ponens,[status(thm)],[2, 9416])).
% 28.17/18.38 tff(9418,plain,
% 28.17/18.38 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | big_f(c2, f7(c2)) | (~(c2 = f4(f7(c2)))) | (~(f7(c2) = c4)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | big_f(c2, f7(c2)) | (~(c2 = f4(f7(c2)))) | (~(f7(c2) = c4)))),
% 28.17/18.38 inference(rewrite,[status(thm)],[])).
% 28.17/18.38 tff(9419,plain,
% 28.17/18.38 (((c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f7(c2) = c4)) | big_f(c2, f7(c2)) | (~(c2 = f4(f7(c2))))) <=> ((c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | big_f(c2, f7(c2)) | (~(c2 = f4(f7(c2)))) | (~(f7(c2) = c4)))),
% 28.17/18.38 inference(rewrite,[status(thm)],[])).
% 28.17/18.38 tff(9420,plain,
% 28.17/18.38 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f7(c2) = c4)) | big_f(c2, f7(c2)) | (~(c2 = f4(f7(c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | big_f(c2, f7(c2)) | (~(c2 = f4(f7(c2)))) | (~(f7(c2) = c4))))),
% 28.17/18.38 inference(monotonicity,[status(thm)],[9419])).
% 28.17/18.38 tff(9421,plain,
% 28.17/18.38 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f7(c2) = c4)) | big_f(c2, f7(c2)) | (~(c2 = f4(f7(c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | big_f(c2, f7(c2)) | (~(c2 = f4(f7(c2)))) | (~(f7(c2) = c4)))),
% 28.17/18.38 inference(transitivity,[status(thm)],[9420, 9418])).
% 28.17/18.38 tff(9422,plain,
% 28.17/18.38 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f7(c2) = c4)) | big_f(c2, f7(c2)) | (~(c2 = f4(f7(c2)))))),
% 28.17/18.38 inference(quant_inst,[status(thm)],[])).
% 28.17/18.38 tff(9423,plain,
% 28.17/18.38 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | big_f(c2, f7(c2)) | (~(c2 = f4(f7(c2)))) | (~(f7(c2) = c4))),
% 28.17/18.38 inference(modus_ponens,[status(thm)],[9422, 9421])).
% 28.17/18.38 tff(9424,plain,
% 28.17/18.38 ($false),
% 28.17/18.38 inference(unit_resolution,[status(thm)],[9423, 402, 377, 1828, 9417, 8770, 9332, 9331])).
% 28.17/18.38 tff(9425,plain,((f1(c2, c2) = c2) | (c2 = c3) | (~(f7(c2) = c4)) | (~(c2 = f4(f7(c2)))) | big_f(c2, f7(c2)) | big_f(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 28.17/18.38 tff(9426,plain,
% 28.17/18.38 (f1(c2, c2) = c2),
% 28.17/18.38 inference(unit_resolution,[status(thm)],[9425, 9413, 377, 9409, 9331, 2])).
% 28.17/18.38 tff(9427,plain,
% 28.17/18.38 (big_f(c2, f1(c2, c2)) <=> big_f(c2, c2)),
% 28.17/18.38 inference(monotonicity,[status(thm)],[9426])).
% 28.17/18.38 tff(9428,plain,
% 28.17/18.38 (big_f(c2, c2) <=> big_f(c2, f1(c2, c2))),
% 28.17/18.38 inference(symmetry,[status(thm)],[9427])).
% 28.17/18.38 tff(9429,plain,
% 28.17/18.38 (big_f(c2, f1(c2, c2))),
% 28.17/18.38 inference(modus_ponens,[status(thm)],[1345, 9428])).
% 28.17/18.38 tff(9430,plain,
% 28.17/18.38 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | big_f(c2, f7(c2)) | (~(c2 = f4(f7(c2)))) | (~(f7(c2) = c4)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | big_f(c2, f7(c2)) | (~(c2 = f4(f7(c2)))) | (~(f7(c2) = c4)))),
% 28.17/18.38 inference(rewrite,[status(thm)],[])).
% 28.17/18.38 tff(9431,plain,
% 28.17/18.38 (((c2 = c3) | (~(f7(c2) = c4)) | big_f(c2, f7(c2)) | (~(c2 = f4(f7(c2)))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2)))) <=> ((c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | big_f(c2, f7(c2)) | (~(c2 = f4(f7(c2)))) | (~(f7(c2) = c4)))),
% 28.17/18.38 inference(rewrite,[status(thm)],[])).
% 28.17/18.38 tff(9432,plain,
% 28.17/18.38 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f7(c2) = c4)) | big_f(c2, f7(c2)) | (~(c2 = f4(f7(c2)))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | big_f(c2, f7(c2)) | (~(c2 = f4(f7(c2)))) | (~(f7(c2) = c4))))),
% 28.17/18.38 inference(monotonicity,[status(thm)],[9431])).
% 28.17/18.38 tff(9433,plain,
% 28.17/18.38 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f7(c2) = c4)) | big_f(c2, f7(c2)) | (~(c2 = f4(f7(c2)))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | big_f(c2, f7(c2)) | (~(c2 = f4(f7(c2)))) | (~(f7(c2) = c4)))),
% 28.17/18.38 inference(transitivity,[status(thm)],[9432, 9430])).
% 28.17/18.38 tff(9434,plain,
% 28.17/18.38 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f7(c2) = c4)) | big_f(c2, f7(c2)) | (~(c2 = f4(f7(c2)))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))),
% 28.17/18.38 inference(quant_inst,[status(thm)],[])).
% 28.17/18.38 tff(9435,plain,
% 28.17/18.38 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | big_f(c2, f7(c2)) | (~(c2 = f4(f7(c2)))) | (~(f7(c2) = c4))),
% 28.17/18.38 inference(modus_ponens,[status(thm)],[9434, 9433])).
% 28.17/18.38 tff(9436,plain,
% 28.17/18.38 ($false),
% 28.17/18.38 inference(unit_resolution,[status(thm)],[9435, 447, 377, 9426, 9429, 9413, 9409, 9331])).
% 28.17/18.38 tff(9437,plain,((~(c4 = c1)) | (c2 = c3) | big_f(c2, f7(c2)) | (~big_f(c2, c2)) | big_f(c2, c1) | (~(f7(c2) = c1)) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.17/18.38 tff(9438,plain,
% 28.17/18.38 (~(c4 = c1)),
% 28.17/18.38 inference(unit_resolution,[status(thm)],[9437, 9408, 9314, 1345, 2, 22, 79])).
% 28.17/18.38 tff(9439,plain,
% 28.17/18.38 (c4 = c2),
% 28.17/18.38 inference(unit_resolution,[status(thm)],[461, 9438])).
% 28.17/18.38 tff(9440,plain,
% 28.17/18.38 (c2 = c4),
% 28.17/18.38 inference(modus_ponens,[status(thm)],[9439, 159])).
% 28.17/18.38 tff(9441,plain,
% 28.17/18.38 (c2 = c4),
% 28.17/18.38 inference(symmetry,[status(thm)],[9439])).
% 28.17/18.38 tff(9442,plain,
% 28.17/18.38 (f4(c2) = f4(c4)),
% 28.17/18.38 inference(monotonicity,[status(thm)],[9441])).
% 28.17/18.38 tff(9443,plain,
% 28.17/18.38 (f4(c2) = c2),
% 28.17/18.38 inference(transitivity,[status(thm)],[9442, 79])).
% 28.17/18.38 tff(9444,plain,
% 28.17/18.38 ((c1 = f4(c2)) <=> (f7(c2) = c2)),
% 28.17/18.38 inference(monotonicity,[status(thm)],[125, 9443])).
% 28.17/18.38 tff(9445,plain,
% 28.17/18.38 ((f7(c2) = c2) <=> (c1 = f4(c2))),
% 28.17/18.38 inference(symmetry,[status(thm)],[9444])).
% 28.17/18.38 tff(9446,plain,
% 28.17/18.38 ((f7(c2) = c2) <=> (f7(c2) = f4(c2))),
% 28.17/18.38 inference(transitivity,[status(thm)],[9445, 9302])).
% 28.17/18.38 tff(9447,plain,
% 28.17/18.38 ((~(f7(c2) = c2)) <=> (~(f7(c2) = f4(c2)))),
% 28.17/18.38 inference(monotonicity,[status(thm)],[9446])).
% 28.17/18.38 tff(9448,plain,
% 28.17/18.38 (~(f7(c2) = f4(c2))),
% 28.17/18.38 inference(modus_ponens,[status(thm)],[17, 9447])).
% 28.17/18.38 tff(9449,plain,
% 28.17/18.38 (~(f5(c2) = c1)),
% 28.17/18.38 inference(modus_ponens,[status(thm)],[8392, 9401])).
% 28.17/18.38 tff(9450,plain,
% 28.17/18.38 (f5(c2) = c2),
% 28.17/18.38 inference(unit_resolution,[status(thm)],[1547, 9449])).
% 28.17/18.38 tff(9451,plain,
% 28.17/18.38 (c2 = f5(c2)),
% 28.17/18.38 inference(unit_resolution,[status(thm)],[8113, 9450])).
% 28.17/18.38 tff(9452,plain,
% 28.17/18.38 (big_f(f7(c2), c2)),
% 28.17/18.38 inference(unit_resolution,[status(thm)],[8397, 9451, 17, 122, 1572, 690])).
% 28.17/18.38 tff(9453,plain,
% 28.17/18.38 (c1 = f1(c2, c2)),
% 28.17/18.38 inference(symmetry,[status(thm)],[5298])).
% 28.17/18.38 tff(9454,plain,
% 28.17/18.38 (big_f(c2, c1) <=> big_f(c2, f1(c2, c2))),
% 28.17/18.38 inference(monotonicity,[status(thm)],[9453])).
% 28.17/18.38 tff(9455,plain,
% 28.17/18.38 ((~big_f(c2, c1)) <=> (~big_f(c2, f1(c2, c2)))),
% 28.17/18.38 inference(monotonicity,[status(thm)],[9454])).
% 28.17/18.38 tff(9456,plain,
% 28.17/18.38 (~big_f(c2, f1(c2, c2))),
% 28.17/18.38 inference(modus_ponens,[status(thm)],[2, 9455])).
% 28.17/18.38 tff(9457,plain,
% 28.17/18.38 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c2 = c3) | (~(c2 = c4)) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (~big_f(f7(c2), c2)) | (f7(c2) = f4(c2)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (c2 = c3) | (~(c2 = c4)) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (~big_f(f7(c2), c2)) | (f7(c2) = f4(c2)))),
% 28.17/18.38 inference(rewrite,[status(thm)],[])).
% 28.17/18.38 tff(9458,plain,
% 28.17/18.38 (((c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(c2 = c4)) | (f7(c2) = f4(c2)) | (~big_f(f7(c2), c2))) <=> ((c2 = c3) | (~(c2 = c4)) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (~big_f(f7(c2), c2)) | (f7(c2) = f4(c2)))),
% 28.17/18.38 inference(rewrite,[status(thm)],[])).
% 28.17/18.38 tff(9459,plain,
% 28.17/18.38 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(c2 = c4)) | (f7(c2) = f4(c2)) | (~big_f(f7(c2), c2)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c2 = c3) | (~(c2 = c4)) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (~big_f(f7(c2), c2)) | (f7(c2) = f4(c2))))),
% 28.17/18.38 inference(monotonicity,[status(thm)],[9458])).
% 28.17/18.38 tff(9460,plain,
% 28.17/18.38 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(c2 = c4)) | (f7(c2) = f4(c2)) | (~big_f(f7(c2), c2)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (c2 = c3) | (~(c2 = c4)) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (~big_f(f7(c2), c2)) | (f7(c2) = f4(c2)))),
% 28.17/18.38 inference(transitivity,[status(thm)],[9459, 9457])).
% 28.17/18.38 tff(9461,plain,
% 28.17/18.38 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(c2 = c4)) | (f7(c2) = f4(c2)) | (~big_f(f7(c2), c2)))),
% 28.17/18.38 inference(quant_inst,[status(thm)],[])).
% 28.17/18.38 tff(9462,plain,
% 28.17/18.38 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (c2 = c3) | (~(c2 = c4)) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (~big_f(f7(c2), c2)) | (f7(c2) = f4(c2))),
% 28.17/18.38 inference(modus_ponens,[status(thm)],[9461, 9460])).
% 28.17/18.38 tff(9463,plain,
% 28.17/18.38 ($false),
% 28.17/18.38 inference(unit_resolution,[status(thm)],[9462, 525, 631, 377, 1180, 1828, 9456, 9367])).
% 28.17/18.38 tff(9464,plain,((f1(c2, c2) = c2) | (~(c2 = c4)) | (c2 = c3) | (~big_f(f7(c2), c2)) | (f7(c2) = f4(c2)) | big_f(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 28.17/18.38 tff(9465,plain,
% 28.17/18.38 (f1(c2, c2) = c2),
% 28.17/18.38 inference(unit_resolution,[status(thm)],[9464, 377, 631, 9452, 9367, 2])).
% 28.17/18.38 tff(9466,plain,
% 28.17/18.38 (big_f(c2, f1(c2, c2)) <=> big_f(c2, c2)),
% 28.17/18.38 inference(monotonicity,[status(thm)],[9465])).
% 28.17/18.38 tff(9467,plain,
% 28.17/18.38 (big_f(c2, c2) <=> big_f(c2, f1(c2, c2))),
% 28.17/18.38 inference(symmetry,[status(thm)],[9466])).
% 28.17/18.38 tff(9468,plain,
% 28.17/18.38 (big_f(c2, f1(c2, c2))),
% 28.17/18.38 inference(modus_ponens,[status(thm)],[1345, 9467])).
% 28.17/18.38 tff(9469,plain,
% 28.17/18.38 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c2 = c4)) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (~big_f(f7(c2), c2)) | (f7(c2) = f4(c2)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(c2 = c4)) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (~big_f(f7(c2), c2)) | (f7(c2) = f4(c2)))),
% 28.17/18.38 inference(rewrite,[status(thm)],[])).
% 28.17/18.38 tff(9470,plain,
% 28.17/18.38 (((c2 = c3) | (~(c2 = c4)) | (f7(c2) = f4(c2)) | (~big_f(f7(c2), c2)) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2)))) <=> ((c2 = c3) | (~(c2 = c4)) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (~big_f(f7(c2), c2)) | (f7(c2) = f4(c2)))),
% 28.17/18.38 inference(rewrite,[status(thm)],[])).
% 28.17/18.38 tff(9471,plain,
% 28.17/18.38 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c2 = c4)) | (f7(c2) = f4(c2)) | (~big_f(f7(c2), c2)) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c2 = c4)) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (~big_f(f7(c2), c2)) | (f7(c2) = f4(c2))))),
% 28.20/18.38 inference(monotonicity,[status(thm)],[9470])).
% 28.20/18.38 tff(9472,plain,
% 28.20/18.38 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c2 = c4)) | (f7(c2) = f4(c2)) | (~big_f(f7(c2), c2)) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(c2 = c4)) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (~big_f(f7(c2), c2)) | (f7(c2) = f4(c2)))),
% 28.20/18.38 inference(transitivity,[status(thm)],[9471, 9469])).
% 28.20/18.38 tff(9473,plain,
% 28.20/18.38 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c2 = c4)) | (f7(c2) = f4(c2)) | (~big_f(f7(c2), c2)) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))),
% 28.20/18.38 inference(quant_inst,[status(thm)],[])).
% 28.20/18.38 tff(9474,plain,
% 28.20/18.38 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(c2 = c4)) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (~big_f(f7(c2), c2)) | (f7(c2) = f4(c2))),
% 28.20/18.38 inference(modus_ponens,[status(thm)],[9473, 9472])).
% 28.20/18.38 tff(9475,plain,
% 28.20/18.38 ($false),
% 28.20/18.38 inference(unit_resolution,[status(thm)],[9474, 553, 631, 377, 9452, 9465, 9468, 9367])).
% 28.20/18.38 tff(9476,plain,((c2 = c3) | (~(c2 = c4)) | (f7(c2) = f4(c2)) | (~big_f(c2, c2)) | big_f(c2, c1) | (f7(c2) = c2) | (~(f10(c2) = c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f7(c2) = f5(c2))), inference(lemma,lemma(discharge,[]))).
% 28.20/18.38 tff(9477,plain,
% 28.20/18.38 ($false),
% 28.20/18.38 inference(unit_resolution,[status(thm)],[9476, 9448, 9440, 9408, 1345, 2, 17, 122, 8080, 9298, 9299])).
% 28.20/18.38 tff(9478,plain,(big_f(c2, c1) | (~big_f(c2, c2)) | (f7(c2) = c2) | (~(f10(c2) = c2)) | (~(f4(c4) = c2)) | big_f(f7(c2), c1)), inference(lemma,lemma(discharge,[]))).
% 28.20/18.38 tff(9479,plain,
% 28.20/18.38 (~big_f(c2, c2)),
% 28.20/18.38 inference(unit_resolution,[status(thm)],[9478, 333, 17, 122, 79, 2])).
% 28.20/18.38 tff(9480,plain,
% 28.20/18.38 (~(f7(c1) = c1)),
% 28.20/18.38 inference(unit_resolution,[status(thm)],[8365, 9479, 122, 17, 333, 79])).
% 28.20/18.38 tff(9481,plain,
% 28.20/18.38 (~(c3 = c2)),
% 28.20/18.38 inference(unit_resolution,[status(thm)],[8259, 9479, 2, 79])).
% 28.20/18.38 tff(9482,plain,
% 28.20/18.38 (c3 = c1),
% 28.20/18.38 inference(unit_resolution,[status(thm)],[180, 9481])).
% 28.20/18.38 tff(9483,plain,
% 28.20/18.38 ($false),
% 28.20/18.38 inference(unit_resolution,[status(thm)],[9080, 9482, 9480, 17, 79, 122, 9479])).
% 28.20/18.38 tff(9484,plain,(big_f(f7(c2), c1) | (f7(c2) = c2) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | big_f(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 28.20/18.38 tff(9485,plain,
% 28.20/18.38 (big_f(f7(c2), c1)),
% 28.20/18.38 inference(unit_resolution,[status(thm)],[9484, 2, 79, 122, 17])).
% 28.20/18.38 tff(9486,plain,
% 28.20/18.38 (big_f(f7(c2), f7(c2))),
% 28.20/18.38 inference(modus_ponens,[status(thm)],[9485, 8076])).
% 28.20/18.38 tff(9487,plain,
% 28.20/18.38 (big_f(c1, c1) <=> big_f(f7(c2), c1)),
% 28.20/18.38 inference(monotonicity,[status(thm)],[125])).
% 28.20/18.38 tff(9488,plain,
% 28.20/18.38 (big_f(f7(c2), c1) <=> big_f(c1, c1)),
% 28.20/18.38 inference(symmetry,[status(thm)],[9487])).
% 28.20/18.38 tff(9489,plain,
% 28.20/18.38 (big_f(c1, c1)),
% 28.20/18.38 inference(modus_ponens,[status(thm)],[338, 9488])).
% 28.20/18.38 tff(9490,plain,
% 28.20/18.38 ((c1 = c4) <=> (f7(f4(c4)) = c4)),
% 28.20/18.38 inference(monotonicity,[status(thm)],[8115])).
% 28.20/18.38 tff(9491,plain,
% 28.20/18.38 ((c4 = c1) <=> (f7(c2) = c4)),
% 28.20/18.38 inference(transitivity,[status(thm)],[479, 9490, 9326])).
% 28.20/18.38 tff(9492,plain,
% 28.20/18.38 ((~(c4 = c1)) <=> (~(f7(c2) = c4))),
% 28.20/18.38 inference(monotonicity,[status(thm)],[9491])).
% 28.20/18.38 tff(9493,plain,
% 28.20/18.38 (~(c4 = c1)),
% 28.20/18.38 inference(unit_resolution,[status(thm)],[9437, 377, 9331, 1345, 2, 22, 79])).
% 28.20/18.38 tff(9494,plain,
% 28.20/18.38 (~(f7(c2) = c4)),
% 28.20/18.38 inference(modus_ponens,[status(thm)],[9493, 9492])).
% 28.20/18.38 tff(9495,assumption,(~(f7(c2) = c4)), introduced(assumption)).
% 28.20/18.38 tff(9496,plain,
% 28.20/18.38 (f3(f7(c2), f7(c2)) = f3(c1, c1)),
% 28.20/18.39 inference(monotonicity,[status(thm)],[22, 22])).
% 28.20/18.39 tff(9497,plain,
% 28.20/18.39 (f3(f7(c2), f7(c2)) = c2),
% 28.20/18.39 inference(transitivity,[status(thm)],[9496, 1441])).
% 28.20/18.39 tff(9498,plain,
% 28.20/18.39 ((f3(f7(c2), f7(c2)) = f7(c2)) <=> (c2 = f7(c2))),
% 28.20/18.39 inference(monotonicity,[status(thm)],[9497])).
% 28.20/18.39 tff(9499,plain,
% 28.20/18.39 ((f3(f7(c2), f7(c2)) = f7(c2)) <=> (f7(c2) = c2)),
% 28.20/18.39 inference(transitivity,[status(thm)],[9498, 8409])).
% 28.20/18.39 tff(9500,plain,
% 28.20/18.39 ((f7(c2) = c2) <=> (f3(f7(c2), f7(c2)) = f7(c2))),
% 28.20/18.39 inference(symmetry,[status(thm)],[9499])).
% 28.20/18.39 tff(9501,plain,
% 28.20/18.39 ((~(f7(c2) = c2)) <=> (~(f3(f7(c2), f7(c2)) = f7(c2)))),
% 28.20/18.39 inference(monotonicity,[status(thm)],[9500])).
% 28.20/18.39 tff(9502,plain,
% 28.20/18.39 (~(f3(f7(c2), f7(c2)) = f7(c2))),
% 28.20/18.39 inference(modus_ponens,[status(thm)],[17, 9501])).
% 28.20/18.39 tff(9503,plain,
% 28.20/18.39 (big_f(f3(f7(c2), f7(c2)), f7(c2)) <=> big_f(c2, c1)),
% 28.20/18.39 inference(monotonicity,[status(thm)],[9497, 22])).
% 28.20/18.39 tff(9504,plain,
% 28.20/18.39 (big_f(c2, c1) <=> big_f(f3(f7(c2), f7(c2)), f7(c2))),
% 28.20/18.39 inference(symmetry,[status(thm)],[9503])).
% 28.20/18.39 tff(9505,plain,
% 28.20/18.39 ((~big_f(c2, c1)) <=> (~big_f(f3(f7(c2), f7(c2)), f7(c2)))),
% 28.20/18.39 inference(monotonicity,[status(thm)],[9504])).
% 28.20/18.39 tff(9506,plain,
% 28.20/18.39 (~big_f(f3(f7(c2), f7(c2)), f7(c2))),
% 28.20/18.39 inference(modus_ponens,[status(thm)],[2, 9505])).
% 28.20/18.39 tff(9507,plain,
% 28.20/18.39 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (f7(c2) = c4) | (f3(f7(c2), f7(c2)) = f7(c2)) | big_f(f3(f7(c2), f7(c2)), f7(c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (f7(c2) = c4) | (f3(f7(c2), f7(c2)) = f7(c2)) | big_f(f3(f7(c2), f7(c2)), f7(c2)))),
% 28.20/18.39 inference(rewrite,[status(thm)],[])).
% 28.20/18.39 tff(9508,plain,
% 28.20/18.39 (((f7(c2) = c4) | (f3(f7(c2), f7(c2)) = f7(c2)) | big_f(f3(f7(c2), f7(c2)), f7(c2)) | (c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2))) <=> ((c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (f7(c2) = c4) | (f3(f7(c2), f7(c2)) = f7(c2)) | big_f(f3(f7(c2), f7(c2)), f7(c2)))),
% 28.20/18.39 inference(rewrite,[status(thm)],[])).
% 28.20/18.39 tff(9509,plain,
% 28.20/18.39 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f7(c2) = c4) | (f3(f7(c2), f7(c2)) = f7(c2)) | big_f(f3(f7(c2), f7(c2)), f7(c2)) | (c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (f7(c2) = c4) | (f3(f7(c2), f7(c2)) = f7(c2)) | big_f(f3(f7(c2), f7(c2)), f7(c2))))),
% 28.20/18.39 inference(monotonicity,[status(thm)],[9508])).
% 28.20/18.39 tff(9510,plain,
% 28.20/18.39 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f7(c2) = c4) | (f3(f7(c2), f7(c2)) = f7(c2)) | big_f(f3(f7(c2), f7(c2)), f7(c2)) | (c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (f7(c2) = c4) | (f3(f7(c2), f7(c2)) = f7(c2)) | big_f(f3(f7(c2), f7(c2)), f7(c2)))),
% 28.20/18.39 inference(transitivity,[status(thm)],[9509, 9507])).
% 28.20/18.39 tff(9511,plain,
% 28.20/18.39 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f7(c2) = c4) | (f3(f7(c2), f7(c2)) = f7(c2)) | big_f(f3(f7(c2), f7(c2)), f7(c2)) | (c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)))),
% 28.20/18.39 inference(quant_inst,[status(thm)],[])).
% 28.20/18.39 tff(9512,plain,
% 28.20/18.39 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (f7(c2) = c4) | (f3(f7(c2), f7(c2)) = f7(c2)) | big_f(f3(f7(c2), f7(c2)), f7(c2))),
% 28.20/18.39 inference(modus_ponens,[status(thm)],[9511, 9510])).
% 28.20/18.39 tff(9513,plain,
% 28.20/18.39 ((f3(f7(c2), f7(c2)) = f7(c2)) | big_f(f3(f7(c2), f7(c2)), f7(c2))),
% 28.20/18.39 inference(unit_resolution,[status(thm)],[9512, 1014, 377, 1828, 9456, 9495])).
% 28.20/18.39 tff(9514,plain,
% 28.20/18.39 ($false),
% 28.20/18.39 inference(unit_resolution,[status(thm)],[9513, 9506, 9502])).
% 28.20/18.39 tff(9515,plain,((~(f3(c1, c1) = c2)) | (c2 = c3) | (f1(c2, c2) = c2) | (f7(c2) = c4) | big_f(c2, c1) | (f7(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 28.20/18.39 tff(9516,plain,
% 28.20/18.39 (~(f3(c1, c1) = c2)),
% 28.20/18.39 inference(unit_resolution,[status(thm)],[9515, 1828, 377, 9495, 2, 17])).
% 28.20/18.39 tff(9517,plain,
% 28.20/18.39 (f3(c1, c1) = c1),
% 28.20/18.39 inference(unit_resolution,[status(thm)],[1416, 9516])).
% 28.20/18.39 tff(9518,plain,
% 28.20/18.39 (f3(f7(c2), f7(c2)) = f7(c2)),
% 28.20/18.39 inference(transitivity,[status(thm)],[9496, 9517, 125])).
% 28.20/18.39 tff(9519,plain,
% 28.20/18.39 (big_f(f3(f7(c2), f7(c2)), f7(c2)) <=> big_f(f7(c2), c1)),
% 28.20/18.39 inference(monotonicity,[status(thm)],[9518, 22])).
% 28.20/18.39 tff(9520,plain,
% 28.20/18.39 (big_f(f7(c2), c1) <=> big_f(f3(f7(c2), f7(c2)), f7(c2))),
% 28.20/18.39 inference(symmetry,[status(thm)],[9519])).
% 28.20/18.39 tff(9521,plain,
% 28.20/18.39 (big_f(f3(f7(c2), f7(c2)), f7(c2))),
% 28.20/18.39 inference(modus_ponens,[status(thm)],[338, 9520])).
% 28.20/18.39 tff(9522,plain,
% 28.20/18.39 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (f7(c2) = c4) | (~(f3(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f3(f7(c2), f7(c2)), f7(c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (f7(c2) = c4) | (~(f3(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f3(f7(c2), f7(c2)), f7(c2))))),
% 28.20/18.39 inference(rewrite,[status(thm)],[])).
% 28.20/18.39 tff(9523,plain,
% 28.20/18.39 (((f7(c2) = c4) | (c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f3(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f3(f7(c2), f7(c2)), f7(c2)))) <=> ((c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (f7(c2) = c4) | (~(f3(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f3(f7(c2), f7(c2)), f7(c2))))),
% 28.20/18.39 inference(rewrite,[status(thm)],[])).
% 28.20/18.39 tff(9524,plain,
% 28.20/18.39 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((f7(c2) = c4) | (c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f3(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f3(f7(c2), f7(c2)), f7(c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (f7(c2) = c4) | (~(f3(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f3(f7(c2), f7(c2)), f7(c2)))))),
% 28.20/18.39 inference(monotonicity,[status(thm)],[9523])).
% 28.20/18.39 tff(9525,plain,
% 28.20/18.39 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((f7(c2) = c4) | (c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f3(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f3(f7(c2), f7(c2)), f7(c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (f7(c2) = c4) | (~(f3(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f3(f7(c2), f7(c2)), f7(c2))))),
% 28.20/18.39 inference(transitivity,[status(thm)],[9524, 9522])).
% 28.20/18.39 tff(9526,plain,
% 28.20/18.39 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((f7(c2) = c4) | (c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f3(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f3(f7(c2), f7(c2)), f7(c2))))),
% 28.20/18.39 inference(quant_inst,[status(thm)],[])).
% 28.20/18.39 tff(9527,plain,
% 28.20/18.39 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (f7(c2) = c4) | (~(f3(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f3(f7(c2), f7(c2)), f7(c2)))),
% 28.20/18.39 inference(modus_ponens,[status(thm)],[9526, 9525])).
% 28.20/18.39 tff(9528,plain,
% 28.20/18.39 ((~(f3(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f3(f7(c2), f7(c2)), f7(c2)))),
% 28.20/18.39 inference(unit_resolution,[status(thm)],[9527, 969, 377, 1828, 9456, 9495])).
% 28.20/18.39 tff(9529,plain,
% 28.20/18.39 ($false),
% 28.20/18.39 inference(unit_resolution,[status(thm)],[9528, 9521, 9518])).
% 28.20/18.39 tff(9530,plain,((f1(c2, c2) = c2) | (c2 = c3) | (f7(c2) = c4) | (~big_f(f7(c2), c1)) | big_f(c2, c1) | (f7(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 28.20/18.39 tff(9531,plain,
% 28.20/18.39 (f1(c2, c2) = c2),
% 28.20/18.39 inference(unit_resolution,[status(thm)],[9530, 377, 9494, 338, 2, 17])).
% 28.20/18.39 tff(9532,plain,
% 28.20/18.39 (big_f(c2, f1(c2, c2)) <=> big_f(c2, c2)),
% 28.20/18.39 inference(monotonicity,[status(thm)],[9531])).
% 28.20/18.39 tff(9533,plain,
% 28.20/18.39 (big_f(c2, c2) <=> big_f(c2, f1(c2, c2))),
% 28.20/18.39 inference(symmetry,[status(thm)],[9532])).
% 28.20/18.39 tff(9534,plain,
% 28.20/18.39 (big_f(c2, f1(c2, c2))),
% 28.20/18.39 inference(modus_ponens,[status(thm)],[1345, 9533])).
% 28.20/18.39 tff(9535,plain,
% 28.20/18.39 (f3(f7(c2), f7(c2)) = f3(c1, c1)),
% 28.20/18.39 inference(monotonicity,[status(thm)],[292, 292])).
% 28.20/18.39 tff(9536,plain,
% 28.20/18.39 (f3(f7(c2), f7(c2)) = f7(c2)),
% 28.20/18.39 inference(transitivity,[status(thm)],[9535, 1938, 342])).
% 28.20/18.39 tff(9537,plain,
% 28.20/18.39 (big_f(f3(f7(c2), f7(c2)), f7(c2)) <=> big_f(f7(c2), c1)),
% 28.20/18.39 inference(monotonicity,[status(thm)],[9536, 292])).
% 28.20/18.39 tff(9538,plain,
% 28.20/18.39 (big_f(f7(c2), c1) <=> big_f(f3(f7(c2), f7(c2)), f7(c2))),
% 28.20/18.39 inference(symmetry,[status(thm)],[9537])).
% 28.20/18.39 tff(9539,plain,
% 28.20/18.39 (big_f(f3(f7(c2), f7(c2)), f7(c2))),
% 28.20/18.39 inference(modus_ponens,[status(thm)],[338, 9538])).
% 28.20/18.39 tff(9540,plain,
% 28.20/18.39 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f7(c2) = c4) | (~(f3(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f3(f7(c2), f7(c2)), f7(c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f7(c2) = c4) | (~(f3(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f3(f7(c2), f7(c2)), f7(c2))))),
% 28.20/18.39 inference(rewrite,[status(thm)],[])).
% 28.20/18.39 tff(9541,plain,
% 28.20/18.39 (((f7(c2) = c4) | (c2 = c3) | (~(f3(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f3(f7(c2), f7(c2)), f7(c2))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2)))) <=> ((c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f7(c2) = c4) | (~(f3(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f3(f7(c2), f7(c2)), f7(c2))))),
% 28.20/18.39 inference(rewrite,[status(thm)],[])).
% 28.20/18.39 tff(9542,plain,
% 28.20/18.39 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c2) = c4) | (c2 = c3) | (~(f3(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f3(f7(c2), f7(c2)), f7(c2))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f7(c2) = c4) | (~(f3(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f3(f7(c2), f7(c2)), f7(c2)))))),
% 28.20/18.39 inference(monotonicity,[status(thm)],[9541])).
% 28.20/18.39 tff(9543,plain,
% 28.20/18.39 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c2) = c4) | (c2 = c3) | (~(f3(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f3(f7(c2), f7(c2)), f7(c2))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f7(c2) = c4) | (~(f3(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f3(f7(c2), f7(c2)), f7(c2))))),
% 28.20/18.39 inference(transitivity,[status(thm)],[9542, 9540])).
% 28.20/18.39 tff(9544,plain,
% 28.20/18.39 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c2) = c4) | (c2 = c3) | (~(f3(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f3(f7(c2), f7(c2)), f7(c2))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))),
% 28.20/18.39 inference(quant_inst,[status(thm)],[])).
% 28.20/18.39 tff(9545,plain,
% 28.20/18.39 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f7(c2) = c4) | (~(f3(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f3(f7(c2), f7(c2)), f7(c2)))),
% 28.20/18.39 inference(modus_ponens,[status(thm)],[9544, 9543])).
% 28.20/18.39 tff(9546,plain,
% 28.20/18.39 ((~(f3(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f3(f7(c2), f7(c2)), f7(c2)))),
% 28.20/18.39 inference(unit_resolution,[status(thm)],[9545, 933, 377, 1908, 1907, 9495])).
% 28.20/18.39 tff(9547,plain,
% 28.20/18.39 ($false),
% 28.20/18.39 inference(unit_resolution,[status(thm)],[9546, 9539, 9536])).
% 28.20/18.39 tff(9548,plain,((~(f3(c1, c1) = c1)) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f7(c2) = c4) | (~big_f(f7(c2), c1)) | (~(f7(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.20/18.39 tff(9549,plain,
% 28.20/18.39 (~(f3(c1, c1) = c1)),
% 28.20/18.39 inference(unit_resolution,[status(thm)],[9548, 377, 9531, 9534, 9494, 338, 22])).
% 28.20/18.39 tff(9550,plain,
% 28.20/18.39 (f3(c1, c1) = c2),
% 28.20/18.39 inference(unit_resolution,[status(thm)],[1416, 9549])).
% 28.20/18.39 tff(9551,plain,
% 28.20/18.39 (big_f(f3(c1, c1), c1) <=> big_f(c2, c1)),
% 28.20/18.39 inference(monotonicity,[status(thm)],[9550])).
% 28.20/18.39 tff(9552,plain,
% 28.20/18.39 (big_f(c2, c1) <=> big_f(f3(c1, c1), c1)),
% 28.20/18.39 inference(symmetry,[status(thm)],[9551])).
% 28.20/18.39 tff(9553,plain,
% 28.20/18.39 ((~big_f(c2, c1)) <=> (~big_f(f3(c1, c1), c1))),
% 28.20/18.39 inference(monotonicity,[status(thm)],[9552])).
% 28.20/18.39 tff(9554,plain,
% 28.20/18.39 (~big_f(f3(c1, c1), c1)),
% 28.20/18.39 inference(modus_ponens,[status(thm)],[2, 9553])).
% 28.20/18.39 tff(9555,plain,
% 28.20/18.39 (f1(f9(f10(c2), f4(c4)), c2) = f1(f9(c2, c2), c2)),
% 28.20/18.39 inference(monotonicity,[status(thm)],[2634])).
% 28.20/18.39 tff(9556,plain,
% 28.20/18.39 (big_f(f9(f10(c2), f4(c4)), f1(f9(f10(c2), f4(c4)), c2)) <=> big_f(f9(c2, c2), f1(f9(c2, c2), c2))),
% 28.20/18.39 inference(monotonicity,[status(thm)],[2634, 9555])).
% 28.20/18.39 tff(9557,plain,
% 28.20/18.39 (big_f(f9(c2, c2), f1(f9(c2, c2), c2)) <=> big_f(f9(f10(c2), f4(c4)), f1(f9(f10(c2), f4(c4)), c2))),
% 28.20/18.39 inference(symmetry,[status(thm)],[9556])).
% 28.20/18.39 tff(9558,plain,
% 28.20/18.39 (f1(f9(c2, c2), c2) = f1(c2, c2)),
% 28.20/18.39 inference(monotonicity,[status(thm)],[8067])).
% 28.20/18.39 tff(9559,plain,
% 28.20/18.39 (big_f(f9(c2, c2), f1(f9(c2, c2), c2)) <=> big_f(c2, f1(c2, c2))),
% 28.20/18.39 inference(monotonicity,[status(thm)],[8067, 9558])).
% 28.20/18.39 tff(9560,plain,
% 28.20/18.39 (big_f(c2, f1(c2, c2)) <=> big_f(f9(c2, c2), f1(f9(c2, c2), c2))),
% 28.20/18.39 inference(symmetry,[status(thm)],[9559])).
% 28.20/18.39 tff(9561,plain,
% 28.20/18.39 (big_f(c2, c2) <=> big_f(f9(f10(c2), f4(c4)), f1(f9(f10(c2), f4(c4)), c2))),
% 28.20/18.39 inference(transitivity,[status(thm)],[9533, 9560, 9557])).
% 28.20/18.39 tff(9562,plain,
% 28.20/18.39 (big_f(f9(f10(c2), f4(c4)), f1(f9(f10(c2), f4(c4)), c2))),
% 28.20/18.39 inference(modus_ponens,[status(thm)],[1345, 9561])).
% 28.20/18.39 tff(9563,plain,
% 28.20/18.39 (~(c1 = c4)),
% 28.20/18.39 inference(modus_ponens,[status(thm)],[9493, 1997])).
% 28.20/18.39 tff(9564,plain,
% 28.20/18.39 ((f1(f9(f10(c2), f4(c4)), c2) = c2) <=> (f1(f9(c2, c2), c2) = c2)),
% 28.20/18.39 inference(monotonicity,[status(thm)],[9555])).
% 28.20/18.39 tff(9565,plain,
% 28.20/18.39 ((f1(f9(c2, c2), c2) = c2) <=> (f1(f9(f10(c2), f4(c4)), c2) = c2)),
% 28.20/18.39 inference(symmetry,[status(thm)],[9564])).
% 28.20/18.39 tff(9566,plain,
% 28.20/18.39 ((f1(f9(c2, c2), c2) = c2) <=> (f1(c2, c2) = c2)),
% 28.20/18.39 inference(monotonicity,[status(thm)],[9558])).
% 28.20/18.39 tff(9567,plain,
% 28.20/18.39 ((f1(c2, c2) = c2) <=> (f1(f9(c2, c2), c2) = c2)),
% 28.20/18.39 inference(symmetry,[status(thm)],[9566])).
% 28.20/18.39 tff(9568,plain,
% 28.20/18.39 ((f1(c2, c2) = c2) <=> (f1(f9(f10(c2), f4(c4)), c2) = c2)),
% 28.20/18.39 inference(transitivity,[status(thm)],[9567, 9565])).
% 28.20/18.39 tff(9569,plain,
% 28.20/18.39 (f1(f9(f10(c2), f4(c4)), c2) = c2),
% 28.20/18.39 inference(modus_ponens,[status(thm)],[9531, 9568])).
% 28.20/18.39 tff(9570,plain,
% 28.20/18.39 ((f9(f10(c2), f4(c4)) = c3) <=> (f9(c2, c2) = c3)),
% 28.20/18.39 inference(monotonicity,[status(thm)],[2634])).
% 28.20/18.39 tff(9571,plain,
% 28.20/18.39 ((f9(c2, c2) = c3) <=> (f9(f10(c2), f4(c4)) = c3)),
% 28.20/18.39 inference(symmetry,[status(thm)],[9570])).
% 28.20/18.39 tff(9572,plain,
% 28.20/18.39 ((f9(c2, c2) = c3) <=> (c2 = c3)),
% 28.20/18.39 inference(monotonicity,[status(thm)],[8067])).
% 28.20/18.39 tff(9573,plain,
% 28.20/18.39 ((c2 = c3) <=> (f9(c2, c2) = c3)),
% 28.20/18.39 inference(symmetry,[status(thm)],[9572])).
% 28.20/18.39 tff(9574,plain,
% 28.20/18.39 ((c2 = c3) <=> (f9(f10(c2), f4(c4)) = c3)),
% 28.20/18.39 inference(transitivity,[status(thm)],[9573, 9571])).
% 28.20/18.39 tff(9575,plain,
% 28.20/18.39 ((~(c2 = c3)) <=> (~(f9(f10(c2), f4(c4)) = c3))),
% 28.20/18.39 inference(monotonicity,[status(thm)],[9574])).
% 28.20/18.39 tff(9576,plain,
% 28.20/18.39 (~(f9(f10(c2), f4(c4)) = c3)),
% 28.20/18.39 inference(modus_ponens,[status(thm)],[377, 9575])).
% 28.20/18.39 tff(9577,plain,
% 28.20/18.39 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (big_f(f3(c1, c1), c1) | (f3(c1, c1) = c1) | (c1 = c4) | (~big_f(f9(f10(c2), f4(c4)), f1(f9(f10(c2), f4(c4)), c2))) | (f9(f10(c2), f4(c4)) = c3) | (~(f1(f9(f10(c2), f4(c4)), c2) = c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | big_f(f3(c1, c1), c1) | (f3(c1, c1) = c1) | (c1 = c4) | (~big_f(f9(f10(c2), f4(c4)), f1(f9(f10(c2), f4(c4)), c2))) | (f9(f10(c2), f4(c4)) = c3) | (~(f1(f9(f10(c2), f4(c4)), c2) = c2)))),
% 28.20/18.39 inference(rewrite,[status(thm)],[])).
% 28.20/18.39 tff(9578,plain,
% 28.20/18.39 (((c1 = c4) | (f3(c1, c1) = c1) | big_f(f3(c1, c1), c1) | (f9(f10(c2), f4(c4)) = c3) | (~(f1(f9(f10(c2), f4(c4)), c2) = c2)) | (~big_f(f9(f10(c2), f4(c4)), f1(f9(f10(c2), f4(c4)), c2)))) <=> (big_f(f3(c1, c1), c1) | (f3(c1, c1) = c1) | (c1 = c4) | (~big_f(f9(f10(c2), f4(c4)), f1(f9(f10(c2), f4(c4)), c2))) | (f9(f10(c2), f4(c4)) = c3) | (~(f1(f9(f10(c2), f4(c4)), c2) = c2)))),
% 28.20/18.39 inference(rewrite,[status(thm)],[])).
% 28.20/18.39 tff(9579,plain,
% 28.20/18.39 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c4) | (f3(c1, c1) = c1) | big_f(f3(c1, c1), c1) | (f9(f10(c2), f4(c4)) = c3) | (~(f1(f9(f10(c2), f4(c4)), c2) = c2)) | (~big_f(f9(f10(c2), f4(c4)), f1(f9(f10(c2), f4(c4)), c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (big_f(f3(c1, c1), c1) | (f3(c1, c1) = c1) | (c1 = c4) | (~big_f(f9(f10(c2), f4(c4)), f1(f9(f10(c2), f4(c4)), c2))) | (f9(f10(c2), f4(c4)) = c3) | (~(f1(f9(f10(c2), f4(c4)), c2) = c2))))),
% 28.20/18.40 inference(monotonicity,[status(thm)],[9578])).
% 28.20/18.40 tff(9580,plain,
% 28.20/18.40 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c4) | (f3(c1, c1) = c1) | big_f(f3(c1, c1), c1) | (f9(f10(c2), f4(c4)) = c3) | (~(f1(f9(f10(c2), f4(c4)), c2) = c2)) | (~big_f(f9(f10(c2), f4(c4)), f1(f9(f10(c2), f4(c4)), c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | big_f(f3(c1, c1), c1) | (f3(c1, c1) = c1) | (c1 = c4) | (~big_f(f9(f10(c2), f4(c4)), f1(f9(f10(c2), f4(c4)), c2))) | (f9(f10(c2), f4(c4)) = c3) | (~(f1(f9(f10(c2), f4(c4)), c2) = c2)))),
% 28.20/18.40 inference(transitivity,[status(thm)],[9579, 9577])).
% 28.20/18.40 tff(9581,plain,
% 28.20/18.40 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c4) | (f3(c1, c1) = c1) | big_f(f3(c1, c1), c1) | (f9(f10(c2), f4(c4)) = c3) | (~(f1(f9(f10(c2), f4(c4)), c2) = c2)) | (~big_f(f9(f10(c2), f4(c4)), f1(f9(f10(c2), f4(c4)), c2))))),
% 28.20/18.40 inference(quant_inst,[status(thm)],[])).
% 28.20/18.40 tff(9582,plain,
% 28.20/18.40 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | big_f(f3(c1, c1), c1) | (f3(c1, c1) = c1) | (c1 = c4) | (~big_f(f9(f10(c2), f4(c4)), f1(f9(f10(c2), f4(c4)), c2))) | (f9(f10(c2), f4(c4)) = c3) | (~(f1(f9(f10(c2), f4(c4)), c2) = c2))),
% 28.20/18.40 inference(modus_ponens,[status(thm)],[9581, 9580])).
% 28.20/18.40 tff(9583,plain,
% 28.20/18.40 (big_f(f3(c1, c1), c1) | (f3(c1, c1) = c1) | (c1 = c4) | (~big_f(f9(f10(c2), f4(c4)), f1(f9(f10(c2), f4(c4)), c2))) | (f9(f10(c2), f4(c4)) = c3) | (~(f1(f9(f10(c2), f4(c4)), c2) = c2))),
% 28.20/18.40 inference(unit_resolution,[status(thm)],[9582, 904])).
% 28.20/18.40 tff(9584,plain,
% 28.20/18.40 (big_f(f3(c1, c1), c1)),
% 28.20/18.40 inference(unit_resolution,[status(thm)],[9583, 9549, 9576, 9569, 9563, 9562])).
% 28.20/18.40 tff(9585,plain,
% 28.20/18.40 ($false),
% 28.20/18.40 inference(unit_resolution,[status(thm)],[9584, 9554])).
% 28.20/18.40 tff(9586,plain,((c2 = c3) | big_f(c2, c1) | (~big_f(f7(c2), c1)) | (~big_f(c2, c2)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(c2, f7(c2))), inference(lemma,lemma(discharge,[]))).
% 28.20/18.40 tff(9587,plain,
% 28.20/18.40 (c2 = c3),
% 28.20/18.40 inference(unit_resolution,[status(thm)],[9586, 9314, 338, 1345, 79, 122, 17, 2])).
% 28.20/18.40 tff(9588,plain,
% 28.20/18.40 (c3 = c2),
% 28.20/18.40 inference(symmetry,[status(thm)],[9587])).
% 28.20/18.40 tff(9589,plain,
% 28.20/18.40 ((f7(c2) = c3) <=> (f7(c2) = c2)),
% 28.20/18.40 inference(monotonicity,[status(thm)],[9588])).
% 28.20/18.40 tff(9590,plain,
% 28.20/18.40 ((f7(c2) = c2) <=> (f7(c2) = c3)),
% 28.20/18.40 inference(symmetry,[status(thm)],[9589])).
% 28.20/18.40 tff(9591,plain,
% 28.20/18.40 ((f7(c2) = c2) <=> (c1 = c3)),
% 28.20/18.40 inference(transitivity,[status(thm)],[9590, 9088])).
% 28.20/18.40 tff(9592,plain,
% 28.20/18.40 ((~(f7(c2) = c2)) <=> (~(c1 = c3))),
% 28.20/18.40 inference(monotonicity,[status(thm)],[9591])).
% 28.20/18.40 tff(9593,plain,
% 28.20/18.40 (~(c1 = c3)),
% 28.20/18.40 inference(modus_ponens,[status(thm)],[17, 9592])).
% 28.20/18.40 tff(9594,plain,
% 28.20/18.40 ((f7(f4(c4)) = c4) <=> (c1 = c4)),
% 28.20/18.40 inference(symmetry,[status(thm)],[9490])).
% 28.20/18.40 tff(9595,plain,
% 28.20/18.40 ((~(f7(c2) = c2)) <=> (~(f7(c2) = c3))),
% 28.20/18.40 inference(monotonicity,[status(thm)],[9590])).
% 28.20/18.40 tff(9596,plain,
% 28.20/18.40 (~(f7(c2) = c3)),
% 28.20/18.40 inference(modus_ponens,[status(thm)],[17, 9595])).
% 28.20/18.40 tff(9597,plain,
% 28.20/18.40 ((f7(c2) = f4(f7(c2))) <=> (c1 = f4(c1))),
% 28.20/18.40 inference(monotonicity,[status(thm)],[22, 8758])).
% 28.20/18.40 tff(9598,plain,
% 28.20/18.40 ((c1 = f4(c1)) <=> (f7(c2) = f4(f7(c2)))),
% 28.20/18.40 inference(symmetry,[status(thm)],[9597])).
% 28.20/18.40 tff(9599,plain,
% 28.20/18.40 ((c1 = f4(c1)) <=> (f7(c2) = c2)),
% 28.20/18.40 inference(monotonicity,[status(thm)],[125, 569])).
% 28.20/18.40 tff(9600,plain,
% 28.20/18.40 ((f7(c2) = c2) <=> (c1 = f4(c1))),
% 28.20/18.40 inference(symmetry,[status(thm)],[9599])).
% 28.20/18.40 tff(9601,plain,
% 28.20/18.40 ((f7(c2) = c2) <=> (f7(c2) = f4(f7(c2)))),
% 28.20/18.40 inference(transitivity,[status(thm)],[9600, 9598])).
% 28.20/18.40 tff(9602,plain,
% 28.20/18.40 ((~(f7(c2) = c2)) <=> (~(f7(c2) = f4(f7(c2))))),
% 28.20/18.40 inference(monotonicity,[status(thm)],[9601])).
% 28.20/18.40 tff(9603,plain,
% 28.20/18.40 (~(f7(c2) = f4(f7(c2)))),
% 28.20/18.40 inference(modus_ponens,[status(thm)],[17, 9602])).
% 28.20/18.40 tff(9604,plain,
% 28.20/18.40 (f1(f7(c2), f7(c2)) = f1(c1, c1)),
% 28.20/18.40 inference(monotonicity,[status(thm)],[292, 292])).
% 28.20/18.40 tff(9605,plain,
% 28.20/18.40 (f1(f7(c2), f7(c2)) = f7(c2)),
% 28.20/18.40 inference(transitivity,[status(thm)],[9604, 624, 342])).
% 28.20/18.40 tff(9606,plain,
% 28.20/18.40 (f1(f7(c2), f7(c2)) = c1),
% 28.20/18.40 inference(transitivity,[status(thm)],[9604, 624])).
% 28.20/18.40 tff(9607,plain,
% 28.20/18.40 (big_f(f7(c2), f1(f7(c2), f7(c2))) <=> big_f(f7(c2), c1)),
% 28.20/18.40 inference(monotonicity,[status(thm)],[9606])).
% 28.20/18.40 tff(9608,plain,
% 28.20/18.40 (big_f(f7(c2), c1) <=> big_f(f7(c2), f1(f7(c2), f7(c2)))),
% 28.20/18.40 inference(symmetry,[status(thm)],[9607])).
% 28.20/18.40 tff(9609,plain,
% 28.20/18.40 (big_f(f7(c2), f1(f7(c2), f7(c2)))),
% 28.20/18.40 inference(modus_ponens,[status(thm)],[338, 9608])).
% 28.20/18.40 tff(9610,plain,
% 28.20/18.40 (big_f(f7(c2), f7(c2))),
% 28.20/18.40 inference(modus_ponens,[status(thm)],[338, 8369])).
% 28.20/18.40 tff(9611,plain,
% 28.20/18.40 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c2) = c3) | (~(f7(c2) = c4)) | (~big_f(f7(c2), f7(c2))) | (f7(c2) = f4(f7(c2))) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (f7(c2) = c3) | (~(f7(c2) = c4)) | (~big_f(f7(c2), f7(c2))) | (f7(c2) = f4(f7(c2))) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2)))))),
% 28.20/18.40 inference(rewrite,[status(thm)],[])).
% 28.20/18.40 tff(9612,plain,
% 28.20/18.40 (((f7(c2) = c3) | (~(f7(c2) = c4)) | (f7(c2) = f4(f7(c2))) | (~big_f(f7(c2), f7(c2))) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2))))) <=> ((f7(c2) = c3) | (~(f7(c2) = c4)) | (~big_f(f7(c2), f7(c2))) | (f7(c2) = f4(f7(c2))) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2)))))),
% 28.20/18.40 inference(rewrite,[status(thm)],[])).
% 28.20/18.40 tff(9613,plain,
% 28.20/18.40 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c2) = c3) | (~(f7(c2) = c4)) | (f7(c2) = f4(f7(c2))) | (~big_f(f7(c2), f7(c2))) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c2) = c3) | (~(f7(c2) = c4)) | (~big_f(f7(c2), f7(c2))) | (f7(c2) = f4(f7(c2))) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2))))))),
% 28.20/18.40 inference(monotonicity,[status(thm)],[9612])).
% 28.20/18.40 tff(9614,plain,
% 28.20/18.40 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c2) = c3) | (~(f7(c2) = c4)) | (f7(c2) = f4(f7(c2))) | (~big_f(f7(c2), f7(c2))) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (f7(c2) = c3) | (~(f7(c2) = c4)) | (~big_f(f7(c2), f7(c2))) | (f7(c2) = f4(f7(c2))) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2)))))),
% 28.20/18.40 inference(transitivity,[status(thm)],[9613, 9611])).
% 28.20/18.40 tff(9615,plain,
% 28.20/18.40 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c2) = c3) | (~(f7(c2) = c4)) | (f7(c2) = f4(f7(c2))) | (~big_f(f7(c2), f7(c2))) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2)))))),
% 28.20/18.40 inference(quant_inst,[status(thm)],[])).
% 28.20/18.40 tff(9616,plain,
% 28.20/18.40 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (f7(c2) = c3) | (~(f7(c2) = c4)) | (~big_f(f7(c2), f7(c2))) | (f7(c2) = f4(f7(c2))) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2))))),
% 28.20/18.40 inference(modus_ponens,[status(thm)],[9615, 9614])).
% 28.20/18.40 tff(9617,plain,
% 28.20/18.40 ((~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2))))),
% 28.20/18.40 inference(unit_resolution,[status(thm)],[9616, 553, 9092, 9610, 8770, 8769])).
% 28.20/18.40 tff(9618,plain,
% 28.20/18.40 ($false),
% 28.20/18.40 inference(unit_resolution,[status(thm)],[9617, 9609, 9605])).
% 28.20/18.40 tff(9619,plain,((~(f1(c1, c1) = c1)) | (f7(c2) = c3) | (~(f7(c2) = c4)) | (f7(c2) = f4(f7(c2))) | (~big_f(f7(c2), c1)) | (~(f7(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.20/18.40 tff(9620,plain,
% 28.20/18.40 (~(f1(c1, c1) = c1)),
% 28.20/18.40 inference(unit_resolution,[status(thm)],[9619, 9330, 9092, 9603, 338, 22])).
% 28.20/18.40 tff(9621,plain,
% 28.20/18.40 (f1(c1, c1) = c2),
% 28.20/18.40 inference(unit_resolution,[status(thm)],[601, 9620])).
% 28.20/18.40 tff(9622,plain,
% 28.20/18.40 (f1(f7(c2), f7(c2)) = f1(c1, c1)),
% 28.20/18.40 inference(monotonicity,[status(thm)],[22, 22])).
% 28.20/18.40 tff(9623,plain,
% 28.20/18.40 (f1(f7(c2), f7(c2)) = c2),
% 28.20/18.40 inference(transitivity,[status(thm)],[9622, 9621])).
% 28.20/18.40 tff(9624,plain,
% 28.20/18.40 ((f1(f7(c2), f7(c2)) = f7(c2)) <=> (c2 = f7(c2))),
% 28.20/18.40 inference(monotonicity,[status(thm)],[9623])).
% 28.20/18.40 tff(9625,plain,
% 28.20/18.40 ((f1(f7(c2), f7(c2)) = f7(c2)) <=> (f7(c2) = c2)),
% 28.20/18.40 inference(transitivity,[status(thm)],[9624, 8409])).
% 28.20/18.40 tff(9626,plain,
% 28.20/18.40 ((f7(c2) = c2) <=> (f1(f7(c2), f7(c2)) = f7(c2))),
% 28.20/18.40 inference(symmetry,[status(thm)],[9625])).
% 28.20/18.40 tff(9627,plain,
% 28.20/18.40 ((~(f7(c2) = c2)) <=> (~(f1(f7(c2), f7(c2)) = f7(c2)))),
% 28.20/18.40 inference(monotonicity,[status(thm)],[9626])).
% 28.20/18.40 tff(9628,plain,
% 28.20/18.40 (~(f1(f7(c2), f7(c2)) = f7(c2))),
% 28.20/18.40 inference(modus_ponens,[status(thm)],[17, 9627])).
% 28.20/18.40 tff(9629,plain,
% 28.20/18.40 (big_f(f7(c2), f1(f7(c2), f7(c2))) <=> big_f(f7(c2), c2)),
% 28.20/18.40 inference(monotonicity,[status(thm)],[9623])).
% 28.20/18.40 tff(9630,plain,
% 28.20/18.40 (big_f(f7(c2), c2) <=> big_f(f7(c2), f1(f7(c2), f7(c2)))),
% 28.20/18.40 inference(symmetry,[status(thm)],[9629])).
% 28.20/18.40 tff(9631,plain,
% 28.20/18.40 ((~big_f(f7(c2), c2)) <=> (~big_f(f7(c2), f1(f7(c2), f7(c2))))),
% 28.20/18.40 inference(monotonicity,[status(thm)],[9630])).
% 28.20/18.40 tff(9632,plain,
% 28.20/18.40 (~big_f(f7(c2), f1(f7(c2), f7(c2)))),
% 28.20/18.40 inference(modus_ponens,[status(thm)],[1521, 9631])).
% 28.20/18.40 tff(9633,plain,
% 28.20/18.40 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((f7(c2) = c3) | (~(f7(c2) = c4)) | (~big_f(f7(c2), f7(c2))) | (f7(c2) = f4(f7(c2))) | (f1(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(c2), f1(f7(c2), f7(c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (f7(c2) = c3) | (~(f7(c2) = c4)) | (~big_f(f7(c2), f7(c2))) | (f7(c2) = f4(f7(c2))) | (f1(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(c2), f1(f7(c2), f7(c2))))),
% 28.20/18.40 inference(rewrite,[status(thm)],[])).
% 28.20/18.40 tff(9634,plain,
% 28.20/18.40 (((f7(c2) = c3) | (f1(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(c2), f1(f7(c2), f7(c2))) | (~(f7(c2) = c4)) | (f7(c2) = f4(f7(c2))) | (~big_f(f7(c2), f7(c2)))) <=> ((f7(c2) = c3) | (~(f7(c2) = c4)) | (~big_f(f7(c2), f7(c2))) | (f7(c2) = f4(f7(c2))) | (f1(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(c2), f1(f7(c2), f7(c2))))),
% 28.20/18.40 inference(rewrite,[status(thm)],[])).
% 28.20/18.40 tff(9635,plain,
% 28.20/18.40 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((f7(c2) = c3) | (f1(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(c2), f1(f7(c2), f7(c2))) | (~(f7(c2) = c4)) | (f7(c2) = f4(f7(c2))) | (~big_f(f7(c2), f7(c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((f7(c2) = c3) | (~(f7(c2) = c4)) | (~big_f(f7(c2), f7(c2))) | (f7(c2) = f4(f7(c2))) | (f1(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(c2), f1(f7(c2), f7(c2)))))),
% 28.20/18.40 inference(monotonicity,[status(thm)],[9634])).
% 28.20/18.40 tff(9636,plain,
% 28.20/18.40 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((f7(c2) = c3) | (f1(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(c2), f1(f7(c2), f7(c2))) | (~(f7(c2) = c4)) | (f7(c2) = f4(f7(c2))) | (~big_f(f7(c2), f7(c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (f7(c2) = c3) | (~(f7(c2) = c4)) | (~big_f(f7(c2), f7(c2))) | (f7(c2) = f4(f7(c2))) | (f1(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(c2), f1(f7(c2), f7(c2))))),
% 28.20/18.40 inference(transitivity,[status(thm)],[9635, 9633])).
% 28.20/18.40 tff(9637,plain,
% 28.20/18.40 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((f7(c2) = c3) | (f1(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(c2), f1(f7(c2), f7(c2))) | (~(f7(c2) = c4)) | (f7(c2) = f4(f7(c2))) | (~big_f(f7(c2), f7(c2))))),
% 28.20/18.40 inference(quant_inst,[status(thm)],[])).
% 28.20/18.40 tff(9638,plain,
% 28.20/18.40 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (f7(c2) = c3) | (~(f7(c2) = c4)) | (~big_f(f7(c2), f7(c2))) | (f7(c2) = f4(f7(c2))) | (f1(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(c2), f1(f7(c2), f7(c2)))),
% 28.20/18.40 inference(modus_ponens,[status(thm)],[9637, 9636])).
% 28.20/18.40 tff(9639,plain,
% 28.20/18.40 ((f1(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(c2), f1(f7(c2), f7(c2)))),
% 28.20/18.40 inference(unit_resolution,[status(thm)],[9638, 525, 9092, 8765, 9330, 9603])).
% 28.20/18.40 tff(9640,plain,
% 28.20/18.40 ($false),
% 28.20/18.40 inference(unit_resolution,[status(thm)],[9639, 9632, 9628])).
% 28.20/18.40 tff(9641,plain,((~(c4 = c1)) | (f7(c2) = c3) | big_f(f7(c2), c2) | (f7(c2) = c2) | (~big_f(f7(c2), c1)) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.20/18.40 tff(9642,plain,
% 28.20/18.40 (~(c4 = c1)),
% 28.20/18.40 inference(unit_resolution,[status(thm)],[9641, 9596, 338, 17, 1521, 79])).
% 28.20/18.40 tff(9643,plain,
% 28.20/18.40 (c4 = c2),
% 28.20/18.40 inference(unit_resolution,[status(thm)],[461, 9642])).
% 28.20/18.40 tff(9644,plain,
% 28.20/18.40 ((f7(f4(c4)) = c4) <=> (f7(c2) = c2)),
% 28.20/18.40 inference(monotonicity,[status(thm)],[80, 9643])).
% 28.20/18.40 tff(9645,plain,
% 28.20/18.40 ((f7(c2) = c2) <=> (f7(f4(c4)) = c4)),
% 28.20/18.40 inference(symmetry,[status(thm)],[9644])).
% 28.20/18.40 tff(9646,plain,
% 28.20/18.40 ((f7(c2) = c2) <=> (c1 = c4)),
% 28.20/18.40 inference(transitivity,[status(thm)],[9645, 9594])).
% 28.20/18.40 tff(9647,plain,
% 28.20/18.40 ((~(f7(c2) = c2)) <=> (~(c1 = c4))),
% 28.20/18.40 inference(monotonicity,[status(thm)],[9646])).
% 28.20/18.40 tff(9648,plain,
% 28.20/18.40 (~(c1 = c4)),
% 28.20/18.40 inference(modus_ponens,[status(thm)],[17, 9647])).
% 28.20/18.40 tff(9649,plain,
% 28.20/18.40 ((f7(c2) = c2) <=> (f7(c2) = c4)),
% 28.20/18.40 inference(transitivity,[status(thm)],[9645, 9326])).
% 28.20/18.40 tff(9650,plain,
% 28.20/18.40 ((~(f7(c2) = c2)) <=> (~(f7(c2) = c4))),
% 28.20/18.40 inference(monotonicity,[status(thm)],[9649])).
% 28.20/18.40 tff(9651,plain,
% 28.20/18.40 (~(f7(c2) = c4)),
% 28.20/18.40 inference(modus_ponens,[status(thm)],[17, 9650])).
% 28.20/18.40 tff(9652,plain,
% 28.20/18.40 (big_f(f7(c2), c2) <=> big_f(c1, c2)),
% 28.20/18.40 inference(symmetry,[status(thm)],[126])).
% 28.20/18.40 tff(9653,plain,
% 28.20/18.40 ((~big_f(f7(c2), c2)) <=> (~big_f(c1, c2))),
% 28.20/18.40 inference(monotonicity,[status(thm)],[9652])).
% 28.20/18.40 tff(9654,plain,
% 28.20/18.40 (~big_f(c1, c2)),
% 28.20/18.40 inference(modus_ponens,[status(thm)],[1521, 9653])).
% 28.20/18.40 tff(9655,plain,
% 28.20/18.40 (big_f(f7(c2), f1(f7(c2), f7(c2))) <=> big_f(c1, f1(c1, c1))),
% 28.20/18.40 inference(monotonicity,[status(thm)],[22, 9622])).
% 28.20/18.40 tff(9656,plain,
% 28.20/18.40 ((~big_f(f7(c2), f1(f7(c2), f7(c2)))) <=> (~big_f(c1, f1(c1, c1)))),
% 28.20/18.40 inference(monotonicity,[status(thm)],[9655])).
% 28.20/18.40 tff(9657,plain,
% 28.20/18.40 (f3(f7(c2), f7(c2)) = c2),
% 28.20/18.40 inference(transitivity,[status(thm)],[9496, 1440])).
% 28.20/18.40 tff(9658,plain,
% 28.20/18.40 (big_f(f3(f7(c2), f7(c2)), f7(c2)) <=> big_f(c2, c1)),
% 28.20/18.40 inference(monotonicity,[status(thm)],[9657, 22])).
% 28.20/18.40 tff(9659,plain,
% 28.20/18.40 (big_f(c2, c1) <=> big_f(f3(f7(c2), f7(c2)), f7(c2))),
% 28.20/18.40 inference(symmetry,[status(thm)],[9658])).
% 28.20/18.40 tff(9660,plain,
% 28.20/18.40 ((~big_f(c2, c1)) <=> (~big_f(f3(f7(c2), f7(c2)), f7(c2)))),
% 28.20/18.40 inference(monotonicity,[status(thm)],[9659])).
% 28.20/18.40 tff(9661,plain,
% 28.20/18.40 (~big_f(f3(f7(c2), f7(c2)), f7(c2))),
% 28.20/18.40 inference(modus_ponens,[status(thm)],[2, 9660])).
% 28.20/18.40 tff(9662,plain,
% 28.20/18.40 ((f3(f7(c2), f7(c2)) = f7(c2)) <=> (c2 = f7(c2))),
% 28.20/18.40 inference(monotonicity,[status(thm)],[9657])).
% 28.20/18.40 tff(9663,plain,
% 28.20/18.40 ((f3(f7(c2), f7(c2)) = f7(c2)) <=> (f7(c2) = c2)),
% 28.20/18.40 inference(transitivity,[status(thm)],[9662, 8409])).
% 28.20/18.40 tff(9664,plain,
% 28.20/18.40 ((f7(c2) = c2) <=> (f3(f7(c2), f7(c2)) = f7(c2))),
% 28.20/18.40 inference(symmetry,[status(thm)],[9663])).
% 28.20/18.40 tff(9665,plain,
% 28.20/18.40 ((~(f7(c2) = c2)) <=> (~(f3(f7(c2), f7(c2)) = f7(c2)))),
% 28.20/18.40 inference(monotonicity,[status(thm)],[9664])).
% 28.20/18.40 tff(9666,plain,
% 28.20/18.40 (~(f3(f7(c2), f7(c2)) = f7(c2))),
% 28.20/18.40 inference(modus_ponens,[status(thm)],[17, 9665])).
% 28.20/18.40 tff(9667,plain,
% 28.20/18.40 ((f1(f7(c2), f7(c2)) = f7(c2)) <=> (f1(c1, c1) = c1)),
% 28.20/18.40 inference(monotonicity,[status(thm)],[9622, 22])).
% 28.20/18.40 tff(9668,plain,
% 28.20/18.40 ((f1(c1, c1) = c1) <=> (f1(f7(c2), f7(c2)) = f7(c2))),
% 28.20/18.40 inference(symmetry,[status(thm)],[9667])).
% 28.20/18.40 tff(9669,plain,
% 28.20/18.40 (big_f(f3(c1, c1), c1) <=> big_f(c2, c1)),
% 28.20/18.40 inference(monotonicity,[status(thm)],[1440])).
% 28.20/18.40 tff(9670,plain,
% 28.20/18.40 (big_f(c2, c1) <=> big_f(f3(c1, c1), c1)),
% 28.20/18.40 inference(symmetry,[status(thm)],[9669])).
% 28.20/18.40 tff(9671,plain,
% 28.20/18.40 ((~big_f(c2, c1)) <=> (~big_f(f3(c1, c1), c1))),
% 28.20/18.40 inference(monotonicity,[status(thm)],[9670])).
% 28.20/18.40 tff(9672,plain,
% 28.20/18.40 (~big_f(f3(c1, c1), c1)),
% 28.20/18.40 inference(modus_ponens,[status(thm)],[2, 9671])).
% 28.20/18.40 tff(9673,assumption,(~big_f(c1, f1(c1, c1))), introduced(assumption)).
% 28.20/18.40 tff(9674,plain,
% 28.20/18.40 (big_f(c1, f1(c1, c1)) <=> big_f(c1, c1)),
% 28.20/18.40 inference(monotonicity,[status(thm)],[624])).
% 28.20/18.40 tff(9675,plain,
% 28.20/18.40 (big_f(c1, c1) <=> big_f(c1, f1(c1, c1))),
% 28.20/18.40 inference(symmetry,[status(thm)],[9674])).
% 28.20/18.40 tff(9676,plain,
% 28.20/18.40 (big_f(c1, f1(c1, c1))),
% 28.20/18.40 inference(modus_ponens,[status(thm)],[4932, 9675])).
% 28.20/18.40 tff(9677,plain,
% 28.20/18.40 ($false),
% 28.20/18.40 inference(unit_resolution,[status(thm)],[9673, 9676])).
% 28.20/18.40 tff(9678,plain,((~(f1(c1, c1) = c1)) | big_f(c1, f1(c1, c1)) | (~big_f(c1, c1))), inference(lemma,lemma(discharge,[]))).
% 28.20/18.40 tff(9679,plain,
% 28.20/18.40 (~(f1(c1, c1) = c1)),
% 28.20/18.40 inference(unit_resolution,[status(thm)],[9678, 9673, 4932])).
% 28.20/18.40 tff(9680,plain,
% 28.20/18.40 ($false),
% 28.20/18.40 inference(unit_resolution,[status(thm)],[2005, 9679, 9673, 168, 482, 1431, 1430])).
% 28.20/18.40 tff(9681,plain,(big_f(c1, f1(c1, c1)) | (c1 = c3) | (c1 = c4) | (f3(c1, c1) = c1) | big_f(f3(c1, c1), c1) | (~big_f(c1, c1))), inference(lemma,lemma(discharge,[]))).
% 28.20/18.40 tff(9682,plain,
% 28.20/18.40 (big_f(c1, f1(c1, c1))),
% 28.20/18.40 inference(unit_resolution,[status(thm)],[9681, 1431, 482, 168, 9672, 4932])).
% 28.20/18.40 tff(9683,plain,
% 28.20/18.40 (~(f1(c1, c1) = c2)),
% 28.20/18.40 inference(unit_resolution,[status(thm)],[4561, 9682, 27])).
% 28.20/18.40 tff(9684,plain,
% 28.20/18.40 (f1(c1, c1) = c1),
% 28.20/18.40 inference(unit_resolution,[status(thm)],[601, 9683])).
% 28.20/18.40 tff(9685,plain,
% 28.20/18.40 (f1(f7(c2), f7(c2)) = f7(c2)),
% 28.20/18.40 inference(modus_ponens,[status(thm)],[9684, 9668])).
% 28.20/18.40 tff(9686,plain,
% 28.20/18.40 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c2) = c3) | (f7(c2) = c4) | (f3(f7(c2), f7(c2)) = f7(c2)) | big_f(f3(f7(c2), f7(c2)), f7(c2)) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2)))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (f7(c2) = c3) | (f7(c2) = c4) | (f3(f7(c2), f7(c2)) = f7(c2)) | big_f(f3(f7(c2), f7(c2)), f7(c2)) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2)))))),
% 28.20/18.40 inference(rewrite,[status(thm)],[])).
% 28.20/18.40 tff(9687,plain,
% 28.20/18.40 (((f7(c2) = c4) | (f3(f7(c2), f7(c2)) = f7(c2)) | big_f(f3(f7(c2), f7(c2)), f7(c2)) | (f7(c2) = c3) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2))))) <=> ((f7(c2) = c3) | (f7(c2) = c4) | (f3(f7(c2), f7(c2)) = f7(c2)) | big_f(f3(f7(c2), f7(c2)), f7(c2)) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2)))))),
% 28.20/18.40 inference(rewrite,[status(thm)],[])).
% 28.20/18.40 tff(9688,plain,
% 28.20/18.40 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c2) = c4) | (f3(f7(c2), f7(c2)) = f7(c2)) | big_f(f3(f7(c2), f7(c2)), f7(c2)) | (f7(c2) = c3) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2)))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c2) = c3) | (f7(c2) = c4) | (f3(f7(c2), f7(c2)) = f7(c2)) | big_f(f3(f7(c2), f7(c2)), f7(c2)) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2))))))),
% 28.20/18.40 inference(monotonicity,[status(thm)],[9687])).
% 28.20/18.40 tff(9689,plain,
% 28.20/18.40 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c2) = c4) | (f3(f7(c2), f7(c2)) = f7(c2)) | big_f(f3(f7(c2), f7(c2)), f7(c2)) | (f7(c2) = c3) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2)))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (f7(c2) = c3) | (f7(c2) = c4) | (f3(f7(c2), f7(c2)) = f7(c2)) | big_f(f3(f7(c2), f7(c2)), f7(c2)) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2)))))),
% 28.20/18.41 inference(transitivity,[status(thm)],[9688, 9686])).
% 28.20/18.41 tff(9690,plain,
% 28.20/18.41 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c2) = c4) | (f3(f7(c2), f7(c2)) = f7(c2)) | big_f(f3(f7(c2), f7(c2)), f7(c2)) | (f7(c2) = c3) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2)))))),
% 28.20/18.41 inference(quant_inst,[status(thm)],[])).
% 28.20/18.41 tff(9691,plain,
% 28.20/18.41 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (f7(c2) = c3) | (f7(c2) = c4) | (f3(f7(c2), f7(c2)) = f7(c2)) | big_f(f3(f7(c2), f7(c2)), f7(c2)) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2))))),
% 28.20/18.41 inference(modus_ponens,[status(thm)],[9690, 9689])).
% 28.20/18.41 tff(9692,plain,
% 28.20/18.41 ((f3(f7(c2), f7(c2)) = f7(c2)) | big_f(f3(f7(c2), f7(c2)), f7(c2)) | (~big_f(f7(c2), f1(f7(c2), f7(c2))))),
% 28.20/18.41 inference(unit_resolution,[status(thm)],[9691, 904, 9092, 9495, 9685])).
% 28.20/18.41 tff(9693,plain,
% 28.20/18.41 (~big_f(f7(c2), f1(f7(c2), f7(c2)))),
% 28.20/18.41 inference(unit_resolution,[status(thm)],[9692, 9666, 9661])).
% 28.20/18.41 tff(9694,plain,
% 28.20/18.41 (~big_f(c1, f1(c1, c1))),
% 28.20/18.41 inference(modus_ponens,[status(thm)],[9693, 9656])).
% 28.20/18.41 tff(9695,plain,
% 28.20/18.41 ($false),
% 28.20/18.41 inference(unit_resolution,[status(thm)],[9682, 9694])).
% 28.20/18.41 tff(9696,plain,((f3(c1, c1) = c1) | (f7(c2) = c3) | (f7(c2) = c4) | big_f(c2, c1) | (f7(c2) = c2) | big_f(c1, c2) | (c1 = c4) | (c1 = c3) | (~big_f(c1, c1))), inference(lemma,lemma(discharge,[]))).
% 28.20/18.41 tff(9697,plain,
% 28.20/18.41 (f3(c1, c1) = c1),
% 28.20/18.41 inference(unit_resolution,[status(thm)],[9696, 9654, 9651, 2, 17, 9596, 9648, 9593, 9489])).
% 28.20/18.41 tff(9698,plain,
% 28.20/18.41 (f3(f7(c2), f7(c2)) = f7(c2)),
% 28.20/18.41 inference(transitivity,[status(thm)],[9496, 9697, 125])).
% 28.20/18.41 tff(9699,plain,
% 28.20/18.41 (big_f(f3(f7(c2), f7(c2)), f7(c2)) <=> big_f(f7(c2), c1)),
% 28.20/18.41 inference(monotonicity,[status(thm)],[9698, 22])).
% 28.20/18.41 tff(9700,plain,
% 28.20/18.41 (big_f(f7(c2), c1) <=> big_f(f3(f7(c2), f7(c2)), f7(c2))),
% 28.20/18.41 inference(symmetry,[status(thm)],[9699])).
% 28.20/18.41 tff(9701,plain,
% 28.20/18.41 (big_f(f3(f7(c2), f7(c2)), f7(c2))),
% 28.20/18.41 inference(modus_ponens,[status(thm)],[338, 9700])).
% 28.20/18.41 tff(9702,plain,
% 28.20/18.41 (big_f(f7(c2), f1(f7(c2), f7(c2))) <=> big_f(c1, f1(c1, c1))),
% 28.20/18.41 inference(monotonicity,[status(thm)],[292, 9604])).
% 28.20/18.41 tff(9703,plain,
% 28.20/18.41 (big_f(c1, c1) <=> big_f(f7(c2), c1)),
% 28.20/18.41 inference(monotonicity,[status(thm)],[342])).
% 28.20/18.41 tff(9704,plain,
% 28.20/18.41 (big_f(f7(c2), c1) <=> big_f(c1, c1)),
% 28.20/18.41 inference(symmetry,[status(thm)],[9703])).
% 28.20/18.41 tff(9705,plain,
% 28.20/18.41 (big_f(c1, c1)),
% 28.20/18.41 inference(modus_ponens,[status(thm)],[338, 9704])).
% 28.20/18.41 tff(9706,plain,
% 28.20/18.41 (~(f1(c1, c1) = c1)),
% 28.20/18.41 inference(unit_resolution,[status(thm)],[9678, 9673, 9705])).
% 28.20/18.41 tff(9707,plain,
% 28.20/18.41 ((f1(f7(c2), f7(c2)) = f7(c2)) <=> (f1(c1, c1) = c1)),
% 28.20/18.41 inference(monotonicity,[status(thm)],[9604, 292])).
% 28.20/18.41 tff(9708,assumption,(f1(f7(c2), f7(c2)) = f7(c2)), introduced(assumption)).
% 28.20/18.41 tff(9709,plain,
% 28.20/18.41 (f1(c1, c1) = c1),
% 28.20/18.41 inference(modus_ponens,[status(thm)],[9708, 9707])).
% 28.20/18.41 tff(9710,assumption,(~(f1(c1, c1) = c1)), introduced(assumption)).
% 28.20/18.41 tff(9711,plain,
% 28.20/18.41 ($false),
% 28.20/18.41 inference(unit_resolution,[status(thm)],[9710, 9709])).
% 28.20/18.41 tff(9712,plain,((~(f1(f7(c2), f7(c2)) = f7(c2))) | (f1(c1, c1) = c1) | (~(f7(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.20/18.41 tff(9713,plain,
% 28.20/18.41 (~(f1(f7(c2), f7(c2)) = f7(c2))),
% 28.20/18.41 inference(unit_resolution,[status(thm)],[9712, 9706, 292])).
% 28.20/18.41 tff(9714,plain,
% 28.20/18.41 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((f7(c2) = c3) | (f7(c2) = c4) | (~(f3(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f3(f7(c2), f7(c2)), f7(c2))) | (f1(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(c2), f1(f7(c2), f7(c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (f7(c2) = c3) | (f7(c2) = c4) | (~(f3(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f3(f7(c2), f7(c2)), f7(c2))) | (f1(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(c2), f1(f7(c2), f7(c2))))),
% 28.20/18.41 inference(rewrite,[status(thm)],[])).
% 28.20/18.41 tff(9715,plain,
% 28.20/18.41 (((f7(c2) = c4) | (f7(c2) = c3) | (f1(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(c2), f1(f7(c2), f7(c2))) | (~(f3(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f3(f7(c2), f7(c2)), f7(c2)))) <=> ((f7(c2) = c3) | (f7(c2) = c4) | (~(f3(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f3(f7(c2), f7(c2)), f7(c2))) | (f1(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(c2), f1(f7(c2), f7(c2))))),
% 28.20/18.41 inference(rewrite,[status(thm)],[])).
% 28.20/18.41 tff(9716,plain,
% 28.20/18.41 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((f7(c2) = c4) | (f7(c2) = c3) | (f1(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(c2), f1(f7(c2), f7(c2))) | (~(f3(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f3(f7(c2), f7(c2)), f7(c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((f7(c2) = c3) | (f7(c2) = c4) | (~(f3(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f3(f7(c2), f7(c2)), f7(c2))) | (f1(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(c2), f1(f7(c2), f7(c2)))))),
% 28.20/18.41 inference(monotonicity,[status(thm)],[9715])).
% 28.20/18.41 tff(9717,plain,
% 28.20/18.41 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((f7(c2) = c4) | (f7(c2) = c3) | (f1(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(c2), f1(f7(c2), f7(c2))) | (~(f3(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f3(f7(c2), f7(c2)), f7(c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (f7(c2) = c3) | (f7(c2) = c4) | (~(f3(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f3(f7(c2), f7(c2)), f7(c2))) | (f1(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(c2), f1(f7(c2), f7(c2))))),
% 28.20/18.41 inference(transitivity,[status(thm)],[9716, 9714])).
% 28.20/18.41 tff(9718,plain,
% 28.20/18.41 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((f7(c2) = c4) | (f7(c2) = c3) | (f1(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(c2), f1(f7(c2), f7(c2))) | (~(f3(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f3(f7(c2), f7(c2)), f7(c2))))),
% 28.20/18.41 inference(quant_inst,[status(thm)],[])).
% 28.20/18.41 tff(9719,plain,
% 28.20/18.41 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (f7(c2) = c3) | (f7(c2) = c4) | (~(f3(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f3(f7(c2), f7(c2)), f7(c2))) | (f1(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(c2), f1(f7(c2), f7(c2)))),
% 28.20/18.41 inference(modus_ponens,[status(thm)],[9718, 9717])).
% 28.20/18.41 tff(9720,plain,
% 28.20/18.41 ((~(f3(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f3(f7(c2), f7(c2)), f7(c2))) | (f1(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(c2), f1(f7(c2), f7(c2)))),
% 28.20/18.41 inference(unit_resolution,[status(thm)],[9719, 969, 9092, 9495])).
% 28.20/18.41 tff(9721,plain,
% 28.20/18.41 (big_f(f7(c2), f1(f7(c2), f7(c2)))),
% 28.20/18.41 inference(unit_resolution,[status(thm)],[9720, 9713, 9536, 9539])).
% 28.20/18.41 tff(9722,plain,
% 28.20/18.41 (big_f(c1, f1(c1, c1))),
% 28.20/18.41 inference(modus_ponens,[status(thm)],[9721, 9702])).
% 28.20/18.41 tff(9723,plain,
% 28.20/18.41 ($false),
% 28.20/18.41 inference(unit_resolution,[status(thm)],[9673, 9722])).
% 28.20/18.41 tff(9724,plain,(big_f(c1, f1(c1, c1)) | (~(f7(c2) = c1)) | (f7(c2) = c3) | (f7(c2) = c4) | (~big_f(f7(c2), c1)) | (~(f3(c1, c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.20/18.41 tff(9725,plain,
% 28.20/18.41 (big_f(c1, f1(c1, c1))),
% 28.20/18.41 inference(unit_resolution,[status(thm)],[9724, 9651, 22, 338, 9596, 9697])).
% 28.20/18.41 tff(9726,plain,
% 28.20/18.41 ((~big_f(f7(c2), f1(f7(c2), f7(c2)))) <=> (~big_f(c1, f1(c1, c1)))),
% 28.20/18.41 inference(monotonicity,[status(thm)],[9702])).
% 28.20/18.41 tff(9727,assumption,(~big_f(f7(c2), f1(f7(c2), f7(c2)))), introduced(assumption)).
% 28.20/18.41 tff(9728,plain,
% 28.20/18.41 (~big_f(c1, f1(c1, c1))),
% 28.20/18.41 inference(modus_ponens,[status(thm)],[9727, 9726])).
% 28.20/18.41 tff(9729,plain,
% 28.20/18.41 ($false),
% 28.20/18.41 inference(unit_resolution,[status(thm)],[4559, 9728])).
% 28.20/18.41 tff(9730,plain,(big_f(f7(c2), f1(f7(c2), f7(c2))) | (~big_f(c1, f1(c1, c1))) | (~(f7(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.20/18.41 tff(9731,plain,
% 28.20/18.41 (big_f(f7(c2), f1(f7(c2), f7(c2)))),
% 28.20/18.41 inference(unit_resolution,[status(thm)],[9730, 9725, 22])).
% 28.20/18.41 tff(9732,plain,
% 28.20/18.41 (~(f1(c1, c1) = c2)),
% 28.20/18.41 inference(unit_resolution,[status(thm)],[4561, 9725, 9654])).
% 28.20/18.41 tff(9733,plain,
% 28.20/18.41 (f1(c1, c1) = c1),
% 28.20/18.41 inference(unit_resolution,[status(thm)],[601, 9732])).
% 28.20/18.41 tff(9734,plain,
% 28.20/18.41 (f1(f7(c2), f7(c2)) = f7(c2)),
% 28.20/18.41 inference(modus_ponens,[status(thm)],[9733, 9668])).
% 28.20/18.41 tff(9735,plain,
% 28.20/18.41 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c2) = c3) | (f7(c2) = c4) | (~(f3(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f3(f7(c2), f7(c2)), f7(c2))) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2)))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (f7(c2) = c3) | (f7(c2) = c4) | (~(f3(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f3(f7(c2), f7(c2)), f7(c2))) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2)))))),
% 28.20/18.41 inference(rewrite,[status(thm)],[])).
% 28.20/18.41 tff(9736,plain,
% 28.20/18.41 (((f7(c2) = c4) | (f7(c2) = c3) | (~(f3(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f3(f7(c2), f7(c2)), f7(c2))) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2))))) <=> ((f7(c2) = c3) | (f7(c2) = c4) | (~(f3(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f3(f7(c2), f7(c2)), f7(c2))) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2)))))),
% 28.20/18.41 inference(rewrite,[status(thm)],[])).
% 28.20/18.41 tff(9737,plain,
% 28.20/18.41 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c2) = c4) | (f7(c2) = c3) | (~(f3(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f3(f7(c2), f7(c2)), f7(c2))) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2)))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c2) = c3) | (f7(c2) = c4) | (~(f3(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f3(f7(c2), f7(c2)), f7(c2))) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2))))))),
% 28.20/18.41 inference(monotonicity,[status(thm)],[9736])).
% 28.20/18.41 tff(9738,plain,
% 28.20/18.41 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c2) = c4) | (f7(c2) = c3) | (~(f3(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f3(f7(c2), f7(c2)), f7(c2))) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2)))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (f7(c2) = c3) | (f7(c2) = c4) | (~(f3(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f3(f7(c2), f7(c2)), f7(c2))) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2)))))),
% 28.20/18.41 inference(transitivity,[status(thm)],[9737, 9735])).
% 28.20/18.41 tff(9739,plain,
% 28.20/18.41 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c2) = c4) | (f7(c2) = c3) | (~(f3(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f3(f7(c2), f7(c2)), f7(c2))) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2)))))),
% 28.20/18.41 inference(quant_inst,[status(thm)],[])).
% 28.20/18.41 tff(9740,plain,
% 28.20/18.41 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (f7(c2) = c3) | (f7(c2) = c4) | (~(f3(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f3(f7(c2), f7(c2)), f7(c2))) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2))))),
% 28.20/18.41 inference(modus_ponens,[status(thm)],[9739, 9738])).
% 28.20/18.41 tff(9741,plain,
% 28.20/18.41 ((~(f3(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f3(f7(c2), f7(c2)), f7(c2)))),
% 28.20/18.41 inference(unit_resolution,[status(thm)],[9740, 933, 9596, 9651, 9734, 9731])).
% 28.20/18.41 tff(9742,plain,
% 28.20/18.41 ($false),
% 28.20/18.41 inference(unit_resolution,[status(thm)],[9741, 9701, 9698])).
% 28.20/18.41 tff(9743,plain,(big_f(c2, c1) | (~big_f(f7(c2), c1)) | (f7(c2) = c2) | (~(f4(c4) = c2)) | big_f(f7(c2), c2) | (~big_f(c2, c2)) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.20/18.41 tff(9744,plain,
% 28.20/18.41 (~big_f(c2, c2)),
% 28.20/18.41 inference(unit_resolution,[status(thm)],[9743, 1521, 17, 79, 2, 9485, 122])).
% 28.20/18.41 tff(9745,plain,
% 28.20/18.41 ((~(c2 = c3)) <=> (~(c3 = c2))),
% 28.20/18.41 inference(monotonicity,[status(thm)],[127])).
% 28.20/18.41 tff(9746,plain,
% 28.20/18.41 ((f7(c2) = c3) <=> (f7(c2) = c2)),
% 28.20/18.41 inference(monotonicity,[status(thm)],[1816])).
% 28.20/18.41 tff(9747,plain,
% 28.20/18.41 ((f7(c2) = c2) <=> (f7(c2) = c3)),
% 28.20/18.41 inference(symmetry,[status(thm)],[9746])).
% 28.20/18.41 tff(9748,plain,
% 28.20/18.41 ((~(f7(c2) = c2)) <=> (~(f7(c2) = c3))),
% 28.20/18.41 inference(monotonicity,[status(thm)],[9747])).
% 28.20/18.41 tff(9749,plain,
% 28.20/18.41 (~(f7(c2) = c3)),
% 28.20/18.41 inference(modus_ponens,[status(thm)],[17, 9748])).
% 28.20/18.41 tff(9750,plain,
% 28.20/18.41 ((f7(c2) = c2) <=> (c1 = c3)),
% 28.20/18.41 inference(transitivity,[status(thm)],[9747, 9088])).
% 28.20/18.41 tff(9751,plain,
% 28.20/18.41 ((~(f7(c2) = c2)) <=> (~(c1 = c3))),
% 28.20/18.41 inference(monotonicity,[status(thm)],[9750])).
% 28.20/18.41 tff(9752,plain,
% 28.20/18.41 (~(c1 = c3)),
% 28.20/18.41 inference(modus_ponens,[status(thm)],[17, 9751])).
% 28.20/18.41 tff(9753,plain,
% 28.20/18.41 (~(c4 = c1)),
% 28.20/18.41 inference(unit_resolution,[status(thm)],[9641, 338, 1521, 17, 9092, 79])).
% 28.20/18.41 tff(9754,plain,
% 28.20/18.41 (c4 = c2),
% 28.20/18.41 inference(unit_resolution,[status(thm)],[461, 9753])).
% 28.20/18.41 tff(9755,plain,
% 28.20/18.41 (c2 = c4),
% 28.20/18.41 inference(symmetry,[status(thm)],[9754])).
% 28.20/18.41 tff(9756,plain,
% 28.20/18.41 (f4(c2) = f4(c4)),
% 28.20/18.41 inference(monotonicity,[status(thm)],[9755])).
% 28.20/18.41 tff(9757,plain,
% 28.20/18.41 (f4(c4) = f4(c2)),
% 28.20/18.41 inference(symmetry,[status(thm)],[9756])).
% 28.20/18.41 tff(9758,plain,
% 28.20/18.41 (c2 = f4(c2)),
% 28.20/18.41 inference(transitivity,[status(thm)],[436, 9757])).
% 28.20/18.41 tff(9759,plain,
% 28.20/18.41 (c2 = c4),
% 28.20/18.41 inference(modus_ponens,[status(thm)],[9754, 159])).
% 28.20/18.41 tff(9760,plain,
% 28.20/18.41 (f1(c1, c1) = c2),
% 28.20/18.41 inference(unit_resolution,[status(thm)],[601, 9710])).
% 28.20/18.41 tff(9761,plain,
% 28.20/18.41 (big_f(c1, f1(c1, c1))),
% 28.20/18.41 inference(unit_resolution,[status(thm)],[656, 9710, 121, 168, 631, 630])).
% 28.20/18.41 tff(9762,plain,
% 28.20/18.41 ($false),
% 28.20/18.41 inference(unit_resolution,[status(thm)],[4561, 9761, 9760, 27])).
% 28.20/18.41 tff(9763,plain,((f1(c1, c1) = c1) | big_f(c1, c2) | big_f(c2, c2) | (c1 = c3) | (~(c2 = c4)) | (~(c2 = f4(c2)))), inference(lemma,lemma(discharge,[]))).
% 28.20/18.41 tff(9764,plain,
% 28.20/18.41 (f1(c1, c1) = c1),
% 28.20/18.41 inference(unit_resolution,[status(thm)],[9763, 9654, 121, 168, 9759, 9758])).
% 28.20/18.41 tff(9765,plain,
% 28.20/18.41 (f1(f7(c2), f7(c2)) = f7(c2)),
% 28.20/18.41 inference(transitivity,[status(thm)],[9622, 9764, 125])).
% 28.20/18.41 tff(9766,plain,
% 28.20/18.41 (f1(f7(c2), f7(c2)) = c1),
% 28.20/18.41 inference(transitivity,[status(thm)],[9622, 9764])).
% 28.20/18.41 tff(9767,plain,
% 28.20/18.41 (big_f(f7(c2), f1(f7(c2), f7(c2))) <=> big_f(f7(c2), c1)),
% 28.20/18.41 inference(monotonicity,[status(thm)],[9766])).
% 28.20/18.41 tff(9768,plain,
% 28.20/18.41 (big_f(f7(c2), c1) <=> big_f(f7(c2), f1(f7(c2), f7(c2)))),
% 28.20/18.41 inference(symmetry,[status(thm)],[9767])).
% 28.20/18.41 tff(9769,plain,
% 28.20/18.41 (big_f(f7(c2), f1(f7(c2), f7(c2)))),
% 28.20/18.41 inference(modus_ponens,[status(thm)],[338, 9768])).
% 28.20/18.41 tff(9770,plain,
% 28.20/18.41 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (f7(c2) = c3) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (f7(c2) = c3) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2)))))),
% 28.20/18.41 inference(rewrite,[status(thm)],[])).
% 28.20/18.41 tff(9771,plain,
% 28.20/18.41 (((f7(c2) = c3) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2))))) <=> ((~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (f7(c2) = c3) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2)))))),
% 28.20/18.41 inference(rewrite,[status(thm)],[])).
% 28.20/18.41 tff(9772,plain,
% 28.20/18.41 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c2) = c3) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (f7(c2) = c3) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2))))))),
% 28.20/18.41 inference(monotonicity,[status(thm)],[9771])).
% 28.20/18.41 tff(9773,plain,
% 28.20/18.41 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c2) = c3) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (f7(c2) = c3) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2)))))),
% 28.20/18.41 inference(transitivity,[status(thm)],[9772, 9770])).
% 28.20/18.41 tff(9774,plain,
% 28.20/18.41 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c2) = c3) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2)))))),
% 28.20/18.41 inference(quant_inst,[status(thm)],[])).
% 28.20/18.41 tff(9775,plain,
% 28.20/18.41 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (f7(c2) = c3) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2))))),
% 28.20/18.41 inference(modus_ponens,[status(thm)],[9774, 9773])).
% 28.20/18.41 tff(9776,plain,
% 28.20/18.41 ((~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2))))),
% 28.20/18.41 inference(unit_resolution,[status(thm)],[9775, 447, 9759, 9758, 121, 9092])).
% 28.20/18.41 tff(9777,plain,
% 28.20/18.41 ($false),
% 28.20/18.41 inference(unit_resolution,[status(thm)],[9776, 9769, 9765])).
% 28.20/18.41 tff(9778,plain,((~big_f(f7(c2), c1)) | big_f(c2, c2) | (f7(c2) = c3) | (c1 = c3) | (~(f4(c4) = c2)) | big_f(f7(c2), c2) | (f7(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 28.20/18.41 tff(9779,plain,
% 28.20/18.41 ($false),
% 28.20/18.41 inference(unit_resolution,[status(thm)],[9778, 9752, 9749, 338, 1521, 79, 121, 17])).
% 28.20/18.41 tff(9780,plain,((~(c2 = c3)) | (~big_f(f7(c2), c1)) | big_f(f7(c2), c2) | (~(f4(c4) = c2)) | big_f(c2, c2) | (f7(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 28.20/18.41 tff(9781,plain,
% 28.20/18.41 (~(c2 = c3)),
% 28.20/18.41 inference(unit_resolution,[status(thm)],[9780, 1521, 338, 79, 121, 17])).
% 28.20/18.41 tff(9782,plain,
% 28.20/18.41 (~(c3 = c2)),
% 28.20/18.41 inference(modus_ponens,[status(thm)],[9781, 9745])).
% 28.20/18.41 tff(9783,plain,
% 28.20/18.41 (c3 = c1),
% 28.20/18.41 inference(unit_resolution,[status(thm)],[180, 9782])).
% 28.20/18.41 tff(9784,plain,
% 28.20/18.41 (c1 = c3),
% 28.20/18.41 inference(symmetry,[status(thm)],[9783])).
% 28.20/18.41 tff(9785,plain,
% 28.20/18.41 (f6(c1, c1) = f6(f7(c2), c3)),
% 28.20/18.41 inference(monotonicity,[status(thm)],[125, 9784])).
% 28.20/18.41 tff(9786,plain,
% 28.20/18.41 (f6(f7(c2), c3) = f6(c1, c1)),
% 28.20/18.41 inference(symmetry,[status(thm)],[9785])).
% 28.20/18.41 tff(9787,plain,
% 28.20/18.41 (big_f(f7(f7(c2)), f6(f7(c2), c3)) <=> big_f(f7(c1), f6(c1, c1))),
% 28.20/18.41 inference(monotonicity,[status(thm)],[8077, 9786])).
% 28.20/18.41 tff(9788,plain,
% 28.20/18.41 (big_f(f7(c1), f6(c1, c1)) <=> big_f(f7(f7(c2)), f6(f7(c2), c3))),
% 28.20/18.41 inference(symmetry,[status(thm)],[9787])).
% 28.20/18.41 tff(9789,plain,
% 28.20/18.41 (f6(f7(c2), f7(c2)) = f6(c1, c1)),
% 28.20/18.41 inference(monotonicity,[status(thm)],[22, 22])).
% 28.20/18.41 tff(9790,plain,
% 28.20/18.41 (big_f(f7(f7(c2)), f6(f7(c2), f7(c2))) <=> big_f(f7(c1), f6(c1, c1))),
% 28.20/18.41 inference(monotonicity,[status(thm)],[8077, 9789])).
% 28.20/18.41 tff(9791,plain,
% 28.20/18.41 (big_f(f7(f7(c2)), f6(f7(c2), f7(c2))) <=> big_f(f7(f7(c2)), f6(f7(c2), c3))),
% 28.20/18.41 inference(transitivity,[status(thm)],[9790, 9788])).
% 28.20/18.41 tff(9792,plain,
% 28.20/18.41 ((~big_f(f7(f7(c2)), f6(f7(c2), f7(c2)))) <=> (~big_f(f7(f7(c2)), f6(f7(c2), c3)))),
% 28.20/18.41 inference(monotonicity,[status(thm)],[9791])).
% 28.20/18.41 tff(9793,plain,
% 28.20/18.41 ((~big_f(f7(c2), c2)) <=> (~big_f(c1, f10(f7(f4(c4)))))),
% 28.20/18.41 inference(monotonicity,[status(thm)],[8583])).
% 28.20/18.41 tff(9794,plain,
% 28.20/18.41 (~big_f(c1, f10(f7(f4(c4))))),
% 28.20/18.41 inference(modus_ponens,[status(thm)],[1521, 9793])).
% 28.20/18.41 tff(9795,plain,
% 28.20/18.41 (big_f(c1, f10(c1)) <=> big_f(c1, f10(f7(f4(c4))))),
% 28.20/18.41 inference(monotonicity,[status(thm)],[8504])).
% 28.20/18.41 tff(9796,plain,
% 28.20/18.41 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1))),
% 28.20/18.41 inference(rewrite,[status(thm)],[])).
% 28.20/18.41 tff(9797,plain,
% 28.20/18.41 (((f10(c1) = c1) | big_f(c1, f10(c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1)) | (~(c1 = f8(c1)))) <=> ((f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1))),
% 28.20/18.41 inference(rewrite,[status(thm)],[])).
% 28.20/18.41 tff(9798,plain,
% 28.20/18.41 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | big_f(c1, f10(c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1)) | (~(c1 = f8(c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1)))),
% 28.20/18.41 inference(monotonicity,[status(thm)],[9797])).
% 28.20/18.41 tff(9799,plain,
% 28.20/18.41 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | big_f(c1, f10(c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1)) | (~(c1 = f8(c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1))),
% 28.20/18.41 inference(transitivity,[status(thm)],[9798, 9796])).
% 28.20/18.41 tff(9800,plain,
% 28.20/18.41 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | big_f(c1, f10(c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1)) | (~(c1 = f8(c1))))),
% 28.20/18.41 inference(quant_inst,[status(thm)],[])).
% 28.20/18.41 tff(9801,plain,
% 28.20/18.41 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1)),
% 28.20/18.42 inference(modus_ponens,[status(thm)],[9800, 9799])).
% 28.20/18.42 tff(9802,plain,
% 28.20/18.42 ($false),
% 28.20/18.42 inference(unit_resolution,[status(thm)],[9801, 2994, 4234, 3, 3031, 3030, 65, 28])).
% 28.20/18.42 tff(9803,plain,((f6(c1, c1) = c1) | (~(f7(c1) = c1)) | (f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | big_f(f7(c1), f6(c1, c1))), inference(lemma,lemma(discharge,[]))).
% 28.20/18.42 tff(9804,plain,
% 28.20/18.42 (~(c1 = f8(c1))),
% 28.20/18.42 inference(unit_resolution,[status(thm)],[9803, 28, 3, 3030, 65, 4234])).
% 28.20/18.42 tff(9805,plain,
% 28.20/18.42 (c1 = f8(c1)),
% 28.20/18.42 inference(modus_ponens,[status(thm)],[3018, 3028])).
% 28.20/18.42 tff(9806,assumption,(~(c1 = f8(c1))), introduced(assumption)).
% 28.20/18.42 tff(9807,plain,
% 28.20/18.42 ($false),
% 28.20/18.42 inference(unit_resolution,[status(thm)],[9806, 9805])).
% 28.20/18.42 tff(9808,plain,((~(f8(c1) = c1)) | (c1 = f8(c1))), inference(lemma,lemma(discharge,[]))).
% 28.20/18.42 tff(9809,plain,
% 28.20/18.42 (~(f8(c1) = c1)),
% 28.20/18.42 inference(unit_resolution,[status(thm)],[9808, 9804])).
% 28.20/18.42 tff(9810,plain,
% 28.20/18.42 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1))),
% 28.20/18.42 inference(rewrite,[status(thm)],[])).
% 28.20/18.42 tff(9811,plain,
% 28.20/18.42 (((f10(c1) = c1) | big_f(c2, f10(c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1)) | (~(c2 = f8(c1)))) <=> (big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1))),
% 28.20/18.42 inference(rewrite,[status(thm)],[])).
% 28.20/18.42 tff(9812,plain,
% 28.20/18.42 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | big_f(c2, f10(c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1)) | (~(c2 = f8(c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1)))),
% 28.20/18.42 inference(monotonicity,[status(thm)],[9811])).
% 28.20/18.42 tff(9813,plain,
% 28.20/18.42 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | big_f(c2, f10(c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1)) | (~(c2 = f8(c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1))),
% 28.20/18.42 inference(transitivity,[status(thm)],[9812, 9810])).
% 28.20/18.42 tff(9814,plain,
% 28.20/18.42 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | big_f(c2, f10(c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1)) | (~(c2 = f8(c1))))),
% 28.20/18.42 inference(quant_inst,[status(thm)],[])).
% 28.20/18.42 tff(9815,plain,
% 28.20/18.42 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1)),
% 28.20/18.42 inference(modus_ponens,[status(thm)],[9814, 9813])).
% 28.20/18.42 tff(9816,plain,
% 28.20/18.42 (big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1)),
% 28.20/18.42 inference(unit_resolution,[status(thm)],[9815, 2994])).
% 28.20/18.42 tff(9817,plain,
% 28.20/18.42 (~(c2 = f8(c1))),
% 28.20/18.42 inference(unit_resolution,[status(thm)],[9816, 28, 4234, 2946, 3, 65])).
% 28.20/18.42 tff(9818,plain,
% 28.20/18.42 (~(f8(c1) = c2)),
% 28.20/18.42 inference(unit_resolution,[status(thm)],[1675, 9817])).
% 28.20/18.42 tff(9819,plain,
% 28.20/18.42 ($false),
% 28.20/18.42 inference(unit_resolution,[status(thm)],[1680, 9818, 9809])).
% 28.20/18.42 tff(9820,plain,((f6(c1, c1) = c1) | (~(f7(c1) = c1)) | big_f(c2, f10(c1)) | (f10(c1) = c1) | big_f(f7(c1), f6(c1, c1)) | big_f(c1, f10(c1))), inference(lemma,lemma(discharge,[]))).
% 28.20/18.42 tff(9821,plain,
% 28.20/18.42 (f6(c1, c1) = c1),
% 28.20/18.42 inference(unit_resolution,[status(thm)],[9820, 65, 2946, 3, 4234, 3030])).
% 28.20/18.42 tff(9822,plain,
% 28.20/18.42 (big_f(f7(c1), f6(c1, c1)) <=> big_f(f7(c2), c1)),
% 28.20/18.42 inference(monotonicity,[status(thm)],[8286, 9821])).
% 28.20/18.42 tff(9823,plain,
% 28.20/18.42 (big_f(f7(c2), c1) <=> big_f(f7(c1), f6(c1, c1))),
% 28.20/18.42 inference(symmetry,[status(thm)],[9822])).
% 28.20/18.42 tff(9824,plain,
% 28.20/18.42 (big_f(f7(c1), f6(c1, c1))),
% 28.20/18.42 inference(modus_ponens,[status(thm)],[338, 9823])).
% 28.20/18.42 tff(9825,plain,
% 28.20/18.42 ($false),
% 28.20/18.42 inference(unit_resolution,[status(thm)],[65, 9824])).
% 28.20/18.42 tff(9826,plain,(big_f(f7(c1), f6(c1, c1)) | (~big_f(f7(c2), c1)) | (~(f7(c1) = c1)) | (~(f7(c2) = c1)) | big_f(c2, f10(c1)) | (f10(c1) = c1) | big_f(c1, f10(c1))), inference(lemma,lemma(discharge,[]))).
% 28.20/18.42 tff(9827,plain,
% 28.20/18.42 (big_f(c1, f10(c1))),
% 28.20/18.42 inference(unit_resolution,[status(thm)],[9826, 8451, 4234, 292, 338, 65, 3])).
% 28.20/18.42 tff(9828,plain,
% 28.20/18.42 (big_f(c1, f10(f7(f4(c4))))),
% 28.20/18.42 inference(modus_ponens,[status(thm)],[9827, 9795])).
% 28.20/18.42 tff(9829,plain,
% 28.20/18.42 ($false),
% 28.20/18.42 inference(unit_resolution,[status(thm)],[9828, 9794])).
% 28.20/18.42 tff(9830,plain,((f10(c1) = c1) | big_f(f7(c2), c2) | (~(f7(c2) = c1)) | (~(f4(c4) = c2)) | (~(f7(c1) = c1)) | (~big_f(f7(c2), c1)) | big_f(f7(c1), f6(c1, c1)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 28.20/18.42 tff(9831,plain,
% 28.20/18.42 (big_f(f7(c1), f6(c1, c1))),
% 28.20/18.42 inference(unit_resolution,[status(thm)],[9830, 3, 22, 79, 4234, 338, 1521, 121])).
% 28.20/18.42 tff(9832,plain,
% 28.20/18.42 ((f7(c2) = f8(f7(c2))) <=> (c1 = f8(f7(f4(c4))))),
% 28.20/18.42 inference(monotonicity,[status(thm)],[22, 8536])).
% 28.20/18.42 tff(9833,plain,
% 28.20/18.42 ((f7(c2) = f8(f7(c2))) <=> (f8(f7(f4(c4))) = c1)),
% 28.20/18.42 inference(transitivity,[status(thm)],[9832, 8517])).
% 28.20/18.42 tff(9834,plain,
% 28.20/18.42 ((f8(f7(f4(c4))) = c1) <=> (f7(c2) = f8(f7(c2)))),
% 28.20/18.42 inference(symmetry,[status(thm)],[9833])).
% 28.20/18.42 tff(9835,plain,
% 28.20/18.42 (f8(c1) = f8(f7(f4(c4)))),
% 28.20/18.42 inference(monotonicity,[status(thm)],[8115])).
% 28.20/18.42 tff(9836,plain,
% 28.20/18.42 ((f8(c1) = c1) <=> (f8(f7(f4(c4))) = c1)),
% 28.20/18.42 inference(monotonicity,[status(thm)],[9835])).
% 28.20/18.42 tff(9837,plain,
% 28.20/18.42 ((f8(c1) = c1) <=> (f7(c2) = f8(f7(c2)))),
% 28.20/18.42 inference(transitivity,[status(thm)],[9836, 9834])).
% 28.20/18.42 tff(9838,plain,
% 28.20/18.42 (f6(f7(c2), c3) = f6(c1, c1)),
% 28.20/18.42 inference(symmetry,[status(thm)],[5969])).
% 28.20/18.42 tff(9839,plain,
% 28.20/18.42 (f7(f10(c1)) = f7(c1)),
% 28.20/18.42 inference(transitivity,[status(thm)],[219, 22, 5544])).
% 28.20/18.42 tff(9840,plain,
% 28.20/18.42 (big_f(f7(f10(c1)), f6(f7(c2), c3)) <=> big_f(f7(c1), f6(c1, c1))),
% 28.20/18.42 inference(monotonicity,[status(thm)],[9839, 9838])).
% 28.20/18.42 tff(9841,plain,
% 28.20/18.42 (big_f(f7(c1), f6(c1, c1)) <=> big_f(f7(f10(c1)), f6(f7(c2), c3))),
% 28.20/18.42 inference(symmetry,[status(thm)],[9840])).
% 28.20/18.42 tff(9842,plain,
% 28.20/18.42 (big_f(f7(f10(c1)), f6(f7(c2), c3))),
% 28.20/18.42 inference(modus_ponens,[status(thm)],[5964, 9841])).
% 28.20/18.42 tff(9843,plain,
% 28.20/18.42 ((~(f10(c1) = c1)) <=> (~(f10(f7(c2)) = f7(c2)))),
% 28.20/18.42 inference(monotonicity,[status(thm)],[8182])).
% 28.20/18.42 tff(9844,plain,
% 28.20/18.42 (~(f10(f7(c2)) = f7(c2))),
% 28.20/18.42 inference(modus_ponens,[status(thm)],[3, 9843])).
% 28.20/18.42 tff(9845,plain,
% 28.20/18.42 (big_f(f7(c2), f10(f7(c2))) <=> big_f(c1, f10(f7(f4(c4))))),
% 28.20/18.42 inference(monotonicity,[status(thm)],[22, 8167])).
% 28.20/18.42 tff(9846,plain,
% 28.20/18.42 (big_f(c1, f10(f7(f4(c4)))) <=> big_f(f7(c2), f10(f7(c2)))),
% 28.20/18.42 inference(symmetry,[status(thm)],[9845])).
% 28.20/18.42 tff(9847,plain,
% 28.20/18.42 (f10(f7(f4(c4))) = c2),
% 28.20/18.42 inference(transitivity,[status(thm)],[8082, 15])).
% 28.20/18.42 tff(9848,plain,
% 28.20/18.42 (big_f(c1, f10(f7(f4(c4)))) <=> big_f(f7(c2), c2)),
% 28.20/18.42 inference(monotonicity,[status(thm)],[125, 9847])).
% 28.20/18.42 tff(9849,plain,
% 28.20/18.42 (big_f(f7(c2), c2) <=> big_f(c1, f10(f7(f4(c4))))),
% 28.20/18.42 inference(symmetry,[status(thm)],[9848])).
% 28.20/18.42 tff(9850,plain,
% 28.20/18.42 (big_f(f7(c2), c2) <=> big_f(f7(c2), f10(f7(c2)))),
% 28.20/18.42 inference(transitivity,[status(thm)],[9849, 9846])).
% 28.20/18.42 tff(9851,plain,
% 28.20/18.42 ((~big_f(f7(c2), c2)) <=> (~big_f(f7(c2), f10(f7(c2))))),
% 28.20/18.42 inference(monotonicity,[status(thm)],[9850])).
% 28.20/18.42 tff(9852,plain,
% 28.20/18.42 (~big_f(f7(c2), f10(f7(c2)))),
% 28.20/18.42 inference(modus_ponens,[status(thm)],[1521, 9851])).
% 28.20/18.42 tff(9853,plain,
% 28.20/18.42 (big_f(c2, f10(f7(f4(c4)))) <=> big_f(c2, c2)),
% 28.20/18.42 inference(monotonicity,[status(thm)],[9847])).
% 28.20/18.42 tff(9854,plain,
% 28.20/18.42 (big_f(c2, c2) <=> big_f(c2, f10(f7(f4(c4))))),
% 28.20/18.42 inference(symmetry,[status(thm)],[9853])).
% 28.20/18.42 tff(9855,plain,
% 28.20/18.42 (big_f(c2, c2) <=> big_f(c2, f10(f7(c2)))),
% 28.20/18.42 inference(transitivity,[status(thm)],[9854, 8510])).
% 28.20/18.42 tff(9856,plain,
% 28.20/18.42 ((~big_f(c2, c2)) <=> (~big_f(c2, f10(f7(c2))))),
% 28.20/18.42 inference(monotonicity,[status(thm)],[9855])).
% 28.20/18.42 tff(9857,plain,
% 28.20/18.42 (~big_f(c2, f10(f7(c2)))),
% 28.20/18.42 inference(modus_ponens,[status(thm)],[121, 9856])).
% 28.20/18.42 tff(9858,plain,
% 28.20/18.42 ((c2 = f8(c1)) <=> (c2 = f8(f7(f4(c4))))),
% 28.20/18.42 inference(monotonicity,[status(thm)],[9835])).
% 28.20/18.42 tff(9859,plain,
% 28.20/18.42 ((c2 = f8(f7(f4(c4)))) <=> (c2 = f8(c1))),
% 28.20/18.42 inference(symmetry,[status(thm)],[9858])).
% 28.20/18.42 tff(9860,plain,
% 28.20/18.42 ((c2 = f8(f7(c2))) <=> (f8(c1) = c2)),
% 28.20/18.42 inference(transitivity,[status(thm)],[8537, 9859, 2782])).
% 28.20/18.42 tff(9861,plain,
% 28.20/18.42 ((~(c2 = f8(f7(c2)))) <=> (~(f8(c1) = c2))),
% 28.20/18.42 inference(monotonicity,[status(thm)],[9860])).
% 28.20/18.42 tff(9862,plain,
% 28.20/18.42 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (f10(f7(c2)) = f7(c2)) | big_f(c2, f10(f7(c2))) | (~(c2 = f8(f7(c2)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (f10(f7(c2)) = f7(c2)) | big_f(c2, f10(f7(c2))) | (~(c2 = f8(f7(c2)))))),
% 28.20/18.42 inference(rewrite,[status(thm)],[])).
% 28.20/18.42 tff(9863,plain,
% 28.20/18.42 (((~(c2 = f5(c2))) | (f10(f7(c2)) = f7(c2)) | big_f(c2, f10(f7(c2))) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(c2 = f8(f7(c2))))) <=> ((f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (f10(f7(c2)) = f7(c2)) | big_f(c2, f10(f7(c2))) | (~(c2 = f8(f7(c2)))))),
% 28.20/18.42 inference(rewrite,[status(thm)],[])).
% 28.20/18.42 tff(9864,plain,
% 28.20/18.42 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c2 = f5(c2))) | (f10(f7(c2)) = f7(c2)) | big_f(c2, f10(f7(c2))) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(c2 = f8(f7(c2)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (f10(f7(c2)) = f7(c2)) | big_f(c2, f10(f7(c2))) | (~(c2 = f8(f7(c2))))))),
% 28.20/18.42 inference(monotonicity,[status(thm)],[9863])).
% 28.20/18.42 tff(9865,plain,
% 28.20/18.42 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c2 = f5(c2))) | (f10(f7(c2)) = f7(c2)) | big_f(c2, f10(f7(c2))) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(c2 = f8(f7(c2)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (f10(f7(c2)) = f7(c2)) | big_f(c2, f10(f7(c2))) | (~(c2 = f8(f7(c2)))))),
% 28.20/18.42 inference(transitivity,[status(thm)],[9864, 9862])).
% 28.20/18.42 tff(9866,plain,
% 28.20/18.42 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c2 = f5(c2))) | (f10(f7(c2)) = f7(c2)) | big_f(c2, f10(f7(c2))) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(c2 = f8(f7(c2)))))),
% 28.20/18.42 inference(quant_inst,[status(thm)],[])).
% 28.20/18.42 tff(9867,plain,
% 28.20/18.42 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (f10(f7(c2)) = f7(c2)) | big_f(c2, f10(f7(c2))) | (~(c2 = f8(f7(c2))))),
% 28.20/18.42 inference(modus_ponens,[status(thm)],[9866, 9865])).
% 28.20/18.42 tff(9868,plain,
% 28.20/18.42 ((~(c2 = f5(c2))) | (~(c2 = f8(f7(c2))))),
% 28.20/18.42 inference(unit_resolution,[status(thm)],[9867, 1745, 17, 1521, 8523, 8522])).
% 28.20/18.42 tff(9869,plain,
% 28.20/18.42 (~(c2 = f8(f7(c2)))),
% 28.20/18.42 inference(unit_resolution,[status(thm)],[9868, 5124])).
% 28.20/18.42 tff(9870,plain,
% 28.20/18.42 (~(f8(c1) = c2)),
% 28.20/18.42 inference(modus_ponens,[status(thm)],[9869, 9861])).
% 28.20/18.42 tff(9871,plain,
% 28.20/18.42 ((f8(f7(f4(c4))) = c1) <=> (f8(c1) = c1)),
% 28.20/18.42 inference(symmetry,[status(thm)],[9836])).
% 28.20/18.42 tff(9872,plain,
% 28.20/18.42 ((f7(c2) = f8(f7(c2))) <=> (f8(c1) = c1)),
% 28.20/18.42 inference(transitivity,[status(thm)],[9833, 9871])).
% 28.20/18.42 tff(9873,plain,
% 28.20/18.42 ((~(f7(c2) = f8(f7(c2)))) <=> (~(f8(c1) = c1))),
% 28.20/18.42 inference(monotonicity,[status(thm)],[9872])).
% 28.20/18.42 tff(9874,plain,
% 28.20/18.42 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (f10(f7(c2)) = f7(c2)) | big_f(f7(c2), f10(f7(c2))) | (~(f7(c2) = f8(f7(c2)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (f10(f7(c2)) = f7(c2)) | big_f(f7(c2), f10(f7(c2))) | (~(f7(c2) = f8(f7(c2)))))),
% 28.20/18.42 inference(rewrite,[status(thm)],[])).
% 28.20/18.42 tff(9875,plain,
% 28.20/18.42 (((~(c2 = f5(c2))) | (f10(f7(c2)) = f7(c2)) | big_f(f7(c2), f10(f7(c2))) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(f7(c2) = f8(f7(c2))))) <=> ((f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (f10(f7(c2)) = f7(c2)) | big_f(f7(c2), f10(f7(c2))) | (~(f7(c2) = f8(f7(c2)))))),
% 28.20/18.42 inference(rewrite,[status(thm)],[])).
% 28.20/18.42 tff(9876,plain,
% 28.20/18.42 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c2 = f5(c2))) | (f10(f7(c2)) = f7(c2)) | big_f(f7(c2), f10(f7(c2))) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(f7(c2) = f8(f7(c2)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (f10(f7(c2)) = f7(c2)) | big_f(f7(c2), f10(f7(c2))) | (~(f7(c2) = f8(f7(c2))))))),
% 28.20/18.42 inference(monotonicity,[status(thm)],[9875])).
% 28.20/18.42 tff(9877,plain,
% 28.20/18.42 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c2 = f5(c2))) | (f10(f7(c2)) = f7(c2)) | big_f(f7(c2), f10(f7(c2))) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(f7(c2) = f8(f7(c2)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (f10(f7(c2)) = f7(c2)) | big_f(f7(c2), f10(f7(c2))) | (~(f7(c2) = f8(f7(c2)))))),
% 28.20/18.42 inference(transitivity,[status(thm)],[9876, 9874])).
% 28.20/18.42 tff(9878,plain,
% 28.20/18.42 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c2 = f5(c2))) | (f10(f7(c2)) = f7(c2)) | big_f(f7(c2), f10(f7(c2))) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(f7(c2) = f8(f7(c2)))))),
% 28.20/18.42 inference(quant_inst,[status(thm)],[])).
% 28.20/18.42 tff(9879,plain,
% 28.20/18.42 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (f10(f7(c2)) = f7(c2)) | big_f(f7(c2), f10(f7(c2))) | (~(f7(c2) = f8(f7(c2))))),
% 28.24/18.42 inference(modus_ponens,[status(thm)],[9878, 9877])).
% 28.24/18.42 tff(9880,plain,
% 28.24/18.42 ((~(c2 = f5(c2))) | (~(f7(c2) = f8(f7(c2))))),
% 28.24/18.42 inference(unit_resolution,[status(thm)],[9879, 1745, 17, 1521, 8556, 8523])).
% 28.24/18.42 tff(9881,plain,
% 28.24/18.42 (~(f7(c2) = f8(f7(c2)))),
% 28.24/18.42 inference(unit_resolution,[status(thm)],[9880, 5124])).
% 28.24/18.42 tff(9882,plain,
% 28.24/18.42 (~(f8(c1) = c1)),
% 28.24/18.42 inference(modus_ponens,[status(thm)],[9881, 9873])).
% 28.24/18.42 tff(9883,plain,
% 28.24/18.42 ($false),
% 28.24/18.42 inference(unit_resolution,[status(thm)],[1680, 9882, 9870])).
% 28.24/18.42 tff(9884,plain,((~(c2 = f5(c2))) | (~(f4(c4) = c2)) | (f7(c2) = c2) | big_f(f7(c2), c2) | big_f(f7(c2), f10(f7(c2))) | (f10(f7(c2)) = f7(c2)) | big_f(c2, f10(f7(c2)))), inference(lemma,lemma(discharge,[]))).
% 28.24/18.42 tff(9885,plain,
% 28.24/18.42 (~(c2 = f5(c2))),
% 28.24/18.42 inference(unit_resolution,[status(thm)],[9884, 9857, 17, 1521, 9852, 9844, 79])).
% 28.24/18.42 tff(9886,plain,
% 28.24/18.42 (~(f5(c2) = c2)),
% 28.24/18.42 inference(unit_resolution,[status(thm)],[8113, 9885])).
% 28.24/18.42 tff(9887,plain,
% 28.24/18.42 (f5(c2) = c1),
% 28.24/18.42 inference(unit_resolution,[status(thm)],[1547, 9886])).
% 28.24/18.42 tff(9888,plain,
% 28.24/18.42 (f5(f10(c1)) = f5(c2)),
% 28.24/18.42 inference(monotonicity,[status(thm)],[15])).
% 28.24/18.42 tff(9889,plain,
% 28.24/18.42 (f5(f10(c1)) = c1),
% 28.24/18.42 inference(transitivity,[status(thm)],[9888, 9887])).
% 28.24/18.42 tff(9890,plain,
% 28.24/18.42 ((f6(f7(c2), c3) = f5(f10(c1))) <=> (f6(c1, c1) = c1)),
% 28.24/18.42 inference(monotonicity,[status(thm)],[9838, 9889])).
% 28.24/18.42 tff(9891,plain,
% 28.24/18.42 ((f6(c1, c1) = c1) <=> (f6(f7(c2), c3) = f5(f10(c1)))),
% 28.24/18.42 inference(symmetry,[status(thm)],[9890])).
% 28.24/18.42 tff(9892,plain,
% 28.24/18.42 ((f6(f7(c2), f7(c2)) = f7(c2)) <=> (f6(c1, c1) = c1)),
% 28.24/18.42 inference(monotonicity,[status(thm)],[9789, 22])).
% 28.24/18.42 tff(9893,plain,
% 28.24/18.42 ((f6(f7(c2), f7(c2)) = f7(c2)) <=> (f6(f7(c2), c3) = f5(f10(c1)))),
% 28.24/18.42 inference(transitivity,[status(thm)],[9892, 9891])).
% 28.24/18.42 tff(9894,plain,
% 28.24/18.42 ((~(f6(f7(c2), f7(c2)) = f7(c2))) <=> (~(f6(f7(c2), c3) = f5(f10(c1))))),
% 28.24/18.42 inference(monotonicity,[status(thm)],[9893])).
% 28.24/18.42 tff(9895,plain,
% 28.24/18.42 (big_f(f7(c1), f6(c1, c1)) <=> big_f(f7(f7(c2)), f6(f7(c2), f7(c2)))),
% 28.24/18.42 inference(symmetry,[status(thm)],[9790])).
% 28.24/18.42 tff(9896,plain,
% 28.24/18.42 (big_f(f7(f7(c2)), f6(f7(c2), f7(c2)))),
% 28.24/18.42 inference(modus_ponens,[status(thm)],[5964, 9895])).
% 28.24/18.42 tff(9897,assumption,(big_f(f7(f7(c2)), f6(f7(c2), f7(c2)))), introduced(assumption)).
% 28.24/18.42 tff(9898,assumption,(f6(f7(c2), f7(c2)) = f7(c2)), introduced(assumption)).
% 28.24/18.42 tff(9899,assumption,(f7(f7(c2)) = f7(c2)), introduced(assumption)).
% 28.24/18.42 tff(9900,plain,
% 28.24/18.42 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(f7(c2)) = f7(c2))) | (f10(f7(c2)) = f7(c2)) | big_f(f7(c2), f10(f7(c2))) | (~(f7(c2) = f8(f7(c2)))) | (~(f6(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), f7(c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(f7(c2)) = f7(c2))) | (f10(f7(c2)) = f7(c2)) | big_f(f7(c2), f10(f7(c2))) | (~(f7(c2) = f8(f7(c2)))) | (~(f6(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), f7(c2)))))),
% 28.24/18.42 inference(rewrite,[status(thm)],[])).
% 28.24/18.42 tff(9901,plain,
% 28.24/18.42 (((f10(f7(c2)) = f7(c2)) | big_f(f7(c2), f10(f7(c2))) | (~(f7(f7(c2)) = f7(c2))) | (~(f7(c2) = f8(f7(c2)))) | (~(f6(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), f7(c2))))) <=> ((~(f7(f7(c2)) = f7(c2))) | (f10(f7(c2)) = f7(c2)) | big_f(f7(c2), f10(f7(c2))) | (~(f7(c2) = f8(f7(c2)))) | (~(f6(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), f7(c2)))))),
% 28.24/18.42 inference(rewrite,[status(thm)],[])).
% 28.24/18.42 tff(9902,plain,
% 28.24/18.42 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f7(c2)) = f7(c2)) | big_f(f7(c2), f10(f7(c2))) | (~(f7(f7(c2)) = f7(c2))) | (~(f7(c2) = f8(f7(c2)))) | (~(f6(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), f7(c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(f7(c2)) = f7(c2))) | (f10(f7(c2)) = f7(c2)) | big_f(f7(c2), f10(f7(c2))) | (~(f7(c2) = f8(f7(c2)))) | (~(f6(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), f7(c2))))))),
% 28.24/18.42 inference(monotonicity,[status(thm)],[9901])).
% 28.24/18.42 tff(9903,plain,
% 28.24/18.42 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f7(c2)) = f7(c2)) | big_f(f7(c2), f10(f7(c2))) | (~(f7(f7(c2)) = f7(c2))) | (~(f7(c2) = f8(f7(c2)))) | (~(f6(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), f7(c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(f7(c2)) = f7(c2))) | (f10(f7(c2)) = f7(c2)) | big_f(f7(c2), f10(f7(c2))) | (~(f7(c2) = f8(f7(c2)))) | (~(f6(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), f7(c2)))))),
% 28.24/18.42 inference(transitivity,[status(thm)],[9902, 9900])).
% 28.24/18.42 tff(9904,plain,
% 28.24/18.42 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f7(c2)) = f7(c2)) | big_f(f7(c2), f10(f7(c2))) | (~(f7(f7(c2)) = f7(c2))) | (~(f7(c2) = f8(f7(c2)))) | (~(f6(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), f7(c2)))))),
% 28.24/18.42 inference(quant_inst,[status(thm)],[])).
% 28.24/18.42 tff(9905,plain,
% 28.24/18.42 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(f7(c2)) = f7(c2))) | (f10(f7(c2)) = f7(c2)) | big_f(f7(c2), f10(f7(c2))) | (~(f7(c2) = f8(f7(c2)))) | (~(f6(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), f7(c2))))),
% 28.24/18.42 inference(modus_ponens,[status(thm)],[9904, 9903])).
% 28.24/18.42 tff(9906,plain,
% 28.24/18.42 ((~(f7(c2) = f8(f7(c2)))) | (~(f6(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), f7(c2))))),
% 28.24/18.42 inference(unit_resolution,[status(thm)],[9905, 2963, 9899, 8556, 8523])).
% 28.24/18.42 tff(9907,plain,
% 28.24/18.42 (~(f7(c2) = f8(f7(c2)))),
% 28.24/18.42 inference(unit_resolution,[status(thm)],[9906, 9898, 9897])).
% 28.24/18.42 tff(9908,plain,
% 28.24/18.42 (~(f8(c3) = c1)),
% 28.24/18.42 inference(modus_ponens,[status(thm)],[9907, 8555])).
% 28.24/18.42 tff(9909,plain,
% 28.24/18.42 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(f7(c2)) = f7(c2))) | (f10(f7(c2)) = f7(c2)) | big_f(c2, f10(f7(c2))) | (~(c2 = f8(f7(c2)))) | (~(f6(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), f7(c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(f7(c2)) = f7(c2))) | (f10(f7(c2)) = f7(c2)) | big_f(c2, f10(f7(c2))) | (~(c2 = f8(f7(c2)))) | (~(f6(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), f7(c2)))))),
% 28.24/18.42 inference(rewrite,[status(thm)],[])).
% 28.24/18.42 tff(9910,plain,
% 28.24/18.42 (((f10(f7(c2)) = f7(c2)) | big_f(c2, f10(f7(c2))) | (~(f7(f7(c2)) = f7(c2))) | (~(c2 = f8(f7(c2)))) | (~(f6(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), f7(c2))))) <=> ((~(f7(f7(c2)) = f7(c2))) | (f10(f7(c2)) = f7(c2)) | big_f(c2, f10(f7(c2))) | (~(c2 = f8(f7(c2)))) | (~(f6(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), f7(c2)))))),
% 28.24/18.42 inference(rewrite,[status(thm)],[])).
% 28.24/18.42 tff(9911,plain,
% 28.24/18.42 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f7(c2)) = f7(c2)) | big_f(c2, f10(f7(c2))) | (~(f7(f7(c2)) = f7(c2))) | (~(c2 = f8(f7(c2)))) | (~(f6(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), f7(c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(f7(c2)) = f7(c2))) | (f10(f7(c2)) = f7(c2)) | big_f(c2, f10(f7(c2))) | (~(c2 = f8(f7(c2)))) | (~(f6(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), f7(c2))))))),
% 28.24/18.43 inference(monotonicity,[status(thm)],[9910])).
% 28.24/18.43 tff(9912,plain,
% 28.24/18.43 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f7(c2)) = f7(c2)) | big_f(c2, f10(f7(c2))) | (~(f7(f7(c2)) = f7(c2))) | (~(c2 = f8(f7(c2)))) | (~(f6(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), f7(c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(f7(c2)) = f7(c2))) | (f10(f7(c2)) = f7(c2)) | big_f(c2, f10(f7(c2))) | (~(c2 = f8(f7(c2)))) | (~(f6(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), f7(c2)))))),
% 28.24/18.43 inference(transitivity,[status(thm)],[9911, 9909])).
% 28.24/18.43 tff(9913,plain,
% 28.24/18.43 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f7(c2)) = f7(c2)) | big_f(c2, f10(f7(c2))) | (~(f7(f7(c2)) = f7(c2))) | (~(c2 = f8(f7(c2)))) | (~(f6(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), f7(c2)))))),
% 28.24/18.43 inference(quant_inst,[status(thm)],[])).
% 28.24/18.43 tff(9914,plain,
% 28.24/18.43 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(f7(c2)) = f7(c2))) | (f10(f7(c2)) = f7(c2)) | big_f(c2, f10(f7(c2))) | (~(c2 = f8(f7(c2)))) | (~(f6(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), f7(c2))))),
% 28.24/18.43 inference(modus_ponens,[status(thm)],[9913, 9912])).
% 28.24/18.43 tff(9915,plain,
% 28.24/18.43 ((~(c2 = f8(f7(c2)))) | (~(f6(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), f7(c2))))),
% 28.24/18.43 inference(unit_resolution,[status(thm)],[9914, 2963, 9899, 8523, 8522])).
% 28.24/18.43 tff(9916,plain,
% 28.24/18.43 (~(c2 = f8(f7(c2)))),
% 28.24/18.43 inference(unit_resolution,[status(thm)],[9915, 9898, 9897])).
% 28.24/18.43 tff(9917,plain,
% 28.24/18.43 (~(f8(c3) = c2)),
% 28.24/18.43 inference(modus_ponens,[status(thm)],[9916, 8539])).
% 28.24/18.43 tff(9918,plain,
% 28.24/18.43 ($false),
% 28.24/18.43 inference(unit_resolution,[status(thm)],[8569, 9917, 9908])).
% 28.24/18.43 tff(9919,plain,((~(f6(f7(c2), f7(c2)) = f7(c2))) | (~(f4(c4) = c2)) | (~(c3 = c1)) | (~(f7(c2) = c1)) | (~big_f(f7(f7(c2)), f6(f7(c2), f7(c2)))) | (~(f7(f7(c2)) = f7(c2))) | big_f(f7(c2), f10(f7(c2))) | (f10(f7(c2)) = f7(c2)) | big_f(c2, f10(f7(c2)))), inference(lemma,lemma(discharge,[]))).
% 28.24/18.43 tff(9920,plain,
% 28.24/18.43 (~(f6(f7(c2), f7(c2)) = f7(c2))),
% 28.24/18.43 inference(unit_resolution,[status(thm)],[9919, 9896, 172, 22, 79, 8315, 9852, 9844, 9857])).
% 28.24/18.43 tff(9921,plain,
% 28.24/18.43 (~(f6(f7(c2), c3) = f5(f10(c1)))),
% 28.24/18.43 inference(modus_ponens,[status(thm)],[9920, 9894])).
% 28.24/18.43 tff(9922,plain,
% 28.24/18.43 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | (big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (f7(f10(c1)) = f10(c1)) | (~big_f(f7(f10(c1)), f6(f7(c2), c3))) | (f6(f7(c2), c3) = f5(f10(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (f7(f10(c1)) = f10(c1)) | (~big_f(f7(f10(c1)), f6(f7(c2), c3))) | (f6(f7(c2), c3) = f5(f10(c1))))),
% 28.24/18.43 inference(rewrite,[status(thm)],[])).
% 28.24/18.43 tff(9923,plain,
% 28.24/18.43 (((f10(c1) = c1) | big_f(c2, f10(c1)) | (f7(f10(c1)) = f10(c1)) | (f6(f7(c2), c3) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(f7(c2), c3))) | (~(c2 = f8(c1)))) <=> (big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (f7(f10(c1)) = f10(c1)) | (~big_f(f7(f10(c1)), f6(f7(c2), c3))) | (f6(f7(c2), c3) = f5(f10(c1))))),
% 28.24/18.43 inference(rewrite,[status(thm)],[])).
% 28.24/18.43 tff(9924,plain,
% 28.24/18.43 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | big_f(c2, f10(c1)) | (f7(f10(c1)) = f10(c1)) | (f6(f7(c2), c3) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(f7(c2), c3))) | (~(c2 = f8(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | (big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (f7(f10(c1)) = f10(c1)) | (~big_f(f7(f10(c1)), f6(f7(c2), c3))) | (f6(f7(c2), c3) = f5(f10(c1)))))),
% 28.24/18.43 inference(monotonicity,[status(thm)],[9923])).
% 28.24/18.43 tff(9925,plain,
% 28.24/18.43 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | big_f(c2, f10(c1)) | (f7(f10(c1)) = f10(c1)) | (f6(f7(c2), c3) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(f7(c2), c3))) | (~(c2 = f8(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (f7(f10(c1)) = f10(c1)) | (~big_f(f7(f10(c1)), f6(f7(c2), c3))) | (f6(f7(c2), c3) = f5(f10(c1))))),
% 28.24/18.43 inference(transitivity,[status(thm)],[9924, 9922])).
% 28.24/18.43 tff(9926,plain,
% 28.24/18.43 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | big_f(c2, f10(c1)) | (f7(f10(c1)) = f10(c1)) | (f6(f7(c2), c3) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(f7(c2), c3))) | (~(c2 = f8(c1))))),
% 28.24/18.43 inference(quant_inst,[status(thm)],[])).
% 28.24/18.43 tff(9927,plain,
% 28.24/18.43 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (f7(f10(c1)) = f10(c1)) | (~big_f(f7(f10(c1)), f6(f7(c2), c3))) | (f6(f7(c2), c3) = f5(f10(c1)))),
% 28.24/18.43 inference(modus_ponens,[status(thm)],[9926, 9925])).
% 28.24/18.43 tff(9928,plain,
% 28.24/18.43 (big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (f7(f10(c1)) = f10(c1)) | (~big_f(f7(f10(c1)), f6(f7(c2), c3))) | (f6(f7(c2), c3) = f5(f10(c1)))),
% 28.24/18.43 inference(unit_resolution,[status(thm)],[9927, 2795])).
% 28.24/18.43 tff(9929,plain,
% 28.24/18.43 (~(c2 = f8(c1))),
% 28.24/18.43 inference(unit_resolution,[status(thm)],[9928, 9921, 3, 223, 8451, 9842])).
% 28.24/18.43 tff(9930,plain,
% 28.24/18.43 (~(f8(c1) = c2)),
% 28.24/18.43 inference(unit_resolution,[status(thm)],[1675, 9929])).
% 28.24/18.43 tff(9931,plain,
% 28.24/18.43 (f8(c1) = c1),
% 28.24/18.43 inference(unit_resolution,[status(thm)],[1680, 9930])).
% 28.24/18.43 tff(9932,plain,
% 28.24/18.43 (f7(c2) = f8(f7(c2))),
% 28.24/18.43 inference(modus_ponens,[status(thm)],[9931, 9837])).
% 28.24/18.43 tff(9933,plain,
% 28.24/18.43 (f5(c2) = f5(f10(c1))),
% 28.24/18.43 inference(symmetry,[status(thm)],[9888])).
% 28.24/18.43 tff(9934,plain,
% 28.24/18.43 ((f6(c1, c1) = f5(c2)) <=> (f6(f7(c2), c3) = f5(f10(c1)))),
% 28.24/18.43 inference(monotonicity,[status(thm)],[5969, 9933])).
% 28.24/18.43 tff(9935,plain,
% 28.24/18.43 ((f6(f7(c2), c3) = f5(f10(c1))) <=> (f6(c1, c1) = f5(c2))),
% 28.24/18.43 inference(symmetry,[status(thm)],[9934])).
% 28.24/18.43 tff(9936,plain,
% 28.24/18.43 ((f6(f7(c2), f7(c2)) = f7(c2)) <=> (f6(c1, c1) = f5(c2))),
% 28.24/18.43 inference(transitivity,[status(thm)],[9892, 9891, 9935])).
% 28.24/18.43 tff(9937,plain,
% 28.24/18.43 ((~(f6(f7(c2), f7(c2)) = f7(c2))) <=> (~(f6(c1, c1) = f5(c2)))),
% 28.24/18.43 inference(monotonicity,[status(thm)],[9936])).
% 28.24/18.43 tff(9938,plain,
% 28.24/18.43 (~(f6(c1, c1) = f5(c2))),
% 28.24/18.43 inference(modus_ponens,[status(thm)],[9920, 9937])).
% 28.24/18.43 tff(9939,plain,
% 28.24/18.43 (big_f(f7(c2), f6(c1, c1))),
% 28.24/18.43 inference(modus_ponens,[status(thm)],[5964, 5547])).
% 28.24/18.43 tff(9940,plain,
% 28.24/18.43 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f7(c2) = c2) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))) | (f10(f7(c2)) = f7(c2)) | big_f(f7(c2), f10(f7(c2))) | (~(f7(c2) = f8(f7(c2)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | (f7(c2) = c2) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))) | (f10(f7(c2)) = f7(c2)) | big_f(f7(c2), f10(f7(c2))) | (~(f7(c2) = f8(f7(c2)))))),
% 28.24/18.43 inference(rewrite,[status(thm)],[])).
% 28.24/18.43 tff(9941,plain,
% 28.24/18.43 (((f10(f7(c2)) = f7(c2)) | big_f(f7(c2), f10(f7(c2))) | (f7(c2) = c2) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))) | (~(f7(c2) = f8(f7(c2))))) <=> ((f7(c2) = c2) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))) | (f10(f7(c2)) = f7(c2)) | big_f(f7(c2), f10(f7(c2))) | (~(f7(c2) = f8(f7(c2)))))),
% 28.24/18.43 inference(rewrite,[status(thm)],[])).
% 28.24/18.43 tff(9942,plain,
% 28.24/18.43 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(f7(c2)) = f7(c2)) | big_f(f7(c2), f10(f7(c2))) | (f7(c2) = c2) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))) | (~(f7(c2) = f8(f7(c2)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f7(c2) = c2) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))) | (f10(f7(c2)) = f7(c2)) | big_f(f7(c2), f10(f7(c2))) | (~(f7(c2) = f8(f7(c2))))))),
% 28.24/18.43 inference(monotonicity,[status(thm)],[9941])).
% 28.24/18.43 tff(9943,plain,
% 28.24/18.43 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(f7(c2)) = f7(c2)) | big_f(f7(c2), f10(f7(c2))) | (f7(c2) = c2) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))) | (~(f7(c2) = f8(f7(c2)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | (f7(c2) = c2) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))) | (f10(f7(c2)) = f7(c2)) | big_f(f7(c2), f10(f7(c2))) | (~(f7(c2) = f8(f7(c2)))))),
% 28.24/18.43 inference(transitivity,[status(thm)],[9942, 9940])).
% 28.24/18.43 tff(9944,plain,
% 28.24/18.43 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(f7(c2)) = f7(c2)) | big_f(f7(c2), f10(f7(c2))) | (f7(c2) = c2) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))) | (~(f7(c2) = f8(f7(c2)))))),
% 28.24/18.43 inference(quant_inst,[status(thm)],[])).
% 28.24/18.43 tff(9945,plain,
% 28.24/18.43 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | (f7(c2) = c2) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))) | (f10(f7(c2)) = f7(c2)) | big_f(f7(c2), f10(f7(c2))) | (~(f7(c2) = f8(f7(c2))))),
% 28.24/18.43 inference(modus_ponens,[status(thm)],[9944, 9943])).
% 28.24/18.43 tff(9946,plain,
% 28.24/18.43 ((f6(c1, c1) = f5(c2)) | (~(f7(c2) = f8(f7(c2))))),
% 28.24/18.43 inference(unit_resolution,[status(thm)],[9945, 2795, 17, 9852, 9844, 9939])).
% 28.24/18.43 tff(9947,plain,
% 28.24/18.43 (~(f7(c2) = f8(f7(c2)))),
% 28.24/18.43 inference(unit_resolution,[status(thm)],[9946, 9938])).
% 28.24/18.43 tff(9948,plain,
% 28.24/18.43 ($false),
% 28.24/18.43 inference(unit_resolution,[status(thm)],[9947, 9932])).
% 28.24/18.43 tff(9949,plain,((f10(c1) = c1) | (~(f4(c4) = c2)) | (f7(c2) = c2) | (~(c3 = c1)) | (~big_f(f7(c1), f6(c1, c1))) | big_f(f7(c2), c2) | (~(f7(c1) = c1)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 28.24/18.43 tff(9950,plain,
% 28.24/18.43 ($false),
% 28.24/18.43 inference(unit_resolution,[status(thm)],[9949, 9831, 3, 17, 9783, 79, 1521, 4234, 121])).
% 28.24/18.43 tff(9951,plain,((f10(c1) = c1) | (f7(c2) = c2) | (~(f4(c4) = c2)) | big_f(f7(c2), c2) | (~(f7(c1) = c1)) | big_f(c2, c2) | (~big_f(f7(c2), c1))), inference(lemma,lemma(discharge,[]))).
% 28.24/18.43 tff(9952,plain,
% 28.24/18.43 (f10(c1) = c1),
% 28.24/18.43 inference(unit_resolution,[status(thm)],[9951, 1521, 79, 17, 4234, 121, 338])).
% 28.24/18.43 tff(9953,plain,
% 28.24/18.43 (f10(f7(c2)) = c1),
% 28.24/18.43 inference(transitivity,[status(thm)],[8167, 8082, 9952])).
% 28.24/18.43 tff(9954,plain,
% 28.24/18.43 (f10(c1) = c1),
% 28.24/18.43 inference(unit_resolution,[status(thm)],[9830, 65, 292, 79, 4234, 338, 1521, 121])).
% 28.24/18.43 tff(9955,plain,
% 28.24/18.43 (f9(c1, c1) = f7(c2)),
% 28.24/18.43 inference(transitivity,[status(thm)],[3949, 342])).
% 28.24/18.43 tff(9956,plain,
% 28.24/18.43 (big_f(f9(c1, c1), c1) <=> big_f(f7(c2), c1)),
% 28.24/18.43 inference(monotonicity,[status(thm)],[9955])).
% 28.24/18.43 tff(9957,plain,
% 28.24/18.43 (big_f(f7(c2), c1) <=> big_f(f9(c1, c1), c1)),
% 28.24/18.43 inference(symmetry,[status(thm)],[9956])).
% 28.24/18.43 tff(9958,plain,
% 28.24/18.43 (big_f(f9(c1, c1), c1)),
% 28.24/18.43 inference(modus_ponens,[status(thm)],[338, 9957])).
% 28.24/18.43 tff(9959,plain,
% 28.24/18.43 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (big_f(f7(c1), f6(c1, c1)) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (f6(c1, c1) = c1))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | big_f(f7(c1), f6(c1, c1)) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (f6(c1, c1) = c1))),
% 28.24/18.43 inference(rewrite,[status(thm)],[])).
% 28.24/18.43 tff(9960,plain,
% 28.24/18.43 (((~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1)))) <=> (big_f(f7(c1), f6(c1, c1)) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (f6(c1, c1) = c1))),
% 28.24/18.43 inference(rewrite,[status(thm)],[])).
% 28.24/18.43 tff(9961,plain,
% 28.24/18.43 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (big_f(f7(c1), f6(c1, c1)) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (f6(c1, c1) = c1)))),
% 28.24/18.43 inference(monotonicity,[status(thm)],[9960])).
% 28.24/18.43 tff(9962,plain,
% 28.24/18.43 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | big_f(f7(c1), f6(c1, c1)) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (f6(c1, c1) = c1))),
% 28.24/18.43 inference(transitivity,[status(thm)],[9961, 9959])).
% 28.24/18.43 tff(9963,plain,
% 28.24/18.43 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))),
% 28.24/18.43 inference(quant_inst,[status(thm)],[])).
% 28.24/18.43 tff(9964,plain,
% 28.24/18.43 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | big_f(f7(c1), f6(c1, c1)) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (f6(c1, c1) = c1)),
% 28.24/18.43 inference(modus_ponens,[status(thm)],[9963, 9962])).
% 28.24/18.43 tff(9965,plain,
% 28.24/18.43 ($false),
% 28.24/18.43 inference(unit_resolution,[status(thm)],[9964, 2409, 4234, 3762, 3949, 3948, 65, 28])).
% 28.24/18.43 tff(9966,plain,((f6(c1, c1) = c1) | (~(f7(c1) = c1)) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | big_f(f7(c1), f6(c1, c1))), inference(lemma,lemma(discharge,[]))).
% 28.24/18.43 tff(9967,plain,
% 28.24/18.43 (f6(c1, c1) = c1),
% 28.24/18.43 inference(unit_resolution,[status(thm)],[9966, 65, 3762, 3949, 3948, 4234])).
% 28.24/18.43 tff(9968,plain,
% 28.25/18.43 (big_f(f7(c1), f6(c1, c1)) <=> big_f(f7(c2), c1)),
% 28.25/18.43 inference(monotonicity,[status(thm)],[8286, 9967])).
% 28.25/18.43 tff(9969,plain,
% 28.25/18.43 (big_f(f7(c2), c1) <=> big_f(f7(c1), f6(c1, c1))),
% 28.25/18.43 inference(symmetry,[status(thm)],[9968])).
% 28.25/18.43 tff(9970,plain,
% 28.25/18.43 (big_f(f7(c1), f6(c1, c1))),
% 28.25/18.43 inference(modus_ponens,[status(thm)],[338, 9969])).
% 28.25/18.43 tff(9971,plain,
% 28.25/18.43 ($false),
% 28.25/18.43 inference(unit_resolution,[status(thm)],[65, 9970])).
% 28.25/18.43 tff(9972,plain,(big_f(f7(c1), f6(c1, c1)) | (~big_f(f7(c2), c1)) | (~(f7(c1) = c1)) | (~(f7(c2) = c1)) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1)))), inference(lemma,lemma(discharge,[]))).
% 28.25/18.43 tff(9973,plain,
% 28.25/18.43 (~big_f(f9(c1, c1), f10(c1))),
% 28.25/18.43 inference(unit_resolution,[status(thm)],[9972, 3949, 4234, 292, 338, 65, 3762])).
% 28.25/18.43 tff(9974,plain,
% 28.25/18.43 (~big_f(f9(c1, c1), c1)),
% 28.25/18.43 inference(unit_resolution,[status(thm)],[8716, 9973, 3762])).
% 28.25/18.43 tff(9975,plain,
% 28.25/18.43 ($false),
% 28.25/18.43 inference(unit_resolution,[status(thm)],[9974, 9958])).
% 28.25/18.43 tff(9976,plain,((~(f9(c1, c1) = c1)) | (~big_f(f7(c2), c1)) | (~(f7(c2) = c1)) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c1))), inference(lemma,lemma(discharge,[]))).
% 28.25/18.43 tff(9977,plain,
% 28.25/18.43 (~(f9(c1, c1) = c1)),
% 28.25/18.43 inference(unit_resolution,[status(thm)],[9976, 9954, 292, 338, 4234, 65])).
% 28.25/18.43 tff(9978,plain,
% 28.25/18.43 (big_f(f9(c1, c1), c1) <=> big_f(c2, c1)),
% 28.25/18.43 inference(monotonicity,[status(thm)],[4071])).
% 28.25/18.43 tff(9979,plain,
% 28.25/18.43 (big_f(c2, c1) <=> big_f(f9(c1, c1), c1)),
% 28.25/18.43 inference(symmetry,[status(thm)],[9978])).
% 28.25/18.43 tff(9980,plain,
% 28.25/18.43 ((~big_f(c2, c1)) <=> (~big_f(f9(c1, c1), c1))),
% 28.25/18.43 inference(monotonicity,[status(thm)],[9979])).
% 28.25/18.43 tff(9981,plain,
% 28.25/18.43 (~big_f(f9(c1, c1), c1)),
% 28.25/18.43 inference(modus_ponens,[status(thm)],[2, 9980])).
% 28.25/18.43 tff(9982,plain,
% 28.25/18.43 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (big_f(f7(c1), f6(c1, c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | big_f(f7(c1), f6(c1, c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1))),
% 28.25/18.43 inference(rewrite,[status(thm)],[])).
% 28.25/18.43 tff(9983,plain,
% 28.25/18.43 (((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1))) <=> (big_f(f7(c1), f6(c1, c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1))),
% 28.25/18.43 inference(rewrite,[status(thm)],[])).
% 28.25/18.43 tff(9984,plain,
% 28.25/18.43 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (big_f(f7(c1), f6(c1, c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1)))),
% 28.25/18.43 inference(monotonicity,[status(thm)],[9983])).
% 28.25/18.43 tff(9985,plain,
% 28.25/18.43 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | big_f(f7(c1), f6(c1, c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1))),
% 28.25/18.44 inference(transitivity,[status(thm)],[9984, 9982])).
% 28.25/18.44 tff(9986,plain,
% 28.25/18.44 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1)))),
% 28.25/18.44 inference(quant_inst,[status(thm)],[])).
% 28.25/18.44 tff(9987,plain,
% 28.25/18.44 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | big_f(f7(c1), f6(c1, c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1)),
% 28.25/18.44 inference(modus_ponens,[status(thm)],[9986, 9985])).
% 28.25/18.44 tff(9988,plain,
% 28.25/18.44 (f6(c1, c1) = c1),
% 28.25/18.44 inference(unit_resolution,[status(thm)],[9987, 2492, 4234, 3762, 4070, 8712, 65])).
% 28.25/18.44 tff(9989,plain,
% 28.25/18.44 (big_f(f7(c1), f6(c1, c1)) <=> big_f(f7(c2), c1)),
% 28.25/18.44 inference(monotonicity,[status(thm)],[8286, 9988])).
% 28.25/18.44 tff(9990,plain,
% 28.25/18.44 (big_f(f7(c2), c1) <=> big_f(f7(c1), f6(c1, c1))),
% 28.25/18.44 inference(symmetry,[status(thm)],[9989])).
% 28.25/18.44 tff(9991,plain,
% 28.25/18.44 (big_f(f7(c1), f6(c1, c1))),
% 28.25/18.44 inference(modus_ponens,[status(thm)],[338, 9990])).
% 28.25/18.44 tff(9992,plain,
% 28.25/18.44 ($false),
% 28.25/18.44 inference(unit_resolution,[status(thm)],[65, 9991])).
% 28.25/18.44 tff(9993,plain,(big_f(f7(c1), f6(c1, c1)) | (~big_f(f7(c2), c1)) | (~(f7(c1) = c1)) | (~(f7(c2) = c1)) | (~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1))), inference(lemma,lemma(discharge,[]))).
% 28.25/18.44 tff(9994,plain,
% 28.25/18.44 (big_f(f9(c1, c1), f10(c1))),
% 28.25/18.44 inference(unit_resolution,[status(thm)],[9993, 4070, 292, 4234, 65, 338, 3762])).
% 28.25/18.44 tff(9995,plain,
% 28.25/18.44 (big_f(f9(c1, c1), c1)),
% 28.25/18.44 inference(modus_ponens,[status(thm)],[9994, 3931])).
% 28.25/18.44 tff(9996,plain,
% 28.25/18.44 ($false),
% 28.25/18.44 inference(unit_resolution,[status(thm)],[9995, 9981])).
% 28.25/18.44 tff(9997,plain,((f9(c1, c1) = c1) | big_f(c2, c1) | (~(f10(c1) = c1)) | (~(f7(c2) = c1)) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c1)) | (~big_f(f7(c2), c1))), inference(lemma,lemma(discharge,[]))).
% 28.25/18.44 tff(9998,plain,
% 28.25/18.44 ($false),
% 28.25/18.44 inference(unit_resolution,[status(thm)],[9997, 9977, 9954, 2, 292, 4234, 65, 338])).
% 28.25/18.44 tff(9999,plain,(big_f(f7(c1), f6(c1, c1)) | big_f(c2, c1) | (~(f7(c2) = c1)) | (~(f7(c1) = c1)) | (~big_f(f7(c2), c1)) | (~(f4(c4) = c2)) | big_f(f7(c2), c2) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 28.25/18.44 tff(10000,plain,
% 28.25/18.44 (big_f(f7(c1), f6(c1, c1))),
% 28.25/18.44 inference(unit_resolution,[status(thm)],[9999, 2, 22, 4234, 338, 79, 1521, 121])).
% 28.25/18.44 tff(10001,plain,
% 28.25/18.44 (f10(c1) = c1),
% 28.25/18.44 inference(unit_resolution,[status(thm)],[9949, 10000, 17, 9783, 79, 1521, 4234, 121])).
% 28.25/18.44 tff(10002,plain,
% 28.25/18.44 (f10(f7(c2)) = c1),
% 28.25/18.44 inference(transitivity,[status(thm)],[8167, 8082, 10001])).
% 28.25/18.44 tff(10003,plain,
% 28.25/18.44 (f6(c1, c1) = c2),
% 28.25/18.44 inference(transitivity,[status(thm)],[5958, 2362])).
% 28.25/18.44 tff(10004,plain,
% 28.25/18.44 (big_f(f7(c1), f6(c1, c1)) <=> big_f(f7(c2), c2)),
% 28.25/18.44 inference(monotonicity,[status(thm)],[8286, 10003])).
% 28.25/18.44 tff(10005,plain,
% 28.25/18.44 (big_f(f7(c2), c2) <=> big_f(f7(c1), f6(c1, c1))),
% 28.25/18.44 inference(symmetry,[status(thm)],[10004])).
% 28.25/18.44 tff(10006,plain,
% 28.25/18.44 ((~big_f(f7(c2), c2)) <=> (~big_f(f7(c1), f6(c1, c1)))),
% 28.25/18.44 inference(monotonicity,[status(thm)],[10005])).
% 28.25/18.44 tff(10007,plain,
% 28.25/18.44 (~big_f(f7(c1), f6(c1, c1))),
% 28.25/18.44 inference(modus_ponens,[status(thm)],[1521, 10006])).
% 28.25/18.44 tff(10008,plain,
% 28.25/18.44 ($false),
% 28.25/18.44 inference(unit_resolution,[status(thm)],[5964, 10007])).
% 28.25/18.44 tff(10009,plain,((~(f6(f7(c2), c3) = c2)) | (~big_f(f7(c1), f6(c1, c1))) | big_f(f7(c2), c2) | (~(c3 = c1)) | (~(f7(c2) = c1)) | (~(f7(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.25/18.44 tff(10010,plain,
% 28.25/18.44 (~(f6(f7(c2), c3) = c2)),
% 28.25/18.44 inference(unit_resolution,[status(thm)],[10009, 10000, 1521, 9783, 22, 4234])).
% 28.25/18.44 tff(10011,plain,
% 28.25/18.44 (f6(f7(c2), c3) = c1),
% 28.25/18.44 inference(unit_resolution,[status(thm)],[2391, 10010])).
% 28.25/18.44 tff(10012,plain,
% 28.25/18.44 (f6(f7(c2), c3) = f6(c1, c1)),
% 28.25/18.44 inference(monotonicity,[status(thm)],[292, 172])).
% 28.25/18.44 tff(10013,plain,
% 28.25/18.44 (f6(c1, c1) = f6(f7(c2), c3)),
% 28.25/18.44 inference(symmetry,[status(thm)],[10012])).
% 28.25/18.44 tff(10014,plain,
% 28.25/18.44 ((f6(c1, c1) = c1) <=> (f6(f7(c2), c3) = c1)),
% 28.25/18.44 inference(monotonicity,[status(thm)],[10013])).
% 28.25/18.44 tff(10015,plain,
% 28.25/18.44 ((f6(f7(c2), c3) = c1) <=> (f6(c1, c1) = c1)),
% 28.25/18.44 inference(symmetry,[status(thm)],[10014])).
% 28.25/18.44 tff(10016,plain,
% 28.25/18.44 (f6(c1, c1) = c1),
% 28.25/18.44 inference(modus_ponens,[status(thm)],[2702, 10015])).
% 28.25/18.44 tff(10017,plain,
% 28.25/18.44 ($false),
% 28.25/18.44 inference(unit_resolution,[status(thm)],[28, 10016])).
% 28.25/18.44 tff(10018,plain,((~(f6(f7(c2), c3) = c1)) | (f6(c1, c1) = c1) | (~(c3 = c1)) | (~(f7(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.25/18.44 tff(10019,plain,
% 28.25/18.44 (f6(c1, c1) = c1),
% 28.25/18.44 inference(unit_resolution,[status(thm)],[10018, 10011, 22, 9783])).
% 28.25/18.44 tff(10020,assumption,(~big_f(f9(c1, c1), c1)), introduced(assumption)).
% 28.25/18.44 tff(10021,assumption,(f9(f7(c2), f7(c2)) = f7(c2)), introduced(assumption)).
% 28.25/18.44 tff(10022,plain,
% 28.25/18.44 (f9(c1, c1) = f9(f7(c2), f7(c2))),
% 28.25/18.44 inference(monotonicity,[status(thm)],[342, 342])).
% 28.25/18.44 tff(10023,plain,
% 28.25/18.44 (f9(c1, c1) = f7(c2)),
% 28.25/18.44 inference(transitivity,[status(thm)],[10022, 10021])).
% 28.25/18.44 tff(10024,plain,
% 28.25/18.44 (big_f(f9(c1, c1), c1) <=> big_f(f7(c2), c1)),
% 28.25/18.44 inference(monotonicity,[status(thm)],[10023])).
% 28.25/18.44 tff(10025,plain,
% 28.25/18.44 (big_f(f7(c2), c1) <=> big_f(f9(c1, c1), c1)),
% 28.25/18.44 inference(symmetry,[status(thm)],[10024])).
% 28.25/18.44 tff(10026,plain,
% 28.25/18.44 (big_f(f9(c1, c1), c1)),
% 28.25/18.44 inference(modus_ponens,[status(thm)],[338, 10025])).
% 28.25/18.44 tff(10027,plain,
% 28.25/18.44 ($false),
% 28.25/18.44 inference(unit_resolution,[status(thm)],[10020, 10026])).
% 28.25/18.44 tff(10028,plain,((~(f9(f7(c2), f7(c2)) = f7(c2))) | big_f(f9(c1, c1), c1) | (~big_f(f7(c2), c1)) | (~(f7(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.25/18.44 tff(10029,plain,
% 28.25/18.44 (~(f9(f7(c2), f7(c2)) = f7(c2))),
% 28.25/18.44 inference(unit_resolution,[status(thm)],[10028, 10020, 338, 292])).
% 28.25/18.44 tff(10030,assumption,(f6(c1, c1) = c1), introduced(assumption)).
% 28.25/18.44 tff(10031,plain,
% 28.25/18.44 (big_f(f9(c1, c1), c1)),
% 28.25/18.44 inference(modus_ponens,[status(thm)],[3948, 3931])).
% 28.25/18.44 tff(10032,plain,
% 28.25/18.44 ($false),
% 28.25/18.44 inference(unit_resolution,[status(thm)],[10020, 10031])).
% 28.25/18.44 tff(10033,plain,((~big_f(f9(c1, c1), f10(c1))) | big_f(f9(c1, c1), c1) | (~(f10(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.25/18.44 tff(10034,plain,
% 28.25/18.44 (~big_f(f9(c1, c1), f10(c1))),
% 28.25/18.44 inference(unit_resolution,[status(thm)],[10033, 10020, 3762])).
% 28.25/18.44 tff(10035,plain,
% 28.25/18.44 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)))),
% 28.25/18.44 inference(rewrite,[status(thm)],[])).
% 28.25/18.44 tff(10036,plain,
% 28.25/18.44 (((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1)))) <=> ((f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)))),
% 28.25/18.44 inference(rewrite,[status(thm)],[])).
% 28.25/18.44 tff(10037,plain,
% 28.25/18.44 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1))))),
% 28.25/18.44 inference(monotonicity,[status(thm)],[10036])).
% 28.25/18.44 tff(10038,plain,
% 28.25/18.44 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)))),
% 28.25/18.44 inference(transitivity,[status(thm)],[10037, 10035])).
% 28.25/18.44 tff(10039,plain,
% 28.25/18.44 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))),
% 28.25/18.44 inference(quant_inst,[status(thm)],[])).
% 28.25/18.44 tff(10040,plain,
% 28.25/18.44 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1))),
% 28.25/18.44 inference(modus_ponens,[status(thm)],[10039, 10038])).
% 28.25/18.44 tff(10041,plain,
% 28.25/18.44 ($false),
% 28.25/18.44 inference(unit_resolution,[status(thm)],[10040, 2534, 4234, 3762, 4070, 8712, 5964, 10030])).
% 28.25/18.44 tff(10042,plain,((~(f6(c1, c1) = c1)) | (~(f7(c1) = c1)) | (~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~big_f(f7(c1), f6(c1, c1)))), inference(lemma,lemma(discharge,[]))).
% 28.25/18.44 tff(10043,plain,
% 28.25/18.44 (f9(c1, c1) = c1),
% 28.25/18.44 inference(unit_resolution,[status(thm)],[10042, 10034, 5964, 3762, 10030, 4234])).
% 28.25/18.44 tff(10044,plain,
% 28.25/18.44 ((f9(f7(c2), f7(c2)) = f7(c2)) <=> (f9(c1, c1) = c1)),
% 28.25/18.44 inference(monotonicity,[status(thm)],[8634, 292])).
% 28.25/18.44 tff(10045,plain,
% 28.25/18.44 ((f9(c1, c1) = c1) <=> (f9(f7(c2), f7(c2)) = f7(c2))),
% 28.25/18.44 inference(symmetry,[status(thm)],[10044])).
% 28.25/18.44 tff(10046,plain,
% 28.25/18.44 (f9(f7(c2), f7(c2)) = f7(c2)),
% 28.25/18.44 inference(modus_ponens,[status(thm)],[3949, 10045])).
% 28.25/18.44 tff(10047,assumption,(~(f9(f7(c2), f7(c2)) = f7(c2))), introduced(assumption)).
% 28.25/18.44 tff(10048,plain,
% 28.25/18.44 ($false),
% 28.25/18.44 inference(unit_resolution,[status(thm)],[10047, 10046])).
% 28.25/18.44 tff(10049,plain,((~(f9(c1, c1) = c1)) | (f9(f7(c2), f7(c2)) = f7(c2)) | (~(f7(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.25/18.44 tff(10050,plain,
% 28.25/18.44 ($false),
% 28.25/18.44 inference(unit_resolution,[status(thm)],[10049, 10043, 10029, 292])).
% 28.25/18.44 tff(10051,plain,(big_f(f9(c1, c1), c1) | (~(f7(c2) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f10(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~(f7(c1) = c1)) | (~big_f(f7(c2), c1))), inference(lemma,lemma(discharge,[]))).
% 28.25/18.44 tff(10052,plain,
% 28.25/18.44 (big_f(f9(c1, c1), c1)),
% 28.25/18.44 inference(unit_resolution,[status(thm)],[10051, 10000, 22, 10001, 10019, 4234, 338])).
% 28.25/18.44 tff(10053,plain,
% 28.25/18.44 (big_f(f9(c1, c1), c1) <=> big_f(c2, c1)),
% 28.25/18.44 inference(monotonicity,[status(thm)],[4102])).
% 28.25/18.44 tff(10054,plain,
% 28.25/18.44 (big_f(c2, c1) <=> big_f(f9(c1, c1), c1)),
% 28.25/18.44 inference(symmetry,[status(thm)],[10053])).
% 28.25/18.44 tff(10055,plain,
% 28.25/18.44 ((~big_f(c2, c1)) <=> (~big_f(f9(c1, c1), c1))),
% 28.25/18.44 inference(monotonicity,[status(thm)],[10054])).
% 28.25/18.44 tff(10056,plain,
% 28.25/18.44 (~big_f(f9(c1, c1), c1)),
% 28.25/18.44 inference(modus_ponens,[status(thm)],[2, 10055])).
% 28.25/18.44 tff(10057,plain,
% 28.25/18.44 ($false),
% 28.25/18.44 inference(unit_resolution,[status(thm)],[8714, 10056])).
% 28.25/18.44 tff(10058,plain,((~(f9(c1, c1) = c2)) | (~big_f(f9(c1, c1), c1)) | big_f(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 28.25/18.44 tff(10059,plain,
% 28.25/18.44 (~(f9(c1, c1) = c2)),
% 28.25/18.44 inference(unit_resolution,[status(thm)],[10058, 10052, 2])).
% 28.25/18.44 tff(10060,plain,
% 28.25/18.44 (f9(c1, c1) = c1),
% 28.25/18.44 inference(unit_resolution,[status(thm)],[3939, 10059])).
% 28.25/18.44 tff(10061,plain,
% 28.25/18.44 (f9(f7(c2), f7(c2)) = f7(c2)),
% 28.25/18.44 inference(transitivity,[status(thm)],[8652, 10060, 125])).
% 28.25/18.44 tff(10062,plain,
% 28.25/18.44 (big_f(f9(f7(c2), f7(c2)), f10(f7(c2))) <=> big_f(f7(c2), c1)),
% 28.25/18.44 inference(monotonicity,[status(thm)],[10061, 10002])).
% 28.25/18.44 tff(10063,plain,
% 28.25/18.44 (big_f(f7(c2), c1) <=> big_f(f9(f7(c2), f7(c2)), f10(f7(c2)))),
% 28.25/18.44 inference(symmetry,[status(thm)],[10062])).
% 28.25/18.44 tff(10064,plain,
% 28.25/18.44 (big_f(f9(f7(c2), f7(c2)), f10(f7(c2)))),
% 28.25/18.44 inference(modus_ponens,[status(thm)],[338, 10063])).
% 28.25/18.44 tff(10065,plain,
% 28.25/18.44 (f9(f7(c2), f7(c2)) = f7(c2)),
% 28.25/18.44 inference(unit_resolution,[status(thm)],[10049, 10060, 22])).
% 28.25/18.44 tff(10066,plain,
% 28.25/18.44 (big_f(f7(f7(c2)), f6(f7(c2), f7(c2)))),
% 28.25/18.44 inference(modus_ponens,[status(thm)],[10000, 9895])).
% 28.25/18.44 tff(10067,plain,
% 28.25/18.44 ((f6(c1, c1) = c1) <=> (f6(f7(c2), f7(c2)) = f7(c2))),
% 28.25/18.44 inference(symmetry,[status(thm)],[9892])).
% 28.25/18.44 tff(10068,plain,
% 28.25/18.44 ((f6(c1, c1) = c1) <=> (f6(f7(c2), c3) = c1)),
% 28.25/18.44 inference(monotonicity,[status(thm)],[9785])).
% 28.25/18.44 tff(10069,plain,
% 28.25/18.44 ((f6(f7(c2), c3) = c1) <=> (f6(c1, c1) = c1)),
% 28.25/18.44 inference(symmetry,[status(thm)],[10068])).
% 28.25/18.44 tff(10070,plain,
% 28.25/18.44 ((f6(f7(c2), c3) = c1) <=> (f6(f7(c2), f7(c2)) = f7(c2))),
% 28.25/18.44 inference(transitivity,[status(thm)],[10069, 10067])).
% 28.25/18.44 tff(10071,plain,
% 28.25/18.44 (f6(f7(c2), f7(c2)) = f7(c2)),
% 28.25/18.44 inference(modus_ponens,[status(thm)],[10011, 10070])).
% 28.25/18.44 tff(10072,plain,
% 28.25/18.44 (f10(f7(c2)) = f7(c2)),
% 28.25/18.44 inference(modus_ponens,[status(thm)],[10001, 8182])).
% 28.25/18.44 tff(10073,plain,
% 28.25/18.44 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(f7(c2)) = f7(c2))) | (~(f9(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f9(f7(c2), f7(c2)), f10(f7(c2)))) | (~(f10(f7(c2)) = f7(c2))) | (~(f6(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), f7(c2)))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(f7(c2)) = f7(c2))) | (~(f9(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f9(f7(c2), f7(c2)), f10(f7(c2)))) | (~(f10(f7(c2)) = f7(c2))) | (~(f6(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), f7(c2)))))),
% 28.25/18.44 inference(rewrite,[status(thm)],[])).
% 28.25/18.44 tff(10074,plain,
% 28.25/18.44 (((~(f10(f7(c2)) = f7(c2))) | (~(f7(f7(c2)) = f7(c2))) | (~(f9(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f9(f7(c2), f7(c2)), f10(f7(c2)))) | (~(f6(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), f7(c2))))) <=> ((~(f7(f7(c2)) = f7(c2))) | (~(f9(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f9(f7(c2), f7(c2)), f10(f7(c2)))) | (~(f10(f7(c2)) = f7(c2))) | (~(f6(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), f7(c2)))))),
% 28.25/18.44 inference(rewrite,[status(thm)],[])).
% 28.25/18.44 tff(10075,plain,
% 28.25/18.44 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(f7(c2)) = f7(c2))) | (~(f7(f7(c2)) = f7(c2))) | (~(f9(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f9(f7(c2), f7(c2)), f10(f7(c2)))) | (~(f6(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), f7(c2)))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(f7(c2)) = f7(c2))) | (~(f9(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f9(f7(c2), f7(c2)), f10(f7(c2)))) | (~(f10(f7(c2)) = f7(c2))) | (~(f6(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), f7(c2))))))),
% 28.25/18.44 inference(monotonicity,[status(thm)],[10074])).
% 28.25/18.44 tff(10076,plain,
% 28.25/18.44 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(f7(c2)) = f7(c2))) | (~(f7(f7(c2)) = f7(c2))) | (~(f9(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f9(f7(c2), f7(c2)), f10(f7(c2)))) | (~(f6(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), f7(c2)))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(f7(c2)) = f7(c2))) | (~(f9(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f9(f7(c2), f7(c2)), f10(f7(c2)))) | (~(f10(f7(c2)) = f7(c2))) | (~(f6(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), f7(c2)))))),
% 28.25/18.44 inference(transitivity,[status(thm)],[10075, 10073])).
% 28.25/18.44 tff(10077,plain,
% 28.25/18.44 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(f7(c2)) = f7(c2))) | (~(f7(f7(c2)) = f7(c2))) | (~(f9(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f9(f7(c2), f7(c2)), f10(f7(c2)))) | (~(f6(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), f7(c2)))))),
% 28.25/18.44 inference(quant_inst,[status(thm)],[])).
% 28.25/18.44 tff(10078,plain,
% 28.25/18.44 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(f7(c2)) = f7(c2))) | (~(f9(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f9(f7(c2), f7(c2)), f10(f7(c2)))) | (~(f10(f7(c2)) = f7(c2))) | (~(f6(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), f7(c2))))),
% 28.25/18.44 inference(modus_ponens,[status(thm)],[10077, 10076])).
% 28.25/18.44 tff(10079,plain,
% 28.25/18.44 (~big_f(f9(f7(c2), f7(c2)), f10(f7(c2)))),
% 28.25/18.44 inference(unit_resolution,[status(thm)],[10078, 2378, 8315, 10072, 10071, 10066, 10065])).
% 28.25/18.44 tff(10080,plain,
% 28.25/18.44 ($false),
% 28.25/18.44 inference(unit_resolution,[status(thm)],[10079, 10064])).
% 28.25/18.44 tff(10081,plain,(big_f(c2, c1) | (~big_f(f7(c2), c1)) | (~(f4(c4) = c2)) | (~(f7(c1) = c1)) | big_f(f7(c2), c2) | (f7(c2) = c2) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 28.25/18.44 tff(10082,plain,
% 28.25/18.44 (big_f(c2, c1)),
% 28.25/18.44 inference(unit_resolution,[status(thm)],[10081, 1521, 79, 4234, 338, 17, 121])).
% 28.25/18.44 tff(10083,plain,
% 28.25/18.44 (~(f9(c1, c1) = c1)),
% 28.25/18.44 inference(unit_resolution,[status(thm)],[9976, 65, 22, 338, 4234, 3762])).
% 28.25/18.44 tff(10084,plain,
% 28.25/18.44 (big_f(f9(c1, c1), f10(c1))),
% 28.25/18.44 inference(unit_resolution,[status(thm)],[9993, 10083, 22, 4234, 65, 338, 3762])).
% 28.25/18.44 tff(10085,plain,
% 28.25/18.44 (f9(c1, c1) = c2),
% 28.25/18.44 inference(unit_resolution,[status(thm)],[3939, 10083])).
% 28.25/18.44 tff(10086,plain,
% 28.25/18.44 ((~(f1(c2, f7(c2)) = f7(c2))) <=> (~(f1(c2, c1) = c1))),
% 28.25/18.44 inference(monotonicity,[status(thm)],[8792])).
% 28.25/18.44 tff(10087,plain,
% 28.25/18.44 ((~(f1(c2, f7(c2)) = f7(c2))) <=> (~(f1(c2, c1) = c1))),
% 28.25/18.44 inference(monotonicity,[status(thm)],[8740])).
% 28.25/18.44 tff(10088,plain,
% 28.25/18.44 (~big_f(c2, c4)),
% 28.25/18.44 inference(unit_resolution,[status(thm)],[6521, 803, 79])).
% 28.25/18.44 tff(10089,assumption,(c2 = f4(c4)), introduced(assumption)).
% 28.25/18.44 tff(10090,assumption,(~big_f(c2, f1(c2, c1))), introduced(assumption)).
% 28.25/18.44 tff(10091,plain,
% 28.25/18.44 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | big_f(c2, c4) | (~(c2 = f4(c4))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | big_f(c2, c4) | (~(c2 = f4(c4))))),
% 28.25/18.44 inference(rewrite,[status(thm)],[])).
% 28.25/18.44 tff(10092,plain,
% 28.25/18.44 (((c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | $false | big_f(c2, c4) | (~(c2 = f4(c4)))) <=> ((c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | big_f(c2, c4) | (~(c2 = f4(c4))))),
% 28.25/18.44 inference(rewrite,[status(thm)],[])).
% 28.25/18.44 tff(10093,plain,
% 28.25/18.44 (((c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | (~(c4 = c4)) | big_f(c2, c4) | (~(c2 = f4(c4)))) <=> ((c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | $false | big_f(c2, c4) | (~(c2 = f4(c4))))),
% 28.25/18.44 inference(monotonicity,[status(thm)],[410])).
% 28.25/18.44 tff(10094,plain,
% 28.25/18.44 (((c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | (~(c4 = c4)) | big_f(c2, c4) | (~(c2 = f4(c4)))) <=> ((c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | big_f(c2, c4) | (~(c2 = f4(c4))))),
% 28.25/18.44 inference(transitivity,[status(thm)],[10093, 10092])).
% 28.25/18.44 tff(10095,plain,
% 28.25/18.44 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | (~(c4 = c4)) | big_f(c2, c4) | (~(c2 = f4(c4))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | big_f(c2, c4) | (~(c2 = f4(c4)))))),
% 28.25/18.44 inference(monotonicity,[status(thm)],[10094])).
% 28.25/18.44 tff(10096,plain,
% 28.25/18.44 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | (~(c4 = c4)) | big_f(c2, c4) | (~(c2 = f4(c4))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | big_f(c2, c4) | (~(c2 = f4(c4))))),
% 28.25/18.44 inference(transitivity,[status(thm)],[10095, 10091])).
% 28.25/18.44 tff(10097,plain,
% 28.25/18.44 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | (~(c4 = c4)) | big_f(c2, c4) | (~(c2 = f4(c4))))),
% 28.25/18.44 inference(quant_inst,[status(thm)],[])).
% 28.25/18.44 tff(10098,plain,
% 28.25/18.44 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | big_f(c2, c4) | (~(c2 = f4(c4)))),
% 28.25/18.44 inference(modus_ponens,[status(thm)],[10097, 10096])).
% 28.25/18.44 tff(10099,plain,
% 28.25/18.44 ((c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | big_f(c2, c4) | (~(c2 = f4(c4)))),
% 28.25/18.44 inference(unit_resolution,[status(thm)],[10098, 402])).
% 28.25/18.44 tff(10100,plain,
% 28.25/18.44 (f1(c2, c1) = c1),
% 28.25/18.44 inference(unit_resolution,[status(thm)],[10099, 10090, 10089, 3865, 377])).
% 28.25/18.44 tff(10101,plain,
% 28.25/18.44 (big_f(c2, f1(c2, c1)) <=> big_f(c2, c1)),
% 28.25/18.44 inference(monotonicity,[status(thm)],[10100])).
% 28.25/18.44 tff(10102,plain,
% 28.25/18.44 (big_f(c2, c1) <=> big_f(c2, f1(c2, c1))),
% 28.25/18.44 inference(symmetry,[status(thm)],[10101])).
% 28.25/18.44 tff(10103,plain,
% 28.25/18.44 (big_f(c2, f1(c2, c1))),
% 28.25/18.44 inference(modus_ponens,[status(thm)],[348, 10102])).
% 28.25/18.44 tff(10104,plain,
% 28.25/18.44 ($false),
% 28.25/18.44 inference(unit_resolution,[status(thm)],[10090, 10103])).
% 28.25/18.44 tff(10105,plain,(big_f(c2, f1(c2, c1)) | (~big_f(c2, c1)) | (~(c2 = f4(c4))) | big_f(c2, c4) | (c2 = c3)), inference(lemma,lemma(discharge,[]))).
% 28.25/18.44 tff(10106,plain,
% 28.25/18.44 (big_f(c2, f1(c2, c1))),
% 28.25/18.44 inference(unit_resolution,[status(thm)],[10105, 10088, 2602, 348, 377])).
% 28.25/18.44 tff(10107,plain,
% 28.25/18.44 (big_f(c2, f1(c2, f7(c2)))),
% 28.25/18.44 inference(modus_ponens,[status(thm)],[10106, 8727])).
% 28.25/18.44 tff(10108,plain,
% 28.25/18.44 (~(f1(c2, f7(c2)) = f7(c2))),
% 28.25/18.44 inference(unit_resolution,[status(thm)],[8752, 447, 432, 437, 121, 377, 10107])).
% 28.25/18.44 tff(10109,plain,
% 28.25/18.44 (~(f1(c2, c1) = c1)),
% 28.25/18.44 inference(modus_ponens,[status(thm)],[10108, 10087])).
% 28.25/18.44 tff(10110,plain,
% 28.25/18.44 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f1(c2, c1) = c1) | (f1(c2, c1) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f1(c2, c1) = c1) | (f1(c2, c1) = c2))),
% 28.25/18.44 inference(rewrite,[status(thm)],[])).
% 28.25/18.44 tff(10111,plain,
% 28.25/18.44 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f1(c2, c1) = c1) | (f1(c2, c1) = c2))),
% 28.25/18.44 inference(quant_inst,[status(thm)],[])).
% 28.25/18.44 tff(10112,plain,
% 28.25/18.44 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f1(c2, c1) = c1) | (f1(c2, c1) = c2)),
% 28.25/18.44 inference(modus_ponens,[status(thm)],[10111, 10110])).
% 28.25/18.44 tff(10113,plain,
% 28.25/18.44 ((f1(c2, c1) = c1) | (f1(c2, c1) = c2)),
% 28.25/18.44 inference(unit_resolution,[status(thm)],[10112, 10])).
% 28.25/18.44 tff(10114,plain,
% 28.25/18.44 (f1(c2, c1) = c2),
% 28.25/18.44 inference(unit_resolution,[status(thm)],[10113, 10109])).
% 28.25/18.45 tff(10115,plain,
% 28.25/18.45 (big_f(c2, f1(c2, c1)) <=> big_f(c2, c2)),
% 28.25/18.45 inference(monotonicity,[status(thm)],[10114])).
% 28.25/18.45 tff(10116,plain,
% 28.25/18.45 (big_f(c2, c2) <=> big_f(c2, f1(c2, c1))),
% 28.25/18.45 inference(symmetry,[status(thm)],[10115])).
% 28.25/18.45 tff(10117,plain,
% 28.25/18.45 ((~big_f(c2, c2)) <=> (~big_f(c2, f1(c2, c1)))),
% 28.25/18.45 inference(monotonicity,[status(thm)],[10116])).
% 28.25/18.45 tff(10118,plain,
% 28.25/18.45 (~big_f(c2, f1(c2, c1))),
% 28.25/18.45 inference(modus_ponens,[status(thm)],[121, 10117])).
% 28.25/18.45 tff(10119,plain,
% 28.25/18.45 ($false),
% 28.25/18.45 inference(unit_resolution,[status(thm)],[10106, 10118])).
% 28.25/18.45 tff(10120,plain,((~(c4 = c2)) | big_f(c2, c2) | (~(f7(c2) = c1)) | (c2 = c3) | (~big_f(c2, c1)) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.25/18.45 tff(10121,plain,
% 28.25/18.45 (~(c4 = c2)),
% 28.25/18.45 inference(unit_resolution,[status(thm)],[10120, 377, 22, 121, 348, 79])).
% 28.25/18.45 tff(10122,plain,
% 28.25/18.45 (c4 = c1),
% 28.25/18.45 inference(unit_resolution,[status(thm)],[461, 10121])).
% 28.25/18.45 tff(10123,plain,
% 28.25/18.45 (c1 = c4),
% 28.25/18.45 inference(symmetry,[status(thm)],[10122])).
% 28.25/18.45 tff(10124,plain,
% 28.25/18.45 (f4(c1) = f4(c4)),
% 28.25/18.45 inference(monotonicity,[status(thm)],[10123])).
% 28.25/18.45 tff(10125,plain,
% 28.25/18.45 (f4(c1) = c2),
% 28.25/18.45 inference(transitivity,[status(thm)],[10124, 79])).
% 28.25/18.45 tff(10126,plain,
% 28.25/18.45 ((c1 = f4(c1)) <=> (f7(c2) = c2)),
% 28.25/18.45 inference(monotonicity,[status(thm)],[125, 10125])).
% 28.25/18.45 tff(10127,plain,
% 28.25/18.45 ((f7(c2) = c2) <=> (c1 = f4(c1))),
% 28.25/18.45 inference(symmetry,[status(thm)],[10126])).
% 28.25/18.45 tff(10128,plain,
% 28.25/18.45 ((f7(c2) = c2) <=> (f7(c2) = f4(f7(c2)))),
% 28.25/18.45 inference(transitivity,[status(thm)],[10127, 9598])).
% 28.25/18.45 tff(10129,plain,
% 28.25/18.45 ((~(f7(c2) = c2)) <=> (~(f7(c2) = f4(f7(c2))))),
% 28.25/18.45 inference(monotonicity,[status(thm)],[10128])).
% 28.25/18.45 tff(10130,plain,
% 28.25/18.45 (~(f7(c2) = f4(f7(c2)))),
% 28.25/18.45 inference(modus_ponens,[status(thm)],[17, 10129])).
% 28.25/18.45 tff(10131,plain,
% 28.25/18.45 (c1 = c4),
% 28.25/18.45 inference(unit_resolution,[status(thm)],[484, 10122])).
% 28.25/18.45 tff(10132,plain,
% 28.25/18.45 (f7(c2) = c4),
% 28.25/18.45 inference(modus_ponens,[status(thm)],[10131, 9329])).
% 28.25/18.45 tff(10133,plain,
% 28.25/18.45 (f1(f9(c1, c1), c1) = f1(c2, c1)),
% 28.25/18.45 inference(monotonicity,[status(thm)],[4102])).
% 28.25/18.45 tff(10134,plain,
% 28.25/18.45 ((f1(f9(c1, c1), c1) = c1) <=> (f1(c2, c1) = c1)),
% 28.25/18.45 inference(monotonicity,[status(thm)],[10133])).
% 28.25/18.45 tff(10135,plain,
% 28.25/18.45 ((f1(c2, c1) = c1) <=> (f1(f9(c1, c1), c1) = c1)),
% 28.25/18.45 inference(symmetry,[status(thm)],[10134])).
% 28.25/18.45 tff(10136,plain,
% 28.25/18.45 ((f1(c2, f7(c2)) = f7(c2)) <=> (f1(f9(c1, c1), c1) = c1)),
% 28.25/18.45 inference(transitivity,[status(thm)],[8740, 10135])).
% 28.25/18.45 tff(10137,plain,
% 28.25/18.45 (big_f(c2, f1(c2, c1))),
% 28.25/18.45 inference(modus_ponens,[status(thm)],[8934, 8726])).
% 28.25/18.45 tff(10138,plain,
% 28.25/18.45 ($false),
% 28.25/18.45 inference(unit_resolution,[status(thm)],[10090, 10137])).
% 28.25/18.45 tff(10139,plain,((~big_f(c2, f1(c2, f7(c2)))) | big_f(c2, f1(c2, c1)) | (~(f7(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.25/18.45 tff(10140,plain,
% 28.25/18.45 (~big_f(c2, f1(c2, f7(c2)))),
% 28.25/18.45 inference(unit_resolution,[status(thm)],[10139, 10090, 292])).
% 28.25/18.45 tff(10141,plain,
% 28.25/18.45 (f1(c2, f7(c2)) = f7(c2)),
% 28.25/18.45 inference(unit_resolution,[status(thm)],[8804, 525, 377, 10140, 8372, 8770, 8769])).
% 28.25/18.45 tff(10142,plain,
% 28.25/18.45 (f1(f9(c1, c1), c1) = c1),
% 28.25/18.45 inference(modus_ponens,[status(thm)],[10141, 10136])).
% 28.25/18.45 tff(10143,plain,
% 28.25/18.45 (big_f(f9(c1, c1), f1(f9(c1, c1), c1)) <=> big_f(c2, f1(c2, c1))),
% 28.25/18.45 inference(monotonicity,[status(thm)],[4102, 10133])).
% 28.25/18.45 tff(10144,plain,
% 28.25/18.45 (big_f(c2, f1(c2, c1)) <=> big_f(f9(c1, c1), f1(f9(c1, c1), c1))),
% 28.25/18.45 inference(symmetry,[status(thm)],[10143])).
% 28.25/18.45 tff(10145,plain,
% 28.25/18.45 ((~big_f(c2, f1(c2, c1))) <=> (~big_f(f9(c1, c1), f1(f9(c1, c1), c1)))),
% 28.25/18.45 inference(monotonicity,[status(thm)],[10144])).
% 28.25/18.45 tff(10146,plain,
% 28.25/18.45 (~big_f(f9(c1, c1), f1(f9(c1, c1), c1))),
% 28.25/18.45 inference(modus_ponens,[status(thm)],[10090, 10145])).
% 28.25/18.45 tff(10147,assumption,(f1(f9(c1, c1), c1) = c1), introduced(assumption)).
% 28.25/18.45 tff(10148,plain,
% 28.25/18.45 (big_f(f9(c1, c1), f1(f9(c1, c1), c1)) <=> big_f(f9(c1, c1), c1)),
% 28.25/18.45 inference(monotonicity,[status(thm)],[10147])).
% 28.25/18.45 tff(10149,plain,
% 28.25/18.45 (big_f(f9(c1, c1), c1) <=> big_f(f9(c1, c1), f1(f9(c1, c1), c1))),
% 28.25/18.45 inference(symmetry,[status(thm)],[10148])).
% 28.25/18.45 tff(10150,plain,
% 28.25/18.45 (big_f(f9(c1, c1), f1(f9(c1, c1), c1))),
% 28.25/18.45 inference(modus_ponens,[status(thm)],[8714, 10149])).
% 28.25/18.45 tff(10151,assumption,(~big_f(f9(c1, c1), f1(f9(c1, c1), c1))), introduced(assumption)).
% 28.25/18.45 tff(10152,plain,
% 28.25/18.45 ($false),
% 28.25/18.45 inference(unit_resolution,[status(thm)],[10151, 10150])).
% 28.25/18.45 tff(10153,plain,((~(f1(f9(c1, c1), c1) = c1)) | big_f(f9(c1, c1), f1(f9(c1, c1), c1)) | (~big_f(f9(c1, c1), c1))), inference(lemma,lemma(discharge,[]))).
% 28.25/18.45 tff(10154,plain,
% 28.25/18.45 (~(f1(f9(c1, c1), c1) = c1)),
% 28.25/18.45 inference(unit_resolution,[status(thm)],[10153, 10146, 8714])).
% 28.25/18.45 tff(10155,plain,
% 28.25/18.45 ($false),
% 28.25/18.45 inference(unit_resolution,[status(thm)],[10154, 10142])).
% 28.25/18.45 tff(10156,plain,(big_f(c2, f1(c2, c1)) | (~(f7(c2) = c1)) | (~(f9(c1, c1) = c2)) | (~big_f(f9(c1, c1), c1)) | (c2 = c3) | (~big_f(f7(c2), f7(c2))) | (~(f7(c2) = c4)) | (f7(c2) = f4(f7(c2)))), inference(lemma,lemma(discharge,[]))).
% 28.25/18.45 tff(10157,plain,
% 28.25/18.45 (big_f(c2, f1(c2, c1))),
% 28.25/18.45 inference(unit_resolution,[status(thm)],[10156, 377, 4102, 8714, 22, 8372, 10132, 10130])).
% 28.25/18.45 tff(10158,plain,
% 28.25/18.45 (big_f(c2, f1(c2, f7(c2)))),
% 28.25/18.45 inference(modus_ponens,[status(thm)],[10157, 8768])).
% 28.25/18.45 tff(10159,plain,
% 28.25/18.45 (~(f1(c2, f7(c2)) = f7(c2))),
% 28.25/18.45 inference(unit_resolution,[status(thm)],[8779, 553, 377, 10158, 8372, 10132, 10130])).
% 28.25/18.45 tff(10160,plain,
% 28.25/18.45 (~(f1(c2, c1) = c1)),
% 28.25/18.45 inference(modus_ponens,[status(thm)],[10159, 10086])).
% 28.25/18.45 tff(10161,plain,
% 28.25/18.45 (f1(c2, c1) = c2),
% 28.25/18.45 inference(unit_resolution,[status(thm)],[10113, 10160])).
% 28.25/18.45 tff(10162,plain,
% 28.25/18.45 (big_f(c2, f1(c2, c1)) <=> big_f(c2, c2)),
% 28.25/18.45 inference(monotonicity,[status(thm)],[10161])).
% 28.25/18.45 tff(10163,plain,
% 28.25/18.45 (big_f(c2, c2) <=> big_f(c2, f1(c2, c1))),
% 28.25/18.45 inference(symmetry,[status(thm)],[10162])).
% 28.25/18.45 tff(10164,plain,
% 28.25/18.45 ((~big_f(c2, c2)) <=> (~big_f(c2, f1(c2, c1)))),
% 28.25/18.45 inference(monotonicity,[status(thm)],[10163])).
% 28.25/18.45 tff(10165,plain,
% 28.25/18.45 (~big_f(c2, f1(c2, c1))),
% 28.25/18.45 inference(modus_ponens,[status(thm)],[121, 10164])).
% 28.25/18.45 tff(10166,plain,
% 28.25/18.45 ($false),
% 28.25/18.45 inference(unit_resolution,[status(thm)],[10157, 10165])).
% 28.25/18.45 tff(10167,plain,((c2 = c3) | big_f(c2, c2) | (~big_f(f7(c2), f7(c2))) | (~(f9(c1, c1) = c2)) | (~big_f(f9(c1, c1), c1)) | (f7(c2) = c2) | (~(f4(c4) = c2)) | (~big_f(c2, c1))), inference(lemma,lemma(discharge,[]))).
% 28.25/18.45 tff(10168,plain,
% 28.25/18.45 (~big_f(f9(c1, c1), c1)),
% 28.25/18.45 inference(unit_resolution,[status(thm)],[10167, 10085, 8765, 121, 377, 17, 79, 348])).
% 28.25/18.45 tff(10169,plain,
% 28.25/18.45 ($false),
% 28.25/18.45 inference(unit_resolution,[status(thm)],[10033, 10168, 10084, 3762])).
% 28.25/18.45 tff(10170,plain,(big_f(f7(c1), f6(c1, c1)) | (~(f10(c1) = c1)) | big_f(c2, c2) | (c2 = c3) | (f7(c2) = c2) | (~(f4(c4) = c2)) | (~big_f(c2, c1)) | (~(f7(c1) = c1)) | (~big_f(f7(c2), c1))), inference(lemma,lemma(discharge,[]))).
% 28.25/18.45 tff(10171,plain,
% 28.25/18.45 (big_f(f7(c1), f6(c1, c1))),
% 28.25/18.45 inference(unit_resolution,[status(thm)],[10170, 9952, 121, 9781, 17, 79, 10082, 4234, 338])).
% 28.25/18.45 tff(10172,plain,
% 28.25/18.45 (~(f6(f7(c2), c3) = c2)),
% 28.25/18.45 inference(unit_resolution,[status(thm)],[10009, 10171, 1521, 9783, 22, 4234])).
% 28.25/18.45 tff(10173,plain,
% 28.25/18.45 (f6(f7(c2), c3) = c1),
% 28.25/18.45 inference(unit_resolution,[status(thm)],[2391, 10172])).
% 28.25/18.45 tff(10174,plain,
% 28.25/18.45 (f6(c1, c1) = c1),
% 28.25/18.45 inference(unit_resolution,[status(thm)],[10018, 10173, 22, 9783])).
% 28.25/18.45 tff(10175,plain,
% 28.25/18.45 (big_f(f9(c1, c1), c1)),
% 28.25/18.45 inference(unit_resolution,[status(thm)],[10051, 10174, 22, 9952, 10171, 4234, 338])).
% 28.25/18.45 tff(10176,plain,
% 28.25/18.45 (~(f9(c1, c1) = c2)),
% 28.25/18.45 inference(unit_resolution,[status(thm)],[10167, 10175, 8765, 121, 9781, 17, 79, 10082])).
% 28.25/18.45 tff(10177,plain,
% 28.25/18.45 (f9(c1, c1) = c1),
% 28.25/18.45 inference(unit_resolution,[status(thm)],[3939, 10176])).
% 28.25/18.45 tff(10178,plain,
% 28.25/18.45 (f9(f7(c2), f7(c2)) = f7(c2)),
% 28.25/18.45 inference(transitivity,[status(thm)],[8652, 10177, 125])).
% 28.25/18.45 tff(10179,plain,
% 28.25/18.45 (big_f(f9(f7(c2), f7(c2)), f10(f7(c2))) <=> big_f(f7(c2), c1)),
% 28.25/18.45 inference(monotonicity,[status(thm)],[10178, 9953])).
% 28.25/18.45 tff(10180,plain,
% 28.25/18.45 (big_f(f7(c2), c1) <=> big_f(f9(f7(c2), f7(c2)), f10(f7(c2)))),
% 28.25/18.45 inference(symmetry,[status(thm)],[10179])).
% 28.25/18.45 tff(10181,plain,
% 28.25/18.45 (big_f(f9(f7(c2), f7(c2)), f10(f7(c2)))),
% 28.25/18.45 inference(modus_ponens,[status(thm)],[338, 10180])).
% 28.25/18.45 tff(10182,plain,
% 28.25/18.45 (f9(f7(c2), f7(c2)) = f7(c2)),
% 28.25/18.45 inference(unit_resolution,[status(thm)],[10049, 10177, 22])).
% 28.25/18.45 tff(10183,plain,
% 28.25/18.45 (f6(f7(c2), f7(c2)) = f7(c2)),
% 28.25/18.45 inference(modus_ponens,[status(thm)],[10173, 10070])).
% 28.25/18.45 tff(10184,plain,
% 28.25/18.45 (f10(f7(c2)) = f7(c2)),
% 28.25/18.45 inference(modus_ponens,[status(thm)],[9952, 8182])).
% 28.25/18.45 tff(10185,plain,
% 28.25/18.45 ((~big_f(f9(f7(c2), f7(c2)), f10(f7(c2)))) | (~big_f(f7(f7(c2)), f6(f7(c2), f7(c2))))),
% 28.25/18.45 inference(unit_resolution,[status(thm)],[10078, 2378, 8315, 10184, 10183, 10182])).
% 28.25/18.45 tff(10186,plain,
% 28.25/18.45 (~big_f(f7(f7(c2)), f6(f7(c2), f7(c2)))),
% 28.25/18.45 inference(unit_resolution,[status(thm)],[10185, 10181])).
% 28.25/18.45 tff(10187,plain,
% 28.25/18.45 (~big_f(f7(f7(c2)), f6(f7(c2), c3))),
% 28.25/18.45 inference(modus_ponens,[status(thm)],[10186, 9792])).
% 28.25/18.45 tff(10188,plain,
% 28.25/18.45 (big_f(f7(f7(c2)), f6(f7(c2), c3)) <=> big_f(f7(c1), f6(c1, c1))),
% 28.25/18.45 inference(monotonicity,[status(thm)],[352, 10012])).
% 28.25/18.45 tff(10189,plain,
% 28.25/18.45 (big_f(f7(c1), f6(c1, c1)) <=> big_f(f7(f7(c2)), f6(f7(c2), c3))),
% 28.25/18.45 inference(symmetry,[status(thm)],[10188])).
% 28.25/18.45 tff(10190,plain,
% 28.25/18.45 (big_f(f7(f7(c2)), f6(f7(c2), c3))),
% 28.25/18.45 inference(modus_ponens,[status(thm)],[5964, 10189])).
% 28.25/18.45 tff(10191,plain,
% 28.25/18.45 ($false),
% 28.25/18.45 inference(unit_resolution,[status(thm)],[2472, 10190])).
% 28.25/18.45 tff(10192,plain,((~big_f(f7(c1), f6(c1, c1))) | big_f(f7(f7(c2)), f6(f7(c2), c3)) | (~(c3 = c1)) | (~(f7(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.25/18.45 tff(10193,plain,
% 28.25/18.45 (big_f(f7(f7(c2)), f6(f7(c2), c3))),
% 28.25/18.45 inference(unit_resolution,[status(thm)],[10192, 10171, 22, 9783])).
% 28.25/18.45 tff(10194,plain,
% 28.25/18.45 ($false),
% 28.25/18.45 inference(unit_resolution,[status(thm)],[10193, 10187])).
% 28.25/18.45 tff(10195,plain,(big_f(f7(c2), c2) | (~big_f(f7(c2), c1)) | (~(f4(c4) = c2)) | big_f(c2, c2) | (f7(c2) = c2) | (~(f7(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.25/18.45 tff(10196,plain,
% 28.25/18.45 (~(f7(c1) = c1)),
% 28.25/18.45 inference(unit_resolution,[status(thm)],[10195, 9744, 79, 9485, 17, 1521])).
% 28.25/18.45 tff(10197,plain,
% 28.25/18.45 (~(c3 = c2)),
% 28.25/18.45 inference(unit_resolution,[status(thm)],[8259, 9744, 2, 79])).
% 28.25/18.45 tff(10198,plain,
% 28.25/18.45 (c3 = c1),
% 28.25/18.45 inference(unit_resolution,[status(thm)],[180, 10197])).
% 28.25/18.45 tff(10199,plain,
% 28.25/18.45 ($false),
% 28.25/18.45 inference(unit_resolution,[status(thm)],[9080, 10198, 10196, 17, 79, 122, 9744])).
% 28.25/18.45 tff(10200,plain,(big_f(f7(c2), c2) | (f7(c2) = c2) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | big_f(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 28.25/18.45 tff(10201,plain,
% 28.25/18.45 (big_f(f7(c2), c2)),
% 28.25/18.45 inference(unit_resolution,[status(thm)],[10200, 2, 79, 122, 17])).
% 28.25/18.45 tff(10202,plain,
% 28.25/18.45 (f9(c2, f7(c2)) = f7(c2)),
% 28.25/18.45 inference(modus_ponens,[status(thm)],[736, 8073])).
% 28.25/18.45 tff(10203,plain,
% 28.25/18.45 (f9(c2, c1) = f7(c2)),
% 28.25/18.45 inference(transitivity,[status(thm)],[736, 125])).
% 28.25/18.45 tff(10204,plain,
% 28.25/18.45 (big_f(f9(c2, c1), f10(c2)) <=> big_f(f7(c2), c2)),
% 28.25/18.45 inference(monotonicity,[status(thm)],[10203, 122])).
% 28.25/18.45 tff(10205,plain,
% 28.25/18.45 (big_f(f7(c2), c2) <=> big_f(f9(c2, c1), f10(c2))),
% 28.25/18.45 inference(symmetry,[status(thm)],[10204])).
% 28.25/18.45 tff(10206,plain,
% 28.25/18.45 (big_f(f7(c2), c2) <=> big_f(f9(c2, f7(c2)), f10(c2))),
% 28.25/18.45 inference(transitivity,[status(thm)],[10205, 8309])).
% 28.25/18.45 tff(10207,plain,
% 28.25/18.45 (big_f(f9(c2, f7(c2)), f10(c2))),
% 28.25/18.45 inference(modus_ponens,[status(thm)],[1180, 10206])).
% 28.25/18.45 tff(10208,plain,
% 28.25/18.45 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2))))),
% 28.25/18.45 inference(rewrite,[status(thm)],[])).
% 28.25/18.45 tff(10209,plain,
% 28.25/18.45 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2))))),
% 28.25/18.45 inference(quant_inst,[status(thm)],[])).
% 28.25/18.45 tff(10210,plain,
% 28.25/18.45 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2)))),
% 28.25/18.45 inference(modus_ponens,[status(thm)],[10209, 10208])).
% 28.25/18.45 tff(10211,plain,
% 28.25/18.45 (c2 = f5(c2)),
% 28.25/18.45 inference(unit_resolution,[status(thm)],[10210, 1190, 122, 17, 1180, 10207, 10202])).
% 28.25/18.45 tff(10212,plain,
% 28.25/18.45 (f5(c2) = c2),
% 28.25/18.45 inference(symmetry,[status(thm)],[10211])).
% 28.25/18.45 tff(10213,plain,
% 28.25/18.45 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2))) | (f7(c2) = f5(c2)) | (~big_f(f7(c2), f7(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2))) | (f7(c2) = f5(c2)) | (~big_f(f7(c2), f7(c2))))),
% 28.25/18.45 inference(rewrite,[status(thm)],[])).
% 28.25/18.45 tff(10214,plain,
% 28.25/18.45 (((~(f10(c2) = c2)) | (f7(c2) = c2) | (f7(c2) = f5(c2)) | (~big_f(f7(c2), f7(c2))) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2)))) <=> ((~(f10(c2) = c2)) | (f7(c2) = c2) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2))) | (f7(c2) = f5(c2)) | (~big_f(f7(c2), f7(c2))))),
% 28.25/18.45 inference(rewrite,[status(thm)],[])).
% 28.25/18.45 tff(10215,plain,
% 28.25/18.45 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (f7(c2) = f5(c2)) | (~big_f(f7(c2), f7(c2))) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2))) | (f7(c2) = f5(c2)) | (~big_f(f7(c2), f7(c2)))))),
% 28.25/18.45 inference(monotonicity,[status(thm)],[10214])).
% 28.25/18.45 tff(10216,plain,
% 28.25/18.45 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (f7(c2) = f5(c2)) | (~big_f(f7(c2), f7(c2))) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2))) | (f7(c2) = f5(c2)) | (~big_f(f7(c2), f7(c2))))),
% 28.25/18.45 inference(transitivity,[status(thm)],[10215, 10213])).
% 28.25/18.45 tff(10217,plain,
% 28.25/18.45 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (f7(c2) = f5(c2)) | (~big_f(f7(c2), f7(c2))) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2))))),
% 28.25/18.45 inference(quant_inst,[status(thm)],[])).
% 28.25/18.45 tff(10218,plain,
% 28.25/18.45 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2))) | (f7(c2) = f5(c2)) | (~big_f(f7(c2), f7(c2)))),
% 28.25/18.45 inference(modus_ponens,[status(thm)],[10217, 10216])).
% 28.25/18.45 tff(10219,plain,
% 28.25/18.45 (f7(c2) = f5(c2)),
% 28.25/18.45 inference(unit_resolution,[status(thm)],[10218, 1190, 122, 17, 10207, 10202, 8372])).
% 28.25/18.45 tff(10220,plain,
% 28.25/18.45 (f7(c2) = c2),
% 28.25/18.45 inference(transitivity,[status(thm)],[10219, 10212])).
% 28.25/18.45 tff(10221,plain,
% 28.25/18.45 ($false),
% 28.25/18.45 inference(unit_resolution,[status(thm)],[17, 10220])).
% 28.25/18.45 tff(10222,plain,((~(f9(c2, c1) = c1)) | (f7(c2) = c2) | (~(f10(c2) = c2)) | (~big_f(f7(c2), f7(c2))) | (~big_f(f7(c2), c2))), inference(lemma,lemma(discharge,[]))).
% 28.25/18.45 tff(10223,plain,
% 28.25/18.45 (~(f9(c2, c1) = c1)),
% 28.25/18.45 inference(unit_resolution,[status(thm)],[10222, 9486, 122, 17, 10201])).
% 28.25/18.45 tff(10224,plain,
% 28.25/18.45 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (f7(c2) = f5(c2)) | (~big_f(f7(c2), f7(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (f7(c2) = f5(c2)) | (~big_f(f7(c2), f7(c2))))),
% 28.25/18.45 inference(rewrite,[status(thm)],[])).
% 28.25/18.45 tff(10225,plain,
% 28.25/18.45 (((~(f10(c2) = c2)) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (f7(c2) = c2) | (f7(c2) = f5(c2)) | (~big_f(f7(c2), f7(c2)))) <=> ((~(f10(c2) = c2)) | (f7(c2) = c2) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (f7(c2) = f5(c2)) | (~big_f(f7(c2), f7(c2))))),
% 28.25/18.45 inference(rewrite,[status(thm)],[])).
% 28.25/18.45 tff(10226,plain,
% 28.25/18.45 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (f7(c2) = c2) | (f7(c2) = f5(c2)) | (~big_f(f7(c2), f7(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (f7(c2) = f5(c2)) | (~big_f(f7(c2), f7(c2)))))),
% 28.25/18.45 inference(monotonicity,[status(thm)],[10225])).
% 28.25/18.45 tff(10227,plain,
% 28.25/18.45 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (f7(c2) = c2) | (f7(c2) = f5(c2)) | (~big_f(f7(c2), f7(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (f7(c2) = f5(c2)) | (~big_f(f7(c2), f7(c2))))),
% 28.25/18.45 inference(transitivity,[status(thm)],[10226, 10224])).
% 28.25/18.45 tff(10228,plain,
% 28.25/18.45 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (f7(c2) = c2) | (f7(c2) = f5(c2)) | (~big_f(f7(c2), f7(c2))))),
% 28.25/18.45 inference(quant_inst,[status(thm)],[])).
% 28.25/18.45 tff(10229,plain,
% 28.25/18.45 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (f7(c2) = f5(c2)) | (~big_f(f7(c2), f7(c2)))),
% 28.25/18.45 inference(modus_ponens,[status(thm)],[10228, 10227])).
% 28.25/18.45 tff(10230,plain,
% 28.25/18.45 (f7(c2) = f5(c2)),
% 28.25/18.45 inference(unit_resolution,[status(thm)],[10229, 676, 122, 17, 8312, 8307, 8372])).
% 28.25/18.45 tff(10231,plain,
% 28.25/18.45 (f5(c2) = f7(c2)),
% 28.25/18.45 inference(symmetry,[status(thm)],[10230])).
% 28.25/18.45 tff(10232,plain,
% 28.25/18.45 (f5(c2) = c1),
% 28.25/18.45 inference(transitivity,[status(thm)],[10231, 22])).
% 28.25/18.45 tff(10233,plain,
% 28.25/18.45 ((f6(c1, c1) = f5(c2)) <=> (f6(c1, c1) = c1)),
% 28.25/18.45 inference(monotonicity,[status(thm)],[10232])).
% 28.25/18.45 tff(10234,plain,
% 28.25/18.45 ((f6(c1, c1) = f5(c2)) <=> (f6(f7(c2), f7(c2)) = f7(c2))),
% 28.25/18.45 inference(transitivity,[status(thm)],[10233, 10067])).
% 28.25/18.45 tff(10235,plain,
% 28.25/18.45 (f5(c2) = f7(c2)),
% 28.25/18.45 inference(symmetry,[status(thm)],[8378])).
% 28.25/18.45 tff(10236,plain,
% 28.25/18.45 (f5(c2) = c1),
% 28.25/18.45 inference(transitivity,[status(thm)],[10235, 22])).
% 28.25/18.45 tff(10237,plain,
% 28.25/18.45 ((f6(c1, c1) = f5(c2)) <=> (f6(c1, c1) = c1)),
% 28.25/18.45 inference(monotonicity,[status(thm)],[10236])).
% 28.25/18.45 tff(10238,plain,
% 28.25/18.45 ((f6(c1, c1) = c1) <=> (f6(c1, c1) = f5(c2))),
% 28.25/18.45 inference(symmetry,[status(thm)],[10237])).
% 28.25/18.45 tff(10239,plain,
% 28.25/18.45 ((f6(f7(c2), f7(c2)) = f7(c2)) <=> (f6(c1, c1) = f5(c2))),
% 28.25/18.45 inference(transitivity,[status(thm)],[9892, 10238])).
% 28.25/18.45 tff(10240,plain,
% 28.25/18.45 ((~big_f(f7(c1), f6(c1, c1))) <=> (~big_f(f7(f7(c2)), f6(f7(c2), f7(c2))))),
% 28.25/18.45 inference(monotonicity,[status(thm)],[9895])).
% 28.25/18.45 tff(10241,plain,
% 28.25/18.45 (~big_f(f7(f7(c2)), f6(f7(c2), f7(c2)))),
% 28.25/18.45 inference(modus_ponens,[status(thm)],[65, 10240])).
% 28.25/18.45 tff(10242,assumption,(~(f9(c2, f7(c2)) = f7(c2))), introduced(assumption)).
% 28.25/18.45 tff(10243,assumption,(~big_f(f9(c2, f7(c2)), f10(c2))), introduced(assumption)).
% 28.25/18.45 tff(10244,plain,
% 28.25/18.45 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (f6(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f6(f7(c2), f7(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (f6(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f6(f7(c2), f7(c2))))),
% 28.25/18.45 inference(rewrite,[status(thm)],[])).
% 28.25/18.45 tff(10245,plain,
% 28.25/18.45 (((~(f10(c2) = c2)) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (~(f7(f7(c2)) = f7(c2))) | (f6(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f6(f7(c2), f7(c2)))) <=> ((~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (f6(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f6(f7(c2), f7(c2))))),
% 28.25/18.45 inference(rewrite,[status(thm)],[])).
% 28.25/18.45 tff(10246,plain,
% 28.25/18.45 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (~(f7(f7(c2)) = f7(c2))) | (f6(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f6(f7(c2), f7(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (f6(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f6(f7(c2), f7(c2)))))),
% 28.25/18.45 inference(monotonicity,[status(thm)],[10245])).
% 28.25/18.45 tff(10247,plain,
% 28.25/18.45 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (~(f7(f7(c2)) = f7(c2))) | (f6(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f6(f7(c2), f7(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (f6(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f6(f7(c2), f7(c2))))),
% 28.25/18.45 inference(transitivity,[status(thm)],[10246, 10244])).
% 28.25/18.45 tff(10248,plain,
% 28.25/18.45 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (~(f7(f7(c2)) = f7(c2))) | (f6(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f6(f7(c2), f7(c2))))),
% 28.25/18.46 inference(quant_inst,[status(thm)],[])).
% 28.25/18.46 tff(10249,plain,
% 28.25/18.46 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (f6(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f6(f7(c2), f7(c2)))),
% 28.25/18.46 inference(modus_ponens,[status(thm)],[10248, 10247])).
% 28.25/18.46 tff(10250,plain,
% 28.25/18.46 ((f6(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f6(f7(c2), f7(c2)))),
% 28.25/18.46 inference(unit_resolution,[status(thm)],[10249, 2492, 122, 8315, 10243, 10242])).
% 28.25/18.46 tff(10251,plain,
% 28.25/18.46 (f6(f7(c2), f7(c2)) = f7(c2)),
% 28.25/18.46 inference(unit_resolution,[status(thm)],[10250, 10241])).
% 28.25/18.46 tff(10252,plain,
% 28.25/18.46 (f6(c1, c1) = f5(c2)),
% 28.25/18.46 inference(modus_ponens,[status(thm)],[10251, 10239])).
% 28.25/18.46 tff(10253,plain,
% 28.25/18.46 ((~big_f(f7(c1), f6(c1, c1))) <=> (~big_f(f7(c2), f6(c1, c1)))),
% 28.25/18.46 inference(monotonicity,[status(thm)],[5547])).
% 28.25/18.46 tff(10254,plain,
% 28.25/18.46 (~big_f(f7(c2), f6(c1, c1))),
% 28.25/18.46 inference(modus_ponens,[status(thm)],[65, 10253])).
% 28.25/18.46 tff(10255,plain,
% 28.25/18.46 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f7(c2), f6(c1, c1)) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (~(f6(c1, c1) = f5(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f7(c2), f6(c1, c1)) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (~(f6(c1, c1) = f5(c2))))),
% 28.25/18.46 inference(rewrite,[status(thm)],[])).
% 28.25/18.46 tff(10256,plain,
% 28.25/18.46 (((~(f10(c2) = c2)) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), f6(c1, c1)) | (~(f6(c1, c1) = f5(c2)))) <=> ((~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f7(c2), f6(c1, c1)) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (~(f6(c1, c1) = f5(c2))))),
% 28.25/18.46 inference(rewrite,[status(thm)],[])).
% 28.25/18.46 tff(10257,plain,
% 28.25/18.46 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), f6(c1, c1)) | (~(f6(c1, c1) = f5(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f7(c2), f6(c1, c1)) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (~(f6(c1, c1) = f5(c2)))))),
% 28.25/18.46 inference(monotonicity,[status(thm)],[10256])).
% 28.25/18.46 tff(10258,plain,
% 28.25/18.46 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), f6(c1, c1)) | (~(f6(c1, c1) = f5(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f7(c2), f6(c1, c1)) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (~(f6(c1, c1) = f5(c2))))),
% 28.25/18.46 inference(transitivity,[status(thm)],[10257, 10255])).
% 28.25/18.46 tff(10259,plain,
% 28.25/18.46 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), f6(c1, c1)) | (~(f6(c1, c1) = f5(c2))))),
% 28.25/18.46 inference(quant_inst,[status(thm)],[])).
% 28.25/18.46 tff(10260,plain,
% 28.25/18.46 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f7(c2), f6(c1, c1)) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (~(f6(c1, c1) = f5(c2)))),
% 28.25/18.46 inference(modus_ponens,[status(thm)],[10259, 10258])).
% 28.25/18.46 tff(10261,plain,
% 28.25/18.46 (big_f(f7(c2), f6(c1, c1)) | (~(f6(c1, c1) = f5(c2)))),
% 28.25/18.46 inference(unit_resolution,[status(thm)],[10260, 267, 122, 17, 10243, 10242])).
% 28.25/18.46 tff(10262,plain,
% 28.25/18.46 (~(f6(c1, c1) = f5(c2))),
% 28.25/18.46 inference(unit_resolution,[status(thm)],[10261, 10254])).
% 28.25/18.46 tff(10263,plain,
% 28.25/18.46 ($false),
% 28.25/18.46 inference(unit_resolution,[status(thm)],[10262, 10252])).
% 28.25/18.46 tff(10264,plain,(big_f(f7(c1), f6(c1, c1)) | (~(f7(c2) = f5(c2))) | (~(f10(c2) = c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (f9(c2, f7(c2)) = f7(c2)) | (f7(c2) = c2) | (~(f7(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.25/18.46 tff(10265,plain,
% 28.25/18.46 (big_f(f7(c1), f6(c1, c1))),
% 28.25/18.46 inference(unit_resolution,[status(thm)],[10264, 10230, 122, 8312, 8307, 17, 4234])).
% 28.25/18.46 tff(10266,plain,
% 28.25/18.46 (big_f(f7(c2), f6(c1, c1))),
% 28.25/18.46 inference(modus_ponens,[status(thm)],[10265, 5547])).
% 28.25/18.46 tff(10267,plain,
% 28.25/18.46 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)))),
% 28.25/18.46 inference(rewrite,[status(thm)],[])).
% 28.25/18.46 tff(10268,plain,
% 28.25/18.46 (((~(f10(c2) = c2)) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (f7(c2) = c2) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1)))) <=> ((~(f10(c2) = c2)) | (f7(c2) = c2) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)))),
% 28.25/18.46 inference(rewrite,[status(thm)],[])).
% 28.25/18.46 tff(10269,plain,
% 28.25/18.46 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (f7(c2) = c2) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2))))),
% 28.25/18.46 inference(monotonicity,[status(thm)],[10268])).
% 28.25/18.46 tff(10270,plain,
% 28.25/18.46 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (f7(c2) = c2) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)))),
% 28.25/18.46 inference(transitivity,[status(thm)],[10269, 10267])).
% 28.25/18.46 tff(10271,plain,
% 28.25/18.46 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (f7(c2) = c2) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))))),
% 28.25/18.46 inference(quant_inst,[status(thm)],[])).
% 28.25/18.46 tff(10272,plain,
% 28.25/18.46 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2))),
% 28.25/18.46 inference(modus_ponens,[status(thm)],[10271, 10270])).
% 28.25/18.46 tff(10273,plain,
% 28.25/18.46 ((f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1)))),
% 28.25/18.46 inference(unit_resolution,[status(thm)],[10272, 676, 122, 17, 8312, 8307])).
% 28.25/18.46 tff(10274,plain,
% 28.25/18.46 (f6(c1, c1) = f5(c2)),
% 28.25/18.46 inference(unit_resolution,[status(thm)],[10273, 10266])).
% 28.25/18.46 tff(10275,plain,
% 28.25/18.46 (f6(f7(c2), f7(c2)) = f7(c2)),
% 28.25/18.46 inference(modus_ponens,[status(thm)],[10274, 10234])).
% 28.25/18.46 tff(10276,plain,
% 28.25/18.46 (big_f(f7(f7(c2)), f6(f7(c2), f7(c2)))),
% 28.25/18.46 inference(modus_ponens,[status(thm)],[10265, 9895])).
% 28.25/18.46 tff(10277,plain,
% 28.25/18.46 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (~(f6(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), f7(c2)))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (~(f6(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), f7(c2)))))),
% 28.25/18.46 inference(rewrite,[status(thm)],[])).
% 28.25/18.46 tff(10278,plain,
% 28.25/18.46 (((~(f10(c2) = c2)) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (~(f7(f7(c2)) = f7(c2))) | (~(f6(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), f7(c2))))) <=> ((~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (~(f6(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), f7(c2)))))),
% 28.25/18.46 inference(rewrite,[status(thm)],[])).
% 28.25/18.46 tff(10279,plain,
% 28.25/18.46 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (~(f7(f7(c2)) = f7(c2))) | (~(f6(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), f7(c2)))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (~(f6(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), f7(c2))))))),
% 28.25/18.46 inference(monotonicity,[status(thm)],[10278])).
% 28.25/18.46 tff(10280,plain,
% 28.25/18.46 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (~(f7(f7(c2)) = f7(c2))) | (~(f6(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), f7(c2)))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (~(f6(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), f7(c2)))))),
% 28.25/18.46 inference(transitivity,[status(thm)],[10279, 10277])).
% 28.25/18.46 tff(10281,plain,
% 28.25/18.46 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (~(f7(f7(c2)) = f7(c2))) | (~(f6(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), f7(c2)))))),
% 28.25/18.46 inference(quant_inst,[status(thm)],[])).
% 28.25/18.46 tff(10282,plain,
% 28.25/18.46 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (~(f6(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), f7(c2))))),
% 28.25/18.46 inference(modus_ponens,[status(thm)],[10281, 10280])).
% 28.25/18.46 tff(10283,plain,
% 28.25/18.46 ((~(f6(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), f7(c2))))),
% 28.25/18.46 inference(unit_resolution,[status(thm)],[10282, 2534, 122, 8315, 8312, 8307])).
% 28.25/18.46 tff(10284,plain,
% 28.25/18.46 (~(f6(f7(c2), f7(c2)) = f7(c2))),
% 28.25/18.46 inference(unit_resolution,[status(thm)],[10283, 10276])).
% 28.25/18.46 tff(10285,plain,
% 28.25/18.46 ($false),
% 28.25/18.46 inference(unit_resolution,[status(thm)],[10284, 10275])).
% 28.25/18.46 tff(10286,plain,((f9(c2, c1) = c1) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~(f7(c1) = c1)) | (~big_f(f7(c2), f7(c2))) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 28.25/18.46 tff(10287,plain,
% 28.25/18.46 (~(f7(c1) = c1)),
% 28.25/18.46 inference(unit_resolution,[status(thm)],[10286, 121, 17, 10223, 9486, 122])).
% 28.25/18.46 tff(10288,plain,
% 28.25/18.46 (~(c3 = c2)),
% 28.25/18.46 inference(unit_resolution,[status(thm)],[8259, 121, 2, 79])).
% 28.25/18.46 tff(10289,plain,
% 28.25/18.46 (c3 = c1),
% 28.25/18.46 inference(unit_resolution,[status(thm)],[180, 10288])).
% 28.25/18.46 tff(10290,plain,
% 28.25/18.46 ($false),
% 28.25/18.46 inference(unit_resolution,[status(thm)],[9080, 10289, 10287, 17, 79, 122, 121])).
% 28.25/18.46 tff(10291,plain,(big_f(c2, c2) | (f7(c2) = c2) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | big_f(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 28.25/18.46 tff(10292,plain,
% 28.25/18.46 (big_f(c2, c2)),
% 28.25/18.46 inference(unit_resolution,[status(thm)],[10291, 2, 79, 122, 17])).
% 28.25/18.46 tff(10293,plain,
% 28.25/18.46 (big_f(f9(c2, c2), f10(c2))),
% 28.25/18.46 inference(modus_ponens,[status(thm)],[10292, 8070])).
% 28.25/18.46 tff(10294,plain,
% 28.25/18.46 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f7(c2) = f5(c2)) | (~big_f(f7(c2), f7(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f7(c2) = f5(c2)) | (~big_f(f7(c2), f7(c2))))),
% 28.25/18.46 inference(rewrite,[status(thm)],[])).
% 28.25/18.46 tff(10295,plain,
% 28.25/18.46 (((~(f10(c2) = c2)) | (f7(c2) = c2) | (f7(c2) = f5(c2)) | (~big_f(f7(c2), f7(c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2)))) <=> ((~(f10(c2) = c2)) | (f7(c2) = c2) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f7(c2) = f5(c2)) | (~big_f(f7(c2), f7(c2))))),
% 28.25/18.46 inference(rewrite,[status(thm)],[])).
% 28.25/18.46 tff(10296,plain,
% 28.25/18.46 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (f7(c2) = f5(c2)) | (~big_f(f7(c2), f7(c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f7(c2) = f5(c2)) | (~big_f(f7(c2), f7(c2)))))),
% 28.25/18.46 inference(monotonicity,[status(thm)],[10295])).
% 28.25/18.46 tff(10297,plain,
% 28.25/18.46 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (f7(c2) = f5(c2)) | (~big_f(f7(c2), f7(c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f7(c2) = f5(c2)) | (~big_f(f7(c2), f7(c2))))),
% 28.25/18.46 inference(transitivity,[status(thm)],[10296, 10294])).
% 28.25/18.46 tff(10298,plain,
% 28.25/18.46 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (f7(c2) = f5(c2)) | (~big_f(f7(c2), f7(c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))),
% 28.25/18.46 inference(quant_inst,[status(thm)],[])).
% 28.25/18.46 tff(10299,plain,
% 28.25/18.46 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f7(c2) = f5(c2)) | (~big_f(f7(c2), f7(c2)))),
% 28.25/18.46 inference(modus_ponens,[status(thm)],[10298, 10297])).
% 28.25/18.46 tff(10300,plain,
% 28.25/18.46 ((~big_f(f9(c2, c2), f10(c2))) | (f7(c2) = f5(c2))),
% 28.25/18.46 inference(unit_resolution,[status(thm)],[10299, 1190, 122, 17, 8080, 9486])).
% 28.25/18.46 tff(10301,plain,
% 28.25/18.46 (f7(c2) = f5(c2)),
% 28.25/18.46 inference(unit_resolution,[status(thm)],[10300, 10293])).
% 28.25/18.46 tff(10302,plain,
% 28.25/18.46 (f5(c2) = f7(c2)),
% 28.25/18.46 inference(symmetry,[status(thm)],[10301])).
% 28.25/18.46 tff(10303,plain,
% 28.25/18.46 ((c2 = f5(c2)) <=> (c2 = f7(c2))),
% 28.25/18.46 inference(monotonicity,[status(thm)],[10302])).
% 28.25/18.46 tff(10304,plain,
% 28.25/18.46 ((c2 = f5(c2)) <=> (f7(c2) = c2)),
% 28.25/18.46 inference(transitivity,[status(thm)],[10303, 8409])).
% 28.25/18.46 tff(10305,plain,
% 28.25/18.46 ((f7(c2) = c2) <=> (c2 = f5(c2))),
% 28.25/18.46 inference(symmetry,[status(thm)],[10304])).
% 28.25/18.46 tff(10306,plain,
% 28.25/18.46 ((~(f7(c2) = c2)) <=> (~(c2 = f5(c2)))),
% 28.25/18.46 inference(monotonicity,[status(thm)],[10305])).
% 28.25/18.46 tff(10307,plain,
% 28.25/18.46 (~(c2 = f5(c2))),
% 28.25/18.46 inference(modus_ponens,[status(thm)],[17, 10306])).
% 28.25/18.46 tff(10308,plain,
% 28.25/18.46 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))),
% 28.25/18.46 inference(rewrite,[status(thm)],[])).
% 28.25/18.46 tff(10309,plain,
% 28.25/18.46 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))),
% 28.25/18.46 inference(quant_inst,[status(thm)],[])).
% 28.25/18.46 tff(10310,plain,
% 28.25/18.46 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2)))),
% 28.25/18.46 inference(modus_ponens,[status(thm)],[10309, 10308])).
% 28.25/18.46 tff(10311,plain,
% 28.25/18.46 ((c2 = f5(c2)) | (~big_f(f9(c2, c2), f10(c2)))),
% 28.25/18.46 inference(unit_resolution,[status(thm)],[10310, 1190, 122, 17, 10201, 8080])).
% 28.25/18.46 tff(10312,plain,
% 28.25/18.46 (c2 = f5(c2)),
% 28.25/18.46 inference(unit_resolution,[status(thm)],[10311, 10293])).
% 28.25/18.46 tff(10313,plain,
% 28.25/18.46 ($false),
% 28.25/18.46 inference(unit_resolution,[status(thm)],[10312, 10307])).
% 28.25/18.46 tff(10314,plain,(big_f(c2, c1) | (f7(c2) = c2) | (~(f10(c2) = c2)) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.25/18.47 tff(10315,plain,
% 28.25/18.47 (big_f(c2, c1)),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[10314, 17, 122, 79])).
% 28.25/18.47 tff(10316,plain,
% 28.25/18.47 (big_f(f7(f7(c2)), f7(c2))),
% 28.25/18.47 inference(modus_ponens,[status(thm)],[10315, 9297])).
% 28.25/18.47 tff(10317,plain,
% 28.25/18.47 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))))),
% 28.25/18.47 inference(rewrite,[status(thm)],[])).
% 28.25/18.47 tff(10318,plain,
% 28.25/18.47 (((~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2)))) <=> ((~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))))),
% 28.25/18.47 inference(rewrite,[status(thm)],[])).
% 28.25/18.47 tff(10319,plain,
% 28.25/18.47 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2)))))),
% 28.25/18.47 inference(monotonicity,[status(thm)],[10318])).
% 28.25/18.47 tff(10320,plain,
% 28.25/18.47 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))))),
% 28.25/18.47 inference(transitivity,[status(thm)],[10319, 10317])).
% 28.25/18.47 tff(10321,plain,
% 28.25/18.47 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))),
% 28.25/18.47 inference(quant_inst,[status(thm)],[])).
% 28.25/18.47 tff(10322,plain,
% 28.25/18.47 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2)))),
% 28.25/18.47 inference(modus_ponens,[status(thm)],[10321, 10320])).
% 28.25/18.47 tff(10323,plain,
% 28.25/18.47 (f7(c2) = f5(f7(c2))),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[10322, 1190, 122, 9284, 8080, 9235, 10316])).
% 28.25/18.47 tff(10324,plain,
% 28.25/18.47 (f7(c2) = c2),
% 28.25/18.47 inference(transitivity,[status(thm)],[10323, 9292])).
% 28.25/18.47 tff(10325,plain,
% 28.25/18.47 ($false),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[17, 10324])).
% 28.25/18.47 tff(10326,plain,(big_f(f7(c2), c1) | (f7(c2) = c2) | (~(f10(c2) = c2)) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.25/18.47 tff(10327,plain,
% 28.25/18.47 (big_f(f7(c2), c1)),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[10326, 17, 122, 79])).
% 28.25/18.47 tff(10328,plain,
% 28.25/18.47 (big_f(f7(c2), f7(c2))),
% 28.25/18.47 inference(modus_ponens,[status(thm)],[10327, 8076])).
% 28.25/18.47 tff(10329,plain,
% 28.25/18.47 (~(c4 = c2)),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[10120, 9781, 22, 348, 121, 79])).
% 28.25/18.47 tff(10330,plain,
% 28.25/18.47 (~(f7(c1) = c1)),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[10195, 1521, 79, 338, 17, 121])).
% 28.25/18.47 tff(10331,plain,
% 28.25/18.47 (f7(c1) = c2),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[119, 10330])).
% 28.25/18.47 tff(10332,plain,
% 28.25/18.47 (~(c4 = c1)),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[8806, 10331, 338, 121, 348, 17, 79, 9781])).
% 28.25/18.47 tff(10333,plain,
% 28.25/18.47 ($false),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[461, 10332, 10329])).
% 28.25/18.47 tff(10334,plain,(big_f(f7(c2), c2) | (~big_f(f7(c2), c1)) | big_f(c2, c2) | (~big_f(c2, c1)) | (f7(c2) = c2) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.25/18.47 tff(10335,plain,
% 28.25/18.47 (big_f(f7(c2), c2)),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[10334, 121, 10327, 10315, 17, 79])).
% 28.25/18.47 tff(10336,plain,
% 28.25/18.47 (~(f9(c2, c1) = c1)),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[10222, 10335, 122, 17, 10328])).
% 28.25/18.47 tff(10337,plain,
% 28.25/18.47 (~(f9(c2, f7(c2)) = f7(c2))),
% 28.25/18.47 inference(modus_ponens,[status(thm)],[10336, 8074])).
% 28.25/18.47 tff(10338,plain,
% 28.25/18.47 (f9(c2, c1) = c2),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[3913, 10336])).
% 28.25/18.47 tff(10339,plain,
% 28.25/18.47 (big_f(f9(c2, c1), f10(c2)) <=> big_f(c2, c2)),
% 28.25/18.47 inference(monotonicity,[status(thm)],[10338, 122])).
% 28.25/18.47 tff(10340,plain,
% 28.25/18.47 (big_f(c2, c2) <=> big_f(f9(c2, c1), f10(c2))),
% 28.25/18.47 inference(symmetry,[status(thm)],[10339])).
% 28.25/18.47 tff(10341,plain,
% 28.25/18.47 (big_f(c2, c2) <=> big_f(f9(c2, f7(c2)), f10(c2))),
% 28.25/18.47 inference(transitivity,[status(thm)],[10340, 8309])).
% 28.25/18.47 tff(10342,plain,
% 28.25/18.47 ((~big_f(c2, c2)) <=> (~big_f(f9(c2, f7(c2)), f10(c2)))),
% 28.25/18.47 inference(monotonicity,[status(thm)],[10341])).
% 28.25/18.47 tff(10343,plain,
% 28.25/18.47 (~big_f(f9(c2, f7(c2)), f10(c2))),
% 28.25/18.47 inference(modus_ponens,[status(thm)],[121, 10342])).
% 28.25/18.47 tff(10344,plain,
% 28.25/18.47 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)))),
% 28.25/18.47 inference(rewrite,[status(thm)],[])).
% 28.25/18.47 tff(10345,plain,
% 28.25/18.47 (((~(f10(c2) = c2)) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2))) <=> ((~(f10(c2) = c2)) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)))),
% 28.25/18.47 inference(rewrite,[status(thm)],[])).
% 28.25/18.47 tff(10346,plain,
% 28.25/18.47 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2))))),
% 28.25/18.47 inference(monotonicity,[status(thm)],[10345])).
% 28.25/18.47 tff(10347,plain,
% 28.25/18.47 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)))),
% 28.25/18.47 inference(transitivity,[status(thm)],[10346, 10344])).
% 28.25/18.47 tff(10348,plain,
% 28.25/18.47 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)))),
% 28.25/18.47 inference(quant_inst,[status(thm)],[])).
% 28.25/18.47 tff(10349,plain,
% 28.25/18.47 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2))),
% 28.25/18.47 inference(modus_ponens,[status(thm)],[10348, 10347])).
% 28.25/18.47 tff(10350,plain,
% 28.25/18.47 (c2 = f5(c2)),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[10349, 676, 122, 17, 10335, 10343, 10337])).
% 28.25/18.47 tff(10351,plain,
% 28.25/18.47 (f5(c2) = c2),
% 28.25/18.47 inference(symmetry,[status(thm)],[10350])).
% 28.25/18.47 tff(10352,plain,
% 28.25/18.47 (f7(c2) = f5(c2)),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[10229, 676, 122, 17, 10343, 10337, 10328])).
% 28.25/18.47 tff(10353,plain,
% 28.25/18.47 (f7(c2) = c2),
% 28.25/18.47 inference(transitivity,[status(thm)],[10352, 10351])).
% 28.25/18.47 tff(10354,plain,
% 28.25/18.47 ($false),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[17, 10353])).
% 28.25/18.47 tff(10355,plain,(big_f(c2, c2) | (f7(c2) = c2) | (~(f10(c2) = c2)) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.25/18.47 tff(10356,plain,
% 28.25/18.47 (big_f(c2, c2)),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[10355, 17, 122, 79])).
% 28.25/18.47 tff(10357,plain,
% 28.25/18.47 (big_f(f9(c2, c2), f10(c2))),
% 28.25/18.47 inference(modus_ponens,[status(thm)],[10356, 8070])).
% 28.25/18.47 tff(10358,plain,
% 28.25/18.47 ((~big_f(f9(c2, c2), f10(c2))) | (f7(c2) = f5(c2))),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[10299, 1190, 122, 17, 8080, 10328])).
% 28.25/18.47 tff(10359,plain,
% 28.25/18.47 (f7(c2) = f5(c2)),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[10358, 10357])).
% 28.25/18.47 tff(10360,plain,
% 28.25/18.47 ((c3 = c1) <=> (f7(c2) = c3)),
% 28.25/18.47 inference(transitivity,[status(thm)],[68, 9087])).
% 28.25/18.47 tff(10361,plain,
% 28.25/18.47 ((~(c3 = c1)) <=> (~(f7(c2) = c3))),
% 28.25/18.47 inference(monotonicity,[status(thm)],[10360])).
% 28.25/18.47 tff(10362,plain,
% 28.25/18.47 (~(c3 = c1)),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[9080, 115, 17, 79, 122, 121])).
% 28.25/18.47 tff(10363,plain,
% 28.25/18.47 (~(f7(c2) = c3)),
% 28.25/18.47 inference(modus_ponens,[status(thm)],[10362, 10361])).
% 28.25/18.47 tff(10364,plain,
% 28.25/18.47 (~(c1 = c3)),
% 28.25/18.47 inference(modus_ponens,[status(thm)],[10362, 648])).
% 28.25/18.47 tff(10365,plain,
% 28.25/18.47 (c3 = c2),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[180, 10362])).
% 28.25/18.47 tff(10366,plain,
% 28.25/18.47 (big_f(c2, c1)),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[8259, 10365, 121, 79])).
% 28.25/18.47 tff(10367,plain,
% 28.25/18.47 (~big_f(f7(c2), c1)),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[9778, 1521, 9092, 168, 79, 121, 17])).
% 28.25/18.47 tff(10368,plain,
% 28.25/18.47 (f10(c1) = c1),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[8159, 10367, 17, 1521, 121, 122, 79])).
% 28.25/18.47 tff(10369,plain,
% 28.25/18.47 (~(f5(c2) = c2)),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[9023, 10368, 1521, 17, 348, 10367, 79, 347, 122])).
% 28.25/18.47 tff(10370,plain,
% 28.25/18.47 (~(f5(c2) = c1)),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[9008, 10368, 17, 348, 79, 10367, 347, 122])).
% 28.25/18.47 tff(10371,plain,
% 28.25/18.47 ($false),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[1547, 10370, 10369])).
% 28.25/18.47 tff(10372,plain,(big_f(f7(c2), c2) | (f7(c2) = c2) | (~big_f(c2, c1)) | (~(f4(c4) = c2)) | (~(f7(c1) = c2)) | (~(f10(c2) = c2)) | big_f(c2, c2) | (f7(c2) = c3) | (c1 = c3)), inference(lemma,lemma(discharge,[]))).
% 28.25/18.47 tff(10373,plain,
% 28.25/18.47 (big_f(f7(c2), c2)),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[10372, 10366, 17, 79, 120, 122, 121, 10363, 10364])).
% 28.25/18.47 tff(10374,plain,
% 28.25/18.47 (big_f(f7(c2), c1)),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[9231, 10364, 10373, 121, 10363, 17, 79, 120])).
% 28.25/18.47 tff(10375,plain,
% 28.25/18.47 ((c2 = f5(c1)) <=> (c2 = f5(f7(c2)))),
% 28.25/18.47 inference(symmetry,[status(thm)],[8484])).
% 28.25/18.47 tff(10376,plain,
% 28.25/18.47 ((f5(c1) = c2) <=> (c2 = f5(f7(c2)))),
% 28.25/18.47 inference(transitivity,[status(thm)],[155, 10375])).
% 28.25/18.47 tff(10377,plain,
% 28.25/18.47 (c2 = f5(f7(c2))),
% 28.25/18.47 inference(modus_ponens,[status(thm)],[186, 10376])).
% 28.25/18.47 tff(10378,plain,
% 28.25/18.47 ((f9(c2, f7(c2)) = f7(c2)) <=> (f9(c2, c1) = c1)),
% 28.25/18.47 inference(monotonicity,[status(thm)],[8456, 292])).
% 28.25/18.47 tff(10379,plain,
% 28.25/18.47 ((f9(c2, c1) = c1) <=> (f9(c2, f7(c2)) = f7(c2))),
% 28.25/18.47 inference(symmetry,[status(thm)],[10378])).
% 28.25/18.47 tff(10380,plain,
% 28.25/18.47 (~big_f(f7(c1), f5(c1))),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[1715, 186, 121, 120])).
% 28.25/18.47 tff(10381,plain,
% 28.25/18.47 (f9(c2, c1) = c1),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[8445, 10380, 122, 115, 121])).
% 28.25/18.47 tff(10382,plain,
% 28.25/18.47 (f9(c2, f7(c2)) = f7(c2)),
% 28.25/18.47 inference(modus_ponens,[status(thm)],[10381, 10379])).
% 28.25/18.47 tff(10383,plain,
% 28.25/18.47 (big_f(f9(c2, f7(c2)), f10(c2)) <=> big_f(f9(c2, c1), f10(c2))),
% 28.25/18.47 inference(monotonicity,[status(thm)],[8456])).
% 28.25/18.47 tff(10384,plain,
% 28.25/18.47 (big_f(f9(c2, c1), f10(c2)) <=> big_f(f9(c2, f7(c2)), f10(c2))),
% 28.25/18.47 inference(symmetry,[status(thm)],[10383])).
% 28.25/18.47 tff(10385,plain,
% 28.25/18.47 (f9(c2, c1) = f7(c2)),
% 28.25/18.47 inference(transitivity,[status(thm)],[10381, 342])).
% 28.25/18.47 tff(10386,plain,
% 28.25/18.47 (big_f(f9(c2, c1), f10(c2)) <=> big_f(f7(c2), c2)),
% 28.25/18.47 inference(monotonicity,[status(thm)],[10385, 122])).
% 28.25/18.47 tff(10387,plain,
% 28.25/18.47 (big_f(f7(c2), c2) <=> big_f(f9(c2, c1), f10(c2))),
% 28.25/18.47 inference(symmetry,[status(thm)],[10386])).
% 28.25/18.47 tff(10388,plain,
% 28.25/18.47 (big_f(f7(c2), c2) <=> big_f(f9(c2, f7(c2)), f10(c2))),
% 28.25/18.47 inference(transitivity,[status(thm)],[10387, 10384])).
% 28.25/18.47 tff(10389,plain,
% 28.25/18.47 (big_f(f9(c2, f7(c2)), f10(c2))),
% 28.25/18.47 inference(modus_ponens,[status(thm)],[1180, 10388])).
% 28.25/18.47 tff(10390,plain,
% 28.25/18.47 ($false),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[8493, 783, 122, 8463, 10389, 10382, 8468, 10377])).
% 28.25/18.47 tff(10391,plain,((~(f5(c1) = c2)) | (~(f10(c2) = c2)) | (~big_f(f7(c2), c2)) | (~(f7(c2) = c1)) | (f7(c1) = c1) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 28.25/18.47 tff(10392,plain,
% 28.25/18.47 (~(f5(c1) = c2)),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[10391, 10373, 122, 22, 115, 121])).
% 28.25/18.47 tff(10393,plain,
% 28.25/18.47 (f5(c1) = c1),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[1708, 10392])).
% 28.25/18.47 tff(10394,assumption,(f6(c2, f9(c2, f5(c1))) = c1), introduced(assumption)).
% 28.25/18.47 tff(10395,plain,
% 28.25/18.47 (c2 = f9(c2, c1)),
% 28.25/18.47 inference(symmetry,[status(thm)],[5008])).
% 28.25/18.47 tff(10396,plain,
% 28.25/18.47 (c2 = f9(c2, f5(c1))),
% 28.25/18.47 inference(transitivity,[status(thm)],[10395, 3554])).
% 28.25/18.47 tff(10397,plain,
% 28.25/18.47 (f6(c2, c2) = f6(c2, f9(c2, f5(c1)))),
% 28.25/18.47 inference(monotonicity,[status(thm)],[10396])).
% 28.25/18.47 tff(10398,plain,
% 28.25/18.47 (f6(c2, c2) = c1),
% 28.25/18.47 inference(transitivity,[status(thm)],[10397, 10394])).
% 28.25/18.47 tff(10399,plain,
% 28.25/18.47 (big_f(f7(c2), f6(c2, c2)) <=> big_f(f7(c2), c1)),
% 28.25/18.47 inference(monotonicity,[status(thm)],[10398])).
% 28.25/18.47 tff(10400,plain,
% 28.25/18.47 (big_f(f7(c2), c1) <=> big_f(f7(c2), f6(c2, c2))),
% 28.25/18.47 inference(symmetry,[status(thm)],[10399])).
% 28.25/18.47 tff(10401,plain,
% 28.25/18.47 (big_f(f7(c2), f6(c2, c2))),
% 28.25/18.47 inference(modus_ponens,[status(thm)],[338, 10400])).
% 28.25/18.47 tff(10402,plain,
% 28.25/18.47 ($false),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[2621, 10401])).
% 28.25/18.47 tff(10403,plain,((~(f6(c2, f9(c2, f5(c1))) = c1)) | big_f(f7(c2), f6(c2, c2)) | (~big_f(f7(c2), c1)) | (~(f9(c2, c1) = c2)) | (~(f5(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.25/18.47 tff(10404,plain,
% 28.25/18.47 (~(f6(c2, f9(c2, f5(c1))) = c1)),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[10403, 5008, 338, 2621, 230])).
% 28.25/18.47 tff(10405,plain,
% 28.25/18.47 (f6(c2, f9(c2, f5(c1))) = c2),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[7234, 10404])).
% 28.25/18.47 tff(10406,plain,
% 28.25/18.47 (f6(c2, c2) = c2),
% 28.25/18.47 inference(transitivity,[status(thm)],[10397, 10405])).
% 28.25/18.47 tff(10407,plain,
% 28.25/18.47 (big_f(f7(c2), f6(c2, c2)) <=> big_f(f7(c2), c2)),
% 28.25/18.47 inference(monotonicity,[status(thm)],[10406])).
% 28.25/18.47 tff(10408,plain,
% 28.25/18.47 (big_f(f7(c2), c2) <=> big_f(f7(c2), f6(c2, c2))),
% 28.25/18.47 inference(symmetry,[status(thm)],[10407])).
% 28.25/18.47 tff(10409,plain,
% 28.25/18.47 (big_f(f7(c2), f6(c2, c2))),
% 28.25/18.47 inference(modus_ponens,[status(thm)],[1180, 10408])).
% 28.25/18.47 tff(10410,plain,
% 28.25/18.47 ($false),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[2621, 10409])).
% 28.25/18.47 tff(10411,plain,((~(f9(c2, c1) = c2)) | big_f(f7(c2), f6(c2, c2)) | (~big_f(f7(c2), c2)) | (~(f5(c1) = c1)) | (~big_f(f7(c2), c1))), inference(lemma,lemma(discharge,[]))).
% 28.25/18.47 tff(10412,plain,
% 28.25/18.47 (~(f9(c2, c1) = c2)),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[10411, 10373, 2621, 10393, 10374])).
% 28.25/18.47 tff(10413,plain,
% 28.25/18.47 (f9(c2, c1) = c1),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[3913, 10412])).
% 28.25/18.47 tff(10414,plain,
% 28.25/18.47 (f9(c2, f7(c2)) = f7(c2)),
% 28.25/18.47 inference(modus_ponens,[status(thm)],[10413, 8073])).
% 28.25/18.47 tff(10415,plain,
% 28.25/18.47 (f9(c2, c1) = f7(c2)),
% 28.25/18.47 inference(transitivity,[status(thm)],[10413, 125])).
% 28.25/18.47 tff(10416,plain,
% 28.25/18.47 (big_f(f9(c2, c1), f10(c2)) <=> big_f(f7(c2), c2)),
% 28.25/18.47 inference(monotonicity,[status(thm)],[10415, 122])).
% 28.25/18.47 tff(10417,plain,
% 28.25/18.47 (big_f(f7(c2), c2) <=> big_f(f9(c2, c1), f10(c2))),
% 28.25/18.47 inference(symmetry,[status(thm)],[10416])).
% 28.25/18.47 tff(10418,plain,
% 28.25/18.47 (big_f(f7(c2), c2) <=> big_f(f9(c2, f7(c2)), f10(c2))),
% 28.25/18.47 inference(transitivity,[status(thm)],[10417, 8309])).
% 28.25/18.47 tff(10419,plain,
% 28.25/18.47 (big_f(f9(c2, f7(c2)), f10(c2))),
% 28.25/18.47 inference(modus_ponens,[status(thm)],[10373, 10418])).
% 28.25/18.47 tff(10420,plain,
% 28.25/18.47 (c2 = f5(c2)),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[10210, 1190, 122, 17, 10373, 10419, 10414])).
% 28.25/18.47 tff(10421,plain,
% 28.25/18.47 (f5(c2) = c2),
% 28.25/18.47 inference(symmetry,[status(thm)],[10420])).
% 28.25/18.47 tff(10422,plain,
% 28.25/18.47 (big_f(f7(c2), f7(c2))),
% 28.25/18.47 inference(modus_ponens,[status(thm)],[10374, 8076])).
% 28.25/18.47 tff(10423,plain,
% 28.25/18.47 (f7(c2) = f5(c2)),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[10218, 1190, 122, 17, 10419, 10414, 10422])).
% 28.25/18.47 tff(10424,plain,
% 28.25/18.47 (f7(c2) = c2),
% 28.25/18.47 inference(transitivity,[status(thm)],[10423, 10421])).
% 28.25/18.47 tff(10425,plain,
% 28.25/18.47 ($false),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[17, 10424])).
% 28.25/18.47 tff(10426,plain,((f7(c1) = c1) | (f7(c2) = c2) | (~(f10(c2) = c2)) | big_f(f7(c2), f6(c2, c2)) | big_f(c2, c2) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.25/18.47 tff(10427,plain,
% 28.25/18.47 (f7(c1) = c1),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[10426, 121, 122, 2621, 17, 79])).
% 28.25/18.47 tff(10428,plain,
% 28.25/18.47 (big_f(f7(c2), c1)),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[8365, 10427, 122, 17, 121, 79])).
% 28.25/18.47 tff(10429,plain,
% 28.25/18.47 (big_f(f7(c2), f7(c2))),
% 28.25/18.47 inference(modus_ponens,[status(thm)],[10428, 8076])).
% 28.25/18.47 tff(10430,plain,
% 28.25/18.47 (f9(c2, c1) = c1),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[10286, 10427, 17, 122, 10429, 121])).
% 28.25/18.47 tff(10431,plain,
% 28.25/18.47 (f9(c2, f7(c2)) = f7(c2)),
% 28.25/18.47 inference(modus_ponens,[status(thm)],[10430, 8073])).
% 28.25/18.47 tff(10432,plain,
% 28.25/18.47 (f9(c2, c1) = f7(c2)),
% 28.25/18.47 inference(transitivity,[status(thm)],[10430, 125])).
% 28.25/18.47 tff(10433,plain,
% 28.25/18.47 (big_f(f9(c2, c1), f10(c2)) <=> big_f(f7(c2), c2)),
% 28.25/18.47 inference(monotonicity,[status(thm)],[10432, 122])).
% 28.25/18.47 tff(10434,plain,
% 28.25/18.47 (big_f(f7(c2), c2) <=> big_f(f9(c2, c1), f10(c2))),
% 28.25/18.47 inference(symmetry,[status(thm)],[10433])).
% 28.25/18.47 tff(10435,plain,
% 28.25/18.47 (big_f(f7(c2), c2) <=> big_f(f9(c2, f7(c2)), f10(c2))),
% 28.25/18.47 inference(transitivity,[status(thm)],[10434, 8309])).
% 28.25/18.47 tff(10436,plain,
% 28.25/18.47 (big_f(f7(c2), c2)),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[10195, 10428, 79, 121, 17, 10427])).
% 28.25/18.47 tff(10437,plain,
% 28.25/18.47 (big_f(f9(c2, f7(c2)), f10(c2))),
% 28.25/18.47 inference(modus_ponens,[status(thm)],[10436, 10435])).
% 28.25/18.47 tff(10438,plain,
% 28.25/18.47 (c2 = f5(c2)),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[10210, 1190, 122, 17, 10436, 10437, 10431])).
% 28.25/18.47 tff(10439,plain,
% 28.25/18.47 (f5(c2) = c2),
% 28.25/18.47 inference(symmetry,[status(thm)],[10438])).
% 28.25/18.47 tff(10440,plain,
% 28.25/18.47 ((~big_f(f9(c2, f7(c2)), f10(c2))) | (f7(c2) = f5(c2))),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[10218, 1190, 122, 17, 10431, 10429])).
% 28.25/18.47 tff(10441,plain,
% 28.25/18.47 (f7(c2) = f5(c2)),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[10440, 10437])).
% 28.25/18.47 tff(10442,plain,
% 28.25/18.47 (f7(c2) = c2),
% 28.25/18.47 inference(transitivity,[status(thm)],[10441, 10439])).
% 28.25/18.47 tff(10443,plain,
% 28.25/18.47 ($false),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[17, 10442])).
% 28.25/18.47 tff(10444,plain,(big_f(c2, c2) | (f7(c2) = c2) | (~(f10(c2) = c2)) | (~(f4(c4) = c2)) | big_f(f7(c2), f6(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 28.25/18.47 tff(10445,plain,
% 28.25/18.47 (big_f(c2, c2)),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[10444, 2621, 122, 79, 17])).
% 28.25/18.47 tff(10446,plain,
% 28.25/18.47 (big_f(c2, c2) <=> big_f(f7(f7(c2)), c2)),
% 28.25/18.47 inference(transitivity,[status(thm)],[1724, 8079])).
% 28.25/18.47 tff(10447,plain,
% 28.25/18.47 (big_f(f7(f7(c2)), c2)),
% 28.25/18.47 inference(modus_ponens,[status(thm)],[10445, 10446])).
% 28.25/18.47 tff(10448,plain,
% 28.25/18.47 (big_f(f9(c2, c2), f10(c2))),
% 28.25/18.47 inference(modus_ponens,[status(thm)],[10445, 8070])).
% 28.25/18.47 tff(10449,plain,
% 28.25/18.47 (c2 = f5(f7(c2))),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[9290, 1190, 122, 8615, 8080, 10448, 10447])).
% 28.25/18.47 tff(10450,plain,
% 28.25/18.47 (big_f(f7(f7(c2)), f7(c2)) <=> big_f(c2, c1)),
% 28.25/18.47 inference(transitivity,[status(thm)],[9293, 247])).
% 28.25/18.47 tff(10451,plain,
% 28.25/18.47 ((~big_f(f7(f7(c2)), f7(c2))) <=> (~big_f(c2, c1))),
% 28.25/18.47 inference(monotonicity,[status(thm)],[10450])).
% 28.25/18.47 tff(10452,plain,
% 28.25/18.47 (f5(c1) = f5(f7(c2))),
% 28.25/18.47 inference(monotonicity,[status(thm)],[125])).
% 28.25/18.47 tff(10453,plain,
% 28.25/18.47 (f5(f7(c2)) = f5(c1)),
% 28.25/18.47 inference(symmetry,[status(thm)],[10452])).
% 28.25/18.47 tff(10454,plain,
% 28.25/18.47 ((f7(c2) = f5(f7(c2))) <=> (c1 = f5(c1))),
% 28.25/18.47 inference(monotonicity,[status(thm)],[22, 10453])).
% 28.25/18.47 tff(10455,plain,
% 28.25/18.47 ((f7(c2) = f5(f7(c2))) <=> (f5(c1) = c1)),
% 28.25/18.47 inference(transitivity,[status(thm)],[10454, 128])).
% 28.25/18.47 tff(10456,plain,
% 28.25/18.47 ((f5(c1) = c1) <=> (f7(c2) = f5(f7(c2)))),
% 28.25/18.47 inference(symmetry,[status(thm)],[10455])).
% 28.25/18.47 tff(10457,plain,
% 28.25/18.47 (f5(f7(c2)) = c2),
% 28.25/18.47 inference(symmetry,[status(thm)],[10449])).
% 28.25/18.47 tff(10458,plain,
% 28.25/18.47 (f5(c1) = c2),
% 28.25/18.47 inference(transitivity,[status(thm)],[10452, 10457])).
% 28.25/18.47 tff(10459,plain,
% 28.25/18.47 ((f5(c1) = c1) <=> (c2 = f7(c2))),
% 28.25/18.47 inference(monotonicity,[status(thm)],[10458, 125])).
% 28.25/18.47 tff(10460,plain,
% 28.25/18.47 ((f5(c1) = c1) <=> (f7(c2) = c2)),
% 28.25/18.47 inference(transitivity,[status(thm)],[10459, 8409])).
% 28.25/18.47 tff(10461,plain,
% 28.25/18.47 ((f7(c2) = c2) <=> (f5(c1) = c1)),
% 28.25/18.47 inference(symmetry,[status(thm)],[10460])).
% 28.25/18.47 tff(10462,plain,
% 28.25/18.47 ((f7(c2) = c2) <=> (f7(c2) = f5(f7(c2)))),
% 28.25/18.47 inference(transitivity,[status(thm)],[10461, 10456])).
% 28.25/18.47 tff(10463,plain,
% 28.25/18.47 ((~(f7(c2) = c2)) <=> (~(f7(c2) = f5(f7(c2))))),
% 28.25/18.47 inference(monotonicity,[status(thm)],[10462])).
% 28.25/18.47 tff(10464,plain,
% 28.25/18.47 (~(f7(c2) = f5(f7(c2)))),
% 28.25/18.47 inference(modus_ponens,[status(thm)],[17, 10463])).
% 28.25/18.47 tff(10465,assumption,(big_f(f7(f7(c2)), f7(c2))), introduced(assumption)).
% 28.25/18.47 tff(10466,assumption,(~(f7(c2) = f5(f7(c2)))), introduced(assumption)).
% 28.25/18.47 tff(10467,plain,
% 28.25/18.47 ($false),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[10322, 1190, 122, 8473, 1572, 690, 10466, 10465])).
% 28.25/18.47 tff(10468,plain,((~big_f(f7(f7(c2)), f7(c2))) | (~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f7(c2) = f5(f7(c2)))), inference(lemma,lemma(discharge,[]))).
% 28.25/18.47 tff(10469,plain,
% 28.25/18.47 (~big_f(f7(f7(c2)), f7(c2))),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[10468, 8615, 122, 8080, 10448, 10464])).
% 28.25/18.47 tff(10470,plain,
% 28.25/18.47 (~big_f(c2, c1)),
% 28.25/18.47 inference(modus_ponens,[status(thm)],[10469, 10451])).
% 28.25/18.47 tff(10471,plain,
% 28.25/18.47 (~(f5(c2) = c1)),
% 28.25/18.47 inference(modus_ponens,[status(thm)],[9299, 9401])).
% 28.25/18.47 tff(10472,plain,
% 28.25/18.47 (f5(c2) = c2),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[1547, 10471])).
% 28.25/18.47 tff(10473,plain,
% 28.25/18.47 ((~(c3 = c2)) <=> (~(c2 = c3))),
% 28.25/18.47 inference(monotonicity,[status(thm)],[78])).
% 28.25/18.47 tff(10474,plain,
% 28.25/18.47 (c2 = f5(c2)),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[8113, 10472])).
% 28.25/18.47 tff(10475,plain,
% 28.25/18.47 (big_f(f7(c2), c2)),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[8397, 10474, 17, 122, 8080, 9298])).
% 28.25/18.47 tff(10476,plain,
% 28.25/18.47 (~(c3 = c2)),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[9397, 2, 17, 333, 79, 10475])).
% 28.25/18.47 tff(10477,plain,
% 28.25/18.47 (~(c2 = c3)),
% 28.25/18.47 inference(modus_ponens,[status(thm)],[10476, 10473])).
% 28.25/18.47 tff(10478,plain,
% 28.25/18.47 ((c2 = f5(f7(c2))) <=> (c2 = f5(c1))),
% 28.25/18.47 inference(monotonicity,[status(thm)],[10453])).
% 28.25/18.47 tff(10479,plain,
% 28.25/18.47 ((c2 = f5(f7(c2))) <=> (f5(c1) = c2)),
% 28.25/18.47 inference(transitivity,[status(thm)],[10478, 8483])).
% 28.25/18.47 tff(10480,plain,
% 28.25/18.47 (f5(c1) = c2),
% 28.25/18.47 inference(modus_ponens,[status(thm)],[8686, 10479])).
% 28.25/18.47 tff(10481,plain,
% 28.25/18.47 (c2 = f5(c2)),
% 28.25/18.47 inference(symmetry,[status(thm)],[8109])).
% 28.25/18.47 tff(10482,plain,
% 28.25/18.47 (f1(c2, c2) = f1(f5(c2), f5(c1))),
% 28.25/18.47 inference(monotonicity,[status(thm)],[10481, 1761])).
% 28.25/18.47 tff(10483,plain,
% 28.25/18.47 (f1(f5(c2), f5(c1)) = f1(c2, c2)),
% 28.25/18.47 inference(symmetry,[status(thm)],[10482])).
% 28.25/18.47 tff(10484,assumption,(f1(f5(c2), f5(c1)) = c1), introduced(assumption)).
% 28.25/18.47 tff(10485,plain,
% 28.25/18.47 (c1 = f1(f5(c2), f5(c1))),
% 28.25/18.47 inference(symmetry,[status(thm)],[10484])).
% 28.25/18.47 tff(10486,plain,
% 28.25/18.47 (c1 = f1(c2, c2)),
% 28.25/18.47 inference(transitivity,[status(thm)],[10485, 10483])).
% 28.25/18.47 tff(10487,plain,
% 28.25/18.47 (big_f(c2, c1) <=> big_f(c2, f1(c2, c2))),
% 28.25/18.47 inference(monotonicity,[status(thm)],[10486])).
% 28.25/18.47 tff(10488,plain,
% 28.25/18.47 ((~big_f(c2, c1)) <=> (~big_f(c2, f1(c2, c2)))),
% 28.25/18.47 inference(monotonicity,[status(thm)],[10487])).
% 28.25/18.47 tff(10489,plain,
% 28.25/18.47 (~big_f(c2, f1(c2, c2))),
% 28.25/18.47 inference(modus_ponens,[status(thm)],[2, 10488])).
% 28.25/18.47 tff(10490,plain,
% 28.25/18.47 (f1(c2, c2) = f7(c2)),
% 28.25/18.47 inference(transitivity,[status(thm)],[10482, 10484, 125])).
% 28.25/18.47 tff(10491,plain,
% 28.25/18.47 ((f1(c2, c2) = c2) <=> (f7(c2) = c2)),
% 28.25/18.47 inference(monotonicity,[status(thm)],[10490])).
% 28.25/18.47 tff(10492,plain,
% 28.25/18.47 ((f7(c2) = c2) <=> (f1(c2, c2) = c2)),
% 28.25/18.47 inference(symmetry,[status(thm)],[10491])).
% 28.25/18.47 tff(10493,plain,
% 28.25/18.47 ((~(f7(c2) = c2)) <=> (~(f1(c2, c2) = c2))),
% 28.25/18.47 inference(monotonicity,[status(thm)],[10492])).
% 28.25/18.47 tff(10494,plain,
% 28.25/18.47 (~(f1(c2, c2) = c2)),
% 28.25/18.47 inference(modus_ponens,[status(thm)],[17, 10493])).
% 28.25/18.47 tff(10495,plain,
% 28.25/18.47 ($false),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[9423, 402, 377, 10494, 10489, 8770, 9314, 9332])).
% 28.25/18.47 tff(10496,plain,((~(f1(f5(c2), f5(c1)) = c1)) | (c2 = c3) | (~(f7(c2) = c4)) | (~(c2 = f4(f7(c2)))) | big_f(c2, c1) | (~(f5(c1) = c2)) | (~(f5(c2) = c2)) | (f7(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 28.25/18.47 tff(10497,plain,
% 28.25/18.47 (~(f1(f5(c2), f5(c1)) = c1)),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[10496, 9324, 8109, 377, 2, 10480, 9330, 17])).
% 28.25/18.47 tff(10498,plain,
% 28.25/18.47 (f1(f5(c2), f5(c1)) = c2),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[5191, 10497])).
% 28.25/18.47 tff(10499,plain,
% 28.25/18.47 (c2 = f5(c1)),
% 28.25/18.47 inference(transitivity,[status(thm)],[8686, 10453])).
% 28.25/18.47 tff(10500,plain,
% 28.25/18.47 (f1(f5(f9(f10(c2), f7(c1))), c2) = f1(f5(c2), f5(c1))),
% 28.25/18.47 inference(monotonicity,[status(thm)],[8971, 10499])).
% 28.25/18.47 tff(10501,plain,
% 28.25/18.47 (f5(c2) = f5(f9(f10(c2), f7(c1)))),
% 28.25/18.47 inference(symmetry,[status(thm)],[8971])).
% 28.25/18.47 tff(10502,plain,
% 28.25/18.47 (c2 = f5(f9(f10(c2), f7(c1)))),
% 28.25/18.47 inference(transitivity,[status(thm)],[10481, 10501])).
% 28.25/18.47 tff(10503,plain,
% 28.25/18.47 (f1(c2, c2) = f1(f5(f9(f10(c2), f7(c1))), c2)),
% 28.25/18.47 inference(monotonicity,[status(thm)],[10502])).
% 28.25/18.47 tff(10504,plain,
% 28.25/18.47 (f1(c2, c2) = c2),
% 28.25/18.47 inference(transitivity,[status(thm)],[10503, 10500, 10498])).
% 28.25/18.47 tff(10505,plain,
% 28.25/18.47 (big_f(c2, f1(c2, c2)) <=> big_f(c2, c2)),
% 28.25/18.47 inference(monotonicity,[status(thm)],[10504])).
% 28.25/18.47 tff(10506,plain,
% 28.25/18.47 (big_f(c2, c2) <=> big_f(c2, f1(c2, c2))),
% 28.25/18.47 inference(symmetry,[status(thm)],[10505])).
% 28.25/18.47 tff(10507,plain,
% 28.25/18.47 (big_f(c2, f1(c2, c2))),
% 28.25/18.47 inference(modus_ponens,[status(thm)],[1345, 10506])).
% 28.25/18.47 tff(10508,plain,
% 28.25/18.47 (f1(f5(f9(f10(c2), f7(c1))), c2) = f1(c2, c2)),
% 28.25/18.47 inference(symmetry,[status(thm)],[10503])).
% 28.25/18.47 tff(10509,plain,
% 28.25/18.47 ((f1(f5(f9(f10(c2), f7(c1))), c2) = c2) <=> (f1(c2, c2) = c2)),
% 28.25/18.47 inference(monotonicity,[status(thm)],[10508])).
% 28.25/18.47 tff(10510,plain,
% 28.25/18.47 (f1(f5(c2), f5(c1)) = f1(f5(f9(f10(c2), f7(c1))), c2)),
% 28.25/18.47 inference(symmetry,[status(thm)],[10500])).
% 28.25/18.47 tff(10511,plain,
% 28.25/18.47 ((f1(f5(c2), f5(c1)) = c2) <=> (f1(f5(f9(f10(c2), f7(c1))), c2) = c2)),
% 28.25/18.47 inference(monotonicity,[status(thm)],[10510])).
% 28.25/18.47 tff(10512,plain,
% 28.25/18.47 ((f1(f5(c2), f5(c1)) = c2) <=> (f1(c2, c2) = c2)),
% 28.25/18.47 inference(transitivity,[status(thm)],[10511, 10509])).
% 28.25/18.47 tff(10513,plain,
% 28.25/18.47 (f1(c2, c2) = c2),
% 28.25/18.47 inference(modus_ponens,[status(thm)],[10498, 10512])).
% 28.25/18.47 tff(10514,plain,
% 28.25/18.47 ($false),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[9435, 447, 377, 10513, 10507, 9330, 9324, 9314])).
% 28.25/18.47 tff(10515,plain,((~(c4 = c1)) | (c2 = c3) | (~big_f(c2, c2)) | (~(c2 = f5(f7(c2)))) | (~(f4(c4) = c2)) | (~(f7(c1) = c2)) | (~(f10(c2) = c2)) | (~(f5(c2) = c2)) | big_f(c2, c1) | (f7(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 28.25/18.47 tff(10516,plain,
% 28.25/18.47 (~(c4 = c1)),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[10515, 10477, 1345, 8686, 79, 347, 122, 10472, 2, 17])).
% 28.25/18.47 tff(10517,plain,
% 28.25/18.47 (c4 = c2),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[461, 10516])).
% 28.25/18.47 tff(10518,plain,
% 28.25/18.47 (c2 = c4),
% 28.25/18.47 inference(symmetry,[status(thm)],[10517])).
% 28.25/18.47 tff(10519,plain,
% 28.25/18.47 (f4(c2) = f4(c4)),
% 28.25/18.47 inference(monotonicity,[status(thm)],[10518])).
% 28.25/18.47 tff(10520,plain,
% 28.25/18.47 (f4(c2) = c2),
% 28.25/18.47 inference(transitivity,[status(thm)],[10519, 79])).
% 28.25/18.47 tff(10521,plain,
% 28.25/18.47 ((c1 = f4(c2)) <=> (f7(c2) = c2)),
% 28.25/18.47 inference(monotonicity,[status(thm)],[125, 10520])).
% 28.25/18.47 tff(10522,plain,
% 28.25/18.47 ((f7(c2) = c2) <=> (c1 = f4(c2))),
% 28.25/18.47 inference(symmetry,[status(thm)],[10521])).
% 28.25/18.47 tff(10523,plain,
% 28.25/18.47 ((f7(c2) = c2) <=> (f7(c2) = f4(c2))),
% 28.25/18.47 inference(transitivity,[status(thm)],[10522, 9302])).
% 28.25/18.47 tff(10524,plain,
% 28.25/18.47 ((~(f7(c2) = c2)) <=> (~(f7(c2) = f4(c2)))),
% 28.25/18.47 inference(monotonicity,[status(thm)],[10523])).
% 28.25/18.47 tff(10525,plain,
% 28.25/18.47 (~(f7(c2) = f4(c2))),
% 28.25/18.47 inference(modus_ponens,[status(thm)],[17, 10524])).
% 28.25/18.47 tff(10526,plain,
% 28.25/18.47 (c2 = c4),
% 28.25/18.47 inference(modus_ponens,[status(thm)],[10517, 159])).
% 28.25/18.47 tff(10527,plain,
% 28.25/18.47 (f1(c2, c2) = c1),
% 28.25/18.47 inference(transitivity,[status(thm)],[10503, 10500, 10484])).
% 28.25/18.47 tff(10528,plain,
% 28.25/18.47 (big_f(c2, f1(c2, c2)) <=> big_f(c2, c1)),
% 28.25/18.47 inference(monotonicity,[status(thm)],[10527])).
% 28.25/18.47 tff(10529,plain,
% 28.25/18.47 (big_f(c2, c1) <=> big_f(c2, f1(c2, c2))),
% 28.25/18.47 inference(symmetry,[status(thm)],[10528])).
% 28.25/18.47 tff(10530,plain,
% 28.25/18.47 ((~big_f(c2, c1)) <=> (~big_f(c2, f1(c2, c2)))),
% 28.25/18.47 inference(monotonicity,[status(thm)],[10529])).
% 28.25/18.47 tff(10531,plain,
% 28.25/18.47 (~big_f(c2, f1(c2, c2))),
% 28.25/18.47 inference(modus_ponens,[status(thm)],[2, 10530])).
% 28.25/18.47 tff(10532,plain,
% 28.25/18.47 (f1(c2, c2) = f7(c2)),
% 28.25/18.47 inference(transitivity,[status(thm)],[10503, 10500, 10484, 125])).
% 28.25/18.47 tff(10533,plain,
% 28.25/18.47 ((f1(c2, c2) = c2) <=> (f7(c2) = c2)),
% 28.25/18.47 inference(monotonicity,[status(thm)],[10532])).
% 28.25/18.47 tff(10534,plain,
% 28.25/18.47 ((f7(c2) = c2) <=> (f1(c2, c2) = c2)),
% 28.25/18.47 inference(symmetry,[status(thm)],[10533])).
% 28.25/18.47 tff(10535,plain,
% 28.25/18.47 ((~(f7(c2) = c2)) <=> (~(f1(c2, c2) = c2))),
% 28.25/18.47 inference(monotonicity,[status(thm)],[10534])).
% 28.25/18.47 tff(10536,plain,
% 28.25/18.47 (~(f1(c2, c2) = c2)),
% 28.25/18.47 inference(modus_ponens,[status(thm)],[17, 10535])).
% 28.25/18.47 tff(10537,plain,
% 28.25/18.47 ($false),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[9462, 525, 631, 377, 1180, 10536, 10531, 9367])).
% 28.25/18.47 tff(10538,plain,((~(f1(f5(c2), f5(c1)) = c1)) | (~(c2 = c4)) | (c2 = c3) | (~big_f(f7(c2), c2)) | (f7(c2) = f4(c2)) | big_f(c2, c1) | (~(c2 = f5(f7(c2)))) | (~(f4(c4) = c2)) | (~(f7(c1) = c2)) | (~(f10(c2) = c2)) | (~(f5(c2) = c2)) | (f7(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 28.25/18.47 tff(10539,plain,
% 28.25/18.47 (~(f1(f5(c2), f5(c1)) = c1)),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[10538, 10526, 10477, 10475, 10525, 2, 8686, 79, 347, 122, 10472, 17])).
% 28.25/18.47 tff(10540,plain,
% 28.25/18.47 (f1(f5(c2), f5(c1)) = c2),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[5191, 10539])).
% 28.25/18.47 tff(10541,plain,
% 28.25/18.47 (c2 = f5(c2)),
% 28.25/18.47 inference(symmetry,[status(thm)],[10472])).
% 28.25/18.47 tff(10542,plain,
% 28.25/18.47 (c2 = f5(f9(f10(c2), f7(c1)))),
% 28.25/18.47 inference(transitivity,[status(thm)],[10541, 10501])).
% 28.25/18.47 tff(10543,plain,
% 28.25/18.47 (f1(c2, c2) = f1(f5(f9(f10(c2), f7(c1))), c2)),
% 28.25/18.47 inference(monotonicity,[status(thm)],[10542])).
% 28.25/18.47 tff(10544,plain,
% 28.25/18.47 (f1(c2, c2) = c2),
% 28.25/18.47 inference(transitivity,[status(thm)],[10543, 10500, 10540])).
% 28.25/18.47 tff(10545,plain,
% 28.25/18.47 (big_f(c2, f1(c2, c2)) <=> big_f(c2, c2)),
% 28.25/18.47 inference(monotonicity,[status(thm)],[10544])).
% 28.25/18.47 tff(10546,plain,
% 28.25/18.47 (big_f(c2, c2) <=> big_f(c2, f1(c2, c2))),
% 28.25/18.47 inference(symmetry,[status(thm)],[10545])).
% 28.25/18.47 tff(10547,plain,
% 28.25/18.47 (big_f(c2, f1(c2, c2))),
% 28.25/18.47 inference(modus_ponens,[status(thm)],[1345, 10546])).
% 28.25/18.47 tff(10548,plain,
% 28.25/18.47 (f1(f5(f9(f10(c2), f7(c1))), c2) = f1(c2, c2)),
% 28.25/18.47 inference(symmetry,[status(thm)],[10543])).
% 28.25/18.47 tff(10549,plain,
% 28.25/18.47 ((f1(f5(f9(f10(c2), f7(c1))), c2) = c2) <=> (f1(c2, c2) = c2)),
% 28.25/18.47 inference(monotonicity,[status(thm)],[10548])).
% 28.25/18.47 tff(10550,plain,
% 28.25/18.47 ((f1(f5(c2), f5(c1)) = c2) <=> (f1(c2, c2) = c2)),
% 28.25/18.47 inference(transitivity,[status(thm)],[10511, 10549])).
% 28.25/18.47 tff(10551,plain,
% 28.25/18.47 (f1(c2, c2) = c2),
% 28.25/18.47 inference(modus_ponens,[status(thm)],[10540, 10550])).
% 28.25/18.47 tff(10552,plain,
% 28.25/18.47 ($false),
% 28.25/18.47 inference(unit_resolution,[status(thm)],[9474, 553, 10526, 10477, 10475, 10551, 10547, 10525])).
% 28.25/18.48 tff(10553,plain,(big_f(c2, c1) | (~big_f(c2, c2)) | (~(c2 = f5(f7(c2)))) | (~(f4(c4) = c2)) | (~(f7(c1) = c2)) | (~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f7(c2), c1)), inference(lemma,lemma(discharge,[]))).
% 28.25/18.48 tff(10554,plain,
% 28.25/18.48 (big_f(f7(c2), c1)),
% 28.25/18.48 inference(unit_resolution,[status(thm)],[10553, 10470, 10449, 79, 120, 122, 17, 10445])).
% 28.25/18.48 tff(10555,plain,
% 28.25/18.48 (big_f(c1, c1)),
% 28.25/18.48 inference(modus_ponens,[status(thm)],[10554, 9488])).
% 28.25/18.48 tff(10556,plain,
% 28.25/18.48 (big_f(f7(f7(c2)), f7(c2)) <=> big_f(c2, f7(c2))),
% 28.25/18.48 inference(transitivity,[status(thm)],[9293, 247, 9312])).
% 28.25/18.48 tff(10557,plain,
% 28.25/18.48 ((~big_f(f7(f7(c2)), f7(c2))) <=> (~big_f(c2, f7(c2)))),
% 28.25/18.48 inference(monotonicity,[status(thm)],[10556])).
% 28.25/18.48 tff(10558,plain,
% 28.25/18.48 (~big_f(c2, f7(c2))),
% 28.25/18.48 inference(modus_ponens,[status(thm)],[10469, 10557])).
% 28.25/18.48 tff(10559,plain,
% 28.25/18.48 (c2 = c3),
% 28.25/18.48 inference(unit_resolution,[status(thm)],[9586, 10470, 10554, 10445, 79, 122, 17, 10558])).
% 28.25/18.48 tff(10560,plain,
% 28.25/18.48 (c3 = c2),
% 28.25/18.48 inference(symmetry,[status(thm)],[10559])).
% 28.25/18.48 tff(10561,plain,
% 28.25/18.48 ((f7(c2) = c3) <=> (f7(c2) = c2)),
% 28.25/18.48 inference(monotonicity,[status(thm)],[10560])).
% 28.25/18.48 tff(10562,plain,
% 28.25/18.48 ((f7(c2) = c2) <=> (f7(c2) = c3)),
% 28.25/18.48 inference(symmetry,[status(thm)],[10561])).
% 28.25/18.48 tff(10563,plain,
% 28.25/18.48 ((f7(c2) = c2) <=> (c1 = c3)),
% 28.25/18.48 inference(transitivity,[status(thm)],[10562, 9088])).
% 28.25/18.48 tff(10564,plain,
% 28.25/18.48 ((~(f7(c2) = c2)) <=> (~(c1 = c3))),
% 28.25/18.48 inference(monotonicity,[status(thm)],[10563])).
% 28.25/18.48 tff(10565,plain,
% 28.25/18.48 (~(c1 = c3)),
% 28.25/18.48 inference(modus_ponens,[status(thm)],[17, 10564])).
% 28.25/18.48 tff(10566,plain,
% 28.25/18.48 (big_f(f7(c2), f7(c2))),
% 28.25/18.48 inference(modus_ponens,[status(thm)],[10554, 8076])).
% 28.25/18.48 tff(10567,plain,
% 28.25/18.48 (f7(c2) = f5(c2)),
% 28.25/18.48 inference(unit_resolution,[status(thm)],[10299, 1190, 122, 17, 8080, 10448, 10566])).
% 28.25/18.48 tff(10568,plain,
% 28.25/18.48 (f5(c2) = f7(c2)),
% 28.25/18.48 inference(symmetry,[status(thm)],[10567])).
% 28.25/18.48 tff(10569,plain,
% 28.25/18.48 (f5(c2) = c1),
% 28.25/18.48 inference(transitivity,[status(thm)],[10568, 22])).
% 28.25/18.48 tff(10570,plain,
% 28.25/18.48 (f9(c2, f5(c1)) = f9(c2, c2)),
% 28.25/18.48 inference(monotonicity,[status(thm)],[10458])).
% 28.25/18.48 tff(10571,plain,
% 28.25/18.48 (f9(c2, c2) = f9(c2, f5(c1))),
% 28.25/18.48 inference(symmetry,[status(thm)],[10570])).
% 28.25/18.48 tff(10572,plain,
% 28.25/18.48 (c2 = f9(f10(c2), f4(c4))),
% 28.25/18.48 inference(symmetry,[status(thm)],[8066])).
% 28.25/18.48 tff(10573,plain,
% 28.25/18.48 (c2 = f9(c2, f5(c1))),
% 28.25/18.48 inference(transitivity,[status(thm)],[10572, 2634, 10571])).
% 28.25/18.48 tff(10574,plain,
% 28.25/18.48 (f6(c2, c2) = f6(c2, f9(c2, f5(c1)))),
% 28.25/18.48 inference(monotonicity,[status(thm)],[10573])).
% 28.25/18.48 tff(10575,plain,
% 28.25/18.48 ((f6(c2, c2) = f5(c2)) <=> (f6(c2, f9(c2, f5(c1))) = c1)),
% 28.25/18.48 inference(monotonicity,[status(thm)],[10574, 10569])).
% 28.25/18.48 tff(10576,plain,
% 28.25/18.48 ((~(f6(c2, c2) = f5(c2))) <=> (~(f6(c2, f9(c2, f5(c1))) = c1))),
% 28.25/18.48 inference(monotonicity,[status(thm)],[10575])).
% 28.25/18.48 tff(10577,plain,
% 28.25/18.48 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f6(c2, c2) = f5(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f6(c2, c2) = f5(c2))))),
% 28.25/18.48 inference(rewrite,[status(thm)],[])).
% 28.25/18.48 tff(10578,plain,
% 28.25/18.48 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f6(c2, c2) = f5(c2))))),
% 28.25/18.48 inference(quant_inst,[status(thm)],[])).
% 28.25/18.48 tff(10579,plain,
% 28.25/18.48 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f6(c2, c2) = f5(c2)))),
% 28.25/18.48 inference(modus_ponens,[status(thm)],[10578, 10577])).
% 28.25/18.48 tff(10580,plain,
% 28.25/18.48 (~(f6(c2, c2) = f5(c2))),
% 28.25/18.48 inference(unit_resolution,[status(thm)],[10579, 783, 122, 17, 2621, 8080, 10448])).
% 28.25/18.48 tff(10581,plain,
% 28.25/18.48 (~(f6(c2, f9(c2, f5(c1))) = c1)),
% 28.25/18.48 inference(modus_ponens,[status(thm)],[10580, 10576])).
% 28.25/18.48 tff(10582,plain,
% 28.25/18.48 (f6(c2, f9(c2, f5(c1))) = c2),
% 28.25/18.48 inference(unit_resolution,[status(thm)],[7234, 10581])).
% 28.25/18.48 tff(10583,plain,
% 28.25/18.48 (f6(c2, c2) = c2),
% 28.25/18.48 inference(transitivity,[status(thm)],[10574, 10582])).
% 28.25/18.48 tff(10584,plain,
% 28.25/18.48 (big_f(f7(c2), f6(c2, c2)) <=> big_f(f7(c2), c2)),
% 28.25/18.48 inference(monotonicity,[status(thm)],[10583])).
% 28.25/18.48 tff(10585,plain,
% 28.25/18.48 ((~big_f(f7(c2), f6(c2, c2))) <=> (~big_f(f7(c2), c2))),
% 28.25/18.48 inference(monotonicity,[status(thm)],[10584])).
% 28.25/18.48 tff(10586,plain,
% 28.25/18.48 (~big_f(f7(c2), c2)),
% 28.25/18.48 inference(modus_ponens,[status(thm)],[2621, 10585])).
% 28.25/18.48 tff(10587,plain,
% 28.25/18.48 ((~(f7(c2) = c2)) <=> (~(f7(c2) = c3))),
% 28.25/18.48 inference(monotonicity,[status(thm)],[10562])).
% 28.25/18.48 tff(10588,plain,
% 28.25/18.48 (~(f7(c2) = c3)),
% 28.25/18.48 inference(modus_ponens,[status(thm)],[17, 10587])).
% 28.25/18.48 tff(10589,plain,
% 28.25/18.48 (~(c4 = c1)),
% 28.25/18.48 inference(unit_resolution,[status(thm)],[9641, 10588, 10554, 17, 10586, 79])).
% 28.25/18.48 tff(10590,plain,
% 28.25/18.48 (c4 = c2),
% 28.25/18.48 inference(unit_resolution,[status(thm)],[461, 10589])).
% 28.25/18.48 tff(10591,plain,
% 28.25/18.48 ((f7(f4(c4)) = c4) <=> (f7(c2) = c2)),
% 28.25/18.48 inference(monotonicity,[status(thm)],[80, 10590])).
% 28.25/18.48 tff(10592,plain,
% 28.25/18.48 ((f7(c2) = c2) <=> (f7(f4(c4)) = c4)),
% 28.25/18.48 inference(symmetry,[status(thm)],[10591])).
% 28.25/18.48 tff(10593,plain,
% 28.25/18.48 ((f7(c2) = c2) <=> (c1 = c4)),
% 28.25/18.48 inference(transitivity,[status(thm)],[10592, 9594])).
% 28.25/18.48 tff(10594,plain,
% 28.25/18.48 ((~(f7(c2) = c2)) <=> (~(c1 = c4))),
% 28.25/18.48 inference(monotonicity,[status(thm)],[10593])).
% 28.25/18.48 tff(10595,plain,
% 28.25/18.48 (~(c1 = c4)),
% 28.25/18.48 inference(modus_ponens,[status(thm)],[17, 10594])).
% 28.25/18.48 tff(10596,plain,
% 28.25/18.48 (big_f(f7(c2), f6(c2, c2)) <=> big_f(c1, c2)),
% 28.25/18.48 inference(transitivity,[status(thm)],[10584, 9652])).
% 28.25/18.48 tff(10597,plain,
% 28.25/18.48 ((~big_f(f7(c2), f6(c2, c2))) <=> (~big_f(c1, c2))),
% 28.25/18.48 inference(monotonicity,[status(thm)],[10596])).
% 28.25/18.48 tff(10598,plain,
% 28.25/18.48 (~big_f(c1, c2)),
% 28.25/18.48 inference(modus_ponens,[status(thm)],[2621, 10597])).
% 28.25/18.48 tff(10599,plain,
% 28.25/18.48 ((f7(c2) = c2) <=> (f7(c2) = c4)),
% 28.25/18.48 inference(transitivity,[status(thm)],[10592, 9326])).
% 28.25/18.48 tff(10600,plain,
% 28.25/18.48 ((~(f7(c2) = c2)) <=> (~(f7(c2) = c4))),
% 28.25/18.48 inference(monotonicity,[status(thm)],[10599])).
% 28.25/18.48 tff(10601,plain,
% 28.25/18.48 (~(f7(c2) = c4)),
% 28.25/18.48 inference(modus_ponens,[status(thm)],[17, 10600])).
% 28.25/18.48 tff(10602,plain,
% 28.25/18.48 (f3(c1, c1) = c1),
% 28.25/18.48 inference(unit_resolution,[status(thm)],[9696, 10588, 10601, 10470, 17, 10598, 10595, 10565, 10555])).
% 28.25/18.48 tff(10603,plain,
% 28.25/18.48 (f3(f7(c2), f7(c2)) = f7(c2)),
% 28.25/18.48 inference(transitivity,[status(thm)],[9496, 10602, 125])).
% 28.25/18.48 tff(10604,plain,
% 28.25/18.48 (big_f(f3(f7(c2), f7(c2)), f7(c2)) <=> big_f(f7(c2), c1)),
% 28.25/18.48 inference(monotonicity,[status(thm)],[10603, 22])).
% 28.25/18.48 tff(10605,plain,
% 28.25/18.48 (big_f(f7(c2), c1) <=> big_f(f3(f7(c2), f7(c2)), f7(c2))),
% 28.25/18.48 inference(symmetry,[status(thm)],[10604])).
% 28.25/18.48 tff(10606,plain,
% 28.25/18.48 (big_f(f3(f7(c2), f7(c2)), f7(c2))),
% 28.25/18.48 inference(modus_ponens,[status(thm)],[10554, 10605])).
% 28.25/18.48 tff(10607,plain,
% 28.25/18.48 (big_f(c1, f1(c1, c1)) <=> big_f(f7(c2), f1(f7(c2), f7(c2)))),
% 28.25/18.48 inference(symmetry,[status(thm)],[9655])).
% 28.25/18.48 tff(10608,plain,
% 28.25/18.48 (big_f(c1, f1(c1, c1))),
% 28.25/18.48 inference(unit_resolution,[status(thm)],[9724, 10588, 22, 10601, 10554, 10602])).
% 28.25/18.48 tff(10609,plain,
% 28.25/18.48 (big_f(f7(c2), f1(f7(c2), f7(c2)))),
% 28.25/18.48 inference(modus_ponens,[status(thm)],[10608, 10607])).
% 28.25/18.48 tff(10610,plain,
% 28.25/18.48 (~(f1(c1, c1) = c2)),
% 28.25/18.48 inference(unit_resolution,[status(thm)],[4561, 10608, 10598])).
% 28.25/18.48 tff(10611,plain,
% 28.25/18.48 (f1(c1, c1) = c1),
% 28.25/18.48 inference(unit_resolution,[status(thm)],[601, 10610])).
% 28.25/18.48 tff(10612,plain,
% 28.25/18.48 (f1(f7(c2), f7(c2)) = f7(c2)),
% 28.25/18.48 inference(modus_ponens,[status(thm)],[10611, 9668])).
% 28.25/18.48 tff(10613,plain,
% 28.25/18.48 ((~(f3(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f3(f7(c2), f7(c2)), f7(c2)))),
% 28.25/18.48 inference(unit_resolution,[status(thm)],[9740, 933, 10588, 10601, 10612, 10609])).
% 28.25/18.48 tff(10614,plain,
% 28.25/18.48 ($false),
% 28.25/18.48 inference(unit_resolution,[status(thm)],[10613, 10606, 10603])).
% 28.25/18.48 tff(10615,plain,((f7(c1) = c1) | (f7(c2) = c2) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | big_f(f7(c2), f6(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 28.25/18.48 tff(10616,plain,
% 28.25/18.48 (f7(c1) = c1),
% 28.25/18.48 inference(unit_resolution,[status(thm)],[10615, 2621, 79, 122, 17])).
% 28.25/18.48 tff(10617,plain,
% 28.25/18.48 (big_f(f7(c2), c1)),
% 28.25/18.48 inference(unit_resolution,[status(thm)],[9277, 10448, 8080, 122, 17, 10616])).
% 28.25/18.48 tff(10618,plain,
% 28.25/18.48 (big_f(f7(c2), f7(c2))),
% 28.25/18.48 inference(modus_ponens,[status(thm)],[10617, 8076])).
% 28.25/18.48 tff(10619,plain,
% 28.25/18.48 (f7(c2) = f5(c2)),
% 28.25/18.48 inference(unit_resolution,[status(thm)],[10299, 1190, 122, 17, 8080, 10448, 10618])).
% 28.25/18.48 tff(10620,plain,
% 28.25/18.48 (f5(c2) = f7(c2)),
% 28.25/18.48 inference(symmetry,[status(thm)],[10619])).
% 28.25/18.48 tff(10621,plain,
% 28.25/18.48 (c1 = f7(c1)),
% 28.25/18.48 inference(symmetry,[status(thm)],[10616])).
% 28.25/18.48 tff(10622,plain,
% 28.25/18.48 (f7(c2) = f7(c1)),
% 28.25/18.48 inference(transitivity,[status(thm)],[22, 10621])).
% 28.25/18.48 tff(10623,plain,
% 28.25/18.48 (big_f(f7(c2), f6(c1, c1)) <=> big_f(f7(c1), f6(c1, c1))),
% 28.25/18.48 inference(monotonicity,[status(thm)],[10622])).
% 28.25/18.48 tff(10624,plain,
% 28.25/18.48 (big_f(f7(c1), f6(c1, c1)) <=> big_f(f7(c2), f6(c1, c1))),
% 28.25/18.48 inference(symmetry,[status(thm)],[10623])).
% 28.25/18.48 tff(10625,plain,
% 28.25/18.48 (big_f(f7(f7(c2)), f6(f7(c2), f7(c2))) <=> big_f(f7(c2), f6(c1, c1))),
% 28.25/18.48 inference(transitivity,[status(thm)],[9790, 10624])).
% 28.25/18.48 tff(10626,plain,
% 28.25/18.48 ((~(f6(c1, c1) = c1)) <=> (~(f6(f7(c2), f7(c2)) = f7(c2)))),
% 28.25/18.48 inference(monotonicity,[status(thm)],[10067])).
% 28.25/18.48 tff(10627,plain,
% 28.25/18.48 (f6(f7(c2), f7(c2)) = f6(c1, c1)),
% 28.25/18.48 inference(monotonicity,[status(thm)],[292, 292])).
% 28.25/18.48 tff(10628,plain,
% 28.25/18.48 (big_f(f7(f7(c2)), f6(f7(c2), f7(c2))) <=> big_f(f7(c1), f6(c1, c1))),
% 28.25/18.48 inference(monotonicity,[status(thm)],[352, 10627])).
% 28.25/18.48 tff(10629,plain,
% 28.25/18.48 (big_f(f7(c1), f6(c1, c1)) <=> big_f(f7(f7(c2)), f6(f7(c2), f7(c2)))),
% 28.25/18.48 inference(symmetry,[status(thm)],[10628])).
% 28.25/18.48 tff(10630,plain,
% 28.25/18.48 (big_f(f7(c1), f6(c1, c1)) <=> big_f(f7(c2), f6(c1, c1))),
% 28.25/18.48 inference(monotonicity,[status(thm)],[8286])).
% 28.25/18.48 tff(10631,plain,
% 28.25/18.48 (big_f(f7(c2), f6(c1, c1)) <=> big_f(f7(c1), f6(c1, c1))),
% 28.25/18.48 inference(symmetry,[status(thm)],[10630])).
% 28.25/18.48 tff(10632,plain,
% 28.25/18.48 (big_f(f7(c2), f6(c1, c1)) <=> big_f(f7(c2), c1)),
% 28.25/18.48 inference(monotonicity,[status(thm)],[10030])).
% 28.25/18.48 tff(10633,plain,
% 28.25/18.48 (big_f(f7(c2), c1) <=> big_f(f7(c2), f6(c1, c1))),
% 28.25/18.48 inference(symmetry,[status(thm)],[10632])).
% 28.25/18.48 tff(10634,plain,
% 28.25/18.48 (big_f(f7(c2), c1) <=> big_f(f7(f7(c2)), f6(f7(c2), f7(c2)))),
% 28.25/18.48 inference(transitivity,[status(thm)],[10633, 10631, 10629])).
% 28.25/18.48 tff(10635,plain,
% 28.25/18.48 (big_f(f7(f7(c2)), f6(f7(c2), f7(c2)))),
% 28.25/18.48 inference(modus_ponens,[status(thm)],[338, 10634])).
% 28.25/18.48 tff(10636,plain,
% 28.25/18.48 ((f6(f7(c2), f7(c2)) = f7(c2)) <=> (f6(c1, c1) = c1)),
% 28.25/18.48 inference(monotonicity,[status(thm)],[10627, 292])).
% 28.25/18.48 tff(10637,plain,
% 28.25/18.48 ((f6(c1, c1) = c1) <=> (f6(f7(c2), f7(c2)) = f7(c2))),
% 28.25/18.48 inference(symmetry,[status(thm)],[10636])).
% 28.25/18.48 tff(10638,plain,
% 28.25/18.48 (f6(f7(c2), f7(c2)) = f7(c2)),
% 28.25/18.48 inference(modus_ponens,[status(thm)],[10030, 10637])).
% 28.25/18.48 tff(10639,plain,
% 28.25/18.48 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f6(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), f7(c2)))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f6(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), f7(c2)))))),
% 28.25/18.48 inference(rewrite,[status(thm)],[])).
% 28.25/18.48 tff(10640,plain,
% 28.25/18.48 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f6(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), f7(c2)))))),
% 28.25/18.48 inference(quant_inst,[status(thm)],[])).
% 28.25/18.48 tff(10641,plain,
% 28.25/18.48 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f6(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(f7(c2)), f6(f7(c2), f7(c2))))),
% 28.25/18.48 inference(modus_ponens,[status(thm)],[10640, 10639])).
% 28.25/18.48 tff(10642,plain,
% 28.25/18.48 ($false),
% 28.25/18.48 inference(unit_resolution,[status(thm)],[10641, 2378, 122, 9247, 1572, 690, 10638, 10635])).
% 28.25/18.48 tff(10643,plain,((~(f6(c1, c1) = c1)) | (~(f10(c2) = c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~big_f(f7(c2), c1)) | (~(f7(c1) = c1)) | (~(f7(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.25/18.48 tff(10644,plain,
% 28.25/18.48 (~(f6(c1, c1) = c1)),
% 28.25/18.48 inference(unit_resolution,[status(thm)],[10643, 10448, 8080, 122, 10617, 10616, 22])).
% 28.25/18.48 tff(10645,plain,
% 28.25/18.48 (~(f6(f7(c2), f7(c2)) = f7(c2))),
% 28.25/18.48 inference(modus_ponens,[status(thm)],[10644, 10626])).
% 28.25/18.48 tff(10646,plain,
% 28.25/18.48 (f7(f7(c2)) = f7(c2)),
% 28.25/18.48 inference(modus_ponens,[status(thm)],[10616, 8314])).
% 28.25/18.48 tff(10647,plain,
% 28.25/18.48 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f6(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f6(f7(c2), f7(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f6(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f6(f7(c2), f7(c2))))),
% 28.25/18.48 inference(rewrite,[status(thm)],[])).
% 28.25/18.48 tff(10648,plain,
% 28.25/18.48 (((~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (f6(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f6(f7(c2), f7(c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2)))) <=> ((~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f6(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f6(f7(c2), f7(c2))))),
% 28.25/18.48 inference(rewrite,[status(thm)],[])).
% 28.25/18.48 tff(10649,plain,
% 28.25/18.48 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (f6(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f6(f7(c2), f7(c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f6(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f6(f7(c2), f7(c2)))))),
% 28.25/18.48 inference(monotonicity,[status(thm)],[10648])).
% 28.25/18.48 tff(10650,plain,
% 28.25/18.48 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (f6(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f6(f7(c2), f7(c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f6(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f6(f7(c2), f7(c2))))),
% 28.25/18.48 inference(transitivity,[status(thm)],[10649, 10647])).
% 28.25/18.48 tff(10651,plain,
% 28.25/18.48 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (f6(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f6(f7(c2), f7(c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))),
% 28.25/18.48 inference(quant_inst,[status(thm)],[])).
% 28.25/18.48 tff(10652,plain,
% 28.25/18.48 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (~(f7(f7(c2)) = f7(c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f6(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f6(f7(c2), f7(c2)))),
% 28.25/18.48 inference(modus_ponens,[status(thm)],[10651, 10650])).
% 28.25/18.48 tff(10653,plain,
% 28.25/18.48 (big_f(f7(f7(c2)), f6(f7(c2), f7(c2)))),
% 28.25/18.48 inference(unit_resolution,[status(thm)],[10652, 2409, 122, 10646, 8080, 10448, 10645])).
% 28.25/18.48 tff(10654,plain,
% 28.25/18.48 (big_f(f7(c2), f6(c1, c1))),
% 28.25/18.48 inference(modus_ponens,[status(thm)],[10653, 10625])).
% 28.25/18.48 tff(10655,plain,
% 28.25/18.48 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))))),
% 28.25/18.48 inference(rewrite,[status(thm)],[])).
% 28.25/18.48 tff(10656,plain,
% 28.25/18.48 (((~(f10(c2) = c2)) | (f7(c2) = c2) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2)))) <=> ((~(f10(c2) = c2)) | (f7(c2) = c2) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))))),
% 28.25/18.48 inference(rewrite,[status(thm)],[])).
% 28.25/18.48 tff(10657,plain,
% 28.25/18.48 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1)))))),
% 28.25/18.48 inference(monotonicity,[status(thm)],[10656])).
% 28.25/18.48 tff(10658,plain,
% 28.25/18.48 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))))),
% 28.25/18.48 inference(transitivity,[status(thm)],[10657, 10655])).
% 28.25/18.48 tff(10659,plain,
% 28.25/18.48 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))),
% 28.25/18.48 inference(quant_inst,[status(thm)],[])).
% 28.25/18.48 tff(10660,plain,
% 28.25/18.48 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1)))),
% 28.25/18.48 inference(modus_ponens,[status(thm)],[10659, 10658])).
% 28.25/18.48 tff(10661,plain,
% 28.25/18.48 (f6(c1, c1) = f5(c2)),
% 28.25/18.48 inference(unit_resolution,[status(thm)],[10660, 1190, 122, 17, 8080, 10448, 10654])).
% 28.25/18.48 tff(10662,plain,
% 28.25/18.48 (f6(c1, c1) = c1),
% 28.25/18.48 inference(transitivity,[status(thm)],[10661, 10620, 22])).
% 28.25/18.48 tff(10663,plain,
% 28.25/18.48 ($false),
% 28.25/18.48 inference(unit_resolution,[status(thm)],[10644, 10662])).
% 28.25/18.48 tff(10664,plain,(big_f(f7(c2), f6(c2, c2)) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.25/18.48 tff(10665,plain,
% 28.25/18.48 (big_f(f7(c2), f6(c2, c2))),
% 28.25/18.48 inference(unit_resolution,[status(thm)],[10664, 17, 122, 79])).
% 28.25/18.48 tff(10666,plain,
% 28.25/18.48 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (~big_f(f7(c2), f6(c2, c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f6(c2, c2) = f5(c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~big_f(f7(c2), f6(c2, c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f6(c2, c2) = f5(c2)))),
% 28.25/18.48 inference(rewrite,[status(thm)],[])).
% 28.25/18.48 tff(10667,plain,
% 28.25/18.48 (((~(f10(c2) = c2)) | (f7(c2) = c2) | (f6(c2, c2) = f5(c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2)))) <=> ((~(f10(c2) = c2)) | (f7(c2) = c2) | (~big_f(f7(c2), f6(c2, c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f6(c2, c2) = f5(c2)))),
% 28.25/18.48 inference(rewrite,[status(thm)],[])).
% 28.25/18.48 tff(10668,plain,
% 28.25/18.48 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (f6(c2, c2) = f5(c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (~big_f(f7(c2), f6(c2, c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f6(c2, c2) = f5(c2))))),
% 28.25/18.48 inference(monotonicity,[status(thm)],[10667])).
% 28.25/18.48 tff(10669,plain,
% 28.25/18.48 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (f6(c2, c2) = f5(c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~big_f(f7(c2), f6(c2, c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f6(c2, c2) = f5(c2)))),
% 28.25/18.48 inference(transitivity,[status(thm)],[10668, 10666])).
% 28.25/18.48 tff(10670,plain,
% 28.25/18.48 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (f6(c2, c2) = f5(c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))),
% 28.25/18.48 inference(quant_inst,[status(thm)],[])).
% 28.25/18.48 tff(10671,plain,
% 28.25/18.48 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~big_f(f7(c2), f6(c2, c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f6(c2, c2) = f5(c2))),
% 28.25/18.49 inference(modus_ponens,[status(thm)],[10670, 10669])).
% 28.25/18.49 tff(10672,plain,
% 28.25/18.49 ((~big_f(f9(c2, c2), f10(c2))) | (f6(c2, c2) = f5(c2))),
% 28.25/18.49 inference(unit_resolution,[status(thm)],[10671, 1190, 122, 17, 10665, 8080])).
% 28.25/18.49 tff(10673,plain,
% 28.25/18.49 (f6(c2, c2) = f5(c2)),
% 28.25/18.49 inference(unit_resolution,[status(thm)],[10672, 10357])).
% 28.25/18.49 tff(10674,plain,
% 28.25/18.49 (f5(c2) = f6(c2, c2)),
% 28.25/18.49 inference(symmetry,[status(thm)],[10673])).
% 28.25/18.49 tff(10675,plain,
% 28.25/18.49 (f7(c2) = f6(c2, c2)),
% 28.25/18.49 inference(transitivity,[status(thm)],[10359, 10674])).
% 28.25/18.49 tff(10676,plain,
% 28.25/18.49 ((f7(c2) = c2) <=> (f6(c2, c2) = c2)),
% 28.25/18.49 inference(monotonicity,[status(thm)],[10675])).
% 28.25/18.49 tff(10677,plain,
% 28.25/18.49 ((~(f7(c2) = c2)) <=> (~(f6(c2, c2) = c2))),
% 28.25/18.49 inference(monotonicity,[status(thm)],[10676])).
% 28.25/18.49 tff(10678,plain,
% 28.25/18.49 (~(f6(c2, c2) = c2)),
% 28.25/18.49 inference(modus_ponens,[status(thm)],[17, 10677])).
% 28.25/18.49 tff(10679,assumption,(f6(c2, c2) = f5(c2)), introduced(assumption)).
% 28.25/18.49 tff(10680,plain,
% 28.25/18.49 (f6(c2, c2) = f7(c2)),
% 28.25/18.49 inference(transitivity,[status(thm)],[10679, 10235])).
% 28.25/18.49 tff(10681,plain,
% 28.25/18.49 (f7(f6(c2, c2)) = f7(f7(c2))),
% 28.25/18.49 inference(monotonicity,[status(thm)],[10680])).
% 28.25/18.49 tff(10682,plain,
% 28.25/18.49 (f7(f6(c2, c2)) = c2),
% 28.25/18.49 inference(transitivity,[status(thm)],[10681, 352, 347])).
% 28.25/18.49 tff(10683,plain,
% 28.25/18.49 ((f7(f6(c2, c2)) = f6(c2, c2)) <=> (c2 = f6(c2, c2))),
% 28.25/18.49 inference(monotonicity,[status(thm)],[10682])).
% 28.25/18.49 tff(10684,plain,
% 28.25/18.49 ((f7(f6(c2, c2)) = f6(c2, c2)) <=> (f6(c2, c2) = c2)),
% 28.25/18.49 inference(transitivity,[status(thm)],[10683, 3242])).
% 28.25/18.49 tff(10685,plain,
% 28.25/18.49 ((f6(c2, c2) = c2) <=> (f7(f6(c2, c2)) = f6(c2, c2))),
% 28.25/18.49 inference(symmetry,[status(thm)],[10684])).
% 28.25/18.49 tff(10686,plain,
% 28.25/18.49 ((~(f6(c2, c2) = c2)) <=> (~(f7(f6(c2, c2)) = f6(c2, c2)))),
% 28.25/18.49 inference(monotonicity,[status(thm)],[10685])).
% 28.25/18.49 tff(10687,plain,
% 28.25/18.49 (~(f7(f6(c2, c2)) = f6(c2, c2))),
% 28.25/18.49 inference(modus_ponens,[status(thm)],[2637, 10686])).
% 28.25/18.49 tff(10688,plain,
% 28.25/18.49 (big_f(f7(f6(c2, c2)), c2) <=> big_f(c2, c2)),
% 28.25/18.49 inference(monotonicity,[status(thm)],[10682])).
% 28.25/18.49 tff(10689,plain,
% 28.25/18.49 (big_f(c2, c2) <=> big_f(f7(f6(c2, c2)), c2)),
% 28.25/18.49 inference(symmetry,[status(thm)],[10688])).
% 28.25/18.49 tff(10690,plain,
% 28.25/18.49 (big_f(f7(f6(c2, c2)), c2)),
% 28.25/18.49 inference(modus_ponens,[status(thm)],[1345, 10689])).
% 28.25/18.49 tff(10691,plain,
% 28.25/18.49 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~big_f(f7(f6(c2, c2)), c2)) | (c2 = f5(f6(c2, c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f7(f6(c2, c2)) = f6(c2, c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (~big_f(f7(f6(c2, c2)), c2)) | (c2 = f5(f6(c2, c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f7(f6(c2, c2)) = f6(c2, c2)))),
% 28.25/18.49 inference(rewrite,[status(thm)],[])).
% 28.25/18.49 tff(10692,plain,
% 28.25/18.49 (((~(f10(c2) = c2)) | (f7(f6(c2, c2)) = f6(c2, c2)) | (c2 = f5(f6(c2, c2))) | (~big_f(f7(f6(c2, c2)), c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2)))) <=> ((~(f10(c2) = c2)) | (~big_f(f7(f6(c2, c2)), c2)) | (c2 = f5(f6(c2, c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f7(f6(c2, c2)) = f6(c2, c2)))),
% 28.25/18.49 inference(rewrite,[status(thm)],[])).
% 28.25/18.49 tff(10693,plain,
% 28.25/18.49 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(f6(c2, c2)) = f6(c2, c2)) | (c2 = f5(f6(c2, c2))) | (~big_f(f7(f6(c2, c2)), c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~big_f(f7(f6(c2, c2)), c2)) | (c2 = f5(f6(c2, c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f7(f6(c2, c2)) = f6(c2, c2))))),
% 28.25/18.49 inference(monotonicity,[status(thm)],[10692])).
% 28.25/18.49 tff(10694,plain,
% 28.25/18.49 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(f6(c2, c2)) = f6(c2, c2)) | (c2 = f5(f6(c2, c2))) | (~big_f(f7(f6(c2, c2)), c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (~big_f(f7(f6(c2, c2)), c2)) | (c2 = f5(f6(c2, c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f7(f6(c2, c2)) = f6(c2, c2)))),
% 28.25/18.49 inference(transitivity,[status(thm)],[10693, 10691])).
% 28.25/18.49 tff(10695,plain,
% 28.25/18.49 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(f6(c2, c2)) = f6(c2, c2)) | (c2 = f5(f6(c2, c2))) | (~big_f(f7(f6(c2, c2)), c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))),
% 28.25/18.49 inference(quant_inst,[status(thm)],[])).
% 28.25/18.49 tff(10696,plain,
% 28.25/18.49 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (~big_f(f7(f6(c2, c2)), c2)) | (c2 = f5(f6(c2, c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f7(f6(c2, c2)) = f6(c2, c2))),
% 28.25/18.49 inference(modus_ponens,[status(thm)],[10695, 10694])).
% 28.25/18.49 tff(10697,plain,
% 28.25/18.49 ((~big_f(f7(f6(c2, c2)), c2)) | (c2 = f5(f6(c2, c2))) | (f7(f6(c2, c2)) = f6(c2, c2))),
% 28.25/18.49 inference(unit_resolution,[status(thm)],[10696, 1190, 122, 1572, 690])).
% 28.25/18.49 tff(10698,plain,
% 28.25/18.49 (c2 = f5(f6(c2, c2))),
% 28.25/18.49 inference(unit_resolution,[status(thm)],[10697, 10690, 10687])).
% 28.25/18.49 tff(10699,plain,
% 28.25/18.49 (f5(f6(c2, c2)) = c2),
% 28.25/18.49 inference(symmetry,[status(thm)],[10698])).
% 28.25/18.49 tff(10700,plain,
% 28.25/18.49 (f6(c2, c2) = c1),
% 28.25/18.49 inference(transitivity,[status(thm)],[10679, 10235, 292])).
% 28.25/18.49 tff(10701,plain,
% 28.25/18.49 (big_f(f7(f6(c2, c2)), f6(c2, c2)) <=> big_f(c2, c1)),
% 28.25/18.49 inference(monotonicity,[status(thm)],[10682, 10700])).
% 28.25/18.49 tff(10702,plain,
% 28.25/18.49 (big_f(c2, c1) <=> big_f(f7(f6(c2, c2)), f6(c2, c2))),
% 28.25/18.49 inference(symmetry,[status(thm)],[10701])).
% 28.25/18.49 tff(10703,plain,
% 28.25/18.49 (big_f(f7(f6(c2, c2)), f6(c2, c2))),
% 28.25/18.49 inference(modus_ponens,[status(thm)],[348, 10702])).
% 28.25/18.49 tff(10704,plain,
% 28.25/18.49 ((f6(c2, c2) = f5(f6(c2, c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f7(f6(c2, c2)), f6(c2, c2)))),
% 28.25/18.49 inference(unit_resolution,[status(thm)],[3316, 1190, 122, 1572, 690])).
% 28.25/18.49 tff(10705,plain,
% 28.25/18.49 (f6(c2, c2) = f5(f6(c2, c2))),
% 28.25/18.49 inference(unit_resolution,[status(thm)],[10704, 10687, 10703])).
% 28.25/18.49 tff(10706,plain,
% 28.25/18.49 (f6(c2, c2) = c2),
% 28.25/18.49 inference(transitivity,[status(thm)],[10705, 10699])).
% 28.25/18.49 tff(10707,plain,
% 28.25/18.49 ($false),
% 28.25/18.49 inference(unit_resolution,[status(thm)],[2637, 10706])).
% 28.25/18.49 tff(10708,plain,((~(f7(c1) = c2)) | (f6(c2, c2) = c2) | (~(f10(c2) = c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~big_f(c2, c1)) | (~(f7(c2) = c1)) | (~(f7(c2) = f5(c2))) | (~(f6(c2, c2) = f5(c2))) | (~big_f(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 28.25/18.49 tff(10709,plain,
% 28.25/18.49 (~(f7(c1) = c2)),
% 28.25/18.49 inference(unit_resolution,[status(thm)],[10708, 10678, 122, 8080, 10357, 10315, 22, 10359, 10673, 10356])).
% 28.25/18.49 tff(10710,plain,
% 28.25/18.49 (f7(c1) = c1),
% 28.25/18.49 inference(unit_resolution,[status(thm)],[119, 10709])).
% 28.25/18.49 tff(10711,plain,
% 28.25/18.49 (~(f6(c1, c1) = c1)),
% 28.25/18.49 inference(unit_resolution,[status(thm)],[10643, 10710, 8080, 122, 10327, 10357, 22])).
% 28.25/18.49 tff(10712,assumption,(f6(c1, c1) = f5(c2)), introduced(assumption)).
% 28.25/18.49 tff(10713,plain,
% 28.25/18.49 (f6(c1, c1) = c1),
% 28.25/18.49 inference(transitivity,[status(thm)],[10712, 10235, 292])).
% 28.25/18.49 tff(10714,plain,
% 28.25/18.49 ($false),
% 28.25/18.49 inference(unit_resolution,[status(thm)],[28, 10713])).
% 28.25/18.49 tff(10715,plain,((~(f6(c1, c1) = f5(c2))) | (f6(c1, c1) = c1) | (~(f7(c2) = c1)) | (~(f7(c2) = f5(c2)))), inference(lemma,lemma(discharge,[]))).
% 28.25/18.49 tff(10716,plain,
% 28.25/18.49 (~(f6(c1, c1) = f5(c2))),
% 28.25/18.49 inference(unit_resolution,[status(thm)],[10715, 10711, 22, 10359])).
% 28.25/18.49 tff(10717,plain,
% 28.25/18.49 (f5(c2) = f7(c2)),
% 28.25/18.49 inference(symmetry,[status(thm)],[10359])).
% 28.25/18.49 tff(10718,plain,
% 28.25/18.49 (f6(c2, c2) = c1),
% 28.25/18.49 inference(transitivity,[status(thm)],[10673, 10717, 22])).
% 28.25/18.49 tff(10719,plain,
% 28.25/18.49 (f6(f6(c2, c2), f6(c2, c2)) = f6(c1, c1)),
% 28.25/18.49 inference(monotonicity,[status(thm)],[10718, 10718])).
% 28.25/18.49 tff(10720,plain,
% 28.25/18.49 (f6(c2, c2) = f7(c2)),
% 28.25/18.49 inference(transitivity,[status(thm)],[10673, 10717])).
% 28.25/18.49 tff(10721,plain,
% 28.25/18.49 (f7(f6(c2, c2)) = f7(f7(c2))),
% 28.25/18.49 inference(monotonicity,[status(thm)],[10720])).
% 28.25/18.49 tff(10722,plain,
% 28.25/18.49 (f7(f6(c2, c2)) = f7(c2)),
% 28.25/18.49 inference(transitivity,[status(thm)],[10721, 8077, 10710, 125])).
% 28.25/18.49 tff(10723,plain,
% 28.25/18.49 (big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f6(c2, c2))) <=> big_f(f7(c2), f6(c1, c1))),
% 28.25/18.49 inference(monotonicity,[status(thm)],[10722, 10719])).
% 28.25/18.49 tff(10724,plain,
% 28.25/18.49 (f7(f6(c2, c2)) = f6(c2, c2)),
% 28.25/18.49 inference(transitivity,[status(thm)],[10721, 8077, 10710, 125, 10359, 10674])).
% 28.25/18.49 tff(10725,plain,
% 28.25/18.49 ((f6(f6(c2, c2), f6(c2, c2)) = f6(c2, c2)) <=> (f6(c1, c1) = c1)),
% 28.25/18.49 inference(monotonicity,[status(thm)],[10719, 10718])).
% 28.25/18.49 tff(10726,plain,
% 28.25/18.49 ((f6(c1, c1) = c1) <=> (f6(f6(c2, c2), f6(c2, c2)) = f6(c2, c2))),
% 28.25/18.49 inference(symmetry,[status(thm)],[10725])).
% 28.25/18.49 tff(10727,plain,
% 28.25/18.49 ((~(f6(c1, c1) = c1)) <=> (~(f6(f6(c2, c2), f6(c2, c2)) = f6(c2, c2)))),
% 28.25/18.49 inference(monotonicity,[status(thm)],[10726])).
% 28.25/18.49 tff(10728,plain,
% 28.25/18.49 (~(f6(f6(c2, c2), f6(c2, c2)) = f6(c2, c2))),
% 28.25/18.49 inference(modus_ponens,[status(thm)],[10711, 10727])).
% 28.25/18.49 tff(10729,plain,
% 28.25/18.49 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f7(f6(c2, c2)) = f6(c2, c2))) | (f6(f6(c2, c2), f6(c2, c2)) = f6(c2, c2)) | big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f6(c2, c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f7(f6(c2, c2)) = f6(c2, c2))) | (f6(f6(c2, c2), f6(c2, c2)) = f6(c2, c2)) | big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f6(c2, c2))))),
% 28.25/18.49 inference(rewrite,[status(thm)],[])).
% 28.25/18.49 tff(10730,plain,
% 28.25/18.49 (((~(f10(c2) = c2)) | (~(f7(f6(c2, c2)) = f6(c2, c2))) | (f6(f6(c2, c2), f6(c2, c2)) = f6(c2, c2)) | big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f6(c2, c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2)))) <=> ((~(f10(c2) = c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f7(f6(c2, c2)) = f6(c2, c2))) | (f6(f6(c2, c2), f6(c2, c2)) = f6(c2, c2)) | big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f6(c2, c2))))),
% 28.25/18.49 inference(rewrite,[status(thm)],[])).
% 28.25/18.49 tff(10731,plain,
% 28.25/18.49 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(f6(c2, c2)) = f6(c2, c2))) | (f6(f6(c2, c2), f6(c2, c2)) = f6(c2, c2)) | big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f6(c2, c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f7(f6(c2, c2)) = f6(c2, c2))) | (f6(f6(c2, c2), f6(c2, c2)) = f6(c2, c2)) | big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f6(c2, c2)))))),
% 28.25/18.49 inference(monotonicity,[status(thm)],[10730])).
% 28.25/18.49 tff(10732,plain,
% 28.25/18.49 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(f6(c2, c2)) = f6(c2, c2))) | (f6(f6(c2, c2), f6(c2, c2)) = f6(c2, c2)) | big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f6(c2, c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f7(f6(c2, c2)) = f6(c2, c2))) | (f6(f6(c2, c2), f6(c2, c2)) = f6(c2, c2)) | big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f6(c2, c2))))),
% 28.25/18.49 inference(transitivity,[status(thm)],[10731, 10729])).
% 28.25/18.49 tff(10733,plain,
% 28.25/18.49 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(f6(c2, c2)) = f6(c2, c2))) | (f6(f6(c2, c2), f6(c2, c2)) = f6(c2, c2)) | big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f6(c2, c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))),
% 28.25/18.49 inference(quant_inst,[status(thm)],[])).
% 28.25/18.49 tff(10734,plain,
% 28.25/18.49 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f7(f6(c2, c2)) = f6(c2, c2))) | (f6(f6(c2, c2), f6(c2, c2)) = f6(c2, c2)) | big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f6(c2, c2)))),
% 28.25/18.49 inference(modus_ponens,[status(thm)],[10733, 10732])).
% 28.25/18.49 tff(10735,plain,
% 28.25/18.49 ((~(f7(f6(c2, c2)) = f6(c2, c2))) | (f6(f6(c2, c2), f6(c2, c2)) = f6(c2, c2)) | big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f6(c2, c2)))),
% 28.25/18.49 inference(unit_resolution,[status(thm)],[10734, 2409, 122, 8080, 10357])).
% 28.25/18.49 tff(10736,plain,
% 28.25/18.49 (big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f6(c2, c2)))),
% 28.25/18.49 inference(unit_resolution,[status(thm)],[10735, 10728, 10724])).
% 28.25/18.49 tff(10737,plain,
% 28.25/18.49 (big_f(f7(c2), f6(c1, c1))),
% 28.25/18.49 inference(modus_ponens,[status(thm)],[10736, 10723])).
% 28.25/18.49 tff(10738,plain,
% 28.25/18.49 ($false),
% 28.25/18.49 inference(unit_resolution,[status(thm)],[10660, 1190, 122, 17, 8080, 10357, 10737, 10716])).
% 28.25/18.49 tff(10739,plain,((f7(c2) = c2) | (~(f10(c2) = c2)) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.25/18.49 tff(10740,plain,
% 28.25/18.49 (f7(c2) = c2),
% 28.25/18.49 inference(unit_resolution,[status(thm)],[10739, 122, 79])).
% 28.25/18.49 tff(10741,plain,
% 28.25/18.49 (~(c3 = c2)),
% 28.25/18.49 inference(unit_resolution,[status(thm)],[8259, 2, 121, 79])).
% 28.25/18.49 tff(10742,plain,
% 28.25/18.49 (c3 = c1),
% 28.25/18.49 inference(unit_resolution,[status(thm)],[180, 10741])).
% 28.25/18.49 tff(10743,plain,
% 28.25/18.49 (c1 = c3),
% 28.25/18.49 inference(symmetry,[status(thm)],[10742])).
% 28.25/18.49 tff(10744,plain,
% 28.25/18.49 (f7(f7(c2)) = f7(c2)),
% 28.25/18.49 inference(monotonicity,[status(thm)],[10740])).
% 28.25/18.49 tff(10745,plain,
% 28.25/18.49 (f7(f7(c2)) = c2),
% 28.25/18.49 inference(transitivity,[status(thm)],[10744, 10740])).
% 28.25/18.49 tff(10746,plain,
% 28.25/18.49 ((f7(f7(c2)) = c3) <=> (c2 = c3)),
% 28.25/18.49 inference(monotonicity,[status(thm)],[10745])).
% 28.25/18.49 tff(10747,plain,
% 28.25/18.49 ((c2 = c3) <=> (f7(f7(c2)) = c3)),
% 28.25/18.49 inference(symmetry,[status(thm)],[10746])).
% 28.25/18.49 tff(10748,plain,
% 28.25/18.49 ((c2 = c1) <=> (c2 = c3)),
% 28.25/18.49 inference(monotonicity,[status(thm)],[10743])).
% 28.25/18.49 tff(10749,plain,
% 28.25/18.49 ((c2 = c1) <=> (f7(f7(c2)) = c3)),
% 28.25/18.49 inference(transitivity,[status(thm)],[10748, 10747])).
% 28.25/18.49 tff(10750,plain,
% 28.25/18.49 ((~(c2 = c1)) <=> (~(f7(f7(c2)) = c3))),
% 28.25/18.49 inference(monotonicity,[status(thm)],[10749])).
% 28.25/18.49 tff(10751,plain,
% 28.25/18.49 (~(f7(f7(c2)) = c3)),
% 28.25/18.49 inference(modus_ponens,[status(thm)],[75, 10750])).
% 28.25/18.49 tff(10752,plain,
% 28.25/18.49 (f1(f7(f7(c2)), c1) = c1),
% 28.25/18.49 inference(unit_resolution,[status(thm)],[5433, 10751, 10740, 5577, 121])).
% 28.25/18.49 tff(10753,plain,
% 28.25/18.49 (f1(f7(f7(c2)), c1) = f1(c2, c1)),
% 28.25/18.49 inference(monotonicity,[status(thm)],[10745])).
% 28.25/18.49 tff(10754,plain,
% 28.25/18.49 (f1(c2, c1) = f1(f7(f7(c2)), c1)),
% 28.25/18.49 inference(symmetry,[status(thm)],[10753])).
% 28.25/18.49 tff(10755,plain,
% 28.25/18.49 (f1(c2, c1) = c3),
% 28.25/18.49 inference(transitivity,[status(thm)],[10754, 10752, 10743])).
% 28.25/18.49 tff(10756,plain,
% 28.25/18.49 (big_f(c1, f2(c1))),
% 28.25/18.49 inference(unit_resolution,[status(thm)],[8631, 10742, 8627])).
% 28.25/18.49 tff(10757,plain,
% 28.25/18.49 (c1 = f1(f7(f7(c2)), c1)),
% 28.25/18.49 inference(symmetry,[status(thm)],[10752])).
% 28.25/18.49 tff(10758,plain,
% 28.25/18.49 (c1 = f1(c2, c1)),
% 28.25/18.49 inference(transitivity,[status(thm)],[10757, 10753])).
% 28.25/18.49 tff(10759,plain,
% 28.25/18.49 (big_f(c2, c1) <=> big_f(c2, f1(c2, c1))),
% 28.25/18.49 inference(monotonicity,[status(thm)],[10758])).
% 28.25/18.49 tff(10760,plain,
% 28.25/18.49 ((~big_f(c2, c1)) <=> (~big_f(c2, f1(c2, c1)))),
% 28.25/18.49 inference(monotonicity,[status(thm)],[10759])).
% 28.25/18.49 tff(10761,plain,
% 28.25/18.49 (~big_f(c2, f1(c2, c1))),
% 28.25/18.49 inference(modus_ponens,[status(thm)],[2, 10760])).
% 28.25/18.49 tff(10762,plain,
% 28.25/18.49 (f1(f7(f7(c2)), c1) = f1(c2, c1)),
% 28.25/18.49 inference(monotonicity,[status(thm)],[5429])).
% 28.25/18.49 tff(10763,plain,
% 28.25/18.49 (big_f(f7(c1), c1) <=> big_f(f7(c1), f1(f7(f7(c2)), c1))),
% 28.25/18.49 inference(monotonicity,[status(thm)],[875])).
% 28.25/18.49 tff(10764,plain,
% 28.25/18.49 (big_f(f7(c1), f1(f7(f7(c2)), c1)) <=> big_f(f7(c1), c1)),
% 28.25/18.49 inference(symmetry,[status(thm)],[10763])).
% 28.25/18.49 tff(10765,plain,
% 28.25/18.49 (big_f(f7(c1), f1(f7(f7(c2)), c1)) <=> big_f(c2, f1(c2, c1))),
% 28.25/18.49 inference(monotonicity,[status(thm)],[120, 10762])).
% 28.25/18.49 tff(10766,plain,
% 28.25/18.49 (big_f(c2, f1(c2, c1)) <=> big_f(f7(c1), f1(f7(f7(c2)), c1))),
% 28.25/18.49 inference(symmetry,[status(thm)],[10765])).
% 28.25/18.49 tff(10767,plain,
% 28.25/18.49 (big_f(c2, f1(c2, c1)) <=> big_f(f7(c1), c1)),
% 28.25/18.49 inference(transitivity,[status(thm)],[10766, 10764])).
% 28.25/18.49 tff(10768,plain,
% 28.25/18.49 ((~big_f(c2, f1(c2, c1))) <=> (~big_f(f7(c1), c1))),
% 28.25/18.49 inference(monotonicity,[status(thm)],[10767])).
% 28.25/18.49 tff(10769,plain,
% 28.25/18.49 (~big_f(f7(c1), c1)),
% 28.25/18.49 inference(modus_ponens,[status(thm)],[10090, 10768])).
% 28.25/18.49 tff(10770,plain,
% 28.25/18.49 (~big_f(f7(c1), f5(c1))),
% 28.25/18.49 inference(unit_resolution,[status(thm)],[8430, 10769, 121, 120])).
% 28.25/18.49 tff(10771,plain,
% 28.25/18.49 (f9(c2, c1) = c1),
% 28.25/18.49 inference(unit_resolution,[status(thm)],[8445, 10770, 122, 115, 121])).
% 28.25/18.49 tff(10772,plain,
% 28.25/18.49 (f1(c2, c1) = f1(f7(f7(c2)), c1)),
% 28.25/18.49 inference(symmetry,[status(thm)],[10762])).
% 28.25/18.49 tff(10773,plain,
% 28.25/18.49 (f1(c2, c1) = c1),
% 28.25/18.49 inference(transitivity,[status(thm)],[10772, 874])).
% 28.25/18.49 tff(10774,plain,
% 28.25/18.49 (f9(c2, f1(c2, c1)) = f9(c2, c1)),
% 28.25/18.49 inference(monotonicity,[status(thm)],[10773])).
% 28.25/18.49 tff(10775,plain,
% 28.25/18.49 (f9(c2, f1(c2, c1)) = c1),
% 28.25/18.49 inference(transitivity,[status(thm)],[10774, 10771])).
% 28.25/18.49 tff(10776,plain,
% 28.25/18.49 (big_f(f9(c2, f1(c2, c1)), f10(c2)) <=> big_f(c1, c2)),
% 28.25/18.49 inference(monotonicity,[status(thm)],[10775, 122])).
% 28.25/18.49 tff(10777,plain,
% 28.25/18.49 ((~big_f(f9(c2, f1(c2, c1)), f10(c2))) <=> (~big_f(c1, c2))),
% 28.25/18.49 inference(monotonicity,[status(thm)],[10776])).
% 28.25/18.49 tff(10778,plain,
% 28.25/18.49 (f7(f1(c2, c1)) = f7(c1)),
% 28.25/18.49 inference(monotonicity,[status(thm)],[10773])).
% 28.25/18.49 tff(10779,plain,
% 28.25/18.49 (f7(f1(c2, c1)) = c2),
% 28.25/18.49 inference(transitivity,[status(thm)],[10778, 120])).
% 28.25/18.49 tff(10780,plain,
% 28.25/18.49 (big_f(f7(f1(c2, c1)), c2) <=> big_f(c2, c2)),
% 28.25/18.49 inference(monotonicity,[status(thm)],[10779])).
% 28.25/18.49 tff(10781,plain,
% 28.25/18.49 (big_f(c2, c2) <=> big_f(f7(f1(c2, c1)), c2)),
% 28.25/18.49 inference(symmetry,[status(thm)],[10780])).
% 28.25/18.49 tff(10782,plain,
% 28.25/18.49 ((~big_f(c2, c2)) <=> (~big_f(f7(f1(c2, c1)), c2))),
% 28.25/18.49 inference(monotonicity,[status(thm)],[10781])).
% 28.25/18.49 tff(10783,plain,
% 28.25/18.49 (~big_f(f7(f1(c2, c1)), c2)),
% 28.25/18.49 inference(modus_ponens,[status(thm)],[121, 10782])).
% 28.25/18.49 tff(10784,plain,
% 28.25/18.49 ((c2 = f1(c2, c1)) <=> (f1(c2, c1) = c2)),
% 28.25/18.49 inference(commutativity,[status(thm)],[])).
% 28.25/18.49 tff(10785,plain,
% 28.25/18.49 ((f7(f1(c2, c1)) = f1(c2, c1)) <=> (c2 = f1(c2, c1))),
% 28.25/18.49 inference(monotonicity,[status(thm)],[10779])).
% 28.25/18.49 tff(10786,plain,
% 28.25/18.49 ((f7(f1(c2, c1)) = f1(c2, c1)) <=> (f1(c2, c1) = c2)),
% 28.25/18.49 inference(transitivity,[status(thm)],[10785, 10784])).
% 28.25/18.49 tff(10787,plain,
% 28.25/18.49 ((f1(c2, c1) = c2) <=> (f7(f1(c2, c1)) = f1(c2, c1))),
% 28.25/18.49 inference(symmetry,[status(thm)],[10786])).
% 28.25/18.49 tff(10788,plain,
% 28.25/18.49 ((~(f1(c2, c1) = c2)) <=> (~(f7(f1(c2, c1)) = f1(c2, c1)))),
% 28.25/18.49 inference(monotonicity,[status(thm)],[10787])).
% 28.25/18.49 tff(10789,plain,
% 28.25/18.49 ((f1(c2, c1) = c2) <=> (c1 = c2)),
% 28.25/18.49 inference(monotonicity,[status(thm)],[10773])).
% 28.25/18.49 tff(10790,plain,
% 28.25/18.49 ((f1(c2, c1) = c2) <=> (c2 = c1)),
% 28.25/18.49 inference(transitivity,[status(thm)],[10789, 1])).
% 28.25/18.49 tff(10791,plain,
% 28.25/18.49 ((c2 = c1) <=> (f1(c2, c1) = c2)),
% 28.25/18.49 inference(symmetry,[status(thm)],[10790])).
% 28.25/18.50 tff(10792,plain,
% 28.25/18.50 ((~(c2 = c1)) <=> (~(f1(c2, c1) = c2))),
% 28.25/18.50 inference(monotonicity,[status(thm)],[10791])).
% 28.25/18.50 tff(10793,plain,
% 28.25/18.50 (~(f1(c2, c1) = c2)),
% 28.25/18.50 inference(modus_ponens,[status(thm)],[75, 10792])).
% 28.25/18.50 tff(10794,plain,
% 28.25/18.50 (~(f7(f1(c2, c1)) = f1(c2, c1))),
% 28.25/18.50 inference(modus_ponens,[status(thm)],[10793, 10788])).
% 28.25/18.50 tff(10795,plain,
% 28.25/18.50 (big_f(f7(f1(c2, c1)), f1(c2, c1)) <=> big_f(c2, f1(c2, c1))),
% 28.25/18.50 inference(monotonicity,[status(thm)],[10779])).
% 28.25/18.50 tff(10796,plain,
% 28.25/18.50 (big_f(c2, f1(c2, c1)) <=> big_f(f7(f1(c2, c1)), f1(c2, c1))),
% 28.25/18.50 inference(symmetry,[status(thm)],[10795])).
% 28.25/18.50 tff(10797,plain,
% 28.25/18.50 ((~big_f(c2, f1(c2, c1))) <=> (~big_f(f7(f1(c2, c1)), f1(c2, c1)))),
% 28.25/18.50 inference(monotonicity,[status(thm)],[10796])).
% 28.25/18.50 tff(10798,plain,
% 28.25/18.50 (~big_f(f7(f1(c2, c1)), f1(c2, c1))),
% 28.25/18.50 inference(modus_ponens,[status(thm)],[10090, 10797])).
% 28.25/18.50 tff(10799,plain,
% 28.25/18.50 (f9(c2, f1(c2, c1)) = f1(c2, c1)),
% 28.25/18.50 inference(transitivity,[status(thm)],[10774, 10771, 875, 10762])).
% 28.25/18.50 tff(10800,plain,
% 28.25/18.50 (f5(f1(c2, c1)) = f5(c1)),
% 28.25/18.50 inference(monotonicity,[status(thm)],[10773])).
% 28.25/18.50 tff(10801,plain,
% 28.25/18.50 ((c2 = f5(f1(c2, c1))) <=> (c2 = f5(c1))),
% 28.25/18.50 inference(monotonicity,[status(thm)],[10800])).
% 28.25/18.50 tff(10802,plain,
% 28.25/18.50 ((c2 = f5(f1(c2, c1))) <=> (f5(c1) = c2)),
% 28.25/18.50 inference(transitivity,[status(thm)],[10801, 8483])).
% 28.25/18.50 tff(10803,plain,
% 28.25/18.50 ((~(c2 = f5(f1(c2, c1)))) <=> (~(f5(c1) = c2))),
% 28.25/18.50 inference(monotonicity,[status(thm)],[10802])).
% 28.25/18.50 tff(10804,assumption,(~big_f(f7(f1(c2, c1)), c2)), introduced(assumption)).
% 28.25/18.50 tff(10805,assumption,(~(f7(f1(c2, c1)) = f1(c2, c1))), introduced(assumption)).
% 28.25/18.50 tff(10806,assumption,(f9(c2, f1(c2, c1)) = f1(c2, c1)), introduced(assumption)).
% 28.25/18.50 tff(10807,assumption,(big_f(f9(c2, f1(c2, c1)), f10(c2))), introduced(assumption)).
% 28.25/18.50 tff(10808,plain,
% 28.25/18.50 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (~big_f(f9(c2, f1(c2, c1)), f10(c2))) | (f7(f1(c2, c1)) = f1(c2, c1)) | (~(f9(c2, f1(c2, c1)) = f1(c2, c1))) | (~(c2 = f5(f1(c2, c1)))) | big_f(f7(f1(c2, c1)), c2))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (~big_f(f9(c2, f1(c2, c1)), f10(c2))) | (f7(f1(c2, c1)) = f1(c2, c1)) | (~(f9(c2, f1(c2, c1)) = f1(c2, c1))) | (~(c2 = f5(f1(c2, c1)))) | big_f(f7(f1(c2, c1)), c2))),
% 28.25/18.50 inference(rewrite,[status(thm)],[])).
% 28.25/18.50 tff(10809,plain,
% 28.25/18.50 (((~(f10(c2) = c2)) | (f7(f1(c2, c1)) = f1(c2, c1)) | big_f(f7(f1(c2, c1)), c2) | (~(f9(c2, f1(c2, c1)) = f1(c2, c1))) | (~big_f(f9(c2, f1(c2, c1)), f10(c2))) | (~(c2 = f5(f1(c2, c1))))) <=> ((~(f10(c2) = c2)) | (~big_f(f9(c2, f1(c2, c1)), f10(c2))) | (f7(f1(c2, c1)) = f1(c2, c1)) | (~(f9(c2, f1(c2, c1)) = f1(c2, c1))) | (~(c2 = f5(f1(c2, c1)))) | big_f(f7(f1(c2, c1)), c2))),
% 28.25/18.50 inference(rewrite,[status(thm)],[])).
% 28.25/18.50 tff(10810,plain,
% 28.25/18.50 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(f1(c2, c1)) = f1(c2, c1)) | big_f(f7(f1(c2, c1)), c2) | (~(f9(c2, f1(c2, c1)) = f1(c2, c1))) | (~big_f(f9(c2, f1(c2, c1)), f10(c2))) | (~(c2 = f5(f1(c2, c1)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (~big_f(f9(c2, f1(c2, c1)), f10(c2))) | (f7(f1(c2, c1)) = f1(c2, c1)) | (~(f9(c2, f1(c2, c1)) = f1(c2, c1))) | (~(c2 = f5(f1(c2, c1)))) | big_f(f7(f1(c2, c1)), c2)))),
% 28.25/18.50 inference(monotonicity,[status(thm)],[10809])).
% 28.25/18.50 tff(10811,plain,
% 28.25/18.50 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(f1(c2, c1)) = f1(c2, c1)) | big_f(f7(f1(c2, c1)), c2) | (~(f9(c2, f1(c2, c1)) = f1(c2, c1))) | (~big_f(f9(c2, f1(c2, c1)), f10(c2))) | (~(c2 = f5(f1(c2, c1)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (~big_f(f9(c2, f1(c2, c1)), f10(c2))) | (f7(f1(c2, c1)) = f1(c2, c1)) | (~(f9(c2, f1(c2, c1)) = f1(c2, c1))) | (~(c2 = f5(f1(c2, c1)))) | big_f(f7(f1(c2, c1)), c2))),
% 28.25/18.50 inference(transitivity,[status(thm)],[10810, 10808])).
% 28.25/18.50 tff(10812,plain,
% 28.25/18.50 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(f1(c2, c1)) = f1(c2, c1)) | big_f(f7(f1(c2, c1)), c2) | (~(f9(c2, f1(c2, c1)) = f1(c2, c1))) | (~big_f(f9(c2, f1(c2, c1)), f10(c2))) | (~(c2 = f5(f1(c2, c1)))))),
% 28.25/18.50 inference(quant_inst,[status(thm)],[])).
% 28.25/18.50 tff(10813,plain,
% 28.25/18.50 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (~big_f(f9(c2, f1(c2, c1)), f10(c2))) | (f7(f1(c2, c1)) = f1(c2, c1)) | (~(f9(c2, f1(c2, c1)) = f1(c2, c1))) | (~(c2 = f5(f1(c2, c1)))) | big_f(f7(f1(c2, c1)), c2)),
% 28.25/18.50 inference(modus_ponens,[status(thm)],[10812, 10811])).
% 28.25/18.50 tff(10814,plain,
% 28.25/18.50 ((~big_f(f9(c2, f1(c2, c1)), f10(c2))) | (f7(f1(c2, c1)) = f1(c2, c1)) | (~(f9(c2, f1(c2, c1)) = f1(c2, c1))) | (~(c2 = f5(f1(c2, c1)))) | big_f(f7(f1(c2, c1)), c2)),
% 28.25/18.50 inference(unit_resolution,[status(thm)],[10813, 783, 122])).
% 28.25/18.50 tff(10815,plain,
% 28.25/18.50 (~(c2 = f5(f1(c2, c1)))),
% 28.25/18.50 inference(unit_resolution,[status(thm)],[10814, 10807, 10806, 10805, 10804])).
% 28.25/18.50 tff(10816,plain,
% 28.25/18.50 (~(f5(c1) = c2)),
% 28.25/18.50 inference(modus_ponens,[status(thm)],[10815, 10803])).
% 28.25/18.50 tff(10817,plain,
% 28.25/18.50 ((f1(f7(f7(c2)), c1) = f5(c1)) <=> (c1 = f5(c1))),
% 28.25/18.50 inference(monotonicity,[status(thm)],[874])).
% 28.25/18.50 tff(10818,plain,
% 28.25/18.50 ((f1(f7(f7(c2)), c1) = f5(c1)) <=> (f5(c1) = c1)),
% 28.25/18.50 inference(transitivity,[status(thm)],[10817, 128])).
% 28.25/18.50 tff(10819,plain,
% 28.25/18.50 ((f1(c2, c1) = f5(f1(c2, c1))) <=> (f1(f7(f7(c2)), c1) = f5(c1))),
% 28.25/18.50 inference(monotonicity,[status(thm)],[10772, 10800])).
% 28.25/18.50 tff(10820,plain,
% 28.25/18.50 ((f1(c2, c1) = f5(f1(c2, c1))) <=> (f5(c1) = c1)),
% 28.25/18.50 inference(transitivity,[status(thm)],[10819, 10818])).
% 28.25/18.50 tff(10821,plain,
% 28.25/18.50 ((~(f1(c2, c1) = f5(f1(c2, c1)))) <=> (~(f5(c1) = c1))),
% 28.25/18.50 inference(monotonicity,[status(thm)],[10820])).
% 28.25/18.50 tff(10822,assumption,(~big_f(f7(f1(c2, c1)), f1(c2, c1))), introduced(assumption)).
% 28.25/18.50 tff(10823,plain,
% 28.25/18.50 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | big_f(f7(f1(c2, c1)), f1(c2, c1)) | (~big_f(f9(c2, f1(c2, c1)), f10(c2))) | (f7(f1(c2, c1)) = f1(c2, c1)) | (~(f9(c2, f1(c2, c1)) = f1(c2, c1))) | (~(f1(c2, c1) = f5(f1(c2, c1)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | big_f(f7(f1(c2, c1)), f1(c2, c1)) | (~big_f(f9(c2, f1(c2, c1)), f10(c2))) | (f7(f1(c2, c1)) = f1(c2, c1)) | (~(f9(c2, f1(c2, c1)) = f1(c2, c1))) | (~(f1(c2, c1) = f5(f1(c2, c1)))))),
% 28.25/18.50 inference(rewrite,[status(thm)],[])).
% 28.25/18.50 tff(10824,plain,
% 28.25/18.50 (((~(f10(c2) = c2)) | (f7(f1(c2, c1)) = f1(c2, c1)) | big_f(f7(f1(c2, c1)), f1(c2, c1)) | (~(f9(c2, f1(c2, c1)) = f1(c2, c1))) | (~big_f(f9(c2, f1(c2, c1)), f10(c2))) | (~(f1(c2, c1) = f5(f1(c2, c1))))) <=> ((~(f10(c2) = c2)) | big_f(f7(f1(c2, c1)), f1(c2, c1)) | (~big_f(f9(c2, f1(c2, c1)), f10(c2))) | (f7(f1(c2, c1)) = f1(c2, c1)) | (~(f9(c2, f1(c2, c1)) = f1(c2, c1))) | (~(f1(c2, c1) = f5(f1(c2, c1)))))),
% 28.25/18.50 inference(rewrite,[status(thm)],[])).
% 28.25/18.50 tff(10825,plain,
% 28.25/18.50 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(f1(c2, c1)) = f1(c2, c1)) | big_f(f7(f1(c2, c1)), f1(c2, c1)) | (~(f9(c2, f1(c2, c1)) = f1(c2, c1))) | (~big_f(f9(c2, f1(c2, c1)), f10(c2))) | (~(f1(c2, c1) = f5(f1(c2, c1)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | big_f(f7(f1(c2, c1)), f1(c2, c1)) | (~big_f(f9(c2, f1(c2, c1)), f10(c2))) | (f7(f1(c2, c1)) = f1(c2, c1)) | (~(f9(c2, f1(c2, c1)) = f1(c2, c1))) | (~(f1(c2, c1) = f5(f1(c2, c1))))))),
% 28.25/18.50 inference(monotonicity,[status(thm)],[10824])).
% 28.25/18.50 tff(10826,plain,
% 28.25/18.50 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(f1(c2, c1)) = f1(c2, c1)) | big_f(f7(f1(c2, c1)), f1(c2, c1)) | (~(f9(c2, f1(c2, c1)) = f1(c2, c1))) | (~big_f(f9(c2, f1(c2, c1)), f10(c2))) | (~(f1(c2, c1) = f5(f1(c2, c1)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | big_f(f7(f1(c2, c1)), f1(c2, c1)) | (~big_f(f9(c2, f1(c2, c1)), f10(c2))) | (f7(f1(c2, c1)) = f1(c2, c1)) | (~(f9(c2, f1(c2, c1)) = f1(c2, c1))) | (~(f1(c2, c1) = f5(f1(c2, c1)))))),
% 28.25/18.50 inference(transitivity,[status(thm)],[10825, 10823])).
% 28.25/18.50 tff(10827,plain,
% 28.25/18.50 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(f1(c2, c1)) = f1(c2, c1)) | big_f(f7(f1(c2, c1)), f1(c2, c1)) | (~(f9(c2, f1(c2, c1)) = f1(c2, c1))) | (~big_f(f9(c2, f1(c2, c1)), f10(c2))) | (~(f1(c2, c1) = f5(f1(c2, c1)))))),
% 28.25/18.50 inference(quant_inst,[status(thm)],[])).
% 28.25/18.50 tff(10828,plain,
% 28.25/18.50 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | big_f(f7(f1(c2, c1)), f1(c2, c1)) | (~big_f(f9(c2, f1(c2, c1)), f10(c2))) | (f7(f1(c2, c1)) = f1(c2, c1)) | (~(f9(c2, f1(c2, c1)) = f1(c2, c1))) | (~(f1(c2, c1) = f5(f1(c2, c1))))),
% 28.25/18.50 inference(modus_ponens,[status(thm)],[10827, 10826])).
% 28.25/18.50 tff(10829,plain,
% 28.25/18.50 (big_f(f7(f1(c2, c1)), f1(c2, c1)) | (~big_f(f9(c2, f1(c2, c1)), f10(c2))) | (f7(f1(c2, c1)) = f1(c2, c1)) | (~(f9(c2, f1(c2, c1)) = f1(c2, c1))) | (~(f1(c2, c1) = f5(f1(c2, c1))))),
% 28.25/18.50 inference(unit_resolution,[status(thm)],[10828, 783, 122])).
% 28.25/18.50 tff(10830,plain,
% 28.25/18.50 (~(f1(c2, c1) = f5(f1(c2, c1)))),
% 28.25/18.50 inference(unit_resolution,[status(thm)],[10829, 10807, 10806, 10822, 10805])).
% 28.25/18.50 tff(10831,plain,
% 28.25/18.50 (~(f5(c1) = c1)),
% 28.25/18.50 inference(modus_ponens,[status(thm)],[10830, 10821])).
% 28.25/18.50 tff(10832,plain,
% 28.25/18.50 ($false),
% 28.25/18.50 inference(unit_resolution,[status(thm)],[1708, 10831, 10816])).
% 28.25/18.50 tff(10833,plain,((~big_f(f9(c2, f1(c2, c1)), f10(c2))) | (~(f1(f7(f7(c2)), c1) = c1)) | (~(f7(c2) = c2)) | (~(f9(c2, f1(c2, c1)) = f1(c2, c1))) | big_f(f7(f1(c2, c1)), f1(c2, c1)) | (f7(f1(c2, c1)) = f1(c2, c1)) | (~(f10(c2) = c2)) | big_f(f7(f1(c2, c1)), c2)), inference(lemma,lemma(discharge,[]))).
% 28.25/18.50 tff(10834,plain,
% 28.25/18.50 (~big_f(f9(c2, f1(c2, c1)), f10(c2))),
% 28.25/18.50 inference(unit_resolution,[status(thm)],[10833, 10799, 77, 874, 10798, 10794, 122, 10783])).
% 28.25/18.50 tff(10835,plain,
% 28.25/18.50 (~big_f(c1, c2)),
% 28.25/18.50 inference(modus_ponens,[status(thm)],[10834, 10777])).
% 28.25/18.50 tff(10836,plain,
% 28.25/18.50 (f8(f1(c2, c1)) = f8(c1)),
% 28.25/18.50 inference(monotonicity,[status(thm)],[10773])).
% 28.25/18.50 tff(10837,plain,
% 28.25/18.50 ((f1(c2, c1) = f8(f1(c2, c1))) <=> (c1 = f8(c1))),
% 28.25/18.50 inference(monotonicity,[status(thm)],[10773, 10836])).
% 28.25/18.50 tff(10838,plain,
% 28.25/18.50 ((f1(c2, c1) = f8(f1(c2, c1))) <=> (f8(c1) = c1)),
% 28.25/18.50 inference(transitivity,[status(thm)],[10837, 3027])).
% 28.25/18.50 tff(10839,plain,
% 28.25/18.50 ((f8(c1) = c1) <=> (f1(c2, c1) = f8(f1(c2, c1)))),
% 28.25/18.50 inference(symmetry,[status(thm)],[10838])).
% 28.25/18.50 tff(10840,plain,
% 28.25/18.50 ((f5(c1) = f1(f7(f7(c2)), c1)) <=> (f1(f7(f7(c2)), c1) = f5(c1))),
% 28.25/18.50 inference(commutativity,[status(thm)],[])).
% 28.25/18.50 tff(10841,plain,
% 28.25/18.50 ((f5(c1) = c1) <=> (f5(c1) = f1(f7(f7(c2)), c1))),
% 28.25/18.50 inference(monotonicity,[status(thm)],[875])).
% 28.25/18.50 tff(10842,plain,
% 28.25/18.50 ((f5(c1) = c1) <=> (f1(f7(f7(c2)), c1) = f5(c1))),
% 28.25/18.50 inference(transitivity,[status(thm)],[10841, 10840])).
% 28.25/18.50 tff(10843,plain,
% 28.25/18.50 ((f1(f7(f7(c2)), c1) = f5(c1)) <=> (f5(c1) = c1)),
% 28.25/18.50 inference(symmetry,[status(thm)],[10842])).
% 28.25/18.50 tff(10844,plain,
% 28.25/18.50 ((f1(c2, c1) = f5(f1(c2, c1))) <=> (f5(c1) = c1)),
% 28.25/18.50 inference(transitivity,[status(thm)],[10819, 10843])).
% 28.25/18.50 tff(10845,plain,
% 28.25/18.50 ((~(f1(c2, c1) = f5(f1(c2, c1)))) <=> (~(f5(c1) = c1))),
% 28.25/18.50 inference(monotonicity,[status(thm)],[10844])).
% 28.25/18.50 tff(10846,plain,
% 28.25/18.50 (f10(f1(c2, c1)) = f10(c1)),
% 28.25/18.50 inference(monotonicity,[status(thm)],[10773])).
% 28.25/18.50 tff(10847,plain,
% 28.25/18.50 (f10(f1(c2, c1)) = c2),
% 28.25/18.50 inference(transitivity,[status(thm)],[10846, 15])).
% 28.25/18.50 tff(10848,plain,
% 28.25/18.50 (big_f(c2, f10(f1(c2, c1))) <=> big_f(c2, c2)),
% 28.25/18.50 inference(monotonicity,[status(thm)],[10847])).
% 28.25/18.50 tff(10849,plain,
% 28.25/18.50 (big_f(c2, c2) <=> big_f(c2, f10(f1(c2, c1)))),
% 28.25/18.50 inference(symmetry,[status(thm)],[10848])).
% 28.25/18.50 tff(10850,plain,
% 28.25/18.50 ((~big_f(c2, c2)) <=> (~big_f(c2, f10(f1(c2, c1))))),
% 28.25/18.50 inference(monotonicity,[status(thm)],[10849])).
% 28.25/18.50 tff(10851,plain,
% 28.25/18.50 (~big_f(c2, f10(f1(c2, c1)))),
% 28.25/18.50 inference(modus_ponens,[status(thm)],[121, 10850])).
% 28.25/18.50 tff(10852,plain,
% 28.25/18.50 ((f10(f1(c2, c1)) = f1(c2, c1)) <=> (c2 = f1(c2, c1))),
% 28.25/18.50 inference(monotonicity,[status(thm)],[10847])).
% 28.25/18.50 tff(10853,plain,
% 28.25/18.50 ((f10(f1(c2, c1)) = f1(c2, c1)) <=> (f1(c2, c1) = c2)),
% 28.25/18.50 inference(transitivity,[status(thm)],[10852, 10784])).
% 28.25/18.50 tff(10854,plain,
% 28.25/18.50 ((f1(c2, c1) = c2) <=> (f10(f1(c2, c1)) = f1(c2, c1))),
% 28.25/18.50 inference(symmetry,[status(thm)],[10853])).
% 28.25/18.50 tff(10855,plain,
% 28.25/18.50 ((~(f1(c2, c1) = c2)) <=> (~(f10(f1(c2, c1)) = f1(c2, c1)))),
% 28.25/18.50 inference(monotonicity,[status(thm)],[10854])).
% 28.25/18.50 tff(10856,plain,
% 28.25/18.50 (~(f10(f1(c2, c1)) = f1(c2, c1))),
% 28.25/18.50 inference(modus_ponens,[status(thm)],[10793, 10855])).
% 28.25/18.50 tff(10857,plain,
% 28.25/18.50 (big_f(f1(c2, c1), f10(f1(c2, c1))) <=> big_f(c1, c2)),
% 28.25/18.50 inference(monotonicity,[status(thm)],[10773, 10847])).
% 28.25/18.50 tff(10858,plain,
% 28.25/18.50 (big_f(c1, c2) <=> big_f(f1(c2, c1), f10(f1(c2, c1)))),
% 28.25/18.50 inference(symmetry,[status(thm)],[10857])).
% 28.25/18.50 tff(10859,plain,
% 28.25/18.50 ((~big_f(c1, c2)) <=> (~big_f(f1(c2, c1), f10(f1(c2, c1))))),
% 28.25/18.50 inference(monotonicity,[status(thm)],[10858])).
% 28.25/18.50 tff(10860,plain,
% 28.25/18.50 (~big_f(f1(c2, c1), f10(f1(c2, c1)))),
% 28.25/18.50 inference(modus_ponens,[status(thm)],[27, 10859])).
% 28.25/18.50 tff(10861,plain,
% 28.25/18.50 (f8(c3) = f8(c1)),
% 28.25/18.50 inference(monotonicity,[status(thm)],[172])).
% 28.25/18.50 tff(10862,plain,
% 28.25/18.50 ((f8(c3) = c2) <=> (f8(c1) = c2)),
% 28.25/18.50 inference(monotonicity,[status(thm)],[10861])).
% 28.25/18.50 tff(10863,plain,
% 28.25/18.50 ((f8(c3) = c2) <=> (c2 = f8(c1))),
% 28.25/18.50 inference(transitivity,[status(thm)],[10862, 1670])).
% 28.25/18.50 tff(10864,plain,
% 28.25/18.50 ((c2 = f8(c1)) <=> (f8(c3) = c2)),
% 28.25/18.50 inference(symmetry,[status(thm)],[10863])).
% 28.25/18.50 tff(10865,plain,
% 28.25/18.50 ((c2 = f8(f1(c2, c1))) <=> (c2 = f8(c1))),
% 28.25/18.50 inference(monotonicity,[status(thm)],[10836])).
% 28.25/18.50 tff(10866,plain,
% 28.25/18.50 ((c2 = f8(f1(c2, c1))) <=> (f8(c3) = c2)),
% 28.25/18.50 inference(transitivity,[status(thm)],[10865, 10864])).
% 28.25/18.50 tff(10867,plain,
% 28.25/18.50 ((~(c2 = f8(f1(c2, c1)))) <=> (~(f8(c3) = c2))),
% 28.25/18.50 inference(monotonicity,[status(thm)],[10866])).
% 28.25/18.50 tff(10868,assumption,(~(f10(f1(c2, c1)) = f1(c2, c1))), introduced(assumption)).
% 28.25/18.50 tff(10869,assumption,(~big_f(c2, f10(f1(c2, c1)))), introduced(assumption)).
% 28.25/18.50 tff(10870,assumption,(f1(c2, c1) = f5(f1(c2, c1))), introduced(assumption)).
% 28.25/18.50 tff(10871,plain,
% 28.25/18.50 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (big_f(f7(f1(c2, c1)), f1(c2, c1)) | (f7(f1(c2, c1)) = f1(c2, c1)) | (~(f1(c2, c1) = f5(f1(c2, c1)))) | (f10(f1(c2, c1)) = f1(c2, c1)) | big_f(c2, f10(f1(c2, c1))) | (~(c2 = f8(f1(c2, c1)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | big_f(f7(f1(c2, c1)), f1(c2, c1)) | (f7(f1(c2, c1)) = f1(c2, c1)) | (~(f1(c2, c1) = f5(f1(c2, c1)))) | (f10(f1(c2, c1)) = f1(c2, c1)) | big_f(c2, f10(f1(c2, c1))) | (~(c2 = f8(f1(c2, c1)))))),
% 28.25/18.50 inference(rewrite,[status(thm)],[])).
% 28.25/18.50 tff(10872,plain,
% 28.25/18.50 (((~(f1(c2, c1) = f5(f1(c2, c1)))) | (f10(f1(c2, c1)) = f1(c2, c1)) | big_f(c2, f10(f1(c2, c1))) | (f7(f1(c2, c1)) = f1(c2, c1)) | big_f(f7(f1(c2, c1)), f1(c2, c1)) | (~(c2 = f8(f1(c2, c1))))) <=> (big_f(f7(f1(c2, c1)), f1(c2, c1)) | (f7(f1(c2, c1)) = f1(c2, c1)) | (~(f1(c2, c1) = f5(f1(c2, c1)))) | (f10(f1(c2, c1)) = f1(c2, c1)) | big_f(c2, f10(f1(c2, c1))) | (~(c2 = f8(f1(c2, c1)))))),
% 28.25/18.50 inference(rewrite,[status(thm)],[])).
% 28.25/18.50 tff(10873,plain,
% 28.25/18.50 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(f1(c2, c1) = f5(f1(c2, c1)))) | (f10(f1(c2, c1)) = f1(c2, c1)) | big_f(c2, f10(f1(c2, c1))) | (f7(f1(c2, c1)) = f1(c2, c1)) | big_f(f7(f1(c2, c1)), f1(c2, c1)) | (~(c2 = f8(f1(c2, c1)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (big_f(f7(f1(c2, c1)), f1(c2, c1)) | (f7(f1(c2, c1)) = f1(c2, c1)) | (~(f1(c2, c1) = f5(f1(c2, c1)))) | (f10(f1(c2, c1)) = f1(c2, c1)) | big_f(c2, f10(f1(c2, c1))) | (~(c2 = f8(f1(c2, c1))))))),
% 28.25/18.50 inference(monotonicity,[status(thm)],[10872])).
% 28.25/18.50 tff(10874,plain,
% 28.25/18.50 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(f1(c2, c1) = f5(f1(c2, c1)))) | (f10(f1(c2, c1)) = f1(c2, c1)) | big_f(c2, f10(f1(c2, c1))) | (f7(f1(c2, c1)) = f1(c2, c1)) | big_f(f7(f1(c2, c1)), f1(c2, c1)) | (~(c2 = f8(f1(c2, c1)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | big_f(f7(f1(c2, c1)), f1(c2, c1)) | (f7(f1(c2, c1)) = f1(c2, c1)) | (~(f1(c2, c1) = f5(f1(c2, c1)))) | (f10(f1(c2, c1)) = f1(c2, c1)) | big_f(c2, f10(f1(c2, c1))) | (~(c2 = f8(f1(c2, c1)))))),
% 28.25/18.50 inference(transitivity,[status(thm)],[10873, 10871])).
% 28.25/18.50 tff(10875,plain,
% 28.25/18.50 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(f1(c2, c1) = f5(f1(c2, c1)))) | (f10(f1(c2, c1)) = f1(c2, c1)) | big_f(c2, f10(f1(c2, c1))) | (f7(f1(c2, c1)) = f1(c2, c1)) | big_f(f7(f1(c2, c1)), f1(c2, c1)) | (~(c2 = f8(f1(c2, c1)))))),
% 28.25/18.50 inference(quant_inst,[status(thm)],[])).
% 28.25/18.50 tff(10876,plain,
% 28.25/18.50 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | big_f(f7(f1(c2, c1)), f1(c2, c1)) | (f7(f1(c2, c1)) = f1(c2, c1)) | (~(f1(c2, c1) = f5(f1(c2, c1)))) | (f10(f1(c2, c1)) = f1(c2, c1)) | big_f(c2, f10(f1(c2, c1))) | (~(c2 = f8(f1(c2, c1))))),
% 28.25/18.50 inference(modus_ponens,[status(thm)],[10875, 10874])).
% 28.25/18.50 tff(10877,plain,
% 28.25/18.50 ((~(f1(c2, c1) = f5(f1(c2, c1)))) | (f10(f1(c2, c1)) = f1(c2, c1)) | big_f(c2, f10(f1(c2, c1))) | (~(c2 = f8(f1(c2, c1))))),
% 28.25/18.50 inference(unit_resolution,[status(thm)],[10876, 1745, 10805, 10822])).
% 28.25/18.50 tff(10878,plain,
% 28.25/18.50 (~(c2 = f8(f1(c2, c1)))),
% 28.25/18.50 inference(unit_resolution,[status(thm)],[10877, 10870, 10869, 10868])).
% 28.25/18.50 tff(10879,plain,
% 28.25/18.50 (~(f8(c3) = c2)),
% 28.25/18.50 inference(modus_ponens,[status(thm)],[10878, 10867])).
% 28.25/18.50 tff(10880,plain,
% 28.25/18.50 ((f8(c3) = c1) <=> (f8(c1) = c1)),
% 28.25/18.50 inference(monotonicity,[status(thm)],[10861])).
% 28.25/18.50 tff(10881,plain,
% 28.25/18.50 ((f8(c1) = c1) <=> (f8(c3) = c1)),
% 28.25/18.50 inference(symmetry,[status(thm)],[10880])).
% 28.25/18.50 tff(10882,plain,
% 28.25/18.50 ((f1(c2, c1) = f8(f1(c2, c1))) <=> (f8(c3) = c1)),
% 28.25/18.50 inference(transitivity,[status(thm)],[10838, 10881])).
% 28.25/18.50 tff(10883,plain,
% 28.25/18.50 ((~(f1(c2, c1) = f8(f1(c2, c1)))) <=> (~(f8(c3) = c1))),
% 28.25/18.50 inference(monotonicity,[status(thm)],[10882])).
% 28.25/18.50 tff(10884,assumption,(~big_f(f1(c2, c1), f10(f1(c2, c1)))), introduced(assumption)).
% 28.25/18.50 tff(10885,plain,
% 28.25/18.50 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (big_f(f7(f1(c2, c1)), f1(c2, c1)) | (f7(f1(c2, c1)) = f1(c2, c1)) | (~(f1(c2, c1) = f5(f1(c2, c1)))) | (f10(f1(c2, c1)) = f1(c2, c1)) | big_f(f1(c2, c1), f10(f1(c2, c1))) | (~(f1(c2, c1) = f8(f1(c2, c1)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | big_f(f7(f1(c2, c1)), f1(c2, c1)) | (f7(f1(c2, c1)) = f1(c2, c1)) | (~(f1(c2, c1) = f5(f1(c2, c1)))) | (f10(f1(c2, c1)) = f1(c2, c1)) | big_f(f1(c2, c1), f10(f1(c2, c1))) | (~(f1(c2, c1) = f8(f1(c2, c1)))))),
% 28.25/18.51 inference(rewrite,[status(thm)],[])).
% 28.25/18.51 tff(10886,plain,
% 28.25/18.51 (((~(f1(c2, c1) = f5(f1(c2, c1)))) | (f10(f1(c2, c1)) = f1(c2, c1)) | big_f(f1(c2, c1), f10(f1(c2, c1))) | (f7(f1(c2, c1)) = f1(c2, c1)) | big_f(f7(f1(c2, c1)), f1(c2, c1)) | (~(f1(c2, c1) = f8(f1(c2, c1))))) <=> (big_f(f7(f1(c2, c1)), f1(c2, c1)) | (f7(f1(c2, c1)) = f1(c2, c1)) | (~(f1(c2, c1) = f5(f1(c2, c1)))) | (f10(f1(c2, c1)) = f1(c2, c1)) | big_f(f1(c2, c1), f10(f1(c2, c1))) | (~(f1(c2, c1) = f8(f1(c2, c1)))))),
% 28.25/18.51 inference(rewrite,[status(thm)],[])).
% 28.25/18.51 tff(10887,plain,
% 28.25/18.51 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(f1(c2, c1) = f5(f1(c2, c1)))) | (f10(f1(c2, c1)) = f1(c2, c1)) | big_f(f1(c2, c1), f10(f1(c2, c1))) | (f7(f1(c2, c1)) = f1(c2, c1)) | big_f(f7(f1(c2, c1)), f1(c2, c1)) | (~(f1(c2, c1) = f8(f1(c2, c1)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (big_f(f7(f1(c2, c1)), f1(c2, c1)) | (f7(f1(c2, c1)) = f1(c2, c1)) | (~(f1(c2, c1) = f5(f1(c2, c1)))) | (f10(f1(c2, c1)) = f1(c2, c1)) | big_f(f1(c2, c1), f10(f1(c2, c1))) | (~(f1(c2, c1) = f8(f1(c2, c1))))))),
% 28.25/18.51 inference(monotonicity,[status(thm)],[10886])).
% 28.25/18.51 tff(10888,plain,
% 28.25/18.51 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(f1(c2, c1) = f5(f1(c2, c1)))) | (f10(f1(c2, c1)) = f1(c2, c1)) | big_f(f1(c2, c1), f10(f1(c2, c1))) | (f7(f1(c2, c1)) = f1(c2, c1)) | big_f(f7(f1(c2, c1)), f1(c2, c1)) | (~(f1(c2, c1) = f8(f1(c2, c1)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | big_f(f7(f1(c2, c1)), f1(c2, c1)) | (f7(f1(c2, c1)) = f1(c2, c1)) | (~(f1(c2, c1) = f5(f1(c2, c1)))) | (f10(f1(c2, c1)) = f1(c2, c1)) | big_f(f1(c2, c1), f10(f1(c2, c1))) | (~(f1(c2, c1) = f8(f1(c2, c1)))))),
% 28.25/18.51 inference(transitivity,[status(thm)],[10887, 10885])).
% 28.25/18.51 tff(10889,plain,
% 28.25/18.51 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(f1(c2, c1) = f5(f1(c2, c1)))) | (f10(f1(c2, c1)) = f1(c2, c1)) | big_f(f1(c2, c1), f10(f1(c2, c1))) | (f7(f1(c2, c1)) = f1(c2, c1)) | big_f(f7(f1(c2, c1)), f1(c2, c1)) | (~(f1(c2, c1) = f8(f1(c2, c1)))))),
% 28.25/18.51 inference(quant_inst,[status(thm)],[])).
% 28.25/18.51 tff(10890,plain,
% 28.25/18.51 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | big_f(f7(f1(c2, c1)), f1(c2, c1)) | (f7(f1(c2, c1)) = f1(c2, c1)) | (~(f1(c2, c1) = f5(f1(c2, c1)))) | (f10(f1(c2, c1)) = f1(c2, c1)) | big_f(f1(c2, c1), f10(f1(c2, c1))) | (~(f1(c2, c1) = f8(f1(c2, c1))))),
% 28.25/18.51 inference(modus_ponens,[status(thm)],[10889, 10888])).
% 28.25/18.51 tff(10891,plain,
% 28.25/18.51 ((~(f1(c2, c1) = f5(f1(c2, c1)))) | (f10(f1(c2, c1)) = f1(c2, c1)) | big_f(f1(c2, c1), f10(f1(c2, c1))) | (~(f1(c2, c1) = f8(f1(c2, c1))))),
% 28.25/18.51 inference(unit_resolution,[status(thm)],[10890, 1745, 10805, 10822])).
% 28.25/18.51 tff(10892,plain,
% 28.25/18.51 (~(f1(c2, c1) = f8(f1(c2, c1)))),
% 28.25/18.51 inference(unit_resolution,[status(thm)],[10891, 10870, 10884, 10868])).
% 28.25/18.51 tff(10893,plain,
% 28.25/18.51 (~(f8(c3) = c1)),
% 28.25/18.51 inference(modus_ponens,[status(thm)],[10892, 10883])).
% 28.25/18.51 tff(10894,plain,
% 28.25/18.51 ($false),
% 28.25/18.51 inference(unit_resolution,[status(thm)],[8569, 10893, 10879])).
% 28.25/18.51 tff(10895,plain,((~(f1(c2, c1) = f5(f1(c2, c1)))) | (~(f1(f7(f7(c2)), c1) = c1)) | (~(f7(c2) = c2)) | (~(c3 = c1)) | big_f(f1(c2, c1), f10(f1(c2, c1))) | (f10(f1(c2, c1)) = f1(c2, c1)) | (f7(f1(c2, c1)) = f1(c2, c1)) | big_f(f7(f1(c2, c1)), f1(c2, c1)) | big_f(c2, f10(f1(c2, c1)))), inference(lemma,lemma(discharge,[]))).
% 28.25/18.51 tff(10896,plain,
% 28.25/18.51 (~(f1(c2, c1) = f5(f1(c2, c1)))),
% 28.25/18.51 inference(unit_resolution,[status(thm)],[10895, 10860, 77, 172, 874, 10856, 10794, 10822, 10851])).
% 28.25/18.51 tff(10897,plain,
% 28.25/18.51 (~(f5(c1) = c1)),
% 28.25/18.51 inference(modus_ponens,[status(thm)],[10896, 10845])).
% 28.25/18.51 tff(10898,plain,
% 28.25/18.51 (f5(c1) = c2),
% 28.25/18.51 inference(unit_resolution,[status(thm)],[1708, 10897])).
% 28.25/18.51 tff(10899,plain,
% 28.25/18.51 (c2 = f5(c1)),
% 28.25/18.51 inference(modus_ponens,[status(thm)],[10898, 155])).
% 28.25/18.51 tff(10900,plain,
% 28.25/18.51 (~(c2 = f8(c1))),
% 28.25/18.51 inference(unit_resolution,[status(thm)],[1752, 10899, 115, 1726, 3, 8451])).
% 28.25/18.51 tff(10901,plain,
% 28.25/18.51 (~(f8(c1) = c2)),
% 28.25/18.51 inference(unit_resolution,[status(thm)],[1675, 10900])).
% 28.25/18.51 tff(10902,plain,
% 28.25/18.51 (f8(c1) = c1),
% 28.25/18.51 inference(unit_resolution,[status(thm)],[1680, 10901])).
% 28.25/18.51 tff(10903,plain,
% 28.25/18.51 (f1(c2, c1) = f8(f1(c2, c1))),
% 28.25/18.51 inference(modus_ponens,[status(thm)],[10902, 10839])).
% 28.25/18.51 tff(10904,plain,
% 28.25/18.51 ((c2 = f5(c1)) <=> (c2 = f5(f1(c2, c1)))),
% 28.25/18.51 inference(symmetry,[status(thm)],[10801])).
% 28.25/18.51 tff(10905,plain,
% 28.25/18.51 ((f5(c1) = c2) <=> (c2 = f5(f1(c2, c1)))),
% 28.25/18.51 inference(transitivity,[status(thm)],[155, 10904])).
% 28.25/18.51 tff(10906,plain,
% 28.25/18.51 (c2 = f5(f1(c2, c1))),
% 28.25/18.51 inference(modus_ponens,[status(thm)],[10898, 10905])).
% 28.25/18.51 tff(10907,plain,
% 28.25/18.51 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f7(f1(c2, c1)) = f1(c2, c1)) | (~(c2 = f5(f1(c2, c1)))) | big_f(f7(f1(c2, c1)), c2) | (f10(f1(c2, c1)) = f1(c2, c1)) | big_f(f1(c2, c1), f10(f1(c2, c1))) | (~(f1(c2, c1) = f8(f1(c2, c1)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(f1(c2, c1)) = f1(c2, c1)) | (~(c2 = f5(f1(c2, c1)))) | big_f(f7(f1(c2, c1)), c2) | (f10(f1(c2, c1)) = f1(c2, c1)) | big_f(f1(c2, c1), f10(f1(c2, c1))) | (~(f1(c2, c1) = f8(f1(c2, c1)))))),
% 28.25/18.51 inference(rewrite,[status(thm)],[])).
% 28.25/18.51 tff(10908,plain,
% 28.25/18.51 (((~(c2 = f5(f1(c2, c1)))) | (f10(f1(c2, c1)) = f1(c2, c1)) | big_f(f1(c2, c1), f10(f1(c2, c1))) | (f7(f1(c2, c1)) = f1(c2, c1)) | big_f(f7(f1(c2, c1)), c2) | (~(f1(c2, c1) = f8(f1(c2, c1))))) <=> ((f7(f1(c2, c1)) = f1(c2, c1)) | (~(c2 = f5(f1(c2, c1)))) | big_f(f7(f1(c2, c1)), c2) | (f10(f1(c2, c1)) = f1(c2, c1)) | big_f(f1(c2, c1), f10(f1(c2, c1))) | (~(f1(c2, c1) = f8(f1(c2, c1)))))),
% 28.25/18.51 inference(rewrite,[status(thm)],[])).
% 28.25/18.51 tff(10909,plain,
% 28.25/18.51 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c2 = f5(f1(c2, c1)))) | (f10(f1(c2, c1)) = f1(c2, c1)) | big_f(f1(c2, c1), f10(f1(c2, c1))) | (f7(f1(c2, c1)) = f1(c2, c1)) | big_f(f7(f1(c2, c1)), c2) | (~(f1(c2, c1) = f8(f1(c2, c1)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f7(f1(c2, c1)) = f1(c2, c1)) | (~(c2 = f5(f1(c2, c1)))) | big_f(f7(f1(c2, c1)), c2) | (f10(f1(c2, c1)) = f1(c2, c1)) | big_f(f1(c2, c1), f10(f1(c2, c1))) | (~(f1(c2, c1) = f8(f1(c2, c1))))))),
% 28.25/18.51 inference(monotonicity,[status(thm)],[10908])).
% 28.25/18.51 tff(10910,plain,
% 28.25/18.51 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c2 = f5(f1(c2, c1)))) | (f10(f1(c2, c1)) = f1(c2, c1)) | big_f(f1(c2, c1), f10(f1(c2, c1))) | (f7(f1(c2, c1)) = f1(c2, c1)) | big_f(f7(f1(c2, c1)), c2) | (~(f1(c2, c1) = f8(f1(c2, c1)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(f1(c2, c1)) = f1(c2, c1)) | (~(c2 = f5(f1(c2, c1)))) | big_f(f7(f1(c2, c1)), c2) | (f10(f1(c2, c1)) = f1(c2, c1)) | big_f(f1(c2, c1), f10(f1(c2, c1))) | (~(f1(c2, c1) = f8(f1(c2, c1)))))),
% 28.25/18.51 inference(transitivity,[status(thm)],[10909, 10907])).
% 28.25/18.51 tff(10911,plain,
% 28.25/18.51 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c2 = f5(f1(c2, c1)))) | (f10(f1(c2, c1)) = f1(c2, c1)) | big_f(f1(c2, c1), f10(f1(c2, c1))) | (f7(f1(c2, c1)) = f1(c2, c1)) | big_f(f7(f1(c2, c1)), c2) | (~(f1(c2, c1) = f8(f1(c2, c1)))))),
% 28.25/18.51 inference(quant_inst,[status(thm)],[])).
% 28.25/18.51 tff(10912,plain,
% 28.25/18.51 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(f1(c2, c1)) = f1(c2, c1)) | (~(c2 = f5(f1(c2, c1)))) | big_f(f7(f1(c2, c1)), c2) | (f10(f1(c2, c1)) = f1(c2, c1)) | big_f(f1(c2, c1), f10(f1(c2, c1))) | (~(f1(c2, c1) = f8(f1(c2, c1))))),
% 28.25/18.51 inference(modus_ponens,[status(thm)],[10911, 10910])).
% 28.25/18.51 tff(10913,plain,
% 28.25/18.51 ((~(c2 = f5(f1(c2, c1)))) | (f10(f1(c2, c1)) = f1(c2, c1)) | big_f(f1(c2, c1), f10(f1(c2, c1))) | (~(f1(c2, c1) = f8(f1(c2, c1))))),
% 28.25/18.51 inference(unit_resolution,[status(thm)],[10912, 1745, 10794, 10783])).
% 28.25/18.51 tff(10914,plain,
% 28.25/18.51 (~(f1(c2, c1) = f8(f1(c2, c1)))),
% 28.25/18.51 inference(unit_resolution,[status(thm)],[10913, 10906, 10860, 10856])).
% 28.25/18.51 tff(10915,plain,
% 28.25/18.51 ($false),
% 28.25/18.51 inference(unit_resolution,[status(thm)],[10914, 10903])).
% 28.25/18.51 tff(10916,plain,((f10(c1) = c1) | (~(f1(f7(f7(c2)), c1) = c1)) | (~(f7(c2) = c2)) | (f7(c1) = c1) | (~(c3 = c1)) | big_f(f7(f1(c2, c1)), f1(c2, c1)) | big_f(c1, c2) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 28.25/18.51 tff(10917,plain,
% 28.25/18.51 (f10(c1) = c1),
% 28.25/18.51 inference(unit_resolution,[status(thm)],[10916, 115, 77, 874, 172, 10798, 10835, 121])).
% 28.25/18.51 tff(10918,plain,
% 28.25/18.51 (big_f(c3, c2) <=> big_f(c1, c2)),
% 28.25/18.51 inference(monotonicity,[status(thm)],[172])).
% 28.25/18.51 tff(10919,plain,
% 28.25/18.51 (big_f(c1, c2) <=> big_f(c3, c2)),
% 28.25/18.51 inference(symmetry,[status(thm)],[10918])).
% 28.25/18.51 tff(10920,plain,
% 28.25/18.51 (big_f(f9(c2, f1(c2, c1)), f10(c2)) <=> big_f(c3, c2)),
% 28.25/18.51 inference(transitivity,[status(thm)],[10776, 10919])).
% 28.25/18.51 tff(10921,plain,
% 28.25/18.51 ((~big_f(f9(c2, f1(c2, c1)), f10(c2))) <=> (~big_f(c3, c2))),
% 28.25/18.51 inference(monotonicity,[status(thm)],[10920])).
% 28.25/18.51 tff(10922,plain,
% 28.25/18.51 (~big_f(c3, c2)),
% 28.25/18.51 inference(modus_ponens,[status(thm)],[10834, 10921])).
% 28.25/18.51 tff(10923,plain,
% 28.25/18.51 (~(c2 = f2(c3))),
% 28.25/18.51 inference(unit_resolution,[status(thm)],[2612, 10922, 10089, 3865])).
% 28.25/18.51 tff(10924,plain,
% 28.25/18.51 (~(f2(c3) = c2)),
% 28.25/18.51 inference(modus_ponens,[status(thm)],[10923, 3832])).
% 28.25/18.51 tff(10925,plain,
% 28.25/18.51 (f2(c3) = c1),
% 28.25/18.51 inference(unit_resolution,[status(thm)],[1273, 10924])).
% 28.25/18.51 tff(10926,plain,
% 28.25/18.51 (f2(c1) = c1),
% 28.25/18.51 inference(transitivity,[status(thm)],[5586, 1247])).
% 28.25/18.51 tff(10927,plain,
% 28.25/18.51 (big_f(c1, f2(c1)) <=> big_f(c1, c1)),
% 28.25/18.51 inference(monotonicity,[status(thm)],[10926])).
% 28.25/18.51 tff(10928,plain,
% 28.25/18.51 (big_f(c1, c1) <=> big_f(c1, f2(c1))),
% 28.25/18.51 inference(symmetry,[status(thm)],[10927])).
% 28.25/18.51 tff(10929,plain,
% 28.25/18.51 ((~big_f(c1, c1)) <=> (~big_f(c1, f2(c1)))),
% 28.25/18.51 inference(monotonicity,[status(thm)],[10928])).
% 28.25/18.51 tff(10930,plain,
% 28.25/18.51 (~big_f(c1, f2(c1))),
% 28.25/18.51 inference(modus_ponens,[status(thm)],[66, 10929])).
% 28.25/18.51 tff(10931,plain,
% 28.25/18.51 ($false),
% 28.25/18.51 inference(unit_resolution,[status(thm)],[6546, 10930])).
% 28.25/18.51 tff(10932,plain,((~(f2(c3) = c1)) | (~big_f(c1, f2(c1))) | big_f(c1, c1) | (~(c3 = c1))), inference(lemma,lemma(discharge,[]))).
% 28.25/18.51 tff(10933,plain,
% 28.25/18.51 (big_f(c1, c1)),
% 28.25/18.51 inference(unit_resolution,[status(thm)],[10932, 10925, 6546, 172])).
% 28.25/18.51 tff(10934,plain,
% 28.25/18.51 (big_f(f9(c1, c1), c1) <=> big_f(c1, c1)),
% 28.25/18.51 inference(monotonicity,[status(thm)],[3949])).
% 28.25/18.51 tff(10935,plain,
% 28.25/18.51 (big_f(c1, c1) <=> big_f(f9(c1, c1), c1)),
% 28.25/18.51 inference(symmetry,[status(thm)],[10934])).
% 28.25/18.51 tff(10936,plain,
% 28.25/18.51 (big_f(f9(c1, c1), c1)),
% 28.25/18.51 inference(modus_ponens,[status(thm)],[4932, 10935])).
% 28.25/18.51 tff(10937,plain,
% 28.25/18.51 ($false),
% 28.25/18.51 inference(unit_resolution,[status(thm)],[10020, 10936])).
% 28.25/18.51 tff(10938,plain,((~(f9(c1, c1) = c1)) | big_f(f9(c1, c1), c1) | (~big_f(c1, c1))), inference(lemma,lemma(discharge,[]))).
% 28.25/18.51 tff(10939,plain,
% 28.25/18.51 (big_f(f9(c1, c1), c1)),
% 28.25/18.51 inference(unit_resolution,[status(thm)],[10938, 3949, 4932])).
% 28.25/18.51 tff(10940,plain,
% 28.25/18.51 (~big_f(f9(c1, c1), f10(c1))),
% 28.25/18.51 inference(unit_resolution,[status(thm)],[8709, 3949, 115, 2907, 2908, 3762])).
% 28.25/18.51 tff(10941,plain,
% 28.25/18.51 ($false),
% 28.25/18.51 inference(unit_resolution,[status(thm)],[8716, 10940, 10939, 3762])).
% 28.25/18.51 tff(10942,plain,((~(f9(c1, c1) = c1)) | (~(f10(c1) = c1)) | (f7(c1) = c1) | big_f(f7(c1), c2) | (~(c2 = f5(c1))) | (~big_f(c1, c1))), inference(lemma,lemma(discharge,[]))).
% 28.25/18.51 tff(10943,plain,
% 28.25/18.51 (~(f9(c1, c1) = c1)),
% 28.25/18.51 inference(unit_resolution,[status(thm)],[10942, 1727, 115, 2907, 3762, 4932])).
% 28.25/18.51 tff(10944,plain,
% 28.25/18.51 (f9(c1, c1) = c2),
% 28.25/18.51 inference(unit_resolution,[status(thm)],[3939, 10943])).
% 28.25/18.51 tff(10945,plain,
% 28.25/18.51 (f9(f1(c2, c1), f1(c2, c1)) = f9(c1, c1)),
% 28.25/18.51 inference(monotonicity,[status(thm)],[10773, 10773])).
% 28.25/18.51 tff(10946,plain,
% 28.25/18.51 (f9(f1(c2, c1), f1(c2, c1)) = c2),
% 28.25/18.51 inference(transitivity,[status(thm)],[10945, 10944])).
% 28.25/18.51 tff(10947,plain,
% 28.25/18.51 ((f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1)) <=> (c2 = f1(c2, c1))),
% 28.25/18.51 inference(monotonicity,[status(thm)],[10946])).
% 28.25/18.51 tff(10948,plain,
% 28.25/18.51 ((f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1)) <=> (f1(c2, c1) = c2)),
% 28.25/18.51 inference(transitivity,[status(thm)],[10947, 10784])).
% 28.25/18.51 tff(10949,plain,
% 28.25/18.51 ((f1(c2, c1) = c2) <=> (f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))),
% 28.25/18.51 inference(symmetry,[status(thm)],[10948])).
% 28.25/18.51 tff(10950,plain,
% 28.25/18.51 ((~(f1(c2, c1) = c2)) <=> (~(f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1)))),
% 28.25/18.51 inference(monotonicity,[status(thm)],[10949])).
% 28.25/18.51 tff(10951,plain,
% 28.25/18.51 (~(f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))),
% 28.25/18.51 inference(modus_ponens,[status(thm)],[10793, 10950])).
% 28.25/18.51 tff(10952,plain,
% 28.25/18.51 (f10(f1(c2, c1)) = f1(c2, c1)),
% 28.25/18.51 inference(transitivity,[status(thm)],[10846, 3762, 875, 10762])).
% 28.25/18.51 tff(10953,plain,
% 28.25/18.51 (big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1))) <=> big_f(c2, f1(c2, c1))),
% 28.25/18.51 inference(monotonicity,[status(thm)],[10946, 10952])).
% 28.25/18.51 tff(10954,plain,
% 28.25/18.51 (big_f(c2, f1(c2, c1)) <=> big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1)))),
% 28.25/18.51 inference(symmetry,[status(thm)],[10953])).
% 28.25/18.51 tff(10955,plain,
% 28.25/18.51 ((~big_f(c2, f1(c2, c1))) <=> (~big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1))))),
% 28.25/18.51 inference(monotonicity,[status(thm)],[10954])).
% 28.25/18.51 tff(10956,plain,
% 28.25/18.51 (~big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1)))),
% 28.25/18.51 inference(modus_ponens,[status(thm)],[10090, 10955])).
% 28.25/18.51 tff(10957,plain,
% 28.25/18.51 (c2 = f5(f1(c2, c1))),
% 28.25/18.51 inference(modus_ponens,[status(thm)],[186, 10905])).
% 28.25/18.51 tff(10958,plain,
% 28.25/18.51 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((f7(f1(c2, c1)) = f1(c2, c1)) | (~(c2 = f5(f1(c2, c1)))) | big_f(f7(f1(c2, c1)), c2) | (~(f10(f1(c2, c1)) = f1(c2, c1))) | (f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1)) | big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (f7(f1(c2, c1)) = f1(c2, c1)) | (~(c2 = f5(f1(c2, c1)))) | big_f(f7(f1(c2, c1)), c2) | (~(f10(f1(c2, c1)) = f1(c2, c1))) | (f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1)) | big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1))))),
% 28.25/18.51 inference(rewrite,[status(thm)],[])).
% 28.25/18.51 tff(10959,plain,
% 28.25/18.51 (((~(f10(f1(c2, c1)) = f1(c2, c1))) | (f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1)) | big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1))) | (f7(f1(c2, c1)) = f1(c2, c1)) | big_f(f7(f1(c2, c1)), c2) | (~(c2 = f5(f1(c2, c1))))) <=> ((f7(f1(c2, c1)) = f1(c2, c1)) | (~(c2 = f5(f1(c2, c1)))) | big_f(f7(f1(c2, c1)), c2) | (~(f10(f1(c2, c1)) = f1(c2, c1))) | (f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1)) | big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1))))),
% 28.25/18.51 inference(rewrite,[status(thm)],[])).
% 28.25/18.51 tff(10960,plain,
% 28.25/18.51 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(f1(c2, c1)) = f1(c2, c1))) | (f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1)) | big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1))) | (f7(f1(c2, c1)) = f1(c2, c1)) | big_f(f7(f1(c2, c1)), c2) | (~(c2 = f5(f1(c2, c1)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((f7(f1(c2, c1)) = f1(c2, c1)) | (~(c2 = f5(f1(c2, c1)))) | big_f(f7(f1(c2, c1)), c2) | (~(f10(f1(c2, c1)) = f1(c2, c1))) | (f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1)) | big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1)))))),
% 28.25/18.51 inference(monotonicity,[status(thm)],[10959])).
% 28.25/18.51 tff(10961,plain,
% 28.25/18.51 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(f1(c2, c1)) = f1(c2, c1))) | (f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1)) | big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1))) | (f7(f1(c2, c1)) = f1(c2, c1)) | big_f(f7(f1(c2, c1)), c2) | (~(c2 = f5(f1(c2, c1)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (f7(f1(c2, c1)) = f1(c2, c1)) | (~(c2 = f5(f1(c2, c1)))) | big_f(f7(f1(c2, c1)), c2) | (~(f10(f1(c2, c1)) = f1(c2, c1))) | (f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1)) | big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1))))),
% 28.25/18.51 inference(transitivity,[status(thm)],[10960, 10958])).
% 28.25/18.51 tff(10962,plain,
% 28.25/18.51 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(f1(c2, c1)) = f1(c2, c1))) | (f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1)) | big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1))) | (f7(f1(c2, c1)) = f1(c2, c1)) | big_f(f7(f1(c2, c1)), c2) | (~(c2 = f5(f1(c2, c1)))))),
% 28.25/18.51 inference(quant_inst,[status(thm)],[])).
% 28.25/18.51 tff(10963,plain,
% 28.25/18.51 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (f7(f1(c2, c1)) = f1(c2, c1)) | (~(c2 = f5(f1(c2, c1)))) | big_f(f7(f1(c2, c1)), c2) | (~(f10(f1(c2, c1)) = f1(c2, c1))) | (f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1)) | big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1)))),
% 28.25/18.51 inference(modus_ponens,[status(thm)],[10962, 10961])).
% 28.25/18.51 tff(10964,plain,
% 28.25/18.51 ((f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1)) | big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1)))),
% 28.25/18.51 inference(unit_resolution,[status(thm)],[10963, 267, 10794, 10957, 10804, 10952])).
% 28.25/18.51 tff(10965,plain,
% 28.25/18.51 ($false),
% 28.25/18.51 inference(unit_resolution,[status(thm)],[10964, 10956, 10951])).
% 28.25/18.51 tff(10966,plain,((~(f5(c1) = c2)) | big_f(f7(f1(c2, c1)), c2) | big_f(c2, f1(c2, c1)) | (~(f10(c1) = c1)) | (~(f1(f7(f7(c2)), c1) = c1)) | (~(f7(c2) = c2)) | (f7(c1) = c1) | big_f(f7(c1), c2) | (~big_f(c1, c1))), inference(lemma,lemma(discharge,[]))).
% 28.25/18.51 tff(10967,plain,
% 28.25/18.51 (~(f5(c1) = c2)),
% 28.25/18.51 inference(unit_resolution,[status(thm)],[10966, 10783, 10090, 10917, 874, 77, 115, 1726, 10933])).
% 28.25/18.51 tff(10968,plain,
% 28.25/18.51 (f5(c1) = c1),
% 28.25/18.51 inference(unit_resolution,[status(thm)],[1708, 10967])).
% 28.25/18.51 tff(10969,plain,
% 28.25/18.51 ((f1(f7(f7(c2)), c1) = f5(c1)) <=> (f1(c2, c1) = f5(f1(c2, c1)))),
% 28.25/18.51 inference(symmetry,[status(thm)],[10819])).
% 28.25/18.51 tff(10970,plain,
% 28.25/18.51 ((f5(c1) = c1) <=> (f1(f7(f7(c2)), c1) = f5(c1))),
% 28.25/18.51 inference(symmetry,[status(thm)],[10818])).
% 28.25/18.51 tff(10971,plain,
% 28.25/18.51 ((f5(c1) = c1) <=> (f1(c2, c1) = f5(f1(c2, c1)))),
% 28.25/18.51 inference(transitivity,[status(thm)],[10970, 10969])).
% 28.25/18.51 tff(10972,plain,
% 28.25/18.51 (f1(c2, c1) = f5(f1(c2, c1))),
% 28.25/18.51 inference(modus_ponens,[status(thm)],[230, 10971])).
% 28.25/18.51 tff(10973,assumption,(~(f1(c2, c1) = f5(f1(c2, c1)))), introduced(assumption)).
% 28.25/18.51 tff(10974,plain,
% 28.25/18.51 ($false),
% 28.25/18.51 inference(unit_resolution,[status(thm)],[10973, 10972])).
% 28.25/18.51 tff(10975,plain,((~(f5(c1) = c1)) | (f1(c2, c1) = f5(f1(c2, c1))) | (~(f1(f7(f7(c2)), c1) = c1)) | (~(f7(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.25/18.52 tff(10976,plain,
% 28.25/18.52 (f1(c2, c1) = f5(f1(c2, c1))),
% 28.25/18.52 inference(unit_resolution,[status(thm)],[10975, 10968, 874, 77])).
% 28.25/18.52 tff(10977,plain,
% 28.25/18.52 (f9(f1(c2, c1), f1(c2, c1)) = c2),
% 28.25/18.52 inference(transitivity,[status(thm)],[10945, 4102])).
% 28.25/18.52 tff(10978,plain,
% 28.25/18.52 ((f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1)) <=> (c2 = f1(c2, c1))),
% 28.25/18.52 inference(monotonicity,[status(thm)],[10977])).
% 28.25/18.52 tff(10979,plain,
% 28.25/18.52 ((f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1)) <=> (f1(c2, c1) = c2)),
% 28.25/18.52 inference(transitivity,[status(thm)],[10978, 10784])).
% 28.25/18.52 tff(10980,plain,
% 28.25/18.52 ((f1(c2, c1) = c2) <=> (f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))),
% 28.25/18.52 inference(symmetry,[status(thm)],[10979])).
% 28.25/18.52 tff(10981,plain,
% 28.25/18.52 ((~(f1(c2, c1) = c2)) <=> (~(f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1)))),
% 28.25/18.52 inference(monotonicity,[status(thm)],[10980])).
% 28.25/18.52 tff(10982,plain,
% 28.25/18.52 (~(f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))),
% 28.25/18.52 inference(modus_ponens,[status(thm)],[10793, 10981])).
% 28.25/18.52 tff(10983,plain,
% 28.25/18.52 (big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1))) <=> big_f(c2, f1(c2, c1))),
% 28.25/18.52 inference(monotonicity,[status(thm)],[10977, 10952])).
% 28.25/18.52 tff(10984,plain,
% 28.25/18.52 (big_f(c2, f1(c2, c1)) <=> big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1)))),
% 28.25/18.52 inference(symmetry,[status(thm)],[10983])).
% 28.25/18.52 tff(10985,plain,
% 28.25/18.52 ((~big_f(c2, f1(c2, c1))) <=> (~big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1))))),
% 28.25/18.52 inference(monotonicity,[status(thm)],[10984])).
% 28.25/18.52 tff(10986,plain,
% 28.25/18.52 (~big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1)))),
% 28.25/18.52 inference(modus_ponens,[status(thm)],[10090, 10985])).
% 28.25/18.52 tff(10987,plain,
% 28.25/18.52 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (big_f(f7(f1(c2, c1)), f1(c2, c1)) | (f7(f1(c2, c1)) = f1(c2, c1)) | (~(f1(c2, c1) = f5(f1(c2, c1)))) | (~(f10(f1(c2, c1)) = f1(c2, c1))) | (f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1)) | big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | big_f(f7(f1(c2, c1)), f1(c2, c1)) | (f7(f1(c2, c1)) = f1(c2, c1)) | (~(f1(c2, c1) = f5(f1(c2, c1)))) | (~(f10(f1(c2, c1)) = f1(c2, c1))) | (f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1)) | big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1))))),
% 28.25/18.52 inference(rewrite,[status(thm)],[])).
% 28.25/18.52 tff(10988,plain,
% 28.25/18.52 (((~(f10(f1(c2, c1)) = f1(c2, c1))) | (f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1)) | big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1))) | (f7(f1(c2, c1)) = f1(c2, c1)) | big_f(f7(f1(c2, c1)), f1(c2, c1)) | (~(f1(c2, c1) = f5(f1(c2, c1))))) <=> (big_f(f7(f1(c2, c1)), f1(c2, c1)) | (f7(f1(c2, c1)) = f1(c2, c1)) | (~(f1(c2, c1) = f5(f1(c2, c1)))) | (~(f10(f1(c2, c1)) = f1(c2, c1))) | (f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1)) | big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1))))),
% 28.25/18.52 inference(rewrite,[status(thm)],[])).
% 28.25/18.52 tff(10989,plain,
% 28.25/18.52 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(f1(c2, c1)) = f1(c2, c1))) | (f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1)) | big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1))) | (f7(f1(c2, c1)) = f1(c2, c1)) | big_f(f7(f1(c2, c1)), f1(c2, c1)) | (~(f1(c2, c1) = f5(f1(c2, c1)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (big_f(f7(f1(c2, c1)), f1(c2, c1)) | (f7(f1(c2, c1)) = f1(c2, c1)) | (~(f1(c2, c1) = f5(f1(c2, c1)))) | (~(f10(f1(c2, c1)) = f1(c2, c1))) | (f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1)) | big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1)))))),
% 28.25/18.52 inference(monotonicity,[status(thm)],[10988])).
% 28.25/18.52 tff(10990,plain,
% 28.25/18.52 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(f1(c2, c1)) = f1(c2, c1))) | (f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1)) | big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1))) | (f7(f1(c2, c1)) = f1(c2, c1)) | big_f(f7(f1(c2, c1)), f1(c2, c1)) | (~(f1(c2, c1) = f5(f1(c2, c1)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | big_f(f7(f1(c2, c1)), f1(c2, c1)) | (f7(f1(c2, c1)) = f1(c2, c1)) | (~(f1(c2, c1) = f5(f1(c2, c1)))) | (~(f10(f1(c2, c1)) = f1(c2, c1))) | (f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1)) | big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1))))),
% 28.25/18.52 inference(transitivity,[status(thm)],[10989, 10987])).
% 28.25/18.52 tff(10991,plain,
% 28.25/18.52 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(f1(c2, c1)) = f1(c2, c1))) | (f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1)) | big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1))) | (f7(f1(c2, c1)) = f1(c2, c1)) | big_f(f7(f1(c2, c1)), f1(c2, c1)) | (~(f1(c2, c1) = f5(f1(c2, c1)))))),
% 28.25/18.52 inference(quant_inst,[status(thm)],[])).
% 28.25/18.52 tff(10992,plain,
% 28.25/18.52 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | big_f(f7(f1(c2, c1)), f1(c2, c1)) | (f7(f1(c2, c1)) = f1(c2, c1)) | (~(f1(c2, c1) = f5(f1(c2, c1)))) | (~(f10(f1(c2, c1)) = f1(c2, c1))) | (f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1)) | big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1)))),
% 28.25/18.52 inference(modus_ponens,[status(thm)],[10991, 10990])).
% 28.25/18.52 tff(10993,plain,
% 28.25/18.52 ((f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1)) | big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1)))),
% 28.25/18.52 inference(unit_resolution,[status(thm)],[10992, 267, 10805, 10822, 10870, 10952])).
% 28.25/18.52 tff(10994,plain,
% 28.25/18.52 ($false),
% 28.25/18.52 inference(unit_resolution,[status(thm)],[10993, 10986, 10982])).
% 28.25/18.52 tff(10995,plain,((~(f9(c1, c1) = c2)) | (f7(f1(c2, c1)) = f1(c2, c1)) | big_f(f7(f1(c2, c1)), f1(c2, c1)) | (~(f1(c2, c1) = f5(f1(c2, c1)))) | big_f(c2, f1(c2, c1)) | (~(f10(c1) = c1)) | (~(f1(f7(f7(c2)), c1) = c1)) | (~(f7(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.25/18.52 tff(10996,plain,
% 28.25/18.52 (~(f9(c1, c1) = c2)),
% 28.25/18.52 inference(unit_resolution,[status(thm)],[10995, 10794, 10798, 10976, 10090, 10917, 874, 77])).
% 28.25/18.52 tff(10997,plain,
% 28.25/18.52 (f9(c1, c1) = c1),
% 28.25/18.52 inference(unit_resolution,[status(thm)],[3939, 10996])).
% 28.25/18.52 tff(10998,plain,
% 28.25/18.52 (f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1)),
% 28.25/18.52 inference(transitivity,[status(thm)],[10945, 10997, 875, 10762])).
% 28.25/18.52 tff(10999,plain,
% 28.25/18.52 (f10(f1(c2, c1)) = c1),
% 28.25/18.52 inference(transitivity,[status(thm)],[10846, 10917])).
% 28.25/18.52 tff(11000,plain,
% 28.25/18.52 (f9(f1(c2, c1), f1(c2, c1)) = c1),
% 28.25/18.52 inference(transitivity,[status(thm)],[10945, 10997])).
% 28.25/18.52 tff(11001,plain,
% 28.25/18.52 (big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1))) <=> big_f(c1, c1)),
% 28.25/18.52 inference(monotonicity,[status(thm)],[11000, 10999])).
% 28.25/18.52 tff(11002,plain,
% 28.25/18.52 (big_f(c1, c1) <=> big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1)))),
% 28.25/18.52 inference(symmetry,[status(thm)],[11001])).
% 28.25/18.52 tff(11003,plain,
% 28.25/18.52 (big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1)))),
% 28.25/18.52 inference(modus_ponens,[status(thm)],[10933, 11002])).
% 28.25/18.52 tff(11004,plain,
% 28.25/18.52 (f10(f1(c2, c1)) = f1(c2, c1)),
% 28.25/18.52 inference(transitivity,[status(thm)],[10846, 10917, 875, 10762])).
% 28.25/18.52 tff(11005,plain,
% 28.25/18.52 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (big_f(f7(f1(c2, c1)), f1(c2, c1)) | (f7(f1(c2, c1)) = f1(c2, c1)) | (~(f1(c2, c1) = f5(f1(c2, c1)))) | (~(f10(f1(c2, c1)) = f1(c2, c1))) | (~big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1)))) | (~(f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | big_f(f7(f1(c2, c1)), f1(c2, c1)) | (f7(f1(c2, c1)) = f1(c2, c1)) | (~(f1(c2, c1) = f5(f1(c2, c1)))) | (~(f10(f1(c2, c1)) = f1(c2, c1))) | (~big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1)))) | (~(f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))))),
% 28.25/18.52 inference(rewrite,[status(thm)],[])).
% 28.25/18.52 tff(11006,plain,
% 28.25/18.52 (((~(f10(f1(c2, c1)) = f1(c2, c1))) | (f7(f1(c2, c1)) = f1(c2, c1)) | big_f(f7(f1(c2, c1)), f1(c2, c1)) | (~(f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))) | (~big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1)))) | (~(f1(c2, c1) = f5(f1(c2, c1))))) <=> (big_f(f7(f1(c2, c1)), f1(c2, c1)) | (f7(f1(c2, c1)) = f1(c2, c1)) | (~(f1(c2, c1) = f5(f1(c2, c1)))) | (~(f10(f1(c2, c1)) = f1(c2, c1))) | (~big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1)))) | (~(f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))))),
% 28.25/18.52 inference(rewrite,[status(thm)],[])).
% 28.25/18.52 tff(11007,plain,
% 28.25/18.52 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(f1(c2, c1)) = f1(c2, c1))) | (f7(f1(c2, c1)) = f1(c2, c1)) | big_f(f7(f1(c2, c1)), f1(c2, c1)) | (~(f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))) | (~big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1)))) | (~(f1(c2, c1) = f5(f1(c2, c1)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (big_f(f7(f1(c2, c1)), f1(c2, c1)) | (f7(f1(c2, c1)) = f1(c2, c1)) | (~(f1(c2, c1) = f5(f1(c2, c1)))) | (~(f10(f1(c2, c1)) = f1(c2, c1))) | (~big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1)))) | (~(f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1)))))),
% 28.25/18.52 inference(monotonicity,[status(thm)],[11006])).
% 28.25/18.52 tff(11008,plain,
% 28.25/18.52 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(f1(c2, c1)) = f1(c2, c1))) | (f7(f1(c2, c1)) = f1(c2, c1)) | big_f(f7(f1(c2, c1)), f1(c2, c1)) | (~(f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))) | (~big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1)))) | (~(f1(c2, c1) = f5(f1(c2, c1)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | big_f(f7(f1(c2, c1)), f1(c2, c1)) | (f7(f1(c2, c1)) = f1(c2, c1)) | (~(f1(c2, c1) = f5(f1(c2, c1)))) | (~(f10(f1(c2, c1)) = f1(c2, c1))) | (~big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1)))) | (~(f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))))),
% 28.25/18.52 inference(transitivity,[status(thm)],[11007, 11005])).
% 28.25/18.52 tff(11009,plain,
% 28.25/18.52 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(f1(c2, c1)) = f1(c2, c1))) | (f7(f1(c2, c1)) = f1(c2, c1)) | big_f(f7(f1(c2, c1)), f1(c2, c1)) | (~(f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))) | (~big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1)))) | (~(f1(c2, c1) = f5(f1(c2, c1)))))),
% 28.25/18.52 inference(quant_inst,[status(thm)],[])).
% 28.25/18.52 tff(11010,plain,
% 28.25/18.52 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | big_f(f7(f1(c2, c1)), f1(c2, c1)) | (f7(f1(c2, c1)) = f1(c2, c1)) | (~(f1(c2, c1) = f5(f1(c2, c1)))) | (~(f10(f1(c2, c1)) = f1(c2, c1))) | (~big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1)))) | (~(f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1)))),
% 28.25/18.52 inference(modus_ponens,[status(thm)],[11009, 11008])).
% 28.25/18.52 tff(11011,plain,
% 28.25/18.52 ((~big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1)))) | (~(f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1)))),
% 28.25/18.52 inference(unit_resolution,[status(thm)],[11010, 783, 10794, 10798, 10976, 11004])).
% 28.25/18.52 tff(11012,plain,
% 28.25/18.52 ($false),
% 28.25/18.52 inference(unit_resolution,[status(thm)],[11011, 11003, 10998])).
% 28.25/18.52 tff(11013,plain,((f7(c1) = c1) | (~(f1(f7(f7(c2)), c1) = c1)) | (~(f7(c2) = c2)) | big_f(c2, f1(c2, c1)) | (~(c3 = c1)) | big_f(c2, c2) | (~big_f(c1, f2(c1))) | (~(c2 = f4(c4))) | big_f(c2, c4) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.34/18.52 tff(11014,plain,
% 28.34/18.52 (f7(c1) = c1),
% 28.34/18.52 inference(unit_resolution,[status(thm)],[11013, 10752, 10740, 10761, 10742, 121, 10756, 2602, 8607, 122])).
% 28.34/18.52 tff(11015,plain,
% 28.34/18.52 ((~(c2 = c1)) <=> (~(c2 = c3))),
% 28.34/18.52 inference(monotonicity,[status(thm)],[10748])).
% 28.34/18.52 tff(11016,plain,
% 28.34/18.52 (~(c2 = c3)),
% 28.34/18.52 inference(modus_ponens,[status(thm)],[75, 11015])).
% 28.34/18.52 tff(11017,plain,
% 28.34/18.52 (f4(f1(c2, c1)) = f4(c1)),
% 28.34/18.52 inference(monotonicity,[status(thm)],[10773])).
% 28.34/18.52 tff(11018,plain,
% 28.34/18.52 ((c2 = f4(f1(c2, c1))) <=> (c2 = f4(c1))),
% 28.34/18.52 inference(monotonicity,[status(thm)],[11017])).
% 28.34/18.52 tff(11019,plain,
% 28.34/18.52 ((c2 = f4(c1)) <=> (c2 = f4(f1(c2, c1)))),
% 28.34/18.52 inference(symmetry,[status(thm)],[11018])).
% 28.34/18.52 tff(11020,plain,
% 28.34/18.52 (f1(c2, c2) = f1(c2, c1)),
% 28.34/18.52 inference(transitivity,[status(thm)],[5298, 875, 10762])).
% 28.34/18.52 tff(11021,plain,
% 28.34/18.52 (big_f(c2, f1(c2, c2)) <=> big_f(c2, f1(c2, c1))),
% 28.34/18.52 inference(monotonicity,[status(thm)],[11020])).
% 28.34/18.52 tff(11022,plain,
% 28.34/18.52 (big_f(c2, f1(c2, c1)) <=> big_f(c2, f1(c2, c2))),
% 28.34/18.52 inference(symmetry,[status(thm)],[11021])).
% 28.34/18.52 tff(11023,plain,
% 28.34/18.52 ((~big_f(c2, f1(c2, c1))) <=> (~big_f(c2, f1(c2, c2)))),
% 28.34/18.52 inference(monotonicity,[status(thm)],[11022])).
% 28.34/18.52 tff(11024,plain,
% 28.34/18.52 (~big_f(c2, f1(c2, c2))),
% 28.34/18.52 inference(modus_ponens,[status(thm)],[10090, 11023])).
% 28.34/18.52 tff(11025,plain,
% 28.34/18.52 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c2 = c3) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (c2 = c3) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2))),
% 28.34/18.52 inference(rewrite,[status(thm)],[])).
% 28.34/18.52 tff(11026,plain,
% 28.34/18.52 (((c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2)))) <=> ((c2 = c3) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2))),
% 28.34/18.52 inference(rewrite,[status(thm)],[])).
% 28.34/18.52 tff(11027,plain,
% 28.34/18.52 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c2 = c3) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2)))),
% 28.34/18.52 inference(monotonicity,[status(thm)],[11026])).
% 28.34/18.52 tff(11028,plain,
% 28.34/18.52 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (c2 = c3) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2))),
% 28.34/18.52 inference(transitivity,[status(thm)],[11027, 11025])).
% 28.34/18.52 tff(11029,plain,
% 28.34/18.52 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))))),
% 28.34/18.52 inference(quant_inst,[status(thm)],[])).
% 28.34/18.52 tff(11030,plain,
% 28.34/18.52 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (c2 = c3) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2)),
% 28.34/18.52 inference(modus_ponens,[status(thm)],[11029, 11028])).
% 28.34/18.53 tff(11031,plain,
% 28.34/18.53 ($false),
% 28.34/18.53 inference(unit_resolution,[status(thm)],[11030, 402, 631, 630, 121, 377, 1828, 11024])).
% 28.34/18.53 tff(11032,plain,((f1(c2, c2) = c2) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (c2 = c3) | big_f(c2, f1(c2, c1)) | (~(f1(f7(f7(c2)), c1) = c1)) | (~(f7(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.34/18.53 tff(11033,plain,
% 28.34/18.53 ($false),
% 28.34/18.53 inference(unit_resolution,[status(thm)],[11032, 437, 432, 1828, 121, 377, 10090, 874, 77])).
% 28.34/18.53 tff(11034,plain,((~(c4 = c2)) | (f1(c2, c2) = c2) | big_f(c2, c2) | (c2 = c3) | big_f(c2, f1(c2, c1)) | (~(f1(f7(f7(c2)), c1) = c1)) | (~(f7(c2) = c2)) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.34/18.53 tff(11035,plain,
% 28.34/18.53 (~(c4 = c2)),
% 28.34/18.53 inference(unit_resolution,[status(thm)],[11034, 1828, 121, 377, 10090, 874, 77, 79])).
% 28.34/18.53 tff(11036,plain,
% 28.34/18.53 (c4 = c1),
% 28.34/18.53 inference(unit_resolution,[status(thm)],[461, 11035])).
% 28.34/18.53 tff(11037,plain,
% 28.34/18.53 (c1 = c4),
% 28.34/18.53 inference(symmetry,[status(thm)],[11036])).
% 28.34/18.53 tff(11038,plain,
% 28.34/18.53 (f4(c1) = f4(c4)),
% 28.34/18.53 inference(monotonicity,[status(thm)],[11037])).
% 28.34/18.53 tff(11039,plain,
% 28.34/18.53 (f4(c4) = f4(c1)),
% 28.34/18.53 inference(symmetry,[status(thm)],[11038])).
% 28.34/18.53 tff(11040,plain,
% 28.34/18.53 (c2 = f4(c1)),
% 28.34/18.53 inference(transitivity,[status(thm)],[436, 11039])).
% 28.34/18.53 tff(11041,plain,
% 28.34/18.53 (c2 = f4(f1(c2, c1))),
% 28.34/18.53 inference(modus_ponens,[status(thm)],[11040, 11019])).
% 28.34/18.53 tff(11042,plain,
% 28.34/18.53 (f1(c2, c1) = c4),
% 28.34/18.53 inference(transitivity,[status(thm)],[10772, 874, 11037])).
% 28.34/18.53 tff(11043,plain,
% 28.34/18.53 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c2 = c3) | big_f(c2, f1(c2, c1)) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (~(f1(c2, c1) = c4)) | (~(c2 = f4(f1(c2, c1)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (c2 = c3) | big_f(c2, f1(c2, c1)) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (~(f1(c2, c1) = c4)) | (~(c2 = f4(f1(c2, c1)))))),
% 28.34/18.53 inference(rewrite,[status(thm)],[])).
% 28.34/18.53 tff(11044,plain,
% 28.34/18.53 (((c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f1(c2, c1) = c4)) | big_f(c2, f1(c2, c1)) | (~(c2 = f4(f1(c2, c1))))) <=> ((c2 = c3) | big_f(c2, f1(c2, c1)) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (~(f1(c2, c1) = c4)) | (~(c2 = f4(f1(c2, c1)))))),
% 28.34/18.53 inference(rewrite,[status(thm)],[])).
% 28.34/18.53 tff(11045,plain,
% 28.34/18.53 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f1(c2, c1) = c4)) | big_f(c2, f1(c2, c1)) | (~(c2 = f4(f1(c2, c1)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c2 = c3) | big_f(c2, f1(c2, c1)) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (~(f1(c2, c1) = c4)) | (~(c2 = f4(f1(c2, c1))))))),
% 28.34/18.53 inference(monotonicity,[status(thm)],[11044])).
% 28.34/18.53 tff(11046,plain,
% 28.34/18.53 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f1(c2, c1) = c4)) | big_f(c2, f1(c2, c1)) | (~(c2 = f4(f1(c2, c1)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (c2 = c3) | big_f(c2, f1(c2, c1)) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (~(f1(c2, c1) = c4)) | (~(c2 = f4(f1(c2, c1)))))),
% 28.34/18.53 inference(transitivity,[status(thm)],[11045, 11043])).
% 28.34/18.53 tff(11047,plain,
% 28.34/18.53 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f1(c2, c1) = c4)) | big_f(c2, f1(c2, c1)) | (~(c2 = f4(f1(c2, c1)))))),
% 28.34/18.53 inference(quant_inst,[status(thm)],[])).
% 28.34/18.53 tff(11048,plain,
% 28.34/18.53 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (c2 = c3) | big_f(c2, f1(c2, c1)) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (~(f1(c2, c1) = c4)) | (~(c2 = f4(f1(c2, c1))))),
% 28.34/18.53 inference(modus_ponens,[status(thm)],[11047, 11046])).
% 28.34/18.53 tff(11049,plain,
% 28.34/18.53 ((~(f1(c2, c1) = c4)) | (~(c2 = f4(f1(c2, c1))))),
% 28.34/18.53 inference(unit_resolution,[status(thm)],[11048, 402, 377, 10090, 1828, 11024])).
% 28.34/18.53 tff(11050,plain,
% 28.34/18.53 (~(c2 = f4(f1(c2, c1)))),
% 28.34/18.53 inference(unit_resolution,[status(thm)],[11049, 11042])).
% 28.34/18.53 tff(11051,plain,
% 28.34/18.53 ($false),
% 28.34/18.53 inference(unit_resolution,[status(thm)],[11050, 11041])).
% 28.34/18.53 tff(11052,plain,((f1(c2, c2) = c2) | (~(f1(f7(f7(c2)), c1) = c1)) | (~(f7(c2) = c2)) | (c2 = c3) | big_f(c2, f1(c2, c1)) | (~(f4(c4) = c2)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 28.34/18.53 tff(11053,plain,
% 28.34/18.53 (f1(c2, c2) = c2),
% 28.34/18.53 inference(unit_resolution,[status(thm)],[11052, 10752, 10740, 11016, 10761, 79, 121])).
% 28.34/18.53 tff(11054,plain,
% 28.34/18.53 ((f9(c2, f1(c2, c1)) = f1(c2, c1)) <=> (f9(c2, c1) = c1)),
% 28.34/18.53 inference(monotonicity,[status(thm)],[10774, 10773])).
% 28.34/18.53 tff(11055,plain,
% 28.34/18.53 ((f9(c2, c1) = c1) <=> (f9(c2, f1(c2, c1)) = f1(c2, c1))),
% 28.34/18.53 inference(symmetry,[status(thm)],[11054])).
% 28.34/18.53 tff(11056,plain,
% 28.34/18.53 (~(f2(c3) = c1)),
% 28.34/18.53 inference(unit_resolution,[status(thm)],[10932, 66, 6546, 172])).
% 28.34/18.53 tff(11057,plain,
% 28.34/18.53 (f2(c3) = c2),
% 28.34/18.53 inference(unit_resolution,[status(thm)],[1273, 11056])).
% 28.34/18.53 tff(11058,plain,
% 28.34/18.53 (f2(c1) = c2),
% 28.34/18.53 inference(transitivity,[status(thm)],[5586, 11057])).
% 28.34/18.53 tff(11059,plain,
% 28.34/18.53 (big_f(c1, f2(c1)) <=> big_f(c1, c2)),
% 28.34/18.53 inference(monotonicity,[status(thm)],[11058])).
% 28.34/18.53 tff(11060,plain,
% 28.34/18.53 (big_f(c1, c2)),
% 28.34/18.53 inference(modus_ponens,[status(thm)],[6546, 11059])).
% 28.34/18.53 tff(11061,plain,
% 28.34/18.53 (f6(c1, f1(c2, c2)) = f6(c1, c2)),
% 28.34/18.53 inference(monotonicity,[status(thm)],[1908])).
% 28.34/18.53 tff(11062,plain,
% 28.34/18.53 ((f6(c1, f1(c2, c2)) = f1(c2, c2)) <=> (f6(c1, c2) = c2)),
% 28.34/18.53 inference(monotonicity,[status(thm)],[11061, 1908])).
% 28.34/18.53 tff(11063,plain,
% 28.34/18.53 ((f6(c1, c2) = c2) <=> (f6(c1, f1(c2, c2)) = f1(c2, c2))),
% 28.34/18.53 inference(symmetry,[status(thm)],[11062])).
% 28.34/18.53 tff(11064,plain,
% 28.34/18.53 ((~(f6(c1, c2) = c2)) <=> (~(f6(c1, f1(c2, c2)) = f1(c2, c2)))),
% 28.34/18.53 inference(monotonicity,[status(thm)],[11063])).
% 28.34/18.53 tff(11065,plain,
% 28.34/18.53 (big_f(c1, f6(c1, c2)) <=> big_f(c1, c2)),
% 28.34/18.53 inference(monotonicity,[status(thm)],[36])).
% 28.34/18.53 tff(11066,plain,
% 28.34/18.53 (big_f(c1, c2) <=> big_f(c1, f6(c1, c2))),
% 28.34/18.53 inference(symmetry,[status(thm)],[11065])).
% 28.34/18.53 tff(11067,plain,
% 28.34/18.53 (big_f(c1, f6(c1, c2))),
% 28.34/18.53 inference(modus_ponens,[status(thm)],[2865, 11066])).
% 28.34/18.53 tff(11068,plain,
% 28.34/18.53 (big_f(f7(c1), f6(c1, c2)) <=> big_f(c1, f6(c1, c2))),
% 28.34/18.53 inference(monotonicity,[status(thm)],[4234])).
% 28.34/18.53 tff(11069,plain,
% 28.34/18.53 ((~big_f(f7(c1), f6(c1, c2))) <=> (~big_f(c1, f6(c1, c2)))),
% 28.34/18.53 inference(monotonicity,[status(thm)],[11068])).
% 28.34/18.53 tff(11070,plain,
% 28.34/18.53 (~big_f(c1, f6(c1, c2))),
% 28.34/18.53 inference(modus_ponens,[status(thm)],[8289, 11069])).
% 28.34/18.53 tff(11071,plain,
% 28.34/18.53 ($false),
% 28.34/18.53 inference(unit_resolution,[status(thm)],[11070, 11067])).
% 28.34/18.53 tff(11072,plain,((~(f6(c1, c2) = c2)) | (~big_f(c1, c2)) | (~(f7(c1) = c1)) | (~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2))), inference(lemma,lemma(discharge,[]))).
% 28.34/18.53 tff(11073,plain,
% 28.34/18.53 (~(f6(c1, c2) = c2)),
% 28.34/18.53 inference(unit_resolution,[status(thm)],[11072, 1139, 4234, 122, 2865, 8282])).
% 28.34/18.53 tff(11074,plain,
% 28.34/18.53 (~(f6(c1, f1(c2, c2)) = f1(c2, c2))),
% 28.34/18.53 inference(modus_ponens,[status(thm)],[11073, 11064])).
% 28.34/18.53 tff(11075,plain,
% 28.34/18.53 (big_f(f7(c1), f6(c1, f1(c2, c2))) <=> big_f(c1, f6(c1, c2))),
% 28.34/18.53 inference(monotonicity,[status(thm)],[4234, 11061])).
% 28.34/18.53 tff(11076,plain,
% 28.34/18.53 (big_f(c1, f6(c1, c2)) <=> big_f(f7(c1), f6(c1, f1(c2, c2)))),
% 28.34/18.53 inference(symmetry,[status(thm)],[11075])).
% 28.34/18.53 tff(11077,plain,
% 28.34/18.53 (f6(c1, c2) = c1),
% 28.34/18.53 inference(unit_resolution,[status(thm)],[48, 11073])).
% 28.34/18.53 tff(11078,plain,
% 28.34/18.53 (big_f(c1, f6(c1, c2)) <=> big_f(c1, c1)),
% 28.34/18.53 inference(monotonicity,[status(thm)],[11077])).
% 28.34/18.53 tff(11079,plain,
% 28.34/18.53 (big_f(c1, c1) <=> big_f(c1, f6(c1, c2))),
% 28.34/18.53 inference(symmetry,[status(thm)],[11078])).
% 28.34/18.53 tff(11080,plain,
% 28.34/18.53 (big_f(c1, c1) <=> big_f(f7(c1), f6(c1, f1(c2, c2)))),
% 28.34/18.53 inference(transitivity,[status(thm)],[11079, 11076])).
% 28.34/18.53 tff(11081,plain,
% 28.34/18.53 ((~big_f(c1, c1)) <=> (~big_f(f7(c1), f6(c1, f1(c2, c2))))),
% 28.34/18.53 inference(monotonicity,[status(thm)],[11080])).
% 28.34/18.53 tff(11082,plain,
% 28.34/18.53 (~big_f(f7(c1), f6(c1, f1(c2, c2)))),
% 28.34/18.53 inference(modus_ponens,[status(thm)],[66, 11081])).
% 28.34/18.53 tff(11083,plain,
% 28.34/18.53 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (~(f7(c1) = c1)) | (f6(c1, f1(c2, c2)) = f1(c2, c2)) | big_f(f7(c1), f6(c1, f1(c2, c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (~(f7(c1) = c1)) | (f6(c1, f1(c2, c2)) = f1(c2, c2)) | big_f(f7(c1), f6(c1, f1(c2, c2))))),
% 28.34/18.53 inference(rewrite,[status(thm)],[])).
% 28.34/18.53 tff(11084,plain,
% 28.34/18.53 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (~(f7(c1) = c1)) | (f6(c1, f1(c2, c2)) = f1(c2, c2)) | big_f(f7(c1), f6(c1, f1(c2, c2))))),
% 28.34/18.53 inference(quant_inst,[status(thm)],[])).
% 28.34/18.53 tff(11085,plain,
% 28.34/18.53 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (~(f7(c1) = c1)) | (f6(c1, f1(c2, c2)) = f1(c2, c2)) | big_f(f7(c1), f6(c1, f1(c2, c2)))),
% 28.34/18.53 inference(modus_ponens,[status(thm)],[11084, 11083])).
% 28.34/18.53 tff(11086,plain,
% 28.34/18.53 ((~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (~(f7(c1) = c1)) | (f6(c1, f1(c2, c2)) = f1(c2, c2)) | big_f(f7(c1), f6(c1, f1(c2, c2)))),
% 28.34/18.53 inference(unit_resolution,[status(thm)],[11085, 2492])).
% 28.34/18.53 tff(11087,plain,
% 28.34/18.53 ($false),
% 28.34/18.53 inference(unit_resolution,[status(thm)],[11086, 11082, 11074, 122, 4234, 1139, 8282])).
% 28.34/18.53 tff(11088,plain,((f9(c2, c1) = c1) | (~(f10(c2) = c2)) | (~(f7(c1) = c1)) | big_f(c1, c1) | (~(f1(c2, c2) = c2)) | (~big_f(c1, c2)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 28.34/18.53 tff(11089,plain,
% 28.34/18.53 (f9(c2, c1) = c1),
% 28.34/18.53 inference(unit_resolution,[status(thm)],[11088, 66, 4234, 122, 1908, 11060, 121])).
% 28.34/18.53 tff(11090,plain,
% 28.34/18.53 (f9(c2, f1(c2, c1)) = f1(c2, c1)),
% 28.34/18.53 inference(modus_ponens,[status(thm)],[11089, 11055])).
% 28.34/18.53 tff(11091,plain,
% 28.34/18.53 (big_f(f9(c2, f1(c2, c1)), f10(c2)) <=> big_f(f9(c2, c1), f10(c2))),
% 28.34/18.53 inference(monotonicity,[status(thm)],[10774])).
% 28.34/18.53 tff(11092,plain,
% 28.34/18.53 (big_f(f9(c2, c1), f10(c2)) <=> big_f(f9(c2, f1(c2, c1)), f10(c2))),
% 28.34/18.53 inference(symmetry,[status(thm)],[11091])).
% 28.34/18.53 tff(11093,plain,
% 28.34/18.53 (big_f(f9(c2, c1), f10(c2)) <=> big_f(c1, c2)),
% 28.34/18.53 inference(monotonicity,[status(thm)],[11089, 122])).
% 28.34/18.53 tff(11094,plain,
% 28.34/18.53 (big_f(c1, c2) <=> big_f(f9(c2, c1), f10(c2))),
% 28.34/18.53 inference(symmetry,[status(thm)],[11093])).
% 28.34/18.53 tff(11095,plain,
% 28.34/18.53 (big_f(c1, c2) <=> big_f(f9(c2, f1(c2, c1)), f10(c2))),
% 28.34/18.53 inference(transitivity,[status(thm)],[11094, 11092])).
% 28.34/18.53 tff(11096,plain,
% 28.34/18.53 (big_f(f9(c2, f1(c2, c1)), f10(c2))),
% 28.34/18.53 inference(modus_ponens,[status(thm)],[11060, 11095])).
% 28.34/18.53 tff(11097,plain,
% 28.34/18.53 (f6(f1(c2, c1), c2) = f6(c1, c2)),
% 28.34/18.53 inference(monotonicity,[status(thm)],[10773])).
% 28.34/18.53 tff(11098,plain,
% 28.34/18.53 (f6(f1(c2, c1), c2) = f1(c2, c1)),
% 28.34/18.53 inference(transitivity,[status(thm)],[11097, 6931, 875, 10762])).
% 28.34/18.53 tff(11099,plain,
% 28.34/18.53 ((f6(f1(c2, c1), c2) = c2) <=> (f1(c2, c1) = c2)),
% 28.34/18.53 inference(monotonicity,[status(thm)],[11098])).
% 28.34/18.53 tff(11100,plain,
% 28.34/18.53 ((f1(c2, c1) = c2) <=> (f6(f1(c2, c1), c2) = c2)),
% 28.34/18.53 inference(symmetry,[status(thm)],[11099])).
% 28.34/18.53 tff(11101,plain,
% 28.34/18.53 ((~(f1(c2, c1) = c2)) <=> (~(f6(f1(c2, c1), c2) = c2))),
% 28.34/18.53 inference(monotonicity,[status(thm)],[11100])).
% 28.34/18.53 tff(11102,plain,
% 28.34/18.53 (~(f6(f1(c2, c1), c2) = c2)),
% 28.34/18.53 inference(modus_ponens,[status(thm)],[10793, 11101])).
% 28.34/18.53 tff(11103,plain,
% 28.34/18.53 (f6(f1(c2, c1), c2) = c1),
% 28.34/18.53 inference(transitivity,[status(thm)],[11097, 6931])).
% 28.34/18.53 tff(11104,plain,
% 28.34/18.53 (f7(f1(c2, c1)) = c1),
% 28.34/18.53 inference(transitivity,[status(thm)],[10778, 4234])).
% 28.34/18.53 tff(11105,plain,
% 28.34/18.53 (big_f(f7(f1(c2, c1)), f6(f1(c2, c1), c2)) <=> big_f(c1, c1)),
% 28.34/18.53 inference(monotonicity,[status(thm)],[11104, 11103])).
% 28.34/18.53 tff(11106,plain,
% 28.34/18.53 (big_f(c1, c1) <=> big_f(f7(f1(c2, c1)), f6(f1(c2, c1), c2))),
% 28.34/18.53 inference(symmetry,[status(thm)],[11105])).
% 28.34/18.53 tff(11107,plain,
% 28.34/18.53 ((~big_f(c1, c1)) <=> (~big_f(f7(f1(c2, c1)), f6(f1(c2, c1), c2)))),
% 28.34/18.53 inference(monotonicity,[status(thm)],[11106])).
% 28.34/18.53 tff(11108,plain,
% 28.34/18.53 (~big_f(f7(f1(c2, c1)), f6(f1(c2, c1), c2))),
% 28.34/18.53 inference(modus_ponens,[status(thm)],[66, 11107])).
% 28.34/18.53 tff(11109,plain,
% 28.34/18.53 (f7(f1(c2, c1)) = f1(c2, c1)),
% 28.34/18.53 inference(transitivity,[status(thm)],[10778, 4234, 875, 10762])).
% 28.34/18.53 tff(11110,plain,
% 28.34/18.53 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~big_f(f9(c2, f1(c2, c1)), f10(c2))) | (~(f9(c2, f1(c2, c1)) = f1(c2, c1))) | (~(f7(f1(c2, c1)) = f1(c2, c1))) | (f6(f1(c2, c1), c2) = c2) | big_f(f7(f1(c2, c1)), f6(f1(c2, c1), c2)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (~big_f(f9(c2, f1(c2, c1)), f10(c2))) | (~(f9(c2, f1(c2, c1)) = f1(c2, c1))) | (~(f7(f1(c2, c1)) = f1(c2, c1))) | (f6(f1(c2, c1), c2) = c2) | big_f(f7(f1(c2, c1)), f6(f1(c2, c1), c2)))),
% 28.34/18.53 inference(rewrite,[status(thm)],[])).
% 28.34/18.53 tff(11111,plain,
% 28.34/18.53 (((~(f10(c2) = c2)) | (~(f7(f1(c2, c1)) = f1(c2, c1))) | (f6(f1(c2, c1), c2) = c2) | big_f(f7(f1(c2, c1)), f6(f1(c2, c1), c2)) | (~(f9(c2, f1(c2, c1)) = f1(c2, c1))) | (~big_f(f9(c2, f1(c2, c1)), f10(c2)))) <=> ((~(f10(c2) = c2)) | (~big_f(f9(c2, f1(c2, c1)), f10(c2))) | (~(f9(c2, f1(c2, c1)) = f1(c2, c1))) | (~(f7(f1(c2, c1)) = f1(c2, c1))) | (f6(f1(c2, c1), c2) = c2) | big_f(f7(f1(c2, c1)), f6(f1(c2, c1), c2)))),
% 28.34/18.53 inference(rewrite,[status(thm)],[])).
% 28.34/18.53 tff(11112,plain,
% 28.34/18.53 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(f1(c2, c1)) = f1(c2, c1))) | (f6(f1(c2, c1), c2) = c2) | big_f(f7(f1(c2, c1)), f6(f1(c2, c1), c2)) | (~(f9(c2, f1(c2, c1)) = f1(c2, c1))) | (~big_f(f9(c2, f1(c2, c1)), f10(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~big_f(f9(c2, f1(c2, c1)), f10(c2))) | (~(f9(c2, f1(c2, c1)) = f1(c2, c1))) | (~(f7(f1(c2, c1)) = f1(c2, c1))) | (f6(f1(c2, c1), c2) = c2) | big_f(f7(f1(c2, c1)), f6(f1(c2, c1), c2))))),
% 28.34/18.53 inference(monotonicity,[status(thm)],[11111])).
% 28.34/18.53 tff(11113,plain,
% 28.34/18.53 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(f1(c2, c1)) = f1(c2, c1))) | (f6(f1(c2, c1), c2) = c2) | big_f(f7(f1(c2, c1)), f6(f1(c2, c1), c2)) | (~(f9(c2, f1(c2, c1)) = f1(c2, c1))) | (~big_f(f9(c2, f1(c2, c1)), f10(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (~big_f(f9(c2, f1(c2, c1)), f10(c2))) | (~(f9(c2, f1(c2, c1)) = f1(c2, c1))) | (~(f7(f1(c2, c1)) = f1(c2, c1))) | (f6(f1(c2, c1), c2) = c2) | big_f(f7(f1(c2, c1)), f6(f1(c2, c1), c2)))),
% 28.34/18.53 inference(transitivity,[status(thm)],[11112, 11110])).
% 28.34/18.53 tff(11114,plain,
% 28.34/18.53 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(f1(c2, c1)) = f1(c2, c1))) | (f6(f1(c2, c1), c2) = c2) | big_f(f7(f1(c2, c1)), f6(f1(c2, c1), c2)) | (~(f9(c2, f1(c2, c1)) = f1(c2, c1))) | (~big_f(f9(c2, f1(c2, c1)), f10(c2))))),
% 28.34/18.53 inference(quant_inst,[status(thm)],[])).
% 28.34/18.53 tff(11115,plain,
% 28.34/18.53 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (~big_f(f9(c2, f1(c2, c1)), f10(c2))) | (~(f9(c2, f1(c2, c1)) = f1(c2, c1))) | (~(f7(f1(c2, c1)) = f1(c2, c1))) | (f6(f1(c2, c1), c2) = c2) | big_f(f7(f1(c2, c1)), f6(f1(c2, c1), c2))),
% 28.34/18.53 inference(modus_ponens,[status(thm)],[11114, 11113])).
% 28.34/18.53 tff(11116,plain,
% 28.34/18.53 ((f6(f1(c2, c1), c2) = c2) | big_f(f7(f1(c2, c1)), f6(f1(c2, c1), c2))),
% 28.34/18.53 inference(unit_resolution,[status(thm)],[11115, 2409, 122, 10807, 10806, 11109])).
% 28.34/18.53 tff(11117,plain,
% 28.34/18.53 ($false),
% 28.34/18.53 inference(unit_resolution,[status(thm)],[11116, 11108, 11102])).
% 28.34/18.53 tff(11118,plain,((~(f6(c1, c2) = c1)) | (~(f10(c2) = c2)) | (~big_f(f9(c2, f1(c2, c1)), f10(c2))) | (~(f9(c2, f1(c2, c1)) = f1(c2, c1))) | big_f(c1, c1) | (~(f1(f7(f7(c2)), c1) = c1)) | (~(f7(c2) = c2)) | (~(f7(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.34/18.53 tff(11119,plain,
% 28.34/18.53 (~(f6(c1, c2) = c1)),
% 28.34/18.53 inference(unit_resolution,[status(thm)],[11118, 11096, 122, 11090, 66, 874, 77, 4234])).
% 28.34/18.53 tff(11120,plain,
% 28.34/18.53 (f6(c1, c2) = c2),
% 28.34/18.53 inference(unit_resolution,[status(thm)],[48, 11119])).
% 28.34/18.53 tff(11121,plain,
% 28.34/18.53 (big_f(c1, f6(c1, c2)) <=> big_f(c1, c2)),
% 28.34/18.53 inference(monotonicity,[status(thm)],[11120])).
% 28.34/18.53 tff(11122,plain,
% 28.34/18.53 (big_f(c1, c2) <=> big_f(c1, f6(c1, c2))),
% 28.34/18.53 inference(symmetry,[status(thm)],[11121])).
% 28.34/18.53 tff(11123,plain,
% 28.34/18.53 (big_f(c1, f6(c1, c2))),
% 28.34/18.53 inference(modus_ponens,[status(thm)],[11060, 11122])).
% 28.34/18.53 tff(11124,plain,
% 28.34/18.53 (big_f(f9(c2, c1), f10(c2))),
% 28.34/18.53 inference(modus_ponens,[status(thm)],[11060, 11094])).
% 28.34/18.53 tff(11125,plain,
% 28.34/18.53 (~big_f(f7(c1), f6(c1, c2))),
% 28.34/18.53 inference(unit_resolution,[status(thm)],[5827, 11120, 122, 4234, 11089, 11124])).
% 28.34/18.53 tff(11126,plain,
% 28.34/18.53 (~big_f(c1, f6(c1, c2))),
% 28.34/18.53 inference(modus_ponens,[status(thm)],[11125, 11069])).
% 28.34/18.53 tff(11127,plain,
% 28.34/18.53 ($false),
% 28.34/18.53 inference(unit_resolution,[status(thm)],[11126, 11123])).
% 28.34/18.53 tff(11128,plain,(big_f(c1, c1) | (~(f7(c1) = c1)) | (~(f10(c2) = c2)) | (~(f1(f7(f7(c2)), c1) = c1)) | (~(f7(c2) = c2)) | (~(f1(c2, c2) = c2)) | big_f(c2, c2) | (~big_f(c1, f2(c1))) | (~(c3 = c1))), inference(lemma,lemma(discharge,[]))).
% 28.34/18.53 tff(11129,plain,
% 28.34/18.53 (big_f(c1, c1)),
% 28.34/18.53 inference(unit_resolution,[status(thm)],[11128, 11014, 122, 10752, 10740, 11053, 121, 10756, 10742])).
% 28.34/18.53 tff(11130,plain,
% 28.34/18.53 (big_f(c2, f10(f1(c2, c1))) <=> big_f(c2, f10(c1))),
% 28.34/18.53 inference(monotonicity,[status(thm)],[10846])).
% 28.34/18.53 tff(11131,assumption,(f1(c2, c1) = c3), introduced(assumption)).
% 28.34/18.53 tff(11132,plain,
% 28.34/18.53 (big_f(f1(c2, c1), f1(c2, c1)) <=> big_f(c1, c1)),
% 28.34/18.53 inference(monotonicity,[status(thm)],[10773, 10773])).
% 28.34/18.53 tff(11133,plain,
% 28.34/18.53 (big_f(c1, c1) <=> big_f(f1(c2, c1), f1(c2, c1))),
% 28.34/18.53 inference(symmetry,[status(thm)],[11132])).
% 28.34/18.53 tff(11134,plain,
% 28.34/18.53 (big_f(f1(c2, c1), f1(c2, c1))),
% 28.34/18.53 inference(modus_ponens,[status(thm)],[4932, 11133])).
% 28.34/18.53 tff(11135,assumption,(~(f1(c2, c1) = f2(f1(c2, c1)))), introduced(assumption)).
% 28.34/18.53 tff(11136,assumption,(big_f(f1(c2, c1), f1(c2, c1))), introduced(assumption)).
% 28.34/18.53 tff(11137,plain,
% 28.34/18.53 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (big_f(c2, c4) | (~(c2 = f4(c4))) | (~(f1(c2, c1) = c3)) | (f1(c2, c1) = f2(f1(c2, c1))) | (~big_f(f1(c2, c1), f1(c2, c1))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | big_f(c2, c4) | (~(c2 = f4(c4))) | (~(f1(c2, c1) = c3)) | (f1(c2, c1) = f2(f1(c2, c1))) | (~big_f(f1(c2, c1), f1(c2, c1))))),
% 28.34/18.54 inference(rewrite,[status(thm)],[])).
% 28.34/18.54 tff(11138,plain,
% 28.34/18.54 (((~(f1(c2, c1) = c3)) | $false | big_f(c2, c4) | (~(c2 = f4(c4))) | (f1(c2, c1) = f2(f1(c2, c1))) | (~big_f(f1(c2, c1), f1(c2, c1)))) <=> (big_f(c2, c4) | (~(c2 = f4(c4))) | (~(f1(c2, c1) = c3)) | (f1(c2, c1) = f2(f1(c2, c1))) | (~big_f(f1(c2, c1), f1(c2, c1))))),
% 28.34/18.54 inference(rewrite,[status(thm)],[])).
% 28.34/18.54 tff(11139,plain,
% 28.34/18.54 (((~(f1(c2, c1) = c3)) | (~(c4 = c4)) | big_f(c2, c4) | (~(c2 = f4(c4))) | (f1(c2, c1) = f2(f1(c2, c1))) | (~big_f(f1(c2, c1), f1(c2, c1)))) <=> ((~(f1(c2, c1) = c3)) | $false | big_f(c2, c4) | (~(c2 = f4(c4))) | (f1(c2, c1) = f2(f1(c2, c1))) | (~big_f(f1(c2, c1), f1(c2, c1))))),
% 28.34/18.54 inference(monotonicity,[status(thm)],[410])).
% 28.34/18.54 tff(11140,plain,
% 28.34/18.54 (((~(f1(c2, c1) = c3)) | (~(c4 = c4)) | big_f(c2, c4) | (~(c2 = f4(c4))) | (f1(c2, c1) = f2(f1(c2, c1))) | (~big_f(f1(c2, c1), f1(c2, c1)))) <=> (big_f(c2, c4) | (~(c2 = f4(c4))) | (~(f1(c2, c1) = c3)) | (f1(c2, c1) = f2(f1(c2, c1))) | (~big_f(f1(c2, c1), f1(c2, c1))))),
% 28.34/18.54 inference(transitivity,[status(thm)],[11139, 11138])).
% 28.34/18.54 tff(11141,plain,
% 28.34/18.54 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f1(c2, c1) = c3)) | (~(c4 = c4)) | big_f(c2, c4) | (~(c2 = f4(c4))) | (f1(c2, c1) = f2(f1(c2, c1))) | (~big_f(f1(c2, c1), f1(c2, c1))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (big_f(c2, c4) | (~(c2 = f4(c4))) | (~(f1(c2, c1) = c3)) | (f1(c2, c1) = f2(f1(c2, c1))) | (~big_f(f1(c2, c1), f1(c2, c1)))))),
% 28.34/18.54 inference(monotonicity,[status(thm)],[11140])).
% 28.34/18.54 tff(11142,plain,
% 28.34/18.54 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f1(c2, c1) = c3)) | (~(c4 = c4)) | big_f(c2, c4) | (~(c2 = f4(c4))) | (f1(c2, c1) = f2(f1(c2, c1))) | (~big_f(f1(c2, c1), f1(c2, c1))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | big_f(c2, c4) | (~(c2 = f4(c4))) | (~(f1(c2, c1) = c3)) | (f1(c2, c1) = f2(f1(c2, c1))) | (~big_f(f1(c2, c1), f1(c2, c1))))),
% 28.34/18.54 inference(transitivity,[status(thm)],[11141, 11137])).
% 28.34/18.54 tff(11143,plain,
% 28.34/18.54 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f1(c2, c1) = c3)) | (~(c4 = c4)) | big_f(c2, c4) | (~(c2 = f4(c4))) | (f1(c2, c1) = f2(f1(c2, c1))) | (~big_f(f1(c2, c1), f1(c2, c1))))),
% 28.34/18.54 inference(quant_inst,[status(thm)],[])).
% 28.34/18.54 tff(11144,plain,
% 28.34/18.54 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | big_f(c2, c4) | (~(c2 = f4(c4))) | (~(f1(c2, c1) = c3)) | (f1(c2, c1) = f2(f1(c2, c1))) | (~big_f(f1(c2, c1), f1(c2, c1)))),
% 28.34/18.54 inference(modus_ponens,[status(thm)],[11143, 11142])).
% 28.34/18.54 tff(11145,plain,
% 28.34/18.54 ($false),
% 28.34/18.54 inference(unit_resolution,[status(thm)],[11144, 5622, 3865, 10089, 11136, 11131, 11135])).
% 28.34/18.54 tff(11146,plain,((f1(c2, c1) = f2(f1(c2, c1))) | big_f(c2, c4) | (~(c2 = f4(c4))) | (~big_f(f1(c2, c1), f1(c2, c1))) | (~(f1(c2, c1) = c3))), inference(lemma,lemma(discharge,[]))).
% 28.34/18.54 tff(11147,plain,
% 28.34/18.54 (f1(c2, c1) = f2(f1(c2, c1))),
% 28.34/18.54 inference(unit_resolution,[status(thm)],[11146, 3865, 10089, 11134, 11131])).
% 28.34/18.54 tff(11148,assumption,(f1(c2, c1) = f2(f1(c2, c1))), introduced(assumption)).
% 28.34/18.54 tff(11149,plain,
% 28.34/18.54 (f2(f1(c2, c1)) = f1(c2, c1)),
% 28.34/18.54 inference(symmetry,[status(thm)],[11148])).
% 28.34/18.54 tff(11150,assumption,(big_f(f1(c2, c1), f6(c1, c1))), introduced(assumption)).
% 28.34/18.54 tff(11151,plain,
% 28.34/18.54 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (big_f(c2, c4) | (~(c2 = f4(c4))) | (~(f1(c2, c1) = c3)) | (f6(c1, c1) = f2(f1(c2, c1))) | (~big_f(f1(c2, c1), f6(c1, c1))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | big_f(c2, c4) | (~(c2 = f4(c4))) | (~(f1(c2, c1) = c3)) | (f6(c1, c1) = f2(f1(c2, c1))) | (~big_f(f1(c2, c1), f6(c1, c1))))),
% 28.34/18.54 inference(rewrite,[status(thm)],[])).
% 28.34/18.54 tff(11152,plain,
% 28.34/18.54 (((~(f1(c2, c1) = c3)) | $false | big_f(c2, c4) | (~(c2 = f4(c4))) | (f6(c1, c1) = f2(f1(c2, c1))) | (~big_f(f1(c2, c1), f6(c1, c1)))) <=> (big_f(c2, c4) | (~(c2 = f4(c4))) | (~(f1(c2, c1) = c3)) | (f6(c1, c1) = f2(f1(c2, c1))) | (~big_f(f1(c2, c1), f6(c1, c1))))),
% 28.34/18.54 inference(rewrite,[status(thm)],[])).
% 28.34/18.54 tff(11153,plain,
% 28.34/18.54 (((~(f1(c2, c1) = c3)) | (~(c4 = c4)) | big_f(c2, c4) | (~(c2 = f4(c4))) | (f6(c1, c1) = f2(f1(c2, c1))) | (~big_f(f1(c2, c1), f6(c1, c1)))) <=> ((~(f1(c2, c1) = c3)) | $false | big_f(c2, c4) | (~(c2 = f4(c4))) | (f6(c1, c1) = f2(f1(c2, c1))) | (~big_f(f1(c2, c1), f6(c1, c1))))),
% 28.34/18.54 inference(monotonicity,[status(thm)],[410])).
% 28.34/18.54 tff(11154,plain,
% 28.34/18.54 (((~(f1(c2, c1) = c3)) | (~(c4 = c4)) | big_f(c2, c4) | (~(c2 = f4(c4))) | (f6(c1, c1) = f2(f1(c2, c1))) | (~big_f(f1(c2, c1), f6(c1, c1)))) <=> (big_f(c2, c4) | (~(c2 = f4(c4))) | (~(f1(c2, c1) = c3)) | (f6(c1, c1) = f2(f1(c2, c1))) | (~big_f(f1(c2, c1), f6(c1, c1))))),
% 28.34/18.54 inference(transitivity,[status(thm)],[11153, 11152])).
% 28.34/18.54 tff(11155,plain,
% 28.34/18.54 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f1(c2, c1) = c3)) | (~(c4 = c4)) | big_f(c2, c4) | (~(c2 = f4(c4))) | (f6(c1, c1) = f2(f1(c2, c1))) | (~big_f(f1(c2, c1), f6(c1, c1))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (big_f(c2, c4) | (~(c2 = f4(c4))) | (~(f1(c2, c1) = c3)) | (f6(c1, c1) = f2(f1(c2, c1))) | (~big_f(f1(c2, c1), f6(c1, c1)))))),
% 28.34/18.54 inference(monotonicity,[status(thm)],[11154])).
% 28.34/18.54 tff(11156,plain,
% 28.34/18.54 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f1(c2, c1) = c3)) | (~(c4 = c4)) | big_f(c2, c4) | (~(c2 = f4(c4))) | (f6(c1, c1) = f2(f1(c2, c1))) | (~big_f(f1(c2, c1), f6(c1, c1))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | big_f(c2, c4) | (~(c2 = f4(c4))) | (~(f1(c2, c1) = c3)) | (f6(c1, c1) = f2(f1(c2, c1))) | (~big_f(f1(c2, c1), f6(c1, c1))))),
% 28.34/18.54 inference(transitivity,[status(thm)],[11155, 11151])).
% 28.34/18.54 tff(11157,plain,
% 28.34/18.54 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f1(c2, c1) = c3)) | (~(c4 = c4)) | big_f(c2, c4) | (~(c2 = f4(c4))) | (f6(c1, c1) = f2(f1(c2, c1))) | (~big_f(f1(c2, c1), f6(c1, c1))))),
% 28.34/18.54 inference(quant_inst,[status(thm)],[])).
% 28.34/18.54 tff(11158,plain,
% 28.34/18.54 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | big_f(c2, c4) | (~(c2 = f4(c4))) | (~(f1(c2, c1) = c3)) | (f6(c1, c1) = f2(f1(c2, c1))) | (~big_f(f1(c2, c1), f6(c1, c1)))),
% 28.34/18.54 inference(modus_ponens,[status(thm)],[11157, 11156])).
% 28.34/18.54 tff(11159,plain,
% 28.34/18.54 (f6(c1, c1) = f2(f1(c2, c1))),
% 28.34/18.54 inference(unit_resolution,[status(thm)],[11158, 5622, 3865, 10089, 11131, 11150])).
% 28.34/18.54 tff(11160,plain,
% 28.34/18.54 (f6(c1, c1) = c1),
% 28.34/18.54 inference(transitivity,[status(thm)],[11159, 11149, 10772, 874])).
% 28.34/18.54 tff(11161,plain,
% 28.34/18.54 ($false),
% 28.34/18.54 inference(unit_resolution,[status(thm)],[28, 11160])).
% 28.34/18.54 tff(11162,plain,((~(f1(c2, c1) = f2(f1(c2, c1)))) | (f6(c1, c1) = c1) | (~(f1(f7(f7(c2)), c1) = c1)) | (~(f7(c2) = c2)) | big_f(c2, c4) | (~(c2 = f4(c4))) | (~(f1(c2, c1) = c3)) | (~big_f(f1(c2, c1), f6(c1, c1)))), inference(lemma,lemma(discharge,[]))).
% 28.34/18.54 tff(11163,plain,
% 28.34/18.54 (~big_f(f1(c2, c1), f6(c1, c1))),
% 28.34/18.54 inference(unit_resolution,[status(thm)],[11162, 28, 874, 77, 3865, 10089, 11131, 11148])).
% 28.34/18.54 tff(11164,plain,
% 28.34/18.54 ((~big_f(c1, c2)) <=> (~big_f(c1, f10(c1)))),
% 28.34/18.54 inference(monotonicity,[status(thm)],[3350])).
% 28.34/18.54 tff(11165,plain,
% 28.34/18.54 (big_f(f1(c2, c1), c2) <=> big_f(c1, c2)),
% 28.34/18.54 inference(monotonicity,[status(thm)],[10773])).
% 28.34/18.54 tff(11166,plain,
% 28.34/18.54 ((~big_f(f1(c2, c1), c2)) <=> (~big_f(c1, c2))),
% 28.34/18.54 inference(monotonicity,[status(thm)],[11165])).
% 28.34/18.54 tff(11167,assumption,(big_f(f1(c2, c1), c2)), introduced(assumption)).
% 28.34/18.54 tff(11168,plain,
% 28.34/18.54 ((c2 = f2(f1(c2, c1))) <=> (c2 = f1(c2, c1))),
% 28.34/18.54 inference(monotonicity,[status(thm)],[11149])).
% 28.34/18.54 tff(11169,plain,
% 28.34/18.54 ((c2 = f2(f1(c2, c1))) <=> (f1(c2, c1) = c2)),
% 28.34/18.54 inference(transitivity,[status(thm)],[11168, 10784])).
% 28.34/18.54 tff(11170,plain,
% 28.34/18.54 ((f1(c2, c1) = c2) <=> (c2 = f2(f1(c2, c1)))),
% 28.34/18.54 inference(symmetry,[status(thm)],[11169])).
% 28.34/18.54 tff(11171,plain,
% 28.34/18.54 ((~(f1(c2, c1) = c2)) <=> (~(c2 = f2(f1(c2, c1))))),
% 28.34/18.54 inference(monotonicity,[status(thm)],[11170])).
% 28.34/18.54 tff(11172,assumption,(~(f1(c2, c1) = c2)), introduced(assumption)).
% 28.34/18.54 tff(11173,plain,
% 28.34/18.54 (~(c2 = f2(f1(c2, c1)))),
% 28.34/18.54 inference(modus_ponens,[status(thm)],[11172, 11171])).
% 28.34/18.54 tff(11174,plain,
% 28.34/18.54 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (big_f(c2, c4) | (~(c2 = f4(c4))) | (c2 = f2(f1(c2, c1))) | (~(f1(c2, c1) = c3)) | (~big_f(f1(c2, c1), c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | big_f(c2, c4) | (~(c2 = f4(c4))) | (c2 = f2(f1(c2, c1))) | (~(f1(c2, c1) = c3)) | (~big_f(f1(c2, c1), c2)))),
% 28.34/18.54 inference(rewrite,[status(thm)],[])).
% 28.34/18.54 tff(11175,plain,
% 28.34/18.54 (((~(f1(c2, c1) = c3)) | $false | big_f(c2, c4) | (~(c2 = f4(c4))) | (c2 = f2(f1(c2, c1))) | (~big_f(f1(c2, c1), c2))) <=> (big_f(c2, c4) | (~(c2 = f4(c4))) | (c2 = f2(f1(c2, c1))) | (~(f1(c2, c1) = c3)) | (~big_f(f1(c2, c1), c2)))),
% 28.34/18.54 inference(rewrite,[status(thm)],[])).
% 28.34/18.54 tff(11176,plain,
% 28.34/18.54 (((~(f1(c2, c1) = c3)) | (~(c4 = c4)) | big_f(c2, c4) | (~(c2 = f4(c4))) | (c2 = f2(f1(c2, c1))) | (~big_f(f1(c2, c1), c2))) <=> ((~(f1(c2, c1) = c3)) | $false | big_f(c2, c4) | (~(c2 = f4(c4))) | (c2 = f2(f1(c2, c1))) | (~big_f(f1(c2, c1), c2)))),
% 28.34/18.54 inference(monotonicity,[status(thm)],[410])).
% 28.34/18.54 tff(11177,plain,
% 28.34/18.54 (((~(f1(c2, c1) = c3)) | (~(c4 = c4)) | big_f(c2, c4) | (~(c2 = f4(c4))) | (c2 = f2(f1(c2, c1))) | (~big_f(f1(c2, c1), c2))) <=> (big_f(c2, c4) | (~(c2 = f4(c4))) | (c2 = f2(f1(c2, c1))) | (~(f1(c2, c1) = c3)) | (~big_f(f1(c2, c1), c2)))),
% 28.34/18.54 inference(transitivity,[status(thm)],[11176, 11175])).
% 28.34/18.54 tff(11178,plain,
% 28.34/18.54 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f1(c2, c1) = c3)) | (~(c4 = c4)) | big_f(c2, c4) | (~(c2 = f4(c4))) | (c2 = f2(f1(c2, c1))) | (~big_f(f1(c2, c1), c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (big_f(c2, c4) | (~(c2 = f4(c4))) | (c2 = f2(f1(c2, c1))) | (~(f1(c2, c1) = c3)) | (~big_f(f1(c2, c1), c2))))),
% 28.34/18.54 inference(monotonicity,[status(thm)],[11177])).
% 28.34/18.54 tff(11179,plain,
% 28.34/18.54 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f1(c2, c1) = c3)) | (~(c4 = c4)) | big_f(c2, c4) | (~(c2 = f4(c4))) | (c2 = f2(f1(c2, c1))) | (~big_f(f1(c2, c1), c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | big_f(c2, c4) | (~(c2 = f4(c4))) | (c2 = f2(f1(c2, c1))) | (~(f1(c2, c1) = c3)) | (~big_f(f1(c2, c1), c2)))),
% 28.34/18.54 inference(transitivity,[status(thm)],[11178, 11174])).
% 28.34/18.54 tff(11180,plain,
% 28.34/18.54 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f1(c2, c1) = c3)) | (~(c4 = c4)) | big_f(c2, c4) | (~(c2 = f4(c4))) | (c2 = f2(f1(c2, c1))) | (~big_f(f1(c2, c1), c2)))),
% 28.34/18.54 inference(quant_inst,[status(thm)],[])).
% 28.34/18.54 tff(11181,plain,
% 28.34/18.54 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | big_f(c2, c4) | (~(c2 = f4(c4))) | (c2 = f2(f1(c2, c1))) | (~(f1(c2, c1) = c3)) | (~big_f(f1(c2, c1), c2))),
% 28.34/18.54 inference(modus_ponens,[status(thm)],[11180, 11179])).
% 28.34/18.54 tff(11182,plain,
% 28.34/18.54 ((c2 = f2(f1(c2, c1))) | (~big_f(f1(c2, c1), c2))),
% 28.34/18.54 inference(unit_resolution,[status(thm)],[11181, 5622, 3865, 10089, 11131])).
% 28.34/18.54 tff(11183,plain,
% 28.34/18.54 ($false),
% 28.34/18.54 inference(unit_resolution,[status(thm)],[11182, 11173, 11167])).
% 28.34/18.54 tff(11184,plain,((~big_f(f1(c2, c1), c2)) | big_f(c2, c4) | (~(c2 = f4(c4))) | (~(f1(c2, c1) = c3)) | (f1(c2, c1) = c2) | (~(f1(c2, c1) = f2(f1(c2, c1))))), inference(lemma,lemma(discharge,[]))).
% 28.34/18.54 tff(11185,plain,
% 28.34/18.54 (~big_f(f1(c2, c1), c2)),
% 28.34/18.54 inference(unit_resolution,[status(thm)],[11184, 3865, 10089, 11131, 10793, 11148])).
% 28.34/18.54 tff(11186,plain,
% 28.34/18.54 (~big_f(c1, c2)),
% 28.34/18.54 inference(modus_ponens,[status(thm)],[11185, 11166])).
% 28.34/18.54 tff(11187,plain,
% 28.34/18.54 (~big_f(c1, f10(c1))),
% 28.34/18.54 inference(modus_ponens,[status(thm)],[11186, 11164])).
% 28.34/18.54 tff(11188,plain,
% 28.34/18.54 (big_f(f7(c1), f6(c1, c1))),
% 28.34/18.54 inference(unit_resolution,[status(thm)],[9820, 28, 4234, 2946, 3, 11187])).
% 28.34/18.54 tff(11189,plain,
% 28.34/18.54 (f1(c2, c1) = f7(c1)),
% 28.34/18.54 inference(transitivity,[status(thm)],[10772, 874, 5544])).
% 28.34/18.54 tff(11190,plain,
% 28.34/18.54 (big_f(f1(c2, c1), f6(c1, c1)) <=> big_f(f7(c1), f6(c1, c1))),
% 28.34/18.54 inference(monotonicity,[status(thm)],[11189])).
% 28.34/18.54 tff(11191,plain,
% 28.34/18.54 (big_f(f7(c1), f6(c1, c1)) <=> big_f(f1(c2, c1), f6(c1, c1))),
% 28.34/18.54 inference(symmetry,[status(thm)],[11190])).
% 28.34/18.54 tff(11192,plain,
% 28.34/18.54 (big_f(f1(c2, c1), f6(c1, c1))),
% 28.34/18.54 inference(modus_ponens,[status(thm)],[5964, 11191])).
% 28.34/18.54 tff(11193,assumption,(~big_f(f1(c2, c1), f6(c1, c1))), introduced(assumption)).
% 28.34/18.54 tff(11194,plain,
% 28.34/18.54 ($false),
% 28.34/18.54 inference(unit_resolution,[status(thm)],[11193, 11192])).
% 28.34/18.54 tff(11195,plain,((~big_f(f7(c1), f6(c1, c1))) | big_f(f1(c2, c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (~(f1(f7(f7(c2)), c1) = c1)) | (~(f7(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.34/18.54 tff(11196,plain,
% 28.34/18.54 ($false),
% 28.34/18.54 inference(unit_resolution,[status(thm)],[11195, 11188, 11163, 4234, 874, 77])).
% 28.34/18.54 tff(11197,plain,((f6(c1, c1) = c1) | (~(f7(c1) = c1)) | (~(f1(f7(f7(c2)), c1) = c1)) | (~(f7(c2) = c2)) | big_f(c2, f10(c1)) | (f10(c1) = c1) | big_f(c2, c4) | (~(c2 = f4(c4))) | (~(f1(c2, c1) = c3)) | (~(f1(c2, c1) = f2(f1(c2, c1))))), inference(lemma,lemma(discharge,[]))).
% 28.34/18.54 tff(11198,plain,
% 28.34/18.54 (f6(c1, c1) = c1),
% 28.34/18.54 inference(unit_resolution,[status(thm)],[11197, 8451, 874, 77, 4234, 3, 3865, 10089, 11131, 11147])).
% 28.34/18.54 tff(11199,plain,
% 28.34/18.54 (f6(f1(c2, c1), f1(c2, c1)) = f6(c1, c1)),
% 28.34/18.54 inference(monotonicity,[status(thm)],[10773, 10773])).
% 28.34/18.54 tff(11200,plain,
% 28.34/18.54 (f6(f1(c2, c1), f1(c2, c1)) = c1),
% 28.34/18.54 inference(transitivity,[status(thm)],[11199, 11198])).
% 28.34/18.54 tff(11201,plain,
% 28.34/18.54 (big_f(f7(f1(c2, c1)), f6(f1(c2, c1), f1(c2, c1))) <=> big_f(c1, c1)),
% 28.34/18.54 inference(monotonicity,[status(thm)],[11104, 11200])).
% 28.34/18.54 tff(11202,plain,
% 28.34/18.54 (big_f(c1, c1) <=> big_f(f7(f1(c2, c1)), f6(f1(c2, c1), f1(c2, c1)))),
% 28.34/18.54 inference(symmetry,[status(thm)],[11201])).
% 28.34/18.54 tff(11203,plain,
% 28.34/18.54 (big_f(f7(f1(c2, c1)), f6(f1(c2, c1), f1(c2, c1)))),
% 28.34/18.54 inference(modus_ponens,[status(thm)],[4932, 11202])).
% 28.34/18.54 tff(11204,plain,
% 28.34/18.54 (f6(f1(c2, c1), f1(c2, c1)) = f1(c2, c1)),
% 28.34/18.54 inference(transitivity,[status(thm)],[11199, 11198, 875, 10762])).
% 28.34/18.54 tff(11205,plain,
% 28.34/18.54 ((c2 = f8(c1)) <=> (c2 = f8(f1(c2, c1)))),
% 28.34/18.54 inference(symmetry,[status(thm)],[10865])).
% 28.34/18.54 tff(11206,plain,
% 28.34/18.54 ((~(f1(c2, c1) = f8(f1(c2, c1)))) <=> (~(f8(c1) = c1))),
% 28.34/18.54 inference(monotonicity,[status(thm)],[10838])).
% 28.34/18.54 tff(11207,plain,
% 28.34/18.54 ((f10(f1(c2, c1)) = f1(c2, c1)) <=> (f10(c1) = c1)),
% 28.34/18.54 inference(monotonicity,[status(thm)],[10846, 10773])).
% 28.34/18.54 tff(11208,plain,
% 28.34/18.54 ((f10(c1) = c1) <=> (f10(f1(c2, c1)) = f1(c2, c1))),
% 28.34/18.54 inference(symmetry,[status(thm)],[11207])).
% 28.34/18.54 tff(11209,plain,
% 28.34/18.54 ((~(f10(c1) = c1)) <=> (~(f10(f1(c2, c1)) = f1(c2, c1)))),
% 28.34/18.54 inference(monotonicity,[status(thm)],[11208])).
% 28.34/18.54 tff(11210,plain,
% 28.34/18.54 (~(f10(f1(c2, c1)) = f1(c2, c1))),
% 28.34/18.54 inference(modus_ponens,[status(thm)],[3, 11209])).
% 28.34/18.54 tff(11211,plain,
% 28.34/18.54 (big_f(f1(c2, c1), f10(f1(c2, c1))) <=> big_f(c1, f10(c1))),
% 28.34/18.54 inference(monotonicity,[status(thm)],[10773, 10846])).
% 28.34/18.54 tff(11212,plain,
% 28.34/18.54 (big_f(c1, f10(c1)) <=> big_f(f1(c2, c1), f10(f1(c2, c1)))),
% 28.34/18.54 inference(symmetry,[status(thm)],[11211])).
% 28.34/18.54 tff(11213,plain,
% 28.34/18.54 (big_f(c1, c2) <=> big_f(f1(c2, c1), f10(f1(c2, c1)))),
% 28.34/18.54 inference(transitivity,[status(thm)],[3350, 11212])).
% 28.34/18.54 tff(11214,plain,
% 28.34/18.54 ((~big_f(c1, c2)) <=> (~big_f(f1(c2, c1), f10(f1(c2, c1))))),
% 28.34/18.54 inference(monotonicity,[status(thm)],[11213])).
% 28.34/18.54 tff(11215,plain,
% 28.34/18.54 (~big_f(f1(c2, c1), c2)),
% 28.34/18.54 inference(unit_resolution,[status(thm)],[11184, 3865, 10089, 11131, 10793, 11147])).
% 28.34/18.54 tff(11216,plain,
% 28.34/18.54 (~big_f(c1, c2)),
% 28.34/18.54 inference(modus_ponens,[status(thm)],[11215, 11166])).
% 28.34/18.54 tff(11217,plain,
% 28.34/18.54 (~big_f(f1(c2, c1), f10(f1(c2, c1)))),
% 28.34/18.54 inference(modus_ponens,[status(thm)],[11216, 11214])).
% 28.34/18.54 tff(11218,plain,
% 28.34/18.54 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f1(c2, c1)) = f1(c2, c1)) | big_f(f1(c2, c1), f10(f1(c2, c1))) | (~(f1(c2, c1) = f8(f1(c2, c1)))) | (~(f7(f1(c2, c1)) = f1(c2, c1))) | (~(f6(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))) | (~big_f(f7(f1(c2, c1)), f6(f1(c2, c1), f1(c2, c1)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(f1(c2, c1)) = f1(c2, c1)) | big_f(f1(c2, c1), f10(f1(c2, c1))) | (~(f1(c2, c1) = f8(f1(c2, c1)))) | (~(f7(f1(c2, c1)) = f1(c2, c1))) | (~(f6(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))) | (~big_f(f7(f1(c2, c1)), f6(f1(c2, c1), f1(c2, c1)))))),
% 28.34/18.54 inference(rewrite,[status(thm)],[])).
% 28.34/18.54 tff(11219,plain,
% 28.34/18.54 (((f10(f1(c2, c1)) = f1(c2, c1)) | big_f(f1(c2, c1), f10(f1(c2, c1))) | (~(f7(f1(c2, c1)) = f1(c2, c1))) | (~(f1(c2, c1) = f8(f1(c2, c1)))) | (~(f6(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))) | (~big_f(f7(f1(c2, c1)), f6(f1(c2, c1), f1(c2, c1))))) <=> ((f10(f1(c2, c1)) = f1(c2, c1)) | big_f(f1(c2, c1), f10(f1(c2, c1))) | (~(f1(c2, c1) = f8(f1(c2, c1)))) | (~(f7(f1(c2, c1)) = f1(c2, c1))) | (~(f6(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))) | (~big_f(f7(f1(c2, c1)), f6(f1(c2, c1), f1(c2, c1)))))),
% 28.34/18.54 inference(rewrite,[status(thm)],[])).
% 28.34/18.54 tff(11220,plain,
% 28.34/18.54 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f1(c2, c1)) = f1(c2, c1)) | big_f(f1(c2, c1), f10(f1(c2, c1))) | (~(f7(f1(c2, c1)) = f1(c2, c1))) | (~(f1(c2, c1) = f8(f1(c2, c1)))) | (~(f6(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))) | (~big_f(f7(f1(c2, c1)), f6(f1(c2, c1), f1(c2, c1)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f1(c2, c1)) = f1(c2, c1)) | big_f(f1(c2, c1), f10(f1(c2, c1))) | (~(f1(c2, c1) = f8(f1(c2, c1)))) | (~(f7(f1(c2, c1)) = f1(c2, c1))) | (~(f6(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))) | (~big_f(f7(f1(c2, c1)), f6(f1(c2, c1), f1(c2, c1))))))),
% 28.34/18.54 inference(monotonicity,[status(thm)],[11219])).
% 28.34/18.54 tff(11221,plain,
% 28.34/18.54 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f1(c2, c1)) = f1(c2, c1)) | big_f(f1(c2, c1), f10(f1(c2, c1))) | (~(f7(f1(c2, c1)) = f1(c2, c1))) | (~(f1(c2, c1) = f8(f1(c2, c1)))) | (~(f6(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))) | (~big_f(f7(f1(c2, c1)), f6(f1(c2, c1), f1(c2, c1)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(f1(c2, c1)) = f1(c2, c1)) | big_f(f1(c2, c1), f10(f1(c2, c1))) | (~(f1(c2, c1) = f8(f1(c2, c1)))) | (~(f7(f1(c2, c1)) = f1(c2, c1))) | (~(f6(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))) | (~big_f(f7(f1(c2, c1)), f6(f1(c2, c1), f1(c2, c1)))))),
% 28.34/18.55 inference(transitivity,[status(thm)],[11220, 11218])).
% 28.34/18.55 tff(11222,plain,
% 28.34/18.55 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f1(c2, c1)) = f1(c2, c1)) | big_f(f1(c2, c1), f10(f1(c2, c1))) | (~(f7(f1(c2, c1)) = f1(c2, c1))) | (~(f1(c2, c1) = f8(f1(c2, c1)))) | (~(f6(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))) | (~big_f(f7(f1(c2, c1)), f6(f1(c2, c1), f1(c2, c1)))))),
% 28.34/18.55 inference(quant_inst,[status(thm)],[])).
% 28.34/18.55 tff(11223,plain,
% 28.34/18.55 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(f1(c2, c1)) = f1(c2, c1)) | big_f(f1(c2, c1), f10(f1(c2, c1))) | (~(f1(c2, c1) = f8(f1(c2, c1)))) | (~(f7(f1(c2, c1)) = f1(c2, c1))) | (~(f6(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))) | (~big_f(f7(f1(c2, c1)), f6(f1(c2, c1), f1(c2, c1))))),
% 28.34/18.55 inference(modus_ponens,[status(thm)],[11222, 11221])).
% 28.34/18.55 tff(11224,plain,
% 28.34/18.55 ((~(f1(c2, c1) = f8(f1(c2, c1)))) | (~(f6(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))) | (~big_f(f7(f1(c2, c1)), f6(f1(c2, c1), f1(c2, c1))))),
% 28.34/18.55 inference(unit_resolution,[status(thm)],[11223, 2963, 11109, 11217, 11210])).
% 28.34/18.55 tff(11225,plain,
% 28.34/18.55 (~(f1(c2, c1) = f8(f1(c2, c1)))),
% 28.34/18.55 inference(unit_resolution,[status(thm)],[11224, 11203, 11204])).
% 28.34/18.55 tff(11226,plain,
% 28.34/18.55 (~(f8(c1) = c1)),
% 28.34/18.55 inference(modus_ponens,[status(thm)],[11225, 11206])).
% 28.34/18.55 tff(11227,plain,
% 28.34/18.55 (f8(c1) = c2),
% 28.34/18.55 inference(unit_resolution,[status(thm)],[1680, 11226])).
% 28.34/18.55 tff(11228,plain,
% 28.34/18.55 (c2 = f8(c1)),
% 28.34/18.55 inference(unit_resolution,[status(thm)],[1675, 11227])).
% 28.34/18.55 tff(11229,plain,
% 28.34/18.55 (c2 = f8(f1(c2, c1))),
% 28.34/18.55 inference(modus_ponens,[status(thm)],[11228, 11205])).
% 28.34/18.55 tff(11230,plain,
% 28.34/18.55 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f1(c2, c1)) = f1(c2, c1)) | big_f(c2, f10(f1(c2, c1))) | (~(c2 = f8(f1(c2, c1)))) | (~(f7(f1(c2, c1)) = f1(c2, c1))) | (~(f6(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))) | (~big_f(f7(f1(c2, c1)), f6(f1(c2, c1), f1(c2, c1)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(f1(c2, c1)) = f1(c2, c1)) | big_f(c2, f10(f1(c2, c1))) | (~(c2 = f8(f1(c2, c1)))) | (~(f7(f1(c2, c1)) = f1(c2, c1))) | (~(f6(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))) | (~big_f(f7(f1(c2, c1)), f6(f1(c2, c1), f1(c2, c1)))))),
% 28.34/18.55 inference(rewrite,[status(thm)],[])).
% 28.34/18.55 tff(11231,plain,
% 28.34/18.55 (((f10(f1(c2, c1)) = f1(c2, c1)) | big_f(c2, f10(f1(c2, c1))) | (~(f7(f1(c2, c1)) = f1(c2, c1))) | (~(c2 = f8(f1(c2, c1)))) | (~(f6(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))) | (~big_f(f7(f1(c2, c1)), f6(f1(c2, c1), f1(c2, c1))))) <=> ((f10(f1(c2, c1)) = f1(c2, c1)) | big_f(c2, f10(f1(c2, c1))) | (~(c2 = f8(f1(c2, c1)))) | (~(f7(f1(c2, c1)) = f1(c2, c1))) | (~(f6(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))) | (~big_f(f7(f1(c2, c1)), f6(f1(c2, c1), f1(c2, c1)))))),
% 28.34/18.55 inference(rewrite,[status(thm)],[])).
% 28.34/18.55 tff(11232,plain,
% 28.34/18.55 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f1(c2, c1)) = f1(c2, c1)) | big_f(c2, f10(f1(c2, c1))) | (~(f7(f1(c2, c1)) = f1(c2, c1))) | (~(c2 = f8(f1(c2, c1)))) | (~(f6(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))) | (~big_f(f7(f1(c2, c1)), f6(f1(c2, c1), f1(c2, c1)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f1(c2, c1)) = f1(c2, c1)) | big_f(c2, f10(f1(c2, c1))) | (~(c2 = f8(f1(c2, c1)))) | (~(f7(f1(c2, c1)) = f1(c2, c1))) | (~(f6(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))) | (~big_f(f7(f1(c2, c1)), f6(f1(c2, c1), f1(c2, c1))))))),
% 28.34/18.55 inference(monotonicity,[status(thm)],[11231])).
% 28.34/18.55 tff(11233,plain,
% 28.34/18.55 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f1(c2, c1)) = f1(c2, c1)) | big_f(c2, f10(f1(c2, c1))) | (~(f7(f1(c2, c1)) = f1(c2, c1))) | (~(c2 = f8(f1(c2, c1)))) | (~(f6(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))) | (~big_f(f7(f1(c2, c1)), f6(f1(c2, c1), f1(c2, c1)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(f1(c2, c1)) = f1(c2, c1)) | big_f(c2, f10(f1(c2, c1))) | (~(c2 = f8(f1(c2, c1)))) | (~(f7(f1(c2, c1)) = f1(c2, c1))) | (~(f6(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))) | (~big_f(f7(f1(c2, c1)), f6(f1(c2, c1), f1(c2, c1)))))),
% 28.34/18.55 inference(transitivity,[status(thm)],[11232, 11230])).
% 28.34/18.55 tff(11234,plain,
% 28.34/18.55 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f1(c2, c1)) = f1(c2, c1)) | big_f(c2, f10(f1(c2, c1))) | (~(f7(f1(c2, c1)) = f1(c2, c1))) | (~(c2 = f8(f1(c2, c1)))) | (~(f6(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))) | (~big_f(f7(f1(c2, c1)), f6(f1(c2, c1), f1(c2, c1)))))),
% 28.34/18.55 inference(quant_inst,[status(thm)],[])).
% 28.34/18.55 tff(11235,plain,
% 28.34/18.55 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(f1(c2, c1)) = f1(c2, c1)) | big_f(c2, f10(f1(c2, c1))) | (~(c2 = f8(f1(c2, c1)))) | (~(f7(f1(c2, c1)) = f1(c2, c1))) | (~(f6(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))) | (~big_f(f7(f1(c2, c1)), f6(f1(c2, c1), f1(c2, c1))))),
% 28.34/18.55 inference(modus_ponens,[status(thm)],[11234, 11233])).
% 28.34/18.55 tff(11236,plain,
% 28.34/18.55 (big_f(c2, f10(f1(c2, c1))) | (~(c2 = f8(f1(c2, c1)))) | (~(f6(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))) | (~big_f(f7(f1(c2, c1)), f6(f1(c2, c1), f1(c2, c1))))),
% 28.34/18.55 inference(unit_resolution,[status(thm)],[11235, 2963, 11109, 11210])).
% 28.34/18.55 tff(11237,plain,
% 28.34/18.55 (big_f(c2, f10(f1(c2, c1)))),
% 28.34/18.55 inference(unit_resolution,[status(thm)],[11236, 11229, 11204, 11203])).
% 28.34/18.55 tff(11238,plain,
% 28.34/18.55 (big_f(c2, f10(c1))),
% 28.34/18.55 inference(modus_ponens,[status(thm)],[11237, 11130])).
% 28.34/18.55 tff(11239,plain,
% 28.34/18.55 ($false),
% 28.34/18.55 inference(unit_resolution,[status(thm)],[8451, 11238])).
% 28.34/18.55 tff(11240,plain,((f10(c1) = c1) | (~(f1(f7(f7(c2)), c1) = c1)) | (~(f7(c2) = c2)) | (~big_f(c1, c1)) | (~(f7(c1) = c1)) | big_f(c2, c4) | (~(c2 = f4(c4))) | (~(f1(c2, c1) = c3)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 28.34/18.55 tff(11241,plain,
% 28.34/18.55 (f10(c1) = c1),
% 28.34/18.55 inference(unit_resolution,[status(thm)],[11240, 10752, 10740, 11129, 11014, 8607, 2602, 10755, 121])).
% 28.34/18.55 tff(11242,plain,
% 28.34/18.55 (f1(c2, c1) = c3),
% 28.34/18.55 inference(transitivity,[status(thm)],[10772, 874, 5585])).
% 28.34/18.55 tff(11243,plain,
% 28.34/18.55 (f10(c1) = c1),
% 28.34/18.55 inference(unit_resolution,[status(thm)],[11240, 874, 77, 4932, 4234, 3865, 10089, 11242, 121])).
% 28.34/18.55 tff(11244,plain,
% 28.34/18.55 (f1(c2, c1) = f2(f1(c2, c1))),
% 28.34/18.55 inference(unit_resolution,[status(thm)],[11146, 3865, 10089, 11134, 11242])).
% 28.34/18.55 tff(11245,plain,
% 28.34/18.55 (~big_f(f1(c2, c1), f6(c1, c1))),
% 28.34/18.55 inference(unit_resolution,[status(thm)],[11162, 28, 874, 77, 3865, 10089, 11242, 11244])).
% 28.34/18.55 tff(11246,plain,
% 28.34/18.55 (~big_f(f7(c1), f6(c1, c1))),
% 28.34/18.55 inference(unit_resolution,[status(thm)],[11195, 11245, 4234, 874, 77])).
% 28.34/18.55 tff(11247,plain,
% 28.34/18.55 (~big_f(f9(c1, c1), f10(c1))),
% 28.34/18.55 inference(unit_resolution,[status(thm)],[9966, 3949, 4234, 3762, 65, 28])).
% 28.34/18.55 tff(11248,plain,
% 28.34/18.55 ($false),
% 28.34/18.55 inference(unit_resolution,[status(thm)],[8716, 11247, 10939, 3762])).
% 28.34/18.55 tff(11249,plain,((~(f9(c1, c1) = c1)) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c1)) | (f6(c1, c1) = c1) | (~big_f(c1, c1))), inference(lemma,lemma(discharge,[]))).
% 28.34/18.55 tff(11250,plain,
% 28.34/18.55 (~(f9(c1, c1) = c1)),
% 28.34/18.55 inference(unit_resolution,[status(thm)],[11249, 11246, 4234, 11243, 28, 4932])).
% 28.34/18.55 tff(11251,plain,
% 28.34/18.55 (f9(c1, c1) = c2),
% 28.34/18.55 inference(unit_resolution,[status(thm)],[3939, 11250])).
% 28.34/18.55 tff(11252,plain,
% 28.34/18.55 (~big_f(f9(c1, c1), c1)),
% 28.34/18.55 inference(unit_resolution,[status(thm)],[10058, 11251, 2])).
% 28.34/18.55 tff(11253,plain,
% 28.34/18.55 (~big_f(f9(c1, c1), f10(c1))),
% 28.34/18.55 inference(unit_resolution,[status(thm)],[10033, 11252, 11243])).
% 28.34/18.55 tff(11254,plain,
% 28.34/18.55 (c1 = f1(c2, c1)),
% 28.34/18.55 inference(transitivity,[status(thm)],[875, 10762])).
% 28.34/18.55 tff(11255,plain,
% 28.34/18.55 (big_f(c2, c1) <=> big_f(c2, f1(c2, c1))),
% 28.34/18.55 inference(monotonicity,[status(thm)],[11254])).
% 28.34/18.55 tff(11256,plain,
% 28.34/18.55 ((~big_f(c2, c1)) <=> (~big_f(c2, f1(c2, c1)))),
% 28.34/18.55 inference(monotonicity,[status(thm)],[11255])).
% 28.34/18.55 tff(11257,plain,
% 28.34/18.55 (~big_f(c2, f1(c2, c1))),
% 28.34/18.55 inference(modus_ponens,[status(thm)],[2, 11256])).
% 28.34/18.55 tff(11258,plain,
% 28.34/18.55 (f6(c2, f1(c2, c1)) = f6(c2, c1)),
% 28.34/18.55 inference(monotonicity,[status(thm)],[10773])).
% 28.34/18.55 tff(11259,plain,
% 28.34/18.55 ((f6(c2, f1(c2, c1)) = f1(c2, c1)) <=> (f6(c2, c1) = c1)),
% 28.34/18.55 inference(monotonicity,[status(thm)],[11258, 10773])).
% 28.34/18.55 tff(11260,plain,
% 28.34/18.55 ((f6(c2, f1(c2, c1)) = f1(c2, c1)) <=> (f6(f7(c2), c3) = c1)),
% 28.34/18.55 inference(transitivity,[status(thm)],[11259, 5838])).
% 28.34/18.55 tff(11261,plain,
% 28.34/18.55 ((~(f6(c2, f1(c2, c1)) = f1(c2, c1))) <=> (~(f6(f7(c2), c3) = c1))),
% 28.34/18.55 inference(monotonicity,[status(thm)],[11260])).
% 28.34/18.55 tff(11262,assumption,(~(f6(c2, f1(c2, c1)) = f1(c2, c1))), introduced(assumption)).
% 28.34/18.55 tff(11263,plain,
% 28.34/18.55 (~(f6(f7(c2), c3) = c1)),
% 28.34/18.55 inference(modus_ponens,[status(thm)],[11262, 11261])).
% 28.34/18.55 tff(11264,plain,
% 28.34/18.55 (big_f(f7(c2), f6(c2, f1(c2, c1))) <=> big_f(f7(c2), f6(c2, c1))),
% 28.34/18.55 inference(monotonicity,[status(thm)],[11258])).
% 28.34/18.55 tff(11265,plain,
% 28.34/18.55 (f10(f1(c2, c1)) = f1(c2, c1)),
% 28.34/18.55 inference(modus_ponens,[status(thm)],[3762, 11208])).
% 28.34/18.55 tff(11266,plain,
% 28.34/18.55 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f7(c2) = c2)) | (f6(c2, f1(c2, c1)) = f1(c2, c1)) | big_f(f7(c2), f6(c2, f1(c2, c1))) | (~(f10(f1(c2, c1)) = f1(c2, c1))) | (f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1)) | big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c2) = c2)) | (f6(c2, f1(c2, c1)) = f1(c2, c1)) | big_f(f7(c2), f6(c2, f1(c2, c1))) | (~(f10(f1(c2, c1)) = f1(c2, c1))) | (f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1)) | big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1))))),
% 28.34/18.55 inference(rewrite,[status(thm)],[])).
% 28.34/18.55 tff(11267,plain,
% 28.34/18.55 (((~(f10(f1(c2, c1)) = f1(c2, c1))) | (f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1)) | big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1))) | (~(f7(c2) = c2)) | (f6(c2, f1(c2, c1)) = f1(c2, c1)) | big_f(f7(c2), f6(c2, f1(c2, c1)))) <=> ((~(f7(c2) = c2)) | (f6(c2, f1(c2, c1)) = f1(c2, c1)) | big_f(f7(c2), f6(c2, f1(c2, c1))) | (~(f10(f1(c2, c1)) = f1(c2, c1))) | (f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1)) | big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1))))),
% 28.34/18.55 inference(rewrite,[status(thm)],[])).
% 28.34/18.55 tff(11268,plain,
% 28.34/18.55 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(f1(c2, c1)) = f1(c2, c1))) | (f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1)) | big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1))) | (~(f7(c2) = c2)) | (f6(c2, f1(c2, c1)) = f1(c2, c1)) | big_f(f7(c2), f6(c2, f1(c2, c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f7(c2) = c2)) | (f6(c2, f1(c2, c1)) = f1(c2, c1)) | big_f(f7(c2), f6(c2, f1(c2, c1))) | (~(f10(f1(c2, c1)) = f1(c2, c1))) | (f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1)) | big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1)))))),
% 28.34/18.55 inference(monotonicity,[status(thm)],[11267])).
% 28.34/18.55 tff(11269,plain,
% 28.34/18.55 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(f1(c2, c1)) = f1(c2, c1))) | (f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1)) | big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1))) | (~(f7(c2) = c2)) | (f6(c2, f1(c2, c1)) = f1(c2, c1)) | big_f(f7(c2), f6(c2, f1(c2, c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c2) = c2)) | (f6(c2, f1(c2, c1)) = f1(c2, c1)) | big_f(f7(c2), f6(c2, f1(c2, c1))) | (~(f10(f1(c2, c1)) = f1(c2, c1))) | (f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1)) | big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1))))),
% 28.34/18.55 inference(transitivity,[status(thm)],[11268, 11266])).
% 28.34/18.55 tff(11270,plain,
% 28.34/18.55 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(f1(c2, c1)) = f1(c2, c1))) | (f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1)) | big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1))) | (~(f7(c2) = c2)) | (f6(c2, f1(c2, c1)) = f1(c2, c1)) | big_f(f7(c2), f6(c2, f1(c2, c1))))),
% 28.34/18.55 inference(quant_inst,[status(thm)],[])).
% 28.34/18.55 tff(11271,plain,
% 28.34/18.55 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c2) = c2)) | (f6(c2, f1(c2, c1)) = f1(c2, c1)) | big_f(f7(c2), f6(c2, f1(c2, c1))) | (~(f10(f1(c2, c1)) = f1(c2, c1))) | (f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1)) | big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1)))),
% 28.34/18.55 inference(modus_ponens,[status(thm)],[11270, 11269])).
% 28.34/18.55 tff(11272,plain,
% 28.34/18.55 ((f6(c2, f1(c2, c1)) = f1(c2, c1)) | big_f(f7(c2), f6(c2, f1(c2, c1))) | (f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1)) | big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1)))),
% 28.34/18.55 inference(unit_resolution,[status(thm)],[11271, 2492, 77, 11265])).
% 28.34/18.55 tff(11273,plain,
% 28.34/18.55 (big_f(f7(c2), f6(c2, f1(c2, c1)))),
% 28.34/18.55 inference(unit_resolution,[status(thm)],[11272, 11262, 10982, 10986])).
% 28.34/18.55 tff(11274,plain,
% 28.34/18.55 (big_f(f7(c2), f6(c2, c1))),
% 28.34/18.55 inference(modus_ponens,[status(thm)],[11273, 11264])).
% 28.34/18.55 tff(11275,plain,
% 28.34/18.55 (~(f6(f7(c2), c3) = c2)),
% 28.34/18.55 inference(unit_resolution,[status(thm)],[5848, 11274, 77, 172, 121])).
% 28.34/18.55 tff(11276,plain,
% 28.34/18.55 ($false),
% 28.34/18.55 inference(unit_resolution,[status(thm)],[2391, 11275, 11263])).
% 28.34/18.55 tff(11277,plain,((f6(c2, f1(c2, c1)) = f1(c2, c1)) | (~(f7(c2) = c2)) | (~(c3 = c1)) | big_f(c2, c2) | (~(f1(f7(f7(c2)), c1) = c1)) | big_f(c2, f1(c2, c1)) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.34/18.55 tff(11278,plain,
% 28.34/18.55 (f6(c2, f1(c2, c1)) = f1(c2, c1)),
% 28.34/18.55 inference(unit_resolution,[status(thm)],[11277, 11251, 172, 121, 874, 11257, 11243, 77])).
% 28.34/18.55 tff(11279,plain,
% 28.34/18.55 (f6(c2, c1) = f6(c2, f1(c2, c1))),
% 28.34/18.55 inference(monotonicity,[status(thm)],[11254])).
% 28.34/18.55 tff(11280,plain,
% 28.34/18.55 (f6(c2, c1) = c1),
% 28.34/18.55 inference(transitivity,[status(thm)],[11279, 11278, 10772, 874])).
% 28.34/18.55 tff(11281,plain,
% 28.34/18.55 (f6(c1, f6(c2, c1)) = f6(c1, c1)),
% 28.34/18.55 inference(monotonicity,[status(thm)],[11280])).
% 28.34/18.55 tff(11282,plain,
% 28.34/18.55 ((f6(c1, f6(c2, c1)) = f6(c2, c1)) <=> (f6(c1, c1) = c1)),
% 28.34/18.55 inference(monotonicity,[status(thm)],[11281, 11280])).
% 28.34/18.55 tff(11283,plain,
% 28.34/18.55 ((f6(c1, c1) = c1) <=> (f6(c1, f6(c2, c1)) = f6(c2, c1))),
% 28.34/18.55 inference(symmetry,[status(thm)],[11282])).
% 28.34/18.55 tff(11284,plain,
% 28.34/18.55 ((~(f6(c1, c1) = c1)) <=> (~(f6(c1, f6(c2, c1)) = f6(c2, c1)))),
% 28.34/18.55 inference(monotonicity,[status(thm)],[11283])).
% 28.34/18.55 tff(11285,plain,
% 28.34/18.55 (~(f6(c1, f6(c2, c1)) = f6(c2, c1))),
% 28.34/18.55 inference(modus_ponens,[status(thm)],[28, 11284])).
% 28.34/18.55 tff(11286,plain,
% 28.34/18.55 (big_f(f7(c1), f6(c1, f6(c2, c1))) <=> big_f(f7(c1), f6(c1, c1))),
% 28.34/18.55 inference(monotonicity,[status(thm)],[11281])).
% 28.34/18.55 tff(11287,plain,
% 28.34/18.55 (big_f(f7(c1), f6(c1, c1)) <=> big_f(f7(c1), f6(c1, f6(c2, c1)))),
% 28.34/18.55 inference(symmetry,[status(thm)],[11286])).
% 28.34/18.55 tff(11288,plain,
% 28.34/18.55 ((~big_f(f7(c1), f6(c1, c1))) <=> (~big_f(f7(c1), f6(c1, f6(c2, c1))))),
% 28.34/18.55 inference(monotonicity,[status(thm)],[11287])).
% 28.34/18.55 tff(11289,plain,
% 28.34/18.55 (~big_f(f7(c1), f6(c1, f6(c2, c1)))),
% 28.34/18.55 inference(modus_ponens,[status(thm)],[11246, 11288])).
% 28.34/18.55 tff(11290,plain,
% 28.34/18.55 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (f6(c1, f6(c2, c1)) = f6(c2, c1)) | big_f(f7(c1), f6(c1, f6(c2, c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (f6(c1, f6(c2, c1)) = f6(c2, c1)) | big_f(f7(c1), f6(c1, f6(c2, c1))))),
% 28.34/18.55 inference(rewrite,[status(thm)],[])).
% 28.34/18.55 tff(11291,plain,
% 28.34/18.55 (((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f7(c1) = c1)) | (f6(c1, f6(c2, c1)) = f6(c2, c1)) | big_f(f7(c1), f6(c1, f6(c2, c1)))) <=> ((f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (f6(c1, f6(c2, c1)) = f6(c2, c1)) | big_f(f7(c1), f6(c1, f6(c2, c1))))),
% 28.34/18.55 inference(rewrite,[status(thm)],[])).
% 28.34/18.55 tff(11292,plain,
% 28.34/18.55 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f7(c1) = c1)) | (f6(c1, f6(c2, c1)) = f6(c2, c1)) | big_f(f7(c1), f6(c1, f6(c2, c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (f6(c1, f6(c2, c1)) = f6(c2, c1)) | big_f(f7(c1), f6(c1, f6(c2, c1)))))),
% 28.34/18.55 inference(monotonicity,[status(thm)],[11291])).
% 28.34/18.55 tff(11293,plain,
% 28.34/18.55 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f7(c1) = c1)) | (f6(c1, f6(c2, c1)) = f6(c2, c1)) | big_f(f7(c1), f6(c1, f6(c2, c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (f6(c1, f6(c2, c1)) = f6(c2, c1)) | big_f(f7(c1), f6(c1, f6(c2, c1))))),
% 28.34/18.55 inference(transitivity,[status(thm)],[11292, 11290])).
% 28.34/18.55 tff(11294,plain,
% 28.34/18.55 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f7(c1) = c1)) | (f6(c1, f6(c2, c1)) = f6(c2, c1)) | big_f(f7(c1), f6(c1, f6(c2, c1))))),
% 28.34/18.55 inference(quant_inst,[status(thm)],[])).
% 28.34/18.55 tff(11295,plain,
% 28.34/18.55 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (f6(c1, f6(c2, c1)) = f6(c2, c1)) | big_f(f7(c1), f6(c1, f6(c2, c1)))),
% 28.34/18.55 inference(modus_ponens,[status(thm)],[11294, 11293])).
% 28.34/18.55 tff(11296,plain,
% 28.34/18.55 ((f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (f6(c1, f6(c2, c1)) = f6(c2, c1)) | big_f(f7(c1), f6(c1, f6(c2, c1)))),
% 28.34/18.55 inference(unit_resolution,[status(thm)],[11295, 2492])).
% 28.34/18.55 tff(11297,plain,
% 28.34/18.56 ($false),
% 28.34/18.56 inference(unit_resolution,[status(thm)],[11296, 11289, 11285, 4234, 11243, 11253, 11250])).
% 28.34/18.56 tff(11298,plain,((f6(c1, c1) = c1) | (~(f7(c1) = c1)) | (~(f1(f7(f7(c2)), c1) = c1)) | (~(f7(c2) = c2)) | (~(c3 = c1)) | big_f(c2, c2) | big_f(c2, c1) | (~big_f(c1, c1)) | big_f(c2, c4) | (~(c2 = f4(c4)))), inference(lemma,lemma(discharge,[]))).
% 28.34/18.56 tff(11299,plain,
% 28.34/18.56 (f6(c1, c1) = c1),
% 28.34/18.56 inference(unit_resolution,[status(thm)],[11298, 11014, 10752, 10740, 10742, 121, 2, 11129, 8607, 2602])).
% 28.34/18.56 tff(11300,plain,
% 28.34/18.56 (big_f(f7(c1), f6(c1, c1)) <=> big_f(c1, c1)),
% 28.34/18.56 inference(monotonicity,[status(thm)],[4234, 10030])).
% 28.34/18.56 tff(11301,plain,
% 28.34/18.56 (big_f(c1, c1) <=> big_f(f7(c1), f6(c1, c1))),
% 28.34/18.56 inference(symmetry,[status(thm)],[11300])).
% 28.34/18.56 tff(11302,plain,
% 28.34/18.56 (big_f(f7(c1), f6(c1, c1))),
% 28.34/18.56 inference(modus_ponens,[status(thm)],[4932, 11301])).
% 28.34/18.56 tff(11303,plain,
% 28.34/18.56 ($false),
% 28.34/18.56 inference(unit_resolution,[status(thm)],[65, 11302])).
% 28.34/18.56 tff(11304,plain,(big_f(f7(c1), f6(c1, c1)) | (~big_f(c1, c1)) | (~(f6(c1, c1) = c1)) | (~(f7(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.34/18.56 tff(11305,plain,
% 28.34/18.56 (big_f(f7(c1), f6(c1, c1))),
% 28.34/18.56 inference(unit_resolution,[status(thm)],[11304, 11129, 11299, 11014])).
% 28.34/18.56 tff(11306,plain,
% 28.34/18.56 (f6(f1(c2, c1), f1(c2, c1)) = c1),
% 28.34/18.56 inference(transitivity,[status(thm)],[11199, 10030])).
% 28.34/18.56 tff(11307,plain,
% 28.34/18.56 (big_f(f7(f1(c2, c1)), f6(f1(c2, c1), f1(c2, c1))) <=> big_f(c1, c1)),
% 28.34/18.56 inference(monotonicity,[status(thm)],[11104, 11306])).
% 28.34/18.56 tff(11308,plain,
% 28.34/18.56 (big_f(c1, c1) <=> big_f(f7(f1(c2, c1)), f6(f1(c2, c1), f1(c2, c1)))),
% 28.34/18.56 inference(symmetry,[status(thm)],[11307])).
% 28.34/18.56 tff(11309,plain,
% 28.34/18.56 (big_f(f7(f1(c2, c1)), f6(f1(c2, c1), f1(c2, c1)))),
% 28.34/18.56 inference(modus_ponens,[status(thm)],[4932, 11308])).
% 28.34/18.56 tff(11310,plain,
% 28.34/18.56 (f6(f1(c2, c1), f1(c2, c1)) = f1(c2, c1)),
% 28.34/18.56 inference(transitivity,[status(thm)],[11199, 10030, 875, 10762])).
% 28.34/18.56 tff(11311,plain,
% 28.34/18.56 (f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1)),
% 28.34/18.56 inference(transitivity,[status(thm)],[10945, 3949, 875, 10762])).
% 28.34/18.56 tff(11312,plain,
% 28.34/18.56 (f10(f1(c2, c1)) = c1),
% 28.34/18.56 inference(transitivity,[status(thm)],[10846, 3762])).
% 28.34/18.56 tff(11313,plain,
% 28.34/18.56 (f9(f1(c2, c1), f1(c2, c1)) = c1),
% 28.34/18.56 inference(transitivity,[status(thm)],[10945, 3949])).
% 28.34/18.56 tff(11314,plain,
% 28.34/18.56 (big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1))) <=> big_f(c1, c1)),
% 28.34/18.56 inference(monotonicity,[status(thm)],[11313, 11312])).
% 28.34/18.56 tff(11315,plain,
% 28.34/18.56 (big_f(c1, c1) <=> big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1)))),
% 28.34/18.56 inference(symmetry,[status(thm)],[11314])).
% 28.34/18.56 tff(11316,plain,
% 28.34/18.56 (big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1)))),
% 28.34/18.56 inference(modus_ponens,[status(thm)],[4932, 11315])).
% 28.34/18.56 tff(11317,plain,
% 28.34/18.56 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(f1(c2, c1)) = f1(c2, c1))) | (~big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1)))) | (~(f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))) | (~(f7(f1(c2, c1)) = f1(c2, c1))) | (~(f6(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))) | (~big_f(f7(f1(c2, c1)), f6(f1(c2, c1), f1(c2, c1)))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(f1(c2, c1)) = f1(c2, c1))) | (~big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1)))) | (~(f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))) | (~(f7(f1(c2, c1)) = f1(c2, c1))) | (~(f6(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))) | (~big_f(f7(f1(c2, c1)), f6(f1(c2, c1), f1(c2, c1)))))),
% 28.34/18.56 inference(rewrite,[status(thm)],[])).
% 28.34/18.56 tff(11318,plain,
% 28.34/18.56 (((~(f10(f1(c2, c1)) = f1(c2, c1))) | (~(f7(f1(c2, c1)) = f1(c2, c1))) | (~(f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))) | (~big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1)))) | (~(f6(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))) | (~big_f(f7(f1(c2, c1)), f6(f1(c2, c1), f1(c2, c1))))) <=> ((~(f10(f1(c2, c1)) = f1(c2, c1))) | (~big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1)))) | (~(f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))) | (~(f7(f1(c2, c1)) = f1(c2, c1))) | (~(f6(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))) | (~big_f(f7(f1(c2, c1)), f6(f1(c2, c1), f1(c2, c1)))))),
% 28.34/18.56 inference(rewrite,[status(thm)],[])).
% 28.34/18.56 tff(11319,plain,
% 28.34/18.56 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(f1(c2, c1)) = f1(c2, c1))) | (~(f7(f1(c2, c1)) = f1(c2, c1))) | (~(f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))) | (~big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1)))) | (~(f6(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))) | (~big_f(f7(f1(c2, c1)), f6(f1(c2, c1), f1(c2, c1)))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(f1(c2, c1)) = f1(c2, c1))) | (~big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1)))) | (~(f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))) | (~(f7(f1(c2, c1)) = f1(c2, c1))) | (~(f6(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))) | (~big_f(f7(f1(c2, c1)), f6(f1(c2, c1), f1(c2, c1))))))),
% 28.34/18.56 inference(monotonicity,[status(thm)],[11318])).
% 28.34/18.56 tff(11320,plain,
% 28.34/18.56 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(f1(c2, c1)) = f1(c2, c1))) | (~(f7(f1(c2, c1)) = f1(c2, c1))) | (~(f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))) | (~big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1)))) | (~(f6(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))) | (~big_f(f7(f1(c2, c1)), f6(f1(c2, c1), f1(c2, c1)))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(f1(c2, c1)) = f1(c2, c1))) | (~big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1)))) | (~(f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))) | (~(f7(f1(c2, c1)) = f1(c2, c1))) | (~(f6(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))) | (~big_f(f7(f1(c2, c1)), f6(f1(c2, c1), f1(c2, c1)))))),
% 28.34/18.56 inference(transitivity,[status(thm)],[11319, 11317])).
% 28.34/18.56 tff(11321,plain,
% 28.34/18.56 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(f1(c2, c1)) = f1(c2, c1))) | (~(f7(f1(c2, c1)) = f1(c2, c1))) | (~(f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))) | (~big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1)))) | (~(f6(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))) | (~big_f(f7(f1(c2, c1)), f6(f1(c2, c1), f1(c2, c1)))))),
% 28.34/18.56 inference(quant_inst,[status(thm)],[])).
% 28.34/18.56 tff(11322,plain,
% 28.34/18.56 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(f1(c2, c1)) = f1(c2, c1))) | (~big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1)))) | (~(f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))) | (~(f7(f1(c2, c1)) = f1(c2, c1))) | (~(f6(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))) | (~big_f(f7(f1(c2, c1)), f6(f1(c2, c1), f1(c2, c1))))),
% 28.34/18.56 inference(modus_ponens,[status(thm)],[11321, 11320])).
% 28.34/18.56 tff(11323,plain,
% 28.34/18.56 ((~big_f(f9(f1(c2, c1), f1(c2, c1)), f10(f1(c2, c1)))) | (~(f9(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))) | (~(f6(f1(c2, c1), f1(c2, c1)) = f1(c2, c1))) | (~big_f(f7(f1(c2, c1)), f6(f1(c2, c1), f1(c2, c1))))),
% 28.34/18.56 inference(unit_resolution,[status(thm)],[11322, 2378, 11109, 11265])).
% 28.34/18.56 tff(11324,plain,
% 28.34/18.56 ($false),
% 28.34/18.56 inference(unit_resolution,[status(thm)],[11323, 11316, 11311, 11310, 11309])).
% 28.34/18.56 tff(11325,plain,((~(f9(c1, c1) = c1)) | (~big_f(c1, c1)) | (~(f6(c1, c1) = c1)) | (~(f1(f7(f7(c2)), c1) = c1)) | (~(f7(c2) = c2)) | (~(f7(c1) = c1)) | (~(f10(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.34/18.56 tff(11326,plain,
% 28.34/18.56 (~(f9(c1, c1) = c1)),
% 28.34/18.56 inference(unit_resolution,[status(thm)],[11325, 11129, 11299, 10752, 10740, 11014, 11241])).
% 28.34/18.56 tff(11327,plain,
% 28.34/18.56 (big_f(f9(c1, c1), f10(c1))),
% 28.34/18.56 inference(unit_resolution,[status(thm)],[10042, 11326, 11241, 11299, 11305, 11014])).
% 28.34/18.56 tff(11328,plain,
% 28.34/18.56 (f9(c1, c1) = c2),
% 28.34/18.56 inference(unit_resolution,[status(thm)],[3939, 11326])).
% 28.34/18.56 tff(11329,plain,
% 28.34/18.56 (~big_f(f9(c1, c1), c1)),
% 28.34/18.56 inference(unit_resolution,[status(thm)],[10058, 11328, 2])).
% 28.34/18.56 tff(11330,plain,
% 28.34/18.56 ($false),
% 28.34/18.56 inference(unit_resolution,[status(thm)],[10033, 11329, 11327, 11241])).
% 28.34/18.56 tff(11331,plain,(big_f(c2, c1) | big_f(c2, c2) | (~(f10(c2) = c2)) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.34/18.56 tff(11332,plain,
% 28.34/18.56 (big_f(c2, c1)),
% 28.34/18.56 inference(unit_resolution,[status(thm)],[11331, 121, 122, 79])).
% 28.34/18.56 tff(11333,plain,
% 28.34/18.56 (big_f(f7(c1), f5(c1))),
% 28.34/18.56 inference(unit_resolution,[status(thm)],[8445, 1139, 122, 115, 121])).
% 28.34/18.56 tff(11334,plain,
% 28.34/18.56 (~(f5(c1) = c2)),
% 28.34/18.56 inference(unit_resolution,[status(thm)],[1715, 11333, 121, 120])).
% 28.34/18.56 tff(11335,plain,
% 28.34/18.56 (f5(c1) = c1),
% 28.34/18.56 inference(unit_resolution,[status(thm)],[1708, 11334])).
% 28.34/18.56 tff(11336,plain,
% 28.34/18.56 ((f6(c2, c1) = f5(c1)) <=> (f6(c2, c1) = c1)),
% 28.34/18.56 inference(monotonicity,[status(thm)],[11335])).
% 28.34/18.56 tff(11337,plain,
% 28.34/18.56 ((f6(c2, c1) = c1) <=> (f6(c2, c1) = f5(c1))),
% 28.34/18.56 inference(symmetry,[status(thm)],[11336])).
% 28.34/18.56 tff(11338,plain,
% 28.34/18.56 ((~(f6(c2, c1) = c1)) <=> (~(f6(c2, c1) = f5(c1)))),
% 28.34/18.56 inference(monotonicity,[status(thm)],[11337])).
% 28.34/18.56 tff(11339,plain,
% 28.34/18.56 (f6(c2, c1) = c1),
% 28.34/18.56 inference(unit_resolution,[status(thm)],[3211, 3197, 122, 77, 1139, 731])).
% 28.34/18.56 tff(11340,plain,
% 28.34/18.56 (big_f(f7(c2), f6(c2, c1)) <=> big_f(c2, c1)),
% 28.34/18.56 inference(monotonicity,[status(thm)],[77, 11339])).
% 28.34/18.56 tff(11341,plain,
% 28.34/18.56 (big_f(c2, c1) <=> big_f(f7(c2), f6(c2, c1))),
% 28.34/18.56 inference(symmetry,[status(thm)],[11340])).
% 28.34/18.56 tff(11342,plain,
% 28.34/18.56 (big_f(f7(c2), f6(c2, c1))),
% 28.34/18.56 inference(modus_ponens,[status(thm)],[348, 11341])).
% 28.34/18.56 tff(11343,plain,
% 28.34/18.56 ($false),
% 28.34/18.56 inference(unit_resolution,[status(thm)],[3197, 11342])).
% 28.34/18.56 tff(11344,plain,(big_f(f7(c2), f6(c2, c1)) | (~big_f(c2, c1)) | (~(f7(c2) = c2)) | (~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2))), inference(lemma,lemma(discharge,[]))).
% 28.34/18.56 tff(11345,plain,
% 28.34/18.56 (big_f(f7(c2), f6(c2, c1))),
% 28.34/18.56 inference(unit_resolution,[status(thm)],[11344, 1139, 77, 122, 348, 8282])).
% 28.34/18.56 tff(11346,plain,
% 28.34/18.56 (~(f6(c2, c1) = c1)),
% 28.34/18.56 inference(unit_resolution,[status(thm)],[3084, 11345, 122, 77, 1139, 8282])).
% 28.34/18.56 tff(11347,plain,
% 28.34/18.56 (~(f6(c2, c1) = f5(c1))),
% 28.34/18.56 inference(modus_ponens,[status(thm)],[11346, 11338])).
% 28.34/18.56 tff(11348,plain,
% 28.34/18.56 (big_f(f7(c1), f6(c2, c1)) <=> big_f(f7(c2), f6(c2, c1))),
% 28.34/18.56 inference(monotonicity,[status(thm)],[3229])).
% 28.34/18.56 tff(11349,plain,
% 28.34/18.56 (big_f(f7(c2), f6(c2, c1)) <=> big_f(f7(c1), f6(c2, c1))),
% 28.34/18.56 inference(symmetry,[status(thm)],[11348])).
% 28.34/18.56 tff(11350,plain,
% 28.34/18.56 (big_f(f7(c1), f6(c2, c1))),
% 28.34/18.56 inference(modus_ponens,[status(thm)],[11345, 11349])).
% 28.34/18.56 tff(11351,plain,
% 28.34/18.56 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(c1) = c1) | (~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (f6(c2, c1) = f5(c1)) | (~big_f(f7(c1), f6(c2, c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (f6(c2, c1) = f5(c1)) | (~big_f(f7(c1), f6(c2, c1))))),
% 28.34/18.56 inference(rewrite,[status(thm)],[])).
% 28.34/18.56 tff(11352,plain,
% 28.34/18.56 (((~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (f7(c1) = c1) | (f6(c2, c1) = f5(c1)) | (~big_f(f7(c1), f6(c2, c1)))) <=> ((f7(c1) = c1) | (~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (f6(c2, c1) = f5(c1)) | (~big_f(f7(c1), f6(c2, c1))))),
% 28.34/18.56 inference(rewrite,[status(thm)],[])).
% 28.34/18.56 tff(11353,plain,
% 28.34/18.56 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (f7(c1) = c1) | (f6(c2, c1) = f5(c1)) | (~big_f(f7(c1), f6(c2, c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(c1) = c1) | (~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (f6(c2, c1) = f5(c1)) | (~big_f(f7(c1), f6(c2, c1)))))),
% 28.34/18.56 inference(monotonicity,[status(thm)],[11352])).
% 28.34/18.56 tff(11354,plain,
% 28.34/18.56 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (f7(c1) = c1) | (f6(c2, c1) = f5(c1)) | (~big_f(f7(c1), f6(c2, c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (f6(c2, c1) = f5(c1)) | (~big_f(f7(c1), f6(c2, c1))))),
% 28.34/18.56 inference(transitivity,[status(thm)],[11353, 11351])).
% 28.34/18.56 tff(11355,plain,
% 28.34/18.56 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (f7(c1) = c1) | (f6(c2, c1) = f5(c1)) | (~big_f(f7(c1), f6(c2, c1))))),
% 28.34/18.56 inference(quant_inst,[status(thm)],[])).
% 28.34/18.56 tff(11356,plain,
% 28.34/18.56 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (f6(c2, c1) = f5(c1)) | (~big_f(f7(c1), f6(c2, c1)))),
% 28.34/18.56 inference(modus_ponens,[status(thm)],[11355, 11354])).
% 28.34/18.56 tff(11357,plain,
% 28.34/18.56 ((f6(c2, c1) = f5(c1)) | (~big_f(f7(c1), f6(c2, c1)))),
% 28.34/18.56 inference(unit_resolution,[status(thm)],[11356, 676, 115, 122, 1139, 8282])).
% 28.34/18.56 tff(11358,plain,
% 28.34/18.56 ($false),
% 28.34/18.56 inference(unit_resolution,[status(thm)],[11357, 11350, 11347])).
% 28.34/18.56 tff(11359,plain,((f9(c2, c1) = c1) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~big_f(c2, c1)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 28.34/18.56 tff(11360,plain,
% 28.34/18.56 (f9(c2, c1) = c1),
% 28.34/18.56 inference(unit_resolution,[status(thm)],[11359, 115, 122, 77, 348, 121])).
% 28.34/18.56 tff(11361,plain,
% 28.34/18.56 (~(c2 = f8(c1))),
% 28.34/18.56 inference(unit_resolution,[status(thm)],[3001, 3198, 77, 3, 8451, 3197])).
% 28.34/18.56 tff(11362,plain,
% 28.34/18.56 (~(f8(c1) = c2)),
% 28.34/18.56 inference(unit_resolution,[status(thm)],[1675, 11361])).
% 28.34/18.56 tff(11363,plain,
% 28.34/18.56 (f8(c1) = c1),
% 28.34/18.56 inference(unit_resolution,[status(thm)],[1680, 11362])).
% 28.34/18.56 tff(11364,plain,
% 28.34/18.56 (big_f(f9(c2, c1), f10(c2)) <=> big_f(c1, c2)),
% 28.34/18.56 inference(monotonicity,[status(thm)],[736, 122])).
% 28.34/18.56 tff(11365,plain,
% 28.34/18.56 (big_f(c1, c2) <=> big_f(f9(c2, c1), f10(c2))),
% 28.34/18.56 inference(symmetry,[status(thm)],[11364])).
% 28.34/18.56 tff(11366,plain,
% 28.34/18.56 (big_f(f8(c1), f10(c1)) <=> big_f(c1, c2)),
% 28.34/18.56 inference(monotonicity,[status(thm)],[3018, 15])).
% 28.34/18.56 tff(11367,plain,
% 28.34/18.56 (big_f(f8(c1), f10(c1)) <=> big_f(f9(c2, c1), f10(c2))),
% 28.34/18.56 inference(transitivity,[status(thm)],[11366, 11365])).
% 28.34/18.56 tff(11368,plain,
% 28.34/18.56 (big_f(f8(c1), f10(c1))),
% 28.34/18.56 inference(unit_resolution,[status(thm)],[2848, 10380, 115, 3])).
% 28.34/18.56 tff(11369,plain,
% 28.34/18.56 (big_f(f9(c2, c1), f10(c2))),
% 28.34/18.56 inference(modus_ponens,[status(thm)],[11368, 11367])).
% 28.34/18.56 tff(11370,plain,
% 28.34/18.56 ((~(c2 = f5(c1))) | (~big_f(f9(c2, c1), f10(c2)))),
% 28.34/18.56 inference(unit_resolution,[status(thm)],[2914, 783, 1726, 115, 122, 736])).
% 28.34/18.56 tff(11371,plain,
% 28.34/18.56 ($false),
% 28.34/18.56 inference(unit_resolution,[status(thm)],[11370, 11369, 1727])).
% 28.34/18.56 tff(11372,plain,((~(f5(c1) = c2)) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (~(f9(c2, c1) = c1)) | (~(f8(c1) = c1)) | (f10(c1) = c1) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 28.34/18.56 tff(11373,plain,
% 28.34/18.56 (~(f5(c1) = c2)),
% 28.34/18.56 inference(unit_resolution,[status(thm)],[11372, 11363, 122, 736, 115, 3, 121])).
% 28.34/18.56 tff(11374,plain,
% 28.34/18.56 (f5(c1) = c1),
% 28.34/18.56 inference(unit_resolution,[status(thm)],[1708, 11373])).
% 28.34/18.56 tff(11375,plain,
% 28.34/18.56 (f6(f7(c2), f5(c1)) = f6(c2, c1)),
% 28.34/18.56 inference(monotonicity,[status(thm)],[77, 11374])).
% 28.34/18.56 tff(11376,plain,
% 28.34/18.56 ((f6(f7(c2), f5(c1)) = c1) <=> (f6(c2, c1) = c1)),
% 28.34/18.56 inference(monotonicity,[status(thm)],[11375])).
% 28.34/18.56 tff(11377,plain,
% 28.34/18.56 ((f6(c2, c1) = c1) <=> (f6(f7(c2), f5(c1)) = c1)),
% 28.34/18.56 inference(symmetry,[status(thm)],[11376])).
% 28.34/18.56 tff(11378,plain,
% 28.34/18.56 ((~(f6(c2, c1) = c1)) <=> (~(f6(f7(c2), f5(c1)) = c1))),
% 28.34/18.56 inference(monotonicity,[status(thm)],[11377])).
% 28.34/18.56 tff(11379,plain,
% 28.34/18.56 (~(f6(f7(c2), f5(c1)) = c1)),
% 28.34/18.56 inference(modus_ponens,[status(thm)],[3198, 11378])).
% 28.34/18.56 tff(11380,plain,
% 28.34/18.56 (c1 = f8(c1)),
% 28.34/18.56 inference(unit_resolution,[status(thm)],[9808, 11363])).
% 28.34/18.56 tff(11381,plain,
% 28.34/18.56 (~big_f(c1, c2)),
% 28.34/18.56 inference(unit_resolution,[status(thm)],[3563, 11374, 122, 77, 736, 3197, 3198])).
% 28.34/18.56 tff(11382,plain,
% 28.34/18.56 (~big_f(c1, f10(c1))),
% 28.34/18.56 inference(modus_ponens,[status(thm)],[11381, 11164])).
% 28.34/18.56 tff(11383,plain,
% 28.34/18.56 (~(f6(f7(c2), f5(c1)) = c2)),
% 28.34/18.56 inference(unit_resolution,[status(thm)],[3049, 11382, 77, 121, 3, 11380, 11374])).
% 28.34/18.56 tff(11384,plain,
% 28.34/18.56 ($false),
% 28.34/18.56 inference(unit_resolution,[status(thm)],[2978, 11383, 11379])).
% 28.34/18.56 tff(11385,plain,((f6(c2, c1) = c1) | (~(f7(c2) = c2)) | big_f(c2, c2) | (f10(c1) = c1) | (~(f10(c2) = c2)) | (~(f9(c2, c1) = c1)) | big_f(f7(c2), f6(c2, c1)) | (f7(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 28.34/18.56 tff(11386,plain,
% 28.34/18.56 (f6(c2, c1) = c1),
% 28.34/18.56 inference(unit_resolution,[status(thm)],[11385, 3197, 121, 3, 122, 11360, 77, 115])).
% 28.34/18.56 tff(11387,plain,
% 28.34/18.56 (big_f(f7(c2), f6(c2, c1)) <=> big_f(c2, c1)),
% 28.34/18.56 inference(monotonicity,[status(thm)],[77, 11386])).
% 28.34/18.56 tff(11388,plain,
% 28.34/18.56 (big_f(c2, c1) <=> big_f(f7(c2), f6(c2, c1))),
% 28.34/18.56 inference(symmetry,[status(thm)],[11387])).
% 28.34/18.56 tff(11389,plain,
% 28.34/18.56 (big_f(f7(c2), f6(c2, c1))),
% 28.34/18.56 inference(modus_ponens,[status(thm)],[348, 11388])).
% 28.34/18.56 tff(11390,plain,
% 28.34/18.56 ($false),
% 28.34/18.56 inference(unit_resolution,[status(thm)],[3197, 11389])).
% 28.34/18.56 tff(11391,plain,(big_f(f7(c2), f6(c2, c1)) | (~big_f(c2, c1)) | (~(f7(c2) = c2)) | big_f(c2, c2) | (f10(c1) = c1) | (~(f10(c2) = c2)) | (f7(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 28.34/18.56 tff(11392,plain,
% 28.34/18.56 (big_f(f7(c2), f6(c2, c1))),
% 28.34/18.56 inference(unit_resolution,[status(thm)],[11391, 3, 10740, 121, 11332, 122, 115])).
% 28.34/18.56 tff(11393,plain,
% 28.34/18.56 (~(c3 = c2)),
% 28.34/18.56 inference(unit_resolution,[status(thm)],[3407, 3, 122, 79, 10740, 115])).
% 28.34/18.56 tff(11394,plain,
% 28.34/18.56 (c3 = c1),
% 28.34/18.56 inference(unit_resolution,[status(thm)],[180, 11393])).
% 28.34/18.56 tff(11395,plain,
% 28.34/18.56 (c1 = c3),
% 28.34/18.56 inference(symmetry,[status(thm)],[11394])).
% 28.34/18.56 tff(11396,plain,
% 28.34/18.56 (c2 = f7(c2)),
% 28.34/18.56 inference(symmetry,[status(thm)],[10740])).
% 28.34/18.56 tff(11397,plain,
% 28.34/18.56 (f6(c2, c1) = f6(f7(c2), c3)),
% 28.34/18.56 inference(monotonicity,[status(thm)],[11396, 11395])).
% 28.34/18.56 tff(11398,plain,
% 28.34/18.56 ((f6(c2, c1) = c1) <=> (f6(f7(c2), c3) = c1)),
% 28.34/18.56 inference(monotonicity,[status(thm)],[11397])).
% 28.34/18.56 tff(11399,plain,
% 28.34/18.56 ((f6(f7(c2), c3) = c1) <=> (f6(c2, c1) = c1)),
% 28.34/18.56 inference(symmetry,[status(thm)],[11398])).
% 28.34/18.56 tff(11400,plain,
% 28.34/18.56 (~(f6(f7(c2), c3) = c2)),
% 28.34/18.56 inference(unit_resolution,[status(thm)],[5848, 11392, 10740, 11394, 121])).
% 28.34/18.56 tff(11401,plain,
% 28.34/18.56 (f6(f7(c2), c3) = c1),
% 28.34/18.56 inference(unit_resolution,[status(thm)],[2391, 11400])).
% 28.34/18.56 tff(11402,plain,
% 28.34/18.56 (f6(c2, c1) = c1),
% 28.34/18.56 inference(modus_ponens,[status(thm)],[11401, 11399])).
% 28.34/18.56 tff(11403,plain,
% 28.34/18.56 (f9(c2, c1) = c1),
% 28.34/18.56 inference(unit_resolution,[status(thm)],[11359, 115, 122, 10740, 11332, 121])).
% 28.34/18.56 tff(11404,plain,
% 28.34/18.56 (~big_f(f9(c2, c1), f10(c2))),
% 28.34/18.56 inference(unit_resolution,[status(thm)],[3097, 2378, 122, 11403, 10740, 11402, 11392])).
% 28.34/18.56 tff(11405,plain,
% 28.34/18.56 (~big_f(c1, c2)),
% 28.34/18.56 inference(unit_resolution,[status(thm)],[3090, 11404, 122, 10740, 11402, 11392])).
% 28.34/18.56 tff(11406,plain,
% 28.34/18.56 (~big_f(c1, f10(c1))),
% 28.34/18.56 inference(modus_ponens,[status(thm)],[11405, 11164])).
% 28.34/18.56 tff(11407,plain,
% 28.34/18.56 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1))))),
% 28.34/18.56 inference(rewrite,[status(thm)],[])).
% 28.34/18.56 tff(11408,plain,
% 28.34/18.56 (((f10(c1) = c1) | big_f(c2, f10(c1)) | (~(f7(c2) = c2)) | (~(c2 = f8(c1))) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1)))) <=> (big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1))))),
% 28.34/18.56 inference(rewrite,[status(thm)],[])).
% 28.34/18.56 tff(11409,plain,
% 28.34/18.56 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | big_f(c2, f10(c1)) | (~(f7(c2) = c2)) | (~(c2 = f8(c1))) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1)))))),
% 28.34/18.56 inference(monotonicity,[status(thm)],[11408])).
% 28.34/18.56 tff(11410,plain,
% 28.34/18.56 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | big_f(c2, f10(c1)) | (~(f7(c2) = c2)) | (~(c2 = f8(c1))) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1))))),
% 28.34/18.56 inference(transitivity,[status(thm)],[11409, 11407])).
% 28.34/18.56 tff(11411,plain,
% 28.34/18.56 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | big_f(c2, f10(c1)) | (~(f7(c2) = c2)) | (~(c2 = f8(c1))) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1))))),
% 28.34/18.56 inference(quant_inst,[status(thm)],[])).
% 28.34/18.56 tff(11412,plain,
% 28.34/18.56 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1)))),
% 28.34/18.56 inference(modus_ponens,[status(thm)],[11411, 11410])).
% 28.34/18.56 tff(11413,plain,
% 28.34/18.56 (~(c2 = f8(c1))),
% 28.34/18.56 inference(unit_resolution,[status(thm)],[11412, 2963, 8451, 3, 10740, 11402, 11392])).
% 28.34/18.56 tff(11414,plain,
% 28.34/18.56 (~(f8(c1) = c2)),
% 28.34/18.56 inference(unit_resolution,[status(thm)],[1675, 11413])).
% 28.34/18.56 tff(11415,plain,
% 28.34/18.56 (f8(c1) = c1),
% 28.34/18.56 inference(unit_resolution,[status(thm)],[1680, 11414])).
% 28.34/18.56 tff(11416,plain,
% 28.34/18.56 (c1 = f8(c1)),
% 28.34/18.56 inference(unit_resolution,[status(thm)],[9808, 11415])).
% 28.34/18.56 tff(11417,plain,
% 28.34/18.56 ($false),
% 28.34/18.56 inference(unit_resolution,[status(thm)],[3064, 2963, 3, 10740, 11402, 11392, 11416, 11406])).
% 28.34/18.56 tff(11418,plain,((f10(c1) = c1) | (~(f10(c2) = c2)) | big_f(c2, c2) | (f7(c1) = c1) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.34/18.56 tff(11419,plain,
% 28.34/18.56 (f10(c1) = c1),
% 28.34/18.56 inference(unit_resolution,[status(thm)],[11418, 115, 121, 122, 79])).
% 28.34/18.56 tff(11420,plain,
% 28.34/18.56 ((~big_f(f9(c2, c1), f10(c2))) <=> (~big_f(c1, c2))),
% 28.34/18.56 inference(monotonicity,[status(thm)],[11364])).
% 28.34/18.56 tff(11421,plain,
% 28.34/18.56 (~big_f(f9(c2, c1), f10(c2))),
% 28.34/18.56 inference(unit_resolution,[status(thm)],[3225, 2409, 122, 736, 10740, 3198, 3197])).
% 28.34/18.56 tff(11422,plain,
% 28.34/18.56 (~big_f(c1, c2)),
% 28.34/18.56 inference(modus_ponens,[status(thm)],[11421, 11420])).
% 28.34/18.57 tff(11423,plain,
% 28.34/18.57 (big_f(f9(c1, c2), f10(c1)) <=> big_f(c2, c1)),
% 28.34/18.57 inference(monotonicity,[status(thm)],[3764, 3762])).
% 28.34/18.57 tff(11424,plain,
% 28.34/18.57 (big_f(c2, c1) <=> big_f(f9(c1, c2), f10(c1))),
% 28.34/18.57 inference(symmetry,[status(thm)],[11423])).
% 28.34/18.57 tff(11425,plain,
% 28.34/18.57 (big_f(f9(c1, c2), f10(c1))),
% 28.34/18.57 inference(modus_ponens,[status(thm)],[348, 11424])).
% 28.34/18.57 tff(11426,plain,
% 28.34/18.57 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (~(f10(c1) = c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (~(f10(c1) = c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2)))),
% 28.34/18.57 inference(rewrite,[status(thm)],[])).
% 28.34/18.57 tff(11427,plain,
% 28.34/18.57 (((~(f10(c1) = c1)) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (~(f9(c1, c2) = c2)) | (~big_f(f9(c1, c2), f10(c1)))) <=> ((~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (~(f10(c1) = c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2)))),
% 28.34/18.57 inference(rewrite,[status(thm)],[])).
% 28.34/18.57 tff(11428,plain,
% 28.34/18.57 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c1) = c1)) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (~(f9(c1, c2) = c2)) | (~big_f(f9(c1, c2), f10(c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (~(f10(c1) = c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2))))),
% 28.34/18.57 inference(monotonicity,[status(thm)],[11427])).
% 28.34/18.57 tff(11429,plain,
% 28.34/18.57 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c1) = c1)) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (~(f9(c1, c2) = c2)) | (~big_f(f9(c1, c2), f10(c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (~(f10(c1) = c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2)))),
% 28.34/18.57 inference(transitivity,[status(thm)],[11428, 11426])).
% 28.34/18.57 tff(11430,plain,
% 28.34/18.57 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c1) = c1)) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (~(f9(c1, c2) = c2)) | (~big_f(f9(c1, c2), f10(c1))))),
% 28.34/18.57 inference(quant_inst,[status(thm)],[])).
% 28.34/18.57 tff(11431,plain,
% 28.34/18.57 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (~(f10(c1) = c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2))),
% 28.34/18.57 inference(modus_ponens,[status(thm)],[11430, 11429])).
% 28.34/18.57 tff(11432,plain,
% 28.34/18.57 ((~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (~(f10(c1) = c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2))),
% 28.34/18.57 inference(unit_resolution,[status(thm)],[11431, 2409])).
% 28.34/18.57 tff(11433,plain,
% 28.34/18.57 (~big_f(f9(c1, c2), f10(c1))),
% 28.34/18.57 inference(unit_resolution,[status(thm)],[11432, 3764, 77, 3762, 3197, 3198])).
% 28.34/18.57 tff(11434,plain,
% 28.34/18.57 ($false),
% 28.34/18.57 inference(unit_resolution,[status(thm)],[11433, 11425])).
% 28.34/18.57 tff(11435,plain,((~(f9(c1, c2) = c2)) | (~big_f(c2, c1)) | (~(f10(c1) = c1)) | (~(f7(c2) = c2)) | big_f(f7(c2), f6(c2, c1)) | (f6(c2, c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 28.34/18.57 tff(11436,plain,
% 28.34/18.57 (~(f9(c1, c2) = c2)),
% 28.34/18.57 inference(unit_resolution,[status(thm)],[11435, 3198, 3762, 10740, 3197, 11332])).
% 28.34/18.57 tff(11437,plain,
% 28.34/18.57 (f9(c1, c2) = c1),
% 28.34/18.57 inference(unit_resolution,[status(thm)],[3791, 11436])).
% 28.34/18.57 tff(11438,plain,
% 28.34/18.57 (big_f(f9(c1, c2), f10(c1)) <=> big_f(c1, c1)),
% 28.34/18.57 inference(monotonicity,[status(thm)],[11437, 3762])).
% 28.34/18.57 tff(11439,plain,
% 28.34/18.57 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)))),
% 28.34/18.57 inference(rewrite,[status(thm)],[])).
% 28.34/18.57 tff(11440,plain,
% 28.34/18.57 (((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1))) <=> ((~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)))),
% 28.34/18.57 inference(rewrite,[status(thm)],[])).
% 28.34/18.57 tff(11441,plain,
% 28.34/18.57 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1))))),
% 28.34/18.57 inference(monotonicity,[status(thm)],[11440])).
% 28.34/18.57 tff(11442,plain,
% 28.34/18.57 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)))),
% 28.34/18.57 inference(transitivity,[status(thm)],[11441, 11439])).
% 28.34/18.57 tff(11443,plain,
% 28.34/18.57 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)))),
% 28.34/18.57 inference(quant_inst,[status(thm)],[])).
% 28.34/18.57 tff(11444,plain,
% 28.34/18.57 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1))),
% 28.34/18.57 inference(modus_ponens,[status(thm)],[11443, 11442])).
% 28.34/18.57 tff(11445,plain,
% 28.34/18.57 (big_f(f9(c1, c2), f10(c1))),
% 28.34/18.57 inference(unit_resolution,[status(thm)],[11444, 2492, 3762, 10740, 3198, 3197, 11436])).
% 28.34/18.57 tff(11446,plain,
% 28.34/18.57 (big_f(c1, c1)),
% 28.34/18.57 inference(modus_ponens,[status(thm)],[11445, 11438])).
% 28.34/18.57 tff(11447,plain,
% 28.34/18.57 ((f7(f7(c2)) = c3) <=> (c2 = c3)),
% 28.34/18.57 inference(monotonicity,[status(thm)],[5429])).
% 28.34/18.57 tff(11448,plain,
% 28.34/18.57 ((c2 = c3) <=> (f7(f7(c2)) = c3)),
% 28.34/18.57 inference(symmetry,[status(thm)],[11447])).
% 28.34/18.57 tff(11449,plain,
% 28.34/18.57 ((c2 = c3) <=> (c2 = c1)),
% 28.34/18.57 inference(monotonicity,[status(thm)],[172])).
% 28.34/18.57 tff(11450,plain,
% 28.34/18.57 ((c2 = c1) <=> (c2 = c3)),
% 28.34/18.57 inference(symmetry,[status(thm)],[11449])).
% 28.34/18.57 tff(11451,plain,
% 28.34/18.57 ((c2 = c1) <=> (f7(f7(c2)) = c3)),
% 28.34/18.57 inference(transitivity,[status(thm)],[11450, 11448])).
% 28.34/18.57 tff(11452,plain,
% 28.34/18.57 ((~(c2 = c1)) <=> (~(f7(f7(c2)) = c3))),
% 28.34/18.57 inference(monotonicity,[status(thm)],[11451])).
% 28.34/18.57 tff(11453,plain,
% 28.34/18.57 (~(f7(f7(c2)) = c3)),
% 28.34/18.57 inference(modus_ponens,[status(thm)],[75, 11452])).
% 28.34/18.57 tff(11454,plain,
% 28.34/18.57 ((~(c2 = c1)) <=> (~(c2 = c3))),
% 28.34/18.57 inference(monotonicity,[status(thm)],[11450])).
% 28.34/18.57 tff(11455,plain,
% 28.34/18.57 (~(c2 = c3)),
% 28.34/18.57 inference(modus_ponens,[status(thm)],[75, 11454])).
% 28.34/18.57 tff(11456,plain,
% 28.34/18.57 (big_f(f4(c4), c4)),
% 28.34/18.57 inference(unit_resolution,[status(thm)],[5433, 380, 77, 378, 121])).
% 28.34/18.57 tff(11457,plain,
% 28.34/18.57 (~(c4 = c2)),
% 28.34/18.57 inference(unit_resolution,[status(thm)],[476, 11456, 79, 121])).
% 28.34/18.57 tff(11458,plain,
% 28.34/18.57 (c4 = c1),
% 28.34/18.57 inference(unit_resolution,[status(thm)],[461, 11457])).
% 28.34/18.57 tff(11459,plain,
% 28.34/18.57 (c1 = c4),
% 28.34/18.57 inference(symmetry,[status(thm)],[11458])).
% 28.34/18.57 tff(11460,plain,
% 28.34/18.57 (f4(c1) = f4(c4)),
% 28.34/18.57 inference(monotonicity,[status(thm)],[11459])).
% 28.34/18.57 tff(11461,plain,
% 28.34/18.57 (f4(c1) = c2),
% 28.34/18.57 inference(transitivity,[status(thm)],[11460, 79])).
% 28.34/18.57 tff(11462,plain,
% 28.34/18.57 ((c1 = f4(c1)) <=> (c1 = c2)),
% 28.34/18.57 inference(monotonicity,[status(thm)],[11461])).
% 28.34/18.57 tff(11463,plain,
% 28.34/18.57 ((c1 = f4(c1)) <=> (c2 = c1)),
% 28.34/18.57 inference(transitivity,[status(thm)],[11462, 1])).
% 28.34/18.57 tff(11464,plain,
% 28.34/18.57 ((c2 = c1) <=> (c1 = f4(c1))),
% 28.34/18.57 inference(symmetry,[status(thm)],[11463])).
% 28.34/18.57 tff(11465,plain,
% 28.34/18.57 ((~(c2 = c1)) <=> (~(c1 = f4(c1)))),
% 28.34/18.57 inference(monotonicity,[status(thm)],[11464])).
% 28.34/18.57 tff(11466,plain,
% 28.34/18.57 (~(c1 = f4(c1))),
% 28.34/18.57 inference(modus_ponens,[status(thm)],[75, 11465])).
% 28.34/18.57 tff(11467,plain,
% 28.34/18.57 ((f1(c2, c1) = c1) <=> (c2 = c1)),
% 28.34/18.57 inference(monotonicity,[status(thm)],[5423])).
% 28.34/18.57 tff(11468,plain,
% 28.34/18.57 ((c2 = c1) <=> (f1(c2, c1) = c1)),
% 28.34/18.57 inference(symmetry,[status(thm)],[11467])).
% 28.34/18.57 tff(11469,plain,
% 28.34/18.57 ((~(c2 = c1)) <=> (~(f1(c2, c1) = c1))),
% 28.34/18.57 inference(monotonicity,[status(thm)],[11468])).
% 28.34/18.57 tff(11470,plain,
% 28.34/18.57 (~(f1(c2, c1) = c1)),
% 28.34/18.57 inference(modus_ponens,[status(thm)],[75, 11469])).
% 28.34/18.57 tff(11471,plain,
% 28.34/18.57 (c1 = c4),
% 28.34/18.57 inference(unit_resolution,[status(thm)],[484, 11458])).
% 28.34/18.57 tff(11472,plain,
% 28.34/18.57 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)))),
% 28.34/18.57 inference(rewrite,[status(thm)],[])).
% 28.34/18.57 tff(11473,plain,
% 28.34/18.57 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)))),
% 28.34/18.57 inference(quant_inst,[status(thm)],[])).
% 28.34/18.57 tff(11474,plain,
% 28.34/18.57 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1))),
% 28.34/18.57 inference(modus_ponens,[status(thm)],[11473, 11472])).
% 28.34/18.57 tff(11475,plain,
% 28.34/18.57 ($false),
% 28.34/18.57 inference(unit_resolution,[status(thm)],[11474, 525, 11471, 377, 11470, 5427, 11466, 4932])).
% 28.34/18.57 tff(11476,plain,((f1(f7(f7(c2)), c1) = c1) | (c2 = c3) | (~big_f(c1, c1)) | (~(f4(c4) = c2)) | big_f(c2, c2) | (~(f7(c2) = c2)) | (f7(f7(c2)) = c3)), inference(lemma,lemma(discharge,[]))).
% 28.34/18.57 tff(11477,plain,
% 28.34/18.57 (f1(f7(f7(c2)), c1) = c1),
% 28.34/18.57 inference(unit_resolution,[status(thm)],[11476, 11455, 4932, 79, 121, 77, 11453])).
% 28.34/18.57 tff(11478,plain,
% 28.34/18.57 (f1(c2, c1) = c1),
% 28.34/18.57 inference(transitivity,[status(thm)],[5422, 11477])).
% 28.34/18.57 tff(11479,plain,
% 28.34/18.57 (big_f(c2, f1(c2, c1)) <=> big_f(c2, c1)),
% 28.34/18.57 inference(monotonicity,[status(thm)],[11478])).
% 28.34/18.57 tff(11480,plain,
% 28.34/18.57 (big_f(c2, c1) <=> big_f(c2, f1(c2, c1))),
% 28.34/18.57 inference(symmetry,[status(thm)],[11479])).
% 28.34/18.57 tff(11481,plain,
% 28.34/18.57 (big_f(c2, f1(c2, c1))),
% 28.34/18.57 inference(modus_ponens,[status(thm)],[348, 11480])).
% 28.34/18.57 tff(11482,plain,
% 28.34/18.57 ((f1(f7(f7(c2)), c1) = c1) <=> (f1(c2, c1) = c1)),
% 28.34/18.57 inference(monotonicity,[status(thm)],[5428])).
% 28.34/18.57 tff(11483,plain,
% 28.34/18.57 (f1(c2, c1) = c1),
% 28.34/18.57 inference(modus_ponens,[status(thm)],[11477, 11482])).
% 28.34/18.57 tff(11484,assumption,(big_f(c2, f1(c2, c1))), introduced(assumption)).
% 28.34/18.57 tff(11485,assumption,(f1(c2, c1) = c1), introduced(assumption)).
% 28.34/18.57 tff(11486,plain,
% 28.34/18.57 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1)))),
% 28.34/18.57 inference(rewrite,[status(thm)],[])).
% 28.34/18.57 tff(11487,plain,
% 28.34/18.57 (((c2 = c3) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))) | (~(f1(c2, c1) = c1)) | (~big_f(c2, f1(c2, c1)))) <=> ((c2 = c3) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1)))),
% 28.34/18.57 inference(rewrite,[status(thm)],[])).
% 28.34/18.57 tff(11488,plain,
% 28.34/18.57 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))) | (~(f1(c2, c1) = c1)) | (~big_f(c2, f1(c2, c1))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1))))),
% 28.34/18.57 inference(monotonicity,[status(thm)],[11487])).
% 28.34/18.57 tff(11489,plain,
% 28.34/18.57 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))) | (~(f1(c2, c1) = c1)) | (~big_f(c2, f1(c2, c1))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1)))),
% 28.34/18.57 inference(transitivity,[status(thm)],[11488, 11486])).
% 28.34/18.57 tff(11490,plain,
% 28.34/18.57 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))) | (~(f1(c2, c1) = c1)) | (~big_f(c2, f1(c2, c1))))),
% 28.34/18.57 inference(quant_inst,[status(thm)],[])).
% 28.34/18.57 tff(11491,plain,
% 28.34/18.57 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1))),
% 28.34/18.57 inference(modus_ponens,[status(thm)],[11490, 11489])).
% 28.34/18.57 tff(11492,plain,
% 28.34/18.57 ((~(c2 = c4)) | (~(c2 = f4(c2)))),
% 28.34/18.57 inference(unit_resolution,[status(thm)],[11491, 447, 121, 377, 11485, 11484])).
% 28.34/18.57 tff(11493,plain,
% 28.34/18.57 ($false),
% 28.34/18.57 inference(unit_resolution,[status(thm)],[11492, 437, 432])).
% 28.34/18.57 tff(11494,plain,((~(c4 = c2)) | big_f(c2, c2) | (c2 = c3) | (~(f1(c2, c1) = c1)) | (~big_f(c2, f1(c2, c1))) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.34/18.57 tff(11495,plain,
% 28.34/18.57 (~(c4 = c2)),
% 28.34/18.57 inference(unit_resolution,[status(thm)],[11494, 11455, 121, 11483, 11481, 79])).
% 28.34/18.57 tff(11496,plain,
% 28.34/18.57 (c4 = c1),
% 28.34/18.57 inference(unit_resolution,[status(thm)],[461, 11495])).
% 28.34/18.57 tff(11497,plain,
% 28.34/18.57 (c1 = c4),
% 28.34/18.57 inference(unit_resolution,[status(thm)],[484, 11496])).
% 28.34/18.57 tff(11498,plain,
% 28.34/18.57 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1)))),
% 28.34/18.57 inference(rewrite,[status(thm)],[])).
% 28.34/18.57 tff(11499,plain,
% 28.34/18.57 (((c2 = c3) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (~(f1(c2, c1) = c1)) | (~big_f(c2, f1(c2, c1)))) <=> ((c2 = c3) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1)))),
% 28.34/18.57 inference(rewrite,[status(thm)],[])).
% 28.34/18.57 tff(11500,plain,
% 28.34/18.57 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (~(f1(c2, c1) = c1)) | (~big_f(c2, f1(c2, c1))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1))))),
% 28.34/18.57 inference(monotonicity,[status(thm)],[11499])).
% 28.34/18.57 tff(11501,plain,
% 28.34/18.57 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (~(f1(c2, c1) = c1)) | (~big_f(c2, f1(c2, c1))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1)))),
% 28.34/18.57 inference(transitivity,[status(thm)],[11500, 11498])).
% 28.34/18.57 tff(11502,plain,
% 28.34/18.57 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (~(f1(c2, c1) = c1)) | (~big_f(c2, f1(c2, c1))))),
% 28.34/18.57 inference(quant_inst,[status(thm)],[])).
% 28.34/18.57 tff(11503,plain,
% 28.34/18.57 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1))),
% 28.34/18.57 inference(modus_ponens,[status(thm)],[11502, 11501])).
% 28.34/18.57 tff(11504,plain,
% 28.34/18.57 ((~(c1 = c4)) | (c1 = f4(c1))),
% 28.34/18.57 inference(unit_resolution,[status(thm)],[11503, 553, 11455, 11483, 11481, 4932])).
% 28.34/18.57 tff(11505,plain,
% 28.34/18.57 (c1 = f4(c1)),
% 28.34/18.57 inference(unit_resolution,[status(thm)],[11504, 11497])).
% 28.34/18.57 tff(11506,plain,
% 28.34/18.57 (f4(c1) = c1),
% 28.34/18.57 inference(symmetry,[status(thm)],[11505])).
% 28.34/18.57 tff(11507,plain,
% 28.34/18.57 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c1 = c4)) | (~big_f(c2, c1)) | (c2 = f4(c1)) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(c1 = c4)) | (~big_f(c2, c1)) | (c2 = f4(c1)) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1)))),
% 28.34/18.58 inference(rewrite,[status(thm)],[])).
% 28.34/18.58 tff(11508,plain,
% 28.34/18.58 (((c2 = c3) | (~(c1 = c4)) | (c2 = f4(c1)) | (~big_f(c2, c1)) | (~(f1(c2, c1) = c1)) | (~big_f(c2, f1(c2, c1)))) <=> ((c2 = c3) | (~(c1 = c4)) | (~big_f(c2, c1)) | (c2 = f4(c1)) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1)))),
% 28.34/18.58 inference(rewrite,[status(thm)],[])).
% 28.34/18.58 tff(11509,plain,
% 28.34/18.58 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c1 = c4)) | (c2 = f4(c1)) | (~big_f(c2, c1)) | (~(f1(c2, c1) = c1)) | (~big_f(c2, f1(c2, c1))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c1 = c4)) | (~big_f(c2, c1)) | (c2 = f4(c1)) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1))))),
% 28.34/18.58 inference(monotonicity,[status(thm)],[11508])).
% 28.34/18.58 tff(11510,plain,
% 28.34/18.58 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c1 = c4)) | (c2 = f4(c1)) | (~big_f(c2, c1)) | (~(f1(c2, c1) = c1)) | (~big_f(c2, f1(c2, c1))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(c1 = c4)) | (~big_f(c2, c1)) | (c2 = f4(c1)) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1)))),
% 28.34/18.58 inference(transitivity,[status(thm)],[11509, 11507])).
% 28.34/18.58 tff(11511,plain,
% 28.34/18.58 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c1 = c4)) | (c2 = f4(c1)) | (~big_f(c2, c1)) | (~(f1(c2, c1) = c1)) | (~big_f(c2, f1(c2, c1))))),
% 28.34/18.58 inference(quant_inst,[status(thm)],[])).
% 28.34/18.58 tff(11512,plain,
% 28.34/18.58 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(c1 = c4)) | (~big_f(c2, c1)) | (c2 = f4(c1)) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1))),
% 28.34/18.58 inference(modus_ponens,[status(thm)],[11511, 11510])).
% 28.34/18.58 tff(11513,plain,
% 28.34/18.58 ((~(c1 = c4)) | (c2 = f4(c1))),
% 28.34/18.58 inference(unit_resolution,[status(thm)],[11512, 553, 11455, 11483, 11481, 348])).
% 28.34/18.58 tff(11514,plain,
% 28.34/18.58 (c2 = f4(c1)),
% 28.34/18.58 inference(unit_resolution,[status(thm)],[11513, 11497])).
% 28.34/18.58 tff(11515,plain,
% 28.34/18.58 (c2 = c1),
% 28.34/18.58 inference(transitivity,[status(thm)],[11514, 11506])).
% 28.34/18.58 tff(11516,plain,
% 28.34/18.58 ($false),
% 28.34/18.58 inference(unit_resolution,[status(thm)],[75, 11515])).
% 28.34/18.58 tff(11517,plain,((~(c3 = c1)) | (~big_f(c1, c1)) | (~big_f(c2, c1)) | big_f(c2, c2) | (~(f4(c4) = c2)) | (~(f7(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.34/18.58 tff(11518,plain,
% 28.34/18.58 (~(c3 = c1)),
% 28.34/18.58 inference(unit_resolution,[status(thm)],[11517, 11446, 11332, 121, 79, 10740])).
% 28.34/18.58 tff(11519,plain,
% 28.34/18.58 (~(c1 = c3)),
% 28.34/18.58 inference(modus_ponens,[status(thm)],[11518, 648])).
% 28.34/18.58 tff(11520,plain,
% 28.34/18.58 ((c1 = f4(c1)) <=> (c1 = c2)),
% 28.34/18.58 inference(monotonicity,[status(thm)],[569])).
% 28.34/18.58 tff(11521,plain,
% 28.34/18.58 ((c1 = f4(c1)) <=> (c2 = c1)),
% 28.34/18.58 inference(transitivity,[status(thm)],[11520, 1])).
% 28.34/18.58 tff(11522,plain,
% 28.34/18.58 ((c2 = c1) <=> (c1 = f4(c1))),
% 28.34/18.58 inference(symmetry,[status(thm)],[11521])).
% 28.34/18.58 tff(11523,plain,
% 28.34/18.58 ((~(c2 = c1)) <=> (~(c1 = f4(c1)))),
% 28.34/18.58 inference(monotonicity,[status(thm)],[11522])).
% 28.34/18.58 tff(11524,plain,
% 28.34/18.58 (~(c1 = f4(c1))),
% 28.34/18.58 inference(modus_ponens,[status(thm)],[75, 11523])).
% 28.34/18.58 tff(11525,assumption,(~(c1 = f4(c1))), introduced(assumption)).
% 28.34/18.58 tff(11526,assumption,(c1 = c4), introduced(assumption)).
% 28.34/18.58 tff(11527,plain,
% 28.34/18.58 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((f1(c1, c1) = c1) | (c1 = c3) | big_f(c1, f1(c1, c1)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (f1(c1, c1) = c1) | (c1 = c3) | big_f(c1, f1(c1, c1)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)))),
% 28.34/18.58 inference(rewrite,[status(thm)],[])).
% 28.34/18.58 tff(11528,plain,
% 28.34/18.58 (((c1 = c3) | (f1(c1, c1) = c1) | big_f(c1, f1(c1, c1)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1))) <=> ((f1(c1, c1) = c1) | (c1 = c3) | big_f(c1, f1(c1, c1)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)))),
% 28.34/18.58 inference(rewrite,[status(thm)],[])).
% 28.34/18.58 tff(11529,plain,
% 28.34/18.58 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c1 = c3) | (f1(c1, c1) = c1) | big_f(c1, f1(c1, c1)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((f1(c1, c1) = c1) | (c1 = c3) | big_f(c1, f1(c1, c1)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1))))),
% 28.34/18.58 inference(monotonicity,[status(thm)],[11528])).
% 28.34/18.58 tff(11530,plain,
% 28.34/18.58 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c1 = c3) | (f1(c1, c1) = c1) | big_f(c1, f1(c1, c1)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (f1(c1, c1) = c1) | (c1 = c3) | big_f(c1, f1(c1, c1)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)))),
% 28.34/18.58 inference(transitivity,[status(thm)],[11529, 11527])).
% 28.34/18.58 tff(11531,plain,
% 28.34/18.58 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c1 = c3) | (f1(c1, c1) = c1) | big_f(c1, f1(c1, c1)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)))),
% 28.34/18.58 inference(quant_inst,[status(thm)],[])).
% 28.34/18.58 tff(11532,plain,
% 28.34/18.58 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (f1(c1, c1) = c1) | (c1 = c3) | big_f(c1, f1(c1, c1)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1))),
% 28.34/18.58 inference(modus_ponens,[status(thm)],[11531, 11530])).
% 28.34/18.58 tff(11533,plain,
% 28.34/18.58 ($false),
% 28.34/18.58 inference(unit_resolution,[status(thm)],[11532, 525, 9679, 168, 11526, 9673, 11525, 4932])).
% 28.34/18.58 tff(11534,plain,(big_f(c1, f1(c1, c1)) | (c1 = c3) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1))), inference(lemma,lemma(discharge,[]))).
% 28.34/18.58 tff(11535,plain,
% 28.34/18.58 (big_f(c1, f1(c1, c1))),
% 28.34/18.58 inference(unit_resolution,[status(thm)],[11534, 564, 168, 11524, 4932])).
% 28.34/18.58 tff(11536,plain,
% 28.34/18.58 (~(f1(c1, c1) = c2)),
% 28.34/18.58 inference(unit_resolution,[status(thm)],[4561, 11535, 27])).
% 28.34/18.58 tff(11537,plain,
% 28.34/18.58 (f1(c1, c1) = c1),
% 28.34/18.58 inference(unit_resolution,[status(thm)],[601, 11536])).
% 28.34/18.58 tff(11538,plain,
% 28.34/18.58 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)))),
% 28.34/18.58 inference(rewrite,[status(thm)],[])).
% 28.34/18.58 tff(11539,plain,
% 28.34/18.58 (((c1 = c3) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1)))) <=> ((c1 = c3) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)))),
% 28.34/18.58 inference(rewrite,[status(thm)],[])).
% 28.34/18.58 tff(11540,plain,
% 28.34/18.58 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1))))),
% 28.34/18.58 inference(monotonicity,[status(thm)],[11539])).
% 28.34/18.58 tff(11541,plain,
% 28.34/18.58 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)))),
% 28.34/18.58 inference(transitivity,[status(thm)],[11540, 11538])).
% 28.34/18.58 tff(11542,plain,
% 28.34/18.58 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))))),
% 28.34/18.58 inference(quant_inst,[status(thm)],[])).
% 28.34/18.58 tff(11543,plain,
% 28.34/18.58 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1))),
% 28.34/18.58 inference(modus_ponens,[status(thm)],[11542, 11541])).
% 28.34/18.58 tff(11544,plain,
% 28.34/18.58 ($false),
% 28.34/18.58 inference(unit_resolution,[status(thm)],[11543, 553, 11537, 168, 564, 11535, 11524, 4932])).
% 28.34/18.58 tff(11545,plain,((~(c4 = c1)) | (c1 = c3) | (~big_f(c1, c1)) | big_f(c1, c2) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.34/18.58 tff(11546,plain,
% 28.34/18.58 (~(c4 = c1)),
% 28.34/18.58 inference(unit_resolution,[status(thm)],[11545, 11519, 11446, 11422, 79])).
% 28.34/18.58 tff(11547,plain,
% 28.34/18.58 (c4 = c2),
% 28.34/18.58 inference(unit_resolution,[status(thm)],[461, 11546])).
% 28.34/18.58 tff(11548,plain,
% 28.34/18.58 (c2 = c4),
% 28.34/18.58 inference(symmetry,[status(thm)],[11547])).
% 28.34/18.58 tff(11549,plain,
% 28.34/18.58 (f4(c2) = f4(c4)),
% 28.34/18.58 inference(monotonicity,[status(thm)],[11548])).
% 28.34/18.58 tff(11550,plain,
% 28.34/18.58 (f4(c4) = f4(c2)),
% 28.34/18.58 inference(symmetry,[status(thm)],[11549])).
% 28.34/18.58 tff(11551,plain,
% 28.34/18.58 (c2 = f4(c2)),
% 28.34/18.58 inference(transitivity,[status(thm)],[436, 11550])).
% 28.34/18.58 tff(11552,plain,
% 28.34/18.58 (c2 = c4),
% 28.34/18.58 inference(modus_ponens,[status(thm)],[11547, 159])).
% 28.34/18.58 tff(11553,plain,
% 28.34/18.58 (f1(c1, c1) = c1),
% 28.34/18.58 inference(unit_resolution,[status(thm)],[9763, 11552, 121, 11519, 11422, 11551])).
% 28.34/18.58 tff(11554,plain,
% 28.34/18.58 (big_f(c1, f1(c1, c1))),
% 28.34/18.58 inference(unit_resolution,[status(thm)],[9678, 11553, 11446])).
% 28.34/18.58 tff(11555,plain,
% 28.34/18.58 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))))),
% 28.34/18.58 inference(rewrite,[status(thm)],[])).
% 28.34/18.58 tff(11556,plain,
% 28.34/18.58 (((c1 = c3) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1)))) <=> ((c1 = c3) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))))),
% 28.34/18.58 inference(rewrite,[status(thm)],[])).
% 28.34/18.58 tff(11557,plain,
% 28.34/18.58 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1)))))),
% 28.34/18.58 inference(monotonicity,[status(thm)],[11556])).
% 28.34/18.58 tff(11558,plain,
% 28.34/18.58 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))))),
% 28.34/18.58 inference(transitivity,[status(thm)],[11557, 11555])).
% 28.34/18.58 tff(11559,plain,
% 28.34/18.58 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))))),
% 28.34/18.58 inference(quant_inst,[status(thm)],[])).
% 28.34/18.58 tff(11560,plain,
% 28.34/18.58 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1)))),
% 28.34/18.58 inference(modus_ponens,[status(thm)],[11559, 11558])).
% 28.34/18.58 tff(11561,plain,
% 28.34/18.58 ($false),
% 28.34/18.58 inference(unit_resolution,[status(thm)],[11560, 447, 11553, 11519, 11554, 11552, 11551, 121])).
% 28.34/18.58 tff(11562,plain,((f6(c2, c1) = c1) | big_f(c2, c2) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f9(c2, c1) = c1)) | (~(f10(c1) = c1)) | big_f(f7(c2), f6(c2, c1))), inference(lemma,lemma(discharge,[]))).
% 28.34/18.58 tff(11563,plain,
% 28.34/18.58 (f6(c2, c1) = c1),
% 28.34/18.58 inference(unit_resolution,[status(thm)],[11562, 3197, 79, 122, 736, 3762, 121])).
% 28.34/18.58 tff(11564,plain,
% 28.34/18.58 (big_f(f7(c2), f6(c2, c1)) <=> big_f(c2, c1)),
% 28.34/18.58 inference(monotonicity,[status(thm)],[10740, 11563])).
% 28.34/18.58 tff(11565,plain,
% 28.34/18.58 (big_f(c2, c1) <=> big_f(f7(c2), f6(c2, c1))),
% 28.34/18.58 inference(symmetry,[status(thm)],[11564])).
% 28.34/18.58 tff(11566,plain,
% 28.34/18.58 (big_f(f7(c2), f6(c2, c1))),
% 28.34/18.58 inference(modus_ponens,[status(thm)],[11332, 11565])).
% 28.34/18.58 tff(11567,plain,
% 28.34/18.58 ($false),
% 28.34/18.58 inference(unit_resolution,[status(thm)],[3197, 11566])).
% 28.34/18.58 tff(11568,plain,(big_f(f7(c2), f6(c2, c1)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f9(c2, c1) = c1)) | (~(f10(c1) = c1)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 28.34/18.58 tff(11569,plain,
% 28.34/18.58 (big_f(f7(c2), f6(c2, c1))),
% 28.34/18.58 inference(unit_resolution,[status(thm)],[11568, 11403, 122, 79, 11419, 121])).
% 28.34/18.58 tff(11570,plain,
% 28.34/18.58 (c1 = f10(c1)),
% 28.34/18.58 inference(symmetry,[status(thm)],[3762])).
% 28.34/18.58 tff(11571,plain,
% 28.34/18.58 (f5(c1) = f5(f10(c1))),
% 28.34/18.58 inference(monotonicity,[status(thm)],[11570])).
% 28.34/18.58 tff(11572,plain,
% 28.34/18.58 (f5(f10(c1)) = f5(c1)),
% 28.34/18.58 inference(symmetry,[status(thm)],[11571])).
% 28.34/18.58 tff(11573,plain,
% 28.34/18.58 ((c2 = f5(f10(c1))) <=> (c2 = f5(c1))),
% 28.34/18.58 inference(monotonicity,[status(thm)],[11572])).
% 28.34/18.58 tff(11574,plain,
% 28.34/18.58 ((c2 = f5(c1)) <=> (c2 = f5(f10(c1)))),
% 28.34/18.58 inference(symmetry,[status(thm)],[11573])).
% 28.34/18.58 tff(11575,plain,
% 28.34/18.58 ((c2 = f5(c1)) <=> (f5(f10(c1)) = c2)),
% 28.34/18.58 inference(transitivity,[status(thm)],[11574, 5892])).
% 28.34/18.58 tff(11576,plain,
% 28.34/18.58 ((~(c2 = f5(c1))) <=> (~(f5(f10(c1)) = c2))),
% 28.34/18.58 inference(monotonicity,[status(thm)],[11575])).
% 28.34/18.58 tff(11577,plain,
% 28.34/18.58 (big_f(f9(c1, c2), f10(c1)) <=> big_f(c1, c1)),
% 28.34/18.58 inference(monotonicity,[status(thm)],[4240, 3762])).
% 28.34/18.58 tff(11578,plain,
% 28.34/18.58 (big_f(c1, c1) <=> big_f(f9(c1, c2), f10(c1))),
% 28.34/18.58 inference(symmetry,[status(thm)],[11577])).
% 28.34/18.58 tff(11579,plain,
% 28.34/18.58 ((~big_f(c1, c1)) <=> (~big_f(f9(c1, c2), f10(c1)))),
% 28.40/18.58 inference(monotonicity,[status(thm)],[11578])).
% 28.40/18.58 tff(11580,plain,
% 28.40/18.58 (~big_f(f9(c1, c2), f10(c1))),
% 28.40/18.58 inference(modus_ponens,[status(thm)],[66, 11579])).
% 28.40/18.58 tff(11581,plain,
% 28.40/18.58 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)))),
% 28.40/18.58 inference(rewrite,[status(thm)],[])).
% 28.40/18.58 tff(11582,plain,
% 28.40/18.58 (((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (f7(c1) = c1) | big_f(f7(c1), c2) | (~(c2 = f5(c1)))) <=> ((~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)))),
% 28.40/18.58 inference(rewrite,[status(thm)],[])).
% 28.40/18.58 tff(11583,plain,
% 28.40/18.58 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (f7(c1) = c1) | big_f(f7(c1), c2) | (~(c2 = f5(c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1))))),
% 28.40/18.58 inference(monotonicity,[status(thm)],[11582])).
% 28.40/18.58 tff(11584,plain,
% 28.40/18.58 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (f7(c1) = c1) | big_f(f7(c1), c2) | (~(c2 = f5(c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)))),
% 28.40/18.58 inference(transitivity,[status(thm)],[11583, 11581])).
% 28.40/18.58 tff(11585,plain,
% 28.40/18.58 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (f7(c1) = c1) | big_f(f7(c1), c2) | (~(c2 = f5(c1))))),
% 28.40/18.58 inference(quant_inst,[status(thm)],[])).
% 28.40/18.58 tff(11586,plain,
% 28.40/18.58 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1))),
% 28.40/18.58 inference(modus_ponens,[status(thm)],[11585, 11584])).
% 28.40/18.58 tff(11587,plain,
% 28.40/18.58 ((~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1))),
% 28.40/18.58 inference(unit_resolution,[status(thm)],[11586, 267])).
% 28.40/18.58 tff(11588,plain,
% 28.40/18.58 (big_f(f9(c1, c2), f10(c1))),
% 28.40/18.58 inference(unit_resolution,[status(thm)],[11587, 4236, 115, 2907, 2908, 3762])).
% 28.40/18.58 tff(11589,plain,
% 28.40/18.58 ($false),
% 28.40/18.58 inference(unit_resolution,[status(thm)],[11588, 11580])).
% 28.40/18.58 tff(11590,plain,((f9(c1, c2) = c2) | big_f(c1, c1) | (~(f10(c1) = c1)) | (f7(c1) = c1) | big_f(f7(c1), c2) | (~(c2 = f5(c1)))), inference(lemma,lemma(discharge,[]))).
% 28.40/18.58 tff(11591,plain,
% 28.40/18.58 (f9(c1, c2) = c2),
% 28.40/18.58 inference(unit_resolution,[status(thm)],[11590, 2908, 115, 2907, 3762, 66])).
% 28.40/18.58 tff(11592,plain,
% 28.40/18.58 (big_f(f9(c1, c2), f10(c1)) <=> big_f(c2, c1)),
% 28.40/18.58 inference(monotonicity,[status(thm)],[11591, 3762])).
% 28.40/18.58 tff(11593,plain,
% 28.40/18.58 (big_f(c2, c1) <=> big_f(f9(c1, c2), f10(c1))),
% 28.40/18.59 inference(symmetry,[status(thm)],[11592])).
% 28.40/18.59 tff(11594,plain,
% 28.40/18.59 (big_f(f9(c1, c2), f10(c1))),
% 28.40/18.59 inference(modus_ponens,[status(thm)],[348, 11593])).
% 28.40/18.59 tff(11595,plain,
% 28.40/18.59 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (~(f10(c1) = c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (~(f10(c1) = c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2)))),
% 28.40/18.59 inference(rewrite,[status(thm)],[])).
% 28.40/18.59 tff(11596,plain,
% 28.40/18.59 (((~(f10(c1) = c1)) | (f7(c1) = c1) | big_f(f7(c1), c2) | (~(f9(c1, c2) = c2)) | (~big_f(f9(c1, c2), f10(c1))) | (~(c2 = f5(c1)))) <=> ((~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (~(f10(c1) = c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2)))),
% 28.40/18.59 inference(rewrite,[status(thm)],[])).
% 28.40/18.59 tff(11597,plain,
% 28.40/18.59 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f7(c1) = c1) | big_f(f7(c1), c2) | (~(f9(c1, c2) = c2)) | (~big_f(f9(c1, c2), f10(c1))) | (~(c2 = f5(c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (~(f10(c1) = c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2))))),
% 28.40/18.59 inference(monotonicity,[status(thm)],[11596])).
% 28.40/18.59 tff(11598,plain,
% 28.40/18.59 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f7(c1) = c1) | big_f(f7(c1), c2) | (~(f9(c1, c2) = c2)) | (~big_f(f9(c1, c2), f10(c1))) | (~(c2 = f5(c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (~(f10(c1) = c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2)))),
% 28.40/18.59 inference(transitivity,[status(thm)],[11597, 11595])).
% 28.40/18.59 tff(11599,plain,
% 28.40/18.59 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f7(c1) = c1) | big_f(f7(c1), c2) | (~(f9(c1, c2) = c2)) | (~big_f(f9(c1, c2), f10(c1))) | (~(c2 = f5(c1))))),
% 28.40/18.59 inference(quant_inst,[status(thm)],[])).
% 28.40/18.59 tff(11600,plain,
% 28.40/18.59 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (~(f10(c1) = c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2))),
% 28.40/18.59 inference(modus_ponens,[status(thm)],[11599, 11598])).
% 28.40/18.59 tff(11601,plain,
% 28.40/18.59 ($false),
% 28.40/18.59 inference(unit_resolution,[status(thm)],[11600, 783, 2908, 2907, 115, 3762, 11594, 11591])).
% 28.40/18.59 tff(11602,plain,((~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (~(f10(c1) = c1)) | (~big_f(c2, c1)) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 28.40/18.59 tff(11603,plain,
% 28.40/18.59 (~(c2 = f5(c1))),
% 28.40/18.59 inference(unit_resolution,[status(thm)],[11602, 66, 115, 3762, 348, 1726])).
% 28.40/18.59 tff(11604,plain,
% 28.40/18.59 (~(f5(f10(c1)) = c2)),
% 28.40/18.59 inference(modus_ponens,[status(thm)],[11603, 11576])).
% 28.40/18.59 tff(11605,plain,
% 28.40/18.59 (f5(f10(c1)) = c1),
% 28.40/18.59 inference(unit_resolution,[status(thm)],[326, 11604])).
% 28.40/18.59 tff(11606,plain,
% 28.40/18.59 (c1 = f5(f10(c1))),
% 28.40/18.59 inference(symmetry,[status(thm)],[11605])).
% 28.40/18.59 tff(11607,plain,
% 28.40/18.59 (c1 = f5(c1)),
% 28.40/18.59 inference(transitivity,[status(thm)],[11606, 11572])).
% 28.40/18.59 tff(11608,plain,
% 28.40/18.59 (f6(c2, c1) = f6(f7(c2), f5(c1))),
% 28.40/18.59 inference(monotonicity,[status(thm)],[82, 11607])).
% 28.40/18.59 tff(11609,plain,
% 28.40/18.59 ((f6(c2, c1) = c1) <=> (f6(f7(c2), f5(c1)) = c1)),
% 28.40/18.59 inference(monotonicity,[status(thm)],[11608])).
% 28.40/18.59 tff(11610,plain,
% 28.40/18.59 ((f6(f7(c2), f5(c1)) = c1) <=> (f6(c2, c1) = c1)),
% 28.40/18.59 inference(symmetry,[status(thm)],[11609])).
% 28.40/18.59 tff(11611,plain,
% 28.40/18.59 (c1 = f5(c1)),
% 28.40/18.59 inference(transitivity,[status(thm)],[4462, 11572])).
% 28.40/18.59 tff(11612,plain,
% 28.40/18.59 (f6(c2, c1) = f6(f7(c2), f5(c1))),
% 28.40/18.59 inference(monotonicity,[status(thm)],[82, 11611])).
% 28.40/18.59 tff(11613,plain,
% 28.40/18.59 (f6(c2, c1) = c2),
% 28.40/18.59 inference(transitivity,[status(thm)],[11612, 3032])).
% 28.40/18.59 tff(11614,plain,
% 28.40/18.59 (big_f(f7(c2), f6(c2, c1)) <=> big_f(c2, c2)),
% 28.40/18.59 inference(monotonicity,[status(thm)],[77, 11613])).
% 28.40/18.59 tff(11615,plain,
% 28.40/18.59 (big_f(c2, c2) <=> big_f(f7(c2), f6(c2, c1))),
% 28.40/18.59 inference(symmetry,[status(thm)],[11614])).
% 28.40/18.59 tff(11616,plain,
% 28.40/18.59 ((~big_f(c2, c2)) <=> (~big_f(f7(c2), f6(c2, c1)))),
% 28.40/18.59 inference(monotonicity,[status(thm)],[11615])).
% 28.40/18.59 tff(11617,plain,
% 28.40/18.59 (~big_f(f7(c2), f6(c2, c1))),
% 28.40/18.59 inference(modus_ponens,[status(thm)],[121, 11616])).
% 28.40/18.59 tff(11618,plain,
% 28.40/18.59 ($false),
% 28.40/18.59 inference(unit_resolution,[status(thm)],[3078, 11617])).
% 28.40/18.59 tff(11619,plain,((~(f6(f7(c2), f5(c1)) = c2)) | (~big_f(f7(c2), f6(c2, c1))) | big_f(c2, c2) | (~(f5(f10(c1)) = c1)) | (~(f10(c1) = c1)) | (~(f7(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.40/18.59 tff(11620,plain,
% 28.40/18.59 (~(f6(f7(c2), f5(c1)) = c2)),
% 28.40/18.59 inference(unit_resolution,[status(thm)],[11619, 11605, 121, 3078, 3762, 77])).
% 28.40/18.59 tff(11621,plain,
% 28.40/18.59 (f6(f7(c2), f5(c1)) = c1),
% 28.40/18.59 inference(unit_resolution,[status(thm)],[2978, 11620])).
% 28.40/18.59 tff(11622,plain,
% 28.40/18.59 (f6(c2, c1) = c1),
% 28.40/18.59 inference(modus_ponens,[status(thm)],[11621, 11610])).
% 28.40/18.59 tff(11623,plain,
% 28.40/18.59 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (~big_f(f7(c2), f6(c2, c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (~big_f(f7(c2), f6(c2, c1))))),
% 28.40/18.59 inference(rewrite,[status(thm)],[])).
% 28.40/18.59 tff(11624,plain,
% 28.40/18.59 (((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1)))) <=> ((~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (~big_f(f7(c2), f6(c2, c1))))),
% 28.40/18.59 inference(rewrite,[status(thm)],[])).
% 28.40/18.59 tff(11625,plain,
% 28.40/18.59 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (~big_f(f7(c2), f6(c2, c1)))))),
% 28.40/18.59 inference(monotonicity,[status(thm)],[11624])).
% 28.40/18.59 tff(11626,plain,
% 28.40/18.59 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (~big_f(f7(c2), f6(c2, c1))))),
% 28.40/18.59 inference(transitivity,[status(thm)],[11625, 11623])).
% 28.40/18.59 tff(11627,plain,
% 28.40/18.59 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1))))),
% 28.40/18.59 inference(quant_inst,[status(thm)],[])).
% 28.40/18.59 tff(11628,plain,
% 28.40/18.59 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (~big_f(f7(c2), f6(c2, c1)))),
% 28.40/18.59 inference(modus_ponens,[status(thm)],[11627, 11626])).
% 28.40/18.59 tff(11629,plain,
% 28.40/18.59 ($false),
% 28.40/18.59 inference(unit_resolution,[status(thm)],[11628, 2534, 3762, 77, 3079, 3078, 11580, 4236])).
% 28.40/18.59 tff(11630,plain,((f9(c1, c2) = c2) | (~(f10(c1) = c1)) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1))) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 28.40/18.59 tff(11631,plain,
% 28.40/18.59 (f9(c1, c2) = c2),
% 28.40/18.59 inference(unit_resolution,[status(thm)],[11630, 11622, 77, 3762, 3078, 66])).
% 28.40/18.59 tff(11632,plain,
% 28.40/18.59 (big_f(f9(c1, c2), f10(c1)) <=> big_f(c2, c1)),
% 28.40/18.59 inference(monotonicity,[status(thm)],[11631, 3762])).
% 28.40/18.59 tff(11633,plain,
% 28.40/18.59 (big_f(c2, c1) <=> big_f(f9(c1, c2), f10(c1))),
% 28.40/18.59 inference(symmetry,[status(thm)],[11632])).
% 28.40/18.59 tff(11634,plain,
% 28.40/18.59 (big_f(f9(c1, c2), f10(c1))),
% 28.40/18.59 inference(modus_ponens,[status(thm)],[348, 11633])).
% 28.40/18.59 tff(11635,plain,
% 28.40/18.59 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~(f10(c1) = c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2)) | (~big_f(f7(c2), f6(c2, c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~(f10(c1) = c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2)) | (~big_f(f7(c2), f6(c2, c1))))),
% 28.40/18.59 inference(rewrite,[status(thm)],[])).
% 28.40/18.59 tff(11636,plain,
% 28.40/18.59 (((~(f10(c1) = c1)) | (~(f7(c2) = c2)) | (~(f9(c1, c2) = c2)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1)))) <=> ((~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~(f10(c1) = c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2)) | (~big_f(f7(c2), f6(c2, c1))))),
% 28.40/18.59 inference(rewrite,[status(thm)],[])).
% 28.40/18.59 tff(11637,plain,
% 28.40/18.59 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (~(f7(c2) = c2)) | (~(f9(c1, c2) = c2)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~(f10(c1) = c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2)) | (~big_f(f7(c2), f6(c2, c1)))))),
% 28.40/18.59 inference(monotonicity,[status(thm)],[11636])).
% 28.40/18.59 tff(11638,plain,
% 28.40/18.59 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (~(f7(c2) = c2)) | (~(f9(c1, c2) = c2)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~(f10(c1) = c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2)) | (~big_f(f7(c2), f6(c2, c1))))),
% 28.40/18.59 inference(transitivity,[status(thm)],[11637, 11635])).
% 28.40/18.59 tff(11639,plain,
% 28.40/18.59 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (~(f7(c2) = c2)) | (~(f9(c1, c2) = c2)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1))))),
% 28.40/18.59 inference(quant_inst,[status(thm)],[])).
% 28.40/18.59 tff(11640,plain,
% 28.40/18.59 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~(f10(c1) = c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2)) | (~big_f(f7(c2), f6(c2, c1)))),
% 28.40/18.59 inference(modus_ponens,[status(thm)],[11639, 11638])).
% 28.40/18.59 tff(11641,plain,
% 28.40/18.59 ($false),
% 28.40/18.59 inference(unit_resolution,[status(thm)],[11640, 2378, 3762, 77, 11622, 3078, 11634, 11631])).
% 28.40/18.59 tff(11642,plain,(big_f(c1, c1) | (~(f10(c1) = c1)) | (~(f7(c2) = c2)) | (~big_f(f7(c2), f6(c2, c1))) | (~big_f(c2, c1)) | big_f(c2, c2) | (f7(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 28.40/18.59 tff(11643,plain,
% 28.40/18.59 (big_f(c1, c1)),
% 28.40/18.59 inference(unit_resolution,[status(thm)],[11642, 11419, 10740, 11569, 11332, 121, 115])).
% 28.40/18.59 tff(11644,plain,
% 28.40/18.59 (~(c3 = c1)),
% 28.40/18.59 inference(unit_resolution,[status(thm)],[11517, 11643, 11332, 121, 79, 10740])).
% 28.40/18.59 tff(11645,plain,
% 28.40/18.59 (c3 = c2),
% 28.40/18.59 inference(unit_resolution,[status(thm)],[180, 11644])).
% 28.40/18.59 tff(11646,plain,
% 28.40/18.59 ((c1 = c3) <=> (c1 = c2)),
% 28.40/18.59 inference(monotonicity,[status(thm)],[11645])).
% 28.40/18.59 tff(11647,plain,
% 28.40/18.59 ((c1 = c3) <=> (c2 = c1)),
% 28.40/18.59 inference(transitivity,[status(thm)],[11646, 1])).
% 28.40/18.59 tff(11648,plain,
% 28.40/18.59 ((c2 = c1) <=> (c1 = c3)),
% 28.40/18.59 inference(symmetry,[status(thm)],[11647])).
% 28.40/18.59 tff(11649,plain,
% 28.40/18.59 ((~(c2 = c1)) <=> (~(c1 = c3))),
% 28.40/18.59 inference(monotonicity,[status(thm)],[11648])).
% 28.40/18.59 tff(11650,plain,
% 28.40/18.59 (~(c1 = c3)),
% 28.40/18.59 inference(modus_ponens,[status(thm)],[75, 11649])).
% 28.40/18.59 tff(11651,plain,
% 28.40/18.59 (c2 = f2(c2)),
% 28.40/18.59 inference(unit_resolution,[status(thm)],[4867, 1319, 67])).
% 28.40/18.59 tff(11652,plain,
% 28.40/18.59 (~big_f(c3, f2(c3))),
% 28.40/18.59 inference(unit_resolution,[status(thm)],[7831, 1319, 121, 67])).
% 28.40/18.59 tff(11653,plain,
% 28.40/18.59 (big_f(f4(c4), c4)),
% 28.40/18.59 inference(unit_resolution,[status(thm)],[1315, 11652])).
% 28.40/18.59 tff(11654,plain,
% 28.40/18.59 (~(c4 = c2)),
% 28.40/18.59 inference(unit_resolution,[status(thm)],[476, 11653, 79, 121])).
% 28.40/18.59 tff(11655,plain,
% 28.40/18.59 (c4 = c1),
% 28.40/18.59 inference(unit_resolution,[status(thm)],[461, 11654])).
% 28.40/18.59 tff(11656,plain,
% 28.40/18.59 (c1 = c4),
% 28.40/18.59 inference(unit_resolution,[status(thm)],[484, 11655])).
% 28.40/18.59 tff(11657,plain,
% 28.40/18.59 (^[X12: $i, X3: $i, X10: $i, X2: $i] : refl(((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12)) <=> ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12)))),
% 28.40/18.59 inference(bind,[status(th)],[])).
% 28.40/18.59 tff(11658,plain,
% 28.40/18.59 (![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12)) <=> ![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))),
% 28.40/18.59 inference(quant_intro,[status(thm)],[11657])).
% 28.40/18.59 tff(11659,plain,
% 28.40/18.59 (![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12)) <=> ![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))),
% 28.40/18.59 inference(rewrite,[status(thm)],[])).
% 28.40/18.59 tff(11660,plain,
% 28.40/18.59 (^[X12: $i, X3: $i, X10: $i, X2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((big_f(X10, X12) | (~(X12 = f2(X10)))) <=> ((~(X12 = f2(X10))) | big_f(X10, X12))), (((big_f(X10, X12) | (~(X12 = f2(X10)))) | (~(X10 = c3))) <=> (((~(X12 = f2(X10))) | big_f(X10, X12)) | (~(X10 = c3))))), rewrite((((~(X12 = f2(X10))) | big_f(X10, X12)) | (~(X10 = c3))) <=> ((~(X10 = c3)) | (~(X12 = f2(X10))) | big_f(X10, X12))), (((big_f(X10, X12) | (~(X12 = f2(X10)))) | (~(X10 = c3))) <=> ((~(X10 = c3)) | (~(X12 = f2(X10))) | big_f(X10, X12)))), ((((big_f(X10, X12) | (~(X12 = f2(X10)))) | (~(X10 = c3))) | (~big_f(X3, X2))) <=> (((~(X10 = c3)) | (~(X12 = f2(X10))) | big_f(X10, X12)) | (~big_f(X3, X2))))), rewrite((((~(X10 = c3)) | (~(X12 = f2(X10))) | big_f(X10, X12)) | (~big_f(X3, X2))) <=> ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~big_f(X3, X2)) | big_f(X10, X12))), ((((big_f(X10, X12) | (~(X12 = f2(X10)))) | (~(X10 = c3))) | (~big_f(X3, X2))) <=> ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~big_f(X3, X2)) | big_f(X10, X12)))), (((((big_f(X10, X12) | (~(X12 = f2(X10)))) | (~(X10 = c3))) | (~big_f(X3, X2))) | (X3 = f4(X2))) <=> (((~(X10 = c3)) | (~(X12 = f2(X10))) | (~big_f(X3, X2)) | big_f(X10, X12)) | (X3 = f4(X2))))), rewrite((((~(X10 = c3)) | (~(X12 = f2(X10))) | (~big_f(X3, X2)) | big_f(X10, X12)) | (X3 = f4(X2))) <=> ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))), (((((big_f(X10, X12) | (~(X12 = f2(X10)))) | (~(X10 = c3))) | (~big_f(X3, X2))) | (X3 = f4(X2))) <=> ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12)))), ((((((big_f(X10, X12) | (~(X12 = f2(X10)))) | (~(X10 = c3))) | (~big_f(X3, X2))) | (X3 = f4(X2))) | (~(X2 = c4))) <=> (((~(X10 = c3)) | (~(X12 = f2(X10))) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12)) | (~(X2 = c4))))), rewrite((((~(X10 = c3)) | (~(X12 = f2(X10))) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12)) | (~(X2 = c4))) <=> ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))), ((((((big_f(X10, X12) | (~(X12 = f2(X10)))) | (~(X10 = c3))) | (~big_f(X3, X2))) | (X3 = f4(X2))) | (~(X2 = c4))) <=> ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))))),
% 28.40/18.59 inference(bind,[status(th)],[])).
% 28.40/18.59 tff(11661,plain,
% 28.40/18.59 (![X12: $i, X3: $i, X10: $i, X2: $i] : (((((big_f(X10, X12) | (~(X12 = f2(X10)))) | (~(X10 = c3))) | (~big_f(X3, X2))) | (X3 = f4(X2))) | (~(X2 = c4))) <=> ![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))),
% 28.40/18.59 inference(quant_intro,[status(thm)],[11660])).
% 28.40/18.59 tff(11662,axiom,(![X12: $i, X3: $i, X10: $i, X2: $i] : (((((big_f(X10, X12) | (~(X12 = f2(X10)))) | (~(X10 = c3))) | (~big_f(X3, X2))) | (X3 = f4(X2))) | (~(X2 = c4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_17')).
% 28.40/18.59 tff(11663,plain,
% 28.40/18.59 (![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))),
% 28.40/18.59 inference(modus_ponens,[status(thm)],[11662, 11661])).
% 28.40/18.59 tff(11664,plain,
% 28.40/18.59 (![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))),
% 28.40/18.59 inference(modus_ponens,[status(thm)],[11663, 11659])).
% 28.40/18.59 tff(11665,plain,(
% 28.40/18.59 ![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))),
% 28.40/18.59 inference(skolemize,[status(sab)],[11664])).
% 28.40/18.59 tff(11666,plain,
% 28.40/18.59 (![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))),
% 28.40/18.59 inference(modus_ponens,[status(thm)],[11665, 11658])).
% 28.40/18.59 tff(11667,plain,
% 28.40/18.59 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | (~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)))),
% 28.40/18.59 inference(rewrite,[status(thm)],[])).
% 28.40/18.59 tff(11668,plain,
% 28.40/18.59 (((~(c2 = c3)) | (~(c2 = f2(c2))) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | big_f(c2, c2)) <=> ((~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)))),
% 28.40/18.59 inference(rewrite,[status(thm)],[])).
% 28.40/18.59 tff(11669,plain,
% 28.40/18.59 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | big_f(c2, c2))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1))))),
% 28.40/18.59 inference(monotonicity,[status(thm)],[11668])).
% 28.40/18.59 tff(11670,plain,
% 28.40/18.59 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | big_f(c2, c2))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | (~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)))),
% 28.40/18.59 inference(transitivity,[status(thm)],[11669, 11667])).
% 28.40/18.59 tff(11671,plain,
% 28.40/18.59 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | big_f(c2, c2))),
% 28.40/18.59 inference(quant_inst,[status(thm)],[])).
% 28.40/18.59 tff(11672,plain,
% 28.40/18.59 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | (~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1))),
% 28.40/18.59 inference(modus_ponens,[status(thm)],[11671, 11670])).
% 28.40/18.59 tff(11673,plain,
% 28.40/18.59 ((~(c2 = c3)) | (~(c2 = f2(c2))) | (~(c1 = c4)) | (c1 = f4(c1))),
% 28.40/18.59 inference(unit_resolution,[status(thm)],[11672, 11666, 121, 4932])).
% 28.40/18.59 tff(11674,plain,
% 28.40/18.59 (c1 = f4(c1)),
% 28.40/18.59 inference(unit_resolution,[status(thm)],[11673, 11656, 1335, 11651])).
% 28.40/18.59 tff(11675,plain,
% 28.40/18.59 (f4(c1) = c1),
% 28.40/18.59 inference(symmetry,[status(thm)],[11674])).
% 28.40/18.59 tff(11676,plain,
% 28.40/18.59 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (~(c1 = c4)) | (~big_f(c2, c1)) | (c2 = f4(c1)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | (~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (~(c1 = c4)) | (~big_f(c2, c1)) | (c2 = f4(c1)))),
% 28.40/18.59 inference(rewrite,[status(thm)],[])).
% 28.40/18.59 tff(11677,plain,
% 28.40/18.59 (((~(c2 = c3)) | (~(c2 = f2(c2))) | (~(c1 = c4)) | (c2 = f4(c1)) | (~big_f(c2, c1)) | big_f(c2, c2)) <=> ((~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (~(c1 = c4)) | (~big_f(c2, c1)) | (c2 = f4(c1)))),
% 28.40/18.59 inference(rewrite,[status(thm)],[])).
% 28.40/18.59 tff(11678,plain,
% 28.40/18.59 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | (~(c1 = c4)) | (c2 = f4(c1)) | (~big_f(c2, c1)) | big_f(c2, c2))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (~(c1 = c4)) | (~big_f(c2, c1)) | (c2 = f4(c1))))),
% 28.40/18.59 inference(monotonicity,[status(thm)],[11677])).
% 28.40/18.60 tff(11679,plain,
% 28.40/18.60 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | (~(c1 = c4)) | (c2 = f4(c1)) | (~big_f(c2, c1)) | big_f(c2, c2))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | (~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (~(c1 = c4)) | (~big_f(c2, c1)) | (c2 = f4(c1)))),
% 28.40/18.60 inference(transitivity,[status(thm)],[11678, 11676])).
% 28.40/18.60 tff(11680,plain,
% 28.40/18.60 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | (~(c1 = c4)) | (c2 = f4(c1)) | (~big_f(c2, c1)) | big_f(c2, c2))),
% 28.40/18.60 inference(quant_inst,[status(thm)],[])).
% 28.40/18.60 tff(11681,plain,
% 28.40/18.60 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | (~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (~(c1 = c4)) | (~big_f(c2, c1)) | (c2 = f4(c1))),
% 28.40/18.60 inference(modus_ponens,[status(thm)],[11680, 11679])).
% 28.40/18.60 tff(11682,plain,
% 28.40/18.60 ((~(c2 = c3)) | (~(c2 = f2(c2))) | (~(c1 = c4)) | (c2 = f4(c1))),
% 28.40/18.60 inference(unit_resolution,[status(thm)],[11681, 11666, 121, 348])).
% 28.40/18.60 tff(11683,plain,
% 28.40/18.60 (c2 = f4(c1)),
% 28.40/18.60 inference(unit_resolution,[status(thm)],[11682, 11656, 1335, 11651])).
% 28.40/18.60 tff(11684,plain,
% 28.40/18.60 (c2 = c1),
% 28.40/18.60 inference(transitivity,[status(thm)],[11683, 11675])).
% 28.40/18.60 tff(11685,plain,
% 28.40/18.60 ($false),
% 28.40/18.60 inference(unit_resolution,[status(thm)],[75, 11684])).
% 28.40/18.60 tff(11686,plain,((~(f2(c3) = c2)) | big_f(c2, c2) | (~big_f(c2, c1)) | (~big_f(c1, c1)) | (~(f4(c4) = c2)) | (~(c3 = c2))), inference(lemma,lemma(discharge,[]))).
% 28.40/18.60 tff(11687,plain,
% 28.40/18.60 (~(f2(c3) = c2)),
% 28.40/18.60 inference(unit_resolution,[status(thm)],[11686, 11645, 11332, 121, 79, 11643])).
% 28.40/18.60 tff(11688,plain,
% 28.40/18.60 (f2(c3) = c1),
% 28.40/18.60 inference(unit_resolution,[status(thm)],[1273, 11687])).
% 28.40/18.60 tff(11689,plain,
% 28.40/18.60 (big_f(c2, f6(c2, c1)) <=> big_f(f7(c2), f6(c2, c1))),
% 28.40/18.60 inference(monotonicity,[status(thm)],[11396])).
% 28.40/18.60 tff(11690,plain,
% 28.40/18.60 (big_f(f7(c2), f6(c2, c1)) <=> big_f(c2, f6(c2, c1))),
% 28.40/18.60 inference(symmetry,[status(thm)],[11689])).
% 28.40/18.60 tff(11691,plain,
% 28.40/18.60 (big_f(c2, f6(c2, c1))),
% 28.40/18.60 inference(modus_ponens,[status(thm)],[11569, 11690])).
% 28.40/18.60 tff(11692,assumption,(big_f(c2, f6(c2, c1))), introduced(assumption)).
% 28.40/18.60 tff(11693,plain,
% 28.40/18.60 (f2(c2) = c1),
% 28.40/18.60 inference(transitivity,[status(thm)],[1426, 7833])).
% 28.40/18.60 tff(11694,plain,
% 28.40/18.60 ((f6(c2, c1) = f2(c2)) <=> (f6(c2, c1) = c1)),
% 28.40/18.60 inference(monotonicity,[status(thm)],[11693])).
% 28.40/18.60 tff(11695,plain,
% 28.40/18.60 ((f6(c2, c1) = c1) <=> (f6(c2, c1) = f2(c2))),
% 28.40/18.60 inference(symmetry,[status(thm)],[11694])).
% 28.40/18.60 tff(11696,plain,
% 28.40/18.60 ((~(f6(c2, c1) = c1)) <=> (~(f6(c2, c1) = f2(c2)))),
% 28.40/18.60 inference(monotonicity,[status(thm)],[11695])).
% 28.40/18.60 tff(11697,plain,
% 28.40/18.60 (~(f6(c2, c1) = f2(c2))),
% 28.40/18.60 inference(modus_ponens,[status(thm)],[3198, 11696])).
% 28.40/18.60 tff(11698,plain,
% 28.40/18.60 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (~big_f(c2, f6(c2, c1))) | (f6(c2, c1) = f2(c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (~big_f(c2, f6(c2, c1))) | (f6(c2, c1) = f2(c2)))),
% 28.40/18.60 inference(rewrite,[status(thm)],[])).
% 28.40/18.60 tff(11699,plain,
% 28.40/18.60 (((~(c2 = c3)) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))) | (f6(c2, c1) = f2(c2)) | (~big_f(c2, f6(c2, c1)))) <=> ((~(c2 = c3)) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (~big_f(c2, f6(c2, c1))) | (f6(c2, c1) = f2(c2)))),
% 28.40/18.60 inference(rewrite,[status(thm)],[])).
% 28.40/18.60 tff(11700,plain,
% 28.40/18.60 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))) | (f6(c2, c1) = f2(c2)) | (~big_f(c2, f6(c2, c1))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (~big_f(c2, f6(c2, c1))) | (f6(c2, c1) = f2(c2))))),
% 28.40/18.60 inference(monotonicity,[status(thm)],[11699])).
% 28.40/18.60 tff(11701,plain,
% 28.40/18.60 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))) | (f6(c2, c1) = f2(c2)) | (~big_f(c2, f6(c2, c1))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (~big_f(c2, f6(c2, c1))) | (f6(c2, c1) = f2(c2)))),
% 28.40/18.60 inference(transitivity,[status(thm)],[11700, 11698])).
% 28.40/18.60 tff(11702,plain,
% 28.40/18.60 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))) | (f6(c2, c1) = f2(c2)) | (~big_f(c2, f6(c2, c1))))),
% 28.40/18.60 inference(quant_inst,[status(thm)],[])).
% 28.40/18.60 tff(11703,plain,
% 28.40/18.60 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (~big_f(c2, f6(c2, c1))) | (f6(c2, c1) = f2(c2))),
% 28.40/18.60 inference(modus_ponens,[status(thm)],[11702, 11701])).
% 28.40/18.60 tff(11704,plain,
% 28.40/18.60 ((~(c2 = c3)) | (~(c2 = c4)) | (~(c2 = f4(c2))) | (~big_f(c2, f6(c2, c1))) | (f6(c2, c1) = f2(c2))),
% 28.40/18.60 inference(unit_resolution,[status(thm)],[11703, 5622, 121])).
% 28.40/18.60 tff(11705,plain,
% 28.40/18.60 ($false),
% 28.40/18.60 inference(unit_resolution,[status(thm)],[11704, 437, 432, 1335, 11692, 11697])).
% 28.40/18.60 tff(11706,plain,((~(c4 = c2)) | (~big_f(c2, f6(c2, c1))) | big_f(c2, c2) | (f6(c2, c1) = c1) | (~(c3 = c2)) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.40/18.60 tff(11707,plain,
% 28.40/18.60 (~(c4 = c2)),
% 28.40/18.60 inference(unit_resolution,[status(thm)],[11706, 3198, 121, 11692, 67, 79])).
% 28.40/18.60 tff(11708,plain,
% 28.40/18.60 (c4 = c1),
% 28.40/18.60 inference(unit_resolution,[status(thm)],[461, 11707])).
% 28.40/18.60 tff(11709,plain,
% 28.40/18.60 (c1 = c4),
% 28.40/18.60 inference(unit_resolution,[status(thm)],[484, 11708])).
% 28.40/18.60 tff(11710,plain,
% 28.40/18.60 ((f6(c2, c1) = f2(c2)) <=> (f6(c2, c1) = c1)),
% 28.40/18.60 inference(monotonicity,[status(thm)],[1427])).
% 28.40/18.60 tff(11711,plain,
% 28.40/18.60 ((f6(c2, c1) = c1) <=> (f6(c2, c1) = f2(c2))),
% 28.40/18.60 inference(symmetry,[status(thm)],[11710])).
% 28.40/18.60 tff(11712,plain,
% 28.40/18.60 ((~(f6(c2, c1) = c1)) <=> (~(f6(c2, c1) = f2(c2)))),
% 28.40/18.60 inference(monotonicity,[status(thm)],[11711])).
% 28.40/18.60 tff(11713,plain,
% 28.40/18.60 (~(f6(c2, c1) = f2(c2))),
% 28.40/18.60 inference(modus_ponens,[status(thm)],[3198, 11712])).
% 28.40/18.60 tff(11714,plain,
% 28.40/18.60 (c1 = c4),
% 28.40/18.60 inference(symmetry,[status(thm)],[11708])).
% 28.40/18.60 tff(11715,plain,
% 28.40/18.60 (f4(c1) = f4(c4)),
% 28.40/18.60 inference(monotonicity,[status(thm)],[11714])).
% 28.40/18.60 tff(11716,plain,
% 28.40/18.60 (f4(c1) = c2),
% 28.40/18.60 inference(transitivity,[status(thm)],[11715, 79])).
% 28.40/18.60 tff(11717,plain,
% 28.40/18.60 ((c1 = f4(c1)) <=> (c1 = c2)),
% 28.40/18.60 inference(monotonicity,[status(thm)],[11716])).
% 28.40/18.60 tff(11718,plain,
% 28.40/18.60 ((c1 = f4(c1)) <=> (c2 = c1)),
% 28.40/18.60 inference(transitivity,[status(thm)],[11717, 1])).
% 28.40/18.60 tff(11719,plain,
% 28.40/18.60 ((c2 = c1) <=> (c1 = f4(c1))),
% 28.40/18.60 inference(symmetry,[status(thm)],[11718])).
% 28.40/18.60 tff(11720,plain,
% 28.40/18.60 ((~(c2 = c1)) <=> (~(c1 = f4(c1)))),
% 28.40/18.60 inference(monotonicity,[status(thm)],[11719])).
% 28.40/18.60 tff(11721,plain,
% 28.40/18.60 (~(c1 = f4(c1))),
% 28.40/18.60 inference(modus_ponens,[status(thm)],[75, 11720])).
% 28.40/18.60 tff(11722,plain,
% 28.40/18.60 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (~big_f(c2, f6(c2, c1))) | (f6(c2, c1) = f2(c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (~big_f(c2, f6(c2, c1))) | (f6(c2, c1) = f2(c2)))),
% 28.40/18.60 inference(rewrite,[status(thm)],[])).
% 28.40/18.60 tff(11723,plain,
% 28.40/18.60 (((~(c2 = c3)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (f6(c2, c1) = f2(c2)) | (~big_f(c2, f6(c2, c1)))) <=> ((~(c2 = c3)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (~big_f(c2, f6(c2, c1))) | (f6(c2, c1) = f2(c2)))),
% 28.40/18.60 inference(rewrite,[status(thm)],[])).
% 28.40/18.60 tff(11724,plain,
% 28.40/18.60 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (f6(c2, c1) = f2(c2)) | (~big_f(c2, f6(c2, c1))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (~big_f(c2, f6(c2, c1))) | (f6(c2, c1) = f2(c2))))),
% 28.40/18.60 inference(monotonicity,[status(thm)],[11723])).
% 28.40/18.60 tff(11725,plain,
% 28.40/18.60 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (f6(c2, c1) = f2(c2)) | (~big_f(c2, f6(c2, c1))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (~big_f(c2, f6(c2, c1))) | (f6(c2, c1) = f2(c2)))),
% 28.40/18.60 inference(transitivity,[status(thm)],[11724, 11722])).
% 28.40/18.60 tff(11726,plain,
% 28.40/18.60 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (f6(c2, c1) = f2(c2)) | (~big_f(c2, f6(c2, c1))))),
% 28.40/18.60 inference(quant_inst,[status(thm)],[])).
% 28.40/18.60 tff(11727,plain,
% 28.40/18.60 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (~big_f(c2, f6(c2, c1))) | (f6(c2, c1) = f2(c2))),
% 28.40/18.60 inference(modus_ponens,[status(thm)],[11726, 11725])).
% 28.40/18.60 tff(11728,plain,
% 28.40/18.60 ((~(c1 = c4)) | (c1 = f4(c1)) | (f6(c2, c1) = f2(c2))),
% 28.40/18.60 inference(unit_resolution,[status(thm)],[11727, 1355, 1335, 4932, 11692])).
% 28.40/18.60 tff(11729,plain,
% 28.40/18.60 ($false),
% 28.40/18.60 inference(unit_resolution,[status(thm)],[11728, 11721, 11713, 11709])).
% 28.40/18.60 tff(11730,plain,((f6(c2, c1) = c1) | (~big_f(c1, c1)) | (~big_f(c2, f6(c2, c1))) | (~(f4(c4) = c2)) | (~(f2(c3) = c1)) | (~(c3 = c2)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 28.40/18.60 tff(11731,plain,
% 28.40/18.60 (f6(c2, c1) = c1),
% 28.40/18.60 inference(unit_resolution,[status(thm)],[11730, 11643, 11691, 79, 11688, 11645, 121])).
% 28.40/18.60 tff(11732,plain,
% 28.40/18.60 ((~(f6(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2)))),
% 28.40/18.60 inference(unit_resolution,[status(thm)],[3097, 2378, 122, 11403, 10740, 11569])).
% 28.40/18.60 tff(11733,plain,
% 28.40/18.60 (~big_f(f9(c2, c1), f10(c2))),
% 28.40/18.60 inference(unit_resolution,[status(thm)],[11732, 11731])).
% 28.40/18.60 tff(11734,plain,
% 28.40/18.60 (~big_f(c1, c2)),
% 28.40/18.60 inference(unit_resolution,[status(thm)],[3090, 11731, 122, 10740, 11733, 11569])).
% 28.40/18.60 tff(11735,plain,
% 28.40/18.60 (~(c4 = c1)),
% 28.40/18.60 inference(unit_resolution,[status(thm)],[11545, 11734, 11643, 11650, 79])).
% 28.40/18.60 tff(11736,plain,
% 28.40/18.60 (c4 = c2),
% 28.40/18.60 inference(unit_resolution,[status(thm)],[461, 11735])).
% 28.40/18.60 tff(11737,plain,
% 28.40/18.60 (c2 = c4),
% 28.40/18.60 inference(symmetry,[status(thm)],[11736])).
% 28.40/18.60 tff(11738,plain,
% 28.40/18.60 (f4(c2) = f4(c4)),
% 28.40/18.60 inference(monotonicity,[status(thm)],[11737])).
% 28.40/18.60 tff(11739,plain,
% 28.40/18.60 (f4(c4) = f4(c2)),
% 28.40/18.60 inference(symmetry,[status(thm)],[11738])).
% 28.40/18.60 tff(11740,plain,
% 28.40/18.60 (c2 = f4(c2)),
% 28.40/18.60 inference(transitivity,[status(thm)],[436, 11739])).
% 28.40/18.60 tff(11741,plain,
% 28.40/18.60 (c2 = c4),
% 28.40/18.60 inference(modus_ponens,[status(thm)],[11736, 159])).
% 28.40/18.60 tff(11742,plain,
% 28.40/18.60 (f1(c1, c1) = c1),
% 28.40/18.60 inference(unit_resolution,[status(thm)],[9763, 11741, 121, 11650, 11734, 11740])).
% 28.40/18.60 tff(11743,plain,
% 28.40/18.60 (big_f(c1, f1(c1, c1))),
% 28.40/18.60 inference(unit_resolution,[status(thm)],[9678, 11742, 11643])).
% 28.40/18.60 tff(11744,plain,
% 28.40/18.60 ($false),
% 28.40/18.60 inference(unit_resolution,[status(thm)],[11560, 447, 11742, 11650, 11743, 11741, 11740, 121])).
% 28.40/18.60 tff(11745,plain,((f7(c1) = c1) | big_f(c2, c2) | (~(f4(c4) = c2)) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.40/18.60 tff(11746,plain,
% 28.40/18.60 (~(f4(c4) = c2)),
% 28.40/18.60 inference(unit_resolution,[status(thm)],[11745, 121, 115, 122])).
% 28.40/18.60 tff(11747,plain,
% 28.40/18.60 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f4(c4) = c1) | (f4(c4) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f4(c4) = c1) | (f4(c4) = c2))),
% 28.40/18.60 inference(rewrite,[status(thm)],[])).
% 28.40/18.60 tff(11748,plain,
% 28.40/18.60 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f4(c4) = c1) | (f4(c4) = c2))),
% 28.40/18.60 inference(quant_inst,[status(thm)],[])).
% 28.40/18.60 tff(11749,plain,
% 28.40/18.60 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f4(c4) = c1) | (f4(c4) = c2)),
% 28.40/18.60 inference(modus_ponens,[status(thm)],[11748, 11747])).
% 28.40/18.60 tff(11750,plain,
% 28.40/18.60 ((f4(c4) = c1) | (f4(c4) = c2)),
% 28.40/18.60 inference(unit_resolution,[status(thm)],[11749, 10])).
% 28.40/18.60 tff(11751,plain,
% 28.40/18.60 (f4(c4) = c1),
% 28.40/18.60 inference(unit_resolution,[status(thm)],[11750, 11746])).
% 28.40/18.60 tff(11752,assumption,(f4(c4) = c1), introduced(assumption)).
% 28.40/18.60 tff(11753,plain,
% 28.40/18.60 (~(c3 = c2)),
% 28.40/18.60 inference(modus_ponens,[status(thm)],[377, 9745])).
% 28.40/18.60 tff(11754,plain,
% 28.40/18.60 (c3 = c1),
% 28.40/18.60 inference(unit_resolution,[status(thm)],[180, 11753])).
% 28.40/18.60 tff(11755,plain,
% 28.40/18.60 (big_f(c1, f2(c1)) <=> big_f(c3, f2(c3))),
% 28.40/18.60 inference(symmetry,[status(thm)],[5590])).
% 28.40/18.60 tff(11756,plain,
% 28.40/18.60 (big_f(c1, c1) <=> big_f(c3, f2(c3))),
% 28.40/18.60 inference(transitivity,[status(thm)],[10928, 11755])).
% 28.40/18.60 tff(11757,plain,
% 28.40/18.60 ((~big_f(c1, c1)) <=> (~big_f(c3, f2(c3)))),
% 28.40/18.60 inference(monotonicity,[status(thm)],[11756])).
% 28.40/18.60 tff(11758,plain,
% 28.40/18.60 (~big_f(c3, f2(c3))),
% 28.40/18.60 inference(modus_ponens,[status(thm)],[66, 11757])).
% 28.40/18.60 tff(11759,plain,
% 28.40/18.60 (big_f(f4(c4), c4) <=> big_f(c1, c2)),
% 28.40/18.60 inference(monotonicity,[status(thm)],[11752, 431])).
% 28.40/18.60 tff(11760,plain,
% 28.40/18.60 (big_f(c1, c2) <=> big_f(f4(c4), c4)),
% 28.40/18.60 inference(symmetry,[status(thm)],[11759])).
% 28.40/18.60 tff(11761,plain,
% 28.40/18.60 ((~big_f(c1, c2)) <=> (~big_f(f4(c4), c4))),
% 28.40/18.60 inference(monotonicity,[status(thm)],[11760])).
% 28.40/18.60 tff(11762,plain,
% 28.40/18.60 (~big_f(f4(c4), c4)),
% 28.40/18.60 inference(modus_ponens,[status(thm)],[27, 11761])).
% 28.40/18.60 tff(11763,plain,
% 28.40/18.60 ($false),
% 28.40/18.60 inference(unit_resolution,[status(thm)],[474, 11762])).
% 28.40/18.60 tff(11764,plain,((~(c4 = c2)) | (~big_f(f4(c4), c4)) | big_f(c1, c2) | (~(f4(c4) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.40/18.60 tff(11765,plain,
% 28.40/18.60 (~(c4 = c2)),
% 28.40/18.60 inference(unit_resolution,[status(thm)],[11764, 474, 11752, 27])).
% 28.40/18.60 tff(11766,plain,
% 28.40/18.60 (c4 = c1),
% 28.40/18.60 inference(unit_resolution,[status(thm)],[461, 11765])).
% 28.40/18.60 tff(11767,plain,
% 28.40/18.60 (big_f(f4(c4), c4) <=> big_f(c1, c1)),
% 28.40/18.60 inference(monotonicity,[status(thm)],[11752, 11766])).
% 28.40/18.60 tff(11768,plain,
% 28.40/18.60 (big_f(c1, c1) <=> big_f(f4(c4), c4)),
% 28.40/18.60 inference(symmetry,[status(thm)],[11767])).
% 28.40/18.60 tff(11769,plain,
% 28.40/18.60 ((~big_f(c1, c1)) <=> (~big_f(f4(c4), c4))),
% 28.40/18.60 inference(monotonicity,[status(thm)],[11768])).
% 28.40/18.60 tff(11770,plain,
% 28.40/18.60 (~big_f(f4(c4), c4)),
% 28.40/18.60 inference(modus_ponens,[status(thm)],[66, 11769])).
% 28.40/18.60 tff(11771,plain,
% 28.40/18.60 ($false),
% 28.40/18.60 inference(unit_resolution,[status(thm)],[474, 11770])).
% 28.40/18.60 tff(11772,plain,((~big_f(f4(c4), c4)) | big_f(c1, c1) | (~(f4(c4) = c1)) | big_f(c1, c2)), inference(lemma,lemma(discharge,[]))).
% 28.40/18.60 tff(11773,plain,
% 28.40/18.60 (~big_f(f4(c4), c4)),
% 28.40/18.60 inference(unit_resolution,[status(thm)],[11772, 66, 11752, 27])).
% 28.40/18.60 tff(11774,plain,
% 28.40/18.60 (big_f(c3, f2(c3))),
% 28.40/18.60 inference(unit_resolution,[status(thm)],[1315, 11773])).
% 28.40/18.60 tff(11775,plain,
% 28.40/18.60 ($false),
% 28.40/18.60 inference(unit_resolution,[status(thm)],[11774, 11758])).
% 28.40/18.60 tff(11776,plain,(big_f(c1, c1) | (~(f2(c3) = c1)) | (~(c3 = c1)) | (~(f4(c4) = c1)) | big_f(c1, c2)), inference(lemma,lemma(discharge,[]))).
% 28.40/18.60 tff(11777,plain,
% 28.40/18.60 (~(f2(c3) = c1)),
% 28.40/18.60 inference(unit_resolution,[status(thm)],[11776, 172, 11752, 27, 66])).
% 28.40/18.60 tff(11778,plain,
% 28.40/18.60 (f2(c3) = c2),
% 28.40/18.60 inference(unit_resolution,[status(thm)],[1273, 11777])).
% 28.40/18.60 tff(11779,plain,
% 28.40/18.60 (big_f(c3, f2(c3)) <=> big_f(c1, c2)),
% 28.40/18.60 inference(monotonicity,[status(thm)],[172, 11778])).
% 28.40/18.60 tff(11780,plain,
% 28.40/18.60 (big_f(c1, c2) <=> big_f(c3, f2(c3))),
% 28.40/18.60 inference(symmetry,[status(thm)],[11779])).
% 28.40/18.60 tff(11781,plain,
% 28.40/18.60 ((~big_f(c1, c2)) <=> (~big_f(c3, f2(c3)))),
% 28.40/18.60 inference(monotonicity,[status(thm)],[11780])).
% 28.40/18.60 tff(11782,plain,
% 28.40/18.60 (~big_f(c3, f2(c3))),
% 28.40/18.60 inference(modus_ponens,[status(thm)],[27, 11781])).
% 28.40/18.60 tff(11783,plain,
% 28.40/18.60 ($false),
% 28.40/18.60 inference(unit_resolution,[status(thm)],[11774, 11782])).
% 28.40/18.60 tff(11784,plain,((~(c3 = c1)) | big_f(c1, c2) | (~(f4(c4) = c1)) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 28.40/18.60 tff(11785,plain,
% 28.40/18.60 (big_f(c1, c1)),
% 28.40/18.60 inference(unit_resolution,[status(thm)],[11784, 27, 11752, 11754])).
% 28.40/18.60 tff(11786,plain,
% 28.40/18.60 ((~(c2 = f5(c1))) <=> (~(f5(c1) = c2))),
% 28.40/18.60 inference(monotonicity,[status(thm)],[8483])).
% 28.40/18.60 tff(11787,plain,
% 28.40/18.60 ((c2 = f6(f7(c2), f5(c1))) <=> (f6(f7(c2), f5(c1)) = c2)),
% 28.40/18.60 inference(commutativity,[status(thm)],[])).
% 28.40/18.60 tff(11788,plain,
% 28.40/18.60 (f9(c2, c1) = c1),
% 28.40/18.60 inference(unit_resolution,[status(thm)],[8445, 4990, 115, 122, 121])).
% 28.40/18.60 tff(11789,plain,
% 28.40/18.60 (~(f8(c1) = c1)),
% 28.40/18.60 inference(unit_resolution,[status(thm)],[11372, 11788, 115, 3, 122, 121, 186])).
% 28.40/18.60 tff(11790,plain,
% 28.40/18.60 (f8(c1) = c2),
% 28.40/18.60 inference(unit_resolution,[status(thm)],[1680, 11789])).
% 28.40/18.60 tff(11791,plain,
% 28.40/18.60 (c2 = f8(c1)),
% 28.40/18.60 inference(unit_resolution,[status(thm)],[1675, 11790])).
% 28.40/18.60 tff(11792,plain,
% 28.40/18.60 (~(c2 = f5(c1))),
% 28.40/18.60 inference(unit_resolution,[status(thm)],[1752, 11791, 115, 1726, 6126, 3])).
% 28.40/18.60 tff(11793,plain,
% 28.40/18.60 ($false),
% 28.40/18.60 inference(unit_resolution,[status(thm)],[11792, 1727])).
% 28.40/18.60 tff(11794,plain,((~(f5(c1) = c2)) | (f7(c1) = c1) | (f10(c1) = c1) | (~(f10(c2) = c2)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 28.40/18.60 tff(11795,plain,
% 28.40/18.60 (~(f5(c1) = c2)),
% 28.40/18.60 inference(unit_resolution,[status(thm)],[11794, 121, 3, 122, 115])).
% 28.40/18.60 tff(11796,plain,
% 28.40/18.60 (f5(c1) = c1),
% 28.40/18.60 inference(unit_resolution,[status(thm)],[1708, 11795])).
% 28.40/18.60 tff(11797,plain,
% 28.40/18.60 (~(f10(c2) = c2)),
% 28.40/18.60 inference(unit_resolution,[status(thm)],[10739, 17, 79])).
% 28.40/18.60 tff(11798,plain,
% 28.40/18.60 (~(f10(c2) = c2)),
% 28.40/18.60 inference(unit_resolution,[status(thm)],[11745, 121, 115, 79])).
% 28.40/18.60 tff(11799,plain,
% 28.40/18.60 (f10(c2) = c1),
% 28.40/18.60 inference(unit_resolution,[status(thm)],[93, 11798])).
% 28.40/18.60 tff(11800,plain,
% 28.40/18.60 ((f10(c2) = f4(c2)) <=> (c1 = f4(c2))),
% 28.40/18.60 inference(monotonicity,[status(thm)],[11799])).
% 28.40/18.60 tff(11801,plain,
% 28.40/18.60 ((c1 = f4(c2)) <=> (f10(c2) = f4(c2))),
% 28.40/18.60 inference(symmetry,[status(thm)],[11800])).
% 28.40/18.60 tff(11802,plain,
% 28.40/18.60 (c1 = c3),
% 28.40/18.60 inference(unit_resolution,[status(thm)],[175, 10742])).
% 28.40/18.60 tff(11803,plain,
% 28.40/18.60 (big_f(c1, f7(c1)) <=> big_f(c1, c2)),
% 28.40/18.60 inference(monotonicity,[status(thm)],[120])).
% 28.40/18.60 tff(11804,plain,
% 28.40/18.60 (big_f(c1, c2) <=> big_f(c1, f7(c1))),
% 28.40/18.60 inference(symmetry,[status(thm)],[11803])).
% 28.40/18.60 tff(11805,plain,
% 28.40/18.60 (f7(f10(c2)) = f7(c1)),
% 28.40/18.60 inference(monotonicity,[status(thm)],[11799])).
% 28.40/18.60 tff(11806,plain,
% 28.40/18.60 (f7(f10(c2)) = c2),
% 28.40/18.60 inference(transitivity,[status(thm)],[11805, 120])).
% 28.40/18.60 tff(11807,plain,
% 28.40/18.60 ((f7(f10(c2)) = f10(c2)) <=> (c2 = f10(c2))),
% 28.40/18.60 inference(monotonicity,[status(thm)],[11806])).
% 28.40/18.60 tff(11808,plain,
% 28.40/18.60 ((f7(f10(c2)) = f10(c2)) <=> (f10(c2) = c2)),
% 28.40/18.60 inference(transitivity,[status(thm)],[11807, 4987])).
% 28.40/18.60 tff(11809,plain,
% 28.40/18.60 ((f10(c2) = c2) <=> (f7(f10(c2)) = f10(c2))),
% 28.40/18.60 inference(symmetry,[status(thm)],[11808])).
% 28.40/18.60 tff(11810,plain,
% 28.40/18.60 ((~(f10(c2) = c2)) <=> (~(f7(f10(c2)) = f10(c2)))),
% 28.40/18.60 inference(monotonicity,[status(thm)],[11809])).
% 28.40/18.60 tff(11811,plain,
% 28.40/18.60 (~(f7(f10(c2)) = f10(c2))),
% 28.40/18.60 inference(modus_ponens,[status(thm)],[11798, 11810])).
% 28.40/18.60 tff(11812,plain,
% 28.40/18.60 (f10(f10(c2)) = f10(c1)),
% 28.40/18.60 inference(monotonicity,[status(thm)],[11799])).
% 28.40/18.60 tff(11813,plain,
% 28.40/18.60 (f10(f10(c2)) = c2),
% 28.40/18.60 inference(transitivity,[status(thm)],[11812, 15])).
% 28.40/18.60 tff(11814,plain,
% 28.40/18.60 ((f10(f10(c2)) = f10(c2)) <=> (c2 = f10(c2))),
% 28.40/18.60 inference(monotonicity,[status(thm)],[11813])).
% 28.40/18.60 tff(11815,plain,
% 28.40/18.60 ((f10(f10(c2)) = f10(c2)) <=> (f10(c2) = c2)),
% 28.40/18.60 inference(transitivity,[status(thm)],[11814, 4987])).
% 28.40/18.60 tff(11816,plain,
% 28.40/18.60 ((f10(c2) = c2) <=> (f10(f10(c2)) = f10(c2))),
% 28.40/18.60 inference(symmetry,[status(thm)],[11815])).
% 28.40/18.60 tff(11817,plain,
% 28.40/18.60 ((~(f10(c2) = c2)) <=> (~(f10(f10(c2)) = f10(c2)))),
% 28.40/18.60 inference(monotonicity,[status(thm)],[11816])).
% 28.40/18.60 tff(11818,plain,
% 28.40/18.60 (~(f10(f10(c2)) = f10(c2))),
% 28.40/18.60 inference(modus_ponens,[status(thm)],[11798, 11817])).
% 28.40/18.60 tff(11819,assumption,(f10(c2) = c1), introduced(assumption)).
% 28.40/18.60 tff(11820,plain,
% 28.40/18.60 (f8(f10(c2)) = f8(c1)),
% 28.40/18.60 inference(monotonicity,[status(thm)],[11819])).
% 28.40/18.60 tff(11821,plain,
% 28.40/18.60 ((f10(c2) = f8(f10(c2))) <=> (c1 = f8(c1))),
% 28.40/18.60 inference(monotonicity,[status(thm)],[11819, 11820])).
% 28.40/18.60 tff(11822,plain,
% 28.40/18.60 ((f10(c2) = f8(f10(c2))) <=> (f8(c1) = c1)),
% 28.40/18.60 inference(transitivity,[status(thm)],[11821, 3027])).
% 28.40/18.60 tff(11823,plain,
% 28.40/18.60 ((f8(c1) = c1) <=> (f10(c2) = f8(f10(c2)))),
% 28.40/18.60 inference(symmetry,[status(thm)],[11822])).
% 28.40/18.60 tff(11824,plain,
% 28.40/18.60 ((~big_f(c1, c2)) <=> (~big_f(c1, f7(c1)))),
% 28.40/18.60 inference(monotonicity,[status(thm)],[11804])).
% 28.40/18.60 tff(11825,plain,
% 28.40/18.60 (~big_f(c1, f7(c1))),
% 28.40/18.60 inference(modus_ponens,[status(thm)],[27, 11824])).
% 28.40/18.60 tff(11826,assumption,(c1 = f5(c1)), introduced(assumption)).
% 28.40/18.60 tff(11827,plain,
% 28.40/18.60 (big_f(c1, f10(c1)) <=> big_f(c1, f7(c1))),
% 28.40/18.60 inference(monotonicity,[status(thm)],[2808])).
% 28.40/18.60 tff(11828,plain,
% 28.40/18.60 (big_f(c1, f7(c1)) <=> big_f(c1, f10(c1))),
% 28.40/18.60 inference(symmetry,[status(thm)],[11827])).
% 28.40/18.60 tff(11829,plain,
% 28.40/18.60 ((~big_f(c1, f7(c1))) <=> (~big_f(c1, f10(c1)))),
% 28.40/18.60 inference(monotonicity,[status(thm)],[11828])).
% 28.40/18.60 tff(11830,assumption,(~big_f(c1, f7(c1))), introduced(assumption)).
% 28.40/18.60 tff(11831,plain,
% 28.40/18.60 (~big_f(c1, f10(c1))),
% 28.40/18.60 inference(modus_ponens,[status(thm)],[11830, 11829])).
% 28.40/18.60 tff(11832,plain,
% 28.40/18.60 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f7(c1) = c1) | (f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | big_f(f7(c1), c1) | (~(c1 = f5(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(c1) = c1) | (f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | big_f(f7(c1), c1) | (~(c1 = f5(c1))))),
% 28.40/18.60 inference(rewrite,[status(thm)],[])).
% 28.40/18.60 tff(11833,plain,
% 28.40/18.60 (((~(c1 = f5(c1))) | (f10(c1) = c1) | big_f(c1, f10(c1)) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(c1 = f8(c1)))) <=> ((f7(c1) = c1) | (f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | big_f(f7(c1), c1) | (~(c1 = f5(c1))))),
% 28.40/18.60 inference(rewrite,[status(thm)],[])).
% 28.40/18.60 tff(11834,plain,
% 28.40/18.60 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c1 = f5(c1))) | (f10(c1) = c1) | big_f(c1, f10(c1)) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(c1 = f8(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f7(c1) = c1) | (f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | big_f(f7(c1), c1) | (~(c1 = f5(c1)))))),
% 28.40/18.60 inference(monotonicity,[status(thm)],[11833])).
% 28.40/18.60 tff(11835,plain,
% 28.40/18.60 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c1 = f5(c1))) | (f10(c1) = c1) | big_f(c1, f10(c1)) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(c1 = f8(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(c1) = c1) | (f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | big_f(f7(c1), c1) | (~(c1 = f5(c1))))),
% 28.40/18.60 inference(transitivity,[status(thm)],[11834, 11832])).
% 28.40/18.60 tff(11836,plain,
% 28.40/18.60 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c1 = f5(c1))) | (f10(c1) = c1) | big_f(c1, f10(c1)) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(c1 = f8(c1))))),
% 28.40/18.60 inference(quant_inst,[status(thm)],[])).
% 28.40/18.60 tff(11837,plain,
% 28.40/18.60 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(c1) = c1) | (f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | big_f(f7(c1), c1) | (~(c1 = f5(c1)))),
% 28.40/18.60 inference(modus_ponens,[status(thm)],[11836, 11835])).
% 28.40/18.60 tff(11838,plain,
% 28.40/18.60 (~(c1 = f8(c1))),
% 28.40/18.60 inference(unit_resolution,[status(thm)],[11837, 1745, 115, 3, 11831, 285, 11826])).
% 28.40/18.60 tff(11839,plain,
% 28.40/18.60 ((c2 = f8(f10(c2))) <=> (c2 = f8(c1))),
% 28.40/18.60 inference(monotonicity,[status(thm)],[11820])).
% 28.40/18.60 tff(11840,plain,
% 28.40/18.60 ((c2 = f8(f10(c2))) <=> (f8(c1) = c2)),
% 28.40/18.60 inference(transitivity,[status(thm)],[11839, 2782])).
% 28.40/18.60 tff(11841,plain,
% 28.40/18.60 ((~(c2 = f8(f10(c2)))) <=> (~(f8(c1) = c2))),
% 28.40/18.60 inference(monotonicity,[status(thm)],[11840])).
% 28.40/18.60 tff(11842,plain,
% 28.40/18.60 ((f10(f10(c2)) = f10(c2)) <=> (f10(f10(c2)) = c1)),
% 28.40/18.60 inference(monotonicity,[status(thm)],[11819])).
% 28.40/18.60 tff(11843,plain,
% 28.40/18.60 ((f10(f10(c2)) = c1) <=> (f10(f10(c2)) = f10(c2))),
% 28.40/18.60 inference(symmetry,[status(thm)],[11842])).
% 28.40/18.60 tff(11844,plain,
% 28.40/18.60 (f10(f10(c2)) = f10(c1)),
% 28.40/18.60 inference(monotonicity,[status(thm)],[11819])).
% 28.40/18.60 tff(11845,plain,
% 28.40/18.60 ((f10(f10(c2)) = c1) <=> (f10(c1) = c1)),
% 28.40/18.60 inference(monotonicity,[status(thm)],[11844])).
% 28.40/18.60 tff(11846,plain,
% 28.40/18.60 ((f10(c1) = c1) <=> (f10(f10(c2)) = c1)),
% 28.40/18.60 inference(symmetry,[status(thm)],[11845])).
% 28.40/18.60 tff(11847,plain,
% 28.40/18.60 ((f10(c1) = c1) <=> (f10(f10(c2)) = f10(c2))),
% 28.40/18.60 inference(transitivity,[status(thm)],[11846, 11843])).
% 28.40/18.60 tff(11848,plain,
% 28.40/18.60 ((~(f10(c1) = c1)) <=> (~(f10(f10(c2)) = f10(c2)))),
% 28.40/18.60 inference(monotonicity,[status(thm)],[11847])).
% 28.40/18.60 tff(11849,plain,
% 28.40/18.60 (~(f10(f10(c2)) = f10(c2))),
% 28.40/18.60 inference(modus_ponens,[status(thm)],[3, 11848])).
% 28.40/18.60 tff(11850,plain,
% 28.40/18.60 (big_f(c2, f10(f10(c2))) <=> big_f(c2, f10(c1))),
% 28.40/18.60 inference(monotonicity,[status(thm)],[11844])).
% 28.40/18.60 tff(11851,plain,
% 28.40/18.60 (big_f(c2, f10(c1)) <=> big_f(c2, f10(f10(c2)))),
% 28.40/18.60 inference(symmetry,[status(thm)],[11850])).
% 28.40/18.60 tff(11852,plain,
% 28.40/18.60 (big_f(c2, f10(c1)) <=> big_f(f7(c1), f10(c1))),
% 28.40/18.60 inference(monotonicity,[status(thm)],[2778])).
% 28.40/18.60 tff(11853,plain,
% 28.40/18.60 (big_f(f7(c1), f10(c1)) <=> big_f(c2, f10(c1))),
% 28.40/18.60 inference(symmetry,[status(thm)],[11852])).
% 28.40/18.60 tff(11854,plain,
% 28.40/18.60 (big_f(f7(c1), f10(c1)) <=> big_f(c2, c2)),
% 28.40/18.60 inference(monotonicity,[status(thm)],[120, 15])).
% 28.40/18.60 tff(11855,plain,
% 28.40/18.60 (big_f(c2, c2) <=> big_f(f7(c1), f10(c1))),
% 28.40/18.60 inference(symmetry,[status(thm)],[11854])).
% 28.40/18.60 tff(11856,plain,
% 28.40/18.60 (big_f(c2, c2) <=> big_f(c2, f10(f10(c2)))),
% 28.40/18.60 inference(transitivity,[status(thm)],[11855, 11853, 11851])).
% 28.40/18.60 tff(11857,plain,
% 28.40/18.60 ((~big_f(c2, c2)) <=> (~big_f(c2, f10(f10(c2))))),
% 28.40/18.60 inference(monotonicity,[status(thm)],[11856])).
% 28.40/18.60 tff(11858,plain,
% 28.40/18.60 (~big_f(c2, f10(f10(c2)))),
% 28.40/18.60 inference(modus_ponens,[status(thm)],[121, 11857])).
% 28.40/18.60 tff(11859,plain,
% 28.40/18.60 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f7(c1) = c1) | (f10(f10(c2)) = f10(c2)) | (~(c2 = f8(f10(c2)))) | big_f(f7(c1), c1) | big_f(c2, f10(f10(c2))) | (~(c1 = f5(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(c1) = c1) | (f10(f10(c2)) = f10(c2)) | (~(c2 = f8(f10(c2)))) | big_f(f7(c1), c1) | big_f(c2, f10(f10(c2))) | (~(c1 = f5(c1))))),
% 28.40/18.60 inference(rewrite,[status(thm)],[])).
% 28.40/18.60 tff(11860,plain,
% 28.40/18.60 (((~(c1 = f5(c1))) | (f10(f10(c2)) = f10(c2)) | big_f(c2, f10(f10(c2))) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(c2 = f8(f10(c2))))) <=> ((f7(c1) = c1) | (f10(f10(c2)) = f10(c2)) | (~(c2 = f8(f10(c2)))) | big_f(f7(c1), c1) | big_f(c2, f10(f10(c2))) | (~(c1 = f5(c1))))),
% 28.40/18.60 inference(rewrite,[status(thm)],[])).
% 28.40/18.60 tff(11861,plain,
% 28.40/18.60 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c1 = f5(c1))) | (f10(f10(c2)) = f10(c2)) | big_f(c2, f10(f10(c2))) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(c2 = f8(f10(c2)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f7(c1) = c1) | (f10(f10(c2)) = f10(c2)) | (~(c2 = f8(f10(c2)))) | big_f(f7(c1), c1) | big_f(c2, f10(f10(c2))) | (~(c1 = f5(c1)))))),
% 28.40/18.61 inference(monotonicity,[status(thm)],[11860])).
% 28.40/18.61 tff(11862,plain,
% 28.40/18.61 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c1 = f5(c1))) | (f10(f10(c2)) = f10(c2)) | big_f(c2, f10(f10(c2))) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(c2 = f8(f10(c2)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(c1) = c1) | (f10(f10(c2)) = f10(c2)) | (~(c2 = f8(f10(c2)))) | big_f(f7(c1), c1) | big_f(c2, f10(f10(c2))) | (~(c1 = f5(c1))))),
% 28.40/18.61 inference(transitivity,[status(thm)],[11861, 11859])).
% 28.40/18.61 tff(11863,plain,
% 28.40/18.61 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c1 = f5(c1))) | (f10(f10(c2)) = f10(c2)) | big_f(c2, f10(f10(c2))) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(c2 = f8(f10(c2)))))),
% 28.40/18.61 inference(quant_inst,[status(thm)],[])).
% 28.40/18.61 tff(11864,plain,
% 28.40/18.61 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(c1) = c1) | (f10(f10(c2)) = f10(c2)) | (~(c2 = f8(f10(c2)))) | big_f(f7(c1), c1) | big_f(c2, f10(f10(c2))) | (~(c1 = f5(c1)))),
% 28.40/18.61 inference(modus_ponens,[status(thm)],[11863, 11862])).
% 28.40/18.61 tff(11865,plain,
% 28.40/18.61 ((f7(c1) = c1) | (f10(f10(c2)) = f10(c2)) | (~(c2 = f8(f10(c2)))) | big_f(f7(c1), c1) | big_f(c2, f10(f10(c2))) | (~(c1 = f5(c1)))),
% 28.40/18.61 inference(unit_resolution,[status(thm)],[11864, 1745])).
% 28.40/18.61 tff(11866,plain,
% 28.40/18.61 (~(c2 = f8(f10(c2)))),
% 28.40/18.61 inference(unit_resolution,[status(thm)],[11865, 11858, 115, 285, 11826, 11849])).
% 28.40/18.61 tff(11867,plain,
% 28.40/18.61 (~(f8(c1) = c2)),
% 28.40/18.61 inference(modus_ponens,[status(thm)],[11866, 11841])).
% 28.40/18.61 tff(11868,plain,
% 28.40/18.61 (f8(c1) = c1),
% 28.40/18.61 inference(unit_resolution,[status(thm)],[1680, 11867])).
% 28.40/18.61 tff(11869,plain,
% 28.40/18.61 ($false),
% 28.40/18.61 inference(unit_resolution,[status(thm)],[9808, 11868, 11838])).
% 28.40/18.61 tff(11870,plain,((f10(c1) = c1) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(c1 = f5(c1))) | (~(f10(c2) = c1)) | big_f(c2, c2) | big_f(c1, f7(c1))), inference(lemma,lemma(discharge,[]))).
% 28.40/18.61 tff(11871,plain,
% 28.40/18.61 (~(c1 = f5(c1))),
% 28.40/18.61 inference(unit_resolution,[status(thm)],[11870, 11825, 115, 3, 285, 121, 11819])).
% 28.40/18.61 tff(11872,plain,
% 28.40/18.61 (~(f5(c1) = c1)),
% 28.40/18.61 inference(modus_ponens,[status(thm)],[11871, 2279])).
% 28.40/18.61 tff(11873,plain,
% 28.40/18.61 (f5(c1) = c2),
% 28.40/18.61 inference(unit_resolution,[status(thm)],[1708, 11872])).
% 28.40/18.61 tff(11874,plain,
% 28.40/18.61 (c2 = f5(c1)),
% 28.40/18.61 inference(modus_ponens,[status(thm)],[11873, 155])).
% 28.40/18.61 tff(11875,plain,
% 28.40/18.61 (~(c2 = f8(c1))),
% 28.40/18.61 inference(unit_resolution,[status(thm)],[1752, 11874, 115, 1726, 6126, 3])).
% 28.40/18.61 tff(11876,plain,
% 28.40/18.61 (~(f8(c1) = c2)),
% 28.40/18.61 inference(unit_resolution,[status(thm)],[1675, 11875])).
% 28.40/18.61 tff(11877,plain,
% 28.40/18.61 (f8(c1) = c1),
% 28.40/18.61 inference(unit_resolution,[status(thm)],[1680, 11876])).
% 28.40/18.61 tff(11878,plain,
% 28.40/18.61 (f10(c2) = f8(f10(c2))),
% 28.40/18.61 inference(modus_ponens,[status(thm)],[11877, 11823])).
% 28.40/18.61 tff(11879,plain,
% 28.40/18.61 (f10(f10(c2)) = c2),
% 28.40/18.61 inference(transitivity,[status(thm)],[11844, 15])).
% 28.40/18.61 tff(11880,plain,
% 28.40/18.61 (big_f(f10(c2), f10(f10(c2))) <=> big_f(c1, c2)),
% 28.40/18.61 inference(monotonicity,[status(thm)],[11819, 11879])).
% 28.40/18.61 tff(11881,plain,
% 28.40/18.61 (big_f(c1, c2) <=> big_f(f10(c2), f10(f10(c2)))),
% 28.40/18.61 inference(symmetry,[status(thm)],[11880])).
% 28.40/18.61 tff(11882,plain,
% 28.40/18.61 ((~big_f(c1, c2)) <=> (~big_f(f10(c2), f10(f10(c2))))),
% 28.40/18.61 inference(monotonicity,[status(thm)],[11881])).
% 28.40/18.61 tff(11883,plain,
% 28.40/18.61 (~big_f(f10(c2), f10(f10(c2)))),
% 28.40/18.61 inference(modus_ponens,[status(thm)],[27, 11882])).
% 28.40/18.61 tff(11884,plain,
% 28.40/18.61 (f5(f10(c2)) = f5(c1)),
% 28.40/18.61 inference(monotonicity,[status(thm)],[11819])).
% 28.40/18.61 tff(11885,plain,
% 28.40/18.61 ((c2 = f5(f10(c2))) <=> (c2 = f5(c1))),
% 28.40/18.61 inference(monotonicity,[status(thm)],[11884])).
% 28.40/18.61 tff(11886,plain,
% 28.40/18.61 ((c2 = f5(c1)) <=> (c2 = f5(f10(c2)))),
% 28.40/18.61 inference(symmetry,[status(thm)],[11885])).
% 28.40/18.61 tff(11887,plain,
% 28.40/18.61 ((f5(c1) = c2) <=> (c2 = f5(f10(c2)))),
% 28.40/18.61 inference(transitivity,[status(thm)],[155, 11886])).
% 28.40/18.61 tff(11888,plain,
% 28.40/18.61 (c2 = f5(f10(c2))),
% 28.40/18.61 inference(modus_ponens,[status(thm)],[11873, 11887])).
% 28.40/18.61 tff(11889,plain,
% 28.40/18.61 (f7(f10(c2)) = f7(c1)),
% 28.40/18.61 inference(monotonicity,[status(thm)],[11819])).
% 28.40/18.61 tff(11890,plain,
% 28.40/18.61 (f7(f10(c2)) = c2),
% 28.40/18.61 inference(transitivity,[status(thm)],[11889, 120])).
% 28.40/18.61 tff(11891,plain,
% 28.40/18.61 (big_f(f7(f10(c2)), c2) <=> big_f(c2, c2)),
% 28.40/18.61 inference(monotonicity,[status(thm)],[11890])).
% 28.40/18.61 tff(11892,plain,
% 28.40/18.61 (big_f(c2, c2) <=> big_f(f7(f10(c2)), c2)),
% 28.40/18.61 inference(symmetry,[status(thm)],[11891])).
% 28.40/18.61 tff(11893,plain,
% 28.40/18.61 ((~big_f(c2, c2)) <=> (~big_f(f7(f10(c2)), c2))),
% 28.40/18.61 inference(monotonicity,[status(thm)],[11892])).
% 28.40/18.61 tff(11894,plain,
% 28.40/18.61 (~big_f(f7(f10(c2)), c2)),
% 28.40/18.61 inference(modus_ponens,[status(thm)],[121, 11893])).
% 28.40/18.61 tff(11895,assumption,(~(f7(f10(c2)) = f10(c2))), introduced(assumption)).
% 28.40/18.61 tff(11896,assumption,(~(f10(f10(c2)) = f10(c2))), introduced(assumption)).
% 28.40/18.61 tff(11897,plain,
% 28.40/18.61 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f10(f10(c2)) = f10(c2)) | (~(c2 = f5(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2) | big_f(f10(c2), f10(f10(c2))) | (~(f10(c2) = f8(f10(c2)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(f10(c2)) = f10(c2)) | (~(c2 = f5(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2) | big_f(f10(c2), f10(f10(c2))) | (~(f10(c2) = f8(f10(c2)))))),
% 28.40/18.61 inference(rewrite,[status(thm)],[])).
% 28.40/18.61 tff(11898,plain,
% 28.40/18.61 (((~(c2 = f5(f10(c2)))) | (f10(f10(c2)) = f10(c2)) | big_f(f10(c2), f10(f10(c2))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2) | (~(f10(c2) = f8(f10(c2))))) <=> ((f10(f10(c2)) = f10(c2)) | (~(c2 = f5(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2) | big_f(f10(c2), f10(f10(c2))) | (~(f10(c2) = f8(f10(c2)))))),
% 28.40/18.61 inference(rewrite,[status(thm)],[])).
% 28.40/18.61 tff(11899,plain,
% 28.40/18.61 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c2 = f5(f10(c2)))) | (f10(f10(c2)) = f10(c2)) | big_f(f10(c2), f10(f10(c2))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2) | (~(f10(c2) = f8(f10(c2)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f10(f10(c2)) = f10(c2)) | (~(c2 = f5(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2) | big_f(f10(c2), f10(f10(c2))) | (~(f10(c2) = f8(f10(c2))))))),
% 28.40/18.61 inference(monotonicity,[status(thm)],[11898])).
% 28.40/18.61 tff(11900,plain,
% 28.40/18.61 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c2 = f5(f10(c2)))) | (f10(f10(c2)) = f10(c2)) | big_f(f10(c2), f10(f10(c2))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2) | (~(f10(c2) = f8(f10(c2)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(f10(c2)) = f10(c2)) | (~(c2 = f5(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2) | big_f(f10(c2), f10(f10(c2))) | (~(f10(c2) = f8(f10(c2)))))),
% 28.40/18.61 inference(transitivity,[status(thm)],[11899, 11897])).
% 28.40/18.61 tff(11901,plain,
% 28.40/18.61 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c2 = f5(f10(c2)))) | (f10(f10(c2)) = f10(c2)) | big_f(f10(c2), f10(f10(c2))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2) | (~(f10(c2) = f8(f10(c2)))))),
% 28.40/18.61 inference(quant_inst,[status(thm)],[])).
% 28.40/18.61 tff(11902,plain,
% 28.40/18.61 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(f10(c2)) = f10(c2)) | (~(c2 = f5(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2) | big_f(f10(c2), f10(f10(c2))) | (~(f10(c2) = f8(f10(c2))))),
% 28.40/18.61 inference(modus_ponens,[status(thm)],[11901, 11900])).
% 28.40/18.61 tff(11903,plain,
% 28.40/18.61 ((~(c2 = f5(f10(c2)))) | big_f(f10(c2), f10(f10(c2))) | (~(f10(c2) = f8(f10(c2))))),
% 28.40/18.61 inference(unit_resolution,[status(thm)],[11902, 1745, 11896, 11895, 11894])).
% 28.40/18.61 tff(11904,plain,
% 28.40/18.61 (~(f10(c2) = f8(f10(c2)))),
% 28.40/18.61 inference(unit_resolution,[status(thm)],[11903, 11888, 11883])).
% 28.40/18.61 tff(11905,plain,
% 28.40/18.61 ($false),
% 28.40/18.61 inference(unit_resolution,[status(thm)],[11904, 11878])).
% 28.40/18.61 tff(11906,plain,(big_f(c1, c2) | (~(f10(c2) = c1)) | (f10(f10(c2)) = f10(c2)) | (f7(f10(c2)) = f10(c2)) | (f7(c1) = c1) | (f10(c1) = c1) | big_f(f7(c1), c1) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 28.40/18.61 tff(11907,plain,
% 28.40/18.61 (big_f(c1, c2)),
% 28.40/18.61 inference(unit_resolution,[status(thm)],[11906, 695, 11818, 11811, 115, 3, 11799, 121])).
% 28.40/18.61 tff(11908,plain,
% 28.40/18.61 (big_f(c1, f7(c1))),
% 28.40/18.61 inference(modus_ponens,[status(thm)],[11907, 11804])).
% 28.40/18.61 tff(11909,assumption,(big_f(c1, f7(c1))), introduced(assumption)).
% 28.40/18.61 tff(11910,assumption,(~(f3(f7(c1), c1) = c1)), introduced(assumption)).
% 28.40/18.61 tff(11911,plain,
% 28.40/18.61 (f3(f7(c1), c1) = c2),
% 28.40/18.61 inference(unit_resolution,[status(thm)],[918, 11910])).
% 28.40/18.61 tff(11912,plain,
% 28.40/18.61 (big_f(f3(f7(c1), c1), f7(c1)) <=> big_f(c2, c2)),
% 28.40/18.61 inference(monotonicity,[status(thm)],[11911, 120])).
% 28.40/18.61 tff(11913,plain,
% 28.40/18.61 (big_f(c2, c2) <=> big_f(f3(f7(c1), c1), f7(c1))),
% 28.40/18.61 inference(symmetry,[status(thm)],[11912])).
% 28.40/18.61 tff(11914,plain,
% 28.40/18.61 ((~big_f(c2, c2)) <=> (~big_f(f3(f7(c1), c1), f7(c1)))),
% 28.40/18.61 inference(monotonicity,[status(thm)],[11913])).
% 28.40/18.61 tff(11915,plain,
% 28.40/18.61 (~big_f(f3(f7(c1), c1), f7(c1))),
% 28.40/18.61 inference(modus_ponens,[status(thm)],[121, 11914])).
% 28.40/18.61 tff(11916,plain,
% 28.40/18.61 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (f7(c1) = c4) | (c1 = f2(c1)) | (f3(f7(c1), c1) = c1) | big_f(f3(f7(c1), c1), f7(c1)) | (~big_f(c1, c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c1 = c3)) | (f7(c1) = c4) | (c1 = f2(c1)) | (f3(f7(c1), c1) = c1) | big_f(f3(f7(c1), c1), f7(c1)) | (~big_f(c1, c1)))),
% 28.40/18.61 inference(rewrite,[status(thm)],[])).
% 28.40/18.61 tff(11917,plain,
% 28.40/18.61 (((~(c1 = c3)) | (f7(c1) = c4) | (f3(f7(c1), c1) = c1) | big_f(f3(f7(c1), c1), f7(c1)) | (c1 = f2(c1)) | (~big_f(c1, c1))) <=> ((~(c1 = c3)) | (f7(c1) = c4) | (c1 = f2(c1)) | (f3(f7(c1), c1) = c1) | big_f(f3(f7(c1), c1), f7(c1)) | (~big_f(c1, c1)))),
% 28.40/18.61 inference(rewrite,[status(thm)],[])).
% 28.40/18.61 tff(11918,plain,
% 28.40/18.61 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (f7(c1) = c4) | (f3(f7(c1), c1) = c1) | big_f(f3(f7(c1), c1), f7(c1)) | (c1 = f2(c1)) | (~big_f(c1, c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (f7(c1) = c4) | (c1 = f2(c1)) | (f3(f7(c1), c1) = c1) | big_f(f3(f7(c1), c1), f7(c1)) | (~big_f(c1, c1))))),
% 28.40/18.61 inference(monotonicity,[status(thm)],[11917])).
% 28.40/18.61 tff(11919,plain,
% 28.40/18.61 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (f7(c1) = c4) | (f3(f7(c1), c1) = c1) | big_f(f3(f7(c1), c1), f7(c1)) | (c1 = f2(c1)) | (~big_f(c1, c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c1 = c3)) | (f7(c1) = c4) | (c1 = f2(c1)) | (f3(f7(c1), c1) = c1) | big_f(f3(f7(c1), c1), f7(c1)) | (~big_f(c1, c1)))),
% 28.40/18.61 inference(transitivity,[status(thm)],[11918, 11916])).
% 28.40/18.61 tff(11920,plain,
% 28.40/18.61 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (f7(c1) = c4) | (f3(f7(c1), c1) = c1) | big_f(f3(f7(c1), c1), f7(c1)) | (c1 = f2(c1)) | (~big_f(c1, c1)))),
% 28.40/18.61 inference(quant_inst,[status(thm)],[])).
% 28.40/18.61 tff(11921,plain,
% 28.40/18.61 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c1 = c3)) | (f7(c1) = c4) | (c1 = f2(c1)) | (f3(f7(c1), c1) = c1) | big_f(f3(f7(c1), c1), f7(c1)) | (~big_f(c1, c1))),
% 28.40/18.61 inference(modus_ponens,[status(thm)],[11920, 11919])).
% 28.40/18.61 tff(11922,plain,
% 28.40/18.61 (c1 = f2(c1)),
% 28.40/18.61 inference(unit_resolution,[status(thm)],[11921, 7352, 5080, 1000, 11910, 11915, 4932])).
% 28.40/18.61 tff(11923,plain,
% 28.40/18.61 (f2(c1) = c1),
% 28.40/18.61 inference(symmetry,[status(thm)],[11922])).
% 28.40/18.61 tff(11924,plain,
% 28.40/18.61 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (f7(c1) = c4) | (f3(f7(c1), c1) = c1) | big_f(f3(f7(c1), c1), f7(c1)) | (f7(c1) = f2(c1)) | (~big_f(c1, f7(c1))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c1 = c3)) | (f7(c1) = c4) | (f3(f7(c1), c1) = c1) | big_f(f3(f7(c1), c1), f7(c1)) | (f7(c1) = f2(c1)) | (~big_f(c1, f7(c1))))),
% 28.40/18.61 inference(rewrite,[status(thm)],[])).
% 28.40/18.61 tff(11925,plain,
% 28.40/18.61 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (f7(c1) = c4) | (f3(f7(c1), c1) = c1) | big_f(f3(f7(c1), c1), f7(c1)) | (f7(c1) = f2(c1)) | (~big_f(c1, f7(c1))))),
% 28.40/18.61 inference(quant_inst,[status(thm)],[])).
% 28.40/18.61 tff(11926,plain,
% 28.40/18.61 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c1 = c3)) | (f7(c1) = c4) | (f3(f7(c1), c1) = c1) | big_f(f3(f7(c1), c1), f7(c1)) | (f7(c1) = f2(c1)) | (~big_f(c1, f7(c1)))),
% 28.40/18.61 inference(modus_ponens,[status(thm)],[11925, 11924])).
% 28.40/18.61 tff(11927,plain,
% 28.40/18.61 (f7(c1) = f2(c1)),
% 28.40/18.61 inference(unit_resolution,[status(thm)],[11926, 7352, 5080, 1000, 11910, 11915, 11909])).
% 28.40/18.61 tff(11928,plain,
% 28.40/18.61 (f7(c1) = c1),
% 28.40/18.61 inference(transitivity,[status(thm)],[11927, 11923])).
% 28.40/18.61 tff(11929,plain,
% 28.40/18.61 ($false),
% 28.40/18.61 inference(unit_resolution,[status(thm)],[115, 11928])).
% 28.40/18.61 tff(11930,plain,((f3(f7(c1), c1) = c1) | (f7(c1) = c1) | (~(c1 = c3)) | (f7(c1) = c4) | (~big_f(c1, c1)) | (~big_f(c1, f7(c1))) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 28.40/18.61 tff(11931,plain,
% 28.40/18.61 (f3(f7(c1), c1) = c1),
% 28.40/18.61 inference(unit_resolution,[status(thm)],[11930, 11909, 5080, 1000, 4932, 115, 121])).
% 28.40/18.61 tff(11932,plain,
% 28.40/18.61 (big_f(f3(f7(c1), c1), f7(c1)) <=> big_f(c1, f7(c1))),
% 28.40/18.61 inference(monotonicity,[status(thm)],[11931])).
% 28.40/18.61 tff(11933,plain,
% 28.40/18.61 (big_f(c1, f7(c1)) <=> big_f(f3(f7(c1), c1), f7(c1))),
% 28.40/18.61 inference(symmetry,[status(thm)],[11932])).
% 28.40/18.61 tff(11934,plain,
% 28.40/18.61 (big_f(f3(f7(c1), c1), f7(c1))),
% 28.40/18.61 inference(modus_ponens,[status(thm)],[11909, 11933])).
% 28.40/18.61 tff(11935,plain,
% 28.40/18.61 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (f7(c1) = c4) | (c1 = f2(c1)) | (~big_f(c1, c1)) | (~big_f(f3(f7(c1), c1), f7(c1))) | (~(f3(f7(c1), c1) = c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c1 = c3)) | (f7(c1) = c4) | (c1 = f2(c1)) | (~big_f(c1, c1)) | (~big_f(f3(f7(c1), c1), f7(c1))) | (~(f3(f7(c1), c1) = c1)))),
% 28.40/18.61 inference(rewrite,[status(thm)],[])).
% 28.40/18.61 tff(11936,plain,
% 28.40/18.61 (((~(c1 = c3)) | (f7(c1) = c4) | (~(f3(f7(c1), c1) = c1)) | (~big_f(f3(f7(c1), c1), f7(c1))) | (c1 = f2(c1)) | (~big_f(c1, c1))) <=> ((~(c1 = c3)) | (f7(c1) = c4) | (c1 = f2(c1)) | (~big_f(c1, c1)) | (~big_f(f3(f7(c1), c1), f7(c1))) | (~(f3(f7(c1), c1) = c1)))),
% 28.40/18.61 inference(rewrite,[status(thm)],[])).
% 28.40/18.61 tff(11937,plain,
% 28.40/18.61 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (f7(c1) = c4) | (~(f3(f7(c1), c1) = c1)) | (~big_f(f3(f7(c1), c1), f7(c1))) | (c1 = f2(c1)) | (~big_f(c1, c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (f7(c1) = c4) | (c1 = f2(c1)) | (~big_f(c1, c1)) | (~big_f(f3(f7(c1), c1), f7(c1))) | (~(f3(f7(c1), c1) = c1))))),
% 28.40/18.61 inference(monotonicity,[status(thm)],[11936])).
% 28.40/18.61 tff(11938,plain,
% 28.40/18.61 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (f7(c1) = c4) | (~(f3(f7(c1), c1) = c1)) | (~big_f(f3(f7(c1), c1), f7(c1))) | (c1 = f2(c1)) | (~big_f(c1, c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c1 = c3)) | (f7(c1) = c4) | (c1 = f2(c1)) | (~big_f(c1, c1)) | (~big_f(f3(f7(c1), c1), f7(c1))) | (~(f3(f7(c1), c1) = c1)))),
% 28.40/18.61 inference(transitivity,[status(thm)],[11937, 11935])).
% 28.40/18.61 tff(11939,plain,
% 28.40/18.61 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (f7(c1) = c4) | (~(f3(f7(c1), c1) = c1)) | (~big_f(f3(f7(c1), c1), f7(c1))) | (c1 = f2(c1)) | (~big_f(c1, c1)))),
% 28.40/18.61 inference(quant_inst,[status(thm)],[])).
% 28.40/18.61 tff(11940,plain,
% 28.40/18.61 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c1 = c3)) | (f7(c1) = c4) | (c1 = f2(c1)) | (~big_f(c1, c1)) | (~big_f(f3(f7(c1), c1), f7(c1))) | (~(f3(f7(c1), c1) = c1))),
% 28.40/18.61 inference(modus_ponens,[status(thm)],[11939, 11938])).
% 28.40/18.61 tff(11941,plain,
% 28.40/18.61 (c1 = f2(c1)),
% 28.40/18.61 inference(unit_resolution,[status(thm)],[11940, 7051, 5080, 1000, 11931, 11934, 4932])).
% 28.40/18.61 tff(11942,plain,
% 28.40/18.61 (f2(c1) = c1),
% 28.40/18.61 inference(symmetry,[status(thm)],[11941])).
% 28.40/18.61 tff(11943,plain,
% 28.40/18.61 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (f7(c1) = c4) | (f7(c1) = f2(c1)) | (~big_f(c1, f7(c1))) | (~big_f(f3(f7(c1), c1), f7(c1))) | (~(f3(f7(c1), c1) = c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c1 = c3)) | (f7(c1) = c4) | (f7(c1) = f2(c1)) | (~big_f(c1, f7(c1))) | (~big_f(f3(f7(c1), c1), f7(c1))) | (~(f3(f7(c1), c1) = c1)))),
% 28.40/18.61 inference(rewrite,[status(thm)],[])).
% 28.40/18.61 tff(11944,plain,
% 28.40/18.61 (((~(c1 = c3)) | (f7(c1) = c4) | (~(f3(f7(c1), c1) = c1)) | (~big_f(f3(f7(c1), c1), f7(c1))) | (f7(c1) = f2(c1)) | (~big_f(c1, f7(c1)))) <=> ((~(c1 = c3)) | (f7(c1) = c4) | (f7(c1) = f2(c1)) | (~big_f(c1, f7(c1))) | (~big_f(f3(f7(c1), c1), f7(c1))) | (~(f3(f7(c1), c1) = c1)))),
% 28.40/18.61 inference(rewrite,[status(thm)],[])).
% 28.40/18.61 tff(11945,plain,
% 28.40/18.61 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (f7(c1) = c4) | (~(f3(f7(c1), c1) = c1)) | (~big_f(f3(f7(c1), c1), f7(c1))) | (f7(c1) = f2(c1)) | (~big_f(c1, f7(c1))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (f7(c1) = c4) | (f7(c1) = f2(c1)) | (~big_f(c1, f7(c1))) | (~big_f(f3(f7(c1), c1), f7(c1))) | (~(f3(f7(c1), c1) = c1))))),
% 28.40/18.61 inference(monotonicity,[status(thm)],[11944])).
% 28.40/18.61 tff(11946,plain,
% 28.40/18.61 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (f7(c1) = c4) | (~(f3(f7(c1), c1) = c1)) | (~big_f(f3(f7(c1), c1), f7(c1))) | (f7(c1) = f2(c1)) | (~big_f(c1, f7(c1))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c1 = c3)) | (f7(c1) = c4) | (f7(c1) = f2(c1)) | (~big_f(c1, f7(c1))) | (~big_f(f3(f7(c1), c1), f7(c1))) | (~(f3(f7(c1), c1) = c1)))),
% 28.40/18.61 inference(transitivity,[status(thm)],[11945, 11943])).
% 28.40/18.61 tff(11947,plain,
% 28.40/18.61 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (f7(c1) = c4) | (~(f3(f7(c1), c1) = c1)) | (~big_f(f3(f7(c1), c1), f7(c1))) | (f7(c1) = f2(c1)) | (~big_f(c1, f7(c1))))),
% 28.40/18.61 inference(quant_inst,[status(thm)],[])).
% 28.40/18.61 tff(11948,plain,
% 28.40/18.61 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c1 = c3)) | (f7(c1) = c4) | (f7(c1) = f2(c1)) | (~big_f(c1, f7(c1))) | (~big_f(f3(f7(c1), c1), f7(c1))) | (~(f3(f7(c1), c1) = c1))),
% 28.40/18.61 inference(modus_ponens,[status(thm)],[11947, 11946])).
% 28.40/18.61 tff(11949,plain,
% 28.40/18.61 (f7(c1) = f2(c1)),
% 28.40/18.61 inference(unit_resolution,[status(thm)],[11948, 7051, 5080, 1000, 11931, 11934, 11909])).
% 28.40/18.61 tff(11950,plain,
% 28.40/18.61 (f7(c1) = c1),
% 28.40/18.61 inference(transitivity,[status(thm)],[11949, 11942])).
% 28.40/18.61 tff(11951,plain,
% 28.40/18.61 ($false),
% 28.40/18.61 inference(unit_resolution,[status(thm)],[115, 11950])).
% 28.40/18.61 tff(11952,plain,((~big_f(c1, f7(c1))) | (f7(c1) = c1) | (~(c1 = c3)) | (f7(c1) = c4) | (~big_f(c1, c1)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 28.40/18.61 tff(11953,plain,
% 28.40/18.61 (f7(c1) = c4),
% 28.40/18.61 inference(unit_resolution,[status(thm)],[11952, 11908, 4932, 115, 11802, 121])).
% 28.40/18.61 tff(11954,plain,
% 28.40/18.61 (c2 = c4),
% 28.40/18.61 inference(transitivity,[status(thm)],[2778, 11953])).
% 28.40/18.61 tff(11955,plain,
% 28.40/18.61 (f4(c2) = f4(c4)),
% 28.40/18.61 inference(monotonicity,[status(thm)],[11954])).
% 28.40/18.61 tff(11956,plain,
% 28.40/18.61 (f4(c2) = c2),
% 28.40/18.61 inference(transitivity,[status(thm)],[11955, 79])).
% 28.40/18.61 tff(11957,plain,
% 28.40/18.61 (c1 = f10(c2)),
% 28.40/18.61 inference(symmetry,[status(thm)],[11799])).
% 28.40/18.61 tff(11958,plain,
% 28.40/18.61 ((c1 = f4(c2)) <=> (f10(c2) = c2)),
% 28.40/18.61 inference(monotonicity,[status(thm)],[11957, 11956])).
% 28.40/18.61 tff(11959,plain,
% 28.40/18.61 ((f10(c2) = c2) <=> (c1 = f4(c2))),
% 28.40/18.61 inference(symmetry,[status(thm)],[11958])).
% 28.40/18.61 tff(11960,plain,
% 28.40/18.61 ((f10(c2) = c2) <=> (f10(c2) = f4(c2))),
% 28.40/18.61 inference(transitivity,[status(thm)],[11959, 11801])).
% 28.40/18.61 tff(11961,plain,
% 28.40/18.61 ((~(f10(c2) = c2)) <=> (~(f10(c2) = f4(c2)))),
% 28.40/18.61 inference(monotonicity,[status(thm)],[11960])).
% 28.40/18.61 tff(11962,plain,
% 28.40/18.61 (~(f10(c2) = f4(c2))),
% 28.40/18.61 inference(modus_ponens,[status(thm)],[11798, 11961])).
% 28.40/18.61 tff(11963,plain,
% 28.40/18.61 (c2 = c4),
% 28.40/18.61 inference(modus_ponens,[status(thm)],[11953, 2811])).
% 28.40/18.61 tff(11964,plain,
% 28.40/18.61 (big_f(f10(c2), c2) <=> big_f(c1, c2)),
% 28.40/18.61 inference(monotonicity,[status(thm)],[11799])).
% 28.40/18.61 tff(11965,plain,
% 28.40/18.61 (big_f(c1, c2) <=> big_f(f10(c2), c2)),
% 28.40/18.61 inference(symmetry,[status(thm)],[11964])).
% 28.40/18.61 tff(11966,plain,
% 28.40/18.61 (big_f(f10(c2), c2)),
% 28.40/18.61 inference(modus_ponens,[status(thm)],[11907, 11965])).
% 28.40/18.61 tff(11967,plain,
% 28.40/18.61 (f10(c2) = c3),
% 28.40/18.61 inference(transitivity,[status(thm)],[11799, 10743])).
% 28.40/18.61 tff(11968,plain,
% 28.40/18.61 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c4)) | (~(f10(c2) = c3)) | (~big_f(f10(c2), c2)) | (f10(c2) = f4(c2)) | (c2 = f2(f10(c2))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c4)) | (~(f10(c2) = c3)) | (~big_f(f10(c2), c2)) | (f10(c2) = f4(c2)) | (c2 = f2(f10(c2))))),
% 28.40/18.62 inference(rewrite,[status(thm)],[])).
% 28.40/18.62 tff(11969,plain,
% 28.40/18.62 (((~(f10(c2) = c3)) | (~(c2 = c4)) | (f10(c2) = f4(c2)) | (~big_f(f10(c2), c2)) | (c2 = f2(f10(c2))) | (~big_f(f10(c2), c2))) <=> ((~(c2 = c4)) | (~(f10(c2) = c3)) | (~big_f(f10(c2), c2)) | (f10(c2) = f4(c2)) | (c2 = f2(f10(c2))))),
% 28.40/18.62 inference(rewrite,[status(thm)],[])).
% 28.40/18.62 tff(11970,plain,
% 28.40/18.62 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f10(c2) = c3)) | (~(c2 = c4)) | (f10(c2) = f4(c2)) | (~big_f(f10(c2), c2)) | (c2 = f2(f10(c2))) | (~big_f(f10(c2), c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c4)) | (~(f10(c2) = c3)) | (~big_f(f10(c2), c2)) | (f10(c2) = f4(c2)) | (c2 = f2(f10(c2)))))),
% 28.40/18.62 inference(monotonicity,[status(thm)],[11969])).
% 28.40/18.62 tff(11971,plain,
% 28.40/18.62 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f10(c2) = c3)) | (~(c2 = c4)) | (f10(c2) = f4(c2)) | (~big_f(f10(c2), c2)) | (c2 = f2(f10(c2))) | (~big_f(f10(c2), c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c4)) | (~(f10(c2) = c3)) | (~big_f(f10(c2), c2)) | (f10(c2) = f4(c2)) | (c2 = f2(f10(c2))))),
% 28.40/18.62 inference(transitivity,[status(thm)],[11970, 11968])).
% 28.40/18.62 tff(11972,plain,
% 28.40/18.62 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f10(c2) = c3)) | (~(c2 = c4)) | (f10(c2) = f4(c2)) | (~big_f(f10(c2), c2)) | (c2 = f2(f10(c2))) | (~big_f(f10(c2), c2)))),
% 28.40/18.62 inference(quant_inst,[status(thm)],[])).
% 28.40/18.62 tff(11973,plain,
% 28.40/18.62 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c4)) | (~(f10(c2) = c3)) | (~big_f(f10(c2), c2)) | (f10(c2) = f4(c2)) | (c2 = f2(f10(c2)))),
% 28.40/18.62 inference(modus_ponens,[status(thm)],[11972, 11971])).
% 28.40/18.62 tff(11974,plain,
% 28.40/18.62 ((~(c2 = c4)) | (~big_f(f10(c2), c2)) | (f10(c2) = f4(c2)) | (c2 = f2(f10(c2)))),
% 28.40/18.62 inference(unit_resolution,[status(thm)],[11973, 1355, 11967])).
% 28.40/18.62 tff(11975,plain,
% 28.40/18.62 (c2 = f2(f10(c2))),
% 28.40/18.62 inference(unit_resolution,[status(thm)],[11974, 11966, 11963, 11962])).
% 28.40/18.62 tff(11976,plain,
% 28.40/18.62 (f2(f10(c2)) = c2),
% 28.40/18.62 inference(symmetry,[status(thm)],[11975])).
% 28.40/18.62 tff(11977,plain,
% 28.40/18.62 (big_f(f10(c2), f10(c2)) <=> big_f(c1, c1)),
% 28.40/18.62 inference(monotonicity,[status(thm)],[11799, 11799])).
% 28.40/18.62 tff(11978,plain,
% 28.40/18.62 (big_f(c1, c1) <=> big_f(f10(c2), f10(c2))),
% 28.40/18.62 inference(symmetry,[status(thm)],[11977])).
% 28.40/18.62 tff(11979,plain,
% 28.40/18.62 (big_f(f10(c2), f10(c2))),
% 28.40/18.62 inference(modus_ponens,[status(thm)],[4932, 11978])).
% 28.40/18.62 tff(11980,plain,
% 28.40/18.62 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c4)) | (~(f10(c2) = c3)) | (f10(c2) = f2(f10(c2))) | (~big_f(f10(c2), c2)) | (f10(c2) = f4(c2)) | (~big_f(f10(c2), f10(c2))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c4)) | (~(f10(c2) = c3)) | (f10(c2) = f2(f10(c2))) | (~big_f(f10(c2), c2)) | (f10(c2) = f4(c2)) | (~big_f(f10(c2), f10(c2))))),
% 28.40/18.62 inference(rewrite,[status(thm)],[])).
% 28.40/18.62 tff(11981,plain,
% 28.40/18.62 (((~(f10(c2) = c3)) | (~(c2 = c4)) | (f10(c2) = f4(c2)) | (~big_f(f10(c2), c2)) | (f10(c2) = f2(f10(c2))) | (~big_f(f10(c2), f10(c2)))) <=> ((~(c2 = c4)) | (~(f10(c2) = c3)) | (f10(c2) = f2(f10(c2))) | (~big_f(f10(c2), c2)) | (f10(c2) = f4(c2)) | (~big_f(f10(c2), f10(c2))))),
% 28.40/18.62 inference(rewrite,[status(thm)],[])).
% 28.40/18.62 tff(11982,plain,
% 28.40/18.62 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f10(c2) = c3)) | (~(c2 = c4)) | (f10(c2) = f4(c2)) | (~big_f(f10(c2), c2)) | (f10(c2) = f2(f10(c2))) | (~big_f(f10(c2), f10(c2))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c4)) | (~(f10(c2) = c3)) | (f10(c2) = f2(f10(c2))) | (~big_f(f10(c2), c2)) | (f10(c2) = f4(c2)) | (~big_f(f10(c2), f10(c2)))))),
% 28.40/18.62 inference(monotonicity,[status(thm)],[11981])).
% 28.40/18.62 tff(11983,plain,
% 28.40/18.62 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f10(c2) = c3)) | (~(c2 = c4)) | (f10(c2) = f4(c2)) | (~big_f(f10(c2), c2)) | (f10(c2) = f2(f10(c2))) | (~big_f(f10(c2), f10(c2))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c4)) | (~(f10(c2) = c3)) | (f10(c2) = f2(f10(c2))) | (~big_f(f10(c2), c2)) | (f10(c2) = f4(c2)) | (~big_f(f10(c2), f10(c2))))),
% 28.40/18.62 inference(transitivity,[status(thm)],[11982, 11980])).
% 28.40/18.62 tff(11984,plain,
% 28.40/18.62 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f10(c2) = c3)) | (~(c2 = c4)) | (f10(c2) = f4(c2)) | (~big_f(f10(c2), c2)) | (f10(c2) = f2(f10(c2))) | (~big_f(f10(c2), f10(c2))))),
% 28.40/18.62 inference(quant_inst,[status(thm)],[])).
% 28.40/18.62 tff(11985,plain,
% 28.40/18.62 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c4)) | (~(f10(c2) = c3)) | (f10(c2) = f2(f10(c2))) | (~big_f(f10(c2), c2)) | (f10(c2) = f4(c2)) | (~big_f(f10(c2), f10(c2)))),
% 28.40/18.62 inference(modus_ponens,[status(thm)],[11984, 11983])).
% 28.40/18.62 tff(11986,plain,
% 28.40/18.62 ((~(c2 = c4)) | (f10(c2) = f2(f10(c2))) | (~big_f(f10(c2), c2)) | (f10(c2) = f4(c2))),
% 28.40/18.62 inference(unit_resolution,[status(thm)],[11985, 1355, 11967, 11979])).
% 28.40/18.62 tff(11987,plain,
% 28.40/18.62 (f10(c2) = f2(f10(c2))),
% 28.40/18.62 inference(unit_resolution,[status(thm)],[11986, 11963, 11966, 11962])).
% 28.40/18.62 tff(11988,plain,
% 28.40/18.62 (f10(c2) = c2),
% 28.40/18.62 inference(transitivity,[status(thm)],[11987, 11976])).
% 28.40/18.62 tff(11989,plain,
% 28.40/18.62 ($false),
% 28.40/18.62 inference(unit_resolution,[status(thm)],[11798, 11988])).
% 28.40/18.62 tff(11990,plain,(big_f(c2, c1) | (~(f4(c4) = c2)) | (~big_f(c1, c1)) | (f7(c1) = c1) | big_f(c2, c2) | (f10(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 28.40/18.62 tff(11991,plain,
% 28.40/18.62 (~big_f(c1, c1)),
% 28.40/18.62 inference(unit_resolution,[status(thm)],[11990, 2, 121, 115, 79, 3])).
% 28.40/18.62 tff(11992,plain,
% 28.40/18.62 ((f10(c2) = f8(c2)) <=> (c1 = f8(c2))),
% 28.40/18.62 inference(monotonicity,[status(thm)],[11799])).
% 28.40/18.62 tff(11993,plain,
% 28.40/18.62 ((c1 = f8(c2)) <=> (f10(c2) = f8(c2))),
% 28.40/18.62 inference(symmetry,[status(thm)],[11992])).
% 28.40/18.62 tff(11994,plain,
% 28.40/18.62 (f8(f10(c1)) = f8(c2)),
% 28.40/18.62 inference(monotonicity,[status(thm)],[16])).
% 28.40/18.62 tff(11995,plain,
% 28.40/18.62 ((c1 = f8(f10(c1))) <=> (c1 = f8(c2))),
% 28.40/18.62 inference(monotonicity,[status(thm)],[11994])).
% 28.40/18.62 tff(11996,plain,
% 28.40/18.62 ((f8(f10(c1)) = c1) <=> (c1 = f8(f10(c1)))),
% 28.40/18.62 inference(commutativity,[status(thm)],[])).
% 28.40/18.62 tff(11997,plain,
% 28.40/18.62 ((f8(f10(c1)) = c1) <=> (f10(c2) = f8(c2))),
% 28.40/18.62 inference(transitivity,[status(thm)],[11996, 11995, 11993])).
% 28.40/18.62 tff(11998,plain,
% 28.40/18.62 ((f8(c2) = c2) <=> (c2 = f8(c2))),
% 28.40/18.62 inference(commutativity,[status(thm)],[])).
% 28.40/18.62 tff(11999,plain,
% 28.40/18.62 ((f8(f10(c1)) = c2) <=> (f8(c2) = c2)),
% 28.40/18.62 inference(monotonicity,[status(thm)],[11994])).
% 28.40/18.62 tff(12000,plain,
% 28.40/18.62 ((f8(f10(c1)) = c2) <=> (c2 = f8(c2))),
% 28.40/18.62 inference(transitivity,[status(thm)],[11999, 11998])).
% 28.40/18.62 tff(12001,plain,
% 28.40/18.62 ((c2 = f8(c2)) <=> (f8(f10(c1)) = c2)),
% 28.40/18.62 inference(symmetry,[status(thm)],[12000])).
% 28.40/18.62 tff(12002,plain,
% 28.40/18.62 ((~(c2 = f8(c2))) <=> (~(f8(f10(c1)) = c2))),
% 28.40/18.62 inference(monotonicity,[status(thm)],[12001])).
% 28.40/18.62 tff(12003,plain,
% 28.40/18.62 (big_f(c2, f10(c2)) <=> big_f(c2, c1)),
% 28.40/18.62 inference(monotonicity,[status(thm)],[11799])).
% 28.40/18.62 tff(12004,plain,
% 28.40/18.62 (big_f(c2, c1) <=> big_f(c2, f10(c2))),
% 28.40/18.62 inference(symmetry,[status(thm)],[12003])).
% 28.40/18.62 tff(12005,plain,
% 28.40/18.62 ((~big_f(c2, c1)) <=> (~big_f(c2, f10(c2)))),
% 28.40/18.62 inference(monotonicity,[status(thm)],[12004])).
% 28.40/18.62 tff(12006,plain,
% 28.40/18.62 (~big_f(c2, f10(c2))),
% 28.40/18.62 inference(modus_ponens,[status(thm)],[2, 12005])).
% 28.40/18.62 tff(12007,plain,
% 28.40/18.62 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f7(c1) = c1) | (f10(c2) = c2) | big_f(f7(c1), f5(c1)) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(c1) = c1) | (f10(c2) = c2) | big_f(f7(c1), f5(c1)) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))))),
% 28.40/18.62 inference(rewrite,[status(thm)],[])).
% 28.40/18.62 tff(12008,plain,
% 28.40/18.62 (($false | (f10(c2) = c2) | big_f(c2, f10(c2)) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (~(c2 = f8(c2)))) <=> ((f7(c1) = c1) | (f10(c2) = c2) | big_f(f7(c1), f5(c1)) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))))),
% 28.40/18.62 inference(rewrite,[status(thm)],[])).
% 28.40/18.62 tff(12009,plain,
% 28.40/18.62 (((~(f5(c1) = f5(c1))) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (~(c2 = f8(c2)))) <=> ($false | (f10(c2) = c2) | big_f(c2, f10(c2)) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (~(c2 = f8(c2))))),
% 28.40/18.62 inference(monotonicity,[status(thm)],[273])).
% 28.40/18.62 tff(12010,plain,
% 28.40/18.62 (((~(f5(c1) = f5(c1))) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (~(c2 = f8(c2)))) <=> ((f7(c1) = c1) | (f10(c2) = c2) | big_f(f7(c1), f5(c1)) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))))),
% 28.40/18.62 inference(transitivity,[status(thm)],[12009, 12008])).
% 28.40/18.62 tff(12011,plain,
% 28.40/18.62 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(f5(c1) = f5(c1))) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (~(c2 = f8(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f7(c1) = c1) | (f10(c2) = c2) | big_f(f7(c1), f5(c1)) | big_f(c2, f10(c2)) | (~(c2 = f8(c2)))))),
% 28.40/18.62 inference(monotonicity,[status(thm)],[12010])).
% 28.40/18.62 tff(12012,plain,
% 28.40/18.62 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(f5(c1) = f5(c1))) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (~(c2 = f8(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(c1) = c1) | (f10(c2) = c2) | big_f(f7(c1), f5(c1)) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))))),
% 28.40/18.62 inference(transitivity,[status(thm)],[12011, 12007])).
% 28.40/18.62 tff(12013,plain,
% 28.40/18.62 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(f5(c1) = f5(c1))) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (~(c2 = f8(c2))))),
% 28.40/18.62 inference(quant_inst,[status(thm)],[])).
% 28.40/18.62 tff(12014,plain,
% 28.40/18.62 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(c1) = c1) | (f10(c2) = c2) | big_f(f7(c1), f5(c1)) | big_f(c2, f10(c2)) | (~(c2 = f8(c2)))),
% 28.40/18.62 inference(modus_ponens,[status(thm)],[12013, 12012])).
% 28.40/18.62 tff(12015,plain,
% 28.40/18.62 ((f7(c1) = c1) | (f10(c2) = c2) | big_f(f7(c1), f5(c1)) | big_f(c2, f10(c2)) | (~(c2 = f8(c2)))),
% 28.40/18.62 inference(unit_resolution,[status(thm)],[12014, 1745])).
% 28.40/18.62 tff(12016,plain,
% 28.40/18.62 (~(c2 = f8(c2))),
% 28.40/18.62 inference(unit_resolution,[status(thm)],[12015, 12006, 115, 11798, 1716])).
% 28.40/18.62 tff(12017,plain,
% 28.40/18.62 (~(f8(f10(c1)) = c2)),
% 28.40/18.62 inference(modus_ponens,[status(thm)],[12016, 12002])).
% 28.40/18.62 tff(12018,plain,
% 28.40/18.62 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f8(f10(c1)) = c1) | (f8(f10(c1)) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f8(f10(c1)) = c1) | (f8(f10(c1)) = c2))),
% 28.40/18.62 inference(rewrite,[status(thm)],[])).
% 28.40/18.62 tff(12019,plain,
% 28.40/18.62 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f8(f10(c1)) = c1) | (f8(f10(c1)) = c2))),
% 28.40/18.62 inference(quant_inst,[status(thm)],[])).
% 28.40/18.62 tff(12020,plain,
% 28.40/18.62 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f8(f10(c1)) = c1) | (f8(f10(c1)) = c2)),
% 28.40/18.62 inference(modus_ponens,[status(thm)],[12019, 12018])).
% 28.40/18.62 tff(12021,plain,
% 28.40/18.62 ((f8(f10(c1)) = c1) | (f8(f10(c1)) = c2)),
% 28.40/18.62 inference(unit_resolution,[status(thm)],[12020, 10])).
% 28.40/18.62 tff(12022,plain,
% 28.40/18.62 (f8(f10(c1)) = c1),
% 28.40/18.62 inference(unit_resolution,[status(thm)],[12021, 12017])).
% 28.40/18.62 tff(12023,plain,
% 28.40/18.62 (f10(c2) = f8(c2)),
% 28.40/18.62 inference(modus_ponens,[status(thm)],[12022, 11997])).
% 28.40/18.62 tff(12024,plain,
% 28.40/18.62 ((~big_f(c1, c1)) <=> (~big_f(f10(c2), f10(c2)))),
% 28.40/18.62 inference(monotonicity,[status(thm)],[11978])).
% 28.40/18.62 tff(12025,plain,
% 28.40/18.62 (~big_f(f10(c2), f10(c2))),
% 28.40/18.62 inference(modus_ponens,[status(thm)],[66, 12024])).
% 28.40/18.62 tff(12026,plain,
% 28.40/18.62 (big_f(f7(f10(c2)), c2) <=> big_f(c2, c2)),
% 28.40/18.62 inference(monotonicity,[status(thm)],[11806])).
% 28.40/18.62 tff(12027,plain,
% 28.40/18.62 (big_f(c2, c2) <=> big_f(f7(f10(c2)), c2)),
% 28.40/18.62 inference(symmetry,[status(thm)],[12026])).
% 28.40/18.62 tff(12028,plain,
% 28.40/18.62 ((~big_f(c2, c2)) <=> (~big_f(f7(f10(c2)), c2))),
% 28.40/18.62 inference(monotonicity,[status(thm)],[12027])).
% 28.40/18.62 tff(12029,plain,
% 28.40/18.62 (~big_f(f7(f10(c2)), c2)),
% 28.40/18.62 inference(modus_ponens,[status(thm)],[121, 12028])).
% 28.40/18.62 tff(12030,plain,
% 28.40/18.62 (f5(f10(c2)) = f5(c1)),
% 28.40/18.62 inference(monotonicity,[status(thm)],[11799])).
% 28.40/18.62 tff(12031,plain,
% 28.40/18.62 (f5(c1) = f5(f10(c2))),
% 28.40/18.62 inference(symmetry,[status(thm)],[12030])).
% 28.40/18.62 tff(12032,plain,
% 28.40/18.62 (c2 = f5(f10(c2))),
% 28.40/18.62 inference(transitivity,[status(thm)],[1761, 12031])).
% 28.40/18.62 tff(12033,plain,
% 28.40/18.62 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | big_f(f10(c2), f10(c2)) | (~(c2 = f5(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2) | (~(f10(c2) = f8(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | big_f(f10(c2), f10(c2)) | (~(c2 = f5(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2) | (~(f10(c2) = f8(c2))))),
% 28.40/18.62 inference(rewrite,[status(thm)],[])).
% 28.40/18.62 tff(12034,plain,
% 28.40/18.62 (((~(c2 = f5(f10(c2)))) | (f10(c2) = c2) | big_f(f10(c2), f10(c2)) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2) | (~(f10(c2) = f8(c2)))) <=> ((f10(c2) = c2) | big_f(f10(c2), f10(c2)) | (~(c2 = f5(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2) | (~(f10(c2) = f8(c2))))),
% 28.40/18.62 inference(rewrite,[status(thm)],[])).
% 28.40/18.62 tff(12035,plain,
% 28.40/18.62 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c2 = f5(f10(c2)))) | (f10(c2) = c2) | big_f(f10(c2), f10(c2)) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2) | (~(f10(c2) = f8(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | big_f(f10(c2), f10(c2)) | (~(c2 = f5(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2) | (~(f10(c2) = f8(c2)))))),
% 28.40/18.62 inference(monotonicity,[status(thm)],[12034])).
% 28.40/18.62 tff(12036,plain,
% 28.40/18.62 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c2 = f5(f10(c2)))) | (f10(c2) = c2) | big_f(f10(c2), f10(c2)) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2) | (~(f10(c2) = f8(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | big_f(f10(c2), f10(c2)) | (~(c2 = f5(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2) | (~(f10(c2) = f8(c2))))),
% 28.40/18.62 inference(transitivity,[status(thm)],[12035, 12033])).
% 28.40/18.62 tff(12037,plain,
% 28.40/18.62 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c2 = f5(f10(c2)))) | (f10(c2) = c2) | big_f(f10(c2), f10(c2)) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2) | (~(f10(c2) = f8(c2))))),
% 28.40/18.62 inference(quant_inst,[status(thm)],[])).
% 28.40/18.62 tff(12038,plain,
% 28.40/18.62 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | big_f(f10(c2), f10(c2)) | (~(c2 = f5(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2) | (~(f10(c2) = f8(c2)))),
% 28.40/18.62 inference(modus_ponens,[status(thm)],[12037, 12036])).
% 28.40/18.62 tff(12039,plain,
% 28.40/18.62 (big_f(f10(c2), f10(c2)) | (~(c2 = f5(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2) | (~(f10(c2) = f8(c2)))),
% 28.40/18.62 inference(unit_resolution,[status(thm)],[12038, 1745, 11798])).
% 28.40/18.62 tff(12040,plain,
% 28.40/18.62 (~(f10(c2) = f8(c2))),
% 28.40/18.62 inference(unit_resolution,[status(thm)],[12039, 12032, 11811, 12029, 12025])).
% 28.40/18.62 tff(12041,plain,
% 28.40/18.62 ($false),
% 28.40/18.62 inference(unit_resolution,[status(thm)],[12040, 12023])).
% 28.40/18.62 tff(12042,plain,(big_f(c2, c2) | (~(f10(c1) = c2)) | (~(f5(c1) = c2)) | big_f(c1, c1) | (f7(c1) = c1) | big_f(c2, c1) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.40/18.62 tff(12043,plain,
% 28.40/18.62 (~(f5(c1) = c2)),
% 28.40/18.62 inference(unit_resolution,[status(thm)],[12042, 11991, 121, 2, 115, 15, 79])).
% 28.40/18.62 tff(12044,plain,
% 28.40/18.62 (f5(c1) = c1),
% 28.40/18.62 inference(unit_resolution,[status(thm)],[1708, 12043])).
% 28.40/18.62 tff(12045,plain,
% 28.40/18.62 (c1 = f5(c1)),
% 28.40/18.62 inference(modus_ponens,[status(thm)],[12044, 192])).
% 28.40/18.62 tff(12046,plain,
% 28.40/18.62 (big_f(c1, f10(c2)) <=> big_f(f7(c2), f10(c2))),
% 28.40/18.62 inference(monotonicity,[status(thm)],[342])).
% 28.40/18.62 tff(12047,plain,
% 28.40/18.62 (big_f(f7(c2), f10(c2)) <=> big_f(c1, f10(c2))),
% 28.40/18.62 inference(symmetry,[status(thm)],[12046])).
% 28.40/18.62 tff(12048,plain,
% 28.40/18.62 (f10(c2) = f7(c2)),
% 28.40/18.62 inference(transitivity,[status(thm)],[94, 342])).
% 28.40/18.62 tff(12049,plain,
% 28.40/18.62 (big_f(f7(c2), f10(c2)) <=> big_f(f7(c2), f7(c2))),
% 28.40/18.62 inference(monotonicity,[status(thm)],[12048])).
% 28.40/18.62 tff(12050,plain,
% 28.40/18.62 (big_f(f7(c2), f7(c2)) <=> big_f(f7(c2), f10(c2))),
% 28.40/18.62 inference(symmetry,[status(thm)],[12049])).
% 28.40/18.62 tff(12051,plain,
% 28.40/18.62 (big_f(c1, c1) <=> big_f(f7(c2), f7(c2))),
% 28.40/18.62 inference(monotonicity,[status(thm)],[342, 342])).
% 28.40/18.62 tff(12052,plain,
% 28.40/18.62 (big_f(c1, c1) <=> big_f(c1, f10(c2))),
% 28.40/18.62 inference(transitivity,[status(thm)],[12051, 12050, 12047])).
% 28.40/18.62 tff(12053,plain,
% 28.40/18.62 ((~big_f(c1, c1)) <=> (~big_f(c1, f10(c2)))),
% 28.40/18.62 inference(monotonicity,[status(thm)],[12052])).
% 28.40/18.62 tff(12054,plain,
% 28.40/18.62 (~big_f(c1, f10(c2))),
% 28.40/18.62 inference(modus_ponens,[status(thm)],[11991, 12053])).
% 28.40/18.62 tff(12055,assumption,(~big_f(c1, f10(c2))), introduced(assumption)).
% 28.40/18.62 tff(12056,plain,
% 28.40/18.62 ((c1 = f8(f10(c1))) <=> (f8(f10(c1)) = c1)),
% 28.40/18.62 inference(symmetry,[status(thm)],[11996])).
% 28.40/18.62 tff(12057,plain,
% 28.40/18.62 ((c1 = f8(c2)) <=> (c1 = f8(f10(c1)))),
% 28.40/18.62 inference(symmetry,[status(thm)],[11995])).
% 28.40/18.62 tff(12058,plain,
% 28.40/18.62 ((c1 = f8(c2)) <=> (f8(f10(c1)) = c1)),
% 28.40/18.62 inference(transitivity,[status(thm)],[12057, 12056])).
% 28.40/18.62 tff(12059,plain,
% 28.40/18.62 ((~(c1 = f8(c2))) <=> (~(f8(f10(c1)) = c1))),
% 28.40/18.62 inference(monotonicity,[status(thm)],[12058])).
% 28.40/18.62 tff(12060,plain,
% 28.40/18.62 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f7(c1) = c1) | (f10(c2) = c2) | big_f(f7(c1), c1) | (~(c1 = f5(c1))) | big_f(c1, f10(c2)) | (~(c1 = f8(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(c1) = c1) | (f10(c2) = c2) | big_f(f7(c1), c1) | (~(c1 = f5(c1))) | big_f(c1, f10(c2)) | (~(c1 = f8(c2))))),
% 28.40/18.62 inference(rewrite,[status(thm)],[])).
% 28.40/18.62 tff(12061,plain,
% 28.40/18.62 (((~(c1 = f5(c1))) | (f10(c2) = c2) | big_f(c1, f10(c2)) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(c1 = f8(c2)))) <=> ((f7(c1) = c1) | (f10(c2) = c2) | big_f(f7(c1), c1) | (~(c1 = f5(c1))) | big_f(c1, f10(c2)) | (~(c1 = f8(c2))))),
% 28.40/18.62 inference(rewrite,[status(thm)],[])).
% 28.40/18.62 tff(12062,plain,
% 28.40/18.62 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c1 = f5(c1))) | (f10(c2) = c2) | big_f(c1, f10(c2)) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(c1 = f8(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f7(c1) = c1) | (f10(c2) = c2) | big_f(f7(c1), c1) | (~(c1 = f5(c1))) | big_f(c1, f10(c2)) | (~(c1 = f8(c2)))))),
% 28.40/18.62 inference(monotonicity,[status(thm)],[12061])).
% 28.40/18.62 tff(12063,plain,
% 28.40/18.62 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c1 = f5(c1))) | (f10(c2) = c2) | big_f(c1, f10(c2)) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(c1 = f8(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(c1) = c1) | (f10(c2) = c2) | big_f(f7(c1), c1) | (~(c1 = f5(c1))) | big_f(c1, f10(c2)) | (~(c1 = f8(c2))))),
% 28.40/18.62 inference(transitivity,[status(thm)],[12062, 12060])).
% 28.40/18.62 tff(12064,plain,
% 28.40/18.62 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c1 = f5(c1))) | (f10(c2) = c2) | big_f(c1, f10(c2)) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(c1 = f8(c2))))),
% 28.40/18.62 inference(quant_inst,[status(thm)],[])).
% 28.40/18.62 tff(12065,plain,
% 28.40/18.62 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(c1) = c1) | (f10(c2) = c2) | big_f(f7(c1), c1) | (~(c1 = f5(c1))) | big_f(c1, f10(c2)) | (~(c1 = f8(c2)))),
% 28.40/18.62 inference(modus_ponens,[status(thm)],[12064, 12063])).
% 28.40/18.62 tff(12066,plain,
% 28.40/18.62 (~(c1 = f8(c2))),
% 28.40/18.62 inference(unit_resolution,[status(thm)],[12065, 1745, 115, 89, 285, 11826, 12055])).
% 28.40/18.62 tff(12067,plain,
% 28.40/18.62 (~(f8(f10(c1)) = c1)),
% 28.40/18.62 inference(modus_ponens,[status(thm)],[12066, 12059])).
% 28.40/18.62 tff(12068,plain,
% 28.40/18.62 (big_f(c2, f10(c2)) <=> big_f(c2, c1)),
% 28.40/18.62 inference(monotonicity,[status(thm)],[94])).
% 28.40/18.62 tff(12069,plain,
% 28.40/18.62 (big_f(c2, c1) <=> big_f(c2, f10(c2))),
% 28.40/18.62 inference(symmetry,[status(thm)],[12068])).
% 28.40/18.62 tff(12070,plain,
% 28.40/18.62 ((~big_f(c2, c1)) <=> (~big_f(c2, f10(c2)))),
% 28.40/18.62 inference(monotonicity,[status(thm)],[12069])).
% 28.40/18.62 tff(12071,plain,
% 28.40/18.62 (~big_f(c2, f10(c2))),
% 28.40/18.62 inference(modus_ponens,[status(thm)],[2, 12070])).
% 28.40/18.62 tff(12072,plain,
% 28.40/18.62 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f7(c1) = c1) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | big_f(f7(c1), c1) | (~(c1 = f5(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(c1) = c1) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | big_f(f7(c1), c1) | (~(c1 = f5(c1))))),
% 28.40/18.62 inference(rewrite,[status(thm)],[])).
% 28.40/18.62 tff(12073,plain,
% 28.40/18.62 (((~(c1 = f5(c1))) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(c2 = f8(c2)))) <=> ((f7(c1) = c1) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | big_f(f7(c1), c1) | (~(c1 = f5(c1))))),
% 28.40/18.62 inference(rewrite,[status(thm)],[])).
% 28.40/18.62 tff(12074,plain,
% 28.40/18.62 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c1 = f5(c1))) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(c2 = f8(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f7(c1) = c1) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | big_f(f7(c1), c1) | (~(c1 = f5(c1)))))),
% 28.40/18.63 inference(monotonicity,[status(thm)],[12073])).
% 28.40/18.63 tff(12075,plain,
% 28.40/18.63 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c1 = f5(c1))) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(c2 = f8(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(c1) = c1) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | big_f(f7(c1), c1) | (~(c1 = f5(c1))))),
% 28.40/18.63 inference(transitivity,[status(thm)],[12074, 12072])).
% 28.40/18.63 tff(12076,plain,
% 28.40/18.63 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c1 = f5(c1))) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(c2 = f8(c2))))),
% 28.40/18.63 inference(quant_inst,[status(thm)],[])).
% 28.40/18.63 tff(12077,plain,
% 28.40/18.63 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(c1) = c1) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | big_f(f7(c1), c1) | (~(c1 = f5(c1)))),
% 28.40/18.63 inference(modus_ponens,[status(thm)],[12076, 12075])).
% 28.40/18.63 tff(12078,plain,
% 28.40/18.63 (~(c2 = f8(c2))),
% 28.40/18.63 inference(unit_resolution,[status(thm)],[12077, 1745, 115, 89, 12071, 285, 11826])).
% 28.40/18.63 tff(12079,plain,
% 28.40/18.63 (~(f8(f10(c1)) = c2)),
% 28.40/18.63 inference(modus_ponens,[status(thm)],[12078, 12002])).
% 28.40/18.63 tff(12080,plain,
% 28.40/18.63 ($false),
% 28.40/18.63 inference(unit_resolution,[status(thm)],[12021, 12079, 12067])).
% 28.40/18.63 tff(12081,plain,(big_f(f7(c1), c1) | (~(f10(c1) = c2)) | (f7(c1) = c1) | (f10(c2) = c2) | (~(c1 = f5(c1))) | big_f(c1, f10(c2)) | big_f(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 28.40/18.63 tff(12082,plain,
% 28.40/18.63 (big_f(f7(c1), c1)),
% 28.40/18.63 inference(unit_resolution,[status(thm)],[12081, 2, 115, 89, 11826, 12055, 16])).
% 28.40/18.63 tff(12083,plain,
% 28.40/18.63 ($false),
% 28.40/18.63 inference(unit_resolution,[status(thm)],[12082, 695])).
% 28.40/18.63 tff(12084,plain,(big_f(c2, c1) | (f7(c1) = c1) | (f10(c2) = c2) | (~(c1 = f5(c1))) | big_f(c1, f10(c2)) | (~(f10(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.40/18.63 tff(12085,plain,
% 28.40/18.63 ($false),
% 28.40/18.63 inference(unit_resolution,[status(thm)],[12084, 12054, 12045, 115, 89, 2, 15])).
% 28.40/18.63 tff(12086,plain,(big_f(c2, c1) | (f7(c1) = c1) | (f10(c2) = c2) | (~(f7(c2) = c1)) | big_f(c2, c2) | (~(f4(c4) = c2)) | (f10(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 28.40/18.63 tff(12087,plain,
% 28.40/18.63 (big_f(c2, c1)),
% 28.40/18.63 inference(unit_resolution,[status(thm)],[12086, 121, 11797, 22, 115, 79, 3])).
% 28.40/18.63 tff(12088,plain,
% 28.40/18.63 ((c3 = c2) <=> (f7(f7(c2)) = c3)),
% 28.40/18.63 inference(transitivity,[status(thm)],[78, 8810])).
% 28.40/18.63 tff(12089,plain,
% 28.40/18.63 ((~(c3 = c2)) <=> (~(f7(f7(c2)) = c3))),
% 28.40/18.63 inference(monotonicity,[status(thm)],[12088])).
% 28.40/18.63 tff(12090,plain,
% 28.40/18.63 (big_f(f7(c2), c1) <=> big_f(c1, c1)),
% 28.40/18.63 inference(monotonicity,[status(thm)],[22])).
% 28.40/18.63 tff(12091,plain,
% 28.40/18.63 (big_f(c1, c1) <=> big_f(f7(c2), c1)),
% 28.40/18.63 inference(symmetry,[status(thm)],[12090])).
% 28.40/18.63 tff(12092,plain,
% 28.40/18.63 ((~big_f(c1, c1)) <=> (~big_f(f7(c2), c1))),
% 28.40/18.63 inference(monotonicity,[status(thm)],[12091])).
% 28.40/18.63 tff(12093,plain,
% 28.40/18.63 (~big_f(f7(c2), c1)),
% 28.40/18.63 inference(modus_ponens,[status(thm)],[66, 12092])).
% 28.40/18.63 tff(12094,plain,
% 28.40/18.63 ((c1 = c3) <=> (f10(c2) = c3)),
% 28.40/18.63 inference(monotonicity,[status(thm)],[99])).
% 28.40/18.63 tff(12095,plain,
% 28.40/18.63 ((f10(c2) = c3) <=> (c1 = c3)),
% 28.40/18.63 inference(symmetry,[status(thm)],[12094])).
% 28.40/18.63 tff(12096,plain,
% 28.40/18.63 ((f10(c2) = c3) <=> (f10(c2) = c2)),
% 28.40/18.63 inference(monotonicity,[status(thm)],[67])).
% 28.40/18.63 tff(12097,plain,
% 28.40/18.63 ((f10(c2) = c2) <=> (f10(c2) = c3)),
% 28.40/18.63 inference(symmetry,[status(thm)],[12096])).
% 28.40/18.63 tff(12098,plain,
% 28.40/18.63 ((f10(c2) = c2) <=> (c1 = c3)),
% 28.40/18.63 inference(transitivity,[status(thm)],[12097, 12095])).
% 28.40/18.63 tff(12099,plain,
% 28.40/18.63 ((~(f10(c2) = c2)) <=> (~(c1 = c3))),
% 28.40/18.63 inference(monotonicity,[status(thm)],[12098])).
% 28.40/18.63 tff(12100,plain,
% 28.40/18.63 (~(c1 = c3)),
% 28.40/18.63 inference(modus_ponens,[status(thm)],[89, 12099])).
% 28.40/18.63 tff(12101,plain,
% 28.40/18.63 (f7(c2) = f10(c2)),
% 28.40/18.63 inference(transitivity,[status(thm)],[22, 99])).
% 28.40/18.63 tff(12102,plain,
% 28.40/18.63 ((f7(c2) = c3) <=> (f10(c2) = c3)),
% 28.40/18.63 inference(monotonicity,[status(thm)],[12101])).
% 28.40/18.63 tff(12103,plain,
% 28.40/18.63 ((f10(c2) = c3) <=> (f7(c2) = c3)),
% 28.40/18.63 inference(symmetry,[status(thm)],[12102])).
% 28.40/18.63 tff(12104,plain,
% 28.40/18.63 ((f10(c2) = c2) <=> (f7(c2) = c3)),
% 28.40/18.63 inference(transitivity,[status(thm)],[12097, 12103])).
% 28.40/18.63 tff(12105,plain,
% 28.40/18.63 ((~(f10(c2) = c2)) <=> (~(f7(c2) = c3))),
% 28.40/18.63 inference(monotonicity,[status(thm)],[12104])).
% 28.40/18.63 tff(12106,plain,
% 28.40/18.63 (~(f7(c2) = c3)),
% 28.40/18.63 inference(modus_ponens,[status(thm)],[89, 12105])).
% 28.40/18.63 tff(12107,plain,
% 28.40/18.63 (~big_f(f7(c2), c2)),
% 28.40/18.63 inference(unit_resolution,[status(thm)],[9231, 121, 333, 168, 9092, 17, 79, 347])).
% 28.40/18.63 tff(12108,plain,
% 28.40/18.63 (f10(f7(c2)) = c2),
% 28.40/18.63 inference(transitivity,[status(thm)],[23, 15])).
% 28.40/18.63 tff(12109,plain,
% 28.40/18.63 ((f10(f7(c2)) = f7(c2)) <=> (c2 = c1)),
% 28.40/18.63 inference(monotonicity,[status(thm)],[12108, 22])).
% 28.40/18.63 tff(12110,plain,
% 28.40/18.63 ((c2 = c1) <=> (f10(f7(c2)) = f7(c2))),
% 28.40/18.63 inference(symmetry,[status(thm)],[12109])).
% 28.40/18.63 tff(12111,plain,
% 28.40/18.63 ((~(c2 = c1)) <=> (~(f10(f7(c2)) = f7(c2)))),
% 28.40/18.63 inference(monotonicity,[status(thm)],[12110])).
% 28.40/18.63 tff(12112,plain,
% 28.40/18.63 (~(f10(f7(c2)) = f7(c2))),
% 28.40/18.63 inference(modus_ponens,[status(thm)],[75, 12111])).
% 28.40/18.63 tff(12113,plain,
% 28.40/18.63 (f10(f7(f4(c4))) = f10(f7(c2))),
% 28.40/18.63 inference(monotonicity,[status(thm)],[80])).
% 28.40/18.63 tff(12114,plain,
% 28.40/18.63 (f10(f7(c2)) = f10(f7(f4(c4)))),
% 28.40/18.63 inference(symmetry,[status(thm)],[12113])).
% 28.40/18.63 tff(12115,plain,
% 28.40/18.63 (big_f(f7(c2), f10(f7(c2))) <=> big_f(c1, f10(f7(f4(c4))))),
% 28.40/18.63 inference(monotonicity,[status(thm)],[22, 12114])).
% 28.40/18.63 tff(12116,plain,
% 28.40/18.63 (big_f(c1, f10(f7(f4(c4)))) <=> big_f(f7(c2), f10(f7(c2)))),
% 28.40/18.63 inference(symmetry,[status(thm)],[12115])).
% 28.40/18.63 tff(12117,plain,
% 28.40/18.63 (f10(f7(f4(c4))) = c2),
% 28.40/18.63 inference(transitivity,[status(thm)],[12113, 23, 15])).
% 28.40/18.63 tff(12118,plain,
% 28.40/18.63 (big_f(c1, f10(f7(f4(c4)))) <=> big_f(c1, c2)),
% 28.40/18.63 inference(monotonicity,[status(thm)],[12117])).
% 28.40/18.63 tff(12119,plain,
% 28.40/18.63 (big_f(c1, c2) <=> big_f(c1, f10(f7(f4(c4))))),
% 28.40/18.63 inference(symmetry,[status(thm)],[12118])).
% 28.40/18.63 tff(12120,plain,
% 28.40/18.63 (big_f(f7(c2), c2) <=> big_f(c1, c2)),
% 28.40/18.63 inference(monotonicity,[status(thm)],[22])).
% 28.40/18.63 tff(12121,plain,
% 28.40/18.63 (big_f(f7(c2), c2) <=> big_f(f7(c2), f10(f7(c2)))),
% 28.40/18.63 inference(transitivity,[status(thm)],[12120, 12119, 12116])).
% 28.40/18.63 tff(12122,plain,
% 28.40/18.63 ((~big_f(f7(c2), c2)) <=> (~big_f(f7(c2), f10(f7(c2))))),
% 28.40/18.63 inference(monotonicity,[status(thm)],[12121])).
% 28.40/18.63 tff(12123,plain,
% 28.40/18.63 (~big_f(f7(c2), f10(f7(c2)))),
% 28.40/18.63 inference(modus_ponens,[status(thm)],[12107, 12122])).
% 28.40/18.63 tff(12124,plain,
% 28.40/18.63 (big_f(c2, f10(f7(c2))) <=> big_f(c2, c2)),
% 28.40/18.63 inference(monotonicity,[status(thm)],[12108])).
% 28.40/18.63 tff(12125,plain,
% 28.40/18.63 (big_f(c2, c2) <=> big_f(c2, f10(f7(c2)))),
% 28.40/18.63 inference(symmetry,[status(thm)],[12124])).
% 28.40/18.63 tff(12126,plain,
% 28.40/18.63 ((~big_f(c2, c2)) <=> (~big_f(c2, f10(f7(c2))))),
% 28.40/18.63 inference(monotonicity,[status(thm)],[12125])).
% 28.40/18.63 tff(12127,plain,
% 28.40/18.63 (~big_f(c2, f10(f7(c2)))),
% 28.40/18.63 inference(modus_ponens,[status(thm)],[121, 12126])).
% 28.40/18.63 tff(12128,plain,
% 28.40/18.63 (~(c2 = f5(c2))),
% 28.40/18.63 inference(unit_resolution,[status(thm)],[9884, 12127, 79, 17, 12123, 12112, 12107])).
% 28.40/18.63 tff(12129,plain,
% 28.40/18.63 (~(f5(c2) = c2)),
% 28.40/18.63 inference(unit_resolution,[status(thm)],[8113, 12128])).
% 28.40/18.63 tff(12130,plain,
% 28.40/18.63 (f5(c2) = c1),
% 28.40/18.63 inference(unit_resolution,[status(thm)],[1547, 12129])).
% 28.40/18.63 tff(12131,plain,
% 28.40/18.63 (c1 = f5(c2)),
% 28.40/18.63 inference(unit_resolution,[status(thm)],[8139, 12130])).
% 28.40/18.63 tff(12132,plain,
% 28.40/18.63 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (f7(c2) = c2) | (~(c1 = f5(c2))) | big_f(f7(c2), c1))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (f7(c2) = c2) | (~(c1 = f5(c2))) | big_f(f7(c2), c1))),
% 28.40/18.63 inference(rewrite,[status(thm)],[])).
% 28.40/18.63 tff(12133,plain,
% 28.40/18.63 (((~(c1 = f5(c2))) | (f10(c1) = c1) | big_f(c2, f10(c1)) | (f7(c2) = c2) | big_f(f7(c2), c1) | (~(c2 = f8(c1)))) <=> (big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (f7(c2) = c2) | (~(c1 = f5(c2))) | big_f(f7(c2), c1))),
% 28.40/18.63 inference(rewrite,[status(thm)],[])).
% 28.40/18.63 tff(12134,plain,
% 28.40/18.63 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c1 = f5(c2))) | (f10(c1) = c1) | big_f(c2, f10(c1)) | (f7(c2) = c2) | big_f(f7(c2), c1) | (~(c2 = f8(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (f7(c2) = c2) | (~(c1 = f5(c2))) | big_f(f7(c2), c1)))),
% 28.40/18.63 inference(monotonicity,[status(thm)],[12133])).
% 28.40/18.63 tff(12135,plain,
% 28.40/18.63 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c1 = f5(c2))) | (f10(c1) = c1) | big_f(c2, f10(c1)) | (f7(c2) = c2) | big_f(f7(c2), c1) | (~(c2 = f8(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (f7(c2) = c2) | (~(c1 = f5(c2))) | big_f(f7(c2), c1))),
% 28.40/18.63 inference(transitivity,[status(thm)],[12134, 12132])).
% 28.40/18.63 tff(12136,plain,
% 28.40/18.63 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c1 = f5(c2))) | (f10(c1) = c1) | big_f(c2, f10(c1)) | (f7(c2) = c2) | big_f(f7(c2), c1) | (~(c2 = f8(c1))))),
% 28.40/18.63 inference(quant_inst,[status(thm)],[])).
% 28.40/18.63 tff(12137,plain,
% 28.40/18.63 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (f7(c2) = c2) | (~(c1 = f5(c2))) | big_f(f7(c2), c1)),
% 28.40/18.63 inference(modus_ponens,[status(thm)],[12136, 12135])).
% 28.40/18.63 tff(12138,plain,
% 28.40/18.63 ((~(c2 = f8(c1))) | (~(c1 = f5(c2)))),
% 28.40/18.63 inference(unit_resolution,[status(thm)],[12137, 1745, 6126, 3, 17, 333])).
% 28.40/18.63 tff(12139,plain,
% 28.40/18.63 (~(c2 = f8(c1))),
% 28.40/18.63 inference(unit_resolution,[status(thm)],[12138, 12131])).
% 28.40/18.63 tff(12140,plain,
% 28.40/18.63 (~(f8(c1) = c2)),
% 28.40/18.63 inference(unit_resolution,[status(thm)],[1675, 12139])).
% 28.40/18.63 tff(12141,plain,
% 28.40/18.63 (big_f(f7(c2), c2) <=> big_f(c1, f10(c1))),
% 28.40/18.63 inference(transitivity,[status(thm)],[12120, 3350])).
% 28.40/18.63 tff(12142,plain,
% 28.40/18.63 ((~big_f(f7(c2), c2)) <=> (~big_f(c1, f10(c1)))),
% 28.40/18.63 inference(monotonicity,[status(thm)],[12141])).
% 28.40/18.63 tff(12143,plain,
% 28.40/18.63 (~big_f(c1, f10(c1))),
% 28.40/18.63 inference(modus_ponens,[status(thm)],[12107, 12142])).
% 28.40/18.63 tff(12144,plain,
% 28.40/18.63 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | (f7(c2) = c2) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (~(c1 = f5(c2))) | big_f(f7(c2), c1))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c1) = c1) | (f7(c2) = c2) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (~(c1 = f5(c2))) | big_f(f7(c2), c1))),
% 28.40/18.63 inference(rewrite,[status(thm)],[])).
% 28.40/18.63 tff(12145,plain,
% 28.40/18.63 (((~(c1 = f5(c2))) | (f10(c1) = c1) | big_f(c1, f10(c1)) | (f7(c2) = c2) | big_f(f7(c2), c1) | (~(c1 = f8(c1)))) <=> ((f10(c1) = c1) | (f7(c2) = c2) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (~(c1 = f5(c2))) | big_f(f7(c2), c1))),
% 28.40/18.63 inference(rewrite,[status(thm)],[])).
% 28.40/18.63 tff(12146,plain,
% 28.40/18.63 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c1 = f5(c2))) | (f10(c1) = c1) | big_f(c1, f10(c1)) | (f7(c2) = c2) | big_f(f7(c2), c1) | (~(c1 = f8(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | (f7(c2) = c2) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (~(c1 = f5(c2))) | big_f(f7(c2), c1)))),
% 28.40/18.63 inference(monotonicity,[status(thm)],[12145])).
% 28.40/18.63 tff(12147,plain,
% 28.40/18.63 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c1 = f5(c2))) | (f10(c1) = c1) | big_f(c1, f10(c1)) | (f7(c2) = c2) | big_f(f7(c2), c1) | (~(c1 = f8(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c1) = c1) | (f7(c2) = c2) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (~(c1 = f5(c2))) | big_f(f7(c2), c1))),
% 28.40/18.63 inference(transitivity,[status(thm)],[12146, 12144])).
% 28.40/18.63 tff(12148,plain,
% 28.40/18.63 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c1 = f5(c2))) | (f10(c1) = c1) | big_f(c1, f10(c1)) | (f7(c2) = c2) | big_f(f7(c2), c1) | (~(c1 = f8(c1))))),
% 28.40/18.63 inference(quant_inst,[status(thm)],[])).
% 28.40/18.63 tff(12149,plain,
% 28.40/18.63 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c1) = c1) | (f7(c2) = c2) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (~(c1 = f5(c2))) | big_f(f7(c2), c1)),
% 28.40/18.63 inference(modus_ponens,[status(thm)],[12148, 12147])).
% 28.40/18.63 tff(12150,plain,
% 28.40/18.63 ((~(c1 = f8(c1))) | (~(c1 = f5(c2)))),
% 28.40/18.63 inference(unit_resolution,[status(thm)],[12149, 1745, 3, 17, 12143, 333])).
% 28.40/18.63 tff(12151,plain,
% 28.40/18.63 (~(c1 = f8(c1))),
% 28.40/18.63 inference(unit_resolution,[status(thm)],[12150, 12131])).
% 28.40/18.63 tff(12152,plain,
% 28.40/18.63 (~(f8(c1) = c1)),
% 28.40/18.63 inference(unit_resolution,[status(thm)],[9808, 12151])).
% 28.40/18.63 tff(12153,plain,
% 28.40/18.63 ($false),
% 28.40/18.63 inference(unit_resolution,[status(thm)],[1680, 12152, 12140])).
% 28.40/18.63 tff(12154,plain,(big_f(c2, c2) | (f10(c1) = c1) | (f7(c2) = c2) | big_f(f7(c2), c1) | (~(f4(c4) = c2)) | (c1 = c3) | (f7(c2) = c3) | (~(f7(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.40/18.63 tff(12155,plain,
% 28.40/18.63 ($false),
% 28.40/18.63 inference(unit_resolution,[status(thm)],[12154, 12106, 12100, 121, 17, 79, 3, 333, 347])).
% 28.40/18.63 tff(12156,plain,((~(c3 = c2)) | big_f(c2, c2) | (f7(c2) = c2) | (~(f4(c4) = c2)) | (f10(c1) = c1) | big_f(f7(c2), c1) | (~(f7(c1) = c2)) | (f10(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 28.40/18.63 tff(12157,plain,
% 28.40/18.63 (~(c3 = c2)),
% 28.40/18.63 inference(unit_resolution,[status(thm)],[12156, 17, 121, 79, 3, 12093, 347, 89])).
% 28.40/18.63 tff(12158,plain,
% 28.40/18.63 (~(f7(f7(c2)) = c3)),
% 28.40/18.63 inference(modus_ponens,[status(thm)],[12157, 12089])).
% 28.40/18.63 tff(12159,plain,
% 28.40/18.63 (~(c2 = c3)),
% 28.40/18.63 inference(modus_ponens,[status(thm)],[12157, 10473])).
% 28.40/18.63 tff(12160,plain,
% 28.40/18.63 ((c3 = c2) <=> (f7(c1) = c3)),
% 28.40/18.63 inference(transitivity,[status(thm)],[78, 1002])).
% 28.40/18.63 tff(12161,plain,
% 28.40/18.63 ((~(c3 = c2)) <=> (~(f7(c1) = c3))),
% 28.40/18.63 inference(monotonicity,[status(thm)],[12160])).
% 28.40/18.63 tff(12162,plain,
% 28.40/18.63 (~(f7(c1) = c3)),
% 28.40/18.63 inference(modus_ponens,[status(thm)],[12157, 12161])).
% 28.40/18.63 tff(12163,plain,
% 28.40/18.63 (big_f(c1, c2) <=> big_f(f7(c2), c2)),
% 28.40/18.63 inference(symmetry,[status(thm)],[12120])).
% 28.40/18.63 tff(12164,plain,
% 28.40/18.63 ((~big_f(c1, c2)) <=> (~big_f(f7(c2), c2))),
% 28.40/18.63 inference(monotonicity,[status(thm)],[12163])).
% 28.40/18.63 tff(12165,assumption,(~(f7(c1) = c3)), introduced(assumption)).
% 28.40/18.63 tff(12166,plain,
% 28.40/18.63 (~(c2 = c4)),
% 28.40/18.63 inference(unit_resolution,[status(thm)],[8754, 121, 79, 22, 378, 347, 377, 348])).
% 28.40/18.63 tff(12167,plain,
% 28.40/18.63 (big_f(f7(c2), c2)),
% 28.40/18.63 inference(modus_ponens,[status(thm)],[2865, 12163])).
% 28.40/18.63 tff(12168,plain,
% 28.40/18.63 (~(f3(f7(c1), c1) = c1)),
% 28.40/18.63 inference(unit_resolution,[status(thm)],[9039, 12167, 377, 347, 121, 873, 348, 17])).
% 28.40/18.63 tff(12169,plain,
% 28.40/18.63 (f3(f7(c1), c1) = c2),
% 28.40/18.63 inference(unit_resolution,[status(thm)],[918, 12168])).
% 28.40/18.63 tff(12170,plain,
% 28.40/18.63 (f3(c2, c1) = c2),
% 28.40/18.63 inference(transitivity,[status(thm)],[3125, 12169])).
% 28.40/18.63 tff(12171,plain,
% 28.40/18.63 (big_f(f3(c2, c1), c2) <=> big_f(c2, c2)),
% 28.40/18.63 inference(monotonicity,[status(thm)],[12170])).
% 28.40/18.63 tff(12172,plain,
% 28.40/18.63 (big_f(c2, c2) <=> big_f(f3(c2, c1), c2)),
% 28.40/18.63 inference(symmetry,[status(thm)],[12171])).
% 28.40/18.63 tff(12173,plain,
% 28.40/18.63 ((~big_f(c2, c2)) <=> (~big_f(f3(c2, c1), c2))),
% 28.40/18.63 inference(monotonicity,[status(thm)],[12172])).
% 28.40/18.63 tff(12174,plain,
% 28.40/18.63 (~big_f(f3(c2, c1), c2)),
% 28.40/18.63 inference(modus_ponens,[status(thm)],[121, 12173])).
% 28.40/18.63 tff(12175,assumption,(~big_f(f3(c2, c1), c2)), introduced(assumption)).
% 28.40/18.63 tff(12176,plain,
% 28.40/18.63 ((~(f3(f7(c1), c1) = c1)) <=> (~(f3(c2, c1) = c1))),
% 28.40/18.63 inference(monotonicity,[status(thm)],[9098])).
% 28.40/18.63 tff(12177,plain,
% 28.40/18.63 (f3(c2, c1) = c1),
% 28.40/18.63 inference(transitivity,[status(thm)],[3125, 953])).
% 28.40/18.63 tff(12178,plain,
% 28.40/18.63 (big_f(f3(c2, c1), c2) <=> big_f(c1, c2)),
% 28.40/18.63 inference(monotonicity,[status(thm)],[12177])).
% 28.40/18.63 tff(12179,plain,
% 28.40/18.63 (big_f(c1, c2) <=> big_f(f3(c2, c1), c2)),
% 28.40/18.63 inference(symmetry,[status(thm)],[12178])).
% 28.40/18.63 tff(12180,plain,
% 28.40/18.63 (big_f(f3(c2, c1), c2)),
% 28.40/18.63 inference(modus_ponens,[status(thm)],[2865, 12179])).
% 28.40/18.63 tff(12181,plain,
% 28.40/18.63 ($false),
% 28.40/18.63 inference(unit_resolution,[status(thm)],[12175, 12180])).
% 28.40/18.63 tff(12182,plain,((~(f3(f7(c1), c1) = c1)) | big_f(f3(c2, c1), c2) | (~big_f(c1, c2)) | (~(f7(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.40/18.63 tff(12183,plain,
% 28.40/18.63 (~(f3(f7(c1), c1) = c1)),
% 28.40/18.63 inference(unit_resolution,[status(thm)],[12182, 12175, 2865, 347])).
% 28.40/18.63 tff(12184,plain,
% 28.40/18.63 (~(f3(c2, c1) = c1)),
% 28.40/18.63 inference(modus_ponens,[status(thm)],[12183, 12176])).
% 28.40/18.63 tff(12185,plain,
% 28.40/18.63 ((~(c2 = c4)) <=> (~(f7(c1) = c4))),
% 28.40/18.63 inference(monotonicity,[status(thm)],[869])).
% 28.40/18.63 tff(12186,plain,
% 28.40/18.63 (~(f7(c1) = c4)),
% 28.40/18.63 inference(modus_ponens,[status(thm)],[873, 12185])).
% 28.40/18.63 tff(12187,assumption,(~(f1(c2, c1) = c1)), introduced(assumption)).
% 28.40/18.63 tff(12188,plain,
% 28.40/18.63 (f1(c2, c1) = c2),
% 28.40/18.63 inference(unit_resolution,[status(thm)],[10113, 12187])).
% 28.40/18.63 tff(12189,assumption,(f1(c2, c1) = c2), introduced(assumption)).
% 28.40/18.63 tff(12190,plain,
% 28.40/18.63 (f1(f7(c1), c1) = c2),
% 28.40/18.63 inference(transitivity,[status(thm)],[989, 12189])).
% 28.40/18.63 tff(12191,plain,
% 28.40/18.63 (big_f(f7(c1), f1(f7(c1), c1)) <=> big_f(c2, c2)),
% 28.40/18.63 inference(monotonicity,[status(thm)],[347, 12190])).
% 28.40/18.63 tff(12192,plain,
% 28.40/18.63 (big_f(c2, c2) <=> big_f(f7(c1), f1(f7(c1), c1))),
% 28.40/18.63 inference(symmetry,[status(thm)],[12191])).
% 28.40/18.63 tff(12193,plain,
% 28.40/18.63 ((~big_f(c2, c2)) <=> (~big_f(f7(c1), f1(f7(c1), c1)))),
% 28.40/18.63 inference(monotonicity,[status(thm)],[12192])).
% 28.40/18.63 tff(12194,plain,
% 28.40/18.63 (~big_f(f7(c1), f1(f7(c1), c1))),
% 28.40/18.63 inference(modus_ponens,[status(thm)],[121, 12193])).
% 28.40/18.63 tff(12195,assumption,(big_f(f7(c1), f1(f7(c1), c1))), introduced(assumption)).
% 28.40/18.63 tff(12196,plain,
% 28.40/18.63 ($false),
% 28.40/18.63 inference(unit_resolution,[status(thm)],[12195, 12194])).
% 28.40/18.63 tff(12197,plain,((~(f1(c2, c1) = c2)) | (~big_f(f7(c1), f1(f7(c1), c1))) | big_f(c2, c2) | (~(f7(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.40/18.63 tff(12198,plain,
% 28.40/18.63 (~big_f(f7(c1), f1(f7(c1), c1))),
% 28.40/18.63 inference(unit_resolution,[status(thm)],[12197, 12188, 121, 347])).
% 28.40/18.63 tff(12199,plain,
% 28.40/18.63 (big_f(f3(f7(c1), c1), f7(c1)) <=> big_f(c2, c2)),
% 28.40/18.63 inference(monotonicity,[status(thm)],[11911, 347])).
% 28.40/18.63 tff(12200,plain,
% 28.40/18.63 (big_f(c2, c2) <=> big_f(f3(f7(c1), c1), f7(c1))),
% 28.40/18.63 inference(symmetry,[status(thm)],[12199])).
% 28.40/18.63 tff(12201,plain,
% 28.40/18.63 ((~big_f(c2, c2)) <=> (~big_f(f3(f7(c1), c1), f7(c1)))),
% 28.40/18.63 inference(monotonicity,[status(thm)],[12200])).
% 28.40/18.63 tff(12202,plain,
% 28.40/18.63 (~big_f(f3(f7(c1), c1), f7(c1))),
% 28.40/18.63 inference(modus_ponens,[status(thm)],[121, 12201])).
% 28.40/18.63 tff(12203,assumption,(~(f1(f7(c1), c1) = c1)), introduced(assumption)).
% 28.40/18.63 tff(12204,assumption,(~big_f(f7(c1), f1(f7(c1), c1))), introduced(assumption)).
% 28.40/18.63 tff(12205,plain,
% 28.40/18.63 (big_f(f3(f7(c1), c1), f7(c1))),
% 28.40/18.63 inference(unit_resolution,[status(thm)],[1021, 11910, 12165, 12204, 1000, 12203])).
% 28.40/18.63 tff(12206,plain,
% 28.40/18.63 ($false),
% 28.40/18.63 inference(unit_resolution,[status(thm)],[12205, 12202])).
% 28.40/18.63 tff(12207,plain,((f3(f7(c1), c1) = c1) | big_f(c2, c2) | (~(f7(c1) = c2)) | (f7(c1) = c3) | big_f(f7(c1), f1(f7(c1), c1)) | (f7(c1) = c4) | (f1(f7(c1), c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 28.40/18.63 tff(12208,plain,
% 28.40/18.63 (f1(f7(c1), c1) = c1),
% 28.40/18.63 inference(unit_resolution,[status(thm)],[12207, 12198, 347, 12165, 1000, 11910, 121])).
% 28.40/18.63 tff(12209,plain,
% 28.40/18.63 (f1(c2, c1) = c1),
% 28.40/18.63 inference(modus_ponens,[status(thm)],[12208, 995])).
% 28.40/18.63 tff(12210,plain,
% 28.40/18.63 ($false),
% 28.40/18.63 inference(unit_resolution,[status(thm)],[12187, 12209])).
% 28.40/18.63 tff(12211,plain,((f1(c2, c1) = c1) | (~(f7(c1) = c2)) | (f7(c1) = c3) | (f7(c1) = c4) | (f3(f7(c1), c1) = c1) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 28.40/18.63 tff(12212,plain,
% 28.40/18.63 (f1(c2, c1) = c1),
% 28.40/18.63 inference(unit_resolution,[status(thm)],[12211, 12183, 12165, 12186, 347, 121])).
% 28.40/18.63 tff(12213,plain,
% 28.40/18.63 (big_f(c2, f1(c2, c1)) <=> big_f(c2, c1)),
% 28.40/18.63 inference(monotonicity,[status(thm)],[12212])).
% 28.40/18.63 tff(12214,plain,
% 28.40/18.63 (big_f(c2, c1) <=> big_f(c2, f1(c2, c1))),
% 28.40/18.63 inference(symmetry,[status(thm)],[12213])).
% 28.40/18.63 tff(12215,plain,
% 28.40/18.63 (big_f(c2, f1(c2, c1))),
% 28.40/18.63 inference(modus_ponens,[status(thm)],[348, 12214])).
% 28.40/18.63 tff(12216,plain,
% 28.40/18.63 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (c2 = c4) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1)) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (c2 = c4) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1)) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2))),
% 28.40/18.63 inference(rewrite,[status(thm)],[])).
% 28.40/18.63 tff(12217,plain,
% 28.40/18.63 (((c2 = c4) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2) | (c2 = c3) | (~(f1(c2, c1) = c1)) | (~big_f(c2, f1(c2, c1)))) <=> ((c2 = c3) | (c2 = c4) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1)) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2))),
% 28.40/18.63 inference(rewrite,[status(thm)],[])).
% 28.40/18.63 tff(12218,plain,
% 28.40/18.63 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2) | (c2 = c3) | (~(f1(c2, c1) = c1)) | (~big_f(c2, f1(c2, c1))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (c2 = c4) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1)) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2)))),
% 28.40/18.63 inference(monotonicity,[status(thm)],[12217])).
% 28.40/18.63 tff(12219,plain,
% 28.40/18.63 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2) | (c2 = c3) | (~(f1(c2, c1) = c1)) | (~big_f(c2, f1(c2, c1))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (c2 = c4) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1)) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2))),
% 28.40/18.63 inference(transitivity,[status(thm)],[12218, 12216])).
% 28.40/18.63 tff(12220,plain,
% 28.40/18.63 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2) | (c2 = c3) | (~(f1(c2, c1) = c1)) | (~big_f(c2, f1(c2, c1))))),
% 28.40/18.63 inference(quant_inst,[status(thm)],[])).
% 28.40/18.63 tff(12221,plain,
% 28.40/18.63 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (c2 = c4) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1)) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2)),
% 28.40/18.64 inference(modus_ponens,[status(thm)],[12220, 12219])).
% 28.40/18.64 tff(12222,plain,
% 28.40/18.64 ($false),
% 28.40/18.64 inference(unit_resolution,[status(thm)],[12221, 904, 873, 377, 12212, 12215, 12184, 12175])).
% 28.40/18.64 tff(12223,plain,(big_f(f3(c2, c1), c2) | (c2 = c4) | (c2 = c3) | (~big_f(c2, c1)) | (f7(c1) = c3) | (~(f7(c1) = c2)) | big_f(c2, c2) | (~big_f(c1, c2))), inference(lemma,lemma(discharge,[]))).
% 28.40/18.64 tff(12224,plain,
% 28.40/18.64 (big_f(f3(c2, c1), c2)),
% 28.40/18.64 inference(unit_resolution,[status(thm)],[12223, 2865, 377, 121, 12165, 347, 348, 873])).
% 28.40/18.64 tff(12225,plain,
% 28.40/18.64 ($false),
% 28.40/18.64 inference(unit_resolution,[status(thm)],[12224, 12174])).
% 28.40/18.64 tff(12226,plain,((~big_f(c1, c2)) | big_f(c2, c2) | (~(f7(c1) = c2)) | (c2 = c3) | (c2 = c4) | (~big_f(c2, c1)) | (f7(c2) = c2) | (f7(c1) = c3)), inference(lemma,lemma(discharge,[]))).
% 28.40/18.64 tff(12227,plain,
% 28.40/18.64 (~big_f(c1, c2)),
% 28.40/18.64 inference(unit_resolution,[status(thm)],[12226, 121, 347, 377, 12166, 348, 17, 12165])).
% 28.40/18.64 tff(12228,plain,
% 28.40/18.64 (~big_f(f7(c2), c2)),
% 28.40/18.64 inference(modus_ponens,[status(thm)],[12227, 12164])).
% 28.40/18.64 tff(12229,plain,
% 28.40/18.64 (f10(c2) = c1),
% 28.40/18.64 inference(unit_resolution,[status(thm)],[93, 11797])).
% 28.40/18.64 tff(12230,assumption,(f10(f10(c2)) = c2), introduced(assumption)).
% 28.40/18.64 tff(12231,plain,
% 28.40/18.64 (c1 = f10(c2)),
% 28.40/18.64 inference(symmetry,[status(thm)],[11819])).
% 28.40/18.64 tff(12232,plain,
% 28.40/18.64 (f10(c1) = f10(f10(c2))),
% 28.40/18.64 inference(monotonicity,[status(thm)],[12231])).
% 28.40/18.64 tff(12233,plain,
% 28.40/18.64 (f10(c1) = c2),
% 28.40/18.64 inference(transitivity,[status(thm)],[12232, 12230])).
% 28.40/18.64 tff(12234,plain,
% 28.40/18.64 (big_f(c1, f10(c1)) <=> big_f(c1, c2)),
% 28.40/18.64 inference(monotonicity,[status(thm)],[12233])).
% 28.40/18.64 tff(12235,plain,
% 28.40/18.64 (big_f(c1, c2) <=> big_f(c1, f10(c1))),
% 28.40/18.64 inference(symmetry,[status(thm)],[12234])).
% 28.40/18.64 tff(12236,plain,
% 28.40/18.64 ((~big_f(c1, c2)) <=> (~big_f(c1, f10(c1)))),
% 28.40/18.64 inference(monotonicity,[status(thm)],[12235])).
% 28.40/18.64 tff(12237,plain,
% 28.40/18.64 (~big_f(c1, f10(c1))),
% 28.40/18.64 inference(modus_ponens,[status(thm)],[27, 12236])).
% 28.40/18.64 tff(12238,plain,
% 28.40/18.64 ($false),
% 28.40/18.64 inference(unit_resolution,[status(thm)],[3023, 12237])).
% 28.40/18.64 tff(12239,plain,((~(f10(f10(c2)) = c2)) | (~big_f(c1, f10(c1))) | big_f(c1, c2) | (~(f10(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.40/18.64 tff(12240,plain,
% 28.40/18.64 (~big_f(c1, f10(c1))),
% 28.40/18.64 inference(unit_resolution,[status(thm)],[12239, 27, 11819, 11879])).
% 28.40/18.64 tff(12241,plain,
% 28.40/18.64 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | (f7(c2) = c2) | big_f(f7(c2), f5(c2)) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c1) = c1) | (f7(c2) = c2) | big_f(f7(c2), f5(c2)) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)))),
% 28.40/18.64 inference(rewrite,[status(thm)],[])).
% 28.40/18.64 tff(12242,plain,
% 28.40/18.64 (($false | (f10(c1) = c1) | big_f(c1, f10(c1)) | (f7(c2) = c2) | big_f(f7(c2), f5(c2)) | (~(c1 = f8(c1)))) <=> ((f10(c1) = c1) | (f7(c2) = c2) | big_f(f7(c2), f5(c2)) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)))),
% 28.40/18.64 inference(rewrite,[status(thm)],[])).
% 28.40/18.64 tff(12243,plain,
% 28.40/18.64 (((~(f5(c2) = f5(c2))) | (f10(c1) = c1) | big_f(c1, f10(c1)) | (f7(c2) = c2) | big_f(f7(c2), f5(c2)) | (~(c1 = f8(c1)))) <=> ($false | (f10(c1) = c1) | big_f(c1, f10(c1)) | (f7(c2) = c2) | big_f(f7(c2), f5(c2)) | (~(c1 = f8(c1))))),
% 28.40/18.64 inference(monotonicity,[status(thm)],[4851])).
% 28.40/18.64 tff(12244,plain,
% 28.40/18.64 (((~(f5(c2) = f5(c2))) | (f10(c1) = c1) | big_f(c1, f10(c1)) | (f7(c2) = c2) | big_f(f7(c2), f5(c2)) | (~(c1 = f8(c1)))) <=> ((f10(c1) = c1) | (f7(c2) = c2) | big_f(f7(c2), f5(c2)) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)))),
% 28.40/18.64 inference(transitivity,[status(thm)],[12243, 12242])).
% 28.40/18.64 tff(12245,plain,
% 28.40/18.64 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(f5(c2) = f5(c2))) | (f10(c1) = c1) | big_f(c1, f10(c1)) | (f7(c2) = c2) | big_f(f7(c2), f5(c2)) | (~(c1 = f8(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | (f7(c2) = c2) | big_f(f7(c2), f5(c2)) | (~(c1 = f8(c1))) | big_f(c1, f10(c1))))),
% 28.40/18.64 inference(monotonicity,[status(thm)],[12244])).
% 28.40/18.64 tff(12246,plain,
% 28.40/18.64 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(f5(c2) = f5(c2))) | (f10(c1) = c1) | big_f(c1, f10(c1)) | (f7(c2) = c2) | big_f(f7(c2), f5(c2)) | (~(c1 = f8(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c1) = c1) | (f7(c2) = c2) | big_f(f7(c2), f5(c2)) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)))),
% 28.40/18.64 inference(transitivity,[status(thm)],[12245, 12241])).
% 28.40/18.64 tff(12247,plain,
% 28.40/18.64 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(f5(c2) = f5(c2))) | (f10(c1) = c1) | big_f(c1, f10(c1)) | (f7(c2) = c2) | big_f(f7(c2), f5(c2)) | (~(c1 = f8(c1))))),
% 28.40/18.64 inference(quant_inst,[status(thm)],[])).
% 28.40/18.64 tff(12248,plain,
% 28.40/18.64 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c1) = c1) | (f7(c2) = c2) | big_f(f7(c2), f5(c2)) | (~(c1 = f8(c1))) | big_f(c1, f10(c1))),
% 28.40/18.64 inference(modus_ponens,[status(thm)],[12247, 12246])).
% 28.40/18.64 tff(12249,plain,
% 28.40/18.64 ((f10(c1) = c1) | (f7(c2) = c2) | big_f(f7(c2), f5(c2)) | (~(c1 = f8(c1))) | big_f(c1, f10(c1))),
% 28.40/18.64 inference(unit_resolution,[status(thm)],[12248, 1745])).
% 28.40/18.64 tff(12250,plain,
% 28.40/18.64 (big_f(f7(c2), f5(c2))),
% 28.40/18.64 inference(unit_resolution,[status(thm)],[12249, 12240, 17, 3031, 3])).
% 28.40/18.64 tff(12251,plain,
% 28.40/18.64 (~(f5(f10(c1)) = c1)),
% 28.40/18.64 inference(unit_resolution,[status(thm)],[336, 12250, 333, 15])).
% 28.40/18.64 tff(12252,plain,
% 28.40/18.64 (f5(f10(c1)) = c2),
% 28.40/18.64 inference(unit_resolution,[status(thm)],[326, 12251])).
% 28.40/18.64 tff(12253,plain,
% 28.40/18.64 (f5(c2) = f5(f10(c1))),
% 28.40/18.64 inference(monotonicity,[status(thm)],[5571])).
% 28.40/18.64 tff(12254,plain,
% 28.40/18.64 (f5(c2) = c2),
% 28.40/18.64 inference(transitivity,[status(thm)],[12253, 12252])).
% 28.40/18.64 tff(12255,plain,
% 28.40/18.64 (big_f(f7(c2), f5(c2)) <=> big_f(c1, c2)),
% 28.40/18.64 inference(monotonicity,[status(thm)],[22, 12254])).
% 28.40/18.64 tff(12256,plain,
% 28.40/18.64 (big_f(c1, c2) <=> big_f(f7(c2), f5(c2))),
% 28.40/18.64 inference(symmetry,[status(thm)],[12255])).
% 28.40/18.64 tff(12257,plain,
% 28.40/18.64 ((~big_f(c1, c2)) <=> (~big_f(f7(c2), f5(c2)))),
% 28.40/18.64 inference(monotonicity,[status(thm)],[12256])).
% 28.40/18.64 tff(12258,plain,
% 28.40/18.64 (~big_f(f7(c2), f5(c2))),
% 28.40/18.64 inference(modus_ponens,[status(thm)],[27, 12257])).
% 28.40/18.64 tff(12259,plain,
% 28.40/18.64 ($false),
% 28.40/18.64 inference(unit_resolution,[status(thm)],[12250, 12258])).
% 28.40/18.64 tff(12260,plain,(big_f(c1, c2) | big_f(f7(c2), c1) | (f7(c2) = c2) | (~(c1 = f8(c1))) | (f10(c1) = c1) | (~(f10(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.40/18.64 tff(12261,plain,
% 28.40/18.64 (~(c1 = f8(c1))),
% 28.40/18.64 inference(unit_resolution,[status(thm)],[12260, 12227, 17, 333, 3, 12229])).
% 28.40/18.64 tff(12262,plain,
% 28.40/18.64 (~(f8(c1) = c1)),
% 28.40/18.64 inference(unit_resolution,[status(thm)],[9808, 12261])).
% 28.40/18.64 tff(12263,plain,
% 28.40/18.64 (f8(c1) = c2),
% 28.40/18.64 inference(unit_resolution,[status(thm)],[1680, 12262])).
% 28.40/18.64 tff(12264,plain,
% 28.40/18.64 (c2 = f8(c1)),
% 28.40/18.64 inference(unit_resolution,[status(thm)],[1675, 12263])).
% 28.40/18.64 tff(12265,plain,
% 28.40/18.64 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2))),
% 28.40/18.64 inference(rewrite,[status(thm)],[])).
% 28.40/18.64 tff(12266,plain,
% 28.40/18.64 (((~(c2 = f5(c2))) | (f10(c1) = c1) | big_f(c2, f10(c1)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(c2 = f8(c1)))) <=> (big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2))),
% 28.40/18.64 inference(rewrite,[status(thm)],[])).
% 28.40/18.64 tff(12267,plain,
% 28.40/18.64 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c2 = f5(c2))) | (f10(c1) = c1) | big_f(c2, f10(c1)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(c2 = f8(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2)))),
% 28.40/18.64 inference(monotonicity,[status(thm)],[12266])).
% 28.40/18.64 tff(12268,plain,
% 28.40/18.64 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c2 = f5(c2))) | (f10(c1) = c1) | big_f(c2, f10(c1)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(c2 = f8(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2))),
% 28.40/18.64 inference(transitivity,[status(thm)],[12267, 12265])).
% 28.40/18.64 tff(12269,plain,
% 28.40/18.64 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c2 = f5(c2))) | (f10(c1) = c1) | big_f(c2, f10(c1)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(c2 = f8(c1))))),
% 28.40/18.64 inference(quant_inst,[status(thm)],[])).
% 28.40/18.64 tff(12270,plain,
% 28.40/18.64 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2)),
% 28.40/18.64 inference(modus_ponens,[status(thm)],[12269, 12268])).
% 28.40/18.64 tff(12271,plain,
% 28.40/18.64 (~(c2 = f5(c2))),
% 28.40/18.64 inference(unit_resolution,[status(thm)],[12270, 1745, 6126, 3, 12264, 17, 12228])).
% 28.40/18.64 tff(12272,plain,
% 28.40/18.64 (~(f5(c2) = c2)),
% 28.40/18.64 inference(unit_resolution,[status(thm)],[8113, 12271])).
% 28.40/18.64 tff(12273,plain,
% 28.40/18.64 (~(c1 = f5(c2))),
% 28.40/18.64 inference(unit_resolution,[status(thm)],[12137, 1745, 6126, 3, 12264, 17, 333])).
% 28.40/18.64 tff(12274,plain,
% 28.40/18.64 (~(f5(c2) = c1)),
% 28.40/18.64 inference(unit_resolution,[status(thm)],[8139, 12273])).
% 28.40/18.64 tff(12275,plain,
% 28.40/18.64 ($false),
% 28.40/18.64 inference(unit_resolution,[status(thm)],[1547, 12274, 12272])).
% 28.40/18.64 tff(12276,plain,(big_f(c2, c2) | (f10(c1) = c1) | (f7(c2) = c2) | big_f(f7(c2), c1) | (~(f7(c1) = c2)) | (c2 = c3) | (~big_f(c2, c1)) | (f7(c1) = c3) | (~(f4(c4) = c2)) | (f7(f7(c2)) = c3)), inference(lemma,lemma(discharge,[]))).
% 28.40/18.64 tff(12277,plain,
% 28.40/18.64 ($false),
% 28.40/18.64 inference(unit_resolution,[status(thm)],[12276, 12162, 12159, 3, 121, 347, 17, 348, 12093, 79, 12158])).
% 28.40/18.64 tff(12278,plain,((f7(c2) = c2) | (f10(c1) = c1) | big_f(c2, c2) | (~(f7(c1) = c2)) | (~big_f(c2, c1)) | (~(f4(c4) = c2)) | (f10(c2) = c2) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 28.40/18.64 tff(12279,plain,
% 28.40/18.64 (big_f(c1, c1)),
% 28.40/18.64 inference(unit_resolution,[status(thm)],[12278, 12087, 3, 120, 17, 79, 11797, 121])).
% 28.40/18.64 tff(12280,plain,
% 28.40/18.64 (f8(f7(c1)) = f8(c2)),
% 28.40/18.64 inference(monotonicity,[status(thm)],[120])).
% 28.40/18.64 tff(12281,plain,
% 28.40/18.64 ((c1 = f8(f7(c1))) <=> (c1 = f8(c2))),
% 28.40/18.64 inference(monotonicity,[status(thm)],[12280])).
% 28.40/18.64 tff(12282,plain,
% 28.40/18.64 ((c1 = f8(c2)) <=> (c1 = f8(f7(c1)))),
% 28.40/18.64 inference(symmetry,[status(thm)],[12281])).
% 28.40/18.64 tff(12283,plain,
% 28.40/18.64 (big_f(c2, c1)),
% 28.40/18.64 inference(unit_resolution,[status(thm)],[11990, 121, 4932, 115, 79, 3])).
% 28.40/18.64 tff(12284,plain,
% 28.40/18.64 (big_f(f7(c2), c1)),
% 28.40/18.64 inference(unit_resolution,[status(thm)],[12156, 17, 121, 79, 3, 67, 120, 11798])).
% 28.40/18.64 tff(12285,plain,
% 28.40/18.64 (big_f(f7(c2), c2)),
% 28.40/18.64 inference(unit_resolution,[status(thm)],[10334, 12284, 79, 121, 12283, 17])).
% 28.40/18.64 tff(12286,plain,
% 28.40/18.64 (big_f(c2, f10(c2))),
% 28.40/18.64 inference(modus_ponens,[status(thm)],[12283, 12004])).
% 28.40/18.64 tff(12287,plain,
% 28.40/18.64 (big_f(f7(c2), f10(c2)) <=> big_f(c1, c1)),
% 28.40/18.64 inference(monotonicity,[status(thm)],[22, 11799])).
% 28.40/18.64 tff(12288,plain,
% 28.40/18.64 (big_f(c1, c1) <=> big_f(f7(c2), f10(c2))),
% 28.40/18.64 inference(symmetry,[status(thm)],[12287])).
% 28.40/18.64 tff(12289,plain,
% 28.40/18.64 (big_f(f7(c2), f10(c2))),
% 28.40/18.64 inference(modus_ponens,[status(thm)],[4932, 12288])).
% 28.40/18.64 tff(12290,assumption,(~(c2 = f8(c2))), introduced(assumption)).
% 28.40/18.64 tff(12291,assumption,(big_f(c2, f10(c2))), introduced(assumption)).
% 28.40/18.64 tff(12292,plain,
% 28.40/18.64 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f7(c2) = c2) | (c2 = f5(c2)) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~big_f(f7(c2), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (f7(c2) = c2) | (c2 = f5(c2)) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~big_f(f7(c2), c2)))),
% 28.40/18.64 inference(rewrite,[status(thm)],[])).
% 28.40/18.64 tff(12293,plain,
% 28.40/18.64 (((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2))) <=> ((f10(c2) = c2) | (f7(c2) = c2) | (c2 = f5(c2)) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~big_f(f7(c2), c2)))),
% 28.40/18.64 inference(rewrite,[status(thm)],[])).
% 28.40/18.64 tff(12294,plain,
% 28.40/18.64 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f7(c2) = c2) | (c2 = f5(c2)) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~big_f(f7(c2), c2))))),
% 28.40/18.64 inference(monotonicity,[status(thm)],[12293])).
% 28.40/18.64 tff(12295,plain,
% 28.40/18.64 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (f7(c2) = c2) | (c2 = f5(c2)) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~big_f(f7(c2), c2)))),
% 28.40/18.64 inference(transitivity,[status(thm)],[12294, 12292])).
% 28.40/18.64 tff(12296,plain,
% 28.40/18.64 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)))),
% 28.40/18.64 inference(quant_inst,[status(thm)],[])).
% 28.40/18.64 tff(12297,plain,
% 28.40/18.64 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (f7(c2) = c2) | (c2 = f5(c2)) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~big_f(f7(c2), c2))),
% 28.40/18.64 inference(modus_ponens,[status(thm)],[12296, 12295])).
% 28.40/18.64 tff(12298,plain,
% 28.40/18.64 ((c2 = f5(c2)) | (c2 = f8(c2))),
% 28.40/18.64 inference(unit_resolution,[status(thm)],[12297, 1659, 89, 17, 1180, 12291])).
% 28.40/18.64 tff(12299,plain,
% 28.40/18.64 (c2 = f5(c2)),
% 28.40/18.64 inference(unit_resolution,[status(thm)],[12298, 12290])).
% 28.40/18.64 tff(12300,plain,
% 28.40/18.64 (f5(c2) = c2),
% 28.40/18.64 inference(symmetry,[status(thm)],[12299])).
% 28.40/18.64 tff(12301,assumption,(big_f(f7(c2), f10(c2))), introduced(assumption)).
% 28.40/18.64 tff(12302,plain,
% 28.40/18.64 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f7(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~big_f(f7(c2), f10(c2))) | (f10(c2) = f5(c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (f7(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~big_f(f7(c2), f10(c2))) | (f10(c2) = f5(c2)))),
% 28.40/18.64 inference(rewrite,[status(thm)],[])).
% 28.40/18.64 tff(12303,plain,
% 28.40/18.64 (((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(c2) = c2) | (f10(c2) = f5(c2)) | (~big_f(f7(c2), f10(c2)))) <=> ((f10(c2) = c2) | (f7(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~big_f(f7(c2), f10(c2))) | (f10(c2) = f5(c2)))),
% 28.40/18.64 inference(rewrite,[status(thm)],[])).
% 28.40/18.64 tff(12304,plain,
% 28.40/18.64 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(c2) = c2) | (f10(c2) = f5(c2)) | (~big_f(f7(c2), f10(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f7(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~big_f(f7(c2), f10(c2))) | (f10(c2) = f5(c2))))),
% 28.40/18.64 inference(monotonicity,[status(thm)],[12303])).
% 28.40/18.64 tff(12305,plain,
% 28.40/18.64 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(c2) = c2) | (f10(c2) = f5(c2)) | (~big_f(f7(c2), f10(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (f7(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~big_f(f7(c2), f10(c2))) | (f10(c2) = f5(c2)))),
% 28.40/18.64 inference(transitivity,[status(thm)],[12304, 12302])).
% 28.40/18.64 tff(12306,plain,
% 28.40/18.64 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(c2) = c2) | (f10(c2) = f5(c2)) | (~big_f(f7(c2), f10(c2))))),
% 28.40/18.64 inference(quant_inst,[status(thm)],[])).
% 28.40/18.64 tff(12307,plain,
% 28.40/18.64 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (f7(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~big_f(f7(c2), f10(c2))) | (f10(c2) = f5(c2))),
% 28.40/18.64 inference(modus_ponens,[status(thm)],[12306, 12305])).
% 28.40/18.64 tff(12308,plain,
% 28.40/18.64 ((c2 = f8(c2)) | (~big_f(f7(c2), f10(c2))) | (f10(c2) = f5(c2))),
% 28.40/18.64 inference(unit_resolution,[status(thm)],[12307, 1659, 89, 17, 12291])).
% 28.40/18.64 tff(12309,plain,
% 28.40/18.64 (f10(c2) = f5(c2)),
% 28.40/18.64 inference(unit_resolution,[status(thm)],[12308, 12290, 12301])).
% 28.40/18.64 tff(12310,plain,
% 28.40/18.64 (f10(c2) = c2),
% 28.40/18.64 inference(transitivity,[status(thm)],[12309, 12300])).
% 28.40/18.64 tff(12311,plain,
% 28.40/18.64 ($false),
% 28.40/18.64 inference(unit_resolution,[status(thm)],[89, 12310])).
% 28.40/18.64 tff(12312,plain,((c2 = f8(c2)) | (f10(c2) = c2) | (~big_f(f7(c2), f10(c2))) | (f7(c2) = c2) | (~big_f(c2, f10(c2))) | (~big_f(f7(c2), c2))), inference(lemma,lemma(discharge,[]))).
% 28.40/18.64 tff(12313,plain,
% 28.40/18.64 (c2 = f8(c2)),
% 28.40/18.64 inference(unit_resolution,[status(thm)],[12312, 12289, 11798, 17, 12286, 12285])).
% 28.40/18.64 tff(12314,plain,
% 28.40/18.64 (f8(c2) = c2),
% 28.40/18.64 inference(symmetry,[status(thm)],[12313])).
% 28.40/18.64 tff(12315,plain,
% 28.40/18.64 ((c1 = f8(c2)) <=> (f10(c2) = c2)),
% 28.40/18.64 inference(monotonicity,[status(thm)],[11957, 12314])).
% 28.40/18.64 tff(12316,plain,
% 28.40/18.64 ((f10(c2) = c2) <=> (c1 = f8(c2))),
% 28.40/18.64 inference(symmetry,[status(thm)],[12315])).
% 28.40/18.64 tff(12317,plain,
% 28.40/18.64 ((f10(c2) = c2) <=> (c1 = f8(f7(c1)))),
% 28.40/18.64 inference(transitivity,[status(thm)],[12316, 12282])).
% 28.40/18.64 tff(12318,plain,
% 28.40/18.64 ((~(f10(c2) = c2)) <=> (~(c1 = f8(f7(c1))))),
% 28.40/18.64 inference(monotonicity,[status(thm)],[12317])).
% 28.40/18.64 tff(12319,plain,
% 28.40/18.64 (~(c1 = f8(f7(c1)))),
% 28.40/18.64 inference(modus_ponens,[status(thm)],[11798, 12318])).
% 28.40/18.64 tff(12320,plain,
% 28.40/18.64 (f7(f7(c1)) = f7(c2)),
% 28.40/18.64 inference(monotonicity,[status(thm)],[120])).
% 28.40/18.64 tff(12321,plain,
% 28.40/18.64 (big_f(f7(f7(c1)), c1) <=> big_f(f7(c2), c1)),
% 28.40/18.64 inference(monotonicity,[status(thm)],[12320])).
% 28.40/18.64 tff(12322,plain,
% 28.40/18.64 (big_f(f7(c2), c1) <=> big_f(f7(f7(c1)), c1)),
% 28.40/18.64 inference(symmetry,[status(thm)],[12321])).
% 28.40/18.64 tff(12323,plain,
% 28.40/18.64 (big_f(f7(f7(c1)), c1)),
% 28.40/18.64 inference(modus_ponens,[status(thm)],[12284, 12322])).
% 28.40/18.64 tff(12324,plain,
% 28.40/18.64 (big_f(f7(f7(c1)), f7(c1)) <=> big_f(f7(c2), c2)),
% 28.40/18.64 inference(monotonicity,[status(thm)],[12320, 120])).
% 28.40/18.64 tff(12325,plain,
% 28.40/18.64 (big_f(f7(c2), c2) <=> big_f(f7(f7(c1)), f7(c1))),
% 28.40/18.64 inference(symmetry,[status(thm)],[12324])).
% 28.40/18.64 tff(12326,plain,
% 28.40/18.64 (big_f(f7(f7(c1)), f7(c1))),
% 28.40/18.64 inference(modus_ponens,[status(thm)],[12285, 12325])).
% 28.40/18.64 tff(12327,plain,
% 28.40/18.64 (f10(f7(c1)) = f10(c2)),
% 28.40/18.64 inference(monotonicity,[status(thm)],[120])).
% 28.40/18.64 tff(12328,plain,
% 28.40/18.64 (big_f(c1, f10(f7(c1))) <=> big_f(c1, f10(c2))),
% 28.40/18.64 inference(monotonicity,[status(thm)],[12327])).
% 28.40/18.64 tff(12329,plain,
% 28.40/18.64 (big_f(c1, f10(c2)) <=> big_f(c1, f10(f7(c1)))),
% 28.40/18.64 inference(symmetry,[status(thm)],[12328])).
% 28.40/18.64 tff(12330,plain,
% 28.40/18.64 (big_f(c1, f10(c2)) <=> big_f(c1, c1)),
% 28.40/18.64 inference(monotonicity,[status(thm)],[11799])).
% 28.40/18.64 tff(12331,plain,
% 28.40/18.64 (big_f(c1, c1) <=> big_f(c1, f10(c2))),
% 28.40/18.64 inference(symmetry,[status(thm)],[12330])).
% 28.40/18.64 tff(12332,plain,
% 28.40/18.64 (big_f(c1, c1) <=> big_f(c1, f10(f7(c1)))),
% 28.40/18.64 inference(transitivity,[status(thm)],[12331, 12329])).
% 28.40/18.64 tff(12333,plain,
% 28.40/18.64 (big_f(c1, f10(f7(c1)))),
% 28.40/18.64 inference(modus_ponens,[status(thm)],[4932, 12332])).
% 28.40/18.64 tff(12334,plain,
% 28.40/18.64 ((f10(f7(c1)) = f7(c1)) <=> (f10(c2) = c2)),
% 28.40/18.64 inference(monotonicity,[status(thm)],[12327, 120])).
% 28.40/18.64 tff(12335,plain,
% 28.40/18.64 ((f10(c2) = c2) <=> (f10(f7(c1)) = f7(c1))),
% 28.40/18.64 inference(symmetry,[status(thm)],[12334])).
% 28.40/18.64 tff(12336,plain,
% 28.40/18.64 ((~(f10(c2) = c2)) <=> (~(f10(f7(c1)) = f7(c1)))),
% 28.40/18.64 inference(monotonicity,[status(thm)],[12335])).
% 28.40/18.64 tff(12337,plain,
% 28.40/18.64 (~(f10(f7(c1)) = f7(c1))),
% 28.40/18.64 inference(modus_ponens,[status(thm)],[11798, 12336])).
% 28.40/18.64 tff(12338,plain,
% 28.40/18.64 ((f7(f7(c1)) = f7(c1)) <=> (f7(c2) = c2)),
% 28.40/18.64 inference(monotonicity,[status(thm)],[12320, 120])).
% 28.40/18.64 tff(12339,plain,
% 28.40/18.64 ((f7(c2) = c2) <=> (f7(f7(c1)) = f7(c1))),
% 28.40/18.64 inference(symmetry,[status(thm)],[12338])).
% 28.40/18.64 tff(12340,plain,
% 28.40/18.64 ((~(f7(c2) = c2)) <=> (~(f7(f7(c1)) = f7(c1)))),
% 28.40/18.64 inference(monotonicity,[status(thm)],[12339])).
% 28.40/18.64 tff(12341,plain,
% 28.40/18.64 (~(f7(f7(c1)) = f7(c1))),
% 28.40/18.64 inference(modus_ponens,[status(thm)],[17, 12340])).
% 28.40/18.64 tff(12342,assumption,(big_f(c1, f10(f7(c1)))), introduced(assumption)).
% 28.40/18.64 tff(12343,assumption,(~(c1 = f8(f7(c1)))), introduced(assumption)).
% 28.40/18.64 tff(12344,assumption,(~(f10(f7(c1)) = f7(c1))), introduced(assumption)).
% 28.40/18.64 tff(12345,assumption,(big_f(f7(f7(c1)), c1)), introduced(assumption)).
% 28.40/18.64 tff(12346,assumption,(~(f7(f7(c1)) = f7(c1))), introduced(assumption)).
% 28.40/18.64 tff(12347,plain,
% 28.40/18.64 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~big_f(c1, f10(f7(c1)))) | (f7(f7(c1)) = f7(c1)) | (f10(f7(c1)) = f7(c1)) | (c1 = f8(f7(c1))) | (c1 = f5(f7(c1))) | (~big_f(f7(f7(c1)), c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~big_f(c1, f10(f7(c1)))) | (f7(f7(c1)) = f7(c1)) | (f10(f7(c1)) = f7(c1)) | (c1 = f8(f7(c1))) | (c1 = f5(f7(c1))) | (~big_f(f7(f7(c1)), c1)))),
% 28.40/18.64 inference(rewrite,[status(thm)],[])).
% 28.40/18.64 tff(12348,plain,
% 28.40/18.64 (((f10(f7(c1)) = f7(c1)) | (c1 = f8(f7(c1))) | (~big_f(c1, f10(f7(c1)))) | (f7(f7(c1)) = f7(c1)) | (c1 = f5(f7(c1))) | (~big_f(f7(f7(c1)), c1))) <=> ((~big_f(c1, f10(f7(c1)))) | (f7(f7(c1)) = f7(c1)) | (f10(f7(c1)) = f7(c1)) | (c1 = f8(f7(c1))) | (c1 = f5(f7(c1))) | (~big_f(f7(f7(c1)), c1)))),
% 28.40/18.64 inference(rewrite,[status(thm)],[])).
% 28.40/18.64 tff(12349,plain,
% 28.40/18.64 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f7(c1)) = f7(c1)) | (c1 = f8(f7(c1))) | (~big_f(c1, f10(f7(c1)))) | (f7(f7(c1)) = f7(c1)) | (c1 = f5(f7(c1))) | (~big_f(f7(f7(c1)), c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~big_f(c1, f10(f7(c1)))) | (f7(f7(c1)) = f7(c1)) | (f10(f7(c1)) = f7(c1)) | (c1 = f8(f7(c1))) | (c1 = f5(f7(c1))) | (~big_f(f7(f7(c1)), c1))))),
% 28.40/18.64 inference(monotonicity,[status(thm)],[12348])).
% 28.40/18.64 tff(12350,plain,
% 28.40/18.64 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f7(c1)) = f7(c1)) | (c1 = f8(f7(c1))) | (~big_f(c1, f10(f7(c1)))) | (f7(f7(c1)) = f7(c1)) | (c1 = f5(f7(c1))) | (~big_f(f7(f7(c1)), c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~big_f(c1, f10(f7(c1)))) | (f7(f7(c1)) = f7(c1)) | (f10(f7(c1)) = f7(c1)) | (c1 = f8(f7(c1))) | (c1 = f5(f7(c1))) | (~big_f(f7(f7(c1)), c1)))),
% 28.40/18.64 inference(transitivity,[status(thm)],[12349, 12347])).
% 28.40/18.64 tff(12351,plain,
% 28.40/18.64 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f7(c1)) = f7(c1)) | (c1 = f8(f7(c1))) | (~big_f(c1, f10(f7(c1)))) | (f7(f7(c1)) = f7(c1)) | (c1 = f5(f7(c1))) | (~big_f(f7(f7(c1)), c1)))),
% 28.40/18.64 inference(quant_inst,[status(thm)],[])).
% 28.40/18.64 tff(12352,plain,
% 28.40/18.64 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~big_f(c1, f10(f7(c1)))) | (f7(f7(c1)) = f7(c1)) | (f10(f7(c1)) = f7(c1)) | (c1 = f8(f7(c1))) | (c1 = f5(f7(c1))) | (~big_f(f7(f7(c1)), c1))),
% 28.40/18.64 inference(modus_ponens,[status(thm)],[12351, 12350])).
% 28.40/18.64 tff(12353,plain,
% 28.40/18.64 ((~big_f(c1, f10(f7(c1)))) | (c1 = f8(f7(c1))) | (c1 = f5(f7(c1)))),
% 28.40/18.64 inference(unit_resolution,[status(thm)],[12352, 1659, 12346, 12345, 12344])).
% 28.40/18.64 tff(12354,plain,
% 28.40/18.64 (c1 = f5(f7(c1))),
% 28.40/18.64 inference(unit_resolution,[status(thm)],[12353, 12343, 12342])).
% 28.40/18.64 tff(12355,plain,
% 28.40/18.64 (f5(f7(c1)) = c1),
% 28.40/18.65 inference(symmetry,[status(thm)],[12354])).
% 28.40/18.65 tff(12356,assumption,(big_f(f7(f7(c1)), f7(c1))), introduced(assumption)).
% 28.40/18.65 tff(12357,plain,
% 28.40/18.65 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~big_f(c1, f10(f7(c1)))) | (~big_f(f7(f7(c1)), f7(c1))) | (f7(f7(c1)) = f7(c1)) | (f10(f7(c1)) = f7(c1)) | (c1 = f8(f7(c1))) | (f7(c1) = f5(f7(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~big_f(c1, f10(f7(c1)))) | (~big_f(f7(f7(c1)), f7(c1))) | (f7(f7(c1)) = f7(c1)) | (f10(f7(c1)) = f7(c1)) | (c1 = f8(f7(c1))) | (f7(c1) = f5(f7(c1))))),
% 28.40/18.65 inference(rewrite,[status(thm)],[])).
% 28.40/18.65 tff(12358,plain,
% 28.40/18.65 (((f10(f7(c1)) = f7(c1)) | (c1 = f8(f7(c1))) | (~big_f(c1, f10(f7(c1)))) | (f7(f7(c1)) = f7(c1)) | (f7(c1) = f5(f7(c1))) | (~big_f(f7(f7(c1)), f7(c1)))) <=> ((~big_f(c1, f10(f7(c1)))) | (~big_f(f7(f7(c1)), f7(c1))) | (f7(f7(c1)) = f7(c1)) | (f10(f7(c1)) = f7(c1)) | (c1 = f8(f7(c1))) | (f7(c1) = f5(f7(c1))))),
% 28.40/18.65 inference(rewrite,[status(thm)],[])).
% 28.40/18.65 tff(12359,plain,
% 28.40/18.65 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f7(c1)) = f7(c1)) | (c1 = f8(f7(c1))) | (~big_f(c1, f10(f7(c1)))) | (f7(f7(c1)) = f7(c1)) | (f7(c1) = f5(f7(c1))) | (~big_f(f7(f7(c1)), f7(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~big_f(c1, f10(f7(c1)))) | (~big_f(f7(f7(c1)), f7(c1))) | (f7(f7(c1)) = f7(c1)) | (f10(f7(c1)) = f7(c1)) | (c1 = f8(f7(c1))) | (f7(c1) = f5(f7(c1)))))),
% 28.40/18.65 inference(monotonicity,[status(thm)],[12358])).
% 28.40/18.65 tff(12360,plain,
% 28.40/18.65 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f7(c1)) = f7(c1)) | (c1 = f8(f7(c1))) | (~big_f(c1, f10(f7(c1)))) | (f7(f7(c1)) = f7(c1)) | (f7(c1) = f5(f7(c1))) | (~big_f(f7(f7(c1)), f7(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~big_f(c1, f10(f7(c1)))) | (~big_f(f7(f7(c1)), f7(c1))) | (f7(f7(c1)) = f7(c1)) | (f10(f7(c1)) = f7(c1)) | (c1 = f8(f7(c1))) | (f7(c1) = f5(f7(c1))))),
% 28.40/18.65 inference(transitivity,[status(thm)],[12359, 12357])).
% 28.40/18.65 tff(12361,plain,
% 28.40/18.65 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f7(c1)) = f7(c1)) | (c1 = f8(f7(c1))) | (~big_f(c1, f10(f7(c1)))) | (f7(f7(c1)) = f7(c1)) | (f7(c1) = f5(f7(c1))) | (~big_f(f7(f7(c1)), f7(c1))))),
% 28.40/18.65 inference(quant_inst,[status(thm)],[])).
% 28.40/18.65 tff(12362,plain,
% 28.40/18.65 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~big_f(c1, f10(f7(c1)))) | (~big_f(f7(f7(c1)), f7(c1))) | (f7(f7(c1)) = f7(c1)) | (f10(f7(c1)) = f7(c1)) | (c1 = f8(f7(c1))) | (f7(c1) = f5(f7(c1)))),
% 28.40/18.65 inference(modus_ponens,[status(thm)],[12361, 12360])).
% 28.40/18.65 tff(12363,plain,
% 28.40/18.65 ((~big_f(f7(f7(c1)), f7(c1))) | (c1 = f8(f7(c1))) | (f7(c1) = f5(f7(c1)))),
% 28.40/18.65 inference(unit_resolution,[status(thm)],[12362, 1659, 12346, 12344, 12342])).
% 28.40/18.65 tff(12364,plain,
% 28.40/18.65 (f7(c1) = f5(f7(c1))),
% 28.40/18.65 inference(unit_resolution,[status(thm)],[12363, 12343, 12356])).
% 28.40/18.65 tff(12365,plain,
% 28.40/18.65 (f7(c1) = c1),
% 28.40/18.65 inference(transitivity,[status(thm)],[12364, 12355])).
% 28.40/18.65 tff(12366,plain,
% 28.40/18.65 ($false),
% 28.40/18.65 inference(unit_resolution,[status(thm)],[115, 12365])).
% 28.40/18.65 tff(12367,plain,((c1 = f8(f7(c1))) | (f7(c1) = c1) | (~big_f(f7(f7(c1)), f7(c1))) | (f7(f7(c1)) = f7(c1)) | (f10(f7(c1)) = f7(c1)) | (~big_f(c1, f10(f7(c1)))) | (~big_f(f7(f7(c1)), c1))), inference(lemma,lemma(discharge,[]))).
% 28.40/18.65 tff(12368,plain,
% 28.40/18.65 (c1 = f8(f7(c1))),
% 28.40/18.65 inference(unit_resolution,[status(thm)],[12367, 12341, 12337, 12333, 12326, 12323, 115])).
% 28.40/18.65 tff(12369,plain,
% 28.40/18.65 ($false),
% 28.40/18.65 inference(unit_resolution,[status(thm)],[12368, 12319])).
% 28.40/18.65 tff(12370,plain,((f7(c2) = c2) | (~big_f(c1, c1)) | (f7(c1) = c1) | (~(f4(c4) = c2)) | big_f(c2, c2) | (f10(c1) = c1) | (~(c3 = c2))), inference(lemma,lemma(discharge,[]))).
% 28.40/18.65 tff(12371,plain,
% 28.40/18.65 (~(c3 = c2)),
% 28.40/18.65 inference(unit_resolution,[status(thm)],[12370, 12279, 115, 79, 17, 3, 121])).
% 28.40/18.65 tff(12372,plain,
% 28.40/18.65 (c3 = c1),
% 28.40/18.65 inference(unit_resolution,[status(thm)],[180, 12371])).
% 28.40/18.65 tff(12373,plain,
% 28.40/18.65 (c3 = f7(c2)),
% 28.40/18.65 inference(transitivity,[status(thm)],[12372, 125])).
% 28.40/18.65 tff(12374,plain,
% 28.40/18.65 ((c2 = c3) <=> (c2 = f7(c2))),
% 28.40/18.65 inference(monotonicity,[status(thm)],[12373])).
% 28.40/18.65 tff(12375,plain,
% 28.40/18.65 ((c2 = c3) <=> (f7(c2) = c2)),
% 28.40/18.65 inference(transitivity,[status(thm)],[12374, 8409])).
% 28.40/18.65 tff(12376,plain,
% 28.40/18.65 ((f7(c2) = c2) <=> (c2 = c3)),
% 28.40/18.65 inference(symmetry,[status(thm)],[12375])).
% 28.40/18.65 tff(12377,plain,
% 28.40/18.65 ((~(f7(c2) = c2)) <=> (~(c2 = c3))),
% 28.40/18.65 inference(monotonicity,[status(thm)],[12376])).
% 28.40/18.65 tff(12378,plain,
% 28.40/18.65 (~(c2 = c3)),
% 28.40/18.65 inference(modus_ponens,[status(thm)],[17, 12377])).
% 28.40/18.65 tff(12379,plain,
% 28.40/18.65 ((f7(c2) = c2) <=> (f7(f7(c2)) = c3)),
% 28.40/18.65 inference(transitivity,[status(thm)],[12376, 8408])).
% 28.40/18.65 tff(12380,plain,
% 28.40/18.65 ((~(f7(c2) = c2)) <=> (~(f7(f7(c2)) = c3))),
% 28.40/18.65 inference(monotonicity,[status(thm)],[12379])).
% 28.40/18.65 tff(12381,plain,
% 28.40/18.65 (~(f7(f7(c2)) = c3)),
% 28.40/18.65 inference(modus_ponens,[status(thm)],[17, 12380])).
% 28.40/18.65 tff(12382,plain,
% 28.40/18.65 ((f7(c1) = c3) <=> (c2 = c3)),
% 28.40/18.65 inference(monotonicity,[status(thm)],[120])).
% 28.40/18.65 tff(12383,plain,
% 28.40/18.65 ((c2 = c3) <=> (f7(c1) = c3)),
% 28.40/18.65 inference(symmetry,[status(thm)],[12382])).
% 28.40/18.65 tff(12384,plain,
% 28.40/18.65 ((f7(c2) = c2) <=> (f7(c1) = c3)),
% 28.40/18.65 inference(transitivity,[status(thm)],[12376, 12383])).
% 28.40/18.65 tff(12385,plain,
% 28.40/18.65 ((~(f7(c2) = c2)) <=> (~(f7(c1) = c3))),
% 28.40/18.65 inference(monotonicity,[status(thm)],[12384])).
% 28.40/18.65 tff(12386,plain,
% 28.40/18.65 (~(f7(c1) = c3)),
% 28.40/18.65 inference(modus_ponens,[status(thm)],[17, 12385])).
% 28.40/18.65 tff(12387,plain,
% 28.40/18.65 ((c1 = c3) <=> (c3 = c1)),
% 28.40/18.65 inference(symmetry,[status(thm)],[68])).
% 28.40/18.65 tff(12388,plain,
% 28.40/18.65 (c1 = c3),
% 28.40/18.65 inference(unit_resolution,[status(thm)],[11545, 480, 4932, 27, 79])).
% 28.40/18.65 tff(12389,plain,
% 28.40/18.65 (c3 = c1),
% 28.40/18.65 inference(modus_ponens,[status(thm)],[12388, 12387])).
% 28.40/18.65 tff(12390,plain,
% 28.40/18.65 (~(f7(c2) = c2)),
% 28.40/18.65 inference(unit_resolution,[status(thm)],[11517, 12389, 79, 4932, 121, 348])).
% 28.40/18.65 tff(12391,plain,
% 28.40/18.65 (f7(c2) = c1),
% 28.40/18.65 inference(unit_resolution,[status(thm)],[21, 12390])).
% 28.40/18.65 tff(12392,plain,
% 28.40/18.65 (big_f(f7(c2), c1) <=> big_f(c1, c1)),
% 28.40/18.65 inference(monotonicity,[status(thm)],[12391])).
% 28.40/18.65 tff(12393,plain,
% 28.40/18.65 (big_f(c1, c1) <=> big_f(f7(c2), c1)),
% 28.40/18.65 inference(symmetry,[status(thm)],[12392])).
% 28.40/18.65 tff(12394,plain,
% 28.40/18.65 (big_f(f7(c2), c1)),
% 28.40/18.65 inference(modus_ponens,[status(thm)],[4932, 12393])).
% 28.40/18.65 tff(12395,plain,
% 28.40/18.65 (c3 = c1),
% 28.40/18.65 inference(symmetry,[status(thm)],[12388])).
% 28.40/18.65 tff(12396,plain,
% 28.40/18.65 (c3 = f10(c2)),
% 28.40/18.65 inference(transitivity,[status(thm)],[12395, 99])).
% 28.40/18.65 tff(12397,plain,
% 28.40/18.65 ((c2 = c3) <=> (c2 = f10(c2))),
% 28.40/18.65 inference(monotonicity,[status(thm)],[12396])).
% 28.40/18.65 tff(12398,plain,
% 28.40/18.65 ((c2 = c3) <=> (f10(c2) = c2)),
% 28.40/18.65 inference(transitivity,[status(thm)],[12397, 4987])).
% 28.40/18.65 tff(12399,plain,
% 28.40/18.65 ((f10(c2) = c2) <=> (c2 = c3)),
% 28.40/18.65 inference(symmetry,[status(thm)],[12398])).
% 28.40/18.65 tff(12400,plain,
% 28.40/18.65 ((~(f10(c2) = c2)) <=> (~(c2 = c3))),
% 28.40/18.65 inference(monotonicity,[status(thm)],[12399])).
% 28.40/18.65 tff(12401,plain,
% 28.40/18.65 (~(c2 = c3)),
% 28.40/18.65 inference(modus_ponens,[status(thm)],[89, 12400])).
% 28.40/18.65 tff(12402,plain,
% 28.40/18.65 (~big_f(f7(c2), c1)),
% 28.40/18.65 inference(unit_resolution,[status(thm)],[8806, 12390, 79, 121, 348, 12401, 480, 347])).
% 28.40/18.65 tff(12403,plain,
% 28.40/18.65 ($false),
% 28.40/18.65 inference(unit_resolution,[status(thm)],[12402, 12394])).
% 28.40/18.65 tff(12404,plain,((~(c4 = c1)) | (~big_f(c1, c1)) | (~(f4(c4) = c2)) | big_f(c2, c2) | (~big_f(c2, c1)) | (~(f7(c1) = c2)) | (f10(c2) = c2) | big_f(c1, c2)), inference(lemma,lemma(discharge,[]))).
% 28.40/18.65 tff(12405,plain,
% 28.40/18.65 (~(c4 = c1)),
% 28.40/18.65 inference(unit_resolution,[status(thm)],[12404, 27, 79, 121, 348, 347, 89, 4932])).
% 28.40/18.65 tff(12406,plain,
% 28.40/18.65 (c4 = c2),
% 28.40/18.65 inference(unit_resolution,[status(thm)],[461, 12405])).
% 28.40/18.65 tff(12407,plain,
% 28.40/18.65 (c2 = c4),
% 28.40/18.65 inference(symmetry,[status(thm)],[12406])).
% 28.40/18.65 tff(12408,plain,
% 28.40/18.65 (f4(c2) = f4(c4)),
% 28.40/18.65 inference(monotonicity,[status(thm)],[12407])).
% 28.40/18.65 tff(12409,plain,
% 28.40/18.65 (f4(c4) = f4(c2)),
% 28.40/18.65 inference(symmetry,[status(thm)],[12408])).
% 28.40/18.65 tff(12410,plain,
% 28.40/18.65 (c2 = f4(c2)),
% 28.40/18.65 inference(transitivity,[status(thm)],[436, 12409])).
% 28.40/18.65 tff(12411,plain,
% 28.40/18.65 (c2 = c4),
% 28.40/18.65 inference(modus_ponens,[status(thm)],[12406, 159])).
% 28.40/18.65 tff(12412,plain,
% 28.40/18.65 (f1(c1, c1) = c1),
% 28.40/18.65 inference(unit_resolution,[status(thm)],[9763, 12100, 121, 631, 27, 630])).
% 28.40/18.65 tff(12413,plain,
% 28.40/18.65 (f1(f10(c2), f10(c2)) = f1(c1, c1)),
% 28.40/18.65 inference(monotonicity,[status(thm)],[94, 94])).
% 28.40/18.65 tff(12414,plain,
% 28.40/18.65 (f1(f10(c2), f10(c2)) = f10(c2)),
% 28.40/18.65 inference(transitivity,[status(thm)],[12413, 12412, 99])).
% 28.40/18.65 tff(12415,plain,
% 28.40/18.65 (f1(f10(c2), f10(c2)) = c1),
% 28.40/18.65 inference(transitivity,[status(thm)],[12413, 12412])).
% 28.40/18.65 tff(12416,plain,
% 28.40/18.65 (big_f(f10(c2), f1(f10(c2), f10(c2))) <=> big_f(c1, c1)),
% 28.40/18.65 inference(monotonicity,[status(thm)],[94, 12415])).
% 28.40/18.65 tff(12417,plain,
% 28.40/18.65 (big_f(c1, c1) <=> big_f(f10(c2), f1(f10(c2), f10(c2)))),
% 28.40/18.65 inference(symmetry,[status(thm)],[12416])).
% 28.40/18.65 tff(12418,plain,
% 28.40/18.65 (big_f(f10(c2), f1(f10(c2), f10(c2)))),
% 28.40/18.65 inference(modus_ponens,[status(thm)],[4932, 12417])).
% 28.40/18.65 tff(12419,plain,
% 28.40/18.65 ((~(f10(c2) = c2)) <=> (~(f10(c2) = c3))),
% 28.40/18.65 inference(monotonicity,[status(thm)],[12097])).
% 28.40/18.65 tff(12420,plain,
% 28.40/18.65 (~(f10(c2) = c3)),
% 28.40/18.65 inference(modus_ponens,[status(thm)],[89, 12419])).
% 28.40/18.65 tff(12421,plain,
% 28.40/18.65 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (f10(c2) = c3) | (~(f1(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f10(c2), f1(f10(c2), f10(c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (f10(c2) = c3) | (~(f1(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f10(c2), f1(f10(c2), f10(c2)))))),
% 28.40/18.65 inference(rewrite,[status(thm)],[])).
% 28.40/18.65 tff(12422,plain,
% 28.40/18.65 (((f10(c2) = c3) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))) | (~(f1(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f10(c2), f1(f10(c2), f10(c2))))) <=> ((~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (f10(c2) = c3) | (~(f1(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f10(c2), f1(f10(c2), f10(c2)))))),
% 28.40/18.65 inference(rewrite,[status(thm)],[])).
% 28.40/18.65 tff(12423,plain,
% 28.40/18.65 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f10(c2) = c3) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))) | (~(f1(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f10(c2), f1(f10(c2), f10(c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (f10(c2) = c3) | (~(f1(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f10(c2), f1(f10(c2), f10(c2))))))),
% 28.40/18.65 inference(monotonicity,[status(thm)],[12422])).
% 28.40/18.65 tff(12424,plain,
% 28.40/18.65 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f10(c2) = c3) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))) | (~(f1(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f10(c2), f1(f10(c2), f10(c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (f10(c2) = c3) | (~(f1(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f10(c2), f1(f10(c2), f10(c2)))))),
% 28.40/18.65 inference(transitivity,[status(thm)],[12423, 12421])).
% 28.40/18.65 tff(12425,plain,
% 28.40/18.65 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f10(c2) = c3) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))) | (~(f1(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f10(c2), f1(f10(c2), f10(c2)))))),
% 28.40/18.65 inference(quant_inst,[status(thm)],[])).
% 28.40/18.65 tff(12426,plain,
% 28.40/18.65 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (f10(c2) = c3) | (~(f1(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f10(c2), f1(f10(c2), f10(c2))))),
% 28.40/18.65 inference(modus_ponens,[status(thm)],[12425, 12424])).
% 28.40/18.65 tff(12427,plain,
% 28.40/18.65 ((~(f1(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f10(c2), f1(f10(c2), f10(c2))))),
% 28.40/18.65 inference(unit_resolution,[status(thm)],[12426, 447, 631, 630, 121, 12420])).
% 28.40/18.65 tff(12428,plain,
% 28.40/18.65 ($false),
% 28.40/18.65 inference(unit_resolution,[status(thm)],[12427, 12418, 12414])).
% 28.40/18.65 tff(12429,plain,((~(c3 = c2)) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (~big_f(c1, c1)) | big_f(c1, c2) | (f10(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 28.40/18.65 tff(12430,plain,
% 28.40/18.65 (~(c3 = c2)),
% 28.40/18.65 inference(unit_resolution,[status(thm)],[12429, 12411, 12410, 121, 4932, 27, 89])).
% 28.40/18.65 tff(12431,plain,
% 28.40/18.65 (~(c2 = c3)),
% 28.40/18.65 inference(modus_ponens,[status(thm)],[12430, 10473])).
% 28.40/18.65 tff(12432,plain,
% 28.40/18.65 (c3 = c1),
% 28.40/18.65 inference(unit_resolution,[status(thm)],[180, 12430])).
% 28.40/18.65 tff(12433,plain,
% 28.40/18.65 (~(f7(c2) = c2)),
% 28.40/18.65 inference(unit_resolution,[status(thm)],[11517, 12432, 79, 4932, 121, 348])).
% 28.40/18.65 tff(12434,plain,
% 28.40/18.65 (f7(c2) = c1),
% 28.40/18.65 inference(unit_resolution,[status(thm)],[21, 12433])).
% 28.40/18.65 tff(12435,plain,
% 28.40/18.65 (c2 = c3),
% 28.40/18.65 inference(unit_resolution,[status(thm)],[10120, 12434, 79, 121, 348, 12406])).
% 28.40/18.65 tff(12436,plain,
% 28.40/18.65 ($false),
% 28.40/18.65 inference(unit_resolution,[status(thm)],[12435, 12431])).
% 28.40/18.65 tff(12437,plain,(big_f(c1, c2) | (~(f4(c4) = c2)) | big_f(c2, c2) | (~big_f(c2, c1)) | (~big_f(c1, c1)) | (f10(c2) = c2) | (~(f7(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.40/18.65 tff(12438,plain,
% 28.40/18.65 (big_f(c1, c2)),
% 28.40/18.65 inference(unit_resolution,[status(thm)],[12437, 12279, 79, 121, 12087, 11797, 120])).
% 28.40/18.65 tff(12439,plain,
% 28.40/18.65 (c2 = c4),
% 28.40/18.65 inference(unit_resolution,[status(thm)],[12226, 12378, 120, 121, 12087, 12438, 17, 12386])).
% 28.40/18.65 tff(12440,plain,
% 28.40/18.65 ($false),
% 28.40/18.65 inference(unit_resolution,[status(thm)],[8754, 12439, 12381, 79, 121, 12378, 120, 22, 12087])).
% 28.40/18.65 tff(12441,plain,(big_f(c2, c2) | (~(f4(c4) = c2)) | (f7(c2) = c2) | (f7(c1) = c1) | (f10(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 28.40/18.65 tff(12442,plain,
% 28.40/18.65 (big_f(c2, c2)),
% 28.40/18.65 inference(unit_resolution,[status(thm)],[12441, 17, 79, 115, 3])).
% 28.40/18.65 tff(12443,plain,
% 28.40/18.65 (big_f(f7(f7(c2)), c2)),
% 28.40/18.65 inference(modus_ponens,[status(thm)],[12442, 8617])).
% 28.40/18.65 tff(12444,plain,
% 28.40/18.65 ((f10(f7(c2)) = f7(c2)) <=> (c2 = f7(c2))),
% 28.40/18.65 inference(monotonicity,[status(thm)],[12108])).
% 28.40/18.65 tff(12445,plain,
% 28.40/18.65 ((f10(f7(c2)) = f7(c2)) <=> (f7(c2) = c2)),
% 28.40/18.65 inference(transitivity,[status(thm)],[12444, 8409])).
% 28.40/18.65 tff(12446,plain,
% 28.40/18.65 ((f7(c2) = c2) <=> (f10(f7(c2)) = f7(c2))),
% 28.40/18.65 inference(symmetry,[status(thm)],[12445])).
% 28.40/18.65 tff(12447,plain,
% 28.40/18.65 ((~(f7(c2) = c2)) <=> (~(f10(f7(c2)) = f7(c2)))),
% 28.40/18.65 inference(monotonicity,[status(thm)],[12446])).
% 28.40/18.65 tff(12448,plain,
% 28.40/18.65 (~(f10(f7(c2)) = f7(c2))),
% 28.40/18.65 inference(modus_ponens,[status(thm)],[17, 12447])).
% 28.40/18.65 tff(12449,plain,
% 28.40/18.65 (big_f(f7(f7(c2)), f7(c2)) <=> big_f(c2, f7(c2))),
% 28.40/18.65 inference(monotonicity,[status(thm)],[8406])).
% 28.40/18.65 tff(12450,plain,
% 28.40/18.65 (big_f(c2, f7(c2)) <=> big_f(f7(f7(c2)), f7(c2))),
% 28.40/18.65 inference(symmetry,[status(thm)],[12449])).
% 28.40/18.65 tff(12451,plain,
% 28.40/18.65 (big_f(c2, c1) <=> big_f(f7(f7(c2)), f7(c2))),
% 28.40/18.65 inference(transitivity,[status(thm)],[9312, 12450])).
% 28.40/18.65 tff(12452,plain,
% 28.40/18.65 (big_f(c1, f10(c2)) <=> big_f(f7(c2), f10(c2))),
% 28.40/18.65 inference(monotonicity,[status(thm)],[125])).
% 28.40/18.65 tff(12453,plain,
% 28.40/18.65 (big_f(f7(c2), f10(c2)) <=> big_f(c1, f10(c2))),
% 28.40/18.65 inference(symmetry,[status(thm)],[12452])).
% 28.40/18.65 tff(12454,plain,
% 28.40/18.65 (f10(c2) = f7(c2)),
% 28.40/18.65 inference(transitivity,[status(thm)],[12229, 125])).
% 28.40/18.65 tff(12455,plain,
% 28.40/18.65 (big_f(f7(c2), f10(c2)) <=> big_f(f7(c2), f7(c2))),
% 28.40/18.65 inference(monotonicity,[status(thm)],[12454])).
% 28.40/18.65 tff(12456,plain,
% 28.40/18.65 (big_f(f7(c2), f7(c2)) <=> big_f(f7(c2), f10(c2))),
% 28.40/18.65 inference(symmetry,[status(thm)],[12455])).
% 28.40/18.65 tff(12457,plain,
% 28.40/18.65 (big_f(c1, c1) <=> big_f(f7(c2), f7(c2))),
% 28.40/18.65 inference(monotonicity,[status(thm)],[125, 125])).
% 28.40/18.65 tff(12458,plain,
% 28.40/18.65 (big_f(c1, c1) <=> big_f(c1, f10(c2))),
% 28.40/18.65 inference(transitivity,[status(thm)],[12457, 12456, 12453])).
% 28.40/18.65 tff(12459,plain,
% 28.40/18.65 ((~big_f(c1, c1)) <=> (~big_f(c1, f10(c2)))),
% 28.40/18.65 inference(monotonicity,[status(thm)],[12458])).
% 28.40/18.65 tff(12460,plain,
% 28.40/18.65 ((f7(c2) = f8(f7(c2))) <=> (c1 = f8(f7(f4(c4))))),
% 28.40/18.65 inference(monotonicity,[status(thm)],[22, 108])).
% 28.40/18.65 tff(12461,plain,
% 28.40/18.65 ((f7(c2) = f8(f7(c2))) <=> (f8(f7(f4(c4))) = c1)),
% 28.40/18.65 inference(transitivity,[status(thm)],[12460, 8517])).
% 28.40/18.65 tff(12462,plain,
% 28.40/18.65 ((f8(f7(f4(c4))) = c1) <=> (f7(c2) = f8(f7(c2)))),
% 28.40/18.65 inference(symmetry,[status(thm)],[12461])).
% 28.40/18.65 tff(12463,plain,
% 28.40/18.65 (big_f(f7(c2), f7(c2))),
% 28.40/18.65 inference(modus_ponens,[status(thm)],[4932, 12457])).
% 28.40/18.65 tff(12464,plain,
% 28.40/18.65 (big_f(c2, f10(f7(c2))) <=> big_f(c2, c2)),
% 28.40/18.65 inference(monotonicity,[status(thm)],[24])).
% 28.40/18.65 tff(12465,plain,
% 28.40/18.65 (big_f(c2, c2) <=> big_f(c2, f10(f7(c2)))),
% 28.40/18.65 inference(symmetry,[status(thm)],[12464])).
% 28.40/18.65 tff(12466,plain,
% 28.40/18.65 (big_f(c2, f10(f7(c2)))),
% 28.40/18.65 inference(modus_ponens,[status(thm)],[1345, 12465])).
% 28.40/18.65 tff(12467,plain,
% 28.40/18.65 ((f10(f7(c2)) = f7(c2)) <=> (c2 = f7(c2))),
% 28.40/18.65 inference(monotonicity,[status(thm)],[24])).
% 28.40/18.65 tff(12468,plain,
% 28.40/18.65 ((f10(f7(c2)) = f7(c2)) <=> (f7(c2) = c2)),
% 28.40/18.65 inference(transitivity,[status(thm)],[12467, 8409])).
% 28.40/18.65 tff(12469,plain,
% 28.40/18.65 ((f7(c2) = c2) <=> (f10(f7(c2)) = f7(c2))),
% 28.40/18.65 inference(symmetry,[status(thm)],[12468])).
% 28.40/18.65 tff(12470,plain,
% 28.40/18.65 ((~(f7(c2) = c2)) <=> (~(f10(f7(c2)) = f7(c2)))),
% 28.40/18.65 inference(monotonicity,[status(thm)],[12469])).
% 28.40/18.65 tff(12471,plain,
% 28.40/18.65 (~(f10(f7(c2)) = f7(c2))),
% 28.40/18.65 inference(modus_ponens,[status(thm)],[17, 12470])).
% 28.40/18.65 tff(12472,plain,
% 28.40/18.65 (big_f(f7(f7(c2)), c2) <=> big_f(c2, c2)),
% 28.40/18.65 inference(monotonicity,[status(thm)],[8808])).
% 28.40/18.65 tff(12473,plain,
% 28.40/18.65 (big_f(c2, c2) <=> big_f(f7(f7(c2)), c2)),
% 28.40/18.65 inference(symmetry,[status(thm)],[12472])).
% 28.40/18.65 tff(12474,plain,
% 28.40/18.65 (big_f(f7(f7(c2)), c2)),
% 28.40/18.65 inference(modus_ponens,[status(thm)],[1345, 12473])).
% 28.40/18.65 tff(12475,plain,
% 28.40/18.65 (big_f(f7(c2), f10(c2))),
% 28.40/18.65 inference(modus_ponens,[status(thm)],[12463, 12456])).
% 28.40/18.65 tff(12476,plain,
% 28.40/18.65 (big_f(f7(f7(c2)), f7(c2)) <=> big_f(c2, f7(c2))),
% 28.40/18.65 inference(monotonicity,[status(thm)],[8808])).
% 28.40/18.65 tff(12477,plain,
% 28.40/18.65 (big_f(c2, f7(c2)) <=> big_f(f7(f7(c2)), f7(c2))),
% 28.40/18.65 inference(symmetry,[status(thm)],[12476])).
% 28.40/18.65 tff(12478,plain,
% 28.40/18.65 (big_f(c2, c1) <=> big_f(f7(f7(c2)), f7(c2))),
% 28.40/18.65 inference(transitivity,[status(thm)],[9312, 12477])).
% 28.40/18.65 tff(12479,plain,
% 28.40/18.65 (big_f(f7(f7(c2)), f7(c2))),
% 28.40/18.65 inference(modus_ponens,[status(thm)],[348, 12478])).
% 28.40/18.65 tff(12480,assumption,(big_f(f7(f7(c2)), c2)), introduced(assumption)).
% 28.40/18.65 tff(12481,plain,
% 28.40/18.65 ((f7(f7(c2)) = f7(c2)) <=> (c2 = f7(c2))),
% 28.40/18.65 inference(monotonicity,[status(thm)],[8808])).
% 28.40/18.65 tff(12482,plain,
% 28.40/18.65 ((f7(f7(c2)) = f7(c2)) <=> (f7(c2) = c2)),
% 28.40/18.65 inference(transitivity,[status(thm)],[12481, 8409])).
% 28.40/18.65 tff(12483,plain,
% 28.40/18.65 ((f7(c2) = c2) <=> (f7(f7(c2)) = f7(c2))),
% 28.40/18.65 inference(symmetry,[status(thm)],[12482])).
% 28.40/18.65 tff(12484,plain,
% 28.40/18.65 ((~(f7(c2) = c2)) <=> (~(f7(f7(c2)) = f7(c2)))),
% 28.40/18.65 inference(monotonicity,[status(thm)],[12483])).
% 28.40/18.65 tff(12485,plain,
% 28.40/18.65 (~(f7(f7(c2)) = f7(c2))),
% 28.40/18.65 inference(modus_ponens,[status(thm)],[17, 12484])).
% 28.40/18.65 tff(12486,plain,
% 28.40/18.65 (f10(c2) = f7(c2)),
% 28.40/18.65 inference(transitivity,[status(thm)],[94, 125])).
% 28.40/18.65 tff(12487,plain,
% 28.40/18.65 (big_f(c2, f10(c2)) <=> big_f(c2, f7(c2))),
% 28.40/18.65 inference(monotonicity,[status(thm)],[12486])).
% 28.40/18.65 tff(12488,plain,
% 28.40/18.65 (big_f(c2, f7(c2)) <=> big_f(c2, f10(c2))),
% 28.40/18.65 inference(symmetry,[status(thm)],[12487])).
% 28.40/18.65 tff(12489,plain,
% 28.40/18.65 (big_f(c2, c1) <=> big_f(c2, f10(c2))),
% 28.40/18.65 inference(transitivity,[status(thm)],[9312, 12488])).
% 28.40/18.65 tff(12490,plain,
% 28.40/18.65 (big_f(c2, f10(c2))),
% 28.40/18.65 inference(modus_ponens,[status(thm)],[348, 12489])).
% 28.40/18.65 tff(12491,plain,
% 28.40/18.65 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f7(f7(c2)) = f7(c2)) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (f7(f7(c2)) = f7(c2)) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2)))),
% 28.40/18.65 inference(rewrite,[status(thm)],[])).
% 28.40/18.65 tff(12492,plain,
% 28.40/18.65 (((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(f7(c2)) = f7(c2)) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2))) <=> ((f10(c2) = c2) | (f7(f7(c2)) = f7(c2)) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2)))),
% 28.40/18.65 inference(rewrite,[status(thm)],[])).
% 28.40/18.65 tff(12493,plain,
% 28.40/18.65 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(f7(c2)) = f7(c2)) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f7(f7(c2)) = f7(c2)) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2))))),
% 28.40/18.65 inference(monotonicity,[status(thm)],[12492])).
% 28.40/18.65 tff(12494,plain,
% 28.40/18.65 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(f7(c2)) = f7(c2)) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (f7(f7(c2)) = f7(c2)) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2)))),
% 28.40/18.65 inference(transitivity,[status(thm)],[12493, 12491])).
% 28.40/18.65 tff(12495,plain,
% 28.40/18.65 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(f7(c2)) = f7(c2)) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2)))),
% 28.40/18.65 inference(quant_inst,[status(thm)],[])).
% 28.40/18.65 tff(12496,plain,
% 28.40/18.65 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (f7(f7(c2)) = f7(c2)) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2))),
% 28.40/18.65 inference(modus_ponens,[status(thm)],[12495, 12494])).
% 28.40/18.65 tff(12497,plain,
% 28.40/18.65 ((c2 = f8(c2)) | (c2 = f5(f7(c2)))),
% 28.40/18.65 inference(unit_resolution,[status(thm)],[12496, 1659, 89, 8473, 12291, 12480])).
% 28.40/18.65 tff(12498,plain,
% 28.40/18.65 (c2 = f5(f7(c2))),
% 28.40/18.65 inference(unit_resolution,[status(thm)],[12497, 12290])).
% 28.40/18.65 tff(12499,plain,
% 28.40/18.65 (f5(f7(c2)) = c2),
% 28.40/18.65 inference(symmetry,[status(thm)],[12498])).
% 28.40/18.65 tff(12500,plain,
% 28.40/18.65 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f7(f7(c2)) = f7(c2)) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (f7(f7(c2)) = f7(c2)) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))))),
% 28.40/18.65 inference(rewrite,[status(thm)],[])).
% 28.40/18.65 tff(12501,plain,
% 28.40/18.65 (((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(f7(c2)) = f7(c2)) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2)))) <=> ((f10(c2) = c2) | (f7(f7(c2)) = f7(c2)) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))))),
% 28.40/18.65 inference(rewrite,[status(thm)],[])).
% 28.40/18.65 tff(12502,plain,
% 28.40/18.65 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(f7(c2)) = f7(c2)) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f7(f7(c2)) = f7(c2)) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2)))))),
% 28.40/18.65 inference(monotonicity,[status(thm)],[12501])).
% 28.40/18.65 tff(12503,plain,
% 28.40/18.65 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(f7(c2)) = f7(c2)) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (f7(f7(c2)) = f7(c2)) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))))),
% 28.40/18.65 inference(transitivity,[status(thm)],[12502, 12500])).
% 28.40/18.65 tff(12504,plain,
% 28.40/18.65 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(f7(c2)) = f7(c2)) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))))),
% 28.40/18.65 inference(quant_inst,[status(thm)],[])).
% 28.40/18.65 tff(12505,plain,
% 28.40/18.65 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (f7(f7(c2)) = f7(c2)) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2)))),
% 28.40/18.66 inference(modus_ponens,[status(thm)],[12504, 12503])).
% 28.40/18.66 tff(12506,plain,
% 28.40/18.66 ((c2 = f8(c2)) | (f7(c2) = f5(f7(c2)))),
% 28.40/18.66 inference(unit_resolution,[status(thm)],[12505, 1659, 89, 8473, 12291, 10465])).
% 28.40/18.66 tff(12507,plain,
% 28.40/18.66 (f7(c2) = f5(f7(c2))),
% 28.40/18.66 inference(unit_resolution,[status(thm)],[12506, 12290])).
% 28.40/18.66 tff(12508,plain,
% 28.40/18.66 (f7(c2) = c2),
% 28.40/18.66 inference(transitivity,[status(thm)],[12507, 12499])).
% 28.40/18.66 tff(12509,plain,
% 28.40/18.66 ($false),
% 28.40/18.66 inference(unit_resolution,[status(thm)],[17, 12508])).
% 28.40/18.66 tff(12510,plain,((c2 = f8(c2)) | (f7(c2) = c2) | (f10(c2) = c2) | (f7(f7(c2)) = f7(c2)) | (~big_f(c2, f10(c2))) | (~big_f(f7(f7(c2)), c2)) | (~big_f(f7(f7(c2)), f7(c2)))), inference(lemma,lemma(discharge,[]))).
% 28.40/18.66 tff(12511,plain,
% 28.40/18.66 (c2 = f8(c2)),
% 28.40/18.66 inference(unit_resolution,[status(thm)],[12510, 12490, 89, 12485, 17, 12480, 12479])).
% 28.40/18.66 tff(12512,plain,
% 28.40/18.66 (f8(c2) = c2),
% 28.40/18.66 inference(symmetry,[status(thm)],[12511])).
% 28.40/18.66 tff(12513,plain,
% 28.40/18.66 ((f7(c2) = f8(c2)) <=> (f7(c2) = c2)),
% 28.40/18.66 inference(monotonicity,[status(thm)],[12512])).
% 28.40/18.66 tff(12514,plain,
% 28.40/18.66 ((f7(c2) = c2) <=> (f7(c2) = f8(c2))),
% 28.40/18.66 inference(symmetry,[status(thm)],[12513])).
% 28.40/18.66 tff(12515,plain,
% 28.40/18.66 ((~(f7(c2) = c2)) <=> (~(f7(c2) = f8(c2)))),
% 28.40/18.66 inference(monotonicity,[status(thm)],[12514])).
% 28.40/18.66 tff(12516,plain,
% 28.40/18.66 (~(f7(c2) = f8(c2))),
% 28.40/18.66 inference(modus_ponens,[status(thm)],[17, 12515])).
% 28.40/18.66 tff(12517,plain,
% 28.40/18.66 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f7(f7(c2)) = f7(c2)) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2)) | (f7(c2) = f8(c2)) | (~big_f(f7(c2), f10(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (f7(f7(c2)) = f7(c2)) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2)) | (f7(c2) = f8(c2)) | (~big_f(f7(c2), f10(c2))))),
% 28.40/18.66 inference(rewrite,[status(thm)],[])).
% 28.40/18.66 tff(12518,plain,
% 28.40/18.66 (((f10(c2) = c2) | (f7(c2) = f8(c2)) | (~big_f(f7(c2), f10(c2))) | (f7(f7(c2)) = f7(c2)) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2))) <=> ((f10(c2) = c2) | (f7(f7(c2)) = f7(c2)) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2)) | (f7(c2) = f8(c2)) | (~big_f(f7(c2), f10(c2))))),
% 28.40/18.66 inference(rewrite,[status(thm)],[])).
% 28.40/18.66 tff(12519,plain,
% 28.40/18.66 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f7(c2) = f8(c2)) | (~big_f(f7(c2), f10(c2))) | (f7(f7(c2)) = f7(c2)) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f7(f7(c2)) = f7(c2)) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2)) | (f7(c2) = f8(c2)) | (~big_f(f7(c2), f10(c2)))))),
% 28.40/18.66 inference(monotonicity,[status(thm)],[12518])).
% 28.40/18.66 tff(12520,plain,
% 28.40/18.66 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f7(c2) = f8(c2)) | (~big_f(f7(c2), f10(c2))) | (f7(f7(c2)) = f7(c2)) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (f7(f7(c2)) = f7(c2)) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2)) | (f7(c2) = f8(c2)) | (~big_f(f7(c2), f10(c2))))),
% 28.40/18.66 inference(transitivity,[status(thm)],[12519, 12517])).
% 28.40/18.66 tff(12521,plain,
% 28.40/18.66 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f7(c2) = f8(c2)) | (~big_f(f7(c2), f10(c2))) | (f7(f7(c2)) = f7(c2)) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2)))),
% 28.40/18.66 inference(quant_inst,[status(thm)],[])).
% 28.40/18.66 tff(12522,plain,
% 28.40/18.66 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (f7(f7(c2)) = f7(c2)) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2)) | (f7(c2) = f8(c2)) | (~big_f(f7(c2), f10(c2)))),
% 28.40/18.66 inference(modus_ponens,[status(thm)],[12521, 12520])).
% 28.40/18.66 tff(12523,plain,
% 28.40/18.66 ((c2 = f5(f7(c2))) | (f7(c2) = f8(c2))),
% 28.40/18.66 inference(unit_resolution,[status(thm)],[12522, 1659, 89, 12485, 12480, 12301])).
% 28.40/18.66 tff(12524,plain,
% 28.40/18.66 (c2 = f5(f7(c2))),
% 28.40/18.66 inference(unit_resolution,[status(thm)],[12523, 12516])).
% 28.40/18.66 tff(12525,plain,
% 28.40/18.66 (f5(f7(c2)) = c2),
% 28.40/18.66 inference(symmetry,[status(thm)],[12524])).
% 28.40/18.66 tff(12526,plain,
% 28.40/18.66 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f7(f7(c2)) = f7(c2)) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))) | (f7(c2) = f8(c2)) | (~big_f(f7(c2), f10(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (f7(f7(c2)) = f7(c2)) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))) | (f7(c2) = f8(c2)) | (~big_f(f7(c2), f10(c2))))),
% 28.40/18.66 inference(rewrite,[status(thm)],[])).
% 28.40/18.66 tff(12527,plain,
% 28.40/18.66 (((f10(c2) = c2) | (f7(c2) = f8(c2)) | (~big_f(f7(c2), f10(c2))) | (f7(f7(c2)) = f7(c2)) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2)))) <=> ((f10(c2) = c2) | (f7(f7(c2)) = f7(c2)) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))) | (f7(c2) = f8(c2)) | (~big_f(f7(c2), f10(c2))))),
% 28.40/18.66 inference(rewrite,[status(thm)],[])).
% 28.40/18.66 tff(12528,plain,
% 28.40/18.66 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f7(c2) = f8(c2)) | (~big_f(f7(c2), f10(c2))) | (f7(f7(c2)) = f7(c2)) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f7(f7(c2)) = f7(c2)) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))) | (f7(c2) = f8(c2)) | (~big_f(f7(c2), f10(c2)))))),
% 28.40/18.66 inference(monotonicity,[status(thm)],[12527])).
% 28.40/18.66 tff(12529,plain,
% 28.40/18.66 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f7(c2) = f8(c2)) | (~big_f(f7(c2), f10(c2))) | (f7(f7(c2)) = f7(c2)) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (f7(f7(c2)) = f7(c2)) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))) | (f7(c2) = f8(c2)) | (~big_f(f7(c2), f10(c2))))),
% 28.40/18.66 inference(transitivity,[status(thm)],[12528, 12526])).
% 28.40/18.66 tff(12530,plain,
% 28.40/18.66 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f7(c2) = f8(c2)) | (~big_f(f7(c2), f10(c2))) | (f7(f7(c2)) = f7(c2)) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))))),
% 28.40/18.66 inference(quant_inst,[status(thm)],[])).
% 28.40/18.66 tff(12531,plain,
% 28.40/18.66 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (f7(f7(c2)) = f7(c2)) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))) | (f7(c2) = f8(c2)) | (~big_f(f7(c2), f10(c2)))),
% 28.40/18.66 inference(modus_ponens,[status(thm)],[12530, 12529])).
% 28.40/18.66 tff(12532,plain,
% 28.40/18.66 ((f7(c2) = f5(f7(c2))) | (f7(c2) = f8(c2))),
% 28.40/18.66 inference(unit_resolution,[status(thm)],[12531, 1659, 89, 12485, 12479, 12301])).
% 28.40/18.66 tff(12533,plain,
% 28.40/18.66 (f7(c2) = f5(f7(c2))),
% 28.40/18.66 inference(unit_resolution,[status(thm)],[12532, 12516])).
% 28.40/18.66 tff(12534,plain,
% 28.40/18.66 (f7(c2) = c2),
% 28.40/18.66 inference(transitivity,[status(thm)],[12533, 12525])).
% 28.40/18.66 tff(12535,plain,
% 28.40/18.66 ($false),
% 28.40/18.66 inference(unit_resolution,[status(thm)],[17, 12534])).
% 28.40/18.66 tff(12536,plain,((~big_f(c2, c1)) | (f7(c2) = c2) | (f10(c2) = c2) | (~big_f(f7(c2), f10(c2))) | (~big_f(f7(f7(c2)), c2)) | (~(f7(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.40/18.66 tff(12537,plain,
% 28.40/18.66 (~big_f(c2, c1)),
% 28.40/18.66 inference(unit_resolution,[status(thm)],[12536, 17, 11797, 12475, 12474, 347])).
% 28.40/18.66 tff(12538,plain,
% 28.40/18.66 (big_f(c1, c1) <=> big_f(f7(c2), c1)),
% 28.40/18.66 inference(transitivity,[status(thm)],[12457, 8075])).
% 28.40/18.66 tff(12539,plain,
% 28.40/18.66 (big_f(f7(c2), c1)),
% 28.40/18.66 inference(modus_ponens,[status(thm)],[4932, 12538])).
% 28.40/18.66 tff(12540,plain,
% 28.40/18.66 (~(c4 = c1)),
% 28.40/18.66 inference(unit_resolution,[status(thm)],[9437, 377, 79, 1345, 2, 22, 9314])).
% 28.40/18.66 tff(12541,plain,
% 28.40/18.66 (c4 = c2),
% 28.40/18.66 inference(unit_resolution,[status(thm)],[461, 12540])).
% 28.40/18.66 tff(12542,plain,
% 28.40/18.66 ((f7(c2) = c4) <=> (f7(c2) = c2)),
% 28.40/18.66 inference(monotonicity,[status(thm)],[12541])).
% 28.40/18.66 tff(12543,plain,
% 28.40/18.66 ((f7(c2) = c2) <=> (f7(c2) = c4)),
% 28.40/18.66 inference(symmetry,[status(thm)],[12542])).
% 28.40/18.66 tff(12544,plain,
% 28.40/18.66 ((~(f7(c2) = c2)) <=> (~(f7(c2) = c4))),
% 28.40/18.66 inference(monotonicity,[status(thm)],[12543])).
% 28.40/18.66 tff(12545,plain,
% 28.40/18.66 (~(f7(c2) = c4)),
% 28.40/18.66 inference(modus_ponens,[status(thm)],[17, 12544])).
% 28.40/18.66 tff(12546,plain,
% 28.40/18.66 (f1(c2, c2) = c2),
% 28.40/18.66 inference(unit_resolution,[status(thm)],[9530, 12545, 17, 338, 2, 377])).
% 28.40/18.66 tff(12547,plain,
% 28.40/18.66 (big_f(c2, f1(c2, c2)) <=> big_f(c2, c2)),
% 28.40/18.66 inference(monotonicity,[status(thm)],[12546])).
% 28.40/18.66 tff(12548,plain,
% 28.40/18.66 (big_f(c2, c2) <=> big_f(c2, f1(c2, c2))),
% 28.40/18.66 inference(symmetry,[status(thm)],[12547])).
% 28.40/18.66 tff(12549,plain,
% 28.40/18.66 (big_f(c2, f1(c2, c2))),
% 28.40/18.66 inference(modus_ponens,[status(thm)],[1345, 12548])).
% 28.40/18.66 tff(12550,plain,
% 28.40/18.66 (~(f3(c1, c1) = c1)),
% 28.40/18.66 inference(unit_resolution,[status(thm)],[9548, 12549, 22, 12546, 12545, 338, 377])).
% 28.40/18.66 tff(12551,plain,
% 28.40/18.66 (f3(c1, c1) = c2),
% 28.40/18.66 inference(unit_resolution,[status(thm)],[1416, 12550])).
% 28.40/18.66 tff(12552,plain,
% 28.40/18.66 (f3(f7(c2), f7(c2)) = c2),
% 28.40/18.66 inference(transitivity,[status(thm)],[9496, 12551])).
% 28.40/18.66 tff(12553,plain,
% 28.40/18.66 ((f3(f7(c2), f7(c2)) = f7(c2)) <=> (c2 = f7(c2))),
% 28.40/18.66 inference(monotonicity,[status(thm)],[12552])).
% 28.40/18.66 tff(12554,plain,
% 28.40/18.66 ((f3(f7(c2), f7(c2)) = f7(c2)) <=> (f7(c2) = c2)),
% 28.40/18.66 inference(transitivity,[status(thm)],[12553, 8409])).
% 28.40/18.66 tff(12555,plain,
% 28.40/18.66 ((f7(c2) = c2) <=> (f3(f7(c2), f7(c2)) = f7(c2))),
% 28.40/18.66 inference(symmetry,[status(thm)],[12554])).
% 28.40/18.66 tff(12556,plain,
% 28.40/18.66 ((~(f7(c2) = c2)) <=> (~(f3(f7(c2), f7(c2)) = f7(c2)))),
% 28.40/18.66 inference(monotonicity,[status(thm)],[12555])).
% 28.40/18.66 tff(12557,plain,
% 28.40/18.66 (~(f3(f7(c2), f7(c2)) = f7(c2))),
% 28.40/18.66 inference(modus_ponens,[status(thm)],[17, 12556])).
% 28.40/18.66 tff(12558,plain,
% 28.40/18.66 (big_f(f3(f7(c2), f7(c2)), f7(c2)) <=> big_f(c2, f7(c2))),
% 28.40/18.66 inference(monotonicity,[status(thm)],[12552])).
% 28.40/18.66 tff(12559,plain,
% 28.40/18.66 (big_f(c2, f7(c2)) <=> big_f(f3(f7(c2), f7(c2)), f7(c2))),
% 28.40/18.66 inference(symmetry,[status(thm)],[12558])).
% 28.40/18.66 tff(12560,plain,
% 28.40/18.66 ((~big_f(c2, f7(c2))) <=> (~big_f(f3(f7(c2), f7(c2)), f7(c2)))),
% 28.40/18.66 inference(monotonicity,[status(thm)],[12559])).
% 28.40/18.66 tff(12561,plain,
% 28.40/18.66 (~big_f(f3(f7(c2), f7(c2)), f7(c2))),
% 28.40/18.66 inference(modus_ponens,[status(thm)],[9314, 12560])).
% 28.40/18.66 tff(12562,plain,
% 28.40/18.66 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f7(c2) = c4) | (f3(f7(c2), f7(c2)) = f7(c2)) | big_f(f3(f7(c2), f7(c2)), f7(c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f7(c2) = c4) | (f3(f7(c2), f7(c2)) = f7(c2)) | big_f(f3(f7(c2), f7(c2)), f7(c2)))),
% 28.40/18.66 inference(rewrite,[status(thm)],[])).
% 28.40/18.66 tff(12563,plain,
% 28.40/18.66 (((f7(c2) = c4) | (f3(f7(c2), f7(c2)) = f7(c2)) | big_f(f3(f7(c2), f7(c2)), f7(c2)) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2)))) <=> ((c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f7(c2) = c4) | (f3(f7(c2), f7(c2)) = f7(c2)) | big_f(f3(f7(c2), f7(c2)), f7(c2)))),
% 28.40/18.66 inference(rewrite,[status(thm)],[])).
% 28.40/18.66 tff(12564,plain,
% 28.40/18.66 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c2) = c4) | (f3(f7(c2), f7(c2)) = f7(c2)) | big_f(f3(f7(c2), f7(c2)), f7(c2)) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f7(c2) = c4) | (f3(f7(c2), f7(c2)) = f7(c2)) | big_f(f3(f7(c2), f7(c2)), f7(c2))))),
% 28.40/18.66 inference(monotonicity,[status(thm)],[12563])).
% 28.40/18.66 tff(12565,plain,
% 28.40/18.66 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c2) = c4) | (f3(f7(c2), f7(c2)) = f7(c2)) | big_f(f3(f7(c2), f7(c2)), f7(c2)) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f7(c2) = c4) | (f3(f7(c2), f7(c2)) = f7(c2)) | big_f(f3(f7(c2), f7(c2)), f7(c2)))),
% 28.40/18.66 inference(transitivity,[status(thm)],[12564, 12562])).
% 28.40/18.66 tff(12566,plain,
% 28.40/18.66 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c2) = c4) | (f3(f7(c2), f7(c2)) = f7(c2)) | big_f(f3(f7(c2), f7(c2)), f7(c2)) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))),
% 28.40/18.66 inference(quant_inst,[status(thm)],[])).
% 28.40/18.66 tff(12567,plain,
% 28.40/18.66 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f7(c2) = c4) | (f3(f7(c2), f7(c2)) = f7(c2)) | big_f(f3(f7(c2), f7(c2)), f7(c2))),
% 28.40/18.66 inference(modus_ponens,[status(thm)],[12566, 12565])).
% 28.40/18.66 tff(12568,plain,
% 28.40/18.66 ((f3(f7(c2), f7(c2)) = f7(c2)) | big_f(f3(f7(c2), f7(c2)), f7(c2))),
% 28.40/18.66 inference(unit_resolution,[status(thm)],[12567, 904, 377, 12546, 12549, 12545])).
% 28.40/18.66 tff(12569,plain,
% 28.40/18.66 ($false),
% 28.40/18.66 inference(unit_resolution,[status(thm)],[12568, 12561, 12557])).
% 28.40/18.66 tff(12570,plain,((c2 = c3) | (f7(c2) = c2) | (~big_f(f7(c2), c1)) | (~big_f(c2, c2)) | big_f(c2, c1) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.40/18.66 tff(12571,plain,
% 28.40/18.66 (c2 = c3),
% 28.40/18.66 inference(unit_resolution,[status(thm)],[12570, 2, 12539, 1345, 17, 79])).
% 28.40/18.66 tff(12572,plain,
% 28.40/18.66 (c3 = c2),
% 28.40/18.66 inference(symmetry,[status(thm)],[12571])).
% 28.40/18.66 tff(12573,plain,
% 28.40/18.66 ((f7(c2) = c3) <=> (f7(c2) = c2)),
% 28.40/18.66 inference(monotonicity,[status(thm)],[12572])).
% 28.40/18.66 tff(12574,plain,
% 28.40/18.66 ((f7(c2) = c2) <=> (f7(c2) = c3)),
% 28.40/18.66 inference(symmetry,[status(thm)],[12573])).
% 28.40/18.66 tff(12575,plain,
% 28.40/18.66 ((~(f7(c2) = c2)) <=> (~(f7(c2) = c3))),
% 28.40/18.66 inference(monotonicity,[status(thm)],[12574])).
% 28.40/18.66 tff(12576,plain,
% 28.40/18.66 (~(f7(c2) = c3)),
% 28.40/18.66 inference(modus_ponens,[status(thm)],[17, 12575])).
% 28.40/18.66 tff(12577,plain,
% 28.40/18.66 (~(c4 = c1)),
% 28.40/18.66 inference(unit_resolution,[status(thm)],[9641, 12576, 1512, 17, 12539, 79])).
% 28.40/18.66 tff(12578,plain,
% 28.40/18.66 (c4 = c2),
% 28.40/18.66 inference(unit_resolution,[status(thm)],[461, 12577])).
% 28.40/18.66 tff(12579,plain,
% 28.40/18.66 ((f7(c2) = c4) <=> (f7(c2) = c2)),
% 28.40/18.66 inference(monotonicity,[status(thm)],[12578])).
% 28.40/18.66 tff(12580,plain,
% 28.40/18.66 ((f7(c2) = c2) <=> (f7(c2) = c4)),
% 28.40/18.66 inference(symmetry,[status(thm)],[12579])).
% 28.40/18.66 tff(12581,plain,
% 28.40/18.66 ((~(f7(c2) = c2)) <=> (~(f7(c2) = c4))),
% 28.40/18.66 inference(monotonicity,[status(thm)],[12580])).
% 28.40/18.66 tff(12582,plain,
% 28.40/18.66 (~(f7(c2) = c4)),
% 28.40/18.66 inference(modus_ponens,[status(thm)],[17, 12581])).
% 28.40/18.66 tff(12583,plain,
% 28.40/18.66 ((f7(c2) = c2) <=> (c1 = c3)),
% 28.40/18.66 inference(transitivity,[status(thm)],[12574, 9088])).
% 28.40/18.66 tff(12584,plain,
% 28.40/18.66 ((~(f7(c2) = c2)) <=> (~(c1 = c3))),
% 28.40/18.66 inference(monotonicity,[status(thm)],[12583])).
% 28.40/18.66 tff(12585,plain,
% 28.40/18.66 (~(c1 = c3)),
% 28.40/18.66 inference(modus_ponens,[status(thm)],[17, 12584])).
% 28.40/18.66 tff(12586,plain,
% 28.40/18.66 ((c1 = c4) <=> (f7(c2) = c4)),
% 28.40/18.66 inference(monotonicity,[status(thm)],[125])).
% 28.40/18.66 tff(12587,plain,
% 28.40/18.66 ((f7(c2) = c4) <=> (c1 = c4)),
% 28.40/18.66 inference(symmetry,[status(thm)],[12586])).
% 28.40/18.66 tff(12588,plain,
% 28.40/18.66 ((f7(c2) = c2) <=> (c1 = c4)),
% 28.40/18.66 inference(transitivity,[status(thm)],[12580, 12587])).
% 28.40/18.66 tff(12589,plain,
% 28.40/18.66 ((~(f7(c2) = c2)) <=> (~(c1 = c4))),
% 28.40/18.66 inference(monotonicity,[status(thm)],[12588])).
% 28.40/18.66 tff(12590,plain,
% 28.40/18.66 (~(c1 = c4)),
% 28.40/18.66 inference(modus_ponens,[status(thm)],[17, 12589])).
% 28.40/18.66 tff(12591,plain,
% 28.40/18.66 (f3(c1, c1) = c1),
% 28.40/18.66 inference(unit_resolution,[status(thm)],[9696, 12590, 4932, 27, 17, 2, 12585, 12582, 12576])).
% 28.40/18.66 tff(12592,plain,
% 28.40/18.66 (f3(f7(c2), f7(c2)) = f7(c2)),
% 28.40/18.66 inference(transitivity,[status(thm)],[9496, 12591, 125])).
% 28.40/18.66 tff(12593,plain,
% 28.40/18.66 (big_f(f3(f7(c2), f7(c2)), f7(c2)) <=> big_f(f7(c2), f7(c2))),
% 28.40/18.66 inference(monotonicity,[status(thm)],[12592])).
% 28.40/18.66 tff(12594,plain,
% 28.40/18.66 (big_f(f7(c2), f7(c2)) <=> big_f(f3(f7(c2), f7(c2)), f7(c2))),
% 28.40/18.66 inference(symmetry,[status(thm)],[12593])).
% 28.40/18.66 tff(12595,plain,
% 28.40/18.66 (big_f(f3(f7(c2), f7(c2)), f7(c2))),
% 28.40/18.66 inference(modus_ponens,[status(thm)],[12463, 12594])).
% 28.40/18.66 tff(12596,plain,
% 28.40/18.66 (big_f(c1, f1(c1, c1))),
% 28.40/18.66 inference(unit_resolution,[status(thm)],[9724, 12591, 12576, 12582, 12539, 22])).
% 28.40/18.66 tff(12597,plain,
% 28.40/18.66 (big_f(f7(c2), f1(f7(c2), f7(c2)))),
% 28.40/18.66 inference(unit_resolution,[status(thm)],[9730, 12596, 22])).
% 28.40/18.66 tff(12598,plain,
% 28.40/18.66 (~(f1(c1, c1) = c2)),
% 28.40/18.66 inference(unit_resolution,[status(thm)],[4561, 12596, 27])).
% 28.40/18.66 tff(12599,plain,
% 28.40/18.66 (f1(c1, c1) = c1),
% 28.40/18.66 inference(unit_resolution,[status(thm)],[601, 12598])).
% 28.40/18.66 tff(12600,plain,
% 28.40/18.66 (f1(f7(c2), f7(c2)) = f7(c2)),
% 28.40/18.66 inference(modus_ponens,[status(thm)],[12599, 9668])).
% 28.40/18.66 tff(12601,plain,
% 28.40/18.66 ((~(f3(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f3(f7(c2), f7(c2)), f7(c2)))),
% 28.40/18.66 inference(unit_resolution,[status(thm)],[9740, 933, 12576, 12582, 12600, 12597])).
% 28.40/18.66 tff(12602,plain,
% 28.40/18.66 ($false),
% 28.40/18.66 inference(unit_resolution,[status(thm)],[12601, 12595, 12592])).
% 28.40/18.66 tff(12603,plain,(big_f(c2, c1) | big_f(c1, c2) | (~big_f(c1, c1)) | (f7(c2) = c2) | (~(f4(c4) = c2)) | (~big_f(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 28.40/18.66 tff(12604,plain,
% 28.40/18.66 (big_f(c1, c2)),
% 28.40/18.66 inference(unit_resolution,[status(thm)],[12603, 12537, 4932, 17, 79, 1345])).
% 28.40/18.66 tff(12605,plain,
% 28.40/18.66 (big_f(f7(c2), c2)),
% 28.40/18.66 inference(modus_ponens,[status(thm)],[12604, 126])).
% 28.40/18.66 tff(12606,assumption,(~(c2 = f8(f7(c2)))), introduced(assumption)).
% 28.40/18.66 tff(12607,assumption,(big_f(c2, f10(f7(c2)))), introduced(assumption)).
% 28.40/18.66 tff(12608,plain,
% 28.40/18.66 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (f10(f7(c2)) = f7(c2)) | (c2 = f8(f7(c2))) | (~big_f(c2, f10(f7(c2)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (f10(f7(c2)) = f7(c2)) | (c2 = f8(f7(c2))) | (~big_f(c2, f10(f7(c2)))))),
% 28.40/18.66 inference(rewrite,[status(thm)],[])).
% 28.40/18.66 tff(12609,plain,
% 28.40/18.66 (((f10(f7(c2)) = f7(c2)) | (c2 = f8(f7(c2))) | (~big_f(c2, f10(f7(c2)))) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2))) <=> ((f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (f10(f7(c2)) = f7(c2)) | (c2 = f8(f7(c2))) | (~big_f(c2, f10(f7(c2)))))),
% 28.40/18.66 inference(rewrite,[status(thm)],[])).
% 28.40/18.66 tff(12610,plain,
% 28.40/18.66 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f7(c2)) = f7(c2)) | (c2 = f8(f7(c2))) | (~big_f(c2, f10(f7(c2)))) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (f10(f7(c2)) = f7(c2)) | (c2 = f8(f7(c2))) | (~big_f(c2, f10(f7(c2))))))),
% 28.40/18.66 inference(monotonicity,[status(thm)],[12609])).
% 28.40/18.66 tff(12611,plain,
% 28.40/18.66 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f7(c2)) = f7(c2)) | (c2 = f8(f7(c2))) | (~big_f(c2, f10(f7(c2)))) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (f10(f7(c2)) = f7(c2)) | (c2 = f8(f7(c2))) | (~big_f(c2, f10(f7(c2)))))),
% 28.40/18.66 inference(transitivity,[status(thm)],[12610, 12608])).
% 28.40/18.66 tff(12612,plain,
% 28.40/18.66 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f7(c2)) = f7(c2)) | (c2 = f8(f7(c2))) | (~big_f(c2, f10(f7(c2)))) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)))),
% 28.40/18.66 inference(quant_inst,[status(thm)],[])).
% 28.40/18.66 tff(12613,plain,
% 28.40/18.66 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (f10(f7(c2)) = f7(c2)) | (c2 = f8(f7(c2))) | (~big_f(c2, f10(f7(c2))))),
% 28.40/18.66 inference(modus_ponens,[status(thm)],[12612, 12611])).
% 28.40/18.66 tff(12614,plain,
% 28.40/18.66 ((c2 = f5(c2)) | (c2 = f8(f7(c2)))),
% 28.40/18.66 inference(unit_resolution,[status(thm)],[12613, 1659, 17, 1180, 8523, 12607])).
% 28.40/18.66 tff(12615,plain,
% 28.40/18.66 (c2 = f5(c2)),
% 28.40/18.66 inference(unit_resolution,[status(thm)],[12614, 12606])).
% 28.40/18.66 tff(12616,plain,
% 28.40/18.66 (f5(c2) = c2),
% 28.40/18.66 inference(symmetry,[status(thm)],[12615])).
% 28.40/18.66 tff(12617,plain,
% 28.40/18.66 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(c2) = c2) | (f10(f7(c2)) = f7(c2)) | (c2 = f8(f7(c2))) | (f7(c2) = f5(c2)) | (~big_f(f7(c2), f7(c2))) | (~big_f(c2, f10(f7(c2)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c2) = c2) | (f10(f7(c2)) = f7(c2)) | (c2 = f8(f7(c2))) | (f7(c2) = f5(c2)) | (~big_f(f7(c2), f7(c2))) | (~big_f(c2, f10(f7(c2)))))),
% 28.40/18.66 inference(rewrite,[status(thm)],[])).
% 28.40/18.66 tff(12618,plain,
% 28.40/18.66 (((f10(f7(c2)) = f7(c2)) | (c2 = f8(f7(c2))) | (~big_f(c2, f10(f7(c2)))) | (f7(c2) = c2) | (f7(c2) = f5(c2)) | (~big_f(f7(c2), f7(c2)))) <=> ((f7(c2) = c2) | (f10(f7(c2)) = f7(c2)) | (c2 = f8(f7(c2))) | (f7(c2) = f5(c2)) | (~big_f(f7(c2), f7(c2))) | (~big_f(c2, f10(f7(c2)))))),
% 28.40/18.66 inference(rewrite,[status(thm)],[])).
% 28.40/18.66 tff(12619,plain,
% 28.40/18.66 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f7(c2)) = f7(c2)) | (c2 = f8(f7(c2))) | (~big_f(c2, f10(f7(c2)))) | (f7(c2) = c2) | (f7(c2) = f5(c2)) | (~big_f(f7(c2), f7(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(c2) = c2) | (f10(f7(c2)) = f7(c2)) | (c2 = f8(f7(c2))) | (f7(c2) = f5(c2)) | (~big_f(f7(c2), f7(c2))) | (~big_f(c2, f10(f7(c2))))))),
% 28.40/18.66 inference(monotonicity,[status(thm)],[12618])).
% 28.40/18.66 tff(12620,plain,
% 28.40/18.66 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f7(c2)) = f7(c2)) | (c2 = f8(f7(c2))) | (~big_f(c2, f10(f7(c2)))) | (f7(c2) = c2) | (f7(c2) = f5(c2)) | (~big_f(f7(c2), f7(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c2) = c2) | (f10(f7(c2)) = f7(c2)) | (c2 = f8(f7(c2))) | (f7(c2) = f5(c2)) | (~big_f(f7(c2), f7(c2))) | (~big_f(c2, f10(f7(c2)))))),
% 28.40/18.66 inference(transitivity,[status(thm)],[12619, 12617])).
% 28.40/18.66 tff(12621,plain,
% 28.40/18.66 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f7(c2)) = f7(c2)) | (c2 = f8(f7(c2))) | (~big_f(c2, f10(f7(c2)))) | (f7(c2) = c2) | (f7(c2) = f5(c2)) | (~big_f(f7(c2), f7(c2))))),
% 28.40/18.66 inference(quant_inst,[status(thm)],[])).
% 28.40/18.66 tff(12622,plain,
% 28.40/18.66 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c2) = c2) | (f10(f7(c2)) = f7(c2)) | (c2 = f8(f7(c2))) | (f7(c2) = f5(c2)) | (~big_f(f7(c2), f7(c2))) | (~big_f(c2, f10(f7(c2))))),
% 28.40/18.66 inference(modus_ponens,[status(thm)],[12621, 12620])).
% 28.40/18.66 tff(12623,plain,
% 28.40/18.66 ((c2 = f8(f7(c2))) | (f7(c2) = f5(c2))),
% 28.40/18.66 inference(unit_resolution,[status(thm)],[12622, 1659, 17, 8523, 12607, 8372])).
% 28.40/18.66 tff(12624,plain,
% 28.40/18.66 (f7(c2) = f5(c2)),
% 28.40/18.66 inference(unit_resolution,[status(thm)],[12623, 12606])).
% 28.40/18.66 tff(12625,plain,
% 28.40/18.66 (f7(c2) = c2),
% 28.40/18.66 inference(transitivity,[status(thm)],[12624, 12616])).
% 28.40/18.66 tff(12626,plain,
% 28.40/18.66 ($false),
% 28.40/18.66 inference(unit_resolution,[status(thm)],[17, 12625])).
% 28.40/18.66 tff(12627,plain,((c2 = f8(f7(c2))) | (f7(c2) = c2) | (~big_f(f7(c2), c2)) | (f10(f7(c2)) = f7(c2)) | (~big_f(c2, f10(f7(c2)))) | (~big_f(f7(c2), f7(c2)))), inference(lemma,lemma(discharge,[]))).
% 28.40/18.66 tff(12628,plain,
% 28.40/18.66 (c2 = f8(f7(c2))),
% 28.40/18.66 inference(unit_resolution,[status(thm)],[12627, 17, 12605, 12471, 12466, 12463])).
% 28.40/18.66 tff(12629,plain,
% 28.40/18.66 (f8(f7(c2)) = c2),
% 28.40/18.66 inference(symmetry,[status(thm)],[12628])).
% 28.40/18.66 tff(12630,plain,
% 28.40/18.66 (f8(f7(f4(c4))) = c2),
% 28.40/18.66 inference(transitivity,[status(thm)],[107, 12629])).
% 28.40/18.66 tff(12631,plain,
% 28.40/18.66 ((f8(f7(f4(c4))) = c1) <=> (c2 = f7(c2))),
% 28.40/18.66 inference(monotonicity,[status(thm)],[12630, 125])).
% 28.40/18.66 tff(12632,plain,
% 28.40/18.66 ((f8(f7(f4(c4))) = c1) <=> (f7(c2) = c2)),
% 28.40/18.66 inference(transitivity,[status(thm)],[12631, 8409])).
% 28.40/18.66 tff(12633,plain,
% 28.40/18.66 ((f7(c2) = c2) <=> (f8(f7(f4(c4))) = c1)),
% 28.40/18.66 inference(symmetry,[status(thm)],[12632])).
% 28.40/18.66 tff(12634,plain,
% 28.40/18.66 ((f7(c2) = c2) <=> (f7(c2) = f8(f7(c2)))),
% 28.40/18.66 inference(transitivity,[status(thm)],[12633, 12462])).
% 28.40/18.66 tff(12635,plain,
% 28.40/18.66 ((~(f7(c2) = c2)) <=> (~(f7(c2) = f8(f7(c2))))),
% 28.40/18.66 inference(monotonicity,[status(thm)],[12634])).
% 28.40/18.66 tff(12636,plain,
% 28.40/18.66 (~(f7(c2) = f8(f7(c2)))),
% 28.40/18.66 inference(modus_ponens,[status(thm)],[17, 12635])).
% 28.40/18.66 tff(12637,plain,
% 28.40/18.66 (big_f(f7(c2), f10(f7(c2))) <=> big_f(f7(c2), c2)),
% 28.40/18.66 inference(monotonicity,[status(thm)],[24])).
% 28.40/18.66 tff(12638,plain,
% 28.40/18.66 (big_f(f7(c2), c2) <=> big_f(f7(c2), f10(f7(c2)))),
% 28.40/18.66 inference(symmetry,[status(thm)],[12637])).
% 28.40/18.66 tff(12639,plain,
% 28.40/18.66 (big_f(c1, c2) <=> big_f(f7(c2), f10(f7(c2)))),
% 28.40/18.66 inference(transitivity,[status(thm)],[126, 12638])).
% 28.40/18.66 tff(12640,plain,
% 28.40/18.66 (big_f(f7(c2), f10(f7(c2)))),
% 28.40/18.66 inference(modus_ponens,[status(thm)],[12604, 12639])).
% 28.40/18.66 tff(12641,plain,
% 28.40/18.66 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (f10(f7(c2)) = f7(c2)) | (f7(c2) = f8(f7(c2))) | (~big_f(f7(c2), f10(f7(c2)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (f10(f7(c2)) = f7(c2)) | (f7(c2) = f8(f7(c2))) | (~big_f(f7(c2), f10(f7(c2)))))),
% 28.40/18.66 inference(rewrite,[status(thm)],[])).
% 28.40/18.66 tff(12642,plain,
% 28.40/18.66 (((f10(f7(c2)) = f7(c2)) | (f7(c2) = f8(f7(c2))) | (~big_f(f7(c2), f10(f7(c2)))) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2))) <=> ((f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (f10(f7(c2)) = f7(c2)) | (f7(c2) = f8(f7(c2))) | (~big_f(f7(c2), f10(f7(c2)))))),
% 28.40/18.67 inference(rewrite,[status(thm)],[])).
% 28.40/18.67 tff(12643,plain,
% 28.40/18.67 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f7(c2)) = f7(c2)) | (f7(c2) = f8(f7(c2))) | (~big_f(f7(c2), f10(f7(c2)))) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (f10(f7(c2)) = f7(c2)) | (f7(c2) = f8(f7(c2))) | (~big_f(f7(c2), f10(f7(c2))))))),
% 28.40/18.67 inference(monotonicity,[status(thm)],[12642])).
% 28.40/18.67 tff(12644,plain,
% 28.40/18.67 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f7(c2)) = f7(c2)) | (f7(c2) = f8(f7(c2))) | (~big_f(f7(c2), f10(f7(c2)))) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (f10(f7(c2)) = f7(c2)) | (f7(c2) = f8(f7(c2))) | (~big_f(f7(c2), f10(f7(c2)))))),
% 28.40/18.67 inference(transitivity,[status(thm)],[12643, 12641])).
% 28.40/18.67 tff(12645,plain,
% 28.40/18.67 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f7(c2)) = f7(c2)) | (f7(c2) = f8(f7(c2))) | (~big_f(f7(c2), f10(f7(c2)))) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)))),
% 28.40/18.67 inference(quant_inst,[status(thm)],[])).
% 28.40/18.67 tff(12646,plain,
% 28.40/18.67 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (f10(f7(c2)) = f7(c2)) | (f7(c2) = f8(f7(c2))) | (~big_f(f7(c2), f10(f7(c2))))),
% 28.40/18.67 inference(modus_ponens,[status(thm)],[12645, 12644])).
% 28.40/18.67 tff(12647,plain,
% 28.40/18.67 ((c2 = f5(c2)) | (f7(c2) = f8(f7(c2)))),
% 28.40/18.67 inference(unit_resolution,[status(thm)],[12646, 1659, 17, 12605, 12640, 12471])).
% 28.40/18.67 tff(12648,plain,
% 28.40/18.67 (c2 = f5(c2)),
% 28.40/18.67 inference(unit_resolution,[status(thm)],[12647, 12636])).
% 28.40/18.67 tff(12649,plain,
% 28.40/18.67 (f5(c2) = c2),
% 28.40/18.67 inference(symmetry,[status(thm)],[12648])).
% 28.40/18.67 tff(12650,plain,
% 28.40/18.67 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(c2) = c2) | (f10(f7(c2)) = f7(c2)) | (f7(c2) = f8(f7(c2))) | (f7(c2) = f5(c2)) | (~big_f(f7(c2), f7(c2))) | (~big_f(f7(c2), f10(f7(c2)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c2) = c2) | (f10(f7(c2)) = f7(c2)) | (f7(c2) = f8(f7(c2))) | (f7(c2) = f5(c2)) | (~big_f(f7(c2), f7(c2))) | (~big_f(f7(c2), f10(f7(c2)))))),
% 28.40/18.67 inference(rewrite,[status(thm)],[])).
% 28.40/18.67 tff(12651,plain,
% 28.40/18.67 (((f10(f7(c2)) = f7(c2)) | (f7(c2) = f8(f7(c2))) | (~big_f(f7(c2), f10(f7(c2)))) | (f7(c2) = c2) | (f7(c2) = f5(c2)) | (~big_f(f7(c2), f7(c2)))) <=> ((f7(c2) = c2) | (f10(f7(c2)) = f7(c2)) | (f7(c2) = f8(f7(c2))) | (f7(c2) = f5(c2)) | (~big_f(f7(c2), f7(c2))) | (~big_f(f7(c2), f10(f7(c2)))))),
% 28.40/18.67 inference(rewrite,[status(thm)],[])).
% 28.40/18.67 tff(12652,plain,
% 28.40/18.67 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f7(c2)) = f7(c2)) | (f7(c2) = f8(f7(c2))) | (~big_f(f7(c2), f10(f7(c2)))) | (f7(c2) = c2) | (f7(c2) = f5(c2)) | (~big_f(f7(c2), f7(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(c2) = c2) | (f10(f7(c2)) = f7(c2)) | (f7(c2) = f8(f7(c2))) | (f7(c2) = f5(c2)) | (~big_f(f7(c2), f7(c2))) | (~big_f(f7(c2), f10(f7(c2))))))),
% 28.40/18.67 inference(monotonicity,[status(thm)],[12651])).
% 28.40/18.67 tff(12653,plain,
% 28.40/18.67 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f7(c2)) = f7(c2)) | (f7(c2) = f8(f7(c2))) | (~big_f(f7(c2), f10(f7(c2)))) | (f7(c2) = c2) | (f7(c2) = f5(c2)) | (~big_f(f7(c2), f7(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c2) = c2) | (f10(f7(c2)) = f7(c2)) | (f7(c2) = f8(f7(c2))) | (f7(c2) = f5(c2)) | (~big_f(f7(c2), f7(c2))) | (~big_f(f7(c2), f10(f7(c2)))))),
% 28.40/18.67 inference(transitivity,[status(thm)],[12652, 12650])).
% 28.40/18.67 tff(12654,plain,
% 28.40/18.67 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f7(c2)) = f7(c2)) | (f7(c2) = f8(f7(c2))) | (~big_f(f7(c2), f10(f7(c2)))) | (f7(c2) = c2) | (f7(c2) = f5(c2)) | (~big_f(f7(c2), f7(c2))))),
% 28.40/18.67 inference(quant_inst,[status(thm)],[])).
% 28.40/18.67 tff(12655,plain,
% 28.40/18.67 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c2) = c2) | (f10(f7(c2)) = f7(c2)) | (f7(c2) = f8(f7(c2))) | (f7(c2) = f5(c2)) | (~big_f(f7(c2), f7(c2))) | (~big_f(f7(c2), f10(f7(c2))))),
% 28.40/18.67 inference(modus_ponens,[status(thm)],[12654, 12653])).
% 28.40/18.67 tff(12656,plain,
% 28.40/18.67 ((f7(c2) = f8(f7(c2))) | (f7(c2) = f5(c2))),
% 28.40/18.67 inference(unit_resolution,[status(thm)],[12655, 1659, 17, 12640, 12471, 12463])).
% 28.40/18.67 tff(12657,plain,
% 28.40/18.67 (f7(c2) = f5(c2)),
% 28.40/18.67 inference(unit_resolution,[status(thm)],[12656, 12636])).
% 28.40/18.67 tff(12658,plain,
% 28.40/18.67 (f7(c2) = c2),
% 28.40/18.67 inference(transitivity,[status(thm)],[12657, 12649])).
% 28.40/18.67 tff(12659,plain,
% 28.40/18.67 ($false),
% 28.40/18.67 inference(unit_resolution,[status(thm)],[17, 12658])).
% 28.40/18.67 tff(12660,plain,((f7(c2) = c2) | (~(f4(c4) = c2)) | (~(f10(c1) = c2)) | (~big_f(c1, c1)) | (~big_f(c2, c2)) | (~(f7(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.40/18.67 tff(12661,plain,
% 28.40/18.67 (~big_f(c1, c1)),
% 28.40/18.67 inference(unit_resolution,[status(thm)],[12660, 1345, 16, 79, 17, 120])).
% 28.40/18.67 tff(12662,plain,
% 28.40/18.67 (~big_f(c1, f10(c2))),
% 28.40/18.67 inference(modus_ponens,[status(thm)],[12661, 12459])).
% 28.40/18.67 tff(12663,plain,
% 28.40/18.67 (~(c1 = f5(c1))),
% 28.40/18.67 inference(unit_resolution,[status(thm)],[12084, 2, 115, 11797, 12662, 16])).
% 28.40/18.67 tff(12664,plain,
% 28.40/18.67 (~(f5(c1) = c1)),
% 28.40/18.67 inference(modus_ponens,[status(thm)],[12663, 2279])).
% 28.40/18.67 tff(12665,plain,
% 28.40/18.67 (f5(c1) = c2),
% 28.40/18.67 inference(unit_resolution,[status(thm)],[1708, 12664])).
% 28.40/18.67 tff(12666,plain,
% 28.40/18.67 ((f5(c1) = c3) <=> (c2 = c3)),
% 28.40/18.67 inference(monotonicity,[status(thm)],[12665])).
% 28.40/18.67 tff(12667,plain,
% 28.40/18.67 ((~(f5(c1) = c3)) <=> (~(c2 = c3))),
% 28.40/18.67 inference(monotonicity,[status(thm)],[12666])).
% 28.40/18.67 tff(12668,plain,
% 28.40/18.67 ((~big_f(c1, c1)) <=> (~big_f(f7(c2), c1))),
% 28.40/18.67 inference(monotonicity,[status(thm)],[12538])).
% 28.40/18.67 tff(12669,plain,
% 28.40/18.67 (~big_f(f7(c2), c1)),
% 28.40/18.67 inference(modus_ponens,[status(thm)],[12661, 12668])).
% 28.40/18.67 tff(12670,plain,
% 28.40/18.67 (f8(c2) = f8(f10(c1))),
% 28.40/18.67 inference(monotonicity,[status(thm)],[293])).
% 28.40/18.67 tff(12671,plain,
% 28.40/18.67 (f8(f10(c1)) = f8(c2)),
% 28.40/18.67 inference(symmetry,[status(thm)],[12670])).
% 28.40/18.67 tff(12672,plain,
% 28.40/18.67 ((f8(f10(c1)) = c2) <=> (f8(c2) = c2)),
% 28.40/18.67 inference(monotonicity,[status(thm)],[12671])).
% 28.40/18.67 tff(12673,plain,
% 28.40/18.67 ((f8(f10(c1)) = c2) <=> (c2 = f8(c2))),
% 28.40/18.67 inference(transitivity,[status(thm)],[12672, 11998])).
% 28.40/18.67 tff(12674,plain,
% 28.40/18.67 ((c1 = f8(f10(c1))) <=> (c1 = f8(c2))),
% 28.40/18.67 inference(monotonicity,[status(thm)],[12671])).
% 28.40/18.67 tff(12675,plain,
% 28.40/18.67 ((c1 = f8(c2)) <=> (c1 = f8(f10(c1)))),
% 28.40/18.67 inference(symmetry,[status(thm)],[12674])).
% 28.40/18.67 tff(12676,plain,
% 28.40/18.67 ((f7(c2) = f8(c2)) <=> (c1 = f8(c2))),
% 28.40/18.67 inference(monotonicity,[status(thm)],[22])).
% 28.40/18.67 tff(12677,plain,
% 28.40/18.67 ((f7(c2) = f8(c2)) <=> (f8(f10(c1)) = c1)),
% 28.40/18.67 inference(transitivity,[status(thm)],[12676, 12675, 12056])).
% 28.40/18.67 tff(12678,plain,
% 28.40/18.67 ((~(f7(c2) = f8(c2))) <=> (~(f8(f10(c1)) = c1))),
% 28.40/18.67 inference(monotonicity,[status(thm)],[12677])).
% 28.40/18.67 tff(12679,plain,
% 28.40/18.67 (~big_f(f7(c2), c2)),
% 28.40/18.67 inference(modus_ponens,[status(thm)],[27, 12164])).
% 28.40/18.67 tff(12680,plain,
% 28.40/18.67 ((~big_f(c1, c1)) <=> (~big_f(f7(c2), f7(c2)))),
% 28.40/18.67 inference(monotonicity,[status(thm)],[12457])).
% 28.40/18.67 tff(12681,plain,
% 28.40/18.67 (~big_f(f7(c2), f7(c2))),
% 28.40/18.67 inference(modus_ponens,[status(thm)],[66, 12680])).
% 28.40/18.67 tff(12682,plain,
% 28.40/18.67 (big_f(f7(c2), f10(c2)) <=> big_f(f7(c2), f7(c2))),
% 28.40/18.67 inference(monotonicity,[status(thm)],[12486])).
% 28.40/18.67 tff(12683,plain,
% 28.40/18.67 (big_f(f7(c2), f7(c2)) <=> big_f(f7(c2), f10(c2))),
% 28.40/18.67 inference(symmetry,[status(thm)],[12682])).
% 28.40/18.67 tff(12684,plain,
% 28.40/18.67 ((~big_f(f7(c2), f7(c2))) <=> (~big_f(f7(c2), f10(c2)))),
% 28.40/18.67 inference(monotonicity,[status(thm)],[12683])).
% 28.40/18.67 tff(12685,plain,
% 28.40/18.67 (~big_f(f7(c2), f10(c2))),
% 28.40/18.67 inference(modus_ponens,[status(thm)],[8218, 12684])).
% 28.40/18.67 tff(12686,assumption,(f7(c2) = f8(c2)), introduced(assumption)).
% 28.40/18.67 tff(12687,plain,
% 28.40/18.67 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | big_f(f7(c2), f10(c2)) | (~(f7(c2) = f8(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | big_f(f7(c2), f10(c2)) | (~(f7(c2) = f8(c2))))),
% 28.40/18.67 inference(rewrite,[status(thm)],[])).
% 28.40/18.67 tff(12688,plain,
% 28.40/18.67 (((~(c2 = f5(c2))) | (f10(c2) = c2) | big_f(f7(c2), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(f7(c2) = f8(c2)))) <=> ((f10(c2) = c2) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | big_f(f7(c2), f10(c2)) | (~(f7(c2) = f8(c2))))),
% 28.40/18.67 inference(rewrite,[status(thm)],[])).
% 28.40/18.67 tff(12689,plain,
% 28.40/18.67 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c2 = f5(c2))) | (f10(c2) = c2) | big_f(f7(c2), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(f7(c2) = f8(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | big_f(f7(c2), f10(c2)) | (~(f7(c2) = f8(c2)))))),
% 28.40/18.67 inference(monotonicity,[status(thm)],[12688])).
% 28.40/18.67 tff(12690,plain,
% 28.40/18.67 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c2 = f5(c2))) | (f10(c2) = c2) | big_f(f7(c2), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(f7(c2) = f8(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | big_f(f7(c2), f10(c2)) | (~(f7(c2) = f8(c2))))),
% 28.40/18.67 inference(transitivity,[status(thm)],[12689, 12687])).
% 28.40/18.67 tff(12691,plain,
% 28.40/18.67 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c2 = f5(c2))) | (f10(c2) = c2) | big_f(f7(c2), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(f7(c2) = f8(c2))))),
% 28.40/18.67 inference(quant_inst,[status(thm)],[])).
% 28.40/18.67 tff(12692,plain,
% 28.40/18.67 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | big_f(f7(c2), f10(c2)) | (~(f7(c2) = f8(c2)))),
% 28.40/18.67 inference(modus_ponens,[status(thm)],[12691, 12690])).
% 28.40/18.67 tff(12693,plain,
% 28.40/18.67 ((~(c2 = f5(c2))) | big_f(f7(c2), f10(c2)) | (~(f7(c2) = f8(c2)))),
% 28.40/18.67 inference(unit_resolution,[status(thm)],[12692, 1745, 89, 17, 1521])).
% 28.40/18.67 tff(12694,plain,
% 28.40/18.67 (~(c2 = f5(c2))),
% 28.40/18.67 inference(unit_resolution,[status(thm)],[12693, 12686, 12685])).
% 28.40/18.67 tff(12695,plain,
% 28.40/18.67 (~(f5(c2) = c2)),
% 28.40/18.67 inference(unit_resolution,[status(thm)],[8113, 12694])).
% 28.40/18.67 tff(12696,plain,
% 28.40/18.67 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | (f7(c2) = c2) | (~(f7(c2) = f5(c2))) | big_f(f7(c2), f7(c2)) | big_f(f7(c2), f10(c2)) | (~(f7(c2) = f8(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | (f7(c2) = c2) | (~(f7(c2) = f5(c2))) | big_f(f7(c2), f7(c2)) | big_f(f7(c2), f10(c2)) | (~(f7(c2) = f8(c2))))),
% 28.40/18.67 inference(rewrite,[status(thm)],[])).
% 28.40/18.67 tff(12697,plain,
% 28.40/18.67 (((~(f7(c2) = f5(c2))) | (f10(c2) = c2) | big_f(f7(c2), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), f7(c2)) | (~(f7(c2) = f8(c2)))) <=> ((f10(c2) = c2) | (f7(c2) = c2) | (~(f7(c2) = f5(c2))) | big_f(f7(c2), f7(c2)) | big_f(f7(c2), f10(c2)) | (~(f7(c2) = f8(c2))))),
% 28.40/18.67 inference(rewrite,[status(thm)],[])).
% 28.40/18.67 tff(12698,plain,
% 28.40/18.67 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(f7(c2) = f5(c2))) | (f10(c2) = c2) | big_f(f7(c2), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), f7(c2)) | (~(f7(c2) = f8(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | (f7(c2) = c2) | (~(f7(c2) = f5(c2))) | big_f(f7(c2), f7(c2)) | big_f(f7(c2), f10(c2)) | (~(f7(c2) = f8(c2)))))),
% 28.40/18.67 inference(monotonicity,[status(thm)],[12697])).
% 28.40/18.67 tff(12699,plain,
% 28.40/18.67 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(f7(c2) = f5(c2))) | (f10(c2) = c2) | big_f(f7(c2), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), f7(c2)) | (~(f7(c2) = f8(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | (f7(c2) = c2) | (~(f7(c2) = f5(c2))) | big_f(f7(c2), f7(c2)) | big_f(f7(c2), f10(c2)) | (~(f7(c2) = f8(c2))))),
% 28.40/18.67 inference(transitivity,[status(thm)],[12698, 12696])).
% 28.40/18.67 tff(12700,plain,
% 28.40/18.67 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(f7(c2) = f5(c2))) | (f10(c2) = c2) | big_f(f7(c2), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), f7(c2)) | (~(f7(c2) = f8(c2))))),
% 28.40/18.67 inference(quant_inst,[status(thm)],[])).
% 28.40/18.67 tff(12701,plain,
% 28.40/18.67 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | (f7(c2) = c2) | (~(f7(c2) = f5(c2))) | big_f(f7(c2), f7(c2)) | big_f(f7(c2), f10(c2)) | (~(f7(c2) = f8(c2)))),
% 28.40/18.67 inference(modus_ponens,[status(thm)],[12700, 12699])).
% 28.49/18.67 tff(12702,plain,
% 28.49/18.67 ((~(f7(c2) = f5(c2))) | big_f(f7(c2), f10(c2)) | (~(f7(c2) = f8(c2)))),
% 28.49/18.67 inference(unit_resolution,[status(thm)],[12701, 1745, 89, 17, 8218])).
% 28.49/18.67 tff(12703,plain,
% 28.49/18.67 (~(f7(c2) = f5(c2))),
% 28.49/18.67 inference(unit_resolution,[status(thm)],[12702, 12686, 12685])).
% 28.49/18.67 tff(12704,plain,
% 28.49/18.67 (~(f5(c2) = c1)),
% 28.49/18.67 inference(unit_resolution,[status(thm)],[8394, 12703, 22])).
% 28.49/18.67 tff(12705,plain,
% 28.49/18.67 ($false),
% 28.49/18.67 inference(unit_resolution,[status(thm)],[1547, 12704, 12695])).
% 28.49/18.67 tff(12706,plain,((~(f7(c2) = f8(c2))) | (f10(c2) = c2) | (f7(c2) = c2) | big_f(f7(c2), f7(c2)) | big_f(f7(c2), c2)), inference(lemma,lemma(discharge,[]))).
% 28.49/18.67 tff(12707,plain,
% 28.49/18.67 (~(f7(c2) = f8(c2))),
% 28.49/18.67 inference(unit_resolution,[status(thm)],[12706, 11797, 17, 12681, 12679])).
% 28.49/18.67 tff(12708,plain,
% 28.49/18.67 (~(f8(f10(c1)) = c1)),
% 28.49/18.67 inference(modus_ponens,[status(thm)],[12707, 12678])).
% 28.49/18.67 tff(12709,plain,
% 28.49/18.67 (f8(f10(c1)) = c2),
% 28.49/18.67 inference(unit_resolution,[status(thm)],[12021, 12708])).
% 28.49/18.67 tff(12710,plain,
% 28.49/18.67 (c2 = f8(c2)),
% 28.49/18.67 inference(modus_ponens,[status(thm)],[12709, 12673])).
% 28.49/18.67 tff(12711,plain,
% 28.49/18.67 (big_f(c2, f10(c2)) <=> big_f(c2, f7(c2))),
% 28.49/18.67 inference(monotonicity,[status(thm)],[12454])).
% 28.49/18.67 tff(12712,plain,
% 28.49/18.67 (big_f(c2, f7(c2)) <=> big_f(c2, f10(c2))),
% 28.49/18.67 inference(symmetry,[status(thm)],[12711])).
% 28.49/18.67 tff(12713,plain,
% 28.49/18.67 ((~big_f(c2, f7(c2))) <=> (~big_f(c2, f10(c2)))),
% 28.49/18.67 inference(monotonicity,[status(thm)],[12712])).
% 28.49/18.67 tff(12714,plain,
% 28.49/18.67 (~big_f(c2, f10(c2))),
% 28.49/18.67 inference(modus_ponens,[status(thm)],[9314, 12713])).
% 28.49/18.67 tff(12715,plain,
% 28.49/18.67 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))))),
% 28.49/18.67 inference(rewrite,[status(thm)],[])).
% 28.49/18.67 tff(12716,plain,
% 28.49/18.67 (((~(c2 = f5(c2))) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(c2 = f8(c2)))) <=> ((f10(c2) = c2) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))))),
% 28.49/18.67 inference(rewrite,[status(thm)],[])).
% 28.49/18.67 tff(12717,plain,
% 28.49/18.67 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c2 = f5(c2))) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(c2 = f8(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2)))))),
% 28.49/18.67 inference(monotonicity,[status(thm)],[12716])).
% 28.49/18.67 tff(12718,plain,
% 28.49/18.67 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c2 = f5(c2))) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(c2 = f8(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))))),
% 28.49/18.67 inference(transitivity,[status(thm)],[12717, 12715])).
% 28.49/18.67 tff(12719,plain,
% 28.49/18.67 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c2 = f5(c2))) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(c2 = f8(c2))))),
% 28.49/18.67 inference(quant_inst,[status(thm)],[])).
% 28.49/18.67 tff(12720,plain,
% 28.49/18.67 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2)))),
% 28.49/18.67 inference(modus_ponens,[status(thm)],[12719, 12718])).
% 28.49/18.67 tff(12721,plain,
% 28.49/18.67 ((~(c2 = f5(c2))) | (~(c2 = f8(c2)))),
% 28.49/18.67 inference(unit_resolution,[status(thm)],[12720, 1745, 11797, 17, 12679, 12714])).
% 28.49/18.67 tff(12722,plain,
% 28.49/18.67 (~(c2 = f5(c2))),
% 28.49/18.67 inference(unit_resolution,[status(thm)],[12721, 12710])).
% 28.49/18.67 tff(12723,plain,
% 28.49/18.67 (~(f5(c2) = c2)),
% 28.49/18.67 inference(unit_resolution,[status(thm)],[8113, 12722])).
% 28.49/18.67 tff(12724,plain,
% 28.49/18.67 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | (f7(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (~(f7(c2) = f5(c2))) | big_f(f7(c2), f7(c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | (f7(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (~(f7(c2) = f5(c2))) | big_f(f7(c2), f7(c2)))),
% 28.49/18.67 inference(rewrite,[status(thm)],[])).
% 28.49/18.67 tff(12725,plain,
% 28.49/18.67 (((~(f7(c2) = f5(c2))) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), f7(c2)) | (~(c2 = f8(c2)))) <=> ((f10(c2) = c2) | (f7(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (~(f7(c2) = f5(c2))) | big_f(f7(c2), f7(c2)))),
% 28.49/18.67 inference(rewrite,[status(thm)],[])).
% 28.49/18.67 tff(12726,plain,
% 28.49/18.67 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(f7(c2) = f5(c2))) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), f7(c2)) | (~(c2 = f8(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | (f7(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (~(f7(c2) = f5(c2))) | big_f(f7(c2), f7(c2))))),
% 28.49/18.67 inference(monotonicity,[status(thm)],[12725])).
% 28.49/18.67 tff(12727,plain,
% 28.49/18.67 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(f7(c2) = f5(c2))) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), f7(c2)) | (~(c2 = f8(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | (f7(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (~(f7(c2) = f5(c2))) | big_f(f7(c2), f7(c2)))),
% 28.49/18.67 inference(transitivity,[status(thm)],[12726, 12724])).
% 28.49/18.67 tff(12728,plain,
% 28.49/18.67 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(f7(c2) = f5(c2))) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), f7(c2)) | (~(c2 = f8(c2))))),
% 28.49/18.67 inference(quant_inst,[status(thm)],[])).
% 28.49/18.67 tff(12729,plain,
% 28.49/18.67 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | (f7(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (~(f7(c2) = f5(c2))) | big_f(f7(c2), f7(c2))),
% 28.49/18.67 inference(modus_ponens,[status(thm)],[12728, 12727])).
% 28.49/18.67 tff(12730,plain,
% 28.49/18.67 ((~(c2 = f8(c2))) | (~(f7(c2) = f5(c2)))),
% 28.49/18.67 inference(unit_resolution,[status(thm)],[12729, 1745, 11797, 17, 12714, 12681])).
% 28.49/18.67 tff(12731,plain,
% 28.49/18.67 (~(f7(c2) = f5(c2))),
% 28.49/18.67 inference(unit_resolution,[status(thm)],[12730, 12710])).
% 28.49/18.67 tff(12732,plain,
% 28.49/18.67 (~(f5(c2) = c1)),
% 28.49/18.67 inference(unit_resolution,[status(thm)],[8394, 12731, 22])).
% 28.49/18.67 tff(12733,plain,
% 28.49/18.67 ($false),
% 28.49/18.67 inference(unit_resolution,[status(thm)],[1547, 12732, 12723])).
% 28.49/18.67 tff(12734,plain,((f7(c2) = c2) | (~(f10(c1) = c2)) | big_f(c1, c1) | big_f(c2, c1) | big_f(c1, c2) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.49/18.67 tff(12735,plain,
% 28.49/18.67 (big_f(c1, c2)),
% 28.49/18.67 inference(unit_resolution,[status(thm)],[12734, 2, 17, 12661, 16, 79])).
% 28.49/18.67 tff(12736,plain,
% 28.49/18.67 (big_f(f7(c2), c2)),
% 28.49/18.67 inference(modus_ponens,[status(thm)],[12735, 126])).
% 28.49/18.67 tff(12737,plain,
% 28.49/18.67 (~(c3 = c2)),
% 28.49/18.67 inference(unit_resolution,[status(thm)],[9397, 12736, 17, 12669, 79, 2])).
% 28.49/18.67 tff(12738,plain,
% 28.49/18.67 (c3 = c1),
% 28.49/18.67 inference(unit_resolution,[status(thm)],[180, 12737])).
% 28.49/18.67 tff(12739,plain,
% 28.49/18.67 ((f5(c1) = c3) <=> (f5(c1) = c1)),
% 28.49/18.67 inference(monotonicity,[status(thm)],[172])).
% 28.49/18.67 tff(12740,plain,
% 28.49/18.67 ((f5(c1) = c3) <=> (c1 = f5(c1))),
% 28.49/18.67 inference(transitivity,[status(thm)],[12739, 192])).
% 28.49/18.67 tff(12741,assumption,(f5(c1) = c3), introduced(assumption)).
% 28.49/18.67 tff(12742,plain,
% 28.49/18.67 (c1 = f5(c1)),
% 28.49/18.67 inference(modus_ponens,[status(thm)],[12741, 12740])).
% 28.49/18.67 tff(12743,plain,
% 28.49/18.67 ($false),
% 28.49/18.67 inference(unit_resolution,[status(thm)],[3761, 12742])).
% 28.49/18.67 tff(12744,plain,((~(f5(c1) = c3)) | (c1 = f5(c1)) | (~(c3 = c1))), inference(lemma,lemma(discharge,[]))).
% 28.49/18.67 tff(12745,plain,
% 28.49/18.67 (~(f5(c1) = c3)),
% 28.49/18.68 inference(unit_resolution,[status(thm)],[12744, 12738, 12663])).
% 28.49/18.68 tff(12746,plain,
% 28.49/18.68 (~(c2 = c3)),
% 28.49/18.68 inference(modus_ponens,[status(thm)],[12745, 12667])).
% 28.49/18.68 tff(12747,plain,
% 28.49/18.68 (~(c4 = c1)),
% 28.49/18.68 inference(unit_resolution,[status(thm)],[9437, 12746, 79, 22, 1345, 2, 9314])).
% 28.49/18.68 tff(12748,plain,
% 28.49/18.68 (c4 = c2),
% 28.49/18.68 inference(unit_resolution,[status(thm)],[461, 12747])).
% 28.49/18.68 tff(12749,plain,
% 28.49/18.68 (c2 = c4),
% 28.49/18.68 inference(symmetry,[status(thm)],[12748])).
% 28.49/18.68 tff(12750,plain,
% 28.49/18.68 (f4(c2) = f4(c4)),
% 28.49/18.68 inference(monotonicity,[status(thm)],[12749])).
% 28.49/18.68 tff(12751,plain,
% 28.49/18.68 (f4(c2) = c2),
% 28.49/18.68 inference(transitivity,[status(thm)],[12750, 79])).
% 28.49/18.68 tff(12752,plain,
% 28.49/18.68 ((f7(c2) = f4(c2)) <=> (f7(c2) = c2)),
% 28.49/18.68 inference(monotonicity,[status(thm)],[12751])).
% 28.49/18.68 tff(12753,plain,
% 28.49/18.68 ((f7(c2) = c2) <=> (f7(c2) = f4(c2))),
% 28.49/18.68 inference(symmetry,[status(thm)],[12752])).
% 28.49/18.68 tff(12754,plain,
% 28.49/18.68 ((~(f7(c2) = c2)) <=> (~(f7(c2) = f4(c2)))),
% 28.49/18.68 inference(monotonicity,[status(thm)],[12753])).
% 28.49/18.68 tff(12755,plain,
% 28.49/18.68 (~(f7(c2) = f4(c2))),
% 28.49/18.68 inference(modus_ponens,[status(thm)],[17, 12754])).
% 28.49/18.68 tff(12756,plain,
% 28.49/18.68 (c2 = c4),
% 28.49/18.68 inference(modus_ponens,[status(thm)],[12748, 159])).
% 28.49/18.68 tff(12757,plain,
% 28.49/18.68 (f1(c2, c2) = c2),
% 28.49/18.68 inference(unit_resolution,[status(thm)],[9464, 12755, 12736, 12746, 2, 12756])).
% 28.49/18.68 tff(12758,plain,
% 28.49/18.68 (big_f(c2, f1(c2, c2)) <=> big_f(c2, c2)),
% 28.49/18.68 inference(monotonicity,[status(thm)],[12757])).
% 28.49/18.68 tff(12759,plain,
% 28.49/18.68 (big_f(c2, c2) <=> big_f(c2, f1(c2, c2))),
% 28.49/18.68 inference(symmetry,[status(thm)],[12758])).
% 28.49/18.68 tff(12760,plain,
% 28.49/18.68 (big_f(c2, f1(c2, c2))),
% 28.49/18.68 inference(modus_ponens,[status(thm)],[1345, 12759])).
% 28.49/18.68 tff(12761,plain,
% 28.49/18.68 ($false),
% 28.49/18.68 inference(unit_resolution,[status(thm)],[9474, 553, 12756, 12746, 12736, 12757, 12760, 12755])).
% 28.49/18.68 tff(12762,plain,(big_f(c2, c1) | (~big_f(c2, c2)) | (f7(c2) = c2) | (~(f4(c4) = c2)) | (f7(c1) = c1) | (~(f10(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.49/18.68 tff(12763,plain,
% 28.49/18.68 (big_f(c2, c1)),
% 28.49/18.68 inference(unit_resolution,[status(thm)],[12762, 12442, 17, 79, 115, 15])).
% 28.49/18.68 tff(12764,plain,
% 28.49/18.68 (big_f(f7(f7(c2)), f7(c2))),
% 28.49/18.68 inference(modus_ponens,[status(thm)],[12763, 12451])).
% 28.49/18.68 tff(12765,plain,
% 28.49/18.68 (big_f(f7(c2), f10(f7(c2))) <=> big_f(f7(c2), c2)),
% 28.49/18.68 inference(monotonicity,[status(thm)],[12108])).
% 28.49/18.68 tff(12766,plain,
% 28.49/18.68 (big_f(f7(c2), c2) <=> big_f(f7(c2), f10(f7(c2)))),
% 28.49/18.68 inference(symmetry,[status(thm)],[12765])).
% 28.49/18.68 tff(12767,plain,
% 28.49/18.68 (big_f(c1, c2) <=> big_f(f7(c2), f10(f7(c2)))),
% 28.49/18.68 inference(transitivity,[status(thm)],[126, 12766])).
% 28.49/18.68 tff(12768,plain,
% 28.49/18.68 (~big_f(c1, c1)),
% 28.49/18.68 inference(unit_resolution,[status(thm)],[12660, 12442, 15, 79, 17, 120])).
% 28.49/18.68 tff(12769,plain,
% 28.49/18.68 (~big_f(f7(c2), c1)),
% 28.49/18.68 inference(modus_ponens,[status(thm)],[12768, 12668])).
% 28.49/18.68 tff(12770,plain,
% 28.49/18.68 (~(c1 = f8(c1))),
% 28.49/18.68 inference(unit_resolution,[status(thm)],[12260, 27, 17, 12769, 3, 12229])).
% 28.49/18.68 tff(12771,plain,
% 28.49/18.68 (~(f8(c1) = c1)),
% 28.49/18.68 inference(unit_resolution,[status(thm)],[9808, 12770])).
% 28.49/18.68 tff(12772,plain,
% 28.49/18.68 (f8(c1) = c2),
% 28.49/18.68 inference(unit_resolution,[status(thm)],[1680, 12771])).
% 28.49/18.68 tff(12773,plain,
% 28.49/18.68 (c2 = f8(c1)),
% 28.49/18.68 inference(unit_resolution,[status(thm)],[1675, 12772])).
% 28.49/18.68 tff(12774,plain,
% 28.49/18.68 (big_f(f7(c1), c2)),
% 28.49/18.68 inference(modus_ponens,[status(thm)],[1345, 1724])).
% 28.49/18.68 tff(12775,assumption,(~(c2 = f5(c1))), introduced(assumption)).
% 28.49/18.68 tff(12776,plain,
% 28.49/18.68 (c2 = f8(c1)),
% 28.49/18.68 inference(unit_resolution,[status(thm)],[3393, 1659, 12775, 12774, 115, 3332, 3])).
% 28.49/18.68 tff(12777,assumption,(~(f3(c1, c2) = c2)), introduced(assumption)).
% 28.49/18.68 tff(12778,plain,
% 28.49/18.68 (f8(c3) = c2),
% 28.49/18.68 inference(transitivity,[status(thm)],[10861, 1643])).
% 28.49/18.68 tff(12779,plain,
% 28.49/18.68 (f3(c1, f8(c3)) = f3(c1, c2)),
% 28.49/18.68 inference(monotonicity,[status(thm)],[12778])).
% 28.49/18.68 tff(12780,plain,
% 28.49/18.68 ((f3(c1, f8(c3)) = c2) <=> (f3(c1, c2) = c2)),
% 28.49/18.68 inference(monotonicity,[status(thm)],[12779])).
% 28.49/18.68 tff(12781,assumption,(f3(c1, f8(c3)) = c2), introduced(assumption)).
% 28.49/18.68 tff(12782,plain,
% 28.49/18.68 (f3(c1, c2) = c2),
% 28.49/18.68 inference(modus_ponens,[status(thm)],[12781, 12780])).
% 28.49/18.68 tff(12783,plain,
% 28.49/18.68 ($false),
% 28.49/18.68 inference(unit_resolution,[status(thm)],[12777, 12782])).
% 28.49/18.68 tff(12784,plain,((~(f3(c1, f8(c3)) = c2)) | (f3(c1, c2) = c2) | (~(c2 = f8(c1))) | (~(c3 = c1))), inference(lemma,lemma(discharge,[]))).
% 28.49/18.68 tff(12785,plain,
% 28.49/18.68 (~(f3(c1, f8(c3)) = c2)),
% 28.49/18.68 inference(unit_resolution,[status(thm)],[12784, 12777, 1642, 172])).
% 28.49/18.68 tff(12786,plain,
% 28.49/18.68 (f3(c1, f8(c3)) = c1),
% 28.49/18.68 inference(unit_resolution,[status(thm)],[7123, 12785])).
% 28.49/18.68 tff(12787,plain,
% 28.49/18.68 (f8(c1) = f8(c3)),
% 28.49/18.68 inference(symmetry,[status(thm)],[10861])).
% 28.49/18.68 tff(12788,plain,
% 28.49/18.68 (c2 = f8(c3)),
% 28.49/18.68 inference(transitivity,[status(thm)],[1642, 12787])).
% 28.49/18.68 tff(12789,plain,
% 28.49/18.68 (f3(c1, c2) = f3(c1, f8(c3))),
% 28.49/18.68 inference(monotonicity,[status(thm)],[12788])).
% 28.49/18.68 tff(12790,plain,
% 28.49/18.68 (f3(c1, c2) = c1),
% 28.49/18.68 inference(transitivity,[status(thm)],[12789, 12786])).
% 28.49/18.68 tff(12791,plain,
% 28.49/18.68 (big_f(f3(c1, c2), c1) <=> big_f(c1, c1)),
% 28.49/18.68 inference(monotonicity,[status(thm)],[12790])).
% 28.49/18.68 tff(12792,plain,
% 28.49/18.68 (big_f(c1, c1) <=> big_f(f3(c1, c2), c1)),
% 28.49/18.68 inference(symmetry,[status(thm)],[12791])).
% 28.49/18.68 tff(12793,plain,
% 28.49/18.68 ((~big_f(c1, c1)) <=> (~big_f(f3(c1, c2), c1))),
% 28.49/18.68 inference(monotonicity,[status(thm)],[12792])).
% 28.49/18.68 tff(12794,plain,
% 28.49/18.68 (~big_f(f3(c1, c2), c1)),
% 28.49/18.68 inference(modus_ponens,[status(thm)],[66, 12793])).
% 28.49/18.68 tff(12795,plain,
% 28.49/18.68 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((c1 = c4) | (~(c1 = c3)) | (~(c1 = f2(c1))) | big_f(c1, c1) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (c1 = c4) | (~(c1 = c3)) | (~(c1 = f2(c1))) | big_f(c1, c1) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2))),
% 28.49/18.68 inference(rewrite,[status(thm)],[])).
% 28.49/18.68 tff(12796,plain,
% 28.49/18.68 (((~(c1 = c3)) | (~(c1 = f2(c1))) | (c1 = c4) | (f3(c1, c2) = c2) | big_f(f3(c1, c2), c1) | big_f(c1, c1)) <=> ((c1 = c4) | (~(c1 = c3)) | (~(c1 = f2(c1))) | big_f(c1, c1) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2))),
% 28.49/18.68 inference(rewrite,[status(thm)],[])).
% 28.49/18.68 tff(12797,plain,
% 28.49/18.68 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(c1 = f2(c1))) | (c1 = c4) | (f3(c1, c2) = c2) | big_f(f3(c1, c2), c1) | big_f(c1, c1))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((c1 = c4) | (~(c1 = c3)) | (~(c1 = f2(c1))) | big_f(c1, c1) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2)))),
% 28.49/18.68 inference(monotonicity,[status(thm)],[12796])).
% 28.49/18.68 tff(12798,plain,
% 28.49/18.68 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(c1 = f2(c1))) | (c1 = c4) | (f3(c1, c2) = c2) | big_f(f3(c1, c2), c1) | big_f(c1, c1))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (c1 = c4) | (~(c1 = c3)) | (~(c1 = f2(c1))) | big_f(c1, c1) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2))),
% 28.49/18.68 inference(transitivity,[status(thm)],[12797, 12795])).
% 28.49/18.68 tff(12799,plain,
% 28.49/18.68 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(c1 = f2(c1))) | (c1 = c4) | (f3(c1, c2) = c2) | big_f(f3(c1, c2), c1) | big_f(c1, c1))),
% 28.49/18.68 inference(quant_inst,[status(thm)],[])).
% 28.49/18.68 tff(12800,plain,
% 28.49/18.68 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (c1 = c4) | (~(c1 = c3)) | (~(c1 = f2(c1))) | big_f(c1, c1) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2)),
% 28.49/18.68 inference(modus_ponens,[status(thm)],[12799, 12798])).
% 28.49/18.68 tff(12801,plain,
% 28.49/18.68 ($false),
% 28.49/18.68 inference(unit_resolution,[status(thm)],[12800, 1459, 5611, 482, 12794, 12777, 6632, 66])).
% 28.49/18.68 tff(12802,plain,((f3(c1, c2) = c2) | (c1 = c4) | (~(c1 = f2(c1))) | big_f(c1, c1) | (~(c2 = f8(c1))) | (~(c3 = c1))), inference(lemma,lemma(discharge,[]))).
% 28.49/18.68 tff(12803,plain,
% 28.49/18.68 (f3(c1, c2) = c2),
% 28.49/18.68 inference(unit_resolution,[status(thm)],[12802, 6632, 482, 66, 1642, 172])).
% 28.49/18.68 tff(12804,plain,
% 28.49/18.68 (big_f(f3(c1, c2), c1) <=> big_f(c2, c1)),
% 28.49/18.68 inference(monotonicity,[status(thm)],[12803])).
% 28.49/18.68 tff(12805,plain,
% 28.49/18.68 (big_f(c2, c1) <=> big_f(f3(c1, c2), c1)),
% 28.49/18.68 inference(symmetry,[status(thm)],[12804])).
% 28.49/18.68 tff(12806,plain,
% 28.49/18.68 (big_f(f3(c1, c2), c1)),
% 28.49/18.68 inference(modus_ponens,[status(thm)],[348, 12805])).
% 28.49/18.68 tff(12807,plain,
% 28.49/18.68 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((c1 = c4) | (~(c1 = c3)) | (~(c1 = f2(c1))) | big_f(c1, c1) | (~big_f(f3(c1, c2), c1)) | (~(f3(c1, c2) = c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (c1 = c4) | (~(c1 = c3)) | (~(c1 = f2(c1))) | big_f(c1, c1) | (~big_f(f3(c1, c2), c1)) | (~(f3(c1, c2) = c2)))),
% 28.49/18.68 inference(rewrite,[status(thm)],[])).
% 28.49/18.68 tff(12808,plain,
% 28.49/18.68 (((~(c1 = c3)) | (~(c1 = f2(c1))) | (c1 = c4) | (~(f3(c1, c2) = c2)) | (~big_f(f3(c1, c2), c1)) | big_f(c1, c1)) <=> ((c1 = c4) | (~(c1 = c3)) | (~(c1 = f2(c1))) | big_f(c1, c1) | (~big_f(f3(c1, c2), c1)) | (~(f3(c1, c2) = c2)))),
% 28.49/18.68 inference(rewrite,[status(thm)],[])).
% 28.49/18.68 tff(12809,plain,
% 28.49/18.68 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(c1 = f2(c1))) | (c1 = c4) | (~(f3(c1, c2) = c2)) | (~big_f(f3(c1, c2), c1)) | big_f(c1, c1))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((c1 = c4) | (~(c1 = c3)) | (~(c1 = f2(c1))) | big_f(c1, c1) | (~big_f(f3(c1, c2), c1)) | (~(f3(c1, c2) = c2))))),
% 28.49/18.68 inference(monotonicity,[status(thm)],[12808])).
% 28.49/18.68 tff(12810,plain,
% 28.49/18.68 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(c1 = f2(c1))) | (c1 = c4) | (~(f3(c1, c2) = c2)) | (~big_f(f3(c1, c2), c1)) | big_f(c1, c1))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (c1 = c4) | (~(c1 = c3)) | (~(c1 = f2(c1))) | big_f(c1, c1) | (~big_f(f3(c1, c2), c1)) | (~(f3(c1, c2) = c2)))),
% 28.49/18.68 inference(transitivity,[status(thm)],[12809, 12807])).
% 28.49/18.68 tff(12811,plain,
% 28.49/18.68 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(c1 = f2(c1))) | (c1 = c4) | (~(f3(c1, c2) = c2)) | (~big_f(f3(c1, c2), c1)) | big_f(c1, c1))),
% 28.49/18.68 inference(quant_inst,[status(thm)],[])).
% 28.49/18.68 tff(12812,plain,
% 28.49/18.68 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (c1 = c4) | (~(c1 = c3)) | (~(c1 = f2(c1))) | big_f(c1, c1) | (~big_f(f3(c1, c2), c1)) | (~(f3(c1, c2) = c2))),
% 28.49/18.68 inference(modus_ponens,[status(thm)],[12811, 12810])).
% 28.49/18.68 tff(12813,plain,
% 28.49/18.68 ($false),
% 28.49/18.68 inference(unit_resolution,[status(thm)],[12812, 1398, 5611, 482, 12806, 12803, 6632, 66])).
% 28.49/18.68 tff(12814,plain,((~(c1 = f2(c1))) | (c1 = c4) | big_f(c1, c1) | (~big_f(c2, c1)) | (~(c2 = f8(c1))) | (~(c3 = c1))), inference(lemma,lemma(discharge,[]))).
% 28.49/18.68 tff(12815,plain,
% 28.49/18.68 (~(c1 = f2(c1))),
% 28.49/18.68 inference(unit_resolution,[status(thm)],[12814, 482, 66, 348, 1642, 172])).
% 28.49/18.68 tff(12816,plain,
% 28.49/18.68 (~(f2(c3) = c1)),
% 28.49/18.68 inference(unit_resolution,[status(thm)],[6771, 12815, 172])).
% 28.49/18.68 tff(12817,plain,
% 28.49/18.68 (f2(c3) = c2),
% 28.49/18.68 inference(unit_resolution,[status(thm)],[1273, 12816])).
% 28.49/18.68 tff(12818,plain,
% 28.49/18.68 ((c2 = f2(c3)) <=> (c2 = f2(c1))),
% 28.49/18.68 inference(monotonicity,[status(thm)],[6765])).
% 28.49/18.68 tff(12819,plain,
% 28.49/18.68 ((f2(c3) = c2) <=> (c2 = f2(c1))),
% 28.49/18.68 inference(transitivity,[status(thm)],[1434, 12818])).
% 28.49/18.68 tff(12820,plain,
% 28.49/18.68 (c2 = f2(c1)),
% 28.49/18.68 inference(modus_ponens,[status(thm)],[1319, 12819])).
% 28.49/18.68 tff(12821,assumption,(~(c2 = f2(c1))), introduced(assumption)).
% 28.49/18.68 tff(12822,plain,
% 28.49/18.68 ($false),
% 28.49/18.68 inference(unit_resolution,[status(thm)],[12821, 12820])).
% 28.49/18.68 tff(12823,plain,((~(f2(c3) = c2)) | (c2 = f2(c1)) | (~(c3 = c1))), inference(lemma,lemma(discharge,[]))).
% 28.49/18.68 tff(12824,plain,
% 28.49/18.68 (c2 = f2(c1)),
% 28.49/18.68 inference(unit_resolution,[status(thm)],[12823, 12817, 172])).
% 28.49/18.68 tff(12825,plain,
% 28.49/18.68 (f3(c1, f8(c3)) = f3(c1, c2)),
% 28.49/18.68 inference(symmetry,[status(thm)],[12789])).
% 28.49/18.68 tff(12826,plain,
% 28.49/18.68 (c1 = f3(c1, f8(c3))),
% 28.49/18.68 inference(symmetry,[status(thm)],[12786])).
% 28.49/18.68 tff(12827,plain,
% 28.49/18.68 (c1 = f3(c1, c2)),
% 28.49/18.68 inference(transitivity,[status(thm)],[12826, 12825])).
% 28.49/18.68 tff(12828,plain,
% 28.49/18.68 (big_f(c1, c1) <=> big_f(f3(c1, c2), c1)),
% 28.49/18.68 inference(monotonicity,[status(thm)],[12827])).
% 28.49/18.68 tff(12829,plain,
% 28.49/18.68 ((~big_f(c1, c1)) <=> (~big_f(f3(c1, c2), c1))),
% 28.49/18.68 inference(monotonicity,[status(thm)],[12828])).
% 28.49/18.68 tff(12830,plain,
% 28.49/18.68 (~big_f(f3(c1, c2), c1)),
% 28.49/18.68 inference(modus_ponens,[status(thm)],[66, 12829])).
% 28.49/18.68 tff(12831,assumption,(c2 = f2(c1)), introduced(assumption)).
% 28.49/18.68 tff(12832,plain,
% 28.49/18.68 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((c1 = c4) | (~(c1 = c3)) | big_f(c1, c2) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2) | (~(c2 = f2(c1))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (c1 = c4) | (~(c1 = c3)) | big_f(c1, c2) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2) | (~(c2 = f2(c1))))),
% 28.49/18.68 inference(rewrite,[status(thm)],[])).
% 28.49/18.68 tff(12833,plain,
% 28.49/18.68 (((~(c1 = c3)) | (~(c2 = f2(c1))) | (c1 = c4) | (f3(c1, c2) = c2) | big_f(f3(c1, c2), c1) | big_f(c1, c2)) <=> ((c1 = c4) | (~(c1 = c3)) | big_f(c1, c2) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2) | (~(c2 = f2(c1))))),
% 28.49/18.68 inference(rewrite,[status(thm)],[])).
% 28.49/18.68 tff(12834,plain,
% 28.49/18.68 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(c2 = f2(c1))) | (c1 = c4) | (f3(c1, c2) = c2) | big_f(f3(c1, c2), c1) | big_f(c1, c2))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((c1 = c4) | (~(c1 = c3)) | big_f(c1, c2) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2) | (~(c2 = f2(c1)))))),
% 28.49/18.68 inference(monotonicity,[status(thm)],[12833])).
% 28.49/18.68 tff(12835,plain,
% 28.49/18.68 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(c2 = f2(c1))) | (c1 = c4) | (f3(c1, c2) = c2) | big_f(f3(c1, c2), c1) | big_f(c1, c2))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (c1 = c4) | (~(c1 = c3)) | big_f(c1, c2) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2) | (~(c2 = f2(c1))))),
% 28.49/18.68 inference(transitivity,[status(thm)],[12834, 12832])).
% 28.49/18.68 tff(12836,plain,
% 28.49/18.68 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(c2 = f2(c1))) | (c1 = c4) | (f3(c1, c2) = c2) | big_f(f3(c1, c2), c1) | big_f(c1, c2))),
% 28.49/18.68 inference(quant_inst,[status(thm)],[])).
% 28.49/18.68 tff(12837,plain,
% 28.49/18.68 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (c1 = c4) | (~(c1 = c3)) | big_f(c1, c2) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2) | (~(c2 = f2(c1)))),
% 28.49/18.68 inference(modus_ponens,[status(thm)],[12836, 12835])).
% 28.49/18.68 tff(12838,plain,
% 28.49/18.68 ($false),
% 28.49/18.68 inference(unit_resolution,[status(thm)],[12837, 1459, 5611, 482, 12831, 27, 12830, 12777])).
% 28.49/18.68 tff(12839,plain,((f3(c1, c2) = c2) | (c1 = c4) | (~(c2 = f2(c1))) | big_f(c1, c2) | big_f(c1, c1) | (~(c2 = f8(c1))) | (~(c3 = c1))), inference(lemma,lemma(discharge,[]))).
% 28.49/18.68 tff(12840,plain,
% 28.49/18.68 (f3(c1, c2) = c2),
% 28.49/18.68 inference(unit_resolution,[status(thm)],[12839, 27, 12824, 482, 66, 1642, 172])).
% 28.49/18.68 tff(12841,plain,
% 28.49/18.68 (big_f(f3(c1, c2), c1) <=> big_f(c2, c1)),
% 28.49/18.68 inference(monotonicity,[status(thm)],[12840])).
% 28.49/18.68 tff(12842,plain,
% 28.49/18.68 (big_f(c2, c1) <=> big_f(f3(c1, c2), c1)),
% 28.49/18.68 inference(symmetry,[status(thm)],[12841])).
% 28.49/18.68 tff(12843,plain,
% 28.49/18.68 (big_f(f3(c1, c2), c1)),
% 28.49/18.68 inference(modus_ponens,[status(thm)],[348, 12842])).
% 28.49/18.68 tff(12844,plain,
% 28.49/18.68 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((c1 = c4) | (~(c1 = c3)) | (~big_f(f3(c1, c2), c1)) | big_f(c1, c2) | (~(f3(c1, c2) = c2)) | (~(c2 = f2(c1))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (c1 = c4) | (~(c1 = c3)) | (~big_f(f3(c1, c2), c1)) | big_f(c1, c2) | (~(f3(c1, c2) = c2)) | (~(c2 = f2(c1))))),
% 28.49/18.68 inference(rewrite,[status(thm)],[])).
% 28.49/18.68 tff(12845,plain,
% 28.49/18.68 (((~(c1 = c3)) | (~(c2 = f2(c1))) | (c1 = c4) | (~(f3(c1, c2) = c2)) | (~big_f(f3(c1, c2), c1)) | big_f(c1, c2)) <=> ((c1 = c4) | (~(c1 = c3)) | (~big_f(f3(c1, c2), c1)) | big_f(c1, c2) | (~(f3(c1, c2) = c2)) | (~(c2 = f2(c1))))),
% 28.49/18.68 inference(rewrite,[status(thm)],[])).
% 28.49/18.68 tff(12846,plain,
% 28.49/18.68 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(c2 = f2(c1))) | (c1 = c4) | (~(f3(c1, c2) = c2)) | (~big_f(f3(c1, c2), c1)) | big_f(c1, c2))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((c1 = c4) | (~(c1 = c3)) | (~big_f(f3(c1, c2), c1)) | big_f(c1, c2) | (~(f3(c1, c2) = c2)) | (~(c2 = f2(c1)))))),
% 28.50/18.68 inference(monotonicity,[status(thm)],[12845])).
% 28.50/18.68 tff(12847,plain,
% 28.50/18.68 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(c2 = f2(c1))) | (c1 = c4) | (~(f3(c1, c2) = c2)) | (~big_f(f3(c1, c2), c1)) | big_f(c1, c2))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (c1 = c4) | (~(c1 = c3)) | (~big_f(f3(c1, c2), c1)) | big_f(c1, c2) | (~(f3(c1, c2) = c2)) | (~(c2 = f2(c1))))),
% 28.50/18.68 inference(transitivity,[status(thm)],[12846, 12844])).
% 28.50/18.68 tff(12848,plain,
% 28.50/18.68 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(c2 = f2(c1))) | (c1 = c4) | (~(f3(c1, c2) = c2)) | (~big_f(f3(c1, c2), c1)) | big_f(c1, c2))),
% 28.50/18.68 inference(quant_inst,[status(thm)],[])).
% 28.50/18.68 tff(12849,plain,
% 28.50/18.68 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (c1 = c4) | (~(c1 = c3)) | (~big_f(f3(c1, c2), c1)) | big_f(c1, c2) | (~(f3(c1, c2) = c2)) | (~(c2 = f2(c1)))),
% 28.50/18.68 inference(modus_ponens,[status(thm)],[12848, 12847])).
% 28.50/18.68 tff(12850,plain,
% 28.50/18.68 ($false),
% 28.50/18.68 inference(unit_resolution,[status(thm)],[12849, 1398, 5611, 482, 12824, 27, 12843, 12840])).
% 28.50/18.68 tff(12851,plain,(big_f(c1, c2) | (c1 = c4) | (~big_f(c2, c1)) | big_f(c1, c1) | (~(c2 = f8(c1))) | (~(c3 = c1))), inference(lemma,lemma(discharge,[]))).
% 28.50/18.68 tff(12852,plain,
% 28.50/18.68 (c1 = c4),
% 28.50/18.68 inference(unit_resolution,[status(thm)],[12851, 27, 172, 66, 348, 12776])).
% 28.50/18.69 tff(12853,plain,
% 28.50/18.69 (c4 = c1),
% 28.50/18.69 inference(symmetry,[status(thm)],[12852])).
% 28.50/18.69 tff(12854,plain,
% 28.50/18.69 ((c2 = c4) <=> (c2 = c1)),
% 28.50/18.69 inference(monotonicity,[status(thm)],[12853])).
% 28.50/18.69 tff(12855,plain,
% 28.50/18.69 ((c2 = c1) <=> (c2 = c4)),
% 28.50/18.69 inference(symmetry,[status(thm)],[12854])).
% 28.50/18.69 tff(12856,plain,
% 28.50/18.69 ((~(c2 = c1)) <=> (~(c2 = c4))),
% 28.50/18.69 inference(monotonicity,[status(thm)],[12855])).
% 28.50/18.69 tff(12857,plain,
% 28.50/18.69 (~(c2 = c4)),
% 28.50/18.69 inference(modus_ponens,[status(thm)],[75, 12856])).
% 28.50/18.69 tff(12858,plain,
% 28.50/18.69 ((f3(c2, c2) = f8(c1)) <=> (f3(c2, c2) = c2)),
% 28.50/18.69 inference(monotonicity,[status(thm)],[1643])).
% 28.50/18.69 tff(12859,plain,
% 28.50/18.69 ((f3(c2, c2) = c2) <=> (f3(c2, c2) = f8(c1))),
% 28.50/18.69 inference(symmetry,[status(thm)],[12858])).
% 28.50/18.69 tff(12860,plain,
% 28.50/18.69 ((~(f3(c2, c2) = c2)) <=> (~(f3(c2, c2) = f8(c1)))),
% 28.50/18.69 inference(monotonicity,[status(thm)],[12859])).
% 28.50/18.69 tff(12861,assumption,(~(f3(c2, c2) = c2)), introduced(assumption)).
% 28.50/18.69 tff(12862,plain,
% 28.50/18.69 (~(f3(c2, c2) = f8(c1))),
% 28.50/18.69 inference(modus_ponens,[status(thm)],[12861, 12860])).
% 28.50/18.69 tff(12863,plain,
% 28.50/18.69 (big_f(f3(c2, c2), f10(c1)) <=> big_f(f3(c2, c2), c2)),
% 28.50/18.69 inference(monotonicity,[status(thm)],[15])).
% 28.50/18.69 tff(12864,plain,
% 28.50/18.69 (big_f(f3(c2, c2), c2) <=> big_f(f3(c2, c2), f10(c1))),
% 28.50/18.69 inference(symmetry,[status(thm)],[12863])).
% 28.50/18.69 tff(12865,plain,
% 28.50/18.69 ((~big_f(c1, f10(c1))) <=> (~big_f(c1, c2))),
% 28.50/18.69 inference(monotonicity,[status(thm)],[3349])).
% 28.50/18.69 tff(12866,plain,
% 28.50/18.69 ((f8(c1) = c1) <=> (c2 = c1)),
% 28.50/18.69 inference(monotonicity,[status(thm)],[1643])).
% 28.50/18.69 tff(12867,plain,
% 28.50/18.69 ((c2 = c1) <=> (f8(c1) = c1)),
% 28.50/18.69 inference(symmetry,[status(thm)],[12866])).
% 28.50/18.69 tff(12868,plain,
% 28.50/18.69 ((c2 = c1) <=> (c1 = f8(c1))),
% 28.50/18.69 inference(transitivity,[status(thm)],[12867, 3028])).
% 28.50/18.69 tff(12869,plain,
% 28.50/18.69 ((~(c2 = c1)) <=> (~(c1 = f8(c1)))),
% 28.50/18.69 inference(monotonicity,[status(thm)],[12868])).
% 28.50/18.69 tff(12870,plain,
% 28.50/18.69 (~(c1 = f8(c1))),
% 28.50/18.69 inference(modus_ponens,[status(thm)],[75, 12869])).
% 28.50/18.69 tff(12871,assumption,(big_f(f7(c1), c2)), introduced(assumption)).
% 28.50/18.69 tff(12872,plain,
% 28.50/18.69 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((c2 = f5(c1)) | (f7(c1) = c1) | (f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~big_f(f7(c1), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (c2 = f5(c1)) | (f7(c1) = c1) | (f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~big_f(f7(c1), c2)))),
% 28.50/18.69 inference(rewrite,[status(thm)],[])).
% 28.50/18.69 tff(12873,plain,
% 28.50/18.69 (((f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2))) <=> ((c2 = f5(c1)) | (f7(c1) = c1) | (f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~big_f(f7(c1), c2)))),
% 28.50/18.69 inference(rewrite,[status(thm)],[])).
% 28.50/18.69 tff(12874,plain,
% 28.50/18.69 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((c2 = f5(c1)) | (f7(c1) = c1) | (f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~big_f(f7(c1), c2))))),
% 28.50/18.69 inference(monotonicity,[status(thm)],[12873])).
% 28.50/18.69 tff(12875,plain,
% 28.50/18.69 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (c2 = f5(c1)) | (f7(c1) = c1) | (f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~big_f(f7(c1), c2)))),
% 28.50/18.69 inference(transitivity,[status(thm)],[12874, 12872])).
% 28.50/18.69 tff(12876,plain,
% 28.50/18.69 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)))),
% 28.50/18.69 inference(quant_inst,[status(thm)],[])).
% 28.50/18.69 tff(12877,plain,
% 28.50/18.69 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (c2 = f5(c1)) | (f7(c1) = c1) | (f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~big_f(f7(c1), c2))),
% 28.50/18.69 inference(modus_ponens,[status(thm)],[12876, 12875])).
% 28.50/18.69 tff(12878,plain,
% 28.50/18.69 ($false),
% 28.50/18.69 inference(unit_resolution,[status(thm)],[12877, 1659, 12775, 12871, 115, 3, 9806, 3023])).
% 28.50/18.69 tff(12879,plain,((~big_f(c1, f10(c1))) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)) | (f7(c1) = c1) | (f10(c1) = c1) | (c1 = f8(c1))), inference(lemma,lemma(discharge,[]))).
% 28.50/18.69 tff(12880,plain,
% 28.50/18.69 (~big_f(c1, f10(c1))),
% 28.50/18.69 inference(unit_resolution,[status(thm)],[12879, 12871, 12775, 115, 3, 12870])).
% 28.50/18.69 tff(12881,plain,
% 28.50/18.69 (~big_f(c1, c2)),
% 28.50/18.69 inference(modus_ponens,[status(thm)],[12880, 12865])).
% 28.50/18.69 tff(12882,assumption,(~big_f(f3(c2, c2), c2)), introduced(assumption)).
% 28.50/18.69 tff(12883,plain,
% 28.50/18.69 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((c2 = c4) | (~(c1 = c3)) | (~(c1 = f2(c1))) | big_f(c1, c1) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (c2 = c4) | (~(c1 = c3)) | (~(c1 = f2(c1))) | big_f(c1, c1) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2))),
% 28.50/18.69 inference(rewrite,[status(thm)],[])).
% 28.50/18.69 tff(12884,plain,
% 28.50/18.69 (((~(c1 = c3)) | (~(c1 = f2(c1))) | (c2 = c4) | (f3(c2, c2) = c2) | big_f(f3(c2, c2), c2) | big_f(c1, c1)) <=> ((c2 = c4) | (~(c1 = c3)) | (~(c1 = f2(c1))) | big_f(c1, c1) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2))),
% 28.50/18.69 inference(rewrite,[status(thm)],[])).
% 28.50/18.69 tff(12885,plain,
% 28.50/18.69 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(c1 = f2(c1))) | (c2 = c4) | (f3(c2, c2) = c2) | big_f(f3(c2, c2), c2) | big_f(c1, c1))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((c2 = c4) | (~(c1 = c3)) | (~(c1 = f2(c1))) | big_f(c1, c1) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2)))),
% 28.50/18.69 inference(monotonicity,[status(thm)],[12884])).
% 28.50/18.69 tff(12886,plain,
% 28.50/18.69 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(c1 = f2(c1))) | (c2 = c4) | (f3(c2, c2) = c2) | big_f(f3(c2, c2), c2) | big_f(c1, c1))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (c2 = c4) | (~(c1 = c3)) | (~(c1 = f2(c1))) | big_f(c1, c1) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2))),
% 28.50/18.69 inference(transitivity,[status(thm)],[12885, 12883])).
% 28.50/18.69 tff(12887,plain,
% 28.50/18.69 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(c1 = f2(c1))) | (c2 = c4) | (f3(c2, c2) = c2) | big_f(f3(c2, c2), c2) | big_f(c1, c1))),
% 28.50/18.69 inference(quant_inst,[status(thm)],[])).
% 28.50/18.69 tff(12888,plain,
% 28.50/18.69 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (c2 = c4) | (~(c1 = c3)) | (~(c1 = f2(c1))) | big_f(c1, c1) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2)),
% 28.50/18.69 inference(modus_ponens,[status(thm)],[12887, 12886])).
% 28.50/18.69 tff(12889,plain,
% 28.50/18.69 (~(c1 = f2(c1))),
% 28.50/18.69 inference(unit_resolution,[status(thm)],[12888, 1459, 5611, 873, 66, 12861, 12882])).
% 28.50/18.69 tff(12890,assumption,(~(f2(c3) = c2)), introduced(assumption)).
% 28.50/18.69 tff(12891,plain,
% 28.50/18.69 (f2(c3) = c1),
% 28.50/18.69 inference(unit_resolution,[status(thm)],[1273, 12890])).
% 28.50/18.69 tff(12892,plain,
% 28.50/18.69 ($false),
% 28.50/18.69 inference(unit_resolution,[status(thm)],[6771, 12891, 12889, 172])).
% 28.50/18.69 tff(12893,plain,((f2(c3) = c2) | (~(c3 = c1)) | (c2 = c4) | big_f(c1, c1) | (f3(c2, c2) = c2) | big_f(f3(c2, c2), c2)), inference(lemma,lemma(discharge,[]))).
% 28.50/18.69 tff(12894,plain,
% 28.50/18.69 (f2(c3) = c2),
% 28.50/18.69 inference(unit_resolution,[status(thm)],[12893, 12882, 873, 66, 12861, 172])).
% 28.50/18.69 tff(12895,plain,
% 28.50/18.69 (c2 = f2(c1)),
% 28.50/18.69 inference(unit_resolution,[status(thm)],[12823, 12894, 172])).
% 28.50/18.69 tff(12896,plain,
% 28.50/18.69 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((c2 = c4) | (~(c1 = c3)) | big_f(c1, c2) | (~(c2 = f2(c1))) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (c2 = c4) | (~(c1 = c3)) | big_f(c1, c2) | (~(c2 = f2(c1))) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2))),
% 28.50/18.69 inference(rewrite,[status(thm)],[])).
% 28.50/18.69 tff(12897,plain,
% 28.50/18.69 (((~(c1 = c3)) | (~(c2 = f2(c1))) | (c2 = c4) | (f3(c2, c2) = c2) | big_f(f3(c2, c2), c2) | big_f(c1, c2)) <=> ((c2 = c4) | (~(c1 = c3)) | big_f(c1, c2) | (~(c2 = f2(c1))) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2))),
% 28.50/18.69 inference(rewrite,[status(thm)],[])).
% 28.50/18.69 tff(12898,plain,
% 28.50/18.69 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(c2 = f2(c1))) | (c2 = c4) | (f3(c2, c2) = c2) | big_f(f3(c2, c2), c2) | big_f(c1, c2))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((c2 = c4) | (~(c1 = c3)) | big_f(c1, c2) | (~(c2 = f2(c1))) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2)))),
% 28.50/18.69 inference(monotonicity,[status(thm)],[12897])).
% 28.50/18.69 tff(12899,plain,
% 28.50/18.69 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(c2 = f2(c1))) | (c2 = c4) | (f3(c2, c2) = c2) | big_f(f3(c2, c2), c2) | big_f(c1, c2))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (c2 = c4) | (~(c1 = c3)) | big_f(c1, c2) | (~(c2 = f2(c1))) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2))),
% 28.50/18.69 inference(transitivity,[status(thm)],[12898, 12896])).
% 28.50/18.69 tff(12900,plain,
% 28.50/18.69 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(c2 = f2(c1))) | (c2 = c4) | (f3(c2, c2) = c2) | big_f(f3(c2, c2), c2) | big_f(c1, c2))),
% 28.50/18.69 inference(quant_inst,[status(thm)],[])).
% 28.50/18.69 tff(12901,plain,
% 28.50/18.69 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (c2 = c4) | (~(c1 = c3)) | big_f(c1, c2) | (~(c2 = f2(c1))) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2)),
% 28.50/18.69 inference(modus_ponens,[status(thm)],[12900, 12899])).
% 28.50/18.69 tff(12902,plain,
% 28.50/18.69 ($false),
% 28.50/18.69 inference(unit_resolution,[status(thm)],[12901, 1459, 5611, 873, 12895, 27, 12861, 12882])).
% 28.50/18.69 tff(12903,plain,(big_f(f3(c2, c2), c2) | (c2 = c4) | big_f(c1, c2) | (f3(c2, c2) = c2) | (~(c3 = c1)) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 28.50/18.69 tff(12904,plain,
% 28.50/18.69 (big_f(f3(c2, c2), c2)),
% 28.50/18.69 inference(unit_resolution,[status(thm)],[12903, 12861, 12881, 873, 172, 66])).
% 28.50/18.69 tff(12905,plain,
% 28.50/18.69 (big_f(f3(c2, c2), f10(c1))),
% 28.50/18.69 inference(modus_ponens,[status(thm)],[12904, 12864])).
% 28.50/18.69 tff(12906,plain,
% 28.50/18.69 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((c2 = f5(c1)) | (f7(c1) = c1) | (f10(c1) = c1) | (~big_f(f7(c1), c2)) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (c2 = f5(c1)) | (f7(c1) = c1) | (f10(c1) = c1) | (~big_f(f7(c1), c2)) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1))))),
% 28.50/18.69 inference(rewrite,[status(thm)],[])).
% 28.50/18.69 tff(12907,plain,
% 28.50/18.69 (((f10(c1) = c1) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1))) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2))) <=> ((c2 = f5(c1)) | (f7(c1) = c1) | (f10(c1) = c1) | (~big_f(f7(c1), c2)) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1))))),
% 28.50/18.69 inference(rewrite,[status(thm)],[])).
% 28.50/18.69 tff(12908,plain,
% 28.50/18.69 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c1) = c1) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1))) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((c2 = f5(c1)) | (f7(c1) = c1) | (f10(c1) = c1) | (~big_f(f7(c1), c2)) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1)))))),
% 28.50/18.69 inference(monotonicity,[status(thm)],[12907])).
% 28.50/18.69 tff(12909,plain,
% 28.50/18.69 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c1) = c1) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1))) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (c2 = f5(c1)) | (f7(c1) = c1) | (f10(c1) = c1) | (~big_f(f7(c1), c2)) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1))))),
% 28.50/18.69 inference(transitivity,[status(thm)],[12908, 12906])).
% 28.50/18.69 tff(12910,plain,
% 28.50/18.69 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c1) = c1) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1))) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)))),
% 28.50/18.69 inference(quant_inst,[status(thm)],[])).
% 28.50/18.69 tff(12911,plain,
% 28.50/18.69 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (c2 = f5(c1)) | (f7(c1) = c1) | (f10(c1) = c1) | (~big_f(f7(c1), c2)) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1)))),
% 28.50/18.69 inference(modus_ponens,[status(thm)],[12910, 12909])).
% 28.50/18.69 tff(12912,plain,
% 28.50/18.69 ($false),
% 28.50/18.69 inference(unit_resolution,[status(thm)],[12911, 1659, 12775, 12871, 115, 3, 12905, 12862])).
% 28.50/18.69 tff(12913,plain,((f3(c2, c2) = c2) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)) | (f7(c1) = c1) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (c2 = c4) | (~(c3 = c1)) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 28.50/18.69 tff(12914,plain,
% 28.50/18.69 (f3(c2, c2) = c2),
% 28.50/18.69 inference(unit_resolution,[status(thm)],[12913, 12857, 12775, 115, 3, 12774, 12776, 172, 66])).
% 28.50/18.69 tff(12915,plain,
% 28.50/18.69 (big_f(f3(c2, c2), c2) <=> big_f(c2, c2)),
% 28.50/18.69 inference(monotonicity,[status(thm)],[12914])).
% 28.50/18.69 tff(12916,plain,
% 28.50/18.69 (big_f(c2, c2) <=> big_f(f3(c2, c2), c2)),
% 28.50/18.69 inference(symmetry,[status(thm)],[12915])).
% 28.50/18.69 tff(12917,plain,
% 28.50/18.69 (big_f(f3(c2, c2), c2)),
% 28.50/18.69 inference(modus_ponens,[status(thm)],[1345, 12916])).
% 28.50/18.69 tff(12918,plain,
% 28.50/18.69 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((c2 = c4) | (~(c1 = c3)) | (~(c1 = f2(c1))) | big_f(c1, c1) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (c2 = c4) | (~(c1 = c3)) | (~(c1 = f2(c1))) | big_f(c1, c1) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)))),
% 28.50/18.69 inference(rewrite,[status(thm)],[])).
% 28.50/18.69 tff(12919,plain,
% 28.50/18.69 (((~(c1 = c3)) | (~(c1 = f2(c1))) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | big_f(c1, c1)) <=> ((c2 = c4) | (~(c1 = c3)) | (~(c1 = f2(c1))) | big_f(c1, c1) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)))),
% 28.50/18.69 inference(rewrite,[status(thm)],[])).
% 28.50/18.69 tff(12920,plain,
% 28.50/18.69 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(c1 = f2(c1))) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | big_f(c1, c1))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((c2 = c4) | (~(c1 = c3)) | (~(c1 = f2(c1))) | big_f(c1, c1) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2))))),
% 28.50/18.69 inference(monotonicity,[status(thm)],[12919])).
% 28.50/18.69 tff(12921,plain,
% 28.50/18.69 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(c1 = f2(c1))) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | big_f(c1, c1))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (c2 = c4) | (~(c1 = c3)) | (~(c1 = f2(c1))) | big_f(c1, c1) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)))),
% 28.50/18.69 inference(transitivity,[status(thm)],[12920, 12918])).
% 28.50/18.69 tff(12922,plain,
% 28.50/18.69 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(c1 = f2(c1))) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | big_f(c1, c1))),
% 28.50/18.69 inference(quant_inst,[status(thm)],[])).
% 28.50/18.69 tff(12923,plain,
% 28.50/18.69 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (c2 = c4) | (~(c1 = c3)) | (~(c1 = f2(c1))) | big_f(c1, c1) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2))),
% 28.50/18.69 inference(modus_ponens,[status(thm)],[12922, 12921])).
% 28.50/18.69 tff(12924,plain,
% 28.50/18.69 (~(c1 = f2(c1))),
% 28.50/18.69 inference(unit_resolution,[status(thm)],[12923, 1398, 5611, 12857, 66, 12914, 12917])).
% 28.50/18.69 tff(12925,plain,
% 28.50/18.69 (~(f2(c3) = c1)),
% 28.50/18.69 inference(unit_resolution,[status(thm)],[6771, 12924, 172])).
% 28.50/18.69 tff(12926,plain,
% 28.50/18.69 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((c2 = c4) | (~(c1 = c3)) | big_f(c1, c2) | (~(c2 = f2(c1))) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (c2 = c4) | (~(c1 = c3)) | big_f(c1, c2) | (~(c2 = f2(c1))) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)))),
% 28.50/18.69 inference(rewrite,[status(thm)],[])).
% 28.50/18.69 tff(12927,plain,
% 28.50/18.69 (((~(c1 = c3)) | (~(c2 = f2(c1))) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | big_f(c1, c2)) <=> ((c2 = c4) | (~(c1 = c3)) | big_f(c1, c2) | (~(c2 = f2(c1))) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)))),
% 28.50/18.69 inference(rewrite,[status(thm)],[])).
% 28.50/18.69 tff(12928,plain,
% 28.50/18.69 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(c2 = f2(c1))) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | big_f(c1, c2))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((c2 = c4) | (~(c1 = c3)) | big_f(c1, c2) | (~(c2 = f2(c1))) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2))))),
% 28.50/18.70 inference(monotonicity,[status(thm)],[12927])).
% 28.50/18.70 tff(12929,plain,
% 28.50/18.70 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(c2 = f2(c1))) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | big_f(c1, c2))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (c2 = c4) | (~(c1 = c3)) | big_f(c1, c2) | (~(c2 = f2(c1))) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)))),
% 28.50/18.70 inference(transitivity,[status(thm)],[12928, 12926])).
% 28.50/18.70 tff(12930,plain,
% 28.50/18.70 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(c2 = f2(c1))) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | big_f(c1, c2))),
% 28.50/18.70 inference(quant_inst,[status(thm)],[])).
% 28.50/18.70 tff(12931,plain,
% 28.50/18.70 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (c2 = c4) | (~(c1 = c3)) | big_f(c1, c2) | (~(c2 = f2(c1))) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2))),
% 28.50/18.70 inference(modus_ponens,[status(thm)],[12930, 12929])).
% 28.50/18.70 tff(12932,plain,
% 28.50/18.70 (~(c2 = f2(c1))),
% 28.50/18.70 inference(unit_resolution,[status(thm)],[12931, 1398, 5611, 12857, 27, 12914, 12917])).
% 28.50/18.70 tff(12933,plain,
% 28.50/18.70 (~(f2(c3) = c2)),
% 28.50/18.70 inference(unit_resolution,[status(thm)],[12823, 12932, 172])).
% 28.50/18.70 tff(12934,plain,
% 28.50/18.70 ($false),
% 28.50/18.70 inference(unit_resolution,[status(thm)],[1273, 12933, 12925])).
% 28.50/18.70 tff(12935,plain,(big_f(c1, c2) | (~(c3 = c1)) | big_f(c1, c1) | (~big_f(c2, c2)) | (c2 = f5(c1)) | (f7(c1) = c1) | (f10(c1) = c1) | (~big_f(c2, c1))), inference(lemma,lemma(discharge,[]))).
% 28.50/18.70 tff(12936,plain,
% 28.50/18.70 (c2 = f5(c1)),
% 28.50/18.70 inference(unit_resolution,[status(thm)],[12935, 172, 66, 1345, 27, 115, 3, 348])).
% 28.50/18.70 tff(12937,plain,
% 28.50/18.70 (f5(c1) = c2),
% 28.50/18.70 inference(modus_ponens,[status(thm)],[12936, 8483])).
% 28.50/18.70 tff(12938,plain,
% 28.50/18.70 (big_f(f7(f7(c2)), f7(c2))),
% 28.50/18.70 inference(modus_ponens,[status(thm)],[348, 12451])).
% 28.50/18.70 tff(12939,plain,
% 28.50/18.70 ((f7(f7(c2)) = f7(c2)) <=> (c2 = f7(c2))),
% 28.50/18.70 inference(monotonicity,[status(thm)],[8406])).
% 28.50/18.70 tff(12940,plain,
% 28.50/18.70 ((f7(f7(c2)) = f7(c2)) <=> (f7(c2) = c2)),
% 28.50/18.70 inference(transitivity,[status(thm)],[12939, 8409])).
% 28.50/18.70 tff(12941,plain,
% 28.50/18.70 ((f7(c2) = c2) <=> (f7(f7(c2)) = f7(c2))),
% 28.50/18.70 inference(symmetry,[status(thm)],[12940])).
% 28.50/18.70 tff(12942,plain,
% 28.50/18.70 ((~(f7(c2) = c2)) <=> (~(f7(f7(c2)) = f7(c2)))),
% 28.50/18.70 inference(monotonicity,[status(thm)],[12941])).
% 28.50/18.70 tff(12943,plain,
% 28.50/18.70 (~(f7(f7(c2)) = f7(c2))),
% 28.50/18.70 inference(modus_ponens,[status(thm)],[17, 12942])).
% 28.50/18.70 tff(12944,plain,
% 28.50/18.70 (f2(f7(c2)) = f2(c1)),
% 28.50/18.70 inference(monotonicity,[status(thm)],[22])).
% 28.50/18.70 tff(12945,plain,
% 28.50/18.70 ((f7(c2) = f2(f7(c2))) <=> (c1 = f2(c1))),
% 28.50/18.70 inference(monotonicity,[status(thm)],[22, 12944])).
% 28.50/18.70 tff(12946,plain,
% 28.50/18.70 ((~(f7(c2) = f2(f7(c2)))) <=> (~(c1 = f2(c1)))),
% 28.50/18.70 inference(monotonicity,[status(thm)],[12945])).
% 28.50/18.70 tff(12947,plain,
% 28.50/18.70 (f5(f7(c2)) = c2),
% 28.50/18.70 inference(transitivity,[status(thm)],[8600, 186])).
% 28.50/18.70 tff(12948,plain,
% 28.50/18.70 ((f7(c2) = f5(f7(c2))) <=> (f7(c2) = c2)),
% 28.50/18.70 inference(monotonicity,[status(thm)],[12947])).
% 28.50/18.70 tff(12949,plain,
% 28.50/18.70 ((f7(c2) = c2) <=> (f7(c2) = f5(f7(c2)))),
% 28.50/18.70 inference(symmetry,[status(thm)],[12948])).
% 28.50/18.70 tff(12950,plain,
% 28.50/18.70 ((~(f7(c2) = c2)) <=> (~(f7(c2) = f5(f7(c2))))),
% 28.50/18.70 inference(monotonicity,[status(thm)],[12949])).
% 28.50/18.70 tff(12951,plain,
% 28.50/18.70 (~(f7(c2) = f5(f7(c2)))),
% 28.50/18.70 inference(modus_ponens,[status(thm)],[17, 12950])).
% 28.50/18.70 tff(12952,plain,
% 28.50/18.70 (c1 = c4),
% 28.50/18.70 inference(unit_resolution,[status(thm)],[12851, 172, 348, 66, 27, 1642])).
% 28.50/18.70 tff(12953,plain,
% 28.50/18.70 (c4 = c1),
% 28.50/18.70 inference(symmetry,[status(thm)],[12952])).
% 28.50/18.70 tff(12954,plain,
% 28.50/18.70 (c4 = f7(c2)),
% 28.50/18.70 inference(transitivity,[status(thm)],[12953, 125])).
% 28.50/18.70 tff(12955,plain,
% 28.50/18.70 ((c2 = c4) <=> (c2 = f7(c2))),
% 28.50/18.70 inference(monotonicity,[status(thm)],[12954])).
% 28.50/18.70 tff(12956,plain,
% 28.50/18.70 ((c2 = c4) <=> (f7(c2) = c2)),
% 28.50/18.70 inference(transitivity,[status(thm)],[12955, 8409])).
% 28.50/18.70 tff(12957,plain,
% 28.50/18.70 ((f7(c2) = c2) <=> (c2 = c4)),
% 28.50/18.70 inference(symmetry,[status(thm)],[12956])).
% 28.50/18.70 tff(12958,plain,
% 28.50/18.70 ((~(f7(c2) = c2)) <=> (~(c2 = c4))),
% 28.50/18.70 inference(monotonicity,[status(thm)],[12957])).
% 28.50/18.70 tff(12959,plain,
% 28.50/18.70 (~(c2 = c4)),
% 28.50/18.70 inference(modus_ponens,[status(thm)],[17, 12958])).
% 28.50/18.70 tff(12960,plain,
% 28.50/18.70 (f8(f7(c2)) = f8(c1)),
% 28.50/18.70 inference(monotonicity,[status(thm)],[292])).
% 28.50/18.70 tff(12961,plain,
% 28.50/18.70 (f8(f7(c2)) = c2),
% 28.50/18.70 inference(transitivity,[status(thm)],[12960, 1643])).
% 28.50/18.70 tff(12962,plain,
% 28.50/18.70 ((f3(c2, c2) = f8(f7(c2))) <=> (f3(c2, c2) = c2)),
% 28.50/18.70 inference(monotonicity,[status(thm)],[12961])).
% 28.50/18.70 tff(12963,plain,
% 28.50/18.70 ((f3(c2, c2) = c2) <=> (f3(c2, c2) = f8(f7(c2)))),
% 28.50/18.70 inference(symmetry,[status(thm)],[12962])).
% 28.50/18.70 tff(12964,plain,
% 28.50/18.70 ((~(f3(c2, c2) = c2)) <=> (~(f3(c2, c2) = f8(f7(c2))))),
% 28.50/18.70 inference(monotonicity,[status(thm)],[12963])).
% 28.50/18.70 tff(12965,plain,
% 28.50/18.70 (~(f3(c2, c2) = f8(f7(c2)))),
% 28.50/18.70 inference(modus_ponens,[status(thm)],[12861, 12964])).
% 28.50/18.70 tff(12966,plain,
% 28.50/18.70 (f10(f7(c2)) = f10(c1)),
% 28.50/18.70 inference(monotonicity,[status(thm)],[292])).
% 28.50/18.70 tff(12967,plain,
% 28.50/18.70 (f10(f7(c2)) = c2),
% 28.50/18.70 inference(transitivity,[status(thm)],[12966, 16])).
% 28.50/18.70 tff(12968,plain,
% 28.50/18.70 (big_f(f3(c2, c2), f10(f7(c2))) <=> big_f(f3(c2, c2), c2)),
% 28.50/18.70 inference(monotonicity,[status(thm)],[12967])).
% 28.50/18.70 tff(12969,plain,
% 28.50/18.70 (big_f(f3(c2, c2), c2) <=> big_f(f3(c2, c2), f10(f7(c2)))),
% 28.50/18.70 inference(symmetry,[status(thm)],[12968])).
% 28.50/18.70 tff(12970,plain,
% 28.50/18.70 (big_f(f3(c2, c2), c2)),
% 28.50/18.70 inference(unit_resolution,[status(thm)],[12903, 12861, 873, 27, 172, 66])).
% 28.50/18.70 tff(12971,plain,
% 28.50/18.70 (big_f(f3(c2, c2), f10(f7(c2)))),
% 28.50/18.70 inference(modus_ponens,[status(thm)],[12970, 12969])).
% 28.50/18.70 tff(12972,plain,
% 28.50/18.70 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(f7(c2)) = f7(c2)) | (f10(f7(c2)) = f7(c2)) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))) | (f3(c2, c2) = f8(f7(c2))) | (~big_f(f3(c2, c2), f10(f7(c2)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(f7(c2)) = f7(c2)) | (f10(f7(c2)) = f7(c2)) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))) | (f3(c2, c2) = f8(f7(c2))) | (~big_f(f3(c2, c2), f10(f7(c2)))))),
% 28.50/18.70 inference(rewrite,[status(thm)],[])).
% 28.50/18.70 tff(12973,plain,
% 28.50/18.70 (((f10(f7(c2)) = f7(c2)) | (f3(c2, c2) = f8(f7(c2))) | (~big_f(f3(c2, c2), f10(f7(c2)))) | (f7(f7(c2)) = f7(c2)) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2)))) <=> ((f7(f7(c2)) = f7(c2)) | (f10(f7(c2)) = f7(c2)) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))) | (f3(c2, c2) = f8(f7(c2))) | (~big_f(f3(c2, c2), f10(f7(c2)))))),
% 28.50/18.70 inference(rewrite,[status(thm)],[])).
% 28.50/18.70 tff(12974,plain,
% 28.50/18.70 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f7(c2)) = f7(c2)) | (f3(c2, c2) = f8(f7(c2))) | (~big_f(f3(c2, c2), f10(f7(c2)))) | (f7(f7(c2)) = f7(c2)) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(f7(c2)) = f7(c2)) | (f10(f7(c2)) = f7(c2)) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))) | (f3(c2, c2) = f8(f7(c2))) | (~big_f(f3(c2, c2), f10(f7(c2))))))),
% 28.50/18.70 inference(monotonicity,[status(thm)],[12973])).
% 28.50/18.70 tff(12975,plain,
% 28.50/18.70 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f7(c2)) = f7(c2)) | (f3(c2, c2) = f8(f7(c2))) | (~big_f(f3(c2, c2), f10(f7(c2)))) | (f7(f7(c2)) = f7(c2)) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(f7(c2)) = f7(c2)) | (f10(f7(c2)) = f7(c2)) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))) | (f3(c2, c2) = f8(f7(c2))) | (~big_f(f3(c2, c2), f10(f7(c2)))))),
% 28.50/18.70 inference(transitivity,[status(thm)],[12974, 12972])).
% 28.50/18.70 tff(12976,plain,
% 28.50/18.70 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f7(c2)) = f7(c2)) | (f3(c2, c2) = f8(f7(c2))) | (~big_f(f3(c2, c2), f10(f7(c2)))) | (f7(f7(c2)) = f7(c2)) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))))),
% 28.50/18.70 inference(quant_inst,[status(thm)],[])).
% 28.50/18.70 tff(12977,plain,
% 28.50/18.70 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(f7(c2)) = f7(c2)) | (f10(f7(c2)) = f7(c2)) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))) | (f3(c2, c2) = f8(f7(c2))) | (~big_f(f3(c2, c2), f10(f7(c2))))),
% 28.50/18.70 inference(modus_ponens,[status(thm)],[12976, 12975])).
% 28.50/18.70 tff(12978,plain,
% 28.50/18.70 ((f3(c2, c2) = f8(f7(c2))) | (~big_f(f3(c2, c2), f10(f7(c2))))),
% 28.50/18.70 inference(unit_resolution,[status(thm)],[12977, 1659, 8473, 10466, 10465, 8523])).
% 28.50/18.70 tff(12979,plain,
% 28.50/18.70 ($false),
% 28.50/18.70 inference(unit_resolution,[status(thm)],[12978, 12971, 12965])).
% 28.50/18.70 tff(12980,plain,((f3(c2, c2) = c2) | (f7(f7(c2)) = f7(c2)) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))) | (f10(f7(c2)) = f7(c2)) | (~(f10(c1) = c2)) | (~(f7(c2) = c1)) | (~(c2 = f8(c1))) | (c2 = c4) | big_f(c1, c2) | (~(c3 = c1)) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 28.50/18.70 tff(12981,plain,
% 28.50/18.70 (f3(c2, c2) = c2),
% 28.50/18.70 inference(unit_resolution,[status(thm)],[12980, 12959, 12951, 10465, 12471, 16, 22, 1642, 8473, 27, 172, 66])).
% 28.50/18.70 tff(12982,plain,
% 28.50/18.70 (big_f(f3(c2, c2), c2) <=> big_f(c2, c2)),
% 28.50/18.70 inference(monotonicity,[status(thm)],[12981])).
% 28.50/18.70 tff(12983,plain,
% 28.50/18.70 (big_f(c2, c2) <=> big_f(f3(c2, c2), c2)),
% 28.50/18.70 inference(symmetry,[status(thm)],[12982])).
% 28.50/18.70 tff(12984,plain,
% 28.50/18.70 (big_f(f3(c2, c2), c2)),
% 28.50/18.70 inference(modus_ponens,[status(thm)],[1345, 12983])).
% 28.50/18.70 tff(12985,plain,
% 28.50/18.70 (f7(c2) = c3),
% 28.50/18.70 inference(transitivity,[status(thm)],[22, 5585])).
% 28.50/18.70 tff(12986,plain,
% 28.50/18.70 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~(f7(c2) = f2(f7(c2)))) | (~(f7(c2) = c3)) | big_f(f7(c2), f7(c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~(f7(c2) = f2(f7(c2)))) | (~(f7(c2) = c3)) | big_f(f7(c2), f7(c2)))),
% 28.50/18.70 inference(rewrite,[status(thm)],[])).
% 28.50/18.70 tff(12987,plain,
% 28.50/18.70 (((~(f7(c2) = c3)) | (~(f7(c2) = f2(f7(c2)))) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | big_f(f7(c2), f7(c2))) <=> ((c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~(f7(c2) = f2(f7(c2)))) | (~(f7(c2) = c3)) | big_f(f7(c2), f7(c2)))),
% 28.50/18.70 inference(rewrite,[status(thm)],[])).
% 28.50/18.70 tff(12988,plain,
% 28.50/18.70 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(f7(c2) = c3)) | (~(f7(c2) = f2(f7(c2)))) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | big_f(f7(c2), f7(c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~(f7(c2) = f2(f7(c2)))) | (~(f7(c2) = c3)) | big_f(f7(c2), f7(c2))))),
% 28.50/18.70 inference(monotonicity,[status(thm)],[12987])).
% 28.50/18.70 tff(12989,plain,
% 28.50/18.70 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(f7(c2) = c3)) | (~(f7(c2) = f2(f7(c2)))) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | big_f(f7(c2), f7(c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~(f7(c2) = f2(f7(c2)))) | (~(f7(c2) = c3)) | big_f(f7(c2), f7(c2)))),
% 28.50/18.70 inference(transitivity,[status(thm)],[12988, 12986])).
% 28.50/18.70 tff(12990,plain,
% 28.50/18.70 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(f7(c2) = c3)) | (~(f7(c2) = f2(f7(c2)))) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | big_f(f7(c2), f7(c2)))),
% 28.50/18.70 inference(quant_inst,[status(thm)],[])).
% 28.50/18.70 tff(12991,plain,
% 28.50/18.70 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~(f7(c2) = f2(f7(c2)))) | (~(f7(c2) = c3)) | big_f(f7(c2), f7(c2))),
% 28.50/18.70 inference(modus_ponens,[status(thm)],[12990, 12989])).
% 28.50/18.70 tff(12992,plain,
% 28.50/18.70 (~(f7(c2) = f2(f7(c2)))),
% 28.50/18.70 inference(unit_resolution,[status(thm)],[12991, 1398, 12959, 12985, 12981, 12984, 12681])).
% 28.50/18.70 tff(12993,plain,
% 28.50/18.70 (~(c1 = f2(c1))),
% 28.50/18.70 inference(modus_ponens,[status(thm)],[12992, 12946])).
% 28.50/18.70 tff(12994,plain,
% 28.50/18.70 ((f7(c2) = c2) <=> (f10(c1) = c4)),
% 28.50/18.70 inference(transitivity,[status(thm)],[12957, 1034])).
% 28.50/18.70 tff(12995,plain,
% 28.50/18.70 ((~(f7(c2) = c2)) <=> (~(f10(c1) = c4))),
% 28.50/18.70 inference(monotonicity,[status(thm)],[12994])).
% 28.50/18.70 tff(12996,plain,
% 28.50/18.70 (~(f10(c1) = c4)),
% 28.50/18.70 inference(modus_ponens,[status(thm)],[17, 12995])).
% 28.50/18.70 tff(12997,plain,
% 28.50/18.70 (big_f(c1, f10(c1)) <=> big_f(c1, c2)),
% 28.50/18.70 inference(monotonicity,[status(thm)],[16])).
% 28.50/18.70 tff(12998,plain,
% 28.50/18.70 (big_f(c1, c2) <=> big_f(c1, f10(c1))),
% 28.50/18.70 inference(symmetry,[status(thm)],[12997])).
% 28.50/18.70 tff(12999,plain,
% 28.50/18.70 ((~big_f(c1, c2)) <=> (~big_f(c1, f10(c1)))),
% 28.50/18.70 inference(monotonicity,[status(thm)],[12998])).
% 28.50/18.70 tff(13000,plain,
% 28.50/18.70 (~big_f(c1, f10(c1))),
% 28.50/18.70 inference(modus_ponens,[status(thm)],[27, 12999])).
% 28.50/18.70 tff(13001,plain,
% 28.50/18.70 (f3(f5(c1), f5(c1)) = f3(c2, c2)),
% 28.50/18.70 inference(monotonicity,[status(thm)],[186, 186])).
% 28.50/18.70 tff(13002,plain,
% 28.50/18.70 (f3(c2, c2) = f3(f5(c1), f5(c1))),
% 28.50/18.70 inference(symmetry,[status(thm)],[13001])).
% 28.50/18.70 tff(13003,plain,
% 28.50/18.70 ((f3(c2, c2) = c2) <=> (f3(f5(c1), f5(c1)) = c2)),
% 28.50/18.70 inference(monotonicity,[status(thm)],[13002])).
% 28.50/18.70 tff(13004,plain,
% 28.50/18.70 (f3(f5(c1), f5(c1)) = c2),
% 28.50/18.70 inference(modus_ponens,[status(thm)],[12981, 13003])).
% 28.50/18.70 tff(13005,assumption,(f3(f5(c1), f5(c1)) = c2), introduced(assumption)).
% 28.50/18.70 tff(13006,plain,
% 28.50/18.70 (f10(c3) = f10(c1)),
% 28.50/18.70 inference(monotonicity,[status(thm)],[172])).
% 28.50/18.70 tff(13007,plain,
% 28.50/18.70 (f10(c3) = f5(c1)),
% 28.50/18.70 inference(transitivity,[status(thm)],[13006, 16, 1761])).
% 28.50/18.70 tff(13008,plain,
% 28.50/18.70 (f3(f10(c3), c2) = f3(f5(c1), f5(c1))),
% 28.50/18.70 inference(monotonicity,[status(thm)],[13007, 1761])).
% 28.50/18.70 tff(13009,plain,
% 28.50/18.70 (f10(c1) = f10(c3)),
% 28.50/18.70 inference(symmetry,[status(thm)],[13006])).
% 28.50/18.70 tff(13010,plain,
% 28.50/18.70 (f3(f10(c1), f10(c1)) = f3(f10(c3), c2)),
% 28.50/18.70 inference(monotonicity,[status(thm)],[13009, 16])).
% 28.50/18.70 tff(13011,plain,
% 28.50/18.70 (f3(f10(c1), f10(c1)) = f10(c1)),
% 28.50/18.70 inference(transitivity,[status(thm)],[13010, 13008, 13005, 293])).
% 28.50/18.70 tff(13012,plain,
% 28.50/18.70 (f3(f10(c1), f10(c1)) = c2),
% 28.50/18.70 inference(transitivity,[status(thm)],[13010, 13008, 13005])).
% 28.50/18.70 tff(13013,plain,
% 28.50/18.70 (big_f(f3(f10(c1), f10(c1)), f10(c1)) <=> big_f(c2, c2)),
% 28.50/18.70 inference(monotonicity,[status(thm)],[13012, 16])).
% 28.50/18.70 tff(13014,plain,
% 28.50/18.70 (big_f(c2, c2) <=> big_f(f3(f10(c1), f10(c1)), f10(c1))),
% 28.50/18.70 inference(symmetry,[status(thm)],[13013])).
% 28.50/18.70 tff(13015,plain,
% 28.50/18.70 (big_f(f3(f10(c1), f10(c1)), f10(c1))),
% 28.50/18.70 inference(modus_ponens,[status(thm)],[1345, 13014])).
% 28.50/18.70 tff(13016,plain,
% 28.50/18.70 (c2 = f2(c3)),
% 28.50/18.70 inference(symmetry,[status(thm)],[1319])).
% 28.50/18.70 tff(13017,plain,
% 28.50/18.70 (f10(c1) = f2(c1)),
% 28.50/18.70 inference(transitivity,[status(thm)],[16, 13016, 5589])).
% 28.50/18.70 tff(13018,plain,
% 28.50/18.70 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (f10(c1) = c4) | (~(f10(c1) = f2(c1))) | big_f(c1, f10(c1)) | (~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (~(c1 = c3)) | (f10(c1) = c4) | (~(f10(c1) = f2(c1))) | big_f(c1, f10(c1)) | (~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))))),
% 28.50/18.70 inference(rewrite,[status(thm)],[])).
% 28.50/18.70 tff(13019,plain,
% 28.50/18.70 (((~(c1 = c3)) | (~(f10(c1) = f2(c1))) | (f10(c1) = c4) | (~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))) | big_f(c1, f10(c1))) <=> ((~(c1 = c3)) | (f10(c1) = c4) | (~(f10(c1) = f2(c1))) | big_f(c1, f10(c1)) | (~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))))),
% 28.50/18.70 inference(rewrite,[status(thm)],[])).
% 28.50/18.70 tff(13020,plain,
% 28.50/18.70 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(f10(c1) = f2(c1))) | (f10(c1) = c4) | (~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))) | big_f(c1, f10(c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (f10(c1) = c4) | (~(f10(c1) = f2(c1))) | big_f(c1, f10(c1)) | (~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1)))))),
% 28.50/18.70 inference(monotonicity,[status(thm)],[13019])).
% 28.50/18.70 tff(13021,plain,
% 28.50/18.70 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(f10(c1) = f2(c1))) | (f10(c1) = c4) | (~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))) | big_f(c1, f10(c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (~(c1 = c3)) | (f10(c1) = c4) | (~(f10(c1) = f2(c1))) | big_f(c1, f10(c1)) | (~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))))),
% 28.50/18.70 inference(transitivity,[status(thm)],[13020, 13018])).
% 28.50/18.70 tff(13022,plain,
% 28.50/18.70 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(f10(c1) = f2(c1))) | (f10(c1) = c4) | (~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))) | big_f(c1, f10(c1)))),
% 28.50/18.70 inference(quant_inst,[status(thm)],[])).
% 28.50/18.70 tff(13023,plain,
% 28.50/18.70 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (~(c1 = c3)) | (f10(c1) = c4) | (~(f10(c1) = f2(c1))) | big_f(c1, f10(c1)) | (~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1)))),
% 28.50/18.70 inference(modus_ponens,[status(thm)],[13022, 13021])).
% 28.50/18.70 tff(13024,plain,
% 28.50/18.70 ((~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1)))),
% 28.50/18.70 inference(unit_resolution,[status(thm)],[13023, 1398, 5611, 3030, 1046, 13017])).
% 28.50/18.70 tff(13025,plain,
% 28.50/18.70 ($false),
% 28.50/18.70 inference(unit_resolution,[status(thm)],[13024, 13015, 13011])).
% 28.50/18.70 tff(13026,plain,((~(f3(f5(c1), f5(c1)) = c2)) | big_f(c1, f10(c1)) | (f10(c1) = c4) | (~big_f(c2, c2)) | (~(f10(c1) = c2)) | (~(f5(c1) = c2)) | (~(c3 = c1)) | (~(f2(c3) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.50/18.70 tff(13027,plain,
% 28.50/18.70 (~(f2(c3) = c2)),
% 28.50/18.70 inference(unit_resolution,[status(thm)],[13026, 13004, 186, 1345, 172, 16, 13000, 12996])).
% 28.50/18.70 tff(13028,plain,
% 28.50/18.70 (f2(c3) = c1),
% 28.50/18.70 inference(unit_resolution,[status(thm)],[1273, 13027])).
% 28.50/18.70 tff(13029,plain,
% 28.50/18.70 (c1 = f2(c1)),
% 28.50/18.70 inference(unit_resolution,[status(thm)],[6771, 13028, 172])).
% 28.50/18.70 tff(13030,plain,
% 28.50/18.70 ($false),
% 28.50/18.70 inference(unit_resolution,[status(thm)],[13029, 12993])).
% 28.50/18.70 tff(13031,plain,((~(c3 = c1)) | (~(f5(c1) = c2)) | (~big_f(c2, c2)) | (~(f10(c1) = c2)) | (~big_f(f7(f7(c2)), f7(c2))) | (~(c2 = f8(c1))) | (f7(f7(c2)) = f7(c2)) | big_f(c1, c2) | big_f(c1, c1) | (f7(c2) = c2) | (~big_f(c2, c1))), inference(lemma,lemma(discharge,[]))).
% 28.50/18.70 tff(13032,plain,
% 28.50/18.70 (~(f5(c1) = c2)),
% 28.50/18.70 inference(unit_resolution,[status(thm)],[13031, 172, 12943, 15, 1345, 12938, 1642, 27, 66, 17, 348])).
% 28.50/18.70 tff(13033,plain,
% 28.50/18.70 ($false),
% 28.50/18.70 inference(unit_resolution,[status(thm)],[13032, 12937])).
% 28.50/18.70 tff(13034,plain,((~(c3 = c1)) | (~big_f(c2, c2)) | (~(c2 = f8(c1))) | big_f(c1, c2) | big_f(c1, c1) | (f7(c2) = c2) | (~big_f(c2, c1)) | (f7(c1) = c1) | (f10(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 28.50/18.70 tff(13035,plain,
% 28.50/18.70 (~(c3 = c1)),
% 28.50/18.70 inference(unit_resolution,[status(thm)],[13034, 12773, 12442, 27, 12768, 17, 12763, 115, 3])).
% 28.50/18.70 tff(13036,plain,
% 28.50/18.70 (c3 = c2),
% 28.50/18.70 inference(unit_resolution,[status(thm)],[180, 13035])).
% 28.50/18.70 tff(13037,plain,
% 28.50/18.70 (big_f(c2, c1) <=> big_f(c2, f10(c2))),
% 28.50/18.70 inference(transitivity,[status(thm)],[9312, 12712])).
% 28.50/18.70 tff(13038,plain,
% 28.50/18.70 (big_f(c2, f10(c2))),
% 28.50/18.70 inference(modus_ponens,[status(thm)],[12763, 13037])).
% 28.50/18.70 tff(13039,plain,
% 28.50/18.70 (c2 = f8(c2)),
% 28.50/18.70 inference(unit_resolution,[status(thm)],[12510, 13038, 11797, 12943, 17, 12443, 12764])).
% 28.50/18.70 tff(13040,plain,
% 28.50/18.70 (big_f(c1, f10(c2)) <=> big_f(c1, c1)),
% 28.50/18.70 inference(monotonicity,[status(thm)],[12229])).
% 28.50/18.70 tff(13041,plain,
% 28.50/18.70 (big_f(c1, c1) <=> big_f(c1, f10(c2))),
% 28.50/18.70 inference(symmetry,[status(thm)],[13040])).
% 28.50/18.70 tff(13042,plain,
% 28.50/18.70 ((~big_f(c1, c1)) <=> (~big_f(c1, f10(c2)))),
% 28.50/18.70 inference(monotonicity,[status(thm)],[13041])).
% 28.50/18.70 tff(13043,plain,
% 28.50/18.70 (~big_f(c1, f10(c2))),
% 28.50/18.70 inference(modus_ponens,[status(thm)],[66, 13042])).
% 28.50/18.70 tff(13044,plain,
% 28.50/18.70 ((f8(c2) = c1) <=> (c1 = f8(c2))),
% 28.50/18.70 inference(commutativity,[status(thm)],[])).
% 28.50/18.70 tff(13045,plain,
% 28.50/18.70 (f8(c3) = f8(c2)),
% 28.50/18.70 inference(monotonicity,[status(thm)],[67])).
% 28.50/18.70 tff(13046,plain,
% 28.50/18.70 ((f8(c3) = c1) <=> (f8(c2) = c1)),
% 28.50/18.70 inference(monotonicity,[status(thm)],[13045])).
% 28.50/18.70 tff(13047,plain,
% 28.50/18.70 ((f8(c3) = c1) <=> (c1 = f8(c2))),
% 28.50/18.70 inference(transitivity,[status(thm)],[13046, 13044])).
% 28.50/18.70 tff(13048,plain,
% 28.50/18.70 ((c1 = f8(c2)) <=> (f8(c3) = c1)),
% 28.50/18.70 inference(symmetry,[status(thm)],[13047])).
% 28.50/18.70 tff(13049,plain,
% 28.50/18.70 ((~(c1 = f8(c2))) <=> (~(f8(c3) = c1))),
% 28.50/18.70 inference(monotonicity,[status(thm)],[13048])).
% 28.50/18.70 tff(13050,plain,
% 28.50/18.70 (big_f(c2, c2)),
% 28.50/18.70 inference(unit_resolution,[status(thm)],[8259, 2, 67, 79])).
% 28.50/18.70 tff(13051,plain,
% 28.50/18.70 (big_f(f7(c1), c2)),
% 28.50/18.70 inference(modus_ponens,[status(thm)],[13050, 1724])).
% 28.50/18.70 tff(13052,plain,
% 28.50/18.70 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((c2 = f5(c1)) | (f7(c1) = c1) | (f10(c2) = c2) | (~big_f(f7(c1), c2)) | big_f(c1, f10(c2)) | (~(c1 = f8(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | (c2 = f5(c1)) | (f7(c1) = c1) | (f10(c2) = c2) | (~big_f(f7(c1), c2)) | big_f(c1, f10(c2)) | (~(c1 = f8(c2))))),
% 28.50/18.70 inference(rewrite,[status(thm)],[])).
% 28.50/18.70 tff(13053,plain,
% 28.50/18.70 (((f10(c2) = c2) | big_f(c1, f10(c2)) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)) | (~(c1 = f8(c2)))) <=> ((c2 = f5(c1)) | (f7(c1) = c1) | (f10(c2) = c2) | (~big_f(f7(c1), c2)) | big_f(c1, f10(c2)) | (~(c1 = f8(c2))))),
% 28.50/18.70 inference(rewrite,[status(thm)],[])).
% 28.50/18.70 tff(13054,plain,
% 28.50/18.70 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | big_f(c1, f10(c2)) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)) | (~(c1 = f8(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((c2 = f5(c1)) | (f7(c1) = c1) | (f10(c2) = c2) | (~big_f(f7(c1), c2)) | big_f(c1, f10(c2)) | (~(c1 = f8(c2)))))),
% 28.50/18.71 inference(monotonicity,[status(thm)],[13053])).
% 28.50/18.71 tff(13055,plain,
% 28.50/18.71 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | big_f(c1, f10(c2)) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)) | (~(c1 = f8(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | (c2 = f5(c1)) | (f7(c1) = c1) | (f10(c2) = c2) | (~big_f(f7(c1), c2)) | big_f(c1, f10(c2)) | (~(c1 = f8(c2))))),
% 28.50/18.71 inference(transitivity,[status(thm)],[13054, 13052])).
% 28.50/18.71 tff(13056,plain,
% 28.50/18.71 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | big_f(c1, f10(c2)) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)) | (~(c1 = f8(c2))))),
% 28.50/18.71 inference(quant_inst,[status(thm)],[])).
% 28.50/18.71 tff(13057,plain,
% 28.50/18.71 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | (c2 = f5(c1)) | (f7(c1) = c1) | (f10(c2) = c2) | (~big_f(f7(c1), c2)) | big_f(c1, f10(c2)) | (~(c1 = f8(c2)))),
% 28.50/18.71 inference(modus_ponens,[status(thm)],[13056, 13055])).
% 28.50/18.71 tff(13058,plain,
% 28.50/18.71 (~(c1 = f8(c2))),
% 28.50/18.71 inference(unit_resolution,[status(thm)],[13057, 2795, 12775, 13051, 115, 89, 12055])).
% 28.50/18.71 tff(13059,plain,
% 28.50/18.71 (~(f8(c3) = c1)),
% 28.50/18.71 inference(modus_ponens,[status(thm)],[13058, 13049])).
% 28.50/18.71 tff(13060,plain,
% 28.50/18.71 ((f8(c3) = c2) <=> (f8(c2) = c2)),
% 28.50/18.71 inference(monotonicity,[status(thm)],[13045])).
% 28.50/18.71 tff(13061,plain,
% 28.50/18.71 ((f8(c3) = c2) <=> (c2 = f8(c2))),
% 28.50/18.71 inference(transitivity,[status(thm)],[13060, 11998])).
% 28.50/18.71 tff(13062,plain,
% 28.50/18.71 ((c2 = f8(c2)) <=> (f8(c3) = c2)),
% 28.50/18.71 inference(symmetry,[status(thm)],[13061])).
% 28.50/18.71 tff(13063,plain,
% 28.50/18.71 ((~(c2 = f8(c2))) <=> (~(f8(c3) = c2))),
% 28.50/18.71 inference(monotonicity,[status(thm)],[13062])).
% 28.50/18.71 tff(13064,plain,
% 28.50/18.71 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((c2 = f5(c1)) | (f7(c1) = c1) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (~big_f(f7(c1), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | (c2 = f5(c1)) | (f7(c1) = c1) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (~big_f(f7(c1), c2)))),
% 28.50/18.71 inference(rewrite,[status(thm)],[])).
% 28.50/18.71 tff(13065,plain,
% 28.50/18.71 (((f10(c2) = c2) | big_f(c2, f10(c2)) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)) | (~(c2 = f8(c2)))) <=> ((c2 = f5(c1)) | (f7(c1) = c1) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (~big_f(f7(c1), c2)))),
% 28.50/18.71 inference(rewrite,[status(thm)],[])).
% 28.50/18.71 tff(13066,plain,
% 28.50/18.71 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | big_f(c2, f10(c2)) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)) | (~(c2 = f8(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((c2 = f5(c1)) | (f7(c1) = c1) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (~big_f(f7(c1), c2))))),
% 28.50/18.71 inference(monotonicity,[status(thm)],[13065])).
% 28.50/18.71 tff(13067,plain,
% 28.50/18.71 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | big_f(c2, f10(c2)) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)) | (~(c2 = f8(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | (c2 = f5(c1)) | (f7(c1) = c1) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (~big_f(f7(c1), c2)))),
% 28.50/18.71 inference(transitivity,[status(thm)],[13066, 13064])).
% 28.50/18.71 tff(13068,plain,
% 28.50/18.71 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | big_f(c2, f10(c2)) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)) | (~(c2 = f8(c2))))),
% 28.50/18.71 inference(quant_inst,[status(thm)],[])).
% 28.50/18.71 tff(13069,plain,
% 28.50/18.71 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | (c2 = f5(c1)) | (f7(c1) = c1) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (~big_f(f7(c1), c2))),
% 28.50/18.71 inference(modus_ponens,[status(thm)],[13068, 13067])).
% 28.50/18.71 tff(13070,plain,
% 28.50/18.71 (~(c2 = f8(c2))),
% 28.50/18.71 inference(unit_resolution,[status(thm)],[13069, 2795, 12775, 13051, 115, 89, 12071])).
% 28.50/18.71 tff(13071,plain,
% 28.50/18.71 (~(f8(c3) = c2)),
% 28.50/18.71 inference(modus_ponens,[status(thm)],[13070, 13063])).
% 28.50/18.71 tff(13072,plain,
% 28.50/18.71 ($false),
% 28.50/18.71 inference(unit_resolution,[status(thm)],[8569, 13071, 13059])).
% 28.50/18.71 tff(13073,plain,(big_f(c2, c1) | (~(c3 = c2)) | (c2 = f5(c1)) | (f7(c1) = c1) | (f10(c2) = c2) | big_f(c1, f10(c2)) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.50/18.71 tff(13074,plain,
% 28.50/18.71 (big_f(c2, c1)),
% 28.50/18.71 inference(unit_resolution,[status(thm)],[13073, 67, 12775, 115, 11797, 13043, 79])).
% 28.50/18.71 tff(13075,plain,
% 28.50/18.71 ((f7(c2) = c3) <=> (c1 = c3)),
% 28.50/18.71 inference(monotonicity,[status(thm)],[22])).
% 28.50/18.71 tff(13076,plain,
% 28.50/18.71 ((c1 = c3) <=> (f7(c2) = c3)),
% 28.50/18.71 inference(symmetry,[status(thm)],[13075])).
% 28.50/18.71 tff(13077,plain,
% 28.50/18.71 ((c1 = c3) <=> (c1 = c2)),
% 28.50/18.71 inference(monotonicity,[status(thm)],[67])).
% 28.50/18.71 tff(13078,plain,
% 28.50/18.71 ((c1 = c3) <=> (c2 = c1)),
% 28.50/18.71 inference(transitivity,[status(thm)],[13077, 1])).
% 28.50/18.71 tff(13079,plain,
% 28.50/18.71 ((c2 = c1) <=> (c1 = c3)),
% 28.50/18.71 inference(symmetry,[status(thm)],[13078])).
% 28.50/18.71 tff(13080,plain,
% 28.50/18.71 ((c2 = c1) <=> (f7(c2) = c3)),
% 28.50/18.71 inference(transitivity,[status(thm)],[13079, 13076])).
% 28.50/18.71 tff(13081,plain,
% 28.50/18.71 ((~(c2 = c1)) <=> (~(f7(c2) = c3))),
% 28.50/18.71 inference(monotonicity,[status(thm)],[13080])).
% 28.50/18.71 tff(13082,plain,
% 28.50/18.71 (~(f7(c2) = c3)),
% 28.50/18.71 inference(modus_ponens,[status(thm)],[75, 13081])).
% 28.50/18.71 tff(13083,plain,
% 28.50/18.71 ((~big_f(c1, c1)) <=> (~big_f(f7(c2), c1))),
% 28.50/18.71 inference(monotonicity,[status(thm)],[9487])).
% 28.50/18.71 tff(13084,plain,
% 28.50/18.71 (~big_f(f7(c2), c1)),
% 28.50/18.71 inference(modus_ponens,[status(thm)],[66, 13083])).
% 28.50/18.71 tff(13085,plain,
% 28.50/18.71 ((~(c2 = c1)) <=> (~(c1 = c3))),
% 28.50/18.71 inference(monotonicity,[status(thm)],[13079])).
% 28.50/18.71 tff(13086,plain,
% 28.50/18.71 (~(c1 = c3)),
% 28.50/18.71 inference(modus_ponens,[status(thm)],[75, 13085])).
% 28.50/18.71 tff(13087,plain,
% 28.50/18.71 (big_f(c2, c2)),
% 28.50/18.71 inference(unit_resolution,[status(thm)],[12154, 13086, 17, 13084, 79, 3, 13082, 120])).
% 28.50/18.71 tff(13088,plain,
% 28.50/18.71 (f8(c1) = c2),
% 28.50/18.71 inference(symmetry,[status(thm)],[12776])).
% 28.52/18.71 tff(13089,plain,
% 28.52/18.71 ((f3(c2, c2) = f8(c1)) <=> (f3(c2, c2) = c2)),
% 28.52/18.71 inference(monotonicity,[status(thm)],[13088])).
% 28.52/18.71 tff(13090,plain,
% 28.52/18.71 ((f3(c2, c2) = c2) <=> (f3(c2, c2) = f8(c1))),
% 28.52/18.71 inference(symmetry,[status(thm)],[13089])).
% 28.52/18.71 tff(13091,plain,
% 28.52/18.71 ((~(f3(c2, c2) = c2)) <=> (~(f3(c2, c2) = f8(c1)))),
% 28.52/18.71 inference(monotonicity,[status(thm)],[13090])).
% 28.52/18.71 tff(13092,plain,
% 28.52/18.71 (~(f3(c2, c2) = f8(c1))),
% 28.52/18.71 inference(modus_ponens,[status(thm)],[12861, 13091])).
% 28.52/18.71 tff(13093,plain,
% 28.52/18.71 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = c4) | (c1 = f2(c2)) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2) | (~big_f(c2, c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = c4) | (c1 = f2(c2)) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2) | (~big_f(c2, c1)))),
% 28.52/18.71 inference(rewrite,[status(thm)],[])).
% 28.52/18.71 tff(13094,plain,
% 28.52/18.71 (((~(c2 = c3)) | (c2 = c4) | (f3(c2, c2) = c2) | big_f(f3(c2, c2), c2) | (c1 = f2(c2)) | (~big_f(c2, c1))) <=> ((~(c2 = c3)) | (c2 = c4) | (c1 = f2(c2)) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2) | (~big_f(c2, c1)))),
% 28.52/18.71 inference(rewrite,[status(thm)],[])).
% 28.52/18.71 tff(13095,plain,
% 28.52/18.71 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = c4) | (f3(c2, c2) = c2) | big_f(f3(c2, c2), c2) | (c1 = f2(c2)) | (~big_f(c2, c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = c4) | (c1 = f2(c2)) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2) | (~big_f(c2, c1))))),
% 28.52/18.71 inference(monotonicity,[status(thm)],[13094])).
% 28.52/18.71 tff(13096,plain,
% 28.52/18.71 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = c4) | (f3(c2, c2) = c2) | big_f(f3(c2, c2), c2) | (c1 = f2(c2)) | (~big_f(c2, c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = c4) | (c1 = f2(c2)) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2) | (~big_f(c2, c1)))),
% 28.52/18.71 inference(transitivity,[status(thm)],[13095, 13093])).
% 28.52/18.71 tff(13097,plain,
% 28.52/18.71 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = c4) | (f3(c2, c2) = c2) | big_f(f3(c2, c2), c2) | (c1 = f2(c2)) | (~big_f(c2, c1)))),
% 28.52/18.71 inference(quant_inst,[status(thm)],[])).
% 28.52/18.71 tff(13098,plain,
% 28.52/18.71 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = c4) | (c1 = f2(c2)) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2) | (~big_f(c2, c1))),
% 28.52/18.71 inference(modus_ponens,[status(thm)],[13097, 13096])).
% 28.52/18.71 tff(13099,plain,
% 28.52/18.71 (c1 = f2(c2)),
% 28.52/18.71 inference(unit_resolution,[status(thm)],[13098, 7352, 873, 1344, 348, 12861, 12882])).
% 28.52/18.71 tff(13100,plain,
% 28.52/18.71 (f2(c2) = c1),
% 28.52/18.71 inference(symmetry,[status(thm)],[13099])).
% 28.52/18.71 tff(13101,plain,
% 28.52/18.71 (c2 = c1),
% 28.52/18.71 inference(transitivity,[status(thm)],[2853, 13100])).
% 28.52/18.71 tff(13102,plain,
% 28.52/18.71 ($false),
% 28.52/18.71 inference(unit_resolution,[status(thm)],[75, 13101])).
% 28.52/18.71 tff(13103,plain,((~(c2 = f2(c2))) | (c2 = c4) | (~(c2 = c3)) | (~big_f(c2, c1)) | (f3(c2, c2) = c2) | big_f(f3(c2, c2), c2)), inference(lemma,lemma(discharge,[]))).
% 28.52/18.71 tff(13104,plain,
% 28.52/18.71 (~(c2 = f2(c2))),
% 28.52/18.71 inference(unit_resolution,[status(thm)],[13103, 12882, 1344, 348, 12861, 873])).
% 28.52/18.71 tff(13105,plain,
% 28.52/18.71 ($false),
% 28.52/18.71 inference(unit_resolution,[status(thm)],[7401, 7352, 873, 1345, 1344, 13104, 12861, 12882])).
% 28.52/18.71 tff(13106,plain,(big_f(f3(c2, c2), c2) | (c2 = c4) | (~big_f(c2, c2)) | (~(c2 = c3)) | (f3(c2, c2) = c2) | (~big_f(c2, c1))), inference(lemma,lemma(discharge,[]))).
% 28.52/18.71 tff(13107,plain,
% 28.52/18.71 (big_f(f3(c2, c2), c2)),
% 28.52/18.71 inference(unit_resolution,[status(thm)],[13106, 12861, 1345, 1344, 873, 348])).
% 28.52/18.71 tff(13108,plain,
% 28.52/18.71 (big_f(f3(c2, c2), f10(c1))),
% 28.52/18.71 inference(modus_ponens,[status(thm)],[13107, 12864])).
% 28.52/18.71 tff(13109,plain,
% 28.52/18.71 ($false),
% 28.52/18.71 inference(unit_resolution,[status(thm)],[12911, 1659, 12775, 12774, 115, 3, 13108, 13092])).
% 28.52/18.71 tff(13110,plain,((f3(c2, c2) = c2) | (c2 = f5(c1)) | (f7(c1) = c1) | (f10(c1) = c1) | (~big_f(c2, c2)) | (~(c2 = c3)) | (c2 = c4) | (~big_f(c2, c1))), inference(lemma,lemma(discharge,[]))).
% 28.52/18.71 tff(13111,plain,
% 28.52/18.71 (f3(c2, c2) = c2),
% 28.52/18.71 inference(unit_resolution,[status(thm)],[13110, 873, 115, 3, 1345, 1344, 12775, 348])).
% 28.52/18.71 tff(13112,plain,
% 28.52/18.71 (big_f(f3(c2, c2), c2) <=> big_f(c2, c2)),
% 28.52/18.71 inference(monotonicity,[status(thm)],[13111])).
% 28.52/18.71 tff(13113,plain,
% 28.52/18.71 (big_f(c2, c2) <=> big_f(f3(c2, c2), c2)),
% 28.52/18.71 inference(symmetry,[status(thm)],[13112])).
% 28.52/18.71 tff(13114,plain,
% 28.52/18.71 (big_f(f3(c2, c2), c2)),
% 28.52/18.71 inference(modus_ponens,[status(thm)],[1345, 13113])).
% 28.52/18.71 tff(13115,plain,
% 28.52/18.71 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = c4) | (c1 = f2(c2)) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~big_f(c2, c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = c4) | (c1 = f2(c2)) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~big_f(c2, c1)))),
% 28.52/18.71 inference(rewrite,[status(thm)],[])).
% 28.52/18.71 tff(13116,plain,
% 28.52/18.71 (((~(c2 = c3)) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (c1 = f2(c2)) | (~big_f(c2, c1))) <=> ((~(c2 = c3)) | (c2 = c4) | (c1 = f2(c2)) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~big_f(c2, c1)))),
% 28.52/18.71 inference(rewrite,[status(thm)],[])).
% 28.52/18.71 tff(13117,plain,
% 28.52/18.71 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (c1 = f2(c2)) | (~big_f(c2, c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = c4) | (c1 = f2(c2)) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~big_f(c2, c1))))),
% 28.52/18.71 inference(monotonicity,[status(thm)],[13116])).
% 28.52/18.71 tff(13118,plain,
% 28.52/18.71 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (c1 = f2(c2)) | (~big_f(c2, c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = c4) | (c1 = f2(c2)) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~big_f(c2, c1)))),
% 28.52/18.71 inference(transitivity,[status(thm)],[13117, 13115])).
% 28.52/18.71 tff(13119,plain,
% 28.52/18.71 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (c1 = f2(c2)) | (~big_f(c2, c1)))),
% 28.52/18.71 inference(quant_inst,[status(thm)],[])).
% 28.52/18.71 tff(13120,plain,
% 28.52/18.71 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = c4) | (c1 = f2(c2)) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~big_f(c2, c1))),
% 28.52/18.71 inference(modus_ponens,[status(thm)],[13119, 13118])).
% 28.52/18.71 tff(13121,plain,
% 28.52/18.71 (c1 = f2(c2)),
% 28.52/18.71 inference(unit_resolution,[status(thm)],[13120, 7051, 873, 1344, 348, 13111, 13114])).
% 28.52/18.71 tff(13122,plain,
% 28.52/18.71 (f2(c2) = c1),
% 28.52/18.71 inference(symmetry,[status(thm)],[13121])).
% 28.52/18.71 tff(13123,plain,
% 28.52/18.71 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = f2(c2)) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = f2(c2)) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~big_f(c2, c2)))),
% 28.52/18.71 inference(rewrite,[status(thm)],[])).
% 28.52/18.71 tff(13124,plain,
% 28.52/18.71 (((~(c2 = c3)) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (c2 = f2(c2)) | (~big_f(c2, c2))) <=> ((~(c2 = c3)) | (c2 = f2(c2)) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~big_f(c2, c2)))),
% 28.52/18.71 inference(rewrite,[status(thm)],[])).
% 28.52/18.71 tff(13125,plain,
% 28.52/18.71 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (c2 = f2(c2)) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = f2(c2)) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~big_f(c2, c2))))),
% 28.52/18.71 inference(monotonicity,[status(thm)],[13124])).
% 28.52/18.71 tff(13126,plain,
% 28.52/18.71 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (c2 = f2(c2)) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = f2(c2)) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~big_f(c2, c2)))),
% 28.52/18.71 inference(transitivity,[status(thm)],[13125, 13123])).
% 28.52/18.71 tff(13127,plain,
% 28.52/18.71 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (c2 = f2(c2)) | (~big_f(c2, c2)))),
% 28.52/18.71 inference(quant_inst,[status(thm)],[])).
% 28.52/18.71 tff(13128,plain,
% 28.52/18.71 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = f2(c2)) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~big_f(c2, c2))),
% 28.52/18.71 inference(modus_ponens,[status(thm)],[13127, 13126])).
% 28.52/18.71 tff(13129,plain,
% 28.52/18.71 (c2 = f2(c2)),
% 28.52/18.71 inference(unit_resolution,[status(thm)],[13128, 7051, 873, 1345, 1344, 13111, 13114])).
% 28.52/18.71 tff(13130,plain,
% 28.52/18.71 (c2 = c1),
% 28.52/18.71 inference(transitivity,[status(thm)],[13129, 13122])).
% 28.52/18.71 tff(13131,plain,
% 28.52/18.71 ($false),
% 28.52/18.71 inference(unit_resolution,[status(thm)],[75, 13130])).
% 28.52/18.71 tff(13132,plain,((c2 = c4) | (~(c2 = c3)) | (~big_f(c2, c1)) | (~big_f(c2, c2)) | (f7(c1) = c1) | (f10(c1) = c1) | (c2 = f5(c1))), inference(lemma,lemma(discharge,[]))).
% 28.52/18.71 tff(13133,plain,
% 28.52/18.71 (c2 = c4),
% 28.52/18.71 inference(unit_resolution,[status(thm)],[13132, 13087, 1335, 13074, 115, 3, 12775])).
% 28.52/18.71 tff(13134,plain,
% 28.52/18.71 (c4 = c2),
% 28.52/18.71 inference(symmetry,[status(thm)],[13133])).
% 28.52/18.71 tff(13135,plain,
% 28.52/18.71 ((c1 = c4) <=> (c1 = c2)),
% 28.52/18.71 inference(monotonicity,[status(thm)],[13134])).
% 28.52/18.71 tff(13136,plain,
% 28.52/18.71 ((c1 = c4) <=> (c2 = c1)),
% 28.52/18.71 inference(transitivity,[status(thm)],[13135, 1])).
% 28.52/18.71 tff(13137,plain,
% 28.52/18.71 ((c2 = c1) <=> (c1 = c4)),
% 28.52/18.71 inference(symmetry,[status(thm)],[13136])).
% 28.52/18.71 tff(13138,plain,
% 28.52/18.71 ((~(c2 = c1)) <=> (~(c1 = c4))),
% 28.52/18.71 inference(monotonicity,[status(thm)],[13137])).
% 28.52/18.71 tff(13139,plain,
% 28.52/18.71 (~(c1 = c4)),
% 28.52/18.71 inference(modus_ponens,[status(thm)],[75, 13138])).
% 28.52/18.71 tff(13140,plain,
% 28.52/18.71 (big_f(c2, f10(c2)) <=> big_f(c2, c1)),
% 28.52/18.71 inference(monotonicity,[status(thm)],[12229])).
% 28.52/18.71 tff(13141,plain,
% 28.52/18.71 (big_f(c2, c1) <=> big_f(c2, f10(c2))),
% 28.52/18.71 inference(symmetry,[status(thm)],[13140])).
% 28.52/18.71 tff(13142,plain,
% 28.52/18.71 (big_f(c2, f10(c2))),
% 28.52/18.71 inference(modus_ponens,[status(thm)],[13074, 13141])).
% 28.52/18.71 tff(13143,plain,
% 28.52/18.71 (big_f(f7(c1), c2)),
% 28.52/18.71 inference(modus_ponens,[status(thm)],[13087, 1724])).
% 28.52/18.71 tff(13144,plain,
% 28.52/18.71 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((c2 = f5(c1)) | (f7(c1) = c1) | (f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(f7(c1), c2)) | (~big_f(c2, f10(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (c2 = f5(c1)) | (f7(c1) = c1) | (f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(f7(c1), c2)) | (~big_f(c2, f10(c2))))),
% 28.52/18.72 inference(rewrite,[status(thm)],[])).
% 28.52/18.72 tff(13145,plain,
% 28.52/18.72 (((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2))) <=> ((c2 = f5(c1)) | (f7(c1) = c1) | (f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(f7(c1), c2)) | (~big_f(c2, f10(c2))))),
% 28.52/18.72 inference(rewrite,[status(thm)],[])).
% 28.52/18.72 tff(13146,plain,
% 28.52/18.72 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((c2 = f5(c1)) | (f7(c1) = c1) | (f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(f7(c1), c2)) | (~big_f(c2, f10(c2)))))),
% 28.52/18.72 inference(monotonicity,[status(thm)],[13145])).
% 28.52/18.72 tff(13147,plain,
% 28.52/18.72 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (c2 = f5(c1)) | (f7(c1) = c1) | (f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(f7(c1), c2)) | (~big_f(c2, f10(c2))))),
% 28.52/18.72 inference(transitivity,[status(thm)],[13146, 13144])).
% 28.52/18.72 tff(13148,plain,
% 28.52/18.72 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)))),
% 28.52/18.72 inference(quant_inst,[status(thm)],[])).
% 28.52/18.72 tff(13149,plain,
% 28.52/18.72 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (c2 = f5(c1)) | (f7(c1) = c1) | (f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(f7(c1), c2)) | (~big_f(c2, f10(c2)))),
% 28.52/18.72 inference(modus_ponens,[status(thm)],[13148, 13147])).
% 28.52/18.72 tff(13150,plain,
% 28.52/18.72 (c2 = f8(c2)),
% 28.52/18.72 inference(unit_resolution,[status(thm)],[13149, 1659, 12775, 13143, 115, 11797, 13142])).
% 28.52/18.72 tff(13151,plain,
% 28.52/18.72 ((f3(c1, c2) = c1) <=> (c1 = f3(c1, c2))),
% 28.52/18.72 inference(commutativity,[status(thm)],[])).
% 28.52/18.72 tff(13152,assumption,(c2 = f8(c2)), introduced(assumption)).
% 28.52/18.72 tff(13153,plain,
% 28.52/18.72 (f8(c2) = c2),
% 28.52/18.72 inference(symmetry,[status(thm)],[13152])).
% 28.52/18.72 tff(13154,plain,
% 28.52/18.72 (f8(c3) = c2),
% 28.52/18.72 inference(transitivity,[status(thm)],[13045, 13153])).
% 28.52/18.72 tff(13155,plain,
% 28.52/18.72 (f3(c1, f8(c3)) = f3(c1, c2)),
% 28.52/18.72 inference(monotonicity,[status(thm)],[13154])).
% 28.52/18.72 tff(13156,plain,
% 28.52/18.72 ((f3(c1, f8(c3)) = c1) <=> (f3(c1, c2) = c1)),
% 28.52/18.72 inference(monotonicity,[status(thm)],[13155])).
% 28.52/18.72 tff(13157,plain,
% 28.52/18.72 ((f3(c1, f8(c3)) = c1) <=> (c1 = f3(c1, c2))),
% 28.52/18.72 inference(transitivity,[status(thm)],[13156, 13151])).
% 28.52/18.72 tff(13158,plain,
% 28.52/18.72 ((f3(c1, f8(c3)) = c2) <=> (f3(c1, c2) = c2)),
% 28.52/18.72 inference(monotonicity,[status(thm)],[13155])).
% 28.52/18.72 tff(13159,plain,
% 28.52/18.72 ((f3(c1, c2) = c2) <=> (f3(c1, f8(c3)) = c2)),
% 28.52/18.72 inference(symmetry,[status(thm)],[13158])).
% 28.52/18.72 tff(13160,plain,
% 28.52/18.72 ((~(f3(c1, c2) = c2)) <=> (~(f3(c1, f8(c3)) = c2))),
% 28.52/18.72 inference(monotonicity,[status(thm)],[13159])).
% 28.52/18.72 tff(13161,plain,
% 28.52/18.72 (~(f3(c1, f8(c3)) = c2)),
% 28.52/18.72 inference(modus_ponens,[status(thm)],[12777, 13160])).
% 28.52/18.72 tff(13162,plain,
% 28.52/18.72 (f3(c1, f8(c3)) = c1),
% 28.52/18.72 inference(unit_resolution,[status(thm)],[7123, 13161])).
% 28.52/18.72 tff(13163,plain,
% 28.52/18.72 (c1 = f3(c1, c2)),
% 28.52/18.72 inference(modus_ponens,[status(thm)],[13162, 13157])).
% 28.52/18.72 tff(13164,assumption,(~big_f(f3(c1, c2), c1)), introduced(assumption)).
% 28.52/18.72 tff(13165,plain,
% 28.52/18.72 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c1 = c4) | (c1 = f2(c2)) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2) | (~big_f(c2, c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c1 = c4) | (c1 = f2(c2)) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2) | (~big_f(c2, c1)))),
% 28.52/18.72 inference(rewrite,[status(thm)],[])).
% 28.52/18.72 tff(13166,plain,
% 28.52/18.72 (((~(c2 = c3)) | (c1 = c4) | (f3(c1, c2) = c2) | big_f(f3(c1, c2), c1) | (c1 = f2(c2)) | (~big_f(c2, c1))) <=> ((~(c2 = c3)) | (c1 = c4) | (c1 = f2(c2)) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2) | (~big_f(c2, c1)))),
% 28.52/18.72 inference(rewrite,[status(thm)],[])).
% 28.52/18.72 tff(13167,plain,
% 28.52/18.72 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c1 = c4) | (f3(c1, c2) = c2) | big_f(f3(c1, c2), c1) | (c1 = f2(c2)) | (~big_f(c2, c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c1 = c4) | (c1 = f2(c2)) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2) | (~big_f(c2, c1))))),
% 28.52/18.72 inference(monotonicity,[status(thm)],[13166])).
% 28.52/18.72 tff(13168,plain,
% 28.52/18.72 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c1 = c4) | (f3(c1, c2) = c2) | big_f(f3(c1, c2), c1) | (c1 = f2(c2)) | (~big_f(c2, c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c1 = c4) | (c1 = f2(c2)) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2) | (~big_f(c2, c1)))),
% 28.52/18.72 inference(transitivity,[status(thm)],[13167, 13165])).
% 28.52/18.72 tff(13169,plain,
% 28.52/18.72 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c1 = c4) | (f3(c1, c2) = c2) | big_f(f3(c1, c2), c1) | (c1 = f2(c2)) | (~big_f(c2, c1)))),
% 28.52/18.72 inference(quant_inst,[status(thm)],[])).
% 28.52/18.72 tff(13170,plain,
% 28.52/18.72 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c1 = c4) | (c1 = f2(c2)) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2) | (~big_f(c2, c1))),
% 28.52/18.72 inference(modus_ponens,[status(thm)],[13169, 13168])).
% 28.52/18.72 tff(13171,plain,
% 28.52/18.72 (c1 = f2(c2)),
% 28.52/18.72 inference(unit_resolution,[status(thm)],[13170, 7352, 482, 1344, 13164, 12777, 348])).
% 28.52/18.72 tff(13172,plain,
% 28.52/18.72 (f2(c2) = c1),
% 28.52/18.72 inference(symmetry,[status(thm)],[13171])).
% 28.52/18.72 tff(13173,plain,
% 28.52/18.72 (c2 = c1),
% 28.52/18.72 inference(transitivity,[status(thm)],[2853, 13172])).
% 28.52/18.72 tff(13174,plain,
% 28.52/18.72 ($false),
% 28.52/18.72 inference(unit_resolution,[status(thm)],[75, 13173])).
% 28.52/18.72 tff(13175,plain,((~(c2 = f2(c2))) | (c1 = c4) | (~(c2 = c3)) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2) | (~big_f(c2, c1))), inference(lemma,lemma(discharge,[]))).
% 28.52/18.72 tff(13176,plain,
% 28.52/18.72 (~(c2 = f2(c2))),
% 28.52/18.72 inference(unit_resolution,[status(thm)],[13175, 13164, 1344, 482, 12777, 348])).
% 28.52/18.72 tff(13177,plain,
% 28.52/18.72 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c1 = c4) | (c2 = f2(c2)) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c1 = c4) | (c2 = f2(c2)) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2) | (~big_f(c2, c2)))),
% 28.52/18.72 inference(rewrite,[status(thm)],[])).
% 28.52/18.72 tff(13178,plain,
% 28.52/18.72 (((~(c2 = c3)) | (c1 = c4) | (f3(c1, c2) = c2) | big_f(f3(c1, c2), c1) | (c2 = f2(c2)) | (~big_f(c2, c2))) <=> ((~(c2 = c3)) | (c1 = c4) | (c2 = f2(c2)) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2) | (~big_f(c2, c2)))),
% 28.52/18.72 inference(rewrite,[status(thm)],[])).
% 28.52/18.72 tff(13179,plain,
% 28.52/18.72 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c1 = c4) | (f3(c1, c2) = c2) | big_f(f3(c1, c2), c1) | (c2 = f2(c2)) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c1 = c4) | (c2 = f2(c2)) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2) | (~big_f(c2, c2))))),
% 28.52/18.72 inference(monotonicity,[status(thm)],[13178])).
% 28.52/18.72 tff(13180,plain,
% 28.52/18.72 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c1 = c4) | (f3(c1, c2) = c2) | big_f(f3(c1, c2), c1) | (c2 = f2(c2)) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c1 = c4) | (c2 = f2(c2)) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2) | (~big_f(c2, c2)))),
% 28.52/18.72 inference(transitivity,[status(thm)],[13179, 13177])).
% 28.52/18.72 tff(13181,plain,
% 28.52/18.72 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c1 = c4) | (f3(c1, c2) = c2) | big_f(f3(c1, c2), c1) | (c2 = f2(c2)) | (~big_f(c2, c2)))),
% 28.52/18.72 inference(quant_inst,[status(thm)],[])).
% 28.52/18.72 tff(13182,plain,
% 28.52/18.72 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c1 = c4) | (c2 = f2(c2)) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2) | (~big_f(c2, c2))),
% 28.52/18.72 inference(modus_ponens,[status(thm)],[13181, 13180])).
% 28.52/18.72 tff(13183,plain,
% 28.53/18.72 ($false),
% 28.53/18.72 inference(unit_resolution,[status(thm)],[13182, 7352, 482, 1345, 1344, 13176, 13164, 12777])).
% 28.53/18.72 tff(13184,plain,(big_f(f3(c1, c2), c1) | (c1 = c4) | (~big_f(c2, c2)) | (~(c2 = c3)) | (f3(c1, c2) = c2) | (~big_f(c2, c1))), inference(lemma,lemma(discharge,[]))).
% 28.53/18.72 tff(13185,plain,
% 28.53/18.72 (big_f(f3(c1, c2), c1)),
% 28.53/18.72 inference(unit_resolution,[status(thm)],[13184, 12777, 1345, 1335, 482, 348])).
% 28.53/18.72 tff(13186,plain,
% 28.53/18.72 ((~(big_f(c1, c1) <=> big_f(f3(c1, c2), c1))) | big_f(c1, c1) | (~big_f(f3(c1, c2), c1))),
% 28.53/18.72 inference(tautology,[status(thm)],[])).
% 28.53/18.72 tff(13187,plain,
% 28.53/18.72 (~(big_f(c1, c1) <=> big_f(f3(c1, c2), c1))),
% 28.53/18.72 inference(unit_resolution,[status(thm)],[13186, 13185, 66])).
% 28.53/18.72 tff(13188,assumption,(~(big_f(c1, c1) <=> big_f(f3(c1, c2), c1))), introduced(assumption)).
% 28.53/18.72 tff(13189,assumption,(c1 = f3(c1, c2)), introduced(assumption)).
% 28.53/18.72 tff(13190,plain,
% 28.53/18.72 (big_f(c1, c1) <=> big_f(f3(c1, c2), c1)),
% 28.53/18.72 inference(monotonicity,[status(thm)],[13189])).
% 28.53/18.72 tff(13191,plain,
% 28.53/18.72 ($false),
% 28.53/18.72 inference(unit_resolution,[status(thm)],[13190, 13188])).
% 28.53/18.72 tff(13192,plain,((~(c1 = f3(c1, c2))) | (big_f(c1, c1) <=> big_f(f3(c1, c2), c1))), inference(lemma,lemma(discharge,[]))).
% 28.53/18.72 tff(13193,plain,
% 28.53/18.72 (~(c1 = f3(c1, c2))),
% 28.53/18.72 inference(unit_resolution,[status(thm)],[13192, 13187])).
% 28.53/18.72 tff(13194,plain,
% 28.53/18.72 ($false),
% 28.53/18.72 inference(unit_resolution,[status(thm)],[13193, 13163])).
% 28.53/18.72 tff(13195,plain,((f3(c1, c2) = c2) | (~(c2 = f8(c2))) | (~(c3 = c2)) | big_f(c1, c1) | (~big_f(c2, c2)) | (c1 = c4) | (~big_f(c2, c1))), inference(lemma,lemma(discharge,[]))).
% 28.53/18.72 tff(13196,plain,
% 28.53/18.72 (f3(c1, c2) = c2),
% 28.53/18.72 inference(unit_resolution,[status(thm)],[13195, 13150, 67, 66, 13087, 13139, 13074])).
% 28.53/18.72 tff(13197,plain,
% 28.53/18.72 (big_f(f3(c1, c2), c1) <=> big_f(c2, c1)),
% 28.53/18.72 inference(monotonicity,[status(thm)],[13196])).
% 28.53/18.72 tff(13198,plain,
% 28.53/18.72 (big_f(c2, c1) <=> big_f(f3(c1, c2), c1)),
% 28.53/18.72 inference(symmetry,[status(thm)],[13197])).
% 28.53/18.72 tff(13199,plain,
% 28.53/18.72 (big_f(f3(c1, c2), c1)),
% 28.53/18.72 inference(modus_ponens,[status(thm)],[13074, 13198])).
% 28.53/18.72 tff(13200,plain,
% 28.53/18.72 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c1 = c4) | (~big_f(f3(c1, c2), c1)) | (~(f3(c1, c2) = c2)) | (c1 = f2(c2)) | (~big_f(c2, c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c1 = c4) | (~big_f(f3(c1, c2), c1)) | (~(f3(c1, c2) = c2)) | (c1 = f2(c2)) | (~big_f(c2, c1)))),
% 28.53/18.72 inference(rewrite,[status(thm)],[])).
% 28.53/18.72 tff(13201,plain,
% 28.53/18.72 (((~(c2 = c3)) | (c1 = c4) | (~(f3(c1, c2) = c2)) | (~big_f(f3(c1, c2), c1)) | (c1 = f2(c2)) | (~big_f(c2, c1))) <=> ((~(c2 = c3)) | (c1 = c4) | (~big_f(f3(c1, c2), c1)) | (~(f3(c1, c2) = c2)) | (c1 = f2(c2)) | (~big_f(c2, c1)))),
% 28.53/18.72 inference(rewrite,[status(thm)],[])).
% 28.53/18.72 tff(13202,plain,
% 28.53/18.72 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c1 = c4) | (~(f3(c1, c2) = c2)) | (~big_f(f3(c1, c2), c1)) | (c1 = f2(c2)) | (~big_f(c2, c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c1 = c4) | (~big_f(f3(c1, c2), c1)) | (~(f3(c1, c2) = c2)) | (c1 = f2(c2)) | (~big_f(c2, c1))))),
% 28.53/18.72 inference(monotonicity,[status(thm)],[13201])).
% 28.53/18.72 tff(13203,plain,
% 28.53/18.72 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c1 = c4) | (~(f3(c1, c2) = c2)) | (~big_f(f3(c1, c2), c1)) | (c1 = f2(c2)) | (~big_f(c2, c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c1 = c4) | (~big_f(f3(c1, c2), c1)) | (~(f3(c1, c2) = c2)) | (c1 = f2(c2)) | (~big_f(c2, c1)))),
% 28.53/18.72 inference(transitivity,[status(thm)],[13202, 13200])).
% 28.53/18.72 tff(13204,plain,
% 28.53/18.72 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c1 = c4) | (~(f3(c1, c2) = c2)) | (~big_f(f3(c1, c2), c1)) | (c1 = f2(c2)) | (~big_f(c2, c1)))),
% 28.53/18.72 inference(quant_inst,[status(thm)],[])).
% 28.53/18.72 tff(13205,plain,
% 28.53/18.72 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c1 = c4) | (~big_f(f3(c1, c2), c1)) | (~(f3(c1, c2) = c2)) | (c1 = f2(c2)) | (~big_f(c2, c1))),
% 28.53/18.72 inference(modus_ponens,[status(thm)],[13204, 13203])).
% 28.53/18.72 tff(13206,plain,
% 28.53/18.72 (c1 = f2(c2)),
% 28.53/18.72 inference(unit_resolution,[status(thm)],[13205, 7051, 13139, 1335, 13199, 13196, 13074])).
% 28.53/18.72 tff(13207,plain,
% 28.53/18.72 (f2(c2) = c1),
% 28.53/18.72 inference(symmetry,[status(thm)],[13206])).
% 28.53/18.72 tff(13208,plain,
% 28.53/18.72 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c1 = c4) | (c2 = f2(c2)) | (~big_f(f3(c1, c2), c1)) | (~(f3(c1, c2) = c2)) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c1 = c4) | (c2 = f2(c2)) | (~big_f(f3(c1, c2), c1)) | (~(f3(c1, c2) = c2)) | (~big_f(c2, c2)))),
% 28.53/18.72 inference(rewrite,[status(thm)],[])).
% 28.53/18.72 tff(13209,plain,
% 28.53/18.72 (((~(c2 = c3)) | (c1 = c4) | (~(f3(c1, c2) = c2)) | (~big_f(f3(c1, c2), c1)) | (c2 = f2(c2)) | (~big_f(c2, c2))) <=> ((~(c2 = c3)) | (c1 = c4) | (c2 = f2(c2)) | (~big_f(f3(c1, c2), c1)) | (~(f3(c1, c2) = c2)) | (~big_f(c2, c2)))),
% 28.53/18.72 inference(rewrite,[status(thm)],[])).
% 28.53/18.72 tff(13210,plain,
% 28.53/18.72 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c1 = c4) | (~(f3(c1, c2) = c2)) | (~big_f(f3(c1, c2), c1)) | (c2 = f2(c2)) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c1 = c4) | (c2 = f2(c2)) | (~big_f(f3(c1, c2), c1)) | (~(f3(c1, c2) = c2)) | (~big_f(c2, c2))))),
% 28.53/18.72 inference(monotonicity,[status(thm)],[13209])).
% 28.53/18.72 tff(13211,plain,
% 28.53/18.72 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c1 = c4) | (~(f3(c1, c2) = c2)) | (~big_f(f3(c1, c2), c1)) | (c2 = f2(c2)) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c1 = c4) | (c2 = f2(c2)) | (~big_f(f3(c1, c2), c1)) | (~(f3(c1, c2) = c2)) | (~big_f(c2, c2)))),
% 28.53/18.72 inference(transitivity,[status(thm)],[13210, 13208])).
% 28.53/18.72 tff(13212,plain,
% 28.53/18.72 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c1 = c4) | (~(f3(c1, c2) = c2)) | (~big_f(f3(c1, c2), c1)) | (c2 = f2(c2)) | (~big_f(c2, c2)))),
% 28.53/18.72 inference(quant_inst,[status(thm)],[])).
% 28.53/18.72 tff(13213,plain,
% 28.53/18.72 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c1 = c4) | (c2 = f2(c2)) | (~big_f(f3(c1, c2), c1)) | (~(f3(c1, c2) = c2)) | (~big_f(c2, c2))),
% 28.53/18.72 inference(modus_ponens,[status(thm)],[13212, 13211])).
% 28.53/18.72 tff(13214,plain,
% 28.53/18.72 (c2 = f2(c2)),
% 28.53/18.72 inference(unit_resolution,[status(thm)],[13213, 7051, 13139, 13087, 1335, 13199, 13196])).
% 28.53/18.72 tff(13215,plain,
% 28.53/18.72 (c2 = c1),
% 28.53/18.72 inference(transitivity,[status(thm)],[13214, 13207])).
% 28.53/18.72 tff(13216,plain,
% 28.53/18.72 ($false),
% 28.53/18.72 inference(unit_resolution,[status(thm)],[75, 13215])).
% 28.53/18.72 tff(13217,plain,((~(c3 = c2)) | big_f(c1, c1) | (c2 = f5(c1)) | (f7(c1) = c1) | (f10(c1) = c1) | (f7(c2) = c2) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.53/18.72 tff(13218,plain,
% 28.53/18.72 (c2 = f5(c1)),
% 28.53/18.72 inference(unit_resolution,[status(thm)],[13217, 13036, 12768, 115, 3, 17, 79])).
% 28.53/18.72 tff(13219,plain,
% 28.53/18.72 (f5(c1) = c2),
% 28.53/18.72 inference(symmetry,[status(thm)],[13218])).
% 28.53/18.72 tff(13220,plain,
% 28.53/18.72 (f5(f7(c2)) = c2),
% 28.53/18.72 inference(transitivity,[status(thm)],[8600, 13219])).
% 28.53/18.72 tff(13221,plain,
% 28.53/18.72 ((f7(c2) = f5(f7(c2))) <=> (f7(c2) = c2)),
% 28.53/18.72 inference(monotonicity,[status(thm)],[13220])).
% 28.53/18.72 tff(13222,plain,
% 28.53/18.72 ((f7(c2) = c2) <=> (f7(c2) = f5(f7(c2)))),
% 28.53/18.72 inference(symmetry,[status(thm)],[13221])).
% 28.53/18.72 tff(13223,plain,
% 28.53/18.72 ((~(f7(c2) = c2)) <=> (~(f7(c2) = f5(f7(c2))))),
% 28.53/18.72 inference(monotonicity,[status(thm)],[13222])).
% 28.53/18.72 tff(13224,plain,
% 28.53/18.72 (~(f7(c2) = f5(f7(c2)))),
% 28.53/18.72 inference(modus_ponens,[status(thm)],[17, 13223])).
% 28.53/18.72 tff(13225,plain,
% 28.53/18.72 (c2 = c3),
% 28.53/18.72 inference(modus_ponens,[status(thm)],[13036, 78])).
% 28.53/18.72 tff(13226,plain,
% 28.53/18.72 (f8(f7(c2)) = f8(c1)),
% 28.53/18.72 inference(monotonicity,[status(thm)],[22])).
% 28.53/18.72 tff(13227,plain,
% 28.53/18.72 (f8(f7(c2)) = c2),
% 28.53/18.72 inference(transitivity,[status(thm)],[13226, 1643])).
% 28.53/18.72 tff(13228,plain,
% 28.53/18.72 ((f3(c2, c2) = f8(f7(c2))) <=> (f3(c2, c2) = c2)),
% 28.53/18.72 inference(monotonicity,[status(thm)],[13227])).
% 28.53/18.72 tff(13229,plain,
% 28.53/18.72 (big_f(f3(c2, c2), f10(f7(c2))) <=> big_f(f3(c2, c2), c2)),
% 28.53/18.72 inference(monotonicity,[status(thm)],[24])).
% 28.53/18.72 tff(13230,plain,
% 28.53/18.72 (big_f(f3(c2, c2), c2) <=> big_f(f3(c2, c2), f10(f7(c2)))),
% 28.53/18.72 inference(symmetry,[status(thm)],[13229])).
% 28.53/18.72 tff(13231,plain,
% 28.53/18.72 (f3(c2, c2) = c2),
% 28.53/18.72 inference(unit_resolution,[status(thm)],[13106, 12882, 1345, 1344, 873, 348])).
% 28.53/18.72 tff(13232,plain,
% 28.53/18.72 (big_f(f3(c2, c2), c2) <=> big_f(c2, c2)),
% 28.53/18.72 inference(monotonicity,[status(thm)],[13231])).
% 28.53/18.72 tff(13233,plain,
% 28.53/18.72 (big_f(c2, c2) <=> big_f(f3(c2, c2), c2)),
% 28.53/18.73 inference(symmetry,[status(thm)],[13232])).
% 28.53/18.73 tff(13234,plain,
% 28.53/18.73 (big_f(f3(c2, c2), c2)),
% 28.53/18.73 inference(modus_ponens,[status(thm)],[1345, 13233])).
% 28.53/18.73 tff(13235,plain,
% 28.53/18.73 ($false),
% 28.53/18.73 inference(unit_resolution,[status(thm)],[12882, 13234])).
% 28.53/18.73 tff(13236,plain,(big_f(f3(c2, c2), c2) | (~big_f(c2, c2)) | (~(c2 = c3)) | (c2 = c4) | (~big_f(c2, c1))), inference(lemma,lemma(discharge,[]))).
% 28.53/18.73 tff(13237,plain,
% 28.53/18.73 (big_f(f3(c2, c2), c2)),
% 28.53/18.73 inference(unit_resolution,[status(thm)],[13236, 873, 1344, 1345, 348])).
% 28.53/18.73 tff(13238,plain,
% 28.53/18.73 (big_f(f3(c2, c2), f10(f7(c2)))),
% 28.53/18.73 inference(modus_ponens,[status(thm)],[13237, 13230])).
% 28.53/18.73 tff(13239,plain,
% 28.53/18.73 ((f3(c2, c2) = f8(f7(c2))) | (~big_f(f3(c2, c2), f10(f7(c2))))),
% 28.53/18.73 inference(unit_resolution,[status(thm)],[12977, 1659, 8473, 10466, 10465, 12471])).
% 28.53/18.73 tff(13240,plain,
% 28.53/18.73 (f3(c2, c2) = f8(f7(c2))),
% 28.53/18.73 inference(unit_resolution,[status(thm)],[13239, 13238])).
% 28.53/18.73 tff(13241,plain,
% 28.53/18.73 (f3(c2, c2) = c2),
% 28.53/18.73 inference(modus_ponens,[status(thm)],[13240, 13228])).
% 28.53/18.73 tff(13242,plain,
% 28.53/18.73 ((c2 = f2(c2)) | (~(f3(c2, c2) = c2))),
% 28.53/18.73 inference(unit_resolution,[status(thm)],[13128, 7051, 873, 1345, 1344, 13237])).
% 28.53/18.73 tff(13243,plain,
% 28.53/18.73 (c2 = f2(c2)),
% 28.53/18.73 inference(unit_resolution,[status(thm)],[13242, 13241])).
% 28.53/18.73 tff(13244,plain,
% 28.53/18.73 (f2(c2) = c2),
% 28.53/18.73 inference(symmetry,[status(thm)],[13243])).
% 28.53/18.73 tff(13245,plain,
% 28.53/18.73 (big_f(c2, f7(c2))),
% 28.53/18.73 inference(modus_ponens,[status(thm)],[348, 9312])).
% 28.53/18.73 tff(13246,plain,
% 28.53/18.73 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~big_f(c2, f7(c2))) | (f7(c2) = f2(c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~big_f(c2, f7(c2))) | (f7(c2) = f2(c2)))),
% 28.53/18.73 inference(rewrite,[status(thm)],[])).
% 28.53/18.73 tff(13247,plain,
% 28.53/18.73 (((~(c2 = c3)) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (f7(c2) = f2(c2)) | (~big_f(c2, f7(c2)))) <=> ((~(c2 = c3)) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~big_f(c2, f7(c2))) | (f7(c2) = f2(c2)))),
% 28.53/18.73 inference(rewrite,[status(thm)],[])).
% 28.53/18.73 tff(13248,plain,
% 28.53/18.73 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (f7(c2) = f2(c2)) | (~big_f(c2, f7(c2))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~big_f(c2, f7(c2))) | (f7(c2) = f2(c2))))),
% 28.53/18.73 inference(monotonicity,[status(thm)],[13247])).
% 28.53/18.73 tff(13249,plain,
% 28.53/18.73 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (f7(c2) = f2(c2)) | (~big_f(c2, f7(c2))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~big_f(c2, f7(c2))) | (f7(c2) = f2(c2)))),
% 28.53/18.73 inference(transitivity,[status(thm)],[13248, 13246])).
% 28.53/18.73 tff(13250,plain,
% 28.53/18.73 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (f7(c2) = f2(c2)) | (~big_f(c2, f7(c2))))),
% 28.53/18.73 inference(quant_inst,[status(thm)],[])).
% 28.53/18.73 tff(13251,plain,
% 28.53/18.73 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~big_f(c2, f7(c2))) | (f7(c2) = f2(c2))),
% 28.53/18.73 inference(modus_ponens,[status(thm)],[13250, 13249])).
% 28.53/18.73 tff(13252,plain,
% 28.53/18.73 ((~(f3(c2, c2) = c2)) | (f7(c2) = f2(c2))),
% 28.53/18.73 inference(unit_resolution,[status(thm)],[13251, 7051, 873, 1344, 13237, 13245])).
% 28.53/18.73 tff(13253,plain,
% 28.53/18.73 (f7(c2) = f2(c2)),
% 28.53/18.73 inference(unit_resolution,[status(thm)],[13252, 13241])).
% 28.53/18.73 tff(13254,plain,
% 28.53/18.73 (f7(c2) = c2),
% 28.53/18.73 inference(transitivity,[status(thm)],[13253, 13244])).
% 28.53/18.73 tff(13255,plain,
% 28.53/18.73 ($false),
% 28.53/18.73 inference(unit_resolution,[status(thm)],[17, 13254])).
% 28.53/18.73 tff(13256,plain,((c2 = c4) | (f7(c2) = c2) | (~(c2 = c3)) | (~big_f(c2, c2)) | (~(c2 = f8(c1))) | (f7(f7(c2)) = f7(c2)) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))) | (~(f10(c1) = c2)) | (~big_f(c2, c1))), inference(lemma,lemma(discharge,[]))).
% 28.53/18.73 tff(13257,plain,
% 28.53/18.73 (c2 = c4),
% 28.53/18.73 inference(unit_resolution,[status(thm)],[13256, 13225, 17, 12442, 12764, 12943, 12773, 13224, 15, 12763])).
% 28.53/18.73 tff(13258,plain,
% 28.53/18.73 (c4 = c2),
% 28.53/18.73 inference(symmetry,[status(thm)],[13257])).
% 28.53/18.73 tff(13259,plain,
% 28.53/18.73 ((f7(c2) = c4) <=> (f7(c2) = c2)),
% 28.53/18.73 inference(monotonicity,[status(thm)],[13258])).
% 28.53/18.73 tff(13260,plain,
% 28.53/18.73 ((f7(c2) = c2) <=> (f7(c2) = c4)),
% 28.53/18.73 inference(symmetry,[status(thm)],[13259])).
% 28.53/18.73 tff(13261,plain,
% 28.53/18.73 ((f7(c2) = c2) <=> (c1 = c4)),
% 28.53/18.73 inference(transitivity,[status(thm)],[13260, 12587])).
% 28.53/18.73 tff(13262,plain,
% 28.53/18.73 ((~(f7(c2) = c2)) <=> (~(c1 = c4))),
% 28.53/18.73 inference(monotonicity,[status(thm)],[13261])).
% 28.53/18.73 tff(13263,plain,
% 28.53/18.73 (~(c1 = c4)),
% 28.53/18.73 inference(modus_ponens,[status(thm)],[17, 13262])).
% 28.53/18.73 tff(13264,plain,
% 28.53/18.73 (f3(c1, c2) = c2),
% 28.53/18.73 inference(unit_resolution,[status(thm)],[13195, 13263, 12768, 12442, 13039, 13036, 12763])).
% 28.53/18.73 tff(13265,plain,
% 28.53/18.73 (f3(f7(f4(c4)), f4(c4)) = f3(c1, c2)),
% 28.53/18.73 inference(monotonicity,[status(thm)],[8081, 79])).
% 28.53/18.73 tff(13266,plain,
% 28.53/18.73 (f3(f7(c2), c2) = f3(f7(f4(c4)), f4(c4))),
% 28.53/18.73 inference(monotonicity,[status(thm)],[81, 436])).
% 28.53/18.73 tff(13267,plain,
% 28.53/18.73 (f3(f7(c2), c2) = c2),
% 28.53/18.73 inference(transitivity,[status(thm)],[13266, 13265, 13264])).
% 28.53/18.73 tff(13268,plain,
% 28.53/18.73 (big_f(f3(f7(c2), c2), f7(c2)) <=> big_f(c2, f7(c2))),
% 28.53/18.73 inference(monotonicity,[status(thm)],[13267])).
% 28.53/18.73 tff(13269,plain,
% 28.53/18.73 (big_f(c2, f7(c2)) <=> big_f(f3(f7(c2), c2), f7(c2))),
% 28.53/18.73 inference(symmetry,[status(thm)],[13268])).
% 28.53/18.73 tff(13270,plain,
% 28.53/18.73 (big_f(c2, f7(c2))),
% 28.53/18.73 inference(modus_ponens,[status(thm)],[12763, 9312])).
% 28.53/18.73 tff(13271,plain,
% 28.53/18.73 (big_f(f3(f7(c2), c2), f7(c2))),
% 28.53/18.73 inference(modus_ponens,[status(thm)],[13270, 13269])).
% 28.53/18.73 tff(13272,plain,
% 28.53/18.73 ((~(f7(c2) = c2)) <=> (~(f7(c2) = c4))),
% 28.53/18.73 inference(monotonicity,[status(thm)],[13260])).
% 28.53/18.73 tff(13273,plain,
% 28.53/18.73 (~(f7(c2) = c4)),
% 28.53/18.73 inference(modus_ponens,[status(thm)],[17, 13272])).
% 28.53/18.73 tff(13274,plain,
% 28.53/18.73 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (f7(c2) = c4) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (f7(c2) = c4) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2))))),
% 28.53/18.73 inference(rewrite,[status(thm)],[])).
% 28.53/18.73 tff(13275,plain,
% 28.53/18.73 (((~(c2 = c3)) | (f7(c2) = c4) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2))) | (c2 = f2(c2)) | (~big_f(c2, c2))) <=> ((~(c2 = c3)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (f7(c2) = c4) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2))))),
% 28.53/18.73 inference(rewrite,[status(thm)],[])).
% 28.53/18.73 tff(13276,plain,
% 28.53/18.73 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f7(c2) = c4) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2))) | (c2 = f2(c2)) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (f7(c2) = c4) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2)))))),
% 28.53/18.73 inference(monotonicity,[status(thm)],[13275])).
% 28.53/18.73 tff(13277,plain,
% 28.53/18.73 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f7(c2) = c4) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2))) | (c2 = f2(c2)) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (f7(c2) = c4) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2))))),
% 28.53/18.73 inference(transitivity,[status(thm)],[13276, 13274])).
% 28.53/18.73 tff(13278,plain,
% 28.53/18.73 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f7(c2) = c4) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2))) | (c2 = f2(c2)) | (~big_f(c2, c2)))),
% 28.53/18.73 inference(quant_inst,[status(thm)],[])).
% 28.53/18.73 tff(13279,plain,
% 28.53/18.73 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (f7(c2) = c4) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2)))),
% 28.53/18.73 inference(modus_ponens,[status(thm)],[13278, 13277])).
% 28.53/18.73 tff(13280,plain,
% 28.53/18.73 ((c2 = f2(c2)) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2)))),
% 28.53/18.73 inference(unit_resolution,[status(thm)],[13279, 7051, 12442, 13225, 13273])).
% 28.53/18.73 tff(13281,plain,
% 28.53/18.73 (c2 = f2(c2)),
% 28.53/18.73 inference(unit_resolution,[status(thm)],[13280, 13267, 13271])).
% 28.53/18.73 tff(13282,plain,
% 28.53/18.73 (f2(c2) = c2),
% 28.53/18.73 inference(symmetry,[status(thm)],[13281])).
% 28.53/18.73 tff(13283,plain,
% 28.53/18.73 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f7(c2) = c4) | (~big_f(c2, f7(c2))) | (f7(c2) = f2(c2)) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (f7(c2) = c4) | (~big_f(c2, f7(c2))) | (f7(c2) = f2(c2)) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2))))),
% 28.53/18.73 inference(rewrite,[status(thm)],[])).
% 28.53/18.73 tff(13284,plain,
% 28.53/18.73 (((~(c2 = c3)) | (f7(c2) = c4) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2))) | (f7(c2) = f2(c2)) | (~big_f(c2, f7(c2)))) <=> ((~(c2 = c3)) | (f7(c2) = c4) | (~big_f(c2, f7(c2))) | (f7(c2) = f2(c2)) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2))))),
% 28.53/18.73 inference(rewrite,[status(thm)],[])).
% 28.53/18.73 tff(13285,plain,
% 28.53/18.73 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f7(c2) = c4) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2))) | (f7(c2) = f2(c2)) | (~big_f(c2, f7(c2))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f7(c2) = c4) | (~big_f(c2, f7(c2))) | (f7(c2) = f2(c2)) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2)))))),
% 28.53/18.73 inference(monotonicity,[status(thm)],[13284])).
% 28.53/18.73 tff(13286,plain,
% 28.53/18.73 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f7(c2) = c4) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2))) | (f7(c2) = f2(c2)) | (~big_f(c2, f7(c2))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (f7(c2) = c4) | (~big_f(c2, f7(c2))) | (f7(c2) = f2(c2)) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2))))),
% 28.53/18.73 inference(transitivity,[status(thm)],[13285, 13283])).
% 28.53/18.73 tff(13287,plain,
% 28.53/18.73 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f7(c2) = c4) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2))) | (f7(c2) = f2(c2)) | (~big_f(c2, f7(c2))))),
% 28.53/18.73 inference(quant_inst,[status(thm)],[])).
% 28.53/18.73 tff(13288,plain,
% 28.53/18.73 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (f7(c2) = c4) | (~big_f(c2, f7(c2))) | (f7(c2) = f2(c2)) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2)))),
% 28.53/18.73 inference(modus_ponens,[status(thm)],[13287, 13286])).
% 28.53/18.73 tff(13289,plain,
% 28.53/18.73 ((f7(c2) = f2(c2)) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2)))),
% 28.53/18.73 inference(unit_resolution,[status(thm)],[13288, 7051, 13225, 13273, 13270])).
% 28.53/18.73 tff(13290,plain,
% 28.53/18.73 (f7(c2) = f2(c2)),
% 28.53/18.73 inference(unit_resolution,[status(thm)],[13289, 13267, 13271])).
% 28.53/18.73 tff(13291,plain,
% 28.53/18.73 (f7(c2) = c2),
% 28.53/18.73 inference(transitivity,[status(thm)],[13290, 13282])).
% 28.53/18.73 tff(13292,plain,
% 28.53/18.73 ($false),
% 28.53/18.73 inference(unit_resolution,[status(thm)],[17, 13291])).
% 28.53/18.73 tff(13293,plain,(big_f(c1, c2) | (f7(c2) = c2) | (~(f4(c4) = c2)) | (f7(c1) = c1) | (f10(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 28.53/18.73 tff(13294,plain,
% 28.53/18.73 (big_f(c1, c2)),
% 28.53/18.73 inference(unit_resolution,[status(thm)],[13293, 17, 79, 115, 3])).
% 28.53/18.73 tff(13295,plain,
% 28.53/18.73 (big_f(f7(c2), f10(f7(c2)))),
% 28.53/18.73 inference(modus_ponens,[status(thm)],[13294, 12767])).
% 28.53/18.73 tff(13296,assumption,(~(f7(c2) = f8(f7(c2)))), introduced(assumption)).
% 28.53/18.73 tff(13297,assumption,(big_f(f7(c2), f10(f7(c2)))), introduced(assumption)).
% 28.53/18.73 tff(13298,plain,
% 28.53/18.73 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(f7(c2)) = f7(c2)) | (f10(f7(c2)) = f7(c2)) | (c2 = f5(f7(c2))) | (f7(c2) = f8(f7(c2))) | (~big_f(f7(f7(c2)), c2)) | (~big_f(f7(c2), f10(f7(c2)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(f7(c2)) = f7(c2)) | (f10(f7(c2)) = f7(c2)) | (c2 = f5(f7(c2))) | (f7(c2) = f8(f7(c2))) | (~big_f(f7(f7(c2)), c2)) | (~big_f(f7(c2), f10(f7(c2)))))),
% 28.53/18.73 inference(rewrite,[status(thm)],[])).
% 28.53/18.73 tff(13299,plain,
% 28.53/18.73 (((f10(f7(c2)) = f7(c2)) | (f7(c2) = f8(f7(c2))) | (~big_f(f7(c2), f10(f7(c2)))) | (f7(f7(c2)) = f7(c2)) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2))) <=> ((f7(f7(c2)) = f7(c2)) | (f10(f7(c2)) = f7(c2)) | (c2 = f5(f7(c2))) | (f7(c2) = f8(f7(c2))) | (~big_f(f7(f7(c2)), c2)) | (~big_f(f7(c2), f10(f7(c2)))))),
% 28.53/18.73 inference(rewrite,[status(thm)],[])).
% 28.53/18.73 tff(13300,plain,
% 28.53/18.73 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f7(c2)) = f7(c2)) | (f7(c2) = f8(f7(c2))) | (~big_f(f7(c2), f10(f7(c2)))) | (f7(f7(c2)) = f7(c2)) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(f7(c2)) = f7(c2)) | (f10(f7(c2)) = f7(c2)) | (c2 = f5(f7(c2))) | (f7(c2) = f8(f7(c2))) | (~big_f(f7(f7(c2)), c2)) | (~big_f(f7(c2), f10(f7(c2))))))),
% 28.53/18.73 inference(monotonicity,[status(thm)],[13299])).
% 28.53/18.73 tff(13301,plain,
% 28.53/18.73 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f7(c2)) = f7(c2)) | (f7(c2) = f8(f7(c2))) | (~big_f(f7(c2), f10(f7(c2)))) | (f7(f7(c2)) = f7(c2)) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(f7(c2)) = f7(c2)) | (f10(f7(c2)) = f7(c2)) | (c2 = f5(f7(c2))) | (f7(c2) = f8(f7(c2))) | (~big_f(f7(f7(c2)), c2)) | (~big_f(f7(c2), f10(f7(c2)))))),
% 28.53/18.73 inference(transitivity,[status(thm)],[13300, 13298])).
% 28.53/18.73 tff(13302,plain,
% 28.53/18.73 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f7(c2)) = f7(c2)) | (f7(c2) = f8(f7(c2))) | (~big_f(f7(c2), f10(f7(c2)))) | (f7(f7(c2)) = f7(c2)) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2)))),
% 28.53/18.73 inference(quant_inst,[status(thm)],[])).
% 28.53/18.73 tff(13303,plain,
% 28.53/18.73 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(f7(c2)) = f7(c2)) | (f10(f7(c2)) = f7(c2)) | (c2 = f5(f7(c2))) | (f7(c2) = f8(f7(c2))) | (~big_f(f7(f7(c2)), c2)) | (~big_f(f7(c2), f10(f7(c2))))),
% 28.53/18.73 inference(modus_ponens,[status(thm)],[13302, 13301])).
% 28.53/18.73 tff(13304,plain,
% 28.53/18.73 ((c2 = f5(f7(c2))) | (f7(c2) = f8(f7(c2)))),
% 28.53/18.73 inference(unit_resolution,[status(thm)],[13303, 1659, 8473, 13297, 8523, 12480])).
% 28.53/18.73 tff(13305,plain,
% 28.53/18.73 (c2 = f5(f7(c2))),
% 28.53/18.73 inference(unit_resolution,[status(thm)],[13304, 13296])).
% 28.53/18.73 tff(13306,plain,
% 28.53/18.73 (f5(f7(c2)) = c2),
% 28.53/18.73 inference(symmetry,[status(thm)],[13305])).
% 28.53/18.73 tff(13307,plain,
% 28.53/18.73 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(f7(c2)) = f7(c2)) | (f10(f7(c2)) = f7(c2)) | (f7(c2) = f5(f7(c2))) | (f7(c2) = f8(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))) | (~big_f(f7(c2), f10(f7(c2)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(f7(c2)) = f7(c2)) | (f10(f7(c2)) = f7(c2)) | (f7(c2) = f5(f7(c2))) | (f7(c2) = f8(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))) | (~big_f(f7(c2), f10(f7(c2)))))),
% 28.53/18.73 inference(rewrite,[status(thm)],[])).
% 28.53/18.73 tff(13308,plain,
% 28.53/18.73 (((f10(f7(c2)) = f7(c2)) | (f7(c2) = f8(f7(c2))) | (~big_f(f7(c2), f10(f7(c2)))) | (f7(f7(c2)) = f7(c2)) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2)))) <=> ((f7(f7(c2)) = f7(c2)) | (f10(f7(c2)) = f7(c2)) | (f7(c2) = f5(f7(c2))) | (f7(c2) = f8(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))) | (~big_f(f7(c2), f10(f7(c2)))))),
% 28.53/18.73 inference(rewrite,[status(thm)],[])).
% 28.53/18.73 tff(13309,plain,
% 28.53/18.73 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f7(c2)) = f7(c2)) | (f7(c2) = f8(f7(c2))) | (~big_f(f7(c2), f10(f7(c2)))) | (f7(f7(c2)) = f7(c2)) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(f7(c2)) = f7(c2)) | (f10(f7(c2)) = f7(c2)) | (f7(c2) = f5(f7(c2))) | (f7(c2) = f8(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))) | (~big_f(f7(c2), f10(f7(c2))))))),
% 28.53/18.73 inference(monotonicity,[status(thm)],[13308])).
% 28.53/18.73 tff(13310,plain,
% 28.53/18.73 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f7(c2)) = f7(c2)) | (f7(c2) = f8(f7(c2))) | (~big_f(f7(c2), f10(f7(c2)))) | (f7(f7(c2)) = f7(c2)) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(f7(c2)) = f7(c2)) | (f10(f7(c2)) = f7(c2)) | (f7(c2) = f5(f7(c2))) | (f7(c2) = f8(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))) | (~big_f(f7(c2), f10(f7(c2)))))),
% 28.53/18.73 inference(transitivity,[status(thm)],[13309, 13307])).
% 28.53/18.73 tff(13311,plain,
% 28.53/18.73 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f7(c2)) = f7(c2)) | (f7(c2) = f8(f7(c2))) | (~big_f(f7(c2), f10(f7(c2)))) | (f7(f7(c2)) = f7(c2)) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))))),
% 28.53/18.73 inference(quant_inst,[status(thm)],[])).
% 28.53/18.73 tff(13312,plain,
% 28.53/18.73 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(f7(c2)) = f7(c2)) | (f10(f7(c2)) = f7(c2)) | (f7(c2) = f5(f7(c2))) | (f7(c2) = f8(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))) | (~big_f(f7(c2), f10(f7(c2))))),
% 28.53/18.73 inference(modus_ponens,[status(thm)],[13311, 13310])).
% 28.53/18.73 tff(13313,plain,
% 28.53/18.73 ((f7(c2) = f5(f7(c2))) | (f7(c2) = f8(f7(c2)))),
% 28.53/18.73 inference(unit_resolution,[status(thm)],[13312, 1659, 8473, 13297, 10465, 8523])).
% 28.53/18.73 tff(13314,plain,
% 28.53/18.73 (f7(c2) = f5(f7(c2))),
% 28.53/18.73 inference(unit_resolution,[status(thm)],[13313, 13296])).
% 28.53/18.73 tff(13315,plain,
% 28.53/18.73 (f7(c2) = c2),
% 28.53/18.73 inference(transitivity,[status(thm)],[13314, 13306])).
% 28.53/18.73 tff(13316,plain,
% 28.53/18.73 ($false),
% 28.53/18.73 inference(unit_resolution,[status(thm)],[17, 13315])).
% 28.53/18.73 tff(13317,plain,((f7(c2) = f8(f7(c2))) | (f7(c2) = c2) | (f7(f7(c2)) = f7(c2)) | (~big_f(f7(c2), f10(f7(c2)))) | (~big_f(f7(f7(c2)), f7(c2))) | (f10(f7(c2)) = f7(c2)) | (~big_f(f7(f7(c2)), c2))), inference(lemma,lemma(discharge,[]))).
% 28.53/18.73 tff(13318,plain,
% 28.53/18.73 (f7(c2) = f8(f7(c2))),
% 28.53/18.73 inference(unit_resolution,[status(thm)],[13317, 17, 12943, 13295, 12764, 12448, 12443])).
% 28.53/18.73 tff(13319,plain,
% 28.53/18.73 (f8(f7(c2)) = f7(c2)),
% 28.53/18.73 inference(symmetry,[status(thm)],[13318])).
% 28.53/18.73 tff(13320,plain,
% 28.53/18.73 ((c2 = f8(f7(c2))) <=> (c2 = f7(c2))),
% 28.53/18.73 inference(monotonicity,[status(thm)],[13319])).
% 28.53/18.73 tff(13321,plain,
% 28.53/18.73 ((c2 = f8(f7(c2))) <=> (f7(c2) = c2)),
% 28.53/18.73 inference(transitivity,[status(thm)],[13320, 8409])).
% 28.53/18.73 tff(13322,plain,
% 28.53/18.73 ((f7(c2) = c2) <=> (c2 = f8(f7(c2)))),
% 28.53/18.73 inference(symmetry,[status(thm)],[13321])).
% 28.53/18.73 tff(13323,plain,
% 28.53/18.73 ((~(f7(c2) = c2)) <=> (~(c2 = f8(f7(c2))))),
% 28.53/18.73 inference(monotonicity,[status(thm)],[13322])).
% 28.53/18.73 tff(13324,plain,
% 28.53/18.73 (~(c2 = f8(f7(c2)))),
% 28.53/18.73 inference(modus_ponens,[status(thm)],[17, 13323])).
% 28.53/18.73 tff(13325,plain,
% 28.53/18.73 (big_f(c2, f10(f7(c2)))),
% 28.53/18.73 inference(modus_ponens,[status(thm)],[12442, 12125])).
% 28.53/18.73 tff(13326,plain,
% 28.53/18.73 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(f7(c2)) = f7(c2)) | (f10(f7(c2)) = f7(c2)) | (c2 = f5(f7(c2))) | (c2 = f8(f7(c2))) | (~big_f(f7(f7(c2)), c2)) | (~big_f(c2, f10(f7(c2)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(f7(c2)) = f7(c2)) | (f10(f7(c2)) = f7(c2)) | (c2 = f5(f7(c2))) | (c2 = f8(f7(c2))) | (~big_f(f7(f7(c2)), c2)) | (~big_f(c2, f10(f7(c2)))))),
% 28.53/18.73 inference(rewrite,[status(thm)],[])).
% 28.53/18.73 tff(13327,plain,
% 28.53/18.73 (((f10(f7(c2)) = f7(c2)) | (c2 = f8(f7(c2))) | (~big_f(c2, f10(f7(c2)))) | (f7(f7(c2)) = f7(c2)) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2))) <=> ((f7(f7(c2)) = f7(c2)) | (f10(f7(c2)) = f7(c2)) | (c2 = f5(f7(c2))) | (c2 = f8(f7(c2))) | (~big_f(f7(f7(c2)), c2)) | (~big_f(c2, f10(f7(c2)))))),
% 28.53/18.73 inference(rewrite,[status(thm)],[])).
% 28.53/18.73 tff(13328,plain,
% 28.53/18.73 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f7(c2)) = f7(c2)) | (c2 = f8(f7(c2))) | (~big_f(c2, f10(f7(c2)))) | (f7(f7(c2)) = f7(c2)) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(f7(c2)) = f7(c2)) | (f10(f7(c2)) = f7(c2)) | (c2 = f5(f7(c2))) | (c2 = f8(f7(c2))) | (~big_f(f7(f7(c2)), c2)) | (~big_f(c2, f10(f7(c2))))))),
% 28.53/18.74 inference(monotonicity,[status(thm)],[13327])).
% 28.53/18.74 tff(13329,plain,
% 28.53/18.74 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f7(c2)) = f7(c2)) | (c2 = f8(f7(c2))) | (~big_f(c2, f10(f7(c2)))) | (f7(f7(c2)) = f7(c2)) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(f7(c2)) = f7(c2)) | (f10(f7(c2)) = f7(c2)) | (c2 = f5(f7(c2))) | (c2 = f8(f7(c2))) | (~big_f(f7(f7(c2)), c2)) | (~big_f(c2, f10(f7(c2)))))),
% 28.53/18.74 inference(transitivity,[status(thm)],[13328, 13326])).
% 28.53/18.74 tff(13330,plain,
% 28.53/18.74 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f7(c2)) = f7(c2)) | (c2 = f8(f7(c2))) | (~big_f(c2, f10(f7(c2)))) | (f7(f7(c2)) = f7(c2)) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2)))),
% 28.53/18.74 inference(quant_inst,[status(thm)],[])).
% 28.53/18.74 tff(13331,plain,
% 28.53/18.74 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(f7(c2)) = f7(c2)) | (f10(f7(c2)) = f7(c2)) | (c2 = f5(f7(c2))) | (c2 = f8(f7(c2))) | (~big_f(f7(f7(c2)), c2)) | (~big_f(c2, f10(f7(c2))))),
% 28.53/18.74 inference(modus_ponens,[status(thm)],[13330, 13329])).
% 28.53/18.74 tff(13332,plain,
% 28.53/18.74 ((c2 = f5(f7(c2))) | (c2 = f8(f7(c2)))),
% 28.53/18.74 inference(unit_resolution,[status(thm)],[13331, 1659, 12943, 12448, 13325, 12443])).
% 28.53/18.74 tff(13333,plain,
% 28.53/18.74 (c2 = f5(f7(c2))),
% 28.53/18.74 inference(unit_resolution,[status(thm)],[13332, 13324])).
% 28.53/18.74 tff(13334,plain,
% 28.53/18.74 (f5(f7(c2)) = c2),
% 28.53/18.74 inference(symmetry,[status(thm)],[13333])).
% 28.53/18.74 tff(13335,plain,
% 28.53/18.74 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(f7(c2)) = f7(c2)) | (f10(f7(c2)) = f7(c2)) | (c2 = f8(f7(c2))) | (f7(c2) = f5(f7(c2))) | (~big_f(c2, f10(f7(c2)))) | (~big_f(f7(f7(c2)), f7(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(f7(c2)) = f7(c2)) | (f10(f7(c2)) = f7(c2)) | (c2 = f8(f7(c2))) | (f7(c2) = f5(f7(c2))) | (~big_f(c2, f10(f7(c2)))) | (~big_f(f7(f7(c2)), f7(c2))))),
% 28.53/18.74 inference(rewrite,[status(thm)],[])).
% 28.53/18.74 tff(13336,plain,
% 28.53/18.74 (((f10(f7(c2)) = f7(c2)) | (c2 = f8(f7(c2))) | (~big_f(c2, f10(f7(c2)))) | (f7(f7(c2)) = f7(c2)) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2)))) <=> ((f7(f7(c2)) = f7(c2)) | (f10(f7(c2)) = f7(c2)) | (c2 = f8(f7(c2))) | (f7(c2) = f5(f7(c2))) | (~big_f(c2, f10(f7(c2)))) | (~big_f(f7(f7(c2)), f7(c2))))),
% 28.53/18.74 inference(rewrite,[status(thm)],[])).
% 28.53/18.74 tff(13337,plain,
% 28.53/18.74 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f7(c2)) = f7(c2)) | (c2 = f8(f7(c2))) | (~big_f(c2, f10(f7(c2)))) | (f7(f7(c2)) = f7(c2)) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(f7(c2)) = f7(c2)) | (f10(f7(c2)) = f7(c2)) | (c2 = f8(f7(c2))) | (f7(c2) = f5(f7(c2))) | (~big_f(c2, f10(f7(c2)))) | (~big_f(f7(f7(c2)), f7(c2)))))),
% 28.53/18.74 inference(monotonicity,[status(thm)],[13336])).
% 28.53/18.74 tff(13338,plain,
% 28.53/18.74 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f7(c2)) = f7(c2)) | (c2 = f8(f7(c2))) | (~big_f(c2, f10(f7(c2)))) | (f7(f7(c2)) = f7(c2)) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(f7(c2)) = f7(c2)) | (f10(f7(c2)) = f7(c2)) | (c2 = f8(f7(c2))) | (f7(c2) = f5(f7(c2))) | (~big_f(c2, f10(f7(c2)))) | (~big_f(f7(f7(c2)), f7(c2))))),
% 28.53/18.74 inference(transitivity,[status(thm)],[13337, 13335])).
% 28.53/18.74 tff(13339,plain,
% 28.53/18.74 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f7(c2)) = f7(c2)) | (c2 = f8(f7(c2))) | (~big_f(c2, f10(f7(c2)))) | (f7(f7(c2)) = f7(c2)) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))))),
% 28.53/18.74 inference(quant_inst,[status(thm)],[])).
% 28.53/18.74 tff(13340,plain,
% 28.53/18.74 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(f7(c2)) = f7(c2)) | (f10(f7(c2)) = f7(c2)) | (c2 = f8(f7(c2))) | (f7(c2) = f5(f7(c2))) | (~big_f(c2, f10(f7(c2)))) | (~big_f(f7(f7(c2)), f7(c2)))),
% 28.53/18.74 inference(modus_ponens,[status(thm)],[13339, 13338])).
% 28.53/18.74 tff(13341,plain,
% 28.53/18.74 ((c2 = f8(f7(c2))) | (f7(c2) = f5(f7(c2)))),
% 28.53/18.74 inference(unit_resolution,[status(thm)],[13340, 1659, 12943, 12764, 12448, 13325])).
% 28.53/18.74 tff(13342,plain,
% 28.53/18.74 (f7(c2) = f5(f7(c2))),
% 28.53/18.74 inference(unit_resolution,[status(thm)],[13341, 13324])).
% 28.53/18.74 tff(13343,plain,
% 28.53/18.74 (f7(c2) = c2),
% 28.53/18.74 inference(transitivity,[status(thm)],[13342, 13334])).
% 28.53/18.74 tff(13344,plain,
% 28.53/18.74 ($false),
% 28.53/18.74 inference(unit_resolution,[status(thm)],[17, 13343])).
% 28.53/18.74 tff(13345,plain,((f7(c2) = c2) | (~(f4(c4) = c2)) | (f7(c1) = c1) | (f10(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 28.53/18.74 tff(13346,plain,
% 28.53/18.74 (f7(c2) = c2),
% 28.53/18.74 inference(unit_resolution,[status(thm)],[13345, 79, 115, 3])).
% 28.53/18.74 tff(13347,plain,
% 28.53/18.74 (big_f(f7(f10(c2)), f10(c2)) <=> big_f(c2, f10(c2))),
% 28.53/18.74 inference(monotonicity,[status(thm)],[11806])).
% 28.53/18.74 tff(13348,plain,
% 28.53/18.74 (big_f(c2, f10(c2)) <=> big_f(f7(f10(c2)), f10(c2))),
% 28.53/18.74 inference(symmetry,[status(thm)],[13347])).
% 28.53/18.74 tff(13349,plain,
% 28.53/18.74 (big_f(c2, c1) <=> big_f(c2, f10(c2))),
% 28.53/18.74 inference(monotonicity,[status(thm)],[11957])).
% 28.53/18.74 tff(13350,plain,
% 28.53/18.74 (big_f(c1, c1) <=> big_f(c1, f10(c2))),
% 28.53/18.74 inference(monotonicity,[status(thm)],[99])).
% 28.53/18.74 tff(13351,plain,
% 28.53/18.74 (big_f(c1, f10(c2)) <=> big_f(c1, c1)),
% 28.53/18.74 inference(symmetry,[status(thm)],[13350])).
% 28.53/18.74 tff(13352,plain,
% 28.53/18.74 ((c2 = f8(f7(f4(c4)))) <=> (c2 = f8(f7(c2)))),
% 28.53/18.74 inference(monotonicity,[status(thm)],[107])).
% 28.53/18.74 tff(13353,plain,
% 28.53/18.74 ((c2 = f8(f7(c2))) <=> (c2 = f8(f7(f4(c4))))),
% 28.53/18.74 inference(symmetry,[status(thm)],[13352])).
% 28.53/18.74 tff(13354,plain,
% 28.53/18.74 (f8(f7(c2)) = f8(c2)),
% 28.53/18.74 inference(monotonicity,[status(thm)],[77])).
% 28.53/18.74 tff(13355,plain,
% 28.53/18.74 ((c2 = f8(f7(c2))) <=> (c2 = f8(c2))),
% 28.53/18.74 inference(monotonicity,[status(thm)],[13354])).
% 28.53/18.74 tff(13356,plain,
% 28.53/18.74 ((c2 = f8(c2)) <=> (c2 = f8(f7(c2)))),
% 28.53/18.74 inference(symmetry,[status(thm)],[13355])).
% 28.53/18.74 tff(13357,plain,
% 28.53/18.74 ((c2 = f8(c2)) <=> (f8(f7(f4(c4))) = c2)),
% 28.53/18.74 inference(transitivity,[status(thm)],[13356, 13353, 106])).
% 28.53/18.74 tff(13358,plain,
% 28.53/18.74 ((~(c2 = f8(c2))) <=> (~(f8(f7(f4(c4))) = c2))),
% 28.53/18.74 inference(monotonicity,[status(thm)],[13357])).
% 28.53/18.74 tff(13359,plain,
% 28.53/18.74 (~(c2 = f8(c2))),
% 28.53/18.74 inference(unit_resolution,[status(thm)],[12077, 1745, 115, 89, 12071, 695, 11826])).
% 28.53/18.74 tff(13360,plain,
% 28.53/18.74 (~(f8(f7(f4(c4))) = c2)),
% 28.53/18.74 inference(modus_ponens,[status(thm)],[13359, 13358])).
% 28.53/18.74 tff(13361,plain,
% 28.53/18.74 (f8(f7(f4(c4))) = f8(c2)),
% 28.53/18.74 inference(transitivity,[status(thm)],[107, 13354])).
% 28.53/18.74 tff(13362,plain,
% 28.53/18.74 ((f8(f7(f4(c4))) = c1) <=> (f8(c2) = c1)),
% 28.53/18.74 inference(monotonicity,[status(thm)],[13361])).
% 28.53/18.74 tff(13363,plain,
% 28.53/18.74 ((f8(f7(f4(c4))) = c1) <=> (c1 = f8(c2))),
% 28.53/18.74 inference(transitivity,[status(thm)],[13362, 13044])).
% 28.53/18.74 tff(13364,plain,
% 28.53/18.74 ((c1 = f8(c2)) <=> (f8(f7(f4(c4))) = c1)),
% 28.53/18.74 inference(symmetry,[status(thm)],[13363])).
% 28.53/18.74 tff(13365,plain,
% 28.53/18.74 ((~(c1 = f8(c2))) <=> (~(f8(f7(f4(c4))) = c1))),
% 28.53/18.74 inference(monotonicity,[status(thm)],[13364])).
% 28.53/18.74 tff(13366,plain,
% 28.53/18.74 (~(c1 = f8(c2))),
% 28.53/18.74 inference(unit_resolution,[status(thm)],[12065, 1745, 115, 89, 695, 11826, 12055])).
% 28.53/18.74 tff(13367,plain,
% 28.53/18.74 (~(f8(f7(f4(c4))) = c1)),
% 28.53/18.74 inference(modus_ponens,[status(thm)],[13366, 13365])).
% 28.53/18.74 tff(13368,plain,
% 28.53/18.74 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f8(f7(f4(c4))) = c1) | (f8(f7(f4(c4))) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f8(f7(f4(c4))) = c1) | (f8(f7(f4(c4))) = c2))),
% 28.53/18.74 inference(rewrite,[status(thm)],[])).
% 28.53/18.74 tff(13369,plain,
% 28.53/18.74 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f8(f7(f4(c4))) = c1) | (f8(f7(f4(c4))) = c2))),
% 28.53/18.74 inference(quant_inst,[status(thm)],[])).
% 28.53/18.74 tff(13370,plain,
% 28.53/18.74 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f8(f7(f4(c4))) = c1) | (f8(f7(f4(c4))) = c2)),
% 28.53/18.74 inference(modus_ponens,[status(thm)],[13369, 13368])).
% 28.53/18.74 tff(13371,plain,
% 28.53/18.74 ((f8(f7(f4(c4))) = c1) | (f8(f7(f4(c4))) = c2)),
% 28.53/18.74 inference(unit_resolution,[status(thm)],[13370, 10])).
% 28.53/18.74 tff(13372,plain,
% 28.53/18.74 ($false),
% 28.53/18.74 inference(unit_resolution,[status(thm)],[13371, 13367, 13360])).
% 28.53/18.74 tff(13373,plain,(big_f(c2, c1) | (~(f7(c2) = c2)) | (~(f4(c4) = c2)) | (f7(c1) = c1) | (f10(c2) = c2) | (~(c1 = f5(c1))) | big_f(c1, f10(c2))), inference(lemma,lemma(discharge,[]))).
% 28.53/18.74 tff(13374,plain,
% 28.53/18.74 (big_f(c1, f10(c2))),
% 28.53/18.74 inference(unit_resolution,[status(thm)],[13373, 89, 79, 115, 77, 11826, 2])).
% 28.53/18.74 tff(13375,plain,
% 28.53/18.74 (big_f(c1, c1)),
% 28.53/18.74 inference(modus_ponens,[status(thm)],[13374, 13351])).
% 28.53/18.74 tff(13376,plain,
% 28.53/18.74 ($false),
% 28.53/18.74 inference(unit_resolution,[status(thm)],[66, 13375])).
% 28.53/18.74 tff(13377,plain,((f10(c2) = c2) | big_f(c1, c1) | (~(f4(c4) = c2)) | (f7(c1) = c1) | (~(f7(c2) = c2)) | (~(c1 = f5(c1))) | big_f(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 28.53/18.74 tff(13378,plain,
% 28.53/18.74 (~(c1 = f5(c1))),
% 28.53/18.74 inference(unit_resolution,[status(thm)],[13377, 11991, 79, 115, 13346, 11798, 2])).
% 28.53/18.74 tff(13379,plain,
% 28.53/18.74 ($false),
% 28.53/18.74 inference(unit_resolution,[status(thm)],[13378, 12045])).
% 28.53/18.74 tff(13380,plain,(big_f(c2, c1) | big_f(c2, c2) | (f7(c1) = c1) | (~(f4(c4) = c2)) | (f10(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 28.53/18.74 tff(13381,plain,
% 28.53/18.74 (big_f(c2, c1)),
% 28.53/18.74 inference(unit_resolution,[status(thm)],[13380, 121, 115, 79, 3])).
% 28.53/18.74 tff(13382,plain,
% 28.53/18.74 (big_f(c2, f10(c2))),
% 28.53/18.74 inference(modus_ponens,[status(thm)],[13381, 13349])).
% 28.53/18.74 tff(13383,plain,
% 28.53/18.74 (big_f(f7(f10(c2)), f10(c2))),
% 28.53/18.74 inference(modus_ponens,[status(thm)],[13382, 13348])).
% 28.53/18.74 tff(13384,plain,
% 28.53/18.74 (f7(f7(c2)) = f7(c2)),
% 28.53/18.74 inference(monotonicity,[status(thm)],[13346])).
% 28.53/18.74 tff(13385,plain,
% 28.53/18.74 (f7(f7(c2)) = c2),
% 28.53/18.74 inference(transitivity,[status(thm)],[13384, 13346])).
% 28.53/18.74 tff(13386,plain,
% 28.53/18.74 ((f7(f7(c2)) = c3) <=> (c2 = c3)),
% 28.53/18.74 inference(monotonicity,[status(thm)],[13385])).
% 28.53/18.74 tff(13387,plain,
% 28.53/18.74 ((c2 = c3) <=> (f7(f7(c2)) = c3)),
% 28.53/18.74 inference(symmetry,[status(thm)],[13386])).
% 28.53/18.74 tff(13388,plain,
% 28.53/18.74 ((c3 = c2) <=> (f7(f7(c2)) = c3)),
% 28.53/18.74 inference(transitivity,[status(thm)],[78, 13387])).
% 28.53/18.74 tff(13389,plain,
% 28.53/18.74 ((~(c3 = c2)) <=> (~(f7(f7(c2)) = c3))),
% 28.53/18.74 inference(monotonicity,[status(thm)],[13388])).
% 28.53/18.74 tff(13390,plain,
% 28.53/18.74 (~(c2 = f8(c1))),
% 28.53/18.74 inference(unit_resolution,[status(thm)],[1752, 1726, 115, 1727, 6126, 3])).
% 28.53/18.74 tff(13391,plain,
% 28.53/18.74 (~(f8(c1) = c2)),
% 28.53/18.74 inference(unit_resolution,[status(thm)],[1675, 13390])).
% 28.53/18.74 tff(13392,plain,
% 28.53/18.74 (f8(c1) = c1),
% 28.53/18.74 inference(unit_resolution,[status(thm)],[1680, 13391])).
% 28.53/18.74 tff(13393,plain,
% 28.53/18.74 (big_f(f8(c1), f10(c1)) <=> big_f(c1, c2)),
% 28.53/18.74 inference(monotonicity,[status(thm)],[13392, 15])).
% 28.53/18.74 tff(13394,plain,
% 28.53/18.74 (big_f(f8(c1), f10(c1))),
% 28.53/18.74 inference(unit_resolution,[status(thm)],[2848, 1716, 115, 3])).
% 28.53/18.74 tff(13395,plain,
% 28.53/18.74 (big_f(c1, c2)),
% 28.53/18.74 inference(modus_ponens,[status(thm)],[13394, 13393])).
% 28.53/18.74 tff(13396,plain,
% 28.53/18.74 ((c1 = c3) <=> (f10(c2) = c3)),
% 28.53/18.74 inference(monotonicity,[status(thm)],[11957])).
% 28.53/18.74 tff(13397,plain,
% 28.53/18.74 ((f10(c2) = c3) <=> (c1 = c3)),
% 28.53/18.74 inference(symmetry,[status(thm)],[13396])).
% 28.53/18.74 tff(13398,assumption,(c2 = f5(f10(c2))), introduced(assumption)).
% 28.53/18.74 tff(13399,plain,
% 28.53/18.74 (f8(f10(c2)) = c1),
% 28.53/18.74 inference(transitivity,[status(thm)],[11820, 3018])).
% 28.53/18.74 tff(13400,plain,
% 28.53/18.74 ((f3(c2, c1) = f8(f10(c2))) <=> (f3(c2, c1) = c1)),
% 28.53/18.74 inference(monotonicity,[status(thm)],[13399])).
% 28.53/18.74 tff(13401,plain,
% 28.53/18.74 ((f3(c2, c1) = c1) <=> (f3(c2, c1) = f8(f10(c2)))),
% 28.53/18.74 inference(symmetry,[status(thm)],[13400])).
% 28.53/18.74 tff(13402,plain,
% 28.53/18.74 ((~(f3(c2, c1) = c1)) <=> (~(f3(c2, c1) = f8(f10(c2))))),
% 28.53/18.74 inference(monotonicity,[status(thm)],[13401])).
% 28.53/18.74 tff(13403,plain,
% 28.53/18.74 (big_f(f3(c2, c1), c2)),
% 28.53/18.74 inference(unit_resolution,[status(thm)],[12223, 873, 348, 121, 2865, 347, 377, 1004])).
% 28.53/18.74 tff(13404,assumption,(big_f(f3(c2, c1), c2)), introduced(assumption)).
% 28.53/18.74 tff(13405,assumption,(f3(c2, c1) = c1), introduced(assumption)).
% 28.53/18.74 tff(13406,plain,
% 28.53/18.74 ((~big_f(f7(c1), f1(f7(c1), c1))) <=> (~big_f(c2, f1(c2, c1)))),
% 28.53/18.74 inference(monotonicity,[status(thm)],[990])).
% 28.53/18.74 tff(13407,plain,
% 28.53/18.74 (~big_f(c2, f1(c2, c1))),
% 28.53/18.74 inference(modus_ponens,[status(thm)],[12204, 13406])).
% 28.53/18.74 tff(13408,plain,
% 28.53/18.74 ($false),
% 28.53/18.74 inference(unit_resolution,[status(thm)],[11484, 13407])).
% 28.53/18.74 tff(13409,plain,((~big_f(c2, f1(c2, c1))) | big_f(f7(c1), f1(f7(c1), c1)) | (~(f7(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.53/18.74 tff(13410,plain,
% 28.53/18.74 (~big_f(c2, f1(c2, c1))),
% 28.53/18.74 inference(unit_resolution,[status(thm)],[13409, 12198, 347])).
% 28.53/18.74 tff(13411,plain,
% 28.53/18.74 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c3) | (c2 = c4) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c2 = c3) | (c2 = c4) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)))),
% 28.53/18.74 inference(rewrite,[status(thm)],[])).
% 28.53/18.74 tff(13412,plain,
% 28.53/18.74 (((c2 = c4) | (c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2))) <=> ((c2 = c3) | (c2 = c4) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)))),
% 28.53/18.74 inference(rewrite,[status(thm)],[])).
% 28.53/18.74 tff(13413,plain,
% 28.53/18.74 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c4) | (c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c3) | (c2 = c4) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2))))),
% 28.53/18.74 inference(monotonicity,[status(thm)],[13412])).
% 28.53/18.74 tff(13414,plain,
% 28.53/18.74 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c4) | (c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c2 = c3) | (c2 = c4) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)))),
% 28.53/18.74 inference(transitivity,[status(thm)],[13413, 13411])).
% 28.53/18.74 tff(13415,plain,
% 28.53/18.74 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c4) | (c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)))),
% 28.53/18.74 inference(quant_inst,[status(thm)],[])).
% 28.53/18.74 tff(13416,plain,
% 28.53/18.74 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c2 = c3) | (c2 = c4) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2))),
% 28.53/18.74 inference(modus_ponens,[status(thm)],[13415, 13414])).
% 28.53/18.74 tff(13417,plain,
% 28.53/18.74 ($false),
% 28.53/18.74 inference(unit_resolution,[status(thm)],[13416, 969, 873, 377, 12187, 13410, 13405, 13404])).
% 28.53/18.74 tff(13418,plain,((f1(c2, c1) = c1) | (c2 = c4) | (c2 = c3) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)) | (~(f7(c1) = c2)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 28.53/18.74 tff(13419,plain,
% 28.53/18.74 (f1(c2, c1) = c1),
% 28.53/18.74 inference(unit_resolution,[status(thm)],[13418, 13405, 377, 873, 13404, 347, 121])).
% 28.53/18.74 tff(13420,plain,
% 28.53/18.74 (big_f(c2, f1(c2, c1)) <=> big_f(c2, c1)),
% 28.53/18.74 inference(monotonicity,[status(thm)],[13419])).
% 28.53/18.74 tff(13421,plain,
% 28.53/18.74 (big_f(c2, c1) <=> big_f(c2, f1(c2, c1))),
% 28.53/18.74 inference(symmetry,[status(thm)],[13420])).
% 28.53/18.74 tff(13422,plain,
% 28.53/18.74 (big_f(c2, f1(c2, c1))),
% 28.53/18.74 inference(modus_ponens,[status(thm)],[348, 13421])).
% 28.53/18.74 tff(13423,plain,
% 28.53/18.74 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (c2 = c4) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1)) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (c2 = c4) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1)) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)))),
% 28.53/18.74 inference(rewrite,[status(thm)],[])).
% 28.53/18.74 tff(13424,plain,
% 28.53/18.74 (((c2 = c4) | (c2 = c3) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)) | (~(f1(c2, c1) = c1)) | (~big_f(c2, f1(c2, c1)))) <=> ((c2 = c3) | (c2 = c4) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1)) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)))),
% 28.53/18.74 inference(rewrite,[status(thm)],[])).
% 28.53/18.74 tff(13425,plain,
% 28.53/18.74 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (c2 = c3) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)) | (~(f1(c2, c1) = c1)) | (~big_f(c2, f1(c2, c1))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (c2 = c4) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1)) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2))))),
% 28.53/18.74 inference(monotonicity,[status(thm)],[13424])).
% 28.53/18.74 tff(13426,plain,
% 28.53/18.74 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (c2 = c3) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)) | (~(f1(c2, c1) = c1)) | (~big_f(c2, f1(c2, c1))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (c2 = c4) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1)) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)))),
% 28.53/18.74 inference(transitivity,[status(thm)],[13425, 13423])).
% 28.53/18.74 tff(13427,plain,
% 28.53/18.74 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (c2 = c3) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)) | (~(f1(c2, c1) = c1)) | (~big_f(c2, f1(c2, c1))))),
% 28.53/18.74 inference(quant_inst,[status(thm)],[])).
% 28.53/18.74 tff(13428,plain,
% 28.53/18.74 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (c2 = c4) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1)) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2))),
% 28.53/18.74 inference(modus_ponens,[status(thm)],[13427, 13426])).
% 28.53/18.74 tff(13429,plain,
% 28.53/18.74 ($false),
% 28.53/18.74 inference(unit_resolution,[status(thm)],[13428, 933, 873, 377, 13419, 13422, 13405, 13404])).
% 28.53/18.74 tff(13430,plain,((~(f3(c2, c1) = c1)) | (c2 = c4) | (c2 = c3) | (~big_f(f3(c2, c1), c2)) | (~big_f(c2, c1)) | (~(f7(c1) = c2)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 28.53/18.74 tff(13431,plain,
% 28.53/18.74 (~(f3(c2, c1) = c1)),
% 28.53/18.74 inference(unit_resolution,[status(thm)],[13430, 13403, 377, 873, 348, 347, 121])).
% 28.53/18.74 tff(13432,plain,
% 28.53/18.74 (~(f3(c2, c1) = f8(f10(c2)))),
% 28.53/18.74 inference(modus_ponens,[status(thm)],[13431, 13402])).
% 28.53/18.74 tff(13433,plain,
% 28.53/18.74 (f10(f10(c2)) = c2),
% 28.53/18.74 inference(transitivity,[status(thm)],[11844, 16])).
% 28.53/18.74 tff(13434,plain,
% 28.53/18.74 (big_f(f3(c2, c1), f10(f10(c2))) <=> big_f(f3(c2, c1), c2)),
% 28.53/18.74 inference(monotonicity,[status(thm)],[13433])).
% 28.53/18.74 tff(13435,plain,
% 28.53/18.74 (big_f(f3(c2, c1), c2) <=> big_f(f3(c2, c1), f10(f10(c2)))),
% 28.53/18.74 inference(symmetry,[status(thm)],[13434])).
% 28.53/18.74 tff(13436,plain,
% 28.53/18.74 (big_f(f3(c2, c1), f10(f10(c2)))),
% 28.53/18.74 inference(modus_ponens,[status(thm)],[13403, 13435])).
% 28.53/18.74 tff(13437,plain,
% 28.53/18.74 (f7(f10(c2)) = c2),
% 28.53/18.74 inference(transitivity,[status(thm)],[11889, 347])).
% 28.53/18.74 tff(13438,plain,
% 28.53/18.74 (big_f(f7(f10(c2)), c2) <=> big_f(c2, c2)),
% 28.53/18.74 inference(monotonicity,[status(thm)],[13437])).
% 28.53/18.74 tff(13439,plain,
% 28.53/18.74 (big_f(c2, c2) <=> big_f(f7(f10(c2)), c2)),
% 28.53/18.74 inference(symmetry,[status(thm)],[13438])).
% 28.53/18.74 tff(13440,plain,
% 28.53/18.74 ((~big_f(c2, c2)) <=> (~big_f(f7(f10(c2)), c2))),
% 28.53/18.74 inference(monotonicity,[status(thm)],[13439])).
% 28.53/18.74 tff(13441,plain,
% 28.53/18.74 (~big_f(f7(f10(c2)), c2)),
% 28.53/18.74 inference(modus_ponens,[status(thm)],[121, 13440])).
% 28.53/18.74 tff(13442,plain,
% 28.53/18.74 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f10(f10(c2)) = f10(c2)) | (~(c2 = f5(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2) | (f3(c2, c1) = f8(f10(c2))) | (~big_f(f3(c2, c1), f10(f10(c2)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(f10(c2)) = f10(c2)) | (~(c2 = f5(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2) | (f3(c2, c1) = f8(f10(c2))) | (~big_f(f3(c2, c1), f10(f10(c2)))))),
% 28.53/18.74 inference(rewrite,[status(thm)],[])).
% 28.53/18.74 tff(13443,plain,
% 28.53/18.74 (((~(c2 = f5(f10(c2)))) | (f10(f10(c2)) = f10(c2)) | (f3(c2, c1) = f8(f10(c2))) | (~big_f(f3(c2, c1), f10(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2)) <=> ((f10(f10(c2)) = f10(c2)) | (~(c2 = f5(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2) | (f3(c2, c1) = f8(f10(c2))) | (~big_f(f3(c2, c1), f10(f10(c2)))))),
% 28.53/18.74 inference(rewrite,[status(thm)],[])).
% 28.53/18.74 tff(13444,plain,
% 28.53/18.74 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c2 = f5(f10(c2)))) | (f10(f10(c2)) = f10(c2)) | (f3(c2, c1) = f8(f10(c2))) | (~big_f(f3(c2, c1), f10(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f10(f10(c2)) = f10(c2)) | (~(c2 = f5(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2) | (f3(c2, c1) = f8(f10(c2))) | (~big_f(f3(c2, c1), f10(f10(c2))))))),
% 28.53/18.74 inference(monotonicity,[status(thm)],[13443])).
% 28.53/18.74 tff(13445,plain,
% 28.53/18.74 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c2 = f5(f10(c2)))) | (f10(f10(c2)) = f10(c2)) | (f3(c2, c1) = f8(f10(c2))) | (~big_f(f3(c2, c1), f10(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(f10(c2)) = f10(c2)) | (~(c2 = f5(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2) | (f3(c2, c1) = f8(f10(c2))) | (~big_f(f3(c2, c1), f10(f10(c2)))))),
% 28.53/18.74 inference(transitivity,[status(thm)],[13444, 13442])).
% 28.53/18.74 tff(13446,plain,
% 28.53/18.74 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c2 = f5(f10(c2)))) | (f10(f10(c2)) = f10(c2)) | (f3(c2, c1) = f8(f10(c2))) | (~big_f(f3(c2, c1), f10(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2))),
% 28.53/18.75 inference(quant_inst,[status(thm)],[])).
% 28.53/18.75 tff(13447,plain,
% 28.53/18.75 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(f10(c2)) = f10(c2)) | (~(c2 = f5(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2) | (f3(c2, c1) = f8(f10(c2))) | (~big_f(f3(c2, c1), f10(f10(c2))))),
% 28.53/18.75 inference(modus_ponens,[status(thm)],[13446, 13445])).
% 28.53/18.75 tff(13448,plain,
% 28.53/18.75 ((f3(c2, c1) = f8(f10(c2))) | (~big_f(f3(c2, c1), f10(f10(c2))))),
% 28.53/18.75 inference(unit_resolution,[status(thm)],[13447, 705, 11896, 13398, 11895, 13441])).
% 28.53/18.75 tff(13449,plain,
% 28.53/18.75 ($false),
% 28.53/18.75 inference(unit_resolution,[status(thm)],[13448, 13436, 13432])).
% 28.53/18.75 tff(13450,plain,((c2 = c4) | (f10(f10(c2)) = f10(c2)) | (~(c2 = f5(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | (~(f10(c1) = c2)) | (~(f10(c2) = c1)) | (~(f8(c1) = c1)) | (c2 = c3) | (~big_f(c2, c1)) | (~(f7(c1) = c2)) | big_f(c2, c2) | (~big_f(c1, c2))), inference(lemma,lemma(discharge,[]))).
% 28.53/18.75 tff(13451,plain,
% 28.53/18.75 (c2 = c4),
% 28.53/18.75 inference(unit_resolution,[status(thm)],[13450, 377, 13398, 11895, 16, 11819, 3018, 11896, 348, 347, 121, 2865])).
% 28.53/18.75 tff(13452,plain,
% 28.53/18.75 (c4 = c2),
% 28.53/18.75 inference(modus_ponens,[status(thm)],[13451, 8721])).
% 28.53/18.75 tff(13453,plain,
% 28.53/18.75 (c4 = c2),
% 28.53/18.75 inference(symmetry,[status(thm)],[13451])).
% 28.53/18.75 tff(13454,plain,
% 28.53/18.75 (big_f(c2, c4) <=> big_f(c2, c2)),
% 28.53/18.75 inference(monotonicity,[status(thm)],[13453])).
% 28.53/18.75 tff(13455,plain,
% 28.53/18.75 (big_f(c2, c2) <=> big_f(c2, c4)),
% 28.53/18.75 inference(symmetry,[status(thm)],[13454])).
% 28.53/18.75 tff(13456,plain,
% 28.53/18.75 ((~big_f(c2, c2)) <=> (~big_f(c2, c4))),
% 28.53/18.75 inference(monotonicity,[status(thm)],[13455])).
% 28.53/18.75 tff(13457,plain,
% 28.53/18.75 (~big_f(c2, c4)),
% 28.53/18.75 inference(modus_ponens,[status(thm)],[121, 13456])).
% 28.53/18.75 tff(13458,plain,
% 28.53/18.75 (big_f(c2, f1(c2, c1))),
% 28.53/18.75 inference(unit_resolution,[status(thm)],[10105, 13457, 2602, 348, 377])).
% 28.53/18.75 tff(13459,plain,
% 28.53/18.75 (~(f1(c2, c1) = c1)),
% 28.53/18.75 inference(unit_resolution,[status(thm)],[11494, 13458, 79, 121, 377, 13452])).
% 28.53/18.75 tff(13460,plain,
% 28.53/18.75 (big_f(f7(c1), f1(f7(c1), c1))),
% 28.53/18.75 inference(unit_resolution,[status(thm)],[13409, 13458, 347])).
% 28.53/18.75 tff(13461,plain,
% 28.53/18.75 (~(f1(c2, c1) = c2)),
% 28.53/18.75 inference(unit_resolution,[status(thm)],[12197, 13460, 121, 347])).
% 28.53/18.75 tff(13462,plain,
% 28.53/18.75 ($false),
% 28.53/18.75 inference(unit_resolution,[status(thm)],[10113, 13461, 13459])).
% 28.53/18.75 tff(13463,plain,((c2 = c3) | big_f(c2, c2) | (~(f7(c1) = c2)) | (~(f4(c4) = c2)) | (~big_f(c2, c1)) | (~(c2 = f5(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | (~(f10(c1) = c2)) | (~(f10(c2) = c1)) | (~(f8(c1) = c1)) | (f10(f10(c2)) = f10(c2)) | (~big_f(c1, c2))), inference(lemma,lemma(discharge,[]))).
% 28.53/18.75 tff(13464,plain,
% 28.53/18.75 (c2 = c3),
% 28.53/18.75 inference(unit_resolution,[status(thm)],[13463, 121, 120, 79, 348, 12032, 11811, 15, 11799, 13392, 11818, 13395])).
% 28.53/18.75 tff(13465,plain,
% 28.53/18.75 (c3 = c2),
% 28.53/18.75 inference(symmetry,[status(thm)],[13464])).
% 28.53/18.75 tff(13466,plain,
% 28.53/18.75 ((f10(c2) = c3) <=> (f10(c2) = c2)),
% 28.53/18.75 inference(monotonicity,[status(thm)],[13465])).
% 28.53/18.75 tff(13467,plain,
% 28.53/18.75 ((f10(c2) = c2) <=> (f10(c2) = c3)),
% 28.53/18.75 inference(symmetry,[status(thm)],[13466])).
% 28.53/18.75 tff(13468,plain,
% 28.53/18.75 ((f10(c2) = c2) <=> (c1 = c3)),
% 28.53/18.75 inference(transitivity,[status(thm)],[13467, 13397])).
% 28.53/18.75 tff(13469,plain,
% 28.53/18.75 ((~(f10(c2) = c2)) <=> (~(c1 = c3))),
% 28.53/18.75 inference(monotonicity,[status(thm)],[13468])).
% 28.53/18.75 tff(13470,plain,
% 28.53/18.75 (~(c1 = c3)),
% 28.53/18.75 inference(modus_ponens,[status(thm)],[11798, 13469])).
% 28.53/18.75 tff(13471,plain,
% 28.53/18.75 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f1(c1, c2) = c2) | (c1 = c3) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | big_f(c1, f1(c1, c2)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (f1(c1, c2) = c2) | (c1 = c3) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | big_f(c1, f1(c1, c2)))),
% 28.53/18.75 inference(rewrite,[status(thm)],[])).
% 28.53/18.75 tff(13472,plain,
% 28.53/18.75 (((c1 = c3) | (f1(c1, c2) = c2) | big_f(c1, f1(c1, c2)) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2)))) <=> ((f1(c1, c2) = c2) | (c1 = c3) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | big_f(c1, f1(c1, c2)))),
% 28.53/18.75 inference(rewrite,[status(thm)],[])).
% 28.53/18.75 tff(13473,plain,
% 28.53/18.75 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c1 = c3) | (f1(c1, c2) = c2) | big_f(c1, f1(c1, c2)) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f1(c1, c2) = c2) | (c1 = c3) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | big_f(c1, f1(c1, c2))))),
% 28.53/18.75 inference(monotonicity,[status(thm)],[13472])).
% 28.53/18.75 tff(13474,plain,
% 28.53/18.75 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c1 = c3) | (f1(c1, c2) = c2) | big_f(c1, f1(c1, c2)) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (f1(c1, c2) = c2) | (c1 = c3) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | big_f(c1, f1(c1, c2)))),
% 28.53/18.75 inference(transitivity,[status(thm)],[13473, 13471])).
% 28.53/18.75 tff(13475,plain,
% 28.53/18.75 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c1 = c3) | (f1(c1, c2) = c2) | big_f(c1, f1(c1, c2)) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))))),
% 28.53/18.75 inference(quant_inst,[status(thm)],[])).
% 28.53/18.75 tff(13476,plain,
% 28.53/18.75 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (f1(c1, c2) = c2) | (c1 = c3) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | big_f(c1, f1(c1, c2))),
% 28.53/18.75 inference(modus_ponens,[status(thm)],[13475, 13474])).
% 28.53/18.75 tff(13477,plain,
% 28.53/18.75 ($false),
% 28.53/18.75 inference(unit_resolution,[status(thm)],[13476, 402, 168, 631, 630, 121, 1052, 7524])).
% 28.53/18.75 tff(13478,plain,((f1(c1, c2) = c2) | (c1 = c3) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 28.53/18.75 tff(13479,plain,
% 28.53/18.75 (f1(c1, c2) = c2),
% 28.53/18.75 inference(unit_resolution,[status(thm)],[13478, 432, 168, 437, 121, 66])).
% 28.53/18.75 tff(13480,plain,
% 28.53/18.75 (big_f(c1, f1(c1, c2)) <=> big_f(c1, c2)),
% 28.53/18.75 inference(monotonicity,[status(thm)],[13479])).
% 28.53/18.75 tff(13481,plain,
% 28.53/18.75 (big_f(c1, c2) <=> big_f(c1, f1(c1, c2))),
% 28.53/18.75 inference(symmetry,[status(thm)],[13480])).
% 28.53/18.75 tff(13482,plain,
% 28.53/18.75 (big_f(c1, f1(c1, c2))),
% 28.53/18.75 inference(modus_ponens,[status(thm)],[2865, 13481])).
% 28.53/18.75 tff(13483,plain,
% 28.53/18.75 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (~big_f(c1, f1(c1, c2))) | (~(f1(c1, c2) = c2)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (~big_f(c1, f1(c1, c2))) | (~(f1(c1, c2) = c2)))),
% 28.53/18.75 inference(rewrite,[status(thm)],[])).
% 28.53/18.75 tff(13484,plain,
% 28.53/18.75 (((c1 = c3) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))) | (~(f1(c1, c2) = c2)) | (~big_f(c1, f1(c1, c2)))) <=> ((c1 = c3) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (~big_f(c1, f1(c1, c2))) | (~(f1(c1, c2) = c2)))),
% 28.53/18.75 inference(rewrite,[status(thm)],[])).
% 28.53/18.75 tff(13485,plain,
% 28.53/18.75 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))) | (~(f1(c1, c2) = c2)) | (~big_f(c1, f1(c1, c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (~big_f(c1, f1(c1, c2))) | (~(f1(c1, c2) = c2))))),
% 28.53/18.75 inference(monotonicity,[status(thm)],[13484])).
% 28.53/18.75 tff(13486,plain,
% 28.53/18.75 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))) | (~(f1(c1, c2) = c2)) | (~big_f(c1, f1(c1, c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (~big_f(c1, f1(c1, c2))) | (~(f1(c1, c2) = c2)))),
% 28.53/18.75 inference(transitivity,[status(thm)],[13485, 13483])).
% 28.53/18.75 tff(13487,plain,
% 28.53/18.75 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~(c2 = c4)) | big_f(c2, c2) | (~(c2 = f4(c2))) | (~(f1(c1, c2) = c2)) | (~big_f(c1, f1(c1, c2))))),
% 28.53/18.75 inference(quant_inst,[status(thm)],[])).
% 28.53/18.75 tff(13488,plain,
% 28.53/18.75 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (~(c2 = c4)) | (~(c2 = f4(c2))) | big_f(c2, c2) | (~big_f(c1, f1(c1, c2))) | (~(f1(c1, c2) = c2))),
% 28.53/18.75 inference(modus_ponens,[status(thm)],[13487, 13486])).
% 28.53/18.75 tff(13489,plain,
% 28.53/18.75 ($false),
% 28.53/18.75 inference(unit_resolution,[status(thm)],[13488, 447, 168, 432, 437, 121, 13479, 13482])).
% 28.53/18.75 tff(13490,plain,((~(c4 = c2)) | (c1 = c3) | big_f(c2, c2) | (~big_f(c1, c2)) | big_f(c1, c1) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.53/18.75 tff(13491,plain,
% 28.53/18.75 (~(c4 = c2)),
% 28.53/18.75 inference(unit_resolution,[status(thm)],[13490, 13470, 121, 13395, 66, 79])).
% 28.53/18.75 tff(13492,plain,
% 28.53/18.75 (c4 = c1),
% 28.53/18.75 inference(unit_resolution,[status(thm)],[461, 13491])).
% 28.53/18.75 tff(13493,plain,
% 28.53/18.75 (c4 = f10(c2)),
% 28.53/18.75 inference(transitivity,[status(thm)],[13492, 11957])).
% 28.53/18.75 tff(13494,plain,
% 28.53/18.75 ((c2 = c4) <=> (c2 = f10(c2))),
% 28.53/18.75 inference(monotonicity,[status(thm)],[13493])).
% 28.53/18.75 tff(13495,plain,
% 28.53/18.75 ((c2 = c4) <=> (f10(c2) = c2)),
% 28.53/18.75 inference(transitivity,[status(thm)],[13494, 4987])).
% 28.53/18.75 tff(13496,plain,
% 28.53/18.75 ((f10(c2) = c2) <=> (c2 = c4)),
% 28.53/18.75 inference(symmetry,[status(thm)],[13495])).
% 28.53/18.75 tff(13497,plain,
% 28.53/18.75 ((~(f10(c2) = c2)) <=> (~(c2 = c4))),
% 28.53/18.75 inference(monotonicity,[status(thm)],[13496])).
% 28.53/18.75 tff(13498,plain,
% 28.53/18.75 (~(c2 = c4)),
% 28.53/18.75 inference(modus_ponens,[status(thm)],[11798, 13497])).
% 28.53/18.75 tff(13499,plain,
% 28.53/18.75 (f3(c2, c1) = c2),
% 28.53/18.75 inference(transitivity,[status(thm)],[3125, 881])).
% 28.53/18.75 tff(13500,plain,
% 28.53/18.75 (big_f(f3(c2, c1), c2) <=> big_f(c2, c2)),
% 28.53/18.75 inference(monotonicity,[status(thm)],[13499])).
% 28.53/18.75 tff(13501,plain,
% 28.53/18.75 (big_f(c2, c2) <=> big_f(f3(c2, c1), c2)),
% 28.53/18.75 inference(symmetry,[status(thm)],[13500])).
% 28.53/18.75 tff(13502,plain,
% 28.53/18.75 ((~big_f(c2, c2)) <=> (~big_f(f3(c2, c1), c2))),
% 28.53/18.75 inference(monotonicity,[status(thm)],[13501])).
% 28.53/18.75 tff(13503,plain,
% 28.53/18.75 (~big_f(f3(c2, c1), c2)),
% 28.53/18.75 inference(modus_ponens,[status(thm)],[121, 13502])).
% 28.53/18.75 tff(13504,plain,
% 28.53/18.75 ((f3(c2, c1) = c1) <=> (c2 = c1)),
% 28.53/18.75 inference(monotonicity,[status(thm)],[13499])).
% 28.53/18.75 tff(13505,plain,
% 28.53/18.75 ((c2 = c1) <=> (f3(c2, c1) = c1)),
% 28.53/18.75 inference(symmetry,[status(thm)],[13504])).
% 28.53/18.75 tff(13506,plain,
% 28.53/18.75 ((~(c2 = c1)) <=> (~(f3(c2, c1) = c1))),
% 28.53/18.75 inference(monotonicity,[status(thm)],[13505])).
% 28.53/18.75 tff(13507,plain,
% 28.53/18.75 (~(f3(c2, c1) = c1)),
% 28.53/18.75 inference(modus_ponens,[status(thm)],[75, 13506])).
% 28.53/18.75 tff(13508,assumption,(~big_f(c1, f1(c1, c2))), introduced(assumption)).
% 28.53/18.75 tff(13509,plain,
% 28.53/18.75 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f1(c1, c2) = c2) | (c1 = c3) | (c2 = c4) | big_f(c1, f1(c1, c2)) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (f1(c1, c2) = c2) | (c1 = c3) | (c2 = c4) | big_f(c1, f1(c1, c2)) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2))),
% 28.53/18.75 inference(rewrite,[status(thm)],[])).
% 28.53/18.75 tff(13510,plain,
% 28.53/18.75 (((c2 = c4) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2) | (c1 = c3) | (f1(c1, c2) = c2) | big_f(c1, f1(c1, c2))) <=> ((f1(c1, c2) = c2) | (c1 = c3) | (c2 = c4) | big_f(c1, f1(c1, c2)) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2))),
% 28.53/18.75 inference(rewrite,[status(thm)],[])).
% 28.53/18.75 tff(13511,plain,
% 28.53/18.75 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c2 = c4) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2) | (c1 = c3) | (f1(c1, c2) = c2) | big_f(c1, f1(c1, c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f1(c1, c2) = c2) | (c1 = c3) | (c2 = c4) | big_f(c1, f1(c1, c2)) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2)))),
% 28.53/18.75 inference(monotonicity,[status(thm)],[13510])).
% 28.53/18.75 tff(13512,plain,
% 28.53/18.75 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c2 = c4) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2) | (c1 = c3) | (f1(c1, c2) = c2) | big_f(c1, f1(c1, c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (f1(c1, c2) = c2) | (c1 = c3) | (c2 = c4) | big_f(c1, f1(c1, c2)) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2))),
% 28.53/18.75 inference(transitivity,[status(thm)],[13511, 13509])).
% 28.53/18.75 tff(13513,plain,
% 28.53/18.75 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c2 = c4) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2) | (c1 = c3) | (f1(c1, c2) = c2) | big_f(c1, f1(c1, c2)))),
% 28.53/18.75 inference(quant_inst,[status(thm)],[])).
% 28.53/18.75 tff(13514,plain,
% 28.53/18.75 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (f1(c1, c2) = c2) | (c1 = c3) | (c2 = c4) | big_f(c1, f1(c1, c2)) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2)),
% 28.53/18.75 inference(modus_ponens,[status(thm)],[13513, 13512])).
% 28.53/18.75 tff(13515,plain,
% 28.53/18.75 ($false),
% 28.53/18.75 inference(unit_resolution,[status(thm)],[13514, 1014, 168, 873, 1052, 13508, 13507, 13503])).
% 28.53/18.75 tff(13516,plain,((~(f3(f7(c1), c1) = c2)) | (c1 = c3) | (c2 = c4) | (f1(c1, c2) = c2) | big_f(c1, f1(c1, c2)) | big_f(c2, c2) | (~(f7(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.53/18.75 tff(13517,plain,
% 28.53/18.75 (~(f3(f7(c1), c1) = c2)),
% 28.53/18.75 inference(unit_resolution,[status(thm)],[13516, 1052, 873, 168, 7524, 121, 347])).
% 28.53/18.75 tff(13518,plain,
% 28.53/18.75 (f3(f7(c1), c1) = c1),
% 28.53/18.75 inference(unit_resolution,[status(thm)],[918, 13517])).
% 28.53/18.75 tff(13519,plain,
% 28.53/18.75 (f3(c2, c1) = c1),
% 28.53/18.75 inference(transitivity,[status(thm)],[3125, 13518])).
% 28.53/18.75 tff(13520,plain,
% 28.53/18.75 (big_f(f3(c2, c1), c2) <=> big_f(c1, c2)),
% 28.53/18.75 inference(monotonicity,[status(thm)],[13519])).
% 28.53/18.75 tff(13521,plain,
% 28.53/18.75 (big_f(c1, c2) <=> big_f(f3(c2, c1), c2)),
% 28.53/18.75 inference(symmetry,[status(thm)],[13520])).
% 28.53/18.75 tff(13522,plain,
% 28.53/18.75 (big_f(f3(c2, c1), c2)),
% 28.53/18.75 inference(modus_ponens,[status(thm)],[2865, 13521])).
% 28.53/18.75 tff(13523,plain,
% 28.53/18.75 (f3(c2, c1) = c1),
% 28.53/18.75 inference(modus_ponens,[status(thm)],[13518, 9098])).
% 28.53/18.75 tff(13524,plain,
% 28.53/18.75 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((f1(c1, c2) = c2) | (c1 = c3) | (c2 = c4) | big_f(c1, f1(c1, c2)) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (f1(c1, c2) = c2) | (c1 = c3) | (c2 = c4) | big_f(c1, f1(c1, c2)) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)))),
% 28.53/18.75 inference(rewrite,[status(thm)],[])).
% 28.53/18.75 tff(13525,plain,
% 28.53/18.75 (((c2 = c4) | (c1 = c3) | (f1(c1, c2) = c2) | big_f(c1, f1(c1, c2)) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2))) <=> ((f1(c1, c2) = c2) | (c1 = c3) | (c2 = c4) | big_f(c1, f1(c1, c2)) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)))),
% 28.53/18.75 inference(rewrite,[status(thm)],[])).
% 28.53/18.75 tff(13526,plain,
% 28.53/18.75 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c4) | (c1 = c3) | (f1(c1, c2) = c2) | big_f(c1, f1(c1, c2)) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((f1(c1, c2) = c2) | (c1 = c3) | (c2 = c4) | big_f(c1, f1(c1, c2)) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2))))),
% 28.53/18.75 inference(monotonicity,[status(thm)],[13525])).
% 28.53/18.75 tff(13527,plain,
% 28.53/18.75 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c4) | (c1 = c3) | (f1(c1, c2) = c2) | big_f(c1, f1(c1, c2)) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (f1(c1, c2) = c2) | (c1 = c3) | (c2 = c4) | big_f(c1, f1(c1, c2)) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)))),
% 28.53/18.75 inference(transitivity,[status(thm)],[13526, 13524])).
% 28.53/18.75 tff(13528,plain,
% 28.53/18.75 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c4) | (c1 = c3) | (f1(c1, c2) = c2) | big_f(c1, f1(c1, c2)) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)))),
% 28.53/18.75 inference(quant_inst,[status(thm)],[])).
% 28.53/18.75 tff(13529,plain,
% 28.53/18.75 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (f1(c1, c2) = c2) | (c1 = c3) | (c2 = c4) | big_f(c1, f1(c1, c2)) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2))),
% 28.53/18.75 inference(modus_ponens,[status(thm)],[13528, 13527])).
% 28.53/18.75 tff(13530,plain,
% 28.53/18.75 ($false),
% 28.53/18.75 inference(unit_resolution,[status(thm)],[13529, 969, 168, 873, 1052, 7524, 13523, 13522])).
% 28.53/18.75 tff(13531,plain,((f1(c1, c2) = c2) | (c1 = c3) | (c2 = c4) | (~big_f(c1, c2)) | (~(f7(c1) = c2)) | big_f(c2, c2) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 28.53/18.75 tff(13532,plain,
% 28.53/18.75 (f1(c1, c2) = c2),
% 28.53/18.75 inference(unit_resolution,[status(thm)],[13531, 13498, 13470, 13395, 120, 121, 66])).
% 28.53/18.75 tff(13533,plain,
% 28.53/18.75 (f3(c2, c1) = c1),
% 28.53/18.75 inference(modus_ponens,[status(thm)],[953, 9098])).
% 28.53/18.75 tff(13534,plain,
% 28.53/18.75 (big_f(c1, f1(c1, c2)) <=> big_f(c1, c2)),
% 28.53/18.75 inference(monotonicity,[status(thm)],[822])).
% 28.53/18.75 tff(13535,plain,
% 28.53/18.75 (big_f(c1, c2) <=> big_f(c1, f1(c1, c2))),
% 28.53/18.75 inference(symmetry,[status(thm)],[13534])).
% 28.53/18.75 tff(13536,plain,
% 28.53/18.75 (big_f(c1, f1(c1, c2))),
% 28.53/18.75 inference(modus_ponens,[status(thm)],[2865, 13535])).
% 28.53/18.75 tff(13537,plain,
% 28.53/18.75 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (c2 = c4) | (~big_f(c1, f1(c1, c2))) | (~(f1(c1, c2) = c2)) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (c2 = c4) | (~big_f(c1, f1(c1, c2))) | (~(f1(c1, c2) = c2)) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)))),
% 28.53/18.76 inference(rewrite,[status(thm)],[])).
% 28.53/18.76 tff(13538,plain,
% 28.53/18.76 (((c2 = c4) | (c1 = c3) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)) | (~(f1(c1, c2) = c2)) | (~big_f(c1, f1(c1, c2)))) <=> ((c1 = c3) | (c2 = c4) | (~big_f(c1, f1(c1, c2))) | (~(f1(c1, c2) = c2)) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)))),
% 28.53/18.76 inference(rewrite,[status(thm)],[])).
% 28.53/18.76 tff(13539,plain,
% 28.53/18.76 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (c1 = c3) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)) | (~(f1(c1, c2) = c2)) | (~big_f(c1, f1(c1, c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (c2 = c4) | (~big_f(c1, f1(c1, c2))) | (~(f1(c1, c2) = c2)) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2))))),
% 28.53/18.76 inference(monotonicity,[status(thm)],[13538])).
% 28.53/18.76 tff(13540,plain,
% 28.53/18.76 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (c1 = c3) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)) | (~(f1(c1, c2) = c2)) | (~big_f(c1, f1(c1, c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (c2 = c4) | (~big_f(c1, f1(c1, c2))) | (~(f1(c1, c2) = c2)) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)))),
% 28.53/18.76 inference(transitivity,[status(thm)],[13539, 13537])).
% 28.53/18.76 tff(13541,plain,
% 28.53/18.76 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (c1 = c3) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)) | (~(f1(c1, c2) = c2)) | (~big_f(c1, f1(c1, c2))))),
% 28.53/18.76 inference(quant_inst,[status(thm)],[])).
% 28.53/18.76 tff(13542,plain,
% 28.53/18.76 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (c2 = c4) | (~big_f(c1, f1(c1, c2))) | (~(f1(c1, c2) = c2)) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2))),
% 28.53/18.76 inference(modus_ponens,[status(thm)],[13541, 13540])).
% 28.53/18.76 tff(13543,plain,
% 28.53/18.76 ($false),
% 28.53/18.76 inference(unit_resolution,[status(thm)],[13542, 933, 168, 873, 822, 13536, 13533, 12180])).
% 28.53/18.76 tff(13544,plain,((~(f3(f7(c1), c1) = c1)) | (c1 = c3) | (c2 = c4) | (~(f1(c1, c2) = c2)) | (~big_f(c1, c2)) | (~(f7(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.53/18.76 tff(13545,plain,
% 28.53/18.76 (~(f3(f7(c1), c1) = c1)),
% 28.53/18.76 inference(unit_resolution,[status(thm)],[13544, 13532, 13470, 13395, 13498, 120])).
% 28.53/18.76 tff(13546,plain,
% 28.53/18.76 (f3(f7(c1), c1) = c2),
% 28.53/18.76 inference(unit_resolution,[status(thm)],[918, 13545])).
% 28.53/18.76 tff(13547,plain,
% 28.53/18.76 (f3(c2, f10(c2)) = f3(c2, c1)),
% 28.53/18.76 inference(monotonicity,[status(thm)],[11799])).
% 28.53/18.76 tff(13548,plain,
% 28.53/18.76 (f3(c2, f10(c2)) = c2),
% 28.53/18.76 inference(transitivity,[status(thm)],[13547, 2779, 13546])).
% 28.53/18.76 tff(13549,plain,
% 28.53/18.76 (big_f(f3(c2, f10(c2)), c2) <=> big_f(c2, c2)),
% 28.53/18.76 inference(monotonicity,[status(thm)],[13548])).
% 28.53/18.76 tff(13550,plain,
% 28.53/18.76 (big_f(c2, c2) <=> big_f(f3(c2, f10(c2)), c2)),
% 28.53/18.76 inference(symmetry,[status(thm)],[13549])).
% 28.53/18.76 tff(13551,plain,
% 28.53/18.76 ((~big_f(c2, c2)) <=> (~big_f(f3(c2, f10(c2)), c2))),
% 28.53/18.76 inference(monotonicity,[status(thm)],[13550])).
% 28.53/18.76 tff(13552,plain,
% 28.53/18.76 (~big_f(f3(c2, f10(c2)), c2)),
% 28.53/18.76 inference(modus_ponens,[status(thm)],[121, 13551])).
% 28.53/18.76 tff(13553,plain,
% 28.53/18.76 ((f3(c2, f10(c2)) = f10(c2)) <=> (c2 = f10(c2))),
% 28.53/18.76 inference(monotonicity,[status(thm)],[13548])).
% 28.53/18.76 tff(13554,plain,
% 28.53/18.76 ((f3(c2, f10(c2)) = f10(c2)) <=> (f10(c2) = c2)),
% 28.53/18.76 inference(transitivity,[status(thm)],[13553, 4987])).
% 28.53/18.76 tff(13555,plain,
% 28.53/18.76 ((f10(c2) = c2) <=> (f3(c2, f10(c2)) = f10(c2))),
% 28.53/18.76 inference(symmetry,[status(thm)],[13554])).
% 28.53/18.76 tff(13556,plain,
% 28.53/18.76 ((~(f10(c2) = c2)) <=> (~(f3(c2, f10(c2)) = f10(c2)))),
% 28.53/18.76 inference(monotonicity,[status(thm)],[13555])).
% 28.53/18.76 tff(13557,plain,
% 28.53/18.76 (~(f3(c2, f10(c2)) = f10(c2))),
% 28.53/18.76 inference(modus_ponens,[status(thm)],[11798, 13556])).
% 28.53/18.76 tff(13558,plain,
% 28.53/18.76 (f1(f10(c2), c2) = f1(c1, c2)),
% 28.53/18.76 inference(monotonicity,[status(thm)],[11799])).
% 28.53/18.76 tff(13559,plain,
% 28.53/18.76 (f1(f10(c2), c2) = c2),
% 28.53/18.76 inference(transitivity,[status(thm)],[13558, 13532])).
% 28.53/18.76 tff(13560,plain,
% 28.53/18.76 (big_f(f10(c2), f1(f10(c2), c2)) <=> big_f(c1, c2)),
% 28.53/18.76 inference(monotonicity,[status(thm)],[11799, 13559])).
% 28.53/18.76 tff(13561,plain,
% 28.53/18.76 (big_f(c1, c2) <=> big_f(f10(c2), f1(f10(c2), c2))),
% 28.53/18.76 inference(symmetry,[status(thm)],[13560])).
% 28.53/18.76 tff(13562,plain,
% 28.53/18.76 (big_f(f10(c2), f1(f10(c2), c2))),
% 28.53/18.76 inference(modus_ponens,[status(thm)],[13395, 13561])).
% 28.53/18.76 tff(13563,plain,
% 28.53/18.76 ((~(f10(c2) = c2)) <=> (~(f10(c2) = c3))),
% 28.53/18.76 inference(monotonicity,[status(thm)],[13467])).
% 28.53/18.76 tff(13564,plain,
% 28.53/18.76 (~(f10(c2) = c3)),
% 28.53/18.76 inference(modus_ponens,[status(thm)],[11798, 13563])).
% 28.53/18.76 tff(13565,plain,
% 28.53/18.76 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (f10(c2) = c3) | (~(f1(f10(c2), c2) = c2)) | (~big_f(f10(c2), f1(f10(c2), c2))) | (f3(c2, f10(c2)) = f10(c2)) | big_f(f3(c2, f10(c2)), c2))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c4) | (f10(c2) = c3) | (~(f1(f10(c2), c2) = c2)) | (~big_f(f10(c2), f1(f10(c2), c2))) | (f3(c2, f10(c2)) = f10(c2)) | big_f(f3(c2, f10(c2)), c2))),
% 28.53/18.76 inference(rewrite,[status(thm)],[])).
% 28.53/18.76 tff(13566,plain,
% 28.53/18.76 (((c2 = c4) | (f3(c2, f10(c2)) = f10(c2)) | big_f(f3(c2, f10(c2)), c2) | (f10(c2) = c3) | (~(f1(f10(c2), c2) = c2)) | (~big_f(f10(c2), f1(f10(c2), c2)))) <=> ((c2 = c4) | (f10(c2) = c3) | (~(f1(f10(c2), c2) = c2)) | (~big_f(f10(c2), f1(f10(c2), c2))) | (f3(c2, f10(c2)) = f10(c2)) | big_f(f3(c2, f10(c2)), c2))),
% 28.53/18.76 inference(rewrite,[status(thm)],[])).
% 28.53/18.76 tff(13567,plain,
% 28.53/18.76 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (f3(c2, f10(c2)) = f10(c2)) | big_f(f3(c2, f10(c2)), c2) | (f10(c2) = c3) | (~(f1(f10(c2), c2) = c2)) | (~big_f(f10(c2), f1(f10(c2), c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (f10(c2) = c3) | (~(f1(f10(c2), c2) = c2)) | (~big_f(f10(c2), f1(f10(c2), c2))) | (f3(c2, f10(c2)) = f10(c2)) | big_f(f3(c2, f10(c2)), c2)))),
% 28.53/18.76 inference(monotonicity,[status(thm)],[13566])).
% 28.53/18.76 tff(13568,plain,
% 28.53/18.76 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (f3(c2, f10(c2)) = f10(c2)) | big_f(f3(c2, f10(c2)), c2) | (f10(c2) = c3) | (~(f1(f10(c2), c2) = c2)) | (~big_f(f10(c2), f1(f10(c2), c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c4) | (f10(c2) = c3) | (~(f1(f10(c2), c2) = c2)) | (~big_f(f10(c2), f1(f10(c2), c2))) | (f3(c2, f10(c2)) = f10(c2)) | big_f(f3(c2, f10(c2)), c2))),
% 28.53/18.76 inference(transitivity,[status(thm)],[13567, 13565])).
% 28.53/18.76 tff(13569,plain,
% 28.53/18.76 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (f3(c2, f10(c2)) = f10(c2)) | big_f(f3(c2, f10(c2)), c2) | (f10(c2) = c3) | (~(f1(f10(c2), c2) = c2)) | (~big_f(f10(c2), f1(f10(c2), c2))))),
% 28.53/18.76 inference(quant_inst,[status(thm)],[])).
% 28.53/18.76 tff(13570,plain,
% 28.53/18.76 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c4) | (f10(c2) = c3) | (~(f1(f10(c2), c2) = c2)) | (~big_f(f10(c2), f1(f10(c2), c2))) | (f3(c2, f10(c2)) = f10(c2)) | big_f(f3(c2, f10(c2)), c2)),
% 28.53/18.76 inference(modus_ponens,[status(thm)],[13569, 13568])).
% 28.53/18.76 tff(13571,plain,
% 28.53/18.76 ((~(f1(f10(c2), c2) = c2)) | (~big_f(f10(c2), f1(f10(c2), c2))) | (f3(c2, f10(c2)) = f10(c2)) | big_f(f3(c2, f10(c2)), c2)),
% 28.53/18.76 inference(unit_resolution,[status(thm)],[13570, 904, 13498, 13564])).
% 28.53/18.76 tff(13572,plain,
% 28.53/18.76 ($false),
% 28.53/18.76 inference(unit_resolution,[status(thm)],[13571, 13562, 13559, 13557, 13552])).
% 28.53/18.76 tff(13573,plain,(big_f(c2, c2) | big_f(c1, c1) | (~(f4(c4) = c2)) | (~big_f(c2, c1)) | (~(f5(c1) = c2)) | (f7(c1) = c1) | (f10(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 28.53/18.76 tff(13574,plain,
% 28.53/18.76 (~(f5(c1) = c2)),
% 28.53/18.76 inference(unit_resolution,[status(thm)],[13573, 66, 79, 121, 13381, 115, 3])).
% 28.53/18.76 tff(13575,plain,
% 28.53/18.76 (f5(c1) = c1),
% 28.53/18.76 inference(unit_resolution,[status(thm)],[1708, 13574])).
% 28.53/18.76 tff(13576,plain,
% 28.53/18.76 (~(c2 = f8(c1))),
% 28.53/18.76 inference(unit_resolution,[status(thm)],[3003, 348, 230, 77, 121, 3])).
% 28.53/18.76 tff(13577,plain,
% 28.53/18.76 (~(f8(c1) = c2)),
% 28.53/18.76 inference(unit_resolution,[status(thm)],[1675, 13576])).
% 28.53/18.76 tff(13578,plain,
% 28.53/18.76 (f8(c1) = c1),
% 28.53/18.76 inference(unit_resolution,[status(thm)],[1680, 13577])).
% 28.53/18.76 tff(13579,plain,
% 28.53/18.76 (c1 = f8(c1)),
% 28.53/18.76 inference(unit_resolution,[status(thm)],[9808, 13578])).
% 28.53/18.76 tff(13580,plain,
% 28.53/18.76 (big_f(f7(c2), f6(c2, c1)) <=> big_f(c2, f6(c2, c1))),
% 28.53/18.76 inference(monotonicity,[status(thm)],[77])).
% 28.53/18.76 tff(13581,plain,
% 28.53/18.76 (big_f(c2, f6(c2, c1)) <=> big_f(f7(c2), f6(c2, c1))),
% 28.53/18.76 inference(symmetry,[status(thm)],[13580])).
% 28.53/18.76 tff(13582,plain,
% 28.53/18.76 (~(f6(f7(c2), f5(c1)) = c2)),
% 28.53/18.76 inference(unit_resolution,[status(thm)],[3049, 3030, 230, 77, 3, 13579, 121])).
% 28.53/18.76 tff(13583,plain,
% 28.53/18.76 (f6(f7(c2), f5(c1)) = c1),
% 28.53/18.76 inference(unit_resolution,[status(thm)],[2978, 13582])).
% 28.53/18.76 tff(13584,plain,
% 28.53/18.76 (f6(c2, c1) = c1),
% 28.53/18.76 inference(transitivity,[status(thm)],[2942, 13583])).
% 28.53/18.76 tff(13585,plain,
% 28.53/18.76 (big_f(c2, f6(c2, c1)) <=> big_f(c2, c1)),
% 28.53/18.76 inference(monotonicity,[status(thm)],[13584])).
% 28.53/18.76 tff(13586,plain,
% 28.53/18.76 (big_f(c2, c1) <=> big_f(c2, f6(c2, c1))),
% 28.53/18.76 inference(symmetry,[status(thm)],[13585])).
% 28.53/18.76 tff(13587,plain,
% 28.53/18.76 (big_f(c2, c1) <=> big_f(f7(c2), f6(c2, c1))),
% 28.53/18.76 inference(transitivity,[status(thm)],[13586, 13581])).
% 28.53/18.76 tff(13588,plain,
% 28.53/18.76 (big_f(f7(c2), f6(c2, c1))),
% 28.53/18.76 inference(modus_ponens,[status(thm)],[348, 13587])).
% 28.53/18.76 tff(13589,plain,
% 28.53/18.76 (f6(c2, c1) = c1),
% 28.53/18.76 inference(modus_ponens,[status(thm)],[2947, 7250])).
% 28.53/18.76 tff(13590,plain,
% 28.53/18.76 ($false),
% 28.53/18.76 inference(unit_resolution,[status(thm)],[3198, 13589])).
% 28.53/18.76 tff(13591,plain,((~(f6(f7(c2), f5(c1)) = c1)) | (f6(c2, c1) = c1) | (~(f5(c1) = c1)) | (~(f7(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.53/18.76 tff(13592,plain,
% 28.53/18.76 (f6(c2, c1) = c1),
% 28.53/18.76 inference(unit_resolution,[status(thm)],[13591, 13583, 230, 77])).
% 28.53/18.76 tff(13593,plain,
% 28.53/18.76 ($false),
% 28.53/18.76 inference(unit_resolution,[status(thm)],[3064, 2963, 3, 77, 13592, 13588, 13579, 3030])).
% 28.53/18.76 tff(13594,plain,(big_f(c1, f10(c1)) | (f10(c1) = c1) | (~(f7(c2) = c2)) | (~big_f(c2, c1)) | (~(f5(c1) = c1)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 28.53/18.76 tff(13595,plain,
% 28.53/18.76 (big_f(c1, f10(c1))),
% 28.53/18.76 inference(unit_resolution,[status(thm)],[13594, 13575, 121, 3, 13381, 13346])).
% 28.53/18.76 tff(13596,plain,
% 28.53/18.76 (big_f(c1, c2)),
% 28.53/18.76 inference(unit_resolution,[status(thm)],[12239, 13595, 11799, 11813])).
% 28.53/18.76 tff(13597,plain,
% 28.53/18.76 (~(c4 = c2)),
% 28.53/18.76 inference(unit_resolution,[status(thm)],[13490, 12100, 121, 2865, 66, 79])).
% 28.53/18.76 tff(13598,plain,
% 28.53/18.76 (c4 = c1),
% 28.53/18.76 inference(unit_resolution,[status(thm)],[461, 13597])).
% 28.53/18.76 tff(13599,plain,
% 28.53/18.76 (c4 = f10(c2)),
% 28.53/18.76 inference(transitivity,[status(thm)],[13598, 99])).
% 28.53/18.76 tff(13600,plain,
% 28.53/18.76 ((c2 = c4) <=> (c2 = f10(c2))),
% 28.53/18.76 inference(monotonicity,[status(thm)],[13599])).
% 28.53/18.76 tff(13601,plain,
% 28.53/18.76 ((c2 = c4) <=> (f10(c2) = c2)),
% 28.53/18.76 inference(transitivity,[status(thm)],[13600, 4987])).
% 28.53/18.76 tff(13602,plain,
% 28.53/18.76 ((f10(c2) = c2) <=> (c2 = c4)),
% 28.53/18.76 inference(symmetry,[status(thm)],[13601])).
% 28.53/18.76 tff(13603,plain,
% 28.53/18.76 ((~(f10(c2) = c2)) <=> (~(c2 = c4))),
% 28.53/18.76 inference(monotonicity,[status(thm)],[13602])).
% 28.53/18.76 tff(13604,plain,
% 28.53/18.76 (~(c2 = c4)),
% 28.53/18.76 inference(modus_ponens,[status(thm)],[89, 13603])).
% 28.53/18.76 tff(13605,plain,
% 28.53/18.76 (f1(c1, c2) = c2),
% 28.53/18.76 inference(unit_resolution,[status(thm)],[13531, 13604, 2865, 66, 347, 121, 12100])).
% 28.53/18.76 tff(13606,plain,
% 28.53/18.76 (~(f3(f7(c1), c1) = c1)),
% 28.53/18.76 inference(unit_resolution,[status(thm)],[13544, 13605, 2865, 12100, 13604, 347])).
% 28.53/18.76 tff(13607,plain,
% 28.53/18.76 (f3(f7(c1), c1) = c2),
% 28.53/18.76 inference(unit_resolution,[status(thm)],[918, 13606])).
% 28.53/18.76 tff(13608,plain,
% 28.53/18.76 (f3(c2, f10(c2)) = f3(c2, c1)),
% 28.53/18.76 inference(monotonicity,[status(thm)],[94])).
% 28.53/18.76 tff(13609,plain,
% 28.53/18.76 (f3(c2, f10(c2)) = c2),
% 28.53/18.76 inference(transitivity,[status(thm)],[13608, 3125, 13607])).
% 28.53/18.76 tff(13610,plain,
% 28.53/18.76 (big_f(f3(c2, f10(c2)), c2) <=> big_f(c2, c2)),
% 28.53/18.76 inference(monotonicity,[status(thm)],[13609])).
% 28.53/18.76 tff(13611,plain,
% 28.53/18.76 (big_f(c2, c2) <=> big_f(f3(c2, f10(c2)), c2)),
% 28.53/18.76 inference(symmetry,[status(thm)],[13610])).
% 28.53/18.76 tff(13612,plain,
% 28.53/18.76 ((~big_f(c2, c2)) <=> (~big_f(f3(c2, f10(c2)), c2))),
% 28.53/18.76 inference(monotonicity,[status(thm)],[13611])).
% 28.53/18.76 tff(13613,plain,
% 28.53/18.76 (~big_f(f3(c2, f10(c2)), c2)),
% 28.53/18.76 inference(modus_ponens,[status(thm)],[121, 13612])).
% 28.53/18.76 tff(13614,plain,
% 28.53/18.76 ((f3(c2, f10(c2)) = f10(c2)) <=> (c2 = f10(c2))),
% 28.53/18.76 inference(monotonicity,[status(thm)],[13609])).
% 28.53/18.76 tff(13615,plain,
% 28.53/18.76 ((f3(c2, f10(c2)) = f10(c2)) <=> (f10(c2) = c2)),
% 28.53/18.76 inference(transitivity,[status(thm)],[13614, 4987])).
% 28.53/18.76 tff(13616,plain,
% 28.53/18.76 ((f10(c2) = c2) <=> (f3(c2, f10(c2)) = f10(c2))),
% 28.53/18.76 inference(symmetry,[status(thm)],[13615])).
% 28.53/18.76 tff(13617,plain,
% 28.53/18.76 ((~(f10(c2) = c2)) <=> (~(f3(c2, f10(c2)) = f10(c2)))),
% 28.53/18.76 inference(monotonicity,[status(thm)],[13616])).
% 28.53/18.76 tff(13618,plain,
% 28.53/18.76 (~(f3(c2, f10(c2)) = f10(c2))),
% 28.53/18.76 inference(modus_ponens,[status(thm)],[89, 13617])).
% 28.53/18.76 tff(13619,plain,
% 28.53/18.76 (f1(f10(c2), c2) = f1(c1, c2)),
% 28.53/18.76 inference(monotonicity,[status(thm)],[94])).
% 28.53/18.76 tff(13620,plain,
% 28.53/18.76 (f1(f10(c2), c2) = c2),
% 28.53/18.76 inference(transitivity,[status(thm)],[13619, 13605])).
% 28.53/18.76 tff(13621,plain,
% 28.53/18.76 (big_f(f10(c2), f1(f10(c2), c2)) <=> big_f(c1, c2)),
% 28.53/18.76 inference(monotonicity,[status(thm)],[94, 13620])).
% 28.53/18.76 tff(13622,plain,
% 28.53/18.76 (big_f(c1, c2) <=> big_f(f10(c2), f1(f10(c2), c2))),
% 28.53/18.76 inference(symmetry,[status(thm)],[13621])).
% 28.53/18.76 tff(13623,plain,
% 28.53/18.76 (big_f(f10(c2), f1(f10(c2), c2))),
% 28.53/18.76 inference(modus_ponens,[status(thm)],[2865, 13622])).
% 28.53/18.76 tff(13624,plain,
% 28.53/18.76 ((~(f1(f10(c2), c2) = c2)) | (~big_f(f10(c2), f1(f10(c2), c2))) | (f3(c2, f10(c2)) = f10(c2)) | big_f(f3(c2, f10(c2)), c2)),
% 28.53/18.76 inference(unit_resolution,[status(thm)],[13570, 904, 13604, 12420])).
% 28.53/18.76 tff(13625,plain,
% 28.53/18.76 ($false),
% 28.53/18.76 inference(unit_resolution,[status(thm)],[13624, 13623, 13620, 13618, 13613])).
% 28.53/18.76 tff(13626,plain,((~(c3 = c2)) | big_f(c2, c2) | (~(f7(c1) = c2)) | (f10(c2) = c2) | (~big_f(c1, c2)) | big_f(c1, c1) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.53/18.76 tff(13627,plain,
% 28.53/18.76 (~(c3 = c2)),
% 28.53/18.76 inference(unit_resolution,[status(thm)],[13626, 13596, 120, 11798, 121, 66, 79])).
% 28.53/18.76 tff(13628,plain,
% 28.53/18.76 (~(f7(f7(c2)) = c3)),
% 28.53/18.76 inference(modus_ponens,[status(thm)],[13627, 13389])).
% 28.53/18.76 tff(13629,plain,
% 28.53/18.76 (c3 = c1),
% 28.53/18.76 inference(unit_resolution,[status(thm)],[180, 13627])).
% 28.53/18.76 tff(13630,plain,
% 28.53/18.76 (c1 = f5(c1)),
% 28.53/18.76 inference(modus_ponens,[status(thm)],[13575, 192])).
% 28.53/18.76 tff(13631,plain,
% 28.53/18.76 (~(c2 = c3)),
% 28.53/18.76 inference(modus_ponens,[status(thm)],[13627, 10473])).
% 28.53/18.76 tff(13632,plain,
% 28.53/18.76 ((c3 = c2) <=> (f7(c1) = c3)),
% 28.53/18.76 inference(transitivity,[status(thm)],[78, 12383])).
% 28.53/18.76 tff(13633,plain,
% 28.53/18.76 ((~(c3 = c2)) <=> (~(f7(c1) = c3))),
% 28.53/18.76 inference(monotonicity,[status(thm)],[13632])).
% 28.53/18.76 tff(13634,plain,
% 28.53/18.76 (~(f7(c1) = c3)),
% 28.53/18.76 inference(modus_ponens,[status(thm)],[13627, 13633])).
% 28.53/18.76 tff(13635,plain,
% 28.53/18.76 (f3(f7(c1), c1) = f3(c2, c1)),
% 28.53/18.76 inference(symmetry,[status(thm)],[2779])).
% 28.53/18.76 tff(13636,plain,
% 28.53/18.76 ((f3(f7(c1), c1) = c1) <=> (f3(c2, c1) = c1)),
% 28.53/18.76 inference(monotonicity,[status(thm)],[13635])).
% 28.53/18.76 tff(13637,plain,
% 28.53/18.76 ((f3(c2, c1) = c1) <=> (f3(f7(c1), c1) = c1)),
% 28.53/18.76 inference(symmetry,[status(thm)],[13636])).
% 28.53/18.76 tff(13638,plain,
% 28.53/18.76 ((~(f3(c2, c1) = c1)) <=> (~(f3(f7(c1), c1) = c1))),
% 28.53/18.76 inference(monotonicity,[status(thm)],[13637])).
% 28.53/18.76 tff(13639,plain,
% 28.53/18.76 (big_f(c1, c1) <=> big_f(c1, f10(c2))),
% 28.53/18.76 inference(monotonicity,[status(thm)],[11957])).
% 28.53/18.76 tff(13640,plain,
% 28.53/18.76 ((~big_f(c1, c1)) <=> (~big_f(c1, f10(c2)))),
% 28.53/18.76 inference(monotonicity,[status(thm)],[13639])).
% 28.53/18.76 tff(13641,plain,
% 28.53/18.76 (~big_f(c1, f10(c2))),
% 28.53/18.76 inference(modus_ponens,[status(thm)],[66, 13640])).
% 28.53/18.76 tff(13642,plain,
% 28.53/18.76 (big_f(c2, c1)),
% 28.53/18.76 inference(unit_resolution,[status(thm)],[13373, 11798, 79, 115, 77, 692, 13641])).
% 28.53/18.76 tff(13643,plain,
% 28.53/18.76 (big_f(c1, f10(c1))),
% 28.53/18.76 inference(unit_resolution,[status(thm)],[13594, 13642, 77, 3, 230, 121])).
% 28.53/18.76 tff(13644,plain,
% 28.53/18.76 (big_f(c1, c2)),
% 28.53/18.76 inference(unit_resolution,[status(thm)],[12239, 13643, 11799, 11813])).
% 28.53/18.76 tff(13645,plain,
% 28.53/18.76 (big_f(f3(c2, c1), c2)),
% 28.53/18.76 inference(unit_resolution,[status(thm)],[12223, 13642, 377, 873, 12165, 120, 121, 13644])).
% 28.53/18.76 tff(13646,plain,
% 28.53/18.76 (~(f3(c2, c1) = c1)),
% 28.53/18.76 inference(unit_resolution,[status(thm)],[13430, 13645, 377, 873, 13642, 120, 121])).
% 28.53/18.76 tff(13647,plain,
% 28.53/18.76 (~(f3(f7(c1), c1) = c1)),
% 28.53/18.76 inference(modus_ponens,[status(thm)],[13646, 13638])).
% 28.53/18.76 tff(13648,plain,
% 28.53/18.76 (f3(f7(c1), c1) = c2),
% 28.53/18.76 inference(unit_resolution,[status(thm)],[918, 13647])).
% 28.53/18.76 tff(13649,plain,
% 28.53/18.76 (f3(c2, c1) = c2),
% 28.53/18.76 inference(transitivity,[status(thm)],[2779, 13648])).
% 28.53/18.76 tff(13650,plain,
% 28.53/18.76 (big_f(f3(c2, c1), c2) <=> big_f(c2, c2)),
% 28.53/18.76 inference(monotonicity,[status(thm)],[13649])).
% 28.53/18.76 tff(13651,plain,
% 28.53/18.76 (big_f(c2, c2) <=> big_f(f3(c2, c1), c2)),
% 28.53/18.76 inference(symmetry,[status(thm)],[13650])).
% 28.53/18.76 tff(13652,plain,
% 28.53/18.76 ((~big_f(c2, c2)) <=> (~big_f(f3(c2, c1), c2))),
% 28.53/18.76 inference(monotonicity,[status(thm)],[13651])).
% 28.53/18.76 tff(13653,plain,
% 28.53/18.76 (~big_f(f3(c2, c1), c2)),
% 28.53/18.76 inference(modus_ponens,[status(thm)],[121, 13652])).
% 28.53/18.76 tff(13654,plain,
% 28.53/18.76 ($false),
% 28.53/18.76 inference(unit_resolution,[status(thm)],[13645, 13653])).
% 28.53/18.76 tff(13655,plain,(big_f(c2, c2) | (c2 = c3) | (c2 = c4) | (f7(c1) = c3) | (~(f7(c2) = c2)) | (f10(c1) = c1) | (~(f5(c1) = c1)) | (~(f4(c4) = c2)) | (f7(c1) = c1) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 28.53/18.76 tff(13656,plain,
% 28.53/18.76 (c2 = c4),
% 28.53/18.76 inference(unit_resolution,[status(thm)],[13655, 13631, 13346, 121, 13575, 3, 13634, 79, 115, 66])).
% 28.53/18.76 tff(13657,plain,
% 28.53/18.76 (c4 = c2),
% 28.53/18.76 inference(modus_ponens,[status(thm)],[631, 8721])).
% 28.53/18.76 tff(13658,plain,
% 28.53/18.76 (~big_f(f4(c4), c4)),
% 28.53/18.76 inference(unit_resolution,[status(thm)],[476, 121, 79, 13657])).
% 28.53/18.76 tff(13659,plain,
% 28.53/18.76 (~big_f(c2, c4)),
% 28.53/18.76 inference(unit_resolution,[status(thm)],[6521, 13658, 79])).
% 28.53/18.76 tff(13660,plain,
% 28.53/18.76 (f4(c2) = c2),
% 28.53/18.76 inference(transitivity,[status(thm)],[8744, 79])).
% 28.53/18.76 tff(13661,plain,
% 28.53/18.76 ((c1 = f4(c2)) <=> (c1 = c2)),
% 28.53/18.76 inference(monotonicity,[status(thm)],[13660])).
% 28.53/18.76 tff(13662,plain,
% 28.53/18.76 ((c1 = f4(c2)) <=> (c2 = c1)),
% 28.53/18.76 inference(transitivity,[status(thm)],[13661, 1])).
% 28.53/18.76 tff(13663,plain,
% 28.53/18.76 ((c2 = c1) <=> (c1 = f4(c2))),
% 28.53/18.76 inference(symmetry,[status(thm)],[13662])).
% 28.53/18.76 tff(13664,plain,
% 28.53/18.76 ((~(c2 = c1)) <=> (~(c1 = f4(c2)))),
% 28.53/18.76 inference(monotonicity,[status(thm)],[13663])).
% 28.53/18.76 tff(13665,plain,
% 28.53/18.76 (~(c1 = f4(c2))),
% 28.53/18.76 inference(modus_ponens,[status(thm)],[75, 13664])).
% 28.53/18.76 tff(13666,plain,
% 28.53/18.76 ((f7(c1) = f2(c1)) <=> (c2 = f2(c1))),
% 28.53/18.76 inference(monotonicity,[status(thm)],[347])).
% 28.53/18.76 tff(13667,plain,
% 28.53/18.76 ((c2 = f2(c1)) <=> (f7(c1) = f2(c1))),
% 28.53/18.76 inference(symmetry,[status(thm)],[13666])).
% 28.53/18.76 tff(13668,plain,
% 28.53/18.76 ((c2 = f2(c3)) <=> (c2 = f2(c1))),
% 28.53/18.76 inference(monotonicity,[status(thm)],[5589])).
% 28.53/18.76 tff(13669,plain,
% 28.53/18.76 ((c2 = f2(c3)) <=> (f7(c1) = f2(c1))),
% 28.53/18.76 inference(transitivity,[status(thm)],[13668, 13667])).
% 28.53/18.76 tff(13670,plain,
% 28.53/18.76 ((~(c2 = f2(c3))) <=> (~(f7(c1) = f2(c1)))),
% 28.53/18.76 inference(monotonicity,[status(thm)],[13669])).
% 28.53/18.76 tff(13671,plain,
% 28.53/18.76 (~big_f(c2, c4)),
% 28.53/18.76 inference(unit_resolution,[status(thm)],[6521, 379, 79])).
% 28.53/18.76 tff(13672,plain,
% 28.53/18.76 (~(c2 = f2(c3))),
% 28.53/18.76 inference(unit_resolution,[status(thm)],[2612, 13671, 2602, 3833])).
% 28.53/18.76 tff(13673,plain,
% 28.53/18.76 (~(f7(c1) = f2(c1))),
% 28.53/18.76 inference(modus_ponens,[status(thm)],[13672, 13670])).
% 28.53/18.76 tff(13674,plain,
% 28.53/18.76 (big_f(c3, f2(c3))),
% 28.53/18.76 inference(unit_resolution,[status(thm)],[1315, 379])).
% 28.53/18.76 tff(13675,plain,
% 28.53/18.76 (big_f(c1, f2(c1))),
% 28.53/18.76 inference(unit_resolution,[status(thm)],[8631, 13674, 172])).
% 28.53/18.76 tff(13676,plain,
% 28.53/18.76 (~(f2(c3) = c1)),
% 28.53/18.76 inference(unit_resolution,[status(thm)],[10932, 13675, 66, 172])).
% 28.53/18.76 tff(13677,plain,
% 28.53/18.76 (f2(c3) = c2),
% 28.53/18.76 inference(unit_resolution,[status(thm)],[1273, 13676])).
% 28.53/18.76 tff(13678,plain,
% 28.53/18.76 (f2(c1) = f2(c3)),
% 28.53/18.76 inference(symmetry,[status(thm)],[6765])).
% 28.53/18.76 tff(13679,plain,
% 28.53/18.76 ((c2 = f2(c1)) <=> (c2 = f2(c3))),
% 28.53/18.76 inference(monotonicity,[status(thm)],[13678])).
% 28.53/18.76 tff(13680,plain,
% 28.53/18.76 ((c2 = f2(c3)) <=> (c2 = f2(c1))),
% 28.53/18.76 inference(symmetry,[status(thm)],[13679])).
% 28.53/18.76 tff(13681,plain,
% 28.53/18.76 ((f2(c3) = c2) <=> (f7(c1) = f2(c1))),
% 28.53/18.76 inference(transitivity,[status(thm)],[1434, 13680, 13667])).
% 28.53/18.76 tff(13682,plain,
% 28.53/18.76 (f7(c1) = f2(c1)),
% 28.53/18.76 inference(modus_ponens,[status(thm)],[1319, 13681])).
% 28.53/18.76 tff(13683,assumption,(~(f7(c1) = f2(c1))), introduced(assumption)).
% 28.53/18.76 tff(13684,plain,
% 28.53/18.76 ($false),
% 28.53/18.76 inference(unit_resolution,[status(thm)],[13683, 13682])).
% 28.53/18.76 tff(13685,plain,((~(f2(c3) = c2)) | (f7(c1) = f2(c1)) | (~(c3 = c1)) | (~(f7(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.53/18.76 tff(13686,plain,
% 28.53/18.76 (f7(c1) = f2(c1)),
% 28.53/18.76 inference(unit_resolution,[status(thm)],[13685, 13677, 347, 172])).
% 28.53/18.76 tff(13687,plain,
% 28.53/18.76 ($false),
% 28.53/18.76 inference(unit_resolution,[status(thm)],[13686, 13673])).
% 28.53/18.76 tff(13688,plain,(big_f(f4(c4), c4) | (~(f7(c1) = c2)) | (~(c3 = c1)) | big_f(c1, c1) | big_f(c3, c2) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.53/18.76 tff(13689,plain,
% 28.53/18.76 (big_f(c3, c2)),
% 28.53/18.76 inference(unit_resolution,[status(thm)],[13688, 13658, 172, 66, 120, 79])).
% 28.53/18.76 tff(13690,plain,
% 28.53/18.76 (big_f(c1, c2)),
% 28.53/18.76 inference(modus_ponens,[status(thm)],[13689, 10918])).
% 28.53/18.76 tff(13691,plain,
% 28.53/18.76 (f1(f7(f7(c2)), c1) = c1),
% 28.53/18.76 inference(unit_resolution,[status(thm)],[5433, 13658, 77, 378, 121])).
% 28.53/18.76 tff(13692,plain,
% 28.53/18.76 (f1(c2, c1) = c1),
% 28.53/18.76 inference(modus_ponens,[status(thm)],[13691, 11482])).
% 28.53/18.76 tff(13693,plain,
% 28.53/18.76 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c2 = c4)) | (c1 = f4(c2)) | (~big_f(c1, c2)) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(c2 = c4)) | (c1 = f4(c2)) | (~big_f(c1, c2)) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1)))),
% 28.53/18.76 inference(rewrite,[status(thm)],[])).
% 28.53/18.76 tff(13694,plain,
% 28.53/18.76 (((c2 = c3) | (~(c2 = c4)) | (c1 = f4(c2)) | (~big_f(c1, c2)) | (~(f1(c2, c1) = c1)) | (~big_f(c2, f1(c2, c1)))) <=> ((c2 = c3) | (~(c2 = c4)) | (c1 = f4(c2)) | (~big_f(c1, c2)) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1)))),
% 28.53/18.76 inference(rewrite,[status(thm)],[])).
% 28.53/18.76 tff(13695,plain,
% 28.53/18.76 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c2 = c4)) | (c1 = f4(c2)) | (~big_f(c1, c2)) | (~(f1(c2, c1) = c1)) | (~big_f(c2, f1(c2, c1))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c2 = c4)) | (c1 = f4(c2)) | (~big_f(c1, c2)) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1))))),
% 28.53/18.76 inference(monotonicity,[status(thm)],[13694])).
% 28.53/18.76 tff(13696,plain,
% 28.53/18.76 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c2 = c4)) | (c1 = f4(c2)) | (~big_f(c1, c2)) | (~(f1(c2, c1) = c1)) | (~big_f(c2, f1(c2, c1))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(c2 = c4)) | (c1 = f4(c2)) | (~big_f(c1, c2)) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1)))),
% 28.53/18.77 inference(transitivity,[status(thm)],[13695, 13693])).
% 28.53/18.77 tff(13697,plain,
% 28.53/18.77 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c2 = c4)) | (c1 = f4(c2)) | (~big_f(c1, c2)) | (~(f1(c2, c1) = c1)) | (~big_f(c2, f1(c2, c1))))),
% 28.53/18.77 inference(quant_inst,[status(thm)],[])).
% 28.53/18.77 tff(13698,plain,
% 28.53/18.77 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(c2 = c4)) | (c1 = f4(c2)) | (~big_f(c1, c2)) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1))),
% 28.53/18.77 inference(modus_ponens,[status(thm)],[13697, 13696])).
% 28.53/18.77 tff(13699,plain,
% 28.53/18.77 (~big_f(c2, f1(c2, c1))),
% 28.53/18.77 inference(unit_resolution,[status(thm)],[13698, 553, 631, 377, 13692, 13690, 13665])).
% 28.53/18.77 tff(13700,plain,
% 28.53/18.77 (big_f(c2, c1)),
% 28.53/18.77 inference(unit_resolution,[status(thm)],[13373, 13641, 79, 115, 77, 11826, 11798])).
% 28.53/18.77 tff(13701,plain,
% 28.53/18.77 ($false),
% 28.53/18.77 inference(unit_resolution,[status(thm)],[10105, 13700, 13699, 2602, 377, 13659])).
% 28.53/18.77 tff(13702,plain,(big_f(c2, c2) | (c2 = c3) | (~(f4(c4) = c2)) | (f7(c1) = c1) | (~(f7(c2) = c2)) | (~(c1 = f5(c1))) | (~(c2 = c4)) | big_f(c1, c1) | (~(c3 = c1)) | (f7(f7(c2)) = c3)), inference(lemma,lemma(discharge,[]))).
% 28.53/18.77 tff(13703,plain,
% 28.53/18.77 ($false),
% 28.53/18.77 inference(unit_resolution,[status(thm)],[13702, 13656, 13631, 79, 115, 13346, 121, 13630, 66, 13629, 13628])).
% 28.53/18.77 tff(13704,plain,(big_f(c1, c1) | (~(f4(c4) = c2)) | (f7(c1) = c1) | big_f(c2, c2) | (f10(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 28.53/18.77 tff(13705,plain,
% 28.53/18.77 (big_f(c1, c1)),
% 28.53/18.77 inference(unit_resolution,[status(thm)],[13704, 121, 115, 79, 3])).
% 28.53/18.77 tff(13706,plain,
% 28.53/18.77 (~(c3 = c1)),
% 28.53/18.77 inference(unit_resolution,[status(thm)],[11517, 13705, 79, 13346, 121, 13381])).
% 28.53/18.77 tff(13707,plain,
% 28.53/18.77 (c3 = c2),
% 28.53/18.77 inference(unit_resolution,[status(thm)],[180, 13706])).
% 28.53/18.77 tff(13708,plain,
% 28.53/18.77 (~(f2(c3) = c2)),
% 28.53/18.77 inference(unit_resolution,[status(thm)],[11686, 13707, 121, 13705, 79, 13381])).
% 28.53/18.77 tff(13709,plain,
% 28.53/18.77 (f2(c3) = c1),
% 28.53/18.77 inference(unit_resolution,[status(thm)],[1273, 13708])).
% 28.53/18.77 tff(13710,assumption,(~(f10(c2) = f8(c2))), introduced(assumption)).
% 28.53/18.77 tff(13711,plain,
% 28.53/18.77 (f6(c2, f10(c2)) = f6(c2, c1)),
% 28.53/18.77 inference(monotonicity,[status(thm)],[94])).
% 28.53/18.77 tff(13712,plain,
% 28.53/18.77 (big_f(f7(c2), f6(c2, f10(c2))) <=> big_f(c2, f6(c2, c1))),
% 28.53/18.77 inference(monotonicity,[status(thm)],[77, 13711])).
% 28.53/18.77 tff(13713,plain,
% 28.53/18.77 ((f6(c2, f10(c2)) = f10(c2)) <=> (f6(c2, c1) = c1)),
% 28.53/18.77 inference(monotonicity,[status(thm)],[13711, 94])).
% 28.53/18.77 tff(13714,plain,
% 28.53/18.77 ((f6(c2, c1) = c1) <=> (f6(c2, f10(c2)) = f10(c2))),
% 28.53/18.77 inference(symmetry,[status(thm)],[13713])).
% 28.53/18.77 tff(13715,plain,
% 28.53/18.77 ((~(f6(c2, c1) = c1)) <=> (~(f6(c2, f10(c2)) = f10(c2)))),
% 28.53/18.77 inference(monotonicity,[status(thm)],[13714])).
% 28.53/18.77 tff(13716,plain,
% 28.53/18.77 (~(f6(c2, f10(c2)) = f10(c2))),
% 28.53/18.77 inference(modus_ponens,[status(thm)],[3198, 13715])).
% 28.53/18.77 tff(13717,plain,
% 28.53/18.77 (big_f(c1, c1) <=> big_f(f10(c2), f10(c2))),
% 28.53/18.77 inference(monotonicity,[status(thm)],[99, 99])).
% 28.53/18.77 tff(13718,plain,
% 28.53/18.77 (big_f(f10(c2), f10(c2))),
% 28.53/18.77 inference(modus_ponens,[status(thm)],[4932, 13717])).
% 28.53/18.77 tff(13719,plain,
% 28.53/18.77 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (~(f7(c2) = c2)) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (f6(c2, f10(c2)) = f10(c2)) | big_f(f7(c2), f6(c2, f10(c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (f6(c2, f10(c2)) = f10(c2)) | big_f(f7(c2), f6(c2, f10(c2))))),
% 28.53/18.77 inference(rewrite,[status(thm)],[])).
% 28.53/18.77 tff(13720,plain,
% 28.53/18.77 (((f10(c2) = c2) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (~(f7(c2) = c2)) | (f6(c2, f10(c2)) = f10(c2)) | big_f(f7(c2), f6(c2, f10(c2)))) <=> ((f10(c2) = c2) | (~(f7(c2) = c2)) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (f6(c2, f10(c2)) = f10(c2)) | big_f(f7(c2), f6(c2, f10(c2))))),
% 28.53/18.77 inference(rewrite,[status(thm)],[])).
% 28.53/18.77 tff(13721,plain,
% 28.53/18.77 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (~(f7(c2) = c2)) | (f6(c2, f10(c2)) = f10(c2)) | big_f(f7(c2), f6(c2, f10(c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (~(f7(c2) = c2)) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (f6(c2, f10(c2)) = f10(c2)) | big_f(f7(c2), f6(c2, f10(c2)))))),
% 28.53/18.77 inference(monotonicity,[status(thm)],[13720])).
% 28.53/18.77 tff(13722,plain,
% 28.53/18.77 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (~(f7(c2) = c2)) | (f6(c2, f10(c2)) = f10(c2)) | big_f(f7(c2), f6(c2, f10(c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (f6(c2, f10(c2)) = f10(c2)) | big_f(f7(c2), f6(c2, f10(c2))))),
% 28.53/18.77 inference(transitivity,[status(thm)],[13721, 13719])).
% 28.53/18.77 tff(13723,plain,
% 28.53/18.77 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (~(f7(c2) = c2)) | (f6(c2, f10(c2)) = f10(c2)) | big_f(f7(c2), f6(c2, f10(c2))))),
% 28.53/18.77 inference(quant_inst,[status(thm)],[])).
% 28.53/18.77 tff(13724,plain,
% 28.53/18.77 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (f6(c2, f10(c2)) = f10(c2)) | big_f(f7(c2), f6(c2, f10(c2)))),
% 28.53/18.77 inference(modus_ponens,[status(thm)],[13723, 13722])).
% 28.53/18.77 tff(13725,plain,
% 28.53/18.77 ((f6(c2, f10(c2)) = f10(c2)) | big_f(f7(c2), f6(c2, f10(c2)))),
% 28.53/18.77 inference(unit_resolution,[status(thm)],[13724, 2662, 89, 77, 13710, 13718])).
% 28.53/18.77 tff(13726,plain,
% 28.53/18.77 (big_f(f7(c2), f6(c2, f10(c2)))),
% 28.53/18.77 inference(unit_resolution,[status(thm)],[13725, 13716])).
% 28.53/18.77 tff(13727,plain,
% 28.53/18.77 (big_f(c2, f6(c2, c1))),
% 28.53/18.77 inference(modus_ponens,[status(thm)],[13726, 13712])).
% 28.53/18.77 tff(13728,plain,
% 28.53/18.77 (~big_f(c2, f6(c2, c1))),
% 28.53/18.77 inference(unit_resolution,[status(thm)],[11730, 3198, 79, 121, 4932, 67, 1247])).
% 28.53/18.77 tff(13729,plain,
% 28.53/18.77 ($false),
% 28.53/18.77 inference(unit_resolution,[status(thm)],[13728, 13727])).
% 28.53/18.77 tff(13730,plain,((f6(c2, c1) = c1) | (~(f7(c2) = c2)) | (f10(c2) = c2) | (f10(c2) = f8(c2)) | (~(f4(c4) = c2)) | big_f(c2, c2) | (~big_f(c1, c1)) | (~(c3 = c2)) | (~(f2(c3) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.53/18.77 tff(13731,plain,
% 28.53/18.77 (f6(c2, c1) = c1),
% 28.53/18.77 inference(unit_resolution,[status(thm)],[13730, 13710, 89, 77, 79, 121, 4932, 67, 1247])).
% 28.53/18.77 tff(13732,plain,
% 28.53/18.77 (f6(c2, f10(c2)) = f10(c2)),
% 28.53/18.77 inference(transitivity,[status(thm)],[13711, 13731, 99])).
% 28.53/18.77 tff(13733,plain,
% 28.53/18.77 (big_f(f7(c2), f6(c2, f10(c2))) <=> big_f(c2, f10(c2))),
% 28.53/18.77 inference(monotonicity,[status(thm)],[77, 13732])).
% 28.53/18.77 tff(13734,plain,
% 28.53/18.77 (big_f(c2, f10(c2)) <=> big_f(f7(c2), f6(c2, f10(c2)))),
% 28.53/18.77 inference(symmetry,[status(thm)],[13733])).
% 28.53/18.77 tff(13735,plain,
% 28.53/18.77 (big_f(f7(c2), f6(c2, f10(c2)))),
% 28.53/18.77 inference(modus_ponens,[status(thm)],[12291, 13734])).
% 28.53/18.77 tff(13736,plain,
% 28.53/18.77 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (~(f7(c2) = c2)) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (~(f6(c2, f10(c2)) = f10(c2))) | (~big_f(f7(c2), f6(c2, f10(c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (~(f6(c2, f10(c2)) = f10(c2))) | (~big_f(f7(c2), f6(c2, f10(c2)))))),
% 28.53/18.77 inference(rewrite,[status(thm)],[])).
% 28.53/18.77 tff(13737,plain,
% 28.53/18.77 (((f10(c2) = c2) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (~(f7(c2) = c2)) | (~(f6(c2, f10(c2)) = f10(c2))) | (~big_f(f7(c2), f6(c2, f10(c2))))) <=> ((f10(c2) = c2) | (~(f7(c2) = c2)) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (~(f6(c2, f10(c2)) = f10(c2))) | (~big_f(f7(c2), f6(c2, f10(c2)))))),
% 28.53/18.77 inference(rewrite,[status(thm)],[])).
% 28.53/18.77 tff(13738,plain,
% 28.53/18.77 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (~(f7(c2) = c2)) | (~(f6(c2, f10(c2)) = f10(c2))) | (~big_f(f7(c2), f6(c2, f10(c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (~(f7(c2) = c2)) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (~(f6(c2, f10(c2)) = f10(c2))) | (~big_f(f7(c2), f6(c2, f10(c2))))))),
% 28.53/18.77 inference(monotonicity,[status(thm)],[13737])).
% 28.53/18.77 tff(13739,plain,
% 28.53/18.77 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (~(f7(c2) = c2)) | (~(f6(c2, f10(c2)) = f10(c2))) | (~big_f(f7(c2), f6(c2, f10(c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (~(f6(c2, f10(c2)) = f10(c2))) | (~big_f(f7(c2), f6(c2, f10(c2)))))),
% 28.53/18.77 inference(transitivity,[status(thm)],[13738, 13736])).
% 28.53/18.77 tff(13740,plain,
% 28.53/18.77 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (~(f7(c2) = c2)) | (~(f6(c2, f10(c2)) = f10(c2))) | (~big_f(f7(c2), f6(c2, f10(c2)))))),
% 28.53/18.77 inference(quant_inst,[status(thm)],[])).
% 28.53/18.77 tff(13741,plain,
% 28.53/18.77 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (~(f6(c2, f10(c2)) = f10(c2))) | (~big_f(f7(c2), f6(c2, f10(c2))))),
% 28.53/18.77 inference(modus_ponens,[status(thm)],[13740, 13739])).
% 28.53/18.77 tff(13742,plain,
% 28.53/18.77 ((~(f6(c2, f10(c2)) = f10(c2))) | (~big_f(f7(c2), f6(c2, f10(c2))))),
% 28.53/18.77 inference(unit_resolution,[status(thm)],[13741, 2730, 89, 77, 13710, 13718])).
% 28.53/18.77 tff(13743,plain,
% 28.53/18.77 ($false),
% 28.53/18.77 inference(unit_resolution,[status(thm)],[13742, 13735, 13732])).
% 28.53/18.77 tff(13744,plain,((f10(c2) = f8(c2)) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (~big_f(c2, f10(c2))) | (~(f4(c4) = c2)) | big_f(c2, c2) | (~big_f(c1, c1)) | (~(c3 = c2)) | (~(f2(c3) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.53/18.77 tff(13745,plain,
% 28.53/18.77 (f10(c2) = f8(c2)),
% 28.53/18.77 inference(unit_resolution,[status(thm)],[13744, 11798, 13346, 13382, 79, 121, 13705, 13707, 13709])).
% 28.53/18.77 tff(13746,plain,
% 28.53/18.77 (f8(c2) = f10(c2)),
% 28.53/18.77 inference(symmetry,[status(thm)],[13745])).
% 28.53/18.77 tff(13747,plain,
% 28.53/18.77 ((c2 = f8(c2)) <=> (c2 = f10(c2))),
% 28.53/18.77 inference(monotonicity,[status(thm)],[13746])).
% 28.53/18.77 tff(13748,plain,
% 28.53/18.77 ((c2 = f8(c2)) <=> (f10(c2) = c2)),
% 28.53/18.77 inference(transitivity,[status(thm)],[13747, 4987])).
% 28.53/18.77 tff(13749,plain,
% 28.53/18.77 ((f10(c2) = c2) <=> (c2 = f8(c2))),
% 28.53/18.77 inference(symmetry,[status(thm)],[13748])).
% 28.53/18.77 tff(13750,plain,
% 28.53/18.77 ((~(f10(c2) = c2)) <=> (~(c2 = f8(c2)))),
% 28.53/18.77 inference(monotonicity,[status(thm)],[13749])).
% 28.53/18.77 tff(13751,plain,
% 28.53/18.77 (~(c2 = f8(c2))),
% 28.53/18.77 inference(modus_ponens,[status(thm)],[11798, 13750])).
% 28.53/18.77 tff(13752,plain,
% 28.53/18.77 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(f10(c2)) = f10(c2)) | (~big_f(f7(f10(c2)), f10(c2))) | (f10(c2) = f5(f10(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(f10(c2)) = f10(c2)) | (~big_f(f7(f10(c2)), f10(c2))) | (f10(c2) = f5(f10(c2))))),
% 28.53/18.77 inference(rewrite,[status(thm)],[])).
% 28.53/18.77 tff(13753,plain,
% 28.53/18.77 (((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(f10(c2)) = f10(c2)) | (f10(c2) = f5(f10(c2))) | (~big_f(f7(f10(c2)), f10(c2)))) <=> ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(f10(c2)) = f10(c2)) | (~big_f(f7(f10(c2)), f10(c2))) | (f10(c2) = f5(f10(c2))))),
% 28.53/18.77 inference(rewrite,[status(thm)],[])).
% 28.53/18.77 tff(13754,plain,
% 28.53/18.77 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(f10(c2)) = f10(c2)) | (f10(c2) = f5(f10(c2))) | (~big_f(f7(f10(c2)), f10(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(f10(c2)) = f10(c2)) | (~big_f(f7(f10(c2)), f10(c2))) | (f10(c2) = f5(f10(c2)))))),
% 28.53/18.77 inference(monotonicity,[status(thm)],[13753])).
% 28.53/18.77 tff(13755,plain,
% 28.53/18.77 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(f10(c2)) = f10(c2)) | (f10(c2) = f5(f10(c2))) | (~big_f(f7(f10(c2)), f10(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(f10(c2)) = f10(c2)) | (~big_f(f7(f10(c2)), f10(c2))) | (f10(c2) = f5(f10(c2))))),
% 28.53/18.77 inference(transitivity,[status(thm)],[13754, 13752])).
% 28.53/18.77 tff(13756,plain,
% 28.53/18.77 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(f10(c2)) = f10(c2)) | (f10(c2) = f5(f10(c2))) | (~big_f(f7(f10(c2)), f10(c2))))),
% 28.53/18.77 inference(quant_inst,[status(thm)],[])).
% 28.53/18.77 tff(13757,plain,
% 28.53/18.77 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(f10(c2)) = f10(c2)) | (~big_f(f7(f10(c2)), f10(c2))) | (f10(c2) = f5(f10(c2)))),
% 28.53/18.77 inference(modus_ponens,[status(thm)],[13756, 13755])).
% 28.53/18.77 tff(13758,plain,
% 28.53/18.77 ((c2 = f8(c2)) | (~big_f(f7(f10(c2)), f10(c2))) | (f10(c2) = f5(f10(c2)))),
% 28.53/18.77 inference(unit_resolution,[status(thm)],[13757, 1659, 11798, 13382, 11811])).
% 28.53/18.77 tff(13759,plain,
% 28.53/18.77 (f10(c2) = f5(f10(c2))),
% 28.53/18.77 inference(unit_resolution,[status(thm)],[13758, 13751, 13383])).
% 28.53/18.77 tff(13760,plain,
% 28.53/18.77 (f5(c1) = f5(f10(c2))),
% 28.53/18.77 inference(monotonicity,[status(thm)],[99])).
% 28.53/18.77 tff(13761,plain,
% 28.53/18.77 (f5(f10(c2)) = f5(c1)),
% 28.53/18.77 inference(symmetry,[status(thm)],[13760])).
% 28.53/18.77 tff(13762,assumption,(f10(c2) = f5(f10(c2))), introduced(assumption)).
% 28.53/18.77 tff(13763,plain,
% 28.53/18.77 (c1 = f5(c1)),
% 28.53/18.77 inference(transitivity,[status(thm)],[99, 13762, 13761])).
% 28.53/18.77 tff(13764,plain,
% 28.53/18.77 (f6(c2, c1) = f6(f7(c2), f5(c1))),
% 28.53/18.77 inference(monotonicity,[status(thm)],[82, 13763])).
% 28.53/18.77 tff(13765,plain,
% 28.53/18.77 (f6(c2, f10(c2)) = c2),
% 28.53/18.77 inference(transitivity,[status(thm)],[13711, 13764, 3032])).
% 28.53/18.77 tff(13766,plain,
% 28.53/18.77 ((f6(c2, f10(c2)) = f10(c2)) <=> (c2 = f10(c2))),
% 28.53/18.77 inference(monotonicity,[status(thm)],[13765])).
% 28.53/18.77 tff(13767,plain,
% 28.53/18.77 ((f6(c2, f10(c2)) = f10(c2)) <=> (f10(c2) = c2)),
% 28.53/18.77 inference(transitivity,[status(thm)],[13766, 4987])).
% 28.53/18.77 tff(13768,plain,
% 28.53/18.77 ((f10(c2) = c2) <=> (f6(c2, f10(c2)) = f10(c2))),
% 28.53/18.77 inference(symmetry,[status(thm)],[13767])).
% 28.53/18.77 tff(13769,plain,
% 28.53/18.77 ((~(f10(c2) = c2)) <=> (~(f6(c2, f10(c2)) = f10(c2)))),
% 28.53/18.77 inference(monotonicity,[status(thm)],[13768])).
% 28.53/18.77 tff(13770,plain,
% 28.53/18.77 (~(f6(c2, f10(c2)) = f10(c2))),
% 28.53/18.77 inference(modus_ponens,[status(thm)],[89, 13769])).
% 28.53/18.77 tff(13771,plain,
% 28.53/18.77 (big_f(f7(c2), f6(c2, f10(c2))) <=> big_f(c2, c2)),
% 28.53/18.77 inference(monotonicity,[status(thm)],[77, 13765])).
% 28.53/18.77 tff(13772,plain,
% 28.53/18.77 (big_f(c2, c2) <=> big_f(f7(c2), f6(c2, f10(c2)))),
% 28.53/18.77 inference(symmetry,[status(thm)],[13771])).
% 28.53/18.77 tff(13773,plain,
% 28.53/18.77 ((~big_f(c2, c2)) <=> (~big_f(f7(c2), f6(c2, f10(c2))))),
% 28.53/18.77 inference(monotonicity,[status(thm)],[13772])).
% 28.53/18.77 tff(13774,plain,
% 28.53/18.77 (~big_f(f7(c2), f6(c2, f10(c2)))),
% 28.53/18.77 inference(modus_ponens,[status(thm)],[121, 13773])).
% 28.53/18.77 tff(13775,plain,
% 28.53/18.77 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (~(f7(c2) = c2)) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f6(c2, f10(c2)) = f10(c2)) | big_f(f7(c2), f6(c2, f10(c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f6(c2, f10(c2)) = f10(c2)) | big_f(f7(c2), f6(c2, f10(c2))))),
% 28.53/18.77 inference(rewrite,[status(thm)],[])).
% 28.53/18.77 tff(13776,plain,
% 28.53/18.77 (((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c2) = c2)) | (f6(c2, f10(c2)) = f10(c2)) | big_f(f7(c2), f6(c2, f10(c2)))) <=> ((f10(c2) = c2) | (~(f7(c2) = c2)) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f6(c2, f10(c2)) = f10(c2)) | big_f(f7(c2), f6(c2, f10(c2))))),
% 28.53/18.77 inference(rewrite,[status(thm)],[])).
% 28.53/18.77 tff(13777,plain,
% 28.53/18.77 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c2) = c2)) | (f6(c2, f10(c2)) = f10(c2)) | big_f(f7(c2), f6(c2, f10(c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (~(f7(c2) = c2)) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f6(c2, f10(c2)) = f10(c2)) | big_f(f7(c2), f6(c2, f10(c2)))))),
% 28.53/18.77 inference(monotonicity,[status(thm)],[13776])).
% 28.53/18.77 tff(13778,plain,
% 28.53/18.77 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c2) = c2)) | (f6(c2, f10(c2)) = f10(c2)) | big_f(f7(c2), f6(c2, f10(c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f6(c2, f10(c2)) = f10(c2)) | big_f(f7(c2), f6(c2, f10(c2))))),
% 28.53/18.77 inference(transitivity,[status(thm)],[13777, 13775])).
% 28.53/18.77 tff(13779,plain,
% 28.53/18.77 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c2) = c2)) | (f6(c2, f10(c2)) = f10(c2)) | big_f(f7(c2), f6(c2, f10(c2))))),
% 28.53/18.77 inference(quant_inst,[status(thm)],[])).
% 28.53/18.77 tff(13780,plain,
% 28.53/18.77 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f6(c2, f10(c2)) = f10(c2)) | big_f(f7(c2), f6(c2, f10(c2)))),
% 28.53/18.77 inference(modus_ponens,[status(thm)],[13779, 13778])).
% 28.53/18.77 tff(13781,plain,
% 28.53/18.77 ((f6(c2, f10(c2)) = f10(c2)) | big_f(f7(c2), f6(c2, f10(c2)))),
% 28.53/18.77 inference(unit_resolution,[status(thm)],[13780, 2662, 89, 77, 12291, 12290])).
% 28.53/18.77 tff(13782,plain,
% 28.53/18.77 ($false),
% 28.53/18.77 inference(unit_resolution,[status(thm)],[13781, 13774, 13770])).
% 28.53/18.77 tff(13783,plain,((~(f6(f7(c2), f5(c1)) = c2)) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (~big_f(c2, f10(c2))) | (c2 = f8(c2)) | big_f(c2, c2) | (~(f10(c2) = f5(f10(c2))))), inference(lemma,lemma(discharge,[]))).
% 28.53/18.77 tff(13784,plain,
% 28.53/18.77 (~(f6(f7(c2), f5(c1)) = c2)),
% 28.53/18.77 inference(unit_resolution,[status(thm)],[13783, 11798, 13346, 13382, 13751, 121, 13759])).
% 28.53/18.77 tff(13785,plain,
% 28.53/18.77 (f6(f7(c2), f5(c1)) = c1),
% 28.53/18.77 inference(unit_resolution,[status(thm)],[2978, 13784])).
% 28.53/18.77 tff(13786,plain,
% 28.53/18.77 (f5(c1) = f5(f10(c2))),
% 28.53/18.77 inference(monotonicity,[status(thm)],[11957])).
% 28.53/18.77 tff(13787,plain,
% 28.53/18.77 (f5(f10(c2)) = f5(c1)),
% 28.53/18.77 inference(symmetry,[status(thm)],[13786])).
% 28.53/18.77 tff(13788,plain,
% 28.53/18.77 (c1 = f5(c1)),
% 28.53/18.77 inference(transitivity,[status(thm)],[11957, 13759, 13787])).
% 28.53/18.77 tff(13789,plain,
% 28.53/18.77 (c2 = f7(c2)),
% 28.53/18.77 inference(symmetry,[status(thm)],[13346])).
% 28.53/18.77 tff(13790,plain,
% 28.53/18.77 (f6(c2, c1) = f6(f7(c2), f5(c1))),
% 28.53/18.77 inference(monotonicity,[status(thm)],[13789, 13788])).
% 28.53/18.77 tff(13791,plain,
% 28.53/18.77 (f6(c2, f10(c2)) = f6(c2, c1)),
% 28.53/18.77 inference(monotonicity,[status(thm)],[11799])).
% 28.53/18.77 tff(13792,plain,
% 28.53/18.77 (f6(c2, f10(c2)) = f10(c2)),
% 28.53/18.77 inference(transitivity,[status(thm)],[13791, 13790, 13785, 11957])).
% 28.53/18.77 tff(13793,plain,
% 28.53/18.77 (big_f(f7(c2), f6(c2, f10(c2))) <=> big_f(c2, f10(c2))),
% 28.53/18.77 inference(monotonicity,[status(thm)],[13346, 13792])).
% 28.53/18.77 tff(13794,plain,
% 28.53/18.77 (big_f(c2, f10(c2)) <=> big_f(f7(c2), f6(c2, f10(c2)))),
% 28.53/18.77 inference(symmetry,[status(thm)],[13793])).
% 28.53/18.77 tff(13795,plain,
% 28.53/18.77 (big_f(f7(c2), f6(c2, f10(c2)))),
% 28.53/18.77 inference(modus_ponens,[status(thm)],[13382, 13794])).
% 28.53/18.77 tff(13796,plain,
% 28.53/18.77 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (~(f7(c2) = c2)) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f6(c2, f10(c2)) = f10(c2))) | (~big_f(f7(c2), f6(c2, f10(c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f6(c2, f10(c2)) = f10(c2))) | (~big_f(f7(c2), f6(c2, f10(c2)))))),
% 28.53/18.77 inference(rewrite,[status(thm)],[])).
% 28.53/18.77 tff(13797,plain,
% 28.53/18.77 (((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c2) = c2)) | (~(f6(c2, f10(c2)) = f10(c2))) | (~big_f(f7(c2), f6(c2, f10(c2))))) <=> ((f10(c2) = c2) | (~(f7(c2) = c2)) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f6(c2, f10(c2)) = f10(c2))) | (~big_f(f7(c2), f6(c2, f10(c2)))))),
% 28.53/18.77 inference(rewrite,[status(thm)],[])).
% 28.53/18.77 tff(13798,plain,
% 28.53/18.77 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c2) = c2)) | (~(f6(c2, f10(c2)) = f10(c2))) | (~big_f(f7(c2), f6(c2, f10(c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (~(f7(c2) = c2)) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f6(c2, f10(c2)) = f10(c2))) | (~big_f(f7(c2), f6(c2, f10(c2))))))),
% 28.53/18.77 inference(monotonicity,[status(thm)],[13797])).
% 28.53/18.78 tff(13799,plain,
% 28.53/18.78 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c2) = c2)) | (~(f6(c2, f10(c2)) = f10(c2))) | (~big_f(f7(c2), f6(c2, f10(c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f6(c2, f10(c2)) = f10(c2))) | (~big_f(f7(c2), f6(c2, f10(c2)))))),
% 28.53/18.78 inference(transitivity,[status(thm)],[13798, 13796])).
% 28.53/18.78 tff(13800,plain,
% 28.53/18.78 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c2) = c2)) | (~(f6(c2, f10(c2)) = f10(c2))) | (~big_f(f7(c2), f6(c2, f10(c2)))))),
% 28.53/18.78 inference(quant_inst,[status(thm)],[])).
% 28.53/18.78 tff(13801,plain,
% 28.53/18.78 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f6(c2, f10(c2)) = f10(c2))) | (~big_f(f7(c2), f6(c2, f10(c2))))),
% 28.53/18.78 inference(modus_ponens,[status(thm)],[13800, 13799])).
% 28.53/18.78 tff(13802,plain,
% 28.53/18.78 ((~(f6(c2, f10(c2)) = f10(c2))) | (~big_f(f7(c2), f6(c2, f10(c2))))),
% 28.53/18.78 inference(unit_resolution,[status(thm)],[13801, 2730, 11798, 13346, 13382, 13751])).
% 28.53/18.78 tff(13803,plain,
% 28.53/18.78 ($false),
% 28.53/18.78 inference(unit_resolution,[status(thm)],[13802, 13795, 13792])).
% 28.53/18.78 tff(13804,plain,(big_f(c2, c2) | (~(f4(c4) = c2)) | (f7(c1) = c1) | (f10(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 28.53/18.78 tff(13805,plain,
% 28.53/18.78 (big_f(c2, c2)),
% 28.53/18.78 inference(unit_resolution,[status(thm)],[13804, 79, 115, 3])).
% 28.53/18.78 tff(13806,plain,
% 28.53/18.78 ((c3 = c2) <=> (f7(f7(c2)) = c3)),
% 28.53/18.78 inference(transitivity,[status(thm)],[78, 11448])).
% 28.53/18.78 tff(13807,plain,
% 28.53/18.78 ((~(c3 = c2)) <=> (~(f7(f7(c2)) = c3))),
% 28.53/18.78 inference(monotonicity,[status(thm)],[13806])).
% 28.53/18.78 tff(13808,plain,
% 28.53/18.78 ((c2 = f5(c1)) <=> (c2 = c1)),
% 28.53/18.78 inference(monotonicity,[status(thm)],[230])).
% 28.53/18.78 tff(13809,plain,
% 28.53/18.78 ((c2 = c1) <=> (c2 = f5(c1))),
% 28.53/18.78 inference(symmetry,[status(thm)],[13808])).
% 28.53/18.78 tff(13810,plain,
% 28.53/18.78 ((~(c2 = c1)) <=> (~(c2 = f5(c1)))),
% 28.53/18.78 inference(monotonicity,[status(thm)],[13809])).
% 28.53/18.78 tff(13811,plain,
% 28.53/18.78 (~(c2 = f5(c1))),
% 28.53/18.78 inference(modus_ponens,[status(thm)],[75, 13810])).
% 28.53/18.78 tff(13812,plain,
% 28.53/18.78 (~(f10(c2) = c2)),
% 28.53/18.78 inference(unit_resolution,[status(thm)],[3407, 67, 115, 79, 77, 3])).
% 28.53/18.78 tff(13813,plain,
% 28.53/18.78 (f10(c2) = c1),
% 28.53/18.78 inference(unit_resolution,[status(thm)],[93, 13812])).
% 28.53/18.78 tff(13814,plain,
% 28.53/18.78 (f8(c2) = f8(c3)),
% 28.53/18.78 inference(monotonicity,[status(thm)],[69])).
% 28.53/18.78 tff(13815,plain,
% 28.53/18.78 (f8(c3) = f8(c2)),
% 28.53/18.78 inference(symmetry,[status(thm)],[13814])).
% 28.53/18.78 tff(13816,plain,
% 28.53/18.78 ((f8(c3) = c1) <=> (f8(c2) = c1)),
% 28.53/18.78 inference(monotonicity,[status(thm)],[13815])).
% 28.53/18.78 tff(13817,plain,
% 28.53/18.78 ((f8(c3) = c1) <=> (c1 = f8(c2))),
% 28.53/18.78 inference(transitivity,[status(thm)],[13816, 13044])).
% 28.53/18.78 tff(13818,plain,
% 28.53/18.78 ((c1 = f8(c2)) <=> (f8(c3) = c1)),
% 28.53/18.78 inference(symmetry,[status(thm)],[13817])).
% 28.53/18.78 tff(13819,plain,
% 28.53/18.78 ((~(c1 = f8(c2))) <=> (~(f8(c3) = c1))),
% 28.53/18.78 inference(monotonicity,[status(thm)],[13818])).
% 28.53/18.78 tff(13820,plain,
% 28.53/18.78 (c1 = f10(c2)),
% 28.53/18.78 inference(symmetry,[status(thm)],[13813])).
% 28.53/18.78 tff(13821,plain,
% 28.53/18.78 (big_f(c1, c1) <=> big_f(c1, f10(c2))),
% 28.53/18.78 inference(monotonicity,[status(thm)],[13820])).
% 28.53/18.78 tff(13822,plain,
% 28.53/18.78 ((~big_f(c1, c1)) <=> (~big_f(c1, f10(c2)))),
% 28.53/18.78 inference(monotonicity,[status(thm)],[13821])).
% 28.53/18.78 tff(13823,plain,
% 28.53/18.78 (~big_f(c1, f10(c2))),
% 28.53/18.78 inference(modus_ponens,[status(thm)],[66, 13822])).
% 28.53/18.78 tff(13824,plain,
% 28.53/18.78 (~(c1 = f8(c2))),
% 28.53/18.78 inference(unit_resolution,[status(thm)],[13057, 2795, 12775, 12774, 115, 13812, 13823])).
% 28.53/18.78 tff(13825,plain,
% 28.53/18.78 (~(f8(c3) = c1)),
% 28.53/18.78 inference(modus_ponens,[status(thm)],[13824, 13819])).
% 28.53/18.78 tff(13826,plain,
% 28.53/18.78 (f8(c3) = c2),
% 28.53/18.78 inference(unit_resolution,[status(thm)],[8569, 13825])).
% 28.53/18.78 tff(13827,plain,
% 28.53/18.78 (f8(f10(c1)) = f8(c2)),
% 28.53/18.78 inference(monotonicity,[status(thm)],[15])).
% 28.53/18.78 tff(13828,plain,
% 28.53/18.78 (f8(f10(c1)) = c2),
% 28.53/18.78 inference(transitivity,[status(thm)],[13827, 13814, 13826])).
% 28.53/18.78 tff(13829,plain,
% 28.53/18.78 (big_f(f8(f10(c1)), f10(c2)) <=> big_f(c2, c1)),
% 28.53/18.78 inference(monotonicity,[status(thm)],[13828, 13813])).
% 28.53/18.78 tff(13830,plain,
% 28.53/18.78 (f8(c2) = f8(f10(c1))),
% 28.53/18.78 inference(symmetry,[status(thm)],[13827])).
% 28.53/18.78 tff(13831,plain,
% 28.53/18.78 (f8(f7(f4(c4))) = f8(f10(c1))),
% 28.53/18.78 inference(transitivity,[status(thm)],[107, 13354, 13830])).
% 28.53/18.78 tff(13832,plain,
% 28.53/18.78 (big_f(f8(f7(f4(c4))), f10(c2)) <=> big_f(f8(f10(c1)), f10(c2))),
% 28.53/18.78 inference(monotonicity,[status(thm)],[13831])).
% 28.53/18.78 tff(13833,plain,
% 28.53/18.78 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((c2 = f5(c1)) | (f7(c1) = c1) | (f10(c2) = c2) | big_f(f8(f7(f4(c4))), f10(c2)) | (~(f8(f7(f4(c4))) = f8(c2))) | (~big_f(f7(c1), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | (c2 = f5(c1)) | (f7(c1) = c1) | (f10(c2) = c2) | big_f(f8(f7(f4(c4))), f10(c2)) | (~(f8(f7(f4(c4))) = f8(c2))) | (~big_f(f7(c1), c2)))),
% 28.53/18.78 inference(rewrite,[status(thm)],[])).
% 28.53/18.78 tff(13834,plain,
% 28.53/18.78 (((f10(c2) = c2) | big_f(f8(f7(f4(c4))), f10(c2)) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)) | (~(f8(f7(f4(c4))) = f8(c2)))) <=> ((c2 = f5(c1)) | (f7(c1) = c1) | (f10(c2) = c2) | big_f(f8(f7(f4(c4))), f10(c2)) | (~(f8(f7(f4(c4))) = f8(c2))) | (~big_f(f7(c1), c2)))),
% 28.53/18.78 inference(rewrite,[status(thm)],[])).
% 28.53/18.78 tff(13835,plain,
% 28.53/18.78 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | big_f(f8(f7(f4(c4))), f10(c2)) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)) | (~(f8(f7(f4(c4))) = f8(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((c2 = f5(c1)) | (f7(c1) = c1) | (f10(c2) = c2) | big_f(f8(f7(f4(c4))), f10(c2)) | (~(f8(f7(f4(c4))) = f8(c2))) | (~big_f(f7(c1), c2))))),
% 28.53/18.78 inference(monotonicity,[status(thm)],[13834])).
% 28.53/18.78 tff(13836,plain,
% 28.53/18.78 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | big_f(f8(f7(f4(c4))), f10(c2)) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)) | (~(f8(f7(f4(c4))) = f8(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | (c2 = f5(c1)) | (f7(c1) = c1) | (f10(c2) = c2) | big_f(f8(f7(f4(c4))), f10(c2)) | (~(f8(f7(f4(c4))) = f8(c2))) | (~big_f(f7(c1), c2)))),
% 28.53/18.78 inference(transitivity,[status(thm)],[13835, 13833])).
% 28.53/18.78 tff(13837,plain,
% 28.53/18.78 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | big_f(f8(f7(f4(c4))), f10(c2)) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)) | (~(f8(f7(f4(c4))) = f8(c2))))),
% 28.53/18.78 inference(quant_inst,[status(thm)],[])).
% 28.53/18.78 tff(13838,plain,
% 28.53/18.78 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | (c2 = f5(c1)) | (f7(c1) = c1) | (f10(c2) = c2) | big_f(f8(f7(f4(c4))), f10(c2)) | (~(f8(f7(f4(c4))) = f8(c2))) | (~big_f(f7(c1), c2))),
% 28.53/18.78 inference(modus_ponens,[status(thm)],[13837, 13836])).
% 28.53/18.78 tff(13839,plain,
% 28.53/18.78 ((c2 = f5(c1)) | (f7(c1) = c1) | (f10(c2) = c2) | big_f(f8(f7(f4(c4))), f10(c2)) | (~(f8(f7(f4(c4))) = f8(c2))) | (~big_f(f7(c1), c2))),
% 28.53/18.78 inference(unit_resolution,[status(thm)],[13838, 2795])).
% 28.53/18.78 tff(13840,plain,
% 28.53/18.78 (big_f(f8(f7(f4(c4))), f10(c2))),
% 28.53/18.78 inference(unit_resolution,[status(thm)],[13839, 12774, 115, 13812, 12775, 13361])).
% 28.53/18.78 tff(13841,plain,
% 28.53/18.78 (big_f(f8(f10(c1)), f10(c2))),
% 28.53/18.78 inference(modus_ponens,[status(thm)],[13840, 13832])).
% 28.53/18.78 tff(13842,plain,
% 28.53/18.78 (big_f(c2, c1)),
% 28.53/18.78 inference(modus_ponens,[status(thm)],[13841, 13829])).
% 28.53/18.78 tff(13843,plain,
% 28.53/18.78 (~(f8(f7(f4(c4))) = c1)),
% 28.53/18.78 inference(modus_ponens,[status(thm)],[13824, 13365])).
% 28.53/18.78 tff(13844,plain,
% 28.53/18.78 (f8(f7(f4(c4))) = c2),
% 28.53/18.78 inference(unit_resolution,[status(thm)],[13371, 13843])).
% 28.53/18.78 tff(13845,plain,
% 28.53/18.78 (c2 = c4),
% 28.53/18.78 inference(unit_resolution,[status(thm)],[13132, 13842, 1335, 1345, 115, 3, 12775])).
% 28.53/18.78 tff(13846,plain,
% 28.53/18.78 (c4 = c2),
% 28.53/18.78 inference(symmetry,[status(thm)],[13845])).
% 28.53/18.78 tff(13847,plain,
% 28.53/18.78 ((c1 = c4) <=> (c1 = c2)),
% 28.53/18.78 inference(monotonicity,[status(thm)],[13846])).
% 28.53/18.78 tff(13848,plain,
% 28.53/18.78 ((c1 = c4) <=> (c2 = c1)),
% 28.53/18.78 inference(transitivity,[status(thm)],[13847, 1])).
% 28.53/18.78 tff(13849,plain,
% 28.53/18.78 ((c2 = c1) <=> (c1 = c4)),
% 28.53/18.78 inference(symmetry,[status(thm)],[13848])).
% 28.53/18.78 tff(13850,plain,
% 28.53/18.78 ((~(c2 = c1)) <=> (~(c1 = c4))),
% 28.53/18.78 inference(monotonicity,[status(thm)],[13849])).
% 28.53/18.78 tff(13851,plain,
% 28.53/18.78 (~(c1 = c4)),
% 28.53/18.78 inference(modus_ponens,[status(thm)],[75, 13850])).
% 28.53/18.78 tff(13852,assumption,(f8(c3) = c2), introduced(assumption)).
% 28.53/18.78 tff(13853,plain,
% 28.53/18.78 (c2 = f8(c3)),
% 28.53/18.78 inference(symmetry,[status(thm)],[13852])).
% 28.53/18.78 tff(13854,plain,
% 28.53/18.78 (f3(c1, c2) = f3(c1, f8(c3))),
% 28.53/18.78 inference(monotonicity,[status(thm)],[13853])).
% 28.53/18.78 tff(13855,plain,
% 28.53/18.78 (f3(c1, f8(c3)) = f3(c1, c2)),
% 28.53/18.78 inference(symmetry,[status(thm)],[13854])).
% 28.53/18.78 tff(13856,assumption,(f8(f7(f4(c4))) = c2), introduced(assumption)).
% 28.53/18.78 tff(13857,plain,
% 28.53/18.78 (f8(c2) = f8(f7(f4(c4)))),
% 28.53/18.78 inference(monotonicity,[status(thm)],[83])).
% 28.53/18.78 tff(13858,plain,
% 28.53/18.78 (f8(c3) = c2),
% 28.53/18.78 inference(transitivity,[status(thm)],[13045, 13857, 13856])).
% 28.53/18.78 tff(13859,plain,
% 28.53/18.78 (f3(c1, f8(c3)) = f3(c1, c2)),
% 28.53/18.78 inference(monotonicity,[status(thm)],[13858])).
% 28.53/18.78 tff(13860,plain,
% 28.53/18.78 (f3(c1, c2) = f3(c1, f8(c3))),
% 28.53/18.78 inference(symmetry,[status(thm)],[13859])).
% 28.53/18.78 tff(13861,plain,
% 28.53/18.78 ((f3(c1, c2) = c2) <=> (f3(c1, f8(c3)) = c2)),
% 28.53/18.78 inference(monotonicity,[status(thm)],[13860])).
% 28.53/18.78 tff(13862,plain,
% 28.53/18.78 ((f3(c1, f8(c3)) = c2) <=> (f3(c1, c2) = c2)),
% 28.53/18.78 inference(symmetry,[status(thm)],[13861])).
% 28.53/18.78 tff(13863,plain,
% 28.53/18.78 (f3(c1, c2) = c2),
% 28.53/18.78 inference(modus_ponens,[status(thm)],[12781, 13862])).
% 28.53/18.78 tff(13864,plain,
% 28.53/18.78 ($false),
% 28.53/18.78 inference(unit_resolution,[status(thm)],[12777, 13863])).
% 28.53/18.78 tff(13865,plain,((~(f3(c1, f8(c3)) = c2)) | (f3(c1, c2) = c2) | (~(f8(f7(f4(c4))) = c2)) | (~(f7(c2) = c2)) | (~(f4(c4) = c2)) | (~(c3 = c2))), inference(lemma,lemma(discharge,[]))).
% 28.53/18.78 tff(13866,plain,
% 28.53/18.78 (~(f3(c1, f8(c3)) = c2)),
% 28.53/18.78 inference(unit_resolution,[status(thm)],[13865, 12777, 79, 77, 67, 13856])).
% 28.53/18.78 tff(13867,plain,
% 28.53/18.78 (f3(c1, f8(c3)) = c1),
% 28.53/18.78 inference(unit_resolution,[status(thm)],[7123, 13866])).
% 28.53/18.78 tff(13868,plain,
% 28.53/18.78 (c1 = f3(c1, f8(c3))),
% 28.53/18.78 inference(symmetry,[status(thm)],[13867])).
% 28.53/18.78 tff(13869,plain,
% 28.53/18.78 (c1 = f3(c1, c2)),
% 28.53/18.78 inference(transitivity,[status(thm)],[13868, 13855])).
% 28.53/18.78 tff(13870,plain,
% 28.53/18.78 (big_f(c1, c1) <=> big_f(f3(c1, c2), c1)),
% 28.53/18.78 inference(monotonicity,[status(thm)],[13869])).
% 28.53/18.78 tff(13871,plain,
% 28.53/18.78 ((~big_f(c1, c1)) <=> (~big_f(f3(c1, c2), c1))),
% 28.53/18.78 inference(monotonicity,[status(thm)],[13870])).
% 28.53/18.78 tff(13872,plain,
% 28.53/18.78 (~big_f(f3(c1, c2), c1)),
% 28.53/18.78 inference(modus_ponens,[status(thm)],[66, 13871])).
% 28.53/18.78 tff(13873,plain,
% 28.53/18.78 (c1 = f2(c2)),
% 28.53/18.78 inference(unit_resolution,[status(thm)],[13170, 7352, 482, 1335, 13872, 12777, 348])).
% 28.53/18.78 tff(13874,plain,
% 28.53/18.78 (f2(c2) = c1),
% 28.53/18.78 inference(symmetry,[status(thm)],[13873])).
% 28.53/18.78 tff(13875,plain,
% 28.53/18.78 (c2 = f2(c2)),
% 28.53/18.78 inference(unit_resolution,[status(thm)],[13182, 7352, 482, 1345, 1335, 13872, 12777])).
% 28.53/18.78 tff(13876,plain,
% 28.53/18.78 (c2 = c1),
% 28.53/18.78 inference(transitivity,[status(thm)],[13875, 13874])).
% 28.53/18.78 tff(13877,plain,
% 28.53/18.78 ($false),
% 28.53/18.78 inference(unit_resolution,[status(thm)],[75, 13876])).
% 28.53/18.78 tff(13878,plain,((f3(c1, c2) = c2) | (c1 = c4) | (~big_f(c2, c1)) | (~big_f(c2, c2)) | big_f(c1, c1) | (~(f8(c3) = c2)) | (~(f4(c4) = c2)) | (~(f7(c2) = c2)) | (~(c3 = c2)) | (~(f8(f7(f4(c4))) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.53/18.78 tff(13879,plain,
% 28.53/18.78 (f3(c1, c2) = c2),
% 28.53/18.78 inference(unit_resolution,[status(thm)],[13878, 13851, 13842, 1345, 66, 13826, 79, 77, 67, 13844])).
% 28.53/18.78 tff(13880,plain,
% 28.53/18.78 (big_f(f3(c1, c2), c1) <=> big_f(c2, c1)),
% 28.53/18.78 inference(monotonicity,[status(thm)],[13879])).
% 28.53/18.78 tff(13881,plain,
% 28.53/18.78 (big_f(c2, c1) <=> big_f(f3(c1, c2), c1)),
% 28.53/18.78 inference(symmetry,[status(thm)],[13880])).
% 28.53/18.78 tff(13882,plain,
% 28.53/18.78 (big_f(f3(c1, c2), c1)),
% 28.53/18.78 inference(modus_ponens,[status(thm)],[13842, 13881])).
% 28.53/18.78 tff(13883,plain,
% 28.53/18.78 (c1 = f2(c2)),
% 28.53/18.78 inference(unit_resolution,[status(thm)],[13205, 7051, 13851, 1335, 13882, 13879, 13842])).
% 28.53/18.78 tff(13884,plain,
% 28.53/18.78 (f2(c2) = c1),
% 28.53/18.78 inference(symmetry,[status(thm)],[13883])).
% 28.53/18.78 tff(13885,plain,
% 28.53/18.78 (c2 = f2(c2)),
% 28.53/18.78 inference(unit_resolution,[status(thm)],[13213, 7051, 13851, 1345, 1335, 13882, 13879])).
% 28.53/18.78 tff(13886,plain,
% 28.53/18.78 (c2 = c1),
% 28.53/18.78 inference(transitivity,[status(thm)],[13885, 13884])).
% 28.53/18.78 tff(13887,plain,
% 28.53/18.78 ($false),
% 28.53/18.78 inference(unit_resolution,[status(thm)],[75, 13886])).
% 28.53/18.78 tff(13888,plain,((~big_f(c2, c2)) | big_f(c1, c1) | (~(f4(c4) = c2)) | (~(f7(c2) = c2)) | (~(c3 = c2)) | (f7(c1) = c1) | (f10(c1) = c1) | (c2 = f5(c1))), inference(lemma,lemma(discharge,[]))).
% 28.53/18.78 tff(13889,plain,
% 28.53/18.78 (~big_f(c2, c2)),
% 28.53/18.78 inference(unit_resolution,[status(thm)],[13888, 67, 79, 77, 66, 115, 3, 13811])).
% 28.53/18.78 tff(13890,plain,
% 28.53/18.78 (f10(f6(c2, f7(f4(c4)))) = f10(c1)),
% 28.53/18.78 inference(monotonicity,[status(thm)],[6634])).
% 28.53/18.78 tff(13891,plain,
% 28.53/18.78 (f10(f6(c2, f7(f4(c4)))) = c2),
% 28.53/18.78 inference(transitivity,[status(thm)],[13890, 15])).
% 28.53/18.78 tff(13892,plain,
% 28.53/18.78 (big_f(c1, f10(f6(c2, f7(f4(c4))))) <=> big_f(c1, c2)),
% 28.53/18.78 inference(monotonicity,[status(thm)],[13891])).
% 28.53/18.78 tff(13893,plain,
% 28.53/18.78 (f6(c2, f6(c2, f7(f4(c4)))) = f6(c2, c1)),
% 28.53/18.78 inference(monotonicity,[status(thm)],[6634])).
% 28.53/18.78 tff(13894,plain,
% 28.53/18.78 (big_f(f7(c2), f6(c2, f6(c2, f7(f4(c4))))) <=> big_f(f7(c2), f6(c2, c1))),
% 28.53/18.78 inference(monotonicity,[status(thm)],[13893])).
% 28.53/18.78 tff(13895,plain,
% 28.53/18.78 (big_f(f7(c2), f6(c2, c1)) <=> big_f(f7(c2), f6(c2, f6(c2, f7(f4(c4)))))),
% 28.53/18.78 inference(symmetry,[status(thm)],[13894])).
% 28.53/18.78 tff(13896,plain,
% 28.53/18.78 (big_f(c2, c1)),
% 28.53/18.78 inference(unit_resolution,[status(thm)],[8259, 121, 67, 79])).
% 28.53/18.78 tff(13897,plain,
% 28.53/18.78 (~(c2 = f8(c1))),
% 28.53/18.78 inference(unit_resolution,[status(thm)],[3003, 13896, 230, 77, 121, 3])).
% 28.53/18.78 tff(13898,plain,
% 28.53/18.78 (~(f8(c1) = c2)),
% 28.53/18.78 inference(unit_resolution,[status(thm)],[1675, 13897])).
% 28.53/18.78 tff(13899,plain,
% 28.53/18.78 (f8(c1) = c1),
% 28.53/18.78 inference(unit_resolution,[status(thm)],[1680, 13898])).
% 28.53/18.78 tff(13900,plain,
% 28.53/18.78 (c1 = f8(c1)),
% 28.53/18.78 inference(unit_resolution,[status(thm)],[9808, 13899])).
% 28.53/18.78 tff(13901,plain,
% 28.53/18.78 (big_f(c1, f10(c1))),
% 28.53/18.78 inference(unit_resolution,[status(thm)],[3049, 13900, 230, 77, 3, 3032, 121])).
% 28.53/18.78 tff(13902,plain,
% 28.53/18.78 (big_f(c1, c2)),
% 28.53/18.78 inference(unit_resolution,[status(thm)],[12239, 13901, 11819, 11879])).
% 28.53/18.78 tff(13903,plain,
% 28.53/18.78 (~(c4 = c2)),
% 28.53/18.78 inference(unit_resolution,[status(thm)],[13490, 121, 13086, 13902, 66, 79])).
% 28.53/18.78 tff(13904,plain,
% 28.53/18.78 (~(c2 = c4)),
% 28.53/18.78 inference(modus_ponens,[status(thm)],[13903, 797])).
% 28.53/18.78 tff(13905,plain,
% 28.53/18.78 (f1(c1, c2) = c2),
% 28.53/18.78 inference(unit_resolution,[status(thm)],[13531, 13904, 13086, 13902, 347, 121, 66])).
% 28.53/18.78 tff(13906,plain,
% 28.53/18.78 (~(f3(f7(c1), c1) = c1)),
% 28.53/18.78 inference(unit_resolution,[status(thm)],[13544, 13904, 13086, 13905, 13902, 347])).
% 28.53/18.78 tff(13907,plain,
% 28.53/18.78 (f3(f7(c1), c1) = c2),
% 28.53/18.78 inference(unit_resolution,[status(thm)],[918, 13906])).
% 28.53/18.78 tff(13908,plain,
% 28.53/18.78 (f3(c2, c1) = c2),
% 28.53/18.78 inference(transitivity,[status(thm)],[3125, 13907])).
% 28.53/18.78 tff(13909,plain,
% 28.53/18.78 (big_f(f3(c2, c1), c2) <=> big_f(c2, c2)),
% 28.53/18.78 inference(monotonicity,[status(thm)],[13908])).
% 28.53/18.78 tff(13910,plain,
% 28.53/18.78 (big_f(c2, c2) <=> big_f(f3(c2, c1), c2)),
% 28.53/18.78 inference(symmetry,[status(thm)],[13909])).
% 28.53/18.78 tff(13911,plain,
% 28.53/18.78 ((~big_f(c2, c2)) <=> (~big_f(f3(c2, c1), c2))),
% 28.53/18.78 inference(monotonicity,[status(thm)],[13910])).
% 28.53/18.78 tff(13912,plain,
% 28.53/18.78 (~big_f(f3(c2, c1), c2)),
% 28.53/18.78 inference(modus_ponens,[status(thm)],[121, 13911])).
% 28.53/18.78 tff(13913,plain,
% 28.53/18.78 (~(f3(c2, c1) = c1)),
% 28.53/18.78 inference(modus_ponens,[status(thm)],[13906, 12176])).
% 28.53/18.78 tff(13914,plain,
% 28.53/18.78 (big_f(c1, f1(c1, c2)) <=> big_f(c1, c2)),
% 28.53/18.78 inference(monotonicity,[status(thm)],[13905])).
% 28.53/18.78 tff(13915,plain,
% 28.53/18.78 (big_f(c1, c2) <=> big_f(c1, f1(c1, c2))),
% 28.53/18.78 inference(symmetry,[status(thm)],[13914])).
% 28.53/18.78 tff(13916,plain,
% 28.53/18.78 (big_f(c1, f1(c1, c2))),
% 28.53/18.78 inference(modus_ponens,[status(thm)],[13902, 13915])).
% 28.53/18.78 tff(13917,plain,
% 28.53/18.78 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (c2 = c4) | (~big_f(c1, f1(c1, c2))) | (~(f1(c1, c2) = c2)) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (c2 = c4) | (~big_f(c1, f1(c1, c2))) | (~(f1(c1, c2) = c2)) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2))),
% 28.53/18.78 inference(rewrite,[status(thm)],[])).
% 28.53/18.78 tff(13918,plain,
% 28.53/18.78 (((c2 = c4) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2) | (c1 = c3) | (~(f1(c1, c2) = c2)) | (~big_f(c1, f1(c1, c2)))) <=> ((c1 = c3) | (c2 = c4) | (~big_f(c1, f1(c1, c2))) | (~(f1(c1, c2) = c2)) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2))),
% 28.53/18.78 inference(rewrite,[status(thm)],[])).
% 28.53/18.78 tff(13919,plain,
% 28.53/18.78 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2) | (c1 = c3) | (~(f1(c1, c2) = c2)) | (~big_f(c1, f1(c1, c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (c2 = c4) | (~big_f(c1, f1(c1, c2))) | (~(f1(c1, c2) = c2)) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2)))),
% 28.53/18.78 inference(monotonicity,[status(thm)],[13918])).
% 28.53/18.78 tff(13920,plain,
% 28.53/18.78 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2) | (c1 = c3) | (~(f1(c1, c2) = c2)) | (~big_f(c1, f1(c1, c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (c2 = c4) | (~big_f(c1, f1(c1, c2))) | (~(f1(c1, c2) = c2)) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2))),
% 28.53/18.78 inference(transitivity,[status(thm)],[13919, 13917])).
% 28.53/18.78 tff(13921,plain,
% 28.53/18.78 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2) | (c1 = c3) | (~(f1(c1, c2) = c2)) | (~big_f(c1, f1(c1, c2))))),
% 28.53/18.78 inference(quant_inst,[status(thm)],[])).
% 28.53/18.78 tff(13922,plain,
% 28.53/18.78 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (c2 = c4) | (~big_f(c1, f1(c1, c2))) | (~(f1(c1, c2) = c2)) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2)),
% 28.53/18.78 inference(modus_ponens,[status(thm)],[13921, 13920])).
% 28.53/18.78 tff(13923,plain,
% 28.53/18.78 ($false),
% 28.53/18.78 inference(unit_resolution,[status(thm)],[13922, 904, 13086, 13904, 13905, 13916, 13913, 13912])).
% 28.53/18.78 tff(13924,plain,(big_f(c2, c2) | (~(f7(c1) = c2)) | big_f(c1, c1) | (~(f4(c4) = c2)) | (~(f10(c2) = c1)) | (~(f5(c1) = c1)) | (~(f7(c2) = c2)) | (f10(c1) = c1) | (~(f6(f7(c2), f5(c1)) = c2)) | (~(c3 = c2))), inference(lemma,lemma(discharge,[]))).
% 28.53/18.78 tff(13925,plain,
% 28.53/18.78 (~(f6(f7(c2), f5(c1)) = c2)),
% 28.53/18.78 inference(unit_resolution,[status(thm)],[13924, 13889, 66, 79, 13813, 230, 77, 3, 120, 67])).
% 28.53/18.78 tff(13926,plain,
% 28.53/18.78 (f6(f7(c2), f5(c1)) = c1),
% 28.53/18.78 inference(unit_resolution,[status(thm)],[2978, 13925])).
% 28.53/18.78 tff(13927,plain,
% 28.53/18.78 (f6(c2, c1) = c1),
% 28.53/18.78 inference(transitivity,[status(thm)],[2942, 13926])).
% 28.53/18.78 tff(13928,plain,
% 28.53/18.78 (big_f(c2, f6(c2, c1)) <=> big_f(c2, c1)),
% 28.53/18.78 inference(monotonicity,[status(thm)],[13927])).
% 28.53/18.78 tff(13929,plain,
% 28.53/18.78 (big_f(c2, c1) <=> big_f(c2, f6(c2, c1))),
% 28.53/18.78 inference(symmetry,[status(thm)],[13928])).
% 28.53/18.78 tff(13930,plain,
% 28.53/18.78 (big_f(c2, c1) <=> big_f(f7(c2), f6(c2, f6(c2, f7(f4(c4)))))),
% 28.53/18.78 inference(transitivity,[status(thm)],[13929, 13581, 13895])).
% 28.53/18.78 tff(13931,plain,
% 28.53/18.78 (big_f(c2, c1)),
% 28.53/18.78 inference(unit_resolution,[status(thm)],[8259, 13889, 67, 79])).
% 28.53/18.78 tff(13932,plain,
% 28.53/18.78 (big_f(f7(c2), f6(c2, f6(c2, f7(f4(c4)))))),
% 28.53/18.78 inference(modus_ponens,[status(thm)],[13931, 13930])).
% 28.53/18.78 tff(13933,plain,
% 28.53/18.78 (f8(f6(c2, f7(f4(c4)))) = f8(c1)),
% 28.53/18.78 inference(monotonicity,[status(thm)],[6634])).
% 28.53/18.78 tff(13934,plain,
% 28.53/18.78 ((c1 = f8(f6(c2, f7(f4(c4))))) <=> (c1 = f8(c1))),
% 28.53/18.78 inference(monotonicity,[status(thm)],[13933])).
% 28.53/18.78 tff(13935,plain,
% 28.53/18.78 ((c1 = f8(f6(c2, f7(f4(c4))))) <=> (f8(c1) = c1)),
% 28.53/18.78 inference(transitivity,[status(thm)],[13934, 3027])).
% 28.53/18.78 tff(13936,plain,
% 28.53/18.78 ((f8(c1) = c1) <=> (c1 = f8(f6(c2, f7(f4(c4)))))),
% 28.53/18.78 inference(symmetry,[status(thm)],[13935])).
% 28.53/18.78 tff(13937,plain,
% 28.53/18.78 (~(c2 = f8(c1))),
% 28.53/18.78 inference(unit_resolution,[status(thm)],[3003, 13931, 230, 77, 13889, 3])).
% 28.53/18.78 tff(13938,plain,
% 28.53/18.78 (~(f8(c1) = c2)),
% 28.53/18.78 inference(unit_resolution,[status(thm)],[1675, 13937])).
% 28.53/18.78 tff(13939,plain,
% 28.53/18.78 (f8(c1) = c1),
% 28.53/18.78 inference(unit_resolution,[status(thm)],[1680, 13938])).
% 28.53/18.78 tff(13940,plain,
% 28.53/18.78 (c1 = f8(f6(c2, f7(f4(c4))))),
% 28.53/18.78 inference(modus_ponens,[status(thm)],[13939, 13936])).
% 28.53/18.78 tff(13941,plain,
% 28.53/18.78 ((f10(f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4)))) <=> (c2 = c1)),
% 28.53/18.78 inference(monotonicity,[status(thm)],[13891, 6634])).
% 28.53/18.78 tff(13942,plain,
% 28.53/18.78 ((c2 = c1) <=> (f10(f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4))))),
% 28.53/18.78 inference(symmetry,[status(thm)],[13941])).
% 28.53/18.78 tff(13943,plain,
% 28.53/18.78 ((~(c2 = c1)) <=> (~(f10(f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4)))))),
% 28.53/18.78 inference(monotonicity,[status(thm)],[13942])).
% 28.53/18.78 tff(13944,plain,
% 28.53/18.78 (~(f10(f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4))))),
% 28.53/18.78 inference(modus_ponens,[status(thm)],[75, 13943])).
% 28.53/18.78 tff(13945,plain,
% 28.53/18.78 ((f6(c2, f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4)))) <=> (f6(c2, c1) = c1)),
% 28.53/18.78 inference(monotonicity,[status(thm)],[13893, 6634])).
% 28.53/18.78 tff(13946,plain,
% 28.53/18.78 ((f6(c2, c1) = c1) <=> (f6(c2, f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4))))),
% 28.53/18.78 inference(symmetry,[status(thm)],[13945])).
% 28.53/18.78 tff(13947,plain,
% 28.53/18.78 (f6(c2, c1) = c1),
% 28.53/18.78 inference(unit_resolution,[status(thm)],[13591, 13926, 230, 77])).
% 28.53/18.78 tff(13948,plain,
% 28.53/18.78 (f6(c2, f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4)))),
% 28.53/18.78 inference(modus_ponens,[status(thm)],[13947, 13946])).
% 28.53/18.78 tff(13949,plain,
% 28.53/18.78 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(c2) = c2)) | (f10(f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4)))) | big_f(c1, f10(f6(c2, f7(f4(c4))))) | (~(c1 = f8(f6(c2, f7(f4(c4)))))) | (~big_f(f7(c2), f6(c2, f6(c2, f7(f4(c4)))))) | (~(f6(c2, f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4))))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c2) = c2)) | (f10(f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4)))) | big_f(c1, f10(f6(c2, f7(f4(c4))))) | (~(c1 = f8(f6(c2, f7(f4(c4)))))) | (~big_f(f7(c2), f6(c2, f6(c2, f7(f4(c4)))))) | (~(f6(c2, f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4))))))),
% 28.53/18.78 inference(rewrite,[status(thm)],[])).
% 28.53/18.78 tff(13950,plain,
% 28.53/18.78 (((f10(f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4)))) | big_f(c1, f10(f6(c2, f7(f4(c4))))) | (~(f7(c2) = c2)) | (~(c1 = f8(f6(c2, f7(f4(c4)))))) | (~(f6(c2, f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4))))) | (~big_f(f7(c2), f6(c2, f6(c2, f7(f4(c4))))))) <=> ((~(f7(c2) = c2)) | (f10(f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4)))) | big_f(c1, f10(f6(c2, f7(f4(c4))))) | (~(c1 = f8(f6(c2, f7(f4(c4)))))) | (~big_f(f7(c2), f6(c2, f6(c2, f7(f4(c4)))))) | (~(f6(c2, f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4))))))),
% 28.53/18.78 inference(rewrite,[status(thm)],[])).
% 28.53/18.79 tff(13951,plain,
% 28.53/18.79 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4)))) | big_f(c1, f10(f6(c2, f7(f4(c4))))) | (~(f7(c2) = c2)) | (~(c1 = f8(f6(c2, f7(f4(c4)))))) | (~(f6(c2, f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4))))) | (~big_f(f7(c2), f6(c2, f6(c2, f7(f4(c4)))))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(c2) = c2)) | (f10(f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4)))) | big_f(c1, f10(f6(c2, f7(f4(c4))))) | (~(c1 = f8(f6(c2, f7(f4(c4)))))) | (~big_f(f7(c2), f6(c2, f6(c2, f7(f4(c4)))))) | (~(f6(c2, f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4)))))))),
% 28.53/18.79 inference(monotonicity,[status(thm)],[13950])).
% 28.53/18.79 tff(13952,plain,
% 28.53/18.79 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4)))) | big_f(c1, f10(f6(c2, f7(f4(c4))))) | (~(f7(c2) = c2)) | (~(c1 = f8(f6(c2, f7(f4(c4)))))) | (~(f6(c2, f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4))))) | (~big_f(f7(c2), f6(c2, f6(c2, f7(f4(c4)))))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c2) = c2)) | (f10(f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4)))) | big_f(c1, f10(f6(c2, f7(f4(c4))))) | (~(c1 = f8(f6(c2, f7(f4(c4)))))) | (~big_f(f7(c2), f6(c2, f6(c2, f7(f4(c4)))))) | (~(f6(c2, f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4))))))),
% 28.53/18.79 inference(transitivity,[status(thm)],[13951, 13949])).
% 28.53/18.79 tff(13953,plain,
% 28.53/18.79 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4)))) | big_f(c1, f10(f6(c2, f7(f4(c4))))) | (~(f7(c2) = c2)) | (~(c1 = f8(f6(c2, f7(f4(c4)))))) | (~(f6(c2, f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4))))) | (~big_f(f7(c2), f6(c2, f6(c2, f7(f4(c4)))))))),
% 28.53/18.79 inference(quant_inst,[status(thm)],[])).
% 28.53/18.79 tff(13954,plain,
% 28.53/18.79 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c2) = c2)) | (f10(f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4)))) | big_f(c1, f10(f6(c2, f7(f4(c4))))) | (~(c1 = f8(f6(c2, f7(f4(c4)))))) | (~big_f(f7(c2), f6(c2, f6(c2, f7(f4(c4)))))) | (~(f6(c2, f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4)))))),
% 28.53/18.79 inference(modus_ponens,[status(thm)],[13953, 13952])).
% 28.53/18.79 tff(13955,plain,
% 28.53/18.79 ((~(f7(c2) = c2)) | (f10(f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4)))) | big_f(c1, f10(f6(c2, f7(f4(c4))))) | (~(c1 = f8(f6(c2, f7(f4(c4)))))) | (~big_f(f7(c2), f6(c2, f6(c2, f7(f4(c4)))))) | (~(f6(c2, f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4)))))),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[13954, 2963])).
% 28.53/18.79 tff(13956,plain,
% 28.53/18.79 (big_f(c1, f10(f6(c2, f7(f4(c4)))))),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[13955, 13948, 13944, 77, 13940, 13932])).
% 28.53/18.79 tff(13957,plain,
% 28.53/18.79 (big_f(c1, c2)),
% 28.53/18.79 inference(modus_ponens,[status(thm)],[13956, 13892])).
% 28.53/18.79 tff(13958,plain,
% 28.53/18.79 (~(c4 = c2)),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[13490, 13957, 13086, 13889, 66, 79])).
% 28.53/18.79 tff(13959,plain,
% 28.53/18.79 (c4 = c1),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[461, 13958])).
% 28.53/18.79 tff(13960,plain,
% 28.53/18.79 ((c2 = c4) <=> (c2 = c1)),
% 28.53/18.79 inference(monotonicity,[status(thm)],[13959])).
% 28.53/18.79 tff(13961,plain,
% 28.53/18.79 ((c2 = c1) <=> (c2 = c4)),
% 28.53/18.79 inference(symmetry,[status(thm)],[13960])).
% 28.53/18.79 tff(13962,plain,
% 28.53/18.79 ((~(c2 = c1)) <=> (~(c2 = c4))),
% 28.53/18.79 inference(monotonicity,[status(thm)],[13961])).
% 28.53/18.79 tff(13963,plain,
% 28.53/18.79 (~(c2 = c4)),
% 28.53/18.79 inference(modus_ponens,[status(thm)],[75, 13962])).
% 28.53/18.79 tff(13964,plain,
% 28.53/18.79 (f1(c1, c2) = c2),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[13531, 13963, 13086, 13957, 120, 13889, 66])).
% 28.53/18.79 tff(13965,plain,
% 28.53/18.79 (~(f3(f7(c1), c1) = c1)),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[13544, 13964, 13086, 13957, 13963, 120])).
% 28.53/18.79 tff(13966,plain,
% 28.53/18.79 (f3(f7(c1), c1) = c2),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[918, 13965])).
% 28.53/18.79 tff(13967,plain,
% 28.53/18.79 (f3(c2, c1) = c2),
% 28.53/18.79 inference(transitivity,[status(thm)],[2779, 13966])).
% 28.53/18.79 tff(13968,plain,
% 28.53/18.79 (big_f(f3(c2, c1), c2) <=> big_f(c2, c2)),
% 28.53/18.79 inference(monotonicity,[status(thm)],[13967])).
% 28.53/18.79 tff(13969,plain,
% 28.53/18.79 (big_f(c2, c2) <=> big_f(f3(c2, c1), c2)),
% 28.53/18.79 inference(symmetry,[status(thm)],[13968])).
% 28.53/18.79 tff(13970,plain,
% 28.53/18.79 ((~big_f(c2, c2)) <=> (~big_f(f3(c2, c1), c2))),
% 28.53/18.79 inference(monotonicity,[status(thm)],[13969])).
% 28.53/18.79 tff(13971,plain,
% 28.53/18.79 (~big_f(f3(c2, c1), c2)),
% 28.53/18.79 inference(modus_ponens,[status(thm)],[13889, 13970])).
% 28.53/18.79 tff(13972,plain,
% 28.53/18.79 ((f3(c2, c1) = c1) <=> (c2 = c1)),
% 28.53/18.79 inference(monotonicity,[status(thm)],[13967])).
% 28.53/18.79 tff(13973,plain,
% 28.53/18.79 ((c2 = c1) <=> (f3(c2, c1) = c1)),
% 28.53/18.79 inference(symmetry,[status(thm)],[13972])).
% 28.53/18.79 tff(13974,plain,
% 28.53/18.79 ((~(c2 = c1)) <=> (~(f3(c2, c1) = c1))),
% 28.53/18.79 inference(monotonicity,[status(thm)],[13973])).
% 28.53/18.79 tff(13975,plain,
% 28.53/18.79 (~(f3(c2, c1) = c1)),
% 28.53/18.79 inference(modus_ponens,[status(thm)],[75, 13974])).
% 28.53/18.79 tff(13976,plain,
% 28.53/18.79 (big_f(c1, f1(c1, c2)) <=> big_f(c1, c2)),
% 28.53/18.79 inference(monotonicity,[status(thm)],[13964])).
% 28.53/18.79 tff(13977,plain,
% 28.53/18.79 (big_f(c1, c2) <=> big_f(c1, f1(c1, c2))),
% 28.53/18.79 inference(symmetry,[status(thm)],[13976])).
% 28.53/18.79 tff(13978,plain,
% 28.53/18.79 (big_f(c1, f1(c1, c2))),
% 28.53/18.79 inference(modus_ponens,[status(thm)],[13957, 13977])).
% 28.53/18.79 tff(13979,plain,
% 28.53/18.79 ($false),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[13922, 904, 13086, 13963, 13964, 13978, 13975, 13971])).
% 28.53/18.79 tff(13980,plain,((~(c3 = c2)) | big_f(c1, c1) | (~(f4(c4) = c2)) | (~(f6(c2, f7(f4(c4))) = c1)) | (~(f7(c2) = c2)) | (~(f5(c1) = c1)) | (f10(c1) = c1) | (f7(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 28.53/18.79 tff(13981,plain,
% 28.53/18.79 (~(c3 = c2)),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[13980, 77, 79, 6634, 66, 230, 3, 115])).
% 28.53/18.79 tff(13982,plain,
% 28.53/18.79 (~(f7(f7(c2)) = c3)),
% 28.53/18.79 inference(modus_ponens,[status(thm)],[13981, 13807])).
% 28.53/18.79 tff(13983,plain,
% 28.53/18.79 (c3 = c1),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[180, 13981])).
% 28.53/18.79 tff(13984,plain,
% 28.53/18.79 (~(f7(c1) = c3)),
% 28.53/18.79 inference(modus_ponens,[status(thm)],[13981, 13633])).
% 28.53/18.79 tff(13985,plain,
% 28.53/18.79 (~(c2 = c3)),
% 28.53/18.79 inference(modus_ponens,[status(thm)],[13981, 10473])).
% 28.53/18.79 tff(13986,plain,
% 28.53/18.79 (big_f(c2, c2)),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[13655, 873, 377, 12165, 77, 3, 230, 79, 115, 66])).
% 28.53/18.79 tff(13987,plain,
% 28.53/18.79 (big_f(c2, f10(c1))),
% 28.53/18.79 inference(modus_ponens,[status(thm)],[13986, 2719])).
% 28.53/18.79 tff(13988,plain,
% 28.53/18.79 (big_f(f7(c1), c2)),
% 28.53/18.79 inference(modus_ponens,[status(thm)],[13986, 1724])).
% 28.53/18.79 tff(13989,plain,
% 28.53/18.79 (c2 = f8(c1)),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[3393, 1659, 13811, 13988, 115, 13987, 3])).
% 28.53/18.79 tff(13990,plain,
% 28.53/18.79 (f3(c2, c2) = c2),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[12913, 13988, 13811, 115, 3, 13989, 873, 172, 66])).
% 28.53/18.79 tff(13991,plain,
% 28.53/18.79 (big_f(f3(c2, c2), c2) <=> big_f(c2, c2)),
% 28.53/18.79 inference(monotonicity,[status(thm)],[13990])).
% 28.53/18.79 tff(13992,plain,
% 28.53/18.79 (big_f(c2, c2) <=> big_f(f3(c2, c2), c2)),
% 28.53/18.79 inference(symmetry,[status(thm)],[13991])).
% 28.53/18.79 tff(13993,plain,
% 28.53/18.79 (big_f(f3(c2, c2), c2)),
% 28.53/18.79 inference(modus_ponens,[status(thm)],[13986, 13992])).
% 28.53/18.79 tff(13994,plain,
% 28.53/18.79 (f8(c1) = c2),
% 28.53/18.79 inference(symmetry,[status(thm)],[13989])).
% 28.53/18.79 tff(13995,plain,
% 28.53/18.79 ((f8(c1) = c1) <=> (c2 = c1)),
% 28.53/18.79 inference(monotonicity,[status(thm)],[13994])).
% 28.53/18.79 tff(13996,plain,
% 28.53/18.79 ((c2 = c1) <=> (f8(c1) = c1)),
% 28.53/18.79 inference(symmetry,[status(thm)],[13995])).
% 28.53/18.79 tff(13997,plain,
% 28.53/18.79 ((c2 = c1) <=> (c1 = f8(c1))),
% 28.53/18.79 inference(transitivity,[status(thm)],[13996, 3028])).
% 28.53/18.79 tff(13998,plain,
% 28.53/18.79 ((~(c2 = c1)) <=> (~(c1 = f8(c1)))),
% 28.53/18.79 inference(monotonicity,[status(thm)],[13997])).
% 28.53/18.79 tff(13999,plain,
% 28.53/18.79 (~(c1 = f8(c1))),
% 28.53/18.79 inference(modus_ponens,[status(thm)],[75, 13998])).
% 28.53/18.79 tff(14000,plain,
% 28.53/18.79 (~big_f(c1, f10(c1))),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[12879, 13988, 13811, 115, 3, 13999])).
% 28.53/18.79 tff(14001,plain,
% 28.53/18.79 (~big_f(c1, c2)),
% 28.53/18.79 inference(modus_ponens,[status(thm)],[14000, 12865])).
% 28.53/18.79 tff(14002,plain,
% 28.53/18.79 (~(c2 = f2(c1))),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[12931, 1398, 5611, 873, 14001, 13990, 13993])).
% 28.53/18.79 tff(14003,plain,
% 28.53/18.79 (~(f2(c3) = c2)),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[12823, 14002, 172])).
% 28.53/18.79 tff(14004,plain,
% 28.53/18.79 (~(c1 = f2(c1))),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[12923, 1398, 5611, 873, 66, 13990, 13993])).
% 28.53/18.79 tff(14005,plain,
% 28.53/18.79 (~(f2(c3) = c1)),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[6771, 14004, 172])).
% 28.53/18.79 tff(14006,plain,
% 28.53/18.79 ($false),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[1273, 14005, 14003])).
% 28.53/18.79 tff(14007,plain,((c2 = c4) | (~(c3 = c1)) | big_f(c1, c1) | (f7(c1) = c1) | (f10(c1) = c1) | (c2 = c3) | (f7(c1) = c3) | (~(f7(c2) = c2)) | (~(f5(c1) = c1)) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.53/18.79 tff(14008,plain,
% 28.53/18.79 (c2 = c4),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[14007, 13983, 66, 115, 3, 13985, 13984, 77, 230, 79])).
% 28.53/18.79 tff(14009,plain,
% 28.53/18.79 (big_f(c2, c2)),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[13702, 13985, 79, 115, 77, 692, 14008, 66, 13983, 13982])).
% 28.53/18.79 tff(14010,plain,
% 28.53/18.79 (big_f(f7(c1), c2)),
% 28.53/18.79 inference(modus_ponens,[status(thm)],[14009, 1724])).
% 28.53/18.79 tff(14011,plain,
% 28.53/18.79 (big_f(c2, f10(c1))),
% 28.53/18.79 inference(modus_ponens,[status(thm)],[14009, 2719])).
% 28.53/18.79 tff(14012,plain,
% 28.53/18.79 (c2 = f8(c1)),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[3393, 1659, 13811, 14010, 115, 14011, 3])).
% 28.53/18.79 tff(14013,plain,
% 28.53/18.79 (f8(c1) = c2),
% 28.53/18.79 inference(symmetry,[status(thm)],[14012])).
% 28.53/18.79 tff(14014,plain,
% 28.53/18.79 ((f8(c1) = c1) <=> (c2 = c1)),
% 28.53/18.79 inference(monotonicity,[status(thm)],[14013])).
% 28.53/18.79 tff(14015,plain,
% 28.53/18.79 ((c2 = c1) <=> (f8(c1) = c1)),
% 28.53/18.79 inference(symmetry,[status(thm)],[14014])).
% 28.53/18.79 tff(14016,plain,
% 28.53/18.79 ((c2 = c1) <=> (c1 = f8(c1))),
% 28.53/18.79 inference(transitivity,[status(thm)],[14015, 3028])).
% 28.53/18.79 tff(14017,plain,
% 28.53/18.79 ((~(c2 = c1)) <=> (~(c1 = f8(c1)))),
% 28.53/18.79 inference(monotonicity,[status(thm)],[14016])).
% 28.53/18.79 tff(14018,plain,
% 28.53/18.79 (~(c1 = f8(c1))),
% 28.53/18.79 inference(modus_ponens,[status(thm)],[75, 14017])).
% 28.53/18.79 tff(14019,plain,
% 28.53/18.79 (~big_f(c1, f10(c1))),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[12879, 14018, 13811, 115, 3, 14010])).
% 28.53/18.79 tff(14020,plain,
% 28.53/18.79 (~big_f(c1, c2)),
% 28.53/18.79 inference(modus_ponens,[status(thm)],[14019, 12865])).
% 28.53/18.79 tff(14021,plain,
% 28.53/18.79 (f6(c2, c2) = c1),
% 28.53/18.79 inference(transitivity,[status(thm)],[84, 6634])).
% 28.53/18.79 tff(14022,plain,
% 28.53/18.79 (big_f(f7(c2), f6(c2, c2)) <=> big_f(c2, c1)),
% 28.53/18.79 inference(monotonicity,[status(thm)],[77, 14021])).
% 28.53/18.79 tff(14023,plain,
% 28.53/18.79 (big_f(f7(c2), f6(c2, f4(c4))) <=> big_f(c2, c1)),
% 28.53/18.79 inference(transitivity,[status(thm)],[3947, 14022])).
% 28.53/18.79 tff(14024,plain,
% 28.53/18.79 ((f6(c2, c2) = c2) <=> (c1 = c2)),
% 28.53/18.79 inference(monotonicity,[status(thm)],[14021])).
% 28.53/18.79 tff(14025,plain,
% 28.53/18.79 ((f6(c2, c2) = c2) <=> (c2 = c1)),
% 28.53/18.79 inference(transitivity,[status(thm)],[14024, 1])).
% 28.53/18.79 tff(14026,plain,
% 28.53/18.79 ((c2 = c1) <=> (f6(c2, c2) = c2)),
% 28.53/18.79 inference(symmetry,[status(thm)],[14025])).
% 28.53/18.79 tff(14027,plain,
% 28.53/18.79 ((~(c2 = c1)) <=> (~(f6(c2, c2) = c2))),
% 28.53/18.79 inference(monotonicity,[status(thm)],[14026])).
% 28.53/18.79 tff(14028,plain,
% 28.53/18.79 (~(f6(c2, c2) = c2)),
% 28.53/18.79 inference(modus_ponens,[status(thm)],[75, 14027])).
% 28.53/18.79 tff(14029,plain,
% 28.53/18.79 (f10(c2) = c2),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[13377, 2, 79, 115, 77, 11826, 66])).
% 28.53/18.79 tff(14030,plain,
% 28.53/18.79 (f9(f10(c2), f4(c4)) = c2),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[8065, 14029, 79])).
% 28.53/18.79 tff(14031,plain,
% 28.53/18.79 (big_f(f7(c2), f6(c2, c2))),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[2639, 14029, 1345, 14030, 77, 14028, 79])).
% 28.53/18.79 tff(14032,plain,
% 28.53/18.79 ((~big_f(f7(c2), f6(c2, f4(c4)))) <=> (~big_f(f7(c2), f6(c2, c2)))),
% 28.53/18.79 inference(monotonicity,[status(thm)],[3947])).
% 28.53/18.79 tff(14033,assumption,(~big_f(f7(c2), f6(c2, f4(c4)))), introduced(assumption)).
% 28.53/18.79 tff(14034,plain,
% 28.53/18.79 (~big_f(f7(c2), f6(c2, c2))),
% 28.53/18.79 inference(modus_ponens,[status(thm)],[14033, 14032])).
% 28.53/18.79 tff(14035,plain,
% 28.53/18.79 ($false),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[2707, 14034])).
% 28.53/18.79 tff(14036,plain,(big_f(f7(c2), f6(c2, f4(c4))) | (~big_f(f7(c2), f6(c2, c2))) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.53/18.79 tff(14037,plain,
% 28.53/18.79 (big_f(f7(c2), f6(c2, f4(c4)))),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[14036, 14031, 79])).
% 28.53/18.79 tff(14038,plain,
% 28.53/18.79 (big_f(c2, c1)),
% 28.53/18.79 inference(modus_ponens,[status(thm)],[14037, 14023])).
% 28.53/18.79 tff(14039,plain,
% 28.53/18.79 ($false),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[2, 14038])).
% 28.53/18.79 tff(14040,plain,(big_f(c2, c1) | (~(f6(c2, f7(f4(c4))) = c1)) | (~(f7(c2) = c2)) | (~(f4(c4) = c2)) | (~big_f(c2, c2)) | (f7(c1) = c1) | (~(c1 = f5(c1))) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 28.53/18.79 tff(14041,plain,
% 28.53/18.79 (big_f(c2, c1)),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[14040, 77, 6634, 79, 14009, 115, 692, 66])).
% 28.53/18.79 tff(14042,plain,
% 28.53/18.79 (c4 = c2),
% 28.53/18.79 inference(symmetry,[status(thm)],[14008])).
% 28.53/18.79 tff(14043,plain,
% 28.53/18.79 ((c1 = c4) <=> (c1 = c2)),
% 28.53/18.79 inference(monotonicity,[status(thm)],[14042])).
% 28.53/18.79 tff(14044,plain,
% 28.53/18.79 ((c1 = c4) <=> (c2 = c1)),
% 28.53/18.79 inference(transitivity,[status(thm)],[14043, 1])).
% 28.53/18.79 tff(14045,plain,
% 28.53/18.79 ((c2 = c1) <=> (c1 = c4)),
% 28.53/18.79 inference(symmetry,[status(thm)],[14044])).
% 28.53/18.79 tff(14046,plain,
% 28.53/18.79 ((~(c2 = c1)) <=> (~(c1 = c4))),
% 28.53/18.79 inference(monotonicity,[status(thm)],[14045])).
% 28.53/18.79 tff(14047,plain,
% 28.53/18.79 (~(c1 = c4)),
% 28.53/18.79 inference(modus_ponens,[status(thm)],[75, 14046])).
% 28.53/18.79 tff(14048,plain,
% 28.53/18.79 (big_f(c1, c2)),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[12851, 14047, 14041, 66, 14012, 13983])).
% 28.53/18.79 tff(14049,plain,
% 28.53/18.79 ($false),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[14048, 14020])).
% 28.53/18.79 tff(14050,plain,((~(f7(c2) = c2)) | big_f(c1, c1) | (~(f6(c2, f7(f4(c4))) = c1)) | (~(f4(c4) = c2)) | (f7(c1) = c1) | (f10(c1) = c1) | (~(f5(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.53/18.79 tff(14051,plain,
% 28.53/18.79 (~(f7(c2) = c2)),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[14050, 230, 6634, 79, 115, 3, 66])).
% 28.53/18.79 tff(14052,plain,
% 28.53/18.79 (f7(c2) = c1),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[21, 14051])).
% 28.53/18.79 tff(14053,plain,
% 28.53/18.79 (f7(f7(c2)) = f7(c1)),
% 28.53/18.79 inference(monotonicity,[status(thm)],[14052])).
% 28.53/18.79 tff(14054,plain,
% 28.53/18.79 (f7(f7(c2)) = c2),
% 28.53/18.79 inference(transitivity,[status(thm)],[14053, 120])).
% 28.53/18.79 tff(14055,plain,
% 28.53/18.79 ((f7(f7(c2)) = c3) <=> (c2 = c3)),
% 28.53/18.79 inference(monotonicity,[status(thm)],[14054])).
% 28.53/18.79 tff(14056,plain,
% 28.53/18.79 ((c2 = c3) <=> (f7(f7(c2)) = c3)),
% 28.53/18.79 inference(symmetry,[status(thm)],[14055])).
% 28.53/18.79 tff(14057,plain,
% 28.53/18.79 ((c3 = c2) <=> (f7(f7(c2)) = c3)),
% 28.53/18.79 inference(transitivity,[status(thm)],[78, 14056])).
% 28.53/18.79 tff(14058,plain,
% 28.53/18.79 ((~(c3 = c2)) <=> (~(f7(f7(c2)) = c3))),
% 28.53/18.79 inference(monotonicity,[status(thm)],[14057])).
% 28.53/18.79 tff(14059,plain,
% 28.53/18.79 (~(c3 = c2)),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[13217, 13811, 66, 115, 3, 14051, 79])).
% 28.53/18.79 tff(14060,plain,
% 28.53/18.79 (~(f7(f7(c2)) = c3)),
% 28.53/18.79 inference(modus_ponens,[status(thm)],[14059, 14058])).
% 28.53/18.79 tff(14061,plain,
% 28.53/18.79 (~(f7(c1) = c3)),
% 28.53/18.79 inference(modus_ponens,[status(thm)],[14059, 13633])).
% 28.53/18.79 tff(14062,plain,
% 28.53/18.79 (~(f10(c2) = c2)),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[10739, 14051, 79])).
% 28.53/18.79 tff(14063,plain,
% 28.53/18.79 (f10(c2) = c1),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[93, 14062])).
% 28.53/18.79 tff(14064,plain,
% 28.53/18.79 (big_f(c1, f10(c2)) <=> big_f(c1, c1)),
% 28.53/18.79 inference(monotonicity,[status(thm)],[14063])).
% 28.53/18.79 tff(14065,plain,
% 28.53/18.79 (big_f(c1, c1) <=> big_f(c1, f10(c2))),
% 28.53/18.79 inference(symmetry,[status(thm)],[14064])).
% 28.53/18.79 tff(14066,plain,
% 28.53/18.79 ((~big_f(c1, c1)) <=> (~big_f(c1, f10(c2)))),
% 28.53/18.79 inference(monotonicity,[status(thm)],[14065])).
% 28.53/18.79 tff(14067,plain,
% 28.53/18.79 (~big_f(c1, f10(c2))),
% 28.53/18.79 inference(modus_ponens,[status(thm)],[66, 14066])).
% 28.53/18.79 tff(14068,plain,
% 28.53/18.79 (big_f(c2, c1)),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[12084, 14062, 115, 692, 14067, 15])).
% 28.53/18.79 tff(14069,plain,
% 28.53/18.79 (~(c2 = c3)),
% 28.53/18.79 inference(modus_ponens,[status(thm)],[14059, 10473])).
% 28.53/18.79 tff(14070,plain,
% 28.53/18.79 (c1 = f7(c2)),
% 28.53/18.79 inference(symmetry,[status(thm)],[14052])).
% 28.53/18.79 tff(14071,plain,
% 28.53/18.79 (big_f(c1, c1) <=> big_f(f7(c2), c1)),
% 28.53/18.79 inference(monotonicity,[status(thm)],[14070])).
% 28.53/18.79 tff(14072,plain,
% 28.53/18.79 ((~big_f(c1, c1)) <=> (~big_f(f7(c2), c1))),
% 28.53/18.79 inference(monotonicity,[status(thm)],[14071])).
% 28.53/18.79 tff(14073,plain,
% 28.53/18.79 (~big_f(f7(c2), c1)),
% 28.53/18.79 inference(modus_ponens,[status(thm)],[66, 14072])).
% 28.53/18.79 tff(14074,plain,
% 28.53/18.79 (big_f(c2, c2)),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[12276, 14051, 3, 14073, 120, 14069, 14068, 14061, 79, 14060])).
% 28.53/18.79 tff(14075,plain,
% 28.53/18.79 (big_f(f7(c1), c2)),
% 28.53/18.79 inference(modus_ponens,[status(thm)],[14074, 1724])).
% 28.53/18.79 tff(14076,plain,
% 28.53/18.79 (big_f(c2, f10(c1))),
% 28.53/18.79 inference(modus_ponens,[status(thm)],[14074, 2719])).
% 28.53/18.79 tff(14077,plain,
% 28.53/18.79 (c2 = f8(c1)),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[3393, 1659, 13811, 14075, 115, 14076, 3])).
% 28.53/18.79 tff(14078,plain,
% 28.53/18.79 (f8(c1) = c2),
% 28.53/18.79 inference(symmetry,[status(thm)],[14077])).
% 28.53/18.79 tff(14079,plain,
% 28.53/18.79 ((f8(c1) = c1) <=> (c2 = c1)),
% 28.53/18.79 inference(monotonicity,[status(thm)],[14078])).
% 28.53/18.79 tff(14080,plain,
% 28.53/18.79 ((c2 = c1) <=> (f8(c1) = c1)),
% 28.53/18.79 inference(symmetry,[status(thm)],[14079])).
% 28.53/18.79 tff(14081,plain,
% 28.53/18.79 ((c2 = c1) <=> (c1 = f8(c1))),
% 28.53/18.79 inference(transitivity,[status(thm)],[14080, 3028])).
% 28.53/18.79 tff(14082,plain,
% 28.53/18.79 ((~(c2 = c1)) <=> (~(c1 = f8(c1)))),
% 28.53/18.79 inference(monotonicity,[status(thm)],[14081])).
% 28.53/18.79 tff(14083,plain,
% 28.53/18.79 (~(c1 = f8(c1))),
% 28.53/18.79 inference(modus_ponens,[status(thm)],[75, 14082])).
% 28.53/18.79 tff(14084,plain,
% 28.53/18.79 (~big_f(c1, f10(c1))),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[12879, 14083, 13811, 115, 3, 14075])).
% 28.53/18.79 tff(14085,plain,
% 28.53/18.79 (~big_f(c1, c2)),
% 28.53/18.79 inference(modus_ponens,[status(thm)],[14084, 12865])).
% 28.53/18.79 tff(14086,plain,
% 28.53/18.79 (c3 = c1),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[180, 14059])).
% 28.53/18.79 tff(14087,plain,
% 28.53/18.79 (big_f(c1, c2)),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[12935, 14086, 66, 14074, 13811, 115, 3, 14068])).
% 28.53/18.79 tff(14088,plain,
% 28.53/18.79 ($false),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[14087, 14085])).
% 28.53/18.79 tff(14089,plain,((~(f5(c1) = c1)) | big_f(c1, c1) | (f7(c1) = c1) | (f10(c1) = c1) | (~(f4(c4) = c2)) | (~(f6(c2, f7(f4(c4))) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.53/18.79 tff(14090,plain,
% 28.53/18.79 (~(f5(c1) = c1)),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[14089, 66, 115, 3, 79, 6634])).
% 28.53/18.79 tff(14091,plain,
% 28.53/18.79 (~(c1 = f5(c1))),
% 28.53/18.79 inference(modus_ponens,[status(thm)],[14090, 2261])).
% 28.53/18.79 tff(14092,plain,
% 28.53/18.79 (f6(c2, c2) = f6(c2, f7(f4(c4)))),
% 28.53/18.79 inference(symmetry,[status(thm)],[2475])).
% 28.53/18.79 tff(14093,plain,
% 28.53/18.79 (f6(c2, c2) = c1),
% 28.53/18.79 inference(transitivity,[status(thm)],[14092, 6634])).
% 28.53/18.79 tff(14094,plain,
% 28.53/18.79 (big_f(f7(c2), f6(c2, c2)) <=> big_f(c2, c1)),
% 28.53/18.79 inference(monotonicity,[status(thm)],[77, 14093])).
% 28.53/18.79 tff(14095,plain,
% 28.53/18.79 (big_f(c2, c1) <=> big_f(f7(c2), f6(c2, c2))),
% 28.53/18.79 inference(symmetry,[status(thm)],[14094])).
% 28.53/18.79 tff(14096,plain,
% 28.53/18.79 ((~big_f(c2, c1)) <=> (~big_f(f7(c2), f6(c2, c2)))),
% 28.53/18.79 inference(monotonicity,[status(thm)],[14095])).
% 28.53/18.79 tff(14097,plain,
% 28.53/18.79 (~big_f(f7(c2), f6(c2, c2))),
% 28.53/18.79 inference(modus_ponens,[status(thm)],[2, 14096])).
% 28.53/18.79 tff(14098,plain,
% 28.53/18.79 ((f6(c2, c2) = c2) <=> (c1 = c2)),
% 28.53/18.79 inference(monotonicity,[status(thm)],[14093])).
% 28.53/18.79 tff(14099,plain,
% 28.53/18.79 ((f6(c2, c2) = c2) <=> (c2 = c1)),
% 28.53/18.79 inference(transitivity,[status(thm)],[14098, 1])).
% 28.53/18.79 tff(14100,plain,
% 28.53/18.79 ((c2 = c1) <=> (f6(c2, c2) = c2)),
% 28.53/18.79 inference(symmetry,[status(thm)],[14099])).
% 28.53/18.79 tff(14101,plain,
% 28.53/18.79 ((~(c2 = c1)) <=> (~(f6(c2, c2) = c2))),
% 28.53/18.79 inference(monotonicity,[status(thm)],[14100])).
% 28.53/18.79 tff(14102,plain,
% 28.53/18.79 (~(f6(c2, c2) = c2)),
% 28.53/18.79 inference(modus_ponens,[status(thm)],[75, 14101])).
% 28.53/18.79 tff(14103,plain,
% 28.53/18.79 (c1 = f6(c2, f7(f4(c4)))),
% 28.53/18.79 inference(symmetry,[status(thm)],[6634])).
% 28.53/18.79 tff(14104,plain,
% 28.53/18.79 (f5(c1) = c2),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[1708, 14090])).
% 28.53/18.79 tff(14105,plain,
% 28.53/18.79 (big_f(c2, c2)),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[12042, 2, 14104, 66, 115, 15, 79])).
% 28.53/18.79 tff(14106,plain,
% 28.53/18.79 (f6(f7(c2), f5(c1)) = f6(c2, c2)),
% 28.53/18.79 inference(monotonicity,[status(thm)],[77, 14104])).
% 28.53/18.79 tff(14107,plain,
% 28.53/18.79 ((f6(f7(c2), f5(c1)) = c2) <=> (f6(c2, c2) = c2)),
% 28.53/18.79 inference(monotonicity,[status(thm)],[14106])).
% 28.53/18.79 tff(14108,plain,
% 28.53/18.79 ((f6(c2, c2) = c2) <=> (f6(f7(c2), f5(c1)) = c2)),
% 28.53/18.79 inference(symmetry,[status(thm)],[14107])).
% 28.53/18.79 tff(14109,plain,
% 28.53/18.79 ((c2 = c1) <=> (f6(f7(c2), f5(c1)) = c2)),
% 28.53/18.79 inference(transitivity,[status(thm)],[14100, 14108])).
% 28.53/18.79 tff(14110,plain,
% 28.53/18.79 ((~(c2 = c1)) <=> (~(f6(f7(c2), f5(c1)) = c2))),
% 28.53/18.79 inference(monotonicity,[status(thm)],[14109])).
% 28.53/18.79 tff(14111,plain,
% 28.53/18.79 (~(f6(f7(c2), f5(c1)) = c2)),
% 28.53/18.79 inference(modus_ponens,[status(thm)],[75, 14110])).
% 28.53/18.79 tff(14112,plain,
% 28.53/18.79 (~(f10(c2) = c2)),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[3341, 14111, 79, 14104, 115, 3, 14105, 77])).
% 28.53/18.79 tff(14113,plain,
% 28.53/18.79 (f10(c2) = c1),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[93, 14112])).
% 28.53/18.79 tff(14114,plain,
% 28.53/18.79 (f10(c2) = f6(c2, c2)),
% 28.53/18.79 inference(transitivity,[status(thm)],[14113, 14103, 2475])).
% 28.53/18.79 tff(14115,plain,
% 28.53/18.79 (big_f(c2, f10(c2)) <=> big_f(f7(c2), f6(c2, c2))),
% 28.53/18.79 inference(monotonicity,[status(thm)],[82, 14114])).
% 28.53/18.79 tff(14116,plain,
% 28.53/18.79 (big_f(f7(c2), f6(c2, c2)) <=> big_f(c2, f10(c2))),
% 28.53/18.79 inference(symmetry,[status(thm)],[14115])).
% 28.53/18.79 tff(14117,plain,
% 28.53/18.79 ((~big_f(f7(c2), f6(c2, c2))) <=> (~big_f(c2, f10(c2)))),
% 28.53/18.79 inference(monotonicity,[status(thm)],[14116])).
% 28.53/18.79 tff(14118,plain,
% 28.53/18.79 (~big_f(c2, f10(c2))),
% 28.53/18.79 inference(modus_ponens,[status(thm)],[14097, 14117])).
% 28.53/18.79 tff(14119,plain,
% 28.53/18.79 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | (~(f7(c2) = c2)) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)))),
% 28.53/18.79 inference(rewrite,[status(thm)],[])).
% 28.53/18.79 tff(14120,plain,
% 28.53/18.79 (((f10(c2) = c2) | big_f(c2, f10(c2)) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (~(c2 = f8(c2)))) <=> ((f10(c2) = c2) | (~(f7(c2) = c2)) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)))),
% 28.53/18.79 inference(rewrite,[status(thm)],[])).
% 28.53/18.79 tff(14121,plain,
% 28.53/18.79 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | big_f(c2, f10(c2)) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (~(c2 = f8(c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | (~(f7(c2) = c2)) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2))))),
% 28.53/18.79 inference(monotonicity,[status(thm)],[14120])).
% 28.53/18.79 tff(14122,plain,
% 28.53/18.79 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | big_f(c2, f10(c2)) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (~(c2 = f8(c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)))),
% 28.53/18.79 inference(transitivity,[status(thm)],[14121, 14119])).
% 28.53/18.79 tff(14123,plain,
% 28.53/18.79 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | big_f(c2, f10(c2)) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (~(c2 = f8(c2))))),
% 28.53/18.79 inference(quant_inst,[status(thm)],[])).
% 28.53/18.79 tff(14124,plain,
% 28.53/18.79 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2))),
% 28.53/18.79 inference(modus_ponens,[status(thm)],[14123, 14122])).
% 28.53/18.79 tff(14125,plain,
% 28.53/18.79 (~(c2 = f8(c2))),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[14124, 2994, 14112, 77, 14118, 14102, 14097])).
% 28.53/18.79 tff(14126,plain,
% 28.53/18.79 (~(f8(f7(f4(c4))) = c2)),
% 28.53/18.79 inference(modus_ponens,[status(thm)],[14125, 13358])).
% 28.53/18.79 tff(14127,plain,
% 28.53/18.79 ((~(c1 = f8(f7(f4(c4))))) <=> (~(f8(f7(f4(c4))) = c1))),
% 28.53/18.79 inference(monotonicity,[status(thm)],[8517])).
% 28.53/18.79 tff(14128,plain,
% 28.53/18.79 ((f10(f7(f4(c4))) = f7(f4(c4))) <=> (f10(f7(c2)) = f7(c2))),
% 28.53/18.79 inference(monotonicity,[status(thm)],[12113, 80])).
% 28.53/18.79 tff(14129,plain,
% 28.53/18.79 ((f10(f7(c2)) = f7(c2)) <=> (f10(f7(f4(c4))) = f7(f4(c4)))),
% 28.53/18.79 inference(symmetry,[status(thm)],[14128])).
% 28.53/18.79 tff(14130,plain,
% 28.53/18.79 ((f10(f7(c2)) = f7(c2)) <=> (f10(c2) = c2)),
% 28.53/18.79 inference(monotonicity,[status(thm)],[95, 77])).
% 28.53/18.79 tff(14131,plain,
% 28.53/18.79 ((f10(c2) = c2) <=> (f10(f7(c2)) = f7(c2))),
% 28.53/18.79 inference(symmetry,[status(thm)],[14130])).
% 28.53/18.79 tff(14132,plain,
% 28.53/18.79 ((f10(c2) = c2) <=> (f10(f7(f4(c4))) = f7(f4(c4)))),
% 28.53/18.79 inference(transitivity,[status(thm)],[14131, 14129])).
% 28.53/18.79 tff(14133,plain,
% 28.53/18.79 ((~(f10(c2) = c2)) <=> (~(f10(f7(f4(c4))) = f7(f4(c4))))),
% 28.53/18.79 inference(monotonicity,[status(thm)],[14132])).
% 28.53/18.79 tff(14134,plain,
% 28.53/18.79 (~(f10(f7(f4(c4))) = f7(f4(c4)))),
% 28.53/18.79 inference(modus_ponens,[status(thm)],[14112, 14133])).
% 28.53/18.79 tff(14135,plain,
% 28.53/18.79 (big_f(f7(c2), f6(c2, c2)) <=> big_f(f7(c2), f6(c2, f4(c4)))),
% 28.53/18.79 inference(symmetry,[status(thm)],[3947])).
% 28.53/18.79 tff(14136,plain,
% 28.53/18.79 (big_f(c2, c1) <=> big_f(f7(c2), f6(c2, f4(c4)))),
% 28.53/18.79 inference(transitivity,[status(thm)],[14095, 14135])).
% 28.53/18.79 tff(14137,plain,
% 28.53/18.79 ((~big_f(c2, c1)) <=> (~big_f(f7(c2), f6(c2, f4(c4))))),
% 28.53/18.79 inference(monotonicity,[status(thm)],[14136])).
% 28.53/18.79 tff(14138,plain,
% 28.53/18.79 (~big_f(f7(c2), f6(c2, f4(c4)))),
% 28.53/18.79 inference(modus_ponens,[status(thm)],[2, 14137])).
% 28.53/18.79 tff(14139,plain,
% 28.53/18.79 ((c2 = c1) <=> (f6(c2, f4(c4)) = f4(c4))),
% 28.53/18.79 inference(transitivity,[status(thm)],[14100, 3951])).
% 28.53/18.79 tff(14140,plain,
% 28.53/18.79 ((~(c2 = c1)) <=> (~(f6(c2, f4(c4)) = f4(c4)))),
% 28.53/18.79 inference(monotonicity,[status(thm)],[14139])).
% 28.53/18.79 tff(14141,plain,
% 28.53/18.79 (~(f6(c2, f4(c4)) = f4(c4))),
% 28.53/18.79 inference(modus_ponens,[status(thm)],[75, 14140])).
% 28.53/18.79 tff(14142,plain,
% 28.53/18.79 (f10(f7(f4(c4))) = f10(c2)),
% 28.53/18.79 inference(transitivity,[status(thm)],[12113, 95])).
% 28.53/18.79 tff(14143,plain,
% 28.53/18.79 (big_f(c1, f10(f7(f4(c4)))) <=> big_f(c1, f10(c2))),
% 28.53/18.79 inference(monotonicity,[status(thm)],[14142])).
% 28.53/18.79 tff(14144,plain,
% 28.53/18.79 (big_f(c1, f10(c2)) <=> big_f(c1, f10(f7(f4(c4))))),
% 28.53/18.79 inference(symmetry,[status(thm)],[14143])).
% 28.53/18.79 tff(14145,plain,
% 28.53/18.79 (c1 = f10(c2)),
% 28.53/18.79 inference(symmetry,[status(thm)],[14113])).
% 28.53/18.79 tff(14146,plain,
% 28.53/18.79 (big_f(c1, c1) <=> big_f(c1, f10(c2))),
% 28.53/18.79 inference(monotonicity,[status(thm)],[14145])).
% 28.53/18.79 tff(14147,plain,
% 28.53/18.79 (big_f(c1, c1) <=> big_f(c1, f10(f7(f4(c4))))),
% 28.53/18.79 inference(transitivity,[status(thm)],[14146, 14144])).
% 28.53/18.79 tff(14148,plain,
% 28.53/18.79 ((~big_f(c1, c1)) <=> (~big_f(c1, f10(f7(f4(c4)))))),
% 28.53/18.79 inference(monotonicity,[status(thm)],[14147])).
% 28.53/18.79 tff(14149,plain,
% 28.53/18.79 (~big_f(c1, f10(f7(f4(c4))))),
% 28.53/18.79 inference(modus_ponens,[status(thm)],[66, 14148])).
% 28.53/18.79 tff(14150,plain,
% 28.53/18.79 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((~(f7(c2) = c2)) | (f10(f7(f4(c4))) = f7(f4(c4))) | big_f(c1, f10(f7(f4(c4)))) | (~(c1 = f8(f7(f4(c4))))) | big_f(f7(c2), f6(c2, f4(c4))) | (f6(c2, f4(c4)) = f4(c4)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (~(f7(c2) = c2)) | (f10(f7(f4(c4))) = f7(f4(c4))) | big_f(c1, f10(f7(f4(c4)))) | (~(c1 = f8(f7(f4(c4))))) | big_f(f7(c2), f6(c2, f4(c4))) | (f6(c2, f4(c4)) = f4(c4)))),
% 28.53/18.79 inference(rewrite,[status(thm)],[])).
% 28.53/18.79 tff(14151,plain,
% 28.53/18.79 (((f10(f7(f4(c4))) = f7(f4(c4))) | big_f(c1, f10(f7(f4(c4)))) | (~(f7(c2) = c2)) | (f6(c2, f4(c4)) = f4(c4)) | big_f(f7(c2), f6(c2, f4(c4))) | (~(c1 = f8(f7(f4(c4)))))) <=> ((~(f7(c2) = c2)) | (f10(f7(f4(c4))) = f7(f4(c4))) | big_f(c1, f10(f7(f4(c4)))) | (~(c1 = f8(f7(f4(c4))))) | big_f(f7(c2), f6(c2, f4(c4))) | (f6(c2, f4(c4)) = f4(c4)))),
% 28.53/18.79 inference(rewrite,[status(thm)],[])).
% 28.53/18.79 tff(14152,plain,
% 28.53/18.79 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(f7(f4(c4))) = f7(f4(c4))) | big_f(c1, f10(f7(f4(c4)))) | (~(f7(c2) = c2)) | (f6(c2, f4(c4)) = f4(c4)) | big_f(f7(c2), f6(c2, f4(c4))) | (~(c1 = f8(f7(f4(c4))))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((~(f7(c2) = c2)) | (f10(f7(f4(c4))) = f7(f4(c4))) | big_f(c1, f10(f7(f4(c4)))) | (~(c1 = f8(f7(f4(c4))))) | big_f(f7(c2), f6(c2, f4(c4))) | (f6(c2, f4(c4)) = f4(c4))))),
% 28.53/18.79 inference(monotonicity,[status(thm)],[14151])).
% 28.53/18.79 tff(14153,plain,
% 28.53/18.79 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(f7(f4(c4))) = f7(f4(c4))) | big_f(c1, f10(f7(f4(c4)))) | (~(f7(c2) = c2)) | (f6(c2, f4(c4)) = f4(c4)) | big_f(f7(c2), f6(c2, f4(c4))) | (~(c1 = f8(f7(f4(c4))))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (~(f7(c2) = c2)) | (f10(f7(f4(c4))) = f7(f4(c4))) | big_f(c1, f10(f7(f4(c4)))) | (~(c1 = f8(f7(f4(c4))))) | big_f(f7(c2), f6(c2, f4(c4))) | (f6(c2, f4(c4)) = f4(c4)))),
% 28.53/18.79 inference(transitivity,[status(thm)],[14152, 14150])).
% 28.53/18.79 tff(14154,plain,
% 28.53/18.79 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(f7(f4(c4))) = f7(f4(c4))) | big_f(c1, f10(f7(f4(c4)))) | (~(f7(c2) = c2)) | (f6(c2, f4(c4)) = f4(c4)) | big_f(f7(c2), f6(c2, f4(c4))) | (~(c1 = f8(f7(f4(c4))))))),
% 28.53/18.79 inference(quant_inst,[status(thm)],[])).
% 28.53/18.79 tff(14155,plain,
% 28.53/18.79 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (~(f7(c2) = c2)) | (f10(f7(f4(c4))) = f7(f4(c4))) | big_f(c1, f10(f7(f4(c4)))) | (~(c1 = f8(f7(f4(c4))))) | big_f(f7(c2), f6(c2, f4(c4))) | (f6(c2, f4(c4)) = f4(c4))),
% 28.53/18.79 inference(modus_ponens,[status(thm)],[14154, 14153])).
% 28.53/18.79 tff(14156,plain,
% 28.53/18.79 ((~(f7(c2) = c2)) | (f10(f7(f4(c4))) = f7(f4(c4))) | big_f(c1, f10(f7(f4(c4)))) | (~(c1 = f8(f7(f4(c4))))) | big_f(f7(c2), f6(c2, f4(c4))) | (f6(c2, f4(c4)) = f4(c4))),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[14155, 2994])).
% 28.53/18.79 tff(14157,plain,
% 28.53/18.79 (~(c1 = f8(f7(f4(c4))))),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[14156, 14149, 77, 14141, 14138, 14134])).
% 28.53/18.79 tff(14158,plain,
% 28.53/18.79 (~(f8(f7(f4(c4))) = c1)),
% 28.53/18.79 inference(modus_ponens,[status(thm)],[14157, 14127])).
% 28.53/18.79 tff(14159,plain,
% 28.53/18.79 ($false),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[13371, 14158, 14126])).
% 28.53/18.79 tff(14160,plain,((~(f7(c2) = c2)) | (~(f4(c4) = c2)) | big_f(c1, c1) | (~(f6(c2, f7(f4(c4))) = c1)) | (f7(c1) = c1) | (f10(c1) = c1) | big_f(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 28.53/18.79 tff(14161,plain,
% 28.53/18.79 (~(f7(c2) = c2)),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[14160, 2, 66, 6634, 115, 3, 79])).
% 28.53/18.79 tff(14162,plain,
% 28.53/18.79 (f7(c2) = c1),
% 28.53/18.79 inference(unit_resolution,[status(thm)],[21, 14161])).
% 28.53/18.79 tff(14163,plain,
% 28.53/18.79 (big_f(c2, f7(c2)) <=> big_f(c2, c1)),
% 28.53/18.79 inference(monotonicity,[status(thm)],[14162])).
% 28.53/18.79 tff(14164,plain,
% 28.53/18.79 (big_f(c2, c1) <=> big_f(c2, f7(c2))),
% 28.53/18.79 inference(symmetry,[status(thm)],[14163])).
% 28.53/18.79 tff(14165,plain,
% 28.53/18.79 ((~big_f(c2, c1)) <=> (~big_f(c2, f7(c2)))),
% 28.53/18.79 inference(monotonicity,[status(thm)],[14164])).
% 28.53/18.79 tff(14166,plain,
% 28.53/18.79 (~big_f(c2, f7(c2))),
% 28.53/18.79 inference(modus_ponens,[status(thm)],[2, 14165])).
% 28.53/18.79 tff(14167,plain,
% 28.53/18.79 (c1 = f7(c2)),
% 28.53/18.79 inference(symmetry,[status(thm)],[14162])).
% 28.53/18.79 tff(14168,plain,
% 28.53/18.79 (big_f(f7(c2), f7(c2)) <=> big_f(f7(c2), c1)),
% 28.53/18.79 inference(monotonicity,[status(thm)],[14162])).
% 28.53/18.79 tff(14169,plain,
% 28.53/18.79 (big_f(c1, c1) <=> big_f(f7(c2), f7(c2))),
% 28.53/18.79 inference(monotonicity,[status(thm)],[14167, 14167])).
% 28.53/18.79 tff(14170,plain,
% 28.53/18.79 (big_f(c1, c1) <=> big_f(f7(c2), c1)),
% 28.53/18.80 inference(transitivity,[status(thm)],[14169, 14168])).
% 28.53/18.80 tff(14171,plain,
% 28.53/18.80 ((~big_f(c1, c1)) <=> (~big_f(f7(c2), c1))),
% 28.53/18.80 inference(monotonicity,[status(thm)],[14170])).
% 28.53/18.80 tff(14172,plain,
% 28.53/18.80 (~big_f(f7(c2), c1)),
% 28.53/18.80 inference(modus_ponens,[status(thm)],[66, 14171])).
% 28.53/18.80 tff(14173,plain,
% 28.53/18.80 (big_f(f7(c2), c2) <=> big_f(c1, c2)),
% 28.53/18.80 inference(monotonicity,[status(thm)],[14162])).
% 28.53/18.80 tff(14174,plain,
% 28.53/18.80 (big_f(c1, c2) <=> big_f(f7(c2), c2)),
% 28.53/18.80 inference(symmetry,[status(thm)],[14173])).
% 28.53/18.80 tff(14175,plain,
% 28.53/18.80 (big_f(c1, c2)),
% 28.53/18.80 inference(unit_resolution,[status(thm)],[12734, 14161, 66, 2, 15, 79])).
% 28.53/18.80 tff(14176,plain,
% 28.53/18.80 (big_f(f7(c2), c2)),
% 28.53/18.80 inference(modus_ponens,[status(thm)],[14175, 14174])).
% 28.53/18.80 tff(14177,plain,
% 28.53/18.80 (~(c3 = c2)),
% 28.53/18.80 inference(unit_resolution,[status(thm)],[9397, 14176, 14161, 14172, 79, 2])).
% 28.53/18.80 tff(14178,plain,
% 28.53/18.80 (c3 = c1),
% 28.53/18.80 inference(unit_resolution,[status(thm)],[180, 14177])).
% 28.53/18.80 tff(14179,plain,
% 28.53/18.80 (c3 = f7(c2)),
% 28.53/18.80 inference(transitivity,[status(thm)],[14178, 14167])).
% 28.53/18.80 tff(14180,plain,
% 28.53/18.80 ((c2 = c3) <=> (c2 = f7(c2))),
% 28.53/18.80 inference(monotonicity,[status(thm)],[14179])).
% 28.53/18.80 tff(14181,plain,
% 28.53/18.80 ((c2 = c3) <=> (f7(c2) = c2)),
% 28.53/18.80 inference(transitivity,[status(thm)],[14180, 8409])).
% 28.53/18.80 tff(14182,plain,
% 28.53/18.80 ((f7(c2) = c2) <=> (c2 = c3)),
% 28.53/18.80 inference(symmetry,[status(thm)],[14181])).
% 28.53/18.80 tff(14183,plain,
% 28.53/18.80 ((~(f7(c2) = c2)) <=> (~(c2 = c3))),
% 28.53/18.80 inference(monotonicity,[status(thm)],[14182])).
% 28.53/18.80 tff(14184,plain,
% 28.53/18.80 (~(c2 = c3)),
% 28.53/18.80 inference(modus_ponens,[status(thm)],[14161, 14183])).
% 28.53/18.80 tff(14185,plain,
% 28.53/18.80 (~(c4 = c1)),
% 28.53/18.80 inference(unit_resolution,[status(thm)],[9437, 14184, 79, 2, 14105, 14162, 14166])).
% 28.53/18.80 tff(14186,plain,
% 28.53/18.80 (c4 = c2),
% 28.53/18.80 inference(unit_resolution,[status(thm)],[461, 14185])).
% 28.53/18.80 tff(14187,plain,
% 28.53/18.80 (c2 = c4),
% 28.53/18.80 inference(symmetry,[status(thm)],[14186])).
% 28.53/18.80 tff(14188,plain,
% 28.53/18.80 (f4(c2) = f4(c4)),
% 28.53/18.80 inference(monotonicity,[status(thm)],[14187])).
% 28.53/18.80 tff(14189,plain,
% 28.53/18.80 (f4(c2) = c2),
% 28.53/18.80 inference(transitivity,[status(thm)],[14188, 79])).
% 28.53/18.80 tff(14190,plain,
% 28.53/18.80 ((f7(c2) = f4(c2)) <=> (f7(c2) = c2)),
% 28.53/18.80 inference(monotonicity,[status(thm)],[14189])).
% 28.53/18.80 tff(14191,plain,
% 28.53/18.80 ((f7(c2) = c2) <=> (f7(c2) = f4(c2))),
% 28.53/18.80 inference(symmetry,[status(thm)],[14190])).
% 28.53/18.80 tff(14192,plain,
% 28.53/18.80 ((~(f7(c2) = c2)) <=> (~(f7(c2) = f4(c2)))),
% 28.53/18.80 inference(monotonicity,[status(thm)],[14191])).
% 28.53/18.80 tff(14193,plain,
% 28.53/18.80 (~(f7(c2) = f4(c2))),
% 28.53/18.80 inference(modus_ponens,[status(thm)],[14161, 14192])).
% 28.53/18.80 tff(14194,plain,
% 28.53/18.80 (c2 = c4),
% 28.53/18.80 inference(modus_ponens,[status(thm)],[14186, 159])).
% 28.53/18.80 tff(14195,plain,
% 28.53/18.80 (f1(c2, c2) = c2),
% 28.53/18.80 inference(unit_resolution,[status(thm)],[9464, 14193, 14176, 14184, 2, 14194])).
% 28.53/18.80 tff(14196,plain,
% 28.53/18.80 (big_f(c2, f1(c2, c2)) <=> big_f(c2, c2)),
% 28.53/18.80 inference(monotonicity,[status(thm)],[14195])).
% 28.53/18.80 tff(14197,plain,
% 28.53/18.80 (big_f(c2, c2) <=> big_f(c2, f1(c2, c2))),
% 28.53/18.80 inference(symmetry,[status(thm)],[14196])).
% 28.53/18.80 tff(14198,plain,
% 28.53/18.80 (big_f(c2, f1(c2, c2))),
% 28.53/18.80 inference(modus_ponens,[status(thm)],[14105, 14197])).
% 28.53/18.80 tff(14199,plain,
% 28.53/18.80 ($false),
% 28.53/18.80 inference(unit_resolution,[status(thm)],[9474, 553, 14194, 14184, 14176, 14195, 14198, 14193])).
% 28.53/18.80 tff(14200,plain,(big_f(c2, c1) | (~(f4(c4) = c2)) | big_f(c1, c1) | (~(f6(c2, f7(f4(c4))) = c1)) | (f7(c1) = c1) | (f10(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 28.53/18.80 tff(14201,plain,
% 28.53/18.80 (big_f(c2, c1)),
% 28.53/18.80 inference(unit_resolution,[status(thm)],[14200, 66, 79, 6634, 115, 3])).
% 28.53/18.80 tff(14202,plain,
% 28.53/18.80 (big_f(f7(c1), c1)),
% 28.53/18.80 inference(modus_ponens,[status(thm)],[14201, 693])).
% 28.53/18.80 tff(14203,plain,
% 28.53/18.80 (big_f(c2, c2)),
% 28.53/18.80 inference(unit_resolution,[status(thm)],[13573, 66, 79, 14201, 14104, 115, 3])).
% 28.53/18.80 tff(14204,plain,
% 28.53/18.80 (big_f(c2, f10(c1))),
% 28.53/18.80 inference(modus_ponens,[status(thm)],[14203, 2719])).
% 28.53/18.80 tff(14205,plain,
% 28.53/18.80 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(c1) = c1) | (f10(c1) = c1) | (c2 = f8(c1)) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)) | (~big_f(c2, f10(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c1) = c1) | (f10(c1) = c1) | (c2 = f8(c1)) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)) | (~big_f(c2, f10(c1))))),
% 28.53/18.80 inference(rewrite,[status(thm)],[])).
% 28.53/18.80 tff(14206,plain,
% 28.53/18.80 (((f10(c1) = c1) | (c2 = f8(c1)) | (~big_f(c2, f10(c1))) | (f7(c1) = c1) | (c1 = f5(c1)) | (~big_f(f7(c1), c1))) <=> ((f7(c1) = c1) | (f10(c1) = c1) | (c2 = f8(c1)) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)) | (~big_f(c2, f10(c1))))),
% 28.53/18.80 inference(rewrite,[status(thm)],[])).
% 28.53/18.80 tff(14207,plain,
% 28.53/18.80 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c1) = c1) | (c2 = f8(c1)) | (~big_f(c2, f10(c1))) | (f7(c1) = c1) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(c1) = c1) | (f10(c1) = c1) | (c2 = f8(c1)) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)) | (~big_f(c2, f10(c1)))))),
% 28.53/18.80 inference(monotonicity,[status(thm)],[14206])).
% 28.53/18.80 tff(14208,plain,
% 28.53/18.80 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c1) = c1) | (c2 = f8(c1)) | (~big_f(c2, f10(c1))) | (f7(c1) = c1) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c1) = c1) | (f10(c1) = c1) | (c2 = f8(c1)) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)) | (~big_f(c2, f10(c1))))),
% 28.53/18.80 inference(transitivity,[status(thm)],[14207, 14205])).
% 28.53/18.80 tff(14209,plain,
% 28.53/18.80 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c1) = c1) | (c2 = f8(c1)) | (~big_f(c2, f10(c1))) | (f7(c1) = c1) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)))),
% 28.53/18.80 inference(quant_inst,[status(thm)],[])).
% 28.53/18.80 tff(14210,plain,
% 28.53/18.80 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c1) = c1) | (f10(c1) = c1) | (c2 = f8(c1)) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)) | (~big_f(c2, f10(c1)))),
% 28.53/18.80 inference(modus_ponens,[status(thm)],[14209, 14208])).
% 28.53/18.80 tff(14211,plain,
% 28.53/18.80 (c2 = f8(c1)),
% 28.53/18.80 inference(unit_resolution,[status(thm)],[14210, 1659, 115, 14204, 3, 14202, 14091])).
% 28.53/18.80 tff(14212,plain,
% 28.53/18.80 (big_f(f7(f7(c2)), f7(c2))),
% 28.53/18.80 inference(modus_ponens,[status(thm)],[13245, 12477])).
% 28.53/18.80 tff(14213,plain,
% 28.53/18.80 (~(c3 = c1)),
% 28.53/18.80 inference(unit_resolution,[status(thm)],[13031, 14212, 1345, 16, 186, 1642, 12485, 27, 66, 17, 348])).
% 28.53/18.80 tff(14214,plain,
% 28.53/18.80 (c3 = c2),
% 28.53/18.80 inference(unit_resolution,[status(thm)],[180, 14213])).
% 28.53/18.80 tff(14215,plain,
% 28.53/18.80 (big_f(c2, f10(c2))),
% 28.53/18.80 inference(modus_ponens,[status(thm)],[13245, 12712])).
% 28.53/18.80 tff(14216,plain,
% 28.53/18.80 (c2 = f8(c2)),
% 28.53/18.80 inference(unit_resolution,[status(thm)],[12505, 1659, 11797, 12485, 14215, 12951, 14212])).
% 28.53/18.80 tff(14217,plain,
% 28.53/18.80 (c2 = c3),
% 28.53/18.80 inference(modus_ponens,[status(thm)],[14214, 78])).
% 28.53/18.80 tff(14218,plain,
% 28.53/18.80 (c2 = c4),
% 28.53/18.80 inference(unit_resolution,[status(thm)],[13256, 17, 14217, 1345, 1642, 12485, 12951, 14212, 16, 348])).
% 28.53/18.80 tff(14219,plain,
% 28.53/18.80 (c4 = c2),
% 28.53/18.80 inference(symmetry,[status(thm)],[14218])).
% 28.53/18.80 tff(14220,plain,
% 28.53/18.80 ((f7(c2) = c4) <=> (f7(c2) = c2)),
% 28.53/18.80 inference(monotonicity,[status(thm)],[14219])).
% 28.53/18.80 tff(14221,plain,
% 28.53/18.80 ((f7(c2) = c2) <=> (f7(c2) = c4)),
% 28.53/18.80 inference(symmetry,[status(thm)],[14220])).
% 28.53/18.80 tff(14222,plain,
% 28.53/18.80 ((f7(c2) = c2) <=> (c1 = c4)),
% 28.53/18.80 inference(transitivity,[status(thm)],[14221, 12587])).
% 28.53/18.80 tff(14223,plain,
% 28.53/18.80 ((~(f7(c2) = c2)) <=> (~(c1 = c4))),
% 28.53/18.80 inference(monotonicity,[status(thm)],[14222])).
% 28.53/18.80 tff(14224,plain,
% 28.53/18.80 (~(c1 = c4)),
% 28.53/18.80 inference(modus_ponens,[status(thm)],[17, 14223])).
% 28.53/18.80 tff(14225,plain,
% 28.53/18.80 (f3(c1, c2) = c2),
% 28.53/18.80 inference(unit_resolution,[status(thm)],[13195, 14224, 1345, 66, 14216, 14214, 348])).
% 28.53/18.80 tff(14226,plain,
% 28.53/18.80 (f3(f7(c2), c2) = c2),
% 28.53/18.80 inference(transitivity,[status(thm)],[13266, 13265, 14225])).
% 28.53/18.80 tff(14227,plain,
% 28.53/18.80 (big_f(f3(f7(c2), c2), f7(c2)) <=> big_f(c2, f7(c2))),
% 28.53/18.80 inference(monotonicity,[status(thm)],[14226])).
% 28.53/18.80 tff(14228,plain,
% 28.53/18.80 (big_f(c2, f7(c2)) <=> big_f(f3(f7(c2), c2), f7(c2))),
% 28.53/18.80 inference(symmetry,[status(thm)],[14227])).
% 28.53/18.80 tff(14229,plain,
% 28.53/18.80 (big_f(f3(f7(c2), c2), f7(c2))),
% 28.53/18.80 inference(modus_ponens,[status(thm)],[13245, 14228])).
% 28.53/18.80 tff(14230,plain,
% 28.53/18.80 (f6(c2, c1) = f6(c2, f7(f4(c4)))),
% 28.53/18.80 inference(monotonicity,[status(thm)],[8115])).
% 28.53/18.80 tff(14231,plain,
% 28.53/18.80 (f6(c2, c1) = f7(f4(c4))),
% 28.53/18.80 inference(transitivity,[status(thm)],[14230, 6634, 125, 81])).
% 28.53/18.80 tff(14232,plain,
% 28.53/18.80 (f6(c2, f6(c2, c1)) = f6(c2, f7(f4(c4)))),
% 28.53/18.80 inference(monotonicity,[status(thm)],[14231])).
% 28.53/18.80 tff(14233,plain,
% 28.53/18.80 (f6(c2, f6(c2, c1)) = f7(f4(c4))),
% 28.53/18.80 inference(transitivity,[status(thm)],[14232, 6634, 125, 81])).
% 28.53/18.80 tff(14234,plain,
% 28.53/18.80 (f6(c2, f6(c2, f6(c2, c1))) = f6(c2, f7(f4(c4)))),
% 28.53/18.80 inference(monotonicity,[status(thm)],[14233])).
% 28.53/18.80 tff(14235,plain,
% 28.53/18.80 (f6(c2, f6(c2, f6(c2, c1))) = c1),
% 28.53/18.80 inference(transitivity,[status(thm)],[14234, 6634])).
% 28.53/18.80 tff(14236,plain,
% 28.53/18.80 (f6(c2, f6(c2, f6(c2, c1))) = f7(f4(c4))),
% 28.53/18.80 inference(transitivity,[status(thm)],[14234, 6634, 125, 81])).
% 28.53/18.80 tff(14237,plain,
% 28.53/18.80 (f3(f6(c2, f6(c2, f6(c2, c1))), c2) = f3(f7(f4(c4)), f4(c4))),
% 28.53/18.80 inference(monotonicity,[status(thm)],[14236, 436])).
% 28.53/18.80 tff(14238,plain,
% 28.53/18.80 (f3(f6(c2, f6(c2, f6(c2, c1))), c2) = f3(c1, c2)),
% 28.53/18.80 inference(transitivity,[status(thm)],[14237, 13265])).
% 28.53/18.80 tff(14239,plain,
% 28.53/18.80 (big_f(f3(f6(c2, f6(c2, f6(c2, c1))), c2), f6(c2, f6(c2, f6(c2, c1)))) <=> big_f(f3(c1, c2), c1)),
% 28.53/18.80 inference(monotonicity,[status(thm)],[14238, 14235])).
% 28.53/18.80 tff(14240,plain,
% 28.53/18.80 (big_f(f3(c1, c2), c1) <=> big_f(f3(f6(c2, f6(c2, f6(c2, c1))), c2), f6(c2, f6(c2, f6(c2, c1))))),
% 28.53/18.80 inference(symmetry,[status(thm)],[14239])).
% 28.53/18.80 tff(14241,plain,
% 28.53/18.80 (big_f(f3(c1, c2), c1) <=> big_f(c2, f7(c2))),
% 28.53/18.80 inference(monotonicity,[status(thm)],[14225, 125])).
% 28.53/18.80 tff(14242,plain,
% 28.53/18.80 (big_f(c2, f7(c2)) <=> big_f(f3(c1, c2), c1)),
% 28.53/18.80 inference(symmetry,[status(thm)],[14241])).
% 28.53/18.80 tff(14243,plain,
% 28.53/18.80 (big_f(c2, f7(c2)) <=> big_f(f3(f6(c2, f6(c2, f6(c2, c1))), c2), f6(c2, f6(c2, f6(c2, c1))))),
% 28.53/18.80 inference(transitivity,[status(thm)],[14242, 14240])).
% 28.53/18.80 tff(14244,plain,
% 28.53/18.80 (big_f(f3(f6(c2, f6(c2, f6(c2, c1))), c2), f6(c2, f6(c2, f6(c2, c1))))),
% 28.53/18.80 inference(modus_ponens,[status(thm)],[13245, 14243])).
% 28.53/18.80 tff(14245,plain,
% 28.53/18.80 (f6(c2, f6(c2, f6(c2, c1))) = f7(c2)),
% 28.53/18.80 inference(transitivity,[status(thm)],[14234, 6634, 125])).
% 28.53/18.80 tff(14246,plain,
% 28.53/18.80 ((f6(c2, f6(c2, f6(c2, c1))) = c4) <=> (f7(c2) = c4)),
% 28.53/18.80 inference(monotonicity,[status(thm)],[14245])).
% 28.53/18.80 tff(14247,plain,
% 28.53/18.80 ((f7(c2) = c4) <=> (f6(c2, f6(c2, f6(c2, c1))) = c4)),
% 28.53/18.80 inference(symmetry,[status(thm)],[14246])).
% 28.53/18.80 tff(14248,plain,
% 28.53/18.80 ((f7(c2) = c2) <=> (f6(c2, f6(c2, f6(c2, c1))) = c4)),
% 28.53/18.80 inference(transitivity,[status(thm)],[14221, 14247])).
% 28.53/18.80 tff(14249,plain,
% 28.53/18.80 ((~(f7(c2) = c2)) <=> (~(f6(c2, f6(c2, f6(c2, c1))) = c4))),
% 28.53/18.80 inference(monotonicity,[status(thm)],[14248])).
% 28.53/18.80 tff(14250,plain,
% 28.53/18.80 (~(f6(c2, f6(c2, f6(c2, c1))) = c4)),
% 28.53/18.80 inference(modus_ponens,[status(thm)],[17, 14249])).
% 28.53/18.80 tff(14251,plain,
% 28.53/18.80 ((f3(f6(c2, f6(c2, f6(c2, c1))), c2) = c2) <=> (f3(c1, c2) = c2)),
% 28.53/18.80 inference(monotonicity,[status(thm)],[14238])).
% 28.53/18.80 tff(14252,plain,
% 28.53/18.80 ((f3(c1, c2) = c2) <=> (f3(f6(c2, f6(c2, f6(c2, c1))), c2) = c2)),
% 28.53/18.80 inference(symmetry,[status(thm)],[14251])).
% 28.53/18.80 tff(14253,plain,
% 28.53/18.80 (f3(f6(c2, f6(c2, f6(c2, c1))), c2) = c2),
% 28.53/18.80 inference(modus_ponens,[status(thm)],[14225, 14252])).
% 28.53/18.80 tff(14254,plain,
% 28.53/18.80 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c1 = f2(c2)) | (~big_f(c2, c1)) | (~(f3(f6(c2, f6(c2, f6(c2, c1))), c2) = c2)) | (f6(c2, f6(c2, f6(c2, c1))) = c4) | (~big_f(f3(f6(c2, f6(c2, f6(c2, c1))), c2), f6(c2, f6(c2, f6(c2, c1))))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c1 = f2(c2)) | (~big_f(c2, c1)) | (~(f3(f6(c2, f6(c2, f6(c2, c1))), c2) = c2)) | (f6(c2, f6(c2, f6(c2, c1))) = c4) | (~big_f(f3(f6(c2, f6(c2, f6(c2, c1))), c2), f6(c2, f6(c2, f6(c2, c1))))))),
% 28.53/18.80 inference(rewrite,[status(thm)],[])).
% 28.53/18.80 tff(14255,plain,
% 28.53/18.80 (((~(c2 = c3)) | (f6(c2, f6(c2, f6(c2, c1))) = c4) | (~(f3(f6(c2, f6(c2, f6(c2, c1))), c2) = c2)) | (~big_f(f3(f6(c2, f6(c2, f6(c2, c1))), c2), f6(c2, f6(c2, f6(c2, c1))))) | (c1 = f2(c2)) | (~big_f(c2, c1))) <=> ((~(c2 = c3)) | (c1 = f2(c2)) | (~big_f(c2, c1)) | (~(f3(f6(c2, f6(c2, f6(c2, c1))), c2) = c2)) | (f6(c2, f6(c2, f6(c2, c1))) = c4) | (~big_f(f3(f6(c2, f6(c2, f6(c2, c1))), c2), f6(c2, f6(c2, f6(c2, c1))))))),
% 28.53/18.80 inference(rewrite,[status(thm)],[])).
% 28.53/18.80 tff(14256,plain,
% 28.53/18.80 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f6(c2, f6(c2, f6(c2, c1))) = c4) | (~(f3(f6(c2, f6(c2, f6(c2, c1))), c2) = c2)) | (~big_f(f3(f6(c2, f6(c2, f6(c2, c1))), c2), f6(c2, f6(c2, f6(c2, c1))))) | (c1 = f2(c2)) | (~big_f(c2, c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c1 = f2(c2)) | (~big_f(c2, c1)) | (~(f3(f6(c2, f6(c2, f6(c2, c1))), c2) = c2)) | (f6(c2, f6(c2, f6(c2, c1))) = c4) | (~big_f(f3(f6(c2, f6(c2, f6(c2, c1))), c2), f6(c2, f6(c2, f6(c2, c1)))))))),
% 28.53/18.80 inference(monotonicity,[status(thm)],[14255])).
% 28.53/18.80 tff(14257,plain,
% 28.53/18.80 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f6(c2, f6(c2, f6(c2, c1))) = c4) | (~(f3(f6(c2, f6(c2, f6(c2, c1))), c2) = c2)) | (~big_f(f3(f6(c2, f6(c2, f6(c2, c1))), c2), f6(c2, f6(c2, f6(c2, c1))))) | (c1 = f2(c2)) | (~big_f(c2, c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c1 = f2(c2)) | (~big_f(c2, c1)) | (~(f3(f6(c2, f6(c2, f6(c2, c1))), c2) = c2)) | (f6(c2, f6(c2, f6(c2, c1))) = c4) | (~big_f(f3(f6(c2, f6(c2, f6(c2, c1))), c2), f6(c2, f6(c2, f6(c2, c1))))))),
% 28.53/18.80 inference(transitivity,[status(thm)],[14256, 14254])).
% 28.53/18.80 tff(14258,plain,
% 28.53/18.80 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f6(c2, f6(c2, f6(c2, c1))) = c4) | (~(f3(f6(c2, f6(c2, f6(c2, c1))), c2) = c2)) | (~big_f(f3(f6(c2, f6(c2, f6(c2, c1))), c2), f6(c2, f6(c2, f6(c2, c1))))) | (c1 = f2(c2)) | (~big_f(c2, c1)))),
% 28.53/18.80 inference(quant_inst,[status(thm)],[])).
% 28.53/18.80 tff(14259,plain,
% 28.53/18.80 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c1 = f2(c2)) | (~big_f(c2, c1)) | (~(f3(f6(c2, f6(c2, f6(c2, c1))), c2) = c2)) | (f6(c2, f6(c2, f6(c2, c1))) = c4) | (~big_f(f3(f6(c2, f6(c2, f6(c2, c1))), c2), f6(c2, f6(c2, f6(c2, c1)))))),
% 28.53/18.80 inference(modus_ponens,[status(thm)],[14258, 14257])).
% 28.53/18.80 tff(14260,plain,
% 28.53/18.80 ((~(c2 = c3)) | (c1 = f2(c2)) | (~big_f(c2, c1)) | (~(f3(f6(c2, f6(c2, f6(c2, c1))), c2) = c2)) | (f6(c2, f6(c2, f6(c2, c1))) = c4) | (~big_f(f3(f6(c2, f6(c2, f6(c2, c1))), c2), f6(c2, f6(c2, f6(c2, c1)))))),
% 28.53/18.80 inference(unit_resolution,[status(thm)],[14259, 7051])).
% 28.53/18.80 tff(14261,plain,
% 28.53/18.80 (c1 = f2(c2)),
% 28.53/18.80 inference(unit_resolution,[status(thm)],[14260, 14253, 14217, 348, 14250, 14244])).
% 28.53/18.80 tff(14262,plain,
% 28.53/18.80 (f2(c2) = c1),
% 28.53/18.80 inference(symmetry,[status(thm)],[14261])).
% 28.53/18.80 tff(14263,plain,
% 28.53/18.80 (f2(c2) = f7(c2)),
% 28.53/18.80 inference(transitivity,[status(thm)],[14262, 125])).
% 28.53/18.80 tff(14264,plain,
% 28.53/18.80 ((c2 = f2(c2)) <=> (c2 = f7(c2))),
% 28.53/18.80 inference(monotonicity,[status(thm)],[14263])).
% 28.53/18.80 tff(14265,plain,
% 28.53/18.80 ((c2 = f2(c2)) <=> (f7(c2) = c2)),
% 28.53/18.80 inference(transitivity,[status(thm)],[14264, 8409])).
% 28.53/18.80 tff(14266,plain,
% 28.53/18.80 ((f7(c2) = c2) <=> (c2 = f2(c2))),
% 28.53/18.80 inference(symmetry,[status(thm)],[14265])).
% 28.53/18.80 tff(14267,plain,
% 28.53/18.80 ((~(f7(c2) = c2)) <=> (~(c2 = f2(c2)))),
% 28.53/18.80 inference(monotonicity,[status(thm)],[14266])).
% 28.53/18.80 tff(14268,plain,
% 28.53/18.80 (~(c2 = f2(c2))),
% 28.53/18.80 inference(modus_ponens,[status(thm)],[17, 14267])).
% 28.53/18.80 tff(14269,plain,
% 28.53/18.80 ((~(f7(c2) = c2)) <=> (~(f7(c2) = c4))),
% 28.53/18.80 inference(monotonicity,[status(thm)],[14221])).
% 28.53/18.80 tff(14270,plain,
% 28.53/18.80 (~(f7(c2) = c4)),
% 28.53/18.80 inference(modus_ponens,[status(thm)],[17, 14269])).
% 28.53/18.80 tff(14271,plain,
% 28.53/18.80 ((c2 = f2(c2)) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2)))),
% 28.53/18.80 inference(unit_resolution,[status(thm)],[13279, 7051, 1345, 14217, 14270])).
% 28.53/18.80 tff(14272,plain,
% 28.53/18.80 ($false),
% 28.53/18.80 inference(unit_resolution,[status(thm)],[14271, 14268, 14226, 14229])).
% 28.53/18.80 tff(14273,plain,((f7(c2) = c2) | (~big_f(c2, c2)) | (~(f4(c4) = c2)) | (~big_f(c2, c1)) | (~(f6(c2, f7(f4(c4))) = c1)) | big_f(c1, c1) | (~(c2 = f8(c1))) | (~(f10(c1) = c2)) | (~(f5(c1) = c2)) | big_f(c1, c2) | (~(f7(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.53/18.80 tff(14274,plain,
% 28.53/18.80 (f7(c2) = c2),
% 28.53/18.80 inference(unit_resolution,[status(thm)],[14273, 27, 79, 348, 6634, 66, 1642, 16, 186, 1345, 120])).
% 28.53/18.80 tff(14275,plain,
% 28.53/18.80 (c2 = f7(c2)),
% 28.53/18.80 inference(symmetry,[status(thm)],[14274])).
% 28.53/18.80 tff(14276,plain,
% 28.53/18.80 (c2 = f7(f4(c4))),
% 28.53/18.80 inference(transitivity,[status(thm)],[14275, 81])).
% 28.53/18.80 tff(14277,plain,
% 28.53/18.80 (f6(c2, c2) = f6(c2, f7(f4(c4)))),
% 28.53/18.80 inference(monotonicity,[status(thm)],[14276])).
% 28.53/18.80 tff(14278,plain,
% 28.53/18.80 (f6(f7(c2), f5(c1)) = f6(c2, c2)),
% 28.53/18.80 inference(monotonicity,[status(thm)],[14274, 186])).
% 28.53/18.80 tff(14279,plain,
% 28.53/18.80 (f6(f7(c2), f5(c1)) = c1),
% 28.53/18.80 inference(transitivity,[status(thm)],[14278, 14277, 6634])).
% 28.53/18.80 tff(14280,plain,
% 28.53/18.80 (f3(f6(f7(c2), f5(c1)), c2) = f3(c1, c2)),
% 28.53/18.80 inference(monotonicity,[status(thm)],[14279])).
% 28.53/18.80 tff(14281,plain,
% 28.53/18.80 ((f3(f6(f7(c2), f5(c1)), c2) = c2) <=> (f3(c1, c2) = c2)),
% 28.53/18.80 inference(monotonicity,[status(thm)],[14280])).
% 28.53/18.80 tff(14282,plain,
% 28.53/18.80 ((f3(c1, c2) = c2) <=> (f3(f6(f7(c2), f5(c1)), c2) = c2)),
% 28.53/18.80 inference(symmetry,[status(thm)],[14281])).
% 28.53/18.80 tff(14283,plain,
% 28.53/18.80 (f6(c2, c2) = f6(f7(c2), f5(c1))),
% 28.53/18.80 inference(symmetry,[status(thm)],[14278])).
% 28.53/18.80 tff(14284,plain,
% 28.53/18.80 (f6(c2, f7(f4(c4))) = f6(c2, c2)),
% 28.53/18.80 inference(symmetry,[status(thm)],[14277])).
% 28.53/18.80 tff(14285,plain,
% 28.53/18.80 (c1 = f6(f7(c2), f5(c1))),
% 28.53/18.80 inference(transitivity,[status(thm)],[14103, 14284, 14283])).
% 28.53/18.80 tff(14286,plain,
% 28.53/18.80 ((c1 = c4) <=> (f6(f7(c2), f5(c1)) = c4)),
% 28.53/18.80 inference(monotonicity,[status(thm)],[14285])).
% 28.53/18.80 tff(14287,plain,
% 28.53/18.80 ((f6(f7(c2), f5(c1)) = c4) <=> (c1 = c4)),
% 28.53/18.80 inference(symmetry,[status(thm)],[14286])).
% 28.53/18.80 tff(14288,plain,
% 28.53/18.80 (f7(f4(c4)) = c2),
% 28.53/18.80 inference(transitivity,[status(thm)],[80, 14274])).
% 28.53/18.80 tff(14289,plain,
% 28.53/18.80 (f6(c2, f7(f4(c4))) = f6(c2, c2)),
% 28.53/18.80 inference(monotonicity,[status(thm)],[14288])).
% 28.53/18.80 tff(14290,plain,
% 28.53/18.80 (f6(c2, c2) = f6(c2, f7(f4(c4)))),
% 28.53/18.80 inference(symmetry,[status(thm)],[14289])).
% 28.53/18.80 tff(14291,plain,
% 28.53/18.80 (f6(c2, c2) = c1),
% 28.53/18.80 inference(transitivity,[status(thm)],[14290, 6634])).
% 28.53/18.80 tff(14292,plain,
% 28.53/18.80 (f7(f6(c2, c2)) = f7(c1)),
% 28.53/18.80 inference(monotonicity,[status(thm)],[14291])).
% 28.53/18.80 tff(14293,plain,
% 28.53/18.80 (f7(f6(c2, c2)) = f7(c2)),
% 28.53/18.80 inference(transitivity,[status(thm)],[14292, 120, 14275])).
% 28.53/18.80 tff(14294,plain,
% 28.53/18.80 (big_f(f7(f6(c2, c2)), f6(c2, c2)) <=> big_f(f7(c2), f6(c2, c2))),
% 28.53/18.80 inference(monotonicity,[status(thm)],[14293])).
% 28.53/18.80 tff(14295,plain,
% 28.53/18.80 (big_f(f7(c2), f6(c2, c2)) <=> big_f(f7(f6(c2, c2)), f6(c2, c2))),
% 28.53/18.80 inference(symmetry,[status(thm)],[14294])).
% 28.53/18.80 tff(14296,plain,
% 28.53/18.80 (big_f(f7(c2), f6(c2, c2)) <=> big_f(c2, c1)),
% 28.53/18.80 inference(monotonicity,[status(thm)],[14274, 14291])).
% 28.53/18.80 tff(14297,plain,
% 28.53/18.80 (big_f(c2, c1) <=> big_f(f7(c2), f6(c2, c2))),
% 28.53/18.80 inference(symmetry,[status(thm)],[14296])).
% 28.53/18.80 tff(14298,plain,
% 28.53/18.80 (big_f(f7(c2), f6(c2, c2))),
% 28.53/18.80 inference(modus_ponens,[status(thm)],[348, 14297])).
% 28.53/18.80 tff(14299,plain,
% 28.53/18.80 (big_f(f7(f6(c2, c2)), f6(c2, c2))),
% 28.53/18.80 inference(modus_ponens,[status(thm)],[14298, 14295])).
% 28.53/18.80 tff(14300,plain,
% 28.53/18.80 (f10(f6(c2, c2)) = f10(c1)),
% 28.53/18.80 inference(monotonicity,[status(thm)],[14093])).
% 28.53/18.80 tff(14301,plain,
% 28.53/18.80 (f10(f6(c2, c2)) = c2),
% 28.53/18.80 inference(transitivity,[status(thm)],[14300, 16])).
% 28.53/18.80 tff(14302,plain,
% 28.53/18.80 (big_f(f3(c2, c2), f10(f6(c2, c2))) <=> big_f(f3(c2, c2), c2)),
% 28.53/18.80 inference(monotonicity,[status(thm)],[14301])).
% 28.53/18.80 tff(14303,plain,
% 28.53/18.80 (big_f(f3(c2, c2), c2) <=> big_f(f3(c2, c2), f10(f6(c2, c2)))),
% 28.53/18.80 inference(symmetry,[status(thm)],[14302])).
% 28.53/18.80 tff(14304,plain,
% 28.53/18.80 (f3(c2, c2) = c2),
% 28.53/18.80 inference(unit_resolution,[status(thm)],[12903, 12882, 873, 27, 172, 66])).
% 28.53/18.80 tff(14305,plain,
% 28.53/18.80 (big_f(f3(c2, c2), c2) <=> big_f(c2, c2)),
% 28.53/18.80 inference(monotonicity,[status(thm)],[14304])).
% 28.53/18.80 tff(14306,plain,
% 28.53/18.80 (big_f(c2, c2) <=> big_f(f3(c2, c2), c2)),
% 28.53/18.80 inference(symmetry,[status(thm)],[14305])).
% 28.53/18.80 tff(14307,plain,
% 28.53/18.80 (big_f(f3(c2, c2), c2)),
% 28.53/18.80 inference(modus_ponens,[status(thm)],[1345, 14306])).
% 28.53/18.80 tff(14308,plain,
% 28.53/18.80 ($false),
% 28.53/18.80 inference(unit_resolution,[status(thm)],[12882, 14307])).
% 28.53/18.80 tff(14309,plain,(big_f(f3(c2, c2), c2) | (~big_f(c2, c2)) | (c2 = c4) | big_f(c1, c2) | (~(c3 = c1)) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 28.53/18.80 tff(14310,plain,
% 28.53/18.80 (big_f(f3(c2, c2), c2)),
% 28.53/18.80 inference(unit_resolution,[status(thm)],[14309, 172, 873, 27, 1345, 66])).
% 28.53/18.80 tff(14311,plain,
% 28.53/18.80 (big_f(f3(c2, c2), f10(f6(c2, c2)))),
% 28.53/18.80 inference(modus_ponens,[status(thm)],[14310, 14303])).
% 28.53/18.80 tff(14312,plain,
% 28.53/18.80 ((f10(f6(c2, c2)) = f6(c2, c2)) <=> (c2 = f6(c2, c2))),
% 28.53/18.80 inference(monotonicity,[status(thm)],[14301])).
% 28.53/18.80 tff(14313,plain,
% 28.53/18.80 ((f10(f6(c2, c2)) = f6(c2, c2)) <=> (f6(c2, c2) = c2)),
% 28.53/18.80 inference(transitivity,[status(thm)],[14312, 3242])).
% 28.53/18.80 tff(14314,plain,
% 28.53/18.80 ((f6(c2, c2) = c2) <=> (f10(f6(c2, c2)) = f6(c2, c2))),
% 28.53/18.80 inference(symmetry,[status(thm)],[14313])).
% 28.53/18.80 tff(14315,plain,
% 28.53/18.80 ((~(f6(c2, c2) = c2)) <=> (~(f10(f6(c2, c2)) = f6(c2, c2)))),
% 28.53/18.80 inference(monotonicity,[status(thm)],[14314])).
% 28.53/18.80 tff(14316,plain,
% 28.53/18.80 (~(f10(f6(c2, c2)) = f6(c2, c2))),
% 28.53/18.80 inference(modus_ponens,[status(thm)],[14102, 14315])).
% 28.53/18.80 tff(14317,plain,
% 28.53/18.80 (f8(f6(c2, c2)) = f8(c1)),
% 28.53/18.80 inference(monotonicity,[status(thm)],[14093])).
% 28.53/18.80 tff(14318,plain,
% 28.53/18.80 (f8(f6(c2, c2)) = c2),
% 28.53/18.80 inference(transitivity,[status(thm)],[14317, 1643])).
% 28.53/18.80 tff(14319,plain,
% 28.53/18.80 ((f3(c2, c2) = f8(f6(c2, c2))) <=> (f3(c2, c2) = c2)),
% 28.53/18.80 inference(monotonicity,[status(thm)],[14318])).
% 28.53/18.80 tff(14320,plain,
% 28.53/18.80 ((f3(c2, c2) = c2) <=> (f3(c2, c2) = f8(f6(c2, c2)))),
% 28.53/18.80 inference(symmetry,[status(thm)],[14319])).
% 28.53/18.80 tff(14321,plain,
% 28.53/18.80 ((~(f3(c2, c2) = c2)) <=> (~(f3(c2, c2) = f8(f6(c2, c2))))),
% 28.53/18.80 inference(monotonicity,[status(thm)],[14320])).
% 28.53/18.80 tff(14322,plain,
% 28.53/18.80 (f2(f6(c2, c2)) = f2(c1)),
% 28.53/18.80 inference(monotonicity,[status(thm)],[14093])).
% 28.53/18.80 tff(14323,plain,
% 28.53/18.80 ((f6(c2, c2) = f2(f6(c2, c2))) <=> (c1 = f2(c1))),
% 28.53/18.80 inference(monotonicity,[status(thm)],[14093, 14322])).
% 28.53/18.80 tff(14324,plain,
% 28.53/18.80 ((c1 = f2(c1)) <=> (f6(c2, c2) = f2(f6(c2, c2)))),
% 28.53/18.80 inference(symmetry,[status(thm)],[14323])).
% 28.53/18.81 tff(14325,plain,
% 28.53/18.81 ((~(c2 = c4)) <=> (~(f7(c1) = c4))),
% 28.53/18.81 inference(monotonicity,[status(thm)],[2812])).
% 28.53/18.81 tff(14326,plain,
% 28.53/18.81 (~(f7(c1) = c4)),
% 28.53/18.81 inference(modus_ponens,[status(thm)],[873, 14325])).
% 28.53/18.81 tff(14327,plain,
% 28.53/18.81 (f2(c1) = c2),
% 28.53/18.81 inference(transitivity,[status(thm)],[5586, 1319])).
% 28.53/18.81 tff(14328,plain,
% 28.53/18.81 (big_f(c1, f2(c1)) <=> big_f(c1, c2)),
% 28.53/18.81 inference(monotonicity,[status(thm)],[14327])).
% 28.53/18.81 tff(14329,plain,
% 28.53/18.81 (big_f(c1, c2) <=> big_f(c1, f2(c1))),
% 28.53/18.81 inference(symmetry,[status(thm)],[14328])).
% 28.53/18.81 tff(14330,plain,
% 28.53/18.81 ((~big_f(c1, c2)) <=> (~big_f(c1, f2(c1)))),
% 28.53/18.81 inference(monotonicity,[status(thm)],[14329])).
% 28.53/18.81 tff(14331,plain,
% 28.53/18.81 (~big_f(c1, f2(c1))),
% 28.53/18.81 inference(modus_ponens,[status(thm)],[27, 14330])).
% 28.53/18.81 tff(14332,plain,
% 28.53/18.81 ((f7(c1) = f5(c1)) <=> (c2 = f5(c1))),
% 28.53/18.81 inference(monotonicity,[status(thm)],[120])).
% 28.53/18.81 tff(14333,plain,
% 28.53/18.81 ((c2 = f5(c1)) <=> (f7(c1) = f5(c1))),
% 28.53/18.81 inference(symmetry,[status(thm)],[14332])).
% 28.53/18.81 tff(14334,plain,
% 28.53/18.81 ((f5(c1) = c2) <=> (f7(c1) = f5(c1))),
% 28.53/18.81 inference(transitivity,[status(thm)],[155, 14333])).
% 28.53/18.81 tff(14335,plain,
% 28.53/18.81 (f7(c1) = f5(c1)),
% 28.53/18.81 inference(modus_ponens,[status(thm)],[186, 14334])).
% 28.53/18.81 tff(14336,plain,
% 28.53/18.81 ((c1 = f7(c1)) <=> (f7(c1) = c1)),
% 28.53/18.81 inference(commutativity,[status(thm)],[])).
% 28.53/18.81 tff(14337,assumption,(f3(f5(c1), f5(c1)) = c1), introduced(assumption)).
% 28.53/18.81 tff(14338,assumption,(f7(c1) = f5(c1)), introduced(assumption)).
% 28.53/18.81 tff(14339,plain,
% 28.53/18.81 (c2 = f5(c1)),
% 28.53/18.81 inference(transitivity,[status(thm)],[2778, 14338])).
% 28.53/18.81 tff(14340,plain,
% 28.53/18.81 (f10(c3) = f5(c1)),
% 28.53/18.81 inference(transitivity,[status(thm)],[13006, 16, 2778, 14338])).
% 28.53/18.81 tff(14341,plain,
% 28.53/18.81 (f3(f10(c3), c2) = f3(f5(c1), f5(c1))),
% 28.53/18.81 inference(monotonicity,[status(thm)],[14340, 14339])).
% 28.53/18.81 tff(14342,plain,
% 28.53/18.81 (f7(c1) = f10(c3)),
% 28.53/18.81 inference(transitivity,[status(thm)],[120, 293, 13009])).
% 28.53/18.81 tff(14343,plain,
% 28.53/18.81 (f3(f7(c1), f7(c1)) = f3(f10(c3), c2)),
% 28.53/18.81 inference(monotonicity,[status(thm)],[14342, 120])).
% 28.53/18.81 tff(14344,plain,
% 28.53/18.81 (f3(f7(c1), f7(c1)) = c1),
% 28.53/18.81 inference(transitivity,[status(thm)],[14343, 14341, 14337])).
% 28.53/18.81 tff(14345,plain,
% 28.53/18.81 ((f3(f7(c1), f7(c1)) = f7(c1)) <=> (c1 = f7(c1))),
% 28.53/18.81 inference(monotonicity,[status(thm)],[14344])).
% 28.53/18.81 tff(14346,plain,
% 28.53/18.81 ((f3(f7(c1), f7(c1)) = f7(c1)) <=> (f7(c1) = c1)),
% 28.53/18.81 inference(transitivity,[status(thm)],[14345, 14336])).
% 28.53/18.81 tff(14347,plain,
% 28.53/18.81 ((f7(c1) = c1) <=> (f3(f7(c1), f7(c1)) = f7(c1))),
% 28.53/18.81 inference(symmetry,[status(thm)],[14346])).
% 28.53/18.81 tff(14348,plain,
% 28.53/18.81 ((~(f7(c1) = c1)) <=> (~(f3(f7(c1), f7(c1)) = f7(c1)))),
% 28.53/18.81 inference(monotonicity,[status(thm)],[14347])).
% 28.53/18.81 tff(14349,plain,
% 28.53/18.81 (~(f3(f7(c1), f7(c1)) = f7(c1))),
% 28.53/18.81 inference(modus_ponens,[status(thm)],[115, 14348])).
% 28.53/18.81 tff(14350,plain,
% 28.53/18.81 (f7(c1) = f2(c3)),
% 28.53/18.81 inference(transitivity,[status(thm)],[120, 13016])).
% 28.53/18.81 tff(14351,plain,
% 28.53/18.81 (f3(f7(c1), f7(c1)) = c3),
% 28.53/18.81 inference(transitivity,[status(thm)],[14343, 14341, 14337, 5585])).
% 28.53/18.81 tff(14352,plain,
% 28.53/18.81 (big_f(f3(f7(c1), f7(c1)), f7(c1)) <=> big_f(c3, f2(c3))),
% 28.53/18.81 inference(monotonicity,[status(thm)],[14351, 14350])).
% 28.53/18.81 tff(14353,plain,
% 28.53/18.81 (big_f(c3, f2(c3)) <=> big_f(f3(f7(c1), f7(c1)), f7(c1))),
% 28.53/18.81 inference(symmetry,[status(thm)],[14352])).
% 28.53/18.81 tff(14354,plain,
% 28.53/18.81 ((~big_f(c3, f2(c3))) <=> (~big_f(f3(f7(c1), f7(c1)), f7(c1)))),
% 28.53/18.81 inference(monotonicity,[status(thm)],[14353])).
% 28.53/18.81 tff(14355,plain,
% 28.53/18.81 (~big_f(f3(f7(c1), f7(c1)), f7(c1))),
% 28.53/18.81 inference(modus_ponens,[status(thm)],[1286, 14354])).
% 28.53/18.81 tff(14356,plain,
% 28.53/18.81 (big_f(c1, f7(c1)) <=> big_f(c3, f2(c3))),
% 28.53/18.81 inference(monotonicity,[status(thm)],[5585, 14350])).
% 28.53/18.81 tff(14357,plain,
% 28.53/18.81 (big_f(c3, f2(c3)) <=> big_f(c1, f7(c1))),
% 28.53/18.81 inference(symmetry,[status(thm)],[14356])).
% 28.53/18.81 tff(14358,plain,
% 28.53/18.81 ((~big_f(c3, f2(c3))) <=> (~big_f(c1, f7(c1)))),
% 28.53/18.81 inference(monotonicity,[status(thm)],[14357])).
% 28.53/18.81 tff(14359,plain,
% 28.53/18.81 (~big_f(c1, f7(c1))),
% 28.53/18.81 inference(modus_ponens,[status(thm)],[1286, 14358])).
% 28.53/18.81 tff(14360,plain,
% 28.53/18.81 (f7(c1) = f2(c1)),
% 28.53/18.81 inference(transitivity,[status(thm)],[120, 13016, 5589])).
% 28.53/18.81 tff(14361,plain,
% 28.53/18.81 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c1 = c3)) | (f7(c1) = c4) | (~(f7(c1) = f2(c1))) | big_f(c1, f7(c1)) | (f3(f7(c1), f7(c1)) = f7(c1)) | big_f(f3(f7(c1), f7(c1)), f7(c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (~(c1 = c3)) | (f7(c1) = c4) | (~(f7(c1) = f2(c1))) | big_f(c1, f7(c1)) | (f3(f7(c1), f7(c1)) = f7(c1)) | big_f(f3(f7(c1), f7(c1)), f7(c1)))),
% 28.53/18.81 inference(rewrite,[status(thm)],[])).
% 28.53/18.81 tff(14362,plain,
% 28.53/18.81 (((~(c1 = c3)) | (~(f7(c1) = f2(c1))) | (f7(c1) = c4) | (f3(f7(c1), f7(c1)) = f7(c1)) | big_f(f3(f7(c1), f7(c1)), f7(c1)) | big_f(c1, f7(c1))) <=> ((~(c1 = c3)) | (f7(c1) = c4) | (~(f7(c1) = f2(c1))) | big_f(c1, f7(c1)) | (f3(f7(c1), f7(c1)) = f7(c1)) | big_f(f3(f7(c1), f7(c1)), f7(c1)))),
% 28.53/18.81 inference(rewrite,[status(thm)],[])).
% 28.53/18.81 tff(14363,plain,
% 28.53/18.81 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(f7(c1) = f2(c1))) | (f7(c1) = c4) | (f3(f7(c1), f7(c1)) = f7(c1)) | big_f(f3(f7(c1), f7(c1)), f7(c1)) | big_f(c1, f7(c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c1 = c3)) | (f7(c1) = c4) | (~(f7(c1) = f2(c1))) | big_f(c1, f7(c1)) | (f3(f7(c1), f7(c1)) = f7(c1)) | big_f(f3(f7(c1), f7(c1)), f7(c1))))),
% 28.62/18.81 inference(monotonicity,[status(thm)],[14362])).
% 28.62/18.81 tff(14364,plain,
% 28.62/18.81 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(f7(c1) = f2(c1))) | (f7(c1) = c4) | (f3(f7(c1), f7(c1)) = f7(c1)) | big_f(f3(f7(c1), f7(c1)), f7(c1)) | big_f(c1, f7(c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (~(c1 = c3)) | (f7(c1) = c4) | (~(f7(c1) = f2(c1))) | big_f(c1, f7(c1)) | (f3(f7(c1), f7(c1)) = f7(c1)) | big_f(f3(f7(c1), f7(c1)), f7(c1)))),
% 28.62/18.81 inference(transitivity,[status(thm)],[14363, 14361])).
% 28.62/18.81 tff(14365,plain,
% 28.62/18.81 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(f7(c1) = f2(c1))) | (f7(c1) = c4) | (f3(f7(c1), f7(c1)) = f7(c1)) | big_f(f3(f7(c1), f7(c1)), f7(c1)) | big_f(c1, f7(c1)))),
% 28.62/18.81 inference(quant_inst,[status(thm)],[])).
% 28.62/18.81 tff(14366,plain,
% 28.62/18.81 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (~(c1 = c3)) | (f7(c1) = c4) | (~(f7(c1) = f2(c1))) | big_f(c1, f7(c1)) | (f3(f7(c1), f7(c1)) = f7(c1)) | big_f(f3(f7(c1), f7(c1)), f7(c1))),
% 28.62/18.81 inference(modus_ponens,[status(thm)],[14365, 14364])).
% 28.62/18.81 tff(14367,plain,
% 28.62/18.81 ((f3(f7(c1), f7(c1)) = f7(c1)) | big_f(f3(f7(c1), f7(c1)), f7(c1))),
% 28.62/18.81 inference(unit_resolution,[status(thm)],[14366, 1459, 5611, 1000, 14360, 14359])).
% 28.62/18.81 tff(14368,plain,
% 28.62/18.81 ($false),
% 28.62/18.81 inference(unit_resolution,[status(thm)],[14367, 14355, 14349])).
% 28.62/18.81 tff(14369,plain,((~(f3(f5(c1), f5(c1)) = c1)) | (f7(c1) = c4) | big_f(c3, f2(c3)) | (~(f2(c3) = c2)) | (~(c3 = c1)) | (~(f7(c1) = f5(c1))) | (~(f10(c1) = c2)) | (f7(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 28.62/18.81 tff(14370,plain,
% 28.62/18.81 (~(f3(f5(c1), f5(c1)) = c1)),
% 28.62/18.81 inference(unit_resolution,[status(thm)],[14369, 14335, 1286, 1319, 172, 1000, 16, 115])).
% 28.62/18.81 tff(14371,plain,
% 28.62/18.81 (f3(f5(c1), f5(c1)) = c2),
% 28.62/18.81 inference(unit_resolution,[status(thm)],[7625, 14370])).
% 28.62/18.81 tff(14372,plain,
% 28.62/18.81 (f3(f7(c1), f7(c1)) = c2),
% 28.62/18.81 inference(transitivity,[status(thm)],[14343, 13008, 14371])).
% 28.62/18.81 tff(14373,plain,
% 28.62/18.81 (big_f(f3(f7(c1), f7(c1)), f7(c1)) <=> big_f(c2, c2)),
% 28.62/18.81 inference(monotonicity,[status(thm)],[14372, 120])).
% 28.62/18.81 tff(14374,plain,
% 28.62/18.81 (big_f(c2, c2) <=> big_f(f3(f7(c1), f7(c1)), f7(c1))),
% 28.62/18.81 inference(symmetry,[status(thm)],[14373])).
% 28.62/18.81 tff(14375,plain,
% 28.62/18.81 (big_f(f3(f7(c1), f7(c1)), f7(c1))),
% 28.62/18.81 inference(modus_ponens,[status(thm)],[1345, 14374])).
% 28.62/18.81 tff(14376,plain,
% 28.62/18.81 (f3(f7(c1), f7(c1)) = f7(c1)),
% 28.62/18.81 inference(transitivity,[status(thm)],[14343, 13008, 14371, 2778])).
% 28.62/18.81 tff(14377,plain,
% 28.62/18.81 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (f7(c1) = c4) | (~(f7(c1) = f2(c1))) | big_f(c1, f7(c1)) | (~(f3(f7(c1), f7(c1)) = f7(c1))) | (~big_f(f3(f7(c1), f7(c1)), f7(c1))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (~(c1 = c3)) | (f7(c1) = c4) | (~(f7(c1) = f2(c1))) | big_f(c1, f7(c1)) | (~(f3(f7(c1), f7(c1)) = f7(c1))) | (~big_f(f3(f7(c1), f7(c1)), f7(c1))))),
% 28.62/18.81 inference(rewrite,[status(thm)],[])).
% 28.62/18.81 tff(14378,plain,
% 28.62/18.81 (((~(c1 = c3)) | (~(f7(c1) = f2(c1))) | (f7(c1) = c4) | (~(f3(f7(c1), f7(c1)) = f7(c1))) | (~big_f(f3(f7(c1), f7(c1)), f7(c1))) | big_f(c1, f7(c1))) <=> ((~(c1 = c3)) | (f7(c1) = c4) | (~(f7(c1) = f2(c1))) | big_f(c1, f7(c1)) | (~(f3(f7(c1), f7(c1)) = f7(c1))) | (~big_f(f3(f7(c1), f7(c1)), f7(c1))))),
% 28.62/18.81 inference(rewrite,[status(thm)],[])).
% 28.62/18.81 tff(14379,plain,
% 28.62/18.81 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(f7(c1) = f2(c1))) | (f7(c1) = c4) | (~(f3(f7(c1), f7(c1)) = f7(c1))) | (~big_f(f3(f7(c1), f7(c1)), f7(c1))) | big_f(c1, f7(c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (f7(c1) = c4) | (~(f7(c1) = f2(c1))) | big_f(c1, f7(c1)) | (~(f3(f7(c1), f7(c1)) = f7(c1))) | (~big_f(f3(f7(c1), f7(c1)), f7(c1)))))),
% 28.62/18.81 inference(monotonicity,[status(thm)],[14378])).
% 28.62/18.81 tff(14380,plain,
% 28.62/18.81 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(f7(c1) = f2(c1))) | (f7(c1) = c4) | (~(f3(f7(c1), f7(c1)) = f7(c1))) | (~big_f(f3(f7(c1), f7(c1)), f7(c1))) | big_f(c1, f7(c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (~(c1 = c3)) | (f7(c1) = c4) | (~(f7(c1) = f2(c1))) | big_f(c1, f7(c1)) | (~(f3(f7(c1), f7(c1)) = f7(c1))) | (~big_f(f3(f7(c1), f7(c1)), f7(c1))))),
% 28.62/18.81 inference(transitivity,[status(thm)],[14379, 14377])).
% 28.62/18.81 tff(14381,plain,
% 28.62/18.81 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(f7(c1) = f2(c1))) | (f7(c1) = c4) | (~(f3(f7(c1), f7(c1)) = f7(c1))) | (~big_f(f3(f7(c1), f7(c1)), f7(c1))) | big_f(c1, f7(c1)))),
% 28.62/18.81 inference(quant_inst,[status(thm)],[])).
% 28.62/18.81 tff(14382,plain,
% 28.62/18.81 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (~(c1 = c3)) | (f7(c1) = c4) | (~(f7(c1) = f2(c1))) | big_f(c1, f7(c1)) | (~(f3(f7(c1), f7(c1)) = f7(c1))) | (~big_f(f3(f7(c1), f7(c1)), f7(c1)))),
% 28.62/18.81 inference(modus_ponens,[status(thm)],[14381, 14380])).
% 28.62/18.81 tff(14383,plain,
% 28.62/18.81 (big_f(c1, f7(c1)) | (~(f3(f7(c1), f7(c1)) = f7(c1))) | (~big_f(f3(f7(c1), f7(c1)), f7(c1)))),
% 28.62/18.81 inference(unit_resolution,[status(thm)],[14382, 1398, 5611, 1000, 14360])).
% 28.62/18.81 tff(14384,plain,
% 28.62/18.81 ($false),
% 28.62/18.81 inference(unit_resolution,[status(thm)],[14383, 14376, 14359, 14375])).
% 28.62/18.81 tff(14385,plain,((~(f5(c1) = c2)) | (f7(c1) = c4) | (~big_f(c2, c2)) | (~(f10(c1) = c2)) | (~(c3 = c1)) | big_f(c3, f2(c3)) | (~(f2(c3) = c2)) | (f7(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 28.62/18.81 tff(14386,plain,
% 28.62/18.81 (big_f(c3, f2(c3))),
% 28.62/18.81 inference(unit_resolution,[status(thm)],[14385, 1319, 115, 186, 1345, 16, 172, 1000])).
% 28.62/18.81 tff(14387,plain,
% 28.62/18.81 (big_f(c1, f2(c1))),
% 28.62/18.81 inference(unit_resolution,[status(thm)],[8631, 14386, 172])).
% 28.62/18.81 tff(14388,plain,
% 28.62/18.81 ($false),
% 28.62/18.81 inference(unit_resolution,[status(thm)],[14387, 14331])).
% 28.62/18.81 tff(14389,plain,((~(f2(c3) = c2)) | big_f(c1, c2) | (~(c3 = c1)) | (f7(c1) = c1) | (~(f5(c1) = c2)) | (~big_f(c2, c2)) | (~(f10(c1) = c2)) | (f7(c1) = c4)), inference(lemma,lemma(discharge,[]))).
% 28.62/18.81 tff(14390,plain,
% 28.62/18.81 (~(f2(c3) = c2)),
% 28.62/18.81 inference(unit_resolution,[status(thm)],[14389, 172, 27, 115, 186, 1345, 16, 14326])).
% 28.62/18.81 tff(14391,plain,
% 28.62/18.81 (f2(c3) = c1),
% 28.62/18.81 inference(unit_resolution,[status(thm)],[1273, 14390])).
% 28.62/18.81 tff(14392,plain,
% 28.62/18.81 (c1 = f2(c1)),
% 28.62/18.81 inference(unit_resolution,[status(thm)],[6771, 14391, 172])).
% 28.62/18.81 tff(14393,plain,
% 28.62/18.81 (f6(c2, c2) = f2(f6(c2, c2))),
% 28.62/18.81 inference(modus_ponens,[status(thm)],[14392, 14324])).
% 28.62/18.81 tff(14394,plain,
% 28.62/18.81 (big_f(f6(c2, c2), f6(c2, c2)) <=> big_f(c1, c1)),
% 28.62/18.81 inference(monotonicity,[status(thm)],[14093, 14093])).
% 28.62/18.81 tff(14395,plain,
% 28.62/18.81 (big_f(c1, c1) <=> big_f(f6(c2, c2), f6(c2, c2))),
% 28.62/18.81 inference(symmetry,[status(thm)],[14394])).
% 28.62/18.81 tff(14396,plain,
% 28.62/18.81 ((~big_f(c1, c1)) <=> (~big_f(f6(c2, c2), f6(c2, c2)))),
% 28.62/18.81 inference(monotonicity,[status(thm)],[14395])).
% 28.62/18.81 tff(14397,plain,
% 28.62/18.81 (~big_f(f6(c2, c2), f6(c2, c2))),
% 28.62/18.81 inference(modus_ponens,[status(thm)],[66, 14396])).
% 28.62/18.81 tff(14398,plain,
% 28.62/18.81 ((f6(c2, c2) = c3) <=> (f6(f7(c2), f5(c1)) = c3)),
% 28.62/18.81 inference(monotonicity,[status(thm)],[3245])).
% 28.62/18.81 tff(14399,plain,
% 28.62/18.81 ((f6(f7(c2), f5(c1)) = c3) <=> (f6(c2, c2) = c3)),
% 28.62/18.81 inference(symmetry,[status(thm)],[14398])).
% 28.62/18.81 tff(14400,plain,
% 28.62/18.81 (f6(f7(c2), f5(c1)) = c1),
% 28.62/18.81 inference(transitivity,[status(thm)],[3236, 14092, 6634])).
% 28.62/18.81 tff(14401,plain,
% 28.62/18.81 ((f6(f7(c2), f5(c1)) = c3) <=> (c1 = c3)),
% 28.62/18.81 inference(monotonicity,[status(thm)],[14400])).
% 28.62/18.81 tff(14402,plain,
% 28.62/18.81 ((c1 = c3) <=> (f6(f7(c2), f5(c1)) = c3)),
% 28.62/18.81 inference(symmetry,[status(thm)],[14401])).
% 28.62/18.81 tff(14403,plain,
% 28.62/18.81 ((c1 = c3) <=> (f6(c2, c2) = c3)),
% 28.62/18.81 inference(transitivity,[status(thm)],[14402, 14399])).
% 28.62/18.81 tff(14404,plain,
% 28.62/18.81 (f6(c2, c2) = c3),
% 28.62/18.81 inference(modus_ponens,[status(thm)],[5611, 14403])).
% 28.62/18.81 tff(14405,plain,
% 28.62/18.81 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~(f6(c2, c2) = c3)) | big_f(f6(c2, c2), f6(c2, c2)) | (~(f6(c2, c2) = f2(f6(c2, c2)))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~(f6(c2, c2) = c3)) | big_f(f6(c2, c2), f6(c2, c2)) | (~(f6(c2, c2) = f2(f6(c2, c2)))))),
% 28.62/18.81 inference(rewrite,[status(thm)],[])).
% 28.62/18.81 tff(14406,plain,
% 28.62/18.81 (((~(f6(c2, c2) = c3)) | (~(f6(c2, c2) = f2(f6(c2, c2)))) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | big_f(f6(c2, c2), f6(c2, c2))) <=> ((c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~(f6(c2, c2) = c3)) | big_f(f6(c2, c2), f6(c2, c2)) | (~(f6(c2, c2) = f2(f6(c2, c2)))))),
% 28.62/18.81 inference(rewrite,[status(thm)],[])).
% 28.62/18.81 tff(14407,plain,
% 28.62/18.81 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(f6(c2, c2) = c3)) | (~(f6(c2, c2) = f2(f6(c2, c2)))) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | big_f(f6(c2, c2), f6(c2, c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~(f6(c2, c2) = c3)) | big_f(f6(c2, c2), f6(c2, c2)) | (~(f6(c2, c2) = f2(f6(c2, c2))))))),
% 28.62/18.81 inference(monotonicity,[status(thm)],[14406])).
% 28.62/18.81 tff(14408,plain,
% 28.62/18.81 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(f6(c2, c2) = c3)) | (~(f6(c2, c2) = f2(f6(c2, c2)))) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | big_f(f6(c2, c2), f6(c2, c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~(f6(c2, c2) = c3)) | big_f(f6(c2, c2), f6(c2, c2)) | (~(f6(c2, c2) = f2(f6(c2, c2)))))),
% 28.62/18.81 inference(transitivity,[status(thm)],[14407, 14405])).
% 28.62/18.81 tff(14409,plain,
% 28.62/18.81 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(f6(c2, c2) = c3)) | (~(f6(c2, c2) = f2(f6(c2, c2)))) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | big_f(f6(c2, c2), f6(c2, c2)))),
% 28.62/18.81 inference(quant_inst,[status(thm)],[])).
% 28.62/18.81 tff(14410,plain,
% 28.62/18.81 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~(f6(c2, c2) = c3)) | big_f(f6(c2, c2), f6(c2, c2)) | (~(f6(c2, c2) = f2(f6(c2, c2))))),
% 28.62/18.81 inference(modus_ponens,[status(thm)],[14409, 14408])).
% 28.62/18.81 tff(14411,plain,
% 28.62/18.81 (~(f3(c2, c2) = c2)),
% 28.62/18.81 inference(unit_resolution,[status(thm)],[14410, 1398, 873, 14310, 14404, 14397, 14393])).
% 28.62/18.81 tff(14412,plain,
% 28.62/18.81 (~(f3(c2, c2) = f8(f6(c2, c2)))),
% 28.62/18.81 inference(modus_ponens,[status(thm)],[14411, 14321])).
% 28.62/18.81 tff(14413,assumption,(big_f(f7(f6(c2, c2)), f6(c2, c2))), introduced(assumption)).
% 28.62/18.81 tff(14414,plain,
% 28.62/18.81 (f5(f6(c2, c2)) = f5(c1)),
% 28.62/18.81 inference(monotonicity,[status(thm)],[14093])).
% 28.62/18.81 tff(14415,plain,
% 28.62/18.81 (f5(f6(c2, c2)) = c2),
% 28.62/18.81 inference(transitivity,[status(thm)],[14414, 186])).
% 28.62/18.81 tff(14416,plain,
% 28.62/18.81 ((f6(c2, c2) = f5(f6(c2, c2))) <=> (f6(c2, c2) = c2)),
% 28.62/18.81 inference(monotonicity,[status(thm)],[14415])).
% 28.62/18.81 tff(14417,plain,
% 28.62/18.81 ((f6(c2, c2) = c2) <=> (f6(c2, c2) = f5(f6(c2, c2)))),
% 28.62/18.81 inference(symmetry,[status(thm)],[14416])).
% 28.62/18.81 tff(14418,plain,
% 28.62/18.81 ((~(f6(c2, c2) = c2)) <=> (~(f6(c2, c2) = f5(f6(c2, c2))))),
% 28.62/18.81 inference(monotonicity,[status(thm)],[14417])).
% 28.62/18.81 tff(14419,plain,
% 28.62/18.81 (~(f6(c2, c2) = f5(f6(c2, c2)))),
% 28.62/18.81 inference(modus_ponens,[status(thm)],[14102, 14418])).
% 28.62/18.81 tff(14420,plain,
% 28.62/18.81 (f7(f6(c2, c2)) = f7(c1)),
% 28.62/18.81 inference(monotonicity,[status(thm)],[14093])).
% 28.62/18.81 tff(14421,plain,
% 28.62/18.81 (f7(f6(c2, c2)) = c2),
% 28.62/18.81 inference(transitivity,[status(thm)],[14420, 120])).
% 28.62/18.81 tff(14422,plain,
% 28.62/18.81 ((f7(f6(c2, c2)) = f6(c2, c2)) <=> (c2 = f6(c2, c2))),
% 28.62/18.81 inference(monotonicity,[status(thm)],[14421])).
% 28.62/18.81 tff(14423,plain,
% 28.62/18.81 ((f7(f6(c2, c2)) = f6(c2, c2)) <=> (f6(c2, c2) = c2)),
% 28.62/18.81 inference(transitivity,[status(thm)],[14422, 3242])).
% 28.62/18.81 tff(14424,plain,
% 28.62/18.81 ((f6(c2, c2) = c2) <=> (f7(f6(c2, c2)) = f6(c2, c2))),
% 28.62/18.81 inference(symmetry,[status(thm)],[14423])).
% 28.62/18.81 tff(14425,plain,
% 28.62/18.81 ((~(f6(c2, c2) = c2)) <=> (~(f7(f6(c2, c2)) = f6(c2, c2)))),
% 28.62/18.81 inference(monotonicity,[status(thm)],[14424])).
% 28.62/18.81 tff(14426,plain,
% 28.62/18.81 (~(f7(f6(c2, c2)) = f6(c2, c2))),
% 28.62/18.81 inference(modus_ponens,[status(thm)],[14102, 14425])).
% 28.62/18.81 tff(14427,plain,
% 28.62/18.81 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f6(c2, c2)) = f6(c2, c2)) | (f6(c2, c2) = f5(f6(c2, c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f7(f6(c2, c2)), f6(c2, c2))) | (f3(c2, c2) = f8(f6(c2, c2))) | (~big_f(f3(c2, c2), f10(f6(c2, c2)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(f6(c2, c2)) = f6(c2, c2)) | (f6(c2, c2) = f5(f6(c2, c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f7(f6(c2, c2)), f6(c2, c2))) | (f3(c2, c2) = f8(f6(c2, c2))) | (~big_f(f3(c2, c2), f10(f6(c2, c2)))))),
% 28.62/18.81 inference(rewrite,[status(thm)],[])).
% 28.62/18.81 tff(14428,plain,
% 28.62/18.81 (((f10(f6(c2, c2)) = f6(c2, c2)) | (f3(c2, c2) = f8(f6(c2, c2))) | (~big_f(f3(c2, c2), f10(f6(c2, c2)))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (f6(c2, c2) = f5(f6(c2, c2))) | (~big_f(f7(f6(c2, c2)), f6(c2, c2)))) <=> ((f10(f6(c2, c2)) = f6(c2, c2)) | (f6(c2, c2) = f5(f6(c2, c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f7(f6(c2, c2)), f6(c2, c2))) | (f3(c2, c2) = f8(f6(c2, c2))) | (~big_f(f3(c2, c2), f10(f6(c2, c2)))))),
% 28.62/18.81 inference(rewrite,[status(thm)],[])).
% 28.62/18.81 tff(14429,plain,
% 28.62/18.81 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f6(c2, c2)) = f6(c2, c2)) | (f3(c2, c2) = f8(f6(c2, c2))) | (~big_f(f3(c2, c2), f10(f6(c2, c2)))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (f6(c2, c2) = f5(f6(c2, c2))) | (~big_f(f7(f6(c2, c2)), f6(c2, c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f6(c2, c2)) = f6(c2, c2)) | (f6(c2, c2) = f5(f6(c2, c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f7(f6(c2, c2)), f6(c2, c2))) | (f3(c2, c2) = f8(f6(c2, c2))) | (~big_f(f3(c2, c2), f10(f6(c2, c2))))))),
% 28.62/18.82 inference(monotonicity,[status(thm)],[14428])).
% 28.62/18.82 tff(14430,plain,
% 28.62/18.82 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f6(c2, c2)) = f6(c2, c2)) | (f3(c2, c2) = f8(f6(c2, c2))) | (~big_f(f3(c2, c2), f10(f6(c2, c2)))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (f6(c2, c2) = f5(f6(c2, c2))) | (~big_f(f7(f6(c2, c2)), f6(c2, c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(f6(c2, c2)) = f6(c2, c2)) | (f6(c2, c2) = f5(f6(c2, c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f7(f6(c2, c2)), f6(c2, c2))) | (f3(c2, c2) = f8(f6(c2, c2))) | (~big_f(f3(c2, c2), f10(f6(c2, c2)))))),
% 28.62/18.82 inference(transitivity,[status(thm)],[14429, 14427])).
% 28.62/18.82 tff(14431,plain,
% 28.62/18.82 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f6(c2, c2)) = f6(c2, c2)) | (f3(c2, c2) = f8(f6(c2, c2))) | (~big_f(f3(c2, c2), f10(f6(c2, c2)))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (f6(c2, c2) = f5(f6(c2, c2))) | (~big_f(f7(f6(c2, c2)), f6(c2, c2))))),
% 28.62/18.82 inference(quant_inst,[status(thm)],[])).
% 28.62/18.82 tff(14432,plain,
% 28.62/18.82 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(f6(c2, c2)) = f6(c2, c2)) | (f6(c2, c2) = f5(f6(c2, c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f7(f6(c2, c2)), f6(c2, c2))) | (f3(c2, c2) = f8(f6(c2, c2))) | (~big_f(f3(c2, c2), f10(f6(c2, c2))))),
% 28.62/18.82 inference(modus_ponens,[status(thm)],[14431, 14430])).
% 28.62/18.82 tff(14433,plain,
% 28.62/18.82 ((f10(f6(c2, c2)) = f6(c2, c2)) | (f3(c2, c2) = f8(f6(c2, c2))) | (~big_f(f3(c2, c2), f10(f6(c2, c2))))),
% 28.62/18.82 inference(unit_resolution,[status(thm)],[14432, 1659, 14426, 14419, 14413])).
% 28.62/18.82 tff(14434,plain,
% 28.62/18.82 ($false),
% 28.62/18.82 inference(unit_resolution,[status(thm)],[14433, 14412, 14316, 14311])).
% 28.62/18.82 tff(14435,plain,((~(c3 = c1)) | (~big_f(f7(f6(c2, c2)), f6(c2, c2))) | (~(c2 = f8(c1))) | (~(f6(c2, f7(f4(c4))) = c1)) | (~(f7(c2) = c2)) | (~(f4(c4) = c2)) | (~(f10(c1) = c2)) | (c2 = c4) | big_f(c1, c2) | (~big_f(c2, c2)) | big_f(c1, c1) | (f7(c1) = c1) | (~(f5(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.62/18.82 tff(14436,plain,
% 28.62/18.82 (~(c3 = c1)),
% 28.62/18.82 inference(unit_resolution,[status(thm)],[14435, 873, 1642, 6634, 14274, 79, 16, 14299, 27, 1345, 66, 115, 186])).
% 28.62/18.82 tff(14437,plain,
% 28.62/18.82 (c3 = c2),
% 28.62/18.82 inference(unit_resolution,[status(thm)],[180, 14436])).
% 28.62/18.82 tff(14438,plain,
% 28.62/18.82 ((f3(c2, c2) = c3) <=> (f3(c2, c2) = c2)),
% 28.62/18.82 inference(monotonicity,[status(thm)],[14437])).
% 28.62/18.82 tff(14439,plain,
% 28.62/18.82 ((f3(c2, c2) = c2) <=> (f3(c2, c2) = c3)),
% 28.62/18.82 inference(symmetry,[status(thm)],[14438])).
% 28.62/18.82 tff(14440,plain,
% 28.62/18.82 (f8(f6(c2, c2)) = f8(c1)),
% 28.62/18.82 inference(monotonicity,[status(thm)],[14291])).
% 28.62/18.82 tff(14441,plain,
% 28.62/18.82 (f8(f6(c2, c2)) = c2),
% 28.62/18.82 inference(transitivity,[status(thm)],[14440, 1643])).
% 28.62/18.82 tff(14442,plain,
% 28.62/18.82 ((f3(c2, c2) = f8(f6(c2, c2))) <=> (f3(c2, c2) = c2)),
% 28.62/18.82 inference(monotonicity,[status(thm)],[14441])).
% 28.62/18.82 tff(14443,plain,
% 28.62/18.82 ((f3(c2, c2) = f8(f6(c2, c2))) <=> (f3(c2, c2) = c3)),
% 28.62/18.82 inference(transitivity,[status(thm)],[14442, 14439])).
% 28.62/18.82 tff(14444,plain,
% 28.62/18.82 (f10(f6(c2, c2)) = f10(c1)),
% 28.62/18.82 inference(monotonicity,[status(thm)],[14291])).
% 28.62/18.82 tff(14445,plain,
% 28.62/18.82 (f10(f6(c2, c2)) = c2),
% 28.62/18.82 inference(transitivity,[status(thm)],[14444, 16])).
% 28.62/18.82 tff(14446,plain,
% 28.62/18.82 (big_f(f3(c2, c2), f10(f6(c2, c2))) <=> big_f(f3(c2, c2), c2)),
% 28.62/18.82 inference(monotonicity,[status(thm)],[14445])).
% 28.62/18.82 tff(14447,plain,
% 28.62/18.82 (big_f(f3(c2, c2), c2) <=> big_f(f3(c2, c2), f10(f6(c2, c2)))),
% 28.62/18.82 inference(symmetry,[status(thm)],[14446])).
% 28.62/18.82 tff(14448,plain,
% 28.62/18.82 (c2 = c3),
% 28.62/18.82 inference(modus_ponens,[status(thm)],[14437, 78])).
% 28.62/18.82 tff(14449,plain,
% 28.62/18.82 (big_f(f3(c2, c2), c2)),
% 28.62/18.82 inference(unit_resolution,[status(thm)],[13236, 14448, 873, 1345, 348])).
% 28.62/18.82 tff(14450,plain,
% 28.62/18.82 (big_f(f3(c2, c2), f10(f6(c2, c2)))),
% 28.62/18.82 inference(modus_ponens,[status(thm)],[14449, 14447])).
% 28.62/18.82 tff(14451,plain,
% 28.62/18.82 ((f10(f6(c2, c2)) = f6(c2, c2)) <=> (c2 = f6(c2, c2))),
% 28.62/18.82 inference(monotonicity,[status(thm)],[14445])).
% 28.62/18.82 tff(14452,plain,
% 28.62/18.82 ((f10(f6(c2, c2)) = f6(c2, c2)) <=> (f6(c2, c2) = c2)),
% 28.62/18.82 inference(transitivity,[status(thm)],[14451, 3242])).
% 28.62/18.82 tff(14453,plain,
% 28.62/18.82 ((f6(c2, c2) = c2) <=> (f10(f6(c2, c2)) = f6(c2, c2))),
% 28.62/18.82 inference(symmetry,[status(thm)],[14452])).
% 28.62/18.82 tff(14454,plain,
% 28.62/18.82 ((~(f6(c2, c2) = c2)) <=> (~(f10(f6(c2, c2)) = f6(c2, c2)))),
% 28.62/18.82 inference(monotonicity,[status(thm)],[14453])).
% 28.62/18.82 tff(14455,plain,
% 28.62/18.82 ((f6(c2, c2) = c2) <=> (c1 = c2)),
% 28.62/18.82 inference(monotonicity,[status(thm)],[14291])).
% 28.62/18.82 tff(14456,plain,
% 28.62/18.82 ((f6(c2, c2) = c2) <=> (c2 = c1)),
% 28.62/18.82 inference(transitivity,[status(thm)],[14455, 1])).
% 28.62/18.82 tff(14457,plain,
% 28.62/18.82 ((c2 = c1) <=> (f6(c2, c2) = c2)),
% 28.62/18.82 inference(symmetry,[status(thm)],[14456])).
% 28.62/18.82 tff(14458,plain,
% 28.62/18.82 ((~(c2 = c1)) <=> (~(f6(c2, c2) = c2))),
% 28.62/18.82 inference(monotonicity,[status(thm)],[14457])).
% 28.62/18.82 tff(14459,plain,
% 28.62/18.82 (~(f6(c2, c2) = c2)),
% 28.62/18.82 inference(modus_ponens,[status(thm)],[75, 14458])).
% 28.62/18.82 tff(14460,plain,
% 28.62/18.82 (~(f10(f6(c2, c2)) = f6(c2, c2))),
% 28.62/18.82 inference(modus_ponens,[status(thm)],[14459, 14454])).
% 28.62/18.82 tff(14461,plain,
% 28.62/18.82 (f5(f6(c2, c2)) = f5(c1)),
% 28.62/18.82 inference(monotonicity,[status(thm)],[14291])).
% 28.62/18.82 tff(14462,plain,
% 28.62/18.82 (f5(f6(c2, c2)) = c2),
% 28.62/18.82 inference(transitivity,[status(thm)],[14461, 186])).
% 28.62/18.82 tff(14463,plain,
% 28.62/18.82 ((f6(c2, c2) = f5(f6(c2, c2))) <=> (f6(c2, c2) = c2)),
% 28.62/18.82 inference(monotonicity,[status(thm)],[14462])).
% 28.62/18.82 tff(14464,plain,
% 28.62/18.82 ((f6(c2, c2) = c2) <=> (f6(c2, c2) = f5(f6(c2, c2)))),
% 28.62/18.82 inference(symmetry,[status(thm)],[14463])).
% 28.62/18.82 tff(14465,plain,
% 28.62/18.82 ((~(f6(c2, c2) = c2)) <=> (~(f6(c2, c2) = f5(f6(c2, c2))))),
% 28.62/18.82 inference(monotonicity,[status(thm)],[14464])).
% 28.62/18.82 tff(14466,plain,
% 28.62/18.82 (~(f6(c2, c2) = f5(f6(c2, c2)))),
% 28.62/18.82 inference(modus_ponens,[status(thm)],[14459, 14465])).
% 28.62/18.82 tff(14467,plain,
% 28.62/18.82 (f7(f6(c2, c2)) = c2),
% 28.62/18.82 inference(transitivity,[status(thm)],[14292, 120])).
% 28.62/18.82 tff(14468,plain,
% 28.62/18.82 ((f7(f6(c2, c2)) = f6(c2, c2)) <=> (c2 = f6(c2, c2))),
% 28.62/18.82 inference(monotonicity,[status(thm)],[14467])).
% 28.62/18.82 tff(14469,plain,
% 28.62/18.82 ((f7(f6(c2, c2)) = f6(c2, c2)) <=> (f6(c2, c2) = c2)),
% 28.62/18.82 inference(transitivity,[status(thm)],[14468, 3242])).
% 28.62/18.82 tff(14470,plain,
% 28.62/18.82 ((f6(c2, c2) = c2) <=> (f7(f6(c2, c2)) = f6(c2, c2))),
% 28.62/18.82 inference(symmetry,[status(thm)],[14469])).
% 28.62/18.82 tff(14471,plain,
% 28.62/18.82 ((~(f6(c2, c2) = c2)) <=> (~(f7(f6(c2, c2)) = f6(c2, c2)))),
% 28.62/18.82 inference(monotonicity,[status(thm)],[14470])).
% 28.62/18.82 tff(14472,plain,
% 28.62/18.82 (~(f7(f6(c2, c2)) = f6(c2, c2))),
% 28.62/18.82 inference(modus_ponens,[status(thm)],[14459, 14471])).
% 28.62/18.82 tff(14473,plain,
% 28.62/18.82 ((f10(f6(c2, c2)) = f6(c2, c2)) | (f3(c2, c2) = f8(f6(c2, c2))) | (~big_f(f3(c2, c2), f10(f6(c2, c2))))),
% 28.62/18.82 inference(unit_resolution,[status(thm)],[14432, 1659, 14472, 14466, 14299])).
% 28.62/18.82 tff(14474,plain,
% 28.62/18.82 (f3(c2, c2) = f8(f6(c2, c2))),
% 28.62/18.82 inference(unit_resolution,[status(thm)],[14473, 14460, 14450])).
% 28.62/18.82 tff(14475,plain,
% 28.62/18.82 (f3(c2, c2) = c3),
% 28.62/18.82 inference(modus_ponens,[status(thm)],[14474, 14443])).
% 28.62/18.82 tff(14476,plain,
% 28.62/18.82 (f3(c2, c2) = c2),
% 28.62/18.82 inference(modus_ponens,[status(thm)],[14474, 14442])).
% 28.62/18.82 tff(14477,plain,
% 28.62/18.82 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~(f3(c2, c2) = c3)) | (c2 = f2(f3(c2, c2))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~(f3(c2, c2) = c3)) | (c2 = f2(f3(c2, c2))))),
% 28.62/18.82 inference(rewrite,[status(thm)],[])).
% 28.62/18.82 tff(14478,plain,
% 28.62/18.82 (((~(f3(c2, c2) = c3)) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (c2 = f2(f3(c2, c2))) | (~big_f(f3(c2, c2), c2))) <=> ((c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~(f3(c2, c2) = c3)) | (c2 = f2(f3(c2, c2))))),
% 28.62/18.82 inference(rewrite,[status(thm)],[])).
% 28.62/18.82 tff(14479,plain,
% 28.62/18.82 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f3(c2, c2) = c3)) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (c2 = f2(f3(c2, c2))) | (~big_f(f3(c2, c2), c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~(f3(c2, c2) = c3)) | (c2 = f2(f3(c2, c2)))))),
% 28.62/18.82 inference(monotonicity,[status(thm)],[14478])).
% 28.62/18.82 tff(14480,plain,
% 28.62/18.82 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f3(c2, c2) = c3)) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (c2 = f2(f3(c2, c2))) | (~big_f(f3(c2, c2), c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~(f3(c2, c2) = c3)) | (c2 = f2(f3(c2, c2))))),
% 28.62/18.82 inference(transitivity,[status(thm)],[14479, 14477])).
% 28.62/18.82 tff(14481,plain,
% 28.62/18.82 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f3(c2, c2) = c3)) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (c2 = f2(f3(c2, c2))) | (~big_f(f3(c2, c2), c2)))),
% 28.62/18.82 inference(quant_inst,[status(thm)],[])).
% 28.62/18.82 tff(14482,plain,
% 28.62/18.82 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~(f3(c2, c2) = c3)) | (c2 = f2(f3(c2, c2)))),
% 28.62/18.82 inference(modus_ponens,[status(thm)],[14481, 14480])).
% 28.62/18.82 tff(14483,plain,
% 28.62/18.82 ((~(f3(c2, c2) = c2)) | (~(f3(c2, c2) = c3)) | (c2 = f2(f3(c2, c2)))),
% 28.62/18.82 inference(unit_resolution,[status(thm)],[14482, 7051, 873, 14449])).
% 28.62/18.82 tff(14484,plain,
% 28.62/18.82 (c2 = f2(f3(c2, c2))),
% 28.62/18.82 inference(unit_resolution,[status(thm)],[14483, 14476, 14475])).
% 28.62/18.82 tff(14485,plain,
% 28.62/18.82 (f2(f3(c2, c2)) = c2),
% 28.62/18.82 inference(symmetry,[status(thm)],[14484])).
% 28.62/18.82 tff(14486,plain,
% 28.62/18.82 (f8(f6(c2, c2)) = f3(c2, c2)),
% 28.62/18.82 inference(symmetry,[status(thm)],[14474])).
% 28.62/18.82 tff(14487,plain,
% 28.62/18.82 (f8(c1) = f8(f6(c2, c2))),
% 28.62/18.82 inference(symmetry,[status(thm)],[14440])).
% 28.62/18.82 tff(14488,plain,
% 28.62/18.82 (c2 = f3(c2, c2)),
% 28.62/18.82 inference(transitivity,[status(thm)],[1642, 14487, 14486])).
% 28.62/18.82 tff(14489,plain,
% 28.62/18.82 (f2(c2) = f2(f3(c2, c2))),
% 28.62/18.82 inference(monotonicity,[status(thm)],[14488])).
% 28.62/18.82 tff(14490,plain,
% 28.62/18.82 (big_f(c2, f6(c2, c2)) <=> big_f(f7(c2), f6(c2, c2))),
% 28.62/18.82 inference(monotonicity,[status(thm)],[14275])).
% 28.62/18.82 tff(14491,plain,
% 28.62/18.82 (big_f(f7(c2), f6(c2, c2)) <=> big_f(c2, f6(c2, c2))),
% 28.62/18.82 inference(symmetry,[status(thm)],[14490])).
% 28.62/18.82 tff(14492,plain,
% 28.62/18.82 (big_f(c2, f6(c2, c2))),
% 28.62/18.82 inference(modus_ponens,[status(thm)],[14298, 14491])).
% 28.62/18.82 tff(14493,plain,
% 28.62/18.82 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = c4) | (f6(c2, c2) = f2(c2)) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~big_f(c2, f6(c2, c2))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = c4) | (f6(c2, c2) = f2(c2)) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~big_f(c2, f6(c2, c2))))),
% 28.62/18.82 inference(rewrite,[status(thm)],[])).
% 28.62/18.82 tff(14494,plain,
% 28.62/18.82 (((~(c2 = c3)) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (f6(c2, c2) = f2(c2)) | (~big_f(c2, f6(c2, c2)))) <=> ((~(c2 = c3)) | (c2 = c4) | (f6(c2, c2) = f2(c2)) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~big_f(c2, f6(c2, c2))))),
% 28.62/18.82 inference(rewrite,[status(thm)],[])).
% 28.62/18.82 tff(14495,plain,
% 28.62/18.82 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (f6(c2, c2) = f2(c2)) | (~big_f(c2, f6(c2, c2))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = c4) | (f6(c2, c2) = f2(c2)) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~big_f(c2, f6(c2, c2)))))),
% 28.62/18.82 inference(monotonicity,[status(thm)],[14494])).
% 28.62/18.82 tff(14496,plain,
% 28.62/18.82 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (f6(c2, c2) = f2(c2)) | (~big_f(c2, f6(c2, c2))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = c4) | (f6(c2, c2) = f2(c2)) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~big_f(c2, f6(c2, c2))))),
% 28.62/18.82 inference(transitivity,[status(thm)],[14495, 14493])).
% 28.62/18.82 tff(14497,plain,
% 28.62/18.82 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (f6(c2, c2) = f2(c2)) | (~big_f(c2, f6(c2, c2))))),
% 28.62/18.82 inference(quant_inst,[status(thm)],[])).
% 28.62/18.82 tff(14498,plain,
% 28.62/18.82 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = c4) | (f6(c2, c2) = f2(c2)) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~big_f(c2, f6(c2, c2)))),
% 28.62/18.82 inference(modus_ponens,[status(thm)],[14497, 14496])).
% 28.62/18.82 tff(14499,plain,
% 28.62/18.82 ((f6(c2, c2) = f2(c2)) | (~(f3(c2, c2) = c2))),
% 28.62/18.82 inference(unit_resolution,[status(thm)],[14498, 7051, 873, 14448, 14449, 14492])).
% 28.62/18.82 tff(14500,plain,
% 28.62/18.82 (f6(c2, c2) = f2(c2)),
% 28.62/18.82 inference(unit_resolution,[status(thm)],[14499, 14476])).
% 28.62/18.82 tff(14501,plain,
% 28.62/18.82 (f6(c2, c2) = c2),
% 28.62/18.82 inference(transitivity,[status(thm)],[14500, 14489, 14485])).
% 28.62/18.82 tff(14502,plain,
% 28.62/18.82 ($false),
% 28.62/18.82 inference(unit_resolution,[status(thm)],[14459, 14501])).
% 28.62/18.82 tff(14503,plain,((c2 = c4) | (~(c2 = f8(c1))) | (~(f6(c2, f7(f4(c4))) = c1)) | (~(f4(c4) = c2)) | (~(f10(c1) = c2)) | (~big_f(c2, c2)) | (~big_f(c2, c1)) | big_f(c1, c2) | big_f(c1, c1) | (f7(c1) = c1) | (~(f5(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.62/18.82 tff(14504,plain,
% 28.62/18.82 (c2 = c4),
% 28.62/18.82 inference(unit_resolution,[status(thm)],[14503, 27, 6634, 79, 16, 1345, 348, 1642, 66, 115, 186])).
% 28.62/18.82 tff(14505,plain,
% 28.62/18.82 (c4 = c2),
% 28.62/18.82 inference(symmetry,[status(thm)],[14504])).
% 28.62/18.82 tff(14506,plain,
% 28.62/18.82 ((f6(f7(c2), f5(c1)) = c4) <=> (f6(c2, c2) = c2)),
% 28.62/18.82 inference(monotonicity,[status(thm)],[14278, 14505])).
% 28.62/18.82 tff(14507,plain,
% 28.62/18.82 ((f6(c2, c2) = c2) <=> (f6(f7(c2), f5(c1)) = c4)),
% 28.62/18.82 inference(symmetry,[status(thm)],[14506])).
% 28.62/18.82 tff(14508,plain,
% 28.62/18.82 ((f6(c2, c2) = c2) <=> (c1 = c4)),
% 28.62/18.82 inference(transitivity,[status(thm)],[14507, 14287])).
% 28.62/18.82 tff(14509,plain,
% 28.62/18.82 ((~(f6(c2, c2) = c2)) <=> (~(c1 = c4))),
% 28.62/18.82 inference(monotonicity,[status(thm)],[14508])).
% 28.62/18.82 tff(14510,plain,
% 28.62/18.82 (f6(c2, c2) = c1),
% 28.62/18.82 inference(transitivity,[status(thm)],[14277, 6634])).
% 28.62/18.82 tff(14511,plain,
% 28.62/18.82 ((f6(c2, c2) = c2) <=> (c1 = c2)),
% 28.62/18.82 inference(monotonicity,[status(thm)],[14510])).
% 28.62/18.82 tff(14512,plain,
% 28.62/18.82 ((f6(c2, c2) = c2) <=> (c2 = c1)),
% 28.62/18.82 inference(transitivity,[status(thm)],[14511, 1])).
% 28.62/18.82 tff(14513,plain,
% 28.62/18.82 ((c2 = c1) <=> (f6(c2, c2) = c2)),
% 28.62/18.82 inference(symmetry,[status(thm)],[14512])).
% 28.62/18.82 tff(14514,plain,
% 28.62/18.82 ((~(c2 = c1)) <=> (~(f6(c2, c2) = c2))),
% 28.62/18.82 inference(monotonicity,[status(thm)],[14513])).
% 28.62/18.82 tff(14515,plain,
% 28.62/18.82 (~(f6(c2, c2) = c2)),
% 28.62/18.82 inference(modus_ponens,[status(thm)],[75, 14514])).
% 28.62/18.82 tff(14516,plain,
% 28.62/18.82 (~(c1 = c4)),
% 28.62/18.82 inference(modus_ponens,[status(thm)],[14515, 14509])).
% 28.62/18.82 tff(14517,plain,
% 28.62/18.82 (f7(f6(c2, c2)) = f7(c1)),
% 28.62/18.82 inference(monotonicity,[status(thm)],[14510])).
% 28.62/18.82 tff(14518,plain,
% 28.62/18.82 (f7(f6(c2, c2)) = f7(c2)),
% 28.62/18.82 inference(transitivity,[status(thm)],[14517, 120, 14275])).
% 28.62/18.82 tff(14519,plain,
% 28.62/18.82 (big_f(f7(f6(c2, c2)), f6(c2, c2)) <=> big_f(f7(c2), f6(c2, c2))),
% 28.62/18.82 inference(monotonicity,[status(thm)],[14518])).
% 28.62/18.82 tff(14520,plain,
% 28.62/18.82 (big_f(f7(c2), f6(c2, c2)) <=> big_f(f7(f6(c2, c2)), f6(c2, c2))),
% 28.62/18.82 inference(symmetry,[status(thm)],[14519])).
% 28.62/18.82 tff(14521,plain,
% 28.62/18.82 (big_f(f7(c2), f6(c2, c2)) <=> big_f(c2, c1)),
% 28.62/18.82 inference(monotonicity,[status(thm)],[14274, 14510])).
% 28.62/18.82 tff(14522,plain,
% 28.62/18.82 (big_f(c2, c1) <=> big_f(f7(c2), f6(c2, c2))),
% 28.62/18.82 inference(symmetry,[status(thm)],[14521])).
% 28.62/18.82 tff(14523,plain,
% 28.62/18.82 (big_f(f7(c2), f6(c2, c2))),
% 28.62/18.82 inference(modus_ponens,[status(thm)],[348, 14522])).
% 28.62/18.82 tff(14524,plain,
% 28.62/18.82 (big_f(f7(f6(c2, c2)), f6(c2, c2))),
% 28.62/18.82 inference(modus_ponens,[status(thm)],[14523, 14520])).
% 28.62/18.82 tff(14525,plain,
% 28.62/18.82 (f5(f6(c2, c2)) = f5(c1)),
% 28.62/18.82 inference(monotonicity,[status(thm)],[14510])).
% 28.62/18.82 tff(14526,plain,
% 28.62/18.82 (f5(f6(c2, c2)) = c2),
% 28.62/18.82 inference(transitivity,[status(thm)],[14525, 186])).
% 28.62/18.82 tff(14527,plain,
% 28.62/18.82 ((f6(c2, c2) = f5(f6(c2, c2))) <=> (f6(c2, c2) = c2)),
% 28.62/18.82 inference(monotonicity,[status(thm)],[14526])).
% 28.62/18.82 tff(14528,plain,
% 28.62/18.82 ((f6(c2, c2) = c2) <=> (f6(c2, c2) = f5(f6(c2, c2)))),
% 28.62/18.82 inference(symmetry,[status(thm)],[14527])).
% 28.62/18.82 tff(14529,plain,
% 28.62/18.82 ((~(f6(c2, c2) = c2)) <=> (~(f6(c2, c2) = f5(f6(c2, c2))))),
% 28.62/18.82 inference(monotonicity,[status(thm)],[14528])).
% 28.62/18.82 tff(14530,plain,
% 28.62/18.82 (~(f6(c2, c2) = f5(f6(c2, c2)))),
% 28.62/18.82 inference(modus_ponens,[status(thm)],[14515, 14529])).
% 28.62/18.82 tff(14531,plain,
% 28.62/18.82 (f7(f6(c2, c2)) = c2),
% 28.62/18.82 inference(transitivity,[status(thm)],[14517, 120])).
% 28.62/18.82 tff(14532,plain,
% 28.62/18.82 ((f7(f6(c2, c2)) = f6(c2, c2)) <=> (c2 = f6(c2, c2))),
% 28.62/18.82 inference(monotonicity,[status(thm)],[14531])).
% 28.62/18.82 tff(14533,plain,
% 28.62/18.82 ((f7(f6(c2, c2)) = f6(c2, c2)) <=> (f6(c2, c2) = c2)),
% 28.62/18.82 inference(transitivity,[status(thm)],[14532, 3242])).
% 28.62/18.82 tff(14534,plain,
% 28.62/18.82 ((f6(c2, c2) = c2) <=> (f7(f6(c2, c2)) = f6(c2, c2))),
% 28.62/18.82 inference(symmetry,[status(thm)],[14533])).
% 28.62/18.82 tff(14535,plain,
% 28.62/18.82 ((~(f6(c2, c2) = c2)) <=> (~(f7(f6(c2, c2)) = f6(c2, c2)))),
% 28.62/18.82 inference(monotonicity,[status(thm)],[14534])).
% 28.62/18.82 tff(14536,plain,
% 28.62/18.82 (~(f7(f6(c2, c2)) = f6(c2, c2))),
% 28.62/18.82 inference(modus_ponens,[status(thm)],[14515, 14535])).
% 28.62/18.82 tff(14537,plain,
% 28.62/18.82 (f8(c1) = c2),
% 28.62/18.82 inference(modus_ponens,[status(thm)],[1642, 2782])).
% 28.62/18.82 tff(14538,plain,
% 28.62/18.82 (~(f10(c2) = c2)),
% 28.62/18.82 inference(unit_resolution,[status(thm)],[3321, 14279, 120, 79, 16, 186, 14537, 1345, 14274])).
% 28.62/18.82 tff(14539,plain,
% 28.62/18.82 (f10(c2) = c1),
% 28.62/18.82 inference(unit_resolution,[status(thm)],[93, 14538])).
% 28.62/18.82 tff(14540,plain,
% 28.62/18.82 (f10(c2) = f6(c2, c2)),
% 28.62/18.82 inference(transitivity,[status(thm)],[14539, 14103, 14284])).
% 28.62/18.82 tff(14541,plain,
% 28.62/18.82 (big_f(c2, f10(c2)) <=> big_f(f7(c2), f6(c2, c2))),
% 28.62/18.82 inference(monotonicity,[status(thm)],[14275, 14540])).
% 28.62/18.82 tff(14542,plain,
% 28.62/18.82 (big_f(f7(c2), f6(c2, c2)) <=> big_f(c2, f10(c2))),
% 28.62/18.82 inference(symmetry,[status(thm)],[14541])).
% 28.62/18.82 tff(14543,plain,
% 28.62/18.82 (big_f(c2, f10(c2))),
% 28.62/18.82 inference(modus_ponens,[status(thm)],[14523, 14542])).
% 28.62/18.82 tff(14544,plain,
% 28.62/18.82 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f6(c2, c2) = f5(f6(c2, c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f7(f6(c2, c2)), f6(c2, c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f6(c2, c2) = f5(f6(c2, c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f7(f6(c2, c2)), f6(c2, c2))))),
% 28.62/18.83 inference(rewrite,[status(thm)],[])).
% 28.62/18.83 tff(14545,plain,
% 28.62/18.83 (((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (f6(c2, c2) = f5(f6(c2, c2))) | (~big_f(f7(f6(c2, c2)), f6(c2, c2)))) <=> ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f6(c2, c2) = f5(f6(c2, c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f7(f6(c2, c2)), f6(c2, c2))))),
% 28.62/18.83 inference(rewrite,[status(thm)],[])).
% 28.62/18.83 tff(14546,plain,
% 28.62/18.83 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (f6(c2, c2) = f5(f6(c2, c2))) | (~big_f(f7(f6(c2, c2)), f6(c2, c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f6(c2, c2) = f5(f6(c2, c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f7(f6(c2, c2)), f6(c2, c2)))))),
% 28.62/18.83 inference(monotonicity,[status(thm)],[14545])).
% 28.62/18.83 tff(14547,plain,
% 28.62/18.83 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (f6(c2, c2) = f5(f6(c2, c2))) | (~big_f(f7(f6(c2, c2)), f6(c2, c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f6(c2, c2) = f5(f6(c2, c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f7(f6(c2, c2)), f6(c2, c2))))),
% 28.62/18.83 inference(transitivity,[status(thm)],[14546, 14544])).
% 28.62/18.83 tff(14548,plain,
% 28.62/18.83 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (f6(c2, c2) = f5(f6(c2, c2))) | (~big_f(f7(f6(c2, c2)), f6(c2, c2))))),
% 28.62/18.83 inference(quant_inst,[status(thm)],[])).
% 28.62/18.83 tff(14549,plain,
% 28.62/18.83 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f6(c2, c2) = f5(f6(c2, c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f7(f6(c2, c2)), f6(c2, c2)))),
% 28.62/18.83 inference(modus_ponens,[status(thm)],[14548, 14547])).
% 28.62/18.83 tff(14550,plain,
% 28.62/18.83 ((c2 = f8(c2)) | (f6(c2, c2) = f5(f6(c2, c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f7(f6(c2, c2)), f6(c2, c2)))),
% 28.62/18.83 inference(unit_resolution,[status(thm)],[14549, 1659, 14538, 14543])).
% 28.62/18.83 tff(14551,plain,
% 28.62/18.83 (c2 = f8(c2)),
% 28.62/18.83 inference(unit_resolution,[status(thm)],[14550, 14536, 14530, 14524])).
% 28.62/18.83 tff(14552,plain,
% 28.62/18.83 (~(c3 = c1)),
% 28.62/18.83 inference(unit_resolution,[status(thm)],[12851, 14516, 348, 66, 27, 1642])).
% 28.62/18.83 tff(14553,plain,
% 28.62/18.83 (c3 = c2),
% 28.62/18.83 inference(unit_resolution,[status(thm)],[180, 14552])).
% 28.62/18.83 tff(14554,plain,
% 28.62/18.83 (f3(c1, c2) = c2),
% 28.62/18.83 inference(unit_resolution,[status(thm)],[13195, 14553, 1345, 66, 14551, 14516, 348])).
% 28.62/18.83 tff(14555,plain,
% 28.62/18.83 (f3(f6(f7(c2), f5(c1)), c2) = c2),
% 28.62/18.83 inference(modus_ponens,[status(thm)],[14554, 14282])).
% 28.62/18.83 tff(14556,plain,
% 28.62/18.83 (c2 = c3),
% 28.62/18.83 inference(modus_ponens,[status(thm)],[14553, 78])).
% 28.62/18.83 tff(14557,plain,
% 28.62/18.83 ((~(f6(c2, c2) = c2)) <=> (~(f6(f7(c2), f5(c1)) = c4))),
% 28.62/18.83 inference(monotonicity,[status(thm)],[14507])).
% 28.62/18.83 tff(14558,plain,
% 28.62/18.83 (~(f6(f7(c2), f5(c1)) = c4)),
% 28.62/18.83 inference(modus_ponens,[status(thm)],[14515, 14557])).
% 28.62/18.83 tff(14559,plain,
% 28.62/18.83 (big_f(f3(f6(f7(c2), f5(c1)), c2), f6(f7(c2), f5(c1))) <=> big_f(f3(c1, c2), c1)),
% 28.62/18.83 inference(monotonicity,[status(thm)],[14280, 14279])).
% 28.62/18.83 tff(14560,plain,
% 28.62/18.83 (big_f(f3(c1, c2), c1) <=> big_f(f3(f6(f7(c2), f5(c1)), c2), f6(f7(c2), f5(c1)))),
% 28.62/18.83 inference(symmetry,[status(thm)],[14559])).
% 28.62/18.83 tff(14561,plain,
% 28.62/18.83 (c1 = f6(c2, c2)),
% 28.62/18.83 inference(transitivity,[status(thm)],[14103, 14284])).
% 28.62/18.83 tff(14562,plain,
% 28.62/18.83 (f3(c1, c2) = f7(c2)),
% 28.62/18.83 inference(transitivity,[status(thm)],[14554, 14275])).
% 28.62/18.83 tff(14563,plain,
% 28.62/18.83 (big_f(f3(c1, c2), c1) <=> big_f(f7(c2), f6(c2, c2))),
% 28.62/18.83 inference(monotonicity,[status(thm)],[14562, 14561])).
% 28.62/18.83 tff(14564,plain,
% 28.62/18.83 (big_f(f7(c2), f6(c2, c2)) <=> big_f(f3(c1, c2), c1)),
% 28.62/18.83 inference(symmetry,[status(thm)],[14563])).
% 28.62/18.83 tff(14565,plain,
% 28.62/18.83 (big_f(f7(c2), f6(c2, c2)) <=> big_f(f3(f6(f7(c2), f5(c1)), c2), f6(f7(c2), f5(c1)))),
% 28.62/18.83 inference(transitivity,[status(thm)],[14564, 14560])).
% 28.62/18.83 tff(14566,plain,
% 28.62/18.83 (big_f(f3(f6(f7(c2), f5(c1)), c2), f6(f7(c2), f5(c1)))),
% 28.62/18.83 inference(modus_ponens,[status(thm)],[14523, 14565])).
% 28.62/18.83 tff(14567,plain,
% 28.62/18.83 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (~big_f(f3(f6(f7(c2), f5(c1)), c2), f6(f7(c2), f5(c1)))) | (~(f3(f6(f7(c2), f5(c1)), c2) = c2)) | (f6(f7(c2), f5(c1)) = c4))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (~big_f(f3(f6(f7(c2), f5(c1)), c2), f6(f7(c2), f5(c1)))) | (~(f3(f6(f7(c2), f5(c1)), c2) = c2)) | (f6(f7(c2), f5(c1)) = c4))),
% 28.62/18.83 inference(rewrite,[status(thm)],[])).
% 28.62/18.83 tff(14568,plain,
% 28.62/18.83 (((~(c2 = c3)) | (f6(f7(c2), f5(c1)) = c4) | (~(f3(f6(f7(c2), f5(c1)), c2) = c2)) | (~big_f(f3(f6(f7(c2), f5(c1)), c2), f6(f7(c2), f5(c1)))) | (c2 = f2(c2)) | (~big_f(c2, c2))) <=> ((~(c2 = c3)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (~big_f(f3(f6(f7(c2), f5(c1)), c2), f6(f7(c2), f5(c1)))) | (~(f3(f6(f7(c2), f5(c1)), c2) = c2)) | (f6(f7(c2), f5(c1)) = c4))),
% 28.62/18.83 inference(rewrite,[status(thm)],[])).
% 28.62/18.83 tff(14569,plain,
% 28.62/18.83 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f6(f7(c2), f5(c1)) = c4) | (~(f3(f6(f7(c2), f5(c1)), c2) = c2)) | (~big_f(f3(f6(f7(c2), f5(c1)), c2), f6(f7(c2), f5(c1)))) | (c2 = f2(c2)) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (~big_f(f3(f6(f7(c2), f5(c1)), c2), f6(f7(c2), f5(c1)))) | (~(f3(f6(f7(c2), f5(c1)), c2) = c2)) | (f6(f7(c2), f5(c1)) = c4)))),
% 28.62/18.83 inference(monotonicity,[status(thm)],[14568])).
% 28.62/18.83 tff(14570,plain,
% 28.62/18.83 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f6(f7(c2), f5(c1)) = c4) | (~(f3(f6(f7(c2), f5(c1)), c2) = c2)) | (~big_f(f3(f6(f7(c2), f5(c1)), c2), f6(f7(c2), f5(c1)))) | (c2 = f2(c2)) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (~big_f(f3(f6(f7(c2), f5(c1)), c2), f6(f7(c2), f5(c1)))) | (~(f3(f6(f7(c2), f5(c1)), c2) = c2)) | (f6(f7(c2), f5(c1)) = c4))),
% 28.62/18.83 inference(transitivity,[status(thm)],[14569, 14567])).
% 28.62/18.83 tff(14571,plain,
% 28.62/18.83 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f6(f7(c2), f5(c1)) = c4) | (~(f3(f6(f7(c2), f5(c1)), c2) = c2)) | (~big_f(f3(f6(f7(c2), f5(c1)), c2), f6(f7(c2), f5(c1)))) | (c2 = f2(c2)) | (~big_f(c2, c2)))),
% 28.62/18.83 inference(quant_inst,[status(thm)],[])).
% 28.62/18.83 tff(14572,plain,
% 28.62/18.83 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (~big_f(f3(f6(f7(c2), f5(c1)), c2), f6(f7(c2), f5(c1)))) | (~(f3(f6(f7(c2), f5(c1)), c2) = c2)) | (f6(f7(c2), f5(c1)) = c4)),
% 28.62/18.83 inference(modus_ponens,[status(thm)],[14571, 14570])).
% 28.62/18.83 tff(14573,plain,
% 28.62/18.83 ((~(c2 = c3)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (~big_f(f3(f6(f7(c2), f5(c1)), c2), f6(f7(c2), f5(c1)))) | (~(f3(f6(f7(c2), f5(c1)), c2) = c2)) | (f6(f7(c2), f5(c1)) = c4)),
% 28.62/18.83 inference(unit_resolution,[status(thm)],[14572, 7051])).
% 28.62/18.83 tff(14574,plain,
% 28.62/18.83 (c2 = f2(c2)),
% 28.62/18.83 inference(unit_resolution,[status(thm)],[14573, 14566, 1345, 14558, 14556, 14555])).
% 28.62/18.83 tff(14575,plain,
% 28.62/18.83 (f2(c2) = c2),
% 28.62/18.83 inference(symmetry,[status(thm)],[14574])).
% 28.62/18.83 tff(14576,plain,
% 28.62/18.83 (big_f(c2, c1) <=> big_f(f7(c2), f6(c2, f4(c4)))),
% 28.62/18.83 inference(transitivity,[status(thm)],[14522, 14135])).
% 28.62/18.83 tff(14577,plain,
% 28.62/18.83 (big_f(f7(c2), f6(c2, f4(c4)))),
% 28.62/18.83 inference(modus_ponens,[status(thm)],[348, 14576])).
% 28.62/18.83 tff(14578,plain,
% 28.62/18.83 (big_f(c2, f6(f7(c2), c3)) <=> big_f(f7(c2), f6(c2, c2))),
% 28.62/18.83 inference(monotonicity,[status(thm)],[82, 2361])).
% 28.62/18.83 tff(14579,plain,
% 28.62/18.83 (big_f(c2, f6(f7(c2), c3)) <=> big_f(f7(c2), f6(c2, f4(c4)))),
% 28.62/18.83 inference(transitivity,[status(thm)],[14578, 14135])).
% 28.62/18.83 tff(14580,plain,
% 28.62/18.83 ((~big_f(c2, f6(f7(c2), c3))) <=> (~big_f(f7(c2), f6(c2, f4(c4))))),
% 28.62/18.83 inference(monotonicity,[status(thm)],[14579])).
% 28.62/18.83 tff(14581,assumption,(~big_f(c2, f6(f7(c2), c3))), introduced(assumption)).
% 28.62/18.83 tff(14582,plain,
% 28.62/18.83 (~big_f(f7(c2), f6(c2, f4(c4)))),
% 28.62/18.83 inference(modus_ponens,[status(thm)],[14581, 14580])).
% 28.62/18.83 tff(14583,assumption,(big_f(f7(c2), f6(c2, f4(c4)))), introduced(assumption)).
% 28.62/18.83 tff(14584,plain,
% 28.62/18.83 ($false),
% 28.62/18.83 inference(unit_resolution,[status(thm)],[14583, 14582])).
% 28.62/18.83 tff(14585,plain,(big_f(c2, f6(f7(c2), c3)) | (~big_f(f7(c2), f6(c2, f4(c4)))) | (~(f4(c4) = c2)) | (~(c3 = c2)) | (~(f7(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.62/18.83 tff(14586,plain,
% 28.62/18.83 (big_f(c2, f6(f7(c2), c3))),
% 28.62/18.83 inference(unit_resolution,[status(thm)],[14585, 14553, 79, 14274, 14577])).
% 28.62/18.83 tff(14587,plain,
% 28.62/18.83 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f6(f7(c2), c3) = f2(c2)) | (~big_f(c2, f6(f7(c2), c3))) | (~big_f(f3(f6(f7(c2), f5(c1)), c2), f6(f7(c2), f5(c1)))) | (~(f3(f6(f7(c2), f5(c1)), c2) = c2)) | (f6(f7(c2), f5(c1)) = c4))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (f6(f7(c2), c3) = f2(c2)) | (~big_f(c2, f6(f7(c2), c3))) | (~big_f(f3(f6(f7(c2), f5(c1)), c2), f6(f7(c2), f5(c1)))) | (~(f3(f6(f7(c2), f5(c1)), c2) = c2)) | (f6(f7(c2), f5(c1)) = c4))),
% 28.62/18.83 inference(rewrite,[status(thm)],[])).
% 28.62/18.83 tff(14588,plain,
% 28.62/18.83 (((~(c2 = c3)) | (f6(f7(c2), f5(c1)) = c4) | (~(f3(f6(f7(c2), f5(c1)), c2) = c2)) | (~big_f(f3(f6(f7(c2), f5(c1)), c2), f6(f7(c2), f5(c1)))) | (f6(f7(c2), c3) = f2(c2)) | (~big_f(c2, f6(f7(c2), c3)))) <=> ((~(c2 = c3)) | (f6(f7(c2), c3) = f2(c2)) | (~big_f(c2, f6(f7(c2), c3))) | (~big_f(f3(f6(f7(c2), f5(c1)), c2), f6(f7(c2), f5(c1)))) | (~(f3(f6(f7(c2), f5(c1)), c2) = c2)) | (f6(f7(c2), f5(c1)) = c4))),
% 28.62/18.83 inference(rewrite,[status(thm)],[])).
% 28.62/18.83 tff(14589,plain,
% 28.62/18.83 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f6(f7(c2), f5(c1)) = c4) | (~(f3(f6(f7(c2), f5(c1)), c2) = c2)) | (~big_f(f3(f6(f7(c2), f5(c1)), c2), f6(f7(c2), f5(c1)))) | (f6(f7(c2), c3) = f2(c2)) | (~big_f(c2, f6(f7(c2), c3))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f6(f7(c2), c3) = f2(c2)) | (~big_f(c2, f6(f7(c2), c3))) | (~big_f(f3(f6(f7(c2), f5(c1)), c2), f6(f7(c2), f5(c1)))) | (~(f3(f6(f7(c2), f5(c1)), c2) = c2)) | (f6(f7(c2), f5(c1)) = c4)))),
% 28.62/18.83 inference(monotonicity,[status(thm)],[14588])).
% 28.62/18.83 tff(14590,plain,
% 28.62/18.83 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f6(f7(c2), f5(c1)) = c4) | (~(f3(f6(f7(c2), f5(c1)), c2) = c2)) | (~big_f(f3(f6(f7(c2), f5(c1)), c2), f6(f7(c2), f5(c1)))) | (f6(f7(c2), c3) = f2(c2)) | (~big_f(c2, f6(f7(c2), c3))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (f6(f7(c2), c3) = f2(c2)) | (~big_f(c2, f6(f7(c2), c3))) | (~big_f(f3(f6(f7(c2), f5(c1)), c2), f6(f7(c2), f5(c1)))) | (~(f3(f6(f7(c2), f5(c1)), c2) = c2)) | (f6(f7(c2), f5(c1)) = c4))),
% 28.62/18.83 inference(transitivity,[status(thm)],[14589, 14587])).
% 28.62/18.83 tff(14591,plain,
% 28.62/18.83 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f6(f7(c2), f5(c1)) = c4) | (~(f3(f6(f7(c2), f5(c1)), c2) = c2)) | (~big_f(f3(f6(f7(c2), f5(c1)), c2), f6(f7(c2), f5(c1)))) | (f6(f7(c2), c3) = f2(c2)) | (~big_f(c2, f6(f7(c2), c3))))),
% 28.62/18.83 inference(quant_inst,[status(thm)],[])).
% 28.62/18.83 tff(14592,plain,
% 28.62/18.83 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (f6(f7(c2), c3) = f2(c2)) | (~big_f(c2, f6(f7(c2), c3))) | (~big_f(f3(f6(f7(c2), f5(c1)), c2), f6(f7(c2), f5(c1)))) | (~(f3(f6(f7(c2), f5(c1)), c2) = c2)) | (f6(f7(c2), f5(c1)) = c4)),
% 28.62/18.83 inference(modus_ponens,[status(thm)],[14591, 14590])).
% 28.62/18.83 tff(14593,plain,
% 28.62/18.83 ((~(c2 = c3)) | (f6(f7(c2), c3) = f2(c2)) | (~big_f(c2, f6(f7(c2), c3))) | (~big_f(f3(f6(f7(c2), f5(c1)), c2), f6(f7(c2), f5(c1)))) | (~(f3(f6(f7(c2), f5(c1)), c2) = c2)) | (f6(f7(c2), f5(c1)) = c4)),
% 28.62/18.83 inference(unit_resolution,[status(thm)],[14592, 7051])).
% 28.62/18.83 tff(14594,plain,
% 28.62/18.83 (f6(f7(c2), c3) = f2(c2)),
% 28.62/18.83 inference(unit_resolution,[status(thm)],[14593, 14566, 14556, 14558, 14555, 14586])).
% 28.62/18.83 tff(14595,plain,
% 28.62/18.83 (~(f6(f7(c2), c3) = c2)),
% 28.62/18.83 inference(unit_resolution,[status(thm)],[2716, 14553, 14274, 14515])).
% 28.62/18.83 tff(14596,plain,
% 28.62/18.83 (f6(f7(c2), c3) = c1),
% 28.62/18.83 inference(unit_resolution,[status(thm)],[2391, 14595])).
% 28.62/18.83 tff(14597,plain,
% 28.62/18.83 (c1 = f6(f7(c2), c3)),
% 28.62/18.83 inference(symmetry,[status(thm)],[14596])).
% 28.62/18.83 tff(14598,plain,
% 28.62/18.83 (f6(c2, c2) = c2),
% 28.62/18.83 inference(transitivity,[status(thm)],[14277, 6634, 14597, 14594, 14575])).
% 28.62/18.83 tff(14599,plain,
% 28.62/18.83 ($false),
% 28.62/18.83 inference(unit_resolution,[status(thm)],[14515, 14598])).
% 28.62/18.83 tff(14600,plain,(big_f(c1, c2) | (~(f6(c2, f7(f4(c4))) = c1)) | (~(f4(c4) = c2)) | (~big_f(c2, c2)) | (~(f5(c1) = c2)) | big_f(c1, c1) | (~big_f(c2, c1)) | (~(c2 = f8(c1))) | (~(f10(c1) = c2)) | (f7(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 28.62/18.83 tff(14601,plain,
% 28.62/18.83 (big_f(c1, c2)),
% 28.62/18.83 inference(unit_resolution,[status(thm)],[14600, 14203, 79, 6634, 14104, 66, 14201, 14211, 15, 115])).
% 28.62/18.83 tff(14602,plain,
% 28.62/18.83 (big_f(c1, f10(c1))),
% 28.62/18.83 inference(modus_ponens,[status(thm)],[14601, 3350])).
% 28.62/18.83 tff(14603,plain,
% 28.62/18.83 (f8(c1) = c2),
% 28.62/18.83 inference(symmetry,[status(thm)],[14211])).
% 28.62/18.83 tff(14604,plain,
% 28.62/18.83 ((f8(c1) = c1) <=> (c2 = c1)),
% 28.62/18.83 inference(monotonicity,[status(thm)],[14603])).
% 28.62/18.83 tff(14605,plain,
% 28.62/18.83 ((c2 = c1) <=> (f8(c1) = c1)),
% 28.62/18.83 inference(symmetry,[status(thm)],[14604])).
% 28.62/18.83 tff(14606,plain,
% 28.62/18.83 ((c2 = c1) <=> (c1 = f8(c1))),
% 28.62/18.83 inference(transitivity,[status(thm)],[14605, 3028])).
% 28.62/18.83 tff(14607,plain,
% 28.62/18.83 ((~(c2 = c1)) <=> (~(c1 = f8(c1)))),
% 28.62/18.83 inference(monotonicity,[status(thm)],[14606])).
% 28.62/18.83 tff(14608,plain,
% 28.62/18.83 (~(c1 = f8(c1))),
% 28.62/18.83 inference(modus_ponens,[status(thm)],[75, 14607])).
% 28.62/18.83 tff(14609,plain,
% 28.62/18.83 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(c1) = c1) | (f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c1) = c1) | (f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)))),
% 28.62/18.83 inference(rewrite,[status(thm)],[])).
% 28.62/18.83 tff(14610,plain,
% 28.62/18.83 (((f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (f7(c1) = c1) | (c1 = f5(c1)) | (~big_f(f7(c1), c1))) <=> ((f7(c1) = c1) | (f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)))),
% 28.62/18.83 inference(rewrite,[status(thm)],[])).
% 28.62/18.83 tff(14611,plain,
% 28.62/18.83 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (f7(c1) = c1) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(c1) = c1) | (f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (c1 = f5(c1)) | (~big_f(f7(c1), c1))))),
% 28.62/18.83 inference(monotonicity,[status(thm)],[14610])).
% 28.62/18.83 tff(14612,plain,
% 28.62/18.83 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (f7(c1) = c1) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c1) = c1) | (f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)))),
% 28.62/18.83 inference(transitivity,[status(thm)],[14611, 14609])).
% 28.62/18.83 tff(14613,plain,
% 28.62/18.83 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (f7(c1) = c1) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)))),
% 28.62/18.83 inference(quant_inst,[status(thm)],[])).
% 28.62/18.83 tff(14614,plain,
% 28.62/18.83 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c1) = c1) | (f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (c1 = f5(c1)) | (~big_f(f7(c1), c1))),
% 28.62/18.83 inference(modus_ponens,[status(thm)],[14613, 14612])).
% 28.62/18.83 tff(14615,plain,
% 28.62/18.83 ($false),
% 28.62/18.83 inference(unit_resolution,[status(thm)],[14614, 1659, 115, 3, 14608, 14602, 14202, 14091])).
% 28.62/18.83 tff(14616,plain,(big_f(c1, c1) | (f7(c1) = c1) | (f10(c1) = c1) | (~(f4(c4) = c2)) | (~(f6(c2, f7(f4(c4))) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.62/18.83 tff(14617,plain,
% 28.62/18.83 (big_f(c1, c1)),
% 28.62/18.83 inference(unit_resolution,[status(thm)],[14616, 6634, 3, 79, 115])).
% 28.62/18.83 tff(14618,plain,
% 28.62/18.83 (big_f(c2, c1)),
% 28.62/18.83 inference(unit_resolution,[status(thm)],[11990, 121, 14617, 115, 79, 3])).
% 28.62/18.83 tff(14619,plain,
% 28.62/18.83 (f7(c2) = c2),
% 28.62/18.83 inference(unit_resolution,[status(thm)],[12370, 67, 115, 79, 121, 3, 14617])).
% 28.62/18.83 tff(14620,plain,
% 28.62/18.83 (big_f(f7(c2), f6(c2, f10(c2))) <=> big_f(c2, f6(c2, c1))),
% 28.62/18.83 inference(monotonicity,[status(thm)],[14619, 13791])).
% 28.62/18.83 tff(14621,plain,
% 28.62/18.83 ((f6(c2, f10(c2)) = f10(c2)) <=> (f6(c2, c1) = c1)),
% 28.62/18.83 inference(monotonicity,[status(thm)],[13791, 11799])).
% 28.62/18.83 tff(14622,plain,
% 28.62/18.83 ((f6(c2, c1) = c1) <=> (f6(c2, f10(c2)) = f10(c2))),
% 28.62/18.83 inference(symmetry,[status(thm)],[14621])).
% 28.62/18.83 tff(14623,plain,
% 28.62/18.83 ((~(f6(c2, c1) = c1)) <=> (~(f6(c2, f10(c2)) = f10(c2)))),
% 28.62/18.83 inference(monotonicity,[status(thm)],[14622])).
% 28.62/18.83 tff(14624,plain,
% 28.62/18.83 ((c1 = f6(c2, c1)) <=> (f6(c2, c1) = c1)),
% 28.62/18.83 inference(commutativity,[status(thm)],[])).
% 28.62/18.83 tff(14625,plain,
% 28.62/18.83 (big_f(f10(c2), f10(c2))),
% 28.62/18.83 inference(modus_ponens,[status(thm)],[14617, 11978])).
% 28.62/18.83 tff(14626,plain,
% 28.62/18.83 (~(f2(c3) = c2)),
% 28.62/18.83 inference(unit_resolution,[status(thm)],[11686, 67, 14617, 121, 79, 14618])).
% 28.62/18.83 tff(14627,plain,
% 28.62/18.83 (f2(c3) = c1),
% 28.62/18.83 inference(unit_resolution,[status(thm)],[1273, 14626])).
% 28.62/18.83 tff(14628,plain,
% 28.62/18.83 (big_f(c2, f10(c2))),
% 28.62/18.83 inference(modus_ponens,[status(thm)],[14618, 12004])).
% 28.62/18.83 tff(14629,assumption,(f6(c2, f6(c2, c1)) = c2), introduced(assumption)).
% 28.62/18.83 tff(14630,plain,
% 28.62/18.83 (big_f(f7(c2), f6(c2, f6(c2, c1))) <=> big_f(c2, f6(c2, f6(c2, c1)))),
% 28.62/18.83 inference(monotonicity,[status(thm)],[77])).
% 28.62/18.83 tff(14631,plain,
% 28.62/18.83 (big_f(c2, f6(c2, f6(c2, c1))) <=> big_f(f7(c2), f6(c2, f6(c2, c1)))),
% 28.62/18.83 inference(symmetry,[status(thm)],[14630])).
% 28.62/18.83 tff(14632,plain,
% 28.62/18.83 (big_f(c2, f6(c2, f6(c2, c1))) <=> big_f(c2, c2)),
% 28.62/18.83 inference(monotonicity,[status(thm)],[14629])).
% 28.62/18.83 tff(14633,plain,
% 28.62/18.83 (big_f(c2, c2) <=> big_f(c2, f6(c2, f6(c2, c1)))),
% 28.62/18.83 inference(symmetry,[status(thm)],[14632])).
% 28.62/18.83 tff(14634,plain,
% 28.62/18.83 (big_f(c2, c2) <=> big_f(f7(c2), f6(c2, f6(c2, c1)))),
% 28.62/18.83 inference(transitivity,[status(thm)],[14633, 14631])).
% 28.62/18.83 tff(14635,plain,
% 28.62/18.83 ((~big_f(c2, c2)) <=> (~big_f(f7(c2), f6(c2, f6(c2, c1))))),
% 28.62/18.83 inference(monotonicity,[status(thm)],[14634])).
% 28.62/18.83 tff(14636,plain,
% 28.62/18.84 (~big_f(f7(c2), f6(c2, f6(c2, c1)))),
% 28.62/18.84 inference(modus_ponens,[status(thm)],[121, 14635])).
% 28.62/18.84 tff(14637,plain,
% 28.62/18.84 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (~(f7(c2) = c2)) | (c2 = f8(c2)) | big_f(f7(c2), f6(c2, f6(c2, c1))) | (f6(c2, f6(c2, c1)) = f6(c2, c1)) | (~big_f(c2, f10(c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (c2 = f8(c2)) | big_f(f7(c2), f6(c2, f6(c2, c1))) | (f6(c2, f6(c2, c1)) = f6(c2, c1)) | (~big_f(c2, f10(c2))))),
% 28.62/18.84 inference(rewrite,[status(thm)],[])).
% 28.62/18.84 tff(14638,plain,
% 28.62/18.84 (((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c2) = c2)) | (f6(c2, f6(c2, c1)) = f6(c2, c1)) | big_f(f7(c2), f6(c2, f6(c2, c1)))) <=> ((f10(c2) = c2) | (~(f7(c2) = c2)) | (c2 = f8(c2)) | big_f(f7(c2), f6(c2, f6(c2, c1))) | (f6(c2, f6(c2, c1)) = f6(c2, c1)) | (~big_f(c2, f10(c2))))),
% 28.62/18.84 inference(rewrite,[status(thm)],[])).
% 28.62/18.84 tff(14639,plain,
% 28.62/18.84 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c2) = c2)) | (f6(c2, f6(c2, c1)) = f6(c2, c1)) | big_f(f7(c2), f6(c2, f6(c2, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (~(f7(c2) = c2)) | (c2 = f8(c2)) | big_f(f7(c2), f6(c2, f6(c2, c1))) | (f6(c2, f6(c2, c1)) = f6(c2, c1)) | (~big_f(c2, f10(c2)))))),
% 28.62/18.84 inference(monotonicity,[status(thm)],[14638])).
% 28.62/18.84 tff(14640,plain,
% 28.62/18.84 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c2) = c2)) | (f6(c2, f6(c2, c1)) = f6(c2, c1)) | big_f(f7(c2), f6(c2, f6(c2, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (c2 = f8(c2)) | big_f(f7(c2), f6(c2, f6(c2, c1))) | (f6(c2, f6(c2, c1)) = f6(c2, c1)) | (~big_f(c2, f10(c2))))),
% 28.62/18.84 inference(transitivity,[status(thm)],[14639, 14637])).
% 28.62/18.84 tff(14641,plain,
% 28.62/18.84 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c2) = c2)) | (f6(c2, f6(c2, c1)) = f6(c2, c1)) | big_f(f7(c2), f6(c2, f6(c2, c1))))),
% 28.62/18.84 inference(quant_inst,[status(thm)],[])).
% 28.62/18.84 tff(14642,plain,
% 28.62/18.84 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (c2 = f8(c2)) | big_f(f7(c2), f6(c2, f6(c2, c1))) | (f6(c2, f6(c2, c1)) = f6(c2, c1)) | (~big_f(c2, f10(c2)))),
% 28.62/18.84 inference(modus_ponens,[status(thm)],[14641, 14640])).
% 28.62/18.84 tff(14643,plain,
% 28.62/18.84 (big_f(f7(c2), f6(c2, f6(c2, c1))) | (f6(c2, f6(c2, c1)) = f6(c2, c1))),
% 28.62/18.84 inference(unit_resolution,[status(thm)],[14642, 2662, 89, 77, 12291, 12290])).
% 28.62/18.84 tff(14644,plain,
% 28.62/18.84 (f6(c2, f6(c2, c1)) = f6(c2, c1)),
% 28.62/18.84 inference(unit_resolution,[status(thm)],[14643, 14636])).
% 28.62/18.84 tff(14645,plain,
% 28.62/18.84 (c2 = f6(c2, f6(c2, c1))),
% 28.62/18.84 inference(symmetry,[status(thm)],[14629])).
% 28.62/18.84 tff(14646,plain,
% 28.62/18.84 (c2 = f6(c2, c1)),
% 28.62/18.84 inference(transitivity,[status(thm)],[14645, 14644])).
% 28.62/18.84 tff(14647,plain,
% 28.62/18.84 (f6(c2, c2) = f6(c2, f6(c2, c1))),
% 28.62/18.84 inference(monotonicity,[status(thm)],[14646])).
% 28.62/18.84 tff(14648,plain,
% 28.62/18.84 (f10(c2) = c2),
% 28.62/18.84 inference(transitivity,[status(thm)],[94, 14103, 2475, 14647, 14629])).
% 28.62/18.84 tff(14649,plain,
% 28.62/18.84 ($false),
% 28.62/18.84 inference(unit_resolution,[status(thm)],[89, 14648])).
% 28.62/18.84 tff(14650,plain,((~(f6(c2, f6(c2, c1)) = c2)) | (f10(c2) = c2) | (~(f6(c2, f7(f4(c4))) = c1)) | (~(f7(c2) = c2)) | (~(f4(c4) = c2)) | (~big_f(c2, f10(c2))) | (c2 = f8(c2)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 28.62/18.84 tff(14651,plain,
% 28.62/18.84 (~(f6(c2, f6(c2, c1)) = c2)),
% 28.62/18.84 inference(unit_resolution,[status(thm)],[14650, 12290, 6634, 77, 79, 12291, 89, 121])).
% 28.62/18.84 tff(14652,plain,
% 28.62/18.84 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f6(c2, f6(c2, c1)) = c1) | (f6(c2, f6(c2, c1)) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f6(c2, f6(c2, c1)) = c1) | (f6(c2, f6(c2, c1)) = c2))),
% 28.62/18.84 inference(rewrite,[status(thm)],[])).
% 28.62/18.84 tff(14653,plain,
% 28.62/18.84 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f6(c2, f6(c2, c1)) = c1) | (f6(c2, f6(c2, c1)) = c2))),
% 28.62/18.84 inference(quant_inst,[status(thm)],[])).
% 28.62/18.84 tff(14654,plain,
% 28.62/18.84 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f6(c2, f6(c2, c1)) = c1) | (f6(c2, f6(c2, c1)) = c2)),
% 28.62/18.84 inference(modus_ponens,[status(thm)],[14653, 14652])).
% 28.62/18.84 tff(14655,plain,
% 28.62/18.84 ((f6(c2, f6(c2, c1)) = c1) | (f6(c2, f6(c2, c1)) = c2)),
% 28.62/18.84 inference(unit_resolution,[status(thm)],[14654, 10])).
% 28.62/18.84 tff(14656,plain,
% 28.62/18.84 (f6(c2, f6(c2, c1)) = c1),
% 28.62/18.84 inference(unit_resolution,[status(thm)],[14655, 14651])).
% 28.62/18.84 tff(14657,plain,
% 28.62/18.84 ((f6(c2, f6(c2, c1)) = f6(c2, c1)) <=> (c1 = f6(c2, c1))),
% 28.62/18.84 inference(monotonicity,[status(thm)],[14656])).
% 28.62/18.84 tff(14658,plain,
% 28.62/18.84 ((f6(c2, f6(c2, c1)) = f6(c2, c1)) <=> (f6(c2, c1) = c1)),
% 28.62/18.84 inference(transitivity,[status(thm)],[14657, 14624])).
% 28.62/18.84 tff(14659,plain,
% 28.62/18.84 ((~(f6(c2, f6(c2, c1)) = f6(c2, c1))) <=> (~(f6(c2, c1) = c1))),
% 28.62/18.84 inference(monotonicity,[status(thm)],[14658])).
% 28.62/18.84 tff(14660,plain,
% 28.62/18.84 (f6(c2, f6(c2, c1)) = f10(c2)),
% 28.62/18.84 inference(transitivity,[status(thm)],[14656, 99])).
% 28.62/18.84 tff(14661,plain,
% 28.62/18.84 (big_f(c2, f6(c2, f6(c2, c1))) <=> big_f(c2, f10(c2))),
% 28.62/18.84 inference(monotonicity,[status(thm)],[14660])).
% 28.62/18.84 tff(14662,plain,
% 28.62/18.84 (big_f(c2, f10(c2)) <=> big_f(c2, f6(c2, f6(c2, c1)))),
% 28.62/18.84 inference(symmetry,[status(thm)],[14661])).
% 28.62/18.84 tff(14663,plain,
% 28.62/18.84 (big_f(c2, f10(c2)) <=> big_f(f7(c2), f6(c2, f6(c2, c1)))),
% 28.62/18.84 inference(transitivity,[status(thm)],[14662, 14631])).
% 28.62/18.84 tff(14664,plain,
% 28.62/18.84 (big_f(f7(c2), f6(c2, f6(c2, c1)))),
% 28.62/18.84 inference(modus_ponens,[status(thm)],[12291, 14663])).
% 28.62/18.84 tff(14665,plain,
% 28.62/18.84 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (~(f7(c2) = c2)) | (c2 = f8(c2)) | (~big_f(f7(c2), f6(c2, f6(c2, c1)))) | (~big_f(c2, f10(c2))) | (~(f6(c2, f6(c2, c1)) = f6(c2, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (c2 = f8(c2)) | (~big_f(f7(c2), f6(c2, f6(c2, c1)))) | (~big_f(c2, f10(c2))) | (~(f6(c2, f6(c2, c1)) = f6(c2, c1))))),
% 28.62/18.84 inference(rewrite,[status(thm)],[])).
% 28.62/18.84 tff(14666,plain,
% 28.62/18.84 (((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c2) = c2)) | (~(f6(c2, f6(c2, c1)) = f6(c2, c1))) | (~big_f(f7(c2), f6(c2, f6(c2, c1))))) <=> ((f10(c2) = c2) | (~(f7(c2) = c2)) | (c2 = f8(c2)) | (~big_f(f7(c2), f6(c2, f6(c2, c1)))) | (~big_f(c2, f10(c2))) | (~(f6(c2, f6(c2, c1)) = f6(c2, c1))))),
% 28.62/18.84 inference(rewrite,[status(thm)],[])).
% 28.62/18.84 tff(14667,plain,
% 28.62/18.84 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c2) = c2)) | (~(f6(c2, f6(c2, c1)) = f6(c2, c1))) | (~big_f(f7(c2), f6(c2, f6(c2, c1)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (~(f7(c2) = c2)) | (c2 = f8(c2)) | (~big_f(f7(c2), f6(c2, f6(c2, c1)))) | (~big_f(c2, f10(c2))) | (~(f6(c2, f6(c2, c1)) = f6(c2, c1)))))),
% 28.62/18.84 inference(monotonicity,[status(thm)],[14666])).
% 28.62/18.84 tff(14668,plain,
% 28.62/18.84 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c2) = c2)) | (~(f6(c2, f6(c2, c1)) = f6(c2, c1))) | (~big_f(f7(c2), f6(c2, f6(c2, c1)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (c2 = f8(c2)) | (~big_f(f7(c2), f6(c2, f6(c2, c1)))) | (~big_f(c2, f10(c2))) | (~(f6(c2, f6(c2, c1)) = f6(c2, c1))))),
% 28.62/18.84 inference(transitivity,[status(thm)],[14667, 14665])).
% 28.62/18.84 tff(14669,plain,
% 28.62/18.84 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c2) = c2)) | (~(f6(c2, f6(c2, c1)) = f6(c2, c1))) | (~big_f(f7(c2), f6(c2, f6(c2, c1)))))),
% 28.62/18.84 inference(quant_inst,[status(thm)],[])).
% 28.62/18.84 tff(14670,plain,
% 28.62/18.84 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (c2 = f8(c2)) | (~big_f(f7(c2), f6(c2, f6(c2, c1)))) | (~big_f(c2, f10(c2))) | (~(f6(c2, f6(c2, c1)) = f6(c2, c1)))),
% 28.62/18.84 inference(modus_ponens,[status(thm)],[14669, 14668])).
% 28.62/18.84 tff(14671,plain,
% 28.62/18.84 (~(f6(c2, f6(c2, c1)) = f6(c2, c1))),
% 28.62/18.84 inference(unit_resolution,[status(thm)],[14670, 2730, 89, 77, 12291, 12290, 14664])).
% 28.62/18.84 tff(14672,plain,
% 28.62/18.84 (~(f6(c2, c1) = c1)),
% 28.62/18.84 inference(modus_ponens,[status(thm)],[14671, 14659])).
% 28.62/18.84 tff(14673,plain,
% 28.62/18.84 (~(f6(c2, f10(c2)) = f10(c2))),
% 28.62/18.84 inference(modus_ponens,[status(thm)],[14672, 13715])).
% 28.62/18.84 tff(14674,plain,
% 28.62/18.84 (big_f(f7(c2), f6(c2, f10(c2)))),
% 28.62/18.84 inference(unit_resolution,[status(thm)],[13781, 14673])).
% 28.62/18.84 tff(14675,plain,
% 28.62/18.84 (big_f(c2, f6(c2, c1))),
% 28.62/18.84 inference(modus_ponens,[status(thm)],[14674, 13712])).
% 28.62/18.84 tff(14676,plain,
% 28.62/18.84 (~big_f(c2, f6(c2, c1))),
% 28.62/18.84 inference(unit_resolution,[status(thm)],[11730, 14672, 79, 4932, 121, 67, 1247])).
% 28.62/18.84 tff(14677,plain,
% 28.62/18.84 ($false),
% 28.62/18.84 inference(unit_resolution,[status(thm)],[14676, 14675])).
% 28.62/18.84 tff(14678,plain,((c2 = f8(c2)) | (~(f7(c2) = c2)) | (f10(c2) = c2) | (~big_f(c2, f10(c2))) | (~(f4(c4) = c2)) | (~big_f(c1, c1)) | big_f(c2, c2) | (~(c3 = c2)) | (~(f2(c3) = c1)) | (~(f6(c2, f7(f4(c4))) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.62/18.84 tff(14679,plain,
% 28.62/18.84 (c2 = f8(c2)),
% 28.62/18.84 inference(unit_resolution,[status(thm)],[14678, 14619, 11798, 14628, 79, 14617, 121, 67, 14627, 6634])).
% 28.62/18.84 tff(14680,plain,
% 28.62/18.84 (f8(c2) = c2),
% 28.62/18.84 inference(symmetry,[status(thm)],[14679])).
% 28.62/18.84 tff(14681,plain,
% 28.62/18.84 ((c1 = f8(c2)) <=> (f10(c2) = c2)),
% 28.62/18.84 inference(monotonicity,[status(thm)],[11957, 14680])).
% 28.62/18.84 tff(14682,plain,
% 28.62/18.84 ((f10(c2) = c2) <=> (c1 = f8(c2))),
% 28.62/18.84 inference(symmetry,[status(thm)],[14681])).
% 28.62/18.84 tff(14683,plain,
% 28.62/18.84 ((f10(c2) = c2) <=> (f10(c2) = f8(c2))),
% 28.62/18.84 inference(transitivity,[status(thm)],[14682, 11993])).
% 28.62/18.84 tff(14684,plain,
% 28.62/18.84 ((~(f10(c2) = c2)) <=> (~(f10(c2) = f8(c2)))),
% 28.62/18.84 inference(monotonicity,[status(thm)],[14683])).
% 28.62/18.84 tff(14685,plain,
% 28.62/18.84 (~(f10(c2) = f8(c2))),
% 28.62/18.84 inference(modus_ponens,[status(thm)],[11798, 14684])).
% 28.62/18.84 tff(14686,assumption,(big_f(f10(c2), f10(c2))), introduced(assumption)).
% 28.62/18.84 tff(14687,plain,
% 28.62/18.84 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (~(f7(c2) = c2)) | big_f(f7(c2), f6(c2, f6(c2, c1))) | (f6(c2, f6(c2, c1)) = f6(c2, c1)) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | big_f(f7(c2), f6(c2, f6(c2, c1))) | (f6(c2, f6(c2, c1)) = f6(c2, c1)) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))))),
% 28.62/18.84 inference(rewrite,[status(thm)],[])).
% 28.62/18.84 tff(14688,plain,
% 28.62/18.84 (((f10(c2) = c2) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (~(f7(c2) = c2)) | (f6(c2, f6(c2, c1)) = f6(c2, c1)) | big_f(f7(c2), f6(c2, f6(c2, c1)))) <=> ((f10(c2) = c2) | (~(f7(c2) = c2)) | big_f(f7(c2), f6(c2, f6(c2, c1))) | (f6(c2, f6(c2, c1)) = f6(c2, c1)) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))))),
% 28.62/18.84 inference(rewrite,[status(thm)],[])).
% 28.62/18.84 tff(14689,plain,
% 28.62/18.84 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (~(f7(c2) = c2)) | (f6(c2, f6(c2, c1)) = f6(c2, c1)) | big_f(f7(c2), f6(c2, f6(c2, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (~(f7(c2) = c2)) | big_f(f7(c2), f6(c2, f6(c2, c1))) | (f6(c2, f6(c2, c1)) = f6(c2, c1)) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2)))))),
% 28.62/18.84 inference(monotonicity,[status(thm)],[14688])).
% 28.62/18.84 tff(14690,plain,
% 28.62/18.84 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (~(f7(c2) = c2)) | (f6(c2, f6(c2, c1)) = f6(c2, c1)) | big_f(f7(c2), f6(c2, f6(c2, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | big_f(f7(c2), f6(c2, f6(c2, c1))) | (f6(c2, f6(c2, c1)) = f6(c2, c1)) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))))),
% 28.62/18.84 inference(transitivity,[status(thm)],[14689, 14687])).
% 28.62/18.84 tff(14691,plain,
% 28.62/18.84 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (~(f7(c2) = c2)) | (f6(c2, f6(c2, c1)) = f6(c2, c1)) | big_f(f7(c2), f6(c2, f6(c2, c1))))),
% 28.62/18.84 inference(quant_inst,[status(thm)],[])).
% 28.62/18.84 tff(14692,plain,
% 28.62/18.84 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | big_f(f7(c2), f6(c2, f6(c2, c1))) | (f6(c2, f6(c2, c1)) = f6(c2, c1)) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2)))),
% 28.62/18.84 inference(modus_ponens,[status(thm)],[14691, 14690])).
% 28.62/18.84 tff(14693,plain,
% 28.62/18.84 (big_f(f7(c2), f6(c2, f6(c2, c1))) | (f6(c2, f6(c2, c1)) = f6(c2, c1))),
% 28.62/18.84 inference(unit_resolution,[status(thm)],[14692, 2662, 89, 77, 13710, 14686])).
% 28.62/18.84 tff(14694,plain,
% 28.62/18.84 (f6(c2, f6(c2, c1)) = f6(c2, c1)),
% 28.62/18.84 inference(unit_resolution,[status(thm)],[14693, 14636])).
% 28.62/18.84 tff(14695,plain,
% 28.62/18.84 (c2 = f6(c2, c1)),
% 28.62/18.84 inference(transitivity,[status(thm)],[14645, 14694])).
% 28.62/18.84 tff(14696,plain,
% 28.62/18.84 (f6(c2, c2) = f6(c2, f6(c2, c1))),
% 28.62/18.84 inference(monotonicity,[status(thm)],[14695])).
% 28.62/18.84 tff(14697,plain,
% 28.62/18.84 (f10(c2) = c2),
% 28.62/18.84 inference(transitivity,[status(thm)],[94, 14103, 2475, 14696, 14629])).
% 28.62/18.84 tff(14698,plain,
% 28.62/18.84 ($false),
% 28.62/18.84 inference(unit_resolution,[status(thm)],[89, 14697])).
% 28.62/18.84 tff(14699,plain,((~(f6(c2, f6(c2, c1)) = c2)) | (f10(c2) = c2) | (~(f6(c2, f7(f4(c4))) = c1)) | (~(f7(c2) = c2)) | (~(f4(c4) = c2)) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 28.62/18.84 tff(14700,plain,
% 28.62/18.84 (~(f6(c2, f6(c2, c1)) = c2)),
% 28.62/18.84 inference(unit_resolution,[status(thm)],[14699, 14619, 6634, 11798, 79, 14685, 14625, 121])).
% 28.62/18.84 tff(14701,plain,
% 28.62/18.84 (f6(c2, f6(c2, c1)) = c1),
% 28.62/18.84 inference(unit_resolution,[status(thm)],[14655, 14700])).
% 28.62/18.84 tff(14702,plain,
% 28.62/18.84 ((f6(c2, f6(c2, c1)) = f6(c2, c1)) <=> (c1 = f6(c2, c1))),
% 28.62/18.84 inference(monotonicity,[status(thm)],[14701])).
% 28.62/18.84 tff(14703,plain,
% 28.62/18.84 ((f6(c2, f6(c2, c1)) = f6(c2, c1)) <=> (f6(c2, c1) = c1)),
% 28.62/18.84 inference(transitivity,[status(thm)],[14702, 14624])).
% 28.62/18.84 tff(14704,plain,
% 28.62/18.84 ((~(f6(c2, f6(c2, c1)) = f6(c2, c1))) <=> (~(f6(c2, c1) = c1))),
% 28.62/18.84 inference(monotonicity,[status(thm)],[14703])).
% 28.62/18.84 tff(14705,plain,
% 28.62/18.84 (big_f(f7(c2), f6(c2, f6(c2, c1))) <=> big_f(c2, f6(c2, f6(c2, c1)))),
% 28.62/18.84 inference(monotonicity,[status(thm)],[14619])).
% 28.62/18.84 tff(14706,plain,
% 28.62/18.84 (big_f(c2, f6(c2, f6(c2, c1))) <=> big_f(f7(c2), f6(c2, f6(c2, c1)))),
% 28.62/18.84 inference(symmetry,[status(thm)],[14705])).
% 28.62/18.84 tff(14707,plain,
% 28.62/18.84 (f6(c2, f6(c2, c1)) = f10(c2)),
% 28.62/18.84 inference(transitivity,[status(thm)],[14701, 11957])).
% 28.62/18.84 tff(14708,plain,
% 28.62/18.84 (big_f(c2, f6(c2, f6(c2, c1))) <=> big_f(c2, f10(c2))),
% 28.62/18.84 inference(monotonicity,[status(thm)],[14707])).
% 28.62/18.84 tff(14709,plain,
% 28.62/18.84 (big_f(c2, f10(c2)) <=> big_f(c2, f6(c2, f6(c2, c1)))),
% 28.62/18.84 inference(symmetry,[status(thm)],[14708])).
% 28.62/18.84 tff(14710,plain,
% 28.62/18.84 (big_f(c2, f10(c2)) <=> big_f(f7(c2), f6(c2, f6(c2, c1)))),
% 28.62/18.84 inference(transitivity,[status(thm)],[14709, 14706])).
% 28.62/18.84 tff(14711,plain,
% 28.62/18.84 (big_f(f7(c2), f6(c2, f6(c2, c1)))),
% 28.62/18.84 inference(modus_ponens,[status(thm)],[14628, 14710])).
% 28.62/18.84 tff(14712,plain,
% 28.62/18.84 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (~(f7(c2) = c2)) | (~big_f(f7(c2), f6(c2, f6(c2, c1)))) | (~(f6(c2, f6(c2, c1)) = f6(c2, c1))) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (~big_f(f7(c2), f6(c2, f6(c2, c1)))) | (~(f6(c2, f6(c2, c1)) = f6(c2, c1))) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))))),
% 28.62/18.84 inference(rewrite,[status(thm)],[])).
% 28.62/18.84 tff(14713,plain,
% 28.62/18.84 (((f10(c2) = c2) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (~(f7(c2) = c2)) | (~(f6(c2, f6(c2, c1)) = f6(c2, c1))) | (~big_f(f7(c2), f6(c2, f6(c2, c1))))) <=> ((f10(c2) = c2) | (~(f7(c2) = c2)) | (~big_f(f7(c2), f6(c2, f6(c2, c1)))) | (~(f6(c2, f6(c2, c1)) = f6(c2, c1))) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))))),
% 28.62/18.84 inference(rewrite,[status(thm)],[])).
% 28.62/18.84 tff(14714,plain,
% 28.62/18.84 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (~(f7(c2) = c2)) | (~(f6(c2, f6(c2, c1)) = f6(c2, c1))) | (~big_f(f7(c2), f6(c2, f6(c2, c1)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (~(f7(c2) = c2)) | (~big_f(f7(c2), f6(c2, f6(c2, c1)))) | (~(f6(c2, f6(c2, c1)) = f6(c2, c1))) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2)))))),
% 28.62/18.84 inference(monotonicity,[status(thm)],[14713])).
% 28.62/18.84 tff(14715,plain,
% 28.62/18.84 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (~(f7(c2) = c2)) | (~(f6(c2, f6(c2, c1)) = f6(c2, c1))) | (~big_f(f7(c2), f6(c2, f6(c2, c1)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (~big_f(f7(c2), f6(c2, f6(c2, c1)))) | (~(f6(c2, f6(c2, c1)) = f6(c2, c1))) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))))),
% 28.62/18.84 inference(transitivity,[status(thm)],[14714, 14712])).
% 28.62/18.84 tff(14716,plain,
% 28.62/18.84 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (~(f7(c2) = c2)) | (~(f6(c2, f6(c2, c1)) = f6(c2, c1))) | (~big_f(f7(c2), f6(c2, f6(c2, c1)))))),
% 28.62/18.84 inference(quant_inst,[status(thm)],[])).
% 28.62/18.84 tff(14717,plain,
% 28.62/18.84 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (~big_f(f7(c2), f6(c2, f6(c2, c1)))) | (~(f6(c2, f6(c2, c1)) = f6(c2, c1))) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2)))),
% 28.62/18.84 inference(modus_ponens,[status(thm)],[14716, 14715])).
% 28.62/18.84 tff(14718,plain,
% 28.62/18.84 (~(f6(c2, f6(c2, c1)) = f6(c2, c1))),
% 28.62/18.84 inference(unit_resolution,[status(thm)],[14717, 2730, 11798, 14619, 14711, 14685, 14625])).
% 28.62/18.84 tff(14719,plain,
% 28.62/18.84 (~(f6(c2, c1) = c1)),
% 28.62/18.84 inference(modus_ponens,[status(thm)],[14718, 14704])).
% 28.62/18.84 tff(14720,plain,
% 28.62/18.84 (~(f6(c2, f10(c2)) = f10(c2))),
% 28.62/18.84 inference(modus_ponens,[status(thm)],[14719, 14623])).
% 28.62/18.84 tff(14721,plain,
% 28.62/18.84 ((f6(c2, f10(c2)) = f10(c2)) | big_f(f7(c2), f6(c2, f10(c2)))),
% 28.62/18.84 inference(unit_resolution,[status(thm)],[13724, 2662, 11798, 14619, 14685, 14625])).
% 28.62/18.84 tff(14722,plain,
% 28.62/18.84 (big_f(f7(c2), f6(c2, f10(c2)))),
% 28.62/18.84 inference(unit_resolution,[status(thm)],[14721, 14720])).
% 28.62/18.84 tff(14723,plain,
% 28.62/18.84 (big_f(c2, f6(c2, c1))),
% 28.62/18.84 inference(modus_ponens,[status(thm)],[14722, 14620])).
% 28.62/18.84 tff(14724,plain,
% 28.62/18.84 (~big_f(c2, f6(c2, c1))),
% 28.62/18.84 inference(unit_resolution,[status(thm)],[11730, 14719, 79, 14617, 121, 67, 14627])).
% 28.62/18.84 tff(14725,plain,
% 28.62/18.84 ($false),
% 28.62/18.84 inference(unit_resolution,[status(thm)],[14724, 14723])).
% 28.62/18.84 tff(14726,plain,((~(c3 = c2)) | (~(f4(c4) = c2)) | big_f(c2, c2) | (~(f6(c2, f7(f4(c4))) = c1)) | (f7(c1) = c1) | (f10(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 28.62/18.84 tff(14727,plain,
% 28.62/18.84 (~(c3 = c2)),
% 28.62/18.84 inference(unit_resolution,[status(thm)],[14726, 121, 79, 6634, 115, 3])).
% 28.62/18.84 tff(14728,plain,
% 28.62/18.84 (c3 = c1),
% 28.62/18.84 inference(unit_resolution,[status(thm)],[180, 14727])).
% 28.62/18.84 tff(14729,plain,
% 28.62/18.84 (~(f7(c2) = c2)),
% 28.62/18.84 inference(unit_resolution,[status(thm)],[11517, 14728, 79, 14617, 121, 14618])).
% 28.62/18.84 tff(14730,plain,
% 28.62/18.84 (f7(c2) = c1),
% 28.62/18.84 inference(unit_resolution,[status(thm)],[21, 14729])).
% 28.62/18.84 tff(14731,plain,
% 28.62/18.84 (~(c2 = c3)),
% 28.62/18.84 inference(modus_ponens,[status(thm)],[14727, 10473])).
% 28.62/18.84 tff(14732,plain,
% 28.62/18.84 ((f7(c1) = c4) <=> (c4 = c2)),
% 28.62/18.84 inference(transitivity,[status(thm)],[2811, 8721])).
% 28.62/18.84 tff(14733,plain,
% 28.62/18.84 (big_f(c1, c2)),
% 28.62/18.84 inference(unit_resolution,[status(thm)],[12437, 121, 79, 14618, 14617, 11798, 120])).
% 28.62/18.84 tff(14734,plain,
% 28.62/18.84 (big_f(c1, f7(c1))),
% 28.62/18.84 inference(modus_ponens,[status(thm)],[14733, 11804])).
% 28.62/18.84 tff(14735,plain,
% 28.62/18.84 (c1 = c3),
% 28.62/18.84 inference(unit_resolution,[status(thm)],[175, 14728])).
% 28.62/18.84 tff(14736,plain,
% 28.62/18.84 (f7(c1) = c4),
% 28.62/18.84 inference(unit_resolution,[status(thm)],[11952, 14735, 14617, 115, 14734, 121])).
% 28.62/18.84 tff(14737,plain,
% 28.62/18.84 (c4 = c2),
% 28.62/18.84 inference(modus_ponens,[status(thm)],[14736, 14732])).
% 28.62/18.84 tff(14738,plain,
% 28.62/18.84 ($false),
% 28.62/18.84 inference(unit_resolution,[status(thm)],[10120, 14737, 14731, 79, 121, 14618, 14730])).
% 28.62/18.84 tff(14739,plain,(big_f(c2, c2) | (~(f4(c4) = c2)) | (f7(c1) = c1) | (~(f6(c2, f7(f4(c4))) = c1)) | (f10(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 28.62/18.85 tff(14740,plain,
% 28.62/18.85 (big_f(c2, c2)),
% 28.62/18.85 inference(unit_resolution,[status(thm)],[14739, 6634, 115, 79, 3])).
% 28.62/18.85 tff(14741,plain,
% 28.62/18.85 (f7(c2) = c2),
% 28.62/18.85 inference(unit_resolution,[status(thm)],[12660, 14617, 15, 79, 14740, 120])).
% 28.62/18.85 tff(14742,plain,
% 28.62/18.85 (f7(f4(c4)) = c2),
% 28.62/18.85 inference(transitivity,[status(thm)],[80, 14741])).
% 28.62/18.85 tff(14743,plain,
% 28.62/18.85 (f6(c2, f7(f4(c4))) = f6(c2, c2)),
% 28.62/18.85 inference(monotonicity,[status(thm)],[14742])).
% 28.62/18.85 tff(14744,plain,
% 28.62/18.85 (f7(f6(c2, c2)) = c2),
% 28.62/18.85 inference(transitivity,[status(thm)],[14420, 347])).
% 28.62/18.85 tff(14745,plain,
% 28.62/18.85 ((f7(f6(c2, c2)) = f6(c2, c2)) <=> (c2 = f6(c2, c2))),
% 28.62/18.85 inference(monotonicity,[status(thm)],[14744])).
% 28.62/18.85 tff(14746,plain,
% 28.62/18.85 ((f7(f6(c2, c2)) = f6(c2, c2)) <=> (f6(c2, c2) = c2)),
% 28.62/18.85 inference(transitivity,[status(thm)],[14745, 3242])).
% 28.62/18.85 tff(14747,plain,
% 28.62/18.85 ((f6(c2, c2) = c2) <=> (f7(f6(c2, c2)) = f6(c2, c2))),
% 28.62/18.85 inference(symmetry,[status(thm)],[14746])).
% 28.62/18.85 tff(14748,plain,
% 28.62/18.85 ((~(f6(c2, c2) = c2)) <=> (~(f7(f6(c2, c2)) = f6(c2, c2)))),
% 28.62/18.85 inference(monotonicity,[status(thm)],[14747])).
% 28.62/18.85 tff(14749,plain,
% 28.62/18.85 (~(f7(f6(c2, c2)) = f6(c2, c2))),
% 28.62/18.85 inference(modus_ponens,[status(thm)],[14102, 14748])).
% 28.62/18.85 tff(14750,plain,
% 28.62/18.85 (big_f(f7(f6(c2, c2)), c2) <=> big_f(c2, c2)),
% 28.62/18.85 inference(monotonicity,[status(thm)],[14744])).
% 28.62/18.85 tff(14751,plain,
% 28.62/18.85 (big_f(c2, c2) <=> big_f(f7(f6(c2, c2)), c2)),
% 28.62/18.85 inference(symmetry,[status(thm)],[14750])).
% 28.62/18.85 tff(14752,plain,
% 28.62/18.85 (big_f(f7(f6(c2, c2)), c2)),
% 28.62/18.85 inference(modus_ponens,[status(thm)],[1345, 14751])).
% 28.62/18.85 tff(14753,plain,
% 28.62/18.85 (big_f(f9(c2, c2), c2) <=> big_f(c2, c2)),
% 28.62/18.85 inference(monotonicity,[status(thm)],[8080])).
% 28.62/18.85 tff(14754,plain,
% 28.62/18.85 (big_f(c2, c2) <=> big_f(f9(c2, c2), c2)),
% 28.62/18.85 inference(symmetry,[status(thm)],[14753])).
% 28.62/18.85 tff(14755,plain,
% 28.62/18.85 (big_f(c2, c2) <=> big_f(f9(c2, c2), f10(c2))),
% 28.62/18.85 inference(transitivity,[status(thm)],[14754, 130])).
% 28.62/18.85 tff(14756,plain,
% 28.62/18.85 (big_f(f9(c2, c2), f10(c2))),
% 28.62/18.85 inference(modus_ponens,[status(thm)],[1345, 14755])).
% 28.62/18.85 tff(14757,plain,
% 28.62/18.85 (c2 = f5(f6(c2, c2))),
% 28.62/18.85 inference(unit_resolution,[status(thm)],[10696, 1190, 122, 8080, 14756, 14752, 14749])).
% 28.62/18.85 tff(14758,plain,
% 28.62/18.85 (f5(f6(c2, c2)) = c2),
% 28.62/18.85 inference(symmetry,[status(thm)],[14757])).
% 28.62/18.85 tff(14759,plain,
% 28.62/18.85 (f7(f6(c2, c2)) = f7(c2)),
% 28.62/18.85 inference(transitivity,[status(thm)],[14420, 347, 82])).
% 28.62/18.85 tff(14760,plain,
% 28.62/18.85 (big_f(f7(f6(c2, c2)), f6(c2, c2)) <=> big_f(f7(c2), f6(c2, c2))),
% 28.62/18.85 inference(monotonicity,[status(thm)],[14759])).
% 28.62/18.85 tff(14761,plain,
% 28.62/18.85 (big_f(f7(c2), f6(c2, c2)) <=> big_f(f7(f6(c2, c2)), f6(c2, c2))),
% 28.62/18.85 inference(symmetry,[status(thm)],[14760])).
% 28.62/18.85 tff(14762,plain,
% 28.62/18.85 (big_f(f7(c2), f6(c2, c2))),
% 28.62/18.85 inference(unit_resolution,[status(thm)],[2639, 122, 1345, 8066, 77, 14102, 79])).
% 28.62/18.85 tff(14763,plain,
% 28.62/18.85 (big_f(f7(f6(c2, c2)), f6(c2, c2))),
% 28.62/18.85 inference(modus_ponens,[status(thm)],[14762, 14761])).
% 28.62/18.85 tff(14764,plain,
% 28.62/18.85 (f6(c2, c2) = f5(f6(c2, c2))),
% 28.62/18.85 inference(unit_resolution,[status(thm)],[3316, 1190, 122, 8080, 14756, 14763, 14749])).
% 28.62/18.85 tff(14765,plain,
% 28.62/18.85 (f6(c2, c2) = c2),
% 28.62/18.85 inference(transitivity,[status(thm)],[14764, 14758])).
% 28.62/18.85 tff(14766,plain,
% 28.62/18.85 ($false),
% 28.62/18.85 inference(unit_resolution,[status(thm)],[14102, 14765])).
% 28.62/18.85 tff(14767,plain,((~(f10(c2) = c2)) | (~big_f(c2, c2)) | (~(f7(c2) = c2)) | (~(f7(c1) = c2)) | (~(f6(c2, f7(f4(c4))) = c1)) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.62/18.85 tff(14768,plain,
% 28.62/18.85 (~(f10(c2) = c2)),
% 28.62/18.85 inference(unit_resolution,[status(thm)],[14767, 14740, 14741, 120, 6634, 79])).
% 28.62/18.85 tff(14769,plain,
% 28.62/18.85 (f10(c2) = c1),
% 28.62/18.85 inference(unit_resolution,[status(thm)],[93, 14768])).
% 28.62/18.85 tff(14770,plain,
% 28.62/18.85 (f10(c2) = f6(c2, c2)),
% 28.62/18.85 inference(transitivity,[status(thm)],[14769, 14103, 14743])).
% 28.62/18.85 tff(14771,plain,
% 28.62/18.85 (big_f(f6(c2, c2), f10(c2)) <=> big_f(f6(c2, c2), f6(c2, c2))),
% 28.62/18.85 inference(monotonicity,[status(thm)],[14770])).
% 28.62/18.85 tff(14772,plain,
% 28.62/18.85 (big_f(f6(c2, c2), f6(c2, c2)) <=> big_f(f6(c2, c2), f10(c2))),
% 28.62/18.85 inference(symmetry,[status(thm)],[14771])).
% 28.62/18.85 tff(14773,plain,
% 28.62/18.85 (c1 = f6(c2, c2)),
% 28.62/18.85 inference(transitivity,[status(thm)],[14103, 14743])).
% 28.62/18.85 tff(14774,plain,
% 28.62/18.85 (big_f(c1, c1) <=> big_f(f6(c2, c2), f6(c2, c2))),
% 28.62/18.85 inference(monotonicity,[status(thm)],[14773, 14773])).
% 28.62/18.85 tff(14775,plain,
% 28.62/18.85 (big_f(f6(c2, c2), f6(c2, c2))),
% 28.62/18.85 inference(modus_ponens,[status(thm)],[14617, 14774])).
% 28.62/18.85 tff(14776,plain,
% 28.62/18.85 (big_f(f6(c2, c2), f10(c2))),
% 28.62/18.85 inference(modus_ponens,[status(thm)],[14775, 14772])).
% 28.62/18.85 tff(14777,plain,
% 28.62/18.85 (f6(c2, c2) = f6(c2, f7(f4(c4)))),
% 28.62/18.85 inference(symmetry,[status(thm)],[14743])).
% 28.62/18.85 tff(14778,plain,
% 28.62/18.85 (f6(c2, c2) = c1),
% 28.62/18.85 inference(transitivity,[status(thm)],[14777, 6634])).
% 28.62/18.85 tff(14779,plain,
% 28.62/18.85 ((f6(c2, c2) = f8(c2)) <=> (c1 = f8(c2))),
% 28.62/18.85 inference(monotonicity,[status(thm)],[14778])).
% 28.62/18.85 tff(14780,plain,
% 28.62/18.85 ((c1 = f8(c2)) <=> (f6(c2, c2) = f8(c2))),
% 28.62/18.85 inference(symmetry,[status(thm)],[14779])).
% 28.62/18.85 tff(14781,plain,
% 28.62/18.85 (c2 = f7(c2)),
% 28.62/18.85 inference(symmetry,[status(thm)],[14741])).
% 28.62/18.85 tff(14782,plain,
% 28.62/18.85 (f7(f6(c2, c2)) = f7(c1)),
% 28.62/18.85 inference(monotonicity,[status(thm)],[14778])).
% 28.62/18.85 tff(14783,plain,
% 28.62/18.85 (f7(f6(c2, c2)) = f7(c2)),
% 28.62/18.85 inference(transitivity,[status(thm)],[14782, 120, 14781])).
% 28.62/18.85 tff(14784,plain,
% 28.62/18.85 (big_f(f7(f6(c2, c2)), f6(c2, c2)) <=> big_f(f7(c2), f6(c2, c2))),
% 28.62/18.85 inference(monotonicity,[status(thm)],[14783])).
% 28.62/18.85 tff(14785,plain,
% 28.62/18.85 (big_f(f7(c2), f6(c2, c2)) <=> big_f(f7(f6(c2, c2)), f6(c2, c2))),
% 28.62/18.85 inference(symmetry,[status(thm)],[14784])).
% 28.62/18.85 tff(14786,plain,
% 28.62/18.85 (big_f(f7(c2), f6(c2, c2)) <=> big_f(c2, c1)),
% 28.62/18.85 inference(monotonicity,[status(thm)],[14741, 14778])).
% 28.62/18.85 tff(14787,plain,
% 28.62/18.85 (big_f(c2, c1) <=> big_f(f7(c2), f6(c2, c2))),
% 28.62/18.85 inference(symmetry,[status(thm)],[14786])).
% 28.62/18.85 tff(14788,plain,
% 28.62/18.85 (big_f(c2, c1) <=> big_f(f7(f6(c2, c2)), f6(c2, c2))),
% 28.62/18.85 inference(transitivity,[status(thm)],[14787, 14785])).
% 28.62/18.85 tff(14789,plain,
% 28.62/18.85 (big_f(c2, f10(c1))),
% 28.62/18.85 inference(modus_ponens,[status(thm)],[14740, 2719])).
% 28.62/18.85 tff(14790,plain,
% 28.62/18.85 (f10(f6(c2, c2)) = f10(c1)),
% 28.62/18.85 inference(monotonicity,[status(thm)],[14778])).
% 28.62/18.85 tff(14791,plain,
% 28.62/18.85 (f10(f6(c2, c2)) = c2),
% 28.62/18.85 inference(transitivity,[status(thm)],[14790, 15])).
% 28.62/18.85 tff(14792,plain,
% 28.62/18.85 (big_f(f6(c2, c2), f10(f6(c2, c2))) <=> big_f(c1, c2)),
% 28.62/18.85 inference(monotonicity,[status(thm)],[14778, 14791])).
% 28.62/18.85 tff(14793,plain,
% 28.62/18.85 (big_f(c1, c2) <=> big_f(f6(c2, c2), f10(f6(c2, c2)))),
% 28.62/18.85 inference(symmetry,[status(thm)],[14792])).
% 28.62/18.85 tff(14794,plain,
% 28.62/18.85 (f7(c2) = c2),
% 28.62/18.85 inference(unit_resolution,[status(thm)],[12660, 4932, 15, 79, 1345, 347])).
% 28.62/18.85 tff(14795,plain,
% 28.62/18.85 (f7(f4(c4)) = c2),
% 28.62/18.85 inference(transitivity,[status(thm)],[80, 14794])).
% 28.62/18.85 tff(14796,plain,
% 28.62/18.85 (f6(c2, f7(f4(c4))) = f6(c2, c2)),
% 28.62/18.85 inference(monotonicity,[status(thm)],[14795])).
% 28.62/18.85 tff(14797,plain,
% 28.62/18.85 (f10(c2) = f6(c2, c2)),
% 28.62/18.85 inference(transitivity,[status(thm)],[94, 14103, 14796])).
% 28.62/18.85 tff(14798,plain,
% 28.62/18.85 (big_f(f6(c2, c2), f10(c2)) <=> big_f(f6(c2, c2), f6(c2, c2))),
% 28.62/18.85 inference(monotonicity,[status(thm)],[14797])).
% 28.62/18.85 tff(14799,plain,
% 28.62/18.85 (big_f(f6(c2, c2), f6(c2, c2)) <=> big_f(f6(c2, c2), f10(c2))),
% 28.62/18.85 inference(symmetry,[status(thm)],[14798])).
% 28.62/18.85 tff(14800,plain,
% 28.62/18.85 (c1 = f6(c2, c2)),
% 28.62/18.85 inference(transitivity,[status(thm)],[14103, 14796])).
% 28.62/18.85 tff(14801,plain,
% 28.62/18.85 (big_f(c1, c1) <=> big_f(f6(c2, c2), f6(c2, c2))),
% 28.62/18.85 inference(monotonicity,[status(thm)],[14800, 14800])).
% 28.62/18.85 tff(14802,plain,
% 28.62/18.85 (big_f(f6(c2, c2), f6(c2, c2))),
% 28.62/18.85 inference(modus_ponens,[status(thm)],[4932, 14801])).
% 28.62/18.85 tff(14803,plain,
% 28.62/18.85 (big_f(f6(c2, c2), f10(c2))),
% 28.62/18.85 inference(modus_ponens,[status(thm)],[14802, 14799])).
% 28.62/18.85 tff(14804,plain,
% 28.62/18.85 (f6(c2, c2) = f6(c2, f7(f4(c4)))),
% 28.62/18.85 inference(symmetry,[status(thm)],[14796])).
% 28.62/18.85 tff(14805,plain,
% 28.62/18.85 (f6(c2, c2) = c1),
% 28.62/18.85 inference(transitivity,[status(thm)],[14804, 6634])).
% 28.62/18.85 tff(14806,plain,
% 28.62/18.85 ((f6(c2, c2) = f8(c2)) <=> (c1 = f8(c2))),
% 28.62/18.85 inference(monotonicity,[status(thm)],[14805])).
% 28.62/18.85 tff(14807,plain,
% 28.62/18.85 ((c1 = f8(c2)) <=> (f6(c2, c2) = f8(c2))),
% 28.62/18.85 inference(symmetry,[status(thm)],[14806])).
% 28.62/18.85 tff(14808,plain,
% 28.62/18.85 (c2 = f7(c2)),
% 28.62/18.85 inference(symmetry,[status(thm)],[14794])).
% 28.62/18.85 tff(14809,plain,
% 28.62/18.85 (f7(f6(c2, c2)) = f7(c1)),
% 28.62/18.85 inference(monotonicity,[status(thm)],[14805])).
% 28.62/18.85 tff(14810,plain,
% 28.62/18.85 (f7(f6(c2, c2)) = f7(c2)),
% 28.62/18.85 inference(transitivity,[status(thm)],[14809, 347, 14808])).
% 28.62/18.85 tff(14811,plain,
% 28.62/18.85 (big_f(f7(f6(c2, c2)), f6(c2, c2)) <=> big_f(f7(c2), f6(c2, c2))),
% 28.62/18.85 inference(monotonicity,[status(thm)],[14810])).
% 28.62/18.85 tff(14812,plain,
% 28.62/18.85 (big_f(f7(c2), f6(c2, c2)) <=> big_f(f7(f6(c2, c2)), f6(c2, c2))),
% 28.62/18.85 inference(symmetry,[status(thm)],[14811])).
% 28.62/18.85 tff(14813,plain,
% 28.62/18.85 (big_f(f7(c2), f6(c2, c2)) <=> big_f(c2, c1)),
% 28.62/18.85 inference(monotonicity,[status(thm)],[14794, 14805])).
% 28.62/18.85 tff(14814,plain,
% 28.62/18.85 (big_f(c2, c1) <=> big_f(f7(c2), f6(c2, c2))),
% 28.62/18.85 inference(symmetry,[status(thm)],[14813])).
% 28.62/18.85 tff(14815,plain,
% 28.62/18.85 (big_f(c2, c1) <=> big_f(f7(f6(c2, c2)), f6(c2, c2))),
% 28.62/18.85 inference(transitivity,[status(thm)],[14814, 14812])).
% 28.62/18.85 tff(14816,plain,
% 28.62/18.85 (f10(c2) = f6(c2, c2)),
% 28.62/18.85 inference(transitivity,[status(thm)],[94, 14103, 2475])).
% 28.62/18.85 tff(14817,plain,
% 28.62/18.85 (big_f(f6(c2, c2), f10(c2)) <=> big_f(f6(c2, c2), f6(c2, c2))),
% 28.62/18.85 inference(monotonicity,[status(thm)],[14816])).
% 28.62/18.85 tff(14818,plain,
% 28.62/18.85 (big_f(f6(c2, c2), f6(c2, c2)) <=> big_f(f6(c2, c2), f10(c2))),
% 28.62/18.85 inference(symmetry,[status(thm)],[14817])).
% 28.62/18.85 tff(14819,plain,
% 28.62/18.85 (c1 = f6(c2, c2)),
% 28.62/18.85 inference(transitivity,[status(thm)],[14103, 2475])).
% 28.62/18.85 tff(14820,plain,
% 28.62/18.85 (big_f(c1, c1) <=> big_f(f6(c2, c2), f6(c2, c2))),
% 28.62/18.85 inference(monotonicity,[status(thm)],[14819, 14819])).
% 28.62/18.85 tff(14821,plain,
% 28.62/18.85 (big_f(f6(c2, c2), f6(c2, c2))),
% 28.62/18.85 inference(modus_ponens,[status(thm)],[4932, 14820])).
% 28.62/18.85 tff(14822,plain,
% 28.62/18.85 (big_f(f6(c2, c2), f10(c2))),
% 28.62/18.85 inference(modus_ponens,[status(thm)],[14821, 14818])).
% 28.62/18.85 tff(14823,plain,
% 28.62/18.85 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | (f6(c2, c2) = f8(c2)) | big_f(f7(c2), f6(c2, c2)) | (~big_f(f6(c2, c2), f10(c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | (f6(c2, c2) = f8(c2)) | big_f(f7(c2), f6(c2, c2)) | (~big_f(f6(c2, c2), f10(c2))))),
% 28.62/18.85 inference(rewrite,[status(thm)],[])).
% 28.62/18.85 tff(14824,plain,
% 28.62/18.85 (((f10(c2) = c2) | (f6(c2, c2) = f8(c2)) | (~big_f(f6(c2, c2), f10(c2))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2))) <=> ((f10(c2) = c2) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | (f6(c2, c2) = f8(c2)) | big_f(f7(c2), f6(c2, c2)) | (~big_f(f6(c2, c2), f10(c2))))),
% 28.62/18.85 inference(rewrite,[status(thm)],[])).
% 28.62/18.85 tff(14825,plain,
% 28.62/18.85 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (f6(c2, c2) = f8(c2)) | (~big_f(f6(c2, c2), f10(c2))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | (f6(c2, c2) = f8(c2)) | big_f(f7(c2), f6(c2, c2)) | (~big_f(f6(c2, c2), f10(c2)))))),
% 28.62/18.85 inference(monotonicity,[status(thm)],[14824])).
% 28.62/18.85 tff(14826,plain,
% 28.62/18.85 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (f6(c2, c2) = f8(c2)) | (~big_f(f6(c2, c2), f10(c2))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | (f6(c2, c2) = f8(c2)) | big_f(f7(c2), f6(c2, c2)) | (~big_f(f6(c2, c2), f10(c2))))),
% 28.62/18.85 inference(transitivity,[status(thm)],[14825, 14823])).
% 28.62/18.85 tff(14827,plain,
% 28.62/18.85 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (f6(c2, c2) = f8(c2)) | (~big_f(f6(c2, c2), f10(c2))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)))),
% 28.62/18.85 inference(quant_inst,[status(thm)],[])).
% 28.62/18.85 tff(14828,plain,
% 28.62/18.85 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | (f6(c2, c2) = f8(c2)) | big_f(f7(c2), f6(c2, c2)) | (~big_f(f6(c2, c2), f10(c2)))),
% 28.62/18.85 inference(modus_ponens,[status(thm)],[14827, 14826])).
% 28.62/18.85 tff(14829,plain,
% 28.62/18.85 ((f6(c2, c2) = f8(c2)) | big_f(f7(c2), f6(c2, c2)) | (~big_f(f6(c2, c2), f10(c2)))),
% 28.62/18.85 inference(unit_resolution,[status(thm)],[14828, 2662, 89, 77, 14102])).
% 28.62/18.85 tff(14830,plain,
% 28.62/18.85 (f6(c2, c2) = f8(c2)),
% 28.62/18.85 inference(unit_resolution,[status(thm)],[14829, 14097, 14822])).
% 28.62/18.85 tff(14831,plain,
% 28.62/18.85 (f8(c2) = f6(c2, c2)),
% 28.62/18.85 inference(symmetry,[status(thm)],[14830])).
% 28.62/18.85 tff(14832,plain,
% 28.62/18.85 (f8(f7(f4(c4))) = c1),
% 28.62/18.85 inference(transitivity,[status(thm)],[107, 13354, 14831, 14092, 6634])).
% 28.62/18.85 tff(14833,plain,
% 28.62/18.85 (f1(f8(c3), f8(f7(f4(c4)))) = f1(f8(c3), c1)),
% 28.62/18.85 inference(monotonicity,[status(thm)],[14832])).
% 28.62/18.85 tff(14834,plain,
% 28.62/18.85 (big_f(f8(c3), f1(f8(c3), f8(f7(f4(c4))))) <=> big_f(f8(c3), f1(f8(c3), c1))),
% 28.62/18.85 inference(monotonicity,[status(thm)],[14833])).
% 28.62/18.85 tff(14835,plain,
% 28.62/18.85 (big_f(f8(c3), f1(f8(c3), c1)) <=> big_f(f8(c3), f1(f8(c3), f8(f7(f4(c4)))))),
% 28.62/18.85 inference(symmetry,[status(thm)],[14834])).
% 28.62/18.85 tff(14836,plain,
% 28.62/18.85 ((c1 = f7(c2)) <=> (f7(c2) = c1)),
% 28.62/18.85 inference(commutativity,[status(thm)],[])).
% 28.62/18.85 tff(14837,plain,
% 28.62/18.85 (f6(c2, f7(c2)) = f6(c2, f7(f4(c4)))),
% 28.62/18.85 inference(monotonicity,[status(thm)],[81])).
% 28.62/18.85 tff(14838,plain,
% 28.62/18.85 (f6(c2, f7(c2)) = c1),
% 28.62/18.85 inference(transitivity,[status(thm)],[14837, 6634])).
% 28.62/18.85 tff(14839,plain,
% 28.62/18.85 ((f6(c2, f7(c2)) = f7(c2)) <=> (c1 = f7(c2))),
% 28.62/18.85 inference(monotonicity,[status(thm)],[14838])).
% 28.62/18.85 tff(14840,plain,
% 28.62/18.85 ((f6(c2, f7(c2)) = f7(c2)) <=> (f7(c2) = c1)),
% 28.62/18.85 inference(transitivity,[status(thm)],[14839, 14836])).
% 28.62/18.85 tff(14841,plain,
% 28.62/18.85 ((f7(c2) = c1) <=> (f6(c2, f7(c2)) = f7(c2))),
% 28.62/18.85 inference(symmetry,[status(thm)],[14840])).
% 28.62/18.85 tff(14842,plain,
% 28.62/18.85 ((f7(c2) = c1) <=> (c2 = c1)),
% 28.62/18.85 inference(monotonicity,[status(thm)],[77])).
% 28.62/18.85 tff(14843,plain,
% 28.62/18.85 ((c2 = c1) <=> (f7(c2) = c1)),
% 28.62/18.85 inference(symmetry,[status(thm)],[14842])).
% 28.62/18.85 tff(14844,plain,
% 28.62/18.85 ((c2 = c1) <=> (f6(c2, f7(c2)) = f7(c2))),
% 28.62/18.85 inference(transitivity,[status(thm)],[14843, 14841])).
% 28.62/18.85 tff(14845,plain,
% 28.62/18.85 ((~(c2 = c1)) <=> (~(f6(c2, f7(c2)) = f7(c2)))),
% 28.62/18.85 inference(monotonicity,[status(thm)],[14844])).
% 28.62/18.85 tff(14846,plain,
% 28.62/18.85 (~(f6(c2, f7(c2)) = f7(c2))),
% 28.62/18.85 inference(modus_ponens,[status(thm)],[75, 14845])).
% 28.62/18.85 tff(14847,plain,
% 28.62/18.85 (big_f(f7(c2), f6(c2, f7(c2))) <=> big_f(f7(c2), c1)),
% 28.62/18.85 inference(monotonicity,[status(thm)],[14838])).
% 28.62/18.85 tff(14848,plain,
% 28.62/18.85 (big_f(f7(c2), c1) <=> big_f(f7(c2), f6(c2, f7(c2)))),
% 28.62/18.85 inference(symmetry,[status(thm)],[14847])).
% 28.62/18.85 tff(14849,plain,
% 28.62/18.85 (big_f(c2, c1) <=> big_f(f7(c2), c1)),
% 28.62/18.85 inference(monotonicity,[status(thm)],[82])).
% 28.62/18.85 tff(14850,plain,
% 28.62/18.85 (big_f(c2, c1) <=> big_f(f7(c2), f6(c2, f7(c2)))),
% 28.62/18.85 inference(transitivity,[status(thm)],[14849, 14848])).
% 28.62/18.85 tff(14851,plain,
% 28.62/18.85 ((~big_f(c2, c1)) <=> (~big_f(f7(c2), f6(c2, f7(c2))))),
% 28.62/18.85 inference(monotonicity,[status(thm)],[14850])).
% 28.62/18.85 tff(14852,plain,
% 28.62/18.85 (~big_f(f7(c2), f6(c2, f7(c2)))),
% 28.62/18.85 inference(modus_ponens,[status(thm)],[2, 14851])).
% 28.62/18.85 tff(14853,plain,
% 28.62/18.85 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (c2 = f8(c1)) | (~(f7(c2) = c2)) | (~big_f(c2, f10(c1))) | (f6(c2, f7(c2)) = f7(c2)) | big_f(f7(c2), f6(c2, f7(c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c1) = c1) | (c2 = f8(c1)) | (~(f7(c2) = c2)) | (~big_f(c2, f10(c1))) | (f6(c2, f7(c2)) = f7(c2)) | big_f(f7(c2), f6(c2, f7(c2))))),
% 28.62/18.85 inference(rewrite,[status(thm)],[])).
% 28.62/18.85 tff(14854,plain,
% 28.62/18.85 (((f10(c1) = c1) | (c2 = f8(c1)) | (~big_f(c2, f10(c1))) | (~(f7(c2) = c2)) | (f6(c2, f7(c2)) = f7(c2)) | big_f(f7(c2), f6(c2, f7(c2)))) <=> ((f10(c1) = c1) | (c2 = f8(c1)) | (~(f7(c2) = c2)) | (~big_f(c2, f10(c1))) | (f6(c2, f7(c2)) = f7(c2)) | big_f(f7(c2), f6(c2, f7(c2))))),
% 28.62/18.85 inference(rewrite,[status(thm)],[])).
% 28.62/18.85 tff(14855,plain,
% 28.62/18.85 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (c2 = f8(c1)) | (~big_f(c2, f10(c1))) | (~(f7(c2) = c2)) | (f6(c2, f7(c2)) = f7(c2)) | big_f(f7(c2), f6(c2, f7(c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (c2 = f8(c1)) | (~(f7(c2) = c2)) | (~big_f(c2, f10(c1))) | (f6(c2, f7(c2)) = f7(c2)) | big_f(f7(c2), f6(c2, f7(c2)))))),
% 28.62/18.85 inference(monotonicity,[status(thm)],[14854])).
% 28.62/18.85 tff(14856,plain,
% 28.62/18.85 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (c2 = f8(c1)) | (~big_f(c2, f10(c1))) | (~(f7(c2) = c2)) | (f6(c2, f7(c2)) = f7(c2)) | big_f(f7(c2), f6(c2, f7(c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c1) = c1) | (c2 = f8(c1)) | (~(f7(c2) = c2)) | (~big_f(c2, f10(c1))) | (f6(c2, f7(c2)) = f7(c2)) | big_f(f7(c2), f6(c2, f7(c2))))),
% 28.62/18.85 inference(transitivity,[status(thm)],[14855, 14853])).
% 28.62/18.85 tff(14857,plain,
% 28.62/18.85 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (c2 = f8(c1)) | (~big_f(c2, f10(c1))) | (~(f7(c2) = c2)) | (f6(c2, f7(c2)) = f7(c2)) | big_f(f7(c2), f6(c2, f7(c2))))),
% 28.62/18.85 inference(quant_inst,[status(thm)],[])).
% 28.62/18.85 tff(14858,plain,
% 28.62/18.85 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c1) = c1) | (c2 = f8(c1)) | (~(f7(c2) = c2)) | (~big_f(c2, f10(c1))) | (f6(c2, f7(c2)) = f7(c2)) | big_f(f7(c2), f6(c2, f7(c2)))),
% 28.62/18.85 inference(modus_ponens,[status(thm)],[14857, 14856])).
% 28.62/18.85 tff(14859,plain,
% 28.62/18.85 ((c2 = f8(c1)) | (~(f7(c2) = c2)) | (f6(c2, f7(c2)) = f7(c2)) | big_f(f7(c2), f6(c2, f7(c2)))),
% 28.62/18.85 inference(unit_resolution,[status(thm)],[14858, 2662, 3332, 3])).
% 28.62/18.85 tff(14860,plain,
% 28.62/18.85 (c2 = f8(c1)),
% 28.62/18.85 inference(unit_resolution,[status(thm)],[14859, 14852, 77, 14846])).
% 28.62/18.85 tff(14861,plain,
% 28.62/18.85 ((f6(c2, c2) = c4) <=> (c1 = c4)),
% 28.62/18.85 inference(monotonicity,[status(thm)],[14093])).
% 28.62/18.85 tff(14862,plain,
% 28.62/18.85 ((c1 = c4) <=> (f6(c2, c2) = c4)),
% 28.62/18.85 inference(symmetry,[status(thm)],[14861])).
% 28.62/18.85 tff(14863,plain,
% 28.62/18.85 ((c4 = c1) <=> (f6(c2, c2) = c4)),
% 28.62/18.85 inference(transitivity,[status(thm)],[479, 14862])).
% 28.62/18.85 tff(14864,plain,
% 28.62/18.85 ((~(c4 = c1)) <=> (~(f6(c2, c2) = c4))),
% 28.62/18.85 inference(monotonicity,[status(thm)],[14863])).
% 28.62/18.85 tff(14865,assumption,(big_f(f6(c2, c2), f6(c2, c2))), introduced(assumption)).
% 28.62/18.85 tff(14866,plain,
% 28.62/18.85 (c3 = f6(c2, c2)),
% 28.62/18.85 inference(transitivity,[status(thm)],[172, 14103, 2475])).
% 28.62/18.85 tff(14867,plain,
% 28.62/18.85 ((c2 = c3) <=> (c2 = f6(c2, c2))),
% 28.62/18.85 inference(monotonicity,[status(thm)],[14866])).
% 28.62/18.85 tff(14868,plain,
% 28.62/18.85 ((c2 = c3) <=> (f6(c2, c2) = c2)),
% 28.62/18.85 inference(transitivity,[status(thm)],[14867, 3242])).
% 28.62/18.85 tff(14869,plain,
% 28.62/18.85 ((f6(c2, c2) = c2) <=> (c2 = c3)),
% 28.62/18.85 inference(symmetry,[status(thm)],[14868])).
% 28.62/18.85 tff(14870,plain,
% 28.62/18.85 ((~(f6(c2, c2) = c2)) <=> (~(c2 = c3))),
% 28.62/18.85 inference(monotonicity,[status(thm)],[14869])).
% 28.62/18.85 tff(14871,plain,
% 28.62/18.85 (~(c2 = c3)),
% 28.62/18.85 inference(modus_ponens,[status(thm)],[14102, 14870])).
% 28.62/18.85 tff(14872,plain,
% 28.62/18.85 (f4(f6(c2, c2)) = f4(c1)),
% 28.62/18.85 inference(monotonicity,[status(thm)],[14093])).
% 28.62/18.85 tff(14873,plain,
% 28.62/18.85 ((f6(c2, c2) = f4(f6(c2, c2))) <=> (c1 = f4(c1))),
% 28.62/18.85 inference(monotonicity,[status(thm)],[14093, 14872])).
% 28.62/18.85 tff(14874,plain,
% 28.62/18.85 ((c1 = f4(c1)) <=> (f6(c2, c2) = f4(f6(c2, c2)))),
% 28.62/18.85 inference(symmetry,[status(thm)],[14873])).
% 28.62/18.85 tff(14875,plain,
% 28.62/18.85 ((c1 = f4(c1)) <=> (f6(c2, c2) = c2)),
% 28.62/18.85 inference(monotonicity,[status(thm)],[14819, 569])).
% 28.62/18.85 tff(14876,plain,
% 28.62/18.85 ((f6(c2, c2) = c2) <=> (c1 = f4(c1))),
% 28.62/18.85 inference(symmetry,[status(thm)],[14875])).
% 28.62/18.85 tff(14877,plain,
% 28.62/18.85 ((f6(c2, c2) = c2) <=> (f6(c2, c2) = f4(f6(c2, c2)))),
% 28.62/18.85 inference(transitivity,[status(thm)],[14876, 14874])).
% 28.62/18.85 tff(14878,plain,
% 28.62/18.85 ((~(f6(c2, c2) = c2)) <=> (~(f6(c2, c2) = f4(f6(c2, c2))))),
% 28.62/18.85 inference(monotonicity,[status(thm)],[14877])).
% 28.62/18.85 tff(14879,plain,
% 28.62/18.85 (~(f6(c2, c2) = f4(f6(c2, c2)))),
% 28.62/18.85 inference(modus_ponens,[status(thm)],[14102, 14878])).
% 28.62/18.85 tff(14880,plain,
% 28.62/18.85 (f6(c2, c2) = c4),
% 28.62/18.85 inference(modus_ponens,[status(thm)],[564, 14862])).
% 28.62/18.85 tff(14881,plain,
% 28.62/18.85 (~big_f(c2, c4)),
% 28.62/18.85 inference(unit_resolution,[status(thm)],[6521, 9310, 79])).
% 28.62/18.85 tff(14882,assumption,(~(f6(c2, c2) = f4(f6(c2, c2)))), introduced(assumption)).
% 28.62/18.85 tff(14883,assumption,(f6(c2, c2) = c4), introduced(assumption)).
% 28.62/18.85 tff(14884,assumption,(f1(c2, c2) = c1), introduced(assumption)).
% 28.62/18.85 tff(14885,plain,
% 28.62/18.85 (c1 = f1(c2, c2)),
% 28.62/18.85 inference(symmetry,[status(thm)],[14884])).
% 28.62/18.85 tff(14886,plain,
% 28.62/18.85 (c4 = f1(c2, c2)),
% 28.62/18.85 inference(transitivity,[status(thm)],[480, 14885])).
% 28.62/18.85 tff(14887,plain,
% 28.62/18.85 (big_f(c2, c4) <=> big_f(c2, f1(c2, c2))),
% 28.62/18.85 inference(monotonicity,[status(thm)],[14886])).
% 28.62/18.85 tff(14888,plain,
% 28.62/18.85 (big_f(c2, f1(c2, c2)) <=> big_f(c2, c4)),
% 28.62/18.85 inference(symmetry,[status(thm)],[14887])).
% 28.62/18.85 tff(14889,plain,
% 28.62/18.85 (big_f(c2, c4)),
% 28.62/18.85 inference(modus_ponens,[status(thm)],[1907, 14888])).
% 28.62/18.85 tff(14890,plain,
% 28.62/18.85 ($false),
% 28.62/18.85 inference(unit_resolution,[status(thm)],[3865, 14889])).
% 28.62/18.85 tff(14891,plain,((~(c4 = c1)) | big_f(c2, c4) | (~big_f(c2, f1(c2, c2))) | (~(f1(c2, c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.62/18.85 tff(14892,plain,
% 28.62/18.85 (~big_f(c2, f1(c2, c2))),
% 28.62/18.85 inference(unit_resolution,[status(thm)],[14891, 5298, 480, 3865])).
% 28.62/18.85 tff(14893,plain,
% 28.62/18.85 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (~(f6(c2, c2) = c4)) | (f6(c2, c2) = f4(f6(c2, c2))) | (~big_f(f6(c2, c2), f6(c2, c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (~(f6(c2, c2) = c4)) | (f6(c2, c2) = f4(f6(c2, c2))) | (~big_f(f6(c2, c2), f6(c2, c2))))),
% 28.62/18.85 inference(rewrite,[status(thm)],[])).
% 28.62/18.85 tff(14894,plain,
% 28.62/18.85 (((c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f6(c2, c2) = c4)) | (f6(c2, c2) = f4(f6(c2, c2))) | (~big_f(f6(c2, c2), f6(c2, c2)))) <=> ((c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (~(f6(c2, c2) = c4)) | (f6(c2, c2) = f4(f6(c2, c2))) | (~big_f(f6(c2, c2), f6(c2, c2))))),
% 28.62/18.85 inference(rewrite,[status(thm)],[])).
% 28.62/18.85 tff(14895,plain,
% 28.62/18.85 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f6(c2, c2) = c4)) | (f6(c2, c2) = f4(f6(c2, c2))) | (~big_f(f6(c2, c2), f6(c2, c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (~(f6(c2, c2) = c4)) | (f6(c2, c2) = f4(f6(c2, c2))) | (~big_f(f6(c2, c2), f6(c2, c2)))))),
% 28.62/18.85 inference(monotonicity,[status(thm)],[14894])).
% 28.62/18.85 tff(14896,plain,
% 28.62/18.85 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f6(c2, c2) = c4)) | (f6(c2, c2) = f4(f6(c2, c2))) | (~big_f(f6(c2, c2), f6(c2, c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (~(f6(c2, c2) = c4)) | (f6(c2, c2) = f4(f6(c2, c2))) | (~big_f(f6(c2, c2), f6(c2, c2))))),
% 28.62/18.86 inference(transitivity,[status(thm)],[14895, 14893])).
% 28.62/18.86 tff(14897,plain,
% 28.62/18.86 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f6(c2, c2) = c4)) | (f6(c2, c2) = f4(f6(c2, c2))) | (~big_f(f6(c2, c2), f6(c2, c2))))),
% 28.62/18.86 inference(quant_inst,[status(thm)],[])).
% 28.62/18.86 tff(14898,plain,
% 28.62/18.86 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (~(f6(c2, c2) = c4)) | (f6(c2, c2) = f4(f6(c2, c2))) | (~big_f(f6(c2, c2), f6(c2, c2)))),
% 28.62/18.86 inference(modus_ponens,[status(thm)],[14897, 14896])).
% 28.62/18.86 tff(14899,plain,
% 28.62/18.86 ($false),
% 28.62/18.86 inference(unit_resolution,[status(thm)],[14898, 525, 377, 1828, 14892, 14865, 14883, 14882])).
% 28.62/18.86 tff(14900,plain,((f1(c2, c2) = c2) | (c2 = c3) | (~big_f(f6(c2, c2), f6(c2, c2))) | (~(f6(c2, c2) = c4)) | (f6(c2, c2) = f4(f6(c2, c2))) | (~(c4 = c1)) | big_f(c2, c4)), inference(lemma,lemma(discharge,[]))).
% 28.62/18.86 tff(14901,plain,
% 28.62/18.86 (f1(c2, c2) = c2),
% 28.62/18.86 inference(unit_resolution,[status(thm)],[14900, 14880, 14865, 377, 14879, 480, 14881])).
% 28.62/18.86 tff(14902,plain,
% 28.62/18.86 (big_f(c2, f1(c2, c2)) <=> big_f(c2, c2)),
% 28.62/18.86 inference(monotonicity,[status(thm)],[14901])).
% 28.62/18.86 tff(14903,plain,
% 28.62/18.86 (big_f(c2, c2) <=> big_f(c2, f1(c2, c2))),
% 28.62/18.86 inference(symmetry,[status(thm)],[14902])).
% 28.62/18.86 tff(14904,plain,
% 28.62/18.86 (big_f(c2, f1(c2, c2))),
% 28.62/18.86 inference(modus_ponens,[status(thm)],[1345, 14903])).
% 28.62/18.86 tff(14905,plain,
% 28.62/18.86 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (~(f6(c2, c2) = c4)) | (f6(c2, c2) = f4(f6(c2, c2))) | (~big_f(f6(c2, c2), f6(c2, c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (~(f6(c2, c2) = c4)) | (f6(c2, c2) = f4(f6(c2, c2))) | (~big_f(f6(c2, c2), f6(c2, c2))))),
% 28.62/18.86 inference(rewrite,[status(thm)],[])).
% 28.62/18.86 tff(14906,plain,
% 28.62/18.86 (((c2 = c3) | (~(f6(c2, c2) = c4)) | (f6(c2, c2) = f4(f6(c2, c2))) | (~big_f(f6(c2, c2), f6(c2, c2))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2)))) <=> ((c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (~(f6(c2, c2) = c4)) | (f6(c2, c2) = f4(f6(c2, c2))) | (~big_f(f6(c2, c2), f6(c2, c2))))),
% 28.62/18.86 inference(rewrite,[status(thm)],[])).
% 28.62/18.86 tff(14907,plain,
% 28.62/18.86 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f6(c2, c2) = c4)) | (f6(c2, c2) = f4(f6(c2, c2))) | (~big_f(f6(c2, c2), f6(c2, c2))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (~(f6(c2, c2) = c4)) | (f6(c2, c2) = f4(f6(c2, c2))) | (~big_f(f6(c2, c2), f6(c2, c2)))))),
% 28.62/18.86 inference(monotonicity,[status(thm)],[14906])).
% 28.62/18.86 tff(14908,plain,
% 28.62/18.86 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f6(c2, c2) = c4)) | (f6(c2, c2) = f4(f6(c2, c2))) | (~big_f(f6(c2, c2), f6(c2, c2))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (~(f6(c2, c2) = c4)) | (f6(c2, c2) = f4(f6(c2, c2))) | (~big_f(f6(c2, c2), f6(c2, c2))))),
% 28.62/18.86 inference(transitivity,[status(thm)],[14907, 14905])).
% 28.62/18.86 tff(14909,plain,
% 28.62/18.86 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f6(c2, c2) = c4)) | (f6(c2, c2) = f4(f6(c2, c2))) | (~big_f(f6(c2, c2), f6(c2, c2))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))),
% 28.62/18.86 inference(quant_inst,[status(thm)],[])).
% 28.62/18.86 tff(14910,plain,
% 28.62/18.86 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (~(f6(c2, c2) = c4)) | (f6(c2, c2) = f4(f6(c2, c2))) | (~big_f(f6(c2, c2), f6(c2, c2)))),
% 28.62/18.86 inference(modus_ponens,[status(thm)],[14909, 14908])).
% 28.62/18.86 tff(14911,plain,
% 28.62/18.86 ($false),
% 28.62/18.86 inference(unit_resolution,[status(thm)],[14910, 553, 377, 14901, 14904, 14865, 14880, 14879])).
% 28.62/18.86 tff(14912,plain,((~(c4 = c1)) | (c2 = c3) | (~big_f(f6(c2, c2), f6(c2, c2))) | (~big_f(c2, c2)) | (~(f4(c4) = c2)) | (~(f6(c2, f7(f4(c4))) = c1)) | (~(f7(c2) = c2)) | big_f(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 28.62/18.86 tff(14913,plain,
% 28.62/18.86 (~(c4 = c1)),
% 28.62/18.86 inference(unit_resolution,[status(thm)],[14912, 14871, 14865, 1345, 79, 6634, 77, 2])).
% 28.62/18.86 tff(14914,plain,
% 28.62/18.86 (~(f6(c2, c2) = c4)),
% 28.62/18.86 inference(modus_ponens,[status(thm)],[14913, 14864])).
% 28.62/18.86 tff(14915,plain,
% 28.62/18.86 (~(c1 = c4)),
% 28.62/18.86 inference(modus_ponens,[status(thm)],[14913, 1997])).
% 28.62/18.86 tff(14916,plain,
% 28.62/18.86 (f8(f6(c2, f7(f4(c4)))) = c2),
% 28.62/18.86 inference(transitivity,[status(thm)],[13933, 1643])).
% 28.62/18.86 tff(14917,plain,
% 28.62/18.86 ((f8(f6(c2, f7(f4(c4)))) = c3) <=> (c2 = c3)),
% 28.62/18.86 inference(monotonicity,[status(thm)],[14916])).
% 28.62/18.86 tff(14918,plain,
% 28.62/18.86 ((c2 = c3) <=> (f8(f6(c2, f7(f4(c4)))) = c3)),
% 28.62/18.86 inference(symmetry,[status(thm)],[14917])).
% 28.62/18.86 tff(14919,plain,
% 28.62/18.86 ((f6(c2, c2) = c2) <=> (f8(f6(c2, f7(f4(c4)))) = c3)),
% 28.62/18.86 inference(transitivity,[status(thm)],[14869, 14918])).
% 28.62/18.86 tff(14920,plain,
% 28.62/18.86 ((~(f6(c2, c2) = c2)) <=> (~(f8(f6(c2, f7(f4(c4)))) = c3))),
% 28.62/18.86 inference(monotonicity,[status(thm)],[14919])).
% 28.62/18.86 tff(14921,plain,
% 28.62/18.86 (~(f8(f6(c2, f7(f4(c4)))) = c3)),
% 28.62/18.86 inference(modus_ponens,[status(thm)],[14102, 14920])).
% 28.62/18.86 tff(14922,plain,
% 28.62/18.86 (f1(f8(f6(c2, f7(f4(c4)))), c2) = f1(c2, c2)),
% 28.62/18.86 inference(monotonicity,[status(thm)],[14916])).
% 28.62/18.86 tff(14923,plain,
% 28.62/18.86 (big_f(f8(f6(c2, f7(f4(c4)))), f1(f8(f6(c2, f7(f4(c4)))), c2)) <=> big_f(c2, f1(c2, c2))),
% 28.62/18.86 inference(monotonicity,[status(thm)],[14916, 14922])).
% 28.62/18.86 tff(14924,plain,
% 28.62/18.86 (big_f(c2, f1(c2, c2)) <=> big_f(f8(f6(c2, f7(f4(c4)))), f1(f8(f6(c2, f7(f4(c4)))), c2))),
% 28.62/18.86 inference(symmetry,[status(thm)],[14923])).
% 28.62/18.86 tff(14925,plain,
% 28.62/18.86 (f1(c2, c2) = f6(c2, c2)),
% 28.62/18.86 inference(transitivity,[status(thm)],[5298, 14103, 2475])).
% 28.62/18.86 tff(14926,plain,
% 28.62/18.86 (big_f(c2, f1(c2, c2)) <=> big_f(f7(c2), f6(c2, c2))),
% 28.62/18.86 inference(monotonicity,[status(thm)],[82, 14925])).
% 28.62/18.86 tff(14927,plain,
% 28.62/18.86 (big_f(f7(c2), f6(c2, c2)) <=> big_f(c2, f1(c2, c2))),
% 28.62/18.86 inference(symmetry,[status(thm)],[14926])).
% 28.62/18.86 tff(14928,plain,
% 28.62/18.86 (big_f(f7(c2), f6(c2, c2)) <=> big_f(f8(f6(c2, f7(f4(c4)))), f1(f8(f6(c2, f7(f4(c4)))), c2))),
% 28.62/18.86 inference(transitivity,[status(thm)],[14927, 14924])).
% 28.62/18.86 tff(14929,plain,
% 28.62/18.86 ((~big_f(f7(c2), f6(c2, c2))) <=> (~big_f(f8(f6(c2, f7(f4(c4)))), f1(f8(f6(c2, f7(f4(c4)))), c2)))),
% 28.62/18.86 inference(monotonicity,[status(thm)],[14928])).
% 28.62/18.86 tff(14930,plain,
% 28.62/18.86 (~big_f(f8(f6(c2, f7(f4(c4)))), f1(f8(f6(c2, f7(f4(c4)))), c2))),
% 28.62/18.86 inference(modus_ponens,[status(thm)],[2621, 14929])).
% 28.62/18.86 tff(14931,assumption,(~(f8(f6(c2, f7(f4(c4)))) = c3)), introduced(assumption)).
% 28.62/18.86 tff(14932,plain,
% 28.62/18.86 ((f1(f8(f6(c2, f7(f4(c4)))), c2) = c2) <=> (f1(c2, c2) = c2)),
% 28.62/18.86 inference(monotonicity,[status(thm)],[14922])).
% 28.62/18.86 tff(14933,plain,
% 28.62/18.86 ((f1(c2, c2) = c2) <=> (f1(f8(f6(c2, f7(f4(c4)))), c2) = c2)),
% 28.62/18.86 inference(symmetry,[status(thm)],[14932])).
% 28.62/18.86 tff(14934,plain,
% 28.62/18.86 ((~(f1(c2, c2) = c2)) <=> (~(f1(f8(f6(c2, f7(f4(c4)))), c2) = c2))),
% 28.62/18.86 inference(monotonicity,[status(thm)],[14933])).
% 28.62/18.86 tff(14935,plain,
% 28.62/18.86 (~(f1(f8(f6(c2, f7(f4(c4)))), c2) = c2)),
% 28.62/18.86 inference(modus_ponens,[status(thm)],[1828, 14934])).
% 28.62/18.86 tff(14936,plain,
% 28.62/18.86 (f3(c1, c1) = f7(c2)),
% 28.62/18.86 inference(transitivity,[status(thm)],[1440, 82])).
% 28.62/18.86 tff(14937,plain,
% 28.62/18.86 (big_f(f3(c1, c1), c1) <=> big_f(f7(c2), f6(c2, c2))),
% 28.62/18.86 inference(monotonicity,[status(thm)],[14936, 14819])).
% 28.62/18.86 tff(14938,plain,
% 28.62/18.86 (big_f(f7(c2), f6(c2, c2)) <=> big_f(f3(c1, c1), c1)),
% 28.62/18.86 inference(symmetry,[status(thm)],[14937])).
% 28.62/18.86 tff(14939,plain,
% 28.62/18.86 ((~big_f(f7(c2), f6(c2, c2))) <=> (~big_f(f3(c1, c1), c1))),
% 28.62/18.86 inference(monotonicity,[status(thm)],[14938])).
% 28.62/18.86 tff(14940,plain,
% 28.62/18.86 (~big_f(f3(c1, c1), c1)),
% 28.62/18.86 inference(modus_ponens,[status(thm)],[2621, 14939])).
% 28.62/18.86 tff(14941,assumption,(~big_f(f8(f6(c2, f7(f4(c4)))), f1(f8(f6(c2, f7(f4(c4)))), c2))), introduced(assumption)).
% 28.62/18.86 tff(14942,assumption,(~(f1(f8(f6(c2, f7(f4(c4)))), c2) = c2)), introduced(assumption)).
% 28.62/18.86 tff(14943,plain,
% 28.62/18.86 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c1 = c4) | (f3(c1, c1) = c1) | big_f(f3(c1, c1), c1) | (f8(f6(c2, f7(f4(c4)))) = c3) | (f1(f8(f6(c2, f7(f4(c4)))), c2) = c2) | big_f(f8(f6(c2, f7(f4(c4)))), f1(f8(f6(c2, f7(f4(c4)))), c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (c1 = c4) | (f3(c1, c1) = c1) | big_f(f3(c1, c1), c1) | (f8(f6(c2, f7(f4(c4)))) = c3) | (f1(f8(f6(c2, f7(f4(c4)))), c2) = c2) | big_f(f8(f6(c2, f7(f4(c4)))), f1(f8(f6(c2, f7(f4(c4)))), c2)))),
% 28.62/18.86 inference(rewrite,[status(thm)],[])).
% 28.62/18.86 tff(14944,plain,
% 28.62/18.86 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c1 = c4) | (f3(c1, c1) = c1) | big_f(f3(c1, c1), c1) | (f8(f6(c2, f7(f4(c4)))) = c3) | (f1(f8(f6(c2, f7(f4(c4)))), c2) = c2) | big_f(f8(f6(c2, f7(f4(c4)))), f1(f8(f6(c2, f7(f4(c4)))), c2)))),
% 28.62/18.86 inference(quant_inst,[status(thm)],[])).
% 28.62/18.86 tff(14945,plain,
% 28.62/18.86 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (c1 = c4) | (f3(c1, c1) = c1) | big_f(f3(c1, c1), c1) | (f8(f6(c2, f7(f4(c4)))) = c3) | (f1(f8(f6(c2, f7(f4(c4)))), c2) = c2) | big_f(f8(f6(c2, f7(f4(c4)))), f1(f8(f6(c2, f7(f4(c4)))), c2))),
% 28.62/18.86 inference(modus_ponens,[status(thm)],[14944, 14943])).
% 28.62/18.86 tff(14946,plain,
% 28.62/18.86 ((c1 = c4) | (f3(c1, c1) = c1) | big_f(f3(c1, c1), c1) | (f8(f6(c2, f7(f4(c4)))) = c3) | (f1(f8(f6(c2, f7(f4(c4)))), c2) = c2) | big_f(f8(f6(c2, f7(f4(c4)))), f1(f8(f6(c2, f7(f4(c4)))), c2))),
% 28.62/18.86 inference(unit_resolution,[status(thm)],[14945, 1014])).
% 28.62/18.86 tff(14947,plain,
% 28.62/18.86 (big_f(f3(c1, c1), c1)),
% 28.62/18.86 inference(unit_resolution,[status(thm)],[14946, 1431, 14931, 482, 14942, 14941])).
% 28.62/18.86 tff(14948,plain,
% 28.62/18.86 ($false),
% 28.62/18.86 inference(unit_resolution,[status(thm)],[14947, 14940])).
% 28.62/18.86 tff(14949,plain,((f3(c1, c1) = c1) | big_f(f7(c2), f6(c2, c2)) | (~(f6(c2, f7(f4(c4))) = c1)) | (~(f7(c2) = c2)) | (~(f4(c4) = c2)) | (f8(f6(c2, f7(f4(c4)))) = c3) | (c1 = c4) | (f1(f8(f6(c2, f7(f4(c4)))), c2) = c2) | big_f(f8(f6(c2, f7(f4(c4)))), f1(f8(f6(c2, f7(f4(c4)))), c2))), inference(lemma,lemma(discharge,[]))).
% 28.62/18.86 tff(14950,plain,
% 28.62/18.86 (f3(c1, c1) = c1),
% 28.62/18.86 inference(unit_resolution,[status(thm)],[14949, 14935, 6634, 77, 79, 14931, 482, 2621, 14930])).
% 28.62/18.86 tff(14951,plain,
% 28.62/18.86 (f3(f6(c2, c2), f6(c2, c2)) = f3(c1, c1)),
% 28.62/18.86 inference(monotonicity,[status(thm)],[14093, 14093])).
% 28.62/18.86 tff(14952,plain,
% 28.62/18.86 (f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2)),
% 28.62/18.86 inference(transitivity,[status(thm)],[14951, 14950, 14103, 2475])).
% 28.62/18.86 tff(14953,plain,
% 28.62/18.86 (big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2)) <=> big_f(f6(c2, c2), f6(c2, c2))),
% 28.62/18.86 inference(monotonicity,[status(thm)],[14952])).
% 28.62/18.86 tff(14954,plain,
% 28.62/18.86 (big_f(f6(c2, c2), f6(c2, c2)) <=> big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2))),
% 28.62/18.86 inference(symmetry,[status(thm)],[14953])).
% 28.62/18.86 tff(14955,plain,
% 28.62/18.86 (big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2))),
% 28.62/18.86 inference(modus_ponens,[status(thm)],[14865, 14954])).
% 28.62/18.86 tff(14956,assumption,(~(f6(c2, c2) = c4)), introduced(assumption)).
% 28.62/18.86 tff(14957,plain,
% 28.62/18.86 ((~big_f(f7(c2), f6(c2, c2))) <=> (~big_f(c2, f1(c2, c2)))),
% 28.62/18.86 inference(monotonicity,[status(thm)],[14927])).
% 28.62/18.86 tff(14958,plain,
% 28.62/18.86 (~big_f(c2, f1(c2, c2))),
% 28.62/18.86 inference(modus_ponens,[status(thm)],[2621, 14957])).
% 28.62/18.86 tff(14959,plain,
% 28.62/18.86 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (f6(c2, c2) = c4) | (~(f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2))) | (~big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (f6(c2, c2) = c4) | (~(f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2))) | (~big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2))))),
% 28.62/18.86 inference(rewrite,[status(thm)],[])).
% 28.62/18.86 tff(14960,plain,
% 28.62/18.86 (((f6(c2, c2) = c4) | (c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2))) | (~big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2)))) <=> ((c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (f6(c2, c2) = c4) | (~(f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2))) | (~big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2))))),
% 28.62/18.86 inference(rewrite,[status(thm)],[])).
% 28.62/18.86 tff(14961,plain,
% 28.62/18.86 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((f6(c2, c2) = c4) | (c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2))) | (~big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (f6(c2, c2) = c4) | (~(f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2))) | (~big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2)))))),
% 28.62/18.86 inference(monotonicity,[status(thm)],[14960])).
% 28.62/18.86 tff(14962,plain,
% 28.62/18.86 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((f6(c2, c2) = c4) | (c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2))) | (~big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (f6(c2, c2) = c4) | (~(f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2))) | (~big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2))))),
% 28.62/18.86 inference(transitivity,[status(thm)],[14961, 14959])).
% 28.62/18.86 tff(14963,plain,
% 28.62/18.86 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((f6(c2, c2) = c4) | (c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2))) | (~big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2))))),
% 28.62/18.86 inference(quant_inst,[status(thm)],[])).
% 28.62/18.86 tff(14964,plain,
% 28.62/18.86 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (f6(c2, c2) = c4) | (~(f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2))) | (~big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2)))),
% 28.62/18.86 inference(modus_ponens,[status(thm)],[14963, 14962])).
% 28.62/18.86 tff(14965,plain,
% 28.62/18.86 ((~(f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2))) | (~big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2)))),
% 28.62/18.86 inference(unit_resolution,[status(thm)],[14964, 969, 377, 1828, 14958, 14956])).
% 28.62/18.86 tff(14966,plain,
% 28.62/18.86 ($false),
% 28.62/18.86 inference(unit_resolution,[status(thm)],[14965, 14955, 14952])).
% 28.62/18.86 tff(14967,plain,((f1(c2, c2) = c2) | (c2 = c3) | (f6(c2, c2) = c4) | (~big_f(f6(c2, c2), f6(c2, c2))) | (~(f6(c2, f7(f4(c4))) = c1)) | (~(f7(c2) = c2)) | (~(f4(c4) = c2)) | (f8(f6(c2, f7(f4(c4)))) = c3) | (c1 = c4) | big_f(f7(c2), f6(c2, c2)) | (~(c2 = f8(c1)))), inference(lemma,lemma(discharge,[]))).
% 28.62/18.86 tff(14968,plain,
% 28.62/18.86 (f1(c2, c2) = c2),
% 28.62/18.86 inference(unit_resolution,[status(thm)],[14967, 14871, 14914, 14865, 6634, 77, 79, 14921, 14915, 14097, 1642])).
% 28.62/18.86 tff(14969,plain,
% 28.62/18.86 (big_f(c2, f1(c2, c2)) <=> big_f(c2, c2)),
% 28.62/18.86 inference(monotonicity,[status(thm)],[14968])).
% 28.62/18.86 tff(14970,plain,
% 28.62/18.86 (big_f(c2, c2) <=> big_f(c2, f1(c2, c2))),
% 28.62/18.86 inference(symmetry,[status(thm)],[14969])).
% 28.62/18.86 tff(14971,plain,
% 28.62/18.86 (big_f(c2, f1(c2, c2))),
% 28.62/18.86 inference(modus_ponens,[status(thm)],[1345, 14970])).
% 28.62/18.86 tff(14972,plain,
% 28.62/18.86 (f3(f6(c2, c2), f6(c2, c2)) = c2),
% 28.62/18.86 inference(transitivity,[status(thm)],[14951, 1441])).
% 28.62/18.86 tff(14973,plain,
% 28.62/18.86 ((f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2)) <=> (c2 = f6(c2, c2))),
% 28.62/18.86 inference(monotonicity,[status(thm)],[14972])).
% 28.62/18.86 tff(14974,plain,
% 28.62/18.86 ((f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2)) <=> (f6(c2, c2) = c2)),
% 28.62/18.86 inference(transitivity,[status(thm)],[14973, 3242])).
% 28.62/18.86 tff(14975,plain,
% 28.62/18.86 ((f6(c2, c2) = c2) <=> (f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2))),
% 28.62/18.86 inference(symmetry,[status(thm)],[14974])).
% 28.62/18.86 tff(14976,plain,
% 28.62/18.86 ((~(f6(c2, c2) = c2)) <=> (~(f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2)))),
% 28.62/18.86 inference(monotonicity,[status(thm)],[14975])).
% 28.62/18.86 tff(14977,plain,
% 28.62/18.86 (~(f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2))),
% 28.62/18.86 inference(modus_ponens,[status(thm)],[14102, 14976])).
% 28.62/18.86 tff(14978,plain,
% 28.62/18.86 (f3(f6(c2, c2), f6(c2, c2)) = f7(c2)),
% 28.62/18.86 inference(transitivity,[status(thm)],[14951, 1441, 82])).
% 28.62/18.86 tff(14979,plain,
% 28.62/18.86 (big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2)) <=> big_f(f7(c2), f6(c2, c2))),
% 28.62/18.86 inference(monotonicity,[status(thm)],[14978])).
% 28.62/18.86 tff(14980,plain,
% 28.62/18.86 (big_f(f7(c2), f6(c2, c2)) <=> big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2))),
% 28.62/18.86 inference(symmetry,[status(thm)],[14979])).
% 28.62/18.86 tff(14981,plain,
% 28.62/18.86 ((~big_f(f7(c2), f6(c2, c2))) <=> (~big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2)))),
% 28.62/18.86 inference(monotonicity,[status(thm)],[14980])).
% 28.62/18.86 tff(14982,plain,
% 28.62/18.86 (~big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2))),
% 28.62/18.86 inference(modus_ponens,[status(thm)],[2621, 14981])).
% 28.62/18.86 tff(14983,plain,
% 28.62/18.86 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f6(c2, c2) = c4) | (f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2)) | big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f6(c2, c2) = c4) | (f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2)) | big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2)))),
% 28.62/18.86 inference(rewrite,[status(thm)],[])).
% 28.62/18.86 tff(14984,plain,
% 28.62/18.86 (((f6(c2, c2) = c4) | (f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2)) | big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2)) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2)))) <=> ((c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f6(c2, c2) = c4) | (f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2)) | big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2)))),
% 28.62/18.87 inference(rewrite,[status(thm)],[])).
% 28.62/18.87 tff(14985,plain,
% 28.62/18.87 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f6(c2, c2) = c4) | (f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2)) | big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2)) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f6(c2, c2) = c4) | (f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2)) | big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2))))),
% 28.62/18.87 inference(monotonicity,[status(thm)],[14984])).
% 28.62/18.87 tff(14986,plain,
% 28.62/18.87 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f6(c2, c2) = c4) | (f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2)) | big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2)) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f6(c2, c2) = c4) | (f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2)) | big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2)))),
% 28.62/18.87 inference(transitivity,[status(thm)],[14985, 14983])).
% 28.62/18.87 tff(14987,plain,
% 28.62/18.87 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f6(c2, c2) = c4) | (f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2)) | big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2)) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))),
% 28.62/18.87 inference(quant_inst,[status(thm)],[])).
% 28.62/18.87 tff(14988,plain,
% 28.62/18.87 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f6(c2, c2) = c4) | (f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2)) | big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2))),
% 28.62/18.87 inference(modus_ponens,[status(thm)],[14987, 14986])).
% 28.62/18.87 tff(14989,plain,
% 28.62/18.87 ((f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2)) | big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2))),
% 28.62/18.87 inference(unit_resolution,[status(thm)],[14988, 904, 377, 1908, 1907, 14956])).
% 28.62/18.87 tff(14990,plain,
% 28.62/18.87 ($false),
% 28.62/18.87 inference(unit_resolution,[status(thm)],[14989, 14982, 14977])).
% 28.62/18.87 tff(14991,plain,((~(f3(c1, c1) = c2)) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f6(c2, c2) = c4) | big_f(f7(c2), f6(c2, c2)) | (~(f7(c2) = c2)) | (~(f6(c2, f7(f4(c4))) = c1)) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.62/18.87 tff(14992,plain,
% 28.62/18.87 (~(f3(c1, c1) = c2)),
% 28.62/18.87 inference(unit_resolution,[status(thm)],[14991, 14871, 14968, 14971, 14914, 14097, 77, 6634, 79])).
% 28.62/18.87 tff(14993,plain,
% 28.62/18.87 (f3(c1, c1) = c1),
% 28.62/18.87 inference(unit_resolution,[status(thm)],[1416, 14992])).
% 28.62/18.87 tff(14994,plain,
% 28.62/18.87 (f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2)),
% 28.62/18.87 inference(transitivity,[status(thm)],[14951, 14993, 14103, 2475])).
% 28.62/18.87 tff(14995,plain,
% 28.62/18.87 (big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2)) <=> big_f(f6(c2, c2), f6(c2, c2))),
% 28.62/18.87 inference(monotonicity,[status(thm)],[14994])).
% 28.62/18.87 tff(14996,plain,
% 28.62/18.87 (big_f(f6(c2, c2), f6(c2, c2)) <=> big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2))),
% 28.62/18.87 inference(symmetry,[status(thm)],[14995])).
% 28.62/18.87 tff(14997,plain,
% 28.62/18.87 (big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2))),
% 28.62/18.87 inference(modus_ponens,[status(thm)],[14865, 14996])).
% 28.62/18.87 tff(14998,plain,
% 28.62/18.87 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f6(c2, c2) = c4) | (~(f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2))) | (~big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f6(c2, c2) = c4) | (~(f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2))) | (~big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2))))),
% 28.62/18.87 inference(rewrite,[status(thm)],[])).
% 28.62/18.87 tff(14999,plain,
% 28.62/18.87 (((f6(c2, c2) = c4) | (c2 = c3) | (~(f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2))) | (~big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2)))) <=> ((c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f6(c2, c2) = c4) | (~(f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2))) | (~big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2))))),
% 28.62/18.87 inference(rewrite,[status(thm)],[])).
% 28.62/18.87 tff(15000,plain,
% 28.62/18.87 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f6(c2, c2) = c4) | (c2 = c3) | (~(f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2))) | (~big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f6(c2, c2) = c4) | (~(f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2))) | (~big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2)))))),
% 28.62/18.87 inference(monotonicity,[status(thm)],[14999])).
% 28.62/18.87 tff(15001,plain,
% 28.62/18.87 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f6(c2, c2) = c4) | (c2 = c3) | (~(f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2))) | (~big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f6(c2, c2) = c4) | (~(f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2))) | (~big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2))))),
% 28.62/18.87 inference(transitivity,[status(thm)],[15000, 14998])).
% 28.62/18.87 tff(15002,plain,
% 28.62/18.87 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f6(c2, c2) = c4) | (c2 = c3) | (~(f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2))) | (~big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))),
% 28.62/18.87 inference(quant_inst,[status(thm)],[])).
% 28.62/18.87 tff(15003,plain,
% 28.62/18.87 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f6(c2, c2) = c4) | (~(f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2))) | (~big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2)))),
% 28.62/18.87 inference(modus_ponens,[status(thm)],[15002, 15001])).
% 28.62/18.87 tff(15004,plain,
% 28.62/18.87 ((~(f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2))) | (~big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2)))),
% 28.62/18.87 inference(unit_resolution,[status(thm)],[15003, 933, 14871, 14968, 14971, 14914])).
% 28.62/18.87 tff(15005,plain,
% 28.62/18.87 ($false),
% 28.62/18.87 inference(unit_resolution,[status(thm)],[15004, 14997, 14994])).
% 28.62/18.87 tff(15006,plain,((~(c3 = c1)) | (~big_f(f6(c2, c2), f6(c2, c2))) | (~(f6(c2, f7(f4(c4))) = c1)) | (~(f7(c2) = c2)) | (~(f4(c4) = c2)) | (~big_f(c2, c2)) | (~(c2 = f8(c1))) | big_f(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 28.62/18.87 tff(15007,plain,
% 28.62/18.87 (~(c3 = c1)),
% 28.62/18.87 inference(unit_resolution,[status(thm)],[15006, 14860, 6634, 77, 79, 1345, 14821, 2])).
% 28.62/18.87 tff(15008,plain,
% 28.62/18.87 (c3 = c2),
% 28.62/18.87 inference(unit_resolution,[status(thm)],[180, 15007])).
% 28.62/18.87 tff(15009,plain,
% 28.62/18.87 (f8(c3) = f8(c2)),
% 28.62/18.87 inference(monotonicity,[status(thm)],[15008])).
% 28.62/18.87 tff(15010,plain,
% 28.62/18.87 (f8(c3) = c1),
% 28.62/18.87 inference(transitivity,[status(thm)],[15009, 14831, 14092, 6634])).
% 28.62/18.87 tff(15011,plain,
% 28.62/18.87 (f1(f8(c3), c1) = f1(c1, c1)),
% 28.62/18.87 inference(monotonicity,[status(thm)],[15010])).
% 28.62/18.87 tff(15012,plain,
% 28.62/18.87 (big_f(f8(c3), f1(f8(c3), c1)) <=> big_f(c1, f1(c1, c1))),
% 28.62/18.87 inference(monotonicity,[status(thm)],[15010, 15011])).
% 28.62/18.87 tff(15013,plain,
% 28.62/18.87 (big_f(c1, f1(c1, c1)) <=> big_f(f8(c3), f1(f8(c3), c1))),
% 28.62/18.87 inference(symmetry,[status(thm)],[15012])).
% 28.62/18.87 tff(15014,plain,
% 28.62/18.87 (big_f(c1, f1(c1, c1)) <=> big_f(f8(c3), f1(f8(c3), f8(f7(f4(c4)))))),
% 28.62/18.87 inference(transitivity,[status(thm)],[15013, 14835])).
% 28.62/18.87 tff(15015,plain,
% 28.62/18.87 ((~big_f(c1, f1(c1, c1))) <=> (~big_f(f8(c3), f1(f8(c3), f8(f7(f4(c4))))))),
% 28.62/18.87 inference(monotonicity,[status(thm)],[15014])).
% 28.62/18.87 tff(15016,plain,
% 28.62/18.87 (~(c1 = c3)),
% 28.62/18.87 inference(modus_ponens,[status(thm)],[15007, 648])).
% 28.62/18.87 tff(15017,plain,
% 28.62/18.87 ((c1 = c3) <=> (f6(c2, c2) = c3)),
% 28.62/18.87 inference(monotonicity,[status(thm)],[14819])).
% 28.62/18.87 tff(15018,plain,
% 28.62/18.87 ((c3 = c1) <=> (f6(c2, c2) = c3)),
% 28.62/18.87 inference(transitivity,[status(thm)],[68, 15017])).
% 28.62/18.87 tff(15019,plain,
% 28.62/18.87 ((~(c3 = c1)) <=> (~(f6(c2, c2) = c3))),
% 28.62/18.87 inference(monotonicity,[status(thm)],[15018])).
% 28.62/18.87 tff(15020,plain,
% 28.62/18.87 (~(f6(c2, c2) = c3)),
% 28.62/18.87 inference(modus_ponens,[status(thm)],[15007, 15019])).
% 28.62/18.87 tff(15021,plain,
% 28.62/18.87 (~(c4 = c1)),
% 28.62/18.87 inference(unit_resolution,[status(thm)],[11545, 168, 4932, 27, 79])).
% 28.62/18.87 tff(15022,plain,
% 28.62/18.87 (c4 = c2),
% 28.62/18.87 inference(unit_resolution,[status(thm)],[461, 15021])).
% 28.62/18.87 tff(15023,plain,
% 28.62/18.87 ((c1 = c4) <=> (f6(c2, c2) = c2)),
% 28.62/18.87 inference(monotonicity,[status(thm)],[14819, 15022])).
% 28.62/18.87 tff(15024,plain,
% 28.62/18.87 ((f6(c2, c2) = c2) <=> (c1 = c4)),
% 28.62/18.87 inference(symmetry,[status(thm)],[15023])).
% 28.62/18.87 tff(15025,plain,
% 28.62/18.87 ((~(f6(c2, c2) = c2)) <=> (~(c1 = c4))),
% 28.62/18.87 inference(monotonicity,[status(thm)],[15024])).
% 28.62/18.87 tff(15026,plain,
% 28.62/18.87 (~(c1 = c4)),
% 28.62/18.87 inference(modus_ponens,[status(thm)],[14102, 15025])).
% 28.62/18.87 tff(15027,plain,
% 28.62/18.87 (big_f(c1, f1(c1, c1))),
% 28.62/18.87 inference(unit_resolution,[status(thm)],[9681, 14940, 4932, 168, 15026, 1431])).
% 28.62/18.87 tff(15028,plain,
% 28.62/18.87 (~(f1(c1, c1) = c2)),
% 28.62/18.87 inference(unit_resolution,[status(thm)],[4561, 15027, 27])).
% 28.62/18.87 tff(15029,plain,
% 28.62/18.87 (f1(c1, c1) = c1),
% 28.62/18.87 inference(unit_resolution,[status(thm)],[601, 15028])).
% 28.62/18.87 tff(15030,plain,
% 28.62/18.87 (f1(f6(c2, c2), f6(c2, c2)) = f1(c1, c1)),
% 28.62/18.87 inference(monotonicity,[status(thm)],[14093, 14093])).
% 28.62/18.87 tff(15031,plain,
% 28.62/18.87 (f1(f6(c2, c2), f6(c2, c2)) = f6(c2, c2)),
% 28.62/18.87 inference(transitivity,[status(thm)],[15030, 15029, 14103, 2475])).
% 28.62/18.87 tff(15032,plain,
% 28.62/18.87 (big_f(f6(c2, c2), f1(f6(c2, c2), f6(c2, c2))) <=> big_f(f6(c2, c2), f6(c2, c2))),
% 28.62/18.87 inference(monotonicity,[status(thm)],[15031])).
% 28.62/18.87 tff(15033,plain,
% 28.62/18.87 (big_f(f6(c2, c2), f6(c2, c2)) <=> big_f(f6(c2, c2), f1(f6(c2, c2), f6(c2, c2)))),
% 28.62/18.87 inference(symmetry,[status(thm)],[15032])).
% 28.62/18.87 tff(15034,plain,
% 28.62/18.87 (big_f(f6(c2, c2), f1(f6(c2, c2), f6(c2, c2)))),
% 28.62/18.87 inference(modus_ponens,[status(thm)],[14821, 15033])).
% 28.62/18.87 tff(15035,plain,
% 28.62/18.87 (f3(f6(c2, c2), f6(c2, c2)) = f7(c2)),
% 28.62/18.87 inference(transitivity,[status(thm)],[14951, 1440, 82])).
% 28.62/18.87 tff(15036,plain,
% 28.62/18.87 (big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2)) <=> big_f(f7(c2), f6(c2, c2))),
% 28.62/18.87 inference(monotonicity,[status(thm)],[15035])).
% 28.62/18.87 tff(15037,plain,
% 28.62/18.87 (big_f(f7(c2), f6(c2, c2)) <=> big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2))),
% 28.62/18.87 inference(symmetry,[status(thm)],[15036])).
% 28.62/18.87 tff(15038,plain,
% 28.62/18.87 ((~big_f(f7(c2), f6(c2, c2))) <=> (~big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2)))),
% 28.62/18.87 inference(monotonicity,[status(thm)],[15037])).
% 28.62/18.87 tff(15039,plain,
% 28.62/18.87 (~big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2))),
% 28.62/18.87 inference(modus_ponens,[status(thm)],[2621, 15038])).
% 28.62/18.87 tff(15040,plain,
% 28.62/18.87 (f3(f6(c2, c2), f6(c2, c2)) = c2),
% 28.62/18.87 inference(transitivity,[status(thm)],[14951, 1440])).
% 28.62/18.87 tff(15041,plain,
% 28.62/18.87 ((f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2)) <=> (c2 = f6(c2, c2))),
% 28.62/18.87 inference(monotonicity,[status(thm)],[15040])).
% 28.62/18.87 tff(15042,plain,
% 28.62/18.87 ((f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2)) <=> (f6(c2, c2) = c2)),
% 28.62/18.87 inference(transitivity,[status(thm)],[15041, 3242])).
% 28.62/18.87 tff(15043,plain,
% 28.62/18.87 ((f6(c2, c2) = c2) <=> (f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2))),
% 28.62/18.87 inference(symmetry,[status(thm)],[15042])).
% 28.62/18.87 tff(15044,plain,
% 28.62/18.87 ((~(f6(c2, c2) = c2)) <=> (~(f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2)))),
% 28.62/18.87 inference(monotonicity,[status(thm)],[15043])).
% 28.62/18.87 tff(15045,plain,
% 28.62/18.87 (~(f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2))),
% 28.62/18.87 inference(modus_ponens,[status(thm)],[14102, 15044])).
% 28.62/18.87 tff(15046,plain,
% 28.62/18.87 ((f6(c2, c2) = c2) <=> (f6(c2, c2) = c4)),
% 28.62/18.87 inference(transitivity,[status(thm)],[15024, 14862])).
% 28.62/18.87 tff(15047,plain,
% 28.62/18.87 ((~(f6(c2, c2) = c2)) <=> (~(f6(c2, c2) = c4))),
% 28.62/18.87 inference(monotonicity,[status(thm)],[15046])).
% 28.62/18.87 tff(15048,plain,
% 28.62/18.87 (~(f6(c2, c2) = c4)),
% 28.62/18.87 inference(modus_ponens,[status(thm)],[14102, 15047])).
% 28.62/18.87 tff(15049,assumption,(~(f6(c2, c2) = c3)), introduced(assumption)).
% 28.62/18.87 tff(15050,plain,
% 28.62/18.87 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f6(c2, c2) = c4) | (f6(c2, c2) = c3) | (f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2)) | big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2)) | (~(f1(f6(c2, c2), f6(c2, c2)) = f6(c2, c2))) | (~big_f(f6(c2, c2), f1(f6(c2, c2), f6(c2, c2)))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (f6(c2, c2) = c4) | (f6(c2, c2) = c3) | (f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2)) | big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2)) | (~(f1(f6(c2, c2), f6(c2, c2)) = f6(c2, c2))) | (~big_f(f6(c2, c2), f1(f6(c2, c2), f6(c2, c2)))))),
% 28.62/18.87 inference(rewrite,[status(thm)],[])).
% 28.62/18.87 tff(15051,plain,
% 28.62/18.87 (((f6(c2, c2) = c4) | (f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2)) | big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2)) | (f6(c2, c2) = c3) | (~(f1(f6(c2, c2), f6(c2, c2)) = f6(c2, c2))) | (~big_f(f6(c2, c2), f1(f6(c2, c2), f6(c2, c2))))) <=> ((f6(c2, c2) = c4) | (f6(c2, c2) = c3) | (f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2)) | big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2)) | (~(f1(f6(c2, c2), f6(c2, c2)) = f6(c2, c2))) | (~big_f(f6(c2, c2), f1(f6(c2, c2), f6(c2, c2)))))),
% 28.62/18.87 inference(rewrite,[status(thm)],[])).
% 28.62/18.87 tff(15052,plain,
% 28.62/18.87 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f6(c2, c2) = c4) | (f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2)) | big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2)) | (f6(c2, c2) = c3) | (~(f1(f6(c2, c2), f6(c2, c2)) = f6(c2, c2))) | (~big_f(f6(c2, c2), f1(f6(c2, c2), f6(c2, c2)))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f6(c2, c2) = c4) | (f6(c2, c2) = c3) | (f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2)) | big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2)) | (~(f1(f6(c2, c2), f6(c2, c2)) = f6(c2, c2))) | (~big_f(f6(c2, c2), f1(f6(c2, c2), f6(c2, c2))))))),
% 28.62/18.87 inference(monotonicity,[status(thm)],[15051])).
% 28.62/18.87 tff(15053,plain,
% 28.62/18.87 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f6(c2, c2) = c4) | (f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2)) | big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2)) | (f6(c2, c2) = c3) | (~(f1(f6(c2, c2), f6(c2, c2)) = f6(c2, c2))) | (~big_f(f6(c2, c2), f1(f6(c2, c2), f6(c2, c2)))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (f6(c2, c2) = c4) | (f6(c2, c2) = c3) | (f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2)) | big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2)) | (~(f1(f6(c2, c2), f6(c2, c2)) = f6(c2, c2))) | (~big_f(f6(c2, c2), f1(f6(c2, c2), f6(c2, c2)))))),
% 28.62/18.88 inference(transitivity,[status(thm)],[15052, 15050])).
% 28.62/18.88 tff(15054,plain,
% 28.62/18.88 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f6(c2, c2) = c4) | (f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2)) | big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2)) | (f6(c2, c2) = c3) | (~(f1(f6(c2, c2), f6(c2, c2)) = f6(c2, c2))) | (~big_f(f6(c2, c2), f1(f6(c2, c2), f6(c2, c2)))))),
% 28.62/18.88 inference(quant_inst,[status(thm)],[])).
% 28.62/18.88 tff(15055,plain,
% 28.62/18.88 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (f6(c2, c2) = c4) | (f6(c2, c2) = c3) | (f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2)) | big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2)) | (~(f1(f6(c2, c2), f6(c2, c2)) = f6(c2, c2))) | (~big_f(f6(c2, c2), f1(f6(c2, c2), f6(c2, c2))))),
% 28.62/18.88 inference(modus_ponens,[status(thm)],[15054, 15053])).
% 28.62/18.88 tff(15056,plain,
% 28.62/18.88 ((~(f1(f6(c2, c2), f6(c2, c2)) = f6(c2, c2))) | (~big_f(f6(c2, c2), f1(f6(c2, c2), f6(c2, c2))))),
% 28.62/18.88 inference(unit_resolution,[status(thm)],[15055, 904, 15049, 15048, 15045, 15039])).
% 28.62/18.88 tff(15057,plain,
% 28.62/18.88 ($false),
% 28.62/18.88 inference(unit_resolution,[status(thm)],[15056, 15034, 15031])).
% 28.62/18.88 tff(15058,plain,((f3(c1, c1) = c1) | (f6(c2, c2) = c3) | (~(f6(c2, f7(f4(c4))) = c1)) | (~(f7(c2) = c2)) | (~(f4(c4) = c2)) | big_f(f7(c2), f6(c2, c2)) | big_f(c1, c2) | (~big_f(c1, c1)) | (c1 = c3)), inference(lemma,lemma(discharge,[]))).
% 28.62/18.88 tff(15059,plain,
% 28.62/18.88 (f3(c1, c1) = c1),
% 28.62/18.88 inference(unit_resolution,[status(thm)],[15058, 15020, 6634, 77, 79, 14097, 27, 4932, 15016])).
% 28.62/18.88 tff(15060,plain,
% 28.62/18.88 (f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2)),
% 28.62/18.88 inference(transitivity,[status(thm)],[14951, 15059, 14103, 2475])).
% 28.62/18.88 tff(15061,plain,
% 28.62/18.88 (big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2)) <=> big_f(f6(c2, c2), f6(c2, c2))),
% 28.62/18.88 inference(monotonicity,[status(thm)],[15060])).
% 28.62/18.88 tff(15062,plain,
% 28.62/18.88 (big_f(f6(c2, c2), f6(c2, c2)) <=> big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2))),
% 28.62/18.88 inference(symmetry,[status(thm)],[15061])).
% 28.62/18.88 tff(15063,plain,
% 28.62/18.88 (big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2))),
% 28.62/18.88 inference(modus_ponens,[status(thm)],[14821, 15062])).
% 28.62/18.88 tff(15064,plain,
% 28.62/18.88 (~(c4 = c1)),
% 28.62/18.88 inference(unit_resolution,[status(thm)],[11545, 15016, 4932, 27, 79])).
% 28.62/18.88 tff(15065,plain,
% 28.62/18.88 (c4 = c2),
% 28.62/18.88 inference(unit_resolution,[status(thm)],[461, 15064])).
% 28.62/18.88 tff(15066,plain,
% 28.62/18.88 ((c1 = c4) <=> (f6(c2, c2) = c2)),
% 28.62/18.88 inference(monotonicity,[status(thm)],[14819, 15065])).
% 28.62/18.88 tff(15067,plain,
% 28.62/18.88 ((f6(c2, c2) = c2) <=> (c1 = c4)),
% 28.62/18.88 inference(symmetry,[status(thm)],[15066])).
% 28.62/18.88 tff(15068,plain,
% 28.62/18.88 ((f6(c2, c2) = c2) <=> (f6(c2, c2) = c4)),
% 28.62/18.88 inference(transitivity,[status(thm)],[15067, 14862])).
% 28.62/18.88 tff(15069,plain,
% 28.62/18.88 ((~(f6(c2, c2) = c2)) <=> (~(f6(c2, c2) = c4))),
% 28.62/18.88 inference(monotonicity,[status(thm)],[15068])).
% 28.62/18.88 tff(15070,plain,
% 28.62/18.88 (~(f6(c2, c2) = c4)),
% 28.62/18.88 inference(modus_ponens,[status(thm)],[14102, 15069])).
% 28.62/18.88 tff(15071,plain,
% 28.62/18.88 (f1(f6(c2, c2), f6(c2, c2)) = f6(c2, c2)),
% 28.62/18.88 inference(transitivity,[status(thm)],[15030, 624, 14103, 2475])).
% 28.62/18.88 tff(15072,plain,
% 28.62/18.88 (big_f(f6(c2, c2), f1(f6(c2, c2), f6(c2, c2))) <=> big_f(f6(c2, c2), f6(c2, c2))),
% 28.62/18.88 inference(monotonicity,[status(thm)],[15071])).
% 28.62/18.88 tff(15073,plain,
% 28.62/18.88 (big_f(f6(c2, c2), f6(c2, c2)) <=> big_f(f6(c2, c2), f1(f6(c2, c2), f6(c2, c2)))),
% 28.62/18.88 inference(symmetry,[status(thm)],[15072])).
% 28.62/18.88 tff(15074,plain,
% 28.62/18.88 (big_f(f6(c2, c2), f1(f6(c2, c2), f6(c2, c2)))),
% 28.62/18.88 inference(modus_ponens,[status(thm)],[14865, 15073])).
% 28.62/18.88 tff(15075,assumption,(big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2))), introduced(assumption)).
% 28.62/18.88 tff(15076,assumption,(f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2)), introduced(assumption)).
% 28.62/18.88 tff(15077,plain,
% 28.62/18.88 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f6(c2, c2) = c4) | (f6(c2, c2) = c3) | (~(f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2))) | (~big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2))) | (~(f1(f6(c2, c2), f6(c2, c2)) = f6(c2, c2))) | (~big_f(f6(c2, c2), f1(f6(c2, c2), f6(c2, c2)))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (f6(c2, c2) = c4) | (f6(c2, c2) = c3) | (~(f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2))) | (~big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2))) | (~(f1(f6(c2, c2), f6(c2, c2)) = f6(c2, c2))) | (~big_f(f6(c2, c2), f1(f6(c2, c2), f6(c2, c2)))))),
% 28.62/18.88 inference(rewrite,[status(thm)],[])).
% 28.62/18.88 tff(15078,plain,
% 28.62/18.88 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f6(c2, c2) = c4) | (f6(c2, c2) = c3) | (~(f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2))) | (~big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2))) | (~(f1(f6(c2, c2), f6(c2, c2)) = f6(c2, c2))) | (~big_f(f6(c2, c2), f1(f6(c2, c2), f6(c2, c2)))))),
% 28.62/18.88 inference(quant_inst,[status(thm)],[])).
% 28.62/18.88 tff(15079,plain,
% 28.62/18.88 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (f6(c2, c2) = c4) | (f6(c2, c2) = c3) | (~(f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2))) | (~big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2))) | (~(f1(f6(c2, c2), f6(c2, c2)) = f6(c2, c2))) | (~big_f(f6(c2, c2), f1(f6(c2, c2), f6(c2, c2))))),
% 28.62/18.88 inference(modus_ponens,[status(thm)],[15078, 15077])).
% 28.62/18.88 tff(15080,plain,
% 28.62/18.88 ((~(f1(f6(c2, c2), f6(c2, c2)) = f6(c2, c2))) | (~big_f(f6(c2, c2), f1(f6(c2, c2), f6(c2, c2))))),
% 28.62/18.88 inference(unit_resolution,[status(thm)],[15079, 933, 15049, 14956, 15076, 15075])).
% 28.62/18.88 tff(15081,plain,
% 28.62/18.88 ($false),
% 28.62/18.88 inference(unit_resolution,[status(thm)],[15080, 15074, 15071])).
% 28.62/18.88 tff(15082,plain,((~(f1(c1, c1) = c1)) | (f6(c2, c2) = c3) | (f6(c2, c2) = c4) | (~(f3(f6(c2, c2), f6(c2, c2)) = f6(c2, c2))) | (~big_f(f3(f6(c2, c2), f6(c2, c2)), f6(c2, c2))) | (~big_f(f6(c2, c2), f6(c2, c2))) | (~(f6(c2, f7(f4(c4))) = c1)) | (~(f7(c2) = c2)) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.62/18.88 tff(15083,plain,
% 28.62/18.88 (~(f1(c1, c1) = c1)),
% 28.62/18.88 inference(unit_resolution,[status(thm)],[15082, 15020, 15070, 15060, 15063, 14821, 6634, 77, 79])).
% 28.62/18.88 tff(15084,plain,
% 28.62/18.88 (f1(c1, c1) = c2),
% 28.62/18.88 inference(unit_resolution,[status(thm)],[601, 15083])).
% 28.62/18.88 tff(15085,plain,
% 28.62/18.88 (~big_f(c1, f1(c1, c1))),
% 28.62/18.88 inference(unit_resolution,[status(thm)],[4561, 15084, 27])).
% 28.62/18.88 tff(15086,plain,
% 28.62/18.88 (~big_f(f8(c3), f1(f8(c3), f8(f7(f4(c4)))))),
% 28.62/18.88 inference(modus_ponens,[status(thm)],[15085, 15015])).
% 28.62/18.88 tff(15087,plain,
% 28.62/18.88 (f3(c1, f8(c3)) = f3(c1, c1)),
% 28.62/18.88 inference(monotonicity,[status(thm)],[15010])).
% 28.62/18.88 tff(15088,plain,
% 28.62/18.88 (f3(c1, f8(c3)) = c1),
% 28.62/18.88 inference(transitivity,[status(thm)],[15087, 15059])).
% 28.62/18.88 tff(15089,plain,
% 28.62/18.88 (f3(c1, f3(c1, f8(c3))) = f3(c1, c1)),
% 28.62/18.88 inference(monotonicity,[status(thm)],[15088])).
% 28.62/18.88 tff(15090,plain,
% 28.62/18.88 (f3(c1, f3(c1, f8(c3))) = f6(c2, c2)),
% 28.62/18.88 inference(transitivity,[status(thm)],[15089, 15059, 14103, 2475])).
% 28.62/18.88 tff(15091,plain,
% 28.62/18.88 (big_f(f3(c1, f3(c1, f8(c3))), c1) <=> big_f(f6(c2, c2), f6(c2, c2))),
% 28.62/18.88 inference(monotonicity,[status(thm)],[15090, 14819])).
% 28.62/18.88 tff(15092,plain,
% 28.62/18.88 (big_f(f6(c2, c2), f6(c2, c2)) <=> big_f(f3(c1, f3(c1, f8(c3))), c1)),
% 28.62/18.88 inference(symmetry,[status(thm)],[15091])).
% 28.62/18.88 tff(15093,plain,
% 28.62/18.88 (big_f(f3(c1, f3(c1, f8(c3))), c1)),
% 28.62/18.88 inference(modus_ponens,[status(thm)],[14821, 15092])).
% 28.62/18.88 tff(15094,plain,
% 28.62/18.88 ((f3(c1, f3(c1, f8(c3))) = f3(c1, f8(c3))) <=> (f3(c1, f3(c1, f8(c3))) = c1)),
% 28.62/18.88 inference(monotonicity,[status(thm)],[15088])).
% 28.62/18.88 tff(15095,plain,
% 28.62/18.88 ((f3(c1, f3(c1, f8(c3))) = c1) <=> (f3(c1, f3(c1, f8(c3))) = f3(c1, f8(c3)))),
% 28.62/18.88 inference(symmetry,[status(thm)],[15094])).
% 28.62/18.88 tff(15096,plain,
% 28.62/18.88 (f3(c1, f3(c1, f8(c3))) = c1),
% 28.62/18.88 inference(transitivity,[status(thm)],[15089, 15059])).
% 28.62/18.88 tff(15097,plain,
% 28.62/18.88 (f3(c1, f3(c1, f8(c3))) = f3(c1, f8(c3))),
% 28.62/18.88 inference(modus_ponens,[status(thm)],[15096, 15095])).
% 28.62/18.88 tff(15098,plain,
% 28.62/18.88 ((~(f6(c2, c2) = c2)) <=> (~(c1 = c4))),
% 28.62/18.88 inference(monotonicity,[status(thm)],[15067])).
% 28.62/18.88 tff(15099,plain,
% 28.62/18.88 (~(c1 = c4)),
% 28.62/18.88 inference(modus_ponens,[status(thm)],[14102, 15098])).
% 28.62/18.88 tff(15100,plain,
% 28.62/18.88 ((f8(c3) = c3) <=> (f8(c3) = c2)),
% 28.62/18.88 inference(monotonicity,[status(thm)],[15008])).
% 28.62/18.88 tff(15101,plain,
% 28.62/18.88 ((f8(c3) = c2) <=> (f8(c3) = c3)),
% 28.62/18.88 inference(symmetry,[status(thm)],[15100])).
% 28.62/18.88 tff(15102,plain,
% 28.62/18.88 (f8(c3) = f6(c2, c2)),
% 28.62/18.88 inference(transitivity,[status(thm)],[15009, 14831])).
% 28.62/18.88 tff(15103,plain,
% 28.62/18.88 ((f8(c3) = c2) <=> (f6(c2, c2) = c2)),
% 28.62/18.88 inference(monotonicity,[status(thm)],[15102])).
% 28.62/18.88 tff(15104,plain,
% 28.62/18.88 ((f6(c2, c2) = c2) <=> (f8(c3) = c2)),
% 28.62/18.88 inference(symmetry,[status(thm)],[15103])).
% 28.62/18.88 tff(15105,plain,
% 28.62/18.88 ((f6(c2, c2) = c2) <=> (f8(c3) = c3)),
% 28.62/18.88 inference(transitivity,[status(thm)],[15104, 15101])).
% 28.62/18.88 tff(15106,plain,
% 28.62/18.88 ((~(f6(c2, c2) = c2)) <=> (~(f8(c3) = c3))),
% 28.62/18.88 inference(monotonicity,[status(thm)],[15105])).
% 28.62/18.88 tff(15107,plain,
% 28.62/18.88 (~(f8(c3) = c3)),
% 28.62/18.88 inference(modus_ponens,[status(thm)],[14102, 15106])).
% 28.62/18.88 tff(15108,plain,
% 28.62/18.88 ((f1(f8(c3), f8(f7(f4(c4)))) = f8(f7(f4(c4)))) <=> (f1(f8(c3), c1) = c1)),
% 28.62/18.88 inference(monotonicity,[status(thm)],[14833, 14832])).
% 28.62/18.88 tff(15109,plain,
% 28.62/18.88 ((f1(f8(c3), c1) = c1) <=> (f1(f8(c3), f8(f7(f4(c4)))) = f8(f7(f4(c4))))),
% 28.62/18.88 inference(symmetry,[status(thm)],[15108])).
% 28.62/18.88 tff(15110,plain,
% 28.62/18.88 ((f1(f8(c3), c1) = c1) <=> (f1(c1, c1) = c1)),
% 28.62/18.88 inference(monotonicity,[status(thm)],[15011])).
% 28.62/18.88 tff(15111,plain,
% 28.62/18.88 ((f1(c1, c1) = c1) <=> (f1(f8(c3), c1) = c1)),
% 28.62/18.88 inference(symmetry,[status(thm)],[15110])).
% 28.62/18.88 tff(15112,plain,
% 28.62/18.88 ((f1(c1, c1) = c1) <=> (f1(f8(c3), f8(f7(f4(c4)))) = f8(f7(f4(c4))))),
% 28.62/18.88 inference(transitivity,[status(thm)],[15111, 15109])).
% 28.62/18.88 tff(15113,plain,
% 28.62/18.88 ((~(f1(c1, c1) = c1)) <=> (~(f1(f8(c3), f8(f7(f4(c4)))) = f8(f7(f4(c4)))))),
% 28.62/18.88 inference(monotonicity,[status(thm)],[15112])).
% 28.62/18.88 tff(15114,plain,
% 28.62/18.88 (~(f1(f8(c3), f8(f7(f4(c4)))) = f8(f7(f4(c4))))),
% 28.62/18.88 inference(modus_ponens,[status(thm)],[15083, 15113])).
% 28.62/18.88 tff(15115,plain,
% 28.62/18.88 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c1 = c4) | (f8(c3) = c3) | (f1(f8(c3), f8(f7(f4(c4)))) = f8(f7(f4(c4)))) | big_f(f8(c3), f1(f8(c3), f8(f7(f4(c4))))) | (~big_f(f3(c1, f3(c1, f8(c3))), c1)) | (~(f3(c1, f3(c1, f8(c3))) = f3(c1, f8(c3)))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c1 = c4) | (f8(c3) = c3) | (f1(f8(c3), f8(f7(f4(c4)))) = f8(f7(f4(c4)))) | big_f(f8(c3), f1(f8(c3), f8(f7(f4(c4))))) | (~big_f(f3(c1, f3(c1, f8(c3))), c1)) | (~(f3(c1, f3(c1, f8(c3))) = f3(c1, f8(c3)))))),
% 28.62/18.88 inference(rewrite,[status(thm)],[])).
% 28.62/18.88 tff(15116,plain,
% 28.62/18.88 (((c1 = c4) | (f8(c3) = c3) | (f1(f8(c3), f8(f7(f4(c4)))) = f8(f7(f4(c4)))) | big_f(f8(c3), f1(f8(c3), f8(f7(f4(c4))))) | (~(f3(c1, f3(c1, f8(c3))) = f3(c1, f8(c3)))) | (~big_f(f3(c1, f3(c1, f8(c3))), c1))) <=> ((c1 = c4) | (f8(c3) = c3) | (f1(f8(c3), f8(f7(f4(c4)))) = f8(f7(f4(c4)))) | big_f(f8(c3), f1(f8(c3), f8(f7(f4(c4))))) | (~big_f(f3(c1, f3(c1, f8(c3))), c1)) | (~(f3(c1, f3(c1, f8(c3))) = f3(c1, f8(c3)))))),
% 28.62/18.88 inference(rewrite,[status(thm)],[])).
% 28.62/18.88 tff(15117,plain,
% 28.62/18.88 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c1 = c4) | (f8(c3) = c3) | (f1(f8(c3), f8(f7(f4(c4)))) = f8(f7(f4(c4)))) | big_f(f8(c3), f1(f8(c3), f8(f7(f4(c4))))) | (~(f3(c1, f3(c1, f8(c3))) = f3(c1, f8(c3)))) | (~big_f(f3(c1, f3(c1, f8(c3))), c1)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c1 = c4) | (f8(c3) = c3) | (f1(f8(c3), f8(f7(f4(c4)))) = f8(f7(f4(c4)))) | big_f(f8(c3), f1(f8(c3), f8(f7(f4(c4))))) | (~big_f(f3(c1, f3(c1, f8(c3))), c1)) | (~(f3(c1, f3(c1, f8(c3))) = f3(c1, f8(c3))))))),
% 28.62/18.88 inference(monotonicity,[status(thm)],[15116])).
% 28.62/18.88 tff(15118,plain,
% 28.62/18.88 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c1 = c4) | (f8(c3) = c3) | (f1(f8(c3), f8(f7(f4(c4)))) = f8(f7(f4(c4)))) | big_f(f8(c3), f1(f8(c3), f8(f7(f4(c4))))) | (~(f3(c1, f3(c1, f8(c3))) = f3(c1, f8(c3)))) | (~big_f(f3(c1, f3(c1, f8(c3))), c1)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c1 = c4) | (f8(c3) = c3) | (f1(f8(c3), f8(f7(f4(c4)))) = f8(f7(f4(c4)))) | big_f(f8(c3), f1(f8(c3), f8(f7(f4(c4))))) | (~big_f(f3(c1, f3(c1, f8(c3))), c1)) | (~(f3(c1, f3(c1, f8(c3))) = f3(c1, f8(c3)))))),
% 28.62/18.88 inference(transitivity,[status(thm)],[15117, 15115])).
% 28.62/18.88 tff(15119,plain,
% 28.62/18.88 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c1 = c4) | (f8(c3) = c3) | (f1(f8(c3), f8(f7(f4(c4)))) = f8(f7(f4(c4)))) | big_f(f8(c3), f1(f8(c3), f8(f7(f4(c4))))) | (~(f3(c1, f3(c1, f8(c3))) = f3(c1, f8(c3)))) | (~big_f(f3(c1, f3(c1, f8(c3))), c1)))),
% 28.62/18.88 inference(quant_inst,[status(thm)],[])).
% 28.62/18.88 tff(15120,plain,
% 28.62/18.88 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c1 = c4) | (f8(c3) = c3) | (f1(f8(c3), f8(f7(f4(c4)))) = f8(f7(f4(c4)))) | big_f(f8(c3), f1(f8(c3), f8(f7(f4(c4))))) | (~big_f(f3(c1, f3(c1, f8(c3))), c1)) | (~(f3(c1, f3(c1, f8(c3))) = f3(c1, f8(c3))))),
% 28.62/18.88 inference(modus_ponens,[status(thm)],[15119, 15118])).
% 28.62/18.88 tff(15121,plain,
% 28.62/18.88 ((c1 = c4) | (f8(c3) = c3) | (f1(f8(c3), f8(f7(f4(c4)))) = f8(f7(f4(c4)))) | big_f(f8(c3), f1(f8(c3), f8(f7(f4(c4))))) | (~big_f(f3(c1, f3(c1, f8(c3))), c1)) | (~(f3(c1, f3(c1, f8(c3))) = f3(c1, f8(c3))))),
% 28.62/18.88 inference(unit_resolution,[status(thm)],[15120, 969])).
% 28.62/18.88 tff(15122,plain,
% 28.62/18.88 (big_f(f8(c3), f1(f8(c3), f8(f7(f4(c4)))))),
% 28.62/18.88 inference(unit_resolution,[status(thm)],[15121, 15114, 15107, 15099, 15097, 15093])).
% 28.62/18.88 tff(15123,plain,
% 28.62/18.88 ($false),
% 28.62/18.88 inference(unit_resolution,[status(thm)],[15122, 15086])).
% 28.62/18.88 tff(15124,plain,(big_f(c2, c1) | (~(f6(c2, f7(f4(c4))) = c1)) | (~(f7(c2) = c2)) | (~(f4(c4) = c2)) | big_f(c1, c2) | (~big_f(c1, c1)) | (~big_f(c2, c2)) | (f10(c2) = c2) | (f10(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 28.62/18.88 tff(15125,plain,
% 28.62/18.88 (big_f(c2, c1)),
% 28.62/18.88 inference(unit_resolution,[status(thm)],[15124, 89, 14794, 79, 27, 4932, 1345, 6634, 3])).
% 28.62/18.88 tff(15126,plain,
% 28.62/18.88 (big_f(f7(f6(c2, c2)), f6(c2, c2))),
% 28.62/18.88 inference(modus_ponens,[status(thm)],[15125, 14815])).
% 28.62/18.88 tff(15127,plain,
% 28.62/18.88 (f7(f6(c2, c2)) = c2),
% 28.62/18.88 inference(transitivity,[status(thm)],[14809, 347])).
% 28.62/18.88 tff(15128,plain,
% 28.62/18.88 ((f7(f6(c2, c2)) = f6(c2, c2)) <=> (c2 = f6(c2, c2))),
% 28.62/18.88 inference(monotonicity,[status(thm)],[15127])).
% 28.62/18.88 tff(15129,plain,
% 28.62/18.88 ((f7(f6(c2, c2)) = f6(c2, c2)) <=> (f6(c2, c2) = c2)),
% 28.62/18.88 inference(transitivity,[status(thm)],[15128, 3242])).
% 28.62/18.88 tff(15130,plain,
% 28.62/18.88 ((f6(c2, c2) = c2) <=> (f7(f6(c2, c2)) = f6(c2, c2))),
% 28.62/18.88 inference(symmetry,[status(thm)],[15129])).
% 28.62/18.88 tff(15131,plain,
% 28.62/18.88 ((~(f6(c2, c2) = c2)) <=> (~(f7(f6(c2, c2)) = f6(c2, c2)))),
% 28.62/18.88 inference(monotonicity,[status(thm)],[15130])).
% 28.62/18.88 tff(15132,plain,
% 28.62/18.88 ((f6(c2, c2) = c2) <=> (c1 = c2)),
% 28.62/18.88 inference(monotonicity,[status(thm)],[14805])).
% 28.62/18.88 tff(15133,plain,
% 28.62/18.88 ((f6(c2, c2) = c2) <=> (c2 = c1)),
% 28.62/18.88 inference(transitivity,[status(thm)],[15132, 1])).
% 28.62/18.88 tff(15134,plain,
% 28.62/18.88 ((c2 = c1) <=> (f6(c2, c2) = c2)),
% 28.62/18.88 inference(symmetry,[status(thm)],[15133])).
% 28.62/18.88 tff(15135,plain,
% 28.62/18.88 ((~(c2 = c1)) <=> (~(f6(c2, c2) = c2))),
% 28.62/18.88 inference(monotonicity,[status(thm)],[15134])).
% 28.62/18.88 tff(15136,plain,
% 28.62/18.88 (~(f6(c2, c2) = c2)),
% 28.62/18.88 inference(modus_ponens,[status(thm)],[75, 15135])).
% 28.62/18.88 tff(15137,plain,
% 28.62/18.88 (~(f7(f6(c2, c2)) = f6(c2, c2))),
% 28.62/18.88 inference(modus_ponens,[status(thm)],[15136, 15131])).
% 28.62/18.88 tff(15138,plain,
% 28.62/18.88 (big_f(f7(f6(c2, c2)), c2) <=> big_f(c2, c2)),
% 28.62/18.88 inference(monotonicity,[status(thm)],[15127])).
% 28.62/18.88 tff(15139,plain,
% 28.62/18.88 (big_f(c2, c2) <=> big_f(f7(f6(c2, c2)), c2)),
% 28.62/18.88 inference(symmetry,[status(thm)],[15138])).
% 28.62/18.88 tff(15140,plain,
% 28.62/18.88 (big_f(f7(f6(c2, c2)), c2)),
% 28.62/18.88 inference(modus_ponens,[status(thm)],[1345, 15139])).
% 28.62/18.88 tff(15141,plain,
% 28.62/18.88 (big_f(c2, f10(c2)) <=> big_f(f7(c2), f6(c2, c2))),
% 28.62/18.88 inference(monotonicity,[status(thm)],[14808, 14797])).
% 28.62/18.88 tff(15142,plain,
% 28.62/18.88 (big_f(f7(c2), f6(c2, c2)) <=> big_f(c2, f10(c2))),
% 28.62/18.88 inference(symmetry,[status(thm)],[15141])).
% 28.62/18.88 tff(15143,plain,
% 28.62/18.88 (big_f(c2, c1) <=> big_f(c2, f10(c2))),
% 28.62/18.88 inference(transitivity,[status(thm)],[14814, 15142])).
% 28.62/18.88 tff(15144,plain,
% 28.62/18.88 (big_f(c2, f10(c2))),
% 28.62/18.88 inference(modus_ponens,[status(thm)],[15125, 15143])).
% 28.62/18.88 tff(15145,assumption,(~(f7(f6(c2, c2)) = f6(c2, c2))), introduced(assumption)).
% 28.62/18.88 tff(15146,assumption,(big_f(f7(f6(c2, c2)), c2)), introduced(assumption)).
% 28.62/18.88 tff(15147,plain,
% 28.62/18.88 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(f7(f6(c2, c2)), c2)) | (c2 = f5(f6(c2, c2))) | (~big_f(c2, f10(c2))) | (f7(f6(c2, c2)) = f6(c2, c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(f7(f6(c2, c2)), c2)) | (c2 = f5(f6(c2, c2))) | (~big_f(c2, f10(c2))) | (f7(f6(c2, c2)) = f6(c2, c2)))),
% 28.62/18.88 inference(rewrite,[status(thm)],[])).
% 28.62/18.88 tff(15148,plain,
% 28.62/18.88 (((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (c2 = f5(f6(c2, c2))) | (~big_f(f7(f6(c2, c2)), c2))) <=> ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(f7(f6(c2, c2)), c2)) | (c2 = f5(f6(c2, c2))) | (~big_f(c2, f10(c2))) | (f7(f6(c2, c2)) = f6(c2, c2)))),
% 28.62/18.88 inference(rewrite,[status(thm)],[])).
% 28.62/18.88 tff(15149,plain,
% 28.62/18.88 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (c2 = f5(f6(c2, c2))) | (~big_f(f7(f6(c2, c2)), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(f7(f6(c2, c2)), c2)) | (c2 = f5(f6(c2, c2))) | (~big_f(c2, f10(c2))) | (f7(f6(c2, c2)) = f6(c2, c2))))),
% 28.62/18.88 inference(monotonicity,[status(thm)],[15148])).
% 28.62/18.88 tff(15150,plain,
% 28.62/18.88 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (c2 = f5(f6(c2, c2))) | (~big_f(f7(f6(c2, c2)), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(f7(f6(c2, c2)), c2)) | (c2 = f5(f6(c2, c2))) | (~big_f(c2, f10(c2))) | (f7(f6(c2, c2)) = f6(c2, c2)))),
% 28.62/18.88 inference(transitivity,[status(thm)],[15149, 15147])).
% 28.62/18.88 tff(15151,plain,
% 28.62/18.88 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (c2 = f5(f6(c2, c2))) | (~big_f(f7(f6(c2, c2)), c2)))),
% 28.62/18.88 inference(quant_inst,[status(thm)],[])).
% 28.62/18.88 tff(15152,plain,
% 28.62/18.88 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(f7(f6(c2, c2)), c2)) | (c2 = f5(f6(c2, c2))) | (~big_f(c2, f10(c2))) | (f7(f6(c2, c2)) = f6(c2, c2))),
% 28.70/18.88 inference(modus_ponens,[status(thm)],[15151, 15150])).
% 28.70/18.88 tff(15153,plain,
% 28.70/18.88 ((c2 = f8(c2)) | (c2 = f5(f6(c2, c2)))),
% 28.70/18.88 inference(unit_resolution,[status(thm)],[15152, 1659, 89, 12291, 15146, 15145])).
% 28.70/18.88 tff(15154,plain,
% 28.70/18.88 (c2 = f5(f6(c2, c2))),
% 28.70/18.88 inference(unit_resolution,[status(thm)],[15153, 12290])).
% 28.70/18.88 tff(15155,plain,
% 28.70/18.88 (f5(f6(c2, c2)) = c2),
% 28.70/18.88 inference(symmetry,[status(thm)],[15154])).
% 28.70/18.88 tff(15156,plain,
% 28.70/18.88 ((c2 = f8(c2)) | (f6(c2, c2) = f5(f6(c2, c2)))),
% 28.70/18.88 inference(unit_resolution,[status(thm)],[14549, 1659, 89, 12291, 14413, 15145])).
% 28.70/18.88 tff(15157,plain,
% 28.70/18.88 (f6(c2, c2) = f5(f6(c2, c2))),
% 28.70/18.88 inference(unit_resolution,[status(thm)],[15156, 12290])).
% 28.70/18.88 tff(15158,plain,
% 28.70/18.88 (f6(c2, c2) = c2),
% 28.70/18.88 inference(transitivity,[status(thm)],[15157, 15155])).
% 28.70/18.88 tff(15159,plain,
% 28.70/18.88 ($false),
% 28.70/18.88 inference(unit_resolution,[status(thm)],[2637, 15158])).
% 28.70/18.88 tff(15160,plain,((c2 = f8(c2)) | (f6(c2, c2) = c2) | (f10(c2) = c2) | (~big_f(c2, f10(c2))) | (~big_f(f7(f6(c2, c2)), c2)) | (f7(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f7(f6(c2, c2)), f6(c2, c2)))), inference(lemma,lemma(discharge,[]))).
% 28.70/18.88 tff(15161,plain,
% 28.70/18.88 (c2 = f8(c2)),
% 28.70/18.88 inference(unit_resolution,[status(thm)],[15160, 89, 15136, 15144, 15140, 15137, 15126])).
% 28.70/18.88 tff(15162,plain,
% 28.70/18.88 (f8(c2) = c2),
% 28.70/18.88 inference(symmetry,[status(thm)],[15161])).
% 28.70/18.88 tff(15163,plain,
% 28.70/18.88 ((c1 = f8(c2)) <=> (f6(c2, c2) = c2)),
% 28.70/18.88 inference(monotonicity,[status(thm)],[14800, 15162])).
% 28.70/18.88 tff(15164,plain,
% 28.70/18.88 ((f6(c2, c2) = c2) <=> (c1 = f8(c2))),
% 28.70/18.88 inference(symmetry,[status(thm)],[15163])).
% 28.70/18.88 tff(15165,plain,
% 28.70/18.88 ((f6(c2, c2) = c2) <=> (f6(c2, c2) = f8(c2))),
% 28.70/18.88 inference(transitivity,[status(thm)],[15164, 14807])).
% 28.70/18.88 tff(15166,plain,
% 28.70/18.88 ((~(f6(c2, c2) = c2)) <=> (~(f6(c2, c2) = f8(c2)))),
% 28.70/18.88 inference(monotonicity,[status(thm)],[15165])).
% 28.70/18.88 tff(15167,plain,
% 28.70/18.88 (~(f6(c2, c2) = f8(c2))),
% 28.70/18.88 inference(modus_ponens,[status(thm)],[15136, 15166])).
% 28.70/18.88 tff(15168,plain,
% 28.70/18.88 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (~big_f(f7(f6(c2, c2)), c2)) | (c2 = f5(f6(c2, c2))) | (f6(c2, c2) = f8(c2)) | (f7(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f6(c2, c2), f10(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (~big_f(f7(f6(c2, c2)), c2)) | (c2 = f5(f6(c2, c2))) | (f6(c2, c2) = f8(c2)) | (f7(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f6(c2, c2), f10(c2))))),
% 28.70/18.89 inference(rewrite,[status(thm)],[])).
% 28.70/18.89 tff(15169,plain,
% 28.70/18.89 (((f10(c2) = c2) | (f6(c2, c2) = f8(c2)) | (~big_f(f6(c2, c2), f10(c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (c2 = f5(f6(c2, c2))) | (~big_f(f7(f6(c2, c2)), c2))) <=> ((f10(c2) = c2) | (~big_f(f7(f6(c2, c2)), c2)) | (c2 = f5(f6(c2, c2))) | (f6(c2, c2) = f8(c2)) | (f7(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f6(c2, c2), f10(c2))))),
% 28.70/18.89 inference(rewrite,[status(thm)],[])).
% 28.70/18.89 tff(15170,plain,
% 28.70/18.89 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f6(c2, c2) = f8(c2)) | (~big_f(f6(c2, c2), f10(c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (c2 = f5(f6(c2, c2))) | (~big_f(f7(f6(c2, c2)), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (~big_f(f7(f6(c2, c2)), c2)) | (c2 = f5(f6(c2, c2))) | (f6(c2, c2) = f8(c2)) | (f7(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f6(c2, c2), f10(c2)))))),
% 28.70/18.89 inference(monotonicity,[status(thm)],[15169])).
% 28.70/18.89 tff(15171,plain,
% 28.70/18.89 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f6(c2, c2) = f8(c2)) | (~big_f(f6(c2, c2), f10(c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (c2 = f5(f6(c2, c2))) | (~big_f(f7(f6(c2, c2)), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (~big_f(f7(f6(c2, c2)), c2)) | (c2 = f5(f6(c2, c2))) | (f6(c2, c2) = f8(c2)) | (f7(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f6(c2, c2), f10(c2))))),
% 28.70/18.89 inference(transitivity,[status(thm)],[15170, 15168])).
% 28.70/18.89 tff(15172,plain,
% 28.70/18.89 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f6(c2, c2) = f8(c2)) | (~big_f(f6(c2, c2), f10(c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (c2 = f5(f6(c2, c2))) | (~big_f(f7(f6(c2, c2)), c2)))),
% 28.70/18.89 inference(quant_inst,[status(thm)],[])).
% 28.70/18.89 tff(15173,plain,
% 28.70/18.89 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (~big_f(f7(f6(c2, c2)), c2)) | (c2 = f5(f6(c2, c2))) | (f6(c2, c2) = f8(c2)) | (f7(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f6(c2, c2), f10(c2)))),
% 28.70/18.89 inference(modus_ponens,[status(thm)],[15172, 15171])).
% 28.70/18.89 tff(15174,plain,
% 28.70/18.89 ((c2 = f5(f6(c2, c2))) | (f6(c2, c2) = f8(c2)) | (~big_f(f6(c2, c2), f10(c2)))),
% 28.70/18.89 inference(unit_resolution,[status(thm)],[15173, 1659, 89, 15140, 15137])).
% 28.70/18.89 tff(15175,plain,
% 28.70/18.89 (c2 = f5(f6(c2, c2))),
% 28.70/18.89 inference(unit_resolution,[status(thm)],[15174, 15167, 14803])).
% 28.70/18.89 tff(15176,plain,
% 28.70/18.89 (f5(f6(c2, c2)) = c2),
% 28.70/18.89 inference(symmetry,[status(thm)],[15175])).
% 28.70/18.89 tff(15177,plain,
% 28.70/18.89 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f6(c2, c2) = f8(c2)) | (f6(c2, c2) = f5(f6(c2, c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f7(f6(c2, c2)), f6(c2, c2))) | (~big_f(f6(c2, c2), f10(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (f6(c2, c2) = f8(c2)) | (f6(c2, c2) = f5(f6(c2, c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f7(f6(c2, c2)), f6(c2, c2))) | (~big_f(f6(c2, c2), f10(c2))))),
% 28.70/18.89 inference(rewrite,[status(thm)],[])).
% 28.70/18.89 tff(15178,plain,
% 28.70/18.89 (((f10(c2) = c2) | (f6(c2, c2) = f8(c2)) | (~big_f(f6(c2, c2), f10(c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (f6(c2, c2) = f5(f6(c2, c2))) | (~big_f(f7(f6(c2, c2)), f6(c2, c2)))) <=> ((f10(c2) = c2) | (f6(c2, c2) = f8(c2)) | (f6(c2, c2) = f5(f6(c2, c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f7(f6(c2, c2)), f6(c2, c2))) | (~big_f(f6(c2, c2), f10(c2))))),
% 28.70/18.89 inference(rewrite,[status(thm)],[])).
% 28.70/18.89 tff(15179,plain,
% 28.70/18.89 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f6(c2, c2) = f8(c2)) | (~big_f(f6(c2, c2), f10(c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (f6(c2, c2) = f5(f6(c2, c2))) | (~big_f(f7(f6(c2, c2)), f6(c2, c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f6(c2, c2) = f8(c2)) | (f6(c2, c2) = f5(f6(c2, c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f7(f6(c2, c2)), f6(c2, c2))) | (~big_f(f6(c2, c2), f10(c2)))))),
% 28.70/18.89 inference(monotonicity,[status(thm)],[15178])).
% 28.70/18.89 tff(15180,plain,
% 28.70/18.89 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f6(c2, c2) = f8(c2)) | (~big_f(f6(c2, c2), f10(c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (f6(c2, c2) = f5(f6(c2, c2))) | (~big_f(f7(f6(c2, c2)), f6(c2, c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (f6(c2, c2) = f8(c2)) | (f6(c2, c2) = f5(f6(c2, c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f7(f6(c2, c2)), f6(c2, c2))) | (~big_f(f6(c2, c2), f10(c2))))),
% 28.70/18.89 inference(transitivity,[status(thm)],[15179, 15177])).
% 28.70/18.89 tff(15181,plain,
% 28.70/18.89 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f6(c2, c2) = f8(c2)) | (~big_f(f6(c2, c2), f10(c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (f6(c2, c2) = f5(f6(c2, c2))) | (~big_f(f7(f6(c2, c2)), f6(c2, c2))))),
% 28.70/18.89 inference(quant_inst,[status(thm)],[])).
% 28.70/18.89 tff(15182,plain,
% 28.70/18.89 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (f6(c2, c2) = f8(c2)) | (f6(c2, c2) = f5(f6(c2, c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f7(f6(c2, c2)), f6(c2, c2))) | (~big_f(f6(c2, c2), f10(c2)))),
% 28.70/18.89 inference(modus_ponens,[status(thm)],[15181, 15180])).
% 28.70/18.89 tff(15183,plain,
% 28.70/18.89 ((f6(c2, c2) = f8(c2)) | (f6(c2, c2) = f5(f6(c2, c2)))),
% 28.70/18.89 inference(unit_resolution,[status(thm)],[15182, 1659, 89, 15126, 15137, 14803])).
% 28.70/18.89 tff(15184,plain,
% 28.70/18.89 (f6(c2, c2) = f5(f6(c2, c2))),
% 28.70/18.89 inference(unit_resolution,[status(thm)],[15183, 15167])).
% 28.70/18.89 tff(15185,plain,
% 28.70/18.89 (f6(c2, c2) = c2),
% 28.70/18.89 inference(transitivity,[status(thm)],[15184, 15176])).
% 28.70/18.89 tff(15186,plain,
% 28.70/18.89 ($false),
% 28.70/18.89 inference(unit_resolution,[status(thm)],[15136, 15185])).
% 28.70/18.89 tff(15187,plain,((f10(c2) = c2) | (~(f6(c2, f7(f4(c4))) = c1)) | (~(f4(c4) = c2)) | (~(f7(c1) = c2)) | big_f(c1, c2) | (~big_f(c1, c1)) | (~big_f(c2, c2)) | (f10(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 28.70/18.89 tff(15188,plain,
% 28.70/18.89 (big_f(c1, c2)),
% 28.70/18.89 inference(unit_resolution,[status(thm)],[15187, 14768, 79, 120, 6634, 14617, 14740, 3])).
% 28.70/18.89 tff(15189,plain,
% 28.70/18.89 (big_f(f6(c2, c2), f10(f6(c2, c2)))),
% 28.70/18.89 inference(modus_ponens,[status(thm)],[15188, 14793])).
% 28.70/18.89 tff(15190,plain,
% 28.70/18.89 ((c2 = f8(c1)) | (~(f7(c2) = c2)) | (f6(c2, f7(c2)) = f7(c2)) | big_f(f7(c2), f6(c2, f7(c2)))),
% 28.70/18.89 inference(unit_resolution,[status(thm)],[14858, 2662, 6122, 3])).
% 28.70/18.89 tff(15191,plain,
% 28.70/18.89 (c2 = f8(c1)),
% 28.70/18.89 inference(unit_resolution,[status(thm)],[15190, 14852, 77, 14846])).
% 28.70/18.89 tff(15192,plain,
% 28.70/18.89 (f8(c1) = c2),
% 28.70/18.89 inference(symmetry,[status(thm)],[15191])).
% 28.70/18.89 tff(15193,assumption,(big_f(f6(c2, c2), f10(f6(c2, c2)))), introduced(assumption)).
% 28.70/18.89 tff(15194,plain,
% 28.70/18.89 (f10(f6(c2, c2)) = c2),
% 28.70/18.89 inference(transitivity,[status(thm)],[14300, 15])).
% 28.70/18.89 tff(15195,plain,
% 28.70/18.89 ((f10(f6(c2, c2)) = f6(c2, c2)) <=> (c2 = f6(c2, c2))),
% 28.70/18.89 inference(monotonicity,[status(thm)],[15194])).
% 28.70/18.89 tff(15196,plain,
% 28.70/18.89 ((f10(f6(c2, c2)) = f6(c2, c2)) <=> (f6(c2, c2) = c2)),
% 28.70/18.89 inference(transitivity,[status(thm)],[15195, 3242])).
% 28.70/18.89 tff(15197,plain,
% 28.70/18.89 ((f6(c2, c2) = c2) <=> (f10(f6(c2, c2)) = f6(c2, c2))),
% 28.70/18.89 inference(symmetry,[status(thm)],[15196])).
% 28.70/18.89 tff(15198,plain,
% 28.70/18.89 ((~(f6(c2, c2) = c2)) <=> (~(f10(f6(c2, c2)) = f6(c2, c2)))),
% 28.70/18.89 inference(monotonicity,[status(thm)],[15197])).
% 28.70/18.89 tff(15199,plain,
% 28.70/18.89 (~(f10(f6(c2, c2)) = f6(c2, c2))),
% 28.70/18.89 inference(modus_ponens,[status(thm)],[14102, 15198])).
% 28.70/18.89 tff(15200,plain,
% 28.70/18.89 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (f10(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f6(c2, c2), f10(f6(c2, c2)))) | (f6(c2, c2) = f8(f6(c2, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (f10(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f6(c2, c2), f10(f6(c2, c2)))) | (f6(c2, c2) = f8(f6(c2, c2))))),
% 28.70/18.89 inference(rewrite,[status(thm)],[])).
% 28.70/18.89 tff(15201,plain,
% 28.70/18.89 (((f10(f6(c2, c2)) = f6(c2, c2)) | (f6(c2, c2) = f8(f6(c2, c2))) | (~big_f(f6(c2, c2), f10(f6(c2, c2)))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2))) <=> ((~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (f10(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f6(c2, c2), f10(f6(c2, c2)))) | (f6(c2, c2) = f8(f6(c2, c2))))),
% 28.70/18.89 inference(rewrite,[status(thm)],[])).
% 28.70/18.89 tff(15202,plain,
% 28.70/18.89 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f6(c2, c2)) = f6(c2, c2)) | (f6(c2, c2) = f8(f6(c2, c2))) | (~big_f(f6(c2, c2), f10(f6(c2, c2)))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (f10(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f6(c2, c2), f10(f6(c2, c2)))) | (f6(c2, c2) = f8(f6(c2, c2)))))),
% 28.70/18.89 inference(monotonicity,[status(thm)],[15201])).
% 28.70/18.89 tff(15203,plain,
% 28.70/18.89 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f6(c2, c2)) = f6(c2, c2)) | (f6(c2, c2) = f8(f6(c2, c2))) | (~big_f(f6(c2, c2), f10(f6(c2, c2)))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (f10(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f6(c2, c2), f10(f6(c2, c2)))) | (f6(c2, c2) = f8(f6(c2, c2))))),
% 28.70/18.89 inference(transitivity,[status(thm)],[15202, 15200])).
% 28.70/18.89 tff(15204,plain,
% 28.70/18.89 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f6(c2, c2)) = f6(c2, c2)) | (f6(c2, c2) = f8(f6(c2, c2))) | (~big_f(f6(c2, c2), f10(f6(c2, c2)))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)))),
% 28.70/18.89 inference(quant_inst,[status(thm)],[])).
% 28.70/18.89 tff(15205,plain,
% 28.70/18.89 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (f10(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f6(c2, c2), f10(f6(c2, c2)))) | (f6(c2, c2) = f8(f6(c2, c2)))),
% 28.70/18.89 inference(modus_ponens,[status(thm)],[15204, 15203])).
% 28.70/18.89 tff(15206,plain,
% 28.70/18.89 (big_f(f7(c2), f6(c2, c2)) | (f6(c2, c2) = f8(f6(c2, c2)))),
% 28.70/18.89 inference(unit_resolution,[status(thm)],[15205, 2662, 77, 14102, 15199, 15193])).
% 28.70/18.89 tff(15207,plain,
% 28.70/18.89 (f6(c2, c2) = f8(f6(c2, c2))),
% 28.70/18.89 inference(unit_resolution,[status(thm)],[15206, 14097])).
% 28.70/18.89 tff(15208,plain,
% 28.70/18.89 (f6(c2, c2) = c2),
% 28.70/18.89 inference(transitivity,[status(thm)],[15207, 14317, 15192])).
% 28.70/18.89 tff(15209,plain,
% 28.70/18.89 ($false),
% 28.70/18.89 inference(unit_resolution,[status(thm)],[14102, 15208])).
% 28.70/18.89 tff(15210,plain,(big_f(c2, c1) | (~(f6(c2, f7(f4(c4))) = c1)) | (~(f7(c2) = c2)) | (~(f4(c4) = c2)) | (~big_f(f6(c2, c2), f10(f6(c2, c2)))) | (~big_f(c2, f10(c1))) | (f10(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 28.70/18.89 tff(15211,plain,
% 28.70/18.89 (big_f(c2, c1)),
% 28.70/18.89 inference(unit_resolution,[status(thm)],[15210, 6634, 14741, 79, 15189, 14789, 3])).
% 28.70/18.89 tff(15212,plain,
% 28.70/18.89 (big_f(f7(f6(c2, c2)), f6(c2, c2))),
% 28.70/18.89 inference(modus_ponens,[status(thm)],[15211, 14788])).
% 28.70/18.89 tff(15213,plain,
% 28.70/18.89 (f7(f6(c2, c2)) = c2),
% 28.70/18.89 inference(transitivity,[status(thm)],[14782, 120])).
% 28.70/18.89 tff(15214,plain,
% 28.70/18.89 ((f7(f6(c2, c2)) = f6(c2, c2)) <=> (c2 = f6(c2, c2))),
% 28.70/18.89 inference(monotonicity,[status(thm)],[15213])).
% 28.70/18.89 tff(15215,plain,
% 28.70/18.89 ((f7(f6(c2, c2)) = f6(c2, c2)) <=> (f6(c2, c2) = c2)),
% 28.70/18.89 inference(transitivity,[status(thm)],[15214, 3242])).
% 28.70/18.89 tff(15216,plain,
% 28.70/18.89 ((f6(c2, c2) = c2) <=> (f7(f6(c2, c2)) = f6(c2, c2))),
% 28.70/18.89 inference(symmetry,[status(thm)],[15215])).
% 28.70/18.89 tff(15217,plain,
% 28.70/18.89 ((~(f6(c2, c2) = c2)) <=> (~(f7(f6(c2, c2)) = f6(c2, c2)))),
% 28.70/18.89 inference(monotonicity,[status(thm)],[15216])).
% 28.70/18.89 tff(15218,plain,
% 28.70/18.89 ((f6(c2, c2) = c2) <=> (c1 = c2)),
% 28.70/18.89 inference(monotonicity,[status(thm)],[14778])).
% 28.70/18.89 tff(15219,plain,
% 28.70/18.89 ((f6(c2, c2) = c2) <=> (c2 = c1)),
% 28.70/18.89 inference(transitivity,[status(thm)],[15218, 1])).
% 28.70/18.89 tff(15220,plain,
% 28.70/18.89 ((c2 = c1) <=> (f6(c2, c2) = c2)),
% 28.70/18.89 inference(symmetry,[status(thm)],[15219])).
% 28.70/18.89 tff(15221,plain,
% 28.70/18.89 ((~(c2 = c1)) <=> (~(f6(c2, c2) = c2))),
% 28.70/18.89 inference(monotonicity,[status(thm)],[15220])).
% 28.70/18.89 tff(15222,plain,
% 28.70/18.89 (~(f6(c2, c2) = c2)),
% 28.70/18.89 inference(modus_ponens,[status(thm)],[75, 15221])).
% 28.70/18.89 tff(15223,plain,
% 28.70/18.89 (~(f7(f6(c2, c2)) = f6(c2, c2))),
% 28.70/18.89 inference(modus_ponens,[status(thm)],[15222, 15217])).
% 28.70/18.89 tff(15224,plain,
% 28.70/18.89 (big_f(f7(f6(c2, c2)), c2) <=> big_f(c2, c2)),
% 28.70/18.89 inference(monotonicity,[status(thm)],[15213])).
% 28.70/18.89 tff(15225,plain,
% 28.70/18.89 (big_f(c2, c2) <=> big_f(f7(f6(c2, c2)), c2)),
% 28.70/18.89 inference(symmetry,[status(thm)],[15224])).
% 28.70/18.89 tff(15226,plain,
% 28.70/18.89 (big_f(f7(f6(c2, c2)), c2)),
% 28.70/18.89 inference(modus_ponens,[status(thm)],[14740, 15225])).
% 28.70/18.89 tff(15227,plain,
% 28.70/18.89 (big_f(c2, f10(c2)) <=> big_f(f7(c2), f6(c2, c2))),
% 28.70/18.89 inference(monotonicity,[status(thm)],[14781, 14770])).
% 28.70/18.89 tff(15228,plain,
% 28.70/18.89 (big_f(f7(c2), f6(c2, c2)) <=> big_f(c2, f10(c2))),
% 28.70/18.89 inference(symmetry,[status(thm)],[15227])).
% 28.70/18.89 tff(15229,plain,
% 28.70/18.89 (big_f(c2, c1) <=> big_f(c2, f10(c2))),
% 28.70/18.89 inference(transitivity,[status(thm)],[14787, 15228])).
% 28.70/18.89 tff(15230,plain,
% 28.70/18.89 (big_f(c2, f10(c2))),
% 28.70/18.89 inference(modus_ponens,[status(thm)],[15211, 15229])).
% 28.70/18.89 tff(15231,plain,
% 28.70/18.89 (c2 = f8(c2)),
% 28.70/18.89 inference(unit_resolution,[status(thm)],[15160, 15230, 15222, 14768, 15226, 15223, 15212])).
% 28.70/18.89 tff(15232,plain,
% 28.70/18.89 (f8(c2) = c2),
% 28.70/18.89 inference(symmetry,[status(thm)],[15231])).
% 28.70/18.89 tff(15233,plain,
% 28.70/18.89 ((c1 = f8(c2)) <=> (f6(c2, c2) = c2)),
% 28.70/18.89 inference(monotonicity,[status(thm)],[14773, 15232])).
% 28.70/18.89 tff(15234,plain,
% 28.70/18.89 ((f6(c2, c2) = c2) <=> (c1 = f8(c2))),
% 28.70/18.89 inference(symmetry,[status(thm)],[15233])).
% 28.70/18.89 tff(15235,plain,
% 28.70/18.89 ((f6(c2, c2) = c2) <=> (f6(c2, c2) = f8(c2))),
% 28.70/18.89 inference(transitivity,[status(thm)],[15234, 14780])).
% 28.70/18.89 tff(15236,plain,
% 28.70/18.89 ((~(f6(c2, c2) = c2)) <=> (~(f6(c2, c2) = f8(c2)))),
% 28.70/18.89 inference(monotonicity,[status(thm)],[15235])).
% 28.70/18.89 tff(15237,plain,
% 28.70/18.89 (~(f6(c2, c2) = f8(c2))),
% 28.70/18.89 inference(modus_ponens,[status(thm)],[15222, 15236])).
% 28.70/18.89 tff(15238,plain,
% 28.70/18.89 ((c2 = f5(f6(c2, c2))) | (f6(c2, c2) = f8(c2)) | (~big_f(f6(c2, c2), f10(c2)))),
% 28.70/18.89 inference(unit_resolution,[status(thm)],[15173, 1659, 14768, 15226, 15223])).
% 28.70/18.89 tff(15239,plain,
% 28.70/18.89 (c2 = f5(f6(c2, c2))),
% 28.70/18.89 inference(unit_resolution,[status(thm)],[15238, 15237, 14776])).
% 28.70/18.89 tff(15240,plain,
% 28.70/18.89 (f5(f6(c2, c2)) = c2),
% 28.70/18.89 inference(symmetry,[status(thm)],[15239])).
% 28.70/18.89 tff(15241,plain,
% 28.70/18.89 ((f6(c2, c2) = f8(c2)) | (f6(c2, c2) = f5(f6(c2, c2)))),
% 28.70/18.89 inference(unit_resolution,[status(thm)],[15182, 1659, 14768, 15212, 15223, 14776])).
% 28.70/18.89 tff(15242,plain,
% 28.70/18.89 (f6(c2, c2) = f5(f6(c2, c2))),
% 28.70/18.89 inference(unit_resolution,[status(thm)],[15241, 15237])).
% 28.70/18.89 tff(15243,plain,
% 28.70/18.89 (f6(c2, c2) = c2),
% 28.70/18.89 inference(transitivity,[status(thm)],[15242, 15240])).
% 28.70/18.89 tff(15244,plain,
% 28.70/18.89 ($false),
% 28.70/18.89 inference(unit_resolution,[status(thm)],[15222, 15243])).
% 28.70/18.89 tff(15245,plain,((~(f6(c2, f7(f4(c4))) = c1)) | (~(f4(c4) = c2)) | (f10(c1) = c1) | (f7(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 28.70/18.89 tff(15246,plain,
% 28.70/18.89 (~(f6(c2, f7(f4(c4))) = c1)),
% 28.70/18.89 inference(unit_resolution,[status(thm)],[15245, 79, 3, 115])).
% 28.70/18.89 tff(15247,plain,
% 28.70/18.89 (f6(c2, f7(f4(c4))) = c2),
% 28.70/18.89 inference(unit_resolution,[status(thm)],[6601, 15246])).
% 28.70/18.89 tff(15248,plain,
% 28.70/18.89 (c2 = f7(f4(c4))),
% 28.70/18.89 inference(transitivity,[status(thm)],[13789, 81])).
% 28.70/18.89 tff(15249,plain,
% 28.70/18.89 (f6(c2, c2) = f6(c2, f7(f4(c4)))),
% 28.70/18.89 inference(monotonicity,[status(thm)],[15248])).
% 28.70/18.89 tff(15250,plain,
% 28.70/18.89 (f6(c2, c2) = c2),
% 28.70/18.89 inference(transitivity,[status(thm)],[15249, 15247])).
% 28.70/18.89 tff(15251,plain,
% 28.70/18.89 (big_f(f7(c2), f6(c2, c2))),
% 28.70/18.89 inference(unit_resolution,[status(thm)],[2627, 13805, 13346, 15250])).
% 28.70/18.89 tff(15252,plain,
% 28.70/18.89 (big_f(c2, c1) <=> big_f(c2, f10(c2))),
% 28.70/18.89 inference(monotonicity,[status(thm)],[99])).
% 28.70/18.89 tff(15253,plain,
% 28.70/18.89 (big_f(c2, f10(c2)) <=> big_f(c2, c1)),
% 28.70/18.89 inference(symmetry,[status(thm)],[15252])).
% 28.70/18.89 tff(15254,plain,
% 28.70/18.89 (f8(c2) = f8(f7(c2))),
% 28.70/18.89 inference(monotonicity,[status(thm)],[13789])).
% 28.70/18.89 tff(15255,plain,
% 28.70/18.89 (f8(f7(c2)) = f8(c2)),
% 28.70/18.89 inference(symmetry,[status(thm)],[15254])).
% 28.70/18.89 tff(15256,plain,
% 28.70/18.89 (f8(f7(f4(c4))) = f8(f7(c2))),
% 28.70/18.89 inference(symmetry,[status(thm)],[8536])).
% 28.70/18.89 tff(15257,plain,
% 28.70/18.89 (f8(f7(f4(c4))) = f8(c2)),
% 28.70/18.89 inference(transitivity,[status(thm)],[15256, 15255])).
% 28.70/18.89 tff(15258,plain,
% 28.70/18.89 ((f8(f7(f4(c4))) = c1) <=> (f8(c2) = c1)),
% 28.70/18.89 inference(monotonicity,[status(thm)],[15257])).
% 28.70/18.89 tff(15259,plain,
% 28.70/18.89 ((f8(f7(f4(c4))) = c1) <=> (c1 = f8(c2))),
% 28.70/18.89 inference(transitivity,[status(thm)],[15258, 13044])).
% 28.70/18.89 tff(15260,plain,
% 28.70/18.89 ((c1 = f8(c2)) <=> (f8(f7(f4(c4))) = c1)),
% 28.70/18.89 inference(symmetry,[status(thm)],[15259])).
% 28.70/18.89 tff(15261,plain,
% 28.70/18.89 ((c1 = f8(c2)) <=> (f10(c2) = f8(c2))),
% 28.70/18.89 inference(monotonicity,[status(thm)],[99])).
% 28.70/18.89 tff(15262,plain,
% 28.70/18.89 ((f10(c2) = f8(c2)) <=> (c1 = f8(c2))),
% 28.70/18.89 inference(symmetry,[status(thm)],[15261])).
% 28.70/18.89 tff(15263,plain,
% 28.70/18.89 ((f10(c2) = f8(c2)) <=> (f8(f7(f4(c4))) = c1)),
% 28.70/18.89 inference(transitivity,[status(thm)],[15262, 15260])).
% 28.70/18.89 tff(15264,plain,
% 28.70/18.89 ((~(f10(c2) = f8(c2))) <=> (~(f8(f7(f4(c4))) = c1))),
% 28.70/18.89 inference(monotonicity,[status(thm)],[15263])).
% 28.70/18.89 tff(15265,plain,
% 28.70/18.89 ((~big_f(c1, c1)) <=> (~big_f(f10(c2), f10(c2)))),
% 28.70/18.89 inference(monotonicity,[status(thm)],[13717])).
% 28.70/18.89 tff(15266,plain,
% 28.70/18.89 (~big_f(f10(c2), f10(c2))),
% 28.70/18.89 inference(modus_ponens,[status(thm)],[66, 15265])).
% 28.70/18.89 tff(15267,plain,
% 28.70/18.89 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f8(c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f8(c2))))),
% 28.70/18.89 inference(rewrite,[status(thm)],[])).
% 28.70/18.89 tff(15268,plain,
% 28.70/18.89 (((f10(c2) = c2) | big_f(f10(c2), f10(c2)) | (~(f7(c2) = c2)) | (~(f10(c2) = f8(c2))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2)))) <=> ((f10(c2) = c2) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f8(c2))))),
% 28.70/18.89 inference(rewrite,[status(thm)],[])).
% 28.70/18.89 tff(15269,plain,
% 28.70/18.89 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | big_f(f10(c2), f10(c2)) | (~(f7(c2) = c2)) | (~(f10(c2) = f8(c2))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f8(c2)))))),
% 28.70/18.89 inference(monotonicity,[status(thm)],[15268])).
% 28.70/18.89 tff(15270,plain,
% 28.70/18.89 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | big_f(f10(c2), f10(c2)) | (~(f7(c2) = c2)) | (~(f10(c2) = f8(c2))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f8(c2))))),
% 28.70/18.89 inference(transitivity,[status(thm)],[15269, 15267])).
% 28.70/18.89 tff(15271,plain,
% 28.70/18.89 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | big_f(f10(c2), f10(c2)) | (~(f7(c2) = c2)) | (~(f10(c2) = f8(c2))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))),
% 28.70/18.90 inference(quant_inst,[status(thm)],[])).
% 28.70/18.90 tff(15272,plain,
% 28.70/18.90 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f8(c2)))),
% 28.70/18.90 inference(modus_ponens,[status(thm)],[15271, 15270])).
% 28.70/18.90 tff(15273,plain,
% 28.70/18.90 (~(f10(c2) = f8(c2))),
% 28.70/18.90 inference(unit_resolution,[status(thm)],[15272, 2963, 89, 13346, 15250, 15251, 15266])).
% 28.70/18.90 tff(15274,plain,
% 28.70/18.90 (~(f8(f7(f4(c4))) = c1)),
% 28.70/18.90 inference(modus_ponens,[status(thm)],[15273, 15264])).
% 28.70/18.90 tff(15275,plain,
% 28.70/18.90 (f8(f7(f4(c4))) = c2),
% 28.70/18.90 inference(unit_resolution,[status(thm)],[13371, 15274])).
% 28.70/18.90 tff(15276,plain,
% 28.70/18.90 (f8(f10(c1)) = c2),
% 28.70/18.90 inference(transitivity,[status(thm)],[13827, 15254, 8536, 15275])).
% 28.70/18.90 tff(15277,plain,
% 28.70/18.90 (big_f(f8(f10(c1)), f10(c2)) <=> big_f(c2, f10(c2))),
% 28.70/18.90 inference(monotonicity,[status(thm)],[15276])).
% 28.70/18.90 tff(15278,plain,
% 28.70/18.90 (big_f(f8(f10(c1)), f10(c2)) <=> big_f(c2, c1)),
% 28.70/18.90 inference(transitivity,[status(thm)],[15277, 15253])).
% 28.70/18.90 tff(15279,plain,
% 28.70/18.90 (f8(f7(f4(c4))) = f8(f10(c1))),
% 28.70/18.90 inference(transitivity,[status(thm)],[15256, 15255, 13830])).
% 28.70/18.90 tff(15280,plain,
% 28.70/18.90 (big_f(f8(f7(f4(c4))), f10(c2)) <=> big_f(f8(f10(c1)), f10(c2))),
% 28.70/18.90 inference(monotonicity,[status(thm)],[15279])).
% 28.70/18.90 tff(15281,plain,
% 28.70/18.90 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (~(f7(c2) = c2)) | big_f(f8(f7(f4(c4))), f10(c2)) | (~(f8(f7(f4(c4))) = f8(c2))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | big_f(f8(f7(f4(c4))), f10(c2)) | (~(f8(f7(f4(c4))) = f8(c2))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))),
% 28.70/18.90 inference(rewrite,[status(thm)],[])).
% 28.70/18.90 tff(15282,plain,
% 28.70/18.90 (((f10(c2) = c2) | big_f(f8(f7(f4(c4))), f10(c2)) | (~(f7(c2) = c2)) | (~(f8(f7(f4(c4))) = f8(c2))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2)))) <=> ((f10(c2) = c2) | (~(f7(c2) = c2)) | big_f(f8(f7(f4(c4))), f10(c2)) | (~(f8(f7(f4(c4))) = f8(c2))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))),
% 28.70/18.90 inference(rewrite,[status(thm)],[])).
% 28.70/18.90 tff(15283,plain,
% 28.70/18.90 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | big_f(f8(f7(f4(c4))), f10(c2)) | (~(f7(c2) = c2)) | (~(f8(f7(f4(c4))) = f8(c2))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (~(f7(c2) = c2)) | big_f(f8(f7(f4(c4))), f10(c2)) | (~(f8(f7(f4(c4))) = f8(c2))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2)))))),
% 28.70/18.90 inference(monotonicity,[status(thm)],[15282])).
% 28.70/18.90 tff(15284,plain,
% 28.70/18.90 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | big_f(f8(f7(f4(c4))), f10(c2)) | (~(f7(c2) = c2)) | (~(f8(f7(f4(c4))) = f8(c2))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | big_f(f8(f7(f4(c4))), f10(c2)) | (~(f8(f7(f4(c4))) = f8(c2))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))),
% 28.70/18.90 inference(transitivity,[status(thm)],[15283, 15281])).
% 28.70/18.90 tff(15285,plain,
% 28.70/18.90 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | big_f(f8(f7(f4(c4))), f10(c2)) | (~(f7(c2) = c2)) | (~(f8(f7(f4(c4))) = f8(c2))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))),
% 28.70/18.90 inference(quant_inst,[status(thm)],[])).
% 28.70/18.90 tff(15286,plain,
% 28.70/18.90 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | big_f(f8(f7(f4(c4))), f10(c2)) | (~(f8(f7(f4(c4))) = f8(c2))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2)))),
% 28.70/18.90 inference(modus_ponens,[status(thm)],[15285, 15284])).
% 28.70/18.90 tff(15287,plain,
% 28.70/18.90 ((f10(c2) = c2) | (~(f7(c2) = c2)) | big_f(f8(f7(f4(c4))), f10(c2)) | (~(f8(f7(f4(c4))) = f8(c2))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2)))),
% 28.70/18.90 inference(unit_resolution,[status(thm)],[15286, 2963])).
% 28.70/18.90 tff(15288,plain,
% 28.70/18.90 (big_f(f8(f7(f4(c4))), f10(c2))),
% 28.70/18.90 inference(unit_resolution,[status(thm)],[15287, 89, 13346, 15250, 15251, 15257])).
% 28.70/18.90 tff(15289,plain,
% 28.70/18.90 (big_f(f8(f10(c1)), f10(c2))),
% 28.70/18.90 inference(modus_ponens,[status(thm)],[15288, 15280])).
% 28.70/18.90 tff(15290,plain,
% 28.70/18.90 (big_f(c2, c1)),
% 28.70/18.90 inference(modus_ponens,[status(thm)],[15289, 15278])).
% 28.70/18.90 tff(15291,plain,
% 28.70/18.90 (big_f(c2, f10(c1))),
% 28.70/18.90 inference(modus_ponens,[status(thm)],[13805, 2719])).
% 28.70/18.90 tff(15292,plain,
% 28.70/18.90 (c2 = f8(c1)),
% 28.70/18.90 inference(unit_resolution,[status(thm)],[2736, 2730, 15291, 3, 13346, 15250, 15251])).
% 28.70/18.90 tff(15293,plain,
% 28.70/18.90 (f8(f10(c2)) = f8(c1)),
% 28.70/18.90 inference(monotonicity,[status(thm)],[94])).
% 28.70/18.90 tff(15294,plain,
% 28.70/18.90 (f8(f10(c2)) = c2),
% 28.70/18.90 inference(transitivity,[status(thm)],[15293, 1643])).
% 28.70/18.90 tff(15295,plain,
% 28.70/18.90 ((f10(c2) = f8(f10(c2))) <=> (f10(c2) = c2)),
% 28.70/18.90 inference(monotonicity,[status(thm)],[15294])).
% 28.70/18.90 tff(15296,plain,
% 28.70/18.90 ((f10(c2) = c2) <=> (f10(c2) = f8(f10(c2)))),
% 28.70/18.90 inference(symmetry,[status(thm)],[15295])).
% 28.70/18.90 tff(15297,plain,
% 28.70/18.90 ((~(f10(c2) = c2)) <=> (~(f10(c2) = f8(f10(c2))))),
% 28.70/18.90 inference(monotonicity,[status(thm)],[15296])).
% 28.70/18.90 tff(15298,plain,
% 28.70/18.90 (~(f10(c2) = f8(f10(c2)))),
% 28.70/18.90 inference(modus_ponens,[status(thm)],[89, 15297])).
% 28.70/18.90 tff(15299,plain,
% 28.70/18.90 (f10(f10(c2)) = f10(c1)),
% 28.70/18.90 inference(monotonicity,[status(thm)],[94])).
% 28.70/18.90 tff(15300,plain,
% 28.70/18.90 (f10(f10(c2)) = c2),
% 28.70/18.90 inference(transitivity,[status(thm)],[15299, 16])).
% 28.70/18.90 tff(15301,plain,
% 28.70/18.90 (big_f(f10(c2), f10(f10(c2))) <=> big_f(c1, c2)),
% 28.70/18.90 inference(monotonicity,[status(thm)],[94, 15300])).
% 28.70/18.90 tff(15302,plain,
% 28.70/18.90 (big_f(c1, c2) <=> big_f(f10(c2), f10(f10(c2)))),
% 28.70/18.90 inference(symmetry,[status(thm)],[15301])).
% 28.70/18.90 tff(15303,plain,
% 28.70/18.90 (big_f(f10(c2), f10(f10(c2)))),
% 28.70/18.90 inference(modus_ponens,[status(thm)],[2865, 15302])).
% 28.70/18.90 tff(15304,plain,
% 28.70/18.90 ((f10(f10(c2)) = f10(c2)) <=> (c2 = f10(c2))),
% 28.70/18.90 inference(monotonicity,[status(thm)],[15300])).
% 28.70/18.90 tff(15305,plain,
% 28.70/18.90 ((f10(f10(c2)) = f10(c2)) <=> (f10(c2) = c2)),
% 28.70/18.90 inference(transitivity,[status(thm)],[15304, 4987])).
% 28.70/18.90 tff(15306,plain,
% 28.70/18.90 ((f10(c2) = c2) <=> (f10(f10(c2)) = f10(c2))),
% 28.70/18.90 inference(symmetry,[status(thm)],[15305])).
% 28.70/18.90 tff(15307,plain,
% 28.70/18.90 ((~(f10(c2) = c2)) <=> (~(f10(f10(c2)) = f10(c2)))),
% 28.70/18.90 inference(monotonicity,[status(thm)],[15306])).
% 28.70/18.90 tff(15308,plain,
% 28.70/18.90 (~(f10(f10(c2)) = f10(c2))),
% 28.70/18.90 inference(modus_ponens,[status(thm)],[89, 15307])).
% 28.70/18.90 tff(15309,plain,
% 28.70/18.90 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(c2) = c2)) | (f10(f10(c2)) = f10(c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (f10(c2) = f8(f10(c2))) | (~big_f(f10(c2), f10(f10(c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c2) = c2)) | (f10(f10(c2)) = f10(c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (f10(c2) = f8(f10(c2))) | (~big_f(f10(c2), f10(f10(c2)))))),
% 28.70/18.90 inference(rewrite,[status(thm)],[])).
% 28.70/18.90 tff(15310,plain,
% 28.70/18.90 (((f10(f10(c2)) = f10(c2)) | (f10(c2) = f8(f10(c2))) | (~big_f(f10(c2), f10(f10(c2)))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2)))) <=> ((~(f7(c2) = c2)) | (f10(f10(c2)) = f10(c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (f10(c2) = f8(f10(c2))) | (~big_f(f10(c2), f10(f10(c2)))))),
% 28.70/18.90 inference(rewrite,[status(thm)],[])).
% 28.70/18.90 tff(15311,plain,
% 28.70/18.90 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f10(c2)) = f10(c2)) | (f10(c2) = f8(f10(c2))) | (~big_f(f10(c2), f10(f10(c2)))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(c2) = c2)) | (f10(f10(c2)) = f10(c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (f10(c2) = f8(f10(c2))) | (~big_f(f10(c2), f10(f10(c2))))))),
% 28.70/18.90 inference(monotonicity,[status(thm)],[15310])).
% 28.70/18.90 tff(15312,plain,
% 28.70/18.90 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f10(c2)) = f10(c2)) | (f10(c2) = f8(f10(c2))) | (~big_f(f10(c2), f10(f10(c2)))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c2) = c2)) | (f10(f10(c2)) = f10(c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (f10(c2) = f8(f10(c2))) | (~big_f(f10(c2), f10(f10(c2)))))),
% 28.70/18.90 inference(transitivity,[status(thm)],[15311, 15309])).
% 28.70/18.90 tff(15313,plain,
% 28.70/18.90 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f10(c2)) = f10(c2)) | (f10(c2) = f8(f10(c2))) | (~big_f(f10(c2), f10(f10(c2)))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))),
% 28.70/18.90 inference(quant_inst,[status(thm)],[])).
% 28.70/18.90 tff(15314,plain,
% 28.70/18.90 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c2) = c2)) | (f10(f10(c2)) = f10(c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (f10(c2) = f8(f10(c2))) | (~big_f(f10(c2), f10(f10(c2))))),
% 28.70/18.90 inference(modus_ponens,[status(thm)],[15313, 15312])).
% 28.70/18.90 tff(15315,plain,
% 28.70/18.90 ((f10(c2) = f8(f10(c2))) | (~big_f(f10(c2), f10(f10(c2))))),
% 28.70/18.90 inference(unit_resolution,[status(thm)],[15314, 2730, 77, 15308, 2622, 2707])).
% 28.70/18.90 tff(15316,plain,
% 28.70/18.90 ($false),
% 28.70/18.90 inference(unit_resolution,[status(thm)],[15315, 15303, 15298])).
% 28.70/18.90 tff(15317,plain,((~big_f(c1, c2)) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~(f10(c1) = c2)) | (f10(c2) = c2) | (~(c2 = f8(c1)))), inference(lemma,lemma(discharge,[]))).
% 28.70/18.90 tff(15318,plain,
% 28.70/18.90 (~big_f(c1, c2)),
% 28.70/18.90 inference(unit_resolution,[status(thm)],[15317, 89, 15250, 15251, 15, 13346, 15292])).
% 28.70/18.90 tff(15319,plain,
% 28.70/18.90 (f2(f10(c2)) = f2(c1)),
% 28.70/18.90 inference(monotonicity,[status(thm)],[94])).
% 28.70/18.90 tff(15320,plain,
% 28.70/18.90 ((f10(c2) = f2(f10(c2))) <=> (c1 = f2(c1))),
% 28.70/18.90 inference(monotonicity,[status(thm)],[94, 15319])).
% 28.70/18.90 tff(15321,plain,
% 28.70/18.90 ((c1 = f2(c1)) <=> (f10(c2) = f2(f10(c2)))),
% 28.70/18.90 inference(symmetry,[status(thm)],[15320])).
% 28.70/18.90 tff(15322,plain,
% 28.70/18.90 (c1 = c4),
% 28.70/18.90 inference(unit_resolution,[status(thm)],[12851, 27, 66, 15290, 172, 15292])).
% 28.70/18.90 tff(15323,plain,
% 28.70/18.90 (c4 = c1),
% 28.70/18.90 inference(symmetry,[status(thm)],[15322])).
% 28.70/18.90 tff(15324,plain,
% 28.70/18.90 (c4 = f10(c2)),
% 28.70/18.90 inference(transitivity,[status(thm)],[15323, 99])).
% 28.70/18.90 tff(15325,plain,
% 28.70/18.90 ((c2 = c4) <=> (c2 = f10(c2))),
% 28.70/18.90 inference(monotonicity,[status(thm)],[15324])).
% 28.70/18.90 tff(15326,plain,
% 28.70/18.90 ((c2 = c4) <=> (f10(c2) = c2)),
% 28.70/18.90 inference(transitivity,[status(thm)],[15325, 4987])).
% 28.70/18.90 tff(15327,plain,
% 28.70/18.90 ((f10(c2) = c2) <=> (c2 = c4)),
% 28.70/18.90 inference(symmetry,[status(thm)],[15326])).
% 28.70/18.90 tff(15328,plain,
% 28.70/18.90 ((f10(c2) = c2) <=> (f7(c1) = c4)),
% 28.70/18.90 inference(transitivity,[status(thm)],[15327, 2812])).
% 28.70/18.90 tff(15329,plain,
% 28.70/18.90 ((~(f10(c2) = c2)) <=> (~(f7(c1) = c4))),
% 28.70/18.90 inference(monotonicity,[status(thm)],[15328])).
% 28.70/18.90 tff(15330,plain,
% 28.70/18.90 (~(f7(c1) = c4)),
% 28.70/18.90 inference(modus_ponens,[status(thm)],[89, 15329])).
% 28.70/18.90 tff(15331,plain,
% 28.70/18.90 (c3 = f10(c2)),
% 28.70/18.90 inference(transitivity,[status(thm)],[172, 99])).
% 28.70/18.90 tff(15332,plain,
% 28.70/18.90 ((c2 = c3) <=> (c2 = f10(c2))),
% 28.70/18.90 inference(monotonicity,[status(thm)],[15331])).
% 28.70/18.90 tff(15333,plain,
% 28.70/18.90 ((c2 = c3) <=> (f10(c2) = c2)),
% 28.70/18.90 inference(transitivity,[status(thm)],[15332, 4987])).
% 28.70/18.90 tff(15334,plain,
% 28.70/18.90 ((f10(c2) = c2) <=> (c2 = c3)),
% 28.70/18.90 inference(symmetry,[status(thm)],[15333])).
% 28.70/18.90 tff(15335,plain,
% 28.70/18.90 ((~(f10(c2) = c2)) <=> (~(c2 = c3))),
% 28.70/18.90 inference(monotonicity,[status(thm)],[15334])).
% 28.70/18.90 tff(15336,plain,
% 28.70/18.90 (~(c2 = c3)),
% 28.70/18.90 inference(modus_ponens,[status(thm)],[89, 15335])).
% 28.70/18.90 tff(15337,plain,
% 28.70/18.90 ((f10(c2) = c2) <=> (f7(c1) = c3)),
% 28.70/18.90 inference(transitivity,[status(thm)],[15334, 12383])).
% 28.70/18.90 tff(15338,plain,
% 28.70/18.90 ((~(f10(c2) = c2)) <=> (~(f7(c1) = c3))),
% 28.70/18.90 inference(monotonicity,[status(thm)],[15337])).
% 28.70/18.90 tff(15339,plain,
% 28.70/18.90 (~(f7(c1) = c3)),
% 28.70/18.90 inference(modus_ponens,[status(thm)],[89, 15338])).
% 28.70/18.90 tff(15340,plain,
% 28.70/18.90 ((~(f10(c2) = c2)) <=> (~(c2 = c4))),
% 28.70/18.90 inference(monotonicity,[status(thm)],[15327])).
% 28.70/18.90 tff(15341,plain,
% 28.70/18.90 (~(c2 = c4)),
% 28.70/18.90 inference(modus_ponens,[status(thm)],[89, 15340])).
% 28.70/18.90 tff(15342,plain,
% 28.70/18.90 (~(f5(c1) = c1)),
% 28.70/18.90 inference(unit_resolution,[status(thm)],[14007, 15341, 13346, 115, 3, 66, 15339, 15336, 172, 79])).
% 28.70/18.90 tff(15343,plain,
% 28.70/18.90 (f5(c1) = c2),
% 28.70/18.90 inference(unit_resolution,[status(thm)],[1708, 15342])).
% 28.70/18.90 tff(15344,plain,
% 28.70/18.90 (~(f2(c3) = c2)),
% 28.70/18.90 inference(unit_resolution,[status(thm)],[14389, 15343, 27, 115, 172, 13805, 15, 15330])).
% 28.70/18.90 tff(15345,plain,
% 28.70/18.90 (f2(c3) = c1),
% 28.70/18.90 inference(unit_resolution,[status(thm)],[1273, 15344])).
% 28.70/18.90 tff(15346,plain,
% 28.70/18.90 (c1 = f2(c1)),
% 28.70/18.90 inference(unit_resolution,[status(thm)],[6771, 15345, 172])).
% 28.70/18.90 tff(15347,plain,
% 28.70/18.90 (f10(c2) = f2(f10(c2))),
% 28.70/18.90 inference(modus_ponens,[status(thm)],[15346, 15321])).
% 28.70/18.90 tff(15348,plain,
% 28.70/18.90 (big_f(f3(c2, c2), c2)),
% 28.70/18.90 inference(unit_resolution,[status(thm)],[14309, 15341, 13805, 66, 27, 172])).
% 28.70/18.90 tff(15349,plain,
% 28.70/18.90 (f3(c2, c2) = f3(f7(f4(c4)), f4(c4))),
% 28.70/18.90 inference(monotonicity,[status(thm)],[83, 436])).
% 28.70/18.90 tff(15350,plain,
% 28.70/18.90 (f3(f7(f4(c4)), f4(c4)) = f3(c2, c2)),
% 28.70/18.90 inference(symmetry,[status(thm)],[15349])).
% 28.70/18.90 tff(15351,assumption,(f3(f7(f4(c4)), f4(c4)) = c1), introduced(assumption)).
% 28.70/18.90 tff(15352,plain,
% 28.70/18.90 (c1 = f3(f7(f4(c4)), f4(c4))),
% 28.70/18.90 inference(symmetry,[status(thm)],[15351])).
% 28.70/18.90 tff(15353,plain,
% 28.70/18.90 (c1 = f3(c2, c2)),
% 28.70/18.90 inference(transitivity,[status(thm)],[15352, 15350])).
% 28.70/18.90 tff(15354,plain,
% 28.70/18.90 (big_f(c1, c2) <=> big_f(f3(c2, c2), c2)),
% 28.70/18.90 inference(monotonicity,[status(thm)],[15353])).
% 28.70/18.90 tff(15355,plain,
% 28.70/18.90 (big_f(f3(c2, c2), c2) <=> big_f(c1, c2)),
% 28.70/18.90 inference(symmetry,[status(thm)],[15354])).
% 28.70/18.90 tff(15356,assumption,(big_f(f3(c2, c2), c2)), introduced(assumption)).
% 28.70/18.90 tff(15357,plain,
% 28.70/18.90 (big_f(c1, c2)),
% 28.70/18.90 inference(modus_ponens,[status(thm)],[15356, 15355])).
% 28.70/18.90 tff(15358,plain,
% 28.70/18.90 ($false),
% 28.70/18.90 inference(unit_resolution,[status(thm)],[27, 15357])).
% 28.70/18.90 tff(15359,plain,((~(f3(f7(f4(c4)), f4(c4)) = c1)) | big_f(c1, c2) | (~big_f(f3(c2, c2), c2)) | (~(f4(c4) = c2)) | (~(f7(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.70/18.90 tff(15360,plain,
% 28.70/18.90 (~(f3(f7(f4(c4)), f4(c4)) = c1)),
% 28.70/18.90 inference(unit_resolution,[status(thm)],[15359, 27, 15348, 79, 13346])).
% 28.70/18.90 tff(15361,plain,
% 28.70/18.90 (f3(f7(f4(c4)), f4(c4)) = c2),
% 28.70/18.90 inference(unit_resolution,[status(thm)],[7693, 15360])).
% 28.70/18.90 tff(15362,plain,
% 28.70/18.90 ((f3(c2, c2) = c2) <=> (f3(f7(f4(c4)), f4(c4)) = c2)),
% 28.70/18.90 inference(monotonicity,[status(thm)],[7441])).
% 28.70/18.90 tff(15363,plain,
% 28.70/18.90 ((f3(f7(f4(c4)), f4(c4)) = c2) <=> (f3(c2, c2) = c2)),
% 28.70/18.90 inference(symmetry,[status(thm)],[15362])).
% 28.70/18.90 tff(15364,assumption,(f3(f7(f4(c4)), f4(c4)) = c2), introduced(assumption)).
% 28.70/18.90 tff(15365,plain,
% 28.70/18.90 (f3(c2, c2) = c2),
% 28.70/18.90 inference(modus_ponens,[status(thm)],[15364, 15363])).
% 28.70/18.90 tff(15366,plain,
% 28.70/18.90 ($false),
% 28.70/18.90 inference(unit_resolution,[status(thm)],[12861, 15365])).
% 28.70/18.90 tff(15367,plain,((~(f3(f7(f4(c4)), f4(c4)) = c2)) | (f3(c2, c2) = c2) | (~(f4(c4) = c2)) | (~(f7(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.70/18.90 tff(15368,plain,
% 28.70/18.90 (f3(c2, c2) = c2),
% 28.70/18.90 inference(unit_resolution,[status(thm)],[15367, 15361, 79, 13346])).
% 28.70/18.90 tff(15369,plain,
% 28.70/18.90 (f10(c2) = c3),
% 28.70/18.90 inference(transitivity,[status(thm)],[94, 5585])).
% 28.70/18.90 tff(15370,plain,
% 28.70/18.90 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~(f10(c2) = c3)) | (~(f10(c2) = f2(f10(c2)))) | big_f(f10(c2), f10(c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~(f10(c2) = c3)) | (~(f10(c2) = f2(f10(c2)))) | big_f(f10(c2), f10(c2)))),
% 28.70/18.90 inference(rewrite,[status(thm)],[])).
% 28.70/18.90 tff(15371,plain,
% 28.70/18.90 (((~(f10(c2) = c3)) | (~(f10(c2) = f2(f10(c2)))) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | big_f(f10(c2), f10(c2))) <=> ((c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~(f10(c2) = c3)) | (~(f10(c2) = f2(f10(c2)))) | big_f(f10(c2), f10(c2)))),
% 28.70/18.90 inference(rewrite,[status(thm)],[])).
% 28.70/18.90 tff(15372,plain,
% 28.70/18.90 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(f10(c2) = c3)) | (~(f10(c2) = f2(f10(c2)))) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | big_f(f10(c2), f10(c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~(f10(c2) = c3)) | (~(f10(c2) = f2(f10(c2)))) | big_f(f10(c2), f10(c2))))),
% 28.70/18.90 inference(monotonicity,[status(thm)],[15371])).
% 28.70/18.90 tff(15373,plain,
% 28.70/18.90 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(f10(c2) = c3)) | (~(f10(c2) = f2(f10(c2)))) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | big_f(f10(c2), f10(c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~(f10(c2) = c3)) | (~(f10(c2) = f2(f10(c2)))) | big_f(f10(c2), f10(c2)))),
% 28.70/18.90 inference(transitivity,[status(thm)],[15372, 15370])).
% 28.70/18.90 tff(15374,plain,
% 28.70/18.90 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(f10(c2) = c3)) | (~(f10(c2) = f2(f10(c2)))) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | big_f(f10(c2), f10(c2)))),
% 28.70/18.90 inference(quant_inst,[status(thm)],[])).
% 28.70/18.90 tff(15375,plain,
% 28.70/18.90 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~(f10(c2) = c3)) | (~(f10(c2) = f2(f10(c2)))) | big_f(f10(c2), f10(c2))),
% 28.70/18.90 inference(modus_ponens,[status(thm)],[15374, 15373])).
% 28.70/18.90 tff(15376,plain,
% 28.70/18.90 ($false),
% 28.70/18.90 inference(unit_resolution,[status(thm)],[15375, 1398, 15341, 15369, 15368, 15348, 15266, 15347])).
% 28.70/18.90 tff(15377,plain,(big_f(c1, c2) | (~(f4(c4) = c2)) | (~(c3 = c1)) | (f7(c1) = c1) | big_f(c1, c1) | (f10(c1) = c1) | (f10(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 28.70/18.90 tff(15378,plain,
% 28.70/18.90 (~(c3 = c1)),
% 28.70/18.90 inference(unit_resolution,[status(thm)],[15377, 66, 79, 115, 15318, 3, 89])).
% 28.70/18.90 tff(15379,plain,
% 28.70/18.90 (c3 = c2),
% 28.70/18.90 inference(unit_resolution,[status(thm)],[180, 15378])).
% 28.70/18.90 tff(15380,plain,
% 28.70/18.90 ((c2 = f8(f7(c2))) <=> (c2 = f8(c2))),
% 28.70/18.90 inference(monotonicity,[status(thm)],[15255])).
% 28.70/18.90 tff(15381,plain,
% 28.70/18.90 ((c2 = f8(f7(f4(c4)))) <=> (c2 = f8(f7(c2)))),
% 28.70/18.90 inference(monotonicity,[status(thm)],[15256])).
% 28.70/18.90 tff(15382,plain,
% 28.70/18.90 ((f8(f7(f4(c4))) = c2) <=> (c2 = f8(c2))),
% 28.70/18.90 inference(transitivity,[status(thm)],[105, 15381, 15380])).
% 28.70/18.90 tff(15383,plain,
% 28.70/18.90 (c2 = f8(c2)),
% 28.70/18.90 inference(modus_ponens,[status(thm)],[15275, 15382])).
% 28.70/18.90 tff(15384,plain,
% 28.70/18.90 ((c1 = c4) <=> (f10(c2) = c4)),
% 28.70/18.90 inference(monotonicity,[status(thm)],[99])).
% 28.70/18.90 tff(15385,plain,
% 28.70/18.90 ((f10(c2) = c4) <=> (c1 = c4)),
% 28.70/18.90 inference(symmetry,[status(thm)],[15384])).
% 28.70/18.90 tff(15386,plain,
% 28.70/18.90 (big_f(c2, f10(c2))),
% 28.70/18.90 inference(modus_ponens,[status(thm)],[15289, 15277])).
% 28.70/18.90 tff(15387,assumption,(~(f10(c2) = f2(c2))), introduced(assumption)).
% 28.70/18.90 tff(15388,plain,
% 28.70/18.90 (big_f(f3(c2, c2), c2)),
% 28.70/18.90 inference(unit_resolution,[status(thm)],[13236, 873, 1345, 1344, 348])).
% 28.70/18.90 tff(15389,plain,
% 28.70/18.90 (~(f3(f7(f4(c4)), f4(c4)) = c1)),
% 28.70/18.90 inference(unit_resolution,[status(thm)],[15359, 15388, 27, 79, 77])).
% 28.70/18.90 tff(15390,plain,
% 28.70/18.90 (f3(f7(f4(c4)), f4(c4)) = c2),
% 28.70/18.90 inference(unit_resolution,[status(thm)],[7693, 15389])).
% 28.70/18.90 tff(15391,plain,
% 28.70/18.90 (f3(c2, c2) = c2),
% 28.70/18.90 inference(unit_resolution,[status(thm)],[15367, 15390, 79, 77])).
% 28.70/18.90 tff(15392,plain,
% 28.70/18.90 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (f10(c2) = f2(c2)) | (~big_f(f3(c2, c2), c2)) | (~big_f(c2, f10(c2))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (f10(c2) = f2(c2)) | (~big_f(f3(c2, c2), c2)) | (~big_f(c2, f10(c2))))),
% 28.70/18.90 inference(rewrite,[status(thm)],[])).
% 28.70/18.90 tff(15393,plain,
% 28.70/18.90 (((~(c2 = c3)) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (f10(c2) = f2(c2)) | (~big_f(c2, f10(c2)))) <=> ((~(c2 = c3)) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (f10(c2) = f2(c2)) | (~big_f(f3(c2, c2), c2)) | (~big_f(c2, f10(c2))))),
% 28.70/18.90 inference(rewrite,[status(thm)],[])).
% 28.70/18.90 tff(15394,plain,
% 28.70/18.90 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (f10(c2) = f2(c2)) | (~big_f(c2, f10(c2))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (f10(c2) = f2(c2)) | (~big_f(f3(c2, c2), c2)) | (~big_f(c2, f10(c2)))))),
% 28.70/18.90 inference(monotonicity,[status(thm)],[15393])).
% 28.70/18.90 tff(15395,plain,
% 28.70/18.90 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (f10(c2) = f2(c2)) | (~big_f(c2, f10(c2))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (f10(c2) = f2(c2)) | (~big_f(f3(c2, c2), c2)) | (~big_f(c2, f10(c2))))),
% 28.70/18.90 inference(transitivity,[status(thm)],[15394, 15392])).
% 28.70/18.90 tff(15396,plain,
% 28.70/18.90 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (f10(c2) = f2(c2)) | (~big_f(c2, f10(c2))))),
% 28.70/18.90 inference(quant_inst,[status(thm)],[])).
% 28.70/18.90 tff(15397,plain,
% 28.70/18.91 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (f10(c2) = f2(c2)) | (~big_f(f3(c2, c2), c2)) | (~big_f(c2, f10(c2)))),
% 28.70/18.91 inference(modus_ponens,[status(thm)],[15396, 15395])).
% 28.70/18.91 tff(15398,plain,
% 28.70/18.91 ($false),
% 28.70/18.91 inference(unit_resolution,[status(thm)],[15397, 7051, 873, 1344, 12291, 15391, 15388, 15387])).
% 28.70/18.91 tff(15399,plain,((c2 = c4) | (~(c2 = c3)) | (~big_f(c2, f10(c2))) | (f10(c2) = f2(c2)) | (~(f4(c4) = c2)) | (~(f7(c2) = c2)) | big_f(c1, c2) | (~big_f(c2, c2)) | (~big_f(c2, c1))), inference(lemma,lemma(discharge,[]))).
% 28.70/18.91 tff(15400,plain,
% 28.70/18.91 (c2 = c4),
% 28.70/18.91 inference(unit_resolution,[status(thm)],[15399, 15387, 12291, 1335, 79, 77, 27, 1345, 348])).
% 28.70/18.91 tff(15401,plain,
% 28.70/18.91 (c4 = c2),
% 28.70/18.91 inference(symmetry,[status(thm)],[15400])).
% 28.70/18.91 tff(15402,plain,
% 28.70/18.91 ((f10(c2) = c4) <=> (f10(c2) = c2)),
% 28.70/18.91 inference(monotonicity,[status(thm)],[15401])).
% 28.70/18.91 tff(15403,plain,
% 28.70/18.91 ((f10(c2) = c2) <=> (f10(c2) = c4)),
% 28.70/18.91 inference(symmetry,[status(thm)],[15402])).
% 28.70/18.91 tff(15404,plain,
% 28.70/18.91 ((f10(c2) = c2) <=> (c1 = c4)),
% 28.70/18.91 inference(transitivity,[status(thm)],[15403, 15385])).
% 28.70/18.91 tff(15405,plain,
% 28.70/18.91 ((~(f10(c2) = c2)) <=> (~(c1 = c4))),
% 28.70/18.91 inference(monotonicity,[status(thm)],[15404])).
% 28.70/18.91 tff(15406,plain,
% 28.70/18.91 (~(c1 = c4)),
% 28.70/18.91 inference(modus_ponens,[status(thm)],[89, 15405])).
% 28.70/18.91 tff(15407,plain,
% 28.70/18.91 (f3(c1, c2) = c2),
% 28.70/18.91 inference(unit_resolution,[status(thm)],[13195, 15406, 66, 1345, 13152, 67, 348])).
% 28.70/18.91 tff(15408,plain,
% 28.70/18.91 (f3(f10(c2), c2) = f3(c1, c2)),
% 28.70/18.91 inference(monotonicity,[status(thm)],[94])).
% 28.70/18.91 tff(15409,plain,
% 28.70/18.91 (f3(f10(c2), c2) = c2),
% 28.70/18.91 inference(transitivity,[status(thm)],[15408, 15407])).
% 28.70/18.91 tff(15410,plain,
% 28.70/18.91 (big_f(f3(f10(c2), c2), f10(c2)) <=> big_f(c2, f10(c2))),
% 28.70/18.91 inference(monotonicity,[status(thm)],[15409])).
% 28.70/18.91 tff(15411,plain,
% 28.70/18.91 (big_f(c2, f10(c2)) <=> big_f(f3(f10(c2), c2), f10(c2))),
% 28.70/18.91 inference(symmetry,[status(thm)],[15410])).
% 28.70/18.91 tff(15412,plain,
% 28.70/18.91 (big_f(f3(f10(c2), c2), f10(c2))),
% 28.70/18.91 inference(modus_ponens,[status(thm)],[12291, 15411])).
% 28.70/18.91 tff(15413,plain,
% 28.70/18.91 ((~(f10(c2) = c2)) <=> (~(f10(c2) = c4))),
% 28.70/18.91 inference(monotonicity,[status(thm)],[15403])).
% 28.70/18.91 tff(15414,plain,
% 28.70/18.91 (~(f10(c2) = c4)),
% 28.70/18.91 inference(modus_ponens,[status(thm)],[89, 15413])).
% 28.70/18.91 tff(15415,plain,
% 28.70/18.91 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f10(c2) = c4) | (f10(c2) = f2(c2)) | (~big_f(c2, f10(c2))) | (~(f3(f10(c2), c2) = c2)) | (~big_f(f3(f10(c2), c2), f10(c2))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (f10(c2) = c4) | (f10(c2) = f2(c2)) | (~big_f(c2, f10(c2))) | (~(f3(f10(c2), c2) = c2)) | (~big_f(f3(f10(c2), c2), f10(c2))))),
% 28.70/18.91 inference(rewrite,[status(thm)],[])).
% 28.70/18.91 tff(15416,plain,
% 28.70/18.91 (((~(c2 = c3)) | (f10(c2) = c4) | (~(f3(f10(c2), c2) = c2)) | (~big_f(f3(f10(c2), c2), f10(c2))) | (f10(c2) = f2(c2)) | (~big_f(c2, f10(c2)))) <=> ((~(c2 = c3)) | (f10(c2) = c4) | (f10(c2) = f2(c2)) | (~big_f(c2, f10(c2))) | (~(f3(f10(c2), c2) = c2)) | (~big_f(f3(f10(c2), c2), f10(c2))))),
% 28.70/18.91 inference(rewrite,[status(thm)],[])).
% 28.70/18.91 tff(15417,plain,
% 28.70/18.91 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f10(c2) = c4) | (~(f3(f10(c2), c2) = c2)) | (~big_f(f3(f10(c2), c2), f10(c2))) | (f10(c2) = f2(c2)) | (~big_f(c2, f10(c2))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f10(c2) = c4) | (f10(c2) = f2(c2)) | (~big_f(c2, f10(c2))) | (~(f3(f10(c2), c2) = c2)) | (~big_f(f3(f10(c2), c2), f10(c2)))))),
% 28.70/18.91 inference(monotonicity,[status(thm)],[15416])).
% 28.70/18.91 tff(15418,plain,
% 28.70/18.91 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f10(c2) = c4) | (~(f3(f10(c2), c2) = c2)) | (~big_f(f3(f10(c2), c2), f10(c2))) | (f10(c2) = f2(c2)) | (~big_f(c2, f10(c2))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (f10(c2) = c4) | (f10(c2) = f2(c2)) | (~big_f(c2, f10(c2))) | (~(f3(f10(c2), c2) = c2)) | (~big_f(f3(f10(c2), c2), f10(c2))))),
% 28.70/18.91 inference(transitivity,[status(thm)],[15417, 15415])).
% 28.70/18.91 tff(15419,plain,
% 28.70/18.91 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f10(c2) = c4) | (~(f3(f10(c2), c2) = c2)) | (~big_f(f3(f10(c2), c2), f10(c2))) | (f10(c2) = f2(c2)) | (~big_f(c2, f10(c2))))),
% 28.70/18.91 inference(quant_inst,[status(thm)],[])).
% 28.70/18.91 tff(15420,plain,
% 28.70/18.91 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (f10(c2) = c4) | (f10(c2) = f2(c2)) | (~big_f(c2, f10(c2))) | (~(f3(f10(c2), c2) = c2)) | (~big_f(f3(f10(c2), c2), f10(c2)))),
% 28.70/18.91 inference(modus_ponens,[status(thm)],[15419, 15418])).
% 28.70/18.91 tff(15421,plain,
% 28.70/18.91 ((~(f3(f10(c2), c2) = c2)) | (~big_f(f3(f10(c2), c2), f10(c2)))),
% 28.70/18.91 inference(unit_resolution,[status(thm)],[15420, 7051, 1335, 15414, 12291, 15387])).
% 28.70/18.91 tff(15422,plain,
% 28.70/18.91 ($false),
% 28.70/18.91 inference(unit_resolution,[status(thm)],[15421, 15412, 15409])).
% 28.70/18.91 tff(15423,plain,((f10(c2) = f2(c2)) | (~big_f(c2, f10(c2))) | big_f(c1, c1) | (~big_f(c2, c2)) | (~(c2 = f8(c2))) | (~(c3 = c2)) | (~big_f(c2, c1)) | (f10(c2) = c2) | (~(f4(c4) = c2)) | (~(f7(c2) = c2)) | big_f(c1, c2)), inference(lemma,lemma(discharge,[]))).
% 28.70/18.91 tff(15424,plain,
% 28.70/18.91 (f10(c2) = f2(c2)),
% 28.70/18.91 inference(unit_resolution,[status(thm)],[15423, 15386, 66, 13805, 15383, 15379, 15290, 89, 79, 13346, 15318])).
% 28.70/18.91 tff(15425,plain,
% 28.70/18.91 (f2(c2) = f10(c2)),
% 28.70/18.91 inference(symmetry,[status(thm)],[15424])).
% 28.70/18.91 tff(15426,plain,
% 28.70/18.91 ((c2 = f2(c2)) <=> (c2 = f10(c2))),
% 28.70/18.91 inference(monotonicity,[status(thm)],[15425])).
% 28.70/18.91 tff(15427,plain,
% 28.70/18.91 ((c2 = f2(c2)) <=> (f10(c2) = c2)),
% 28.70/18.91 inference(transitivity,[status(thm)],[15426, 4987])).
% 28.70/18.91 tff(15428,plain,
% 28.70/18.91 ((f10(c2) = c2) <=> (c2 = f2(c2))),
% 28.70/18.91 inference(symmetry,[status(thm)],[15427])).
% 28.70/18.91 tff(15429,plain,
% 28.70/18.91 ((~(f10(c2) = c2)) <=> (~(c2 = f2(c2)))),
% 28.70/18.91 inference(monotonicity,[status(thm)],[15428])).
% 28.70/18.91 tff(15430,plain,
% 28.70/18.91 (~(c2 = f2(c2))),
% 28.70/18.91 inference(modus_ponens,[status(thm)],[89, 15429])).
% 28.70/18.91 tff(15431,plain,
% 28.70/18.91 (c2 = c3),
% 28.70/18.91 inference(modus_ponens,[status(thm)],[15379, 78])).
% 28.70/18.91 tff(15432,plain,
% 28.70/18.91 ($false),
% 28.70/18.91 inference(unit_resolution,[status(thm)],[13128, 7051, 873, 1345, 1344, 1342, 15391, 15388])).
% 28.70/18.91 tff(15433,plain,((c2 = c4) | (~big_f(c2, c2)) | (~(c2 = c3)) | (c2 = f2(c2)) | (~(f4(c4) = c2)) | (~(f7(c2) = c2)) | big_f(c1, c2) | (~big_f(c2, c1))), inference(lemma,lemma(discharge,[]))).
% 28.70/18.91 tff(15434,plain,
% 28.70/18.91 (c2 = c4),
% 28.70/18.91 inference(unit_resolution,[status(thm)],[15433, 15431, 13805, 15430, 79, 13346, 15318, 15290])).
% 28.70/18.91 tff(15435,plain,
% 28.70/18.91 (c4 = c2),
% 28.70/18.91 inference(symmetry,[status(thm)],[15434])).
% 28.70/18.91 tff(15436,plain,
% 28.70/18.91 ((f10(c2) = c4) <=> (f10(c2) = c2)),
% 28.70/18.91 inference(monotonicity,[status(thm)],[15435])).
% 28.70/18.91 tff(15437,plain,
% 28.70/18.91 ((f10(c2) = c2) <=> (f10(c2) = c4)),
% 28.70/18.91 inference(symmetry,[status(thm)],[15436])).
% 28.70/18.91 tff(15438,plain,
% 28.70/18.91 ((f10(c2) = c2) <=> (c1 = c4)),
% 28.70/18.91 inference(transitivity,[status(thm)],[15437, 15385])).
% 28.70/18.91 tff(15439,plain,
% 28.70/18.91 ((~(f10(c2) = c2)) <=> (~(c1 = c4))),
% 28.70/18.91 inference(monotonicity,[status(thm)],[15438])).
% 28.70/18.91 tff(15440,plain,
% 28.70/18.91 (~(c1 = c4)),
% 28.70/18.91 inference(modus_ponens,[status(thm)],[89, 15439])).
% 28.70/18.91 tff(15441,plain,
% 28.70/18.91 (f3(c1, c2) = c2),
% 28.70/18.91 inference(unit_resolution,[status(thm)],[13195, 15440, 66, 13805, 15383, 15379, 15290])).
% 28.70/18.91 tff(15442,plain,
% 28.70/18.91 (f3(f10(c2), c2) = c2),
% 28.70/18.91 inference(transitivity,[status(thm)],[15408, 15441])).
% 28.70/18.91 tff(15443,plain,
% 28.70/18.91 (big_f(f3(f10(c2), c2), f10(c2)) <=> big_f(c2, f10(c2))),
% 28.70/18.91 inference(monotonicity,[status(thm)],[15442])).
% 28.70/18.91 tff(15444,plain,
% 28.70/18.91 (big_f(c2, f10(c2)) <=> big_f(f3(f10(c2), c2), f10(c2))),
% 28.70/18.91 inference(symmetry,[status(thm)],[15443])).
% 28.70/18.91 tff(15445,plain,
% 28.70/18.91 (big_f(f3(f10(c2), c2), f10(c2))),
% 28.70/18.91 inference(modus_ponens,[status(thm)],[15386, 15444])).
% 28.70/18.91 tff(15446,plain,
% 28.70/18.91 ((~(f10(c2) = c2)) <=> (~(f10(c2) = c4))),
% 28.70/18.91 inference(monotonicity,[status(thm)],[15437])).
% 28.70/18.91 tff(15447,plain,
% 28.70/18.91 (~(f10(c2) = c4)),
% 28.70/18.91 inference(modus_ponens,[status(thm)],[89, 15446])).
% 28.70/18.91 tff(15448,plain,
% 28.70/18.91 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = f2(c2)) | (f10(c2) = c4) | (~big_f(c2, c2)) | (~(f3(f10(c2), c2) = c2)) | (~big_f(f3(f10(c2), c2), f10(c2))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = f2(c2)) | (f10(c2) = c4) | (~big_f(c2, c2)) | (~(f3(f10(c2), c2) = c2)) | (~big_f(f3(f10(c2), c2), f10(c2))))),
% 28.70/18.91 inference(rewrite,[status(thm)],[])).
% 28.70/18.91 tff(15449,plain,
% 28.70/18.91 (((~(c2 = c3)) | (f10(c2) = c4) | (~(f3(f10(c2), c2) = c2)) | (~big_f(f3(f10(c2), c2), f10(c2))) | (c2 = f2(c2)) | (~big_f(c2, c2))) <=> ((~(c2 = c3)) | (c2 = f2(c2)) | (f10(c2) = c4) | (~big_f(c2, c2)) | (~(f3(f10(c2), c2) = c2)) | (~big_f(f3(f10(c2), c2), f10(c2))))),
% 28.70/18.91 inference(rewrite,[status(thm)],[])).
% 28.70/18.91 tff(15450,plain,
% 28.70/18.91 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f10(c2) = c4) | (~(f3(f10(c2), c2) = c2)) | (~big_f(f3(f10(c2), c2), f10(c2))) | (c2 = f2(c2)) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = f2(c2)) | (f10(c2) = c4) | (~big_f(c2, c2)) | (~(f3(f10(c2), c2) = c2)) | (~big_f(f3(f10(c2), c2), f10(c2)))))),
% 28.70/18.91 inference(monotonicity,[status(thm)],[15449])).
% 28.70/18.91 tff(15451,plain,
% 28.70/18.91 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f10(c2) = c4) | (~(f3(f10(c2), c2) = c2)) | (~big_f(f3(f10(c2), c2), f10(c2))) | (c2 = f2(c2)) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = f2(c2)) | (f10(c2) = c4) | (~big_f(c2, c2)) | (~(f3(f10(c2), c2) = c2)) | (~big_f(f3(f10(c2), c2), f10(c2))))),
% 28.70/18.91 inference(transitivity,[status(thm)],[15450, 15448])).
% 28.70/18.91 tff(15452,plain,
% 28.70/18.91 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f10(c2) = c4) | (~(f3(f10(c2), c2) = c2)) | (~big_f(f3(f10(c2), c2), f10(c2))) | (c2 = f2(c2)) | (~big_f(c2, c2)))),
% 28.70/18.91 inference(quant_inst,[status(thm)],[])).
% 28.70/18.91 tff(15453,plain,
% 28.70/18.91 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = f2(c2)) | (f10(c2) = c4) | (~big_f(c2, c2)) | (~(f3(f10(c2), c2) = c2)) | (~big_f(f3(f10(c2), c2), f10(c2)))),
% 28.70/18.91 inference(modus_ponens,[status(thm)],[15452, 15451])).
% 28.70/18.91 tff(15454,plain,
% 28.70/18.91 ((~(f3(f10(c2), c2) = c2)) | (~big_f(f3(f10(c2), c2), f10(c2)))),
% 28.70/18.91 inference(unit_resolution,[status(thm)],[15453, 7051, 13805, 15431, 15430, 15447])).
% 28.70/18.91 tff(15455,plain,
% 28.70/18.91 ($false),
% 28.70/18.91 inference(unit_resolution,[status(thm)],[15454, 15445, 15442])).
% 28.70/18.91 tff(15456,plain,(big_f(c1, c1) | (f10(c2) = c2) | (~(f4(c4) = c2)) | (f7(c1) = c1) | (f10(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 28.70/18.91 tff(15457,plain,
% 28.70/18.91 (big_f(c1, c1)),
% 28.70/18.91 inference(unit_resolution,[status(thm)],[15456, 89, 79, 115, 3])).
% 28.70/18.91 tff(15458,plain,
% 28.70/18.91 (big_f(f10(c2), f10(c2))),
% 28.70/18.91 inference(modus_ponens,[status(thm)],[15457, 13717])).
% 28.70/18.91 tff(15459,plain,
% 28.70/18.91 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))))),
% 28.70/18.91 inference(rewrite,[status(thm)],[])).
% 28.70/18.91 tff(15460,plain,
% 28.70/18.91 (((f10(c2) = c2) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2)))) <=> ((f10(c2) = c2) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))))),
% 28.70/18.91 inference(rewrite,[status(thm)],[])).
% 28.70/18.91 tff(15461,plain,
% 28.70/18.91 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2)))))),
% 28.70/18.91 inference(monotonicity,[status(thm)],[15460])).
% 28.70/18.91 tff(15462,plain,
% 28.70/18.91 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))))),
% 28.70/18.91 inference(transitivity,[status(thm)],[15461, 15459])).
% 28.70/18.91 tff(15463,plain,
% 28.70/18.91 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))),
% 28.70/18.91 inference(quant_inst,[status(thm)],[])).
% 28.70/18.91 tff(15464,plain,
% 28.70/18.91 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2)))),
% 28.70/18.91 inference(modus_ponens,[status(thm)],[15463, 15462])).
% 28.70/18.91 tff(15465,plain,
% 28.70/18.91 (f10(c2) = f8(c2)),
% 28.70/18.91 inference(unit_resolution,[status(thm)],[15464, 2730, 89, 13346, 15250, 15251, 15458])).
% 28.70/18.91 tff(15466,plain,
% 28.70/18.91 (f8(c2) = f10(c2)),
% 28.70/18.91 inference(symmetry,[status(thm)],[15465])).
% 28.70/18.91 tff(15467,plain,
% 28.70/18.91 ((c2 = f8(c2)) <=> (c2 = f10(c2))),
% 28.70/18.91 inference(monotonicity,[status(thm)],[15466])).
% 28.70/18.91 tff(15468,plain,
% 28.70/18.91 ((c2 = f8(c2)) <=> (f10(c2) = c2)),
% 28.70/18.91 inference(transitivity,[status(thm)],[15467, 4987])).
% 28.70/18.91 tff(15469,plain,
% 28.70/18.91 ((f10(c2) = c2) <=> (c2 = f8(c2))),
% 28.70/18.91 inference(symmetry,[status(thm)],[15468])).
% 28.70/18.91 tff(15470,plain,
% 28.70/18.91 ((~(f10(c2) = c2)) <=> (~(c2 = f8(c2)))),
% 28.70/18.91 inference(monotonicity,[status(thm)],[15469])).
% 28.70/18.91 tff(15471,plain,
% 28.70/18.91 (~(c2 = f8(c2))),
% 28.70/18.91 inference(modus_ponens,[status(thm)],[89, 15470])).
% 28.70/18.91 tff(15472,plain,
% 28.70/18.91 ((~big_f(c2, c1)) <=> (~big_f(c2, f10(c2)))),
% 28.70/18.91 inference(monotonicity,[status(thm)],[15252])).
% 28.70/18.91 tff(15473,plain,
% 28.70/18.91 (~big_f(c2, f10(c2))),
% 28.70/18.91 inference(modus_ponens,[status(thm)],[2, 15472])).
% 28.70/18.91 tff(15474,plain,
% 28.70/18.91 ((c4 = c1) <=> (f10(c2) = c4)),
% 28.70/18.91 inference(transitivity,[status(thm)],[479, 15384])).
% 28.70/18.91 tff(15475,plain,
% 28.70/18.91 ((~(c4 = c1)) <=> (~(f10(c2) = c4))),
% 28.70/18.91 inference(monotonicity,[status(thm)],[15474])).
% 28.70/18.91 tff(15476,plain,
% 28.70/18.91 (f10(c2) = c4),
% 28.70/18.91 inference(transitivity,[status(thm)],[94, 567])).
% 28.70/18.91 tff(15477,plain,
% 28.70/18.91 (f4(f10(c2)) = f4(c4)),
% 28.70/18.91 inference(monotonicity,[status(thm)],[15476])).
% 28.70/18.91 tff(15478,plain,
% 28.70/18.91 (f4(f10(c2)) = c2),
% 28.70/18.91 inference(transitivity,[status(thm)],[15477, 79])).
% 28.70/18.91 tff(15479,plain,
% 28.70/18.91 ((f10(c2) = f4(f10(c2))) <=> (f10(c2) = c2)),
% 28.70/18.91 inference(monotonicity,[status(thm)],[15478])).
% 28.70/18.91 tff(15480,plain,
% 28.70/18.91 ((f10(c2) = c2) <=> (f10(c2) = f4(f10(c2)))),
% 28.70/18.91 inference(symmetry,[status(thm)],[15479])).
% 28.70/18.91 tff(15481,plain,
% 28.70/18.91 ((~(f10(c2) = c2)) <=> (~(f10(c2) = f4(f10(c2))))),
% 28.70/18.91 inference(monotonicity,[status(thm)],[15480])).
% 28.70/18.91 tff(15482,plain,
% 28.70/18.91 (~(f10(c2) = f4(f10(c2)))),
% 28.70/18.91 inference(modus_ponens,[status(thm)],[89, 15481])).
% 28.70/18.91 tff(15483,assumption,(~(f10(c2) = f4(f10(c2)))), introduced(assumption)).
% 28.70/18.91 tff(15484,assumption,(f10(c2) = c4), introduced(assumption)).
% 28.70/18.91 tff(15485,plain,
% 28.70/18.91 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c2 = c3) | (~(f10(c2) = c4)) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (f10(c2) = f4(f10(c2))) | (~big_f(f10(c2), f10(c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (c2 = c3) | (~(f10(c2) = c4)) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (f10(c2) = f4(f10(c2))) | (~big_f(f10(c2), f10(c2))))),
% 28.70/18.91 inference(rewrite,[status(thm)],[])).
% 28.70/18.91 tff(15486,plain,
% 28.70/18.91 (((c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f10(c2) = c4)) | (f10(c2) = f4(f10(c2))) | (~big_f(f10(c2), f10(c2)))) <=> ((c2 = c3) | (~(f10(c2) = c4)) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (f10(c2) = f4(f10(c2))) | (~big_f(f10(c2), f10(c2))))),
% 28.70/18.91 inference(rewrite,[status(thm)],[])).
% 28.70/18.91 tff(15487,plain,
% 28.70/18.91 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f10(c2) = c4)) | (f10(c2) = f4(f10(c2))) | (~big_f(f10(c2), f10(c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c2 = c3) | (~(f10(c2) = c4)) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (f10(c2) = f4(f10(c2))) | (~big_f(f10(c2), f10(c2)))))),
% 28.70/18.91 inference(monotonicity,[status(thm)],[15486])).
% 28.70/18.91 tff(15488,plain,
% 28.70/18.91 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f10(c2) = c4)) | (f10(c2) = f4(f10(c2))) | (~big_f(f10(c2), f10(c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (c2 = c3) | (~(f10(c2) = c4)) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (f10(c2) = f4(f10(c2))) | (~big_f(f10(c2), f10(c2))))),
% 28.70/18.91 inference(transitivity,[status(thm)],[15487, 15485])).
% 28.70/18.91 tff(15489,plain,
% 28.70/18.91 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f10(c2) = c4)) | (f10(c2) = f4(f10(c2))) | (~big_f(f10(c2), f10(c2))))),
% 28.70/18.91 inference(quant_inst,[status(thm)],[])).
% 28.70/18.91 tff(15490,plain,
% 28.70/18.91 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (c2 = c3) | (~(f10(c2) = c4)) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (f10(c2) = f4(f10(c2))) | (~big_f(f10(c2), f10(c2)))),
% 28.70/18.91 inference(modus_ponens,[status(thm)],[15489, 15488])).
% 28.70/18.91 tff(15491,plain,
% 28.70/18.91 ($false),
% 28.70/18.91 inference(unit_resolution,[status(thm)],[15490, 525, 377, 15484, 1828, 14892, 14686, 15483])).
% 28.70/18.91 tff(15492,plain,((f1(c2, c2) = c2) | (c2 = c3) | (~(f10(c2) = c4)) | (~big_f(f10(c2), f10(c2))) | (f10(c2) = f4(f10(c2))) | (~(c4 = c1)) | big_f(c2, c4)), inference(lemma,lemma(discharge,[]))).
% 28.70/18.91 tff(15493,plain,
% 28.70/18.91 (f1(c2, c2) = c2),
% 28.70/18.91 inference(unit_resolution,[status(thm)],[15492, 15476, 377, 14686, 15482, 480, 14881])).
% 28.70/18.91 tff(15494,plain,
% 28.70/18.91 (big_f(c2, f1(c2, c2)) <=> big_f(c2, c2)),
% 28.70/18.91 inference(monotonicity,[status(thm)],[15493])).
% 28.70/18.91 tff(15495,plain,
% 28.70/18.91 (big_f(c2, c2) <=> big_f(c2, f1(c2, c2))),
% 28.70/18.91 inference(symmetry,[status(thm)],[15494])).
% 28.70/18.91 tff(15496,plain,
% 28.70/18.91 (big_f(c2, f1(c2, c2))),
% 28.70/18.91 inference(modus_ponens,[status(thm)],[1345, 15495])).
% 28.70/18.91 tff(15497,plain,
% 28.70/18.91 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f10(c2) = c4)) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f10(c2) = f4(f10(c2))) | (~big_f(f10(c2), f10(c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(f10(c2) = c4)) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f10(c2) = f4(f10(c2))) | (~big_f(f10(c2), f10(c2))))),
% 28.70/18.91 inference(rewrite,[status(thm)],[])).
% 28.70/18.91 tff(15498,plain,
% 28.70/18.91 (((c2 = c3) | (~(f10(c2) = c4)) | (f10(c2) = f4(f10(c2))) | (~big_f(f10(c2), f10(c2))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2)))) <=> ((c2 = c3) | (~(f10(c2) = c4)) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f10(c2) = f4(f10(c2))) | (~big_f(f10(c2), f10(c2))))),
% 28.70/18.91 inference(rewrite,[status(thm)],[])).
% 28.70/18.91 tff(15499,plain,
% 28.70/18.91 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f10(c2) = c4)) | (f10(c2) = f4(f10(c2))) | (~big_f(f10(c2), f10(c2))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f10(c2) = c4)) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f10(c2) = f4(f10(c2))) | (~big_f(f10(c2), f10(c2)))))),
% 28.70/18.91 inference(monotonicity,[status(thm)],[15498])).
% 28.70/18.91 tff(15500,plain,
% 28.70/18.91 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f10(c2) = c4)) | (f10(c2) = f4(f10(c2))) | (~big_f(f10(c2), f10(c2))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(f10(c2) = c4)) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f10(c2) = f4(f10(c2))) | (~big_f(f10(c2), f10(c2))))),
% 28.70/18.91 inference(transitivity,[status(thm)],[15499, 15497])).
% 28.70/18.91 tff(15501,plain,
% 28.70/18.91 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f10(c2) = c4)) | (f10(c2) = f4(f10(c2))) | (~big_f(f10(c2), f10(c2))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))),
% 28.70/18.91 inference(quant_inst,[status(thm)],[])).
% 28.70/18.91 tff(15502,plain,
% 28.70/18.91 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(f10(c2) = c4)) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f10(c2) = f4(f10(c2))) | (~big_f(f10(c2), f10(c2)))),
% 28.70/18.92 inference(modus_ponens,[status(thm)],[15501, 15500])).
% 28.70/18.92 tff(15503,plain,
% 28.70/18.92 ($false),
% 28.70/18.92 inference(unit_resolution,[status(thm)],[15502, 553, 377, 15476, 15493, 15496, 14686, 15482])).
% 28.70/18.92 tff(15504,plain,((~(c4 = c1)) | (c2 = c3) | (~big_f(f10(c2), f10(c2))) | (~big_f(c2, c2)) | (f10(c2) = c2) | (~(f4(c4) = c2)) | big_f(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 28.70/18.92 tff(15505,plain,
% 28.70/18.92 (~(c4 = c1)),
% 28.70/18.92 inference(unit_resolution,[status(thm)],[15504, 377, 14686, 1345, 89, 79, 2])).
% 28.70/18.92 tff(15506,plain,
% 28.70/18.92 (~(f10(c2) = c4)),
% 28.70/18.92 inference(modus_ponens,[status(thm)],[15505, 15475])).
% 28.70/18.92 tff(15507,plain,
% 28.70/18.92 (f3(f10(c2), f10(c2)) = f3(c1, c1)),
% 28.70/18.92 inference(monotonicity,[status(thm)],[94, 94])).
% 28.70/18.92 tff(15508,plain,
% 28.70/18.92 (f3(f10(c2), f10(c2)) = c2),
% 28.70/18.92 inference(transitivity,[status(thm)],[15507, 1441])).
% 28.70/18.92 tff(15509,plain,
% 28.70/18.92 ((f3(f10(c2), f10(c2)) = f10(c2)) <=> (c2 = f10(c2))),
% 28.70/18.92 inference(monotonicity,[status(thm)],[15508])).
% 28.70/18.92 tff(15510,plain,
% 28.70/18.92 ((f3(f10(c2), f10(c2)) = f10(c2)) <=> (f10(c2) = c2)),
% 28.70/18.92 inference(transitivity,[status(thm)],[15509, 4987])).
% 28.70/18.92 tff(15511,plain,
% 28.70/18.92 ((f10(c2) = c2) <=> (f3(f10(c2), f10(c2)) = f10(c2))),
% 28.70/18.92 inference(symmetry,[status(thm)],[15510])).
% 28.70/18.92 tff(15512,plain,
% 28.70/18.92 ((~(f10(c2) = c2)) <=> (~(f3(f10(c2), f10(c2)) = f10(c2)))),
% 28.70/18.92 inference(monotonicity,[status(thm)],[15511])).
% 28.70/18.92 tff(15513,plain,
% 28.70/18.92 (~(f3(f10(c2), f10(c2)) = f10(c2))),
% 28.70/18.92 inference(modus_ponens,[status(thm)],[89, 15512])).
% 28.70/18.92 tff(15514,plain,
% 28.70/18.92 (big_f(f3(f10(c2), f10(c2)), f10(c2)) <=> big_f(c2, f10(c2))),
% 28.70/18.92 inference(monotonicity,[status(thm)],[15508])).
% 28.70/18.92 tff(15515,plain,
% 28.70/18.92 (big_f(c2, f10(c2)) <=> big_f(f3(f10(c2), f10(c2)), f10(c2))),
% 28.70/18.92 inference(symmetry,[status(thm)],[15514])).
% 28.70/18.92 tff(15516,plain,
% 28.70/18.92 ((~big_f(c2, f10(c2))) <=> (~big_f(f3(f10(c2), f10(c2)), f10(c2)))),
% 28.70/18.92 inference(monotonicity,[status(thm)],[15515])).
% 28.70/18.92 tff(15517,assumption,(~big_f(c2, f10(c2))), introduced(assumption)).
% 28.70/18.92 tff(15518,plain,
% 28.70/18.92 (~big_f(f3(f10(c2), f10(c2)), f10(c2))),
% 28.70/18.92 inference(modus_ponens,[status(thm)],[15517, 15516])).
% 28.70/18.92 tff(15519,assumption,(~(f10(c2) = c4)), introduced(assumption)).
% 28.70/18.92 tff(15520,plain,
% 28.70/18.92 (f1(c2, c2) = f10(c2)),
% 28.70/18.92 inference(transitivity,[status(thm)],[5298, 99])).
% 28.70/18.92 tff(15521,plain,
% 28.70/18.92 (big_f(c2, f1(c2, c2)) <=> big_f(c2, f10(c2))),
% 28.70/18.92 inference(monotonicity,[status(thm)],[15520])).
% 28.70/18.92 tff(15522,plain,
% 28.70/18.92 (big_f(c2, f10(c2)) <=> big_f(c2, f1(c2, c2))),
% 28.70/18.92 inference(symmetry,[status(thm)],[15521])).
% 28.70/18.92 tff(15523,plain,
% 28.70/18.92 ((~big_f(c2, f10(c2))) <=> (~big_f(c2, f1(c2, c2)))),
% 28.70/18.92 inference(monotonicity,[status(thm)],[15522])).
% 28.70/18.92 tff(15524,plain,
% 28.70/18.92 (~big_f(c2, f1(c2, c2))),
% 28.70/18.92 inference(modus_ponens,[status(thm)],[15517, 15523])).
% 28.70/18.92 tff(15525,plain,
% 28.70/18.92 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c2 = c3) | (f10(c2) = c4) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (c2 = c3) | (f10(c2) = c4) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2)))),
% 28.70/18.92 inference(rewrite,[status(thm)],[])).
% 28.70/18.92 tff(15526,plain,
% 28.70/18.92 (((f10(c2) = c4) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2)) | (c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2))) <=> ((c2 = c3) | (f10(c2) = c4) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2)))),
% 28.70/18.92 inference(rewrite,[status(thm)],[])).
% 28.70/18.92 tff(15527,plain,
% 28.70/18.92 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f10(c2) = c4) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2)) | (c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c2 = c3) | (f10(c2) = c4) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2))))),
% 28.70/18.92 inference(monotonicity,[status(thm)],[15526])).
% 28.70/18.92 tff(15528,plain,
% 28.70/18.92 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f10(c2) = c4) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2)) | (c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (c2 = c3) | (f10(c2) = c4) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2)))),
% 28.70/18.92 inference(transitivity,[status(thm)],[15527, 15525])).
% 28.70/18.92 tff(15529,plain,
% 28.70/18.92 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f10(c2) = c4) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2)) | (c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)))),
% 28.70/18.92 inference(quant_inst,[status(thm)],[])).
% 28.70/18.92 tff(15530,plain,
% 28.70/18.92 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (c2 = c3) | (f10(c2) = c4) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2))),
% 28.70/18.92 inference(modus_ponens,[status(thm)],[15529, 15528])).
% 28.70/18.92 tff(15531,plain,
% 28.70/18.92 ((f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2))),
% 28.70/18.92 inference(unit_resolution,[status(thm)],[15530, 1014, 377, 15519, 1828, 15524])).
% 28.70/18.92 tff(15532,plain,
% 28.70/18.92 ($false),
% 28.70/18.92 inference(unit_resolution,[status(thm)],[15531, 15518, 15513])).
% 28.70/18.92 tff(15533,plain,((f1(c2, c2) = c2) | (c2 = c3) | (f10(c2) = c4) | big_f(c2, f10(c2)) | (~(f3(c1, c1) = c2)) | (f10(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 28.70/18.92 tff(15534,plain,
% 28.70/18.92 (f1(c2, c2) = c2),
% 28.70/18.92 inference(unit_resolution,[status(thm)],[15533, 1441, 15519, 15517, 377, 89])).
% 28.70/18.92 tff(15535,plain,
% 28.70/18.92 (big_f(c2, f1(c2, c2)) <=> big_f(c2, c2)),
% 28.70/18.92 inference(monotonicity,[status(thm)],[15534])).
% 28.70/18.92 tff(15536,plain,
% 28.70/18.92 (big_f(c2, c2) <=> big_f(c2, f1(c2, c2))),
% 28.70/18.92 inference(symmetry,[status(thm)],[15535])).
% 28.70/18.92 tff(15537,plain,
% 28.70/18.92 (big_f(c2, f1(c2, c2))),
% 28.70/18.92 inference(modus_ponens,[status(thm)],[1345, 15536])).
% 28.70/18.92 tff(15538,plain,
% 28.70/18.92 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (f10(c2) = c4) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (f10(c2) = c4) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2)))),
% 28.70/18.92 inference(rewrite,[status(thm)],[])).
% 28.70/18.92 tff(15539,plain,
% 28.70/18.92 (((f10(c2) = c4) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2)) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2)))) <=> ((c2 = c3) | (f10(c2) = c4) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2)))),
% 28.70/18.92 inference(rewrite,[status(thm)],[])).
% 28.70/18.92 tff(15540,plain,
% 28.70/18.92 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f10(c2) = c4) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2)) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (f10(c2) = c4) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2))))),
% 28.70/18.92 inference(monotonicity,[status(thm)],[15539])).
% 28.70/18.92 tff(15541,plain,
% 28.70/18.92 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f10(c2) = c4) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2)) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (f10(c2) = c4) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2)))),
% 28.70/18.92 inference(transitivity,[status(thm)],[15540, 15538])).
% 28.70/18.92 tff(15542,plain,
% 28.70/18.92 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f10(c2) = c4) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2)) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))),
% 28.70/18.92 inference(quant_inst,[status(thm)],[])).
% 28.70/18.92 tff(15543,plain,
% 28.70/18.92 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (f10(c2) = c4) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2))),
% 28.70/18.92 inference(modus_ponens,[status(thm)],[15542, 15541])).
% 28.70/18.92 tff(15544,plain,
% 28.70/18.92 ((f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2))),
% 28.70/18.92 inference(unit_resolution,[status(thm)],[15543, 904, 377, 15519, 15534, 15537])).
% 28.70/18.92 tff(15545,plain,
% 28.70/18.92 ($false),
% 28.70/18.92 inference(unit_resolution,[status(thm)],[15544, 15518, 15513])).
% 28.70/18.92 tff(15546,plain,((~(f3(c1, c1) = c2)) | (c2 = c3) | (f10(c2) = c4) | big_f(c2, f10(c2)) | (f10(c2) = c2) | (~big_f(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 28.70/18.92 tff(15547,plain,
% 28.70/18.92 (~(f3(c1, c1) = c2)),
% 28.70/18.92 inference(unit_resolution,[status(thm)],[15546, 377, 15506, 15473, 89, 1345])).
% 28.70/18.92 tff(15548,plain,
% 28.70/18.92 (f3(c1, c1) = c1),
% 28.70/18.92 inference(unit_resolution,[status(thm)],[1416, 15547])).
% 28.70/18.92 tff(15549,plain,
% 28.70/18.92 (f3(f10(c2), f10(c2)) = f10(c2)),
% 28.70/18.92 inference(transitivity,[status(thm)],[15507, 15548, 99])).
% 28.70/18.92 tff(15550,plain,
% 28.70/18.92 (big_f(f3(f10(c2), f10(c2)), f10(c2)) <=> big_f(f10(c2), f10(c2))),
% 28.70/18.92 inference(monotonicity,[status(thm)],[15549])).
% 28.70/18.92 tff(15551,plain,
% 28.70/18.92 (big_f(f10(c2), f10(c2)) <=> big_f(f3(f10(c2), f10(c2)), f10(c2))),
% 28.70/18.92 inference(symmetry,[status(thm)],[15550])).
% 28.70/18.92 tff(15552,plain,
% 28.70/18.92 (big_f(f3(f10(c2), f10(c2)), f10(c2))),
% 28.70/18.92 inference(modus_ponens,[status(thm)],[14686, 15551])).
% 28.70/18.92 tff(15553,plain,
% 28.70/18.92 (f3(f10(c2), f10(c2)) = f3(c1, c1)),
% 28.70/18.92 inference(monotonicity,[status(thm)],[11819, 11819])).
% 28.70/18.92 tff(15554,plain,
% 28.70/18.92 (f3(f10(c2), f10(c2)) = f10(c2)),
% 28.70/18.92 inference(transitivity,[status(thm)],[15553, 1938, 12231])).
% 28.70/18.92 tff(15555,plain,
% 28.70/18.92 (big_f(f3(f10(c2), f10(c2)), f10(c2)) <=> big_f(f10(c2), f10(c2))),
% 28.70/18.92 inference(monotonicity,[status(thm)],[15554])).
% 28.70/18.92 tff(15556,plain,
% 28.70/18.92 (big_f(f10(c2), f10(c2)) <=> big_f(f3(f10(c2), f10(c2)), f10(c2))),
% 28.70/18.92 inference(symmetry,[status(thm)],[15555])).
% 28.70/18.92 tff(15557,plain,
% 28.70/18.92 (big_f(f3(f10(c2), f10(c2)), f10(c2))),
% 28.70/18.92 inference(modus_ponens,[status(thm)],[14686, 15556])).
% 28.70/18.92 tff(15558,plain,
% 28.70/18.92 (f1(c2, c2) = f10(c2)),
% 28.70/18.92 inference(transitivity,[status(thm)],[5298, 12231])).
% 28.70/18.92 tff(15559,plain,
% 28.70/18.92 (big_f(c2, f1(c2, c2)) <=> big_f(c2, f10(c2))),
% 28.70/18.92 inference(monotonicity,[status(thm)],[15558])).
% 28.70/18.92 tff(15560,plain,
% 28.70/18.92 (big_f(c2, f10(c2)) <=> big_f(c2, f1(c2, c2))),
% 28.70/18.92 inference(symmetry,[status(thm)],[15559])).
% 28.70/18.92 tff(15561,plain,
% 28.70/18.92 ((~big_f(c2, f10(c2))) <=> (~big_f(c2, f1(c2, c2)))),
% 28.70/18.92 inference(monotonicity,[status(thm)],[15560])).
% 28.70/18.92 tff(15562,plain,
% 28.70/18.92 (~big_f(c2, f1(c2, c2))),
% 28.70/18.92 inference(modus_ponens,[status(thm)],[15517, 15561])).
% 28.70/18.92 tff(15563,plain,
% 28.70/18.92 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c3) | (f10(c2) = c4) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c2 = c3) | (f10(c2) = c4) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))))),
% 28.70/18.92 inference(rewrite,[status(thm)],[])).
% 28.70/18.92 tff(15564,plain,
% 28.70/18.92 (((f10(c2) = c4) | (c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2)))) <=> ((c2 = c3) | (f10(c2) = c4) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))))),
% 28.70/18.92 inference(rewrite,[status(thm)],[])).
% 28.70/18.92 tff(15565,plain,
% 28.70/18.92 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((f10(c2) = c4) | (c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c3) | (f10(c2) = c4) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2)))))),
% 28.70/18.92 inference(monotonicity,[status(thm)],[15564])).
% 28.70/18.92 tff(15566,plain,
% 28.70/18.92 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((f10(c2) = c4) | (c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c2 = c3) | (f10(c2) = c4) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))))),
% 28.70/18.92 inference(transitivity,[status(thm)],[15565, 15563])).
% 28.70/18.92 tff(15567,plain,
% 28.70/18.92 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((f10(c2) = c4) | (c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))))),
% 28.70/18.92 inference(quant_inst,[status(thm)],[])).
% 28.70/18.92 tff(15568,plain,
% 28.70/18.92 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c2 = c3) | (f10(c2) = c4) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2)))),
% 28.70/18.92 inference(modus_ponens,[status(thm)],[15567, 15566])).
% 28.70/18.92 tff(15569,plain,
% 28.70/18.92 ((~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2)))),
% 28.70/18.92 inference(unit_resolution,[status(thm)],[15568, 969, 377, 15519, 1828, 15562])).
% 28.70/18.92 tff(15570,plain,
% 28.70/18.92 ($false),
% 28.70/18.92 inference(unit_resolution,[status(thm)],[15569, 15557, 15554])).
% 28.70/18.92 tff(15571,plain,((f1(c2, c2) = c2) | (c2 = c3) | (f10(c2) = c4) | (~big_f(f10(c2), f10(c2))) | (~(f3(c1, c1) = c1)) | (~(f10(c2) = c1)) | big_f(c2, f10(c2))), inference(lemma,lemma(discharge,[]))).
% 28.70/18.92 tff(15572,plain,
% 28.70/18.92 (f1(c2, c2) = c2),
% 28.70/18.92 inference(unit_resolution,[status(thm)],[15571, 377, 15506, 14686, 15548, 94, 15473])).
% 28.70/18.92 tff(15573,plain,
% 28.70/18.92 (big_f(c2, f1(c2, c2)) <=> big_f(c2, c2)),
% 28.70/18.92 inference(monotonicity,[status(thm)],[15572])).
% 28.70/18.92 tff(15574,plain,
% 28.70/18.92 (big_f(c2, c2) <=> big_f(c2, f1(c2, c2))),
% 28.70/18.92 inference(symmetry,[status(thm)],[15573])).
% 28.70/18.92 tff(15575,plain,
% 28.70/18.92 (big_f(c2, f1(c2, c2))),
% 28.70/18.92 inference(modus_ponens,[status(thm)],[1345, 15574])).
% 28.70/18.92 tff(15576,plain,
% 28.70/18.92 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (f10(c2) = c4) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (f10(c2) = c4) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))))),
% 28.70/18.92 inference(rewrite,[status(thm)],[])).
% 28.70/18.92 tff(15577,plain,
% 28.70/18.92 (((f10(c2) = c4) | (c2 = c3) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2)))) <=> ((c2 = c3) | (f10(c2) = c4) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))))),
% 28.70/18.92 inference(rewrite,[status(thm)],[])).
% 28.70/18.92 tff(15578,plain,
% 28.70/18.92 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f10(c2) = c4) | (c2 = c3) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (f10(c2) = c4) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2)))))),
% 28.70/18.92 inference(monotonicity,[status(thm)],[15577])).
% 28.70/18.92 tff(15579,plain,
% 28.70/18.92 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f10(c2) = c4) | (c2 = c3) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (f10(c2) = c4) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))))),
% 28.70/18.92 inference(transitivity,[status(thm)],[15578, 15576])).
% 28.70/18.92 tff(15580,plain,
% 28.70/18.92 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f10(c2) = c4) | (c2 = c3) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))),
% 28.70/18.92 inference(quant_inst,[status(thm)],[])).
% 28.70/18.92 tff(15581,plain,
% 28.70/18.92 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (f10(c2) = c4) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2)))),
% 28.70/18.93 inference(modus_ponens,[status(thm)],[15580, 15579])).
% 28.70/18.93 tff(15582,plain,
% 28.70/18.93 ((~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2)))),
% 28.70/18.93 inference(unit_resolution,[status(thm)],[15581, 933, 377, 15506, 15572, 15575])).
% 28.70/18.93 tff(15583,plain,
% 28.70/18.93 ($false),
% 28.70/18.93 inference(unit_resolution,[status(thm)],[15582, 15552, 15549])).
% 28.70/18.93 tff(15584,plain,((c2 = c3) | (~big_f(f10(c2), f10(c2))) | (~big_f(c2, c2)) | (f10(c2) = c2) | (~(f4(c4) = c2)) | big_f(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 28.70/18.93 tff(15585,plain,
% 28.70/18.93 (c2 = c3),
% 28.70/18.93 inference(unit_resolution,[status(thm)],[15584, 2, 1345, 89, 79, 13718])).
% 28.70/18.93 tff(15586,assumption,(f10(c2) = f8(c2)), introduced(assumption)).
% 28.70/18.93 tff(15587,plain,
% 28.70/18.93 (c3 = c2),
% 28.70/18.93 inference(symmetry,[status(thm)],[15585])).
% 28.70/18.93 tff(15588,plain,
% 28.70/18.93 ((f10(c2) = c3) <=> (f10(c2) = c2)),
% 28.70/18.93 inference(monotonicity,[status(thm)],[15587])).
% 28.70/18.93 tff(15589,plain,
% 28.70/18.93 ((f10(c2) = c2) <=> (f10(c2) = c3)),
% 28.70/18.93 inference(symmetry,[status(thm)],[15588])).
% 28.70/18.93 tff(15590,plain,
% 28.70/18.93 ((f10(c2) = c2) <=> (c1 = c3)),
% 28.70/18.93 inference(transitivity,[status(thm)],[15589, 12095])).
% 28.70/18.93 tff(15591,plain,
% 28.70/18.93 ((~(f10(c2) = c2)) <=> (~(c1 = c3))),
% 28.70/18.93 inference(monotonicity,[status(thm)],[15590])).
% 28.70/18.93 tff(15592,plain,
% 28.70/18.93 (~(c1 = c3)),
% 28.70/18.93 inference(modus_ponens,[status(thm)],[89, 15591])).
% 28.70/18.93 tff(15593,plain,
% 28.70/18.93 (~(c4 = c1)),
% 28.70/18.93 inference(unit_resolution,[status(thm)],[11545, 15592, 27, 4932, 79])).
% 28.70/18.93 tff(15594,plain,
% 28.70/18.93 (c4 = c2),
% 28.70/18.93 inference(unit_resolution,[status(thm)],[461, 15593])).
% 28.70/18.93 tff(15595,plain,
% 28.70/18.93 ((f10(c2) = c4) <=> (f10(c2) = c2)),
% 28.70/18.93 inference(monotonicity,[status(thm)],[15594])).
% 28.70/18.93 tff(15596,plain,
% 28.70/18.93 ((f10(c2) = c2) <=> (f10(c2) = c4)),
% 28.70/18.93 inference(symmetry,[status(thm)],[15595])).
% 28.70/18.93 tff(15597,plain,
% 28.70/18.93 ((f10(c2) = c2) <=> (c1 = c4)),
% 28.70/18.93 inference(transitivity,[status(thm)],[15596, 15385])).
% 28.70/18.93 tff(15598,plain,
% 28.70/18.93 ((~(f10(c2) = c2)) <=> (~(c1 = c4))),
% 28.70/18.93 inference(monotonicity,[status(thm)],[15597])).
% 28.70/18.93 tff(15599,plain,
% 28.70/18.93 (~(c1 = c4)),
% 28.70/18.93 inference(modus_ponens,[status(thm)],[89, 15598])).
% 28.70/18.93 tff(15600,plain,
% 28.70/18.93 ((~(f10(c2) = c2)) <=> (~(f10(c2) = c4))),
% 28.70/18.93 inference(monotonicity,[status(thm)],[15596])).
% 28.70/18.93 tff(15601,plain,
% 28.70/18.93 (~(f10(c2) = c4)),
% 28.70/18.93 inference(modus_ponens,[status(thm)],[89, 15600])).
% 28.70/18.93 tff(15602,plain,
% 28.70/18.93 ((f10(c2) = c3) <=> (f10(c2) = c2)),
% 28.70/18.93 inference(monotonicity,[status(thm)],[1816])).
% 28.70/18.93 tff(15603,plain,
% 28.70/18.93 ((f10(c2) = c2) <=> (f10(c2) = c3)),
% 28.70/18.93 inference(symmetry,[status(thm)],[15602])).
% 28.70/18.93 tff(15604,plain,
% 28.70/18.93 ((f10(c2) = c2) <=> (c1 = c3)),
% 28.70/18.93 inference(transitivity,[status(thm)],[15603, 12095])).
% 28.70/18.93 tff(15605,plain,
% 28.70/18.93 ((~(f10(c2) = c2)) <=> (~(c1 = c3))),
% 28.70/18.93 inference(monotonicity,[status(thm)],[15604])).
% 28.70/18.93 tff(15606,plain,
% 28.70/18.93 (~(c1 = c3)),
% 28.70/18.93 inference(modus_ponens,[status(thm)],[89, 15605])).
% 28.70/18.93 tff(15607,plain,
% 28.70/18.93 (f8(c2) = f10(c2)),
% 28.70/18.93 inference(symmetry,[status(thm)],[15586])).
% 28.70/18.93 tff(15608,plain,
% 28.70/18.93 (f8(c3) = f8(c2)),
% 28.70/18.93 inference(monotonicity,[status(thm)],[1816])).
% 28.70/18.93 tff(15609,plain,
% 28.70/18.93 (f8(c3) = c1),
% 28.70/18.93 inference(transitivity,[status(thm)],[15608, 15607, 94])).
% 28.70/18.93 tff(15610,plain,
% 28.70/18.93 (f3(f10(c2), f8(c3)) = f3(c1, c1)),
% 28.70/18.93 inference(monotonicity,[status(thm)],[94, 15609])).
% 28.70/18.93 tff(15611,plain,
% 28.70/18.93 (f3(c1, c1) = f3(f10(c2), f8(c3))),
% 28.70/18.93 inference(symmetry,[status(thm)],[15610])).
% 28.70/18.93 tff(15612,plain,
% 28.70/18.93 (big_f(f3(c1, c1), c1) <=> big_f(f3(f10(c2), f8(c3)), f10(c2))),
% 28.70/18.93 inference(monotonicity,[status(thm)],[15611, 99])).
% 28.70/18.93 tff(15613,plain,
% 28.70/18.93 (big_f(f3(f10(c2), f8(c3)), f10(c2)) <=> big_f(f3(c1, c1), c1)),
% 28.70/18.93 inference(symmetry,[status(thm)],[15612])).
% 28.70/18.93 tff(15614,plain,
% 28.70/18.93 (f3(f10(c2), f8(c3)) = c2),
% 28.70/18.93 inference(transitivity,[status(thm)],[15610, 1440])).
% 28.70/18.93 tff(15615,plain,
% 28.70/18.93 (big_f(f3(f10(c2), f8(c3)), f10(c2)) <=> big_f(c2, f10(c2))),
% 28.70/18.93 inference(monotonicity,[status(thm)],[15614])).
% 28.70/18.93 tff(15616,plain,
% 28.70/18.93 (big_f(c2, f10(c2)) <=> big_f(f3(f10(c2), f8(c3)), f10(c2))),
% 28.70/18.93 inference(symmetry,[status(thm)],[15615])).
% 28.70/18.93 tff(15617,plain,
% 28.70/18.93 (big_f(c2, f10(c2)) <=> big_f(f3(c1, c1), c1)),
% 28.70/18.93 inference(transitivity,[status(thm)],[15616, 15613])).
% 28.70/18.93 tff(15618,plain,
% 28.70/18.93 ((~big_f(c2, f10(c2))) <=> (~big_f(f3(c1, c1), c1))),
% 28.70/18.93 inference(monotonicity,[status(thm)],[15617])).
% 28.70/18.93 tff(15619,plain,
% 28.70/18.93 (~big_f(f3(c1, c1), c1)),
% 28.70/18.93 inference(modus_ponens,[status(thm)],[15517, 15618])).
% 28.70/18.93 tff(15620,plain,
% 28.70/18.93 (big_f(c1, f1(c1, c1))),
% 28.70/18.93 inference(unit_resolution,[status(thm)],[9681, 15619, 4932, 15606, 482, 1431])).
% 28.70/18.93 tff(15621,plain,
% 28.70/18.93 (~(f1(c1, c1) = c2)),
% 28.70/18.93 inference(unit_resolution,[status(thm)],[4561, 15620, 27])).
% 28.70/18.93 tff(15622,plain,
% 28.70/18.93 (f1(c1, c1) = c1),
% 28.70/18.93 inference(unit_resolution,[status(thm)],[601, 15621])).
% 28.70/18.93 tff(15623,plain,
% 28.70/18.93 (f1(f10(c2), f10(c2)) = f10(c2)),
% 28.70/18.93 inference(transitivity,[status(thm)],[12413, 15622, 99])).
% 28.70/18.93 tff(15624,plain,
% 28.70/18.93 (big_f(f10(c2), f1(f10(c2), f10(c2))) <=> big_f(f10(c2), f10(c2))),
% 28.70/18.93 inference(monotonicity,[status(thm)],[15623])).
% 28.70/18.93 tff(15625,plain,
% 28.70/18.93 (big_f(f10(c2), f10(c2)) <=> big_f(f10(c2), f1(f10(c2), f10(c2)))),
% 28.70/18.93 inference(symmetry,[status(thm)],[15624])).
% 28.70/18.93 tff(15626,plain,
% 28.70/18.93 (big_f(f10(c2), f1(f10(c2), f10(c2)))),
% 28.70/18.93 inference(modus_ponens,[status(thm)],[13718, 15625])).
% 28.70/18.93 tff(15627,plain,
% 28.70/18.93 (f3(f10(c2), f10(c2)) = c2),
% 28.70/18.93 inference(transitivity,[status(thm)],[15507, 1440])).
% 28.70/18.93 tff(15628,plain,
% 28.70/18.93 (big_f(f3(f10(c2), f10(c2)), f10(c2)) <=> big_f(c2, f10(c2))),
% 28.70/18.93 inference(monotonicity,[status(thm)],[15627])).
% 28.70/18.93 tff(15629,plain,
% 28.70/18.93 (big_f(c2, f10(c2)) <=> big_f(f3(f10(c2), f10(c2)), f10(c2))),
% 28.70/18.93 inference(symmetry,[status(thm)],[15628])).
% 28.70/18.93 tff(15630,plain,
% 28.70/18.93 ((~big_f(c2, f10(c2))) <=> (~big_f(f3(f10(c2), f10(c2)), f10(c2)))),
% 28.70/18.93 inference(monotonicity,[status(thm)],[15629])).
% 28.70/18.93 tff(15631,plain,
% 28.70/18.93 (~big_f(f3(f10(c2), f10(c2)), f10(c2))),
% 28.70/18.93 inference(modus_ponens,[status(thm)],[15517, 15630])).
% 28.70/18.93 tff(15632,plain,
% 28.70/18.93 ((f3(f10(c2), f10(c2)) = f10(c2)) <=> (c2 = f10(c2))),
% 28.70/18.93 inference(monotonicity,[status(thm)],[15627])).
% 28.70/18.93 tff(15633,plain,
% 28.70/18.93 ((f3(f10(c2), f10(c2)) = f10(c2)) <=> (f10(c2) = c2)),
% 28.70/18.93 inference(transitivity,[status(thm)],[15632, 4987])).
% 28.70/18.93 tff(15634,plain,
% 28.70/18.93 ((f10(c2) = c2) <=> (f3(f10(c2), f10(c2)) = f10(c2))),
% 28.70/18.93 inference(symmetry,[status(thm)],[15633])).
% 28.70/18.93 tff(15635,plain,
% 28.70/18.93 ((~(f10(c2) = c2)) <=> (~(f3(f10(c2), f10(c2)) = f10(c2)))),
% 28.70/18.93 inference(monotonicity,[status(thm)],[15634])).
% 28.70/18.93 tff(15636,plain,
% 28.70/18.93 (~(f3(f10(c2), f10(c2)) = f10(c2))),
% 28.70/18.93 inference(modus_ponens,[status(thm)],[89, 15635])).
% 28.70/18.93 tff(15637,plain,
% 28.70/18.93 ((~(f10(c2) = c2)) <=> (~(f10(c2) = c3))),
% 28.70/18.93 inference(monotonicity,[status(thm)],[15603])).
% 28.70/18.93 tff(15638,plain,
% 28.70/18.93 (~(f10(c2) = c3)),
% 28.70/18.93 inference(modus_ponens,[status(thm)],[89, 15637])).
% 28.70/18.93 tff(15639,plain,
% 28.70/18.93 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f10(c2) = c4) | (f10(c2) = c3) | (~(f1(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f10(c2), f1(f10(c2), f10(c2)))) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (f10(c2) = c4) | (f10(c2) = c3) | (~(f1(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f10(c2), f1(f10(c2), f10(c2)))) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2)))),
% 28.70/18.93 inference(rewrite,[status(thm)],[])).
% 28.70/18.93 tff(15640,plain,
% 28.70/18.93 (((f10(c2) = c4) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2)) | (f10(c2) = c3) | (~(f1(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f10(c2), f1(f10(c2), f10(c2))))) <=> ((f10(c2) = c4) | (f10(c2) = c3) | (~(f1(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f10(c2), f1(f10(c2), f10(c2)))) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2)))),
% 28.70/18.93 inference(rewrite,[status(thm)],[])).
% 28.70/18.93 tff(15641,plain,
% 28.70/18.93 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f10(c2) = c4) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2)) | (f10(c2) = c3) | (~(f1(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f10(c2), f1(f10(c2), f10(c2)))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f10(c2) = c4) | (f10(c2) = c3) | (~(f1(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f10(c2), f1(f10(c2), f10(c2)))) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2))))),
% 28.70/18.93 inference(monotonicity,[status(thm)],[15640])).
% 28.70/18.93 tff(15642,plain,
% 28.70/18.93 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f10(c2) = c4) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2)) | (f10(c2) = c3) | (~(f1(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f10(c2), f1(f10(c2), f10(c2)))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (f10(c2) = c4) | (f10(c2) = c3) | (~(f1(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f10(c2), f1(f10(c2), f10(c2)))) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2)))),
% 28.70/18.93 inference(transitivity,[status(thm)],[15641, 15639])).
% 28.70/18.93 tff(15643,plain,
% 28.70/18.93 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f10(c2) = c4) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2)) | (f10(c2) = c3) | (~(f1(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f10(c2), f1(f10(c2), f10(c2)))))),
% 28.70/18.93 inference(quant_inst,[status(thm)],[])).
% 28.70/18.93 tff(15644,plain,
% 28.70/18.93 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (f10(c2) = c4) | (f10(c2) = c3) | (~(f1(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f10(c2), f1(f10(c2), f10(c2)))) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2))),
% 28.70/18.93 inference(modus_ponens,[status(thm)],[15643, 15642])).
% 28.70/18.93 tff(15645,plain,
% 28.70/18.93 ((~(f1(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f10(c2), f1(f10(c2), f10(c2))))),
% 28.70/18.93 inference(unit_resolution,[status(thm)],[15644, 904, 15519, 15638, 15636, 15631])).
% 28.70/18.93 tff(15646,plain,
% 28.70/18.93 ($false),
% 28.70/18.93 inference(unit_resolution,[status(thm)],[15645, 15626, 15623])).
% 28.70/18.93 tff(15647,plain,((f3(c1, c1) = c1) | (f10(c2) = c4) | big_f(c2, f10(c2)) | (f10(c2) = c2) | big_f(c1, c2) | (~big_f(c1, c1)) | (c1 = c4) | (~(f10(c2) = f8(c2))) | (~(c2 = c3))), inference(lemma,lemma(discharge,[]))).
% 28.70/18.93 tff(15648,plain,
% 28.70/18.93 (f3(c1, c1) = c1),
% 28.70/18.93 inference(unit_resolution,[status(thm)],[15647, 15601, 15473, 89, 27, 4932, 15599, 15586, 15585])).
% 28.70/18.93 tff(15649,plain,
% 28.70/18.93 (f3(f10(c2), f10(c2)) = f10(c2)),
% 28.70/18.93 inference(transitivity,[status(thm)],[15507, 15648, 99])).
% 28.70/18.93 tff(15650,plain,
% 28.70/18.93 (big_f(f3(f10(c2), f10(c2)), f10(c2)) <=> big_f(f10(c2), f10(c2))),
% 28.70/18.93 inference(monotonicity,[status(thm)],[15649])).
% 28.70/18.93 tff(15651,plain,
% 28.70/18.93 (big_f(f10(c2), f10(c2)) <=> big_f(f3(f10(c2), f10(c2)), f10(c2))),
% 28.70/18.93 inference(symmetry,[status(thm)],[15650])).
% 28.70/18.93 tff(15652,plain,
% 28.70/18.93 (big_f(f3(f10(c2), f10(c2)), f10(c2))),
% 28.70/18.93 inference(modus_ponens,[status(thm)],[13718, 15651])).
% 28.70/18.93 tff(15653,plain,
% 28.70/18.93 ((~(f10(c2) = c2)) <=> (~(f10(c2) = c3))),
% 28.70/18.93 inference(monotonicity,[status(thm)],[15589])).
% 28.70/18.93 tff(15654,plain,
% 28.70/18.93 (~(f10(c2) = c3)),
% 28.70/18.93 inference(modus_ponens,[status(thm)],[89, 15653])).
% 28.70/18.93 tff(15655,plain,
% 28.70/18.93 (f1(f10(c2), f10(c2)) = c2),
% 28.70/18.93 inference(transitivity,[status(thm)],[12413, 575])).
% 28.70/18.93 tff(15656,plain,
% 28.70/18.93 ((f1(f10(c2), f10(c2)) = f10(c2)) <=> (c2 = f10(c2))),
% 28.70/18.93 inference(monotonicity,[status(thm)],[15655])).
% 28.70/18.93 tff(15657,plain,
% 28.70/18.93 ((f1(f10(c2), f10(c2)) = f10(c2)) <=> (f10(c2) = c2)),
% 28.70/18.93 inference(transitivity,[status(thm)],[15656, 4987])).
% 28.70/18.93 tff(15658,plain,
% 28.70/18.93 ((f10(c2) = c2) <=> (f1(f10(c2), f10(c2)) = f10(c2))),
% 28.70/18.93 inference(symmetry,[status(thm)],[15657])).
% 28.70/18.93 tff(15659,plain,
% 28.70/18.93 ((~(f10(c2) = c2)) <=> (~(f1(f10(c2), f10(c2)) = f10(c2)))),
% 28.70/18.93 inference(monotonicity,[status(thm)],[15658])).
% 28.70/18.93 tff(15660,plain,
% 28.70/18.93 (~(f1(f10(c2), f10(c2)) = f10(c2))),
% 28.70/18.93 inference(modus_ponens,[status(thm)],[89, 15659])).
% 28.70/18.93 tff(15661,plain,
% 28.70/18.93 (big_f(f10(c2), f1(f10(c2), f10(c2))) <=> big_f(c1, c2)),
% 28.70/18.93 inference(monotonicity,[status(thm)],[94, 15655])).
% 28.70/18.93 tff(15662,plain,
% 28.70/18.93 (big_f(c1, c2) <=> big_f(f10(c2), f1(f10(c2), f10(c2)))),
% 28.70/18.93 inference(symmetry,[status(thm)],[15661])).
% 28.70/18.93 tff(15663,plain,
% 28.70/18.93 ((~big_f(c1, c2)) <=> (~big_f(f10(c2), f1(f10(c2), f10(c2))))),
% 28.70/18.93 inference(monotonicity,[status(thm)],[15662])).
% 28.70/18.93 tff(15664,plain,
% 28.70/18.93 (~big_f(f10(c2), f1(f10(c2), f10(c2)))),
% 28.70/18.93 inference(modus_ponens,[status(thm)],[27, 15663])).
% 28.70/18.93 tff(15665,assumption,(big_f(f3(f10(c2), f10(c2)), f10(c2))), introduced(assumption)).
% 28.70/18.93 tff(15666,assumption,(f3(f10(c2), f10(c2)) = f10(c2)), introduced(assumption)).
% 28.70/18.93 tff(15667,assumption,(~(f10(c2) = c3)), introduced(assumption)).
% 28.70/18.93 tff(15668,plain,
% 28.70/18.93 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((f10(c2) = c4) | (f10(c2) = c3) | (f1(f10(c2), f10(c2)) = f10(c2)) | big_f(f10(c2), f1(f10(c2), f10(c2))) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (f10(c2) = c4) | (f10(c2) = c3) | (f1(f10(c2), f10(c2)) = f10(c2)) | big_f(f10(c2), f1(f10(c2), f10(c2))) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))))),
% 28.70/18.93 inference(rewrite,[status(thm)],[])).
% 28.70/18.93 tff(15669,plain,
% 28.70/18.93 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((f10(c2) = c4) | (f10(c2) = c3) | (f1(f10(c2), f10(c2)) = f10(c2)) | big_f(f10(c2), f1(f10(c2), f10(c2))) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))))),
% 28.70/18.93 inference(quant_inst,[status(thm)],[])).
% 28.70/18.93 tff(15670,plain,
% 28.70/18.93 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (f10(c2) = c4) | (f10(c2) = c3) | (f1(f10(c2), f10(c2)) = f10(c2)) | big_f(f10(c2), f1(f10(c2), f10(c2))) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2)))),
% 28.70/18.93 inference(modus_ponens,[status(thm)],[15669, 15668])).
% 28.70/18.93 tff(15671,plain,
% 28.70/18.93 ((f1(f10(c2), f10(c2)) = f10(c2)) | big_f(f10(c2), f1(f10(c2), f10(c2)))),
% 28.70/18.93 inference(unit_resolution,[status(thm)],[15670, 969, 15519, 15667, 15666, 15665])).
% 28.70/18.93 tff(15672,plain,
% 28.70/18.93 ($false),
% 28.70/18.93 inference(unit_resolution,[status(thm)],[15671, 15664, 15660])).
% 28.70/18.93 tff(15673,plain,((~(f1(c1, c1) = c2)) | (f10(c2) = c4) | (f10(c2) = c3) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))) | big_f(c1, c2) | (f10(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 28.70/18.93 tff(15674,plain,
% 28.70/18.93 (~(f1(c1, c1) = c2)),
% 28.70/18.93 inference(unit_resolution,[status(thm)],[15673, 15601, 15654, 15649, 15652, 27, 89])).
% 28.70/18.93 tff(15675,plain,
% 28.70/18.93 (f1(c1, c1) = c1),
% 28.70/18.93 inference(unit_resolution,[status(thm)],[601, 15674])).
% 28.70/18.93 tff(15676,plain,
% 28.70/18.93 (f1(f10(c2), f10(c2)) = f10(c2)),
% 28.70/18.93 inference(transitivity,[status(thm)],[12413, 15675, 99])).
% 28.70/18.93 tff(15677,plain,
% 28.70/18.93 (big_f(f10(c2), f1(f10(c2), f10(c2))) <=> big_f(f10(c2), f10(c2))),
% 28.70/18.93 inference(monotonicity,[status(thm)],[15676])).
% 28.70/18.93 tff(15678,plain,
% 28.70/18.93 (big_f(f10(c2), f10(c2)) <=> big_f(f10(c2), f1(f10(c2), f10(c2)))),
% 28.70/18.93 inference(symmetry,[status(thm)],[15677])).
% 28.70/18.93 tff(15679,plain,
% 28.70/18.93 (big_f(f10(c2), f1(f10(c2), f10(c2)))),
% 28.70/18.93 inference(modus_ponens,[status(thm)],[13718, 15678])).
% 28.70/18.93 tff(15680,plain,
% 28.70/18.93 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f10(c2) = c4) | (f10(c2) = c3) | (~(f1(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f10(c2), f1(f10(c2), f10(c2)))) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (f10(c2) = c4) | (f10(c2) = c3) | (~(f1(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f10(c2), f1(f10(c2), f10(c2)))) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))))),
% 28.70/18.93 inference(rewrite,[status(thm)],[])).
% 28.70/18.93 tff(15681,plain,
% 28.70/18.93 (((f10(c2) = c4) | (f10(c2) = c3) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))) | (~(f1(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f10(c2), f1(f10(c2), f10(c2))))) <=> ((f10(c2) = c4) | (f10(c2) = c3) | (~(f1(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f10(c2), f1(f10(c2), f10(c2)))) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))))),
% 28.70/18.93 inference(rewrite,[status(thm)],[])).
% 28.70/18.93 tff(15682,plain,
% 28.70/18.93 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f10(c2) = c4) | (f10(c2) = c3) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))) | (~(f1(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f10(c2), f1(f10(c2), f10(c2)))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f10(c2) = c4) | (f10(c2) = c3) | (~(f1(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f10(c2), f1(f10(c2), f10(c2)))) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2)))))),
% 28.70/18.93 inference(monotonicity,[status(thm)],[15681])).
% 28.70/18.93 tff(15683,plain,
% 28.70/18.93 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f10(c2) = c4) | (f10(c2) = c3) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))) | (~(f1(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f10(c2), f1(f10(c2), f10(c2)))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (f10(c2) = c4) | (f10(c2) = c3) | (~(f1(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f10(c2), f1(f10(c2), f10(c2)))) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))))),
% 28.70/18.93 inference(transitivity,[status(thm)],[15682, 15680])).
% 28.70/18.93 tff(15684,plain,
% 28.70/18.93 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f10(c2) = c4) | (f10(c2) = c3) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))) | (~(f1(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f10(c2), f1(f10(c2), f10(c2)))))),
% 28.70/18.93 inference(quant_inst,[status(thm)],[])).
% 28.70/18.93 tff(15685,plain,
% 28.70/18.93 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (f10(c2) = c4) | (f10(c2) = c3) | (~(f1(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f10(c2), f1(f10(c2), f10(c2)))) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2)))),
% 28.70/18.93 inference(modus_ponens,[status(thm)],[15684, 15683])).
% 28.70/18.93 tff(15686,plain,
% 28.70/18.93 ((~(f1(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f10(c2), f1(f10(c2), f10(c2))))),
% 28.70/18.93 inference(unit_resolution,[status(thm)],[15685, 933, 15601, 15654, 15649, 15652])).
% 28.70/18.93 tff(15687,plain,
% 28.70/18.93 ($false),
% 28.70/18.93 inference(unit_resolution,[status(thm)],[15686, 15679, 15676])).
% 28.70/18.93 tff(15688,plain,(big_f(c2, c1) | big_f(c1, c2) | (f10(c2) = c2) | (~big_f(c1, c1)) | (~(f10(c2) = f8(c2))) | (~(f4(c4) = c2)) | (~big_f(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 28.70/18.93 tff(15689,plain,
% 28.70/18.93 (big_f(c2, c1)),
% 28.70/18.93 inference(unit_resolution,[status(thm)],[15688, 15318, 89, 15457, 15465, 79, 13805])).
% 28.70/18.93 tff(15690,plain,
% 28.70/18.93 (big_f(c2, f10(c2))),
% 28.70/18.93 inference(modus_ponens,[status(thm)],[15689, 15252])).
% 28.70/18.93 tff(15691,plain,
% 28.70/18.93 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (~(f7(c2) = c2)) | (c2 = f8(c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~big_f(c2, f10(c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (c2 = f8(c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~big_f(c2, f10(c2))))),
% 28.70/18.93 inference(rewrite,[status(thm)],[])).
% 28.70/18.93 tff(15692,plain,
% 28.70/18.93 (((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2)))) <=> ((f10(c2) = c2) | (~(f7(c2) = c2)) | (c2 = f8(c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~big_f(c2, f10(c2))))),
% 28.70/18.93 inference(rewrite,[status(thm)],[])).
% 28.70/18.93 tff(15693,plain,
% 28.70/18.93 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (~(f7(c2) = c2)) | (c2 = f8(c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~big_f(c2, f10(c2)))))),
% 28.70/18.93 inference(monotonicity,[status(thm)],[15692])).
% 28.70/18.93 tff(15694,plain,
% 28.70/18.93 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (c2 = f8(c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~big_f(c2, f10(c2))))),
% 28.70/18.93 inference(transitivity,[status(thm)],[15693, 15691])).
% 28.70/18.93 tff(15695,plain,
% 28.70/18.93 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))),
% 28.70/18.93 inference(quant_inst,[status(thm)],[])).
% 28.70/18.93 tff(15696,plain,
% 28.70/18.93 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (c2 = f8(c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~big_f(c2, f10(c2)))),
% 28.70/18.93 inference(modus_ponens,[status(thm)],[15695, 15694])).
% 28.70/18.93 tff(15697,plain,
% 28.70/18.93 ($false),
% 28.70/18.93 inference(unit_resolution,[status(thm)],[15696, 2730, 89, 13346, 15690, 15471, 15250, 15251])).
% 28.70/18.93 tff(15698,plain,((f10(c2) = c2) | (~(f4(c4) = c2)) | (f7(c1) = c1) | (f10(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 28.70/18.93 tff(15699,plain,
% 28.70/18.93 (f10(c2) = c2),
% 28.70/18.93 inference(unit_resolution,[status(thm)],[15698, 79, 115, 3])).
% 28.70/18.93 tff(15700,plain,
% 28.70/18.93 (big_f(f9(c2, c2), f10(c2))),
% 28.70/18.93 inference(unit_resolution,[status(thm)],[2750, 15699, 15250, 15251, 13805, 13346])).
% 28.70/18.93 tff(15701,plain,
% 28.70/18.93 (f9(f10(c2), f4(c4)) = c2),
% 28.70/18.93 inference(unit_resolution,[status(thm)],[8065, 15699, 79])).
% 28.70/18.93 tff(15702,plain,
% 28.70/18.93 (f9(c2, c2) = c2),
% 28.70/18.93 inference(unit_resolution,[status(thm)],[1606, 15701, 79, 15699])).
% 28.70/18.93 tff(15703,plain,
% 28.70/18.93 ($false),
% 28.70/18.93 inference(unit_resolution,[status(thm)],[2384, 2378, 15699, 13346, 15250, 15251, 15702, 15700])).
% 28.70/18.93 tff(15704,plain,((~(f4(c4) = c2)) | (f7(c1) = c1) | (f10(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 28.70/18.93 tff(15705,plain,
% 28.70/18.93 (~(f4(c4) = c2)),
% 28.70/18.93 inference(unit_resolution,[status(thm)],[15704, 3, 115])).
% 28.70/18.93 tff(15706,plain,
% 28.70/18.93 (f4(c4) = c1),
% 28.70/18.93 inference(unit_resolution,[status(thm)],[11750, 15705])).
% 28.70/18.93 tff(15707,plain,
% 28.70/18.93 (big_f(f7(f10(c1)), f5(f10(c1))) <=> big_f(f7(c2), f5(c2))),
% 28.70/18.93 inference(monotonicity,[status(thm)],[219, 9888])).
% 28.70/18.93 tff(15708,plain,
% 28.70/18.93 (big_f(f7(c2), f5(c2)) <=> big_f(f7(f10(c1)), f5(f10(c1)))),
% 28.70/18.93 inference(symmetry,[status(thm)],[15707])).
% 28.70/18.93 tff(15709,assumption,(big_f(f8(c1), f10(c1))), introduced(assumption)).
% 28.70/18.93 tff(15710,plain,
% 28.70/18.93 (f8(c1) = f7(c2)),
% 28.70/18.93 inference(transitivity,[status(thm)],[3018, 342])).
% 28.70/18.93 tff(15711,plain,
% 28.70/18.93 (big_f(f8(c1), f10(c1)) <=> big_f(f7(c2), c2)),
% 28.70/18.93 inference(monotonicity,[status(thm)],[15710, 16])).
% 28.70/18.93 tff(15712,plain,
% 28.70/18.93 (big_f(f7(c2), c2) <=> big_f(f8(c1), f10(c1))),
% 28.70/18.93 inference(symmetry,[status(thm)],[15711])).
% 28.70/18.93 tff(15713,plain,
% 28.70/18.93 ((~big_f(f7(c2), c2)) <=> (~big_f(f8(c1), f10(c1)))),
% 28.70/18.93 inference(monotonicity,[status(thm)],[15712])).
% 28.70/18.93 tff(15714,plain,
% 28.70/18.93 (~big_f(f8(c1), f10(c1))),
% 28.70/18.93 inference(modus_ponens,[status(thm)],[1521, 15713])).
% 28.70/18.93 tff(15715,plain,
% 28.70/18.93 ($false),
% 28.70/18.93 inference(unit_resolution,[status(thm)],[15709, 15714])).
% 28.70/18.93 tff(15716,plain,((~(f8(c1) = c1)) | (~big_f(f8(c1), f10(c1))) | big_f(f7(c2), c2) | (~(f10(c1) = c2)) | (~(f7(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.70/18.93 tff(15717,plain,
% 28.70/18.93 (~(f8(c1) = c1)),
% 28.70/18.93 inference(unit_resolution,[status(thm)],[15716, 15709, 1521, 16, 292])).
% 28.70/18.93 tff(15718,plain,
% 28.70/18.93 (f8(c1) = c2),
% 28.70/18.93 inference(unit_resolution,[status(thm)],[1680, 15717])).
% 28.70/18.93 tff(15719,plain,
% 28.70/18.93 (big_f(f8(c1), f10(c1)) <=> big_f(c2, c2)),
% 28.70/18.93 inference(monotonicity,[status(thm)],[15718, 16])).
% 28.70/18.93 tff(15720,plain,
% 28.70/18.93 (big_f(c2, c2) <=> big_f(f8(c1), f10(c1))),
% 28.70/18.94 inference(symmetry,[status(thm)],[15719])).
% 28.70/18.94 tff(15721,plain,
% 28.70/18.94 ((~big_f(c2, c2)) <=> (~big_f(f8(c1), f10(c1)))),
% 28.70/18.94 inference(monotonicity,[status(thm)],[15720])).
% 28.70/18.94 tff(15722,plain,
% 28.70/18.94 (~big_f(f8(c1), f10(c1))),
% 28.70/18.94 inference(modus_ponens,[status(thm)],[121, 15721])).
% 28.70/18.94 tff(15723,plain,
% 28.70/18.94 ($false),
% 28.70/18.94 inference(unit_resolution,[status(thm)],[15709, 15722])).
% 28.70/18.94 tff(15724,plain,((~big_f(f8(c1), f10(c1))) | big_f(c2, c2) | (~(f10(c1) = c2)) | big_f(f7(c2), c2) | (~(f7(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.70/18.94 tff(15725,plain,
% 28.70/18.94 (~big_f(f8(c1), f10(c1))),
% 28.70/18.94 inference(unit_resolution,[status(thm)],[15724, 12679, 15, 121, 22])).
% 28.70/18.94 tff(15726,plain,
% 28.70/18.94 (~(c2 = f5(c2))),
% 28.70/18.94 inference(unit_resolution,[status(thm)],[8107, 15725, 17, 12679, 3])).
% 28.70/18.94 tff(15727,plain,
% 28.70/18.94 (~(f5(c2) = c2)),
% 28.70/18.94 inference(unit_resolution,[status(thm)],[8113, 15726])).
% 28.70/18.94 tff(15728,plain,
% 28.70/18.94 (f5(c2) = c1),
% 28.70/18.94 inference(unit_resolution,[status(thm)],[1547, 15727])).
% 28.70/18.94 tff(15729,plain,
% 28.70/18.94 (f5(c2) = f7(c2)),
% 28.70/18.94 inference(transitivity,[status(thm)],[15728, 125])).
% 28.70/18.94 tff(15730,plain,
% 28.70/18.94 (big_f(f7(c2), f5(c2)) <=> big_f(f7(c2), f7(c2))),
% 28.70/18.94 inference(monotonicity,[status(thm)],[15729])).
% 28.70/18.94 tff(15731,plain,
% 28.70/18.94 (big_f(f7(c2), f7(c2)) <=> big_f(f7(c2), f5(c2))),
% 28.70/18.94 inference(symmetry,[status(thm)],[15730])).
% 28.70/18.94 tff(15732,plain,
% 28.70/18.94 (big_f(f7(c1), f5(c1))),
% 28.70/18.94 inference(unit_resolution,[status(thm)],[2848, 15725, 115, 3])).
% 28.70/18.94 tff(15733,plain,
% 28.70/18.94 (big_f(f7(c1), c1)),
% 28.70/18.94 inference(unit_resolution,[status(thm)],[8430, 15732, 120, 121])).
% 28.70/18.94 tff(15734,plain,
% 28.70/18.94 (big_f(f7(c1), c1) <=> big_f(c2, c1)),
% 28.70/18.94 inference(monotonicity,[status(thm)],[347])).
% 28.70/18.94 tff(15735,assumption,(big_f(f7(c1), c1)), introduced(assumption)).
% 28.70/18.94 tff(15736,plain,
% 28.70/18.94 (big_f(c2, c1)),
% 28.70/18.94 inference(modus_ponens,[status(thm)],[15735, 15734])).
% 28.70/18.94 tff(15737,plain,
% 28.70/18.94 ($false),
% 28.70/18.94 inference(unit_resolution,[status(thm)],[2, 15736])).
% 28.70/18.94 tff(15738,plain,((~big_f(f7(c1), c1)) | big_f(c2, c1) | (~(f7(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.70/18.94 tff(15739,plain,
% 28.70/18.94 (big_f(c2, c1)),
% 28.70/18.94 inference(unit_resolution,[status(thm)],[15738, 15733, 120])).
% 28.70/18.94 tff(15740,plain,
% 28.70/18.94 (big_f(c2, f7(c2))),
% 28.70/18.94 inference(modus_ponens,[status(thm)],[15739, 9312])).
% 28.70/18.94 tff(15741,assumption,(big_f(c2, f7(c2))), introduced(assumption)).
% 28.70/18.94 tff(15742,plain,
% 28.70/18.94 (f4(f7(c2)) = f4(c4)),
% 28.70/18.94 inference(monotonicity,[status(thm)],[8764])).
% 28.70/18.94 tff(15743,plain,
% 28.70/18.94 (f4(f7(c2)) = f7(c2)),
% 28.70/18.94 inference(transitivity,[status(thm)],[15742, 11752, 125])).
% 28.70/18.94 tff(15744,plain,
% 28.70/18.94 ((c2 = f4(f7(c2))) <=> (c2 = f7(c2))),
% 28.70/18.94 inference(monotonicity,[status(thm)],[15743])).
% 28.70/18.94 tff(15745,plain,
% 28.70/18.94 ((c2 = f4(f7(c2))) <=> (f7(c2) = c2)),
% 28.70/18.94 inference(transitivity,[status(thm)],[15744, 8409])).
% 28.70/18.94 tff(15746,plain,
% 28.70/18.94 ((f7(c2) = c2) <=> (c2 = f4(f7(c2)))),
% 28.70/18.94 inference(symmetry,[status(thm)],[15745])).
% 28.70/18.94 tff(15747,plain,
% 28.70/18.94 ((~(f7(c2) = c2)) <=> (~(c2 = f4(f7(c2))))),
% 28.70/18.94 inference(monotonicity,[status(thm)],[15746])).
% 28.70/18.94 tff(15748,plain,
% 28.70/18.94 (~(c2 = f4(f7(c2)))),
% 28.70/18.94 inference(modus_ponens,[status(thm)],[17, 15747])).
% 28.70/18.94 tff(15749,plain,
% 28.70/18.94 (f1(c2, c1) = f7(c2)),
% 28.70/18.94 inference(transitivity,[status(thm)],[11485, 342])).
% 28.70/18.94 tff(15750,plain,
% 28.70/18.94 (big_f(c2, f1(c2, c1)) <=> big_f(c2, f7(c2))),
% 28.70/18.94 inference(monotonicity,[status(thm)],[15749])).
% 28.70/18.94 tff(15751,plain,
% 28.70/18.94 (big_f(c2, f7(c2)) <=> big_f(c2, f1(c2, c1))),
% 28.70/18.94 inference(symmetry,[status(thm)],[15750])).
% 28.70/18.94 tff(15752,plain,
% 28.70/18.94 (big_f(c2, f7(c2)) <=> big_f(c2, f1(c2, f7(c2)))),
% 28.70/18.94 inference(transitivity,[status(thm)],[15751, 8727])).
% 28.70/18.94 tff(15753,plain,
% 28.70/18.94 (big_f(c2, f1(c2, f7(c2)))),
% 28.70/18.94 inference(modus_ponens,[status(thm)],[15741, 15752])).
% 28.70/18.94 tff(15754,plain,
% 28.70/18.94 (f1(c2, f7(c2)) = f7(c2)),
% 28.70/18.94 inference(modus_ponens,[status(thm)],[11485, 8741])).
% 28.70/18.94 tff(15755,plain,
% 28.70/18.94 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~big_f(c2, f1(c2, f7(c2)))) | (~(f1(c2, f7(c2)) = f7(c2))) | (c2 = f4(f7(c2))) | (~(f7(c2) = c4)) | (~big_f(c2, f7(c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~big_f(c2, f1(c2, f7(c2)))) | (~(f1(c2, f7(c2)) = f7(c2))) | (c2 = f4(f7(c2))) | (~(f7(c2) = c4)) | (~big_f(c2, f7(c2))))),
% 28.70/18.94 inference(rewrite,[status(thm)],[])).
% 28.70/18.94 tff(15756,plain,
% 28.70/18.94 (((c2 = c3) | (~(f7(c2) = c4)) | (c2 = f4(f7(c2))) | (~big_f(c2, f7(c2))) | (~(f1(c2, f7(c2)) = f7(c2))) | (~big_f(c2, f1(c2, f7(c2))))) <=> ((c2 = c3) | (~big_f(c2, f1(c2, f7(c2)))) | (~(f1(c2, f7(c2)) = f7(c2))) | (c2 = f4(f7(c2))) | (~(f7(c2) = c4)) | (~big_f(c2, f7(c2))))),
% 28.70/18.94 inference(rewrite,[status(thm)],[])).
% 28.70/18.94 tff(15757,plain,
% 28.70/18.94 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f7(c2) = c4)) | (c2 = f4(f7(c2))) | (~big_f(c2, f7(c2))) | (~(f1(c2, f7(c2)) = f7(c2))) | (~big_f(c2, f1(c2, f7(c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~big_f(c2, f1(c2, f7(c2)))) | (~(f1(c2, f7(c2)) = f7(c2))) | (c2 = f4(f7(c2))) | (~(f7(c2) = c4)) | (~big_f(c2, f7(c2)))))),
% 28.70/18.94 inference(monotonicity,[status(thm)],[15756])).
% 28.70/18.94 tff(15758,plain,
% 28.70/18.94 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f7(c2) = c4)) | (c2 = f4(f7(c2))) | (~big_f(c2, f7(c2))) | (~(f1(c2, f7(c2)) = f7(c2))) | (~big_f(c2, f1(c2, f7(c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~big_f(c2, f1(c2, f7(c2)))) | (~(f1(c2, f7(c2)) = f7(c2))) | (c2 = f4(f7(c2))) | (~(f7(c2) = c4)) | (~big_f(c2, f7(c2))))),
% 28.70/18.94 inference(transitivity,[status(thm)],[15757, 15755])).
% 28.70/18.94 tff(15759,plain,
% 28.70/18.94 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f7(c2) = c4)) | (c2 = f4(f7(c2))) | (~big_f(c2, f7(c2))) | (~(f1(c2, f7(c2)) = f7(c2))) | (~big_f(c2, f1(c2, f7(c2)))))),
% 28.70/18.94 inference(quant_inst,[status(thm)],[])).
% 28.70/18.94 tff(15760,plain,
% 28.70/18.94 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~big_f(c2, f1(c2, f7(c2)))) | (~(f1(c2, f7(c2)) = f7(c2))) | (c2 = f4(f7(c2))) | (~(f7(c2) = c4)) | (~big_f(c2, f7(c2)))),
% 28.70/18.94 inference(modus_ponens,[status(thm)],[15759, 15758])).
% 28.70/18.94 tff(15761,plain,
% 28.70/18.94 ($false),
% 28.70/18.94 inference(unit_resolution,[status(thm)],[15760, 553, 377, 15754, 15753, 8770, 9319, 15741])).
% 28.70/18.94 tff(15762,plain,((~(f1(c2, c1) = c1)) | (c2 = c3) | (~(f7(c2) = c4)) | (c2 = f4(f7(c2))) | (~big_f(c2, f7(c2))) | (~(f7(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.70/18.94 tff(15763,plain,
% 28.70/18.94 (~(f1(c2, c1) = c1)),
% 28.70/18.94 inference(unit_resolution,[status(thm)],[15762, 377, 8770, 9319, 15741, 292])).
% 28.70/18.94 tff(15764,plain,
% 28.70/18.94 (f1(c2, c1) = c2),
% 28.70/18.94 inference(unit_resolution,[status(thm)],[10113, 15763])).
% 28.70/18.94 tff(15765,plain,
% 28.70/18.94 (~big_f(f7(c1), f1(f7(c1), c1))),
% 28.70/18.94 inference(unit_resolution,[status(thm)],[12197, 15764, 121, 347])).
% 28.70/18.94 tff(15766,plain,
% 28.70/18.94 (~big_f(c2, f1(c2, c1))),
% 28.70/18.94 inference(unit_resolution,[status(thm)],[13409, 15765, 347])).
% 28.70/18.94 tff(15767,plain,
% 28.70/18.94 (~big_f(c2, f1(c2, f7(c2)))),
% 28.70/18.94 inference(unit_resolution,[status(thm)],[10139, 15766, 292])).
% 28.70/18.94 tff(15768,plain,
% 28.70/18.94 ((~(f1(c2, c1) = c1)) <=> (~(f1(c2, f7(c2)) = f7(c2)))),
% 28.70/18.94 inference(monotonicity,[status(thm)],[8741])).
% 28.70/18.94 tff(15769,plain,
% 28.70/18.94 (~(f1(c2, f7(c2)) = f7(c2))),
% 28.70/18.94 inference(modus_ponens,[status(thm)],[15763, 15768])).
% 28.70/18.94 tff(15770,plain,
% 28.70/18.94 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c2 = c3) | (f1(c2, f7(c2)) = f7(c2)) | big_f(c2, f1(c2, f7(c2))) | (c2 = f4(f7(c2))) | (~(f7(c2) = c4)) | (~big_f(c2, f7(c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (c2 = c3) | (f1(c2, f7(c2)) = f7(c2)) | big_f(c2, f1(c2, f7(c2))) | (c2 = f4(f7(c2))) | (~(f7(c2) = c4)) | (~big_f(c2, f7(c2))))),
% 28.70/18.94 inference(rewrite,[status(thm)],[])).
% 28.70/18.94 tff(15771,plain,
% 28.70/18.94 (((c2 = c3) | (f1(c2, f7(c2)) = f7(c2)) | big_f(c2, f1(c2, f7(c2))) | (~(f7(c2) = c4)) | (c2 = f4(f7(c2))) | (~big_f(c2, f7(c2)))) <=> ((c2 = c3) | (f1(c2, f7(c2)) = f7(c2)) | big_f(c2, f1(c2, f7(c2))) | (c2 = f4(f7(c2))) | (~(f7(c2) = c4)) | (~big_f(c2, f7(c2))))),
% 28.70/18.94 inference(rewrite,[status(thm)],[])).
% 28.70/18.94 tff(15772,plain,
% 28.70/18.94 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c2 = c3) | (f1(c2, f7(c2)) = f7(c2)) | big_f(c2, f1(c2, f7(c2))) | (~(f7(c2) = c4)) | (c2 = f4(f7(c2))) | (~big_f(c2, f7(c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c2 = c3) | (f1(c2, f7(c2)) = f7(c2)) | big_f(c2, f1(c2, f7(c2))) | (c2 = f4(f7(c2))) | (~(f7(c2) = c4)) | (~big_f(c2, f7(c2)))))),
% 28.70/18.94 inference(monotonicity,[status(thm)],[15771])).
% 28.70/18.94 tff(15773,plain,
% 28.70/18.94 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c2 = c3) | (f1(c2, f7(c2)) = f7(c2)) | big_f(c2, f1(c2, f7(c2))) | (~(f7(c2) = c4)) | (c2 = f4(f7(c2))) | (~big_f(c2, f7(c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (c2 = c3) | (f1(c2, f7(c2)) = f7(c2)) | big_f(c2, f1(c2, f7(c2))) | (c2 = f4(f7(c2))) | (~(f7(c2) = c4)) | (~big_f(c2, f7(c2))))),
% 28.70/18.94 inference(transitivity,[status(thm)],[15772, 15770])).
% 28.70/18.94 tff(15774,plain,
% 28.70/18.94 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c2 = c3) | (f1(c2, f7(c2)) = f7(c2)) | big_f(c2, f1(c2, f7(c2))) | (~(f7(c2) = c4)) | (c2 = f4(f7(c2))) | (~big_f(c2, f7(c2))))),
% 28.70/18.94 inference(quant_inst,[status(thm)],[])).
% 28.70/18.94 tff(15775,plain,
% 28.70/18.94 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (c2 = c3) | (f1(c2, f7(c2)) = f7(c2)) | big_f(c2, f1(c2, f7(c2))) | (c2 = f4(f7(c2))) | (~(f7(c2) = c4)) | (~big_f(c2, f7(c2)))),
% 28.70/18.94 inference(modus_ponens,[status(thm)],[15774, 15773])).
% 28.70/18.94 tff(15776,plain,
% 28.70/18.94 ($false),
% 28.70/18.94 inference(unit_resolution,[status(thm)],[15775, 525, 377, 15769, 15767, 8770, 9319, 15741])).
% 28.70/18.94 tff(15777,plain,((c2 = c3) | (~(f7(c2) = c4)) | (c2 = f4(f7(c2))) | (~big_f(c2, f7(c2))) | (~(f7(c2) = c1)) | (~(f7(c1) = c2)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 28.70/18.94 tff(15778,plain,
% 28.70/18.94 (c2 = c3),
% 28.70/18.94 inference(unit_resolution,[status(thm)],[15777, 8764, 15748, 15741, 22, 347, 121])).
% 28.70/18.94 tff(15779,plain,
% 28.70/18.94 (c3 = c2),
% 28.70/18.94 inference(symmetry,[status(thm)],[15778])).
% 28.70/18.94 tff(15780,plain,
% 28.70/18.94 ((f7(c2) = c3) <=> (f7(c2) = c2)),
% 28.70/18.94 inference(monotonicity,[status(thm)],[15779])).
% 28.70/18.94 tff(15781,plain,
% 28.70/18.94 ((f7(c2) = c2) <=> (f7(c2) = c3)),
% 28.70/18.94 inference(symmetry,[status(thm)],[15780])).
% 28.70/18.94 tff(15782,plain,
% 28.70/18.94 ((~(f7(c2) = c2)) <=> (~(f7(c2) = c3))),
% 28.70/18.94 inference(monotonicity,[status(thm)],[15781])).
% 28.70/18.94 tff(15783,plain,
% 28.70/18.94 (~(f7(c2) = c3)),
% 28.70/18.94 inference(modus_ponens,[status(thm)],[17, 15782])).
% 28.70/18.94 tff(15784,plain,
% 28.70/18.94 (~(f1(f7(c2), f7(c2)) = f7(c2))),
% 28.70/18.94 inference(unit_resolution,[status(thm)],[9712, 9710, 292])).
% 28.70/18.94 tff(15785,plain,
% 28.70/18.94 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((f7(c2) = c3) | (c2 = f4(f7(c2))) | (~(f7(c2) = c4)) | (~big_f(c2, f7(c2))) | (f1(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(c2), f1(f7(c2), f7(c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (f7(c2) = c3) | (c2 = f4(f7(c2))) | (~(f7(c2) = c4)) | (~big_f(c2, f7(c2))) | (f1(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(c2), f1(f7(c2), f7(c2))))),
% 28.70/18.94 inference(rewrite,[status(thm)],[])).
% 28.70/18.94 tff(15786,plain,
% 28.70/18.94 (((f7(c2) = c3) | (f1(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(c2), f1(f7(c2), f7(c2))) | (~(f7(c2) = c4)) | (c2 = f4(f7(c2))) | (~big_f(c2, f7(c2)))) <=> ((f7(c2) = c3) | (c2 = f4(f7(c2))) | (~(f7(c2) = c4)) | (~big_f(c2, f7(c2))) | (f1(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(c2), f1(f7(c2), f7(c2))))),
% 28.70/18.94 inference(rewrite,[status(thm)],[])).
% 28.70/18.94 tff(15787,plain,
% 28.70/18.94 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((f7(c2) = c3) | (f1(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(c2), f1(f7(c2), f7(c2))) | (~(f7(c2) = c4)) | (c2 = f4(f7(c2))) | (~big_f(c2, f7(c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((f7(c2) = c3) | (c2 = f4(f7(c2))) | (~(f7(c2) = c4)) | (~big_f(c2, f7(c2))) | (f1(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(c2), f1(f7(c2), f7(c2)))))),
% 28.70/18.94 inference(monotonicity,[status(thm)],[15786])).
% 28.70/18.94 tff(15788,plain,
% 28.70/18.94 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((f7(c2) = c3) | (f1(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(c2), f1(f7(c2), f7(c2))) | (~(f7(c2) = c4)) | (c2 = f4(f7(c2))) | (~big_f(c2, f7(c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (f7(c2) = c3) | (c2 = f4(f7(c2))) | (~(f7(c2) = c4)) | (~big_f(c2, f7(c2))) | (f1(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(c2), f1(f7(c2), f7(c2))))),
% 28.70/18.94 inference(transitivity,[status(thm)],[15787, 15785])).
% 28.70/18.94 tff(15789,plain,
% 28.70/18.94 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((f7(c2) = c3) | (f1(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(c2), f1(f7(c2), f7(c2))) | (~(f7(c2) = c4)) | (c2 = f4(f7(c2))) | (~big_f(c2, f7(c2))))),
% 28.70/18.94 inference(quant_inst,[status(thm)],[])).
% 28.70/18.94 tff(15790,plain,
% 28.70/18.94 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (f7(c2) = c3) | (c2 = f4(f7(c2))) | (~(f7(c2) = c4)) | (~big_f(c2, f7(c2))) | (f1(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(c2), f1(f7(c2), f7(c2)))),
% 28.70/18.94 inference(modus_ponens,[status(thm)],[15789, 15788])).
% 28.70/18.94 tff(15791,plain,
% 28.70/18.94 (big_f(f7(c2), f1(f7(c2), f7(c2)))),
% 28.70/18.94 inference(unit_resolution,[status(thm)],[15790, 525, 9092, 8770, 15784, 9319, 15741])).
% 28.70/18.94 tff(15792,plain,
% 28.70/18.94 (big_f(c1, f1(c1, c1))),
% 28.70/18.94 inference(modus_ponens,[status(thm)],[15791, 9702])).
% 28.70/18.94 tff(15793,plain,
% 28.70/18.94 (~big_f(c1, f1(c1, c1))),
% 28.70/18.94 inference(unit_resolution,[status(thm)],[4561, 9760, 27])).
% 28.70/18.94 tff(15794,plain,
% 28.70/18.94 ($false),
% 28.70/18.94 inference(unit_resolution,[status(thm)],[15793, 15792])).
% 28.70/18.94 tff(15795,plain,((f1(c1, c1) = c1) | (~(f7(c2) = c1)) | (f7(c2) = c3) | (~(f7(c2) = c4)) | (c2 = f4(f7(c2))) | (~big_f(c2, f7(c2))) | big_f(c1, c2)), inference(lemma,lemma(discharge,[]))).
% 28.70/18.94 tff(15796,plain,
% 28.70/18.94 (f1(c1, c1) = c1),
% 28.70/18.94 inference(unit_resolution,[status(thm)],[15795, 15783, 22, 8764, 15748, 15741, 27])).
% 28.70/18.94 tff(15797,plain,
% 28.70/18.94 (f1(c1, c1) = f7(c2)),
% 28.70/18.94 inference(transitivity,[status(thm)],[15796, 125])).
% 28.70/18.94 tff(15798,plain,
% 28.70/18.94 (big_f(c1, f1(c1, c1)) <=> big_f(f7(c2), f7(c2))),
% 28.70/18.94 inference(monotonicity,[status(thm)],[125, 15797])).
% 28.70/18.94 tff(15799,plain,
% 28.70/18.94 (big_f(f7(c2), f1(f7(c2), f7(c2))) <=> big_f(f7(f10(c1)), f5(f10(c1)))),
% 28.70/18.94 inference(transitivity,[status(thm)],[9655, 15798, 15731, 15708])).
% 28.70/18.94 tff(15800,plain,
% 28.70/18.94 ((~big_f(f7(c2), f1(f7(c2), f7(c2)))) <=> (~big_f(f7(f10(c1)), f5(f10(c1))))),
% 28.70/18.94 inference(monotonicity,[status(thm)],[15799])).
% 28.70/18.94 tff(15801,plain,
% 28.70/18.94 (f1(f7(c2), f7(c2)) = f7(c2)),
% 28.70/18.94 inference(modus_ponens,[status(thm)],[15796, 9668])).
% 28.70/18.94 tff(15802,plain,
% 28.70/18.94 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c2) = c3) | (c2 = f4(f7(c2))) | (~(f7(c2) = c4)) | (~big_f(c2, f7(c2))) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (f7(c2) = c3) | (c2 = f4(f7(c2))) | (~(f7(c2) = c4)) | (~big_f(c2, f7(c2))) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2)))))),
% 28.70/18.94 inference(rewrite,[status(thm)],[])).
% 28.70/18.94 tff(15803,plain,
% 28.70/18.94 (((f7(c2) = c3) | (~(f7(c2) = c4)) | (c2 = f4(f7(c2))) | (~big_f(c2, f7(c2))) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2))))) <=> ((f7(c2) = c3) | (c2 = f4(f7(c2))) | (~(f7(c2) = c4)) | (~big_f(c2, f7(c2))) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2)))))),
% 28.70/18.94 inference(rewrite,[status(thm)],[])).
% 28.70/18.94 tff(15804,plain,
% 28.70/18.94 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c2) = c3) | (~(f7(c2) = c4)) | (c2 = f4(f7(c2))) | (~big_f(c2, f7(c2))) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c2) = c3) | (c2 = f4(f7(c2))) | (~(f7(c2) = c4)) | (~big_f(c2, f7(c2))) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2))))))),
% 28.70/18.94 inference(monotonicity,[status(thm)],[15803])).
% 28.70/18.94 tff(15805,plain,
% 28.70/18.94 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c2) = c3) | (~(f7(c2) = c4)) | (c2 = f4(f7(c2))) | (~big_f(c2, f7(c2))) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (f7(c2) = c3) | (c2 = f4(f7(c2))) | (~(f7(c2) = c4)) | (~big_f(c2, f7(c2))) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2)))))),
% 28.70/18.94 inference(transitivity,[status(thm)],[15804, 15802])).
% 28.70/18.94 tff(15806,plain,
% 28.70/18.94 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c2) = c3) | (~(f7(c2) = c4)) | (c2 = f4(f7(c2))) | (~big_f(c2, f7(c2))) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2)))))),
% 28.70/18.94 inference(quant_inst,[status(thm)],[])).
% 28.70/18.94 tff(15807,plain,
% 28.70/18.94 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (f7(c2) = c3) | (c2 = f4(f7(c2))) | (~(f7(c2) = c4)) | (~big_f(c2, f7(c2))) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2))))),
% 28.70/18.94 inference(modus_ponens,[status(thm)],[15806, 15805])).
% 28.70/18.94 tff(15808,plain,
% 28.70/18.94 (~big_f(f7(c2), f1(f7(c2), f7(c2)))),
% 28.70/18.94 inference(unit_resolution,[status(thm)],[15807, 553, 15783, 8764, 15801, 15748, 15741])).
% 28.70/18.94 tff(15809,plain,
% 28.70/18.94 (~big_f(f7(f10(c1)), f5(f10(c1)))),
% 28.70/18.94 inference(modus_ponens,[status(thm)],[15808, 15800])).
% 28.70/18.94 tff(15810,plain,
% 28.70/18.94 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), f5(f10(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), f5(f10(c1))))),
% 28.70/18.94 inference(rewrite,[status(thm)],[])).
% 28.70/18.94 tff(15811,plain,
% 28.70/18.94 (($false | (f10(c1) = c1) | big_f(c2, f10(c1)) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), f5(f10(c1))) | (~(c2 = f8(c1)))) <=> (big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), f5(f10(c1))))),
% 28.70/18.94 inference(rewrite,[status(thm)],[])).
% 28.70/18.94 tff(15812,plain,
% 28.70/18.94 (((~(f5(f10(c1)) = f5(f10(c1)))) | (f10(c1) = c1) | big_f(c2, f10(c1)) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), f5(f10(c1))) | (~(c2 = f8(c1)))) <=> ($false | (f10(c1) = c1) | big_f(c2, f10(c1)) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), f5(f10(c1))) | (~(c2 = f8(c1))))),
% 28.70/18.94 inference(monotonicity,[status(thm)],[302])).
% 28.70/18.94 tff(15813,plain,
% 28.70/18.94 (((~(f5(f10(c1)) = f5(f10(c1)))) | (f10(c1) = c1) | big_f(c2, f10(c1)) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), f5(f10(c1))) | (~(c2 = f8(c1)))) <=> (big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), f5(f10(c1))))),
% 28.70/18.94 inference(transitivity,[status(thm)],[15812, 15811])).
% 28.70/18.94 tff(15814,plain,
% 28.70/18.94 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(f5(f10(c1)) = f5(f10(c1)))) | (f10(c1) = c1) | big_f(c2, f10(c1)) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), f5(f10(c1))) | (~(c2 = f8(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), f5(f10(c1)))))),
% 28.70/18.94 inference(monotonicity,[status(thm)],[15813])).
% 28.70/18.94 tff(15815,plain,
% 28.70/18.94 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(f5(f10(c1)) = f5(f10(c1)))) | (f10(c1) = c1) | big_f(c2, f10(c1)) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), f5(f10(c1))) | (~(c2 = f8(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), f5(f10(c1))))),
% 28.70/18.95 inference(transitivity,[status(thm)],[15814, 15810])).
% 28.70/18.95 tff(15816,plain,
% 28.70/18.95 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(f5(f10(c1)) = f5(f10(c1)))) | (f10(c1) = c1) | big_f(c2, f10(c1)) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), f5(f10(c1))) | (~(c2 = f8(c1))))),
% 28.70/18.95 inference(quant_inst,[status(thm)],[])).
% 28.70/18.95 tff(15817,plain,
% 28.70/18.95 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), f5(f10(c1)))),
% 28.70/18.95 inference(modus_ponens,[status(thm)],[15816, 15815])).
% 28.70/18.95 tff(15818,plain,
% 28.70/18.95 (big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), f5(f10(c1)))),
% 28.70/18.95 inference(unit_resolution,[status(thm)],[15817, 1745])).
% 28.70/18.95 tff(15819,plain,
% 28.70/18.95 (~(c2 = f8(c1))),
% 28.70/18.95 inference(unit_resolution,[status(thm)],[15818, 15809, 6126, 3, 223])).
% 28.70/18.95 tff(15820,plain,
% 28.70/18.95 (~(f8(c1) = c2)),
% 28.70/18.95 inference(unit_resolution,[status(thm)],[1675, 15819])).
% 28.70/18.95 tff(15821,plain,
% 28.70/18.95 (~big_f(c1, f10(c1))),
% 28.70/18.95 inference(modus_ponens,[status(thm)],[27, 11164])).
% 28.70/18.95 tff(15822,plain,
% 28.70/18.95 (big_f(f7(c2), f1(f7(c2), f7(c2))) <=> big_f(f7(c2), f5(c2))),
% 28.70/18.95 inference(transitivity,[status(thm)],[9655, 15798, 15731])).
% 28.70/18.95 tff(15823,plain,
% 28.70/18.95 ((~big_f(f7(c2), f1(f7(c2), f7(c2)))) <=> (~big_f(f7(c2), f5(c2)))),
% 28.70/18.95 inference(monotonicity,[status(thm)],[15822])).
% 28.70/18.95 tff(15824,plain,
% 28.70/18.95 (~big_f(f7(c2), f5(c2))),
% 28.70/18.95 inference(modus_ponens,[status(thm)],[15808, 15823])).
% 28.70/18.95 tff(15825,plain,
% 28.70/18.95 (~(c1 = f8(c1))),
% 28.70/18.95 inference(unit_resolution,[status(thm)],[12249, 15824, 17, 15821, 3])).
% 28.70/18.95 tff(15826,plain,
% 28.70/18.95 (~(f8(c1) = c1)),
% 28.70/18.95 inference(unit_resolution,[status(thm)],[9808, 15825])).
% 28.70/18.95 tff(15827,plain,
% 28.70/18.95 ($false),
% 28.70/18.95 inference(unit_resolution,[status(thm)],[1680, 15826, 15820])).
% 28.70/18.95 tff(15828,plain,((~(c4 = c1)) | (f7(c2) = c2) | (f10(c1) = c1) | (~big_f(c2, f7(c2))) | big_f(c1, c2) | (~(f7(c1) = c2)) | big_f(c2, c2) | (~(f4(c4) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.70/18.95 tff(15829,plain,
% 28.70/18.95 (~(c4 = c1)),
% 28.70/18.95 inference(unit_resolution,[status(thm)],[15828, 15740, 3, 17, 27, 120, 121, 15706])).
% 28.70/18.95 tff(15830,plain,
% 28.70/18.95 (c4 = c2),
% 28.70/18.95 inference(unit_resolution,[status(thm)],[461, 15829])).
% 28.70/18.95 tff(15831,plain,
% 28.70/18.95 (c2 = c4),
% 28.70/18.95 inference(symmetry,[status(thm)],[15830])).
% 28.70/18.95 tff(15832,plain,
% 28.70/18.95 (f4(c2) = f4(c4)),
% 28.70/18.95 inference(monotonicity,[status(thm)],[15831])).
% 28.70/18.95 tff(15833,plain,
% 28.70/18.95 (f4(c4) = f4(c2)),
% 28.70/18.95 inference(symmetry,[status(thm)],[15832])).
% 28.70/18.95 tff(15834,plain,
% 28.70/18.95 (c1 = f4(c4)),
% 28.70/18.95 inference(symmetry,[status(thm)],[15706])).
% 28.70/18.95 tff(15835,plain,
% 28.70/18.95 (f7(c2) = f4(c2)),
% 28.70/18.95 inference(transitivity,[status(thm)],[22, 15834, 15833])).
% 28.70/18.95 tff(15836,plain,
% 28.70/18.95 (~big_f(f4(c4), c4)),
% 28.70/18.95 inference(unit_resolution,[status(thm)],[11764, 15830, 15706, 27])).
% 28.70/18.95 tff(15837,plain,
% 28.70/18.95 (c2 = c4),
% 28.70/18.95 inference(modus_ponens,[status(thm)],[15830, 159])).
% 28.70/18.95 tff(15838,assumption,(f7(c2) = f4(c2)), introduced(assumption)).
% 28.70/18.95 tff(15839,plain,
% 28.70/18.95 (f1(c2, c1) = f1(c2, f7(c2))),
% 28.70/18.95 inference(monotonicity,[status(thm)],[342])).
% 28.70/18.95 tff(15840,plain,
% 28.70/18.95 (f1(c2, f7(c2)) = f1(c2, c1)),
% 28.70/18.95 inference(symmetry,[status(thm)],[15839])).
% 28.70/18.95 tff(15841,plain,
% 28.70/18.95 (big_f(c2, f1(c2, f7(c2))) <=> big_f(c2, f1(c2, c1))),
% 28.70/18.95 inference(monotonicity,[status(thm)],[15840])).
% 28.70/18.95 tff(15842,plain,
% 28.70/18.95 (big_f(c2, f1(c2, c1)) <=> big_f(c2, f1(c2, f7(c2)))),
% 28.70/18.95 inference(symmetry,[status(thm)],[15841])).
% 28.70/18.95 tff(15843,plain,
% 28.70/18.95 (f1(c2, f7(c2)) = f1(f7(f7(c2)), c1)),
% 28.70/18.95 inference(monotonicity,[status(thm)],[355, 292])).
% 28.70/18.95 tff(15844,plain,
% 28.70/18.95 (f1(f7(f7(c2)), c1) = f1(c2, f7(c2))),
% 28.70/18.95 inference(symmetry,[status(thm)],[15843])).
% 28.70/18.95 tff(15845,plain,
% 28.70/18.95 ((~(c2 = c3)) <=> (~(f7(f7(c2)) = c3))),
% 28.70/18.95 inference(monotonicity,[status(thm)],[365])).
% 28.70/18.95 tff(15846,plain,
% 28.70/18.95 (~(f7(f7(c2)) = c3)),
% 28.70/18.95 inference(modus_ponens,[status(thm)],[377, 15845])).
% 28.70/18.95 tff(15847,plain,
% 28.70/18.95 (f1(f7(f7(c2)), c1) = c1),
% 28.70/18.95 inference(unit_resolution,[status(thm)],[422, 15846, 121, 379, 347, 292])).
% 28.70/18.95 tff(15848,plain,
% 28.70/18.95 (c1 = f1(f7(f7(c2)), c1)),
% 28.70/18.95 inference(symmetry,[status(thm)],[15847])).
% 28.70/18.95 tff(15849,plain,
% 28.70/18.95 (f7(c2) = f1(c2, c1)),
% 28.70/18.95 inference(transitivity,[status(thm)],[292, 15848, 15844, 15840])).
% 28.70/18.95 tff(15850,plain,
% 28.70/18.95 (big_f(c2, f7(c2)) <=> big_f(c2, f1(c2, c1))),
% 28.70/18.95 inference(monotonicity,[status(thm)],[15849])).
% 28.70/18.95 tff(15851,plain,
% 28.70/18.95 (big_f(c2, f7(c2)) <=> big_f(c2, f1(c2, f7(c2)))),
% 28.70/18.95 inference(transitivity,[status(thm)],[15850, 15842])).
% 28.70/18.95 tff(15852,plain,
% 28.70/18.95 (big_f(c2, c1) <=> big_f(c2, f7(c2))),
% 28.70/18.95 inference(monotonicity,[status(thm)],[342])).
% 28.70/18.95 tff(15853,plain,
% 28.70/18.95 (big_f(c2, c1)),
% 28.70/18.95 inference(unit_resolution,[status(thm)],[15738, 15735, 347])).
% 28.70/18.95 tff(15854,plain,
% 28.70/18.95 (big_f(c2, f7(c2))),
% 28.70/18.95 inference(modus_ponens,[status(thm)],[15853, 15852])).
% 28.70/18.95 tff(15855,plain,
% 28.70/18.95 (big_f(c2, f1(c2, f7(c2)))),
% 28.70/18.95 inference(modus_ponens,[status(thm)],[15854, 15851])).
% 28.70/18.95 tff(15856,plain,
% 28.70/18.95 ((f1(c2, f7(c2)) = f7(c2)) <=> (f1(c2, c1) = c1)),
% 28.70/18.95 inference(monotonicity,[status(thm)],[15840, 292])).
% 28.70/18.95 tff(15857,plain,
% 28.70/18.95 ((f1(c2, c1) = c1) <=> (f1(c2, f7(c2)) = f7(c2))),
% 28.70/18.95 inference(symmetry,[status(thm)],[15856])).
% 28.70/18.95 tff(15858,plain,
% 28.70/18.95 (f1(f7(c1), c1) = f1(f7(f7(c2)), c1)),
% 28.70/18.95 inference(monotonicity,[status(thm)],[353])).
% 28.70/18.95 tff(15859,plain,
% 28.70/18.95 (f1(f7(c1), c1) = c1),
% 28.70/18.95 inference(transitivity,[status(thm)],[15858, 874])).
% 28.70/18.95 tff(15860,plain,
% 28.70/18.95 (big_f(f7(c1), f1(f7(c1), c1)) <=> big_f(f7(c1), c1)),
% 28.70/18.95 inference(monotonicity,[status(thm)],[15859])).
% 28.70/18.95 tff(15861,plain,
% 28.70/18.95 (big_f(f7(c1), c1) <=> big_f(f7(c1), f1(f7(c1), c1))),
% 28.70/18.95 inference(symmetry,[status(thm)],[15860])).
% 28.70/18.95 tff(15862,plain,
% 28.70/18.95 (big_f(f7(c1), f1(f7(c1), c1))),
% 28.70/18.95 inference(modus_ponens,[status(thm)],[15735, 15861])).
% 28.70/18.95 tff(15863,plain,
% 28.70/18.95 ($false),
% 28.70/18.95 inference(unit_resolution,[status(thm)],[12204, 15862])).
% 28.70/18.95 tff(15864,plain,((~(f1(f7(f7(c2)), c1) = c1)) | big_f(f7(c1), f1(f7(c1), c1)) | (~big_f(f7(c1), c1)) | (~(f7(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.70/18.95 tff(15865,plain,
% 28.70/18.95 (big_f(f7(c1), f1(f7(c1), c1))),
% 28.70/18.95 inference(unit_resolution,[status(thm)],[15864, 15847, 292, 15735])).
% 28.70/18.95 tff(15866,plain,
% 28.70/18.95 (~(f1(c2, c1) = c2)),
% 28.70/18.95 inference(unit_resolution,[status(thm)],[12197, 15865, 121, 347])).
% 28.70/18.95 tff(15867,plain,
% 28.70/18.95 (f1(c2, c1) = c1),
% 28.70/18.95 inference(unit_resolution,[status(thm)],[10113, 15866])).
% 28.70/18.95 tff(15868,plain,
% 28.70/18.95 (f1(c2, f7(c2)) = f7(c2)),
% 28.70/18.95 inference(modus_ponens,[status(thm)],[15867, 15857])).
% 28.70/18.95 tff(15869,plain,
% 28.70/18.95 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c2 = c4)) | big_f(f7(c2), c2) | (~big_f(c2, f1(c2, f7(c2)))) | (~(f1(c2, f7(c2)) = f7(c2))) | (~(f7(c2) = f4(c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(c2 = c4)) | big_f(f7(c2), c2) | (~big_f(c2, f1(c2, f7(c2)))) | (~(f1(c2, f7(c2)) = f7(c2))) | (~(f7(c2) = f4(c2))))),
% 28.70/18.95 inference(rewrite,[status(thm)],[])).
% 28.70/18.95 tff(15870,plain,
% 28.70/18.95 (((c2 = c3) | (~(c2 = c4)) | big_f(f7(c2), c2) | (~(f7(c2) = f4(c2))) | (~(f1(c2, f7(c2)) = f7(c2))) | (~big_f(c2, f1(c2, f7(c2))))) <=> ((c2 = c3) | (~(c2 = c4)) | big_f(f7(c2), c2) | (~big_f(c2, f1(c2, f7(c2)))) | (~(f1(c2, f7(c2)) = f7(c2))) | (~(f7(c2) = f4(c2))))),
% 28.70/18.95 inference(rewrite,[status(thm)],[])).
% 28.70/18.95 tff(15871,plain,
% 28.70/18.95 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c2 = c4)) | big_f(f7(c2), c2) | (~(f7(c2) = f4(c2))) | (~(f1(c2, f7(c2)) = f7(c2))) | (~big_f(c2, f1(c2, f7(c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c2 = c4)) | big_f(f7(c2), c2) | (~big_f(c2, f1(c2, f7(c2)))) | (~(f1(c2, f7(c2)) = f7(c2))) | (~(f7(c2) = f4(c2)))))),
% 28.70/18.95 inference(monotonicity,[status(thm)],[15870])).
% 28.70/18.95 tff(15872,plain,
% 28.70/18.95 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c2 = c4)) | big_f(f7(c2), c2) | (~(f7(c2) = f4(c2))) | (~(f1(c2, f7(c2)) = f7(c2))) | (~big_f(c2, f1(c2, f7(c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(c2 = c4)) | big_f(f7(c2), c2) | (~big_f(c2, f1(c2, f7(c2)))) | (~(f1(c2, f7(c2)) = f7(c2))) | (~(f7(c2) = f4(c2))))),
% 28.70/18.95 inference(transitivity,[status(thm)],[15871, 15869])).
% 28.70/18.95 tff(15873,plain,
% 28.70/18.95 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c2 = c4)) | big_f(f7(c2), c2) | (~(f7(c2) = f4(c2))) | (~(f1(c2, f7(c2)) = f7(c2))) | (~big_f(c2, f1(c2, f7(c2)))))),
% 28.70/18.95 inference(quant_inst,[status(thm)],[])).
% 28.70/18.95 tff(15874,plain,
% 28.70/18.95 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(c2 = c4)) | big_f(f7(c2), c2) | (~big_f(c2, f1(c2, f7(c2)))) | (~(f1(c2, f7(c2)) = f7(c2))) | (~(f7(c2) = f4(c2)))),
% 28.70/18.95 inference(modus_ponens,[status(thm)],[15873, 15872])).
% 28.70/18.95 tff(15875,plain,
% 28.70/18.95 ($false),
% 28.70/18.95 inference(unit_resolution,[status(thm)],[15874, 447, 631, 377, 1521, 15868, 15855, 15838])).
% 28.70/18.95 tff(15876,plain,((c2 = c3) | (~(c2 = c4)) | big_f(f7(c2), c2) | (~(f7(c2) = f4(c2))) | (~(f7(c2) = c1)) | (~(f7(c1) = c2)) | big_f(c2, c2) | (~big_f(f7(c1), c1)) | big_f(f4(c4), c4)), inference(lemma,lemma(discharge,[]))).
% 28.70/18.95 tff(15877,plain,
% 28.70/18.95 (c2 = c3),
% 28.70/18.95 inference(unit_resolution,[status(thm)],[15876, 15837, 12679, 15835, 22, 120, 121, 15733, 15836])).
% 28.70/18.95 tff(15878,plain,
% 28.70/18.95 (c3 = c2),
% 28.70/18.95 inference(symmetry,[status(thm)],[15877])).
% 28.70/18.95 tff(15879,plain,
% 28.70/18.95 ((f7(c2) = c3) <=> (f7(c2) = c2)),
% 28.70/18.95 inference(monotonicity,[status(thm)],[15878])).
% 28.70/18.95 tff(15880,plain,
% 28.70/18.95 ((f7(c2) = c2) <=> (f7(c2) = c3)),
% 28.70/18.95 inference(symmetry,[status(thm)],[15879])).
% 28.70/18.95 tff(15881,plain,
% 28.70/18.95 ((~(f7(c2) = c2)) <=> (~(f7(c2) = c3))),
% 28.70/18.95 inference(monotonicity,[status(thm)],[15880])).
% 28.70/18.95 tff(15882,plain,
% 28.70/18.95 (~(f7(c2) = c3)),
% 28.70/18.95 inference(modus_ponens,[status(thm)],[17, 15881])).
% 28.70/18.95 tff(15883,plain,
% 28.70/18.95 (big_f(f7(c2), c2) <=> big_f(c1, c2)),
% 28.70/18.95 inference(monotonicity,[status(thm)],[292])).
% 28.70/18.95 tff(15884,plain,
% 28.70/18.95 (big_f(c1, c2) <=> big_f(f7(c2), c2)),
% 28.70/18.95 inference(symmetry,[status(thm)],[15883])).
% 28.70/18.95 tff(15885,plain,
% 28.70/18.95 ((~big_f(c1, c2)) <=> (~big_f(f7(c2), c2))),
% 28.70/18.95 inference(monotonicity,[status(thm)],[15884])).
% 28.70/18.95 tff(15886,plain,
% 28.70/18.95 (~big_f(f7(c2), c2)),
% 28.70/18.95 inference(modus_ponens,[status(thm)],[27, 15885])).
% 28.70/18.95 tff(15887,plain,
% 28.70/18.95 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((~(c2 = c4)) | (f7(c2) = c3) | big_f(f7(c2), c2) | (~(f7(c2) = f4(c2))) | (f1(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(c2), f1(f7(c2), f7(c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (~(c2 = c4)) | (f7(c2) = c3) | big_f(f7(c2), c2) | (~(f7(c2) = f4(c2))) | (f1(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(c2), f1(f7(c2), f7(c2))))),
% 28.70/18.95 inference(rewrite,[status(thm)],[])).
% 28.70/18.95 tff(15888,plain,
% 28.70/18.95 (((f7(c2) = c3) | (f1(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(c2), f1(f7(c2), f7(c2))) | (~(c2 = c4)) | big_f(f7(c2), c2) | (~(f7(c2) = f4(c2)))) <=> ((~(c2 = c4)) | (f7(c2) = c3) | big_f(f7(c2), c2) | (~(f7(c2) = f4(c2))) | (f1(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(c2), f1(f7(c2), f7(c2))))),
% 28.70/18.95 inference(rewrite,[status(thm)],[])).
% 28.70/18.95 tff(15889,plain,
% 28.70/18.95 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f7(c2) = c3) | (f1(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(c2), f1(f7(c2), f7(c2))) | (~(c2 = c4)) | big_f(f7(c2), c2) | (~(f7(c2) = f4(c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((~(c2 = c4)) | (f7(c2) = c3) | big_f(f7(c2), c2) | (~(f7(c2) = f4(c2))) | (f1(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(c2), f1(f7(c2), f7(c2)))))),
% 28.70/18.95 inference(monotonicity,[status(thm)],[15888])).
% 28.70/18.95 tff(15890,plain,
% 28.70/18.95 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f7(c2) = c3) | (f1(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(c2), f1(f7(c2), f7(c2))) | (~(c2 = c4)) | big_f(f7(c2), c2) | (~(f7(c2) = f4(c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (~(c2 = c4)) | (f7(c2) = c3) | big_f(f7(c2), c2) | (~(f7(c2) = f4(c2))) | (f1(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(c2), f1(f7(c2), f7(c2))))),
% 28.70/18.95 inference(transitivity,[status(thm)],[15889, 15887])).
% 28.70/18.95 tff(15891,plain,
% 28.70/18.95 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f7(c2) = c3) | (f1(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(c2), f1(f7(c2), f7(c2))) | (~(c2 = c4)) | big_f(f7(c2), c2) | (~(f7(c2) = f4(c2))))),
% 28.70/18.95 inference(quant_inst,[status(thm)],[])).
% 28.70/18.95 tff(15892,plain,
% 28.70/18.95 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (~(c2 = c4)) | (f7(c2) = c3) | big_f(f7(c2), c2) | (~(f7(c2) = f4(c2))) | (f1(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(c2), f1(f7(c2), f7(c2)))),
% 28.70/18.95 inference(modus_ponens,[status(thm)],[15891, 15890])).
% 28.70/18.95 tff(15893,plain,
% 28.70/18.95 (big_f(f7(c2), f1(f7(c2), f7(c2)))),
% 28.70/18.95 inference(unit_resolution,[status(thm)],[15892, 402, 631, 9092, 15886, 15784, 15838])).
% 28.70/18.95 tff(15894,plain,
% 28.70/18.95 (big_f(c1, f1(c1, c1))),
% 28.70/18.95 inference(modus_ponens,[status(thm)],[15893, 9702])).
% 28.70/18.95 tff(15895,plain,
% 28.70/18.95 ($false),
% 28.70/18.95 inference(unit_resolution,[status(thm)],[15793, 15894])).
% 28.70/18.95 tff(15896,plain,((f1(c1, c1) = c1) | (~(f7(c2) = c1)) | (~(c2 = c4)) | (f7(c2) = c3) | (~(f7(c2) = f4(c2))) | big_f(c1, c2)), inference(lemma,lemma(discharge,[]))).
% 28.70/18.95 tff(15897,plain,
% 28.70/18.95 (f1(c1, c1) = c1),
% 28.70/18.95 inference(unit_resolution,[status(thm)],[15896, 15837, 22, 15882, 15835, 27])).
% 28.70/18.95 tff(15898,plain,
% 28.70/18.95 (f1(c1, c1) = f7(c2)),
% 28.70/18.95 inference(transitivity,[status(thm)],[15897, 125])).
% 28.70/18.95 tff(15899,plain,
% 28.70/18.95 (big_f(c1, f1(c1, c1)) <=> big_f(f7(c2), f7(c2))),
% 28.70/18.95 inference(monotonicity,[status(thm)],[125, 15898])).
% 28.70/18.95 tff(15900,plain,
% 28.70/18.95 (big_f(f7(c2), f1(f7(c2), f7(c2))) <=> big_f(f7(f10(c1)), f5(f10(c1)))),
% 28.70/18.95 inference(transitivity,[status(thm)],[9655, 15899, 15731, 15708])).
% 28.70/18.95 tff(15901,plain,
% 28.70/18.95 ((~big_f(f7(c2), f1(f7(c2), f7(c2)))) <=> (~big_f(f7(f10(c1)), f5(f10(c1))))),
% 28.70/18.95 inference(monotonicity,[status(thm)],[15900])).
% 28.70/18.95 tff(15902,plain,
% 28.70/18.95 (f1(f7(c2), f7(c2)) = f7(c2)),
% 28.70/18.95 inference(modus_ponens,[status(thm)],[15897, 9668])).
% 28.70/18.95 tff(15903,plain,
% 28.70/18.95 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((~(c2 = c4)) | (f7(c2) = c3) | big_f(f7(c2), c2) | (~(f7(c2) = f4(c2))) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (~(c2 = c4)) | (f7(c2) = c3) | big_f(f7(c2), c2) | (~(f7(c2) = f4(c2))) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2)))))),
% 28.70/18.95 inference(rewrite,[status(thm)],[])).
% 28.70/18.95 tff(15904,plain,
% 28.70/18.95 (((f7(c2) = c3) | (~(c2 = c4)) | big_f(f7(c2), c2) | (~(f7(c2) = f4(c2))) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2))))) <=> ((~(c2 = c4)) | (f7(c2) = c3) | big_f(f7(c2), c2) | (~(f7(c2) = f4(c2))) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2)))))),
% 28.70/18.95 inference(rewrite,[status(thm)],[])).
% 28.70/18.95 tff(15905,plain,
% 28.70/18.95 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c2) = c3) | (~(c2 = c4)) | big_f(f7(c2), c2) | (~(f7(c2) = f4(c2))) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((~(c2 = c4)) | (f7(c2) = c3) | big_f(f7(c2), c2) | (~(f7(c2) = f4(c2))) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2))))))),
% 28.70/18.95 inference(monotonicity,[status(thm)],[15904])).
% 28.70/18.95 tff(15906,plain,
% 28.70/18.95 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c2) = c3) | (~(c2 = c4)) | big_f(f7(c2), c2) | (~(f7(c2) = f4(c2))) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (~(c2 = c4)) | (f7(c2) = c3) | big_f(f7(c2), c2) | (~(f7(c2) = f4(c2))) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2)))))),
% 28.70/18.95 inference(transitivity,[status(thm)],[15905, 15903])).
% 28.70/18.95 tff(15907,plain,
% 28.70/18.95 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c2) = c3) | (~(c2 = c4)) | big_f(f7(c2), c2) | (~(f7(c2) = f4(c2))) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2)))))),
% 28.70/18.95 inference(quant_inst,[status(thm)],[])).
% 28.70/18.95 tff(15908,plain,
% 28.70/18.95 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (~(c2 = c4)) | (f7(c2) = c3) | big_f(f7(c2), c2) | (~(f7(c2) = f4(c2))) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2))))),
% 28.70/18.95 inference(modus_ponens,[status(thm)],[15907, 15906])).
% 28.70/18.95 tff(15909,plain,
% 28.70/18.95 (~big_f(f7(c2), f1(f7(c2), f7(c2)))),
% 28.70/18.95 inference(unit_resolution,[status(thm)],[15908, 447, 15837, 15882, 12679, 15902, 15835])).
% 28.70/18.95 tff(15910,plain,
% 28.70/18.95 (~big_f(f7(f10(c1)), f5(f10(c1)))),
% 28.70/18.95 inference(modus_ponens,[status(thm)],[15909, 15901])).
% 28.70/18.95 tff(15911,plain,
% 28.70/18.95 (~(c2 = f8(c1))),
% 28.70/18.95 inference(unit_resolution,[status(thm)],[15818, 15910, 6126, 3, 223])).
% 28.70/18.95 tff(15912,plain,
% 28.70/18.95 (~(f8(c1) = c2)),
% 28.70/18.95 inference(unit_resolution,[status(thm)],[1675, 15911])).
% 28.70/18.95 tff(15913,plain,
% 28.70/18.95 (big_f(f7(c2), f1(f7(c2), f7(c2))) <=> big_f(f7(c2), f5(c2))),
% 28.70/18.95 inference(transitivity,[status(thm)],[9655, 15899, 15731])).
% 28.70/18.95 tff(15914,plain,
% 28.70/18.95 ((~big_f(f7(c2), f1(f7(c2), f7(c2)))) <=> (~big_f(f7(c2), f5(c2)))),
% 28.70/18.95 inference(monotonicity,[status(thm)],[15913])).
% 28.70/18.95 tff(15915,plain,
% 28.70/18.95 (~big_f(f7(c2), f5(c2))),
% 28.70/18.95 inference(modus_ponens,[status(thm)],[15909, 15914])).
% 28.70/18.95 tff(15916,plain,
% 28.70/18.95 (~(c1 = f8(c1))),
% 28.70/18.95 inference(unit_resolution,[status(thm)],[12249, 15915, 17, 15821, 3])).
% 28.70/18.95 tff(15917,plain,
% 28.70/18.95 (~(f8(c1) = c1)),
% 28.70/18.95 inference(unit_resolution,[status(thm)],[9808, 15916])).
% 28.70/18.95 tff(15918,plain,
% 28.70/18.95 ($false),
% 28.70/18.95 inference(unit_resolution,[status(thm)],[1680, 15917, 15912])).
% 28.70/18.95 tff(15919,plain,(big_f(c1, c2) | (f7(c2) = c2) | (f10(c1) = c1) | big_f(c2, c2) | (f7(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 28.70/18.95 tff(15920,plain,
% 28.70/18.95 (big_f(c1, c2)),
% 28.70/18.95 inference(unit_resolution,[status(thm)],[15919, 121, 3, 17, 115])).
% 28.70/18.95 tff(15921,plain,
% 28.70/18.95 (big_f(f7(c2), c2)),
% 28.70/18.95 inference(modus_ponens,[status(thm)],[15920, 12163])).
% 28.70/18.95 tff(15922,plain,
% 28.70/18.95 (~(f5(c1) = c2)),
% 28.70/18.95 inference(unit_resolution,[status(thm)],[10391, 15921, 122, 22, 115, 121])).
% 28.70/18.95 tff(15923,plain,
% 28.70/18.95 (f5(c1) = c1),
% 28.70/18.95 inference(unit_resolution,[status(thm)],[1708, 15922])).
% 28.70/18.95 tff(15924,plain,
% 28.70/18.95 (~(f5(c1) = c2)),
% 28.70/18.95 inference(unit_resolution,[status(thm)],[10391, 1180, 122, 292, 115, 121])).
% 28.70/18.95 tff(15925,plain,
% 28.70/18.95 (f5(c1) = c1),
% 28.70/18.95 inference(unit_resolution,[status(thm)],[1708, 15924])).
% 28.70/18.95 tff(15926,plain,
% 28.70/18.95 (f5(c1) = f7(c2)),
% 28.70/18.95 inference(transitivity,[status(thm)],[15925, 342])).
% 28.70/18.95 tff(15927,plain,
% 28.70/18.95 (big_f(f7(c1), f5(c1)) <=> big_f(c2, f7(c2))),
% 28.70/18.95 inference(monotonicity,[status(thm)],[120, 15926])).
% 28.70/18.95 tff(15928,plain,
% 28.70/18.95 (big_f(c2, f7(c2)) <=> big_f(f7(c1), f5(c1))),
% 28.70/18.95 inference(symmetry,[status(thm)],[15927])).
% 28.70/18.95 tff(15929,plain,
% 28.70/18.95 ((~big_f(c2, f7(c2))) <=> (~big_f(f7(c1), f5(c1)))),
% 28.70/18.95 inference(monotonicity,[status(thm)],[15928])).
% 28.70/18.95 tff(15930,plain,
% 28.70/18.95 (~big_f(f7(c1), f5(c1))),
% 28.70/18.95 inference(modus_ponens,[status(thm)],[9331, 15929])).
% 28.70/18.95 tff(15931,plain,
% 28.70/18.95 (f9(c2, c1) = c1),
% 28.70/18.95 inference(unit_resolution,[status(thm)],[8445, 15930, 115, 122, 121])).
% 28.70/18.95 tff(15932,plain,
% 28.70/18.95 (f9(c2, f7(c2)) = f7(c2)),
% 28.70/18.95 inference(modus_ponens,[status(thm)],[15931, 10379])).
% 28.70/18.95 tff(15933,plain,
% 28.70/18.95 (f9(c2, c1) = f7(c2)),
% 28.70/18.95 inference(transitivity,[status(thm)],[15931, 342])).
% 28.70/18.95 tff(15934,plain,
% 28.70/18.95 (big_f(f9(c2, c1), f10(c2)) <=> big_f(f7(c2), c2)),
% 28.70/18.95 inference(monotonicity,[status(thm)],[15933, 122])).
% 28.70/18.95 tff(15935,plain,
% 28.70/18.95 (big_f(f7(c2), c2) <=> big_f(f9(c2, c1), f10(c2))),
% 28.70/18.95 inference(symmetry,[status(thm)],[15934])).
% 28.70/18.95 tff(15936,plain,
% 28.70/18.95 (big_f(f7(c2), c2) <=> big_f(f9(c2, f7(c2)), f10(c2))),
% 28.70/18.95 inference(transitivity,[status(thm)],[15935, 10384])).
% 28.70/18.95 tff(15937,plain,
% 28.70/18.95 (big_f(f9(c2, f7(c2)), f10(c2))),
% 28.70/18.95 inference(modus_ponens,[status(thm)],[1180, 15936])).
% 28.70/18.95 tff(15938,plain,
% 28.70/18.95 (big_f(f7(f7(c2)), f7(c2)) <=> big_f(c2, f7(c2))),
% 28.70/18.95 inference(monotonicity,[status(thm)],[363])).
% 28.70/18.95 tff(15939,plain,
% 28.70/18.95 (big_f(c2, f7(c2))),
% 28.70/18.95 inference(modus_ponens,[status(thm)],[10465, 15938])).
% 28.70/18.95 tff(15940,plain,
% 28.70/18.95 ($false),
% 28.70/18.95 inference(unit_resolution,[status(thm)],[9331, 15939])).
% 28.70/18.95 tff(15941,plain,((~big_f(f7(f7(c2)), f7(c2))) | big_f(c2, f7(c2)) | (~(f7(c1) = c2)) | (~(f7(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.70/18.95 tff(15942,plain,
% 28.70/18.95 (~big_f(f7(f7(c2)), f7(c2))),
% 28.70/18.95 inference(unit_resolution,[status(thm)],[15941, 9331, 120, 292])).
% 28.70/18.95 tff(15943,plain,
% 28.70/18.95 ((f5(c1) = c1) <=> (f7(c2) = f5(f7(c2)))),
% 28.70/18.95 inference(symmetry,[status(thm)],[8471])).
% 28.70/18.95 tff(15944,plain,
% 28.70/18.95 (f7(c2) = f5(f7(c2))),
% 28.70/18.95 inference(modus_ponens,[status(thm)],[15925, 15943])).
% 28.70/18.95 tff(15945,plain,
% 28.70/18.95 ($false),
% 28.70/18.95 inference(unit_resolution,[status(thm)],[8479, 783, 122, 8473, 15944, 15942, 15937, 15932])).
% 28.70/18.95 tff(15946,plain,(big_f(c2, f7(c2)) | (~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | (~big_f(f7(c2), c2)) | (~(f7(c2) = c1)) | (f7(c1) = c1) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 28.70/18.95 tff(15947,plain,
% 28.70/18.95 (big_f(c2, f7(c2))),
% 28.70/18.95 inference(unit_resolution,[status(thm)],[15946, 15921, 12943, 122, 22, 115, 121])).
% 28.70/18.95 tff(15948,plain,
% 28.70/18.95 (~(f9(c2, c1) = c1)),
% 28.70/18.95 inference(unit_resolution,[status(thm)],[10222, 8372, 122, 17, 1180])).
% 28.70/18.95 tff(15949,plain,
% 28.70/18.95 (~(f9(c2, f7(c2)) = f7(c2))),
% 28.70/18.95 inference(modus_ponens,[status(thm)],[15948, 8074])).
% 28.70/18.95 tff(15950,plain,
% 28.70/18.95 (f9(c2, c1) = c2),
% 28.70/18.95 inference(unit_resolution,[status(thm)],[3913, 15948])).
% 28.70/18.95 tff(15951,plain,
% 28.70/18.95 (big_f(f9(c2, c1), f10(c2)) <=> big_f(c2, c2)),
% 28.70/18.95 inference(monotonicity,[status(thm)],[15950, 122])).
% 28.70/18.95 tff(15952,plain,
% 28.70/18.95 (big_f(c2, c2) <=> big_f(f9(c2, c1), f10(c2))),
% 28.70/18.95 inference(symmetry,[status(thm)],[15951])).
% 28.70/18.95 tff(15953,plain,
% 28.70/18.95 (big_f(c2, c2) <=> big_f(f9(c2, f7(c2)), f10(c2))),
% 28.70/18.96 inference(transitivity,[status(thm)],[15952, 8309])).
% 28.70/18.96 tff(15954,plain,
% 28.70/18.96 ((~big_f(c2, c2)) <=> (~big_f(f9(c2, f7(c2)), f10(c2)))),
% 28.70/18.96 inference(monotonicity,[status(thm)],[15953])).
% 28.70/18.96 tff(15955,plain,
% 28.70/18.96 (~big_f(f9(c2, f7(c2)), f10(c2))),
% 28.70/18.96 inference(modus_ponens,[status(thm)],[121, 15954])).
% 28.70/18.96 tff(15956,plain,
% 28.70/18.96 (c2 = f5(c2)),
% 28.70/18.96 inference(unit_resolution,[status(thm)],[10349, 676, 122, 17, 1180, 15955, 15949])).
% 28.70/18.96 tff(15957,plain,
% 28.70/18.96 (f5(c2) = c2),
% 28.70/18.96 inference(symmetry,[status(thm)],[15956])).
% 28.70/18.96 tff(15958,plain,
% 28.70/18.96 (f7(c2) = f5(c2)),
% 28.70/18.96 inference(unit_resolution,[status(thm)],[10229, 676, 122, 17, 15955, 15949, 8372])).
% 28.70/18.96 tff(15959,plain,
% 28.70/18.96 (f7(c2) = c2),
% 28.70/18.96 inference(transitivity,[status(thm)],[15958, 15957])).
% 28.70/18.96 tff(15960,plain,
% 28.70/18.96 ($false),
% 28.70/18.96 inference(unit_resolution,[status(thm)],[17, 15959])).
% 28.70/18.96 tff(15961,plain,((~big_f(f7(c2), f7(c2))) | (f7(c2) = c2) | (~(f10(c2) = c2)) | (~big_f(f7(c2), c2)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 28.70/18.96 tff(15962,plain,
% 28.70/18.96 (~big_f(f7(c2), f7(c2))),
% 28.70/18.96 inference(unit_resolution,[status(thm)],[15961, 12167, 122, 17, 121])).
% 28.70/18.96 tff(15963,plain,
% 28.70/18.96 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (~(f7(c2) = f5(c2))) | big_f(f7(c2), f7(c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (~(f7(c2) = f5(c2))) | big_f(f7(c2), f7(c2)))),
% 28.70/18.96 inference(rewrite,[status(thm)],[])).
% 28.70/18.96 tff(15964,plain,
% 28.70/18.96 (((~(f10(c2) = c2)) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), f7(c2)) | (~(f7(c2) = f5(c2)))) <=> ((~(f10(c2) = c2)) | (f7(c2) = c2) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (~(f7(c2) = f5(c2))) | big_f(f7(c2), f7(c2)))),
% 28.70/18.96 inference(rewrite,[status(thm)],[])).
% 28.70/18.96 tff(15965,plain,
% 28.70/18.96 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), f7(c2)) | (~(f7(c2) = f5(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (~(f7(c2) = f5(c2))) | big_f(f7(c2), f7(c2))))),
% 28.70/18.96 inference(monotonicity,[status(thm)],[15964])).
% 28.70/18.96 tff(15966,plain,
% 28.70/18.96 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), f7(c2)) | (~(f7(c2) = f5(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (~(f7(c2) = f5(c2))) | big_f(f7(c2), f7(c2)))),
% 28.70/18.96 inference(transitivity,[status(thm)],[15965, 15963])).
% 28.70/18.96 tff(15967,plain,
% 28.70/18.96 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), f7(c2)) | (~(f7(c2) = f5(c2))))),
% 28.70/18.96 inference(quant_inst,[status(thm)],[])).
% 28.70/18.96 tff(15968,plain,
% 28.70/18.96 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (f9(c2, f7(c2)) = f7(c2)) | big_f(f9(c2, f7(c2)), f10(c2)) | (~(f7(c2) = f5(c2))) | big_f(f7(c2), f7(c2))),
% 28.70/18.96 inference(modus_ponens,[status(thm)],[15967, 15966])).
% 28.70/18.96 tff(15969,plain,
% 28.70/18.96 ($false),
% 28.70/18.96 inference(unit_resolution,[status(thm)],[15968, 267, 122, 17, 8312, 8307, 8218, 8378])).
% 28.70/18.96 tff(15970,plain,((f9(c2, c1) = c1) | (~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f7(c2), f7(c2)) | (~(f7(c2) = f5(c2))) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 28.70/18.96 tff(15971,plain,
% 28.70/18.96 (f9(c2, c1) = c1),
% 28.70/18.96 inference(unit_resolution,[status(thm)],[15970, 8378, 17, 8218, 122, 121])).
% 28.70/18.96 tff(15972,plain,
% 28.70/18.96 (f9(c2, f7(c2)) = f7(c2)),
% 28.70/18.96 inference(modus_ponens,[status(thm)],[15971, 8073])).
% 28.70/18.96 tff(15973,plain,
% 28.70/18.96 (f9(c2, c1) = f7(c2)),
% 28.70/18.96 inference(transitivity,[status(thm)],[15971, 125])).
% 28.70/18.96 tff(15974,plain,
% 28.70/18.96 (big_f(f9(c2, c1), f10(c2)) <=> big_f(f7(c2), c2)),
% 28.70/18.96 inference(monotonicity,[status(thm)],[15973, 122])).
% 28.70/18.96 tff(15975,plain,
% 28.70/18.96 (big_f(f7(c2), c2) <=> big_f(f9(c2, c1), f10(c2))),
% 28.70/18.96 inference(symmetry,[status(thm)],[15974])).
% 28.70/18.96 tff(15976,plain,
% 28.70/18.96 (big_f(f7(c2), c2) <=> big_f(f9(c2, f7(c2)), f10(c2))),
% 28.70/18.96 inference(transitivity,[status(thm)],[15975, 8309])).
% 28.70/18.96 tff(15977,plain,
% 28.70/18.96 (big_f(f9(c2, f7(c2)), f10(c2))),
% 28.70/18.96 inference(modus_ponens,[status(thm)],[1180, 15976])).
% 28.70/18.96 tff(15978,plain,
% 28.70/18.96 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2))) | (~(f7(c2) = f5(c2))) | big_f(f7(c2), f7(c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2))) | (~(f7(c2) = f5(c2))) | big_f(f7(c2), f7(c2)))),
% 28.70/18.96 inference(rewrite,[status(thm)],[])).
% 28.70/18.96 tff(15979,plain,
% 28.70/18.96 (((~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f7(c2), f7(c2)) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2))) | (~(f7(c2) = f5(c2)))) <=> ((~(f10(c2) = c2)) | (f7(c2) = c2) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2))) | (~(f7(c2) = f5(c2))) | big_f(f7(c2), f7(c2)))),
% 28.70/18.96 inference(rewrite,[status(thm)],[])).
% 28.70/18.96 tff(15980,plain,
% 28.70/18.96 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f7(c2), f7(c2)) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2))) | (~(f7(c2) = f5(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2))) | (~(f7(c2) = f5(c2))) | big_f(f7(c2), f7(c2))))),
% 28.70/18.96 inference(monotonicity,[status(thm)],[15979])).
% 28.70/18.96 tff(15981,plain,
% 28.70/18.96 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f7(c2), f7(c2)) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2))) | (~(f7(c2) = f5(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2))) | (~(f7(c2) = f5(c2))) | big_f(f7(c2), f7(c2)))),
% 28.70/18.96 inference(transitivity,[status(thm)],[15980, 15978])).
% 28.70/18.96 tff(15982,plain,
% 28.70/18.96 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f7(c2), f7(c2)) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2))) | (~(f7(c2) = f5(c2))))),
% 28.70/18.96 inference(quant_inst,[status(thm)],[])).
% 28.70/18.96 tff(15983,plain,
% 28.70/18.96 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~(f9(c2, f7(c2)) = f7(c2))) | (~big_f(f9(c2, f7(c2)), f10(c2))) | (~(f7(c2) = f5(c2))) | big_f(f7(c2), f7(c2))),
% 28.70/18.96 inference(modus_ponens,[status(thm)],[15982, 15981])).
% 28.70/18.96 tff(15984,plain,
% 28.70/18.96 ($false),
% 28.70/18.96 inference(unit_resolution,[status(thm)],[15983, 783, 122, 17, 15977, 15972, 8218, 8378])).
% 28.70/18.96 tff(15985,plain,((~(f7(c2) = f5(c2))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f7(c2), f7(c2)) | (~big_f(f7(c2), c2)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 28.70/18.96 tff(15986,plain,
% 28.70/18.96 (~(f7(c2) = f5(c2))),
% 28.70/18.96 inference(unit_resolution,[status(thm)],[15985, 15962, 122, 17, 121, 12167])).
% 28.70/18.96 tff(15987,plain,
% 28.70/18.96 (~(f5(c2) = c1)),
% 28.70/18.96 inference(unit_resolution,[status(thm)],[8394, 15986, 22])).
% 28.70/18.96 tff(15988,plain,
% 28.70/18.96 (f5(c2) = c2),
% 28.70/18.96 inference(unit_resolution,[status(thm)],[1547, 15987])).
% 28.70/18.96 tff(15989,plain,
% 28.70/18.96 (big_f(f7(c2), f7(c2)) <=> big_f(c1, c1)),
% 28.70/18.96 inference(symmetry,[status(thm)],[12457])).
% 28.70/18.96 tff(15990,plain,
% 28.70/18.96 ((~big_f(f7(c2), f7(c2))) <=> (~big_f(c1, c1))),
% 28.70/18.96 inference(monotonicity,[status(thm)],[15989])).
% 28.70/18.96 tff(15991,plain,
% 28.70/18.96 (~big_f(c1, c1)),
% 28.70/18.96 inference(modus_ponens,[status(thm)],[15962, 15990])).
% 28.70/18.96 tff(15992,plain,
% 28.70/18.96 (big_f(c2, c1) <=> big_f(f7(c1), c1)),
% 28.70/18.96 inference(symmetry,[status(thm)],[15734])).
% 28.70/18.96 tff(15993,plain,
% 28.70/18.96 (big_f(c2, c1) <=> big_f(c2, f7(c2))),
% 28.70/18.96 inference(monotonicity,[status(thm)],[125])).
% 28.70/18.96 tff(15994,plain,
% 28.70/18.96 (big_f(c2, f7(c2)) <=> big_f(c2, c1)),
% 28.70/18.96 inference(symmetry,[status(thm)],[15993])).
% 28.70/18.96 tff(15995,plain,
% 28.70/18.96 (big_f(c2, f7(c2)) <=> big_f(f7(c1), c1)),
% 28.70/18.96 inference(transitivity,[status(thm)],[15994, 15992])).
% 28.70/18.96 tff(15996,plain,
% 28.70/18.96 (big_f(f7(c1), c1)),
% 28.70/18.96 inference(modus_ponens,[status(thm)],[15741, 15995])).
% 28.70/18.96 tff(15997,plain,
% 28.70/18.96 (big_f(c2, c1)),
% 28.70/18.96 inference(modus_ponens,[status(thm)],[15741, 15994])).
% 28.70/18.96 tff(15998,plain,
% 28.70/18.96 (c2 = c4),
% 28.70/18.96 inference(unit_resolution,[status(thm)],[12226, 1004, 347, 17, 121, 2865, 15997, 377])).
% 28.70/18.96 tff(15999,plain,
% 28.70/18.96 ((f7(c2) = c4) <=> (f7(c2) = c2)),
% 28.70/18.96 inference(monotonicity,[status(thm)],[8728])).
% 28.70/18.96 tff(16000,plain,
% 28.70/18.96 ((f7(c2) = c2) <=> (f7(c2) = c4)),
% 28.70/18.96 inference(symmetry,[status(thm)],[15999])).
% 28.70/18.96 tff(16001,plain,
% 28.70/18.96 ((f7(c2) = c2) <=> (c1 = c4)),
% 28.70/18.96 inference(transitivity,[status(thm)],[16000, 12587])).
% 28.70/18.96 tff(16002,plain,
% 28.70/18.96 ((~(f7(c2) = c2)) <=> (~(c1 = c4))),
% 28.70/18.96 inference(monotonicity,[status(thm)],[16001])).
% 28.70/18.96 tff(16003,plain,
% 28.70/18.96 (~(c1 = c4)),
% 28.70/18.96 inference(modus_ponens,[status(thm)],[17, 16002])).
% 28.70/18.96 tff(16004,assumption,(f1(f7(c1), c1) = c1), introduced(assumption)).
% 28.70/18.96 tff(16005,plain,
% 28.70/18.96 (f1(c2, c1) = c1),
% 28.70/18.96 inference(modus_ponens,[status(thm)],[16004, 995])).
% 28.70/18.96 tff(16006,plain,
% 28.70/18.96 ($false),
% 28.70/18.96 inference(unit_resolution,[status(thm)],[12187, 16005])).
% 28.70/18.96 tff(16007,plain,((~(f1(f7(c1), c1) = c1)) | (f1(c2, c1) = c1) | (~(f7(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.70/18.96 tff(16008,plain,
% 28.70/18.96 (~(f1(f7(c1), c1) = c1)),
% 28.70/18.96 inference(unit_resolution,[status(thm)],[16007, 12187, 347])).
% 28.70/18.96 tff(16009,plain,
% 28.70/18.96 (~big_f(f7(c2), f7(c2))),
% 28.70/18.96 inference(unit_resolution,[status(thm)],[15961, 1180, 122, 17, 121])).
% 28.70/18.96 tff(16010,plain,
% 28.70/18.96 ((f3(c1, f1(f5(c2), f5(c1))) = c4) <=> (f3(c1, f1(f5(c2), f5(c1))) = c2)),
% 28.70/18.96 inference(monotonicity,[status(thm)],[8728])).
% 28.70/18.96 tff(16011,plain,
% 28.70/18.96 ((f3(c1, f1(f5(c2), f5(c1))) = c2) <=> (f3(c1, f1(f5(c2), f5(c1))) = c4)),
% 28.70/18.96 inference(symmetry,[status(thm)],[16010])).
% 28.70/18.96 tff(16012,plain,
% 28.70/18.96 (f5(f10(c1)) = f5(c2)),
% 28.70/18.96 inference(monotonicity,[status(thm)],[16])).
% 28.70/18.96 tff(16013,plain,
% 28.70/18.96 (f5(c2) = f5(f10(c1))),
% 28.70/18.96 inference(symmetry,[status(thm)],[16012])).
% 28.70/18.96 tff(16014,plain,
% 28.70/18.96 (f1(f5(c2), f5(c1)) = f1(f5(f10(c1)), c1)),
% 28.70/18.96 inference(monotonicity,[status(thm)],[16013, 230])).
% 28.70/18.96 tff(16015,plain,
% 28.70/18.96 (f1(f5(f10(c1)), c1) = f1(f5(c2), f5(c1))),
% 28.70/18.96 inference(symmetry,[status(thm)],[16014])).
% 28.70/18.96 tff(16016,plain,
% 28.70/18.96 (~(f7(c2) = f5(c2))),
% 28.70/18.96 inference(unit_resolution,[status(thm)],[15985, 8218, 122, 17, 121, 1180])).
% 28.70/18.96 tff(16017,plain,
% 28.70/18.96 (~(f5(c2) = c1)),
% 28.70/18.96 inference(unit_resolution,[status(thm)],[8394, 16016, 22])).
% 28.70/18.96 tff(16018,plain,
% 28.70/18.96 (f5(c2) = c2),
% 28.70/18.96 inference(unit_resolution,[status(thm)],[1547, 16017])).
% 28.70/18.96 tff(16019,plain,
% 28.70/18.96 (c2 = f5(c2)),
% 28.70/18.96 inference(unit_resolution,[status(thm)],[8113, 16018])).
% 28.70/18.96 tff(16020,plain,
% 28.70/18.96 (f5(c2) = c2),
% 28.70/18.96 inference(symmetry,[status(thm)],[16019])).
% 28.70/18.96 tff(16021,plain,
% 28.70/18.96 (f5(f10(c1)) = c2),
% 28.70/18.96 inference(transitivity,[status(thm)],[16012, 16020])).
% 28.70/18.96 tff(16022,plain,
% 28.70/18.96 (f1(f5(f10(c1)), c1) = f1(c2, f7(c2))),
% 28.70/18.96 inference(monotonicity,[status(thm)],[16021, 125])).
% 28.70/18.96 tff(16023,plain,
% 28.70/18.96 (f1(c2, f7(c2)) = f1(f5(f10(c1)), c1)),
% 28.70/18.96 inference(symmetry,[status(thm)],[16022])).
% 28.70/18.96 tff(16024,plain,
% 28.70/18.96 (f1(c2, c1) = f1(c2, f7(c2))),
% 28.70/18.96 inference(symmetry,[status(thm)],[8766])).
% 28.70/18.96 tff(16025,plain,
% 28.70/18.96 (c2 = f1(c2, c1)),
% 28.70/18.96 inference(symmetry,[status(thm)],[12188])).
% 28.70/18.96 tff(16026,plain,
% 28.70/18.96 (c2 = f1(f5(c2), f5(c1))),
% 28.70/18.96 inference(transitivity,[status(thm)],[16025, 16024, 16023, 16015])).
% 28.70/18.96 tff(16027,plain,
% 28.70/18.96 (f3(c1, c2) = f3(c1, f1(f5(c2), f5(c1)))),
% 28.70/18.96 inference(monotonicity,[status(thm)],[16026])).
% 28.70/18.96 tff(16028,plain,
% 28.70/18.96 (f3(c1, f1(f5(c2), f5(c1))) = f3(c1, c2)),
% 28.70/18.96 inference(symmetry,[status(thm)],[16027])).
% 28.70/18.96 tff(16029,plain,
% 28.70/18.96 ((f3(c1, f1(f5(c2), f5(c1))) = c2) <=> (f3(c1, c2) = c2)),
% 28.70/18.96 inference(monotonicity,[status(thm)],[16028])).
% 28.70/18.96 tff(16030,plain,
% 28.70/18.96 ((f3(c1, c2) = c2) <=> (f3(c1, f1(f5(c2), f5(c1))) = c2)),
% 28.70/18.96 inference(symmetry,[status(thm)],[16029])).
% 28.70/18.96 tff(16031,plain,
% 28.70/18.96 ((f3(c1, c2) = c2) <=> (f3(c1, f1(f5(c2), f5(c1))) = c4)),
% 28.70/18.96 inference(transitivity,[status(thm)],[16030, 16011])).
% 28.70/18.96 tff(16032,plain,
% 28.70/18.96 ((~(f3(c1, c2) = c2)) <=> (~(f3(c1, f1(f5(c2), f5(c1))) = c4))),
% 28.70/18.96 inference(monotonicity,[status(thm)],[16031])).
% 28.70/18.96 tff(16033,plain,
% 28.70/18.96 (~(f3(c1, f1(f5(c2), f5(c1))) = c4)),
% 28.70/18.96 inference(modus_ponens,[status(thm)],[12777, 16032])).
% 28.70/18.96 tff(16034,plain,
% 28.70/18.96 ((c1 = f3(c1, f1(f5(c2), f5(c1)))) <=> (f3(c1, f1(f5(c2), f5(c1))) = c1)),
% 28.70/18.96 inference(commutativity,[status(thm)],[])).
% 28.70/18.96 tff(16035,plain,
% 28.70/18.96 ((c1 = f3(c1, c2)) <=> (c1 = f3(c1, f1(f5(c2), f5(c1))))),
% 28.70/18.96 inference(monotonicity,[status(thm)],[16027])).
% 28.70/18.96 tff(16036,plain,
% 28.70/18.96 ((c1 = f3(c1, c2)) <=> (f3(c1, f1(f5(c2), f5(c1))) = c1)),
% 28.70/18.96 inference(transitivity,[status(thm)],[16035, 16034])).
% 28.70/18.96 tff(16037,plain,
% 28.70/18.96 (f5(f7(c1)) = f5(c2)),
% 28.70/18.96 inference(monotonicity,[status(thm)],[347])).
% 28.70/18.96 tff(16038,plain,
% 28.70/18.96 ((f7(c1) = f5(f7(c1))) <=> (c2 = f5(c2))),
% 28.70/18.96 inference(monotonicity,[status(thm)],[347, 16037])).
% 28.70/18.96 tff(16039,plain,
% 28.70/18.96 ((c2 = f5(c2)) <=> (f7(c1) = f5(f7(c1)))),
% 28.70/18.96 inference(symmetry,[status(thm)],[16038])).
% 28.70/18.96 tff(16040,plain,
% 28.70/18.96 (f7(c1) = f5(f7(c1))),
% 28.70/18.96 inference(modus_ponens,[status(thm)],[9020, 16039])).
% 28.70/18.96 tff(16041,assumption,(~(c1 = f3(c1, c2))), introduced(assumption)).
% 28.70/18.96 tff(16042,assumption,(f7(c1) = f5(f7(c1))), introduced(assumption)).
% 28.70/18.96 tff(16043,plain,
% 28.70/18.96 (f5(f7(c1)) = f7(c1)),
% 28.70/18.96 inference(symmetry,[status(thm)],[16042])).
% 28.70/18.96 tff(16044,plain,
% 28.70/18.96 (f5(c2) = f5(f7(c1))),
% 28.70/18.96 inference(monotonicity,[status(thm)],[354])).
% 28.70/18.96 tff(16045,plain,
% 28.70/18.96 (f5(c2) = f7(c1)),
% 28.70/18.96 inference(transitivity,[status(thm)],[16044, 16043])).
% 28.70/18.96 tff(16046,plain,
% 28.70/18.96 (f1(f5(c2), f5(c1)) = f1(f7(c1), c1)),
% 28.70/18.96 inference(monotonicity,[status(thm)],[16045, 230])).
% 28.70/18.96 tff(16047,plain,
% 28.70/18.96 (f1(f5(c2), f5(c1)) = c1),
% 28.70/18.96 inference(transitivity,[status(thm)],[16046, 989, 11485])).
% 28.70/18.96 tff(16048,plain,
% 28.70/18.96 (f3(f1(f5(c2), f5(c1)), c2) = f3(c1, c2)),
% 28.70/18.96 inference(monotonicity,[status(thm)],[16047])).
% 28.70/18.96 tff(16049,plain,
% 28.70/18.96 ((f3(f1(f5(c2), f5(c1)), c2) = c2) <=> (f3(c1, c2) = c2)),
% 28.70/18.96 inference(monotonicity,[status(thm)],[16048])).
% 28.70/18.96 tff(16050,plain,
% 28.70/18.96 ((f3(c1, c2) = c2) <=> (f3(f1(f5(c2), f5(c1)), c2) = c2)),
% 28.70/18.96 inference(symmetry,[status(thm)],[16049])).
% 28.70/18.96 tff(16051,plain,
% 28.70/18.96 ((~(f3(c1, c2) = c2)) <=> (~(f3(f1(f5(c2), f5(c1)), c2) = c2))),
% 28.70/18.96 inference(monotonicity,[status(thm)],[16050])).
% 28.70/18.96 tff(16052,plain,
% 28.70/18.96 (~(f3(f1(f5(c2), f5(c1)), c2) = c2)),
% 28.70/18.96 inference(modus_ponens,[status(thm)],[12777, 16051])).
% 28.70/18.96 tff(16053,plain,
% 28.70/18.96 ((f3(f1(f5(c2), f5(c1)), c2) = c1) <=> (f3(c1, c2) = c1)),
% 28.70/18.96 inference(monotonicity,[status(thm)],[16048])).
% 28.70/18.96 tff(16054,plain,
% 28.70/18.96 ((f3(f1(f5(c2), f5(c1)), c2) = c1) <=> (c1 = f3(c1, c2))),
% 28.70/18.96 inference(transitivity,[status(thm)],[16053, 13151])).
% 28.70/18.96 tff(16055,plain,
% 28.70/18.96 ((c1 = f3(c1, c2)) <=> (f3(f1(f5(c2), f5(c1)), c2) = c1)),
% 28.70/18.96 inference(symmetry,[status(thm)],[16054])).
% 28.70/18.96 tff(16056,plain,
% 28.70/18.96 ((~(c1 = f3(c1, c2))) <=> (~(f3(f1(f5(c2), f5(c1)), c2) = c1))),
% 28.70/18.96 inference(monotonicity,[status(thm)],[16055])).
% 28.70/18.96 tff(16057,plain,
% 28.70/18.96 (~(f3(f1(f5(c2), f5(c1)), c2) = c1)),
% 28.70/18.96 inference(modus_ponens,[status(thm)],[16041, 16056])).
% 28.70/18.96 tff(16058,plain,
% 28.70/18.96 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f3(f1(f5(c2), f5(c1)), c2) = c1) | (f3(f1(f5(c2), f5(c1)), c2) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f3(f1(f5(c2), f5(c1)), c2) = c1) | (f3(f1(f5(c2), f5(c1)), c2) = c2))),
% 28.70/18.96 inference(rewrite,[status(thm)],[])).
% 28.70/18.96 tff(16059,plain,
% 28.70/18.96 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f3(f1(f5(c2), f5(c1)), c2) = c1) | (f3(f1(f5(c2), f5(c1)), c2) = c2))),
% 28.70/18.96 inference(quant_inst,[status(thm)],[])).
% 28.70/18.96 tff(16060,plain,
% 28.70/18.96 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f3(f1(f5(c2), f5(c1)), c2) = c1) | (f3(f1(f5(c2), f5(c1)), c2) = c2)),
% 28.70/18.96 inference(modus_ponens,[status(thm)],[16059, 16058])).
% 28.70/18.96 tff(16061,plain,
% 28.70/18.96 ((f3(f1(f5(c2), f5(c1)), c2) = c1) | (f3(f1(f5(c2), f5(c1)), c2) = c2)),
% 28.70/18.96 inference(unit_resolution,[status(thm)],[16060, 10])).
% 28.70/18.96 tff(16062,plain,
% 28.70/18.96 ($false),
% 28.70/18.96 inference(unit_resolution,[status(thm)],[16061, 16057, 16052])).
% 28.70/18.96 tff(16063,plain,((~(f5(c1) = c1)) | (c1 = f3(c1, c2)) | (~(f1(c2, c1) = c1)) | (~(f7(c1) = c2)) | (~(f7(c1) = f5(f7(c1)))) | (f3(c1, c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 28.70/18.96 tff(16064,plain,
% 28.70/18.96 (~(f1(c2, c1) = c1)),
% 28.70/18.96 inference(unit_resolution,[status(thm)],[16063, 16041, 230, 347, 12777, 16040])).
% 28.70/18.96 tff(16065,plain,
% 28.70/18.96 (f1(c2, c1) = c2),
% 28.70/18.96 inference(unit_resolution,[status(thm)],[10113, 16064])).
% 28.70/18.96 tff(16066,plain,
% 28.70/18.96 (f5(f10(c1)) = c2),
% 28.70/18.96 inference(transitivity,[status(thm)],[16012, 8109])).
% 28.70/18.96 tff(16067,plain,
% 28.70/18.96 (f1(f5(f10(c1)), c1) = f1(c2, c1)),
% 28.70/18.96 inference(monotonicity,[status(thm)],[16066])).
% 28.70/18.96 tff(16068,plain,
% 28.70/18.96 (f1(f5(c2), f5(c1)) = c2),
% 28.70/18.96 inference(transitivity,[status(thm)],[16014, 16067, 16065])).
% 28.70/18.96 tff(16069,plain,
% 28.70/18.96 (f3(c1, f1(f5(c2), f5(c1))) = f3(c1, c2)),
% 28.70/18.96 inference(monotonicity,[status(thm)],[16068])).
% 28.70/18.96 tff(16070,plain,
% 28.70/18.96 ((f3(c1, f1(f5(c2), f5(c1))) = c1) <=> (f3(c1, c2) = c1)),
% 28.70/18.96 inference(monotonicity,[status(thm)],[16069])).
% 28.70/18.96 tff(16071,plain,
% 28.70/18.96 ((f3(c1, f1(f5(c2), f5(c1))) = c1) <=> (c1 = f3(c1, c2))),
% 28.70/18.96 inference(transitivity,[status(thm)],[16070, 13151])).
% 28.70/18.96 tff(16072,plain,
% 28.70/18.96 ((c1 = f3(c1, c2)) <=> (f3(c1, f1(f5(c2), f5(c1))) = c1)),
% 28.70/18.96 inference(symmetry,[status(thm)],[16071])).
% 28.70/18.96 tff(16073,plain,
% 28.70/18.96 ((~(c1 = f3(c1, c2))) <=> (~(f3(c1, f1(f5(c2), f5(c1))) = c1))),
% 28.70/18.96 inference(monotonicity,[status(thm)],[16072])).
% 28.70/18.96 tff(16074,plain,
% 28.70/18.96 (~(f3(c1, f1(f5(c2), f5(c1))) = c1)),
% 28.70/18.96 inference(modus_ponens,[status(thm)],[16041, 16073])).
% 28.70/18.96 tff(16075,plain,
% 28.70/18.96 ((f3(c1, f1(f5(c2), f5(c1))) = c2) <=> (f3(c1, c2) = c2)),
% 28.70/18.96 inference(monotonicity,[status(thm)],[16069])).
% 28.70/18.96 tff(16076,plain,
% 28.70/18.96 ((f3(c1, c2) = c2) <=> (f3(c1, f1(f5(c2), f5(c1))) = c2)),
% 28.70/18.96 inference(symmetry,[status(thm)],[16075])).
% 28.70/18.96 tff(16077,plain,
% 28.70/18.96 ((~(f3(c1, c2) = c2)) <=> (~(f3(c1, f1(f5(c2), f5(c1))) = c2))),
% 28.70/18.96 inference(monotonicity,[status(thm)],[16076])).
% 28.70/18.96 tff(16078,plain,
% 28.70/18.96 (~(f3(c1, f1(f5(c2), f5(c1))) = c2)),
% 28.70/18.96 inference(modus_ponens,[status(thm)],[12777, 16077])).
% 28.70/18.96 tff(16079,plain,
% 28.70/18.96 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f3(c1, f1(f5(c2), f5(c1))) = c1) | (f3(c1, f1(f5(c2), f5(c1))) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f3(c1, f1(f5(c2), f5(c1))) = c1) | (f3(c1, f1(f5(c2), f5(c1))) = c2))),
% 28.70/18.96 inference(rewrite,[status(thm)],[])).
% 28.70/18.96 tff(16080,plain,
% 28.70/18.96 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f3(c1, f1(f5(c2), f5(c1))) = c1) | (f3(c1, f1(f5(c2), f5(c1))) = c2))),
% 28.70/18.96 inference(quant_inst,[status(thm)],[])).
% 28.70/18.96 tff(16081,plain,
% 28.70/18.96 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f3(c1, f1(f5(c2), f5(c1))) = c1) | (f3(c1, f1(f5(c2), f5(c1))) = c2)),
% 28.70/18.96 inference(modus_ponens,[status(thm)],[16080, 16079])).
% 28.70/18.96 tff(16082,plain,
% 28.70/18.96 ((f3(c1, f1(f5(c2), f5(c1))) = c1) | (f3(c1, f1(f5(c2), f5(c1))) = c2)),
% 28.70/18.96 inference(unit_resolution,[status(thm)],[16081, 10])).
% 28.70/18.96 tff(16083,plain,
% 28.70/18.96 ($false),
% 28.70/18.96 inference(unit_resolution,[status(thm)],[16082, 16078, 16074])).
% 28.70/18.96 tff(16084,plain,((c1 = f3(c1, c2)) | (f3(c1, c2) = c2) | (~(f5(c2) = c2)) | (~(f10(c1) = c2)) | (~(f5(c1) = c1)) | (~(f7(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.70/18.96 tff(16085,plain,
% 28.70/18.96 (c1 = f3(c1, c2)),
% 28.70/18.96 inference(unit_resolution,[status(thm)],[16084, 16018, 12777, 16, 230, 347])).
% 28.70/18.96 tff(16086,plain,
% 28.70/18.96 (f3(c1, f1(f5(c2), f5(c1))) = c1),
% 28.70/18.96 inference(modus_ponens,[status(thm)],[16085, 16036])).
% 28.70/18.96 tff(16087,plain,
% 28.70/18.96 (f3(f3(c1, f1(f5(c2), f5(c1))), c2) = f3(c1, c2)),
% 28.70/18.96 inference(monotonicity,[status(thm)],[16086])).
% 28.70/18.96 tff(16088,plain,
% 28.70/18.96 (f3(f3(c1, f1(f5(c2), f5(c1))), c2) = f7(c2)),
% 28.70/18.96 inference(transitivity,[status(thm)],[16087, 16027, 16086, 125])).
% 28.70/18.96 tff(16089,plain,
% 28.70/18.96 ((f3(f3(c1, f1(f5(c2), f5(c1))), c2) = c2) <=> (f7(c2) = c2)),
% 28.70/18.96 inference(monotonicity,[status(thm)],[16088])).
% 28.70/18.96 tff(16090,plain,
% 28.70/18.96 ((f7(c2) = c2) <=> (f3(f3(c1, f1(f5(c2), f5(c1))), c2) = c2)),
% 28.70/18.96 inference(symmetry,[status(thm)],[16089])).
% 28.70/18.96 tff(16091,plain,
% 28.70/18.96 ((~(f7(c2) = c2)) <=> (~(f3(f3(c1, f1(f5(c2), f5(c1))), c2) = c2))),
% 28.70/18.96 inference(monotonicity,[status(thm)],[16090])).
% 28.70/18.96 tff(16092,plain,
% 28.70/18.96 (~(f3(f3(c1, f1(f5(c2), f5(c1))), c2) = c2)),
% 28.70/18.96 inference(modus_ponens,[status(thm)],[17, 16091])).
% 28.70/18.96 tff(16093,plain,
% 28.70/18.96 (f3(c1, f1(f5(c2), f5(c1))) = f7(c2)),
% 28.70/18.96 inference(transitivity,[status(thm)],[16086, 125])).
% 28.70/18.96 tff(16094,plain,
% 28.70/18.96 (big_f(f3(f3(c1, f1(f5(c2), f5(c1))), c2), f3(c1, f1(f5(c2), f5(c1)))) <=> big_f(f7(c2), f7(c2))),
% 28.70/18.96 inference(monotonicity,[status(thm)],[16088, 16093])).
% 28.70/18.96 tff(16095,plain,
% 28.70/18.96 (big_f(f7(c2), f7(c2)) <=> big_f(f3(f3(c1, f1(f5(c2), f5(c1))), c2), f3(c1, f1(f5(c2), f5(c1))))),
% 28.70/18.96 inference(symmetry,[status(thm)],[16094])).
% 28.70/18.96 tff(16096,plain,
% 28.70/18.96 ((~big_f(f7(c2), f7(c2))) <=> (~big_f(f3(f3(c1, f1(f5(c2), f5(c1))), c2), f3(c1, f1(f5(c2), f5(c1)))))),
% 28.70/18.96 inference(monotonicity,[status(thm)],[16095])).
% 28.70/18.96 tff(16097,plain,
% 28.70/18.96 (~big_f(f3(f3(c1, f1(f5(c2), f5(c1))), c2), f3(c1, f1(f5(c2), f5(c1))))),
% 28.70/18.96 inference(modus_ponens,[status(thm)],[8218, 16096])).
% 28.70/18.96 tff(16098,plain,
% 28.70/18.96 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | (f3(c1, f1(f5(c2), f5(c1))) = c4) | (f3(f3(c1, f1(f5(c2), f5(c1))), c2) = c2) | big_f(f3(f3(c1, f1(f5(c2), f5(c1))), c2), f3(c1, f1(f5(c2), f5(c1)))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | (f3(c1, f1(f5(c2), f5(c1))) = c4) | (f3(f3(c1, f1(f5(c2), f5(c1))), c2) = c2) | big_f(f3(f3(c1, f1(f5(c2), f5(c1))), c2), f3(c1, f1(f5(c2), f5(c1)))))),
% 28.70/18.96 inference(rewrite,[status(thm)],[])).
% 28.70/18.96 tff(16099,plain,
% 28.70/18.96 (((f3(c1, f1(f5(c2), f5(c1))) = c4) | (f3(f3(c1, f1(f5(c2), f5(c1))), c2) = c2) | big_f(f3(f3(c1, f1(f5(c2), f5(c1))), c2), f3(c1, f1(f5(c2), f5(c1)))) | (c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1))) <=> ((c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | (f3(c1, f1(f5(c2), f5(c1))) = c4) | (f3(f3(c1, f1(f5(c2), f5(c1))), c2) = c2) | big_f(f3(f3(c1, f1(f5(c2), f5(c1))), c2), f3(c1, f1(f5(c2), f5(c1)))))),
% 28.70/18.96 inference(rewrite,[status(thm)],[])).
% 28.70/18.96 tff(16100,plain,
% 28.70/18.96 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f3(c1, f1(f5(c2), f5(c1))) = c4) | (f3(f3(c1, f1(f5(c2), f5(c1))), c2) = c2) | big_f(f3(f3(c1, f1(f5(c2), f5(c1))), c2), f3(c1, f1(f5(c2), f5(c1)))) | (c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | (f3(c1, f1(f5(c2), f5(c1))) = c4) | (f3(f3(c1, f1(f5(c2), f5(c1))), c2) = c2) | big_f(f3(f3(c1, f1(f5(c2), f5(c1))), c2), f3(c1, f1(f5(c2), f5(c1))))))),
% 28.70/18.97 inference(monotonicity,[status(thm)],[16099])).
% 28.70/18.97 tff(16101,plain,
% 28.70/18.97 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f3(c1, f1(f5(c2), f5(c1))) = c4) | (f3(f3(c1, f1(f5(c2), f5(c1))), c2) = c2) | big_f(f3(f3(c1, f1(f5(c2), f5(c1))), c2), f3(c1, f1(f5(c2), f5(c1)))) | (c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | (f3(c1, f1(f5(c2), f5(c1))) = c4) | (f3(f3(c1, f1(f5(c2), f5(c1))), c2) = c2) | big_f(f3(f3(c1, f1(f5(c2), f5(c1))), c2), f3(c1, f1(f5(c2), f5(c1)))))),
% 28.70/18.97 inference(transitivity,[status(thm)],[16100, 16098])).
% 28.70/18.97 tff(16102,plain,
% 28.70/18.97 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f3(c1, f1(f5(c2), f5(c1))) = c4) | (f3(f3(c1, f1(f5(c2), f5(c1))), c2) = c2) | big_f(f3(f3(c1, f1(f5(c2), f5(c1))), c2), f3(c1, f1(f5(c2), f5(c1)))) | (c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)))),
% 28.70/18.97 inference(quant_inst,[status(thm)],[])).
% 28.70/18.97 tff(16103,plain,
% 28.70/18.97 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | (f3(c1, f1(f5(c2), f5(c1))) = c4) | (f3(f3(c1, f1(f5(c2), f5(c1))), c2) = c2) | big_f(f3(f3(c1, f1(f5(c2), f5(c1))), c2), f3(c1, f1(f5(c2), f5(c1))))),
% 28.70/18.97 inference(modus_ponens,[status(thm)],[16102, 16101])).
% 28.70/18.97 tff(16104,plain,
% 28.70/18.97 ((c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | (f3(c1, f1(f5(c2), f5(c1))) = c4) | (f3(f3(c1, f1(f5(c2), f5(c1))), c2) = c2) | big_f(f3(f3(c1, f1(f5(c2), f5(c1))), c2), f3(c1, f1(f5(c2), f5(c1))))),
% 28.70/18.97 inference(unit_resolution,[status(thm)],[16103, 1014])).
% 28.70/18.97 tff(16105,plain,
% 28.70/18.97 ($false),
% 28.70/18.97 inference(unit_resolution,[status(thm)],[16104, 16097, 16092, 377, 13410, 16033, 12187])).
% 28.70/18.97 tff(16106,plain,(big_f(f7(c2), f7(c2)) | (c2 = c3) | (f1(c2, c1) = c1) | (~(f10(c1) = c2)) | (~(f5(c1) = c1)) | (f7(c2) = c2) | (f3(c1, c2) = c2) | (~(c2 = c4)) | (~(f7(c1) = c2)) | (~(f10(c2) = c2)) | big_f(c2, c2) | (~big_f(f7(c2), c2))), inference(lemma,lemma(discharge,[]))).
% 28.70/18.97 tff(16107,plain,
% 28.70/18.97 (f3(c1, c2) = c2),
% 28.70/18.97 inference(unit_resolution,[status(thm)],[16106, 12187, 16009, 16, 230, 17, 377, 631, 347, 122, 121, 1180])).
% 28.70/18.97 tff(16108,plain,
% 28.70/18.97 (f3(c1, f7(c1)) = f3(c1, c2)),
% 28.70/18.97 inference(monotonicity,[status(thm)],[347])).
% 28.70/18.97 tff(16109,plain,
% 28.70/18.97 (big_f(f3(c1, f7(c1)), c1) <=> big_f(f3(c1, c2), c1)),
% 28.70/18.97 inference(monotonicity,[status(thm)],[16108])).
% 28.70/18.97 tff(16110,plain,
% 28.70/18.97 (big_f(f3(c1, c2), c1) <=> big_f(f3(c1, f7(c1)), c1)),
% 28.70/18.97 inference(symmetry,[status(thm)],[16109])).
% 28.70/18.97 tff(16111,assumption,(f3(c1, c2) = c2), introduced(assumption)).
% 28.70/18.97 tff(16112,plain,
% 28.70/18.97 (f3(c1, c2) = f7(c1)),
% 28.70/18.97 inference(transitivity,[status(thm)],[16111, 354])).
% 28.70/18.97 tff(16113,plain,
% 28.70/18.97 (big_f(f3(c1, c2), c1) <=> big_f(f7(c1), c1)),
% 28.70/18.97 inference(monotonicity,[status(thm)],[16112])).
% 28.70/18.97 tff(16114,plain,
% 28.70/18.97 (big_f(f7(c1), c1) <=> big_f(f3(c1, c2), c1)),
% 28.70/18.97 inference(symmetry,[status(thm)],[16113])).
% 28.70/18.97 tff(16115,plain,
% 28.70/18.97 (big_f(f7(c1), c1) <=> big_f(f3(c1, f7(c1)), c1)),
% 28.70/18.97 inference(transitivity,[status(thm)],[16114, 16110])).
% 28.70/18.97 tff(16116,plain,
% 28.70/18.97 (big_f(f3(c1, f7(c1)), c1)),
% 28.70/18.97 inference(modus_ponens,[status(thm)],[15735, 16115])).
% 28.70/18.97 tff(16117,plain,
% 28.70/18.97 ((f3(c1, f7(c1)) = f7(c1)) <=> (f3(c1, c2) = c2)),
% 28.70/18.97 inference(monotonicity,[status(thm)],[16108, 347])).
% 28.70/18.97 tff(16118,plain,
% 28.70/18.97 ((f3(c1, c2) = c2) <=> (f3(c1, f7(c1)) = f7(c1))),
% 28.70/18.97 inference(symmetry,[status(thm)],[16117])).
% 28.70/18.97 tff(16119,plain,
% 28.70/18.97 (f3(c1, f7(c1)) = f7(c1)),
% 28.70/18.97 inference(modus_ponens,[status(thm)],[16111, 16118])).
% 28.70/18.97 tff(16120,plain,
% 28.70/18.97 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c1 = c4) | (f7(c1) = c3) | (f1(f7(c1), c1) = c1) | big_f(f7(c1), f1(f7(c1), c1)) | (~(f3(c1, f7(c1)) = f7(c1))) | (~big_f(f3(c1, f7(c1)), c1)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c1 = c4) | (f7(c1) = c3) | (f1(f7(c1), c1) = c1) | big_f(f7(c1), f1(f7(c1), c1)) | (~(f3(c1, f7(c1)) = f7(c1))) | (~big_f(f3(c1, f7(c1)), c1)))),
% 28.70/18.97 inference(rewrite,[status(thm)],[])).
% 28.70/18.97 tff(16121,plain,
% 28.70/18.97 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c1 = c4) | (f7(c1) = c3) | (f1(f7(c1), c1) = c1) | big_f(f7(c1), f1(f7(c1), c1)) | (~(f3(c1, f7(c1)) = f7(c1))) | (~big_f(f3(c1, f7(c1)), c1)))),
% 28.70/18.97 inference(quant_inst,[status(thm)],[])).
% 28.70/18.97 tff(16122,plain,
% 28.70/18.97 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c1 = c4) | (f7(c1) = c3) | (f1(f7(c1), c1) = c1) | big_f(f7(c1), f1(f7(c1), c1)) | (~(f3(c1, f7(c1)) = f7(c1))) | (~big_f(f3(c1, f7(c1)), c1))),
% 28.70/18.97 inference(modus_ponens,[status(thm)],[16121, 16120])).
% 28.70/18.97 tff(16123,plain,
% 28.70/18.97 ($false),
% 28.70/18.97 inference(unit_resolution,[status(thm)],[16122, 969, 482, 12165, 12203, 12204, 16119, 16116])).
% 28.70/18.97 tff(16124,plain,((~(f3(c1, c2) = c2)) | (c1 = c4) | (f7(c1) = c3) | (f1(f7(c1), c1) = c1) | big_f(f7(c1), f1(f7(c1), c1)) | (~big_f(f7(c1), c1)) | (~(f7(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.70/18.97 tff(16125,plain,
% 28.70/18.97 ($false),
% 28.70/18.97 inference(unit_resolution,[status(thm)],[16124, 16107, 16008, 1004, 16003, 12198, 15735, 347])).
% 28.70/18.97 tff(16126,plain,((f1(c2, c1) = c1) | (~big_f(f7(c1), c1)) | (~(f7(c1) = c2)) | big_f(c2, c2) | (~(f10(c1) = c2)) | (~(f5(c1) = c1)) | (f7(c2) = c2) | (c2 = c3) | (~(c2 = c4)) | (~(f10(c2) = c2)) | (~big_f(f7(c2), c2))), inference(lemma,lemma(discharge,[]))).
% 28.70/18.97 tff(16127,plain,
% 28.70/18.97 (f1(c2, c1) = c1),
% 28.70/18.97 inference(unit_resolution,[status(thm)],[16126, 377, 347, 121, 16, 230, 17, 15996, 15998, 122, 12167])).
% 28.70/18.97 tff(16128,plain,
% 28.70/18.97 (c4 = c2),
% 28.70/18.97 inference(symmetry,[status(thm)],[15998])).
% 28.70/18.97 tff(16129,plain,
% 28.70/18.97 ((f7(c2) = c4) <=> (f7(c2) = c2)),
% 28.70/18.97 inference(monotonicity,[status(thm)],[16128])).
% 28.70/18.97 tff(16130,plain,
% 28.70/18.97 ((f7(c2) = c2) <=> (f7(c2) = c4)),
% 28.70/18.97 inference(symmetry,[status(thm)],[16129])).
% 28.70/18.97 tff(16131,plain,
% 28.70/18.97 ((f7(c2) = c2) <=> (c1 = c4)),
% 28.70/18.97 inference(transitivity,[status(thm)],[16130, 12587])).
% 28.70/18.97 tff(16132,plain,
% 28.70/18.97 ((~(f7(c2) = c2)) <=> (~(c1 = c4))),
% 28.70/18.97 inference(monotonicity,[status(thm)],[16131])).
% 28.70/18.97 tff(16133,plain,
% 28.70/18.97 (~(c1 = c4)),
% 28.70/18.97 inference(modus_ponens,[status(thm)],[17, 16132])).
% 28.70/18.97 tff(16134,plain,
% 28.70/18.97 (c1 = f1(c2, c1)),
% 28.70/18.97 inference(symmetry,[status(thm)],[16127])).
% 28.70/18.97 tff(16135,plain,
% 28.70/18.97 (f7(c2) = f1(c2, c1)),
% 28.70/18.97 inference(transitivity,[status(thm)],[22, 16134])).
% 28.70/18.97 tff(16136,plain,
% 28.70/18.97 (big_f(c2, f7(c2)) <=> big_f(c2, f1(c2, c1))),
% 28.70/18.97 inference(monotonicity,[status(thm)],[16135])).
% 28.70/18.97 tff(16137,plain,
% 28.70/18.97 (big_f(c2, f1(c2, c1))),
% 28.70/18.97 inference(modus_ponens,[status(thm)],[15741, 16136])).
% 28.70/18.97 tff(16138,plain,
% 28.70/18.97 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (c1 = c4) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (c1 = c4) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1)))),
% 28.70/18.97 inference(rewrite,[status(thm)],[])).
% 28.70/18.97 tff(16139,plain,
% 28.70/18.97 (((c1 = c4) | (f3(c1, c2) = c2) | big_f(f3(c1, c2), c1) | (c2 = c3) | (~(f1(c2, c1) = c1)) | (~big_f(c2, f1(c2, c1)))) <=> ((c2 = c3) | (c1 = c4) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1)))),
% 28.70/18.97 inference(rewrite,[status(thm)],[])).
% 28.70/18.97 tff(16140,plain,
% 28.70/18.97 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c4) | (f3(c1, c2) = c2) | big_f(f3(c1, c2), c1) | (c2 = c3) | (~(f1(c2, c1) = c1)) | (~big_f(c2, f1(c2, c1))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (c1 = c4) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1))))),
% 28.70/18.97 inference(monotonicity,[status(thm)],[16139])).
% 28.70/18.97 tff(16141,plain,
% 28.70/18.97 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c4) | (f3(c1, c2) = c2) | big_f(f3(c1, c2), c1) | (c2 = c3) | (~(f1(c2, c1) = c1)) | (~big_f(c2, f1(c2, c1))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (c1 = c4) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1)))),
% 28.70/18.97 inference(transitivity,[status(thm)],[16140, 16138])).
% 28.70/18.97 tff(16142,plain,
% 28.70/18.97 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c4) | (f3(c1, c2) = c2) | big_f(f3(c1, c2), c1) | (c2 = c3) | (~(f1(c2, c1) = c1)) | (~big_f(c2, f1(c2, c1))))),
% 28.70/18.97 inference(quant_inst,[status(thm)],[])).
% 28.70/18.97 tff(16143,plain,
% 28.70/18.97 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (c1 = c4) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1))),
% 28.70/18.97 inference(modus_ponens,[status(thm)],[16142, 16141])).
% 28.70/18.97 tff(16144,plain,
% 28.70/18.97 ((c2 = c3) | (c1 = c4) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1))),
% 28.70/18.97 inference(unit_resolution,[status(thm)],[16143, 904])).
% 28.70/18.97 tff(16145,plain,
% 28.70/18.97 (f3(c1, c2) = c2),
% 28.70/18.97 inference(unit_resolution,[status(thm)],[16144, 13164, 377, 11485, 11484, 482])).
% 28.70/18.97 tff(16146,plain,
% 28.70/18.97 (f3(c1, c2) = f7(c1)),
% 28.70/18.97 inference(transitivity,[status(thm)],[16145, 354])).
% 28.70/18.97 tff(16147,plain,
% 28.70/18.97 (big_f(f3(c1, c2), c1) <=> big_f(f7(c1), c1)),
% 28.70/18.97 inference(monotonicity,[status(thm)],[16146])).
% 28.70/18.97 tff(16148,plain,
% 28.70/18.97 (big_f(f7(c1), c1) <=> big_f(f3(c1, c2), c1)),
% 28.70/18.97 inference(symmetry,[status(thm)],[16147])).
% 28.70/18.97 tff(16149,plain,
% 28.70/18.97 (big_f(f3(c1, c2), c1)),
% 28.70/18.97 inference(modus_ponens,[status(thm)],[15735, 16148])).
% 28.70/18.97 tff(16150,plain,
% 28.70/18.97 ($false),
% 28.70/18.97 inference(unit_resolution,[status(thm)],[13164, 16149])).
% 28.70/18.97 tff(16151,plain,(big_f(f3(c1, c2), c1) | (~big_f(f7(c1), c1)) | (~(f7(c1) = c2)) | (c2 = c3) | (~(f1(c2, c1) = c1)) | (~big_f(c2, f1(c2, c1))) | (c1 = c4)), inference(lemma,lemma(discharge,[]))).
% 28.70/18.97 tff(16152,plain,
% 28.70/18.97 (big_f(f3(c1, c2), c1)),
% 28.70/18.97 inference(unit_resolution,[status(thm)],[16151, 16137, 347, 16133, 377, 16127, 15996])).
% 28.70/18.97 tff(16153,plain,
% 28.70/18.97 (~(big_f(c1, c1) <=> big_f(f3(c1, c2), c1))),
% 28.70/18.97 inference(unit_resolution,[status(thm)],[13186, 16152, 15991])).
% 28.79/18.97 tff(16154,plain,
% 28.79/18.97 (~(c1 = f3(c1, c2))),
% 28.79/18.97 inference(unit_resolution,[status(thm)],[13192, 16153])).
% 28.79/18.97 tff(16155,plain,
% 28.79/18.97 (f3(c1, c2) = c2),
% 28.79/18.97 inference(unit_resolution,[status(thm)],[16084, 16154, 15988, 16, 230, 347])).
% 28.79/18.97 tff(16156,plain,
% 28.79/18.97 (f3(f7(c2), c2) = f3(c1, c2)),
% 28.79/18.97 inference(monotonicity,[status(thm)],[22])).
% 28.79/18.97 tff(16157,plain,
% 28.79/18.97 (f3(f7(c2), c2) = c2),
% 28.79/18.97 inference(transitivity,[status(thm)],[16156, 16155])).
% 28.79/18.97 tff(16158,plain,
% 28.79/18.97 (big_f(f3(f7(c2), c2), f7(c2)) <=> big_f(c2, f7(c2))),
% 28.79/18.97 inference(monotonicity,[status(thm)],[16157])).
% 28.79/18.97 tff(16159,plain,
% 28.79/18.97 (big_f(c2, f7(c2)) <=> big_f(f3(f7(c2), c2), f7(c2))),
% 28.79/18.97 inference(symmetry,[status(thm)],[16158])).
% 28.79/18.97 tff(16160,plain,
% 28.79/18.97 (big_f(f3(f7(c2), c2), f7(c2))),
% 28.79/18.97 inference(modus_ponens,[status(thm)],[15741, 16159])).
% 28.79/18.97 tff(16161,plain,
% 28.79/18.97 ((~(f7(c2) = c2)) <=> (~(f7(c2) = c4))),
% 28.79/18.97 inference(monotonicity,[status(thm)],[16130])).
% 28.79/18.97 tff(16162,plain,
% 28.79/18.97 (~(f7(c2) = c4)),
% 28.79/18.97 inference(modus_ponens,[status(thm)],[17, 16161])).
% 28.79/18.97 tff(16163,plain,
% 28.79/18.97 (big_f(c2, f7(c2)) <=> big_f(c2, f1(c2, f7(c2)))),
% 28.79/18.97 inference(transitivity,[status(thm)],[16136, 8768])).
% 28.79/18.97 tff(16164,plain,
% 28.79/18.97 (big_f(c2, f1(c2, f7(c2)))),
% 28.79/18.97 inference(modus_ponens,[status(thm)],[15741, 16163])).
% 28.79/18.97 tff(16165,plain,
% 28.79/18.97 (f1(c2, f7(c2)) = f7(c2)),
% 28.79/18.97 inference(modus_ponens,[status(thm)],[16127, 8793])).
% 28.79/18.97 tff(16166,plain,
% 28.79/18.97 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~big_f(c2, f1(c2, f7(c2)))) | (~(f1(c2, f7(c2)) = f7(c2))) | (f7(c2) = c4) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~big_f(c2, f1(c2, f7(c2)))) | (~(f1(c2, f7(c2)) = f7(c2))) | (f7(c2) = c4) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2))))),
% 28.79/18.97 inference(rewrite,[status(thm)],[])).
% 28.79/18.97 tff(16167,plain,
% 28.79/18.97 (((f7(c2) = c4) | (c2 = c3) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2))) | (~(f1(c2, f7(c2)) = f7(c2))) | (~big_f(c2, f1(c2, f7(c2))))) <=> ((c2 = c3) | (~big_f(c2, f1(c2, f7(c2)))) | (~(f1(c2, f7(c2)) = f7(c2))) | (f7(c2) = c4) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2))))),
% 28.79/18.97 inference(rewrite,[status(thm)],[])).
% 28.79/18.97 tff(16168,plain,
% 28.79/18.97 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c2) = c4) | (c2 = c3) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2))) | (~(f1(c2, f7(c2)) = f7(c2))) | (~big_f(c2, f1(c2, f7(c2)))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~big_f(c2, f1(c2, f7(c2)))) | (~(f1(c2, f7(c2)) = f7(c2))) | (f7(c2) = c4) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2)))))),
% 28.79/18.97 inference(monotonicity,[status(thm)],[16167])).
% 28.79/18.97 tff(16169,plain,
% 28.79/18.97 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c2) = c4) | (c2 = c3) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2))) | (~(f1(c2, f7(c2)) = f7(c2))) | (~big_f(c2, f1(c2, f7(c2)))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~big_f(c2, f1(c2, f7(c2)))) | (~(f1(c2, f7(c2)) = f7(c2))) | (f7(c2) = c4) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2))))),
% 28.79/18.97 inference(transitivity,[status(thm)],[16168, 16166])).
% 28.79/18.97 tff(16170,plain,
% 28.79/18.97 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c2) = c4) | (c2 = c3) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2))) | (~(f1(c2, f7(c2)) = f7(c2))) | (~big_f(c2, f1(c2, f7(c2)))))),
% 28.79/18.97 inference(quant_inst,[status(thm)],[])).
% 28.79/18.97 tff(16171,plain,
% 28.79/18.97 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~big_f(c2, f1(c2, f7(c2)))) | (~(f1(c2, f7(c2)) = f7(c2))) | (f7(c2) = c4) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2)))),
% 28.79/18.97 inference(modus_ponens,[status(thm)],[16170, 16169])).
% 28.79/18.97 tff(16172,plain,
% 28.79/18.97 ((~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2)))),
% 28.79/18.97 inference(unit_resolution,[status(thm)],[16171, 933, 377, 16165, 16164, 16162])).
% 28.79/18.97 tff(16173,plain,
% 28.79/18.97 ($false),
% 28.79/18.97 inference(unit_resolution,[status(thm)],[16172, 16160, 16157])).
% 28.79/18.97 tff(16174,plain,((c2 = c3) | (~big_f(c2, f7(c2))) | (~(f10(c1) = c2)) | (~(f5(c1) = c1)) | (~(f7(c1) = c2)) | big_f(c2, c2) | (f7(c2) = c2) | (~(f10(c2) = c2)) | (~big_f(c1, c2))), inference(lemma,lemma(discharge,[]))).
% 28.79/18.97 tff(16175,plain,
% 28.79/18.97 (c2 = c3),
% 28.79/18.97 inference(unit_resolution,[status(thm)],[16174, 15947, 15, 15923, 120, 121, 17, 122, 15920])).
% 28.79/18.97 tff(16176,plain,
% 28.79/18.97 (c3 = c2),
% 28.79/18.97 inference(symmetry,[status(thm)],[16175])).
% 28.79/18.97 tff(16177,plain,
% 28.79/18.97 ((f7(c2) = c3) <=> (f7(c2) = c2)),
% 28.79/18.97 inference(monotonicity,[status(thm)],[16176])).
% 28.79/18.97 tff(16178,plain,
% 28.79/18.97 ((f7(c2) = c2) <=> (f7(c2) = c3)),
% 28.79/18.97 inference(symmetry,[status(thm)],[16177])).
% 28.79/18.97 tff(16179,plain,
% 28.79/18.97 ((f7(c2) = c2) <=> (c1 = c3)),
% 28.79/18.97 inference(transitivity,[status(thm)],[16178, 9088])).
% 28.79/18.97 tff(16180,plain,
% 28.79/18.97 ((~(f7(c2) = c2)) <=> (~(c1 = c3))),
% 28.79/18.97 inference(monotonicity,[status(thm)],[16179])).
% 28.79/18.97 tff(16181,plain,
% 28.79/18.97 (~(c1 = c3)),
% 28.79/18.97 inference(modus_ponens,[status(thm)],[17, 16180])).
% 28.79/18.97 tff(16182,plain,
% 28.79/18.97 (~big_f(f7(c2), f7(c2))),
% 28.79/18.97 inference(unit_resolution,[status(thm)],[15961, 15921, 122, 17, 121])).
% 28.79/18.97 tff(16183,plain,
% 28.79/18.97 (~big_f(c1, c1)),
% 28.79/18.97 inference(modus_ponens,[status(thm)],[16182, 15990])).
% 28.79/18.97 tff(16184,plain,
% 28.79/18.97 (f1(f5(c2), f5(c1)) = f1(f5(f10(c1)), c1)),
% 28.79/18.97 inference(monotonicity,[status(thm)],[9933, 15923])).
% 28.79/18.97 tff(16185,plain,
% 28.79/18.97 ((f1(f5(c2), f5(c1)) = c1) <=> (f1(f5(f10(c1)), c1) = c1)),
% 28.79/18.97 inference(monotonicity,[status(thm)],[16184])).
% 28.79/18.97 tff(16186,plain,
% 28.79/18.97 ((f1(f5(f10(c1)), c1) = c1) <=> (f1(f5(c2), f5(c1)) = c1)),
% 28.79/18.97 inference(symmetry,[status(thm)],[16185])).
% 28.79/18.97 tff(16187,plain,
% 28.79/18.97 (~(f7(c2) = f5(c2))),
% 28.79/18.97 inference(unit_resolution,[status(thm)],[15985, 16182, 122, 17, 121, 15921])).
% 28.79/18.97 tff(16188,plain,
% 28.79/18.97 (~(f5(c2) = c1)),
% 28.79/18.97 inference(unit_resolution,[status(thm)],[8394, 16187, 22])).
% 28.79/18.97 tff(16189,plain,
% 28.79/18.97 (f5(c2) = c2),
% 28.79/18.97 inference(unit_resolution,[status(thm)],[1547, 16188])).
% 28.79/18.97 tff(16190,plain,
% 28.79/18.97 (f5(f10(c1)) = c2),
% 28.79/18.97 inference(transitivity,[status(thm)],[9888, 16189])).
% 28.79/18.97 tff(16191,plain,
% 28.79/18.97 (f1(f5(f10(c1)), c1) = f1(c2, f7(c2))),
% 28.79/18.97 inference(monotonicity,[status(thm)],[16190, 125])).
% 28.79/18.97 tff(16192,plain,
% 28.79/18.97 (f1(f5(f10(c1)), c1) = f1(c2, c1)),
% 28.79/18.97 inference(transitivity,[status(thm)],[16191, 8766])).
% 28.79/18.97 tff(16193,plain,
% 28.79/18.97 ((f1(f5(f10(c1)), c1) = c1) <=> (f1(c2, c1) = c1)),
% 28.79/18.97 inference(monotonicity,[status(thm)],[16192])).
% 28.79/18.97 tff(16194,plain,
% 28.79/18.97 ((f1(c2, c1) = c1) <=> (f1(f5(f10(c1)), c1) = c1)),
% 28.79/18.97 inference(symmetry,[status(thm)],[16193])).
% 28.79/18.97 tff(16195,plain,
% 28.79/18.97 ((f1(c2, c1) = c1) <=> (f1(f5(c2), f5(c1)) = c1)),
% 28.79/18.97 inference(transitivity,[status(thm)],[16194, 16186])).
% 28.79/18.97 tff(16196,plain,
% 28.79/18.97 ((~(f7(c2) = c2)) <=> (~(f7(c2) = c3))),
% 28.79/18.97 inference(monotonicity,[status(thm)],[16178])).
% 28.79/18.97 tff(16197,plain,
% 28.79/18.97 (~(f7(c2) = c3)),
% 28.79/18.97 inference(modus_ponens,[status(thm)],[17, 16196])).
% 28.79/18.97 tff(16198,plain,
% 28.79/18.97 ((~big_f(f7(c2), f7(c2))) <=> (~big_f(f7(c2), c1))),
% 28.79/18.97 inference(monotonicity,[status(thm)],[8075])).
% 28.79/18.97 tff(16199,plain,
% 28.79/18.97 (~big_f(f7(c2), c1)),
% 28.79/18.97 inference(modus_ponens,[status(thm)],[16182, 16198])).
% 28.79/18.97 tff(16200,plain,
% 28.79/18.97 (c2 = c4),
% 28.79/18.97 inference(unit_resolution,[status(thm)],[9203, 16181, 121, 15921, 16199, 16197, 120, 17])).
% 28.79/18.98 tff(16201,plain,
% 28.79/18.98 (c4 = c2),
% 28.79/18.98 inference(symmetry,[status(thm)],[16200])).
% 28.79/18.98 tff(16202,plain,
% 28.79/18.98 ((f7(c2) = c4) <=> (f7(c2) = c2)),
% 28.79/18.98 inference(monotonicity,[status(thm)],[16201])).
% 28.79/18.98 tff(16203,plain,
% 28.79/18.98 ((f7(c2) = c2) <=> (f7(c2) = c4)),
% 28.79/18.98 inference(symmetry,[status(thm)],[16202])).
% 28.79/18.98 tff(16204,plain,
% 28.79/18.98 ((~(f7(c2) = c2)) <=> (~(f7(c2) = c4))),
% 28.79/18.98 inference(monotonicity,[status(thm)],[16203])).
% 28.79/18.98 tff(16205,plain,
% 28.79/18.98 (~(f7(c2) = c4)),
% 28.79/18.98 inference(modus_ponens,[status(thm)],[17, 16204])).
% 28.79/18.98 tff(16206,plain,
% 28.79/18.98 (f3(f7(c2), c2) = c2),
% 28.79/18.98 inference(transitivity,[status(thm)],[16156, 16111])).
% 28.79/18.98 tff(16207,plain,
% 28.79/18.98 (big_f(f3(f7(c2), c2), f7(c2)) <=> big_f(c2, f7(c2))),
% 28.79/18.98 inference(monotonicity,[status(thm)],[16206])).
% 28.79/18.98 tff(16208,plain,
% 28.79/18.98 (big_f(c2, f7(c2)) <=> big_f(f3(f7(c2), c2), f7(c2))),
% 28.79/18.98 inference(symmetry,[status(thm)],[16207])).
% 28.79/18.98 tff(16209,plain,
% 28.79/18.98 (big_f(f3(f7(c2), c2), f7(c2))),
% 28.79/18.98 inference(modus_ponens,[status(thm)],[15741, 16208])).
% 28.79/18.98 tff(16210,assumption,(big_f(f3(f7(c2), c2), f7(c2))), introduced(assumption)).
% 28.79/18.98 tff(16211,assumption,(f3(f7(c2), c2) = c2), introduced(assumption)).
% 28.79/18.98 tff(16212,plain,
% 28.79/18.98 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c2) = c3) | (f7(c2) = c4) | (~big_f(f7(c2), f1(f7(c2), c2))) | (~(f1(f7(c2), c2) = c2)) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (f7(c2) = c3) | (f7(c2) = c4) | (~big_f(f7(c2), f1(f7(c2), c2))) | (~(f1(f7(c2), c2) = c2)) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2))))),
% 28.79/18.98 inference(rewrite,[status(thm)],[])).
% 28.79/18.98 tff(16213,plain,
% 28.79/18.98 (((f7(c2) = c4) | (f7(c2) = c3) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2))) | (~(f1(f7(c2), c2) = c2)) | (~big_f(f7(c2), f1(f7(c2), c2)))) <=> ((f7(c2) = c3) | (f7(c2) = c4) | (~big_f(f7(c2), f1(f7(c2), c2))) | (~(f1(f7(c2), c2) = c2)) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2))))),
% 28.79/18.98 inference(rewrite,[status(thm)],[])).
% 28.79/18.98 tff(16214,plain,
% 28.79/18.98 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c2) = c4) | (f7(c2) = c3) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2))) | (~(f1(f7(c2), c2) = c2)) | (~big_f(f7(c2), f1(f7(c2), c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c2) = c3) | (f7(c2) = c4) | (~big_f(f7(c2), f1(f7(c2), c2))) | (~(f1(f7(c2), c2) = c2)) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2)))))),
% 28.79/18.98 inference(monotonicity,[status(thm)],[16213])).
% 28.79/18.98 tff(16215,plain,
% 28.79/18.98 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c2) = c4) | (f7(c2) = c3) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2))) | (~(f1(f7(c2), c2) = c2)) | (~big_f(f7(c2), f1(f7(c2), c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (f7(c2) = c3) | (f7(c2) = c4) | (~big_f(f7(c2), f1(f7(c2), c2))) | (~(f1(f7(c2), c2) = c2)) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2))))),
% 28.79/18.98 inference(transitivity,[status(thm)],[16214, 16212])).
% 28.79/18.98 tff(16216,plain,
% 28.79/18.98 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c2) = c4) | (f7(c2) = c3) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2))) | (~(f1(f7(c2), c2) = c2)) | (~big_f(f7(c2), f1(f7(c2), c2))))),
% 28.79/18.98 inference(quant_inst,[status(thm)],[])).
% 28.79/18.98 tff(16217,plain,
% 28.79/18.98 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (f7(c2) = c3) | (f7(c2) = c4) | (~big_f(f7(c2), f1(f7(c2), c2))) | (~(f1(f7(c2), c2) = c2)) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2)))),
% 28.79/18.98 inference(modus_ponens,[status(thm)],[16216, 16215])).
% 28.79/18.98 tff(16218,plain,
% 28.79/18.98 ((~big_f(f7(c2), f1(f7(c2), c2))) | (~(f1(f7(c2), c2) = c2))),
% 28.79/18.98 inference(unit_resolution,[status(thm)],[16217, 933, 9092, 9495, 16211, 16210])).
% 28.79/18.98 tff(16219,plain,
% 28.79/18.98 ($false),
% 28.79/18.98 inference(unit_resolution,[status(thm)],[16218, 9366, 9363])).
% 28.79/18.98 tff(16220,plain,((~(f1(c1, c2) = c2)) | (f7(c2) = c3) | (f7(c2) = c4) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2))) | (~big_f(f7(c2), c2)) | (~(f7(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.79/18.98 tff(16221,plain,
% 28.79/18.98 (~(f1(c1, c2) = c2)),
% 28.79/18.98 inference(unit_resolution,[status(thm)],[16220, 16206, 9495, 9092, 16209, 1180, 22])).
% 28.79/18.98 tff(16222,plain,
% 28.79/18.98 (f1(c1, c2) = c1),
% 28.79/18.98 inference(unit_resolution,[status(thm)],[841, 16221])).
% 28.79/18.98 tff(16223,plain,
% 28.79/18.98 (f1(f7(c2), c2) = f7(c2)),
% 28.79/18.98 inference(transitivity,[status(thm)],[9112, 16222, 125])).
% 28.79/18.98 tff(16224,plain,
% 28.79/18.98 (big_f(f7(c2), f1(f7(c2), c2)) <=> big_f(f7(c2), f7(c2))),
% 28.79/18.98 inference(monotonicity,[status(thm)],[16223])).
% 28.79/18.98 tff(16225,plain,
% 28.79/18.98 (big_f(f7(c2), f7(c2)) <=> big_f(f7(c2), f1(f7(c2), c2))),
% 28.79/18.98 inference(symmetry,[status(thm)],[16224])).
% 28.79/18.98 tff(16226,plain,
% 28.79/18.98 ((~big_f(f7(c2), f7(c2))) <=> (~big_f(f7(c2), f1(f7(c2), c2)))),
% 28.79/18.98 inference(monotonicity,[status(thm)],[16225])).
% 28.79/18.98 tff(16227,plain,
% 28.79/18.98 (~big_f(f7(c2), f1(f7(c2), c2))),
% 28.79/18.98 inference(modus_ponens,[status(thm)],[8218, 16226])).
% 28.79/18.98 tff(16228,plain,
% 28.79/18.98 ((f1(f7(c2), c2) = c2) <=> (f7(c2) = c2)),
% 28.79/18.98 inference(monotonicity,[status(thm)],[16223])).
% 28.79/18.98 tff(16229,plain,
% 28.79/18.98 ((f7(c2) = c2) <=> (f1(f7(c2), c2) = c2)),
% 28.79/18.98 inference(symmetry,[status(thm)],[16228])).
% 28.79/18.98 tff(16230,plain,
% 28.79/18.98 ((~(f7(c2) = c2)) <=> (~(f1(f7(c2), c2) = c2))),
% 28.79/18.98 inference(monotonicity,[status(thm)],[16229])).
% 28.79/18.98 tff(16231,plain,
% 28.79/18.98 (~(f1(f7(c2), c2) = c2)),
% 28.79/18.98 inference(modus_ponens,[status(thm)],[17, 16230])).
% 28.79/18.98 tff(16232,plain,
% 28.79/18.98 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((f7(c2) = c3) | (f7(c2) = c4) | big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (f7(c2) = c3) | (f7(c2) = c4) | big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2))))),
% 28.79/18.98 inference(rewrite,[status(thm)],[])).
% 28.79/18.98 tff(16233,plain,
% 28.79/18.98 (((f7(c2) = c4) | (f7(c2) = c3) | (f1(f7(c2), c2) = c2) | big_f(f7(c2), f1(f7(c2), c2)) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2)))) <=> ((f7(c2) = c3) | (f7(c2) = c4) | big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2))))),
% 28.79/18.98 inference(rewrite,[status(thm)],[])).
% 28.79/18.98 tff(16234,plain,
% 28.79/18.98 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((f7(c2) = c4) | (f7(c2) = c3) | (f1(f7(c2), c2) = c2) | big_f(f7(c2), f1(f7(c2), c2)) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((f7(c2) = c3) | (f7(c2) = c4) | big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2)))))),
% 28.79/18.98 inference(monotonicity,[status(thm)],[16233])).
% 28.79/18.98 tff(16235,plain,
% 28.79/18.98 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((f7(c2) = c4) | (f7(c2) = c3) | (f1(f7(c2), c2) = c2) | big_f(f7(c2), f1(f7(c2), c2)) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (f7(c2) = c3) | (f7(c2) = c4) | big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2))))),
% 28.79/18.98 inference(transitivity,[status(thm)],[16234, 16232])).
% 28.79/18.98 tff(16236,plain,
% 28.79/18.98 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((f7(c2) = c4) | (f7(c2) = c3) | (f1(f7(c2), c2) = c2) | big_f(f7(c2), f1(f7(c2), c2)) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2))))),
% 28.79/18.98 inference(quant_inst,[status(thm)],[])).
% 28.79/18.98 tff(16237,plain,
% 28.79/18.98 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (f7(c2) = c3) | (f7(c2) = c4) | big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2) | (~(f3(f7(c2), c2) = c2)) | (~big_f(f3(f7(c2), c2), f7(c2)))),
% 28.79/18.98 inference(modus_ponens,[status(thm)],[16236, 16235])).
% 28.79/18.98 tff(16238,plain,
% 28.79/18.98 (big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2)),
% 28.79/18.98 inference(unit_resolution,[status(thm)],[16237, 969, 9092, 9495, 16206, 16209])).
% 28.79/18.98 tff(16239,plain,
% 28.79/18.98 ($false),
% 28.79/18.98 inference(unit_resolution,[status(thm)],[16238, 16231, 16227])).
% 28.79/18.98 tff(16240,plain,((~(f3(c1, c2) = c2)) | (f7(c2) = c3) | (f7(c2) = c4) | (f7(c2) = c2) | big_f(f7(c2), f7(c2)) | (~big_f(f7(c2), c2)) | (~big_f(c2, f7(c2)))), inference(lemma,lemma(discharge,[]))).
% 28.79/18.98 tff(16241,plain,
% 28.79/18.98 (~(f3(c1, c2) = c2)),
% 28.79/18.98 inference(unit_resolution,[status(thm)],[16240, 16197, 16205, 17, 16182, 15921, 15947])).
% 28.79/18.98 tff(16242,plain,
% 28.79/18.98 (f8(c2) = f8(c3)),
% 28.79/18.98 inference(symmetry,[status(thm)],[15608])).
% 28.79/18.98 tff(16243,plain,
% 28.79/18.98 (f7(f4(c4)) = f7(c1)),
% 28.79/18.98 inference(monotonicity,[status(thm)],[11752])).
% 28.79/18.98 tff(16244,plain,
% 28.79/18.98 (f7(c1) = f7(f4(c4))),
% 28.79/18.98 inference(symmetry,[status(thm)],[16243])).
% 28.79/18.98 tff(16245,plain,
% 28.79/18.98 (c2 = f7(f4(c4))),
% 28.79/18.98 inference(transitivity,[status(thm)],[354, 16244])).
% 28.79/18.98 tff(16246,plain,
% 28.79/18.98 (f8(c2) = f8(f7(f4(c4)))),
% 28.79/18.98 inference(monotonicity,[status(thm)],[16245])).
% 28.79/18.98 tff(16247,plain,
% 28.79/18.98 (f8(f7(f4(c4))) = f8(c2)),
% 28.79/18.98 inference(symmetry,[status(thm)],[16246])).
% 28.79/18.98 tff(16248,plain,
% 28.79/18.98 (f1(f5(f10(c1)), c1) = f1(c2, f7(c2))),
% 28.79/18.98 inference(monotonicity,[status(thm)],[16066, 125])).
% 28.79/18.98 tff(16249,plain,
% 28.79/18.98 (f1(c2, f7(c2)) = f1(f5(f10(c1)), c1)),
% 28.79/18.98 inference(symmetry,[status(thm)],[16248])).
% 28.79/18.98 tff(16250,plain,
% 28.79/18.98 (c2 = f1(c2, c1)),
% 28.79/18.98 inference(symmetry,[status(thm)],[12189])).
% 28.79/18.98 tff(16251,plain,
% 28.79/18.98 (c2 = f1(f5(c2), f5(c1))),
% 28.79/18.98 inference(transitivity,[status(thm)],[16250, 16024, 16249, 16015])).
% 28.79/18.98 tff(16252,plain,
% 28.79/18.98 (f3(c1, c2) = f3(c1, f1(f5(c2), f5(c1)))),
% 28.79/18.98 inference(monotonicity,[status(thm)],[16251])).
% 28.79/18.98 tff(16253,plain,
% 28.79/18.98 (f3(c1, f1(f5(c2), f5(c1))) = f3(c1, c2)),
% 28.79/18.98 inference(symmetry,[status(thm)],[16252])).
% 28.79/18.98 tff(16254,plain,
% 28.79/18.98 ((f3(c1, f1(f5(c2), f5(c1))) = c2) <=> (f3(c1, c2) = c2)),
% 28.79/18.98 inference(monotonicity,[status(thm)],[16253])).
% 28.79/18.98 tff(16255,plain,
% 28.79/18.98 ((f3(c1, c2) = c2) <=> (f3(c1, f1(f5(c2), f5(c1))) = c2)),
% 28.79/18.98 inference(symmetry,[status(thm)],[16254])).
% 28.79/18.98 tff(16256,plain,
% 28.79/18.98 ((~(f3(c1, c2) = c2)) <=> (~(f3(c1, f1(f5(c2), f5(c1))) = c2))),
% 28.79/18.98 inference(monotonicity,[status(thm)],[16255])).
% 28.79/18.98 tff(16257,plain,
% 28.79/18.98 (~(f3(c1, f1(f5(c2), f5(c1))) = c2)),
% 28.79/18.98 inference(modus_ponens,[status(thm)],[12777, 16256])).
% 28.79/18.98 tff(16258,plain,
% 28.79/18.98 (f3(c1, f1(f5(c2), f5(c1))) = c1),
% 28.79/18.98 inference(unit_resolution,[status(thm)],[16082, 16257])).
% 28.79/18.98 tff(16259,plain,
% 28.79/18.98 (f3(f7(c2), c2) = f7(c2)),
% 28.79/18.98 inference(transitivity,[status(thm)],[16156, 16252, 16258, 125])).
% 28.79/18.98 tff(16260,plain,
% 28.79/18.98 (big_f(f3(f7(c2), c2), f7(c2)) <=> big_f(f7(c2), f7(c2))),
% 28.79/18.98 inference(monotonicity,[status(thm)],[16259])).
% 28.79/18.98 tff(16261,plain,
% 28.79/18.98 (big_f(f7(c2), f7(c2)) <=> big_f(f3(f7(c2), c2), f7(c2))),
% 28.79/18.98 inference(symmetry,[status(thm)],[16260])).
% 28.79/18.98 tff(16262,plain,
% 28.79/18.98 ((~big_f(f7(c2), f7(c2))) <=> (~big_f(f3(f7(c2), c2), f7(c2)))),
% 28.79/18.98 inference(monotonicity,[status(thm)],[16261])).
% 28.79/18.98 tff(16263,plain,
% 28.79/18.98 (~big_f(f3(f7(c2), c2), f7(c2))),
% 28.79/18.98 inference(modus_ponens,[status(thm)],[8218, 16262])).
% 28.79/18.98 tff(16264,plain,
% 28.79/18.98 ((f3(f7(c2), c2) = c2) <=> (f7(c2) = c2)),
% 28.79/18.98 inference(monotonicity,[status(thm)],[16259])).
% 28.79/18.98 tff(16265,plain,
% 28.79/18.98 ((f7(c2) = c2) <=> (f3(f7(c2), c2) = c2)),
% 28.79/18.98 inference(symmetry,[status(thm)],[16264])).
% 28.79/18.98 tff(16266,plain,
% 28.79/18.98 ((~(f7(c2) = c2)) <=> (~(f3(f7(c2), c2) = c2))),
% 28.79/18.98 inference(monotonicity,[status(thm)],[16265])).
% 28.79/18.98 tff(16267,plain,
% 28.79/18.98 (~(f3(f7(c2), c2) = c2)),
% 28.79/18.98 inference(modus_ponens,[status(thm)],[17, 16266])).
% 28.79/18.98 tff(16268,assumption,(f8(f7(f4(c4))) = c1), introduced(assumption)).
% 28.79/18.98 tff(16269,plain,
% 28.79/18.98 (f8(c3) = c1),
% 28.79/18.98 inference(transitivity,[status(thm)],[15608, 16246, 16268])).
% 28.79/18.98 tff(16270,plain,
% 28.79/18.98 (f3(c1, f8(c3)) = f3(c1, c1)),
% 28.79/18.98 inference(monotonicity,[status(thm)],[16269])).
% 28.79/18.98 tff(16271,plain,
% 28.79/18.98 (f3(c1, c1) = f3(c1, f8(c3))),
% 28.79/18.98 inference(symmetry,[status(thm)],[16270])).
% 28.79/18.98 tff(16272,plain,
% 28.79/18.98 (c2 = f3(c1, f8(c3))),
% 28.79/18.98 inference(transitivity,[status(thm)],[1442, 16271])).
% 28.79/18.98 tff(16273,plain,
% 28.79/18.98 (f3(c1, c2) = f3(c1, f3(c1, f8(c3)))),
% 28.79/18.98 inference(monotonicity,[status(thm)],[16272])).
% 28.79/18.98 tff(16274,plain,
% 28.79/18.98 (f3(c1, f3(c1, f8(c3))) = f3(c1, c2)),
% 28.79/18.98 inference(symmetry,[status(thm)],[16273])).
% 28.79/18.98 tff(16275,plain,
% 28.79/18.98 ((f3(c1, f3(c1, f8(c3))) = c1) <=> (f3(c1, c2) = c1)),
% 28.79/18.98 inference(monotonicity,[status(thm)],[16274])).
% 28.79/18.98 tff(16276,plain,
% 28.79/18.98 ((f3(c1, f3(c1, f8(c3))) = c1) <=> (c1 = f3(c1, c2))),
% 28.79/18.98 inference(transitivity,[status(thm)],[16275, 13151])).
% 28.79/18.98 tff(16277,plain,
% 28.79/18.98 ((c1 = f3(c1, c2)) <=> (f3(c1, f3(c1, f8(c3))) = c1)),
% 28.79/18.98 inference(symmetry,[status(thm)],[16276])).
% 28.79/18.98 tff(16278,plain,
% 28.79/18.98 (c1 = f3(c1, c2)),
% 28.79/18.98 inference(unit_resolution,[status(thm)],[16084, 12777, 8109, 16, 230, 347])).
% 28.79/18.98 tff(16279,plain,
% 28.79/18.98 (f3(c1, f3(c1, f8(c3))) = c1),
% 28.79/18.98 inference(modus_ponens,[status(thm)],[16278, 16277])).
% 28.79/18.98 tff(16280,plain,
% 28.79/18.98 (f3(f7(c2), c2) = f7(c2)),
% 28.79/18.98 inference(transitivity,[status(thm)],[16156, 16273, 16279, 125])).
% 28.79/18.98 tff(16281,plain,
% 28.79/18.98 (big_f(f3(f7(c2), c2), f7(c2)) <=> big_f(f7(c2), f7(c2))),
% 28.79/18.98 inference(monotonicity,[status(thm)],[16280])).
% 28.79/18.98 tff(16282,plain,
% 28.79/18.98 (big_f(f7(c2), f7(c2)) <=> big_f(f3(f7(c2), c2), f7(c2))),
% 28.79/18.98 inference(symmetry,[status(thm)],[16281])).
% 28.79/18.98 tff(16283,plain,
% 28.79/18.98 ((~big_f(f7(c2), f7(c2))) <=> (~big_f(f3(f7(c2), c2), f7(c2)))),
% 28.79/18.98 inference(monotonicity,[status(thm)],[16282])).
% 28.79/18.98 tff(16284,plain,
% 28.79/18.98 (~big_f(f3(f7(c2), c2), f7(c2))),
% 28.79/18.98 inference(modus_ponens,[status(thm)],[8218, 16283])).
% 28.79/18.98 tff(16285,plain,
% 28.79/18.98 ((f3(f7(c2), c2) = c2) <=> (f7(c2) = c2)),
% 28.79/18.98 inference(monotonicity,[status(thm)],[16280])).
% 28.79/18.98 tff(16286,plain,
% 28.79/18.98 ((f7(c2) = c2) <=> (f3(f7(c2), c2) = c2)),
% 28.79/18.98 inference(symmetry,[status(thm)],[16285])).
% 28.79/18.98 tff(16287,plain,
% 28.79/18.98 ((~(f7(c2) = c2)) <=> (~(f3(f7(c2), c2) = c2))),
% 28.79/18.98 inference(monotonicity,[status(thm)],[16286])).
% 28.79/18.98 tff(16288,plain,
% 28.79/18.98 (~(f3(f7(c2), c2) = c2)),
% 28.79/18.98 inference(modus_ponens,[status(thm)],[17, 16287])).
% 28.79/18.98 tff(16289,plain,
% 28.79/18.98 (f1(f5(c2), f5(c1)) = c2),
% 28.79/18.98 inference(transitivity,[status(thm)],[16014, 16248, 8766, 12189])).
% 28.79/18.98 tff(16290,plain,
% 28.79/18.98 (f3(c1, f1(f5(c2), f5(c1))) = f3(c1, c2)),
% 28.79/18.98 inference(monotonicity,[status(thm)],[16289])).
% 28.79/18.98 tff(16291,plain,
% 28.79/18.98 (f3(c1, c2) = f3(c1, f1(f5(c2), f5(c1)))),
% 28.79/18.98 inference(symmetry,[status(thm)],[16290])).
% 28.79/18.98 tff(16292,plain,
% 28.79/18.98 (f3(c1, f3(c1, f8(c3))) = f3(c1, f1(f5(c2), f5(c1)))),
% 28.79/18.98 inference(transitivity,[status(thm)],[16274, 16291])).
% 28.79/18.98 tff(16293,plain,
% 28.79/18.98 (f3(f3(c1, f3(c1, f8(c3))), c2) = f3(f3(c1, f1(f5(c2), f5(c1))), c2)),
% 28.79/18.98 inference(monotonicity,[status(thm)],[16292])).
% 28.79/18.98 tff(16294,plain,
% 28.79/18.98 (big_f(f3(f3(c1, f3(c1, f8(c3))), c2), f3(c1, f3(c1, f8(c3)))) <=> big_f(f3(f3(c1, f1(f5(c2), f5(c1))), c2), f3(c1, f1(f5(c2), f5(c1))))),
% 28.79/18.98 inference(monotonicity,[status(thm)],[16293, 16292])).
% 28.79/18.98 tff(16295,plain,
% 28.79/18.98 (big_f(f3(f3(c1, f1(f5(c2), f5(c1))), c2), f3(c1, f1(f5(c2), f5(c1)))) <=> big_f(f3(f3(c1, f3(c1, f8(c3))), c2), f3(c1, f3(c1, f8(c3))))),
% 28.79/18.98 inference(symmetry,[status(thm)],[16294])).
% 28.79/18.98 tff(16296,plain,
% 28.79/18.98 (f3(c1, f1(f5(c2), f5(c1))) = f7(c2)),
% 28.79/18.98 inference(transitivity,[status(thm)],[16290, 16273, 16279, 125])).
% 28.79/18.98 tff(16297,plain,
% 28.79/18.98 (f3(c1, f1(f5(c2), f5(c1))) = c1),
% 28.79/18.98 inference(transitivity,[status(thm)],[16290, 16273, 16279])).
% 28.79/18.98 tff(16298,plain,
% 28.79/18.98 (f3(f3(c1, f1(f5(c2), f5(c1))), c2) = f3(c1, c2)),
% 28.79/18.98 inference(monotonicity,[status(thm)],[16297])).
% 28.79/18.98 tff(16299,plain,
% 28.79/18.98 (f3(f3(c1, f1(f5(c2), f5(c1))), c2) = f7(c2)),
% 28.79/18.98 inference(transitivity,[status(thm)],[16298, 16273, 16279, 125])).
% 28.79/18.98 tff(16300,plain,
% 28.79/18.98 (big_f(f3(f3(c1, f1(f5(c2), f5(c1))), c2), f3(c1, f1(f5(c2), f5(c1)))) <=> big_f(f7(c2), f7(c2))),
% 28.79/18.98 inference(monotonicity,[status(thm)],[16299, 16296])).
% 28.79/18.98 tff(16301,plain,
% 28.79/18.98 (big_f(f7(c2), f7(c2)) <=> big_f(f3(f3(c1, f1(f5(c2), f5(c1))), c2), f3(c1, f1(f5(c2), f5(c1))))),
% 28.79/18.98 inference(symmetry,[status(thm)],[16300])).
% 28.79/18.98 tff(16302,plain,
% 28.79/18.98 (big_f(f7(c2), f7(c2)) <=> big_f(f3(f3(c1, f3(c1, f8(c3))), c2), f3(c1, f3(c1, f8(c3))))),
% 28.79/18.98 inference(transitivity,[status(thm)],[16301, 16295])).
% 28.79/18.98 tff(16303,plain,
% 28.79/18.98 ((~big_f(f7(c2), f7(c2))) <=> (~big_f(f3(f3(c1, f3(c1, f8(c3))), c2), f3(c1, f3(c1, f8(c3)))))),
% 28.79/18.98 inference(monotonicity,[status(thm)],[16302])).
% 28.79/18.98 tff(16304,plain,
% 28.79/18.98 (~big_f(f3(f3(c1, f3(c1, f8(c3))), c2), f3(c1, f3(c1, f8(c3))))),
% 28.79/18.98 inference(modus_ponens,[status(thm)],[8218, 16303])).
% 28.79/18.98 tff(16305,plain,
% 28.79/18.98 ((f3(f3(c1, f3(c1, f8(c3))), c2) = c2) <=> (f3(f3(c1, f1(f5(c2), f5(c1))), c2) = c2)),
% 28.79/18.98 inference(monotonicity,[status(thm)],[16293])).
% 28.79/18.98 tff(16306,plain,
% 28.79/18.98 ((f3(f3(c1, f1(f5(c2), f5(c1))), c2) = c2) <=> (f3(f3(c1, f3(c1, f8(c3))), c2) = c2)),
% 28.79/18.98 inference(symmetry,[status(thm)],[16305])).
% 28.79/18.98 tff(16307,plain,
% 28.79/18.98 ((f3(f3(c1, f1(f5(c2), f5(c1))), c2) = c2) <=> (f7(c2) = c2)),
% 28.79/18.98 inference(monotonicity,[status(thm)],[16299])).
% 28.79/18.98 tff(16308,plain,
% 28.79/18.98 ((f7(c2) = c2) <=> (f3(f3(c1, f1(f5(c2), f5(c1))), c2) = c2)),
% 28.79/18.98 inference(symmetry,[status(thm)],[16307])).
% 28.79/18.98 tff(16309,plain,
% 28.79/18.98 ((f7(c2) = c2) <=> (f3(f3(c1, f3(c1, f8(c3))), c2) = c2)),
% 28.79/18.98 inference(transitivity,[status(thm)],[16308, 16306])).
% 28.79/18.98 tff(16310,plain,
% 28.79/18.98 ((~(f7(c2) = c2)) <=> (~(f3(f3(c1, f3(c1, f8(c3))), c2) = c2))),
% 28.79/18.98 inference(monotonicity,[status(thm)],[16309])).
% 28.79/18.98 tff(16311,plain,
% 28.79/18.98 (~(f3(f3(c1, f3(c1, f8(c3))), c2) = c2)),
% 28.79/18.98 inference(modus_ponens,[status(thm)],[17, 16310])).
% 28.79/18.98 tff(16312,plain,
% 28.79/18.98 ((f3(c1, f3(c1, f8(c3))) = c4) <=> (f3(c1, f3(c1, f8(c3))) = c2)),
% 28.79/18.98 inference(monotonicity,[status(thm)],[8728])).
% 28.79/18.98 tff(16313,plain,
% 28.79/18.98 ((f3(c1, f3(c1, f8(c3))) = c2) <=> (f3(c1, f3(c1, f8(c3))) = c4)),
% 28.79/18.98 inference(symmetry,[status(thm)],[16312])).
% 28.79/18.98 tff(16314,plain,
% 28.79/18.98 ((f3(c1, f3(c1, f8(c3))) = c2) <=> (f3(c1, c2) = c2)),
% 28.79/18.98 inference(monotonicity,[status(thm)],[16274])).
% 28.79/18.98 tff(16315,plain,
% 28.79/18.98 ((f3(c1, c2) = c2) <=> (f3(c1, f3(c1, f8(c3))) = c2)),
% 28.79/18.98 inference(symmetry,[status(thm)],[16314])).
% 28.79/18.98 tff(16316,plain,
% 28.79/18.98 ((f3(c1, c2) = c2) <=> (f3(c1, f3(c1, f8(c3))) = c4)),
% 28.79/18.98 inference(transitivity,[status(thm)],[16315, 16313])).
% 28.79/18.98 tff(16317,plain,
% 28.79/18.98 ((~(f3(c1, c2) = c2)) <=> (~(f3(c1, f3(c1, f8(c3))) = c4))),
% 28.79/18.98 inference(monotonicity,[status(thm)],[16316])).
% 28.79/18.98 tff(16318,plain,
% 28.79/18.98 (~(f3(c1, f3(c1, f8(c3))) = c4)),
% 28.79/18.98 inference(modus_ponens,[status(thm)],[12777, 16317])).
% 28.79/18.98 tff(16319,plain,
% 28.79/18.98 (big_f(f7(c2), f1(c1, c2)) <=> big_f(f7(c2), c2)),
% 28.79/18.98 inference(monotonicity,[status(thm)],[822])).
% 28.79/18.98 tff(16320,plain,
% 28.79/18.98 (big_f(f7(c2), c2) <=> big_f(f7(c2), f1(c1, c2))),
% 28.79/18.98 inference(symmetry,[status(thm)],[16319])).
% 28.79/18.98 tff(16321,plain,
% 28.79/18.98 (big_f(f7(c2), f1(c1, c2))),
% 28.79/18.98 inference(modus_ponens,[status(thm)],[1180, 16320])).
% 28.79/18.98 tff(16322,plain,
% 28.79/18.98 ((~big_f(c1, f1(c1, c2))) <=> (~big_f(f7(c2), f1(c1, c2)))),
% 28.79/18.98 inference(monotonicity,[status(thm)],[9167])).
% 28.79/18.98 tff(16323,assumption,(~big_f(f3(f3(c1, f3(c1, f8(c3))), c2), f3(c1, f3(c1, f8(c3))))), introduced(assumption)).
% 28.80/18.98 tff(16324,assumption,(~(f3(f3(c1, f3(c1, f8(c3))), c2) = c2)), introduced(assumption)).
% 28.80/18.98 tff(16325,assumption,(~(f3(c1, f3(c1, f8(c3))) = c4)), introduced(assumption)).
% 28.80/18.98 tff(16326,plain,
% 28.80/18.98 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~big_f(c1, f1(c1, c2))) | (~(f1(c1, c2) = c2)) | (f3(f3(c1, f3(c1, f8(c3))), c2) = c2) | big_f(f3(f3(c1, f3(c1, f8(c3))), c2), f3(c1, f3(c1, f8(c3)))) | (f3(c1, f3(c1, f8(c3))) = c4))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (~big_f(c1, f1(c1, c2))) | (~(f1(c1, c2) = c2)) | (f3(f3(c1, f3(c1, f8(c3))), c2) = c2) | big_f(f3(f3(c1, f3(c1, f8(c3))), c2), f3(c1, f3(c1, f8(c3)))) | (f3(c1, f3(c1, f8(c3))) = c4))),
% 28.80/18.98 inference(rewrite,[status(thm)],[])).
% 28.80/18.98 tff(16327,plain,
% 28.80/18.98 (((f3(c1, f3(c1, f8(c3))) = c4) | (f3(f3(c1, f3(c1, f8(c3))), c2) = c2) | big_f(f3(f3(c1, f3(c1, f8(c3))), c2), f3(c1, f3(c1, f8(c3)))) | (c1 = c3) | (~(f1(c1, c2) = c2)) | (~big_f(c1, f1(c1, c2)))) <=> ((c1 = c3) | (~big_f(c1, f1(c1, c2))) | (~(f1(c1, c2) = c2)) | (f3(f3(c1, f3(c1, f8(c3))), c2) = c2) | big_f(f3(f3(c1, f3(c1, f8(c3))), c2), f3(c1, f3(c1, f8(c3)))) | (f3(c1, f3(c1, f8(c3))) = c4))),
% 28.80/18.98 inference(rewrite,[status(thm)],[])).
% 28.80/18.98 tff(16328,plain,
% 28.80/18.98 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f3(c1, f3(c1, f8(c3))) = c4) | (f3(f3(c1, f3(c1, f8(c3))), c2) = c2) | big_f(f3(f3(c1, f3(c1, f8(c3))), c2), f3(c1, f3(c1, f8(c3)))) | (c1 = c3) | (~(f1(c1, c2) = c2)) | (~big_f(c1, f1(c1, c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~big_f(c1, f1(c1, c2))) | (~(f1(c1, c2) = c2)) | (f3(f3(c1, f3(c1, f8(c3))), c2) = c2) | big_f(f3(f3(c1, f3(c1, f8(c3))), c2), f3(c1, f3(c1, f8(c3)))) | (f3(c1, f3(c1, f8(c3))) = c4)))),
% 28.80/18.98 inference(monotonicity,[status(thm)],[16327])).
% 28.80/18.98 tff(16329,plain,
% 28.80/18.98 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f3(c1, f3(c1, f8(c3))) = c4) | (f3(f3(c1, f3(c1, f8(c3))), c2) = c2) | big_f(f3(f3(c1, f3(c1, f8(c3))), c2), f3(c1, f3(c1, f8(c3)))) | (c1 = c3) | (~(f1(c1, c2) = c2)) | (~big_f(c1, f1(c1, c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (~big_f(c1, f1(c1, c2))) | (~(f1(c1, c2) = c2)) | (f3(f3(c1, f3(c1, f8(c3))), c2) = c2) | big_f(f3(f3(c1, f3(c1, f8(c3))), c2), f3(c1, f3(c1, f8(c3)))) | (f3(c1, f3(c1, f8(c3))) = c4))),
% 28.80/18.98 inference(transitivity,[status(thm)],[16328, 16326])).
% 28.80/18.98 tff(16330,plain,
% 28.80/18.98 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f3(c1, f3(c1, f8(c3))) = c4) | (f3(f3(c1, f3(c1, f8(c3))), c2) = c2) | big_f(f3(f3(c1, f3(c1, f8(c3))), c2), f3(c1, f3(c1, f8(c3)))) | (c1 = c3) | (~(f1(c1, c2) = c2)) | (~big_f(c1, f1(c1, c2))))),
% 28.80/18.98 inference(quant_inst,[status(thm)],[])).
% 28.80/18.98 tff(16331,plain,
% 28.80/18.98 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (~big_f(c1, f1(c1, c2))) | (~(f1(c1, c2) = c2)) | (f3(f3(c1, f3(c1, f8(c3))), c2) = c2) | big_f(f3(f3(c1, f3(c1, f8(c3))), c2), f3(c1, f3(c1, f8(c3)))) | (f3(c1, f3(c1, f8(c3))) = c4)),
% 28.80/18.98 inference(modus_ponens,[status(thm)],[16330, 16329])).
% 28.80/18.98 tff(16332,plain,
% 28.80/18.98 ((c1 = c3) | (~big_f(c1, f1(c1, c2))) | (~(f1(c1, c2) = c2)) | (f3(f3(c1, f3(c1, f8(c3))), c2) = c2) | big_f(f3(f3(c1, f3(c1, f8(c3))), c2), f3(c1, f3(c1, f8(c3)))) | (f3(c1, f3(c1, f8(c3))) = c4)),
% 28.80/18.99 inference(unit_resolution,[status(thm)],[16331, 904])).
% 28.80/18.99 tff(16333,plain,
% 28.80/18.99 (~big_f(c1, f1(c1, c2))),
% 28.80/18.99 inference(unit_resolution,[status(thm)],[16332, 822, 168, 16325, 16324, 16323])).
% 28.80/18.99 tff(16334,plain,
% 28.80/18.99 (~big_f(f7(c2), f1(c1, c2))),
% 28.80/18.99 inference(modus_ponens,[status(thm)],[16333, 16322])).
% 28.80/18.99 tff(16335,plain,
% 28.80/18.99 ($false),
% 28.80/18.99 inference(unit_resolution,[status(thm)],[16334, 16321])).
% 28.80/18.99 tff(16336,plain,((~(f1(c1, c2) = c2)) | (~big_f(f7(c2), c2)) | (~(f7(c2) = c1)) | (c1 = c3) | (f3(c1, f3(c1, f8(c3))) = c4) | (f3(f3(c1, f3(c1, f8(c3))), c2) = c2) | big_f(f3(f3(c1, f3(c1, f8(c3))), c2), f3(c1, f3(c1, f8(c3))))), inference(lemma,lemma(discharge,[]))).
% 28.80/18.99 tff(16337,plain,
% 28.80/18.99 (~(f1(c1, c2) = c2)),
% 28.80/18.99 inference(unit_resolution,[status(thm)],[16336, 16318, 22, 9752, 1180, 16311, 16304])).
% 28.80/18.99 tff(16338,plain,
% 28.80/18.99 (f1(c1, c2) = c1),
% 28.80/18.99 inference(unit_resolution,[status(thm)],[841, 16337])).
% 28.80/18.99 tff(16339,plain,
% 28.80/18.99 (f1(f7(c2), c2) = f7(c2)),
% 28.80/18.99 inference(transitivity,[status(thm)],[9112, 16338, 125])).
% 28.80/18.99 tff(16340,plain,
% 28.80/18.99 (big_f(f7(c2), f1(f7(c2), c2)) <=> big_f(f7(c2), f7(c2))),
% 28.80/18.99 inference(monotonicity,[status(thm)],[16339])).
% 28.80/18.99 tff(16341,plain,
% 28.80/18.99 (big_f(f7(c2), f7(c2)) <=> big_f(f7(c2), f1(f7(c2), c2))),
% 28.80/18.99 inference(symmetry,[status(thm)],[16340])).
% 28.80/18.99 tff(16342,plain,
% 28.80/18.99 ((~big_f(f7(c2), f7(c2))) <=> (~big_f(f7(c2), f1(f7(c2), c2)))),
% 28.80/18.99 inference(monotonicity,[status(thm)],[16341])).
% 28.80/18.99 tff(16343,plain,
% 28.80/18.99 (~big_f(f7(c2), f1(f7(c2), c2))),
% 28.80/18.99 inference(modus_ponens,[status(thm)],[8218, 16342])).
% 28.80/18.99 tff(16344,plain,
% 28.80/18.99 ((f1(f7(c2), c2) = c2) <=> (f7(c2) = c2)),
% 28.80/18.99 inference(monotonicity,[status(thm)],[16339])).
% 28.80/18.99 tff(16345,plain,
% 28.80/18.99 ((f7(c2) = c2) <=> (f1(f7(c2), c2) = c2)),
% 28.80/18.99 inference(symmetry,[status(thm)],[16344])).
% 28.80/18.99 tff(16346,plain,
% 28.80/18.99 ((~(f7(c2) = c2)) <=> (~(f1(f7(c2), c2) = c2))),
% 28.80/18.99 inference(monotonicity,[status(thm)],[16345])).
% 28.80/18.99 tff(16347,plain,
% 28.80/18.99 (~(f1(f7(c2), c2) = c2)),
% 28.80/18.99 inference(modus_ponens,[status(thm)],[17, 16346])).
% 28.80/18.99 tff(16348,plain,
% 28.80/18.99 ((~(f7(c2) = c2)) <=> (~(f7(c2) = c4))),
% 28.80/18.99 inference(monotonicity,[status(thm)],[16000])).
% 28.80/18.99 tff(16349,plain,
% 28.80/18.99 (~(f7(c2) = c4)),
% 28.80/18.99 inference(modus_ponens,[status(thm)],[17, 16348])).
% 28.80/18.99 tff(16350,plain,
% 28.80/18.99 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f7(c2) = c3) | (f7(c2) = c4) | big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2) | (f3(f7(c2), c2) = c2) | big_f(f3(f7(c2), c2), f7(c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (f7(c2) = c3) | (f7(c2) = c4) | big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2) | (f3(f7(c2), c2) = c2) | big_f(f3(f7(c2), c2), f7(c2)))),
% 28.80/18.99 inference(rewrite,[status(thm)],[])).
% 28.80/18.99 tff(16351,plain,
% 28.80/18.99 (((f7(c2) = c4) | (f3(f7(c2), c2) = c2) | big_f(f3(f7(c2), c2), f7(c2)) | (f7(c2) = c3) | (f1(f7(c2), c2) = c2) | big_f(f7(c2), f1(f7(c2), c2))) <=> ((f7(c2) = c3) | (f7(c2) = c4) | big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2) | (f3(f7(c2), c2) = c2) | big_f(f3(f7(c2), c2), f7(c2)))),
% 28.80/18.99 inference(rewrite,[status(thm)],[])).
% 28.80/18.99 tff(16352,plain,
% 28.80/18.99 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f7(c2) = c4) | (f3(f7(c2), c2) = c2) | big_f(f3(f7(c2), c2), f7(c2)) | (f7(c2) = c3) | (f1(f7(c2), c2) = c2) | big_f(f7(c2), f1(f7(c2), c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f7(c2) = c3) | (f7(c2) = c4) | big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2) | (f3(f7(c2), c2) = c2) | big_f(f3(f7(c2), c2), f7(c2))))),
% 28.80/18.99 inference(monotonicity,[status(thm)],[16351])).
% 28.80/18.99 tff(16353,plain,
% 28.80/18.99 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f7(c2) = c4) | (f3(f7(c2), c2) = c2) | big_f(f3(f7(c2), c2), f7(c2)) | (f7(c2) = c3) | (f1(f7(c2), c2) = c2) | big_f(f7(c2), f1(f7(c2), c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (f7(c2) = c3) | (f7(c2) = c4) | big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2) | (f3(f7(c2), c2) = c2) | big_f(f3(f7(c2), c2), f7(c2)))),
% 28.80/18.99 inference(transitivity,[status(thm)],[16352, 16350])).
% 28.80/18.99 tff(16354,plain,
% 28.80/18.99 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f7(c2) = c4) | (f3(f7(c2), c2) = c2) | big_f(f3(f7(c2), c2), f7(c2)) | (f7(c2) = c3) | (f1(f7(c2), c2) = c2) | big_f(f7(c2), f1(f7(c2), c2)))),
% 28.80/18.99 inference(quant_inst,[status(thm)],[])).
% 28.80/18.99 tff(16355,plain,
% 28.80/18.99 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (f7(c2) = c3) | (f7(c2) = c4) | big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2) | (f3(f7(c2), c2) = c2) | big_f(f3(f7(c2), c2), f7(c2))),
% 28.80/18.99 inference(modus_ponens,[status(thm)],[16354, 16353])).
% 28.80/18.99 tff(16356,plain,
% 28.80/18.99 (big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2) | (f3(f7(c2), c2) = c2) | big_f(f3(f7(c2), c2), f7(c2))),
% 28.80/18.99 inference(unit_resolution,[status(thm)],[16355, 1014, 9749, 16349])).
% 28.80/18.99 tff(16357,plain,
% 28.80/18.99 ($false),
% 28.80/18.99 inference(unit_resolution,[status(thm)],[16356, 16347, 16343, 16288, 16284])).
% 28.80/18.99 tff(16358,plain,((~(f3(c1, c1) = c2)) | big_f(f7(c2), f7(c2)) | (~(f8(f7(f4(c4))) = c1)) | (~(f7(c1) = c2)) | (~(f4(c4) = c1)) | (~(c2 = c3)) | (f7(c2) = c2) | (~big_f(f7(c2), c2)) | (~(f1(c2, c1) = c2)) | (~(f5(c2) = c2)) | (~(f10(c1) = c2)) | (~(f5(c1) = c1)) | (f3(c1, c2) = c2) | (~(c2 = c4))), inference(lemma,lemma(discharge,[]))).
% 28.80/18.99 tff(16359,plain,
% 28.80/18.99 (~(f3(c1, c1) = c2)),
% 28.80/18.99 inference(unit_resolution,[status(thm)],[16358, 16268, 8218, 347, 11752, 1344, 17, 1180, 12189, 8109, 16, 230, 12777, 631])).
% 28.80/18.99 tff(16360,plain,
% 28.80/18.99 (f3(c1, c1) = c1),
% 28.80/18.99 inference(unit_resolution,[status(thm)],[1416, 16359])).
% 28.80/18.99 tff(16361,plain,
% 28.80/18.99 (f3(c1, f8(c3)) = c1),
% 28.80/18.99 inference(transitivity,[status(thm)],[16270, 16360])).
% 28.80/18.99 tff(16362,plain,
% 28.80/18.99 (f3(c1, f3(c1, f8(c3))) = f3(c1, c1)),
% 28.80/18.99 inference(monotonicity,[status(thm)],[16361])).
% 28.80/18.99 tff(16363,plain,
% 28.80/18.99 (f3(c1, f3(c1, f8(c3))) = c1),
% 28.80/18.99 inference(transitivity,[status(thm)],[16362, 16360])).
% 28.80/18.99 tff(16364,plain,
% 28.80/18.99 (f3(f3(c1, f3(c1, f8(c3))), c2) = f3(c1, c2)),
% 28.80/18.99 inference(monotonicity,[status(thm)],[16363])).
% 28.80/18.99 tff(16365,plain,
% 28.80/18.99 (big_f(f3(f3(c1, f3(c1, f8(c3))), c2), f3(c1, f3(c1, f8(c3)))) <=> big_f(f3(c1, c2), c1)),
% 28.80/18.99 inference(monotonicity,[status(thm)],[16364, 16363])).
% 28.80/18.99 tff(16366,plain,
% 28.80/18.99 (big_f(f3(c1, c2), c1) <=> big_f(f3(f3(c1, f3(c1, f8(c3))), c2), f3(c1, f3(c1, f8(c3))))),
% 28.80/18.99 inference(symmetry,[status(thm)],[16365])).
% 28.80/18.99 tff(16367,plain,
% 28.80/18.99 ((~big_f(f3(c1, c2), c1)) <=> (~big_f(f3(f3(c1, f3(c1, f8(c3))), c2), f3(c1, f3(c1, f8(c3)))))),
% 28.80/18.99 inference(monotonicity,[status(thm)],[16366])).
% 28.80/18.99 tff(16368,plain,
% 28.80/18.99 (~big_f(c1, c1)),
% 28.80/18.99 inference(modus_ponens,[status(thm)],[8218, 15990])).
% 28.80/18.99 tff(16369,plain,
% 28.80/18.99 (big_f(c1, c1) <=> big_f(f3(c1, c2), c1)),
% 28.80/18.99 inference(unit_resolution,[status(thm)],[13192, 16278])).
% 28.80/18.99 tff(16370,plain,
% 28.80/18.99 (~big_f(f3(c1, c2), c1)),
% 28.80/18.99 inference(unit_resolution,[status(thm)],[13186, 16369, 16368])).
% 28.80/18.99 tff(16371,plain,
% 28.80/18.99 (~big_f(f3(f3(c1, f3(c1, f8(c3))), c2), f3(c1, f3(c1, f8(c3))))),
% 28.80/18.99 inference(modus_ponens,[status(thm)],[16370, 16367])).
% 28.80/18.99 tff(16372,plain,
% 28.80/18.99 ((f3(f3(c1, f3(c1, f8(c3))), c2) = c2) <=> (f3(c1, c2) = c2)),
% 28.80/18.99 inference(monotonicity,[status(thm)],[16364])).
% 28.80/18.99 tff(16373,plain,
% 28.80/18.99 ((f3(c1, c2) = c2) <=> (f3(f3(c1, f3(c1, f8(c3))), c2) = c2)),
% 28.80/18.99 inference(symmetry,[status(thm)],[16372])).
% 28.80/18.99 tff(16374,plain,
% 28.80/18.99 ((~(f3(c1, c2) = c2)) <=> (~(f3(f3(c1, f3(c1, f8(c3))), c2) = c2))),
% 28.80/18.99 inference(monotonicity,[status(thm)],[16373])).
% 28.80/18.99 tff(16375,plain,
% 28.80/18.99 (~(f3(f3(c1, f3(c1, f8(c3))), c2) = c2)),
% 28.80/18.99 inference(modus_ponens,[status(thm)],[12777, 16374])).
% 28.80/18.99 tff(16376,plain,
% 28.80/18.99 (f3(c1, f3(c1, f8(c3))) = f7(c2)),
% 28.80/18.99 inference(transitivity,[status(thm)],[16362, 16360, 125])).
% 28.80/18.99 tff(16377,plain,
% 28.80/18.99 ((f3(c1, f3(c1, f8(c3))) = c2) <=> (f7(c2) = c2)),
% 28.80/18.99 inference(monotonicity,[status(thm)],[16376])).
% 28.80/18.99 tff(16378,plain,
% 28.80/18.99 ((f7(c2) = c2) <=> (f3(c1, f3(c1, f8(c3))) = c2)),
% 28.80/18.99 inference(symmetry,[status(thm)],[16377])).
% 28.80/18.99 tff(16379,plain,
% 28.80/18.99 ((f7(c2) = c2) <=> (f3(c1, f3(c1, f8(c3))) = c4)),
% 28.80/18.99 inference(transitivity,[status(thm)],[16378, 16313])).
% 28.80/18.99 tff(16380,plain,
% 28.80/18.99 ((~(f7(c2) = c2)) <=> (~(f3(c1, f3(c1, f8(c3))) = c4))),
% 28.80/18.99 inference(monotonicity,[status(thm)],[16379])).
% 28.80/18.99 tff(16381,plain,
% 28.80/18.99 (~(f3(c1, f3(c1, f8(c3))) = c4)),
% 28.80/18.99 inference(modus_ponens,[status(thm)],[17, 16380])).
% 28.80/18.99 tff(16382,plain,
% 28.80/18.99 (~(f1(c1, c2) = c2)),
% 28.80/18.99 inference(unit_resolution,[status(thm)],[16336, 16381, 22, 9752, 1180, 16375, 16371])).
% 28.80/18.99 tff(16383,plain,
% 28.80/18.99 (f1(c1, c2) = c1),
% 28.80/18.99 inference(unit_resolution,[status(thm)],[841, 16382])).
% 28.80/18.99 tff(16384,plain,
% 28.80/18.99 (f1(f7(c2), c2) = f7(c2)),
% 28.80/18.99 inference(transitivity,[status(thm)],[9112, 16383, 125])).
% 28.80/18.99 tff(16385,plain,
% 28.80/18.99 (big_f(f7(c2), f1(f7(c2), c2)) <=> big_f(f7(c2), f7(c2))),
% 28.80/18.99 inference(monotonicity,[status(thm)],[16384])).
% 28.80/18.99 tff(16386,plain,
% 28.80/18.99 (big_f(f7(c2), f7(c2)) <=> big_f(f7(c2), f1(f7(c2), c2))),
% 28.80/18.99 inference(symmetry,[status(thm)],[16385])).
% 28.80/18.99 tff(16387,plain,
% 28.80/18.99 ((~big_f(f7(c2), f7(c2))) <=> (~big_f(f7(c2), f1(f7(c2), c2)))),
% 28.80/18.99 inference(monotonicity,[status(thm)],[16386])).
% 28.80/18.99 tff(16388,plain,
% 28.80/18.99 (~big_f(f7(c2), f1(f7(c2), c2))),
% 28.80/18.99 inference(modus_ponens,[status(thm)],[8218, 16387])).
% 28.80/18.99 tff(16389,plain,
% 28.80/18.99 ((f1(f7(c2), c2) = c2) <=> (f7(c2) = c2)),
% 28.80/18.99 inference(monotonicity,[status(thm)],[16384])).
% 28.80/18.99 tff(16390,plain,
% 28.80/18.99 ((f7(c2) = c2) <=> (f1(f7(c2), c2) = c2)),
% 28.80/18.99 inference(symmetry,[status(thm)],[16389])).
% 28.80/18.99 tff(16391,plain,
% 28.80/18.99 ((~(f7(c2) = c2)) <=> (~(f1(f7(c2), c2) = c2))),
% 28.80/18.99 inference(monotonicity,[status(thm)],[16390])).
% 28.80/18.99 tff(16392,plain,
% 28.80/18.99 (~(f1(f7(c2), c2) = c2)),
% 28.80/18.99 inference(modus_ponens,[status(thm)],[17, 16391])).
% 28.80/18.99 tff(16393,plain,
% 28.80/18.99 ($false),
% 28.80/18.99 inference(unit_resolution,[status(thm)],[16356, 16392, 16388, 16267, 16263])).
% 28.80/18.99 tff(16394,plain,((~(f8(f7(f4(c4))) = c1)) | big_f(f7(c2), f7(c2)) | (~(f1(c2, c1) = c2)) | (~(f5(c2) = c2)) | (~(f10(c1) = c2)) | (~(f5(c1) = c1)) | (f7(c2) = c2) | (~big_f(f7(c2), c2)) | (~(f7(c1) = c2)) | (~(f4(c4) = c1)) | (~(c2 = c3)) | (f3(c1, c2) = c2) | (~(c2 = c4))), inference(lemma,lemma(discharge,[]))).
% 28.80/18.99 tff(16395,plain,
% 28.80/18.99 (~(f8(f7(f4(c4))) = c1)),
% 28.80/18.99 inference(unit_resolution,[status(thm)],[16394, 12777, 12189, 8109, 16, 230, 17, 1180, 347, 11752, 1344, 8218, 631])).
% 28.80/18.99 tff(16396,plain,
% 28.80/18.99 (f8(f7(f4(c4))) = c2),
% 28.80/18.99 inference(unit_resolution,[status(thm)],[13371, 16395])).
% 28.80/18.99 tff(16397,plain,
% 28.80/18.99 (c2 = f8(f7(f4(c4)))),
% 28.80/18.99 inference(symmetry,[status(thm)],[16396])).
% 28.80/18.99 tff(16398,plain,
% 28.80/18.99 (c2 = f8(c3)),
% 28.80/18.99 inference(transitivity,[status(thm)],[16397, 16247, 16242])).
% 28.80/18.99 tff(16399,plain,
% 28.80/18.99 (f3(c1, c2) = f3(c1, f8(c3))),
% 28.80/18.99 inference(monotonicity,[status(thm)],[16398])).
% 28.80/18.99 tff(16400,plain,
% 28.80/18.99 (f3(c1, f8(c3)) = f3(c1, c2)),
% 28.80/18.99 inference(symmetry,[status(thm)],[16399])).
% 28.80/18.99 tff(16401,plain,
% 28.80/18.99 ((f3(c1, f8(c3)) = c1) <=> (f3(c1, c2) = c1)),
% 28.80/18.99 inference(monotonicity,[status(thm)],[16400])).
% 28.80/18.99 tff(16402,plain,
% 28.80/18.99 ((f3(c1, f8(c3)) = c1) <=> (c1 = f3(c1, c2))),
% 28.80/18.99 inference(transitivity,[status(thm)],[16401, 13151])).
% 28.80/18.99 tff(16403,plain,
% 28.80/18.99 ((c1 = f3(c1, c2)) <=> (f3(c1, f8(c3)) = c1)),
% 28.80/18.99 inference(symmetry,[status(thm)],[16402])).
% 28.80/18.99 tff(16404,plain,
% 28.80/18.99 (f3(c1, f8(c3)) = c1),
% 28.80/18.99 inference(modus_ponens,[status(thm)],[16278, 16403])).
% 28.80/18.99 tff(16405,plain,
% 28.80/18.99 (f3(f7(c2), c2) = f7(c2)),
% 28.80/18.99 inference(transitivity,[status(thm)],[16156, 16399, 16404, 125])).
% 28.80/18.99 tff(16406,plain,
% 28.80/18.99 (big_f(f3(f7(c2), c2), f7(c2)) <=> big_f(f7(c2), f7(c2))),
% 28.80/18.99 inference(monotonicity,[status(thm)],[16405])).
% 28.80/18.99 tff(16407,plain,
% 28.80/18.99 (big_f(f7(c2), f7(c2)) <=> big_f(f3(f7(c2), c2), f7(c2))),
% 28.80/18.99 inference(symmetry,[status(thm)],[16406])).
% 28.80/18.99 tff(16408,plain,
% 28.80/18.99 ((~big_f(f7(c2), f7(c2))) <=> (~big_f(f3(f7(c2), c2), f7(c2)))),
% 28.80/18.99 inference(monotonicity,[status(thm)],[16407])).
% 28.80/18.99 tff(16409,plain,
% 28.80/18.99 (~big_f(f3(f7(c2), c2), f7(c2))),
% 28.80/18.99 inference(modus_ponens,[status(thm)],[8218, 16408])).
% 28.80/18.99 tff(16410,plain,
% 28.80/18.99 ((f3(f7(c2), c2) = c2) <=> (f7(c2) = c2)),
% 28.80/18.99 inference(monotonicity,[status(thm)],[16405])).
% 28.80/18.99 tff(16411,plain,
% 28.80/18.99 ((f7(c2) = c2) <=> (f3(f7(c2), c2) = c2)),
% 28.80/18.99 inference(symmetry,[status(thm)],[16410])).
% 28.80/18.99 tff(16412,plain,
% 28.80/18.99 ((~(f7(c2) = c2)) <=> (~(f3(f7(c2), c2) = c2))),
% 28.80/18.99 inference(monotonicity,[status(thm)],[16411])).
% 28.80/18.99 tff(16413,plain,
% 28.80/18.99 (~(f3(f7(c2), c2) = c2)),
% 28.80/18.99 inference(modus_ponens,[status(thm)],[17, 16412])).
% 28.80/18.99 tff(16414,assumption,(f3(c1, f8(c3)) = c1), introduced(assumption)).
% 28.80/18.99 tff(16415,plain,
% 28.80/18.99 (c2 = f8(f7(f4(c4)))),
% 28.80/18.99 inference(symmetry,[status(thm)],[13856])).
% 28.80/18.99 tff(16416,plain,
% 28.80/18.99 (c2 = f8(c3)),
% 28.80/18.99 inference(transitivity,[status(thm)],[16415, 16247, 16242])).
% 28.80/18.99 tff(16417,plain,
% 28.80/18.99 (f3(c1, c2) = f3(c1, f8(c3))),
% 28.80/18.99 inference(monotonicity,[status(thm)],[16416])).
% 28.80/18.99 tff(16418,plain,
% 28.80/18.99 (f3(f7(c2), c2) = f7(c2)),
% 28.80/18.99 inference(transitivity,[status(thm)],[16156, 16417, 16414, 125])).
% 28.80/18.99 tff(16419,plain,
% 28.80/18.99 (big_f(f3(f7(c2), c2), f7(c2)) <=> big_f(f7(c2), f7(c2))),
% 28.80/18.99 inference(monotonicity,[status(thm)],[16418])).
% 28.80/18.99 tff(16420,plain,
% 28.80/18.99 (big_f(f7(c2), f7(c2)) <=> big_f(f3(f7(c2), c2), f7(c2))),
% 28.80/18.99 inference(symmetry,[status(thm)],[16419])).
% 28.80/18.99 tff(16421,plain,
% 28.80/18.99 ((~big_f(f7(c2), f7(c2))) <=> (~big_f(f3(f7(c2), c2), f7(c2)))),
% 28.80/18.99 inference(monotonicity,[status(thm)],[16420])).
% 28.80/18.99 tff(16422,plain,
% 28.80/18.99 (~big_f(f3(f7(c2), c2), f7(c2))),
% 28.80/18.99 inference(modus_ponens,[status(thm)],[8218, 16421])).
% 28.80/18.99 tff(16423,plain,
% 28.80/18.99 ((f3(f7(c2), c2) = c2) <=> (f7(c2) = c2)),
% 28.80/18.99 inference(monotonicity,[status(thm)],[16418])).
% 28.80/18.99 tff(16424,plain,
% 28.80/18.99 ((f7(c2) = c2) <=> (f3(f7(c2), c2) = c2)),
% 28.80/18.99 inference(symmetry,[status(thm)],[16423])).
% 28.80/18.99 tff(16425,plain,
% 28.80/18.99 ((~(f7(c2) = c2)) <=> (~(f3(f7(c2), c2) = c2))),
% 28.80/18.99 inference(monotonicity,[status(thm)],[16424])).
% 28.80/18.99 tff(16426,plain,
% 28.80/18.99 (~(f3(f7(c2), c2) = c2)),
% 28.80/18.99 inference(modus_ponens,[status(thm)],[17, 16425])).
% 28.80/18.99 tff(16427,plain,
% 28.80/18.99 (big_f(f7(c2), f1(f7(c2), c2)) <=> big_f(f7(c2), f7(c2))),
% 28.80/18.99 inference(monotonicity,[status(thm)],[9118])).
% 28.80/18.99 tff(16428,plain,
% 28.80/18.99 (big_f(f7(c2), f7(c2)) <=> big_f(f7(c2), f1(f7(c2), c2))),
% 28.80/18.99 inference(symmetry,[status(thm)],[16427])).
% 28.80/18.99 tff(16429,plain,
% 28.80/18.99 ((~big_f(f7(c2), f7(c2))) <=> (~big_f(f7(c2), f1(f7(c2), c2)))),
% 28.80/18.99 inference(monotonicity,[status(thm)],[16428])).
% 28.80/18.99 tff(16430,plain,
% 28.80/18.99 (~big_f(f7(c2), f1(f7(c2), c2))),
% 28.80/18.99 inference(modus_ponens,[status(thm)],[8218, 16429])).
% 28.80/18.99 tff(16431,plain,
% 28.80/18.99 (big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2) | (f3(f7(c2), c2) = c2) | big_f(f3(f7(c2), c2), f7(c2))),
% 28.80/18.99 inference(unit_resolution,[status(thm)],[16355, 1014, 9749, 9495])).
% 28.80/18.99 tff(16432,plain,
% 28.80/18.99 ($false),
% 28.80/18.99 inference(unit_resolution,[status(thm)],[16431, 9122, 16430, 16426, 16422])).
% 28.80/18.99 tff(16433,plain,((~(f1(c1, c2) = c1)) | (f7(c2) = c4) | big_f(f7(c2), f7(c2)) | (~(f3(c1, f8(c3)) = c1)) | (~(f8(f7(f4(c4))) = c2)) | (~(f7(c1) = c2)) | (~(f4(c4) = c1)) | (~(c2 = c3)) | (f7(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 28.80/18.99 tff(16434,plain,
% 28.80/18.99 (~(f1(c1, c2) = c1)),
% 28.80/18.99 inference(unit_resolution,[status(thm)],[16433, 16404, 8218, 16349, 16396, 347, 11752, 1344, 17])).
% 28.80/18.99 tff(16435,plain,
% 28.80/18.99 (f1(c1, c2) = c2),
% 28.80/18.99 inference(unit_resolution,[status(thm)],[841, 16434])).
% 28.80/18.99 tff(16436,plain,
% 28.80/18.99 (f1(f7(c2), c2) = c2),
% 28.80/18.99 inference(transitivity,[status(thm)],[9112, 16435])).
% 28.80/18.99 tff(16437,plain,
% 28.80/18.99 (big_f(f7(c2), f1(f7(c2), c2)) <=> big_f(f7(c2), c2)),
% 28.80/18.99 inference(monotonicity,[status(thm)],[16436])).
% 28.80/18.99 tff(16438,plain,
% 28.80/18.99 (big_f(f7(c2), c2) <=> big_f(f7(c2), f1(f7(c2), c2))),
% 28.80/18.99 inference(symmetry,[status(thm)],[16437])).
% 28.80/18.99 tff(16439,plain,
% 28.80/18.99 (big_f(f7(c2), f1(f7(c2), c2))),
% 28.80/18.99 inference(modus_ponens,[status(thm)],[1180, 16438])).
% 28.80/18.99 tff(16440,plain,
% 28.80/18.99 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c2) = c3) | (f7(c2) = c4) | (~big_f(f7(c2), f1(f7(c2), c2))) | (~(f1(f7(c2), c2) = c2)) | (f3(f7(c2), c2) = c2) | big_f(f3(f7(c2), c2), f7(c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (f7(c2) = c3) | (f7(c2) = c4) | (~big_f(f7(c2), f1(f7(c2), c2))) | (~(f1(f7(c2), c2) = c2)) | (f3(f7(c2), c2) = c2) | big_f(f3(f7(c2), c2), f7(c2)))),
% 28.80/18.99 inference(rewrite,[status(thm)],[])).
% 28.80/18.99 tff(16441,plain,
% 28.80/18.99 (((f7(c2) = c4) | (f3(f7(c2), c2) = c2) | big_f(f3(f7(c2), c2), f7(c2)) | (f7(c2) = c3) | (~(f1(f7(c2), c2) = c2)) | (~big_f(f7(c2), f1(f7(c2), c2)))) <=> ((f7(c2) = c3) | (f7(c2) = c4) | (~big_f(f7(c2), f1(f7(c2), c2))) | (~(f1(f7(c2), c2) = c2)) | (f3(f7(c2), c2) = c2) | big_f(f3(f7(c2), c2), f7(c2)))),
% 28.80/18.99 inference(rewrite,[status(thm)],[])).
% 28.80/18.99 tff(16442,plain,
% 28.80/18.99 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c2) = c4) | (f3(f7(c2), c2) = c2) | big_f(f3(f7(c2), c2), f7(c2)) | (f7(c2) = c3) | (~(f1(f7(c2), c2) = c2)) | (~big_f(f7(c2), f1(f7(c2), c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c2) = c3) | (f7(c2) = c4) | (~big_f(f7(c2), f1(f7(c2), c2))) | (~(f1(f7(c2), c2) = c2)) | (f3(f7(c2), c2) = c2) | big_f(f3(f7(c2), c2), f7(c2))))),
% 28.80/18.99 inference(monotonicity,[status(thm)],[16441])).
% 28.80/18.99 tff(16443,plain,
% 28.80/18.99 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c2) = c4) | (f3(f7(c2), c2) = c2) | big_f(f3(f7(c2), c2), f7(c2)) | (f7(c2) = c3) | (~(f1(f7(c2), c2) = c2)) | (~big_f(f7(c2), f1(f7(c2), c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (f7(c2) = c3) | (f7(c2) = c4) | (~big_f(f7(c2), f1(f7(c2), c2))) | (~(f1(f7(c2), c2) = c2)) | (f3(f7(c2), c2) = c2) | big_f(f3(f7(c2), c2), f7(c2)))),
% 28.80/18.99 inference(transitivity,[status(thm)],[16442, 16440])).
% 28.80/18.99 tff(16444,plain,
% 28.80/18.99 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c2) = c4) | (f3(f7(c2), c2) = c2) | big_f(f3(f7(c2), c2), f7(c2)) | (f7(c2) = c3) | (~(f1(f7(c2), c2) = c2)) | (~big_f(f7(c2), f1(f7(c2), c2))))),
% 28.80/18.99 inference(quant_inst,[status(thm)],[])).
% 28.80/18.99 tff(16445,plain,
% 28.80/18.99 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (f7(c2) = c3) | (f7(c2) = c4) | (~big_f(f7(c2), f1(f7(c2), c2))) | (~(f1(f7(c2), c2) = c2)) | (f3(f7(c2), c2) = c2) | big_f(f3(f7(c2), c2), f7(c2))),
% 28.80/18.99 inference(modus_ponens,[status(thm)],[16444, 16443])).
% 28.80/18.99 tff(16446,plain,
% 28.80/18.99 ((~big_f(f7(c2), f1(f7(c2), c2))) | (~(f1(f7(c2), c2) = c2)) | (f3(f7(c2), c2) = c2) | big_f(f3(f7(c2), c2), f7(c2))),
% 28.80/18.99 inference(unit_resolution,[status(thm)],[16445, 904, 9749, 16349])).
% 28.80/18.99 tff(16447,plain,
% 28.80/18.99 ($false),
% 28.80/18.99 inference(unit_resolution,[status(thm)],[16446, 16439, 16436, 16413, 16409])).
% 28.80/18.99 tff(16448,plain,((f3(c1, c2) = c2) | big_f(f7(c2), f7(c2)) | (~(f7(c1) = c2)) | (~(f4(c4) = c1)) | (~(c2 = c3)) | (f7(c2) = c2) | (~big_f(f7(c2), c2)) | (~(f1(c2, c1) = c2)) | (~(f5(c2) = c2)) | (~(f10(c1) = c2)) | (~(f5(c1) = c1)) | (~(c2 = c4))), inference(lemma,lemma(discharge,[]))).
% 28.80/18.99 tff(16449,plain,
% 28.80/18.99 (~(f1(c2, c1) = c2)),
% 28.80/18.99 inference(unit_resolution,[status(thm)],[16448, 16241, 120, 15706, 16175, 17, 15921, 16182, 16189, 15, 15923, 16200])).
% 28.80/19.00 tff(16450,plain,
% 28.80/19.00 (f1(c2, c1) = c1),
% 28.80/19.00 inference(unit_resolution,[status(thm)],[10113, 16449])).
% 28.80/19.00 tff(16451,plain,
% 28.80/19.00 (f1(f5(c2), f5(c1)) = c1),
% 28.80/19.00 inference(modus_ponens,[status(thm)],[16450, 16195])).
% 28.80/19.00 tff(16452,plain,
% 28.80/19.00 ((f7(c2) = c2) <=> (c1 = c4)),
% 28.80/19.00 inference(transitivity,[status(thm)],[16203, 12587])).
% 28.80/19.00 tff(16453,plain,
% 28.80/19.00 ((~(f7(c2) = c2)) <=> (~(c1 = c4))),
% 28.80/19.00 inference(monotonicity,[status(thm)],[16452])).
% 28.80/19.00 tff(16454,plain,
% 28.80/19.00 (~(c1 = c4)),
% 28.80/19.00 inference(modus_ponens,[status(thm)],[17, 16453])).
% 28.80/19.00 tff(16455,plain,
% 28.80/19.00 (f1(f5(f10(c1)), c1) = f1(f5(c2), f5(c1))),
% 28.80/19.00 inference(symmetry,[status(thm)],[16184])).
% 28.80/19.00 tff(16456,plain,
% 28.80/19.00 (f1(c2, f7(c2)) = f1(f5(f10(c1)), c1)),
% 28.80/19.00 inference(symmetry,[status(thm)],[16191])).
% 28.80/19.00 tff(16457,plain,
% 28.80/19.00 (f1(c2, c1) = f1(f5(c2), f5(c1))),
% 28.80/19.00 inference(transitivity,[status(thm)],[16024, 16456, 16455])).
% 28.80/19.00 tff(16458,plain,
% 28.80/19.00 (f3(f1(c2, c1), c2) = f3(f1(f5(c2), f5(c1)), c2)),
% 28.80/19.00 inference(monotonicity,[status(thm)],[16457])).
% 28.80/19.00 tff(16459,plain,
% 28.80/19.00 (f3(f1(f5(c2), f5(c1)), c2) = f3(f1(c2, c1), c2)),
% 28.80/19.00 inference(symmetry,[status(thm)],[16458])).
% 28.80/19.00 tff(16460,plain,
% 28.80/19.00 ((f3(f1(f5(c2), f5(c1)), c2) = c2) <=> (f3(f1(c2, c1), c2) = c2)),
% 28.80/19.00 inference(monotonicity,[status(thm)],[16459])).
% 28.80/19.00 tff(16461,plain,
% 28.80/19.00 ((f3(f1(c2, c1), c2) = c2) <=> (f3(f1(f5(c2), f5(c1)), c2) = c2)),
% 28.80/19.00 inference(symmetry,[status(thm)],[16460])).
% 28.80/19.00 tff(16462,plain,
% 28.80/19.00 (c1 = f1(c2, c1)),
% 28.80/19.00 inference(symmetry,[status(thm)],[16450])).
% 28.80/19.00 tff(16463,plain,
% 28.80/19.00 (f3(c1, c2) = f3(f1(c2, c1), c2)),
% 28.80/19.00 inference(monotonicity,[status(thm)],[16462])).
% 28.80/19.00 tff(16464,plain,
% 28.80/19.00 (f3(f1(c2, c1), c2) = f3(c1, c2)),
% 28.80/19.00 inference(symmetry,[status(thm)],[16463])).
% 28.80/19.00 tff(16465,plain,
% 28.80/19.00 ((f3(f1(c2, c1), c2) = c2) <=> (f3(c1, c2) = c2)),
% 28.80/19.00 inference(monotonicity,[status(thm)],[16464])).
% 28.80/19.00 tff(16466,plain,
% 28.80/19.00 ((f3(c1, c2) = c2) <=> (f3(f1(c2, c1), c2) = c2)),
% 28.80/19.00 inference(symmetry,[status(thm)],[16465])).
% 28.80/19.00 tff(16467,plain,
% 28.80/19.00 ((f3(c1, c2) = c2) <=> (f3(f1(f5(c2), f5(c1)), c2) = c2)),
% 28.80/19.00 inference(transitivity,[status(thm)],[16466, 16461])).
% 28.80/19.00 tff(16468,plain,
% 28.80/19.00 ((~(f3(c1, c2) = c2)) <=> (~(f3(f1(f5(c2), f5(c1)), c2) = c2))),
% 28.80/19.00 inference(monotonicity,[status(thm)],[16467])).
% 28.80/19.00 tff(16469,plain,
% 28.80/19.00 (~(f3(f1(f5(c2), f5(c1)), c2) = c2)),
% 28.80/19.00 inference(modus_ponens,[status(thm)],[16241, 16468])).
% 28.80/19.00 tff(16470,plain,
% 28.80/19.00 (f3(c1, c2) = f3(f1(f5(c2), f5(c1)), c2)),
% 28.80/19.00 inference(monotonicity,[status(thm)],[10485])).
% 28.80/19.00 tff(16471,plain,
% 28.80/19.00 (f3(f1(f5(c2), f5(c1)), c2) = f3(c1, c2)),
% 28.80/19.00 inference(symmetry,[status(thm)],[16470])).
% 28.80/19.00 tff(16472,plain,
% 28.80/19.00 ((f3(f1(f5(c2), f5(c1)), c2) = c2) <=> (f3(c1, c2) = c2)),
% 28.80/19.00 inference(monotonicity,[status(thm)],[16471])).
% 28.80/19.00 tff(16473,plain,
% 28.80/19.00 ((~(f3(f1(f5(c2), f5(c1)), c2) = c2)) <=> (~(f3(c1, c2) = c2))),
% 28.80/19.00 inference(monotonicity,[status(thm)],[16472])).
% 28.80/19.00 tff(16474,assumption,(~(f3(f1(f5(c2), f5(c1)), c2) = c2)), introduced(assumption)).
% 28.80/19.00 tff(16475,plain,
% 28.80/19.00 (~(f3(c1, c2) = c2)),
% 28.80/19.00 inference(modus_ponens,[status(thm)],[16474, 16473])).
% 28.80/19.00 tff(16476,plain,
% 28.80/19.00 (f3(f1(f5(c2), f5(c1)), c2) = c1),
% 28.80/19.00 inference(unit_resolution,[status(thm)],[16061, 16474])).
% 28.80/19.00 tff(16477,plain,
% 28.80/19.00 (c1 = f3(f1(f5(c2), f5(c1)), c2)),
% 28.80/19.00 inference(symmetry,[status(thm)],[16476])).
% 28.80/19.00 tff(16478,plain,
% 28.80/19.00 (c1 = f3(c1, c2)),
% 28.80/19.00 inference(transitivity,[status(thm)],[16477, 16471])).
% 28.80/19.00 tff(16479,plain,
% 28.80/19.00 (big_f(c1, c1) <=> big_f(f3(c1, c2), c1)),
% 28.80/19.00 inference(monotonicity,[status(thm)],[16478])).
% 28.80/19.00 tff(16480,plain,
% 28.80/19.00 ((~big_f(c1, c1)) <=> (~big_f(f3(c1, c2), c1))),
% 28.80/19.00 inference(monotonicity,[status(thm)],[16479])).
% 28.80/19.00 tff(16481,plain,
% 28.80/19.00 (~big_f(f3(c1, c2), c1)),
% 28.80/19.00 inference(modus_ponens,[status(thm)],[66, 16480])).
% 28.80/19.00 tff(16482,plain,
% 28.80/19.00 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f1(c1, c2) = c2) | (c1 = c3) | (c1 = c4) | big_f(c1, f1(c1, c2)) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (f1(c1, c2) = c2) | (c1 = c3) | (c1 = c4) | big_f(c1, f1(c1, c2)) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2))),
% 28.80/19.00 inference(rewrite,[status(thm)],[])).
% 28.80/19.00 tff(16483,plain,
% 28.80/19.00 (((c1 = c4) | (f3(c1, c2) = c2) | big_f(f3(c1, c2), c1) | (c1 = c3) | (f1(c1, c2) = c2) | big_f(c1, f1(c1, c2))) <=> ((f1(c1, c2) = c2) | (c1 = c3) | (c1 = c4) | big_f(c1, f1(c1, c2)) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2))),
% 28.80/19.00 inference(rewrite,[status(thm)],[])).
% 28.80/19.00 tff(16484,plain,
% 28.80/19.00 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c1 = c4) | (f3(c1, c2) = c2) | big_f(f3(c1, c2), c1) | (c1 = c3) | (f1(c1, c2) = c2) | big_f(c1, f1(c1, c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f1(c1, c2) = c2) | (c1 = c3) | (c1 = c4) | big_f(c1, f1(c1, c2)) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2)))),
% 28.80/19.00 inference(monotonicity,[status(thm)],[16483])).
% 28.80/19.00 tff(16485,plain,
% 28.80/19.00 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c1 = c4) | (f3(c1, c2) = c2) | big_f(f3(c1, c2), c1) | (c1 = c3) | (f1(c1, c2) = c2) | big_f(c1, f1(c1, c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (f1(c1, c2) = c2) | (c1 = c3) | (c1 = c4) | big_f(c1, f1(c1, c2)) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2))),
% 28.80/19.00 inference(transitivity,[status(thm)],[16484, 16482])).
% 28.80/19.00 tff(16486,plain,
% 28.80/19.00 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c1 = c4) | (f3(c1, c2) = c2) | big_f(f3(c1, c2), c1) | (c1 = c3) | (f1(c1, c2) = c2) | big_f(c1, f1(c1, c2)))),
% 28.80/19.00 inference(quant_inst,[status(thm)],[])).
% 28.80/19.00 tff(16487,plain,
% 28.80/19.00 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (f1(c1, c2) = c2) | (c1 = c3) | (c1 = c4) | big_f(c1, f1(c1, c2)) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2)),
% 28.80/19.00 inference(modus_ponens,[status(thm)],[16486, 16485])).
% 28.80/19.00 tff(16488,plain,
% 28.80/19.00 ($false),
% 28.80/19.00 inference(unit_resolution,[status(thm)],[16487, 1014, 168, 482, 1052, 7524, 16481, 16475])).
% 28.80/19.00 tff(16489,plain,((f3(f1(f5(c2), f5(c1)), c2) = c2) | (c1 = c3) | (c1 = c4) | (f1(c1, c2) = c2) | big_f(c1, c1) | (~(f1(f5(c2), f5(c1)) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.80/19.00 tff(16490,plain,
% 28.80/19.00 (f1(c1, c2) = c2),
% 28.80/19.00 inference(unit_resolution,[status(thm)],[16489, 16469, 16454, 16451, 16183, 16181])).
% 28.80/19.00 tff(16491,plain,
% 28.80/19.00 (f1(f7(c2), c2) = c2),
% 28.80/19.00 inference(transitivity,[status(thm)],[9112, 16490])).
% 28.80/19.00 tff(16492,plain,
% 28.80/19.00 (big_f(f7(c2), f1(f7(c2), c2)) <=> big_f(f7(c2), c2)),
% 28.80/19.00 inference(monotonicity,[status(thm)],[16491])).
% 28.80/19.00 tff(16493,plain,
% 28.80/19.00 (big_f(f7(c2), c2) <=> big_f(f7(c2), f1(f7(c2), c2))),
% 28.80/19.00 inference(symmetry,[status(thm)],[16492])).
% 28.80/19.00 tff(16494,plain,
% 28.80/19.00 (big_f(f7(c2), f1(f7(c2), c2))),
% 28.80/19.00 inference(modus_ponens,[status(thm)],[15921, 16493])).
% 28.80/19.00 tff(16495,plain,
% 28.80/19.00 (big_f(f3(f7(c2), c2), f7(c2)) <=> big_f(f3(c1, c2), c1)),
% 28.80/19.00 inference(monotonicity,[status(thm)],[16156, 22])).
% 28.80/19.00 tff(16496,plain,
% 28.80/19.00 (big_f(f3(c1, c2), c1) <=> big_f(f3(f7(c2), c2), f7(c2))),
% 28.80/19.00 inference(symmetry,[status(thm)],[16495])).
% 28.80/19.00 tff(16497,plain,
% 28.80/19.00 ((~big_f(f3(c1, c2), c1)) <=> (~big_f(f3(f7(c2), c2), f7(c2)))),
% 28.80/19.00 inference(monotonicity,[status(thm)],[16496])).
% 28.80/19.00 tff(16498,plain,
% 28.80/19.00 (c1 = f3(c1, c2)),
% 28.80/19.00 inference(unit_resolution,[status(thm)],[16084, 16241, 16189, 15, 15923, 120])).
% 28.80/19.00 tff(16499,plain,
% 28.80/19.00 (big_f(c1, c1) <=> big_f(f3(c1, c2), c1)),
% 28.80/19.00 inference(unit_resolution,[status(thm)],[13192, 16498])).
% 28.80/19.00 tff(16500,plain,
% 28.80/19.00 (~big_f(f3(c1, c2), c1)),
% 28.80/19.00 inference(unit_resolution,[status(thm)],[13186, 16499, 16183])).
% 28.80/19.00 tff(16501,plain,
% 28.80/19.00 (~big_f(f3(f7(c2), c2), f7(c2))),
% 28.80/19.00 inference(modus_ponens,[status(thm)],[16500, 16497])).
% 28.80/19.00 tff(16502,plain,
% 28.80/19.00 ((f3(f7(c2), c2) = c2) <=> (f3(c1, c2) = c2)),
% 28.80/19.00 inference(monotonicity,[status(thm)],[16156])).
% 28.80/19.00 tff(16503,plain,
% 28.80/19.00 ((f3(c1, c2) = c2) <=> (f3(f7(c2), c2) = c2)),
% 28.80/19.00 inference(symmetry,[status(thm)],[16502])).
% 28.80/19.00 tff(16504,plain,
% 28.80/19.00 ((~(f3(c1, c2) = c2)) <=> (~(f3(f7(c2), c2) = c2))),
% 28.80/19.00 inference(monotonicity,[status(thm)],[16503])).
% 28.80/19.00 tff(16505,plain,
% 28.80/19.00 (~(f3(f7(c2), c2) = c2)),
% 28.80/19.00 inference(modus_ponens,[status(thm)],[16241, 16504])).
% 28.80/19.00 tff(16506,plain,
% 28.80/19.00 ((~big_f(f7(c2), f1(f7(c2), c2))) | (~(f1(f7(c2), c2) = c2))),
% 28.80/19.00 inference(unit_resolution,[status(thm)],[16445, 904, 16197, 16205, 16505, 16501])).
% 28.80/19.00 tff(16507,plain,
% 28.80/19.00 ($false),
% 28.80/19.00 inference(unit_resolution,[status(thm)],[16506, 16494, 16491])).
% 28.80/19.00 tff(16508,plain,(big_f(c2, c2) | (f7(c2) = c2) | (~(f10(c2) = c2)) | (f7(c1) = c1) | (f10(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 28.80/19.00 tff(16509,plain,
% 28.80/19.00 (big_f(c2, c2)),
% 28.80/19.00 inference(unit_resolution,[status(thm)],[16508, 17, 122, 115, 3])).
% 28.80/19.00 tff(16510,plain,
% 28.80/19.00 (big_f(c2, f10(f7(c2)))),
% 28.80/19.00 inference(modus_ponens,[status(thm)],[16509, 12125])).
% 28.80/19.00 tff(16511,plain,
% 28.80/19.00 (c4 = f7(c2)),
% 28.80/19.00 inference(transitivity,[status(thm)],[9094, 125])).
% 28.80/19.00 tff(16512,plain,
% 28.80/19.00 (f4(c4) = f7(c2)),
% 28.80/19.00 inference(transitivity,[status(thm)],[15706, 125])).
% 28.80/19.00 tff(16513,plain,
% 28.80/19.00 (big_f(f4(c4), c4) <=> big_f(f7(c2), f7(c2))),
% 28.80/19.00 inference(monotonicity,[status(thm)],[16512, 16511])).
% 28.80/19.00 tff(16514,plain,
% 28.80/19.00 (big_f(f7(c2), f7(c2)) <=> big_f(f4(c4), c4)),
% 28.80/19.00 inference(symmetry,[status(thm)],[16513])).
% 28.80/19.00 tff(16515,plain,
% 28.80/19.00 (big_f(f7(c2), c1) <=> big_f(f7(c2), f7(c2))),
% 28.80/19.00 inference(monotonicity,[status(thm)],[125])).
% 28.80/19.00 tff(16516,plain,
% 28.80/19.00 (big_f(f7(c2), c1) <=> big_f(f4(c4), c4)),
% 28.80/19.00 inference(transitivity,[status(thm)],[16515, 16514])).
% 28.80/19.00 tff(16517,plain,
% 28.80/19.00 ((~big_f(f7(f7(c2)), f7(c2))) <=> (~big_f(c2, f7(c2)))),
% 28.80/19.00 inference(monotonicity,[status(thm)],[12449])).
% 28.80/19.00 tff(16518,assumption,(~(f5(c1) = c1)), introduced(assumption)).
% 28.80/19.00 tff(16519,plain,
% 28.80/19.00 (f5(c1) = c2),
% 28.80/19.00 inference(unit_resolution,[status(thm)],[1708, 16518])).
% 28.80/19.00 tff(16520,plain,
% 28.80/19.00 (f9(c2, c2) = f9(c2, f5(c1))),
% 28.80/19.00 inference(monotonicity,[status(thm)],[1761])).
% 28.80/19.00 tff(16521,plain,
% 28.80/19.00 (f9(c2, f5(c1)) = f9(c2, c2)),
% 28.80/19.00 inference(symmetry,[status(thm)],[16520])).
% 28.80/19.00 tff(16522,plain,
% 28.80/19.00 ((f9(c2, f5(c1)) = c2) <=> (f9(c2, c2) = c2)),
% 28.80/19.00 inference(monotonicity,[status(thm)],[16521])).
% 28.80/19.00 tff(16523,plain,
% 28.80/19.00 ((f9(c2, c2) = c2) <=> (f9(c2, f5(c1)) = c2)),
% 28.80/19.00 inference(symmetry,[status(thm)],[16522])).
% 28.80/19.00 tff(16524,plain,
% 28.80/19.00 ((~(f9(c2, c2) = c2)) <=> (~(f9(c2, f5(c1)) = c2))),
% 28.80/19.00 inference(monotonicity,[status(thm)],[16523])).
% 28.80/19.00 tff(16525,plain,
% 28.80/19.00 (~(f9(c2, f5(c1)) = c2)),
% 28.80/19.00 inference(modus_ponens,[status(thm)],[1209, 16524])).
% 28.80/19.00 tff(16526,plain,
% 28.80/19.00 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f9(c2, f5(c1)) = c1) | (f9(c2, f5(c1)) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f9(c2, f5(c1)) = c1) | (f9(c2, f5(c1)) = c2))),
% 28.80/19.00 inference(rewrite,[status(thm)],[])).
% 28.80/19.00 tff(16527,plain,
% 28.80/19.00 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f9(c2, f5(c1)) = c1) | (f9(c2, f5(c1)) = c2))),
% 28.80/19.00 inference(quant_inst,[status(thm)],[])).
% 28.80/19.00 tff(16528,plain,
% 28.80/19.00 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f9(c2, f5(c1)) = c1) | (f9(c2, f5(c1)) = c2)),
% 28.80/19.00 inference(modus_ponens,[status(thm)],[16527, 16526])).
% 28.80/19.00 tff(16529,plain,
% 28.80/19.00 ((f9(c2, f5(c1)) = c1) | (f9(c2, f5(c1)) = c2)),
% 28.80/19.00 inference(unit_resolution,[status(thm)],[16528, 10])).
% 28.80/19.00 tff(16530,plain,
% 28.80/19.00 (f9(c2, f5(c1)) = c1),
% 28.80/19.00 inference(unit_resolution,[status(thm)],[16529, 16525])).
% 28.80/19.00 tff(16531,plain,
% 28.80/19.00 (f9(c2, c2) = f7(c2)),
% 28.80/19.00 inference(transitivity,[status(thm)],[16520, 16530, 342])).
% 28.80/19.00 tff(16532,plain,
% 28.80/19.00 (big_f(f9(c2, c2), c2) <=> big_f(f7(c2), c2)),
% 28.80/19.00 inference(monotonicity,[status(thm)],[16531])).
% 28.80/19.00 tff(16533,plain,
% 28.80/19.00 (big_f(f7(c2), c2) <=> big_f(f9(c2, c2), c2)),
% 28.80/19.00 inference(symmetry,[status(thm)],[16532])).
% 28.80/19.00 tff(16534,plain,
% 28.80/19.00 ((~big_f(f7(c2), c2)) <=> (~big_f(f9(c2, c2), c2))),
% 28.80/19.00 inference(monotonicity,[status(thm)],[16533])).
% 28.80/19.00 tff(16535,plain,
% 28.80/19.00 (~big_f(f9(c2, c2), c2)),
% 28.80/19.00 inference(modus_ponens,[status(thm)],[1521, 16534])).
% 28.80/19.00 tff(16536,plain,
% 28.80/19.00 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))))),
% 28.80/19.00 inference(rewrite,[status(thm)],[])).
% 28.80/19.00 tff(16537,plain,
% 28.80/19.00 (((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f7(c2)) = f7(c2)) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2)))) <=> ((~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))))),
% 28.80/19.00 inference(rewrite,[status(thm)],[])).
% 28.80/19.00 tff(16538,plain,
% 28.80/19.00 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f7(c2)) = f7(c2)) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2)))))),
% 28.80/19.00 inference(monotonicity,[status(thm)],[16537])).
% 28.80/19.00 tff(16539,plain,
% 28.80/19.00 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f7(c2)) = f7(c2)) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))))),
% 28.80/19.00 inference(transitivity,[status(thm)],[16538, 16536])).
% 28.80/19.00 tff(16540,plain,
% 28.80/19.00 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f7(c2)) = f7(c2)) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2))))),
% 28.80/19.00 inference(quant_inst,[status(thm)],[])).
% 28.80/19.00 tff(16541,plain,
% 28.80/19.00 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2)))),
% 28.80/19.00 inference(modus_ponens,[status(thm)],[16540, 16539])).
% 28.80/19.00 tff(16542,plain,
% 28.80/19.00 ((f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2))),
% 28.80/19.00 inference(unit_resolution,[status(thm)],[16541, 676, 122, 8473, 10466, 10465])).
% 28.80/19.00 tff(16543,plain,
% 28.80/19.00 (big_f(f9(c2, c2), f10(c2))),
% 28.80/19.00 inference(unit_resolution,[status(thm)],[16542, 1209])).
% 28.80/19.00 tff(16544,plain,
% 28.80/19.00 (big_f(f9(c2, c2), c2)),
% 28.80/19.00 inference(unit_resolution,[status(thm)],[3687, 16543, 122])).
% 28.80/19.00 tff(16545,plain,
% 28.80/19.00 ($false),
% 28.80/19.00 inference(unit_resolution,[status(thm)],[16544, 16535])).
% 28.80/19.00 tff(16546,plain,((f9(c2, c2) = c2) | big_f(f7(c2), c2) | (~(f7(c2) = c1)) | (~(f5(c1) = c2)) | (~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(f7(c2)), f7(c2)))), inference(lemma,lemma(discharge,[]))).
% 28.80/19.00 tff(16547,plain,
% 28.80/19.00 (f9(c2, c2) = c2),
% 28.80/19.00 inference(unit_resolution,[status(thm)],[16546, 10466, 292, 186, 122, 8473, 1521, 10465])).
% 28.80/19.00 tff(16548,plain,
% 28.80/19.00 (big_f(f9(c2, c2), c2) <=> big_f(c2, c2)),
% 28.80/19.00 inference(monotonicity,[status(thm)],[16547])).
% 28.80/19.00 tff(16549,plain,
% 28.80/19.00 (big_f(c2, c2) <=> big_f(f9(c2, c2), c2)),
% 28.80/19.00 inference(symmetry,[status(thm)],[16548])).
% 28.80/19.00 tff(16550,plain,
% 28.80/19.00 (big_f(f9(c2, c2), c2)),
% 28.80/19.00 inference(modus_ponens,[status(thm)],[1345, 16549])).
% 28.80/19.00 tff(16551,plain,
% 28.80/19.00 (~big_f(f9(c2, c2), f10(c2))),
% 28.80/19.00 inference(unit_resolution,[status(thm)],[10468, 16547, 8473, 10466, 10465, 122])).
% 28.80/19.00 tff(16552,plain,
% 28.80/19.00 (~big_f(f9(c2, c2), c2)),
% 28.80/19.00 inference(unit_resolution,[status(thm)],[6482, 16551, 122])).
% 28.80/19.00 tff(16553,plain,
% 28.80/19.00 ($false),
% 28.80/19.00 inference(unit_resolution,[status(thm)],[16552, 16550])).
% 28.80/19.00 tff(16554,plain,((f7(c2) = f5(f7(c2))) | (~big_f(c2, c2)) | (~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | (~big_f(f7(f7(c2)), f7(c2))) | (~(f7(c2) = c1)) | (~(f5(c1) = c2)) | big_f(f7(c2), c2)), inference(lemma,lemma(discharge,[]))).
% 28.80/19.00 tff(16555,plain,
% 28.80/19.00 (f7(c2) = f5(f7(c2))),
% 28.80/19.00 inference(unit_resolution,[status(thm)],[16554, 16519, 122, 8473, 10465, 292, 1345, 1521])).
% 28.80/19.00 tff(16556,plain,
% 28.80/19.00 (f5(c1) = c1),
% 28.80/19.00 inference(modus_ponens,[status(thm)],[16555, 8471])).
% 28.80/19.00 tff(16557,plain,
% 28.80/19.00 ($false),
% 28.80/19.00 inference(unit_resolution,[status(thm)],[16518, 16556])).
% 28.80/19.00 tff(16558,plain,((f5(c1) = c1) | (~(f7(c2) = c1)) | (~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | (~big_f(f7(f7(c2)), f7(c2))) | (~big_f(c2, c2)) | big_f(f7(c2), c2)), inference(lemma,lemma(discharge,[]))).
% 28.80/19.00 tff(16559,plain,
% 28.80/19.00 (f5(c1) = c1),
% 28.80/19.00 inference(unit_resolution,[status(thm)],[16558, 10465, 122, 12943, 22, 1345, 1521])).
% 28.80/19.00 tff(16560,plain,
% 28.80/19.00 (f5(c1) = f7(c2)),
% 28.80/19.00 inference(transitivity,[status(thm)],[16559, 125])).
% 28.80/19.00 tff(16561,plain,
% 28.80/19.00 ((c2 = f5(c1)) <=> (c2 = f7(c2))),
% 28.80/19.00 inference(monotonicity,[status(thm)],[16560])).
% 28.80/19.00 tff(16562,plain,
% 28.80/19.00 ((c2 = f5(c1)) <=> (f7(c2) = c2)),
% 28.80/19.00 inference(transitivity,[status(thm)],[16561, 8409])).
% 28.80/19.00 tff(16563,plain,
% 28.80/19.00 ((f7(c2) = c2) <=> (c2 = f5(c1))),
% 28.80/19.00 inference(symmetry,[status(thm)],[16562])).
% 28.80/19.00 tff(16564,plain,
% 28.80/19.00 ((f7(c2) = c2) <=> (c2 = f5(f7(c2)))),
% 28.80/19.00 inference(transitivity,[status(thm)],[16563, 8602])).
% 28.80/19.00 tff(16565,plain,
% 28.80/19.00 ((~(f7(c2) = c2)) <=> (~(c2 = f5(f7(c2))))),
% 28.80/19.00 inference(monotonicity,[status(thm)],[16564])).
% 28.80/19.00 tff(16566,plain,
% 28.80/19.00 (~(c2 = f5(f7(c2)))),
% 28.80/19.00 inference(modus_ponens,[status(thm)],[17, 16565])).
% 28.80/19.00 tff(16567,plain,
% 28.80/19.00 (big_f(f7(f7(c2)), c2)),
% 28.80/19.00 inference(modus_ponens,[status(thm)],[1345, 8617])).
% 28.80/19.00 tff(16568,plain,
% 28.80/19.00 (f10(c3) = f10(f7(c2))),
% 28.80/19.00 inference(monotonicity,[status(thm)],[8410])).
% 28.80/19.00 tff(16569,plain,
% 28.80/19.00 (f10(c3) = c2),
% 28.80/19.00 inference(transitivity,[status(thm)],[16568, 23, 16])).
% 28.80/19.00 tff(16570,plain,
% 28.80/19.00 ((f10(c3) = c1) <=> (c2 = f7(c2))),
% 28.80/19.00 inference(monotonicity,[status(thm)],[16569, 125])).
% 28.80/19.00 tff(16571,plain,
% 28.80/19.00 ((f10(c3) = c1) <=> (f7(c2) = c2)),
% 28.80/19.00 inference(transitivity,[status(thm)],[16570, 8409])).
% 28.80/19.00 tff(16572,plain,
% 28.80/19.00 ((f7(c2) = c2) <=> (f10(c3) = c1)),
% 28.80/19.00 inference(symmetry,[status(thm)],[16571])).
% 28.80/19.00 tff(16573,plain,
% 28.80/19.00 ((f7(c2) = c2) <=> (f10(c3) = c3)),
% 28.80/19.00 inference(transitivity,[status(thm)],[16572, 8827])).
% 28.80/19.00 tff(16574,plain,
% 28.80/19.00 ((~(f7(c2) = c2)) <=> (~(f10(c3) = c3))),
% 28.80/19.00 inference(monotonicity,[status(thm)],[16573])).
% 28.80/19.00 tff(16575,plain,
% 28.80/19.00 (~(f10(c3) = c3)),
% 28.80/19.00 inference(modus_ponens,[status(thm)],[17, 16574])).
% 28.80/19.00 tff(16576,plain,
% 28.80/19.00 (big_f(c2, f10(c3)) <=> big_f(c2, c2)),
% 28.80/19.00 inference(monotonicity,[status(thm)],[16569])).
% 28.80/19.00 tff(16577,plain,
% 28.80/19.00 (big_f(c2, c2) <=> big_f(c2, f10(c3))),
% 28.80/19.00 inference(symmetry,[status(thm)],[16576])).
% 28.80/19.00 tff(16578,plain,
% 28.80/19.00 (big_f(c2, f10(c3))),
% 28.80/19.00 inference(modus_ponens,[status(thm)],[1345, 16577])).
% 28.80/19.00 tff(16579,assumption,(big_f(c2, f10(c3))), introduced(assumption)).
% 28.80/19.00 tff(16580,plain,
% 28.80/19.00 ((f8(f7(c2)) = c2) <=> (c2 = f8(f7(c2)))),
% 28.80/19.00 inference(commutativity,[status(thm)],[])).
% 28.80/19.00 tff(16581,plain,
% 28.80/19.00 (f8(c3) = f8(f7(c2))),
% 28.80/19.00 inference(monotonicity,[status(thm)],[8410])).
% 28.80/19.00 tff(16582,plain,
% 28.80/19.00 ((f8(c3) = c2) <=> (f8(f7(c2)) = c2)),
% 28.80/19.00 inference(monotonicity,[status(thm)],[16581])).
% 28.80/19.00 tff(16583,plain,
% 28.80/19.00 ((f8(c3) = c2) <=> (c2 = f8(f7(c2)))),
% 28.80/19.00 inference(transitivity,[status(thm)],[16582, 16580])).
% 28.80/19.00 tff(16584,plain,
% 28.80/19.00 ((c2 = f8(f7(c2))) <=> (f8(c3) = c2)),
% 28.80/19.00 inference(symmetry,[status(thm)],[16583])).
% 28.80/19.00 tff(16585,plain,
% 28.80/19.00 (f8(f7(c2)) = f7(c2)),
% 28.80/19.00 inference(transitivity,[status(thm)],[13226, 3018, 125])).
% 28.80/19.00 tff(16586,plain,
% 28.80/19.00 ((c2 = f8(f7(c2))) <=> (c2 = f7(c2))),
% 28.80/19.00 inference(monotonicity,[status(thm)],[16585])).
% 28.80/19.00 tff(16587,plain,
% 28.80/19.00 ((c2 = f8(f7(c2))) <=> (f7(c2) = c2)),
% 28.80/19.00 inference(transitivity,[status(thm)],[16586, 8409])).
% 28.80/19.00 tff(16588,plain,
% 28.80/19.00 ((f7(c2) = c2) <=> (c2 = f8(f7(c2)))),
% 28.80/19.00 inference(symmetry,[status(thm)],[16587])).
% 28.80/19.00 tff(16589,plain,
% 28.80/19.00 ((f7(c2) = c2) <=> (c2 = f8(c3))),
% 28.80/19.00 inference(transitivity,[status(thm)],[16588, 16584, 209])).
% 28.80/19.00 tff(16590,plain,
% 28.80/19.00 ((~(f7(c2) = c2)) <=> (~(c2 = f8(c3)))),
% 28.80/19.00 inference(monotonicity,[status(thm)],[16589])).
% 28.80/19.00 tff(16591,plain,
% 28.80/19.00 (~(c2 = f8(c3))),
% 28.80/19.00 inference(modus_ponens,[status(thm)],[17, 16590])).
% 28.80/19.00 tff(16592,plain,
% 28.80/19.00 (c2 = f5(c1)),
% 28.80/19.00 inference(unit_resolution,[status(thm)],[3528, 16591, 115, 12871, 2828, 16579])).
% 28.80/19.00 tff(16593,plain,
% 28.80/19.00 (f5(c1) = c2),
% 28.80/19.00 inference(symmetry,[status(thm)],[16592])).
% 28.80/19.00 tff(16594,plain,
% 28.80/19.00 ((~(f7(c2) = c2)) <=> (~(c2 = f8(f7(c2))))),
% 28.80/19.00 inference(monotonicity,[status(thm)],[16588])).
% 28.80/19.00 tff(16595,plain,
% 28.80/19.00 (~(c2 = f8(f7(c2)))),
% 28.80/19.00 inference(modus_ponens,[status(thm)],[17, 16594])).
% 28.80/19.00 tff(16596,plain,
% 28.80/19.00 ((c2 = f8(f7(c2))) | (f7(c2) = f5(f7(c2)))),
% 28.80/19.00 inference(unit_resolution,[status(thm)],[13340, 1659, 12943, 10465, 8523, 12607])).
% 28.80/19.00 tff(16597,plain,
% 28.80/19.00 (f7(c2) = f5(f7(c2))),
% 28.80/19.00 inference(unit_resolution,[status(thm)],[16596, 16595])).
% 28.80/19.00 tff(16598,plain,
% 28.80/19.00 (f7(c2) = c2),
% 28.80/19.00 inference(transitivity,[status(thm)],[16597, 8600, 16593])).
% 28.80/19.00 tff(16599,plain,
% 28.80/19.00 ($false),
% 28.80/19.00 inference(unit_resolution,[status(thm)],[17, 16598])).
% 28.80/19.00 tff(16600,plain,((~(f8(c1) = c1)) | (f7(c2) = c2) | (f7(c1) = c1) | (~big_f(f7(c1), c2)) | (f10(c3) = c3) | (~big_f(c2, f10(c3))) | (~big_f(f7(f7(c2)), f7(c2))) | (f10(f7(c2)) = f7(c2)) | (~big_f(c2, f10(f7(c2)))) | (~(c3 = c1))), inference(lemma,lemma(discharge,[]))).
% 28.80/19.00 tff(16601,plain,
% 28.80/19.00 (~(f8(c1) = c1)),
% 28.80/19.00 inference(unit_resolution,[status(thm)],[16600, 10465, 115, 17, 12774, 16578, 16575, 12471, 12466, 172])).
% 28.80/19.00 tff(16602,plain,
% 28.80/19.00 (f8(c1) = c2),
% 28.80/19.00 inference(unit_resolution,[status(thm)],[1680, 16601])).
% 28.80/19.00 tff(16603,plain,
% 28.80/19.00 (f8(f7(c2)) = c2),
% 28.80/19.00 inference(transitivity,[status(thm)],[12960, 1671])).
% 28.80/19.00 tff(16604,plain,
% 28.80/19.00 ((f9(c2, c2) = f8(f7(c2))) <=> (f9(c2, c2) = c2)),
% 28.80/19.00 inference(monotonicity,[status(thm)],[16603])).
% 28.80/19.00 tff(16605,plain,
% 28.80/19.00 ((f9(c2, c2) = c2) <=> (f9(c2, c2) = f8(f7(c2)))),
% 28.80/19.00 inference(symmetry,[status(thm)],[16604])).
% 28.80/19.00 tff(16606,plain,
% 28.80/19.00 ((~(f9(c2, c2) = c2)) <=> (~(f9(c2, c2) = f8(f7(c2))))),
% 28.80/19.00 inference(monotonicity,[status(thm)],[16605])).
% 28.80/19.00 tff(16607,plain,
% 28.80/19.00 (~(f9(c2, c2) = f8(f7(c2)))),
% 28.80/19.00 inference(modus_ponens,[status(thm)],[1209, 16606])).
% 28.80/19.00 tff(16608,plain,
% 28.80/19.00 (big_f(f9(c2, c2), f10(f7(c2))) <=> big_f(f9(c2, c2), c2)),
% 28.80/19.00 inference(monotonicity,[status(thm)],[12967])).
% 28.80/19.00 tff(16609,plain,
% 28.80/19.00 (big_f(f9(c2, c2), c2) <=> big_f(f9(c2, c2), f10(f7(c2)))),
% 28.80/19.00 inference(symmetry,[status(thm)],[16608])).
% 28.80/19.00 tff(16610,assumption,(~(c2 = f5(f7(c2)))), introduced(assumption)).
% 28.80/19.00 tff(16611,plain,
% 28.80/19.00 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2)))),
% 28.80/19.01 inference(rewrite,[status(thm)],[])).
% 28.80/19.01 tff(16612,plain,
% 28.80/19.01 (((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f7(c2)) = f7(c2)) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2))) <=> ((~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2)))),
% 28.80/19.01 inference(rewrite,[status(thm)],[])).
% 28.80/19.01 tff(16613,plain,
% 28.80/19.01 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f7(c2)) = f7(c2)) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2))))),
% 28.80/19.01 inference(monotonicity,[status(thm)],[16612])).
% 28.80/19.01 tff(16614,plain,
% 28.80/19.01 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f7(c2)) = f7(c2)) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2)))),
% 28.80/19.01 inference(transitivity,[status(thm)],[16613, 16611])).
% 28.80/19.01 tff(16615,plain,
% 28.80/19.01 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(f7(c2)) = f7(c2)) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2)))),
% 28.80/19.01 inference(quant_inst,[status(thm)],[])).
% 28.80/19.01 tff(16616,plain,
% 28.80/19.01 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2))),
% 28.80/19.01 inference(modus_ponens,[status(thm)],[16615, 16614])).
% 28.80/19.01 tff(16617,plain,
% 28.80/19.01 ($false),
% 28.80/19.01 inference(unit_resolution,[status(thm)],[16616, 676, 122, 8473, 1209, 256, 12480, 16610])).
% 28.80/19.01 tff(16618,plain,(big_f(f9(c2, c2), f10(c2)) | (~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | (f9(c2, c2) = c2) | (~big_f(f7(f7(c2)), c2)) | (c2 = f5(f7(c2)))), inference(lemma,lemma(discharge,[]))).
% 28.80/19.01 tff(16619,plain,
% 28.80/19.01 (big_f(f9(c2, c2), f10(c2))),
% 28.80/19.01 inference(unit_resolution,[status(thm)],[16618, 1209, 8473, 122, 12480, 16610])).
% 28.80/19.01 tff(16620,plain,
% 28.80/19.01 (big_f(f9(c2, c2), c2)),
% 28.80/19.01 inference(unit_resolution,[status(thm)],[3687, 16619, 122])).
% 28.80/19.01 tff(16621,plain,
% 28.80/19.01 (big_f(f9(c2, c2), f10(f7(c2)))),
% 28.80/19.01 inference(modus_ponens,[status(thm)],[16620, 16609])).
% 28.80/19.01 tff(16622,plain,
% 28.80/19.01 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(f7(c2)) = f7(c2)) | (f10(f7(c2)) = f7(c2)) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2)) | (f9(c2, c2) = f8(f7(c2))) | (~big_f(f9(c2, c2), f10(f7(c2)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(f7(c2)) = f7(c2)) | (f10(f7(c2)) = f7(c2)) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2)) | (f9(c2, c2) = f8(f7(c2))) | (~big_f(f9(c2, c2), f10(f7(c2)))))),
% 28.80/19.01 inference(rewrite,[status(thm)],[])).
% 28.80/19.01 tff(16623,plain,
% 28.80/19.01 (((f10(f7(c2)) = f7(c2)) | (f9(c2, c2) = f8(f7(c2))) | (~big_f(f9(c2, c2), f10(f7(c2)))) | (f7(f7(c2)) = f7(c2)) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2))) <=> ((f7(f7(c2)) = f7(c2)) | (f10(f7(c2)) = f7(c2)) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2)) | (f9(c2, c2) = f8(f7(c2))) | (~big_f(f9(c2, c2), f10(f7(c2)))))),
% 28.80/19.01 inference(rewrite,[status(thm)],[])).
% 28.80/19.01 tff(16624,plain,
% 28.80/19.01 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f7(c2)) = f7(c2)) | (f9(c2, c2) = f8(f7(c2))) | (~big_f(f9(c2, c2), f10(f7(c2)))) | (f7(f7(c2)) = f7(c2)) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(f7(c2)) = f7(c2)) | (f10(f7(c2)) = f7(c2)) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2)) | (f9(c2, c2) = f8(f7(c2))) | (~big_f(f9(c2, c2), f10(f7(c2))))))),
% 28.80/19.01 inference(monotonicity,[status(thm)],[16623])).
% 28.80/19.01 tff(16625,plain,
% 28.80/19.01 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f7(c2)) = f7(c2)) | (f9(c2, c2) = f8(f7(c2))) | (~big_f(f9(c2, c2), f10(f7(c2)))) | (f7(f7(c2)) = f7(c2)) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(f7(c2)) = f7(c2)) | (f10(f7(c2)) = f7(c2)) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2)) | (f9(c2, c2) = f8(f7(c2))) | (~big_f(f9(c2, c2), f10(f7(c2)))))),
% 28.80/19.01 inference(transitivity,[status(thm)],[16624, 16622])).
% 28.80/19.01 tff(16626,plain,
% 28.80/19.01 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f7(c2)) = f7(c2)) | (f9(c2, c2) = f8(f7(c2))) | (~big_f(f9(c2, c2), f10(f7(c2)))) | (f7(f7(c2)) = f7(c2)) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2)))),
% 28.80/19.01 inference(quant_inst,[status(thm)],[])).
% 28.80/19.01 tff(16627,plain,
% 28.80/19.01 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(f7(c2)) = f7(c2)) | (f10(f7(c2)) = f7(c2)) | (c2 = f5(f7(c2))) | (~big_f(f7(f7(c2)), c2)) | (f9(c2, c2) = f8(f7(c2))) | (~big_f(f9(c2, c2), f10(f7(c2))))),
% 28.80/19.01 inference(modus_ponens,[status(thm)],[16626, 16625])).
% 28.80/19.01 tff(16628,plain,
% 28.80/19.01 ((f9(c2, c2) = f8(f7(c2))) | (~big_f(f9(c2, c2), f10(f7(c2))))),
% 28.80/19.01 inference(unit_resolution,[status(thm)],[16627, 1659, 8473, 8523, 12480, 16610])).
% 28.80/19.01 tff(16629,plain,
% 28.80/19.01 ($false),
% 28.80/19.01 inference(unit_resolution,[status(thm)],[16628, 16621, 16607])).
% 28.80/19.01 tff(16630,plain,((f9(c2, c2) = c2) | (f7(f7(c2)) = f7(c2)) | (f10(f7(c2)) = f7(c2)) | (~big_f(f7(f7(c2)), c2)) | (c2 = f5(f7(c2))) | (~(f10(c1) = c2)) | (~(f7(c2) = c1)) | (~(f8(c1) = c2)) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.80/19.01 tff(16631,plain,
% 28.80/19.01 (f9(c2, c2) = c2),
% 28.80/19.01 inference(unit_resolution,[status(thm)],[16630, 16566, 12471, 16567, 12943, 16, 22, 16602, 122])).
% 28.80/19.01 tff(16632,plain,
% 28.80/19.01 (big_f(f9(c2, c2), c2) <=> big_f(c2, c2)),
% 28.80/19.01 inference(monotonicity,[status(thm)],[16631])).
% 28.80/19.01 tff(16633,plain,
% 28.80/19.01 (big_f(c2, c2) <=> big_f(f9(c2, c2), c2)),
% 28.80/19.01 inference(symmetry,[status(thm)],[16632])).
% 28.80/19.01 tff(16634,plain,
% 28.80/19.01 (big_f(c2, c2) <=> big_f(f9(c2, c2), f10(c2))),
% 28.80/19.01 inference(transitivity,[status(thm)],[16633, 130])).
% 28.80/19.01 tff(16635,plain,
% 28.80/19.01 (big_f(f9(c2, c2), f10(c2))),
% 28.80/19.01 inference(modus_ponens,[status(thm)],[1345, 16634])).
% 28.80/19.01 tff(16636,plain,
% 28.80/19.01 ($false),
% 28.80/19.01 inference(unit_resolution,[status(thm)],[9290, 1190, 122, 12943, 16631, 16635, 16567, 16566])).
% 28.80/19.01 tff(16637,plain,((~big_f(f7(f7(c2)), f7(c2))) | (~(f10(c2) = c2)) | (~big_f(c2, c2)) | (~(f10(c1) = c2)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (f7(c1) = c1) | (~(c3 = c1))), inference(lemma,lemma(discharge,[]))).
% 28.80/19.01 tff(16638,plain,
% 28.80/19.01 (~big_f(f7(f7(c2)), f7(c2))),
% 28.80/19.01 inference(unit_resolution,[status(thm)],[16637, 11754, 16509, 15, 17, 1521, 115, 122])).
% 28.80/19.01 tff(16639,plain,
% 28.82/19.01 ((f5(c1) = c1) <=> (f7(c2) = f5(f7(c2)))),
% 28.82/19.01 inference(symmetry,[status(thm)],[8605])).
% 28.82/19.01 tff(16640,plain,
% 28.82/19.01 (big_f(f7(f7(c2)), f7(c2)) <=> big_f(c2, c1)),
% 28.82/19.01 inference(transitivity,[status(thm)],[12449, 9311])).
% 28.82/19.01 tff(16641,plain,
% 28.82/19.01 ((~big_f(f7(f7(c2)), f7(c2))) <=> (~big_f(c2, c1))),
% 28.82/19.01 inference(monotonicity,[status(thm)],[16640])).
% 28.82/19.01 tff(16642,plain,
% 28.82/19.01 (~big_f(c2, c1)),
% 28.82/19.01 inference(modus_ponens,[status(thm)],[16638, 16641])).
% 28.82/19.01 tff(16643,plain,
% 28.82/19.01 (f7(c2) = c4),
% 28.82/19.01 inference(transitivity,[status(thm)],[292, 567])).
% 28.82/19.01 tff(16644,plain,
% 28.82/19.01 ($false),
% 28.82/19.01 inference(unit_resolution,[status(thm)],[9495, 16643])).
% 28.82/19.01 tff(16645,plain,((~(c4 = c1)) | (f7(c2) = c4) | (~(f7(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.82/19.01 tff(16646,plain,
% 28.82/19.01 (~(c4 = c1)),
% 28.82/19.01 inference(unit_resolution,[status(thm)],[16645, 9495, 22])).
% 28.82/19.01 tff(16647,plain,
% 28.82/19.01 (c4 = c2),
% 28.82/19.01 inference(unit_resolution,[status(thm)],[461, 16646])).
% 28.82/19.01 tff(16648,plain,
% 28.82/19.01 (c2 = c4),
% 28.82/19.01 inference(symmetry,[status(thm)],[16647])).
% 28.82/19.01 tff(16649,plain,
% 28.82/19.01 (f4(c2) = f4(c4)),
% 28.82/19.01 inference(monotonicity,[status(thm)],[16648])).
% 28.82/19.01 tff(16650,plain,
% 28.82/19.01 (f4(c4) = f4(c2)),
% 28.82/19.01 inference(symmetry,[status(thm)],[16649])).
% 28.82/19.01 tff(16651,plain,
% 28.82/19.01 (c1 = f4(c4)),
% 28.82/19.01 inference(symmetry,[status(thm)],[11752])).
% 28.82/19.01 tff(16652,plain,
% 28.82/19.01 (f7(c2) = f4(c2)),
% 28.82/19.01 inference(transitivity,[status(thm)],[22, 16651, 16650])).
% 28.82/19.01 tff(16653,plain,
% 28.82/19.01 ((~big_f(f7(c2), c2)) <=> (~big_f(c1, c2))),
% 28.82/19.01 inference(monotonicity,[status(thm)],[12120])).
% 28.82/19.01 tff(16654,plain,
% 28.82/19.01 (~big_f(c1, c2)),
% 28.82/19.01 inference(modus_ponens,[status(thm)],[1521, 16653])).
% 28.82/19.01 tff(16655,plain,
% 28.82/19.01 (~(f2(c3) = c1)),
% 28.82/19.01 inference(unit_resolution,[status(thm)],[11776, 66, 11752, 27, 172])).
% 28.82/19.01 tff(16656,plain,
% 28.82/19.01 (f2(c3) = c2),
% 28.82/19.01 inference(unit_resolution,[status(thm)],[1273, 16655])).
% 28.82/19.01 tff(16657,plain,
% 28.82/19.01 (f2(c1) = c2),
% 28.82/19.01 inference(transitivity,[status(thm)],[5586, 16656])).
% 28.82/19.01 tff(16658,plain,
% 28.82/19.01 (big_f(c1, f2(c1)) <=> big_f(f7(c2), c2)),
% 28.82/19.01 inference(monotonicity,[status(thm)],[342, 16657])).
% 28.82/19.01 tff(16659,plain,
% 28.82/19.01 (big_f(f7(c2), c2) <=> big_f(c1, f2(c1))),
% 28.82/19.01 inference(symmetry,[status(thm)],[16658])).
% 28.82/19.01 tff(16660,plain,
% 28.82/19.01 ((~big_f(f7(c2), c2)) <=> (~big_f(c1, f2(c1)))),
% 28.82/19.01 inference(monotonicity,[status(thm)],[16659])).
% 28.82/19.01 tff(16661,plain,
% 28.82/19.01 (~big_f(c1, f2(c1))),
% 28.82/19.01 inference(modus_ponens,[status(thm)],[15886, 16660])).
% 28.82/19.01 tff(16662,plain,
% 28.82/19.01 (big_f(c1, f2(c1))),
% 28.82/19.01 inference(unit_resolution,[status(thm)],[8631, 11774, 172])).
% 28.82/19.01 tff(16663,plain,
% 28.82/19.01 ($false),
% 28.82/19.01 inference(unit_resolution,[status(thm)],[16662, 16661])).
% 28.82/19.01 tff(16664,plain,(big_f(c1, c1) | (~(c3 = c1)) | (~(f7(c2) = c1)) | (~(f4(c4) = c1)) | big_f(c1, c2)), inference(lemma,lemma(discharge,[]))).
% 28.82/19.01 tff(16665,plain,
% 28.82/19.01 (big_f(c1, c1)),
% 28.82/19.01 inference(unit_resolution,[status(thm)],[16664, 16654, 22, 11752, 11754])).
% 28.82/19.01 tff(16666,plain,
% 28.82/19.01 (big_f(f7(c2), c1)),
% 28.82/19.01 inference(modus_ponens,[status(thm)],[16665, 12538])).
% 28.82/19.01 tff(16667,plain,
% 28.82/19.01 (f1(c2, c2) = c2),
% 28.82/19.01 inference(unit_resolution,[status(thm)],[9530, 9495, 17, 2, 377, 16666])).
% 28.82/19.01 tff(16668,plain,
% 28.82/19.01 (big_f(c2, f1(c2, c2)) <=> big_f(c2, c2)),
% 28.82/19.01 inference(monotonicity,[status(thm)],[16667])).
% 28.82/19.01 tff(16669,plain,
% 28.82/19.01 (big_f(c2, c2) <=> big_f(c2, f1(c2, c2))),
% 28.82/19.01 inference(symmetry,[status(thm)],[16668])).
% 28.82/19.01 tff(16670,plain,
% 28.82/19.01 (big_f(c2, f1(c2, c2))),
% 28.82/19.01 inference(modus_ponens,[status(thm)],[1345, 16669])).
% 28.82/19.01 tff(16671,plain,
% 28.82/19.01 (c2 = c4),
% 28.82/19.01 inference(modus_ponens,[status(thm)],[16647, 159])).
% 28.82/19.01 tff(16672,plain,
% 28.82/19.01 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c2 = c4)) | big_f(f7(c2), c2) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (~(f7(c2) = f4(c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(c2 = c4)) | big_f(f7(c2), c2) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (~(f7(c2) = f4(c2))))),
% 28.82/19.01 inference(rewrite,[status(thm)],[])).
% 28.82/19.01 tff(16673,plain,
% 28.82/19.01 (((c2 = c3) | (~(c2 = c4)) | big_f(f7(c2), c2) | (~(f7(c2) = f4(c2))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2)))) <=> ((c2 = c3) | (~(c2 = c4)) | big_f(f7(c2), c2) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (~(f7(c2) = f4(c2))))),
% 28.82/19.01 inference(rewrite,[status(thm)],[])).
% 28.82/19.01 tff(16674,plain,
% 28.82/19.01 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c2 = c4)) | big_f(f7(c2), c2) | (~(f7(c2) = f4(c2))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c2 = c4)) | big_f(f7(c2), c2) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (~(f7(c2) = f4(c2)))))),
% 28.82/19.01 inference(monotonicity,[status(thm)],[16673])).
% 28.82/19.01 tff(16675,plain,
% 28.82/19.01 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c2 = c4)) | big_f(f7(c2), c2) | (~(f7(c2) = f4(c2))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(c2 = c4)) | big_f(f7(c2), c2) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (~(f7(c2) = f4(c2))))),
% 28.82/19.01 inference(transitivity,[status(thm)],[16674, 16672])).
% 28.82/19.01 tff(16676,plain,
% 28.82/19.01 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c2 = c4)) | big_f(f7(c2), c2) | (~(f7(c2) = f4(c2))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))),
% 28.82/19.01 inference(quant_inst,[status(thm)],[])).
% 28.82/19.01 tff(16677,plain,
% 28.82/19.01 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(c2 = c4)) | big_f(f7(c2), c2) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (~(f7(c2) = f4(c2)))),
% 28.82/19.01 inference(modus_ponens,[status(thm)],[16676, 16675])).
% 28.82/19.01 tff(16678,plain,
% 28.82/19.01 ($false),
% 28.82/19.01 inference(unit_resolution,[status(thm)],[16677, 447, 16671, 377, 1521, 16667, 16670, 16652])).
% 28.82/19.01 tff(16679,plain,((f7(c2) = c4) | (c2 = c3) | big_f(f7(c2), c2) | (~(f4(c4) = c1)) | (~big_f(c2, c2)) | (f7(c2) = c2) | big_f(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 28.82/19.01 tff(16680,plain,
% 28.82/19.01 (f7(c2) = c4),
% 28.82/19.01 inference(unit_resolution,[status(thm)],[16679, 377, 1521, 15706, 16509, 17, 16642])).
% 28.82/19.01 tff(16681,plain,
% 28.82/19.01 (c4 = f7(c2)),
% 28.82/19.01 inference(symmetry,[status(thm)],[16680])).
% 28.82/19.01 tff(16682,plain,
% 28.82/19.01 (big_f(c2, c4) <=> big_f(c2, f7(c2))),
% 28.82/19.01 inference(monotonicity,[status(thm)],[16681])).
% 28.82/19.01 tff(16683,plain,
% 28.82/19.01 (big_f(c2, f7(c2)) <=> big_f(c2, c4)),
% 28.82/19.01 inference(symmetry,[status(thm)],[16682])).
% 28.82/19.01 tff(16684,plain,
% 28.82/19.01 ((~big_f(c2, f7(c2))) <=> (~big_f(c2, c4))),
% 28.82/19.01 inference(monotonicity,[status(thm)],[16683])).
% 28.82/19.01 tff(16685,plain,
% 28.82/19.01 (~big_f(c2, f7(c2))),
% 28.82/19.01 inference(modus_ponens,[status(thm)],[16638, 16517])).
% 28.82/19.01 tff(16686,plain,
% 28.82/19.01 (~big_f(c2, c4)),
% 28.82/19.01 inference(modus_ponens,[status(thm)],[16685, 16684])).
% 28.82/19.01 tff(16687,plain,
% 28.82/19.01 ((f7(c2) = c4) <=> (c1 = c4)),
% 28.82/19.01 inference(monotonicity,[status(thm)],[22])).
% 28.82/19.01 tff(16688,plain,
% 28.82/19.01 ((f7(c2) = c4) <=> (c4 = c1)),
% 28.82/19.01 inference(transitivity,[status(thm)],[16687, 4135])).
% 28.82/19.01 tff(16689,plain,
% 28.82/19.01 (c4 = c1),
% 28.82/19.01 inference(modus_ponens,[status(thm)],[16680, 16688])).
% 28.82/19.01 tff(16690,plain,
% 28.82/19.01 ((c2 = c4) <=> (c2 = f7(c2))),
% 28.82/19.01 inference(monotonicity,[status(thm)],[16681])).
% 28.82/19.01 tff(16691,plain,
% 28.82/19.01 ((c2 = c4) <=> (f7(c2) = c2)),
% 28.82/19.01 inference(transitivity,[status(thm)],[16690, 8409])).
% 28.82/19.01 tff(16692,plain,
% 28.82/19.01 ((f7(c2) = c2) <=> (c2 = c4)),
% 28.82/19.01 inference(symmetry,[status(thm)],[16691])).
% 28.82/19.01 tff(16693,plain,
% 28.82/19.01 ((~(f7(c2) = c2)) <=> (~(c2 = c4))),
% 28.82/19.01 inference(monotonicity,[status(thm)],[16692])).
% 28.82/19.01 tff(16694,plain,
% 28.82/19.01 (~(c2 = c4)),
% 28.82/19.01 inference(modus_ponens,[status(thm)],[17, 16693])).
% 28.82/19.01 tff(16695,plain,
% 28.82/19.01 (f3(c2, c2) = f3(f5(c1), f5(c1))),
% 28.82/19.01 inference(monotonicity,[status(thm)],[1761, 1761])).
% 28.82/19.01 tff(16696,plain,
% 28.82/19.01 (f3(f5(c1), f5(c1)) = f3(c2, c2)),
% 28.82/19.01 inference(symmetry,[status(thm)],[16695])).
% 28.82/19.01 tff(16697,plain,
% 28.82/19.01 ((f3(f5(c1), f5(c1)) = c2) <=> (f3(c2, c2) = c2)),
% 28.82/19.01 inference(monotonicity,[status(thm)],[16696])).
% 28.82/19.01 tff(16698,plain,
% 28.82/19.01 ((f3(c2, c2) = c2) <=> (f3(f5(c1), f5(c1)) = c2)),
% 28.82/19.01 inference(symmetry,[status(thm)],[16697])).
% 28.82/19.01 tff(16699,plain,
% 28.82/19.01 ((~(f3(c2, c2) = c2)) <=> (~(f3(f5(c1), f5(c1)) = c2))),
% 28.82/19.01 inference(monotonicity,[status(thm)],[16698])).
% 28.82/19.01 tff(16700,plain,
% 28.82/19.01 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c2 = c3) | (c2 = c4) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (c2 = c3) | (c2 = c4) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2))),
% 28.82/19.01 inference(rewrite,[status(thm)],[])).
% 28.82/19.01 tff(16701,plain,
% 28.82/19.01 (((c2 = c4) | (f3(c2, c2) = c2) | big_f(f3(c2, c2), c2) | (c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2))) <=> ((c2 = c3) | (c2 = c4) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2))),
% 28.82/19.01 inference(rewrite,[status(thm)],[])).
% 28.82/19.01 tff(16702,plain,
% 28.82/19.01 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c2 = c4) | (f3(c2, c2) = c2) | big_f(f3(c2, c2), c2) | (c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c2 = c3) | (c2 = c4) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2)))),
% 28.82/19.01 inference(monotonicity,[status(thm)],[16701])).
% 28.82/19.01 tff(16703,plain,
% 28.82/19.01 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c2 = c4) | (f3(c2, c2) = c2) | big_f(f3(c2, c2), c2) | (c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (c2 = c3) | (c2 = c4) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2))),
% 28.82/19.01 inference(transitivity,[status(thm)],[16702, 16700])).
% 28.82/19.01 tff(16704,plain,
% 28.82/19.01 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c2 = c4) | (f3(c2, c2) = c2) | big_f(f3(c2, c2), c2) | (c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)))),
% 28.82/19.01 inference(quant_inst,[status(thm)],[])).
% 28.82/19.01 tff(16705,plain,
% 28.82/19.01 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (c2 = c3) | (c2 = c4) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2)),
% 28.82/19.01 inference(modus_ponens,[status(thm)],[16704, 16703])).
% 28.82/19.01 tff(16706,plain,
% 28.82/19.01 ($false),
% 28.82/19.01 inference(unit_resolution,[status(thm)],[16705, 1014, 873, 377, 1828, 1862, 12861, 12882])).
% 28.82/19.01 tff(16707,plain,((f3(c2, c2) = c2) | (c2 = c4) | (c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | big_f(f3(c2, c2), c2)), inference(lemma,lemma(discharge,[]))).
% 28.82/19.01 tff(16708,plain,
% 28.82/19.01 (f3(c2, c2) = c2),
% 28.82/19.01 inference(unit_resolution,[status(thm)],[16707, 12882, 377, 1828, 1862, 873])).
% 28.82/19.01 tff(16709,plain,
% 28.82/19.01 (big_f(f3(c2, c2), c2) <=> big_f(c2, c2)),
% 28.82/19.01 inference(monotonicity,[status(thm)],[16708])).
% 28.82/19.01 tff(16710,plain,
% 28.82/19.01 (big_f(c2, c2) <=> big_f(f3(c2, c2), c2)),
% 28.82/19.01 inference(symmetry,[status(thm)],[16709])).
% 28.82/19.01 tff(16711,plain,
% 28.82/19.01 (big_f(f3(c2, c2), c2)),
% 28.82/19.01 inference(modus_ponens,[status(thm)],[1345, 16710])).
% 28.82/19.01 tff(16712,plain,
% 28.82/19.01 ($false),
% 28.82/19.01 inference(unit_resolution,[status(thm)],[12882, 16711])).
% 28.82/19.01 tff(16713,plain,(big_f(f3(c2, c2), c2) | (~big_f(c2, c2)) | (c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (c2 = c4)), inference(lemma,lemma(discharge,[]))).
% 28.82/19.01 tff(16714,plain,
% 28.82/19.01 (big_f(f3(c2, c2), c2)),
% 28.82/19.01 inference(unit_resolution,[status(thm)],[16713, 1828, 377, 1345, 14892, 873])).
% 28.82/19.01 tff(16715,plain,
% 28.82/19.01 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c3) | (c2 = c4) | (~(f3(c2, c2) = c2)) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (~big_f(f3(c2, c2), c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c2 = c3) | (c2 = c4) | (~(f3(c2, c2) = c2)) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (~big_f(f3(c2, c2), c2)))),
% 28.82/19.01 inference(rewrite,[status(thm)],[])).
% 28.82/19.01 tff(16716,plain,
% 28.82/19.01 (((c2 = c4) | (c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2))) <=> ((c2 = c3) | (c2 = c4) | (~(f3(c2, c2) = c2)) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (~big_f(f3(c2, c2), c2)))),
% 28.82/19.01 inference(rewrite,[status(thm)],[])).
% 28.82/19.01 tff(16717,plain,
% 28.82/19.01 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c4) | (c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c3) | (c2 = c4) | (~(f3(c2, c2) = c2)) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (~big_f(f3(c2, c2), c2))))),
% 28.82/19.01 inference(monotonicity,[status(thm)],[16716])).
% 28.82/19.01 tff(16718,plain,
% 28.82/19.01 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c4) | (c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c2 = c3) | (c2 = c4) | (~(f3(c2, c2) = c2)) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (~big_f(f3(c2, c2), c2)))),
% 28.82/19.01 inference(transitivity,[status(thm)],[16717, 16715])).
% 28.82/19.01 tff(16719,plain,
% 28.82/19.01 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c4) | (c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)))),
% 28.82/19.01 inference(quant_inst,[status(thm)],[])).
% 28.82/19.01 tff(16720,plain,
% 28.82/19.01 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c2 = c3) | (c2 = c4) | (~(f3(c2, c2) = c2)) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (~big_f(f3(c2, c2), c2))),
% 28.82/19.01 inference(modus_ponens,[status(thm)],[16719, 16718])).
% 28.82/19.01 tff(16721,plain,
% 28.82/19.01 (~(f3(c2, c2) = c2)),
% 28.82/19.01 inference(unit_resolution,[status(thm)],[16720, 969, 873, 377, 1828, 14892, 16714])).
% 28.82/19.01 tff(16722,plain,
% 28.82/19.01 (~(f3(f5(c1), f5(c1)) = c2)),
% 28.82/19.01 inference(modus_ponens,[status(thm)],[16721, 16699])).
% 28.82/19.01 tff(16723,plain,
% 28.82/19.01 (f3(f5(c1), f5(c1)) = c1),
% 28.82/19.01 inference(unit_resolution,[status(thm)],[7625, 16722])).
% 28.82/19.01 tff(16724,plain,
% 28.82/19.01 (f3(c2, c2) = f7(c2)),
% 28.82/19.01 inference(transitivity,[status(thm)],[16695, 16723, 342])).
% 28.82/19.02 tff(16725,plain,
% 28.82/19.02 (big_f(f3(c2, c2), c2) <=> big_f(f7(c2), c2)),
% 28.82/19.02 inference(monotonicity,[status(thm)],[16724])).
% 28.82/19.02 tff(16726,plain,
% 28.82/19.02 (big_f(f7(c2), c2) <=> big_f(f3(c2, c2), c2)),
% 28.82/19.02 inference(symmetry,[status(thm)],[16725])).
% 28.82/19.02 tff(16727,plain,
% 28.82/19.02 ((~big_f(f7(c2), c2)) <=> (~big_f(f3(c2, c2), c2))),
% 28.82/19.02 inference(monotonicity,[status(thm)],[16726])).
% 28.82/19.02 tff(16728,plain,
% 28.82/19.02 (~big_f(f3(c2, c2), c2)),
% 28.82/19.02 inference(modus_ponens,[status(thm)],[1521, 16727])).
% 28.82/19.02 tff(16729,plain,
% 28.82/19.02 ($false),
% 28.82/19.02 inference(unit_resolution,[status(thm)],[16714, 16728])).
% 28.82/19.02 tff(16730,plain,((f1(c2, c2) = c2) | big_f(f7(c2), c2) | (~(f7(c2) = c1)) | (~(f5(c1) = c2)) | (c2 = c4) | (c2 = c3) | (~big_f(c2, c2)) | (~(c4 = c1)) | big_f(c2, c4)), inference(lemma,lemma(discharge,[]))).
% 28.82/19.02 tff(16731,plain,
% 28.82/19.02 (f1(c2, c2) = c2),
% 28.82/19.02 inference(unit_resolution,[status(thm)],[16730, 186, 292, 1521, 873, 377, 1345, 480, 3865])).
% 28.82/19.02 tff(16732,plain,
% 28.82/19.02 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (c2 = c4) | (~(f1(c2, c2) = c2)) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2) | (~big_f(c2, f1(c2, c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (c2 = c4) | (~(f1(c2, c2) = c2)) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2) | (~big_f(c2, f1(c2, c2))))),
% 28.82/19.02 inference(rewrite,[status(thm)],[])).
% 28.82/19.02 tff(16733,plain,
% 28.82/19.02 (((c2 = c4) | (f3(c2, c2) = c2) | big_f(f3(c2, c2), c2) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2)))) <=> ((c2 = c3) | (c2 = c4) | (~(f1(c2, c2) = c2)) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2) | (~big_f(c2, f1(c2, c2))))),
% 28.82/19.02 inference(rewrite,[status(thm)],[])).
% 28.82/19.02 tff(16734,plain,
% 28.82/19.02 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (f3(c2, c2) = c2) | big_f(f3(c2, c2), c2) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (c2 = c4) | (~(f1(c2, c2) = c2)) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2) | (~big_f(c2, f1(c2, c2)))))),
% 28.82/19.02 inference(monotonicity,[status(thm)],[16733])).
% 28.82/19.02 tff(16735,plain,
% 28.82/19.02 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (f3(c2, c2) = c2) | big_f(f3(c2, c2), c2) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (c2 = c4) | (~(f1(c2, c2) = c2)) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2) | (~big_f(c2, f1(c2, c2))))),
% 28.82/19.02 inference(transitivity,[status(thm)],[16734, 16732])).
% 28.82/19.02 tff(16736,plain,
% 28.82/19.02 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (f3(c2, c2) = c2) | big_f(f3(c2, c2), c2) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))),
% 28.82/19.02 inference(quant_inst,[status(thm)],[])).
% 28.82/19.02 tff(16737,plain,
% 28.82/19.02 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (c2 = c4) | (~(f1(c2, c2) = c2)) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2) | (~big_f(c2, f1(c2, c2)))),
% 28.82/19.02 inference(modus_ponens,[status(thm)],[16736, 16735])).
% 28.82/19.02 tff(16738,plain,
% 28.82/19.02 ($false),
% 28.82/19.02 inference(unit_resolution,[status(thm)],[16737, 904, 873, 377, 1908, 1907, 12861, 12882])).
% 28.82/19.02 tff(16739,plain,((f3(c2, c2) = c2) | (c2 = c4) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | big_f(f3(c2, c2), c2)), inference(lemma,lemma(discharge,[]))).
% 28.82/19.02 tff(16740,plain,
% 28.82/19.02 (f3(c2, c2) = c2),
% 28.82/19.02 inference(unit_resolution,[status(thm)],[16739, 12882, 377, 1908, 5263, 873])).
% 28.82/19.02 tff(16741,plain,
% 28.82/19.02 (big_f(f3(c2, c2), c2) <=> big_f(c2, c2)),
% 28.82/19.02 inference(monotonicity,[status(thm)],[16740])).
% 28.82/19.02 tff(16742,plain,
% 28.82/19.02 (big_f(c2, c2) <=> big_f(f3(c2, c2), c2)),
% 28.82/19.02 inference(symmetry,[status(thm)],[16741])).
% 28.82/19.02 tff(16743,plain,
% 28.82/19.02 (big_f(f3(c2, c2), c2)),
% 28.82/19.02 inference(modus_ponens,[status(thm)],[1345, 16742])).
% 28.82/19.02 tff(16744,plain,
% 28.82/19.02 ($false),
% 28.82/19.02 inference(unit_resolution,[status(thm)],[12882, 16743])).
% 28.82/19.02 tff(16745,plain,(big_f(f3(c2, c2), c2) | (~big_f(c2, c2)) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (c2 = c4)), inference(lemma,lemma(discharge,[]))).
% 28.82/19.02 tff(16746,plain,
% 28.82/19.02 (big_f(f3(c2, c2), c2)),
% 28.82/19.02 inference(unit_resolution,[status(thm)],[16745, 16731, 377, 1345, 873])).
% 28.82/19.02 tff(16747,plain,
% 28.82/19.02 (big_f(c2, f1(c2, c2)) <=> big_f(c2, c2)),
% 28.82/19.02 inference(monotonicity,[status(thm)],[16731])).
% 28.82/19.02 tff(16748,plain,
% 28.82/19.02 (big_f(c2, c2) <=> big_f(c2, f1(c2, c2))),
% 28.82/19.02 inference(symmetry,[status(thm)],[16747])).
% 28.82/19.02 tff(16749,plain,
% 28.82/19.02 (big_f(c2, f1(c2, c2))),
% 28.82/19.02 inference(modus_ponens,[status(thm)],[1345, 16748])).
% 28.82/19.02 tff(16750,plain,
% 28.82/19.02 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~(f1(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~big_f(c2, f1(c2, c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~(f1(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~big_f(c2, f1(c2, c2))))),
% 28.82/19.02 inference(rewrite,[status(thm)],[])).
% 28.82/19.02 tff(16751,plain,
% 28.82/19.02 (((c2 = c4) | (c2 = c3) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2)))) <=> ((c2 = c3) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~(f1(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~big_f(c2, f1(c2, c2))))),
% 28.82/19.02 inference(rewrite,[status(thm)],[])).
% 28.82/19.02 tff(16752,plain,
% 28.82/19.02 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (c2 = c3) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~(f1(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~big_f(c2, f1(c2, c2)))))),
% 28.82/19.02 inference(monotonicity,[status(thm)],[16751])).
% 28.82/19.02 tff(16753,plain,
% 28.82/19.02 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (c2 = c3) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~(f1(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~big_f(c2, f1(c2, c2))))),
% 28.82/19.02 inference(transitivity,[status(thm)],[16752, 16750])).
% 28.82/19.02 tff(16754,plain,
% 28.82/19.02 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (c2 = c3) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))),
% 28.82/19.02 inference(quant_inst,[status(thm)],[])).
% 28.82/19.02 tff(16755,plain,
% 28.82/19.02 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~(f1(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~big_f(c2, f1(c2, c2)))),
% 28.82/19.02 inference(modus_ponens,[status(thm)],[16754, 16753])).
% 28.82/19.02 tff(16756,plain,
% 28.82/19.02 (~(f3(c2, c2) = c2)),
% 28.82/19.02 inference(unit_resolution,[status(thm)],[16755, 933, 873, 377, 16731, 16749, 16746])).
% 28.82/19.02 tff(16757,plain,
% 28.82/19.02 (~(f3(f5(c1), f5(c1)) = c2)),
% 28.82/19.02 inference(modus_ponens,[status(thm)],[16756, 16699])).
% 28.82/19.02 tff(16758,plain,
% 28.82/19.02 (f3(f5(c1), f5(c1)) = c1),
% 28.82/19.02 inference(unit_resolution,[status(thm)],[7625, 16757])).
% 28.82/19.02 tff(16759,plain,
% 28.82/19.02 (f3(c2, c2) = f7(c2)),
% 28.82/19.02 inference(transitivity,[status(thm)],[16695, 16758, 342])).
% 28.82/19.02 tff(16760,plain,
% 28.82/19.02 (big_f(f3(c2, c2), c2) <=> big_f(f7(c2), c2)),
% 28.82/19.02 inference(monotonicity,[status(thm)],[16759])).
% 28.82/19.02 tff(16761,plain,
% 28.82/19.02 (big_f(f7(c2), c2) <=> big_f(f3(c2, c2), c2)),
% 28.82/19.02 inference(symmetry,[status(thm)],[16760])).
% 28.82/19.02 tff(16762,plain,
% 28.82/19.02 ((~big_f(f7(c2), c2)) <=> (~big_f(f3(c2, c2), c2))),
% 28.82/19.02 inference(monotonicity,[status(thm)],[16761])).
% 28.82/19.02 tff(16763,plain,
% 28.82/19.02 (~big_f(f3(c2, c2), c2)),
% 28.82/19.02 inference(modus_ponens,[status(thm)],[1521, 16762])).
% 28.82/19.02 tff(16764,plain,
% 28.82/19.02 ($false),
% 28.82/19.02 inference(unit_resolution,[status(thm)],[16746, 16763])).
% 28.82/19.02 tff(16765,plain,((~(f5(c1) = c2)) | big_f(f7(c2), c2) | (~(f7(c2) = c1)) | (c2 = c4) | (c2 = c3) | (~big_f(c2, c2)) | (~(c4 = c1)) | big_f(c2, c4)), inference(lemma,lemma(discharge,[]))).
% 28.82/19.02 tff(16766,plain,
% 28.82/19.02 (~(f5(c1) = c2)),
% 28.82/19.02 inference(unit_resolution,[status(thm)],[16765, 16694, 22, 1521, 377, 16509, 16689, 16686])).
% 28.82/19.02 tff(16767,plain,
% 28.82/19.02 (f5(c1) = c1),
% 28.82/19.02 inference(unit_resolution,[status(thm)],[1708, 16766])).
% 28.82/19.02 tff(16768,plain,
% 28.82/19.02 (f7(c2) = f5(f7(c2))),
% 28.82/19.02 inference(modus_ponens,[status(thm)],[16767, 16639])).
% 28.82/19.02 tff(16769,plain,
% 28.82/19.02 (big_f(f7(f7(c2)), f7(c2)) <=> big_f(f7(c1), c1)),
% 28.82/19.02 inference(transitivity,[status(thm)],[12449, 9311, 693])).
% 28.82/19.02 tff(16770,plain,
% 28.82/19.02 ((~big_f(f7(f7(c2)), f7(c2))) <=> (~big_f(f7(c1), c1))),
% 28.82/19.02 inference(monotonicity,[status(thm)],[16769])).
% 28.82/19.02 tff(16771,plain,
% 28.82/19.02 (~big_f(f7(c1), c1)),
% 28.82/19.02 inference(modus_ponens,[status(thm)],[16638, 16770])).
% 28.82/19.02 tff(16772,plain,
% 28.82/19.02 (~big_f(f7(c1), f5(c1))),
% 28.82/19.02 inference(unit_resolution,[status(thm)],[289, 16767, 16771])).
% 28.82/19.02 tff(16773,plain,
% 28.82/19.02 (big_f(f8(c1), f10(c1))),
% 28.82/19.02 inference(unit_resolution,[status(thm)],[2848, 16772, 115, 3])).
% 28.82/19.02 tff(16774,plain,
% 28.82/19.02 (~(f8(c1) = c1)),
% 28.82/19.02 inference(unit_resolution,[status(thm)],[15716, 16773, 1521, 15, 22])).
% 28.82/19.02 tff(16775,plain,
% 28.82/19.02 (f8(c1) = c2),
% 28.82/19.02 inference(unit_resolution,[status(thm)],[1680, 16774])).
% 28.82/19.02 tff(16776,plain,
% 28.82/19.02 (big_f(f7(f7(c2)), c2)),
% 28.82/19.02 inference(modus_ponens,[status(thm)],[16509, 8617])).
% 28.82/19.02 tff(16777,plain,
% 28.82/19.02 ((~(f5(c1) = c2)) <=> (~(c2 = f5(f7(c2))))),
% 28.82/19.02 inference(monotonicity,[status(thm)],[8603])).
% 28.82/19.02 tff(16778,plain,
% 28.82/19.02 (~(c2 = f5(f7(c2)))),
% 28.82/19.02 inference(modus_ponens,[status(thm)],[16766, 16777])).
% 28.82/19.02 tff(16779,plain,
% 28.82/19.02 (f9(c2, c2) = c2),
% 28.82/19.02 inference(unit_resolution,[status(thm)],[16630, 16778, 12448, 16776, 12943, 15, 22, 16775, 122])).
% 28.82/19.02 tff(16780,plain,
% 28.82/19.02 (big_f(f9(c2, c2), c2) <=> big_f(c2, c2)),
% 28.82/19.02 inference(monotonicity,[status(thm)],[16779])).
% 28.82/19.02 tff(16781,plain,
% 28.82/19.02 (big_f(c2, c2) <=> big_f(f9(c2, c2), c2)),
% 28.82/19.02 inference(symmetry,[status(thm)],[16780])).
% 28.82/19.02 tff(16782,plain,
% 28.82/19.02 (big_f(c2, c2) <=> big_f(f9(c2, c2), f10(c2))),
% 28.82/19.02 inference(transitivity,[status(thm)],[16781, 130])).
% 28.82/19.02 tff(16783,plain,
% 28.82/19.02 (big_f(f9(c2, c2), f10(c2))),
% 28.82/19.02 inference(modus_ponens,[status(thm)],[16509, 16782])).
% 28.82/19.02 tff(16784,plain,
% 28.82/19.02 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | big_f(f7(f7(c2)), f7(c2)) | (~(f7(c2) = f5(f7(c2)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | big_f(f7(f7(c2)), f7(c2)) | (~(f7(c2) = f5(f7(c2)))))),
% 28.82/19.02 inference(rewrite,[status(thm)],[])).
% 28.82/19.02 tff(16785,plain,
% 28.82/19.02 (((~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f7(c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f7(c2) = f5(f7(c2))))) <=> ((~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | big_f(f7(f7(c2)), f7(c2)) | (~(f7(c2) = f5(f7(c2)))))),
% 28.82/19.02 inference(rewrite,[status(thm)],[])).
% 28.82/19.02 tff(16786,plain,
% 28.82/19.02 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f7(c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f7(c2) = f5(f7(c2)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | big_f(f7(f7(c2)), f7(c2)) | (~(f7(c2) = f5(f7(c2))))))),
% 28.82/19.02 inference(monotonicity,[status(thm)],[16785])).
% 28.82/19.02 tff(16787,plain,
% 28.82/19.02 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f7(c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f7(c2) = f5(f7(c2)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | big_f(f7(f7(c2)), f7(c2)) | (~(f7(c2) = f5(f7(c2)))))),
% 28.82/19.02 inference(transitivity,[status(thm)],[16786, 16784])).
% 28.82/19.02 tff(16788,plain,
% 28.82/19.02 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | big_f(f7(f7(c2)), f7(c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f7(c2) = f5(f7(c2)))))),
% 28.82/19.02 inference(quant_inst,[status(thm)],[])).
% 28.82/19.02 tff(16789,plain,
% 28.82/19.02 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | big_f(f7(f7(c2)), f7(c2)) | (~(f7(c2) = f5(f7(c2))))),
% 28.82/19.02 inference(modus_ponens,[status(thm)],[16788, 16787])).
% 28.82/19.02 tff(16790,plain,
% 28.82/19.02 ($false),
% 28.82/19.02 inference(unit_resolution,[status(thm)],[16789, 783, 122, 12943, 16779, 16783, 16768, 16638])).
% 28.82/19.02 tff(16791,plain,((c2 = c3) | (~(f10(c2) = c2)) | big_f(f7(c2), c2) | (f7(c1) = c1) | (f10(c1) = c1) | (f7(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 28.82/19.02 tff(16792,plain,
% 28.82/19.02 (big_f(f7(c2), c2)),
% 28.82/19.02 inference(unit_resolution,[status(thm)],[16791, 377, 122, 115, 3, 17])).
% 28.82/19.02 tff(16793,plain,
% 28.82/19.02 (big_f(f7(c2), f10(f7(c2)))),
% 28.82/19.02 inference(modus_ponens,[status(thm)],[16792, 12766])).
% 28.82/19.02 tff(16794,plain,
% 28.82/19.02 (f8(c1) = f8(f7(c2))),
% 28.82/19.02 inference(monotonicity,[status(thm)],[342])).
% 28.82/19.02 tff(16795,plain,
% 28.82/19.02 (f8(f7(c2)) = f8(c1)),
% 28.82/19.02 inference(symmetry,[status(thm)],[16794])).
% 28.82/19.02 tff(16796,plain,
% 28.82/19.02 ((c2 = f8(f7(c2))) <=> (c2 = f8(c1))),
% 28.82/19.02 inference(monotonicity,[status(thm)],[16795])).
% 28.82/19.02 tff(16797,plain,
% 28.82/19.02 ((c2 = f8(f7(c2))) <=> (f8(c1) = c2)),
% 28.82/19.02 inference(transitivity,[status(thm)],[16796, 2782])).
% 28.82/19.02 tff(16798,plain,
% 28.82/19.02 (big_f(c2, f10(f7(c2))) <=> big_f(c2, c2)),
% 28.82/19.02 inference(monotonicity,[status(thm)],[12967])).
% 28.82/19.02 tff(16799,plain,
% 28.82/19.02 (big_f(c2, c2) <=> big_f(c2, f10(f7(c2)))),
% 28.82/19.02 inference(symmetry,[status(thm)],[16798])).
% 28.82/19.02 tff(16800,plain,
% 28.82/19.02 (big_f(c2, f10(f7(c2)))),
% 28.82/19.02 inference(modus_ponens,[status(thm)],[1345, 16799])).
% 28.82/19.02 tff(16801,plain,
% 28.82/19.02 ((c2 = f5(f7(c2))) | (c2 = f8(f7(c2)))),
% 28.82/19.02 inference(unit_resolution,[status(thm)],[13331, 1659, 8473, 8523, 16800, 12480])).
% 28.82/19.02 tff(16802,plain,
% 28.82/19.02 (c2 = f8(f7(c2))),
% 28.82/19.02 inference(unit_resolution,[status(thm)],[16801, 16610])).
% 28.82/19.02 tff(16803,plain,
% 28.82/19.02 (f8(c1) = c2),
% 28.82/19.02 inference(modus_ponens,[status(thm)],[16802, 16797])).
% 28.82/19.02 tff(16804,plain,
% 28.82/19.02 (f9(c2, c2) = c2),
% 28.82/19.02 inference(unit_resolution,[status(thm)],[16630, 16803, 8523, 12480, 8473, 16, 292, 16610, 122])).
% 28.82/19.02 tff(16805,plain,
% 28.82/19.02 (big_f(f9(c2, c2), c2) <=> big_f(c2, c2)),
% 28.82/19.02 inference(monotonicity,[status(thm)],[16804])).
% 28.82/19.02 tff(16806,plain,
% 28.82/19.02 (big_f(c2, c2) <=> big_f(f9(c2, c2), c2)),
% 28.82/19.02 inference(symmetry,[status(thm)],[16805])).
% 28.82/19.02 tff(16807,plain,
% 28.82/19.02 (big_f(c2, c2) <=> big_f(f9(c2, c2), f10(c2))),
% 28.82/19.02 inference(transitivity,[status(thm)],[16806, 130])).
% 28.82/19.02 tff(16808,plain,
% 28.82/19.02 (big_f(f9(c2, c2), f10(c2))),
% 28.82/19.02 inference(modus_ponens,[status(thm)],[1345, 16807])).
% 28.82/19.02 tff(16809,plain,
% 28.82/19.02 ($false),
% 28.82/19.02 inference(unit_resolution,[status(thm)],[9290, 1190, 122, 8473, 16804, 16808, 12480, 16610])).
% 28.82/19.02 tff(16810,plain,((c2 = f5(f7(c2))) | (~(f10(c2) = c2)) | (f7(f7(c2)) = f7(c2)) | (~big_f(f7(f7(c2)), c2)) | (~big_f(c2, c2)) | (f10(f7(c2)) = f7(c2)) | (~(f10(c1) = c2)) | (~(f7(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.82/19.02 tff(16811,plain,
% 28.82/19.02 (c2 = f5(f7(c2))),
% 28.82/19.02 inference(unit_resolution,[status(thm)],[16810, 12943, 122, 16776, 16509, 12448, 15, 22])).
% 28.82/19.02 tff(16812,plain,
% 28.82/19.02 (f5(f7(c2)) = c2),
% 28.82/19.02 inference(symmetry,[status(thm)],[16811])).
% 28.82/19.02 tff(16813,plain,
% 28.82/19.02 (f5(c1) = c2),
% 28.82/19.02 inference(transitivity,[status(thm)],[10452, 16812])).
% 28.82/19.02 tff(16814,plain,
% 28.82/19.02 ((f5(c1) = c1) <=> (c2 = f7(c2))),
% 28.82/19.02 inference(monotonicity,[status(thm)],[16813, 125])).
% 28.82/19.02 tff(16815,plain,
% 28.82/19.02 ((f5(c1) = c1) <=> (f7(c2) = c2)),
% 28.82/19.02 inference(transitivity,[status(thm)],[16814, 8409])).
% 28.82/19.02 tff(16816,plain,
% 28.82/19.02 ((f7(c2) = c2) <=> (f5(c1) = c1)),
% 28.82/19.02 inference(symmetry,[status(thm)],[16815])).
% 28.82/19.02 tff(16817,plain,
% 28.82/19.02 ((f7(c2) = c2) <=> (f7(c2) = f5(f7(c2)))),
% 28.82/19.02 inference(transitivity,[status(thm)],[16816, 10456])).
% 28.82/19.02 tff(16818,plain,
% 28.82/19.02 ((~(f7(c2) = c2)) <=> (~(f7(c2) = f5(f7(c2))))),
% 28.82/19.02 inference(monotonicity,[status(thm)],[16817])).
% 28.82/19.02 tff(16819,plain,
% 28.82/19.02 (~(f7(c2) = f5(f7(c2)))),
% 28.82/19.02 inference(modus_ponens,[status(thm)],[17, 16818])).
% 28.82/19.02 tff(16820,plain,
% 28.82/19.02 ((f10(c3) = c3) <=> (f10(c3) = c1)),
% 28.82/19.02 inference(monotonicity,[status(thm)],[11754])).
% 28.82/19.02 tff(16821,plain,
% 28.82/19.02 ((f10(c3) = c1) <=> (f10(c3) = c3)),
% 28.82/19.02 inference(symmetry,[status(thm)],[16820])).
% 28.82/19.02 tff(16822,plain,
% 28.82/19.02 (c3 = f7(c2)),
% 28.82/19.02 inference(transitivity,[status(thm)],[11754, 125])).
% 28.82/19.02 tff(16823,plain,
% 28.82/19.02 (f10(c3) = f10(f7(c2))),
% 28.82/19.02 inference(monotonicity,[status(thm)],[16822])).
% 28.82/19.02 tff(16824,plain,
% 28.82/19.02 (f10(c3) = c2),
% 28.82/19.02 inference(transitivity,[status(thm)],[16823, 23, 15])).
% 28.82/19.02 tff(16825,plain,
% 28.82/19.02 ((f10(c3) = c1) <=> (c2 = f7(c2))),
% 28.82/19.02 inference(monotonicity,[status(thm)],[16824, 125])).
% 28.82/19.02 tff(16826,plain,
% 28.82/19.02 ((f10(c3) = c1) <=> (f7(c2) = c2)),
% 28.82/19.02 inference(transitivity,[status(thm)],[16825, 8409])).
% 28.82/19.02 tff(16827,plain,
% 28.82/19.02 ((f7(c2) = c2) <=> (f10(c3) = c1)),
% 28.82/19.02 inference(symmetry,[status(thm)],[16826])).
% 28.82/19.02 tff(16828,plain,
% 28.82/19.02 ((f7(c2) = c2) <=> (f10(c3) = c3)),
% 28.82/19.02 inference(transitivity,[status(thm)],[16827, 16821])).
% 28.82/19.02 tff(16829,plain,
% 28.82/19.02 ((~(f7(c2) = c2)) <=> (~(f10(c3) = c3))),
% 28.82/19.02 inference(monotonicity,[status(thm)],[16828])).
% 28.82/19.02 tff(16830,plain,
% 28.82/19.02 (~(f10(c3) = c3)),
% 28.82/19.02 inference(modus_ponens,[status(thm)],[17, 16829])).
% 28.82/19.02 tff(16831,plain,
% 28.82/19.02 (big_f(f7(c1), c2)),
% 28.82/19.02 inference(modus_ponens,[status(thm)],[16509, 1724])).
% 28.82/19.02 tff(16832,plain,
% 28.82/19.02 (big_f(c2, f10(c3)) <=> big_f(c2, c2)),
% 28.82/19.02 inference(monotonicity,[status(thm)],[16824])).
% 28.82/19.02 tff(16833,plain,
% 28.82/19.02 (big_f(c2, c2) <=> big_f(c2, f10(c3))),
% 28.82/19.02 inference(symmetry,[status(thm)],[16832])).
% 28.82/19.02 tff(16834,plain,
% 28.82/19.02 (big_f(c2, f10(c3))),
% 28.82/19.02 inference(modus_ponens,[status(thm)],[16509, 16833])).
% 28.82/19.02 tff(16835,plain,
% 28.82/19.02 (f8(c1) = f8(f7(c2))),
% 28.82/19.02 inference(monotonicity,[status(thm)],[125])).
% 28.82/19.02 tff(16836,plain,
% 28.82/19.02 (f8(f7(c2)) = f8(c1)),
% 28.82/19.02 inference(symmetry,[status(thm)],[16835])).
% 28.82/19.02 tff(16837,plain,
% 28.82/19.02 ((f7(c2) = f8(f7(c2))) <=> (c1 = f8(c1))),
% 28.82/19.02 inference(monotonicity,[status(thm)],[22, 16836])).
% 28.82/19.02 tff(16838,plain,
% 28.82/19.02 ((f7(c2) = f8(f7(c2))) <=> (f8(c1) = c1)),
% 28.82/19.02 inference(transitivity,[status(thm)],[16837, 3027])).
% 28.82/19.02 tff(16839,plain,
% 28.82/19.02 (f7(c2) = f8(f7(c2))),
% 28.82/19.02 inference(unit_resolution,[status(thm)],[13312, 1659, 12943, 10466, 13297, 10465, 8523])).
% 28.82/19.02 tff(16840,plain,
% 28.82/19.02 (f8(c1) = c1),
% 28.82/19.02 inference(modus_ponens,[status(thm)],[16839, 16838])).
% 28.82/19.02 tff(16841,plain,
% 28.82/19.02 (~(f8(c1) = c1)),
% 28.82/19.02 inference(unit_resolution,[status(thm)],[16600, 10465, 115, 17, 12871, 16579, 2828, 8523, 12607, 172])).
% 28.82/19.02 tff(16842,plain,
% 28.82/19.02 ($false),
% 28.82/19.02 inference(unit_resolution,[status(thm)],[16841, 16840])).
% 28.82/19.02 tff(16843,plain,((~big_f(f7(f7(c2)), f7(c2))) | (f7(c1) = c1) | (f7(c2) = c2) | (~big_f(f7(c1), c2)) | (~big_f(c2, f10(c3))) | (f10(c3) = c3) | (f10(f7(c2)) = f7(c2)) | (~big_f(c2, f10(f7(c2)))) | (~(c3 = c1)) | (f7(c2) = f5(f7(c2))) | (~big_f(f7(c2), f10(f7(c2))))), inference(lemma,lemma(discharge,[]))).
% 28.82/19.02 tff(16844,plain,
% 28.82/19.02 (~big_f(f7(f7(c2)), f7(c2))),
% 28.82/19.02 inference(unit_resolution,[status(thm)],[16843, 16834, 17, 16831, 115, 16830, 12448, 16510, 11754, 16819, 16793])).
% 28.82/19.02 tff(16845,plain,
% 28.82/19.02 (~big_f(c2, f7(c2))),
% 28.82/19.02 inference(modus_ponens,[status(thm)],[16844, 16517])).
% 28.82/19.02 tff(16846,plain,
% 28.82/19.02 (f4(c2) = f7(c2)),
% 28.82/19.02 inference(transitivity,[status(thm)],[8744, 11752, 125])).
% 28.82/19.02 tff(16847,plain,
% 28.82/19.02 ((c2 = f4(c2)) <=> (c2 = f7(c2))),
% 28.82/19.02 inference(monotonicity,[status(thm)],[16846])).
% 28.82/19.02 tff(16848,plain,
% 28.82/19.02 ((c2 = f4(c2)) <=> (f7(c2) = c2)),
% 28.82/19.02 inference(transitivity,[status(thm)],[16847, 8409])).
% 28.82/19.02 tff(16849,plain,
% 28.82/19.02 ((f7(c2) = c2) <=> (c2 = f4(c2))),
% 28.82/19.02 inference(symmetry,[status(thm)],[16848])).
% 28.82/19.02 tff(16850,plain,
% 28.82/19.02 ((~(f7(c2) = c2)) <=> (~(c2 = f4(c2)))),
% 28.82/19.02 inference(monotonicity,[status(thm)],[16849])).
% 28.82/19.02 tff(16851,plain,
% 28.82/19.02 (~(c2 = f4(c2))),
% 28.82/19.02 inference(modus_ponens,[status(thm)],[17, 16850])).
% 28.82/19.02 tff(16852,plain,
% 28.82/19.02 (f1(c2, c2) = f7(c2)),
% 28.82/19.02 inference(transitivity,[status(thm)],[5298, 342])).
% 28.82/19.02 tff(16853,plain,
% 28.82/19.02 (big_f(c2, f1(c2, c2)) <=> big_f(c2, f7(c2))),
% 28.82/19.02 inference(monotonicity,[status(thm)],[16852])).
% 28.82/19.02 tff(16854,plain,
% 28.82/19.02 (big_f(c2, f7(c2)) <=> big_f(c2, f1(c2, c2))),
% 28.82/19.02 inference(symmetry,[status(thm)],[16853])).
% 28.82/19.02 tff(16855,plain,
% 28.82/19.02 ((~big_f(c2, f7(c2))) <=> (~big_f(c2, f1(c2, c2)))),
% 28.82/19.02 inference(monotonicity,[status(thm)],[16854])).
% 28.82/19.02 tff(16856,plain,
% 28.82/19.02 (~big_f(c2, f1(c2, c2))),
% 28.82/19.02 inference(modus_ponens,[status(thm)],[9331, 16855])).
% 28.82/19.02 tff(16857,assumption,(~(c2 = f4(c2))), introduced(assumption)).
% 28.82/19.02 tff(16858,plain,
% 28.82/19.02 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c2 = c3) | (~(c2 = c4)) | (c2 = f4(c2)) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (~big_f(c2, c2)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (c2 = c3) | (~(c2 = c4)) | (c2 = f4(c2)) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (~big_f(c2, c2)))),
% 28.82/19.02 inference(rewrite,[status(thm)],[])).
% 28.82/19.02 tff(16859,plain,
% 28.82/19.02 (((c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2))) <=> ((c2 = c3) | (~(c2 = c4)) | (c2 = f4(c2)) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (~big_f(c2, c2)))),
% 28.82/19.02 inference(rewrite,[status(thm)],[])).
% 28.82/19.02 tff(16860,plain,
% 28.82/19.02 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c2 = c3) | (~(c2 = c4)) | (c2 = f4(c2)) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (~big_f(c2, c2))))),
% 28.82/19.02 inference(monotonicity,[status(thm)],[16859])).
% 28.82/19.03 tff(16861,plain,
% 28.82/19.03 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (c2 = c3) | (~(c2 = c4)) | (c2 = f4(c2)) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (~big_f(c2, c2)))),
% 28.82/19.03 inference(transitivity,[status(thm)],[16860, 16858])).
% 28.82/19.03 tff(16862,plain,
% 28.82/19.03 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)))),
% 28.82/19.03 inference(quant_inst,[status(thm)],[])).
% 28.82/19.03 tff(16863,plain,
% 28.82/19.03 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (c2 = c3) | (~(c2 = c4)) | (c2 = f4(c2)) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (~big_f(c2, c2))),
% 28.82/19.03 inference(modus_ponens,[status(thm)],[16862, 16861])).
% 28.82/19.03 tff(16864,plain,
% 28.82/19.03 ($false),
% 28.82/19.03 inference(unit_resolution,[status(thm)],[16863, 525, 631, 16857, 1345, 377, 1828, 16856])).
% 28.82/19.03 tff(16865,plain,((f1(c2, c2) = c2) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)) | (c2 = c3) | big_f(c2, f7(c2)) | (~(f7(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.82/19.03 tff(16866,plain,
% 28.82/19.03 (f1(c2, c2) = c2),
% 28.82/19.03 inference(unit_resolution,[status(thm)],[16865, 631, 16851, 1345, 377, 9331, 22])).
% 28.82/19.03 tff(16867,plain,
% 28.82/19.03 (big_f(c2, f1(c2, c2)) <=> big_f(c2, c2)),
% 28.82/19.03 inference(monotonicity,[status(thm)],[16866])).
% 28.82/19.03 tff(16868,plain,
% 28.82/19.03 (big_f(c2, c2) <=> big_f(c2, f1(c2, c2))),
% 28.82/19.03 inference(symmetry,[status(thm)],[16867])).
% 28.82/19.03 tff(16869,plain,
% 28.82/19.03 (big_f(c2, f1(c2, c2))),
% 28.82/19.03 inference(modus_ponens,[status(thm)],[1345, 16868])).
% 28.82/19.03 tff(16870,plain,
% 28.82/19.03 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c2 = c4)) | (c2 = f4(c2)) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (~big_f(c2, c2)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(c2 = c4)) | (c2 = f4(c2)) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (~big_f(c2, c2)))),
% 28.82/19.03 inference(rewrite,[status(thm)],[])).
% 28.82/19.03 tff(16871,plain,
% 28.82/19.03 (((c2 = c3) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2)))) <=> ((c2 = c3) | (~(c2 = c4)) | (c2 = f4(c2)) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (~big_f(c2, c2)))),
% 28.82/19.03 inference(rewrite,[status(thm)],[])).
% 28.82/19.03 tff(16872,plain,
% 28.82/19.03 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c2 = c4)) | (c2 = f4(c2)) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (~big_f(c2, c2))))),
% 28.82/19.03 inference(monotonicity,[status(thm)],[16871])).
% 28.82/19.03 tff(16873,plain,
% 28.82/19.03 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(c2 = c4)) | (c2 = f4(c2)) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (~big_f(c2, c2)))),
% 28.82/19.03 inference(transitivity,[status(thm)],[16872, 16870])).
% 28.82/19.03 tff(16874,plain,
% 28.82/19.03 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))),
% 28.82/19.03 inference(quant_inst,[status(thm)],[])).
% 28.82/19.03 tff(16875,plain,
% 28.82/19.03 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(c2 = c4)) | (c2 = f4(c2)) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (~big_f(c2, c2))),
% 28.82/19.03 inference(modus_ponens,[status(thm)],[16874, 16873])).
% 28.82/19.03 tff(16876,plain,
% 28.82/19.03 ($false),
% 28.82/19.03 inference(unit_resolution,[status(thm)],[16875, 553, 631, 16851, 1345, 377, 16866, 16869])).
% 28.82/19.03 tff(16877,plain,((~(c2 = c4)) | (~big_f(c2, c2)) | (c2 = c3) | big_f(c2, f7(c2)) | (f7(c2) = c2) | (~(f4(c4) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.82/19.03 tff(16878,plain,
% 28.82/19.03 (~(c2 = c4)),
% 28.82/19.03 inference(unit_resolution,[status(thm)],[16877, 377, 16509, 16845, 17, 15706])).
% 28.82/19.03 tff(16879,plain,
% 28.82/19.03 (~(c4 = c2)),
% 28.82/19.03 inference(modus_ponens,[status(thm)],[16878, 8722])).
% 28.82/19.03 tff(16880,plain,
% 28.82/19.03 (c4 = c1),
% 28.82/19.03 inference(unit_resolution,[status(thm)],[461, 16879])).
% 28.82/19.03 tff(16881,plain,
% 28.82/19.03 (c1 = c4),
% 28.82/19.03 inference(symmetry,[status(thm)],[16880])).
% 28.82/19.03 tff(16882,plain,
% 28.82/19.03 (f7(c2) = c4),
% 28.82/19.03 inference(transitivity,[status(thm)],[22, 16881])).
% 28.82/19.03 tff(16883,plain,
% 28.82/19.03 (f4(f7(c2)) = f4(c4)),
% 28.82/19.03 inference(monotonicity,[status(thm)],[16882])).
% 28.82/19.03 tff(16884,plain,
% 28.82/19.03 (f4(c4) = f4(f7(c2))),
% 28.82/19.03 inference(symmetry,[status(thm)],[16883])).
% 28.82/19.03 tff(16885,plain,
% 28.82/19.03 (f7(c2) = f4(f7(c2))),
% 28.82/19.03 inference(transitivity,[status(thm)],[22, 15834, 16884])).
% 28.82/19.03 tff(16886,plain,
% 28.82/19.03 (f7(c2) = c4),
% 28.82/19.03 inference(unit_resolution,[status(thm)],[16645, 16880, 22])).
% 28.82/19.03 tff(16887,plain,
% 28.82/19.03 (c2 = f8(f7(c2))),
% 28.82/19.03 inference(unit_resolution,[status(thm)],[12627, 8372, 17, 8523, 12607, 1180])).
% 28.82/19.03 tff(16888,plain,
% 28.82/19.03 (f8(f7(c2)) = c2),
% 28.82/19.03 inference(symmetry,[status(thm)],[16887])).
% 28.82/19.03 tff(16889,plain,
% 28.82/19.03 ((f7(c2) = f8(f7(c2))) <=> (f7(c2) = c2)),
% 28.82/19.03 inference(monotonicity,[status(thm)],[16888])).
% 28.82/19.03 tff(16890,plain,
% 28.82/19.03 ((f7(c2) = c2) <=> (f7(c2) = f8(f7(c2)))),
% 28.82/19.03 inference(symmetry,[status(thm)],[16889])).
% 28.82/19.03 tff(16891,plain,
% 28.82/19.03 ((~(f7(c2) = c2)) <=> (~(f7(c2) = f8(f7(c2))))),
% 28.82/19.03 inference(monotonicity,[status(thm)],[16890])).
% 28.82/19.03 tff(16892,plain,
% 28.82/19.03 (~(f7(c2) = f8(f7(c2)))),
% 28.82/19.03 inference(modus_ponens,[status(thm)],[17, 16891])).
% 28.82/19.03 tff(16893,plain,
% 28.82/19.03 ((c2 = f5(c2)) | (f7(c2) = f8(f7(c2)))),
% 28.82/19.03 inference(unit_resolution,[status(thm)],[12646, 1659, 17, 1180, 13297, 8523])).
% 28.82/19.03 tff(16894,plain,
% 28.82/19.03 (c2 = f5(c2)),
% 28.82/19.03 inference(unit_resolution,[status(thm)],[16893, 16892])).
% 28.82/19.03 tff(16895,plain,
% 28.82/19.03 (f5(c2) = c2),
% 28.82/19.03 inference(symmetry,[status(thm)],[16894])).
% 28.82/19.03 tff(16896,plain,
% 28.82/19.03 (f7(c2) = f5(c2)),
% 28.82/19.03 inference(unit_resolution,[status(thm)],[12655, 1659, 17, 13297, 8523, 8372, 16892])).
% 28.82/19.03 tff(16897,plain,
% 28.82/19.03 (f7(c2) = c2),
% 28.82/19.03 inference(transitivity,[status(thm)],[16896, 16895])).
% 28.82/19.03 tff(16898,plain,
% 28.82/19.03 ($false),
% 28.82/19.03 inference(unit_resolution,[status(thm)],[17, 16897])).
% 28.82/19.03 tff(16899,plain,((~big_f(f7(c2), f7(c2))) | (f7(c2) = c2) | (~big_f(f7(c2), c2)) | (~big_f(f7(c2), f10(f7(c2)))) | (f10(f7(c2)) = f7(c2)) | (~big_f(c2, f10(f7(c2))))), inference(lemma,lemma(discharge,[]))).
% 28.82/19.03 tff(16900,plain,
% 28.82/19.03 (~big_f(f7(c2), f7(c2))),
% 28.82/19.03 inference(unit_resolution,[status(thm)],[16899, 16792, 17, 16793, 12448, 16510])).
% 28.82/19.03 tff(16901,plain,
% 28.82/19.03 (c4 = f7(c2)),
% 28.82/19.03 inference(transitivity,[status(thm)],[16880, 125])).
% 28.82/19.03 tff(16902,plain,
% 28.82/19.03 (big_f(c2, c4) <=> big_f(c2, f7(c2))),
% 28.82/19.03 inference(monotonicity,[status(thm)],[16901])).
% 28.82/19.03 tff(16903,plain,
% 28.82/19.03 (big_f(c2, f7(c2)) <=> big_f(c2, c4)),
% 28.82/19.03 inference(symmetry,[status(thm)],[16902])).
% 28.82/19.03 tff(16904,plain,
% 28.82/19.03 ((~big_f(c2, f7(c2))) <=> (~big_f(c2, c4))),
% 28.82/19.03 inference(monotonicity,[status(thm)],[16903])).
% 28.82/19.03 tff(16905,plain,
% 28.82/19.03 (~big_f(c2, c4)),
% 28.82/19.03 inference(modus_ponens,[status(thm)],[16845, 16904])).
% 28.82/19.03 tff(16906,assumption,(f7(c2) = f4(f7(c2))), introduced(assumption)).
% 28.82/19.03 tff(16907,plain,
% 28.82/19.03 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (~(f7(c2) = c4)) | (~(f7(c2) = f4(f7(c2)))) | big_f(f7(c2), f7(c2)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (~(f7(c2) = c4)) | (~(f7(c2) = f4(f7(c2)))) | big_f(f7(c2), f7(c2)))),
% 28.82/19.03 inference(rewrite,[status(thm)],[])).
% 28.82/19.03 tff(16908,plain,
% 28.82/19.03 (((c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f7(c2) = c4)) | big_f(f7(c2), f7(c2)) | (~(f7(c2) = f4(f7(c2))))) <=> ((c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (~(f7(c2) = c4)) | (~(f7(c2) = f4(f7(c2)))) | big_f(f7(c2), f7(c2)))),
% 28.82/19.03 inference(rewrite,[status(thm)],[])).
% 28.82/19.03 tff(16909,plain,
% 28.82/19.03 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f7(c2) = c4)) | big_f(f7(c2), f7(c2)) | (~(f7(c2) = f4(f7(c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (~(f7(c2) = c4)) | (~(f7(c2) = f4(f7(c2)))) | big_f(f7(c2), f7(c2))))),
% 28.82/19.03 inference(monotonicity,[status(thm)],[16908])).
% 28.82/19.03 tff(16910,plain,
% 28.82/19.03 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f7(c2) = c4)) | big_f(f7(c2), f7(c2)) | (~(f7(c2) = f4(f7(c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (~(f7(c2) = c4)) | (~(f7(c2) = f4(f7(c2)))) | big_f(f7(c2), f7(c2)))),
% 28.82/19.03 inference(transitivity,[status(thm)],[16909, 16907])).
% 28.82/19.03 tff(16911,plain,
% 28.82/19.03 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f7(c2) = c4)) | big_f(f7(c2), f7(c2)) | (~(f7(c2) = f4(f7(c2)))))),
% 28.82/19.03 inference(quant_inst,[status(thm)],[])).
% 28.82/19.03 tff(16912,plain,
% 28.82/19.03 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (c2 = c3) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | (~(f7(c2) = c4)) | (~(f7(c2) = f4(f7(c2)))) | big_f(f7(c2), f7(c2))),
% 28.82/19.03 inference(modus_ponens,[status(thm)],[16911, 16910])).
% 28.82/19.03 tff(16913,plain,
% 28.82/19.03 ($false),
% 28.82/19.03 inference(unit_resolution,[status(thm)],[16912, 402, 377, 1828, 1862, 8218, 8770, 16906])).
% 28.82/19.03 tff(16914,plain,(big_f(f7(c2), f7(c2)) | (c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f7(c2) = c4)) | (~(f7(c2) = f4(f7(c2))))), inference(lemma,lemma(discharge,[]))).
% 28.82/19.03 tff(16915,plain,
% 28.82/19.03 (big_f(c2, f1(c2, c2))),
% 28.82/19.03 inference(unit_resolution,[status(thm)],[16914, 1828, 377, 8218, 8770, 16906])).
% 28.82/19.03 tff(16916,plain,
% 28.82/19.03 ($false),
% 28.82/19.03 inference(unit_resolution,[status(thm)],[14891, 16915, 5298, 480, 3865])).
% 28.82/19.03 tff(16917,plain,((f1(c2, c2) = c2) | (~(c4 = c1)) | big_f(c2, c4) | (c2 = c3) | big_f(f7(c2), f7(c2)) | (~(f7(c2) = c4)) | (~(f7(c2) = f4(f7(c2))))), inference(lemma,lemma(discharge,[]))).
% 28.82/19.03 tff(16918,plain,
% 28.82/19.03 (f1(c2, c2) = c2),
% 28.82/19.03 inference(unit_resolution,[status(thm)],[16917, 16880, 16905, 377, 16900, 16886, 16885])).
% 28.82/19.03 tff(16919,plain,
% 28.82/19.03 (big_f(c2, f1(c2, c2)) <=> big_f(c2, c2)),
% 28.82/19.03 inference(monotonicity,[status(thm)],[16918])).
% 28.82/19.03 tff(16920,plain,
% 28.82/19.03 (big_f(c2, c2) <=> big_f(c2, f1(c2, c2))),
% 28.82/19.03 inference(symmetry,[status(thm)],[16919])).
% 28.82/19.03 tff(16921,plain,
% 28.82/19.03 (big_f(c2, f1(c2, c2))),
% 28.82/19.03 inference(modus_ponens,[status(thm)],[16509, 16920])).
% 28.82/19.03 tff(16922,plain,
% 28.82/19.03 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (~(f7(c2) = c4)) | (~(f7(c2) = f4(f7(c2)))) | big_f(f7(c2), f7(c2)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (~(f7(c2) = c4)) | (~(f7(c2) = f4(f7(c2)))) | big_f(f7(c2), f7(c2)))),
% 28.82/19.03 inference(rewrite,[status(thm)],[])).
% 28.82/19.03 tff(16923,plain,
% 28.82/19.03 (((c2 = c3) | (~(f7(c2) = c4)) | big_f(f7(c2), f7(c2)) | (~(f7(c2) = f4(f7(c2)))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2)))) <=> ((c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (~(f7(c2) = c4)) | (~(f7(c2) = f4(f7(c2)))) | big_f(f7(c2), f7(c2)))),
% 28.82/19.03 inference(rewrite,[status(thm)],[])).
% 28.82/19.03 tff(16924,plain,
% 28.82/19.03 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f7(c2) = c4)) | big_f(f7(c2), f7(c2)) | (~(f7(c2) = f4(f7(c2)))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (~(f7(c2) = c4)) | (~(f7(c2) = f4(f7(c2)))) | big_f(f7(c2), f7(c2))))),
% 28.82/19.03 inference(monotonicity,[status(thm)],[16923])).
% 28.82/19.03 tff(16925,plain,
% 28.82/19.03 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f7(c2) = c4)) | big_f(f7(c2), f7(c2)) | (~(f7(c2) = f4(f7(c2)))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (~(f7(c2) = c4)) | (~(f7(c2) = f4(f7(c2)))) | big_f(f7(c2), f7(c2)))),
% 28.82/19.03 inference(transitivity,[status(thm)],[16924, 16922])).
% 28.82/19.03 tff(16926,plain,
% 28.82/19.03 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f7(c2) = c4)) | big_f(f7(c2), f7(c2)) | (~(f7(c2) = f4(f7(c2)))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))),
% 28.82/19.03 inference(quant_inst,[status(thm)],[])).
% 28.82/19.03 tff(16927,plain,
% 28.82/19.03 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | (~(f7(c2) = c4)) | (~(f7(c2) = f4(f7(c2)))) | big_f(f7(c2), f7(c2))),
% 28.82/19.03 inference(modus_ponens,[status(thm)],[16926, 16925])).
% 28.82/19.03 tff(16928,plain,
% 28.82/19.03 ($false),
% 28.82/19.03 inference(unit_resolution,[status(thm)],[16927, 447, 377, 16918, 16921, 16900, 16886, 16885])).
% 28.82/19.03 tff(16929,plain,((c2 = c3) | (f7(c2) = c2) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (f10(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 28.82/19.03 tff(16930,plain,
% 28.82/19.03 (c2 = c3),
% 28.82/19.03 inference(unit_resolution,[status(thm)],[16929, 17, 115, 122, 3])).
% 28.82/19.03 tff(16931,plain,
% 28.82/19.03 (c3 = c2),
% 28.82/19.03 inference(modus_ponens,[status(thm)],[16930, 127])).
% 28.82/19.03 tff(16932,plain,
% 28.82/19.03 (f5(c1) = c2),
% 28.82/19.03 inference(modus_ponens,[status(thm)],[16811, 10479])).
% 28.82/19.03 tff(16933,plain,
% 28.82/19.03 (c2 = f5(c1)),
% 28.82/19.03 inference(transitivity,[status(thm)],[16811, 10453])).
% 28.82/19.03 tff(16934,plain,
% 28.82/19.03 (f3(c2, c2) = f3(f5(c1), f5(c1))),
% 28.82/19.03 inference(monotonicity,[status(thm)],[16933, 16933])).
% 28.85/19.03 tff(16935,plain,
% 28.85/19.03 (f3(f5(c1), f5(c1)) = f3(c2, c2)),
% 28.85/19.03 inference(symmetry,[status(thm)],[16934])).
% 28.85/19.03 tff(16936,plain,
% 28.85/19.03 ((f3(f5(c1), f5(c1)) = c2) <=> (f3(c2, c2) = c2)),
% 28.85/19.03 inference(monotonicity,[status(thm)],[16935])).
% 28.85/19.03 tff(16937,plain,
% 28.85/19.03 (f7(c2) = c4),
% 28.85/19.03 inference(unit_resolution,[status(thm)],[16645, 9094, 22])).
% 28.85/19.03 tff(16938,plain,
% 28.85/19.03 (c1 = c4),
% 28.85/19.03 inference(symmetry,[status(thm)],[9094])).
% 28.85/19.03 tff(16939,plain,
% 28.85/19.03 (f7(c2) = c4),
% 28.85/19.03 inference(transitivity,[status(thm)],[22, 16938])).
% 28.85/19.03 tff(16940,plain,
% 28.85/19.03 (f4(f7(c2)) = f4(c4)),
% 28.85/19.03 inference(monotonicity,[status(thm)],[16939])).
% 28.85/19.03 tff(16941,plain,
% 28.85/19.03 (f4(c4) = f4(f7(c2))),
% 28.85/19.03 inference(symmetry,[status(thm)],[16940])).
% 28.85/19.03 tff(16942,plain,
% 28.85/19.03 (f7(c2) = f4(f7(c2))),
% 28.85/19.03 inference(transitivity,[status(thm)],[22, 15834, 16941])).
% 28.85/19.03 tff(16943,plain,
% 28.85/19.03 (c2 = c3),
% 28.85/19.03 inference(unit_resolution,[status(thm)],[16791, 1521, 122, 115, 3, 17])).
% 28.85/19.03 tff(16944,plain,
% 28.85/19.03 (c3 = c2),
% 28.85/19.03 inference(symmetry,[status(thm)],[16943])).
% 28.85/19.03 tff(16945,plain,
% 28.85/19.03 ((f7(c2) = c3) <=> (f7(c2) = c2)),
% 28.85/19.03 inference(monotonicity,[status(thm)],[16944])).
% 28.85/19.03 tff(16946,plain,
% 28.85/19.03 ((f7(c2) = c2) <=> (f7(c2) = c3)),
% 28.85/19.03 inference(symmetry,[status(thm)],[16945])).
% 28.85/19.03 tff(16947,plain,
% 28.85/19.03 ((f7(c2) = c2) <=> (c1 = c3)),
% 28.85/19.03 inference(transitivity,[status(thm)],[16946, 9088])).
% 28.85/19.03 tff(16948,plain,
% 28.85/19.03 ((~(f7(c2) = c2)) <=> (~(c1 = c3))),
% 28.85/19.03 inference(monotonicity,[status(thm)],[16947])).
% 28.85/19.03 tff(16949,plain,
% 28.85/19.03 (~(c1 = c3)),
% 28.85/19.03 inference(modus_ponens,[status(thm)],[17, 16948])).
% 28.85/19.03 tff(16950,plain,
% 28.85/19.03 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f1(c1, c1) = c1) | (c1 = c3) | (c2 = c4) | big_f(c1, f1(c1, c1)) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (f1(c1, c1) = c1) | (c1 = c3) | (c2 = c4) | big_f(c1, f1(c1, c1)) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2))),
% 28.85/19.03 inference(rewrite,[status(thm)],[])).
% 28.85/19.03 tff(16951,plain,
% 28.85/19.03 (((c2 = c4) | (f3(c2, c2) = c2) | big_f(f3(c2, c2), c2) | (c1 = c3) | (f1(c1, c1) = c1) | big_f(c1, f1(c1, c1))) <=> ((f1(c1, c1) = c1) | (c1 = c3) | (c2 = c4) | big_f(c1, f1(c1, c1)) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2))),
% 28.85/19.03 inference(rewrite,[status(thm)],[])).
% 28.85/19.03 tff(16952,plain,
% 28.85/19.03 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c2 = c4) | (f3(c2, c2) = c2) | big_f(f3(c2, c2), c2) | (c1 = c3) | (f1(c1, c1) = c1) | big_f(c1, f1(c1, c1)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f1(c1, c1) = c1) | (c1 = c3) | (c2 = c4) | big_f(c1, f1(c1, c1)) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2)))),
% 28.85/19.03 inference(monotonicity,[status(thm)],[16951])).
% 28.85/19.03 tff(16953,plain,
% 28.85/19.03 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c2 = c4) | (f3(c2, c2) = c2) | big_f(f3(c2, c2), c2) | (c1 = c3) | (f1(c1, c1) = c1) | big_f(c1, f1(c1, c1)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (f1(c1, c1) = c1) | (c1 = c3) | (c2 = c4) | big_f(c1, f1(c1, c1)) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2))),
% 28.85/19.03 inference(transitivity,[status(thm)],[16952, 16950])).
% 28.85/19.03 tff(16954,plain,
% 28.85/19.03 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c2 = c4) | (f3(c2, c2) = c2) | big_f(f3(c2, c2), c2) | (c1 = c3) | (f1(c1, c1) = c1) | big_f(c1, f1(c1, c1)))),
% 28.85/19.03 inference(quant_inst,[status(thm)],[])).
% 28.85/19.03 tff(16955,plain,
% 28.85/19.03 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (f1(c1, c1) = c1) | (c1 = c3) | (c2 = c4) | big_f(c1, f1(c1, c1)) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2)),
% 28.85/19.04 inference(modus_ponens,[status(thm)],[16954, 16953])).
% 28.85/19.04 tff(16956,plain,
% 28.85/19.04 ($false),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[16955, 1014, 9710, 168, 15793, 873, 12861, 12882])).
% 28.85/19.04 tff(16957,plain,((f1(c1, c1) = c1) | (c1 = c3) | (c2 = c4) | (f3(c2, c2) = c2) | big_f(f3(c2, c2), c2) | big_f(c1, c2)), inference(lemma,lemma(discharge,[]))).
% 28.85/19.04 tff(16958,plain,
% 28.85/19.04 (f1(c1, c1) = c1),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[16957, 873, 16654, 16949, 12882, 12861])).
% 28.85/19.04 tff(16959,plain,
% 28.85/19.04 (c1 = f1(c1, c1)),
% 28.85/19.04 inference(symmetry,[status(thm)],[16958])).
% 28.85/19.04 tff(16960,plain,
% 28.85/19.04 (f7(c2) = f1(c1, c1)),
% 28.85/19.04 inference(transitivity,[status(thm)],[22, 16959])).
% 28.85/19.04 tff(16961,plain,
% 28.85/19.04 (big_f(f7(c2), f7(c2)) <=> big_f(c1, f1(c1, c1))),
% 28.85/19.04 inference(monotonicity,[status(thm)],[22, 16960])).
% 28.85/19.04 tff(16962,plain,
% 28.85/19.04 (big_f(c1, f1(c1, c1)) <=> big_f(f7(c2), f7(c2))),
% 28.85/19.04 inference(symmetry,[status(thm)],[16961])).
% 28.85/19.04 tff(16963,plain,
% 28.85/19.04 ((~big_f(c1, f1(c1, c1))) <=> (~big_f(f7(c2), f7(c2)))),
% 28.85/19.04 inference(monotonicity,[status(thm)],[16962])).
% 28.85/19.04 tff(16964,plain,
% 28.85/19.04 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (c2 = c4) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (c2 = c4) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2))),
% 28.85/19.04 inference(rewrite,[status(thm)],[])).
% 28.85/19.04 tff(16965,plain,
% 28.85/19.04 (((c2 = c4) | (f3(c2, c2) = c2) | big_f(f3(c2, c2), c2) | (c1 = c3) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1)))) <=> ((c1 = c3) | (c2 = c4) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2))),
% 28.85/19.04 inference(rewrite,[status(thm)],[])).
% 28.85/19.04 tff(16966,plain,
% 28.85/19.04 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (f3(c2, c2) = c2) | big_f(f3(c2, c2), c2) | (c1 = c3) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (c2 = c4) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2)))),
% 28.85/19.04 inference(monotonicity,[status(thm)],[16965])).
% 28.85/19.04 tff(16967,plain,
% 28.85/19.04 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (f3(c2, c2) = c2) | big_f(f3(c2, c2), c2) | (c1 = c3) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (c2 = c4) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2))),
% 28.85/19.04 inference(transitivity,[status(thm)],[16966, 16964])).
% 28.85/19.04 tff(16968,plain,
% 28.85/19.04 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (f3(c2, c2) = c2) | big_f(f3(c2, c2), c2) | (c1 = c3) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))))),
% 28.85/19.04 inference(quant_inst,[status(thm)],[])).
% 28.85/19.04 tff(16969,plain,
% 28.85/19.04 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (c2 = c4) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2)),
% 28.85/19.04 inference(modus_ponens,[status(thm)],[16968, 16967])).
% 28.85/19.04 tff(16970,plain,
% 28.85/19.04 ((c1 = c3) | (c2 = c4) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2)),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[16969, 904])).
% 28.85/19.04 tff(16971,plain,
% 28.85/19.04 (~big_f(c1, f1(c1, c1))),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[16970, 16958, 16949, 12882, 12861, 873])).
% 28.85/19.04 tff(16972,plain,
% 28.85/19.04 (~big_f(f7(c2), f7(c2))),
% 28.85/19.04 inference(modus_ponens,[status(thm)],[16971, 16963])).
% 28.85/19.04 tff(16973,plain,
% 28.85/19.04 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (~(f7(c2) = c4)) | (~(f7(c2) = f4(f7(c2)))) | big_f(f7(c2), f7(c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (~(f7(c2) = c4)) | (~(f7(c2) = f4(f7(c2)))) | big_f(f7(c2), f7(c2)))),
% 28.85/19.04 inference(rewrite,[status(thm)],[])).
% 28.85/19.04 tff(16974,plain,
% 28.85/19.04 (((~(c2 = c3)) | (~(f7(c2) = c4)) | big_f(f7(c2), f7(c2)) | (~(f7(c2) = f4(f7(c2)))) | (c2 = f2(c2)) | (~big_f(c2, c2))) <=> ((~(c2 = c3)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (~(f7(c2) = c4)) | (~(f7(c2) = f4(f7(c2)))) | big_f(f7(c2), f7(c2)))),
% 28.85/19.04 inference(rewrite,[status(thm)],[])).
% 28.85/19.04 tff(16975,plain,
% 28.85/19.04 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(f7(c2) = c4)) | big_f(f7(c2), f7(c2)) | (~(f7(c2) = f4(f7(c2)))) | (c2 = f2(c2)) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (~(f7(c2) = c4)) | (~(f7(c2) = f4(f7(c2)))) | big_f(f7(c2), f7(c2))))),
% 28.85/19.04 inference(monotonicity,[status(thm)],[16974])).
% 28.85/19.04 tff(16976,plain,
% 28.85/19.04 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(f7(c2) = c4)) | big_f(f7(c2), f7(c2)) | (~(f7(c2) = f4(f7(c2)))) | (c2 = f2(c2)) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (~(f7(c2) = c4)) | (~(f7(c2) = f4(f7(c2)))) | big_f(f7(c2), f7(c2)))),
% 28.85/19.04 inference(transitivity,[status(thm)],[16975, 16973])).
% 28.85/19.04 tff(16977,plain,
% 28.85/19.04 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(f7(c2) = c4)) | big_f(f7(c2), f7(c2)) | (~(f7(c2) = f4(f7(c2)))) | (c2 = f2(c2)) | (~big_f(c2, c2)))),
% 28.85/19.04 inference(quant_inst,[status(thm)],[])).
% 28.85/19.04 tff(16978,plain,
% 28.85/19.04 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (~(f7(c2) = c4)) | (~(f7(c2) = f4(f7(c2)))) | big_f(f7(c2), f7(c2))),
% 28.85/19.04 inference(modus_ponens,[status(thm)],[16977, 16976])).
% 28.85/19.04 tff(16979,plain,
% 28.85/19.04 ((c2 = f2(c2)) | (~(f7(c2) = c4)) | (~(f7(c2) = f4(f7(c2))))),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[16978, 5622, 16509, 16943, 16972])).
% 28.85/19.04 tff(16980,plain,
% 28.85/19.04 (c2 = f2(c2)),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[16979, 16942, 16937])).
% 28.85/19.04 tff(16981,plain,
% 28.85/19.04 (c3 = c2),
% 28.85/19.04 inference(modus_ponens,[status(thm)],[16943, 127])).
% 28.85/19.04 tff(16982,plain,
% 28.85/19.04 (~big_f(c2, c1)),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[13236, 873, 16509, 16943, 12882])).
% 28.85/19.04 tff(16983,plain,
% 28.85/19.04 (~big_f(f7(c1), c1)),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[15738, 16982, 120])).
% 28.85/19.04 tff(16984,plain,
% 28.85/19.04 ((~big_f(c2, c1)) <=> (~big_f(f7(f7(c2)), f7(c2)))),
% 28.85/19.04 inference(monotonicity,[status(thm)],[12451])).
% 28.85/19.04 tff(16985,plain,
% 28.85/19.04 (~big_f(f7(f7(c2)), f7(c2))),
% 28.85/19.04 inference(modus_ponens,[status(thm)],[16982, 16984])).
% 28.85/19.04 tff(16986,plain,
% 28.85/19.04 (f7(c2) = f5(f7(c2))),
% 28.85/19.04 inference(modus_ponens,[status(thm)],[230, 16639])).
% 28.85/19.04 tff(16987,plain,
% 28.85/19.04 (~big_f(f7(c1), f5(c1))),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[289, 230, 285])).
% 28.85/19.04 tff(16988,plain,
% 28.85/19.04 (big_f(f8(c1), f10(c1))),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[2848, 16987, 115, 3])).
% 28.85/19.04 tff(16989,plain,
% 28.85/19.04 (~(f8(c1) = c1)),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[15716, 16988, 1521, 15, 22])).
% 28.85/19.04 tff(16990,plain,
% 28.85/19.04 (f8(c1) = c2),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[1680, 16989])).
% 28.85/19.04 tff(16991,plain,
% 28.85/19.04 (f5(c1) = f7(c2)),
% 28.85/19.04 inference(transitivity,[status(thm)],[230, 125])).
% 28.85/19.04 tff(16992,plain,
% 28.85/19.04 ((c2 = f5(c1)) <=> (c2 = f7(c2))),
% 28.85/19.04 inference(monotonicity,[status(thm)],[16991])).
% 28.85/19.04 tff(16993,plain,
% 28.85/19.04 ((c2 = f5(c1)) <=> (f7(c2) = c2)),
% 28.85/19.04 inference(transitivity,[status(thm)],[16992, 8409])).
% 28.85/19.04 tff(16994,plain,
% 28.85/19.04 ((f7(c2) = c2) <=> (c2 = f5(c1))),
% 28.85/19.04 inference(symmetry,[status(thm)],[16993])).
% 28.85/19.04 tff(16995,plain,
% 28.85/19.04 ((f7(c2) = c2) <=> (c2 = f5(f7(c2)))),
% 28.85/19.04 inference(transitivity,[status(thm)],[16994, 8602])).
% 28.85/19.04 tff(16996,plain,
% 28.85/19.04 ((~(f7(c2) = c2)) <=> (~(c2 = f5(f7(c2))))),
% 28.85/19.04 inference(monotonicity,[status(thm)],[16995])).
% 28.85/19.04 tff(16997,plain,
% 28.85/19.04 (~(c2 = f5(f7(c2)))),
% 28.85/19.04 inference(modus_ponens,[status(thm)],[17, 16996])).
% 28.85/19.04 tff(16998,plain,
% 28.85/19.04 (f9(c2, c2) = c2),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[16630, 16997, 12448, 16776, 12943, 15, 22, 16990, 122])).
% 28.85/19.04 tff(16999,plain,
% 28.85/19.04 (big_f(f9(c2, c2), c2) <=> big_f(c2, c2)),
% 28.85/19.04 inference(monotonicity,[status(thm)],[16998])).
% 28.85/19.04 tff(17000,plain,
% 28.85/19.04 (big_f(c2, c2) <=> big_f(f9(c2, c2), c2)),
% 28.85/19.04 inference(symmetry,[status(thm)],[16999])).
% 28.85/19.04 tff(17001,plain,
% 28.85/19.04 (big_f(c2, c2) <=> big_f(f9(c2, c2), f10(c2))),
% 28.85/19.04 inference(transitivity,[status(thm)],[17000, 130])).
% 28.85/19.04 tff(17002,plain,
% 28.85/19.04 (big_f(f9(c2, c2), f10(c2))),
% 28.85/19.04 inference(modus_ponens,[status(thm)],[16509, 17001])).
% 28.85/19.04 tff(17003,plain,
% 28.85/19.04 ($false),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[16789, 783, 122, 12943, 16998, 17002, 16986, 8452])).
% 28.85/19.04 tff(17004,plain,((~(f5(c1) = c1)) | (~(f10(c2) = c2)) | big_f(f7(f7(c2)), f7(c2)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (f7(c1) = c1) | (f10(c1) = c1) | big_f(f7(c1), c1)), inference(lemma,lemma(discharge,[]))).
% 28.85/19.04 tff(17005,plain,
% 28.85/19.04 (~(f5(c1) = c1)),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[17004, 16985, 122, 17, 1521, 115, 3, 16983])).
% 28.85/19.04 tff(17006,plain,
% 28.85/19.04 (f5(c1) = c2),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[1708, 17005])).
% 28.85/19.04 tff(17007,plain,
% 28.85/19.04 ((~big_f(f7(c2), c2)) <=> (~big_f(f7(c2), f5(c2)))),
% 28.85/19.04 inference(monotonicity,[status(thm)],[9012])).
% 28.85/19.04 tff(17008,plain,
% 28.85/19.04 (~big_f(f7(c2), f5(c2))),
% 28.85/19.04 inference(modus_ponens,[status(thm)],[1521, 17007])).
% 28.85/19.04 tff(17009,plain,
% 28.85/19.04 ((f9(c2, f5(c1)) = c2) <=> (f9(c2, c2) = c2)),
% 28.85/19.04 inference(monotonicity,[status(thm)],[7218])).
% 28.85/19.04 tff(17010,assumption,(f9(c2, f5(c1)) = c2), introduced(assumption)).
% 28.85/19.04 tff(17011,plain,
% 28.85/19.04 (f9(c2, c2) = c2),
% 28.85/19.04 inference(modus_ponens,[status(thm)],[17010, 17009])).
% 28.85/19.04 tff(17012,plain,
% 28.85/19.04 ($false),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[1209, 17011])).
% 28.85/19.04 tff(17013,plain,((~(f9(c2, f5(c1)) = c2)) | (f9(c2, c2) = c2) | (~(f5(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.85/19.04 tff(17014,plain,
% 28.85/19.04 (~(f9(c2, f5(c1)) = c2)),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[17013, 1209, 186])).
% 28.85/19.04 tff(17015,plain,
% 28.85/19.04 (f9(c2, f5(c1)) = c1),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[16529, 17014])).
% 28.85/19.04 tff(17016,plain,
% 28.85/19.04 (f9(c2, c2) = f7(c2)),
% 28.85/19.04 inference(transitivity,[status(thm)],[16520, 17015, 125])).
% 28.85/19.04 tff(17017,plain,
% 28.85/19.04 (big_f(f9(c2, c2), c2) <=> big_f(f7(c2), c2)),
% 28.85/19.04 inference(monotonicity,[status(thm)],[17016])).
% 28.85/19.04 tff(17018,plain,
% 28.85/19.04 (big_f(f7(c2), c2) <=> big_f(f9(c2, c2), c2)),
% 28.85/19.04 inference(symmetry,[status(thm)],[17017])).
% 28.85/19.04 tff(17019,plain,
% 28.85/19.04 ((~big_f(f7(c2), c2)) <=> (~big_f(f9(c2, c2), c2))),
% 28.85/19.04 inference(monotonicity,[status(thm)],[17018])).
% 28.85/19.04 tff(17020,plain,
% 28.85/19.04 (~big_f(f9(c2, c2), c2)),
% 28.85/19.04 inference(modus_ponens,[status(thm)],[1521, 17019])).
% 28.85/19.04 tff(17021,plain,
% 28.85/19.04 (big_f(f9(c2, c2), c2)),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[4860, 1209, 122, 17, 67, 2853, 4829])).
% 28.85/19.04 tff(17022,plain,
% 28.85/19.04 ($false),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[17021, 17020])).
% 28.85/19.04 tff(17023,plain,((f9(c2, c2) = c2) | big_f(f7(c2), c2) | (~(f5(c1) = c2)) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~(c3 = c2)) | (~(c2 = f2(c2))) | big_f(f7(c2), f5(c2))), inference(lemma,lemma(discharge,[]))).
% 28.85/19.04 tff(17024,plain,
% 28.85/19.04 (f9(c2, c2) = c2),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[17023, 17008, 186, 122, 17, 67, 2853, 1521])).
% 28.85/19.04 tff(17025,plain,
% 28.85/19.04 (big_f(f9(c2, c2), c2) <=> big_f(c2, c2)),
% 28.85/19.04 inference(monotonicity,[status(thm)],[17024])).
% 28.85/19.04 tff(17026,plain,
% 28.85/19.04 (big_f(c2, c2) <=> big_f(f9(c2, c2), c2)),
% 28.85/19.04 inference(symmetry,[status(thm)],[17025])).
% 28.85/19.04 tff(17027,plain,
% 28.85/19.04 (big_f(f9(c2, c2), c2)),
% 28.85/19.04 inference(modus_ponens,[status(thm)],[1345, 17026])).
% 28.85/19.04 tff(17028,plain,
% 28.85/19.04 (~big_f(f9(c2, c2), f10(c2))),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[8397, 17024, 122, 17, 1521, 9020])).
% 28.85/19.04 tff(17029,plain,
% 28.85/19.04 (~big_f(f9(c2, c2), c2)),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[6482, 17028, 122])).
% 28.85/19.04 tff(17030,plain,
% 28.85/19.04 ($false),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[17029, 17027])).
% 28.85/19.04 tff(17031,plain,((~(f5(c2) = c2)) | (~big_f(c2, c2)) | (~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(f5(c1) = c2)) | (~(c3 = c2)) | (~(c2 = f2(c2)))), inference(lemma,lemma(discharge,[]))).
% 28.85/19.04 tff(17032,plain,
% 28.85/19.04 (~(f5(c2) = c2)),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[17031, 17006, 122, 17, 1521, 16509, 16981, 16980])).
% 28.85/19.04 tff(17033,plain,
% 28.85/19.04 (f5(c2) = c1),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[1547, 17032])).
% 28.85/19.04 tff(17034,plain,
% 28.85/19.04 (f5(c2) = f7(c2)),
% 28.85/19.04 inference(transitivity,[status(thm)],[17033, 125])).
% 28.85/19.04 tff(17035,plain,
% 28.85/19.04 (big_f(f7(c2), f5(c2)) <=> big_f(f7(c2), f7(c2))),
% 28.85/19.04 inference(monotonicity,[status(thm)],[17034])).
% 28.85/19.04 tff(17036,plain,
% 28.85/19.04 (big_f(f7(c2), f7(c2)) <=> big_f(f7(c2), f5(c2))),
% 28.85/19.04 inference(symmetry,[status(thm)],[17035])).
% 28.85/19.04 tff(17037,plain,
% 28.85/19.04 ((~big_f(f7(c2), f7(c2))) <=> (~big_f(f7(c2), f5(c2)))),
% 28.85/19.04 inference(monotonicity,[status(thm)],[17036])).
% 28.85/19.04 tff(17038,plain,
% 28.85/19.04 (~big_f(f7(c2), f5(c2))),
% 28.85/19.04 inference(modus_ponens,[status(thm)],[16972, 17037])).
% 28.85/19.04 tff(17039,plain,
% 28.85/19.04 (f9(c2, c2) = c2),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[17023, 17038, 17006, 122, 17, 16981, 16980, 1521])).
% 28.85/19.04 tff(17040,plain,
% 28.85/19.04 (big_f(f9(c2, c2), c2) <=> big_f(c2, c2)),
% 28.85/19.04 inference(monotonicity,[status(thm)],[17039])).
% 28.85/19.04 tff(17041,plain,
% 28.85/19.04 (big_f(c2, c2) <=> big_f(f9(c2, c2), c2)),
% 28.85/19.04 inference(symmetry,[status(thm)],[17040])).
% 28.85/19.04 tff(17042,plain,
% 28.85/19.04 (big_f(f9(c2, c2), c2)),
% 28.85/19.04 inference(modus_ponens,[status(thm)],[16509, 17041])).
% 28.85/19.04 tff(17043,plain,
% 28.85/19.04 (f7(c2) = f5(c2)),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[8394, 17033, 22])).
% 28.85/19.04 tff(17044,plain,
% 28.85/19.04 (~big_f(f9(c2, c2), f10(c2))),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[8386, 17039, 122, 17, 17043, 16972])).
% 28.85/19.04 tff(17045,plain,
% 28.85/19.04 (~big_f(f9(c2, c2), c2)),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[6482, 17044, 122])).
% 28.85/19.04 tff(17046,plain,
% 28.85/19.04 ($false),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[17045, 17042])).
% 28.85/19.04 tff(17047,plain,((c2 = c4) | (~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (f7(c1) = c1) | (f10(c1) = c1) | big_f(f3(c2, c2), c2) | (f3(c2, c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 28.85/19.04 tff(17048,plain,
% 28.85/19.04 (f3(c2, c2) = c2),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[17047, 12882, 17, 873, 115, 3, 1521, 122])).
% 28.85/19.04 tff(17049,plain,
% 28.85/19.04 (big_f(f3(c2, c2), c2) <=> big_f(c2, c2)),
% 28.85/19.04 inference(monotonicity,[status(thm)],[17048])).
% 28.85/19.04 tff(17050,plain,
% 28.85/19.04 (big_f(c2, c2) <=> big_f(f3(c2, c2), c2)),
% 28.85/19.04 inference(symmetry,[status(thm)],[17049])).
% 28.85/19.04 tff(17051,plain,
% 28.85/19.04 (big_f(f3(c2, c2), c2)),
% 28.85/19.04 inference(modus_ponens,[status(thm)],[16509, 17050])).
% 28.85/19.04 tff(17052,plain,
% 28.85/19.04 ($false),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[12882, 17051])).
% 28.85/19.04 tff(17053,plain,(big_f(f3(c2, c2), c2) | (f7(c2) = c2) | (c2 = c4) | (f7(c1) = c1) | (f10(c1) = c1) | big_f(f7(c2), c2) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.85/19.04 tff(17054,plain,
% 28.85/19.04 (big_f(f3(c2, c2), c2)),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[17053, 1521, 873, 115, 3, 17, 122])).
% 28.85/19.04 tff(17055,plain,
% 28.85/19.04 (f5(c1) = f5(f7(c2))),
% 28.85/19.04 inference(monotonicity,[status(thm)],[342])).
% 28.85/19.04 tff(17056,plain,
% 28.85/19.04 (f5(f7(c2)) = f5(c1)),
% 28.85/19.04 inference(symmetry,[status(thm)],[17055])).
% 28.85/19.04 tff(17057,plain,
% 28.85/19.04 (c2 = f5(c1)),
% 28.85/19.04 inference(transitivity,[status(thm)],[8686, 17056])).
% 28.85/19.04 tff(17058,plain,
% 28.85/19.04 (f3(c2, c2) = f3(f5(c1), f5(c1))),
% 28.85/19.04 inference(monotonicity,[status(thm)],[17057, 17057])).
% 28.85/19.04 tff(17059,plain,
% 28.85/19.04 (f3(c2, c2) = f7(c2)),
% 28.85/19.04 inference(transitivity,[status(thm)],[17058, 14337, 342])).
% 28.85/19.04 tff(17060,plain,
% 28.85/19.04 (big_f(f3(c2, c2), c2) <=> big_f(f7(c2), c2)),
% 28.85/19.04 inference(monotonicity,[status(thm)],[17059])).
% 28.85/19.04 tff(17061,plain,
% 28.85/19.04 (big_f(f7(c2), c2) <=> big_f(f3(c2, c2), c2)),
% 28.85/19.04 inference(symmetry,[status(thm)],[17060])).
% 28.85/19.04 tff(17062,plain,
% 28.85/19.04 ((~big_f(f7(c2), c2)) <=> (~big_f(f3(c2, c2), c2))),
% 28.85/19.04 inference(monotonicity,[status(thm)],[17061])).
% 28.85/19.04 tff(17063,plain,
% 28.85/19.04 (~big_f(f3(c2, c2), c2)),
% 28.85/19.04 inference(modus_ponens,[status(thm)],[1521, 17062])).
% 28.85/19.04 tff(17064,plain,
% 28.85/19.04 ($false),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[15356, 17063])).
% 28.85/19.04 tff(17065,plain,((~(f3(f5(c1), f5(c1)) = c1)) | (~big_f(f3(c2, c2), c2)) | big_f(f7(c2), c2) | (~(f7(c2) = c1)) | (~(c2 = f5(f7(c2))))), inference(lemma,lemma(discharge,[]))).
% 28.85/19.04 tff(17066,plain,
% 28.85/19.04 (~(f3(f5(c1), f5(c1)) = c1)),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[17065, 17054, 1521, 22, 16811])).
% 28.85/19.04 tff(17067,plain,
% 28.85/19.04 (f3(f5(c1), f5(c1)) = c2),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[7625, 17066])).
% 28.85/19.04 tff(17068,plain,
% 28.85/19.04 (f3(c2, c2) = c2),
% 28.85/19.04 inference(modus_ponens,[status(thm)],[17067, 16936])).
% 28.85/19.04 tff(17069,plain,
% 28.85/19.04 ((c2 = f2(c2)) | (~(f3(c2, c2) = c2))),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[13128, 7051, 873, 16509, 16930, 17054])).
% 28.85/19.04 tff(17070,plain,
% 28.85/19.04 (c2 = f2(c2)),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[17069, 17068])).
% 28.85/19.04 tff(17071,plain,
% 28.85/19.04 ((f5(f10(c1)) = c1) <=> (f5(c2) = c1)),
% 28.85/19.04 inference(monotonicity,[status(thm)],[16012])).
% 28.85/19.04 tff(17072,plain,
% 28.85/19.04 ((f5(c2) = c1) <=> (f5(f10(c1)) = c1)),
% 28.85/19.04 inference(symmetry,[status(thm)],[17071])).
% 28.85/19.04 tff(17073,plain,
% 28.85/19.04 (~(f5(c2) = c2)),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[17031, 2853, 122, 17, 186, 1345, 67, 1521])).
% 28.85/19.04 tff(17074,plain,
% 28.85/19.04 (f5(c2) = c1),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[1547, 17073])).
% 28.85/19.04 tff(17075,plain,
% 28.85/19.04 (f5(f10(c1)) = c1),
% 28.85/19.04 inference(modus_ponens,[status(thm)],[17074, 17072])).
% 28.85/19.04 tff(17076,plain,
% 28.85/19.04 ((~big_f(f7(c2), f7(c2))) <=> (~big_f(f7(c2), c1))),
% 28.85/19.04 inference(monotonicity,[status(thm)],[8368])).
% 28.85/19.04 tff(17077,plain,
% 28.85/19.04 (~big_f(f7(c2), c1)),
% 28.85/19.04 inference(modus_ponens,[status(thm)],[8218, 17076])).
% 28.85/19.04 tff(17078,plain,
% 28.85/19.04 ($false),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[338, 17077])).
% 28.85/19.04 tff(17079,plain,((~big_f(f7(c2), c1)) | big_f(f7(c2), f7(c2)) | (~(f7(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.85/19.04 tff(17080,plain,
% 28.85/19.04 (~big_f(f7(c2), c1)),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[17079, 8218, 22])).
% 28.85/19.04 tff(17081,plain,
% 28.85/19.04 (~big_f(f7(c2), f5(c2))),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[336, 17080, 17075, 16])).
% 28.85/19.04 tff(17082,plain,
% 28.85/19.04 (f9(c2, c2) = c2),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[17023, 17081, 186, 122, 17, 67, 2853, 1521])).
% 28.85/19.04 tff(17083,plain,
% 28.85/19.04 (big_f(f9(c2, c2), c2) <=> big_f(c2, c2)),
% 28.85/19.04 inference(monotonicity,[status(thm)],[17082])).
% 28.85/19.04 tff(17084,plain,
% 28.85/19.04 (big_f(c2, c2) <=> big_f(f9(c2, c2), c2)),
% 28.85/19.04 inference(symmetry,[status(thm)],[17083])).
% 28.85/19.04 tff(17085,plain,
% 28.85/19.04 (big_f(f9(c2, c2), c2)),
% 28.85/19.04 inference(modus_ponens,[status(thm)],[1345, 17084])).
% 28.85/19.04 tff(17086,plain,
% 28.85/19.04 (f7(c2) = f5(c2)),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[8394, 17074, 22])).
% 28.85/19.04 tff(17087,plain,
% 28.85/19.04 (~big_f(f9(c2, c2), f10(c2))),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[8386, 17082, 122, 17, 17086, 8218])).
% 28.85/19.04 tff(17088,plain,
% 28.85/19.04 (~big_f(f9(c2, c2), c2)),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[6482, 17087, 122])).
% 28.85/19.04 tff(17089,plain,
% 28.85/19.04 ($false),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[17088, 17085])).
% 28.85/19.04 tff(17090,plain,(big_f(f7(c2), f7(c2)) | (~big_f(c2, c2)) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~(f5(c1) = c2)) | (~(c3 = c2)) | (~(c2 = f2(c2))) | big_f(f7(c2), c2) | (~(f10(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.85/19.04 tff(17091,plain,
% 28.85/19.04 (big_f(f7(c2), f7(c2))),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[17090, 17070, 122, 17, 16932, 16931, 16509, 1521, 15])).
% 28.85/19.04 tff(17092,plain,
% 28.85/19.04 (big_f(f7(c2), c1)),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[8374, 17091, 22])).
% 28.85/19.04 tff(17093,plain,
% 28.85/19.04 (big_f(f4(c4), c4)),
% 28.85/19.04 inference(modus_ponens,[status(thm)],[17092, 16516])).
% 28.85/19.04 tff(17094,plain,
% 28.85/19.04 (c1 = c4),
% 28.85/19.04 inference(unit_resolution,[status(thm)],[484, 9094])).
% 28.85/19.04 tff(17095,plain,
% 28.85/19.04 (c3 = c2),
% 28.85/19.04 inference(symmetry,[status(thm)],[16930])).
% 28.85/19.04 tff(17096,plain,
% 28.85/19.04 ((f7(c2) = c3) <=> (f7(c2) = c2)),
% 28.85/19.04 inference(monotonicity,[status(thm)],[17095])).
% 28.85/19.04 tff(17097,plain,
% 28.85/19.04 ((f7(c2) = c2) <=> (f7(c2) = c3)),
% 28.85/19.04 inference(symmetry,[status(thm)],[17096])).
% 28.85/19.04 tff(17098,plain,
% 28.85/19.04 ((~(f7(c2) = c2)) <=> (~(f7(c2) = c3))),
% 28.85/19.04 inference(monotonicity,[status(thm)],[17097])).
% 28.85/19.04 tff(17099,plain,
% 28.85/19.04 (~(f7(c2) = c3)),
% 28.85/19.04 inference(modus_ponens,[status(thm)],[17, 17098])).
% 28.85/19.04 tff(17100,plain,
% 28.85/19.04 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c4) | (f7(c2) = c3) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (f1(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(c2), f1(f7(c2), f7(c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c2 = c4) | (f7(c2) = c3) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (f1(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(c2), f1(f7(c2), f7(c2))))),
% 28.85/19.04 inference(rewrite,[status(thm)],[])).
% 28.85/19.04 tff(17101,plain,
% 28.85/19.04 (((c2 = c4) | (f7(c2) = c3) | (f1(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(c2), f1(f7(c2), f7(c2))) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2))) <=> ((c2 = c4) | (f7(c2) = c3) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (f1(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(c2), f1(f7(c2), f7(c2))))),
% 28.85/19.04 inference(rewrite,[status(thm)],[])).
% 28.85/19.04 tff(17102,plain,
% 28.85/19.04 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c4) | (f7(c2) = c3) | (f1(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(c2), f1(f7(c2), f7(c2))) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c4) | (f7(c2) = c3) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (f1(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(c2), f1(f7(c2), f7(c2)))))),
% 28.85/19.04 inference(monotonicity,[status(thm)],[17101])).
% 28.85/19.04 tff(17103,plain,
% 28.85/19.04 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c4) | (f7(c2) = c3) | (f1(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(c2), f1(f7(c2), f7(c2))) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c2 = c4) | (f7(c2) = c3) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (f1(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(c2), f1(f7(c2), f7(c2))))),
% 28.85/19.04 inference(transitivity,[status(thm)],[17102, 17100])).
% 28.85/19.04 tff(17104,plain,
% 28.85/19.04 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c4) | (f7(c2) = c3) | (f1(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(c2), f1(f7(c2), f7(c2))) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)))),
% 28.85/19.05 inference(quant_inst,[status(thm)],[])).
% 28.85/19.05 tff(17105,plain,
% 28.85/19.05 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c2 = c4) | (f7(c2) = c3) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (f1(f7(c2), f7(c2)) = f7(c2)) | big_f(f7(c2), f1(f7(c2), f7(c2)))),
% 28.85/19.05 inference(modus_ponens,[status(thm)],[17104, 17103])).
% 28.85/19.05 tff(17106,plain,
% 28.85/19.05 (big_f(f7(c2), f1(f7(c2), f7(c2)))),
% 28.85/19.05 inference(unit_resolution,[status(thm)],[17105, 969, 873, 9092, 7387, 15356, 15784])).
% 28.85/19.05 tff(17107,plain,
% 28.85/19.05 (big_f(c1, f1(c1, c1))),
% 28.85/19.05 inference(modus_ponens,[status(thm)],[17106, 9702])).
% 28.85/19.05 tff(17108,plain,
% 28.85/19.05 ($false),
% 28.85/19.05 inference(unit_resolution,[status(thm)],[15793, 17107])).
% 28.85/19.05 tff(17109,plain,((f1(c1, c1) = c1) | (~(f7(c2) = c1)) | (c2 = c4) | (f7(c2) = c3) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | big_f(c1, c2)), inference(lemma,lemma(discharge,[]))).
% 28.85/19.05 tff(17110,plain,
% 28.85/19.05 (f1(c1, c1) = c1),
% 28.85/19.05 inference(unit_resolution,[status(thm)],[17109, 17068, 873, 17099, 22, 17054, 16654])).
% 28.85/19.05 tff(17111,plain,
% 28.85/19.05 (c1 = f1(c1, c1)),
% 28.85/19.05 inference(symmetry,[status(thm)],[624])).
% 28.85/19.05 tff(17112,plain,
% 28.85/19.05 (c4 = c1),
% 28.85/19.05 inference(symmetry,[status(thm)],[11526])).
% 28.85/19.05 tff(17113,plain,
% 28.85/19.05 (c4 = f1(c1, c1)),
% 28.85/19.05 inference(transitivity,[status(thm)],[17112, 17111])).
% 28.85/19.05 tff(17114,plain,
% 28.85/19.05 (big_f(f4(c4), c4) <=> big_f(c1, f1(c1, c1))),
% 28.85/19.05 inference(monotonicity,[status(thm)],[11752, 17113])).
% 28.85/19.05 tff(17115,plain,
% 28.85/19.05 (big_f(c1, f1(c1, c1)) <=> big_f(f4(c4), c4)),
% 28.85/19.05 inference(symmetry,[status(thm)],[17114])).
% 28.85/19.05 tff(17116,plain,
% 28.85/19.05 ((~big_f(c1, f1(c1, c1))) <=> (~big_f(f4(c4), c4))),
% 28.85/19.05 inference(monotonicity,[status(thm)],[17115])).
% 28.85/19.05 tff(17117,plain,
% 28.85/19.05 (~big_f(f4(c4), c4)),
% 28.85/19.05 inference(modus_ponens,[status(thm)],[9673, 17116])).
% 28.85/19.05 tff(17118,plain,
% 28.85/19.05 ($false),
% 28.85/19.05 inference(unit_resolution,[status(thm)],[474, 17117])).
% 28.85/19.05 tff(17119,plain,((~(f1(c1, c1) = c1)) | (~big_f(f4(c4), c4)) | big_f(c1, f1(c1, c1)) | (~(c1 = c4)) | (~(f4(c4) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.85/19.05 tff(17120,plain,
% 28.85/19.05 (big_f(c1, f1(c1, c1))),
% 28.85/19.05 inference(unit_resolution,[status(thm)],[17119, 17110, 15706, 17094, 17093])).
% 28.85/19.05 tff(17121,plain,
% 28.85/19.05 (big_f(f7(c2), f1(f7(c2), f7(c2)))),
% 28.85/19.05 inference(unit_resolution,[status(thm)],[9730, 17120, 22])).
% 28.85/19.05 tff(17122,plain,
% 28.85/19.05 (f1(f7(c2), f7(c2)) = f7(c2)),
% 28.85/19.05 inference(modus_ponens,[status(thm)],[17110, 9668])).
% 28.85/19.05 tff(17123,plain,
% 28.85/19.05 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (f7(c2) = c3) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2)))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c4) | (f7(c2) = c3) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2)))))),
% 28.85/19.05 inference(rewrite,[status(thm)],[])).
% 28.85/19.05 tff(17124,plain,
% 28.85/19.05 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (f7(c2) = c3) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2)))))),
% 28.85/19.05 inference(quant_inst,[status(thm)],[])).
% 28.85/19.05 tff(17125,plain,
% 28.85/19.05 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c4) | (f7(c2) = c3) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~(f1(f7(c2), f7(c2)) = f7(c2))) | (~big_f(f7(c2), f1(f7(c2), f7(c2))))),
% 28.85/19.05 inference(modus_ponens,[status(thm)],[17124, 17123])).
% 28.85/19.05 tff(17126,plain,
% 28.85/19.05 ($false),
% 28.85/19.05 inference(unit_resolution,[status(thm)],[17125, 933, 873, 17099, 17068, 17054, 17122, 17121])).
% 28.85/19.05 tff(17127,plain,(big_f(f7(c2), c2) | (c2 = c4) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (f7(c1) = c1) | (f10(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 28.85/19.05 tff(17128,plain,
% 28.85/19.05 (big_f(f7(c2), c2)),
% 28.85/19.05 inference(unit_resolution,[status(thm)],[17127, 873, 122, 17, 115, 3])).
% 28.85/19.05 tff(17129,plain,
% 28.85/19.05 (big_f(f7(c2), f10(f7(c2)))),
% 28.85/19.05 inference(modus_ponens,[status(thm)],[17128, 12766])).
% 28.85/19.05 tff(17130,plain,
% 28.85/19.05 (~big_f(f7(c2), f7(c2))),
% 28.85/19.05 inference(unit_resolution,[status(thm)],[16899, 17129, 17, 17128, 12448, 16510])).
% 28.85/19.05 tff(17131,plain,
% 28.85/19.05 (c4 = f7(c2)),
% 28.85/19.05 inference(transitivity,[status(thm)],[480, 342])).
% 28.85/19.05 tff(17132,plain,
% 28.85/19.05 (f4(c4) = f7(c2)),
% 28.85/19.05 inference(transitivity,[status(thm)],[11752, 342])).
% 28.85/19.05 tff(17133,plain,
% 28.85/19.05 (big_f(f4(c4), c4) <=> big_f(f7(c2), f7(c2))),
% 28.85/19.05 inference(monotonicity,[status(thm)],[17132, 17131])).
% 28.85/19.05 tff(17134,plain,
% 28.85/19.05 (big_f(f7(c2), f7(c2))),
% 28.85/19.05 inference(modus_ponens,[status(thm)],[474, 17133])).
% 28.85/19.05 tff(17135,plain,
% 28.85/19.05 ($false),
% 28.85/19.05 inference(unit_resolution,[status(thm)],[8218, 17134])).
% 28.85/19.05 tff(17136,plain,((~big_f(f4(c4), c4)) | big_f(f7(c2), f7(c2)) | (~(c4 = c1)) | (~(f7(c2) = c1)) | (~(f4(c4) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.85/19.05 tff(17137,plain,
% 28.85/19.05 (~big_f(f4(c4), c4)),
% 28.85/19.05 inference(unit_resolution,[status(thm)],[17136, 17130, 9094, 22, 15706])).
% 28.85/19.05 tff(17138,plain,
% 28.85/19.05 ((f7(c2) = c2) <=> (c1 = c3)),
% 28.85/19.05 inference(transitivity,[status(thm)],[17097, 9088])).
% 28.85/19.05 tff(17139,plain,
% 28.85/19.05 ((~(f7(c2) = c2)) <=> (~(c1 = c3))),
% 28.85/19.05 inference(monotonicity,[status(thm)],[17138])).
% 28.85/19.05 tff(17140,plain,
% 28.85/19.05 (~(c1 = c3)),
% 28.85/19.05 inference(modus_ponens,[status(thm)],[17, 17139])).
% 28.85/19.05 tff(17141,plain,
% 28.85/19.05 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f7(c2) = c3) | (~(f7(c2) = c4)) | (~(f7(c2) = f4(f7(c2)))) | big_f(f7(c2), f7(c2)) | big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (f7(c2) = c3) | (~(f7(c2) = c4)) | (~(f7(c2) = f4(f7(c2)))) | big_f(f7(c2), f7(c2)) | big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2))),
% 28.85/19.05 inference(rewrite,[status(thm)],[])).
% 28.85/19.05 tff(17142,plain,
% 28.85/19.05 (((f7(c2) = c3) | (f1(f7(c2), c2) = c2) | big_f(f7(c2), f1(f7(c2), c2)) | (~(f7(c2) = c4)) | big_f(f7(c2), f7(c2)) | (~(f7(c2) = f4(f7(c2))))) <=> ((f7(c2) = c3) | (~(f7(c2) = c4)) | (~(f7(c2) = f4(f7(c2)))) | big_f(f7(c2), f7(c2)) | big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2))),
% 28.85/19.05 inference(rewrite,[status(thm)],[])).
% 28.85/19.05 tff(17143,plain,
% 28.85/19.05 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f7(c2) = c3) | (f1(f7(c2), c2) = c2) | big_f(f7(c2), f1(f7(c2), c2)) | (~(f7(c2) = c4)) | big_f(f7(c2), f7(c2)) | (~(f7(c2) = f4(f7(c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f7(c2) = c3) | (~(f7(c2) = c4)) | (~(f7(c2) = f4(f7(c2)))) | big_f(f7(c2), f7(c2)) | big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2)))),
% 28.85/19.05 inference(monotonicity,[status(thm)],[17142])).
% 28.85/19.05 tff(17144,plain,
% 28.85/19.05 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f7(c2) = c3) | (f1(f7(c2), c2) = c2) | big_f(f7(c2), f1(f7(c2), c2)) | (~(f7(c2) = c4)) | big_f(f7(c2), f7(c2)) | (~(f7(c2) = f4(f7(c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (f7(c2) = c3) | (~(f7(c2) = c4)) | (~(f7(c2) = f4(f7(c2)))) | big_f(f7(c2), f7(c2)) | big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2))),
% 28.85/19.05 inference(transitivity,[status(thm)],[17143, 17141])).
% 28.85/19.05 tff(17145,plain,
% 28.85/19.05 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f7(c2) = c3) | (f1(f7(c2), c2) = c2) | big_f(f7(c2), f1(f7(c2), c2)) | (~(f7(c2) = c4)) | big_f(f7(c2), f7(c2)) | (~(f7(c2) = f4(f7(c2)))))),
% 28.85/19.05 inference(quant_inst,[status(thm)],[])).
% 28.85/19.05 tff(17146,plain,
% 28.85/19.05 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (f7(c2) = c3) | (~(f7(c2) = c4)) | (~(f7(c2) = f4(f7(c2)))) | big_f(f7(c2), f7(c2)) | big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2)),
% 28.85/19.05 inference(modus_ponens,[status(thm)],[17145, 17144])).
% 28.85/19.05 tff(17147,plain,
% 28.85/19.05 (big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2)),
% 28.85/19.05 inference(unit_resolution,[status(thm)],[17146, 402, 9092, 8218, 8770, 16906])).
% 28.85/19.05 tff(17148,plain,
% 28.85/19.05 ($false),
% 28.85/19.05 inference(unit_resolution,[status(thm)],[17147, 9122, 16430])).
% 28.85/19.05 tff(17149,plain,((~(f1(c1, c2) = c1)) | (f7(c2) = c3) | big_f(f7(c2), f7(c2)) | (~(f7(c2) = c4)) | (~(f7(c2) = f4(f7(c2)))) | (f7(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 28.85/19.05 tff(17150,plain,
% 28.85/19.05 (~(f1(c1, c2) = c1)),
% 28.85/19.05 inference(unit_resolution,[status(thm)],[17149, 17130, 17099, 16937, 16942, 17])).
% 28.85/19.05 tff(17151,plain,
% 28.85/19.05 (f1(c1, c2) = c2),
% 28.85/19.05 inference(unit_resolution,[status(thm)],[841, 17150])).
% 28.85/19.05 tff(17152,plain,
% 28.85/19.05 (f1(c1, f1(c1, c2)) = f1(c1, c2)),
% 28.85/19.05 inference(monotonicity,[status(thm)],[17151])).
% 28.85/19.05 tff(17153,plain,
% 28.85/19.05 (f1(c1, f1(c1, c2)) = c2),
% 28.85/19.05 inference(transitivity,[status(thm)],[17152, 17151])).
% 28.85/19.05 tff(17154,plain,
% 28.85/19.05 (big_f(c1, f1(c1, f1(c1, c2))) <=> big_f(f7(c2), c2)),
% 28.85/19.05 inference(monotonicity,[status(thm)],[125, 17153])).
% 28.85/19.05 tff(17155,plain,
% 28.85/19.05 (big_f(f7(c2), c2) <=> big_f(c1, f1(c1, f1(c1, c2)))),
% 28.85/19.05 inference(symmetry,[status(thm)],[17154])).
% 28.85/19.05 tff(17156,plain,
% 28.85/19.05 (big_f(c1, f1(c1, f1(c1, c2)))),
% 28.85/19.05 inference(modus_ponens,[status(thm)],[17128, 17155])).
% 28.85/19.05 tff(17157,plain,
% 28.85/19.05 ($false),
% 28.85/19.05 inference(unit_resolution,[status(thm)],[2254, 17156, 17152, 17140, 17137])).
% 28.85/19.05 tff(17158,plain,((c2 = c4) | (f7(c2) = c2) | (~(f10(c2) = c2)) | (f7(c1) = c1) | (f10(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 28.85/19.05 tff(17159,plain,
% 28.85/19.05 (c2 = c4),
% 28.85/19.05 inference(unit_resolution,[status(thm)],[17158, 17, 122, 115, 3])).
% 28.85/19.05 tff(17160,plain,
% 28.85/19.05 (f4(c2) = f4(c4)),
% 28.85/19.05 inference(monotonicity,[status(thm)],[17159])).
% 28.85/19.05 tff(17161,plain,
% 28.85/19.05 (f4(c2) = f7(c2)),
% 28.85/19.05 inference(transitivity,[status(thm)],[17160, 15706, 125])).
% 28.85/19.05 tff(17162,plain,
% 28.85/19.05 ((c2 = f4(c2)) <=> (c2 = f7(c2))),
% 28.85/19.05 inference(monotonicity,[status(thm)],[17161])).
% 28.85/19.05 tff(17163,plain,
% 28.85/19.05 ((c2 = f4(c2)) <=> (f7(c2) = c2)),
% 28.85/19.05 inference(transitivity,[status(thm)],[17162, 8409])).
% 28.85/19.05 tff(17164,plain,
% 28.85/19.05 ((f7(c2) = c2) <=> (c2 = f4(c2))),
% 28.85/19.05 inference(symmetry,[status(thm)],[17163])).
% 28.85/19.05 tff(17165,plain,
% 28.85/19.05 ((~(f7(c2) = c2)) <=> (~(c2 = f4(c2)))),
% 28.85/19.05 inference(monotonicity,[status(thm)],[17164])).
% 28.85/19.05 tff(17166,plain,
% 28.85/19.05 (~(c2 = f4(c2))),
% 28.85/19.05 inference(modus_ponens,[status(thm)],[17, 17165])).
% 28.85/19.05 tff(17167,plain,
% 28.85/19.05 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c2 = c4)) | (c2 = f4(c2)) | (c2 = f2(c2)) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (~(c2 = c4)) | (c2 = f4(c2)) | (c2 = f2(c2)) | (~big_f(c2, c2)))),
% 28.85/19.05 inference(rewrite,[status(thm)],[])).
% 28.85/19.05 tff(17168,plain,
% 28.85/19.05 (((~(c2 = c3)) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)) | (c2 = f2(c2)) | (~big_f(c2, c2))) <=> ((~(c2 = c3)) | (~(c2 = c4)) | (c2 = f4(c2)) | (c2 = f2(c2)) | (~big_f(c2, c2)))),
% 28.85/19.05 inference(rewrite,[status(thm)],[])).
% 28.85/19.05 tff(17169,plain,
% 28.85/19.05 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)) | (c2 = f2(c2)) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c2 = c4)) | (c2 = f4(c2)) | (c2 = f2(c2)) | (~big_f(c2, c2))))),
% 28.85/19.05 inference(monotonicity,[status(thm)],[17168])).
% 28.85/19.05 tff(17170,plain,
% 28.85/19.05 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)) | (c2 = f2(c2)) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (~(c2 = c4)) | (c2 = f4(c2)) | (c2 = f2(c2)) | (~big_f(c2, c2)))),
% 28.85/19.05 inference(transitivity,[status(thm)],[17169, 17167])).
% 28.85/19.05 tff(17171,plain,
% 28.85/19.05 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)) | (c2 = f2(c2)) | (~big_f(c2, c2)))),
% 28.85/19.05 inference(quant_inst,[status(thm)],[])).
% 28.85/19.05 tff(17172,plain,
% 28.85/19.05 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (~(c2 = c4)) | (c2 = f4(c2)) | (c2 = f2(c2)) | (~big_f(c2, c2))),
% 28.85/19.05 inference(modus_ponens,[status(thm)],[17171, 17170])).
% 28.85/19.05 tff(17173,plain,
% 28.85/19.05 ((~(c2 = c3)) | (~(c2 = c4)) | (c2 = f4(c2)) | (c2 = f2(c2))),
% 28.85/19.05 inference(unit_resolution,[status(thm)],[17172, 1355, 16509])).
% 28.85/19.05 tff(17174,plain,
% 28.85/19.05 (c2 = f2(c2)),
% 28.85/19.05 inference(unit_resolution,[status(thm)],[17173, 17166, 16930, 17159])).
% 28.85/19.05 tff(17175,plain,
% 28.85/19.05 (f4(c4) = f4(c2)),
% 28.85/19.05 inference(symmetry,[status(thm)],[17160])).
% 28.85/19.05 tff(17176,plain,
% 28.85/19.05 (f7(c2) = f4(c2)),
% 28.85/19.05 inference(transitivity,[status(thm)],[22, 15834, 17175])).
% 28.85/19.05 tff(17177,plain,
% 28.85/19.05 (big_f(f7(c2), c1) <=> big_f(c1, c1)),
% 28.85/19.05 inference(transitivity,[status(thm)],[8076, 15989])).
% 28.85/19.05 tff(17178,plain,
% 28.85/19.05 (big_f(f7(c2), f7(c2))),
% 28.85/19.05 inference(unit_resolution,[status(thm)],[17090, 1521, 122, 17, 186, 67, 1345, 2853, 16])).
% 28.85/19.05 tff(17179,plain,
% 28.85/19.05 (big_f(f7(c2), c1)),
% 28.85/19.05 inference(unit_resolution,[status(thm)],[8374, 17178, 22])).
% 28.85/19.05 tff(17180,plain,
% 28.85/19.05 (big_f(c1, c1)),
% 28.85/19.05 inference(modus_ponens,[status(thm)],[17179, 17177])).
% 28.85/19.05 tff(17181,plain,
% 28.85/19.05 (big_f(c1, f1(c1, c1))),
% 28.85/19.05 inference(unit_resolution,[status(thm)],[9678, 624, 4932])).
% 28.85/19.05 tff(17182,plain,
% 28.85/19.05 (big_f(f7(c2), f1(f7(c2), f7(c2)))),
% 28.85/19.05 inference(unit_resolution,[status(thm)],[9730, 17181, 292])).
% 28.85/19.05 tff(17183,plain,
% 28.85/19.05 ((f1(c1, c1) = c1) <=> (f1(f7(c2), f7(c2)) = f7(c2))),
% 28.85/19.05 inference(symmetry,[status(thm)],[9707])).
% 28.85/19.05 tff(17184,plain,
% 28.85/19.05 (f1(f7(c2), f7(c2)) = f7(c2)),
% 28.85/19.05 inference(modus_ponens,[status(thm)],[624, 17183])).
% 28.85/19.05 tff(17185,plain,
% 28.85/19.05 ($false),
% 28.85/19.05 inference(unit_resolution,[status(thm)],[15908, 447, 631, 9092, 1521, 17184, 17182, 15838])).
% 28.85/19.05 tff(17186,plain,((~(f1(c1, c1) = c1)) | (~(c2 = c4)) | (f7(c2) = c3) | big_f(f7(c2), c2) | (~(f7(c2) = f4(c2))) | (~(f7(c2) = c1)) | (~big_f(c1, c1))), inference(lemma,lemma(discharge,[]))).
% 28.85/19.05 tff(17187,plain,
% 28.85/19.05 (~(f1(c1, c1) = c1)),
% 28.85/19.05 inference(unit_resolution,[status(thm)],[17186, 1521, 9092, 631, 15838, 22, 17180])).
% 28.85/19.05 tff(17188,plain,
% 28.85/19.05 (big_f(c1, c2)),
% 28.85/19.05 inference(unit_resolution,[status(thm)],[15896, 17187, 22, 631, 9092, 15838])).
% 28.85/19.05 tff(17189,plain,
% 28.85/19.05 ($false),
% 28.85/19.05 inference(unit_resolution,[status(thm)],[17188, 16654])).
% 28.85/19.05 tff(17190,plain,(big_f(f7(c2), c2) | (~(c2 = c4)) | (f7(c2) = c3) | (~(f7(c2) = f4(c2))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~(f5(c1) = c2)) | (~(c3 = c2)) | (~big_f(c2, c2)) | (~(c2 = f2(c2))) | (~(f10(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.85/19.05 tff(17191,plain,
% 28.85/19.05 (big_f(f7(c2), c2)),
% 28.85/19.05 inference(unit_resolution,[status(thm)],[17190, 17159, 17099, 17176, 122, 17, 16932, 16931, 16509, 17174, 15])).
% 28.85/19.05 tff(17192,plain,
% 28.85/19.05 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((~(c2 = c4)) | (c2 = f4(c2)) | (f7(c2) = c3) | (~big_f(c2, c2)) | (~big_f(f7(c2), f1(f7(c2), c2))) | (~(f1(f7(c2), c2) = c2)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (~(c2 = c4)) | (c2 = f4(c2)) | (f7(c2) = c3) | (~big_f(c2, c2)) | (~big_f(f7(c2), f1(f7(c2), c2))) | (~(f1(f7(c2), c2) = c2)))),
% 28.85/19.05 inference(rewrite,[status(thm)],[])).
% 28.85/19.05 tff(17193,plain,
% 28.85/19.05 (((f7(c2) = c3) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)) | (~(f1(f7(c2), c2) = c2)) | (~big_f(f7(c2), f1(f7(c2), c2)))) <=> ((~(c2 = c4)) | (c2 = f4(c2)) | (f7(c2) = c3) | (~big_f(c2, c2)) | (~big_f(f7(c2), f1(f7(c2), c2))) | (~(f1(f7(c2), c2) = c2)))),
% 28.85/19.05 inference(rewrite,[status(thm)],[])).
% 28.85/19.05 tff(17194,plain,
% 28.85/19.05 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c2) = c3) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)) | (~(f1(f7(c2), c2) = c2)) | (~big_f(f7(c2), f1(f7(c2), c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((~(c2 = c4)) | (c2 = f4(c2)) | (f7(c2) = c3) | (~big_f(c2, c2)) | (~big_f(f7(c2), f1(f7(c2), c2))) | (~(f1(f7(c2), c2) = c2))))),
% 28.85/19.05 inference(monotonicity,[status(thm)],[17193])).
% 28.85/19.05 tff(17195,plain,
% 28.85/19.05 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c2) = c3) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)) | (~(f1(f7(c2), c2) = c2)) | (~big_f(f7(c2), f1(f7(c2), c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (~(c2 = c4)) | (c2 = f4(c2)) | (f7(c2) = c3) | (~big_f(c2, c2)) | (~big_f(f7(c2), f1(f7(c2), c2))) | (~(f1(f7(c2), c2) = c2)))),
% 28.85/19.05 inference(transitivity,[status(thm)],[17194, 17192])).
% 28.85/19.05 tff(17196,plain,
% 28.85/19.05 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c2) = c3) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)) | (~(f1(f7(c2), c2) = c2)) | (~big_f(f7(c2), f1(f7(c2), c2))))),
% 28.85/19.05 inference(quant_inst,[status(thm)],[])).
% 28.85/19.05 tff(17197,plain,
% 28.85/19.05 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (~(c2 = c4)) | (c2 = f4(c2)) | (f7(c2) = c3) | (~big_f(c2, c2)) | (~big_f(f7(c2), f1(f7(c2), c2))) | (~(f1(f7(c2), c2) = c2))),
% 28.85/19.05 inference(modus_ponens,[status(thm)],[17196, 17195])).
% 28.85/19.05 tff(17198,plain,
% 28.85/19.05 ((~big_f(f7(c2), f1(f7(c2), c2))) | (~(f1(f7(c2), c2) = c2))),
% 28.85/19.05 inference(unit_resolution,[status(thm)],[17197, 553, 631, 16857, 1345, 9092])).
% 28.85/19.05 tff(17199,plain,
% 28.85/19.05 ($false),
% 28.85/19.05 inference(unit_resolution,[status(thm)],[17198, 9366, 9363])).
% 28.85/19.05 tff(17200,plain,((~(f1(c1, c2) = c2)) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)) | (f7(c2) = c3) | (~big_f(f7(c2), c2)) | (~(f7(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.85/19.05 tff(17201,plain,
% 28.85/19.05 (~(f1(c1, c2) = c2)),
% 28.85/19.05 inference(unit_resolution,[status(thm)],[17200, 17159, 17166, 16509, 17099, 17191, 22])).
% 28.85/19.05 tff(17202,plain,
% 28.85/19.05 (f1(c1, c2) = c1),
% 28.85/19.05 inference(unit_resolution,[status(thm)],[841, 17201])).
% 28.85/19.05 tff(17203,plain,
% 28.85/19.05 (f1(f7(c2), c2) = f7(c2)),
% 28.85/19.05 inference(transitivity,[status(thm)],[9112, 17202, 125])).
% 28.85/19.05 tff(17204,plain,
% 28.85/19.05 (big_f(f7(c2), f1(f7(c2), c2)) <=> big_f(f7(c2), f7(c2))),
% 28.85/19.05 inference(monotonicity,[status(thm)],[17203])).
% 28.85/19.05 tff(17205,plain,
% 28.85/19.05 (big_f(f7(c2), f7(c2)) <=> big_f(f7(c2), f1(f7(c2), c2))),
% 28.85/19.05 inference(symmetry,[status(thm)],[17204])).
% 28.85/19.05 tff(17206,plain,
% 28.85/19.05 ((~big_f(f7(c2), f7(c2))) <=> (~big_f(f7(c2), f1(f7(c2), c2)))),
% 28.85/19.06 inference(monotonicity,[status(thm)],[17205])).
% 28.85/19.06 tff(17207,plain,
% 28.85/19.06 (big_f(f7(c2), f10(f7(c2)))),
% 28.85/19.06 inference(modus_ponens,[status(thm)],[17191, 12766])).
% 28.85/19.06 tff(17208,plain,
% 28.85/19.06 (~big_f(f7(c2), f7(c2))),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[16899, 17207, 17, 17191, 12448, 16510])).
% 28.85/19.06 tff(17209,plain,
% 28.85/19.06 (~big_f(f7(c2), f1(f7(c2), c2))),
% 28.85/19.06 inference(modus_ponens,[status(thm)],[17208, 17206])).
% 28.85/19.06 tff(17210,plain,
% 28.85/19.06 ((f1(f7(c2), c2) = c2) <=> (f7(c2) = c2)),
% 28.85/19.06 inference(monotonicity,[status(thm)],[17203])).
% 28.85/19.06 tff(17211,plain,
% 28.85/19.06 ((f7(c2) = c2) <=> (f1(f7(c2), c2) = c2)),
% 28.85/19.06 inference(symmetry,[status(thm)],[17210])).
% 28.85/19.06 tff(17212,plain,
% 28.85/19.06 ((~(f7(c2) = c2)) <=> (~(f1(f7(c2), c2) = c2))),
% 28.85/19.06 inference(monotonicity,[status(thm)],[17211])).
% 28.85/19.06 tff(17213,plain,
% 28.85/19.06 (~(f1(f7(c2), c2) = c2)),
% 28.85/19.06 inference(modus_ponens,[status(thm)],[17, 17212])).
% 28.85/19.06 tff(17214,plain,
% 28.85/19.06 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((~(c2 = c4)) | (c2 = f4(c2)) | (f7(c2) = c3) | (~big_f(c2, c2)) | big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (~(c2 = c4)) | (c2 = f4(c2)) | (f7(c2) = c3) | (~big_f(c2, c2)) | big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2))),
% 28.85/19.06 inference(rewrite,[status(thm)],[])).
% 28.85/19.06 tff(17215,plain,
% 28.85/19.06 (((f7(c2) = c3) | (f1(f7(c2), c2) = c2) | big_f(f7(c2), f1(f7(c2), c2)) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2))) <=> ((~(c2 = c4)) | (c2 = f4(c2)) | (f7(c2) = c3) | (~big_f(c2, c2)) | big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2))),
% 28.85/19.06 inference(rewrite,[status(thm)],[])).
% 28.85/19.06 tff(17216,plain,
% 28.85/19.06 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((f7(c2) = c3) | (f1(f7(c2), c2) = c2) | big_f(f7(c2), f1(f7(c2), c2)) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((~(c2 = c4)) | (c2 = f4(c2)) | (f7(c2) = c3) | (~big_f(c2, c2)) | big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2)))),
% 28.85/19.06 inference(monotonicity,[status(thm)],[17215])).
% 28.85/19.06 tff(17217,plain,
% 28.85/19.06 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((f7(c2) = c3) | (f1(f7(c2), c2) = c2) | big_f(f7(c2), f1(f7(c2), c2)) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (~(c2 = c4)) | (c2 = f4(c2)) | (f7(c2) = c3) | (~big_f(c2, c2)) | big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2))),
% 28.85/19.06 inference(transitivity,[status(thm)],[17216, 17214])).
% 28.85/19.06 tff(17218,plain,
% 28.85/19.06 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((f7(c2) = c3) | (f1(f7(c2), c2) = c2) | big_f(f7(c2), f1(f7(c2), c2)) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)))),
% 28.85/19.06 inference(quant_inst,[status(thm)],[])).
% 28.85/19.06 tff(17219,plain,
% 28.85/19.06 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (~(c2 = c4)) | (c2 = f4(c2)) | (f7(c2) = c3) | (~big_f(c2, c2)) | big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2)),
% 28.85/19.06 inference(modus_ponens,[status(thm)],[17218, 17217])).
% 28.85/19.06 tff(17220,plain,
% 28.85/19.06 (big_f(f7(c2), f1(f7(c2), c2)) | (f1(f7(c2), c2) = c2)),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[17219, 525, 17159, 17166, 16509, 17099])).
% 28.85/19.06 tff(17221,plain,
% 28.85/19.06 ($false),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[17220, 17213, 17209])).
% 28.85/19.06 tff(17222,plain,((f7(c2) = c2) | (~(f10(c2) = c2)) | (f7(c1) = c1) | (f10(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 28.85/19.06 tff(17223,plain,
% 28.85/19.06 (f7(c2) = c2),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[17222, 122, 115, 3])).
% 28.85/19.06 tff(17224,plain,
% 28.85/19.06 (f6(f7(c2), f5(c1)) = f6(c2, c1)),
% 28.85/19.06 inference(monotonicity,[status(thm)],[17223, 11796])).
% 28.85/19.06 tff(17225,plain,
% 28.85/19.06 (f6(c2, c1) = f6(f7(c2), f5(c1))),
% 28.85/19.06 inference(symmetry,[status(thm)],[17224])).
% 28.85/19.06 tff(17226,plain,
% 28.85/19.06 ((c2 = f6(c2, c1)) <=> (c2 = f6(f7(c2), f5(c1)))),
% 28.85/19.06 inference(monotonicity,[status(thm)],[17225])).
% 28.85/19.06 tff(17227,plain,
% 28.85/19.06 ((c2 = f6(c2, c1)) <=> (f6(f7(c2), f5(c1)) = c2)),
% 28.85/19.06 inference(transitivity,[status(thm)],[17226, 11787])).
% 28.85/19.06 tff(17228,plain,
% 28.85/19.06 ((f6(f7(c2), f5(c1)) = c2) <=> (c2 = f6(c2, c1))),
% 28.85/19.06 inference(symmetry,[status(thm)],[17227])).
% 28.85/19.06 tff(17229,plain,
% 28.85/19.06 (big_f(f8(c1), f10(c1)) <=> big_f(c2, c2)),
% 28.85/19.06 inference(monotonicity,[status(thm)],[1671, 15])).
% 28.85/19.06 tff(17230,plain,
% 28.85/19.06 (big_f(c2, c2) <=> big_f(f8(c1), f10(c1))),
% 28.85/19.06 inference(symmetry,[status(thm)],[17229])).
% 28.85/19.06 tff(17231,plain,
% 28.85/19.06 ((~big_f(c2, c2)) <=> (~big_f(f8(c1), f10(c1)))),
% 28.85/19.06 inference(monotonicity,[status(thm)],[17230])).
% 28.85/19.06 tff(17232,plain,
% 28.85/19.06 (~big_f(f8(c1), f10(c1))),
% 28.85/19.06 inference(modus_ponens,[status(thm)],[121, 17231])).
% 28.85/19.06 tff(17233,plain,
% 28.85/19.06 (c2 = f8(c1)),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[1675, 1671])).
% 28.85/19.06 tff(17234,plain,
% 28.85/19.06 (~big_f(c2, c1)),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[3003, 17233, 77, 121, 230, 3])).
% 28.85/19.06 tff(17235,plain,
% 28.85/19.06 (~big_f(f7(c1), c1)),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[15738, 17234, 120])).
% 28.85/19.06 tff(17236,plain,
% 28.85/19.06 (~big_f(f7(c1), f5(c1))),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[8430, 17235, 120, 121])).
% 28.85/19.06 tff(17237,plain,
% 28.85/19.06 (big_f(f8(c1), f10(c1))),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[2848, 17236, 115, 3])).
% 28.85/19.06 tff(17238,plain,
% 28.85/19.06 ($false),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[17237, 17232])).
% 28.85/19.06 tff(17239,plain,((~(f8(c1) = c2)) | big_f(c2, c2) | (f7(c1) = c1) | (f10(c1) = c1) | (~(f7(c2) = c2)) | (~(f5(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.85/19.06 tff(17240,plain,
% 28.85/19.06 (~(f8(c1) = c2)),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[17239, 121, 115, 3, 17223, 11796])).
% 28.85/19.06 tff(17241,plain,
% 28.85/19.06 (f8(c1) = c1),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[1680, 17240])).
% 28.85/19.06 tff(17242,plain,
% 28.85/19.06 (c1 = f5(c1)),
% 28.85/19.06 inference(modus_ponens,[status(thm)],[11796, 192])).
% 28.85/19.06 tff(17243,plain,
% 28.85/19.06 (~big_f(f7(c1), f5(c1))),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[8430, 285, 120, 121])).
% 28.85/19.06 tff(17244,plain,
% 28.85/19.06 (f9(c2, c1) = c1),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[8445, 17243, 115, 122, 121])).
% 28.85/19.06 tff(17245,plain,
% 28.85/19.06 (big_f(f9(c2, c1), f10(c2)) <=> big_f(c1, c2)),
% 28.85/19.06 inference(monotonicity,[status(thm)],[17244, 122])).
% 28.85/19.06 tff(17246,plain,
% 28.85/19.06 (big_f(c1, c2) <=> big_f(f9(c2, c1), f10(c2))),
% 28.85/19.06 inference(symmetry,[status(thm)],[17245])).
% 28.85/19.06 tff(17247,plain,
% 28.85/19.06 (big_f(f8(c1), f10(c1)) <=> big_f(c1, c2)),
% 28.85/19.06 inference(monotonicity,[status(thm)],[17241, 15])).
% 28.85/19.06 tff(17248,plain,
% 28.85/19.06 (big_f(f8(c1), f10(c1))),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[2848, 17243, 115, 3])).
% 28.85/19.06 tff(17249,plain,
% 28.85/19.06 (big_f(c1, c2)),
% 28.85/19.06 inference(modus_ponens,[status(thm)],[17248, 17247])).
% 28.85/19.06 tff(17250,plain,
% 28.85/19.06 (big_f(f9(c2, c1), f10(c2))),
% 28.85/19.06 inference(modus_ponens,[status(thm)],[17249, 17246])).
% 28.85/19.06 tff(17251,plain,
% 28.85/19.06 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((f7(c1) = c1) | (~(f10(c2) = c2)) | big_f(f7(c1), c1) | (~(c1 = f5(c1))) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (f7(c1) = c1) | (~(f10(c2) = c2)) | big_f(f7(c1), c1) | (~(c1 = f5(c1))) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))))),
% 28.85/19.06 inference(rewrite,[status(thm)],[])).
% 28.85/19.06 tff(17252,plain,
% 28.85/19.06 (((~(f10(c2) = c2)) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))) | (~(c1 = f5(c1)))) <=> ((f7(c1) = c1) | (~(f10(c2) = c2)) | big_f(f7(c1), c1) | (~(c1 = f5(c1))) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))))),
% 28.85/19.06 inference(rewrite,[status(thm)],[])).
% 28.85/19.06 tff(17253,plain,
% 28.85/19.06 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))) | (~(c1 = f5(c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((f7(c1) = c1) | (~(f10(c2) = c2)) | big_f(f7(c1), c1) | (~(c1 = f5(c1))) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2)))))),
% 28.85/19.06 inference(monotonicity,[status(thm)],[17252])).
% 28.85/19.06 tff(17254,plain,
% 28.85/19.06 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))) | (~(c1 = f5(c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (f7(c1) = c1) | (~(f10(c2) = c2)) | big_f(f7(c1), c1) | (~(c1 = f5(c1))) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))))),
% 28.85/19.06 inference(transitivity,[status(thm)],[17253, 17251])).
% 28.85/19.06 tff(17255,plain,
% 28.85/19.06 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))) | (~(c1 = f5(c1))))),
% 28.85/19.06 inference(quant_inst,[status(thm)],[])).
% 28.85/19.06 tff(17256,plain,
% 28.85/19.06 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (f7(c1) = c1) | (~(f10(c2) = c2)) | big_f(f7(c1), c1) | (~(c1 = f5(c1))) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2)))),
% 28.85/19.06 inference(modus_ponens,[status(thm)],[17255, 17254])).
% 28.85/19.06 tff(17257,plain,
% 28.85/19.06 ($false),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[17256, 783, 115, 122, 17244, 17250, 285, 17242])).
% 28.85/19.06 tff(17258,plain,(big_f(f7(c1), c1) | (f7(c1) = c1) | (~(f10(c2) = c2)) | big_f(c2, c2) | (f10(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 28.85/19.06 tff(17259,plain,
% 28.85/19.06 (big_f(f7(c1), c1)),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[17258, 121, 122, 115, 3])).
% 28.85/19.06 tff(17260,plain,
% 28.85/19.06 (big_f(c2, c1)),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[15738, 17259, 120])).
% 28.85/19.06 tff(17261,plain,
% 28.85/19.06 (big_f(f7(c2), f6(c2, c1))),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[11391, 348, 115, 122, 17223, 121, 3])).
% 28.85/19.06 tff(17262,plain,
% 28.85/19.06 (~(f6(f7(c2), c3) = c2)),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[5848, 172, 77, 3078, 121])).
% 28.85/19.06 tff(17263,plain,
% 28.85/19.06 (f6(f7(c2), c3) = c1),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[2391, 17262])).
% 28.85/19.06 tff(17264,plain,
% 28.85/19.06 (f6(c2, c1) = c1),
% 28.85/19.06 inference(transitivity,[status(thm)],[5841, 17263])).
% 28.85/19.06 tff(17265,plain,
% 28.85/19.06 ($false),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[3198, 17264])).
% 28.85/19.06 tff(17266,plain,((~(c3 = c1)) | (f6(c2, c1) = c1) | (~(f7(c2) = c2)) | (~big_f(f7(c2), f6(c2, c1))) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 28.85/19.06 tff(17267,plain,
% 28.85/19.06 (f6(c2, c1) = c1),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[17266, 17261, 17223, 121, 172])).
% 28.85/19.06 tff(17268,plain,
% 28.85/19.06 (f9(c2, c1) = c1),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[11359, 348, 115, 17223, 122, 121])).
% 28.85/19.06 tff(17269,plain,
% 28.85/19.06 (big_f(f9(c2, c1), f10(c2)) <=> big_f(c1, c2)),
% 28.85/19.06 inference(monotonicity,[status(thm)],[17268, 122])).
% 28.85/19.06 tff(17270,plain,
% 28.85/19.06 (big_f(c1, c2) <=> big_f(f9(c2, c1), f10(c2))),
% 28.85/19.06 inference(symmetry,[status(thm)],[17269])).
% 28.85/19.06 tff(17271,plain,
% 28.85/19.06 (~(c2 = f8(c1))),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[3003, 348, 17223, 121, 230, 3])).
% 28.85/19.06 tff(17272,plain,
% 28.85/19.06 (~(f8(c1) = c2)),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[1675, 17271])).
% 28.85/19.06 tff(17273,plain,
% 28.85/19.06 (f8(c1) = c1),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[1680, 17272])).
% 28.85/19.06 tff(17274,plain,
% 28.85/19.06 (big_f(f8(c1), f10(c1)) <=> big_f(c1, c2)),
% 28.85/19.06 inference(monotonicity,[status(thm)],[17273, 15])).
% 28.85/19.06 tff(17275,plain,
% 28.85/19.06 (big_f(f8(c1), f10(c1)) <=> big_f(f9(c2, c1), f10(c2))),
% 28.85/19.06 inference(transitivity,[status(thm)],[17274, 17270])).
% 28.85/19.06 tff(17276,plain,
% 28.85/19.06 (big_f(c1, f10(c1))),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[13594, 348, 17223, 3, 121, 230])).
% 28.85/19.06 tff(17277,plain,
% 28.85/19.06 (big_f(f8(c1), f10(c1))),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[3025, 17273, 17276])).
% 28.85/19.06 tff(17278,plain,
% 28.85/19.06 (big_f(f9(c2, c1), f10(c2))),
% 28.85/19.06 inference(modus_ponens,[status(thm)],[17277, 17275])).
% 28.85/19.06 tff(17279,plain,
% 28.85/19.06 ($false),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[3097, 2378, 122, 17268, 17278, 17223, 17267, 17261])).
% 28.85/19.06 tff(17280,plain,((~big_f(c2, c1)) | (~(f10(c2) = c2)) | big_f(c2, c2) | (~(c3 = c1)) | (~(f5(c1) = c1)) | (f10(c1) = c1) | (f7(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 28.85/19.06 tff(17281,plain,
% 28.85/19.06 (~big_f(c2, c1)),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[17280, 230, 121, 172, 122, 3, 115])).
% 28.85/19.06 tff(17282,plain,
% 28.85/19.06 (~big_f(f7(c1), c1)),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[15738, 17281, 120])).
% 28.85/19.06 tff(17283,plain,
% 28.85/19.06 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f7(c1) = c1) | big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | big_f(f7(c1), c1) | (~(c1 = f5(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(c1) = c1) | big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | big_f(f7(c1), c1) | (~(c1 = f5(c1))))),
% 28.85/19.06 inference(rewrite,[status(thm)],[])).
% 28.85/19.06 tff(17284,plain,
% 28.85/19.06 (((~(c1 = f5(c1))) | (f10(c1) = c1) | big_f(c2, f10(c1)) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(c2 = f8(c1)))) <=> ((f7(c1) = c1) | big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | big_f(f7(c1), c1) | (~(c1 = f5(c1))))),
% 28.85/19.06 inference(rewrite,[status(thm)],[])).
% 28.85/19.06 tff(17285,plain,
% 28.85/19.06 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c1 = f5(c1))) | (f10(c1) = c1) | big_f(c2, f10(c1)) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(c2 = f8(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f7(c1) = c1) | big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | big_f(f7(c1), c1) | (~(c1 = f5(c1)))))),
% 28.85/19.06 inference(monotonicity,[status(thm)],[17284])).
% 28.85/19.06 tff(17286,plain,
% 28.85/19.06 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c1 = f5(c1))) | (f10(c1) = c1) | big_f(c2, f10(c1)) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(c2 = f8(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(c1) = c1) | big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | big_f(f7(c1), c1) | (~(c1 = f5(c1))))),
% 28.85/19.06 inference(transitivity,[status(thm)],[17285, 17283])).
% 28.85/19.06 tff(17287,plain,
% 28.85/19.06 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c1 = f5(c1))) | (f10(c1) = c1) | big_f(c2, f10(c1)) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(c2 = f8(c1))))),
% 28.85/19.06 inference(quant_inst,[status(thm)],[])).
% 28.85/19.06 tff(17288,plain,
% 28.85/19.06 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(c1) = c1) | big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | big_f(f7(c1), c1) | (~(c1 = f5(c1)))),
% 28.85/19.06 inference(modus_ponens,[status(thm)],[17287, 17286])).
% 28.85/19.06 tff(17289,plain,
% 28.85/19.06 (~(c2 = f8(c1))),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[17288, 1745, 115, 6126, 3, 17282, 692])).
% 28.85/19.06 tff(17290,plain,
% 28.85/19.06 (~(f8(c1) = c2)),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[1675, 17289])).
% 28.85/19.06 tff(17291,plain,
% 28.85/19.06 (f8(c1) = c1),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[1680, 17290])).
% 28.85/19.06 tff(17292,plain,
% 28.85/19.06 (big_f(f8(c1), f10(c1)) <=> big_f(c1, c2)),
% 28.85/19.06 inference(monotonicity,[status(thm)],[17291, 15])).
% 28.85/19.06 tff(17293,plain,
% 28.85/19.06 (big_f(c1, c2) <=> big_f(f8(c1), f10(c1))),
% 28.85/19.06 inference(symmetry,[status(thm)],[17292])).
% 28.85/19.06 tff(17294,plain,
% 28.85/19.06 ((~big_f(c1, c2)) <=> (~big_f(f8(c1), f10(c1)))),
% 28.85/19.06 inference(monotonicity,[status(thm)],[17293])).
% 28.85/19.06 tff(17295,plain,
% 28.85/19.06 (~big_f(f7(c1), f5(c1))),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[8430, 17282, 120, 121])).
% 28.85/19.06 tff(17296,plain,
% 28.85/19.06 (f9(c2, c1) = c1),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[8445, 17295, 115, 122, 121])).
% 28.85/19.06 tff(17297,plain,
% 28.85/19.06 (big_f(f9(c2, c1), f10(c2)) <=> big_f(c1, c2)),
% 28.85/19.06 inference(monotonicity,[status(thm)],[17296, 122])).
% 28.85/19.06 tff(17298,plain,
% 28.85/19.06 ((~big_f(f9(c2, c1), f10(c2))) <=> (~big_f(c1, c2))),
% 28.85/19.06 inference(monotonicity,[status(thm)],[17297])).
% 28.85/19.06 tff(17299,plain,
% 28.85/19.06 (~big_f(f9(c2, c1), f10(c2))),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[17256, 783, 115, 122, 17296, 17282, 692])).
% 28.85/19.06 tff(17300,plain,
% 28.85/19.06 (~big_f(c1, c2)),
% 28.85/19.06 inference(modus_ponens,[status(thm)],[17299, 17298])).
% 28.85/19.06 tff(17301,plain,
% 28.85/19.06 (~big_f(f8(c1), f10(c1))),
% 28.85/19.06 inference(modus_ponens,[status(thm)],[17300, 17294])).
% 28.85/19.06 tff(17302,plain,
% 28.85/19.06 (big_f(f8(c1), f10(c1))),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[2848, 17295, 115, 3])).
% 28.85/19.06 tff(17303,plain,
% 28.85/19.06 ($false),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[17302, 17301])).
% 28.85/19.06 tff(17304,plain,((~(f5(c1) = c1)) | (~(f10(c2) = c2)) | (f7(c1) = c1) | (f10(c1) = c1) | big_f(c2, c2) | (~(c3 = c1))), inference(lemma,lemma(discharge,[]))).
% 28.85/19.06 tff(17305,plain,
% 28.85/19.06 (~(c3 = c1)),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[17304, 11796, 115, 3, 121, 122])).
% 28.85/19.06 tff(17306,plain,
% 28.85/19.06 (c3 = c2),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[180, 17305])).
% 28.85/19.06 tff(17307,plain,
% 28.85/19.06 (f10(c3) = c3),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[2830, 17306, 122])).
% 28.85/19.06 tff(17308,plain,
% 28.85/19.06 (big_f(c1, c2)),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[3066, 17260, 17223, 11796, 121, 3, 17307, 17306])).
% 28.85/19.06 tff(17309,plain,
% 28.85/19.06 (~(f6(f7(c2), f5(c1)) = c1)),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[3111, 17308, 122, 17223, 17260, 3, 11796, 17241])).
% 28.85/19.06 tff(17310,plain,
% 28.85/19.06 (f6(f7(c2), f5(c1)) = c2),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[2978, 17309])).
% 28.85/19.06 tff(17311,plain,
% 28.85/19.06 (c2 = f6(c2, c1)),
% 28.85/19.06 inference(modus_ponens,[status(thm)],[17310, 17228])).
% 28.85/19.06 tff(17312,plain,
% 28.85/19.06 ((f7(c2) = c2) <=> (c2 = f7(c2))),
% 28.85/19.06 inference(symmetry,[status(thm)],[8409])).
% 28.85/19.06 tff(17313,plain,
% 28.85/19.06 (c2 = f7(c2)),
% 28.85/19.06 inference(modus_ponens,[status(thm)],[17223, 17312])).
% 28.85/19.06 tff(17314,plain,
% 28.85/19.06 (big_f(f7(c2), f6(c2, c1))),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[11391, 17260, 115, 122, 17223, 121, 3])).
% 28.85/19.06 tff(17315,plain,
% 28.85/19.06 ((~(big_f(c2, c2) <=> big_f(f7(c2), f6(c2, c1)))) | big_f(c2, c2) | (~big_f(f7(c2), f6(c2, c1)))),
% 28.85/19.06 inference(tautology,[status(thm)],[])).
% 28.85/19.06 tff(17316,plain,
% 28.85/19.06 (~(big_f(c2, c2) <=> big_f(f7(c2), f6(c2, c1)))),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[17315, 17314, 121])).
% 28.85/19.06 tff(17317,assumption,(~(big_f(c2, c2) <=> big_f(f7(c2), f6(c2, c1)))), introduced(assumption)).
% 28.85/19.06 tff(17318,assumption,(c2 = f6(c2, c1)), introduced(assumption)).
% 28.85/19.06 tff(17319,assumption,(c2 = f7(c2)), introduced(assumption)).
% 28.85/19.06 tff(17320,plain,
% 28.85/19.06 (big_f(c2, c2) <=> big_f(f7(c2), f6(c2, c1))),
% 28.85/19.06 inference(monotonicity,[status(thm)],[17319, 17318])).
% 28.85/19.06 tff(17321,plain,
% 28.85/19.06 ($false),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[17320, 17317])).
% 28.85/19.06 tff(17322,plain,((~(c2 = f7(c2))) | (~(c2 = f6(c2, c1))) | (big_f(c2, c2) <=> big_f(f7(c2), f6(c2, c1)))), inference(lemma,lemma(discharge,[]))).
% 28.85/19.06 tff(17323,plain,
% 28.85/19.06 (~(c2 = f6(c2, c1))),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[17322, 17316, 17313])).
% 28.85/19.06 tff(17324,plain,
% 28.85/19.06 ($false),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[17323, 17311])).
% 28.85/19.06 tff(17325,plain,(big_f(c2, c2) | (~(f10(c2) = c2)) | (f10(c1) = c1) | (f7(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 28.85/19.06 tff(17326,plain,
% 28.85/19.06 (big_f(c2, c2)),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[17325, 122, 3, 115])).
% 28.85/19.06 tff(17327,plain,
% 28.85/19.06 (big_f(c2, f10(c1))),
% 28.85/19.06 inference(modus_ponens,[status(thm)],[17326, 2719])).
% 28.85/19.06 tff(17328,plain,
% 28.85/19.06 (big_f(f7(c1), c2)),
% 28.85/19.06 inference(modus_ponens,[status(thm)],[17326, 1724])).
% 28.85/19.06 tff(17329,plain,
% 28.85/19.06 ((c2 = f5(c1)) | (c2 = f8(c1))),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[3393, 1659, 17328, 115, 17327, 3])).
% 28.85/19.06 tff(17330,plain,
% 28.85/19.06 (c2 = f8(c1)),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[17329, 12775])).
% 28.85/19.06 tff(17331,plain,
% 28.85/19.06 (f8(c1) = c2),
% 28.85/19.06 inference(symmetry,[status(thm)],[17330])).
% 28.85/19.06 tff(17332,plain,
% 28.85/19.06 ((f9(c2, c2) = f8(c1)) <=> (f9(c2, c2) = c2)),
% 28.85/19.06 inference(monotonicity,[status(thm)],[17331])).
% 28.85/19.06 tff(17333,plain,
% 28.85/19.06 ((f9(c2, c2) = c2) <=> (f9(c2, c2) = f8(c1))),
% 28.85/19.06 inference(symmetry,[status(thm)],[17332])).
% 28.85/19.06 tff(17334,plain,
% 28.85/19.06 ((~(f9(c2, c2) = c2)) <=> (~(f9(c2, c2) = f8(c1)))),
% 28.85/19.06 inference(monotonicity,[status(thm)],[17333])).
% 28.85/19.06 tff(17335,plain,
% 28.85/19.06 (~(f9(c2, c2) = f8(c1))),
% 28.85/19.06 inference(modus_ponens,[status(thm)],[1209, 17334])).
% 28.85/19.06 tff(17336,plain,
% 28.85/19.06 (big_f(f9(c2, c2), f10(c1)) <=> big_f(f9(c2, c2), c2)),
% 28.85/19.06 inference(monotonicity,[status(thm)],[15])).
% 28.85/19.06 tff(17337,plain,
% 28.85/19.06 (big_f(f9(c2, c2), c2) <=> big_f(f9(c2, c2), f10(c1))),
% 28.85/19.06 inference(symmetry,[status(thm)],[17336])).
% 28.85/19.06 tff(17338,plain,
% 28.85/19.06 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((c2 = f5(c1)) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (~big_f(f7(c1), c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (c2 = f5(c1)) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (~big_f(f7(c1), c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)))),
% 28.85/19.06 inference(rewrite,[status(thm)],[])).
% 28.85/19.06 tff(17339,plain,
% 28.85/19.06 (((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2))) <=> ((c2 = f5(c1)) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (~big_f(f7(c1), c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)))),
% 28.85/19.06 inference(rewrite,[status(thm)],[])).
% 28.85/19.06 tff(17340,plain,
% 28.85/19.06 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((c2 = f5(c1)) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (~big_f(f7(c1), c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2))))),
% 28.85/19.06 inference(monotonicity,[status(thm)],[17339])).
% 28.85/19.06 tff(17341,plain,
% 28.85/19.06 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (c2 = f5(c1)) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (~big_f(f7(c1), c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)))),
% 28.85/19.06 inference(transitivity,[status(thm)],[17340, 17338])).
% 28.85/19.06 tff(17342,plain,
% 28.85/19.06 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)))),
% 28.85/19.06 inference(quant_inst,[status(thm)],[])).
% 28.85/19.06 tff(17343,plain,
% 28.85/19.06 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (c2 = f5(c1)) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (~big_f(f7(c1), c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2))),
% 28.85/19.06 inference(modus_ponens,[status(thm)],[17342, 17341])).
% 28.85/19.06 tff(17344,plain,
% 28.85/19.06 ($false),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[17343, 676, 12775, 12871, 115, 122, 1209, 256])).
% 28.85/19.06 tff(17345,plain,(big_f(f9(c2, c2), f10(c2)) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (f9(c2, c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 28.85/19.06 tff(17346,plain,
% 28.85/19.06 (big_f(f9(c2, c2), f10(c2))),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[17345, 1209, 17328, 115, 122, 12775])).
% 28.85/19.06 tff(17347,plain,
% 28.85/19.06 (big_f(f9(c2, c2), c2)),
% 28.85/19.06 inference(unit_resolution,[status(thm)],[3687, 17346, 122])).
% 28.85/19.06 tff(17348,plain,
% 28.85/19.06 (big_f(f9(c2, c2), f10(c1))),
% 28.85/19.06 inference(modus_ponens,[status(thm)],[17347, 17337])).
% 28.85/19.06 tff(17349,plain,
% 28.85/19.06 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((c2 = f5(c1)) | (f7(c1) = c1) | (f10(c1) = c1) | (~big_f(f7(c1), c2)) | (f9(c2, c2) = f8(c1)) | (~big_f(f9(c2, c2), f10(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (c2 = f5(c1)) | (f7(c1) = c1) | (f10(c1) = c1) | (~big_f(f7(c1), c2)) | (f9(c2, c2) = f8(c1)) | (~big_f(f9(c2, c2), f10(c1))))),
% 28.85/19.06 inference(rewrite,[status(thm)],[])).
% 28.85/19.06 tff(17350,plain,
% 28.85/19.06 (((f10(c1) = c1) | (f9(c2, c2) = f8(c1)) | (~big_f(f9(c2, c2), f10(c1))) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2))) <=> ((c2 = f5(c1)) | (f7(c1) = c1) | (f10(c1) = c1) | (~big_f(f7(c1), c2)) | (f9(c2, c2) = f8(c1)) | (~big_f(f9(c2, c2), f10(c1))))),
% 28.85/19.06 inference(rewrite,[status(thm)],[])).
% 28.85/19.06 tff(17351,plain,
% 28.85/19.06 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c1) = c1) | (f9(c2, c2) = f8(c1)) | (~big_f(f9(c2, c2), f10(c1))) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((c2 = f5(c1)) | (f7(c1) = c1) | (f10(c1) = c1) | (~big_f(f7(c1), c2)) | (f9(c2, c2) = f8(c1)) | (~big_f(f9(c2, c2), f10(c1)))))),
% 28.85/19.06 inference(monotonicity,[status(thm)],[17350])).
% 28.85/19.06 tff(17352,plain,
% 28.85/19.06 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c1) = c1) | (f9(c2, c2) = f8(c1)) | (~big_f(f9(c2, c2), f10(c1))) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (c2 = f5(c1)) | (f7(c1) = c1) | (f10(c1) = c1) | (~big_f(f7(c1), c2)) | (f9(c2, c2) = f8(c1)) | (~big_f(f9(c2, c2), f10(c1))))),
% 28.85/19.06 inference(transitivity,[status(thm)],[17351, 17349])).
% 28.85/19.06 tff(17353,plain,
% 28.85/19.06 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c1) = c1) | (f9(c2, c2) = f8(c1)) | (~big_f(f9(c2, c2), f10(c1))) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)))),
% 28.85/19.06 inference(quant_inst,[status(thm)],[])).
% 28.85/19.06 tff(17354,plain,
% 28.85/19.06 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (c2 = f5(c1)) | (f7(c1) = c1) | (f10(c1) = c1) | (~big_f(f7(c1), c2)) | (f9(c2, c2) = f8(c1)) | (~big_f(f9(c2, c2), f10(c1)))),
% 28.85/19.07 inference(modus_ponens,[status(thm)],[17353, 17352])).
% 28.85/19.07 tff(17355,plain,
% 28.85/19.07 ((f9(c2, c2) = f8(c1)) | (~big_f(f9(c2, c2), f10(c1)))),
% 28.85/19.07 inference(unit_resolution,[status(thm)],[17354, 1659, 12775, 17328, 115, 3])).
% 28.85/19.07 tff(17356,plain,
% 28.85/19.07 ($false),
% 28.85/19.07 inference(unit_resolution,[status(thm)],[17355, 17348, 17335])).
% 28.85/19.07 tff(17357,plain,((f9(c2, c2) = c2) | (c2 = f5(c1)) | (f7(c1) = c1) | (f10(c1) = c1) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.85/19.07 tff(17358,plain,
% 28.85/19.07 (f9(c2, c2) = c2),
% 28.85/19.07 inference(unit_resolution,[status(thm)],[17357, 12775, 115, 3, 122])).
% 28.85/19.07 tff(17359,plain,
% 28.85/19.07 (big_f(f9(c2, c2), c2) <=> big_f(c2, c2)),
% 28.85/19.07 inference(monotonicity,[status(thm)],[17358])).
% 28.85/19.07 tff(17360,plain,
% 28.85/19.07 (big_f(c2, c2) <=> big_f(f9(c2, c2), c2)),
% 28.85/19.07 inference(symmetry,[status(thm)],[17359])).
% 28.85/19.07 tff(17361,plain,
% 28.85/19.07 (big_f(c2, c2) <=> big_f(f9(c2, c2), f10(c2))),
% 28.85/19.07 inference(transitivity,[status(thm)],[17360, 130])).
% 28.85/19.07 tff(17362,plain,
% 28.85/19.07 (big_f(f9(c2, c2), f10(c2))),
% 28.85/19.07 inference(modus_ponens,[status(thm)],[17326, 17361])).
% 28.85/19.07 tff(17363,plain,
% 28.85/19.07 ($false),
% 28.85/19.07 inference(unit_resolution,[status(thm)],[3405, 1190, 12775, 17328, 115, 122, 17358, 17362])).
% 28.85/19.07 tff(17364,plain,((c2 = f5(c1)) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (f10(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 28.85/19.07 tff(17365,plain,
% 28.85/19.07 (c2 = f5(c1)),
% 28.85/19.07 inference(unit_resolution,[status(thm)],[17364, 122, 115, 3])).
% 28.85/19.07 tff(17366,plain,
% 28.85/19.07 (f5(c1) = c2),
% 28.85/19.07 inference(symmetry,[status(thm)],[17365])).
% 28.85/19.07 tff(17367,plain,
% 28.85/19.07 ((f5(c1) = c1) <=> (c2 = c1)),
% 28.85/19.07 inference(monotonicity,[status(thm)],[17366])).
% 28.85/19.07 tff(17368,plain,
% 28.85/19.07 ((c2 = c1) <=> (f5(c1) = c1)),
% 28.85/19.07 inference(symmetry,[status(thm)],[17367])).
% 28.85/19.07 tff(17369,plain,
% 28.85/19.07 ((c2 = c1) <=> (c1 = f5(c1))),
% 28.85/19.07 inference(transitivity,[status(thm)],[17368, 192])).
% 28.85/19.07 tff(17370,plain,
% 28.85/19.07 ((~(c2 = c1)) <=> (~(c1 = f5(c1)))),
% 28.85/19.07 inference(monotonicity,[status(thm)],[17369])).
% 28.85/19.07 tff(17371,plain,
% 28.85/19.07 (~(c1 = f5(c1))),
% 28.85/19.07 inference(modus_ponens,[status(thm)],[75, 17370])).
% 28.85/19.07 tff(17372,plain,
% 28.85/19.07 (f5(c1) = c2),
% 28.85/19.07 inference(modus_ponens,[status(thm)],[2908, 8483])).
% 28.85/19.07 tff(17373,plain,
% 28.85/19.07 (~(f9(c2, f5(c1)) = c2)),
% 28.85/19.07 inference(unit_resolution,[status(thm)],[17013, 1209, 17372])).
% 28.85/19.07 tff(17374,plain,
% 28.85/19.07 (f9(c2, f5(c1)) = c1),
% 28.85/19.07 inference(unit_resolution,[status(thm)],[16529, 17373])).
% 28.85/19.07 tff(17375,plain,
% 28.85/19.07 (f5(c1) = c2),
% 28.85/19.07 inference(symmetry,[status(thm)],[2908])).
% 28.85/19.07 tff(17376,plain,
% 28.85/19.07 (f9(c2, f5(c1)) = f9(c2, c2)),
% 28.85/19.07 inference(monotonicity,[status(thm)],[17375])).
% 28.85/19.07 tff(17377,plain,
% 28.85/19.07 (f9(c2, c2) = f9(c2, f5(c1))),
% 28.85/19.07 inference(symmetry,[status(thm)],[17376])).
% 28.85/19.07 tff(17378,plain,
% 28.85/19.07 (f9(c2, c2) = c1),
% 28.85/19.07 inference(transitivity,[status(thm)],[17377, 17374])).
% 28.85/19.07 tff(17379,plain,
% 28.85/19.07 (big_f(c2, f9(c2, c2)) <=> big_f(c2, c1)),
% 28.85/19.07 inference(monotonicity,[status(thm)],[17378])).
% 28.85/19.07 tff(17380,plain,
% 28.85/19.07 (big_f(c2, c1) <=> big_f(c2, f9(c2, c2))),
% 28.85/19.07 inference(symmetry,[status(thm)],[17379])).
% 28.85/19.07 tff(17381,plain,
% 28.85/19.07 ((~big_f(c2, c1)) <=> (~big_f(c2, f9(c2, c2)))),
% 28.85/19.07 inference(monotonicity,[status(thm)],[17380])).
% 28.85/19.07 tff(17382,plain,
% 28.85/19.07 (~big_f(c2, f9(c2, c2))),
% 28.85/19.07 inference(modus_ponens,[status(thm)],[2, 17381])).
% 28.85/19.07 tff(17383,plain,
% 28.85/19.07 (f10(f9(c2, c2)) = f10(c1)),
% 28.85/19.07 inference(monotonicity,[status(thm)],[17378])).
% 28.85/19.07 tff(17384,plain,
% 28.85/19.07 (f10(f9(c2, c2)) = c2),
% 28.85/19.07 inference(transitivity,[status(thm)],[17383, 16])).
% 28.85/19.07 tff(17385,plain,
% 28.85/19.07 (big_f(f9(c2, c2), f10(f9(c2, c2))) <=> big_f(f9(c2, c2), c2)),
% 28.85/19.07 inference(monotonicity,[status(thm)],[17384])).
% 28.85/19.07 tff(17386,plain,
% 28.85/19.07 (big_f(f9(c2, c2), c2) <=> big_f(f9(c2, c2), f10(f9(c2, c2)))),
% 28.85/19.07 inference(symmetry,[status(thm)],[17385])).
% 28.85/19.07 tff(17387,plain,
% 28.85/19.07 (f7(f4(c4)) = c2),
% 28.85/19.07 inference(transitivity,[status(thm)],[16243, 347])).
% 28.85/19.07 tff(17388,plain,
% 28.85/19.07 ((f6(c2, f7(f4(c4))) = f7(f4(c4))) <=> (f6(c2, f7(f4(c4))) = c2)),
% 28.85/19.07 inference(monotonicity,[status(thm)],[17387])).
% 28.85/19.07 tff(17389,plain,
% 28.85/19.07 (big_f(f7(c2), f6(c2, c2))),
% 28.85/19.07 inference(unit_resolution,[status(thm)],[5485, 256, 77, 1345, 122, 1209])).
% 28.85/19.07 tff(17390,plain,
% 28.85/19.07 (~(f6(f7(c2), f5(c1)) = c1)),
% 28.85/19.07 inference(unit_resolution,[status(thm)],[3286, 17389, 77, 186, 347, 122, 1209, 256])).
% 28.85/19.07 tff(17391,plain,
% 28.85/19.07 (f6(f7(c2), f5(c1)) = c2),
% 28.85/19.07 inference(unit_resolution,[status(thm)],[2978, 17390])).
% 28.85/19.07 tff(17392,plain,
% 28.85/19.07 ((f6(c2, f7(f4(c4))) = c2) <=> (f6(c2, f7(f4(c4))) = f7(f4(c4)))),
% 28.85/19.07 inference(symmetry,[status(thm)],[17388])).
% 28.85/19.07 tff(17393,plain,
% 28.85/19.07 (f6(c2, f7(f4(c4))) = f6(c2, c2)),
% 28.85/19.07 inference(monotonicity,[status(thm)],[17387])).
% 28.85/19.07 tff(17394,plain,
% 28.85/19.07 ((f6(c2, f7(f4(c4))) = c2) <=> (f6(c2, c2) = c2)),
% 28.85/19.07 inference(monotonicity,[status(thm)],[17393])).
% 28.85/19.07 tff(17395,plain,
% 28.85/19.07 ((f6(c2, c2) = c2) <=> (f6(c2, f7(f4(c4))) = c2)),
% 28.85/19.07 inference(symmetry,[status(thm)],[17394])).
% 28.85/19.07 tff(17396,plain,
% 28.85/19.07 ((f6(c2, c2) = c2) <=> (f6(f7(c2), f5(c1)) = c2)),
% 28.85/19.07 inference(monotonicity,[status(thm)],[3245])).
% 28.85/19.07 tff(17397,plain,
% 28.85/19.07 ((f6(f7(c2), f5(c1)) = c2) <=> (f6(c2, c2) = c2)),
% 28.85/19.07 inference(symmetry,[status(thm)],[17396])).
% 28.85/19.07 tff(17398,plain,
% 28.85/19.07 ((f6(f7(c2), f5(c1)) = c2) <=> (f6(c2, f7(f4(c4))) = f7(f4(c4)))),
% 28.85/19.07 inference(transitivity,[status(thm)],[17397, 17395, 17392])).
% 28.85/19.07 tff(17399,plain,
% 28.85/19.07 (f6(c2, f7(f4(c4))) = f7(f4(c4))),
% 28.85/19.07 inference(modus_ponens,[status(thm)],[3032, 17398])).
% 28.85/19.07 tff(17400,assumption,(~(f6(c2, f7(f4(c4))) = f7(f4(c4)))), introduced(assumption)).
% 28.85/19.07 tff(17401,plain,
% 28.85/19.07 ($false),
% 28.85/19.07 inference(unit_resolution,[status(thm)],[17400, 17399])).
% 28.85/19.07 tff(17402,plain,((~(f6(f7(c2), f5(c1)) = c2)) | (f6(c2, f7(f4(c4))) = f7(f4(c4))) | (~(f5(c1) = c2)) | (~(f7(c2) = c2)) | (~(f7(c1) = c2)) | (~(f4(c4) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.85/19.07 tff(17403,plain,
% 28.85/19.07 (f6(c2, f7(f4(c4))) = f7(f4(c4))),
% 28.85/19.07 inference(unit_resolution,[status(thm)],[17402, 17391, 347, 77, 186, 11752])).
% 28.85/19.07 tff(17404,plain,
% 28.85/19.07 (f6(c2, f7(f4(c4))) = c2),
% 28.85/19.07 inference(modus_ponens,[status(thm)],[17403, 17388])).
% 28.85/19.07 tff(17405,plain,
% 28.85/19.07 (~(f6(c2, c2) = c2)),
% 28.85/19.07 inference(unit_resolution,[status(thm)],[2744, 17389, 77, 1209, 256, 122])).
% 28.85/19.07 tff(17406,plain,
% 28.85/19.07 (f6(c2, c2) = f6(c2, f7(f4(c4)))),
% 28.85/19.07 inference(symmetry,[status(thm)],[17393])).
% 28.85/19.07 tff(17407,plain,
% 28.85/19.07 ((f6(c2, c2) = c2) <=> (f6(c2, f7(f4(c4))) = c2)),
% 28.85/19.07 inference(monotonicity,[status(thm)],[17406])).
% 28.85/19.07 tff(17408,plain,
% 28.85/19.07 ((f6(c2, f7(f4(c4))) = c2) <=> (f6(c2, c2) = c2)),
% 28.85/19.07 inference(symmetry,[status(thm)],[17407])).
% 28.85/19.07 tff(17409,assumption,(f6(c2, f7(f4(c4))) = c2), introduced(assumption)).
% 28.85/19.07 tff(17410,plain,
% 28.85/19.07 (f6(c2, c2) = c2),
% 28.85/19.07 inference(modus_ponens,[status(thm)],[17409, 17408])).
% 28.85/19.07 tff(17411,plain,
% 28.85/19.07 ($false),
% 28.85/19.07 inference(unit_resolution,[status(thm)],[2637, 17410])).
% 28.85/19.07 tff(17412,plain,((~(f6(c2, f7(f4(c4))) = c2)) | (f6(c2, c2) = c2) | (~(f7(c1) = c2)) | (~(f4(c4) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.85/19.07 tff(17413,plain,
% 28.85/19.07 (~(f6(c2, f7(f4(c4))) = c2)),
% 28.85/19.07 inference(unit_resolution,[status(thm)],[17412, 17405, 347, 11752])).
% 28.85/19.07 tff(17414,plain,
% 28.85/19.07 ($false),
% 28.85/19.07 inference(unit_resolution,[status(thm)],[17413, 17404])).
% 28.85/19.07 tff(17415,plain,(big_f(f9(c2, c2), f10(c2)) | (~(f7(c1) = c2)) | (~(f4(c4) = c1)) | (~(f7(c2) = c2)) | (~(f5(c1) = c2)) | (f9(c2, c2) = c2) | (~(f10(c2) = c2)) | (~big_f(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 28.85/19.07 tff(17416,plain,
% 28.85/19.07 (big_f(f9(c2, c2), f10(c2))),
% 28.85/19.07 inference(unit_resolution,[status(thm)],[17415, 1209, 11752, 77, 17372, 347, 122, 1345])).
% 28.85/19.07 tff(17417,plain,
% 28.85/19.07 (big_f(f9(c2, c2), c2)),
% 28.85/19.07 inference(unit_resolution,[status(thm)],[3687, 17416, 122])).
% 28.85/19.07 tff(17418,plain,
% 28.85/19.07 (big_f(f9(c2, c2), f10(f9(c2, c2)))),
% 28.85/19.07 inference(modus_ponens,[status(thm)],[17417, 17386])).
% 28.85/19.07 tff(17419,plain,
% 28.85/19.07 ((f10(f9(c2, c2)) = f9(c2, c2)) <=> (c2 = f9(c2, c2))),
% 28.85/19.07 inference(monotonicity,[status(thm)],[17384])).
% 28.85/19.07 tff(17420,plain,
% 28.85/19.07 ((f10(f9(c2, c2)) = f9(c2, c2)) <=> (f9(c2, c2) = c2)),
% 28.85/19.07 inference(transitivity,[status(thm)],[17419, 167])).
% 28.85/19.07 tff(17421,plain,
% 28.85/19.07 ((f9(c2, c2) = c2) <=> (f10(f9(c2, c2)) = f9(c2, c2))),
% 28.85/19.07 inference(symmetry,[status(thm)],[17420])).
% 28.85/19.07 tff(17422,plain,
% 28.85/19.07 ((~(f9(c2, c2) = c2)) <=> (~(f10(f9(c2, c2)) = f9(c2, c2)))),
% 28.85/19.07 inference(monotonicity,[status(thm)],[17421])).
% 28.85/19.07 tff(17423,plain,
% 28.85/19.07 (~(f10(f9(c2, c2)) = f9(c2, c2))),
% 28.85/19.07 inference(modus_ponens,[status(thm)],[1209, 17422])).
% 28.85/19.07 tff(17424,assumption,(f9(c2, f5(c1)) = c1), introduced(assumption)).
% 28.85/19.07 tff(17425,plain,
% 28.85/19.07 (c1 = f9(c2, f5(c1))),
% 28.85/19.07 inference(symmetry,[status(thm)],[17424])).
% 28.85/19.07 tff(17426,plain,
% 28.85/19.07 (f6(c2, c2) = f6(f7(c2), f5(c1))),
% 28.85/19.07 inference(monotonicity,[status(thm)],[82, 2908])).
% 28.85/19.07 tff(17427,plain,
% 28.85/19.07 (f6(c2, c2) = c2),
% 28.85/19.07 inference(transitivity,[status(thm)],[17426, 3032])).
% 28.85/19.07 tff(17428,plain,
% 28.85/19.07 (big_f(f7(c2), f6(c2, c2)) <=> big_f(c2, c2)),
% 28.85/19.07 inference(monotonicity,[status(thm)],[77, 17427])).
% 28.85/19.07 tff(17429,plain,
% 28.85/19.07 (big_f(c2, c2) <=> big_f(f7(c2), f6(c2, c2))),
% 28.85/19.07 inference(symmetry,[status(thm)],[17428])).
% 28.85/19.07 tff(17430,plain,
% 28.85/19.07 (big_f(f7(c2), f6(c2, c2))),
% 28.85/19.07 inference(modus_ponens,[status(thm)],[1345, 17429])).
% 28.85/19.07 tff(17431,plain,
% 28.85/19.07 (f6(f7(c2), f5(c1)) = f6(c2, c2)),
% 28.85/19.07 inference(symmetry,[status(thm)],[17426])).
% 28.85/19.07 tff(17432,plain,
% 28.85/19.07 ((f6(f7(c2), f5(c1)) = c2) <=> (f6(c2, c2) = c2)),
% 28.85/19.07 inference(monotonicity,[status(thm)],[17431])).
% 28.85/19.07 tff(17433,plain,
% 28.85/19.07 (f6(c2, c2) = c2),
% 28.85/19.07 inference(modus_ponens,[status(thm)],[3032, 17432])).
% 28.85/19.07 tff(17434,plain,
% 28.85/19.07 ($false),
% 28.85/19.07 inference(unit_resolution,[status(thm)],[3632, 2730, 77, 17433, 17430, 1767, 2026, 2137])).
% 28.85/19.07 tff(17435,plain,((~(f6(f7(c2), f5(c1)) = c2)) | (~(f7(c2) = c2)) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | (f9(c2, c2) = f8(f9(c2, c2))) | (~big_f(c2, c2)) | (~(c2 = f5(c1)))), inference(lemma,lemma(discharge,[]))).
% 28.85/19.07 tff(17436,plain,
% 28.85/19.07 (~(f6(f7(c2), f5(c1)) = c2)),
% 28.85/19.07 inference(unit_resolution,[status(thm)],[17435, 2137, 1767, 2026, 77, 1345, 2908])).
% 28.85/19.07 tff(17437,plain,
% 28.85/19.07 (f6(f7(c2), f5(c1)) = c1),
% 28.85/19.07 inference(unit_resolution,[status(thm)],[2978, 17436])).
% 28.85/19.07 tff(17438,plain,
% 28.85/19.07 (f6(c2, c2) = f9(c2, c2)),
% 28.85/19.07 inference(transitivity,[status(thm)],[17426, 17437, 17425, 17376])).
% 28.85/19.07 tff(17439,plain,
% 28.85/19.07 (big_f(f7(c2), f6(c2, c2)) <=> big_f(c2, f9(c2, c2))),
% 28.85/19.07 inference(monotonicity,[status(thm)],[77, 17438])).
% 28.85/19.07 tff(17440,plain,
% 28.85/19.07 (big_f(c2, f9(c2, c2)) <=> big_f(f7(c2), f6(c2, c2))),
% 28.85/19.07 inference(symmetry,[status(thm)],[17439])).
% 28.85/19.07 tff(17441,plain,
% 28.85/19.07 ((~big_f(c2, f9(c2, c2))) <=> (~big_f(f7(c2), f6(c2, c2)))),
% 28.85/19.07 inference(monotonicity,[status(thm)],[17440])).
% 28.85/19.07 tff(17442,plain,
% 28.85/19.07 (~big_f(f7(c2), f6(c2, c2))),
% 28.85/19.07 inference(modus_ponens,[status(thm)],[2040, 17441])).
% 28.85/19.07 tff(17443,plain,
% 28.85/19.07 ((~(f6(f7(c2), f5(c1)) = c2)) <=> (~(f6(c2, c2) = c2))),
% 28.85/19.07 inference(monotonicity,[status(thm)],[17432])).
% 28.85/19.07 tff(17444,plain,
% 28.85/19.07 (~(f6(c2, c2) = c2)),
% 28.85/19.07 inference(modus_ponens,[status(thm)],[17436, 17443])).
% 28.85/19.07 tff(17445,plain,
% 28.85/19.07 ($false),
% 28.85/19.07 inference(unit_resolution,[status(thm)],[2680, 2662, 77, 17444, 17442, 1767, 2026, 2137])).
% 28.85/19.07 tff(17446,plain,((f9(c2, c2) = f8(f9(c2, c2))) | (~(f7(c2) = c2)) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~big_f(f9(c2, c2), f10(f9(c2, c2)))) | big_f(c2, f9(c2, c2)) | (~(f9(c2, f5(c1)) = c1)) | (~(c2 = f5(c1))) | (~big_f(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 28.85/19.07 tff(17447,plain,
% 28.85/19.07 (f9(c2, c2) = f8(f9(c2, c2))),
% 28.85/19.07 inference(unit_resolution,[status(thm)],[17446, 17423, 77, 17418, 17382, 17374, 2908, 1345])).
% 28.85/19.07 tff(17448,plain,
% 28.85/19.07 (f8(f9(c2, c2)) = f9(c2, c2)),
% 28.85/19.07 inference(symmetry,[status(thm)],[17447])).
% 28.85/19.07 tff(17449,plain,
% 28.85/19.07 ((c2 = f8(f9(c2, c2))) <=> (c2 = f9(c2, c2))),
% 28.85/19.07 inference(monotonicity,[status(thm)],[17448])).
% 28.85/19.07 tff(17450,plain,
% 28.85/19.07 ((c2 = f8(f9(c2, c2))) <=> (f9(c2, c2) = c2)),
% 28.85/19.07 inference(transitivity,[status(thm)],[17449, 167])).
% 28.85/19.07 tff(17451,plain,
% 28.85/19.07 ((f9(c2, c2) = c2) <=> (c2 = f8(f9(c2, c2)))),
% 28.85/19.07 inference(symmetry,[status(thm)],[17450])).
% 28.85/19.07 tff(17452,plain,
% 28.85/19.07 ((~(f9(c2, c2) = c2)) <=> (~(c2 = f8(f9(c2, c2))))),
% 28.85/19.07 inference(monotonicity,[status(thm)],[17451])).
% 28.85/19.07 tff(17453,plain,
% 28.85/19.07 (~(c2 = f8(f9(c2, c2)))),
% 28.85/19.07 inference(modus_ponens,[status(thm)],[1209, 17452])).
% 28.85/19.07 tff(17454,plain,
% 28.85/19.07 (big_f(c2, f10(f9(c2, c2))) <=> big_f(c2, c2)),
% 28.85/19.07 inference(monotonicity,[status(thm)],[17384])).
% 28.85/19.07 tff(17455,plain,
% 28.85/19.07 (big_f(c2, c2) <=> big_f(c2, f10(f9(c2, c2)))),
% 28.85/19.07 inference(symmetry,[status(thm)],[17454])).
% 28.85/19.07 tff(17456,plain,
% 28.85/19.07 (big_f(c2, f10(f9(c2, c2)))),
% 28.85/19.07 inference(modus_ponens,[status(thm)],[1345, 17455])).
% 28.85/19.07 tff(17457,plain,
% 28.85/19.07 (c1 = f9(c2, f5(c1))),
% 28.85/19.07 inference(symmetry,[status(thm)],[17374])).
% 28.85/19.07 tff(17458,plain,
% 28.85/19.07 (f6(c2, c2) = f9(c2, c2)),
% 28.85/19.07 inference(transitivity,[status(thm)],[17426, 2947, 17457, 17376])).
% 28.85/19.07 tff(17459,plain,
% 28.85/19.07 (big_f(f7(c2), f6(c2, c2)) <=> big_f(c2, f9(c2, c2))),
% 28.85/19.07 inference(monotonicity,[status(thm)],[77, 17458])).
% 28.85/19.07 tff(17460,plain,
% 28.85/19.07 (big_f(c2, f9(c2, c2)) <=> big_f(f7(c2), f6(c2, c2))),
% 28.85/19.07 inference(symmetry,[status(thm)],[17459])).
% 28.85/19.07 tff(17461,plain,
% 28.85/19.07 ((~big_f(c2, f9(c2, c2))) <=> (~big_f(f7(c2), f6(c2, c2)))),
% 28.85/19.07 inference(monotonicity,[status(thm)],[17460])).
% 28.85/19.07 tff(17462,plain,
% 28.85/19.07 (~big_f(f7(c2), f6(c2, c2))),
% 28.85/19.07 inference(modus_ponens,[status(thm)],[2040, 17461])).
% 28.85/19.07 tff(17463,plain,
% 28.85/19.07 ((f6(c2, c2) = c2) <=> (f9(c2, c2) = c2)),
% 28.85/19.07 inference(monotonicity,[status(thm)],[17458])).
% 28.85/19.07 tff(17464,plain,
% 28.85/19.07 ((f9(c2, c2) = c2) <=> (f6(c2, c2) = c2)),
% 28.85/19.07 inference(symmetry,[status(thm)],[17463])).
% 28.85/19.07 tff(17465,plain,
% 28.85/19.07 ((~(f9(c2, c2) = c2)) <=> (~(f6(c2, c2) = c2))),
% 28.85/19.07 inference(monotonicity,[status(thm)],[17464])).
% 28.85/19.07 tff(17466,plain,
% 28.85/19.07 (~(f6(c2, c2) = c2)),
% 28.85/19.07 inference(modus_ponens,[status(thm)],[1209, 17465])).
% 28.85/19.07 tff(17467,plain,
% 28.85/19.07 ($false),
% 28.85/19.07 inference(unit_resolution,[status(thm)],[2668, 2662, 77, 17466, 17462, 1767, 2016, 6888])).
% 28.85/19.07 tff(17468,plain,((~(f6(f7(c2), f5(c1)) = c1)) | (~(f7(c2) = c2)) | (f10(f9(c2, c2)) = f9(c2, c2)) | (~big_f(c2, f10(f9(c2, c2)))) | (c2 = f8(f9(c2, c2))) | big_f(c2, f9(c2, c2)) | (~(c2 = f5(c1))) | (f9(c2, c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 28.85/19.07 tff(17469,plain,
% 28.85/19.07 (~(f6(f7(c2), f5(c1)) = c1)),
% 28.85/19.07 inference(unit_resolution,[status(thm)],[17468, 17423, 77, 17456, 17453, 17382, 2908, 1209])).
% 28.85/19.07 tff(17470,plain,
% 28.85/19.07 (f6(f7(c2), f5(c1)) = c2),
% 28.85/19.07 inference(unit_resolution,[status(thm)],[2978, 17469])).
% 28.85/19.07 tff(17471,plain,
% 28.85/19.07 (f6(c2, c2) = c2),
% 28.85/19.07 inference(transitivity,[status(thm)],[17426, 17470])).
% 28.85/19.07 tff(17472,plain,
% 28.85/19.07 (big_f(f7(c2), f6(c2, c2)) <=> big_f(c2, c2)),
% 28.85/19.07 inference(monotonicity,[status(thm)],[77, 17471])).
% 28.85/19.07 tff(17473,plain,
% 28.85/19.07 (big_f(c2, c2) <=> big_f(f7(c2), f6(c2, c2))),
% 28.85/19.07 inference(symmetry,[status(thm)],[17472])).
% 28.85/19.07 tff(17474,plain,
% 28.85/19.07 (big_f(f7(c2), f6(c2, c2))),
% 28.85/19.07 inference(modus_ponens,[status(thm)],[1345, 17473])).
% 28.85/19.07 tff(17475,plain,
% 28.85/19.07 (f6(c2, c2) = c2),
% 28.85/19.07 inference(modus_ponens,[status(thm)],[17470, 17432])).
% 28.85/19.07 tff(17476,plain,
% 28.85/19.07 ($false),
% 28.85/19.07 inference(unit_resolution,[status(thm)],[3618, 2730, 77, 17475, 17474, 17423, 17456, 17453])).
% 28.85/19.07 tff(17477,plain,((f9(c2, c2) = c2) | (~(f7(c2) = c2)) | (~big_f(c2, c2)) | (~(c2 = f5(c1))) | (~(f10(c1) = c2)) | (~(f10(c2) = c2)) | (~(f4(c4) = c1)) | (~(f7(c1) = c2)) | big_f(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 28.85/19.07 tff(17478,plain,
% 28.85/19.07 (f9(c2, c2) = c2),
% 28.85/19.07 inference(unit_resolution,[status(thm)],[17477, 2, 1345, 2908, 16, 122, 11752, 347, 77])).
% 28.85/19.07 tff(17479,plain,
% 28.85/19.07 (big_f(f9(c2, c2), c2) <=> big_f(c2, c2)),
% 28.85/19.07 inference(monotonicity,[status(thm)],[17478])).
% 28.85/19.07 tff(17480,plain,
% 28.85/19.07 (big_f(c2, c2) <=> big_f(f9(c2, c2), c2)),
% 28.85/19.07 inference(symmetry,[status(thm)],[17479])).
% 28.85/19.07 tff(17481,plain,
% 28.85/19.07 (big_f(c2, c2) <=> big_f(f9(c2, c2), f10(c2))),
% 28.85/19.07 inference(transitivity,[status(thm)],[17480, 130])).
% 28.85/19.07 tff(17482,plain,
% 28.85/19.07 (big_f(f9(c2, c2), f10(c2))),
% 28.85/19.07 inference(modus_ponens,[status(thm)],[1345, 17481])).
% 28.85/19.07 tff(17483,plain,
% 28.85/19.07 (~(f6(c2, f7(f4(c4))) = c2)),
% 28.85/19.07 inference(unit_resolution,[status(thm)],[17412, 2637, 347, 11752])).
% 28.85/19.07 tff(17484,plain,
% 28.85/19.07 (f6(c2, f7(f4(c4))) = c1),
% 28.85/19.07 inference(unit_resolution,[status(thm)],[6601, 17483])).
% 28.85/19.07 tff(17485,plain,
% 28.85/19.07 (c1 = f6(c2, f7(f4(c4)))),
% 28.85/19.07 inference(symmetry,[status(thm)],[17484])).
% 28.85/19.07 tff(17486,plain,
% 28.85/19.07 (c1 = f6(c2, c2)),
% 28.85/19.07 inference(transitivity,[status(thm)],[17485, 17393])).
% 28.85/19.07 tff(17487,plain,
% 28.85/19.07 (big_f(c2, c1) <=> big_f(f7(c2), f6(c2, c2))),
% 28.85/19.07 inference(monotonicity,[status(thm)],[82, 17486])).
% 28.85/19.07 tff(17488,plain,
% 28.85/19.07 ((~big_f(c2, c1)) <=> (~big_f(f7(c2), f6(c2, c2)))),
% 28.85/19.07 inference(monotonicity,[status(thm)],[17487])).
% 28.85/19.07 tff(17489,plain,
% 28.85/19.07 (~big_f(f7(c2), f6(c2, c2))),
% 28.85/19.07 inference(modus_ponens,[status(thm)],[2, 17488])).
% 28.85/19.07 tff(17490,plain,
% 28.85/19.07 ($false),
% 28.85/19.07 inference(unit_resolution,[status(thm)],[2412, 2409, 122, 77, 2637, 17489, 1572, 690])).
% 28.85/19.07 tff(17491,plain,((f6(c2, c2) = c2) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | big_f(c2, c1) | (~(f7(c1) = c2)) | (~(f4(c4) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.85/19.07 tff(17492,plain,
% 28.85/19.07 (f6(c2, c2) = c2),
% 28.85/19.07 inference(unit_resolution,[status(thm)],[17491, 17478, 77, 122, 17482, 2, 347, 11752])).
% 28.85/19.07 tff(17493,plain,
% 28.85/19.07 (big_f(f7(c2), f6(c2, c2))),
% 28.85/19.07 inference(unit_resolution,[status(thm)],[2627, 17492, 77, 1345])).
% 28.85/19.07 tff(17494,plain,
% 28.85/19.07 ($false),
% 28.85/19.07 inference(unit_resolution,[status(thm)],[2384, 2378, 122, 77, 17492, 17493, 17478, 17482])).
% 28.85/19.07 tff(17495,plain,(big_f(c2, c1) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~big_f(c2, c2)) | (~(f7(c1) = c2)) | (~(f4(c4) = c1)) | (~(c2 = f5(c1))) | (~(f10(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.85/19.07 tff(17496,plain,
% 28.85/19.07 (big_f(c2, c1)),
% 28.85/19.07 inference(unit_resolution,[status(thm)],[17495, 122, 17223, 17326, 120, 15706, 17365, 15])).
% 28.85/19.07 tff(17497,plain,
% 28.85/19.07 (big_f(f7(c1), c1)),
% 28.85/19.07 inference(modus_ponens,[status(thm)],[17496, 693])).
% 28.85/19.07 tff(17498,plain,
% 28.85/19.07 (c2 = f8(c1)),
% 28.85/19.07 inference(unit_resolution,[status(thm)],[14210, 1659, 115, 17327, 3, 17497, 17371])).
% 28.85/19.07 tff(17499,plain,
% 28.85/19.07 (f7(f9(c2, c2)) = f7(c1)),
% 28.85/19.07 inference(monotonicity,[status(thm)],[17378])).
% 28.85/19.07 tff(17500,plain,
% 28.85/19.07 (f7(f9(c2, c2)) = c2),
% 28.85/19.07 inference(transitivity,[status(thm)],[17499, 347])).
% 28.85/19.07 tff(17501,plain,
% 28.85/19.07 (big_f(f7(f9(c2, c2)), f9(c2, c2)) <=> big_f(c2, f9(c2, c2))),
% 28.85/19.07 inference(monotonicity,[status(thm)],[17500])).
% 28.85/19.07 tff(17502,plain,
% 28.85/19.07 (big_f(c2, f9(c2, c2)) <=> big_f(f7(f9(c2, c2)), f9(c2, c2))),
% 28.85/19.07 inference(symmetry,[status(thm)],[17501])).
% 28.85/19.07 tff(17503,plain,
% 28.85/19.07 (big_f(c2, c1)),
% 28.85/19.07 inference(unit_resolution,[status(thm)],[17495, 122, 77, 1345, 347, 11752, 2908, 16])).
% 28.85/19.07 tff(17504,plain,
% 28.85/19.07 (big_f(c2, f9(c2, c2))),
% 28.85/19.07 inference(modus_ponens,[status(thm)],[17503, 17380])).
% 28.85/19.07 tff(17505,plain,
% 28.85/19.07 (big_f(f7(f9(c2, c2)), f9(c2, c2))),
% 28.85/19.07 inference(modus_ponens,[status(thm)],[17504, 17502])).
% 28.85/19.07 tff(17506,plain,
% 28.85/19.07 ((f7(f9(c2, c2)) = f9(c2, c2)) <=> (c2 = f9(c2, c2))),
% 28.85/19.07 inference(monotonicity,[status(thm)],[17500])).
% 28.85/19.07 tff(17507,plain,
% 28.85/19.07 ((f7(f9(c2, c2)) = f9(c2, c2)) <=> (f9(c2, c2) = c2)),
% 28.85/19.07 inference(transitivity,[status(thm)],[17506, 167])).
% 28.85/19.07 tff(17508,plain,
% 28.85/19.07 ((f9(c2, c2) = c2) <=> (f7(f9(c2, c2)) = f9(c2, c2))),
% 28.85/19.07 inference(symmetry,[status(thm)],[17507])).
% 28.85/19.07 tff(17509,plain,
% 28.85/19.07 ((~(f9(c2, c2) = c2)) <=> (~(f7(f9(c2, c2)) = f9(c2, c2)))),
% 28.85/19.07 inference(monotonicity,[status(thm)],[17508])).
% 28.85/19.07 tff(17510,plain,
% 28.85/19.07 (~(f7(f9(c2, c2)) = f9(c2, c2))),
% 28.85/19.07 inference(modus_ponens,[status(thm)],[1209, 17509])).
% 28.85/19.07 tff(17511,plain,
% 28.85/19.07 (f8(f9(c2, c2)) = f8(c1)),
% 28.85/19.07 inference(monotonicity,[status(thm)],[17378])).
% 28.85/19.07 tff(17512,plain,
% 28.85/19.07 (f8(f9(c2, c2)) = c2),
% 28.85/19.07 inference(transitivity,[status(thm)],[17511, 1643])).
% 28.85/19.07 tff(17513,plain,
% 28.85/19.07 ((f9(c2, c2) = f8(f9(c2, c2))) <=> (f9(c2, c2) = c2)),
% 28.85/19.07 inference(monotonicity,[status(thm)],[17512])).
% 28.85/19.07 tff(17514,plain,
% 28.85/19.07 ((f9(c2, c2) = c2) <=> (f9(c2, c2) = f8(f9(c2, c2)))),
% 28.85/19.07 inference(symmetry,[status(thm)],[17513])).
% 28.85/19.07 tff(17515,plain,
% 28.85/19.07 ((~(f9(c2, c2) = c2)) <=> (~(f9(c2, c2) = f8(f9(c2, c2))))),
% 28.85/19.07 inference(monotonicity,[status(thm)],[17514])).
% 28.85/19.07 tff(17516,plain,
% 28.85/19.07 (~(f9(c2, c2) = f8(f9(c2, c2)))),
% 28.85/19.07 inference(modus_ponens,[status(thm)],[1209, 17515])).
% 28.85/19.07 tff(17517,plain,
% 28.85/19.07 (f5(f9(c2, c2)) = f5(c1)),
% 28.85/19.07 inference(monotonicity,[status(thm)],[17378])).
% 28.85/19.07 tff(17518,plain,
% 28.85/19.07 (f5(f9(c2, c2)) = c2),
% 28.85/19.07 inference(transitivity,[status(thm)],[17517, 17375])).
% 28.85/19.07 tff(17519,plain,
% 28.85/19.07 ((f9(c2, c2) = f5(f9(c2, c2))) <=> (f9(c2, c2) = c2)),
% 28.85/19.07 inference(monotonicity,[status(thm)],[17518])).
% 28.85/19.07 tff(17520,plain,
% 28.85/19.07 ((f9(c2, c2) = c2) <=> (f9(c2, c2) = f5(f9(c2, c2)))),
% 28.85/19.07 inference(symmetry,[status(thm)],[17519])).
% 28.85/19.07 tff(17521,plain,
% 28.85/19.07 ((~(f9(c2, c2) = c2)) <=> (~(f9(c2, c2) = f5(f9(c2, c2))))),
% 28.85/19.07 inference(monotonicity,[status(thm)],[17520])).
% 28.85/19.07 tff(17522,plain,
% 28.85/19.07 (~(f9(c2, c2) = f5(f9(c2, c2)))),
% 28.85/19.07 inference(modus_ponens,[status(thm)],[1209, 17521])).
% 28.85/19.07 tff(17523,plain,
% 28.85/19.07 ($false),
% 28.85/19.07 inference(unit_resolution,[status(thm)],[2032, 1659, 17522, 17423, 17418, 17516, 17510, 17505])).
% 28.85/19.07 tff(17524,plain,((f9(c2, c2) = c2) | (~(c2 = f8(c1))) | (~(c2 = f5(c1))) | (~(f10(c1) = c2)) | (~(f7(c1) = c2)) | (~(f10(c2) = c2)) | (~(f4(c4) = c1)) | (~(f7(c2) = c2)) | (~big_f(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 28.85/19.07 tff(17525,plain,
% 28.85/19.07 (f9(c2, c2) = c2),
% 28.85/19.07 inference(unit_resolution,[status(thm)],[17524, 17498, 17365, 15, 120, 122, 15706, 17223, 17326])).
% 28.85/19.07 tff(17526,plain,
% 28.85/19.07 (big_f(f9(c2, c2), c2) <=> big_f(c2, c2)),
% 28.85/19.07 inference(monotonicity,[status(thm)],[17525])).
% 28.85/19.07 tff(17527,plain,
% 28.85/19.07 (big_f(c2, c2) <=> big_f(f9(c2, c2), c2)),
% 28.85/19.07 inference(symmetry,[status(thm)],[17526])).
% 28.85/19.07 tff(17528,plain,
% 28.85/19.07 (big_f(c2, c2) <=> big_f(f9(c2, c2), f10(c2))),
% 28.85/19.07 inference(transitivity,[status(thm)],[17527, 130])).
% 28.85/19.07 tff(17529,plain,
% 28.85/19.07 (big_f(f9(c2, c2), f10(c2))),
% 28.85/19.07 inference(modus_ponens,[status(thm)],[17326, 17528])).
% 28.85/19.07 tff(17530,plain,
% 28.85/19.07 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((f7(c1) = c1) | (~(f10(c2) = c2)) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))),
% 28.85/19.07 inference(rewrite,[status(thm)],[])).
% 28.85/19.07 tff(17531,plain,
% 28.85/19.07 (((~(f10(c2) = c2)) | (f7(c1) = c1) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2)))) <=> ((f7(c1) = c1) | (~(f10(c2) = c2)) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))),
% 28.85/19.07 inference(rewrite,[status(thm)],[])).
% 28.85/19.07 tff(17532,plain,
% 28.85/19.07 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c1) = c1) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((f7(c1) = c1) | (~(f10(c2) = c2)) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2)))))),
% 28.85/19.07 inference(monotonicity,[status(thm)],[17531])).
% 28.85/19.07 tff(17533,plain,
% 28.85/19.07 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c1) = c1) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))),
% 28.85/19.07 inference(transitivity,[status(thm)],[17532, 17530])).
% 28.85/19.07 tff(17534,plain,
% 28.85/19.07 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c1) = c1) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))),
% 28.85/19.07 inference(quant_inst,[status(thm)],[])).
% 28.85/19.07 tff(17535,plain,
% 28.85/19.07 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2)))),
% 28.85/19.07 inference(modus_ponens,[status(thm)],[17534, 17533])).
% 28.85/19.07 tff(17536,plain,
% 28.85/19.07 ($false),
% 28.85/19.07 inference(unit_resolution,[status(thm)],[17535, 1190, 115, 122, 17497, 17371, 17525, 17529])).
% 28.85/19.07 tff(17537,plain,((~(f10(c2) = c2)) | (f7(c1) = c1) | (f10(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 28.85/19.07 tff(17538,plain,
% 28.85/19.07 (~(f10(c2) = c2)),
% 28.85/19.07 inference(unit_resolution,[status(thm)],[17537, 3, 115])).
% 28.85/19.07 tff(17539,plain,
% 28.85/19.07 (f10(c2) = c1),
% 28.85/19.07 inference(unit_resolution,[status(thm)],[93, 17538])).
% 28.85/19.07 tff(17540,plain,
% 28.85/19.07 (f10(f10(c2)) = f10(c1)),
% 28.85/19.07 inference(monotonicity,[status(thm)],[17539])).
% 28.85/19.07 tff(17541,plain,
% 28.85/19.07 (c1 = f10(c2)),
% 28.85/19.07 inference(symmetry,[status(thm)],[17539])).
% 28.85/19.07 tff(17542,plain,
% 28.85/19.07 (big_f(c2, c1) <=> big_f(c2, f10(c2))),
% 28.85/19.07 inference(monotonicity,[status(thm)],[17541])).
% 28.85/19.07 tff(17543,plain,
% 28.85/19.07 (big_f(c2, f10(c2)) <=> big_f(c2, c1)),
% 28.85/19.07 inference(symmetry,[status(thm)],[17542])).
% 28.85/19.07 tff(17544,plain,
% 28.85/19.07 (f7(f10(c2)) = f7(c1)),
% 28.85/19.07 inference(monotonicity,[status(thm)],[17539])).
% 28.85/19.07 tff(17545,plain,
% 28.85/19.07 (f7(f10(c2)) = c2),
% 28.85/19.07 inference(transitivity,[status(thm)],[17544, 120])).
% 28.85/19.07 tff(17546,plain,
% 28.85/19.07 (big_f(f7(f10(c2)), c2) <=> big_f(c2, c2)),
% 28.85/19.07 inference(monotonicity,[status(thm)],[17545])).
% 28.85/19.07 tff(17547,plain,
% 28.85/19.07 (big_f(c2, c2) <=> big_f(f7(f10(c2)), c2)),
% 28.85/19.07 inference(symmetry,[status(thm)],[17546])).
% 28.85/19.07 tff(17548,plain,
% 28.85/19.07 (f7(c2) = f10(c2)),
% 28.85/19.07 inference(transitivity,[status(thm)],[22, 17541])).
% 28.85/19.07 tff(17549,plain,
% 28.85/19.07 ((f7(c2) = c3) <=> (f10(c2) = c3)),
% 28.85/19.07 inference(monotonicity,[status(thm)],[17548])).
% 28.85/19.07 tff(17550,plain,
% 28.85/19.07 ((f10(c2) = c3) <=> (f7(c2) = c3)),
% 28.85/19.07 inference(symmetry,[status(thm)],[17549])).
% 28.85/19.07 tff(17551,plain,
% 28.85/19.07 (big_f(c1, c2) <=> big_f(f7(f7(c1)), f7(c1))),
% 28.85/19.07 inference(transitivity,[status(thm)],[12163, 12325])).
% 28.85/19.07 tff(17552,plain,
% 28.85/19.07 (big_f(f7(f7(c1)), f7(c1))),
% 28.85/19.07 inference(modus_ponens,[status(thm)],[15920, 17551])).
% 28.85/19.07 tff(17553,plain,
% 28.85/19.07 (f7(f10(c2)) = f7(c1)),
% 28.85/19.07 inference(monotonicity,[status(thm)],[94])).
% 28.85/19.07 tff(17554,plain,
% 28.85/19.07 (f7(f10(c2)) = c2),
% 28.85/19.07 inference(transitivity,[status(thm)],[17553, 120])).
% 28.85/19.08 tff(17555,plain,
% 28.85/19.08 (big_f(f7(f10(c2)), c2) <=> big_f(c2, c2)),
% 28.85/19.08 inference(monotonicity,[status(thm)],[17554])).
% 28.85/19.08 tff(17556,plain,
% 28.85/19.08 (big_f(c2, c2) <=> big_f(f7(f10(c2)), c2)),
% 28.85/19.08 inference(symmetry,[status(thm)],[17555])).
% 28.85/19.08 tff(17557,plain,
% 28.85/19.08 ((~big_f(c2, c2)) <=> (~big_f(f7(f10(c2)), c2))),
% 28.85/19.08 inference(monotonicity,[status(thm)],[17556])).
% 28.85/19.08 tff(17558,plain,
% 28.85/19.08 (~big_f(f7(f10(c2)), c2)),
% 28.85/19.08 inference(modus_ponens,[status(thm)],[121, 17557])).
% 28.85/19.08 tff(17559,plain,
% 28.85/19.08 ((f7(f10(c2)) = f10(c2)) <=> (c2 = f10(c2))),
% 28.85/19.08 inference(monotonicity,[status(thm)],[17554])).
% 28.85/19.08 tff(17560,plain,
% 28.85/19.08 ((f7(f10(c2)) = f10(c2)) <=> (f10(c2) = c2)),
% 28.85/19.08 inference(transitivity,[status(thm)],[17559, 4987])).
% 28.85/19.08 tff(17561,plain,
% 28.85/19.08 ((f10(c2) = c2) <=> (f7(f10(c2)) = f10(c2))),
% 28.85/19.08 inference(symmetry,[status(thm)],[17560])).
% 28.85/19.08 tff(17562,plain,
% 28.85/19.08 ((~(f10(c2) = c2)) <=> (~(f7(f10(c2)) = f10(c2)))),
% 28.85/19.08 inference(monotonicity,[status(thm)],[17561])).
% 28.85/19.08 tff(17563,plain,
% 28.85/19.08 (~(f7(f10(c2)) = f10(c2))),
% 28.85/19.08 inference(modus_ponens,[status(thm)],[89, 17562])).
% 28.85/19.08 tff(17564,plain,
% 28.85/19.08 (f5(f10(c2)) = f5(c1)),
% 28.85/19.08 inference(monotonicity,[status(thm)],[94])).
% 28.85/19.08 tff(17565,plain,
% 28.85/19.08 ((c2 = f5(f10(c2))) <=> (c2 = f5(c1))),
% 28.85/19.08 inference(monotonicity,[status(thm)],[17564])).
% 28.85/19.08 tff(17566,plain,
% 28.85/19.08 ((c2 = f5(c1)) <=> (c2 = f5(f10(c2)))),
% 28.85/19.08 inference(symmetry,[status(thm)],[17565])).
% 28.85/19.08 tff(17567,plain,
% 28.85/19.08 ((f5(c1) = c2) <=> (c2 = f5(f10(c2)))),
% 28.85/19.08 inference(transitivity,[status(thm)],[155, 17566])).
% 28.85/19.08 tff(17568,plain,
% 28.85/19.08 (big_f(f10(c2), f10(c2)) <=> big_f(c1, c1)),
% 28.85/19.08 inference(symmetry,[status(thm)],[13717])).
% 28.85/19.08 tff(17569,plain,
% 28.85/19.08 (big_f(f7(c2), f10(c2)) <=> big_f(f10(c2), f10(c2))),
% 28.85/19.08 inference(monotonicity,[status(thm)],[12101])).
% 28.85/19.08 tff(17570,plain,
% 28.85/19.08 (big_f(f7(c2), c1) <=> big_f(f7(c2), f10(c2))),
% 28.85/19.08 inference(monotonicity,[status(thm)],[99])).
% 28.85/19.08 tff(17571,plain,
% 28.85/19.08 (big_f(f7(c2), c1) <=> big_f(c1, c1)),
% 28.85/19.08 inference(transitivity,[status(thm)],[17570, 17569, 17568])).
% 28.85/19.08 tff(17572,plain,
% 28.85/19.08 ((~big_f(f7(c2), c1)) <=> (~big_f(c1, c1))),
% 28.85/19.08 inference(monotonicity,[status(thm)],[17571])).
% 28.85/19.08 tff(17573,plain,
% 28.85/19.08 (big_f(f7(f7(c1)), f7(c1))),
% 28.85/19.08 inference(modus_ponens,[status(thm)],[2865, 17551])).
% 28.85/19.08 tff(17574,plain,
% 28.85/19.08 (~big_f(f7(c1), c1)),
% 28.85/19.08 inference(unit_resolution,[status(thm)],[15738, 2, 120])).
% 28.85/19.08 tff(17575,plain,
% 28.85/19.08 (~big_f(f7(c1), f5(c1))),
% 28.85/19.08 inference(unit_resolution,[status(thm)],[8430, 17574, 120, 121])).
% 28.85/19.08 tff(17576,plain,
% 28.85/19.08 (~(c2 = f8(c2))),
% 28.85/19.08 inference(unit_resolution,[status(thm)],[12015, 15473, 115, 89, 17575])).
% 28.85/19.08 tff(17577,plain,
% 28.85/19.08 (f8(f7(f4(c4))) = f8(c2)),
% 28.85/19.08 inference(monotonicity,[status(thm)],[17387])).
% 28.85/19.08 tff(17578,plain,
% 28.85/19.08 ((c2 = f8(f7(f4(c4)))) <=> (c2 = f8(c2))),
% 28.85/19.08 inference(monotonicity,[status(thm)],[17577])).
% 28.85/19.08 tff(17579,plain,
% 28.85/19.08 ((f8(f7(f4(c4))) = c2) <=> (c2 = f8(c2))),
% 28.85/19.08 inference(transitivity,[status(thm)],[105, 17578])).
% 28.85/19.08 tff(17580,plain,
% 28.85/19.08 (c2 = f8(c2)),
% 28.85/19.08 inference(modus_ponens,[status(thm)],[13856, 17579])).
% 28.85/19.08 tff(17581,plain,
% 28.85/19.08 ($false),
% 28.85/19.08 inference(unit_resolution,[status(thm)],[12290, 17580])).
% 28.85/19.08 tff(17582,plain,((~(f8(f7(f4(c4))) = c2)) | (c2 = f8(c2)) | (~(f7(c1) = c2)) | (~(f4(c4) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.85/19.08 tff(17583,plain,
% 28.85/19.08 (~(f8(f7(f4(c4))) = c2)),
% 28.85/19.08 inference(unit_resolution,[status(thm)],[17582, 17576, 120, 11752])).
% 28.85/19.08 tff(17584,plain,
% 28.85/19.08 (f8(f7(f4(c4))) = c1),
% 28.85/19.08 inference(unit_resolution,[status(thm)],[13371, 17583])).
% 28.85/19.08 tff(17585,plain,
% 28.85/19.08 (c2 = f7(f4(c4))),
% 28.85/19.08 inference(transitivity,[status(thm)],[2778, 16244])).
% 28.85/19.08 tff(17586,plain,
% 28.85/19.08 (f8(c2) = f8(f7(f4(c4)))),
% 28.85/19.08 inference(monotonicity,[status(thm)],[17585])).
% 28.85/19.08 tff(17587,plain,
% 28.85/19.08 (big_f(f7(f10(c2)), f10(c2)) <=> big_f(c2, f10(c2))),
% 28.85/19.08 inference(monotonicity,[status(thm)],[17554])).
% 28.85/19.08 tff(17588,plain,
% 28.85/19.08 (big_f(c2, f10(c2)) <=> big_f(f7(f10(c2)), f10(c2))),
% 28.85/19.08 inference(symmetry,[status(thm)],[17587])).
% 28.85/19.08 tff(17589,plain,
% 28.85/19.08 ((~big_f(c2, f10(c2))) <=> (~big_f(f7(f10(c2)), f10(c2)))),
% 28.85/19.08 inference(monotonicity,[status(thm)],[17588])).
% 28.85/19.08 tff(17590,plain,
% 28.85/19.08 (~big_f(f7(f10(c2)), f10(c2))),
% 28.85/19.08 inference(modus_ponens,[status(thm)],[15473, 17589])).
% 28.85/19.08 tff(17591,plain,
% 28.85/19.08 (f3(c1, c1) = f3(f10(c2), f10(c2))),
% 28.85/19.08 inference(monotonicity,[status(thm)],[99, 99])).
% 28.85/19.08 tff(17592,plain,
% 28.85/19.08 (big_f(f3(c1, c1), c1) <=> big_f(f3(f10(c2), f10(c2)), f10(c2))),
% 28.85/19.08 inference(monotonicity,[status(thm)],[17591, 99])).
% 28.85/19.08 tff(17593,plain,
% 28.85/19.08 (big_f(f10(c2), f10(c2)) <=> big_f(c1, f10(c2))),
% 28.85/19.08 inference(monotonicity,[status(thm)],[94])).
% 28.85/19.08 tff(17594,plain,
% 28.85/19.08 (big_f(c1, f10(c2)) <=> big_f(f10(c2), f10(c2))),
% 28.85/19.08 inference(symmetry,[status(thm)],[17593])).
% 28.85/19.08 tff(17595,plain,
% 28.85/19.08 (big_f(c1, f10(c2)) <=> big_f(c1, c1)),
% 28.85/19.08 inference(transitivity,[status(thm)],[17594, 17568])).
% 28.85/19.08 tff(17596,plain,
% 28.85/19.08 (big_f(c1, f10(c2))),
% 28.85/19.08 inference(unit_resolution,[status(thm)],[12084, 2, 115, 89, 692, 16])).
% 28.85/19.08 tff(17597,plain,
% 28.85/19.08 (big_f(c1, c1)),
% 28.85/19.08 inference(modus_ponens,[status(thm)],[17596, 17595])).
% 28.85/19.08 tff(17598,plain,
% 28.85/19.08 ((c1 = f2(c2)) <=> (f10(c2) = f2(c2))),
% 28.85/19.08 inference(monotonicity,[status(thm)],[12231])).
% 28.85/19.08 tff(17599,plain,
% 28.85/19.08 ((f10(c2) = f2(c2)) <=> (c1 = f2(c2))),
% 28.85/19.08 inference(symmetry,[status(thm)],[17598])).
% 28.85/19.08 tff(17600,plain,
% 28.85/19.08 ((f2(c2) = f10(c2)) <=> (f10(c2) = f2(c2))),
% 28.85/19.08 inference(commutativity,[status(thm)],[])).
% 28.85/19.08 tff(17601,plain,
% 28.85/19.08 (big_f(c1, f7(c1))),
% 28.85/19.08 inference(modus_ponens,[status(thm)],[2865, 11804])).
% 28.85/19.08 tff(17602,plain,
% 28.85/19.08 (~(c1 = c3)),
% 28.85/19.08 inference(unit_resolution,[status(thm)],[11952, 14326, 121, 115, 17601, 4932])).
% 28.85/19.08 tff(17603,plain,
% 28.85/19.08 (~(c3 = c1)),
% 28.85/19.08 inference(unit_resolution,[status(thm)],[175, 17602])).
% 28.85/19.08 tff(17604,plain,
% 28.85/19.08 (c3 = c2),
% 28.85/19.08 inference(unit_resolution,[status(thm)],[180, 17603])).
% 28.85/19.08 tff(17605,plain,
% 28.85/19.08 (f2(c3) = f2(c2)),
% 28.85/19.08 inference(monotonicity,[status(thm)],[17604])).
% 28.85/19.08 tff(17606,plain,
% 28.85/19.08 ((f2(c3) = c1) <=> (f2(c2) = f10(c2))),
% 28.85/19.08 inference(monotonicity,[status(thm)],[17605, 12231])).
% 28.85/19.08 tff(17607,plain,
% 28.85/19.08 ((f2(c3) = c1) <=> (f10(c2) = f2(c2))),
% 28.85/19.08 inference(transitivity,[status(thm)],[17606, 17600])).
% 28.85/19.08 tff(17608,plain,
% 28.85/19.08 ((f2(c3) = c1) <=> (c1 = f2(c2))),
% 28.85/19.08 inference(transitivity,[status(thm)],[17607, 17599])).
% 28.85/19.08 tff(17609,plain,
% 28.85/19.08 (big_f(c2, c1) <=> big_f(c2, f10(c2))),
% 28.85/19.08 inference(monotonicity,[status(thm)],[12231])).
% 28.85/19.08 tff(17610,plain,
% 28.85/19.08 ((~big_f(c2, c1)) <=> (~big_f(c2, f10(c2)))),
% 28.85/19.08 inference(monotonicity,[status(thm)],[17609])).
% 28.85/19.08 tff(17611,plain,
% 28.85/19.08 (~big_f(c2, f10(c2))),
% 28.85/19.08 inference(modus_ponens,[status(thm)],[2, 17610])).
% 28.85/19.08 tff(17612,plain,
% 28.85/19.08 ((f2(c3) = c1) <=> (f2(c2) = f10(c2))),
% 28.85/19.08 inference(monotonicity,[status(thm)],[1221, 12231])).
% 28.85/19.08 tff(17613,plain,
% 28.85/19.08 ((f2(c3) = c1) <=> (f10(c2) = f2(c2))),
% 28.85/19.08 inference(transitivity,[status(thm)],[17612, 17600])).
% 28.85/19.08 tff(17614,plain,
% 28.85/19.08 (f3(c2, f10(c2)) = f3(c2, c1)),
% 28.85/19.08 inference(monotonicity,[status(thm)],[11819])).
% 28.85/19.08 tff(17615,plain,
% 28.85/19.08 (f3(c2, f10(c2)) = c1),
% 28.85/19.08 inference(transitivity,[status(thm)],[17614, 3125, 953])).
% 28.85/19.08 tff(17616,plain,
% 28.85/19.08 (big_f(f3(c2, f10(c2)), c2) <=> big_f(c1, c2)),
% 28.85/19.08 inference(monotonicity,[status(thm)],[17615])).
% 28.85/19.08 tff(17617,plain,
% 28.85/19.08 (big_f(c1, c2) <=> big_f(f3(c2, f10(c2)), c2)),
% 28.85/19.08 inference(symmetry,[status(thm)],[17616])).
% 28.85/19.08 tff(17618,plain,
% 28.85/19.08 (big_f(f3(c2, f10(c2)), c2)),
% 28.85/19.08 inference(modus_ponens,[status(thm)],[2865, 17617])).
% 28.85/19.08 tff(17619,plain,
% 28.85/19.08 (f3(c2, f10(c2)) = f10(c2)),
% 28.85/19.08 inference(transitivity,[status(thm)],[17614, 3125, 953, 12231])).
% 28.85/19.08 tff(17620,plain,
% 28.85/19.08 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (c2 = c4) | (~(f3(c2, f10(c2)) = f10(c2))) | (~big_f(f3(c2, f10(c2)), c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (c2 = c4) | (~(f3(c2, f10(c2)) = f10(c2))) | (~big_f(f3(c2, f10(c2)), c2)))),
% 28.85/19.08 inference(rewrite,[status(thm)],[])).
% 28.85/19.08 tff(17621,plain,
% 28.85/19.08 (((~(c2 = c3)) | (~(c2 = f2(c2))) | (c2 = c4) | (~(f3(c2, f10(c2)) = f10(c2))) | (~big_f(f3(c2, f10(c2)), c2)) | big_f(c2, c2)) <=> ((~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (c2 = c4) | (~(f3(c2, f10(c2)) = f10(c2))) | (~big_f(f3(c2, f10(c2)), c2)))),
% 28.85/19.08 inference(rewrite,[status(thm)],[])).
% 28.85/19.08 tff(17622,plain,
% 28.85/19.08 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | (c2 = c4) | (~(f3(c2, f10(c2)) = f10(c2))) | (~big_f(f3(c2, f10(c2)), c2)) | big_f(c2, c2))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (c2 = c4) | (~(f3(c2, f10(c2)) = f10(c2))) | (~big_f(f3(c2, f10(c2)), c2))))),
% 28.85/19.08 inference(monotonicity,[status(thm)],[17621])).
% 28.85/19.08 tff(17623,plain,
% 28.85/19.08 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | (c2 = c4) | (~(f3(c2, f10(c2)) = f10(c2))) | (~big_f(f3(c2, f10(c2)), c2)) | big_f(c2, c2))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (c2 = c4) | (~(f3(c2, f10(c2)) = f10(c2))) | (~big_f(f3(c2, f10(c2)), c2)))),
% 28.85/19.08 inference(transitivity,[status(thm)],[17622, 17620])).
% 28.85/19.08 tff(17624,plain,
% 28.85/19.08 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | (c2 = c4) | (~(f3(c2, f10(c2)) = f10(c2))) | (~big_f(f3(c2, f10(c2)), c2)) | big_f(c2, c2))),
% 28.85/19.08 inference(quant_inst,[status(thm)],[])).
% 28.85/19.08 tff(17625,plain,
% 28.85/19.08 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (c2 = c4) | (~(f3(c2, f10(c2)) = f10(c2))) | (~big_f(f3(c2, f10(c2)), c2))),
% 28.85/19.08 inference(modus_ponens,[status(thm)],[17624, 17623])).
% 28.85/19.08 tff(17626,plain,
% 28.85/19.08 ((~(c2 = f2(c2))) | (~(f3(c2, f10(c2)) = f10(c2))) | (~big_f(f3(c2, f10(c2)), c2))),
% 28.85/19.08 inference(unit_resolution,[status(thm)],[17625, 1398, 873, 121, 1335])).
% 28.85/19.08 tff(17627,plain,
% 28.85/19.08 (~(c2 = f2(c2))),
% 28.85/19.08 inference(unit_resolution,[status(thm)],[17626, 17619, 17618])).
% 28.85/19.08 tff(17628,plain,
% 28.85/19.08 (~(f2(c3) = c2)),
% 28.85/19.08 inference(unit_resolution,[status(thm)],[4867, 17627, 67])).
% 28.85/19.08 tff(17629,plain,
% 28.85/19.08 (f2(c3) = c1),
% 28.85/19.08 inference(unit_resolution,[status(thm)],[1273, 17628])).
% 28.85/19.08 tff(17630,plain,
% 28.85/19.08 (f10(c2) = f2(c2)),
% 28.85/19.08 inference(modus_ponens,[status(thm)],[17629, 17613])).
% 28.85/19.08 tff(17631,plain,
% 28.85/19.08 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (c2 = c4) | big_f(c2, f10(c2)) | (~(f10(c2) = f2(c2))) | (~(f3(c2, f10(c2)) = f10(c2))) | (~big_f(f3(c2, f10(c2)), c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (~(c2 = c3)) | (c2 = c4) | big_f(c2, f10(c2)) | (~(f10(c2) = f2(c2))) | (~(f3(c2, f10(c2)) = f10(c2))) | (~big_f(f3(c2, f10(c2)), c2)))),
% 28.85/19.08 inference(rewrite,[status(thm)],[])).
% 28.85/19.08 tff(17632,plain,
% 28.85/19.08 (((~(c2 = c3)) | (~(f10(c2) = f2(c2))) | (c2 = c4) | (~(f3(c2, f10(c2)) = f10(c2))) | (~big_f(f3(c2, f10(c2)), c2)) | big_f(c2, f10(c2))) <=> ((~(c2 = c3)) | (c2 = c4) | big_f(c2, f10(c2)) | (~(f10(c2) = f2(c2))) | (~(f3(c2, f10(c2)) = f10(c2))) | (~big_f(f3(c2, f10(c2)), c2)))),
% 28.85/19.08 inference(rewrite,[status(thm)],[])).
% 28.85/19.08 tff(17633,plain,
% 28.85/19.08 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(f10(c2) = f2(c2))) | (c2 = c4) | (~(f3(c2, f10(c2)) = f10(c2))) | (~big_f(f3(c2, f10(c2)), c2)) | big_f(c2, f10(c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (c2 = c4) | big_f(c2, f10(c2)) | (~(f10(c2) = f2(c2))) | (~(f3(c2, f10(c2)) = f10(c2))) | (~big_f(f3(c2, f10(c2)), c2))))),
% 28.85/19.08 inference(monotonicity,[status(thm)],[17632])).
% 28.85/19.08 tff(17634,plain,
% 28.85/19.08 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(f10(c2) = f2(c2))) | (c2 = c4) | (~(f3(c2, f10(c2)) = f10(c2))) | (~big_f(f3(c2, f10(c2)), c2)) | big_f(c2, f10(c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (~(c2 = c3)) | (c2 = c4) | big_f(c2, f10(c2)) | (~(f10(c2) = f2(c2))) | (~(f3(c2, f10(c2)) = f10(c2))) | (~big_f(f3(c2, f10(c2)), c2)))),
% 28.85/19.08 inference(transitivity,[status(thm)],[17633, 17631])).
% 28.85/19.08 tff(17635,plain,
% 28.85/19.08 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(f10(c2) = f2(c2))) | (c2 = c4) | (~(f3(c2, f10(c2)) = f10(c2))) | (~big_f(f3(c2, f10(c2)), c2)) | big_f(c2, f10(c2)))),
% 28.85/19.08 inference(quant_inst,[status(thm)],[])).
% 28.85/19.08 tff(17636,plain,
% 28.85/19.08 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (~(c2 = c3)) | (c2 = c4) | big_f(c2, f10(c2)) | (~(f10(c2) = f2(c2))) | (~(f3(c2, f10(c2)) = f10(c2))) | (~big_f(f3(c2, f10(c2)), c2))),
% 28.85/19.08 inference(modus_ponens,[status(thm)],[17635, 17634])).
% 28.85/19.08 tff(17637,plain,
% 28.85/19.08 ((~(f10(c2) = f2(c2))) | (~(f3(c2, f10(c2)) = f10(c2))) | (~big_f(f3(c2, f10(c2)), c2))),
% 28.85/19.08 inference(unit_resolution,[status(thm)],[17636, 1398, 873, 1335, 15517])).
% 28.85/19.08 tff(17638,plain,
% 28.85/19.08 (~(f10(c2) = f2(c2))),
% 28.85/19.08 inference(unit_resolution,[status(thm)],[17637, 17619, 17618])).
% 28.85/19.08 tff(17639,plain,
% 28.85/19.08 ($false),
% 28.85/19.08 inference(unit_resolution,[status(thm)],[17638, 17630])).
% 28.85/19.08 tff(17640,plain,((~(f3(f7(c1), c1) = c1)) | (~(f10(c2) = c1)) | (~(c3 = c2)) | (c2 = c4) | big_f(c2, f10(c2)) | big_f(c2, c2) | (~big_f(c1, c2)) | (~(f7(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.85/19.08 tff(17641,plain,
% 28.85/19.08 (~(f3(f7(c1), c1) = c1)),
% 28.85/19.08 inference(unit_resolution,[status(thm)],[17640, 17604, 11819, 873, 17611, 121, 2865, 120])).
% 28.85/19.08 tff(17642,plain,
% 28.85/19.08 (c2 = c3),
% 28.85/19.08 inference(modus_ponens,[status(thm)],[17604, 78])).
% 28.85/19.08 tff(17643,plain,
% 28.85/19.08 (big_f(f3(f7(c1), c1), f7(c1)) <=> big_f(f3(c2, c1), c2)),
% 28.85/19.08 inference(monotonicity,[status(thm)],[13635, 120])).
% 28.85/19.08 tff(17644,plain,
% 28.85/19.08 (big_f(f3(c2, c1), c2) <=> big_f(f3(f7(c1), c1), f7(c1))),
% 28.85/19.08 inference(symmetry,[status(thm)],[17643])).
% 28.85/19.08 tff(17645,plain,
% 28.85/19.08 (f3(f7(c1), c1) = c2),
% 28.85/19.08 inference(unit_resolution,[status(thm)],[918, 17641])).
% 28.85/19.08 tff(17646,plain,
% 28.85/19.08 (f3(c2, c1) = c2),
% 28.85/19.08 inference(transitivity,[status(thm)],[2779, 17645])).
% 28.85/19.08 tff(17647,plain,
% 28.85/19.08 (big_f(f3(c2, c1), c2) <=> big_f(c2, c2)),
% 28.85/19.08 inference(monotonicity,[status(thm)],[17646])).
% 28.85/19.08 tff(17648,plain,
% 28.85/19.08 (big_f(c2, c2) <=> big_f(f3(c2, c1), c2)),
% 28.85/19.08 inference(symmetry,[status(thm)],[17647])).
% 28.85/19.08 tff(17649,plain,
% 28.85/19.08 (big_f(c2, c2) <=> big_f(f3(f7(c1), c1), f7(c1))),
% 28.85/19.08 inference(transitivity,[status(thm)],[17648, 17644])).
% 28.85/19.08 tff(17650,plain,
% 28.85/19.08 ((~big_f(c2, c2)) <=> (~big_f(f3(f7(c1), c1), f7(c1)))),
% 28.85/19.08 inference(monotonicity,[status(thm)],[17649])).
% 28.85/19.08 tff(17651,plain,
% 28.85/19.08 (~big_f(f3(f7(c1), c1), f7(c1))),
% 28.85/19.08 inference(modus_ponens,[status(thm)],[121, 17650])).
% 28.85/19.08 tff(17652,plain,
% 28.85/19.08 (~(c2 = f2(c2))),
% 28.85/19.08 inference(unit_resolution,[status(thm)],[2861, 17651, 121, 17642, 14326, 17641])).
% 28.85/19.08 tff(17653,plain,
% 28.85/19.08 (~(f2(c3) = c2)),
% 28.85/19.08 inference(unit_resolution,[status(thm)],[4867, 17652, 17604])).
% 28.85/19.08 tff(17654,plain,
% 28.85/19.08 (f2(c3) = c1),
% 28.85/19.08 inference(unit_resolution,[status(thm)],[1273, 17653])).
% 28.85/19.08 tff(17655,plain,
% 28.85/19.08 (c1 = f2(c2)),
% 28.85/19.08 inference(modus_ponens,[status(thm)],[17654, 17608])).
% 28.85/19.08 tff(17656,plain,
% 28.85/19.08 (f3(f10(c1), c1) = f3(c2, c1)),
% 28.85/19.08 inference(monotonicity,[status(thm)],[16])).
% 28.85/19.08 tff(17657,plain,
% 28.85/19.08 ((f3(f10(c1), c1) = c1) <=> (f3(c2, c1) = c1)),
% 28.85/19.08 inference(monotonicity,[status(thm)],[17656])).
% 28.85/19.08 tff(17658,plain,
% 28.85/19.08 ((f3(c2, c1) = c1) <=> (f3(f10(c1), c1) = c1)),
% 28.85/19.08 inference(symmetry,[status(thm)],[17657])).
% 28.85/19.08 tff(17659,plain,
% 28.85/19.08 ((f3(f7(c1), c1) = c1) <=> (f3(f10(c1), c1) = c1)),
% 28.85/19.08 inference(transitivity,[status(thm)],[13636, 17658])).
% 28.85/19.08 tff(17660,plain,
% 28.85/19.08 ((~(f3(f7(c1), c1) = c1)) <=> (~(f3(f10(c1), c1) = c1))),
% 28.85/19.08 inference(monotonicity,[status(thm)],[17659])).
% 28.85/19.08 tff(17661,plain,
% 28.85/19.08 (~(f3(f10(c1), c1) = c1)),
% 28.85/19.08 inference(modus_ponens,[status(thm)],[17641, 17660])).
% 28.85/19.08 tff(17662,plain,
% 28.85/19.08 ((~(c2 = c4)) <=> (~(f10(c1) = c4))),
% 28.85/19.08 inference(monotonicity,[status(thm)],[1034])).
% 28.85/19.08 tff(17663,plain,
% 28.85/19.08 (~(f10(c1) = c4)),
% 28.85/19.08 inference(modus_ponens,[status(thm)],[873, 17662])).
% 28.85/19.08 tff(17664,plain,
% 28.85/19.08 (big_f(f3(f10(c1), c1), f10(c1)) <=> big_f(f3(c2, c1), c2)),
% 28.85/19.08 inference(monotonicity,[status(thm)],[17656, 16])).
% 28.85/19.08 tff(17665,plain,
% 28.85/19.08 (big_f(f3(c2, c1), c2) <=> big_f(f3(f10(c1), c1), f10(c1))),
% 28.85/19.08 inference(symmetry,[status(thm)],[17664])).
% 28.85/19.08 tff(17666,plain,
% 28.85/19.08 (big_f(c2, c2) <=> big_f(f3(f10(c1), c1), f10(c1))),
% 28.85/19.08 inference(transitivity,[status(thm)],[17648, 17665])).
% 28.85/19.08 tff(17667,plain,
% 28.85/19.08 ((~big_f(c2, c2)) <=> (~big_f(f3(f10(c1), c1), f10(c1)))),
% 28.85/19.08 inference(monotonicity,[status(thm)],[17666])).
% 28.85/19.08 tff(17668,plain,
% 28.85/19.08 (~big_f(f3(f10(c1), c1), f10(c1))),
% 28.85/19.08 inference(modus_ponens,[status(thm)],[121, 17667])).
% 28.85/19.08 tff(17669,plain,
% 28.85/19.08 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c2 = c3)) | (f10(c1) = c4) | big_f(c2, c1) | (~(c1 = f2(c2))) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (~(c2 = c3)) | (f10(c1) = c4) | big_f(c2, c1) | (~(c1 = f2(c2))) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1)))),
% 28.85/19.08 inference(rewrite,[status(thm)],[])).
% 28.85/19.08 tff(17670,plain,
% 28.85/19.08 (((~(c2 = c3)) | (~(c1 = f2(c2))) | (f10(c1) = c4) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1)) | big_f(c2, c1)) <=> ((~(c2 = c3)) | (f10(c1) = c4) | big_f(c2, c1) | (~(c1 = f2(c2))) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1)))),
% 28.85/19.08 inference(rewrite,[status(thm)],[])).
% 28.85/19.08 tff(17671,plain,
% 28.85/19.08 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c1 = f2(c2))) | (f10(c1) = c4) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1)) | big_f(c2, c1))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c2 = c3)) | (f10(c1) = c4) | big_f(c2, c1) | (~(c1 = f2(c2))) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1))))),
% 28.85/19.08 inference(monotonicity,[status(thm)],[17670])).
% 28.85/19.08 tff(17672,plain,
% 28.85/19.08 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c1 = f2(c2))) | (f10(c1) = c4) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1)) | big_f(c2, c1))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (~(c2 = c3)) | (f10(c1) = c4) | big_f(c2, c1) | (~(c1 = f2(c2))) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1)))),
% 28.85/19.08 inference(transitivity,[status(thm)],[17671, 17669])).
% 28.85/19.08 tff(17673,plain,
% 28.85/19.08 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c1 = f2(c2))) | (f10(c1) = c4) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1)) | big_f(c2, c1))),
% 28.85/19.08 inference(quant_inst,[status(thm)],[])).
% 28.85/19.08 tff(17674,plain,
% 28.85/19.08 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (~(c2 = c3)) | (f10(c1) = c4) | big_f(c2, c1) | (~(c1 = f2(c2))) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1))),
% 28.85/19.08 inference(modus_ponens,[status(thm)],[17673, 17672])).
% 28.85/19.08 tff(17675,plain,
% 28.85/19.08 ((~(c2 = c3)) | (f10(c1) = c4) | big_f(c2, c1) | (~(c1 = f2(c2))) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1))),
% 28.85/19.08 inference(unit_resolution,[status(thm)],[17674, 1459])).
% 28.85/19.08 tff(17676,plain,
% 28.85/19.08 (~(c1 = f2(c2))),
% 28.85/19.08 inference(unit_resolution,[status(thm)],[17675, 17668, 17642, 2, 17663, 17661])).
% 28.85/19.08 tff(17677,plain,
% 28.85/19.08 ($false),
% 28.85/19.08 inference(unit_resolution,[status(thm)],[17676, 17655])).
% 28.85/19.08 tff(17678,plain,((c2 = c4) | (~(f10(c2) = c1)) | big_f(c2, c2) | big_f(c2, c1) | (~(f10(c1) = c2)) | (~big_f(c1, c2)) | (f7(c1) = c1) | (~big_f(c1, c1))), inference(lemma,lemma(discharge,[]))).
% 28.85/19.08 tff(17679,plain,
% 28.85/19.08 (c2 = c4),
% 28.85/19.08 inference(unit_resolution,[status(thm)],[17678, 2, 121, 94, 16, 2865, 115, 17597])).
% 28.85/19.08 tff(17680,plain,
% 28.85/19.08 (c4 = c2),
% 28.85/19.08 inference(symmetry,[status(thm)],[17679])).
% 28.85/19.08 tff(17681,plain,
% 28.85/19.08 ((f10(c2) = c4) <=> (f10(c2) = c2)),
% 28.85/19.08 inference(monotonicity,[status(thm)],[17680])).
% 28.85/19.08 tff(17682,plain,
% 28.85/19.08 ((f10(c2) = c2) <=> (f10(c2) = c4)),
% 28.85/19.08 inference(symmetry,[status(thm)],[17681])).
% 28.85/19.08 tff(17683,plain,
% 28.85/19.08 ((f10(c2) = c2) <=> (c1 = c4)),
% 28.85/19.08 inference(transitivity,[status(thm)],[17682, 15385])).
% 28.85/19.08 tff(17684,plain,
% 28.85/19.08 ((~(f10(c2) = c2)) <=> (~(c1 = c4))),
% 28.85/19.08 inference(monotonicity,[status(thm)],[17683])).
% 28.85/19.08 tff(17685,plain,
% 28.85/19.08 (~(c1 = c4)),
% 28.85/19.08 inference(modus_ponens,[status(thm)],[89, 17684])).
% 28.85/19.08 tff(17686,plain,
% 28.85/19.08 ((f8(c1) = c3) <=> (f8(c1) = c1)),
% 28.85/19.08 inference(monotonicity,[status(thm)],[172])).
% 28.85/19.08 tff(17687,plain,
% 28.85/19.08 ((f8(c1) = c1) <=> (f8(c1) = c3)),
% 28.85/19.08 inference(symmetry,[status(thm)],[17686])).
% 28.85/19.08 tff(17688,plain,
% 28.85/19.08 ((c2 = f8(f10(c2))) <=> (c2 = f8(c1))),
% 28.85/19.08 inference(monotonicity,[status(thm)],[15293])).
% 28.85/19.08 tff(17689,plain,
% 28.85/19.08 ((c2 = f8(f10(c2))) <=> (f8(c1) = c2)),
% 28.85/19.08 inference(transitivity,[status(thm)],[17688, 2782])).
% 28.85/19.08 tff(17690,plain,
% 28.85/19.08 ((~(c2 = f8(f10(c2)))) <=> (~(f8(c1) = c2))),
% 28.85/19.08 inference(monotonicity,[status(thm)],[17689])).
% 28.85/19.08 tff(17691,plain,
% 28.85/19.08 ((f10(f10(c2)) = f10(c2)) <=> (f10(f10(c2)) = c1)),
% 28.85/19.08 inference(monotonicity,[status(thm)],[94])).
% 28.85/19.08 tff(17692,plain,
% 28.85/19.08 ((f10(f10(c2)) = c1) <=> (f10(f10(c2)) = f10(c2))),
% 28.85/19.08 inference(symmetry,[status(thm)],[17691])).
% 28.85/19.08 tff(17693,plain,
% 28.85/19.08 ((f10(f10(c2)) = c1) <=> (f10(c1) = c1)),
% 28.85/19.08 inference(monotonicity,[status(thm)],[15299])).
% 28.85/19.08 tff(17694,plain,
% 28.85/19.08 ((f10(c1) = c1) <=> (f10(f10(c2)) = c1)),
% 28.85/19.08 inference(symmetry,[status(thm)],[17693])).
% 28.85/19.08 tff(17695,plain,
% 28.85/19.08 ((f10(c1) = c1) <=> (f10(f10(c2)) = f10(c2))),
% 28.85/19.08 inference(transitivity,[status(thm)],[17694, 17692])).
% 28.85/19.08 tff(17696,plain,
% 28.85/19.08 ((~(f10(c1) = c1)) <=> (~(f10(f10(c2)) = f10(c2)))),
% 28.85/19.08 inference(monotonicity,[status(thm)],[17695])).
% 28.85/19.08 tff(17697,plain,
% 28.85/19.08 (~big_f(f7(c1), f5(c1))),
% 28.85/19.08 inference(unit_resolution,[status(thm)],[8430, 285, 121, 120])).
% 28.85/19.08 tff(17698,plain,
% 28.85/19.08 (big_f(f7(c2), c1)),
% 28.85/19.08 inference(modus_ponens,[status(thm)],[4932, 12091])).
% 28.85/19.08 tff(17699,plain,
% 28.85/19.08 (f8(f7(c1)) = f8(f7(f4(c4)))),
% 28.85/19.08 inference(monotonicity,[status(thm)],[16244])).
% 28.85/19.08 tff(17700,plain,
% 28.85/19.08 (f8(f7(f4(c4))) = f8(f7(c1))),
% 28.85/19.08 inference(symmetry,[status(thm)],[17699])).
% 28.85/19.08 tff(17701,plain,
% 28.85/19.08 ((c2 = f8(f7(f4(c4)))) <=> (f7(c1) = f8(f7(c1)))),
% 28.85/19.08 inference(monotonicity,[status(thm)],[2778, 17700])).
% 28.85/19.08 tff(17702,plain,
% 28.85/19.08 ((f7(c1) = f8(f7(c1))) <=> (c2 = f8(f7(f4(c4))))),
% 28.85/19.08 inference(symmetry,[status(thm)],[17701])).
% 28.85/19.08 tff(17703,plain,
% 28.85/19.08 (f8(c2) = f8(f7(c1))),
% 28.85/19.08 inference(monotonicity,[status(thm)],[2778])).
% 28.85/19.08 tff(17704,plain,
% 28.85/19.08 ((c2 = f8(c2)) <=> (f7(c1) = f8(f7(c1)))),
% 28.85/19.08 inference(monotonicity,[status(thm)],[2778, 17703])).
% 28.85/19.08 tff(17705,plain,
% 28.85/19.08 ((c2 = f8(c2)) <=> (f8(f7(f4(c4))) = c2)),
% 28.85/19.08 inference(transitivity,[status(thm)],[17704, 17702, 106])).
% 28.85/19.08 tff(17706,plain,
% 28.85/19.08 ((~(c2 = f8(c2))) <=> (~(f8(f7(f4(c4))) = c2))),
% 28.85/19.08 inference(monotonicity,[status(thm)],[17705])).
% 28.85/19.08 tff(17707,plain,
% 28.85/19.08 (big_f(f7(c1), c1) <=> big_f(c2, f10(c2))),
% 28.85/19.08 inference(transitivity,[status(thm)],[247, 12069])).
% 28.85/19.08 tff(17708,plain,
% 28.85/19.08 ((~big_f(f7(c1), c1)) <=> (~big_f(c2, f10(c2)))),
% 28.85/19.08 inference(monotonicity,[status(thm)],[17707])).
% 28.85/19.08 tff(17709,plain,
% 28.85/19.08 (~big_f(c2, f10(c2))),
% 28.85/19.08 inference(modus_ponens,[status(thm)],[285, 17708])).
% 28.85/19.08 tff(17710,plain,
% 28.85/19.08 (~(c2 = f8(c2))),
% 28.85/19.08 inference(unit_resolution,[status(thm)],[12015, 17709, 89, 115, 17697])).
% 28.85/19.08 tff(17711,plain,
% 28.85/19.08 (~(f8(f7(f4(c4))) = c2)),
% 28.85/19.08 inference(modus_ponens,[status(thm)],[17710, 17706])).
% 28.85/19.08 tff(17712,plain,
% 28.85/19.08 (f8(f7(f4(c4))) = c1),
% 28.85/19.08 inference(unit_resolution,[status(thm)],[13371, 17711])).
% 28.85/19.08 tff(17713,plain,
% 28.85/19.08 ((f3(c1, c1) = c3) <=> (f3(c1, c1) = c1)),
% 28.85/19.08 inference(monotonicity,[status(thm)],[172])).
% 28.85/19.08 tff(17714,plain,
% 28.85/19.08 ((f3(c1, c1) = c1) <=> (f3(c1, c1) = c3)),
% 28.85/19.08 inference(symmetry,[status(thm)],[17713])).
% 28.85/19.08 tff(17715,plain,
% 28.85/19.08 (f8(f7(c1)) = c1),
% 28.85/19.08 inference(transitivity,[status(thm)],[17699, 16268])).
% 28.85/19.08 tff(17716,plain,
% 28.85/19.08 ((f3(c1, c1) = f8(f7(c1))) <=> (f3(c1, c1) = c1)),
% 28.85/19.08 inference(monotonicity,[status(thm)],[17715])).
% 28.85/19.08 tff(17717,plain,
% 28.85/19.08 ((f3(c1, c1) = f8(f7(c1))) <=> (f3(c1, c1) = c3)),
% 28.85/19.08 inference(transitivity,[status(thm)],[17716, 17714])).
% 28.85/19.08 tff(17718,plain,
% 28.85/19.08 (f10(f7(c1)) = c1),
% 28.85/19.08 inference(transitivity,[status(thm)],[12327, 11819])).
% 28.85/19.08 tff(17719,plain,
% 28.85/19.08 (big_f(f3(c1, c1), f10(f7(c1))) <=> big_f(f3(c1, c1), c1)),
% 28.85/19.08 inference(monotonicity,[status(thm)],[17718])).
% 28.85/19.08 tff(17720,plain,
% 28.85/19.08 (big_f(f3(c1, c1), c1) <=> big_f(f3(c1, c1), f10(f7(c1)))),
% 28.85/19.08 inference(symmetry,[status(thm)],[17719])).
% 28.85/19.08 tff(17721,plain,
% 28.85/19.08 (big_f(c2, c2) <=> big_f(f7(c1), c2)),
% 28.85/19.08 inference(monotonicity,[status(thm)],[2778])).
% 28.85/19.08 tff(17722,plain,
% 28.85/19.08 ((~big_f(c2, c2)) <=> (~big_f(f7(c1), c2))),
% 28.85/19.09 inference(monotonicity,[status(thm)],[17721])).
% 28.85/19.09 tff(17723,plain,
% 28.85/19.09 (~big_f(f7(c1), c2)),
% 28.85/19.09 inference(modus_ponens,[status(thm)],[121, 17722])).
% 28.85/19.09 tff(17724,plain,
% 28.85/19.09 (~(f9(c1, c1) = c1)),
% 28.85/19.09 inference(unit_resolution,[status(thm)],[10942, 3762, 115, 17723, 1727, 4932])).
% 28.85/19.09 tff(17725,plain,
% 28.85/19.09 ((c1 = f9(c1, c1)) <=> (f9(c1, c1) = c1)),
% 28.85/19.09 inference(commutativity,[status(thm)],[])).
% 28.85/19.09 tff(17726,plain,
% 28.85/19.09 (f9(f10(c2), f4(c4)) = f9(c1, c1)),
% 28.85/19.09 inference(monotonicity,[status(thm)],[11819, 11752])).
% 28.85/19.09 tff(17727,plain,
% 28.85/19.09 (f9(c1, c1) = f9(f10(c2), f4(c4))),
% 28.85/19.09 inference(symmetry,[status(thm)],[17726])).
% 28.85/19.09 tff(17728,plain,
% 28.85/19.09 (f9(c1, c1) = c2),
% 28.85/19.09 inference(transitivity,[status(thm)],[17727, 1498])).
% 28.85/19.09 tff(17729,plain,
% 28.85/19.09 (f7(f9(c1, c1)) = f7(c2)),
% 28.85/19.09 inference(monotonicity,[status(thm)],[17728])).
% 28.85/19.09 tff(17730,plain,
% 28.85/19.09 (f7(f9(c1, c1)) = c1),
% 28.85/19.09 inference(transitivity,[status(thm)],[17729, 22])).
% 28.85/19.09 tff(17731,plain,
% 28.85/19.09 (big_f(f7(f9(c1, c1)), f9(c1, c1)) <=> big_f(c1, f9(c1, c1))),
% 28.85/19.09 inference(monotonicity,[status(thm)],[17730])).
% 28.85/19.09 tff(17732,plain,
% 28.85/19.09 (big_f(c1, f9(c1, c1)) <=> big_f(f7(f9(c1, c1)), f9(c1, c1))),
% 28.85/19.09 inference(symmetry,[status(thm)],[17731])).
% 28.85/19.09 tff(17733,plain,
% 28.85/19.09 (c2 = f9(f10(c2), f4(c4))),
% 28.85/19.09 inference(symmetry,[status(thm)],[1498])).
% 28.85/19.09 tff(17734,plain,
% 28.85/19.09 (c2 = f9(c1, c1)),
% 28.85/19.09 inference(transitivity,[status(thm)],[17733, 17726])).
% 28.85/19.09 tff(17735,plain,
% 28.85/19.09 ((c2 = c3) <=> (f9(c1, c1) = c3)),
% 28.85/19.09 inference(monotonicity,[status(thm)],[17734])).
% 28.85/19.09 tff(17736,plain,
% 28.85/19.09 ((c3 = c2) <=> (f9(c1, c1) = c3)),
% 28.85/19.09 inference(transitivity,[status(thm)],[78, 17735])).
% 28.85/19.09 tff(17737,plain,
% 28.85/19.09 (big_f(f7(c2), c2) <=> big_f(f7(c2), f9(c1, c1))),
% 28.85/19.09 inference(monotonicity,[status(thm)],[17734])).
% 28.85/19.09 tff(17738,plain,
% 28.85/19.09 (big_f(f7(c2), f9(c1, c1)) <=> big_f(f7(c2), c2)),
% 28.85/19.09 inference(symmetry,[status(thm)],[17737])).
% 28.85/19.09 tff(17739,plain,
% 28.85/19.09 (f7(c2) = f7(f9(c1, c1))),
% 28.85/19.09 inference(symmetry,[status(thm)],[17729])).
% 28.85/19.09 tff(17740,plain,
% 28.85/19.09 (big_f(f7(c2), f9(c1, c1)) <=> big_f(f7(f9(c1, c1)), f9(c1, c1))),
% 28.85/19.09 inference(monotonicity,[status(thm)],[17739])).
% 28.85/19.09 tff(17741,plain,
% 28.85/19.09 (big_f(f7(f9(c1, c1)), f9(c1, c1)) <=> big_f(f7(c2), f9(c1, c1))),
% 28.85/19.09 inference(symmetry,[status(thm)],[17740])).
% 28.85/19.09 tff(17742,plain,
% 28.85/19.09 (big_f(c1, f9(c1, c1)) <=> big_f(f7(c2), c2)),
% 28.85/19.09 inference(transitivity,[status(thm)],[17732, 17741, 17738])).
% 28.85/19.09 tff(17743,plain,
% 28.85/19.09 ((~big_f(c1, f9(c1, c1))) <=> (~big_f(f7(c2), c2))),
% 28.85/19.09 inference(monotonicity,[status(thm)],[17742])).
% 28.85/19.09 tff(17744,plain,
% 28.85/19.09 (~big_f(f7(c2), c2)),
% 28.85/19.09 inference(modus_ponens,[status(thm)],[4686, 17743])).
% 28.85/19.09 tff(17745,plain,
% 28.85/19.09 (big_f(c1, c2) <=> big_f(c1, f9(c1, c1))),
% 28.85/19.09 inference(monotonicity,[status(thm)],[17734])).
% 28.85/19.09 tff(17746,plain,
% 28.85/19.09 (big_f(c1, f9(c1, c1))),
% 28.85/19.09 inference(modus_ponens,[status(thm)],[2865, 17745])).
% 28.85/19.09 tff(17747,plain,
% 28.85/19.09 ($false),
% 28.85/19.09 inference(unit_resolution,[status(thm)],[4686, 17746])).
% 28.85/19.09 tff(17748,plain,((~big_f(c1, c2)) | big_f(c1, f9(c1, c1)) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.85/19.09 tff(17749,plain,
% 28.85/19.09 (~big_f(c1, c2)),
% 28.85/19.09 inference(unit_resolution,[status(thm)],[17748, 4686, 1498, 11752, 11819])).
% 28.85/19.09 tff(17750,plain,
% 28.85/19.09 (big_f(f7(c1), f9(c1, c1)) <=> big_f(f7(c1), c2)),
% 28.85/19.09 inference(monotonicity,[status(thm)],[17728])).
% 28.85/19.09 tff(17751,plain,
% 28.85/19.09 (big_f(f7(c1), c2) <=> big_f(f7(c1), f9(c1, c1))),
% 28.85/19.09 inference(symmetry,[status(thm)],[17750])).
% 28.85/19.09 tff(17752,plain,
% 28.85/19.09 (f9(c1, c1) = f7(c1)),
% 28.85/19.09 inference(transitivity,[status(thm)],[17727, 1498, 2778])).
% 28.85/19.09 tff(17753,plain,
% 28.85/19.09 (big_f(f9(c1, c1), f9(c1, c1)) <=> big_f(f7(c1), c2)),
% 28.85/19.09 inference(monotonicity,[status(thm)],[17752, 17728])).
% 28.85/19.09 tff(17754,plain,
% 28.85/19.09 (big_f(f9(c1, c1), f9(c1, c1)) <=> big_f(f7(c1), f9(c1, c1))),
% 28.85/19.09 inference(transitivity,[status(thm)],[17753, 17751])).
% 28.85/19.09 tff(17755,plain,
% 28.85/19.09 ((~big_f(f9(c1, c1), f9(c1, c1))) <=> (~big_f(f7(c1), f9(c1, c1)))),
% 28.85/19.09 inference(monotonicity,[status(thm)],[17754])).
% 28.85/19.09 tff(17756,plain,
% 28.85/19.09 (big_f(c2, c2) <=> big_f(f9(c1, c1), f9(c1, c1))),
% 28.85/19.09 inference(monotonicity,[status(thm)],[17734, 17734])).
% 28.85/19.09 tff(17757,plain,
% 28.85/19.09 ((~big_f(c2, c2)) <=> (~big_f(f9(c1, c1), f9(c1, c1)))),
% 28.85/19.09 inference(monotonicity,[status(thm)],[17756])).
% 28.85/19.09 tff(17758,plain,
% 28.85/19.09 (~big_f(f9(c1, c1), f9(c1, c1))),
% 28.85/19.09 inference(modus_ponens,[status(thm)],[121, 17757])).
% 28.85/19.09 tff(17759,assumption,(big_f(f9(c1, c1), f9(c1, c1))), introduced(assumption)).
% 28.85/19.09 tff(17760,plain,
% 28.85/19.09 ($false),
% 28.85/19.09 inference(unit_resolution,[status(thm)],[17759, 17758])).
% 28.85/19.09 tff(17761,plain,((~big_f(f9(c1, c1), f9(c1, c1))) | big_f(c2, c2) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.85/19.09 tff(17762,plain,
% 28.85/19.09 (~big_f(f9(c1, c1), f9(c1, c1))),
% 28.85/19.09 inference(unit_resolution,[status(thm)],[17761, 121, 1498, 11752, 11819])).
% 28.85/19.09 tff(17763,plain,
% 28.85/19.09 (~big_f(f7(c1), f9(c1, c1))),
% 28.85/19.09 inference(modus_ponens,[status(thm)],[17762, 17755])).
% 28.85/19.09 tff(17764,plain,
% 28.85/19.09 (f9(c1, c1) = f5(c1)),
% 28.85/19.09 inference(transitivity,[status(thm)],[17727, 1498, 1761])).
% 28.85/19.09 tff(17765,plain,
% 28.85/19.09 (f10(f9(c1, c1)) = f10(c2)),
% 28.85/19.09 inference(monotonicity,[status(thm)],[17728])).
% 28.85/19.09 tff(17766,plain,
% 28.85/19.09 (f10(f9(c1, c1)) = c1),
% 28.85/19.09 inference(transitivity,[status(thm)],[17765, 11819])).
% 28.85/19.09 tff(17767,plain,
% 28.85/19.09 (big_f(f9(c1, c1), f10(f9(c1, c1))) <=> big_f(f9(c1, c1), c1)),
% 28.85/19.09 inference(monotonicity,[status(thm)],[17766])).
% 28.85/19.09 tff(17768,plain,
% 28.85/19.09 (big_f(f9(c1, c1), c1) <=> big_f(f9(c1, c1), f10(f9(c1, c1)))),
% 28.85/19.09 inference(symmetry,[status(thm)],[17767])).
% 28.85/19.09 tff(17769,plain,
% 28.85/19.09 (f9(f10(c2), f10(c2)) = f9(c1, c1)),
% 28.85/19.09 inference(monotonicity,[status(thm)],[11819, 11819])).
% 28.85/19.09 tff(17770,plain,
% 28.85/19.09 (big_f(f9(f10(c2), f10(c2)), f10(f10(c2))) <=> big_f(f9(c1, c1), f10(c1))),
% 28.85/19.09 inference(monotonicity,[status(thm)],[17769, 11844])).
% 28.85/19.09 tff(17771,plain,
% 28.85/19.09 (big_f(f9(f10(c2), f10(c2)), f10(f10(c2))) <=> big_f(f9(c1, c1), f10(f9(c1, c1)))),
% 28.85/19.09 inference(transitivity,[status(thm)],[17770, 3931, 17768])).
% 28.85/19.09 tff(17772,plain,
% 28.85/19.09 ((f9(f10(c2), f10(c2)) = f10(c2)) <=> (f9(c1, c1) = c1)),
% 28.85/19.09 inference(monotonicity,[status(thm)],[17769, 11819])).
% 28.85/19.09 tff(17773,plain,
% 28.85/19.09 ((f9(c1, c1) = c1) <=> (f9(f10(c2), f10(c2)) = f10(c2))),
% 28.85/19.09 inference(symmetry,[status(thm)],[17772])).
% 28.85/19.09 tff(17774,plain,
% 28.85/19.09 ((f9(c1, c1) = c1) <=> (c2 = c1)),
% 28.85/19.09 inference(monotonicity,[status(thm)],[17728])).
% 28.85/19.09 tff(17775,plain,
% 28.85/19.09 ((c2 = c1) <=> (f9(c1, c1) = c1)),
% 28.85/19.09 inference(symmetry,[status(thm)],[17774])).
% 28.85/19.09 tff(17776,plain,
% 28.85/19.09 ((c2 = c1) <=> (f9(f10(c2), f10(c2)) = f10(c2))),
% 28.85/19.09 inference(transitivity,[status(thm)],[17775, 17773])).
% 28.85/19.09 tff(17777,plain,
% 28.85/19.09 ((~(c2 = c1)) <=> (~(f9(f10(c2), f10(c2)) = f10(c2)))),
% 28.85/19.09 inference(monotonicity,[status(thm)],[17776])).
% 28.85/19.09 tff(17778,plain,
% 28.85/19.09 (~(f9(f10(c2), f10(c2)) = f10(c2))),
% 28.85/19.09 inference(modus_ponens,[status(thm)],[75, 17777])).
% 28.85/19.09 tff(17779,plain,
% 28.85/19.09 (f10(c1) = f10(f10(c2))),
% 28.85/19.09 inference(symmetry,[status(thm)],[11844])).
% 28.85/19.09 tff(17780,plain,
% 28.85/19.09 ((f10(c1) = c1) <=> (f10(f10(c2)) = c1)),
% 28.85/19.09 inference(monotonicity,[status(thm)],[17779])).
% 28.85/19.09 tff(17781,plain,
% 28.85/19.09 ((f10(c1) = c1) <=> (f10(f10(c2)) = f10(c2))),
% 28.85/19.09 inference(transitivity,[status(thm)],[17780, 11843])).
% 28.85/19.09 tff(17782,plain,
% 28.85/19.09 (f10(f10(c2)) = f10(c2)),
% 28.85/19.09 inference(modus_ponens,[status(thm)],[3762, 17781])).
% 28.85/19.09 tff(17783,plain,
% 28.85/19.09 (~big_f(f7(c1), f5(c1))),
% 28.85/19.09 inference(unit_resolution,[status(thm)],[1715, 120, 121, 186])).
% 28.85/19.09 tff(17784,plain,
% 28.85/19.09 (big_f(f9(f10(c2), f10(c2)), f10(f10(c2)))),
% 28.85/19.09 inference(unit_resolution,[status(thm)],[280, 17783, 17782, 115, 17778])).
% 28.85/19.09 tff(17785,plain,
% 28.85/19.09 (big_f(f9(c1, c1), f10(f9(c1, c1)))),
% 28.85/19.09 inference(modus_ponens,[status(thm)],[17784, 17771])).
% 28.85/19.09 tff(17786,plain,
% 28.85/19.09 ((f10(f9(c1, c1)) = f9(c1, c1)) <=> (c1 = f9(c1, c1))),
% 28.85/19.09 inference(monotonicity,[status(thm)],[17766])).
% 28.85/19.09 tff(17787,plain,
% 28.85/19.09 ((f10(f9(c1, c1)) = f9(c1, c1)) <=> (f9(c1, c1) = c1)),
% 28.85/19.09 inference(transitivity,[status(thm)],[17786, 17725])).
% 28.85/19.09 tff(17788,plain,
% 28.85/19.09 ((f9(c1, c1) = c1) <=> (f10(f9(c1, c1)) = f9(c1, c1))),
% 28.85/19.09 inference(symmetry,[status(thm)],[17787])).
% 28.85/19.09 tff(17789,plain,
% 28.85/19.09 ((~(f9(c1, c1) = c1)) <=> (~(f10(f9(c1, c1)) = f9(c1, c1)))),
% 28.85/19.09 inference(monotonicity,[status(thm)],[17788])).
% 28.85/19.09 tff(17790,plain,
% 28.85/19.09 ((~(c2 = c1)) <=> (~(f9(c1, c1) = c1))),
% 28.85/19.09 inference(monotonicity,[status(thm)],[17775])).
% 28.85/19.09 tff(17791,plain,
% 28.85/19.09 (~(f9(c1, c1) = c1)),
% 28.85/19.09 inference(modus_ponens,[status(thm)],[75, 17790])).
% 28.85/19.09 tff(17792,plain,
% 28.85/19.09 (~(f10(f9(c1, c1)) = f9(c1, c1))),
% 28.85/19.09 inference(modus_ponens,[status(thm)],[17791, 17789])).
% 28.85/19.09 tff(17793,plain,
% 28.85/19.09 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f7(c1) = c1) | big_f(f7(c1), f9(c1, c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~(f9(c1, c1) = f5(c1))) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f7(c1) = c1) | big_f(f7(c1), f9(c1, c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~(f9(c1, c1) = f5(c1))) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))))),
% 28.85/19.09 inference(rewrite,[status(thm)],[])).
% 28.85/19.09 tff(17794,plain,
% 28.85/19.09 (((~(f9(c1, c1) = f5(c1))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (f7(c1) = c1) | big_f(f7(c1), f9(c1, c1))) <=> ((f7(c1) = c1) | big_f(f7(c1), f9(c1, c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~(f9(c1, c1) = f5(c1))) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))))),
% 28.85/19.09 inference(rewrite,[status(thm)],[])).
% 28.85/19.09 tff(17795,plain,
% 28.85/19.09 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(f9(c1, c1) = f5(c1))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (f7(c1) = c1) | big_f(f7(c1), f9(c1, c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f7(c1) = c1) | big_f(f7(c1), f9(c1, c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~(f9(c1, c1) = f5(c1))) | (~big_f(f9(c1, c1), f10(f9(c1, c1))))))),
% 28.85/19.09 inference(monotonicity,[status(thm)],[17794])).
% 28.85/19.09 tff(17796,plain,
% 28.85/19.09 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(f9(c1, c1) = f5(c1))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (f7(c1) = c1) | big_f(f7(c1), f9(c1, c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f7(c1) = c1) | big_f(f7(c1), f9(c1, c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~(f9(c1, c1) = f5(c1))) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))))),
% 28.85/19.09 inference(transitivity,[status(thm)],[17795, 17793])).
% 28.85/19.09 tff(17797,plain,
% 28.85/19.09 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(f9(c1, c1) = f5(c1))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (f7(c1) = c1) | big_f(f7(c1), f9(c1, c1)))),
% 28.85/19.09 inference(quant_inst,[status(thm)],[])).
% 28.85/19.09 tff(17798,plain,
% 28.85/19.09 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f7(c1) = c1) | big_f(f7(c1), f9(c1, c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~(f9(c1, c1) = f5(c1))) | (~big_f(f9(c1, c1), f10(f9(c1, c1))))),
% 28.85/19.09 inference(modus_ponens,[status(thm)],[17797, 17796])).
% 28.85/19.09 tff(17799,plain,
% 28.85/19.09 (f9(c1, c1) = f8(f9(c1, c1))),
% 28.85/19.09 inference(unit_resolution,[status(thm)],[17798, 705, 115, 17792, 17785, 17764, 17763])).
% 28.85/19.09 tff(17800,plain,
% 28.85/19.09 (f8(f9(c1, c1)) = f9(c1, c1)),
% 28.85/19.09 inference(symmetry,[status(thm)],[17799])).
% 28.85/19.09 tff(17801,plain,
% 28.85/19.09 ((c1 = f8(f9(c1, c1))) <=> (c1 = f9(c1, c1))),
% 28.85/19.09 inference(monotonicity,[status(thm)],[17800])).
% 28.85/19.09 tff(17802,plain,
% 28.85/19.09 ((c1 = f8(f9(c1, c1))) <=> (f9(c1, c1) = c1)),
% 28.85/19.09 inference(transitivity,[status(thm)],[17801, 17725])).
% 28.85/19.09 tff(17803,plain,
% 28.85/19.09 ((f9(c1, c1) = c1) <=> (c1 = f8(f9(c1, c1)))),
% 28.85/19.09 inference(symmetry,[status(thm)],[17802])).
% 28.85/19.09 tff(17804,plain,
% 28.85/19.09 ((~(f9(c1, c1) = c1)) <=> (~(c1 = f8(f9(c1, c1))))),
% 28.85/19.09 inference(monotonicity,[status(thm)],[17803])).
% 28.85/19.09 tff(17805,plain,
% 28.85/19.09 (~(c1 = f8(f9(c1, c1)))),
% 28.85/19.09 inference(modus_ponens,[status(thm)],[17791, 17804])).
% 28.85/19.09 tff(17806,plain,
% 28.85/19.09 (big_f(f9(f10(c2), f10(c2)), f10(f10(c2))) <=> big_f(f9(c1, c1), c1)),
% 28.85/19.09 inference(transitivity,[status(thm)],[17770, 3931])).
% 28.85/19.09 tff(17807,plain,
% 28.85/19.09 (big_f(f9(c1, c1), c1)),
% 28.85/19.09 inference(modus_ponens,[status(thm)],[17784, 17806])).
% 28.85/19.09 tff(17808,plain,
% 28.85/19.09 (big_f(f7(f9(c1, c1)), c1) <=> big_f(f7(c2), c1)),
% 28.85/19.09 inference(monotonicity,[status(thm)],[17729])).
% 28.85/19.09 tff(17809,plain,
% 28.85/19.09 (big_f(f7(c2), c1) <=> big_f(f7(f9(c1, c1)), c1)),
% 28.85/19.09 inference(symmetry,[status(thm)],[17808])).
% 28.85/19.09 tff(17810,plain,
% 28.85/19.09 ((~big_f(f7(c2), c1)) <=> (~big_f(f7(f9(c1, c1)), c1))),
% 28.85/19.09 inference(monotonicity,[status(thm)],[17809])).
% 28.85/19.09 tff(17811,plain,
% 28.85/19.09 (~big_f(f7(f9(c1, c1)), c1)),
% 28.85/19.09 inference(modus_ponens,[status(thm)],[333, 17810])).
% 28.85/19.09 tff(17812,assumption,(big_f(f7(f9(c1, c1)), c1)), introduced(assumption)).
% 28.85/19.09 tff(17813,plain,
% 28.85/19.09 ($false),
% 28.85/19.09 inference(unit_resolution,[status(thm)],[17812, 17811])).
% 28.85/19.09 tff(17814,plain,((~big_f(f7(f9(c1, c1)), c1)) | big_f(f7(c2), c1) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.85/19.09 tff(17815,plain,
% 28.85/19.09 (~big_f(f7(f9(c1, c1)), c1)),
% 28.85/19.09 inference(unit_resolution,[status(thm)],[17814, 333, 11819, 11752, 1498])).
% 28.85/19.09 tff(17816,plain,
% 28.85/19.09 ((f7(c2) = c2) <=> (f7(f9(c1, c1)) = f9(c1, c1))),
% 28.85/19.09 inference(monotonicity,[status(thm)],[17739, 17734])).
% 28.85/19.09 tff(17817,plain,
% 28.85/19.09 ((~(f7(c2) = c2)) <=> (~(f7(f9(c1, c1)) = f9(c1, c1)))),
% 28.85/19.09 inference(monotonicity,[status(thm)],[17816])).
% 28.85/19.09 tff(17818,plain,
% 28.85/19.09 (~(f7(f9(c1, c1)) = f9(c1, c1))),
% 28.85/19.09 inference(modus_ponens,[status(thm)],[17, 17817])).
% 28.85/19.09 tff(17819,assumption,(big_f(f9(c1, c1), f10(f9(c1, c1)))), introduced(assumption)).
% 28.85/19.09 tff(17820,plain,
% 28.85/19.09 ((c2 = c1) <=> (f9(c1, c1) = c1)),
% 28.85/19.09 inference(monotonicity,[status(thm)],[17734])).
% 28.85/19.09 tff(17821,plain,
% 28.85/19.09 ((~(c2 = c1)) <=> (~(f9(c1, c1) = c1))),
% 28.85/19.09 inference(monotonicity,[status(thm)],[17820])).
% 28.85/19.09 tff(17822,plain,
% 28.85/19.09 (~(f9(c1, c1) = c1)),
% 28.85/19.09 inference(modus_ponens,[status(thm)],[75, 17821])).
% 28.85/19.09 tff(17823,plain,
% 28.85/19.09 (~(f10(f9(c1, c1)) = f9(c1, c1))),
% 28.85/19.09 inference(modus_ponens,[status(thm)],[17822, 17789])).
% 28.85/19.09 tff(17824,plain,
% 28.85/19.09 (big_f(f7(c2), c2) <=> big_f(f7(f9(c1, c1)), f9(c1, c1))),
% 28.85/19.09 inference(monotonicity,[status(thm)],[17739, 17734])).
% 28.85/19.09 tff(17825,plain,
% 28.85/19.09 ((~big_f(f7(c2), c2)) <=> (~big_f(f7(f9(c1, c1)), f9(c1, c1)))),
% 28.85/19.09 inference(monotonicity,[status(thm)],[17824])).
% 28.85/19.09 tff(17826,plain,
% 28.85/19.09 (~big_f(f7(f9(c1, c1)), f9(c1, c1))),
% 28.85/19.09 inference(modus_ponens,[status(thm)],[1521, 17825])).
% 28.85/19.09 tff(17827,plain,
% 28.85/19.09 (f5(f9(c1, c1)) = f5(c2)),
% 28.85/19.09 inference(monotonicity,[status(thm)],[17728])).
% 28.85/19.09 tff(17828,plain,
% 28.85/19.09 ((f9(c1, c1) = f5(f9(c1, c1))) <=> (c2 = f5(c2))),
% 28.85/19.09 inference(monotonicity,[status(thm)],[17728, 17827])).
% 28.85/19.09 tff(17829,plain,
% 28.85/19.09 ((f9(c1, c1) = f5(f9(c1, c1))) <=> (f5(c2) = c2)),
% 28.85/19.09 inference(transitivity,[status(thm)],[17828, 1280])).
% 28.85/19.09 tff(17830,plain,
% 28.85/19.09 ((~(f9(c1, c1) = f5(f9(c1, c1)))) <=> (~(f5(c2) = c2))),
% 28.85/19.09 inference(monotonicity,[status(thm)],[17829])).
% 28.85/19.09 tff(17831,assumption,(~(f9(c1, c1) = f8(f9(c1, c1)))), introduced(assumption)).
% 28.85/19.09 tff(17832,assumption,(~(f7(f9(c1, c1)) = f9(c1, c1))), introduced(assumption)).
% 28.85/19.09 tff(17833,assumption,(~big_f(f7(f9(c1, c1)), f9(c1, c1))), introduced(assumption)).
% 28.85/19.09 tff(17834,assumption,(~(f10(f9(c1, c1)) = f9(c1, c1))), introduced(assumption)).
% 28.85/19.09 tff(17835,plain,
% 28.85/19.09 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f9(c1, c1) = f8(f9(c1, c1))) | big_f(f7(f9(c1, c1)), f9(c1, c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~(f9(c1, c1) = f5(f9(c1, c1)))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f9(c1, c1) = f8(f9(c1, c1))) | big_f(f7(f9(c1, c1)), f9(c1, c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~(f9(c1, c1) = f5(f9(c1, c1)))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))))),
% 28.85/19.09 inference(rewrite,[status(thm)],[])).
% 28.85/19.09 tff(17836,plain,
% 28.85/19.09 (((~(f9(c1, c1) = f5(f9(c1, c1)))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), f9(c1, c1))) <=> ((f9(c1, c1) = f8(f9(c1, c1))) | big_f(f7(f9(c1, c1)), f9(c1, c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~(f9(c1, c1) = f5(f9(c1, c1)))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))))),
% 28.85/19.09 inference(rewrite,[status(thm)],[])).
% 28.85/19.09 tff(17837,plain,
% 28.85/19.09 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(f9(c1, c1) = f5(f9(c1, c1)))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), f9(c1, c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f9(c1, c1) = f8(f9(c1, c1))) | big_f(f7(f9(c1, c1)), f9(c1, c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~(f9(c1, c1) = f5(f9(c1, c1)))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1))))))),
% 28.85/19.09 inference(monotonicity,[status(thm)],[17836])).
% 28.85/19.09 tff(17838,plain,
% 28.85/19.09 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(f9(c1, c1) = f5(f9(c1, c1)))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), f9(c1, c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f9(c1, c1) = f8(f9(c1, c1))) | big_f(f7(f9(c1, c1)), f9(c1, c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~(f9(c1, c1) = f5(f9(c1, c1)))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))))),
% 28.85/19.09 inference(transitivity,[status(thm)],[17837, 17835])).
% 28.85/19.09 tff(17839,plain,
% 28.85/19.09 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(f9(c1, c1) = f5(f9(c1, c1)))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), f9(c1, c1)))),
% 28.85/19.09 inference(quant_inst,[status(thm)],[])).
% 28.85/19.09 tff(17840,plain,
% 28.85/19.09 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f9(c1, c1) = f8(f9(c1, c1))) | big_f(f7(f9(c1, c1)), f9(c1, c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~(f9(c1, c1) = f5(f9(c1, c1)))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1))))),
% 28.85/19.09 inference(modus_ponens,[status(thm)],[17839, 17838])).
% 28.85/19.09 tff(17841,plain,
% 28.85/19.09 ((f9(c1, c1) = f8(f9(c1, c1))) | (~(f9(c1, c1) = f5(f9(c1, c1))))),
% 28.85/19.09 inference(unit_resolution,[status(thm)],[17840, 705, 17834, 17819, 17833, 17832])).
% 28.85/19.09 tff(17842,plain,
% 28.85/19.09 (~(f9(c1, c1) = f5(f9(c1, c1)))),
% 28.85/19.09 inference(unit_resolution,[status(thm)],[17841, 17831])).
% 28.85/19.09 tff(17843,plain,
% 28.85/19.09 (~(f5(c2) = c2)),
% 28.85/19.09 inference(modus_ponens,[status(thm)],[17842, 17830])).
% 28.85/19.09 tff(17844,plain,
% 28.85/19.09 ((c1 = f5(f9(c1, c1))) <=> (c1 = f5(c2))),
% 28.85/19.09 inference(monotonicity,[status(thm)],[17827])).
% 28.85/19.09 tff(17845,plain,
% 28.85/19.09 ((c1 = f5(f9(c1, c1))) <=> (f5(c2) = c1)),
% 28.85/19.09 inference(transitivity,[status(thm)],[17844, 1531])).
% 28.85/19.10 tff(17846,plain,
% 28.85/19.10 ((~(c1 = f5(f9(c1, c1)))) <=> (~(f5(c2) = c1))),
% 28.85/19.10 inference(monotonicity,[status(thm)],[17845])).
% 28.85/19.10 tff(17847,assumption,(~big_f(f7(f9(c1, c1)), c1)), introduced(assumption)).
% 28.85/19.10 tff(17848,plain,
% 28.85/19.10 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f9(c1, c1) = f8(f9(c1, c1))) | (f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), c1) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (~(c1 = f5(f9(c1, c1)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f9(c1, c1) = f8(f9(c1, c1))) | (f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), c1) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (~(c1 = f5(f9(c1, c1)))))),
% 28.85/19.10 inference(rewrite,[status(thm)],[])).
% 28.85/19.10 tff(17849,plain,
% 28.85/19.10 (((~(c1 = f5(f9(c1, c1)))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), c1)) <=> ((f9(c1, c1) = f8(f9(c1, c1))) | (f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), c1) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (~(c1 = f5(f9(c1, c1)))))),
% 28.85/19.10 inference(rewrite,[status(thm)],[])).
% 28.85/19.10 tff(17850,plain,
% 28.85/19.10 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c1 = f5(f9(c1, c1)))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), c1))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f9(c1, c1) = f8(f9(c1, c1))) | (f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), c1) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (~(c1 = f5(f9(c1, c1))))))),
% 28.85/19.10 inference(monotonicity,[status(thm)],[17849])).
% 28.85/19.10 tff(17851,plain,
% 28.85/19.10 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c1 = f5(f9(c1, c1)))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), c1))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f9(c1, c1) = f8(f9(c1, c1))) | (f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), c1) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (~(c1 = f5(f9(c1, c1)))))),
% 28.85/19.10 inference(transitivity,[status(thm)],[17850, 17848])).
% 28.85/19.10 tff(17852,plain,
% 28.85/19.10 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c1 = f5(f9(c1, c1)))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), c1))),
% 28.85/19.10 inference(quant_inst,[status(thm)],[])).
% 28.85/19.10 tff(17853,plain,
% 28.85/19.10 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f9(c1, c1) = f8(f9(c1, c1))) | (f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), c1) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (~(c1 = f5(f9(c1, c1))))),
% 28.85/19.10 inference(modus_ponens,[status(thm)],[17852, 17851])).
% 28.85/19.10 tff(17854,plain,
% 28.85/19.10 ((f9(c1, c1) = f8(f9(c1, c1))) | (~(c1 = f5(f9(c1, c1))))),
% 28.85/19.10 inference(unit_resolution,[status(thm)],[17853, 705, 17834, 17819, 17832, 17847])).
% 28.85/19.10 tff(17855,plain,
% 28.85/19.10 (~(c1 = f5(f9(c1, c1)))),
% 28.85/19.10 inference(unit_resolution,[status(thm)],[17854, 17831])).
% 28.85/19.10 tff(17856,plain,
% 28.85/19.10 (~(f5(c2) = c1)),
% 28.85/19.10 inference(modus_ponens,[status(thm)],[17855, 17846])).
% 28.85/19.10 tff(17857,plain,
% 28.85/19.10 ($false),
% 28.85/19.10 inference(unit_resolution,[status(thm)],[1547, 17856, 17843])).
% 28.85/19.10 tff(17858,plain,((f9(c1, c1) = f8(f9(c1, c1))) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), c1) | big_f(f7(f9(c1, c1)), f9(c1, c1))), inference(lemma,lemma(discharge,[]))).
% 28.85/19.10 tff(17859,plain,
% 28.85/19.10 (f9(c1, c1) = f8(f9(c1, c1))),
% 28.85/19.10 inference(unit_resolution,[status(thm)],[17858, 17826, 11752, 11819, 17823, 17819, 17818, 17815, 1498])).
% 28.85/19.10 tff(17860,assumption,(f9(c1, c1) = f8(f9(c1, c1))), introduced(assumption)).
% 28.85/19.10 tff(17861,plain,
% 28.85/19.10 (f8(f9(c1, c1)) = f9(c1, c1)),
% 28.85/19.10 inference(symmetry,[status(thm)],[17860])).
% 28.85/19.10 tff(17862,plain,
% 28.85/19.10 (f8(c2) = f8(f9(c1, c1))),
% 28.85/19.10 inference(monotonicity,[status(thm)],[17734])).
% 28.85/19.10 tff(17863,plain,
% 28.85/19.10 (f8(c2) = c2),
% 28.85/19.10 inference(transitivity,[status(thm)],[17862, 17861, 17727, 1498])).
% 28.85/19.10 tff(17864,plain,
% 28.85/19.10 (f9(c1, f8(c2)) = f9(c1, c2)),
% 28.85/19.10 inference(monotonicity,[status(thm)],[17863])).
% 28.85/19.10 tff(17865,plain,
% 28.85/19.10 ((f9(c1, f8(c2)) = f8(c2)) <=> (f9(c1, c2) = c2)),
% 28.85/19.10 inference(monotonicity,[status(thm)],[17864, 17863])).
% 28.85/19.10 tff(17866,plain,
% 28.85/19.10 ((f9(c1, c2) = c2) <=> (f9(c1, f8(c2)) = f8(c2))),
% 28.85/19.10 inference(symmetry,[status(thm)],[17865])).
% 28.85/19.10 tff(17867,plain,
% 28.85/19.10 (c1 = f5(c2)),
% 28.85/19.10 inference(unit_resolution,[status(thm)],[8139, 1569])).
% 28.85/19.10 tff(17868,assumption,(~(f9(c1, f8(c2)) = f8(c2))), introduced(assumption)).
% 28.85/19.10 tff(17869,plain,
% 28.85/19.10 (f8(f9(f10(c2), f10(c2))) = f8(f9(c1, c1))),
% 28.85/19.10 inference(monotonicity,[status(thm)],[17769])).
% 28.85/19.10 tff(17870,plain,
% 28.85/19.10 (f9(c1, c1) = f9(f10(c2), f10(c2))),
% 28.85/19.10 inference(symmetry,[status(thm)],[17769])).
% 28.85/19.10 tff(17871,plain,
% 28.85/19.10 (c2 = f9(f10(c2), f10(c2))),
% 28.85/19.10 inference(transitivity,[status(thm)],[17733, 17726, 17870])).
% 28.85/19.10 tff(17872,plain,
% 28.85/19.10 (f8(c2) = f8(f9(f10(c2), f10(c2)))),
% 28.85/19.10 inference(monotonicity,[status(thm)],[17871])).
% 28.85/19.10 tff(17873,plain,
% 28.85/19.10 (f8(c2) = c2),
% 28.85/19.10 inference(transitivity,[status(thm)],[17872, 17869, 17861, 17727, 1498])).
% 28.85/19.10 tff(17874,plain,
% 28.85/19.10 (f9(c1, f8(c2)) = f9(c1, c2)),
% 28.85/19.10 inference(monotonicity,[status(thm)],[17873])).
% 28.85/19.10 tff(17875,plain,
% 28.85/19.10 ((f9(c1, f8(c2)) = f8(c2)) <=> (f9(c1, c2) = c2)),
% 28.85/19.10 inference(monotonicity,[status(thm)],[17874, 17873])).
% 28.85/19.10 tff(17876,plain,
% 28.85/19.10 ((f9(c1, c2) = c2) <=> (f9(c1, f8(c2)) = f8(c2))),
% 28.85/19.10 inference(symmetry,[status(thm)],[17875])).
% 28.85/19.10 tff(17877,plain,
% 28.85/19.10 (f8(f9(c1, c1)) = c2),
% 28.85/19.10 inference(transitivity,[status(thm)],[17861, 17727, 1498])).
% 28.85/19.10 tff(17878,plain,
% 28.85/19.10 ((f9(c1, c2) = f8(f9(c1, c1))) <=> (f9(c1, c2) = c2)),
% 28.85/19.10 inference(monotonicity,[status(thm)],[17877])).
% 28.85/19.10 tff(17879,plain,
% 28.85/19.10 ((f9(c1, c2) = f8(f9(c1, c1))) <=> (f9(c1, f8(c2)) = f8(c2))),
% 28.85/19.10 inference(transitivity,[status(thm)],[17878, 17876])).
% 28.85/19.10 tff(17880,assumption,(f9(c1, c2) = f8(f9(c1, c1))), introduced(assumption)).
% 28.85/19.10 tff(17881,plain,
% 28.85/19.10 (f9(c1, f8(c2)) = f8(c2)),
% 28.85/19.10 inference(modus_ponens,[status(thm)],[17880, 17879])).
% 28.85/19.10 tff(17882,plain,
% 28.85/19.10 ($false),
% 28.85/19.10 inference(unit_resolution,[status(thm)],[17868, 17881])).
% 28.85/19.10 tff(17883,plain,((~(f9(c1, c2) = f8(f9(c1, c1)))) | (f9(c1, f8(c2)) = f8(c2)) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f9(c1, c1) = f8(f9(c1, c1)))) | (~(f4(c4) = c1)) | (~(f10(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.85/19.10 tff(17884,plain,
% 28.85/19.10 (~(f9(c1, c2) = f8(f9(c1, c1)))),
% 28.85/19.10 inference(unit_resolution,[status(thm)],[17883, 17868, 11819, 1498, 11752, 17860])).
% 28.85/19.10 tff(17885,plain,
% 28.85/19.10 (f10(f9(c1, c1)) = f10(c1)),
% 28.85/19.10 inference(transitivity,[status(thm)],[17765, 11819, 11570])).
% 28.85/19.10 tff(17886,plain,
% 28.85/19.10 (big_f(f9(c1, c2), f10(f9(c1, c1))) <=> big_f(f9(c1, c2), f10(c1))),
% 28.85/19.10 inference(monotonicity,[status(thm)],[17885])).
% 28.85/19.10 tff(17887,plain,
% 28.85/19.10 (big_f(f9(c1, c2), f10(c1)) <=> big_f(f9(c1, c2), f10(f9(c1, c1)))),
% 28.85/19.10 inference(symmetry,[status(thm)],[17886])).
% 28.85/19.10 tff(17888,assumption,(big_f(f9(c1, c2), f10(c1))), introduced(assumption)).
% 28.85/19.10 tff(17889,plain,
% 28.85/19.10 (big_f(f9(c1, c2), f10(f9(c1, c1)))),
% 28.85/19.10 inference(modus_ponens,[status(thm)],[17888, 17887])).
% 28.85/19.10 tff(17890,plain,
% 28.85/19.10 (f5(c2) = f5(f9(c1, c1))),
% 28.85/19.10 inference(symmetry,[status(thm)],[17827])).
% 28.85/19.10 tff(17891,plain,
% 28.85/19.10 (c1 = f5(f9(c1, c1))),
% 28.85/19.10 inference(transitivity,[status(thm)],[1570, 17890])).
% 28.85/19.10 tff(17892,assumption,(~(f9(c1, c2) = f8(f9(c1, c1)))), introduced(assumption)).
% 28.85/19.10 tff(17893,plain,
% 28.85/19.10 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), c1) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~(c1 = f5(f9(c1, c1)))) | (~big_f(f9(c1, c2), f10(f9(c1, c1)))) | (f9(c1, c2) = f8(f9(c1, c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), c1) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~(c1 = f5(f9(c1, c1)))) | (~big_f(f9(c1, c2), f10(f9(c1, c1)))) | (f9(c1, c2) = f8(f9(c1, c1))))),
% 28.85/19.10 inference(rewrite,[status(thm)],[])).
% 28.85/19.10 tff(17894,plain,
% 28.85/19.10 (((~(c1 = f5(f9(c1, c1)))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c2) = f8(f9(c1, c1))) | (~big_f(f9(c1, c2), f10(f9(c1, c1)))) | (f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), c1)) <=> ((f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), c1) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~(c1 = f5(f9(c1, c1)))) | (~big_f(f9(c1, c2), f10(f9(c1, c1)))) | (f9(c1, c2) = f8(f9(c1, c1))))),
% 28.85/19.10 inference(rewrite,[status(thm)],[])).
% 28.85/19.10 tff(17895,plain,
% 28.85/19.10 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c1 = f5(f9(c1, c1)))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c2) = f8(f9(c1, c1))) | (~big_f(f9(c1, c2), f10(f9(c1, c1)))) | (f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), c1))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), c1) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~(c1 = f5(f9(c1, c1)))) | (~big_f(f9(c1, c2), f10(f9(c1, c1)))) | (f9(c1, c2) = f8(f9(c1, c1)))))),
% 28.85/19.10 inference(monotonicity,[status(thm)],[17894])).
% 28.85/19.10 tff(17896,plain,
% 28.85/19.10 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c1 = f5(f9(c1, c1)))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c2) = f8(f9(c1, c1))) | (~big_f(f9(c1, c2), f10(f9(c1, c1)))) | (f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), c1))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), c1) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~(c1 = f5(f9(c1, c1)))) | (~big_f(f9(c1, c2), f10(f9(c1, c1)))) | (f9(c1, c2) = f8(f9(c1, c1))))),
% 28.85/19.10 inference(transitivity,[status(thm)],[17895, 17893])).
% 28.85/19.10 tff(17897,plain,
% 28.85/19.10 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c1 = f5(f9(c1, c1)))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c2) = f8(f9(c1, c1))) | (~big_f(f9(c1, c2), f10(f9(c1, c1)))) | (f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), c1))),
% 28.85/19.10 inference(quant_inst,[status(thm)],[])).
% 28.85/19.10 tff(17898,plain,
% 28.85/19.10 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), c1) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~(c1 = f5(f9(c1, c1)))) | (~big_f(f9(c1, c2), f10(f9(c1, c1)))) | (f9(c1, c2) = f8(f9(c1, c1)))),
% 28.85/19.10 inference(modus_ponens,[status(thm)],[17897, 17896])).
% 28.85/19.10 tff(17899,plain,
% 28.85/19.10 (~big_f(f9(c1, c2), f10(f9(c1, c1)))),
% 28.85/19.10 inference(unit_resolution,[status(thm)],[17898, 705, 17823, 17847, 17832, 17892, 17891])).
% 28.85/19.10 tff(17900,plain,
% 28.85/19.10 ($false),
% 28.85/19.10 inference(unit_resolution,[status(thm)],[17899, 17889])).
% 28.85/19.10 tff(17901,plain,((~big_f(f9(c1, c2), f10(c1))) | (~(f10(c1) = c1)) | (~(f10(c2) = c1)) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | big_f(f7(f9(c1, c1)), c1) | (f7(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c2) = f8(f9(c1, c1))) | (~(f5(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.85/19.10 tff(17902,plain,
% 28.85/19.10 (~big_f(f9(c1, c2), f10(c1))),
% 28.85/19.10 inference(unit_resolution,[status(thm)],[17901, 17884, 11819, 1498, 11752, 17815, 17818, 3762, 1569])).
% 28.85/19.10 tff(17903,plain,
% 28.85/19.10 (f9(c1, c2) = c2),
% 28.85/19.10 inference(unit_resolution,[status(thm)],[8242, 17902, 17, 3762, 17867, 333])).
% 28.85/19.10 tff(17904,plain,
% 28.85/19.10 (f9(c1, f8(c2)) = f8(c2)),
% 28.85/19.10 inference(modus_ponens,[status(thm)],[17903, 17866])).
% 28.85/19.10 tff(17905,plain,
% 28.85/19.10 ($false),
% 28.85/19.10 inference(unit_resolution,[status(thm)],[17868, 17904])).
% 28.85/19.10 tff(17906,plain,((f9(c1, f8(c2)) = f8(c2)) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f9(c1, c1) = f8(f9(c1, c1)))) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | (f7(c2) = c2) | (~(f10(c1) = c1)) | big_f(f7(c2), c1) | (~(f5(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.85/19.10 tff(17907,plain,
% 28.85/19.10 (f9(c1, f8(c2)) = f8(c2)),
% 28.85/19.10 inference(unit_resolution,[status(thm)],[17906, 1569, 17860, 11752, 11819, 17, 3762, 333, 1498])).
% 28.85/19.10 tff(17908,plain,
% 28.85/19.10 (f8(f9(c1, c1)) = f8(c2)),
% 28.85/19.10 inference(symmetry,[status(thm)],[17862])).
% 28.85/19.10 tff(17909,plain,
% 28.85/19.10 (c2 = f8(c2)),
% 28.85/19.10 inference(transitivity,[status(thm)],[17733, 17726, 17860, 17908])).
% 28.85/19.10 tff(17910,plain,
% 28.85/19.10 (f9(c1, c2) = f9(c1, f8(c2))),
% 28.85/19.10 inference(monotonicity,[status(thm)],[17909])).
% 28.85/19.10 tff(17911,plain,
% 28.85/19.10 (f9(c1, f9(c1, c1)) = f9(c1, c2)),
% 28.85/19.10 inference(monotonicity,[status(thm)],[17728])).
% 28.85/19.10 tff(17912,plain,
% 28.85/19.10 (f9(c1, f9(c1, c1)) = f9(c1, c1)),
% 28.85/19.10 inference(transitivity,[status(thm)],[17911, 17910, 17907, 17862, 17861])).
% 28.85/19.10 tff(17913,plain,
% 28.85/19.10 (big_f(f9(c1, f9(c1, c1)), f10(c1)) <=> big_f(f9(c1, c1), c1)),
% 28.85/19.10 inference(monotonicity,[status(thm)],[17912, 3762])).
% 28.85/19.10 tff(17914,plain,
% 28.85/19.10 (big_f(f9(c1, c1), c1) <=> big_f(f9(c1, f9(c1, c1)), f10(c1))),
% 28.85/19.10 inference(symmetry,[status(thm)],[17913])).
% 28.85/19.10 tff(17915,plain,
% 28.85/19.10 (big_f(f9(c1, f9(c1, c1)), f10(c1))),
% 28.85/19.10 inference(modus_ponens,[status(thm)],[8714, 17914])).
% 28.85/19.10 tff(17916,plain,
% 28.85/19.10 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), c1) | (~(c1 = f5(f9(c1, c1)))) | (~(f9(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f9(c1, f9(c1, c1)), f10(c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (~(f10(c1) = c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), c1) | (~(c1 = f5(f9(c1, c1)))) | (~(f9(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f9(c1, f9(c1, c1)), f10(c1))))),
% 28.85/19.10 inference(rewrite,[status(thm)],[])).
% 28.85/19.10 tff(17917,plain,
% 28.85/19.10 (((~(f10(c1) = c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), c1) | (~(f9(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f9(c1, f9(c1, c1)), f10(c1))) | (~(c1 = f5(f9(c1, c1))))) <=> ((~(f10(c1) = c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), c1) | (~(c1 = f5(f9(c1, c1)))) | (~(f9(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f9(c1, f9(c1, c1)), f10(c1))))),
% 28.85/19.10 inference(rewrite,[status(thm)],[])).
% 28.85/19.10 tff(17918,plain,
% 28.85/19.10 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), c1) | (~(f9(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f9(c1, f9(c1, c1)), f10(c1))) | (~(c1 = f5(f9(c1, c1)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), c1) | (~(c1 = f5(f9(c1, c1)))) | (~(f9(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f9(c1, f9(c1, c1)), f10(c1)))))),
% 28.85/19.10 inference(monotonicity,[status(thm)],[17917])).
% 28.85/19.10 tff(17919,plain,
% 28.85/19.10 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), c1) | (~(f9(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f9(c1, f9(c1, c1)), f10(c1))) | (~(c1 = f5(f9(c1, c1)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (~(f10(c1) = c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), c1) | (~(c1 = f5(f9(c1, c1)))) | (~(f9(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f9(c1, f9(c1, c1)), f10(c1))))),
% 28.85/19.10 inference(transitivity,[status(thm)],[17918, 17916])).
% 28.85/19.10 tff(17920,plain,
% 28.85/19.10 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), c1) | (~(f9(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f9(c1, f9(c1, c1)), f10(c1))) | (~(c1 = f5(f9(c1, c1)))))),
% 28.85/19.10 inference(quant_inst,[status(thm)],[])).
% 28.85/19.10 tff(17921,plain,
% 28.85/19.10 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (~(f10(c1) = c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), c1) | (~(c1 = f5(f9(c1, c1)))) | (~(f9(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f9(c1, f9(c1, c1)), f10(c1)))),
% 28.85/19.10 inference(modus_ponens,[status(thm)],[17920, 17919])).
% 28.85/19.10 tff(17922,plain,
% 28.85/19.10 ((~(f9(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f9(c1, f9(c1, c1)), f10(c1)))),
% 28.85/19.10 inference(unit_resolution,[status(thm)],[17921, 783, 3762, 17815, 17818, 17891])).
% 28.85/19.10 tff(17923,plain,
% 28.85/19.10 ($false),
% 28.85/19.10 inference(unit_resolution,[status(thm)],[17922, 17915, 17912])).
% 28.85/19.10 tff(17924,plain,((~(f5(c2) = c1)) | (~(f10(c1) = c1)) | (~big_f(f9(c1, c1), c1)) | (~(f9(c1, c1) = f8(f9(c1, c1)))) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | (f7(c2) = c2) | big_f(f7(c2), c1)), inference(lemma,lemma(discharge,[]))).
% 28.85/19.10 tff(17925,plain,
% 28.85/19.10 (~(f5(c2) = c1)),
% 28.85/19.10 inference(unit_resolution,[status(thm)],[17924, 17859, 8714, 3762, 1498, 11752, 11819, 17, 333])).
% 28.85/19.10 tff(17926,plain,
% 28.85/19.10 (f5(c2) = c2),
% 28.85/19.10 inference(unit_resolution,[status(thm)],[1547, 17925])).
% 28.85/19.10 tff(17927,plain,
% 28.85/19.10 (c2 = f5(c2)),
% 28.85/19.10 inference(modus_ponens,[status(thm)],[17926, 1279])).
% 28.85/19.10 tff(17928,plain,
% 28.85/19.10 (f8(f9(c1, c1)) = f9(c1, c1)),
% 28.85/19.10 inference(symmetry,[status(thm)],[17859])).
% 28.85/19.10 tff(17929,plain,
% 28.85/19.10 (f8(f9(c1, c1)) = c2),
% 28.85/19.10 inference(transitivity,[status(thm)],[17928, 17727, 1498])).
% 28.85/19.10 tff(17930,plain,
% 28.85/19.10 ((f9(c1, c2) = f8(f9(c1, c1))) <=> (f9(c1, c2) = c2)),
% 28.85/19.10 inference(monotonicity,[status(thm)],[17929])).
% 28.85/19.10 tff(17931,plain,
% 28.85/19.10 ((c2 = f5(c2)) <=> (f9(c1, c1) = f5(f9(c1, c1)))),
% 28.85/19.10 inference(symmetry,[status(thm)],[17828])).
% 28.85/19.10 tff(17932,plain,
% 28.85/19.10 ((f5(c2) = c2) <=> (f9(c1, c1) = f5(f9(c1, c1)))),
% 28.85/19.10 inference(transitivity,[status(thm)],[1279, 17931])).
% 28.85/19.10 tff(17933,plain,
% 28.85/19.10 (f9(c1, c1) = f5(f9(c1, c1))),
% 28.85/19.10 inference(modus_ponens,[status(thm)],[17926, 17932])).
% 28.85/19.10 tff(17934,assumption,(f9(c1, c1) = f5(f9(c1, c1))), introduced(assumption)).
% 28.85/19.10 tff(17935,plain,
% 28.85/19.10 ((f9(c1, f9(c1, c1)) = f9(c1, c1)) <=> (f9(c1, c2) = c2)),
% 28.85/19.10 inference(monotonicity,[status(thm)],[17911, 17728])).
% 28.85/19.10 tff(17936,plain,
% 28.85/19.10 ((f9(c1, c2) = c2) <=> (f9(c1, f9(c1, c1)) = f9(c1, c1))),
% 28.85/19.10 inference(symmetry,[status(thm)],[17935])).
% 28.85/19.10 tff(17937,plain,
% 28.85/19.10 ((~(f9(c1, c2) = c2)) <=> (~(f9(c1, f9(c1, c1)) = f9(c1, c1)))),
% 28.85/19.10 inference(monotonicity,[status(thm)],[17936])).
% 28.85/19.10 tff(17938,plain,
% 28.85/19.10 ((~(f9(c1, c2) = f8(f9(c1, c1)))) <=> (~(f9(c1, c2) = c2))),
% 28.85/19.10 inference(monotonicity,[status(thm)],[17878])).
% 28.85/19.10 tff(17939,plain,
% 28.85/19.10 (~(f9(c1, c2) = c2)),
% 28.85/19.10 inference(modus_ponens,[status(thm)],[17892, 17938])).
% 28.85/19.11 tff(17940,plain,
% 28.85/19.11 (~(f9(c1, f9(c1, c1)) = f9(c1, c1))),
% 28.85/19.11 inference(modus_ponens,[status(thm)],[17939, 17937])).
% 28.85/19.11 tff(17941,plain,
% 28.85/19.11 (big_f(f9(c1, f9(c1, c1)), f10(c1)) <=> big_f(f9(c1, c2), f10(c1))),
% 28.85/19.11 inference(monotonicity,[status(thm)],[17911])).
% 28.85/19.11 tff(17942,plain,
% 28.85/19.11 (big_f(f9(c1, c2), f10(c1)) <=> big_f(f9(c1, f9(c1, c1)), f10(c1))),
% 28.85/19.11 inference(symmetry,[status(thm)],[17941])).
% 28.85/19.11 tff(17943,plain,
% 28.85/19.11 ((~big_f(f9(c1, c2), f10(c1))) <=> (~big_f(f9(c1, f9(c1, c1)), f10(c1)))),
% 28.85/19.11 inference(monotonicity,[status(thm)],[17942])).
% 28.85/19.11 tff(17944,assumption,(~big_f(f9(c1, c2), f10(c1))), introduced(assumption)).
% 28.85/19.11 tff(17945,plain,
% 28.85/19.11 (~big_f(f9(c1, f9(c1, c1)), f10(c1))),
% 28.85/19.11 inference(modus_ponens,[status(thm)],[17944, 17943])).
% 28.85/19.11 tff(17946,plain,
% 28.85/19.11 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | big_f(f7(f9(c1, c1)), f9(c1, c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~(f9(c1, c1) = f5(f9(c1, c1)))) | (f9(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f9(c1, f9(c1, c1)), f10(c1)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (~(f10(c1) = c1)) | big_f(f7(f9(c1, c1)), f9(c1, c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~(f9(c1, c1) = f5(f9(c1, c1)))) | (f9(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f9(c1, f9(c1, c1)), f10(c1)))),
% 28.85/19.11 inference(rewrite,[status(thm)],[])).
% 28.85/19.11 tff(17947,plain,
% 28.85/19.11 (((~(f10(c1) = c1)) | (f9(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f9(c1, f9(c1, c1)), f10(c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), f9(c1, c1)) | (~(f9(c1, c1) = f5(f9(c1, c1))))) <=> ((~(f10(c1) = c1)) | big_f(f7(f9(c1, c1)), f9(c1, c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~(f9(c1, c1) = f5(f9(c1, c1)))) | (f9(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f9(c1, f9(c1, c1)), f10(c1)))),
% 28.85/19.11 inference(rewrite,[status(thm)],[])).
% 28.85/19.11 tff(17948,plain,
% 28.85/19.11 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f9(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f9(c1, f9(c1, c1)), f10(c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), f9(c1, c1)) | (~(f9(c1, c1) = f5(f9(c1, c1)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | big_f(f7(f9(c1, c1)), f9(c1, c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~(f9(c1, c1) = f5(f9(c1, c1)))) | (f9(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f9(c1, f9(c1, c1)), f10(c1))))),
% 28.85/19.11 inference(monotonicity,[status(thm)],[17947])).
% 28.85/19.11 tff(17949,plain,
% 28.85/19.11 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f9(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f9(c1, f9(c1, c1)), f10(c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), f9(c1, c1)) | (~(f9(c1, c1) = f5(f9(c1, c1)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (~(f10(c1) = c1)) | big_f(f7(f9(c1, c1)), f9(c1, c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~(f9(c1, c1) = f5(f9(c1, c1)))) | (f9(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f9(c1, f9(c1, c1)), f10(c1)))),
% 28.85/19.11 inference(transitivity,[status(thm)],[17948, 17946])).
% 28.85/19.11 tff(17950,plain,
% 28.85/19.11 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f9(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f9(c1, f9(c1, c1)), f10(c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), f9(c1, c1)) | (~(f9(c1, c1) = f5(f9(c1, c1)))))),
% 28.85/19.11 inference(quant_inst,[status(thm)],[])).
% 28.85/19.11 tff(17951,plain,
% 28.85/19.11 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (~(f10(c1) = c1)) | big_f(f7(f9(c1, c1)), f9(c1, c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~(f9(c1, c1) = f5(f9(c1, c1)))) | (f9(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f9(c1, f9(c1, c1)), f10(c1))),
% 28.85/19.11 inference(modus_ponens,[status(thm)],[17950, 17949])).
% 28.85/19.11 tff(17952,plain,
% 28.85/19.11 ((f9(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f9(c1, f9(c1, c1)), f10(c1))),
% 28.85/19.11 inference(unit_resolution,[status(thm)],[17951, 267, 3762, 17832, 17833, 17934])).
% 28.85/19.11 tff(17953,plain,
% 28.85/19.11 ($false),
% 28.85/19.11 inference(unit_resolution,[status(thm)],[17952, 17945, 17940])).
% 28.85/19.11 tff(17954,plain,(big_f(f9(c1, c2), f10(c1)) | (~(f10(c1) = c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), f9(c1, c1)) | (~(f9(c1, c1) = f5(f9(c1, c1)))) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | (f9(c1, c2) = f8(f9(c1, c1))) | (~(f9(c1, c1) = f8(f9(c1, c1))))), inference(lemma,lemma(discharge,[]))).
% 28.85/19.11 tff(17955,plain,
% 28.85/19.11 (big_f(f9(c1, c2), f10(c1))),
% 28.85/19.11 inference(unit_resolution,[status(thm)],[17954, 17892, 17832, 17833, 17934, 1498, 11752, 11819, 3762, 17860])).
% 28.85/19.11 tff(17956,plain,
% 28.85/19.11 (big_f(f9(c1, c2), f10(f9(c1, c1)))),
% 28.85/19.11 inference(modus_ponens,[status(thm)],[17955, 17887])).
% 28.85/19.11 tff(17957,plain,
% 28.85/19.11 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (big_f(f7(f9(c1, c1)), f9(c1, c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~(f9(c1, c1) = f5(f9(c1, c1)))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c2), f10(f9(c1, c1)))) | (f9(c1, c2) = f8(f9(c1, c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | big_f(f7(f9(c1, c1)), f9(c1, c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~(f9(c1, c1) = f5(f9(c1, c1)))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c2), f10(f9(c1, c1)))) | (f9(c1, c2) = f8(f9(c1, c1))))),
% 28.85/19.11 inference(rewrite,[status(thm)],[])).
% 28.85/19.11 tff(17958,plain,
% 28.85/19.11 (((~(f9(c1, c1) = f5(f9(c1, c1)))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c2) = f8(f9(c1, c1))) | (~big_f(f9(c1, c2), f10(f9(c1, c1)))) | (f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), f9(c1, c1))) <=> (big_f(f7(f9(c1, c1)), f9(c1, c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~(f9(c1, c1) = f5(f9(c1, c1)))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c2), f10(f9(c1, c1)))) | (f9(c1, c2) = f8(f9(c1, c1))))),
% 28.85/19.11 inference(rewrite,[status(thm)],[])).
% 28.85/19.11 tff(17959,plain,
% 28.85/19.11 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(f9(c1, c1) = f5(f9(c1, c1)))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c2) = f8(f9(c1, c1))) | (~big_f(f9(c1, c2), f10(f9(c1, c1)))) | (f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), f9(c1, c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (big_f(f7(f9(c1, c1)), f9(c1, c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~(f9(c1, c1) = f5(f9(c1, c1)))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c2), f10(f9(c1, c1)))) | (f9(c1, c2) = f8(f9(c1, c1)))))),
% 28.85/19.11 inference(monotonicity,[status(thm)],[17958])).
% 28.85/19.11 tff(17960,plain,
% 28.85/19.11 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(f9(c1, c1) = f5(f9(c1, c1)))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c2) = f8(f9(c1, c1))) | (~big_f(f9(c1, c2), f10(f9(c1, c1)))) | (f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), f9(c1, c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | big_f(f7(f9(c1, c1)), f9(c1, c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~(f9(c1, c1) = f5(f9(c1, c1)))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c2), f10(f9(c1, c1)))) | (f9(c1, c2) = f8(f9(c1, c1))))),
% 28.85/19.11 inference(transitivity,[status(thm)],[17959, 17957])).
% 28.85/19.11 tff(17961,plain,
% 28.85/19.11 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(f9(c1, c1) = f5(f9(c1, c1)))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c2) = f8(f9(c1, c1))) | (~big_f(f9(c1, c2), f10(f9(c1, c1)))) | (f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), f9(c1, c1)))),
% 28.85/19.11 inference(quant_inst,[status(thm)],[])).
% 28.85/19.11 tff(17962,plain,
% 28.85/19.11 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | big_f(f7(f9(c1, c1)), f9(c1, c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~(f9(c1, c1) = f5(f9(c1, c1)))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c2), f10(f9(c1, c1)))) | (f9(c1, c2) = f8(f9(c1, c1)))),
% 28.85/19.11 inference(modus_ponens,[status(thm)],[17961, 17960])).
% 28.85/19.11 tff(17963,plain,
% 28.85/19.11 (~big_f(f9(c1, c2), f10(f9(c1, c1)))),
% 28.85/19.11 inference(unit_resolution,[status(thm)],[17962, 705, 17823, 17832, 17833, 17892, 17934])).
% 28.85/19.11 tff(17964,plain,
% 28.85/19.11 ($false),
% 28.85/19.11 inference(unit_resolution,[status(thm)],[17963, 17956])).
% 28.85/19.11 tff(17965,plain,((f9(c1, c2) = f8(f9(c1, c1))) | (~(f10(c1) = c1)) | (~(f10(c2) = c1)) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), f9(c1, c1)) | (~(f9(c1, c1) = f5(f9(c1, c1)))) | (~(f9(c1, c1) = f8(f9(c1, c1))))), inference(lemma,lemma(discharge,[]))).
% 28.85/19.11 tff(17966,plain,
% 28.85/19.11 (f9(c1, c2) = f8(f9(c1, c1))),
% 28.85/19.11 inference(unit_resolution,[status(thm)],[17965, 17826, 11819, 1498, 11752, 17818, 3762, 17933, 17859])).
% 28.85/19.11 tff(17967,plain,
% 28.85/19.11 (f9(c1, c2) = c2),
% 28.85/19.11 inference(modus_ponens,[status(thm)],[17966, 17930])).
% 28.85/19.11 tff(17968,plain,
% 28.85/19.11 (f9(c1, c2) = f9(c1, c1)),
% 28.85/19.11 inference(transitivity,[status(thm)],[17966, 17928])).
% 28.85/19.11 tff(17969,plain,
% 28.85/19.11 (big_f(f9(c1, c2), f10(c1)) <=> big_f(f9(c1, c1), c1)),
% 28.85/19.11 inference(monotonicity,[status(thm)],[17968, 3762])).
% 28.85/19.11 tff(17970,plain,
% 28.85/19.11 (big_f(f9(c1, c1), c1) <=> big_f(f9(c1, c2), f10(c1))),
% 28.85/19.11 inference(symmetry,[status(thm)],[17969])).
% 28.85/19.11 tff(17971,plain,
% 28.85/19.11 (big_f(f9(c1, c2), f10(c1))),
% 28.85/19.11 inference(modus_ponens,[status(thm)],[8714, 17970])).
% 28.85/19.11 tff(17972,plain,
% 28.85/19.11 ($false),
% 28.85/19.11 inference(unit_resolution,[status(thm)],[8204, 17971, 17967, 3762, 17, 1521, 17927])).
% 28.85/19.11 tff(17973,plain,(big_f(f7(c2), c2) | (~(f10(c1) = c1)) | (f7(c2) = c2) | (~big_f(f9(c1, c1), c1)) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | big_f(f7(c2), c1) | (~big_f(f9(c1, c1), f10(f9(c1, c1))))), inference(lemma,lemma(discharge,[]))).
% 28.85/19.11 tff(17974,plain,
% 28.85/19.11 (big_f(f7(c2), c1)),
% 28.85/19.11 inference(unit_resolution,[status(thm)],[17973, 17785, 1498, 17, 3762, 11752, 11819, 1521, 17807])).
% 28.85/19.11 tff(17975,plain,
% 28.85/19.11 (big_f(f9(c1, c1), f10(f9(c1, c1)))),
% 28.85/19.11 inference(modus_ponens,[status(thm)],[8714, 17768])).
% 28.85/19.11 tff(17976,plain,
% 28.85/19.11 (c1 = f7(f9(c1, c1))),
% 28.85/19.11 inference(transitivity,[status(thm)],[342, 17739])).
% 28.85/19.11 tff(17977,plain,
% 28.85/19.11 (big_f(c1, c2) <=> big_f(f7(f9(c1, c1)), f9(c1, c1))),
% 28.85/19.11 inference(monotonicity,[status(thm)],[17976, 17734])).
% 28.85/19.11 tff(17978,plain,
% 28.85/19.11 (big_f(f7(f9(c1, c1)), f9(c1, c1)) <=> big_f(c1, c2)),
% 28.85/19.11 inference(symmetry,[status(thm)],[17977])).
% 28.85/19.11 tff(17979,plain,
% 28.85/19.11 ((~big_f(f7(f9(c1, c1)), f9(c1, c1))) <=> (~big_f(c1, c2))),
% 28.85/19.11 inference(monotonicity,[status(thm)],[17978])).
% 28.85/19.11 tff(17980,plain,
% 28.85/19.11 (big_f(f7(c2), c1) <=> big_f(f7(f9(c1, c1)), c1)),
% 28.85/19.11 inference(monotonicity,[status(thm)],[17739])).
% 28.85/19.11 tff(17981,plain,
% 28.85/19.11 (big_f(f7(f9(c1, c1)), c1)),
% 28.85/19.11 inference(modus_ponens,[status(thm)],[338, 17980])).
% 28.85/19.11 tff(17982,plain,
% 28.85/19.11 (big_f(c1, f10(f9(c1, c1))) <=> big_f(c1, c1)),
% 28.85/19.11 inference(monotonicity,[status(thm)],[17766])).
% 28.85/19.11 tff(17983,plain,
% 28.85/19.11 (big_f(c1, c1) <=> big_f(c1, f10(f9(c1, c1)))),
% 28.85/19.11 inference(symmetry,[status(thm)],[17982])).
% 28.85/19.11 tff(17984,plain,
% 28.85/19.11 (f7(f9(c1, c1)) = c1),
% 28.85/19.11 inference(transitivity,[status(thm)],[17729, 292])).
% 28.85/19.11 tff(17985,plain,
% 28.85/19.11 (big_f(f7(f9(c1, c1)), c1) <=> big_f(c1, c1)),
% 28.85/19.11 inference(monotonicity,[status(thm)],[17984])).
% 28.85/19.11 tff(17986,plain,
% 28.85/19.11 (big_f(f7(c2), c1) <=> big_f(c1, f10(f9(c1, c1)))),
% 28.85/19.11 inference(transitivity,[status(thm)],[17980, 17985, 17983])).
% 28.85/19.11 tff(17987,plain,
% 28.85/19.11 (big_f(c1, f10(f9(c1, c1)))),
% 28.85/19.11 inference(modus_ponens,[status(thm)],[338, 17986])).
% 28.85/19.11 tff(17988,plain,
% 28.85/19.11 ((c1 = f8(c3)) <=> (f8(c3) = c1)),
% 28.85/19.11 inference(commutativity,[status(thm)],[])).
% 28.85/19.11 tff(17989,plain,
% 28.85/19.11 (c3 = f9(c1, c1)),
% 28.85/19.11 inference(transitivity,[status(thm)],[67, 17733, 17726])).
% 28.85/19.11 tff(17990,plain,
% 28.85/19.11 (f8(c3) = f8(f9(c1, c1))),
% 28.85/19.11 inference(monotonicity,[status(thm)],[17989])).
% 28.85/19.11 tff(17991,plain,
% 28.85/19.11 (f8(f9(c1, c1)) = f8(c3)),
% 28.85/19.11 inference(symmetry,[status(thm)],[17990])).
% 28.85/19.11 tff(17992,plain,
% 28.85/19.11 ((c1 = f8(f9(c1, c1))) <=> (c1 = f8(c3))),
% 28.85/19.11 inference(monotonicity,[status(thm)],[17991])).
% 28.85/19.11 tff(17993,plain,
% 28.85/19.11 ((c1 = f8(f9(c1, c1))) <=> (f8(c3) = c1)),
% 28.85/19.11 inference(transitivity,[status(thm)],[17992, 17988])).
% 28.85/19.11 tff(17994,plain,
% 28.85/19.11 ((f8(c3) = c1) <=> (c1 = f8(f9(c1, c1)))),
% 28.85/19.11 inference(symmetry,[status(thm)],[17993])).
% 28.85/19.11 tff(17995,assumption,(big_f(f7(f9(c1, c1)), f9(c1, c1))), introduced(assumption)).
% 28.85/19.11 tff(17996,plain,
% 28.85/19.11 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f9(c1, c1) = f8(f9(c1, c1))) | (f7(f9(c1, c1)) = f9(c1, c1)) | (c1 = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f9(c1, c1) = f8(f9(c1, c1))) | (f7(f9(c1, c1)) = f9(c1, c1)) | (c1 = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))))),
% 28.85/19.11 inference(rewrite,[status(thm)],[])).
% 28.85/19.11 tff(17997,plain,
% 28.85/19.11 (((f10(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (f7(f9(c1, c1)) = f9(c1, c1)) | (c1 = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), c1))) <=> ((f9(c1, c1) = f8(f9(c1, c1))) | (f7(f9(c1, c1)) = f9(c1, c1)) | (c1 = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))))),
% 28.85/19.11 inference(rewrite,[status(thm)],[])).
% 28.85/19.11 tff(17998,plain,
% 28.85/19.11 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (f7(f9(c1, c1)) = f9(c1, c1)) | (c1 = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f9(c1, c1) = f8(f9(c1, c1))) | (f7(f9(c1, c1)) = f9(c1, c1)) | (c1 = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1))))))),
% 28.85/19.11 inference(monotonicity,[status(thm)],[17997])).
% 28.85/19.11 tff(17999,plain,
% 28.85/19.11 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (f7(f9(c1, c1)) = f9(c1, c1)) | (c1 = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f9(c1, c1) = f8(f9(c1, c1))) | (f7(f9(c1, c1)) = f9(c1, c1)) | (c1 = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))))),
% 28.85/19.11 inference(transitivity,[status(thm)],[17998, 17996])).
% 28.85/19.11 tff(18000,plain,
% 28.85/19.11 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (f7(f9(c1, c1)) = f9(c1, c1)) | (c1 = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), c1)))),
% 28.85/19.11 inference(quant_inst,[status(thm)],[])).
% 28.85/19.11 tff(18001,plain,
% 28.85/19.11 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f9(c1, c1) = f8(f9(c1, c1))) | (f7(f9(c1, c1)) = f9(c1, c1)) | (c1 = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1))))),
% 28.85/19.11 inference(modus_ponens,[status(thm)],[18000, 17999])).
% 28.85/19.11 tff(18002,plain,
% 28.85/19.11 ((f9(c1, c1) = f8(f9(c1, c1))) | (c1 = f5(f9(c1, c1)))),
% 28.85/19.11 inference(unit_resolution,[status(thm)],[18001, 1659, 17834, 17819, 17812, 17832])).
% 28.85/19.11 tff(18003,plain,
% 28.85/19.11 (c1 = f5(f9(c1, c1))),
% 28.85/19.11 inference(unit_resolution,[status(thm)],[18002, 17831])).
% 28.85/19.11 tff(18004,plain,
% 28.85/19.11 (f5(f9(c1, c1)) = c1),
% 28.85/19.11 inference(symmetry,[status(thm)],[18003])).
% 28.85/19.11 tff(18005,plain,
% 28.85/19.11 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f9(c1, c1) = f8(f9(c1, c1))) | (f9(c1, c1) = f5(f9(c1, c1))) | (f7(f9(c1, c1)) = f9(c1, c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (~big_f(f7(f9(c1, c1)), f9(c1, c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f9(c1, c1) = f8(f9(c1, c1))) | (f9(c1, c1) = f5(f9(c1, c1))) | (f7(f9(c1, c1)) = f9(c1, c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (~big_f(f7(f9(c1, c1)), f9(c1, c1))))),
% 28.85/19.11 inference(rewrite,[status(thm)],[])).
% 28.85/19.11 tff(18006,plain,
% 28.85/19.11 (((f10(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (f7(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c1) = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), f9(c1, c1)))) <=> ((f9(c1, c1) = f8(f9(c1, c1))) | (f9(c1, c1) = f5(f9(c1, c1))) | (f7(f9(c1, c1)) = f9(c1, c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (~big_f(f7(f9(c1, c1)), f9(c1, c1))))),
% 28.85/19.11 inference(rewrite,[status(thm)],[])).
% 28.85/19.11 tff(18007,plain,
% 28.85/19.11 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (f7(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c1) = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), f9(c1, c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f9(c1, c1) = f8(f9(c1, c1))) | (f9(c1, c1) = f5(f9(c1, c1))) | (f7(f9(c1, c1)) = f9(c1, c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (~big_f(f7(f9(c1, c1)), f9(c1, c1)))))),
% 28.85/19.11 inference(monotonicity,[status(thm)],[18006])).
% 28.85/19.11 tff(18008,plain,
% 28.85/19.11 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (f7(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c1) = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), f9(c1, c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f9(c1, c1) = f8(f9(c1, c1))) | (f9(c1, c1) = f5(f9(c1, c1))) | (f7(f9(c1, c1)) = f9(c1, c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (~big_f(f7(f9(c1, c1)), f9(c1, c1))))),
% 28.85/19.11 inference(transitivity,[status(thm)],[18007, 18005])).
% 28.85/19.11 tff(18009,plain,
% 28.85/19.11 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (f7(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c1) = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), f9(c1, c1))))),
% 28.85/19.12 inference(quant_inst,[status(thm)],[])).
% 28.85/19.12 tff(18010,plain,
% 28.85/19.12 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f9(c1, c1) = f8(f9(c1, c1))) | (f9(c1, c1) = f5(f9(c1, c1))) | (f7(f9(c1, c1)) = f9(c1, c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (~big_f(f7(f9(c1, c1)), f9(c1, c1)))),
% 28.85/19.12 inference(modus_ponens,[status(thm)],[18009, 18008])).
% 28.85/19.12 tff(18011,plain,
% 28.85/19.12 ((f9(c1, c1) = f8(f9(c1, c1))) | (f9(c1, c1) = f5(f9(c1, c1)))),
% 28.85/19.12 inference(unit_resolution,[status(thm)],[18010, 1659, 17834, 17819, 17832, 17995])).
% 28.85/19.12 tff(18012,plain,
% 28.85/19.12 (f9(c1, c1) = f5(f9(c1, c1))),
% 28.85/19.12 inference(unit_resolution,[status(thm)],[18011, 17831])).
% 28.85/19.12 tff(18013,plain,
% 28.85/19.12 (f9(c1, c1) = c1),
% 28.85/19.12 inference(transitivity,[status(thm)],[18012, 18004])).
% 28.85/19.12 tff(18014,plain,
% 28.85/19.12 ($false),
% 28.85/19.12 inference(unit_resolution,[status(thm)],[4070, 18013])).
% 28.85/19.12 tff(18015,plain,((f9(c1, c1) = f8(f9(c1, c1))) | (f9(c1, c1) = c1) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f7(f9(c1, c1)), f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), c1))), inference(lemma,lemma(discharge,[]))).
% 28.85/19.12 tff(18016,plain,
% 28.85/19.12 (f9(c1, c1) = f8(f9(c1, c1))),
% 28.85/19.12 inference(unit_resolution,[status(thm)],[18015, 17995, 17823, 17819, 17832, 17822, 17812])).
% 28.85/19.12 tff(18017,plain,
% 28.85/19.12 (f8(f9(c1, c1)) = f9(c1, c1)),
% 28.85/19.12 inference(symmetry,[status(thm)],[18016])).
% 28.85/19.12 tff(18018,plain,
% 28.85/19.12 (f8(c3) = f9(c1, c1)),
% 28.85/19.12 inference(transitivity,[status(thm)],[17990, 18017])).
% 28.85/19.12 tff(18019,plain,
% 28.85/19.12 ((f8(c3) = c1) <=> (f9(c1, c1) = c1)),
% 28.85/19.12 inference(monotonicity,[status(thm)],[18018])).
% 28.85/19.12 tff(18020,plain,
% 28.85/19.12 ((f9(c1, c1) = c1) <=> (f8(c3) = c1)),
% 28.85/19.12 inference(symmetry,[status(thm)],[18019])).
% 28.85/19.12 tff(18021,plain,
% 28.85/19.12 ((f9(c1, c1) = c1) <=> (c1 = f8(f9(c1, c1)))),
% 28.85/19.12 inference(transitivity,[status(thm)],[18020, 17994])).
% 28.85/19.12 tff(18022,plain,
% 28.85/19.12 ((~(f9(c1, c1) = c1)) <=> (~(c1 = f8(f9(c1, c1))))),
% 28.85/19.12 inference(monotonicity,[status(thm)],[18021])).
% 28.85/19.12 tff(18023,plain,
% 28.85/19.12 (~(c1 = f8(f9(c1, c1)))),
% 28.85/19.12 inference(modus_ponens,[status(thm)],[17822, 18022])).
% 28.85/19.12 tff(18024,assumption,(big_f(c1, f10(f9(c1, c1)))), introduced(assumption)).
% 28.85/19.12 tff(18025,plain,
% 28.85/19.12 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(f9(c1, c1)) = f9(c1, c1)) | (c1 = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(c1, f10(f9(c1, c1)))) | (c1 = f8(f9(c1, c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(f9(c1, c1)) = f9(c1, c1)) | (c1 = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(c1, f10(f9(c1, c1)))) | (c1 = f8(f9(c1, c1))))),
% 28.85/19.12 inference(rewrite,[status(thm)],[])).
% 28.85/19.12 tff(18026,plain,
% 28.85/19.12 (((f10(f9(c1, c1)) = f9(c1, c1)) | (c1 = f8(f9(c1, c1))) | (~big_f(c1, f10(f9(c1, c1)))) | (f7(f9(c1, c1)) = f9(c1, c1)) | (c1 = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), c1))) <=> ((f7(f9(c1, c1)) = f9(c1, c1)) | (c1 = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(c1, f10(f9(c1, c1)))) | (c1 = f8(f9(c1, c1))))),
% 28.85/19.12 inference(rewrite,[status(thm)],[])).
% 28.85/19.12 tff(18027,plain,
% 28.85/19.12 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f9(c1, c1)) = f9(c1, c1)) | (c1 = f8(f9(c1, c1))) | (~big_f(c1, f10(f9(c1, c1)))) | (f7(f9(c1, c1)) = f9(c1, c1)) | (c1 = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(f9(c1, c1)) = f9(c1, c1)) | (c1 = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(c1, f10(f9(c1, c1)))) | (c1 = f8(f9(c1, c1)))))),
% 28.85/19.12 inference(monotonicity,[status(thm)],[18026])).
% 28.85/19.12 tff(18028,plain,
% 28.85/19.12 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f9(c1, c1)) = f9(c1, c1)) | (c1 = f8(f9(c1, c1))) | (~big_f(c1, f10(f9(c1, c1)))) | (f7(f9(c1, c1)) = f9(c1, c1)) | (c1 = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(f9(c1, c1)) = f9(c1, c1)) | (c1 = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(c1, f10(f9(c1, c1)))) | (c1 = f8(f9(c1, c1))))),
% 28.85/19.12 inference(transitivity,[status(thm)],[18027, 18025])).
% 28.85/19.12 tff(18029,plain,
% 28.85/19.12 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f9(c1, c1)) = f9(c1, c1)) | (c1 = f8(f9(c1, c1))) | (~big_f(c1, f10(f9(c1, c1)))) | (f7(f9(c1, c1)) = f9(c1, c1)) | (c1 = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), c1)))),
% 28.85/19.12 inference(quant_inst,[status(thm)],[])).
% 28.85/19.12 tff(18030,plain,
% 28.85/19.12 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(f9(c1, c1)) = f9(c1, c1)) | (c1 = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(c1, f10(f9(c1, c1)))) | (c1 = f8(f9(c1, c1)))),
% 28.85/19.12 inference(modus_ponens,[status(thm)],[18029, 18028])).
% 28.85/19.12 tff(18031,plain,
% 28.85/19.12 ((c1 = f5(f9(c1, c1))) | (c1 = f8(f9(c1, c1)))),
% 28.85/19.12 inference(unit_resolution,[status(thm)],[18030, 1659, 17823, 18024, 17812, 17832])).
% 28.85/19.12 tff(18032,plain,
% 28.85/19.12 (c1 = f5(f9(c1, c1))),
% 28.85/19.12 inference(unit_resolution,[status(thm)],[18031, 18023])).
% 28.85/19.12 tff(18033,plain,
% 28.85/19.12 (f5(f9(c1, c1)) = c1),
% 28.85/19.12 inference(symmetry,[status(thm)],[18032])).
% 28.85/19.12 tff(18034,plain,
% 28.85/19.12 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f9(c1, c1) = f5(f9(c1, c1))) | (f7(f9(c1, c1)) = f9(c1, c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(c1, f10(f9(c1, c1)))) | (c1 = f8(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), f9(c1, c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f9(c1, c1) = f5(f9(c1, c1))) | (f7(f9(c1, c1)) = f9(c1, c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(c1, f10(f9(c1, c1)))) | (c1 = f8(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), f9(c1, c1))))),
% 28.85/19.12 inference(rewrite,[status(thm)],[])).
% 28.85/19.12 tff(18035,plain,
% 28.85/19.12 (((f10(f9(c1, c1)) = f9(c1, c1)) | (c1 = f8(f9(c1, c1))) | (~big_f(c1, f10(f9(c1, c1)))) | (f7(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c1) = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), f9(c1, c1)))) <=> ((f9(c1, c1) = f5(f9(c1, c1))) | (f7(f9(c1, c1)) = f9(c1, c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(c1, f10(f9(c1, c1)))) | (c1 = f8(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), f9(c1, c1))))),
% 28.85/19.12 inference(rewrite,[status(thm)],[])).
% 28.85/19.12 tff(18036,plain,
% 28.85/19.12 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f9(c1, c1)) = f9(c1, c1)) | (c1 = f8(f9(c1, c1))) | (~big_f(c1, f10(f9(c1, c1)))) | (f7(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c1) = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), f9(c1, c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f9(c1, c1) = f5(f9(c1, c1))) | (f7(f9(c1, c1)) = f9(c1, c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(c1, f10(f9(c1, c1)))) | (c1 = f8(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), f9(c1, c1)))))),
% 28.85/19.12 inference(monotonicity,[status(thm)],[18035])).
% 28.85/19.12 tff(18037,plain,
% 28.85/19.12 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f9(c1, c1)) = f9(c1, c1)) | (c1 = f8(f9(c1, c1))) | (~big_f(c1, f10(f9(c1, c1)))) | (f7(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c1) = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), f9(c1, c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f9(c1, c1) = f5(f9(c1, c1))) | (f7(f9(c1, c1)) = f9(c1, c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(c1, f10(f9(c1, c1)))) | (c1 = f8(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), f9(c1, c1))))),
% 28.85/19.12 inference(transitivity,[status(thm)],[18036, 18034])).
% 28.85/19.12 tff(18038,plain,
% 28.85/19.12 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f9(c1, c1)) = f9(c1, c1)) | (c1 = f8(f9(c1, c1))) | (~big_f(c1, f10(f9(c1, c1)))) | (f7(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c1) = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), f9(c1, c1))))),
% 28.85/19.12 inference(quant_inst,[status(thm)],[])).
% 28.85/19.12 tff(18039,plain,
% 28.85/19.12 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f9(c1, c1) = f5(f9(c1, c1))) | (f7(f9(c1, c1)) = f9(c1, c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(c1, f10(f9(c1, c1)))) | (c1 = f8(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), f9(c1, c1)))),
% 28.85/19.12 inference(modus_ponens,[status(thm)],[18038, 18037])).
% 28.85/19.12 tff(18040,plain,
% 28.85/19.12 ((f9(c1, c1) = f5(f9(c1, c1))) | (c1 = f8(f9(c1, c1)))),
% 28.85/19.12 inference(unit_resolution,[status(thm)],[18039, 1659, 17823, 18024, 17832, 17995])).
% 28.85/19.12 tff(18041,plain,
% 28.85/19.12 (f9(c1, c1) = f5(f9(c1, c1))),
% 28.85/19.12 inference(unit_resolution,[status(thm)],[18040, 18023])).
% 28.85/19.12 tff(18042,plain,
% 28.85/19.12 (f9(c1, c1) = c1),
% 28.85/19.12 inference(transitivity,[status(thm)],[18041, 18033])).
% 28.85/19.12 tff(18043,plain,
% 28.85/19.12 ($false),
% 28.85/19.12 inference(unit_resolution,[status(thm)],[17822, 18042])).
% 28.85/19.12 tff(18044,plain,((~big_f(f7(f9(c1, c1)), f9(c1, c1))) | (~big_f(c1, f10(f9(c1, c1)))) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f7(f9(c1, c1)), c1)) | (~(c3 = c2)) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1))))), inference(lemma,lemma(discharge,[]))).
% 28.85/19.12 tff(18045,plain,
% 28.85/19.12 (~big_f(f7(f9(c1, c1)), f9(c1, c1))),
% 28.85/19.12 inference(unit_resolution,[status(thm)],[18044, 17987, 17832, 17981, 67, 1498, 11752, 11819, 17819])).
% 28.85/19.12 tff(18046,plain,
% 28.85/19.12 (~big_f(c1, c2)),
% 28.85/19.12 inference(modus_ponens,[status(thm)],[18045, 17979])).
% 28.85/19.12 tff(18047,plain,
% 28.85/19.12 ((f4(c4) = c3) <=> (c1 = c3)),
% 28.85/19.12 inference(monotonicity,[status(thm)],[11752])).
% 28.85/19.12 tff(18048,plain,
% 28.85/19.12 ((c1 = c3) <=> (f4(c4) = c3)),
% 28.85/19.12 inference(symmetry,[status(thm)],[18047])).
% 28.85/19.12 tff(18049,plain,
% 28.85/19.12 ((c1 = c3) <=> (c1 = f9(c1, c1))),
% 28.85/19.12 inference(monotonicity,[status(thm)],[17989])).
% 28.85/19.12 tff(18050,plain,
% 28.85/19.12 ((c1 = c3) <=> (f9(c1, c1) = c1)),
% 28.85/19.12 inference(transitivity,[status(thm)],[18049, 17725])).
% 28.85/19.12 tff(18051,plain,
% 28.85/19.12 ((f9(c1, c1) = c1) <=> (c1 = c3)),
% 28.85/19.12 inference(symmetry,[status(thm)],[18050])).
% 28.85/19.12 tff(18052,plain,
% 28.85/19.12 ((f9(c1, c1) = c1) <=> (f4(c4) = c3)),
% 28.85/19.12 inference(transitivity,[status(thm)],[18051, 18048])).
% 28.85/19.12 tff(18053,plain,
% 28.85/19.12 ((~(f9(c1, c1) = c1)) <=> (~(f4(c4) = c3))),
% 28.85/19.12 inference(monotonicity,[status(thm)],[18052])).
% 28.85/19.12 tff(18054,plain,
% 28.85/19.12 (~(f4(c4) = c3)),
% 28.85/19.12 inference(modus_ponens,[status(thm)],[17822, 18053])).
% 28.85/19.12 tff(18055,plain,
% 28.85/19.12 ((~(f9(c1, c1) = c1)) <=> (~(c1 = c3))),
% 28.85/19.12 inference(monotonicity,[status(thm)],[18051])).
% 28.85/19.12 tff(18056,plain,
% 28.85/19.12 (~(c1 = c3)),
% 28.85/19.12 inference(modus_ponens,[status(thm)],[17822, 18055])).
% 28.85/19.12 tff(18057,plain,
% 28.85/19.12 (big_f(f7(c2), c1) <=> big_f(c1, c1)),
% 28.85/19.12 inference(transitivity,[status(thm)],[17980, 17985])).
% 28.85/19.12 tff(18058,plain,
% 28.85/19.12 (big_f(c1, c1)),
% 28.85/19.12 inference(modus_ponens,[status(thm)],[338, 18057])).
% 28.85/19.12 tff(18059,assumption,(~(f4(c4) = c3)), introduced(assumption)).
% 28.85/19.12 tff(18060,plain,
% 28.94/19.12 (f1(f4(c4), c1) = f1(c1, c1)),
% 28.94/19.12 inference(monotonicity,[status(thm)],[11752])).
% 28.94/19.12 tff(18061,plain,
% 28.94/19.12 (big_f(f4(c4), f1(f4(c4), c1)) <=> big_f(c1, f1(c1, c1))),
% 28.94/19.12 inference(monotonicity,[status(thm)],[11752, 18060])).
% 28.94/19.12 tff(18062,plain,
% 28.94/19.12 (big_f(c1, f1(c1, c1)) <=> big_f(f4(c4), f1(f4(c4), c1))),
% 28.94/19.12 inference(symmetry,[status(thm)],[18061])).
% 28.94/19.12 tff(18063,plain,
% 28.94/19.12 ((~big_f(c1, f1(c1, c1))) <=> (~big_f(f4(c4), f1(f4(c4), c1)))),
% 28.94/19.12 inference(monotonicity,[status(thm)],[18062])).
% 28.94/19.12 tff(18064,plain,
% 28.94/19.12 (~big_f(f4(c4), f1(f4(c4), c1))),
% 28.94/19.12 inference(modus_ponens,[status(thm)],[9673, 18063])).
% 28.94/19.12 tff(18065,plain,
% 28.94/19.12 ((f1(f4(c4), c1) = c1) <=> (f1(c1, c1) = c1)),
% 28.94/19.12 inference(monotonicity,[status(thm)],[18060])).
% 28.94/19.12 tff(18066,plain,
% 28.94/19.12 ((f1(c1, c1) = c1) <=> (f1(f4(c4), c1) = c1)),
% 28.94/19.12 inference(symmetry,[status(thm)],[18065])).
% 28.94/19.12 tff(18067,plain,
% 28.94/19.12 ((~(f1(c1, c1) = c1)) <=> (~(f1(f4(c4), c1) = c1))),
% 28.94/19.12 inference(monotonicity,[status(thm)],[18066])).
% 28.94/19.12 tff(18068,plain,
% 28.94/19.12 (~(f1(f4(c4), c1) = c1)),
% 28.94/19.12 inference(modus_ponens,[status(thm)],[9679, 18067])).
% 28.94/19.12 tff(18069,plain,
% 28.94/19.12 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f4(c4) = c3) | big_f(f4(c4), c4) | (f1(f4(c4), c1) = c1) | big_f(f4(c4), f1(f4(c4), c1)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (f4(c4) = c3) | big_f(f4(c4), c4) | (f1(f4(c4), c1) = c1) | big_f(f4(c4), f1(f4(c4), c1)))),
% 28.94/19.12 inference(rewrite,[status(thm)],[])).
% 28.94/19.12 tff(18070,plain,
% 28.94/19.12 (((f4(c4) = c3) | (f1(f4(c4), c1) = c1) | big_f(f4(c4), f1(f4(c4), c1)) | $false | big_f(f4(c4), c4) | $false) <=> ((f4(c4) = c3) | big_f(f4(c4), c4) | (f1(f4(c4), c1) = c1) | big_f(f4(c4), f1(f4(c4), c1)))),
% 28.94/19.12 inference(rewrite,[status(thm)],[])).
% 28.94/19.12 tff(18071,plain,
% 28.94/19.12 (((f4(c4) = c3) | (f1(f4(c4), c1) = c1) | big_f(f4(c4), f1(f4(c4), c1)) | (~(c4 = c4)) | big_f(f4(c4), c4) | (~(f4(c4) = f4(c4)))) <=> ((f4(c4) = c3) | (f1(f4(c4), c1) = c1) | big_f(f4(c4), f1(f4(c4), c1)) | $false | big_f(f4(c4), c4) | $false)),
% 28.94/19.12 inference(monotonicity,[status(thm)],[410, 407])).
% 28.94/19.12 tff(18072,plain,
% 28.94/19.12 (((f4(c4) = c3) | (f1(f4(c4), c1) = c1) | big_f(f4(c4), f1(f4(c4), c1)) | (~(c4 = c4)) | big_f(f4(c4), c4) | (~(f4(c4) = f4(c4)))) <=> ((f4(c4) = c3) | big_f(f4(c4), c4) | (f1(f4(c4), c1) = c1) | big_f(f4(c4), f1(f4(c4), c1)))),
% 28.94/19.12 inference(transitivity,[status(thm)],[18071, 18070])).
% 28.94/19.12 tff(18073,plain,
% 28.94/19.12 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f4(c4) = c3) | (f1(f4(c4), c1) = c1) | big_f(f4(c4), f1(f4(c4), c1)) | (~(c4 = c4)) | big_f(f4(c4), c4) | (~(f4(c4) = f4(c4))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f4(c4) = c3) | big_f(f4(c4), c4) | (f1(f4(c4), c1) = c1) | big_f(f4(c4), f1(f4(c4), c1))))),
% 28.94/19.12 inference(monotonicity,[status(thm)],[18072])).
% 28.94/19.12 tff(18074,plain,
% 28.94/19.12 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f4(c4) = c3) | (f1(f4(c4), c1) = c1) | big_f(f4(c4), f1(f4(c4), c1)) | (~(c4 = c4)) | big_f(f4(c4), c4) | (~(f4(c4) = f4(c4))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (f4(c4) = c3) | big_f(f4(c4), c4) | (f1(f4(c4), c1) = c1) | big_f(f4(c4), f1(f4(c4), c1)))),
% 28.94/19.12 inference(transitivity,[status(thm)],[18073, 18069])).
% 28.94/19.12 tff(18075,plain,
% 28.94/19.12 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f4(c4) = c3) | (f1(f4(c4), c1) = c1) | big_f(f4(c4), f1(f4(c4), c1)) | (~(c4 = c4)) | big_f(f4(c4), c4) | (~(f4(c4) = f4(c4))))),
% 28.94/19.12 inference(quant_inst,[status(thm)],[])).
% 28.94/19.12 tff(18076,plain,
% 28.94/19.12 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (f4(c4) = c3) | big_f(f4(c4), c4) | (f1(f4(c4), c1) = c1) | big_f(f4(c4), f1(f4(c4), c1))),
% 28.94/19.12 inference(modus_ponens,[status(thm)],[18075, 18074])).
% 28.94/19.12 tff(18077,plain,
% 28.94/19.12 ((f4(c4) = c3) | big_f(f4(c4), c4) | (f1(f4(c4), c1) = c1) | big_f(f4(c4), f1(f4(c4), c1))),
% 28.94/19.12 inference(unit_resolution,[status(thm)],[18076, 402])).
% 28.94/19.12 tff(18078,plain,
% 28.94/19.12 (big_f(f4(c4), c4)),
% 28.94/19.12 inference(unit_resolution,[status(thm)],[18077, 18068, 18064, 18059])).
% 28.94/19.12 tff(18079,plain,
% 28.94/19.12 (~(c4 = c2)),
% 28.94/19.12 inference(unit_resolution,[status(thm)],[11764, 18078, 27, 11752])).
% 28.94/19.12 tff(18080,plain,
% 28.94/19.12 (c4 = c1),
% 28.94/19.12 inference(unit_resolution,[status(thm)],[461, 18079])).
% 28.94/19.12 tff(18081,plain,
% 28.94/19.12 (c1 = c4),
% 28.94/19.12 inference(unit_resolution,[status(thm)],[484, 18080])).
% 28.94/19.12 tff(18082,plain,
% 28.94/19.12 ((~(c1 = c4)) | (c1 = f4(c1))),
% 28.94/19.12 inference(unit_resolution,[status(thm)],[11532, 525, 9679, 168, 9673, 4932])).
% 28.94/19.12 tff(18083,plain,
% 28.94/19.12 (c1 = f4(c1)),
% 28.94/19.12 inference(unit_resolution,[status(thm)],[18082, 18081])).
% 28.94/19.12 tff(18084,plain,
% 28.94/19.12 (f4(c1) = c1),
% 28.94/19.12 inference(symmetry,[status(thm)],[18083])).
% 28.94/19.12 tff(18085,assumption,(~(f9(c1, c1) = f4(c1))), introduced(assumption)).
% 28.94/19.12 tff(18086,plain,
% 28.94/19.12 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((f1(c1, c1) = c1) | (c1 = c3) | big_f(c1, f1(c1, c1)) | (~(c1 = c4)) | (~big_f(f9(c1, c1), c1)) | (f9(c1, c1) = f4(c1)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (f1(c1, c1) = c1) | (c1 = c3) | big_f(c1, f1(c1, c1)) | (~(c1 = c4)) | (~big_f(f9(c1, c1), c1)) | (f9(c1, c1) = f4(c1)))),
% 28.94/19.12 inference(rewrite,[status(thm)],[])).
% 28.94/19.12 tff(18087,plain,
% 28.94/19.12 (((c1 = c3) | (f1(c1, c1) = c1) | big_f(c1, f1(c1, c1)) | (~(c1 = c4)) | (f9(c1, c1) = f4(c1)) | (~big_f(f9(c1, c1), c1))) <=> ((f1(c1, c1) = c1) | (c1 = c3) | big_f(c1, f1(c1, c1)) | (~(c1 = c4)) | (~big_f(f9(c1, c1), c1)) | (f9(c1, c1) = f4(c1)))),
% 28.94/19.12 inference(rewrite,[status(thm)],[])).
% 28.94/19.12 tff(18088,plain,
% 28.94/19.12 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c1 = c3) | (f1(c1, c1) = c1) | big_f(c1, f1(c1, c1)) | (~(c1 = c4)) | (f9(c1, c1) = f4(c1)) | (~big_f(f9(c1, c1), c1)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((f1(c1, c1) = c1) | (c1 = c3) | big_f(c1, f1(c1, c1)) | (~(c1 = c4)) | (~big_f(f9(c1, c1), c1)) | (f9(c1, c1) = f4(c1))))),
% 28.94/19.12 inference(monotonicity,[status(thm)],[18087])).
% 28.94/19.12 tff(18089,plain,
% 28.94/19.12 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c1 = c3) | (f1(c1, c1) = c1) | big_f(c1, f1(c1, c1)) | (~(c1 = c4)) | (f9(c1, c1) = f4(c1)) | (~big_f(f9(c1, c1), c1)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (f1(c1, c1) = c1) | (c1 = c3) | big_f(c1, f1(c1, c1)) | (~(c1 = c4)) | (~big_f(f9(c1, c1), c1)) | (f9(c1, c1) = f4(c1)))),
% 28.94/19.12 inference(transitivity,[status(thm)],[18088, 18086])).
% 28.94/19.12 tff(18090,plain,
% 28.94/19.12 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c1 = c3) | (f1(c1, c1) = c1) | big_f(c1, f1(c1, c1)) | (~(c1 = c4)) | (f9(c1, c1) = f4(c1)) | (~big_f(f9(c1, c1), c1)))),
% 28.94/19.12 inference(quant_inst,[status(thm)],[])).
% 28.94/19.12 tff(18091,plain,
% 28.94/19.12 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (f1(c1, c1) = c1) | (c1 = c3) | big_f(c1, f1(c1, c1)) | (~(c1 = c4)) | (~big_f(f9(c1, c1), c1)) | (f9(c1, c1) = f4(c1))),
% 28.94/19.13 inference(modus_ponens,[status(thm)],[18090, 18089])).
% 28.94/19.13 tff(18092,plain,
% 28.94/19.13 ($false),
% 28.94/19.13 inference(unit_resolution,[status(thm)],[18091, 525, 9710, 168, 11526, 9673, 8714, 18085])).
% 28.94/19.13 tff(18093,plain,((f1(c1, c1) = c1) | (c1 = c3) | (~(c1 = c4)) | big_f(c1, f1(c1, c1)) | (~big_f(f9(c1, c1), c1)) | (f9(c1, c1) = f4(c1))), inference(lemma,lemma(discharge,[]))).
% 28.94/19.13 tff(18094,plain,
% 28.94/19.13 (f9(c1, c1) = f4(c1)),
% 28.94/19.13 inference(unit_resolution,[status(thm)],[18093, 18081, 9673, 9679, 8714, 168])).
% 28.94/19.13 tff(18095,plain,
% 28.94/19.13 (f9(c1, c1) = c1),
% 28.94/19.13 inference(transitivity,[status(thm)],[18094, 18084])).
% 28.94/19.13 tff(18096,plain,
% 28.94/19.13 ($false),
% 28.94/19.13 inference(unit_resolution,[status(thm)],[4070, 18095])).
% 28.94/19.13 tff(18097,plain,(big_f(c1, f1(c1, c1)) | (f9(c1, c1) = c1) | (c1 = c3) | (~big_f(c1, c1)) | (~big_f(f9(c1, c1), c1)) | big_f(c1, c2) | (~(f4(c4) = c1)) | (f4(c4) = c3)), inference(lemma,lemma(discharge,[]))).
% 28.94/19.13 tff(18098,plain,
% 28.94/19.13 (big_f(c1, f1(c1, c1))),
% 28.94/19.13 inference(unit_resolution,[status(thm)],[18097, 18058, 18056, 17822, 8714, 18046, 11752, 18054])).
% 28.94/19.13 tff(18099,plain,
% 28.94/19.13 (~(f1(c1, c1) = c2)),
% 28.94/19.13 inference(unit_resolution,[status(thm)],[4561, 18098, 18046])).
% 28.94/19.13 tff(18100,plain,
% 28.94/19.13 (f1(c1, c1) = c1),
% 28.94/19.13 inference(unit_resolution,[status(thm)],[601, 18099])).
% 28.94/19.13 tff(18101,plain,
% 28.94/19.13 (big_f(c1, f9(c1, c1)) <=> big_f(c1, c2)),
% 28.94/19.13 inference(monotonicity,[status(thm)],[17728])).
% 28.94/19.13 tff(18102,plain,
% 28.94/19.13 (big_f(c1, c2) <=> big_f(c1, f9(c1, c1))),
% 28.94/19.13 inference(symmetry,[status(thm)],[18101])).
% 28.94/19.13 tff(18103,plain,
% 28.94/19.13 (big_f(f7(f9(c1, c1)), f9(c1, c1)) <=> big_f(c1, f9(c1, c1))),
% 28.94/19.13 inference(transitivity,[status(thm)],[17978, 18102])).
% 28.94/19.13 tff(18104,plain,
% 28.94/19.13 ((~big_f(f7(f9(c1, c1)), f9(c1, c1))) <=> (~big_f(c1, f9(c1, c1)))),
% 28.94/19.13 inference(monotonicity,[status(thm)],[18103])).
% 28.94/19.13 tff(18105,plain,
% 28.94/19.13 (~big_f(c1, f9(c1, c1))),
% 28.94/19.13 inference(modus_ponens,[status(thm)],[18045, 18104])).
% 28.94/19.13 tff(18106,plain,
% 28.94/19.13 (c1 = f4(c2)),
% 28.94/19.13 inference(transitivity,[status(thm)],[16651, 435])).
% 28.94/19.13 tff(18107,plain,
% 28.94/19.13 ((c2 = c4) <=> (f9(c1, c1) = c4)),
% 28.94/19.13 inference(monotonicity,[status(thm)],[17734])).
% 28.94/19.13 tff(18108,plain,
% 28.94/19.13 ((c4 = c2) <=> (f9(c1, c1) = c4)),
% 28.94/19.13 inference(transitivity,[status(thm)],[159, 18107])).
% 28.94/19.13 tff(18109,plain,
% 28.94/19.13 (f9(c1, c1) = c4),
% 28.94/19.13 inference(modus_ponens,[status(thm)],[431, 18108])).
% 28.94/19.13 tff(18110,plain,
% 28.94/19.13 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))) | (~(f9(c1, c1) = c4)) | (~(c1 = f4(f9(c1, c1)))) | big_f(c1, f9(c1, c1)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))) | (~(f9(c1, c1) = c4)) | (~(c1 = f4(f9(c1, c1)))) | big_f(c1, f9(c1, c1)))),
% 28.94/19.13 inference(rewrite,[status(thm)],[])).
% 28.94/19.13 tff(18111,plain,
% 28.94/19.13 (((c1 = c3) | (~(f9(c1, c1) = c4)) | big_f(c1, f9(c1, c1)) | (~(c1 = f4(f9(c1, c1)))) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1)))) <=> ((c1 = c3) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))) | (~(f9(c1, c1) = c4)) | (~(c1 = f4(f9(c1, c1)))) | big_f(c1, f9(c1, c1)))),
% 28.94/19.13 inference(rewrite,[status(thm)],[])).
% 28.94/19.13 tff(18112,plain,
% 28.94/19.13 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~(f9(c1, c1) = c4)) | big_f(c1, f9(c1, c1)) | (~(c1 = f4(f9(c1, c1)))) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))) | (~(f9(c1, c1) = c4)) | (~(c1 = f4(f9(c1, c1)))) | big_f(c1, f9(c1, c1))))),
% 28.94/19.13 inference(monotonicity,[status(thm)],[18111])).
% 28.94/19.13 tff(18113,plain,
% 28.94/19.13 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~(f9(c1, c1) = c4)) | big_f(c1, f9(c1, c1)) | (~(c1 = f4(f9(c1, c1)))) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))) | (~(f9(c1, c1) = c4)) | (~(c1 = f4(f9(c1, c1)))) | big_f(c1, f9(c1, c1)))),
% 28.94/19.13 inference(transitivity,[status(thm)],[18112, 18110])).
% 28.94/19.13 tff(18114,plain,
% 28.94/19.13 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~(f9(c1, c1) = c4)) | big_f(c1, f9(c1, c1)) | (~(c1 = f4(f9(c1, c1)))) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))))),
% 28.94/19.13 inference(quant_inst,[status(thm)],[])).
% 28.94/19.13 tff(18115,plain,
% 28.94/19.13 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))) | (~(f9(c1, c1) = c4)) | (~(c1 = f4(f9(c1, c1)))) | big_f(c1, f9(c1, c1))),
% 28.94/19.13 inference(modus_ponens,[status(thm)],[18114, 18113])).
% 28.94/19.13 tff(18116,plain,
% 28.94/19.13 ((~(f1(c1, c1) = c1)) | (~(f9(c1, c1) = c4)) | (~(c1 = f4(f9(c1, c1))))),
% 28.94/19.13 inference(unit_resolution,[status(thm)],[18115, 447, 168, 4559, 4686])).
% 28.94/19.13 tff(18117,plain,
% 28.94/19.13 (~(c1 = f4(f9(c1, c1)))),
% 28.94/19.13 inference(unit_resolution,[status(thm)],[18116, 18109, 624])).
% 28.94/19.13 tff(18118,plain,
% 28.94/19.13 (f4(f9(c1, c1)) = f4(c2)),
% 28.94/19.13 inference(monotonicity,[status(thm)],[17728])).
% 28.94/19.13 tff(18119,plain,
% 28.94/19.13 ((c1 = f4(f9(c1, c1))) <=> (c1 = f4(c2))),
% 28.94/19.13 inference(monotonicity,[status(thm)],[18118])).
% 28.94/19.13 tff(18120,plain,
% 28.94/19.13 ((~(c1 = f4(f9(c1, c1)))) <=> (~(c1 = f4(c2)))),
% 28.94/19.13 inference(monotonicity,[status(thm)],[18119])).
% 28.94/19.13 tff(18121,assumption,(~(c1 = f4(f9(c1, c1)))), introduced(assumption)).
% 28.94/19.13 tff(18122,plain,
% 28.94/19.13 (~(c1 = f4(c2))),
% 28.94/19.13 inference(modus_ponens,[status(thm)],[18121, 18120])).
% 28.94/19.13 tff(18123,assumption,(c1 = f4(c2)), introduced(assumption)).
% 28.94/19.13 tff(18124,plain,
% 28.94/19.13 ($false),
% 28.94/19.13 inference(unit_resolution,[status(thm)],[18123, 18122])).
% 28.94/19.13 tff(18125,plain,((c1 = f4(f9(c1, c1))) | (~(c1 = f4(c2))) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.94/19.13 tff(18126,plain,
% 28.94/19.13 ($false),
% 28.94/19.13 inference(unit_resolution,[status(thm)],[18125, 18117, 18106, 1498, 11752, 11819])).
% 28.94/19.13 tff(18127,plain,((~(c4 = c2)) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | (~(f1(c1, c1) = c1)) | (c1 = c3) | (~big_f(c1, f1(c1, c1))) | big_f(c1, f9(c1, c1))), inference(lemma,lemma(discharge,[]))).
% 28.94/19.13 tff(18128,plain,
% 28.94/19.13 (~(c4 = c2)),
% 28.94/19.13 inference(unit_resolution,[status(thm)],[18127, 18100, 11752, 11819, 1498, 18056, 18098, 18105])).
% 28.94/19.13 tff(18129,plain,
% 28.94/19.13 (c4 = c1),
% 28.94/19.13 inference(unit_resolution,[status(thm)],[461, 18128])).
% 28.94/19.13 tff(18130,plain,
% 28.94/19.13 (c1 = c4),
% 28.94/19.13 inference(unit_resolution,[status(thm)],[484, 18129])).
% 28.94/19.13 tff(18131,plain,
% 28.94/19.13 ((~(f1(c1, c1) = c1)) | (~(c1 = c4)) | (c1 = f4(c1))),
% 28.94/19.13 inference(unit_resolution,[status(thm)],[11543, 553, 18056, 18098, 18058])).
% 28.94/19.13 tff(18132,plain,
% 28.94/19.13 (c1 = f4(c1)),
% 28.94/19.13 inference(unit_resolution,[status(thm)],[18131, 18130, 18100])).
% 28.94/19.13 tff(18133,plain,
% 28.94/19.13 (f4(c1) = c1),
% 28.94/19.13 inference(symmetry,[status(thm)],[18132])).
% 28.94/19.13 tff(18134,plain,
% 28.94/19.13 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))) | (~(c1 = c4)) | (~big_f(f9(c1, c1), c1)) | (f9(c1, c1) = f4(c1)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))) | (~(c1 = c4)) | (~big_f(f9(c1, c1), c1)) | (f9(c1, c1) = f4(c1)))),
% 28.94/19.13 inference(rewrite,[status(thm)],[])).
% 28.94/19.13 tff(18135,plain,
% 28.94/19.13 (((c1 = c3) | (~(c1 = c4)) | (f9(c1, c1) = f4(c1)) | (~big_f(f9(c1, c1), c1)) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1)))) <=> ((c1 = c3) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))) | (~(c1 = c4)) | (~big_f(f9(c1, c1), c1)) | (f9(c1, c1) = f4(c1)))),
% 28.94/19.13 inference(rewrite,[status(thm)],[])).
% 28.94/19.13 tff(18136,plain,
% 28.94/19.13 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~(c1 = c4)) | (f9(c1, c1) = f4(c1)) | (~big_f(f9(c1, c1), c1)) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))) | (~(c1 = c4)) | (~big_f(f9(c1, c1), c1)) | (f9(c1, c1) = f4(c1))))),
% 28.94/19.13 inference(monotonicity,[status(thm)],[18135])).
% 28.94/19.13 tff(18137,plain,
% 28.94/19.13 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~(c1 = c4)) | (f9(c1, c1) = f4(c1)) | (~big_f(f9(c1, c1), c1)) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))) | (~(c1 = c4)) | (~big_f(f9(c1, c1), c1)) | (f9(c1, c1) = f4(c1)))),
% 28.94/19.13 inference(transitivity,[status(thm)],[18136, 18134])).
% 28.94/19.13 tff(18138,plain,
% 28.94/19.13 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~(c1 = c4)) | (f9(c1, c1) = f4(c1)) | (~big_f(f9(c1, c1), c1)) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))))),
% 28.94/19.13 inference(quant_inst,[status(thm)],[])).
% 28.94/19.13 tff(18139,plain,
% 28.94/19.13 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))) | (~(c1 = c4)) | (~big_f(f9(c1, c1), c1)) | (f9(c1, c1) = f4(c1))),
% 28.94/19.13 inference(modus_ponens,[status(thm)],[18138, 18137])).
% 28.94/19.13 tff(18140,plain,
% 28.94/19.13 ((~(f1(c1, c1) = c1)) | (~(c1 = c4)) | (f9(c1, c1) = f4(c1))),
% 28.94/19.13 inference(unit_resolution,[status(thm)],[18139, 553, 18056, 18098, 8714])).
% 28.94/19.13 tff(18141,plain,
% 28.94/19.13 (f9(c1, c1) = f4(c1)),
% 28.94/19.13 inference(unit_resolution,[status(thm)],[18140, 18130, 18100])).
% 28.94/19.13 tff(18142,plain,
% 28.94/19.13 (f9(c1, c1) = c1),
% 28.94/19.13 inference(transitivity,[status(thm)],[18141, 18133])).
% 28.94/19.13 tff(18143,plain,
% 28.94/19.13 ($false),
% 28.94/19.13 inference(unit_resolution,[status(thm)],[17822, 18142])).
% 28.94/19.13 tff(18144,plain,((~big_f(f7(c2), c1)) | (~big_f(f9(c1, c1), c1)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f7(c2) = c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~(c3 = c2)) | (~big_f(f9(c1, c1), f10(f9(c1, c1))))), inference(lemma,lemma(discharge,[]))).
% 28.94/19.13 tff(18145,plain,
% 28.94/19.13 (~big_f(f9(c1, c1), f10(f9(c1, c1)))),
% 28.94/19.13 inference(unit_resolution,[status(thm)],[18144, 8714, 11752, 11819, 1498, 292, 17832, 67, 338])).
% 28.94/19.13 tff(18146,plain,
% 28.94/19.13 ($false),
% 28.94/19.13 inference(unit_resolution,[status(thm)],[18145, 17975])).
% 28.94/19.13 tff(18147,plain,((~big_f(f9(c1, c1), c1)) | (~(f10(c2) = c1)) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f7(c2) = c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~(c3 = c2)) | (~big_f(f7(c2), c1))), inference(lemma,lemma(discharge,[]))).
% 28.94/19.13 tff(18148,plain,
% 28.94/19.13 (~(c3 = c2)),
% 28.94/19.13 inference(unit_resolution,[status(thm)],[18147, 17807, 1498, 11752, 22, 17818, 17974, 11819])).
% 28.94/19.13 tff(18149,plain,
% 28.94/19.13 (c3 = c1),
% 28.94/19.13 inference(unit_resolution,[status(thm)],[180, 18148])).
% 28.94/19.13 tff(18150,assumption,(~(f2(c3) = c1)), introduced(assumption)).
% 28.94/19.13 tff(18151,plain,
% 28.94/19.13 (f2(c3) = c2),
% 28.94/19.13 inference(unit_resolution,[status(thm)],[1273, 18150])).
% 28.94/19.13 tff(18152,plain,
% 28.94/19.13 (f2(c1) = c2),
% 28.94/19.13 inference(transitivity,[status(thm)],[13678, 18151])).
% 28.94/19.13 tff(18153,plain,
% 28.94/19.13 (big_f(c1, f2(c1)) <=> big_f(c1, c2)),
% 28.94/19.13 inference(monotonicity,[status(thm)],[18152])).
% 28.94/19.13 tff(18154,plain,
% 28.94/19.13 (big_f(c1, c2) <=> big_f(c1, f2(c1))),
% 28.94/19.13 inference(symmetry,[status(thm)],[18153])).
% 28.94/19.13 tff(18155,plain,
% 28.94/19.13 ((~big_f(c1, c2)) <=> (~big_f(c1, f2(c1)))),
% 28.94/19.13 inference(monotonicity,[status(thm)],[18154])).
% 28.94/19.13 tff(18156,plain,
% 28.94/19.13 (~big_f(c1, f2(c1))),
% 28.94/19.13 inference(modus_ponens,[status(thm)],[27, 18155])).
% 28.94/19.13 tff(18157,plain,
% 28.94/19.13 (big_f(c3, f2(c3)) <=> big_f(c1, f2(c1))),
% 28.94/19.13 inference(monotonicity,[status(thm)],[172, 6765])).
% 28.94/19.13 tff(18158,plain,
% 28.94/19.13 (c4 = f2(c3)),
% 28.94/19.13 inference(transitivity,[status(thm)],[431, 13016])).
% 28.94/19.13 tff(18159,plain,
% 28.94/19.13 (f4(c4) = c3),
% 28.94/19.13 inference(transitivity,[status(thm)],[11752, 5585])).
% 28.94/19.13 tff(18160,plain,
% 28.94/19.13 (big_f(f4(c4), c4) <=> big_f(c3, f2(c3))),
% 28.94/19.13 inference(monotonicity,[status(thm)],[18159, 18158])).
% 28.94/19.13 tff(18161,plain,
% 28.94/19.13 (big_f(c3, f2(c3)) <=> big_f(f4(c4), c4)),
% 28.94/19.13 inference(symmetry,[status(thm)],[18160])).
% 28.94/19.13 tff(18162,plain,
% 28.94/19.13 ((~big_f(c3, f2(c3))) <=> (~big_f(f4(c4), c4))),
% 28.94/19.13 inference(monotonicity,[status(thm)],[18161])).
% 28.94/19.13 tff(18163,plain,
% 28.94/19.13 (~big_f(f4(c4), c4)),
% 28.94/19.13 inference(modus_ponens,[status(thm)],[1286, 18162])).
% 28.94/19.13 tff(18164,plain,
% 28.94/19.13 ($false),
% 28.94/19.13 inference(unit_resolution,[status(thm)],[1316, 18163])).
% 28.94/19.13 tff(18165,plain,((~(c4 = c2)) | big_f(c3, f2(c3)) | (~(f2(c3) = c2)) | (~(c3 = c1)) | (~(f4(c4) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.94/19.13 tff(18166,plain,
% 28.94/19.13 (~(c4 = c2)),
% 28.94/19.13 inference(unit_resolution,[status(thm)],[18165, 1286, 18151, 172, 11752])).
% 28.94/19.13 tff(18167,plain,
% 28.94/19.13 (c4 = c1),
% 28.94/19.13 inference(unit_resolution,[status(thm)],[461, 18166])).
% 28.94/19.13 tff(18168,plain,
% 28.94/19.13 (big_f(c1, f2(c1)) <=> big_f(c3, f2(c3))),
% 28.94/19.13 inference(monotonicity,[status(thm)],[5585, 13678])).
% 28.94/19.13 tff(18169,plain,
% 28.94/19.13 (big_f(c3, f2(c3)) <=> big_f(c1, f2(c1))),
% 28.94/19.13 inference(symmetry,[status(thm)],[18168])).
% 28.94/19.13 tff(18170,plain,
% 28.94/19.13 ((~big_f(c3, f2(c3))) <=> (~big_f(c1, f2(c1)))),
% 28.94/19.13 inference(monotonicity,[status(thm)],[18169])).
% 28.94/19.13 tff(18171,plain,
% 28.94/19.13 (~big_f(c1, f2(c1))),
% 28.94/19.13 inference(modus_ponens,[status(thm)],[1286, 18170])).
% 28.94/19.13 tff(18172,plain,
% 28.94/19.13 ($false),
% 28.94/19.13 inference(unit_resolution,[status(thm)],[6546, 18171])).
% 28.94/19.13 tff(18173,plain,((~big_f(c1, f2(c1))) | big_f(c3, f2(c3)) | (~(c3 = c1))), inference(lemma,lemma(discharge,[]))).
% 28.94/19.13 tff(18174,plain,
% 28.94/19.13 (~big_f(c1, f2(c1))),
% 28.94/19.13 inference(unit_resolution,[status(thm)],[18173, 1286, 172])).
% 28.94/19.13 tff(18175,plain,
% 28.94/19.13 (big_f(f2(c1), c1) <=> big_f(c2, c1)),
% 28.94/19.13 inference(monotonicity,[status(thm)],[18152])).
% 28.94/19.13 tff(18176,plain,
% 28.94/19.13 (big_f(c2, c1) <=> big_f(f2(c1), c1)),
% 28.94/19.13 inference(symmetry,[status(thm)],[18175])).
% 28.94/19.13 tff(18177,plain,
% 28.94/19.13 (big_f(f2(c1), c1)),
% 28.94/19.13 inference(modus_ponens,[status(thm)],[348, 18176])).
% 28.94/19.13 tff(18178,plain,
% 28.94/19.13 (f4(c1) = c1),
% 28.94/19.13 inference(transitivity,[status(thm)],[568, 11752])).
% 28.94/19.13 tff(18179,plain,
% 28.94/19.13 ((f2(c1) = f4(c1)) <=> (f2(c3) = c1)),
% 28.94/19.13 inference(monotonicity,[status(thm)],[13678, 18178])).
% 28.94/19.13 tff(18180,plain,
% 28.94/19.13 ((f2(c3) = c1) <=> (f2(c1) = f4(c1))),
% 28.94/19.13 inference(symmetry,[status(thm)],[18179])).
% 28.94/19.13 tff(18181,plain,
% 28.94/19.13 ((~(f2(c3) = c1)) <=> (~(f2(c1) = f4(c1)))),
% 28.94/19.13 inference(monotonicity,[status(thm)],[18180])).
% 28.94/19.13 tff(18182,plain,
% 28.94/19.13 (~(f2(c1) = f4(c1))),
% 28.94/19.13 inference(modus_ponens,[status(thm)],[18150, 18181])).
% 28.94/19.13 tff(18183,plain,
% 28.94/19.13 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(c1 = c4)) | big_f(c1, f2(c1)) | (f2(c1) = f4(c1)) | (~big_f(f2(c1), c1)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | (~(c1 = c3)) | (~(c1 = c4)) | big_f(c1, f2(c1)) | (f2(c1) = f4(c1)) | (~big_f(f2(c1), c1)))),
% 28.94/19.13 inference(rewrite,[status(thm)],[])).
% 28.94/19.13 tff(18184,plain,
% 28.94/19.13 (((~(c1 = c3)) | $false | (~(c1 = c4)) | (f2(c1) = f4(c1)) | (~big_f(f2(c1), c1)) | big_f(c1, f2(c1))) <=> ((~(c1 = c3)) | (~(c1 = c4)) | big_f(c1, f2(c1)) | (f2(c1) = f4(c1)) | (~big_f(f2(c1), c1)))),
% 28.94/19.13 inference(rewrite,[status(thm)],[])).
% 28.94/19.13 tff(18185,plain,
% 28.94/19.13 ((f2(c1) = f2(c1)) <=> $true),
% 28.94/19.13 inference(rewrite,[status(thm)],[])).
% 28.94/19.13 tff(18186,plain,
% 28.94/19.13 ((~(f2(c1) = f2(c1))) <=> (~$true)),
% 28.94/19.13 inference(monotonicity,[status(thm)],[18185])).
% 28.94/19.13 tff(18187,plain,
% 28.94/19.13 ((~(f2(c1) = f2(c1))) <=> $false),
% 28.94/19.13 inference(transitivity,[status(thm)],[18186, 270])).
% 28.94/19.13 tff(18188,plain,
% 28.94/19.13 (((~(c1 = c3)) | (~(f2(c1) = f2(c1))) | (~(c1 = c4)) | (f2(c1) = f4(c1)) | (~big_f(f2(c1), c1)) | big_f(c1, f2(c1))) <=> ((~(c1 = c3)) | $false | (~(c1 = c4)) | (f2(c1) = f4(c1)) | (~big_f(f2(c1), c1)) | big_f(c1, f2(c1)))),
% 28.94/19.13 inference(monotonicity,[status(thm)],[18187])).
% 28.94/19.13 tff(18189,plain,
% 28.94/19.13 (((~(c1 = c3)) | (~(f2(c1) = f2(c1))) | (~(c1 = c4)) | (f2(c1) = f4(c1)) | (~big_f(f2(c1), c1)) | big_f(c1, f2(c1))) <=> ((~(c1 = c3)) | (~(c1 = c4)) | big_f(c1, f2(c1)) | (f2(c1) = f4(c1)) | (~big_f(f2(c1), c1)))),
% 28.94/19.13 inference(transitivity,[status(thm)],[18188, 18184])).
% 28.94/19.13 tff(18190,plain,
% 28.94/19.13 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(f2(c1) = f2(c1))) | (~(c1 = c4)) | (f2(c1) = f4(c1)) | (~big_f(f2(c1), c1)) | big_f(c1, f2(c1)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(c1 = c4)) | big_f(c1, f2(c1)) | (f2(c1) = f4(c1)) | (~big_f(f2(c1), c1))))),
% 28.94/19.13 inference(monotonicity,[status(thm)],[18189])).
% 28.94/19.13 tff(18191,plain,
% 28.94/19.13 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(f2(c1) = f2(c1))) | (~(c1 = c4)) | (f2(c1) = f4(c1)) | (~big_f(f2(c1), c1)) | big_f(c1, f2(c1)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | (~(c1 = c3)) | (~(c1 = c4)) | big_f(c1, f2(c1)) | (f2(c1) = f4(c1)) | (~big_f(f2(c1), c1)))),
% 28.94/19.13 inference(transitivity,[status(thm)],[18190, 18183])).
% 28.94/19.13 tff(18192,plain,
% 28.94/19.13 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(f2(c1) = f2(c1))) | (~(c1 = c4)) | (f2(c1) = f4(c1)) | (~big_f(f2(c1), c1)) | big_f(c1, f2(c1)))),
% 28.94/19.13 inference(quant_inst,[status(thm)],[])).
% 28.94/19.13 tff(18193,plain,
% 28.94/19.13 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | (~(c1 = c3)) | (~(c1 = c4)) | big_f(c1, f2(c1)) | (f2(c1) = f4(c1)) | (~big_f(f2(c1), c1))),
% 28.94/19.13 inference(modus_ponens,[status(thm)],[18192, 18191])).
% 28.94/19.13 tff(18194,plain,
% 28.94/19.13 (big_f(c1, f2(c1)) | (f2(c1) = f4(c1)) | (~big_f(f2(c1), c1))),
% 28.94/19.13 inference(unit_resolution,[status(thm)],[18193, 11666, 5611, 564])).
% 28.94/19.13 tff(18195,plain,
% 28.94/19.13 ($false),
% 28.94/19.13 inference(unit_resolution,[status(thm)],[18194, 18182, 8629, 18177])).
% 28.94/19.13 tff(18196,plain,(big_f(c1, f2(c1)) | (f2(c3) = c1) | (~(f4(c4) = c1)) | (~(c4 = c1)) | (~(c3 = c1)) | (~big_f(c2, c1))), inference(lemma,lemma(discharge,[]))).
% 28.94/19.13 tff(18197,plain,
% 28.94/19.13 (~big_f(c2, c1)),
% 28.94/19.13 inference(unit_resolution,[status(thm)],[18196, 18174, 11752, 18167, 172, 18150])).
% 28.94/19.13 tff(18198,plain,
% 28.94/19.13 (f7(c1) = f10(c3)),
% 28.94/19.13 inference(transitivity,[status(thm)],[120, 5571, 13009])).
% 28.94/19.13 tff(18199,plain,
% 28.94/19.13 (f3(f7(c1), f7(c1)) = f3(f10(c3), c2)),
% 28.94/19.13 inference(monotonicity,[status(thm)],[18198, 120])).
% 28.94/19.13 tff(18200,plain,
% 28.94/19.13 ((f3(f7(c1), f7(c1)) = f7(c1)) <=> (f3(f10(c3), c2) = c2)),
% 28.94/19.13 inference(monotonicity,[status(thm)],[18199, 120])).
% 28.94/19.13 tff(18201,plain,
% 28.94/19.13 ((f3(f10(c3), c2) = c2) <=> (f3(f7(c1), f7(c1)) = f7(c1))),
% 28.94/19.13 inference(symmetry,[status(thm)],[18200])).
% 28.94/19.13 tff(18202,plain,
% 28.94/19.13 ((~(c1 = f8(c1))) <=> (~(f8(c1) = c1))),
% 28.94/19.13 inference(monotonicity,[status(thm)],[3027])).
% 28.94/19.13 tff(18203,plain,
% 28.94/19.13 (~(c4 = c2)),
% 28.94/19.13 inference(unit_resolution,[status(thm)],[18165, 1286, 1319, 172, 11752])).
% 28.94/19.13 tff(18204,plain,
% 28.94/19.13 (c4 = c1),
% 28.94/19.13 inference(unit_resolution,[status(thm)],[461, 18203])).
% 28.94/19.13 tff(18205,plain,
% 28.94/19.13 ((f7(c1) = c4) <=> (f7(c1) = c1)),
% 28.94/19.13 inference(monotonicity,[status(thm)],[18204])).
% 28.94/19.13 tff(18206,plain,
% 28.94/19.13 ((f7(c1) = c1) <=> (f7(c1) = c4)),
% 28.94/19.13 inference(symmetry,[status(thm)],[18205])).
% 28.94/19.13 tff(18207,plain,
% 28.94/19.13 ((~(f7(c1) = c1)) <=> (~(f7(c1) = c4))),
% 28.94/19.13 inference(monotonicity,[status(thm)],[18206])).
% 28.94/19.13 tff(18208,plain,
% 28.94/19.13 (~(f7(c1) = c4)),
% 28.94/19.13 inference(modus_ponens,[status(thm)],[115, 18207])).
% 28.94/19.13 tff(18209,plain,
% 28.94/19.13 (f10(c1) = f2(c3)),
% 28.94/19.13 inference(transitivity,[status(thm)],[15, 13016])).
% 28.94/19.13 tff(18210,plain,
% 28.94/19.13 (big_f(c1, f10(c1)) <=> big_f(c3, f2(c3))),
% 28.94/19.13 inference(monotonicity,[status(thm)],[5585, 18209])).
% 28.94/19.13 tff(18211,plain,
% 28.94/19.13 (big_f(c3, f2(c3)) <=> big_f(c1, f10(c1))),
% 28.94/19.13 inference(symmetry,[status(thm)],[18210])).
% 28.94/19.13 tff(18212,plain,
% 28.94/19.13 ((~big_f(c3, f2(c3))) <=> (~big_f(c1, f10(c1)))),
% 28.94/19.13 inference(monotonicity,[status(thm)],[18211])).
% 28.94/19.13 tff(18213,plain,
% 28.94/19.13 (~big_f(c1, f10(c1))),
% 28.94/19.13 inference(modus_ponens,[status(thm)],[1286, 18212])).
% 28.94/19.13 tff(18214,plain,
% 28.94/19.13 (c1 = c4),
% 28.94/19.13 inference(unit_resolution,[status(thm)],[484, 18204])).
% 28.94/19.13 tff(18215,plain,
% 28.94/19.13 (big_f(f7(f4(c4)), c2) <=> big_f(f7(c1), c2)),
% 28.94/19.13 inference(monotonicity,[status(thm)],[16243])).
% 28.94/19.13 tff(18216,plain,
% 28.94/19.13 (big_f(f7(c1), c2) <=> big_f(f7(f4(c4)), c2)),
% 28.94/19.13 inference(symmetry,[status(thm)],[18215])).
% 28.94/19.13 tff(18217,plain,
% 28.94/19.13 (big_f(c2, c2) <=> big_f(f7(f4(c4)), c2)),
% 28.94/19.13 inference(transitivity,[status(thm)],[17721, 18216])).
% 28.94/19.13 tff(18218,plain,
% 28.94/19.13 ((~big_f(c2, c2)) <=> (~big_f(f7(f4(c4)), c2))),
% 28.94/19.13 inference(monotonicity,[status(thm)],[18217])).
% 28.94/19.13 tff(18219,plain,
% 28.94/19.13 (~big_f(f7(f4(c4)), c2)),
% 28.94/19.13 inference(modus_ponens,[status(thm)],[121, 18218])).
% 28.94/19.13 tff(18220,plain,
% 28.94/19.13 (big_f(c2, c2) <=> big_f(c2, f10(f10(c2)))),
% 28.94/19.13 inference(transitivity,[status(thm)],[2719, 11851])).
% 28.94/19.13 tff(18221,plain,
% 28.94/19.13 ((~big_f(c2, c2)) <=> (~big_f(c2, f10(f10(c2))))),
% 28.94/19.13 inference(monotonicity,[status(thm)],[18220])).
% 28.94/19.13 tff(18222,plain,
% 28.94/19.13 (~big_f(c2, f10(f10(c2)))),
% 28.94/19.13 inference(modus_ponens,[status(thm)],[121, 18221])).
% 28.94/19.13 tff(18223,plain,
% 28.94/19.13 ((c2 = f8(c1)) <=> (c2 = f8(f10(c2)))),
% 28.94/19.13 inference(symmetry,[status(thm)],[11839])).
% 28.94/19.13 tff(18224,plain,
% 28.94/19.13 ((f8(c1) = c2) <=> (c2 = f8(f10(c2)))),
% 28.94/19.13 inference(transitivity,[status(thm)],[1670, 18223])).
% 28.94/19.13 tff(18225,plain,
% 28.94/19.13 (big_f(c2, c1) <=> big_f(f7(c1), f5(c1))),
% 28.94/19.13 inference(transitivity,[status(thm)],[693, 283])).
% 28.94/19.13 tff(18226,plain,
% 28.94/19.13 ((~big_f(c2, c1)) <=> (~big_f(f7(c1), f5(c1)))),
% 28.94/19.13 inference(monotonicity,[status(thm)],[18225])).
% 28.94/19.13 tff(18227,plain,
% 28.94/19.13 (~big_f(f7(c1), f5(c1))),
% 28.94/19.13 inference(modus_ponens,[status(thm)],[2, 18226])).
% 28.94/19.13 tff(18228,assumption,(f10(f10(c2)) = c1), introduced(assumption)).
% 28.94/19.13 tff(18229,plain,
% 28.94/19.13 (f10(c1) = c4),
% 28.94/19.13 inference(transitivity,[status(thm)],[12232, 18228, 11526])).
% 28.94/19.13 tff(18230,plain,
% 28.94/19.13 (big_f(c1, f10(c1)) <=> big_f(f4(c4), c4)),
% 28.94/19.13 inference(monotonicity,[status(thm)],[16651, 18229])).
% 28.94/19.13 tff(18231,plain,
% 28.94/19.13 (big_f(f4(c4), c4) <=> big_f(c1, f10(c1))),
% 28.94/19.13 inference(symmetry,[status(thm)],[18230])).
% 28.94/19.13 tff(18232,plain,
% 28.94/19.13 (big_f(c1, f10(c1))),
% 28.94/19.13 inference(modus_ponens,[status(thm)],[474, 18231])).
% 28.94/19.13 tff(18233,plain,
% 28.94/19.13 ($false),
% 28.94/19.13 inference(unit_resolution,[status(thm)],[3030, 18232])).
% 28.94/19.13 tff(18234,plain,((~(f10(f10(c2)) = c1)) | big_f(c1, f10(c1)) | (~big_f(f4(c4), c4)) | (~(c1 = c4)) | (~(f10(c2) = c1)) | (~(f4(c4) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.94/19.13 tff(18235,plain,
% 28.94/19.13 (~(f10(f10(c2)) = c1)),
% 28.94/19.13 inference(unit_resolution,[status(thm)],[18234, 3030, 474, 11526, 11819, 11752])).
% 28.94/19.13 tff(18236,plain,
% 28.94/19.13 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f10(f10(c2)) = c1) | (f10(f10(c2)) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f10(f10(c2)) = c1) | (f10(f10(c2)) = c2))),
% 28.94/19.13 inference(rewrite,[status(thm)],[])).
% 28.94/19.13 tff(18237,plain,
% 28.94/19.13 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f10(f10(c2)) = c1) | (f10(f10(c2)) = c2))),
% 28.94/19.13 inference(quant_inst,[status(thm)],[])).
% 28.94/19.13 tff(18238,plain,
% 28.94/19.13 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f10(f10(c2)) = c1) | (f10(f10(c2)) = c2)),
% 28.94/19.14 inference(modus_ponens,[status(thm)],[18237, 18236])).
% 28.94/19.14 tff(18239,plain,
% 28.94/19.14 ((f10(f10(c2)) = c1) | (f10(f10(c2)) = c2)),
% 28.94/19.14 inference(unit_resolution,[status(thm)],[18238, 10])).
% 28.94/19.14 tff(18240,plain,
% 28.94/19.14 (f10(f10(c2)) = c2),
% 28.94/19.14 inference(unit_resolution,[status(thm)],[18239, 18235])).
% 28.94/19.14 tff(18241,plain,
% 28.94/19.14 (f10(c1) = c2),
% 28.94/19.14 inference(transitivity,[status(thm)],[12232, 18240])).
% 28.94/19.14 tff(18242,plain,
% 28.94/19.14 ((f10(c1) = c1) <=> (c2 = c4)),
% 28.94/19.14 inference(monotonicity,[status(thm)],[18241, 11526])).
% 28.94/19.14 tff(18243,plain,
% 28.94/19.14 ((c2 = c4) <=> (f10(c1) = c1)),
% 28.94/19.14 inference(symmetry,[status(thm)],[18242])).
% 28.94/19.14 tff(18244,plain,
% 28.94/19.14 ((~(c2 = c4)) <=> (~(f10(c1) = c1))),
% 28.94/19.14 inference(monotonicity,[status(thm)],[18243])).
% 28.94/19.14 tff(18245,plain,
% 28.94/19.14 ((c2 = c1) <=> (c2 = c4)),
% 28.94/19.14 inference(monotonicity,[status(thm)],[11526])).
% 28.94/19.14 tff(18246,plain,
% 28.94/19.14 ((~(c2 = c1)) <=> (~(c2 = c4))),
% 28.94/19.14 inference(monotonicity,[status(thm)],[18245])).
% 28.94/19.14 tff(18247,plain,
% 28.94/19.14 (~(c2 = c4)),
% 28.94/19.14 inference(modus_ponens,[status(thm)],[75, 18246])).
% 28.94/19.14 tff(18248,plain,
% 28.94/19.14 (~(f10(c1) = c1)),
% 28.94/19.14 inference(modus_ponens,[status(thm)],[18247, 18244])).
% 28.94/19.14 tff(18249,plain,
% 28.94/19.14 (big_f(f8(c1), f10(c1))),
% 28.94/19.14 inference(unit_resolution,[status(thm)],[2848, 18248, 730, 115])).
% 28.94/19.14 tff(18250,plain,
% 28.94/19.14 (big_f(c1, f10(c1))),
% 28.94/19.14 inference(modus_ponens,[status(thm)],[18249, 3019])).
% 28.94/19.14 tff(18251,plain,
% 28.94/19.14 ($false),
% 28.94/19.14 inference(unit_resolution,[status(thm)],[3030, 18250])).
% 28.94/19.14 tff(18252,plain,(big_f(c1, f10(c1)) | (~(f8(c1) = c1)) | big_f(f7(c1), f5(c1)) | (f7(c1) = c1) | (~(c1 = c4)) | (~(f10(c2) = c1)) | (~big_f(f4(c4), c4)) | (~(f4(c4) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.94/19.14 tff(18253,plain,
% 28.94/19.14 (~(f8(c1) = c1)),
% 28.94/19.14 inference(unit_resolution,[status(thm)],[18252, 18227, 11526, 3030, 115, 11819, 474, 11752])).
% 28.94/19.14 tff(18254,plain,
% 28.94/19.14 (f8(c1) = c2),
% 28.94/19.14 inference(unit_resolution,[status(thm)],[1680, 18253])).
% 28.94/19.14 tff(18255,plain,
% 28.94/19.14 (c2 = f8(f10(c2))),
% 28.94/19.14 inference(modus_ponens,[status(thm)],[18254, 18224])).
% 28.94/19.14 tff(18256,assumption,(~big_f(c2, f10(f10(c2)))), introduced(assumption)).
% 28.94/19.14 tff(18257,plain,
% 28.94/19.14 (~(c2 = f8(f10(c2)))),
% 28.94/19.14 inference(unit_resolution,[status(thm)],[11865, 695, 11896, 18256, 115, 692])).
% 28.94/19.14 tff(18258,plain,
% 28.94/19.14 ($false),
% 28.94/19.14 inference(unit_resolution,[status(thm)],[18257, 18255])).
% 28.94/19.14 tff(18259,plain,((f7(c1) = c1) | (~(f10(c2) = c1)) | (~(c1 = c4)) | big_f(c1, f10(c1)) | (~big_f(f4(c4), c4)) | (~(f4(c4) = c1)) | (f10(f10(c2)) = f10(c2)) | big_f(c2, f10(f10(c2))) | big_f(c2, c1) | (~(f5(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.94/19.14 tff(18260,plain,
% 28.94/19.14 (~(f5(c1) = c1)),
% 28.94/19.14 inference(unit_resolution,[status(thm)],[18259, 18213, 18214, 11819, 1316, 11752, 115, 18222, 2, 11849])).
% 28.94/19.14 tff(18261,plain,
% 28.94/19.14 (f5(c1) = c2),
% 28.94/19.14 inference(unit_resolution,[status(thm)],[1708, 18260])).
% 28.94/19.14 tff(18262,plain,
% 28.94/19.14 (big_f(f7(c1), f5(c1)) <=> big_f(f7(c1), c2)),
% 28.94/19.14 inference(monotonicity,[status(thm)],[186])).
% 28.94/19.14 tff(18263,plain,
% 28.94/19.14 (big_f(f7(c1), f5(c1)) <=> big_f(f7(f4(c4)), c2)),
% 28.94/19.14 inference(transitivity,[status(thm)],[18262, 18216])).
% 28.94/19.14 tff(18264,plain,
% 28.94/19.14 (big_f(f7(f4(c4)), c2)),
% 28.94/19.14 inference(modus_ponens,[status(thm)],[287, 18263])).
% 28.94/19.14 tff(18265,assumption,(~big_f(f7(f4(c4)), c2)), introduced(assumption)).
% 28.94/19.14 tff(18266,plain,
% 28.94/19.14 ($false),
% 28.94/19.14 inference(unit_resolution,[status(thm)],[18265, 18264])).
% 28.94/19.14 tff(18267,plain,((~big_f(f7(c1), f5(c1))) | big_f(f7(f4(c4)), c2) | (~(f4(c4) = c1)) | (~(f5(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.94/19.14 tff(18268,plain,
% 28.94/19.14 (~big_f(f7(c1), f5(c1))),
% 28.94/19.14 inference(unit_resolution,[status(thm)],[18267, 18261, 11752, 18219])).
% 28.94/19.14 tff(18269,plain,
% 28.94/19.14 (~(f8(c1) = c1)),
% 28.94/19.14 inference(unit_resolution,[status(thm)],[18252, 18268, 18214, 18213, 115, 11819, 1316, 11752])).
% 28.94/19.14 tff(18270,plain,
% 28.94/19.14 (f8(c1) = c2),
% 28.94/19.14 inference(unit_resolution,[status(thm)],[1680, 18269])).
% 28.94/19.14 tff(18271,plain,
% 28.94/19.14 (big_f(f8(c1), f10(c1)) <=> big_f(c2, c2)),
% 28.94/19.14 inference(monotonicity,[status(thm)],[18270, 15])).
% 28.94/19.14 tff(18272,plain,
% 28.94/19.14 (big_f(c2, c2) <=> big_f(f8(c1), f10(c1))),
% 28.94/19.14 inference(symmetry,[status(thm)],[18271])).
% 28.94/19.14 tff(18273,plain,
% 28.94/19.14 ((~big_f(c2, c2)) <=> (~big_f(f8(c1), f10(c1)))),
% 28.94/19.14 inference(monotonicity,[status(thm)],[18272])).
% 28.94/19.14 tff(18274,plain,
% 28.94/19.14 (~big_f(f8(c1), f10(c1))),
% 28.94/19.14 inference(modus_ponens,[status(thm)],[121, 18273])).
% 28.94/19.14 tff(18275,plain,
% 28.94/19.14 (big_f(f8(c1), f10(c1))),
% 28.94/19.14 inference(unit_resolution,[status(thm)],[2848, 18268, 3, 115])).
% 28.94/19.14 tff(18276,plain,
% 28.94/19.14 ($false),
% 28.94/19.14 inference(unit_resolution,[status(thm)],[18275, 18274])).
% 28.94/19.14 tff(18277,plain,((f10(c1) = c1) | big_f(c2, c2) | (f7(c1) = c1) | (~(f10(c2) = c1)) | (~(f4(c4) = c1)) | big_f(c2, c1) | big_f(c3, f2(c3)) | (~(f2(c3) = c2)) | (~(c3 = c1))), inference(lemma,lemma(discharge,[]))).
% 28.94/19.14 tff(18278,plain,
% 28.94/19.14 (big_f(c2, c2)),
% 28.94/19.14 inference(unit_resolution,[status(thm)],[18277, 3, 2, 11819, 11752, 115, 1286, 1319, 172])).
% 28.94/19.14 tff(18279,plain,
% 28.94/19.14 (big_f(f7(c1), f7(c1)) <=> big_f(c2, c2)),
% 28.94/19.14 inference(monotonicity,[status(thm)],[120, 120])).
% 28.94/19.14 tff(18280,plain,
% 28.94/19.14 (big_f(c2, c2) <=> big_f(f7(c1), f7(c1))),
% 28.94/19.14 inference(symmetry,[status(thm)],[18279])).
% 28.94/19.14 tff(18281,plain,
% 28.94/19.14 (big_f(f7(c1), f7(c1))),
% 28.94/19.14 inference(modus_ponens,[status(thm)],[1345, 18280])).
% 28.94/19.14 tff(18282,plain,
% 28.94/19.14 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f7(c1) = c1) | (f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (f7(c1) = f5(c1)) | (~big_f(f7(c1), f7(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | (f7(c1) = c1) | (f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (f7(c1) = f5(c1)) | (~big_f(f7(c1), f7(c1))))),
% 28.94/19.14 inference(rewrite,[status(thm)],[])).
% 28.94/19.14 tff(18283,plain,
% 28.94/19.14 (((f10(c1) = c1) | big_f(c1, f10(c1)) | (f7(c1) = c1) | (f7(c1) = f5(c1)) | (~big_f(f7(c1), f7(c1))) | (~(c1 = f8(c1)))) <=> ((f7(c1) = c1) | (f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (f7(c1) = f5(c1)) | (~big_f(f7(c1), f7(c1))))),
% 28.94/19.14 inference(rewrite,[status(thm)],[])).
% 28.94/19.14 tff(18284,plain,
% 28.94/19.14 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | big_f(c1, f10(c1)) | (f7(c1) = c1) | (f7(c1) = f5(c1)) | (~big_f(f7(c1), f7(c1))) | (~(c1 = f8(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f7(c1) = c1) | (f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (f7(c1) = f5(c1)) | (~big_f(f7(c1), f7(c1)))))),
% 28.94/19.14 inference(monotonicity,[status(thm)],[18283])).
% 28.94/19.14 tff(18285,plain,
% 28.94/19.14 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | big_f(c1, f10(c1)) | (f7(c1) = c1) | (f7(c1) = f5(c1)) | (~big_f(f7(c1), f7(c1))) | (~(c1 = f8(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | (f7(c1) = c1) | (f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (f7(c1) = f5(c1)) | (~big_f(f7(c1), f7(c1))))),
% 28.94/19.14 inference(transitivity,[status(thm)],[18284, 18282])).
% 28.94/19.14 tff(18286,plain,
% 28.94/19.14 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | big_f(c1, f10(c1)) | (f7(c1) = c1) | (f7(c1) = f5(c1)) | (~big_f(f7(c1), f7(c1))) | (~(c1 = f8(c1))))),
% 28.94/19.14 inference(quant_inst,[status(thm)],[])).
% 28.94/19.14 tff(18287,plain,
% 28.94/19.14 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | (f7(c1) = c1) | (f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (f7(c1) = f5(c1)) | (~big_f(f7(c1), f7(c1)))),
% 28.94/19.14 inference(modus_ponens,[status(thm)],[18286, 18285])).
% 28.94/19.14 tff(18288,plain,
% 28.94/19.14 ((~(c1 = f8(c1))) | (f7(c1) = f5(c1)) | (~big_f(f7(c1), f7(c1)))),
% 28.94/19.14 inference(unit_resolution,[status(thm)],[18287, 2795, 115, 3, 18213])).
% 28.94/19.14 tff(18289,plain,
% 28.94/19.14 (f7(c1) = f5(c1)),
% 28.94/19.14 inference(unit_resolution,[status(thm)],[18288, 3031, 18281])).
% 28.94/19.14 tff(18290,plain,
% 28.94/19.14 (~(f3(f5(c1), f5(c1)) = c1)),
% 28.94/19.14 inference(unit_resolution,[status(thm)],[14369, 18289, 1286, 1319, 172, 1000, 15, 115])).
% 28.94/19.14 tff(18291,plain,
% 28.94/19.14 (f3(f5(c1), f5(c1)) = c2),
% 28.94/19.14 inference(unit_resolution,[status(thm)],[7625, 18290])).
% 28.94/19.14 tff(18292,plain,
% 28.94/19.14 (c2 = f5(c1)),
% 28.94/19.14 inference(transitivity,[status(thm)],[2778, 18289])).
% 28.94/19.14 tff(18293,plain,
% 28.94/19.14 (f10(c3) = f5(c1)),
% 28.94/19.14 inference(transitivity,[status(thm)],[13006, 15, 2778, 18289])).
% 28.94/19.14 tff(18294,plain,
% 28.94/19.14 (f3(f10(c3), c2) = f3(f5(c1), f5(c1))),
% 28.94/19.14 inference(monotonicity,[status(thm)],[18293, 18292])).
% 28.94/19.14 tff(18295,plain,
% 28.94/19.14 (f3(f7(c1), f7(c1)) = f7(c1)),
% 28.94/19.14 inference(transitivity,[status(thm)],[18199, 18294, 18291, 2778])).
% 28.94/19.14 tff(18296,plain,
% 28.94/19.14 (f3(f7(c1), f7(c1)) = c2),
% 28.94/19.14 inference(transitivity,[status(thm)],[18199, 18294, 18291])).
% 28.94/19.14 tff(18297,plain,
% 28.94/19.14 (big_f(f3(f7(c1), f7(c1)), f7(c1)) <=> big_f(c2, c2)),
% 28.94/19.14 inference(monotonicity,[status(thm)],[18296, 120])).
% 28.94/19.14 tff(18298,plain,
% 28.94/19.14 (big_f(c2, c2) <=> big_f(f3(f7(c1), f7(c1)), f7(c1))),
% 28.94/19.14 inference(symmetry,[status(thm)],[18297])).
% 28.94/19.14 tff(18299,plain,
% 28.94/19.14 (big_f(f3(f7(c1), f7(c1)), f7(c1))),
% 28.94/19.14 inference(modus_ponens,[status(thm)],[1345, 18298])).
% 28.94/19.14 tff(18300,plain,
% 28.94/19.14 ((~(f3(f7(c1), f7(c1)) = f7(c1))) | (~big_f(f3(f7(c1), f7(c1)), f7(c1)))),
% 28.94/19.14 inference(unit_resolution,[status(thm)],[14382, 1398, 5611, 1000, 14360, 14359])).
% 28.94/19.14 tff(18301,plain,
% 28.94/19.14 ($false),
% 28.94/19.14 inference(unit_resolution,[status(thm)],[18300, 18299, 18295])).
% 28.94/19.14 tff(18302,plain,((~(c1 = f8(c1))) | (f7(c1) = c4) | (~big_f(c2, c2)) | (~(c3 = c1)) | big_f(c3, f2(c3)) | (~(f2(c3) = c2)) | (f7(c1) = c1) | (f10(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 28.94/19.14 tff(18303,plain,
% 28.94/19.14 (~(c1 = f8(c1))),
% 28.94/19.14 inference(unit_resolution,[status(thm)],[18302, 18278, 18208, 172, 1286, 1319, 115, 3])).
% 28.94/19.14 tff(18304,plain,
% 28.94/19.14 (~(f8(c1) = c1)),
% 28.94/19.14 inference(modus_ponens,[status(thm)],[18303, 18202])).
% 28.94/19.14 tff(18305,plain,
% 28.94/19.14 (f8(c1) = c2),
% 28.94/19.14 inference(unit_resolution,[status(thm)],[1680, 18304])).
% 28.94/19.14 tff(18306,plain,
% 28.94/19.14 ((f3(f10(c3), c2) = f8(c1)) <=> (f3(f10(c3), c2) = c2)),
% 28.94/19.14 inference(monotonicity,[status(thm)],[18305])).
% 28.94/19.14 tff(18307,plain,
% 28.94/19.14 ((f3(f10(c3), c2) = f8(c1)) <=> (f3(f7(c1), f7(c1)) = f7(c1))),
% 28.94/19.14 inference(transitivity,[status(thm)],[18306, 18201])).
% 28.94/19.14 tff(18308,plain,
% 28.94/19.14 (big_f(f3(f10(c3), c2), f10(c1)) <=> big_f(f3(f10(c3), c2), f10(c3))),
% 28.94/19.14 inference(monotonicity,[status(thm)],[13009])).
% 28.94/19.14 tff(18309,plain,
% 28.94/19.14 (big_f(f3(f10(c3), c2), f10(c3)) <=> big_f(f3(f10(c3), c2), f10(c1))),
% 28.94/19.14 inference(symmetry,[status(thm)],[18308])).
% 28.94/19.14 tff(18310,plain,
% 28.94/19.14 ((f10(f10(c2)) = c4) <=> (f10(c1) = c4)),
% 28.94/19.14 inference(monotonicity,[status(thm)],[11844])).
% 28.94/19.14 tff(18311,plain,
% 28.94/19.14 ((f10(c1) = c4) <=> (f10(f10(c2)) = c4)),
% 28.94/19.14 inference(symmetry,[status(thm)],[18310])).
% 28.94/19.14 tff(18312,plain,
% 28.94/19.14 ((f10(c1) = c4) <=> (f10(c1) = c1)),
% 28.94/19.14 inference(monotonicity,[status(thm)],[18204])).
% 28.94/19.14 tff(18313,plain,
% 28.94/19.14 ((f10(c1) = c1) <=> (f10(c1) = c4)),
% 28.94/19.14 inference(symmetry,[status(thm)],[18312])).
% 28.94/19.14 tff(18314,plain,
% 28.94/19.14 ((f10(c1) = c1) <=> (f10(f10(c2)) = c4)),
% 28.94/19.14 inference(transitivity,[status(thm)],[18313, 18311])).
% 28.94/19.14 tff(18315,plain,
% 28.94/19.14 ((~(f10(c1) = c1)) <=> (~(f10(f10(c2)) = c4))),
% 28.94/19.14 inference(monotonicity,[status(thm)],[18314])).
% 28.94/19.14 tff(18316,plain,
% 28.94/19.14 (~(f10(f10(c2)) = c4)),
% 28.94/19.14 inference(modus_ponens,[status(thm)],[3, 18315])).
% 28.94/19.14 tff(18317,plain,
% 28.94/19.14 (f10(c3) = c2),
% 28.94/19.14 inference(transitivity,[status(thm)],[13006, 16])).
% 28.94/19.14 tff(18318,assumption,(~(f10(f10(c2)) = c4)), introduced(assumption)).
% 28.94/19.14 tff(18319,assumption,(c2 = f2(c3)), introduced(assumption)).
% 28.94/19.14 tff(18320,plain,
% 28.94/19.14 (f10(f10(c2)) = f10(c3)),
% 28.94/19.14 inference(transitivity,[status(thm)],[11844, 13009])).
% 28.94/19.14 tff(18321,plain,
% 28.94/19.14 (f8(c3) = c2),
% 28.94/19.14 inference(transitivity,[status(thm)],[10861, 1671])).
% 28.94/19.14 tff(18322,plain,
% 28.94/19.14 (f3(f10(f10(c2)), f8(c3)) = f3(f10(c3), c2)),
% 28.94/19.14 inference(monotonicity,[status(thm)],[18320, 18321])).
% 28.94/19.14 tff(18323,plain,
% 28.94/19.14 (big_f(f3(f10(f10(c2)), f8(c3)), f10(f10(c2))) <=> big_f(f3(f10(c3), c2), f10(c3))),
% 28.94/19.14 inference(monotonicity,[status(thm)],[18322, 18320])).
% 28.94/19.14 tff(18324,assumption,(big_f(f3(f10(f10(c2)), f8(c3)), f10(f10(c2)))), introduced(assumption)).
% 28.94/19.14 tff(18325,plain,
% 28.94/19.14 (big_f(f3(f10(c3), c2), f10(c3))),
% 28.94/19.14 inference(modus_ponens,[status(thm)],[18324, 18323])).
% 28.94/19.14 tff(18326,plain,
% 28.94/19.14 ($false),
% 28.94/19.14 inference(unit_resolution,[status(thm)],[7385, 18325])).
% 28.94/19.14 tff(18327,plain,((~big_f(f3(f10(f10(c2)), f8(c3)), f10(f10(c2)))) | big_f(f3(f10(c3), c2), f10(c3)) | (~(f10(c2) = c1)) | (~(c3 = c1)) | (~(f8(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.94/19.14 tff(18328,plain,
% 28.94/19.14 (~big_f(f3(f10(f10(c2)), f8(c3)), f10(f10(c2)))),
% 28.94/19.14 inference(unit_resolution,[status(thm)],[18327, 7385, 11819, 172, 1671])).
% 28.94/19.14 tff(18329,plain,
% 28.94/19.14 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c2 = f2(c3))) | big_f(c3, c2) | big_f(f3(f10(f10(c2)), f8(c3)), f10(f10(c2))) | (f10(f10(c2)) = c4) | (f3(f10(f10(c2)), f8(c3)) = f8(c3)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (~(c2 = f2(c3))) | big_f(c3, c2) | big_f(f3(f10(f10(c2)), f8(c3)), f10(f10(c2))) | (f10(f10(c2)) = c4) | (f3(f10(f10(c2)), f8(c3)) = f8(c3)))),
% 28.94/19.14 inference(rewrite,[status(thm)],[])).
% 28.94/19.14 tff(18330,plain,
% 28.94/19.14 (($false | (~(c2 = f2(c3))) | (f10(f10(c2)) = c4) | (f3(f10(f10(c2)), f8(c3)) = f8(c3)) | big_f(f3(f10(f10(c2)), f8(c3)), f10(f10(c2))) | big_f(c3, c2)) <=> ((~(c2 = f2(c3))) | big_f(c3, c2) | big_f(f3(f10(f10(c2)), f8(c3)), f10(f10(c2))) | (f10(f10(c2)) = c4) | (f3(f10(f10(c2)), f8(c3)) = f8(c3)))),
% 28.94/19.14 inference(rewrite,[status(thm)],[])).
% 28.94/19.14 tff(18331,plain,
% 28.94/19.14 (((~(c3 = c3)) | (~(c2 = f2(c3))) | (f10(f10(c2)) = c4) | (f3(f10(f10(c2)), f8(c3)) = f8(c3)) | big_f(f3(f10(f10(c2)), f8(c3)), f10(f10(c2))) | big_f(c3, c2)) <=> ($false | (~(c2 = f2(c3))) | (f10(f10(c2)) = c4) | (f3(f10(f10(c2)), f8(c3)) = f8(c3)) | big_f(f3(f10(f10(c2)), f8(c3)), f10(f10(c2))) | big_f(c3, c2))),
% 28.94/19.14 inference(monotonicity,[status(thm)],[1308])).
% 28.94/19.14 tff(18332,plain,
% 28.94/19.14 (((~(c3 = c3)) | (~(c2 = f2(c3))) | (f10(f10(c2)) = c4) | (f3(f10(f10(c2)), f8(c3)) = f8(c3)) | big_f(f3(f10(f10(c2)), f8(c3)), f10(f10(c2))) | big_f(c3, c2)) <=> ((~(c2 = f2(c3))) | big_f(c3, c2) | big_f(f3(f10(f10(c2)), f8(c3)), f10(f10(c2))) | (f10(f10(c2)) = c4) | (f3(f10(f10(c2)), f8(c3)) = f8(c3)))),
% 28.94/19.14 inference(transitivity,[status(thm)],[18331, 18330])).
% 28.94/19.14 tff(18333,plain,
% 28.94/19.14 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c3 = c3)) | (~(c2 = f2(c3))) | (f10(f10(c2)) = c4) | (f3(f10(f10(c2)), f8(c3)) = f8(c3)) | big_f(f3(f10(f10(c2)), f8(c3)), f10(f10(c2))) | big_f(c3, c2))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c2 = f2(c3))) | big_f(c3, c2) | big_f(f3(f10(f10(c2)), f8(c3)), f10(f10(c2))) | (f10(f10(c2)) = c4) | (f3(f10(f10(c2)), f8(c3)) = f8(c3))))),
% 28.94/19.14 inference(monotonicity,[status(thm)],[18332])).
% 28.94/19.14 tff(18334,plain,
% 28.94/19.14 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c3 = c3)) | (~(c2 = f2(c3))) | (f10(f10(c2)) = c4) | (f3(f10(f10(c2)), f8(c3)) = f8(c3)) | big_f(f3(f10(f10(c2)), f8(c3)), f10(f10(c2))) | big_f(c3, c2))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (~(c2 = f2(c3))) | big_f(c3, c2) | big_f(f3(f10(f10(c2)), f8(c3)), f10(f10(c2))) | (f10(f10(c2)) = c4) | (f3(f10(f10(c2)), f8(c3)) = f8(c3)))),
% 28.94/19.14 inference(transitivity,[status(thm)],[18333, 18329])).
% 28.94/19.14 tff(18335,plain,
% 28.94/19.14 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c3 = c3)) | (~(c2 = f2(c3))) | (f10(f10(c2)) = c4) | (f3(f10(f10(c2)), f8(c3)) = f8(c3)) | big_f(f3(f10(f10(c2)), f8(c3)), f10(f10(c2))) | big_f(c3, c2))),
% 28.94/19.14 inference(quant_inst,[status(thm)],[])).
% 28.94/19.14 tff(18336,plain,
% 28.94/19.14 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (~(c2 = f2(c3))) | big_f(c3, c2) | big_f(f3(f10(f10(c2)), f8(c3)), f10(f10(c2))) | (f10(f10(c2)) = c4) | (f3(f10(f10(c2)), f8(c3)) = f8(c3))),
% 28.94/19.14 inference(modus_ponens,[status(thm)],[18335, 18334])).
% 28.94/19.14 tff(18337,plain,
% 28.94/19.14 ((~(c2 = f2(c3))) | big_f(c3, c2) | big_f(f3(f10(f10(c2)), f8(c3)), f10(f10(c2))) | (f10(f10(c2)) = c4) | (f3(f10(f10(c2)), f8(c3)) = f8(c3))),
% 28.94/19.14 inference(unit_resolution,[status(thm)],[18336, 1459])).
% 28.94/19.14 tff(18338,plain,
% 28.94/19.14 (f3(f10(f10(c2)), f8(c3)) = f8(c3)),
% 28.94/19.14 inference(unit_resolution,[status(thm)],[18337, 18328, 3833, 18319, 18318])).
% 28.94/19.14 tff(18339,plain,
% 28.94/19.14 (c2 = f8(c3)),
% 28.94/19.14 inference(transitivity,[status(thm)],[7098, 12787])).
% 28.94/19.14 tff(18340,plain,
% 28.94/19.14 (f10(c3) = f10(f10(c2))),
% 28.94/19.14 inference(transitivity,[status(thm)],[13006, 17779])).
% 28.94/19.14 tff(18341,plain,
% 28.94/19.14 (f3(f10(c3), c2) = f3(f10(f10(c2)), f8(c3))),
% 28.94/19.14 inference(monotonicity,[status(thm)],[18340, 18339])).
% 28.94/19.14 tff(18342,plain,
% 28.94/19.14 (f3(f10(c3), c2) = c2),
% 28.94/19.14 inference(transitivity,[status(thm)],[18341, 18338, 10861, 1671])).
% 28.94/19.14 tff(18343,plain,
% 28.94/19.14 (big_f(f3(f10(c3), c2), f10(c3)) <=> big_f(c2, c2)),
% 28.94/19.14 inference(monotonicity,[status(thm)],[18342, 18317])).
% 28.94/19.14 tff(18344,plain,
% 28.94/19.14 (big_f(c2, c2) <=> big_f(f3(f10(c3), c2), f10(c3))),
% 28.94/19.14 inference(symmetry,[status(thm)],[18343])).
% 28.94/19.14 tff(18345,plain,
% 28.94/19.14 (big_f(f3(f10(c3), c2), f10(c3))),
% 28.94/19.14 inference(modus_ponens,[status(thm)],[1345, 18344])).
% 28.94/19.14 tff(18346,plain,
% 28.94/19.14 ($false),
% 28.94/19.14 inference(unit_resolution,[status(thm)],[7385, 18345])).
% 28.94/19.14 tff(18347,plain,(big_f(f3(f10(c3), c2), f10(c3)) | (~big_f(c2, c2)) | (~(f10(c1) = c2)) | (~(c3 = c1)) | (~(f8(c1) = c2)) | (~(f10(c2) = c1)) | big_f(c3, c2) | (~(c2 = f2(c3))) | (f10(f10(c2)) = c4)), inference(lemma,lemma(discharge,[]))).
% 28.94/19.14 tff(18348,plain,
% 28.94/19.14 (big_f(f3(f10(c3), c2), f10(c3))),
% 28.94/19.14 inference(unit_resolution,[status(thm)],[18347, 18278, 15, 172, 18305, 11819, 2603, 2600, 18316])).
% 28.94/19.14 tff(18349,plain,
% 28.94/19.14 (big_f(f3(f10(c3), c2), f10(c1))),
% 28.94/19.14 inference(modus_ponens,[status(thm)],[18348, 18309])).
% 28.94/19.14 tff(18350,plain,
% 28.94/19.14 (big_f(f7(c1), f7(c1))),
% 28.94/19.14 inference(modus_ponens,[status(thm)],[18278, 18280])).
% 28.94/19.14 tff(18351,plain,
% 28.94/19.14 ((~(f5(c1) = c2)) <=> (~(f7(c1) = f5(c1)))),
% 28.94/19.14 inference(monotonicity,[status(thm)],[14334])).
% 28.94/19.14 tff(18352,plain,
% 28.94/19.14 (~(f5(c1) = c2)),
% 28.94/19.14 inference(unit_resolution,[status(thm)],[14385, 18278, 18208, 15, 172, 1286, 1319, 115])).
% 28.94/19.14 tff(18353,plain,
% 28.94/19.14 (~(f7(c1) = f5(c1))),
% 28.94/19.14 inference(modus_ponens,[status(thm)],[18352, 18351])).
% 28.94/19.14 tff(18354,plain,
% 28.94/19.14 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(c1) = c1) | (f10(c1) = c1) | (f7(c1) = f5(c1)) | (~big_f(f7(c1), f7(c1))) | (f3(f10(c3), c2) = f8(c1)) | (~big_f(f3(f10(c3), c2), f10(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c1) = c1) | (f10(c1) = c1) | (f7(c1) = f5(c1)) | (~big_f(f7(c1), f7(c1))) | (f3(f10(c3), c2) = f8(c1)) | (~big_f(f3(f10(c3), c2), f10(c1))))),
% 28.94/19.14 inference(rewrite,[status(thm)],[])).
% 28.94/19.14 tff(18355,plain,
% 28.94/19.14 (((f10(c1) = c1) | (f3(f10(c3), c2) = f8(c1)) | (~big_f(f3(f10(c3), c2), f10(c1))) | (f7(c1) = c1) | (f7(c1) = f5(c1)) | (~big_f(f7(c1), f7(c1)))) <=> ((f7(c1) = c1) | (f10(c1) = c1) | (f7(c1) = f5(c1)) | (~big_f(f7(c1), f7(c1))) | (f3(f10(c3), c2) = f8(c1)) | (~big_f(f3(f10(c3), c2), f10(c1))))),
% 28.94/19.14 inference(rewrite,[status(thm)],[])).
% 28.94/19.14 tff(18356,plain,
% 28.94/19.14 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c1) = c1) | (f3(f10(c3), c2) = f8(c1)) | (~big_f(f3(f10(c3), c2), f10(c1))) | (f7(c1) = c1) | (f7(c1) = f5(c1)) | (~big_f(f7(c1), f7(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(c1) = c1) | (f10(c1) = c1) | (f7(c1) = f5(c1)) | (~big_f(f7(c1), f7(c1))) | (f3(f10(c3), c2) = f8(c1)) | (~big_f(f3(f10(c3), c2), f10(c1)))))),
% 28.94/19.14 inference(monotonicity,[status(thm)],[18355])).
% 28.94/19.14 tff(18357,plain,
% 28.94/19.14 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c1) = c1) | (f3(f10(c3), c2) = f8(c1)) | (~big_f(f3(f10(c3), c2), f10(c1))) | (f7(c1) = c1) | (f7(c1) = f5(c1)) | (~big_f(f7(c1), f7(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c1) = c1) | (f10(c1) = c1) | (f7(c1) = f5(c1)) | (~big_f(f7(c1), f7(c1))) | (f3(f10(c3), c2) = f8(c1)) | (~big_f(f3(f10(c3), c2), f10(c1))))),
% 28.94/19.14 inference(transitivity,[status(thm)],[18356, 18354])).
% 28.94/19.14 tff(18358,plain,
% 28.94/19.14 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c1) = c1) | (f3(f10(c3), c2) = f8(c1)) | (~big_f(f3(f10(c3), c2), f10(c1))) | (f7(c1) = c1) | (f7(c1) = f5(c1)) | (~big_f(f7(c1), f7(c1))))),
% 28.94/19.14 inference(quant_inst,[status(thm)],[])).
% 28.94/19.14 tff(18359,plain,
% 28.94/19.14 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c1) = c1) | (f10(c1) = c1) | (f7(c1) = f5(c1)) | (~big_f(f7(c1), f7(c1))) | (f3(f10(c3), c2) = f8(c1)) | (~big_f(f3(f10(c3), c2), f10(c1)))),
% 28.94/19.14 inference(modus_ponens,[status(thm)],[18358, 18357])).
% 28.94/19.14 tff(18360,plain,
% 28.94/19.14 ((f3(f10(c3), c2) = f8(c1)) | (~big_f(f3(f10(c3), c2), f10(c1)))),
% 28.94/19.14 inference(unit_resolution,[status(thm)],[18359, 1659, 115, 3, 18353, 18350])).
% 28.94/19.14 tff(18361,plain,
% 28.94/19.14 (f3(f10(c3), c2) = f8(c1)),
% 28.94/19.14 inference(unit_resolution,[status(thm)],[18360, 18349])).
% 28.94/19.14 tff(18362,plain,
% 28.94/19.14 (f3(f7(c1), f7(c1)) = f7(c1)),
% 28.94/19.14 inference(modus_ponens,[status(thm)],[18361, 18307])).
% 28.94/19.14 tff(18363,plain,
% 28.94/19.14 (big_f(f3(f7(c1), f7(c1)), f7(c1)) <=> big_f(f3(f10(c3), c2), f10(c3))),
% 28.94/19.14 inference(monotonicity,[status(thm)],[18199, 18198])).
% 28.94/19.14 tff(18364,plain,
% 28.94/19.14 (big_f(f3(f10(c3), c2), f10(c3)) <=> big_f(f3(f7(c1), f7(c1)), f7(c1))),
% 28.94/19.14 inference(symmetry,[status(thm)],[18363])).
% 28.94/19.14 tff(18365,plain,
% 28.94/19.14 (big_f(f3(f7(c1), f7(c1)), f7(c1))),
% 28.94/19.14 inference(modus_ponens,[status(thm)],[18348, 18364])).
% 28.94/19.14 tff(18366,plain,
% 28.94/19.14 (big_f(c1, f7(c1)) | (~(f3(f7(c1), f7(c1)) = f7(c1))) | (~big_f(f3(f7(c1), f7(c1)), f7(c1)))),
% 28.94/19.14 inference(unit_resolution,[status(thm)],[14382, 1398, 5611, 18208, 14360])).
% 28.94/19.14 tff(18367,plain,
% 28.94/19.14 (~(f3(f7(c1), f7(c1)) = f7(c1))),
% 28.94/19.14 inference(unit_resolution,[status(thm)],[18366, 18365, 14359])).
% 28.94/19.14 tff(18368,plain,
% 28.94/19.14 ($false),
% 28.94/19.14 inference(unit_resolution,[status(thm)],[18367, 18362])).
% 28.94/19.14 tff(18369,plain,((f10(c1) = c1) | (~(c3 = c1)) | (f7(c1) = c1) | big_f(c3, f2(c3)) | (~(f2(c3) = c2)) | (~(f10(c2) = c1)) | big_f(c2, c1) | (~(f4(c4) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.94/19.14 tff(18370,plain,
% 28.94/19.14 (f10(c1) = c1),
% 28.94/19.14 inference(unit_resolution,[status(thm)],[18369, 115, 172, 1286, 18151, 11819, 18197, 11752])).
% 28.94/19.14 tff(18371,plain,
% 28.94/19.14 (c1 = f10(c1)),
% 28.94/19.14 inference(symmetry,[status(thm)],[18370])).
% 28.94/19.14 tff(18372,plain,
% 28.94/19.14 (f7(f4(c4)) = c2),
% 28.94/19.14 inference(transitivity,[status(thm)],[16243, 120])).
% 28.94/19.14 tff(18373,plain,
% 28.94/19.14 (f10(f7(f4(c4))) = f10(c2)),
% 28.94/19.14 inference(monotonicity,[status(thm)],[18372])).
% 28.94/19.14 tff(18374,plain,
% 28.94/19.14 (f10(f7(c1)) = f10(f7(f4(c4)))),
% 28.94/19.14 inference(monotonicity,[status(thm)],[16244])).
% 28.94/19.14 tff(18375,plain,
% 28.94/19.14 (f10(f7(c1)) = f10(c1)),
% 28.94/19.14 inference(transitivity,[status(thm)],[18374, 18373, 11819, 18371])).
% 28.94/19.14 tff(18376,plain,
% 28.94/19.14 (big_f(f9(c1, c1), f10(f7(c1))) <=> big_f(f9(c1, c1), f10(c1))),
% 28.94/19.14 inference(monotonicity,[status(thm)],[18375])).
% 28.94/19.14 tff(18377,plain,
% 28.94/19.14 (big_f(f9(c1, c1), f10(c1)) <=> big_f(f9(c1, c1), f10(f7(c1)))),
% 28.94/19.14 inference(symmetry,[status(thm)],[18376])).
% 28.94/19.14 tff(18378,plain,
% 28.94/19.14 (f4(c4) = f7(c2)),
% 28.94/19.14 inference(transitivity,[status(thm)],[11752, 125])).
% 28.94/19.14 tff(18379,plain,
% 28.94/19.14 (big_f(f4(c4), c4) <=> big_f(f7(c2), c1)),
% 28.94/19.14 inference(monotonicity,[status(thm)],[18378, 18167])).
% 28.94/19.14 tff(18380,plain,
% 28.94/19.14 (big_f(f7(c2), c1)),
% 28.94/19.14 inference(modus_ponens,[status(thm)],[1316, 18379])).
% 28.94/19.14 tff(18381,plain,
% 28.94/19.14 (~big_f(f7(c1), c1)),
% 28.94/19.14 inference(modus_ponens,[status(thm)],[18197, 694])).
% 28.94/19.14 tff(18382,plain,
% 28.94/19.14 (big_f(c3, f2(c3)) <=> big_f(c1, c2)),
% 28.94/19.14 inference(monotonicity,[status(thm)],[172, 18151])).
% 28.94/19.14 tff(18383,plain,
% 28.94/19.14 ((~big_f(c3, f2(c3))) <=> (~big_f(c1, c2))),
% 28.94/19.14 inference(monotonicity,[status(thm)],[18382])).
% 28.94/19.14 tff(18384,plain,
% 28.94/19.14 (~big_f(c1, c2)),
% 28.94/19.14 inference(modus_ponens,[status(thm)],[1286, 18383])).
% 28.94/19.14 tff(18385,plain,
% 28.94/19.14 (c1 = c4),
% 28.94/19.14 inference(unit_resolution,[status(thm)],[484, 18167])).
% 28.94/19.14 tff(18386,plain,
% 28.94/19.14 (f5(f2(c1)) = f5(c2)),
% 28.94/19.14 inference(monotonicity,[status(thm)],[18152])).
% 28.94/19.14 tff(18387,plain,
% 28.94/19.14 ((f2(c1) = f5(f2(c1))) <=> (c2 = f5(c2))),
% 28.94/19.14 inference(monotonicity,[status(thm)],[18152, 18386])).
% 28.94/19.14 tff(18388,plain,
% 28.94/19.14 ((c2 = f5(c2)) <=> (f2(c1) = f5(f2(c1)))),
% 28.94/19.14 inference(symmetry,[status(thm)],[18387])).
% 28.94/19.14 tff(18389,plain,
% 28.94/19.14 ((f5(c2) = c2) <=> (f2(c1) = f5(f2(c1)))),
% 28.94/19.14 inference(transitivity,[status(thm)],[1279, 18388])).
% 28.94/19.14 tff(18390,plain,
% 28.94/19.14 (f2(c1) = f5(f2(c1))),
% 28.94/19.14 inference(modus_ponens,[status(thm)],[8109, 18389])).
% 28.94/19.14 tff(18391,plain,
% 28.94/19.14 (f10(f10(c2)) = f10(c1)),
% 28.94/19.14 inference(symmetry,[status(thm)],[12232])).
% 28.94/19.14 tff(18392,plain,
% 28.94/19.14 ((f10(f10(c2)) = c1) <=> (f10(c1) = c1)),
% 28.94/19.14 inference(monotonicity,[status(thm)],[18391])).
% 28.94/19.14 tff(18393,plain,
% 28.94/19.14 ((f10(f10(c2)) = f10(c2)) <=> (f10(c1) = c1)),
% 28.94/19.14 inference(transitivity,[status(thm)],[11842, 18392])).
% 28.94/19.14 tff(18394,plain,
% 28.94/19.14 ((~(f10(f10(c2)) = f10(c2))) <=> (~(f10(c1) = c1))),
% 28.94/19.14 inference(monotonicity,[status(thm)],[18393])).
% 28.94/19.14 tff(18395,plain,
% 28.94/19.14 (~(f10(c1) = c1)),
% 28.94/19.14 inference(modus_ponens,[status(thm)],[11896, 18394])).
% 28.94/19.14 tff(18396,plain,
% 28.94/19.14 (c2 = f2(c3)),
% 28.94/19.14 inference(symmetry,[status(thm)],[18151])).
% 28.94/19.14 tff(18397,plain,
% 28.94/19.14 (f5(c2) = f2(c3)),
% 28.94/19.14 inference(transitivity,[status(thm)],[8109, 18396])).
% 28.94/19.14 tff(18398,plain,
% 28.94/19.14 (big_f(f7(c2), f5(c2)) <=> big_f(c3, f2(c3))),
% 28.94/19.14 inference(monotonicity,[status(thm)],[12985, 18397])).
% 28.94/19.14 tff(18399,plain,
% 28.94/19.14 (big_f(c3, f2(c3)) <=> big_f(f7(c2), f5(c2))),
% 28.94/19.14 inference(symmetry,[status(thm)],[18398])).
% 28.94/19.14 tff(18400,plain,
% 28.94/19.14 ((~big_f(c3, f2(c3))) <=> (~big_f(f7(c2), f5(c2)))),
% 28.94/19.14 inference(monotonicity,[status(thm)],[18399])).
% 28.94/19.14 tff(18401,plain,
% 28.94/19.14 (~big_f(f7(c2), f5(c2))),
% 28.94/19.14 inference(modus_ponens,[status(thm)],[1286, 18400])).
% 28.94/19.14 tff(18402,plain,
% 28.94/19.14 ((~(f10(f10(c2)) = f10(c2))) <=> (~(f10(f10(c2)) = c1))),
% 28.94/19.14 inference(monotonicity,[status(thm)],[11842])).
% 28.94/19.14 tff(18403,plain,
% 28.94/19.14 (~(f10(f10(c2)) = c1)),
% 28.94/19.14 inference(modus_ponens,[status(thm)],[11896, 18402])).
% 28.94/19.14 tff(18404,plain,
% 28.94/19.14 (f10(f10(c2)) = c2),
% 28.94/19.14 inference(unit_resolution,[status(thm)],[18239, 18403])).
% 28.94/19.14 tff(18405,plain,
% 28.94/19.14 (~big_f(c1, f10(c1))),
% 28.94/19.14 inference(unit_resolution,[status(thm)],[12239, 18404, 11819, 18384])).
% 28.94/19.14 tff(18406,plain,
% 28.94/19.14 (~(c1 = f8(c1))),
% 28.94/19.14 inference(unit_resolution,[status(thm)],[12249, 18405, 18401, 17, 18395])).
% 28.94/19.14 tff(18407,plain,
% 28.94/19.14 (~(f8(c1) = c1)),
% 28.94/19.14 inference(modus_ponens,[status(thm)],[18406, 18202])).
% 28.94/19.14 tff(18408,plain,
% 28.94/19.14 (f8(c1) = c2),
% 28.94/19.14 inference(unit_resolution,[status(thm)],[1680, 18407])).
% 28.94/19.14 tff(18409,plain,
% 28.94/19.14 (c2 = f8(c1)),
% 28.94/19.14 inference(modus_ponens,[status(thm)],[18408, 1670])).
% 28.94/19.14 tff(18410,plain,
% 28.94/19.14 (f10(c1) = c2),
% 28.94/19.14 inference(transitivity,[status(thm)],[12232, 18404])).
% 28.94/19.14 tff(18411,plain,
% 28.94/19.14 (f5(f10(c1)) = f5(c2)),
% 28.94/19.14 inference(monotonicity,[status(thm)],[18410])).
% 28.94/19.14 tff(18412,plain,
% 28.94/19.14 (f5(f10(c1)) = f2(c3)),
% 28.94/19.14 inference(transitivity,[status(thm)],[18411, 8109, 18396])).
% 28.94/19.14 tff(18413,plain,
% 28.94/19.14 (f7(f10(c1)) = f7(c2)),
% 28.94/19.14 inference(monotonicity,[status(thm)],[18410])).
% 28.94/19.14 tff(18414,plain,
% 28.94/19.15 (f7(f10(c1)) = c3),
% 28.94/19.15 inference(transitivity,[status(thm)],[18413, 22, 5585])).
% 28.94/19.15 tff(18415,plain,
% 28.94/19.15 (big_f(f7(f10(c1)), f5(f10(c1))) <=> big_f(c3, f2(c3))),
% 28.94/19.15 inference(monotonicity,[status(thm)],[18414, 18412])).
% 28.94/19.15 tff(18416,plain,
% 28.94/19.15 (big_f(c3, f2(c3)) <=> big_f(f7(f10(c1)), f5(f10(c1)))),
% 28.94/19.15 inference(symmetry,[status(thm)],[18415])).
% 28.94/19.15 tff(18417,plain,
% 28.94/19.15 ((~big_f(c3, f2(c3))) <=> (~big_f(f7(f10(c1)), f5(f10(c1))))),
% 28.94/19.15 inference(monotonicity,[status(thm)],[18416])).
% 28.94/19.15 tff(18418,plain,
% 28.94/19.15 (~big_f(f7(f10(c1)), f5(f10(c1)))),
% 28.94/19.15 inference(modus_ponens,[status(thm)],[1286, 18417])).
% 28.94/19.15 tff(18419,plain,
% 28.94/19.15 (f10(c1) = f2(c3)),
% 28.94/19.15 inference(transitivity,[status(thm)],[12232, 18404, 18396])).
% 28.94/19.15 tff(18420,plain,
% 28.94/19.15 (f7(f10(c1)) = c1),
% 28.94/19.15 inference(transitivity,[status(thm)],[18413, 22])).
% 28.94/19.15 tff(18421,plain,
% 28.94/19.15 ((f7(f10(c1)) = f10(c1)) <=> (c1 = f2(c3))),
% 28.94/19.15 inference(monotonicity,[status(thm)],[18420, 18419])).
% 28.94/19.15 tff(18422,plain,
% 28.94/19.15 ((f7(f10(c1)) = f10(c1)) <=> (f2(c3) = c1)),
% 28.94/19.15 inference(transitivity,[status(thm)],[18421, 1436])).
% 28.94/19.15 tff(18423,plain,
% 28.94/19.15 ((f2(c3) = c1) <=> (f7(f10(c1)) = f10(c1))),
% 28.94/19.15 inference(symmetry,[status(thm)],[18422])).
% 28.94/19.15 tff(18424,plain,
% 28.94/19.15 ((~(f2(c3) = c1)) <=> (~(f7(f10(c1)) = f10(c1)))),
% 28.94/19.15 inference(monotonicity,[status(thm)],[18423])).
% 28.94/19.15 tff(18425,plain,
% 28.94/19.15 (~(f7(f10(c1)) = f10(c1))),
% 28.94/19.15 inference(modus_ponens,[status(thm)],[18150, 18424])).
% 28.94/19.15 tff(18426,plain,
% 28.94/19.15 (c2 = f10(f10(c2))),
% 28.94/19.15 inference(symmetry,[status(thm)],[18404])).
% 28.94/19.15 tff(18427,plain,
% 28.94/19.15 (c2 = f10(c1)),
% 28.94/19.15 inference(transitivity,[status(thm)],[18426, 18391])).
% 28.94/19.15 tff(18428,plain,
% 28.94/19.15 (big_f(c2, c2) <=> big_f(c2, f10(c1))),
% 28.94/19.15 inference(monotonicity,[status(thm)],[18427])).
% 28.94/19.15 tff(18429,plain,
% 28.94/19.15 ((~big_f(c2, c2)) <=> (~big_f(c2, f10(c1)))),
% 28.94/19.15 inference(monotonicity,[status(thm)],[18428])).
% 28.94/19.15 tff(18430,plain,
% 28.94/19.15 (~big_f(c2, f10(c1))),
% 28.94/19.15 inference(modus_ponens,[status(thm)],[121, 18429])).
% 28.94/19.15 tff(18431,plain,
% 28.94/19.15 (~(c2 = f8(c1))),
% 28.94/19.15 inference(unit_resolution,[status(thm)],[15818, 18430, 18395, 18425, 18418])).
% 28.94/19.15 tff(18432,plain,
% 28.94/19.15 ($false),
% 28.94/19.15 inference(unit_resolution,[status(thm)],[18431, 18409])).
% 28.94/19.15 tff(18433,plain,((f10(f10(c2)) = f10(c2)) | big_f(c3, f2(c3)) | (~(f5(c2) = c2)) | (~(f10(c2) = c1)) | (~(c3 = c1)) | (f2(c3) = c1) | big_f(c2, c2) | (f7(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 28.94/19.15 tff(18434,plain,
% 28.94/19.15 (f10(f10(c2)) = f10(c2)),
% 28.94/19.15 inference(unit_resolution,[status(thm)],[18433, 8109, 1286, 11819, 172, 18150, 121, 17])).
% 28.94/19.15 tff(18435,plain,
% 28.94/19.15 (f10(c1) = c1),
% 28.94/19.15 inference(modus_ponens,[status(thm)],[18434, 18393])).
% 28.94/19.15 tff(18436,plain,
% 28.94/19.15 (f9(c1, c1) = f9(f10(c2), f4(c4))),
% 28.94/19.15 inference(monotonicity,[status(thm)],[12231, 16651])).
% 28.94/19.15 tff(18437,plain,
% 28.94/19.15 (f9(c1, c1) = c2),
% 28.94/19.15 inference(transitivity,[status(thm)],[18436, 1498])).
% 28.94/19.15 tff(18438,plain,
% 28.94/19.15 (big_f(f9(c1, c1), f10(c1)) <=> big_f(c2, f10(c1))),
% 28.94/19.15 inference(monotonicity,[status(thm)],[18437])).
% 28.94/19.15 tff(18439,plain,
% 28.94/19.15 (big_f(c2, f10(c1)) <=> big_f(f9(c1, c1), f10(c1))),
% 28.94/19.15 inference(symmetry,[status(thm)],[18438])).
% 28.94/19.15 tff(18440,plain,
% 28.94/19.15 (f10(c1) = c1),
% 28.94/19.15 inference(transitivity,[status(thm)],[12232, 18434, 11819])).
% 28.94/19.15 tff(18441,plain,
% 28.94/19.15 (big_f(c2, f10(c1)) <=> big_f(c2, c1)),
% 28.94/19.15 inference(monotonicity,[status(thm)],[18440])).
% 28.94/19.15 tff(18442,plain,
% 28.94/19.15 (big_f(c2, c1) <=> big_f(c2, f10(c1))),
% 28.94/19.15 inference(symmetry,[status(thm)],[18441])).
% 28.94/19.15 tff(18443,plain,
% 28.94/19.15 (big_f(c2, c1) <=> big_f(f9(c1, c1), f10(c1))),
% 28.94/19.15 inference(transitivity,[status(thm)],[18442, 18439])).
% 28.94/19.15 tff(18444,plain,
% 28.94/19.15 ((~big_f(c2, c1)) <=> (~big_f(f9(c1, c1), f10(c1)))),
% 28.94/19.15 inference(monotonicity,[status(thm)],[18443])).
% 28.94/19.15 tff(18445,plain,
% 28.94/19.15 (~big_f(f9(c1, c1), f10(c1))),
% 28.94/19.15 inference(modus_ponens,[status(thm)],[2, 18444])).
% 28.94/19.15 tff(18446,plain,
% 28.94/19.15 (f7(f2(c1)) = f7(c2)),
% 28.94/19.15 inference(monotonicity,[status(thm)],[18152])).
% 28.94/19.15 tff(18447,plain,
% 28.94/19.15 (f7(f2(c1)) = c1),
% 28.94/19.15 inference(transitivity,[status(thm)],[18446, 22])).
% 28.94/19.15 tff(18448,plain,
% 28.94/19.15 ((f7(f2(c1)) = f2(c1)) <=> (c1 = f2(c3))),
% 28.94/19.15 inference(monotonicity,[status(thm)],[18447, 13678])).
% 28.94/19.15 tff(18449,plain,
% 28.94/19.15 ((f7(f2(c1)) = f2(c1)) <=> (f2(c3) = c1)),
% 28.94/19.15 inference(transitivity,[status(thm)],[18448, 1436])).
% 28.94/19.15 tff(18450,plain,
% 28.94/19.15 ((f2(c3) = c1) <=> (f7(f2(c1)) = f2(c1))),
% 28.94/19.15 inference(symmetry,[status(thm)],[18449])).
% 28.94/19.15 tff(18451,plain,
% 28.94/19.15 ((~(f2(c3) = c1)) <=> (~(f7(f2(c1)) = f2(c1)))),
% 28.94/19.15 inference(monotonicity,[status(thm)],[18450])).
% 28.94/19.15 tff(18452,plain,
% 28.94/19.15 (~(f7(f2(c1)) = f2(c1))),
% 28.94/19.15 inference(modus_ponens,[status(thm)],[18150, 18451])).
% 28.94/19.15 tff(18453,plain,
% 28.94/19.15 (f7(f2(c1)) = c3),
% 28.94/19.15 inference(transitivity,[status(thm)],[18446, 22, 5585])).
% 28.94/19.15 tff(18454,plain,
% 28.94/19.15 (big_f(f7(f2(c1)), f2(c1)) <=> big_f(c3, f2(c3))),
% 28.94/19.15 inference(monotonicity,[status(thm)],[18453, 13678])).
% 28.94/19.15 tff(18455,plain,
% 28.94/19.15 (big_f(c3, f2(c3)) <=> big_f(f7(f2(c1)), f2(c1))),
% 28.94/19.15 inference(symmetry,[status(thm)],[18454])).
% 28.94/19.15 tff(18456,plain,
% 28.94/19.15 ((~big_f(c3, f2(c3))) <=> (~big_f(f7(f2(c1)), f2(c1)))),
% 28.94/19.15 inference(monotonicity,[status(thm)],[18455])).
% 28.94/19.15 tff(18457,plain,
% 28.94/19.15 (~big_f(f7(f2(c1)), f2(c1))),
% 28.94/19.15 inference(modus_ponens,[status(thm)],[1286, 18456])).
% 28.94/19.15 tff(18458,plain,
% 28.94/19.15 (f9(c1, c1) = f2(c3)),
% 28.94/19.15 inference(transitivity,[status(thm)],[18436, 1498, 18396])).
% 28.94/19.15 tff(18459,plain,
% 28.94/19.15 ((f9(c1, c1) = c1) <=> (f2(c3) = c1)),
% 28.94/19.15 inference(monotonicity,[status(thm)],[18458])).
% 28.94/19.15 tff(18460,plain,
% 28.94/19.15 ((f2(c3) = c1) <=> (f9(c1, c1) = c1)),
% 28.94/19.15 inference(symmetry,[status(thm)],[18459])).
% 28.94/19.15 tff(18461,plain,
% 28.94/19.15 ((~(f2(c3) = c1)) <=> (~(f9(c1, c1) = c1))),
% 28.94/19.15 inference(monotonicity,[status(thm)],[18460])).
% 28.94/19.15 tff(18462,plain,
% 28.94/19.15 (~(f9(c1, c1) = c1)),
% 28.94/19.15 inference(modus_ponens,[status(thm)],[18150, 18461])).
% 28.94/19.15 tff(18463,plain,
% 28.94/19.15 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f2(c1) = f5(f2(c1)))) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | big_f(f7(f2(c1)), f2(c1)) | (f7(f2(c1)) = f2(c1)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (~(f2(c1) = f5(f2(c1)))) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | big_f(f7(f2(c1)), f2(c1)) | (f7(f2(c1)) = f2(c1)))),
% 28.94/19.15 inference(rewrite,[status(thm)],[])).
% 28.94/19.15 tff(18464,plain,
% 28.94/19.15 (((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(f2(c1)) = f2(c1)) | big_f(f7(f2(c1)), f2(c1)) | (~(f2(c1) = f5(f2(c1))))) <=> ((~(f2(c1) = f5(f2(c1)))) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | big_f(f7(f2(c1)), f2(c1)) | (f7(f2(c1)) = f2(c1)))),
% 28.94/19.15 inference(rewrite,[status(thm)],[])).
% 28.94/19.15 tff(18465,plain,
% 28.94/19.15 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(f2(c1)) = f2(c1)) | big_f(f7(f2(c1)), f2(c1)) | (~(f2(c1) = f5(f2(c1)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f2(c1) = f5(f2(c1)))) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | big_f(f7(f2(c1)), f2(c1)) | (f7(f2(c1)) = f2(c1))))),
% 28.94/19.15 inference(monotonicity,[status(thm)],[18464])).
% 28.94/19.15 tff(18466,plain,
% 28.94/19.15 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(f2(c1)) = f2(c1)) | big_f(f7(f2(c1)), f2(c1)) | (~(f2(c1) = f5(f2(c1)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (~(f2(c1) = f5(f2(c1)))) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | big_f(f7(f2(c1)), f2(c1)) | (f7(f2(c1)) = f2(c1)))),
% 28.94/19.15 inference(transitivity,[status(thm)],[18465, 18463])).
% 28.94/19.15 tff(18467,plain,
% 28.94/19.15 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(f2(c1)) = f2(c1)) | big_f(f7(f2(c1)), f2(c1)) | (~(f2(c1) = f5(f2(c1)))))),
% 28.94/19.15 inference(quant_inst,[status(thm)],[])).
% 28.94/19.15 tff(18468,plain,
% 28.94/19.15 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (~(f2(c1) = f5(f2(c1)))) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | big_f(f7(f2(c1)), f2(c1)) | (f7(f2(c1)) = f2(c1))),
% 28.94/19.15 inference(modus_ponens,[status(thm)],[18467, 18466])).
% 28.94/19.15 tff(18469,plain,
% 28.94/19.15 ((~(f2(c1) = f5(f2(c1)))) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1))),
% 28.94/19.15 inference(unit_resolution,[status(thm)],[18468, 267, 18462, 18457, 18452])).
% 28.94/19.15 tff(18470,plain,
% 28.94/19.15 ($false),
% 28.94/19.15 inference(unit_resolution,[status(thm)],[18469, 18445, 18435, 18390])).
% 28.94/19.15 tff(18471,plain,((~(f5(c2) = c2)) | big_f(c2, c1) | (~(f10(c2) = c1)) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | big_f(c3, f2(c3)) | (~(c3 = c1)) | (f2(c3) = c1) | big_f(c2, c2) | (f7(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 28.94/19.15 tff(18472,plain,
% 28.94/19.15 (~(f5(c2) = c2)),
% 28.94/19.15 inference(unit_resolution,[status(thm)],[18471, 2, 11819, 1498, 11752, 1286, 172, 18150, 121, 17])).
% 28.94/19.15 tff(18473,plain,
% 28.94/19.15 (f5(c2) = c1),
% 28.94/19.15 inference(unit_resolution,[status(thm)],[1547, 18472])).
% 28.94/19.15 tff(18474,plain,
% 28.94/19.15 (f5(f2(c1)) = c1),
% 28.94/19.15 inference(transitivity,[status(thm)],[18386, 1569])).
% 28.94/19.15 tff(18475,plain,
% 28.94/19.15 ((f6(c1, c1) = f5(f2(c1))) <=> (f6(c1, c1) = c1)),
% 28.94/19.15 inference(monotonicity,[status(thm)],[18474])).
% 28.94/19.15 tff(18476,plain,
% 28.94/19.15 (f7(c2) = f7(f10(c1))),
% 28.94/19.15 inference(symmetry,[status(thm)],[18413])).
% 28.94/19.15 tff(18477,plain,
% 28.94/19.15 (f7(f2(c1)) = f7(f10(c1))),
% 28.94/19.15 inference(transitivity,[status(thm)],[18446, 18476])).
% 28.94/19.15 tff(18478,plain,
% 28.94/19.15 (big_f(f7(f2(c1)), f6(c1, c1)) <=> big_f(f7(f10(c1)), f6(f7(c2), c3))),
% 28.94/19.15 inference(monotonicity,[status(thm)],[18477, 10013])).
% 28.94/19.15 tff(18479,plain,
% 28.94/19.15 (big_f(f7(f10(c1)), f6(f7(c2), c3)) <=> big_f(f7(f2(c1)), f6(c1, c1))),
% 28.94/19.15 inference(symmetry,[status(thm)],[18478])).
% 28.94/19.15 tff(18480,plain,
% 28.94/19.15 (big_f(c2, f10(f10(c2))) <=> big_f(c2, f10(c1))),
% 28.94/19.15 inference(monotonicity,[status(thm)],[18391])).
% 28.94/19.15 tff(18481,plain,
% 28.94/19.15 (big_f(c2, f10(c1)) <=> big_f(c2, f10(f10(c2)))),
% 28.94/19.15 inference(symmetry,[status(thm)],[18480])).
% 28.94/19.15 tff(18482,plain,
% 28.94/19.15 (big_f(c2, c2) <=> big_f(c2, f10(f10(c2)))),
% 28.94/19.15 inference(transitivity,[status(thm)],[18428, 18481])).
% 28.94/19.15 tff(18483,plain,
% 28.94/19.15 ((~big_f(c2, c2)) <=> (~big_f(c2, f10(f10(c2))))),
% 28.94/19.15 inference(monotonicity,[status(thm)],[18482])).
% 28.94/19.15 tff(18484,plain,
% 28.94/19.15 (~big_f(c2, f10(f10(c2)))),
% 28.94/19.15 inference(modus_ponens,[status(thm)],[121, 18483])).
% 28.94/19.15 tff(18485,plain,
% 28.94/19.15 (~big_f(c1, f10(c1))),
% 28.94/19.15 inference(unit_resolution,[status(thm)],[12239, 18404, 11819, 27])).
% 28.94/19.15 tff(18486,plain,
% 28.94/19.15 (f7(c1) = c1),
% 28.94/19.15 inference(unit_resolution,[status(thm)],[18259, 18485, 11526, 11819, 474, 11752, 11896, 18484, 2, 230])).
% 28.94/19.15 tff(18487,plain,
% 28.94/19.15 (c1 = f7(c1)),
% 28.94/19.15 inference(symmetry,[status(thm)],[18486])).
% 28.94/19.15 tff(18488,plain,
% 28.94/19.15 (f7(f10(c1)) = f7(c1)),
% 28.94/19.15 inference(transitivity,[status(thm)],[18413, 292, 18487])).
% 28.94/19.15 tff(18489,plain,
% 28.94/19.15 (big_f(f7(f10(c1)), f6(f7(c2), c3)) <=> big_f(f7(c1), f6(c1, c1))),
% 28.94/19.15 inference(monotonicity,[status(thm)],[18488, 10012])).
% 28.94/19.15 tff(18490,plain,
% 28.94/19.15 (big_f(f7(c1), f6(c1, c1)) <=> big_f(f7(f10(c1)), f6(f7(c2), c3))),
% 28.94/19.15 inference(symmetry,[status(thm)],[18489])).
% 28.94/19.15 tff(18491,plain,
% 28.94/19.15 (f6(f7(c2), c3) = f6(c1, c1)),
% 28.94/19.15 inference(symmetry,[status(thm)],[5958])).
% 28.94/19.15 tff(18492,plain,
% 28.94/19.15 ((f6(f7(c2), c3) = c1) <=> (f6(c1, c1) = c1)),
% 28.94/19.15 inference(monotonicity,[status(thm)],[18491])).
% 28.94/19.15 tff(18493,plain,
% 28.94/19.15 ((f6(f7(c2), c3) = c3) <=> (f6(f7(c2), c3) = c1)),
% 28.94/19.15 inference(monotonicity,[status(thm)],[172])).
% 28.94/19.15 tff(18494,plain,
% 28.94/19.15 ((f6(f7(c2), c3) = c3) <=> (f6(c1, c1) = c1)),
% 28.94/19.15 inference(transitivity,[status(thm)],[18493, 18492])).
% 28.94/19.15 tff(18495,plain,
% 28.94/19.15 ((~(f6(f7(c2), c3) = c3)) <=> (~(f6(c1, c1) = c1))),
% 28.94/19.15 inference(monotonicity,[status(thm)],[18494])).
% 28.94/19.15 tff(18496,plain,
% 28.94/19.15 (big_f(f7(f7(c2)), f6(f7(c2), c3)) <=> big_f(f7(c1), f6(c1, c1))),
% 28.94/19.15 inference(monotonicity,[status(thm)],[352, 18491])).
% 28.94/19.15 tff(18497,plain,
% 28.94/19.15 (big_f(f7(c1), f6(c1, c1)) <=> big_f(f7(f7(c2)), f6(f7(c2), c3))),
% 28.94/19.15 inference(symmetry,[status(thm)],[18496])).
% 28.94/19.15 tff(18498,plain,
% 28.94/19.15 (f7(f10(c1)) = f7(c2)),
% 28.94/19.15 inference(monotonicity,[status(thm)],[12233])).
% 28.94/19.15 tff(18499,plain,
% 28.94/19.15 (f7(c2) = f7(f10(c1))),
% 28.94/19.15 inference(symmetry,[status(thm)],[18498])).
% 28.94/19.15 tff(18500,plain,
% 28.94/19.15 (f7(c1) = f7(f10(c1))),
% 28.94/19.15 inference(transitivity,[status(thm)],[4234, 342, 18499])).
% 28.94/19.15 tff(18501,plain,
% 28.94/19.15 (big_f(f7(c1), f6(c1, c1)) <=> big_f(f7(f10(c1)), f6(f7(c2), c3))),
% 28.94/19.15 inference(monotonicity,[status(thm)],[18500, 5958])).
% 28.94/19.15 tff(18502,plain,
% 28.94/19.15 (big_f(f7(f10(c1)), f6(f7(c2), c3)) <=> big_f(f7(c1), f6(c1, c1))),
% 28.94/19.15 inference(symmetry,[status(thm)],[18501])).
% 28.94/19.15 tff(18503,assumption,(f6(f7(c2), c3) = c3), introduced(assumption)).
% 28.94/19.15 tff(18504,plain,
% 28.94/19.15 (f6(f7(c2), c3) = c1),
% 28.94/19.15 inference(transitivity,[status(thm)],[18503, 172])).
% 28.94/19.15 tff(18505,plain,
% 28.94/19.15 (big_f(f7(f10(c1)), f6(f7(c2), c3)) <=> big_f(f7(c2), c1)),
% 28.94/19.15 inference(monotonicity,[status(thm)],[18498, 18504])).
% 28.94/19.15 tff(18506,plain,
% 28.94/19.15 (big_f(f7(c2), c1) <=> big_f(f7(f10(c1)), f6(f7(c2), c3))),
% 28.94/19.15 inference(symmetry,[status(thm)],[18505])).
% 28.94/19.15 tff(18507,plain,
% 28.94/19.15 (big_f(f7(c2), c1) <=> big_f(f7(f7(c2)), f6(f7(c2), c3))),
% 28.94/19.15 inference(transitivity,[status(thm)],[18506, 18502, 18497])).
% 28.94/19.15 tff(18508,plain,
% 28.94/19.15 (big_f(f7(f7(c2)), f6(f7(c2), c3))),
% 28.94/19.15 inference(modus_ponens,[status(thm)],[338, 18507])).
% 28.94/19.15 tff(18509,plain,
% 28.94/19.15 ($false),
% 28.94/19.15 inference(unit_resolution,[status(thm)],[2472, 18508])).
% 28.94/19.15 tff(18510,plain,((~(f6(f7(c2), c3) = c3)) | big_f(f7(f7(c2)), f6(f7(c2), c3)) | (~big_f(f7(c2), c1)) | (~(c3 = c1)) | (~(f10(f10(c2)) = c2)) | (~(f10(c2) = c1)) | (~(f7(c1) = c1)) | (~(f7(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.94/19.15 tff(18511,plain,
% 28.94/19.15 (~(f6(f7(c2), c3) = c3)),
% 28.94/19.15 inference(unit_resolution,[status(thm)],[18510, 4234, 338, 172, 12230, 11819, 2472, 292])).
% 28.94/19.15 tff(18512,plain,
% 28.94/19.15 (~(f6(c1, c1) = c1)),
% 28.94/19.15 inference(modus_ponens,[status(thm)],[18511, 18495])).
% 28.94/19.15 tff(18513,plain,
% 28.94/19.15 ((~big_f(f7(f7(c2)), f6(f7(c2), c3))) <=> (~big_f(f7(c1), f6(c1, c1)))),
% 28.94/19.15 inference(monotonicity,[status(thm)],[18496])).
% 28.94/19.15 tff(18514,plain,
% 28.94/19.15 (~big_f(f7(c1), f6(c1, c1))),
% 28.94/19.15 inference(modus_ponens,[status(thm)],[2472, 18513])).
% 28.94/19.15 tff(18515,plain,
% 28.94/19.15 (~(c1 = f8(c1))),
% 28.94/19.15 inference(unit_resolution,[status(thm)],[9801, 2994, 4234, 3, 3030, 18514, 18512])).
% 28.94/19.15 tff(18516,plain,
% 28.94/19.15 (~(f8(c1) = c1)),
% 28.94/19.15 inference(modus_ponens,[status(thm)],[18515, 18202])).
% 28.94/19.15 tff(18517,plain,
% 28.94/19.15 (~(c2 = f8(c1))),
% 28.94/19.15 inference(unit_resolution,[status(thm)],[9816, 18512, 2946, 3, 4234, 18514])).
% 28.94/19.15 tff(18518,plain,
% 28.94/19.15 (~(f8(c1) = c2)),
% 28.94/19.15 inference(modus_ponens,[status(thm)],[18517, 2783])).
% 28.94/19.15 tff(18519,plain,
% 28.94/19.15 ($false),
% 28.94/19.15 inference(unit_resolution,[status(thm)],[1680, 18518, 18516])).
% 28.94/19.15 tff(18520,plain,((~(f7(c1) = c1)) | big_f(c2, f10(c1)) | (f10(c1) = c1) | big_f(c1, f10(c1)) | (~(f7(c2) = c1)) | (~(c3 = c1)) | big_f(f7(f7(c2)), f6(f7(c2), c3)) | (~big_f(f7(c2), c1)) | (~(f10(f10(c2)) = c2)) | (~(f10(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.94/19.15 tff(18521,plain,
% 28.94/19.15 (big_f(f7(f7(c2)), f6(f7(c2), c3))),
% 28.94/19.15 inference(unit_resolution,[status(thm)],[18520, 18486, 18395, 18485, 292, 172, 18430, 338, 18404, 11819])).
% 28.94/19.15 tff(18522,plain,
% 28.94/19.15 (big_f(f7(c1), f6(c1, c1))),
% 28.94/19.15 inference(modus_ponens,[status(thm)],[18521, 10188])).
% 28.94/19.15 tff(18523,plain,
% 28.94/19.15 (big_f(f7(f10(c1)), f6(f7(c2), c3))),
% 28.94/19.15 inference(modus_ponens,[status(thm)],[18522, 18490])).
% 28.94/19.15 tff(18524,plain,
% 28.94/19.15 (big_f(f7(f2(c1)), f6(c1, c1))),
% 28.94/19.15 inference(modus_ponens,[status(thm)],[18523, 18479])).
% 28.94/19.15 tff(18525,plain,
% 28.94/19.15 (f7(f10(c1)) = c1),
% 28.94/19.15 inference(transitivity,[status(thm)],[18413, 292])).
% 28.94/19.15 tff(18526,plain,
% 28.94/19.15 ((f7(f10(c1)) = f10(c1)) <=> (c1 = f2(c3))),
% 28.94/19.15 inference(monotonicity,[status(thm)],[18525, 18419])).
% 28.94/19.15 tff(18527,plain,
% 28.94/19.15 ((f7(f10(c1)) = f10(c1)) <=> (f2(c3) = c1)),
% 28.94/19.15 inference(transitivity,[status(thm)],[18526, 1436])).
% 28.94/19.15 tff(18528,plain,
% 28.94/19.15 ((f2(c3) = c1) <=> (f7(f10(c1)) = f10(c1))),
% 28.94/19.15 inference(symmetry,[status(thm)],[18527])).
% 28.94/19.15 tff(18529,plain,
% 28.94/19.15 ((~(f2(c3) = c1)) <=> (~(f7(f10(c1)) = f10(c1)))),
% 28.94/19.15 inference(monotonicity,[status(thm)],[18528])).
% 28.94/19.15 tff(18530,plain,
% 28.94/19.15 (~(f7(f10(c1)) = f10(c1))),
% 28.94/19.15 inference(modus_ponens,[status(thm)],[18150, 18529])).
% 28.94/19.15 tff(18531,plain,
% 28.94/19.15 (big_f(f2(c1), f10(c1)) <=> big_f(c2, c2)),
% 28.94/19.15 inference(monotonicity,[status(thm)],[18152, 18410])).
% 28.94/19.15 tff(18532,plain,
% 28.94/19.15 (big_f(c2, c2) <=> big_f(f2(c1), f10(c1))),
% 28.94/19.15 inference(symmetry,[status(thm)],[18531])).
% 28.94/19.15 tff(18533,plain,
% 28.94/19.15 ((~big_f(c2, c2)) <=> (~big_f(f2(c1), f10(c1)))),
% 28.94/19.15 inference(monotonicity,[status(thm)],[18532])).
% 28.94/19.15 tff(18534,plain,
% 28.94/19.15 (~big_f(f2(c1), f10(c1))),
% 28.94/19.15 inference(modus_ponens,[status(thm)],[121, 18533])).
% 28.94/19.15 tff(18535,plain,
% 28.94/19.15 (f5(f10(c1)) = f5(c2)),
% 28.94/19.15 inference(monotonicity,[status(thm)],[12233])).
% 28.94/19.15 tff(18536,plain,
% 28.94/19.15 (f5(f10(c1)) = c1),
% 28.94/19.15 inference(transitivity,[status(thm)],[18535, 1569])).
% 28.94/19.15 tff(18537,plain,
% 28.94/19.15 ((f6(f7(c2), c3) = f5(f10(c1))) <=> (f6(c1, c1) = c1)),
% 28.94/19.15 inference(monotonicity,[status(thm)],[10012, 18536])).
% 28.94/19.15 tff(18538,plain,
% 28.94/19.15 (f7(f10(c1)) = f7(c1)),
% 28.94/19.15 inference(transitivity,[status(thm)],[18498, 292, 5544])).
% 28.94/19.15 tff(18539,plain,
% 28.94/19.15 (big_f(f7(f10(c1)), f6(f7(c2), c3)) <=> big_f(f7(c1), f6(c1, c1))),
% 28.94/19.15 inference(monotonicity,[status(thm)],[18538, 10012])).
% 28.94/19.15 tff(18540,plain,
% 28.94/19.15 (big_f(f7(c1), f6(c1, c1)) <=> big_f(f7(f10(c1)), f6(f7(c2), c3))),
% 28.94/19.15 inference(symmetry,[status(thm)],[18539])).
% 28.94/19.15 tff(18541,plain,
% 28.94/19.15 (big_f(f7(f10(c1)), f6(f7(c2), c3))),
% 28.94/19.15 inference(modus_ponens,[status(thm)],[5964, 18540])).
% 28.94/19.15 tff(18542,plain,
% 28.94/19.15 (f6(f7(c2), c3) = f5(f10(c1))),
% 28.94/19.15 inference(unit_resolution,[status(thm)],[9928, 1672, 3, 297, 2946, 18541])).
% 28.94/19.15 tff(18543,plain,
% 28.94/19.15 (f6(c1, c1) = c1),
% 28.94/19.15 inference(modus_ponens,[status(thm)],[18542, 18537])).
% 28.94/19.15 tff(18544,assumption,(~big_f(f2(c1), f10(c1))), introduced(assumption)).
% 28.94/19.15 tff(18545,plain,
% 28.94/19.15 (f2(c1) = c2),
% 28.94/19.15 inference(transitivity,[status(thm)],[13678, 1319])).
% 28.94/19.15 tff(18546,plain,
% 28.94/19.15 ((f2(c1) = f8(c1)) <=> (c2 = f8(c1))),
% 28.94/19.15 inference(monotonicity,[status(thm)],[18545])).
% 28.94/19.15 tff(18547,plain,
% 28.94/19.15 ((c2 = f8(c1)) <=> (f2(c1) = f8(c1))),
% 28.94/19.15 inference(symmetry,[status(thm)],[18546])).
% 28.94/19.15 tff(18548,plain,
% 28.94/19.15 ((f8(c1) = c2) <=> (f2(c1) = f8(c1))),
% 28.94/19.15 inference(transitivity,[status(thm)],[1670, 18547])).
% 28.94/19.15 tff(18549,plain,
% 28.94/19.15 (f2(c1) = f8(c1)),
% 28.94/19.15 inference(modus_ponens,[status(thm)],[1671, 18548])).
% 28.94/19.15 tff(18550,plain,
% 28.94/19.15 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (~(f7(c1) = c1)) | (~(f2(c1) = f8(c1))) | big_f(f2(c1), f10(c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(f7(c1) = c1)) | (~(f2(c1) = f8(c1))) | big_f(f2(c1), f10(c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)))),
% 28.94/19.15 inference(rewrite,[status(thm)],[])).
% 28.94/19.15 tff(18551,plain,
% 28.94/19.15 (((f10(c1) = c1) | big_f(f2(c1), f10(c1)) | (~(f7(c1) = c1)) | (~(f2(c1) = f8(c1))) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1)))) <=> ((f10(c1) = c1) | (~(f7(c1) = c1)) | (~(f2(c1) = f8(c1))) | big_f(f2(c1), f10(c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)))),
% 28.94/19.15 inference(rewrite,[status(thm)],[])).
% 28.94/19.15 tff(18552,plain,
% 28.94/19.15 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | big_f(f2(c1), f10(c1)) | (~(f7(c1) = c1)) | (~(f2(c1) = f8(c1))) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (~(f7(c1) = c1)) | (~(f2(c1) = f8(c1))) | big_f(f2(c1), f10(c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1))))),
% 28.94/19.15 inference(monotonicity,[status(thm)],[18551])).
% 28.94/19.15 tff(18553,plain,
% 28.94/19.15 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | big_f(f2(c1), f10(c1)) | (~(f7(c1) = c1)) | (~(f2(c1) = f8(c1))) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(f7(c1) = c1)) | (~(f2(c1) = f8(c1))) | big_f(f2(c1), f10(c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)))),
% 28.94/19.15 inference(transitivity,[status(thm)],[18552, 18550])).
% 28.94/19.15 tff(18554,plain,
% 28.94/19.15 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | big_f(f2(c1), f10(c1)) | (~(f7(c1) = c1)) | (~(f2(c1) = f8(c1))) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))),
% 28.94/19.15 inference(quant_inst,[status(thm)],[])).
% 28.94/19.15 tff(18555,plain,
% 28.94/19.15 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(f7(c1) = c1)) | (~(f2(c1) = f8(c1))) | big_f(f2(c1), f10(c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1))),
% 28.94/19.15 inference(modus_ponens,[status(thm)],[18554, 18553])).
% 28.94/19.15 tff(18556,plain,
% 28.94/19.15 ((~(f2(c1) = f8(c1))) | big_f(f2(c1), f10(c1)) | (~(f6(c1, c1) = c1))),
% 28.94/19.15 inference(unit_resolution,[status(thm)],[18555, 2963, 4234, 3, 5964])).
% 28.94/19.15 tff(18557,plain,
% 28.94/19.15 (~(f6(c1, c1) = c1)),
% 28.94/19.15 inference(unit_resolution,[status(thm)],[18556, 18549, 18544])).
% 28.94/19.15 tff(18558,plain,
% 28.94/19.15 ($false),
% 28.94/19.15 inference(unit_resolution,[status(thm)],[18557, 18543])).
% 28.94/19.15 tff(18559,plain,((~(f8(c1) = c2)) | (~(f5(c2) = c1)) | (~(f10(f10(c2)) = c2)) | (~(f10(c2) = c1)) | (~(c3 = c1)) | (~(f7(c2) = c1)) | big_f(f2(c1), f10(c1)) | (~(f7(c1) = c1)) | (f10(c1) = c1) | (~big_f(f7(c1), f6(c1, c1))) | (f7(f10(c1)) = f10(c1)) | big_f(c2, f10(c1)) | (~(f2(c3) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.94/19.15 tff(18560,plain,
% 28.94/19.15 (~(f8(c1) = c2)),
% 28.94/19.15 inference(unit_resolution,[status(thm)],[18559, 18404, 1569, 11819, 172, 292, 18534, 18486, 18395, 18522, 18530, 18430, 18151])).
% 28.94/19.15 tff(18561,plain,
% 28.94/19.15 (f8(c1) = c1),
% 28.94/19.15 inference(unit_resolution,[status(thm)],[1680, 18560])).
% 28.94/19.15 tff(18562,plain,
% 28.94/19.15 (c1 = f8(c1)),
% 28.94/19.15 inference(modus_ponens,[status(thm)],[18561, 3028])).
% 28.94/19.15 tff(18563,plain,
% 28.94/19.15 (f7(f2(c1)) = c1),
% 28.94/19.15 inference(transitivity,[status(thm)],[18446, 292])).
% 28.94/19.15 tff(18564,plain,
% 28.94/19.15 ((f7(f2(c1)) = f2(c1)) <=> (c1 = f2(c3))),
% 28.94/19.15 inference(monotonicity,[status(thm)],[18563, 13678])).
% 28.94/19.15 tff(18565,plain,
% 28.94/19.15 ((f7(f2(c1)) = f2(c1)) <=> (f2(c3) = c1)),
% 28.94/19.15 inference(transitivity,[status(thm)],[18564, 1436])).
% 28.94/19.15 tff(18566,plain,
% 28.94/19.15 ((f2(c3) = c1) <=> (f7(f2(c1)) = f2(c1))),
% 28.94/19.15 inference(symmetry,[status(thm)],[18565])).
% 28.94/19.15 tff(18567,plain,
% 28.94/19.15 ((~(f2(c3) = c1)) <=> (~(f7(f2(c1)) = f2(c1)))),
% 28.94/19.15 inference(monotonicity,[status(thm)],[18566])).
% 28.94/19.15 tff(18568,plain,
% 28.94/19.15 (~(f7(f2(c1)) = f2(c1))),
% 28.94/19.15 inference(modus_ponens,[status(thm)],[18150, 18567])).
% 28.94/19.15 tff(18569,plain,
% 28.94/19.15 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (~big_f(f7(f2(c1)), f6(c1, c1))) | (f6(c1, c1) = f5(f2(c1))) | (f7(f2(c1)) = f2(c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | (f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (~big_f(f7(f2(c1)), f6(c1, c1))) | (f6(c1, c1) = f5(f2(c1))) | (f7(f2(c1)) = f2(c1)))),
% 28.94/19.15 inference(rewrite,[status(thm)],[])).
% 28.94/19.15 tff(18570,plain,
% 28.94/19.15 (((f10(c1) = c1) | big_f(c1, f10(c1)) | (f7(f2(c1)) = f2(c1)) | (f6(c1, c1) = f5(f2(c1))) | (~big_f(f7(f2(c1)), f6(c1, c1))) | (~(c1 = f8(c1)))) <=> ((f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (~big_f(f7(f2(c1)), f6(c1, c1))) | (f6(c1, c1) = f5(f2(c1))) | (f7(f2(c1)) = f2(c1)))),
% 28.94/19.16 inference(rewrite,[status(thm)],[])).
% 28.94/19.16 tff(18571,plain,
% 28.94/19.16 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | big_f(c1, f10(c1)) | (f7(f2(c1)) = f2(c1)) | (f6(c1, c1) = f5(f2(c1))) | (~big_f(f7(f2(c1)), f6(c1, c1))) | (~(c1 = f8(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (~big_f(f7(f2(c1)), f6(c1, c1))) | (f6(c1, c1) = f5(f2(c1))) | (f7(f2(c1)) = f2(c1))))),
% 28.94/19.16 inference(monotonicity,[status(thm)],[18570])).
% 28.94/19.16 tff(18572,plain,
% 28.94/19.16 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | big_f(c1, f10(c1)) | (f7(f2(c1)) = f2(c1)) | (f6(c1, c1) = f5(f2(c1))) | (~big_f(f7(f2(c1)), f6(c1, c1))) | (~(c1 = f8(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | (f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (~big_f(f7(f2(c1)), f6(c1, c1))) | (f6(c1, c1) = f5(f2(c1))) | (f7(f2(c1)) = f2(c1)))),
% 28.94/19.16 inference(transitivity,[status(thm)],[18571, 18569])).
% 28.94/19.16 tff(18573,plain,
% 28.94/19.16 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | big_f(c1, f10(c1)) | (f7(f2(c1)) = f2(c1)) | (f6(c1, c1) = f5(f2(c1))) | (~big_f(f7(f2(c1)), f6(c1, c1))) | (~(c1 = f8(c1))))),
% 28.94/19.16 inference(quant_inst,[status(thm)],[])).
% 28.94/19.16 tff(18574,plain,
% 28.94/19.16 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | (f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (~big_f(f7(f2(c1)), f6(c1, c1))) | (f6(c1, c1) = f5(f2(c1))) | (f7(f2(c1)) = f2(c1))),
% 28.94/19.16 inference(modus_ponens,[status(thm)],[18573, 18572])).
% 28.94/19.16 tff(18575,plain,
% 28.94/19.16 ((~(c1 = f8(c1))) | (~big_f(f7(f2(c1)), f6(c1, c1))) | (f6(c1, c1) = f5(f2(c1)))),
% 28.94/19.16 inference(unit_resolution,[status(thm)],[18574, 2795, 18395, 18485, 18568])).
% 28.94/19.16 tff(18576,plain,
% 28.94/19.16 (f6(c1, c1) = f5(f2(c1))),
% 28.94/19.16 inference(unit_resolution,[status(thm)],[18575, 18562, 18524])).
% 28.94/19.16 tff(18577,plain,
% 28.94/19.16 (f6(c1, c1) = c1),
% 28.94/19.16 inference(modus_ponens,[status(thm)],[18576, 18475])).
% 28.94/19.16 tff(18578,plain,
% 28.94/19.16 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)))),
% 28.94/19.16 inference(rewrite,[status(thm)],[])).
% 28.94/19.16 tff(18579,plain,
% 28.94/19.16 (((f10(c1) = c1) | big_f(c1, f10(c1)) | (~(f7(c1) = c1)) | (~(c1 = f8(c1))) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1)))) <=> ((f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)))),
% 28.94/19.16 inference(rewrite,[status(thm)],[])).
% 28.94/19.16 tff(18580,plain,
% 28.94/19.16 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | big_f(c1, f10(c1)) | (~(f7(c1) = c1)) | (~(c1 = f8(c1))) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1))))),
% 28.94/19.16 inference(monotonicity,[status(thm)],[18579])).
% 28.94/19.16 tff(18581,plain,
% 28.94/19.16 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | big_f(c1, f10(c1)) | (~(f7(c1) = c1)) | (~(c1 = f8(c1))) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)))),
% 28.94/19.16 inference(transitivity,[status(thm)],[18580, 18578])).
% 28.94/19.16 tff(18582,plain,
% 28.94/19.16 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | big_f(c1, f10(c1)) | (~(f7(c1) = c1)) | (~(c1 = f8(c1))) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))),
% 28.94/19.16 inference(quant_inst,[status(thm)],[])).
% 28.94/19.16 tff(18583,plain,
% 28.94/19.16 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1))),
% 28.94/19.16 inference(modus_ponens,[status(thm)],[18582, 18581])).
% 28.94/19.16 tff(18584,plain,
% 28.94/19.16 ((~(c1 = f8(c1))) | (~(f6(c1, c1) = c1))),
% 28.94/19.16 inference(unit_resolution,[status(thm)],[18583, 2963, 18486, 18395, 18485, 18522])).
% 28.94/19.16 tff(18585,plain,
% 28.94/19.16 (~(f6(c1, c1) = c1)),
% 28.94/19.16 inference(unit_resolution,[status(thm)],[18584, 18562])).
% 28.94/19.16 tff(18586,plain,
% 28.94/19.16 ($false),
% 28.94/19.16 inference(unit_resolution,[status(thm)],[18585, 18577])).
% 28.94/19.16 tff(18587,plain,((f10(f10(c2)) = f10(c2)) | (~(f5(c2) = c1)) | (~(c3 = c1)) | (~(f10(c2) = c1)) | (~(f7(c2) = c1)) | big_f(c2, c2) | (~big_f(f7(c2), c1)) | (~(c1 = c4)) | (~big_f(f4(c4), c4)) | (~(f4(c4) = c1)) | big_f(c2, c1) | (~(f5(c1) = c1)) | (f2(c3) = c1) | big_f(c1, c2)), inference(lemma,lemma(discharge,[]))).
% 28.94/19.16 tff(18588,plain,
% 28.94/19.16 (f10(f10(c2)) = f10(c2)),
% 28.94/19.16 inference(unit_resolution,[status(thm)],[18587, 18473, 172, 11819, 22, 121, 18380, 18385, 1316, 11752, 2, 230, 18150, 18384])).
% 28.94/19.16 tff(18589,plain,
% 28.94/19.16 (f10(c1) = c1),
% 28.94/19.16 inference(transitivity,[status(thm)],[12232, 18588, 11819])).
% 28.94/19.16 tff(18590,plain,
% 28.94/19.16 (f10(f10(c2)) = c1),
% 28.94/19.16 inference(transitivity,[status(thm)],[18588, 11819])).
% 28.94/19.16 tff(18591,plain,
% 28.94/19.16 (f9(c1, f10(f10(c2))) = f9(c1, c1)),
% 28.94/19.16 inference(monotonicity,[status(thm)],[18590])).
% 28.94/19.16 tff(18592,plain,
% 28.94/19.16 (f9(c1, f10(f10(c2))) = c2),
% 28.94/19.16 inference(transitivity,[status(thm)],[18591, 18436, 1498])).
% 28.94/19.16 tff(18593,plain,
% 28.94/19.16 (big_f(f9(c1, f10(f10(c2))), f10(c1)) <=> big_f(c2, c1)),
% 28.94/19.16 inference(monotonicity,[status(thm)],[18592, 18589])).
% 28.94/19.16 tff(18594,plain,
% 28.94/19.16 (big_f(c2, c1) <=> big_f(f9(c1, f10(f10(c2))), f10(c1))),
% 28.94/19.16 inference(symmetry,[status(thm)],[18593])).
% 28.94/19.16 tff(18595,plain,
% 28.94/19.16 ((~big_f(c2, c1)) <=> (~big_f(f9(c1, f10(f10(c2))), f10(c1)))),
% 28.94/19.16 inference(monotonicity,[status(thm)],[18594])).
% 28.94/19.16 tff(18596,plain,
% 28.94/19.16 (~big_f(f9(c1, f10(f10(c2))), f10(c1))),
% 28.94/19.16 inference(modus_ponens,[status(thm)],[2, 18595])).
% 28.94/19.16 tff(18597,plain,
% 28.94/19.16 (f9(c1, f10(f10(c2))) = f2(c3)),
% 28.94/19.16 inference(transitivity,[status(thm)],[18591, 18436, 1498, 18396])).
% 28.94/19.16 tff(18598,plain,
% 28.94/19.16 ((f9(c1, f10(f10(c2))) = f10(f10(c2))) <=> (f2(c3) = c1)),
% 28.94/19.16 inference(monotonicity,[status(thm)],[18597, 18590])).
% 28.94/19.16 tff(18599,plain,
% 28.94/19.16 ((f2(c3) = c1) <=> (f9(c1, f10(f10(c2))) = f10(f10(c2)))),
% 28.94/19.16 inference(symmetry,[status(thm)],[18598])).
% 28.94/19.16 tff(18600,plain,
% 28.94/19.16 ((~(f2(c3) = c1)) <=> (~(f9(c1, f10(f10(c2))) = f10(f10(c2))))),
% 28.94/19.16 inference(monotonicity,[status(thm)],[18599])).
% 28.94/19.16 tff(18601,plain,
% 28.94/19.16 (~(f9(c1, f10(f10(c2))) = f10(f10(c2)))),
% 28.94/19.16 inference(modus_ponens,[status(thm)],[18150, 18600])).
% 28.94/19.16 tff(18602,plain,
% 28.94/19.16 (f10(c1) = c1),
% 28.94/19.16 inference(modus_ponens,[status(thm)],[18588, 18393])).
% 28.94/19.16 tff(18603,assumption,(~big_f(f9(c1, f10(f10(c2))), f10(c1))), introduced(assumption)).
% 28.94/19.16 tff(18604,assumption,(~(f9(c1, f10(f10(c2))) = f10(f10(c2)))), introduced(assumption)).
% 28.94/19.16 tff(18605,plain,
% 28.94/19.16 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((f7(c1) = c1) | big_f(f7(c1), c1) | (~(f10(c1) = c1)) | (f9(c1, f10(f10(c2))) = f10(f10(c2))) | big_f(f9(c1, f10(f10(c2))), f10(c1)) | (~(c1 = f5(c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(f10(c1) = c1)) | (f9(c1, f10(f10(c2))) = f10(f10(c2))) | big_f(f9(c1, f10(f10(c2))), f10(c1)) | (~(c1 = f5(c1))))),
% 28.94/19.16 inference(rewrite,[status(thm)],[])).
% 28.94/19.16 tff(18606,plain,
% 28.94/19.16 (((~(f10(c1) = c1)) | (f9(c1, f10(f10(c2))) = f10(f10(c2))) | big_f(f9(c1, f10(f10(c2))), f10(c1)) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(c1 = f5(c1)))) <=> ((f7(c1) = c1) | big_f(f7(c1), c1) | (~(f10(c1) = c1)) | (f9(c1, f10(f10(c2))) = f10(f10(c2))) | big_f(f9(c1, f10(f10(c2))), f10(c1)) | (~(c1 = f5(c1))))),
% 28.94/19.16 inference(rewrite,[status(thm)],[])).
% 28.94/19.16 tff(18607,plain,
% 28.94/19.16 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f9(c1, f10(f10(c2))) = f10(f10(c2))) | big_f(f9(c1, f10(f10(c2))), f10(c1)) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(c1 = f5(c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((f7(c1) = c1) | big_f(f7(c1), c1) | (~(f10(c1) = c1)) | (f9(c1, f10(f10(c2))) = f10(f10(c2))) | big_f(f9(c1, f10(f10(c2))), f10(c1)) | (~(c1 = f5(c1)))))),
% 28.94/19.16 inference(monotonicity,[status(thm)],[18606])).
% 28.94/19.16 tff(18608,plain,
% 28.94/19.16 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f9(c1, f10(f10(c2))) = f10(f10(c2))) | big_f(f9(c1, f10(f10(c2))), f10(c1)) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(c1 = f5(c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(f10(c1) = c1)) | (f9(c1, f10(f10(c2))) = f10(f10(c2))) | big_f(f9(c1, f10(f10(c2))), f10(c1)) | (~(c1 = f5(c1))))),
% 28.94/19.16 inference(transitivity,[status(thm)],[18607, 18605])).
% 28.94/19.16 tff(18609,plain,
% 28.94/19.16 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f9(c1, f10(f10(c2))) = f10(f10(c2))) | big_f(f9(c1, f10(f10(c2))), f10(c1)) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(c1 = f5(c1))))),
% 28.94/19.16 inference(quant_inst,[status(thm)],[])).
% 28.94/19.16 tff(18610,plain,
% 28.94/19.16 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(f10(c1) = c1)) | (f9(c1, f10(f10(c2))) = f10(f10(c2))) | big_f(f9(c1, f10(f10(c2))), f10(c1)) | (~(c1 = f5(c1)))),
% 28.94/19.16 inference(modus_ponens,[status(thm)],[18609, 18608])).
% 28.94/19.16 tff(18611,plain,
% 28.94/19.16 ((f7(c1) = c1) | big_f(f7(c1), c1) | (~(f10(c1) = c1)) | (f9(c1, f10(f10(c2))) = f10(f10(c2))) | big_f(f9(c1, f10(f10(c2))), f10(c1)) | (~(c1 = f5(c1)))),
% 28.94/19.16 inference(unit_resolution,[status(thm)],[18610, 267])).
% 28.94/19.16 tff(18612,plain,
% 28.94/19.16 (big_f(f7(c1), c1)),
% 28.94/19.16 inference(unit_resolution,[status(thm)],[18611, 115, 11826, 3762, 18604, 18603])).
% 28.94/19.16 tff(18613,plain,
% 28.94/19.16 ($false),
% 28.94/19.16 inference(unit_resolution,[status(thm)],[18612, 695])).
% 28.94/19.16 tff(18614,plain,((f7(c1) = c1) | big_f(c2, c1) | (~(c1 = f5(c1))) | (~(f10(c1) = c1)) | (f9(c1, f10(f10(c2))) = f10(f10(c2))) | big_f(f9(c1, f10(f10(c2))), f10(c1))), inference(lemma,lemma(discharge,[]))).
% 28.94/19.16 tff(18615,plain,
% 28.94/19.16 (f7(c1) = c1),
% 28.94/19.16 inference(unit_resolution,[status(thm)],[18614, 2, 692, 18602, 18601, 18596])).
% 28.94/19.16 tff(18616,plain,
% 28.94/19.16 (c1 = f7(c1)),
% 28.94/19.16 inference(symmetry,[status(thm)],[18615])).
% 28.94/19.16 tff(18617,plain,
% 28.94/19.16 (f7(f2(c1)) = f7(c1)),
% 28.94/19.16 inference(transitivity,[status(thm)],[18446, 22, 18616])).
% 28.94/19.16 tff(18618,plain,
% 28.94/19.16 (big_f(f7(f2(c1)), f6(c1, c1)) <=> big_f(f7(c1), f6(c1, c1))),
% 28.94/19.16 inference(monotonicity,[status(thm)],[18617])).
% 28.94/19.16 tff(18619,plain,
% 28.94/19.16 (big_f(f7(c1), f6(c1, c1)) <=> big_f(f7(f2(c1)), f6(c1, c1))),
% 28.94/19.16 inference(symmetry,[status(thm)],[18618])).
% 28.94/19.16 tff(18620,plain,
% 28.94/19.16 (big_f(c2, f10(c1)) <=> big_f(c2, c1)),
% 28.94/19.16 inference(monotonicity,[status(thm)],[18589])).
% 28.94/19.16 tff(18621,plain,
% 28.94/19.16 (big_f(c2, c1) <=> big_f(c2, f10(c1))),
% 28.94/19.16 inference(symmetry,[status(thm)],[18620])).
% 28.94/19.16 tff(18622,plain,
% 28.94/19.16 (big_f(c2, c1) <=> big_f(f9(c1, c1), f10(c1))),
% 28.94/19.16 inference(transitivity,[status(thm)],[18621, 18439])).
% 28.94/19.16 tff(18623,plain,
% 28.94/19.16 ((~big_f(c2, c1)) <=> (~big_f(f9(c1, c1), f10(c1)))),
% 28.94/19.16 inference(monotonicity,[status(thm)],[18622])).
% 28.94/19.16 tff(18624,plain,
% 28.94/19.16 (~big_f(f9(c1, c1), f10(c1))),
% 28.94/19.16 inference(modus_ponens,[status(thm)],[2, 18623])).
% 28.94/19.16 tff(18625,plain,
% 28.94/19.16 (big_f(f7(c1), f6(c1, c1))),
% 28.94/19.16 inference(unit_resolution,[status(thm)],[9993, 18615, 18380, 22, 18602, 18462, 18624])).
% 28.94/19.16 tff(18626,plain,
% 28.94/19.16 (big_f(f7(f2(c1)), f6(c1, c1))),
% 28.94/19.16 inference(modus_ponens,[status(thm)],[18625, 18619])).
% 28.94/19.16 tff(18627,plain,
% 28.94/19.16 (f5(f2(c1)) = c1),
% 28.94/19.16 inference(transitivity,[status(thm)],[18386, 18473])).
% 28.94/19.16 tff(18628,plain,
% 28.94/19.16 ((f6(c1, c1) = f5(f2(c1))) <=> (f6(c1, c1) = c1)),
% 28.94/19.16 inference(monotonicity,[status(thm)],[18627])).
% 28.94/19.16 tff(18629,plain,
% 28.94/19.16 ((f6(c1, c1) = c1) <=> (f6(c1, c1) = f5(f2(c1)))),
% 28.94/19.16 inference(symmetry,[status(thm)],[18628])).
% 28.94/19.16 tff(18630,plain,
% 28.94/19.16 ((~(f6(c1, c1) = c1)) <=> (~(f6(c1, c1) = f5(f2(c1))))),
% 28.94/19.16 inference(monotonicity,[status(thm)],[18629])).
% 28.94/19.16 tff(18631,plain,
% 28.94/19.16 (~(f6(c1, c1) = c1)),
% 28.94/19.16 inference(unit_resolution,[status(thm)],[10040, 2534, 18615, 18602, 18462, 18624, 18625])).
% 28.94/19.16 tff(18632,plain,
% 28.94/19.16 (~(f6(c1, c1) = f5(f2(c1)))),
% 28.94/19.16 inference(modus_ponens,[status(thm)],[18631, 18630])).
% 28.94/19.16 tff(18633,plain,
% 28.94/19.16 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~big_f(f7(f2(c1)), f6(c1, c1))) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (f6(c1, c1) = f5(f2(c1))) | (f7(f2(c1)) = f2(c1)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~big_f(f7(f2(c1)), f6(c1, c1))) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (f6(c1, c1) = f5(f2(c1))) | (f7(f2(c1)) = f2(c1)))),
% 28.94/19.16 inference(rewrite,[status(thm)],[])).
% 28.94/19.16 tff(18634,plain,
% 28.94/19.16 (((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(f2(c1)) = f2(c1)) | (f6(c1, c1) = f5(f2(c1))) | (~big_f(f7(f2(c1)), f6(c1, c1)))) <=> ((~big_f(f7(f2(c1)), f6(c1, c1))) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (f6(c1, c1) = f5(f2(c1))) | (f7(f2(c1)) = f2(c1)))),
% 28.94/19.16 inference(rewrite,[status(thm)],[])).
% 28.94/19.16 tff(18635,plain,
% 28.94/19.16 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(f2(c1)) = f2(c1)) | (f6(c1, c1) = f5(f2(c1))) | (~big_f(f7(f2(c1)), f6(c1, c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~big_f(f7(f2(c1)), f6(c1, c1))) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (f6(c1, c1) = f5(f2(c1))) | (f7(f2(c1)) = f2(c1))))),
% 28.94/19.16 inference(monotonicity,[status(thm)],[18634])).
% 28.94/19.16 tff(18636,plain,
% 28.94/19.16 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(f2(c1)) = f2(c1)) | (f6(c1, c1) = f5(f2(c1))) | (~big_f(f7(f2(c1)), f6(c1, c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~big_f(f7(f2(c1)), f6(c1, c1))) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (f6(c1, c1) = f5(f2(c1))) | (f7(f2(c1)) = f2(c1)))),
% 28.94/19.16 inference(transitivity,[status(thm)],[18635, 18633])).
% 28.94/19.16 tff(18637,plain,
% 28.94/19.16 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(f2(c1)) = f2(c1)) | (f6(c1, c1) = f5(f2(c1))) | (~big_f(f7(f2(c1)), f6(c1, c1))))),
% 28.94/19.16 inference(quant_inst,[status(thm)],[])).
% 28.94/19.16 tff(18638,plain,
% 28.94/19.16 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~big_f(f7(f2(c1)), f6(c1, c1))) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (f6(c1, c1) = f5(f2(c1))) | (f7(f2(c1)) = f2(c1))),
% 28.94/19.16 inference(modus_ponens,[status(thm)],[18637, 18636])).
% 28.94/19.16 tff(18639,plain,
% 28.94/19.16 ((~big_f(f7(f2(c1)), f6(c1, c1))) | (f6(c1, c1) = f5(f2(c1)))),
% 28.94/19.16 inference(unit_resolution,[status(thm)],[18638, 676, 18602, 18462, 18624, 18452])).
% 28.94/19.16 tff(18640,plain,
% 28.94/19.16 ($false),
% 28.94/19.16 inference(unit_resolution,[status(thm)],[18639, 18632, 18626])).
% 28.94/19.16 tff(18641,plain,(big_f(c2, c1) | (~(c3 = c1)) | (~(f10(c2) = c1)) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (f2(c3) = c1) | big_f(c2, c2) | (~(f5(c1) = c1)) | big_f(c3, f2(c3)) | (f7(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 28.94/19.16 tff(18642,plain,
% 28.94/19.16 (~(f9(f10(c2), f4(c4)) = c2)),
% 28.94/19.16 inference(unit_resolution,[status(thm)],[18641, 230, 11819, 18197, 11752, 18150, 121, 172, 1286, 17])).
% 28.94/19.16 tff(18643,plain,
% 28.94/19.16 (f9(f10(c2), f4(c4)) = c1),
% 28.94/19.16 inference(unit_resolution,[status(thm)],[146, 18642])).
% 28.94/19.16 tff(18644,plain,
% 28.94/19.16 (f9(c1, c1) = f7(c2)),
% 28.94/19.16 inference(transitivity,[status(thm)],[18436, 18643, 125])).
% 28.94/19.16 tff(18645,plain,
% 28.94/19.16 (big_f(f9(c1, c1), f10(c1)) <=> big_f(f7(c2), c1)),
% 28.94/19.16 inference(monotonicity,[status(thm)],[18644, 18370])).
% 28.94/19.16 tff(18646,plain,
% 28.94/19.16 (big_f(f7(c2), c1) <=> big_f(f9(c1, c1), f10(c1))),
% 28.94/19.16 inference(symmetry,[status(thm)],[18645])).
% 28.94/19.16 tff(18647,plain,
% 28.94/19.16 (big_f(f9(c1, c1), f10(c1))),
% 28.94/19.16 inference(modus_ponens,[status(thm)],[18380, 18646])).
% 28.94/19.16 tff(18648,plain,
% 28.94/19.16 ((f9(c1, c1) = c1) <=> (f9(f10(c2), f4(c4)) = c1)),
% 28.94/19.16 inference(monotonicity,[status(thm)],[18436])).
% 28.94/19.16 tff(18649,plain,
% 28.94/19.16 ((f9(f10(c2), f4(c4)) = c1) <=> (f9(c1, c1) = c1)),
% 28.94/19.16 inference(symmetry,[status(thm)],[18648])).
% 28.94/19.16 tff(18650,plain,
% 28.94/19.16 (f9(c1, c1) = c1),
% 28.94/19.16 inference(modus_ponens,[status(thm)],[18643, 18649])).
% 28.94/19.16 tff(18651,plain,
% 28.94/19.16 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((f7(c1) = c1) | big_f(f7(c1), c1) | (~(f10(c1) = c1)) | (~(c1 = f5(c1))) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(f10(c1) = c1)) | (~(c1 = f5(c1))) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))),
% 28.94/19.16 inference(rewrite,[status(thm)],[])).
% 28.94/19.16 tff(18652,plain,
% 28.94/19.16 (((~(f10(c1) = c1)) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(c1 = f5(c1)))) <=> ((f7(c1) = c1) | big_f(f7(c1), c1) | (~(f10(c1) = c1)) | (~(c1 = f5(c1))) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))),
% 28.94/19.16 inference(rewrite,[status(thm)],[])).
% 28.94/19.16 tff(18653,plain,
% 28.94/19.16 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(c1 = f5(c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((f7(c1) = c1) | big_f(f7(c1), c1) | (~(f10(c1) = c1)) | (~(c1 = f5(c1))) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1)))))),
% 28.94/19.16 inference(monotonicity,[status(thm)],[18652])).
% 28.94/19.16 tff(18654,plain,
% 28.94/19.16 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(c1 = f5(c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(f10(c1) = c1)) | (~(c1 = f5(c1))) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))),
% 28.94/19.16 inference(transitivity,[status(thm)],[18653, 18651])).
% 28.94/19.16 tff(18655,plain,
% 28.94/19.16 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(c1 = f5(c1))))),
% 28.94/19.16 inference(quant_inst,[status(thm)],[])).
% 28.94/19.16 tff(18656,plain,
% 28.94/19.16 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(f10(c1) = c1)) | (~(c1 = f5(c1))) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1)))),
% 28.94/19.16 inference(modus_ponens,[status(thm)],[18655, 18654])).
% 28.94/19.16 tff(18657,plain,
% 28.94/19.16 ($false),
% 28.94/19.16 inference(unit_resolution,[status(thm)],[18656, 783, 115, 18370, 18650, 18647, 18381, 692])).
% 28.94/19.16 tff(18658,plain,((~(f5(c1) = c1)) | (f7(c1) = c1) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | (f2(c3) = c1) | big_f(c2, c2) | (~(c3 = c1)) | big_f(c3, f2(c3)) | (f7(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 28.94/19.16 tff(18659,plain,
% 28.94/19.16 (~(f5(c1) = c1)),
% 28.94/19.16 inference(unit_resolution,[status(thm)],[18658, 121, 11752, 11819, 18150, 115, 172, 1286, 17])).
% 28.94/19.16 tff(18660,plain,
% 28.94/19.16 (f5(c1) = c2),
% 28.94/19.16 inference(unit_resolution,[status(thm)],[1708, 18659])).
% 28.94/19.16 tff(18661,plain,
% 28.94/19.16 (big_f(f7(c1), f5(c1)) <=> big_f(c2, c2)),
% 28.94/19.16 inference(monotonicity,[status(thm)],[120, 18660])).
% 28.94/19.16 tff(18662,plain,
% 28.94/19.16 (big_f(c2, c2) <=> big_f(f7(c1), f5(c1))),
% 28.94/19.16 inference(symmetry,[status(thm)],[18661])).
% 28.94/19.16 tff(18663,plain,
% 28.94/19.16 (big_f(f7(c1), c2) <=> big_f(c2, c2)),
% 28.94/19.16 inference(symmetry,[status(thm)],[17721])).
% 28.94/19.16 tff(18664,plain,
% 28.94/19.16 (big_f(f7(c1), c2) <=> big_f(f7(c1), f5(c1))),
% 28.94/19.16 inference(transitivity,[status(thm)],[18663, 18662])).
% 28.94/19.16 tff(18665,plain,
% 28.94/19.16 (big_f(f7(c1), c2) <=> big_f(c2, c2)),
% 28.94/19.16 inference(monotonicity,[status(thm)],[347])).
% 28.94/19.16 tff(18666,plain,
% 28.94/19.16 (big_f(f7(f4(c4)), c2) <=> big_f(c2, c2)),
% 28.94/19.16 inference(transitivity,[status(thm)],[18215, 18665])).
% 28.94/19.16 tff(18667,assumption,(big_f(f7(f4(c4)), c2)), introduced(assumption)).
% 28.94/19.16 tff(18668,plain,
% 28.94/19.16 (big_f(c2, c2)),
% 28.94/19.16 inference(modus_ponens,[status(thm)],[18667, 18666])).
% 28.94/19.16 tff(18669,plain,
% 28.94/19.16 ($false),
% 28.94/19.16 inference(unit_resolution,[status(thm)],[121, 18668])).
% 28.94/19.16 tff(18670,plain,((~big_f(f7(f4(c4)), c2)) | big_f(c2, c2) | (~(f7(c1) = c2)) | (~(f4(c4) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.94/19.16 tff(18671,plain,
% 28.94/19.16 (~big_f(f7(f4(c4)), c2)),
% 28.94/19.17 inference(unit_resolution,[status(thm)],[18670, 121, 120, 11752])).
% 28.94/19.17 tff(18672,plain,
% 28.94/19.17 (~big_f(f7(c1), f5(c1))),
% 28.94/19.17 inference(unit_resolution,[status(thm)],[18267, 18660, 11752, 18671])).
% 28.94/19.17 tff(18673,plain,
% 28.94/19.17 (f10(f10(c2)) = f10(c2)),
% 28.94/19.17 inference(modus_ponens,[status(thm)],[3762, 11847])).
% 28.94/19.17 tff(18674,plain,
% 28.94/19.17 (f9(c1, c1) = f9(f10(c2), f10(c2))),
% 28.94/19.17 inference(monotonicity,[status(thm)],[12231, 12231])).
% 28.94/19.17 tff(18675,plain,
% 28.94/19.17 (f9(f10(c2), f10(c2)) = f9(c1, c1)),
% 28.94/19.17 inference(symmetry,[status(thm)],[18674])).
% 28.94/19.17 tff(18676,plain,
% 28.94/19.17 (big_f(f9(f10(c2), f10(c2)), f10(f10(c2))) <=> big_f(f9(c1, c1), f10(c1))),
% 28.94/19.17 inference(monotonicity,[status(thm)],[18675, 11844])).
% 28.94/19.17 tff(18677,plain,
% 28.94/19.17 (big_f(f9(c1, c1), f10(c1)) <=> big_f(f9(f10(c2), f10(c2)), f10(f10(c2)))),
% 28.94/19.17 inference(symmetry,[status(thm)],[18676])).
% 28.94/19.17 tff(18678,plain,
% 28.94/19.17 ((~big_f(f9(c1, c1), f10(c1))) <=> (~big_f(f9(f10(c2), f10(c2)), f10(f10(c2))))),
% 28.94/19.17 inference(monotonicity,[status(thm)],[18677])).
% 28.94/19.17 tff(18679,plain,
% 28.94/19.17 (~big_f(f9(f10(c2), f10(c2)), f10(f10(c2)))),
% 28.94/19.17 inference(modus_ponens,[status(thm)],[8712, 18678])).
% 28.94/19.17 tff(18680,plain,
% 28.94/19.17 (f9(f10(c2), f10(c2)) = f10(c2)),
% 28.94/19.17 inference(unit_resolution,[status(thm)],[280, 18679, 115, 18673, 730])).
% 28.94/19.17 tff(18681,plain,
% 28.94/19.17 (f9(c1, c1) = f7(c2)),
% 28.94/19.17 inference(transitivity,[status(thm)],[18674, 18680, 11819, 342])).
% 28.94/19.17 tff(18682,plain,
% 28.94/19.17 (big_f(f9(c1, c1), f10(c1)) <=> big_f(f7(c2), c1)),
% 28.94/19.17 inference(monotonicity,[status(thm)],[18681, 3762])).
% 28.94/19.17 tff(18683,plain,
% 28.94/19.17 (big_f(f7(c2), c1) <=> big_f(f9(c1, c1), f10(c1))),
% 28.94/19.17 inference(symmetry,[status(thm)],[18682])).
% 28.94/19.17 tff(18684,plain,
% 28.94/19.17 (big_f(f9(c1, c1), f10(c1))),
% 28.94/19.17 inference(modus_ponens,[status(thm)],[338, 18683])).
% 28.94/19.17 tff(18685,plain,
% 28.94/19.17 ($false),
% 28.94/19.17 inference(unit_resolution,[status(thm)],[8712, 18684])).
% 28.94/19.17 tff(18686,plain,(big_f(f9(c1, c1), f10(c1)) | (~big_f(f7(c2), c1)) | (~(f10(c1) = c1)) | (~(f7(c2) = c1)) | (~(f10(c2) = c1)) | (f7(c1) = c1) | big_f(f7(c1), f5(c1))), inference(lemma,lemma(discharge,[]))).
% 28.94/19.17 tff(18687,plain,
% 28.94/19.17 (big_f(f9(c1, c1), f10(c1))),
% 28.94/19.17 inference(unit_resolution,[status(thm)],[18686, 18672, 18370, 22, 11819, 115, 18380])).
% 28.94/19.17 tff(18688,plain,
% 28.94/19.17 (c2 = f5(c1)),
% 28.94/19.17 inference(modus_ponens,[status(thm)],[18660, 155])).
% 28.94/19.17 tff(18689,plain,
% 28.94/19.17 (c1 = c4),
% 28.94/19.17 inference(symmetry,[status(thm)],[18167])).
% 28.94/19.17 tff(18690,plain,
% 28.94/19.17 (f4(c1) = f4(c4)),
% 28.94/19.17 inference(monotonicity,[status(thm)],[18689])).
% 28.94/19.17 tff(18691,plain,
% 28.94/19.17 (f4(c1) = c1),
% 28.94/19.17 inference(transitivity,[status(thm)],[18690, 11752])).
% 28.94/19.17 tff(18692,plain,
% 28.94/19.17 ((f9(c1, c1) = f4(c1)) <=> (f9(c1, c1) = c1)),
% 28.94/19.17 inference(monotonicity,[status(thm)],[18691])).
% 28.94/19.17 tff(18693,plain,
% 28.94/19.17 (f7(c1) = f2(c3)),
% 28.94/19.17 inference(transitivity,[status(thm)],[120, 18396])).
% 28.94/19.17 tff(18694,plain,
% 28.94/19.17 (big_f(c1, f7(c1)) <=> big_f(c3, f2(c3))),
% 28.94/19.17 inference(monotonicity,[status(thm)],[5585, 18693])).
% 28.94/19.17 tff(18695,plain,
% 28.94/19.17 (big_f(c3, f2(c3)) <=> big_f(c1, f7(c1))),
% 28.94/19.17 inference(symmetry,[status(thm)],[18694])).
% 28.94/19.17 tff(18696,plain,
% 28.94/19.17 ((~big_f(c3, f2(c3))) <=> (~big_f(c1, f7(c1)))),
% 28.94/19.17 inference(monotonicity,[status(thm)],[18695])).
% 28.94/19.17 tff(18697,plain,
% 28.94/19.17 (~big_f(c1, f7(c1))),
% 28.94/19.17 inference(modus_ponens,[status(thm)],[1286, 18696])).
% 28.94/19.17 tff(18698,plain,
% 28.94/19.17 (big_f(f9(c1, c1), c1) <=> big_f(f9(c1, c1), f10(c1))),
% 28.94/19.17 inference(monotonicity,[status(thm)],[18371])).
% 28.94/19.17 tff(18699,plain,
% 28.94/19.17 (big_f(f9(c1, c1), f10(c1)) <=> big_f(f9(c1, c1), c1)),
% 28.94/19.17 inference(symmetry,[status(thm)],[18698])).
% 28.94/19.17 tff(18700,plain,
% 28.94/19.17 (big_f(f9(c1, c1), c1)),
% 28.94/19.17 inference(modus_ponens,[status(thm)],[18687, 18699])).
% 28.94/19.17 tff(18701,plain,
% 28.94/19.17 (f7(c1) = f2(c1)),
% 28.94/19.17 inference(transitivity,[status(thm)],[120, 18396, 5589])).
% 28.94/19.17 tff(18702,plain,
% 28.94/19.17 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(c1 = c4)) | (~big_f(f9(c1, c1), c1)) | (f9(c1, c1) = f4(c1)) | (~(f7(c1) = f2(c1))) | big_f(c1, f7(c1)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | (~(c1 = c3)) | (~(c1 = c4)) | (~big_f(f9(c1, c1), c1)) | (f9(c1, c1) = f4(c1)) | (~(f7(c1) = f2(c1))) | big_f(c1, f7(c1)))),
% 28.94/19.17 inference(rewrite,[status(thm)],[])).
% 28.94/19.17 tff(18703,plain,
% 28.94/19.17 (((~(c1 = c3)) | (~(f7(c1) = f2(c1))) | (~(c1 = c4)) | (f9(c1, c1) = f4(c1)) | (~big_f(f9(c1, c1), c1)) | big_f(c1, f7(c1))) <=> ((~(c1 = c3)) | (~(c1 = c4)) | (~big_f(f9(c1, c1), c1)) | (f9(c1, c1) = f4(c1)) | (~(f7(c1) = f2(c1))) | big_f(c1, f7(c1)))),
% 28.94/19.17 inference(rewrite,[status(thm)],[])).
% 28.94/19.17 tff(18704,plain,
% 28.94/19.17 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(f7(c1) = f2(c1))) | (~(c1 = c4)) | (f9(c1, c1) = f4(c1)) | (~big_f(f9(c1, c1), c1)) | big_f(c1, f7(c1)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(c1 = c4)) | (~big_f(f9(c1, c1), c1)) | (f9(c1, c1) = f4(c1)) | (~(f7(c1) = f2(c1))) | big_f(c1, f7(c1))))),
% 28.94/19.17 inference(monotonicity,[status(thm)],[18703])).
% 28.94/19.17 tff(18705,plain,
% 28.94/19.17 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(f7(c1) = f2(c1))) | (~(c1 = c4)) | (f9(c1, c1) = f4(c1)) | (~big_f(f9(c1, c1), c1)) | big_f(c1, f7(c1)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | (~(c1 = c3)) | (~(c1 = c4)) | (~big_f(f9(c1, c1), c1)) | (f9(c1, c1) = f4(c1)) | (~(f7(c1) = f2(c1))) | big_f(c1, f7(c1)))),
% 28.94/19.17 inference(transitivity,[status(thm)],[18704, 18702])).
% 28.94/19.17 tff(18706,plain,
% 28.94/19.17 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(f7(c1) = f2(c1))) | (~(c1 = c4)) | (f9(c1, c1) = f4(c1)) | (~big_f(f9(c1, c1), c1)) | big_f(c1, f7(c1)))),
% 28.94/19.17 inference(quant_inst,[status(thm)],[])).
% 28.94/19.17 tff(18707,plain,
% 28.94/19.17 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | (~(c1 = c3)) | (~(c1 = c4)) | (~big_f(f9(c1, c1), c1)) | (f9(c1, c1) = f4(c1)) | (~(f7(c1) = f2(c1))) | big_f(c1, f7(c1))),
% 28.94/19.17 inference(modus_ponens,[status(thm)],[18706, 18705])).
% 28.94/19.17 tff(18708,plain,
% 28.94/19.17 ((~big_f(f9(c1, c1), c1)) | (f9(c1, c1) = f4(c1)) | big_f(c1, f7(c1))),
% 28.94/19.17 inference(unit_resolution,[status(thm)],[18707, 11666, 5611, 18385, 18701])).
% 28.94/19.17 tff(18709,plain,
% 28.94/19.17 (f9(c1, c1) = f4(c1)),
% 28.94/19.17 inference(unit_resolution,[status(thm)],[18708, 18700, 18697])).
% 28.94/19.17 tff(18710,plain,
% 28.94/19.17 (f9(c1, c1) = c1),
% 28.94/19.17 inference(modus_ponens,[status(thm)],[18709, 18692])).
% 28.94/19.17 tff(18711,plain,
% 28.94/19.17 (big_f(f7(c1), c2)),
% 28.94/19.17 inference(unit_resolution,[status(thm)],[8709, 18710, 115, 18688, 18370, 18687])).
% 28.94/19.17 tff(18712,plain,
% 28.94/19.17 (big_f(f7(c1), f5(c1))),
% 28.94/19.17 inference(modus_ponens,[status(thm)],[18711, 18664])).
% 28.94/19.17 tff(18713,plain,
% 28.94/19.17 ($false),
% 28.94/19.17 inference(unit_resolution,[status(thm)],[18672, 18712])).
% 28.94/19.17 tff(18714,plain,(big_f(c2, c2) | (f7(c1) = c1) | (~(f4(c4) = c1)) | big_f(c3, f2(c3)) | (~(c3 = c1)) | (~(f10(c2) = c1)) | (f2(c3) = c1) | (f7(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 28.94/19.17 tff(18715,plain,
% 28.94/19.17 (big_f(c2, c2)),
% 28.94/19.17 inference(unit_resolution,[status(thm)],[18714, 115, 11752, 1286, 172, 11819, 18150, 17])).
% 28.94/19.17 tff(18716,plain,
% 28.94/19.17 ((f7(c1) = c4) <=> (f7(c1) = c1)),
% 28.94/19.17 inference(monotonicity,[status(thm)],[18167])).
% 28.94/19.17 tff(18717,plain,
% 28.94/19.17 ((f7(c1) = c1) <=> (f7(c1) = c4)),
% 28.94/19.17 inference(symmetry,[status(thm)],[18716])).
% 28.94/19.17 tff(18718,plain,
% 28.94/19.17 ((~(f7(c1) = c1)) <=> (~(f7(c1) = c4))),
% 28.94/19.17 inference(monotonicity,[status(thm)],[18717])).
% 28.94/19.17 tff(18719,plain,
% 28.94/19.17 (~(f7(c1) = c4)),
% 28.94/19.17 inference(modus_ponens,[status(thm)],[115, 18718])).
% 28.94/19.17 tff(18720,plain,
% 28.94/19.17 (f5(c1) = c2),
% 28.94/19.17 inference(unit_resolution,[status(thm)],[1708, 8428])).
% 28.94/19.17 tff(18721,plain,
% 28.94/19.17 (f7(c1) = f5(c1)),
% 28.94/19.17 inference(transitivity,[status(thm)],[347, 1761])).
% 28.94/19.17 tff(18722,plain,
% 28.94/19.17 (f3(f7(c1), f7(c1)) = f3(f5(c1), f5(c1))),
% 28.94/19.17 inference(monotonicity,[status(thm)],[18721, 18721])).
% 28.94/19.17 tff(18723,plain,
% 28.94/19.17 (f3(f7(c1), f7(c1)) = f7(c1)),
% 28.94/19.17 inference(transitivity,[status(thm)],[18722, 13005, 354])).
% 28.94/19.17 tff(18724,plain,
% 28.94/19.17 (f3(f7(c1), f7(c1)) = c2),
% 28.94/19.17 inference(transitivity,[status(thm)],[18722, 13005])).
% 28.94/19.17 tff(18725,plain,
% 28.94/19.17 (big_f(f3(f7(c1), f7(c1)), f7(c1)) <=> big_f(c2, c2)),
% 28.94/19.17 inference(monotonicity,[status(thm)],[18724, 347])).
% 28.94/19.17 tff(18726,plain,
% 28.94/19.17 (big_f(c2, c2) <=> big_f(f3(f7(c1), f7(c1)), f7(c1))),
% 28.94/19.17 inference(symmetry,[status(thm)],[18725])).
% 28.94/19.17 tff(18727,plain,
% 28.94/19.17 (big_f(f3(f7(c1), f7(c1)), f7(c1))),
% 28.94/19.17 inference(modus_ponens,[status(thm)],[1345, 18726])).
% 28.94/19.17 tff(18728,assumption,(f7(c1) = f2(c1)), introduced(assumption)).
% 28.94/19.17 tff(18729,plain,
% 28.94/19.17 ((~(f3(f7(c1), f7(c1)) = f7(c1))) | (~big_f(f3(f7(c1), f7(c1)), f7(c1)))),
% 28.94/19.17 inference(unit_resolution,[status(thm)],[14382, 1398, 5080, 1000, 18728, 11830])).
% 28.94/19.17 tff(18730,plain,
% 28.94/19.17 ($false),
% 28.94/19.17 inference(unit_resolution,[status(thm)],[18729, 18727, 18723])).
% 28.94/19.17 tff(18731,plain,((~(f3(f5(c1), f5(c1)) = c2)) | (~(c1 = c3)) | (f7(c1) = c4) | (~(f7(c1) = f2(c1))) | big_f(c1, f7(c1)) | (~big_f(c2, c2)) | (~(f7(c1) = c2)) | (~(f5(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.94/19.17 tff(18732,plain,
% 28.94/19.17 (~(f3(f5(c1), f5(c1)) = c2)),
% 28.94/19.17 inference(unit_resolution,[status(thm)],[18731, 14360, 1000, 5611, 14359, 1345, 120, 18720])).
% 28.94/19.17 tff(18733,plain,
% 28.94/19.17 (f3(f5(c1), f5(c1)) = c1),
% 28.94/19.17 inference(unit_resolution,[status(thm)],[7625, 18732])).
% 28.94/19.17 tff(18734,plain,
% 28.94/19.17 (c2 = f5(c1)),
% 28.94/19.17 inference(symmetry,[status(thm)],[18720])).
% 28.94/19.17 tff(18735,plain,
% 28.94/19.17 (f7(c1) = f5(c1)),
% 28.94/19.17 inference(transitivity,[status(thm)],[120, 18734])).
% 28.94/19.17 tff(18736,plain,
% 28.94/19.17 (f3(f7(c1), f7(c1)) = f3(f5(c1), f5(c1))),
% 28.94/19.17 inference(monotonicity,[status(thm)],[18735, 18735])).
% 28.94/19.17 tff(18737,plain,
% 28.94/19.17 (f3(f7(c1), f7(c1)) = c1),
% 28.94/19.17 inference(transitivity,[status(thm)],[18736, 18733])).
% 28.94/19.17 tff(18738,plain,
% 28.94/19.17 ((f3(f7(c1), f7(c1)) = f7(c1)) <=> (c1 = f7(c1))),
% 28.94/19.17 inference(monotonicity,[status(thm)],[18737])).
% 28.94/19.17 tff(18739,plain,
% 28.94/19.17 ((f3(f7(c1), f7(c1)) = f7(c1)) <=> (f7(c1) = c1)),
% 28.94/19.17 inference(transitivity,[status(thm)],[18738, 14336])).
% 28.94/19.17 tff(18740,plain,
% 28.94/19.17 ((f7(c1) = c1) <=> (f3(f7(c1), f7(c1)) = f7(c1))),
% 28.94/19.17 inference(symmetry,[status(thm)],[18739])).
% 28.94/19.17 tff(18741,plain,
% 28.94/19.17 ((~(f7(c1) = c1)) <=> (~(f3(f7(c1), f7(c1)) = f7(c1)))),
% 28.94/19.17 inference(monotonicity,[status(thm)],[18740])).
% 28.94/19.17 tff(18742,plain,
% 28.94/19.17 (~(f3(f7(c1), f7(c1)) = f7(c1))),
% 28.94/19.17 inference(modus_ponens,[status(thm)],[115, 18741])).
% 28.94/19.17 tff(18743,plain,
% 28.94/19.17 (f3(f7(c1), f7(c1)) = c3),
% 28.94/19.17 inference(transitivity,[status(thm)],[18736, 18733, 5585])).
% 28.94/19.17 tff(18744,plain,
% 28.94/19.17 (big_f(f3(f7(c1), f7(c1)), f7(c1)) <=> big_f(c3, f2(c3))),
% 28.94/19.17 inference(monotonicity,[status(thm)],[18743, 14350])).
% 28.94/19.17 tff(18745,plain,
% 28.94/19.17 (big_f(c3, f2(c3)) <=> big_f(f3(f7(c1), f7(c1)), f7(c1))),
% 28.94/19.17 inference(symmetry,[status(thm)],[18744])).
% 28.94/19.17 tff(18746,plain,
% 28.94/19.17 ((~big_f(c3, f2(c3))) <=> (~big_f(f3(f7(c1), f7(c1)), f7(c1)))),
% 28.94/19.17 inference(monotonicity,[status(thm)],[18745])).
% 28.94/19.17 tff(18747,plain,
% 28.94/19.17 (~big_f(f3(f7(c1), f7(c1)), f7(c1))),
% 28.94/19.17 inference(modus_ponens,[status(thm)],[1286, 18746])).
% 28.94/19.17 tff(18748,plain,
% 28.94/19.17 ($false),
% 28.94/19.17 inference(unit_resolution,[status(thm)],[14367, 18747, 18742])).
% 28.94/19.17 tff(18749,plain,((~big_f(f7(c1), f5(c1))) | (f7(c1) = c4) | big_f(c3, f2(c3)) | (~(f2(c3) = c2)) | (~(c3 = c1)) | (f7(c1) = c1) | (~big_f(c2, c2)) | big_f(f7(c1), c1)), inference(lemma,lemma(discharge,[]))).
% 28.94/19.17 tff(18750,plain,
% 28.94/19.17 (~big_f(f7(c1), f5(c1))),
% 28.94/19.17 inference(unit_resolution,[status(thm)],[18749, 18719, 1286, 18151, 172, 115, 18715, 18381])).
% 28.94/19.17 tff(18751,plain,
% 28.94/19.17 (big_f(f9(c1, c1), f10(c1))),
% 28.94/19.17 inference(unit_resolution,[status(thm)],[18686, 18750, 18370, 22, 11819, 115, 18380])).
% 28.94/19.17 tff(18752,plain,
% 28.94/19.17 (big_f(f9(c1, c1), f10(f7(c1)))),
% 28.94/19.17 inference(modus_ponens,[status(thm)],[18751, 18377])).
% 28.94/19.17 tff(18753,plain,
% 28.94/19.17 (f10(f7(c1)) = c1),
% 28.94/19.17 inference(transitivity,[status(thm)],[18374, 18373, 11819])).
% 28.94/19.17 tff(18754,plain,
% 28.94/19.17 ((f10(f7(c1)) = f7(c1)) <=> (c1 = f7(c1))),
% 28.94/19.17 inference(monotonicity,[status(thm)],[18753])).
% 28.94/19.17 tff(18755,plain,
% 28.94/19.17 ((f10(f7(c1)) = f7(c1)) <=> (f7(c1) = c1)),
% 28.94/19.17 inference(transitivity,[status(thm)],[18754, 14336])).
% 28.94/19.17 tff(18756,plain,
% 28.94/19.17 ((f7(c1) = c1) <=> (f10(f7(c1)) = f7(c1))),
% 28.94/19.17 inference(symmetry,[status(thm)],[18755])).
% 28.94/19.17 tff(18757,plain,
% 28.94/19.17 ((~(f7(c1) = c1)) <=> (~(f10(f7(c1)) = f7(c1)))),
% 28.94/19.17 inference(monotonicity,[status(thm)],[18756])).
% 28.94/19.17 tff(18758,plain,
% 28.94/19.17 (~(f10(f7(c1)) = f7(c1))),
% 28.94/19.17 inference(modus_ponens,[status(thm)],[115, 18757])).
% 28.94/19.17 tff(18759,plain,
% 28.94/19.17 (big_f(c1, f10(f7(c1))) <=> big_f(f7(c2), c1)),
% 28.94/19.17 inference(monotonicity,[status(thm)],[125, 18753])).
% 28.94/19.17 tff(18760,plain,
% 28.94/19.17 (big_f(f7(c2), c1) <=> big_f(c1, f10(f7(c1)))),
% 28.94/19.17 inference(symmetry,[status(thm)],[18759])).
% 28.94/19.17 tff(18761,plain,
% 28.94/19.17 (big_f(c1, f10(f7(c1)))),
% 28.94/19.17 inference(modus_ponens,[status(thm)],[18380, 18760])).
% 28.94/19.17 tff(18762,plain,
% 28.94/19.17 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (~big_f(c1, f10(f7(c1)))) | (f10(f7(c1)) = f7(c1)) | (c1 = f8(f7(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (~big_f(c1, f10(f7(c1)))) | (f10(f7(c1)) = f7(c1)) | (c1 = f8(f7(c1))))),
% 28.94/19.17 inference(rewrite,[status(thm)],[])).
% 28.94/19.17 tff(18763,plain,
% 28.94/19.17 (($false | (f10(f7(c1)) = f7(c1)) | (c1 = f8(f7(c1))) | (~big_f(c1, f10(f7(c1)))) | (f7(c1) = c1) | big_f(f7(c1), f5(c1))) <=> ((f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (~big_f(c1, f10(f7(c1)))) | (f10(f7(c1)) = f7(c1)) | (c1 = f8(f7(c1))))),
% 28.94/19.17 inference(rewrite,[status(thm)],[])).
% 28.94/19.17 tff(18764,plain,
% 28.94/19.17 (((~(f5(c1) = f5(c1))) | (f10(f7(c1)) = f7(c1)) | (c1 = f8(f7(c1))) | (~big_f(c1, f10(f7(c1)))) | (f7(c1) = c1) | big_f(f7(c1), f5(c1))) <=> ($false | (f10(f7(c1)) = f7(c1)) | (c1 = f8(f7(c1))) | (~big_f(c1, f10(f7(c1)))) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)))),
% 28.94/19.17 inference(monotonicity,[status(thm)],[273])).
% 28.94/19.17 tff(18765,plain,
% 28.94/19.17 (((~(f5(c1) = f5(c1))) | (f10(f7(c1)) = f7(c1)) | (c1 = f8(f7(c1))) | (~big_f(c1, f10(f7(c1)))) | (f7(c1) = c1) | big_f(f7(c1), f5(c1))) <=> ((f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (~big_f(c1, f10(f7(c1)))) | (f10(f7(c1)) = f7(c1)) | (c1 = f8(f7(c1))))),
% 28.94/19.17 inference(transitivity,[status(thm)],[18764, 18763])).
% 28.94/19.17 tff(18766,plain,
% 28.94/19.17 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(f5(c1) = f5(c1))) | (f10(f7(c1)) = f7(c1)) | (c1 = f8(f7(c1))) | (~big_f(c1, f10(f7(c1)))) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (~big_f(c1, f10(f7(c1)))) | (f10(f7(c1)) = f7(c1)) | (c1 = f8(f7(c1)))))),
% 28.94/19.17 inference(monotonicity,[status(thm)],[18765])).
% 28.94/19.17 tff(18767,plain,
% 28.94/19.17 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(f5(c1) = f5(c1))) | (f10(f7(c1)) = f7(c1)) | (c1 = f8(f7(c1))) | (~big_f(c1, f10(f7(c1)))) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (~big_f(c1, f10(f7(c1)))) | (f10(f7(c1)) = f7(c1)) | (c1 = f8(f7(c1))))),
% 28.94/19.17 inference(transitivity,[status(thm)],[18766, 18762])).
% 28.94/19.17 tff(18768,plain,
% 28.94/19.17 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(f5(c1) = f5(c1))) | (f10(f7(c1)) = f7(c1)) | (c1 = f8(f7(c1))) | (~big_f(c1, f10(f7(c1)))) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)))),
% 28.94/19.17 inference(quant_inst,[status(thm)],[])).
% 28.94/19.17 tff(18769,plain,
% 28.94/19.17 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (~big_f(c1, f10(f7(c1)))) | (f10(f7(c1)) = f7(c1)) | (c1 = f8(f7(c1)))),
% 28.94/19.17 inference(modus_ponens,[status(thm)],[18768, 18767])).
% 28.94/19.17 tff(18770,plain,
% 28.94/19.17 (c1 = f8(f7(c1))),
% 28.94/19.17 inference(unit_resolution,[status(thm)],[18769, 705, 115, 18750, 18761, 18758])).
% 28.94/19.17 tff(18771,plain,
% 28.94/19.17 (f8(f7(c1)) = c1),
% 28.94/19.17 inference(symmetry,[status(thm)],[18770])).
% 28.94/19.17 tff(18772,plain,
% 28.94/19.17 ((f9(c1, c1) = f8(f7(c1))) <=> (f9(c1, c1) = c1)),
% 28.94/19.17 inference(monotonicity,[status(thm)],[18771])).
% 28.94/19.17 tff(18773,plain,
% 28.94/19.17 ((f9(c1, c1) = c1) <=> (f9(c1, c1) = f8(f7(c1)))),
% 28.94/19.17 inference(symmetry,[status(thm)],[18772])).
% 28.94/19.17 tff(18774,plain,
% 28.94/19.17 ((~(f9(c1, c1) = c1)) <=> (~(f9(c1, c1) = f8(f7(c1))))),
% 28.94/19.17 inference(monotonicity,[status(thm)],[18773])).
% 28.94/19.17 tff(18775,plain,
% 28.94/19.17 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))),
% 28.94/19.17 inference(rewrite,[status(thm)],[])).
% 28.94/19.17 tff(18776,plain,
% 28.94/19.17 (((~(f10(c1) = c1)) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | $false) <=> ((f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))),
% 28.94/19.17 inference(rewrite,[status(thm)],[])).
% 28.94/19.17 tff(18777,plain,
% 28.94/19.17 (((~(f10(c1) = c1)) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(f5(c1) = f5(c1)))) <=> ((~(f10(c1) = c1)) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | $false)),
% 28.94/19.17 inference(monotonicity,[status(thm)],[273])).
% 28.94/19.17 tff(18778,plain,
% 28.94/19.17 (((~(f10(c1) = c1)) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(f5(c1) = f5(c1)))) <=> ((f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))),
% 28.94/19.17 inference(transitivity,[status(thm)],[18777, 18776])).
% 28.94/19.17 tff(18779,plain,
% 28.94/19.17 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(f5(c1) = f5(c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1)))))),
% 28.94/19.17 inference(monotonicity,[status(thm)],[18778])).
% 28.94/19.17 tff(18780,plain,
% 28.94/19.17 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(f5(c1) = f5(c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))),
% 28.94/19.17 inference(transitivity,[status(thm)],[18779, 18775])).
% 28.94/19.17 tff(18781,plain,
% 28.94/19.17 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(f5(c1) = f5(c1))))),
% 28.94/19.17 inference(quant_inst,[status(thm)],[])).
% 28.94/19.17 tff(18782,plain,
% 28.94/19.17 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1)))),
% 28.94/19.17 inference(modus_ponens,[status(thm)],[18781, 18780])).
% 28.94/19.17 tff(18783,plain,
% 28.94/19.17 (~(f9(c1, c1) = c1)),
% 28.94/19.17 inference(unit_resolution,[status(thm)],[18782, 783, 115, 18370, 18750, 18751])).
% 28.94/19.17 tff(18784,plain,
% 28.94/19.17 (~(f9(c1, c1) = f8(f7(c1)))),
% 28.94/19.17 inference(modus_ponens,[status(thm)],[18783, 18774])).
% 28.94/19.17 tff(18785,plain,
% 28.94/19.17 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (f10(f7(c1)) = f7(c1)) | (~big_f(f9(c1, c1), f10(f7(c1)))) | (f9(c1, c1) = f8(f7(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (f10(f7(c1)) = f7(c1)) | (~big_f(f9(c1, c1), f10(f7(c1)))) | (f9(c1, c1) = f8(f7(c1))))),
% 28.94/19.17 inference(rewrite,[status(thm)],[])).
% 28.94/19.17 tff(18786,plain,
% 28.94/19.17 (($false | (f10(f7(c1)) = f7(c1)) | (f9(c1, c1) = f8(f7(c1))) | (~big_f(f9(c1, c1), f10(f7(c1)))) | (f7(c1) = c1) | big_f(f7(c1), f5(c1))) <=> ((f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (f10(f7(c1)) = f7(c1)) | (~big_f(f9(c1, c1), f10(f7(c1)))) | (f9(c1, c1) = f8(f7(c1))))),
% 28.94/19.17 inference(rewrite,[status(thm)],[])).
% 28.94/19.17 tff(18787,plain,
% 28.94/19.17 (((~(f5(c1) = f5(c1))) | (f10(f7(c1)) = f7(c1)) | (f9(c1, c1) = f8(f7(c1))) | (~big_f(f9(c1, c1), f10(f7(c1)))) | (f7(c1) = c1) | big_f(f7(c1), f5(c1))) <=> ($false | (f10(f7(c1)) = f7(c1)) | (f9(c1, c1) = f8(f7(c1))) | (~big_f(f9(c1, c1), f10(f7(c1)))) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)))),
% 28.94/19.17 inference(monotonicity,[status(thm)],[273])).
% 28.94/19.17 tff(18788,plain,
% 28.94/19.17 (((~(f5(c1) = f5(c1))) | (f10(f7(c1)) = f7(c1)) | (f9(c1, c1) = f8(f7(c1))) | (~big_f(f9(c1, c1), f10(f7(c1)))) | (f7(c1) = c1) | big_f(f7(c1), f5(c1))) <=> ((f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (f10(f7(c1)) = f7(c1)) | (~big_f(f9(c1, c1), f10(f7(c1)))) | (f9(c1, c1) = f8(f7(c1))))),
% 28.94/19.17 inference(transitivity,[status(thm)],[18787, 18786])).
% 28.94/19.17 tff(18789,plain,
% 28.94/19.17 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(f5(c1) = f5(c1))) | (f10(f7(c1)) = f7(c1)) | (f9(c1, c1) = f8(f7(c1))) | (~big_f(f9(c1, c1), f10(f7(c1)))) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (f10(f7(c1)) = f7(c1)) | (~big_f(f9(c1, c1), f10(f7(c1)))) | (f9(c1, c1) = f8(f7(c1)))))),
% 28.94/19.17 inference(monotonicity,[status(thm)],[18788])).
% 28.94/19.17 tff(18790,plain,
% 28.94/19.17 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(f5(c1) = f5(c1))) | (f10(f7(c1)) = f7(c1)) | (f9(c1, c1) = f8(f7(c1))) | (~big_f(f9(c1, c1), f10(f7(c1)))) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (f10(f7(c1)) = f7(c1)) | (~big_f(f9(c1, c1), f10(f7(c1)))) | (f9(c1, c1) = f8(f7(c1))))),
% 28.94/19.17 inference(transitivity,[status(thm)],[18789, 18785])).
% 28.94/19.17 tff(18791,plain,
% 28.94/19.17 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(f5(c1) = f5(c1))) | (f10(f7(c1)) = f7(c1)) | (f9(c1, c1) = f8(f7(c1))) | (~big_f(f9(c1, c1), f10(f7(c1)))) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)))),
% 28.94/19.18 inference(quant_inst,[status(thm)],[])).
% 28.94/19.18 tff(18792,plain,
% 28.94/19.18 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (f10(f7(c1)) = f7(c1)) | (~big_f(f9(c1, c1), f10(f7(c1)))) | (f9(c1, c1) = f8(f7(c1)))),
% 28.94/19.18 inference(modus_ponens,[status(thm)],[18791, 18790])).
% 28.94/19.18 tff(18793,plain,
% 28.94/19.18 ((~big_f(f9(c1, c1), f10(f7(c1)))) | (f9(c1, c1) = f8(f7(c1)))),
% 28.94/19.18 inference(unit_resolution,[status(thm)],[18792, 705, 115, 18750, 18758])).
% 28.94/19.18 tff(18794,plain,
% 28.94/19.18 ($false),
% 28.94/19.18 inference(unit_resolution,[status(thm)],[18793, 18784, 18752])).
% 28.94/19.18 tff(18795,plain,((f7(c1) = c1) | (~(f10(c2) = c1)) | (~(f4(c4) = c1)) | big_f(c3, f2(c3)) | (~(c3 = c1)) | (f2(c3) = c1) | (f7(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 28.94/19.18 tff(18796,plain,
% 28.94/19.18 (f7(c1) = c1),
% 28.94/19.18 inference(unit_resolution,[status(thm)],[18795, 1286, 11752, 11819, 172, 18150, 17])).
% 28.94/19.18 tff(18797,plain,
% 28.94/19.18 (~(f5(c2) = c2)),
% 28.94/19.18 inference(unit_resolution,[status(thm)],[18433, 11849, 1286, 11819, 172, 18150, 121, 17])).
% 28.94/19.18 tff(18798,plain,
% 28.94/19.18 (f5(c2) = c1),
% 28.94/19.18 inference(unit_resolution,[status(thm)],[1547, 18797])).
% 28.94/19.18 tff(18799,plain,
% 28.94/19.18 (f5(f10(c1)) = c1),
% 28.94/19.18 inference(transitivity,[status(thm)],[9888, 18798])).
% 28.94/19.18 tff(18800,plain,
% 28.94/19.18 ((f6(c1, c1) = f5(f10(c1))) <=> (f6(c1, c1) = c1)),
% 28.94/19.18 inference(monotonicity,[status(thm)],[18799])).
% 28.94/19.18 tff(18801,plain,
% 28.94/19.18 (big_f(f7(f10(c1)), f6(c1, c1)) <=> big_f(f7(c1), f6(c1, c1))),
% 28.94/19.18 inference(monotonicity,[status(thm)],[9839])).
% 28.94/19.18 tff(18802,plain,
% 28.94/19.18 (big_f(f7(c1), f6(c1, c1)) <=> big_f(f7(f10(c1)), f6(c1, c1))),
% 28.94/19.18 inference(symmetry,[status(thm)],[18801])).
% 28.94/19.18 tff(18803,plain,
% 28.94/19.18 (f6(f7(c2), c3) = f6(c1, c1)),
% 28.94/19.18 inference(monotonicity,[status(thm)],[22, 172])).
% 28.94/19.18 tff(18804,plain,
% 28.94/19.18 (big_f(f7(f7(c2)), f6(f7(c2), c3)) <=> big_f(f7(c1), f6(c1, c1))),
% 28.94/19.18 inference(monotonicity,[status(thm)],[8077, 18803])).
% 28.94/19.18 tff(18805,plain,
% 28.94/19.18 ((f10(f10(c2)) = c2) <=> (f10(c1) = c2)),
% 28.94/19.18 inference(monotonicity,[status(thm)],[11844])).
% 28.94/19.18 tff(18806,plain,
% 28.94/19.18 ((f10(c1) = c2) <=> (f10(f10(c2)) = c2)),
% 28.94/19.18 inference(symmetry,[status(thm)],[18805])).
% 28.94/19.18 tff(18807,plain,
% 28.94/19.18 (f10(f10(c2)) = c2),
% 28.94/19.18 inference(modus_ponens,[status(thm)],[15, 18806])).
% 28.94/19.18 tff(18808,plain,
% 28.94/19.18 (big_f(c2, c2) <=> big_f(c2, f10(c1))),
% 28.94/19.18 inference(monotonicity,[status(thm)],[5571])).
% 28.94/19.18 tff(18809,plain,
% 28.94/19.18 ((~big_f(c2, c2)) <=> (~big_f(c2, f10(c1)))),
% 28.94/19.18 inference(monotonicity,[status(thm)],[18808])).
% 28.94/19.18 tff(18810,plain,
% 28.94/19.18 (~big_f(c2, f10(c1))),
% 28.94/19.18 inference(modus_ponens,[status(thm)],[121, 18809])).
% 28.94/19.18 tff(18811,plain,
% 28.94/19.18 (f10(c1) = f2(c3)),
% 28.94/19.18 inference(transitivity,[status(thm)],[15, 18396])).
% 28.94/19.18 tff(18812,plain,
% 28.94/19.18 (big_f(c1, f10(c1)) <=> big_f(c3, f2(c3))),
% 28.94/19.18 inference(monotonicity,[status(thm)],[5585, 18811])).
% 28.94/19.18 tff(18813,plain,
% 28.94/19.18 (big_f(c3, f2(c3)) <=> big_f(c1, f10(c1))),
% 28.94/19.18 inference(symmetry,[status(thm)],[18812])).
% 28.94/19.18 tff(18814,plain,
% 28.94/19.18 ((~big_f(c3, f2(c3))) <=> (~big_f(c1, f10(c1)))),
% 28.94/19.18 inference(monotonicity,[status(thm)],[18813])).
% 28.94/19.18 tff(18815,plain,
% 28.94/19.18 (~big_f(c1, f10(c1))),
% 28.94/19.18 inference(modus_ponens,[status(thm)],[1286, 18814])).
% 28.94/19.18 tff(18816,plain,
% 28.94/19.18 (big_f(f7(f7(c2)), f6(f7(c2), c3))),
% 28.94/19.18 inference(unit_resolution,[status(thm)],[18520, 18815, 4234, 3, 22, 172, 18810, 338, 18807, 11819])).
% 28.94/19.18 tff(18817,plain,
% 28.94/19.18 (big_f(f7(c1), f6(c1, c1))),
% 28.94/19.18 inference(modus_ponens,[status(thm)],[18816, 18804])).
% 28.94/19.18 tff(18818,plain,
% 28.94/19.18 (big_f(f7(f10(c1)), f6(c1, c1))),
% 28.94/19.18 inference(modus_ponens,[status(thm)],[18817, 18802])).
% 28.94/19.18 tff(18819,plain,
% 28.94/19.18 ((c1 = f10(c1)) <=> (f10(c1) = c1)),
% 28.94/19.18 inference(commutativity,[status(thm)],[])).
% 28.94/19.18 tff(18820,plain,
% 28.94/19.18 (f7(f10(c1)) = c1),
% 28.94/19.18 inference(transitivity,[status(thm)],[219, 22])).
% 28.94/19.18 tff(18821,plain,
% 28.94/19.18 ((f7(f10(c1)) = f10(c1)) <=> (c1 = f10(c1))),
% 28.94/19.18 inference(monotonicity,[status(thm)],[18820])).
% 28.94/19.18 tff(18822,plain,
% 28.94/19.18 ((f7(f10(c1)) = f10(c1)) <=> (f10(c1) = c1)),
% 28.94/19.18 inference(transitivity,[status(thm)],[18821, 18819])).
% 28.94/19.18 tff(18823,plain,
% 28.94/19.18 ((f10(c1) = c1) <=> (f7(f10(c1)) = f10(c1))),
% 28.94/19.18 inference(symmetry,[status(thm)],[18822])).
% 28.94/19.18 tff(18824,plain,
% 28.94/19.18 ((~(f10(c1) = c1)) <=> (~(f7(f10(c1)) = f10(c1)))),
% 28.94/19.18 inference(monotonicity,[status(thm)],[18823])).
% 28.94/19.18 tff(18825,plain,
% 28.94/19.18 (~(f7(f10(c1)) = f10(c1))),
% 28.94/19.18 inference(modus_ponens,[status(thm)],[3, 18824])).
% 28.94/19.18 tff(18826,plain,
% 28.94/19.18 (f2(c1) = c2),
% 28.94/19.18 inference(transitivity,[status(thm)],[5586, 18151])).
% 28.94/19.18 tff(18827,plain,
% 28.94/19.18 (big_f(f2(c1), f10(c1)) <=> big_f(c2, f10(c1))),
% 28.94/19.18 inference(monotonicity,[status(thm)],[18826])).
% 28.94/19.18 tff(18828,plain,
% 28.94/19.18 (big_f(c2, f10(c1)) <=> big_f(f2(c1), f10(c1))),
% 28.94/19.18 inference(symmetry,[status(thm)],[18827])).
% 28.94/19.18 tff(18829,plain,
% 28.94/19.18 (big_f(c2, c2) <=> big_f(f2(c1), f10(c1))),
% 28.94/19.18 inference(transitivity,[status(thm)],[18808, 18828])).
% 28.94/19.18 tff(18830,plain,
% 28.94/19.18 ((~big_f(c2, c2)) <=> (~big_f(f2(c1), f10(c1)))),
% 28.94/19.18 inference(monotonicity,[status(thm)],[18829])).
% 28.94/19.18 tff(18831,plain,
% 28.94/19.18 (~big_f(f2(c1), f10(c1))),
% 28.94/19.18 inference(modus_ponens,[status(thm)],[121, 18830])).
% 28.94/19.18 tff(18832,plain,
% 28.94/19.18 (~(f8(c1) = c2)),
% 28.94/19.18 inference(unit_resolution,[status(thm)],[18559, 18817, 18810, 11819, 172, 22, 18831, 4234, 3, 18807, 18825, 18798, 18151])).
% 28.94/19.18 tff(18833,plain,
% 28.94/19.18 (f8(c1) = c1),
% 28.94/19.18 inference(unit_resolution,[status(thm)],[1680, 18832])).
% 28.94/19.18 tff(18834,plain,
% 28.94/19.18 (c1 = f8(c1)),
% 28.94/19.18 inference(modus_ponens,[status(thm)],[18833, 3028])).
% 28.94/19.18 tff(18835,plain,
% 28.94/19.18 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | (f7(f10(c1)) = f10(c1)) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (f6(c1, c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | (f10(c1) = c1) | (f7(f10(c1)) = f10(c1)) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (f6(c1, c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, c1))))),
% 28.94/19.18 inference(rewrite,[status(thm)],[])).
% 28.94/19.18 tff(18836,plain,
% 28.94/19.18 (((f10(c1) = c1) | big_f(c1, f10(c1)) | (f7(f10(c1)) = f10(c1)) | (f6(c1, c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, c1))) | (~(c1 = f8(c1)))) <=> ((f10(c1) = c1) | (f7(f10(c1)) = f10(c1)) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (f6(c1, c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, c1))))),
% 28.94/19.18 inference(rewrite,[status(thm)],[])).
% 28.94/19.18 tff(18837,plain,
% 28.94/19.18 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | big_f(c1, f10(c1)) | (f7(f10(c1)) = f10(c1)) | (f6(c1, c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, c1))) | (~(c1 = f8(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | (f7(f10(c1)) = f10(c1)) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (f6(c1, c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, c1)))))),
% 28.94/19.18 inference(monotonicity,[status(thm)],[18836])).
% 28.94/19.18 tff(18838,plain,
% 28.94/19.18 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | big_f(c1, f10(c1)) | (f7(f10(c1)) = f10(c1)) | (f6(c1, c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, c1))) | (~(c1 = f8(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | (f10(c1) = c1) | (f7(f10(c1)) = f10(c1)) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (f6(c1, c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, c1))))),
% 28.94/19.18 inference(transitivity,[status(thm)],[18837, 18835])).
% 28.94/19.18 tff(18839,plain,
% 28.94/19.18 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | big_f(c1, f10(c1)) | (f7(f10(c1)) = f10(c1)) | (f6(c1, c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, c1))) | (~(c1 = f8(c1))))),
% 28.94/19.18 inference(quant_inst,[status(thm)],[])).
% 28.94/19.18 tff(18840,plain,
% 28.94/19.18 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | (f10(c1) = c1) | (f7(f10(c1)) = f10(c1)) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (f6(c1, c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, c1)))),
% 28.94/19.18 inference(modus_ponens,[status(thm)],[18839, 18838])).
% 28.94/19.18 tff(18841,plain,
% 28.94/19.18 ((~(c1 = f8(c1))) | (f6(c1, c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, c1)))),
% 28.94/19.18 inference(unit_resolution,[status(thm)],[18840, 2795, 3, 18815, 18825])).
% 28.94/19.18 tff(18842,plain,
% 28.94/19.18 (f6(c1, c1) = f5(f10(c1))),
% 28.94/19.18 inference(unit_resolution,[status(thm)],[18841, 18834, 18818])).
% 28.94/19.18 tff(18843,plain,
% 28.94/19.18 (f6(c1, c1) = c1),
% 28.94/19.18 inference(modus_ponens,[status(thm)],[18842, 18800])).
% 28.94/19.18 tff(18844,plain,
% 28.94/19.18 ((~(c1 = f8(c1))) | (~(f6(c1, c1) = c1))),
% 28.94/19.18 inference(unit_resolution,[status(thm)],[18583, 2963, 4234, 3, 18815, 18817])).
% 28.94/19.18 tff(18845,plain,
% 28.94/19.18 (~(f6(c1, c1) = c1)),
% 28.94/19.18 inference(unit_resolution,[status(thm)],[18844, 18834])).
% 28.94/19.18 tff(18846,plain,
% 28.94/19.18 ($false),
% 28.94/19.18 inference(unit_resolution,[status(thm)],[18845, 18843])).
% 28.94/19.18 tff(18847,plain,((f10(c1) = c1) | (~(f7(c1) = c1)) | (~(f10(c2) = c1)) | (~(c3 = c1)) | (~big_f(f7(c2), c1)) | big_f(c3, f2(c3)) | (f2(c3) = c1) | big_f(c2, c2) | (f7(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 28.94/19.18 tff(18848,plain,
% 28.94/19.18 (f10(c1) = c1),
% 28.94/19.18 inference(unit_resolution,[status(thm)],[18847, 121, 11819, 172, 18380, 1286, 18150, 18796, 17])).
% 28.94/19.18 tff(18849,plain,
% 28.94/19.18 (f7(c1) = c3),
% 28.94/19.18 inference(transitivity,[status(thm)],[18796, 5585])).
% 28.94/19.18 tff(18850,plain,
% 28.94/19.18 (big_f(f7(c1), c2) <=> big_f(c3, f2(c3))),
% 28.94/19.18 inference(monotonicity,[status(thm)],[18849, 18396])).
% 28.94/19.18 tff(18851,plain,
% 28.94/19.18 (big_f(c3, f2(c3)) <=> big_f(f7(c1), c2)),
% 28.94/19.18 inference(symmetry,[status(thm)],[18850])).
% 28.94/19.18 tff(18852,plain,
% 28.94/19.18 (big_f(c3, f2(c3)) <=> big_f(f7(f4(c4)), c2)),
% 28.94/19.18 inference(transitivity,[status(thm)],[18851, 18216])).
% 28.94/19.18 tff(18853,plain,
% 28.94/19.18 ((~big_f(c3, f2(c3))) <=> (~big_f(f7(f4(c4)), c2))),
% 28.94/19.18 inference(monotonicity,[status(thm)],[18852])).
% 28.94/19.18 tff(18854,plain,
% 28.94/19.18 (~big_f(f7(f4(c4)), c2)),
% 28.94/19.18 inference(modus_ponens,[status(thm)],[1286, 18853])).
% 28.94/19.18 tff(18855,plain,
% 28.94/19.18 (big_f(f7(c1), f5(c1)) <=> big_f(f7(c2), c1)),
% 28.94/19.18 inference(monotonicity,[status(thm)],[8286, 230])).
% 28.94/19.18 tff(18856,plain,
% 28.94/19.18 (big_f(f7(c2), c1) <=> big_f(f7(c1), f5(c1))),
% 28.94/19.18 inference(symmetry,[status(thm)],[18855])).
% 28.94/19.18 tff(18857,plain,
% 28.94/19.18 (big_f(f7(c1), f5(c1))),
% 28.94/19.18 inference(modus_ponens,[status(thm)],[338, 18856])).
% 28.94/19.18 tff(18858,plain,
% 28.94/19.18 ($false),
% 28.94/19.18 inference(unit_resolution,[status(thm)],[730, 18857])).
% 28.94/19.18 tff(18859,plain,((~(f5(c1) = c1)) | big_f(f7(c1), f5(c1)) | (~big_f(f7(c2), c1)) | (~(f7(c1) = c1)) | (~(f7(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.94/19.18 tff(18860,plain,
% 28.94/19.18 (~(f5(c1) = c1)),
% 28.94/19.18 inference(unit_resolution,[status(thm)],[18859, 730, 338, 4234, 292])).
% 28.94/19.18 tff(18861,plain,
% 28.94/19.18 (f5(c1) = c2),
% 28.94/19.18 inference(unit_resolution,[status(thm)],[1708, 18860])).
% 28.94/19.18 tff(18862,plain,
% 28.94/19.18 (big_f(f7(c1), f6(c1, c1))),
% 28.94/19.18 inference(unit_resolution,[status(thm)],[9993, 4070, 338, 292, 4234, 3762, 8712])).
% 28.94/19.18 tff(18863,plain,
% 28.94/19.18 (~(f6(f7(c2), c3) = c2)),
% 28.94/19.18 inference(unit_resolution,[status(thm)],[5966, 18862, 730, 18861, 172, 292])).
% 28.94/19.18 tff(18864,plain,
% 28.94/19.18 (f6(f7(c2), c3) = c1),
% 28.94/19.18 inference(unit_resolution,[status(thm)],[2391, 18863])).
% 28.94/19.18 tff(18865,plain,
% 28.94/19.18 (f6(c1, c1) = c1),
% 28.94/19.18 inference(unit_resolution,[status(thm)],[10018, 18864, 172, 292])).
% 28.94/19.18 tff(18866,plain,
% 28.94/19.18 ($false),
% 28.94/19.18 inference(unit_resolution,[status(thm)],[10040, 2534, 4234, 3762, 4070, 8712, 18862, 18865])).
% 28.94/19.18 tff(18867,plain,((f9(c1, c1) = c1) | (~(f7(c1) = c1)) | (~(f10(c1) = c1)) | big_f(f9(c1, c1), f10(c1)) | (~(c3 = c1)) | (~(f7(c2) = c1)) | big_f(f7(c1), f5(c1)) | (~big_f(f7(c2), c1))), inference(lemma,lemma(discharge,[]))).
% 28.94/19.18 tff(18868,plain,
% 28.94/19.18 (f9(c1, c1) = c1),
% 28.94/19.18 inference(unit_resolution,[status(thm)],[18867, 8712, 3762, 4234, 172, 292, 730, 338])).
% 28.94/19.18 tff(18869,plain,
% 28.94/19.18 (f9(c1, c1) = f7(c2)),
% 28.94/19.18 inference(transitivity,[status(thm)],[18868, 342])).
% 28.94/19.18 tff(18870,plain,
% 28.94/19.18 (big_f(f9(c1, c1), f10(c1)) <=> big_f(f7(c2), c1)),
% 28.94/19.18 inference(monotonicity,[status(thm)],[18869, 3762])).
% 28.94/19.18 tff(18871,plain,
% 28.94/19.18 (big_f(f7(c2), c1) <=> big_f(f9(c1, c1), f10(c1))),
% 28.94/19.18 inference(symmetry,[status(thm)],[18870])).
% 28.94/19.18 tff(18872,plain,
% 28.94/19.18 (big_f(f9(c1, c1), f10(c1))),
% 28.94/19.18 inference(modus_ponens,[status(thm)],[338, 18871])).
% 28.94/19.18 tff(18873,plain,
% 28.94/19.18 ($false),
% 28.94/19.18 inference(unit_resolution,[status(thm)],[8712, 18872])).
% 28.94/19.18 tff(18874,plain,(big_f(f9(c1, c1), f10(c1)) | (~big_f(f7(c2), c1)) | (~(f10(c1) = c1)) | (~(f7(c2) = c1)) | (~(f7(c1) = c1)) | (~(c3 = c1)) | big_f(f7(c1), f5(c1))), inference(lemma,lemma(discharge,[]))).
% 28.94/19.18 tff(18875,plain,
% 28.94/19.18 (big_f(f9(c1, c1), f10(c1))),
% 28.94/19.18 inference(unit_resolution,[status(thm)],[18874, 730, 3762, 292, 4234, 172, 338])).
% 28.94/19.18 tff(18876,plain,
% 28.94/19.18 ((f9(c1, c1) = f4(c1)) <=> (f9(c1, c1) = c1)),
% 28.94/19.18 inference(monotonicity,[status(thm)],[18178])).
% 28.94/19.18 tff(18877,plain,
% 28.94/19.18 (big_f(f9(c1, c1), c1) <=> big_f(f9(c1, c1), f10(c1))),
% 28.94/19.18 inference(monotonicity,[status(thm)],[11570])).
% 28.94/19.18 tff(18878,plain,
% 28.94/19.18 (big_f(f9(c1, c1), f10(c1)) <=> big_f(f9(c1, c1), c1)),
% 28.94/19.18 inference(symmetry,[status(thm)],[18877])).
% 28.94/19.18 tff(18879,plain,
% 28.94/19.18 (big_f(f9(c1, c1), c1)),
% 28.94/19.18 inference(modus_ponens,[status(thm)],[18875, 18878])).
% 28.94/19.18 tff(18880,plain,
% 28.94/19.18 (f5(c1) = f2(c1)),
% 28.94/19.18 inference(transitivity,[status(thm)],[18861, 13016, 5589])).
% 28.94/19.18 tff(18881,plain,
% 28.94/19.18 (big_f(c1, f5(c1)) <=> big_f(f7(c1), f5(c1))),
% 28.94/19.18 inference(monotonicity,[status(thm)],[5544])).
% 28.94/19.18 tff(18882,plain,
% 28.94/19.18 (big_f(f7(c1), f5(c1)) <=> big_f(c1, f5(c1))),
% 28.94/19.18 inference(symmetry,[status(thm)],[18881])).
% 28.94/19.18 tff(18883,plain,
% 28.94/19.18 ((~big_f(f7(c1), f5(c1))) <=> (~big_f(c1, f5(c1)))),
% 28.94/19.18 inference(monotonicity,[status(thm)],[18882])).
% 28.94/19.18 tff(18884,plain,
% 28.94/19.18 (~big_f(c1, f5(c1))),
% 28.94/19.18 inference(modus_ponens,[status(thm)],[730, 18883])).
% 28.94/19.18 tff(18885,assumption,(big_f(c1, f5(c1))), introduced(assumption)).
% 28.94/19.18 tff(18886,plain,
% 28.94/19.18 ($false),
% 28.94/19.18 inference(unit_resolution,[status(thm)],[18885, 18884])).
% 28.94/19.18 tff(18887,plain,((~big_f(c1, f5(c1))) | big_f(f7(c1), f5(c1)) | (~(f7(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.94/19.18 tff(18888,plain,
% 28.94/19.18 (~big_f(c1, f5(c1))),
% 28.94/19.18 inference(unit_resolution,[status(thm)],[18887, 730, 4234])).
% 28.94/19.18 tff(18889,plain,
% 28.94/19.18 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(c1 = c4)) | (~big_f(f9(c1, c1), c1)) | (f9(c1, c1) = f4(c1)) | (~(f5(c1) = f2(c1))) | big_f(c1, f5(c1)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | (~(c1 = c3)) | (~(c1 = c4)) | (~big_f(f9(c1, c1), c1)) | (f9(c1, c1) = f4(c1)) | (~(f5(c1) = f2(c1))) | big_f(c1, f5(c1)))),
% 28.94/19.18 inference(rewrite,[status(thm)],[])).
% 28.94/19.18 tff(18890,plain,
% 28.94/19.18 (((~(c1 = c3)) | (~(f5(c1) = f2(c1))) | (~(c1 = c4)) | (f9(c1, c1) = f4(c1)) | (~big_f(f9(c1, c1), c1)) | big_f(c1, f5(c1))) <=> ((~(c1 = c3)) | (~(c1 = c4)) | (~big_f(f9(c1, c1), c1)) | (f9(c1, c1) = f4(c1)) | (~(f5(c1) = f2(c1))) | big_f(c1, f5(c1)))),
% 28.94/19.18 inference(rewrite,[status(thm)],[])).
% 28.94/19.18 tff(18891,plain,
% 28.94/19.18 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(f5(c1) = f2(c1))) | (~(c1 = c4)) | (f9(c1, c1) = f4(c1)) | (~big_f(f9(c1, c1), c1)) | big_f(c1, f5(c1)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(c1 = c4)) | (~big_f(f9(c1, c1), c1)) | (f9(c1, c1) = f4(c1)) | (~(f5(c1) = f2(c1))) | big_f(c1, f5(c1))))),
% 28.94/19.18 inference(monotonicity,[status(thm)],[18890])).
% 28.94/19.18 tff(18892,plain,
% 28.94/19.18 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(f5(c1) = f2(c1))) | (~(c1 = c4)) | (f9(c1, c1) = f4(c1)) | (~big_f(f9(c1, c1), c1)) | big_f(c1, f5(c1)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | (~(c1 = c3)) | (~(c1 = c4)) | (~big_f(f9(c1, c1), c1)) | (f9(c1, c1) = f4(c1)) | (~(f5(c1) = f2(c1))) | big_f(c1, f5(c1)))),
% 28.94/19.18 inference(transitivity,[status(thm)],[18891, 18889])).
% 28.94/19.18 tff(18893,plain,
% 28.94/19.18 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(f5(c1) = f2(c1))) | (~(c1 = c4)) | (f9(c1, c1) = f4(c1)) | (~big_f(f9(c1, c1), c1)) | big_f(c1, f5(c1)))),
% 28.94/19.18 inference(quant_inst,[status(thm)],[])).
% 28.94/19.18 tff(18894,plain,
% 28.94/19.18 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | (~(c1 = c3)) | (~(c1 = c4)) | (~big_f(f9(c1, c1), c1)) | (f9(c1, c1) = f4(c1)) | (~(f5(c1) = f2(c1))) | big_f(c1, f5(c1))),
% 28.94/19.18 inference(modus_ponens,[status(thm)],[18893, 18892])).
% 28.94/19.18 tff(18895,plain,
% 28.94/19.18 ((~big_f(f9(c1, c1), c1)) | (f9(c1, c1) = f4(c1))),
% 28.94/19.18 inference(unit_resolution,[status(thm)],[18894, 11666, 5611, 564, 18888, 18880])).
% 28.94/19.18 tff(18896,plain,
% 28.94/19.18 (f9(c1, c1) = f4(c1)),
% 28.94/19.18 inference(unit_resolution,[status(thm)],[18895, 18879])).
% 28.94/19.18 tff(18897,plain,
% 28.94/19.18 (f9(c1, c1) = c1),
% 28.94/19.18 inference(modus_ponens,[status(thm)],[18896, 18876])).
% 28.94/19.18 tff(18898,plain,
% 28.94/19.18 (big_f(f7(c1), f6(c1, c1))),
% 28.94/19.18 inference(unit_resolution,[status(thm)],[9972, 18897, 4234, 292, 3762, 338, 18875])).
% 28.94/19.18 tff(18899,plain,
% 28.94/19.18 (~(f6(f7(c2), c3) = c2)),
% 28.94/19.18 inference(unit_resolution,[status(thm)],[5966, 18898, 730, 18861, 172, 292])).
% 28.94/19.18 tff(18900,plain,
% 28.94/19.18 (f6(f7(c2), c3) = c1),
% 28.94/19.18 inference(unit_resolution,[status(thm)],[2391, 18899])).
% 28.94/19.18 tff(18901,plain,
% 28.94/19.18 (f6(c1, c1) = c1),
% 28.94/19.18 inference(unit_resolution,[status(thm)],[10018, 18900, 172, 292])).
% 28.94/19.18 tff(18902,plain,
% 28.94/19.18 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)))),
% 28.94/19.18 inference(rewrite,[status(thm)],[])).
% 28.94/19.18 tff(18903,plain,
% 28.94/19.18 (((~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1)))) <=> ((~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)))),
% 28.94/19.18 inference(rewrite,[status(thm)],[])).
% 28.94/19.18 tff(18904,plain,
% 28.94/19.18 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1))))),
% 28.94/19.18 inference(monotonicity,[status(thm)],[18903])).
% 28.94/19.18 tff(18905,plain,
% 28.94/19.18 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)))),
% 28.94/19.18 inference(transitivity,[status(thm)],[18904, 18902])).
% 28.94/19.18 tff(18906,plain,
% 28.94/19.18 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))),
% 28.94/19.18 inference(quant_inst,[status(thm)],[])).
% 28.94/19.18 tff(18907,plain,
% 28.94/19.18 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1))),
% 28.94/19.18 inference(modus_ponens,[status(thm)],[18906, 18905])).
% 28.94/19.18 tff(18908,plain,
% 28.94/19.18 ($false),
% 28.94/19.18 inference(unit_resolution,[status(thm)],[18907, 2378, 4234, 3762, 18897, 18875, 18898, 18901])).
% 28.94/19.18 tff(18909,plain,(big_f(f7(c1), f5(c1)) | (~(f7(c1) = c1)) | (~(f10(c1) = c1)) | (~(c3 = c1)) | (~(f7(c2) = c1)) | (~big_f(f7(c2), c1)) | (~(f4(c4) = c1)) | (~(c4 = c1)) | (~(f2(c3) = c2))), inference(lemma,lemma(discharge,[]))).
% 28.94/19.18 tff(18910,plain,
% 28.94/19.18 (big_f(f7(c1), f5(c1))),
% 28.94/19.18 inference(unit_resolution,[status(thm)],[18909, 18848, 18796, 172, 22, 18380, 11752, 18167, 18151])).
% 28.94/19.18 tff(18911,plain,
% 28.94/19.18 (~(f5(c1) = c2)),
% 28.94/19.18 inference(unit_resolution,[status(thm)],[18267, 18910, 11752, 18854])).
% 28.94/19.18 tff(18912,plain,
% 28.94/19.18 (f5(c1) = c1),
% 28.94/19.18 inference(unit_resolution,[status(thm)],[1708, 18911])).
% 28.94/19.18 tff(18913,plain,
% 28.94/19.18 (~(f9(f10(c2), f4(c4)) = c2)),
% 28.94/19.18 inference(unit_resolution,[status(thm)],[18641, 18912, 11819, 18197, 11752, 18150, 121, 172, 1286, 17])).
% 28.94/19.18 tff(18914,plain,
% 28.94/19.18 (f9(f10(c2), f4(c4)) = c1),
% 28.94/19.18 inference(unit_resolution,[status(thm)],[146, 18913])).
% 28.94/19.18 tff(18915,plain,
% 28.94/19.18 (f9(c1, c1) = f7(c2)),
% 28.94/19.18 inference(transitivity,[status(thm)],[18436, 18914, 125])).
% 28.94/19.18 tff(18916,plain,
% 28.94/19.18 (big_f(f9(c1, c1), f10(c1)) <=> big_f(f7(c2), c1)),
% 28.94/19.18 inference(monotonicity,[status(thm)],[18915, 18848])).
% 28.94/19.18 tff(18917,plain,
% 28.94/19.18 (big_f(f7(c2), c1) <=> big_f(f9(c1, c1), f10(c1))),
% 28.94/19.18 inference(symmetry,[status(thm)],[18916])).
% 28.94/19.18 tff(18918,plain,
% 28.94/19.18 (big_f(f9(c1, c1), f10(c1))),
% 28.94/19.18 inference(modus_ponens,[status(thm)],[18380, 18917])).
% 28.94/19.18 tff(18919,plain,
% 28.94/19.18 (f9(c1, c1) = c1),
% 28.94/19.18 inference(modus_ponens,[status(thm)],[18914, 18649])).
% 28.94/19.18 tff(18920,plain,
% 28.94/19.18 (big_f(f7(c1), f6(c1, c1))),
% 28.94/19.18 inference(unit_resolution,[status(thm)],[9972, 18919, 18796, 22, 18848, 18380, 18918])).
% 28.94/19.18 tff(18921,plain,
% 28.94/19.18 (f6(c1, c1) = f2(c3)),
% 28.94/19.18 inference(transitivity,[status(thm)],[5958, 2362, 13016])).
% 28.94/19.18 tff(18922,plain,
% 28.94/19.18 (f7(c1) = c3),
% 28.94/19.18 inference(transitivity,[status(thm)],[4234, 5585])).
% 28.94/19.18 tff(18923,plain,
% 28.94/19.18 (big_f(f7(c1), f6(c1, c1)) <=> big_f(c3, f2(c3))),
% 28.94/19.18 inference(monotonicity,[status(thm)],[18922, 18921])).
% 28.94/19.18 tff(18924,plain,
% 28.94/19.18 (big_f(c3, f2(c3)) <=> big_f(f7(c1), f6(c1, c1))),
% 28.94/19.18 inference(symmetry,[status(thm)],[18923])).
% 28.94/19.18 tff(18925,plain,
% 28.94/19.18 ((~big_f(c3, f2(c3))) <=> (~big_f(f7(c1), f6(c1, c1)))),
% 28.94/19.18 inference(monotonicity,[status(thm)],[18924])).
% 28.94/19.18 tff(18926,plain,
% 28.94/19.18 (~big_f(f7(c1), f6(c1, c1))),
% 28.94/19.18 inference(modus_ponens,[status(thm)],[1286, 18925])).
% 28.94/19.18 tff(18927,plain,
% 28.94/19.18 ($false),
% 28.94/19.18 inference(unit_resolution,[status(thm)],[5964, 18926])).
% 28.94/19.18 tff(18928,plain,((~(f6(f7(c2), c3) = c2)) | (~big_f(f7(c1), f6(c1, c1))) | big_f(c3, f2(c3)) | (~(f2(c3) = c2)) | (~(c3 = c1)) | (~(f7(c2) = c1)) | (~(f7(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.94/19.18 tff(18929,plain,
% 28.94/19.18 (~(f6(f7(c2), c3) = c2)),
% 28.94/19.18 inference(unit_resolution,[status(thm)],[18928, 18920, 1286, 18151, 172, 22, 18796])).
% 28.94/19.19 tff(18930,plain,
% 28.94/19.19 (f6(f7(c2), c3) = c1),
% 28.94/19.19 inference(unit_resolution,[status(thm)],[2391, 18929])).
% 28.94/19.19 tff(18931,plain,
% 28.94/19.19 (f6(c1, c1) = c1),
% 28.94/19.19 inference(unit_resolution,[status(thm)],[10018, 18930, 172, 22])).
% 28.94/19.19 tff(18932,plain,
% 28.94/19.19 ($false),
% 28.94/19.19 inference(unit_resolution,[status(thm)],[18907, 2378, 18796, 18848, 18919, 18918, 18920, 18931])).
% 28.94/19.19 tff(18933,plain,(big_f(c2, c2) | (~(c3 = c1)) | big_f(c3, f2(c3)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | (f2(c3) = c1) | (f7(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 28.94/19.19 tff(18934,plain,
% 28.94/19.19 (big_f(c2, c2)),
% 28.94/19.19 inference(unit_resolution,[status(thm)],[18933, 1286, 172, 11752, 11819, 18150, 17])).
% 28.94/19.19 tff(18935,plain,
% 28.94/19.19 (f3(f10(c1), f10(c1)) = f3(f10(c3), c2)),
% 28.94/19.19 inference(monotonicity,[status(thm)],[13009, 15])).
% 28.94/19.19 tff(18936,plain,
% 28.94/19.19 ((f3(f10(c1), f10(c1)) = f10(c1)) <=> (f3(f10(c3), c2) = c2)),
% 28.94/19.19 inference(monotonicity,[status(thm)],[18935, 15])).
% 28.94/19.19 tff(18937,plain,
% 28.94/19.19 ((f3(f10(c3), c2) = c2) <=> (f3(f10(c1), f10(c1)) = f10(c1))),
% 28.94/19.19 inference(symmetry,[status(thm)],[18936])).
% 28.94/19.19 tff(18938,plain,
% 28.94/19.19 (big_f(f10(c1), f10(c1)) <=> big_f(c2, c2)),
% 28.94/19.19 inference(monotonicity,[status(thm)],[15, 15])).
% 28.94/19.19 tff(18939,plain,
% 28.94/19.19 (big_f(c2, c2) <=> big_f(f10(c1), f10(c1))),
% 28.94/19.19 inference(symmetry,[status(thm)],[18938])).
% 28.94/19.19 tff(18940,plain,
% 28.94/19.19 (big_f(f10(c1), f10(c1))),
% 28.94/19.19 inference(modus_ponens,[status(thm)],[1345, 18939])).
% 28.94/19.19 tff(18941,plain,
% 28.94/19.19 ((f10(c1) = c4) <=> (f10(c1) = c1)),
% 28.94/19.19 inference(monotonicity,[status(thm)],[480])).
% 28.94/19.19 tff(18942,plain,
% 28.94/19.19 ((f10(c1) = c1) <=> (f10(c1) = c4)),
% 28.94/19.19 inference(symmetry,[status(thm)],[18941])).
% 28.94/19.19 tff(18943,plain,
% 28.94/19.19 ((f10(c1) = c1) <=> (f10(f10(c2)) = c4)),
% 28.94/19.19 inference(transitivity,[status(thm)],[18942, 18311])).
% 28.94/19.19 tff(18944,plain,
% 28.94/19.19 ((~(f10(c1) = c1)) <=> (~(f10(f10(c2)) = c4))),
% 28.94/19.19 inference(monotonicity,[status(thm)],[18943])).
% 28.94/19.19 tff(18945,plain,
% 28.94/19.19 (~(f10(f10(c2)) = c4)),
% 28.94/19.19 inference(modus_ponens,[status(thm)],[3, 18944])).
% 28.94/19.19 tff(18946,plain,
% 28.94/19.19 ((~(f10(c1) = c1)) <=> (~(f10(c1) = c4))),
% 28.94/19.19 inference(monotonicity,[status(thm)],[18942])).
% 28.94/19.19 tff(18947,plain,
% 28.94/19.19 (~(f10(c1) = c4)),
% 28.94/19.19 inference(modus_ponens,[status(thm)],[3, 18946])).
% 28.94/19.19 tff(18948,plain,
% 28.94/19.19 (~(f6(f7(c2), c3) = c1)),
% 28.94/19.19 inference(unit_resolution,[status(thm)],[10018, 28, 172, 292])).
% 28.94/19.19 tff(18949,plain,
% 28.94/19.19 (f6(f7(c2), c3) = c2),
% 28.94/19.19 inference(unit_resolution,[status(thm)],[2391, 18948])).
% 28.94/19.19 tff(18950,plain,
% 28.94/19.19 (c2 = f6(f7(c2), c3)),
% 28.94/19.19 inference(symmetry,[status(thm)],[18949])).
% 28.94/19.19 tff(18951,plain,
% 28.94/19.19 (f10(c3) = f6(f7(c2), c3)),
% 28.94/19.19 inference(transitivity,[status(thm)],[13006, 15, 18950])).
% 28.94/19.19 tff(18952,plain,
% 28.94/19.19 (f3(f10(c3), c2) = f3(f6(f7(c2), c3), c2)),
% 28.94/19.19 inference(monotonicity,[status(thm)],[18951])).
% 28.94/19.19 tff(18953,plain,
% 28.94/19.19 (f3(f10(c1), f10(c1)) = f3(f6(f7(c2), c3), c2)),
% 28.94/19.19 inference(transitivity,[status(thm)],[18935, 18952])).
% 28.94/19.19 tff(18954,plain,
% 28.94/19.19 ((f3(f10(c1), f10(c1)) = f10(c1)) <=> (f3(f6(f7(c2), c3), c2) = c2)),
% 28.94/19.19 inference(monotonicity,[status(thm)],[18953, 15])).
% 28.94/19.19 tff(18955,plain,
% 28.94/19.19 ((f3(f6(f7(c2), c3), c2) = c2) <=> (f3(f10(c1), f10(c1)) = f10(c1))),
% 28.94/19.19 inference(symmetry,[status(thm)],[18954])).
% 28.94/19.19 tff(18956,plain,
% 28.94/19.19 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | (~big_f(f10(c1), f10(c1))) | (f10(c1) = f8(c1)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c1) = c1) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | (~big_f(f10(c1), f10(c1))) | (f10(c1) = f8(c1)))),
% 28.94/19.19 inference(rewrite,[status(thm)],[])).
% 28.94/19.19 tff(18957,plain,
% 28.94/19.19 (((f10(c1) = c1) | (f10(c1) = f8(c1)) | (~big_f(f10(c1), f10(c1))) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1))) <=> ((f10(c1) = c1) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | (~big_f(f10(c1), f10(c1))) | (f10(c1) = f8(c1)))),
% 28.94/19.19 inference(rewrite,[status(thm)],[])).
% 28.94/19.19 tff(18958,plain,
% 28.94/19.19 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (f10(c1) = f8(c1)) | (~big_f(f10(c1), f10(c1))) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | (~big_f(f10(c1), f10(c1))) | (f10(c1) = f8(c1))))),
% 28.94/19.19 inference(monotonicity,[status(thm)],[18957])).
% 28.94/19.19 tff(18959,plain,
% 28.94/19.19 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (f10(c1) = f8(c1)) | (~big_f(f10(c1), f10(c1))) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c1) = c1) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | (~big_f(f10(c1), f10(c1))) | (f10(c1) = f8(c1)))),
% 28.94/19.19 inference(transitivity,[status(thm)],[18958, 18956])).
% 28.94/19.19 tff(18960,plain,
% 28.94/19.19 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (f10(c1) = f8(c1)) | (~big_f(f10(c1), f10(c1))) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1)))),
% 28.94/19.19 inference(quant_inst,[status(thm)],[])).
% 28.94/19.19 tff(18961,plain,
% 28.94/19.19 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c1) = c1) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | (~big_f(f10(c1), f10(c1))) | (f10(c1) = f8(c1))),
% 28.94/19.19 inference(modus_ponens,[status(thm)],[18960, 18959])).
% 28.94/19.19 tff(18962,plain,
% 28.94/19.19 (f10(c1) = f8(c1)),
% 28.94/19.19 inference(unit_resolution,[status(thm)],[18961, 2662, 4234, 3, 65, 28, 18940])).
% 28.94/19.19 tff(18963,plain,
% 28.94/19.19 (f8(c1) = f10(c1)),
% 28.94/19.19 inference(symmetry,[status(thm)],[18962])).
% 28.94/19.19 tff(18964,plain,
% 28.94/19.19 (f8(c1) = c2),
% 28.94/19.19 inference(transitivity,[status(thm)],[18963, 15])).
% 28.94/19.19 tff(18965,plain,
% 28.94/19.19 ((f3(f6(f7(c2), c3), c2) = f8(c1)) <=> (f3(f6(f7(c2), c3), c2) = c2)),
% 28.94/19.19 inference(monotonicity,[status(thm)],[18964])).
% 28.94/19.19 tff(18966,plain,
% 28.94/19.19 ((f3(f6(f7(c2), c3), c2) = f8(c1)) <=> (f3(f10(c1), f10(c1)) = f10(c1))),
% 28.94/19.19 inference(transitivity,[status(thm)],[18965, 18955])).
% 28.94/19.19 tff(18967,plain,
% 28.94/19.19 (f10(c1) = f6(f7(c2), c3)),
% 28.94/19.19 inference(transitivity,[status(thm)],[15, 18950])).
% 28.94/19.19 tff(18968,plain,
% 28.94/19.19 (big_f(f3(f6(f7(c2), c3), c2), f10(c1)) <=> big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))),
% 28.94/19.19 inference(monotonicity,[status(thm)],[18967])).
% 28.94/19.19 tff(18969,plain,
% 28.94/19.19 (big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3)) <=> big_f(f3(f6(f7(c2), c3), c2), f10(c1))),
% 28.94/19.19 inference(symmetry,[status(thm)],[18968])).
% 28.94/19.19 tff(18970,plain,
% 28.94/19.19 (big_f(f3(f10(c3), c2), f10(c3)) <=> big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))),
% 28.94/19.19 inference(monotonicity,[status(thm)],[18952, 18951])).
% 28.94/19.19 tff(18971,plain,
% 28.94/19.19 ((f10(c1) = f8(c1)) <=> (c2 = f8(c1))),
% 28.94/19.19 inference(monotonicity,[status(thm)],[15])).
% 28.94/19.19 tff(18972,plain,
% 28.94/19.19 ((f10(c1) = f8(c1)) <=> (f8(c1) = c2)),
% 28.94/19.19 inference(transitivity,[status(thm)],[18971, 2782])).
% 28.94/19.19 tff(18973,plain,
% 28.94/19.19 (f8(c1) = c2),
% 28.94/19.19 inference(modus_ponens,[status(thm)],[18962, 18972])).
% 28.94/19.19 tff(18974,plain,
% 28.94/19.19 (big_f(f3(f10(c3), c2), f10(c3))),
% 28.94/19.19 inference(unit_resolution,[status(thm)],[18347, 18973, 1345, 172, 15, 11819, 3833, 2600, 18318])).
% 28.94/19.19 tff(18975,plain,
% 28.94/19.19 (big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))),
% 28.94/19.19 inference(modus_ponens,[status(thm)],[18974, 18970])).
% 28.94/19.19 tff(18976,plain,
% 28.94/19.19 (big_f(f3(f6(f7(c2), c3), c2), f10(c1))),
% 28.94/19.19 inference(modus_ponens,[status(thm)],[18975, 18969])).
% 28.94/19.19 tff(18977,plain,
% 28.94/19.19 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | (f3(f6(f7(c2), c3), c2) = f8(c1)) | (~big_f(f3(f6(f7(c2), c3), c2), f10(c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c1) = c1) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | (f3(f6(f7(c2), c3), c2) = f8(c1)) | (~big_f(f3(f6(f7(c2), c3), c2), f10(c1))))),
% 28.94/19.19 inference(rewrite,[status(thm)],[])).
% 28.94/19.19 tff(18978,plain,
% 28.94/19.19 (((f10(c1) = c1) | (f3(f6(f7(c2), c3), c2) = f8(c1)) | (~big_f(f3(f6(f7(c2), c3), c2), f10(c1))) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1))) <=> ((f10(c1) = c1) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | (f3(f6(f7(c2), c3), c2) = f8(c1)) | (~big_f(f3(f6(f7(c2), c3), c2), f10(c1))))),
% 28.94/19.19 inference(rewrite,[status(thm)],[])).
% 28.94/19.19 tff(18979,plain,
% 28.94/19.19 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (f3(f6(f7(c2), c3), c2) = f8(c1)) | (~big_f(f3(f6(f7(c2), c3), c2), f10(c1))) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | (f3(f6(f7(c2), c3), c2) = f8(c1)) | (~big_f(f3(f6(f7(c2), c3), c2), f10(c1)))))),
% 28.94/19.19 inference(monotonicity,[status(thm)],[18978])).
% 28.94/19.19 tff(18980,plain,
% 28.94/19.19 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (f3(f6(f7(c2), c3), c2) = f8(c1)) | (~big_f(f3(f6(f7(c2), c3), c2), f10(c1))) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c1) = c1) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | (f3(f6(f7(c2), c3), c2) = f8(c1)) | (~big_f(f3(f6(f7(c2), c3), c2), f10(c1))))),
% 28.94/19.19 inference(transitivity,[status(thm)],[18979, 18977])).
% 28.94/19.19 tff(18981,plain,
% 28.94/19.19 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (f3(f6(f7(c2), c3), c2) = f8(c1)) | (~big_f(f3(f6(f7(c2), c3), c2), f10(c1))) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1)))),
% 28.94/19.19 inference(quant_inst,[status(thm)],[])).
% 28.94/19.19 tff(18982,plain,
% 28.94/19.19 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c1) = c1) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | (f3(f6(f7(c2), c3), c2) = f8(c1)) | (~big_f(f3(f6(f7(c2), c3), c2), f10(c1)))),
% 28.94/19.19 inference(modus_ponens,[status(thm)],[18981, 18980])).
% 28.94/19.19 tff(18983,plain,
% 28.94/19.19 ((f3(f6(f7(c2), c3), c2) = f8(c1)) | (~big_f(f3(f6(f7(c2), c3), c2), f10(c1)))),
% 28.94/19.19 inference(unit_resolution,[status(thm)],[18982, 2662, 4234, 3, 65, 28])).
% 28.94/19.19 tff(18984,plain,
% 28.94/19.19 (f3(f6(f7(c2), c3), c2) = f8(c1)),
% 28.94/19.19 inference(unit_resolution,[status(thm)],[18983, 18976])).
% 28.94/19.19 tff(18985,plain,
% 28.94/19.19 (f3(f10(c1), f10(c1)) = f10(c1)),
% 28.94/19.19 inference(modus_ponens,[status(thm)],[18984, 18966])).
% 28.94/19.19 tff(18986,plain,
% 28.94/19.19 (big_f(f3(f10(c1), f10(c1)), f10(c1)) <=> big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))),
% 28.94/19.19 inference(monotonicity,[status(thm)],[18953, 18967])).
% 28.94/19.19 tff(18987,plain,
% 28.94/19.19 (big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3)) <=> big_f(f3(f10(c1), f10(c1)), f10(c1))),
% 28.94/19.19 inference(symmetry,[status(thm)],[18986])).
% 28.94/19.19 tff(18988,plain,
% 28.94/19.19 (big_f(f3(f10(c1), f10(c1)), f10(c1))),
% 28.94/19.19 inference(modus_ponens,[status(thm)],[18975, 18987])).
% 28.94/19.19 tff(18989,plain,
% 28.94/19.19 (f10(c1) = f2(c1)),
% 28.94/19.19 inference(transitivity,[status(thm)],[15, 13016, 5589])).
% 28.94/19.19 tff(18990,plain,
% 28.94/19.19 ((~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1)))),
% 28.94/19.19 inference(unit_resolution,[status(thm)],[13023, 1398, 5611, 3030, 1046, 18989])).
% 28.94/19.19 tff(18991,plain,
% 28.94/19.19 (~(f3(f10(c1), f10(c1)) = f10(c1))),
% 28.94/19.19 inference(unit_resolution,[status(thm)],[18990, 18988])).
% 28.94/19.19 tff(18992,plain,
% 28.94/19.19 ($false),
% 28.94/19.19 inference(unit_resolution,[status(thm)],[18991, 18985])).
% 28.94/19.19 tff(18993,plain,((f6(c1, c1) = c1) | (~(c3 = c1)) | big_f(c1, f10(c1)) | (f10(c1) = c4) | (~(f7(c1) = c1)) | (f10(c1) = c1) | big_f(f7(c1), f6(c1, c1)) | (~(f2(c3) = c2)) | (~big_f(c2, c2)) | (~(f10(c2) = c1)) | big_f(c3, c2) | (f10(f10(c2)) = c4) | (~(f7(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.94/19.19 tff(18994,plain,
% 28.94/19.19 (f6(c1, c1) = c1),
% 28.94/19.19 inference(unit_resolution,[status(thm)],[18993, 65, 3030, 1046, 4234, 3, 172, 1319, 1345, 11819, 3833, 18318, 292])).
% 28.94/19.19 tff(18995,plain,
% 28.94/19.19 (big_f(f7(c1), f6(c1, c1)) <=> big_f(f7(c2), c1)),
% 28.94/19.19 inference(monotonicity,[status(thm)],[8286, 18994])).
% 28.94/19.19 tff(18996,plain,
% 28.94/19.19 (big_f(f7(c2), c1) <=> big_f(f7(c1), f6(c1, c1))),
% 28.94/19.19 inference(symmetry,[status(thm)],[18995])).
% 28.94/19.19 tff(18997,plain,
% 28.94/19.19 (big_f(f7(c1), f6(c1, c1))),
% 28.94/19.19 inference(modus_ponens,[status(thm)],[338, 18996])).
% 28.94/19.19 tff(18998,plain,
% 28.94/19.19 ($false),
% 28.94/19.19 inference(unit_resolution,[status(thm)],[65, 18997])).
% 28.94/19.19 tff(18999,plain,(big_f(f7(c1), f6(c1, c1)) | (~big_f(f7(c2), c1)) | (~(f7(c1) = c1)) | (~(f7(c2) = c1)) | big_f(c1, f10(c1)) | (f10(c1) = c4) | (f10(c1) = c1) | (~(c3 = c1)) | (~(f2(c3) = c2)) | (~big_f(c2, c2)) | (~(f10(c2) = c1)) | big_f(c3, c2) | (f10(f10(c2)) = c4)), inference(lemma,lemma(discharge,[]))).
% 28.94/19.19 tff(19000,plain,
% 28.94/19.19 (big_f(f7(c1), f6(c1, c1))),
% 28.94/19.19 inference(unit_resolution,[status(thm)],[18999, 18213, 4234, 292, 338, 18947, 3, 172, 1319, 1345, 11819, 2603, 18945])).
% 28.94/19.19 tff(19001,plain,
% 28.94/19.19 (~(f6(f7(c2), c3) = c2)),
% 28.94/19.19 inference(unit_resolution,[status(thm)],[18928, 19000, 1286, 1319, 172, 292, 4234])).
% 28.94/19.19 tff(19002,plain,
% 28.94/19.19 (f6(f7(c2), c3) = c1),
% 28.94/19.19 inference(unit_resolution,[status(thm)],[2391, 19001])).
% 28.94/19.19 tff(19003,plain,
% 28.94/19.19 (f6(c1, c1) = c1),
% 28.94/19.19 inference(unit_resolution,[status(thm)],[10018, 19002, 172, 292])).
% 28.94/19.19 tff(19004,plain,
% 28.94/19.19 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (~big_f(f10(c1), f10(c1))) | (f10(c1) = f8(c1)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (~big_f(f10(c1), f10(c1))) | (f10(c1) = f8(c1)))),
% 28.94/19.19 inference(rewrite,[status(thm)],[])).
% 28.94/19.19 tff(19005,plain,
% 28.94/19.19 (((f10(c1) = c1) | (f10(c1) = f8(c1)) | (~big_f(f10(c1), f10(c1))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1)))) <=> ((f10(c1) = c1) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (~big_f(f10(c1), f10(c1))) | (f10(c1) = f8(c1)))),
% 28.94/19.19 inference(rewrite,[status(thm)],[])).
% 28.94/19.19 tff(19006,plain,
% 28.94/19.19 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (f10(c1) = f8(c1)) | (~big_f(f10(c1), f10(c1))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (~big_f(f10(c1), f10(c1))) | (f10(c1) = f8(c1))))),
% 28.94/19.19 inference(monotonicity,[status(thm)],[19005])).
% 28.94/19.19 tff(19007,plain,
% 28.94/19.19 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (f10(c1) = f8(c1)) | (~big_f(f10(c1), f10(c1))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (~big_f(f10(c1), f10(c1))) | (f10(c1) = f8(c1)))),
% 28.94/19.19 inference(transitivity,[status(thm)],[19006, 19004])).
% 28.94/19.19 tff(19008,plain,
% 28.94/19.19 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (f10(c1) = f8(c1)) | (~big_f(f10(c1), f10(c1))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))),
% 28.94/19.19 inference(quant_inst,[status(thm)],[])).
% 28.94/19.19 tff(19009,plain,
% 28.94/19.19 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (~big_f(f10(c1), f10(c1))) | (f10(c1) = f8(c1))),
% 28.94/19.19 inference(modus_ponens,[status(thm)],[19008, 19007])).
% 28.94/19.19 tff(19010,plain,
% 28.94/19.19 (f10(c1) = f8(c1)),
% 28.94/19.19 inference(unit_resolution,[status(thm)],[19009, 2730, 4234, 3, 19000, 19003, 18940])).
% 28.94/19.19 tff(19011,plain,
% 28.94/19.19 (f8(c1) = f10(c1)),
% 28.94/19.19 inference(symmetry,[status(thm)],[19010])).
% 28.94/19.19 tff(19012,plain,
% 28.94/19.19 (f8(c1) = c2),
% 28.94/19.19 inference(transitivity,[status(thm)],[19011, 15])).
% 28.94/19.19 tff(19013,plain,
% 28.94/19.19 ((f3(f10(c3), c2) = f8(c1)) <=> (f3(f10(c3), c2) = c2)),
% 28.94/19.19 inference(monotonicity,[status(thm)],[19012])).
% 28.94/19.19 tff(19014,plain,
% 28.94/19.19 ((f3(f10(c3), c2) = f8(c1)) <=> (f3(f10(c1), f10(c1)) = f10(c1))),
% 28.94/19.19 inference(transitivity,[status(thm)],[19013, 18937])).
% 28.94/19.19 tff(19015,plain,
% 28.94/19.19 (f8(c1) = c2),
% 28.94/19.19 inference(modus_ponens,[status(thm)],[19010, 18972])).
% 28.94/19.19 tff(19016,plain,
% 28.94/19.19 (big_f(f3(f10(c3), c2), f10(c3))),
% 28.94/19.19 inference(unit_resolution,[status(thm)],[18347, 19015, 1345, 172, 15, 11819, 2603, 2600, 18945])).
% 28.94/19.19 tff(19017,plain,
% 28.94/19.19 (big_f(f3(f10(c3), c2), f10(c1))),
% 28.94/19.19 inference(modus_ponens,[status(thm)],[19016, 18309])).
% 28.94/19.19 tff(19018,plain,
% 28.94/19.19 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (f3(f10(c3), c2) = f8(c1)) | (~big_f(f3(f10(c3), c2), f10(c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (f3(f10(c3), c2) = f8(c1)) | (~big_f(f3(f10(c3), c2), f10(c1))))),
% 28.94/19.19 inference(rewrite,[status(thm)],[])).
% 28.94/19.19 tff(19019,plain,
% 28.94/19.19 (((f10(c1) = c1) | (f3(f10(c3), c2) = f8(c1)) | (~big_f(f3(f10(c3), c2), f10(c1))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1)))) <=> ((f10(c1) = c1) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (f3(f10(c3), c2) = f8(c1)) | (~big_f(f3(f10(c3), c2), f10(c1))))),
% 28.94/19.19 inference(rewrite,[status(thm)],[])).
% 28.94/19.19 tff(19020,plain,
% 28.94/19.19 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (f3(f10(c3), c2) = f8(c1)) | (~big_f(f3(f10(c3), c2), f10(c1))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (f3(f10(c3), c2) = f8(c1)) | (~big_f(f3(f10(c3), c2), f10(c1)))))),
% 28.94/19.19 inference(monotonicity,[status(thm)],[19019])).
% 28.94/19.19 tff(19021,plain,
% 28.94/19.19 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (f3(f10(c3), c2) = f8(c1)) | (~big_f(f3(f10(c3), c2), f10(c1))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (f3(f10(c3), c2) = f8(c1)) | (~big_f(f3(f10(c3), c2), f10(c1))))),
% 28.94/19.19 inference(transitivity,[status(thm)],[19020, 19018])).
% 28.94/19.19 tff(19022,plain,
% 28.94/19.19 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (f3(f10(c3), c2) = f8(c1)) | (~big_f(f3(f10(c3), c2), f10(c1))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))),
% 28.94/19.19 inference(quant_inst,[status(thm)],[])).
% 28.94/19.19 tff(19023,plain,
% 28.94/19.19 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (f3(f10(c3), c2) = f8(c1)) | (~big_f(f3(f10(c3), c2), f10(c1)))),
% 28.94/19.19 inference(modus_ponens,[status(thm)],[19022, 19021])).
% 28.94/19.19 tff(19024,plain,
% 28.94/19.19 ((f3(f10(c3), c2) = f8(c1)) | (~big_f(f3(f10(c3), c2), f10(c1)))),
% 28.94/19.19 inference(unit_resolution,[status(thm)],[19023, 2730, 4234, 3, 19000, 19003])).
% 28.94/19.19 tff(19025,plain,
% 28.94/19.19 (f3(f10(c3), c2) = f8(c1)),
% 28.94/19.19 inference(unit_resolution,[status(thm)],[19024, 19017])).
% 28.94/19.19 tff(19026,plain,
% 28.94/19.19 (f3(f10(c1), f10(c1)) = f10(c1)),
% 28.94/19.19 inference(modus_ponens,[status(thm)],[19025, 19014])).
% 28.94/19.19 tff(19027,plain,
% 28.94/19.19 (big_f(f3(f10(c1), f10(c1)), f10(c1)) <=> big_f(f3(f10(c3), c2), f10(c3))),
% 28.94/19.19 inference(monotonicity,[status(thm)],[18935, 13009])).
% 28.94/19.19 tff(19028,plain,
% 28.94/19.19 (big_f(f3(f10(c3), c2), f10(c3)) <=> big_f(f3(f10(c1), f10(c1)), f10(c1))),
% 28.94/19.19 inference(symmetry,[status(thm)],[19027])).
% 28.94/19.19 tff(19029,plain,
% 28.94/19.19 (big_f(f3(f10(c1), f10(c1)), f10(c1))),
% 28.94/19.19 inference(modus_ponens,[status(thm)],[19016, 19028])).
% 28.94/19.19 tff(19030,plain,
% 28.94/19.19 ((~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1)))),
% 28.94/19.19 inference(unit_resolution,[status(thm)],[13023, 1398, 5611, 18213, 18947, 18989])).
% 28.94/19.19 tff(19031,plain,
% 28.94/19.19 (~(f3(f10(c1), f10(c1)) = f10(c1))),
% 28.94/19.19 inference(unit_resolution,[status(thm)],[19030, 19029])).
% 28.94/19.19 tff(19032,plain,
% 28.94/19.19 ($false),
% 28.94/19.19 inference(unit_resolution,[status(thm)],[19031, 19026])).
% 28.94/19.19 tff(19033,plain,((f10(c1) = c1) | (~(c3 = c1)) | (~(f7(c1) = c1)) | (~(f2(c3) = c2)) | (~big_f(c2, c2)) | (~(f10(c2) = c1)) | (~(f7(c2) = c1)) | big_f(c3, f2(c3)) | (~big_f(f7(c2), c1)) | (~(c4 = c1))), inference(lemma,lemma(discharge,[]))).
% 28.94/19.19 tff(19034,plain,
% 28.94/19.19 (f10(c1) = c1),
% 28.94/19.19 inference(unit_resolution,[status(thm)],[19033, 18796, 172, 18151, 18934, 11819, 22, 1286, 18380, 18167])).
% 28.94/19.19 tff(19035,plain,
% 28.94/19.19 ((f9(c1, c1) = c1) <=> (f9(f10(c2), f4(c4)) = c1)),
% 28.94/19.19 inference(monotonicity,[status(thm)],[17727])).
% 28.94/19.19 tff(19036,plain,
% 28.94/19.19 (f9(c1, c1) = c1),
% 28.94/19.19 inference(unit_resolution,[status(thm)],[9993, 8712, 338, 292, 4234, 3762, 65])).
% 28.94/19.19 tff(19037,plain,
% 28.94/19.19 (f9(f10(c2), f4(c4)) = c1),
% 28.94/19.19 inference(modus_ponens,[status(thm)],[19036, 19035])).
% 28.94/19.19 tff(19038,plain,
% 28.94/19.19 (f9(c1, c1) = f7(c2)),
% 28.94/19.19 inference(transitivity,[status(thm)],[18436, 148, 342])).
% 28.94/19.19 tff(19039,plain,
% 28.94/19.19 (big_f(f9(c1, c1), f10(c1)) <=> big_f(f7(c2), c1)),
% 28.94/19.19 inference(monotonicity,[status(thm)],[19038, 3762])).
% 28.94/19.19 tff(19040,plain,
% 28.94/19.19 (big_f(f7(c2), c1) <=> big_f(f9(c1, c1), f10(c1))),
% 28.94/19.20 inference(symmetry,[status(thm)],[19039])).
% 28.94/19.20 tff(19041,plain,
% 28.94/19.20 (big_f(f9(c1, c1), f10(c1))),
% 28.94/19.20 inference(modus_ponens,[status(thm)],[338, 19040])).
% 28.94/19.20 tff(19042,plain,
% 28.94/19.20 ($false),
% 28.94/19.20 inference(unit_resolution,[status(thm)],[8712, 19041])).
% 28.94/19.20 tff(19043,plain,((~(f9(f10(c2), f4(c4)) = c1)) | big_f(f9(c1, c1), f10(c1)) | (~big_f(f7(c2), c1)) | (~(f10(c1) = c1)) | (~(f7(c2) = c1)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 28.94/19.20 tff(19044,plain,
% 28.94/19.20 (~(f9(f10(c2), f4(c4)) = c1)),
% 28.94/19.20 inference(unit_resolution,[status(thm)],[19043, 8712, 338, 3762, 292, 11752, 11819])).
% 28.94/19.20 tff(19045,plain,
% 28.94/19.20 ($false),
% 28.94/19.20 inference(unit_resolution,[status(thm)],[19044, 19037])).
% 28.94/19.20 tff(19046,plain,(big_f(f9(c1, c1), f10(c1)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | (~big_f(f7(c2), c1)) | (~(f10(c1) = c1)) | (~(f7(c2) = c1)) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c1))), inference(lemma,lemma(discharge,[]))).
% 28.94/19.20 tff(19047,plain,
% 28.94/19.20 (big_f(f9(c1, c1), f10(c1))),
% 28.94/19.20 inference(unit_resolution,[status(thm)],[19046, 65, 11819, 338, 3762, 292, 4234, 11752])).
% 28.94/19.20 tff(19048,plain,
% 28.94/19.20 (big_f(f9(c1, c1), c1)),
% 28.94/19.20 inference(modus_ponens,[status(thm)],[19047, 18878])).
% 28.94/19.20 tff(19049,plain,
% 28.94/19.20 ((f9(c1, c1) = c1) <=> (f9(c1, c1) = f4(c1))),
% 28.94/19.20 inference(symmetry,[status(thm)],[18876])).
% 28.94/19.20 tff(19050,plain,
% 28.94/19.20 ((~(f9(c1, c1) = c1)) <=> (~(f9(c1, c1) = f4(c1)))),
% 28.94/19.20 inference(monotonicity,[status(thm)],[19049])).
% 28.94/19.20 tff(19051,plain,
% 28.94/19.20 (~(f9(c1, c1) = c1)),
% 28.94/19.20 inference(unit_resolution,[status(thm)],[9972, 19047, 4234, 292, 3762, 338, 65])).
% 28.94/19.20 tff(19052,plain,
% 28.94/19.20 (~(f9(c1, c1) = f4(c1))),
% 28.94/19.20 inference(modus_ponens,[status(thm)],[19051, 19050])).
% 28.94/19.20 tff(19053,plain,
% 28.94/19.20 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(c1 = c4)) | (~big_f(f9(c1, c1), c1)) | big_f(c1, f2(c1)) | (f9(c1, c1) = f4(c1)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | (~(c1 = c3)) | (~(c1 = c4)) | (~big_f(f9(c1, c1), c1)) | big_f(c1, f2(c1)) | (f9(c1, c1) = f4(c1)))),
% 28.94/19.20 inference(rewrite,[status(thm)],[])).
% 28.94/19.20 tff(19054,plain,
% 28.94/19.20 (((~(c1 = c3)) | $false | (~(c1 = c4)) | (f9(c1, c1) = f4(c1)) | (~big_f(f9(c1, c1), c1)) | big_f(c1, f2(c1))) <=> ((~(c1 = c3)) | (~(c1 = c4)) | (~big_f(f9(c1, c1), c1)) | big_f(c1, f2(c1)) | (f9(c1, c1) = f4(c1)))),
% 28.94/19.20 inference(rewrite,[status(thm)],[])).
% 28.94/19.20 tff(19055,plain,
% 28.94/19.20 (((~(c1 = c3)) | (~(f2(c1) = f2(c1))) | (~(c1 = c4)) | (f9(c1, c1) = f4(c1)) | (~big_f(f9(c1, c1), c1)) | big_f(c1, f2(c1))) <=> ((~(c1 = c3)) | $false | (~(c1 = c4)) | (f9(c1, c1) = f4(c1)) | (~big_f(f9(c1, c1), c1)) | big_f(c1, f2(c1)))),
% 28.94/19.20 inference(monotonicity,[status(thm)],[18187])).
% 28.94/19.20 tff(19056,plain,
% 28.94/19.20 (((~(c1 = c3)) | (~(f2(c1) = f2(c1))) | (~(c1 = c4)) | (f9(c1, c1) = f4(c1)) | (~big_f(f9(c1, c1), c1)) | big_f(c1, f2(c1))) <=> ((~(c1 = c3)) | (~(c1 = c4)) | (~big_f(f9(c1, c1), c1)) | big_f(c1, f2(c1)) | (f9(c1, c1) = f4(c1)))),
% 29.01/19.20 inference(transitivity,[status(thm)],[19055, 19054])).
% 29.01/19.20 tff(19057,plain,
% 29.01/19.20 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(f2(c1) = f2(c1))) | (~(c1 = c4)) | (f9(c1, c1) = f4(c1)) | (~big_f(f9(c1, c1), c1)) | big_f(c1, f2(c1)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(c1 = c4)) | (~big_f(f9(c1, c1), c1)) | big_f(c1, f2(c1)) | (f9(c1, c1) = f4(c1))))),
% 29.01/19.20 inference(monotonicity,[status(thm)],[19056])).
% 29.01/19.20 tff(19058,plain,
% 29.01/19.20 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(f2(c1) = f2(c1))) | (~(c1 = c4)) | (f9(c1, c1) = f4(c1)) | (~big_f(f9(c1, c1), c1)) | big_f(c1, f2(c1)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | (~(c1 = c3)) | (~(c1 = c4)) | (~big_f(f9(c1, c1), c1)) | big_f(c1, f2(c1)) | (f9(c1, c1) = f4(c1)))),
% 29.01/19.20 inference(transitivity,[status(thm)],[19057, 19053])).
% 29.01/19.20 tff(19059,plain,
% 29.01/19.20 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(f2(c1) = f2(c1))) | (~(c1 = c4)) | (f9(c1, c1) = f4(c1)) | (~big_f(f9(c1, c1), c1)) | big_f(c1, f2(c1)))),
% 29.01/19.20 inference(quant_inst,[status(thm)],[])).
% 29.01/19.20 tff(19060,plain,
% 29.01/19.20 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | (~(c1 = c3)) | (~(c1 = c4)) | (~big_f(f9(c1, c1), c1)) | big_f(c1, f2(c1)) | (f9(c1, c1) = f4(c1))),
% 29.01/19.20 inference(modus_ponens,[status(thm)],[19059, 19058])).
% 29.01/19.20 tff(19061,plain,
% 29.01/19.20 ((~big_f(f9(c1, c1), c1)) | (f9(c1, c1) = f4(c1))),
% 29.01/19.20 inference(unit_resolution,[status(thm)],[19060, 11666, 5080, 564, 8629])).
% 29.01/19.20 tff(19062,plain,
% 29.01/19.20 ($false),
% 29.01/19.20 inference(unit_resolution,[status(thm)],[19061, 19052, 19048])).
% 29.01/19.20 tff(19063,plain,(big_f(f7(c1), f6(c1, c1)) | (~(c1 = c3)) | big_f(c1, f2(c1)) | (~(f4(c4) = c1)) | (~(c4 = c1)) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~(f7(c2) = c1)) | (~big_f(f7(c2), c1)) | (~(f10(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.01/19.20 tff(19064,plain,
% 29.01/19.20 (big_f(f7(c1), f6(c1, c1))),
% 29.01/19.20 inference(unit_resolution,[status(thm)],[19063, 18174, 5611, 11752, 18167, 19034, 18796, 22, 18380, 11819])).
% 29.01/19.20 tff(19065,plain,
% 29.01/19.20 (~(f6(f7(c2), c3) = c2)),
% 29.01/19.20 inference(unit_resolution,[status(thm)],[18928, 19064, 1286, 18151, 172, 22, 18796])).
% 29.01/19.20 tff(19066,plain,
% 29.01/19.20 (f6(f7(c2), c3) = c1),
% 29.01/19.20 inference(unit_resolution,[status(thm)],[2391, 19065])).
% 29.01/19.20 tff(19067,plain,
% 29.01/19.20 (f6(c1, c1) = c1),
% 29.01/19.20 inference(unit_resolution,[status(thm)],[10018, 19066, 172, 22])).
% 29.01/19.20 tff(19068,plain,
% 29.01/19.20 (f9(f10(c2), f4(c4)) = c2),
% 29.01/19.20 inference(unit_resolution,[status(thm)],[146, 19044])).
% 29.01/19.20 tff(19069,plain,
% 29.01/19.20 (f9(c1, c1) = f2(c3)),
% 29.01/19.20 inference(transitivity,[status(thm)],[17727, 19068, 18396])).
% 29.01/19.20 tff(19070,plain,
% 29.01/19.20 ((f9(c1, c1) = c1) <=> (f2(c3) = c1)),
% 29.01/19.20 inference(monotonicity,[status(thm)],[19069])).
% 29.01/19.20 tff(19071,plain,
% 29.01/19.20 ((f2(c3) = c1) <=> (f9(c1, c1) = c1)),
% 29.01/19.20 inference(symmetry,[status(thm)],[19070])).
% 29.01/19.20 tff(19072,plain,
% 29.01/19.20 ((~(f2(c3) = c1)) <=> (~(f9(c1, c1) = c1))),
% 29.01/19.20 inference(monotonicity,[status(thm)],[19071])).
% 29.01/19.20 tff(19073,plain,
% 29.01/19.20 (~(f9(c1, c1) = c1)),
% 29.01/19.20 inference(modus_ponens,[status(thm)],[18150, 19072])).
% 29.01/19.20 tff(19074,plain,
% 29.01/19.20 ($false),
% 29.01/19.20 inference(unit_resolution,[status(thm)],[10040, 2534, 4234, 3762, 19073, 8712, 5964, 10030])).
% 29.01/19.20 tff(19075,plain,(big_f(f9(c1, c1), f10(c1)) | (~(f7(c1) = c1)) | (~(f10(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (f2(c3) = c1) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | (~big_f(f7(c2), c1)) | (~(f7(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.01/19.20 tff(19076,plain,
% 29.01/19.20 (big_f(f9(c1, c1), f10(c1))),
% 29.01/19.20 inference(unit_resolution,[status(thm)],[19075, 18796, 19034, 19064, 19067, 18150, 11752, 11819, 18380, 22])).
% 29.01/19.20 tff(19077,plain,
% 29.01/19.20 (big_f(f9(c1, c1), f10(c1)) <=> big_f(c2, c1)),
% 29.01/19.20 inference(monotonicity,[status(thm)],[17728, 3762])).
% 29.01/19.20 tff(19078,plain,
% 29.01/19.20 (big_f(c2, c1) <=> big_f(f9(c1, c1), f10(c1))),
% 29.01/19.20 inference(symmetry,[status(thm)],[19077])).
% 29.01/19.20 tff(19079,plain,
% 29.01/19.20 ((~big_f(c2, c1)) <=> (~big_f(f9(c1, c1), f10(c1)))),
% 29.01/19.20 inference(monotonicity,[status(thm)],[19078])).
% 29.01/19.20 tff(19080,plain,
% 29.01/19.20 (~big_f(f9(c1, c1), f10(c1))),
% 29.01/19.20 inference(modus_ponens,[status(thm)],[2, 19079])).
% 29.01/19.20 tff(19081,plain,
% 29.01/19.20 ($false),
% 29.01/19.20 inference(unit_resolution,[status(thm)],[3948, 19080])).
% 29.01/19.20 tff(19082,plain,((~(f9(f10(c2), f4(c4)) = c2)) | (~big_f(f9(c1, c1), f10(c1))) | big_f(c2, c1) | (~(f10(c1) = c1)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.01/19.20 tff(19083,plain,
% 29.01/19.20 (~(f9(f10(c2), f4(c4)) = c2)),
% 29.01/19.20 inference(unit_resolution,[status(thm)],[19082, 19076, 18197, 19034, 11752, 11819])).
% 29.01/19.20 tff(19084,plain,
% 29.01/19.20 (f9(f10(c2), f4(c4)) = c1),
% 29.01/19.20 inference(unit_resolution,[status(thm)],[146, 19083])).
% 29.01/19.20 tff(19085,plain,
% 29.01/19.20 (f9(c1, c1) = c1),
% 29.01/19.20 inference(modus_ponens,[status(thm)],[19084, 18649])).
% 29.01/19.20 tff(19086,plain,
% 29.01/19.20 ($false),
% 29.01/19.20 inference(unit_resolution,[status(thm)],[18907, 2378, 18796, 19034, 19085, 19076, 19064, 19067])).
% 29.01/19.20 tff(19087,plain,(big_f(c3, f2(c3)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | (f2(c3) = c1) | (~(c3 = c1)) | (f7(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 29.01/19.20 tff(19088,plain,
% 29.01/19.20 (big_f(c3, f2(c3))),
% 29.01/19.20 inference(unit_resolution,[status(thm)],[19087, 18150, 17, 11819, 172, 11752])).
% 29.01/19.20 tff(19089,plain,
% 29.01/19.20 (big_f(c1, f2(c1))),
% 29.01/19.20 inference(modus_ponens,[status(thm)],[19088, 18157])).
% 29.01/19.20 tff(19090,plain,
% 29.01/19.20 ($false),
% 29.01/19.20 inference(unit_resolution,[status(thm)],[19089, 18156])).
% 29.01/19.20 tff(19091,plain,((f2(c3) = c1) | big_f(c1, c2) | (~(c3 = c1)) | (f7(c2) = c2) | (~(f10(c2) = c1)) | (~(f4(c4) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.01/19.20 tff(19092,plain,
% 29.01/19.20 (f2(c3) = c1),
% 29.01/19.20 inference(unit_resolution,[status(thm)],[19091, 18149, 11819, 17, 27, 11752])).
% 29.01/19.20 tff(19093,plain,
% 29.01/19.20 ($false),
% 29.01/19.20 inference(unit_resolution,[status(thm)],[66, 18058])).
% 29.01/19.20 tff(19094,plain,((~big_f(f7(c2), c1)) | big_f(c1, c1) | (~(f7(c2) = c1)) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.01/19.20 tff(19095,plain,
% 29.01/19.20 (big_f(c1, c1)),
% 29.01/19.20 inference(unit_resolution,[status(thm)],[19094, 17974, 1498, 22, 11752, 11819])).
% 29.01/19.20 tff(19096,plain,
% 29.01/19.20 (~big_f(c3, f2(c3))),
% 29.01/19.20 inference(unit_resolution,[status(thm)],[8631, 8629, 172])).
% 29.01/19.20 tff(19097,plain,
% 29.01/19.20 (f2(c3) = c1),
% 29.01/19.20 inference(unit_resolution,[status(thm)],[18795, 19096, 11752, 11819, 172, 115, 17])).
% 29.01/19.20 tff(19098,plain,
% 29.01/19.20 (f2(c1) = c1),
% 29.01/19.20 inference(transitivity,[status(thm)],[5586, 19097])).
% 29.01/19.20 tff(19099,plain,
% 29.01/19.20 (big_f(c1, f2(c1)) <=> big_f(c1, c1)),
% 29.01/19.20 inference(monotonicity,[status(thm)],[19098])).
% 29.01/19.20 tff(19100,plain,
% 29.01/19.20 (big_f(c1, c1) <=> big_f(c1, f2(c1))),
% 29.01/19.20 inference(symmetry,[status(thm)],[19099])).
% 29.01/19.20 tff(19101,plain,
% 29.01/19.20 (big_f(c1, f2(c1))),
% 29.01/19.20 inference(modus_ponens,[status(thm)],[4932, 19100])).
% 29.01/19.20 tff(19102,plain,
% 29.01/19.20 ($false),
% 29.01/19.20 inference(unit_resolution,[status(thm)],[8629, 19101])).
% 29.01/19.20 tff(19103,plain,(big_f(c1, f2(c1)) | (~big_f(c1, c1)) | (~(c3 = c1)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | (f7(c1) = c1) | (f7(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 29.01/19.20 tff(19104,plain,
% 29.01/19.20 (big_f(c1, f2(c1))),
% 29.01/19.20 inference(unit_resolution,[status(thm)],[19103, 18149, 19095, 11752, 11819, 115, 17])).
% 29.01/19.20 tff(19105,plain,
% 29.01/19.20 (big_f(c3, f2(c3))),
% 29.01/19.20 inference(unit_resolution,[status(thm)],[18173, 19104, 18149])).
% 29.01/19.20 tff(19106,plain,
% 29.01/19.20 (big_f(c3, f2(c3)) <=> big_f(c1, f10(f9(c1, c1)))),
% 29.01/19.20 inference(transitivity,[status(thm)],[5590, 10927, 17983])).
% 29.01/19.20 tff(19107,plain,
% 29.01/19.20 (big_f(c1, f10(f9(c1, c1)))),
% 29.01/19.20 inference(modus_ponens,[status(thm)],[2274, 19106])).
% 29.01/19.20 tff(19108,assumption,(~big_f(c1, f10(f9(c1, c1)))), introduced(assumption)).
% 29.01/19.20 tff(19109,plain,
% 29.01/19.20 ($false),
% 29.01/19.20 inference(unit_resolution,[status(thm)],[19108, 19107])).
% 29.01/19.20 tff(19110,plain,((~big_f(c3, f2(c3))) | big_f(c1, f10(f9(c1, c1))) | (~(f10(c2) = c1)) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f2(c3) = c1)) | (~(c3 = c1))), inference(lemma,lemma(discharge,[]))).
% 29.01/19.20 tff(19111,plain,
% 29.01/19.20 (big_f(c1, f10(f9(c1, c1)))),
% 29.01/19.20 inference(unit_resolution,[status(thm)],[19110, 19105, 11819, 1498, 11752, 19092, 18149])).
% 29.01/19.20 tff(19112,plain,
% 29.01/19.20 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f7(c1) = c1) | big_f(f7(c1), f9(c1, c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~(f9(c1, c1) = f5(c1))) | (~big_f(c1, f10(f9(c1, c1)))) | (c1 = f8(f9(c1, c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f7(c1) = c1) | big_f(f7(c1), f9(c1, c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~(f9(c1, c1) = f5(c1))) | (~big_f(c1, f10(f9(c1, c1)))) | (c1 = f8(f9(c1, c1))))),
% 29.01/19.20 inference(rewrite,[status(thm)],[])).
% 29.01/19.20 tff(19113,plain,
% 29.01/19.20 (((~(f9(c1, c1) = f5(c1))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (c1 = f8(f9(c1, c1))) | (~big_f(c1, f10(f9(c1, c1)))) | (f7(c1) = c1) | big_f(f7(c1), f9(c1, c1))) <=> ((f7(c1) = c1) | big_f(f7(c1), f9(c1, c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~(f9(c1, c1) = f5(c1))) | (~big_f(c1, f10(f9(c1, c1)))) | (c1 = f8(f9(c1, c1))))),
% 29.01/19.20 inference(rewrite,[status(thm)],[])).
% 29.01/19.20 tff(19114,plain,
% 29.01/19.20 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(f9(c1, c1) = f5(c1))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (c1 = f8(f9(c1, c1))) | (~big_f(c1, f10(f9(c1, c1)))) | (f7(c1) = c1) | big_f(f7(c1), f9(c1, c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f7(c1) = c1) | big_f(f7(c1), f9(c1, c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~(f9(c1, c1) = f5(c1))) | (~big_f(c1, f10(f9(c1, c1)))) | (c1 = f8(f9(c1, c1)))))),
% 29.01/19.20 inference(monotonicity,[status(thm)],[19113])).
% 29.01/19.20 tff(19115,plain,
% 29.01/19.20 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(f9(c1, c1) = f5(c1))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (c1 = f8(f9(c1, c1))) | (~big_f(c1, f10(f9(c1, c1)))) | (f7(c1) = c1) | big_f(f7(c1), f9(c1, c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f7(c1) = c1) | big_f(f7(c1), f9(c1, c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~(f9(c1, c1) = f5(c1))) | (~big_f(c1, f10(f9(c1, c1)))) | (c1 = f8(f9(c1, c1))))),
% 29.01/19.20 inference(transitivity,[status(thm)],[19114, 19112])).
% 29.01/19.20 tff(19116,plain,
% 29.01/19.20 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(f9(c1, c1) = f5(c1))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (c1 = f8(f9(c1, c1))) | (~big_f(c1, f10(f9(c1, c1)))) | (f7(c1) = c1) | big_f(f7(c1), f9(c1, c1)))),
% 29.01/19.20 inference(quant_inst,[status(thm)],[])).
% 29.01/19.20 tff(19117,plain,
% 29.01/19.20 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f7(c1) = c1) | big_f(f7(c1), f9(c1, c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~(f9(c1, c1) = f5(c1))) | (~big_f(c1, f10(f9(c1, c1)))) | (c1 = f8(f9(c1, c1)))),
% 29.01/19.20 inference(modus_ponens,[status(thm)],[19116, 19115])).
% 29.01/19.20 tff(19118,plain,
% 29.01/19.20 ($false),
% 29.01/19.20 inference(unit_resolution,[status(thm)],[19117, 705, 115, 17792, 19111, 17805, 17764, 17763])).
% 29.01/19.20 tff(19119,plain,((f7(c1) = c1) | (~(f10(c2) = c1)) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (f7(c2) = c2) | big_f(c1, c2) | (~(f10(c1) = c1)) | big_f(f7(c2), c2) | big_f(c2, c2) | (~(f5(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.01/19.20 tff(19120,plain,
% 29.01/19.20 (f7(c1) = c1),
% 29.01/19.20 inference(unit_resolution,[status(thm)],[19119, 17749, 1498, 11752, 17, 11819, 3762, 17744, 121, 186])).
% 29.01/19.20 tff(19121,plain,
% 29.01/19.20 (big_f(f9(c1, c1), c1) <=> big_f(c2, c1)),
% 29.01/19.20 inference(monotonicity,[status(thm)],[17728])).
% 29.01/19.20 tff(19122,plain,
% 29.01/19.20 (big_f(c2, c1) <=> big_f(f9(c1, c1), c1)),
% 29.01/19.20 inference(symmetry,[status(thm)],[19121])).
% 29.01/19.20 tff(19123,plain,
% 29.01/19.20 (big_f(c2, c1) <=> big_f(f9(c1, c1), f10(f9(c1, c1)))),
% 29.01/19.20 inference(transitivity,[status(thm)],[19122, 17768])).
% 29.01/19.20 tff(19124,plain,
% 29.01/19.20 (f2(c3) = c1),
% 29.01/19.20 inference(unit_resolution,[status(thm)],[19091, 27, 11819, 17, 172, 11752])).
% 29.01/19.20 tff(19125,plain,
% 29.01/19.20 ($false),
% 29.01/19.20 inference(unit_resolution,[status(thm)],[11776, 19124, 27, 172, 11752, 66])).
% 29.01/19.20 tff(19126,plain,(big_f(c1, c2) | (~(c3 = c1)) | (~(f4(c4) = c1)) | big_f(c1, c1) | (~(f10(c2) = c1)) | (f7(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 29.01/19.20 tff(19127,plain,
% 29.01/19.20 (big_f(c1, c1)),
% 29.01/19.20 inference(unit_resolution,[status(thm)],[19126, 172, 11752, 17749, 11819, 17])).
% 29.01/19.20 tff(19128,plain,
% 29.01/19.20 ((~big_f(f7(c2), c1)) <=> (~big_f(c1, c1))),
% 29.01/19.20 inference(monotonicity,[status(thm)],[18057])).
% 29.01/19.20 tff(19129,plain,
% 29.01/19.20 (~big_f(c1, c1)),
% 29.01/19.20 inference(modus_ponens,[status(thm)],[333, 19128])).
% 29.01/19.20 tff(19130,plain,
% 29.01/19.20 ($false),
% 29.01/19.20 inference(unit_resolution,[status(thm)],[4932, 19129])).
% 29.01/19.20 tff(19131,plain,((~big_f(c1, c1)) | big_f(f7(c2), c1) | (~(f7(c2) = c1)) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.01/19.20 tff(19132,plain,
% 29.01/19.20 (big_f(f7(c2), c1)),
% 29.01/19.20 inference(unit_resolution,[status(thm)],[19131, 4932, 1498, 292, 11752, 11819])).
% 29.01/19.20 tff(19133,plain,
% 29.01/19.20 (~big_f(f9(c1, c1), f10(c1))),
% 29.01/19.20 inference(unit_resolution,[status(thm)],[19082, 3762, 1498, 2, 11752, 11819])).
% 29.01/19.20 tff(19134,plain,
% 29.01/19.20 ($false),
% 29.01/19.20 inference(unit_resolution,[status(thm)],[18686, 19133, 3762, 11819, 338, 292, 115, 730])).
% 29.01/19.20 tff(19135,plain,((~(f10(c1) = c1)) | (~(f10(c2) = c1)) | (~big_f(f7(c2), c1)) | (~(f7(c2) = c1)) | (f7(c1) = c1) | big_f(f7(c1), f5(c1)) | (~(f9(f10(c2), f4(c4)) = c2)) | big_f(c2, c1) | (~(f4(c4) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.01/19.20 tff(19136,plain,
% 29.01/19.20 (~(f10(c1) = c1)),
% 29.01/19.20 inference(unit_resolution,[status(thm)],[19135, 115, 338, 292, 11819, 17783, 1498, 2, 11752])).
% 29.01/19.20 tff(19137,plain,
% 29.01/19.20 (f10(c1) = c2),
% 29.01/19.20 inference(unit_resolution,[status(thm)],[14, 19136])).
% 29.01/19.20 tff(19138,plain,
% 29.01/19.20 (f10(c1) = f9(c1, c1)),
% 29.01/19.20 inference(transitivity,[status(thm)],[19137, 17733, 17726])).
% 29.01/19.20 tff(19139,plain,
% 29.01/19.20 (f7(c1) = f9(c1, c1)),
% 29.01/19.20 inference(transitivity,[status(thm)],[120, 17733, 17726])).
% 29.01/19.20 tff(19140,plain,
% 29.01/19.20 (big_f(f7(c1), c2) <=> big_f(f9(c1, c1), f9(c1, c1))),
% 29.01/19.20 inference(monotonicity,[status(thm)],[19139, 17734])).
% 29.01/19.20 tff(19141,plain,
% 29.01/19.20 (big_f(f9(c1, c1), f9(c1, c1)) <=> big_f(f7(c1), c2)),
% 29.01/19.20 inference(symmetry,[status(thm)],[19140])).
% 29.01/19.20 tff(19142,plain,
% 29.01/19.20 ((~big_f(f9(c1, c1), f9(c1, c1))) <=> (~big_f(f7(c1), c2))),
% 29.01/19.20 inference(monotonicity,[status(thm)],[19141])).
% 29.01/19.20 tff(19143,plain,
% 29.01/19.20 (~big_f(f7(c1), c2)),
% 29.01/19.20 inference(modus_ponens,[status(thm)],[17762, 19142])).
% 29.01/19.20 tff(19144,plain,
% 29.01/19.20 (~big_f(c2, f10(c1))),
% 29.01/19.20 inference(unit_resolution,[status(thm)],[6125, 19137, 121])).
% 29.01/19.20 tff(19145,plain,
% 29.01/19.20 (~(c2 = f8(c1))),
% 29.01/19.20 inference(unit_resolution,[status(thm)],[1752, 19144, 1727, 115, 19136, 19143])).
% 29.01/19.20 tff(19146,plain,
% 29.01/19.20 (~(f8(c1) = c2)),
% 29.01/19.20 inference(unit_resolution,[status(thm)],[1675, 19145])).
% 29.01/19.20 tff(19147,plain,
% 29.01/19.20 (f8(c1) = c1),
% 29.01/19.20 inference(unit_resolution,[status(thm)],[1680, 19146])).
% 29.01/19.20 tff(19148,plain,
% 29.01/19.20 (big_f(f8(c1), f10(c1)) <=> big_f(c1, f9(c1, c1))),
% 29.01/19.20 inference(monotonicity,[status(thm)],[19147, 19138])).
% 29.01/19.20 tff(19149,plain,
% 29.01/19.20 (big_f(c1, f9(c1, c1)) <=> big_f(f8(c1), f10(c1))),
% 29.01/19.20 inference(symmetry,[status(thm)],[19148])).
% 29.01/19.20 tff(19150,plain,
% 29.01/19.20 ((~big_f(c1, f9(c1, c1))) <=> (~big_f(f8(c1), f10(c1)))),
% 29.01/19.20 inference(monotonicity,[status(thm)],[19149])).
% 29.01/19.20 tff(19151,plain,
% 29.01/19.20 (~big_f(f8(c1), f10(c1))),
% 29.01/19.20 inference(modus_ponens,[status(thm)],[4686, 19150])).
% 29.01/19.20 tff(19152,plain,
% 29.01/19.20 (big_f(f8(c1), f10(c1))),
% 29.01/19.20 inference(unit_resolution,[status(thm)],[2848, 19136, 115, 17783])).
% 29.01/19.20 tff(19153,plain,
% 29.01/19.20 ($false),
% 29.01/19.20 inference(unit_resolution,[status(thm)],[19152, 19151])).
% 29.01/19.20 tff(19154,plain,((f7(c1) = c1) | big_f(c1, f9(c1, c1)) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | big_f(c2, c2) | (~big_f(f7(c2), c1)) | (~(f7(c2) = c1)) | big_f(c2, c1) | (~(f5(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.01/19.20 tff(19155,plain,
% 29.01/19.20 (f7(c1) = c1),
% 29.01/19.20 inference(unit_resolution,[status(thm)],[19154, 4686, 1498, 11752, 11819, 121, 19132, 292, 2, 186])).
% 29.01/19.20 tff(19156,plain,
% 29.01/19.20 (f10(c1) = f9(c1, c1)),
% 29.01/19.20 inference(transitivity,[status(thm)],[15, 17733, 17726])).
% 29.01/19.20 tff(19157,plain,
% 29.01/19.20 (big_f(c1, f10(c1)) <=> big_f(c1, f9(c1, c1))),
% 29.01/19.20 inference(monotonicity,[status(thm)],[19156])).
% 29.01/19.20 tff(19158,plain,
% 29.01/19.20 (big_f(c1, f9(c1, c1)) <=> big_f(c1, f10(c1))),
% 29.01/19.20 inference(symmetry,[status(thm)],[19157])).
% 29.01/19.20 tff(19159,plain,
% 29.01/19.20 ((~big_f(c1, f9(c1, c1))) <=> (~big_f(c1, f10(c1)))),
% 29.01/19.20 inference(monotonicity,[status(thm)],[19158])).
% 29.01/19.20 tff(19160,plain,
% 29.01/19.20 (~big_f(c1, f10(c1))),
% 29.01/19.21 inference(modus_ponens,[status(thm)],[4686, 19159])).
% 29.01/19.21 tff(19161,plain,
% 29.01/19.21 (big_f(f7(f9(c1, c1)), f9(c1, c1)) <=> big_f(c1, f9(c1, c1))),
% 29.01/19.21 inference(monotonicity,[status(thm)],[17984])).
% 29.01/19.21 tff(19162,plain,
% 29.01/19.21 (big_f(c1, f9(c1, c1)) <=> big_f(f7(f9(c1, c1)), f9(c1, c1))),
% 29.01/19.21 inference(symmetry,[status(thm)],[19161])).
% 29.01/19.21 tff(19163,plain,
% 29.01/19.21 ((~big_f(c1, f9(c1, c1))) <=> (~big_f(f7(f9(c1, c1)), f9(c1, c1)))),
% 29.01/19.21 inference(monotonicity,[status(thm)],[19162])).
% 29.01/19.21 tff(19164,plain,
% 29.01/19.21 (~big_f(f7(f9(c1, c1)), f9(c1, c1))),
% 29.01/19.21 inference(modus_ponens,[status(thm)],[4686, 19163])).
% 29.01/19.21 tff(19165,plain,
% 29.01/19.21 (f9(c1, c1) = f10(c1)),
% 29.01/19.21 inference(transitivity,[status(thm)],[17727, 1498, 5571])).
% 29.01/19.21 tff(19166,plain,
% 29.01/19.21 (big_f(f9(c1, c1), f9(c1, c1)) <=> big_f(f9(c1, c1), f10(c1))),
% 29.01/19.21 inference(monotonicity,[status(thm)],[19165])).
% 29.01/19.21 tff(19167,plain,
% 29.01/19.21 ((~big_f(f9(c1, c1), f9(c1, c1))) <=> (~big_f(f9(c1, c1), f10(c1)))),
% 29.01/19.21 inference(monotonicity,[status(thm)],[19166])).
% 29.01/19.21 tff(19168,plain,
% 29.01/19.21 (~big_f(f9(c1, c1), f10(c1))),
% 29.01/19.21 inference(modus_ponens,[status(thm)],[17762, 19167])).
% 29.01/19.21 tff(19169,plain,
% 29.01/19.21 ((f9(c1, c1) = f8(c1)) <=> (c2 = f8(c1))),
% 29.01/19.21 inference(monotonicity,[status(thm)],[17728])).
% 29.01/19.21 tff(19170,plain,
% 29.01/19.21 ((c2 = f8(c1)) <=> (f9(c1, c1) = f8(c1))),
% 29.01/19.21 inference(symmetry,[status(thm)],[19169])).
% 29.01/19.21 tff(19171,plain,
% 29.01/19.21 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | big_f(f7(f9(c1, c1)), f9(c1, c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~(f9(c1, c1) = f5(f9(c1, c1)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | big_f(f7(f9(c1, c1)), f9(c1, c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~(f9(c1, c1) = f5(f9(c1, c1)))))),
% 29.01/19.21 inference(rewrite,[status(thm)],[])).
% 29.01/19.21 tff(19172,plain,
% 29.01/19.21 (((~(f9(c1, c1) = f5(f9(c1, c1)))) | (f10(c1) = c1) | big_f(c1, f10(c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), f9(c1, c1)) | (~(c1 = f8(c1)))) <=> ((f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | big_f(f7(f9(c1, c1)), f9(c1, c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~(f9(c1, c1) = f5(f9(c1, c1)))))),
% 29.01/19.21 inference(rewrite,[status(thm)],[])).
% 29.01/19.21 tff(19173,plain,
% 29.01/19.21 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(f9(c1, c1) = f5(f9(c1, c1)))) | (f10(c1) = c1) | big_f(c1, f10(c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), f9(c1, c1)) | (~(c1 = f8(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | big_f(f7(f9(c1, c1)), f9(c1, c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~(f9(c1, c1) = f5(f9(c1, c1))))))),
% 29.01/19.21 inference(monotonicity,[status(thm)],[19172])).
% 29.01/19.21 tff(19174,plain,
% 29.01/19.21 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(f9(c1, c1) = f5(f9(c1, c1)))) | (f10(c1) = c1) | big_f(c1, f10(c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), f9(c1, c1)) | (~(c1 = f8(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | big_f(f7(f9(c1, c1)), f9(c1, c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~(f9(c1, c1) = f5(f9(c1, c1)))))),
% 29.01/19.21 inference(transitivity,[status(thm)],[19173, 19171])).
% 29.01/19.21 tff(19175,plain,
% 29.01/19.21 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(f9(c1, c1) = f5(f9(c1, c1)))) | (f10(c1) = c1) | big_f(c1, f10(c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), f9(c1, c1)) | (~(c1 = f8(c1))))),
% 29.01/19.21 inference(quant_inst,[status(thm)],[])).
% 29.01/19.21 tff(19176,plain,
% 29.01/19.21 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | big_f(f7(f9(c1, c1)), f9(c1, c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~(f9(c1, c1) = f5(f9(c1, c1))))),
% 29.01/19.21 inference(modus_ponens,[status(thm)],[19175, 19174])).
% 29.01/19.21 tff(19177,plain,
% 29.01/19.21 ((~(c1 = f8(c1))) | (~(f9(c1, c1) = f5(f9(c1, c1))))),
% 29.01/19.21 inference(unit_resolution,[status(thm)],[19176, 1745, 3, 3030, 17832, 17833])).
% 29.01/19.21 tff(19178,plain,
% 29.01/19.21 (~(c1 = f8(c1))),
% 29.01/19.21 inference(unit_resolution,[status(thm)],[19177, 17934])).
% 29.01/19.21 tff(19179,plain,
% 29.01/19.21 (~(f8(c1) = c1)),
% 29.01/19.21 inference(unit_resolution,[status(thm)],[9808, 19178])).
% 29.01/19.21 tff(19180,plain,
% 29.01/19.21 (f8(c1) = c2),
% 29.01/19.21 inference(unit_resolution,[status(thm)],[1680, 19179])).
% 29.01/19.21 tff(19181,plain,
% 29.01/19.21 (c2 = f8(c1)),
% 29.01/19.21 inference(unit_resolution,[status(thm)],[1675, 19180])).
% 29.01/19.21 tff(19182,plain,
% 29.01/19.21 (f9(c1, c1) = f8(c1)),
% 29.01/19.21 inference(modus_ponens,[status(thm)],[19181, 19170])).
% 29.01/19.21 tff(19183,plain,
% 29.01/19.21 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | big_f(f9(c1, c1), f10(c1)) | big_f(f7(f9(c1, c1)), f9(c1, c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~(f9(c1, c1) = f5(f9(c1, c1)))) | (~(f9(c1, c1) = f8(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c1) = c1) | big_f(f9(c1, c1), f10(c1)) | big_f(f7(f9(c1, c1)), f9(c1, c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~(f9(c1, c1) = f5(f9(c1, c1)))) | (~(f9(c1, c1) = f8(c1))))),
% 29.01/19.21 inference(rewrite,[status(thm)],[])).
% 29.01/19.21 tff(19184,plain,
% 29.01/19.21 (((~(f9(c1, c1) = f5(f9(c1, c1)))) | (f10(c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), f9(c1, c1)) | (~(f9(c1, c1) = f8(c1)))) <=> ((f10(c1) = c1) | big_f(f9(c1, c1), f10(c1)) | big_f(f7(f9(c1, c1)), f9(c1, c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~(f9(c1, c1) = f5(f9(c1, c1)))) | (~(f9(c1, c1) = f8(c1))))),
% 29.01/19.21 inference(rewrite,[status(thm)],[])).
% 29.01/19.21 tff(19185,plain,
% 29.01/19.21 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(f9(c1, c1) = f5(f9(c1, c1)))) | (f10(c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), f9(c1, c1)) | (~(f9(c1, c1) = f8(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | big_f(f9(c1, c1), f10(c1)) | big_f(f7(f9(c1, c1)), f9(c1, c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~(f9(c1, c1) = f5(f9(c1, c1)))) | (~(f9(c1, c1) = f8(c1)))))),
% 29.01/19.21 inference(monotonicity,[status(thm)],[19184])).
% 29.01/19.21 tff(19186,plain,
% 29.01/19.21 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(f9(c1, c1) = f5(f9(c1, c1)))) | (f10(c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), f9(c1, c1)) | (~(f9(c1, c1) = f8(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c1) = c1) | big_f(f9(c1, c1), f10(c1)) | big_f(f7(f9(c1, c1)), f9(c1, c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~(f9(c1, c1) = f5(f9(c1, c1)))) | (~(f9(c1, c1) = f8(c1))))),
% 29.01/19.21 inference(transitivity,[status(thm)],[19185, 19183])).
% 29.01/19.21 tff(19187,plain,
% 29.01/19.21 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(f9(c1, c1) = f5(f9(c1, c1)))) | (f10(c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), f9(c1, c1)) | (~(f9(c1, c1) = f8(c1))))),
% 29.01/19.21 inference(quant_inst,[status(thm)],[])).
% 29.01/19.21 tff(19188,plain,
% 29.01/19.21 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c1) = c1) | big_f(f9(c1, c1), f10(c1)) | big_f(f7(f9(c1, c1)), f9(c1, c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~(f9(c1, c1) = f5(f9(c1, c1)))) | (~(f9(c1, c1) = f8(c1)))),
% 29.01/19.21 inference(modus_ponens,[status(thm)],[19187, 19186])).
% 29.01/19.21 tff(19189,plain,
% 29.01/19.21 ((~(f9(c1, c1) = f5(f9(c1, c1)))) | (~(f9(c1, c1) = f8(c1)))),
% 29.01/19.21 inference(unit_resolution,[status(thm)],[19188, 1745, 3, 8712, 17832, 17833])).
% 29.01/19.21 tff(19190,plain,
% 29.01/19.21 (~(f9(c1, c1) = f8(c1))),
% 29.01/19.21 inference(unit_resolution,[status(thm)],[19189, 17934])).
% 29.01/19.21 tff(19191,plain,
% 29.01/19.21 ($false),
% 29.01/19.21 inference(unit_resolution,[status(thm)],[19190, 19182])).
% 29.01/19.21 tff(19192,plain,((~(f9(c1, c1) = f5(f9(c1, c1)))) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | (f10(c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | big_f(f7(f9(c1, c1)), f9(c1, c1)) | big_f(c1, f10(c1))), inference(lemma,lemma(discharge,[]))).
% 29.01/19.21 tff(19193,plain,
% 29.01/19.21 (~(f9(c1, c1) = f5(f9(c1, c1)))),
% 29.01/19.21 inference(unit_resolution,[status(thm)],[19192, 19168, 11752, 11819, 1498, 19164, 17832, 3, 19160])).
% 29.01/19.21 tff(19194,plain,
% 29.01/19.21 (f5(c2) = f5(f9(c1, c1))),
% 29.01/19.21 inference(monotonicity,[status(thm)],[17734])).
% 29.01/19.21 tff(19195,plain,
% 29.01/19.21 (f5(f9(c1, c1)) = f5(c2)),
% 29.01/19.21 inference(symmetry,[status(thm)],[19194])).
% 29.01/19.21 tff(19196,plain,
% 29.01/19.21 ((f9(c1, c1) = f5(f9(c1, c1))) <=> (c2 = f5(c2))),
% 29.01/19.21 inference(monotonicity,[status(thm)],[17728, 19195])).
% 29.01/19.21 tff(19197,plain,
% 29.01/19.21 ((c2 = f5(c2)) <=> (f9(c1, c1) = f5(f9(c1, c1)))),
% 29.01/19.21 inference(symmetry,[status(thm)],[19196])).
% 29.01/19.21 tff(19198,plain,
% 29.01/19.21 ((f5(c2) = c2) <=> (f9(c1, c1) = f5(f9(c1, c1)))),
% 29.01/19.21 inference(transitivity,[status(thm)],[1279, 19197])).
% 29.01/19.21 tff(19199,plain,
% 29.01/19.21 (f9(c1, c1) = f5(f9(c1, c1))),
% 29.01/19.21 inference(modus_ponens,[status(thm)],[8109, 19198])).
% 29.01/19.21 tff(19200,assumption,(~(f9(c1, c1) = f5(f9(c1, c1)))), introduced(assumption)).
% 29.01/19.21 tff(19201,plain,
% 29.01/19.21 ($false),
% 29.01/19.21 inference(unit_resolution,[status(thm)],[19200, 19199])).
% 29.01/19.21 tff(19202,plain,((~(f5(c2) = c2)) | (f9(c1, c1) = f5(f9(c1, c1))) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.01/19.21 tff(19203,plain,
% 29.01/19.21 (~(f5(c2) = c2)),
% 29.01/19.21 inference(unit_resolution,[status(thm)],[19202, 19193, 1498, 11752, 11819])).
% 29.01/19.21 tff(19204,plain,
% 29.01/19.21 (f5(c2) = c1),
% 29.01/19.21 inference(unit_resolution,[status(thm)],[1547, 19203])).
% 29.01/19.21 tff(19205,plain,
% 29.01/19.21 (f7(c1) = f7(f9(c1, c1))),
% 29.01/19.21 inference(transitivity,[status(thm)],[4234, 342, 17739])).
% 29.01/19.21 tff(19206,plain,
% 29.01/19.21 (big_f(f7(c1), f6(c1, c1)) <=> big_f(f7(f9(c1, c1)), f6(c1, c1))),
% 29.01/19.21 inference(monotonicity,[status(thm)],[19205])).
% 29.01/19.21 tff(19207,plain,
% 29.01/19.21 (f9(c1, c1) = f8(c1)),
% 29.01/19.21 inference(transitivity,[status(thm)],[17727, 1498, 7098])).
% 29.01/19.21 tff(19208,plain,
% 29.01/19.21 (big_f(f7(f9(c1, c1)), f6(c1, c1)) <=> big_f(f7(c1), f6(c1, c1))),
% 29.01/19.21 inference(symmetry,[status(thm)],[19206])).
% 29.01/19.21 tff(19209,plain,
% 29.01/19.21 (f6(c1, c1) = c1),
% 29.01/19.21 inference(unit_resolution,[status(thm)],[9816, 65, 4234, 3, 2946, 1642])).
% 29.01/19.21 tff(19210,plain,
% 29.01/19.21 (big_f(f7(f9(c1, c1)), f6(c1, c1)) <=> big_f(c1, c1)),
% 29.01/19.21 inference(monotonicity,[status(thm)],[17984, 19209])).
% 29.01/19.21 tff(19211,plain,
% 29.01/19.21 (big_f(c1, c1) <=> big_f(f7(f9(c1, c1)), f6(c1, c1))),
% 29.01/19.21 inference(symmetry,[status(thm)],[19210])).
% 29.01/19.21 tff(19212,plain,
% 29.01/19.21 (big_f(c1, c1) <=> big_f(f7(c1), f6(c1, c1))),
% 29.01/19.21 inference(transitivity,[status(thm)],[19211, 19208])).
% 29.01/19.21 tff(19213,plain,
% 29.01/19.21 (big_f(f7(c1), f6(c1, c1))),
% 29.01/19.21 inference(modus_ponens,[status(thm)],[4932, 19212])).
% 29.01/19.21 tff(19214,plain,
% 29.01/19.21 ($false),
% 29.01/19.21 inference(unit_resolution,[status(thm)],[65, 19213])).
% 29.01/19.21 tff(19215,plain,(big_f(f7(c1), f6(c1, c1)) | (~big_f(c1, c1)) | (~(f7(c2) = c1)) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | (~(f7(c1) = c1)) | (f10(c1) = c1) | big_f(c2, f10(c1)) | (~(c2 = f8(c1)))), inference(lemma,lemma(discharge,[]))).
% 29.01/19.21 tff(19216,plain,
% 29.01/19.21 (big_f(f7(c1), f6(c1, c1))),
% 29.01/19.21 inference(unit_resolution,[status(thm)],[19215, 17233, 292, 1498, 11752, 11819, 4234, 3, 2946, 4932])).
% 29.01/19.21 tff(19217,plain,
% 29.01/19.21 (big_f(f7(f9(c1, c1)), f6(c1, c1))),
% 29.01/19.21 inference(modus_ponens,[status(thm)],[19216, 19206])).
% 29.01/19.21 tff(19218,plain,
% 29.01/19.21 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f7(f9(c1, c1)), f6(c1, c1))) | (f6(c1, c1) = f5(f9(c1, c1))) | (~(f9(c1, c1) = f8(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | (f10(c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f7(f9(c1, c1)), f6(c1, c1))) | (f6(c1, c1) = f5(f9(c1, c1))) | (~(f9(c1, c1) = f8(c1))))),
% 29.01/19.21 inference(rewrite,[status(thm)],[])).
% 29.01/19.21 tff(19219,plain,
% 29.01/19.21 (((f10(c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (f6(c1, c1) = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), f6(c1, c1))) | (~(f9(c1, c1) = f8(c1)))) <=> ((f10(c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f7(f9(c1, c1)), f6(c1, c1))) | (f6(c1, c1) = f5(f9(c1, c1))) | (~(f9(c1, c1) = f8(c1))))),
% 29.01/19.21 inference(rewrite,[status(thm)],[])).
% 29.01/19.21 tff(19220,plain,
% 29.01/19.21 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (f6(c1, c1) = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), f6(c1, c1))) | (~(f9(c1, c1) = f8(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f7(f9(c1, c1)), f6(c1, c1))) | (f6(c1, c1) = f5(f9(c1, c1))) | (~(f9(c1, c1) = f8(c1)))))),
% 29.01/19.21 inference(monotonicity,[status(thm)],[19219])).
% 29.01/19.21 tff(19221,plain,
% 29.01/19.21 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (f6(c1, c1) = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), f6(c1, c1))) | (~(f9(c1, c1) = f8(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | (f10(c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f7(f9(c1, c1)), f6(c1, c1))) | (f6(c1, c1) = f5(f9(c1, c1))) | (~(f9(c1, c1) = f8(c1))))),
% 29.01/19.21 inference(transitivity,[status(thm)],[19220, 19218])).
% 29.01/19.21 tff(19222,plain,
% 29.01/19.21 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (f6(c1, c1) = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), f6(c1, c1))) | (~(f9(c1, c1) = f8(c1))))),
% 29.01/19.21 inference(quant_inst,[status(thm)],[])).
% 29.01/19.21 tff(19223,plain,
% 29.01/19.21 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | (f10(c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f7(f9(c1, c1)), f6(c1, c1))) | (f6(c1, c1) = f5(f9(c1, c1))) | (~(f9(c1, c1) = f8(c1)))),
% 29.01/19.21 inference(modus_ponens,[status(thm)],[19222, 19221])).
% 29.01/19.21 tff(19224,plain,
% 29.01/19.21 (f6(c1, c1) = f5(f9(c1, c1))),
% 29.01/19.21 inference(unit_resolution,[status(thm)],[19223, 2795, 3, 8712, 17832, 19217, 19207])).
% 29.01/19.21 tff(19225,plain,
% 29.01/19.21 (f6(c1, c1) = c1),
% 29.01/19.21 inference(transitivity,[status(thm)],[19224, 17827, 1569])).
% 29.01/19.21 tff(19226,assumption,(f9(c1, c1) = f8(c1)), introduced(assumption)).
% 29.01/19.21 tff(19227,plain,
% 29.01/19.21 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (~(f9(c1, c1) = f8(c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (~(f9(c1, c1) = f8(c1))))),
% 29.01/19.21 inference(rewrite,[status(thm)],[])).
% 29.01/19.21 tff(19228,plain,
% 29.01/19.21 (((f10(c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f7(c1) = c1)) | (~(f9(c1, c1) = f8(c1))) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1)))) <=> ((f10(c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (~(f9(c1, c1) = f8(c1))))),
% 29.01/19.21 inference(rewrite,[status(thm)],[])).
% 29.01/19.21 tff(19229,plain,
% 29.01/19.21 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f7(c1) = c1)) | (~(f9(c1, c1) = f8(c1))) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (~(f9(c1, c1) = f8(c1)))))),
% 29.01/19.21 inference(monotonicity,[status(thm)],[19228])).
% 29.01/19.21 tff(19230,plain,
% 29.01/19.21 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f7(c1) = c1)) | (~(f9(c1, c1) = f8(c1))) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (~(f9(c1, c1) = f8(c1))))),
% 29.01/19.21 inference(transitivity,[status(thm)],[19229, 19227])).
% 29.01/19.21 tff(19231,plain,
% 29.01/19.21 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f7(c1) = c1)) | (~(f9(c1, c1) = f8(c1))) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))),
% 29.01/19.21 inference(quant_inst,[status(thm)],[])).
% 29.01/19.21 tff(19232,plain,
% 29.01/19.21 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (~(f9(c1, c1) = f8(c1)))),
% 29.01/19.21 inference(modus_ponens,[status(thm)],[19231, 19230])).
% 29.01/19.21 tff(19233,plain,
% 29.01/19.21 ($false),
% 29.01/19.21 inference(unit_resolution,[status(thm)],[19232, 2963, 4234, 3, 8712, 5964, 10030, 19226])).
% 29.01/19.21 tff(19234,plain,(big_f(f9(c1, c1), f10(c1)) | (~(f7(c1) = c1)) | (f10(c1) = c1) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (~(f9(c1, c1) = f8(c1)))), inference(lemma,lemma(discharge,[]))).
% 29.01/19.21 tff(19235,plain,
% 29.01/19.21 (~(f6(c1, c1) = c1)),
% 29.01/19.21 inference(unit_resolution,[status(thm)],[19234, 19216, 3, 8712, 19207, 4234])).
% 29.01/19.21 tff(19236,plain,
% 29.01/19.21 ($false),
% 29.01/19.21 inference(unit_resolution,[status(thm)],[19235, 19225])).
% 29.01/19.21 tff(19237,plain,((~(f8(c1) = c2)) | (~(f5(c2) = c1)) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | (f10(c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~(f7(c1) = c1)) | (~(f7(c2) = c1)) | big_f(c2, f10(c1)) | (~big_f(c1, c1))), inference(lemma,lemma(discharge,[]))).
% 29.01/19.22 tff(19238,plain,
% 29.01/19.22 (~(f8(c1) = c2)),
% 29.01/19.22 inference(unit_resolution,[status(thm)],[19237, 19204, 1498, 11752, 11819, 3, 19168, 17832, 4234, 292, 8451, 4932])).
% 29.01/19.22 tff(19239,plain,
% 29.01/19.22 (f8(c1) = c1),
% 29.01/19.22 inference(unit_resolution,[status(thm)],[1680, 19238])).
% 29.01/19.22 tff(19240,plain,
% 29.01/19.22 (c1 = f8(c1)),
% 29.01/19.22 inference(unit_resolution,[status(thm)],[9808, 19239])).
% 29.01/19.22 tff(19241,plain,
% 29.01/19.22 (f6(c1, c1) = c1),
% 29.01/19.22 inference(unit_resolution,[status(thm)],[9803, 65, 3, 3031, 3030, 4234])).
% 29.01/19.22 tff(19242,plain,
% 29.01/19.22 (big_f(f7(f9(c1, c1)), f6(c1, c1)) <=> big_f(c1, c1)),
% 29.01/19.22 inference(monotonicity,[status(thm)],[17984, 19241])).
% 29.01/19.22 tff(19243,plain,
% 29.01/19.22 (big_f(c1, c1) <=> big_f(f7(f9(c1, c1)), f6(c1, c1))),
% 29.01/19.22 inference(symmetry,[status(thm)],[19242])).
% 29.01/19.22 tff(19244,plain,
% 29.01/19.22 (big_f(c1, c1) <=> big_f(f7(c1), f6(c1, c1))),
% 29.01/19.22 inference(transitivity,[status(thm)],[19243, 19208])).
% 29.01/19.22 tff(19245,plain,
% 29.01/19.22 (big_f(f7(c1), f6(c1, c1))),
% 29.01/19.22 inference(modus_ponens,[status(thm)],[4932, 19244])).
% 29.01/19.22 tff(19246,plain,
% 29.01/19.22 ($false),
% 29.01/19.22 inference(unit_resolution,[status(thm)],[65, 19245])).
% 29.01/19.22 tff(19247,plain,(big_f(f7(c1), f6(c1, c1)) | (~big_f(c1, c1)) | (~(f7(c2) = c1)) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | (~(f7(c1) = c1)) | (f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1))), inference(lemma,lemma(discharge,[]))).
% 29.01/19.22 tff(19248,plain,
% 29.01/19.22 (big_f(f7(c1), f6(c1, c1))),
% 29.01/19.22 inference(unit_resolution,[status(thm)],[19247, 3, 292, 1498, 11752, 11819, 4234, 4932, 19240, 19160])).
% 29.01/19.22 tff(19249,plain,
% 29.01/19.22 (big_f(f7(f9(c1, c1)), f6(c1, c1))),
% 29.01/19.22 inference(modus_ponens,[status(thm)],[19248, 19206])).
% 29.01/19.22 tff(19250,plain,
% 29.01/19.22 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f7(f9(c1, c1)), f6(c1, c1))) | (f6(c1, c1) = f5(f9(c1, c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | (f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f7(f9(c1, c1)), f6(c1, c1))) | (f6(c1, c1) = f5(f9(c1, c1))))),
% 29.01/19.22 inference(rewrite,[status(thm)],[])).
% 29.01/19.22 tff(19251,plain,
% 29.01/19.22 (((f10(c1) = c1) | big_f(c1, f10(c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (f6(c1, c1) = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), f6(c1, c1))) | (~(c1 = f8(c1)))) <=> ((f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f7(f9(c1, c1)), f6(c1, c1))) | (f6(c1, c1) = f5(f9(c1, c1))))),
% 29.01/19.22 inference(rewrite,[status(thm)],[])).
% 29.01/19.22 tff(19252,plain,
% 29.01/19.22 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | big_f(c1, f10(c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (f6(c1, c1) = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), f6(c1, c1))) | (~(c1 = f8(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f7(f9(c1, c1)), f6(c1, c1))) | (f6(c1, c1) = f5(f9(c1, c1)))))),
% 29.01/19.22 inference(monotonicity,[status(thm)],[19251])).
% 29.01/19.22 tff(19253,plain,
% 29.01/19.22 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | big_f(c1, f10(c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (f6(c1, c1) = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), f6(c1, c1))) | (~(c1 = f8(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | (f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f7(f9(c1, c1)), f6(c1, c1))) | (f6(c1, c1) = f5(f9(c1, c1))))),
% 29.01/19.22 inference(transitivity,[status(thm)],[19252, 19250])).
% 29.01/19.22 tff(19254,plain,
% 29.01/19.22 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | big_f(c1, f10(c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (f6(c1, c1) = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), f6(c1, c1))) | (~(c1 = f8(c1))))),
% 29.01/19.22 inference(quant_inst,[status(thm)],[])).
% 29.01/19.22 tff(19255,plain,
% 29.01/19.22 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | (f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f7(f9(c1, c1)), f6(c1, c1))) | (f6(c1, c1) = f5(f9(c1, c1)))),
% 29.01/19.22 inference(modus_ponens,[status(thm)],[19254, 19253])).
% 29.01/19.22 tff(19256,plain,
% 29.01/19.22 (f6(c1, c1) = f5(f9(c1, c1))),
% 29.01/19.22 inference(unit_resolution,[status(thm)],[19255, 2795, 3, 19240, 19160, 17832, 19249])).
% 29.01/19.22 tff(19257,plain,
% 29.01/19.22 (f6(c1, c1) = c1),
% 29.01/19.22 inference(transitivity,[status(thm)],[19256, 17827, 19204])).
% 29.01/19.22 tff(19258,plain,
% 29.01/19.22 (~(f6(c1, c1) = c1)),
% 29.01/19.22 inference(unit_resolution,[status(thm)],[18583, 2963, 4234, 3, 19240, 19160, 19248])).
% 29.01/19.22 tff(19259,plain,
% 29.01/19.22 ($false),
% 29.01/19.22 inference(unit_resolution,[status(thm)],[19258, 19257])).
% 29.01/19.22 tff(19260,plain,((f10(c1) = c1) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | (~(f7(c1) = c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~(f7(c2) = c1)) | (~big_f(c1, c1)) | big_f(c1, f9(c1, c1)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 29.01/19.22 tff(19261,plain,
% 29.01/19.22 (f10(c1) = c1),
% 29.01/19.22 inference(unit_resolution,[status(thm)],[19260, 19155, 11752, 11819, 1498, 17832, 292, 4932, 4686, 121])).
% 29.01/19.22 tff(19262,plain,
% 29.01/19.22 (big_f(f7(c1), c2) <=> big_f(f7(c1), f5(c1))),
% 29.01/19.22 inference(symmetry,[status(thm)],[18262])).
% 29.01/19.22 tff(19263,plain,
% 29.01/19.22 (big_f(f7(c1), c2) <=> big_f(c1, f9(c1, c1))),
% 29.01/19.22 inference(monotonicity,[status(thm)],[19155, 17734])).
% 29.01/19.22 tff(19264,plain,
% 29.01/19.22 (big_f(c1, f9(c1, c1)) <=> big_f(f7(c1), c2)),
% 29.01/19.22 inference(symmetry,[status(thm)],[19263])).
% 29.01/19.22 tff(19265,plain,
% 29.01/19.22 (big_f(c1, f9(c1, c1)) <=> big_f(f7(c1), f5(c1))),
% 29.01/19.22 inference(transitivity,[status(thm)],[19264, 19262])).
% 29.01/19.22 tff(19266,plain,
% 29.01/19.22 ((~big_f(c1, f9(c1, c1))) <=> (~big_f(f7(c1), f5(c1)))),
% 29.01/19.22 inference(monotonicity,[status(thm)],[19265])).
% 29.01/19.22 tff(19267,plain,
% 29.01/19.22 (~big_f(f7(c1), f5(c1))),
% 29.01/19.22 inference(modus_ponens,[status(thm)],[4686, 19266])).
% 29.01/19.22 tff(19268,plain,
% 29.01/19.22 (~big_f(f9(c1, c1), f10(c1))),
% 29.01/19.22 inference(unit_resolution,[status(thm)],[19082, 19261, 1498, 2, 11752, 11819])).
% 29.01/19.22 tff(19269,plain,
% 29.01/19.22 ((c2 = c1) <=> (f9(f10(c2), f10(c2)) = f10(c2))),
% 29.01/19.22 inference(transitivity,[status(thm)],[17820, 17773])).
% 29.01/19.22 tff(19270,plain,
% 29.01/19.22 ((~(c2 = c1)) <=> (~(f9(f10(c2), f10(c2)) = f10(c2)))),
% 29.01/19.22 inference(monotonicity,[status(thm)],[19269])).
% 29.01/19.22 tff(19271,plain,
% 29.01/19.22 (~(f9(f10(c2), f10(c2)) = f10(c2))),
% 29.01/19.22 inference(modus_ponens,[status(thm)],[75, 19270])).
% 29.01/19.22 tff(19272,plain,
% 29.01/19.22 (big_f(f9(c1, c1), f10(c1)) <=> big_f(f9(f10(c2), f10(c2)), f10(f10(c2)))),
% 29.01/19.22 inference(symmetry,[status(thm)],[17770])).
% 29.01/19.22 tff(19273,plain,
% 29.01/19.22 (big_f(c2, c1) <=> big_f(f9(f10(c2), f10(c2)), f10(f10(c2)))),
% 29.01/19.22 inference(transitivity,[status(thm)],[19078, 19272])).
% 29.01/19.22 tff(19274,plain,
% 29.01/19.22 ((~big_f(c2, c1)) <=> (~big_f(f9(f10(c2), f10(c2)), f10(f10(c2))))),
% 29.01/19.22 inference(monotonicity,[status(thm)],[19273])).
% 29.01/19.22 tff(19275,plain,
% 29.01/19.22 (~big_f(f9(f10(c2), f10(c2)), f10(f10(c2)))),
% 29.01/19.22 inference(modus_ponens,[status(thm)],[2, 19274])).
% 29.01/19.22 tff(19276,plain,
% 29.01/19.22 (f10(f10(c2)) = c1),
% 29.01/19.22 inference(transitivity,[status(thm)],[11844, 3762])).
% 29.01/19.22 tff(19277,plain,
% 29.01/19.22 (f9(c1, f10(f10(c2))) = f9(c1, c1)),
% 29.01/19.22 inference(monotonicity,[status(thm)],[19276])).
% 29.01/19.22 tff(19278,plain,
% 29.01/19.22 ((f9(c1, f10(f10(c2))) = f10(f10(c2))) <=> (f9(c1, c1) = c1)),
% 29.01/19.22 inference(monotonicity,[status(thm)],[19277, 19276])).
% 29.01/19.22 tff(19279,plain,
% 29.01/19.22 ((f9(c1, c1) = c1) <=> (f9(c1, f10(f10(c2))) = f10(f10(c2)))),
% 29.01/19.22 inference(symmetry,[status(thm)],[19278])).
% 29.01/19.22 tff(19280,plain,
% 29.01/19.22 ((~(f9(c1, c1) = c1)) <=> (~(f9(c1, f10(f10(c2))) = f10(f10(c2))))),
% 29.01/19.22 inference(monotonicity,[status(thm)],[19279])).
% 29.01/19.22 tff(19281,plain,
% 29.01/19.22 (~(f9(c1, f10(f10(c2))) = f10(f10(c2)))),
% 29.01/19.22 inference(modus_ponens,[status(thm)],[17822, 19280])).
% 29.01/19.22 tff(19282,plain,
% 29.01/19.22 (f9(c1, f10(f10(c2))) = c2),
% 29.01/19.22 inference(transitivity,[status(thm)],[19277, 17727, 1498])).
% 29.01/19.22 tff(19283,plain,
% 29.01/19.22 (big_f(f9(c1, f10(f10(c2))), f10(c1)) <=> big_f(c2, c1)),
% 29.01/19.22 inference(monotonicity,[status(thm)],[19282, 3762])).
% 29.01/19.22 tff(19284,plain,
% 29.01/19.22 (big_f(c2, c1) <=> big_f(f9(c1, f10(f10(c2))), f10(c1))),
% 29.01/19.22 inference(symmetry,[status(thm)],[19283])).
% 29.01/19.22 tff(19285,plain,
% 29.01/19.22 ((~big_f(c2, c1)) <=> (~big_f(f9(c1, f10(f10(c2))), f10(c1)))),
% 29.01/19.22 inference(monotonicity,[status(thm)],[19284])).
% 29.01/19.22 tff(19286,plain,
% 29.01/19.22 (~big_f(f9(c1, f10(f10(c2))), f10(c1))),
% 29.01/19.22 inference(modus_ponens,[status(thm)],[2, 19285])).
% 29.01/19.22 tff(19287,plain,
% 29.01/19.22 (big_f(f7(c1), f5(c1))),
% 29.01/19.22 inference(unit_resolution,[status(thm)],[280, 115, 2471, 1515, 158])).
% 29.01/19.22 tff(19288,plain,
% 29.01/19.22 (~(f5(c1) = c2)),
% 29.01/19.22 inference(unit_resolution,[status(thm)],[1715, 19287, 121, 120])).
% 29.01/19.22 tff(19289,plain,
% 29.01/19.22 (f5(c1) = c1),
% 29.01/19.22 inference(unit_resolution,[status(thm)],[1708, 19288])).
% 29.01/19.22 tff(19290,plain,
% 29.01/19.22 (c1 = f5(c1)),
% 29.01/19.22 inference(modus_ponens,[status(thm)],[19289, 192])).
% 29.01/19.22 tff(19291,plain,
% 29.01/19.22 (~(c1 = f5(c1))),
% 29.01/19.22 inference(unit_resolution,[status(thm)],[18614, 115, 3762, 2, 18603, 18604])).
% 29.01/19.22 tff(19292,plain,
% 29.01/19.22 ($false),
% 29.01/19.22 inference(unit_resolution,[status(thm)],[19291, 19290])).
% 29.01/19.22 tff(19293,plain,((f7(c1) = c1) | big_f(c2, c2) | (~(f10(c1) = c1)) | big_f(c2, c1) | big_f(f9(c1, f10(f10(c2))), f10(c1)) | (f9(c1, f10(f10(c2))) = f10(f10(c2))) | (~(f10(f10(c2)) = f10(c2))) | big_f(f9(f10(c2), f10(c2)), f10(f10(c2))) | (f9(f10(c2), f10(c2)) = f10(c2))), inference(lemma,lemma(discharge,[]))).
% 29.01/19.22 tff(19294,plain,
% 29.01/19.22 (f7(c1) = c1),
% 29.01/19.22 inference(unit_resolution,[status(thm)],[19293, 2, 3762, 121, 19286, 19281, 17782, 19275, 19271])).
% 29.01/19.22 tff(19295,plain,
% 29.01/19.22 (c1 = f7(c1)),
% 29.01/19.22 inference(symmetry,[status(thm)],[19294])).
% 29.01/19.22 tff(19296,plain,
% 29.01/19.22 (f7(f9(c1, c1)) = f7(c1)),
% 29.01/19.22 inference(transitivity,[status(thm)],[17729, 292, 19295])).
% 29.01/19.22 tff(19297,plain,
% 29.01/19.22 (big_f(f7(f9(c1, c1)), f6(c1, c1)) <=> big_f(f7(c1), f6(c1, c1))),
% 29.01/19.22 inference(monotonicity,[status(thm)],[19296])).
% 29.01/19.22 tff(19298,plain,
% 29.01/19.22 (big_f(f7(c1), f6(c1, c1)) <=> big_f(f7(f9(c1, c1)), f6(c1, c1))),
% 29.01/19.22 inference(symmetry,[status(thm)],[19297])).
% 29.01/19.22 tff(19299,plain,
% 29.01/19.22 (~big_f(f9(c1, c1), f10(c1))),
% 29.01/19.22 inference(unit_resolution,[status(thm)],[19082, 2, 3762, 1498, 11752, 11819])).
% 29.01/19.22 tff(19300,plain,
% 29.01/19.22 (big_f(f7(f9(c1, c1)), c1) <=> big_f(f7(c2), c1)),
% 29.01/19.22 inference(symmetry,[status(thm)],[17980])).
% 29.01/19.22 tff(19301,plain,
% 29.01/19.22 (big_f(c1, f10(f9(c1, c1))) <=> big_f(f7(f9(c1, c1)), c1)),
% 29.01/19.22 inference(monotonicity,[status(thm)],[17976, 17766])).
% 29.01/19.22 tff(19302,plain,
% 29.01/19.22 (f10(c2) = f10(f9(c1, c1))),
% 29.01/19.22 inference(symmetry,[status(thm)],[17765])).
% 29.01/19.22 tff(19303,plain,
% 29.01/19.22 (f7(f9(c1, c1)) = f4(c4)),
% 29.01/19.22 inference(transitivity,[status(thm)],[17729, 292, 16651])).
% 29.01/19.22 tff(19304,plain,
% 29.01/19.22 (big_f(f7(f9(c1, c1)), c4) <=> big_f(f4(c4), c4)),
% 29.01/19.22 inference(monotonicity,[status(thm)],[19303])).
% 29.01/19.22 tff(19305,plain,
% 29.01/19.22 (big_f(f4(c4), c4) <=> big_f(f7(f9(c1, c1)), c4)),
% 29.01/19.22 inference(symmetry,[status(thm)],[19304])).
% 29.01/19.22 tff(19306,plain,
% 29.01/19.22 (~big_f(c3, f2(c3))),
% 29.01/19.22 inference(unit_resolution,[status(thm)],[8256, 2, 67, 121])).
% 29.01/19.22 tff(19307,plain,
% 29.01/19.22 (big_f(f4(c4), c4)),
% 29.01/19.22 inference(unit_resolution,[status(thm)],[1315, 19306])).
% 29.01/19.22 tff(19308,plain,
% 29.01/19.22 (big_f(f7(f9(c1, c1)), c4)),
% 29.01/19.22 inference(modus_ponens,[status(thm)],[19307, 19305])).
% 29.01/19.22 tff(19309,plain,
% 29.01/19.22 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~big_f(f7(f9(c1, c1)), c4)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (c4 = f5(f9(c1, c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~big_f(f7(f9(c1, c1)), c4)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (c4 = f5(f9(c1, c1))))),
% 29.01/19.22 inference(rewrite,[status(thm)],[])).
% 29.01/19.22 tff(19310,plain,
% 29.01/19.22 (((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (c4 = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), c4))) <=> ((f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~big_f(f7(f9(c1, c1)), c4)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (c4 = f5(f9(c1, c1))))),
% 29.01/19.22 inference(rewrite,[status(thm)],[])).
% 29.01/19.22 tff(19311,plain,
% 29.01/19.22 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (c4 = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), c4)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~big_f(f7(f9(c1, c1)), c4)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (c4 = f5(f9(c1, c1)))))),
% 29.01/19.22 inference(monotonicity,[status(thm)],[19310])).
% 29.01/19.22 tff(19312,plain,
% 29.01/19.22 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (c4 = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), c4)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~big_f(f7(f9(c1, c1)), c4)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (c4 = f5(f9(c1, c1))))),
% 29.01/19.22 inference(transitivity,[status(thm)],[19311, 19309])).
% 29.01/19.22 tff(19313,plain,
% 29.01/19.22 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (c4 = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), c4)))),
% 29.01/19.22 inference(quant_inst,[status(thm)],[])).
% 29.01/19.22 tff(19314,plain,
% 29.01/19.22 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~big_f(f7(f9(c1, c1)), c4)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (c4 = f5(f9(c1, c1)))),
% 29.01/19.22 inference(modus_ponens,[status(thm)],[19313, 19312])).
% 29.01/19.22 tff(19315,plain,
% 29.01/19.22 ((~big_f(f7(f9(c1, c1)), c4)) | (c4 = f5(f9(c1, c1)))),
% 29.01/19.22 inference(unit_resolution,[status(thm)],[19314, 676, 3762, 17822, 19299, 17832])).
% 29.01/19.22 tff(19316,plain,
% 29.01/19.22 (c4 = f5(f9(c1, c1))),
% 29.01/19.22 inference(unit_resolution,[status(thm)],[19315, 19308])).
% 29.01/19.22 tff(19317,plain,
% 29.01/19.22 (c4 = f5(c2)),
% 29.01/19.22 inference(transitivity,[status(thm)],[19316, 19195])).
% 29.01/19.22 tff(19318,plain,
% 29.01/19.22 (big_f(f4(c4), c4) <=> big_f(f7(c2), f5(c2))),
% 29.01/19.22 inference(monotonicity,[status(thm)],[17132, 19317])).
% 29.01/19.22 tff(19319,plain,
% 29.01/19.22 (big_f(f7(c2), f5(c2))),
% 29.01/19.22 inference(modus_ponens,[status(thm)],[19307, 19318])).
% 29.01/19.22 tff(19320,plain,
% 29.01/19.22 (f10(f9(c1, c1)) = f10(c2)),
% 29.01/19.22 inference(monotonicity,[status(thm)],[18437])).
% 29.01/19.22 tff(19321,plain,
% 29.01/19.22 (f10(f9(c1, c1)) = c1),
% 29.01/19.22 inference(transitivity,[status(thm)],[19320, 11819])).
% 29.01/19.22 tff(19322,plain,
% 29.01/19.22 (f7(f9(c1, c1)) = f7(c2)),
% 29.01/19.22 inference(monotonicity,[status(thm)],[18437])).
% 29.01/19.22 tff(19323,plain,
% 29.01/19.22 (f7(c2) = f7(f9(c1, c1))),
% 29.01/19.22 inference(symmetry,[status(thm)],[19322])).
% 29.01/19.22 tff(19324,plain,
% 29.01/19.22 (c1 = f7(f9(c1, c1))),
% 29.01/19.22 inference(transitivity,[status(thm)],[342, 19323])).
% 29.01/19.22 tff(19325,plain,
% 29.01/19.22 (big_f(c1, f10(f9(c1, c1))) <=> big_f(f7(f9(c1, c1)), c1)),
% 29.01/19.22 inference(monotonicity,[status(thm)],[19324, 19321])).
% 29.01/19.22 tff(19326,plain,
% 29.01/19.22 (f10(c2) = f10(f9(c1, c1))),
% 29.01/19.22 inference(symmetry,[status(thm)],[19320])).
% 29.01/19.22 tff(19327,assumption,(c4 = f5(f9(c1, c1))), introduced(assumption)).
% 29.01/19.22 tff(19328,plain,
% 29.01/19.22 (f5(f9(c1, c1)) = c4),
% 29.01/19.22 inference(symmetry,[status(thm)],[19327])).
% 29.01/19.22 tff(19329,plain,
% 29.01/19.22 (f9(f10(c2), f4(c4)) = f9(c1, c1)),
% 29.01/19.22 inference(symmetry,[status(thm)],[18436])).
% 29.01/19.22 tff(19330,plain,
% 29.01/19.22 (c2 = f9(c1, c1)),
% 29.01/19.22 inference(transitivity,[status(thm)],[17733, 19329])).
% 29.01/19.22 tff(19331,plain,
% 29.01/19.22 (f5(c2) = f5(f9(c1, c1))),
% 29.01/19.22 inference(monotonicity,[status(thm)],[19330])).
% 29.01/19.22 tff(19332,plain,
% 29.01/19.22 (f5(c2) = c2),
% 29.01/19.22 inference(transitivity,[status(thm)],[19331, 19328, 431])).
% 29.01/19.22 tff(19333,plain,
% 29.01/19.22 (big_f(f7(c2), f5(c2)) <=> big_f(c1, c2)),
% 29.01/19.22 inference(monotonicity,[status(thm)],[292, 19332])).
% 29.01/19.22 tff(19334,plain,
% 29.01/19.22 (big_f(c1, c2)),
% 29.01/19.22 inference(modus_ponens,[status(thm)],[319, 19333])).
% 29.01/19.22 tff(19335,plain,
% 29.01/19.22 (f6(c1, c2) = f6(f7(c2), c3)),
% 29.01/19.22 inference(monotonicity,[status(thm)],[342, 69])).
% 29.01/19.22 tff(19336,plain,
% 29.01/19.22 (f6(c1, f9(c1, c1)) = f6(c1, c2)),
% 29.01/19.22 inference(monotonicity,[status(thm)],[17728])).
% 29.01/19.22 tff(19337,plain,
% 29.01/19.22 (f6(c1, f9(c1, c1)) = f9(c1, c1)),
% 29.01/19.22 inference(transitivity,[status(thm)],[19336, 19335, 2362, 17733, 17726])).
% 29.01/19.22 tff(19338,plain,
% 29.01/19.22 (f6(c1, f9(c1, c1)) = c2),
% 29.01/19.22 inference(transitivity,[status(thm)],[19336, 19335, 2362])).
% 29.01/19.22 tff(19339,plain,
% 29.01/19.22 (big_f(f7(c1), f6(c1, f9(c1, c1))) <=> big_f(c1, c2)),
% 29.01/19.22 inference(monotonicity,[status(thm)],[4234, 19338])).
% 29.01/19.22 tff(19340,plain,
% 29.01/19.22 (big_f(c1, c2) <=> big_f(f7(c1), f6(c1, f9(c1, c1)))),
% 29.01/19.22 inference(symmetry,[status(thm)],[19339])).
% 29.01/19.22 tff(19341,plain,
% 29.01/19.22 (big_f(f7(c1), f6(c1, f9(c1, c1)))),
% 29.01/19.22 inference(modus_ponens,[status(thm)],[2865, 19340])).
% 29.01/19.22 tff(19342,plain,
% 29.01/19.22 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f7(c1), f6(c1, f9(c1, c1)))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f7(c1), f6(c1, f9(c1, c1)))))),
% 29.01/19.22 inference(rewrite,[status(thm)],[])).
% 29.01/19.22 tff(19343,plain,
% 29.01/19.22 (((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f7(c1) = c1)) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f7(c1), f6(c1, f9(c1, c1))))) <=> ((f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f7(c1), f6(c1, f9(c1, c1)))))),
% 29.01/19.22 inference(rewrite,[status(thm)],[])).
% 29.01/19.22 tff(19344,plain,
% 29.01/19.22 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f7(c1) = c1)) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f7(c1), f6(c1, f9(c1, c1)))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f7(c1), f6(c1, f9(c1, c1))))))),
% 29.01/19.22 inference(monotonicity,[status(thm)],[19343])).
% 29.01/19.22 tff(19345,plain,
% 29.01/19.22 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f7(c1) = c1)) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f7(c1), f6(c1, f9(c1, c1)))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f7(c1), f6(c1, f9(c1, c1)))))),
% 29.01/19.22 inference(transitivity,[status(thm)],[19344, 19342])).
% 29.01/19.22 tff(19346,plain,
% 29.01/19.22 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f7(c1) = c1)) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f7(c1), f6(c1, f9(c1, c1)))))),
% 29.01/19.22 inference(quant_inst,[status(thm)],[])).
% 29.01/19.22 tff(19347,plain,
% 29.01/19.22 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f7(c1), f6(c1, f9(c1, c1))))),
% 29.01/19.22 inference(modus_ponens,[status(thm)],[19346, 19345])).
% 29.01/19.22 tff(19348,plain,
% 29.01/19.22 ((~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f7(c1), f6(c1, f9(c1, c1))))),
% 29.01/19.22 inference(unit_resolution,[status(thm)],[19347, 2534, 4234, 3762, 17822, 8712])).
% 29.01/19.22 tff(19349,plain,
% 29.01/19.22 ($false),
% 29.01/19.22 inference(unit_resolution,[status(thm)],[19348, 19341, 19337])).
% 29.01/19.22 tff(19350,plain,((~(f6(f7(c2), c3) = c2)) | (~(f7(c1) = c1)) | (~(f10(c1) = c1)) | big_f(f9(c1, c1), f10(c1)) | (~big_f(c1, c2)) | (~(c3 = c2)) | (~(f7(c2) = c1)) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.01/19.22 tff(19351,plain,
% 29.01/19.22 (~(f6(f7(c2), c3) = c2)),
% 29.01/19.22 inference(unit_resolution,[status(thm)],[19350, 19334, 3762, 8712, 4234, 67, 292, 1498, 11752, 11819])).
% 29.01/19.22 tff(19352,plain,
% 29.01/19.22 (f6(f7(c2), c3) = c1),
% 29.01/19.22 inference(unit_resolution,[status(thm)],[2391, 19351])).
% 29.01/19.22 tff(19353,plain,
% 29.01/19.22 (f6(c1, c2) = f10(f9(c1, c1))),
% 29.01/19.22 inference(transitivity,[status(thm)],[19335, 19352, 12231, 19326])).
% 29.01/19.22 tff(19354,plain,
% 29.01/19.22 (big_f(f7(c1), f6(c1, c2)) <=> big_f(c1, f10(f9(c1, c1)))),
% 29.01/19.22 inference(monotonicity,[status(thm)],[4234, 19353])).
% 29.01/19.22 tff(19355,plain,
% 29.01/19.22 (f6(f7(c2), c3) = f6(c1, c2)),
% 29.01/19.22 inference(symmetry,[status(thm)],[19335])).
% 29.01/19.22 tff(19356,plain,
% 29.01/19.22 (big_f(f7(f7(c2)), f6(f7(c2), c3)) <=> big_f(f7(c1), f6(c1, c2))),
% 29.01/19.22 inference(monotonicity,[status(thm)],[352, 19355])).
% 29.01/19.22 tff(19357,plain,
% 29.01/19.22 (big_f(f7(f7(c2)), f6(f7(c2), c3)) <=> big_f(f7(f9(c1, c1)), c1)),
% 29.01/19.22 inference(transitivity,[status(thm)],[19356, 19354, 19325])).
% 29.01/19.22 tff(19358,plain,
% 29.01/19.22 (big_f(f7(c1), f6(c1, c2)) <=> big_f(f7(f7(c2)), f6(f7(c2), c3))),
% 29.01/19.22 inference(symmetry,[status(thm)],[19356])).
% 29.01/19.22 tff(19359,plain,
% 29.01/19.22 (big_f(c1, f10(f9(c1, c1))) <=> big_f(f7(c1), f6(c1, c2))),
% 29.01/19.22 inference(symmetry,[status(thm)],[19354])).
% 29.01/19.22 tff(19360,plain,
% 29.01/19.22 (big_f(c1, f10(f9(c1, c1))) <=> big_f(f7(f7(c2)), f6(f7(c2), c3))),
% 29.01/19.22 inference(transitivity,[status(thm)],[19359, 19358])).
% 29.01/19.22 tff(19361,plain,
% 29.01/19.22 (f6(c1, f9(c1, c1)) = c1),
% 29.01/19.22 inference(transitivity,[status(thm)],[19336, 19335, 2702])).
% 29.01/19.22 tff(19362,plain,
% 29.01/19.22 ((f6(c1, f9(c1, c1)) = f9(c1, c1)) <=> (c1 = f9(c1, c1))),
% 29.01/19.22 inference(monotonicity,[status(thm)],[19361])).
% 29.01/19.22 tff(19363,plain,
% 29.01/19.22 ((f6(c1, f9(c1, c1)) = f9(c1, c1)) <=> (f9(c1, c1) = c1)),
% 29.01/19.22 inference(transitivity,[status(thm)],[19362, 17725])).
% 29.01/19.22 tff(19364,plain,
% 29.01/19.22 ((f9(c1, c1) = c1) <=> (f6(c1, f9(c1, c1)) = f9(c1, c1))),
% 29.01/19.22 inference(symmetry,[status(thm)],[19363])).
% 29.01/19.22 tff(19365,plain,
% 29.01/19.22 ((~(f9(c1, c1) = c1)) <=> (~(f6(c1, f9(c1, c1)) = f9(c1, c1)))),
% 29.01/19.22 inference(monotonicity,[status(thm)],[19364])).
% 29.01/19.22 tff(19366,plain,
% 29.01/19.22 (~(f6(c1, f9(c1, c1)) = f9(c1, c1))),
% 29.01/19.22 inference(modus_ponens,[status(thm)],[17822, 19365])).
% 29.01/19.22 tff(19367,plain,
% 29.01/19.22 (f6(c1, f9(c1, c1)) = f10(f9(c1, c1))),
% 29.01/19.22 inference(transitivity,[status(thm)],[19336, 19335, 2702, 12231, 19302])).
% 29.01/19.22 tff(19368,plain,
% 29.01/19.22 (big_f(f7(c1), f6(c1, f9(c1, c1))) <=> big_f(c1, f10(f9(c1, c1)))),
% 29.01/19.22 inference(monotonicity,[status(thm)],[4234, 19367])).
% 29.01/19.22 tff(19369,plain,
% 29.01/19.22 (big_f(c1, f10(f9(c1, c1))) <=> big_f(f7(c1), f6(c1, f9(c1, c1)))),
% 29.01/19.23 inference(symmetry,[status(thm)],[19368])).
% 29.01/19.23 tff(19370,plain,
% 29.01/19.23 ((~big_f(c1, f10(f9(c1, c1)))) <=> (~big_f(f7(c1), f6(c1, f9(c1, c1))))),
% 29.01/19.23 inference(monotonicity,[status(thm)],[19369])).
% 29.01/19.23 tff(19371,plain,
% 29.01/19.23 (~big_f(f7(c1), f6(c1, f9(c1, c1)))),
% 29.01/19.23 inference(modus_ponens,[status(thm)],[19108, 19370])).
% 29.01/19.23 tff(19372,plain,
% 29.01/19.23 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (f6(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f7(c1), f6(c1, f9(c1, c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (f6(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f7(c1), f6(c1, f9(c1, c1))))),
% 29.01/19.23 inference(rewrite,[status(thm)],[])).
% 29.01/19.23 tff(19373,plain,
% 29.01/19.23 (((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f7(c1) = c1)) | (f6(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f7(c1), f6(c1, f9(c1, c1)))) <=> ((f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (f6(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f7(c1), f6(c1, f9(c1, c1))))),
% 29.01/19.23 inference(rewrite,[status(thm)],[])).
% 29.01/19.23 tff(19374,plain,
% 29.01/19.23 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f7(c1) = c1)) | (f6(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f7(c1), f6(c1, f9(c1, c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (f6(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f7(c1), f6(c1, f9(c1, c1)))))),
% 29.01/19.23 inference(monotonicity,[status(thm)],[19373])).
% 29.01/19.23 tff(19375,plain,
% 29.01/19.23 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f7(c1) = c1)) | (f6(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f7(c1), f6(c1, f9(c1, c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (f6(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f7(c1), f6(c1, f9(c1, c1))))),
% 29.01/19.23 inference(transitivity,[status(thm)],[19374, 19372])).
% 29.01/19.23 tff(19376,plain,
% 29.01/19.23 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f7(c1) = c1)) | (f6(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f7(c1), f6(c1, f9(c1, c1))))),
% 29.01/19.23 inference(quant_inst,[status(thm)],[])).
% 29.01/19.23 tff(19377,plain,
% 29.01/19.23 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (f6(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f7(c1), f6(c1, f9(c1, c1)))),
% 29.01/19.23 inference(modus_ponens,[status(thm)],[19376, 19375])).
% 29.01/19.23 tff(19378,plain,
% 29.01/19.23 ((f6(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f7(c1), f6(c1, f9(c1, c1)))),
% 29.01/19.23 inference(unit_resolution,[status(thm)],[19377, 2492, 4234, 3762, 17822, 8712])).
% 29.01/19.23 tff(19379,plain,
% 29.01/19.23 ($false),
% 29.01/19.23 inference(unit_resolution,[status(thm)],[19378, 19371, 19366])).
% 29.01/19.23 tff(19380,plain,((~(f6(f7(c2), c3) = c1)) | (~(f7(c1) = c1)) | (~(f10(c1) = c1)) | big_f(f9(c1, c1), f10(c1)) | big_f(c1, f10(f9(c1, c1))) | (~(f10(c2) = c1)) | (~(c3 = c2)) | (~(f7(c2) = c1)) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.01/19.23 tff(19381,plain,
% 29.01/19.23 (big_f(c1, f10(f9(c1, c1)))),
% 29.01/19.23 inference(unit_resolution,[status(thm)],[19380, 19352, 3762, 8712, 4234, 11819, 67, 292, 1498, 11752])).
% 29.01/19.23 tff(19382,plain,
% 29.01/19.23 (big_f(f7(f7(c2)), f6(f7(c2), c3))),
% 29.01/19.23 inference(modus_ponens,[status(thm)],[19381, 19360])).
% 29.01/19.23 tff(19383,plain,
% 29.01/19.23 (big_f(f7(f9(c1, c1)), c1)),
% 29.01/19.23 inference(modus_ponens,[status(thm)],[19382, 19357])).
% 29.01/19.23 tff(19384,plain,
% 29.01/19.23 ((c2 = c1) <=> (f9(c1, c1) = c1)),
% 29.01/19.23 inference(monotonicity,[status(thm)],[19330])).
% 29.01/19.23 tff(19385,plain,
% 29.01/19.23 ((~(c2 = c1)) <=> (~(f9(c1, c1) = c1))),
% 29.01/19.23 inference(monotonicity,[status(thm)],[19384])).
% 29.01/19.23 tff(19386,plain,
% 29.01/19.23 (~(f9(c1, c1) = c1)),
% 29.01/19.23 inference(modus_ponens,[status(thm)],[75, 19385])).
% 29.01/19.23 tff(19387,plain,
% 29.01/19.23 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (c1 = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), c1)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (c1 = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), c1)))),
% 29.01/19.23 inference(rewrite,[status(thm)],[])).
% 29.01/19.23 tff(19388,plain,
% 29.01/19.23 (((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (c1 = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), c1))) <=> ((f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (c1 = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), c1)))),
% 29.01/19.23 inference(rewrite,[status(thm)],[])).
% 29.01/19.23 tff(19389,plain,
% 29.01/19.23 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (c1 = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), c1)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (c1 = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), c1))))),
% 29.01/19.23 inference(monotonicity,[status(thm)],[19388])).
% 29.01/19.23 tff(19390,plain,
% 29.01/19.23 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (c1 = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), c1)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (c1 = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), c1)))),
% 29.01/19.23 inference(transitivity,[status(thm)],[19389, 19387])).
% 29.01/19.23 tff(19391,plain,
% 29.01/19.23 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (c1 = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), c1)))),
% 29.01/19.23 inference(quant_inst,[status(thm)],[])).
% 29.01/19.23 tff(19392,plain,
% 29.01/19.23 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (c1 = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), c1))),
% 29.01/19.23 inference(modus_ponens,[status(thm)],[19391, 19390])).
% 29.01/19.23 tff(19393,plain,
% 29.01/19.23 (c1 = f5(f9(c1, c1))),
% 29.01/19.23 inference(unit_resolution,[status(thm)],[19392, 676, 3762, 19386, 8712, 19383, 17832])).
% 29.01/19.23 tff(19394,plain,
% 29.01/19.23 (f5(f9(c1, c1)) = c1),
% 29.01/19.23 inference(symmetry,[status(thm)],[19393])).
% 29.01/19.23 tff(19395,plain,
% 29.01/19.23 (f9(c1, c1) = c1),
% 29.01/19.23 inference(transitivity,[status(thm)],[18436, 1498, 433, 19327, 19394])).
% 29.01/19.23 tff(19396,plain,
% 29.01/19.23 ($false),
% 29.01/19.23 inference(unit_resolution,[status(thm)],[19386, 19395])).
% 29.01/19.23 tff(19397,plain,((~(c4 = c2)) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(c4 = f5(f9(c1, c1)))) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | (~(f10(c1) = c1)) | big_f(f9(c1, c1), f10(c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~(f7(c2) = c1)) | (~(c3 = c2)) | (~(f7(c1) = c1)) | (~big_f(f7(c2), f5(c2)))), inference(lemma,lemma(discharge,[]))).
% 29.01/19.23 tff(19398,plain,
% 29.01/19.23 (~(c4 = c2)),
% 29.01/19.23 inference(unit_resolution,[status(thm)],[19397, 19316, 1498, 11752, 11819, 3762, 19299, 17832, 292, 67, 19294, 19319])).
% 29.01/19.23 tff(19399,plain,
% 29.01/19.23 (c4 = c1),
% 29.01/19.23 inference(unit_resolution,[status(thm)],[461, 19398])).
% 29.01/19.23 tff(19400,plain,
% 29.01/19.23 (f5(f9(c1, c1)) = c4),
% 29.01/19.23 inference(symmetry,[status(thm)],[19316])).
% 29.01/19.23 tff(19401,plain,
% 29.01/19.23 (f5(c2) = f10(f9(c1, c1))),
% 29.01/19.23 inference(transitivity,[status(thm)],[19194, 19400, 19399, 12231, 19302])).
% 29.01/19.23 tff(19402,plain,
% 29.01/19.23 (big_f(f7(c2), f5(c2)) <=> big_f(c1, f10(f9(c1, c1)))),
% 29.01/19.23 inference(monotonicity,[status(thm)],[292, 19401])).
% 29.01/19.23 tff(19403,plain,
% 29.01/19.23 (big_f(f7(c2), f5(c2)) <=> big_f(f7(c2), c1)),
% 29.01/19.23 inference(transitivity,[status(thm)],[19402, 19301, 19300])).
% 29.01/19.23 tff(19404,plain,
% 29.01/19.23 (big_f(f7(c2), c1)),
% 29.01/19.23 inference(modus_ponens,[status(thm)],[19319, 19403])).
% 29.01/19.23 tff(19405,plain,
% 29.01/19.23 (big_f(f7(c1), f6(c1, c1))),
% 29.01/19.23 inference(unit_resolution,[status(thm)],[19046, 19404, 11819, 19299, 3762, 292, 19294, 11752])).
% 29.01/19.23 tff(19406,plain,
% 29.01/19.23 (big_f(f7(f9(c1, c1)), f6(c1, c1))),
% 29.01/19.23 inference(modus_ponens,[status(thm)],[19405, 19298])).
% 29.01/19.23 tff(19407,plain,
% 29.01/19.23 (~(f6(c1, c1) = c1)),
% 29.01/19.23 inference(unit_resolution,[status(thm)],[10042, 19405, 3762, 17822, 19299, 19294])).
% 29.01/19.23 tff(19408,assumption,(big_f(f7(f9(c1, c1)), f6(c1, c1))), introduced(assumption)).
% 29.01/19.23 tff(19409,plain,
% 29.01/19.23 (f5(f9(c1, c1)) = c1),
% 29.01/19.23 inference(transitivity,[status(thm)],[19328, 480])).
% 29.01/19.23 tff(19410,plain,
% 29.01/19.23 ((f6(c1, c1) = f5(f9(c1, c1))) <=> (f6(c1, c1) = c1)),
% 29.01/19.23 inference(monotonicity,[status(thm)],[19409])).
% 29.01/19.23 tff(19411,plain,
% 29.01/19.23 ((f6(c1, c1) = c1) <=> (f6(c1, c1) = f5(f9(c1, c1)))),
% 29.01/19.23 inference(symmetry,[status(thm)],[19410])).
% 29.01/19.23 tff(19412,plain,
% 29.01/19.23 ((~(f6(c1, c1) = c1)) <=> (~(f6(c1, c1) = f5(f9(c1, c1))))),
% 29.01/19.23 inference(monotonicity,[status(thm)],[19411])).
% 29.01/19.23 tff(19413,plain,
% 29.01/19.23 (~(f6(c1, c1) = f5(f9(c1, c1)))),
% 29.01/19.23 inference(modus_ponens,[status(thm)],[28, 19412])).
% 29.01/19.23 tff(19414,plain,
% 29.01/19.23 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f7(f9(c1, c1)), f6(c1, c1))) | (f6(c1, c1) = f5(f9(c1, c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f7(f9(c1, c1)), f6(c1, c1))) | (f6(c1, c1) = f5(f9(c1, c1))))),
% 29.01/19.23 inference(rewrite,[status(thm)],[])).
% 29.01/19.23 tff(19415,plain,
% 29.01/19.23 (((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (f6(c1, c1) = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), f6(c1, c1)))) <=> ((f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f7(f9(c1, c1)), f6(c1, c1))) | (f6(c1, c1) = f5(f9(c1, c1))))),
% 29.01/19.23 inference(rewrite,[status(thm)],[])).
% 29.01/19.23 tff(19416,plain,
% 29.01/19.23 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (f6(c1, c1) = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), f6(c1, c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f7(f9(c1, c1)), f6(c1, c1))) | (f6(c1, c1) = f5(f9(c1, c1)))))),
% 29.01/19.23 inference(monotonicity,[status(thm)],[19415])).
% 29.01/19.23 tff(19417,plain,
% 29.01/19.23 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (f6(c1, c1) = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), f6(c1, c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f7(f9(c1, c1)), f6(c1, c1))) | (f6(c1, c1) = f5(f9(c1, c1))))),
% 29.01/19.23 inference(transitivity,[status(thm)],[19416, 19414])).
% 29.01/19.23 tff(19418,plain,
% 29.01/19.23 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (f6(c1, c1) = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), f6(c1, c1))))),
% 29.01/19.23 inference(quant_inst,[status(thm)],[])).
% 29.01/19.23 tff(19419,plain,
% 29.01/19.23 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f7(f9(c1, c1)), f6(c1, c1))) | (f6(c1, c1) = f5(f9(c1, c1)))),
% 29.01/19.23 inference(modus_ponens,[status(thm)],[19418, 19417])).
% 29.01/19.23 tff(19420,plain,
% 29.01/19.23 ((~big_f(f7(f9(c1, c1)), f6(c1, c1))) | (f6(c1, c1) = f5(f9(c1, c1)))),
% 29.01/19.23 inference(unit_resolution,[status(thm)],[19419, 676, 3762, 4070, 8712, 17832])).
% 29.01/19.23 tff(19421,plain,
% 29.01/19.23 ($false),
% 29.01/19.23 inference(unit_resolution,[status(thm)],[19420, 19413, 19408])).
% 29.01/19.23 tff(19422,plain,((~big_f(f7(f9(c1, c1)), f6(c1, c1))) | (~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (f6(c1, c1) = c1) | (~(c4 = f5(f9(c1, c1)))) | (~(c4 = c1))), inference(lemma,lemma(discharge,[]))).
% 29.01/19.23 tff(19423,plain,
% 29.01/19.23 (~big_f(f7(f9(c1, c1)), f6(c1, c1))),
% 29.01/19.23 inference(unit_resolution,[status(thm)],[19422, 19299, 17822, 3762, 17832, 19407, 19316, 19399])).
% 29.01/19.23 tff(19424,plain,
% 29.01/19.23 ($false),
% 29.01/19.23 inference(unit_resolution,[status(thm)],[19423, 19406])).
% 29.01/19.23 tff(19425,plain,(big_f(c2, c1) | (~(f7(c2) = c1)) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | (~(f10(c1) = c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~(c3 = c2)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 29.01/19.23 tff(19426,plain,
% 29.01/19.23 (~(c3 = c2)),
% 29.01/19.23 inference(unit_resolution,[status(thm)],[19425, 19261, 1498, 11752, 11819, 121, 292, 17832, 2])).
% 29.01/19.23 tff(19427,plain,
% 29.01/19.23 (c3 = c1),
% 29.01/19.23 inference(unit_resolution,[status(thm)],[180, 19426])).
% 29.01/19.23 tff(19428,plain,
% 29.01/19.23 ($false),
% 29.01/19.23 inference(unit_resolution,[status(thm)],[18874, 19427, 19268, 292, 19267, 19261, 19132, 19155])).
% 29.01/19.23 tff(19429,plain,(big_f(c1, f9(c1, c1)) | (~(f7(c2) = c1)) | (~(f9(f10(c2), f4(c4)) = c2)) | big_f(c2, c1) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | big_f(c2, c2) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~big_f(c1, c1)) | (~(f5(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.01/19.23 tff(19430,plain,
% 29.01/19.23 (big_f(c2, c1)),
% 29.01/19.23 inference(unit_resolution,[status(thm)],[19429, 19127, 1498, 22, 11752, 11819, 121, 17818, 4686, 186])).
% 29.01/19.23 tff(19431,plain,
% 29.01/19.23 (big_f(f9(c1, c1), f10(f9(c1, c1)))),
% 29.01/19.23 inference(modus_ponens,[status(thm)],[19430, 19123])).
% 29.01/19.23 tff(19432,plain,
% 29.01/19.23 (big_f(c1, f10(f9(c1, c1)))),
% 29.01/19.23 inference(modus_ponens,[status(thm)],[4932, 17983])).
% 29.01/19.23 tff(19433,plain,
% 29.01/19.23 (~(f6(f7(c2), c3) = c1)),
% 29.01/19.23 inference(unit_resolution,[status(thm)],[10018, 28, 292, 172])).
% 29.01/19.23 tff(19434,plain,
% 29.01/19.23 (f6(f7(c2), c3) = c2),
% 29.01/19.23 inference(unit_resolution,[status(thm)],[2391, 19433])).
% 29.01/19.23 tff(19435,plain,
% 29.01/19.23 (f6(c1, c1) = f9(c1, c1)),
% 29.01/19.23 inference(transitivity,[status(thm)],[5958, 19434, 17733, 17726])).
% 29.01/19.23 tff(19436,plain,
% 29.01/19.23 (big_f(f7(f9(c1, c1)), f6(c1, c1)) <=> big_f(c1, f9(c1, c1))),
% 29.01/19.23 inference(monotonicity,[status(thm)],[17984, 19435])).
% 29.01/19.23 tff(19437,plain,
% 29.01/19.23 (big_f(c1, f9(c1, c1)) <=> big_f(f7(f9(c1, c1)), f6(c1, c1))),
% 29.01/19.23 inference(symmetry,[status(thm)],[19436])).
% 29.01/19.23 tff(19438,plain,
% 29.01/19.23 (big_f(c1, f9(c1, c1)) <=> big_f(f7(f7(c2)), f6(f7(c2), c3))),
% 29.01/19.23 inference(transitivity,[status(thm)],[19437, 19208, 18497])).
% 29.01/19.23 tff(19439,plain,
% 29.01/19.23 ((~big_f(c1, f9(c1, c1))) <=> (~big_f(f7(f7(c2)), f6(f7(c2), c3)))),
% 29.01/19.23 inference(monotonicity,[status(thm)],[19438])).
% 29.01/19.23 tff(19440,plain,
% 29.01/19.23 (~big_f(f7(f7(c2)), f6(f7(c2), c3))),
% 29.01/19.23 inference(modus_ponens,[status(thm)],[4686, 19439])).
% 29.01/19.23 tff(19441,plain,
% 29.01/19.23 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(c1, f10(f9(c1, c1)))) | (c1 = f8(f9(c1, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(c1, f10(f9(c1, c1)))) | (c1 = f8(f9(c1, c1))))),
% 29.01/19.23 inference(rewrite,[status(thm)],[])).
% 29.01/19.23 tff(19442,plain,
% 29.01/19.23 (((f10(f9(c1, c1)) = f9(c1, c1)) | (c1 = f8(f9(c1, c1))) | (~big_f(c1, f10(f9(c1, c1)))) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1))) <=> (big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(c1, f10(f9(c1, c1)))) | (c1 = f8(f9(c1, c1))))),
% 29.01/19.23 inference(rewrite,[status(thm)],[])).
% 29.01/19.23 tff(19443,plain,
% 29.01/19.23 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f9(c1, c1)) = f9(c1, c1)) | (c1 = f8(f9(c1, c1))) | (~big_f(c1, f10(f9(c1, c1)))) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(c1, f10(f9(c1, c1)))) | (c1 = f8(f9(c1, c1)))))),
% 29.01/19.23 inference(monotonicity,[status(thm)],[19442])).
% 29.01/19.23 tff(19444,plain,
% 29.01/19.23 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f9(c1, c1)) = f9(c1, c1)) | (c1 = f8(f9(c1, c1))) | (~big_f(c1, f10(f9(c1, c1)))) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(c1, f10(f9(c1, c1)))) | (c1 = f8(f9(c1, c1))))),
% 29.01/19.23 inference(transitivity,[status(thm)],[19443, 19441])).
% 29.01/19.23 tff(19445,plain,
% 29.01/19.23 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f9(c1, c1)) = f9(c1, c1)) | (c1 = f8(f9(c1, c1))) | (~big_f(c1, f10(f9(c1, c1)))) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1)))),
% 29.01/19.24 inference(quant_inst,[status(thm)],[])).
% 29.01/19.24 tff(19446,plain,
% 29.01/19.24 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(c1, f10(f9(c1, c1)))) | (c1 = f8(f9(c1, c1)))),
% 29.01/19.24 inference(modus_ponens,[status(thm)],[19445, 19444])).
% 29.01/19.24 tff(19447,plain,
% 29.01/19.24 (c1 = f8(f9(c1, c1))),
% 29.01/19.24 inference(unit_resolution,[status(thm)],[19446, 2662, 4234, 65, 28, 17834, 18024])).
% 29.01/19.24 tff(19448,plain,
% 29.01/19.24 (f8(f9(c1, c1)) = c1),
% 29.01/19.24 inference(symmetry,[status(thm)],[19447])).
% 29.01/19.24 tff(19449,plain,
% 29.01/19.24 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (f6(c1, c1) = c1) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (f6(c1, c1) = c1) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))))),
% 29.01/19.24 inference(rewrite,[status(thm)],[])).
% 29.01/19.24 tff(19450,plain,
% 29.01/19.24 (((f10(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1))) <=> (big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (f6(c1, c1) = c1) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))))),
% 29.01/19.24 inference(rewrite,[status(thm)],[])).
% 29.01/19.24 tff(19451,plain,
% 29.01/19.24 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (f6(c1, c1) = c1) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1))))))),
% 29.01/19.24 inference(monotonicity,[status(thm)],[19450])).
% 29.01/19.24 tff(19452,plain,
% 29.01/19.24 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (f6(c1, c1) = c1) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))))),
% 29.01/19.24 inference(transitivity,[status(thm)],[19451, 19449])).
% 29.01/19.24 tff(19453,plain,
% 29.01/19.24 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1)))),
% 29.01/19.24 inference(quant_inst,[status(thm)],[])).
% 29.01/19.24 tff(19454,plain,
% 29.01/19.24 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (f6(c1, c1) = c1) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1))))),
% 29.01/19.24 inference(modus_ponens,[status(thm)],[19453, 19452])).
% 29.01/19.24 tff(19455,plain,
% 29.01/19.24 (f9(c1, c1) = f8(f9(c1, c1))),
% 29.01/19.24 inference(unit_resolution,[status(thm)],[19454, 2662, 4234, 65, 28, 17834, 17819])).
% 29.01/19.24 tff(19456,plain,
% 29.01/19.24 (f9(c1, c1) = c1),
% 29.01/19.24 inference(transitivity,[status(thm)],[19455, 19448])).
% 29.01/19.24 tff(19457,plain,
% 29.01/19.24 ($false),
% 29.01/19.24 inference(unit_resolution,[status(thm)],[4070, 19456])).
% 29.01/19.24 tff(19458,plain,((f6(c1, c1) = c1) | (f9(c1, c1) = c1) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(c1, f10(f9(c1, c1)))) | (~big_f(f9(c1, c1), f10(f9(c1, c1))))), inference(lemma,lemma(discharge,[]))).
% 29.01/19.24 tff(19459,plain,
% 29.01/19.24 (big_f(f7(c1), f6(c1, c1))),
% 29.01/19.24 inference(unit_resolution,[status(thm)],[19458, 28, 17823, 18024, 17819, 4234, 17822])).
% 29.01/19.24 tff(19460,plain,
% 29.01/19.24 (big_f(f7(f7(c2)), f6(f7(c2), c3))),
% 29.01/19.24 inference(unit_resolution,[status(thm)],[10192, 19459, 292, 172])).
% 29.01/19.24 tff(19461,plain,
% 29.01/19.24 ($false),
% 29.01/19.24 inference(unit_resolution,[status(thm)],[19460, 19440])).
% 29.01/19.24 tff(19462,plain,((f6(c1, c1) = c1) | big_f(c1, f9(c1, c1)) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | (~(c3 = c1)) | (~(f7(c2) = c1)) | (~(f7(c1) = c1)) | (~big_f(c1, f10(f9(c1, c1)))) | (~big_f(f9(c1, c1), f10(f9(c1, c1))))), inference(lemma,lemma(discharge,[]))).
% 29.01/19.24 tff(19463,plain,
% 29.01/19.24 (f6(c1, c1) = c1),
% 29.01/19.24 inference(unit_resolution,[status(thm)],[19462, 4234, 1498, 11752, 11819, 172, 292, 4686, 19432, 17819])).
% 29.01/19.24 tff(19464,plain,
% 29.01/19.24 (big_f(f7(f9(c1, c1)), f6(c1, c1)) <=> big_f(c1, c1)),
% 29.01/19.24 inference(monotonicity,[status(thm)],[17984, 19463])).
% 29.01/19.24 tff(19465,plain,
% 29.01/19.24 (big_f(c1, c1) <=> big_f(f7(f9(c1, c1)), f6(c1, c1))),
% 29.01/19.24 inference(symmetry,[status(thm)],[19464])).
% 29.01/19.24 tff(19466,plain,
% 29.01/19.24 (big_f(c1, c1) <=> big_f(f7(c1), f6(c1, c1))),
% 29.01/19.24 inference(transitivity,[status(thm)],[19465, 19208])).
% 29.01/19.24 tff(19467,plain,
% 29.01/19.24 (big_f(f7(c1), f6(c1, c1))),
% 29.01/19.24 inference(modus_ponens,[status(thm)],[4932, 19466])).
% 29.01/19.24 tff(19468,plain,
% 29.01/19.24 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(c1, f10(f9(c1, c1)))) | (c1 = f8(f9(c1, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(c1, f10(f9(c1, c1)))) | (c1 = f8(f9(c1, c1))))),
% 29.01/19.24 inference(rewrite,[status(thm)],[])).
% 29.01/19.24 tff(19469,plain,
% 29.01/19.24 (((f10(f9(c1, c1)) = f9(c1, c1)) | (c1 = f8(f9(c1, c1))) | (~big_f(c1, f10(f9(c1, c1)))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1)))) <=> ((~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(c1, f10(f9(c1, c1)))) | (c1 = f8(f9(c1, c1))))),
% 29.01/19.24 inference(rewrite,[status(thm)],[])).
% 29.01/19.24 tff(19470,plain,
% 29.01/19.24 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f9(c1, c1)) = f9(c1, c1)) | (c1 = f8(f9(c1, c1))) | (~big_f(c1, f10(f9(c1, c1)))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(c1, f10(f9(c1, c1)))) | (c1 = f8(f9(c1, c1)))))),
% 29.01/19.24 inference(monotonicity,[status(thm)],[19469])).
% 29.01/19.24 tff(19471,plain,
% 29.01/19.24 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f9(c1, c1)) = f9(c1, c1)) | (c1 = f8(f9(c1, c1))) | (~big_f(c1, f10(f9(c1, c1)))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(c1, f10(f9(c1, c1)))) | (c1 = f8(f9(c1, c1))))),
% 29.01/19.24 inference(transitivity,[status(thm)],[19470, 19468])).
% 29.01/19.24 tff(19472,plain,
% 29.01/19.24 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f9(c1, c1)) = f9(c1, c1)) | (c1 = f8(f9(c1, c1))) | (~big_f(c1, f10(f9(c1, c1)))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))),
% 29.01/19.24 inference(quant_inst,[status(thm)],[])).
% 29.01/19.24 tff(19473,plain,
% 29.01/19.24 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(c1, f10(f9(c1, c1)))) | (c1 = f8(f9(c1, c1)))),
% 29.01/19.24 inference(modus_ponens,[status(thm)],[19472, 19471])).
% 29.01/19.24 tff(19474,plain,
% 29.01/19.24 (c1 = f8(f9(c1, c1))),
% 29.01/19.24 inference(unit_resolution,[status(thm)],[19473, 2730, 4234, 19467, 19463, 17823, 19432])).
% 29.01/19.24 tff(19475,plain,
% 29.01/19.24 (f8(f9(c1, c1)) = c1),
% 29.01/19.24 inference(symmetry,[status(thm)],[19474])).
% 29.01/19.24 tff(19476,plain,
% 29.01/19.24 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (f9(c1, c1) = f8(f9(c1, c1))) | (~(f6(c1, c1) = c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (f9(c1, c1) = f8(f9(c1, c1))) | (~(f6(c1, c1) = c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))))),
% 29.01/19.24 inference(rewrite,[status(thm)],[])).
% 29.01/19.24 tff(19477,plain,
% 29.01/19.24 (((f10(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1)))) <=> ((~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (f9(c1, c1) = f8(f9(c1, c1))) | (~(f6(c1, c1) = c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))))),
% 29.01/19.24 inference(rewrite,[status(thm)],[])).
% 29.01/19.24 tff(19478,plain,
% 29.01/19.24 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (f9(c1, c1) = f8(f9(c1, c1))) | (~(f6(c1, c1) = c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1))))))),
% 29.01/19.24 inference(monotonicity,[status(thm)],[19477])).
% 29.01/19.24 tff(19479,plain,
% 29.01/19.24 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (f9(c1, c1) = f8(f9(c1, c1))) | (~(f6(c1, c1) = c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))))),
% 29.01/19.24 inference(transitivity,[status(thm)],[19478, 19476])).
% 29.01/19.24 tff(19480,plain,
% 29.01/19.24 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))),
% 29.01/19.24 inference(quant_inst,[status(thm)],[])).
% 29.01/19.24 tff(19481,plain,
% 29.01/19.24 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (f9(c1, c1) = f8(f9(c1, c1))) | (~(f6(c1, c1) = c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1))))),
% 29.01/19.24 inference(modus_ponens,[status(thm)],[19480, 19479])).
% 29.01/19.24 tff(19482,plain,
% 29.01/19.24 (f9(c1, c1) = f8(f9(c1, c1))),
% 29.01/19.24 inference(unit_resolution,[status(thm)],[19481, 2730, 4234, 19467, 19463, 17823, 17819])).
% 29.01/19.24 tff(19483,plain,
% 29.01/19.24 (f9(c1, c1) = c1),
% 29.01/19.24 inference(transitivity,[status(thm)],[19482, 19475])).
% 29.01/19.24 tff(19484,plain,
% 29.01/19.24 ($false),
% 29.01/19.24 inference(unit_resolution,[status(thm)],[17822, 19483])).
% 29.01/19.24 tff(19485,plain,((~(f7(c1) = c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (~big_f(c1, c1)) | (~(f7(c2) = c1)) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | (~(c3 = c1)) | big_f(c1, f9(c1, c1))), inference(lemma,lemma(discharge,[]))).
% 29.01/19.24 tff(19486,plain,
% 29.01/19.24 (~big_f(f9(c1, c1), f10(f9(c1, c1)))),
% 29.01/19.24 inference(unit_resolution,[status(thm)],[19485, 172, 1498, 22, 4234, 11752, 11819, 4686, 19127])).
% 29.01/19.24 tff(19487,plain,
% 29.01/19.24 ($false),
% 29.01/19.24 inference(unit_resolution,[status(thm)],[19486, 19431])).
% 29.01/19.24 tff(19488,plain,((~(c3 = c1)) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | big_f(c2, c2) | big_f(c1, f9(c1, c1)) | (~(f5(c1) = c2)) | (~(f7(c1) = c1)) | (f7(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 29.01/19.24 tff(19489,plain,
% 29.01/19.24 (~(c3 = c1)),
% 29.01/19.24 inference(unit_resolution,[status(thm)],[19488, 4686, 11752, 11819, 121, 1498, 186, 19120, 17])).
% 29.01/19.24 tff(19490,plain,
% 29.01/19.24 (c3 = c2),
% 29.01/19.24 inference(unit_resolution,[status(thm)],[180, 19489])).
% 29.01/19.24 tff(19491,plain,
% 29.01/19.24 (f9(c1, c1) = c3),
% 29.01/19.24 inference(modus_ponens,[status(thm)],[19490, 17736])).
% 29.01/19.24 tff(19492,plain,
% 29.01/19.24 (big_f(c2, c1)),
% 29.01/19.24 inference(unit_resolution,[status(thm)],[19425, 19490, 1498, 11752, 11819, 121, 22, 17818, 3762])).
% 29.01/19.24 tff(19493,plain,
% 29.01/19.24 ((~big_f(f9(c1, c1), c1)) <=> (~big_f(c2, c1))),
% 29.01/19.24 inference(monotonicity,[status(thm)],[19121])).
% 29.01/19.24 tff(19494,plain,
% 29.01/19.24 (~big_f(c2, c1)),
% 29.01/19.24 inference(modus_ponens,[status(thm)],[10020, 19493])).
% 29.01/19.24 tff(19495,plain,
% 29.01/19.24 ($false),
% 29.01/19.24 inference(unit_resolution,[status(thm)],[348, 19494])).
% 29.01/19.24 tff(19496,plain,((~big_f(c2, c1)) | big_f(f9(c1, c1), c1) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.01/19.24 tff(19497,plain,
% 29.01/19.24 (big_f(f9(c1, c1), c1)),
% 29.01/19.24 inference(unit_resolution,[status(thm)],[19496, 19492, 1498, 11752, 11819])).
% 29.01/19.24 tff(19498,plain,
% 29.01/19.24 (~big_f(f7(c2), c1)),
% 29.01/19.24 inference(unit_resolution,[status(thm)],[18147, 19497, 1498, 11752, 22, 17818, 19490, 11819])).
% 29.01/19.24 tff(19499,plain,
% 29.01/19.24 (~big_f(c1, c1)),
% 29.01/19.24 inference(unit_resolution,[status(thm)],[19131, 19498, 1498, 22, 11752, 11819])).
% 29.01/19.24 tff(19500,plain,
% 29.01/19.24 (big_f(c1, f9(c1, c1)) <=> big_f(c1, c2)),
% 29.01/19.24 inference(symmetry,[status(thm)],[17745])).
% 29.01/19.24 tff(19501,plain,
% 29.01/19.24 (c1 = f7(f9(c1, c1))),
% 29.01/19.24 inference(transitivity,[status(thm)],[125, 17739])).
% 29.01/19.24 tff(19502,plain,
% 29.01/19.24 (big_f(c1, f9(c1, c1)) <=> big_f(f7(f9(c1, c1)), f9(c1, c1))),
% 29.01/19.24 inference(monotonicity,[status(thm)],[19501])).
% 29.01/19.24 tff(19503,plain,
% 29.01/19.24 (big_f(f7(f9(c1, c1)), f9(c1, c1)) <=> big_f(c1, f9(c1, c1))),
% 29.01/19.24 inference(symmetry,[status(thm)],[19502])).
% 29.01/19.24 tff(19504,plain,
% 29.01/19.24 (big_f(f7(f9(c1, c1)), f9(c1, c1)) <=> big_f(f7(c2), f9(c1, c1))),
% 29.01/19.24 inference(monotonicity,[status(thm)],[17729])).
% 29.01/19.24 tff(19505,plain,
% 29.01/19.24 (big_f(f7(c2), f9(c1, c1)) <=> big_f(f7(f9(c1, c1)), f9(c1, c1))),
% 29.01/19.24 inference(symmetry,[status(thm)],[19504])).
% 29.01/19.24 tff(19506,plain,
% 29.01/19.24 (big_f(f7(c2), c2) <=> big_f(c1, c2)),
% 29.01/19.24 inference(transitivity,[status(thm)],[17737, 19505, 19503, 19500])).
% 29.01/19.24 tff(19507,plain,
% 29.01/19.24 (~big_f(f7(c2), c1)),
% 29.01/19.24 inference(unit_resolution,[status(thm)],[19094, 66, 22, 1498, 11752, 11819])).
% 29.01/19.24 tff(19508,assumption,(f9(c1, c1) = c3), introduced(assumption)).
% 29.01/19.24 tff(19509,plain,
% 29.01/19.24 (big_f(f9(c1, c1), f10(c1)) <=> big_f(f9(c1, c1), f9(c1, c1))),
% 29.01/19.24 inference(symmetry,[status(thm)],[19166])).
% 29.01/19.24 tff(19510,plain,
% 29.01/19.24 (big_f(c1, c2) <=> big_f(f7(f9(c1, c1)), f9(c1, c1))),
% 29.01/19.24 inference(transitivity,[status(thm)],[17745, 19502])).
% 29.01/19.24 tff(19511,plain,
% 29.01/19.24 ((~big_f(c1, c2)) <=> (~big_f(f7(f9(c1, c1)), f9(c1, c1)))),
% 29.01/19.24 inference(monotonicity,[status(thm)],[19510])).
% 29.01/19.24 tff(19512,plain,
% 29.01/19.24 (~big_f(f7(f9(c1, c1)), f9(c1, c1))),
% 29.01/19.24 inference(modus_ponens,[status(thm)],[17749, 19511])).
% 29.01/19.24 tff(19513,plain,
% 29.01/19.24 (~big_f(c1, f10(c1))),
% 29.01/19.24 inference(unit_resolution,[status(thm)],[12239, 17749, 11819, 18807])).
% 29.01/19.24 tff(19514,plain,
% 29.01/19.24 (f5(f10(c1)) = f5(f9(c1, c1))),
% 29.01/19.24 inference(monotonicity,[status(thm)],[19156])).
% 29.01/19.24 tff(19515,plain,
% 29.01/19.24 (f5(f10(c1)) = f5(c2)),
% 29.01/19.24 inference(transitivity,[status(thm)],[19514, 17827])).
% 29.01/19.24 tff(19516,plain,
% 29.01/19.24 (f7(f10(c1)) = f7(f9(c1, c1))),
% 29.01/19.24 inference(monotonicity,[status(thm)],[19156])).
% 29.01/19.24 tff(19517,plain,
% 29.01/19.24 (f7(f10(c1)) = f7(c2)),
% 29.01/19.24 inference(transitivity,[status(thm)],[19516, 17729])).
% 29.01/19.24 tff(19518,plain,
% 29.01/19.24 (big_f(f7(f10(c1)), f5(f10(c1))) <=> big_f(f7(c2), f5(c2))),
% 29.01/19.24 inference(monotonicity,[status(thm)],[19517, 19515])).
% 29.01/19.24 tff(19519,plain,
% 29.01/19.24 (f7(f10(c1)) = c1),
% 29.01/19.24 inference(transitivity,[status(thm)],[19516, 17729, 22])).
% 29.01/19.24 tff(19520,plain,
% 29.01/19.24 ((f7(f10(c1)) = f10(c1)) <=> (c1 = f9(c1, c1))),
% 29.01/19.24 inference(monotonicity,[status(thm)],[19519, 19156])).
% 29.01/19.24 tff(19521,plain,
% 29.01/19.24 ((f7(f10(c1)) = f10(c1)) <=> (f9(c1, c1) = c1)),
% 29.01/19.24 inference(transitivity,[status(thm)],[19520, 17725])).
% 29.01/19.24 tff(19522,plain,
% 29.01/19.24 ((f9(c1, c1) = c1) <=> (f7(f10(c1)) = f10(c1))),
% 29.01/19.24 inference(symmetry,[status(thm)],[19521])).
% 29.01/19.24 tff(19523,plain,
% 29.01/19.24 ((~(f9(c1, c1) = c1)) <=> (~(f7(f10(c1)) = f10(c1)))),
% 29.01/19.24 inference(monotonicity,[status(thm)],[19522])).
% 29.01/19.24 tff(19524,plain,
% 29.01/19.24 (~(f7(f10(c1)) = f10(c1))),
% 29.01/19.24 inference(modus_ponens,[status(thm)],[17791, 19523])).
% 29.01/19.24 tff(19525,plain,
% 29.01/19.24 (big_f(f9(c1, c1), f10(c1)) <=> big_f(c2, c2)),
% 29.01/19.24 inference(monotonicity,[status(thm)],[18437, 16])).
% 29.01/19.24 tff(19526,plain,
% 29.01/19.24 (big_f(c2, c2) <=> big_f(f9(c1, c1), f10(c1))),
% 29.01/19.24 inference(symmetry,[status(thm)],[19525])).
% 29.01/19.24 tff(19527,plain,
% 29.01/19.24 (big_f(f9(c1, c1), f10(c1))),
% 29.01/19.24 inference(modus_ponens,[status(thm)],[1345, 19526])).
% 29.01/19.24 tff(19528,plain,
% 29.01/19.24 ($false),
% 29.01/19.24 inference(unit_resolution,[status(thm)],[8712, 19527])).
% 29.01/19.24 tff(19529,plain,((~(f9(f10(c2), f4(c4)) = c2)) | big_f(f9(c1, c1), f10(c1)) | (~big_f(c2, c2)) | (~(f10(c1) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.01/19.24 tff(19530,plain,
% 29.01/19.24 (~big_f(c2, c2)),
% 29.01/19.24 inference(unit_resolution,[status(thm)],[19529, 8712, 11752, 1498, 15, 11819])).
% 29.01/19.24 tff(19531,plain,
% 29.01/19.24 (~big_f(c2, f10(c1))),
% 29.01/19.24 inference(unit_resolution,[status(thm)],[6125, 19530, 15])).
% 29.01/19.24 tff(19532,plain,
% 29.01/19.24 ((c2 = f5(f10(c1))) <=> (f9(c1, c1) = f5(f9(c1, c1)))),
% 29.01/19.24 inference(monotonicity,[status(thm)],[17734, 19514])).
% 29.01/19.24 tff(19533,plain,
% 29.01/19.24 ((f9(c1, c1) = f5(f9(c1, c1))) <=> (c2 = f5(f10(c1)))),
% 29.01/19.24 inference(symmetry,[status(thm)],[19532])).
% 29.01/19.24 tff(19534,plain,
% 29.01/19.24 ((f9(c1, c1) = f5(f9(c1, c1))) <=> (f5(f10(c1)) = c2)),
% 29.01/19.24 inference(transitivity,[status(thm)],[19533, 5892])).
% 29.01/19.24 tff(19535,plain,
% 29.01/19.24 ((~(f9(c1, c1) = f5(f9(c1, c1)))) <=> (~(f5(f10(c1)) = c2))),
% 29.01/19.24 inference(monotonicity,[status(thm)],[19534])).
% 29.01/19.24 tff(19536,plain,
% 29.01/19.24 (~(f9(c1, c1) = f5(f9(c1, c1)))),
% 29.01/19.24 inference(unit_resolution,[status(thm)],[19192, 8712, 11752, 11819, 1498, 3, 17818, 17833, 3030])).
% 29.01/19.24 tff(19537,plain,
% 29.01/19.24 (~(f5(f10(c1)) = c2)),
% 29.01/19.24 inference(modus_ponens,[status(thm)],[19536, 19535])).
% 29.01/19.24 tff(19538,plain,
% 29.01/19.24 (f5(f10(c1)) = c1),
% 29.01/19.24 inference(unit_resolution,[status(thm)],[326, 19537])).
% 29.01/19.24 tff(19539,plain,
% 29.01/19.24 (~big_f(f7(c2), f5(c2))),
% 29.01/19.24 inference(unit_resolution,[status(thm)],[336, 19538, 15, 333])).
% 29.01/19.24 tff(19540,plain,
% 29.01/19.24 (~(c1 = f8(c1))),
% 29.01/19.24 inference(unit_resolution,[status(thm)],[12249, 19539, 17, 3, 3030])).
% 29.01/19.24 tff(19541,plain,
% 29.01/19.24 (~(f8(c1) = c1)),
% 29.01/19.24 inference(unit_resolution,[status(thm)],[9808, 19540])).
% 29.01/19.24 tff(19542,plain,
% 29.01/19.24 (f8(c1) = c2),
% 29.01/19.24 inference(unit_resolution,[status(thm)],[1680, 19541])).
% 29.01/19.24 tff(19543,plain,
% 29.01/19.24 (c2 = f8(c1)),
% 29.01/19.24 inference(unit_resolution,[status(thm)],[1675, 19542])).
% 29.01/19.24 tff(19544,plain,
% 29.01/19.24 (big_f(f7(f10(c1)), f5(f10(c1)))),
% 29.01/19.24 inference(unit_resolution,[status(thm)],[15818, 19543, 3, 19531, 19524])).
% 29.01/19.24 tff(19545,plain,
% 29.01/19.24 (big_f(f7(c2), f5(c2))),
% 29.01/19.24 inference(modus_ponens,[status(thm)],[19544, 19518])).
% 29.01/19.24 tff(19546,plain,
% 29.01/19.24 ($false),
% 29.01/19.24 inference(unit_resolution,[status(thm)],[19539, 19545])).
% 29.01/19.24 tff(19547,plain,(big_f(f9(c1, c1), f10(c1)) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | (f10(c1) = c1) | (f7(c2) = c2) | big_f(c1, f10(c1)) | big_f(f7(c2), c1) | big_f(f7(f9(c1, c1)), f9(c1, c1))), inference(lemma,lemma(discharge,[]))).
% 29.01/19.24 tff(19548,plain,
% 29.01/19.24 (big_f(f9(c1, c1), f10(c1))),
% 29.01/19.24 inference(unit_resolution,[status(thm)],[19547, 19513, 11752, 11819, 3, 17, 1498, 19507, 19512])).
% 29.01/19.24 tff(19549,plain,
% 29.01/19.24 (big_f(f9(c1, c1), f9(c1, c1))),
% 29.01/19.24 inference(modus_ponens,[status(thm)],[19548, 19509])).
% 29.01/19.24 tff(19550,plain,
% 29.01/19.24 (f9(c1, c1) = c4),
% 29.01/19.24 inference(transitivity,[status(thm)],[17727, 1498, 433])).
% 29.01/19.24 tff(19551,plain,
% 29.01/19.24 (f4(f9(c1, c1)) = f4(c4)),
% 29.01/19.24 inference(monotonicity,[status(thm)],[19550])).
% 29.01/19.24 tff(19552,plain,
% 29.01/19.24 (f4(c4) = f4(f9(c1, c1))),
% 29.01/19.24 inference(symmetry,[status(thm)],[19551])).
% 29.01/19.24 tff(19553,plain,
% 29.01/19.24 (c1 = f4(f9(c1, c1))),
% 29.01/19.24 inference(transitivity,[status(thm)],[16651, 19552])).
% 29.01/19.24 tff(19554,plain,
% 29.01/19.24 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c1, c1) = c3)) | (c1 = f2(f9(c1, c1))) | (~big_f(f9(c1, c1), c1)) | (~(f9(c1, c1) = c4)) | (~(c1 = f4(f9(c1, c1)))) | big_f(c1, f9(c1, c1)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(f9(c1, c1) = c3)) | (c1 = f2(f9(c1, c1))) | (~big_f(f9(c1, c1), c1)) | (~(f9(c1, c1) = c4)) | (~(c1 = f4(f9(c1, c1)))) | big_f(c1, f9(c1, c1)))),
% 29.01/19.24 inference(rewrite,[status(thm)],[])).
% 29.01/19.24 tff(19555,plain,
% 29.01/19.24 (((~(f9(c1, c1) = c3)) | (~(f9(c1, c1) = c4)) | big_f(c1, f9(c1, c1)) | (~(c1 = f4(f9(c1, c1)))) | (c1 = f2(f9(c1, c1))) | (~big_f(f9(c1, c1), c1))) <=> ((~(f9(c1, c1) = c3)) | (c1 = f2(f9(c1, c1))) | (~big_f(f9(c1, c1), c1)) | (~(f9(c1, c1) = c4)) | (~(c1 = f4(f9(c1, c1)))) | big_f(c1, f9(c1, c1)))),
% 29.01/19.24 inference(rewrite,[status(thm)],[])).
% 29.01/19.24 tff(19556,plain,
% 29.01/19.24 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c1, c1) = c3)) | (~(f9(c1, c1) = c4)) | big_f(c1, f9(c1, c1)) | (~(c1 = f4(f9(c1, c1)))) | (c1 = f2(f9(c1, c1))) | (~big_f(f9(c1, c1), c1)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c1, c1) = c3)) | (c1 = f2(f9(c1, c1))) | (~big_f(f9(c1, c1), c1)) | (~(f9(c1, c1) = c4)) | (~(c1 = f4(f9(c1, c1)))) | big_f(c1, f9(c1, c1))))),
% 29.01/19.24 inference(monotonicity,[status(thm)],[19555])).
% 29.01/19.24 tff(19557,plain,
% 29.01/19.24 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c1, c1) = c3)) | (~(f9(c1, c1) = c4)) | big_f(c1, f9(c1, c1)) | (~(c1 = f4(f9(c1, c1)))) | (c1 = f2(f9(c1, c1))) | (~big_f(f9(c1, c1), c1)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(f9(c1, c1) = c3)) | (c1 = f2(f9(c1, c1))) | (~big_f(f9(c1, c1), c1)) | (~(f9(c1, c1) = c4)) | (~(c1 = f4(f9(c1, c1)))) | big_f(c1, f9(c1, c1)))),
% 29.01/19.25 inference(transitivity,[status(thm)],[19556, 19554])).
% 29.01/19.25 tff(19558,plain,
% 29.01/19.25 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c1, c1) = c3)) | (~(f9(c1, c1) = c4)) | big_f(c1, f9(c1, c1)) | (~(c1 = f4(f9(c1, c1)))) | (c1 = f2(f9(c1, c1))) | (~big_f(f9(c1, c1), c1)))),
% 29.01/19.25 inference(quant_inst,[status(thm)],[])).
% 29.01/19.25 tff(19559,plain,
% 29.01/19.25 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(f9(c1, c1) = c3)) | (c1 = f2(f9(c1, c1))) | (~big_f(f9(c1, c1), c1)) | (~(f9(c1, c1) = c4)) | (~(c1 = f4(f9(c1, c1)))) | big_f(c1, f9(c1, c1))),
% 29.01/19.25 inference(modus_ponens,[status(thm)],[19558, 19557])).
% 29.01/19.25 tff(19560,plain,
% 29.01/19.25 ((c1 = f2(f9(c1, c1))) | (~(f9(c1, c1) = c4)) | (~(c1 = f4(f9(c1, c1))))),
% 29.01/19.25 inference(unit_resolution,[status(thm)],[19559, 5622, 19508, 8714, 4686])).
% 29.01/19.25 tff(19561,plain,
% 29.01/19.25 (c1 = f2(f9(c1, c1))),
% 29.01/19.25 inference(unit_resolution,[status(thm)],[19560, 18109, 19553])).
% 29.01/19.25 tff(19562,plain,
% 29.01/19.25 (f2(f9(c1, c1)) = c1),
% 29.01/19.25 inference(symmetry,[status(thm)],[19561])).
% 29.01/19.25 tff(19563,plain,
% 29.01/19.25 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c1, c1) = c3)) | (~(f9(c1, c1) = c4)) | (~(c1 = f4(f9(c1, c1)))) | (f9(c1, c1) = f2(f9(c1, c1))) | big_f(c1, f9(c1, c1)) | (~big_f(f9(c1, c1), f9(c1, c1))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(f9(c1, c1) = c3)) | (~(f9(c1, c1) = c4)) | (~(c1 = f4(f9(c1, c1)))) | (f9(c1, c1) = f2(f9(c1, c1))) | big_f(c1, f9(c1, c1)) | (~big_f(f9(c1, c1), f9(c1, c1))))),
% 29.01/19.25 inference(rewrite,[status(thm)],[])).
% 29.01/19.25 tff(19564,plain,
% 29.01/19.25 (((~(f9(c1, c1) = c3)) | (~(f9(c1, c1) = c4)) | big_f(c1, f9(c1, c1)) | (~(c1 = f4(f9(c1, c1)))) | (f9(c1, c1) = f2(f9(c1, c1))) | (~big_f(f9(c1, c1), f9(c1, c1)))) <=> ((~(f9(c1, c1) = c3)) | (~(f9(c1, c1) = c4)) | (~(c1 = f4(f9(c1, c1)))) | (f9(c1, c1) = f2(f9(c1, c1))) | big_f(c1, f9(c1, c1)) | (~big_f(f9(c1, c1), f9(c1, c1))))),
% 29.01/19.25 inference(rewrite,[status(thm)],[])).
% 29.01/19.25 tff(19565,plain,
% 29.01/19.25 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c1, c1) = c3)) | (~(f9(c1, c1) = c4)) | big_f(c1, f9(c1, c1)) | (~(c1 = f4(f9(c1, c1)))) | (f9(c1, c1) = f2(f9(c1, c1))) | (~big_f(f9(c1, c1), f9(c1, c1))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c1, c1) = c3)) | (~(f9(c1, c1) = c4)) | (~(c1 = f4(f9(c1, c1)))) | (f9(c1, c1) = f2(f9(c1, c1))) | big_f(c1, f9(c1, c1)) | (~big_f(f9(c1, c1), f9(c1, c1)))))),
% 29.01/19.25 inference(monotonicity,[status(thm)],[19564])).
% 29.01/19.25 tff(19566,plain,
% 29.01/19.25 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c1, c1) = c3)) | (~(f9(c1, c1) = c4)) | big_f(c1, f9(c1, c1)) | (~(c1 = f4(f9(c1, c1)))) | (f9(c1, c1) = f2(f9(c1, c1))) | (~big_f(f9(c1, c1), f9(c1, c1))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(f9(c1, c1) = c3)) | (~(f9(c1, c1) = c4)) | (~(c1 = f4(f9(c1, c1)))) | (f9(c1, c1) = f2(f9(c1, c1))) | big_f(c1, f9(c1, c1)) | (~big_f(f9(c1, c1), f9(c1, c1))))),
% 29.01/19.25 inference(transitivity,[status(thm)],[19565, 19563])).
% 29.01/19.25 tff(19567,plain,
% 29.01/19.25 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c1, c1) = c3)) | (~(f9(c1, c1) = c4)) | big_f(c1, f9(c1, c1)) | (~(c1 = f4(f9(c1, c1)))) | (f9(c1, c1) = f2(f9(c1, c1))) | (~big_f(f9(c1, c1), f9(c1, c1))))),
% 29.01/19.25 inference(quant_inst,[status(thm)],[])).
% 29.01/19.25 tff(19568,plain,
% 29.01/19.25 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(f9(c1, c1) = c3)) | (~(f9(c1, c1) = c4)) | (~(c1 = f4(f9(c1, c1)))) | (f9(c1, c1) = f2(f9(c1, c1))) | big_f(c1, f9(c1, c1)) | (~big_f(f9(c1, c1), f9(c1, c1)))),
% 29.01/19.25 inference(modus_ponens,[status(thm)],[19567, 19566])).
% 29.01/19.25 tff(19569,plain,
% 29.01/19.25 ((~(f9(c1, c1) = c4)) | (~(c1 = f4(f9(c1, c1)))) | (f9(c1, c1) = f2(f9(c1, c1)))),
% 29.01/19.25 inference(unit_resolution,[status(thm)],[19568, 5622, 19508, 17759, 4686])).
% 29.01/19.25 tff(19570,plain,
% 29.01/19.25 (f9(c1, c1) = f2(f9(c1, c1))),
% 29.01/19.25 inference(unit_resolution,[status(thm)],[19569, 18109, 19553])).
% 29.01/19.25 tff(19571,plain,
% 29.01/19.25 (f9(c1, c1) = c1),
% 29.01/19.25 inference(transitivity,[status(thm)],[19570, 19562])).
% 29.01/19.25 tff(19572,plain,
% 29.01/19.25 ($false),
% 29.01/19.25 inference(unit_resolution,[status(thm)],[17791, 19571])).
% 29.01/19.25 tff(19573,plain,((~(c4 = c2)) | (~(f9(c1, c1) = c3)) | (~big_f(f9(c1, c1), f9(c1, c1))) | big_f(c1, f9(c1, c1)) | (~big_f(f9(c1, c1), c1)) | (~(f4(c4) = c1)) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f10(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.01/19.25 tff(19574,plain,
% 29.01/19.25 (~(c4 = c2)),
% 29.01/19.25 inference(unit_resolution,[status(thm)],[19573, 19549, 19508, 4686, 8714, 11752, 1498, 11819])).
% 29.01/19.25 tff(19575,plain,
% 29.01/19.25 (c4 = c1),
% 29.01/19.25 inference(unit_resolution,[status(thm)],[461, 19574])).
% 29.01/19.25 tff(19576,plain,
% 29.01/19.25 (c1 = c4),
% 29.01/19.25 inference(unit_resolution,[status(thm)],[484, 19575])).
% 29.01/19.25 tff(19577,plain,
% 29.01/19.25 (c1 = c4),
% 29.01/19.25 inference(symmetry,[status(thm)],[19575])).
% 29.01/19.25 tff(19578,plain,
% 29.01/19.25 (f4(c1) = f4(c4)),
% 29.01/19.25 inference(monotonicity,[status(thm)],[19577])).
% 29.01/19.25 tff(19579,plain,
% 29.01/19.25 (f4(c4) = f4(c1)),
% 29.01/19.25 inference(symmetry,[status(thm)],[19578])).
% 29.01/19.25 tff(19580,plain,
% 29.01/19.25 (c1 = f4(c1)),
% 29.01/19.25 inference(transitivity,[status(thm)],[16651, 19579])).
% 29.01/19.25 tff(19581,plain,
% 29.01/19.25 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (~(f9(c1, c1) = c3)) | (c1 = f2(f9(c1, c1))) | (~big_f(f9(c1, c1), c1)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (~(f9(c1, c1) = c3)) | (c1 = f2(f9(c1, c1))) | (~big_f(f9(c1, c1), c1)))),
% 29.01/19.25 inference(rewrite,[status(thm)],[])).
% 29.01/19.25 tff(19582,plain,
% 29.01/19.25 (((~(f9(c1, c1) = c3)) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (c1 = f2(f9(c1, c1))) | (~big_f(f9(c1, c1), c1))) <=> ((~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (~(f9(c1, c1) = c3)) | (c1 = f2(f9(c1, c1))) | (~big_f(f9(c1, c1), c1)))),
% 29.01/19.25 inference(rewrite,[status(thm)],[])).
% 29.01/19.25 tff(19583,plain,
% 29.01/19.25 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c1, c1) = c3)) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (c1 = f2(f9(c1, c1))) | (~big_f(f9(c1, c1), c1)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (~(f9(c1, c1) = c3)) | (c1 = f2(f9(c1, c1))) | (~big_f(f9(c1, c1), c1))))),
% 29.01/19.25 inference(monotonicity,[status(thm)],[19582])).
% 29.01/19.25 tff(19584,plain,
% 29.01/19.25 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c1, c1) = c3)) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (c1 = f2(f9(c1, c1))) | (~big_f(f9(c1, c1), c1)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (~(f9(c1, c1) = c3)) | (c1 = f2(f9(c1, c1))) | (~big_f(f9(c1, c1), c1)))),
% 29.01/19.25 inference(transitivity,[status(thm)],[19583, 19581])).
% 29.01/19.25 tff(19585,plain,
% 29.01/19.25 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c1, c1) = c3)) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (c1 = f2(f9(c1, c1))) | (~big_f(f9(c1, c1), c1)))),
% 29.01/19.25 inference(quant_inst,[status(thm)],[])).
% 29.01/19.25 tff(19586,plain,
% 29.01/19.25 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (~(f9(c1, c1) = c3)) | (c1 = f2(f9(c1, c1))) | (~big_f(f9(c1, c1), c1))),
% 29.01/19.25 inference(modus_ponens,[status(thm)],[19585, 19584])).
% 29.01/19.25 tff(19587,plain,
% 29.01/19.25 ((~(c1 = c4)) | (~(c1 = f4(c1))) | (c1 = f2(f9(c1, c1)))),
% 29.01/19.25 inference(unit_resolution,[status(thm)],[19586, 5622, 19508, 8714, 66])).
% 29.01/19.25 tff(19588,plain,
% 29.01/19.25 (c1 = f2(f9(c1, c1))),
% 29.01/19.25 inference(unit_resolution,[status(thm)],[19587, 19580, 19576])).
% 29.01/19.25 tff(19589,plain,
% 29.01/19.25 (f2(f9(c1, c1)) = c1),
% 29.01/19.25 inference(symmetry,[status(thm)],[19588])).
% 29.01/19.25 tff(19590,plain,
% 29.01/19.25 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (~(f9(c1, c1) = c3)) | (f9(c1, c1) = f2(f9(c1, c1))) | (~big_f(f9(c1, c1), f9(c1, c1))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (~(f9(c1, c1) = c3)) | (f9(c1, c1) = f2(f9(c1, c1))) | (~big_f(f9(c1, c1), f9(c1, c1))))),
% 29.01/19.25 inference(rewrite,[status(thm)],[])).
% 29.01/19.25 tff(19591,plain,
% 29.01/19.25 (((~(f9(c1, c1) = c3)) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (f9(c1, c1) = f2(f9(c1, c1))) | (~big_f(f9(c1, c1), f9(c1, c1)))) <=> ((~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (~(f9(c1, c1) = c3)) | (f9(c1, c1) = f2(f9(c1, c1))) | (~big_f(f9(c1, c1), f9(c1, c1))))),
% 29.01/19.25 inference(rewrite,[status(thm)],[])).
% 29.01/19.25 tff(19592,plain,
% 29.01/19.25 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c1, c1) = c3)) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (f9(c1, c1) = f2(f9(c1, c1))) | (~big_f(f9(c1, c1), f9(c1, c1))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (~(f9(c1, c1) = c3)) | (f9(c1, c1) = f2(f9(c1, c1))) | (~big_f(f9(c1, c1), f9(c1, c1)))))),
% 29.01/19.25 inference(monotonicity,[status(thm)],[19591])).
% 29.01/19.25 tff(19593,plain,
% 29.01/19.25 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c1, c1) = c3)) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (f9(c1, c1) = f2(f9(c1, c1))) | (~big_f(f9(c1, c1), f9(c1, c1))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (~(f9(c1, c1) = c3)) | (f9(c1, c1) = f2(f9(c1, c1))) | (~big_f(f9(c1, c1), f9(c1, c1))))),
% 29.01/19.25 inference(transitivity,[status(thm)],[19592, 19590])).
% 29.01/19.25 tff(19594,plain,
% 29.01/19.25 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c1, c1) = c3)) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (f9(c1, c1) = f2(f9(c1, c1))) | (~big_f(f9(c1, c1), f9(c1, c1))))),
% 29.01/19.25 inference(quant_inst,[status(thm)],[])).
% 29.01/19.25 tff(19595,plain,
% 29.01/19.25 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (~(f9(c1, c1) = c3)) | (f9(c1, c1) = f2(f9(c1, c1))) | (~big_f(f9(c1, c1), f9(c1, c1)))),
% 29.01/19.25 inference(modus_ponens,[status(thm)],[19594, 19593])).
% 29.01/19.25 tff(19596,plain,
% 29.01/19.25 ((~(c1 = c4)) | (~(c1 = f4(c1))) | (f9(c1, c1) = f2(f9(c1, c1)))),
% 29.01/19.25 inference(unit_resolution,[status(thm)],[19595, 5622, 19508, 19549, 66])).
% 29.01/19.25 tff(19597,plain,
% 29.01/19.25 (f9(c1, c1) = f2(f9(c1, c1))),
% 29.01/19.25 inference(unit_resolution,[status(thm)],[19596, 19580, 19576])).
% 29.01/19.25 tff(19598,plain,
% 29.01/19.25 (f9(c1, c1) = c1),
% 29.01/19.25 inference(transitivity,[status(thm)],[19597, 19589])).
% 29.01/19.25 tff(19599,plain,
% 29.01/19.25 ($false),
% 29.01/19.25 inference(unit_resolution,[status(thm)],[17791, 19598])).
% 29.01/19.25 tff(19600,plain,(big_f(c1, f9(c1, c1)) | (~(f9(c1, c1) = c3)) | big_f(c1, c1) | (~big_f(f9(c1, c1), c1)) | (~(f4(c4) = c1)) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f10(c2) = c1)) | (f10(c1) = c1) | (f7(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 29.01/19.25 tff(19601,plain,
% 29.01/19.25 (f10(c1) = c1),
% 29.01/19.25 inference(unit_resolution,[status(thm)],[19600, 4686, 19508, 66, 11752, 1498, 11819, 8714, 17])).
% 29.01/19.25 tff(19602,plain,
% 29.01/19.25 (big_f(f7(c2), c2)),
% 29.01/19.25 inference(unit_resolution,[status(thm)],[17973, 19601, 1498, 17, 17975, 11752, 11819, 19507, 8714])).
% 29.01/19.25 tff(19603,plain,
% 29.01/19.25 (big_f(c1, c2)),
% 29.01/19.25 inference(modus_ponens,[status(thm)],[19602, 19506])).
% 29.01/19.25 tff(19604,plain,
% 29.01/19.25 ($false),
% 29.01/19.25 inference(unit_resolution,[status(thm)],[17749, 19603])).
% 29.01/19.25 tff(19605,plain,(big_f(c1, f9(c1, c1)) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | (f7(c2) = c2) | (~big_f(f9(c1, c1), c1)) | (~(f9(c1, c1) = c3)) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 29.01/19.25 tff(19606,plain,
% 29.01/19.25 (~(f9(c1, c1) = c3)),
% 29.01/19.25 inference(unit_resolution,[status(thm)],[19605, 19499, 11752, 11819, 17, 1498, 19497, 4686])).
% 29.01/19.25 tff(19607,plain,
% 29.01/19.25 ($false),
% 29.01/19.25 inference(unit_resolution,[status(thm)],[19606, 19491])).
% 29.01/19.25 tff(19608,plain,(big_f(c1, f9(c1, c1)) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | (f7(c2) = c2) | big_f(c2, c2) | (~(f10(c1) = c1)) | (~(f5(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.01/19.25 tff(19609,plain,
% 29.01/19.25 (big_f(c1, f9(c1, c1))),
% 29.01/19.25 inference(unit_resolution,[status(thm)],[19608, 3762, 11752, 11819, 17, 121, 1498, 186])).
% 29.01/19.25 tff(19610,plain,
% 29.01/19.25 (big_f(f7(f9(c1, c1)), f9(c1, c1))),
% 29.01/19.25 inference(modus_ponens,[status(thm)],[19609, 17732])).
% 29.01/19.25 tff(19611,plain,
% 29.01/19.25 (big_f(f7(f9(c1, c1)), c1) <=> big_f(c1, c1)),
% 29.01/19.25 inference(monotonicity,[status(thm)],[17730])).
% 29.01/19.25 tff(19612,plain,
% 29.01/19.25 (big_f(c1, c1) <=> big_f(f7(f9(c1, c1)), c1)),
% 29.01/19.25 inference(symmetry,[status(thm)],[19611])).
% 29.01/19.25 tff(19613,plain,
% 29.01/19.25 ((f9(c1, c1) = c3) <=> (c2 = c3)),
% 29.01/19.25 inference(symmetry,[status(thm)],[17735])).
% 29.01/19.25 tff(19614,plain,
% 29.01/19.25 ((f9(c1, c1) = c3) <=> (c3 = c2)),
% 29.01/19.25 inference(transitivity,[status(thm)],[19613, 127])).
% 29.01/19.25 tff(19615,plain,
% 29.01/19.25 ((f7(f7(c2)) = c3) <=> (f7(c1) = c3)),
% 29.01/19.25 inference(monotonicity,[status(thm)],[352])).
% 29.01/19.25 tff(19616,plain,
% 29.01/19.25 ((f7(c1) = c3) <=> (f7(f7(c2)) = c3)),
% 29.01/19.25 inference(symmetry,[status(thm)],[19615])).
% 29.01/19.25 tff(19617,plain,
% 29.01/19.25 ((f7(c1) = c3) <=> (f9(c1, c1) = c3)),
% 29.01/19.25 inference(monotonicity,[status(thm)],[19139])).
% 29.01/19.25 tff(19618,plain,
% 29.01/19.25 ((f9(c1, c1) = c3) <=> (f7(c1) = c3)),
% 29.01/19.25 inference(symmetry,[status(thm)],[19617])).
% 29.01/19.25 tff(19619,plain,
% 29.01/19.25 ((f9(c1, c1) = c3) <=> (f7(f7(c2)) = c3)),
% 29.01/19.25 inference(transitivity,[status(thm)],[19618, 19616])).
% 29.01/19.25 tff(19620,plain,
% 29.01/19.25 ((~(f9(c1, c1) = c3)) <=> (~(f7(f7(c2)) = c3))),
% 29.01/19.25 inference(monotonicity,[status(thm)],[19619])).
% 29.01/19.25 tff(19621,assumption,(~(f9(c1, c1) = c3)), introduced(assumption)).
% 29.01/19.25 tff(19622,plain,
% 29.01/19.25 (~(f7(f7(c2)) = c3)),
% 29.01/19.25 inference(modus_ponens,[status(thm)],[19621, 19620])).
% 29.01/19.25 tff(19623,plain,
% 29.01/19.25 ((~big_f(c1, f10(f9(c1, c1)))) <=> (~big_f(c1, c1))),
% 29.01/19.25 inference(monotonicity,[status(thm)],[17982])).
% 29.01/19.25 tff(19624,assumption,(f9(c1, c1) = f5(c1)), introduced(assumption)).
% 29.01/19.25 tff(19625,plain,
% 29.01/19.25 ((c1 = f8(f9(c1, c1))) <=> (c1 = f9(c1, c1))),
% 29.01/19.25 inference(monotonicity,[status(thm)],[17861])).
% 29.01/19.25 tff(19626,plain,
% 29.01/19.25 ((c1 = f8(f9(c1, c1))) <=> (f9(c1, c1) = c1)),
% 29.01/19.25 inference(transitivity,[status(thm)],[19625, 17725])).
% 29.01/19.25 tff(19627,plain,
% 29.01/19.25 ((f9(c1, c1) = c1) <=> (c1 = f8(f9(c1, c1)))),
% 29.01/19.25 inference(symmetry,[status(thm)],[19626])).
% 29.01/19.25 tff(19628,plain,
% 29.01/19.25 ((~(f9(c1, c1) = c1)) <=> (~(c1 = f8(f9(c1, c1))))),
% 29.01/19.25 inference(monotonicity,[status(thm)],[19627])).
% 29.01/19.25 tff(19629,plain,
% 29.01/19.25 (~(c1 = f8(f9(c1, c1)))),
% 29.01/19.25 inference(modus_ponens,[status(thm)],[17791, 19628])).
% 29.01/19.25 tff(19630,assumption,(~big_f(f7(c1), f9(c1, c1))), introduced(assumption)).
% 29.01/19.25 tff(19631,assumption,(~(c1 = f8(f9(c1, c1)))), introduced(assumption)).
% 29.01/19.25 tff(19632,plain,
% 29.01/19.25 ($false),
% 29.01/19.25 inference(unit_resolution,[status(thm)],[19117, 705, 115, 17834, 18024, 19631, 19624, 19630])).
% 29.01/19.25 tff(19633,plain,((~big_f(c1, f10(f9(c1, c1)))) | (f7(c1) = c1) | (f10(f9(c1, c1)) = f9(c1, c1)) | (c1 = f8(f9(c1, c1))) | (~(f9(c1, c1) = f5(c1))) | big_f(f7(c1), f9(c1, c1))), inference(lemma,lemma(discharge,[]))).
% 29.01/19.25 tff(19634,plain,
% 29.01/19.25 (~big_f(c1, f10(f9(c1, c1)))),
% 29.01/19.25 inference(unit_resolution,[status(thm)],[19633, 115, 17792, 19629, 19624, 17763])).
% 29.01/19.25 tff(19635,plain,
% 29.01/19.25 (~big_f(c1, c1)),
% 29.01/19.25 inference(modus_ponens,[status(thm)],[19634, 19623])).
% 29.01/19.25 tff(19636,plain,
% 29.01/19.25 (f9(c1, c1) = c3),
% 29.01/19.25 inference(modus_ponens,[status(thm)],[1344, 17735])).
% 29.01/19.25 tff(19637,plain,
% 29.01/19.25 ($false),
% 29.01/19.25 inference(unit_resolution,[status(thm)],[19621, 19636])).
% 29.01/19.25 tff(19638,plain,((~(c2 = c3)) | (f9(c1, c1) = c3) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.01/19.25 tff(19639,plain,
% 29.01/19.25 (~(c2 = c3)),
% 29.01/19.25 inference(unit_resolution,[status(thm)],[19638, 19621, 1498, 11752, 11819])).
% 29.01/19.25 tff(19640,plain,
% 29.01/19.25 ((f3(c1, f9(c1, c1)) = f8(f9(c1, c1))) <=> (f3(c1, f9(c1, c1)) = f9(c1, c1))),
% 29.01/19.25 inference(monotonicity,[status(thm)],[17861])).
% 29.01/19.25 tff(19641,plain,
% 29.01/19.25 (big_f(f3(c1, f9(c1, c1)), f10(f9(c1, c1))) <=> big_f(f3(c1, f9(c1, c1)), c1)),
% 29.01/19.25 inference(monotonicity,[status(thm)],[17766])).
% 29.01/19.25 tff(19642,plain,
% 29.01/19.25 (big_f(f3(c1, f9(c1, c1)), c1) <=> big_f(f3(c1, f9(c1, c1)), f10(f9(c1, c1)))),
% 29.01/19.25 inference(symmetry,[status(thm)],[19641])).
% 29.01/19.25 tff(19643,plain,
% 29.01/19.25 (f3(c1, c2) = f3(c1, f9(c1, c1))),
% 29.01/19.25 inference(monotonicity,[status(thm)],[17734])).
% 29.01/19.25 tff(19644,plain,
% 29.01/19.25 (big_f(f3(c1, c2), c1) <=> big_f(f3(c1, f9(c1, c1)), c1)),
% 29.01/19.25 inference(monotonicity,[status(thm)],[19643])).
% 29.01/19.25 tff(19645,plain,
% 29.01/19.25 (big_f(f3(c1, c2), c1) <=> big_f(f3(c1, f9(c1, c1)), f10(f9(c1, c1)))),
% 29.01/19.25 inference(transitivity,[status(thm)],[19644, 19642])).
% 29.01/19.25 tff(19646,plain,
% 29.01/19.25 (big_f(c1, f10(c1)) <=> big_f(c1, c1)),
% 29.01/19.25 inference(monotonicity,[status(thm)],[3762])).
% 29.01/19.25 tff(19647,plain,
% 29.01/19.25 (big_f(c1, c1) <=> big_f(c1, f10(c1))),
% 29.01/19.25 inference(symmetry,[status(thm)],[19646])).
% 29.01/19.25 tff(19648,plain,
% 29.01/19.25 ((~big_f(c1, c1)) <=> (~big_f(c1, f10(c1)))),
% 29.01/19.25 inference(monotonicity,[status(thm)],[19647])).
% 29.01/19.25 tff(19649,plain,
% 29.01/19.25 (~big_f(c1, f10(c1))),
% 29.01/19.25 inference(modus_ponens,[status(thm)],[66, 19648])).
% 29.01/19.25 tff(19650,plain,
% 29.01/19.25 (f10(f10(c2)) = c1),
% 29.01/19.25 inference(modus_ponens,[status(thm)],[3762, 17780])).
% 29.01/19.25 tff(19651,plain,
% 29.01/19.25 (~big_f(f4(c4), c4)),
% 29.01/19.25 inference(unit_resolution,[status(thm)],[18234, 11526, 18228, 3030, 11819, 11752])).
% 29.01/19.25 tff(19652,plain,
% 29.01/19.25 (f1(f7(f7(c2)), c1) = c1),
% 29.01/19.25 inference(unit_resolution,[status(thm)],[422, 19651, 121, 292, 347, 378])).
% 29.01/19.25 tff(19653,plain,
% 29.01/19.25 (f9(c1, c1) = f7(c1)),
% 29.01/19.25 inference(transitivity,[status(thm)],[17727, 1498, 354])).
% 29.01/19.25 tff(19654,plain,
% 29.01/19.25 (f1(f9(c1, c1), c1) = f1(f7(c1), c1)),
% 29.01/19.25 inference(monotonicity,[status(thm)],[19653])).
% 29.01/19.25 tff(19655,plain,
% 29.01/19.25 (f1(f9(c1, c1), c1) = c1),
% 29.01/19.25 inference(transitivity,[status(thm)],[19654, 15858, 19652])).
% 29.01/19.25 tff(19656,plain,
% 29.01/19.25 (big_f(f9(c1, c1), f1(f9(c1, c1), c1)) <=> big_f(f9(c1, c1), c1)),
% 29.01/19.25 inference(monotonicity,[status(thm)],[19655])).
% 29.01/19.25 tff(19657,plain,
% 29.01/19.25 (big_f(f9(c1, c1), c1) <=> big_f(f9(c1, c1), f1(f9(c1, c1), c1))),
% 29.01/19.25 inference(symmetry,[status(thm)],[19656])).
% 29.01/19.25 tff(19658,plain,
% 29.01/19.25 (big_f(f9(c1, c1), f1(f9(c1, c1), c1))),
% 29.01/19.25 inference(modus_ponens,[status(thm)],[8714, 19657])).
% 29.01/19.25 tff(19659,plain,
% 29.01/19.25 (f1(f7(c1), c1) = f1(f9(c1, c1), c1)),
% 29.01/19.25 inference(symmetry,[status(thm)],[19654])).
% 29.01/19.25 tff(19660,plain,
% 29.01/19.25 ((f1(f7(c1), c1) = c1) <=> (f1(f9(c1, c1), c1) = c1)),
% 29.01/19.25 inference(monotonicity,[status(thm)],[19659])).
% 29.01/19.26 tff(19661,plain,
% 29.01/19.26 (f1(f7(f7(c2)), c1) = f1(f7(c1), c1)),
% 29.01/19.26 inference(symmetry,[status(thm)],[15858])).
% 29.01/19.26 tff(19662,plain,
% 29.01/19.26 ((f1(f7(f7(c2)), c1) = c1) <=> (f1(f7(c1), c1) = c1)),
% 29.01/19.26 inference(monotonicity,[status(thm)],[19661])).
% 29.01/19.26 tff(19663,plain,
% 29.01/19.26 ((f1(f7(f7(c2)), c1) = c1) <=> (f1(f9(c1, c1), c1) = c1)),
% 29.01/19.26 inference(transitivity,[status(thm)],[19662, 19660])).
% 29.01/19.26 tff(19664,plain,
% 29.01/19.26 (f1(f9(c1, c1), c1) = c1),
% 29.01/19.26 inference(modus_ponens,[status(thm)],[19652, 19663])).
% 29.01/19.26 tff(19665,plain,
% 29.01/19.26 (f4(c1) = f4(c4)),
% 29.01/19.26 inference(monotonicity,[status(thm)],[11526])).
% 29.01/19.26 tff(19666,plain,
% 29.01/19.26 (f4(c4) = f4(c1)),
% 29.01/19.26 inference(symmetry,[status(thm)],[19665])).
% 29.01/19.26 tff(19667,plain,
% 29.01/19.26 (c1 = f4(c1)),
% 29.01/19.26 inference(transitivity,[status(thm)],[16651, 19666])).
% 29.01/19.26 tff(19668,plain,
% 29.01/19.26 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (f9(c1, c1) = c3) | (~big_f(f9(c1, c1), f1(f9(c1, c1), c1))) | (~(f1(f9(c1, c1), c1) = c1)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (f9(c1, c1) = c3) | (~big_f(f9(c1, c1), f1(f9(c1, c1), c1))) | (~(f1(f9(c1, c1), c1) = c1)))),
% 29.01/19.26 inference(rewrite,[status(thm)],[])).
% 29.01/19.26 tff(19669,plain,
% 29.01/19.26 (((f9(c1, c1) = c3) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (~(f1(f9(c1, c1), c1) = c1)) | (~big_f(f9(c1, c1), f1(f9(c1, c1), c1)))) <=> ((~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (f9(c1, c1) = c3) | (~big_f(f9(c1, c1), f1(f9(c1, c1), c1))) | (~(f1(f9(c1, c1), c1) = c1)))),
% 29.01/19.26 inference(rewrite,[status(thm)],[])).
% 29.01/19.26 tff(19670,plain,
% 29.01/19.26 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f9(c1, c1) = c3) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (~(f1(f9(c1, c1), c1) = c1)) | (~big_f(f9(c1, c1), f1(f9(c1, c1), c1))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (f9(c1, c1) = c3) | (~big_f(f9(c1, c1), f1(f9(c1, c1), c1))) | (~(f1(f9(c1, c1), c1) = c1))))),
% 29.01/19.26 inference(monotonicity,[status(thm)],[19669])).
% 29.01/19.26 tff(19671,plain,
% 29.01/19.26 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f9(c1, c1) = c3) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (~(f1(f9(c1, c1), c1) = c1)) | (~big_f(f9(c1, c1), f1(f9(c1, c1), c1))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (f9(c1, c1) = c3) | (~big_f(f9(c1, c1), f1(f9(c1, c1), c1))) | (~(f1(f9(c1, c1), c1) = c1)))),
% 29.01/19.26 inference(transitivity,[status(thm)],[19670, 19668])).
% 29.01/19.26 tff(19672,plain,
% 29.01/19.26 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f9(c1, c1) = c3) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (~(f1(f9(c1, c1), c1) = c1)) | (~big_f(f9(c1, c1), f1(f9(c1, c1), c1))))),
% 29.01/19.26 inference(quant_inst,[status(thm)],[])).
% 29.01/19.26 tff(19673,plain,
% 29.01/19.26 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (f9(c1, c1) = c3) | (~big_f(f9(c1, c1), f1(f9(c1, c1), c1))) | (~(f1(f9(c1, c1), c1) = c1))),
% 29.01/19.26 inference(modus_ponens,[status(thm)],[19672, 19671])).
% 29.01/19.26 tff(19674,plain,
% 29.01/19.26 ($false),
% 29.01/19.26 inference(unit_resolution,[status(thm)],[19673, 447, 11526, 19667, 19621, 66, 19664, 19658])).
% 29.01/19.26 tff(19675,plain,((~(c1 = c4)) | (f9(c1, c1) = c3) | big_f(c1, c1) | (~big_f(f9(c1, c1), c1)) | (~(f7(c2) = c1)) | (~(f7(c1) = c2)) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | big_f(c2, c2) | (f7(f7(c2)) = c3) | (~(f10(f10(c2)) = c1)) | big_f(c1, f10(c1))), inference(lemma,lemma(discharge,[]))).
% 29.01/19.26 tff(19676,plain,
% 29.01/19.26 (~(c1 = c4)),
% 29.01/19.26 inference(unit_resolution,[status(thm)],[19675, 66, 19621, 8714, 292, 120, 1498, 11752, 11819, 121, 378, 19650, 19649])).
% 29.01/19.26 tff(19677,plain,
% 29.01/19.26 (c2 = f1(f5(c2), f5(c1))),
% 29.01/19.26 inference(symmetry,[status(thm)],[5131])).
% 29.01/19.26 tff(19678,plain,
% 29.01/19.26 (f9(c1, c1) = f1(f5(c2), f5(c1))),
% 29.01/19.26 inference(transitivity,[status(thm)],[17727, 1498, 19677])).
% 29.01/19.26 tff(19679,plain,
% 29.01/19.26 (f3(c1, f9(c1, c1)) = f3(c1, f1(f5(c2), f5(c1)))),
% 29.01/19.26 inference(monotonicity,[status(thm)],[19678])).
% 29.01/19.26 tff(19680,plain,
% 29.01/19.26 (f3(c1, f1(f5(c2), f5(c1))) = f3(c1, f9(c1, c1))),
% 29.01/19.26 inference(symmetry,[status(thm)],[19679])).
% 29.01/19.26 tff(19681,plain,
% 29.01/19.26 ((f3(c1, f1(f5(c2), f5(c1))) = c2) <=> (f3(c1, f9(c1, c1)) = f9(c1, c1))),
% 29.01/19.26 inference(monotonicity,[status(thm)],[19680, 17734])).
% 29.01/19.26 tff(19682,plain,
% 29.01/19.26 ((f3(c1, f9(c1, c1)) = f9(c1, c1)) <=> (f3(c1, f1(f5(c2), f5(c1))) = c2)),
% 29.01/19.26 inference(symmetry,[status(thm)],[19681])).
% 29.01/19.26 tff(19683,plain,
% 29.01/19.26 ((~(f3(c1, f9(c1, c1)) = f9(c1, c1))) <=> (~(f3(c1, f1(f5(c2), f5(c1))) = c2))),
% 29.01/19.26 inference(monotonicity,[status(thm)],[19682])).
% 29.01/19.26 tff(19684,plain,
% 29.01/19.26 (~(f1(f9(c1, c1), c1) = c1)),
% 29.01/19.26 inference(unit_resolution,[status(thm)],[10153, 10151, 8714])).
% 29.01/19.26 tff(19685,assumption,(~(f1(f9(c1, c1), c1) = c1)), introduced(assumption)).
% 29.01/19.26 tff(19686,plain,
% 29.01/19.26 (f3(c1, f9(c1, c1)) = f3(c1, c2)),
% 29.01/19.26 inference(monotonicity,[status(thm)],[17728])).
% 29.01/19.26 tff(19687,plain,
% 29.01/19.26 (big_f(f3(c1, f9(c1, c1)), c1) <=> big_f(f3(c1, c2), c1)),
% 29.01/19.26 inference(monotonicity,[status(thm)],[19686])).
% 29.01/19.26 tff(19688,assumption,(big_f(f3(c1, f9(c1, c1)), c1)), introduced(assumption)).
% 29.01/19.26 tff(19689,plain,
% 29.01/19.26 (big_f(f3(c1, c2), c1)),
% 29.01/19.26 inference(modus_ponens,[status(thm)],[19688, 19687])).
% 29.01/19.26 tff(19690,plain,
% 29.01/19.26 ($false),
% 29.01/19.26 inference(unit_resolution,[status(thm)],[13164, 19689])).
% 29.01/19.26 tff(19691,plain,((~big_f(f3(c1, f9(c1, c1)), c1)) | big_f(f3(c1, c2), c1) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.01/19.26 tff(19692,plain,
% 29.01/19.26 (~big_f(f3(c1, f9(c1, c1)), c1)),
% 29.01/19.26 inference(unit_resolution,[status(thm)],[19691, 13164, 1498, 11752, 11819])).
% 29.01/19.26 tff(19693,assumption,(~big_f(f3(c1, f9(c1, c1)), c1)), introduced(assumption)).
% 29.01/19.26 tff(19694,assumption,(~(f3(c1, f9(c1, c1)) = f9(c1, c1))), introduced(assumption)).
% 29.01/19.26 tff(19695,plain,
% 29.01/19.26 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c1 = c4) | (f9(c1, c1) = c3) | big_f(f3(c1, f9(c1, c1)), c1) | (f3(c1, f9(c1, c1)) = f9(c1, c1)) | (f1(f9(c1, c1), c1) = c1) | big_f(f9(c1, c1), f1(f9(c1, c1), c1)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (c1 = c4) | (f9(c1, c1) = c3) | big_f(f3(c1, f9(c1, c1)), c1) | (f3(c1, f9(c1, c1)) = f9(c1, c1)) | (f1(f9(c1, c1), c1) = c1) | big_f(f9(c1, c1), f1(f9(c1, c1), c1)))),
% 29.01/19.26 inference(rewrite,[status(thm)],[])).
% 29.01/19.26 tff(19696,plain,
% 29.01/19.26 (((c1 = c4) | (f3(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f3(c1, f9(c1, c1)), c1) | (f9(c1, c1) = c3) | (f1(f9(c1, c1), c1) = c1) | big_f(f9(c1, c1), f1(f9(c1, c1), c1))) <=> ((c1 = c4) | (f9(c1, c1) = c3) | big_f(f3(c1, f9(c1, c1)), c1) | (f3(c1, f9(c1, c1)) = f9(c1, c1)) | (f1(f9(c1, c1), c1) = c1) | big_f(f9(c1, c1), f1(f9(c1, c1), c1)))),
% 29.01/19.26 inference(rewrite,[status(thm)],[])).
% 29.01/19.26 tff(19697,plain,
% 29.01/19.26 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c1 = c4) | (f3(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f3(c1, f9(c1, c1)), c1) | (f9(c1, c1) = c3) | (f1(f9(c1, c1), c1) = c1) | big_f(f9(c1, c1), f1(f9(c1, c1), c1)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c1 = c4) | (f9(c1, c1) = c3) | big_f(f3(c1, f9(c1, c1)), c1) | (f3(c1, f9(c1, c1)) = f9(c1, c1)) | (f1(f9(c1, c1), c1) = c1) | big_f(f9(c1, c1), f1(f9(c1, c1), c1))))),
% 29.01/19.26 inference(monotonicity,[status(thm)],[19696])).
% 29.01/19.26 tff(19698,plain,
% 29.01/19.26 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c1 = c4) | (f3(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f3(c1, f9(c1, c1)), c1) | (f9(c1, c1) = c3) | (f1(f9(c1, c1), c1) = c1) | big_f(f9(c1, c1), f1(f9(c1, c1), c1)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (c1 = c4) | (f9(c1, c1) = c3) | big_f(f3(c1, f9(c1, c1)), c1) | (f3(c1, f9(c1, c1)) = f9(c1, c1)) | (f1(f9(c1, c1), c1) = c1) | big_f(f9(c1, c1), f1(f9(c1, c1), c1)))),
% 29.01/19.26 inference(transitivity,[status(thm)],[19697, 19695])).
% 29.01/19.26 tff(19699,plain,
% 29.01/19.26 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c1 = c4) | (f3(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f3(c1, f9(c1, c1)), c1) | (f9(c1, c1) = c3) | (f1(f9(c1, c1), c1) = c1) | big_f(f9(c1, c1), f1(f9(c1, c1), c1)))),
% 29.01/19.26 inference(quant_inst,[status(thm)],[])).
% 29.01/19.26 tff(19700,plain,
% 29.01/19.26 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (c1 = c4) | (f9(c1, c1) = c3) | big_f(f3(c1, f9(c1, c1)), c1) | (f3(c1, f9(c1, c1)) = f9(c1, c1)) | (f1(f9(c1, c1), c1) = c1) | big_f(f9(c1, c1), f1(f9(c1, c1), c1))),
% 29.01/19.26 inference(modus_ponens,[status(thm)],[19699, 19698])).
% 29.01/19.26 tff(19701,plain,
% 29.01/19.26 ($false),
% 29.01/19.26 inference(unit_resolution,[status(thm)],[19700, 1014, 482, 19621, 19685, 10151, 19694, 19693])).
% 29.01/19.26 tff(19702,plain,(big_f(f3(c1, f9(c1, c1)), c1) | (c1 = c4) | (f9(c1, c1) = c3) | (f1(f9(c1, c1), c1) = c1) | big_f(f9(c1, c1), f1(f9(c1, c1), c1)) | (f3(c1, f9(c1, c1)) = f9(c1, c1))), inference(lemma,lemma(discharge,[]))).
% 29.01/19.26 tff(19703,plain,
% 29.01/19.26 (f3(c1, f9(c1, c1)) = f9(c1, c1)),
% 29.01/19.26 inference(unit_resolution,[status(thm)],[19702, 19692, 19621, 19685, 10151, 482])).
% 29.01/19.26 tff(19704,plain,
% 29.01/19.26 (f3(c1, c2) = f9(c1, c1)),
% 29.01/19.26 inference(transitivity,[status(thm)],[19643, 19703])).
% 29.01/19.26 tff(19705,plain,
% 29.01/19.26 (big_f(f3(c1, c2), c1) <=> big_f(f9(c1, c1), c1)),
% 29.01/19.26 inference(monotonicity,[status(thm)],[19704])).
% 29.01/19.26 tff(19706,plain,
% 29.01/19.26 (big_f(f9(c1, c1), c1) <=> big_f(f3(c1, c2), c1)),
% 29.01/19.26 inference(symmetry,[status(thm)],[19705])).
% 29.01/19.26 tff(19707,plain,
% 29.01/19.26 (big_f(f3(c1, c2), c1)),
% 29.01/19.26 inference(modus_ponens,[status(thm)],[8714, 19706])).
% 29.01/19.26 tff(19708,plain,
% 29.01/19.26 ($false),
% 29.01/19.26 inference(unit_resolution,[status(thm)],[13164, 19707])).
% 29.01/19.26 tff(19709,plain,(big_f(f3(c1, c2), c1) | (~big_f(f9(c1, c1), c1)) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | (f9(c1, c1) = c3) | (f1(f9(c1, c1), c1) = c1) | big_f(f9(c1, c1), f1(f9(c1, c1), c1)) | (c1 = c4)), inference(lemma,lemma(discharge,[]))).
% 29.01/19.26 tff(19710,plain,
% 29.01/19.26 (big_f(f3(c1, c2), c1)),
% 29.01/19.26 inference(unit_resolution,[status(thm)],[19709, 482, 1498, 11752, 11819, 19621, 8714, 10151, 19684])).
% 29.01/19.26 tff(19711,plain,
% 29.01/19.26 (big_f(f3(c1, f9(c1, c1)), c1)),
% 29.01/19.26 inference(modus_ponens,[status(thm)],[19710, 19644])).
% 29.01/19.26 tff(19712,plain,
% 29.01/19.26 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c1 = c4) | (f9(c1, c1) = c3) | (~(f3(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f3(c1, f9(c1, c1)), c1)) | (f1(f9(c1, c1), c1) = c1) | big_f(f9(c1, c1), f1(f9(c1, c1), c1)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c1 = c4) | (f9(c1, c1) = c3) | (~(f3(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f3(c1, f9(c1, c1)), c1)) | (f1(f9(c1, c1), c1) = c1) | big_f(f9(c1, c1), f1(f9(c1, c1), c1)))),
% 29.01/19.26 inference(rewrite,[status(thm)],[])).
% 29.01/19.26 tff(19713,plain,
% 29.01/19.26 (((c1 = c4) | (f9(c1, c1) = c3) | (f1(f9(c1, c1), c1) = c1) | big_f(f9(c1, c1), f1(f9(c1, c1), c1)) | (~(f3(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f3(c1, f9(c1, c1)), c1))) <=> ((c1 = c4) | (f9(c1, c1) = c3) | (~(f3(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f3(c1, f9(c1, c1)), c1)) | (f1(f9(c1, c1), c1) = c1) | big_f(f9(c1, c1), f1(f9(c1, c1), c1)))),
% 29.01/19.26 inference(rewrite,[status(thm)],[])).
% 29.01/19.26 tff(19714,plain,
% 29.01/19.26 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c1 = c4) | (f9(c1, c1) = c3) | (f1(f9(c1, c1), c1) = c1) | big_f(f9(c1, c1), f1(f9(c1, c1), c1)) | (~(f3(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f3(c1, f9(c1, c1)), c1)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c1 = c4) | (f9(c1, c1) = c3) | (~(f3(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f3(c1, f9(c1, c1)), c1)) | (f1(f9(c1, c1), c1) = c1) | big_f(f9(c1, c1), f1(f9(c1, c1), c1))))),
% 29.01/19.26 inference(monotonicity,[status(thm)],[19713])).
% 29.01/19.26 tff(19715,plain,
% 29.01/19.26 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c1 = c4) | (f9(c1, c1) = c3) | (f1(f9(c1, c1), c1) = c1) | big_f(f9(c1, c1), f1(f9(c1, c1), c1)) | (~(f3(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f3(c1, f9(c1, c1)), c1)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c1 = c4) | (f9(c1, c1) = c3) | (~(f3(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f3(c1, f9(c1, c1)), c1)) | (f1(f9(c1, c1), c1) = c1) | big_f(f9(c1, c1), f1(f9(c1, c1), c1)))),
% 29.01/19.26 inference(transitivity,[status(thm)],[19714, 19712])).
% 29.01/19.26 tff(19716,plain,
% 29.01/19.26 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c1 = c4) | (f9(c1, c1) = c3) | (f1(f9(c1, c1), c1) = c1) | big_f(f9(c1, c1), f1(f9(c1, c1), c1)) | (~(f3(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f3(c1, f9(c1, c1)), c1)))),
% 29.01/19.26 inference(quant_inst,[status(thm)],[])).
% 29.01/19.26 tff(19717,plain,
% 29.01/19.26 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c1 = c4) | (f9(c1, c1) = c3) | (~(f3(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f3(c1, f9(c1, c1)), c1)) | (f1(f9(c1, c1), c1) = c1) | big_f(f9(c1, c1), f1(f9(c1, c1), c1))),
% 29.01/19.26 inference(modus_ponens,[status(thm)],[19716, 19715])).
% 29.01/19.26 tff(19718,plain,
% 29.01/19.26 (~(f3(c1, f9(c1, c1)) = f9(c1, c1))),
% 29.01/19.26 inference(unit_resolution,[status(thm)],[19717, 969, 482, 19621, 19684, 10151, 19711])).
% 29.01/19.26 tff(19719,plain,
% 29.01/19.26 (~(f3(c1, f1(f5(c2), f5(c1))) = c2)),
% 29.01/19.26 inference(modus_ponens,[status(thm)],[19718, 19683])).
% 29.01/19.26 tff(19720,plain,
% 29.01/19.26 (f3(c1, f1(f5(c2), f5(c1))) = c1),
% 29.01/19.26 inference(unit_resolution,[status(thm)],[16082, 19719])).
% 29.01/19.26 tff(19721,plain,
% 29.01/19.26 (f3(c1, f9(c1, c1)) = c1),
% 29.01/19.26 inference(transitivity,[status(thm)],[19679, 19720])).
% 29.01/19.26 tff(19722,plain,
% 29.01/19.26 (big_f(f3(c1, f9(c1, c1)), c1) <=> big_f(c1, c1)),
% 29.01/19.26 inference(monotonicity,[status(thm)],[19721])).
% 29.01/19.26 tff(19723,plain,
% 29.01/19.26 (big_f(c1, c1) <=> big_f(f3(c1, f9(c1, c1)), c1)),
% 29.01/19.26 inference(symmetry,[status(thm)],[19722])).
% 29.01/19.26 tff(19724,plain,
% 29.01/19.26 ((~big_f(c1, c1)) <=> (~big_f(f3(c1, f9(c1, c1)), c1))),
% 29.01/19.26 inference(monotonicity,[status(thm)],[19723])).
% 29.01/19.26 tff(19725,plain,
% 29.01/19.26 (~big_f(f3(c1, f9(c1, c1)), c1)),
% 29.01/19.26 inference(modus_ponens,[status(thm)],[66, 19724])).
% 29.01/19.26 tff(19726,plain,
% 29.01/19.26 ($false),
% 29.01/19.26 inference(unit_resolution,[status(thm)],[19711, 19725])).
% 29.01/19.26 tff(19727,plain,((c1 = c4) | big_f(c1, c1) | (~(f1(f5(c2), f5(c1)) = c2)) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | (f9(c1, c1) = c3) | big_f(f9(c1, c1), f1(f9(c1, c1), c1)) | (~big_f(f9(c1, c1), c1))), inference(lemma,lemma(discharge,[]))).
% 29.01/19.26 tff(19728,plain,
% 29.01/19.26 (~(f1(f5(c2), f5(c1)) = c2)),
% 29.01/19.26 inference(unit_resolution,[status(thm)],[19727, 10151, 1498, 66, 11752, 11819, 19621, 8714, 482])).
% 29.01/19.26 tff(19729,plain,
% 29.01/19.26 (f1(f5(c2), f5(c1)) = c1),
% 29.01/19.26 inference(unit_resolution,[status(thm)],[5191, 19728])).
% 29.01/19.26 tff(19730,plain,
% 29.01/19.26 (big_f(f3(c1, c2), c1)),
% 29.01/19.26 inference(unit_resolution,[status(thm)],[19709, 19684, 1498, 11752, 11819, 8714, 19621, 482, 10151])).
% 29.01/19.26 tff(19731,plain,
% 29.01/19.26 (big_f(f3(c1, f9(c1, c1)), c1)),
% 29.01/19.26 inference(modus_ponens,[status(thm)],[19730, 19644])).
% 29.01/19.26 tff(19732,assumption,(f3(c1, f9(c1, c1)) = f9(c1, c1)), introduced(assumption)).
% 29.01/19.26 tff(19733,plain,
% 29.01/19.26 ($false),
% 29.01/19.26 inference(unit_resolution,[status(thm)],[19717, 969, 482, 19621, 19685, 10151, 19732, 19688])).
% 29.01/19.26 tff(19734,plain,((~(f3(c1, f9(c1, c1)) = f9(c1, c1))) | (c1 = c4) | (f9(c1, c1) = c3) | (f1(f9(c1, c1), c1) = c1) | big_f(f9(c1, c1), f1(f9(c1, c1), c1)) | (~big_f(f3(c1, f9(c1, c1)), c1))), inference(lemma,lemma(discharge,[]))).
% 29.01/19.26 tff(19735,plain,
% 29.01/19.26 (~(f3(c1, f9(c1, c1)) = f9(c1, c1))),
% 29.01/19.26 inference(unit_resolution,[status(thm)],[19734, 19731, 19621, 19684, 10151, 482])).
% 29.01/19.26 tff(19736,plain,
% 29.01/19.26 (f3(c1, f9(c1, c1)) = f3(f1(f5(c2), f5(c1)), c2)),
% 29.01/19.26 inference(monotonicity,[status(thm)],[10485, 17728])).
% 29.01/19.26 tff(19737,plain,
% 29.01/19.26 (f3(f1(f5(c2), f5(c1)), c2) = f3(c1, f9(c1, c1))),
% 29.01/19.26 inference(symmetry,[status(thm)],[19736])).
% 29.01/19.26 tff(19738,plain,
% 29.01/19.26 ((f3(f1(f5(c2), f5(c1)), c2) = c2) <=> (f3(c1, f9(c1, c1)) = f9(c1, c1))),
% 29.01/19.26 inference(monotonicity,[status(thm)],[19737, 17734])).
% 29.01/19.26 tff(19739,plain,
% 29.01/19.26 ((f3(c1, f9(c1, c1)) = f9(c1, c1)) <=> (f3(f1(f5(c2), f5(c1)), c2) = c2)),
% 29.01/19.26 inference(symmetry,[status(thm)],[19738])).
% 29.01/19.26 tff(19740,plain,
% 29.01/19.26 ((~(f3(c1, f9(c1, c1)) = f9(c1, c1))) <=> (~(f3(f1(f5(c2), f5(c1)), c2) = c2))),
% 29.01/19.27 inference(monotonicity,[status(thm)],[19739])).
% 29.01/19.27 tff(19741,plain,
% 29.01/19.27 (~(f3(f1(f5(c2), f5(c1)), c2) = c2)),
% 29.01/19.27 inference(modus_ponens,[status(thm)],[19694, 19740])).
% 29.01/19.27 tff(19742,plain,
% 29.01/19.27 (f3(f1(f5(c2), f5(c1)), c2) = c1),
% 29.01/19.27 inference(unit_resolution,[status(thm)],[16061, 19741])).
% 29.01/19.27 tff(19743,plain,
% 29.01/19.27 (f3(c1, f9(c1, c1)) = c1),
% 29.01/19.27 inference(transitivity,[status(thm)],[19736, 19742])).
% 29.01/19.27 tff(19744,plain,
% 29.01/19.27 (big_f(f3(c1, f9(c1, c1)), c1) <=> big_f(c1, c1)),
% 29.01/19.27 inference(monotonicity,[status(thm)],[19743])).
% 29.01/19.27 tff(19745,plain,
% 29.01/19.27 (big_f(c1, c1) <=> big_f(f3(c1, f9(c1, c1)), c1)),
% 29.01/19.27 inference(symmetry,[status(thm)],[19744])).
% 29.01/19.27 tff(19746,plain,
% 29.01/19.27 ((~big_f(c1, c1)) <=> (~big_f(f3(c1, f9(c1, c1)), c1))),
% 29.01/19.27 inference(monotonicity,[status(thm)],[19745])).
% 29.01/19.27 tff(19747,plain,
% 29.01/19.27 (~big_f(f3(c1, f9(c1, c1)), c1)),
% 29.01/19.27 inference(modus_ponens,[status(thm)],[66, 19746])).
% 29.01/19.27 tff(19748,plain,
% 29.01/19.27 ($false),
% 29.01/19.27 inference(unit_resolution,[status(thm)],[19688, 19747])).
% 29.01/19.27 tff(19749,plain,((~(f1(f5(c2), f5(c1)) = c1)) | (~big_f(f3(c1, f9(c1, c1)), c1)) | big_f(c1, c1) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | (f3(c1, f9(c1, c1)) = f9(c1, c1))), inference(lemma,lemma(discharge,[]))).
% 29.01/19.27 tff(19750,plain,
% 29.01/19.27 ($false),
% 29.01/19.27 inference(unit_resolution,[status(thm)],[19749, 19735, 19731, 1498, 66, 11752, 11819, 19729])).
% 29.01/19.27 tff(19751,plain,(big_f(f9(c1, c1), f1(f9(c1, c1), c1)) | (~(f9(f10(c2), f4(c4)) = c2)) | big_f(c1, c1) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | (f9(c1, c1) = c3) | (c1 = c4) | (~big_f(f9(c1, c1), c1))), inference(lemma,lemma(discharge,[]))).
% 29.01/19.27 tff(19752,plain,
% 29.01/19.27 (big_f(f9(c1, c1), f1(f9(c1, c1), c1))),
% 29.01/19.27 inference(unit_resolution,[status(thm)],[19751, 66, 1498, 11752, 11819, 19621, 19676, 8714])).
% 29.01/19.27 tff(19753,plain,
% 29.01/19.27 (f1(f9(c1, c1), c1) = f1(c2, c1)),
% 29.01/19.27 inference(monotonicity,[status(thm)],[17728])).
% 29.01/19.27 tff(19754,plain,
% 29.01/19.27 (f1(f9(c1, c1), c1) = f9(c1, c1)),
% 29.01/19.27 inference(transitivity,[status(thm)],[19753, 12189, 17733, 17726])).
% 29.01/19.27 tff(19755,plain,
% 29.01/19.27 (big_f(f9(c1, c1), f1(f9(c1, c1), c1)) <=> big_f(f9(c1, c1), f9(c1, c1))),
% 29.01/19.27 inference(monotonicity,[status(thm)],[19754])).
% 29.01/19.27 tff(19756,plain,
% 29.01/19.27 (big_f(f9(c1, c1), f9(c1, c1)) <=> big_f(f9(c1, c1), f1(f9(c1, c1), c1))),
% 29.01/19.27 inference(symmetry,[status(thm)],[19755])).
% 29.01/19.27 tff(19757,plain,
% 29.01/19.27 ((~big_f(f9(c1, c1), f9(c1, c1))) <=> (~big_f(f9(c1, c1), f1(f9(c1, c1), c1)))),
% 29.01/19.27 inference(monotonicity,[status(thm)],[19756])).
% 29.01/19.27 tff(19758,assumption,(~big_f(f9(c1, c1), f9(c1, c1))), introduced(assumption)).
% 29.01/19.27 tff(19759,plain,
% 29.01/19.27 (~big_f(f9(c1, c1), f1(f9(c1, c1), c1))),
% 29.01/19.27 inference(modus_ponens,[status(thm)],[19758, 19757])).
% 29.01/19.27 tff(19760,assumption,(big_f(f9(c1, c1), f1(f9(c1, c1), c1))), introduced(assumption)).
% 29.01/19.27 tff(19761,plain,
% 29.01/19.27 ($false),
% 29.01/19.27 inference(unit_resolution,[status(thm)],[19760, 19759])).
% 29.01/19.27 tff(19762,plain,((~(f1(c2, c1) = c2)) | (~big_f(f9(c1, c1), f1(f9(c1, c1), c1))) | big_f(f9(c1, c1), f9(c1, c1)) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.01/19.27 tff(19763,plain,
% 29.01/19.27 (~(f1(c2, c1) = c2)),
% 29.01/19.27 inference(unit_resolution,[status(thm)],[19762, 19752, 17762, 1498, 11752, 11819])).
% 29.01/19.27 tff(19764,plain,
% 29.01/19.27 (f1(c2, c1) = c1),
% 29.01/19.27 inference(unit_resolution,[status(thm)],[10113, 19763])).
% 29.01/19.27 tff(19765,plain,
% 29.01/19.27 (f1(c2, c1) = f1(f9(c1, c1), c1)),
% 29.01/19.27 inference(symmetry,[status(thm)],[19753])).
% 29.01/19.27 tff(19766,plain,
% 29.01/19.27 (big_f(c2, f1(c2, c1)) <=> big_f(f9(c1, c1), f1(f9(c1, c1), c1))),
% 29.01/19.27 inference(monotonicity,[status(thm)],[17734, 19765])).
% 29.01/19.27 tff(19767,plain,
% 29.01/19.27 (big_f(f9(c1, c1), f1(f9(c1, c1), c1)) <=> big_f(c2, f1(c2, c1))),
% 29.01/19.27 inference(symmetry,[status(thm)],[19766])).
% 29.01/19.27 tff(19768,plain,
% 29.01/19.27 (big_f(c2, f1(c2, c1))),
% 29.01/19.27 inference(modus_ponens,[status(thm)],[19752, 19767])).
% 29.01/19.27 tff(19769,plain,
% 29.01/19.27 (f3(c1, c2) = c2),
% 29.01/19.27 inference(unit_resolution,[status(thm)],[16144, 13164, 377, 11484, 11485, 482])).
% 29.01/19.27 tff(19770,plain,
% 29.01/19.27 (f3(c1, c2) = f9(c1, c1)),
% 29.01/19.27 inference(transitivity,[status(thm)],[19769, 17733, 17726])).
% 29.01/19.27 tff(19771,plain,
% 29.01/19.27 (big_f(f3(c1, c2), c1) <=> big_f(f9(c1, c1), c1)),
% 29.01/19.27 inference(monotonicity,[status(thm)],[19770])).
% 29.01/19.27 tff(19772,plain,
% 29.01/19.27 (big_f(f9(c1, c1), c1) <=> big_f(f3(c1, c2), c1)),
% 29.01/19.27 inference(symmetry,[status(thm)],[19771])).
% 29.01/19.27 tff(19773,plain,
% 29.01/19.27 (big_f(f3(c1, c2), c1)),
% 29.01/19.27 inference(modus_ponens,[status(thm)],[8714, 19772])).
% 29.01/19.27 tff(19774,plain,
% 29.01/19.27 ($false),
% 29.01/19.27 inference(unit_resolution,[status(thm)],[13164, 19773])).
% 29.01/19.27 tff(19775,plain,(big_f(f3(c1, c2), c1) | (~big_f(f9(c1, c1), c1)) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | (c2 = c3) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1)) | (c1 = c4)), inference(lemma,lemma(discharge,[]))).
% 29.01/19.27 tff(19776,plain,
% 29.01/19.27 (big_f(f3(c1, c2), c1)),
% 29.01/19.27 inference(unit_resolution,[status(thm)],[19775, 19768, 1498, 11752, 11819, 377, 8714, 19676, 19764])).
% 29.01/19.27 tff(19777,plain,
% 29.01/19.27 (big_f(f3(c1, f9(c1, c1)), f10(f9(c1, c1)))),
% 29.01/19.27 inference(modus_ponens,[status(thm)],[19776, 19645])).
% 29.01/19.27 tff(19778,plain,
% 29.01/19.27 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f7(c1) = c1) | big_f(f7(c1), f9(c1, c1)) | (f3(c1, f9(c1, c1)) = f8(f9(c1, c1))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~(f9(c1, c1) = f5(c1))) | (~big_f(f3(c1, f9(c1, c1)), f10(f9(c1, c1)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f7(c1) = c1) | big_f(f7(c1), f9(c1, c1)) | (f3(c1, f9(c1, c1)) = f8(f9(c1, c1))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~(f9(c1, c1) = f5(c1))) | (~big_f(f3(c1, f9(c1, c1)), f10(f9(c1, c1)))))),
% 29.01/19.27 inference(rewrite,[status(thm)],[])).
% 29.01/19.27 tff(19779,plain,
% 29.01/19.27 (((~(f9(c1, c1) = f5(c1))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (f3(c1, f9(c1, c1)) = f8(f9(c1, c1))) | (~big_f(f3(c1, f9(c1, c1)), f10(f9(c1, c1)))) | (f7(c1) = c1) | big_f(f7(c1), f9(c1, c1))) <=> ((f7(c1) = c1) | big_f(f7(c1), f9(c1, c1)) | (f3(c1, f9(c1, c1)) = f8(f9(c1, c1))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~(f9(c1, c1) = f5(c1))) | (~big_f(f3(c1, f9(c1, c1)), f10(f9(c1, c1)))))),
% 29.01/19.27 inference(rewrite,[status(thm)],[])).
% 29.01/19.27 tff(19780,plain,
% 29.01/19.27 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(f9(c1, c1) = f5(c1))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (f3(c1, f9(c1, c1)) = f8(f9(c1, c1))) | (~big_f(f3(c1, f9(c1, c1)), f10(f9(c1, c1)))) | (f7(c1) = c1) | big_f(f7(c1), f9(c1, c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f7(c1) = c1) | big_f(f7(c1), f9(c1, c1)) | (f3(c1, f9(c1, c1)) = f8(f9(c1, c1))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~(f9(c1, c1) = f5(c1))) | (~big_f(f3(c1, f9(c1, c1)), f10(f9(c1, c1))))))),
% 29.01/19.27 inference(monotonicity,[status(thm)],[19779])).
% 29.01/19.27 tff(19781,plain,
% 29.01/19.27 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(f9(c1, c1) = f5(c1))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (f3(c1, f9(c1, c1)) = f8(f9(c1, c1))) | (~big_f(f3(c1, f9(c1, c1)), f10(f9(c1, c1)))) | (f7(c1) = c1) | big_f(f7(c1), f9(c1, c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f7(c1) = c1) | big_f(f7(c1), f9(c1, c1)) | (f3(c1, f9(c1, c1)) = f8(f9(c1, c1))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~(f9(c1, c1) = f5(c1))) | (~big_f(f3(c1, f9(c1, c1)), f10(f9(c1, c1)))))),
% 29.01/19.27 inference(transitivity,[status(thm)],[19780, 19778])).
% 29.01/19.27 tff(19782,plain,
% 29.01/19.27 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(f9(c1, c1) = f5(c1))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (f3(c1, f9(c1, c1)) = f8(f9(c1, c1))) | (~big_f(f3(c1, f9(c1, c1)), f10(f9(c1, c1)))) | (f7(c1) = c1) | big_f(f7(c1), f9(c1, c1)))),
% 29.01/19.27 inference(quant_inst,[status(thm)],[])).
% 29.01/19.27 tff(19783,plain,
% 29.01/19.27 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f7(c1) = c1) | big_f(f7(c1), f9(c1, c1)) | (f3(c1, f9(c1, c1)) = f8(f9(c1, c1))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~(f9(c1, c1) = f5(c1))) | (~big_f(f3(c1, f9(c1, c1)), f10(f9(c1, c1))))),
% 29.01/19.27 inference(modus_ponens,[status(thm)],[19782, 19781])).
% 29.01/19.27 tff(19784,plain,
% 29.01/19.27 (f3(c1, f9(c1, c1)) = f8(f9(c1, c1))),
% 29.01/19.27 inference(unit_resolution,[status(thm)],[19783, 705, 115, 17792, 19777, 19624, 17763])).
% 29.01/19.27 tff(19785,plain,
% 29.01/19.27 (f3(c1, f9(c1, c1)) = f9(c1, c1)),
% 29.01/19.27 inference(modus_ponens,[status(thm)],[19784, 19640])).
% 29.01/19.27 tff(19786,plain,
% 29.01/19.27 (big_f(f3(c1, f9(c1, c1)), c1)),
% 29.01/19.27 inference(modus_ponens,[status(thm)],[19776, 19644])).
% 29.01/19.27 tff(19787,plain,
% 29.01/19.27 ((f1(c2, c1) = c1) <=> (f1(f9(c1, c1), c1) = c1)),
% 29.01/19.27 inference(monotonicity,[status(thm)],[19765])).
% 29.01/19.27 tff(19788,plain,
% 29.01/19.27 (f1(f9(c1, c1), c1) = c1),
% 29.01/19.27 inference(modus_ponens,[status(thm)],[19764, 19787])).
% 29.01/19.27 tff(19789,plain,
% 29.01/19.27 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c4) | (f9(c1, c1) = c3) | (~big_f(f9(c1, c1), f1(f9(c1, c1), c1))) | (~(f3(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f3(c1, f9(c1, c1)), c1)) | (~(f1(f9(c1, c1), c1) = c1)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c4) | (f9(c1, c1) = c3) | (~big_f(f9(c1, c1), f1(f9(c1, c1), c1))) | (~(f3(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f3(c1, f9(c1, c1)), c1)) | (~(f1(f9(c1, c1), c1) = c1)))),
% 29.01/19.27 inference(rewrite,[status(thm)],[])).
% 29.01/19.27 tff(19790,plain,
% 29.01/19.27 (((c1 = c4) | (f9(c1, c1) = c3) | (~(f3(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f3(c1, f9(c1, c1)), c1)) | (~(f1(f9(c1, c1), c1) = c1)) | (~big_f(f9(c1, c1), f1(f9(c1, c1), c1)))) <=> ((c1 = c4) | (f9(c1, c1) = c3) | (~big_f(f9(c1, c1), f1(f9(c1, c1), c1))) | (~(f3(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f3(c1, f9(c1, c1)), c1)) | (~(f1(f9(c1, c1), c1) = c1)))),
% 29.09/19.27 inference(rewrite,[status(thm)],[])).
% 29.09/19.27 tff(19791,plain,
% 29.09/19.27 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c4) | (f9(c1, c1) = c3) | (~(f3(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f3(c1, f9(c1, c1)), c1)) | (~(f1(f9(c1, c1), c1) = c1)) | (~big_f(f9(c1, c1), f1(f9(c1, c1), c1))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c4) | (f9(c1, c1) = c3) | (~big_f(f9(c1, c1), f1(f9(c1, c1), c1))) | (~(f3(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f3(c1, f9(c1, c1)), c1)) | (~(f1(f9(c1, c1), c1) = c1))))),
% 29.09/19.27 inference(monotonicity,[status(thm)],[19790])).
% 29.09/19.27 tff(19792,plain,
% 29.09/19.27 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c4) | (f9(c1, c1) = c3) | (~(f3(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f3(c1, f9(c1, c1)), c1)) | (~(f1(f9(c1, c1), c1) = c1)) | (~big_f(f9(c1, c1), f1(f9(c1, c1), c1))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c4) | (f9(c1, c1) = c3) | (~big_f(f9(c1, c1), f1(f9(c1, c1), c1))) | (~(f3(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f3(c1, f9(c1, c1)), c1)) | (~(f1(f9(c1, c1), c1) = c1)))),
% 29.09/19.27 inference(transitivity,[status(thm)],[19791, 19789])).
% 29.09/19.27 tff(19793,plain,
% 29.09/19.27 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c4) | (f9(c1, c1) = c3) | (~(f3(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f3(c1, f9(c1, c1)), c1)) | (~(f1(f9(c1, c1), c1) = c1)) | (~big_f(f9(c1, c1), f1(f9(c1, c1), c1))))),
% 29.09/19.27 inference(quant_inst,[status(thm)],[])).
% 29.09/19.27 tff(19794,plain,
% 29.09/19.27 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c4) | (f9(c1, c1) = c3) | (~big_f(f9(c1, c1), f1(f9(c1, c1), c1))) | (~(f3(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f3(c1, f9(c1, c1)), c1)) | (~(f1(f9(c1, c1), c1) = c1))),
% 29.09/19.27 inference(modus_ponens,[status(thm)],[19793, 19792])).
% 29.09/19.27 tff(19795,plain,
% 29.09/19.27 (~(f3(c1, f9(c1, c1)) = f9(c1, c1))),
% 29.09/19.27 inference(unit_resolution,[status(thm)],[19794, 933, 19676, 19621, 19788, 19752, 19786])).
% 29.09/19.27 tff(19796,plain,
% 29.09/19.27 ($false),
% 29.09/19.27 inference(unit_resolution,[status(thm)],[19795, 19785])).
% 29.09/19.27 tff(19797,plain,(big_f(c1, c1) | (~(f9(c1, c1) = f8(f9(c1, c1)))) | (f9(c1, c1) = c3) | (f7(c1) = c1) | (~(f9(c1, c1) = f5(c1))) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | (c2 = c3) | (~big_f(f9(c1, c1), c1)) | (~(f7(c2) = c1)) | big_f(c2, c2) | (f7(f7(c2)) = c3) | (~(f10(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.09/19.27 tff(19798,plain,
% 29.09/19.27 (f7(f7(c2)) = c3),
% 29.09/19.27 inference(unit_resolution,[status(thm)],[19797, 19639, 17860, 115, 19624, 1498, 11752, 11819, 19635, 8714, 292, 121, 19621, 3762])).
% 29.09/19.27 tff(19799,plain,
% 29.09/19.27 ($false),
% 29.09/19.27 inference(unit_resolution,[status(thm)],[19798, 19622])).
% 29.09/19.27 tff(19800,plain,((f9(c1, c1) = c3) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | (~(f7(c2) = c1)) | (~(f9(c1, c1) = f8(f9(c1, c1)))) | (f7(c1) = c1) | (~(f9(c1, c1) = f5(c1))) | (~big_f(f9(c1, c1), c1)) | big_f(c2, c2) | (~(f10(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.09/19.27 tff(19801,plain,
% 29.09/19.27 (f9(c1, c1) = c3),
% 29.09/19.27 inference(unit_resolution,[status(thm)],[19800, 17799, 11752, 11819, 292, 1498, 115, 17764, 17807, 121, 3762])).
% 29.09/19.27 tff(19802,plain,
% 29.09/19.27 (c3 = c2),
% 29.09/19.27 inference(modus_ponens,[status(thm)],[19801, 19614])).
% 29.09/19.27 tff(19803,assumption,(big_f(c1, f9(c1, c1))), introduced(assumption)).
% 29.09/19.27 tff(19804,plain,
% 29.09/19.27 (c3 = f9(c1, c1)),
% 29.09/19.27 inference(symmetry,[status(thm)],[19801])).
% 29.09/19.27 tff(19805,plain,
% 29.09/19.27 ((c1 = c3) <=> (c1 = f9(c1, c1))),
% 29.09/19.27 inference(monotonicity,[status(thm)],[19804])).
% 29.09/19.27 tff(19806,plain,
% 29.09/19.27 ((c1 = c3) <=> (f9(c1, c1) = c1)),
% 29.09/19.27 inference(transitivity,[status(thm)],[19805, 17725])).
% 29.09/19.27 tff(19807,plain,
% 29.09/19.27 ((f9(c1, c1) = c1) <=> (c1 = c3)),
% 29.09/19.27 inference(symmetry,[status(thm)],[19806])).
% 29.09/19.27 tff(19808,plain,
% 29.09/19.27 ((~(f9(c1, c1) = c1)) <=> (~(c1 = c3))),
% 29.09/19.27 inference(monotonicity,[status(thm)],[19807])).
% 29.09/19.27 tff(19809,plain,
% 29.09/19.27 (~(c1 = c3)),
% 29.09/19.27 inference(modus_ponens,[status(thm)],[17791, 19808])).
% 29.09/19.27 tff(19810,plain,
% 29.09/19.27 (~big_f(c1, f10(f9(c1, c1)))),
% 29.09/19.27 inference(unit_resolution,[status(thm)],[19633, 115, 17792, 17805, 17764, 17763])).
% 29.09/19.27 tff(19811,plain,
% 29.09/19.27 (~big_f(c1, c1)),
% 29.09/19.27 inference(modus_ponens,[status(thm)],[19810, 19623])).
% 29.09/19.27 tff(19812,plain,
% 29.09/19.27 ((f7(f4(c4)) = f4(c4)) <=> (f7(c1) = c1)),
% 29.09/19.27 inference(monotonicity,[status(thm)],[16243, 11752])).
% 29.09/19.27 tff(19813,plain,
% 29.09/19.27 ((f7(c1) = c1) <=> (f7(f4(c4)) = f4(c4))),
% 29.09/19.27 inference(symmetry,[status(thm)],[19812])).
% 29.09/19.27 tff(19814,plain,
% 29.09/19.27 ((~(f7(c1) = c1)) <=> (~(f7(f4(c4)) = f4(c4)))),
% 29.09/19.27 inference(monotonicity,[status(thm)],[19813])).
% 29.09/19.27 tff(19815,plain,
% 29.09/19.27 (~(f7(f4(c4)) = f4(c4))),
% 29.09/19.27 inference(modus_ponens,[status(thm)],[115, 19814])).
% 29.09/19.27 tff(19816,plain,
% 29.09/19.27 (big_f(c1, c2)),
% 29.09/19.27 inference(modus_ponens,[status(thm)],[19803, 19500])).
% 29.09/19.27 tff(19817,plain,
% 29.09/19.27 (big_f(c1, c1) <=> big_f(f7(f9(c1, c1)), c1)),
% 29.09/19.27 inference(symmetry,[status(thm)],[17985])).
% 29.09/19.27 tff(19818,plain,
% 29.09/19.27 (big_f(c1, f10(f9(c1, c1))) <=> big_f(f7(c2), c1)),
% 29.09/19.27 inference(transitivity,[status(thm)],[17982, 19817, 19300])).
% 29.09/19.27 tff(19819,plain,
% 29.09/19.27 ((~big_f(c1, f10(f9(c1, c1)))) <=> (~big_f(f7(c2), c1))),
% 29.09/19.27 inference(monotonicity,[status(thm)],[19818])).
% 29.09/19.27 tff(19820,plain,
% 29.09/19.27 (~big_f(f7(c2), c1)),
% 29.09/19.27 inference(modus_ponens,[status(thm)],[19810, 19819])).
% 29.09/19.27 tff(19821,plain,
% 29.09/19.27 (big_f(c1, f10(f9(c1, c1))) <=> big_f(c1, f10(c1))),
% 29.09/19.27 inference(transitivity,[status(thm)],[17982, 19647])).
% 29.09/19.27 tff(19822,plain,
% 29.09/19.27 ((~big_f(c1, f10(f9(c1, c1)))) <=> (~big_f(c1, f10(c1)))),
% 29.09/19.27 inference(monotonicity,[status(thm)],[19821])).
% 29.09/19.27 tff(19823,plain,
% 29.09/19.27 (~big_f(c1, f10(c1))),
% 29.09/19.27 inference(modus_ponens,[status(thm)],[19810, 19822])).
% 29.09/19.27 tff(19824,plain,
% 29.09/19.27 (~big_f(f4(c4), c4)),
% 29.09/19.27 inference(unit_resolution,[status(thm)],[18234, 564, 18228, 3030, 11819, 11752])).
% 29.09/19.27 tff(19825,plain,
% 29.09/19.27 (c1 = f4(c1)),
% 29.09/19.27 inference(transitivity,[status(thm)],[16651, 3840])).
% 29.09/19.27 tff(19826,plain,
% 29.09/19.27 ((f9(f10(c2), f4(c4)) = c1) <=> (f9(c1, c1) = c1)),
% 29.09/19.27 inference(monotonicity,[status(thm)],[17726])).
% 29.09/19.27 tff(19827,plain,
% 29.09/19.27 (f9(c1, c1) = c1),
% 29.09/19.27 inference(modus_ponens,[status(thm)],[148, 19826])).
% 29.09/19.27 tff(19828,plain,
% 29.09/19.27 ($false),
% 29.09/19.27 inference(unit_resolution,[status(thm)],[4070, 19827])).
% 29.09/19.27 tff(19829,plain,((~(f9(f10(c2), f4(c4)) = c1)) | (f9(c1, c1) = c1) | (~(f4(c4) = c1)) | (~(f10(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.09/19.27 tff(19830,plain,
% 29.09/19.27 (~(f9(f10(c2), f4(c4)) = c1)),
% 29.09/19.27 inference(unit_resolution,[status(thm)],[19829, 4070, 11752, 11819])).
% 29.09/19.27 tff(19831,plain,
% 29.09/19.27 (f9(f10(c2), f4(c4)) = c2),
% 29.09/19.27 inference(unit_resolution,[status(thm)],[146, 19830])).
% 29.09/19.27 tff(19832,plain,
% 29.09/19.27 (f9(c1, c1) = c2),
% 29.09/19.27 inference(transitivity,[status(thm)],[17727, 19831])).
% 29.09/19.27 tff(19833,plain,
% 29.09/19.27 (f1(c1, f9(c1, c1)) = f1(c1, c2)),
% 29.09/19.27 inference(monotonicity,[status(thm)],[19832])).
% 29.09/19.27 tff(19834,plain,
% 29.09/19.27 (f1(c1, f9(c1, c1)) = c1),
% 29.09/19.27 inference(transitivity,[status(thm)],[19833, 1095])).
% 29.09/19.27 tff(19835,plain,
% 29.09/19.27 ((f1(c1, f9(c1, c1)) = f9(c1, c1)) <=> (c1 = f9(c1, c1))),
% 29.09/19.27 inference(monotonicity,[status(thm)],[19834])).
% 29.09/19.27 tff(19836,plain,
% 29.09/19.27 ((f1(c1, f9(c1, c1)) = f9(c1, c1)) <=> (f9(c1, c1) = c1)),
% 29.09/19.27 inference(transitivity,[status(thm)],[19835, 17725])).
% 29.09/19.27 tff(19837,plain,
% 29.09/19.27 ((f9(c1, c1) = c1) <=> (f1(c1, f9(c1, c1)) = f9(c1, c1))),
% 29.09/19.27 inference(symmetry,[status(thm)],[19836])).
% 29.09/19.27 tff(19838,plain,
% 29.09/19.27 ((~(f9(c1, c1) = c1)) <=> (~(f1(c1, f9(c1, c1)) = f9(c1, c1)))),
% 29.09/19.27 inference(monotonicity,[status(thm)],[19837])).
% 29.09/19.27 tff(19839,plain,
% 29.09/19.27 (~(f1(c1, f9(c1, c1)) = f9(c1, c1))),
% 29.09/19.27 inference(modus_ponens,[status(thm)],[4070, 19838])).
% 29.09/19.27 tff(19840,plain,
% 29.09/19.27 (big_f(c1, f1(c1, f9(c1, c1))) <=> big_f(f7(c2), c1)),
% 29.09/19.27 inference(monotonicity,[status(thm)],[342, 19834])).
% 29.09/19.27 tff(19841,plain,
% 29.09/19.27 (big_f(f7(c2), c1) <=> big_f(c1, f1(c1, f9(c1, c1)))),
% 29.09/19.27 inference(symmetry,[status(thm)],[19840])).
% 29.09/19.27 tff(19842,plain,
% 29.09/19.27 ((~big_f(f7(c2), c1)) <=> (~big_f(c1, f1(c1, f9(c1, c1))))),
% 29.09/19.27 inference(monotonicity,[status(thm)],[19841])).
% 29.09/19.27 tff(19843,plain,
% 29.09/19.27 (~big_f(c1, f1(c1, f9(c1, c1)))),
% 29.09/19.27 inference(modus_ponens,[status(thm)],[333, 19842])).
% 29.09/19.27 tff(19844,assumption,(c1 = f4(c1)), introduced(assumption)).
% 29.09/19.27 tff(19845,plain,
% 29.09/19.27 ((~big_f(f7(c2), c1)) <=> (~big_f(c1, c1))),
% 29.09/19.27 inference(monotonicity,[status(thm)],[9704])).
% 29.09/19.27 tff(19846,plain,
% 29.09/19.27 (~big_f(c1, c1)),
% 29.09/19.27 inference(modus_ponens,[status(thm)],[333, 19845])).
% 29.09/19.27 tff(19847,plain,
% 29.09/19.27 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c1 = c3) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (f1(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(c1, f1(c1, f9(c1, c1))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (c1 = c3) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (f1(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(c1, f1(c1, f9(c1, c1))))),
% 29.09/19.28 inference(rewrite,[status(thm)],[])).
% 29.09/19.28 tff(19848,plain,
% 29.09/19.28 (((c1 = c3) | (f1(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(c1, f1(c1, f9(c1, c1))) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1)))) <=> ((c1 = c3) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (f1(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(c1, f1(c1, f9(c1, c1))))),
% 29.09/19.28 inference(rewrite,[status(thm)],[])).
% 29.09/19.28 tff(19849,plain,
% 29.09/19.28 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c1 = c3) | (f1(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(c1, f1(c1, f9(c1, c1))) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c1 = c3) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (f1(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(c1, f1(c1, f9(c1, c1)))))),
% 29.09/19.28 inference(monotonicity,[status(thm)],[19848])).
% 29.09/19.28 tff(19850,plain,
% 29.09/19.28 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c1 = c3) | (f1(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(c1, f1(c1, f9(c1, c1))) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (c1 = c3) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (f1(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(c1, f1(c1, f9(c1, c1))))),
% 29.09/19.28 inference(transitivity,[status(thm)],[19849, 19847])).
% 29.09/19.28 tff(19851,plain,
% 29.09/19.28 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c1 = c3) | (f1(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(c1, f1(c1, f9(c1, c1))) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))))),
% 29.09/19.28 inference(quant_inst,[status(thm)],[])).
% 29.09/19.28 tff(19852,plain,
% 29.09/19.28 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (c1 = c3) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (f1(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(c1, f1(c1, f9(c1, c1)))),
% 29.09/19.28 inference(modus_ponens,[status(thm)],[19851, 19850])).
% 29.09/19.28 tff(19853,plain,
% 29.09/19.28 ((f1(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(c1, f1(c1, f9(c1, c1)))),
% 29.09/19.28 inference(unit_resolution,[status(thm)],[19852, 402, 168, 11526, 19846, 19844])).
% 29.09/19.28 tff(19854,plain,
% 29.09/19.28 ($false),
% 29.09/19.28 inference(unit_resolution,[status(thm)],[19853, 19843, 19839])).
% 29.09/19.28 tff(19855,plain,((~(f1(c1, c2) = c1)) | (c1 = c3) | (~(c1 = c4)) | (~(c1 = f4(c1))) | big_f(f7(c2), c1) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | (~(f7(c2) = c1)) | (f9(c1, c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.09/19.28 tff(19856,plain,
% 29.09/19.28 (~(f1(c1, c2) = c1)),
% 29.09/19.28 inference(unit_resolution,[status(thm)],[19855, 19825, 4070, 333, 564, 11752, 11819, 292, 168])).
% 29.09/19.28 tff(19857,plain,
% 29.09/19.28 (f1(c1, c2) = c2),
% 29.09/19.28 inference(unit_resolution,[status(thm)],[841, 19856])).
% 29.09/19.28 tff(19858,plain,
% 29.09/19.28 (f1(c1, f1(c1, c2)) = f1(c1, c2)),
% 29.09/19.28 inference(monotonicity,[status(thm)],[19857])).
% 29.09/19.28 tff(19859,plain,
% 29.09/19.28 (f1(c1, f1(c1, c2)) = c2),
% 29.09/19.28 inference(transitivity,[status(thm)],[19858, 19857])).
% 29.09/19.28 tff(19860,plain,
% 29.09/19.28 (big_f(c1, f1(c1, f1(c1, c2))) <=> big_f(c1, c2)),
% 29.09/19.28 inference(monotonicity,[status(thm)],[19859])).
% 29.09/19.28 tff(19861,plain,
% 29.09/19.28 (big_f(c1, c2) <=> big_f(c1, f1(c1, f1(c1, c2)))),
% 29.09/19.28 inference(symmetry,[status(thm)],[19860])).
% 29.09/19.28 tff(19862,plain,
% 29.09/19.28 (big_f(c1, f1(c1, f1(c1, c2)))),
% 29.09/19.28 inference(modus_ponens,[status(thm)],[2865, 19861])).
% 29.09/19.28 tff(19863,plain,
% 29.09/19.28 ($false),
% 29.09/19.28 inference(unit_resolution,[status(thm)],[2254, 19862, 19858, 168, 19824])).
% 29.09/19.28 tff(19864,plain,((~(c4 = c1)) | (c1 = c3) | (~big_f(c1, c2)) | (f9(c1, c1) = c1) | big_f(f7(c2), c1) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | (~(f7(c2) = c1)) | (~(f10(f10(c2)) = c1)) | big_f(c1, f10(c1))), inference(lemma,lemma(discharge,[]))).
% 29.09/19.28 tff(19865,plain,
% 29.09/19.28 (~(c4 = c1)),
% 29.09/19.28 inference(unit_resolution,[status(thm)],[19864, 19809, 11752, 19650, 19823, 17791, 11819, 292, 19820, 19816])).
% 29.09/19.28 tff(19866,plain,
% 29.09/19.28 (c4 = c2),
% 29.09/19.28 inference(unit_resolution,[status(thm)],[461, 19865])).
% 29.09/19.28 tff(19867,plain,
% 29.09/19.28 (f7(c1) = c4),
% 29.09/19.28 inference(modus_ponens,[status(thm)],[431, 870])).
% 29.09/19.28 tff(19868,plain,
% 29.09/19.28 ($false),
% 29.09/19.28 inference(unit_resolution,[status(thm)],[1000, 19867])).
% 29.09/19.28 tff(19869,plain,((~(c4 = c2)) | (f7(c1) = c4) | (~(f7(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.09/19.28 tff(19870,plain,
% 29.09/19.28 (f7(c1) = c4),
% 29.09/19.28 inference(unit_resolution,[status(thm)],[19869, 19866, 120])).
% 29.09/19.28 tff(19871,plain,
% 29.09/19.28 ((f7(f4(c4)) = c4) <=> (f7(c1) = c4)),
% 29.09/19.28 inference(monotonicity,[status(thm)],[16243])).
% 29.09/19.28 tff(19872,plain,
% 29.09/19.28 (f4(c4) = c4),
% 29.09/19.28 inference(transitivity,[status(thm)],[11752, 11526])).
% 29.09/19.28 tff(19873,plain,
% 29.09/19.28 ((f7(f4(c4)) = f4(c4)) <=> (f7(f4(c4)) = c4)),
% 29.09/19.28 inference(monotonicity,[status(thm)],[19872])).
% 29.09/19.28 tff(19874,plain,
% 29.09/19.28 ((f7(f4(c4)) = f4(c4)) <=> (f7(c1) = c4)),
% 29.09/19.28 inference(transitivity,[status(thm)],[19873, 19871])).
% 29.09/19.28 tff(19875,plain,
% 29.09/19.28 ((~(f7(f4(c4)) = f4(c4))) <=> (~(f7(c1) = c4))),
% 29.09/19.28 inference(monotonicity,[status(thm)],[19874])).
% 29.09/19.28 tff(19876,assumption,(~(f7(f4(c4)) = f4(c4))), introduced(assumption)).
% 29.09/19.28 tff(19877,plain,
% 29.09/19.28 (~(f7(c1) = c4)),
% 29.09/19.28 inference(modus_ponens,[status(thm)],[19876, 19875])).
% 29.09/19.28 tff(19878,assumption,(f7(c1) = c4), introduced(assumption)).
% 29.09/19.28 tff(19879,plain,
% 29.09/19.28 ($false),
% 29.09/19.28 inference(unit_resolution,[status(thm)],[19878, 19877])).
% 29.09/19.28 tff(19880,plain,((~(f7(c1) = c4)) | (f7(f4(c4)) = f4(c4)) | (~(f4(c4) = c1)) | (~(c1 = c4))), inference(lemma,lemma(discharge,[]))).
% 29.09/19.28 tff(19881,plain,
% 29.09/19.28 (~(c1 = c4)),
% 29.09/19.28 inference(unit_resolution,[status(thm)],[19880, 19870, 11752, 19815])).
% 29.09/19.28 tff(19882,plain,
% 29.09/19.28 (big_f(f3(c1, f9(c1, c1)), c1) <=> big_f(f9(c1, c1), c1)),
% 29.09/19.28 inference(monotonicity,[status(thm)],[19732])).
% 29.09/19.28 tff(19883,plain,
% 29.09/19.28 (big_f(f9(c1, c1), c1) <=> big_f(f3(c1, f9(c1, c1)), c1)),
% 29.09/19.28 inference(symmetry,[status(thm)],[19882])).
% 29.09/19.28 tff(19884,plain,
% 29.09/19.28 (big_f(f3(c1, f9(c1, c1)), c1)),
% 29.09/19.28 inference(modus_ponens,[status(thm)],[8714, 19883])).
% 29.09/19.28 tff(19885,plain,
% 29.09/19.28 (f1(c1, f9(c1, c1)) = f1(c1, c2)),
% 29.09/19.28 inference(monotonicity,[status(thm)],[17728])).
% 29.09/19.28 tff(19886,plain,
% 29.09/19.28 (f1(c1, f9(c1, c1)) = c1),
% 29.09/19.28 inference(transitivity,[status(thm)],[19885, 1095])).
% 29.09/19.28 tff(19887,plain,
% 29.09/19.28 ((f1(c1, f9(c1, c1)) = f9(c1, c1)) <=> (c1 = f9(c1, c1))),
% 29.09/19.28 inference(monotonicity,[status(thm)],[19886])).
% 29.09/19.28 tff(19888,plain,
% 29.09/19.28 ((f1(c1, f9(c1, c1)) = f9(c1, c1)) <=> (f9(c1, c1) = c1)),
% 29.09/19.28 inference(transitivity,[status(thm)],[19887, 17725])).
% 29.09/19.28 tff(19889,plain,
% 29.09/19.28 ((f9(c1, c1) = c1) <=> (f1(c1, f9(c1, c1)) = f9(c1, c1))),
% 29.09/19.28 inference(symmetry,[status(thm)],[19888])).
% 29.09/19.28 tff(19890,plain,
% 29.09/19.28 ((~(f9(c1, c1) = c1)) <=> (~(f1(c1, f9(c1, c1)) = f9(c1, c1)))),
% 29.09/19.28 inference(monotonicity,[status(thm)],[19889])).
% 29.09/19.28 tff(19891,plain,
% 29.09/19.28 (~(f1(c1, f9(c1, c1)) = f9(c1, c1))),
% 29.09/19.28 inference(modus_ponens,[status(thm)],[17791, 19890])).
% 29.09/19.28 tff(19892,plain,
% 29.09/19.28 (big_f(c1, f1(c1, f9(c1, c1))) <=> big_f(c1, c1)),
% 29.09/19.28 inference(monotonicity,[status(thm)],[19886])).
% 29.09/19.28 tff(19893,plain,
% 29.09/19.28 (big_f(c1, c1) <=> big_f(c1, f1(c1, f9(c1, c1)))),
% 29.09/19.28 inference(symmetry,[status(thm)],[19892])).
% 29.09/19.28 tff(19894,plain,
% 29.09/19.28 ((~big_f(c1, c1)) <=> (~big_f(c1, f1(c1, f9(c1, c1))))),
% 29.09/19.28 inference(monotonicity,[status(thm)],[19893])).
% 29.09/19.28 tff(19895,plain,
% 29.09/19.28 (~big_f(c1, f1(c1, f9(c1, c1)))),
% 29.09/19.28 inference(modus_ponens,[status(thm)],[66, 19894])).
% 29.09/19.28 tff(19896,plain,
% 29.09/19.28 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c1 = c3) | (c1 = c4) | (~(f3(c1, f9(c1, c1)) = f9(c1, c1))) | (f1(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(c1, f1(c1, f9(c1, c1))) | (~big_f(f3(c1, f9(c1, c1)), c1)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c1 = c3) | (c1 = c4) | (~(f3(c1, f9(c1, c1)) = f9(c1, c1))) | (f1(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(c1, f1(c1, f9(c1, c1))) | (~big_f(f3(c1, f9(c1, c1)), c1)))),
% 29.09/19.28 inference(rewrite,[status(thm)],[])).
% 29.09/19.28 tff(19897,plain,
% 29.09/19.28 (((c1 = c4) | (c1 = c3) | (f1(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(c1, f1(c1, f9(c1, c1))) | (~(f3(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f3(c1, f9(c1, c1)), c1))) <=> ((c1 = c3) | (c1 = c4) | (~(f3(c1, f9(c1, c1)) = f9(c1, c1))) | (f1(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(c1, f1(c1, f9(c1, c1))) | (~big_f(f3(c1, f9(c1, c1)), c1)))),
% 29.09/19.28 inference(rewrite,[status(thm)],[])).
% 29.09/19.28 tff(19898,plain,
% 29.09/19.28 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c1 = c4) | (c1 = c3) | (f1(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(c1, f1(c1, f9(c1, c1))) | (~(f3(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f3(c1, f9(c1, c1)), c1)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c1 = c3) | (c1 = c4) | (~(f3(c1, f9(c1, c1)) = f9(c1, c1))) | (f1(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(c1, f1(c1, f9(c1, c1))) | (~big_f(f3(c1, f9(c1, c1)), c1))))),
% 29.09/19.28 inference(monotonicity,[status(thm)],[19897])).
% 29.09/19.28 tff(19899,plain,
% 29.09/19.28 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c1 = c4) | (c1 = c3) | (f1(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(c1, f1(c1, f9(c1, c1))) | (~(f3(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f3(c1, f9(c1, c1)), c1)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c1 = c3) | (c1 = c4) | (~(f3(c1, f9(c1, c1)) = f9(c1, c1))) | (f1(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(c1, f1(c1, f9(c1, c1))) | (~big_f(f3(c1, f9(c1, c1)), c1)))),
% 29.09/19.28 inference(transitivity,[status(thm)],[19898, 19896])).
% 29.09/19.28 tff(19900,plain,
% 29.09/19.28 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c1 = c4) | (c1 = c3) | (f1(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(c1, f1(c1, f9(c1, c1))) | (~(f3(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f3(c1, f9(c1, c1)), c1)))),
% 29.09/19.28 inference(quant_inst,[status(thm)],[])).
% 29.09/19.28 tff(19901,plain,
% 29.09/19.28 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c1 = c3) | (c1 = c4) | (~(f3(c1, f9(c1, c1)) = f9(c1, c1))) | (f1(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(c1, f1(c1, f9(c1, c1))) | (~big_f(f3(c1, f9(c1, c1)), c1))),
% 29.09/19.28 inference(modus_ponens,[status(thm)],[19900, 19899])).
% 29.09/19.28 tff(19902,plain,
% 29.09/19.28 ((f1(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(c1, f1(c1, f9(c1, c1)))),
% 29.09/19.28 inference(unit_resolution,[status(thm)],[19901, 969, 168, 482, 19732, 19688])).
% 29.09/19.28 tff(19903,plain,
% 29.09/19.28 ($false),
% 29.09/19.28 inference(unit_resolution,[status(thm)],[19902, 19895, 19891])).
% 29.09/19.28 tff(19904,plain,((~(f1(c1, c2) = c1)) | (c1 = c3) | (c1 = c4) | (~(f3(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f3(c1, f9(c1, c1)), c1)) | big_f(c1, c1) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.09/19.28 tff(19905,plain,
% 29.09/19.28 (~(f1(c1, c2) = c1)),
% 29.09/19.28 inference(unit_resolution,[status(thm)],[19904, 19732, 482, 168, 19884, 66, 1498, 11752, 11819])).
% 29.09/19.28 tff(19906,plain,
% 29.09/19.28 (f1(c1, c2) = c2),
% 29.09/19.28 inference(unit_resolution,[status(thm)],[841, 19905])).
% 29.09/19.28 tff(19907,plain,
% 29.09/19.28 (f1(c1, f9(c1, c1)) = f9(c1, c1)),
% 29.09/19.28 inference(transitivity,[status(thm)],[19885, 19906, 17733, 17726])).
% 29.09/19.28 tff(19908,plain,
% 29.09/19.28 (big_f(c1, f1(c1, f9(c1, c1))) <=> big_f(c1, f9(c1, c1))),
% 29.09/19.28 inference(monotonicity,[status(thm)],[19907])).
% 29.09/19.28 tff(19909,plain,
% 29.09/19.28 (big_f(c1, f9(c1, c1)) <=> big_f(c1, f1(c1, f9(c1, c1)))),
% 29.09/19.28 inference(symmetry,[status(thm)],[19908])).
% 29.09/19.28 tff(19910,plain,
% 29.09/19.28 (big_f(c1, f1(c1, f9(c1, c1)))),
% 29.09/19.28 inference(modus_ponens,[status(thm)],[19803, 19909])).
% 29.09/19.28 tff(19911,plain,
% 29.09/19.28 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (c1 = c4) | (~(f3(c1, f9(c1, c1)) = f9(c1, c1))) | (~(f1(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(c1, f1(c1, f9(c1, c1)))) | (~big_f(f3(c1, f9(c1, c1)), c1)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (c1 = c4) | (~(f3(c1, f9(c1, c1)) = f9(c1, c1))) | (~(f1(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(c1, f1(c1, f9(c1, c1)))) | (~big_f(f3(c1, f9(c1, c1)), c1)))),
% 29.09/19.28 inference(rewrite,[status(thm)],[])).
% 29.09/19.28 tff(19912,plain,
% 29.09/19.28 (((c1 = c4) | (c1 = c3) | (~(f3(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f3(c1, f9(c1, c1)), c1)) | (~(f1(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(c1, f1(c1, f9(c1, c1))))) <=> ((c1 = c3) | (c1 = c4) | (~(f3(c1, f9(c1, c1)) = f9(c1, c1))) | (~(f1(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(c1, f1(c1, f9(c1, c1)))) | (~big_f(f3(c1, f9(c1, c1)), c1)))),
% 29.09/19.28 inference(rewrite,[status(thm)],[])).
% 29.09/19.28 tff(19913,plain,
% 29.09/19.28 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c4) | (c1 = c3) | (~(f3(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f3(c1, f9(c1, c1)), c1)) | (~(f1(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(c1, f1(c1, f9(c1, c1)))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (c1 = c4) | (~(f3(c1, f9(c1, c1)) = f9(c1, c1))) | (~(f1(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(c1, f1(c1, f9(c1, c1)))) | (~big_f(f3(c1, f9(c1, c1)), c1))))),
% 29.09/19.28 inference(monotonicity,[status(thm)],[19912])).
% 29.09/19.28 tff(19914,plain,
% 29.09/19.28 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c4) | (c1 = c3) | (~(f3(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f3(c1, f9(c1, c1)), c1)) | (~(f1(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(c1, f1(c1, f9(c1, c1)))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (c1 = c4) | (~(f3(c1, f9(c1, c1)) = f9(c1, c1))) | (~(f1(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(c1, f1(c1, f9(c1, c1)))) | (~big_f(f3(c1, f9(c1, c1)), c1)))),
% 29.09/19.28 inference(transitivity,[status(thm)],[19913, 19911])).
% 29.09/19.28 tff(19915,plain,
% 29.09/19.28 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c4) | (c1 = c3) | (~(f3(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f3(c1, f9(c1, c1)), c1)) | (~(f1(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(c1, f1(c1, f9(c1, c1)))))),
% 29.09/19.28 inference(quant_inst,[status(thm)],[])).
% 29.09/19.28 tff(19916,plain,
% 29.09/19.28 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (c1 = c4) | (~(f3(c1, f9(c1, c1)) = f9(c1, c1))) | (~(f1(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(c1, f1(c1, f9(c1, c1)))) | (~big_f(f3(c1, f9(c1, c1)), c1))),
% 29.09/19.28 inference(modus_ponens,[status(thm)],[19915, 19914])).
% 29.09/19.28 tff(19917,plain,
% 29.09/19.28 ((~(f1(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(c1, f1(c1, f9(c1, c1))))),
% 29.09/19.28 inference(unit_resolution,[status(thm)],[19916, 933, 168, 482, 19732, 19884])).
% 29.09/19.28 tff(19918,plain,
% 29.09/19.28 ($false),
% 29.09/19.28 inference(unit_resolution,[status(thm)],[19917, 19910, 19907])).
% 29.09/19.28 tff(19919,plain,((~(f3(c1, f9(c1, c1)) = f9(c1, c1))) | (c1 = c3) | (c1 = c4) | (~big_f(c1, f9(c1, c1))) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | big_f(c1, c1) | (~big_f(f9(c1, c1), c1))), inference(lemma,lemma(discharge,[]))).
% 29.09/19.28 tff(19920,plain,
% 29.09/19.28 (~(f3(c1, f9(c1, c1)) = f9(c1, c1))),
% 29.09/19.28 inference(unit_resolution,[status(thm)],[19919, 19881, 19811, 19809, 1498, 11752, 11819, 19803, 17807])).
% 29.09/19.28 tff(19921,plain,
% 29.09/19.28 (f8(c3) = f9(c1, c1)),
% 29.09/19.28 inference(transitivity,[status(thm)],[17990, 17861])).
% 29.09/19.28 tff(19922,plain,
% 29.09/19.28 (f3(c1, f8(c3)) = f3(c1, f9(c1, c1))),
% 29.09/19.28 inference(monotonicity,[status(thm)],[19921])).
% 29.09/19.28 tff(19923,plain,
% 29.09/19.28 ((f3(c1, f8(c3)) = c2) <=> (f3(c1, f9(c1, c1)) = f9(c1, c1))),
% 29.09/19.28 inference(monotonicity,[status(thm)],[19922, 17734])).
% 29.09/19.28 tff(19924,plain,
% 29.09/19.28 ((f3(c1, f9(c1, c1)) = f9(c1, c1)) <=> (f3(c1, f8(c3)) = c2)),
% 29.09/19.28 inference(symmetry,[status(thm)],[19923])).
% 29.09/19.28 tff(19925,plain,
% 29.09/19.28 ((~(f3(c1, f9(c1, c1)) = f9(c1, c1))) <=> (~(f3(c1, f8(c3)) = c2))),
% 29.09/19.28 inference(monotonicity,[status(thm)],[19924])).
% 29.09/19.28 tff(19926,plain,
% 29.09/19.28 (~(f3(c1, f8(c3)) = c2)),
% 29.09/19.28 inference(modus_ponens,[status(thm)],[19694, 19925])).
% 29.09/19.28 tff(19927,plain,
% 29.09/19.28 ($false),
% 29.09/19.28 inference(unit_resolution,[status(thm)],[12781, 19926])).
% 29.09/19.28 tff(19928,plain,((~(f3(c1, f8(c3)) = c2)) | (f3(c1, f9(c1, c1)) = f9(c1, c1)) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | (~(f9(c1, c1) = f8(f9(c1, c1)))) | (~(c3 = c2))), inference(lemma,lemma(discharge,[]))).
% 29.09/19.28 tff(19929,plain,
% 29.09/19.28 (~(f3(c1, f8(c3)) = c2)),
% 29.09/19.28 inference(unit_resolution,[status(thm)],[19928, 19920, 1498, 11752, 11819, 17799, 19802])).
% 29.09/19.28 tff(19930,plain,
% 29.09/19.28 (f3(c1, f8(c3)) = c1),
% 29.09/19.28 inference(unit_resolution,[status(thm)],[7123, 19929])).
% 29.09/19.28 tff(19931,plain,
% 29.09/19.28 (f8(c3) = f8(f9(c1, c1))),
% 29.09/19.28 inference(monotonicity,[status(thm)],[19804])).
% 29.09/19.28 tff(19932,plain,
% 29.09/19.28 (f8(f9(c1, c1)) = f8(c3)),
% 29.09/19.28 inference(symmetry,[status(thm)],[19931])).
% 29.09/19.28 tff(19933,plain,
% 29.09/19.28 (f9(c1, c1) = f8(c3)),
% 29.09/19.28 inference(transitivity,[status(thm)],[17799, 19932])).
% 29.09/19.28 tff(19934,plain,
% 29.09/19.28 (f3(c1, f9(c1, c1)) = f3(c1, f8(c3))),
% 29.09/19.28 inference(monotonicity,[status(thm)],[19933])).
% 29.09/19.28 tff(19935,plain,
% 29.09/19.28 (f3(c1, f9(c1, c1)) = c1),
% 29.09/19.28 inference(transitivity,[status(thm)],[19934, 19930])).
% 29.09/19.28 tff(19936,plain,
% 29.09/19.28 (big_f(f3(c1, f9(c1, c1)), c1) <=> big_f(c1, c1)),
% 29.09/19.28 inference(monotonicity,[status(thm)],[19935])).
% 29.09/19.28 tff(19937,plain,
% 29.09/19.28 (big_f(c1, c1) <=> big_f(f3(c1, f9(c1, c1)), c1)),
% 29.09/19.28 inference(symmetry,[status(thm)],[19936])).
% 29.09/19.28 tff(19938,plain,
% 29.09/19.28 ((~big_f(c1, c1)) <=> (~big_f(f3(c1, f9(c1, c1)), c1))),
% 29.09/19.28 inference(monotonicity,[status(thm)],[19937])).
% 29.09/19.28 tff(19939,plain,
% 29.09/19.28 (~big_f(f3(c1, f9(c1, c1)), c1)),
% 29.09/19.29 inference(modus_ponens,[status(thm)],[19811, 19938])).
% 29.09/19.29 tff(19940,plain,
% 29.09/19.29 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c1 = c3) | (c1 = c4) | (f1(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(c1, f1(c1, f9(c1, c1))) | big_f(f3(c1, f9(c1, c1)), c1) | (f3(c1, f9(c1, c1)) = f9(c1, c1)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (c1 = c3) | (c1 = c4) | (f1(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(c1, f1(c1, f9(c1, c1))) | big_f(f3(c1, f9(c1, c1)), c1) | (f3(c1, f9(c1, c1)) = f9(c1, c1)))),
% 29.09/19.29 inference(rewrite,[status(thm)],[])).
% 29.09/19.29 tff(19941,plain,
% 29.09/19.29 (((c1 = c4) | (f3(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f3(c1, f9(c1, c1)), c1) | (c1 = c3) | (f1(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(c1, f1(c1, f9(c1, c1)))) <=> ((c1 = c3) | (c1 = c4) | (f1(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(c1, f1(c1, f9(c1, c1))) | big_f(f3(c1, f9(c1, c1)), c1) | (f3(c1, f9(c1, c1)) = f9(c1, c1)))),
% 29.09/19.29 inference(rewrite,[status(thm)],[])).
% 29.09/19.29 tff(19942,plain,
% 29.09/19.29 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c1 = c4) | (f3(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f3(c1, f9(c1, c1)), c1) | (c1 = c3) | (f1(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(c1, f1(c1, f9(c1, c1))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c1 = c3) | (c1 = c4) | (f1(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(c1, f1(c1, f9(c1, c1))) | big_f(f3(c1, f9(c1, c1)), c1) | (f3(c1, f9(c1, c1)) = f9(c1, c1))))),
% 29.09/19.29 inference(monotonicity,[status(thm)],[19941])).
% 29.09/19.29 tff(19943,plain,
% 29.09/19.29 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c1 = c4) | (f3(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f3(c1, f9(c1, c1)), c1) | (c1 = c3) | (f1(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(c1, f1(c1, f9(c1, c1))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (c1 = c3) | (c1 = c4) | (f1(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(c1, f1(c1, f9(c1, c1))) | big_f(f3(c1, f9(c1, c1)), c1) | (f3(c1, f9(c1, c1)) = f9(c1, c1)))),
% 29.09/19.29 inference(transitivity,[status(thm)],[19942, 19940])).
% 29.09/19.29 tff(19944,plain,
% 29.09/19.29 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c1 = c4) | (f3(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f3(c1, f9(c1, c1)), c1) | (c1 = c3) | (f1(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(c1, f1(c1, f9(c1, c1))))),
% 29.09/19.29 inference(quant_inst,[status(thm)],[])).
% 29.09/19.29 tff(19945,plain,
% 29.09/19.29 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (c1 = c3) | (c1 = c4) | (f1(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(c1, f1(c1, f9(c1, c1))) | big_f(f3(c1, f9(c1, c1)), c1) | (f3(c1, f9(c1, c1)) = f9(c1, c1))),
% 29.09/19.29 inference(modus_ponens,[status(thm)],[19944, 19943])).
% 29.09/19.29 tff(19946,plain,
% 29.09/19.29 ((f1(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(c1, f1(c1, f9(c1, c1)))),
% 29.09/19.29 inference(unit_resolution,[status(thm)],[19945, 1014, 168, 482, 19694, 19693])).
% 29.09/19.29 tff(19947,plain,
% 29.09/19.29 ($false),
% 29.09/19.29 inference(unit_resolution,[status(thm)],[19946, 19895, 19891])).
% 29.09/19.29 tff(19948,plain,((~(f1(c1, c2) = c1)) | (c1 = c3) | (c1 = c4) | (f3(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f3(c1, f9(c1, c1)), c1) | big_f(c1, c1) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.09/19.29 tff(19949,plain,
% 29.09/19.29 (~(f1(c1, c2) = c1)),
% 29.09/19.29 inference(unit_resolution,[status(thm)],[19948, 19809, 19881, 19920, 19939, 19811, 1498, 11752, 11819])).
% 29.09/19.29 tff(19950,plain,
% 29.09/19.29 (f1(c1, c2) = c2),
% 29.09/19.29 inference(unit_resolution,[status(thm)],[841, 19949])).
% 29.09/19.29 tff(19951,plain,
% 29.09/19.29 (f1(c1, c2) = f9(c1, c1)),
% 29.09/19.29 inference(transitivity,[status(thm)],[19950, 17733, 17726])).
% 29.09/19.29 tff(19952,plain,
% 29.09/19.29 (f3(f10(c2), f1(c1, c2)) = f3(c1, f9(c1, c1))),
% 29.09/19.29 inference(monotonicity,[status(thm)],[11819, 19951])).
% 29.09/19.29 tff(19953,plain,
% 29.09/19.29 (f3(f10(c2), f1(c1, c2)) = c1),
% 29.09/19.29 inference(transitivity,[status(thm)],[19952, 19934, 19930])).
% 29.09/19.29 tff(19954,plain,
% 29.09/19.29 (big_f(f3(f10(c2), f1(c1, c2)), f10(c2)) <=> big_f(c1, c1)),
% 29.09/19.29 inference(monotonicity,[status(thm)],[19953, 11819])).
% 29.09/19.29 tff(19955,plain,
% 29.09/19.29 (big_f(c1, c1) <=> big_f(f3(f10(c2), f1(c1, c2)), f10(c2))),
% 29.09/19.29 inference(symmetry,[status(thm)],[19954])).
% 29.09/19.29 tff(19956,plain,
% 29.09/19.29 ((~big_f(c1, c1)) <=> (~big_f(f3(f10(c2), f1(c1, c2)), f10(c2)))),
% 29.09/19.29 inference(monotonicity,[status(thm)],[19955])).
% 29.09/19.29 tff(19957,plain,
% 29.09/19.29 (~big_f(f3(f10(c2), f1(c1, c2)), f10(c2))),
% 29.09/19.29 inference(modus_ponens,[status(thm)],[19811, 19956])).
% 29.09/19.29 tff(19958,plain,
% 29.09/19.29 ((f3(f10(c2), f1(c1, c2)) = f1(c1, c2)) <=> (f3(f10(c2), f1(c1, c2)) = c2)),
% 29.09/19.29 inference(monotonicity,[status(thm)],[19950])).
% 29.09/19.29 tff(19959,plain,
% 29.09/19.29 ((f3(f10(c2), f1(c1, c2)) = c2) <=> (f3(f10(c2), f1(c1, c2)) = f1(c1, c2))),
% 29.09/19.29 inference(symmetry,[status(thm)],[19958])).
% 29.09/19.29 tff(19960,plain,
% 29.09/19.29 ((f3(f10(c2), f1(c1, c2)) = c2) <=> (c1 = f9(c1, c1))),
% 29.09/19.29 inference(monotonicity,[status(thm)],[19953, 17734])).
% 29.09/19.29 tff(19961,plain,
% 29.09/19.29 ((f3(f10(c2), f1(c1, c2)) = c2) <=> (f9(c1, c1) = c1)),
% 29.09/19.29 inference(transitivity,[status(thm)],[19960, 17725])).
% 29.09/19.29 tff(19962,plain,
% 29.09/19.29 ((f9(c1, c1) = c1) <=> (f3(f10(c2), f1(c1, c2)) = c2)),
% 29.09/19.29 inference(symmetry,[status(thm)],[19961])).
% 29.09/19.29 tff(19963,plain,
% 29.09/19.29 ((f9(c1, c1) = c1) <=> (f3(f10(c2), f1(c1, c2)) = f1(c1, c2))),
% 29.09/19.29 inference(transitivity,[status(thm)],[19962, 19959])).
% 29.09/19.29 tff(19964,plain,
% 29.09/19.29 ((~(f9(c1, c1) = c1)) <=> (~(f3(f10(c2), f1(c1, c2)) = f1(c1, c2)))),
% 29.09/19.29 inference(monotonicity,[status(thm)],[19963])).
% 29.09/19.29 tff(19965,plain,
% 29.09/19.29 (~(f3(f10(c2), f1(c1, c2)) = f1(c1, c2))),
% 29.09/19.29 inference(modus_ponens,[status(thm)],[17791, 19964])).
% 29.09/19.29 tff(19966,plain,
% 29.09/19.29 ((f10(c2) = c4) <=> (c1 = c4)),
% 29.09/19.29 inference(monotonicity,[status(thm)],[11819])).
% 29.09/19.29 tff(19967,plain,
% 29.09/19.29 ((c1 = c4) <=> (f10(c2) = c4)),
% 29.09/19.29 inference(symmetry,[status(thm)],[19966])).
% 29.09/19.29 tff(19968,plain,
% 29.09/19.29 ((~(c1 = c4)) <=> (~(f10(c2) = c4))),
% 29.09/19.29 inference(monotonicity,[status(thm)],[19967])).
% 29.09/19.29 tff(19969,plain,
% 29.09/19.29 (~(f10(c2) = c4)),
% 29.09/19.29 inference(modus_ponens,[status(thm)],[19881, 19968])).
% 29.09/19.29 tff(19970,plain,
% 29.09/19.29 (f1(c1, f1(c1, c2)) = f1(c1, c2)),
% 29.09/19.29 inference(monotonicity,[status(thm)],[19950])).
% 29.09/19.29 tff(19971,plain,
% 29.09/19.29 (f1(c1, f1(c1, c2)) = f9(c1, c1)),
% 29.09/19.29 inference(transitivity,[status(thm)],[19970, 19950, 17733, 17726])).
% 29.09/19.29 tff(19972,plain,
% 29.09/19.29 (big_f(c1, f1(c1, f1(c1, c2))) <=> big_f(c1, f9(c1, c1))),
% 29.09/19.29 inference(monotonicity,[status(thm)],[19971])).
% 29.09/19.29 tff(19973,plain,
% 29.09/19.29 (big_f(c1, f9(c1, c1)) <=> big_f(c1, f1(c1, f1(c1, c2)))),
% 29.09/19.29 inference(symmetry,[status(thm)],[19972])).
% 29.09/19.29 tff(19974,plain,
% 29.09/19.29 (big_f(c1, f1(c1, f1(c1, c2)))),
% 29.09/19.29 inference(modus_ponens,[status(thm)],[19803, 19973])).
% 29.09/19.29 tff(19975,plain,
% 29.09/19.29 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~(f1(c1, f1(c1, c2)) = f1(c1, c2))) | big_f(f3(f10(c2), f1(c1, c2)), f10(c2)) | (f3(f10(c2), f1(c1, c2)) = f1(c1, c2)) | (f10(c2) = c4) | (~big_f(c1, f1(c1, f1(c1, c2)))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (~(f1(c1, f1(c1, c2)) = f1(c1, c2))) | big_f(f3(f10(c2), f1(c1, c2)), f10(c2)) | (f3(f10(c2), f1(c1, c2)) = f1(c1, c2)) | (f10(c2) = c4) | (~big_f(c1, f1(c1, f1(c1, c2)))))),
% 29.09/19.29 inference(rewrite,[status(thm)],[])).
% 29.09/19.29 tff(19976,plain,
% 29.09/19.29 (((f10(c2) = c4) | (f3(f10(c2), f1(c1, c2)) = f1(c1, c2)) | big_f(f3(f10(c2), f1(c1, c2)), f10(c2)) | (c1 = c3) | (~(f1(c1, f1(c1, c2)) = f1(c1, c2))) | (~big_f(c1, f1(c1, f1(c1, c2))))) <=> ((c1 = c3) | (~(f1(c1, f1(c1, c2)) = f1(c1, c2))) | big_f(f3(f10(c2), f1(c1, c2)), f10(c2)) | (f3(f10(c2), f1(c1, c2)) = f1(c1, c2)) | (f10(c2) = c4) | (~big_f(c1, f1(c1, f1(c1, c2)))))),
% 29.09/19.29 inference(rewrite,[status(thm)],[])).
% 29.09/19.29 tff(19977,plain,
% 29.09/19.29 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f10(c2) = c4) | (f3(f10(c2), f1(c1, c2)) = f1(c1, c2)) | big_f(f3(f10(c2), f1(c1, c2)), f10(c2)) | (c1 = c3) | (~(f1(c1, f1(c1, c2)) = f1(c1, c2))) | (~big_f(c1, f1(c1, f1(c1, c2)))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~(f1(c1, f1(c1, c2)) = f1(c1, c2))) | big_f(f3(f10(c2), f1(c1, c2)), f10(c2)) | (f3(f10(c2), f1(c1, c2)) = f1(c1, c2)) | (f10(c2) = c4) | (~big_f(c1, f1(c1, f1(c1, c2))))))),
% 29.09/19.29 inference(monotonicity,[status(thm)],[19976])).
% 29.09/19.29 tff(19978,plain,
% 29.09/19.29 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f10(c2) = c4) | (f3(f10(c2), f1(c1, c2)) = f1(c1, c2)) | big_f(f3(f10(c2), f1(c1, c2)), f10(c2)) | (c1 = c3) | (~(f1(c1, f1(c1, c2)) = f1(c1, c2))) | (~big_f(c1, f1(c1, f1(c1, c2)))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (~(f1(c1, f1(c1, c2)) = f1(c1, c2))) | big_f(f3(f10(c2), f1(c1, c2)), f10(c2)) | (f3(f10(c2), f1(c1, c2)) = f1(c1, c2)) | (f10(c2) = c4) | (~big_f(c1, f1(c1, f1(c1, c2)))))),
% 29.09/19.29 inference(transitivity,[status(thm)],[19977, 19975])).
% 29.09/19.29 tff(19979,plain,
% 29.09/19.29 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f10(c2) = c4) | (f3(f10(c2), f1(c1, c2)) = f1(c1, c2)) | big_f(f3(f10(c2), f1(c1, c2)), f10(c2)) | (c1 = c3) | (~(f1(c1, f1(c1, c2)) = f1(c1, c2))) | (~big_f(c1, f1(c1, f1(c1, c2)))))),
% 29.09/19.29 inference(quant_inst,[status(thm)],[])).
% 29.09/19.29 tff(19980,plain,
% 29.09/19.29 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (~(f1(c1, f1(c1, c2)) = f1(c1, c2))) | big_f(f3(f10(c2), f1(c1, c2)), f10(c2)) | (f3(f10(c2), f1(c1, c2)) = f1(c1, c2)) | (f10(c2) = c4) | (~big_f(c1, f1(c1, f1(c1, c2))))),
% 29.09/19.29 inference(modus_ponens,[status(thm)],[19979, 19978])).
% 29.09/19.29 tff(19981,plain,
% 29.09/19.29 ((c1 = c3) | (~(f1(c1, f1(c1, c2)) = f1(c1, c2))) | big_f(f3(f10(c2), f1(c1, c2)), f10(c2)) | (f3(f10(c2), f1(c1, c2)) = f1(c1, c2)) | (f10(c2) = c4) | (~big_f(c1, f1(c1, f1(c1, c2))))),
% 29.09/19.29 inference(unit_resolution,[status(thm)],[19980, 904])).
% 29.09/19.29 tff(19982,plain,
% 29.09/19.29 ($false),
% 29.09/19.29 inference(unit_resolution,[status(thm)],[19981, 19974, 19970, 19809, 19969, 19965, 19957])).
% 29.09/19.29 tff(19983,plain,((f7(c1) = c1) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | (~big_f(c1, f9(c1, c1))) | (~(f7(c2) = c1)) | big_f(c2, c2) | (~(f10(c1) = c1)) | (~(f5(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.09/19.29 tff(19984,plain,
% 29.09/19.29 (f7(c1) = c1),
% 29.09/19.29 inference(unit_resolution,[status(thm)],[19983, 19609, 11752, 11819, 1498, 22, 121, 3762, 186])).
% 29.09/19.29 tff(19985,plain,
% 29.09/19.29 (big_f(f7(c1), f6(c1, f9(c1, c1))) <=> big_f(c1, f6(c1, c2))),
% 29.09/19.29 inference(monotonicity,[status(thm)],[4234, 19336])).
% 29.09/19.29 tff(19986,plain,
% 29.09/19.29 (big_f(c1, f6(c1, c2)) <=> big_f(f7(c1), f6(c1, f9(c1, c1)))),
% 29.09/19.29 inference(symmetry,[status(thm)],[19985])).
% 29.09/19.29 tff(19987,plain,
% 29.09/19.29 (big_f(f9(c1, c1), f10(c1))),
% 29.09/19.29 inference(unit_resolution,[status(thm)],[8716, 8714, 3762])).
% 29.09/19.29 tff(19988,plain,
% 29.09/19.29 (big_f(c2, c1)),
% 29.09/19.29 inference(unit_resolution,[status(thm)],[19082, 19987, 1498, 3762, 11752, 11819])).
% 29.09/19.29 tff(19989,plain,
% 29.09/19.29 (big_f(f9(c1, c1), f10(f9(c1, c1)))),
% 29.09/19.29 inference(modus_ponens,[status(thm)],[19988, 19123])).
% 29.09/19.29 tff(19990,plain,
% 29.09/19.29 (f6(c1, f9(c1, c1)) = c1),
% 29.09/19.29 inference(transitivity,[status(thm)],[19336, 6931])).
% 29.09/19.29 tff(19991,plain,
% 29.09/19.29 ((f6(c1, f9(c1, c1)) = f9(c1, c1)) <=> (c1 = f9(c1, c1))),
% 29.09/19.29 inference(monotonicity,[status(thm)],[19990])).
% 29.09/19.29 tff(19992,plain,
% 29.09/19.29 ((f6(c1, f9(c1, c1)) = f9(c1, c1)) <=> (f9(c1, c1) = c1)),
% 29.09/19.29 inference(transitivity,[status(thm)],[19991, 17725])).
% 29.09/19.29 tff(19993,plain,
% 29.09/19.29 ((f9(c1, c1) = c1) <=> (f6(c1, f9(c1, c1)) = f9(c1, c1))),
% 29.09/19.29 inference(symmetry,[status(thm)],[19992])).
% 29.09/19.29 tff(19994,plain,
% 29.09/19.29 ((~(f9(c1, c1) = c1)) <=> (~(f6(c1, f9(c1, c1)) = f9(c1, c1)))),
% 29.09/19.29 inference(monotonicity,[status(thm)],[19993])).
% 29.09/19.29 tff(19995,plain,
% 29.09/19.29 (~(f6(c1, f9(c1, c1)) = f9(c1, c1))),
% 29.09/19.29 inference(modus_ponens,[status(thm)],[17791, 19994])).
% 29.09/19.29 tff(19996,plain,
% 29.09/19.29 (big_f(f7(c1), f6(c1, f9(c1, c1))) <=> big_f(c1, c1)),
% 29.09/19.29 inference(monotonicity,[status(thm)],[4234, 19990])).
% 29.09/19.29 tff(19997,plain,
% 29.09/19.29 (big_f(c1, c1) <=> big_f(f7(c1), f6(c1, f9(c1, c1)))),
% 29.09/19.29 inference(symmetry,[status(thm)],[19996])).
% 29.09/19.29 tff(19998,plain,
% 29.09/19.29 ((~big_f(c1, c1)) <=> (~big_f(f7(c1), f6(c1, f9(c1, c1))))),
% 29.09/19.29 inference(monotonicity,[status(thm)],[19997])).
% 29.09/19.29 tff(19999,plain,
% 29.09/19.29 (~big_f(f7(c1), f6(c1, f9(c1, c1)))),
% 29.09/19.29 inference(modus_ponens,[status(thm)],[66, 19998])).
% 29.09/19.29 tff(20000,plain,
% 29.09/19.29 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f7(c1) = c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (f6(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f7(c1), f6(c1, f9(c1, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c1) = c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (f6(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f7(c1), f6(c1, f9(c1, c1))))),
% 29.09/19.29 inference(rewrite,[status(thm)],[])).
% 29.09/19.29 tff(20001,plain,
% 29.09/19.29 (((f10(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (~(f7(c1) = c1)) | (f6(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f7(c1), f6(c1, f9(c1, c1)))) <=> ((~(f7(c1) = c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (f6(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f7(c1), f6(c1, f9(c1, c1))))),
% 29.09/19.29 inference(rewrite,[status(thm)],[])).
% 29.09/19.29 tff(20002,plain,
% 29.09/19.29 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (~(f7(c1) = c1)) | (f6(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f7(c1), f6(c1, f9(c1, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f7(c1) = c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (f6(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f7(c1), f6(c1, f9(c1, c1)))))),
% 29.09/19.29 inference(monotonicity,[status(thm)],[20001])).
% 29.09/19.29 tff(20003,plain,
% 29.09/19.29 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (~(f7(c1) = c1)) | (f6(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f7(c1), f6(c1, f9(c1, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c1) = c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (f6(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f7(c1), f6(c1, f9(c1, c1))))),
% 29.09/19.29 inference(transitivity,[status(thm)],[20002, 20000])).
% 29.09/19.29 tff(20004,plain,
% 29.09/19.29 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (~(f7(c1) = c1)) | (f6(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f7(c1), f6(c1, f9(c1, c1))))),
% 29.09/19.29 inference(quant_inst,[status(thm)],[])).
% 29.09/19.29 tff(20005,plain,
% 29.09/19.29 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c1) = c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (f6(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f7(c1), f6(c1, f9(c1, c1)))),
% 29.09/19.29 inference(modus_ponens,[status(thm)],[20004, 20003])).
% 29.09/19.29 tff(20006,plain,
% 29.09/19.29 ((f6(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f7(c1), f6(c1, f9(c1, c1)))),
% 29.09/19.29 inference(unit_resolution,[status(thm)],[20005, 2662, 4234, 17792, 17819, 17831])).
% 29.09/19.29 tff(20007,plain,
% 29.09/19.29 ($false),
% 29.09/19.29 inference(unit_resolution,[status(thm)],[20006, 19999, 19995])).
% 29.09/19.29 tff(20008,plain,((~(f6(c1, c2) = c1)) | (~(f7(c1) = c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (f9(c1, c1) = f8(f9(c1, c1))) | big_f(c1, c1) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.09/19.29 tff(20009,plain,
% 29.09/19.29 (~(f6(c1, c2) = c1)),
% 29.09/19.29 inference(unit_resolution,[status(thm)],[20008, 17831, 17819, 4234, 66, 1498, 11752, 11819])).
% 29.09/19.29 tff(20010,plain,
% 29.09/19.29 (f6(c1, c2) = c2),
% 29.09/19.29 inference(unit_resolution,[status(thm)],[48, 20009])).
% 29.09/19.29 tff(20011,plain,
% 29.09/19.29 (f6(c1, f9(c1, c1)) = f9(c1, c1)),
% 29.09/19.29 inference(transitivity,[status(thm)],[19336, 20010, 17733, 17726])).
% 29.09/19.29 tff(20012,plain,
% 29.09/19.29 (big_f(f7(c1), f6(c1, f9(c1, c1))) <=> big_f(c1, f9(c1, c1))),
% 29.09/19.29 inference(monotonicity,[status(thm)],[4234, 20011])).
% 29.09/19.29 tff(20013,plain,
% 29.09/19.29 (big_f(c1, f9(c1, c1)) <=> big_f(f7(c1), f6(c1, f9(c1, c1)))),
% 29.09/19.29 inference(symmetry,[status(thm)],[20012])).
% 29.09/19.29 tff(20014,plain,
% 29.09/19.29 (big_f(f7(c1), f6(c1, f9(c1, c1)))),
% 29.09/19.29 inference(modus_ponens,[status(thm)],[19803, 20013])).
% 29.09/19.29 tff(20015,plain,
% 29.09/19.29 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(c1) = c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f7(c1), f6(c1, f9(c1, c1)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c1) = c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f7(c1), f6(c1, f9(c1, c1)))))),
% 29.09/19.29 inference(rewrite,[status(thm)],[])).
% 29.09/19.29 tff(20016,plain,
% 29.09/19.29 (((f10(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (~(f7(c1) = c1)) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f7(c1), f6(c1, f9(c1, c1))))) <=> ((~(f7(c1) = c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f7(c1), f6(c1, f9(c1, c1)))))),
% 29.09/19.29 inference(rewrite,[status(thm)],[])).
% 29.09/19.29 tff(20017,plain,
% 29.09/19.29 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (~(f7(c1) = c1)) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f7(c1), f6(c1, f9(c1, c1)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(c1) = c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f7(c1), f6(c1, f9(c1, c1))))))),
% 29.09/19.30 inference(monotonicity,[status(thm)],[20016])).
% 29.09/19.30 tff(20018,plain,
% 29.09/19.30 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (~(f7(c1) = c1)) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f7(c1), f6(c1, f9(c1, c1)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c1) = c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f7(c1), f6(c1, f9(c1, c1)))))),
% 29.09/19.30 inference(transitivity,[status(thm)],[20017, 20015])).
% 29.09/19.30 tff(20019,plain,
% 29.09/19.30 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (~(f7(c1) = c1)) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f7(c1), f6(c1, f9(c1, c1)))))),
% 29.09/19.30 inference(quant_inst,[status(thm)],[])).
% 29.09/19.30 tff(20020,plain,
% 29.09/19.30 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c1) = c1)) | (f9(c1, c1) = f8(f9(c1, c1))) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f7(c1), f6(c1, f9(c1, c1))))),
% 29.09/19.30 inference(modus_ponens,[status(thm)],[20019, 20018])).
% 29.09/19.30 tff(20021,plain,
% 29.09/19.30 ((~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f7(c1), f6(c1, f9(c1, c1))))),
% 29.09/19.30 inference(unit_resolution,[status(thm)],[20020, 2730, 4234, 17792, 17819, 17831])).
% 29.09/19.30 tff(20022,plain,
% 29.09/19.30 ($false),
% 29.09/19.30 inference(unit_resolution,[status(thm)],[20021, 20014, 20011])).
% 29.09/19.30 tff(20023,plain,((f9(c1, c1) = f8(f9(c1, c1))) | (~(f7(c1) = c1)) | (~big_f(f9(c1, c1), f10(f9(c1, c1)))) | (~big_f(c1, f9(c1, c1))) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 29.09/19.30 tff(20024,plain,
% 29.09/19.30 (f9(c1, c1) = f8(f9(c1, c1))),
% 29.09/19.30 inference(unit_resolution,[status(thm)],[20023, 4234, 19989, 19803, 1498, 11752, 11819, 66])).
% 29.09/19.30 tff(20025,plain,
% 29.09/19.30 (f8(f9(c1, c1)) = f9(c1, c1)),
% 29.09/19.30 inference(symmetry,[status(thm)],[20024])).
% 29.09/19.30 tff(20026,plain,
% 29.09/19.30 (f8(f9(c1, c1)) = c2),
% 29.09/19.30 inference(transitivity,[status(thm)],[20025, 17727, 1498])).
% 29.09/19.30 tff(20027,plain,
% 29.09/19.30 ((f9(c1, c2) = f8(f9(c1, c1))) <=> (f9(c1, c2) = c2)),
% 29.09/19.30 inference(monotonicity,[status(thm)],[20026])).
% 29.09/19.30 tff(20028,plain,
% 29.09/19.30 ((f9(c1, c2) = f8(f9(c1, c1))) <=> (f9(c1, f9(c1, c1)) = f9(c1, c1))),
% 29.09/19.30 inference(transitivity,[status(thm)],[20027, 17936])).
% 29.09/19.30 tff(20029,plain,
% 29.09/19.30 (big_f(f7(c1), f6(c1, f8(c2))) <=> big_f(c1, f6(c1, f8(c2)))),
% 29.09/19.30 inference(monotonicity,[status(thm)],[4234])).
% 29.09/19.30 tff(20030,plain,
% 29.09/19.30 (big_f(c1, f6(c1, f8(c2))) <=> big_f(f7(c1), f6(c1, f8(c2)))),
% 29.09/19.30 inference(symmetry,[status(thm)],[20029])).
% 29.09/19.30 tff(20031,plain,
% 29.09/19.30 ((f9(c1, c2) = f8(f9(c1, c1))) <=> (f9(c1, f9(c1, c1)) = f9(c1, c1))),
% 29.09/19.30 inference(transitivity,[status(thm)],[17878, 17936])).
% 29.09/19.30 tff(20032,plain,
% 29.09/19.30 (f6(c1, f9(c1, c1)) = f9(c1, c1)),
% 29.09/19.30 inference(transitivity,[status(thm)],[19336, 36, 17733, 17726])).
% 29.09/19.30 tff(20033,plain,
% 29.09/19.30 (big_f(f7(c1), f6(c1, f9(c1, c1))) <=> big_f(c1, f9(c1, c1))),
% 29.09/19.30 inference(monotonicity,[status(thm)],[4234, 20032])).
% 29.09/19.30 tff(20034,plain,
% 29.09/19.30 (big_f(c1, f9(c1, c1)) <=> big_f(f7(c1), f6(c1, f9(c1, c1)))),
% 29.09/19.30 inference(symmetry,[status(thm)],[20033])).
% 29.09/19.30 tff(20035,plain,
% 29.09/19.30 (big_f(f7(c1), f6(c1, f9(c1, c1)))),
% 29.09/19.30 inference(modus_ponens,[status(thm)],[19803, 20034])).
% 29.09/19.30 tff(20036,plain,
% 29.09/19.30 ((f9(c1, c2) = c2) <=> (f9(c1, c2) = f8(f9(c1, c1)))),
% 29.09/19.30 inference(symmetry,[status(thm)],[17878])).
% 29.09/19.30 tff(20037,plain,
% 29.09/19.30 ((f9(c1, f9(c1, c1)) = f9(c1, c1)) <=> (f9(c1, c2) = f8(f9(c1, c1)))),
% 29.09/19.30 inference(transitivity,[status(thm)],[17935, 20036])).
% 29.09/19.30 tff(20038,assumption,(big_f(f7(c1), f6(c1, f9(c1, c1)))), introduced(assumption)).
% 29.09/19.30 tff(20039,assumption,(f6(c1, f9(c1, c1)) = f9(c1, c1)), introduced(assumption)).
% 29.09/19.30 tff(20040,plain,
% 29.09/19.30 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (f9(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f9(c1, f9(c1, c1)), f10(c1)) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f7(c1), f6(c1, f9(c1, c1)))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (f9(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f9(c1, f9(c1, c1)), f10(c1)) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f7(c1), f6(c1, f9(c1, c1)))))),
% 29.09/19.30 inference(rewrite,[status(thm)],[])).
% 29.09/19.30 tff(20041,plain,
% 29.09/19.30 (((~(f10(c1) = c1)) | (f9(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f9(c1, f9(c1, c1)), f10(c1)) | (~(f7(c1) = c1)) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f7(c1), f6(c1, f9(c1, c1))))) <=> ((~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (f9(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f9(c1, f9(c1, c1)), f10(c1)) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f7(c1), f6(c1, f9(c1, c1)))))),
% 29.09/19.30 inference(rewrite,[status(thm)],[])).
% 29.09/19.30 tff(20042,plain,
% 29.09/19.30 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (f9(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f9(c1, f9(c1, c1)), f10(c1)) | (~(f7(c1) = c1)) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f7(c1), f6(c1, f9(c1, c1)))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (f9(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f9(c1, f9(c1, c1)), f10(c1)) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f7(c1), f6(c1, f9(c1, c1))))))),
% 29.09/19.30 inference(monotonicity,[status(thm)],[20041])).
% 29.09/19.30 tff(20043,plain,
% 29.09/19.30 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (f9(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f9(c1, f9(c1, c1)), f10(c1)) | (~(f7(c1) = c1)) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f7(c1), f6(c1, f9(c1, c1)))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (f9(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f9(c1, f9(c1, c1)), f10(c1)) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f7(c1), f6(c1, f9(c1, c1)))))),
% 29.09/19.30 inference(transitivity,[status(thm)],[20042, 20040])).
% 29.09/19.30 tff(20044,plain,
% 29.09/19.30 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (f9(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f9(c1, f9(c1, c1)), f10(c1)) | (~(f7(c1) = c1)) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f7(c1), f6(c1, f9(c1, c1)))))),
% 29.09/19.30 inference(quant_inst,[status(thm)],[])).
% 29.09/19.30 tff(20045,plain,
% 29.09/19.30 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (f9(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f9(c1, f9(c1, c1)), f10(c1)) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f7(c1), f6(c1, f9(c1, c1))))),
% 29.09/19.30 inference(modus_ponens,[status(thm)],[20044, 20043])).
% 29.09/19.30 tff(20046,plain,
% 29.09/19.30 ((f9(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f9(c1, f9(c1, c1)), f10(c1))),
% 29.09/19.30 inference(unit_resolution,[status(thm)],[20045, 2534, 4234, 3762, 20039, 20038])).
% 29.09/19.30 tff(20047,plain,
% 29.09/19.30 (f9(c1, f9(c1, c1)) = f9(c1, c1)),
% 29.09/19.30 inference(unit_resolution,[status(thm)],[20046, 17945])).
% 29.09/19.30 tff(20048,plain,
% 29.09/19.30 (f9(c1, c2) = f8(f9(c1, c1))),
% 29.09/19.30 inference(modus_ponens,[status(thm)],[20047, 20037])).
% 29.09/19.30 tff(20049,plain,
% 29.09/19.30 ((~big_f(f9(c1, c2), f10(c1))) <=> (~big_f(f9(c1, c2), f10(f9(c1, c1))))),
% 29.09/19.30 inference(monotonicity,[status(thm)],[17887])).
% 29.09/19.30 tff(20050,plain,
% 29.09/19.30 (~big_f(f9(c1, c2), f10(f9(c1, c1)))),
% 29.09/19.30 inference(modus_ponens,[status(thm)],[17944, 20049])).
% 29.09/19.30 tff(20051,plain,
% 29.09/19.30 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(c1) = c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | big_f(f9(c1, c2), f10(f9(c1, c1))) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~(f9(c1, c2) = f8(f9(c1, c1)))) | (~big_f(f7(c1), f6(c1, f9(c1, c1)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c1) = c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | big_f(f9(c1, c2), f10(f9(c1, c1))) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~(f9(c1, c2) = f8(f9(c1, c1)))) | (~big_f(f7(c1), f6(c1, f9(c1, c1)))))),
% 29.09/19.30 inference(rewrite,[status(thm)],[])).
% 29.09/19.30 tff(20052,plain,
% 29.09/19.30 (((f10(f9(c1, c1)) = f9(c1, c1)) | big_f(f9(c1, c2), f10(f9(c1, c1))) | (~(f7(c1) = c1)) | (~(f9(c1, c2) = f8(f9(c1, c1)))) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f7(c1), f6(c1, f9(c1, c1))))) <=> ((~(f7(c1) = c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | big_f(f9(c1, c2), f10(f9(c1, c1))) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~(f9(c1, c2) = f8(f9(c1, c1)))) | (~big_f(f7(c1), f6(c1, f9(c1, c1)))))),
% 29.09/19.30 inference(rewrite,[status(thm)],[])).
% 29.09/19.30 tff(20053,plain,
% 29.09/19.30 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f9(c1, c1)) = f9(c1, c1)) | big_f(f9(c1, c2), f10(f9(c1, c1))) | (~(f7(c1) = c1)) | (~(f9(c1, c2) = f8(f9(c1, c1)))) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f7(c1), f6(c1, f9(c1, c1)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(c1) = c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | big_f(f9(c1, c2), f10(f9(c1, c1))) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~(f9(c1, c2) = f8(f9(c1, c1)))) | (~big_f(f7(c1), f6(c1, f9(c1, c1))))))),
% 29.09/19.30 inference(monotonicity,[status(thm)],[20052])).
% 29.09/19.30 tff(20054,plain,
% 29.09/19.30 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f9(c1, c1)) = f9(c1, c1)) | big_f(f9(c1, c2), f10(f9(c1, c1))) | (~(f7(c1) = c1)) | (~(f9(c1, c2) = f8(f9(c1, c1)))) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f7(c1), f6(c1, f9(c1, c1)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c1) = c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | big_f(f9(c1, c2), f10(f9(c1, c1))) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~(f9(c1, c2) = f8(f9(c1, c1)))) | (~big_f(f7(c1), f6(c1, f9(c1, c1)))))),
% 29.09/19.30 inference(transitivity,[status(thm)],[20053, 20051])).
% 29.09/19.30 tff(20055,plain,
% 29.09/19.30 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f9(c1, c1)) = f9(c1, c1)) | big_f(f9(c1, c2), f10(f9(c1, c1))) | (~(f7(c1) = c1)) | (~(f9(c1, c2) = f8(f9(c1, c1)))) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f7(c1), f6(c1, f9(c1, c1)))))),
% 29.09/19.30 inference(quant_inst,[status(thm)],[])).
% 29.09/19.30 tff(20056,plain,
% 29.09/19.30 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c1) = c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | big_f(f9(c1, c2), f10(f9(c1, c1))) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~(f9(c1, c2) = f8(f9(c1, c1)))) | (~big_f(f7(c1), f6(c1, f9(c1, c1))))),
% 29.09/19.30 inference(modus_ponens,[status(thm)],[20055, 20054])).
% 29.09/19.30 tff(20057,plain,
% 29.09/19.30 (big_f(f9(c1, c2), f10(f9(c1, c1))) | (~(f9(c1, c2) = f8(f9(c1, c1))))),
% 29.09/19.30 inference(unit_resolution,[status(thm)],[20056, 2963, 4234, 17792, 20039, 20038])).
% 29.09/19.30 tff(20058,plain,
% 29.09/19.30 (~(f9(c1, c2) = f8(f9(c1, c1)))),
% 29.09/19.30 inference(unit_resolution,[status(thm)],[20057, 20050])).
% 29.09/19.30 tff(20059,plain,
% 29.09/19.30 ($false),
% 29.09/19.30 inference(unit_resolution,[status(thm)],[20058, 20048])).
% 29.09/19.30 tff(20060,plain,(big_f(f9(c1, c2), f10(c1)) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | (~(f9(c1, c1) = f8(f9(c1, c1)))) | (~(f7(c1) = c1)) | (~(f10(c1) = c1)) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f7(c1), f6(c1, f9(c1, c1))))), inference(lemma,lemma(discharge,[]))).
% 29.09/19.30 tff(20061,plain,
% 29.09/19.30 (big_f(f9(c1, c2), f10(c1))),
% 29.09/19.30 inference(unit_resolution,[status(thm)],[20060, 20032, 11752, 11819, 17860, 4234, 3762, 1498, 20035])).
% 29.09/19.30 tff(20062,plain,
% 29.09/19.30 (big_f(f9(c1, c2), f10(f9(c1, c1)))),
% 29.09/19.30 inference(modus_ponens,[status(thm)],[20061, 17887])).
% 29.09/19.30 tff(20063,plain,
% 29.09/19.30 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(c1) = c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c2), f10(f9(c1, c1)))) | (f9(c1, c2) = f8(f9(c1, c1))) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f7(c1), f6(c1, f9(c1, c1)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c1) = c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c2), f10(f9(c1, c1)))) | (f9(c1, c2) = f8(f9(c1, c1))) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f7(c1), f6(c1, f9(c1, c1)))))),
% 29.09/19.30 inference(rewrite,[status(thm)],[])).
% 29.09/19.30 tff(20064,plain,
% 29.09/19.30 (((f10(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c2) = f8(f9(c1, c1))) | (~big_f(f9(c1, c2), f10(f9(c1, c1)))) | (~(f7(c1) = c1)) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f7(c1), f6(c1, f9(c1, c1))))) <=> ((~(f7(c1) = c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c2), f10(f9(c1, c1)))) | (f9(c1, c2) = f8(f9(c1, c1))) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f7(c1), f6(c1, f9(c1, c1)))))),
% 29.09/19.30 inference(rewrite,[status(thm)],[])).
% 29.09/19.30 tff(20065,plain,
% 29.09/19.30 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c2) = f8(f9(c1, c1))) | (~big_f(f9(c1, c2), f10(f9(c1, c1)))) | (~(f7(c1) = c1)) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f7(c1), f6(c1, f9(c1, c1)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(c1) = c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c2), f10(f9(c1, c1)))) | (f9(c1, c2) = f8(f9(c1, c1))) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f7(c1), f6(c1, f9(c1, c1))))))),
% 29.09/19.30 inference(monotonicity,[status(thm)],[20064])).
% 29.09/19.30 tff(20066,plain,
% 29.09/19.30 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c2) = f8(f9(c1, c1))) | (~big_f(f9(c1, c2), f10(f9(c1, c1)))) | (~(f7(c1) = c1)) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f7(c1), f6(c1, f9(c1, c1)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c1) = c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c2), f10(f9(c1, c1)))) | (f9(c1, c2) = f8(f9(c1, c1))) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f7(c1), f6(c1, f9(c1, c1)))))),
% 29.09/19.30 inference(transitivity,[status(thm)],[20065, 20063])).
% 29.09/19.30 tff(20067,plain,
% 29.09/19.30 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c2) = f8(f9(c1, c1))) | (~big_f(f9(c1, c2), f10(f9(c1, c1)))) | (~(f7(c1) = c1)) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f7(c1), f6(c1, f9(c1, c1)))))),
% 29.09/19.30 inference(quant_inst,[status(thm)],[])).
% 29.09/19.30 tff(20068,plain,
% 29.09/19.30 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c1) = c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c2), f10(f9(c1, c1)))) | (f9(c1, c2) = f8(f9(c1, c1))) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f7(c1), f6(c1, f9(c1, c1))))),
% 29.09/19.30 inference(modus_ponens,[status(thm)],[20067, 20066])).
% 29.09/19.30 tff(20069,plain,
% 29.09/19.30 ((~big_f(f9(c1, c2), f10(f9(c1, c1)))) | (f9(c1, c2) = f8(f9(c1, c1)))),
% 29.09/19.30 inference(unit_resolution,[status(thm)],[20068, 2730, 4234, 17792, 20032, 20035])).
% 29.09/19.30 tff(20070,plain,
% 29.09/19.30 (f9(c1, c2) = f8(f9(c1, c1))),
% 29.09/19.30 inference(unit_resolution,[status(thm)],[20069, 20062])).
% 29.09/19.30 tff(20071,plain,
% 29.09/19.30 (f9(c1, f9(c1, c1)) = f9(c1, c1)),
% 29.09/19.30 inference(modus_ponens,[status(thm)],[20070, 20031])).
% 29.09/19.30 tff(20072,plain,
% 29.09/19.30 (big_f(f9(c1, f9(c1, c1)), f10(c1))),
% 29.09/19.30 inference(modus_ponens,[status(thm)],[20061, 17942])).
% 29.09/19.30 tff(20073,plain,
% 29.09/19.30 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~(f9(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f9(c1, f9(c1, c1)), f10(c1))) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f7(c1), f6(c1, f9(c1, c1)))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~(f9(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f9(c1, f9(c1, c1)), f10(c1))) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f7(c1), f6(c1, f9(c1, c1)))))),
% 29.09/19.30 inference(rewrite,[status(thm)],[])).
% 29.09/19.30 tff(20074,plain,
% 29.09/19.30 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~(f9(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f9(c1, f9(c1, c1)), f10(c1))) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f7(c1), f6(c1, f9(c1, c1)))))),
% 29.09/19.30 inference(quant_inst,[status(thm)],[])).
% 29.09/19.30 tff(20075,plain,
% 29.09/19.30 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~(f9(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f9(c1, f9(c1, c1)), f10(c1))) | (~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f7(c1), f6(c1, f9(c1, c1))))),
% 29.09/19.30 inference(modus_ponens,[status(thm)],[20074, 20073])).
% 29.09/19.30 tff(20076,plain,
% 29.09/19.30 ((~(f9(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f9(c1, f9(c1, c1)), f10(c1)))),
% 29.09/19.30 inference(unit_resolution,[status(thm)],[20075, 2378, 4234, 3762, 20032, 20035])).
% 29.09/19.30 tff(20077,plain,
% 29.09/19.30 (~(f9(c1, f9(c1, c1)) = f9(c1, c1))),
% 29.09/19.30 inference(unit_resolution,[status(thm)],[20076, 20072])).
% 29.09/19.30 tff(20078,plain,
% 29.09/19.30 ($false),
% 29.09/19.30 inference(unit_resolution,[status(thm)],[20077, 20071])).
% 29.09/19.31 tff(20079,plain,((~(f6(c1, c2) = c2)) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | (~(f9(c1, c1) = f8(f9(c1, c1)))) | (~(f7(c1) = c1)) | (~(f10(c1) = c1)) | (~big_f(c1, f9(c1, c1)))), inference(lemma,lemma(discharge,[]))).
% 29.09/19.31 tff(20080,plain,
% 29.09/19.31 (~(f6(c1, c2) = c2)),
% 29.09/19.31 inference(unit_resolution,[status(thm)],[20079, 20024, 11752, 11819, 1498, 4234, 3762, 19803])).
% 29.09/19.31 tff(20081,plain,
% 29.09/19.31 (f6(c1, c2) = c1),
% 29.09/19.31 inference(unit_resolution,[status(thm)],[48, 20080])).
% 29.09/19.31 tff(20082,plain,
% 29.09/19.31 (f8(c2) = c2),
% 29.09/19.31 inference(transitivity,[status(thm)],[17862, 20025, 17727, 1498])).
% 29.09/19.31 tff(20083,plain,
% 29.09/19.31 (f6(c1, f8(c2)) = f6(c1, c2)),
% 29.09/19.31 inference(monotonicity,[status(thm)],[20082])).
% 29.09/19.31 tff(20084,plain,
% 29.09/19.31 (f6(c1, f8(c2)) = c1),
% 29.09/19.31 inference(transitivity,[status(thm)],[20083, 20081])).
% 29.09/19.31 tff(20085,plain,
% 29.09/19.31 (big_f(c1, f6(c1, f8(c2))) <=> big_f(c1, c1)),
% 29.09/19.31 inference(monotonicity,[status(thm)],[20084])).
% 29.09/19.31 tff(20086,plain,
% 29.09/19.31 (big_f(c1, c1) <=> big_f(c1, f6(c1, f8(c2)))),
% 29.09/19.31 inference(symmetry,[status(thm)],[20085])).
% 29.09/19.31 tff(20087,plain,
% 29.09/19.31 (big_f(c1, c1) <=> big_f(f7(c1), f6(c1, f8(c2)))),
% 29.09/19.31 inference(transitivity,[status(thm)],[20086, 20030])).
% 29.09/19.31 tff(20088,plain,
% 29.09/19.31 ((~big_f(c1, c1)) <=> (~big_f(f7(c1), f6(c1, f8(c2))))),
% 29.09/19.31 inference(monotonicity,[status(thm)],[20087])).
% 29.09/19.31 tff(20089,plain,
% 29.09/19.31 (~big_f(f7(c1), f6(c1, f8(c2)))),
% 29.09/19.31 inference(modus_ponens,[status(thm)],[66, 20088])).
% 29.09/19.31 tff(20090,plain,
% 29.09/19.31 ((f6(c1, f8(c2)) = f8(c2)) <=> (f6(c1, f8(c2)) = c2)),
% 29.09/19.31 inference(monotonicity,[status(thm)],[20082])).
% 29.09/19.31 tff(20091,plain,
% 29.09/19.31 ((f6(c1, f8(c2)) = c2) <=> (f6(c1, f8(c2)) = f8(c2))),
% 29.09/19.31 inference(symmetry,[status(thm)],[20090])).
% 29.09/19.31 tff(20092,plain,
% 29.09/19.31 ((f6(c1, f8(c2)) = c2) <=> (c1 = f9(c1, c1))),
% 29.09/19.31 inference(monotonicity,[status(thm)],[20084, 17734])).
% 29.09/19.31 tff(20093,plain,
% 29.09/19.31 ((f6(c1, f8(c2)) = c2) <=> (f9(c1, c1) = c1)),
% 29.09/19.31 inference(transitivity,[status(thm)],[20092, 17725])).
% 29.09/19.31 tff(20094,plain,
% 29.09/19.31 ((f9(c1, c1) = c1) <=> (f6(c1, f8(c2)) = c2)),
% 29.09/19.31 inference(symmetry,[status(thm)],[20093])).
% 29.09/19.31 tff(20095,plain,
% 29.09/19.31 ((f9(c1, c1) = c1) <=> (f6(c1, f8(c2)) = f8(c2))),
% 29.09/19.31 inference(transitivity,[status(thm)],[20094, 20091])).
% 29.09/19.31 tff(20096,plain,
% 29.09/19.31 ((~(f9(c1, c1) = c1)) <=> (~(f6(c1, f8(c2)) = f8(c2)))),
% 29.09/19.31 inference(monotonicity,[status(thm)],[20095])).
% 29.09/19.31 tff(20097,plain,
% 29.09/19.31 (~(f6(c1, f8(c2)) = f8(c2))),
% 29.09/19.31 inference(modus_ponens,[status(thm)],[17791, 20096])).
% 29.09/19.31 tff(20098,assumption,(~big_f(f7(c1), f6(c1, f8(c2)))), introduced(assumption)).
% 29.09/19.31 tff(20099,assumption,(~(f6(c1, f8(c2)) = f8(c2))), introduced(assumption)).
% 29.09/19.31 tff(20100,plain,
% 29.09/19.31 (f9(c1, f8(c2)) = f9(c1, c2)),
% 29.09/19.31 inference(symmetry,[status(thm)],[17910])).
% 29.09/19.31 tff(20101,plain,
% 29.09/19.31 (big_f(f9(c1, f8(c2)), f10(c1)) <=> big_f(f9(c1, c2), f10(c1))),
% 29.09/19.31 inference(monotonicity,[status(thm)],[20100])).
% 29.09/19.31 tff(20102,plain,
% 29.09/19.31 (big_f(f9(c1, c2), f10(c1)) <=> big_f(f9(c1, f8(c2)), f10(c1))),
% 29.09/19.31 inference(symmetry,[status(thm)],[20101])).
% 29.09/19.31 tff(20103,plain,
% 29.09/19.31 ((~big_f(f9(c1, c2), f10(c1))) <=> (~big_f(f9(c1, f8(c2)), f10(c1)))),
% 29.09/19.31 inference(monotonicity,[status(thm)],[20102])).
% 29.09/19.31 tff(20104,plain,
% 29.09/19.31 (~big_f(f9(c1, f8(c2)), f10(c1))),
% 29.09/19.31 inference(modus_ponens,[status(thm)],[17944, 20103])).
% 29.09/19.31 tff(20105,plain,
% 29.09/19.31 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c1) = c1)) | big_f(f7(c1), f6(c1, f8(c2))) | (~(f7(c1) = c1)) | (f6(c1, f8(c2)) = f8(c2)) | big_f(f9(c1, f8(c2)), f10(c1)) | (f9(c1, f8(c2)) = f8(c2)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f10(c1) = c1)) | big_f(f7(c1), f6(c1, f8(c2))) | (~(f7(c1) = c1)) | (f6(c1, f8(c2)) = f8(c2)) | big_f(f9(c1, f8(c2)), f10(c1)) | (f9(c1, f8(c2)) = f8(c2)))),
% 29.09/19.31 inference(rewrite,[status(thm)],[])).
% 29.09/19.31 tff(20106,plain,
% 29.09/19.31 (((~(f10(c1) = c1)) | (f9(c1, f8(c2)) = f8(c2)) | big_f(f9(c1, f8(c2)), f10(c1)) | (~(f7(c1) = c1)) | (f6(c1, f8(c2)) = f8(c2)) | big_f(f7(c1), f6(c1, f8(c2)))) <=> ((~(f10(c1) = c1)) | big_f(f7(c1), f6(c1, f8(c2))) | (~(f7(c1) = c1)) | (f6(c1, f8(c2)) = f8(c2)) | big_f(f9(c1, f8(c2)), f10(c1)) | (f9(c1, f8(c2)) = f8(c2)))),
% 29.09/19.31 inference(rewrite,[status(thm)],[])).
% 29.09/19.31 tff(20107,plain,
% 29.09/19.31 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c1) = c1)) | (f9(c1, f8(c2)) = f8(c2)) | big_f(f9(c1, f8(c2)), f10(c1)) | (~(f7(c1) = c1)) | (f6(c1, f8(c2)) = f8(c2)) | big_f(f7(c1), f6(c1, f8(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c1) = c1)) | big_f(f7(c1), f6(c1, f8(c2))) | (~(f7(c1) = c1)) | (f6(c1, f8(c2)) = f8(c2)) | big_f(f9(c1, f8(c2)), f10(c1)) | (f9(c1, f8(c2)) = f8(c2))))),
% 29.09/19.31 inference(monotonicity,[status(thm)],[20106])).
% 29.09/19.31 tff(20108,plain,
% 29.09/19.31 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c1) = c1)) | (f9(c1, f8(c2)) = f8(c2)) | big_f(f9(c1, f8(c2)), f10(c1)) | (~(f7(c1) = c1)) | (f6(c1, f8(c2)) = f8(c2)) | big_f(f7(c1), f6(c1, f8(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f10(c1) = c1)) | big_f(f7(c1), f6(c1, f8(c2))) | (~(f7(c1) = c1)) | (f6(c1, f8(c2)) = f8(c2)) | big_f(f9(c1, f8(c2)), f10(c1)) | (f9(c1, f8(c2)) = f8(c2)))),
% 29.09/19.31 inference(transitivity,[status(thm)],[20107, 20105])).
% 29.09/19.31 tff(20109,plain,
% 29.09/19.31 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c1) = c1)) | (f9(c1, f8(c2)) = f8(c2)) | big_f(f9(c1, f8(c2)), f10(c1)) | (~(f7(c1) = c1)) | (f6(c1, f8(c2)) = f8(c2)) | big_f(f7(c1), f6(c1, f8(c2))))),
% 29.09/19.31 inference(quant_inst,[status(thm)],[])).
% 29.09/19.31 tff(20110,plain,
% 29.09/19.31 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f10(c1) = c1)) | big_f(f7(c1), f6(c1, f8(c2))) | (~(f7(c1) = c1)) | (f6(c1, f8(c2)) = f8(c2)) | big_f(f9(c1, f8(c2)), f10(c1)) | (f9(c1, f8(c2)) = f8(c2))),
% 29.09/19.31 inference(modus_ponens,[status(thm)],[20109, 20108])).
% 29.09/19.31 tff(20111,plain,
% 29.09/19.31 ((~(f10(c1) = c1)) | big_f(f7(c1), f6(c1, f8(c2))) | (~(f7(c1) = c1)) | (f6(c1, f8(c2)) = f8(c2)) | big_f(f9(c1, f8(c2)), f10(c1)) | (f9(c1, f8(c2)) = f8(c2))),
% 29.09/19.31 inference(unit_resolution,[status(thm)],[20110, 2492])).
% 29.09/19.31 tff(20112,plain,
% 29.09/19.31 (f9(c1, f8(c2)) = f8(c2)),
% 29.09/19.31 inference(unit_resolution,[status(thm)],[20111, 20104, 3762, 4234, 20099, 20098])).
% 29.09/19.31 tff(20113,plain,
% 29.09/19.31 (f9(c1, c2) = f9(c1, c1)),
% 29.09/19.31 inference(transitivity,[status(thm)],[17910, 20112, 17862, 17861])).
% 29.09/19.31 tff(20114,plain,
% 29.09/19.31 (big_f(f9(c1, c2), f10(c1)) <=> big_f(f9(c1, c1), c1)),
% 29.09/19.31 inference(monotonicity,[status(thm)],[20113, 3762])).
% 29.09/19.31 tff(20115,plain,
% 29.09/19.31 (big_f(f9(c1, c1), c1) <=> big_f(f9(c1, c2), f10(c1))),
% 29.09/19.31 inference(symmetry,[status(thm)],[20114])).
% 29.09/19.31 tff(20116,plain,
% 29.09/19.31 (big_f(f9(c1, c2), f10(c1))),
% 29.09/19.31 inference(modus_ponens,[status(thm)],[8714, 20115])).
% 29.09/19.31 tff(20117,plain,
% 29.09/19.31 ($false),
% 29.09/19.31 inference(unit_resolution,[status(thm)],[17944, 20116])).
% 29.09/19.31 tff(20118,plain,(big_f(f9(c1, c2), f10(c1)) | (~big_f(f9(c1, c1), c1)) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = f8(f9(c1, c1)))) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | (~(f7(c1) = c1)) | (f6(c1, f8(c2)) = f8(c2)) | big_f(f7(c1), f6(c1, f8(c2)))), inference(lemma,lemma(discharge,[]))).
% 29.09/19.31 tff(20119,plain,
% 29.09/19.31 (big_f(f9(c1, c2), f10(c1))),
% 29.09/19.31 inference(unit_resolution,[status(thm)],[20118, 20024, 3762, 8714, 1498, 11752, 11819, 4234, 20097, 20089])).
% 29.09/19.31 tff(20120,plain,
% 29.09/19.31 (big_f(f9(c1, c2), f10(f9(c1, c1)))),
% 29.09/19.31 inference(modus_ponens,[status(thm)],[20119, 17887])).
% 29.09/19.31 tff(20121,plain,
% 29.09/19.31 (f6(c1, f9(c1, c1)) = c1),
% 29.09/19.31 inference(transitivity,[status(thm)],[19336, 20081])).
% 29.09/19.31 tff(20122,plain,
% 29.09/19.31 (big_f(f7(c1), f6(c1, f9(c1, c1))) <=> big_f(c1, c1)),
% 29.09/19.31 inference(monotonicity,[status(thm)],[4234, 20121])).
% 29.09/19.31 tff(20123,plain,
% 29.09/19.31 (big_f(c1, c1) <=> big_f(f7(c1), f6(c1, f9(c1, c1)))),
% 29.09/19.31 inference(symmetry,[status(thm)],[20122])).
% 29.09/19.31 tff(20124,plain,
% 29.09/19.31 ((~big_f(c1, c1)) <=> (~big_f(f7(c1), f6(c1, f9(c1, c1))))),
% 29.09/19.31 inference(monotonicity,[status(thm)],[20123])).
% 29.09/19.31 tff(20125,plain,
% 29.09/19.31 (~big_f(f7(c1), f6(c1, f9(c1, c1)))),
% 29.09/19.31 inference(modus_ponens,[status(thm)],[66, 20124])).
% 29.09/19.31 tff(20126,plain,
% 29.09/19.31 ((f6(c1, f9(c1, c1)) = f9(c1, c1)) <=> (c1 = f9(c1, c1))),
% 29.09/19.31 inference(monotonicity,[status(thm)],[20121])).
% 29.09/19.31 tff(20127,plain,
% 29.09/19.31 ((f6(c1, f9(c1, c1)) = f9(c1, c1)) <=> (f9(c1, c1) = c1)),
% 29.09/19.31 inference(transitivity,[status(thm)],[20126, 17725])).
% 29.09/19.31 tff(20128,plain,
% 29.09/19.31 ((f9(c1, c1) = c1) <=> (f6(c1, f9(c1, c1)) = f9(c1, c1))),
% 29.09/19.31 inference(symmetry,[status(thm)],[20127])).
% 29.09/19.31 tff(20129,plain,
% 29.09/19.31 ((~(f9(c1, c1) = c1)) <=> (~(f6(c1, f9(c1, c1)) = f9(c1, c1)))),
% 29.09/19.31 inference(monotonicity,[status(thm)],[20128])).
% 29.09/19.31 tff(20130,plain,
% 29.09/19.31 (~(f6(c1, f9(c1, c1)) = f9(c1, c1))),
% 29.09/19.31 inference(modus_ponens,[status(thm)],[17791, 20129])).
% 29.09/19.31 tff(20131,plain,
% 29.09/19.31 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f7(c1) = c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c2), f10(f9(c1, c1)))) | (f9(c1, c2) = f8(f9(c1, c1))) | (f6(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f7(c1), f6(c1, f9(c1, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c1) = c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c2), f10(f9(c1, c1)))) | (f9(c1, c2) = f8(f9(c1, c1))) | (f6(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f7(c1), f6(c1, f9(c1, c1))))),
% 29.09/19.31 inference(rewrite,[status(thm)],[])).
% 29.09/19.31 tff(20132,plain,
% 29.09/19.31 (((f10(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c2) = f8(f9(c1, c1))) | (~big_f(f9(c1, c2), f10(f9(c1, c1)))) | (~(f7(c1) = c1)) | (f6(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f7(c1), f6(c1, f9(c1, c1)))) <=> ((~(f7(c1) = c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c2), f10(f9(c1, c1)))) | (f9(c1, c2) = f8(f9(c1, c1))) | (f6(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f7(c1), f6(c1, f9(c1, c1))))),
% 29.09/19.31 inference(rewrite,[status(thm)],[])).
% 29.09/19.31 tff(20133,plain,
% 29.09/19.31 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c2) = f8(f9(c1, c1))) | (~big_f(f9(c1, c2), f10(f9(c1, c1)))) | (~(f7(c1) = c1)) | (f6(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f7(c1), f6(c1, f9(c1, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f7(c1) = c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c2), f10(f9(c1, c1)))) | (f9(c1, c2) = f8(f9(c1, c1))) | (f6(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f7(c1), f6(c1, f9(c1, c1)))))),
% 29.09/19.31 inference(monotonicity,[status(thm)],[20132])).
% 29.09/19.31 tff(20134,plain,
% 29.09/19.31 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c2) = f8(f9(c1, c1))) | (~big_f(f9(c1, c2), f10(f9(c1, c1)))) | (~(f7(c1) = c1)) | (f6(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f7(c1), f6(c1, f9(c1, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c1) = c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c2), f10(f9(c1, c1)))) | (f9(c1, c2) = f8(f9(c1, c1))) | (f6(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f7(c1), f6(c1, f9(c1, c1))))),
% 29.09/19.31 inference(transitivity,[status(thm)],[20133, 20131])).
% 29.09/19.31 tff(20135,plain,
% 29.09/19.31 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c2) = f8(f9(c1, c1))) | (~big_f(f9(c1, c2), f10(f9(c1, c1)))) | (~(f7(c1) = c1)) | (f6(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f7(c1), f6(c1, f9(c1, c1))))),
% 29.09/19.31 inference(quant_inst,[status(thm)],[])).
% 29.09/19.31 tff(20136,plain,
% 29.09/19.31 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c1) = c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f9(c1, c2), f10(f9(c1, c1)))) | (f9(c1, c2) = f8(f9(c1, c1))) | (f6(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f7(c1), f6(c1, f9(c1, c1)))),
% 29.09/19.31 inference(modus_ponens,[status(thm)],[20135, 20134])).
% 29.09/19.31 tff(20137,plain,
% 29.09/19.31 ((~big_f(f9(c1, c2), f10(f9(c1, c1)))) | (f9(c1, c2) = f8(f9(c1, c1)))),
% 29.09/19.31 inference(unit_resolution,[status(thm)],[20136, 2662, 4234, 17792, 20130, 20125])).
% 29.09/19.31 tff(20138,plain,
% 29.09/19.31 (f9(c1, c2) = f8(f9(c1, c1))),
% 29.09/19.31 inference(unit_resolution,[status(thm)],[20137, 20120])).
% 29.09/19.31 tff(20139,plain,
% 29.09/19.31 (f9(c1, f9(c1, c1)) = f9(c1, c1)),
% 29.09/19.31 inference(modus_ponens,[status(thm)],[20138, 20028])).
% 29.09/19.31 tff(20140,plain,
% 29.09/19.31 (big_f(f9(c1, f9(c1, c1)), f10(c1))),
% 29.09/19.31 inference(modus_ponens,[status(thm)],[20119, 17942])).
% 29.09/19.31 tff(20141,plain,
% 29.09/19.31 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (f6(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f7(c1), f6(c1, f9(c1, c1))) | (~(f9(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f9(c1, f9(c1, c1)), f10(c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (f6(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f7(c1), f6(c1, f9(c1, c1))) | (~(f9(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f9(c1, f9(c1, c1)), f10(c1))))),
% 29.09/19.31 inference(rewrite,[status(thm)],[])).
% 29.09/19.31 tff(20142,plain,
% 29.09/19.31 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (f6(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f7(c1), f6(c1, f9(c1, c1))) | (~(f9(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f9(c1, f9(c1, c1)), f10(c1))))),
% 29.09/19.31 inference(quant_inst,[status(thm)],[])).
% 29.09/19.31 tff(20143,plain,
% 29.09/19.31 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (f6(c1, f9(c1, c1)) = f9(c1, c1)) | big_f(f7(c1), f6(c1, f9(c1, c1))) | (~(f9(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f9(c1, f9(c1, c1)), f10(c1)))),
% 29.09/19.31 inference(modus_ponens,[status(thm)],[20142, 20141])).
% 29.09/19.31 tff(20144,plain,
% 29.09/19.31 ((~(f9(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f9(c1, f9(c1, c1)), f10(c1)))),
% 29.09/19.31 inference(unit_resolution,[status(thm)],[20143, 2409, 4234, 3762, 20130, 20125])).
% 29.09/19.31 tff(20145,plain,
% 29.09/19.31 (~(f9(c1, f9(c1, c1)) = f9(c1, c1))),
% 29.09/19.31 inference(unit_resolution,[status(thm)],[20144, 20140])).
% 29.09/19.31 tff(20146,plain,
% 29.09/19.31 ($false),
% 29.09/19.31 inference(unit_resolution,[status(thm)],[20145, 20139])).
% 29.09/19.31 tff(20147,plain,((~(f7(c1) = c1)) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | (~(f10(c1) = c1)) | (~big_f(f9(c1, c1), c1)) | big_f(c1, c1) | (~big_f(c1, f9(c1, c1)))), inference(lemma,lemma(discharge,[]))).
% 29.09/19.31 tff(20148,plain,
% 29.09/19.31 (~big_f(f9(c1, c1), c1)),
% 29.09/19.31 inference(unit_resolution,[status(thm)],[20147, 66, 11752, 11819, 3762, 1498, 19803, 4234])).
% 29.09/19.31 tff(20149,plain,
% 29.09/19.31 (~big_f(c2, c1)),
% 29.09/19.31 inference(unit_resolution,[status(thm)],[19496, 20148, 1498, 11752, 11819])).
% 29.09/19.31 tff(20150,plain,
% 29.09/19.31 (~big_f(f9(c1, c1), f10(c1))),
% 29.09/19.31 inference(unit_resolution,[status(thm)],[19082, 20149, 1498, 3762, 11752, 11819])).
% 29.09/19.31 tff(20151,plain,
% 29.09/19.31 ((~(f6(c1, f9(c1, c1)) = f9(c1, c1))) | (~big_f(f7(c1), f6(c1, f9(c1, c1))))),
% 29.09/19.31 inference(unit_resolution,[status(thm)],[19347, 2534, 4234, 3762, 17791, 8712])).
% 29.09/19.31 tff(20152,plain,
% 29.09/19.31 ($false),
% 29.09/19.31 inference(unit_resolution,[status(thm)],[20151, 20035, 20032])).
% 29.09/19.31 tff(20153,plain,((~(f6(c1, c2) = c2)) | (~(f7(c1) = c1)) | (~(f10(c1) = c1)) | big_f(f9(c1, c1), f10(c1)) | (~big_f(c1, f9(c1, c1))) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.09/19.31 tff(20154,plain,
% 29.09/19.31 (~(f6(c1, c2) = c2)),
% 29.09/19.31 inference(unit_resolution,[status(thm)],[20153, 20150, 3762, 19803, 4234, 1498, 11752, 11819])).
% 29.09/19.31 tff(20155,plain,
% 29.09/19.31 (f6(c1, c2) = c1),
% 29.09/19.31 inference(unit_resolution,[status(thm)],[48, 20154])).
% 29.09/19.31 tff(20156,plain,
% 29.09/19.31 (big_f(c1, f6(c1, c2)) <=> big_f(c1, c1)),
% 29.09/19.31 inference(monotonicity,[status(thm)],[20155])).
% 29.09/19.31 tff(20157,plain,
% 29.09/19.31 (big_f(c1, c1) <=> big_f(c1, f6(c1, c2))),
% 29.09/19.31 inference(symmetry,[status(thm)],[20156])).
% 29.09/19.31 tff(20158,plain,
% 29.09/19.31 (big_f(c1, c1) <=> big_f(f7(c1), f6(c1, f9(c1, c1)))),
% 29.09/19.31 inference(transitivity,[status(thm)],[20157, 19986])).
% 29.09/19.31 tff(20159,plain,
% 29.09/19.31 ((~big_f(c1, c1)) <=> (~big_f(f7(c1), f6(c1, f9(c1, c1))))),
% 29.09/19.31 inference(monotonicity,[status(thm)],[20158])).
% 29.09/19.31 tff(20160,plain,
% 29.09/19.31 (~big_f(f7(c1), f6(c1, f9(c1, c1)))),
% 29.09/19.31 inference(modus_ponens,[status(thm)],[66, 20159])).
% 29.09/19.31 tff(20161,plain,
% 29.09/19.31 (f6(c1, f9(c1, c1)) = c1),
% 29.09/19.31 inference(transitivity,[status(thm)],[19336, 20155])).
% 29.09/19.31 tff(20162,plain,
% 29.09/19.31 ((f6(c1, f9(c1, c1)) = f9(c1, c1)) <=> (c1 = f9(c1, c1))),
% 29.09/19.31 inference(monotonicity,[status(thm)],[20161])).
% 29.09/19.31 tff(20163,plain,
% 29.09/19.31 ((f6(c1, f9(c1, c1)) = f9(c1, c1)) <=> (f9(c1, c1) = c1)),
% 29.09/19.31 inference(transitivity,[status(thm)],[20162, 17725])).
% 29.09/19.31 tff(20164,plain,
% 29.09/19.31 ((f9(c1, c1) = c1) <=> (f6(c1, f9(c1, c1)) = f9(c1, c1))),
% 29.09/19.31 inference(symmetry,[status(thm)],[20163])).
% 29.09/19.31 tff(20165,plain,
% 29.09/19.31 ((~(f9(c1, c1) = c1)) <=> (~(f6(c1, f9(c1, c1)) = f9(c1, c1)))),
% 29.09/19.31 inference(monotonicity,[status(thm)],[20164])).
% 29.09/19.31 tff(20166,plain,
% 29.09/19.31 (~(f6(c1, f9(c1, c1)) = f9(c1, c1))),
% 29.09/19.31 inference(modus_ponens,[status(thm)],[17791, 20165])).
% 29.09/19.31 tff(20167,plain,
% 29.09/19.31 ($false),
% 29.09/19.31 inference(unit_resolution,[status(thm)],[19377, 2492, 4234, 3762, 17791, 20150, 20166, 20160])).
% 29.09/19.31 tff(20168,plain,(big_f(c1, c1) | (~(f7(c1) = c1)) | (~(f10(c1) = c1)) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | (~big_f(c1, f9(c1, c1)))), inference(lemma,lemma(discharge,[]))).
% 29.09/19.31 tff(20169,plain,
% 29.09/19.31 (big_f(c1, c1)),
% 29.09/19.31 inference(unit_resolution,[status(thm)],[20168, 19984, 3762, 1498, 11752, 11819, 19609])).
% 29.09/19.31 tff(20170,plain,
% 29.09/19.31 (big_f(f7(f9(c1, c1)), c1)),
% 29.09/19.31 inference(modus_ponens,[status(thm)],[20169, 19612])).
% 29.09/19.31 tff(20171,plain,
% 29.09/19.31 (big_f(f9(c1, c1), f10(c1)) | (c1 = f5(f9(c1, c1)))),
% 29.09/19.31 inference(unit_resolution,[status(thm)],[19392, 676, 3762, 4070, 17812, 17832])).
% 29.09/19.31 tff(20172,plain,
% 29.09/19.31 (c1 = f5(f9(c1, c1))),
% 29.09/19.31 inference(unit_resolution,[status(thm)],[20171, 8712])).
% 29.09/19.31 tff(20173,plain,
% 29.09/19.31 (f5(f9(c1, c1)) = c1),
% 29.09/19.31 inference(symmetry,[status(thm)],[20172])).
% 29.09/19.31 tff(20174,plain,
% 29.09/19.31 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (f9(c1, c1) = f5(f9(c1, c1))) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f7(f9(c1, c1)), f9(c1, c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (f9(c1, c1) = f5(f9(c1, c1))) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f7(f9(c1, c1)), f9(c1, c1))))),
% 29.09/19.31 inference(rewrite,[status(thm)],[])).
% 29.09/19.31 tff(20175,plain,
% 29.09/19.31 (((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c1) = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), f9(c1, c1)))) <=> ((f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (f9(c1, c1) = f5(f9(c1, c1))) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f7(f9(c1, c1)), f9(c1, c1))))),
% 29.09/19.32 inference(rewrite,[status(thm)],[])).
% 29.09/19.32 tff(20176,plain,
% 29.09/19.32 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c1) = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), f9(c1, c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (f9(c1, c1) = f5(f9(c1, c1))) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f7(f9(c1, c1)), f9(c1, c1)))))),
% 29.09/19.32 inference(monotonicity,[status(thm)],[20175])).
% 29.09/19.32 tff(20177,plain,
% 29.09/19.32 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c1) = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), f9(c1, c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (f9(c1, c1) = f5(f9(c1, c1))) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f7(f9(c1, c1)), f9(c1, c1))))),
% 29.09/19.32 inference(transitivity,[status(thm)],[20176, 20174])).
% 29.09/19.32 tff(20178,plain,
% 29.09/19.32 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (f9(c1, c1) = f5(f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), f9(c1, c1))))),
% 29.09/19.32 inference(quant_inst,[status(thm)],[])).
% 29.09/19.32 tff(20179,plain,
% 29.09/19.32 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (f9(c1, c1) = f5(f9(c1, c1))) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f7(f9(c1, c1)), f9(c1, c1)))),
% 29.09/19.32 inference(modus_ponens,[status(thm)],[20178, 20177])).
% 29.09/19.32 tff(20180,plain,
% 29.09/19.32 (big_f(f9(c1, c1), f10(c1)) | (f9(c1, c1) = f5(f9(c1, c1)))),
% 29.09/19.32 inference(unit_resolution,[status(thm)],[20179, 676, 3762, 4070, 17832, 17995])).
% 29.09/19.32 tff(20181,plain,
% 29.09/19.32 (f9(c1, c1) = f5(f9(c1, c1))),
% 29.09/19.32 inference(unit_resolution,[status(thm)],[20180, 8712])).
% 29.09/19.32 tff(20182,plain,
% 29.09/19.32 (f9(c1, c1) = c1),
% 29.09/19.32 inference(transitivity,[status(thm)],[20181, 20173])).
% 29.09/19.32 tff(20183,plain,
% 29.09/19.32 ($false),
% 29.09/19.32 inference(unit_resolution,[status(thm)],[4070, 20182])).
% 29.09/19.32 tff(20184,plain,(big_f(f9(c1, c1), f10(c1)) | (f9(c1, c1) = c1) | (~(f10(c1) = c1)) | (f7(f9(c1, c1)) = f9(c1, c1)) | (~big_f(f7(f9(c1, c1)), f9(c1, c1))) | (~big_f(f7(f9(c1, c1)), c1))), inference(lemma,lemma(discharge,[]))).
% 29.09/19.32 tff(20185,plain,
% 29.09/19.32 (big_f(f9(c1, c1), f10(c1))),
% 29.09/19.32 inference(unit_resolution,[status(thm)],[20184, 20170, 3762, 17791, 17818, 19610])).
% 29.09/19.32 tff(20186,plain,
% 29.09/19.32 (big_f(c2, c1)),
% 29.09/19.32 inference(unit_resolution,[status(thm)],[19082, 20185, 1498, 3762, 11752, 11819])).
% 29.09/19.32 tff(20187,plain,
% 29.09/19.32 (big_f(f9(c1, c1), f10(f9(c1, c1)))),
% 29.09/19.32 inference(modus_ponens,[status(thm)],[20186, 19123])).
% 29.09/19.32 tff(20188,plain,
% 29.09/19.32 (f9(c1, c1) = f8(f9(c1, c1))),
% 29.09/19.32 inference(unit_resolution,[status(thm)],[18015, 20187, 17792, 20170, 17818, 17791, 19610])).
% 29.09/19.32 tff(20189,plain,
% 29.09/19.32 (f8(f9(c1, c1)) = f9(c1, c1)),
% 29.09/19.32 inference(symmetry,[status(thm)],[20188])).
% 29.09/19.32 tff(20190,plain,
% 29.09/19.32 ((c1 = f8(f9(c1, c1))) <=> (c1 = f9(c1, c1))),
% 29.09/19.32 inference(monotonicity,[status(thm)],[20189])).
% 29.09/19.32 tff(20191,plain,
% 29.09/19.32 ((c1 = f8(f9(c1, c1))) <=> (f9(c1, c1) = c1)),
% 29.09/19.32 inference(transitivity,[status(thm)],[20190, 17725])).
% 29.09/19.32 tff(20192,plain,
% 29.09/19.32 ((f9(c1, c1) = c1) <=> (c1 = f8(f9(c1, c1)))),
% 29.09/19.32 inference(symmetry,[status(thm)],[20191])).
% 29.09/19.32 tff(20193,plain,
% 29.09/19.32 ((~(f9(c1, c1) = c1)) <=> (~(c1 = f8(f9(c1, c1))))),
% 29.09/19.32 inference(monotonicity,[status(thm)],[20192])).
% 29.09/19.32 tff(20194,plain,
% 29.09/19.32 (~(c1 = f8(f9(c1, c1)))),
% 29.09/19.32 inference(modus_ponens,[status(thm)],[17791, 20193])).
% 29.09/19.32 tff(20195,plain,
% 29.09/19.32 (big_f(c1, f10(f9(c1, c1)))),
% 29.09/19.32 inference(modus_ponens,[status(thm)],[20169, 17983])).
% 29.09/19.32 tff(20196,plain,
% 29.09/19.32 ((c1 = f5(f9(c1, c1))) | (c1 = f8(f9(c1, c1)))),
% 29.09/19.32 inference(unit_resolution,[status(thm)],[18030, 1659, 17792, 20195, 20170, 17818])).
% 29.09/19.32 tff(20197,plain,
% 29.09/19.32 (c1 = f5(f9(c1, c1))),
% 29.09/19.32 inference(unit_resolution,[status(thm)],[20196, 20194])).
% 29.09/19.32 tff(20198,plain,
% 29.09/19.32 (f5(f9(c1, c1)) = c1),
% 29.09/19.32 inference(symmetry,[status(thm)],[20197])).
% 29.09/19.32 tff(20199,plain,
% 29.09/19.32 ((f9(c1, c1) = f5(f9(c1, c1))) | (c1 = f8(f9(c1, c1)))),
% 29.09/19.32 inference(unit_resolution,[status(thm)],[18039, 1659, 17792, 20195, 17818, 19610])).
% 29.09/19.32 tff(20200,plain,
% 29.09/19.32 (f9(c1, c1) = f5(f9(c1, c1))),
% 29.09/19.32 inference(unit_resolution,[status(thm)],[20199, 20194])).
% 29.09/19.32 tff(20201,plain,
% 29.09/19.32 (f9(c1, c1) = c1),
% 29.09/19.32 inference(transitivity,[status(thm)],[20200, 20198])).
% 29.09/19.32 tff(20202,plain,
% 29.09/19.32 ($false),
% 29.09/19.32 inference(unit_resolution,[status(thm)],[17791, 20201])).
% 29.09/19.32 tff(20203,plain,((~(f10(c1) = c1)) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | big_f(c2, c2) | (~(f5(c1) = c2)) | (f7(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 29.09/19.32 tff(20204,plain,
% 29.09/19.32 (~(f9(f10(c2), f4(c4)) = c2)),
% 29.09/19.32 inference(unit_resolution,[status(thm)],[20203, 3762, 17, 11819, 121, 11752, 186])).
% 29.09/19.32 tff(20205,plain,
% 29.09/19.32 (f9(f10(c2), f4(c4)) = c1),
% 29.09/19.32 inference(unit_resolution,[status(thm)],[146, 20204])).
% 29.09/19.32 tff(20206,plain,
% 29.09/19.32 ($false),
% 29.09/19.32 inference(unit_resolution,[status(thm)],[19829, 20205, 17724, 11752, 11819])).
% 29.09/19.32 tff(20207,plain,((~(f10(c1) = c1)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | (f7(c1) = c1) | (~big_f(c1, c1)) | (f7(c2) = c2) | big_f(c2, c2) | (~(f5(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.09/19.32 tff(20208,plain,
% 29.09/19.32 (~(f10(c1) = c1)),
% 29.09/19.32 inference(unit_resolution,[status(thm)],[20207, 186, 11819, 115, 4932, 17, 121, 11752])).
% 29.09/19.32 tff(20209,plain,
% 29.09/19.32 (f10(c1) = c2),
% 29.09/19.32 inference(unit_resolution,[status(thm)],[14, 20208])).
% 29.09/19.32 tff(20210,plain,
% 29.09/19.32 (f10(c1) = f7(c1)),
% 29.09/19.32 inference(transitivity,[status(thm)],[20209, 2778])).
% 29.09/19.32 tff(20211,plain,
% 29.09/19.32 (~big_f(c2, f10(c1))),
% 29.09/19.32 inference(unit_resolution,[status(thm)],[6125, 20209, 121])).
% 29.09/19.32 tff(20212,plain,
% 29.09/19.32 (~(c2 = f8(c1))),
% 29.09/19.32 inference(unit_resolution,[status(thm)],[1752, 20211, 115, 17723, 1727, 20208])).
% 29.09/19.32 tff(20213,plain,
% 29.09/19.32 (~(f8(c1) = c2)),
% 29.09/19.32 inference(unit_resolution,[status(thm)],[1675, 20212])).
% 29.09/19.32 tff(20214,plain,
% 29.09/19.32 (f8(c1) = c1),
% 29.09/19.32 inference(unit_resolution,[status(thm)],[1680, 20213])).
% 29.09/19.32 tff(20215,plain,
% 29.09/19.32 (big_f(f8(c1), f10(c1)) <=> big_f(c1, f7(c1))),
% 29.09/19.32 inference(monotonicity,[status(thm)],[20214, 20210])).
% 29.09/19.32 tff(20216,plain,
% 29.09/19.32 (big_f(f8(c1), f10(c1))),
% 29.09/19.32 inference(unit_resolution,[status(thm)],[2848, 20208, 115, 730])).
% 29.09/19.32 tff(20217,plain,
% 29.09/19.32 (big_f(c1, f7(c1))),
% 29.09/19.32 inference(modus_ponens,[status(thm)],[20216, 20215])).
% 29.09/19.32 tff(20218,plain,
% 29.09/19.32 (big_f(f7(c2), c1) <=> big_f(c1, c1)),
% 29.09/19.32 inference(monotonicity,[status(thm)],[292])).
% 29.09/19.32 tff(20219,plain,
% 29.09/19.32 (big_f(c1, c1) <=> big_f(f7(c2), c1)),
% 29.09/19.32 inference(symmetry,[status(thm)],[20218])).
% 29.09/19.32 tff(20220,plain,
% 29.09/19.32 (big_f(f7(c2), c1)),
% 29.09/19.32 inference(modus_ponens,[status(thm)],[4932, 20219])).
% 29.09/19.32 tff(20221,plain,
% 29.09/19.32 (f3(c1, c1) = f7(c2)),
% 29.09/19.32 inference(transitivity,[status(thm)],[1938, 342])).
% 29.09/19.32 tff(20222,plain,
% 29.09/19.32 (big_f(f3(c1, c1), c1) <=> big_f(f7(c2), c1)),
% 29.09/19.32 inference(monotonicity,[status(thm)],[20221])).
% 29.09/19.32 tff(20223,plain,
% 29.09/19.32 (big_f(f7(c2), c1) <=> big_f(f3(c1, c1), c1)),
% 29.09/19.32 inference(symmetry,[status(thm)],[20222])).
% 29.09/19.32 tff(20224,plain,
% 29.09/19.32 (big_f(f3(c1, c1), c1)),
% 29.09/19.32 inference(modus_ponens,[status(thm)],[338, 20223])).
% 29.09/19.32 tff(20225,plain,
% 29.09/19.32 ($false),
% 29.09/19.32 inference(unit_resolution,[status(thm)],[1430, 20224])).
% 29.09/19.32 tff(20226,plain,((~(f3(c1, c1) = c1)) | big_f(f3(c1, c1), c1) | (~big_f(f7(c2), c1)) | (~(f7(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.09/19.32 tff(20227,plain,
% 29.09/19.32 (~(f3(c1, c1) = c1)),
% 29.09/19.32 inference(unit_resolution,[status(thm)],[20226, 1430, 292, 20220])).
% 29.09/19.32 tff(20228,plain,
% 29.09/19.32 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (big_f(f3(c1, c1), c1) | (f3(c1, c1) = c1) | (c1 = c4) | (~(c1 = c3)) | (c1 = f2(c1)) | (~big_f(c1, c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | big_f(f3(c1, c1), c1) | (f3(c1, c1) = c1) | (c1 = c4) | (~(c1 = c3)) | (c1 = f2(c1)) | (~big_f(c1, c1)))),
% 29.09/19.32 inference(rewrite,[status(thm)],[])).
% 29.09/19.32 tff(20229,plain,
% 29.09/19.32 (((~(c1 = c3)) | (c1 = c4) | (f3(c1, c1) = c1) | big_f(f3(c1, c1), c1) | (c1 = f2(c1)) | (~big_f(c1, c1))) <=> (big_f(f3(c1, c1), c1) | (f3(c1, c1) = c1) | (c1 = c4) | (~(c1 = c3)) | (c1 = f2(c1)) | (~big_f(c1, c1)))),
% 29.09/19.32 inference(rewrite,[status(thm)],[])).
% 29.09/19.32 tff(20230,plain,
% 29.09/19.32 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c1 = c4) | (f3(c1, c1) = c1) | big_f(f3(c1, c1), c1) | (c1 = f2(c1)) | (~big_f(c1, c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (big_f(f3(c1, c1), c1) | (f3(c1, c1) = c1) | (c1 = c4) | (~(c1 = c3)) | (c1 = f2(c1)) | (~big_f(c1, c1))))),
% 29.09/19.32 inference(monotonicity,[status(thm)],[20229])).
% 29.09/19.32 tff(20231,plain,
% 29.09/19.32 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c1 = c4) | (f3(c1, c1) = c1) | big_f(f3(c1, c1), c1) | (c1 = f2(c1)) | (~big_f(c1, c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | big_f(f3(c1, c1), c1) | (f3(c1, c1) = c1) | (c1 = c4) | (~(c1 = c3)) | (c1 = f2(c1)) | (~big_f(c1, c1)))),
% 29.09/19.32 inference(transitivity,[status(thm)],[20230, 20228])).
% 29.09/19.32 tff(20232,plain,
% 29.09/19.32 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c1 = c4) | (f3(c1, c1) = c1) | big_f(f3(c1, c1), c1) | (c1 = f2(c1)) | (~big_f(c1, c1)))),
% 29.09/19.32 inference(quant_inst,[status(thm)],[])).
% 29.09/19.32 tff(20233,plain,
% 29.09/19.32 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | big_f(f3(c1, c1), c1) | (f3(c1, c1) = c1) | (c1 = c4) | (~(c1 = c3)) | (c1 = f2(c1)) | (~big_f(c1, c1))),
% 29.09/19.32 inference(modus_ponens,[status(thm)],[20232, 20231])).
% 29.09/19.32 tff(20234,plain,
% 29.09/19.32 (c1 = f2(c1)),
% 29.09/19.32 inference(unit_resolution,[status(thm)],[20233, 7352, 1430, 5080, 20227, 482, 4932])).
% 29.09/19.32 tff(20235,plain,
% 29.09/19.32 (f2(c1) = c1),
% 29.09/19.32 inference(symmetry,[status(thm)],[20234])).
% 29.09/19.32 tff(20236,plain,
% 29.09/19.32 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (big_f(f3(c1, c1), c1) | (f3(c1, c1) = c1) | (c1 = c4) | (~(c1 = c3)) | (f7(c1) = f2(c1)) | (~big_f(c1, f7(c1))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | big_f(f3(c1, c1), c1) | (f3(c1, c1) = c1) | (c1 = c4) | (~(c1 = c3)) | (f7(c1) = f2(c1)) | (~big_f(c1, f7(c1))))),
% 29.09/19.32 inference(rewrite,[status(thm)],[])).
% 29.09/19.32 tff(20237,plain,
% 29.09/19.32 (((~(c1 = c3)) | (c1 = c4) | (f3(c1, c1) = c1) | big_f(f3(c1, c1), c1) | (f7(c1) = f2(c1)) | (~big_f(c1, f7(c1)))) <=> (big_f(f3(c1, c1), c1) | (f3(c1, c1) = c1) | (c1 = c4) | (~(c1 = c3)) | (f7(c1) = f2(c1)) | (~big_f(c1, f7(c1))))),
% 29.09/19.32 inference(rewrite,[status(thm)],[])).
% 29.09/19.32 tff(20238,plain,
% 29.09/19.32 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c1 = c4) | (f3(c1, c1) = c1) | big_f(f3(c1, c1), c1) | (f7(c1) = f2(c1)) | (~big_f(c1, f7(c1))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (big_f(f3(c1, c1), c1) | (f3(c1, c1) = c1) | (c1 = c4) | (~(c1 = c3)) | (f7(c1) = f2(c1)) | (~big_f(c1, f7(c1)))))),
% 29.09/19.32 inference(monotonicity,[status(thm)],[20237])).
% 29.09/19.32 tff(20239,plain,
% 29.09/19.32 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c1 = c4) | (f3(c1, c1) = c1) | big_f(f3(c1, c1), c1) | (f7(c1) = f2(c1)) | (~big_f(c1, f7(c1))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | big_f(f3(c1, c1), c1) | (f3(c1, c1) = c1) | (c1 = c4) | (~(c1 = c3)) | (f7(c1) = f2(c1)) | (~big_f(c1, f7(c1))))),
% 29.09/19.32 inference(transitivity,[status(thm)],[20238, 20236])).
% 29.09/19.32 tff(20240,plain,
% 29.09/19.32 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c1 = c4) | (f3(c1, c1) = c1) | big_f(f3(c1, c1), c1) | (f7(c1) = f2(c1)) | (~big_f(c1, f7(c1))))),
% 29.09/19.32 inference(quant_inst,[status(thm)],[])).
% 29.09/19.32 tff(20241,plain,
% 29.09/19.32 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | big_f(f3(c1, c1), c1) | (f3(c1, c1) = c1) | (c1 = c4) | (~(c1 = c3)) | (f7(c1) = f2(c1)) | (~big_f(c1, f7(c1)))),
% 29.09/19.32 inference(modus_ponens,[status(thm)],[20240, 20239])).
% 29.09/19.32 tff(20242,plain,
% 29.09/19.32 (f7(c1) = f2(c1)),
% 29.09/19.32 inference(unit_resolution,[status(thm)],[20241, 7352, 1430, 5080, 20227, 482, 11909])).
% 29.09/19.32 tff(20243,plain,
% 29.09/19.32 (f7(c1) = c1),
% 29.09/19.32 inference(transitivity,[status(thm)],[20242, 20235])).
% 29.09/19.32 tff(20244,plain,
% 29.09/19.32 ($false),
% 29.09/19.32 inference(unit_resolution,[status(thm)],[115, 20243])).
% 29.09/19.32 tff(20245,plain,(big_f(f3(c1, c1), c1) | (f7(c1) = c1) | (~(c1 = c3)) | (c1 = c4) | (~big_f(c1, c1)) | (~big_f(c1, f7(c1))) | (~(f7(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.09/19.32 tff(20246,plain,
% 29.09/19.32 (big_f(f3(c1, c1), c1)),
% 29.09/19.32 inference(unit_resolution,[status(thm)],[20245, 20217, 5611, 482, 4932, 115, 22])).
% 29.09/19.32 tff(20247,plain,
% 29.09/19.32 (big_f(f3(c1, c1), f10(f7(c1)))),
% 29.09/19.32 inference(modus_ponens,[status(thm)],[20246, 17720])).
% 29.09/19.32 tff(20248,plain,
% 29.09/19.32 ((~big_f(c2, c2)) <=> (~big_f(f7(c1), f7(c1)))),
% 29.09/19.32 inference(monotonicity,[status(thm)],[18280])).
% 29.09/19.32 tff(20249,plain,
% 29.09/19.32 (~big_f(f7(c1), f7(c1))),
% 29.09/19.32 inference(modus_ponens,[status(thm)],[121, 20248])).
% 29.09/19.32 tff(20250,plain,
% 29.09/19.32 ((f10(f7(c1)) = f7(c1)) <=> (c1 = f7(c1))),
% 29.09/19.32 inference(monotonicity,[status(thm)],[17718])).
% 29.09/19.32 tff(20251,plain,
% 29.09/19.32 ((f10(f7(c1)) = f7(c1)) <=> (f7(c1) = c1)),
% 29.09/19.32 inference(transitivity,[status(thm)],[20250, 14336])).
% 29.09/19.32 tff(20252,plain,
% 29.09/19.32 ((f7(c1) = c1) <=> (f10(f7(c1)) = f7(c1))),
% 29.09/19.32 inference(symmetry,[status(thm)],[20251])).
% 29.09/19.32 tff(20253,plain,
% 29.09/19.32 ((~(f7(c1) = c1)) <=> (~(f10(f7(c1)) = f7(c1)))),
% 29.09/19.32 inference(monotonicity,[status(thm)],[20252])).
% 29.09/19.32 tff(20254,plain,
% 29.09/19.32 (~(f10(f7(c1)) = f7(c1))),
% 29.09/19.32 inference(modus_ponens,[status(thm)],[115, 20253])).
% 29.09/19.32 tff(20255,plain,
% 29.09/19.32 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f7(c1) = c1) | (f10(f7(c1)) = f7(c1)) | big_f(f7(c1), f7(c1)) | (~(f7(c1) = f5(c1))) | (f3(c1, c1) = f8(f7(c1))) | (~big_f(f3(c1, c1), f10(f7(c1)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f7(c1) = c1) | (f10(f7(c1)) = f7(c1)) | big_f(f7(c1), f7(c1)) | (~(f7(c1) = f5(c1))) | (f3(c1, c1) = f8(f7(c1))) | (~big_f(f3(c1, c1), f10(f7(c1)))))),
% 29.09/19.32 inference(rewrite,[status(thm)],[])).
% 29.09/19.32 tff(20256,plain,
% 29.09/19.32 (((~(f7(c1) = f5(c1))) | (f10(f7(c1)) = f7(c1)) | (f3(c1, c1) = f8(f7(c1))) | (~big_f(f3(c1, c1), f10(f7(c1)))) | (f7(c1) = c1) | big_f(f7(c1), f7(c1))) <=> ((f7(c1) = c1) | (f10(f7(c1)) = f7(c1)) | big_f(f7(c1), f7(c1)) | (~(f7(c1) = f5(c1))) | (f3(c1, c1) = f8(f7(c1))) | (~big_f(f3(c1, c1), f10(f7(c1)))))),
% 29.09/19.32 inference(rewrite,[status(thm)],[])).
% 29.09/19.32 tff(20257,plain,
% 29.09/19.32 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(f7(c1) = f5(c1))) | (f10(f7(c1)) = f7(c1)) | (f3(c1, c1) = f8(f7(c1))) | (~big_f(f3(c1, c1), f10(f7(c1)))) | (f7(c1) = c1) | big_f(f7(c1), f7(c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f7(c1) = c1) | (f10(f7(c1)) = f7(c1)) | big_f(f7(c1), f7(c1)) | (~(f7(c1) = f5(c1))) | (f3(c1, c1) = f8(f7(c1))) | (~big_f(f3(c1, c1), f10(f7(c1))))))),
% 29.09/19.32 inference(monotonicity,[status(thm)],[20256])).
% 29.09/19.32 tff(20258,plain,
% 29.09/19.32 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(f7(c1) = f5(c1))) | (f10(f7(c1)) = f7(c1)) | (f3(c1, c1) = f8(f7(c1))) | (~big_f(f3(c1, c1), f10(f7(c1)))) | (f7(c1) = c1) | big_f(f7(c1), f7(c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f7(c1) = c1) | (f10(f7(c1)) = f7(c1)) | big_f(f7(c1), f7(c1)) | (~(f7(c1) = f5(c1))) | (f3(c1, c1) = f8(f7(c1))) | (~big_f(f3(c1, c1), f10(f7(c1)))))),
% 29.09/19.32 inference(transitivity,[status(thm)],[20257, 20255])).
% 29.09/19.32 tff(20259,plain,
% 29.09/19.32 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(f7(c1) = f5(c1))) | (f10(f7(c1)) = f7(c1)) | (f3(c1, c1) = f8(f7(c1))) | (~big_f(f3(c1, c1), f10(f7(c1)))) | (f7(c1) = c1) | big_f(f7(c1), f7(c1)))),
% 29.09/19.32 inference(quant_inst,[status(thm)],[])).
% 29.09/19.32 tff(20260,plain,
% 29.09/19.32 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f7(c1) = c1) | (f10(f7(c1)) = f7(c1)) | big_f(f7(c1), f7(c1)) | (~(f7(c1) = f5(c1))) | (f3(c1, c1) = f8(f7(c1))) | (~big_f(f3(c1, c1), f10(f7(c1))))),
% 29.09/19.32 inference(modus_ponens,[status(thm)],[20259, 20258])).
% 29.09/19.32 tff(20261,plain,
% 29.09/19.32 ((f3(c1, c1) = f8(f7(c1))) | (~big_f(f3(c1, c1), f10(f7(c1))))),
% 29.09/19.32 inference(unit_resolution,[status(thm)],[20260, 705, 115, 14335, 20254, 20249])).
% 29.09/19.32 tff(20262,plain,
% 29.09/19.32 (f3(c1, c1) = f8(f7(c1))),
% 29.09/19.32 inference(unit_resolution,[status(thm)],[20261, 20247])).
% 29.09/19.32 tff(20263,plain,
% 29.09/19.32 (f3(c1, c1) = c3),
% 29.09/19.32 inference(modus_ponens,[status(thm)],[20262, 17717])).
% 29.09/19.32 tff(20264,plain,
% 29.09/19.32 (f3(c1, c1) = c1),
% 29.09/19.32 inference(modus_ponens,[status(thm)],[20262, 17716])).
% 29.09/19.32 tff(20265,plain,
% 29.09/19.32 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((c1 = c4) | (~big_f(f3(c1, c1), c1)) | (~(f3(c1, c1) = c1)) | (c1 = f2(f3(c1, c1))) | (~(f3(c1, c1) = c3)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (c1 = c4) | (~big_f(f3(c1, c1), c1)) | (~(f3(c1, c1) = c1)) | (c1 = f2(f3(c1, c1))) | (~(f3(c1, c1) = c3)))),
% 29.09/19.32 inference(rewrite,[status(thm)],[])).
% 29.09/19.32 tff(20266,plain,
% 29.09/19.32 (((~(f3(c1, c1) = c3)) | (c1 = c4) | (~(f3(c1, c1) = c1)) | (~big_f(f3(c1, c1), c1)) | (c1 = f2(f3(c1, c1))) | (~big_f(f3(c1, c1), c1))) <=> ((c1 = c4) | (~big_f(f3(c1, c1), c1)) | (~(f3(c1, c1) = c1)) | (c1 = f2(f3(c1, c1))) | (~(f3(c1, c1) = c3)))),
% 29.09/19.33 inference(rewrite,[status(thm)],[])).
% 29.09/19.33 tff(20267,plain,
% 29.09/19.33 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f3(c1, c1) = c3)) | (c1 = c4) | (~(f3(c1, c1) = c1)) | (~big_f(f3(c1, c1), c1)) | (c1 = f2(f3(c1, c1))) | (~big_f(f3(c1, c1), c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((c1 = c4) | (~big_f(f3(c1, c1), c1)) | (~(f3(c1, c1) = c1)) | (c1 = f2(f3(c1, c1))) | (~(f3(c1, c1) = c3))))),
% 29.09/19.33 inference(monotonicity,[status(thm)],[20266])).
% 29.09/19.33 tff(20268,plain,
% 29.09/19.33 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f3(c1, c1) = c3)) | (c1 = c4) | (~(f3(c1, c1) = c1)) | (~big_f(f3(c1, c1), c1)) | (c1 = f2(f3(c1, c1))) | (~big_f(f3(c1, c1), c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (c1 = c4) | (~big_f(f3(c1, c1), c1)) | (~(f3(c1, c1) = c1)) | (c1 = f2(f3(c1, c1))) | (~(f3(c1, c1) = c3)))),
% 29.09/19.33 inference(transitivity,[status(thm)],[20267, 20265])).
% 29.09/19.33 tff(20269,plain,
% 29.09/19.33 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f3(c1, c1) = c3)) | (c1 = c4) | (~(f3(c1, c1) = c1)) | (~big_f(f3(c1, c1), c1)) | (c1 = f2(f3(c1, c1))) | (~big_f(f3(c1, c1), c1)))),
% 29.09/19.33 inference(quant_inst,[status(thm)],[])).
% 29.09/19.33 tff(20270,plain,
% 29.09/19.33 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (c1 = c4) | (~big_f(f3(c1, c1), c1)) | (~(f3(c1, c1) = c1)) | (c1 = f2(f3(c1, c1))) | (~(f3(c1, c1) = c3))),
% 29.09/19.33 inference(modus_ponens,[status(thm)],[20269, 20268])).
% 29.09/19.33 tff(20271,plain,
% 29.09/19.33 ((~(f3(c1, c1) = c1)) | (c1 = f2(f3(c1, c1))) | (~(f3(c1, c1) = c3))),
% 29.09/19.33 inference(unit_resolution,[status(thm)],[20270, 7051, 20246, 482])).
% 29.09/19.33 tff(20272,plain,
% 29.09/19.33 (c1 = f2(f3(c1, c1))),
% 29.09/19.33 inference(unit_resolution,[status(thm)],[20271, 20264, 20263])).
% 29.09/19.33 tff(20273,plain,
% 29.09/19.33 (f2(f3(c1, c1)) = c1),
% 29.09/19.33 inference(symmetry,[status(thm)],[20272])).
% 29.09/19.33 tff(20274,plain,
% 29.09/19.33 (f8(f7(c1)) = f3(c1, c1)),
% 29.09/19.33 inference(symmetry,[status(thm)],[20262])).
% 29.09/19.33 tff(20275,plain,
% 29.09/19.33 (c1 = f8(f7(f4(c4)))),
% 29.09/19.33 inference(symmetry,[status(thm)],[16268])).
% 29.09/19.33 tff(20276,plain,
% 29.09/19.33 (c1 = f3(c1, c1)),
% 29.09/19.33 inference(transitivity,[status(thm)],[20275, 17700, 20274])).
% 29.09/19.33 tff(20277,plain,
% 29.09/19.33 (f2(c1) = f2(f3(c1, c1))),
% 29.09/19.33 inference(monotonicity,[status(thm)],[20276])).
% 29.09/19.33 tff(20278,plain,
% 29.09/19.33 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((c1 = c4) | (~(c1 = c3)) | (~big_f(f3(c1, c1), c1)) | (~(f3(c1, c1) = c1)) | (f7(c1) = f2(c1)) | (~big_f(c1, f7(c1))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (c1 = c4) | (~(c1 = c3)) | (~big_f(f3(c1, c1), c1)) | (~(f3(c1, c1) = c1)) | (f7(c1) = f2(c1)) | (~big_f(c1, f7(c1))))),
% 29.09/19.33 inference(rewrite,[status(thm)],[])).
% 29.09/19.33 tff(20279,plain,
% 29.09/19.33 (((~(c1 = c3)) | (c1 = c4) | (~(f3(c1, c1) = c1)) | (~big_f(f3(c1, c1), c1)) | (f7(c1) = f2(c1)) | (~big_f(c1, f7(c1)))) <=> ((c1 = c4) | (~(c1 = c3)) | (~big_f(f3(c1, c1), c1)) | (~(f3(c1, c1) = c1)) | (f7(c1) = f2(c1)) | (~big_f(c1, f7(c1))))),
% 29.09/19.33 inference(rewrite,[status(thm)],[])).
% 29.09/19.33 tff(20280,plain,
% 29.09/19.33 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c1 = c4) | (~(f3(c1, c1) = c1)) | (~big_f(f3(c1, c1), c1)) | (f7(c1) = f2(c1)) | (~big_f(c1, f7(c1))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((c1 = c4) | (~(c1 = c3)) | (~big_f(f3(c1, c1), c1)) | (~(f3(c1, c1) = c1)) | (f7(c1) = f2(c1)) | (~big_f(c1, f7(c1)))))),
% 29.09/19.33 inference(monotonicity,[status(thm)],[20279])).
% 29.09/19.33 tff(20281,plain,
% 29.09/19.33 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c1 = c4) | (~(f3(c1, c1) = c1)) | (~big_f(f3(c1, c1), c1)) | (f7(c1) = f2(c1)) | (~big_f(c1, f7(c1))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (c1 = c4) | (~(c1 = c3)) | (~big_f(f3(c1, c1), c1)) | (~(f3(c1, c1) = c1)) | (f7(c1) = f2(c1)) | (~big_f(c1, f7(c1))))),
% 29.09/19.33 inference(transitivity,[status(thm)],[20280, 20278])).
% 29.09/19.33 tff(20282,plain,
% 29.09/19.33 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c1 = c4) | (~(f3(c1, c1) = c1)) | (~big_f(f3(c1, c1), c1)) | (f7(c1) = f2(c1)) | (~big_f(c1, f7(c1))))),
% 29.09/19.33 inference(quant_inst,[status(thm)],[])).
% 29.09/19.33 tff(20283,plain,
% 29.09/19.33 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (c1 = c4) | (~(c1 = c3)) | (~big_f(f3(c1, c1), c1)) | (~(f3(c1, c1) = c1)) | (f7(c1) = f2(c1)) | (~big_f(c1, f7(c1)))),
% 29.09/19.33 inference(modus_ponens,[status(thm)],[20282, 20281])).
% 29.09/19.33 tff(20284,plain,
% 29.09/19.33 ((~(f3(c1, c1) = c1)) | (f7(c1) = f2(c1))),
% 29.09/19.33 inference(unit_resolution,[status(thm)],[20283, 7051, 20246, 5611, 482, 20217])).
% 29.09/19.33 tff(20285,plain,
% 29.09/19.33 (f7(c1) = f2(c1)),
% 29.09/19.33 inference(unit_resolution,[status(thm)],[20284, 20264])).
% 29.09/19.33 tff(20286,plain,
% 29.09/19.33 (f7(c1) = c1),
% 29.09/19.33 inference(transitivity,[status(thm)],[20285, 20277, 20273])).
% 29.09/19.33 tff(20287,plain,
% 29.09/19.33 ($false),
% 29.09/19.33 inference(unit_resolution,[status(thm)],[115, 20286])).
% 29.09/19.33 tff(20288,plain,((~(f5(c1) = c2)) | (f7(c1) = c1) | (~(f8(f7(f4(c4))) = c1)) | (~(f4(c4) = c1)) | (c1 = c4) | (~(c3 = c1)) | (~(f10(c2) = c1)) | (~big_f(c1, c1)) | big_f(c2, c2) | big_f(f7(c1), f5(c1)) | (f7(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 29.09/19.33 tff(20289,plain,
% 29.09/19.33 (~(f5(c1) = c2)),
% 29.09/19.33 inference(unit_resolution,[status(thm)],[20288, 17712, 115, 11752, 482, 172, 94, 4932, 121, 17697, 17])).
% 29.09/19.33 tff(20290,plain,
% 29.09/19.33 (f5(c1) = c1),
% 29.09/19.33 inference(unit_resolution,[status(thm)],[1708, 20289])).
% 29.09/19.33 tff(20291,plain,
% 29.09/19.33 (c1 = f5(c1)),
% 29.09/19.33 inference(modus_ponens,[status(thm)],[20290, 192])).
% 29.09/19.33 tff(20292,plain,
% 29.09/19.33 (big_f(f9(c1, c1), f10(c1))),
% 29.09/19.33 inference(unit_resolution,[status(thm)],[18686, 3762, 11819, 115, 292, 338, 730])).
% 29.09/19.33 tff(20293,plain,
% 29.09/19.33 ((~big_f(f7(c1), c1)) <=> (~big_f(c2, c1))),
% 29.09/19.33 inference(monotonicity,[status(thm)],[247])).
% 29.09/19.33 tff(20294,plain,
% 29.09/19.33 (~big_f(c2, c1)),
% 29.09/19.33 inference(modus_ponens,[status(thm)],[285, 20293])).
% 29.09/19.33 tff(20295,plain,
% 29.09/19.33 (~(f9(f10(c2), f4(c4)) = c2)),
% 29.09/19.33 inference(unit_resolution,[status(thm)],[19135, 3762, 11819, 292, 115, 338, 20294, 730, 11752])).
% 29.09/19.33 tff(20296,plain,
% 29.09/19.33 (f9(f10(c2), f4(c4)) = c1),
% 29.09/19.33 inference(unit_resolution,[status(thm)],[146, 20295])).
% 29.09/19.33 tff(20297,plain,
% 29.09/19.33 (f9(c1, c1) = c1),
% 29.09/19.33 inference(unit_resolution,[status(thm)],[19829, 20296, 11752, 11819])).
% 29.09/19.33 tff(20298,plain,
% 29.09/19.33 ($false),
% 29.09/19.33 inference(unit_resolution,[status(thm)],[18656, 783, 115, 3762, 20297, 20292, 285, 11826])).
% 29.09/19.33 tff(20299,plain,((~(f10(c1) = c1)) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(c1 = f5(c1))) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | (~(f7(c2) = c1)) | (~big_f(f7(c2), c1)) | big_f(f7(c1), f5(c1))), inference(lemma,lemma(discharge,[]))).
% 29.09/19.33 tff(20300,plain,
% 29.09/19.33 (~(f10(c1) = c1)),
% 29.09/19.33 inference(unit_resolution,[status(thm)],[20299, 285, 115, 20291, 11752, 94, 22, 17698, 17697])).
% 29.09/19.33 tff(20301,plain,
% 29.09/19.33 (~(f10(f10(c2)) = f10(c2))),
% 29.09/19.33 inference(modus_ponens,[status(thm)],[20300, 17696])).
% 29.09/19.33 tff(20302,plain,
% 29.09/19.33 (big_f(c2, f10(f10(c2))) <=> big_f(c2, f10(c1))),
% 29.09/19.33 inference(monotonicity,[status(thm)],[15299])).
% 29.09/19.33 tff(20303,plain,
% 29.09/19.33 (big_f(c2, f10(c1)) <=> big_f(c2, f10(f10(c2)))),
% 29.09/19.33 inference(symmetry,[status(thm)],[20302])).
% 29.09/19.33 tff(20304,plain,
% 29.09/19.33 (f10(c1) = c2),
% 29.09/19.33 inference(unit_resolution,[status(thm)],[14, 20300])).
% 29.09/19.33 tff(20305,plain,
% 29.09/19.33 (big_f(f7(c1), f10(c1)) <=> big_f(c2, c2)),
% 29.09/19.33 inference(monotonicity,[status(thm)],[120, 20304])).
% 29.09/19.33 tff(20306,plain,
% 29.09/19.33 (big_f(c2, c2) <=> big_f(f7(c1), f10(c1))),
% 29.09/19.33 inference(symmetry,[status(thm)],[20305])).
% 29.09/19.33 tff(20307,plain,
% 29.09/19.33 (big_f(c2, c2) <=> big_f(c2, f10(f10(c2)))),
% 29.09/19.33 inference(transitivity,[status(thm)],[20306, 11853, 20303])).
% 29.09/19.33 tff(20308,plain,
% 29.09/19.33 ((~big_f(c2, c2)) <=> (~big_f(c2, f10(f10(c2))))),
% 29.09/19.33 inference(monotonicity,[status(thm)],[20307])).
% 29.09/19.33 tff(20309,plain,
% 29.09/19.33 (~big_f(c2, f10(f10(c2)))),
% 29.09/19.33 inference(modus_ponens,[status(thm)],[121, 20308])).
% 29.09/19.33 tff(20310,plain,
% 29.09/19.33 (~(c2 = f8(f10(c2)))),
% 29.09/19.33 inference(unit_resolution,[status(thm)],[11865, 20309, 115, 285, 20291, 20301])).
% 29.09/19.33 tff(20311,plain,
% 29.09/19.33 (~(f8(c1) = c2)),
% 29.09/19.33 inference(modus_ponens,[status(thm)],[20310, 17690])).
% 29.09/19.33 tff(20312,plain,
% 29.09/19.33 (f8(c1) = c1),
% 29.09/19.33 inference(unit_resolution,[status(thm)],[1680, 20311])).
% 29.09/19.33 tff(20313,plain,
% 29.09/19.33 (f8(c1) = c3),
% 29.09/19.33 inference(modus_ponens,[status(thm)],[20312, 17687])).
% 29.09/19.33 tff(20314,plain,
% 29.09/19.33 (c2 = f10(c1)),
% 29.09/19.33 inference(symmetry,[status(thm)],[20304])).
% 29.09/19.33 tff(20315,plain,
% 29.09/19.33 (f7(c1) = f10(c1)),
% 29.09/19.33 inference(transitivity,[status(thm)],[120, 20314])).
% 29.09/19.33 tff(20316,plain,
% 29.09/19.33 (big_f(f8(c1), f7(c1)) <=> big_f(f8(c1), f10(c1))),
% 29.09/19.33 inference(monotonicity,[status(thm)],[20315])).
% 29.09/19.33 tff(20317,plain,
% 29.09/19.33 (big_f(f8(c1), f10(c1)) <=> big_f(f8(c1), f7(c1))),
% 29.09/19.33 inference(symmetry,[status(thm)],[20316])).
% 29.09/19.33 tff(20318,plain,
% 29.09/19.33 (big_f(f8(c1), f10(c1))),
% 29.09/19.33 inference(unit_resolution,[status(thm)],[2848, 20300, 115, 17697])).
% 29.09/19.33 tff(20319,plain,
% 29.09/19.33 (big_f(f8(c1), f7(c1))),
% 29.09/19.33 inference(modus_ponens,[status(thm)],[20318, 20317])).
% 29.09/19.33 tff(20320,plain,
% 29.09/19.33 (f8(f7(c1)) = c1),
% 29.09/19.33 inference(transitivity,[status(thm)],[17699, 17712])).
% 29.09/19.33 tff(20321,plain,
% 29.09/19.33 ((f3(c1, c1) = f8(f7(c1))) <=> (f3(c1, c1) = c1)),
% 29.09/19.33 inference(monotonicity,[status(thm)],[20320])).
% 29.09/19.33 tff(20322,plain,
% 29.09/19.33 (f10(f7(c1)) = c1),
% 29.09/19.33 inference(transitivity,[status(thm)],[12327, 94])).
% 29.09/19.33 tff(20323,plain,
% 29.09/19.33 (big_f(f3(c1, c1), f10(f7(c1))) <=> big_f(f3(c1, c1), c1)),
% 29.09/19.33 inference(monotonicity,[status(thm)],[20322])).
% 29.09/19.33 tff(20324,plain,
% 29.09/19.33 (big_f(f3(c1, c1), c1) <=> big_f(f3(c1, c1), f10(f7(c1)))),
% 29.09/19.33 inference(symmetry,[status(thm)],[20323])).
% 29.09/19.33 tff(20325,plain,
% 29.09/19.33 (big_f(c1, f7(c1))),
% 29.09/19.33 inference(unit_resolution,[status(thm)],[11870, 20300, 285, 20291, 94, 121, 115])).
% 29.09/19.33 tff(20326,plain,
% 29.09/19.33 (big_f(f3(c1, c1), c1)),
% 29.09/19.33 inference(unit_resolution,[status(thm)],[20245, 20325, 5611, 482, 4932, 115, 22])).
% 29.09/19.33 tff(20327,plain,
% 29.09/19.33 (big_f(f3(c1, c1), f10(f7(c1)))),
% 29.09/19.33 inference(modus_ponens,[status(thm)],[20326, 20324])).
% 29.09/19.33 tff(20328,plain,
% 29.09/19.33 ((f10(f7(c1)) = f7(c1)) <=> (c1 = f7(c1))),
% 29.09/19.33 inference(monotonicity,[status(thm)],[20322])).
% 29.09/19.33 tff(20329,plain,
% 29.09/19.33 ((f10(f7(c1)) = f7(c1)) <=> (f7(c1) = c1)),
% 29.09/19.33 inference(transitivity,[status(thm)],[20328, 14336])).
% 29.09/19.33 tff(20330,plain,
% 29.09/19.33 ((f7(c1) = c1) <=> (f10(f7(c1)) = f7(c1))),
% 29.09/19.33 inference(symmetry,[status(thm)],[20329])).
% 29.09/19.33 tff(20331,plain,
% 29.09/19.33 ((~(f7(c1) = c1)) <=> (~(f10(f7(c1)) = f7(c1)))),
% 29.09/19.33 inference(monotonicity,[status(thm)],[20330])).
% 29.09/19.33 tff(20332,plain,
% 29.09/19.33 (~(f10(f7(c1)) = f7(c1))),
% 29.09/19.33 inference(modus_ponens,[status(thm)],[115, 20331])).
% 29.09/19.33 tff(20333,plain,
% 29.09/19.33 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f7(c1) = c1) | big_f(f7(c1), c1) | (~(c1 = f5(c1))) | (f10(f7(c1)) = f7(c1)) | (f3(c1, c1) = f8(f7(c1))) | (~big_f(f3(c1, c1), f10(f7(c1)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(c1 = f5(c1))) | (f10(f7(c1)) = f7(c1)) | (f3(c1, c1) = f8(f7(c1))) | (~big_f(f3(c1, c1), f10(f7(c1)))))),
% 29.09/19.33 inference(rewrite,[status(thm)],[])).
% 29.09/19.33 tff(20334,plain,
% 29.09/19.33 (((~(c1 = f5(c1))) | (f10(f7(c1)) = f7(c1)) | (f3(c1, c1) = f8(f7(c1))) | (~big_f(f3(c1, c1), f10(f7(c1)))) | (f7(c1) = c1) | big_f(f7(c1), c1)) <=> ((f7(c1) = c1) | big_f(f7(c1), c1) | (~(c1 = f5(c1))) | (f10(f7(c1)) = f7(c1)) | (f3(c1, c1) = f8(f7(c1))) | (~big_f(f3(c1, c1), f10(f7(c1)))))),
% 29.09/19.33 inference(rewrite,[status(thm)],[])).
% 29.09/19.33 tff(20335,plain,
% 29.09/19.33 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c1 = f5(c1))) | (f10(f7(c1)) = f7(c1)) | (f3(c1, c1) = f8(f7(c1))) | (~big_f(f3(c1, c1), f10(f7(c1)))) | (f7(c1) = c1) | big_f(f7(c1), c1))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f7(c1) = c1) | big_f(f7(c1), c1) | (~(c1 = f5(c1))) | (f10(f7(c1)) = f7(c1)) | (f3(c1, c1) = f8(f7(c1))) | (~big_f(f3(c1, c1), f10(f7(c1))))))),
% 29.09/19.33 inference(monotonicity,[status(thm)],[20334])).
% 29.09/19.33 tff(20336,plain,
% 29.09/19.33 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c1 = f5(c1))) | (f10(f7(c1)) = f7(c1)) | (f3(c1, c1) = f8(f7(c1))) | (~big_f(f3(c1, c1), f10(f7(c1)))) | (f7(c1) = c1) | big_f(f7(c1), c1))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(c1 = f5(c1))) | (f10(f7(c1)) = f7(c1)) | (f3(c1, c1) = f8(f7(c1))) | (~big_f(f3(c1, c1), f10(f7(c1)))))),
% 29.09/19.33 inference(transitivity,[status(thm)],[20335, 20333])).
% 29.09/19.33 tff(20337,plain,
% 29.09/19.33 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c1 = f5(c1))) | (f10(f7(c1)) = f7(c1)) | (f3(c1, c1) = f8(f7(c1))) | (~big_f(f3(c1, c1), f10(f7(c1)))) | (f7(c1) = c1) | big_f(f7(c1), c1))),
% 29.09/19.33 inference(quant_inst,[status(thm)],[])).
% 29.09/19.33 tff(20338,plain,
% 29.09/19.33 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(c1 = f5(c1))) | (f10(f7(c1)) = f7(c1)) | (f3(c1, c1) = f8(f7(c1))) | (~big_f(f3(c1, c1), f10(f7(c1))))),
% 29.09/19.33 inference(modus_ponens,[status(thm)],[20337, 20336])).
% 29.09/19.33 tff(20339,plain,
% 29.09/19.33 ((f3(c1, c1) = f8(f7(c1))) | (~big_f(f3(c1, c1), f10(f7(c1))))),
% 29.09/19.33 inference(unit_resolution,[status(thm)],[20338, 705, 115, 285, 20291, 20332])).
% 29.09/19.33 tff(20340,plain,
% 29.09/19.33 (f3(c1, c1) = f8(f7(c1))),
% 29.09/19.33 inference(unit_resolution,[status(thm)],[20339, 20327])).
% 29.09/19.33 tff(20341,plain,
% 29.09/19.33 (f3(c1, c1) = c1),
% 29.09/19.33 inference(modus_ponens,[status(thm)],[20340, 20321])).
% 29.09/19.33 tff(20342,plain,
% 29.09/19.33 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((c1 = c4) | (~big_f(f3(c1, c1), c1)) | (~(f3(c1, c1) = c1)) | (~(f8(c1) = c3)) | (f7(c1) = f2(f8(c1))) | (~big_f(f8(c1), f7(c1))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (c1 = c4) | (~big_f(f3(c1, c1), c1)) | (~(f3(c1, c1) = c1)) | (~(f8(c1) = c3)) | (f7(c1) = f2(f8(c1))) | (~big_f(f8(c1), f7(c1))))),
% 29.09/19.33 inference(rewrite,[status(thm)],[])).
% 29.09/19.33 tff(20343,plain,
% 29.09/19.33 (((~(f8(c1) = c3)) | (c1 = c4) | (~(f3(c1, c1) = c1)) | (~big_f(f3(c1, c1), c1)) | (f7(c1) = f2(f8(c1))) | (~big_f(f8(c1), f7(c1)))) <=> ((c1 = c4) | (~big_f(f3(c1, c1), c1)) | (~(f3(c1, c1) = c1)) | (~(f8(c1) = c3)) | (f7(c1) = f2(f8(c1))) | (~big_f(f8(c1), f7(c1))))),
% 29.09/19.33 inference(rewrite,[status(thm)],[])).
% 29.09/19.33 tff(20344,plain,
% 29.09/19.33 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f8(c1) = c3)) | (c1 = c4) | (~(f3(c1, c1) = c1)) | (~big_f(f3(c1, c1), c1)) | (f7(c1) = f2(f8(c1))) | (~big_f(f8(c1), f7(c1))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((c1 = c4) | (~big_f(f3(c1, c1), c1)) | (~(f3(c1, c1) = c1)) | (~(f8(c1) = c3)) | (f7(c1) = f2(f8(c1))) | (~big_f(f8(c1), f7(c1)))))),
% 29.09/19.33 inference(monotonicity,[status(thm)],[20343])).
% 29.09/19.33 tff(20345,plain,
% 29.09/19.33 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f8(c1) = c3)) | (c1 = c4) | (~(f3(c1, c1) = c1)) | (~big_f(f3(c1, c1), c1)) | (f7(c1) = f2(f8(c1))) | (~big_f(f8(c1), f7(c1))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (c1 = c4) | (~big_f(f3(c1, c1), c1)) | (~(f3(c1, c1) = c1)) | (~(f8(c1) = c3)) | (f7(c1) = f2(f8(c1))) | (~big_f(f8(c1), f7(c1))))),
% 29.09/19.33 inference(transitivity,[status(thm)],[20344, 20342])).
% 29.09/19.33 tff(20346,plain,
% 29.09/19.33 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f8(c1) = c3)) | (c1 = c4) | (~(f3(c1, c1) = c1)) | (~big_f(f3(c1, c1), c1)) | (f7(c1) = f2(f8(c1))) | (~big_f(f8(c1), f7(c1))))),
% 29.09/19.33 inference(quant_inst,[status(thm)],[])).
% 29.09/19.33 tff(20347,plain,
% 29.09/19.33 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (c1 = c4) | (~big_f(f3(c1, c1), c1)) | (~(f3(c1, c1) = c1)) | (~(f8(c1) = c3)) | (f7(c1) = f2(f8(c1))) | (~big_f(f8(c1), f7(c1)))),
% 29.09/19.33 inference(modus_ponens,[status(thm)],[20346, 20345])).
% 29.09/19.33 tff(20348,plain,
% 29.09/19.33 ((~(f3(c1, c1) = c1)) | (~(f8(c1) = c3)) | (f7(c1) = f2(f8(c1))) | (~big_f(f8(c1), f7(c1)))),
% 29.09/19.33 inference(unit_resolution,[status(thm)],[20347, 7051, 20326, 482])).
% 29.09/19.33 tff(20349,plain,
% 29.09/19.33 (f7(c1) = f2(f8(c1))),
% 29.09/19.33 inference(unit_resolution,[status(thm)],[20348, 20341, 20319, 20313])).
% 29.09/19.33 tff(20350,plain,
% 29.09/19.33 (f2(f8(c1)) = f7(c1)),
% 29.09/19.33 inference(symmetry,[status(thm)],[20349])).
% 29.09/19.33 tff(20351,plain,
% 29.09/19.33 (f10(c1) = f7(c1)),
% 29.09/19.33 inference(transitivity,[status(thm)],[20304, 2778])).
% 29.09/19.33 tff(20352,plain,
% 29.09/19.33 (big_f(c1, f10(c1)) <=> big_f(c1, f7(c1))),
% 29.09/19.33 inference(monotonicity,[status(thm)],[20351])).
% 29.09/19.33 tff(20353,plain,
% 29.09/19.33 (big_f(c1, f7(c1)) <=> big_f(c1, f10(c1))),
% 29.09/19.33 inference(symmetry,[status(thm)],[20352])).
% 29.09/19.33 tff(20354,plain,
% 29.09/19.33 (big_f(c1, f10(c1))),
% 29.09/19.33 inference(modus_ponens,[status(thm)],[20325, 20353])).
% 29.09/19.33 tff(20355,plain,
% 29.09/19.33 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f7(c1) = c1) | (f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | big_f(f7(c1), c1) | (~(c1 = f5(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f7(c1) = c1) | (f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | big_f(f7(c1), c1) | (~(c1 = f5(c1))))),
% 29.09/19.33 inference(rewrite,[status(thm)],[])).
% 29.09/19.33 tff(20356,plain,
% 29.09/19.33 (((~(c1 = f5(c1))) | (f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (f7(c1) = c1) | big_f(f7(c1), c1)) <=> ((f7(c1) = c1) | (f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | big_f(f7(c1), c1) | (~(c1 = f5(c1))))),
% 29.09/19.33 inference(rewrite,[status(thm)],[])).
% 29.09/19.33 tff(20357,plain,
% 29.09/19.33 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c1 = f5(c1))) | (f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (f7(c1) = c1) | big_f(f7(c1), c1))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f7(c1) = c1) | (f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | big_f(f7(c1), c1) | (~(c1 = f5(c1)))))),
% 29.09/19.33 inference(monotonicity,[status(thm)],[20356])).
% 29.09/19.33 tff(20358,plain,
% 29.09/19.33 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c1 = f5(c1))) | (f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (f7(c1) = c1) | big_f(f7(c1), c1))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f7(c1) = c1) | (f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | big_f(f7(c1), c1) | (~(c1 = f5(c1))))),
% 29.09/19.33 inference(transitivity,[status(thm)],[20357, 20355])).
% 29.09/19.33 tff(20359,plain,
% 29.09/19.33 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c1 = f5(c1))) | (f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (f7(c1) = c1) | big_f(f7(c1), c1))),
% 29.09/19.33 inference(quant_inst,[status(thm)],[])).
% 29.09/19.33 tff(20360,plain,
% 29.09/19.33 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f7(c1) = c1) | (f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | big_f(f7(c1), c1) | (~(c1 = f5(c1)))),
% 29.09/19.33 inference(modus_ponens,[status(thm)],[20359, 20358])).
% 29.09/19.33 tff(20361,plain,
% 29.09/19.33 (c1 = f8(c1)),
% 29.09/19.33 inference(unit_resolution,[status(thm)],[20360, 705, 115, 20300, 20354, 285, 20291])).
% 29.09/19.33 tff(20362,plain,
% 29.09/19.33 (f8(c1) = c1),
% 29.09/19.33 inference(symmetry,[status(thm)],[20361])).
% 29.09/19.33 tff(20363,plain,
% 29.09/19.33 (f2(f8(c1)) = f2(c1)),
% 29.09/19.33 inference(monotonicity,[status(thm)],[20362])).
% 29.09/19.33 tff(20364,plain,
% 29.09/19.33 (f2(c1) = f2(f8(c1))),
% 29.09/19.33 inference(symmetry,[status(thm)],[20363])).
% 29.09/19.33 tff(20365,plain,
% 29.09/19.33 ((f10(f10(c2)) = c2) <=> (f10(c1) = c2)),
% 29.09/19.33 inference(monotonicity,[status(thm)],[15299])).
% 29.09/19.33 tff(20366,plain,
% 29.09/19.33 ((f10(c1) = c2) <=> (f10(f10(c2)) = c2)),
% 29.09/19.33 inference(symmetry,[status(thm)],[20365])).
% 29.09/19.33 tff(20367,plain,
% 29.09/19.33 (f10(f10(c2)) = c2),
% 29.09/19.33 inference(modus_ponens,[status(thm)],[20304, 20366])).
% 29.09/19.33 tff(20368,plain,
% 29.09/19.33 (big_f(c1, c2)),
% 29.09/19.33 inference(unit_resolution,[status(thm)],[12239, 20354, 94, 20367])).
% 29.09/19.33 tff(20369,plain,
% 29.09/19.33 (big_f(c1, f1(c1, c1))),
% 29.09/19.33 inference(modus_ponens,[status(thm)],[2865, 4556])).
% 29.09/19.33 tff(20370,plain,
% 29.09/19.33 ($false),
% 29.09/19.33 inference(unit_resolution,[status(thm)],[9673, 20369])).
% 29.09/19.33 tff(20371,plain,((~(f1(c1, c1) = c2)) | big_f(c1, f1(c1, c1)) | (~big_f(c1, c2))), inference(lemma,lemma(discharge,[]))).
% 29.09/19.33 tff(20372,plain,
% 29.09/19.33 (~(f1(c1, c1) = c2)),
% 29.09/19.33 inference(unit_resolution,[status(thm)],[20371, 9673, 2865])).
% 29.09/19.33 tff(20373,plain,
% 29.09/19.33 ($false),
% 29.09/19.33 inference(unit_resolution,[status(thm)],[601, 20372, 9679])).
% 29.09/19.33 tff(20374,plain,(big_f(c1, f1(c1, c1)) | (~big_f(c1, c2)) | (~big_f(c1, c1))), inference(lemma,lemma(discharge,[]))).
% 29.09/19.33 tff(20375,plain,
% 29.09/19.33 (big_f(c1, f1(c1, c1))),
% 29.09/19.33 inference(unit_resolution,[status(thm)],[20374, 20368, 4932])).
% 29.09/19.33 tff(20376,plain,
% 29.09/19.33 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((c1 = c4) | (~big_f(c1, f1(c1, c1))) | (~(c1 = c3)) | (~big_f(f3(c1, c1), c1)) | (~(f3(c1, c1) = c1)) | (f1(c1, c1) = f2(c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (c1 = c4) | (~big_f(c1, f1(c1, c1))) | (~(c1 = c3)) | (~big_f(f3(c1, c1), c1)) | (~(f3(c1, c1) = c1)) | (f1(c1, c1) = f2(c1)))),
% 29.09/19.33 inference(rewrite,[status(thm)],[])).
% 29.09/19.33 tff(20377,plain,
% 29.09/19.33 (((~(c1 = c3)) | (c1 = c4) | (~(f3(c1, c1) = c1)) | (~big_f(f3(c1, c1), c1)) | (f1(c1, c1) = f2(c1)) | (~big_f(c1, f1(c1, c1)))) <=> ((c1 = c4) | (~big_f(c1, f1(c1, c1))) | (~(c1 = c3)) | (~big_f(f3(c1, c1), c1)) | (~(f3(c1, c1) = c1)) | (f1(c1, c1) = f2(c1)))),
% 29.09/19.34 inference(rewrite,[status(thm)],[])).
% 29.09/19.34 tff(20378,plain,
% 29.09/19.34 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c1 = c4) | (~(f3(c1, c1) = c1)) | (~big_f(f3(c1, c1), c1)) | (f1(c1, c1) = f2(c1)) | (~big_f(c1, f1(c1, c1))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((c1 = c4) | (~big_f(c1, f1(c1, c1))) | (~(c1 = c3)) | (~big_f(f3(c1, c1), c1)) | (~(f3(c1, c1) = c1)) | (f1(c1, c1) = f2(c1))))),
% 29.09/19.34 inference(monotonicity,[status(thm)],[20377])).
% 29.09/19.34 tff(20379,plain,
% 29.09/19.34 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c1 = c4) | (~(f3(c1, c1) = c1)) | (~big_f(f3(c1, c1), c1)) | (f1(c1, c1) = f2(c1)) | (~big_f(c1, f1(c1, c1))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (c1 = c4) | (~big_f(c1, f1(c1, c1))) | (~(c1 = c3)) | (~big_f(f3(c1, c1), c1)) | (~(f3(c1, c1) = c1)) | (f1(c1, c1) = f2(c1)))),
% 29.09/19.34 inference(transitivity,[status(thm)],[20378, 20376])).
% 29.09/19.34 tff(20380,plain,
% 29.09/19.34 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c1 = c4) | (~(f3(c1, c1) = c1)) | (~big_f(f3(c1, c1), c1)) | (f1(c1, c1) = f2(c1)) | (~big_f(c1, f1(c1, c1))))),
% 29.09/19.34 inference(quant_inst,[status(thm)],[])).
% 29.09/19.34 tff(20381,plain,
% 29.09/19.34 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (c1 = c4) | (~big_f(c1, f1(c1, c1))) | (~(c1 = c3)) | (~big_f(f3(c1, c1), c1)) | (~(f3(c1, c1) = c1)) | (f1(c1, c1) = f2(c1))),
% 29.09/19.34 inference(modus_ponens,[status(thm)],[20380, 20379])).
% 29.09/19.34 tff(20382,plain,
% 29.09/19.34 (f1(c1, c1) = f2(c1)),
% 29.09/19.34 inference(unit_resolution,[status(thm)],[20381, 7051, 20326, 5611, 20341, 482, 20375])).
% 29.09/19.34 tff(20383,plain,
% 29.09/19.34 (f1(c1, c1) = f7(c1)),
% 29.09/19.34 inference(transitivity,[status(thm)],[20382, 20364, 20350])).
% 29.09/19.34 tff(20384,plain,
% 29.09/19.34 ((f1(c1, c1) = c1) <=> (f7(c1) = c1)),
% 29.09/19.34 inference(monotonicity,[status(thm)],[20383])).
% 29.09/19.34 tff(20385,plain,
% 29.09/19.34 ((f7(c1) = c1) <=> (f1(c1, c1) = c1)),
% 29.09/19.34 inference(symmetry,[status(thm)],[20384])).
% 29.09/19.34 tff(20386,plain,
% 29.09/19.34 ((~(f7(c1) = c1)) <=> (~(f1(c1, c1) = c1))),
% 29.09/19.34 inference(monotonicity,[status(thm)],[20385])).
% 29.09/19.34 tff(20387,plain,
% 29.09/19.34 (~(f1(c1, c1) = c1)),
% 29.09/19.34 inference(modus_ponens,[status(thm)],[115, 20386])).
% 29.09/19.34 tff(20388,plain,
% 29.09/19.34 ((f3(c1, c1) = f8(f7(c1))) <=> (f3(c1, c1) = c3)),
% 29.09/19.34 inference(transitivity,[status(thm)],[20321, 17714])).
% 29.09/19.34 tff(20389,plain,
% 29.09/19.34 (f3(c1, c1) = c3),
% 29.09/19.34 inference(modus_ponens,[status(thm)],[20340, 20388])).
% 29.09/19.34 tff(20390,plain,
% 29.09/19.34 ((~(f3(c1, c1) = c1)) | (c1 = f2(f3(c1, c1))) | (~(f3(c1, c1) = c3))),
% 29.09/19.34 inference(unit_resolution,[status(thm)],[20270, 7051, 20326, 482])).
% 29.09/19.34 tff(20391,plain,
% 29.09/19.34 (c1 = f2(f3(c1, c1))),
% 29.09/19.34 inference(unit_resolution,[status(thm)],[20390, 20341, 20389])).
% 29.09/19.34 tff(20392,plain,
% 29.09/19.34 (f2(f3(c1, c1)) = c1),
% 29.09/19.34 inference(symmetry,[status(thm)],[20391])).
% 29.09/19.34 tff(20393,plain,
% 29.09/19.34 (f8(f7(c1)) = f3(c1, c1)),
% 29.09/19.34 inference(symmetry,[status(thm)],[20340])).
% 29.09/19.34 tff(20394,plain,
% 29.09/19.34 (c1 = f8(f7(f4(c4)))),
% 29.09/19.34 inference(symmetry,[status(thm)],[17712])).
% 29.09/19.34 tff(20395,plain,
% 29.09/19.34 (c1 = f3(c1, c1)),
% 29.09/19.34 inference(transitivity,[status(thm)],[20394, 17700, 20393])).
% 29.09/19.34 tff(20396,plain,
% 29.09/19.34 (f2(c1) = f2(f3(c1, c1))),
% 29.09/19.34 inference(monotonicity,[status(thm)],[20395])).
% 29.09/19.34 tff(20397,plain,
% 29.09/19.34 (f1(c1, c1) = c1),
% 29.09/19.34 inference(transitivity,[status(thm)],[20382, 20396, 20392])).
% 29.09/19.34 tff(20398,plain,
% 29.09/19.34 ($false),
% 29.09/19.34 inference(unit_resolution,[status(thm)],[20397, 20387])).
% 29.09/19.34 tff(20399,plain,(big_f(f7(c1), c1) | (f7(c1) = c1) | (~(f4(c4) = c1)) | (c1 = c4) | (~(c3 = c1)) | (~big_f(c1, c1)) | big_f(c2, c2) | (f7(c2) = c2) | (f10(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 29.09/19.34 tff(20400,plain,
% 29.09/19.34 (~(c3 = c1)),
% 29.09/19.34 inference(unit_resolution,[status(thm)],[20399, 17685, 115, 11752, 89, 17574, 121, 17, 17597])).
% 29.09/19.34 tff(20401,plain,
% 29.09/19.34 (c3 = c2),
% 29.09/19.34 inference(unit_resolution,[status(thm)],[180, 20400])).
% 29.09/19.34 tff(20402,plain,
% 29.09/19.34 (~big_f(c3, f2(c3))),
% 29.09/19.34 inference(unit_resolution,[status(thm)],[8256, 20401, 121, 2])).
% 29.09/19.34 tff(20403,plain,
% 29.09/19.34 ((c2 = f8(c2)) <=> (c2 = f8(f7(f4(c4))))),
% 29.09/19.34 inference(monotonicity,[status(thm)],[17586])).
% 29.09/19.34 tff(20404,plain,
% 29.09/19.34 ((c2 = f8(c2)) <=> (f8(f7(f4(c4))) = c2)),
% 29.09/19.34 inference(transitivity,[status(thm)],[20403, 106])).
% 29.09/19.34 tff(20405,plain,
% 29.09/19.34 ((~(c2 = f8(c2))) <=> (~(f8(f7(f4(c4))) = c2))),
% 29.09/19.34 inference(monotonicity,[status(thm)],[20404])).
% 29.09/19.34 tff(20406,plain,
% 29.09/19.34 (big_f(f7(c1), f5(c1)) <=> big_f(c2, f10(c2))),
% 29.09/19.34 inference(transitivity,[status(thm)],[282, 247, 12069])).
% 29.09/19.34 tff(20407,plain,
% 29.09/19.34 ((~big_f(f7(c1), f5(c1))) <=> (~big_f(c2, f10(c2)))),
% 29.09/19.34 inference(monotonicity,[status(thm)],[20406])).
% 29.09/19.34 tff(20408,plain,
% 29.09/19.34 (~big_f(c2, f10(c2))),
% 29.09/19.34 inference(modus_ponens,[status(thm)],[730, 20407])).
% 29.09/19.34 tff(20409,plain,
% 29.09/19.34 (~(c2 = f8(c2))),
% 29.09/19.34 inference(unit_resolution,[status(thm)],[12015, 20408, 89, 730, 115])).
% 29.09/19.34 tff(20410,plain,
% 29.09/19.34 (~(f8(f7(f4(c4))) = c2)),
% 29.09/19.34 inference(modus_ponens,[status(thm)],[20409, 20405])).
% 29.09/19.34 tff(20411,plain,
% 29.09/19.34 (f8(f7(f4(c4))) = c1),
% 29.09/19.34 inference(unit_resolution,[status(thm)],[13371, 20410])).
% 29.09/19.34 tff(20412,plain,
% 29.09/19.34 (f8(f7(f4(c4))) = f7(c2)),
% 29.09/19.34 inference(transitivity,[status(thm)],[20411, 342])).
% 29.09/19.34 tff(20413,plain,
% 29.09/19.34 (big_f(f8(f7(f4(c4))), f10(c2)) <=> big_f(f7(c2), c1)),
% 29.09/19.34 inference(monotonicity,[status(thm)],[20412, 94])).
% 29.09/19.34 tff(20414,plain,
% 29.09/19.34 (big_f(f7(c2), c1) <=> big_f(f8(f7(f4(c4))), f10(c2))),
% 29.09/19.34 inference(symmetry,[status(thm)],[20413])).
% 29.09/19.34 tff(20415,plain,
% 29.09/19.34 ((~big_f(f7(c2), c1)) <=> (~big_f(f8(f7(f4(c4))), f10(c2)))),
% 29.09/19.34 inference(monotonicity,[status(thm)],[20414])).
% 29.09/19.34 tff(20416,plain,
% 29.09/19.34 (~big_f(f8(f7(f4(c4))), f10(c2))),
% 29.09/19.34 inference(modus_ponens,[status(thm)],[333, 20415])).
% 29.09/19.34 tff(20417,plain,
% 29.09/19.34 (f8(f7(f4(c4))) = f8(c2)),
% 29.09/19.34 inference(symmetry,[status(thm)],[17586])).
% 29.09/19.34 tff(20418,plain,
% 29.09/19.34 ((~big_f(f7(c1), f5(c1))) <=> (~big_f(f7(c1), c1))),
% 29.09/19.34 inference(monotonicity,[status(thm)],[282])).
% 29.09/19.34 tff(20419,plain,
% 29.09/19.34 (~big_f(f7(c1), c1)),
% 29.09/19.34 inference(modus_ponens,[status(thm)],[730, 20418])).
% 29.09/19.34 tff(20420,plain,
% 29.09/19.34 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f7(c1) = c1) | (f10(c2) = c2) | big_f(f8(f7(f4(c4))), f10(c2)) | (~(f8(f7(f4(c4))) = f8(c2))) | big_f(f7(c1), c1) | (~(c1 = f5(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(c1) = c1) | (f10(c2) = c2) | big_f(f8(f7(f4(c4))), f10(c2)) | (~(f8(f7(f4(c4))) = f8(c2))) | big_f(f7(c1), c1) | (~(c1 = f5(c1))))),
% 29.09/19.34 inference(rewrite,[status(thm)],[])).
% 29.09/19.34 tff(20421,plain,
% 29.09/19.34 (((~(c1 = f5(c1))) | (f10(c2) = c2) | big_f(f8(f7(f4(c4))), f10(c2)) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(f8(f7(f4(c4))) = f8(c2)))) <=> ((f7(c1) = c1) | (f10(c2) = c2) | big_f(f8(f7(f4(c4))), f10(c2)) | (~(f8(f7(f4(c4))) = f8(c2))) | big_f(f7(c1), c1) | (~(c1 = f5(c1))))),
% 29.09/19.34 inference(rewrite,[status(thm)],[])).
% 29.09/19.34 tff(20422,plain,
% 29.09/19.34 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c1 = f5(c1))) | (f10(c2) = c2) | big_f(f8(f7(f4(c4))), f10(c2)) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(f8(f7(f4(c4))) = f8(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f7(c1) = c1) | (f10(c2) = c2) | big_f(f8(f7(f4(c4))), f10(c2)) | (~(f8(f7(f4(c4))) = f8(c2))) | big_f(f7(c1), c1) | (~(c1 = f5(c1)))))),
% 29.09/19.34 inference(monotonicity,[status(thm)],[20421])).
% 29.09/19.34 tff(20423,plain,
% 29.09/19.34 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c1 = f5(c1))) | (f10(c2) = c2) | big_f(f8(f7(f4(c4))), f10(c2)) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(f8(f7(f4(c4))) = f8(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(c1) = c1) | (f10(c2) = c2) | big_f(f8(f7(f4(c4))), f10(c2)) | (~(f8(f7(f4(c4))) = f8(c2))) | big_f(f7(c1), c1) | (~(c1 = f5(c1))))),
% 29.09/19.34 inference(transitivity,[status(thm)],[20422, 20420])).
% 29.09/19.34 tff(20424,plain,
% 29.09/19.34 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c1 = f5(c1))) | (f10(c2) = c2) | big_f(f8(f7(f4(c4))), f10(c2)) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(f8(f7(f4(c4))) = f8(c2))))),
% 29.09/19.34 inference(quant_inst,[status(thm)],[])).
% 29.09/19.34 tff(20425,plain,
% 29.09/19.34 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(c1) = c1) | (f10(c2) = c2) | big_f(f8(f7(f4(c4))), f10(c2)) | (~(f8(f7(f4(c4))) = f8(c2))) | big_f(f7(c1), c1) | (~(c1 = f5(c1)))),
% 29.09/19.34 inference(modus_ponens,[status(thm)],[20424, 20423])).
% 29.09/19.34 tff(20426,plain,
% 29.09/19.34 ((f7(c1) = c1) | (f10(c2) = c2) | big_f(f8(f7(f4(c4))), f10(c2)) | (~(f8(f7(f4(c4))) = f8(c2))) | big_f(f7(c1), c1) | (~(c1 = f5(c1)))),
% 29.09/19.34 inference(unit_resolution,[status(thm)],[20425, 1745])).
% 29.09/19.34 tff(20427,plain,
% 29.09/19.34 (big_f(f8(f7(f4(c4))), f10(c2))),
% 29.09/19.34 inference(unit_resolution,[status(thm)],[20426, 692, 89, 115, 20419, 20417])).
% 29.09/19.34 tff(20428,plain,
% 29.09/19.34 ($false),
% 29.09/19.34 inference(unit_resolution,[status(thm)],[20427, 20416])).
% 29.09/19.34 tff(20429,plain,((~(f5(c1) = c1)) | big_f(f7(c2), c1) | (~(f7(c2) = c1)) | (~(f4(c4) = c1)) | (f10(c2) = c2) | big_f(f7(c1), f5(c1)) | (f7(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.09/19.34 tff(20430,plain,
% 29.09/19.34 (big_f(f7(c2), c1)),
% 29.09/19.34 inference(unit_resolution,[status(thm)],[20429, 17575, 115, 11752, 89, 22, 230])).
% 29.09/19.34 tff(20431,plain,
% 29.09/19.34 ($false),
% 29.09/19.34 inference(unit_resolution,[status(thm)],[20226, 1483, 1430, 292, 338])).
% 29.09/19.34 tff(20432,plain,(big_f(f3(c1, c1), c1) | (~(f7(c2) = c1)) | (~big_f(f7(c2), c1)) | (c1 = c4) | big_f(c3, f2(c3)) | (~(c3 = c2))), inference(lemma,lemma(discharge,[]))).
% 29.09/19.34 tff(20433,plain,
% 29.09/19.34 (big_f(f3(c1, c1), c1)),
% 29.09/19.34 inference(unit_resolution,[status(thm)],[20432, 20430, 22, 17685, 20402, 20401])).
% 29.09/19.34 tff(20434,plain,
% 29.09/19.34 (big_f(f3(f10(c2), f10(c2)), f10(c2))),
% 29.09/19.34 inference(modus_ponens,[status(thm)],[20433, 17592])).
% 29.09/19.34 tff(20435,plain,
% 29.09/19.34 ((f10(c2) = f5(f10(c2))) <=> (c1 = f5(c1))),
% 29.09/19.34 inference(monotonicity,[status(thm)],[94, 17564])).
% 29.09/19.34 tff(20436,plain,
% 29.09/19.34 ((f10(c2) = f5(f10(c2))) <=> (f5(c1) = c1)),
% 29.09/19.34 inference(transitivity,[status(thm)],[20435, 128])).
% 29.09/19.34 tff(20437,plain,
% 29.09/19.34 ((f5(c1) = c1) <=> (f10(c2) = f5(f10(c2)))),
% 29.09/19.34 inference(symmetry,[status(thm)],[20436])).
% 29.09/19.34 tff(20438,plain,
% 29.09/19.34 (f10(c2) = f5(f10(c2))),
% 29.09/19.34 inference(modus_ponens,[status(thm)],[230, 20437])).
% 29.09/19.34 tff(20439,plain,
% 29.09/19.34 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f10(c2) = c2) | (f7(f10(c2)) = f10(c2)) | (~(f10(c2) = f5(f10(c2)))) | big_f(f7(f10(c2)), f10(c2)) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))) | (f3(f10(c2), f10(c2)) = f8(c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(c2) = c2) | (f7(f10(c2)) = f10(c2)) | (~(f10(c2) = f5(f10(c2)))) | big_f(f7(f10(c2)), f10(c2)) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))) | (f3(f10(c2), f10(c2)) = f8(c2)))),
% 29.09/19.34 inference(rewrite,[status(thm)],[])).
% 29.09/19.34 tff(20440,plain,
% 29.09/19.34 (((~(f10(c2) = f5(f10(c2)))) | (f10(c2) = c2) | (f3(f10(c2), f10(c2)) = f8(c2)) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), f10(c2))) <=> ((f10(c2) = c2) | (f7(f10(c2)) = f10(c2)) | (~(f10(c2) = f5(f10(c2)))) | big_f(f7(f10(c2)), f10(c2)) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))) | (f3(f10(c2), f10(c2)) = f8(c2)))),
% 29.09/19.34 inference(rewrite,[status(thm)],[])).
% 29.09/19.34 tff(20441,plain,
% 29.09/19.34 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(f10(c2) = f5(f10(c2)))) | (f10(c2) = c2) | (f3(f10(c2), f10(c2)) = f8(c2)) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), f10(c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f10(c2) = c2) | (f7(f10(c2)) = f10(c2)) | (~(f10(c2) = f5(f10(c2)))) | big_f(f7(f10(c2)), f10(c2)) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))) | (f3(f10(c2), f10(c2)) = f8(c2))))),
% 29.09/19.34 inference(monotonicity,[status(thm)],[20440])).
% 29.09/19.34 tff(20442,plain,
% 29.09/19.34 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(f10(c2) = f5(f10(c2)))) | (f10(c2) = c2) | (f3(f10(c2), f10(c2)) = f8(c2)) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), f10(c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(c2) = c2) | (f7(f10(c2)) = f10(c2)) | (~(f10(c2) = f5(f10(c2)))) | big_f(f7(f10(c2)), f10(c2)) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))) | (f3(f10(c2), f10(c2)) = f8(c2)))),
% 29.09/19.34 inference(transitivity,[status(thm)],[20441, 20439])).
% 29.09/19.34 tff(20443,plain,
% 29.09/19.34 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(f10(c2) = f5(f10(c2)))) | (f10(c2) = c2) | (f3(f10(c2), f10(c2)) = f8(c2)) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), f10(c2)))),
% 29.09/19.34 inference(quant_inst,[status(thm)],[])).
% 29.09/19.34 tff(20444,plain,
% 29.09/19.34 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(c2) = c2) | (f7(f10(c2)) = f10(c2)) | (~(f10(c2) = f5(f10(c2)))) | big_f(f7(f10(c2)), f10(c2)) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))) | (f3(f10(c2), f10(c2)) = f8(c2))),
% 29.09/19.34 inference(modus_ponens,[status(thm)],[20443, 20442])).
% 29.09/19.34 tff(20445,plain,
% 29.09/19.34 (f3(f10(c2), f10(c2)) = f8(c2)),
% 29.09/19.34 inference(unit_resolution,[status(thm)],[20444, 705, 89, 17563, 20438, 20434, 17590])).
% 29.09/19.34 tff(20446,plain,
% 29.09/19.34 (f3(f10(c2), f10(c2)) = f10(c2)),
% 29.09/19.34 inference(transitivity,[status(thm)],[20445, 17586, 17584, 99])).
% 29.09/19.34 tff(20447,plain,
% 29.09/19.34 ((~(f10(c2) = c2)) <=> (~(f10(c2) = c4))),
% 29.09/19.34 inference(monotonicity,[status(thm)],[17682])).
% 29.09/19.34 tff(20448,plain,
% 29.09/19.34 (~(f10(c2) = c4)),
% 29.09/19.34 inference(modus_ponens,[status(thm)],[89, 20447])).
% 29.09/19.34 tff(20449,plain,
% 29.09/19.34 (c4 = c2),
% 29.09/19.34 inference(modus_ponens,[status(thm)],[17679, 8721])).
% 29.09/19.34 tff(20450,plain,
% 29.09/19.34 (~(f2(c3) = c1)),
% 29.09/19.34 inference(unit_resolution,[status(thm)],[1424, 20433, 20449, 20401, 20402])).
% 29.09/19.34 tff(20451,plain,
% 29.09/19.34 (f2(c3) = c2),
% 29.09/19.34 inference(unit_resolution,[status(thm)],[1273, 20450])).
% 29.09/19.34 tff(20452,plain,
% 29.09/19.34 (c2 = f2(c2)),
% 29.09/19.34 inference(unit_resolution,[status(thm)],[4867, 20451, 20401])).
% 29.09/19.34 tff(20453,plain,
% 29.09/19.34 (c2 = c3),
% 29.09/19.34 inference(modus_ponens,[status(thm)],[20401, 78])).
% 29.09/19.34 tff(20454,plain,
% 29.09/19.34 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (f10(c2) = c4) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (f10(c2) = c4) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))))),
% 29.09/19.34 inference(rewrite,[status(thm)],[])).
% 29.09/19.34 tff(20455,plain,
% 29.09/19.34 (((~(c2 = c3)) | (~(c2 = f2(c2))) | (f10(c2) = c4) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))) | big_f(c2, c2)) <=> ((~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (f10(c2) = c4) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))))),
% 29.09/19.34 inference(rewrite,[status(thm)],[])).
% 29.09/19.34 tff(20456,plain,
% 29.09/19.34 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | (f10(c2) = c4) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))) | big_f(c2, c2))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (f10(c2) = c4) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2)))))),
% 29.09/19.34 inference(monotonicity,[status(thm)],[20455])).
% 29.09/19.34 tff(20457,plain,
% 29.09/19.34 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | (f10(c2) = c4) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))) | big_f(c2, c2))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (f10(c2) = c4) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))))),
% 29.09/19.34 inference(transitivity,[status(thm)],[20456, 20454])).
% 29.09/19.34 tff(20458,plain,
% 29.09/19.34 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | (f10(c2) = c4) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))) | big_f(c2, c2))),
% 29.09/19.34 inference(quant_inst,[status(thm)],[])).
% 29.09/19.34 tff(20459,plain,
% 29.09/19.34 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (f10(c2) = c4) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2)))),
% 29.09/19.34 inference(modus_ponens,[status(thm)],[20458, 20457])).
% 29.09/19.34 tff(20460,plain,
% 29.09/19.34 (~(f3(f10(c2), f10(c2)) = f10(c2))),
% 29.09/19.34 inference(unit_resolution,[status(thm)],[20459, 1398, 121, 20453, 20452, 20448, 20434])).
% 29.09/19.34 tff(20461,plain,
% 29.09/19.34 ($false),
% 29.09/19.34 inference(unit_resolution,[status(thm)],[20460, 20446])).
% 29.09/19.34 tff(20462,plain,(big_f(c2, c1) | (~(f4(c4) = c1)) | big_f(c2, c2) | (f10(c2) = c2) | (f7(c1) = c1) | (f7(c2) = c2) | (~(f10(c1) = c2)) | (~big_f(c1, c2)) | (~(f5(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.09/19.34 tff(20463,plain,
% 29.09/19.34 (big_f(c2, c1)),
% 29.09/19.34 inference(unit_resolution,[status(thm)],[20462, 230, 121, 89, 115, 17, 16, 2865, 11752])).
% 29.09/19.34 tff(20464,plain,
% 29.09/19.34 (big_f(c2, f10(c2))),
% 29.09/19.34 inference(modus_ponens,[status(thm)],[20463, 15252])).
% 29.09/19.34 tff(20465,plain,
% 29.09/19.34 (big_f(f7(c2), f10(c2))),
% 29.09/19.34 inference(modus_ponens,[status(thm)],[338, 17570])).
% 29.09/19.34 tff(20466,plain,
% 29.09/19.34 (c2 = f8(c2)),
% 29.09/19.34 inference(unit_resolution,[status(thm)],[12312, 20465, 89, 17, 1180, 12291])).
% 29.09/19.34 tff(20467,plain,
% 29.09/19.34 (f8(c2) = c2),
% 29.09/19.34 inference(symmetry,[status(thm)],[20466])).
% 29.09/19.34 tff(20468,plain,
% 29.09/19.34 ((f10(c2) = f8(c2)) <=> (f10(c2) = c2)),
% 29.09/19.34 inference(monotonicity,[status(thm)],[20467])).
% 29.09/19.34 tff(20469,plain,
% 29.09/19.34 ((f10(c2) = c2) <=> (f10(c2) = f8(c2))),
% 29.09/19.34 inference(symmetry,[status(thm)],[20468])).
% 29.09/19.34 tff(20470,plain,
% 29.09/19.34 ((f10(c2) = c2) <=> (c1 = f8(f7(c1)))),
% 29.09/19.34 inference(transitivity,[status(thm)],[20469, 15262, 12282])).
% 29.09/19.34 tff(20471,plain,
% 29.09/19.34 ((~(f10(c2) = c2)) <=> (~(c1 = f8(f7(c1))))),
% 29.09/19.34 inference(monotonicity,[status(thm)],[20470])).
% 29.09/19.34 tff(20472,plain,
% 29.09/19.34 (~(c1 = f8(f7(c1)))),
% 29.09/19.34 inference(modus_ponens,[status(thm)],[89, 20471])).
% 29.09/19.34 tff(20473,plain,
% 29.09/19.34 (big_f(f7(f7(c1)), c1)),
% 29.09/19.34 inference(modus_ponens,[status(thm)],[338, 12322])).
% 29.09/19.34 tff(20474,plain,
% 29.09/19.34 (~(f10(f7(c1)) = f7(c1))),
% 29.09/19.34 inference(modus_ponens,[status(thm)],[89, 12336])).
% 29.09/19.34 tff(20475,plain,
% 29.09/19.34 (big_f(f7(c2), c1) <=> big_f(c1, f10(f7(c1)))),
% 29.09/19.34 inference(transitivity,[status(thm)],[17570, 17569, 17593, 12329])).
% 29.09/19.34 tff(20476,plain,
% 29.09/19.34 (big_f(c1, f10(f7(c1)))),
% 29.09/19.34 inference(modus_ponens,[status(thm)],[338, 20475])).
% 29.09/19.34 tff(20477,plain,
% 29.09/19.34 (c1 = f8(f7(c1))),
% 29.09/19.34 inference(unit_resolution,[status(thm)],[12367, 20476, 20474, 12341, 12356, 20473, 115])).
% 29.09/19.34 tff(20478,plain,
% 29.09/19.34 ($false),
% 29.09/19.34 inference(unit_resolution,[status(thm)],[20477, 20472])).
% 29.09/19.34 tff(20479,plain,((~big_f(f7(c2), c1)) | (f10(c2) = c2) | (f7(c2) = c2) | (~big_f(f7(c2), c2)) | (~big_f(c2, f10(c2))) | (~big_f(f7(f7(c1)), f7(c1))) | (f7(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.09/19.34 tff(20480,plain,
% 29.09/19.34 (~big_f(f7(c2), c1)),
% 29.09/19.34 inference(unit_resolution,[status(thm)],[20479, 20464, 17, 12167, 89, 17573, 115])).
% 29.09/19.34 tff(20481,plain,
% 29.09/19.34 (~big_f(c1, c1)),
% 29.09/19.34 inference(modus_ponens,[status(thm)],[20480, 17572])).
% 29.09/19.34 tff(20482,plain,
% 29.09/19.34 ((f7(c1) = c3) <=> (f7(c1) = c1)),
% 29.09/19.34 inference(monotonicity,[status(thm)],[172])).
% 29.09/19.34 tff(20483,plain,
% 29.09/19.34 ((f7(c1) = c1) <=> (f7(c1) = c3)),
% 29.09/19.34 inference(symmetry,[status(thm)],[20482])).
% 29.09/19.34 tff(20484,plain,
% 29.09/19.34 ((~(f7(c1) = c1)) <=> (~(f7(c1) = c3))),
% 29.09/19.34 inference(monotonicity,[status(thm)],[20483])).
% 29.09/19.34 tff(20485,plain,
% 29.09/19.34 (~(f7(c1) = c3)),
% 29.09/19.34 inference(modus_ponens,[status(thm)],[115, 20484])).
% 29.09/19.34 tff(20486,plain,
% 29.09/19.34 (f7(f7(c1)) = c1),
% 29.09/19.34 inference(transitivity,[status(thm)],[12320, 22])).
% 29.09/19.34 tff(20487,plain,
% 29.09/19.34 (big_f(f7(f7(c1)), f7(c1)) <=> big_f(c1, f7(c1))),
% 29.09/19.34 inference(monotonicity,[status(thm)],[20486])).
% 29.09/19.34 tff(20488,plain,
% 29.09/19.34 (big_f(c1, f7(c1)) <=> big_f(f7(f7(c1)), f7(c1))),
% 29.09/19.34 inference(symmetry,[status(thm)],[20487])).
% 29.09/19.34 tff(20489,plain,
% 29.09/19.34 (big_f(c1, c2) <=> big_f(c1, f7(c1))),
% 29.09/19.34 inference(monotonicity,[status(thm)],[2778])).
% 29.09/19.34 tff(20490,plain,
% 29.09/19.34 (big_f(c1, c2) <=> big_f(f7(f7(c1)), f7(c1))),
% 29.09/19.34 inference(transitivity,[status(thm)],[20489, 20488])).
% 29.09/19.34 tff(20491,plain,
% 29.09/19.34 (big_f(c1, c2)),
% 29.09/19.34 inference(unit_resolution,[status(thm)],[19126, 66, 17, 172, 94, 11752])).
% 29.09/19.34 tff(20492,plain,
% 29.09/19.34 (big_f(f7(f7(c1)), f7(c1))),
% 29.09/19.34 inference(modus_ponens,[status(thm)],[20491, 20490])).
% 29.09/19.34 tff(20493,plain,
% 29.09/19.34 (f10(f7(f4(c4))) = f10(f7(c1))),
% 29.09/19.34 inference(monotonicity,[status(thm)],[16243])).
% 29.09/19.34 tff(20494,plain,
% 29.09/19.34 (big_f(c1, f10(f7(f4(c4)))) <=> big_f(c1, f10(f7(c1)))),
% 29.09/19.34 inference(monotonicity,[status(thm)],[20493])).
% 29.09/19.34 tff(20495,plain,
% 29.09/19.34 (big_f(c1, f10(f7(c1))) <=> big_f(c1, f10(f7(f4(c4))))),
% 29.09/19.34 inference(symmetry,[status(thm)],[20494])).
% 29.09/19.34 tff(20496,plain,
% 29.09/19.34 (big_f(c1, f10(f7(c1))) <=> big_f(c1, c1)),
% 29.09/19.34 inference(monotonicity,[status(thm)],[20322])).
% 29.09/19.34 tff(20497,plain,
% 29.09/19.34 (big_f(c1, c1) <=> big_f(c1, f10(f7(c1)))),
% 29.09/19.34 inference(symmetry,[status(thm)],[20496])).
% 29.09/19.34 tff(20498,plain,
% 29.09/19.34 (big_f(c1, c1) <=> big_f(c1, f10(f7(f4(c4))))),
% 29.09/19.34 inference(transitivity,[status(thm)],[20497, 20495])).
% 29.09/19.34 tff(20499,plain,
% 29.09/19.34 ((~big_f(c1, c1)) <=> (~big_f(c1, f10(f7(f4(c4)))))),
% 29.09/19.34 inference(monotonicity,[status(thm)],[20498])).
% 29.09/19.34 tff(20500,plain,
% 29.09/19.34 (~big_f(c1, f10(f7(f4(c4))))),
% 29.09/19.34 inference(modus_ponens,[status(thm)],[66, 20499])).
% 29.09/19.34 tff(20501,plain,
% 29.09/19.34 (f8(f7(f4(c4))) = f8(f7(c1))),
% 29.09/19.34 inference(monotonicity,[status(thm)],[16243])).
% 29.09/19.34 tff(20502,plain,
% 29.09/19.34 (f8(f7(c1)) = f8(f7(f4(c4)))),
% 29.09/19.34 inference(symmetry,[status(thm)],[20501])).
% 29.09/19.34 tff(20503,plain,
% 29.09/19.34 ((f7(c1) = f8(f7(c1))) <=> (c2 = f8(f7(f4(c4))))),
% 29.09/19.34 inference(monotonicity,[status(thm)],[120, 20502])).
% 29.09/19.34 tff(20504,plain,
% 29.09/19.34 ((f7(c1) = f8(f7(c1))) <=> (f8(f7(f4(c4))) = c2)),
% 29.09/19.34 inference(transitivity,[status(thm)],[20503, 106])).
% 29.09/19.34 tff(20505,plain,
% 29.09/19.34 ((~(f7(c1) = f8(f7(c1)))) <=> (~(f8(f7(f4(c4))) = c2))),
% 29.09/19.34 inference(monotonicity,[status(thm)],[20504])).
% 29.09/19.34 tff(20506,plain,
% 29.09/19.34 (big_f(f7(c1), f10(f7(c1))) <=> big_f(f7(c1), c1)),
% 29.09/19.34 inference(monotonicity,[status(thm)],[20322])).
% 29.09/19.34 tff(20507,plain,
% 29.09/19.34 (big_f(f7(c1), c1) <=> big_f(f7(c1), f10(f7(c1)))),
% 29.09/19.34 inference(symmetry,[status(thm)],[20506])).
% 29.09/19.34 tff(20508,plain,
% 29.09/19.34 ((~big_f(f7(c1), c1)) <=> (~big_f(f7(c1), f10(f7(c1))))),
% 29.09/19.34 inference(monotonicity,[status(thm)],[20507])).
% 29.09/19.34 tff(20509,plain,
% 29.09/19.34 (~big_f(f7(c1), f10(f7(c1)))),
% 29.09/19.34 inference(modus_ponens,[status(thm)],[285, 20508])).
% 29.09/19.34 tff(20510,plain,
% 29.09/19.34 (~(f5(c1) = c1)),
% 29.09/19.34 inference(unit_resolution,[status(thm)],[20429, 17697, 11752, 292, 89, 115, 333])).
% 29.09/19.34 tff(20511,plain,
% 29.09/19.34 (f5(c1) = c2),
% 29.09/19.34 inference(unit_resolution,[status(thm)],[1708, 20510])).
% 29.09/19.34 tff(20512,plain,
% 29.09/19.34 (f7(c1) = f5(c1)),
% 29.09/19.34 inference(modus_ponens,[status(thm)],[20511, 14334])).
% 29.09/19.34 tff(20513,plain,
% 29.09/19.34 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f7(c1) = c1) | (f10(f7(c1)) = f7(c1)) | big_f(f7(c1), f7(c1)) | big_f(f7(c1), f10(f7(c1))) | (~(f7(c1) = f8(f7(c1)))) | (~(f7(c1) = f5(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(c1) = c1) | (f10(f7(c1)) = f7(c1)) | big_f(f7(c1), f7(c1)) | big_f(f7(c1), f10(f7(c1))) | (~(f7(c1) = f8(f7(c1)))) | (~(f7(c1) = f5(c1))))),
% 29.09/19.35 inference(rewrite,[status(thm)],[])).
% 29.09/19.35 tff(20514,plain,
% 29.09/19.35 (((~(f7(c1) = f5(c1))) | (f10(f7(c1)) = f7(c1)) | big_f(f7(c1), f10(f7(c1))) | (f7(c1) = c1) | big_f(f7(c1), f7(c1)) | (~(f7(c1) = f8(f7(c1))))) <=> ((f7(c1) = c1) | (f10(f7(c1)) = f7(c1)) | big_f(f7(c1), f7(c1)) | big_f(f7(c1), f10(f7(c1))) | (~(f7(c1) = f8(f7(c1)))) | (~(f7(c1) = f5(c1))))),
% 29.09/19.35 inference(rewrite,[status(thm)],[])).
% 29.09/19.35 tff(20515,plain,
% 29.09/19.35 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(f7(c1) = f5(c1))) | (f10(f7(c1)) = f7(c1)) | big_f(f7(c1), f10(f7(c1))) | (f7(c1) = c1) | big_f(f7(c1), f7(c1)) | (~(f7(c1) = f8(f7(c1)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f7(c1) = c1) | (f10(f7(c1)) = f7(c1)) | big_f(f7(c1), f7(c1)) | big_f(f7(c1), f10(f7(c1))) | (~(f7(c1) = f8(f7(c1)))) | (~(f7(c1) = f5(c1)))))),
% 29.09/19.35 inference(monotonicity,[status(thm)],[20514])).
% 29.09/19.35 tff(20516,plain,
% 29.09/19.35 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(f7(c1) = f5(c1))) | (f10(f7(c1)) = f7(c1)) | big_f(f7(c1), f10(f7(c1))) | (f7(c1) = c1) | big_f(f7(c1), f7(c1)) | (~(f7(c1) = f8(f7(c1)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(c1) = c1) | (f10(f7(c1)) = f7(c1)) | big_f(f7(c1), f7(c1)) | big_f(f7(c1), f10(f7(c1))) | (~(f7(c1) = f8(f7(c1)))) | (~(f7(c1) = f5(c1))))),
% 29.09/19.35 inference(transitivity,[status(thm)],[20515, 20513])).
% 29.09/19.35 tff(20517,plain,
% 29.09/19.35 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(f7(c1) = f5(c1))) | (f10(f7(c1)) = f7(c1)) | big_f(f7(c1), f10(f7(c1))) | (f7(c1) = c1) | big_f(f7(c1), f7(c1)) | (~(f7(c1) = f8(f7(c1)))))),
% 29.09/19.35 inference(quant_inst,[status(thm)],[])).
% 29.09/19.35 tff(20518,plain,
% 29.09/19.35 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(c1) = c1) | (f10(f7(c1)) = f7(c1)) | big_f(f7(c1), f7(c1)) | big_f(f7(c1), f10(f7(c1))) | (~(f7(c1) = f8(f7(c1)))) | (~(f7(c1) = f5(c1)))),
% 29.09/19.35 inference(modus_ponens,[status(thm)],[20517, 20516])).
% 29.09/19.35 tff(20519,plain,
% 29.09/19.35 (~(f7(c1) = f8(f7(c1)))),
% 29.09/19.35 inference(unit_resolution,[status(thm)],[20518, 1745, 115, 20512, 20332, 20509, 20249])).
% 29.09/19.35 tff(20520,plain,
% 29.09/19.35 (~(f8(f7(f4(c4))) = c2)),
% 29.09/19.35 inference(modus_ponens,[status(thm)],[20519, 20505])).
% 29.09/19.35 tff(20521,assumption,(~big_f(c1, f10(f7(f4(c4))))), introduced(assumption)).
% 29.09/19.35 tff(20522,plain,
% 29.09/19.35 ((f10(f7(f4(c4))) = f7(f4(c4))) <=> (f10(f7(c1)) = f7(c1))),
% 29.09/19.35 inference(monotonicity,[status(thm)],[20493, 16243])).
% 29.09/19.35 tff(20523,plain,
% 29.09/19.35 ((f10(f7(c1)) = f7(c1)) <=> (f10(f7(f4(c4))) = f7(f4(c4)))),
% 29.09/19.35 inference(symmetry,[status(thm)],[20522])).
% 29.09/19.35 tff(20524,plain,
% 29.09/19.35 ((f7(c1) = c1) <=> (f10(f7(f4(c4))) = f7(f4(c4)))),
% 29.09/19.35 inference(transitivity,[status(thm)],[20330, 20523])).
% 29.09/19.35 tff(20525,plain,
% 29.09/19.35 ((~(f7(c1) = c1)) <=> (~(f10(f7(f4(c4))) = f7(f4(c4))))),
% 29.09/19.35 inference(monotonicity,[status(thm)],[20524])).
% 29.09/19.35 tff(20526,plain,
% 29.09/19.35 (~(f10(f7(f4(c4))) = f7(f4(c4)))),
% 29.09/19.35 inference(modus_ponens,[status(thm)],[115, 20525])).
% 29.09/19.35 tff(20527,plain,
% 29.09/19.35 (c2 = f5(c1)),
% 29.09/19.35 inference(modus_ponens,[status(thm)],[20511, 155])).
% 29.09/19.35 tff(20528,plain,
% 29.09/19.35 (~(c1 = f8(f7(f4(c4))))),
% 29.09/19.35 inference(unit_resolution,[status(thm)],[8593, 20527, 115, 17723, 20526, 20521])).
% 29.09/19.35 tff(20529,plain,
% 29.09/19.35 (~(f8(f7(f4(c4))) = c1)),
% 29.09/19.35 inference(modus_ponens,[status(thm)],[20528, 14127])).
% 29.09/19.35 tff(20530,plain,
% 29.09/19.35 ($false),
% 29.09/19.35 inference(unit_resolution,[status(thm)],[13371, 20529, 20520])).
% 29.09/19.35 tff(20531,plain,(big_f(f7(c1), c1) | (~(f4(c4) = c1)) | (f7(c1) = c1) | big_f(c1, f10(f7(f4(c4)))) | (~(f7(c2) = c1)) | (f10(c2) = c2) | big_f(f7(c2), c1) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 29.09/19.35 tff(20532,plain,
% 29.09/19.35 (big_f(f7(c1), c1)),
% 29.09/19.35 inference(unit_resolution,[status(thm)],[20531, 20500, 115, 11752, 22, 89, 12093, 121])).
% 29.09/19.35 tff(20533,plain,
% 29.09/19.35 (f3(c1, f7(c1)) = f3(c1, c2)),
% 29.09/19.35 inference(monotonicity,[status(thm)],[120])).
% 29.09/19.35 tff(20534,plain,
% 29.09/19.35 ((f3(c1, f7(c1)) = f7(c1)) <=> (f3(c1, c2) = c2)),
% 29.09/19.35 inference(monotonicity,[status(thm)],[20533, 120])).
% 29.09/19.35 tff(20535,plain,
% 29.09/19.35 ((~(f3(c1, f7(c1)) = f7(c1))) <=> (~(f3(c1, c2) = c2))),
% 29.09/19.35 inference(monotonicity,[status(thm)],[20534])).
% 29.09/19.35 tff(20536,plain,
% 29.09/19.35 (big_f(f3(c1, f7(c1)), c1) <=> big_f(f3(c1, c2), c1)),
% 29.09/19.35 inference(monotonicity,[status(thm)],[20533])).
% 29.09/19.35 tff(20537,plain,
% 29.09/19.35 (big_f(f3(c1, c2), c1) <=> big_f(f3(c1, f7(c1)), c1)),
% 29.09/19.35 inference(symmetry,[status(thm)],[20536])).
% 29.09/19.35 tff(20538,plain,
% 29.09/19.35 (~(f1(f7(f7(c2)), c1) = c1)),
% 29.09/19.35 inference(unit_resolution,[status(thm)],[15864, 12204, 15735, 292])).
% 29.09/19.35 tff(20539,plain,
% 29.09/19.35 (f1(f7(f7(c2)), c1) = c2),
% 29.09/19.35 inference(unit_resolution,[status(thm)],[384, 20538])).
% 29.09/19.35 tff(20540,plain,
% 29.09/19.35 (f1(f7(c1), c1) = f7(c1)),
% 29.09/19.35 inference(transitivity,[status(thm)],[15858, 20539, 2778])).
% 29.09/19.35 tff(20541,plain,
% 29.09/19.35 ((f1(f7(c1), c1) = c1) <=> (f7(c1) = c1)),
% 29.09/19.35 inference(monotonicity,[status(thm)],[20540])).
% 29.09/19.35 tff(20542,plain,
% 29.09/19.35 ((f7(c1) = c1) <=> (f1(f7(c1), c1) = c1)),
% 29.09/19.35 inference(symmetry,[status(thm)],[20541])).
% 29.09/19.35 tff(20543,plain,
% 29.09/19.35 ((~(f7(c1) = c1)) <=> (~(f1(f7(c1), c1) = c1))),
% 29.09/19.35 inference(monotonicity,[status(thm)],[20542])).
% 29.09/19.35 tff(20544,plain,
% 29.09/19.35 (~(f1(f7(c1), c1) = c1)),
% 29.09/19.35 inference(modus_ponens,[status(thm)],[115, 20543])).
% 29.09/19.35 tff(20545,plain,
% 29.09/19.35 (~(f3(c1, c2) = c2)),
% 29.09/19.35 inference(unit_resolution,[status(thm)],[16124, 20544, 12165, 482, 12204, 15735, 120])).
% 29.09/19.35 tff(20546,plain,
% 29.09/19.35 (f7(f7(c1)) = c1),
% 29.09/19.35 inference(transitivity,[status(thm)],[12320, 292])).
% 29.09/19.35 tff(20547,plain,
% 29.09/19.35 ((f7(f7(c1)) = f7(c1)) <=> (c1 = f7(c1))),
% 29.09/19.35 inference(monotonicity,[status(thm)],[20546])).
% 29.09/19.35 tff(20548,plain,
% 29.09/19.35 ((f7(f7(c1)) = f7(c1)) <=> (f7(c1) = c1)),
% 29.09/19.35 inference(transitivity,[status(thm)],[20547, 14336])).
% 29.09/19.35 tff(20549,plain,
% 29.09/19.35 ((f7(c1) = c1) <=> (f7(f7(c1)) = f7(c1))),
% 29.09/19.35 inference(symmetry,[status(thm)],[20548])).
% 29.09/19.35 tff(20550,plain,
% 29.09/19.35 ((~(f7(c1) = c1)) <=> (~(f7(f7(c1)) = f7(c1)))),
% 29.09/19.35 inference(monotonicity,[status(thm)],[20549])).
% 29.09/19.35 tff(20551,plain,
% 29.09/19.35 (~(f7(f7(c1)) = f7(c1))),
% 29.09/19.35 inference(modus_ponens,[status(thm)],[115, 20550])).
% 29.09/19.35 tff(20552,plain,
% 29.09/19.35 (big_f(f7(c1), f10(f7(c1))) <=> big_f(f7(c1), c1)),
% 29.09/19.35 inference(monotonicity,[status(thm)],[17718])).
% 29.09/19.35 tff(20553,plain,
% 29.09/19.35 (big_f(f7(c1), c1) <=> big_f(f7(c1), f10(f7(c1)))),
% 29.09/19.35 inference(symmetry,[status(thm)],[20552])).
% 29.09/19.35 tff(20554,plain,
% 29.09/19.35 (big_f(f7(c1), f10(f7(c1)))),
% 29.09/19.35 inference(modus_ponens,[status(thm)],[15735, 20553])).
% 29.09/19.35 tff(20555,plain,
% 29.09/19.35 (big_f(f3(c1, c2), f10(f7(c1))) <=> big_f(f3(c1, c2), c1)),
% 29.09/19.35 inference(monotonicity,[status(thm)],[17718])).
% 29.09/19.35 tff(20556,plain,
% 29.09/19.35 (big_f(f3(c1, c2), c1) <=> big_f(f3(c1, c2), f10(f7(c1)))),
% 29.09/19.35 inference(symmetry,[status(thm)],[20555])).
% 29.09/19.35 tff(20557,plain,
% 29.09/19.35 (big_f(f3(c1, f7(c1)), c1) <=> big_f(f3(c1, c2), f10(f7(c1)))),
% 29.09/19.35 inference(transitivity,[status(thm)],[20536, 20556])).
% 29.09/19.35 tff(20558,plain,
% 29.09/19.35 ((f3(c1, c2) = c2) <=> (f3(c1, f7(c1)) = f7(c1))),
% 29.09/19.35 inference(symmetry,[status(thm)],[20534])).
% 29.09/19.35 tff(20559,plain,
% 29.09/19.35 ((~(f3(c1, c2) = c2)) <=> (~(f3(c1, f7(c1)) = f7(c1)))),
% 29.09/19.35 inference(monotonicity,[status(thm)],[20558])).
% 29.09/19.35 tff(20560,plain,
% 29.09/19.35 (~(f3(c1, f7(c1)) = f7(c1))),
% 29.09/19.35 inference(modus_ponens,[status(thm)],[20545, 20559])).
% 29.09/19.35 tff(20561,plain,
% 29.09/19.35 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c1 = c4) | (f7(c1) = c3) | (f1(f7(c1), c1) = c1) | big_f(f7(c1), f1(f7(c1), c1)) | (f3(c1, f7(c1)) = f7(c1)) | big_f(f3(c1, f7(c1)), c1))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (c1 = c4) | (f7(c1) = c3) | (f1(f7(c1), c1) = c1) | big_f(f7(c1), f1(f7(c1), c1)) | (f3(c1, f7(c1)) = f7(c1)) | big_f(f3(c1, f7(c1)), c1))),
% 29.09/19.35 inference(rewrite,[status(thm)],[])).
% 29.09/19.35 tff(20562,plain,
% 29.09/19.35 (((c1 = c4) | (f3(c1, f7(c1)) = f7(c1)) | big_f(f3(c1, f7(c1)), c1) | (f7(c1) = c3) | (f1(f7(c1), c1) = c1) | big_f(f7(c1), f1(f7(c1), c1))) <=> ((c1 = c4) | (f7(c1) = c3) | (f1(f7(c1), c1) = c1) | big_f(f7(c1), f1(f7(c1), c1)) | (f3(c1, f7(c1)) = f7(c1)) | big_f(f3(c1, f7(c1)), c1))),
% 29.09/19.35 inference(rewrite,[status(thm)],[])).
% 29.09/19.35 tff(20563,plain,
% 29.09/19.35 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c1 = c4) | (f3(c1, f7(c1)) = f7(c1)) | big_f(f3(c1, f7(c1)), c1) | (f7(c1) = c3) | (f1(f7(c1), c1) = c1) | big_f(f7(c1), f1(f7(c1), c1)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c1 = c4) | (f7(c1) = c3) | (f1(f7(c1), c1) = c1) | big_f(f7(c1), f1(f7(c1), c1)) | (f3(c1, f7(c1)) = f7(c1)) | big_f(f3(c1, f7(c1)), c1)))),
% 29.09/19.35 inference(monotonicity,[status(thm)],[20562])).
% 29.09/19.35 tff(20564,plain,
% 29.09/19.35 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c1 = c4) | (f3(c1, f7(c1)) = f7(c1)) | big_f(f3(c1, f7(c1)), c1) | (f7(c1) = c3) | (f1(f7(c1), c1) = c1) | big_f(f7(c1), f1(f7(c1), c1)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (c1 = c4) | (f7(c1) = c3) | (f1(f7(c1), c1) = c1) | big_f(f7(c1), f1(f7(c1), c1)) | (f3(c1, f7(c1)) = f7(c1)) | big_f(f3(c1, f7(c1)), c1))),
% 29.09/19.35 inference(transitivity,[status(thm)],[20563, 20561])).
% 29.09/19.35 tff(20565,plain,
% 29.09/19.35 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c1 = c4) | (f3(c1, f7(c1)) = f7(c1)) | big_f(f3(c1, f7(c1)), c1) | (f7(c1) = c3) | (f1(f7(c1), c1) = c1) | big_f(f7(c1), f1(f7(c1), c1)))),
% 29.09/19.35 inference(quant_inst,[status(thm)],[])).
% 29.09/19.35 tff(20566,plain,
% 29.09/19.35 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (c1 = c4) | (f7(c1) = c3) | (f1(f7(c1), c1) = c1) | big_f(f7(c1), f1(f7(c1), c1)) | (f3(c1, f7(c1)) = f7(c1)) | big_f(f3(c1, f7(c1)), c1)),
% 29.09/19.35 inference(modus_ponens,[status(thm)],[20565, 20564])).
% 29.09/19.35 tff(20567,plain,
% 29.09/19.35 (big_f(f3(c1, f7(c1)), c1)),
% 29.09/19.35 inference(unit_resolution,[status(thm)],[20566, 1014, 482, 12165, 20544, 12204, 20560])).
% 29.09/19.35 tff(20568,plain,
% 29.09/19.35 (big_f(f3(c1, c2), f10(f7(c1)))),
% 29.09/19.35 inference(modus_ponens,[status(thm)],[20567, 20557])).
% 29.09/19.35 tff(20569,assumption,(~(f7(c1) = f5(f7(c1)))), introduced(assumption)).
% 29.09/19.35 tff(20570,assumption,(big_f(f7(c1), f10(f7(c1)))), introduced(assumption)).
% 29.09/19.35 tff(20571,plain,
% 29.09/19.35 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~big_f(f7(f7(c1)), f7(c1))) | (f7(f7(c1)) = f7(c1)) | (f10(f7(c1)) = f7(c1)) | (f7(c1) = f5(f7(c1))) | (f7(c1) = f8(f7(c1))) | (~big_f(f7(c1), f10(f7(c1)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~big_f(f7(f7(c1)), f7(c1))) | (f7(f7(c1)) = f7(c1)) | (f10(f7(c1)) = f7(c1)) | (f7(c1) = f5(f7(c1))) | (f7(c1) = f8(f7(c1))) | (~big_f(f7(c1), f10(f7(c1)))))),
% 29.09/19.35 inference(rewrite,[status(thm)],[])).
% 29.09/19.35 tff(20572,plain,
% 29.09/19.35 (((f10(f7(c1)) = f7(c1)) | (f7(c1) = f8(f7(c1))) | (~big_f(f7(c1), f10(f7(c1)))) | (f7(f7(c1)) = f7(c1)) | (f7(c1) = f5(f7(c1))) | (~big_f(f7(f7(c1)), f7(c1)))) <=> ((~big_f(f7(f7(c1)), f7(c1))) | (f7(f7(c1)) = f7(c1)) | (f10(f7(c1)) = f7(c1)) | (f7(c1) = f5(f7(c1))) | (f7(c1) = f8(f7(c1))) | (~big_f(f7(c1), f10(f7(c1)))))),
% 29.09/19.35 inference(rewrite,[status(thm)],[])).
% 29.09/19.35 tff(20573,plain,
% 29.09/19.35 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f7(c1)) = f7(c1)) | (f7(c1) = f8(f7(c1))) | (~big_f(f7(c1), f10(f7(c1)))) | (f7(f7(c1)) = f7(c1)) | (f7(c1) = f5(f7(c1))) | (~big_f(f7(f7(c1)), f7(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~big_f(f7(f7(c1)), f7(c1))) | (f7(f7(c1)) = f7(c1)) | (f10(f7(c1)) = f7(c1)) | (f7(c1) = f5(f7(c1))) | (f7(c1) = f8(f7(c1))) | (~big_f(f7(c1), f10(f7(c1))))))),
% 29.09/19.35 inference(monotonicity,[status(thm)],[20572])).
% 29.09/19.35 tff(20574,plain,
% 29.09/19.35 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f7(c1)) = f7(c1)) | (f7(c1) = f8(f7(c1))) | (~big_f(f7(c1), f10(f7(c1)))) | (f7(f7(c1)) = f7(c1)) | (f7(c1) = f5(f7(c1))) | (~big_f(f7(f7(c1)), f7(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~big_f(f7(f7(c1)), f7(c1))) | (f7(f7(c1)) = f7(c1)) | (f10(f7(c1)) = f7(c1)) | (f7(c1) = f5(f7(c1))) | (f7(c1) = f8(f7(c1))) | (~big_f(f7(c1), f10(f7(c1)))))),
% 29.09/19.35 inference(transitivity,[status(thm)],[20573, 20571])).
% 29.09/19.35 tff(20575,plain,
% 29.09/19.35 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f7(c1)) = f7(c1)) | (f7(c1) = f8(f7(c1))) | (~big_f(f7(c1), f10(f7(c1)))) | (f7(f7(c1)) = f7(c1)) | (f7(c1) = f5(f7(c1))) | (~big_f(f7(f7(c1)), f7(c1))))),
% 29.09/19.35 inference(quant_inst,[status(thm)],[])).
% 29.09/19.35 tff(20576,plain,
% 29.09/19.35 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~big_f(f7(f7(c1)), f7(c1))) | (f7(f7(c1)) = f7(c1)) | (f10(f7(c1)) = f7(c1)) | (f7(c1) = f5(f7(c1))) | (f7(c1) = f8(f7(c1))) | (~big_f(f7(c1), f10(f7(c1))))),
% 29.09/19.35 inference(modus_ponens,[status(thm)],[20575, 20574])).
% 29.09/19.35 tff(20577,plain,
% 29.09/19.35 ((f7(c1) = f5(f7(c1))) | (f7(c1) = f8(f7(c1)))),
% 29.09/19.35 inference(unit_resolution,[status(thm)],[20576, 1659, 12346, 12344, 20570, 12356])).
% 29.09/19.35 tff(20578,plain,
% 29.09/19.35 (f7(c1) = f8(f7(c1))),
% 29.09/19.35 inference(unit_resolution,[status(thm)],[20577, 20569])).
% 29.09/19.35 tff(20579,plain,
% 29.09/19.35 (f8(f7(c1)) = f7(c1)),
% 29.09/19.35 inference(symmetry,[status(thm)],[20578])).
% 29.09/19.35 tff(20580,assumption,(big_f(f3(c1, c2), f10(f7(c1)))), introduced(assumption)).
% 29.09/19.35 tff(20581,plain,
% 29.09/19.35 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~big_f(f7(f7(c1)), f7(c1))) | (f7(f7(c1)) = f7(c1)) | (f10(f7(c1)) = f7(c1)) | (f7(c1) = f5(f7(c1))) | (f3(c1, c2) = f8(f7(c1))) | (~big_f(f3(c1, c2), f10(f7(c1)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~big_f(f7(f7(c1)), f7(c1))) | (f7(f7(c1)) = f7(c1)) | (f10(f7(c1)) = f7(c1)) | (f7(c1) = f5(f7(c1))) | (f3(c1, c2) = f8(f7(c1))) | (~big_f(f3(c1, c2), f10(f7(c1)))))),
% 29.09/19.35 inference(rewrite,[status(thm)],[])).
% 29.09/19.35 tff(20582,plain,
% 29.09/19.35 (((f10(f7(c1)) = f7(c1)) | (f3(c1, c2) = f8(f7(c1))) | (~big_f(f3(c1, c2), f10(f7(c1)))) | (f7(f7(c1)) = f7(c1)) | (f7(c1) = f5(f7(c1))) | (~big_f(f7(f7(c1)), f7(c1)))) <=> ((~big_f(f7(f7(c1)), f7(c1))) | (f7(f7(c1)) = f7(c1)) | (f10(f7(c1)) = f7(c1)) | (f7(c1) = f5(f7(c1))) | (f3(c1, c2) = f8(f7(c1))) | (~big_f(f3(c1, c2), f10(f7(c1)))))),
% 29.09/19.35 inference(rewrite,[status(thm)],[])).
% 29.09/19.35 tff(20583,plain,
% 29.09/19.35 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f7(c1)) = f7(c1)) | (f3(c1, c2) = f8(f7(c1))) | (~big_f(f3(c1, c2), f10(f7(c1)))) | (f7(f7(c1)) = f7(c1)) | (f7(c1) = f5(f7(c1))) | (~big_f(f7(f7(c1)), f7(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~big_f(f7(f7(c1)), f7(c1))) | (f7(f7(c1)) = f7(c1)) | (f10(f7(c1)) = f7(c1)) | (f7(c1) = f5(f7(c1))) | (f3(c1, c2) = f8(f7(c1))) | (~big_f(f3(c1, c2), f10(f7(c1))))))),
% 29.09/19.35 inference(monotonicity,[status(thm)],[20582])).
% 29.09/19.35 tff(20584,plain,
% 29.09/19.35 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f7(c1)) = f7(c1)) | (f3(c1, c2) = f8(f7(c1))) | (~big_f(f3(c1, c2), f10(f7(c1)))) | (f7(f7(c1)) = f7(c1)) | (f7(c1) = f5(f7(c1))) | (~big_f(f7(f7(c1)), f7(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~big_f(f7(f7(c1)), f7(c1))) | (f7(f7(c1)) = f7(c1)) | (f10(f7(c1)) = f7(c1)) | (f7(c1) = f5(f7(c1))) | (f3(c1, c2) = f8(f7(c1))) | (~big_f(f3(c1, c2), f10(f7(c1)))))),
% 29.09/19.35 inference(transitivity,[status(thm)],[20583, 20581])).
% 29.09/19.35 tff(20585,plain,
% 29.09/19.35 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f7(c1)) = f7(c1)) | (f3(c1, c2) = f8(f7(c1))) | (~big_f(f3(c1, c2), f10(f7(c1)))) | (f7(f7(c1)) = f7(c1)) | (f7(c1) = f5(f7(c1))) | (~big_f(f7(f7(c1)), f7(c1))))),
% 29.09/19.35 inference(quant_inst,[status(thm)],[])).
% 29.09/19.35 tff(20586,plain,
% 29.09/19.35 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (~big_f(f7(f7(c1)), f7(c1))) | (f7(f7(c1)) = f7(c1)) | (f10(f7(c1)) = f7(c1)) | (f7(c1) = f5(f7(c1))) | (f3(c1, c2) = f8(f7(c1))) | (~big_f(f3(c1, c2), f10(f7(c1))))),
% 29.09/19.35 inference(modus_ponens,[status(thm)],[20585, 20584])).
% 29.09/19.35 tff(20587,plain,
% 29.09/19.35 ((f7(c1) = f5(f7(c1))) | (f3(c1, c2) = f8(f7(c1))) | (~big_f(f3(c1, c2), f10(f7(c1))))),
% 29.09/19.35 inference(unit_resolution,[status(thm)],[20586, 1659, 12346, 12344, 12356])).
% 29.09/19.35 tff(20588,plain,
% 29.09/19.35 (f3(c1, c2) = f8(f7(c1))),
% 29.09/19.35 inference(unit_resolution,[status(thm)],[20587, 20569, 20580])).
% 29.09/19.35 tff(20589,plain,
% 29.09/19.35 (f3(c1, c2) = c2),
% 29.09/19.35 inference(transitivity,[status(thm)],[20588, 20579, 347])).
% 29.09/19.35 tff(20590,plain,
% 29.09/19.35 ($false),
% 29.09/19.35 inference(unit_resolution,[status(thm)],[12777, 20589])).
% 29.09/19.35 tff(20591,plain,((f7(c1) = f5(f7(c1))) | (f3(c1, c2) = c2) | (~(f7(c1) = c2)) | (~big_f(f3(c1, c2), f10(f7(c1)))) | (f7(f7(c1)) = f7(c1)) | (f10(f7(c1)) = f7(c1)) | (~big_f(f7(f7(c1)), f7(c1))) | (~big_f(f7(c1), f10(f7(c1))))), inference(lemma,lemma(discharge,[]))).
% 29.09/19.35 tff(20592,plain,
% 29.09/19.35 (f7(c1) = f5(f7(c1))),
% 29.09/19.35 inference(unit_resolution,[status(thm)],[20591, 20568, 120, 20554, 20551, 20254, 12356, 20545])).
% 29.09/19.35 tff(20593,plain,
% 29.09/19.35 (big_f(f3(c1, c2), c1)),
% 29.09/19.35 inference(modus_ponens,[status(thm)],[20567, 20536])).
% 29.09/19.35 tff(20594,plain,
% 29.09/19.35 ((~(big_f(c1, c1) <=> big_f(f3(c1, c2), c1))) | (~big_f(f3(c1, c2), c1))),
% 29.09/19.35 inference(unit_resolution,[status(thm)],[13186, 66])).
% 29.09/19.35 tff(20595,plain,
% 29.09/19.35 (~(big_f(c1, c1) <=> big_f(f3(c1, c2), c1))),
% 29.09/19.35 inference(unit_resolution,[status(thm)],[20594, 20593])).
% 29.09/19.35 tff(20596,plain,
% 29.09/19.35 (~(c1 = f3(c1, c2))),
% 29.09/19.35 inference(unit_resolution,[status(thm)],[13192, 20595])).
% 29.09/19.35 tff(20597,plain,
% 29.09/19.35 (f1(f5(c2), f5(c1)) = c2),
% 29.09/19.35 inference(transitivity,[status(thm)],[16046, 15858, 499])).
% 29.09/19.35 tff(20598,plain,
% 29.09/19.35 (f3(c1, f1(f5(c2), f5(c1))) = f3(c1, c2)),
% 29.09/19.35 inference(monotonicity,[status(thm)],[20597])).
% 29.09/19.35 tff(20599,plain,
% 29.09/19.35 ((f3(c1, f1(f5(c2), f5(c1))) = c1) <=> (f3(c1, c2) = c1)),
% 29.09/19.35 inference(monotonicity,[status(thm)],[20598])).
% 29.09/19.35 tff(20600,plain,
% 29.09/19.35 ((f3(c1, f1(f5(c2), f5(c1))) = c1) <=> (c1 = f3(c1, c2))),
% 29.09/19.35 inference(transitivity,[status(thm)],[20599, 13151])).
% 29.09/19.35 tff(20601,plain,
% 29.09/19.35 ((c1 = f3(c1, c2)) <=> (f3(c1, f1(f5(c2), f5(c1))) = c1)),
% 29.09/19.35 inference(symmetry,[status(thm)],[20600])).
% 29.09/19.35 tff(20602,plain,
% 29.09/19.35 ((~(c1 = f3(c1, c2))) <=> (~(f3(c1, f1(f5(c2), f5(c1))) = c1))),
% 29.09/19.35 inference(monotonicity,[status(thm)],[20601])).
% 29.09/19.35 tff(20603,plain,
% 29.09/19.35 (~(f3(c1, f1(f5(c2), f5(c1))) = c1)),
% 29.09/19.35 inference(modus_ponens,[status(thm)],[16041, 20602])).
% 29.09/19.35 tff(20604,plain,
% 29.09/19.35 (f3(c1, c2) = f3(c1, f1(f5(c2), f5(c1)))),
% 29.09/19.35 inference(symmetry,[status(thm)],[20598])).
% 29.09/19.35 tff(20605,plain,
% 29.09/19.35 ((f3(c1, c2) = c2) <=> (f3(c1, f1(f5(c2), f5(c1))) = c2)),
% 29.09/19.35 inference(monotonicity,[status(thm)],[20604])).
% 29.09/19.35 tff(20606,plain,
% 29.09/19.35 ((~(f3(c1, c2) = c2)) <=> (~(f3(c1, f1(f5(c2), f5(c1))) = c2))),
% 29.09/19.35 inference(monotonicity,[status(thm)],[20605])).
% 29.09/19.35 tff(20607,plain,
% 29.09/19.35 (~(f3(c1, f1(f5(c2), f5(c1))) = c2)),
% 29.09/19.35 inference(modus_ponens,[status(thm)],[12777, 20606])).
% 29.09/19.35 tff(20608,plain,
% 29.09/19.35 ($false),
% 29.09/19.35 inference(unit_resolution,[status(thm)],[16082, 20607, 20603])).
% 29.09/19.35 tff(20609,plain,((~(f5(c1) = c1)) | (f3(c1, c2) = c2) | (~(f1(f7(f7(c2)), c1) = c2)) | (~(f7(c2) = c1)) | (~(f7(c1) = f5(f7(c1)))) | (~(f7(c1) = c2)) | (c1 = f3(c1, c2))), inference(lemma,lemma(discharge,[]))).
% 29.09/19.35 tff(20610,plain,
% 29.09/19.35 (~(f5(c1) = c1)),
% 29.09/19.35 inference(unit_resolution,[status(thm)],[20609, 20545, 20539, 292, 20592, 120, 20596])).
% 29.09/19.35 tff(20611,plain,
% 29.09/19.35 (f5(c1) = c2),
% 29.09/19.35 inference(unit_resolution,[status(thm)],[1708, 20610])).
% 29.09/19.35 tff(20612,plain,
% 29.09/19.35 (f5(c2) = c2),
% 29.09/19.35 inference(transitivity,[status(thm)],[16044, 16043, 347])).
% 29.09/19.35 tff(20613,plain,
% 29.09/19.35 (f1(f5(c2), f5(c1)) = f1(c2, c2)),
% 29.09/19.35 inference(monotonicity,[status(thm)],[20612, 186])).
% 29.09/19.35 tff(20614,plain,
% 29.09/19.35 (f1(f5(c2), f5(c1)) = c1),
% 29.09/19.35 inference(transitivity,[status(thm)],[20613, 14884])).
% 29.09/19.35 tff(20615,plain,
% 29.09/19.35 (f3(f1(f5(c2), f5(c1)), c2) = f3(c1, c2)),
% 29.09/19.35 inference(monotonicity,[status(thm)],[20614])).
% 29.09/19.35 tff(20616,plain,
% 29.09/19.35 ((f3(f1(f5(c2), f5(c1)), c2) = c2) <=> (f3(c1, c2) = c2)),
% 29.09/19.35 inference(monotonicity,[status(thm)],[20615])).
% 29.09/19.35 tff(20617,plain,
% 29.09/19.35 ((f3(c1, c2) = c2) <=> (f3(f1(f5(c2), f5(c1)), c2) = c2)),
% 29.09/19.35 inference(symmetry,[status(thm)],[20616])).
% 29.09/19.35 tff(20618,plain,
% 29.09/19.35 ((~(f3(c1, c2) = c2)) <=> (~(f3(f1(f5(c2), f5(c1)), c2) = c2))),
% 29.09/19.35 inference(monotonicity,[status(thm)],[20617])).
% 29.09/19.35 tff(20619,plain,
% 29.09/19.35 (~(f3(f1(f5(c2), f5(c1)), c2) = c2)),
% 29.09/19.35 inference(modus_ponens,[status(thm)],[12777, 20618])).
% 29.09/19.35 tff(20620,plain,
% 29.09/19.35 (f1(c2, c2) = f1(f5(c2), f5(c1))),
% 29.09/19.35 inference(symmetry,[status(thm)],[20613])).
% 29.09/19.35 tff(20621,plain,
% 29.09/19.35 (c1 = f1(f5(c2), f5(c1))),
% 29.09/19.35 inference(transitivity,[status(thm)],[14885, 20620])).
% 29.09/19.35 tff(20622,plain,
% 29.09/19.35 (f3(c1, c2) = f3(f1(f5(c2), f5(c1)), c2)),
% 29.09/19.35 inference(monotonicity,[status(thm)],[20621])).
% 29.09/19.35 tff(20623,plain,
% 29.09/19.35 (f3(c1, c2) = c1),
% 29.09/19.35 inference(transitivity,[status(thm)],[20622, 16476])).
% 29.09/19.35 tff(20624,plain,
% 29.09/19.35 (big_f(f3(c1, c2), c1) <=> big_f(c1, c1)),
% 29.09/19.35 inference(monotonicity,[status(thm)],[20623])).
% 29.09/19.35 tff(20625,plain,
% 29.09/19.35 (big_f(c1, c1) <=> big_f(f3(c1, c2), c1)),
% 29.09/19.36 inference(symmetry,[status(thm)],[20624])).
% 29.09/19.36 tff(20626,plain,
% 29.09/19.36 ((~big_f(c1, c1)) <=> (~big_f(f3(c1, c2), c1))),
% 29.09/19.36 inference(monotonicity,[status(thm)],[20625])).
% 29.09/19.36 tff(20627,plain,
% 29.09/19.36 (~big_f(f3(c1, c2), c1)),
% 29.09/19.36 inference(modus_ponens,[status(thm)],[66, 20626])).
% 29.09/19.36 tff(20628,plain,
% 29.09/19.36 ((~(f3(c1, c2) = c2)) <=> (~(f3(c1, f7(c1)) = f7(c1)))),
% 29.09/19.36 inference(monotonicity,[status(thm)],[16118])).
% 29.09/19.36 tff(20629,plain,
% 29.09/19.36 (~(f3(c1, f7(c1)) = f7(c1))),
% 29.09/19.36 inference(modus_ponens,[status(thm)],[12777, 20628])).
% 29.09/19.36 tff(20630,plain,
% 29.09/19.36 (big_f(f3(c1, f7(c1)), c1)),
% 29.09/19.36 inference(unit_resolution,[status(thm)],[20566, 1014, 482, 12165, 12203, 12204, 20629])).
% 29.09/19.36 tff(20631,plain,
% 29.09/19.36 (big_f(f3(c1, c2), c1)),
% 29.09/19.36 inference(modus_ponens,[status(thm)],[20630, 16109])).
% 29.09/19.36 tff(20632,plain,
% 29.09/19.36 ($false),
% 29.09/19.36 inference(unit_resolution,[status(thm)],[20631, 20627])).
% 29.09/19.36 tff(20633,plain,((f3(f1(f5(c2), f5(c1)), c2) = c2) | big_f(c1, c1) | (~(f1(c2, c2) = c1)) | (~(f5(c1) = c2)) | (~(f7(c1) = c2)) | (~(f7(c1) = f5(f7(c1)))) | (c1 = c4) | (f7(c1) = c3) | (f1(f7(c1), c1) = c1) | big_f(f7(c1), f1(f7(c1), c1)) | (f3(c1, c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 29.09/19.36 tff(20634,plain,
% 29.09/19.36 (f3(f1(f5(c2), f5(c1)), c2) = c2),
% 29.09/19.36 inference(unit_resolution,[status(thm)],[20633, 12777, 14884, 186, 347, 16042, 482, 12165, 12203, 12204, 66])).
% 29.09/19.36 tff(20635,plain,
% 29.09/19.36 ($false),
% 29.09/19.36 inference(unit_resolution,[status(thm)],[20634, 20619])).
% 29.09/19.36 tff(20636,plain,((f3(c1, c2) = c2) | (~(f1(c2, c2) = c1)) | (~(f5(c1) = c2)) | (~(f7(c1) = c2)) | (~(f7(c1) = f5(f7(c1)))) | (c1 = c4) | (f7(c1) = c3) | (f1(f7(c1), c1) = c1) | big_f(f7(c1), f1(f7(c1), c1)) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 29.09/19.36 tff(20637,plain,
% 29.09/19.36 (~(f1(c2, c2) = c1)),
% 29.09/19.36 inference(unit_resolution,[status(thm)],[20636, 20611, 20545, 120, 20592, 482, 12165, 20544, 12204, 66])).
% 29.09/19.36 tff(20638,plain,
% 29.09/19.36 (f1(c2, c2) = c2),
% 29.09/19.36 inference(unit_resolution,[status(thm)],[5270, 20637])).
% 29.09/19.36 tff(20639,plain,
% 29.09/19.36 (f5(f7(c1)) = f7(c1)),
% 29.09/19.36 inference(symmetry,[status(thm)],[20592])).
% 29.09/19.36 tff(20640,plain,
% 29.09/19.36 (f5(c2) = f5(f7(c1))),
% 29.09/19.36 inference(monotonicity,[status(thm)],[2778])).
% 29.09/19.36 tff(20641,plain,
% 29.09/19.36 (f5(c2) = c2),
% 29.09/19.36 inference(transitivity,[status(thm)],[20640, 20639, 120])).
% 29.09/19.36 tff(20642,plain,
% 29.09/19.36 (f1(f5(c2), f5(c1)) = f1(c2, c2)),
% 29.09/19.36 inference(monotonicity,[status(thm)],[20641, 20611])).
% 29.09/19.36 tff(20643,plain,
% 29.09/19.36 (f1(f5(c2), f5(c1)) = c2),
% 29.09/19.36 inference(transitivity,[status(thm)],[20642, 20638])).
% 29.09/19.36 tff(20644,plain,
% 29.09/19.36 (f3(c1, f1(f5(c2), f5(c1))) = f3(c1, c2)),
% 29.09/19.36 inference(monotonicity,[status(thm)],[20643])).
% 29.09/19.36 tff(20645,plain,
% 29.09/19.36 ((f3(c1, f1(f5(c2), f5(c1))) = c1) <=> (f3(c1, c2) = c1)),
% 29.09/19.36 inference(monotonicity,[status(thm)],[20644])).
% 29.09/19.36 tff(20646,plain,
% 29.09/19.36 ((f3(c1, f1(f5(c2), f5(c1))) = c1) <=> (c1 = f3(c1, c2))),
% 29.09/19.36 inference(transitivity,[status(thm)],[20645, 13151])).
% 29.09/19.36 tff(20647,plain,
% 29.09/19.36 ((c1 = f3(c1, c2)) <=> (f3(c1, f1(f5(c2), f5(c1))) = c1)),
% 29.09/19.36 inference(symmetry,[status(thm)],[20646])).
% 29.09/19.36 tff(20648,plain,
% 29.09/19.36 ((~(c1 = f3(c1, c2))) <=> (~(f3(c1, f1(f5(c2), f5(c1))) = c1))),
% 29.09/19.36 inference(monotonicity,[status(thm)],[20647])).
% 29.09/19.36 tff(20649,plain,
% 29.09/19.36 (~(f3(c1, f1(f5(c2), f5(c1))) = c1)),
% 29.09/19.36 inference(modus_ponens,[status(thm)],[20596, 20648])).
% 29.09/19.36 tff(20650,plain,
% 29.09/19.36 (f3(c1, c2) = f3(c1, f1(f5(c2), f5(c1)))),
% 29.09/19.36 inference(symmetry,[status(thm)],[20644])).
% 29.09/19.36 tff(20651,plain,
% 29.09/19.36 ((f3(c1, c2) = c2) <=> (f3(c1, f1(f5(c2), f5(c1))) = c2)),
% 29.09/19.36 inference(monotonicity,[status(thm)],[20650])).
% 29.09/19.36 tff(20652,plain,
% 29.09/19.36 ((~(f3(c1, c2) = c2)) <=> (~(f3(c1, f1(f5(c2), f5(c1))) = c2))),
% 29.09/19.36 inference(monotonicity,[status(thm)],[20651])).
% 29.09/19.36 tff(20653,plain,
% 29.09/19.36 (~(f3(c1, f1(f5(c2), f5(c1))) = c2)),
% 29.09/19.36 inference(modus_ponens,[status(thm)],[20545, 20652])).
% 29.09/19.36 tff(20654,plain,
% 29.09/19.36 ($false),
% 29.09/19.36 inference(unit_resolution,[status(thm)],[16082, 20653, 20649])).
% 29.09/19.36 tff(20655,plain,(big_f(f7(c1), f1(f7(c1), c1)) | (c1 = c4) | (f7(c1) = c3) | big_f(c1, c1) | (~(f7(c2) = c1)) | (~big_f(f7(f7(c1)), f7(c1))) | (~(f10(c2) = c1)) | (~big_f(f7(c1), c1)) | (f7(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.09/19.36 tff(20656,plain,
% 29.09/19.36 (big_f(f7(c1), f1(f7(c1), c1))),
% 29.09/19.36 inference(unit_resolution,[status(thm)],[20655, 482, 12165, 66, 292, 12356, 11819, 15735, 115])).
% 29.09/19.36 tff(20657,plain,
% 29.09/19.36 (~(f1(c2, c1) = c2)),
% 29.09/19.36 inference(unit_resolution,[status(thm)],[12197, 20656, 121, 120])).
% 29.09/19.36 tff(20658,plain,
% 29.09/19.36 (f1(c2, c1) = c1),
% 29.09/19.36 inference(unit_resolution,[status(thm)],[10113, 20657])).
% 29.09/19.36 tff(20659,plain,
% 29.09/19.36 (f1(f7(c1), c1) = f1(c2, c1)),
% 29.09/19.36 inference(monotonicity,[status(thm)],[120])).
% 29.09/19.36 tff(20660,plain,
% 29.09/19.36 (f1(c2, c1) = f1(f7(c1), c1)),
% 29.09/19.36 inference(symmetry,[status(thm)],[20659])).
% 29.09/19.36 tff(20661,plain,
% 29.09/19.36 (big_f(c2, f1(c2, c1)) <=> big_f(f7(c1), f1(f7(c1), c1))),
% 29.09/19.36 inference(monotonicity,[status(thm)],[2778, 20660])).
% 29.09/19.36 tff(20662,plain,
% 29.09/19.36 (big_f(f7(c1), f1(f7(c1), c1)) <=> big_f(c2, f1(c2, c1))),
% 29.09/19.36 inference(symmetry,[status(thm)],[20661])).
% 29.09/19.36 tff(20663,plain,
% 29.09/19.36 (big_f(c2, f1(c2, c1))),
% 29.09/19.36 inference(modus_ponens,[status(thm)],[20656, 20662])).
% 29.09/19.36 tff(20664,plain,
% 29.09/19.36 (big_f(f3(c1, c2), c1)),
% 29.09/19.36 inference(unit_resolution,[status(thm)],[16151, 20663, 120, 377, 482, 20658, 15735])).
% 29.09/19.36 tff(20665,plain,
% 29.09/19.36 (big_f(f3(c1, f7(c1)), c1)),
% 29.09/19.36 inference(modus_ponens,[status(thm)],[20664, 20537])).
% 29.09/19.36 tff(20666,plain,
% 29.09/19.36 (f1(c2, c1) = f1(f7(c1), c1)),
% 29.09/19.36 inference(monotonicity,[status(thm)],[354])).
% 29.09/19.36 tff(20667,plain,
% 29.09/19.36 ((f1(c2, c1) = c1) <=> (f1(f7(c1), c1) = c1)),
% 29.09/19.36 inference(monotonicity,[status(thm)],[20666])).
% 29.09/19.36 tff(20668,plain,
% 29.09/19.36 (f1(f7(c1), c1) = c1),
% 29.09/19.36 inference(modus_ponens,[status(thm)],[11485, 20667])).
% 29.09/19.36 tff(20669,plain,
% 29.09/19.36 ($false),
% 29.09/19.36 inference(unit_resolution,[status(thm)],[12203, 20668])).
% 29.09/19.36 tff(20670,plain,((~(f1(c2, c1) = c1)) | (f1(f7(c1), c1) = c1) | (~(f7(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.09/19.36 tff(20671,plain,
% 29.09/19.36 (f1(f7(c1), c1) = c1),
% 29.09/19.36 inference(unit_resolution,[status(thm)],[20670, 20658, 120])).
% 29.09/19.36 tff(20672,plain,
% 29.09/19.36 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c4) | (f7(c1) = c3) | (~(f1(f7(c1), c1) = c1)) | (~big_f(f7(c1), f1(f7(c1), c1))) | (~(f3(c1, f7(c1)) = f7(c1))) | (~big_f(f3(c1, f7(c1)), c1)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c4) | (f7(c1) = c3) | (~(f1(f7(c1), c1) = c1)) | (~big_f(f7(c1), f1(f7(c1), c1))) | (~(f3(c1, f7(c1)) = f7(c1))) | (~big_f(f3(c1, f7(c1)), c1)))),
% 29.09/19.36 inference(rewrite,[status(thm)],[])).
% 29.09/19.36 tff(20673,plain,
% 29.09/19.36 (((c1 = c4) | (f7(c1) = c3) | (~(f3(c1, f7(c1)) = f7(c1))) | (~big_f(f3(c1, f7(c1)), c1)) | (~(f1(f7(c1), c1) = c1)) | (~big_f(f7(c1), f1(f7(c1), c1)))) <=> ((c1 = c4) | (f7(c1) = c3) | (~(f1(f7(c1), c1) = c1)) | (~big_f(f7(c1), f1(f7(c1), c1))) | (~(f3(c1, f7(c1)) = f7(c1))) | (~big_f(f3(c1, f7(c1)), c1)))),
% 29.09/19.36 inference(rewrite,[status(thm)],[])).
% 29.09/19.36 tff(20674,plain,
% 29.09/19.36 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c4) | (f7(c1) = c3) | (~(f3(c1, f7(c1)) = f7(c1))) | (~big_f(f3(c1, f7(c1)), c1)) | (~(f1(f7(c1), c1) = c1)) | (~big_f(f7(c1), f1(f7(c1), c1))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c4) | (f7(c1) = c3) | (~(f1(f7(c1), c1) = c1)) | (~big_f(f7(c1), f1(f7(c1), c1))) | (~(f3(c1, f7(c1)) = f7(c1))) | (~big_f(f3(c1, f7(c1)), c1))))),
% 29.09/19.36 inference(monotonicity,[status(thm)],[20673])).
% 29.09/19.36 tff(20675,plain,
% 29.09/19.36 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c4) | (f7(c1) = c3) | (~(f3(c1, f7(c1)) = f7(c1))) | (~big_f(f3(c1, f7(c1)), c1)) | (~(f1(f7(c1), c1) = c1)) | (~big_f(f7(c1), f1(f7(c1), c1))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c4) | (f7(c1) = c3) | (~(f1(f7(c1), c1) = c1)) | (~big_f(f7(c1), f1(f7(c1), c1))) | (~(f3(c1, f7(c1)) = f7(c1))) | (~big_f(f3(c1, f7(c1)), c1)))),
% 29.09/19.36 inference(transitivity,[status(thm)],[20674, 20672])).
% 29.09/19.36 tff(20676,plain,
% 29.09/19.36 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c4) | (f7(c1) = c3) | (~(f3(c1, f7(c1)) = f7(c1))) | (~big_f(f3(c1, f7(c1)), c1)) | (~(f1(f7(c1), c1) = c1)) | (~big_f(f7(c1), f1(f7(c1), c1))))),
% 29.09/19.36 inference(quant_inst,[status(thm)],[])).
% 29.09/19.36 tff(20677,plain,
% 29.09/19.36 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c4) | (f7(c1) = c3) | (~(f1(f7(c1), c1) = c1)) | (~big_f(f7(c1), f1(f7(c1), c1))) | (~(f3(c1, f7(c1)) = f7(c1))) | (~big_f(f3(c1, f7(c1)), c1))),
% 29.09/19.36 inference(modus_ponens,[status(thm)],[20676, 20675])).
% 29.09/19.36 tff(20678,plain,
% 29.09/19.36 (~(f3(c1, f7(c1)) = f7(c1))),
% 29.09/19.36 inference(unit_resolution,[status(thm)],[20677, 933, 482, 12165, 20671, 20656, 20665])).
% 29.09/19.36 tff(20679,plain,
% 29.09/19.36 (~(f3(c1, c2) = c2)),
% 29.09/19.36 inference(modus_ponens,[status(thm)],[20678, 20535])).
% 29.09/19.36 tff(20680,plain,
% 29.09/19.36 (big_f(f3(c1, c2), f10(f7(c1)))),
% 29.09/19.36 inference(modus_ponens,[status(thm)],[20664, 20556])).
% 29.09/19.36 tff(20681,plain,
% 29.09/19.36 (f7(c1) = f5(f7(c1))),
% 29.09/19.36 inference(unit_resolution,[status(thm)],[20591, 20679, 120, 20554, 20551, 20254, 12356, 20680])).
% 29.09/19.36 tff(20682,plain,
% 29.09/19.36 (~(big_f(c1, c1) <=> big_f(f3(c1, c2), c1))),
% 29.09/19.36 inference(unit_resolution,[status(thm)],[20594, 20664])).
% 29.09/19.36 tff(20683,plain,
% 29.09/19.36 (~(c1 = f3(c1, c2))),
% 29.09/19.36 inference(unit_resolution,[status(thm)],[13192, 20682])).
% 29.09/19.36 tff(20684,plain,
% 29.09/19.36 (~(f5(c1) = c1)),
% 29.09/19.36 inference(unit_resolution,[status(thm)],[16063, 20683, 20658, 120, 20681, 20679])).
% 29.09/19.36 tff(20685,plain,
% 29.09/19.36 (~(c1 = f5(c1))),
% 29.09/19.36 inference(modus_ponens,[status(thm)],[20684, 2261])).
% 29.09/19.36 tff(20686,plain,
% 29.09/19.36 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(c1) = c1) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)) | (f10(f7(c1)) = f7(c1)) | (f7(c1) = f8(f7(c1))) | (~big_f(f7(c1), f10(f7(c1)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c1) = c1) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)) | (f10(f7(c1)) = f7(c1)) | (f7(c1) = f8(f7(c1))) | (~big_f(f7(c1), f10(f7(c1)))))),
% 29.09/19.36 inference(rewrite,[status(thm)],[])).
% 29.09/19.36 tff(20687,plain,
% 29.09/19.36 (((f10(f7(c1)) = f7(c1)) | (f7(c1) = f8(f7(c1))) | (~big_f(f7(c1), f10(f7(c1)))) | (f7(c1) = c1) | (c1 = f5(c1)) | (~big_f(f7(c1), c1))) <=> ((f7(c1) = c1) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)) | (f10(f7(c1)) = f7(c1)) | (f7(c1) = f8(f7(c1))) | (~big_f(f7(c1), f10(f7(c1)))))),
% 29.09/19.36 inference(rewrite,[status(thm)],[])).
% 29.09/19.36 tff(20688,plain,
% 29.09/19.36 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f7(c1)) = f7(c1)) | (f7(c1) = f8(f7(c1))) | (~big_f(f7(c1), f10(f7(c1)))) | (f7(c1) = c1) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(c1) = c1) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)) | (f10(f7(c1)) = f7(c1)) | (f7(c1) = f8(f7(c1))) | (~big_f(f7(c1), f10(f7(c1))))))),
% 29.09/19.36 inference(monotonicity,[status(thm)],[20687])).
% 29.09/19.36 tff(20689,plain,
% 29.09/19.36 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f7(c1)) = f7(c1)) | (f7(c1) = f8(f7(c1))) | (~big_f(f7(c1), f10(f7(c1)))) | (f7(c1) = c1) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c1) = c1) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)) | (f10(f7(c1)) = f7(c1)) | (f7(c1) = f8(f7(c1))) | (~big_f(f7(c1), f10(f7(c1)))))),
% 29.09/19.36 inference(transitivity,[status(thm)],[20688, 20686])).
% 29.09/19.36 tff(20690,plain,
% 29.09/19.36 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f7(c1)) = f7(c1)) | (f7(c1) = f8(f7(c1))) | (~big_f(f7(c1), f10(f7(c1)))) | (f7(c1) = c1) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)))),
% 29.09/19.36 inference(quant_inst,[status(thm)],[])).
% 29.09/19.36 tff(20691,plain,
% 29.09/19.36 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c1) = c1) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)) | (f10(f7(c1)) = f7(c1)) | (f7(c1) = f8(f7(c1))) | (~big_f(f7(c1), f10(f7(c1))))),
% 29.09/19.36 inference(modus_ponens,[status(thm)],[20690, 20689])).
% 29.09/19.36 tff(20692,plain,
% 29.09/19.36 ((c1 = f5(c1)) | (f7(c1) = f8(f7(c1)))),
% 29.09/19.36 inference(unit_resolution,[status(thm)],[20691, 1659, 115, 15735, 20254, 20554])).
% 29.09/19.36 tff(20693,plain,
% 29.09/19.36 (f7(c1) = f8(f7(c1))),
% 29.09/19.36 inference(unit_resolution,[status(thm)],[20692, 20685])).
% 29.09/19.36 tff(20694,plain,
% 29.09/19.36 (f8(f7(c1)) = f7(c1)),
% 29.09/19.36 inference(symmetry,[status(thm)],[20693])).
% 29.09/19.36 tff(20695,plain,
% 29.09/19.36 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(c1) = c1) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)) | (f10(f7(c1)) = f7(c1)) | (f3(c1, c2) = f8(f7(c1))) | (~big_f(f3(c1, c2), f10(f7(c1)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c1) = c1) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)) | (f10(f7(c1)) = f7(c1)) | (f3(c1, c2) = f8(f7(c1))) | (~big_f(f3(c1, c2), f10(f7(c1)))))),
% 29.09/19.36 inference(rewrite,[status(thm)],[])).
% 29.09/19.36 tff(20696,plain,
% 29.09/19.36 (((f10(f7(c1)) = f7(c1)) | (f3(c1, c2) = f8(f7(c1))) | (~big_f(f3(c1, c2), f10(f7(c1)))) | (f7(c1) = c1) | (c1 = f5(c1)) | (~big_f(f7(c1), c1))) <=> ((f7(c1) = c1) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)) | (f10(f7(c1)) = f7(c1)) | (f3(c1, c2) = f8(f7(c1))) | (~big_f(f3(c1, c2), f10(f7(c1)))))),
% 29.09/19.36 inference(rewrite,[status(thm)],[])).
% 29.09/19.36 tff(20697,plain,
% 29.09/19.36 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f7(c1)) = f7(c1)) | (f3(c1, c2) = f8(f7(c1))) | (~big_f(f3(c1, c2), f10(f7(c1)))) | (f7(c1) = c1) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(c1) = c1) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)) | (f10(f7(c1)) = f7(c1)) | (f3(c1, c2) = f8(f7(c1))) | (~big_f(f3(c1, c2), f10(f7(c1))))))),
% 29.09/19.36 inference(monotonicity,[status(thm)],[20696])).
% 29.09/19.36 tff(20698,plain,
% 29.09/19.36 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f7(c1)) = f7(c1)) | (f3(c1, c2) = f8(f7(c1))) | (~big_f(f3(c1, c2), f10(f7(c1)))) | (f7(c1) = c1) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c1) = c1) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)) | (f10(f7(c1)) = f7(c1)) | (f3(c1, c2) = f8(f7(c1))) | (~big_f(f3(c1, c2), f10(f7(c1)))))),
% 29.09/19.36 inference(transitivity,[status(thm)],[20697, 20695])).
% 29.09/19.36 tff(20699,plain,
% 29.09/19.36 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f7(c1)) = f7(c1)) | (f3(c1, c2) = f8(f7(c1))) | (~big_f(f3(c1, c2), f10(f7(c1)))) | (f7(c1) = c1) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)))),
% 29.09/19.36 inference(quant_inst,[status(thm)],[])).
% 29.09/19.36 tff(20700,plain,
% 29.09/19.36 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c1) = c1) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)) | (f10(f7(c1)) = f7(c1)) | (f3(c1, c2) = f8(f7(c1))) | (~big_f(f3(c1, c2), f10(f7(c1))))),
% 29.09/19.36 inference(modus_ponens,[status(thm)],[20699, 20698])).
% 29.09/19.36 tff(20701,plain,
% 29.09/19.36 ((c1 = f5(c1)) | (f3(c1, c2) = f8(f7(c1)))),
% 29.09/19.36 inference(unit_resolution,[status(thm)],[20700, 1659, 115, 15735, 20254, 20680])).
% 29.09/19.36 tff(20702,plain,
% 29.09/19.36 (f3(c1, c2) = f8(f7(c1))),
% 29.09/19.36 inference(unit_resolution,[status(thm)],[20701, 20685])).
% 29.09/19.36 tff(20703,plain,
% 29.09/19.36 (f3(c1, c2) = c2),
% 29.09/19.36 inference(transitivity,[status(thm)],[20702, 20694, 120])).
% 29.09/19.36 tff(20704,plain,
% 29.09/19.36 ($false),
% 29.09/19.36 inference(unit_resolution,[status(thm)],[20679, 20703])).
% 29.09/19.36 tff(20705,plain,((c1 = c4) | (f7(c1) = c1) | (~big_f(f7(c1), c1)) | (~big_f(f7(f7(c1)), f7(c1))) | (f7(c1) = c3) | (~(f10(c2) = c1)) | big_f(c1, c1) | (c2 = c3) | big_f(c2, c2) | (~(f7(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.09/19.36 tff(20706,plain,
% 29.09/19.36 (c1 = c4),
% 29.09/19.36 inference(unit_resolution,[status(thm)],[20705, 20532, 115, 20492, 20485, 94, 66, 11455, 121, 22])).
% 29.09/19.36 tff(20707,plain,
% 29.09/19.36 (f4(c1) = f4(c4)),
% 29.09/19.36 inference(monotonicity,[status(thm)],[20706])).
% 29.09/19.36 tff(20708,plain,
% 29.09/19.36 (f4(c4) = f4(c1)),
% 29.09/19.36 inference(symmetry,[status(thm)],[20707])).
% 29.09/19.36 tff(20709,plain,
% 29.09/19.36 (c1 = f4(c1)),
% 29.09/19.36 inference(transitivity,[status(thm)],[16651, 20708])).
% 29.09/19.36 tff(20710,plain,
% 29.09/19.36 ((f7(f7(c2)) = c3) <=> (f7(c1) = c3)),
% 29.09/19.36 inference(monotonicity,[status(thm)],[8077])).
% 29.09/19.36 tff(20711,plain,
% 29.09/19.36 ((f7(c1) = c3) <=> (f7(f7(c2)) = c3)),
% 29.09/19.36 inference(symmetry,[status(thm)],[20710])).
% 29.09/19.36 tff(20712,plain,
% 29.09/19.36 ((f7(c1) = c1) <=> (f7(f7(c2)) = c3)),
% 29.09/19.36 inference(transitivity,[status(thm)],[20483, 20711])).
% 29.09/19.36 tff(20713,plain,
% 29.09/19.36 ((~(f7(c1) = c1)) <=> (~(f7(f7(c2)) = c3))),
% 29.09/19.36 inference(monotonicity,[status(thm)],[20712])).
% 29.09/19.36 tff(20714,plain,
% 29.09/19.36 (~(f7(f7(c2)) = c3)),
% 29.09/19.36 inference(modus_ponens,[status(thm)],[115, 20713])).
% 29.09/19.36 tff(20715,plain,
% 29.09/19.36 (c4 = c1),
% 29.09/19.36 inference(symmetry,[status(thm)],[20706])).
% 29.09/19.36 tff(20716,plain,
% 29.09/19.36 (big_f(f4(c4), c4) <=> big_f(c1, c1)),
% 29.09/19.36 inference(monotonicity,[status(thm)],[11752, 20715])).
% 29.09/19.36 tff(20717,plain,
% 29.09/19.36 (big_f(c1, c1) <=> big_f(f4(c4), c4)),
% 29.09/19.36 inference(symmetry,[status(thm)],[20716])).
% 29.09/19.36 tff(20718,plain,
% 29.09/19.36 ((~big_f(c1, c1)) <=> (~big_f(f4(c4), c4))),
% 29.09/19.36 inference(monotonicity,[status(thm)],[20717])).
% 29.09/19.36 tff(20719,plain,
% 29.09/19.36 (~big_f(f4(c4), c4)),
% 29.09/19.36 inference(modus_ponens,[status(thm)],[66, 20718])).
% 29.09/19.36 tff(20720,plain,
% 29.09/19.36 (f1(f7(f7(c2)), c1) = c1),
% 29.09/19.36 inference(unit_resolution,[status(thm)],[422, 20719, 22, 121, 120, 20714])).
% 29.09/19.36 tff(20721,plain,
% 29.09/19.36 (big_f(f7(c1), f1(f7(c1), c1))),
% 29.09/19.36 inference(unit_resolution,[status(thm)],[15864, 20720, 20532, 22])).
% 29.09/19.36 tff(20722,plain,
% 29.09/19.36 (~(f1(c2, c1) = c2)),
% 29.09/19.36 inference(unit_resolution,[status(thm)],[12197, 20721, 121, 120])).
% 29.09/19.36 tff(20723,plain,
% 29.09/19.36 (f1(c2, c1) = c1),
% 29.09/19.36 inference(unit_resolution,[status(thm)],[10113, 20722])).
% 29.09/19.36 tff(20724,plain,
% 29.09/19.36 (f1(f7(c1), c1) = c1),
% 29.09/19.36 inference(unit_resolution,[status(thm)],[20670, 20723, 120])).
% 29.09/19.36 tff(20725,plain,
% 29.09/19.36 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c1) = c3) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (~(f1(f7(c1), c1) = c1)) | (~big_f(f7(c1), f1(f7(c1), c1))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (f7(c1) = c3) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (~(f1(f7(c1), c1) = c1)) | (~big_f(f7(c1), f1(f7(c1), c1))))),
% 29.09/19.36 inference(rewrite,[status(thm)],[])).
% 29.09/19.36 tff(20726,plain,
% 29.09/19.36 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c1) = c3) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (~(f1(f7(c1), c1) = c1)) | (~big_f(f7(c1), f1(f7(c1), c1))))),
% 29.09/19.36 inference(quant_inst,[status(thm)],[])).
% 29.09/19.36 tff(20727,plain,
% 29.09/19.36 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (f7(c1) = c3) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (~(f1(f7(c1), c1) = c1)) | (~big_f(f7(c1), f1(f7(c1), c1)))),
% 29.09/19.36 inference(modus_ponens,[status(thm)],[20726, 20725])).
% 29.09/19.36 tff(20728,plain,
% 29.09/19.36 ($false),
% 29.09/19.36 inference(unit_resolution,[status(thm)],[20727, 447, 20706, 20485, 20724, 20721, 20709, 66])).
% 29.09/19.36 tff(20729,plain,(big_f(c1, c1) | big_f(c2, c2) | (~(f4(c4) = c1)) | (f7(c1) = c1) | (f10(c2) = c2) | (f7(c2) = c2) | (~(c3 = c1))), inference(lemma,lemma(discharge,[]))).
% 29.09/19.36 tff(20730,plain,
% 29.09/19.36 (~(c3 = c1)),
% 29.09/19.36 inference(unit_resolution,[status(thm)],[20729, 20481, 115, 11752, 89, 17, 121])).
% 29.09/19.36 tff(20731,plain,
% 29.09/19.36 (c3 = c2),
% 29.09/19.36 inference(unit_resolution,[status(thm)],[180, 20730])).
% 29.09/19.36 tff(20732,plain,
% 29.09/19.36 ((f10(c2) = c3) <=> (f10(c2) = c2)),
% 29.09/19.36 inference(monotonicity,[status(thm)],[20731])).
% 29.09/19.36 tff(20733,plain,
% 29.09/19.36 ((f10(c2) = c2) <=> (f10(c2) = c3)),
% 29.09/19.36 inference(symmetry,[status(thm)],[20732])).
% 29.09/19.36 tff(20734,plain,
% 29.09/19.36 ((f10(c2) = c2) <=> (f7(c2) = c3)),
% 29.09/19.36 inference(transitivity,[status(thm)],[20733, 12103])).
% 29.09/19.36 tff(20735,plain,
% 29.09/19.36 ((~(f10(c2) = c2)) <=> (~(f7(c2) = c3))),
% 29.09/19.36 inference(monotonicity,[status(thm)],[20734])).
% 29.09/19.36 tff(20736,plain,
% 29.09/19.36 (~(f7(c2) = c3)),
% 29.09/19.36 inference(modus_ponens,[status(thm)],[89, 20735])).
% 29.09/19.36 tff(20737,plain,
% 29.09/19.36 ((f10(c2) = c2) <=> (c1 = c3)),
% 29.09/19.36 inference(transitivity,[status(thm)],[20733, 12095])).
% 29.09/19.36 tff(20738,plain,
% 29.09/19.36 ((~(f10(c2) = c2)) <=> (~(c1 = c3))),
% 29.09/19.36 inference(monotonicity,[status(thm)],[20737])).
% 29.09/19.36 tff(20739,plain,
% 29.09/19.36 (~(c1 = c3)),
% 29.09/19.36 inference(modus_ponens,[status(thm)],[89, 20738])).
% 29.09/19.36 tff(20740,plain,
% 29.09/19.36 (c2 = c4),
% 29.09/19.36 inference(unit_resolution,[status(thm)],[9203, 20739, 121, 12167, 20480, 20736, 120, 17])).
% 29.09/19.36 tff(20741,plain,
% 29.09/19.36 (~big_f(f7(c2), f7(c2))),
% 29.09/19.36 inference(unit_resolution,[status(thm)],[8374, 20480, 22])).
% 29.09/19.36 tff(20742,plain,
% 29.09/19.36 (big_f(c2, f7(c2)) <=> big_f(c2, f10(c2))),
% 29.09/19.36 inference(monotonicity,[status(thm)],[12101])).
% 29.09/19.36 tff(20743,plain,
% 29.09/19.36 (big_f(c2, f10(c2)) <=> big_f(c2, f7(c2))),
% 29.09/19.36 inference(symmetry,[status(thm)],[20742])).
% 29.09/19.36 tff(20744,plain,
% 29.09/19.36 (big_f(c2, c1) <=> big_f(c2, f7(c2))),
% 29.09/19.36 inference(transitivity,[status(thm)],[15252, 20743])).
% 29.09/19.36 tff(20745,plain,
% 29.09/19.36 (big_f(c2, f7(c2))),
% 29.09/19.36 inference(modus_ponens,[status(thm)],[20463, 20744])).
% 29.09/19.36 tff(20746,plain,
% 29.09/19.36 ((f7(c2) = c4) <=> (f10(c2) = c4)),
% 29.09/19.36 inference(monotonicity,[status(thm)],[12101])).
% 29.09/19.36 tff(20747,plain,
% 29.09/19.36 ((f10(c2) = c4) <=> (f7(c2) = c4)),
% 29.09/19.36 inference(symmetry,[status(thm)],[20746])).
% 29.09/19.36 tff(20748,plain,
% 29.09/19.36 (c4 = c2),
% 29.09/19.36 inference(symmetry,[status(thm)],[20740])).
% 29.09/19.36 tff(20749,plain,
% 29.09/19.36 ((f10(c2) = c4) <=> (f10(c2) = c2)),
% 29.09/19.36 inference(monotonicity,[status(thm)],[20748])).
% 29.09/19.36 tff(20750,plain,
% 29.09/19.36 ((f10(c2) = c2) <=> (f10(c2) = c4)),
% 29.09/19.36 inference(symmetry,[status(thm)],[20749])).
% 29.09/19.36 tff(20751,plain,
% 29.09/19.36 ((f10(c2) = c2) <=> (f7(c2) = c4)),
% 29.09/19.36 inference(transitivity,[status(thm)],[20750, 20747])).
% 29.09/19.36 tff(20752,plain,
% 29.09/19.36 ((~(f10(c2) = c2)) <=> (~(f7(c2) = c4))),
% 29.09/19.36 inference(monotonicity,[status(thm)],[20751])).
% 29.09/19.36 tff(20753,plain,
% 29.09/19.36 (~(f7(c2) = c4)),
% 29.09/19.36 inference(modus_ponens,[status(thm)],[89, 20752])).
% 29.09/19.36 tff(20754,plain,
% 29.09/19.36 (~(f3(c1, c2) = c2)),
% 29.09/19.36 inference(unit_resolution,[status(thm)],[16240, 20753, 17, 20745, 20736, 12167, 20741])).
% 29.09/19.36 tff(20755,plain,
% 29.09/19.36 (c2 = c3),
% 29.09/19.36 inference(modus_ponens,[status(thm)],[20731, 78])).
% 29.09/19.36 tff(20756,plain,
% 29.09/19.36 (big_f(f7(c2), c1) <=> big_f(f10(c2), f10(c2))),
% 29.09/19.36 inference(transitivity,[status(thm)],[17570, 17569])).
% 29.09/19.36 tff(20757,plain,
% 29.09/19.36 ((~big_f(f7(c2), c1)) <=> (~big_f(f10(c2), f10(c2)))),
% 29.09/19.36 inference(monotonicity,[status(thm)],[20756])).
% 29.09/19.36 tff(20758,plain,
% 29.09/19.36 (~big_f(f10(c2), f10(c2))),
% 29.09/19.36 inference(modus_ponens,[status(thm)],[20480, 20757])).
% 29.09/19.36 tff(20759,plain,
% 29.09/19.36 ((~(f10(c2) = c2)) <=> (~(f10(c2) = c4))),
% 29.09/19.36 inference(monotonicity,[status(thm)],[20750])).
% 29.09/19.36 tff(20760,plain,
% 29.09/19.36 (~(f10(c2) = c4)),
% 29.09/19.36 inference(modus_ponens,[status(thm)],[89, 20759])).
% 29.09/19.36 tff(20761,plain,
% 29.09/19.36 (f8(c2) = f8(c3)),
% 29.09/19.36 inference(symmetry,[status(thm)],[13045])).
% 29.09/19.36 tff(20762,plain,
% 29.09/19.36 (c2 = f8(c3)),
% 29.09/19.36 inference(transitivity,[status(thm)],[13152, 20761])).
% 29.09/19.36 tff(20763,plain,
% 29.09/19.36 (f3(c1, c2) = f3(f10(c2), f8(c3))),
% 29.09/19.36 inference(monotonicity,[status(thm)],[99, 20762])).
% 29.09/19.36 tff(20764,plain,
% 29.09/19.36 (f3(f10(c2), f8(c3)) = f3(c1, c2)),
% 29.09/19.36 inference(symmetry,[status(thm)],[20763])).
% 29.09/19.36 tff(20765,plain,
% 29.09/19.36 (f3(f10(c2), f8(c3)) = f3(c1, f8(c3))),
% 29.09/19.36 inference(monotonicity,[status(thm)],[94])).
% 29.09/19.36 tff(20766,plain,
% 29.09/19.36 (f3(c1, f8(c3)) = f3(f10(c2), f8(c3))),
% 29.09/19.36 inference(symmetry,[status(thm)],[20765])).
% 29.09/19.36 tff(20767,plain,
% 29.09/19.36 (f3(c1, f8(c3)) = f3(c1, c2)),
% 29.09/19.36 inference(transitivity,[status(thm)],[20766, 20764])).
% 29.09/19.36 tff(20768,plain,
% 29.09/19.36 ((f3(c1, f8(c3)) = c2) <=> (f3(c1, c2) = c2)),
% 29.09/19.36 inference(monotonicity,[status(thm)],[20767])).
% 29.09/19.36 tff(20769,plain,
% 29.09/19.36 ((f3(c1, c2) = c2) <=> (f3(c1, f8(c3)) = c2)),
% 29.09/19.36 inference(symmetry,[status(thm)],[20768])).
% 29.09/19.36 tff(20770,plain,
% 29.09/19.36 ((~(f3(c1, c2) = c2)) <=> (~(f3(c1, f8(c3)) = c2))),
% 29.09/19.36 inference(monotonicity,[status(thm)],[20769])).
% 29.09/19.36 tff(20771,plain,
% 29.09/19.36 (~(f3(c1, f8(c3)) = c2)),
% 29.09/19.36 inference(modus_ponens,[status(thm)],[12777, 20770])).
% 29.09/19.36 tff(20772,plain,
% 29.09/19.36 (f3(c1, f8(c3)) = c1),
% 29.09/19.36 inference(unit_resolution,[status(thm)],[7123, 20771])).
% 29.09/19.36 tff(20773,plain,
% 29.09/19.36 ((c2 = f8(c2)) <=> (c2 = f8(f7(f4(c4))))),
% 29.09/19.36 inference(symmetry,[status(thm)],[17578])).
% 29.09/19.36 tff(20774,plain,
% 29.09/19.36 ((c2 = f8(c2)) <=> (f8(f7(f4(c4))) = c2)),
% 29.09/19.36 inference(transitivity,[status(thm)],[20773, 106])).
% 29.09/19.36 tff(20775,plain,
% 29.09/19.36 (f8(f7(f4(c4))) = c2),
% 29.09/19.36 inference(modus_ponens,[status(thm)],[13152, 20774])).
% 29.09/19.36 tff(20776,plain,
% 29.09/19.36 (~(f1(c1, c2) = c1)),
% 29.09/19.36 inference(unit_resolution,[status(thm)],[16433, 20772, 8218, 9495, 20775, 347, 11752, 1335, 17])).
% 29.09/19.36 tff(20777,plain,
% 29.09/19.36 (f1(c1, c2) = c2),
% 29.09/19.36 inference(unit_resolution,[status(thm)],[841, 20776])).
% 29.09/19.36 tff(20778,plain,
% 29.09/19.36 (f3(f10(c2), f1(c1, c2)) = f3(c1, c2)),
% 29.09/19.36 inference(monotonicity,[status(thm)],[94, 20777])).
% 29.09/19.36 tff(20779,plain,
% 29.09/19.36 (f3(f10(c2), f1(c1, c2)) = f10(c2)),
% 29.09/19.36 inference(transitivity,[status(thm)],[20778, 20763, 20765, 20772, 99])).
% 29.09/19.36 tff(20780,plain,
% 29.09/19.36 (big_f(f3(f10(c2), f1(c1, c2)), f10(c2)) <=> big_f(f10(c2), f10(c2))),
% 29.09/19.36 inference(monotonicity,[status(thm)],[20779])).
% 29.09/19.36 tff(20781,plain,
% 29.09/19.36 (big_f(f10(c2), f10(c2)) <=> big_f(f3(f10(c2), f1(c1, c2)), f10(c2))),
% 29.09/19.36 inference(symmetry,[status(thm)],[20780])).
% 29.09/19.36 tff(20782,plain,
% 29.09/19.36 ((~big_f(f10(c2), f10(c2))) <=> (~big_f(f3(f10(c2), f1(c1, c2)), f10(c2)))),
% 29.09/19.36 inference(monotonicity,[status(thm)],[20781])).
% 29.09/19.36 tff(20783,assumption,(~big_f(f10(c2), f10(c2))), introduced(assumption)).
% 29.09/19.36 tff(20784,plain,
% 29.09/19.36 (~big_f(f3(f10(c2), f1(c1, c2)), f10(c2))),
% 29.09/19.36 inference(modus_ponens,[status(thm)],[20783, 20782])).
% 29.09/19.36 tff(20785,plain,
% 29.09/19.36 (f1(c1, f1(c1, c2)) = f1(c1, c2)),
% 29.09/19.36 inference(monotonicity,[status(thm)],[20777])).
% 29.09/19.36 tff(20786,plain,
% 29.09/19.36 (f1(c1, f1(c1, c2)) = c2),
% 29.09/19.36 inference(transitivity,[status(thm)],[20785, 20777])).
% 29.09/19.36 tff(20787,plain,
% 29.09/19.36 (big_f(c1, f1(c1, f1(c1, c2))) <=> big_f(c1, c2)),
% 29.09/19.36 inference(monotonicity,[status(thm)],[20786])).
% 29.09/19.36 tff(20788,plain,
% 29.09/19.36 (big_f(c1, c2) <=> big_f(c1, f1(c1, f1(c1, c2)))),
% 29.09/19.36 inference(symmetry,[status(thm)],[20787])).
% 29.09/19.36 tff(20789,plain,
% 29.09/19.36 (big_f(c1, f1(c1, f1(c1, c2)))),
% 29.09/19.36 inference(modus_ponens,[status(thm)],[2865, 20788])).
% 29.09/19.36 tff(20790,plain,
% 29.09/19.36 ((f3(f10(c2), f1(c1, c2)) = f1(c1, c2)) <=> (f3(f10(c2), f1(c1, c2)) = c2)),
% 29.09/19.36 inference(monotonicity,[status(thm)],[20777])).
% 29.09/19.36 tff(20791,plain,
% 29.09/19.36 ((f3(f10(c2), f1(c1, c2)) = c2) <=> (f3(f10(c2), f1(c1, c2)) = f1(c1, c2))),
% 29.09/19.36 inference(symmetry,[status(thm)],[20790])).
% 29.09/19.36 tff(20792,plain,
% 29.09/19.36 ((f3(f10(c2), f1(c1, c2)) = c2) <=> (f10(c2) = c2)),
% 29.09/19.36 inference(monotonicity,[status(thm)],[20779])).
% 29.09/19.36 tff(20793,plain,
% 29.09/19.36 ((f10(c2) = c2) <=> (f3(f10(c2), f1(c1, c2)) = c2)),
% 29.09/19.36 inference(symmetry,[status(thm)],[20792])).
% 29.09/19.36 tff(20794,plain,
% 29.09/19.36 ((f10(c2) = c2) <=> (f3(f10(c2), f1(c1, c2)) = f1(c1, c2))),
% 29.09/19.36 inference(transitivity,[status(thm)],[20793, 20791])).
% 29.09/19.37 tff(20795,plain,
% 29.09/19.37 ((~(f10(c2) = c2)) <=> (~(f3(f10(c2), f1(c1, c2)) = f1(c1, c2)))),
% 29.09/19.37 inference(monotonicity,[status(thm)],[20794])).
% 29.09/19.37 tff(20796,plain,
% 29.09/19.37 (~(f3(f10(c2), f1(c1, c2)) = f1(c1, c2))),
% 29.09/19.37 inference(modus_ponens,[status(thm)],[89, 20795])).
% 29.09/19.37 tff(20797,plain,
% 29.09/19.37 ($false),
% 29.09/19.37 inference(unit_resolution,[status(thm)],[19981, 20796, 20785, 15519, 12100, 20789, 20784])).
% 29.09/19.37 tff(20798,plain,((~(c2 = f8(c2))) | (f10(c2) = c4) | (f10(c2) = c2) | (~(c3 = c2)) | big_f(f10(c2), f10(c2)) | (~big_f(c1, c2)) | big_f(f7(c2), f7(c2)) | (f7(c2) = c4) | (~(f7(c1) = c2)) | (~(f4(c4) = c1)) | (f7(c2) = c2) | (f3(c1, c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 29.09/19.37 tff(20799,plain,
% 29.09/19.37 (~(c2 = f8(c2))),
% 29.09/19.37 inference(unit_resolution,[status(thm)],[20798, 20760, 89, 20731, 20758, 2865, 20741, 20753, 120, 11752, 17, 20754])).
% 29.09/19.37 tff(20800,plain,
% 29.09/19.37 ((c2 = f5(c2)) | (c2 = f8(c2))),
% 29.09/19.37 inference(unit_resolution,[status(thm)],[12297, 1659, 89, 17, 12167, 20464])).
% 29.09/19.37 tff(20801,plain,
% 29.09/19.37 (c2 = f5(c2)),
% 29.09/19.37 inference(unit_resolution,[status(thm)],[20800, 20799])).
% 29.09/19.37 tff(20802,plain,
% 29.09/19.37 (f5(c2) = c2),
% 29.09/19.37 inference(modus_ponens,[status(thm)],[20801, 1280])).
% 29.09/19.37 tff(20803,plain,
% 29.09/19.37 (~(f1(c2, c1) = c2)),
% 29.09/19.37 inference(unit_resolution,[status(thm)],[16448, 20802, 120, 11752, 20755, 17, 12167, 20741, 20754, 16, 230, 20740])).
% 29.09/19.37 tff(20804,plain,
% 29.09/19.37 (f1(c2, c1) = c1),
% 29.09/19.37 inference(unit_resolution,[status(thm)],[10113, 20803])).
% 29.09/19.37 tff(20805,plain,
% 29.09/19.37 (c1 = f1(c2, c1)),
% 29.09/19.37 inference(symmetry,[status(thm)],[20804])).
% 29.09/19.37 tff(20806,plain,
% 29.09/19.37 (f3(c1, c2) = f3(f1(c2, c1), c2)),
% 29.09/19.37 inference(monotonicity,[status(thm)],[20805])).
% 29.09/19.37 tff(20807,plain,
% 29.09/19.37 (f3(f1(c2, c1), c2) = f3(c1, c2)),
% 29.09/19.37 inference(symmetry,[status(thm)],[20806])).
% 29.09/19.37 tff(20808,plain,
% 29.09/19.37 (f5(c2) = c2),
% 29.09/19.37 inference(symmetry,[status(thm)],[20801])).
% 29.09/19.37 tff(20809,plain,
% 29.09/19.37 (f5(f10(c1)) = c2),
% 29.09/19.37 inference(transitivity,[status(thm)],[16012, 20808])).
% 29.09/19.37 tff(20810,plain,
% 29.09/19.37 (f1(f5(f10(c1)), c1) = f1(c2, c1)),
% 29.09/19.37 inference(monotonicity,[status(thm)],[20809])).
% 29.09/19.37 tff(20811,plain,
% 29.09/19.37 (f1(c2, c1) = f1(f5(f10(c1)), c1)),
% 29.09/19.37 inference(symmetry,[status(thm)],[20810])).
% 29.09/19.37 tff(20812,plain,
% 29.09/19.37 (f1(c2, c1) = f1(f5(c2), f5(c1))),
% 29.09/19.37 inference(transitivity,[status(thm)],[20811, 16015])).
% 29.09/19.37 tff(20813,plain,
% 29.09/19.37 (f3(f1(c2, c1), c2) = f3(f1(f5(c2), f5(c1)), c2)),
% 29.09/19.37 inference(monotonicity,[status(thm)],[20812])).
% 29.09/19.37 tff(20814,plain,
% 29.09/19.37 (f3(f1(f5(c2), f5(c1)), c2) = f3(f1(c2, c1), c2)),
% 29.09/19.37 inference(symmetry,[status(thm)],[20813])).
% 29.09/19.37 tff(20815,plain,
% 29.09/19.37 (f3(f1(f5(c2), f5(c1)), c2) = f3(c1, c2)),
% 29.09/19.37 inference(transitivity,[status(thm)],[20814, 20807])).
% 29.09/19.37 tff(20816,plain,
% 29.09/19.37 ((f3(f1(f5(c2), f5(c1)), c2) = c1) <=> (f3(c1, c2) = c1)),
% 29.09/19.37 inference(monotonicity,[status(thm)],[20815])).
% 29.09/19.37 tff(20817,plain,
% 29.09/19.37 ((f3(f1(f5(c2), f5(c1)), c2) = c1) <=> (c1 = f3(c1, c2))),
% 29.09/19.37 inference(transitivity,[status(thm)],[20816, 13151])).
% 29.09/19.37 tff(20818,plain,
% 29.09/19.37 ((c1 = f3(c1, c2)) <=> (f3(f1(f5(c2), f5(c1)), c2) = c1)),
% 29.09/19.37 inference(symmetry,[status(thm)],[20817])).
% 29.09/19.37 tff(20819,plain,
% 29.09/19.37 (c1 = f3(c1, c2)),
% 29.09/19.37 inference(unit_resolution,[status(thm)],[16084, 20802, 20754, 16, 230, 120])).
% 29.09/19.37 tff(20820,plain,
% 29.09/19.37 (f3(f1(f5(c2), f5(c1)), c2) = c1),
% 29.09/19.37 inference(modus_ponens,[status(thm)],[20819, 20818])).
% 29.09/19.37 tff(20821,plain,
% 29.09/19.37 ((f1(f5(c2), f5(c1)) = c1) <=> (f1(f5(f10(c1)), c1) = c1)),
% 29.09/19.37 inference(monotonicity,[status(thm)],[16014])).
% 29.09/19.37 tff(20822,plain,
% 29.09/19.37 ((f1(f5(f10(c1)), c1) = c1) <=> (f1(f5(c2), f5(c1)) = c1)),
% 29.09/19.37 inference(symmetry,[status(thm)],[20821])).
% 29.09/19.37 tff(20823,plain,
% 29.09/19.37 ((f1(f5(f10(c1)), c1) = c1) <=> (f1(c2, c1) = c1)),
% 29.09/19.37 inference(monotonicity,[status(thm)],[20810])).
% 29.09/19.37 tff(20824,plain,
% 29.09/19.37 ((f1(c2, c1) = c1) <=> (f1(f5(f10(c1)), c1) = c1)),
% 29.09/19.37 inference(symmetry,[status(thm)],[20823])).
% 29.09/19.37 tff(20825,plain,
% 29.09/19.37 ((f1(c2, c1) = c1) <=> (f1(f5(c2), f5(c1)) = c1)),
% 29.09/19.37 inference(transitivity,[status(thm)],[20824, 20822])).
% 29.09/19.37 tff(20826,plain,
% 29.09/19.37 (f1(f5(c2), f5(c1)) = c1),
% 29.09/19.37 inference(modus_ponens,[status(thm)],[20804, 20825])).
% 29.09/19.37 tff(20827,plain,
% 29.09/19.37 ((f10(c2) = c2) <=> (c1 = c4)),
% 29.09/19.37 inference(transitivity,[status(thm)],[20750, 15385])).
% 29.09/19.37 tff(20828,plain,
% 29.09/19.37 ((~(f10(c2) = c2)) <=> (~(c1 = c4))),
% 29.09/19.37 inference(monotonicity,[status(thm)],[20827])).
% 29.09/19.37 tff(20829,plain,
% 29.09/19.37 (~(c1 = c4)),
% 29.09/19.37 inference(modus_ponens,[status(thm)],[89, 20828])).
% 29.09/19.37 tff(20830,plain,
% 29.09/19.37 ((f3(f1(f5(c2), f5(c1)), c2) = c2) <=> (f3(f1(c2, c1), c2) = c2)),
% 29.09/19.37 inference(monotonicity,[status(thm)],[20814])).
% 29.09/19.37 tff(20831,plain,
% 29.09/19.37 ((f3(f1(c2, c1), c2) = c2) <=> (f3(f1(f5(c2), f5(c1)), c2) = c2)),
% 29.09/19.37 inference(symmetry,[status(thm)],[20830])).
% 29.09/19.37 tff(20832,plain,
% 29.09/19.37 ((f3(f1(c2, c1), c2) = c2) <=> (f3(c1, c2) = c2)),
% 29.09/19.37 inference(monotonicity,[status(thm)],[20807])).
% 29.09/19.37 tff(20833,plain,
% 29.09/19.37 ((f3(c1, c2) = c2) <=> (f3(f1(c2, c1), c2) = c2)),
% 29.09/19.37 inference(symmetry,[status(thm)],[20832])).
% 29.09/19.37 tff(20834,plain,
% 29.09/19.37 ((f3(c1, c2) = c2) <=> (f3(f1(f5(c2), f5(c1)), c2) = c2)),
% 29.09/19.37 inference(transitivity,[status(thm)],[20833, 20831])).
% 29.09/19.37 tff(20835,plain,
% 29.09/19.37 ((~(f3(c1, c2) = c2)) <=> (~(f3(f1(f5(c2), f5(c1)), c2) = c2))),
% 29.09/19.37 inference(monotonicity,[status(thm)],[20834])).
% 29.09/19.37 tff(20836,plain,
% 29.09/19.37 (~(f3(f1(f5(c2), f5(c1)), c2) = c2)),
% 29.09/19.37 inference(modus_ponens,[status(thm)],[20754, 20835])).
% 29.09/19.37 tff(20837,plain,
% 29.09/19.37 (f1(c1, c2) = c2),
% 29.09/19.37 inference(unit_resolution,[status(thm)],[16489, 20836, 20481, 20829, 20826, 20739])).
% 29.09/19.37 tff(20838,plain,
% 29.09/19.37 (f3(f10(c2), f1(c1, c2)) = f3(c1, c2)),
% 29.09/19.37 inference(monotonicity,[status(thm)],[94, 20837])).
% 29.09/19.37 tff(20839,plain,
% 29.09/19.37 (f3(f10(c2), f1(c1, c2)) = f10(c2)),
% 29.09/19.37 inference(transitivity,[status(thm)],[20838, 20806, 20813, 20820, 99])).
% 29.09/19.37 tff(20840,plain,
% 29.09/19.37 (big_f(f3(f10(c2), f1(c1, c2)), f10(c2)) <=> big_f(f10(c2), f10(c2))),
% 29.09/19.37 inference(monotonicity,[status(thm)],[20839])).
% 29.09/19.37 tff(20841,plain,
% 29.09/19.37 (big_f(f10(c2), f10(c2)) <=> big_f(f3(f10(c2), f1(c1, c2)), f10(c2))),
% 29.09/19.37 inference(symmetry,[status(thm)],[20840])).
% 29.09/19.37 tff(20842,plain,
% 29.09/19.37 ((~big_f(f10(c2), f10(c2))) <=> (~big_f(f3(f10(c2), f1(c1, c2)), f10(c2)))),
% 29.09/19.37 inference(monotonicity,[status(thm)],[20841])).
% 29.09/19.37 tff(20843,plain,
% 29.09/19.37 (~big_f(f3(f10(c2), f1(c1, c2)), f10(c2))),
% 29.09/19.37 inference(modus_ponens,[status(thm)],[20758, 20842])).
% 29.09/19.37 tff(20844,plain,
% 29.09/19.37 (f1(c1, f1(c1, c2)) = f1(c1, c2)),
% 29.09/19.37 inference(monotonicity,[status(thm)],[20837])).
% 29.09/19.37 tff(20845,plain,
% 29.09/19.37 (f1(c1, f1(c1, c2)) = c2),
% 29.09/19.37 inference(transitivity,[status(thm)],[20844, 20837])).
% 29.09/19.37 tff(20846,plain,
% 29.09/19.37 (big_f(c1, f1(c1, f1(c1, c2))) <=> big_f(c1, c2)),
% 29.09/19.37 inference(monotonicity,[status(thm)],[20845])).
% 29.09/19.37 tff(20847,plain,
% 29.09/19.37 (big_f(c1, c2) <=> big_f(c1, f1(c1, f1(c1, c2)))),
% 29.09/19.37 inference(symmetry,[status(thm)],[20846])).
% 29.09/19.37 tff(20848,plain,
% 29.09/19.37 (big_f(c1, f1(c1, f1(c1, c2)))),
% 29.09/19.37 inference(modus_ponens,[status(thm)],[2865, 20847])).
% 29.09/19.37 tff(20849,plain,
% 29.09/19.37 ((f3(f10(c2), f1(c1, c2)) = f1(c1, c2)) <=> (f3(f10(c2), f1(c1, c2)) = c2)),
% 29.09/19.37 inference(monotonicity,[status(thm)],[20837])).
% 29.09/19.37 tff(20850,plain,
% 29.09/19.37 ((f3(f10(c2), f1(c1, c2)) = c2) <=> (f3(f10(c2), f1(c1, c2)) = f1(c1, c2))),
% 29.09/19.37 inference(symmetry,[status(thm)],[20849])).
% 29.09/19.37 tff(20851,plain,
% 29.09/19.37 ((f3(f10(c2), f1(c1, c2)) = c2) <=> (f10(c2) = c2)),
% 29.09/19.37 inference(monotonicity,[status(thm)],[20839])).
% 29.09/19.37 tff(20852,plain,
% 29.09/19.37 ((f10(c2) = c2) <=> (f3(f10(c2), f1(c1, c2)) = c2)),
% 29.09/19.37 inference(symmetry,[status(thm)],[20851])).
% 29.09/19.37 tff(20853,plain,
% 29.09/19.37 ((f10(c2) = c2) <=> (f3(f10(c2), f1(c1, c2)) = f1(c1, c2))),
% 29.09/19.37 inference(transitivity,[status(thm)],[20852, 20850])).
% 29.09/19.37 tff(20854,plain,
% 29.09/19.37 ((~(f10(c2) = c2)) <=> (~(f3(f10(c2), f1(c1, c2)) = f1(c1, c2)))),
% 29.09/19.37 inference(monotonicity,[status(thm)],[20853])).
% 29.09/19.37 tff(20855,plain,
% 29.09/19.37 (~(f3(f10(c2), f1(c1, c2)) = f1(c1, c2))),
% 29.09/19.37 inference(modus_ponens,[status(thm)],[89, 20854])).
% 29.09/19.37 tff(20856,plain,
% 29.09/19.37 ($false),
% 29.09/19.37 inference(unit_resolution,[status(thm)],[19981, 20855, 20844, 20760, 20739, 20848, 20843])).
% 29.09/19.37 tff(20857,plain,((~(f5(c1) = c1)) | (f10(c2) = c2) | (~(f10(c1) = c2)) | (~big_f(c1, c2)) | (~(f4(c4) = c1)) | (f7(c2) = c2) | big_f(c2, c2) | (f7(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.09/19.37 tff(20858,plain,
% 29.09/19.37 (~(f5(c1) = c1)),
% 29.09/19.37 inference(unit_resolution,[status(thm)],[20857, 2865, 16, 89, 11752, 17, 121, 115])).
% 29.09/19.37 tff(20859,plain,
% 29.09/19.37 (f5(c1) = c2),
% 29.09/19.37 inference(unit_resolution,[status(thm)],[1708, 20858])).
% 29.09/19.37 tff(20860,plain,
% 29.09/19.37 (c2 = f5(f10(c2))),
% 29.09/19.37 inference(modus_ponens,[status(thm)],[20859, 17567])).
% 29.09/19.37 tff(20861,plain,
% 29.09/19.37 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (~(c2 = f5(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (~(c2 = f5(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2))),
% 29.09/19.37 inference(rewrite,[status(thm)],[])).
% 29.09/19.37 tff(20862,plain,
% 29.09/19.37 (((~(c2 = f5(f10(c2)))) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2) | (~(c2 = f8(c2)))) <=> ((f10(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (~(c2 = f5(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2))),
% 29.09/19.37 inference(rewrite,[status(thm)],[])).
% 29.09/19.37 tff(20863,plain,
% 29.09/19.37 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c2 = f5(f10(c2)))) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2) | (~(c2 = f8(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (~(c2 = f5(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2)))),
% 29.09/19.37 inference(monotonicity,[status(thm)],[20862])).
% 29.09/19.37 tff(20864,plain,
% 29.09/19.37 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c2 = f5(f10(c2)))) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2) | (~(c2 = f8(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (~(c2 = f5(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2))),
% 29.09/19.37 inference(transitivity,[status(thm)],[20863, 20861])).
% 29.09/19.37 tff(20865,plain,
% 29.09/19.37 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c2 = f5(f10(c2)))) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2) | (~(c2 = f8(c2))))),
% 29.09/19.37 inference(quant_inst,[status(thm)],[])).
% 29.09/19.37 tff(20866,plain,
% 29.09/19.37 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (~(c2 = f5(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2)),
% 29.09/19.37 inference(modus_ponens,[status(thm)],[20865, 20864])).
% 29.09/19.37 tff(20867,plain,
% 29.09/19.37 (~(c2 = f8(c2))),
% 29.09/19.37 inference(unit_resolution,[status(thm)],[20866, 1745, 89, 15473, 20860, 17563, 17558])).
% 29.09/19.37 tff(20868,plain,
% 29.09/19.37 (~(f8(f7(f4(c4))) = c2)),
% 29.09/19.37 inference(unit_resolution,[status(thm)],[17582, 20867, 120, 11752])).
% 29.09/19.37 tff(20869,plain,
% 29.09/19.37 (f8(f7(f4(c4))) = c1),
% 29.09/19.37 inference(unit_resolution,[status(thm)],[13371, 20868])).
% 29.09/19.37 tff(20870,plain,
% 29.09/19.37 (big_f(c1, f10(f7(f4(c4)))) <=> big_f(c1, f10(c2))),
% 29.09/19.37 inference(monotonicity,[status(thm)],[18373])).
% 29.09/19.37 tff(20871,plain,
% 29.09/19.37 (big_f(c1, f10(f7(f4(c4)))) <=> big_f(c1, c1)),
% 29.09/19.37 inference(transitivity,[status(thm)],[20870, 17594, 17568])).
% 29.09/19.37 tff(20872,plain,
% 29.09/19.37 ((f10(f7(f4(c4))) = f7(f4(c4))) <=> (f10(c2) = c2)),
% 29.09/19.37 inference(monotonicity,[status(thm)],[18373, 18372])).
% 29.09/19.37 tff(20873,plain,
% 29.09/19.37 ((f10(c2) = c2) <=> (f10(f7(f4(c4))) = f7(f4(c4)))),
% 29.09/19.37 inference(symmetry,[status(thm)],[20872])).
% 29.09/19.37 tff(20874,plain,
% 29.09/19.37 ((~(f10(c2) = c2)) <=> (~(f10(f7(f4(c4))) = f7(f4(c4))))),
% 29.19/19.37 inference(monotonicity,[status(thm)],[20873])).
% 29.19/19.37 tff(20875,plain,
% 29.19/19.37 (~(f10(f7(f4(c4))) = f7(f4(c4)))),
% 29.19/19.37 inference(modus_ponens,[status(thm)],[89, 20874])).
% 29.19/19.37 tff(20876,plain,
% 29.19/19.37 (c2 = f5(c1)),
% 29.19/19.37 inference(modus_ponens,[status(thm)],[20859, 155])).
% 29.19/19.37 tff(20877,plain,
% 29.19/19.37 (c1 = f8(f7(f4(c4)))),
% 29.19/19.37 inference(modus_ponens,[status(thm)],[20869, 8518])).
% 29.19/19.37 tff(20878,plain,
% 29.19/19.37 (big_f(c1, f10(f7(f4(c4))))),
% 29.19/19.37 inference(unit_resolution,[status(thm)],[8593, 20877, 115, 1726, 20876, 20875])).
% 29.19/19.37 tff(20879,plain,
% 29.19/19.37 (big_f(c1, c1)),
% 29.19/19.37 inference(modus_ponens,[status(thm)],[20878, 20871])).
% 29.19/19.37 tff(20880,plain,
% 29.19/19.37 (c2 = c4),
% 29.19/19.37 inference(unit_resolution,[status(thm)],[17678, 20879, 121, 94, 16, 2865, 115, 2])).
% 29.19/19.37 tff(20881,plain,
% 29.19/19.37 (c4 = c2),
% 29.19/19.37 inference(symmetry,[status(thm)],[20880])).
% 29.19/19.37 tff(20882,plain,
% 29.19/19.37 ((f10(c2) = c4) <=> (f10(c2) = c2)),
% 29.19/19.37 inference(monotonicity,[status(thm)],[20881])).
% 29.19/19.37 tff(20883,plain,
% 29.19/19.37 ((f10(c2) = c2) <=> (f10(c2) = c4)),
% 29.19/19.37 inference(symmetry,[status(thm)],[20882])).
% 29.19/19.37 tff(20884,plain,
% 29.19/19.37 ((f10(c2) = c2) <=> (c1 = c4)),
% 29.19/19.37 inference(transitivity,[status(thm)],[20883, 15385])).
% 29.19/19.37 tff(20885,plain,
% 29.19/19.37 ((~(f10(c2) = c2)) <=> (~(c1 = c4))),
% 29.19/19.37 inference(monotonicity,[status(thm)],[20884])).
% 29.19/19.37 tff(20886,plain,
% 29.19/19.37 (~(c1 = c4)),
% 29.19/19.37 inference(modus_ponens,[status(thm)],[89, 20885])).
% 29.19/19.37 tff(20887,plain,
% 29.19/19.37 (~(c3 = c1)),
% 29.19/19.37 inference(unit_resolution,[status(thm)],[20399, 20886, 115, 11752, 89, 17574, 121, 17, 20879])).
% 29.19/19.37 tff(20888,plain,
% 29.19/19.37 (c3 = c2),
% 29.19/19.37 inference(unit_resolution,[status(thm)],[180, 20887])).
% 29.19/19.37 tff(20889,plain,
% 29.19/19.37 (big_f(f7(c2), f10(c2)) <=> big_f(f7(c2), c1)),
% 29.19/19.37 inference(symmetry,[status(thm)],[17570])).
% 29.19/19.37 tff(20890,plain,
% 29.19/19.37 (big_f(f10(c2), f10(c2)) <=> big_f(f7(c2), f10(c2))),
% 29.19/19.37 inference(symmetry,[status(thm)],[17569])).
% 29.19/19.37 tff(20891,plain,
% 29.19/19.37 (big_f(c1, f10(f7(f4(c4)))) <=> big_f(f7(c2), c1)),
% 29.19/19.37 inference(transitivity,[status(thm)],[20870, 17594, 20890, 20889])).
% 29.19/19.37 tff(20892,plain,
% 29.19/19.37 (big_f(f7(c2), c1)),
% 29.19/19.37 inference(modus_ponens,[status(thm)],[20878, 20891])).
% 29.19/19.37 tff(20893,plain,
% 29.19/19.37 (~big_f(c3, f2(c3))),
% 29.19/19.37 inference(unit_resolution,[status(thm)],[8256, 20888, 121, 2])).
% 29.19/19.37 tff(20894,plain,
% 29.19/19.37 (big_f(f3(c1, c1), c1)),
% 29.19/19.37 inference(unit_resolution,[status(thm)],[20432, 20893, 22, 20892, 20886, 20888])).
% 29.19/19.37 tff(20895,plain,
% 29.19/19.37 (big_f(f3(f10(c2), f10(c2)), f10(c2))),
% 29.19/19.37 inference(modus_ponens,[status(thm)],[20894, 17592])).
% 29.19/19.37 tff(20896,plain,
% 29.19/19.37 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f10(c2) = c2) | (~(c2 = f5(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))) | (f3(f10(c2), f10(c2)) = f8(c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(c2) = c2) | (~(c2 = f5(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))) | (f3(f10(c2), f10(c2)) = f8(c2)))),
% 29.19/19.37 inference(rewrite,[status(thm)],[])).
% 29.19/19.37 tff(20897,plain,
% 29.19/19.37 (((~(c2 = f5(f10(c2)))) | (f10(c2) = c2) | (f3(f10(c2), f10(c2)) = f8(c2)) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2)) <=> ((f10(c2) = c2) | (~(c2 = f5(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))) | (f3(f10(c2), f10(c2)) = f8(c2)))),
% 29.19/19.37 inference(rewrite,[status(thm)],[])).
% 29.19/19.37 tff(20898,plain,
% 29.19/19.37 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c2 = f5(f10(c2)))) | (f10(c2) = c2) | (f3(f10(c2), f10(c2)) = f8(c2)) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f10(c2) = c2) | (~(c2 = f5(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))) | (f3(f10(c2), f10(c2)) = f8(c2))))),
% 29.19/19.37 inference(monotonicity,[status(thm)],[20897])).
% 29.19/19.37 tff(20899,plain,
% 29.19/19.37 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c2 = f5(f10(c2)))) | (f10(c2) = c2) | (f3(f10(c2), f10(c2)) = f8(c2)) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(c2) = c2) | (~(c2 = f5(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))) | (f3(f10(c2), f10(c2)) = f8(c2)))),
% 29.19/19.37 inference(transitivity,[status(thm)],[20898, 20896])).
% 29.19/19.37 tff(20900,plain,
% 29.19/19.37 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c2 = f5(f10(c2)))) | (f10(c2) = c2) | (f3(f10(c2), f10(c2)) = f8(c2)) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2))),
% 29.19/19.37 inference(quant_inst,[status(thm)],[])).
% 29.19/19.37 tff(20901,plain,
% 29.19/19.37 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(c2) = c2) | (~(c2 = f5(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))) | (f3(f10(c2), f10(c2)) = f8(c2))),
% 29.19/19.37 inference(modus_ponens,[status(thm)],[20900, 20899])).
% 29.19/19.37 tff(20902,plain,
% 29.19/19.37 (f3(f10(c2), f10(c2)) = f8(c2)),
% 29.19/19.37 inference(unit_resolution,[status(thm)],[20901, 705, 89, 20860, 17563, 20895, 17558])).
% 29.19/19.37 tff(20903,plain,
% 29.19/19.37 (f3(f10(c2), f10(c2)) = f10(c2)),
% 29.19/19.37 inference(transitivity,[status(thm)],[20902, 17586, 20869, 99])).
% 29.19/19.37 tff(20904,plain,
% 29.19/19.37 ((~(f10(c2) = c2)) <=> (~(f10(c2) = c4))),
% 29.19/19.37 inference(monotonicity,[status(thm)],[20883])).
% 29.19/19.37 tff(20905,plain,
% 29.19/19.37 (~(f10(c2) = c4)),
% 29.19/19.37 inference(modus_ponens,[status(thm)],[89, 20904])).
% 29.19/19.37 tff(20906,plain,
% 29.19/19.37 (c4 = c2),
% 29.19/19.37 inference(modus_ponens,[status(thm)],[20880, 8721])).
% 29.19/19.37 tff(20907,plain,
% 29.19/19.37 (~(f2(c3) = c1)),
% 29.19/19.37 inference(unit_resolution,[status(thm)],[1424, 20894, 20906, 20888, 20893])).
% 29.19/19.37 tff(20908,plain,
% 29.19/19.37 (f2(c3) = c2),
% 29.19/19.37 inference(unit_resolution,[status(thm)],[1273, 20907])).
% 29.19/19.37 tff(20909,plain,
% 29.19/19.37 (c2 = f2(c2)),
% 29.19/19.37 inference(unit_resolution,[status(thm)],[4867, 20908, 20888])).
% 29.19/19.37 tff(20910,plain,
% 29.19/19.37 (c2 = c3),
% 29.19/19.37 inference(modus_ponens,[status(thm)],[20888, 78])).
% 29.19/19.37 tff(20911,plain,
% 29.19/19.37 (~(f3(f10(c2), f10(c2)) = f10(c2))),
% 29.19/19.37 inference(unit_resolution,[status(thm)],[20459, 1398, 121, 20910, 20909, 20905, 20895])).
% 29.19/19.37 tff(20912,plain,
% 29.19/19.37 ($false),
% 29.19/19.37 inference(unit_resolution,[status(thm)],[20911, 20903])).
% 29.19/19.37 tff(20913,plain,(big_f(c2, c1) | (~(f4(c4) = c1)) | big_f(c2, c2) | (f10(c2) = c2) | (f7(c1) = c1) | (f7(c2) = c2) | (~(f10(c1) = c2)) | (~big_f(c1, c2))), inference(lemma,lemma(discharge,[]))).
% 29.19/19.37 tff(20914,plain,
% 29.19/19.37 (big_f(c2, c1)),
% 29.19/19.37 inference(unit_resolution,[status(thm)],[20913, 121, 15706, 17538, 115, 17, 15, 15920])).
% 29.19/19.37 tff(20915,plain,
% 29.19/19.37 (big_f(c2, f10(c2))),
% 29.19/19.37 inference(modus_ponens,[status(thm)],[20914, 17542])).
% 29.19/19.37 tff(20916,plain,
% 29.19/19.37 (~big_f(f7(c2), c1)),
% 29.19/19.37 inference(unit_resolution,[status(thm)],[20479, 20915, 17, 15921, 17538, 17552, 115])).
% 29.19/19.37 tff(20917,plain,
% 29.19/19.37 (big_f(f7(c2), c1) <=> big_f(f7(c2), f10(c2))),
% 29.19/19.37 inference(monotonicity,[status(thm)],[12231])).
% 29.19/19.37 tff(20918,plain,
% 29.19/19.37 (big_f(f7(c2), f10(c2)) <=> big_f(f7(c2), c1)),
% 29.19/19.37 inference(symmetry,[status(thm)],[20917])).
% 29.19/19.37 tff(20919,plain,
% 29.19/19.37 (f7(c2) = f10(c2)),
% 29.19/19.37 inference(transitivity,[status(thm)],[292, 12231])).
% 29.19/19.37 tff(20920,plain,
% 29.19/19.37 (big_f(f7(c2), f10(c2)) <=> big_f(f10(c2), f10(c2))),
% 29.19/19.37 inference(monotonicity,[status(thm)],[20919])).
% 29.19/19.37 tff(20921,plain,
% 29.19/19.37 (big_f(f10(c2), f10(c2)) <=> big_f(f7(c2), f10(c2))),
% 29.19/19.37 inference(symmetry,[status(thm)],[20920])).
% 29.19/19.37 tff(20922,plain,
% 29.19/19.37 (big_f(c1, c1) <=> big_f(f10(c2), f10(c2))),
% 29.19/19.37 inference(monotonicity,[status(thm)],[12231, 12231])).
% 29.19/19.37 tff(20923,plain,
% 29.19/19.37 (big_f(c1, c1) <=> big_f(f7(c2), c1)),
% 29.19/19.37 inference(transitivity,[status(thm)],[20922, 20921, 20918])).
% 29.19/19.37 tff(20924,plain,
% 29.19/19.37 (big_f(f7(c2), c1)),
% 29.19/19.37 inference(modus_ponens,[status(thm)],[4932, 20923])).
% 29.19/19.37 tff(20925,plain,
% 29.19/19.37 ($false),
% 29.19/19.37 inference(unit_resolution,[status(thm)],[333, 20924])).
% 29.19/19.37 tff(20926,plain,((~big_f(c1, c1)) | big_f(f7(c2), c1) | (~(f7(c2) = c1)) | (~(f10(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.19/19.37 tff(20927,plain,
% 29.19/19.37 (~big_f(c1, c1)),
% 29.19/19.37 inference(unit_resolution,[status(thm)],[20926, 20916, 22, 17539])).
% 29.19/19.37 tff(20928,plain,
% 29.19/19.37 (~(c3 = c1)),
% 29.19/19.37 inference(unit_resolution,[status(thm)],[20729, 20927, 115, 15706, 17538, 17, 121])).
% 29.19/19.37 tff(20929,plain,
% 29.19/19.37 (c3 = c2),
% 29.19/19.37 inference(unit_resolution,[status(thm)],[180, 20928])).
% 29.19/19.37 tff(20930,plain,
% 29.19/19.37 ((f10(c2) = c3) <=> (f10(c2) = c2)),
% 29.19/19.37 inference(monotonicity,[status(thm)],[20929])).
% 29.19/19.37 tff(20931,plain,
% 29.19/19.37 ((f10(c2) = c2) <=> (f10(c2) = c3)),
% 29.19/19.37 inference(symmetry,[status(thm)],[20930])).
% 29.19/19.37 tff(20932,plain,
% 29.19/19.37 ((f10(c2) = c2) <=> (f7(c2) = c3)),
% 29.19/19.37 inference(transitivity,[status(thm)],[20931, 17550])).
% 29.19/19.37 tff(20933,plain,
% 29.19/19.37 ((~(f10(c2) = c2)) <=> (~(f7(c2) = c3))),
% 29.19/19.37 inference(monotonicity,[status(thm)],[20932])).
% 29.19/19.37 tff(20934,plain,
% 29.19/19.37 (~(f7(c2) = c3)),
% 29.19/19.37 inference(modus_ponens,[status(thm)],[17538, 20933])).
% 29.19/19.37 tff(20935,plain,
% 29.19/19.37 ((c1 = c3) <=> (f10(c2) = c3)),
% 29.19/19.37 inference(monotonicity,[status(thm)],[17541])).
% 29.19/19.37 tff(20936,plain,
% 29.19/19.37 ((f10(c2) = c3) <=> (c1 = c3)),
% 29.19/19.37 inference(symmetry,[status(thm)],[20935])).
% 29.19/19.37 tff(20937,plain,
% 29.19/19.37 ((f10(c2) = c2) <=> (c1 = c3)),
% 29.19/19.37 inference(transitivity,[status(thm)],[20931, 20936])).
% 29.19/19.37 tff(20938,plain,
% 29.19/19.37 ((~(f10(c2) = c2)) <=> (~(c1 = c3))),
% 29.19/19.37 inference(monotonicity,[status(thm)],[20937])).
% 29.19/19.37 tff(20939,plain,
% 29.19/19.37 (~(c1 = c3)),
% 29.19/19.37 inference(modus_ponens,[status(thm)],[17538, 20938])).
% 29.19/19.37 tff(20940,plain,
% 29.19/19.37 (c2 = c4),
% 29.19/19.37 inference(unit_resolution,[status(thm)],[9203, 20939, 121, 15921, 20916, 20934, 120, 17])).
% 29.19/19.37 tff(20941,plain,
% 29.19/19.37 (c4 = c2),
% 29.19/19.37 inference(symmetry,[status(thm)],[20940])).
% 29.19/19.37 tff(20942,plain,
% 29.19/19.37 ((f10(c2) = c4) <=> (f10(c2) = c2)),
% 29.19/19.37 inference(monotonicity,[status(thm)],[20941])).
% 29.19/19.37 tff(20943,plain,
% 29.19/19.37 ((f10(c2) = c2) <=> (f10(c2) = c4)),
% 29.19/19.37 inference(symmetry,[status(thm)],[20942])).
% 29.19/19.37 tff(20944,plain,
% 29.19/19.37 ((~(f10(c2) = c2)) <=> (~(f10(c2) = c4))),
% 29.19/19.37 inference(monotonicity,[status(thm)],[20943])).
% 29.19/19.37 tff(20945,plain,
% 29.19/19.37 (~(f10(c2) = c4)),
% 29.19/19.37 inference(modus_ponens,[status(thm)],[17538, 20944])).
% 29.19/19.37 tff(20946,plain,
% 29.19/19.37 (big_f(f7(c2), f10(c2)) <=> big_f(f10(c2), f10(c2))),
% 29.19/19.37 inference(monotonicity,[status(thm)],[17548])).
% 29.19/19.37 tff(20947,plain,
% 29.19/19.37 (big_f(f7(c2), c1) <=> big_f(f7(c2), f10(c2))),
% 29.19/19.37 inference(monotonicity,[status(thm)],[17541])).
% 29.19/19.37 tff(20948,plain,
% 29.19/19.37 (big_f(f7(c2), c1) <=> big_f(f10(c2), f10(c2))),
% 29.19/19.37 inference(transitivity,[status(thm)],[20947, 20946])).
% 29.19/19.37 tff(20949,plain,
% 29.19/19.37 ((~big_f(f7(c2), c1)) <=> (~big_f(f10(c2), f10(c2)))),
% 29.19/19.37 inference(monotonicity,[status(thm)],[20948])).
% 29.19/19.37 tff(20950,plain,
% 29.19/19.37 (~big_f(f10(c2), f10(c2))),
% 29.19/19.37 inference(modus_ponens,[status(thm)],[20916, 20949])).
% 29.19/19.37 tff(20951,plain,
% 29.19/19.37 (~big_f(f7(c2), f7(c2))),
% 29.19/19.37 inference(unit_resolution,[status(thm)],[8374, 20916, 22])).
% 29.19/19.37 tff(20952,plain,
% 29.19/19.37 ((~big_f(c2, c2)) <=> (~big_f(f7(f10(c2)), c2))),
% 29.19/19.37 inference(monotonicity,[status(thm)],[17547])).
% 29.19/19.37 tff(20953,plain,
% 29.19/19.37 (~big_f(f7(f10(c2)), c2)),
% 29.19/19.37 inference(modus_ponens,[status(thm)],[121, 20952])).
% 29.19/19.37 tff(20954,plain,
% 29.19/19.37 ((f7(f10(c2)) = f10(c2)) <=> (c2 = f10(c2))),
% 29.19/19.37 inference(monotonicity,[status(thm)],[17545])).
% 29.19/19.37 tff(20955,plain,
% 29.19/19.37 ((f7(f10(c2)) = f10(c2)) <=> (f10(c2) = c2)),
% 29.19/19.37 inference(transitivity,[status(thm)],[20954, 4987])).
% 29.19/19.37 tff(20956,plain,
% 29.19/19.37 ((f10(c2) = c2) <=> (f7(f10(c2)) = f10(c2))),
% 29.19/19.37 inference(symmetry,[status(thm)],[20955])).
% 29.19/19.37 tff(20957,plain,
% 29.19/19.37 ((~(f10(c2) = c2)) <=> (~(f7(f10(c2)) = f10(c2)))),
% 29.19/19.37 inference(monotonicity,[status(thm)],[20956])).
% 29.19/19.37 tff(20958,plain,
% 29.19/19.37 (~(f7(f10(c2)) = f10(c2))),
% 29.19/19.37 inference(modus_ponens,[status(thm)],[17538, 20957])).
% 29.19/19.38 tff(20959,plain,
% 29.19/19.38 (f5(f10(c2)) = f5(c1)),
% 29.19/19.38 inference(monotonicity,[status(thm)],[17539])).
% 29.19/19.38 tff(20960,plain,
% 29.19/19.38 ((c2 = f5(f10(c2))) <=> (c2 = f5(c1))),
% 29.19/19.38 inference(monotonicity,[status(thm)],[20959])).
% 29.19/19.38 tff(20961,plain,
% 29.19/19.38 ((c2 = f5(c1)) <=> (c2 = f5(f10(c2)))),
% 29.19/19.38 inference(symmetry,[status(thm)],[20960])).
% 29.19/19.38 tff(20962,plain,
% 29.19/19.38 ((f5(c1) = c2) <=> (c2 = f5(f10(c2)))),
% 29.19/19.38 inference(transitivity,[status(thm)],[155, 20961])).
% 29.19/19.38 tff(20963,plain,
% 29.19/19.38 (~(f5(c1) = c1)),
% 29.19/19.38 inference(unit_resolution,[status(thm)],[20857, 15920, 15, 17538, 15706, 17, 121, 115])).
% 29.19/19.38 tff(20964,plain,
% 29.19/19.38 (f5(c1) = c2),
% 29.19/19.38 inference(unit_resolution,[status(thm)],[1708, 20963])).
% 29.19/19.38 tff(20965,plain,
% 29.19/19.38 (c2 = f5(f10(c2))),
% 29.19/19.38 inference(modus_ponens,[status(thm)],[20964, 20962])).
% 29.19/19.38 tff(20966,plain,
% 29.19/19.38 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(c2 = f5(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(c2 = f5(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2))),
% 29.19/19.38 inference(rewrite,[status(thm)],[])).
% 29.19/19.38 tff(20967,plain,
% 29.19/19.38 (((~(c2 = f5(f10(c2)))) | (f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2)) <=> ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(c2 = f5(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2))),
% 29.19/19.38 inference(rewrite,[status(thm)],[])).
% 29.19/19.38 tff(20968,plain,
% 29.19/19.38 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c2 = f5(f10(c2)))) | (f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(c2 = f5(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2)))),
% 29.19/19.38 inference(monotonicity,[status(thm)],[20967])).
% 29.19/19.38 tff(20969,plain,
% 29.19/19.38 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c2 = f5(f10(c2)))) | (f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(c2 = f5(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2))),
% 29.19/19.38 inference(transitivity,[status(thm)],[20968, 20966])).
% 29.19/19.38 tff(20970,plain,
% 29.19/19.38 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c2 = f5(f10(c2)))) | (f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2))),
% 29.19/19.38 inference(quant_inst,[status(thm)],[])).
% 29.19/19.38 tff(20971,plain,
% 29.19/19.38 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(c2 = f5(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2)),
% 29.19/19.38 inference(modus_ponens,[status(thm)],[20970, 20969])).
% 29.19/19.38 tff(20972,plain,
% 29.19/19.38 (c2 = f8(c2)),
% 29.19/19.38 inference(unit_resolution,[status(thm)],[20971, 705, 17538, 20915, 20965, 20958, 20953])).
% 29.19/19.38 tff(20973,plain,
% 29.19/19.38 ((f7(c2) = c4) <=> (f10(c2) = c4)),
% 29.19/19.38 inference(monotonicity,[status(thm)],[17548])).
% 29.19/19.38 tff(20974,plain,
% 29.19/19.38 ((f10(c2) = c4) <=> (f7(c2) = c4)),
% 29.19/19.38 inference(symmetry,[status(thm)],[20973])).
% 29.19/19.38 tff(20975,plain,
% 29.19/19.38 ((f10(c2) = c2) <=> (f7(c2) = c4)),
% 29.19/19.38 inference(transitivity,[status(thm)],[20943, 20974])).
% 29.19/19.38 tff(20976,plain,
% 29.19/19.38 ((~(f10(c2) = c2)) <=> (~(f7(c2) = c4))),
% 29.19/19.38 inference(monotonicity,[status(thm)],[20975])).
% 29.19/19.38 tff(20977,plain,
% 29.19/19.38 (~(f7(c2) = c4)),
% 29.19/19.38 inference(modus_ponens,[status(thm)],[17538, 20976])).
% 29.19/19.38 tff(20978,plain,
% 29.19/19.38 (big_f(c2, f7(c2)) <=> big_f(c2, f10(c2))),
% 29.19/19.38 inference(monotonicity,[status(thm)],[17548])).
% 29.19/19.38 tff(20979,plain,
% 29.19/19.38 (big_f(c2, f10(c2)) <=> big_f(c2, f7(c2))),
% 29.19/19.38 inference(symmetry,[status(thm)],[20978])).
% 29.19/19.38 tff(20980,plain,
% 29.19/19.38 (big_f(c2, c1) <=> big_f(c2, f7(c2))),
% 29.19/19.38 inference(transitivity,[status(thm)],[17542, 20979])).
% 29.19/19.38 tff(20981,plain,
% 29.19/19.38 (big_f(c2, f7(c2))),
% 29.19/19.38 inference(modus_ponens,[status(thm)],[20914, 20980])).
% 29.19/19.38 tff(20982,plain,
% 29.19/19.38 (~(f3(c1, c2) = c2)),
% 29.19/19.38 inference(unit_resolution,[status(thm)],[16240, 20977, 17, 20981, 20934, 15921, 20951])).
% 29.19/19.38 tff(20983,plain,
% 29.19/19.38 ($false),
% 29.19/19.38 inference(unit_resolution,[status(thm)],[20798, 20982, 20977, 17538, 20972, 20929, 15920, 20951, 20950, 120, 15706, 17, 20945])).
% 29.19/19.38 tff(20984,plain,(big_f(c2, c2) | (f7(c2) = c2) | (f7(c1) = c1) | (f10(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.19/19.38 tff(20985,plain,
% 29.19/19.38 (big_f(c2, c2)),
% 29.19/19.38 inference(unit_resolution,[status(thm)],[20984, 17, 115, 3])).
% 29.19/19.38 tff(20986,plain,
% 29.19/19.38 (big_f(f7(f10(c2)), c2)),
% 29.19/19.38 inference(modus_ponens,[status(thm)],[20985, 17547])).
% 29.19/19.38 tff(20987,plain,
% 29.19/19.38 (f10(f7(c2)) = f10(f10(c2))),
% 29.19/19.38 inference(monotonicity,[status(thm)],[17548])).
% 29.19/19.38 tff(20988,plain,
% 29.19/19.38 (f10(f7(c2)) = c2),
% 29.19/19.38 inference(transitivity,[status(thm)],[20987, 17540, 15])).
% 29.19/19.38 tff(20989,plain,
% 29.19/19.38 ((f10(f7(c2)) = f7(c2)) <=> (c2 = f10(c2))),
% 29.19/19.38 inference(monotonicity,[status(thm)],[20988, 17548])).
% 29.19/19.38 tff(20990,plain,
% 29.19/19.38 ((f10(f7(c2)) = f7(c2)) <=> (f10(c2) = c2)),
% 29.19/19.38 inference(transitivity,[status(thm)],[20989, 4987])).
% 29.19/19.38 tff(20991,plain,
% 29.19/19.38 ((f10(c2) = c2) <=> (f10(f7(c2)) = f7(c2))),
% 29.19/19.38 inference(symmetry,[status(thm)],[20990])).
% 29.19/19.38 tff(20992,plain,
% 29.19/19.38 ((~(f10(c2) = c2)) <=> (~(f10(f7(c2)) = f7(c2)))),
% 29.19/19.38 inference(monotonicity,[status(thm)],[20991])).
% 29.19/19.38 tff(20993,plain,
% 29.19/19.38 (~(f10(f7(c2)) = f7(c2))),
% 29.19/19.38 inference(modus_ponens,[status(thm)],[17538, 20992])).
% 29.19/19.38 tff(20994,plain,
% 29.19/19.38 (f7(f7(c2)) = f7(f10(c2))),
% 29.19/19.38 inference(monotonicity,[status(thm)],[17548])).
% 29.19/19.38 tff(20995,plain,
% 29.19/19.38 (f7(f7(c2)) = c2),
% 29.19/19.38 inference(transitivity,[status(thm)],[20994, 17544, 120])).
% 29.19/19.38 tff(20996,plain,
% 29.19/19.38 (big_f(f7(f7(c2)), f7(c2)) <=> big_f(c2, f10(c2))),
% 29.19/19.38 inference(monotonicity,[status(thm)],[20995, 17548])).
% 29.19/19.38 tff(20997,plain,
% 29.19/19.38 (big_f(c2, f10(c2)) <=> big_f(f7(f7(c2)), f7(c2))),
% 29.19/19.38 inference(symmetry,[status(thm)],[20996])).
% 29.19/19.38 tff(20998,plain,
% 29.19/19.38 (big_f(c2, c1) <=> big_f(f7(f7(c2)), f7(c2))),
% 29.19/19.38 inference(transitivity,[status(thm)],[17542, 20997])).
% 29.19/19.38 tff(20999,plain,
% 29.19/19.38 ((c3 = c1) <=> (f7(c2) = c3)),
% 29.19/19.38 inference(transitivity,[status(thm)],[68, 12094, 12103])).
% 29.19/19.38 tff(21000,plain,
% 29.19/19.38 ((~(c3 = c1)) <=> (~(f7(c2) = c3))),
% 29.19/19.38 inference(monotonicity,[status(thm)],[20999])).
% 29.19/19.38 tff(21001,plain,
% 29.19/19.38 ((~big_f(c2, c1)) <=> (~big_f(c2, f7(c2)))),
% 29.19/19.38 inference(monotonicity,[status(thm)],[20744])).
% 29.19/19.38 tff(21002,plain,
% 29.19/19.38 (~big_f(c2, f7(c2))),
% 29.19/19.38 inference(modus_ponens,[status(thm)],[2, 21001])).
% 29.19/19.38 tff(21003,plain,
% 29.19/19.38 (~(c2 = c4)),
% 29.19/19.38 inference(unit_resolution,[status(thm)],[16877, 15336, 1345, 9331, 17, 11752])).
% 29.19/19.38 tff(21004,plain,
% 29.19/19.38 (~(c4 = c2)),
% 29.19/19.38 inference(modus_ponens,[status(thm)],[21003, 8722])).
% 29.19/19.38 tff(21005,plain,
% 29.19/19.38 (c4 = c1),
% 29.19/19.38 inference(unit_resolution,[status(thm)],[461, 21004])).
% 29.19/19.38 tff(21006,plain,
% 29.19/19.38 (c1 = c4),
% 29.19/19.38 inference(symmetry,[status(thm)],[21005])).
% 29.19/19.38 tff(21007,plain,
% 29.19/19.38 (f10(c2) = c4),
% 29.19/19.38 inference(transitivity,[status(thm)],[94, 21006])).
% 29.19/19.38 tff(21008,plain,
% 29.19/19.38 (f4(f10(c2)) = f4(c4)),
% 29.19/19.38 inference(monotonicity,[status(thm)],[21007])).
% 29.19/19.38 tff(21009,plain,
% 29.19/19.38 (f4(c4) = f4(f10(c2))),
% 29.19/19.38 inference(symmetry,[status(thm)],[21008])).
% 29.19/19.38 tff(21010,plain,
% 29.19/19.38 (f10(c2) = f4(f10(c2))),
% 29.19/19.38 inference(transitivity,[status(thm)],[94, 16651, 21009])).
% 29.19/19.38 tff(21011,plain,
% 29.19/19.38 (f10(f7(c2)) = f10(f10(c2))),
% 29.19/19.38 inference(monotonicity,[status(thm)],[12101])).
% 29.19/19.38 tff(21012,plain,
% 29.19/19.38 (f10(f7(c2)) = c2),
% 29.19/19.38 inference(transitivity,[status(thm)],[21011, 15299, 16])).
% 29.19/19.38 tff(21013,plain,
% 29.19/19.38 (big_f(f7(c2), f10(f7(c2))) <=> big_f(c1, c2)),
% 29.19/19.38 inference(monotonicity,[status(thm)],[22, 21012])).
% 29.19/19.38 tff(21014,plain,
% 29.19/19.38 (big_f(c1, c2) <=> big_f(f7(c2), f10(f7(c2)))),
% 29.19/19.38 inference(symmetry,[status(thm)],[21013])).
% 29.19/19.38 tff(21015,plain,
% 29.19/19.38 (c4 = f10(c2)),
% 29.19/19.38 inference(transitivity,[status(thm)],[21005, 99])).
% 29.19/19.38 tff(21016,plain,
% 29.19/19.38 (big_f(c2, c4) <=> big_f(c2, f10(c2))),
% 29.19/19.38 inference(monotonicity,[status(thm)],[21015])).
% 29.19/19.38 tff(21017,plain,
% 29.19/19.38 (big_f(c2, f10(c2)) <=> big_f(c2, c4)),
% 29.19/19.38 inference(symmetry,[status(thm)],[21016])).
% 29.19/19.38 tff(21018,plain,
% 29.19/19.38 ((~big_f(c2, f10(c2))) <=> (~big_f(c2, c4))),
% 29.19/19.38 inference(monotonicity,[status(thm)],[21017])).
% 29.19/19.38 tff(21019,plain,
% 29.19/19.38 (~big_f(c2, c4)),
% 29.19/19.38 inference(modus_ponens,[status(thm)],[15517, 21018])).
% 29.19/19.38 tff(21020,plain,
% 29.19/19.38 (~(f1(c2, c2) = c2)),
% 29.19/19.38 inference(unit_resolution,[status(thm)],[16745, 873, 377, 1345, 12882])).
% 29.19/19.38 tff(21021,plain,
% 29.19/19.38 (f1(c2, c2) = c1),
% 29.19/19.38 inference(unit_resolution,[status(thm)],[5270, 21020])).
% 29.19/19.38 tff(21022,plain,
% 29.19/19.38 (f1(c2, c2) = f7(c2)),
% 29.19/19.38 inference(transitivity,[status(thm)],[21021, 342])).
% 29.19/19.38 tff(21023,plain,
% 29.19/19.38 (big_f(c2, f1(c2, c2)) <=> big_f(c2, f7(c2))),
% 29.19/19.38 inference(monotonicity,[status(thm)],[21022])).
% 29.19/19.38 tff(21024,plain,
% 29.19/19.38 (big_f(c2, f7(c2)) <=> big_f(c2, f1(c2, c2))),
% 29.19/19.38 inference(symmetry,[status(thm)],[21023])).
% 29.19/19.38 tff(21025,plain,
% 29.19/19.38 ((~big_f(c2, f7(c2))) <=> (~big_f(c2, f1(c2, c2)))),
% 29.19/19.38 inference(monotonicity,[status(thm)],[21024])).
% 29.19/19.38 tff(21026,plain,
% 29.19/19.38 (~big_f(c2, f1(c2, c2))),
% 29.19/19.38 inference(modus_ponens,[status(thm)],[9331, 21025])).
% 29.19/19.38 tff(21027,plain,
% 29.19/19.38 (big_f(c2, f1(c2, c2))),
% 29.19/19.38 inference(unit_resolution,[status(thm)],[16713, 21020, 377, 1345, 12882, 873])).
% 29.19/19.38 tff(21028,plain,
% 29.19/19.38 ($false),
% 29.19/19.38 inference(unit_resolution,[status(thm)],[21027, 21026])).
% 29.19/19.38 tff(21029,plain,((c2 = c4) | big_f(c2, f7(c2)) | (~(f7(c2) = c1)) | (c2 = c3) | (~big_f(c2, c2)) | big_f(f3(c2, c2), c2)), inference(lemma,lemma(discharge,[]))).
% 29.19/19.38 tff(21030,plain,
% 29.19/19.38 (big_f(f3(c2, c2), c2)),
% 29.19/19.38 inference(unit_resolution,[status(thm)],[21029, 15336, 22, 21003, 1345, 9331])).
% 29.19/19.38 tff(21031,plain,
% 29.19/19.38 (~big_f(c2, f1(c2, c2))),
% 29.19/19.38 inference(unit_resolution,[status(thm)],[14891, 5298, 9094, 3865])).
% 29.19/19.38 tff(21032,plain,
% 29.19/19.38 ($false),
% 29.19/19.38 inference(unit_resolution,[status(thm)],[16720, 969, 873, 377, 1828, 21031, 7387, 15356])).
% 29.19/19.38 tff(21033,plain,((f1(c2, c2) = c2) | (c2 = c4) | (c2 = c3) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | big_f(c2, c4)), inference(lemma,lemma(discharge,[]))).
% 29.19/19.38 tff(21034,plain,
% 29.19/19.38 (f1(c2, c2) = c2),
% 29.19/19.38 inference(unit_resolution,[status(thm)],[21033, 7387, 377, 873, 15356, 3865])).
% 29.19/19.38 tff(21035,plain,
% 29.19/19.38 (big_f(c2, f1(c2, c2)) <=> big_f(c2, c2)),
% 29.19/19.38 inference(monotonicity,[status(thm)],[21034])).
% 29.19/19.38 tff(21036,plain,
% 29.19/19.38 (big_f(c2, c2) <=> big_f(c2, f1(c2, c2))),
% 29.19/19.38 inference(symmetry,[status(thm)],[21035])).
% 29.19/19.38 tff(21037,plain,
% 29.19/19.38 (big_f(c2, f1(c2, c2))),
% 29.19/19.38 inference(modus_ponens,[status(thm)],[1345, 21036])).
% 29.19/19.38 tff(21038,plain,
% 29.19/19.38 ($false),
% 29.19/19.38 inference(unit_resolution,[status(thm)],[16755, 933, 873, 377, 21034, 21037, 7387, 15356])).
% 29.19/19.38 tff(21039,plain,((~(f3(c2, c2) = c2)) | (c2 = c4) | (c2 = c3) | (~big_f(f3(c2, c2), c2)) | (~big_f(c2, c2)) | big_f(c2, c4)), inference(lemma,lemma(discharge,[]))).
% 29.19/19.38 tff(21040,plain,
% 29.19/19.38 (~(f3(c2, c2) = c2)),
% 29.19/19.38 inference(unit_resolution,[status(thm)],[21039, 21003, 15336, 21030, 1345, 21019])).
% 29.19/19.38 tff(21041,plain,
% 29.19/19.38 (~big_f(f7(f10(c2)), f10(c2))),
% 29.19/19.38 inference(modus_ponens,[status(thm)],[15517, 17589])).
% 29.19/19.38 tff(21042,plain,
% 29.19/19.38 (big_f(f3(c2, c2), f10(f10(c2))) <=> big_f(f3(c2, c2), c2)),
% 29.19/19.38 inference(monotonicity,[status(thm)],[15300])).
% 29.19/19.38 tff(21043,plain,
% 29.19/19.38 (big_f(f3(c2, c2), c2) <=> big_f(f3(c2, c2), f10(f10(c2)))),
% 29.19/19.38 inference(symmetry,[status(thm)],[21042])).
% 29.19/19.38 tff(21044,plain,
% 29.19/19.38 (big_f(f3(c2, c2), f10(f10(c2)))),
% 29.19/19.38 inference(modus_ponens,[status(thm)],[21030, 21043])).
% 29.19/19.38 tff(21045,assumption,(big_f(f3(c2, c2), f10(f10(c2)))), introduced(assumption)).
% 29.19/19.38 tff(21046,plain,
% 29.19/19.38 ((f10(c2) = f5(f10(c2))) <=> (c1 = f5(c1))),
% 29.19/19.38 inference(monotonicity,[status(thm)],[11819, 11884])).
% 29.19/19.38 tff(21047,plain,
% 29.19/19.38 ((f10(c2) = f5(f10(c2))) <=> (f5(c1) = c1)),
% 29.19/19.38 inference(transitivity,[status(thm)],[21046, 128])).
% 29.19/19.38 tff(21048,plain,
% 29.19/19.38 ((f5(c1) = c1) <=> (f10(c2) = f5(f10(c2)))),
% 29.19/19.38 inference(symmetry,[status(thm)],[21047])).
% 29.19/19.38 tff(21049,plain,
% 29.19/19.38 (~(f5(c1) = c2)),
% 29.19/19.38 inference(unit_resolution,[status(thm)],[16765, 12679, 22, 377, 873, 1345, 9094, 3865])).
% 29.19/19.38 tff(21050,plain,
% 29.19/19.38 (f5(c1) = c1),
% 29.19/19.38 inference(unit_resolution,[status(thm)],[1708, 21049])).
% 29.19/19.38 tff(21051,plain,
% 29.19/19.38 (f10(c2) = f5(f10(c2))),
% 29.19/19.38 inference(modus_ponens,[status(thm)],[21050, 21048])).
% 29.19/19.38 tff(21052,plain,
% 29.19/19.38 ((f3(c2, c2) = f8(f10(c2))) <=> (f3(c2, c2) = f8(c1))),
% 29.19/19.38 inference(monotonicity,[status(thm)],[11820])).
% 29.19/19.38 tff(21053,plain,
% 29.19/19.38 ((f3(c2, c2) = f8(c1)) <=> (f3(c2, c2) = f8(f10(c2)))),
% 29.19/19.38 inference(symmetry,[status(thm)],[21052])).
% 29.19/19.38 tff(21054,plain,
% 29.19/19.38 (c4 = f10(c2)),
% 29.19/19.38 inference(transitivity,[status(thm)],[9094, 12231])).
% 29.19/19.38 tff(21055,plain,
% 29.19/19.38 (f4(c4) = f10(c2)),
% 29.19/19.38 inference(transitivity,[status(thm)],[11752, 12231])).
% 29.19/19.38 tff(21056,plain,
% 29.19/19.38 (big_f(f4(c4), c4) <=> big_f(f10(c2), f10(c2))),
% 29.19/19.38 inference(monotonicity,[status(thm)],[21055, 21054])).
% 29.19/19.38 tff(21057,plain,
% 29.19/19.38 (big_f(f10(c2), f10(c2)) <=> big_f(f4(c4), c4)),
% 29.19/19.38 inference(symmetry,[status(thm)],[21056])).
% 29.19/19.38 tff(21058,plain,
% 29.19/19.38 (big_f(c1, c1) <=> big_f(f4(c4), c4)),
% 29.19/19.38 inference(transitivity,[status(thm)],[20922, 21057])).
% 29.19/19.38 tff(21059,plain,
% 29.19/19.38 (big_f(c1, c1)),
% 29.19/19.38 inference(unit_resolution,[status(thm)],[19126, 27, 11752, 11819, 17, 172])).
% 29.19/19.38 tff(21060,plain,
% 29.19/19.38 (big_f(f4(c4), c4)),
% 29.19/19.38 inference(modus_ponens,[status(thm)],[21059, 21058])).
% 29.19/19.38 tff(21061,plain,
% 29.19/19.38 (~big_f(c1, f10(c1))),
% 29.19/19.38 inference(unit_resolution,[status(thm)],[12239, 27, 11819, 12230])).
% 29.19/19.38 tff(21062,plain,
% 29.19/19.38 (~big_f(f7(c1), f5(c1))),
% 29.19/19.38 inference(unit_resolution,[status(thm)],[289, 21050, 285])).
% 29.19/19.38 tff(21063,plain,
% 29.19/19.38 (~(f8(c1) = c1)),
% 29.19/19.38 inference(unit_resolution,[status(thm)],[18252, 21062, 115, 11819, 21061, 17094, 21060, 11752])).
% 29.19/19.38 tff(21064,plain,
% 29.19/19.38 (f8(c1) = c2),
% 29.19/19.38 inference(unit_resolution,[status(thm)],[1680, 21063])).
% 29.19/19.38 tff(21065,plain,
% 29.19/19.38 ((f3(c2, c2) = f8(c1)) <=> (f3(c2, c2) = c2)),
% 29.19/19.38 inference(monotonicity,[status(thm)],[21064])).
% 29.19/19.38 tff(21066,plain,
% 29.19/19.38 ((f3(c2, c2) = c2) <=> (f3(c2, c2) = f8(c1))),
% 29.19/19.38 inference(symmetry,[status(thm)],[21065])).
% 29.19/19.38 tff(21067,plain,
% 29.19/19.38 ((f3(c2, c2) = c2) <=> (f3(c2, c2) = f8(f10(c2)))),
% 29.19/19.38 inference(transitivity,[status(thm)],[21066, 21053])).
% 29.19/19.38 tff(21068,plain,
% 29.19/19.38 ((~(f3(c2, c2) = c2)) <=> (~(f3(c2, c2) = f8(f10(c2))))),
% 29.19/19.38 inference(monotonicity,[status(thm)],[21067])).
% 29.19/19.38 tff(21069,plain,
% 29.19/19.38 (~(f3(c2, c2) = f8(f10(c2)))),
% 29.19/19.38 inference(modus_ponens,[status(thm)],[12861, 21068])).
% 29.19/19.38 tff(21070,assumption,(~big_f(f7(f10(c2)), f10(c2))), introduced(assumption)).
% 29.19/19.38 tff(21071,plain,
% 29.19/19.38 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f10(f10(c2)) = f10(c2)) | (f7(f10(c2)) = f10(c2)) | (~(f10(c2) = f5(f10(c2)))) | big_f(f7(f10(c2)), f10(c2)) | (f3(c2, c2) = f8(f10(c2))) | (~big_f(f3(c2, c2), f10(f10(c2)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(f10(c2)) = f10(c2)) | (f7(f10(c2)) = f10(c2)) | (~(f10(c2) = f5(f10(c2)))) | big_f(f7(f10(c2)), f10(c2)) | (f3(c2, c2) = f8(f10(c2))) | (~big_f(f3(c2, c2), f10(f10(c2)))))),
% 29.19/19.38 inference(rewrite,[status(thm)],[])).
% 29.19/19.38 tff(21072,plain,
% 29.19/19.38 (((~(f10(c2) = f5(f10(c2)))) | (f10(f10(c2)) = f10(c2)) | (f3(c2, c2) = f8(f10(c2))) | (~big_f(f3(c2, c2), f10(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), f10(c2))) <=> ((f10(f10(c2)) = f10(c2)) | (f7(f10(c2)) = f10(c2)) | (~(f10(c2) = f5(f10(c2)))) | big_f(f7(f10(c2)), f10(c2)) | (f3(c2, c2) = f8(f10(c2))) | (~big_f(f3(c2, c2), f10(f10(c2)))))),
% 29.19/19.38 inference(rewrite,[status(thm)],[])).
% 29.19/19.38 tff(21073,plain,
% 29.19/19.38 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(f10(c2) = f5(f10(c2)))) | (f10(f10(c2)) = f10(c2)) | (f3(c2, c2) = f8(f10(c2))) | (~big_f(f3(c2, c2), f10(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), f10(c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f10(f10(c2)) = f10(c2)) | (f7(f10(c2)) = f10(c2)) | (~(f10(c2) = f5(f10(c2)))) | big_f(f7(f10(c2)), f10(c2)) | (f3(c2, c2) = f8(f10(c2))) | (~big_f(f3(c2, c2), f10(f10(c2))))))),
% 29.19/19.38 inference(monotonicity,[status(thm)],[21072])).
% 29.19/19.38 tff(21074,plain,
% 29.19/19.38 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(f10(c2) = f5(f10(c2)))) | (f10(f10(c2)) = f10(c2)) | (f3(c2, c2) = f8(f10(c2))) | (~big_f(f3(c2, c2), f10(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), f10(c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(f10(c2)) = f10(c2)) | (f7(f10(c2)) = f10(c2)) | (~(f10(c2) = f5(f10(c2)))) | big_f(f7(f10(c2)), f10(c2)) | (f3(c2, c2) = f8(f10(c2))) | (~big_f(f3(c2, c2), f10(f10(c2)))))),
% 29.19/19.38 inference(transitivity,[status(thm)],[21073, 21071])).
% 29.19/19.38 tff(21075,plain,
% 29.19/19.38 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(f10(c2) = f5(f10(c2)))) | (f10(f10(c2)) = f10(c2)) | (f3(c2, c2) = f8(f10(c2))) | (~big_f(f3(c2, c2), f10(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), f10(c2)))),
% 29.19/19.38 inference(quant_inst,[status(thm)],[])).
% 29.19/19.38 tff(21076,plain,
% 29.19/19.38 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(f10(c2)) = f10(c2)) | (f7(f10(c2)) = f10(c2)) | (~(f10(c2) = f5(f10(c2)))) | big_f(f7(f10(c2)), f10(c2)) | (f3(c2, c2) = f8(f10(c2))) | (~big_f(f3(c2, c2), f10(f10(c2))))),
% 29.19/19.38 inference(modus_ponens,[status(thm)],[21075, 21074])).
% 29.19/19.38 tff(21077,plain,
% 29.19/19.38 ((~(f10(c2) = f5(f10(c2)))) | (f3(c2, c2) = f8(f10(c2))) | (~big_f(f3(c2, c2), f10(f10(c2))))),
% 29.19/19.38 inference(unit_resolution,[status(thm)],[21076, 705, 11896, 11895, 21070])).
% 29.19/19.38 tff(21078,plain,
% 29.19/19.38 ($false),
% 29.19/19.38 inference(unit_resolution,[status(thm)],[21077, 21069, 21051, 21045])).
% 29.19/19.38 tff(21079,plain,(big_f(c1, c2) | (~big_f(f3(c2, c2), f10(f10(c2)))) | (f10(f10(c2)) = f10(c2)) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), f10(c2)) | (f3(c2, c2) = c2) | (~(f10(c2) = c1)) | (f7(c1) = c1) | (~(f4(c4) = c1)) | big_f(f7(c1), c1) | (c2 = c3) | (c2 = c4) | (~big_f(c2, c2)) | big_f(c2, c4) | (f7(c2) = c2) | (~(c3 = c1)) | (~(f10(f10(c2)) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.19/19.38 tff(21080,plain,
% 29.19/19.38 (big_f(c1, c2)),
% 29.19/19.38 inference(unit_resolution,[status(thm)],[21079, 21044, 15308, 17563, 21041, 21040, 94, 115, 11752, 285, 15336, 21003, 1345, 21019, 17, 172, 15300])).
% 29.19/19.38 tff(21081,plain,
% 29.19/19.38 (big_f(f7(c2), f10(f7(c2)))),
% 29.19/19.38 inference(modus_ponens,[status(thm)],[21080, 21014])).
% 29.19/19.38 tff(21082,plain,
% 29.19/19.38 ((f10(f7(c2)) = f7(c2)) <=> (c2 = f10(c2))),
% 29.19/19.38 inference(monotonicity,[status(thm)],[21012, 12101])).
% 29.19/19.38 tff(21083,plain,
% 29.19/19.38 ((f10(f7(c2)) = f7(c2)) <=> (f10(c2) = c2)),
% 29.19/19.38 inference(transitivity,[status(thm)],[21082, 4987])).
% 29.19/19.38 tff(21084,plain,
% 29.19/19.38 ((f10(c2) = c2) <=> (f10(f7(c2)) = f7(c2))),
% 29.19/19.38 inference(symmetry,[status(thm)],[21083])).
% 29.19/19.38 tff(21085,plain,
% 29.19/19.38 ((~(f10(c2) = c2)) <=> (~(f10(f7(c2)) = f7(c2)))),
% 29.19/19.38 inference(monotonicity,[status(thm)],[21084])).
% 29.19/19.38 tff(21086,plain,
% 29.19/19.38 (~(f10(f7(c2)) = f7(c2))),
% 29.19/19.38 inference(modus_ponens,[status(thm)],[89, 21085])).
% 29.19/19.38 tff(21087,plain,
% 29.19/19.38 (big_f(c2, f10(f7(c2))) <=> big_f(c2, c2)),
% 29.19/19.38 inference(monotonicity,[status(thm)],[21012])).
% 29.19/19.38 tff(21088,plain,
% 29.19/19.38 (big_f(c2, c2) <=> big_f(c2, f10(f7(c2)))),
% 29.19/19.38 inference(symmetry,[status(thm)],[21087])).
% 29.19/19.38 tff(21089,plain,
% 29.19/19.38 (big_f(c2, f10(f7(c2)))),
% 29.19/19.38 inference(modus_ponens,[status(thm)],[1345, 21088])).
% 29.19/19.38 tff(21090,plain,
% 29.19/19.38 (big_f(f7(c2), c2)),
% 29.19/19.38 inference(modus_ponens,[status(thm)],[21080, 12163])).
% 29.19/19.38 tff(21091,plain,
% 29.19/19.38 (~big_f(f7(c2), f7(c2))),
% 29.19/19.38 inference(unit_resolution,[status(thm)],[16899, 21090, 17, 21089, 21086, 21081])).
% 29.19/19.38 tff(21092,plain,
% 29.19/19.38 (~big_f(f7(c2), c1)),
% 29.19/19.38 inference(unit_resolution,[status(thm)],[17079, 21091, 22])).
% 29.19/19.38 tff(21093,plain,
% 29.19/19.38 (~big_f(c1, c1)),
% 29.19/19.38 inference(unit_resolution,[status(thm)],[20926, 21092, 22, 94])).
% 29.19/19.38 tff(21094,plain,
% 29.19/19.38 (~big_f(f10(c2), f10(c2))),
% 29.19/19.38 inference(modus_ponens,[status(thm)],[21093, 15265])).
% 29.19/19.38 tff(21095,assumption,(f10(c2) = f4(f10(c2))), introduced(assumption)).
% 29.19/19.38 tff(21096,plain,
% 29.19/19.38 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c2 = c3) | (~(f10(c2) = c4)) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (c2 = c3) | (~(f10(c2) = c4)) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2)))))),
% 29.19/19.38 inference(rewrite,[status(thm)],[])).
% 29.19/19.38 tff(21097,plain,
% 29.19/19.38 (((c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f10(c2) = c4)) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2))))) <=> ((c2 = c3) | (~(f10(c2) = c4)) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2)))))),
% 29.19/19.38 inference(rewrite,[status(thm)],[])).
% 29.19/19.38 tff(21098,plain,
% 29.19/19.38 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f10(c2) = c4)) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c2 = c3) | (~(f10(c2) = c4)) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2))))))),
% 29.19/19.38 inference(monotonicity,[status(thm)],[21097])).
% 29.19/19.38 tff(21099,plain,
% 29.19/19.38 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f10(c2) = c4)) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (c2 = c3) | (~(f10(c2) = c4)) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2)))))),
% 29.19/19.38 inference(transitivity,[status(thm)],[21098, 21096])).
% 29.19/19.38 tff(21100,plain,
% 29.19/19.38 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(f10(c2) = c4)) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2)))))),
% 29.19/19.38 inference(quant_inst,[status(thm)],[])).
% 29.19/19.38 tff(21101,plain,
% 29.19/19.38 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (c2 = c3) | (~(f10(c2) = c4)) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2))))),
% 29.19/19.38 inference(modus_ponens,[status(thm)],[21100, 21099])).
% 29.19/19.38 tff(21102,plain,
% 29.19/19.38 ($false),
% 29.19/19.38 inference(unit_resolution,[status(thm)],[21101, 402, 377, 15484, 1828, 14892, 20783, 21095])).
% 29.19/19.38 tff(21103,plain,((f1(c2, c2) = c2) | (c2 = c3) | (~(f10(c2) = c4)) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2)))) | (~(c4 = c1)) | big_f(c2, c4)), inference(lemma,lemma(discharge,[]))).
% 29.19/19.38 tff(21104,plain,
% 29.19/19.38 (f1(c2, c2) = c2),
% 29.19/19.38 inference(unit_resolution,[status(thm)],[21103, 15336, 21007, 21094, 21010, 21005, 21019])).
% 29.19/19.38 tff(21105,plain,
% 29.19/19.38 (big_f(c2, f1(c2, c2)) <=> big_f(c2, c2)),
% 29.19/19.38 inference(monotonicity,[status(thm)],[21104])).
% 29.19/19.38 tff(21106,plain,
% 29.19/19.38 (big_f(c2, c2) <=> big_f(c2, f1(c2, c2))),
% 29.19/19.38 inference(symmetry,[status(thm)],[21105])).
% 29.19/19.38 tff(21107,plain,
% 29.19/19.38 (big_f(c2, f1(c2, c2))),
% 29.19/19.38 inference(modus_ponens,[status(thm)],[1345, 21106])).
% 29.19/19.38 tff(21108,plain,
% 29.19/19.38 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f10(c2) = c4)) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(f10(c2) = c4)) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2)))))),
% 29.19/19.38 inference(rewrite,[status(thm)],[])).
% 29.19/19.38 tff(21109,plain,
% 29.19/19.38 (((c2 = c3) | (~(f10(c2) = c4)) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2)))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2)))) <=> ((c2 = c3) | (~(f10(c2) = c4)) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2)))))),
% 29.19/19.38 inference(rewrite,[status(thm)],[])).
% 29.19/19.38 tff(21110,plain,
% 29.19/19.38 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f10(c2) = c4)) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2)))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f10(c2) = c4)) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2))))))),
% 29.19/19.38 inference(monotonicity,[status(thm)],[21109])).
% 29.19/19.38 tff(21111,plain,
% 29.19/19.38 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f10(c2) = c4)) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2)))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(f10(c2) = c4)) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2)))))),
% 29.19/19.38 inference(transitivity,[status(thm)],[21110, 21108])).
% 29.19/19.38 tff(21112,plain,
% 29.19/19.38 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f10(c2) = c4)) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2)))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))),
% 29.19/19.38 inference(quant_inst,[status(thm)],[])).
% 29.19/19.38 tff(21113,plain,
% 29.19/19.38 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(f10(c2) = c4)) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2))))),
% 29.19/19.38 inference(modus_ponens,[status(thm)],[21112, 21111])).
% 29.19/19.38 tff(21114,plain,
% 29.19/19.38 ($false),
% 29.19/19.38 inference(unit_resolution,[status(thm)],[21113, 447, 15336, 21007, 21104, 21107, 21094, 21010])).
% 29.19/19.38 tff(21115,plain,((~(c3 = c1)) | (~big_f(c2, c2)) | (f7(c2) = c2) | (~(f10(c1) = c2)) | (f7(c1) = c1) | (~(f4(c4) = c1)) | big_f(f7(c1), c1) | big_f(c2, f10(c2)) | big_f(c2, f7(c2)) | (f10(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 29.19/19.38 tff(21116,plain,
% 29.19/19.38 (~(c3 = c1)),
% 29.19/19.38 inference(unit_resolution,[status(thm)],[21115, 17574, 17, 16, 115, 11752, 1345, 15473, 21002, 89])).
% 29.19/19.39 tff(21117,plain,
% 29.19/19.39 (~(f7(c2) = c3)),
% 29.19/19.39 inference(modus_ponens,[status(thm)],[21116, 21000])).
% 29.19/19.39 tff(21118,plain,
% 29.19/19.39 (~(c1 = c3)),
% 29.19/19.39 inference(modus_ponens,[status(thm)],[21116, 648])).
% 29.19/19.39 tff(21119,plain,
% 29.19/19.39 ((c3 = c1) <=> (f10(c2) = c3)),
% 29.19/19.39 inference(transitivity,[status(thm)],[68, 12094])).
% 29.19/19.39 tff(21120,plain,
% 29.19/19.39 ((~(c3 = c1)) <=> (~(f10(c2) = c3))),
% 29.19/19.39 inference(monotonicity,[status(thm)],[21119])).
% 29.19/19.39 tff(21121,plain,
% 29.19/19.39 (~(f10(c2) = c3)),
% 29.19/19.39 inference(modus_ponens,[status(thm)],[21116, 21120])).
% 29.19/19.39 tff(21122,plain,
% 29.19/19.39 (c4 = f10(c2)),
% 29.19/19.39 inference(transitivity,[status(thm)],[9094, 99])).
% 29.19/19.39 tff(21123,plain,
% 29.19/19.39 (f4(c4) = f10(c2)),
% 29.19/19.39 inference(transitivity,[status(thm)],[11752, 99])).
% 29.19/19.39 tff(21124,plain,
% 29.19/19.39 (big_f(f4(c4), c4) <=> big_f(f10(c2), f10(c2))),
% 29.19/19.39 inference(monotonicity,[status(thm)],[21123, 21122])).
% 29.19/19.39 tff(21125,plain,
% 29.19/19.39 ((~big_f(f4(c4), c4)) <=> (~big_f(f10(c2), f10(c2)))),
% 29.19/19.39 inference(monotonicity,[status(thm)],[21124])).
% 29.19/19.39 tff(21126,plain,
% 29.19/19.39 ($false),
% 29.19/19.39 inference(unit_resolution,[status(thm)],[1180, 15886])).
% 29.19/19.39 tff(21127,plain,((~big_f(f7(c2), c2)) | big_f(c1, c2) | (~(f7(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.19/19.39 tff(21128,plain,
% 29.19/19.39 (~big_f(f7(c2), c2)),
% 29.19/19.39 inference(unit_resolution,[status(thm)],[21127, 27, 22])).
% 29.19/19.39 tff(21129,plain,
% 29.19/19.39 ((c2 = f5(f10(c1))) <=> (c2 = f5(c2))),
% 29.19/19.39 inference(monotonicity,[status(thm)],[16012])).
% 29.19/19.39 tff(21130,plain,
% 29.19/19.39 ((f5(f10(c1)) = c2) <=> (f5(c2) = c2)),
% 29.19/19.39 inference(transitivity,[status(thm)],[5891, 21129, 1280])).
% 29.19/19.39 tff(21131,plain,
% 29.19/19.39 (~(f7(c2) = f8(c2))),
% 29.19/19.39 inference(unit_resolution,[status(thm)],[12706, 1521, 89, 17, 8375])).
% 29.19/19.39 tff(21132,plain,
% 29.19/19.39 ((f7(c2) = f8(c2)) <=> (f10(c2) = f8(c2))),
% 29.19/19.39 inference(monotonicity,[status(thm)],[20919])).
% 29.19/19.39 tff(21133,plain,
% 29.19/19.39 ((f10(c2) = f8(c2)) <=> (f7(c2) = f8(c2))),
% 29.19/19.39 inference(symmetry,[status(thm)],[21132])).
% 29.19/19.39 tff(21134,plain,
% 29.19/19.39 ((f10(c2) = f8(c2)) <=> (c1 = f8(c2))),
% 29.19/19.39 inference(monotonicity,[status(thm)],[11819])).
% 29.19/19.39 tff(21135,plain,
% 29.19/19.39 ((c1 = f8(c2)) <=> (f10(c2) = f8(c2))),
% 29.19/19.39 inference(symmetry,[status(thm)],[21134])).
% 29.19/19.39 tff(21136,plain,
% 29.19/19.39 ((f8(f7(f4(c4))) = c1) <=> (f8(c2) = c1)),
% 29.19/19.39 inference(monotonicity,[status(thm)],[17577])).
% 29.19/19.39 tff(21137,plain,
% 29.19/19.39 ((f8(f7(f4(c4))) = c1) <=> (c1 = f8(c2))),
% 29.19/19.39 inference(transitivity,[status(thm)],[21136, 13044])).
% 29.19/19.39 tff(21138,plain,
% 29.19/19.39 ((f8(f7(f4(c4))) = c1) <=> (f7(c2) = f8(c2))),
% 29.19/19.39 inference(transitivity,[status(thm)],[21137, 21135, 21133])).
% 29.19/19.39 tff(21139,plain,
% 29.19/19.39 (f7(c2) = f8(c2)),
% 29.19/19.39 inference(modus_ponens,[status(thm)],[16268, 21138])).
% 29.19/19.39 tff(21140,assumption,(~(f7(c2) = f8(c2))), introduced(assumption)).
% 29.19/19.39 tff(21141,plain,
% 29.19/19.39 ($false),
% 29.19/19.39 inference(unit_resolution,[status(thm)],[21140, 21139])).
% 29.19/19.39 tff(21142,plain,((~(f8(f7(f4(c4))) = c1)) | (f7(c2) = f8(c2)) | (~(f10(c2) = c1)) | (~(f7(c2) = c1)) | (~(f7(c1) = c2)) | (~(f4(c4) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.19/19.39 tff(21143,plain,
% 29.19/19.39 (~(f8(f7(f4(c4))) = c1)),
% 29.19/19.39 inference(unit_resolution,[status(thm)],[21142, 21131, 94, 22, 347, 11752])).
% 29.19/19.39 tff(21144,plain,
% 29.19/19.39 (f8(f7(f4(c4))) = c2),
% 29.19/19.39 inference(unit_resolution,[status(thm)],[13371, 21143])).
% 29.19/19.39 tff(21145,plain,
% 29.19/19.39 (c2 = f8(c2)),
% 29.19/19.39 inference(unit_resolution,[status(thm)],[17582, 21144, 347, 11752])).
% 29.19/19.39 tff(21146,plain,
% 29.19/19.39 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | (f7(c2) = c2) | big_f(f7(c2), f5(c2)) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | (f7(c2) = c2) | big_f(f7(c2), f5(c2)) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))))),
% 29.19/19.39 inference(rewrite,[status(thm)],[])).
% 29.19/19.39 tff(21147,plain,
% 29.19/19.39 (($false | (f10(c2) = c2) | big_f(c2, f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), f5(c2)) | (~(c2 = f8(c2)))) <=> ((f10(c2) = c2) | (f7(c2) = c2) | big_f(f7(c2), f5(c2)) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))))),
% 29.19/19.39 inference(rewrite,[status(thm)],[])).
% 29.19/19.39 tff(21148,plain,
% 29.19/19.39 (((~(f5(c2) = f5(c2))) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), f5(c2)) | (~(c2 = f8(c2)))) <=> ($false | (f10(c2) = c2) | big_f(c2, f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), f5(c2)) | (~(c2 = f8(c2))))),
% 29.19/19.39 inference(monotonicity,[status(thm)],[4851])).
% 29.19/19.39 tff(21149,plain,
% 29.19/19.39 (((~(f5(c2) = f5(c2))) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), f5(c2)) | (~(c2 = f8(c2)))) <=> ((f10(c2) = c2) | (f7(c2) = c2) | big_f(f7(c2), f5(c2)) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))))),
% 29.19/19.39 inference(transitivity,[status(thm)],[21148, 21147])).
% 29.19/19.39 tff(21150,plain,
% 29.19/19.39 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(f5(c2) = f5(c2))) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), f5(c2)) | (~(c2 = f8(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | (f7(c2) = c2) | big_f(f7(c2), f5(c2)) | big_f(c2, f10(c2)) | (~(c2 = f8(c2)))))),
% 29.19/19.39 inference(monotonicity,[status(thm)],[21149])).
% 29.19/19.39 tff(21151,plain,
% 29.19/19.39 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(f5(c2) = f5(c2))) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), f5(c2)) | (~(c2 = f8(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | (f7(c2) = c2) | big_f(f7(c2), f5(c2)) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))))),
% 29.19/19.39 inference(transitivity,[status(thm)],[21150, 21146])).
% 29.19/19.39 tff(21152,plain,
% 29.19/19.39 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(f5(c2) = f5(c2))) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), f5(c2)) | (~(c2 = f8(c2))))),
% 29.19/19.39 inference(quant_inst,[status(thm)],[])).
% 29.19/19.39 tff(21153,plain,
% 29.19/19.39 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | (f7(c2) = c2) | big_f(f7(c2), f5(c2)) | big_f(c2, f10(c2)) | (~(c2 = f8(c2)))),
% 29.19/19.39 inference(modus_ponens,[status(thm)],[21152, 21151])).
% 29.19/19.39 tff(21154,plain,
% 29.19/19.39 ((f10(c2) = c2) | (f7(c2) = c2) | big_f(f7(c2), f5(c2)) | big_f(c2, f10(c2)) | (~(c2 = f8(c2)))),
% 29.19/19.39 inference(unit_resolution,[status(thm)],[21153, 1745])).
% 29.19/19.39 tff(21155,plain,
% 29.19/19.39 (big_f(f7(c2), f5(c2))),
% 29.19/19.39 inference(unit_resolution,[status(thm)],[21154, 21145, 89, 15517, 17])).
% 29.19/19.39 tff(21156,plain,
% 29.19/19.39 (~(f5(f10(c1)) = c1)),
% 29.19/19.39 inference(unit_resolution,[status(thm)],[336, 21155, 333, 16])).
% 29.19/19.39 tff(21157,plain,
% 29.19/19.39 (f5(f10(c1)) = c2),
% 29.19/19.39 inference(unit_resolution,[status(thm)],[326, 21156])).
% 29.19/19.39 tff(21158,plain,
% 29.19/19.39 (f5(c2) = c2),
% 29.19/19.39 inference(modus_ponens,[status(thm)],[21157, 21130])).
% 29.19/19.39 tff(21159,plain,
% 29.19/19.39 ((~(c2 = f5(c2))) | (~(c2 = f8(c2)))),
% 29.19/19.39 inference(unit_resolution,[status(thm)],[12720, 1745, 89, 17, 1521, 15517])).
% 29.19/19.39 tff(21160,plain,
% 29.19/19.39 (~(c2 = f5(c2))),
% 29.19/19.39 inference(unit_resolution,[status(thm)],[21159, 21145])).
% 29.19/19.39 tff(21161,plain,
% 29.19/19.39 (~(f5(c2) = c2)),
% 29.19/19.39 inference(unit_resolution,[status(thm)],[8113, 21160])).
% 29.19/19.39 tff(21162,plain,
% 29.19/19.39 ($false),
% 29.19/19.39 inference(unit_resolution,[status(thm)],[21161, 21158])).
% 29.19/19.39 tff(21163,plain,(big_f(f7(c2), c2) | (~(f10(c1) = c2)) | big_f(f7(c2), c1) | (f10(c2) = c2) | (f7(c2) = c2) | big_f(c2, f10(c2)) | (~(f7(c1) = c2)) | (~(f4(c4) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.19/19.39 tff(21164,plain,
% 29.19/19.39 (big_f(f7(c2), c1)),
% 29.19/19.39 inference(unit_resolution,[status(thm)],[21163, 21128, 16, 89, 17, 15517, 120, 11752])).
% 29.19/19.39 tff(21165,plain,
% 29.19/19.39 (big_f(c1, c1)),
% 29.19/19.39 inference(modus_ponens,[status(thm)],[21164, 17571])).
% 29.19/19.39 tff(21166,plain,
% 29.19/19.39 (big_f(f7(f10(c2)), c2)),
% 29.19/19.39 inference(modus_ponens,[status(thm)],[1345, 17556])).
% 29.19/19.39 tff(21167,plain,
% 29.19/19.39 (big_f(f10(c2), f10(c2)) <=> big_f(f4(c4), c4)),
% 29.19/19.39 inference(symmetry,[status(thm)],[21124])).
% 29.19/19.39 tff(21168,plain,
% 29.19/19.39 (big_f(f7(c2), c1) <=> big_f(f4(c4), c4)),
% 29.19/19.39 inference(transitivity,[status(thm)],[17570, 17569, 21167])).
% 29.19/19.39 tff(21169,plain,
% 29.19/19.39 (big_f(f4(c4), c4)),
% 29.19/19.39 inference(modus_ponens,[status(thm)],[21164, 21168])).
% 29.19/19.39 tff(21170,plain,
% 29.19/19.39 ((~(f5(c1) = c2)) <=> (~(c2 = f5(f10(c2))))),
% 29.19/19.39 inference(monotonicity,[status(thm)],[11887])).
% 29.19/19.39 tff(21171,plain,
% 29.19/19.39 (~big_f(f7(c2), c2)),
% 29.19/19.39 inference(unit_resolution,[status(thm)],[21127, 27, 292])).
% 29.19/19.39 tff(21172,plain,
% 29.19/19.39 (f1(c1, c1) = c1),
% 29.19/19.39 inference(unit_resolution,[status(thm)],[16957, 12882, 168, 873, 27, 12861])).
% 29.19/19.39 tff(21173,plain,
% 29.19/19.39 ($false),
% 29.19/19.39 inference(unit_resolution,[status(thm)],[16970, 17181, 624, 12861, 168, 12882, 873])).
% 29.19/19.39 tff(21174,plain,((~(f1(c1, c1) = c1)) | (f3(c2, c2) = c2) | (c1 = c3) | big_f(f3(c2, c2), c2) | (c2 = c4) | (~big_f(c1, c1))), inference(lemma,lemma(discharge,[]))).
% 29.19/19.39 tff(21175,plain,
% 29.19/19.39 ($false),
% 29.19/19.39 inference(unit_resolution,[status(thm)],[21174, 21172, 12882, 168, 873, 4932, 12861])).
% 29.19/19.39 tff(21176,plain,(big_f(f3(c2, c2), c2) | (c1 = c3) | (c2 = c4) | (~big_f(c1, c1)) | (f3(c2, c2) = c2) | big_f(c1, c2)), inference(lemma,lemma(discharge,[]))).
% 29.19/19.39 tff(21177,plain,
% 29.19/19.39 (big_f(f3(c2, c2), c2)),
% 29.19/19.39 inference(unit_resolution,[status(thm)],[21176, 12861, 873, 4932, 168, 27])).
% 29.19/19.39 tff(21178,plain,
% 29.19/19.39 ((~(f3(c2, c2) = c2)) <=> (~(f3(f5(c1), f5(c1)) = c2))),
% 29.19/19.39 inference(monotonicity,[status(thm)],[13003])).
% 29.19/19.39 tff(21179,plain,
% 29.19/19.39 (~(f3(f5(c1), f5(c1)) = c2)),
% 29.19/19.39 inference(modus_ponens,[status(thm)],[12861, 21178])).
% 29.19/19.39 tff(21180,plain,
% 29.19/19.39 (f5(f7(c2)) = f5(f10(c2))),
% 29.19/19.39 inference(monotonicity,[status(thm)],[20919])).
% 29.19/19.39 tff(21181,plain,
% 29.19/19.39 (f5(f7(c2)) = f5(c1)),
% 29.19/19.39 inference(transitivity,[status(thm)],[21180, 11884])).
% 29.19/19.39 tff(21182,plain,
% 29.19/19.39 ((c2 = f5(f7(c2))) <=> (c2 = f5(c1))),
% 29.19/19.39 inference(monotonicity,[status(thm)],[21181])).
% 29.19/19.39 tff(21183,plain,
% 29.19/19.39 ((c2 = f5(c1)) <=> (c2 = f5(f7(c2)))),
% 29.19/19.39 inference(symmetry,[status(thm)],[21182])).
% 29.19/19.39 tff(21184,plain,
% 29.19/19.39 ((f5(c1) = c2) <=> (c2 = f5(f7(c2)))),
% 29.19/19.39 inference(transitivity,[status(thm)],[155, 21183])).
% 29.19/19.39 tff(21185,plain,
% 29.19/19.39 (c2 = f5(f7(c2))),
% 29.19/19.39 inference(modus_ponens,[status(thm)],[186, 21184])).
% 29.19/19.39 tff(21186,plain,
% 29.19/19.39 (~(f3(f5(c1), f5(c1)) = c1)),
% 29.19/19.39 inference(unit_resolution,[status(thm)],[17065, 21185, 1521, 292, 15356])).
% 29.19/19.39 tff(21187,plain,
% 29.19/19.39 ($false),
% 29.19/19.39 inference(unit_resolution,[status(thm)],[7625, 21186, 21179])).
% 29.19/19.39 tff(21188,plain,((~(f5(c1) = c2)) | big_f(f7(c2), c2) | (~(f7(c2) = c1)) | (~big_f(f3(c2, c2), c2)) | (f3(c2, c2) = c2) | (~(f10(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.19/19.39 tff(21189,plain,
% 29.19/19.39 (~(f5(c1) = c2)),
% 29.19/19.39 inference(unit_resolution,[status(thm)],[21188, 21177, 292, 21171, 12861, 11819])).
% 29.19/19.39 tff(21190,plain,
% 29.19/19.39 (~(c2 = f5(f10(c2)))),
% 29.19/19.39 inference(modus_ponens,[status(thm)],[21189, 21170])).
% 29.19/19.39 tff(21191,plain,
% 29.19/19.39 (~big_f(c1, f10(c1))),
% 29.19/19.39 inference(unit_resolution,[status(thm)],[12239, 27, 11819, 13433])).
% 29.19/19.39 tff(21192,plain,
% 29.19/19.39 (f5(c1) = c1),
% 29.19/19.39 inference(unit_resolution,[status(thm)],[1708, 21189])).
% 29.19/19.39 tff(21193,plain,
% 29.19/19.39 (~big_f(f7(c1), f5(c1))),
% 29.19/19.39 inference(unit_resolution,[status(thm)],[289, 21192, 285])).
% 29.19/19.39 tff(21194,plain,
% 29.19/19.39 (~(f8(c1) = c1)),
% 29.19/19.39 inference(unit_resolution,[status(thm)],[18252, 21193, 115, 11819, 21191, 17094, 474, 11752])).
% 29.19/19.39 tff(21195,plain,
% 29.19/19.39 (f8(c1) = c2),
% 29.19/19.39 inference(unit_resolution,[status(thm)],[1680, 21194])).
% 29.19/19.39 tff(21196,plain,
% 29.19/19.39 ((f3(c2, c2) = f8(c1)) <=> (f3(c2, c2) = c2)),
% 29.19/19.39 inference(monotonicity,[status(thm)],[21195])).
% 29.19/19.39 tff(21197,plain,
% 29.19/19.39 ((f3(c2, c2) = c2) <=> (f3(c2, c2) = f8(c1))),
% 29.19/19.39 inference(symmetry,[status(thm)],[21196])).
% 29.19/19.39 tff(21198,plain,
% 29.19/19.39 ((f3(c2, c2) = c2) <=> (f3(c2, c2) = f8(f10(c2)))),
% 29.19/19.39 inference(transitivity,[status(thm)],[21197, 21053])).
% 29.19/19.39 tff(21199,plain,
% 29.19/19.39 ((~(f3(c2, c2) = c2)) <=> (~(f3(c2, c2) = f8(f10(c2))))),
% 29.19/19.39 inference(monotonicity,[status(thm)],[21198])).
% 29.19/19.39 tff(21200,plain,
% 29.19/19.39 (~(f3(c2, c2) = f8(f10(c2)))),
% 29.19/19.39 inference(modus_ponens,[status(thm)],[12861, 21199])).
% 29.19/19.39 tff(21201,plain,
% 29.19/19.39 (big_f(f3(c2, c2), f10(f10(c2))) <=> big_f(f3(c2, c2), c2)),
% 29.19/19.39 inference(monotonicity,[status(thm)],[13433])).
% 29.19/19.39 tff(21202,plain,
% 29.19/19.39 (big_f(f3(c2, c2), c2) <=> big_f(f3(c2, c2), f10(f10(c2)))),
% 29.19/19.39 inference(symmetry,[status(thm)],[21201])).
% 29.19/19.39 tff(21203,plain,
% 29.19/19.39 (big_f(f3(c2, c2), f10(f10(c2)))),
% 29.19/19.39 inference(modus_ponens,[status(thm)],[21177, 21202])).
% 29.19/19.39 tff(21204,assumption,(big_f(f7(f10(c2)), c2)), introduced(assumption)).
% 29.19/19.39 tff(21205,plain,
% 29.19/19.39 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f10(c2)) = f10(c2)) | (c2 = f5(f10(c2))) | (f7(f10(c2)) = f10(c2)) | (~big_f(f7(f10(c2)), c2)) | (f3(c2, c2) = f8(f10(c2))) | (~big_f(f3(c2, c2), f10(f10(c2)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(f10(c2)) = f10(c2)) | (c2 = f5(f10(c2))) | (f7(f10(c2)) = f10(c2)) | (~big_f(f7(f10(c2)), c2)) | (f3(c2, c2) = f8(f10(c2))) | (~big_f(f3(c2, c2), f10(f10(c2)))))),
% 29.19/19.39 inference(rewrite,[status(thm)],[])).
% 29.19/19.39 tff(21206,plain,
% 29.19/19.39 (((f10(f10(c2)) = f10(c2)) | (f3(c2, c2) = f8(f10(c2))) | (~big_f(f3(c2, c2), f10(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | (c2 = f5(f10(c2))) | (~big_f(f7(f10(c2)), c2))) <=> ((f10(f10(c2)) = f10(c2)) | (c2 = f5(f10(c2))) | (f7(f10(c2)) = f10(c2)) | (~big_f(f7(f10(c2)), c2)) | (f3(c2, c2) = f8(f10(c2))) | (~big_f(f3(c2, c2), f10(f10(c2)))))),
% 29.19/19.39 inference(rewrite,[status(thm)],[])).
% 29.19/19.39 tff(21207,plain,
% 29.19/19.39 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f10(c2)) = f10(c2)) | (f3(c2, c2) = f8(f10(c2))) | (~big_f(f3(c2, c2), f10(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | (c2 = f5(f10(c2))) | (~big_f(f7(f10(c2)), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f10(c2)) = f10(c2)) | (c2 = f5(f10(c2))) | (f7(f10(c2)) = f10(c2)) | (~big_f(f7(f10(c2)), c2)) | (f3(c2, c2) = f8(f10(c2))) | (~big_f(f3(c2, c2), f10(f10(c2))))))),
% 29.19/19.39 inference(monotonicity,[status(thm)],[21206])).
% 29.19/19.39 tff(21208,plain,
% 29.19/19.39 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f10(c2)) = f10(c2)) | (f3(c2, c2) = f8(f10(c2))) | (~big_f(f3(c2, c2), f10(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | (c2 = f5(f10(c2))) | (~big_f(f7(f10(c2)), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(f10(c2)) = f10(c2)) | (c2 = f5(f10(c2))) | (f7(f10(c2)) = f10(c2)) | (~big_f(f7(f10(c2)), c2)) | (f3(c2, c2) = f8(f10(c2))) | (~big_f(f3(c2, c2), f10(f10(c2)))))),
% 29.19/19.39 inference(transitivity,[status(thm)],[21207, 21205])).
% 29.19/19.39 tff(21209,plain,
% 29.19/19.39 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f10(c2)) = f10(c2)) | (f3(c2, c2) = f8(f10(c2))) | (~big_f(f3(c2, c2), f10(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | (c2 = f5(f10(c2))) | (~big_f(f7(f10(c2)), c2)))),
% 29.19/19.39 inference(quant_inst,[status(thm)],[])).
% 29.19/19.39 tff(21210,plain,
% 29.19/19.39 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(f10(c2)) = f10(c2)) | (c2 = f5(f10(c2))) | (f7(f10(c2)) = f10(c2)) | (~big_f(f7(f10(c2)), c2)) | (f3(c2, c2) = f8(f10(c2))) | (~big_f(f3(c2, c2), f10(f10(c2))))),
% 29.19/19.39 inference(modus_ponens,[status(thm)],[21209, 21208])).
% 29.19/19.39 tff(21211,plain,
% 29.19/19.39 ((c2 = f5(f10(c2))) | (f3(c2, c2) = f8(f10(c2)))),
% 29.19/19.39 inference(unit_resolution,[status(thm)],[21210, 1659, 11896, 11895, 21204, 21203])).
% 29.19/19.39 tff(21212,plain,
% 29.19/19.39 ($false),
% 29.19/19.39 inference(unit_resolution,[status(thm)],[21211, 21200, 21190])).
% 29.19/19.39 tff(21213,plain,((f3(c2, c2) = c2) | (f10(f10(c2)) = f10(c2)) | (f7(f10(c2)) = f10(c2)) | (~big_f(f7(f10(c2)), c2)) | (~(f10(c2) = c1)) | (f7(c1) = c1) | (~big_f(f4(c4), c4)) | (~(f4(c4) = c1)) | big_f(f7(c1), c1) | (~(f7(c2) = c1)) | (~(f10(c1) = c2)) | (c2 = c4) | (~big_f(c1, c1)) | (c1 = c3) | big_f(c1, c2)), inference(lemma,lemma(discharge,[]))).
% 29.19/19.39 tff(21214,plain,
% 29.19/19.39 (f3(c2, c2) = c2),
% 29.19/19.39 inference(unit_resolution,[status(thm)],[21213, 21169, 17563, 21166, 94, 115, 15308, 11752, 285, 22, 16, 873, 21165, 168, 27])).
% 29.19/19.39 tff(21215,plain,
% 29.19/19.39 (big_f(f3(c2, c2), c2) <=> big_f(c2, c2)),
% 29.19/19.39 inference(monotonicity,[status(thm)],[21214])).
% 29.19/19.39 tff(21216,plain,
% 29.19/19.39 (big_f(c2, c2) <=> big_f(f3(c2, c2), c2)),
% 29.19/19.39 inference(symmetry,[status(thm)],[21215])).
% 29.19/19.39 tff(21217,plain,
% 29.19/19.39 (big_f(f3(c2, c2), c2)),
% 29.19/19.39 inference(modus_ponens,[status(thm)],[1345, 21216])).
% 29.19/19.39 tff(21218,plain,
% 29.19/19.39 (f1(c1, c1) = c1),
% 29.19/19.39 inference(unit_resolution,[status(thm)],[17109, 21217, 9092, 873, 22, 21214, 27])).
% 29.19/19.39 tff(21219,plain,
% 29.19/19.39 (f1(f10(c2), f10(c2)) = f10(c2)),
% 29.19/19.39 inference(transitivity,[status(thm)],[12413, 21218, 99])).
% 29.19/19.39 tff(21220,plain,
% 29.19/19.39 (big_f(f10(c2), f1(f10(c2), f10(c2))) <=> big_f(f10(c2), f10(c2))),
% 29.19/19.39 inference(monotonicity,[status(thm)],[21219])).
% 29.19/19.39 tff(21221,plain,
% 29.19/19.39 (big_f(f10(c2), f10(c2)) <=> big_f(f10(c2), f1(f10(c2), f10(c2)))),
% 29.19/19.39 inference(symmetry,[status(thm)],[21220])).
% 29.19/19.39 tff(21222,plain,
% 29.19/19.39 (big_f(f10(c2), f10(c2))),
% 29.19/19.39 inference(modus_ponens,[status(thm)],[21164, 20756])).
% 29.19/19.39 tff(21223,plain,
% 29.19/19.39 (big_f(f10(c2), f1(f10(c2), f10(c2)))),
% 29.19/19.39 inference(modus_ponens,[status(thm)],[21222, 21221])).
% 29.19/19.39 tff(21224,plain,
% 29.19/19.39 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (f10(c2) = c3) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~(f1(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f10(c2), f1(f10(c2), f10(c2)))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c4) | (f10(c2) = c3) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~(f1(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f10(c2), f1(f10(c2), f10(c2)))))),
% 29.19/19.39 inference(rewrite,[status(thm)],[])).
% 29.19/19.39 tff(21225,plain,
% 29.19/19.39 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (f10(c2) = c3) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~(f1(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f10(c2), f1(f10(c2), f10(c2)))))),
% 29.19/19.39 inference(quant_inst,[status(thm)],[])).
% 29.19/19.39 tff(21226,plain,
% 29.19/19.39 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c4) | (f10(c2) = c3) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~(f1(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f10(c2), f1(f10(c2), f10(c2))))),
% 29.19/19.39 inference(modus_ponens,[status(thm)],[21225, 21224])).
% 29.19/19.39 tff(21227,plain,
% 29.19/19.39 ((~(f1(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f10(c2), f1(f10(c2), f10(c2))))),
% 29.19/19.39 inference(unit_resolution,[status(thm)],[21226, 933, 873, 15667, 21214, 21217])).
% 29.19/19.39 tff(21228,plain,
% 29.19/19.39 ($false),
% 29.19/19.39 inference(unit_resolution,[status(thm)],[21227, 21223, 21219])).
% 29.19/19.39 tff(21229,plain,(big_f(c1, c2) | (c2 = c4) | (f10(c2) = c3) | (f7(c2) = c3) | (~big_f(c2, c2)) | (f7(c1) = c1) | (~(f4(c4) = c1)) | big_f(f7(c1), c1) | (~(f10(c1) = c2)) | (c1 = c3) | (f10(c2) = c2) | (f7(c2) = c2) | big_f(c2, f10(c2))), inference(lemma,lemma(discharge,[]))).
% 29.19/19.39 tff(21230,plain,
% 29.19/19.39 (big_f(c1, c2)),
% 29.19/19.39 inference(unit_resolution,[status(thm)],[21229, 873, 15667, 9092, 1345, 115, 11752, 285, 16, 168, 89, 17, 15517])).
% 29.19/19.39 tff(21231,plain,
% 29.19/19.39 (big_f(f7(c2), f10(f7(c2)))),
% 29.19/19.39 inference(modus_ponens,[status(thm)],[21230, 21014])).
% 29.19/19.39 tff(21232,plain,
% 29.19/19.39 (big_f(f7(c2), c2)),
% 29.19/19.39 inference(modus_ponens,[status(thm)],[21230, 12163])).
% 29.19/19.39 tff(21233,plain,
% 29.19/19.39 (~big_f(f7(c2), f7(c2))),
% 29.19/19.39 inference(unit_resolution,[status(thm)],[16899, 21232, 17, 21089, 21086, 21231])).
% 29.19/19.39 tff(21234,plain,
% 29.19/19.39 (~big_f(f4(c4), c4)),
% 29.19/19.39 inference(unit_resolution,[status(thm)],[17136, 21233, 22, 9094, 11752])).
% 29.19/19.39 tff(21235,plain,
% 29.19/19.39 (~big_f(f10(c2), f10(c2))),
% 29.19/19.39 inference(modus_ponens,[status(thm)],[21234, 21125])).
% 29.19/19.39 tff(21236,plain,
% 29.19/19.39 (f10(c2) = c4),
% 29.19/19.39 inference(transitivity,[status(thm)],[94, 16938])).
% 29.19/19.39 tff(21237,plain,
% 29.19/19.39 (f4(f10(c2)) = f4(c4)),
% 29.19/19.39 inference(monotonicity,[status(thm)],[21236])).
% 29.19/19.39 tff(21238,plain,
% 29.19/19.39 (f4(c4) = f4(f10(c2))),
% 29.19/19.39 inference(symmetry,[status(thm)],[21237])).
% 29.19/19.39 tff(21239,plain,
% 29.19/19.39 (f10(c2) = f4(f10(c2))),
% 29.19/19.39 inference(transitivity,[status(thm)],[94, 16651, 21238])).
% 29.19/19.39 tff(21240,plain,
% 29.19/19.39 (f1(c1, f1(c1, c2)) = f1(c1, c2)),
% 29.19/19.39 inference(monotonicity,[status(thm)],[822])).
% 29.19/19.39 tff(21241,plain,
% 29.19/19.39 (f1(c1, f1(c1, c2)) = c2),
% 29.19/19.39 inference(transitivity,[status(thm)],[21240, 822])).
% 29.19/19.39 tff(21242,plain,
% 29.19/19.39 (big_f(c1, f1(c1, f1(c1, c2))) <=> big_f(c1, c2)),
% 29.19/19.39 inference(monotonicity,[status(thm)],[21241])).
% 29.19/19.39 tff(21243,plain,
% 29.19/19.39 (big_f(c1, c2) <=> big_f(c1, f1(c1, f1(c1, c2)))),
% 29.19/19.39 inference(symmetry,[status(thm)],[21242])).
% 29.19/19.39 tff(21244,plain,
% 29.19/19.39 (big_f(c1, f1(c1, f1(c1, c2)))),
% 29.19/19.39 inference(modus_ponens,[status(thm)],[2865, 21243])).
% 29.19/19.39 tff(21245,plain,
% 29.19/19.39 ($false),
% 29.19/19.39 inference(unit_resolution,[status(thm)],[2254, 21244, 21240, 168, 379])).
% 29.19/19.39 tff(21246,plain,((~(f1(c1, c2) = c2)) | (c1 = c3) | big_f(f4(c4), c4) | (~big_f(c1, c2))), inference(lemma,lemma(discharge,[]))).
% 29.19/19.39 tff(21247,plain,
% 29.19/19.39 (~(f1(c1, c2) = c2)),
% 29.19/19.39 inference(unit_resolution,[status(thm)],[21246, 21234, 168, 21230])).
% 29.19/19.39 tff(21248,plain,
% 29.19/19.39 (f1(c1, c2) = c1),
% 29.19/19.39 inference(unit_resolution,[status(thm)],[841, 21247])).
% 29.19/19.39 tff(21249,plain,
% 29.19/19.39 (f1(f10(c2), c2) = f10(c2)),
% 29.19/19.39 inference(transitivity,[status(thm)],[13619, 1095, 99])).
% 29.19/19.39 tff(21250,plain,
% 29.19/19.39 (big_f(f10(c2), f1(f10(c2), c2)) <=> big_f(f10(c2), f10(c2))),
% 29.19/19.39 inference(monotonicity,[status(thm)],[21249])).
% 29.19/19.39 tff(21251,plain,
% 29.19/19.39 (big_f(f10(c2), f10(c2)) <=> big_f(f10(c2), f1(f10(c2), c2))),
% 29.19/19.39 inference(symmetry,[status(thm)],[21250])).
% 29.19/19.39 tff(21252,plain,
% 29.19/19.39 ((~big_f(f10(c2), f10(c2))) <=> (~big_f(f10(c2), f1(f10(c2), c2)))),
% 29.19/19.39 inference(monotonicity,[status(thm)],[21251])).
% 29.19/19.39 tff(21253,plain,
% 29.19/19.39 (~big_f(f10(c2), f1(f10(c2), c2))),
% 29.19/19.39 inference(modus_ponens,[status(thm)],[20783, 21252])).
% 29.19/19.39 tff(21254,plain,
% 29.19/19.39 ((f1(f10(c2), c2) = c2) <=> (f10(c2) = c2)),
% 29.19/19.39 inference(monotonicity,[status(thm)],[21249])).
% 29.19/19.39 tff(21255,plain,
% 29.19/19.39 ((f10(c2) = c2) <=> (f1(f10(c2), c2) = c2)),
% 29.19/19.39 inference(symmetry,[status(thm)],[21254])).
% 29.19/19.39 tff(21256,plain,
% 29.19/19.39 ((~(f10(c2) = c2)) <=> (~(f1(f10(c2), c2) = c2))),
% 29.19/19.39 inference(monotonicity,[status(thm)],[21255])).
% 29.19/19.39 tff(21257,plain,
% 29.19/19.39 (~(f1(f10(c2), c2) = c2)),
% 29.19/19.39 inference(modus_ponens,[status(thm)],[89, 21256])).
% 29.19/19.39 tff(21258,plain,
% 29.19/19.39 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f10(c2) = c3) | (~(f10(c2) = c4)) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2)))) | big_f(f10(c2), f1(f10(c2), c2)) | (f1(f10(c2), c2) = c2))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (f10(c2) = c3) | (~(f10(c2) = c4)) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2)))) | big_f(f10(c2), f1(f10(c2), c2)) | (f1(f10(c2), c2) = c2))),
% 29.19/19.39 inference(rewrite,[status(thm)],[])).
% 29.19/19.39 tff(21259,plain,
% 29.19/19.39 (((f10(c2) = c3) | (f1(f10(c2), c2) = c2) | big_f(f10(c2), f1(f10(c2), c2)) | (~(f10(c2) = c4)) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2))))) <=> ((f10(c2) = c3) | (~(f10(c2) = c4)) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2)))) | big_f(f10(c2), f1(f10(c2), c2)) | (f1(f10(c2), c2) = c2))),
% 29.19/19.39 inference(rewrite,[status(thm)],[])).
% 29.19/19.39 tff(21260,plain,
% 29.19/19.39 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f10(c2) = c3) | (f1(f10(c2), c2) = c2) | big_f(f10(c2), f1(f10(c2), c2)) | (~(f10(c2) = c4)) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f10(c2) = c3) | (~(f10(c2) = c4)) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2)))) | big_f(f10(c2), f1(f10(c2), c2)) | (f1(f10(c2), c2) = c2)))),
% 29.21/19.40 inference(monotonicity,[status(thm)],[21259])).
% 29.21/19.40 tff(21261,plain,
% 29.21/19.40 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f10(c2) = c3) | (f1(f10(c2), c2) = c2) | big_f(f10(c2), f1(f10(c2), c2)) | (~(f10(c2) = c4)) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (f10(c2) = c3) | (~(f10(c2) = c4)) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2)))) | big_f(f10(c2), f1(f10(c2), c2)) | (f1(f10(c2), c2) = c2))),
% 29.21/19.40 inference(transitivity,[status(thm)],[21260, 21258])).
% 29.21/19.40 tff(21262,plain,
% 29.21/19.40 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f10(c2) = c3) | (f1(f10(c2), c2) = c2) | big_f(f10(c2), f1(f10(c2), c2)) | (~(f10(c2) = c4)) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2)))))),
% 29.21/19.40 inference(quant_inst,[status(thm)],[])).
% 29.21/19.40 tff(21263,plain,
% 29.21/19.40 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (f10(c2) = c3) | (~(f10(c2) = c4)) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2)))) | big_f(f10(c2), f1(f10(c2), c2)) | (f1(f10(c2), c2) = c2)),
% 29.21/19.40 inference(modus_ponens,[status(thm)],[21262, 21261])).
% 29.21/19.40 tff(21264,plain,
% 29.21/19.40 (big_f(f10(c2), f1(f10(c2), c2)) | (f1(f10(c2), c2) = c2)),
% 29.21/19.40 inference(unit_resolution,[status(thm)],[21263, 402, 15484, 15667, 20783, 21095])).
% 29.21/19.40 tff(21265,plain,
% 29.21/19.40 ($false),
% 29.21/19.40 inference(unit_resolution,[status(thm)],[21264, 21257, 21253])).
% 29.21/19.40 tff(21266,plain,((~(f1(c1, c2) = c1)) | (~(f10(c2) = c4)) | (f10(c2) = c3) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2)))) | (f10(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 29.21/19.40 tff(21267,plain,
% 29.21/19.40 (big_f(f10(c2), f10(c2))),
% 29.21/19.40 inference(unit_resolution,[status(thm)],[21266, 21248, 15667, 21236, 21239, 89])).
% 29.21/19.40 tff(21268,plain,
% 29.21/19.40 ($false),
% 29.21/19.40 inference(unit_resolution,[status(thm)],[21267, 21235])).
% 29.21/19.40 tff(21269,plain,((c2 = c4) | (~(f4(c4) = c1)) | (f10(c2) = c3) | (f10(c2) = c2) | (c1 = c3) | (f7(c2) = c2) | (~(f10(c1) = c2)) | (f7(c2) = c3) | (~big_f(c2, c2)) | (f7(c1) = c1) | big_f(f7(c1), c1) | big_f(c2, f10(c2))), inference(lemma,lemma(discharge,[]))).
% 29.21/19.40 tff(21270,plain,
% 29.21/19.40 (c2 = c4),
% 29.21/19.40 inference(unit_resolution,[status(thm)],[21269, 21121, 11752, 89, 21118, 17, 16, 21117, 1345, 115, 17574, 15473])).
% 29.21/19.40 tff(21271,plain,
% 29.21/19.40 (f4(c2) = f4(c4)),
% 29.21/19.40 inference(monotonicity,[status(thm)],[21270])).
% 29.21/19.40 tff(21272,plain,
% 29.21/19.40 (f4(c2) = f10(c2)),
% 29.21/19.40 inference(transitivity,[status(thm)],[21271, 11752, 99])).
% 29.21/19.40 tff(21273,plain,
% 29.21/19.40 ((c2 = f4(c2)) <=> (c2 = f10(c2))),
% 29.21/19.40 inference(monotonicity,[status(thm)],[21272])).
% 29.21/19.40 tff(21274,plain,
% 29.21/19.40 ((c2 = f4(c2)) <=> (f10(c2) = c2)),
% 29.21/19.40 inference(transitivity,[status(thm)],[21273, 4987])).
% 29.21/19.40 tff(21275,plain,
% 29.21/19.40 ((f10(c2) = c2) <=> (c2 = f4(c2))),
% 29.21/19.40 inference(symmetry,[status(thm)],[21274])).
% 29.21/19.40 tff(21276,plain,
% 29.21/19.40 ((~(f10(c2) = c2)) <=> (~(c2 = f4(c2)))),
% 29.21/19.40 inference(monotonicity,[status(thm)],[21275])).
% 29.21/19.40 tff(21277,plain,
% 29.21/19.40 (~(c2 = f4(c2))),
% 29.21/19.40 inference(modus_ponens,[status(thm)],[89, 21276])).
% 29.21/19.40 tff(21278,plain,
% 29.21/19.40 (big_f(f7(c2), c1)),
% 29.21/19.40 inference(unit_resolution,[status(thm)],[21163, 21128, 16, 89, 17, 15517, 347, 11752])).
% 29.21/19.40 tff(21279,plain,
% 29.21/19.40 (big_f(c1, c1)),
% 29.21/19.40 inference(modus_ponens,[status(thm)],[21278, 17571])).
% 29.21/19.40 tff(21280,plain,
% 29.21/19.40 (c1 = f4(c2)),
% 29.21/19.40 inference(transitivity,[status(thm)],[16651, 8745])).
% 29.21/19.40 tff(21281,plain,
% 29.21/19.40 (f7(c2) = f4(c2)),
% 29.21/19.40 inference(modus_ponens,[status(thm)],[21280, 9302])).
% 29.21/19.40 tff(21282,plain,
% 29.21/19.40 (f1(c1, c1) = c1),
% 29.21/19.40 inference(unit_resolution,[status(thm)],[15896, 27, 22, 631, 9092, 21281])).
% 29.21/19.40 tff(21283,plain,
% 29.21/19.40 (~big_f(c1, c1)),
% 29.21/19.40 inference(unit_resolution,[status(thm)],[17186, 21282, 631, 9092, 21281, 22, 21128])).
% 29.21/19.40 tff(21284,plain,
% 29.21/19.40 ($false),
% 29.21/19.40 inference(unit_resolution,[status(thm)],[21283, 21279])).
% 29.21/19.40 tff(21285,plain,(big_f(c1, c2) | (~(c2 = c4)) | (f7(c2) = c3) | (~(f10(c1) = c2)) | (f10(c2) = c2) | (f7(c2) = c2) | big_f(c2, f10(c2)) | (~(f7(c1) = c2)) | (~(f4(c4) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.21/19.40 tff(21286,plain,
% 29.21/19.40 (big_f(c1, c2)),
% 29.21/19.40 inference(unit_resolution,[status(thm)],[21285, 21270, 21117, 16, 89, 17, 15473, 120, 11752])).
% 29.21/19.40 tff(21287,plain,
% 29.21/19.40 (big_f(f7(c2), c2)),
% 29.21/19.40 inference(modus_ponens,[status(thm)],[21286, 12163])).
% 29.21/19.40 tff(21288,plain,
% 29.21/19.40 (~(f1(c1, c2) = c2)),
% 29.21/19.40 inference(unit_resolution,[status(thm)],[17200, 21287, 1345, 21270, 21117, 21277, 22])).
% 29.21/19.40 tff(21289,plain,
% 29.21/19.40 (f1(c1, c2) = c1),
% 29.21/19.40 inference(unit_resolution,[status(thm)],[841, 21288])).
% 29.21/19.40 tff(21290,plain,
% 29.21/19.40 (f1(f10(c2), c2) = f10(c2)),
% 29.21/19.40 inference(transitivity,[status(thm)],[13619, 21289, 99])).
% 29.21/19.40 tff(21291,plain,
% 29.21/19.40 (big_f(f10(c2), f1(f10(c2), c2)) <=> big_f(f10(c2), f10(c2))),
% 29.21/19.40 inference(monotonicity,[status(thm)],[21290])).
% 29.21/19.40 tff(21292,plain,
% 29.21/19.40 (big_f(f10(c2), f1(f10(c2), c2)) <=> big_f(f7(c2), c1)),
% 29.21/19.40 inference(transitivity,[status(thm)],[21291, 20890, 20889])).
% 29.21/19.40 tff(21293,plain,
% 29.21/19.40 ((f1(f10(c2), c2) = c2) <=> (f10(c2) = c2)),
% 29.21/19.40 inference(monotonicity,[status(thm)],[21290])).
% 29.21/19.40 tff(21294,plain,
% 29.21/19.40 ((f10(c2) = c2) <=> (f1(f10(c2), c2) = c2)),
% 29.21/19.40 inference(symmetry,[status(thm)],[21293])).
% 29.21/19.40 tff(21295,plain,
% 29.21/19.40 ((~(f10(c2) = c2)) <=> (~(f1(f10(c2), c2) = c2))),
% 29.21/19.40 inference(monotonicity,[status(thm)],[21294])).
% 29.21/19.40 tff(21296,plain,
% 29.21/19.40 (~(f1(f10(c2), c2) = c2)),
% 29.21/19.40 inference(modus_ponens,[status(thm)],[89, 21295])).
% 29.21/19.40 tff(21297,plain,
% 29.21/19.40 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((~(c2 = c4)) | (c2 = f4(c2)) | (f10(c2) = c3) | (~big_f(c2, c2)) | big_f(f10(c2), f1(f10(c2), c2)) | (f1(f10(c2), c2) = c2))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (~(c2 = c4)) | (c2 = f4(c2)) | (f10(c2) = c3) | (~big_f(c2, c2)) | big_f(f10(c2), f1(f10(c2), c2)) | (f1(f10(c2), c2) = c2))),
% 29.21/19.40 inference(rewrite,[status(thm)],[])).
% 29.21/19.40 tff(21298,plain,
% 29.21/19.40 (((f10(c2) = c3) | (f1(f10(c2), c2) = c2) | big_f(f10(c2), f1(f10(c2), c2)) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2))) <=> ((~(c2 = c4)) | (c2 = f4(c2)) | (f10(c2) = c3) | (~big_f(c2, c2)) | big_f(f10(c2), f1(f10(c2), c2)) | (f1(f10(c2), c2) = c2))),
% 29.21/19.40 inference(rewrite,[status(thm)],[])).
% 29.21/19.40 tff(21299,plain,
% 29.21/19.40 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((f10(c2) = c3) | (f1(f10(c2), c2) = c2) | big_f(f10(c2), f1(f10(c2), c2)) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((~(c2 = c4)) | (c2 = f4(c2)) | (f10(c2) = c3) | (~big_f(c2, c2)) | big_f(f10(c2), f1(f10(c2), c2)) | (f1(f10(c2), c2) = c2)))),
% 29.21/19.40 inference(monotonicity,[status(thm)],[21298])).
% 29.21/19.40 tff(21300,plain,
% 29.21/19.40 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((f10(c2) = c3) | (f1(f10(c2), c2) = c2) | big_f(f10(c2), f1(f10(c2), c2)) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (~(c2 = c4)) | (c2 = f4(c2)) | (f10(c2) = c3) | (~big_f(c2, c2)) | big_f(f10(c2), f1(f10(c2), c2)) | (f1(f10(c2), c2) = c2))),
% 29.21/19.40 inference(transitivity,[status(thm)],[21299, 21297])).
% 29.21/19.40 tff(21301,plain,
% 29.21/19.40 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((f10(c2) = c3) | (f1(f10(c2), c2) = c2) | big_f(f10(c2), f1(f10(c2), c2)) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)))),
% 29.21/19.40 inference(quant_inst,[status(thm)],[])).
% 29.21/19.40 tff(21302,plain,
% 29.21/19.40 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (~(c2 = c4)) | (c2 = f4(c2)) | (f10(c2) = c3) | (~big_f(c2, c2)) | big_f(f10(c2), f1(f10(c2), c2)) | (f1(f10(c2), c2) = c2)),
% 29.21/19.40 inference(modus_ponens,[status(thm)],[21301, 21300])).
% 29.21/19.40 tff(21303,plain,
% 29.21/19.40 (big_f(f10(c2), f1(f10(c2), c2)) | (f1(f10(c2), c2) = c2)),
% 29.21/19.40 inference(unit_resolution,[status(thm)],[21302, 525, 21270, 21277, 1345, 21121])).
% 29.21/19.40 tff(21304,plain,
% 29.21/19.40 (big_f(f10(c2), f1(f10(c2), c2))),
% 29.21/19.40 inference(unit_resolution,[status(thm)],[21303, 21296])).
% 29.21/19.40 tff(21305,plain,
% 29.21/19.40 (big_f(f7(c2), c1)),
% 29.21/19.40 inference(modus_ponens,[status(thm)],[21304, 21292])).
% 29.21/19.40 tff(21306,plain,
% 29.21/19.40 (big_f(f7(c2), f10(f7(c2)))),
% 29.21/19.40 inference(modus_ponens,[status(thm)],[21286, 21014])).
% 29.21/19.40 tff(21307,plain,
% 29.21/19.40 (~big_f(f7(c2), f7(c2))),
% 29.21/19.40 inference(unit_resolution,[status(thm)],[16899, 21287, 17, 21089, 21086, 21306])).
% 29.21/19.40 tff(21308,plain,
% 29.21/19.40 (~big_f(f7(c2), c1)),
% 29.21/19.40 inference(unit_resolution,[status(thm)],[17079, 21307, 22])).
% 29.21/19.40 tff(21309,plain,
% 29.21/19.40 ($false),
% 29.21/19.40 inference(unit_resolution,[status(thm)],[21308, 21305])).
% 29.21/19.40 tff(21310,plain,(big_f(c2, c1) | (~big_f(c2, c2)) | (f10(c2) = c2) | (f7(c2) = c2) | (~(f10(c1) = c2)) | (~(f4(c4) = c1)) | (f7(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.21/19.40 tff(21311,plain,
% 29.21/19.40 (big_f(c2, c1)),
% 29.21/19.40 inference(unit_resolution,[status(thm)],[21310, 20985, 17538, 17, 15, 15706, 115])).
% 29.21/19.40 tff(21312,plain,
% 29.21/19.40 (big_f(f7(f7(c2)), f7(c2))),
% 29.21/19.40 inference(modus_ponens,[status(thm)],[21311, 20998])).
% 29.21/19.40 tff(21313,plain,
% 29.21/19.40 (big_f(f7(f7(c2)), c2) <=> big_f(c2, c2)),
% 29.21/19.40 inference(monotonicity,[status(thm)],[20995])).
% 29.21/19.40 tff(21314,plain,
% 29.21/19.40 (big_f(c2, c2) <=> big_f(f7(f7(c2)), c2)),
% 29.21/19.40 inference(symmetry,[status(thm)],[21313])).
% 29.21/19.40 tff(21315,plain,
% 29.21/19.40 (big_f(f7(f7(c2)), c2)),
% 29.21/19.40 inference(modus_ponens,[status(thm)],[20985, 21314])).
% 29.21/19.40 tff(21316,plain,
% 29.21/19.40 ((f7(f7(c2)) = f7(c2)) <=> (f7(f7(c2)) = c1)),
% 29.21/19.40 inference(monotonicity,[status(thm)],[22])).
% 29.21/19.40 tff(21317,plain,
% 29.21/19.40 ((f7(f7(c2)) = c1) <=> (f7(f7(c2)) = f7(c2))),
% 29.21/19.40 inference(symmetry,[status(thm)],[21316])).
% 29.21/19.40 tff(21318,plain,
% 29.21/19.40 ((f7(f7(c2)) = c1) <=> (c2 = f10(c2))),
% 29.21/19.40 inference(monotonicity,[status(thm)],[20995, 17541])).
% 29.21/19.40 tff(21319,plain,
% 29.21/19.40 ((f7(f7(c2)) = c1) <=> (f10(c2) = c2)),
% 29.21/19.40 inference(transitivity,[status(thm)],[21318, 4987])).
% 29.21/19.40 tff(21320,plain,
% 29.21/19.40 ((f10(c2) = c2) <=> (f7(f7(c2)) = c1)),
% 29.21/19.40 inference(symmetry,[status(thm)],[21319])).
% 29.21/19.40 tff(21321,plain,
% 29.21/19.40 ((f10(c2) = c2) <=> (f7(f7(c2)) = f7(c2))),
% 29.21/19.40 inference(transitivity,[status(thm)],[21320, 21317])).
% 29.21/19.40 tff(21322,plain,
% 29.21/19.40 ((~(f10(c2) = c2)) <=> (~(f7(f7(c2)) = f7(c2)))),
% 29.21/19.40 inference(monotonicity,[status(thm)],[21321])).
% 29.21/19.40 tff(21323,plain,
% 29.21/19.40 (~(f7(f7(c2)) = f7(c2))),
% 29.21/19.40 inference(modus_ponens,[status(thm)],[17538, 21322])).
% 29.21/19.40 tff(21324,plain,
% 29.21/19.40 (big_f(f7(c2), f10(f7(c2))) <=> big_f(c1, c2)),
% 29.21/19.40 inference(monotonicity,[status(thm)],[22, 20988])).
% 29.21/19.40 tff(21325,plain,
% 29.21/19.40 (big_f(c1, c2) <=> big_f(f7(c2), f10(f7(c2)))),
% 29.21/19.40 inference(symmetry,[status(thm)],[21324])).
% 29.21/19.40 tff(21326,plain,
% 29.21/19.40 (~big_f(f7(c2), f10(c2))),
% 29.21/19.40 inference(unit_resolution,[status(thm)],[12536, 21311, 17538, 21315, 17, 120])).
% 29.21/19.40 tff(21327,plain,
% 29.21/19.40 ((~big_f(f7(c2), f10(c2))) <=> (~big_f(f7(c2), c1))),
% 29.21/19.40 inference(monotonicity,[status(thm)],[20918])).
% 29.21/19.40 tff(21328,assumption,(~big_f(f7(c2), f10(c2))), introduced(assumption)).
% 29.21/19.40 tff(21329,plain,
% 29.21/19.40 (~big_f(f7(c2), c1)),
% 29.21/19.40 inference(modus_ponens,[status(thm)],[21328, 21327])).
% 29.21/19.40 tff(21330,plain,
% 29.21/19.40 ($false),
% 29.21/19.40 inference(unit_resolution,[status(thm)],[338, 21329])).
% 29.21/19.40 tff(21331,plain,((~big_f(f7(c2), c1)) | big_f(f7(c2), f10(c2)) | (~(f10(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.21/19.40 tff(21332,plain,
% 29.21/19.40 (~big_f(f7(c2), c1)),
% 29.21/19.40 inference(unit_resolution,[status(thm)],[21331, 21326, 17539])).
% 29.21/19.40 tff(21333,plain,
% 29.21/19.40 (~big_f(c1, c1)),
% 29.21/19.40 inference(unit_resolution,[status(thm)],[20926, 21332, 22, 17539])).
% 29.21/19.40 tff(21334,plain,
% 29.21/19.40 (big_f(c2, f10(c2))),
% 29.21/19.40 inference(modus_ponens,[status(thm)],[21311, 17542])).
% 29.21/19.40 tff(21335,plain,
% 29.21/19.40 (f4(c4) = f4(f10(c2))),
% 29.21/19.40 inference(symmetry,[status(thm)],[15477])).
% 29.21/19.40 tff(21336,plain,
% 29.21/19.40 (f10(c2) = f4(f10(c2))),
% 29.21/19.40 inference(transitivity,[status(thm)],[94, 16651, 21335])).
% 29.21/19.40 tff(21337,plain,
% 29.21/19.40 (~(c3 = c1)),
% 29.21/19.40 inference(unit_resolution,[status(thm)],[19126, 66, 11752, 94, 17, 27])).
% 29.21/19.40 tff(21338,plain,
% 29.21/19.40 (c3 = c2),
% 29.21/19.40 inference(unit_resolution,[status(thm)],[180, 21337])).
% 29.21/19.40 tff(21339,plain,
% 29.21/19.40 (c2 = c3),
% 29.21/19.40 inference(modus_ponens,[status(thm)],[21338, 78])).
% 29.21/19.40 tff(21340,plain,
% 29.21/19.40 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = f2(c2)) | (~(f10(c2) = c4)) | (~big_f(c2, c2)) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2)))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = f2(c2)) | (~(f10(c2) = c4)) | (~big_f(c2, c2)) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2)))))),
% 29.21/19.40 inference(rewrite,[status(thm)],[])).
% 29.21/19.40 tff(21341,plain,
% 29.21/19.40 (((~(c2 = c3)) | (~(f10(c2) = c4)) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2)))) | (c2 = f2(c2)) | (~big_f(c2, c2))) <=> ((~(c2 = c3)) | (c2 = f2(c2)) | (~(f10(c2) = c4)) | (~big_f(c2, c2)) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2)))))),
% 29.21/19.40 inference(rewrite,[status(thm)],[])).
% 29.21/19.40 tff(21342,plain,
% 29.21/19.40 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(f10(c2) = c4)) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2)))) | (c2 = f2(c2)) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = f2(c2)) | (~(f10(c2) = c4)) | (~big_f(c2, c2)) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2))))))),
% 29.21/19.40 inference(monotonicity,[status(thm)],[21341])).
% 29.21/19.40 tff(21343,plain,
% 29.21/19.40 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(f10(c2) = c4)) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2)))) | (c2 = f2(c2)) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = f2(c2)) | (~(f10(c2) = c4)) | (~big_f(c2, c2)) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2)))))),
% 29.21/19.40 inference(transitivity,[status(thm)],[21342, 21340])).
% 29.21/19.40 tff(21344,plain,
% 29.21/19.40 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(f10(c2) = c4)) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2)))) | (c2 = f2(c2)) | (~big_f(c2, c2)))),
% 29.21/19.40 inference(quant_inst,[status(thm)],[])).
% 29.21/19.40 tff(21345,plain,
% 29.21/19.40 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = f2(c2)) | (~(f10(c2) = c4)) | (~big_f(c2, c2)) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2))))),
% 29.21/19.40 inference(modus_ponens,[status(thm)],[21344, 21343])).
% 29.21/19.40 tff(21346,plain,
% 29.21/19.40 (c2 = f2(c2)),
% 29.21/19.40 inference(unit_resolution,[status(thm)],[21345, 5622, 1345, 21339, 15484, 15266, 21095])).
% 29.21/19.40 tff(21347,plain,
% 29.21/19.40 (f2(c2) = c2),
% 29.21/19.40 inference(symmetry,[status(thm)],[21346])).
% 29.21/19.40 tff(21348,plain,
% 29.21/19.40 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(f10(c2) = c4)) | (f10(c2) = f2(c2)) | (~big_f(c2, f10(c2))) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2)))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (~(f10(c2) = c4)) | (f10(c2) = f2(c2)) | (~big_f(c2, f10(c2))) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2)))))),
% 29.21/19.40 inference(rewrite,[status(thm)],[])).
% 29.21/19.40 tff(21349,plain,
% 29.21/19.40 (((~(c2 = c3)) | (~(f10(c2) = c4)) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2)))) | (f10(c2) = f2(c2)) | (~big_f(c2, f10(c2)))) <=> ((~(c2 = c3)) | (~(f10(c2) = c4)) | (f10(c2) = f2(c2)) | (~big_f(c2, f10(c2))) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2)))))),
% 29.21/19.40 inference(rewrite,[status(thm)],[])).
% 29.21/19.40 tff(21350,plain,
% 29.21/19.40 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(f10(c2) = c4)) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2)))) | (f10(c2) = f2(c2)) | (~big_f(c2, f10(c2))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(f10(c2) = c4)) | (f10(c2) = f2(c2)) | (~big_f(c2, f10(c2))) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2))))))),
% 29.21/19.40 inference(monotonicity,[status(thm)],[21349])).
% 29.21/19.40 tff(21351,plain,
% 29.21/19.40 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(f10(c2) = c4)) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2)))) | (f10(c2) = f2(c2)) | (~big_f(c2, f10(c2))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (~(f10(c2) = c4)) | (f10(c2) = f2(c2)) | (~big_f(c2, f10(c2))) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2)))))),
% 29.21/19.40 inference(transitivity,[status(thm)],[21350, 21348])).
% 29.21/19.40 tff(21352,plain,
% 29.21/19.40 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(f10(c2) = c4)) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2)))) | (f10(c2) = f2(c2)) | (~big_f(c2, f10(c2))))),
% 29.21/19.40 inference(quant_inst,[status(thm)],[])).
% 29.21/19.40 tff(21353,plain,
% 29.21/19.40 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (~(f10(c2) = c4)) | (f10(c2) = f2(c2)) | (~big_f(c2, f10(c2))) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2))))),
% 29.21/19.40 inference(modus_ponens,[status(thm)],[21352, 21351])).
% 29.21/19.40 tff(21354,plain,
% 29.21/19.40 (f10(c2) = f2(c2)),
% 29.21/19.40 inference(unit_resolution,[status(thm)],[21353, 5622, 21339, 15484, 12291, 15266, 21095])).
% 29.21/19.40 tff(21355,plain,
% 29.21/19.40 (f10(c2) = c2),
% 29.21/19.40 inference(transitivity,[status(thm)],[21354, 21347])).
% 29.21/19.40 tff(21356,plain,
% 29.21/19.40 ($false),
% 29.21/19.40 inference(unit_resolution,[status(thm)],[89, 21355])).
% 29.21/19.40 tff(21357,plain,(big_f(c1, c1) | (f10(c2) = c2) | (~(f10(c2) = c4)) | (~big_f(c2, f10(c2))) | (~(f10(c2) = f4(f10(c2)))) | (~big_f(c2, c2)) | (~(f4(c4) = c1)) | (f7(c2) = c2) | big_f(c1, c2)), inference(lemma,lemma(discharge,[]))).
% 29.21/19.40 tff(21358,plain,
% 29.21/19.40 ($false),
% 29.21/19.40 inference(unit_resolution,[status(thm)],[21357, 21336, 15476, 89, 12291, 66, 1345, 11752, 17, 27])).
% 29.21/19.40 tff(21359,plain,((~(c4 = c1)) | (f10(c2) = c2) | (~big_f(c2, f10(c2))) | big_f(c1, c1) | (~big_f(c2, c2)) | (~(f4(c4) = c1)) | (f7(c2) = c2) | big_f(c1, c2)), inference(lemma,lemma(discharge,[]))).
% 29.21/19.40 tff(21360,plain,
% 29.21/19.40 (~(c4 = c1)),
% 29.21/19.40 inference(unit_resolution,[status(thm)],[21359, 27, 12291, 66, 1345, 11752, 17, 89])).
% 29.21/19.40 tff(21361,plain,
% 29.21/19.40 (c4 = c2),
% 29.21/19.40 inference(unit_resolution,[status(thm)],[461, 21360])).
% 29.21/19.40 tff(21362,plain,
% 29.21/19.40 (c2 = c4),
% 29.21/19.40 inference(modus_ponens,[status(thm)],[21361, 159])).
% 29.21/19.40 tff(21363,plain,
% 29.21/19.40 (~(c3 = c1)),
% 29.21/19.40 inference(unit_resolution,[status(thm)],[19126, 27, 11752, 94, 17, 66])).
% 29.21/19.40 tff(21364,plain,
% 29.21/19.40 (c3 = c2),
% 29.21/19.40 inference(unit_resolution,[status(thm)],[180, 21363])).
% 29.21/19.40 tff(21365,plain,
% 29.21/19.40 (c2 = c3),
% 29.21/19.40 inference(modus_ponens,[status(thm)],[21364, 78])).
% 29.21/19.40 tff(21366,plain,
% 29.21/19.40 (c2 = c4),
% 29.21/19.40 inference(symmetry,[status(thm)],[21361])).
% 29.21/19.40 tff(21367,plain,
% 29.21/19.40 (f4(c2) = f4(c4)),
% 29.21/19.40 inference(monotonicity,[status(thm)],[21366])).
% 29.21/19.40 tff(21368,plain,
% 29.21/19.40 (f4(c2) = f10(c2)),
% 29.21/19.40 inference(transitivity,[status(thm)],[21367, 11752, 99])).
% 29.21/19.40 tff(21369,plain,
% 29.21/19.40 ((c2 = f4(c2)) <=> (c2 = f10(c2))),
% 29.21/19.40 inference(monotonicity,[status(thm)],[21368])).
% 29.21/19.40 tff(21370,plain,
% 29.21/19.40 ((c2 = f4(c2)) <=> (f10(c2) = c2)),
% 29.21/19.40 inference(transitivity,[status(thm)],[21369, 4987])).
% 29.21/19.40 tff(21371,plain,
% 29.21/19.40 ((f10(c2) = c2) <=> (c2 = f4(c2))),
% 29.21/19.40 inference(symmetry,[status(thm)],[21370])).
% 29.21/19.40 tff(21372,plain,
% 29.21/19.40 ((~(f10(c2) = c2)) <=> (~(c2 = f4(c2)))),
% 29.21/19.40 inference(monotonicity,[status(thm)],[21371])).
% 29.21/19.40 tff(21373,plain,
% 29.21/19.40 (~(c2 = f4(c2))),
% 29.21/19.40 inference(modus_ponens,[status(thm)],[89, 21372])).
% 29.21/19.40 tff(21374,plain,
% 29.21/19.40 ((~(c2 = c3)) | (~(c2 = c4)) | (c2 = f4(c2)) | (c2 = f2(c2))),
% 29.21/19.40 inference(unit_resolution,[status(thm)],[17172, 1355, 1345])).
% 29.21/19.40 tff(21375,plain,
% 29.21/19.40 (c2 = f2(c2)),
% 29.21/19.40 inference(unit_resolution,[status(thm)],[21374, 21373, 21365, 21362])).
% 29.21/19.40 tff(21376,plain,
% 29.21/19.40 (f2(c2) = c2),
% 29.21/19.40 inference(symmetry,[status(thm)],[21375])).
% 29.21/19.40 tff(21377,plain,
% 29.21/19.40 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c2 = c4)) | (c2 = f4(c2)) | (f10(c2) = f2(c2)) | (~big_f(c2, f10(c2))) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (~(c2 = c4)) | (c2 = f4(c2)) | (f10(c2) = f2(c2)) | (~big_f(c2, f10(c2))) | (~big_f(c2, c2)))),
% 29.21/19.40 inference(rewrite,[status(thm)],[])).
% 29.21/19.40 tff(21378,plain,
% 29.21/19.40 (((~(c2 = c3)) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)) | (f10(c2) = f2(c2)) | (~big_f(c2, f10(c2)))) <=> ((~(c2 = c3)) | (~(c2 = c4)) | (c2 = f4(c2)) | (f10(c2) = f2(c2)) | (~big_f(c2, f10(c2))) | (~big_f(c2, c2)))),
% 29.21/19.40 inference(rewrite,[status(thm)],[])).
% 29.21/19.40 tff(21379,plain,
% 29.21/19.40 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)) | (f10(c2) = f2(c2)) | (~big_f(c2, f10(c2))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c2 = c4)) | (c2 = f4(c2)) | (f10(c2) = f2(c2)) | (~big_f(c2, f10(c2))) | (~big_f(c2, c2))))),
% 29.21/19.40 inference(monotonicity,[status(thm)],[21378])).
% 29.21/19.40 tff(21380,plain,
% 29.21/19.40 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)) | (f10(c2) = f2(c2)) | (~big_f(c2, f10(c2))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (~(c2 = c4)) | (c2 = f4(c2)) | (f10(c2) = f2(c2)) | (~big_f(c2, f10(c2))) | (~big_f(c2, c2)))),
% 29.21/19.40 inference(transitivity,[status(thm)],[21379, 21377])).
% 29.21/19.40 tff(21381,plain,
% 29.21/19.40 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)) | (f10(c2) = f2(c2)) | (~big_f(c2, f10(c2))))),
% 29.21/19.40 inference(quant_inst,[status(thm)],[])).
% 29.21/19.40 tff(21382,plain,
% 29.21/19.40 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (~(c2 = c4)) | (c2 = f4(c2)) | (f10(c2) = f2(c2)) | (~big_f(c2, f10(c2))) | (~big_f(c2, c2))),
% 29.21/19.41 inference(modus_ponens,[status(thm)],[21381, 21380])).
% 29.21/19.41 tff(21383,plain,
% 29.21/19.41 ((~(c2 = c3)) | (~(c2 = c4)) | (c2 = f4(c2)) | (f10(c2) = f2(c2))),
% 29.21/19.41 inference(unit_resolution,[status(thm)],[21382, 1355, 1345, 12291])).
% 29.21/19.41 tff(21384,plain,
% 29.21/19.41 (f10(c2) = f2(c2)),
% 29.21/19.41 inference(unit_resolution,[status(thm)],[21383, 21373, 21365, 21362])).
% 29.21/19.41 tff(21385,plain,
% 29.21/19.41 (f10(c2) = c2),
% 29.21/19.41 inference(transitivity,[status(thm)],[21384, 21376])).
% 29.21/19.41 tff(21386,plain,
% 29.21/19.41 ($false),
% 29.21/19.41 inference(unit_resolution,[status(thm)],[89, 21385])).
% 29.21/19.41 tff(21387,plain,(big_f(c1, c2) | (f10(c2) = c2) | (~big_f(c2, c2)) | (~big_f(c2, f10(c2))) | (~(f4(c4) = c1)) | big_f(c1, c1) | (f7(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 29.21/19.41 tff(21388,plain,
% 29.21/19.41 (big_f(c1, c2)),
% 29.21/19.41 inference(unit_resolution,[status(thm)],[21387, 20985, 17538, 21334, 15706, 21333, 17])).
% 29.21/19.41 tff(21389,plain,
% 29.21/19.41 (big_f(f7(c2), f10(f7(c2)))),
% 29.21/19.41 inference(modus_ponens,[status(thm)],[21388, 21325])).
% 29.21/19.41 tff(21390,plain,
% 29.21/19.41 (f7(c2) = f8(f7(c2))),
% 29.21/19.41 inference(unit_resolution,[status(thm)],[13317, 21389, 21323, 21315, 21312, 20993, 17])).
% 29.21/19.41 tff(21391,plain,
% 29.21/19.41 (f8(f7(c2)) = f7(c2)),
% 29.21/19.41 inference(symmetry,[status(thm)],[21390])).
% 29.21/19.41 tff(21392,plain,
% 29.21/19.41 (f10(c2) = f7(c2)),
% 29.21/19.41 inference(transitivity,[status(thm)],[17539, 125])).
% 29.21/19.41 tff(21393,plain,
% 29.21/19.41 (f8(f10(c2)) = f8(f7(c2))),
% 29.21/19.41 inference(monotonicity,[status(thm)],[21392])).
% 29.21/19.41 tff(21394,plain,
% 29.21/19.41 (f8(f10(c2)) = f10(c2)),
% 29.21/19.41 inference(transitivity,[status(thm)],[21393, 21391, 22, 17541])).
% 29.21/19.41 tff(21395,plain,
% 29.21/19.41 ((c2 = f8(f10(c2))) <=> (c2 = f10(c2))),
% 29.21/19.41 inference(monotonicity,[status(thm)],[21394])).
% 29.21/19.41 tff(21396,plain,
% 29.21/19.41 ((c2 = f8(f10(c2))) <=> (f10(c2) = c2)),
% 29.21/19.41 inference(transitivity,[status(thm)],[21395, 4987])).
% 29.21/19.41 tff(21397,plain,
% 29.21/19.41 ((f10(c2) = c2) <=> (c2 = f8(f10(c2)))),
% 29.21/19.41 inference(symmetry,[status(thm)],[21396])).
% 29.21/19.41 tff(21398,plain,
% 29.21/19.41 ((~(f10(c2) = c2)) <=> (~(c2 = f8(f10(c2))))),
% 29.21/19.41 inference(monotonicity,[status(thm)],[21397])).
% 29.21/19.41 tff(21399,plain,
% 29.21/19.41 (~(c2 = f8(f10(c2)))),
% 29.21/19.41 inference(modus_ponens,[status(thm)],[17538, 21398])).
% 29.21/19.41 tff(21400,plain,
% 29.21/19.41 (f10(f10(c2)) = c2),
% 29.21/19.41 inference(transitivity,[status(thm)],[17540, 15])).
% 29.21/19.41 tff(21401,plain,
% 29.21/19.41 (big_f(c2, f10(f10(c2))) <=> big_f(c2, c2)),
% 29.21/19.41 inference(monotonicity,[status(thm)],[21400])).
% 29.21/19.41 tff(21402,plain,
% 29.21/19.41 (big_f(c2, c2) <=> big_f(c2, f10(f10(c2)))),
% 29.21/19.41 inference(symmetry,[status(thm)],[21401])).
% 29.21/19.41 tff(21403,plain,
% 29.21/19.41 (big_f(c2, f10(f10(c2)))),
% 29.21/19.41 inference(modus_ponens,[status(thm)],[20985, 21402])).
% 29.21/19.41 tff(21404,plain,
% 29.21/19.41 ((f10(f10(c2)) = f10(c2)) <=> (c2 = f10(c2))),
% 29.21/19.41 inference(monotonicity,[status(thm)],[21400])).
% 29.21/19.41 tff(21405,plain,
% 29.21/19.41 ((f10(f10(c2)) = f10(c2)) <=> (f10(c2) = c2)),
% 29.21/19.41 inference(transitivity,[status(thm)],[21404, 4987])).
% 29.21/19.41 tff(21406,plain,
% 29.21/19.41 ((f10(c2) = c2) <=> (f10(f10(c2)) = f10(c2))),
% 29.21/19.41 inference(symmetry,[status(thm)],[21405])).
% 29.21/19.41 tff(21407,plain,
% 29.21/19.41 ((~(f10(c2) = c2)) <=> (~(f10(f10(c2)) = f10(c2)))),
% 29.21/19.41 inference(monotonicity,[status(thm)],[21406])).
% 29.21/19.41 tff(21408,plain,
% 29.21/19.41 (~(f10(f10(c2)) = f10(c2))),
% 29.21/19.41 inference(modus_ponens,[status(thm)],[17538, 21407])).
% 29.21/19.41 tff(21409,plain,
% 29.21/19.41 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f10(c2)) = f10(c2)) | (c2 = f8(f10(c2))) | (~big_f(c2, f10(f10(c2)))) | (c2 = f5(f10(c2))) | (f7(f10(c2)) = f10(c2)) | (~big_f(f7(f10(c2)), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(f10(c2)) = f10(c2)) | (c2 = f8(f10(c2))) | (~big_f(c2, f10(f10(c2)))) | (c2 = f5(f10(c2))) | (f7(f10(c2)) = f10(c2)) | (~big_f(f7(f10(c2)), c2)))),
% 29.21/19.41 inference(rewrite,[status(thm)],[])).
% 29.21/19.41 tff(21410,plain,
% 29.21/19.41 (((f10(f10(c2)) = f10(c2)) | (c2 = f8(f10(c2))) | (~big_f(c2, f10(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | (c2 = f5(f10(c2))) | (~big_f(f7(f10(c2)), c2))) <=> ((f10(f10(c2)) = f10(c2)) | (c2 = f8(f10(c2))) | (~big_f(c2, f10(f10(c2)))) | (c2 = f5(f10(c2))) | (f7(f10(c2)) = f10(c2)) | (~big_f(f7(f10(c2)), c2)))),
% 29.21/19.41 inference(rewrite,[status(thm)],[])).
% 29.21/19.41 tff(21411,plain,
% 29.21/19.41 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f10(c2)) = f10(c2)) | (c2 = f8(f10(c2))) | (~big_f(c2, f10(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | (c2 = f5(f10(c2))) | (~big_f(f7(f10(c2)), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f10(c2)) = f10(c2)) | (c2 = f8(f10(c2))) | (~big_f(c2, f10(f10(c2)))) | (c2 = f5(f10(c2))) | (f7(f10(c2)) = f10(c2)) | (~big_f(f7(f10(c2)), c2))))),
% 29.21/19.41 inference(monotonicity,[status(thm)],[21410])).
% 29.21/19.41 tff(21412,plain,
% 29.21/19.41 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f10(c2)) = f10(c2)) | (c2 = f8(f10(c2))) | (~big_f(c2, f10(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | (c2 = f5(f10(c2))) | (~big_f(f7(f10(c2)), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(f10(c2)) = f10(c2)) | (c2 = f8(f10(c2))) | (~big_f(c2, f10(f10(c2)))) | (c2 = f5(f10(c2))) | (f7(f10(c2)) = f10(c2)) | (~big_f(f7(f10(c2)), c2)))),
% 29.21/19.41 inference(transitivity,[status(thm)],[21411, 21409])).
% 29.21/19.41 tff(21413,plain,
% 29.21/19.41 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f10(c2)) = f10(c2)) | (c2 = f8(f10(c2))) | (~big_f(c2, f10(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | (c2 = f5(f10(c2))) | (~big_f(f7(f10(c2)), c2)))),
% 29.21/19.41 inference(quant_inst,[status(thm)],[])).
% 29.21/19.41 tff(21414,plain,
% 29.21/19.41 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(f10(c2)) = f10(c2)) | (c2 = f8(f10(c2))) | (~big_f(c2, f10(f10(c2)))) | (c2 = f5(f10(c2))) | (f7(f10(c2)) = f10(c2)) | (~big_f(f7(f10(c2)), c2))),
% 29.21/19.41 inference(modus_ponens,[status(thm)],[21413, 21412])).
% 29.21/19.41 tff(21415,plain,
% 29.21/19.41 ((c2 = f8(f10(c2))) | (c2 = f5(f10(c2))) | (~big_f(f7(f10(c2)), c2))),
% 29.21/19.41 inference(unit_resolution,[status(thm)],[21414, 1659, 21408, 21403, 20958])).
% 29.21/19.41 tff(21416,plain,
% 29.21/19.41 (c2 = f5(f10(c2))),
% 29.21/19.41 inference(unit_resolution,[status(thm)],[21415, 21399, 20986])).
% 29.21/19.41 tff(21417,plain,
% 29.21/19.41 (f5(f10(c2)) = c2),
% 29.21/19.41 inference(symmetry,[status(thm)],[21416])).
% 29.21/19.41 tff(21418,plain,
% 29.21/19.41 (big_f(f7(f10(c2)), f10(c2)) <=> big_f(c2, f10(c2))),
% 29.21/19.41 inference(monotonicity,[status(thm)],[17545])).
% 29.21/19.41 tff(21419,plain,
% 29.21/19.41 (big_f(c2, f10(c2)) <=> big_f(f7(f10(c2)), f10(c2))),
% 29.21/19.41 inference(symmetry,[status(thm)],[21418])).
% 29.21/19.41 tff(21420,plain,
% 29.21/19.41 (big_f(f7(f10(c2)), f10(c2))),
% 29.21/19.41 inference(modus_ponens,[status(thm)],[21334, 21419])).
% 29.21/19.41 tff(21421,plain,
% 29.21/19.41 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f10(c2)) = f10(c2)) | (c2 = f8(f10(c2))) | (~big_f(c2, f10(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | (~big_f(f7(f10(c2)), f10(c2))) | (f10(c2) = f5(f10(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(f10(c2)) = f10(c2)) | (c2 = f8(f10(c2))) | (~big_f(c2, f10(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | (~big_f(f7(f10(c2)), f10(c2))) | (f10(c2) = f5(f10(c2))))),
% 29.21/19.41 inference(rewrite,[status(thm)],[])).
% 29.21/19.41 tff(21422,plain,
% 29.21/19.41 (((f10(f10(c2)) = f10(c2)) | (c2 = f8(f10(c2))) | (~big_f(c2, f10(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | (f10(c2) = f5(f10(c2))) | (~big_f(f7(f10(c2)), f10(c2)))) <=> ((f10(f10(c2)) = f10(c2)) | (c2 = f8(f10(c2))) | (~big_f(c2, f10(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | (~big_f(f7(f10(c2)), f10(c2))) | (f10(c2) = f5(f10(c2))))),
% 29.21/19.41 inference(rewrite,[status(thm)],[])).
% 29.21/19.41 tff(21423,plain,
% 29.21/19.41 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f10(c2)) = f10(c2)) | (c2 = f8(f10(c2))) | (~big_f(c2, f10(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | (f10(c2) = f5(f10(c2))) | (~big_f(f7(f10(c2)), f10(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f10(c2)) = f10(c2)) | (c2 = f8(f10(c2))) | (~big_f(c2, f10(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | (~big_f(f7(f10(c2)), f10(c2))) | (f10(c2) = f5(f10(c2)))))),
% 29.21/19.41 inference(monotonicity,[status(thm)],[21422])).
% 29.21/19.41 tff(21424,plain,
% 29.21/19.41 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f10(c2)) = f10(c2)) | (c2 = f8(f10(c2))) | (~big_f(c2, f10(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | (f10(c2) = f5(f10(c2))) | (~big_f(f7(f10(c2)), f10(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(f10(c2)) = f10(c2)) | (c2 = f8(f10(c2))) | (~big_f(c2, f10(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | (~big_f(f7(f10(c2)), f10(c2))) | (f10(c2) = f5(f10(c2))))),
% 29.21/19.41 inference(transitivity,[status(thm)],[21423, 21421])).
% 29.21/19.41 tff(21425,plain,
% 29.21/19.41 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f10(c2)) = f10(c2)) | (c2 = f8(f10(c2))) | (~big_f(c2, f10(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | (f10(c2) = f5(f10(c2))) | (~big_f(f7(f10(c2)), f10(c2))))),
% 29.21/19.41 inference(quant_inst,[status(thm)],[])).
% 29.21/19.41 tff(21426,plain,
% 29.21/19.41 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(f10(c2)) = f10(c2)) | (c2 = f8(f10(c2))) | (~big_f(c2, f10(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | (~big_f(f7(f10(c2)), f10(c2))) | (f10(c2) = f5(f10(c2)))),
% 29.21/19.41 inference(modus_ponens,[status(thm)],[21425, 21424])).
% 29.21/19.41 tff(21427,plain,
% 29.21/19.41 ((c2 = f8(f10(c2))) | (f10(c2) = f5(f10(c2)))),
% 29.21/19.41 inference(unit_resolution,[status(thm)],[21426, 1659, 21408, 21403, 20958, 21420])).
% 29.21/19.41 tff(21428,plain,
% 29.21/19.41 (f10(c2) = f5(f10(c2))),
% 29.21/19.41 inference(unit_resolution,[status(thm)],[21427, 21399])).
% 29.21/19.41 tff(21429,plain,
% 29.21/19.41 (f10(c2) = c2),
% 29.21/19.41 inference(transitivity,[status(thm)],[21428, 21417])).
% 29.21/19.41 tff(21430,plain,
% 29.21/19.41 ($false),
% 29.21/19.41 inference(unit_resolution,[status(thm)],[17538, 21429])).
% 29.21/19.41 tff(21431,plain,((f7(c2) = c2) | (f7(c1) = c1) | (f10(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.21/19.41 tff(21432,plain,
% 29.21/19.41 (f7(c2) = c2),
% 29.21/19.41 inference(unit_resolution,[status(thm)],[21431, 3, 115])).
% 29.21/19.41 tff(21433,plain,
% 29.21/19.41 (~big_f(c1, f10(c1))),
% 29.21/19.41 inference(unit_resolution,[status(thm)],[12239, 27, 17539, 21400])).
% 29.21/19.41 tff(21434,plain,
% 29.21/19.41 (big_f(f7(c1), c1)),
% 29.21/19.41 inference(unit_resolution,[status(thm)],[11906, 121, 21408, 20958, 115, 3, 27, 17539])).
% 29.21/19.41 tff(21435,plain,
% 29.21/19.41 (big_f(c2, c1)),
% 29.21/19.41 inference(unit_resolution,[status(thm)],[15738, 21434, 120])).
% 29.21/19.41 tff(21436,plain,
% 29.21/19.41 (~(f5(c1) = c1)),
% 29.21/19.41 inference(unit_resolution,[status(thm)],[13594, 21435, 21432, 3, 21433, 121])).
% 29.21/19.41 tff(21437,plain,
% 29.21/19.41 (f5(c1) = c2),
% 29.21/19.41 inference(unit_resolution,[status(thm)],[1708, 21436])).
% 29.21/19.41 tff(21438,plain,
% 29.21/19.41 (c2 = f5(c1)),
% 29.21/19.41 inference(modus_ponens,[status(thm)],[21437, 155])).
% 29.21/19.41 tff(21439,plain,
% 29.21/19.41 (~(c2 = f8(c1))),
% 29.21/19.41 inference(unit_resolution,[status(thm)],[1752, 1726, 115, 21438, 6126, 3])).
% 29.21/19.41 tff(21440,plain,
% 29.21/19.41 (~(f8(c1) = c2)),
% 29.21/19.41 inference(unit_resolution,[status(thm)],[1675, 21439])).
% 29.21/19.41 tff(21441,plain,
% 29.21/19.41 (f8(c1) = c1),
% 29.21/19.41 inference(unit_resolution,[status(thm)],[1680, 21440])).
% 29.21/19.41 tff(21442,plain,
% 29.21/19.41 (big_f(f8(c1), f10(c1)) <=> big_f(c1, c2)),
% 29.21/19.41 inference(monotonicity,[status(thm)],[21441, 15])).
% 29.21/19.41 tff(21443,plain,
% 29.21/19.41 (big_f(c1, c2) <=> big_f(f8(c1), f10(c1))),
% 29.21/19.41 inference(symmetry,[status(thm)],[21442])).
% 29.21/19.41 tff(21444,plain,
% 29.21/19.41 ((~big_f(c1, c2)) <=> (~big_f(f8(c1), f10(c1)))),
% 29.21/19.41 inference(monotonicity,[status(thm)],[21443])).
% 29.21/19.41 tff(21445,plain,
% 29.21/19.41 (~big_f(f8(c1), f10(c1))),
% 29.21/19.41 inference(modus_ponens,[status(thm)],[27, 21444])).
% 29.21/19.41 tff(21446,plain,
% 29.21/19.41 (~big_f(f7(c1), f5(c1))),
% 29.21/19.41 inference(unit_resolution,[status(thm)],[1715, 21437, 120, 121])).
% 29.21/19.41 tff(21447,plain,
% 29.21/19.41 (big_f(f8(c1), f10(c1))),
% 29.21/19.41 inference(unit_resolution,[status(thm)],[2848, 21446, 115, 3])).
% 29.21/19.41 tff(21448,plain,
% 29.21/19.41 ($false),
% 29.21/19.41 inference(unit_resolution,[status(thm)],[21447, 21445])).
% 29.21/19.41 tff(21449,plain,(big_f(c2, c2) | big_f(c1, c2) | (f7(c1) = c1) | (f10(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.21/19.41 tff(21450,plain,
% 29.21/19.41 (big_f(c2, c2)),
% 29.21/19.41 inference(unit_resolution,[status(thm)],[21449, 27, 115, 3])).
% 29.21/19.41 tff(21451,plain,
% 29.21/19.41 (f10(c3) = f10(f10(c2))),
% 29.21/19.41 inference(monotonicity,[status(thm)],[15331])).
% 29.21/19.41 tff(21452,plain,
% 29.21/19.41 (f10(c3) = c2),
% 29.21/19.41 inference(transitivity,[status(thm)],[21451, 15299, 16])).
% 29.21/19.41 tff(21453,plain,
% 29.21/19.41 ((f10(c3) = c1) <=> (c2 = f10(c2))),
% 29.21/19.41 inference(monotonicity,[status(thm)],[21452, 99])).
% 29.21/19.41 tff(21454,plain,
% 29.21/19.41 ((f10(c3) = c1) <=> (f10(c2) = c2)),
% 29.21/19.41 inference(transitivity,[status(thm)],[21453, 4987])).
% 29.21/19.41 tff(21455,plain,
% 29.21/19.41 ((f10(c2) = c2) <=> (f10(c3) = c1)),
% 29.21/19.41 inference(symmetry,[status(thm)],[21454])).
% 29.21/19.41 tff(21456,plain,
% 29.21/19.41 ((f10(c2) = c2) <=> (f10(c3) = c3)),
% 29.21/19.41 inference(transitivity,[status(thm)],[21455, 8827])).
% 29.21/19.41 tff(21457,plain,
% 29.21/19.41 ((~(f10(c2) = c2)) <=> (~(f10(c3) = c3))),
% 29.21/19.41 inference(monotonicity,[status(thm)],[21456])).
% 29.21/19.41 tff(21458,plain,
% 29.21/19.41 (~(f10(c3) = c3)),
% 29.21/19.41 inference(modus_ponens,[status(thm)],[89, 21457])).
% 29.21/19.41 tff(21459,plain,
% 29.21/19.41 (big_f(c2, f10(f10(c2))) <=> big_f(c2, c2)),
% 29.21/19.41 inference(monotonicity,[status(thm)],[13433])).
% 29.21/19.41 tff(21460,plain,
% 29.21/19.41 (big_f(c2, c2) <=> big_f(c2, f10(f10(c2)))),
% 29.21/19.41 inference(symmetry,[status(thm)],[21459])).
% 29.21/19.41 tff(21461,plain,
% 29.21/19.41 (big_f(c2, f10(f10(c2)))),
% 29.21/19.41 inference(modus_ponens,[status(thm)],[1345, 21460])).
% 29.21/19.41 tff(21462,plain,
% 29.21/19.41 (big_f(c2, c4) <=> big_f(c2, f10(c2))),
% 29.21/19.41 inference(monotonicity,[status(thm)],[21054])).
% 29.21/19.41 tff(21463,plain,
% 29.21/19.41 (big_f(c2, f10(c2)) <=> big_f(c2, c4)),
% 29.21/19.41 inference(symmetry,[status(thm)],[21462])).
% 29.21/19.41 tff(21464,plain,
% 29.21/19.41 ((~big_f(c2, f10(c2))) <=> (~big_f(c2, c4))),
% 29.21/19.41 inference(monotonicity,[status(thm)],[21463])).
% 29.21/19.41 tff(21465,plain,
% 29.21/19.41 (~big_f(c2, c4)),
% 29.21/19.41 inference(modus_ponens,[status(thm)],[15517, 21464])).
% 29.21/19.41 tff(21466,plain,
% 29.21/19.41 (~(f1(c2, c2) = c2)),
% 29.21/19.41 inference(unit_resolution,[status(thm)],[16745, 12882, 1345, 377, 873])).
% 29.21/19.41 tff(21467,plain,
% 29.21/19.41 (f1(c2, c2) = c1),
% 29.21/19.41 inference(unit_resolution,[status(thm)],[5270, 21466])).
% 29.21/19.41 tff(21468,plain,
% 29.21/19.41 (big_f(c2, f1(c2, c2))),
% 29.21/19.41 inference(unit_resolution,[status(thm)],[16713, 21466, 1345, 377, 873, 12882])).
% 29.21/19.41 tff(21469,plain,
% 29.21/19.41 ($false),
% 29.21/19.41 inference(unit_resolution,[status(thm)],[14891, 21468, 21467, 9094, 3865])).
% 29.21/19.41 tff(21470,plain,(big_f(f3(c2, c2), c2) | big_f(c2, c4) | (~big_f(c2, c2)) | (c2 = c3) | (c2 = c4)), inference(lemma,lemma(discharge,[]))).
% 29.21/19.41 tff(21471,plain,
% 29.21/19.41 (big_f(f3(c2, c2), c2)),
% 29.21/19.41 inference(unit_resolution,[status(thm)],[21470, 21465, 1345, 377, 873])).
% 29.21/19.41 tff(21472,plain,
% 29.21/19.41 (~(f3(c2, c2) = c2)),
% 29.21/19.41 inference(unit_resolution,[status(thm)],[21039, 21471, 873, 377, 1345, 21465])).
% 29.21/19.41 tff(21473,plain,
% 29.21/19.41 (f6(c2, c2) = f6(c2, f7(f4(c4)))),
% 29.21/19.41 inference(monotonicity,[status(thm)],[16245])).
% 29.21/19.41 tff(21474,plain,
% 29.21/19.41 (f6(c2, c2) = f10(c2)),
% 29.21/19.41 inference(transitivity,[status(thm)],[21473, 17484, 12231])).
% 29.21/19.41 tff(21475,plain,
% 29.21/19.41 (big_f(f7(c2), f6(c2, c2)) <=> big_f(c2, f10(c2))),
% 29.21/19.41 inference(monotonicity,[status(thm)],[77, 21474])).
% 29.21/19.41 tff(21476,plain,
% 29.21/19.41 (big_f(c2, f10(c2)) <=> big_f(f7(c2), f6(c2, c2))),
% 29.21/19.41 inference(symmetry,[status(thm)],[21475])).
% 29.21/19.41 tff(21477,plain,
% 29.21/19.41 ((~big_f(c2, f10(c2))) <=> (~big_f(f7(c2), f6(c2, c2)))),
% 29.21/19.41 inference(monotonicity,[status(thm)],[21476])).
% 29.21/19.41 tff(21478,plain,
% 29.21/19.41 (~big_f(f7(c2), f6(c2, c2))),
% 29.21/19.41 inference(modus_ponens,[status(thm)],[15517, 21477])).
% 29.21/19.41 tff(21479,assumption,(big_f(c2, f10(f10(c2)))), introduced(assumption)).
% 29.21/19.41 tff(21480,plain,
% 29.21/19.41 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f7(c2) = c2)) | (f10(f10(c2)) = f10(c2)) | (f6(c2, c2) = c2) | (c2 = f8(f10(c2))) | big_f(f7(c2), f6(c2, c2)) | (~big_f(c2, f10(f10(c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c2) = c2)) | (f10(f10(c2)) = f10(c2)) | (f6(c2, c2) = c2) | (c2 = f8(f10(c2))) | big_f(f7(c2), f6(c2, c2)) | (~big_f(c2, f10(f10(c2)))))),
% 29.21/19.41 inference(rewrite,[status(thm)],[])).
% 29.21/19.41 tff(21481,plain,
% 29.21/19.41 (((f10(f10(c2)) = f10(c2)) | (c2 = f8(f10(c2))) | (~big_f(c2, f10(f10(c2)))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2))) <=> ((~(f7(c2) = c2)) | (f10(f10(c2)) = f10(c2)) | (f6(c2, c2) = c2) | (c2 = f8(f10(c2))) | big_f(f7(c2), f6(c2, c2)) | (~big_f(c2, f10(f10(c2)))))),
% 29.21/19.41 inference(rewrite,[status(thm)],[])).
% 29.21/19.41 tff(21482,plain,
% 29.21/19.41 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f10(c2)) = f10(c2)) | (c2 = f8(f10(c2))) | (~big_f(c2, f10(f10(c2)))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f7(c2) = c2)) | (f10(f10(c2)) = f10(c2)) | (f6(c2, c2) = c2) | (c2 = f8(f10(c2))) | big_f(f7(c2), f6(c2, c2)) | (~big_f(c2, f10(f10(c2))))))),
% 29.21/19.41 inference(monotonicity,[status(thm)],[21481])).
% 29.21/19.41 tff(21483,plain,
% 29.21/19.41 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f10(c2)) = f10(c2)) | (c2 = f8(f10(c2))) | (~big_f(c2, f10(f10(c2)))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c2) = c2)) | (f10(f10(c2)) = f10(c2)) | (f6(c2, c2) = c2) | (c2 = f8(f10(c2))) | big_f(f7(c2), f6(c2, c2)) | (~big_f(c2, f10(f10(c2)))))),
% 29.21/19.41 inference(transitivity,[status(thm)],[21482, 21480])).
% 29.21/19.41 tff(21484,plain,
% 29.21/19.41 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f10(c2)) = f10(c2)) | (c2 = f8(f10(c2))) | (~big_f(c2, f10(f10(c2)))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)))),
% 29.21/19.41 inference(quant_inst,[status(thm)],[])).
% 29.21/19.41 tff(21485,plain,
% 29.21/19.41 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c2) = c2)) | (f10(f10(c2)) = f10(c2)) | (f6(c2, c2) = c2) | (c2 = f8(f10(c2))) | big_f(f7(c2), f6(c2, c2)) | (~big_f(c2, f10(f10(c2))))),
% 29.21/19.41 inference(modus_ponens,[status(thm)],[21484, 21483])).
% 29.21/19.41 tff(21486,plain,
% 29.21/19.41 (c2 = f8(f10(c2))),
% 29.21/19.41 inference(unit_resolution,[status(thm)],[21485, 2662, 77, 11896, 21479, 2637, 21478])).
% 29.21/19.41 tff(21487,plain,
% 29.21/19.41 (f8(f10(c2)) = c2),
% 29.21/19.41 inference(symmetry,[status(thm)],[21486])).
% 29.21/19.41 tff(21488,plain,
% 29.21/19.41 (big_f(f3(c2, c2), f10(f10(c2)))),
% 29.21/19.41 inference(modus_ponens,[status(thm)],[15356, 21202])).
% 29.21/19.41 tff(21489,plain,
% 29.21/19.41 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f7(c2) = c2)) | (f10(f10(c2)) = f10(c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (f3(c2, c2) = f8(f10(c2))) | (~big_f(f3(c2, c2), f10(f10(c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c2) = c2)) | (f10(f10(c2)) = f10(c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (f3(c2, c2) = f8(f10(c2))) | (~big_f(f3(c2, c2), f10(f10(c2)))))),
% 29.21/19.41 inference(rewrite,[status(thm)],[])).
% 29.21/19.41 tff(21490,plain,
% 29.21/19.41 (((f10(f10(c2)) = f10(c2)) | (f3(c2, c2) = f8(f10(c2))) | (~big_f(f3(c2, c2), f10(f10(c2)))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2))) <=> ((~(f7(c2) = c2)) | (f10(f10(c2)) = f10(c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (f3(c2, c2) = f8(f10(c2))) | (~big_f(f3(c2, c2), f10(f10(c2)))))),
% 29.21/19.41 inference(rewrite,[status(thm)],[])).
% 29.21/19.41 tff(21491,plain,
% 29.21/19.41 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f10(c2)) = f10(c2)) | (f3(c2, c2) = f8(f10(c2))) | (~big_f(f3(c2, c2), f10(f10(c2)))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f7(c2) = c2)) | (f10(f10(c2)) = f10(c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (f3(c2, c2) = f8(f10(c2))) | (~big_f(f3(c2, c2), f10(f10(c2))))))),
% 29.21/19.41 inference(monotonicity,[status(thm)],[21490])).
% 29.21/19.41 tff(21492,plain,
% 29.21/19.41 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f10(c2)) = f10(c2)) | (f3(c2, c2) = f8(f10(c2))) | (~big_f(f3(c2, c2), f10(f10(c2)))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c2) = c2)) | (f10(f10(c2)) = f10(c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (f3(c2, c2) = f8(f10(c2))) | (~big_f(f3(c2, c2), f10(f10(c2)))))),
% 29.21/19.41 inference(transitivity,[status(thm)],[21491, 21489])).
% 29.21/19.41 tff(21493,plain,
% 29.21/19.41 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f10(c2)) = f10(c2)) | (f3(c2, c2) = f8(f10(c2))) | (~big_f(f3(c2, c2), f10(f10(c2)))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)))),
% 29.21/19.41 inference(quant_inst,[status(thm)],[])).
% 29.21/19.41 tff(21494,plain,
% 29.21/19.41 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c2) = c2)) | (f10(f10(c2)) = f10(c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (f3(c2, c2) = f8(f10(c2))) | (~big_f(f3(c2, c2), f10(f10(c2))))),
% 29.21/19.41 inference(modus_ponens,[status(thm)],[21493, 21492])).
% 29.21/19.41 tff(21495,plain,
% 29.21/19.41 (f3(c2, c2) = f8(f10(c2))),
% 29.21/19.41 inference(unit_resolution,[status(thm)],[21494, 2662, 77, 11896, 2637, 21478, 21488])).
% 29.21/19.41 tff(21496,plain,
% 29.21/19.41 (f3(c2, c2) = c2),
% 29.21/19.41 inference(transitivity,[status(thm)],[21495, 21487])).
% 29.21/19.41 tff(21497,plain,
% 29.21/19.41 ($false),
% 29.21/19.41 inference(unit_resolution,[status(thm)],[12861, 21496])).
% 29.21/19.41 tff(21498,plain,((f6(c2, c2) = c2) | (f3(c2, c2) = c2) | (~(f7(c2) = c2)) | (f10(f10(c2)) = f10(c2)) | (~big_f(f3(c2, c2), c2)) | (~(f10(c1) = c2)) | (~(f10(c2) = c1)) | (~big_f(c2, f10(f10(c2)))) | big_f(c2, f10(c2)) | (~(f7(c1) = c2)) | (~(f4(c4) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.21/19.41 tff(21499,plain,
% 29.21/19.41 (f6(c2, c2) = c2),
% 29.21/19.41 inference(unit_resolution,[status(thm)],[21498, 21472, 77, 11896, 21471, 16, 11819, 21461, 15517, 347, 11752])).
% 29.21/19.41 tff(21500,plain,
% 29.21/19.41 (big_f(f7(c2), f6(c2, c2))),
% 29.21/19.41 inference(unit_resolution,[status(thm)],[2627, 21499, 77, 1345])).
% 29.21/19.41 tff(21501,plain,
% 29.21/19.41 (c3 = f10(c2)),
% 29.21/19.41 inference(transitivity,[status(thm)],[172, 12231])).
% 29.21/19.41 tff(21502,plain,
% 29.21/19.41 (f10(c3) = f10(f10(c2))),
% 29.21/19.41 inference(monotonicity,[status(thm)],[21501])).
% 29.21/19.42 tff(21503,plain,
% 29.21/19.42 (f10(c3) = c2),
% 29.21/19.42 inference(transitivity,[status(thm)],[21502, 11844, 16])).
% 29.21/19.42 tff(21504,plain,
% 29.21/19.42 (big_f(c2, f10(c3)) <=> big_f(c2, c2)),
% 29.21/19.42 inference(monotonicity,[status(thm)],[21503])).
% 29.21/19.42 tff(21505,plain,
% 29.21/19.42 (big_f(c2, c2) <=> big_f(c2, f10(c3))),
% 29.21/19.42 inference(symmetry,[status(thm)],[21504])).
% 29.21/19.42 tff(21506,plain,
% 29.21/19.42 (big_f(c2, f10(c3))),
% 29.21/19.42 inference(modus_ponens,[status(thm)],[1345, 21505])).
% 29.21/19.42 tff(21507,plain,
% 29.21/19.42 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(c2) = c2)) | (f10(c3) = c3) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~big_f(c2, f10(c3))) | (c2 = f8(c3)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c2) = c2)) | (f10(c3) = c3) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~big_f(c2, f10(c3))) | (c2 = f8(c3)))),
% 29.21/19.42 inference(rewrite,[status(thm)],[])).
% 29.21/19.42 tff(21508,plain,
% 29.21/19.42 (((f10(c3) = c3) | (c2 = f8(c3)) | (~big_f(c2, f10(c3))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2)))) <=> ((~(f7(c2) = c2)) | (f10(c3) = c3) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~big_f(c2, f10(c3))) | (c2 = f8(c3)))),
% 29.21/19.42 inference(rewrite,[status(thm)],[])).
% 29.21/19.42 tff(21509,plain,
% 29.21/19.42 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c3) = c3) | (c2 = f8(c3)) | (~big_f(c2, f10(c3))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(c2) = c2)) | (f10(c3) = c3) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~big_f(c2, f10(c3))) | (c2 = f8(c3))))),
% 29.21/19.42 inference(monotonicity,[status(thm)],[21508])).
% 29.21/19.42 tff(21510,plain,
% 29.21/19.42 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c3) = c3) | (c2 = f8(c3)) | (~big_f(c2, f10(c3))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c2) = c2)) | (f10(c3) = c3) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~big_f(c2, f10(c3))) | (c2 = f8(c3)))),
% 29.21/19.42 inference(transitivity,[status(thm)],[21509, 21507])).
% 29.21/19.42 tff(21511,plain,
% 29.21/19.42 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c3) = c3) | (c2 = f8(c3)) | (~big_f(c2, f10(c3))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))),
% 29.21/19.42 inference(quant_inst,[status(thm)],[])).
% 29.21/19.42 tff(21512,plain,
% 29.21/19.42 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c2) = c2)) | (f10(c3) = c3) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~big_f(c2, f10(c3))) | (c2 = f8(c3))),
% 29.21/19.42 inference(modus_ponens,[status(thm)],[21511, 21510])).
% 29.21/19.42 tff(21513,plain,
% 29.21/19.42 ((~(f7(c2) = c2)) | (f10(c3) = c3) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~big_f(c2, f10(c3))) | (c2 = f8(c3))),
% 29.21/19.42 inference(unit_resolution,[status(thm)],[21512, 2730])).
% 29.21/19.42 tff(21514,plain,
% 29.21/19.42 (c2 = f8(c3)),
% 29.21/19.42 inference(unit_resolution,[status(thm)],[21513, 21499, 77, 21506, 21500, 2828])).
% 29.21/19.42 tff(21515,plain,
% 29.21/19.42 (f8(c3) = c2),
% 29.21/19.42 inference(symmetry,[status(thm)],[21514])).
% 29.21/19.42 tff(21516,plain,
% 29.21/19.42 (f10(c2) = c3),
% 29.21/19.42 inference(transitivity,[status(thm)],[11819, 5585])).
% 29.21/19.42 tff(21517,plain,
% 29.21/19.42 (f8(f10(c2)) = f8(c3)),
% 29.21/19.42 inference(monotonicity,[status(thm)],[21516])).
% 29.21/19.42 tff(21518,plain,
% 29.21/19.42 (big_f(f3(c2, c2), f10(f10(c2)))),
% 29.21/19.42 inference(modus_ponens,[status(thm)],[21471, 21202])).
% 29.21/19.42 tff(21519,plain,
% 29.21/19.42 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(c2) = c2)) | (f10(f10(c2)) = f10(c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (f3(c2, c2) = f8(f10(c2))) | (~big_f(f3(c2, c2), f10(f10(c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c2) = c2)) | (f10(f10(c2)) = f10(c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (f3(c2, c2) = f8(f10(c2))) | (~big_f(f3(c2, c2), f10(f10(c2)))))),
% 29.21/19.42 inference(rewrite,[status(thm)],[])).
% 29.21/19.42 tff(21520,plain,
% 29.21/19.42 (((f10(f10(c2)) = f10(c2)) | (f3(c2, c2) = f8(f10(c2))) | (~big_f(f3(c2, c2), f10(f10(c2)))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2)))) <=> ((~(f7(c2) = c2)) | (f10(f10(c2)) = f10(c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (f3(c2, c2) = f8(f10(c2))) | (~big_f(f3(c2, c2), f10(f10(c2)))))),
% 29.21/19.42 inference(rewrite,[status(thm)],[])).
% 29.21/19.42 tff(21521,plain,
% 29.21/19.42 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f10(c2)) = f10(c2)) | (f3(c2, c2) = f8(f10(c2))) | (~big_f(f3(c2, c2), f10(f10(c2)))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(c2) = c2)) | (f10(f10(c2)) = f10(c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (f3(c2, c2) = f8(f10(c2))) | (~big_f(f3(c2, c2), f10(f10(c2))))))),
% 29.21/19.42 inference(monotonicity,[status(thm)],[21520])).
% 29.21/19.42 tff(21522,plain,
% 29.21/19.42 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f10(c2)) = f10(c2)) | (f3(c2, c2) = f8(f10(c2))) | (~big_f(f3(c2, c2), f10(f10(c2)))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c2) = c2)) | (f10(f10(c2)) = f10(c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (f3(c2, c2) = f8(f10(c2))) | (~big_f(f3(c2, c2), f10(f10(c2)))))),
% 29.21/19.42 inference(transitivity,[status(thm)],[21521, 21519])).
% 29.21/19.42 tff(21523,plain,
% 29.21/19.42 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f10(c2)) = f10(c2)) | (f3(c2, c2) = f8(f10(c2))) | (~big_f(f3(c2, c2), f10(f10(c2)))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))),
% 29.21/19.42 inference(quant_inst,[status(thm)],[])).
% 29.21/19.42 tff(21524,plain,
% 29.21/19.42 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c2) = c2)) | (f10(f10(c2)) = f10(c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (f3(c2, c2) = f8(f10(c2))) | (~big_f(f3(c2, c2), f10(f10(c2))))),
% 29.21/19.42 inference(modus_ponens,[status(thm)],[21523, 21522])).
% 29.21/19.42 tff(21525,plain,
% 29.21/19.42 (f3(c2, c2) = f8(f10(c2))),
% 29.21/19.42 inference(unit_resolution,[status(thm)],[21524, 2730, 77, 11896, 21499, 21500, 21518])).
% 29.21/19.42 tff(21526,plain,
% 29.21/19.42 (f3(c2, c2) = c2),
% 29.21/19.42 inference(transitivity,[status(thm)],[21525, 21517, 21515])).
% 29.21/19.42 tff(21527,plain,
% 29.21/19.42 ($false),
% 29.21/19.42 inference(unit_resolution,[status(thm)],[21472, 21526])).
% 29.21/19.42 tff(21528,plain,((c2 = c4) | (~(c3 = c1)) | (~(f10(c2) = c1)) | (~(f7(c2) = c2)) | (f10(f10(c2)) = f10(c2)) | (~(f10(c1) = c2)) | (f10(c3) = c3) | (~big_f(c2, c2)) | big_f(c2, f10(c2)) | (~(f7(c1) = c2)) | (~(f4(c4) = c1)) | (c2 = c3)), inference(lemma,lemma(discharge,[]))).
% 29.21/19.42 tff(21529,plain,
% 29.21/19.42 (c2 = c4),
% 29.21/19.42 inference(unit_resolution,[status(thm)],[21528, 172, 94, 77, 15308, 16, 21458, 1345, 15517, 347, 11752, 15336])).
% 29.21/19.42 tff(21530,plain,
% 29.21/19.42 (big_f(f7(c2), c2) <=> big_f(c2, c2)),
% 29.21/19.42 inference(monotonicity,[status(thm)],[77])).
% 29.21/19.42 tff(21531,plain,
% 29.21/19.42 (big_f(c2, c2) <=> big_f(f7(c2), c2)),
% 29.21/19.42 inference(symmetry,[status(thm)],[21530])).
% 29.21/19.42 tff(21532,plain,
% 29.21/19.42 (big_f(f7(c2), c2)),
% 29.21/19.42 inference(modus_ponens,[status(thm)],[1345, 21531])).
% 29.21/19.42 tff(21533,plain,
% 29.21/19.42 ((~big_f(c2, f10(c2))) <=> (~big_f(c2, c1))),
% 29.21/19.42 inference(monotonicity,[status(thm)],[15253])).
% 29.21/19.42 tff(21534,plain,
% 29.21/19.42 (~big_f(c2, c1)),
% 29.21/19.42 inference(modus_ponens,[status(thm)],[15517, 21533])).
% 29.21/19.42 tff(21535,plain,
% 29.21/19.42 ((f7(c2) = f4(c2)) <=> (c2 = f4(c2))),
% 29.21/19.42 inference(monotonicity,[status(thm)],[77])).
% 29.21/19.42 tff(21536,plain,
% 29.21/19.42 ((c2 = f4(c2)) <=> (f7(c2) = f4(c2))),
% 29.21/19.42 inference(symmetry,[status(thm)],[21535])).
% 29.21/19.42 tff(21537,plain,
% 29.21/19.42 (f4(c2) = f4(c4)),
% 29.21/19.42 inference(monotonicity,[status(thm)],[21529])).
% 29.21/19.42 tff(21538,plain,
% 29.21/19.42 (f4(c2) = f10(c2)),
% 29.21/19.42 inference(transitivity,[status(thm)],[21537, 11752, 99])).
% 29.21/19.42 tff(21539,plain,
% 29.21/19.42 ((c2 = f4(c2)) <=> (c2 = f10(c2))),
% 29.21/19.42 inference(monotonicity,[status(thm)],[21538])).
% 29.21/19.42 tff(21540,plain,
% 29.21/19.42 ((c2 = f4(c2)) <=> (f10(c2) = c2)),
% 29.21/19.42 inference(transitivity,[status(thm)],[21539, 4987])).
% 29.21/19.42 tff(21541,plain,
% 29.21/19.42 ((f10(c2) = c2) <=> (c2 = f4(c2))),
% 29.21/19.42 inference(symmetry,[status(thm)],[21540])).
% 29.21/19.42 tff(21542,plain,
% 29.21/19.42 ((f10(c2) = c2) <=> (f7(c2) = f4(c2))),
% 29.21/19.42 inference(transitivity,[status(thm)],[21541, 21536])).
% 29.21/19.42 tff(21543,plain,
% 29.21/19.42 ((~(f10(c2) = c2)) <=> (~(f7(c2) = f4(c2)))),
% 29.21/19.42 inference(monotonicity,[status(thm)],[21542])).
% 29.21/19.42 tff(21544,plain,
% 29.21/19.42 (~(f7(c2) = f4(c2))),
% 29.21/19.42 inference(modus_ponens,[status(thm)],[89, 21543])).
% 29.21/19.42 tff(21545,plain,
% 29.21/19.42 (f1(c2, c2) = c2),
% 29.21/19.42 inference(unit_resolution,[status(thm)],[9464, 21544, 15336, 21534, 21532, 21529])).
% 29.21/19.42 tff(21546,plain,
% 29.21/19.42 (big_f(c2, f1(c2, c2)) <=> big_f(c2, c2)),
% 29.21/19.42 inference(monotonicity,[status(thm)],[21545])).
% 29.21/19.42 tff(21547,plain,
% 29.21/19.42 (big_f(c2, c2) <=> big_f(c2, f1(c2, c2))),
% 29.21/19.42 inference(symmetry,[status(thm)],[21546])).
% 29.21/19.42 tff(21548,plain,
% 29.21/19.42 (big_f(c2, f1(c2, c2))),
% 29.21/19.42 inference(modus_ponens,[status(thm)],[1345, 21547])).
% 29.21/19.42 tff(21549,plain,
% 29.21/19.42 ((~(f10(c2) = c2)) <=> (~(c2 = f4(c2)))),
% 29.21/19.42 inference(monotonicity,[status(thm)],[21541])).
% 29.21/19.42 tff(21550,plain,
% 29.21/19.42 (~(c2 = f4(c2))),
% 29.21/19.42 inference(modus_ponens,[status(thm)],[89, 21549])).
% 29.21/19.42 tff(21551,plain,
% 29.21/19.42 ($false),
% 29.21/19.42 inference(unit_resolution,[status(thm)],[16875, 553, 21529, 21550, 1345, 15336, 21545, 21548])).
% 29.21/19.42 tff(21552,plain,((~(c3 = c1)) | (~big_f(c2, c2)) | (f10(c2) = c2) | (~(f4(c4) = c1)) | (~(f7(c2) = c2)) | (~(f10(c1) = c2)) | big_f(c2, f10(c2)) | (~(f7(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.21/19.42 tff(21553,plain,
% 29.21/19.42 (~(c3 = c1)),
% 29.21/19.42 inference(unit_resolution,[status(thm)],[21552, 15517, 89, 11752, 77, 16, 1345, 347])).
% 29.21/19.42 tff(21554,plain,
% 29.21/19.42 (~(c1 = c3)),
% 29.21/19.42 inference(modus_ponens,[status(thm)],[21553, 648])).
% 29.21/19.42 tff(21555,plain,
% 29.21/19.42 (f8(c2) = f8(f10(c1))),
% 29.21/19.42 inference(symmetry,[status(thm)],[11994])).
% 29.21/19.42 tff(21556,plain,
% 29.21/19.42 (f8(f7(f4(c4))) = f8(f10(c1))),
% 29.21/19.42 inference(transitivity,[status(thm)],[16247, 21555])).
% 29.21/19.42 tff(21557,plain,
% 29.21/19.42 (big_f(f8(f7(f4(c4))), f10(c2)) <=> big_f(f8(f10(c1)), f10(c2))),
% 29.21/19.42 inference(monotonicity,[status(thm)],[21556])).
% 29.21/19.42 tff(21558,plain,
% 29.21/19.42 (big_f(f8(f10(c1)), f10(c2)) <=> big_f(f8(f7(f4(c4))), f10(c2))),
% 29.21/19.42 inference(symmetry,[status(thm)],[21557])).
% 29.21/19.42 tff(21559,plain,
% 29.21/19.42 (f8(f10(c1)) = f10(c2)),
% 29.21/19.42 inference(transitivity,[status(thm)],[11994, 16246, 16268, 99])).
% 29.21/19.42 tff(21560,plain,
% 29.21/19.42 (big_f(f8(f10(c1)), f10(c2)) <=> big_f(f10(c2), f10(c2))),
% 29.21/19.42 inference(monotonicity,[status(thm)],[21559])).
% 29.21/19.42 tff(21561,plain,
% 29.21/19.42 (big_f(f10(c2), f10(c2)) <=> big_f(f8(f10(c1)), f10(c2))),
% 29.21/19.42 inference(symmetry,[status(thm)],[21560])).
% 29.21/19.42 tff(21562,plain,
% 29.21/19.42 (big_f(f10(c2), f10(c2)) <=> big_f(f8(f7(f4(c4))), f10(c2))),
% 29.23/19.42 inference(transitivity,[status(thm)],[21561, 21558])).
% 29.23/19.42 tff(21563,plain,
% 29.23/19.42 ((~big_f(f10(c2), f10(c2))) <=> (~big_f(f8(f7(f4(c4))), f10(c2)))),
% 29.23/19.42 inference(monotonicity,[status(thm)],[21562])).
% 29.23/19.42 tff(21564,plain,
% 29.23/19.42 (~big_f(f8(f7(f4(c4))), f10(c2))),
% 29.23/19.42 inference(modus_ponens,[status(thm)],[20783, 21563])).
% 29.23/19.42 tff(21565,plain,
% 29.23/19.42 ((f10(c2) = f8(c2)) <=> (c1 = f8(c2))),
% 29.23/19.42 inference(monotonicity,[status(thm)],[94])).
% 29.23/19.42 tff(21566,plain,
% 29.23/19.42 ((c1 = f8(c2)) <=> (f10(c2) = f8(c2))),
% 29.23/19.42 inference(symmetry,[status(thm)],[21565])).
% 29.23/19.42 tff(21567,plain,
% 29.23/19.42 ((f8(f7(f4(c4))) = c1) <=> (f8(c2) = c1)),
% 29.23/19.42 inference(monotonicity,[status(thm)],[16247])).
% 29.23/19.42 tff(21568,plain,
% 29.23/19.42 ((f8(f7(f4(c4))) = c1) <=> (c1 = f8(c2))),
% 29.23/19.42 inference(transitivity,[status(thm)],[21567, 13044])).
% 29.23/19.42 tff(21569,plain,
% 29.23/19.42 ((f8(f7(f4(c4))) = c1) <=> (f10(c2) = f8(c2))),
% 29.23/19.42 inference(transitivity,[status(thm)],[21568, 21566])).
% 29.23/19.42 tff(21570,plain,
% 29.23/19.42 (f10(c2) = f8(c2)),
% 29.23/19.42 inference(modus_ponens,[status(thm)],[16268, 21569])).
% 29.23/19.42 tff(21571,plain,
% 29.23/19.42 (~big_f(f7(c2), f6(c2, c2))),
% 29.23/19.42 inference(unit_resolution,[status(thm)],[7213, 2637, 77, 2, 67])).
% 29.23/19.42 tff(21572,plain,
% 29.23/19.42 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f8(c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f8(c2))))),
% 29.23/19.42 inference(rewrite,[status(thm)],[])).
% 29.23/19.42 tff(21573,plain,
% 29.23/19.42 (((f10(c2) = c2) | big_f(f10(c2), f10(c2)) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (~(f10(c2) = f8(c2)))) <=> ((f10(c2) = c2) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f8(c2))))),
% 29.23/19.42 inference(rewrite,[status(thm)],[])).
% 29.23/19.42 tff(21574,plain,
% 29.23/19.42 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | big_f(f10(c2), f10(c2)) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (~(f10(c2) = f8(c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f8(c2)))))),
% 29.23/19.42 inference(monotonicity,[status(thm)],[21573])).
% 29.23/19.42 tff(21575,plain,
% 29.23/19.42 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | big_f(f10(c2), f10(c2)) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (~(f10(c2) = f8(c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f8(c2))))),
% 29.23/19.42 inference(transitivity,[status(thm)],[21574, 21572])).
% 29.23/19.42 tff(21576,plain,
% 29.23/19.42 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | big_f(f10(c2), f10(c2)) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (~(f10(c2) = f8(c2))))),
% 29.23/19.42 inference(quant_inst,[status(thm)],[])).
% 29.23/19.42 tff(21577,plain,
% 29.23/19.42 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f8(c2)))),
% 29.24/19.42 inference(modus_ponens,[status(thm)],[21576, 21575])).
% 29.24/19.42 tff(21578,plain,
% 29.24/19.42 ($false),
% 29.24/19.42 inference(unit_resolution,[status(thm)],[21577, 2994, 89, 77, 2637, 21571, 15586, 20783])).
% 29.24/19.42 tff(21579,plain,((f6(c2, c2) = c2) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (~(f10(c2) = f8(c2))) | big_f(f10(c2), f10(c2)) | big_f(c2, c1) | (~(c3 = c2))), inference(lemma,lemma(discharge,[]))).
% 29.24/19.42 tff(21580,plain,
% 29.24/19.42 (f6(c2, c2) = c2),
% 29.24/19.42 inference(unit_resolution,[status(thm)],[21579, 21570, 77, 89, 20783, 2, 67])).
% 29.24/19.42 tff(21581,plain,
% 29.24/19.42 (big_f(f7(c2), f6(c2, c2))),
% 29.24/19.42 inference(unit_resolution,[status(thm)],[2627, 21580, 77, 1345])).
% 29.24/19.42 tff(21582,plain,
% 29.24/19.42 ($false),
% 29.24/19.42 inference(unit_resolution,[status(thm)],[15287, 21581, 21580, 89, 77, 21564, 16247])).
% 29.24/19.42 tff(21583,plain,((~(f8(f7(f4(c4))) = c1)) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (~big_f(c2, c2)) | big_f(f10(c2), f10(c2)) | big_f(c2, c1) | (~(c3 = c2)) | (~(f7(c1) = c2)) | (~(f4(c4) = c1)) | (~(f10(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.24/19.42 tff(21584,plain,
% 29.24/19.42 (~(f8(f7(f4(c4))) = c1)),
% 29.24/19.42 inference(unit_resolution,[status(thm)],[21583, 67, 77, 1345, 20783, 21534, 89, 347, 11752, 16])).
% 29.24/19.42 tff(21585,plain,
% 29.24/19.42 (f8(f7(f4(c4))) = c2),
% 29.24/19.42 inference(unit_resolution,[status(thm)],[13371, 21584])).
% 29.24/19.42 tff(21586,plain,
% 29.24/19.42 (f8(f10(c1)) = c2),
% 29.24/19.42 inference(transitivity,[status(thm)],[11994, 16246, 21585])).
% 29.24/19.42 tff(21587,plain,
% 29.24/19.42 (big_f(f8(f10(c1)), f10(c2)) <=> big_f(c2, f10(c2))),
% 29.24/19.42 inference(monotonicity,[status(thm)],[21586])).
% 29.24/19.42 tff(21588,plain,
% 29.24/19.42 (big_f(c2, f10(c2)) <=> big_f(f8(f10(c1)), f10(c2))),
% 29.24/19.42 inference(symmetry,[status(thm)],[21587])).
% 29.24/19.42 tff(21589,plain,
% 29.24/19.42 (big_f(c2, f10(c2)) <=> big_f(f8(f7(f4(c4))), f10(c2))),
% 29.24/19.42 inference(transitivity,[status(thm)],[21588, 21558])).
% 29.24/19.42 tff(21590,plain,
% 29.24/19.42 ((~big_f(c2, f10(c2))) <=> (~big_f(f8(f7(f4(c4))), f10(c2)))),
% 29.24/19.42 inference(monotonicity,[status(thm)],[21589])).
% 29.24/19.42 tff(21591,plain,
% 29.24/19.42 (~big_f(f8(f7(f4(c4))), f10(c2))),
% 29.24/19.42 inference(modus_ponens,[status(thm)],[15517, 21590])).
% 29.24/19.42 tff(21592,plain,
% 29.24/19.42 (c2 = f8(c2)),
% 29.24/19.42 inference(unit_resolution,[status(thm)],[17582, 21585, 347, 11752])).
% 29.24/19.42 tff(21593,plain,
% 29.24/19.42 (~big_f(f7(c2), f6(c2, c2))),
% 29.24/19.42 inference(unit_resolution,[status(thm)],[7213, 2637, 77, 21534, 67])).
% 29.24/19.42 tff(21594,plain,
% 29.24/19.42 ($false),
% 29.24/19.42 inference(unit_resolution,[status(thm)],[14124, 2994, 89, 77, 15517, 13152, 2637, 21593])).
% 29.24/19.42 tff(21595,plain,((f6(c2, c2) = c2) | (f10(c2) = c2) | (~(f7(c2) = c2)) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (~(c3 = c2))), inference(lemma,lemma(discharge,[]))).
% 29.24/19.42 tff(21596,plain,
% 29.24/19.42 (f6(c2, c2) = c2),
% 29.24/19.42 inference(unit_resolution,[status(thm)],[21595, 21592, 77, 15517, 89, 67])).
% 29.24/19.42 tff(21597,plain,
% 29.24/19.42 (big_f(f7(c2), f6(c2, c2))),
% 29.24/19.42 inference(unit_resolution,[status(thm)],[2627, 21596, 77, 1345])).
% 29.24/19.42 tff(21598,plain,
% 29.24/19.42 ($false),
% 29.24/19.42 inference(unit_resolution,[status(thm)],[15287, 21597, 21596, 89, 77, 21591, 16247])).
% 29.24/19.42 tff(21599,plain,((~(c3 = c2)) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (~big_f(c2, c2)) | big_f(c2, f10(c2)) | (~(f7(c1) = c2)) | (~(f4(c4) = c1)) | (~(f10(c1) = c2)) | big_f(f10(c2), f10(c2))), inference(lemma,lemma(discharge,[]))).
% 29.24/19.42 tff(21600,plain,
% 29.24/19.42 (~(c3 = c2)),
% 29.24/19.42 inference(unit_resolution,[status(thm)],[21599, 15266, 77, 1345, 15517, 347, 11752, 16, 89])).
% 29.24/19.42 tff(21601,plain,
% 29.24/19.42 (c3 = c1),
% 29.24/19.42 inference(unit_resolution,[status(thm)],[180, 21600])).
% 29.24/19.42 tff(21602,plain,
% 29.24/19.42 (~(f2(c3) = c1)),
% 29.24/19.42 inference(unit_resolution,[status(thm)],[11776, 21601, 11752, 27, 66])).
% 29.24/19.42 tff(21603,plain,
% 29.24/19.42 (f2(c3) = c2),
% 29.24/19.42 inference(unit_resolution,[status(thm)],[1273, 21602])).
% 29.24/19.42 tff(21604,plain,
% 29.24/19.42 (big_f(c3, f2(c3)) <=> big_f(c1, c2)),
% 29.24/19.42 inference(monotonicity,[status(thm)],[21601, 21603])).
% 29.24/19.42 tff(21605,plain,
% 29.24/19.42 (big_f(c1, c2) <=> big_f(c3, f2(c3))),
% 29.24/19.42 inference(symmetry,[status(thm)],[21604])).
% 29.24/19.42 tff(21606,plain,
% 29.24/19.42 ((~big_f(c1, c2)) <=> (~big_f(c3, f2(c3)))),
% 29.24/19.42 inference(monotonicity,[status(thm)],[21605])).
% 29.24/19.42 tff(21607,plain,
% 29.24/19.42 (~big_f(c3, f2(c3))),
% 29.24/19.42 inference(modus_ponens,[status(thm)],[27, 21606])).
% 29.24/19.42 tff(21608,plain,
% 29.24/19.42 ($false),
% 29.24/19.42 inference(unit_resolution,[status(thm)],[11774, 21607])).
% 29.24/19.42 tff(21609,plain,(big_f(c1, c1) | big_f(c1, c2) | (~(f4(c4) = c1)) | (~(f7(c2) = c2)) | (~big_f(c2, c2)) | big_f(c2, f10(c2)) | (~(f7(c1) = c2)) | (~(f10(c1) = c2)) | (f10(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 29.24/19.42 tff(21610,plain,
% 29.24/19.42 (big_f(c1, c1)),
% 29.24/19.42 inference(unit_resolution,[status(thm)],[21609, 15517, 11752, 77, 1345, 27, 347, 16, 89])).
% 29.24/19.42 tff(21611,plain,
% 29.24/19.42 (big_f(c2, f10(f10(c2))) <=> big_f(c2, c2)),
% 29.24/19.42 inference(monotonicity,[status(thm)],[15300])).
% 29.24/19.42 tff(21612,plain,
% 29.24/19.42 (big_f(c2, c2) <=> big_f(c2, f10(f10(c2)))),
% 29.24/19.42 inference(symmetry,[status(thm)],[21611])).
% 29.24/19.42 tff(21613,plain,
% 29.24/19.42 (big_f(c2, f10(f10(c2)))),
% 29.24/19.42 inference(modus_ponens,[status(thm)],[1345, 21612])).
% 29.24/19.42 tff(21614,plain,
% 29.24/19.42 (big_f(f10(c2), f10(c2))),
% 29.24/19.42 inference(modus_ponens,[status(thm)],[21610, 13717])).
% 29.24/19.42 tff(21615,plain,
% 29.24/19.42 (~(f10(c2) = c3)),
% 29.24/19.42 inference(modus_ponens,[status(thm)],[21553, 21120])).
% 29.24/19.42 tff(21616,plain,
% 29.24/19.42 (big_f(f3(c2, c2), c2) <=> big_f(c2, c2)),
% 29.24/19.42 inference(monotonicity,[status(thm)],[7387])).
% 29.24/19.42 tff(21617,plain,
% 29.24/19.42 (big_f(c2, c2) <=> big_f(f3(c2, c2), c2)),
% 29.24/19.42 inference(symmetry,[status(thm)],[21616])).
% 29.24/19.42 tff(21618,plain,
% 29.24/19.42 (big_f(f3(c2, c2), c2)),
% 29.24/19.42 inference(modus_ponens,[status(thm)],[1345, 21617])).
% 29.24/19.42 tff(21619,plain,
% 29.24/19.42 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c4) | (f10(c2) = c3) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (f1(f10(c2), f10(c2)) = f10(c2)) | big_f(f10(c2), f1(f10(c2), f10(c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c2 = c4) | (f10(c2) = c3) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (f1(f10(c2), f10(c2)) = f10(c2)) | big_f(f10(c2), f1(f10(c2), f10(c2))))),
% 29.24/19.42 inference(rewrite,[status(thm)],[])).
% 29.24/19.42 tff(21620,plain,
% 29.24/19.42 (((c2 = c4) | (f10(c2) = c3) | (f1(f10(c2), f10(c2)) = f10(c2)) | big_f(f10(c2), f1(f10(c2), f10(c2))) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2))) <=> ((c2 = c4) | (f10(c2) = c3) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (f1(f10(c2), f10(c2)) = f10(c2)) | big_f(f10(c2), f1(f10(c2), f10(c2))))),
% 29.24/19.42 inference(rewrite,[status(thm)],[])).
% 29.24/19.42 tff(21621,plain,
% 29.24/19.42 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c4) | (f10(c2) = c3) | (f1(f10(c2), f10(c2)) = f10(c2)) | big_f(f10(c2), f1(f10(c2), f10(c2))) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c4) | (f10(c2) = c3) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (f1(f10(c2), f10(c2)) = f10(c2)) | big_f(f10(c2), f1(f10(c2), f10(c2)))))),
% 29.24/19.42 inference(monotonicity,[status(thm)],[21620])).
% 29.24/19.42 tff(21622,plain,
% 29.24/19.42 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c4) | (f10(c2) = c3) | (f1(f10(c2), f10(c2)) = f10(c2)) | big_f(f10(c2), f1(f10(c2), f10(c2))) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c2 = c4) | (f10(c2) = c3) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (f1(f10(c2), f10(c2)) = f10(c2)) | big_f(f10(c2), f1(f10(c2), f10(c2))))),
% 29.24/19.42 inference(transitivity,[status(thm)],[21621, 21619])).
% 29.24/19.42 tff(21623,plain,
% 29.24/19.42 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c2 = c4) | (f10(c2) = c3) | (f1(f10(c2), f10(c2)) = f10(c2)) | big_f(f10(c2), f1(f10(c2), f10(c2))) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)))),
% 29.24/19.43 inference(quant_inst,[status(thm)],[])).
% 29.24/19.43 tff(21624,plain,
% 29.24/19.43 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c2 = c4) | (f10(c2) = c3) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (f1(f10(c2), f10(c2)) = f10(c2)) | big_f(f10(c2), f1(f10(c2), f10(c2)))),
% 29.24/19.43 inference(modus_ponens,[status(thm)],[21623, 21622])).
% 29.24/19.43 tff(21625,plain,
% 29.24/19.43 ((f1(f10(c2), f10(c2)) = f10(c2)) | big_f(f10(c2), f1(f10(c2), f10(c2)))),
% 29.24/19.43 inference(unit_resolution,[status(thm)],[21624, 969, 873, 15667, 7387, 15356])).
% 29.24/19.43 tff(21626,plain,
% 29.24/19.43 ($false),
% 29.24/19.43 inference(unit_resolution,[status(thm)],[21625, 15664, 15660])).
% 29.24/19.43 tff(21627,plain,((~(f1(c1, c1) = c2)) | (c2 = c4) | (f10(c2) = c3) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | big_f(c1, c2) | (f10(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 29.24/19.43 tff(21628,plain,
% 29.24/19.43 (~(f1(c1, c1) = c2)),
% 29.24/19.43 inference(unit_resolution,[status(thm)],[21627, 7387, 15667, 873, 21618, 27, 89])).
% 29.24/19.43 tff(21629,plain,
% 29.24/19.43 (f1(c1, c1) = c1),
% 29.24/19.43 inference(unit_resolution,[status(thm)],[601, 21628])).
% 29.24/19.43 tff(21630,plain,
% 29.24/19.43 (f1(f10(c2), f10(c2)) = f10(c2)),
% 29.24/19.43 inference(transitivity,[status(thm)],[12413, 21629, 99])).
% 29.24/19.43 tff(21631,plain,
% 29.24/19.43 (big_f(f10(c2), f1(f10(c2), f10(c2))) <=> big_f(f10(c2), f10(c2))),
% 29.24/19.43 inference(monotonicity,[status(thm)],[21630])).
% 29.24/19.43 tff(21632,plain,
% 29.24/19.43 (big_f(f10(c2), f10(c2)) <=> big_f(f10(c2), f1(f10(c2), f10(c2)))),
% 29.24/19.43 inference(symmetry,[status(thm)],[21631])).
% 29.24/19.43 tff(21633,plain,
% 29.24/19.43 (big_f(f10(c2), f1(f10(c2), f10(c2)))),
% 29.24/19.43 inference(modus_ponens,[status(thm)],[14686, 21632])).
% 29.24/19.43 tff(21634,plain,
% 29.24/19.43 ((~(f1(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f10(c2), f1(f10(c2), f10(c2))))),
% 29.24/19.43 inference(unit_resolution,[status(thm)],[21226, 933, 873, 15667, 7387, 21618])).
% 29.24/19.43 tff(21635,plain,
% 29.24/19.43 ($false),
% 29.24/19.43 inference(unit_resolution,[status(thm)],[21634, 21633, 21630])).
% 29.24/19.43 tff(21636,plain,((~(f3(c2, c2) = c2)) | (c2 = c4) | (f10(c2) = c3) | (~big_f(f10(c2), f10(c2))) | big_f(c1, c2) | (f10(c2) = c2) | (~big_f(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 29.24/19.43 tff(21637,plain,
% 29.24/19.43 (~(f3(c2, c2) = c2)),
% 29.24/19.43 inference(unit_resolution,[status(thm)],[21636, 873, 21615, 21614, 27, 89, 1345])).
% 29.24/19.43 tff(21638,plain,
% 29.24/19.43 (big_f(f3(c2, c2), c2)),
% 29.24/19.43 inference(unit_resolution,[status(thm)],[21176, 12861, 4932, 873, 168, 27])).
% 29.24/19.43 tff(21639,plain,
% 29.24/19.43 ($false),
% 29.24/19.43 inference(unit_resolution,[status(thm)],[21498, 21638, 12861, 77, 11896, 2637, 16, 11819, 21479, 15517, 347, 11752])).
% 29.24/19.43 tff(21640,plain,((f3(c2, c2) = c2) | (~(f7(c2) = c2)) | (f10(f10(c2)) = f10(c2)) | (f6(c2, c2) = c2) | (~(f10(c1) = c2)) | (~(f10(c2) = c1)) | (~big_f(c2, f10(f10(c2)))) | big_f(c2, f10(c2)) | (~(f7(c1) = c2)) | (~(f4(c4) = c1)) | (~big_f(c1, c1)) | (c2 = c4) | (c1 = c3) | big_f(c1, c2)), inference(lemma,lemma(discharge,[]))).
% 29.24/19.43 tff(21641,plain,
% 29.24/19.43 (f6(c2, c2) = c2),
% 29.24/19.43 inference(unit_resolution,[status(thm)],[21640, 21637, 15308, 77, 16, 94, 21613, 15517, 347, 11752, 21610, 873, 21554, 27])).
% 29.24/19.43 tff(21642,plain,
% 29.24/19.43 (big_f(f7(c2), f6(c2, c2))),
% 29.24/19.43 inference(unit_resolution,[status(thm)],[2627, 21641, 77, 1345])).
% 29.24/19.43 tff(21643,plain,
% 29.24/19.43 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(c2) = c2)) | (f10(f10(c2)) = f10(c2)) | (c2 = f8(f10(c2))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~big_f(c2, f10(f10(c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c2) = c2)) | (f10(f10(c2)) = f10(c2)) | (c2 = f8(f10(c2))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~big_f(c2, f10(f10(c2)))))),
% 29.24/19.43 inference(rewrite,[status(thm)],[])).
% 29.24/19.43 tff(21644,plain,
% 29.24/19.43 (((f10(f10(c2)) = f10(c2)) | (c2 = f8(f10(c2))) | (~big_f(c2, f10(f10(c2)))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2)))) <=> ((~(f7(c2) = c2)) | (f10(f10(c2)) = f10(c2)) | (c2 = f8(f10(c2))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~big_f(c2, f10(f10(c2)))))),
% 29.24/19.43 inference(rewrite,[status(thm)],[])).
% 29.24/19.43 tff(21645,plain,
% 29.24/19.43 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f10(c2)) = f10(c2)) | (c2 = f8(f10(c2))) | (~big_f(c2, f10(f10(c2)))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(c2) = c2)) | (f10(f10(c2)) = f10(c2)) | (c2 = f8(f10(c2))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~big_f(c2, f10(f10(c2))))))),
% 29.24/19.43 inference(monotonicity,[status(thm)],[21644])).
% 29.24/19.43 tff(21646,plain,
% 29.24/19.43 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f10(c2)) = f10(c2)) | (c2 = f8(f10(c2))) | (~big_f(c2, f10(f10(c2)))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c2) = c2)) | (f10(f10(c2)) = f10(c2)) | (c2 = f8(f10(c2))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~big_f(c2, f10(f10(c2)))))),
% 29.24/19.43 inference(transitivity,[status(thm)],[21645, 21643])).
% 29.24/19.43 tff(21647,plain,
% 29.24/19.43 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f10(c2)) = f10(c2)) | (c2 = f8(f10(c2))) | (~big_f(c2, f10(f10(c2)))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))),
% 29.24/19.43 inference(quant_inst,[status(thm)],[])).
% 29.24/19.43 tff(21648,plain,
% 29.24/19.43 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c2) = c2)) | (f10(f10(c2)) = f10(c2)) | (c2 = f8(f10(c2))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~big_f(c2, f10(f10(c2))))),
% 29.24/19.43 inference(modus_ponens,[status(thm)],[21647, 21646])).
% 29.24/19.43 tff(21649,plain,
% 29.24/19.43 (c2 = f8(f10(c2))),
% 29.24/19.43 inference(unit_resolution,[status(thm)],[21648, 2730, 77, 15308, 21613, 21641, 21642])).
% 29.24/19.43 tff(21650,plain,
% 29.24/19.43 (f8(f10(c2)) = c2),
% 29.24/19.43 inference(symmetry,[status(thm)],[21649])).
% 29.24/19.43 tff(21651,plain,
% 29.24/19.43 (big_f(f3(c2, c2), c2)),
% 29.24/19.43 inference(unit_resolution,[status(thm)],[21176, 21637, 21610, 873, 21554, 27])).
% 29.24/19.43 tff(21652,plain,
% 29.24/19.43 (big_f(f3(c2, c2), f10(f10(c2)))),
% 29.24/19.43 inference(modus_ponens,[status(thm)],[21651, 21043])).
% 29.24/19.43 tff(21653,plain,
% 29.24/19.43 (f3(c2, c2) = f8(f10(c2))),
% 29.24/19.43 inference(unit_resolution,[status(thm)],[21524, 2730, 77, 15308, 21641, 21642, 21652])).
% 29.24/19.43 tff(21654,plain,
% 29.24/19.43 (f3(c2, c2) = c2),
% 29.24/19.43 inference(transitivity,[status(thm)],[21653, 21650])).
% 29.24/19.43 tff(21655,plain,
% 29.24/19.43 ($false),
% 29.24/19.43 inference(unit_resolution,[status(thm)],[21637, 21654])).
% 29.24/19.43 tff(21656,plain,((c2 = c4) | (~(f7(c2) = c2)) | (~(f10(c1) = c2)) | (~big_f(c2, c2)) | big_f(c2, f10(c2)) | (~(f7(c1) = c2)) | (~(f4(c4) = c1)) | big_f(c1, c2) | (f10(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 29.24/19.43 tff(21657,plain,
% 29.24/19.43 (c2 = c4),
% 29.24/19.43 inference(unit_resolution,[status(thm)],[21656, 15517, 16, 1345, 77, 347, 11752, 27, 89])).
% 29.24/19.43 tff(21658,plain,
% 29.24/19.43 (c4 = c2),
% 29.24/19.43 inference(symmetry,[status(thm)],[21657])).
% 29.24/19.43 tff(21659,plain,
% 29.24/19.43 (big_f(f4(c4), c4) <=> big_f(c1, c2)),
% 29.24/19.43 inference(monotonicity,[status(thm)],[11752, 21658])).
% 29.24/19.43 tff(21660,plain,
% 29.24/19.43 (big_f(c1, c2) <=> big_f(f4(c4), c4)),
% 29.24/19.43 inference(symmetry,[status(thm)],[21659])).
% 29.24/19.43 tff(21661,plain,
% 29.24/19.43 ((~big_f(c1, c2)) <=> (~big_f(f4(c4), c4))),
% 29.24/19.43 inference(monotonicity,[status(thm)],[21660])).
% 29.24/19.43 tff(21662,plain,
% 29.24/19.43 (~big_f(f4(c4), c4)),
% 29.24/19.43 inference(modus_ponens,[status(thm)],[27, 21661])).
% 29.24/19.43 tff(21663,plain,
% 29.24/19.43 ((c3 = c1) <=> (f4(c4) = c3)),
% 29.24/19.43 inference(transitivity,[status(thm)],[68, 18048])).
% 29.24/19.43 tff(21664,plain,
% 29.24/19.43 ((~(c3 = c1)) <=> (~(f4(c4) = c3))),
% 29.24/19.43 inference(monotonicity,[status(thm)],[21663])).
% 29.24/19.43 tff(21665,plain,
% 29.24/19.43 (~(f4(c4) = c3)),
% 29.24/19.43 inference(modus_ponens,[status(thm)],[21553, 21664])).
% 29.24/19.43 tff(21666,plain,
% 29.24/19.43 (f4(c2) = f4(c4)),
% 29.24/19.43 inference(monotonicity,[status(thm)],[21657])).
% 29.24/19.43 tff(21667,plain,
% 29.24/19.43 (f4(c2) = f10(c2)),
% 29.24/19.43 inference(transitivity,[status(thm)],[21666, 11752, 99])).
% 29.24/19.43 tff(21668,plain,
% 29.24/19.43 ((c2 = f4(c2)) <=> (c2 = f10(c2))),
% 29.24/19.43 inference(monotonicity,[status(thm)],[21667])).
% 29.24/19.43 tff(21669,plain,
% 29.24/19.43 ((c2 = f4(c2)) <=> (f10(c2) = c2)),
% 29.24/19.43 inference(transitivity,[status(thm)],[21668, 4987])).
% 29.24/19.43 tff(21670,plain,
% 29.24/19.43 ((f10(c2) = c2) <=> (c2 = f4(c2))),
% 29.24/19.43 inference(symmetry,[status(thm)],[21669])).
% 29.24/19.43 tff(21671,plain,
% 29.24/19.43 ((~(f10(c2) = c2)) <=> (~(c2 = f4(c2)))),
% 29.24/19.43 inference(monotonicity,[status(thm)],[21670])).
% 29.24/19.43 tff(21672,plain,
% 29.24/19.43 (~(c2 = f4(c2))),
% 29.24/19.43 inference(modus_ponens,[status(thm)],[89, 21671])).
% 29.24/19.43 tff(21673,plain,
% 29.24/19.43 (f1(f10(c2), f10(c2)) = f1(c1, c1)),
% 29.24/19.43 inference(monotonicity,[status(thm)],[11819, 11819])).
% 29.24/19.43 tff(21674,plain,
% 29.24/19.43 (f1(f10(c2), f10(c2)) = f10(c2)),
% 29.24/19.43 inference(transitivity,[status(thm)],[21673, 624, 12231])).
% 29.24/19.43 tff(21675,plain,
% 29.24/19.43 (big_f(f10(c2), f1(f10(c2), f10(c2))) <=> big_f(f10(c2), f10(c2))),
% 29.24/19.43 inference(monotonicity,[status(thm)],[21674])).
% 29.24/19.43 tff(21676,plain,
% 29.24/19.43 (big_f(f10(c2), f10(c2)) <=> big_f(f10(c2), f1(f10(c2), f10(c2)))),
% 29.24/19.43 inference(symmetry,[status(thm)],[21675])).
% 29.24/19.43 tff(21677,plain,
% 29.24/19.43 (big_f(f10(c2), f1(f10(c2), f10(c2)))),
% 29.24/19.43 inference(modus_ponens,[status(thm)],[14686, 21676])).
% 29.24/19.43 tff(21678,plain,
% 29.24/19.43 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((~(c2 = c4)) | (c2 = f4(c2)) | (f10(c2) = c3) | (~big_f(c2, c2)) | (~(f1(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f10(c2), f1(f10(c2), f10(c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (~(c2 = c4)) | (c2 = f4(c2)) | (f10(c2) = c3) | (~big_f(c2, c2)) | (~(f1(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f10(c2), f1(f10(c2), f10(c2)))))),
% 29.24/19.43 inference(rewrite,[status(thm)],[])).
% 29.24/19.43 tff(21679,plain,
% 29.24/19.43 (((f10(c2) = c3) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)) | (~(f1(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f10(c2), f1(f10(c2), f10(c2))))) <=> ((~(c2 = c4)) | (c2 = f4(c2)) | (f10(c2) = c3) | (~big_f(c2, c2)) | (~(f1(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f10(c2), f1(f10(c2), f10(c2)))))),
% 29.24/19.43 inference(rewrite,[status(thm)],[])).
% 29.24/19.43 tff(21680,plain,
% 29.24/19.43 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f10(c2) = c3) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)) | (~(f1(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f10(c2), f1(f10(c2), f10(c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((~(c2 = c4)) | (c2 = f4(c2)) | (f10(c2) = c3) | (~big_f(c2, c2)) | (~(f1(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f10(c2), f1(f10(c2), f10(c2))))))),
% 29.24/19.43 inference(monotonicity,[status(thm)],[21679])).
% 29.24/19.43 tff(21681,plain,
% 29.24/19.43 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f10(c2) = c3) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)) | (~(f1(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f10(c2), f1(f10(c2), f10(c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (~(c2 = c4)) | (c2 = f4(c2)) | (f10(c2) = c3) | (~big_f(c2, c2)) | (~(f1(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f10(c2), f1(f10(c2), f10(c2)))))),
% 29.24/19.43 inference(transitivity,[status(thm)],[21680, 21678])).
% 29.24/19.43 tff(21682,plain,
% 29.24/19.43 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f10(c2) = c3) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)) | (~(f1(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f10(c2), f1(f10(c2), f10(c2)))))),
% 29.24/19.43 inference(quant_inst,[status(thm)],[])).
% 29.24/19.43 tff(21683,plain,
% 29.24/19.43 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (~(c2 = c4)) | (c2 = f4(c2)) | (f10(c2) = c3) | (~big_f(c2, c2)) | (~(f1(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f10(c2), f1(f10(c2), f10(c2))))),
% 29.24/19.43 inference(modus_ponens,[status(thm)],[21682, 21681])).
% 29.24/19.43 tff(21684,plain,
% 29.24/19.43 ((~(f1(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f10(c2), f1(f10(c2), f10(c2))))),
% 29.24/19.43 inference(unit_resolution,[status(thm)],[21683, 553, 631, 16857, 1345, 15667])).
% 29.24/19.43 tff(21685,plain,
% 29.24/19.43 ($false),
% 29.24/19.43 inference(unit_resolution,[status(thm)],[21684, 21677, 21674])).
% 29.24/19.43 tff(21686,plain,((~(f1(c1, c1) = c1)) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)) | (f10(c2) = c3) | (~big_f(f10(c2), f10(c2))) | (~(f10(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.24/19.43 tff(21687,plain,
% 29.24/19.43 (~(f1(c1, c1) = c1)),
% 29.24/19.43 inference(unit_resolution,[status(thm)],[21686, 21657, 21672, 1345, 21615, 21614, 94])).
% 29.24/19.43 tff(21688,plain,
% 29.24/19.43 (~(f1(f4(c4), c1) = c1)),
% 29.24/19.43 inference(modus_ponens,[status(thm)],[21687, 18067])).
% 29.24/19.43 tff(21689,plain,
% 29.24/19.43 (big_f(f4(c4), f1(f4(c4), c1))),
% 29.24/19.43 inference(unit_resolution,[status(thm)],[18077, 21688, 21665, 21662])).
% 29.24/19.43 tff(21690,plain,
% 29.24/19.43 (big_f(c1, f1(c1, c1))),
% 29.24/19.43 inference(modus_ponens,[status(thm)],[21689, 18061])).
% 29.24/19.43 tff(21691,plain,
% 29.24/19.43 (f1(c1, c1) = c2),
% 29.24/19.43 inference(unit_resolution,[status(thm)],[601, 21687])).
% 29.24/19.43 tff(21692,plain,
% 29.24/19.43 (~big_f(c1, f1(c1, c1))),
% 29.24/19.43 inference(unit_resolution,[status(thm)],[4561, 21691, 27])).
% 29.24/19.43 tff(21693,plain,
% 29.24/19.43 ($false),
% 29.24/19.43 inference(unit_resolution,[status(thm)],[21692, 21690])).
% 29.24/19.43 tff(21694,plain,(big_f(c2, f10(c2)) | (~(f4(c4) = c1)) | big_f(c1, c2) | (~big_f(c2, c2)) | (f10(c2) = c2) | (~(f10(c1) = c2)) | (~(f7(c2) = c2)) | (~(f7(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.24/19.43 tff(21695,plain,
% 29.24/19.43 (big_f(c2, f10(c2))),
% 29.24/19.43 inference(unit_resolution,[status(thm)],[21694, 27, 15706, 21450, 17538, 15, 21432, 120])).
% 29.24/19.43 tff(21696,plain,
% 29.24/19.43 (big_f(c2, c1)),
% 29.24/19.43 inference(modus_ponens,[status(thm)],[21695, 17543])).
% 29.24/19.43 tff(21697,plain,
% 29.24/19.43 (big_f(f7(f10(c2)), c2)),
% 29.24/19.43 inference(modus_ponens,[status(thm)],[21450, 17547])).
% 29.24/19.43 tff(21698,plain,
% 29.24/19.43 (big_f(f7(f10(c2)), f10(c2))),
% 29.24/19.43 inference(modus_ponens,[status(thm)],[21695, 21419])).
% 29.24/19.43 tff(21699,plain,
% 29.24/19.43 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (c2 = f5(f10(c2))) | (f7(f10(c2)) = f10(c2)) | (~big_f(f7(f10(c2)), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (c2 = f5(f10(c2))) | (f7(f10(c2)) = f10(c2)) | (~big_f(f7(f10(c2)), c2)))),
% 29.24/19.43 inference(rewrite,[status(thm)],[])).
% 29.24/19.43 tff(21700,plain,
% 29.24/19.43 (((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(f10(c2)) = f10(c2)) | (c2 = f5(f10(c2))) | (~big_f(f7(f10(c2)), c2))) <=> ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (c2 = f5(f10(c2))) | (f7(f10(c2)) = f10(c2)) | (~big_f(f7(f10(c2)), c2)))),
% 29.24/19.43 inference(rewrite,[status(thm)],[])).
% 29.24/19.43 tff(21701,plain,
% 29.24/19.43 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(f10(c2)) = f10(c2)) | (c2 = f5(f10(c2))) | (~big_f(f7(f10(c2)), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (c2 = f5(f10(c2))) | (f7(f10(c2)) = f10(c2)) | (~big_f(f7(f10(c2)), c2))))),
% 29.24/19.43 inference(monotonicity,[status(thm)],[21700])).
% 29.24/19.43 tff(21702,plain,
% 29.24/19.43 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(f10(c2)) = f10(c2)) | (c2 = f5(f10(c2))) | (~big_f(f7(f10(c2)), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (c2 = f5(f10(c2))) | (f7(f10(c2)) = f10(c2)) | (~big_f(f7(f10(c2)), c2)))),
% 29.24/19.43 inference(transitivity,[status(thm)],[21701, 21699])).
% 29.24/19.43 tff(21703,plain,
% 29.24/19.43 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(f10(c2)) = f10(c2)) | (c2 = f5(f10(c2))) | (~big_f(f7(f10(c2)), c2)))),
% 29.24/19.43 inference(quant_inst,[status(thm)],[])).
% 29.24/19.43 tff(21704,plain,
% 29.24/19.43 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (c2 = f5(f10(c2))) | (f7(f10(c2)) = f10(c2)) | (~big_f(f7(f10(c2)), c2))),
% 29.24/19.43 inference(modus_ponens,[status(thm)],[21703, 21702])).
% 29.24/19.43 tff(21705,plain,
% 29.24/19.43 ((c2 = f8(c2)) | (c2 = f5(f10(c2)))),
% 29.24/19.43 inference(unit_resolution,[status(thm)],[21704, 1659, 89, 12291, 11895, 21204])).
% 29.24/19.43 tff(21706,plain,
% 29.24/19.43 (c2 = f5(f10(c2))),
% 29.24/19.43 inference(unit_resolution,[status(thm)],[21705, 12290])).
% 29.24/19.43 tff(21707,plain,
% 29.24/19.43 (f5(f10(c2)) = c2),
% 29.24/19.43 inference(symmetry,[status(thm)],[21706])).
% 29.24/19.43 tff(21708,assumption,(big_f(f7(f10(c2)), f10(c2))), introduced(assumption)).
% 29.24/19.43 tff(21709,plain,
% 29.24/19.43 ((c2 = f8(c2)) | (f10(c2) = f5(f10(c2)))),
% 29.24/19.43 inference(unit_resolution,[status(thm)],[13757, 1659, 89, 12291, 11895, 21708])).
% 29.24/19.43 tff(21710,plain,
% 29.24/19.43 (f10(c2) = f5(f10(c2))),
% 29.24/19.43 inference(unit_resolution,[status(thm)],[21709, 12290])).
% 29.24/19.43 tff(21711,plain,
% 29.24/19.43 (f10(c2) = c2),
% 29.24/19.43 inference(transitivity,[status(thm)],[21710, 21707])).
% 29.24/19.43 tff(21712,plain,
% 29.24/19.43 ($false),
% 29.24/19.43 inference(unit_resolution,[status(thm)],[89, 21711])).
% 29.24/19.43 tff(21713,plain,((c2 = f8(c2)) | (f10(c2) = c2) | (~big_f(c2, f10(c2))) | (f7(f10(c2)) = f10(c2)) | (~big_f(f7(f10(c2)), c2)) | (~big_f(f7(f10(c2)), f10(c2)))), inference(lemma,lemma(discharge,[]))).
% 29.24/19.43 tff(21714,plain,
% 29.24/19.43 (c2 = f8(c2)),
% 29.24/19.43 inference(unit_resolution,[status(thm)],[21713, 21695, 17538, 20958, 21697, 21698])).
% 29.24/19.43 tff(21715,plain,
% 29.24/19.43 (f8(c2) = c2),
% 29.24/19.43 inference(symmetry,[status(thm)],[21714])).
% 29.24/19.43 tff(21716,plain,
% 29.24/19.43 ((f10(c2) = f8(c2)) <=> (f10(c2) = c2)),
% 29.24/19.43 inference(monotonicity,[status(thm)],[21715])).
% 29.24/19.43 tff(21717,plain,
% 29.24/19.43 ((f10(c2) = c2) <=> (f10(c2) = f8(c2))),
% 29.24/19.43 inference(symmetry,[status(thm)],[21716])).
% 29.24/19.43 tff(21718,plain,
% 29.24/19.43 ((~(f10(c2) = c2)) <=> (~(f10(c2) = f8(c2)))),
% 29.24/19.43 inference(monotonicity,[status(thm)],[21717])).
% 29.24/19.43 tff(21719,plain,
% 29.24/19.43 (~(f10(c2) = f8(c2))),
% 29.24/19.43 inference(modus_ponens,[status(thm)],[17538, 21718])).
% 29.24/19.43 tff(21720,plain,
% 29.24/19.43 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c2 = f5(f10(c2))) | (f7(f10(c2)) = f10(c2)) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (~big_f(f7(f10(c2)), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (c2 = f5(f10(c2))) | (f7(f10(c2)) = f10(c2)) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (~big_f(f7(f10(c2)), c2)))),
% 29.24/19.43 inference(rewrite,[status(thm)],[])).
% 29.24/19.43 tff(21721,plain,
% 29.24/19.43 (((f10(c2) = c2) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (f7(f10(c2)) = f10(c2)) | (c2 = f5(f10(c2))) | (~big_f(f7(f10(c2)), c2))) <=> ((f10(c2) = c2) | (c2 = f5(f10(c2))) | (f7(f10(c2)) = f10(c2)) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (~big_f(f7(f10(c2)), c2)))),
% 29.24/19.43 inference(rewrite,[status(thm)],[])).
% 29.24/19.43 tff(21722,plain,
% 29.24/19.43 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (f7(f10(c2)) = f10(c2)) | (c2 = f5(f10(c2))) | (~big_f(f7(f10(c2)), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c2 = f5(f10(c2))) | (f7(f10(c2)) = f10(c2)) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (~big_f(f7(f10(c2)), c2))))),
% 29.24/19.43 inference(monotonicity,[status(thm)],[21721])).
% 29.24/19.43 tff(21723,plain,
% 29.24/19.43 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (f7(f10(c2)) = f10(c2)) | (c2 = f5(f10(c2))) | (~big_f(f7(f10(c2)), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (c2 = f5(f10(c2))) | (f7(f10(c2)) = f10(c2)) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (~big_f(f7(f10(c2)), c2)))),
% 29.24/19.43 inference(transitivity,[status(thm)],[21722, 21720])).
% 29.24/19.43 tff(21724,plain,
% 29.24/19.43 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (f7(f10(c2)) = f10(c2)) | (c2 = f5(f10(c2))) | (~big_f(f7(f10(c2)), c2)))),
% 29.24/19.43 inference(quant_inst,[status(thm)],[])).
% 29.24/19.43 tff(21725,plain,
% 29.24/19.43 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (c2 = f5(f10(c2))) | (f7(f10(c2)) = f10(c2)) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (~big_f(f7(f10(c2)), c2))),
% 29.24/19.43 inference(modus_ponens,[status(thm)],[21724, 21723])).
% 29.24/19.43 tff(21726,plain,
% 29.24/19.43 ((c2 = f5(f10(c2))) | (f10(c2) = f8(c2))),
% 29.24/19.43 inference(unit_resolution,[status(thm)],[21725, 1659, 89, 11895, 14686, 21204])).
% 29.24/19.43 tff(21727,plain,
% 29.24/19.43 (c2 = f5(f10(c2))),
% 29.24/19.43 inference(unit_resolution,[status(thm)],[21726, 13710])).
% 29.24/19.43 tff(21728,plain,
% 29.24/19.43 (f5(f10(c2)) = c2),
% 29.24/19.43 inference(symmetry,[status(thm)],[21727])).
% 29.24/19.43 tff(21729,plain,
% 29.24/19.43 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f7(f10(c2)) = f10(c2)) | (f10(c2) = f8(c2)) | (~big_f(f7(f10(c2)), f10(c2))) | (f10(c2) = f5(f10(c2))) | (~big_f(f10(c2), f10(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (f7(f10(c2)) = f10(c2)) | (f10(c2) = f8(c2)) | (~big_f(f7(f10(c2)), f10(c2))) | (f10(c2) = f5(f10(c2))) | (~big_f(f10(c2), f10(c2))))),
% 29.24/19.43 inference(rewrite,[status(thm)],[])).
% 29.24/19.43 tff(21730,plain,
% 29.24/19.43 (((f10(c2) = c2) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (f7(f10(c2)) = f10(c2)) | (f10(c2) = f5(f10(c2))) | (~big_f(f7(f10(c2)), f10(c2)))) <=> ((f10(c2) = c2) | (f7(f10(c2)) = f10(c2)) | (f10(c2) = f8(c2)) | (~big_f(f7(f10(c2)), f10(c2))) | (f10(c2) = f5(f10(c2))) | (~big_f(f10(c2), f10(c2))))),
% 29.24/19.43 inference(rewrite,[status(thm)],[])).
% 29.24/19.43 tff(21731,plain,
% 29.24/19.43 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (f7(f10(c2)) = f10(c2)) | (f10(c2) = f5(f10(c2))) | (~big_f(f7(f10(c2)), f10(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f7(f10(c2)) = f10(c2)) | (f10(c2) = f8(c2)) | (~big_f(f7(f10(c2)), f10(c2))) | (f10(c2) = f5(f10(c2))) | (~big_f(f10(c2), f10(c2)))))),
% 29.24/19.44 inference(monotonicity,[status(thm)],[21730])).
% 29.24/19.44 tff(21732,plain,
% 29.24/19.44 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (f7(f10(c2)) = f10(c2)) | (f10(c2) = f5(f10(c2))) | (~big_f(f7(f10(c2)), f10(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (f7(f10(c2)) = f10(c2)) | (f10(c2) = f8(c2)) | (~big_f(f7(f10(c2)), f10(c2))) | (f10(c2) = f5(f10(c2))) | (~big_f(f10(c2), f10(c2))))),
% 29.24/19.44 inference(transitivity,[status(thm)],[21731, 21729])).
% 29.24/19.44 tff(21733,plain,
% 29.24/19.44 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (f7(f10(c2)) = f10(c2)) | (f10(c2) = f5(f10(c2))) | (~big_f(f7(f10(c2)), f10(c2))))),
% 29.24/19.44 inference(quant_inst,[status(thm)],[])).
% 29.24/19.44 tff(21734,plain,
% 29.24/19.44 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (f7(f10(c2)) = f10(c2)) | (f10(c2) = f8(c2)) | (~big_f(f7(f10(c2)), f10(c2))) | (f10(c2) = f5(f10(c2))) | (~big_f(f10(c2), f10(c2)))),
% 29.24/19.44 inference(modus_ponens,[status(thm)],[21733, 21732])).
% 29.24/19.44 tff(21735,plain,
% 29.24/19.44 ((f10(c2) = f8(c2)) | (f10(c2) = f5(f10(c2)))),
% 29.24/19.44 inference(unit_resolution,[status(thm)],[21734, 1659, 89, 11895, 14686, 21708])).
% 29.24/19.44 tff(21736,plain,
% 29.24/19.44 (f10(c2) = f5(f10(c2))),
% 29.24/19.44 inference(unit_resolution,[status(thm)],[21735, 13710])).
% 29.24/19.44 tff(21737,plain,
% 29.24/19.44 (f10(c2) = c2),
% 29.24/19.44 inference(transitivity,[status(thm)],[21736, 21728])).
% 29.24/19.44 tff(21738,plain,
% 29.24/19.44 ($false),
% 29.24/19.44 inference(unit_resolution,[status(thm)],[89, 21737])).
% 29.24/19.44 tff(21739,plain,((f10(c2) = f8(c2)) | (f10(c2) = c2) | (f7(f10(c2)) = f10(c2)) | (~big_f(f10(c2), f10(c2))) | (~big_f(f7(f10(c2)), f10(c2))) | (~big_f(f7(f10(c2)), c2))), inference(lemma,lemma(discharge,[]))).
% 29.24/19.44 tff(21740,plain,
% 29.24/19.44 (~big_f(f10(c2), f10(c2))),
% 29.24/19.44 inference(unit_resolution,[status(thm)],[21739, 21719, 20958, 17538, 21698, 21697])).
% 29.24/19.44 tff(21741,plain,
% 29.24/19.44 (big_f(f10(c2), f10(c2))),
% 29.24/19.44 inference(modus_ponens,[status(thm)],[4932, 20922])).
% 29.24/19.44 tff(21742,plain,
% 29.24/19.44 ($false),
% 29.24/19.44 inference(unit_resolution,[status(thm)],[20783, 21741])).
% 29.24/19.44 tff(21743,plain,((~big_f(c1, c1)) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.24/19.44 tff(21744,plain,
% 29.24/19.44 (~big_f(c1, c1)),
% 29.24/19.44 inference(unit_resolution,[status(thm)],[21743, 21740, 17539])).
% 29.24/19.44 tff(21745,plain,
% 29.24/19.44 (f4(c1) = f4(f10(c2))),
% 29.24/19.44 inference(monotonicity,[status(thm)],[17541])).
% 29.24/19.44 tff(21746,plain,
% 29.24/19.44 (f4(f10(c2)) = f4(c1)),
% 29.24/19.44 inference(symmetry,[status(thm)],[21745])).
% 29.24/19.44 tff(21747,plain,
% 29.24/19.44 ((c2 = f4(f10(c2))) <=> (c2 = f4(c1))),
% 29.24/19.44 inference(monotonicity,[status(thm)],[21746])).
% 29.24/19.44 tff(21748,plain,
% 29.24/19.44 ((c2 = f4(c1)) <=> (c2 = f4(f10(c2)))),
% 29.24/19.44 inference(symmetry,[status(thm)],[21747])).
% 29.24/19.44 tff(21749,plain,
% 29.24/19.44 (f10(c2) = c4),
% 29.24/19.44 inference(transitivity,[status(thm)],[17539, 16938])).
% 29.24/19.44 tff(21750,plain,
% 29.24/19.44 (f4(f10(c2)) = f4(c4)),
% 29.24/19.44 inference(monotonicity,[status(thm)],[21749])).
% 29.24/19.44 tff(21751,plain,
% 29.24/19.44 (f4(c1) = f10(c2)),
% 29.24/19.44 inference(transitivity,[status(thm)],[21745, 21750, 15706, 17541])).
% 29.24/19.44 tff(21752,plain,
% 29.24/19.44 ((c2 = f4(c1)) <=> (c2 = f10(c2))),
% 29.24/19.44 inference(monotonicity,[status(thm)],[21751])).
% 29.24/19.44 tff(21753,plain,
% 29.24/19.44 ((c2 = f4(c1)) <=> (f10(c2) = c2)),
% 29.24/19.44 inference(transitivity,[status(thm)],[21752, 4987])).
% 29.24/19.44 tff(21754,plain,
% 29.24/19.44 ((f10(c2) = c2) <=> (c2 = f4(c1))),
% 29.24/19.44 inference(symmetry,[status(thm)],[21753])).
% 29.24/19.44 tff(21755,plain,
% 29.24/19.44 ((f10(c2) = c2) <=> (c2 = f4(f10(c2)))),
% 29.24/19.44 inference(transitivity,[status(thm)],[21754, 21748])).
% 29.24/19.44 tff(21756,plain,
% 29.24/19.44 ((~(f10(c2) = c2)) <=> (~(c2 = f4(f10(c2))))),
% 29.24/19.44 inference(monotonicity,[status(thm)],[21755])).
% 29.24/19.44 tff(21757,plain,
% 29.24/19.44 (~(c2 = f4(f10(c2)))),
% 29.24/19.44 inference(modus_ponens,[status(thm)],[17538, 21756])).
% 29.24/19.44 tff(21758,assumption,(~(c2 = f4(f10(c2)))), introduced(assumption)).
% 29.24/19.44 tff(21759,plain,
% 29.24/19.44 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = f2(c2)) | (~(f10(c2) = c4)) | (c2 = f4(f10(c2))) | (~big_f(c2, f10(c2))) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = f2(c2)) | (~(f10(c2) = c4)) | (c2 = f4(f10(c2))) | (~big_f(c2, f10(c2))) | (~big_f(c2, c2)))),
% 29.24/19.44 inference(rewrite,[status(thm)],[])).
% 29.24/19.44 tff(21760,plain,
% 29.24/19.44 (((~(c2 = c3)) | (~(f10(c2) = c4)) | (c2 = f4(f10(c2))) | (~big_f(c2, f10(c2))) | (c2 = f2(c2)) | (~big_f(c2, c2))) <=> ((~(c2 = c3)) | (c2 = f2(c2)) | (~(f10(c2) = c4)) | (c2 = f4(f10(c2))) | (~big_f(c2, f10(c2))) | (~big_f(c2, c2)))),
% 29.24/19.44 inference(rewrite,[status(thm)],[])).
% 29.24/19.44 tff(21761,plain,
% 29.24/19.44 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(f10(c2) = c4)) | (c2 = f4(f10(c2))) | (~big_f(c2, f10(c2))) | (c2 = f2(c2)) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = f2(c2)) | (~(f10(c2) = c4)) | (c2 = f4(f10(c2))) | (~big_f(c2, f10(c2))) | (~big_f(c2, c2))))),
% 29.24/19.44 inference(monotonicity,[status(thm)],[21760])).
% 29.24/19.44 tff(21762,plain,
% 29.24/19.44 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(f10(c2) = c4)) | (c2 = f4(f10(c2))) | (~big_f(c2, f10(c2))) | (c2 = f2(c2)) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = f2(c2)) | (~(f10(c2) = c4)) | (c2 = f4(f10(c2))) | (~big_f(c2, f10(c2))) | (~big_f(c2, c2)))),
% 29.24/19.44 inference(transitivity,[status(thm)],[21761, 21759])).
% 29.24/19.44 tff(21763,plain,
% 29.24/19.44 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(f10(c2) = c4)) | (c2 = f4(f10(c2))) | (~big_f(c2, f10(c2))) | (c2 = f2(c2)) | (~big_f(c2, c2)))),
% 29.24/19.44 inference(quant_inst,[status(thm)],[])).
% 29.24/19.44 tff(21764,plain,
% 29.24/19.44 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = f2(c2)) | (~(f10(c2) = c4)) | (c2 = f4(f10(c2))) | (~big_f(c2, f10(c2))) | (~big_f(c2, c2))),
% 29.24/19.44 inference(modus_ponens,[status(thm)],[21763, 21762])).
% 29.24/19.44 tff(21765,plain,
% 29.24/19.44 ((~(c2 = c3)) | (c2 = f2(c2)) | (~(f10(c2) = c4)) | (c2 = f4(f10(c2)))),
% 29.24/19.44 inference(unit_resolution,[status(thm)],[21764, 1355, 1345, 12291])).
% 29.24/19.44 tff(21766,plain,
% 29.24/19.44 (c2 = f2(c2)),
% 29.24/19.44 inference(unit_resolution,[status(thm)],[21765, 1344, 15484, 21758])).
% 29.24/19.44 tff(21767,plain,
% 29.24/19.44 (f2(c2) = c2),
% 29.24/19.44 inference(symmetry,[status(thm)],[21766])).
% 29.24/19.44 tff(21768,plain,
% 29.24/19.44 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(f10(c2) = c4)) | (f10(c2) = f2(c2)) | (c2 = f4(f10(c2))) | (~big_f(c2, f10(c2))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (~(f10(c2) = c4)) | (f10(c2) = f2(c2)) | (c2 = f4(f10(c2))) | (~big_f(c2, f10(c2))))),
% 29.24/19.44 inference(rewrite,[status(thm)],[])).
% 29.24/19.44 tff(21769,plain,
% 29.24/19.44 (((~(c2 = c3)) | (~(f10(c2) = c4)) | (c2 = f4(f10(c2))) | (~big_f(c2, f10(c2))) | (f10(c2) = f2(c2)) | (~big_f(c2, f10(c2)))) <=> ((~(c2 = c3)) | (~(f10(c2) = c4)) | (f10(c2) = f2(c2)) | (c2 = f4(f10(c2))) | (~big_f(c2, f10(c2))))),
% 29.24/19.44 inference(rewrite,[status(thm)],[])).
% 29.24/19.44 tff(21770,plain,
% 29.24/19.44 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(f10(c2) = c4)) | (c2 = f4(f10(c2))) | (~big_f(c2, f10(c2))) | (f10(c2) = f2(c2)) | (~big_f(c2, f10(c2))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(f10(c2) = c4)) | (f10(c2) = f2(c2)) | (c2 = f4(f10(c2))) | (~big_f(c2, f10(c2)))))),
% 29.24/19.44 inference(monotonicity,[status(thm)],[21769])).
% 29.24/19.44 tff(21771,plain,
% 29.24/19.44 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(f10(c2) = c4)) | (c2 = f4(f10(c2))) | (~big_f(c2, f10(c2))) | (f10(c2) = f2(c2)) | (~big_f(c2, f10(c2))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (~(f10(c2) = c4)) | (f10(c2) = f2(c2)) | (c2 = f4(f10(c2))) | (~big_f(c2, f10(c2))))),
% 29.24/19.44 inference(transitivity,[status(thm)],[21770, 21768])).
% 29.24/19.44 tff(21772,plain,
% 29.24/19.44 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(f10(c2) = c4)) | (c2 = f4(f10(c2))) | (~big_f(c2, f10(c2))) | (f10(c2) = f2(c2)) | (~big_f(c2, f10(c2))))),
% 29.24/19.44 inference(quant_inst,[status(thm)],[])).
% 29.24/19.44 tff(21773,plain,
% 29.24/19.44 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (~(f10(c2) = c4)) | (f10(c2) = f2(c2)) | (c2 = f4(f10(c2))) | (~big_f(c2, f10(c2)))),
% 29.24/19.44 inference(modus_ponens,[status(thm)],[21772, 21771])).
% 29.24/19.44 tff(21774,plain,
% 29.24/19.44 ((~(c2 = c3)) | (~(f10(c2) = c4)) | (f10(c2) = f2(c2)) | (c2 = f4(f10(c2)))),
% 29.24/19.44 inference(unit_resolution,[status(thm)],[21773, 1355, 12291])).
% 29.24/19.44 tff(21775,plain,
% 29.24/19.44 (f10(c2) = f2(c2)),
% 29.24/19.44 inference(unit_resolution,[status(thm)],[21774, 1344, 15484, 21758])).
% 29.24/19.44 tff(21776,plain,
% 29.24/19.44 (f10(c2) = c2),
% 29.24/19.44 inference(transitivity,[status(thm)],[21775, 21767])).
% 29.24/19.44 tff(21777,plain,
% 29.24/19.44 ($false),
% 29.24/19.44 inference(unit_resolution,[status(thm)],[89, 21776])).
% 29.24/19.44 tff(21778,plain,((~(c2 = c3)) | (f10(c2) = c2) | (~(f10(c2) = c4)) | (c2 = f4(f10(c2))) | (~big_f(c2, c2)) | (~big_f(c2, f10(c2)))), inference(lemma,lemma(discharge,[]))).
% 29.24/19.44 tff(21779,plain,
% 29.24/19.44 (~(c2 = c3)),
% 29.24/19.44 inference(unit_resolution,[status(thm)],[21778, 21749, 17538, 21757, 21450, 21695])).
% 29.24/19.44 tff(21780,plain,
% 29.24/19.44 (~(c3 = c2)),
% 29.24/19.44 inference(modus_ponens,[status(thm)],[21779, 9745])).
% 29.24/19.44 tff(21781,plain,
% 29.24/19.44 (c3 = c1),
% 29.24/19.44 inference(unit_resolution,[status(thm)],[180, 21780])).
% 29.24/19.44 tff(21782,plain,
% 29.24/19.44 (c2 = f5(c1)),
% 29.24/19.44 inference(unit_resolution,[status(thm)],[12935, 21781, 27, 21450, 21744, 115, 3, 21696])).
% 29.24/19.44 tff(21783,plain,
% 29.24/19.44 (f5(c1) = c2),
% 29.24/19.44 inference(modus_ponens,[status(thm)],[21782, 8483])).
% 29.24/19.44 tff(21784,plain,
% 29.24/19.44 (~(f2(c3) = c1)),
% 29.24/19.44 inference(unit_resolution,[status(thm)],[11776, 21781, 15706, 27, 21744])).
% 29.24/19.44 tff(21785,plain,
% 29.24/19.44 (f2(c3) = c2),
% 29.24/19.44 inference(unit_resolution,[status(thm)],[1273, 21784])).
% 29.24/19.44 tff(21786,plain,
% 29.24/19.44 (~(f5(c1) = c2)),
% 29.24/19.44 inference(unit_resolution,[status(thm)],[14389, 21785, 27, 115, 21450, 14326, 15, 21781])).
% 29.24/19.44 tff(21787,plain,
% 29.24/19.44 ($false),
% 29.24/19.44 inference(unit_resolution,[status(thm)],[21786, 21783])).
% 29.24/19.44 tff(21788,plain,((c2 = c4) | big_f(c1, c2) | (f7(c1) = c1) | (f10(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.24/19.44 tff(21789,plain,
% 29.24/19.44 (c2 = c4),
% 29.24/19.44 inference(unit_resolution,[status(thm)],[21788, 27, 115, 3])).
% 29.24/19.44 tff(21790,plain,
% 29.24/19.44 (f4(c2) = f4(c4)),
% 29.24/19.44 inference(monotonicity,[status(thm)],[21789])).
% 29.24/19.44 tff(21791,plain,
% 29.24/19.44 (f4(c2) = f10(c2)),
% 29.24/19.44 inference(transitivity,[status(thm)],[21790, 15706, 17541])).
% 29.24/19.44 tff(21792,plain,
% 29.24/19.44 ((c2 = f4(c2)) <=> (c2 = f10(c2))),
% 29.24/19.44 inference(monotonicity,[status(thm)],[21791])).
% 29.24/19.44 tff(21793,plain,
% 29.24/19.44 ((c2 = f4(c2)) <=> (f10(c2) = c2)),
% 29.24/19.44 inference(transitivity,[status(thm)],[21792, 4987])).
% 29.24/19.44 tff(21794,plain,
% 29.24/19.44 ((f10(c2) = c2) <=> (c2 = f4(c2))),
% 29.24/19.44 inference(symmetry,[status(thm)],[21793])).
% 29.24/19.44 tff(21795,plain,
% 29.24/19.44 ((~(f10(c2) = c2)) <=> (~(c2 = f4(c2)))),
% 29.24/19.44 inference(monotonicity,[status(thm)],[21794])).
% 29.24/19.44 tff(21796,plain,
% 29.24/19.44 (~(c2 = f4(c2))),
% 29.24/19.44 inference(modus_ponens,[status(thm)],[17538, 21795])).
% 29.24/19.44 tff(21797,plain,
% 29.24/19.44 (~(c3 = c1)),
% 29.24/19.44 inference(unit_resolution,[status(thm)],[11784, 27, 15706, 21744])).
% 29.24/19.44 tff(21798,plain,
% 29.24/19.44 (c3 = c2),
% 29.24/19.44 inference(unit_resolution,[status(thm)],[180, 21797])).
% 29.24/19.44 tff(21799,plain,
% 29.24/19.44 (c2 = c3),
% 29.24/19.44 inference(modus_ponens,[status(thm)],[21798, 78])).
% 29.24/19.44 tff(21800,plain,
% 29.24/19.44 ((~(c2 = c3)) | (~(c2 = c4)) | (c2 = f4(c2)) | (c2 = f2(c2))),
% 29.24/19.44 inference(unit_resolution,[status(thm)],[17172, 1355, 21450])).
% 29.24/19.44 tff(21801,plain,
% 29.24/19.44 (c2 = f2(c2)),
% 29.24/19.44 inference(unit_resolution,[status(thm)],[21800, 21799, 21796, 21789])).
% 29.24/19.44 tff(21802,plain,
% 29.24/19.44 (f2(c2) = c2),
% 29.24/19.44 inference(symmetry,[status(thm)],[21801])).
% 29.24/19.44 tff(21803,plain,
% 29.24/19.44 ((~(c2 = c3)) | (~(c2 = c4)) | (c2 = f4(c2)) | (f10(c2) = f2(c2))),
% 29.24/19.44 inference(unit_resolution,[status(thm)],[21382, 1355, 21450, 21695])).
% 29.24/19.44 tff(21804,plain,
% 29.24/19.44 (f10(c2) = f2(c2)),
% 29.24/19.44 inference(unit_resolution,[status(thm)],[21803, 21799, 21789, 21796])).
% 29.24/19.44 tff(21805,plain,
% 29.24/19.44 (f10(c2) = c2),
% 29.24/19.44 inference(transitivity,[status(thm)],[21804, 21802])).
% 29.24/19.44 tff(21806,plain,
% 29.24/19.44 ($false),
% 29.24/19.44 inference(unit_resolution,[status(thm)],[17538, 21805])).
% 29.24/19.44 tff(21807,plain,(big_f(c1, c2) | (f7(c1) = c1) | (f10(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.24/19.44 tff(21808,plain,
% 29.24/19.44 (big_f(c1, c2)),
% 29.24/19.44 inference(unit_resolution,[status(thm)],[21807, 3, 115])).
% 29.24/19.44 tff(21809,plain,
% 29.24/19.44 (big_f(f10(c2), c2) <=> big_f(c1, c2)),
% 29.24/19.44 inference(monotonicity,[status(thm)],[17539])).
% 29.24/19.44 tff(21810,plain,
% 29.24/19.44 (big_f(c1, c2) <=> big_f(f10(c2), c2)),
% 29.24/19.44 inference(symmetry,[status(thm)],[21809])).
% 29.24/19.44 tff(21811,plain,
% 29.24/19.44 (big_f(f10(c2), c2)),
% 29.24/19.44 inference(modus_ponens,[status(thm)],[21808, 21810])).
% 29.24/19.44 tff(21812,plain,
% 29.24/19.44 ((~big_f(c2, f10(c2))) <=> (~big_f(f7(f10(c2)), f10(c2)))),
% 29.24/19.44 inference(monotonicity,[status(thm)],[21419])).
% 29.24/19.44 tff(21813,plain,
% 29.24/19.44 (~big_f(f7(f10(c2)), f10(c2))),
% 29.24/19.44 inference(modus_ponens,[status(thm)],[15517, 21812])).
% 29.24/19.44 tff(21814,plain,
% 29.24/19.44 ((f10(c2) = f8(c2)) <=> (c1 = f8(c2))),
% 29.24/19.44 inference(monotonicity,[status(thm)],[17539])).
% 29.24/19.44 tff(21815,plain,
% 29.24/19.44 ((c1 = f8(c2)) <=> (f10(c2) = f8(c2))),
% 29.24/19.44 inference(symmetry,[status(thm)],[21814])).
% 29.24/19.44 tff(21816,plain,
% 29.24/19.44 (f7(f4(c4)) = f7(c1)),
% 29.24/19.44 inference(monotonicity,[status(thm)],[15706])).
% 29.24/19.44 tff(21817,plain,
% 29.24/19.44 (f7(c1) = f7(f4(c4))),
% 29.24/19.44 inference(symmetry,[status(thm)],[21816])).
% 29.24/19.44 tff(21818,plain,
% 29.24/19.44 (c2 = f7(f4(c4))),
% 29.24/19.44 inference(transitivity,[status(thm)],[2778, 21817])).
% 29.24/19.44 tff(21819,plain,
% 29.24/19.44 (f8(c2) = f8(f7(f4(c4)))),
% 29.24/19.44 inference(monotonicity,[status(thm)],[21818])).
% 29.24/19.44 tff(21820,plain,
% 29.24/19.44 (f8(f7(f4(c4))) = f8(c2)),
% 29.24/19.44 inference(symmetry,[status(thm)],[21819])).
% 29.24/19.44 tff(21821,plain,
% 29.24/19.44 ((f8(f7(f4(c4))) = c1) <=> (f8(c2) = c1)),
% 29.24/19.44 inference(monotonicity,[status(thm)],[21820])).
% 29.24/19.44 tff(21822,plain,
% 29.24/19.44 ((f8(f7(f4(c4))) = c1) <=> (c1 = f8(c2))),
% 29.24/19.44 inference(transitivity,[status(thm)],[21821, 13044])).
% 29.24/19.44 tff(21823,plain,
% 29.24/19.44 ((f8(f7(f4(c4))) = c1) <=> (f10(c2) = f8(c2))),
% 29.24/19.44 inference(transitivity,[status(thm)],[21822, 21815])).
% 29.24/19.44 tff(21824,plain,
% 29.24/19.44 (big_f(c2, f10(c2)) <=> big_f(f7(c1), c1)),
% 29.24/19.44 inference(transitivity,[status(thm)],[17543, 693])).
% 29.24/19.44 tff(21825,plain,
% 29.24/19.44 ((~big_f(c2, f10(c2))) <=> (~big_f(f7(c1), c1))),
% 29.24/19.44 inference(monotonicity,[status(thm)],[21824])).
% 29.24/19.44 tff(21826,plain,
% 29.24/19.44 (~big_f(f7(c1), c1)),
% 29.24/19.44 inference(modus_ponens,[status(thm)],[15517, 21825])).
% 29.24/19.44 tff(21827,plain,
% 29.24/19.44 (~big_f(f7(c1), f5(c1))),
% 29.24/19.44 inference(unit_resolution,[status(thm)],[8430, 21826, 120, 121])).
% 29.24/19.44 tff(21828,plain,
% 29.24/19.44 (~(c2 = f8(c2))),
% 29.24/19.44 inference(unit_resolution,[status(thm)],[12015, 21827, 115, 17538, 15517])).
% 29.24/19.44 tff(21829,plain,
% 29.24/19.44 (~(f8(f7(f4(c4))) = c2)),
% 29.24/19.44 inference(unit_resolution,[status(thm)],[17582, 21828, 120, 15706])).
% 29.24/19.44 tff(21830,plain,
% 29.24/19.44 (f8(f7(f4(c4))) = c1),
% 29.24/19.44 inference(unit_resolution,[status(thm)],[13371, 21829])).
% 29.24/19.44 tff(21831,plain,
% 29.24/19.44 (f10(c2) = f8(c2)),
% 29.24/19.44 inference(modus_ponens,[status(thm)],[21830, 21823])).
% 29.24/19.44 tff(21832,plain,
% 29.24/19.44 (c1 = f8(f7(f4(c4)))),
% 29.24/19.44 inference(modus_ponens,[status(thm)],[21830, 8518])).
% 29.24/19.44 tff(21833,plain,
% 29.24/19.44 ((~(f10(c2) = f5(f10(c2)))) <=> (~(f5(c1) = c1))),
% 29.24/19.44 inference(monotonicity,[status(thm)],[20436])).
% 29.24/19.44 tff(21834,plain,
% 29.24/19.44 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | big_f(f10(c2), f10(c2)) | (f7(f10(c2)) = f10(c2)) | (~(f10(c2) = f8(c2))) | (~(f10(c2) = f5(f10(c2)))) | big_f(f7(f10(c2)), f10(c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | big_f(f10(c2), f10(c2)) | (f7(f10(c2)) = f10(c2)) | (~(f10(c2) = f8(c2))) | (~(f10(c2) = f5(f10(c2)))) | big_f(f7(f10(c2)), f10(c2)))),
% 29.24/19.44 inference(rewrite,[status(thm)],[])).
% 29.24/19.44 tff(21835,plain,
% 29.24/19.44 (((~(f10(c2) = f5(f10(c2)))) | (f10(c2) = c2) | big_f(f10(c2), f10(c2)) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), f10(c2)) | (~(f10(c2) = f8(c2)))) <=> ((f10(c2) = c2) | big_f(f10(c2), f10(c2)) | (f7(f10(c2)) = f10(c2)) | (~(f10(c2) = f8(c2))) | (~(f10(c2) = f5(f10(c2)))) | big_f(f7(f10(c2)), f10(c2)))),
% 29.24/19.44 inference(rewrite,[status(thm)],[])).
% 29.24/19.44 tff(21836,plain,
% 29.24/19.44 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(f10(c2) = f5(f10(c2)))) | (f10(c2) = c2) | big_f(f10(c2), f10(c2)) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), f10(c2)) | (~(f10(c2) = f8(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | big_f(f10(c2), f10(c2)) | (f7(f10(c2)) = f10(c2)) | (~(f10(c2) = f8(c2))) | (~(f10(c2) = f5(f10(c2)))) | big_f(f7(f10(c2)), f10(c2))))),
% 29.24/19.44 inference(monotonicity,[status(thm)],[21835])).
% 29.24/19.44 tff(21837,plain,
% 29.24/19.44 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(f10(c2) = f5(f10(c2)))) | (f10(c2) = c2) | big_f(f10(c2), f10(c2)) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), f10(c2)) | (~(f10(c2) = f8(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | big_f(f10(c2), f10(c2)) | (f7(f10(c2)) = f10(c2)) | (~(f10(c2) = f8(c2))) | (~(f10(c2) = f5(f10(c2)))) | big_f(f7(f10(c2)), f10(c2)))),
% 29.24/19.44 inference(transitivity,[status(thm)],[21836, 21834])).
% 29.24/19.44 tff(21838,plain,
% 29.24/19.44 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(f10(c2) = f5(f10(c2)))) | (f10(c2) = c2) | big_f(f10(c2), f10(c2)) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), f10(c2)) | (~(f10(c2) = f8(c2))))),
% 29.24/19.44 inference(quant_inst,[status(thm)],[])).
% 29.24/19.44 tff(21839,plain,
% 29.24/19.44 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | big_f(f10(c2), f10(c2)) | (f7(f10(c2)) = f10(c2)) | (~(f10(c2) = f8(c2))) | (~(f10(c2) = f5(f10(c2)))) | big_f(f7(f10(c2)), f10(c2))),
% 29.24/19.44 inference(modus_ponens,[status(thm)],[21838, 21837])).
% 29.24/19.44 tff(21840,plain,
% 29.24/19.44 (~(f10(c2) = f5(f10(c2)))),
% 29.24/19.44 inference(unit_resolution,[status(thm)],[21839, 1745, 89, 17563, 15586, 15266, 21070])).
% 29.24/19.44 tff(21841,plain,
% 29.24/19.44 (~(f5(c1) = c1)),
% 29.24/19.44 inference(modus_ponens,[status(thm)],[21840, 21833])).
% 29.24/19.44 tff(21842,assumption,(c1 = f8(f7(f4(c4)))), introduced(assumption)).
% 29.24/19.44 tff(21843,plain,
% 29.24/19.44 (big_f(c1, f10(c2)) <=> big_f(c1, f10(f7(f4(c4))))),
% 29.24/19.44 inference(symmetry,[status(thm)],[20870])).
% 29.24/19.44 tff(21844,plain,
% 29.24/19.44 (big_f(c1, c1) <=> big_f(c1, f10(f7(f4(c4))))),
% 29.24/19.44 inference(transitivity,[status(thm)],[13717, 17593, 21843])).
% 29.24/19.44 tff(21845,plain,
% 29.24/19.44 ((~big_f(c1, c1)) <=> (~big_f(c1, f10(f7(f4(c4)))))),
% 29.24/19.44 inference(monotonicity,[status(thm)],[21844])).
% 29.24/19.44 tff(21846,plain,
% 29.24/19.44 (~big_f(c1, f10(f7(f4(c4))))),
% 29.24/19.44 inference(modus_ponens,[status(thm)],[66, 21845])).
% 29.24/19.44 tff(21847,plain,
% 29.24/19.44 (~(c2 = f5(c1))),
% 29.24/19.44 inference(unit_resolution,[status(thm)],[8593, 21846, 115, 2907, 21842, 20875])).
% 29.24/19.44 tff(21848,plain,
% 29.24/19.44 (~(f5(c1) = c2)),
% 29.24/19.44 inference(modus_ponens,[status(thm)],[21847, 11786])).
% 29.24/19.44 tff(21849,plain,
% 29.24/19.44 ($false),
% 29.24/19.44 inference(unit_resolution,[status(thm)],[1708, 21848, 21841])).
% 29.24/19.44 tff(21850,plain,(big_f(c1, c1) | (f7(c1) = c1) | big_f(f7(c1), c2) | (~(c1 = f8(f7(f4(c4))))) | (f10(c2) = c2) | (~(f10(c2) = f8(c2))) | big_f(f7(f10(c2)), f10(c2)) | (~(f4(c4) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.24/19.44 tff(21851,plain,
% 29.24/19.44 (big_f(c1, c1)),
% 29.24/19.44 inference(unit_resolution,[status(thm)],[21850, 21832, 1726, 115, 17538, 21831, 21813, 15706])).
% 29.24/19.44 tff(21852,plain,
% 29.24/19.44 (big_f(f10(c2), f10(c2))),
% 29.24/19.44 inference(unit_resolution,[status(thm)],[21743, 21851, 17539])).
% 29.24/19.44 tff(21853,plain,
% 29.24/19.44 ((~big_f(c2, f10(c2))) <=> (~big_f(c2, c1))),
% 29.24/19.44 inference(monotonicity,[status(thm)],[17543])).
% 29.24/19.44 tff(21854,plain,
% 29.24/19.44 (~big_f(c2, c1)),
% 29.24/19.44 inference(modus_ponens,[status(thm)],[15517, 21853])).
% 29.24/19.44 tff(21855,plain,
% 29.24/19.44 (c2 = c4),
% 29.24/19.44 inference(unit_resolution,[status(thm)],[17678, 21851, 121, 17539, 15, 21808, 115, 21854])).
% 29.24/19.44 tff(21856,plain,
% 29.24/19.44 (c4 = c2),
% 29.24/19.44 inference(symmetry,[status(thm)],[21855])).
% 29.24/19.44 tff(21857,plain,
% 29.24/19.44 ((f10(c2) = c4) <=> (f10(c2) = c2)),
% 29.24/19.44 inference(monotonicity,[status(thm)],[21856])).
% 29.24/19.44 tff(21858,plain,
% 29.24/19.44 ((f10(c2) = c2) <=> (f10(c2) = c4)),
% 29.24/19.44 inference(symmetry,[status(thm)],[21857])).
% 29.24/19.44 tff(21859,plain,
% 29.24/19.44 ((~(f10(c2) = c2)) <=> (~(f10(c2) = c4))),
% 29.24/19.44 inference(monotonicity,[status(thm)],[21858])).
% 29.24/19.44 tff(21860,plain,
% 29.24/19.44 (~(f10(c2) = c4)),
% 29.24/19.44 inference(modus_ponens,[status(thm)],[17538, 21859])).
% 29.24/19.44 tff(21861,plain,
% 29.24/19.44 ((c1 = c4) <=> (f10(c2) = c4)),
% 29.24/19.44 inference(monotonicity,[status(thm)],[17541])).
% 29.24/19.44 tff(21862,plain,
% 29.24/19.44 ((f10(c2) = c4) <=> (c1 = c4)),
% 29.24/19.44 inference(symmetry,[status(thm)],[21861])).
% 29.24/19.44 tff(21863,plain,
% 29.24/19.44 ((f10(c2) = c2) <=> (c1 = c4)),
% 29.24/19.44 inference(transitivity,[status(thm)],[21858, 21862])).
% 29.24/19.44 tff(21864,plain,
% 29.24/19.44 ((~(f10(c2) = c2)) <=> (~(c1 = c4))),
% 29.24/19.44 inference(monotonicity,[status(thm)],[21863])).
% 29.24/19.44 tff(21865,plain,
% 29.24/19.44 (~(c1 = c4)),
% 29.24/19.44 inference(modus_ponens,[status(thm)],[17538, 21864])).
% 29.24/19.44 tff(21866,plain,
% 29.24/19.44 (c4 = c2),
% 29.24/19.44 inference(modus_ponens,[status(thm)],[21855, 8721])).
% 29.24/19.44 tff(21867,plain,
% 29.24/19.44 (f7(f10(c2)) = c2),
% 29.24/19.44 inference(transitivity,[status(thm)],[17553, 347])).
% 29.24/19.44 tff(21868,plain,
% 29.24/19.44 (big_f(f7(f10(c2)), c2) <=> big_f(c2, c2)),
% 29.24/19.44 inference(monotonicity,[status(thm)],[21867])).
% 29.24/19.44 tff(21869,plain,
% 29.24/19.44 (big_f(c2, c2) <=> big_f(f7(f10(c2)), c2)),
% 29.24/19.44 inference(symmetry,[status(thm)],[21868])).
% 29.24/19.44 tff(21870,plain,
% 29.24/19.44 ((~big_f(c2, c2)) <=> (~big_f(f7(f10(c2)), c2))),
% 29.24/19.44 inference(monotonicity,[status(thm)],[21869])).
% 29.24/19.44 tff(21871,plain,
% 29.24/19.44 (~big_f(f7(f10(c2)), c2)),
% 29.24/19.44 inference(modus_ponens,[status(thm)],[121, 21870])).
% 29.24/19.44 tff(21872,plain,
% 29.24/19.44 (~big_f(c3, f2(c3))),
% 29.24/19.44 inference(unit_resolution,[status(thm)],[8256, 67, 121, 21534])).
% 29.24/19.44 tff(21873,plain,
% 29.24/19.44 (f3(c1, c1) = f3(f10(c2), f10(c2))),
% 29.24/19.44 inference(symmetry,[status(thm)],[15553])).
% 29.24/19.44 tff(21874,plain,
% 29.24/19.44 (big_f(f3(c1, c1), c1) <=> big_f(f3(f10(c2), f10(c2)), f10(c2))),
% 29.24/19.44 inference(monotonicity,[status(thm)],[21873, 12231])).
% 29.24/19.44 tff(21875,plain,
% 29.24/19.44 (big_f(f3(f10(c2), f10(c2)), f10(c2)) <=> big_f(f3(c1, c1), c1)),
% 29.24/19.44 inference(symmetry,[status(thm)],[21874])).
% 29.24/19.44 tff(21876,plain,
% 29.24/19.44 (f3(f10(c2), f10(c2)) = f10(c2)),
% 29.24/19.44 inference(transitivity,[status(thm)],[15553, 1483, 12231])).
% 29.24/19.44 tff(21877,plain,
% 29.24/19.44 (big_f(f3(f10(c2), f10(c2)), f10(c2)) <=> big_f(f10(c2), f10(c2))),
% 29.24/19.44 inference(monotonicity,[status(thm)],[21876])).
% 29.24/19.44 tff(21878,plain,
% 29.24/19.44 (big_f(f10(c2), f10(c2)) <=> big_f(f3(f10(c2), f10(c2)), f10(c2))),
% 29.24/19.44 inference(symmetry,[status(thm)],[21877])).
% 29.24/19.44 tff(21879,plain,
% 29.24/19.44 (big_f(f10(c2), f10(c2)) <=> big_f(f3(c1, c1), c1)),
% 29.24/19.44 inference(transitivity,[status(thm)],[21878, 21875])).
% 29.24/19.44 tff(21880,plain,
% 29.24/19.44 (big_f(f3(c1, c1), c1)),
% 29.24/19.44 inference(modus_ponens,[status(thm)],[14686, 21879])).
% 29.24/19.44 tff(21881,plain,
% 29.24/19.44 ($false),
% 29.24/19.44 inference(unit_resolution,[status(thm)],[1430, 21880])).
% 29.24/19.44 tff(21882,plain,(big_f(f3(c1, c1), c1) | (~big_f(f10(c2), f10(c2))) | (~(f10(c2) = c1)) | (c1 = c4) | big_f(c3, f2(c3)) | (~(c3 = c2))), inference(lemma,lemma(discharge,[]))).
% 29.24/19.44 tff(21883,plain,
% 29.24/19.44 (big_f(f3(c1, c1), c1)),
% 29.24/19.44 inference(unit_resolution,[status(thm)],[21882, 21872, 94, 482, 14686, 67])).
% 29.24/19.44 tff(21884,plain,
% 29.24/19.44 (big_f(f3(f10(c2), f10(c2)), f10(c2))),
% 29.24/19.44 inference(modus_ponens,[status(thm)],[21883, 17592])).
% 29.24/19.44 tff(21885,plain,
% 29.24/19.44 ((f7(f10(c2)) = f10(c2)) <=> (c2 = f10(c2))),
% 29.24/19.44 inference(monotonicity,[status(thm)],[21867])).
% 29.24/19.44 tff(21886,plain,
% 29.24/19.44 ((f7(f10(c2)) = f10(c2)) <=> (f10(c2) = c2)),
% 29.24/19.44 inference(transitivity,[status(thm)],[21885, 4987])).
% 29.24/19.44 tff(21887,plain,
% 29.24/19.44 ((f10(c2) = c2) <=> (f7(f10(c2)) = f10(c2))),
% 29.24/19.44 inference(symmetry,[status(thm)],[21886])).
% 29.24/19.44 tff(21888,plain,
% 29.24/19.44 ((~(f10(c2) = c2)) <=> (~(f7(f10(c2)) = f10(c2)))),
% 29.24/19.44 inference(monotonicity,[status(thm)],[21887])).
% 29.24/19.44 tff(21889,plain,
% 29.24/19.44 (~(f7(f10(c2)) = f10(c2))),
% 29.24/19.44 inference(modus_ponens,[status(thm)],[89, 21888])).
% 29.24/19.44 tff(21890,plain,
% 29.24/19.44 (~(f2(c3) = c1)),
% 29.24/19.44 inference(unit_resolution,[status(thm)],[1424, 21883, 67, 431, 21872])).
% 29.24/19.44 tff(21891,plain,
% 29.24/19.44 (f2(c3) = c2),
% 29.24/19.44 inference(unit_resolution,[status(thm)],[1273, 21890])).
% 29.24/19.44 tff(21892,plain,
% 29.24/19.44 (c2 = f2(c2)),
% 29.24/19.44 inference(unit_resolution,[status(thm)],[4867, 21891, 67])).
% 29.24/19.44 tff(21893,plain,
% 29.24/19.44 (f10(c2) = f5(c1)),
% 29.24/19.44 inference(transitivity,[status(thm)],[94, 2941])).
% 29.24/19.44 tff(21894,plain,
% 29.24/19.44 (f3(f10(c2), f10(c2)) = f3(f5(c1), f5(c1))),
% 29.24/19.44 inference(monotonicity,[status(thm)],[21893, 21893])).
% 29.24/19.44 tff(21895,plain,
% 29.24/19.44 (f3(f10(c2), f10(c2)) = c2),
% 29.24/19.44 inference(transitivity,[status(thm)],[21894, 13005])).
% 29.24/19.44 tff(21896,plain,
% 29.24/19.44 (big_f(f3(f10(c2), f10(c2)), f10(c2)) <=> big_f(c2, f10(c2))),
% 29.24/19.44 inference(monotonicity,[status(thm)],[21895])).
% 29.24/19.44 tff(21897,plain,
% 29.24/19.44 (big_f(c2, f10(c2)) <=> big_f(f3(f10(c2), f10(c2)), f10(c2))),
% 29.24/19.44 inference(symmetry,[status(thm)],[21896])).
% 29.24/19.44 tff(21898,plain,
% 29.24/19.44 ((~big_f(c2, f10(c2))) <=> (~big_f(f3(f10(c2), f10(c2)), f10(c2)))),
% 29.24/19.44 inference(monotonicity,[status(thm)],[21897])).
% 29.24/19.44 tff(21899,plain,
% 29.24/19.44 (~big_f(f3(f10(c2), f10(c2)), f10(c2))),
% 29.24/19.44 inference(modus_ponens,[status(thm)],[15517, 21898])).
% 29.24/19.44 tff(21900,plain,
% 29.24/19.44 ((f3(f10(c2), f10(c2)) = f10(c2)) <=> (c2 = f10(c2))),
% 29.24/19.44 inference(monotonicity,[status(thm)],[21895])).
% 29.24/19.44 tff(21901,plain,
% 29.24/19.44 ((f3(f10(c2), f10(c2)) = f10(c2)) <=> (f10(c2) = c2)),
% 29.24/19.44 inference(transitivity,[status(thm)],[21900, 4987])).
% 29.24/19.44 tff(21902,plain,
% 29.24/19.44 ((f10(c2) = c2) <=> (f3(f10(c2), f10(c2)) = f10(c2))),
% 29.24/19.44 inference(symmetry,[status(thm)],[21901])).
% 29.24/19.44 tff(21903,plain,
% 29.24/19.44 ((~(f10(c2) = c2)) <=> (~(f3(f10(c2), f10(c2)) = f10(c2)))),
% 29.24/19.44 inference(monotonicity,[status(thm)],[21902])).
% 29.24/19.44 tff(21904,plain,
% 29.24/19.44 (~(f3(f10(c2), f10(c2)) = f10(c2))),
% 29.24/19.44 inference(modus_ponens,[status(thm)],[89, 21903])).
% 29.24/19.44 tff(21905,plain,
% 29.24/19.44 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (f10(c2) = c4) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (f10(c2) = c4) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2)))),
% 29.24/19.45 inference(rewrite,[status(thm)],[])).
% 29.24/19.45 tff(21906,plain,
% 29.24/19.45 (((~(c2 = c3)) | (~(c2 = f2(c2))) | (f10(c2) = c4) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2)) | big_f(c2, c2)) <=> ((~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (f10(c2) = c4) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2)))),
% 29.24/19.45 inference(rewrite,[status(thm)],[])).
% 29.24/19.45 tff(21907,plain,
% 29.24/19.45 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | (f10(c2) = c4) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2)) | big_f(c2, c2))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (f10(c2) = c4) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2))))),
% 29.24/19.45 inference(monotonicity,[status(thm)],[21906])).
% 29.24/19.45 tff(21908,plain,
% 29.24/19.45 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | (f10(c2) = c4) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2)) | big_f(c2, c2))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (f10(c2) = c4) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2)))),
% 29.24/19.45 inference(transitivity,[status(thm)],[21907, 21905])).
% 29.24/19.45 tff(21909,plain,
% 29.24/19.45 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | (f10(c2) = c4) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2)) | big_f(c2, c2))),
% 29.24/19.45 inference(quant_inst,[status(thm)],[])).
% 29.24/19.45 tff(21910,plain,
% 29.24/19.45 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (f10(c2) = c4) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2))),
% 29.24/19.45 inference(modus_ponens,[status(thm)],[21909, 21908])).
% 29.24/19.45 tff(21911,plain,
% 29.24/19.45 ($false),
% 29.24/19.45 inference(unit_resolution,[status(thm)],[21910, 1459, 121, 1344, 2853, 15519, 21904, 21899])).
% 29.24/19.45 tff(21912,plain,((~(f3(f5(c1), f5(c1)) = c2)) | big_f(c2, c2) | (~(c2 = c3)) | (~(c2 = f2(c2))) | (f10(c2) = c4) | big_f(c2, f10(c2)) | (~(f5(c1) = c1)) | (f10(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 29.24/19.45 tff(21913,plain,
% 29.24/19.45 (~(f3(f5(c1), f5(c1)) = c2)),
% 29.24/19.45 inference(unit_resolution,[status(thm)],[21912, 2853, 1344, 121, 15519, 15517, 230, 89])).
% 29.24/19.45 tff(21914,plain,
% 29.24/19.45 (f3(f5(c1), f5(c1)) = c1),
% 29.24/19.45 inference(unit_resolution,[status(thm)],[7625, 21913])).
% 29.24/19.45 tff(21915,plain,
% 29.24/19.45 (f3(f10(c2), f10(c2)) = f10(c2)),
% 29.24/19.45 inference(transitivity,[status(thm)],[21894, 21914, 99])).
% 29.24/19.45 tff(21916,plain,
% 29.24/19.45 (big_f(f3(f10(c2), f10(c2)), f10(c2)) <=> big_f(f10(c2), f10(c2))),
% 29.24/19.45 inference(monotonicity,[status(thm)],[21915])).
% 29.24/19.45 tff(21917,plain,
% 29.24/19.45 (big_f(f10(c2), f10(c2)) <=> big_f(f3(f10(c2), f10(c2)), f10(c2))),
% 29.24/19.45 inference(symmetry,[status(thm)],[21916])).
% 29.24/19.45 tff(21918,plain,
% 29.24/19.45 (big_f(f3(f10(c2), f10(c2)), f10(c2))),
% 29.24/19.45 inference(modus_ponens,[status(thm)],[14686, 21917])).
% 29.24/19.45 tff(21919,plain,
% 29.24/19.45 (f3(f5(c1), f5(c1)) = f3(f10(c2), f10(c2))),
% 29.24/19.45 inference(symmetry,[status(thm)],[21894])).
% 29.24/19.45 tff(21920,plain,
% 29.24/19.45 ((f3(f5(c1), f5(c1)) = c1) <=> (f3(f10(c2), f10(c2)) = f10(c2))),
% 29.24/19.45 inference(monotonicity,[status(thm)],[21919, 99])).
% 29.24/19.45 tff(21921,plain,
% 29.24/19.45 (f3(f10(c2), f10(c2)) = f10(c2)),
% 29.24/19.45 inference(modus_ponens,[status(thm)],[21914, 21920])).
% 29.24/19.45 tff(21922,plain,
% 29.24/19.45 ($false),
% 29.24/19.45 inference(unit_resolution,[status(thm)],[20459, 1398, 121, 1344, 2853, 15519, 21921, 21918])).
% 29.24/19.45 tff(21923,plain,((~(c2 = f2(c2))) | big_f(c2, c2) | (~(c2 = c3)) | (f10(c2) = c4) | (~big_f(f10(c2), f10(c2))) | (~(f5(c1) = c1)) | big_f(c2, f10(c2)) | (f10(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 29.24/19.45 tff(21924,plain,
% 29.24/19.45 (~(f5(c1) = c1)),
% 29.24/19.45 inference(unit_resolution,[status(thm)],[21923, 21892, 1335, 15519, 14686, 121, 15517, 89])).
% 29.24/19.45 tff(21925,plain,
% 29.24/19.45 (f5(c1) = c2),
% 29.24/19.45 inference(unit_resolution,[status(thm)],[1708, 21924])).
% 29.24/19.45 tff(21926,plain,
% 29.24/19.45 (c2 = f5(f10(c2))),
% 29.24/19.45 inference(modus_ponens,[status(thm)],[21925, 17567])).
% 29.24/19.45 tff(21927,plain,
% 29.24/19.45 (f3(f10(c2), f10(c2)) = f8(c2)),
% 29.24/19.45 inference(unit_resolution,[status(thm)],[20901, 705, 89, 21926, 21889, 21884, 21871])).
% 29.24/19.45 tff(21928,plain,
% 29.24/19.45 (f3(f10(c2), f10(c2)) = f10(c2)),
% 29.24/19.45 inference(transitivity,[status(thm)],[21927, 16246, 16268, 99])).
% 29.24/19.45 tff(21929,plain,
% 29.24/19.45 (~(f3(f10(c2), f10(c2)) = f10(c2))),
% 29.24/19.45 inference(unit_resolution,[status(thm)],[20459, 1398, 121, 1335, 21892, 15519, 21884])).
% 29.24/19.45 tff(21930,plain,
% 29.24/19.45 ($false),
% 29.24/19.45 inference(unit_resolution,[status(thm)],[21929, 21928])).
% 29.24/19.45 tff(21931,plain,((~(c3 = c2)) | (~(f8(f7(f4(c4))) = c1)) | (~(f7(c1) = c2)) | (~(f4(c4) = c1)) | big_f(c2, c2) | (f10(c2) = c4) | (f10(c2) = c2) | (~big_f(f10(c2), f10(c2))) | big_f(c2, f10(c2)) | (~(c4 = c2)) | (c1 = c4)), inference(lemma,lemma(discharge,[]))).
% 29.24/19.45 tff(21932,plain,
% 29.24/19.45 (~(c3 = c2)),
% 29.24/19.45 inference(unit_resolution,[status(thm)],[21931, 21830, 120, 15706, 121, 21860, 17538, 21852, 15517, 21866, 21865])).
% 29.24/19.45 tff(21933,plain,
% 29.24/19.45 (c3 = c1),
% 29.24/19.45 inference(unit_resolution,[status(thm)],[180, 21932])).
% 29.24/19.45 tff(21934,plain,
% 29.24/19.45 ((c2 = f5(f10(c2))) <=> (f5(c1) = c2)),
% 29.24/19.45 inference(transitivity,[status(thm)],[20960, 8483])).
% 29.24/19.45 tff(21935,plain,
% 29.24/19.45 ((~(c2 = f5(f10(c2)))) <=> (~(f5(c1) = c2))),
% 29.24/19.45 inference(monotonicity,[status(thm)],[21934])).
% 29.24/19.45 tff(21936,plain,
% 29.24/19.45 (big_f(f10(c2), f10(f10(c2))) <=> big_f(c1, c2)),
% 29.24/19.45 inference(monotonicity,[status(thm)],[17539, 21400])).
% 29.24/19.45 tff(21937,plain,
% 29.24/19.45 (big_f(c1, c2) <=> big_f(f10(c2), f10(f10(c2)))),
% 29.24/19.45 inference(symmetry,[status(thm)],[21936])).
% 29.24/19.45 tff(21938,plain,
% 29.24/19.45 (big_f(f10(c2), f10(f10(c2)))),
% 29.24/19.45 inference(modus_ponens,[status(thm)],[21808, 21937])).
% 29.24/19.45 tff(21939,plain,
% 29.24/19.45 (f2(c1) = f2(f10(c2))),
% 29.24/19.45 inference(monotonicity,[status(thm)],[99])).
% 29.24/19.45 tff(21940,plain,
% 29.24/19.45 (f2(f10(c2)) = f2(c1)),
% 29.24/19.45 inference(symmetry,[status(thm)],[21939])).
% 29.24/19.45 tff(21941,plain,
% 29.24/19.45 ((c2 = f2(f10(c2))) <=> (c2 = f2(c1))),
% 29.24/19.45 inference(monotonicity,[status(thm)],[21940])).
% 29.24/19.45 tff(21942,plain,
% 29.24/19.45 ((c2 = f2(c1)) <=> (c2 = f2(f10(c2)))),
% 29.24/19.45 inference(symmetry,[status(thm)],[21941])).
% 29.24/19.45 tff(21943,assumption,(~big_f(f7(f10(c2)), c2)), introduced(assumption)).
% 29.24/19.45 tff(21944,assumption,(big_f(f10(c2), f10(f10(c2)))), introduced(assumption)).
% 29.24/19.45 tff(21945,plain,
% 29.24/19.45 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f10(f10(c2)) = f10(c2)) | (~(c2 = f5(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2) | (f10(c2) = f8(f10(c2))) | (~big_f(f10(c2), f10(f10(c2)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(f10(c2)) = f10(c2)) | (~(c2 = f5(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2) | (f10(c2) = f8(f10(c2))) | (~big_f(f10(c2), f10(f10(c2)))))),
% 29.24/19.45 inference(rewrite,[status(thm)],[])).
% 29.24/19.45 tff(21946,plain,
% 29.24/19.45 (((~(c2 = f5(f10(c2)))) | (f10(f10(c2)) = f10(c2)) | (f10(c2) = f8(f10(c2))) | (~big_f(f10(c2), f10(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2)) <=> ((f10(f10(c2)) = f10(c2)) | (~(c2 = f5(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2) | (f10(c2) = f8(f10(c2))) | (~big_f(f10(c2), f10(f10(c2)))))),
% 29.24/19.45 inference(rewrite,[status(thm)],[])).
% 29.24/19.45 tff(21947,plain,
% 29.24/19.45 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c2 = f5(f10(c2)))) | (f10(f10(c2)) = f10(c2)) | (f10(c2) = f8(f10(c2))) | (~big_f(f10(c2), f10(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f10(f10(c2)) = f10(c2)) | (~(c2 = f5(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2) | (f10(c2) = f8(f10(c2))) | (~big_f(f10(c2), f10(f10(c2))))))),
% 29.24/19.45 inference(monotonicity,[status(thm)],[21946])).
% 29.24/19.45 tff(21948,plain,
% 29.24/19.45 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c2 = f5(f10(c2)))) | (f10(f10(c2)) = f10(c2)) | (f10(c2) = f8(f10(c2))) | (~big_f(f10(c2), f10(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(f10(c2)) = f10(c2)) | (~(c2 = f5(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2) | (f10(c2) = f8(f10(c2))) | (~big_f(f10(c2), f10(f10(c2)))))),
% 29.24/19.45 inference(transitivity,[status(thm)],[21947, 21945])).
% 29.24/19.45 tff(21949,plain,
% 29.24/19.45 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c2 = f5(f10(c2)))) | (f10(f10(c2)) = f10(c2)) | (f10(c2) = f8(f10(c2))) | (~big_f(f10(c2), f10(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2))),
% 29.24/19.45 inference(quant_inst,[status(thm)],[])).
% 29.24/19.45 tff(21950,plain,
% 29.24/19.45 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(f10(c2)) = f10(c2)) | (~(c2 = f5(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2) | (f10(c2) = f8(f10(c2))) | (~big_f(f10(c2), f10(f10(c2))))),
% 29.24/19.45 inference(modus_ponens,[status(thm)],[21949, 21948])).
% 29.24/19.45 tff(21951,plain,
% 29.24/19.45 ((~(c2 = f5(f10(c2)))) | (f10(c2) = f8(f10(c2))) | (~big_f(f10(c2), f10(f10(c2))))),
% 29.24/19.45 inference(unit_resolution,[status(thm)],[21950, 705, 11896, 21889, 21943])).
% 29.24/19.45 tff(21952,plain,
% 29.24/19.45 (f10(c2) = f8(f10(c2))),
% 29.24/19.45 inference(unit_resolution,[status(thm)],[21951, 13398, 21944])).
% 29.24/19.45 tff(21953,plain,
% 29.24/19.45 (f3(c1, f8(c3)) = f3(f10(c2), f8(c3))),
% 29.24/19.45 inference(monotonicity,[status(thm)],[99])).
% 29.24/19.45 tff(21954,plain,
% 29.24/19.45 (f3(f10(c2), f8(c3)) = f3(c1, f8(c3))),
% 29.24/19.45 inference(symmetry,[status(thm)],[21953])).
% 29.24/19.45 tff(21955,plain,
% 29.24/19.45 (f8(c3) = f8(f10(c2))),
% 29.24/19.45 inference(monotonicity,[status(thm)],[15331])).
% 29.24/19.45 tff(21956,plain,
% 29.24/19.45 (f8(f10(c2)) = f8(c3)),
% 29.24/19.45 inference(symmetry,[status(thm)],[21955])).
% 29.24/19.45 tff(21957,assumption,(f10(c2) = f8(f10(c2))), introduced(assumption)).
% 29.24/19.45 tff(21958,plain,
% 29.24/19.45 (f10(c2) = f8(c3)),
% 29.24/19.45 inference(transitivity,[status(thm)],[21957, 21956])).
% 29.24/19.45 tff(21959,plain,
% 29.24/19.45 (f3(f10(c2), f10(c2)) = f3(f10(c2), f8(c3))),
% 29.24/19.45 inference(monotonicity,[status(thm)],[21958])).
% 29.24/19.45 tff(21960,plain,
% 29.24/19.45 (f3(f10(c2), f10(c2)) = f3(c1, f8(c3))),
% 29.24/19.45 inference(transitivity,[status(thm)],[21959, 21954])).
% 29.24/19.45 tff(21961,plain,
% 29.24/19.45 ((f3(f10(c2), f10(c2)) = f10(c2)) <=> (f3(c1, f8(c3)) = c1)),
% 29.24/19.45 inference(monotonicity,[status(thm)],[21960, 94])).
% 29.24/19.45 tff(21962,plain,
% 29.24/19.45 ((~(f3(f10(c2), f10(c2)) = f10(c2))) <=> (~(f3(c1, f8(c3)) = c1))),
% 29.24/19.45 inference(monotonicity,[status(thm)],[21961])).
% 29.24/19.45 tff(21963,assumption,(~(f10(c2) = f2(f10(c2)))), introduced(assumption)).
% 29.24/19.45 tff(21964,assumption,(~big_f(f3(f10(c2), f10(c2)), f10(c2))), introduced(assumption)).
% 29.24/19.45 tff(21965,assumption,(~(f3(f10(c2), f10(c2)) = f10(c2))), introduced(assumption)).
% 29.24/19.45 tff(21966,assumption,(f10(c2) = c3), introduced(assumption)).
% 29.24/19.45 tff(21967,plain,
% 29.24/19.45 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((f10(c2) = c4) | (~(f10(c2) = c3)) | (f10(c2) = f2(f10(c2))) | (~big_f(f10(c2), f10(c2))) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (f10(c2) = c4) | (~(f10(c2) = c3)) | (f10(c2) = f2(f10(c2))) | (~big_f(f10(c2), f10(c2))) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2)))),
% 29.24/19.45 inference(rewrite,[status(thm)],[])).
% 29.24/19.45 tff(21968,plain,
% 29.24/19.45 (((~(f10(c2) = c3)) | (f10(c2) = c4) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2)) | (f10(c2) = f2(f10(c2))) | (~big_f(f10(c2), f10(c2)))) <=> ((f10(c2) = c4) | (~(f10(c2) = c3)) | (f10(c2) = f2(f10(c2))) | (~big_f(f10(c2), f10(c2))) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2)))),
% 29.24/19.45 inference(rewrite,[status(thm)],[])).
% 29.24/19.45 tff(21969,plain,
% 29.24/19.45 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f10(c2) = c3)) | (f10(c2) = c4) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2)) | (f10(c2) = f2(f10(c2))) | (~big_f(f10(c2), f10(c2))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((f10(c2) = c4) | (~(f10(c2) = c3)) | (f10(c2) = f2(f10(c2))) | (~big_f(f10(c2), f10(c2))) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2))))),
% 29.24/19.45 inference(monotonicity,[status(thm)],[21968])).
% 29.24/19.45 tff(21970,plain,
% 29.24/19.45 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f10(c2) = c3)) | (f10(c2) = c4) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2)) | (f10(c2) = f2(f10(c2))) | (~big_f(f10(c2), f10(c2))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (f10(c2) = c4) | (~(f10(c2) = c3)) | (f10(c2) = f2(f10(c2))) | (~big_f(f10(c2), f10(c2))) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2)))),
% 29.24/19.45 inference(transitivity,[status(thm)],[21969, 21967])).
% 29.24/19.45 tff(21971,plain,
% 29.24/19.45 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f10(c2) = c3)) | (f10(c2) = c4) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2)) | (f10(c2) = f2(f10(c2))) | (~big_f(f10(c2), f10(c2))))),
% 29.24/19.45 inference(quant_inst,[status(thm)],[])).
% 29.24/19.45 tff(21972,plain,
% 29.24/19.45 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (f10(c2) = c4) | (~(f10(c2) = c3)) | (f10(c2) = f2(f10(c2))) | (~big_f(f10(c2), f10(c2))) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2))),
% 29.24/19.45 inference(modus_ponens,[status(thm)],[21971, 21970])).
% 29.24/19.45 tff(21973,plain,
% 29.24/19.45 ($false),
% 29.24/19.45 inference(unit_resolution,[status(thm)],[21972, 7352, 15519, 21966, 14686, 21965, 21964, 21963])).
% 29.24/19.45 tff(21974,plain,((f3(f10(c2), f10(c2)) = f10(c2)) | (f10(c2) = c4) | (~(f10(c2) = c3)) | (~big_f(f10(c2), f10(c2))) | big_f(f3(f10(c2), f10(c2)), f10(c2)) | (f10(c2) = f2(f10(c2)))), inference(lemma,lemma(discharge,[]))).
% 29.24/19.45 tff(21975,plain,
% 29.24/19.45 (f3(f10(c2), f10(c2)) = f10(c2)),
% 29.24/19.45 inference(unit_resolution,[status(thm)],[21974, 21964, 21516, 14686, 15519, 21963])).
% 29.24/19.45 tff(21976,plain,
% 29.24/19.45 (f8(f10(c2)) = f10(c2)),
% 29.24/19.45 inference(symmetry,[status(thm)],[21957])).
% 29.24/19.45 tff(21977,plain,
% 29.24/19.45 (f8(c3) = f8(f10(c2))),
% 29.24/19.45 inference(monotonicity,[status(thm)],[21501])).
% 29.24/19.45 tff(21978,plain,
% 29.24/19.45 (f8(c3) = f10(c2)),
% 29.24/19.45 inference(transitivity,[status(thm)],[21977, 21976])).
% 29.24/19.45 tff(21979,plain,
% 29.24/19.45 (f3(f10(c2), f8(c3)) = f3(f10(c2), f10(c2))),
% 29.24/19.45 inference(monotonicity,[status(thm)],[21978])).
% 29.24/19.45 tff(21980,plain,
% 29.24/19.45 (f3(f10(c2), f8(c3)) = f10(c2)),
% 29.24/19.45 inference(transitivity,[status(thm)],[21979, 21975])).
% 29.24/19.45 tff(21981,plain,
% 29.24/19.45 (big_f(f3(f10(c2), f8(c3)), f10(c2)) <=> big_f(f10(c2), f10(c2))),
% 29.24/19.45 inference(monotonicity,[status(thm)],[21980])).
% 29.24/19.45 tff(21982,plain,
% 29.24/19.45 (big_f(f10(c2), f10(c2)) <=> big_f(f3(f10(c2), f8(c3)), f10(c2))),
% 29.24/19.45 inference(symmetry,[status(thm)],[21981])).
% 29.24/19.45 tff(21983,plain,
% 29.24/19.45 (big_f(f3(f10(c2), f8(c3)), f10(c2))),
% 29.24/19.45 inference(modus_ponens,[status(thm)],[14686, 21982])).
% 29.24/19.45 tff(21984,plain,
% 29.24/19.45 (f3(f10(c2), f10(c2)) = f3(f10(c2), f8(c3))),
% 29.24/19.45 inference(symmetry,[status(thm)],[21979])).
% 29.24/19.45 tff(21985,plain,
% 29.24/19.45 (big_f(f3(f10(c2), f10(c2)), f10(c2)) <=> big_f(f3(f10(c2), f8(c3)), f10(c2))),
% 29.24/19.45 inference(monotonicity,[status(thm)],[21984])).
% 29.24/19.45 tff(21986,plain,
% 29.24/19.45 ((~big_f(f3(f10(c2), f10(c2)), f10(c2))) <=> (~big_f(f3(f10(c2), f8(c3)), f10(c2)))),
% 29.24/19.45 inference(monotonicity,[status(thm)],[21985])).
% 29.24/19.45 tff(21987,plain,
% 29.24/19.45 (~big_f(f3(f10(c2), f8(c3)), f10(c2))),
% 29.24/19.45 inference(modus_ponens,[status(thm)],[21964, 21986])).
% 29.24/19.45 tff(21988,plain,
% 29.24/19.45 ($false),
% 29.24/19.45 inference(unit_resolution,[status(thm)],[21987, 21983])).
% 29.24/19.45 tff(21989,plain,(big_f(f3(f10(c2), f10(c2)), f10(c2)) | (~big_f(f10(c2), f10(c2))) | (~(f10(c2) = f8(f10(c2)))) | (~(c3 = c1)) | (~(f10(c2) = c1)) | (f10(c2) = c4) | (f10(c2) = f2(f10(c2)))), inference(lemma,lemma(discharge,[]))).
% 29.24/19.45 tff(21990,plain,
% 29.24/19.45 (big_f(f3(f10(c2), f10(c2)), f10(c2))),
% 29.24/19.45 inference(unit_resolution,[status(thm)],[21989, 21963, 21957, 172, 94, 15519, 14686])).
% 29.24/19.45 tff(21991,plain,
% 29.24/19.45 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((f10(c2) = c4) | (~(f10(c2) = c3)) | (f10(c2) = f2(f10(c2))) | (~big_f(f10(c2), f10(c2))) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (f10(c2) = c4) | (~(f10(c2) = c3)) | (f10(c2) = f2(f10(c2))) | (~big_f(f10(c2), f10(c2))) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))))),
% 29.24/19.45 inference(rewrite,[status(thm)],[])).
% 29.24/19.45 tff(21992,plain,
% 29.24/19.45 (((~(f10(c2) = c3)) | (f10(c2) = c4) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))) | (f10(c2) = f2(f10(c2))) | (~big_f(f10(c2), f10(c2)))) <=> ((f10(c2) = c4) | (~(f10(c2) = c3)) | (f10(c2) = f2(f10(c2))) | (~big_f(f10(c2), f10(c2))) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))))),
% 29.24/19.45 inference(rewrite,[status(thm)],[])).
% 29.24/19.45 tff(21993,plain,
% 29.24/19.45 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f10(c2) = c3)) | (f10(c2) = c4) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))) | (f10(c2) = f2(f10(c2))) | (~big_f(f10(c2), f10(c2))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((f10(c2) = c4) | (~(f10(c2) = c3)) | (f10(c2) = f2(f10(c2))) | (~big_f(f10(c2), f10(c2))) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2)))))),
% 29.24/19.45 inference(monotonicity,[status(thm)],[21992])).
% 29.24/19.45 tff(21994,plain,
% 29.24/19.45 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f10(c2) = c3)) | (f10(c2) = c4) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))) | (f10(c2) = f2(f10(c2))) | (~big_f(f10(c2), f10(c2))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (f10(c2) = c4) | (~(f10(c2) = c3)) | (f10(c2) = f2(f10(c2))) | (~big_f(f10(c2), f10(c2))) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))))),
% 29.24/19.45 inference(transitivity,[status(thm)],[21993, 21991])).
% 29.24/19.45 tff(21995,plain,
% 29.24/19.45 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f10(c2) = c3)) | (f10(c2) = c4) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))) | (f10(c2) = f2(f10(c2))) | (~big_f(f10(c2), f10(c2))))),
% 29.24/19.45 inference(quant_inst,[status(thm)],[])).
% 29.24/19.45 tff(21996,plain,
% 29.24/19.45 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (f10(c2) = c4) | (~(f10(c2) = c3)) | (f10(c2) = f2(f10(c2))) | (~big_f(f10(c2), f10(c2))) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2)))),
% 29.24/19.45 inference(modus_ponens,[status(thm)],[21995, 21994])).
% 29.24/19.45 tff(21997,plain,
% 29.24/19.45 (~(f3(f10(c2), f10(c2)) = f10(c2))),
% 29.24/19.45 inference(unit_resolution,[status(thm)],[21996, 7051, 15519, 15369, 14686, 21990, 21963])).
% 29.24/19.45 tff(21998,plain,
% 29.24/19.45 (~(f3(c1, f8(c3)) = c1)),
% 29.24/19.45 inference(modus_ponens,[status(thm)],[21997, 21962])).
% 29.24/19.45 tff(21999,plain,
% 29.24/19.45 (big_f(f3(f10(c2), f10(c2)), f10(c2)) <=> big_f(f3(f10(c2), f8(c3)), f10(c2))),
% 29.24/19.45 inference(monotonicity,[status(thm)],[21959])).
% 29.24/19.45 tff(22000,plain,
% 29.24/19.45 (big_f(f3(f10(c2), f8(c3)), f10(c2))),
% 29.24/19.45 inference(modus_ponens,[status(thm)],[21990, 21999])).
% 29.24/19.45 tff(22001,plain,
% 29.24/19.45 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f10(c2) = c2) | (~(c2 = f5(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2) | (~big_f(f3(f10(c2), f8(c3)), f10(c2))) | (f3(f10(c2), f8(c3)) = f8(c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(c2) = c2) | (~(c2 = f5(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2) | (~big_f(f3(f10(c2), f8(c3)), f10(c2))) | (f3(f10(c2), f8(c3)) = f8(c2)))),
% 29.24/19.45 inference(rewrite,[status(thm)],[])).
% 29.24/19.45 tff(22002,plain,
% 29.24/19.45 (((~(c2 = f5(f10(c2)))) | (f10(c2) = c2) | (f3(f10(c2), f8(c3)) = f8(c2)) | (~big_f(f3(f10(c2), f8(c3)), f10(c2))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2)) <=> ((f10(c2) = c2) | (~(c2 = f5(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2) | (~big_f(f3(f10(c2), f8(c3)), f10(c2))) | (f3(f10(c2), f8(c3)) = f8(c2)))),
% 29.24/19.45 inference(rewrite,[status(thm)],[])).
% 29.24/19.45 tff(22003,plain,
% 29.24/19.45 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c2 = f5(f10(c2)))) | (f10(c2) = c2) | (f3(f10(c2), f8(c3)) = f8(c2)) | (~big_f(f3(f10(c2), f8(c3)), f10(c2))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f10(c2) = c2) | (~(c2 = f5(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2) | (~big_f(f3(f10(c2), f8(c3)), f10(c2))) | (f3(f10(c2), f8(c3)) = f8(c2))))),
% 29.24/19.45 inference(monotonicity,[status(thm)],[22002])).
% 29.24/19.45 tff(22004,plain,
% 29.24/19.45 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c2 = f5(f10(c2)))) | (f10(c2) = c2) | (f3(f10(c2), f8(c3)) = f8(c2)) | (~big_f(f3(f10(c2), f8(c3)), f10(c2))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(c2) = c2) | (~(c2 = f5(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2) | (~big_f(f3(f10(c2), f8(c3)), f10(c2))) | (f3(f10(c2), f8(c3)) = f8(c2)))),
% 29.24/19.45 inference(transitivity,[status(thm)],[22003, 22001])).
% 29.24/19.45 tff(22005,plain,
% 29.24/19.45 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c2 = f5(f10(c2)))) | (f10(c2) = c2) | (f3(f10(c2), f8(c3)) = f8(c2)) | (~big_f(f3(f10(c2), f8(c3)), f10(c2))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2))),
% 29.24/19.46 inference(quant_inst,[status(thm)],[])).
% 29.24/19.46 tff(22006,plain,
% 29.24/19.46 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(c2) = c2) | (~(c2 = f5(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), c2) | (~big_f(f3(f10(c2), f8(c3)), f10(c2))) | (f3(f10(c2), f8(c3)) = f8(c2))),
% 29.24/19.46 inference(modus_ponens,[status(thm)],[22005, 22004])).
% 29.24/19.46 tff(22007,plain,
% 29.24/19.46 (f3(f10(c2), f8(c3)) = f8(c2)),
% 29.24/19.46 inference(unit_resolution,[status(thm)],[22006, 705, 89, 22000, 13398, 21889, 21943])).
% 29.24/19.46 tff(22008,plain,
% 29.24/19.46 (f3(c1, f8(c3)) = c1),
% 29.24/19.46 inference(transitivity,[status(thm)],[21953, 22007, 16246, 16268])).
% 29.24/19.46 tff(22009,plain,
% 29.24/19.46 ($false),
% 29.24/19.46 inference(unit_resolution,[status(thm)],[22008, 21998])).
% 29.24/19.46 tff(22010,plain,((f10(c2) = f2(f10(c2))) | (~(f10(c2) = f8(f10(c2)))) | (~(c3 = c1)) | (~(f8(f7(f4(c4))) = c1)) | (~(f7(c1) = c2)) | (~(f4(c4) = c1)) | (f10(c2) = c4) | (~big_f(f10(c2), f10(c2))) | (f10(c2) = c2) | (~(c2 = f5(f10(c2)))) | big_f(f7(f10(c2)), c2)), inference(lemma,lemma(discharge,[]))).
% 29.24/19.46 tff(22011,plain,
% 29.24/19.46 (f10(c2) = f2(f10(c2))),
% 29.24/19.46 inference(unit_resolution,[status(thm)],[22010, 21952, 172, 16268, 347, 11752, 15519, 14686, 89, 13398, 21943])).
% 29.24/19.46 tff(22012,plain,
% 29.24/19.46 (f2(f10(c2)) = f10(c2)),
% 29.24/19.46 inference(symmetry,[status(thm)],[22011])).
% 29.24/19.46 tff(22013,plain,
% 29.24/19.46 (f2(c1) = f10(c2)),
% 29.24/19.46 inference(transitivity,[status(thm)],[21939, 22012])).
% 29.24/19.46 tff(22014,plain,
% 29.24/19.46 ((c2 = f2(c1)) <=> (c2 = f10(c2))),
% 29.24/19.46 inference(monotonicity,[status(thm)],[22013])).
% 29.24/19.46 tff(22015,plain,
% 29.24/19.46 ((c2 = f2(c1)) <=> (f10(c2) = c2)),
% 29.24/19.46 inference(transitivity,[status(thm)],[22014, 4987])).
% 29.24/19.46 tff(22016,plain,
% 29.24/19.46 ((f10(c2) = c2) <=> (c2 = f2(c1))),
% 29.24/19.46 inference(symmetry,[status(thm)],[22015])).
% 29.24/19.46 tff(22017,plain,
% 29.24/19.46 ((f10(c2) = c2) <=> (c2 = f2(f10(c2)))),
% 29.24/19.46 inference(transitivity,[status(thm)],[22016, 21942])).
% 29.24/19.46 tff(22018,plain,
% 29.24/19.46 ((~(f10(c2) = c2)) <=> (~(c2 = f2(f10(c2))))),
% 29.24/19.46 inference(monotonicity,[status(thm)],[22017])).
% 29.24/19.46 tff(22019,plain,
% 29.24/19.46 (~(c2 = f2(f10(c2)))),
% 29.24/19.46 inference(modus_ponens,[status(thm)],[89, 22018])).
% 29.24/19.46 tff(22020,assumption,(big_f(f10(c2), c2)), introduced(assumption)).
% 29.24/19.46 tff(22021,plain,
% 29.24/19.46 (f8(f10(c2)) = f10(c2)),
% 29.24/19.46 inference(symmetry,[status(thm)],[21952])).
% 29.24/19.46 tff(22022,plain,
% 29.24/19.46 (f8(c3) = f10(c2)),
% 29.24/19.46 inference(transitivity,[status(thm)],[21955, 22021])).
% 29.24/19.46 tff(22023,plain,
% 29.24/19.46 (f3(f10(c2), f8(c3)) = f3(f10(c2), f10(c2))),
% 29.24/19.46 inference(monotonicity,[status(thm)],[22022])).
% 29.24/19.46 tff(22024,plain,
% 29.24/19.46 (f3(f10(c2), f10(c2)) = f3(f10(c2), f8(c3))),
% 29.24/19.46 inference(symmetry,[status(thm)],[22023])).
% 29.24/19.46 tff(22025,plain,
% 29.24/19.46 (big_f(f3(f10(c2), f10(c2)), f10(c2)) <=> big_f(f3(f10(c2), f8(c3)), f10(c2))),
% 29.24/19.46 inference(monotonicity,[status(thm)],[22024])).
% 29.24/19.46 tff(22026,plain,
% 29.24/19.46 (big_f(f3(f10(c2), f8(c3)), f10(c2)) <=> big_f(f3(f10(c2), f10(c2)), f10(c2))),
% 29.24/19.46 inference(symmetry,[status(thm)],[22025])).
% 29.24/19.46 tff(22027,assumption,(~(c2 = f2(f10(c2)))), introduced(assumption)).
% 29.24/19.46 tff(22028,plain,
% 29.24/19.46 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((f10(c2) = c4) | (~(f10(c2) = c3)) | (~big_f(f10(c2), c2)) | (c2 = f2(f10(c2))) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (f10(c2) = c4) | (~(f10(c2) = c3)) | (~big_f(f10(c2), c2)) | (c2 = f2(f10(c2))) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2)))),
% 29.24/19.46 inference(rewrite,[status(thm)],[])).
% 29.24/19.46 tff(22029,plain,
% 29.24/19.46 (((~(f10(c2) = c3)) | (f10(c2) = c4) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2)) | (c2 = f2(f10(c2))) | (~big_f(f10(c2), c2))) <=> ((f10(c2) = c4) | (~(f10(c2) = c3)) | (~big_f(f10(c2), c2)) | (c2 = f2(f10(c2))) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2)))),
% 29.24/19.46 inference(rewrite,[status(thm)],[])).
% 29.24/19.46 tff(22030,plain,
% 29.24/19.46 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f10(c2) = c3)) | (f10(c2) = c4) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2)) | (c2 = f2(f10(c2))) | (~big_f(f10(c2), c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((f10(c2) = c4) | (~(f10(c2) = c3)) | (~big_f(f10(c2), c2)) | (c2 = f2(f10(c2))) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2))))),
% 29.24/19.46 inference(monotonicity,[status(thm)],[22029])).
% 29.24/19.46 tff(22031,plain,
% 29.24/19.46 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f10(c2) = c3)) | (f10(c2) = c4) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2)) | (c2 = f2(f10(c2))) | (~big_f(f10(c2), c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (f10(c2) = c4) | (~(f10(c2) = c3)) | (~big_f(f10(c2), c2)) | (c2 = f2(f10(c2))) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2)))),
% 29.24/19.46 inference(transitivity,[status(thm)],[22030, 22028])).
% 29.24/19.46 tff(22032,plain,
% 29.24/19.46 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f10(c2) = c3)) | (f10(c2) = c4) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2)) | (c2 = f2(f10(c2))) | (~big_f(f10(c2), c2)))),
% 29.24/19.46 inference(quant_inst,[status(thm)],[])).
% 29.24/19.46 tff(22033,plain,
% 29.24/19.46 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (f10(c2) = c4) | (~(f10(c2) = c3)) | (~big_f(f10(c2), c2)) | (c2 = f2(f10(c2))) | (f3(f10(c2), f10(c2)) = f10(c2)) | big_f(f3(f10(c2), f10(c2)), f10(c2))),
% 29.24/19.46 inference(modus_ponens,[status(thm)],[22032, 22031])).
% 29.24/19.46 tff(22034,plain,
% 29.24/19.46 ($false),
% 29.24/19.46 inference(unit_resolution,[status(thm)],[22033, 7352, 15519, 21966, 21965, 21964, 22020, 22027])).
% 29.24/19.46 tff(22035,plain,(big_f(f3(f10(c2), f10(c2)), f10(c2)) | (f10(c2) = c4) | (~(f10(c2) = c3)) | (f3(f10(c2), f10(c2)) = f10(c2)) | (~big_f(f10(c2), c2)) | (c2 = f2(f10(c2)))), inference(lemma,lemma(discharge,[]))).
% 29.24/19.46 tff(22036,plain,
% 29.24/19.46 (big_f(f3(f10(c2), f10(c2)), f10(c2))),
% 29.24/19.46 inference(unit_resolution,[status(thm)],[22035, 21965, 15369, 15519, 22020, 22027])).
% 29.24/19.46 tff(22037,plain,
% 29.24/19.46 (big_f(f3(f10(c2), f8(c3)), f10(c2))),
% 29.24/19.46 inference(modus_ponens,[status(thm)],[22036, 21999])).
% 29.24/19.46 tff(22038,plain,
% 29.24/19.46 (f3(f10(c2), f8(c3)) = f8(c2)),
% 29.24/19.46 inference(unit_resolution,[status(thm)],[22006, 705, 89, 22037, 13398, 21889, 21943])).
% 29.24/19.46 tff(22039,plain,
% 29.24/19.46 (f3(c1, f8(c3)) = c1),
% 29.24/19.46 inference(transitivity,[status(thm)],[21953, 22038, 16246, 16268])).
% 29.24/19.46 tff(22040,plain,
% 29.24/19.46 (~(f3(c1, f8(c3)) = c1)),
% 29.24/19.46 inference(modus_ponens,[status(thm)],[21965, 21962])).
% 29.24/19.46 tff(22041,plain,
% 29.24/19.46 ($false),
% 29.24/19.46 inference(unit_resolution,[status(thm)],[22040, 22039])).
% 29.24/19.46 tff(22042,plain,((f3(f10(c2), f10(c2)) = f10(c2)) | (~(f8(f7(f4(c4))) = c1)) | (~(f7(c1) = c2)) | (~(f4(c4) = c1)) | (f10(c2) = c2) | (~(c2 = f5(f10(c2)))) | big_f(f7(f10(c2)), c2) | (~(f10(c2) = f8(f10(c2)))) | (~(c3 = c1)) | (f10(c2) = c4) | (~big_f(f10(c2), c2)) | (c2 = f2(f10(c2)))), inference(lemma,lemma(discharge,[]))).
% 29.24/19.46 tff(22043,plain,
% 29.24/19.46 (f3(f10(c2), f10(c2)) = f10(c2)),
% 29.24/19.46 inference(unit_resolution,[status(thm)],[22042, 13398, 347, 11752, 89, 16268, 21943, 21952, 172, 15519, 22020, 22019])).
% 29.24/19.46 tff(22044,plain,
% 29.24/19.46 (f3(f10(c2), f8(c3)) = f10(c2)),
% 29.24/19.46 inference(transitivity,[status(thm)],[22023, 22043])).
% 29.24/19.46 tff(22045,plain,
% 29.24/19.46 (big_f(f3(f10(c2), f8(c3)), f10(c2)) <=> big_f(f10(c2), f10(c2))),
% 29.24/19.46 inference(monotonicity,[status(thm)],[22044])).
% 29.24/19.46 tff(22046,plain,
% 29.24/19.46 (big_f(f10(c2), f10(c2)) <=> big_f(f3(f10(c2), f8(c3)), f10(c2))),
% 29.24/19.46 inference(symmetry,[status(thm)],[22045])).
% 29.24/19.46 tff(22047,plain,
% 29.24/19.46 (big_f(f10(c2), f10(c2)) <=> big_f(f3(f10(c2), f10(c2)), f10(c2))),
% 29.24/19.46 inference(transitivity,[status(thm)],[22046, 22026])).
% 29.24/19.46 tff(22048,plain,
% 29.24/19.46 (big_f(f3(f10(c2), f10(c2)), f10(c2))),
% 29.24/19.46 inference(modus_ponens,[status(thm)],[14686, 22047])).
% 29.24/19.46 tff(22049,plain,
% 29.24/19.46 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((f10(c2) = c4) | (~(f10(c2) = c3)) | (~big_f(f10(c2), c2)) | (c2 = f2(f10(c2))) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (f10(c2) = c4) | (~(f10(c2) = c3)) | (~big_f(f10(c2), c2)) | (c2 = f2(f10(c2))) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))))),
% 29.24/19.46 inference(rewrite,[status(thm)],[])).
% 29.24/19.46 tff(22050,plain,
% 29.24/19.46 (((~(f10(c2) = c3)) | (f10(c2) = c4) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))) | (c2 = f2(f10(c2))) | (~big_f(f10(c2), c2))) <=> ((f10(c2) = c4) | (~(f10(c2) = c3)) | (~big_f(f10(c2), c2)) | (c2 = f2(f10(c2))) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))))),
% 29.24/19.46 inference(rewrite,[status(thm)],[])).
% 29.24/19.46 tff(22051,plain,
% 29.24/19.46 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f10(c2) = c3)) | (f10(c2) = c4) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))) | (c2 = f2(f10(c2))) | (~big_f(f10(c2), c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((f10(c2) = c4) | (~(f10(c2) = c3)) | (~big_f(f10(c2), c2)) | (c2 = f2(f10(c2))) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2)))))),
% 29.24/19.46 inference(monotonicity,[status(thm)],[22050])).
% 29.24/19.46 tff(22052,plain,
% 29.24/19.46 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f10(c2) = c3)) | (f10(c2) = c4) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))) | (c2 = f2(f10(c2))) | (~big_f(f10(c2), c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (f10(c2) = c4) | (~(f10(c2) = c3)) | (~big_f(f10(c2), c2)) | (c2 = f2(f10(c2))) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))))),
% 29.24/19.46 inference(transitivity,[status(thm)],[22051, 22049])).
% 29.24/19.46 tff(22053,plain,
% 29.24/19.46 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f10(c2) = c3)) | (f10(c2) = c4) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2))) | (c2 = f2(f10(c2))) | (~big_f(f10(c2), c2)))),
% 29.24/19.46 inference(quant_inst,[status(thm)],[])).
% 29.24/19.46 tff(22054,plain,
% 29.24/19.46 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (f10(c2) = c4) | (~(f10(c2) = c3)) | (~big_f(f10(c2), c2)) | (c2 = f2(f10(c2))) | (~(f3(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f3(f10(c2), f10(c2)), f10(c2)))),
% 29.24/19.46 inference(modus_ponens,[status(thm)],[22053, 22052])).
% 29.24/19.46 tff(22055,plain,
% 29.24/19.46 ($false),
% 29.24/19.46 inference(unit_resolution,[status(thm)],[22054, 7051, 15519, 15369, 22043, 22048, 22020, 22019])).
% 29.24/19.46 tff(22056,plain,((~(c2 = f5(f10(c2)))) | (f10(c2) = c4) | (~big_f(f10(c2), c2)) | (~big_f(f10(c2), f10(c2))) | (~(c3 = c1)) | (~(f7(c1) = c2)) | (~(f4(c4) = c1)) | (f10(c2) = c2) | (~(f8(f7(f4(c4))) = c1)) | big_f(f7(f10(c2)), c2) | (~big_f(f10(c2), f10(f10(c2)))) | (f10(f10(c2)) = f10(c2))), inference(lemma,lemma(discharge,[]))).
% 29.24/19.46 tff(22057,plain,
% 29.24/19.46 (~(c2 = f5(f10(c2)))),
% 29.24/19.46 inference(unit_resolution,[status(thm)],[22056, 21860, 21811, 21852, 21933, 120, 15706, 17538, 21830, 20953, 21938, 21408])).
% 29.24/19.46 tff(22058,plain,
% 29.24/19.46 (~(f5(c1) = c2)),
% 29.24/19.46 inference(modus_ponens,[status(thm)],[22057, 21935])).
% 29.24/19.46 tff(22059,plain,
% 29.24/19.46 (f5(c1) = c1),
% 29.24/19.46 inference(unit_resolution,[status(thm)],[1708, 22058])).
% 29.24/19.46 tff(22060,plain,
% 29.24/19.46 (~(f8(c1) = c2)),
% 29.24/19.46 inference(unit_resolution,[status(thm)],[17239, 22059, 115, 3, 21432, 121])).
% 29.24/19.46 tff(22061,plain,
% 29.24/19.46 (f8(c1) = c1),
% 29.24/19.46 inference(unit_resolution,[status(thm)],[1680, 22060])).
% 29.24/19.46 tff(22062,plain,
% 29.24/19.46 (f8(c1) = f8(f10(c2))),
% 29.24/19.46 inference(symmetry,[status(thm)],[15293])).
% 29.24/19.46 tff(22063,plain,
% 29.24/19.46 (f10(c2) = f8(c3)),
% 29.24/19.46 inference(transitivity,[status(thm)],[94, 3143, 22062, 21956])).
% 29.24/19.46 tff(22064,plain,
% 29.24/19.46 (f3(f10(c2), f10(c2)) = f3(f10(c2), f8(c3))),
% 29.24/19.46 inference(monotonicity,[status(thm)],[22063])).
% 29.24/19.46 tff(22065,plain,
% 29.24/19.46 (f3(f10(c2), f8(c3)) = f3(f10(c2), f10(c2))),
% 29.24/19.46 inference(symmetry,[status(thm)],[22064])).
% 29.24/19.46 tff(22066,plain,
% 29.24/19.46 (f3(c1, f8(c3)) = f3(f10(c2), f10(c2))),
% 29.24/19.46 inference(transitivity,[status(thm)],[20766, 22065])).
% 29.24/19.46 tff(22067,plain,
% 29.24/19.46 ((f3(c1, f8(c3)) = c1) <=> (f3(f10(c2), f10(c2)) = f10(c2))),
% 29.24/19.46 inference(monotonicity,[status(thm)],[22066, 99])).
% 29.24/19.46 tff(22068,plain,
% 29.24/19.46 ((f3(f10(c2), f10(c2)) = f10(c2)) <=> (f3(c1, f8(c3)) = c1)),
% 29.24/19.46 inference(symmetry,[status(thm)],[22067])).
% 29.24/19.46 tff(22069,plain,
% 29.24/19.46 ((~(f3(f10(c2), f10(c2)) = f10(c2))) <=> (~(f3(c1, f8(c3)) = c1))),
% 29.24/19.46 inference(monotonicity,[status(thm)],[22068])).
% 29.24/19.46 tff(22070,plain,
% 29.24/19.46 (~(f3(c1, f8(c3)) = c1)),
% 29.24/19.46 inference(modus_ponens,[status(thm)],[21965, 22069])).
% 29.24/19.46 tff(22071,plain,
% 29.24/19.46 (f3(c1, f8(c3)) = c2),
% 29.24/19.46 inference(unit_resolution,[status(thm)],[7123, 22070])).
% 29.24/19.46 tff(22072,plain,
% 29.24/19.46 (f3(f10(c2), f10(c2)) = c2),
% 29.24/19.46 inference(transitivity,[status(thm)],[22064, 20765, 22071])).
% 29.24/19.46 tff(22073,plain,
% 29.24/19.46 (big_f(f3(f10(c2), f10(c2)), f10(c2)) <=> big_f(c2, f10(c2))),
% 29.24/19.46 inference(monotonicity,[status(thm)],[22072])).
% 29.24/19.46 tff(22074,plain,
% 29.24/19.46 (big_f(c2, f10(c2)) <=> big_f(f3(f10(c2), f10(c2)), f10(c2))),
% 29.24/19.46 inference(symmetry,[status(thm)],[22073])).
% 29.24/19.46 tff(22075,plain,
% 29.24/19.46 ((~big_f(c2, f10(c2))) <=> (~big_f(f3(f10(c2), f10(c2)), f10(c2)))),
% 29.24/19.46 inference(monotonicity,[status(thm)],[22074])).
% 29.24/19.46 tff(22076,plain,
% 29.24/19.46 (~big_f(f3(f10(c2), f10(c2)), f10(c2))),
% 29.24/19.46 inference(modus_ponens,[status(thm)],[15517, 22075])).
% 29.24/19.46 tff(22077,plain,
% 29.24/19.46 (c2 = f2(f10(c2))),
% 29.24/19.46 inference(unit_resolution,[status(thm)],[22035, 21964, 21966, 15519, 22020, 21965])).
% 29.24/19.46 tff(22078,plain,
% 29.24/19.46 (f2(f10(c2)) = c2),
% 29.24/19.46 inference(symmetry,[status(thm)],[22077])).
% 29.24/19.46 tff(22079,plain,
% 29.24/19.46 (f10(c2) = f2(f10(c2))),
% 29.24/19.46 inference(unit_resolution,[status(thm)],[21974, 21964, 21966, 14686, 15519, 21965])).
% 29.24/19.46 tff(22080,plain,
% 29.24/19.46 (f10(c2) = c2),
% 29.24/19.46 inference(transitivity,[status(thm)],[22079, 22078])).
% 29.24/19.46 tff(22081,plain,
% 29.24/19.46 ($false),
% 29.24/19.46 inference(unit_resolution,[status(thm)],[89, 22080])).
% 29.24/19.46 tff(22082,plain,(big_f(f3(f10(c2), f10(c2)), f10(c2)) | (f10(c2) = c2) | (~(f10(c2) = c3)) | (f10(c2) = c4) | (~big_f(f10(c2), c2)) | (f3(f10(c2), f10(c2)) = f10(c2)) | (~big_f(f10(c2), f10(c2)))), inference(lemma,lemma(discharge,[]))).
% 29.24/19.46 tff(22083,plain,
% 29.24/19.46 (big_f(f3(f10(c2), f10(c2)), f10(c2))),
% 29.24/19.46 inference(unit_resolution,[status(thm)],[22082, 21965, 15369, 15519, 22020, 89, 14686])).
% 29.24/19.46 tff(22084,plain,
% 29.24/19.46 ($false),
% 29.24/19.46 inference(unit_resolution,[status(thm)],[22083, 22076])).
% 29.24/19.46 tff(22085,plain,((f3(f10(c2), f10(c2)) = f10(c2)) | big_f(c2, f10(c2)) | (~(f8(c1) = c1)) | (~(c3 = c1)) | (f10(c2) = c4) | (~big_f(f10(c2), c2)) | (f10(c2) = c2) | (~big_f(f10(c2), f10(c2)))), inference(lemma,lemma(discharge,[]))).
% 29.24/19.46 tff(22086,plain,
% 29.24/19.46 (f3(f10(c2), f10(c2)) = f10(c2)),
% 29.24/19.46 inference(unit_resolution,[status(thm)],[22085, 15517, 22061, 21933, 21860, 21811, 17538, 21852])).
% 29.24/19.46 tff(22087,plain,
% 29.24/19.46 (f10(c2) = f3(f10(c2), f10(c2))),
% 29.24/19.46 inference(symmetry,[status(thm)],[22086])).
% 29.24/19.46 tff(22088,plain,
% 29.24/19.46 (big_f(f10(c2), f10(c2)) <=> big_f(f3(f10(c2), f10(c2)), f10(c2))),
% 29.24/19.46 inference(monotonicity,[status(thm)],[22087])).
% 29.24/19.46 tff(22089,plain,
% 29.24/19.46 (big_f(f3(f10(c2), f10(c2)), f10(c2))),
% 29.24/19.46 inference(modus_ponens,[status(thm)],[21852, 22088])).
% 29.24/19.46 tff(22090,plain,
% 29.24/19.46 (c1 = c3),
% 29.24/19.46 inference(symmetry,[status(thm)],[21933])).
% 29.24/19.46 tff(22091,plain,
% 29.24/19.46 (f10(c2) = c3),
% 29.24/19.46 inference(transitivity,[status(thm)],[17539, 22090])).
% 29.24/19.46 tff(22092,plain,
% 29.24/19.46 (c2 = f2(f10(c2))),
% 29.24/19.46 inference(unit_resolution,[status(thm)],[22054, 7051, 21860, 22091, 22086, 22089, 21811])).
% 29.24/19.46 tff(22093,plain,
% 29.24/19.46 (f2(f10(c2)) = c2),
% 29.24/19.46 inference(symmetry,[status(thm)],[22092])).
% 29.24/19.46 tff(22094,plain,
% 29.24/19.46 (f10(c2) = f2(f10(c2))),
% 29.24/19.46 inference(unit_resolution,[status(thm)],[21996, 7051, 21860, 22091, 21852, 22086, 22089])).
% 29.24/19.46 tff(22095,plain,
% 29.24/19.46 (f10(c2) = c2),
% 29.24/19.46 inference(transitivity,[status(thm)],[22094, 22093])).
% 29.24/19.46 tff(22096,plain,
% 29.24/19.46 ($false),
% 29.24/19.46 inference(unit_resolution,[status(thm)],[17538, 22095])).
% 29.24/19.46 tff(22097,plain,(big_f(c2, f10(c2)) | (f7(c1) = c1) | (f10(c1) = c1) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 29.24/19.46 tff(22098,plain,
% 29.24/19.46 (big_f(c2, f10(c2))),
% 29.24/19.46 inference(unit_resolution,[status(thm)],[22097, 121, 3, 115])).
% 29.24/19.46 tff(22099,plain,
% 29.24/19.46 (big_f(f7(f10(c2)), f10(c2))),
% 29.24/19.46 inference(modus_ponens,[status(thm)],[22098, 21419])).
% 29.24/19.46 tff(22100,plain,
% 29.24/19.46 (~(f6(f7(c2), f5(c1)) = c2)),
% 29.24/19.46 inference(unit_resolution,[status(thm)],[13783, 21710, 77, 121, 12291, 12290, 89])).
% 29.24/19.46 tff(22101,plain,
% 29.24/19.46 (f6(f7(c2), f5(c1)) = c1),
% 29.24/19.46 inference(unit_resolution,[status(thm)],[2978, 22100])).
% 29.24/19.46 tff(22102,plain,
% 29.24/19.46 (c1 = f5(c1)),
% 29.24/19.46 inference(transitivity,[status(thm)],[99, 21710, 13761])).
% 29.24/19.46 tff(22103,plain,
% 29.24/19.46 (f6(c2, c1) = f6(f7(c2), f5(c1))),
% 29.24/19.46 inference(monotonicity,[status(thm)],[82, 22102])).
% 29.24/19.46 tff(22104,plain,
% 29.24/19.46 (f6(c2, f10(c2)) = f10(c2)),
% 29.24/19.46 inference(transitivity,[status(thm)],[13711, 22103, 22101, 99])).
% 29.24/19.46 tff(22105,plain,
% 29.24/19.46 (big_f(f7(c2), f6(c2, f10(c2))) <=> big_f(c2, f10(c2))),
% 29.24/19.46 inference(monotonicity,[status(thm)],[77, 22104])).
% 29.24/19.46 tff(22106,plain,
% 29.24/19.46 (big_f(c2, f10(c2)) <=> big_f(f7(c2), f6(c2, f10(c2)))),
% 29.24/19.46 inference(symmetry,[status(thm)],[22105])).
% 29.24/19.46 tff(22107,plain,
% 29.24/19.46 (big_f(f7(c2), f6(c2, f10(c2)))),
% 29.24/19.46 inference(modus_ponens,[status(thm)],[12291, 22106])).
% 29.24/19.46 tff(22108,plain,
% 29.24/19.46 ((~(f6(c2, f10(c2)) = f10(c2))) | (~big_f(f7(c2), f6(c2, f10(c2))))),
% 29.24/19.46 inference(unit_resolution,[status(thm)],[13801, 2730, 89, 77, 12291, 12290])).
% 29.24/19.46 tff(22109,plain,
% 29.24/19.46 ($false),
% 29.24/19.46 inference(unit_resolution,[status(thm)],[22108, 22107, 22104])).
% 29.24/19.46 tff(22110,plain,((c2 = f8(c2)) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (~big_f(c2, f10(c2))) | big_f(c2, c2) | (f7(f10(c2)) = f10(c2)) | (~big_f(f7(f10(c2)), f10(c2)))), inference(lemma,lemma(discharge,[]))).
% 29.24/19.46 tff(22111,plain,
% 29.24/19.46 (c2 = f8(c2)),
% 29.24/19.46 inference(unit_resolution,[status(thm)],[22110, 22098, 21432, 17538, 121, 20958, 22099])).
% 29.24/19.46 tff(22112,plain,
% 29.24/19.46 (f8(c2) = c2),
% 29.24/19.46 inference(symmetry,[status(thm)],[22111])).
% 29.24/19.46 tff(22113,plain,
% 29.24/19.46 ((f10(c2) = f8(c2)) <=> (f10(c2) = c2)),
% 29.24/19.46 inference(monotonicity,[status(thm)],[22112])).
% 29.24/19.46 tff(22114,plain,
% 29.24/19.46 ((f10(c2) = c2) <=> (f10(c2) = f8(c2))),
% 29.24/19.46 inference(symmetry,[status(thm)],[22113])).
% 29.24/19.46 tff(22115,plain,
% 29.24/19.46 ((~(f10(c2) = c2)) <=> (~(f10(c2) = f8(c2)))),
% 29.24/19.46 inference(monotonicity,[status(thm)],[22114])).
% 29.24/19.46 tff(22116,plain,
% 29.24/19.46 (~(f10(c2) = f8(c2))),
% 29.24/19.46 inference(modus_ponens,[status(thm)],[17538, 22115])).
% 29.24/19.46 tff(22117,plain,
% 29.24/19.46 ((~big_f(f3(c1, c2), c1)) <=> (~big_f(f3(c1, f7(c1)), c1))),
% 29.24/19.46 inference(monotonicity,[status(thm)],[16110])).
% 29.24/19.46 tff(22118,plain,
% 29.24/19.46 (~big_f(c1, c1)),
% 29.24/19.46 inference(unit_resolution,[status(thm)],[21743, 20783, 94])).
% 29.24/19.46 tff(22119,plain,
% 29.24/19.46 (big_f(f7(f10(c2)), f10(c2)) <=> big_f(c2, f10(c2))),
% 29.24/19.46 inference(monotonicity,[status(thm)],[21867])).
% 29.24/19.46 tff(22120,plain,
% 29.24/19.46 (big_f(c2, f10(c2)) <=> big_f(f7(f10(c2)), f10(c2))),
% 29.24/19.46 inference(symmetry,[status(thm)],[22119])).
% 29.24/19.46 tff(22121,plain,
% 29.24/19.46 (big_f(f7(f10(c2)), f10(c2))),
% 29.24/19.46 inference(modus_ponens,[status(thm)],[12291, 22120])).
% 29.24/19.46 tff(22122,plain,
% 29.24/19.46 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | big_f(f10(c2), f10(c2)) | (f7(f10(c2)) = f10(c2)) | (~(f10(c2) = f8(c2))) | (~big_f(f7(f10(c2)), f10(c2))) | (f10(c2) = f5(f10(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | big_f(f10(c2), f10(c2)) | (f7(f10(c2)) = f10(c2)) | (~(f10(c2) = f8(c2))) | (~big_f(f7(f10(c2)), f10(c2))) | (f10(c2) = f5(f10(c2))))),
% 29.24/19.46 inference(rewrite,[status(thm)],[])).
% 29.24/19.46 tff(22123,plain,
% 29.24/19.46 (((f10(c2) = c2) | big_f(f10(c2), f10(c2)) | (f7(f10(c2)) = f10(c2)) | (f10(c2) = f5(f10(c2))) | (~big_f(f7(f10(c2)), f10(c2))) | (~(f10(c2) = f8(c2)))) <=> ((f10(c2) = c2) | big_f(f10(c2), f10(c2)) | (f7(f10(c2)) = f10(c2)) | (~(f10(c2) = f8(c2))) | (~big_f(f7(f10(c2)), f10(c2))) | (f10(c2) = f5(f10(c2))))),
% 29.24/19.46 inference(rewrite,[status(thm)],[])).
% 29.24/19.46 tff(22124,plain,
% 29.24/19.46 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | big_f(f10(c2), f10(c2)) | (f7(f10(c2)) = f10(c2)) | (f10(c2) = f5(f10(c2))) | (~big_f(f7(f10(c2)), f10(c2))) | (~(f10(c2) = f8(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | big_f(f10(c2), f10(c2)) | (f7(f10(c2)) = f10(c2)) | (~(f10(c2) = f8(c2))) | (~big_f(f7(f10(c2)), f10(c2))) | (f10(c2) = f5(f10(c2)))))),
% 29.24/19.46 inference(monotonicity,[status(thm)],[22123])).
% 29.24/19.46 tff(22125,plain,
% 29.24/19.46 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | big_f(f10(c2), f10(c2)) | (f7(f10(c2)) = f10(c2)) | (f10(c2) = f5(f10(c2))) | (~big_f(f7(f10(c2)), f10(c2))) | (~(f10(c2) = f8(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | big_f(f10(c2), f10(c2)) | (f7(f10(c2)) = f10(c2)) | (~(f10(c2) = f8(c2))) | (~big_f(f7(f10(c2)), f10(c2))) | (f10(c2) = f5(f10(c2))))),
% 29.24/19.46 inference(transitivity,[status(thm)],[22124, 22122])).
% 29.24/19.46 tff(22126,plain,
% 29.24/19.46 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | big_f(f10(c2), f10(c2)) | (f7(f10(c2)) = f10(c2)) | (f10(c2) = f5(f10(c2))) | (~big_f(f7(f10(c2)), f10(c2))) | (~(f10(c2) = f8(c2))))),
% 29.24/19.46 inference(quant_inst,[status(thm)],[])).
% 29.24/19.46 tff(22127,plain,
% 29.24/19.46 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | big_f(f10(c2), f10(c2)) | (f7(f10(c2)) = f10(c2)) | (~(f10(c2) = f8(c2))) | (~big_f(f7(f10(c2)), f10(c2))) | (f10(c2) = f5(f10(c2)))),
% 29.24/19.46 inference(modus_ponens,[status(thm)],[22126, 22125])).
% 29.24/19.46 tff(22128,plain,
% 29.24/19.46 ((~(f10(c2) = f8(c2))) | (f10(c2) = f5(f10(c2)))),
% 29.24/19.46 inference(unit_resolution,[status(thm)],[22127, 2795, 89, 21889, 20783, 22121])).
% 29.24/19.46 tff(22129,plain,
% 29.24/19.46 (f10(c2) = f5(f10(c2))),
% 29.24/19.46 inference(unit_resolution,[status(thm)],[22128, 21570])).
% 29.24/19.46 tff(22130,plain,
% 29.24/19.46 (f8(c2) = f10(c2)),
% 29.24/19.46 inference(transitivity,[status(thm)],[16246, 16268, 99])).
% 29.24/19.46 tff(22131,plain,
% 29.24/19.46 ((c2 = f8(c2)) <=> (c2 = f10(c2))),
% 29.24/19.46 inference(monotonicity,[status(thm)],[22130])).
% 29.24/19.46 tff(22132,plain,
% 29.24/19.46 ((c2 = f8(c2)) <=> (f10(c2) = c2)),
% 29.24/19.46 inference(transitivity,[status(thm)],[22131, 4987])).
% 29.24/19.46 tff(22133,plain,
% 29.24/19.46 ((f10(c2) = c2) <=> (c2 = f8(c2))),
% 29.24/19.46 inference(symmetry,[status(thm)],[22132])).
% 29.24/19.46 tff(22134,plain,
% 29.24/19.46 ((~(f10(c2) = c2)) <=> (~(c2 = f8(c2)))),
% 29.24/19.46 inference(monotonicity,[status(thm)],[22133])).
% 29.24/19.47 tff(22135,plain,
% 29.24/19.47 (~(c2 = f8(c2))),
% 29.24/19.47 inference(modus_ponens,[status(thm)],[89, 22134])).
% 29.24/19.47 tff(22136,plain,
% 29.24/19.47 (~(f6(f7(c2), f5(c1)) = c2)),
% 29.24/19.47 inference(unit_resolution,[status(thm)],[13783, 22135, 77, 121, 12291, 22129, 89])).
% 29.24/19.47 tff(22137,plain,
% 29.24/19.47 (f6(f7(c2), f5(c1)) = c1),
% 29.24/19.47 inference(unit_resolution,[status(thm)],[2978, 22136])).
% 29.24/19.47 tff(22138,plain,
% 29.24/19.47 (c1 = f5(c1)),
% 29.24/19.47 inference(transitivity,[status(thm)],[99, 22129, 13761])).
% 29.24/19.47 tff(22139,plain,
% 29.24/19.47 (f6(c2, c1) = f6(f7(c2), f5(c1))),
% 29.24/19.47 inference(monotonicity,[status(thm)],[82, 22138])).
% 29.24/19.47 tff(22140,plain,
% 29.24/19.47 (f6(c2, f10(c2)) = f10(c2)),
% 29.24/19.47 inference(transitivity,[status(thm)],[13711, 22139, 22137, 99])).
% 29.24/19.47 tff(22141,plain,
% 29.24/19.47 (big_f(f7(c2), f6(c2, f10(c2))) <=> big_f(c2, f10(c2))),
% 29.24/19.47 inference(monotonicity,[status(thm)],[77, 22140])).
% 29.24/19.47 tff(22142,plain,
% 29.24/19.47 (big_f(c2, f10(c2)) <=> big_f(f7(c2), f6(c2, f10(c2)))),
% 29.24/19.47 inference(symmetry,[status(thm)],[22141])).
% 29.24/19.47 tff(22143,plain,
% 29.24/19.47 (big_f(f7(c2), f6(c2, f10(c2)))),
% 29.24/19.47 inference(modus_ponens,[status(thm)],[12291, 22142])).
% 29.24/19.47 tff(22144,plain,
% 29.24/19.47 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (~(f7(c2) = c2)) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f8(c2))) | (~(f6(c2, f10(c2)) = f10(c2))) | (~big_f(f7(c2), f6(c2, f10(c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f8(c2))) | (~(f6(c2, f10(c2)) = f10(c2))) | (~big_f(f7(c2), f6(c2, f10(c2)))))),
% 29.24/19.47 inference(rewrite,[status(thm)],[])).
% 29.24/19.47 tff(22145,plain,
% 29.24/19.47 (((f10(c2) = c2) | big_f(f10(c2), f10(c2)) | (~(f7(c2) = c2)) | (~(f10(c2) = f8(c2))) | (~(f6(c2, f10(c2)) = f10(c2))) | (~big_f(f7(c2), f6(c2, f10(c2))))) <=> ((f10(c2) = c2) | (~(f7(c2) = c2)) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f8(c2))) | (~(f6(c2, f10(c2)) = f10(c2))) | (~big_f(f7(c2), f6(c2, f10(c2)))))),
% 29.24/19.47 inference(rewrite,[status(thm)],[])).
% 29.24/19.47 tff(22146,plain,
% 29.24/19.47 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | big_f(f10(c2), f10(c2)) | (~(f7(c2) = c2)) | (~(f10(c2) = f8(c2))) | (~(f6(c2, f10(c2)) = f10(c2))) | (~big_f(f7(c2), f6(c2, f10(c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (~(f7(c2) = c2)) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f8(c2))) | (~(f6(c2, f10(c2)) = f10(c2))) | (~big_f(f7(c2), f6(c2, f10(c2))))))),
% 29.24/19.47 inference(monotonicity,[status(thm)],[22145])).
% 29.24/19.47 tff(22147,plain,
% 29.24/19.47 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | big_f(f10(c2), f10(c2)) | (~(f7(c2) = c2)) | (~(f10(c2) = f8(c2))) | (~(f6(c2, f10(c2)) = f10(c2))) | (~big_f(f7(c2), f6(c2, f10(c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f8(c2))) | (~(f6(c2, f10(c2)) = f10(c2))) | (~big_f(f7(c2), f6(c2, f10(c2)))))),
% 29.24/19.47 inference(transitivity,[status(thm)],[22146, 22144])).
% 29.24/19.47 tff(22148,plain,
% 29.24/19.47 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | big_f(f10(c2), f10(c2)) | (~(f7(c2) = c2)) | (~(f10(c2) = f8(c2))) | (~(f6(c2, f10(c2)) = f10(c2))) | (~big_f(f7(c2), f6(c2, f10(c2)))))),
% 29.24/19.47 inference(quant_inst,[status(thm)],[])).
% 29.24/19.47 tff(22149,plain,
% 29.24/19.47 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f8(c2))) | (~(f6(c2, f10(c2)) = f10(c2))) | (~big_f(f7(c2), f6(c2, f10(c2))))),
% 29.24/19.47 inference(modus_ponens,[status(thm)],[22148, 22147])).
% 29.24/19.47 tff(22150,plain,
% 29.24/19.47 ((~(f6(c2, f10(c2)) = f10(c2))) | (~big_f(f7(c2), f6(c2, f10(c2))))),
% 29.24/19.47 inference(unit_resolution,[status(thm)],[22149, 2963, 89, 77, 21570, 20783])).
% 29.24/19.47 tff(22151,plain,
% 29.24/19.47 ($false),
% 29.24/19.47 inference(unit_resolution,[status(thm)],[22150, 22143, 22140])).
% 29.24/19.47 tff(22152,plain,((~(f8(f7(f4(c4))) = c1)) | (f10(c2) = c2) | (~(f7(c2) = c2)) | big_f(f10(c2), f10(c2)) | (~big_f(c2, f10(c2))) | big_f(c2, c2) | (~(f7(c1) = c2)) | (~(f4(c4) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.24/19.47 tff(22153,plain,
% 29.24/19.47 (~(f8(f7(f4(c4))) = c1)),
% 29.24/19.47 inference(unit_resolution,[status(thm)],[22152, 20783, 77, 89, 12291, 121, 347, 11752])).
% 29.24/19.47 tff(22154,plain,
% 29.24/19.47 (f8(f7(f4(c4))) = c2),
% 29.24/19.47 inference(unit_resolution,[status(thm)],[13371, 22153])).
% 29.24/19.47 tff(22155,plain,
% 29.24/19.47 ((f10(c2) = c4) <=> (c4 = c1)),
% 29.24/19.47 inference(transitivity,[status(thm)],[15385, 4135])).
% 29.24/19.47 tff(22156,plain,
% 29.24/19.47 ((~(f10(c2) = c4)) <=> (~(c4 = c1))),
% 29.24/19.47 inference(monotonicity,[status(thm)],[22155])).
% 29.24/19.47 tff(22157,plain,
% 29.24/19.47 (~(c4 = c1)),
% 29.24/19.47 inference(modus_ponens,[status(thm)],[15519, 22156])).
% 29.24/19.47 tff(22158,plain,
% 29.24/19.47 (c4 = c2),
% 29.24/19.47 inference(unit_resolution,[status(thm)],[461, 22157])).
% 29.24/19.47 tff(22159,plain,
% 29.24/19.47 ((f3(c1, c1) = c4) <=> (f3(c1, c1) = c2)),
% 29.24/19.47 inference(monotonicity,[status(thm)],[22158])).
% 29.24/19.47 tff(22160,plain,
% 29.24/19.47 ((f3(c1, c1) = c2) <=> (f3(c1, c1) = c4)),
% 29.24/19.47 inference(symmetry,[status(thm)],[22159])).
% 29.24/19.47 tff(22161,plain,
% 29.24/19.47 ($false),
% 29.24/19.47 inference(unit_resolution,[status(thm)],[15667, 21516])).
% 29.24/19.47 tff(22162,plain,((~(c3 = c1)) | (f10(c2) = c3) | (~(f10(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.24/19.47 tff(22163,plain,
% 29.24/19.47 (~(c3 = c1)),
% 29.24/19.47 inference(unit_resolution,[status(thm)],[22162, 15667, 94])).
% 29.24/19.47 tff(22164,plain,
% 29.24/19.47 (c3 = c2),
% 29.24/19.47 inference(unit_resolution,[status(thm)],[180, 22163])).
% 29.24/19.47 tff(22165,plain,
% 29.24/19.47 (big_f(c3, c2) <=> big_f(c2, c2)),
% 29.24/19.47 inference(monotonicity,[status(thm)],[22164])).
% 29.24/19.47 tff(22166,plain,
% 29.24/19.47 (big_f(c2, c2) <=> big_f(c3, c2)),
% 29.24/19.47 inference(symmetry,[status(thm)],[22165])).
% 29.24/19.47 tff(22167,plain,
% 29.24/19.47 ((~big_f(c2, c2)) <=> (~big_f(c3, c2))),
% 29.24/19.47 inference(monotonicity,[status(thm)],[22166])).
% 29.24/19.47 tff(22168,plain,
% 29.24/19.47 (~big_f(c3, c2)),
% 29.24/19.47 inference(modus_ponens,[status(thm)],[121, 22167])).
% 29.24/19.47 tff(22169,plain,
% 29.24/19.47 ((f3(c1, c1) = c1) <=> (f3(f10(c2), f10(c2)) = f10(c2))),
% 29.24/19.47 inference(monotonicity,[status(thm)],[21873, 12231])).
% 29.24/19.47 tff(22170,plain,
% 29.24/19.47 ((f3(f10(c2), f10(c2)) = f10(c2)) <=> (f3(c1, c1) = c1)),
% 29.24/19.47 inference(symmetry,[status(thm)],[22169])).
% 29.24/19.47 tff(22171,plain,
% 29.24/19.47 (f3(f10(c2), f10(c2)) = c2),
% 29.24/19.47 inference(transitivity,[status(thm)],[15553, 1440])).
% 29.24/19.47 tff(22172,plain,
% 29.24/19.47 ((f3(f10(c2), f10(c2)) = f10(c2)) <=> (c2 = f10(c2))),
% 29.24/19.47 inference(monotonicity,[status(thm)],[22171])).
% 29.24/19.47 tff(22173,plain,
% 29.24/19.47 ((f3(f10(c2), f10(c2)) = f10(c2)) <=> (f10(c2) = c2)),
% 29.24/19.47 inference(transitivity,[status(thm)],[22172, 4987])).
% 29.24/19.47 tff(22174,plain,
% 29.24/19.47 ((f10(c2) = c2) <=> (f3(f10(c2), f10(c2)) = f10(c2))),
% 29.24/19.47 inference(symmetry,[status(thm)],[22173])).
% 29.24/19.47 tff(22175,plain,
% 29.24/19.47 ((c1 = c3) <=> (f10(c2) = c3)),
% 29.24/19.47 inference(monotonicity,[status(thm)],[12231])).
% 29.24/19.47 tff(22176,plain,
% 29.24/19.47 ((c1 = c3) <=> (f3(c1, c1) = c1)),
% 29.24/19.47 inference(transitivity,[status(thm)],[22175, 12096, 22174, 22170])).
% 29.24/19.47 tff(22177,plain,
% 29.24/19.47 (f3(c1, c1) = c1),
% 29.24/19.47 inference(modus_ponens,[status(thm)],[5080, 22176])).
% 29.24/19.47 tff(22178,plain,
% 29.24/19.47 ($false),
% 29.24/19.47 inference(unit_resolution,[status(thm)],[1431, 22177])).
% 29.24/19.47 tff(22179,plain,((~(c1 = c3)) | (f3(c1, c1) = c1) | (~(c3 = c2)) | (~(f10(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.24/19.47 tff(22180,plain,
% 29.24/19.47 (~(c1 = c3)),
% 29.24/19.47 inference(unit_resolution,[status(thm)],[22179, 22164, 1431, 94])).
% 29.24/19.47 tff(22181,plain,
% 29.24/19.47 ((~(f10(c2) = c4)) <=> (~(c1 = c4))),
% 29.24/19.47 inference(monotonicity,[status(thm)],[15385])).
% 29.24/19.47 tff(22182,plain,
% 29.24/19.47 (~(c1 = c4)),
% 29.24/19.47 inference(modus_ponens,[status(thm)],[15519, 22181])).
% 29.24/19.47 tff(22183,plain,
% 29.24/19.47 (big_f(c2, f10(c2)) <=> big_f(c2, c1)),
% 29.24/19.47 inference(symmetry,[status(thm)],[17609])).
% 29.24/19.47 tff(22184,plain,
% 29.24/19.47 (big_f(c2, c1)),
% 29.24/19.47 inference(modus_ponens,[status(thm)],[12291, 22183])).
% 29.24/19.47 tff(22185,plain,
% 29.24/19.47 (c2 = f8(c3)),
% 29.24/19.47 inference(transitivity,[status(thm)],[16415, 16247, 20761])).
% 29.24/19.47 tff(22186,plain,
% 29.24/19.47 (f3(c1, c2) = f3(f10(c2), f8(c3))),
% 29.24/19.47 inference(monotonicity,[status(thm)],[12231, 22185])).
% 29.24/19.47 tff(22187,plain,
% 29.24/19.47 (f3(f10(c2), f8(c3)) = f3(c1, c2)),
% 29.24/19.47 inference(symmetry,[status(thm)],[22186])).
% 29.24/19.47 tff(22188,plain,
% 29.24/19.47 (f3(f10(c2), f8(c3)) = f3(c1, f8(c3))),
% 29.24/19.47 inference(monotonicity,[status(thm)],[11819])).
% 29.24/19.47 tff(22189,plain,
% 29.24/19.47 (f3(c1, f8(c3)) = f3(f10(c2), f8(c3))),
% 29.24/19.47 inference(symmetry,[status(thm)],[22188])).
% 29.24/19.47 tff(22190,plain,
% 29.24/19.47 (f3(c1, f8(c3)) = f3(c1, c2)),
% 29.24/19.47 inference(transitivity,[status(thm)],[22189, 22187])).
% 29.24/19.47 tff(22191,plain,
% 29.24/19.47 ((f3(c1, f8(c3)) = c2) <=> (f3(c1, c2) = c2)),
% 29.24/19.47 inference(monotonicity,[status(thm)],[22190])).
% 29.24/19.47 tff(22192,plain,
% 29.24/19.47 ((~(f3(c1, f8(c3)) = c2)) <=> (~(f3(c1, c2) = c2))),
% 29.24/19.47 inference(monotonicity,[status(thm)],[22191])).
% 29.24/19.47 tff(22193,plain,
% 29.24/19.47 ((f3(c1, f3(c1, f8(c3))) = f3(c1, f8(c3))) <=> (f3(c1, f3(c1, f8(c3))) = c2)),
% 29.24/19.47 inference(monotonicity,[status(thm)],[12781])).
% 29.24/19.47 tff(22194,plain,
% 29.24/19.47 ((f3(c1, f3(c1, f8(c3))) = c2) <=> (f3(c1, f3(c1, f8(c3))) = f3(c1, f8(c3)))),
% 29.24/19.47 inference(symmetry,[status(thm)],[22193])).
% 29.24/19.47 tff(22195,plain,
% 29.24/19.47 (f3(c1, f3(c1, f8(c3))) = f3(c1, c2)),
% 29.24/19.47 inference(monotonicity,[status(thm)],[12781])).
% 29.24/19.47 tff(22196,plain,
% 29.24/19.47 (f3(c1, f3(c1, f8(c3))) = c2),
% 29.24/19.47 inference(transitivity,[status(thm)],[22195, 22186, 22188, 12781])).
% 29.24/19.47 tff(22197,plain,
% 29.24/19.47 (f3(c1, f3(c1, f8(c3))) = f3(c1, f8(c3))),
% 29.24/19.47 inference(modus_ponens,[status(thm)],[22196, 22194])).
% 29.24/19.47 tff(22198,plain,
% 29.24/19.47 (big_f(f3(c1, f3(c1, f8(c3))), c1) <=> big_f(f3(c1, f3(c1, f8(c3))), f10(c2))),
% 29.24/19.47 inference(monotonicity,[status(thm)],[12231])).
% 29.24/19.47 tff(22199,plain,
% 29.24/19.47 (big_f(f3(c1, f3(c1, f8(c3))), f10(c2)) <=> big_f(f3(c1, f3(c1, f8(c3))), c1)),
% 29.24/19.47 inference(symmetry,[status(thm)],[22198])).
% 29.24/19.47 tff(22200,plain,
% 29.24/19.47 (big_f(f3(c1, f3(c1, f8(c3))), f10(c2)) <=> big_f(c2, f10(c2))),
% 29.24/19.47 inference(monotonicity,[status(thm)],[22196])).
% 29.24/19.47 tff(22201,plain,
% 29.24/19.47 (big_f(c2, f10(c2)) <=> big_f(f3(c1, f3(c1, f8(c3))), f10(c2))),
% 29.24/19.47 inference(symmetry,[status(thm)],[22200])).
% 29.24/19.47 tff(22202,plain,
% 29.24/19.47 (big_f(c2, f10(c2)) <=> big_f(f3(c1, f3(c1, f8(c3))), c1)),
% 29.24/19.47 inference(transitivity,[status(thm)],[22201, 22199])).
% 29.24/19.47 tff(22203,plain,
% 29.24/19.47 (big_f(f3(c1, f3(c1, f8(c3))), c1)),
% 29.24/19.47 inference(modus_ponens,[status(thm)],[12291, 22202])).
% 29.24/19.47 tff(22204,plain,
% 29.24/19.47 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((c1 = c4) | (~(c2 = f2(c3))) | big_f(c3, c2) | (~big_f(f3(c1, f3(c1, f8(c3))), c1)) | (~(f3(c1, f3(c1, f8(c3))) = f3(c1, f8(c3)))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (c1 = c4) | (~(c2 = f2(c3))) | big_f(c3, c2) | (~big_f(f3(c1, f3(c1, f8(c3))), c1)) | (~(f3(c1, f3(c1, f8(c3))) = f3(c1, f8(c3)))))),
% 29.24/19.47 inference(rewrite,[status(thm)],[])).
% 29.24/19.47 tff(22205,plain,
% 29.24/19.47 (($false | (~(c2 = f2(c3))) | (c1 = c4) | (~(f3(c1, f3(c1, f8(c3))) = f3(c1, f8(c3)))) | (~big_f(f3(c1, f3(c1, f8(c3))), c1)) | big_f(c3, c2)) <=> ((c1 = c4) | (~(c2 = f2(c3))) | big_f(c3, c2) | (~big_f(f3(c1, f3(c1, f8(c3))), c1)) | (~(f3(c1, f3(c1, f8(c3))) = f3(c1, f8(c3)))))),
% 29.24/19.47 inference(rewrite,[status(thm)],[])).
% 29.24/19.47 tff(22206,plain,
% 29.24/19.47 (((~(c3 = c3)) | (~(c2 = f2(c3))) | (c1 = c4) | (~(f3(c1, f3(c1, f8(c3))) = f3(c1, f8(c3)))) | (~big_f(f3(c1, f3(c1, f8(c3))), c1)) | big_f(c3, c2)) <=> ($false | (~(c2 = f2(c3))) | (c1 = c4) | (~(f3(c1, f3(c1, f8(c3))) = f3(c1, f8(c3)))) | (~big_f(f3(c1, f3(c1, f8(c3))), c1)) | big_f(c3, c2))),
% 29.24/19.47 inference(monotonicity,[status(thm)],[1308])).
% 29.24/19.47 tff(22207,plain,
% 29.24/19.47 (((~(c3 = c3)) | (~(c2 = f2(c3))) | (c1 = c4) | (~(f3(c1, f3(c1, f8(c3))) = f3(c1, f8(c3)))) | (~big_f(f3(c1, f3(c1, f8(c3))), c1)) | big_f(c3, c2)) <=> ((c1 = c4) | (~(c2 = f2(c3))) | big_f(c3, c2) | (~big_f(f3(c1, f3(c1, f8(c3))), c1)) | (~(f3(c1, f3(c1, f8(c3))) = f3(c1, f8(c3)))))),
% 29.24/19.47 inference(transitivity,[status(thm)],[22206, 22205])).
% 29.24/19.47 tff(22208,plain,
% 29.24/19.47 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c3 = c3)) | (~(c2 = f2(c3))) | (c1 = c4) | (~(f3(c1, f3(c1, f8(c3))) = f3(c1, f8(c3)))) | (~big_f(f3(c1, f3(c1, f8(c3))), c1)) | big_f(c3, c2))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((c1 = c4) | (~(c2 = f2(c3))) | big_f(c3, c2) | (~big_f(f3(c1, f3(c1, f8(c3))), c1)) | (~(f3(c1, f3(c1, f8(c3))) = f3(c1, f8(c3))))))),
% 29.24/19.47 inference(monotonicity,[status(thm)],[22207])).
% 29.24/19.47 tff(22209,plain,
% 29.24/19.47 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c3 = c3)) | (~(c2 = f2(c3))) | (c1 = c4) | (~(f3(c1, f3(c1, f8(c3))) = f3(c1, f8(c3)))) | (~big_f(f3(c1, f3(c1, f8(c3))), c1)) | big_f(c3, c2))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (c1 = c4) | (~(c2 = f2(c3))) | big_f(c3, c2) | (~big_f(f3(c1, f3(c1, f8(c3))), c1)) | (~(f3(c1, f3(c1, f8(c3))) = f3(c1, f8(c3)))))),
% 29.24/19.47 inference(transitivity,[status(thm)],[22208, 22204])).
% 29.24/19.47 tff(22210,plain,
% 29.24/19.47 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c3 = c3)) | (~(c2 = f2(c3))) | (c1 = c4) | (~(f3(c1, f3(c1, f8(c3))) = f3(c1, f8(c3)))) | (~big_f(f3(c1, f3(c1, f8(c3))), c1)) | big_f(c3, c2))),
% 29.24/19.47 inference(quant_inst,[status(thm)],[])).
% 29.24/19.47 tff(22211,plain,
% 29.24/19.47 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (c1 = c4) | (~(c2 = f2(c3))) | big_f(c3, c2) | (~big_f(f3(c1, f3(c1, f8(c3))), c1)) | (~(f3(c1, f3(c1, f8(c3))) = f3(c1, f8(c3))))),
% 29.24/19.47 inference(modus_ponens,[status(thm)],[22210, 22209])).
% 29.24/19.47 tff(22212,plain,
% 29.24/19.47 ((c1 = c4) | (~(c2 = f2(c3))) | big_f(c3, c2) | (~big_f(f3(c1, f3(c1, f8(c3))), c1)) | (~(f3(c1, f3(c1, f8(c3))) = f3(c1, f8(c3))))),
% 29.24/19.47 inference(unit_resolution,[status(thm)],[22211, 1398])).
% 29.24/19.47 tff(22213,plain,
% 29.24/19.47 ($false),
% 29.24/19.47 inference(unit_resolution,[status(thm)],[22212, 22203, 22197, 3833, 482, 18319])).
% 29.24/19.47 tff(22214,plain,((~(f3(c1, f8(c3)) = c2)) | big_f(c3, c2) | (c1 = c4) | (~(c2 = f2(c3))) | (~big_f(c2, f10(c2))) | (~(f8(f7(f4(c4))) = c2)) | (~(f7(c1) = c2)) | (~(f4(c4) = c1)) | (~(c3 = c2)) | (~(f10(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.24/19.47 tff(22215,plain,
% 29.24/19.47 (~(f3(c1, f8(c3)) = c2)),
% 29.24/19.47 inference(unit_resolution,[status(thm)],[22214, 2600, 482, 3833, 12291, 13856, 347, 11752, 67, 11819])).
% 29.24/19.47 tff(22216,plain,
% 29.24/19.47 (~(f3(c1, c2) = c2)),
% 29.24/19.47 inference(modus_ponens,[status(thm)],[22215, 22192])).
% 29.24/19.47 tff(22217,plain,
% 29.24/19.47 (f10(f7(c1)) = f10(c2)),
% 29.24/19.47 inference(monotonicity,[status(thm)],[347])).
% 29.24/19.47 tff(22218,plain,
% 29.24/19.47 (f10(c2) = f10(f7(c1))),
% 29.24/19.47 inference(symmetry,[status(thm)],[22217])).
% 29.24/19.47 tff(22219,plain,
% 29.24/19.47 (c1 = f10(f7(c1))),
% 29.24/19.47 inference(transitivity,[status(thm)],[12231, 22218])).
% 29.24/19.47 tff(22220,plain,
% 29.24/19.47 (big_f(f3(c1, c2), c1) <=> big_f(f3(c1, c2), f10(f7(c1)))),
% 29.24/19.47 inference(monotonicity,[status(thm)],[22219])).
% 29.24/19.47 tff(22221,plain,
% 29.24/19.47 (big_f(f3(c1, c2), f10(f7(c1))) <=> big_f(f3(c1, c2), c1)),
% 29.24/19.47 inference(symmetry,[status(thm)],[22220])).
% 29.24/19.47 tff(22222,plain,
% 29.24/19.47 (f3(c1, f8(c3)) = c1),
% 29.24/19.47 inference(unit_resolution,[status(thm)],[7123, 22215])).
% 29.24/19.47 tff(22223,plain,
% 29.24/19.47 (f3(c1, c2) = f10(c2)),
% 29.24/19.47 inference(transitivity,[status(thm)],[22186, 22188, 22222, 12231])).
% 29.24/19.47 tff(22224,plain,
% 29.24/19.47 (big_f(f3(c1, c2), f10(f7(c1))) <=> big_f(f10(c2), f10(c2))),
% 29.24/19.47 inference(monotonicity,[status(thm)],[22223, 22217])).
% 29.24/19.47 tff(22225,plain,
% 29.24/19.47 (big_f(f10(c2), f10(c2)) <=> big_f(f3(c1, c2), f10(f7(c1)))),
% 29.24/19.47 inference(symmetry,[status(thm)],[22224])).
% 29.24/19.47 tff(22226,plain,
% 29.24/19.47 (big_f(f10(c2), f10(c2)) <=> big_f(f3(c1, c2), c1)),
% 29.24/19.47 inference(transitivity,[status(thm)],[22225, 22221])).
% 29.24/19.47 tff(22227,plain,
% 29.24/19.47 ((~big_f(f10(c2), f10(c2))) <=> (~big_f(f3(c1, c2), c1))),
% 29.24/19.47 inference(monotonicity,[status(thm)],[22226])).
% 29.24/19.47 tff(22228,plain,
% 29.24/19.47 (~big_f(f3(c1, c2), c1)),
% 29.24/19.47 inference(modus_ponens,[status(thm)],[20783, 22227])).
% 29.24/19.47 tff(22229,plain,
% 29.24/19.47 ($false),
% 29.24/19.47 inference(unit_resolution,[status(thm)],[13175, 22228, 22216, 22184, 482, 1335, 11651])).
% 29.24/19.47 tff(22230,plain,((~(f2(c3) = c2)) | (c1 = c4) | big_f(f10(c2), f10(c2)) | (~(f7(c1) = c2)) | (~(f10(c2) = c1)) | (~(f8(f7(f4(c4))) = c2)) | (~(f4(c4) = c1)) | (~(c3 = c2)) | big_f(c3, c2) | (~big_f(c2, f10(c2)))), inference(lemma,lemma(discharge,[]))).
% 29.24/19.47 tff(22231,plain,
% 29.24/19.47 (~(f2(c3) = c2)),
% 29.24/19.47 inference(unit_resolution,[status(thm)],[22230, 13856, 20783, 347, 94, 22182, 11752, 67, 3833, 12291])).
% 29.24/19.47 tff(22232,plain,
% 29.24/19.47 (f2(c3) = c1),
% 29.24/19.47 inference(unit_resolution,[status(thm)],[1273, 22231])).
% 29.24/19.47 tff(22233,plain,
% 29.24/19.47 (big_f(c2, c1)),
% 29.24/19.47 inference(modus_ponens,[status(thm)],[12291, 15253])).
% 29.24/19.47 tff(22234,plain,
% 29.24/19.47 (f3(c1, c2) = f3(f10(c2), f8(c3))),
% 29.24/19.47 inference(monotonicity,[status(thm)],[99, 22185])).
% 29.24/19.47 tff(22235,plain,
% 29.24/19.47 (f3(f10(c2), c2) = c2),
% 29.24/19.47 inference(transitivity,[status(thm)],[15408, 22234, 20765, 12781])).
% 29.24/19.47 tff(22236,plain,
% 29.24/19.47 (big_f(f3(f10(c2), c2), f10(c2)) <=> big_f(c2, f10(c2))),
% 29.24/19.47 inference(monotonicity,[status(thm)],[22235])).
% 29.24/19.47 tff(22237,plain,
% 29.24/19.47 (big_f(c2, f10(c2)) <=> big_f(f3(f10(c2), c2), f10(c2))),
% 29.24/19.47 inference(symmetry,[status(thm)],[22236])).
% 29.24/19.47 tff(22238,plain,
% 29.24/19.47 (big_f(f3(f10(c2), c2), f10(c2))),
% 29.24/19.47 inference(modus_ponens,[status(thm)],[12291, 22237])).
% 29.24/19.47 tff(22239,plain,
% 29.24/19.47 (f10(c3) = c1),
% 29.24/19.47 inference(transitivity,[status(thm)],[2824, 94])).
% 29.24/19.47 tff(22240,plain,
% 29.24/19.47 (f3(f10(c3), c2) = f3(c1, c2)),
% 29.24/19.47 inference(monotonicity,[status(thm)],[22239])).
% 29.24/19.47 tff(22241,plain,
% 29.24/19.47 ((f3(f10(c3), c2) = c2) <=> (f3(c1, c2) = c2)),
% 29.24/19.47 inference(monotonicity,[status(thm)],[22240])).
% 29.24/19.47 tff(22242,plain,
% 29.24/19.47 ((f3(c1, c2) = c2) <=> (f3(f10(c3), c2) = c2)),
% 29.24/19.47 inference(symmetry,[status(thm)],[22241])).
% 29.24/19.47 tff(22243,plain,
% 29.24/19.47 (f3(c1, c2) = f3(c1, f8(c3))),
% 29.24/19.47 inference(transitivity,[status(thm)],[22234, 20765])).
% 29.24/19.47 tff(22244,plain,
% 29.24/19.47 ((f3(c1, c2) = c2) <=> (f3(c1, f8(c3)) = c2)),
% 29.24/19.47 inference(monotonicity,[status(thm)],[22243])).
% 29.24/19.47 tff(22245,plain,
% 29.24/19.47 ((f3(c1, f8(c3)) = c2) <=> (f3(c1, c2) = c2)),
% 29.24/19.47 inference(symmetry,[status(thm)],[22244])).
% 29.24/19.47 tff(22246,plain,
% 29.24/19.47 ((f3(c1, f8(c3)) = c2) <=> (f3(f10(c3), c2) = c2)),
% 29.24/19.47 inference(transitivity,[status(thm)],[22245, 22242])).
% 29.24/19.47 tff(22247,plain,
% 29.24/19.47 (f3(f10(c3), c2) = c2),
% 29.24/19.47 inference(modus_ponens,[status(thm)],[12781, 22246])).
% 29.24/19.47 tff(22248,plain,
% 29.24/19.47 ((f9(f10(c2), f2(c3)) = c3) <=> (f9(f10(c2), f2(c3)) = c2)),
% 29.24/19.47 inference(monotonicity,[status(thm)],[67])).
% 29.24/19.47 tff(22249,plain,
% 29.24/19.47 ((f9(f10(c2), f2(c3)) = c2) <=> (f9(f10(c2), f2(c3)) = c3)),
% 29.24/19.47 inference(symmetry,[status(thm)],[22248])).
% 29.24/19.47 tff(22250,plain,
% 29.24/19.47 (f10(c2) = f4(c4)),
% 29.24/19.47 inference(transitivity,[status(thm)],[94, 16651])).
% 29.24/19.47 tff(22251,plain,
% 29.24/19.47 (f9(f10(c2), f10(c2)) = f9(f10(c2), f4(c4))),
% 29.24/19.47 inference(monotonicity,[status(thm)],[22250])).
% 29.24/19.47 tff(22252,plain,
% 29.24/19.47 (f2(c3) = f10(c2)),
% 29.24/19.47 inference(transitivity,[status(thm)],[1247, 99])).
% 29.24/19.47 tff(22253,plain,
% 29.24/19.47 (f9(f10(c2), f2(c3)) = f9(f10(c2), f10(c2))),
% 29.24/19.47 inference(monotonicity,[status(thm)],[22252])).
% 29.24/19.47 tff(22254,plain,
% 29.24/19.47 (f9(f10(c2), f2(c3)) = f10(c2)),
% 29.24/19.47 inference(transitivity,[status(thm)],[22253, 22251, 148, 99])).
% 29.24/19.47 tff(22255,plain,
% 29.24/19.47 ((f9(f10(c2), f2(c3)) = c2) <=> (f10(c2) = c2)),
% 29.24/19.47 inference(monotonicity,[status(thm)],[22254])).
% 29.24/19.47 tff(22256,plain,
% 29.24/19.47 ((f10(c2) = c2) <=> (f9(f10(c2), f2(c3)) = c2)),
% 29.24/19.47 inference(symmetry,[status(thm)],[22255])).
% 29.24/19.47 tff(22257,plain,
% 29.24/19.47 ((f10(c2) = c2) <=> (f9(f10(c2), f2(c3)) = c3)),
% 29.24/19.47 inference(transitivity,[status(thm)],[22256, 22249])).
% 29.24/19.47 tff(22258,plain,
% 29.24/19.47 ((~(f10(c2) = c2)) <=> (~(f9(f10(c2), f2(c3)) = c3))),
% 29.24/19.47 inference(monotonicity,[status(thm)],[22257])).
% 29.24/19.47 tff(22259,plain,
% 29.24/19.47 (~(f9(f10(c2), f2(c3)) = c3)),
% 29.24/19.47 inference(modus_ponens,[status(thm)],[89, 22258])).
% 29.24/19.47 tff(22260,plain,
% 29.24/19.47 ((f10(c3) = c4) <=> (f10(c3) = c2)),
% 29.24/19.47 inference(monotonicity,[status(thm)],[22158])).
% 29.24/19.47 tff(22261,plain,
% 29.24/19.47 ((f10(c3) = c2) <=> (f10(c3) = c4)),
% 29.24/19.47 inference(symmetry,[status(thm)],[22260])).
% 29.24/19.47 tff(22262,plain,
% 29.24/19.47 ((f10(c3) = c2) <=> (f10(c2) = c2)),
% 29.24/19.47 inference(monotonicity,[status(thm)],[2824])).
% 29.24/19.47 tff(22263,plain,
% 29.24/19.47 ((f10(c2) = c2) <=> (f10(c3) = c2)),
% 29.24/19.47 inference(symmetry,[status(thm)],[22262])).
% 29.24/19.47 tff(22264,plain,
% 29.24/19.47 ((f10(c2) = c2) <=> (f10(c3) = c4)),
% 29.24/19.47 inference(transitivity,[status(thm)],[22263, 22261])).
% 29.24/19.47 tff(22265,plain,
% 29.24/19.47 ((~(f10(c2) = c2)) <=> (~(f10(c3) = c4))),
% 29.24/19.47 inference(monotonicity,[status(thm)],[22264])).
% 29.24/19.47 tff(22266,plain,
% 29.24/19.47 (~(f10(c3) = c4)),
% 29.24/19.47 inference(modus_ponens,[status(thm)],[89, 22265])).
% 29.24/19.47 tff(22267,plain,
% 29.24/19.47 (f10(c3) = f10(f7(c1))),
% 29.24/19.47 inference(transitivity,[status(thm)],[2824, 22218])).
% 29.24/19.47 tff(22268,plain,
% 29.24/19.47 (big_f(f3(f10(c3), c2), f10(c3)) <=> big_f(f3(c1, c2), f10(f7(c1)))),
% 29.24/19.47 inference(monotonicity,[status(thm)],[22240, 22267])).
% 29.24/19.47 tff(22269,plain,
% 29.24/19.47 (big_f(f3(c1, c2), f10(f7(c1))) <=> big_f(f3(f10(c3), c2), f10(c3))),
% 29.24/19.47 inference(symmetry,[status(thm)],[22268])).
% 29.24/19.47 tff(22270,plain,
% 29.24/19.47 (f3(c1, c2) = c2),
% 29.24/19.47 inference(transitivity,[status(thm)],[22234, 20765, 12781])).
% 29.24/19.47 tff(22271,plain,
% 29.24/19.47 (big_f(f3(c1, c2), f10(f7(c1))) <=> big_f(c2, f10(c2))),
% 29.24/19.47 inference(monotonicity,[status(thm)],[22270, 22217])).
% 29.24/19.47 tff(22272,plain,
% 29.24/19.47 (big_f(c2, f10(c2)) <=> big_f(f3(c1, c2), f10(f7(c1)))),
% 29.24/19.47 inference(symmetry,[status(thm)],[22271])).
% 29.24/19.47 tff(22273,plain,
% 29.24/19.47 (big_f(c2, f10(c2)) <=> big_f(f3(f10(c3), c2), f10(c3))),
% 29.24/19.47 inference(transitivity,[status(thm)],[22272, 22269])).
% 29.24/19.47 tff(22274,plain,
% 29.24/19.47 (big_f(f3(f10(c3), c2), f10(c3))),
% 29.24/19.47 inference(modus_ponens,[status(thm)],[12291, 22273])).
% 29.24/19.47 tff(22275,assumption,(f3(f10(c3), c2) = c2), introduced(assumption)).
% 29.24/19.47 tff(22276,assumption,(~(f10(c3) = c4)), introduced(assumption)).
% 29.24/19.47 tff(22277,assumption,(~(f9(f10(c2), f2(c3)) = c3)), introduced(assumption)).
% 29.24/19.47 tff(22278,plain,
% 29.24/19.47 (f10(c2) = f4(c4)),
% 29.24/19.47 inference(transitivity,[status(thm)],[11819, 16651])).
% 29.24/19.47 tff(22279,plain,
% 29.24/19.47 (f9(f10(c2), f10(c2)) = f9(f10(c2), f4(c4))),
% 29.24/19.47 inference(monotonicity,[status(thm)],[22278])).
% 29.24/19.47 tff(22280,plain,
% 29.24/19.47 (f2(c3) = f10(c2)),
% 29.24/19.47 inference(transitivity,[status(thm)],[1247, 12231])).
% 29.24/19.47 tff(22281,plain,
% 29.24/19.47 (f9(f10(c2), f2(c3)) = f9(f10(c2), f10(c2))),
% 29.24/19.47 inference(monotonicity,[status(thm)],[22280])).
% 29.24/19.47 tff(22282,plain,
% 29.24/19.47 (f9(f10(c2), f2(c3)) = c1),
% 29.24/19.47 inference(transitivity,[status(thm)],[22281, 22279, 148])).
% 29.24/19.47 tff(22283,plain,
% 29.24/19.47 (f1(f9(f10(c2), f2(c3)), c2) = f1(c1, c2)),
% 29.24/19.47 inference(monotonicity,[status(thm)],[22282])).
% 29.24/19.47 tff(22284,plain,
% 29.24/19.47 ((f1(f9(f10(c2), f2(c3)), c2) = c2) <=> (f1(c1, c2) = c2)),
% 29.24/19.47 inference(monotonicity,[status(thm)],[22283])).
% 29.24/19.47 tff(22285,plain,
% 29.24/19.47 ((f1(c1, c2) = c2) <=> (f1(f9(f10(c2), f2(c3)), c2) = c2)),
% 29.24/19.47 inference(symmetry,[status(thm)],[22284])).
% 29.24/19.47 tff(22286,plain,
% 29.24/19.47 (f1(f9(f10(c2), f2(c3)), c2) = c2),
% 29.24/19.47 inference(modus_ponens,[status(thm)],[822, 22285])).
% 29.24/19.47 tff(22287,plain,
% 29.24/19.47 (big_f(f9(f10(c2), f2(c3)), f1(f9(f10(c2), f2(c3)), c2)) <=> big_f(c1, f1(c1, c2))),
% 29.24/19.47 inference(monotonicity,[status(thm)],[22282, 22283])).
% 29.24/19.47 tff(22288,plain,
% 29.24/19.47 (big_f(c1, f1(c1, c2)) <=> big_f(f9(f10(c2), f2(c3)), f1(f9(f10(c2), f2(c3)), c2))),
% 29.24/19.47 inference(symmetry,[status(thm)],[22287])).
% 29.24/19.47 tff(22289,plain,
% 29.24/19.47 (big_f(c1, c2) <=> big_f(f9(f10(c2), f2(c3)), f1(f9(f10(c2), f2(c3)), c2))),
% 29.24/19.47 inference(transitivity,[status(thm)],[13535, 22288])).
% 29.24/19.47 tff(22290,plain,
% 29.24/19.47 (big_f(f9(f10(c2), f2(c3)), f1(f9(f10(c2), f2(c3)), c2))),
% 29.24/19.47 inference(modus_ponens,[status(thm)],[2865, 22289])).
% 29.24/19.47 tff(22291,plain,
% 29.24/19.47 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f10(c3) = c4) | (~big_f(f3(f10(c3), c2), f10(c3))) | (f9(f10(c2), f2(c3)) = c3) | (~big_f(f9(f10(c2), f2(c3)), f1(f9(f10(c2), f2(c3)), c2))) | (~(f3(f10(c3), c2) = c2)) | (~(f1(f9(f10(c2), f2(c3)), c2) = c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (f10(c3) = c4) | (~big_f(f3(f10(c3), c2), f10(c3))) | (f9(f10(c2), f2(c3)) = c3) | (~big_f(f9(f10(c2), f2(c3)), f1(f9(f10(c2), f2(c3)), c2))) | (~(f3(f10(c3), c2) = c2)) | (~(f1(f9(f10(c2), f2(c3)), c2) = c2)))),
% 29.24/19.48 inference(rewrite,[status(thm)],[])).
% 29.24/19.48 tff(22292,plain,
% 29.24/19.48 (((f10(c3) = c4) | (f9(f10(c2), f2(c3)) = c3) | (~(f3(f10(c3), c2) = c2)) | (~big_f(f3(f10(c3), c2), f10(c3))) | (~(f1(f9(f10(c2), f2(c3)), c2) = c2)) | (~big_f(f9(f10(c2), f2(c3)), f1(f9(f10(c2), f2(c3)), c2)))) <=> ((f10(c3) = c4) | (~big_f(f3(f10(c3), c2), f10(c3))) | (f9(f10(c2), f2(c3)) = c3) | (~big_f(f9(f10(c2), f2(c3)), f1(f9(f10(c2), f2(c3)), c2))) | (~(f3(f10(c3), c2) = c2)) | (~(f1(f9(f10(c2), f2(c3)), c2) = c2)))),
% 29.24/19.48 inference(rewrite,[status(thm)],[])).
% 29.24/19.48 tff(22293,plain,
% 29.24/19.48 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f10(c3) = c4) | (f9(f10(c2), f2(c3)) = c3) | (~(f3(f10(c3), c2) = c2)) | (~big_f(f3(f10(c3), c2), f10(c3))) | (~(f1(f9(f10(c2), f2(c3)), c2) = c2)) | (~big_f(f9(f10(c2), f2(c3)), f1(f9(f10(c2), f2(c3)), c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f10(c3) = c4) | (~big_f(f3(f10(c3), c2), f10(c3))) | (f9(f10(c2), f2(c3)) = c3) | (~big_f(f9(f10(c2), f2(c3)), f1(f9(f10(c2), f2(c3)), c2))) | (~(f3(f10(c3), c2) = c2)) | (~(f1(f9(f10(c2), f2(c3)), c2) = c2))))),
% 29.24/19.48 inference(monotonicity,[status(thm)],[22292])).
% 29.24/19.48 tff(22294,plain,
% 29.24/19.48 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f10(c3) = c4) | (f9(f10(c2), f2(c3)) = c3) | (~(f3(f10(c3), c2) = c2)) | (~big_f(f3(f10(c3), c2), f10(c3))) | (~(f1(f9(f10(c2), f2(c3)), c2) = c2)) | (~big_f(f9(f10(c2), f2(c3)), f1(f9(f10(c2), f2(c3)), c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (f10(c3) = c4) | (~big_f(f3(f10(c3), c2), f10(c3))) | (f9(f10(c2), f2(c3)) = c3) | (~big_f(f9(f10(c2), f2(c3)), f1(f9(f10(c2), f2(c3)), c2))) | (~(f3(f10(c3), c2) = c2)) | (~(f1(f9(f10(c2), f2(c3)), c2) = c2)))),
% 29.24/19.48 inference(transitivity,[status(thm)],[22293, 22291])).
% 29.24/19.48 tff(22295,plain,
% 29.24/19.48 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f10(c3) = c4) | (f9(f10(c2), f2(c3)) = c3) | (~(f3(f10(c3), c2) = c2)) | (~big_f(f3(f10(c3), c2), f10(c3))) | (~(f1(f9(f10(c2), f2(c3)), c2) = c2)) | (~big_f(f9(f10(c2), f2(c3)), f1(f9(f10(c2), f2(c3)), c2))))),
% 29.24/19.48 inference(quant_inst,[status(thm)],[])).
% 29.24/19.48 tff(22296,plain,
% 29.24/19.48 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (f10(c3) = c4) | (~big_f(f3(f10(c3), c2), f10(c3))) | (f9(f10(c2), f2(c3)) = c3) | (~big_f(f9(f10(c2), f2(c3)), f1(f9(f10(c2), f2(c3)), c2))) | (~(f3(f10(c3), c2) = c2)) | (~(f1(f9(f10(c2), f2(c3)), c2) = c2))),
% 29.24/19.48 inference(modus_ponens,[status(thm)],[22295, 22294])).
% 29.24/19.48 tff(22297,plain,
% 29.24/19.48 ((f10(c3) = c4) | (~big_f(f3(f10(c3), c2), f10(c3))) | (f9(f10(c2), f2(c3)) = c3) | (~big_f(f9(f10(c2), f2(c3)), f1(f9(f10(c2), f2(c3)), c2))) | (~(f3(f10(c3), c2) = c2)) | (~(f1(f9(f10(c2), f2(c3)), c2) = c2))),
% 29.24/19.48 inference(unit_resolution,[status(thm)],[22296, 933])).
% 29.24/19.48 tff(22298,plain,
% 29.24/19.48 ($false),
% 29.24/19.48 inference(unit_resolution,[status(thm)],[22297, 22290, 22286, 22277, 22276, 7426, 22275])).
% 29.24/19.48 tff(22299,plain,((~(f1(c1, c2) = c2)) | (f9(f10(c2), f2(c3)) = c3) | (f10(c3) = c4) | (~big_f(f3(f10(c3), c2), f10(c3))) | (~(f3(f10(c3), c2) = c2)) | (~big_f(c1, c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | (~(f2(c3) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.24/19.48 tff(22300,plain,
% 29.24/19.48 (~(f1(c1, c2) = c2)),
% 29.24/19.48 inference(unit_resolution,[status(thm)],[22299, 22274, 22266, 22259, 22247, 2865, 148, 11752, 94, 1247])).
% 29.24/19.48 tff(22301,plain,
% 29.24/19.48 (f1(c1, c2) = c1),
% 29.24/19.48 inference(unit_resolution,[status(thm)],[841, 22300])).
% 29.24/19.48 tff(22302,plain,
% 29.24/19.48 (f1(f10(c2), c2) = f10(c2)),
% 29.24/19.48 inference(transitivity,[status(thm)],[13619, 22301, 99])).
% 29.24/19.48 tff(22303,plain,
% 29.24/19.48 (big_f(f10(c2), f1(f10(c2), c2)) <=> big_f(f10(c2), f10(c2))),
% 29.24/19.48 inference(monotonicity,[status(thm)],[22302])).
% 29.24/19.48 tff(22304,plain,
% 29.24/19.48 (big_f(f10(c2), f10(c2)) <=> big_f(f10(c2), f1(f10(c2), c2))),
% 29.24/19.48 inference(symmetry,[status(thm)],[22303])).
% 29.24/19.48 tff(22305,plain,
% 29.24/19.48 ((~big_f(f10(c2), f10(c2))) <=> (~big_f(f10(c2), f1(f10(c2), c2)))),
% 29.24/19.48 inference(monotonicity,[status(thm)],[22304])).
% 29.24/19.48 tff(22306,plain,
% 29.24/19.48 (~big_f(f10(c2), f1(f10(c2), c2))),
% 29.24/19.48 inference(modus_ponens,[status(thm)],[20783, 22305])).
% 29.24/19.48 tff(22307,plain,
% 29.24/19.48 ((f1(f10(c2), c2) = c2) <=> (f10(c2) = c2)),
% 29.24/19.48 inference(monotonicity,[status(thm)],[22302])).
% 29.24/19.48 tff(22308,plain,
% 29.24/19.48 ((f10(c2) = c2) <=> (f1(f10(c2), c2) = c2)),
% 29.24/19.48 inference(symmetry,[status(thm)],[22307])).
% 29.24/19.48 tff(22309,plain,
% 29.24/19.48 ((~(f10(c2) = c2)) <=> (~(f1(f10(c2), c2) = c2))),
% 29.24/19.48 inference(monotonicity,[status(thm)],[22308])).
% 29.24/19.48 tff(22310,plain,
% 29.24/19.48 (~(f1(f10(c2), c2) = c2)),
% 29.24/19.48 inference(modus_ponens,[status(thm)],[89, 22309])).
% 29.24/19.48 tff(22311,plain,
% 29.24/19.48 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((f10(c2) = c4) | (f10(c2) = c3) | big_f(f10(c2), f1(f10(c2), c2)) | (f1(f10(c2), c2) = c2) | (~(f3(f10(c2), c2) = c2)) | (~big_f(f3(f10(c2), c2), f10(c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (f10(c2) = c4) | (f10(c2) = c3) | big_f(f10(c2), f1(f10(c2), c2)) | (f1(f10(c2), c2) = c2) | (~(f3(f10(c2), c2) = c2)) | (~big_f(f3(f10(c2), c2), f10(c2))))),
% 29.24/19.48 inference(rewrite,[status(thm)],[])).
% 29.24/19.48 tff(22312,plain,
% 29.24/19.48 (((f10(c2) = c4) | (f10(c2) = c3) | (f1(f10(c2), c2) = c2) | big_f(f10(c2), f1(f10(c2), c2)) | (~(f3(f10(c2), c2) = c2)) | (~big_f(f3(f10(c2), c2), f10(c2)))) <=> ((f10(c2) = c4) | (f10(c2) = c3) | big_f(f10(c2), f1(f10(c2), c2)) | (f1(f10(c2), c2) = c2) | (~(f3(f10(c2), c2) = c2)) | (~big_f(f3(f10(c2), c2), f10(c2))))),
% 29.24/19.48 inference(rewrite,[status(thm)],[])).
% 29.24/19.48 tff(22313,plain,
% 29.24/19.48 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((f10(c2) = c4) | (f10(c2) = c3) | (f1(f10(c2), c2) = c2) | big_f(f10(c2), f1(f10(c2), c2)) | (~(f3(f10(c2), c2) = c2)) | (~big_f(f3(f10(c2), c2), f10(c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((f10(c2) = c4) | (f10(c2) = c3) | big_f(f10(c2), f1(f10(c2), c2)) | (f1(f10(c2), c2) = c2) | (~(f3(f10(c2), c2) = c2)) | (~big_f(f3(f10(c2), c2), f10(c2)))))),
% 29.24/19.48 inference(monotonicity,[status(thm)],[22312])).
% 29.24/19.48 tff(22314,plain,
% 29.24/19.48 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((f10(c2) = c4) | (f10(c2) = c3) | (f1(f10(c2), c2) = c2) | big_f(f10(c2), f1(f10(c2), c2)) | (~(f3(f10(c2), c2) = c2)) | (~big_f(f3(f10(c2), c2), f10(c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (f10(c2) = c4) | (f10(c2) = c3) | big_f(f10(c2), f1(f10(c2), c2)) | (f1(f10(c2), c2) = c2) | (~(f3(f10(c2), c2) = c2)) | (~big_f(f3(f10(c2), c2), f10(c2))))),
% 29.24/19.48 inference(transitivity,[status(thm)],[22313, 22311])).
% 29.24/19.48 tff(22315,plain,
% 29.24/19.48 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((f10(c2) = c4) | (f10(c2) = c3) | (f1(f10(c2), c2) = c2) | big_f(f10(c2), f1(f10(c2), c2)) | (~(f3(f10(c2), c2) = c2)) | (~big_f(f3(f10(c2), c2), f10(c2))))),
% 29.24/19.48 inference(quant_inst,[status(thm)],[])).
% 29.24/19.48 tff(22316,plain,
% 29.24/19.48 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (f10(c2) = c4) | (f10(c2) = c3) | big_f(f10(c2), f1(f10(c2), c2)) | (f1(f10(c2), c2) = c2) | (~(f3(f10(c2), c2) = c2)) | (~big_f(f3(f10(c2), c2), f10(c2)))),
% 29.24/19.48 inference(modus_ponens,[status(thm)],[22315, 22314])).
% 29.24/19.48 tff(22317,plain,
% 29.24/19.48 (big_f(f10(c2), f1(f10(c2), c2)) | (f1(f10(c2), c2) = c2) | (~(f3(f10(c2), c2) = c2)) | (~big_f(f3(f10(c2), c2), f10(c2)))),
% 29.24/19.48 inference(unit_resolution,[status(thm)],[22316, 969, 15519, 15667])).
% 29.24/19.48 tff(22318,plain,
% 29.24/19.48 ($false),
% 29.24/19.48 inference(unit_resolution,[status(thm)],[22317, 22310, 22306, 22235, 22238])).
% 29.24/19.48 tff(22319,plain,((~(f3(c1, f8(c3)) = c2)) | (f10(c2) = c4) | (f10(c2) = c3) | (~big_f(c2, f10(c2))) | (~(f8(f7(f4(c4))) = c2)) | (~(f7(c1) = c2)) | (~(f4(c4) = c1)) | (~(c3 = c2)) | (f10(c2) = c2) | big_f(f10(c2), f10(c2)) | (~big_f(c1, c2)) | (~(f9(f10(c2), f4(c4)) = c1)) | (~(f2(c3) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.24/19.48 tff(22320,plain,
% 29.24/19.48 (~(f9(f10(c2), f4(c4)) = c1)),
% 29.24/19.48 inference(unit_resolution,[status(thm)],[22319, 12781, 15667, 12291, 13856, 347, 11752, 67, 89, 20783, 2865, 1247, 15519])).
% 29.24/19.48 tff(22321,plain,
% 29.24/19.48 (f9(f10(c2), f4(c4)) = c2),
% 29.24/19.48 inference(unit_resolution,[status(thm)],[146, 22320])).
% 29.24/19.48 tff(22322,plain,
% 29.24/19.48 (big_f(f9(c1, c1), c1)),
% 29.24/19.48 inference(unit_resolution,[status(thm)],[19496, 22321, 11752, 94, 22233])).
% 29.24/19.48 tff(22323,plain,
% 29.24/19.48 (big_f(c1, f9(c1, c1))),
% 29.24/19.48 inference(unit_resolution,[status(thm)],[17748, 22321, 11752, 94, 2865])).
% 29.24/19.48 tff(22324,plain,
% 29.24/19.48 (f7(f4(c4)) = f9(c1, c1)),
% 29.24/19.48 inference(transitivity,[status(thm)],[16243, 347, 17733, 17726])).
% 29.24/19.48 tff(22325,plain,
% 29.24/19.48 (f8(f7(f4(c4))) = f8(f9(c1, c1))),
% 29.24/19.48 inference(monotonicity,[status(thm)],[22324])).
% 29.24/19.48 tff(22326,plain,
% 29.24/19.48 ((c2 = f8(f7(f4(c4)))) <=> (f9(c1, c1) = f8(f9(c1, c1)))),
% 29.24/19.48 inference(monotonicity,[status(thm)],[17734, 22325])).
% 29.24/19.48 tff(22327,plain,
% 29.24/19.48 ((f8(f7(f4(c4))) = c2) <=> (f9(c1, c1) = f8(f9(c1, c1)))),
% 29.24/19.48 inference(transitivity,[status(thm)],[105, 22326])).
% 29.24/19.48 tff(22328,plain,
% 29.24/19.48 (f9(c1, c1) = f8(f9(c1, c1))),
% 29.24/19.48 inference(modus_ponens,[status(thm)],[13856, 22327])).
% 29.24/19.48 tff(22329,plain,
% 29.24/19.48 ($false),
% 29.24/19.48 inference(unit_resolution,[status(thm)],[17831, 22328])).
% 29.24/19.48 tff(22330,plain,((~(f8(f7(f4(c4))) = c2)) | (f9(c1, c1) = f8(f9(c1, c1))) | (~(f7(c1) = c2)) | (~(f9(f10(c2), f4(c4)) = c2)) | (~(f10(c2) = c1)) | (~(f4(c4) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.24/19.48 tff(22331,plain,
% 29.24/19.48 (f9(c1, c1) = f8(f9(c1, c1))),
% 29.24/19.48 inference(unit_resolution,[status(thm)],[22330, 22321, 11752, 347, 94, 13856])).
% 29.24/19.48 tff(22332,plain,
% 29.24/19.48 (f3(c1, f9(c1, c1)) = f9(c1, c1)),
% 29.24/19.48 inference(unit_resolution,[status(thm)],[19928, 22321, 11752, 94, 12781, 67, 22331])).
% 29.24/19.48 tff(22333,plain,
% 29.24/19.48 ($false),
% 29.24/19.48 inference(unit_resolution,[status(thm)],[19919, 22332, 22323, 11752, 22118, 22321, 22182, 94, 168, 22322])).
% 29.24/19.48 tff(22334,plain,((~(f3(c1, f8(c3)) = c2)) | (~(f4(c4) = c1)) | (c1 = c3) | (~(c3 = c2)) | (~(f7(c1) = c2)) | (~(f8(f7(f4(c4))) = c2)) | (~big_f(c1, c2)) | (f10(c2) = c3) | (~big_f(c2, f10(c2))) | (f10(c2) = c2) | big_f(f10(c2), f10(c2)) | (~(f2(c3) = c1)) | (f10(c2) = c4)), inference(lemma,lemma(discharge,[]))).
% 29.24/19.48 tff(22335,plain,
% 29.24/19.48 (~(f3(c1, f8(c3)) = c2)),
% 29.24/19.48 inference(unit_resolution,[status(thm)],[22334, 13856, 168, 67, 347, 11752, 2865, 15667, 12291, 89, 20783, 22232, 15519])).
% 29.24/19.48 tff(22336,plain,
% 29.24/19.48 (f3(c1, f8(c3)) = c1),
% 29.24/19.48 inference(unit_resolution,[status(thm)],[7123, 22335])).
% 29.24/19.48 tff(22337,plain,
% 29.24/19.48 (f3(f10(c2), c2) = f10(c2)),
% 29.24/19.48 inference(transitivity,[status(thm)],[15408, 22234, 20765, 16414, 99])).
% 29.24/19.48 tff(22338,plain,
% 29.24/19.48 ((f3(f10(c2), c2) = c2) <=> (f10(c2) = c2)),
% 29.24/19.48 inference(monotonicity,[status(thm)],[22337])).
% 29.24/19.48 tff(22339,plain,
% 29.24/19.48 ((f10(c2) = c2) <=> (f3(f10(c2), c2) = c2)),
% 29.24/19.48 inference(symmetry,[status(thm)],[22338])).
% 29.24/19.48 tff(22340,plain,
% 29.24/19.48 ((~(f10(c2) = c2)) <=> (~(f3(f10(c2), c2) = c2))),
% 29.24/19.48 inference(monotonicity,[status(thm)],[22339])).
% 29.24/19.48 tff(22341,plain,
% 29.24/19.48 (~(f3(f10(c2), c2) = c2)),
% 29.24/19.48 inference(modus_ponens,[status(thm)],[89, 22340])).
% 29.24/19.48 tff(22342,plain,
% 29.24/19.48 (big_f(f3(f10(c2), c2), f10(c2)) <=> big_f(f10(c2), f10(c2))),
% 29.24/19.48 inference(monotonicity,[status(thm)],[22337])).
% 29.24/19.48 tff(22343,plain,
% 29.24/19.48 (big_f(f10(c2), f10(c2)) <=> big_f(f3(f10(c2), c2), f10(c2))),
% 29.24/19.48 inference(symmetry,[status(thm)],[22342])).
% 29.24/19.48 tff(22344,plain,
% 29.24/19.48 ((~big_f(f10(c2), f10(c2))) <=> (~big_f(f3(f10(c2), c2), f10(c2)))),
% 29.24/19.48 inference(monotonicity,[status(thm)],[22343])).
% 29.24/19.48 tff(22345,plain,
% 29.24/19.48 (~big_f(f3(f10(c2), c2), f10(c2))),
% 29.24/19.48 inference(modus_ponens,[status(thm)],[20783, 22344])).
% 29.24/19.48 tff(22346,plain,
% 29.24/19.48 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f10(c2) = c4) | (f10(c2) = c3) | big_f(f10(c2), f1(f10(c2), c2)) | (f1(f10(c2), c2) = c2) | big_f(f3(f10(c2), c2), f10(c2)) | (f3(f10(c2), c2) = c2))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (f10(c2) = c4) | (f10(c2) = c3) | big_f(f10(c2), f1(f10(c2), c2)) | (f1(f10(c2), c2) = c2) | big_f(f3(f10(c2), c2), f10(c2)) | (f3(f10(c2), c2) = c2))),
% 29.24/19.48 inference(rewrite,[status(thm)],[])).
% 29.24/19.48 tff(22347,plain,
% 29.24/19.48 (((f10(c2) = c4) | (f3(f10(c2), c2) = c2) | big_f(f3(f10(c2), c2), f10(c2)) | (f10(c2) = c3) | (f1(f10(c2), c2) = c2) | big_f(f10(c2), f1(f10(c2), c2))) <=> ((f10(c2) = c4) | (f10(c2) = c3) | big_f(f10(c2), f1(f10(c2), c2)) | (f1(f10(c2), c2) = c2) | big_f(f3(f10(c2), c2), f10(c2)) | (f3(f10(c2), c2) = c2))),
% 29.24/19.48 inference(rewrite,[status(thm)],[])).
% 29.24/19.48 tff(22348,plain,
% 29.24/19.48 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f10(c2) = c4) | (f3(f10(c2), c2) = c2) | big_f(f3(f10(c2), c2), f10(c2)) | (f10(c2) = c3) | (f1(f10(c2), c2) = c2) | big_f(f10(c2), f1(f10(c2), c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f10(c2) = c4) | (f10(c2) = c3) | big_f(f10(c2), f1(f10(c2), c2)) | (f1(f10(c2), c2) = c2) | big_f(f3(f10(c2), c2), f10(c2)) | (f3(f10(c2), c2) = c2)))),
% 29.24/19.48 inference(monotonicity,[status(thm)],[22347])).
% 29.24/19.48 tff(22349,plain,
% 29.24/19.48 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f10(c2) = c4) | (f3(f10(c2), c2) = c2) | big_f(f3(f10(c2), c2), f10(c2)) | (f10(c2) = c3) | (f1(f10(c2), c2) = c2) | big_f(f10(c2), f1(f10(c2), c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (f10(c2) = c4) | (f10(c2) = c3) | big_f(f10(c2), f1(f10(c2), c2)) | (f1(f10(c2), c2) = c2) | big_f(f3(f10(c2), c2), f10(c2)) | (f3(f10(c2), c2) = c2))),
% 29.24/19.48 inference(transitivity,[status(thm)],[22348, 22346])).
% 29.24/19.48 tff(22350,plain,
% 29.24/19.48 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((f10(c2) = c4) | (f3(f10(c2), c2) = c2) | big_f(f3(f10(c2), c2), f10(c2)) | (f10(c2) = c3) | (f1(f10(c2), c2) = c2) | big_f(f10(c2), f1(f10(c2), c2)))),
% 29.24/19.48 inference(quant_inst,[status(thm)],[])).
% 29.24/19.48 tff(22351,plain,
% 29.24/19.48 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (f10(c2) = c4) | (f10(c2) = c3) | big_f(f10(c2), f1(f10(c2), c2)) | (f1(f10(c2), c2) = c2) | big_f(f3(f10(c2), c2), f10(c2)) | (f3(f10(c2), c2) = c2)),
% 29.24/19.48 inference(modus_ponens,[status(thm)],[22350, 22349])).
% 29.24/19.48 tff(22352,plain,
% 29.24/19.48 (big_f(f10(c2), f1(f10(c2), c2)) | (f1(f10(c2), c2) = c2) | big_f(f3(f10(c2), c2), f10(c2)) | (f3(f10(c2), c2) = c2)),
% 29.24/19.48 inference(unit_resolution,[status(thm)],[22351, 1014, 15519, 15667])).
% 29.24/19.48 tff(22353,plain,
% 29.24/19.48 ($false),
% 29.24/19.48 inference(unit_resolution,[status(thm)],[22352, 21257, 21253, 22345, 22341])).
% 29.24/19.48 tff(22354,plain,((~(f1(c1, c2) = c1)) | (f10(c2) = c4) | (f10(c2) = c3) | (f10(c2) = c2) | (~(f3(c1, f8(c3)) = c1)) | (~(f8(f7(f4(c4))) = c2)) | (~(f7(c1) = c2)) | (~(f4(c4) = c1)) | (~(c3 = c2)) | big_f(f10(c2), f10(c2))), inference(lemma,lemma(discharge,[]))).
% 29.24/19.48 tff(22355,plain,
% 29.24/19.48 (~(f1(c1, c2) = c1)),
% 29.24/19.48 inference(unit_resolution,[status(thm)],[22354, 22336, 15667, 89, 15519, 13856, 347, 11752, 67, 20783])).
% 29.24/19.48 tff(22356,plain,
% 29.24/19.48 (f1(c1, c2) = c2),
% 29.24/19.48 inference(unit_resolution,[status(thm)],[841, 22355])).
% 29.24/19.48 tff(22357,plain,
% 29.24/19.48 (f3(f10(c2), f1(c1, c2)) = f3(c1, c2)),
% 29.24/19.48 inference(monotonicity,[status(thm)],[94, 22356])).
% 29.24/19.48 tff(22358,plain,
% 29.24/19.48 (f3(f10(c2), f1(c1, c2)) = f10(c2)),
% 29.24/19.48 inference(transitivity,[status(thm)],[22357, 22234, 20765, 22336, 99])).
% 29.24/19.48 tff(22359,plain,
% 29.24/19.48 (big_f(f3(f10(c2), f1(c1, c2)), f10(c2)) <=> big_f(f10(c2), f10(c2))),
% 29.24/19.48 inference(monotonicity,[status(thm)],[22358])).
% 29.24/19.48 tff(22360,plain,
% 29.24/19.48 (big_f(f10(c2), f10(c2)) <=> big_f(f3(f10(c2), f1(c1, c2)), f10(c2))),
% 29.24/19.48 inference(symmetry,[status(thm)],[22359])).
% 29.24/19.48 tff(22361,plain,
% 29.24/19.48 ((~big_f(f10(c2), f10(c2))) <=> (~big_f(f3(f10(c2), f1(c1, c2)), f10(c2)))),
% 29.24/19.48 inference(monotonicity,[status(thm)],[22360])).
% 29.24/19.48 tff(22362,plain,
% 29.24/19.48 (~big_f(f3(f10(c2), f1(c1, c2)), f10(c2))),
% 29.24/19.48 inference(modus_ponens,[status(thm)],[20783, 22361])).
% 29.24/19.48 tff(22363,plain,
% 29.24/19.48 (f1(c1, f1(c1, c2)) = f1(c1, c2)),
% 29.24/19.48 inference(monotonicity,[status(thm)],[22356])).
% 29.24/19.48 tff(22364,plain,
% 29.24/19.48 (f1(c1, f1(c1, c2)) = c2),
% 29.24/19.48 inference(transitivity,[status(thm)],[22363, 22356])).
% 29.24/19.48 tff(22365,plain,
% 29.24/19.48 (big_f(c1, f1(c1, f1(c1, c2))) <=> big_f(c1, c2)),
% 29.24/19.48 inference(monotonicity,[status(thm)],[22364])).
% 29.24/19.48 tff(22366,plain,
% 29.24/19.48 (big_f(c1, c2) <=> big_f(c1, f1(c1, f1(c1, c2)))),
% 29.24/19.48 inference(symmetry,[status(thm)],[22365])).
% 29.24/19.48 tff(22367,plain,
% 29.24/19.48 (big_f(c1, f1(c1, f1(c1, c2)))),
% 29.24/19.48 inference(modus_ponens,[status(thm)],[2865, 22366])).
% 29.24/19.48 tff(22368,plain,
% 29.24/19.48 ((f3(f10(c2), f1(c1, c2)) = f1(c1, c2)) <=> (f3(f10(c2), f1(c1, c2)) = c2)),
% 29.24/19.48 inference(monotonicity,[status(thm)],[22356])).
% 29.24/19.48 tff(22369,plain,
% 29.24/19.48 ((f3(f10(c2), f1(c1, c2)) = c2) <=> (f3(f10(c2), f1(c1, c2)) = f1(c1, c2))),
% 29.24/19.48 inference(symmetry,[status(thm)],[22368])).
% 29.24/19.48 tff(22370,plain,
% 29.24/19.48 ((f3(f10(c2), f1(c1, c2)) = c2) <=> (f10(c2) = c2)),
% 29.24/19.48 inference(monotonicity,[status(thm)],[22358])).
% 29.24/19.48 tff(22371,plain,
% 29.24/19.48 ((f10(c2) = c2) <=> (f3(f10(c2), f1(c1, c2)) = c2)),
% 29.24/19.48 inference(symmetry,[status(thm)],[22370])).
% 29.24/19.48 tff(22372,plain,
% 29.24/19.48 ((f10(c2) = c2) <=> (f3(f10(c2), f1(c1, c2)) = f1(c1, c2))),
% 29.24/19.48 inference(transitivity,[status(thm)],[22371, 22369])).
% 29.24/19.48 tff(22373,plain,
% 29.24/19.48 ((~(f10(c2) = c2)) <=> (~(f3(f10(c2), f1(c1, c2)) = f1(c1, c2)))),
% 29.24/19.48 inference(monotonicity,[status(thm)],[22372])).
% 29.24/19.48 tff(22374,plain,
% 29.24/19.48 (~(f3(f10(c2), f1(c1, c2)) = f1(c1, c2))),
% 29.24/19.48 inference(modus_ponens,[status(thm)],[89, 22373])).
% 29.24/19.48 tff(22375,plain,
% 29.24/19.48 ($false),
% 29.24/19.48 inference(unit_resolution,[status(thm)],[19981, 22374, 22367, 15519, 168, 22363, 22362])).
% 29.24/19.48 tff(22376,plain,((~(f8(f7(f4(c4))) = c2)) | (f10(c2) = c4) | (c1 = c3) | (f10(c2) = c2) | (~(f7(c1) = c2)) | (~(f4(c4) = c1)) | (~(c3 = c2)) | big_f(f10(c2), f10(c2)) | (~big_f(c1, c2)) | (f10(c2) = c3) | (~big_f(c2, f10(c2))) | big_f(c3, c2)), inference(lemma,lemma(discharge,[]))).
% 29.24/19.48 tff(22377,plain,
% 29.24/19.48 (big_f(c3, c2)),
% 29.24/19.48 inference(unit_resolution,[status(thm)],[22376, 22180, 15519, 89, 347, 11752, 13856, 20783, 2865, 15667, 12291, 22164])).
% 29.24/19.48 tff(22378,plain,
% 29.24/19.48 ($false),
% 29.24/19.48 inference(unit_resolution,[status(thm)],[22377, 22168])).
% 29.24/19.48 tff(22379,plain,((f10(c2) = c3) | big_f(c2, c2) | (f10(c2) = c4) | (f10(c2) = c2) | (~(f7(c1) = c2)) | (~(f4(c4) = c1)) | (~(f8(f7(f4(c4))) = c2)) | big_f(f10(c2), f10(c2)) | (~big_f(c1, c2)) | (~big_f(c2, f10(c2))) | (f3(c1, c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.24/19.48 tff(22380,plain,
% 29.24/19.48 (f3(c1, c1) = c1),
% 29.24/19.48 inference(unit_resolution,[status(thm)],[22379, 15667, 13856, 89, 347, 11752, 121, 20783, 2865, 12291, 15519])).
% 29.24/19.48 tff(22381,plain,
% 29.24/19.48 (f3(c1, c1) = f10(c2)),
% 29.24/19.48 inference(transitivity,[status(thm)],[22380, 99])).
% 29.24/19.48 tff(22382,plain,
% 29.24/19.48 ((f3(c1, c1) = c2) <=> (f10(c2) = c2)),
% 29.24/19.48 inference(monotonicity,[status(thm)],[22381])).
% 29.24/19.48 tff(22383,plain,
% 29.24/19.48 ((f10(c2) = c2) <=> (f3(c1, c1) = c2)),
% 29.24/19.48 inference(symmetry,[status(thm)],[22382])).
% 29.24/19.48 tff(22384,plain,
% 29.24/19.48 ((f10(c2) = c3) <=> (f10(c2) = c2)),
% 29.24/19.48 inference(monotonicity,[status(thm)],[22164])).
% 29.24/19.48 tff(22385,plain,
% 29.24/19.48 ((c1 = c3) <=> (f3(c1, c1) = c4)),
% 29.24/19.48 inference(transitivity,[status(thm)],[12094, 22384, 22383, 22160])).
% 29.24/19.48 tff(22386,plain,
% 29.24/19.48 (c1 = c3),
% 29.24/19.48 inference(unit_resolution,[status(thm)],[22376, 22168, 13856, 89, 347, 11752, 15519, 20783, 2865, 15667, 12291, 22164])).
% 29.24/19.48 tff(22387,plain,
% 29.24/19.48 (f3(c1, c1) = c4),
% 29.24/19.48 inference(modus_ponens,[status(thm)],[22386, 22385])).
% 29.24/19.48 tff(22388,plain,
% 29.24/19.48 ((f10(c2) = c2) <=> (f3(c1, c1) = c4)),
% 29.24/19.48 inference(transitivity,[status(thm)],[22383, 22160])).
% 29.24/19.48 tff(22389,plain,
% 29.24/19.48 ((~(f10(c2) = c2)) <=> (~(f3(c1, c1) = c4))),
% 29.24/19.48 inference(monotonicity,[status(thm)],[22388])).
% 29.24/19.48 tff(22390,plain,
% 29.24/19.48 (~(f3(c1, c1) = c4)),
% 29.24/19.48 inference(modus_ponens,[status(thm)],[89, 22389])).
% 29.24/19.48 tff(22391,plain,
% 29.24/19.48 ($false),
% 29.24/19.48 inference(unit_resolution,[status(thm)],[22390, 22387])).
% 29.24/19.48 tff(22392,plain,((f10(c2) = c3) | (~(f8(f7(f4(c4))) = c2)) | (f10(c2) = c2) | (~(f7(c1) = c2)) | (~(f4(c4) = c1)) | (f10(c2) = c4) | big_f(f10(c2), f10(c2)) | (~big_f(c1, c2)) | (~big_f(c2, f10(c2))) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 29.24/19.48 tff(22393,plain,
% 29.24/19.48 (f10(c2) = c3),
% 29.24/19.48 inference(unit_resolution,[status(thm)],[22392, 15519, 89, 347, 11752, 22154, 20783, 2865, 12291, 121])).
% 29.24/19.48 tff(22394,plain,
% 29.24/19.48 (c3 = f10(c2)),
% 29.24/19.48 inference(symmetry,[status(thm)],[22393])).
% 29.24/19.48 tff(22395,plain,
% 29.24/19.48 ((c2 = c3) <=> (c2 = f10(c2))),
% 29.24/19.48 inference(monotonicity,[status(thm)],[22394])).
% 29.24/19.48 tff(22396,plain,
% 29.24/19.48 ((c2 = c3) <=> (f10(c2) = c2)),
% 29.24/19.48 inference(transitivity,[status(thm)],[22395, 4987])).
% 29.24/19.48 tff(22397,plain,
% 29.24/19.48 ((f10(c2) = c2) <=> (c2 = c3)),
% 29.24/19.48 inference(symmetry,[status(thm)],[22396])).
% 29.24/19.48 tff(22398,plain,
% 29.24/19.48 ((f10(c2) = c2) <=> (f7(c1) = c3)),
% 29.24/19.48 inference(transitivity,[status(thm)],[22397, 1002])).
% 29.24/19.48 tff(22399,plain,
% 29.24/19.48 ((~(f10(c2) = c2)) <=> (~(f7(c1) = c3))),
% 29.24/19.48 inference(monotonicity,[status(thm)],[22398])).
% 29.24/19.48 tff(22400,plain,
% 29.24/19.48 (~(f7(c1) = c3)),
% 29.24/19.48 inference(modus_ponens,[status(thm)],[89, 22399])).
% 29.24/19.48 tff(22401,plain,
% 29.24/19.48 ((~(f10(c2) = c2)) <=> (~(c2 = c3))),
% 29.24/19.48 inference(monotonicity,[status(thm)],[22397])).
% 29.24/19.48 tff(22402,plain,
% 29.24/19.48 (~(c2 = c3)),
% 29.24/19.48 inference(modus_ponens,[status(thm)],[89, 22401])).
% 29.24/19.48 tff(22403,plain,
% 29.24/19.48 (big_f(c2, f10(c2)) <=> big_f(f7(c1), c1)),
% 29.24/19.48 inference(transitivity,[status(thm)],[22183, 15992])).
% 29.24/19.48 tff(22404,plain,
% 29.24/19.48 (big_f(f7(c1), c1)),
% 29.24/19.48 inference(modus_ponens,[status(thm)],[12291, 22403])).
% 29.24/19.48 tff(22405,plain,
% 29.24/19.48 ((c1 = c4) <=> (f10(c2) = c4)),
% 29.24/19.48 inference(monotonicity,[status(thm)],[12231])).
% 29.24/19.48 tff(22406,plain,
% 29.24/19.48 ((f10(c2) = c4) <=> (c1 = c4)),
% 29.24/19.48 inference(symmetry,[status(thm)],[22405])).
% 29.24/19.48 tff(22407,plain,
% 29.24/19.48 ((~(f10(c2) = c4)) <=> (~(c1 = c4))),
% 29.24/19.48 inference(monotonicity,[status(thm)],[22406])).
% 29.24/19.48 tff(22408,plain,
% 29.24/19.48 (~(c1 = c4)),
% 29.24/19.48 inference(modus_ponens,[status(thm)],[15519, 22407])).
% 29.24/19.48 tff(22409,plain,
% 29.24/19.48 ($false),
% 29.24/19.48 inference(unit_resolution,[status(thm)],[16124, 12198, 16008, 12165, 482, 16111, 15735, 347])).
% 29.24/19.48 tff(22410,plain,((f1(c2, c1) = c1) | (f7(c1) = c3) | (c1 = c4) | (~(f3(c1, c2) = c2)) | (~big_f(f7(c1), c1)) | (~(f7(c1) = c2)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 29.24/19.49 tff(22411,plain,
% 29.24/19.49 (f1(c2, c1) = c1),
% 29.24/19.49 inference(unit_resolution,[status(thm)],[22410, 16111, 22408, 12165, 22404, 347, 121])).
% 29.24/19.49 tff(22412,plain,
% 29.24/19.49 (f1(c2, f10(c2)) = f1(c2, c1)),
% 29.24/19.49 inference(monotonicity,[status(thm)],[11819])).
% 29.24/19.49 tff(22413,plain,
% 29.24/19.49 (f1(c2, f10(c2)) = f10(c2)),
% 29.24/19.49 inference(transitivity,[status(thm)],[22412, 22411, 12231])).
% 29.24/19.49 tff(22414,plain,
% 29.24/19.49 (big_f(c2, f1(c2, f10(c2))) <=> big_f(c2, f10(c2))),
% 29.24/19.49 inference(monotonicity,[status(thm)],[22413])).
% 29.24/19.49 tff(22415,plain,
% 29.24/19.49 (big_f(c2, f10(c2)) <=> big_f(c2, f1(c2, f10(c2)))),
% 29.24/19.49 inference(symmetry,[status(thm)],[22414])).
% 29.24/19.49 tff(22416,plain,
% 29.24/19.49 (big_f(c2, f1(c2, f10(c2)))),
% 29.24/19.49 inference(modus_ponens,[status(thm)],[12291, 22415])).
% 29.24/19.49 tff(22417,plain,
% 29.24/19.49 (f3(f10(c2), c2) = f3(c1, c2)),
% 29.24/19.49 inference(monotonicity,[status(thm)],[11819])).
% 29.24/19.49 tff(22418,plain,
% 29.24/19.49 ((f3(f10(c2), c2) = c2) <=> (f3(c1, c2) = c2)),
% 29.24/19.49 inference(monotonicity,[status(thm)],[22417])).
% 29.24/19.49 tff(22419,plain,
% 29.24/19.49 ((f3(c1, c2) = c2) <=> (f3(f10(c2), c2) = c2)),
% 29.24/19.49 inference(symmetry,[status(thm)],[22418])).
% 29.24/19.49 tff(22420,plain,
% 29.24/19.49 (f3(f10(c2), c2) = c2),
% 29.24/19.49 inference(modus_ponens,[status(thm)],[16111, 22419])).
% 29.24/19.49 tff(22421,plain,
% 29.24/19.49 (big_f(f3(f10(c2), c2), f10(c2)) <=> big_f(f3(c1, c2), f10(f7(c1)))),
% 29.24/19.49 inference(monotonicity,[status(thm)],[22417, 22218])).
% 29.24/19.49 tff(22422,plain,
% 29.24/19.49 (big_f(f3(c1, c2), f10(f7(c1))) <=> big_f(f3(f10(c2), c2), f10(c2))),
% 29.24/19.49 inference(symmetry,[status(thm)],[22421])).
% 29.24/19.49 tff(22423,plain,
% 29.24/19.49 (big_f(f3(c1, c2), f10(f7(c1))) <=> big_f(c2, f10(c2))),
% 29.24/19.49 inference(monotonicity,[status(thm)],[16111, 22217])).
% 29.24/19.49 tff(22424,plain,
% 29.24/19.49 (big_f(c2, f10(c2)) <=> big_f(f3(c1, c2), f10(f7(c1)))),
% 29.24/19.49 inference(symmetry,[status(thm)],[22423])).
% 29.24/19.49 tff(22425,plain,
% 29.24/19.49 (big_f(c2, f10(c2)) <=> big_f(f3(f10(c2), c2), f10(c2))),
% 29.24/19.49 inference(transitivity,[status(thm)],[22424, 22422])).
% 29.24/19.49 tff(22426,plain,
% 29.24/19.49 (big_f(f3(f10(c2), c2), f10(c2))),
% 29.24/19.49 inference(modus_ponens,[status(thm)],[12291, 22425])).
% 29.24/19.49 tff(22427,plain,
% 29.24/19.49 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (f10(c2) = c4) | (~(f3(f10(c2), c2) = c2)) | (~big_f(f3(f10(c2), c2), f10(c2))) | (~(f1(c2, f10(c2)) = f10(c2))) | (~big_f(c2, f1(c2, f10(c2)))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (f10(c2) = c4) | (~(f3(f10(c2), c2) = c2)) | (~big_f(f3(f10(c2), c2), f10(c2))) | (~(f1(c2, f10(c2)) = f10(c2))) | (~big_f(c2, f1(c2, f10(c2)))))),
% 29.24/19.49 inference(rewrite,[status(thm)],[])).
% 29.24/19.49 tff(22428,plain,
% 29.24/19.49 (((f10(c2) = c4) | (c2 = c3) | (~(f3(f10(c2), c2) = c2)) | (~big_f(f3(f10(c2), c2), f10(c2))) | (~(f1(c2, f10(c2)) = f10(c2))) | (~big_f(c2, f1(c2, f10(c2))))) <=> ((c2 = c3) | (f10(c2) = c4) | (~(f3(f10(c2), c2) = c2)) | (~big_f(f3(f10(c2), c2), f10(c2))) | (~(f1(c2, f10(c2)) = f10(c2))) | (~big_f(c2, f1(c2, f10(c2)))))),
% 29.24/19.49 inference(rewrite,[status(thm)],[])).
% 29.24/19.49 tff(22429,plain,
% 29.24/19.49 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f10(c2) = c4) | (c2 = c3) | (~(f3(f10(c2), c2) = c2)) | (~big_f(f3(f10(c2), c2), f10(c2))) | (~(f1(c2, f10(c2)) = f10(c2))) | (~big_f(c2, f1(c2, f10(c2)))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (f10(c2) = c4) | (~(f3(f10(c2), c2) = c2)) | (~big_f(f3(f10(c2), c2), f10(c2))) | (~(f1(c2, f10(c2)) = f10(c2))) | (~big_f(c2, f1(c2, f10(c2))))))),
% 29.24/19.49 inference(monotonicity,[status(thm)],[22428])).
% 29.24/19.49 tff(22430,plain,
% 29.24/19.49 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f10(c2) = c4) | (c2 = c3) | (~(f3(f10(c2), c2) = c2)) | (~big_f(f3(f10(c2), c2), f10(c2))) | (~(f1(c2, f10(c2)) = f10(c2))) | (~big_f(c2, f1(c2, f10(c2)))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (f10(c2) = c4) | (~(f3(f10(c2), c2) = c2)) | (~big_f(f3(f10(c2), c2), f10(c2))) | (~(f1(c2, f10(c2)) = f10(c2))) | (~big_f(c2, f1(c2, f10(c2)))))),
% 29.24/19.49 inference(transitivity,[status(thm)],[22429, 22427])).
% 29.24/19.49 tff(22431,plain,
% 29.24/19.49 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f10(c2) = c4) | (c2 = c3) | (~(f3(f10(c2), c2) = c2)) | (~big_f(f3(f10(c2), c2), f10(c2))) | (~(f1(c2, f10(c2)) = f10(c2))) | (~big_f(c2, f1(c2, f10(c2)))))),
% 29.24/19.49 inference(quant_inst,[status(thm)],[])).
% 29.24/19.49 tff(22432,plain,
% 29.24/19.49 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (f10(c2) = c4) | (~(f3(f10(c2), c2) = c2)) | (~big_f(f3(f10(c2), c2), f10(c2))) | (~(f1(c2, f10(c2)) = f10(c2))) | (~big_f(c2, f1(c2, f10(c2))))),
% 29.24/19.49 inference(modus_ponens,[status(thm)],[22431, 22430])).
% 29.24/19.49 tff(22433,plain,
% 29.24/19.49 ((~(f1(c2, f10(c2)) = f10(c2))) | (~big_f(c2, f1(c2, f10(c2))))),
% 29.24/19.49 inference(unit_resolution,[status(thm)],[22432, 933, 377, 15519, 22426, 22420])).
% 29.24/19.49 tff(22434,plain,
% 29.24/19.49 ($false),
% 29.24/19.49 inference(unit_resolution,[status(thm)],[22433, 22416, 22413])).
% 29.24/19.49 tff(22435,plain,((~(f3(c1, c2) = c2)) | (c2 = c3) | (f10(c2) = c4) | (~big_f(c2, f10(c2))) | (~(f10(c2) = c1)) | (f7(c1) = c3) | (~(f7(c1) = c2)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 29.24/19.49 tff(22436,plain,
% 29.24/19.49 (~(f3(c1, c2) = c2)),
% 29.24/19.49 inference(unit_resolution,[status(thm)],[22435, 22402, 15519, 12291, 94, 22400, 347, 121])).
% 29.24/19.49 tff(22437,plain,
% 29.24/19.49 (big_f(f3(c1, c2), f10(c2)) <=> big_f(f3(c1, c2), f10(f7(c1)))),
% 29.24/19.49 inference(monotonicity,[status(thm)],[22218])).
% 29.24/19.49 tff(22438,plain,
% 29.24/19.49 (big_f(f3(c1, c2), f10(f7(c1))) <=> big_f(f3(c1, c2), f10(c2))),
% 29.24/19.49 inference(symmetry,[status(thm)],[22437])).
% 29.24/19.49 tff(22439,plain,
% 29.24/19.49 (f10(f7(c1)) = c1),
% 29.24/19.49 inference(transitivity,[status(thm)],[22217, 94])).
% 29.24/19.49 tff(22440,plain,
% 29.24/19.49 (big_f(f3(c1, c2), f10(f7(c1))) <=> big_f(f3(c1, c2), c1)),
% 29.24/19.49 inference(monotonicity,[status(thm)],[22439])).
% 29.24/19.49 tff(22441,plain,
% 29.24/19.49 (big_f(f3(c1, c2), c1) <=> big_f(f3(c1, c2), f10(f7(c1)))),
% 29.24/19.49 inference(symmetry,[status(thm)],[22440])).
% 29.24/19.49 tff(22442,assumption,(big_f(f3(c1, c2), c1)), introduced(assumption)).
% 29.24/19.49 tff(22443,plain,
% 29.24/19.49 (big_f(f3(c1, c2), f10(f7(c1)))),
% 29.24/19.49 inference(modus_ponens,[status(thm)],[22442, 22441])).
% 29.24/19.49 tff(22444,plain,
% 29.24/19.49 (big_f(f3(c1, c2), f10(c2))),
% 29.24/19.49 inference(modus_ponens,[status(thm)],[22443, 22438])).
% 29.24/19.49 tff(22445,plain,
% 29.24/19.49 (f8(c2) = c2),
% 29.24/19.49 inference(transitivity,[status(thm)],[16246, 13856])).
% 29.24/19.49 tff(22446,plain,
% 29.24/19.49 ((f3(c1, c2) = f8(c2)) <=> (f3(c1, c2) = c2)),
% 29.24/19.49 inference(monotonicity,[status(thm)],[22445])).
% 29.24/19.49 tff(22447,plain,
% 29.24/19.49 ((f3(c1, c2) = c2) <=> (f3(c1, c2) = f8(c2))),
% 29.24/19.49 inference(symmetry,[status(thm)],[22446])).
% 29.24/19.49 tff(22448,plain,
% 29.24/19.49 ((~(f3(c1, c2) = c2)) <=> (~(f3(c1, c2) = f8(c2)))),
% 29.24/19.49 inference(monotonicity,[status(thm)],[22447])).
% 29.24/19.49 tff(22449,plain,
% 29.24/19.49 (~(f3(c1, c2) = f8(c2))),
% 29.24/19.49 inference(modus_ponens,[status(thm)],[12777, 22448])).
% 29.24/19.49 tff(22450,plain,
% 29.24/19.49 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f3(c1, c2) = f8(c2)) | (~big_f(f3(c1, c2), f10(c2))) | (f7(f10(c2)) = f10(c2)) | (~big_f(f7(f10(c2)), f10(c2))) | (f10(c2) = f5(f10(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (f3(c1, c2) = f8(c2)) | (~big_f(f3(c1, c2), f10(c2))) | (f7(f10(c2)) = f10(c2)) | (~big_f(f7(f10(c2)), f10(c2))) | (f10(c2) = f5(f10(c2))))),
% 29.24/19.49 inference(rewrite,[status(thm)],[])).
% 29.24/19.49 tff(22451,plain,
% 29.24/19.49 (((f10(c2) = c2) | (f3(c1, c2) = f8(c2)) | (~big_f(f3(c1, c2), f10(c2))) | (f7(f10(c2)) = f10(c2)) | (f10(c2) = f5(f10(c2))) | (~big_f(f7(f10(c2)), f10(c2)))) <=> ((f10(c2) = c2) | (f3(c1, c2) = f8(c2)) | (~big_f(f3(c1, c2), f10(c2))) | (f7(f10(c2)) = f10(c2)) | (~big_f(f7(f10(c2)), f10(c2))) | (f10(c2) = f5(f10(c2))))),
% 29.24/19.49 inference(rewrite,[status(thm)],[])).
% 29.24/19.49 tff(22452,plain,
% 29.24/19.49 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f3(c1, c2) = f8(c2)) | (~big_f(f3(c1, c2), f10(c2))) | (f7(f10(c2)) = f10(c2)) | (f10(c2) = f5(f10(c2))) | (~big_f(f7(f10(c2)), f10(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f3(c1, c2) = f8(c2)) | (~big_f(f3(c1, c2), f10(c2))) | (f7(f10(c2)) = f10(c2)) | (~big_f(f7(f10(c2)), f10(c2))) | (f10(c2) = f5(f10(c2)))))),
% 29.24/19.49 inference(monotonicity,[status(thm)],[22451])).
% 29.24/19.49 tff(22453,plain,
% 29.24/19.49 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f3(c1, c2) = f8(c2)) | (~big_f(f3(c1, c2), f10(c2))) | (f7(f10(c2)) = f10(c2)) | (f10(c2) = f5(f10(c2))) | (~big_f(f7(f10(c2)), f10(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (f3(c1, c2) = f8(c2)) | (~big_f(f3(c1, c2), f10(c2))) | (f7(f10(c2)) = f10(c2)) | (~big_f(f7(f10(c2)), f10(c2))) | (f10(c2) = f5(f10(c2))))),
% 29.24/19.49 inference(transitivity,[status(thm)],[22452, 22450])).
% 29.24/19.49 tff(22454,plain,
% 29.24/19.49 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f3(c1, c2) = f8(c2)) | (~big_f(f3(c1, c2), f10(c2))) | (f7(f10(c2)) = f10(c2)) | (f10(c2) = f5(f10(c2))) | (~big_f(f7(f10(c2)), f10(c2))))),
% 29.24/19.49 inference(quant_inst,[status(thm)],[])).
% 29.24/19.49 tff(22455,plain,
% 29.24/19.49 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (f3(c1, c2) = f8(c2)) | (~big_f(f3(c1, c2), f10(c2))) | (f7(f10(c2)) = f10(c2)) | (~big_f(f7(f10(c2)), f10(c2))) | (f10(c2) = f5(f10(c2)))),
% 29.24/19.49 inference(modus_ponens,[status(thm)],[22454, 22453])).
% 29.24/19.49 tff(22456,plain,
% 29.24/19.49 ((f3(c1, c2) = f8(c2)) | (~big_f(f3(c1, c2), f10(c2))) | (f10(c2) = f5(f10(c2)))),
% 29.24/19.49 inference(unit_resolution,[status(thm)],[22455, 1659, 89, 21889, 21708])).
% 29.24/19.49 tff(22457,plain,
% 29.24/19.49 (f10(c2) = f5(f10(c2))),
% 29.24/19.49 inference(unit_resolution,[status(thm)],[22456, 22449, 22444])).
% 29.24/19.49 tff(22458,plain,
% 29.24/19.49 (~(big_f(c1, c1) <=> big_f(f3(c1, c2), c1))),
% 29.24/19.49 inference(unit_resolution,[status(thm)],[13186, 22442, 66])).
% 29.24/19.49 tff(22459,plain,
% 29.24/19.49 (~(c1 = f3(c1, c2))),
% 29.24/19.49 inference(unit_resolution,[status(thm)],[13192, 22458])).
% 29.24/19.49 tff(22460,plain,
% 29.24/19.49 (f5(c1) = f5(f10(c2))),
% 29.24/19.49 inference(monotonicity,[status(thm)],[12231])).
% 29.24/19.49 tff(22461,plain,
% 29.24/19.49 (f5(f10(c2)) = f5(c1)),
% 29.24/19.49 inference(symmetry,[status(thm)],[22460])).
% 29.24/19.49 tff(22462,plain,
% 29.24/19.49 (c1 = f5(c1)),
% 29.24/19.49 inference(transitivity,[status(thm)],[12231, 13762, 22461])).
% 29.24/19.49 tff(22463,plain,
% 29.24/19.49 (f6(c2, c1) = f6(f7(c2), f5(c1))),
% 29.24/19.49 inference(monotonicity,[status(thm)],[82, 22462])).
% 29.24/19.49 tff(22464,plain,
% 29.24/19.49 (c3 = f10(c2)),
% 29.24/19.49 inference(symmetry,[status(thm)],[21966])).
% 29.24/19.49 tff(22465,plain,
% 29.24/19.49 (c3 = c1),
% 29.24/19.49 inference(transitivity,[status(thm)],[22464, 11819])).
% 29.24/19.49 tff(22466,plain,
% 29.24/19.49 (f6(f7(c2), c3) = f6(c2, c1)),
% 29.24/19.49 inference(monotonicity,[status(thm)],[77, 22465])).
% 29.24/19.49 tff(22467,plain,
% 29.24/19.49 (f6(f7(c2), c3) = c1),
% 29.24/19.49 inference(transitivity,[status(thm)],[22466, 22463, 2947])).
% 29.24/19.49 tff(22468,plain,
% 29.24/19.49 (f3(f6(f7(c2), c3), c2) = f3(c1, c2)),
% 29.24/19.49 inference(monotonicity,[status(thm)],[22467])).
% 29.24/19.49 tff(22469,plain,
% 29.24/19.49 ((f3(f6(f7(c2), c3), c2) = c2) <=> (f3(c1, c2) = c2)),
% 29.24/19.49 inference(monotonicity,[status(thm)],[22468])).
% 29.24/19.49 tff(22470,plain,
% 29.24/19.49 ((f3(c1, c2) = c2) <=> (f3(f6(f7(c2), c3), c2) = c2)),
% 29.24/19.49 inference(symmetry,[status(thm)],[22469])).
% 29.24/19.49 tff(22471,plain,
% 29.24/19.49 ((~(f3(c1, c2) = c2)) <=> (~(f3(f6(f7(c2), c3), c2) = c2))),
% 29.24/19.49 inference(monotonicity,[status(thm)],[22470])).
% 29.24/19.49 tff(22472,plain,
% 29.24/19.49 (~(f3(f6(f7(c2), c3), c2) = c2)),
% 29.24/19.49 inference(modus_ponens,[status(thm)],[12777, 22471])).
% 29.24/19.49 tff(22473,plain,
% 29.24/19.49 ((c1 = f3(f6(f7(c2), c3), c2)) <=> (f3(f6(f7(c2), c3), c2) = c1)),
% 29.24/19.49 inference(commutativity,[status(thm)],[])).
% 29.24/19.49 tff(22474,plain,
% 29.24/19.49 (f3(c1, c2) = f3(f6(f7(c2), c3), c2)),
% 29.24/19.49 inference(symmetry,[status(thm)],[22468])).
% 29.24/19.49 tff(22475,plain,
% 29.24/19.49 ((c1 = f3(c1, c2)) <=> (c1 = f3(f6(f7(c2), c3), c2))),
% 29.24/19.49 inference(monotonicity,[status(thm)],[22474])).
% 29.24/19.49 tff(22476,plain,
% 29.24/19.49 ((c1 = f3(c1, c2)) <=> (f3(f6(f7(c2), c3), c2) = c1)),
% 29.24/19.49 inference(transitivity,[status(thm)],[22475, 22473])).
% 29.24/19.49 tff(22477,plain,
% 29.24/19.49 ((~(c1 = f3(c1, c2))) <=> (~(f3(f6(f7(c2), c3), c2) = c1))),
% 29.24/19.49 inference(monotonicity,[status(thm)],[22476])).
% 29.24/19.49 tff(22478,plain,
% 29.24/19.49 (~(f3(f6(f7(c2), c3), c2) = c1)),
% 29.24/19.49 inference(modus_ponens,[status(thm)],[16041, 22477])).
% 29.24/19.49 tff(22479,plain,
% 29.24/19.49 ($false),
% 29.24/19.49 inference(unit_resolution,[status(thm)],[6749, 22478, 22472])).
% 29.24/19.49 tff(22480,plain,((~(f6(f7(c2), f5(c1)) = c1)) | (c1 = f3(c1, c2)) | (~(f10(c2) = c1)) | (~(f10(c2) = f5(f10(c2)))) | (~(f10(c2) = c3)) | (~(f7(c2) = c2)) | (f3(c1, c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 29.24/19.49 tff(22481,plain,
% 29.24/19.49 (~(f6(f7(c2), f5(c1)) = c1)),
% 29.24/19.49 inference(unit_resolution,[status(thm)],[22480, 22459, 94, 22457, 21966, 77, 12777])).
% 29.24/19.49 tff(22482,plain,
% 29.24/19.49 (f6(f7(c2), f5(c1)) = c2),
% 29.24/19.49 inference(unit_resolution,[status(thm)],[2978, 22481])).
% 29.24/19.49 tff(22483,plain,
% 29.24/19.49 (c1 = f5(c1)),
% 29.24/19.49 inference(transitivity,[status(thm)],[99, 22457, 13761])).
% 29.24/19.49 tff(22484,plain,
% 29.24/19.49 (f6(c2, c1) = f6(f7(c2), f5(c1))),
% 29.24/19.49 inference(monotonicity,[status(thm)],[82, 22483])).
% 29.24/19.49 tff(22485,plain,
% 29.24/19.49 (f6(c2, f10(c2)) = c2),
% 29.24/19.49 inference(transitivity,[status(thm)],[13711, 22484, 22482])).
% 29.24/19.49 tff(22486,plain,
% 29.24/19.49 ((f6(c2, f10(c2)) = f10(c2)) <=> (c2 = f10(c2))),
% 29.24/19.49 inference(monotonicity,[status(thm)],[22485])).
% 29.24/19.49 tff(22487,plain,
% 29.24/19.49 ((f6(c2, f10(c2)) = f10(c2)) <=> (f10(c2) = c2)),
% 29.24/19.49 inference(transitivity,[status(thm)],[22486, 4987])).
% 29.24/19.49 tff(22488,plain,
% 29.24/19.49 ((f10(c2) = c2) <=> (f6(c2, f10(c2)) = f10(c2))),
% 29.24/19.49 inference(symmetry,[status(thm)],[22487])).
% 29.24/19.49 tff(22489,plain,
% 29.24/19.49 ((~(f10(c2) = c2)) <=> (~(f6(c2, f10(c2)) = f10(c2)))),
% 29.24/19.49 inference(monotonicity,[status(thm)],[22488])).
% 29.24/19.49 tff(22490,plain,
% 29.24/19.49 (~(f6(c2, f10(c2)) = f10(c2))),
% 29.24/19.49 inference(modus_ponens,[status(thm)],[89, 22489])).
% 29.24/19.49 tff(22491,plain,
% 29.24/19.49 (big_f(f7(c2), f6(c2, f10(c2))) <=> big_f(c2, c2)),
% 29.24/19.49 inference(monotonicity,[status(thm)],[77, 22485])).
% 29.24/19.49 tff(22492,plain,
% 29.24/19.49 (big_f(c2, c2) <=> big_f(f7(c2), f6(c2, f10(c2)))),
% 29.24/19.49 inference(symmetry,[status(thm)],[22491])).
% 29.24/19.49 tff(22493,plain,
% 29.24/19.49 ((~big_f(c2, c2)) <=> (~big_f(f7(c2), f6(c2, f10(c2))))),
% 29.24/19.49 inference(monotonicity,[status(thm)],[22492])).
% 29.24/19.49 tff(22494,plain,
% 29.24/19.49 (~big_f(f7(c2), f6(c2, f10(c2)))),
% 29.24/19.49 inference(modus_ponens,[status(thm)],[121, 22493])).
% 29.24/19.49 tff(22495,plain,
% 29.24/19.49 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (~(f7(c2) = c2)) | (f3(c1, c2) = f8(c2)) | (~big_f(f3(c1, c2), f10(c2))) | (f6(c2, f10(c2)) = f10(c2)) | big_f(f7(c2), f6(c2, f10(c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (f3(c1, c2) = f8(c2)) | (~big_f(f3(c1, c2), f10(c2))) | (f6(c2, f10(c2)) = f10(c2)) | big_f(f7(c2), f6(c2, f10(c2))))),
% 29.24/19.49 inference(rewrite,[status(thm)],[])).
% 29.24/19.49 tff(22496,plain,
% 29.24/19.49 (((f10(c2) = c2) | (f3(c1, c2) = f8(c2)) | (~big_f(f3(c1, c2), f10(c2))) | (~(f7(c2) = c2)) | (f6(c2, f10(c2)) = f10(c2)) | big_f(f7(c2), f6(c2, f10(c2)))) <=> ((f10(c2) = c2) | (~(f7(c2) = c2)) | (f3(c1, c2) = f8(c2)) | (~big_f(f3(c1, c2), f10(c2))) | (f6(c2, f10(c2)) = f10(c2)) | big_f(f7(c2), f6(c2, f10(c2))))),
% 29.24/19.49 inference(rewrite,[status(thm)],[])).
% 29.24/19.49 tff(22497,plain,
% 29.24/19.49 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (f3(c1, c2) = f8(c2)) | (~big_f(f3(c1, c2), f10(c2))) | (~(f7(c2) = c2)) | (f6(c2, f10(c2)) = f10(c2)) | big_f(f7(c2), f6(c2, f10(c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (~(f7(c2) = c2)) | (f3(c1, c2) = f8(c2)) | (~big_f(f3(c1, c2), f10(c2))) | (f6(c2, f10(c2)) = f10(c2)) | big_f(f7(c2), f6(c2, f10(c2)))))),
% 29.24/19.49 inference(monotonicity,[status(thm)],[22496])).
% 29.24/19.49 tff(22498,plain,
% 29.24/19.49 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (f3(c1, c2) = f8(c2)) | (~big_f(f3(c1, c2), f10(c2))) | (~(f7(c2) = c2)) | (f6(c2, f10(c2)) = f10(c2)) | big_f(f7(c2), f6(c2, f10(c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (f3(c1, c2) = f8(c2)) | (~big_f(f3(c1, c2), f10(c2))) | (f6(c2, f10(c2)) = f10(c2)) | big_f(f7(c2), f6(c2, f10(c2))))),
% 29.24/19.49 inference(transitivity,[status(thm)],[22497, 22495])).
% 29.24/19.49 tff(22499,plain,
% 29.24/19.49 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (f3(c1, c2) = f8(c2)) | (~big_f(f3(c1, c2), f10(c2))) | (~(f7(c2) = c2)) | (f6(c2, f10(c2)) = f10(c2)) | big_f(f7(c2), f6(c2, f10(c2))))),
% 29.24/19.49 inference(quant_inst,[status(thm)],[])).
% 29.24/19.49 tff(22500,plain,
% 29.24/19.49 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (f3(c1, c2) = f8(c2)) | (~big_f(f3(c1, c2), f10(c2))) | (f6(c2, f10(c2)) = f10(c2)) | big_f(f7(c2), f6(c2, f10(c2)))),
% 29.24/19.49 inference(modus_ponens,[status(thm)],[22499, 22498])).
% 29.24/19.49 tff(22501,plain,
% 29.24/19.49 ((f6(c2, f10(c2)) = f10(c2)) | big_f(f7(c2), f6(c2, f10(c2)))),
% 29.24/19.49 inference(unit_resolution,[status(thm)],[22500, 2662, 89, 77, 22449, 22444])).
% 29.24/19.49 tff(22502,plain,
% 29.24/19.49 ($false),
% 29.24/19.49 inference(unit_resolution,[status(thm)],[22501, 22494, 22490])).
% 29.24/19.49 tff(22503,plain,((~big_f(f3(c1, c2), c1)) | (f10(c2) = c2) | (~(f7(c2) = c2)) | big_f(c2, c2) | (~(f10(c2) = c3)) | (f3(c1, c2) = c2) | (~big_f(f7(f10(c2)), f10(c2))) | (~(f7(c1) = c2)) | (~(f8(f7(f4(c4))) = c2)) | (~(f4(c4) = c1)) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 29.24/19.49 tff(22504,plain,
% 29.24/19.49 (~big_f(f3(c1, c2), c1)),
% 29.24/19.49 inference(unit_resolution,[status(thm)],[22503, 22393, 77, 121, 89, 22436, 22121, 347, 22154, 11752, 22118])).
% 29.24/19.49 tff(22505,plain,
% 29.24/19.49 (~big_f(f3(c1, f7(c1)), c1)),
% 29.24/19.49 inference(modus_ponens,[status(thm)],[22504, 22117])).
% 29.24/19.49 tff(22506,plain,
% 29.24/19.49 (big_f(c2, f10(c2)) <=> big_f(f7(c1), c1)),
% 29.24/19.49 inference(transitivity,[status(thm)],[15253, 15992])).
% 29.24/19.49 tff(22507,plain,
% 29.24/19.49 (big_f(f7(c1), c1)),
% 29.24/19.49 inference(modus_ponens,[status(thm)],[12291, 22506])).
% 29.24/19.49 tff(22508,plain,
% 29.24/19.49 (~(f3(c1, f7(c1)) = f7(c1))),
% 29.24/19.49 inference(modus_ponens,[status(thm)],[22436, 20628])).
% 29.24/19.49 tff(22509,plain,
% 29.24/19.49 (f1(c2, c1) = f10(c2)),
% 29.24/19.49 inference(transitivity,[status(thm)],[11485, 12231])).
% 29.24/19.49 tff(22510,plain,
% 29.24/19.49 (big_f(c2, f1(c2, c1)) <=> big_f(c2, f10(c2))),
% 29.24/19.49 inference(monotonicity,[status(thm)],[22509])).
% 29.24/19.49 tff(22511,plain,
% 29.24/19.49 (big_f(c2, f10(c2)) <=> big_f(c2, f1(c2, c1))),
% 29.24/19.49 inference(symmetry,[status(thm)],[22510])).
% 29.24/19.49 tff(22512,plain,
% 29.24/19.49 (big_f(c2, f1(c2, c1))),
% 29.24/19.49 inference(modus_ponens,[status(thm)],[12291, 22511])).
% 29.24/19.49 tff(22513,plain,
% 29.24/19.49 (~big_f(c2, f1(c2, c1))),
% 29.24/19.49 inference(unit_resolution,[status(thm)],[16151, 11485, 347, 377, 482, 13164, 22404])).
% 29.24/19.49 tff(22514,plain,
% 29.24/19.49 ($false),
% 29.24/19.49 inference(unit_resolution,[status(thm)],[22513, 22512])).
% 29.24/19.49 tff(22515,plain,((~(f1(c2, c1) = c1)) | (~big_f(c2, f10(c2))) | (~(f10(c2) = c1)) | (~(f7(c1) = c2)) | (c2 = c3) | (c1 = c4) | big_f(f3(c1, c2), c1)), inference(lemma,lemma(discharge,[]))).
% 29.24/19.49 tff(22516,plain,
% 29.24/19.49 (~(f1(c2, c1) = c1)),
% 29.24/19.49 inference(unit_resolution,[status(thm)],[22515, 22504, 94, 347, 22402, 22182, 12291])).
% 29.24/19.49 tff(22517,plain,
% 29.24/19.49 (f1(c2, c1) = c2),
% 29.24/19.49 inference(unit_resolution,[status(thm)],[10113, 22516])).
% 29.24/19.49 tff(22518,plain,
% 29.24/19.49 (~big_f(f7(c1), f1(f7(c1), c1))),
% 29.24/19.49 inference(unit_resolution,[status(thm)],[12197, 22517, 121, 347])).
% 29.24/19.49 tff(22519,assumption,(~big_f(f3(c1, f7(c1)), c1)), introduced(assumption)).
% 29.24/19.49 tff(22520,assumption,(~(f3(c1, f7(c1)) = f7(c1))), introduced(assumption)).
% 29.24/19.49 tff(22521,plain,
% 29.24/19.49 ($false),
% 29.24/19.49 inference(unit_resolution,[status(thm)],[20566, 1014, 482, 12165, 12203, 12204, 22520, 22519])).
% 29.24/19.49 tff(22522,plain,((f1(f7(c1), c1) = c1) | (c1 = c4) | (f7(c1) = c3) | big_f(f7(c1), f1(f7(c1), c1)) | (f3(c1, f7(c1)) = f7(c1)) | big_f(f3(c1, f7(c1)), c1)), inference(lemma,lemma(discharge,[]))).
% 29.24/19.49 tff(22523,plain,
% 29.24/19.49 (f1(f7(c1), c1) = c1),
% 29.24/19.49 inference(unit_resolution,[status(thm)],[22522, 12204, 12165, 482, 22520, 22519])).
% 29.24/19.49 tff(22524,plain,
% 29.24/19.49 (big_f(f7(c1), f1(f7(c1), c1)) <=> big_f(f7(c1), c1)),
% 29.24/19.49 inference(monotonicity,[status(thm)],[22523])).
% 29.24/19.49 tff(22525,plain,
% 29.24/19.49 (big_f(f7(c1), c1) <=> big_f(f7(c1), f1(f7(c1), c1))),
% 29.24/19.49 inference(symmetry,[status(thm)],[22524])).
% 29.24/19.49 tff(22526,plain,
% 29.24/19.49 (big_f(f7(c1), f1(f7(c1), c1))),
% 29.24/19.49 inference(modus_ponens,[status(thm)],[15735, 22525])).
% 29.24/19.49 tff(22527,plain,
% 29.24/19.49 ($false),
% 29.24/19.49 inference(unit_resolution,[status(thm)],[12204, 22526])).
% 29.24/19.49 tff(22528,plain,(big_f(f7(c1), f1(f7(c1), c1)) | (~big_f(f7(c1), c1)) | (f7(c1) = c3) | (c1 = c4) | (f3(c1, f7(c1)) = f7(c1)) | big_f(f3(c1, f7(c1)), c1)), inference(lemma,lemma(discharge,[]))).
% 29.24/19.49 tff(22529,plain,
% 29.24/19.49 (big_f(f3(c1, f7(c1)), c1)),
% 29.24/19.49 inference(unit_resolution,[status(thm)],[22528, 22518, 22400, 22182, 22508, 22507])).
% 29.24/19.49 tff(22530,plain,
% 29.24/19.49 ($false),
% 29.24/19.49 inference(unit_resolution,[status(thm)],[22529, 22505])).
% 29.24/19.49 tff(22531,plain,((f10(c2) = c4) | (~(f7(c1) = c2)) | big_f(c2, c2) | (~big_f(c2, f10(c2))) | (~(f7(c2) = c2)) | (f10(c2) = c2) | (~(f4(c4) = c1)) | big_f(f10(c2), f10(c2)) | (~big_f(c1, c2))), inference(lemma,lemma(discharge,[]))).
% 29.24/19.49 tff(22532,plain,
% 29.24/19.49 (f10(c2) = c4),
% 29.24/19.49 inference(unit_resolution,[status(thm)],[22531, 20783, 121, 12291, 77, 89, 11752, 347, 2865])).
% 29.24/19.49 tff(22533,plain,
% 29.24/19.49 (c4 = f10(c2)),
% 29.24/19.49 inference(symmetry,[status(thm)],[22532])).
% 29.24/19.49 tff(22534,plain,
% 29.24/19.49 (big_f(f4(c4), c4) <=> big_f(f10(c2), f10(c2))),
% 29.24/19.49 inference(monotonicity,[status(thm)],[21123, 22533])).
% 29.24/19.49 tff(22535,plain,
% 29.24/19.49 (big_f(f10(c2), f10(c2)) <=> big_f(f4(c4), c4)),
% 29.24/19.49 inference(symmetry,[status(thm)],[22534])).
% 29.24/19.49 tff(22536,plain,
% 29.24/19.49 ((~big_f(f10(c2), f10(c2))) <=> (~big_f(f4(c4), c4))),
% 29.24/19.49 inference(monotonicity,[status(thm)],[22535])).
% 29.24/19.49 tff(22537,plain,
% 29.24/19.49 (~big_f(f4(c4), c4)),
% 29.24/19.49 inference(modus_ponens,[status(thm)],[20783, 22536])).
% 29.24/19.49 tff(22538,plain,
% 29.24/19.49 (f4(f10(c2)) = f4(c4)),
% 29.24/19.49 inference(monotonicity,[status(thm)],[22532])).
% 29.24/19.49 tff(22539,plain,
% 29.24/19.49 (f4(c4) = f4(f10(c2))),
% 29.24/19.49 inference(symmetry,[status(thm)],[22538])).
% 29.24/19.49 tff(22540,plain,
% 29.24/19.49 (f10(c2) = f4(f10(c2))),
% 29.24/19.49 inference(transitivity,[status(thm)],[94, 16651, 22539])).
% 29.24/19.49 tff(22541,plain,
% 29.24/19.49 ((f10(c2) = c3) <=> (c1 = c3)),
% 29.24/19.49 inference(monotonicity,[status(thm)],[94])).
% 29.24/19.49 tff(22542,plain,
% 29.24/19.49 ((c1 = c3) <=> (f10(c2) = c3)),
% 29.24/19.49 inference(symmetry,[status(thm)],[22541])).
% 29.24/19.49 tff(22543,plain,
% 29.24/19.49 (~(f1(c1, c2) = c1)),
% 29.24/19.49 inference(unit_resolution,[status(thm)],[21266, 15667, 20783, 15484, 21095, 89])).
% 29.24/19.49 tff(22544,plain,
% 29.24/19.49 (f1(c1, c2) = c2),
% 29.24/19.49 inference(unit_resolution,[status(thm)],[841, 22543])).
% 29.24/19.49 tff(22545,plain,
% 29.24/19.49 (c1 = c3),
% 29.24/19.50 inference(unit_resolution,[status(thm)],[21246, 22544, 2865, 379])).
% 29.24/19.50 tff(22546,plain,
% 29.24/19.50 (f10(c2) = c3),
% 29.24/19.50 inference(modus_ponens,[status(thm)],[22545, 22542])).
% 29.24/19.50 tff(22547,plain,
% 29.24/19.50 ($false),
% 29.24/19.50 inference(unit_resolution,[status(thm)],[15667, 22546])).
% 29.24/19.50 tff(22548,plain,((f10(c2) = c3) | (~big_f(c1, c2)) | big_f(f4(c4), c4) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = c4)) | (~(f10(c2) = f4(f10(c2)))) | (f10(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 29.24/19.50 tff(22549,plain,
% 29.24/19.50 (f10(c2) = c3),
% 29.24/19.50 inference(unit_resolution,[status(thm)],[22548, 22537, 2865, 20783, 22532, 22540, 89])).
% 29.24/19.50 tff(22550,plain,
% 29.24/19.50 (c3 = f10(c2)),
% 29.24/19.50 inference(symmetry,[status(thm)],[22549])).
% 29.24/19.50 tff(22551,plain,
% 29.24/19.50 ((c2 = c3) <=> (c2 = f10(c2))),
% 29.24/19.50 inference(monotonicity,[status(thm)],[22550])).
% 29.24/19.50 tff(22552,plain,
% 29.24/19.50 ((c2 = c3) <=> (f10(c2) = c2)),
% 29.24/19.50 inference(transitivity,[status(thm)],[22551, 4987])).
% 29.24/19.50 tff(22553,plain,
% 29.24/19.50 ((f10(c2) = c2) <=> (c2 = c3)),
% 29.24/19.50 inference(symmetry,[status(thm)],[22552])).
% 29.24/19.50 tff(22554,plain,
% 29.24/19.50 ((f10(c2) = c2) <=> (f7(f7(c2)) = c3)),
% 29.24/19.50 inference(transitivity,[status(thm)],[22553, 11448])).
% 29.24/19.50 tff(22555,plain,
% 29.24/19.50 ((~(f10(c2) = c2)) <=> (~(f7(f7(c2)) = c3))),
% 29.24/19.50 inference(monotonicity,[status(thm)],[22554])).
% 29.24/19.50 tff(22556,plain,
% 29.24/19.50 (~(f7(f7(c2)) = c3)),
% 29.24/19.50 inference(modus_ponens,[status(thm)],[89, 22555])).
% 29.24/19.50 tff(22557,plain,
% 29.24/19.50 (f1(f7(f7(c2)), c1) = c1),
% 29.24/19.50 inference(unit_resolution,[status(thm)],[5433, 22556, 77, 121, 22537])).
% 29.24/19.50 tff(22558,plain,
% 29.24/19.50 (f1(c2, f10(c2)) = f1(c2, c1)),
% 29.24/19.50 inference(monotonicity,[status(thm)],[94])).
% 29.24/19.50 tff(22559,plain,
% 29.24/19.50 (f1(c2, f10(c2)) = f10(c2)),
% 29.24/19.50 inference(transitivity,[status(thm)],[22558, 5422, 22557, 99])).
% 29.24/19.50 tff(22560,plain,
% 29.24/19.50 (big_f(c2, f1(c2, f10(c2))) <=> big_f(c2, f10(c2))),
% 29.24/19.50 inference(monotonicity,[status(thm)],[22559])).
% 29.24/19.50 tff(22561,plain,
% 29.24/19.50 (big_f(c2, f10(c2)) <=> big_f(c2, f1(c2, f10(c2)))),
% 29.24/19.50 inference(symmetry,[status(thm)],[22560])).
% 29.24/19.50 tff(22562,plain,
% 29.24/19.50 (big_f(c2, f1(c2, f10(c2)))),
% 29.24/19.50 inference(modus_ponens,[status(thm)],[12291, 22561])).
% 29.24/19.50 tff(22563,plain,
% 29.24/19.50 ((~(f10(c2) = c2)) <=> (~(c2 = c3))),
% 29.24/19.50 inference(monotonicity,[status(thm)],[22553])).
% 29.24/19.50 tff(22564,plain,
% 29.24/19.50 (~(c2 = c3)),
% 29.24/19.50 inference(modus_ponens,[status(thm)],[89, 22563])).
% 29.24/19.50 tff(22565,plain,
% 29.24/19.50 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f10(c2) = c4)) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2)))) | (~(f1(c2, f10(c2)) = f10(c2))) | (~big_f(c2, f1(c2, f10(c2)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(f10(c2) = c4)) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2)))) | (~(f1(c2, f10(c2)) = f10(c2))) | (~big_f(c2, f1(c2, f10(c2)))))),
% 29.24/19.50 inference(rewrite,[status(thm)],[])).
% 29.24/19.50 tff(22566,plain,
% 29.24/19.50 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(f10(c2) = c4)) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2)))) | (~(f1(c2, f10(c2)) = f10(c2))) | (~big_f(c2, f1(c2, f10(c2)))))),
% 29.24/19.50 inference(quant_inst,[status(thm)],[])).
% 29.24/19.50 tff(22567,plain,
% 29.24/19.50 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(f10(c2) = c4)) | big_f(f10(c2), f10(c2)) | (~(f10(c2) = f4(f10(c2)))) | (~(f1(c2, f10(c2)) = f10(c2))) | (~big_f(c2, f1(c2, f10(c2))))),
% 29.24/19.50 inference(modus_ponens,[status(thm)],[22566, 22565])).
% 29.24/19.50 tff(22568,plain,
% 29.24/19.50 ((~(f1(c2, f10(c2)) = f10(c2))) | (~big_f(c2, f1(c2, f10(c2))))),
% 29.24/19.50 inference(unit_resolution,[status(thm)],[22567, 447, 22564, 22532, 20783, 22540])).
% 29.24/19.50 tff(22569,plain,
% 29.24/19.50 ($false),
% 29.24/19.50 inference(unit_resolution,[status(thm)],[22568, 22562, 22559])).
% 29.24/19.50 tff(22570,plain,(big_f(f10(c2), f10(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c2) = c2)) | big_f(c2, c2) | (f10(c2) = c2) | (~big_f(c1, c2)) | (~(f4(c4) = c1)) | (~(f7(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.31/19.50 tff(22571,plain,
% 29.31/19.50 (big_f(f10(c2), f10(c2))),
% 29.31/19.50 inference(unit_resolution,[status(thm)],[22570, 22098, 21432, 121, 17538, 21808, 15706, 120])).
% 29.31/19.50 tff(22572,plain,
% 29.31/19.50 ((f10(c2) = f8(c2)) | (f10(c2) = f5(f10(c2)))),
% 29.31/19.50 inference(unit_resolution,[status(thm)],[21734, 1659, 17538, 20958, 22571, 22099])).
% 29.31/19.50 tff(22573,plain,
% 29.31/19.50 (f10(c2) = f5(f10(c2))),
% 29.31/19.50 inference(unit_resolution,[status(thm)],[22572, 22116])).
% 29.31/19.50 tff(22574,plain,
% 29.31/19.50 ((f6(c2, f10(c2)) = f10(c2)) | big_f(f7(c2), f6(c2, f10(c2)))),
% 29.31/19.50 inference(unit_resolution,[status(thm)],[13724, 2662, 89, 77, 13710, 14686])).
% 29.31/19.50 tff(22575,plain,
% 29.31/19.50 ($false),
% 29.31/19.50 inference(unit_resolution,[status(thm)],[22574, 13774, 13770])).
% 29.31/19.50 tff(22576,plain,((~(f6(f7(c2), f5(c1)) = c2)) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | big_f(c2, c2) | (~(f10(c2) = f5(f10(c2))))), inference(lemma,lemma(discharge,[]))).
% 29.31/19.50 tff(22577,plain,
% 29.31/19.50 (~(f6(f7(c2), f5(c1)) = c2)),
% 29.31/19.50 inference(unit_resolution,[status(thm)],[22576, 22116, 21432, 17538, 22571, 121, 22573])).
% 29.31/19.50 tff(22578,plain,
% 29.31/19.50 (f6(f7(c2), f5(c1)) = c1),
% 29.31/19.50 inference(unit_resolution,[status(thm)],[2978, 22577])).
% 29.31/19.50 tff(22579,plain,
% 29.31/19.50 (f5(c1) = f5(f10(c2))),
% 29.31/19.50 inference(monotonicity,[status(thm)],[17541])).
% 29.31/19.50 tff(22580,plain,
% 29.31/19.50 (f5(f10(c2)) = f5(c1)),
% 29.31/19.50 inference(symmetry,[status(thm)],[22579])).
% 29.31/19.50 tff(22581,plain,
% 29.31/19.50 (c1 = f5(c1)),
% 29.31/19.50 inference(transitivity,[status(thm)],[17541, 22573, 22580])).
% 29.31/19.50 tff(22582,plain,
% 29.31/19.50 (c2 = f7(c2)),
% 29.31/19.50 inference(symmetry,[status(thm)],[21432])).
% 29.31/19.50 tff(22583,plain,
% 29.31/19.50 (f6(c2, c1) = f6(f7(c2), f5(c1))),
% 29.31/19.50 inference(monotonicity,[status(thm)],[22582, 22581])).
% 29.31/19.50 tff(22584,plain,
% 29.31/19.50 (f6(c2, f10(c2)) = f6(c2, c1)),
% 29.31/19.50 inference(monotonicity,[status(thm)],[17539])).
% 29.31/19.50 tff(22585,plain,
% 29.31/19.50 (f6(c2, f10(c2)) = f10(c2)),
% 29.31/19.50 inference(transitivity,[status(thm)],[22584, 22583, 22578, 17541])).
% 29.31/19.50 tff(22586,plain,
% 29.31/19.50 (big_f(f7(c2), f6(c2, f10(c2))) <=> big_f(c2, f10(c2))),
% 29.31/19.50 inference(monotonicity,[status(thm)],[21432, 22585])).
% 29.31/19.50 tff(22587,plain,
% 29.31/19.50 (big_f(c2, f10(c2)) <=> big_f(f7(c2), f6(c2, f10(c2)))),
% 29.31/19.50 inference(symmetry,[status(thm)],[22586])).
% 29.31/19.50 tff(22588,plain,
% 29.31/19.50 (big_f(f7(c2), f6(c2, f10(c2)))),
% 29.31/19.50 inference(modus_ponens,[status(thm)],[22098, 22587])).
% 29.31/19.50 tff(22589,plain,
% 29.31/19.50 ((~(f6(c2, f10(c2)) = f10(c2))) | (~big_f(f7(c2), f6(c2, f10(c2))))),
% 29.31/19.50 inference(unit_resolution,[status(thm)],[13741, 2730, 17538, 21432, 22116, 22571])).
% 29.31/19.50 tff(22590,plain,
% 29.31/19.50 ($false),
% 29.31/19.50 inference(unit_resolution,[status(thm)],[22589, 22588, 22585])).
% 29.31/19.50 tff(22591,plain,(big_f(c2, c2) | (f10(c1) = c1) | (f7(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.31/19.50 tff(22592,plain,
% 29.31/19.50 (big_f(c2, c2)),
% 29.31/19.50 inference(unit_resolution,[status(thm)],[22591, 3, 115])).
% 29.31/19.50 tff(22593,plain,
% 29.31/19.50 (big_f(c2, f10(f10(c2)))),
% 29.31/19.50 inference(modus_ponens,[status(thm)],[22592, 21402])).
% 29.31/19.50 tff(22594,plain,
% 29.31/19.50 (c2 = f8(f10(c2))),
% 29.31/19.50 inference(unit_resolution,[status(thm)],[21485, 2662, 77, 11896, 21479, 3953, 2621])).
% 29.31/19.50 tff(22595,plain,
% 29.31/19.50 (f8(f10(c2)) = c2),
% 29.31/19.50 inference(symmetry,[status(thm)],[22594])).
% 29.31/19.50 tff(22596,plain,
% 29.31/19.50 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f7(c2) = c2)) | (f10(f10(c2)) = f10(c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (f10(c2) = f8(f10(c2))) | (~big_f(f10(c2), f10(f10(c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c2) = c2)) | (f10(f10(c2)) = f10(c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (f10(c2) = f8(f10(c2))) | (~big_f(f10(c2), f10(f10(c2)))))),
% 29.31/19.50 inference(rewrite,[status(thm)],[])).
% 29.31/19.50 tff(22597,plain,
% 29.31/19.50 (((f10(f10(c2)) = f10(c2)) | (f10(c2) = f8(f10(c2))) | (~big_f(f10(c2), f10(f10(c2)))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2))) <=> ((~(f7(c2) = c2)) | (f10(f10(c2)) = f10(c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (f10(c2) = f8(f10(c2))) | (~big_f(f10(c2), f10(f10(c2)))))),
% 29.31/19.50 inference(rewrite,[status(thm)],[])).
% 29.31/19.50 tff(22598,plain,
% 29.31/19.50 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f10(c2)) = f10(c2)) | (f10(c2) = f8(f10(c2))) | (~big_f(f10(c2), f10(f10(c2)))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f7(c2) = c2)) | (f10(f10(c2)) = f10(c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (f10(c2) = f8(f10(c2))) | (~big_f(f10(c2), f10(f10(c2))))))),
% 29.31/19.50 inference(monotonicity,[status(thm)],[22597])).
% 29.31/19.50 tff(22599,plain,
% 29.31/19.50 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f10(c2)) = f10(c2)) | (f10(c2) = f8(f10(c2))) | (~big_f(f10(c2), f10(f10(c2)))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c2) = c2)) | (f10(f10(c2)) = f10(c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (f10(c2) = f8(f10(c2))) | (~big_f(f10(c2), f10(f10(c2)))))),
% 29.31/19.50 inference(transitivity,[status(thm)],[22598, 22596])).
% 29.31/19.50 tff(22600,plain,
% 29.31/19.50 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f10(c2)) = f10(c2)) | (f10(c2) = f8(f10(c2))) | (~big_f(f10(c2), f10(f10(c2)))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)))),
% 29.31/19.50 inference(quant_inst,[status(thm)],[])).
% 29.31/19.50 tff(22601,plain,
% 29.31/19.50 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c2) = c2)) | (f10(f10(c2)) = f10(c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (f10(c2) = f8(f10(c2))) | (~big_f(f10(c2), f10(f10(c2))))),
% 29.31/19.50 inference(modus_ponens,[status(thm)],[22600, 22599])).
% 29.31/19.50 tff(22602,plain,
% 29.31/19.50 (f10(c2) = f8(f10(c2))),
% 29.31/19.50 inference(unit_resolution,[status(thm)],[22601, 2662, 77, 11896, 3953, 2621, 21944])).
% 29.31/19.50 tff(22603,plain,
% 29.31/19.50 (f10(c2) = c2),
% 29.31/19.50 inference(transitivity,[status(thm)],[22602, 22595])).
% 29.31/19.50 tff(22604,plain,
% 29.31/19.50 ($false),
% 29.31/19.50 inference(unit_resolution,[status(thm)],[89, 22603])).
% 29.31/19.50 tff(22605,plain,(big_f(f7(c2), f6(c2, c2)) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (f10(f10(c2)) = f10(c2)) | (~big_f(c2, f10(f10(c2)))) | (~big_f(f10(c2), f10(f10(c2)))) | (~big_f(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 29.31/19.50 tff(22606,plain,
% 29.31/19.50 (big_f(f7(c2), f6(c2, c2))),
% 29.31/19.50 inference(unit_resolution,[status(thm)],[22605, 17538, 21432, 21408, 22593, 21938, 22592])).
% 29.31/19.50 tff(22607,plain,
% 29.31/19.50 (f8(c1) = f8(f10(c2))),
% 29.31/19.50 inference(monotonicity,[status(thm)],[99])).
% 29.31/19.50 tff(22608,plain,
% 29.31/19.50 (f8(f10(c2)) = f8(c1)),
% 29.31/19.50 inference(symmetry,[status(thm)],[22607])).
% 29.31/19.50 tff(22609,plain,
% 29.31/19.50 ((c2 = f8(f10(c2))) <=> (c2 = f8(c1))),
% 29.31/19.50 inference(monotonicity,[status(thm)],[22608])).
% 29.31/19.50 tff(22610,plain,
% 29.31/19.50 ((c2 = f8(f10(c2))) <=> (f8(c1) = c2)),
% 29.31/19.50 inference(transitivity,[status(thm)],[22609, 2782])).
% 29.31/19.50 tff(22611,plain,
% 29.31/19.50 ((c2 = f8(f10(c2))) | (~(f6(c2, c2) = c2))),
% 29.31/19.50 inference(unit_resolution,[status(thm)],[21648, 2730, 77, 15308, 21479, 2707])).
% 29.31/19.50 tff(22612,plain,
% 29.31/19.50 (c2 = f8(f10(c2))),
% 29.31/19.50 inference(unit_resolution,[status(thm)],[22611, 2622])).
% 29.31/19.50 tff(22613,plain,
% 29.31/19.50 (f8(c1) = c2),
% 29.31/19.50 inference(modus_ponens,[status(thm)],[22612, 22610])).
% 29.31/19.50 tff(22614,plain,
% 29.31/19.50 (~(c2 = f8(c1))),
% 29.31/19.50 inference(unit_resolution,[status(thm)],[15317, 2622, 89, 2865, 16, 77, 2707])).
% 29.31/19.50 tff(22615,plain,
% 29.31/19.50 (~(f8(c1) = c2)),
% 29.31/19.50 inference(unit_resolution,[status(thm)],[1675, 22614])).
% 29.31/19.50 tff(22616,plain,
% 29.31/19.50 ($false),
% 29.31/19.50 inference(unit_resolution,[status(thm)],[22615, 22613])).
% 29.31/19.50 tff(22617,plain,((~(f6(c2, c2) = c2)) | (~(f7(c2) = c2)) | (~big_f(c2, f10(f10(c2)))) | (~big_f(f7(c2), f6(c2, c2))) | (f10(c2) = c2) | (~big_f(c1, c2)) | (~(f10(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.31/19.50 tff(22618,plain,
% 29.31/19.50 (~(f6(c2, c2) = c2)),
% 29.31/19.50 inference(unit_resolution,[status(thm)],[22617, 21432, 22593, 22606, 17538, 21808, 15])).
% 29.31/19.50 tff(22619,plain,
% 29.31/19.50 (~(f6(c2, f7(f4(c4))) = c2)),
% 29.31/19.50 inference(unit_resolution,[status(thm)],[17412, 22618, 120, 15706])).
% 29.31/19.50 tff(22620,plain,
% 29.31/19.50 (f6(c2, f7(f4(c4))) = c1),
% 29.31/19.50 inference(unit_resolution,[status(thm)],[6601, 22619])).
% 29.31/19.50 tff(22621,plain,
% 29.31/19.50 (f6(c2, c2) = f6(c2, f7(f4(c4)))),
% 29.31/19.50 inference(monotonicity,[status(thm)],[21818])).
% 29.31/19.50 tff(22622,plain,
% 29.31/19.50 (f6(c2, c2) = f10(c2)),
% 29.31/19.50 inference(transitivity,[status(thm)],[22621, 22620, 17541])).
% 29.31/19.50 tff(22623,plain,
% 29.31/19.50 (big_f(f7(c2), f6(c2, c2)) <=> big_f(c2, f10(c2))),
% 29.31/19.50 inference(monotonicity,[status(thm)],[21432, 22622])).
% 29.31/19.50 tff(22624,plain,
% 29.31/19.50 (big_f(f7(c2), f6(c2, c2)) <=> big_f(c2, c1)),
% 29.31/19.50 inference(transitivity,[status(thm)],[22623, 17543])).
% 29.31/19.50 tff(22625,plain,
% 29.31/19.50 (big_f(c2, c1)),
% 29.31/19.50 inference(modus_ponens,[status(thm)],[22606, 22624])).
% 29.31/19.50 tff(22626,plain,
% 29.31/19.50 (big_f(f7(c2), f6(c2, c2)) <=> big_f(f7(f10(c2)), f10(c2))),
% 29.31/19.50 inference(transitivity,[status(thm)],[22623, 21419])).
% 29.31/19.50 tff(22627,plain,
% 29.31/19.50 (big_f(f7(f10(c2)), f10(c2))),
% 29.31/19.50 inference(modus_ponens,[status(thm)],[22606, 22626])).
% 29.31/19.50 tff(22628,plain,
% 29.31/19.50 (big_f(f7(f10(c2)), c2)),
% 29.31/19.50 inference(modus_ponens,[status(thm)],[22592, 17547])).
% 29.31/19.50 tff(22629,plain,
% 29.31/19.50 (big_f(c2, f10(c2))),
% 29.31/19.50 inference(modus_ponens,[status(thm)],[22606, 22623])).
% 29.31/19.50 tff(22630,plain,
% 29.31/19.50 (c2 = f8(c2)),
% 29.31/19.50 inference(unit_resolution,[status(thm)],[21713, 22629, 17538, 20958, 22628, 22627])).
% 29.31/19.50 tff(22631,plain,
% 29.31/19.50 (f8(c2) = c2),
% 29.31/19.50 inference(symmetry,[status(thm)],[22630])).
% 29.31/19.50 tff(22632,plain,
% 29.31/19.50 ((f10(c2) = f8(c2)) <=> (f10(c2) = c2)),
% 29.31/19.50 inference(monotonicity,[status(thm)],[22631])).
% 29.31/19.50 tff(22633,plain,
% 29.31/19.50 ((f10(c2) = c2) <=> (f10(c2) = f8(c2))),
% 29.31/19.50 inference(symmetry,[status(thm)],[22632])).
% 29.31/19.50 tff(22634,plain,
% 29.31/19.50 ((~(f10(c2) = c2)) <=> (~(f10(c2) = f8(c2)))),
% 29.31/19.50 inference(monotonicity,[status(thm)],[22633])).
% 29.31/19.50 tff(22635,plain,
% 29.31/19.50 (~(f10(c2) = f8(c2))),
% 29.31/19.50 inference(modus_ponens,[status(thm)],[17538, 22634])).
% 29.31/19.50 tff(22636,plain,
% 29.31/19.50 (~big_f(f10(c2), f10(c2))),
% 29.31/19.50 inference(unit_resolution,[status(thm)],[21739, 22635, 20958, 17538, 22628, 22627])).
% 29.31/19.50 tff(22637,plain,
% 29.31/19.50 (c2 = c3),
% 29.31/19.50 inference(modus_ponens,[status(thm)],[22164, 78])).
% 29.31/19.50 tff(22638,plain,
% 29.31/19.50 (f2(c3) = f2(c2)),
% 29.31/19.50 inference(monotonicity,[status(thm)],[22164])).
% 29.31/19.50 tff(22639,plain,
% 29.31/19.50 ((f2(c3) = c1) <=> (f2(c2) = f10(c2))),
% 29.31/19.50 inference(monotonicity,[status(thm)],[22638, 99])).
% 29.31/19.50 tff(22640,plain,
% 29.31/19.50 ((f2(c3) = c1) <=> (f10(c2) = f2(c2))),
% 29.31/19.50 inference(transitivity,[status(thm)],[22639, 17600])).
% 29.31/19.50 tff(22641,plain,
% 29.31/19.50 ((f10(c2) = f2(c2)) <=> (f2(c3) = c1)),
% 29.31/19.50 inference(symmetry,[status(thm)],[22640])).
% 29.31/19.50 tff(22642,plain,
% 29.31/19.50 ((f3(f10(c2), c2) = c2) <=> (f3(c1, c2) = c2)),
% 29.31/19.50 inference(monotonicity,[status(thm)],[15408])).
% 29.31/19.50 tff(22643,plain,
% 29.31/19.50 ((f3(c1, c2) = c2) <=> (f3(f10(c2), c2) = c2)),
% 29.31/19.50 inference(symmetry,[status(thm)],[22642])).
% 29.31/19.50 tff(22644,plain,
% 29.31/19.50 (f3(c1, c2) = c2),
% 29.31/19.50 inference(unit_resolution,[status(thm)],[13195, 22182, 1345, 13152, 22118, 22164, 348])).
% 29.31/19.50 tff(22645,plain,
% 29.31/19.50 (f3(f10(c2), c2) = c2),
% 29.31/19.50 inference(modus_ponens,[status(thm)],[22644, 22643])).
% 29.31/19.50 tff(22646,plain,
% 29.31/19.50 (big_f(f3(f10(c2), c2), f10(c2)) <=> big_f(f3(c1, c2), f10(f7(c1)))),
% 29.31/19.50 inference(monotonicity,[status(thm)],[15408, 22218])).
% 29.31/19.50 tff(22647,plain,
% 29.31/19.50 (big_f(f3(c1, c2), f10(f7(c1))) <=> big_f(f3(f10(c2), c2), f10(c2))),
% 29.31/19.50 inference(symmetry,[status(thm)],[22646])).
% 29.31/19.50 tff(22648,plain,
% 29.31/19.50 (big_f(f3(c1, c2), f10(f7(c1))) <=> big_f(c2, f10(c2))),
% 29.31/19.50 inference(monotonicity,[status(thm)],[22644, 22217])).
% 29.31/19.50 tff(22649,plain,
% 29.31/19.50 (big_f(c2, f10(c2)) <=> big_f(f3(c1, c2), f10(f7(c1)))),
% 29.31/19.50 inference(symmetry,[status(thm)],[22648])).
% 29.31/19.50 tff(22650,plain,
% 29.31/19.50 (big_f(c2, f10(c2)) <=> big_f(f3(f10(c2), c2), f10(c2))),
% 29.31/19.50 inference(transitivity,[status(thm)],[22649, 22647])).
% 29.31/19.50 tff(22651,plain,
% 29.31/19.50 (big_f(f3(f10(c2), c2), f10(c2))),
% 29.31/19.50 inference(modus_ponens,[status(thm)],[12291, 22650])).
% 29.31/19.50 tff(22652,plain,
% 29.31/19.50 (f10(c2) = f2(c2)),
% 29.31/19.50 inference(unit_resolution,[status(thm)],[15420, 7051, 22637, 15519, 12291, 22651, 22645])).
% 29.31/19.50 tff(22653,plain,
% 29.31/19.50 (f2(c3) = c1),
% 29.31/19.50 inference(modus_ponens,[status(thm)],[22652, 22641])).
% 29.31/19.50 tff(22654,plain,
% 29.31/19.50 ((~(f10(c2) = c3)) <=> (~(c1 = c3))),
% 29.31/19.50 inference(monotonicity,[status(thm)],[12095])).
% 29.31/19.50 tff(22655,plain,
% 29.31/19.50 (~(c1 = c3)),
% 29.31/19.50 inference(modus_ponens,[status(thm)],[15667, 22654])).
% 29.31/19.50 tff(22656,plain,
% 29.31/19.50 (f8(c3) = f8(c2)),
% 29.31/19.50 inference(monotonicity,[status(thm)],[22164])).
% 29.31/19.50 tff(22657,plain,
% 29.31/19.50 (f8(c3) = c2),
% 29.31/19.50 inference(transitivity,[status(thm)],[22656, 13153])).
% 29.31/19.50 tff(22658,plain,
% 29.31/19.50 (f3(f10(c2), f8(c3)) = f3(c1, c2)),
% 29.31/19.50 inference(monotonicity,[status(thm)],[94, 22657])).
% 29.31/19.50 tff(22659,plain,
% 29.31/19.50 (f3(c1, f8(c3)) = f3(c1, c2)),
% 29.31/19.50 inference(transitivity,[status(thm)],[21953, 22658])).
% 29.31/19.50 tff(22660,plain,
% 29.31/19.50 ((f3(c1, f8(c3)) = c2) <=> (f3(c1, c2) = c2)),
% 29.31/19.50 inference(monotonicity,[status(thm)],[22659])).
% 29.31/19.50 tff(22661,plain,
% 29.31/19.50 ((f3(c1, c2) = c2) <=> (f3(c1, f8(c3)) = c2)),
% 29.31/19.50 inference(symmetry,[status(thm)],[22660])).
% 29.31/19.50 tff(22662,plain,
% 29.31/19.50 (f3(c1, f8(c3)) = c2),
% 29.31/19.50 inference(modus_ponens,[status(thm)],[22644, 22661])).
% 29.31/19.50 tff(22663,plain,
% 29.31/19.50 (~(f2(c3) = c1)),
% 29.31/19.50 inference(unit_resolution,[status(thm)],[22334, 22662, 20775, 20783, 347, 11752, 2865, 15667, 12291, 89, 22164, 22655, 15519])).
% 29.31/19.50 tff(22664,plain,
% 29.31/19.50 ($false),
% 29.31/19.50 inference(unit_resolution,[status(thm)],[22663, 22653])).
% 29.31/19.50 tff(22665,plain,((f10(c2) = c4) | big_f(f10(c2), f10(c2)) | (~(f7(c1) = c2)) | (~(f4(c4) = c1)) | (~big_f(c1, c2)) | (f10(c2) = c3) | (~big_f(c2, f10(c2))) | (f10(c2) = c2) | (~(c2 = f8(c2))) | (~big_f(c2, c2)) | (~big_f(c2, c1))), inference(lemma,lemma(discharge,[]))).
% 29.31/19.50 tff(22666,plain,
% 29.31/19.50 (f10(c2) = c4),
% 29.31/19.50 inference(unit_resolution,[status(thm)],[22665, 15667, 347, 11752, 2865, 20783, 12291, 89, 13152, 1345, 348])).
% 29.31/19.50 tff(22667,plain,
% 29.31/19.50 (c2 = f4(f10(c2))),
% 29.31/19.50 inference(unit_resolution,[status(thm)],[21778, 22666, 1345, 12291, 22637, 89])).
% 29.31/19.50 tff(22668,plain,
% 29.31/19.50 (f4(f10(c2)) = c2),
% 29.31/19.50 inference(symmetry,[status(thm)],[22667])).
% 29.31/19.50 tff(22669,plain,
% 29.31/19.50 (c4 = f10(c2)),
% 29.31/19.50 inference(symmetry,[status(thm)],[22666])).
% 29.31/19.50 tff(22670,plain,
% 29.31/19.50 (f4(c4) = f4(f10(c2))),
% 29.31/19.50 inference(monotonicity,[status(thm)],[22669])).
% 29.31/19.50 tff(22671,plain,
% 29.31/19.50 (f10(c2) = c2),
% 29.31/19.50 inference(transitivity,[status(thm)],[94, 16651, 22670, 22668])).
% 29.31/19.50 tff(22672,plain,
% 29.31/19.50 ($false),
% 29.31/19.50 inference(unit_resolution,[status(thm)],[89, 22671])).
% 29.31/19.50 tff(22673,plain,((f10(c2) = c3) | (f10(c2) = c2) | (~(f4(c4) = c1)) | (~big_f(c2, c2)) | (~big_f(c2, f10(c2))) | (~(f7(c1) = c2)) | (~big_f(c1, c2)) | big_f(f10(c2), f10(c2)) | (~(c2 = f8(c2))) | (~big_f(c2, c1))), inference(lemma,lemma(discharge,[]))).
% 29.31/19.50 tff(22674,plain,
% 29.31/19.50 (f10(c2) = c3),
% 29.31/19.50 inference(unit_resolution,[status(thm)],[22673, 17538, 15706, 22592, 22629, 120, 21808, 22636, 22630, 22625])).
% 29.31/19.50 tff(22675,plain,
% 29.31/19.50 (c3 = f10(c2)),
% 29.31/19.50 inference(symmetry,[status(thm)],[22674])).
% 29.31/19.50 tff(22676,plain,
% 29.31/19.50 (f10(c3) = f10(f10(c2))),
% 29.31/19.50 inference(monotonicity,[status(thm)],[22675])).
% 29.31/19.50 tff(22677,plain,
% 29.31/19.50 (f10(c3) = c2),
% 29.31/19.50 inference(transitivity,[status(thm)],[22676, 17540, 15])).
% 29.31/19.50 tff(22678,plain,
% 29.31/19.50 (big_f(c2, f10(c3)) <=> big_f(c2, c2)),
% 29.31/19.50 inference(monotonicity,[status(thm)],[22677])).
% 29.31/19.50 tff(22679,plain,
% 29.31/19.50 (big_f(c2, c2) <=> big_f(c2, f10(c3))),
% 29.31/19.50 inference(symmetry,[status(thm)],[22678])).
% 29.31/19.50 tff(22680,plain,
% 29.31/19.50 (big_f(c2, f10(c3))),
% 29.31/19.50 inference(modus_ponens,[status(thm)],[22592, 22679])).
% 29.31/19.50 tff(22681,plain,
% 29.31/19.50 (c3 = c1),
% 29.31/19.50 inference(transitivity,[status(thm)],[22675, 17539])).
% 29.31/19.50 tff(22682,plain,
% 29.31/19.50 ((f10(c3) = c3) <=> (f10(c3) = c1)),
% 29.31/19.50 inference(monotonicity,[status(thm)],[22681])).
% 29.31/19.50 tff(22683,plain,
% 29.31/19.50 ((f10(c3) = c1) <=> (f10(c3) = c3)),
% 29.31/19.50 inference(symmetry,[status(thm)],[22682])).
% 29.31/19.50 tff(22684,plain,
% 29.31/19.50 ((f10(c3) = c1) <=> (c2 = f10(c2))),
% 29.31/19.50 inference(monotonicity,[status(thm)],[22677, 17541])).
% 29.31/19.50 tff(22685,plain,
% 29.31/19.50 ((f10(c3) = c1) <=> (f10(c2) = c2)),
% 29.31/19.50 inference(transitivity,[status(thm)],[22684, 4987])).
% 29.31/19.50 tff(22686,plain,
% 29.31/19.50 ((f10(c2) = c2) <=> (f10(c3) = c1)),
% 29.31/19.50 inference(symmetry,[status(thm)],[22685])).
% 29.31/19.50 tff(22687,plain,
% 29.31/19.50 ((f10(c2) = c2) <=> (f10(c3) = c3)),
% 29.31/19.50 inference(transitivity,[status(thm)],[22686, 22683])).
% 29.31/19.50 tff(22688,plain,
% 29.31/19.50 ((~(f10(c2) = c2)) <=> (~(f10(c3) = c3))),
% 29.31/19.50 inference(monotonicity,[status(thm)],[22687])).
% 29.31/19.50 tff(22689,plain,
% 29.31/19.50 (~(f10(c3) = c3)),
% 29.31/19.50 inference(modus_ponens,[status(thm)],[17538, 22688])).
% 29.31/19.50 tff(22690,plain,
% 29.31/19.50 (big_f(f7(c1), c2)),
% 29.31/19.50 inference(modus_ponens,[status(thm)],[22592, 1724])).
% 29.31/19.50 tff(22691,assumption,(~(f10(c2) = f5(f10(c2)))), introduced(assumption)).
% 29.31/19.50 tff(22692,plain,
% 29.31/19.50 ((c2 = f8(f10(c2))) | (f10(c2) = f5(f10(c2)))),
% 29.31/19.50 inference(unit_resolution,[status(thm)],[21426, 1659, 11896, 21479, 11895, 21708])).
% 29.31/19.50 tff(22693,plain,
% 29.31/19.50 (c2 = f8(f10(c2))),
% 29.31/19.50 inference(unit_resolution,[status(thm)],[22692, 22691])).
% 29.31/19.50 tff(22694,plain,
% 29.31/19.50 (f8(f10(c2)) = c2),
% 29.31/19.50 inference(symmetry,[status(thm)],[22693])).
% 29.31/19.50 tff(22695,plain,
% 29.31/19.50 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f10(c2)) = f10(c2)) | (f7(f10(c2)) = f10(c2)) | (f10(c2) = f8(f10(c2))) | (~big_f(f10(c2), f10(f10(c2)))) | (~big_f(f7(f10(c2)), f10(c2))) | (f10(c2) = f5(f10(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(f10(c2)) = f10(c2)) | (f7(f10(c2)) = f10(c2)) | (f10(c2) = f8(f10(c2))) | (~big_f(f10(c2), f10(f10(c2)))) | (~big_f(f7(f10(c2)), f10(c2))) | (f10(c2) = f5(f10(c2))))),
% 29.31/19.50 inference(rewrite,[status(thm)],[])).
% 29.31/19.50 tff(22696,plain,
% 29.31/19.50 (((f10(f10(c2)) = f10(c2)) | (f10(c2) = f8(f10(c2))) | (~big_f(f10(c2), f10(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | (f10(c2) = f5(f10(c2))) | (~big_f(f7(f10(c2)), f10(c2)))) <=> ((f10(f10(c2)) = f10(c2)) | (f7(f10(c2)) = f10(c2)) | (f10(c2) = f8(f10(c2))) | (~big_f(f10(c2), f10(f10(c2)))) | (~big_f(f7(f10(c2)), f10(c2))) | (f10(c2) = f5(f10(c2))))),
% 29.31/19.50 inference(rewrite,[status(thm)],[])).
% 29.31/19.50 tff(22697,plain,
% 29.31/19.50 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f10(c2)) = f10(c2)) | (f10(c2) = f8(f10(c2))) | (~big_f(f10(c2), f10(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | (f10(c2) = f5(f10(c2))) | (~big_f(f7(f10(c2)), f10(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f10(c2)) = f10(c2)) | (f7(f10(c2)) = f10(c2)) | (f10(c2) = f8(f10(c2))) | (~big_f(f10(c2), f10(f10(c2)))) | (~big_f(f7(f10(c2)), f10(c2))) | (f10(c2) = f5(f10(c2)))))),
% 29.31/19.50 inference(monotonicity,[status(thm)],[22696])).
% 29.31/19.50 tff(22698,plain,
% 29.31/19.50 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f10(c2)) = f10(c2)) | (f10(c2) = f8(f10(c2))) | (~big_f(f10(c2), f10(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | (f10(c2) = f5(f10(c2))) | (~big_f(f7(f10(c2)), f10(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(f10(c2)) = f10(c2)) | (f7(f10(c2)) = f10(c2)) | (f10(c2) = f8(f10(c2))) | (~big_f(f10(c2), f10(f10(c2)))) | (~big_f(f7(f10(c2)), f10(c2))) | (f10(c2) = f5(f10(c2))))),
% 29.31/19.50 inference(transitivity,[status(thm)],[22697, 22695])).
% 29.31/19.50 tff(22699,plain,
% 29.31/19.50 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f10(c2)) = f10(c2)) | (f10(c2) = f8(f10(c2))) | (~big_f(f10(c2), f10(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | (f10(c2) = f5(f10(c2))) | (~big_f(f7(f10(c2)), f10(c2))))),
% 29.31/19.50 inference(quant_inst,[status(thm)],[])).
% 29.31/19.50 tff(22700,plain,
% 29.31/19.50 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(f10(c2)) = f10(c2)) | (f7(f10(c2)) = f10(c2)) | (f10(c2) = f8(f10(c2))) | (~big_f(f10(c2), f10(f10(c2)))) | (~big_f(f7(f10(c2)), f10(c2))) | (f10(c2) = f5(f10(c2)))),
% 29.31/19.50 inference(modus_ponens,[status(thm)],[22699, 22698])).
% 29.31/19.50 tff(22701,plain,
% 29.31/19.50 ((f10(c2) = f8(f10(c2))) | (f10(c2) = f5(f10(c2)))),
% 29.31/19.50 inference(unit_resolution,[status(thm)],[22700, 1659, 11896, 11895, 21708, 21944])).
% 29.31/19.50 tff(22702,plain,
% 29.31/19.50 (f10(c2) = f8(f10(c2))),
% 29.31/19.50 inference(unit_resolution,[status(thm)],[22701, 22691])).
% 29.31/19.50 tff(22703,plain,
% 29.31/19.50 (f10(c2) = c2),
% 29.31/19.50 inference(transitivity,[status(thm)],[22702, 22694])).
% 29.31/19.50 tff(22704,plain,
% 29.31/19.50 ($false),
% 29.31/19.50 inference(unit_resolution,[status(thm)],[89, 22703])).
% 29.31/19.50 tff(22705,plain,((f10(c2) = f5(f10(c2))) | (f10(c2) = c2) | (f10(f10(c2)) = f10(c2)) | (f7(f10(c2)) = f10(c2)) | (~big_f(f7(f10(c2)), f10(c2))) | (~big_f(f10(c2), f10(f10(c2)))) | (~big_f(c2, f10(f10(c2))))), inference(lemma,lemma(discharge,[]))).
% 29.31/19.50 tff(22706,plain,
% 29.31/19.50 (f10(c2) = f5(f10(c2))),
% 29.31/19.50 inference(unit_resolution,[status(thm)],[22705, 17538, 21408, 20958, 22627, 21938, 22593])).
% 29.31/19.50 tff(22707,plain,
% 29.31/19.50 (f5(f10(c2)) = f10(c2)),
% 29.31/19.50 inference(symmetry,[status(thm)],[22706])).
% 29.31/19.50 tff(22708,plain,
% 29.31/19.50 (f5(c1) = f10(c2)),
% 29.31/19.50 inference(transitivity,[status(thm)],[22579, 22707])).
% 29.31/19.50 tff(22709,plain,
% 29.31/19.50 ((c2 = f5(c1)) <=> (c2 = f10(c2))),
% 29.31/19.50 inference(monotonicity,[status(thm)],[22708])).
% 29.31/19.50 tff(22710,plain,
% 29.31/19.50 ((c2 = f5(c1)) <=> (f10(c2) = c2)),
% 29.31/19.50 inference(transitivity,[status(thm)],[22709, 4987])).
% 29.31/19.50 tff(22711,plain,
% 29.31/19.50 ((f10(c2) = c2) <=> (c2 = f5(c1))),
% 29.31/19.50 inference(symmetry,[status(thm)],[22710])).
% 29.31/19.50 tff(22712,plain,
% 29.31/19.50 ((~(f10(c2) = c2)) <=> (~(c2 = f5(c1)))),
% 29.31/19.50 inference(monotonicity,[status(thm)],[22711])).
% 29.31/19.50 tff(22713,plain,
% 29.31/19.50 (~(c2 = f5(c1))),
% 29.31/19.50 inference(modus_ponens,[status(thm)],[17538, 22712])).
% 29.31/19.50 tff(22714,plain,
% 29.31/19.50 (c2 = f8(c3)),
% 29.31/19.50 inference(unit_resolution,[status(thm)],[3528, 22713, 115, 22690, 22689, 22680])).
% 29.31/19.50 tff(22715,plain,
% 29.31/19.50 (f8(c3) = c2),
% 29.31/19.50 inference(symmetry,[status(thm)],[22714])).
% 29.31/19.50 tff(22716,plain,
% 29.31/19.50 (f8(f10(c2)) = f8(c3)),
% 29.31/19.50 inference(monotonicity,[status(thm)],[22674])).
% 29.31/19.50 tff(22717,plain,
% 29.31/19.50 ((c2 = f5(f10(c2))) <=> (c2 = f5(c1))),
% 29.31/19.50 inference(monotonicity,[status(thm)],[22580])).
% 29.31/19.50 tff(22718,plain,
% 29.31/19.50 ((c2 = f5(c1)) <=> (c2 = f5(f10(c2)))),
% 29.31/19.50 inference(symmetry,[status(thm)],[22717])).
% 29.31/19.50 tff(22719,plain,
% 29.31/19.50 ((f10(c2) = c2) <=> (c2 = f5(f10(c2)))),
% 29.31/19.50 inference(transitivity,[status(thm)],[22711, 22718])).
% 29.31/19.50 tff(22720,plain,
% 29.31/19.50 ((~(f10(c2) = c2)) <=> (~(c2 = f5(f10(c2))))),
% 29.31/19.50 inference(monotonicity,[status(thm)],[22719])).
% 29.31/19.50 tff(22721,plain,
% 29.31/19.50 (~(c2 = f5(f10(c2)))),
% 29.31/19.50 inference(modus_ponens,[status(thm)],[17538, 22720])).
% 29.31/19.50 tff(22722,plain,
% 29.31/19.50 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f10(c2)) = f10(c2)) | (c2 = f5(f10(c2))) | (f7(f10(c2)) = f10(c2)) | (f10(c2) = f8(f10(c2))) | (~big_f(f10(c2), f10(f10(c2)))) | (~big_f(f7(f10(c2)), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(f10(c2)) = f10(c2)) | (c2 = f5(f10(c2))) | (f7(f10(c2)) = f10(c2)) | (f10(c2) = f8(f10(c2))) | (~big_f(f10(c2), f10(f10(c2)))) | (~big_f(f7(f10(c2)), c2)))),
% 29.31/19.50 inference(rewrite,[status(thm)],[])).
% 29.31/19.50 tff(22723,plain,
% 29.31/19.50 (((f10(f10(c2)) = f10(c2)) | (f10(c2) = f8(f10(c2))) | (~big_f(f10(c2), f10(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | (c2 = f5(f10(c2))) | (~big_f(f7(f10(c2)), c2))) <=> ((f10(f10(c2)) = f10(c2)) | (c2 = f5(f10(c2))) | (f7(f10(c2)) = f10(c2)) | (f10(c2) = f8(f10(c2))) | (~big_f(f10(c2), f10(f10(c2)))) | (~big_f(f7(f10(c2)), c2)))),
% 29.31/19.50 inference(rewrite,[status(thm)],[])).
% 29.31/19.50 tff(22724,plain,
% 29.31/19.50 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f10(c2)) = f10(c2)) | (f10(c2) = f8(f10(c2))) | (~big_f(f10(c2), f10(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | (c2 = f5(f10(c2))) | (~big_f(f7(f10(c2)), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f10(c2)) = f10(c2)) | (c2 = f5(f10(c2))) | (f7(f10(c2)) = f10(c2)) | (f10(c2) = f8(f10(c2))) | (~big_f(f10(c2), f10(f10(c2)))) | (~big_f(f7(f10(c2)), c2))))),
% 29.31/19.51 inference(monotonicity,[status(thm)],[22723])).
% 29.31/19.51 tff(22725,plain,
% 29.31/19.51 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f10(c2)) = f10(c2)) | (f10(c2) = f8(f10(c2))) | (~big_f(f10(c2), f10(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | (c2 = f5(f10(c2))) | (~big_f(f7(f10(c2)), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(f10(c2)) = f10(c2)) | (c2 = f5(f10(c2))) | (f7(f10(c2)) = f10(c2)) | (f10(c2) = f8(f10(c2))) | (~big_f(f10(c2), f10(f10(c2)))) | (~big_f(f7(f10(c2)), c2)))),
% 29.31/19.51 inference(transitivity,[status(thm)],[22724, 22722])).
% 29.31/19.51 tff(22726,plain,
% 29.31/19.51 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f10(c2)) = f10(c2)) | (f10(c2) = f8(f10(c2))) | (~big_f(f10(c2), f10(f10(c2)))) | (f7(f10(c2)) = f10(c2)) | (c2 = f5(f10(c2))) | (~big_f(f7(f10(c2)), c2)))),
% 29.31/19.51 inference(quant_inst,[status(thm)],[])).
% 29.31/19.51 tff(22727,plain,
% 29.31/19.51 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(f10(c2)) = f10(c2)) | (c2 = f5(f10(c2))) | (f7(f10(c2)) = f10(c2)) | (f10(c2) = f8(f10(c2))) | (~big_f(f10(c2), f10(f10(c2)))) | (~big_f(f7(f10(c2)), c2))),
% 29.31/19.51 inference(modus_ponens,[status(thm)],[22726, 22725])).
% 29.31/19.51 tff(22728,plain,
% 29.31/19.51 ((c2 = f5(f10(c2))) | (f10(c2) = f8(f10(c2)))),
% 29.31/19.51 inference(unit_resolution,[status(thm)],[22727, 1659, 21408, 20958, 22628, 21938])).
% 29.31/19.51 tff(22729,plain,
% 29.31/19.51 (f10(c2) = f8(f10(c2))),
% 29.31/19.51 inference(unit_resolution,[status(thm)],[22728, 22721])).
% 29.31/19.51 tff(22730,plain,
% 29.31/19.51 (f10(c2) = c2),
% 29.31/19.51 inference(transitivity,[status(thm)],[22729, 22716, 22715])).
% 29.31/19.51 tff(22731,plain,
% 29.31/19.51 ($false),
% 29.31/19.51 inference(unit_resolution,[status(thm)],[17538, 22730])).
% 29.31/19.51 tff(22732,plain,((f10(c1) = c1) | (f7(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.31/19.51 tff(22733,plain,
% 29.31/19.51 (f10(c1) = c1),
% 29.31/19.51 inference(unit_resolution,[status(thm)],[22732, 115])).
% 29.31/19.51 tff(22734,plain,
% 29.31/19.51 (~(f9(c1, c1) = c1)),
% 29.31/19.51 inference(unit_resolution,[status(thm)],[10942, 2908, 115, 22733, 2907, 4932])).
% 29.31/19.51 tff(22735,plain,
% 29.31/19.51 (f9(c1, c1) = c2),
% 29.31/19.51 inference(unit_resolution,[status(thm)],[3939, 22734])).
% 29.31/19.51 tff(22736,plain,
% 29.31/19.51 (~big_f(f9(c1, c1), c1)),
% 29.31/19.51 inference(unit_resolution,[status(thm)],[10058, 22735, 2])).
% 29.31/19.51 tff(22737,plain,
% 29.31/19.51 (~big_f(f9(c1, c1), f10(c1))),
% 29.31/19.51 inference(unit_resolution,[status(thm)],[10033, 22736, 22733])).
% 29.31/19.51 tff(22738,plain,
% 29.31/19.51 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)))),
% 29.31/19.51 inference(rewrite,[status(thm)],[])).
% 29.31/19.51 tff(22739,plain,
% 29.31/19.51 (((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(c1) = c1) | big_f(f7(c1), c2) | (~(c2 = f5(c1)))) <=> ((~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)))),
% 29.31/19.51 inference(rewrite,[status(thm)],[])).
% 29.31/19.51 tff(22740,plain,
% 29.31/19.51 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(c1) = c1) | big_f(f7(c1), c2) | (~(c2 = f5(c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1))))),
% 29.31/19.51 inference(monotonicity,[status(thm)],[22739])).
% 29.31/19.51 tff(22741,plain,
% 29.31/19.51 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(c1) = c1) | big_f(f7(c1), c2) | (~(c2 = f5(c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)))),
% 29.31/19.51 inference(transitivity,[status(thm)],[22740, 22738])).
% 29.31/19.51 tff(22742,plain,
% 29.31/19.51 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(c1) = c1) | big_f(f7(c1), c2) | (~(c2 = f5(c1))))),
% 29.31/19.51 inference(quant_inst,[status(thm)],[])).
% 29.31/19.51 tff(22743,plain,
% 29.31/19.51 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1))),
% 29.31/19.51 inference(modus_ponens,[status(thm)],[22742, 22741])).
% 29.31/19.51 tff(22744,plain,
% 29.31/19.51 ($false),
% 29.31/19.51 inference(unit_resolution,[status(thm)],[22743, 267, 2908, 2907, 115, 22733, 22734, 22737])).
% 29.31/19.51 tff(22745,plain,((~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | big_f(c2, c1) | (~big_f(c1, c1))), inference(lemma,lemma(discharge,[]))).
% 29.31/19.51 tff(22746,plain,
% 29.31/19.51 (~(c2 = f5(c1))),
% 29.31/19.51 inference(unit_resolution,[status(thm)],[22745, 2, 115, 2907, 4932])).
% 29.31/19.51 tff(22747,plain,
% 29.31/19.51 (~(f5(c1) = c2)),
% 29.31/19.51 inference(modus_ponens,[status(thm)],[22746, 11786])).
% 29.31/19.51 tff(22748,plain,
% 29.31/19.51 (f5(c1) = c1),
% 29.31/19.51 inference(unit_resolution,[status(thm)],[1708, 22747])).
% 29.31/19.51 tff(22749,plain,
% 29.31/19.51 (c1 = f5(c1)),
% 29.31/19.51 inference(modus_ponens,[status(thm)],[22748, 192])).
% 29.31/19.51 tff(22750,plain,
% 29.31/19.51 (~big_f(f9(c1, c1), f10(c1))),
% 29.31/19.51 inference(unit_resolution,[status(thm)],[10033, 10020, 22733])).
% 29.31/19.51 tff(22751,plain,
% 29.31/19.51 (~(f9(c1, c1) = c1)),
% 29.31/19.51 inference(unit_resolution,[status(thm)],[10938, 10020, 4932])).
% 29.31/19.51 tff(22752,plain,
% 29.31/19.51 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((f7(c1) = c1) | big_f(f7(c1), c1) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~(c1 = f5(c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (f7(c1) = c1) | big_f(f7(c1), c1) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~(c1 = f5(c1))))),
% 29.31/19.51 inference(rewrite,[status(thm)],[])).
% 29.31/19.51 tff(22753,plain,
% 29.31/19.51 (((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(c1 = f5(c1)))) <=> ((f7(c1) = c1) | big_f(f7(c1), c1) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~(c1 = f5(c1))))),
% 29.31/19.51 inference(rewrite,[status(thm)],[])).
% 29.31/19.51 tff(22754,plain,
% 29.31/19.51 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(c1 = f5(c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((f7(c1) = c1) | big_f(f7(c1), c1) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~(c1 = f5(c1)))))),
% 29.31/19.51 inference(monotonicity,[status(thm)],[22753])).
% 29.31/19.51 tff(22755,plain,
% 29.31/19.51 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(c1 = f5(c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (f7(c1) = c1) | big_f(f7(c1), c1) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~(c1 = f5(c1))))),
% 29.31/19.51 inference(transitivity,[status(thm)],[22754, 22752])).
% 29.31/19.51 tff(22756,plain,
% 29.31/19.51 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(c1 = f5(c1))))),
% 29.31/19.51 inference(quant_inst,[status(thm)],[])).
% 29.31/19.51 tff(22757,plain,
% 29.31/19.51 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (f7(c1) = c1) | big_f(f7(c1), c1) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~(c1 = f5(c1)))),
% 29.31/19.51 inference(modus_ponens,[status(thm)],[22756, 22755])).
% 29.31/19.51 tff(22758,plain,
% 29.31/19.51 ($false),
% 29.31/19.51 inference(unit_resolution,[status(thm)],[22757, 267, 115, 22733, 22751, 22750, 285, 11826])).
% 29.31/19.51 tff(22759,plain,(big_f(f9(c1, c1), c1) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(c1 = f5(c1))) | (~big_f(c1, c1))), inference(lemma,lemma(discharge,[]))).
% 29.31/19.51 tff(22760,plain,
% 29.31/19.51 (big_f(f9(c1, c1), c1)),
% 29.31/19.51 inference(unit_resolution,[status(thm)],[22759, 17574, 115, 22749, 4932])).
% 29.31/19.51 tff(22761,plain,
% 29.31/19.51 (big_f(f9(c1, c1), f10(c1))),
% 29.31/19.51 inference(unit_resolution,[status(thm)],[8716, 22760, 22733])).
% 29.31/19.51 tff(22762,plain,
% 29.31/19.51 (~(f9(c1, c1) = c2)),
% 29.31/19.51 inference(unit_resolution,[status(thm)],[10058, 22760, 2])).
% 29.31/19.51 tff(22763,plain,
% 29.31/19.51 (f9(c1, c1) = c1),
% 29.31/19.51 inference(unit_resolution,[status(thm)],[3939, 22762])).
% 29.31/19.51 tff(22764,plain,
% 29.31/19.51 ($false),
% 29.31/19.51 inference(unit_resolution,[status(thm)],[18656, 783, 115, 22733, 22763, 22761, 17574, 22749])).
% 29.31/19.51 tff(22765,plain,(big_f(c2, c1) | (f7(c1) = c1) | (~big_f(c1, c1)) | big_f(f7(c1), c2)), inference(lemma,lemma(discharge,[]))).
% 29.31/19.51 tff(22766,plain,
% 29.31/19.51 (big_f(c2, c1)),
% 29.31/19.51 inference(unit_resolution,[status(thm)],[22765, 11785, 115, 1726])).
% 29.31/19.51 tff(22767,plain,
% 29.31/19.51 ((c2 = f4(c1)) <=> (c2 = c1)),
% 29.31/19.51 inference(monotonicity,[status(thm)],[18178])).
% 29.31/19.51 tff(22768,plain,
% 29.31/19.51 ((c2 = c1) <=> (c2 = f4(c1))),
% 29.31/19.51 inference(symmetry,[status(thm)],[22767])).
% 29.31/19.51 tff(22769,plain,
% 29.31/19.51 ((~(c2 = c1)) <=> (~(c2 = f4(c1)))),
% 29.31/19.51 inference(monotonicity,[status(thm)],[22768])).
% 29.31/19.51 tff(22770,plain,
% 29.31/19.51 (~(c2 = f4(c1))),
% 29.31/19.51 inference(modus_ponens,[status(thm)],[75, 22769])).
% 29.31/19.51 tff(22771,assumption,(~(c2 = f4(c1))), introduced(assumption)).
% 29.31/19.51 tff(22772,plain,
% 29.31/19.51 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | (~(c1 = c4)) | (~big_f(c2, c1)) | (c2 = f4(c1)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | (~(c1 = c4)) | (~big_f(c2, c1)) | (c2 = f4(c1)))),
% 29.31/19.51 inference(rewrite,[status(thm)],[])).
% 29.31/19.51 tff(22773,plain,
% 29.31/19.51 (((c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | (~(c1 = c4)) | (c2 = f4(c1)) | (~big_f(c2, c1))) <=> ((c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | (~(c1 = c4)) | (~big_f(c2, c1)) | (c2 = f4(c1)))),
% 29.31/19.51 inference(rewrite,[status(thm)],[])).
% 29.31/19.51 tff(22774,plain,
% 29.31/19.51 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | (~(c1 = c4)) | (c2 = f4(c1)) | (~big_f(c2, c1)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | (~(c1 = c4)) | (~big_f(c2, c1)) | (c2 = f4(c1))))),
% 29.31/19.51 inference(monotonicity,[status(thm)],[22773])).
% 29.31/19.51 tff(22775,plain,
% 29.31/19.51 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | (~(c1 = c4)) | (c2 = f4(c1)) | (~big_f(c2, c1)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | (~(c1 = c4)) | (~big_f(c2, c1)) | (c2 = f4(c1)))),
% 29.31/19.51 inference(transitivity,[status(thm)],[22774, 22772])).
% 29.31/19.51 tff(22776,plain,
% 29.31/19.51 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | (~(c1 = c4)) | (c2 = f4(c1)) | (~big_f(c2, c1)))),
% 29.31/19.51 inference(quant_inst,[status(thm)],[])).
% 29.31/19.51 tff(22777,plain,
% 29.31/19.51 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | (~(c1 = c4)) | (~big_f(c2, c1)) | (c2 = f4(c1))),
% 29.31/19.51 inference(modus_ponens,[status(thm)],[22776, 22775])).
% 29.31/19.51 tff(22778,plain,
% 29.31/19.51 ($false),
% 29.31/19.51 inference(unit_resolution,[status(thm)],[22777, 525, 11526, 377, 12187, 13410, 348, 22771])).
% 29.31/19.51 tff(22779,plain,((f1(c2, c1) = c1) | (~(c1 = c4)) | (c2 = c3) | (~big_f(c2, c1)) | (c2 = f4(c1)) | (~(f7(c1) = c2)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 29.31/19.51 tff(22780,plain,
% 29.31/19.51 (f1(c2, c1) = c1),
% 29.31/19.51 inference(unit_resolution,[status(thm)],[22779, 564, 377, 348, 22770, 347, 121])).
% 29.31/19.51 tff(22781,plain,
% 29.31/19.51 (big_f(c2, f1(c2, c1)) <=> big_f(c2, c1)),
% 29.31/19.51 inference(monotonicity,[status(thm)],[22780])).
% 29.31/19.51 tff(22782,plain,
% 29.31/19.51 (big_f(c2, c1) <=> big_f(c2, f1(c2, c1))),
% 29.31/19.51 inference(symmetry,[status(thm)],[22781])).
% 29.31/19.51 tff(22783,plain,
% 29.31/19.51 (big_f(c2, f1(c2, c1))),
% 29.31/19.51 inference(modus_ponens,[status(thm)],[348, 22782])).
% 29.31/19.51 tff(22784,plain,
% 29.31/19.51 ($false),
% 29.31/19.51 inference(unit_resolution,[status(thm)],[11512, 553, 564, 377, 22780, 22783, 348, 22770])).
% 29.31/19.51 tff(22785,plain,((~(c4 = c1)) | (c2 = c3) | (~big_f(c2, c1)) | (~(f7(c1) = c2)) | big_f(c2, c2) | (~(f4(c4) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.31/19.51 tff(22786,plain,
% 29.31/19.51 (~(c4 = c1)),
% 29.31/19.51 inference(unit_resolution,[status(thm)],[22785, 22766, 377, 120, 121, 11752])).
% 29.31/19.51 tff(22787,plain,
% 29.31/19.51 (c4 = c2),
% 29.31/19.51 inference(unit_resolution,[status(thm)],[461, 22786])).
% 29.31/19.51 tff(22788,plain,
% 29.31/19.51 (c2 = c4),
% 29.31/19.51 inference(symmetry,[status(thm)],[22787])).
% 29.31/19.51 tff(22789,plain,
% 29.31/19.51 (f4(c2) = f4(c4)),
% 29.31/19.51 inference(monotonicity,[status(thm)],[22788])).
% 29.31/19.51 tff(22790,plain,
% 29.31/19.51 (f4(c4) = f4(c2)),
% 29.31/19.51 inference(symmetry,[status(thm)],[22789])).
% 29.31/19.51 tff(22791,plain,
% 29.31/19.51 (c1 = f4(c2)),
% 29.31/19.51 inference(transitivity,[status(thm)],[16651, 22790])).
% 29.31/19.51 tff(22792,plain,
% 29.31/19.51 ((f7(f7(c2)) = c3) <=> (f7(f7(c2)) = c1)),
% 29.31/19.51 inference(monotonicity,[status(thm)],[11754])).
% 29.31/19.51 tff(22793,plain,
% 29.31/19.51 ((f7(f7(c2)) = c1) <=> (f7(f7(c2)) = c3)),
% 29.31/19.51 inference(symmetry,[status(thm)],[22792])).
% 29.31/19.51 tff(22794,plain,
% 29.31/19.51 ((c2 = f4(c1)) <=> (c2 = f4(f7(c2)))),
% 29.31/19.51 inference(symmetry,[status(thm)],[9317])).
% 29.31/19.51 tff(22795,plain,
% 29.31/19.51 ((c2 = c1) <=> (c2 = f4(f7(c2)))),
% 29.31/19.51 inference(transitivity,[status(thm)],[22768, 22794])).
% 29.31/19.51 tff(22796,plain,
% 29.31/19.51 ((~(c2 = c1)) <=> (~(c2 = f4(f7(c2))))),
% 29.31/19.51 inference(monotonicity,[status(thm)],[22795])).
% 29.31/19.51 tff(22797,plain,
% 29.31/19.51 (~(c2 = f4(f7(c2)))),
% 29.31/19.51 inference(modus_ponens,[status(thm)],[75, 22796])).
% 29.31/19.51 tff(22798,plain,
% 29.31/19.51 (f7(c2) = c4),
% 29.31/19.51 inference(unit_resolution,[status(thm)],[16645, 480, 292])).
% 29.31/19.51 tff(22799,plain,
% 29.31/19.51 (big_f(f7(f7(c2)), f7(c2)) <=> big_f(c2, c1)),
% 29.31/19.51 inference(monotonicity,[status(thm)],[8464, 292])).
% 29.31/19.51 tff(22800,plain,
% 29.31/19.51 ((~big_f(f7(f7(c2)), f7(c2))) <=> (~big_f(c2, c1))),
% 29.31/19.51 inference(monotonicity,[status(thm)],[22799])).
% 29.31/19.51 tff(22801,plain,
% 29.31/19.51 (~big_f(c2, f7(c2))),
% 29.31/19.51 inference(unit_resolution,[status(thm)],[15777, 377, 121, 9319, 292, 120, 8770])).
% 29.31/19.51 tff(22802,plain,
% 29.31/19.51 (~big_f(f7(f7(c2)), f7(c2))),
% 29.31/19.51 inference(unit_resolution,[status(thm)],[15941, 22801, 120, 292])).
% 29.31/19.51 tff(22803,plain,
% 29.31/19.51 (~big_f(c2, c1)),
% 29.31/19.51 inference(modus_ponens,[status(thm)],[22802, 22800])).
% 29.31/19.51 tff(22804,plain,
% 29.31/19.51 (big_f(c1, c1)),
% 29.31/19.51 inference(unit_resolution,[status(thm)],[16664, 11754, 292, 11752, 27])).
% 29.31/19.51 tff(22805,plain,
% 29.31/19.51 (big_f(c2, c1)),
% 29.31/19.51 inference(unit_resolution,[status(thm)],[22765, 22804, 115, 1726])).
% 29.31/19.51 tff(22806,plain,
% 29.31/19.51 ($false),
% 29.31/19.51 inference(unit_resolution,[status(thm)],[22805, 22803])).
% 29.31/19.51 tff(22807,plain,((c2 = c3) | (~(f7(c2) = c1)) | (f7(c1) = c1) | (~(f4(c4) = c1)) | big_f(c1, c2) | big_f(c2, c2) | (c2 = f4(f7(c2))) | (~(f7(c2) = c4))), inference(lemma,lemma(discharge,[]))).
% 29.31/19.51 tff(22808,plain,
% 29.31/19.51 (c2 = f4(f7(c2))),
% 29.31/19.51 inference(unit_resolution,[status(thm)],[22807, 22798, 115, 11752, 377, 121, 27, 292])).
% 29.31/19.51 tff(22809,plain,
% 29.31/19.51 ($false),
% 29.31/19.51 inference(unit_resolution,[status(thm)],[22808, 22797])).
% 29.31/19.51 tff(22810,plain,((~(c4 = c1)) | (~(f4(c4) = c1)) | (~(f7(c2) = c1)) | (f7(c1) = c1) | (c2 = c3) | big_f(c2, c2) | big_f(c1, c2)), inference(lemma,lemma(discharge,[]))).
% 29.31/19.51 tff(22811,plain,
% 29.31/19.51 (~(c4 = c1)),
% 29.31/19.51 inference(unit_resolution,[status(thm)],[22810, 292, 11752, 115, 377, 121, 27])).
% 29.31/19.51 tff(22812,plain,
% 29.31/19.51 (c4 = c2),
% 29.31/19.51 inference(unit_resolution,[status(thm)],[461, 22811])).
% 29.31/19.51 tff(22813,plain,
% 29.31/19.51 (c2 = c4),
% 29.31/19.51 inference(symmetry,[status(thm)],[22812])).
% 29.31/19.51 tff(22814,plain,
% 29.31/19.51 (f4(c2) = f4(c4)),
% 29.31/19.51 inference(monotonicity,[status(thm)],[22813])).
% 29.31/19.51 tff(22815,plain,
% 29.31/19.51 (f4(c4) = f4(c2)),
% 29.31/19.51 inference(symmetry,[status(thm)],[22814])).
% 29.31/19.51 tff(22816,plain,
% 29.31/19.51 (c1 = f4(c2)),
% 29.31/19.51 inference(transitivity,[status(thm)],[16651, 22815])).
% 29.31/19.51 tff(22817,plain,
% 29.31/19.51 ((f7(f7(c2)) = c1) <=> (c2 = c1)),
% 29.31/19.51 inference(monotonicity,[status(thm)],[8464])).
% 29.31/19.51 tff(22818,plain,
% 29.31/19.51 ((c2 = c1) <=> (f7(f7(c2)) = c1)),
% 29.31/19.51 inference(symmetry,[status(thm)],[22817])).
% 29.31/19.51 tff(22819,plain,
% 29.31/19.51 ((c2 = c1) <=> (f7(f7(c2)) = c3)),
% 29.31/19.51 inference(transitivity,[status(thm)],[22818, 22793])).
% 29.31/19.51 tff(22820,plain,
% 29.31/19.51 ((~(c2 = c1)) <=> (~(f7(f7(c2)) = c3))),
% 29.31/19.51 inference(monotonicity,[status(thm)],[22819])).
% 29.31/19.51 tff(22821,plain,
% 29.31/19.51 (~(f7(f7(c2)) = c3)),
% 29.31/19.51 inference(modus_ponens,[status(thm)],[75, 22820])).
% 29.31/19.51 tff(22822,plain,
% 29.31/19.51 (~big_f(f4(c4), c4)),
% 29.31/19.51 inference(unit_resolution,[status(thm)],[11764, 22812, 11752, 27])).
% 29.31/19.51 tff(22823,plain,
% 29.31/19.51 (f1(f7(f7(c2)), c1) = c1),
% 29.31/19.51 inference(unit_resolution,[status(thm)],[422, 22822, 121, 22821, 120, 292])).
% 29.31/19.51 tff(22824,plain,
% 29.31/19.51 (c2 = f7(f7(c2))),
% 29.31/19.51 inference(transitivity,[status(thm)],[2778, 353])).
% 29.31/19.51 tff(22825,plain,
% 29.31/19.51 (f1(c2, c1) = f1(f7(f7(c2)), c1)),
% 29.31/19.51 inference(monotonicity,[status(thm)],[22824])).
% 29.31/19.51 tff(22826,plain,
% 29.31/19.51 (f1(c2, c1) = c1),
% 29.31/19.51 inference(transitivity,[status(thm)],[22825, 22823])).
% 29.31/19.51 tff(22827,plain,
% 29.31/19.51 (big_f(c2, f1(c2, c1)) <=> big_f(c2, c1)),
% 29.31/19.51 inference(monotonicity,[status(thm)],[22826])).
% 29.31/19.51 tff(22828,plain,
% 29.31/19.51 (big_f(c2, c1) <=> big_f(c2, f1(c2, c1))),
% 29.31/19.51 inference(symmetry,[status(thm)],[22827])).
% 29.31/19.51 tff(22829,plain,
% 29.31/19.51 (big_f(c2, f1(c2, c1))),
% 29.31/19.51 inference(modus_ponens,[status(thm)],[22766, 22828])).
% 29.31/19.51 tff(22830,plain,
% 29.31/19.51 (big_f(f7(c1), c1)),
% 29.31/19.51 inference(modus_ponens,[status(thm)],[22766, 693])).
% 29.31/19.51 tff(22831,plain,
% 29.31/19.51 (big_f(f7(c1), f1(f7(c1), c1))),
% 29.31/19.51 inference(unit_resolution,[status(thm)],[15864, 22823, 22830, 292])).
% 29.31/19.51 tff(22832,plain,
% 29.31/19.51 (~(f1(c2, c1) = c2)),
% 29.31/19.51 inference(unit_resolution,[status(thm)],[12197, 22831, 121, 120])).
% 29.31/19.51 tff(22833,plain,
% 29.31/19.51 (f1(c2, c1) = c1),
% 29.31/19.51 inference(unit_resolution,[status(thm)],[10113, 22832])).
% 29.31/19.51 tff(22834,plain,
% 29.31/19.51 (c2 = c4),
% 29.31/19.51 inference(modus_ponens,[status(thm)],[22812, 159])).
% 29.31/19.51 tff(22835,plain,
% 29.31/19.51 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c2 = c4)) | big_f(c1, c2) | (~(c1 = f4(c2))) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(c2 = c4)) | big_f(c1, c2) | (~(c1 = f4(c2))) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1)))),
% 29.31/19.51 inference(rewrite,[status(thm)],[])).
% 29.31/19.51 tff(22836,plain,
% 29.31/19.51 (((c2 = c3) | (~(c2 = c4)) | big_f(c1, c2) | (~(c1 = f4(c2))) | (~(f1(c2, c1) = c1)) | (~big_f(c2, f1(c2, c1)))) <=> ((c2 = c3) | (~(c2 = c4)) | big_f(c1, c2) | (~(c1 = f4(c2))) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1)))),
% 29.31/19.51 inference(rewrite,[status(thm)],[])).
% 29.31/19.51 tff(22837,plain,
% 29.31/19.51 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c2 = c4)) | big_f(c1, c2) | (~(c1 = f4(c2))) | (~(f1(c2, c1) = c1)) | (~big_f(c2, f1(c2, c1))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c2 = c4)) | big_f(c1, c2) | (~(c1 = f4(c2))) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1))))),
% 29.31/19.51 inference(monotonicity,[status(thm)],[22836])).
% 29.31/19.51 tff(22838,plain,
% 29.31/19.51 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c2 = c4)) | big_f(c1, c2) | (~(c1 = f4(c2))) | (~(f1(c2, c1) = c1)) | (~big_f(c2, f1(c2, c1))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(c2 = c4)) | big_f(c1, c2) | (~(c1 = f4(c2))) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1)))),
% 29.31/19.51 inference(transitivity,[status(thm)],[22837, 22835])).
% 29.31/19.51 tff(22839,plain,
% 29.31/19.51 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c2 = c4)) | big_f(c1, c2) | (~(c1 = f4(c2))) | (~(f1(c2, c1) = c1)) | (~big_f(c2, f1(c2, c1))))),
% 29.31/19.51 inference(quant_inst,[status(thm)],[])).
% 29.31/19.51 tff(22840,plain,
% 29.31/19.51 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(c2 = c4)) | big_f(c1, c2) | (~(c1 = f4(c2))) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1))),
% 29.31/19.51 inference(modus_ponens,[status(thm)],[22839, 22838])).
% 29.31/19.51 tff(22841,plain,
% 29.31/19.51 ($false),
% 29.31/19.51 inference(unit_resolution,[status(thm)],[22840, 447, 22834, 377, 22833, 22829, 27, 22816])).
% 29.31/19.51 tff(22842,plain,((~(f7(c2) = c1)) | (c2 = c3) | big_f(c1, c2) | (~(f4(c4) = c1)) | big_f(c2, c2) | (f7(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.31/19.51 tff(22843,plain,
% 29.31/19.51 (~(f7(c2) = c1)),
% 29.31/19.51 inference(unit_resolution,[status(thm)],[22842, 27, 377, 11752, 121, 115])).
% 29.31/19.51 tff(22844,plain,
% 29.31/19.51 (f7(c2) = c2),
% 29.31/19.51 inference(unit_resolution,[status(thm)],[21, 22843])).
% 29.31/19.51 tff(22845,plain,
% 29.31/19.51 (f7(f7(c2)) = f7(c2)),
% 29.31/19.51 inference(monotonicity,[status(thm)],[22844])).
% 29.31/19.51 tff(22846,plain,
% 29.31/19.51 (f7(f7(c2)) = c2),
% 29.31/19.51 inference(transitivity,[status(thm)],[22845, 22844])).
% 29.31/19.51 tff(22847,plain,
% 29.31/19.51 ((f7(f7(c2)) = c1) <=> (c2 = c1)),
% 29.31/19.51 inference(monotonicity,[status(thm)],[22846])).
% 29.31/19.52 tff(22848,plain,
% 29.31/19.52 ((c2 = c1) <=> (f7(f7(c2)) = c1)),
% 29.31/19.52 inference(symmetry,[status(thm)],[22847])).
% 29.31/19.52 tff(22849,plain,
% 29.31/19.52 ((c2 = c1) <=> (f7(f7(c2)) = c3)),
% 29.31/19.52 inference(transitivity,[status(thm)],[22848, 22793])).
% 29.31/19.52 tff(22850,plain,
% 29.31/19.52 ((~(c2 = c1)) <=> (~(f7(f7(c2)) = c3))),
% 29.31/19.52 inference(monotonicity,[status(thm)],[22849])).
% 29.31/19.52 tff(22851,plain,
% 29.31/19.52 (~(f7(f7(c2)) = c3)),
% 29.31/19.52 inference(modus_ponens,[status(thm)],[75, 22850])).
% 29.31/19.52 tff(22852,plain,
% 29.31/19.52 (~big_f(f4(c4), c4)),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[11764, 22787, 11752, 27])).
% 29.31/19.52 tff(22853,plain,
% 29.31/19.52 (f1(f7(f7(c2)), c1) = c1),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[5433, 22852, 121, 22844, 22851])).
% 29.31/19.52 tff(22854,plain,
% 29.31/19.52 (f7(c2) = f7(f7(c2))),
% 29.31/19.52 inference(symmetry,[status(thm)],[22845])).
% 29.31/19.52 tff(22855,plain,
% 29.31/19.52 (c2 = f7(c2)),
% 29.31/19.52 inference(symmetry,[status(thm)],[22844])).
% 29.31/19.52 tff(22856,plain,
% 29.31/19.52 (c2 = f7(f7(c2))),
% 29.31/19.52 inference(transitivity,[status(thm)],[22855, 22854])).
% 29.31/19.52 tff(22857,plain,
% 29.31/19.52 (f1(c2, c1) = f1(f7(f7(c2)), c1)),
% 29.31/19.52 inference(monotonicity,[status(thm)],[22856])).
% 29.31/19.52 tff(22858,plain,
% 29.31/19.52 (f1(c2, c1) = c1),
% 29.31/19.52 inference(transitivity,[status(thm)],[22857, 22853])).
% 29.31/19.52 tff(22859,plain,
% 29.31/19.52 (big_f(c2, f1(c2, c1)) <=> big_f(c2, c1)),
% 29.31/19.52 inference(monotonicity,[status(thm)],[22858])).
% 29.31/19.52 tff(22860,plain,
% 29.31/19.52 (big_f(c2, c1) <=> big_f(c2, f1(c2, c1))),
% 29.31/19.52 inference(symmetry,[status(thm)],[22859])).
% 29.31/19.52 tff(22861,plain,
% 29.31/19.52 (big_f(c2, f1(c2, c1))),
% 29.31/19.52 inference(modus_ponens,[status(thm)],[22766, 22860])).
% 29.31/19.52 tff(22862,plain,
% 29.31/19.52 ((f1(f7(f7(c2)), c1) = c1) <=> (f1(c2, c1) = c1)),
% 29.31/19.52 inference(monotonicity,[status(thm)],[10762])).
% 29.31/19.52 tff(22863,plain,
% 29.31/19.52 ((f1(f7(f7(c2)), c1) = c1) <=> (f1(f7(c1), c1) = c1)),
% 29.31/19.52 inference(transitivity,[status(thm)],[22862, 996])).
% 29.31/19.52 tff(22864,plain,
% 29.31/19.52 (f1(f7(c1), c1) = c1),
% 29.31/19.52 inference(modus_ponens,[status(thm)],[874, 22863])).
% 29.31/19.52 tff(22865,plain,
% 29.31/19.52 ($false),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[12203, 22864])).
% 29.31/19.52 tff(22866,plain,((~(f1(f7(f7(c2)), c1) = c1)) | (f1(f7(c1), c1) = c1) | (~(f7(c1) = c2)) | (~(f7(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.31/19.52 tff(22867,plain,
% 29.31/19.52 (f1(f7(c1), c1) = c1),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[22866, 22853, 22844, 120])).
% 29.31/19.52 tff(22868,plain,
% 29.31/19.52 (f1(c2, c1) = c1),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[16007, 22867, 120])).
% 29.31/19.52 tff(22869,plain,
% 29.31/19.52 (c2 = c4),
% 29.31/19.52 inference(modus_ponens,[status(thm)],[22787, 159])).
% 29.31/19.52 tff(22870,plain,
% 29.31/19.52 ($false),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[22840, 447, 22869, 377, 22868, 22861, 27, 22791])).
% 29.31/19.52 tff(22871,plain,(big_f(c1, c2) | (c2 = c3) | (~(f4(c4) = c1)) | big_f(c2, c2) | (f7(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.31/19.52 tff(22872,plain,
% 29.31/19.52 (big_f(c1, c2)),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[22871, 377, 11751, 121, 115])).
% 29.31/19.52 tff(22873,plain,
% 29.31/19.52 (big_f(f9(c2, c1), f10(c2))),
% 29.31/19.52 inference(modus_ponens,[status(thm)],[2865, 17246])).
% 29.31/19.52 tff(22874,plain,
% 29.31/19.52 (~(c1 = f5(c1))),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[17256, 783, 115, 122, 17244, 22873, 285])).
% 29.31/19.52 tff(22875,plain,
% 29.31/19.52 (~(f5(c1) = c1)),
% 29.31/19.52 inference(modus_ponens,[status(thm)],[22874, 2279])).
% 29.31/19.52 tff(22876,plain,
% 29.31/19.52 (~(c2 = f5(c1))),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[2914, 783, 1726, 115, 122, 17244, 22873])).
% 29.31/19.52 tff(22877,plain,
% 29.31/19.52 (~(f5(c1) = c2)),
% 29.31/19.52 inference(modus_ponens,[status(thm)],[22876, 11786])).
% 29.31/19.52 tff(22878,plain,
% 29.31/19.52 ($false),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[1708, 22877, 22875])).
% 29.31/19.52 tff(22879,plain,(big_f(f7(c1), c1) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (~big_f(c1, c2)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 29.31/19.52 tff(22880,plain,
% 29.31/19.52 (big_f(f7(c1), c1)),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[22879, 22872, 122, 115, 121])).
% 29.31/19.52 tff(22881,plain,
% 29.31/19.52 (big_f(c2, c1)),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[15738, 22880, 120])).
% 29.31/19.52 tff(22882,plain,
% 29.31/19.52 (big_f(f7(c2), c2)),
% 29.31/19.52 inference(modus_ponens,[status(thm)],[22872, 12163])).
% 29.31/19.52 tff(22883,plain,
% 29.31/19.52 (~big_f(f7(c2), f7(c2))),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[15961, 22882, 122, 121, 17])).
% 29.31/19.52 tff(22884,plain,
% 29.31/19.52 (~big_f(c1, c1)),
% 29.31/19.52 inference(modus_ponens,[status(thm)],[22883, 124])).
% 29.31/19.52 tff(22885,plain,
% 29.31/19.52 (f5(f7(c1)) = f5(c2)),
% 29.31/19.52 inference(monotonicity,[status(thm)],[120])).
% 29.31/19.52 tff(22886,plain,
% 29.31/19.52 ((f7(c1) = f5(f7(c1))) <=> (c2 = f5(c2))),
% 29.31/19.52 inference(monotonicity,[status(thm)],[120, 22885])).
% 29.31/19.52 tff(22887,plain,
% 29.31/19.52 ((c2 = f5(c2)) <=> (f7(c1) = f5(f7(c1)))),
% 29.31/19.52 inference(symmetry,[status(thm)],[22886])).
% 29.31/19.52 tff(22888,plain,
% 29.31/19.52 (~(f7(c2) = f5(c2))),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[15985, 22883, 122, 121, 17, 22882])).
% 29.31/19.52 tff(22889,plain,
% 29.31/19.52 (~(f5(c2) = c1)),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[8394, 22888, 22])).
% 29.31/19.52 tff(22890,plain,
% 29.31/19.52 (f5(c2) = c2),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[1547, 22889])).
% 29.31/19.52 tff(22891,plain,
% 29.31/19.52 (c2 = f5(c2)),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[8113, 22890])).
% 29.31/19.52 tff(22892,plain,
% 29.31/19.52 (f7(c1) = f5(f7(c1))),
% 29.31/19.52 inference(modus_ponens,[status(thm)],[22891, 22887])).
% 29.31/19.52 tff(22893,plain,
% 29.31/19.52 (f7(f4(c4)) = f7(c1)),
% 29.31/19.52 inference(monotonicity,[status(thm)],[11751])).
% 29.31/19.52 tff(22894,plain,
% 29.31/19.52 (f7(f4(c4)) = c2),
% 29.31/19.52 inference(transitivity,[status(thm)],[22893, 120])).
% 29.31/19.52 tff(22895,plain,
% 29.31/19.52 ((f7(f4(c4)) = f4(c4)) <=> (c2 = c1)),
% 29.31/19.52 inference(monotonicity,[status(thm)],[22894, 11751])).
% 29.31/19.52 tff(22896,plain,
% 29.31/19.52 ((c2 = c1) <=> (f7(f4(c4)) = f4(c4))),
% 29.31/19.52 inference(symmetry,[status(thm)],[22895])).
% 29.31/19.52 tff(22897,plain,
% 29.31/19.52 ((~(c2 = c1)) <=> (~(f7(f4(c4)) = f4(c4)))),
% 29.31/19.52 inference(monotonicity,[status(thm)],[22896])).
% 29.31/19.52 tff(22898,plain,
% 29.31/19.52 (~(f7(f4(c4)) = f4(c4))),
% 29.31/19.52 inference(modus_ponens,[status(thm)],[75, 22897])).
% 29.31/19.52 tff(22899,plain,
% 29.31/19.52 (~(c4 = c1)),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[22785, 22881, 377, 120, 121, 11751])).
% 29.31/19.52 tff(22900,plain,
% 29.31/19.52 (c4 = c2),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[461, 22899])).
% 29.31/19.52 tff(22901,plain,
% 29.31/19.52 (f7(c1) = c4),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[19869, 22900, 120])).
% 29.31/19.52 tff(22902,plain,
% 29.31/19.52 (~(c1 = c4)),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[19880, 22901, 11751, 22898])).
% 29.31/19.52 tff(22903,plain,
% 29.31/19.52 (~(f5(c1) = c2)),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[10391, 22882, 122, 121, 115, 22])).
% 29.31/19.52 tff(22904,plain,
% 29.31/19.52 (f5(c1) = c1),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[1708, 22903])).
% 29.31/19.52 tff(22905,plain,
% 29.31/19.52 (~(f3(c1, c2) = c2)),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[22410, 12187, 121, 1004, 15735, 347, 482])).
% 29.31/19.52 tff(22906,plain,
% 29.31/19.52 (~(f1(f7(f7(c2)), c1) = c1)),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[15864, 12198, 15735, 292])).
% 29.31/19.52 tff(22907,plain,
% 29.31/19.52 (f1(f7(f7(c2)), c1) = c2),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[384, 22906])).
% 29.31/19.52 tff(22908,plain,
% 29.31/19.52 (c1 = f3(c1, c2)),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[20609, 22907, 292, 230, 16042, 347, 22905])).
% 29.31/19.52 tff(22909,plain,
% 29.31/19.52 (big_f(c1, c1) <=> big_f(f3(c1, c2), c1)),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[13192, 22908])).
% 29.31/19.52 tff(22910,plain,
% 29.31/19.52 (~big_f(f3(c1, c2), c1)),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[13186, 22909, 66])).
% 29.31/19.52 tff(22911,plain,
% 29.31/19.52 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c2 = c3) | (c1 = c4) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (c2 = c3) | (c1 = c4) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2))),
% 29.31/19.52 inference(rewrite,[status(thm)],[])).
% 29.31/19.52 tff(22912,plain,
% 29.31/19.52 (((c1 = c4) | (f3(c1, c2) = c2) | big_f(f3(c1, c2), c1) | (c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1))) <=> ((c2 = c3) | (c1 = c4) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2))),
% 29.31/19.52 inference(rewrite,[status(thm)],[])).
% 29.31/19.52 tff(22913,plain,
% 29.31/19.52 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c1 = c4) | (f3(c1, c2) = c2) | big_f(f3(c1, c2), c1) | (c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c2 = c3) | (c1 = c4) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2)))),
% 29.31/19.52 inference(monotonicity,[status(thm)],[22912])).
% 29.31/19.52 tff(22914,plain,
% 29.31/19.52 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c1 = c4) | (f3(c1, c2) = c2) | big_f(f3(c1, c2), c1) | (c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (c2 = c3) | (c1 = c4) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2))),
% 29.31/19.52 inference(transitivity,[status(thm)],[22913, 22911])).
% 29.31/19.52 tff(22915,plain,
% 29.31/19.52 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c1 = c4) | (f3(c1, c2) = c2) | big_f(f3(c1, c2), c1) | (c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)))),
% 29.31/19.52 inference(quant_inst,[status(thm)],[])).
% 29.31/19.52 tff(22916,plain,
% 29.31/19.52 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (c2 = c3) | (c1 = c4) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2)),
% 29.31/19.52 inference(modus_ponens,[status(thm)],[22915, 22914])).
% 29.31/19.52 tff(22917,plain,
% 29.31/19.52 ($false),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[22916, 1014, 482, 377, 12187, 13410, 22910, 22905])).
% 29.31/19.52 tff(22918,plain,((f1(c2, c1) = c1) | (c1 = c4) | (c2 = c3) | big_f(c1, c1) | (~(f7(c2) = c1)) | (~(f5(c1) = c1)) | (~(f7(c1) = f5(f7(c1)))) | (~(f7(c1) = c2)) | (~big_f(f7(c1), c1)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 29.31/19.52 tff(22919,plain,
% 29.31/19.52 (f1(c2, c1) = c1),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[22918, 66, 377, 482, 292, 230, 16042, 347, 15735, 121])).
% 29.31/19.52 tff(22920,plain,
% 29.31/19.52 (big_f(c2, f1(c2, c1)) <=> big_f(c2, c1)),
% 29.31/19.52 inference(monotonicity,[status(thm)],[22919])).
% 29.31/19.52 tff(22921,plain,
% 29.31/19.52 (big_f(c2, c1) <=> big_f(c2, f1(c2, c1))),
% 29.31/19.52 inference(symmetry,[status(thm)],[22920])).
% 29.31/19.52 tff(22922,plain,
% 29.31/19.52 (big_f(c2, f1(c2, c1))),
% 29.31/19.52 inference(modus_ponens,[status(thm)],[15853, 22921])).
% 29.31/19.52 tff(22923,plain,
% 29.31/19.52 (big_f(f3(c1, c2), c1)),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[16151, 22922, 347, 22919, 377, 482, 15735])).
% 29.31/19.52 tff(22924,plain,
% 29.31/19.52 (~(big_f(c1, c1) <=> big_f(f3(c1, c2), c1))),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[13186, 22923, 66])).
% 29.31/19.52 tff(22925,plain,
% 29.31/19.52 (~(c1 = f3(c1, c2))),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[13192, 22924])).
% 29.31/19.52 tff(22926,plain,
% 29.31/19.52 (f3(c1, c2) = c2),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[16063, 22925, 230, 347, 16042, 22919])).
% 29.31/19.52 tff(22927,plain,
% 29.31/19.52 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (c1 = c4) | (~big_f(f3(c1, c2), c1)) | (~(f3(c1, c2) = c2)) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (c1 = c4) | (~big_f(f3(c1, c2), c1)) | (~(f3(c1, c2) = c2)) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1)))),
% 29.31/19.52 inference(rewrite,[status(thm)],[])).
% 29.31/19.52 tff(22928,plain,
% 29.31/19.52 (((c1 = c4) | (c2 = c3) | (~(f3(c1, c2) = c2)) | (~big_f(f3(c1, c2), c1)) | (~(f1(c2, c1) = c1)) | (~big_f(c2, f1(c2, c1)))) <=> ((c2 = c3) | (c1 = c4) | (~big_f(f3(c1, c2), c1)) | (~(f3(c1, c2) = c2)) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1)))),
% 29.31/19.52 inference(rewrite,[status(thm)],[])).
% 29.31/19.52 tff(22929,plain,
% 29.31/19.52 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c4) | (c2 = c3) | (~(f3(c1, c2) = c2)) | (~big_f(f3(c1, c2), c1)) | (~(f1(c2, c1) = c1)) | (~big_f(c2, f1(c2, c1))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (c1 = c4) | (~big_f(f3(c1, c2), c1)) | (~(f3(c1, c2) = c2)) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1))))),
% 29.31/19.52 inference(monotonicity,[status(thm)],[22928])).
% 29.31/19.52 tff(22930,plain,
% 29.31/19.52 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c4) | (c2 = c3) | (~(f3(c1, c2) = c2)) | (~big_f(f3(c1, c2), c1)) | (~(f1(c2, c1) = c1)) | (~big_f(c2, f1(c2, c1))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (c1 = c4) | (~big_f(f3(c1, c2), c1)) | (~(f3(c1, c2) = c2)) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1)))),
% 29.31/19.52 inference(transitivity,[status(thm)],[22929, 22927])).
% 29.31/19.52 tff(22931,plain,
% 29.31/19.52 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c4) | (c2 = c3) | (~(f3(c1, c2) = c2)) | (~big_f(f3(c1, c2), c1)) | (~(f1(c2, c1) = c1)) | (~big_f(c2, f1(c2, c1))))),
% 29.31/19.52 inference(quant_inst,[status(thm)],[])).
% 29.31/19.52 tff(22932,plain,
% 29.31/19.52 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (c1 = c4) | (~big_f(f3(c1, c2), c1)) | (~(f3(c1, c2) = c2)) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1))),
% 29.31/19.52 inference(modus_ponens,[status(thm)],[22931, 22930])).
% 29.31/19.52 tff(22933,plain,
% 29.31/19.52 ($false),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[22932, 933, 482, 377, 22919, 22922, 22923, 22926])).
% 29.31/19.52 tff(22934,plain,(big_f(c1, c1) | (c1 = c4) | (c2 = c3) | (~(f5(c1) = c1)) | (~(f7(c1) = c2)) | (~(f7(c1) = f5(f7(c1)))) | (~big_f(f7(c1), c1)) | (~(f7(c2) = c1)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 29.31/19.52 tff(22935,plain,
% 29.31/19.52 (big_f(c1, c1)),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[22934, 22904, 377, 22902, 120, 22892, 22880, 22, 121])).
% 29.31/19.52 tff(22936,plain,
% 29.31/19.52 ($false),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[22935, 22884])).
% 29.31/19.52 tff(22937,plain,((f7(c2) = c2) | (c2 = c3) | big_f(c2, c2) | (~(f10(c2) = c2)) | (f7(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.31/19.52 tff(22938,plain,
% 29.31/19.52 (f7(c2) = c2),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[22937, 377, 121, 122, 115])).
% 29.31/19.52 tff(22939,plain,
% 29.31/19.52 (f9(c2, c1) = c1),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[11359, 22938, 115, 122, 121, 22881])).
% 29.31/19.52 tff(22940,plain,
% 29.31/19.52 (big_f(f9(c2, c1), f10(c2)) <=> big_f(c1, c2)),
% 29.31/19.52 inference(monotonicity,[status(thm)],[22939, 122])).
% 29.31/19.52 tff(22941,plain,
% 29.31/19.52 (big_f(c1, c2) <=> big_f(f9(c2, c1), f10(c2))),
% 29.31/19.52 inference(symmetry,[status(thm)],[22940])).
% 29.31/19.52 tff(22942,plain,
% 29.31/19.52 (big_f(f9(c2, c1), f10(c2))),
% 29.31/19.52 inference(modus_ponens,[status(thm)],[22872, 22941])).
% 29.31/19.52 tff(22943,plain,
% 29.31/19.52 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((f7(c1) = c1) | (~(f10(c2) = c2)) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))))),
% 29.31/19.52 inference(rewrite,[status(thm)],[])).
% 29.31/19.52 tff(22944,plain,
% 29.31/19.52 (((~(f10(c2) = c2)) | (f7(c1) = c1) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2)))) <=> ((f7(c1) = c1) | (~(f10(c2) = c2)) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))))),
% 29.31/19.52 inference(rewrite,[status(thm)],[])).
% 29.31/19.52 tff(22945,plain,
% 29.31/19.52 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c1) = c1) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((f7(c1) = c1) | (~(f10(c2) = c2)) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2)))))),
% 29.31/19.52 inference(monotonicity,[status(thm)],[22944])).
% 29.31/19.52 tff(22946,plain,
% 29.31/19.52 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c1) = c1) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))))),
% 29.31/19.52 inference(transitivity,[status(thm)],[22945, 22943])).
% 29.31/19.52 tff(22947,plain,
% 29.31/19.52 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c1) = c1) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))))),
% 29.31/19.52 inference(quant_inst,[status(thm)],[])).
% 29.31/19.52 tff(22948,plain,
% 29.31/19.52 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2)))),
% 29.31/19.52 inference(modus_ponens,[status(thm)],[22947, 22946])).
% 29.31/19.52 tff(22949,plain,
% 29.31/19.52 (c1 = f5(c1)),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[22948, 1190, 115, 122, 22939, 22942, 22880])).
% 29.31/19.52 tff(22950,plain,
% 29.31/19.52 (f5(c1) = c1),
% 29.31/19.52 inference(modus_ponens,[status(thm)],[22949, 128])).
% 29.31/19.52 tff(22951,plain,
% 29.31/19.52 (big_f(c2, f6(c2, c1)) <=> big_f(f7(c2), f6(c2, c1))),
% 29.31/19.52 inference(monotonicity,[status(thm)],[82])).
% 29.31/19.52 tff(22952,plain,
% 29.31/19.52 (f6(c2, c1) = c1),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[3563, 3197, 122, 77, 2865, 736, 230])).
% 29.31/19.52 tff(22953,plain,
% 29.31/19.52 (c1 = f6(c2, c1)),
% 29.31/19.52 inference(symmetry,[status(thm)],[22952])).
% 29.31/19.52 tff(22954,plain,
% 29.31/19.52 (big_f(c2, c1) <=> big_f(c2, f6(c2, c1))),
% 29.31/19.52 inference(monotonicity,[status(thm)],[22953])).
% 29.31/19.52 tff(22955,plain,
% 29.31/19.52 (big_f(c2, c1) <=> big_f(f7(c2), f6(c2, c1))),
% 29.31/19.52 inference(transitivity,[status(thm)],[22954, 22951])).
% 29.31/19.52 tff(22956,plain,
% 29.31/19.52 (big_f(f7(c2), f6(c2, c1))),
% 29.31/19.52 inference(modus_ponens,[status(thm)],[348, 22955])).
% 29.31/19.52 tff(22957,plain,
% 29.31/19.52 ($false),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[3197, 22956])).
% 29.31/19.52 tff(22958,plain,(big_f(f7(c2), f6(c2, c1)) | (~big_f(c2, c1)) | (~(f7(c2) = c2)) | (~(f10(c2) = c2)) | (~big_f(c1, c2)) | (~(f9(c2, c1) = c1)) | (~(f5(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.31/19.52 tff(22959,plain,
% 29.31/19.52 (big_f(f7(c2), f6(c2, c1))),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[22958, 22881, 22938, 122, 22872, 22939, 22950])).
% 29.31/19.52 tff(22960,plain,
% 29.31/19.52 (f6(c2, c1) = c1),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[17266, 22959, 22938, 121, 11754])).
% 29.31/19.52 tff(22961,plain,
% 29.31/19.52 ($false),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[3097, 2378, 122, 22939, 22942, 22938, 22960, 22959])).
% 29.31/19.52 tff(22962,plain,((c2 = c3) | (~(f10(c2) = c2)) | big_f(c2, c2) | (f7(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.31/19.52 tff(22963,plain,
% 29.31/19.52 (c2 = c3),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[22962, 121, 122, 115])).
% 29.31/19.52 tff(22964,plain,
% 29.31/19.52 (c3 = c2),
% 29.31/19.52 inference(modus_ponens,[status(thm)],[22963, 127])).
% 29.31/19.52 tff(22965,plain,
% 29.31/19.52 ((f4(c4) = c3) <=> (c1 = c3)),
% 29.31/19.52 inference(monotonicity,[status(thm)],[11751])).
% 29.31/19.52 tff(22966,plain,
% 29.31/19.52 ((c1 = c3) <=> (f4(c4) = c3)),
% 29.31/19.52 inference(symmetry,[status(thm)],[22965])).
% 29.31/19.52 tff(22967,plain,
% 29.31/19.52 (c3 = c2),
% 29.31/19.52 inference(symmetry,[status(thm)],[22963])).
% 29.31/19.52 tff(22968,plain,
% 29.31/19.52 ((c1 = c3) <=> (c1 = c2)),
% 29.31/19.52 inference(monotonicity,[status(thm)],[22967])).
% 29.31/19.52 tff(22969,plain,
% 29.31/19.52 ((c1 = c3) <=> (c2 = c1)),
% 29.31/19.52 inference(transitivity,[status(thm)],[22968, 1])).
% 29.31/19.52 tff(22970,plain,
% 29.31/19.52 ((c2 = c1) <=> (c1 = c3)),
% 29.31/19.52 inference(symmetry,[status(thm)],[22969])).
% 29.31/19.52 tff(22971,plain,
% 29.31/19.52 ((c2 = c1) <=> (f4(c4) = c3)),
% 29.31/19.52 inference(transitivity,[status(thm)],[22970, 22966])).
% 29.31/19.52 tff(22972,plain,
% 29.31/19.52 ((~(c2 = c1)) <=> (~(f4(c4) = c3))),
% 29.31/19.52 inference(monotonicity,[status(thm)],[22971])).
% 29.31/19.52 tff(22973,plain,
% 29.31/19.52 (~(f4(c4) = c3)),
% 29.31/19.52 inference(modus_ponens,[status(thm)],[75, 22972])).
% 29.31/19.52 tff(22974,plain,
% 29.31/19.52 ((~(c2 = c1)) <=> (~(c1 = c3))),
% 29.31/19.52 inference(monotonicity,[status(thm)],[22970])).
% 29.31/19.52 tff(22975,plain,
% 29.31/19.52 (~(c1 = c3)),
% 29.31/19.52 inference(modus_ponens,[status(thm)],[75, 22974])).
% 29.31/19.52 tff(22976,plain,
% 29.31/19.52 (~big_f(c1, c1)),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[22765, 2, 115, 1726])).
% 29.31/19.52 tff(22977,plain,
% 29.31/19.52 (~big_f(f4(c4), c4)),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[11772, 22976, 11752, 27])).
% 29.31/19.52 tff(22978,plain,
% 29.31/19.52 ($false),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[1315, 22977, 8257])).
% 29.31/19.52 tff(22979,plain,(big_f(c2, c1) | (~(f4(c4) = c1)) | big_f(c1, c2) | big_f(c2, c2) | (~(c3 = c2)) | (f7(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.31/19.52 tff(22980,plain,
% 29.31/19.52 (big_f(c2, c1)),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[22979, 27, 11751, 121, 22964, 115])).
% 29.31/19.52 tff(22981,plain,
% 29.31/19.52 (~(f1(f4(c4), c1) = c1)),
% 29.31/19.52 inference(modus_ponens,[status(thm)],[9710, 18067])).
% 29.31/19.52 tff(22982,assumption,(big_f(f4(c4), f1(f4(c4), c1))), introduced(assumption)).
% 29.31/19.52 tff(22983,plain,
% 29.31/19.52 (big_f(c1, f1(c1, c1))),
% 29.31/19.52 inference(modus_ponens,[status(thm)],[22982, 18061])).
% 29.31/19.52 tff(22984,plain,
% 29.31/19.52 ($false),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[9673, 22983])).
% 29.31/19.52 tff(22985,plain,((~big_f(f4(c4), f1(f4(c4), c1))) | big_f(c1, f1(c1, c1)) | (~(f4(c4) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.31/19.52 tff(22986,plain,
% 29.31/19.52 (~big_f(f4(c4), f1(f4(c4), c1))),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[22985, 15793, 11752])).
% 29.31/19.52 tff(22987,plain,
% 29.31/19.52 (big_f(f4(c4), c4)),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[18077, 22986, 18059, 22981])).
% 29.31/19.52 tff(22988,plain,
% 29.31/19.52 (~(c4 = c2)),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[11764, 22987, 11752, 27])).
% 29.31/19.52 tff(22989,plain,
% 29.31/19.52 (c4 = c1),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[461, 22988])).
% 29.31/19.52 tff(22990,plain,
% 29.31/19.52 (c1 = c4),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[484, 22989])).
% 29.31/19.52 tff(22991,plain,
% 29.31/19.52 (c1 = f4(c1)),
% 29.31/19.52 inference(unit_resolution,[status(thm)],[11534, 22990, 168, 4932, 15793])).
% 29.31/19.52 tff(22992,plain,
% 29.31/19.52 (f4(c1) = c1),
% 29.31/19.52 inference(symmetry,[status(thm)],[22991])).
% 29.31/19.52 tff(22993,plain,
% 29.31/19.52 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((f1(c1, c1) = c1) | (c1 = c3) | big_f(c1, f1(c1, c1)) | (~(c1 = c4)) | (~big_f(c2, c1)) | (c2 = f4(c1)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (f1(c1, c1) = c1) | (c1 = c3) | big_f(c1, f1(c1, c1)) | (~(c1 = c4)) | (~big_f(c2, c1)) | (c2 = f4(c1)))),
% 29.31/19.52 inference(rewrite,[status(thm)],[])).
% 29.31/19.52 tff(22994,plain,
% 29.31/19.52 (((c1 = c3) | (f1(c1, c1) = c1) | big_f(c1, f1(c1, c1)) | (~(c1 = c4)) | (c2 = f4(c1)) | (~big_f(c2, c1))) <=> ((f1(c1, c1) = c1) | (c1 = c3) | big_f(c1, f1(c1, c1)) | (~(c1 = c4)) | (~big_f(c2, c1)) | (c2 = f4(c1)))),
% 29.31/19.52 inference(rewrite,[status(thm)],[])).
% 29.31/19.53 tff(22995,plain,
% 29.31/19.53 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c1 = c3) | (f1(c1, c1) = c1) | big_f(c1, f1(c1, c1)) | (~(c1 = c4)) | (c2 = f4(c1)) | (~big_f(c2, c1)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((f1(c1, c1) = c1) | (c1 = c3) | big_f(c1, f1(c1, c1)) | (~(c1 = c4)) | (~big_f(c2, c1)) | (c2 = f4(c1))))),
% 29.31/19.53 inference(monotonicity,[status(thm)],[22994])).
% 29.31/19.53 tff(22996,plain,
% 29.31/19.53 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c1 = c3) | (f1(c1, c1) = c1) | big_f(c1, f1(c1, c1)) | (~(c1 = c4)) | (c2 = f4(c1)) | (~big_f(c2, c1)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (f1(c1, c1) = c1) | (c1 = c3) | big_f(c1, f1(c1, c1)) | (~(c1 = c4)) | (~big_f(c2, c1)) | (c2 = f4(c1)))),
% 29.31/19.53 inference(transitivity,[status(thm)],[22995, 22993])).
% 29.31/19.53 tff(22997,plain,
% 29.31/19.53 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c1 = c3) | (f1(c1, c1) = c1) | big_f(c1, f1(c1, c1)) | (~(c1 = c4)) | (c2 = f4(c1)) | (~big_f(c2, c1)))),
% 29.31/19.53 inference(quant_inst,[status(thm)],[])).
% 29.31/19.53 tff(22998,plain,
% 29.31/19.53 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (f1(c1, c1) = c1) | (c1 = c3) | big_f(c1, f1(c1, c1)) | (~(c1 = c4)) | (~big_f(c2, c1)) | (c2 = f4(c1))),
% 29.31/19.53 inference(modus_ponens,[status(thm)],[22997, 22996])).
% 29.31/19.53 tff(22999,plain,
% 29.31/19.53 ((~(c1 = c4)) | (c2 = f4(c1))),
% 29.31/19.53 inference(unit_resolution,[status(thm)],[22998, 525, 9710, 168, 15793, 348])).
% 29.31/19.53 tff(23000,plain,
% 29.31/19.53 (c2 = f4(c1)),
% 29.31/19.53 inference(unit_resolution,[status(thm)],[22999, 22990])).
% 29.31/19.53 tff(23001,plain,
% 29.31/19.53 (c2 = c1),
% 29.31/19.53 inference(transitivity,[status(thm)],[23000, 22992])).
% 29.31/19.53 tff(23002,plain,
% 29.31/19.53 ($false),
% 29.31/19.53 inference(unit_resolution,[status(thm)],[75, 23001])).
% 29.31/19.53 tff(23003,plain,((f1(c1, c1) = c1) | (c1 = c3) | (~big_f(c2, c1)) | (~big_f(c1, c1)) | (~(f4(c4) = c1)) | big_f(c1, c2) | (f4(c4) = c3)), inference(lemma,lemma(discharge,[]))).
% 29.31/19.53 tff(23004,plain,
% 29.31/19.53 (f1(c1, c1) = c1),
% 29.31/19.53 inference(unit_resolution,[status(thm)],[23003, 4932, 348, 168, 11752, 27, 18059])).
% 29.31/19.53 tff(23005,plain,
% 29.31/19.53 (big_f(c1, f1(c1, c1))),
% 29.31/19.53 inference(unit_resolution,[status(thm)],[9678, 23004, 4932])).
% 29.31/19.53 tff(23006,plain,
% 29.31/19.53 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~(c2 = c4)) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))) | big_f(c1, c2) | (~(c1 = f4(c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (~(c2 = c4)) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))) | big_f(c1, c2) | (~(c1 = f4(c2))))),
% 29.31/19.53 inference(rewrite,[status(thm)],[])).
% 29.31/19.53 tff(23007,plain,
% 29.31/19.53 (((c1 = c3) | (~(c2 = c4)) | big_f(c1, c2) | (~(c1 = f4(c2))) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1)))) <=> ((c1 = c3) | (~(c2 = c4)) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))) | big_f(c1, c2) | (~(c1 = f4(c2))))),
% 29.31/19.53 inference(rewrite,[status(thm)],[])).
% 29.31/19.53 tff(23008,plain,
% 29.31/19.53 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~(c2 = c4)) | big_f(c1, c2) | (~(c1 = f4(c2))) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~(c2 = c4)) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))) | big_f(c1, c2) | (~(c1 = f4(c2)))))),
% 29.31/19.53 inference(monotonicity,[status(thm)],[23007])).
% 29.31/19.53 tff(23009,plain,
% 29.31/19.53 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~(c2 = c4)) | big_f(c1, c2) | (~(c1 = f4(c2))) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (~(c2 = c4)) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))) | big_f(c1, c2) | (~(c1 = f4(c2))))),
% 29.31/19.53 inference(transitivity,[status(thm)],[23008, 23006])).
% 29.31/19.53 tff(23010,plain,
% 29.31/19.53 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~(c2 = c4)) | big_f(c1, c2) | (~(c1 = f4(c2))) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))))),
% 29.31/19.53 inference(quant_inst,[status(thm)],[])).
% 29.31/19.53 tff(23011,plain,
% 29.31/19.53 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (~(c2 = c4)) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))) | big_f(c1, c2) | (~(c1 = f4(c2)))),
% 29.31/19.53 inference(modus_ponens,[status(thm)],[23010, 23009])).
% 29.31/19.53 tff(23012,plain,
% 29.31/19.53 (~(f1(c1, c1) = c1)),
% 29.31/19.53 inference(unit_resolution,[status(thm)],[23011, 447, 168, 4559, 631, 27, 18123])).
% 29.31/19.53 tff(23013,plain,
% 29.31/19.53 (~(f1(c1, c1) = c2)),
% 29.31/19.53 inference(unit_resolution,[status(thm)],[4561, 4559, 27])).
% 29.31/19.53 tff(23014,plain,
% 29.31/19.53 ($false),
% 29.31/19.53 inference(unit_resolution,[status(thm)],[601, 23013, 23012])).
% 29.31/19.53 tff(23015,plain,((~big_f(c1, f1(c1, c1))) | big_f(c1, c2) | (c1 = c3) | (~(c2 = c4)) | (~(c1 = f4(c2)))), inference(lemma,lemma(discharge,[]))).
% 29.31/19.53 tff(23016,plain,
% 29.31/19.53 ($false),
% 29.31/19.53 inference(unit_resolution,[status(thm)],[23015, 18106, 432, 168, 27, 4559])).
% 29.31/19.53 tff(23017,plain,((~(c4 = c2)) | (c1 = c3) | big_f(c1, c2) | (~big_f(c1, f1(c1, c1))) | (~(f4(c4) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.31/19.53 tff(23018,plain,
% 29.31/19.53 (~(c4 = c2)),
% 29.31/19.53 inference(unit_resolution,[status(thm)],[23017, 23005, 27, 168, 11752])).
% 29.31/19.53 tff(23019,plain,
% 29.31/19.53 (c4 = c1),
% 29.31/19.53 inference(unit_resolution,[status(thm)],[461, 23018])).
% 29.31/19.53 tff(23020,plain,
% 29.31/19.53 (c1 = c4),
% 29.31/19.53 inference(unit_resolution,[status(thm)],[484, 23019])).
% 29.31/19.53 tff(23021,plain,
% 29.31/19.53 ((~(c1 = c4)) | (c1 = f4(c1))),
% 29.31/19.53 inference(unit_resolution,[status(thm)],[11543, 553, 23004, 168, 23005, 4932])).
% 29.31/19.53 tff(23022,plain,
% 29.31/19.53 (c1 = f4(c1)),
% 29.31/19.53 inference(unit_resolution,[status(thm)],[23021, 23020])).
% 29.31/19.53 tff(23023,plain,
% 29.31/19.53 (f4(c1) = c1),
% 29.31/19.53 inference(symmetry,[status(thm)],[23022])).
% 29.31/19.53 tff(23024,plain,
% 29.31/19.53 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))) | (~(c1 = c4)) | (~big_f(c2, c1)) | (c2 = f4(c1)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))) | (~(c1 = c4)) | (~big_f(c2, c1)) | (c2 = f4(c1)))),
% 29.31/19.53 inference(rewrite,[status(thm)],[])).
% 29.31/19.53 tff(23025,plain,
% 29.31/19.53 (((c1 = c3) | (~(c1 = c4)) | (c2 = f4(c1)) | (~big_f(c2, c1)) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1)))) <=> ((c1 = c3) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))) | (~(c1 = c4)) | (~big_f(c2, c1)) | (c2 = f4(c1)))),
% 29.31/19.53 inference(rewrite,[status(thm)],[])).
% 29.31/19.53 tff(23026,plain,
% 29.31/19.53 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~(c1 = c4)) | (c2 = f4(c1)) | (~big_f(c2, c1)) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))) | (~(c1 = c4)) | (~big_f(c2, c1)) | (c2 = f4(c1))))),
% 29.31/19.53 inference(monotonicity,[status(thm)],[23025])).
% 29.31/19.53 tff(23027,plain,
% 29.31/19.53 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~(c1 = c4)) | (c2 = f4(c1)) | (~big_f(c2, c1)) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))) | (~(c1 = c4)) | (~big_f(c2, c1)) | (c2 = f4(c1)))),
% 29.31/19.53 inference(transitivity,[status(thm)],[23026, 23024])).
% 29.31/19.53 tff(23028,plain,
% 29.31/19.53 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~(c1 = c4)) | (c2 = f4(c1)) | (~big_f(c2, c1)) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))))),
% 29.31/19.53 inference(quant_inst,[status(thm)],[])).
% 29.31/19.53 tff(23029,plain,
% 29.31/19.53 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))) | (~(c1 = c4)) | (~big_f(c2, c1)) | (c2 = f4(c1))),
% 29.31/19.53 inference(modus_ponens,[status(thm)],[23028, 23027])).
% 29.31/19.53 tff(23030,plain,
% 29.31/19.53 ((~(c1 = c4)) | (c2 = f4(c1))),
% 29.31/19.53 inference(unit_resolution,[status(thm)],[23029, 553, 23004, 168, 23005, 348])).
% 29.31/19.53 tff(23031,plain,
% 29.31/19.53 (c2 = f4(c1)),
% 29.31/19.53 inference(unit_resolution,[status(thm)],[23030, 23020])).
% 29.31/19.53 tff(23032,plain,
% 29.31/19.53 (c2 = c1),
% 29.31/19.53 inference(transitivity,[status(thm)],[23031, 23023])).
% 29.31/19.53 tff(23033,plain,
% 29.31/19.53 ($false),
% 29.31/19.53 inference(unit_resolution,[status(thm)],[75, 23032])).
% 29.31/19.53 tff(23034,plain,((~big_f(c1, c1)) | (c1 = c3) | (~big_f(c2, c1)) | big_f(c1, c2) | (~(f4(c4) = c1)) | (f4(c4) = c3)), inference(lemma,lemma(discharge,[]))).
% 29.31/19.53 tff(23035,plain,
% 29.31/19.53 (~big_f(c1, c1)),
% 29.31/19.53 inference(unit_resolution,[status(thm)],[23034, 22980, 22975, 27, 11751, 22973])).
% 29.31/19.53 tff(23036,plain,
% 29.31/19.53 (~big_f(f4(c4), c4)),
% 29.31/19.53 inference(unit_resolution,[status(thm)],[11772, 23035, 11751, 27])).
% 29.31/19.53 tff(23037,plain,
% 29.31/19.53 (big_f(c3, f2(c3))),
% 29.31/19.53 inference(unit_resolution,[status(thm)],[1315, 23036])).
% 29.31/19.53 tff(23038,plain,
% 29.31/19.53 (~(f2(c3) = c2)),
% 29.31/19.53 inference(unit_resolution,[status(thm)],[7831, 23037, 121, 22964])).
% 29.31/19.53 tff(23039,plain,
% 29.31/19.53 (f2(c3) = c1),
% 29.31/19.53 inference(unit_resolution,[status(thm)],[1273, 23038])).
% 29.31/19.53 tff(23040,plain,
% 29.31/19.53 (f2(c2) = f2(c3)),
% 29.31/19.53 inference(monotonicity,[status(thm)],[22963])).
% 29.31/19.53 tff(23041,plain,
% 29.31/19.53 (c1 = f10(c1)),
% 29.31/19.53 inference(symmetry,[status(thm)],[22733])).
% 29.31/19.53 tff(23042,plain,
% 29.31/19.53 (f5(c1) = f5(f10(c1))),
% 29.31/19.53 inference(monotonicity,[status(thm)],[23041])).
% 29.31/19.53 tff(23043,plain,
% 29.31/19.53 (f5(f10(c1)) = f5(c1)),
% 29.31/19.53 inference(symmetry,[status(thm)],[23042])).
% 29.31/19.53 tff(23044,plain,
% 29.31/19.53 ((c2 = f5(f10(c1))) <=> (c2 = f5(c1))),
% 29.31/19.53 inference(monotonicity,[status(thm)],[23043])).
% 29.31/19.53 tff(23045,plain,
% 29.31/19.53 ((c2 = f5(c1)) <=> (c2 = f5(f10(c1)))),
% 29.31/19.53 inference(symmetry,[status(thm)],[23044])).
% 29.31/19.53 tff(23046,plain,
% 29.31/19.53 ((c2 = f5(c1)) <=> (f5(f10(c1)) = c2)),
% 29.31/19.53 inference(transitivity,[status(thm)],[23045, 5892])).
% 29.31/19.53 tff(23047,plain,
% 29.31/19.53 ((~(c2 = f5(c1))) <=> (~(f5(f10(c1)) = c2))),
% 29.31/19.53 inference(monotonicity,[status(thm)],[23046])).
% 29.31/19.53 tff(23048,plain,
% 29.31/19.53 (~(c2 = f5(c1))),
% 29.31/19.53 inference(unit_resolution,[status(thm)],[11602, 23035, 115, 22733, 22980, 1726])).
% 29.31/19.53 tff(23049,plain,
% 29.31/19.53 (~(f5(f10(c1)) = c2)),
% 29.31/19.53 inference(modus_ponens,[status(thm)],[23048, 23047])).
% 29.31/19.53 tff(23050,plain,
% 29.31/19.53 (f5(f10(c1)) = c1),
% 29.31/19.53 inference(unit_resolution,[status(thm)],[326, 23049])).
% 29.31/19.53 tff(23051,plain,
% 29.31/19.53 (f7(f9(f10(c2), f7(c1))) = f7(f9(c2, c2))),
% 29.31/19.53 inference(monotonicity,[status(thm)],[8961])).
% 29.31/19.53 tff(23052,plain,
% 29.31/19.53 ((f7(f9(f10(c2), f7(c1))) = f9(f10(c2), f7(c1))) <=> (f7(f9(c2, c2)) = f9(c2, c2))),
% 29.31/19.53 inference(monotonicity,[status(thm)],[23051, 8961])).
% 29.31/19.53 tff(23053,plain,
% 29.31/19.53 ((f7(f9(c2, c2)) = f9(c2, c2)) <=> (f7(f9(f10(c2), f7(c1))) = f9(f10(c2), f7(c1)))),
% 29.31/19.53 inference(symmetry,[status(thm)],[23052])).
% 29.31/19.53 tff(23054,assumption,(c1 = f5(c2)), introduced(assumption)).
% 29.31/19.53 tff(23055,assumption,(f9(c2, f9(f10(c2), f10(c2))) = c2), introduced(assumption)).
% 29.31/19.53 tff(23056,plain,
% 29.31/19.53 (f9(c2, f9(c2, c2)) = c2),
% 29.31/19.53 inference(transitivity,[status(thm)],[1134, 23055])).
% 29.31/19.53 tff(23057,plain,
% 29.31/19.53 ((f9(c2, f9(c2, c2)) = f9(c2, c2)) <=> (c2 = f9(c2, c2))),
% 29.31/19.53 inference(monotonicity,[status(thm)],[23056])).
% 29.31/19.53 tff(23058,plain,
% 29.31/19.53 ((f9(c2, f9(c2, c2)) = f9(c2, c2)) <=> (f9(c2, c2) = c2)),
% 29.31/19.53 inference(transitivity,[status(thm)],[23057, 167])).
% 29.31/19.53 tff(23059,plain,
% 29.31/19.53 ((f9(c2, c2) = c2) <=> (f9(c2, f9(c2, c2)) = f9(c2, c2))),
% 29.31/19.53 inference(symmetry,[status(thm)],[23058])).
% 29.31/19.53 tff(23060,plain,
% 29.31/19.53 ((~(f9(c2, c2) = c2)) <=> (~(f9(c2, f9(c2, c2)) = f9(c2, c2)))),
% 29.31/19.53 inference(monotonicity,[status(thm)],[23059])).
% 29.31/19.53 tff(23061,plain,
% 29.31/19.53 (~(f9(c2, f9(c2, c2)) = f9(c2, c2))),
% 29.31/19.53 inference(modus_ponens,[status(thm)],[1209, 23060])).
% 29.31/19.53 tff(23062,plain,
% 29.31/19.53 ((f9(c2, f9(f10(c2), f10(c2))) = c2) <=> (f9(c2, f9(c2, c2)) = c2)),
% 29.31/19.53 inference(monotonicity,[status(thm)],[3822])).
% 29.31/19.53 tff(23063,plain,
% 29.31/19.53 ((f9(c2, f9(f10(c2), f10(c2))) = c2) <=> (c2 = f9(c2, f9(c2, c2)))),
% 29.31/19.53 inference(transitivity,[status(thm)],[23062, 5005])).
% 29.31/19.53 tff(23064,plain,
% 29.31/19.53 (c2 = f9(c2, f9(c2, c2))),
% 29.31/19.53 inference(modus_ponens,[status(thm)],[23055, 23063])).
% 29.31/19.53 tff(23065,plain,
% 29.31/19.53 ($false),
% 29.31/19.53 inference(unit_resolution,[status(thm)],[5010, 23064])).
% 29.31/19.53 tff(23066,plain,((~(f9(c2, f9(f10(c2), f10(c2))) = c2)) | (c2 = f9(c2, f9(c2, c2))) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.31/19.53 tff(23067,plain,
% 29.31/19.53 (c2 = f9(c2, f9(c2, c2))),
% 29.31/19.53 inference(unit_resolution,[status(thm)],[23066, 23055, 122])).
% 29.31/19.53 tff(23068,plain,
% 29.31/19.53 (big_f(c2, c2) <=> big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 29.31/19.53 inference(unit_resolution,[status(thm)],[5003, 23067, 4989])).
% 29.31/19.53 tff(23069,plain,
% 29.31/19.53 (~big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 29.31/19.53 inference(unit_resolution,[status(thm)],[4996, 23068, 121])).
% 29.31/19.53 tff(23070,plain,
% 29.31/19.53 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (~(c1 = f5(c2))) | big_f(f7(c2), c1) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~(c1 = f5(c2))) | big_f(f7(c2), c1) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)))),
% 29.31/19.53 inference(rewrite,[status(thm)],[])).
% 29.31/19.53 tff(23071,plain,
% 29.31/19.53 (((~(f10(c2) = c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), c1) | (~(c1 = f5(c2)))) <=> ((~(f10(c2) = c2)) | (f7(c2) = c2) | (~(c1 = f5(c2))) | big_f(f7(c2), c1) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)))),
% 29.31/19.53 inference(rewrite,[status(thm)],[])).
% 29.31/19.53 tff(23072,plain,
% 29.31/19.53 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), c1) | (~(c1 = f5(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (~(c1 = f5(c2))) | big_f(f7(c2), c1) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2))))),
% 29.31/19.53 inference(monotonicity,[status(thm)],[23071])).
% 29.31/19.53 tff(23073,plain,
% 29.31/19.53 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), c1) | (~(c1 = f5(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~(c1 = f5(c2))) | big_f(f7(c2), c1) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)))),
% 29.31/19.53 inference(transitivity,[status(thm)],[23072, 23070])).
% 29.31/19.53 tff(23074,plain,
% 29.31/19.53 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), c1) | (~(c1 = f5(c2))))),
% 29.31/19.53 inference(quant_inst,[status(thm)],[])).
% 29.31/19.53 tff(23075,plain,
% 29.31/19.53 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~(c1 = f5(c2))) | big_f(f7(c2), c1) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2))),
% 29.31/19.53 inference(modus_ponens,[status(thm)],[23074, 23073])).
% 29.31/19.53 tff(23076,plain,
% 29.31/19.53 ($false),
% 29.31/19.53 inference(unit_resolution,[status(thm)],[23075, 267, 122, 17, 23054, 333, 23069, 23061])).
% 29.31/19.53 tff(23077,plain,((~(f9(c2, f9(f10(c2), f10(c2))) = c2)) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~(c1 = f5(c2))) | big_f(f7(c2), c1) | (f9(c2, c2) = c2) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 29.31/19.53 tff(23078,plain,
% 29.31/19.53 (~(f9(c2, f9(f10(c2), f10(c2))) = c2)),
% 29.31/19.53 inference(unit_resolution,[status(thm)],[23077, 1209, 17, 23054, 333, 122, 121])).
% 29.31/19.53 tff(23079,plain,
% 29.31/19.53 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f9(c2, f9(f10(c2), f10(c2))) = c1) | (f9(c2, f9(f10(c2), f10(c2))) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f9(c2, f9(f10(c2), f10(c2))) = c1) | (f9(c2, f9(f10(c2), f10(c2))) = c2))),
% 29.31/19.53 inference(rewrite,[status(thm)],[])).
% 29.31/19.53 tff(23080,plain,
% 29.31/19.53 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f9(c2, f9(f10(c2), f10(c2))) = c1) | (f9(c2, f9(f10(c2), f10(c2))) = c2))),
% 29.31/19.53 inference(quant_inst,[status(thm)],[])).
% 29.31/19.53 tff(23081,plain,
% 29.31/19.53 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f9(c2, f9(f10(c2), f10(c2))) = c1) | (f9(c2, f9(f10(c2), f10(c2))) = c2)),
% 29.31/19.53 inference(modus_ponens,[status(thm)],[23080, 23079])).
% 29.31/19.53 tff(23082,plain,
% 29.31/19.53 ((f9(c2, f9(f10(c2), f10(c2))) = c1) | (f9(c2, f9(f10(c2), f10(c2))) = c2)),
% 29.31/19.53 inference(unit_resolution,[status(thm)],[23081, 10])).
% 29.31/19.53 tff(23083,plain,
% 29.31/19.53 (f9(c2, f9(f10(c2), f10(c2))) = c1),
% 29.31/19.53 inference(unit_resolution,[status(thm)],[23082, 23078])).
% 29.31/19.53 tff(23084,plain,
% 29.31/19.53 (f9(c2, f9(c2, c2)) = c1),
% 29.31/19.53 inference(transitivity,[status(thm)],[1134, 23083])).
% 29.31/19.53 tff(23085,plain,
% 29.31/19.53 (big_f(f9(c2, f9(c2, c2)), f10(c2)) <=> big_f(c1, c2)),
% 29.31/19.53 inference(monotonicity,[status(thm)],[23084, 122])).
% 29.31/19.53 tff(23086,plain,
% 29.31/19.53 (big_f(c1, c2) <=> big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 29.31/19.53 inference(symmetry,[status(thm)],[23085])).
% 29.31/19.53 tff(23087,plain,
% 29.31/19.53 ((~big_f(c1, c2)) <=> (~big_f(f9(c2, f9(c2, c2)), f10(c2)))),
% 29.31/19.53 inference(monotonicity,[status(thm)],[23086])).
% 29.31/19.53 tff(23088,plain,
% 29.31/19.53 (~big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 29.31/19.53 inference(modus_ponens,[status(thm)],[27, 23087])).
% 29.31/19.53 tff(23089,plain,
% 29.31/19.53 (f9(c2, f9(c2, c2)) = f9(c2, c2)),
% 29.31/19.53 inference(unit_resolution,[status(thm)],[23075, 267, 122, 17, 23054, 333, 23088])).
% 29.31/19.53 tff(23090,plain,
% 29.31/19.53 (f9(c2, c2) = f9(c2, f9(c2, c2))),
% 29.31/19.53 inference(symmetry,[status(thm)],[23089])).
% 29.31/19.53 tff(23091,plain,
% 29.31/19.53 (f9(c2, c2) = c1),
% 29.31/19.53 inference(transitivity,[status(thm)],[23090, 1134, 23083])).
% 29.31/19.53 tff(23092,plain,
% 29.31/19.53 (big_f(f9(c2, c2), c2) <=> big_f(c1, c2)),
% 29.31/19.53 inference(monotonicity,[status(thm)],[23091])).
% 29.31/19.53 tff(23093,plain,
% 29.31/19.53 (big_f(c1, c2) <=> big_f(f9(c2, c2), c2)),
% 29.31/19.53 inference(symmetry,[status(thm)],[23092])).
% 29.31/19.53 tff(23094,plain,
% 29.31/19.53 ((~big_f(c1, c2)) <=> (~big_f(f9(c2, c2), c2))),
% 29.31/19.54 inference(monotonicity,[status(thm)],[23093])).
% 29.31/19.54 tff(23095,plain,
% 29.31/19.54 (~big_f(f9(c2, c2), c2)),
% 29.31/19.54 inference(modus_ponens,[status(thm)],[27, 23094])).
% 29.31/19.54 tff(23096,plain,
% 29.31/19.54 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (~(c1 = f5(c2))) | big_f(f7(c2), c1) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~(c1 = f5(c2))) | big_f(f7(c2), c1) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)))),
% 29.31/19.54 inference(rewrite,[status(thm)],[])).
% 29.31/19.54 tff(23097,plain,
% 29.31/19.54 (((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), c1) | (~(c1 = f5(c2)))) <=> ((~(f10(c2) = c2)) | (f7(c2) = c2) | (~(c1 = f5(c2))) | big_f(f7(c2), c1) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)))),
% 29.31/19.54 inference(rewrite,[status(thm)],[])).
% 29.31/19.54 tff(23098,plain,
% 29.31/19.54 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), c1) | (~(c1 = f5(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c2) = c2) | (~(c1 = f5(c2))) | big_f(f7(c2), c1) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2))))),
% 29.31/19.54 inference(monotonicity,[status(thm)],[23097])).
% 29.31/19.54 tff(23099,plain,
% 29.31/19.54 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), c1) | (~(c1 = f5(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~(c1 = f5(c2))) | big_f(f7(c2), c1) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)))),
% 29.31/19.54 inference(transitivity,[status(thm)],[23098, 23096])).
% 29.31/19.54 tff(23100,plain,
% 29.31/19.54 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), c1) | (~(c1 = f5(c2))))),
% 29.31/19.54 inference(quant_inst,[status(thm)],[])).
% 29.31/19.54 tff(23101,plain,
% 29.31/19.54 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~(c1 = f5(c2))) | big_f(f7(c2), c1) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2))),
% 29.31/19.54 inference(modus_ponens,[status(thm)],[23100, 23099])).
% 29.31/19.54 tff(23102,plain,
% 29.31/19.54 ($false),
% 29.31/19.54 inference(unit_resolution,[status(thm)],[23101, 267, 122, 17, 23054, 333, 1209, 256])).
% 29.31/19.54 tff(23103,plain,(big_f(f9(c2, c2), f10(c2)) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~(c1 = f5(c2))) | big_f(f7(c2), c1) | (f9(c2, c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 29.31/19.54 tff(23104,plain,
% 29.31/19.54 (big_f(f9(c2, c2), f10(c2))),
% 29.31/19.54 inference(unit_resolution,[status(thm)],[23103, 1209, 17, 23054, 333, 122])).
% 29.31/19.54 tff(23105,plain,
% 29.31/19.54 (big_f(f9(c2, c2), c2)),
% 29.31/19.54 inference(unit_resolution,[status(thm)],[3687, 23104, 122])).
% 29.31/19.54 tff(23106,plain,
% 29.31/19.54 ($false),
% 29.31/19.54 inference(unit_resolution,[status(thm)],[23105, 23095])).
% 29.31/19.54 tff(23107,plain,((f9(c2, c2) = c2) | big_f(c1, c2) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~(c1 = f5(c2))) | big_f(f7(c2), c1) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 29.31/19.54 tff(23108,plain,
% 29.31/19.54 (f9(c2, c2) = c2),
% 29.31/19.54 inference(unit_resolution,[status(thm)],[23107, 17867, 122, 17, 27, 12093, 121])).
% 29.31/19.54 tff(23109,plain,
% 29.31/19.54 (f5(f9(c2, c2)) = f5(c2)),
% 29.31/19.54 inference(monotonicity,[status(thm)],[23108])).
% 29.31/19.54 tff(23110,plain,
% 29.31/19.54 (f5(f9(f10(c2), f7(c1))) = f5(f9(c2, c2))),
% 29.31/19.54 inference(monotonicity,[status(thm)],[8961])).
% 29.31/19.54 tff(23111,plain,
% 29.31/19.54 (f5(f9(f10(c2), f7(c1))) = c1),
% 29.31/19.54 inference(transitivity,[status(thm)],[23110, 23109, 1569])).
% 29.31/19.54 tff(23112,plain,
% 29.31/19.54 (big_f(f7(f9(f10(c2), f7(c1))), f5(f9(f10(c2), f7(c1)))) <=> big_f(f7(f9(f10(c2), f7(c1))), c1)),
% 29.31/19.54 inference(monotonicity,[status(thm)],[23111])).
% 29.31/19.54 tff(23113,plain,
% 29.31/19.54 (big_f(f7(f9(f10(c2), f7(c1))), c1) <=> big_f(f7(f9(f10(c2), f7(c1))), f5(f9(f10(c2), f7(c1))))),
% 29.31/19.54 inference(symmetry,[status(thm)],[23112])).
% 29.31/19.54 tff(23114,plain,
% 29.31/19.54 (f7(f9(c2, c2)) = f7(c2)),
% 29.31/19.54 inference(monotonicity,[status(thm)],[23108])).
% 29.31/19.54 tff(23115,plain,
% 29.31/19.54 (f7(f9(f10(c2), f7(c1))) = c1),
% 29.31/19.54 inference(transitivity,[status(thm)],[23051, 23114, 22])).
% 29.31/19.54 tff(23116,plain,
% 29.31/19.54 (big_f(f7(f9(f10(c2), f7(c1))), c1) <=> big_f(c1, c1)),
% 29.31/19.54 inference(monotonicity,[status(thm)],[23115])).
% 29.31/19.54 tff(23117,plain,
% 29.31/19.54 (big_f(c1, c1) <=> big_f(f7(f9(f10(c2), f7(c1))), c1)),
% 29.31/19.54 inference(symmetry,[status(thm)],[23116])).
% 29.31/19.54 tff(23118,plain,
% 29.31/19.54 (big_f(c1, c1) <=> big_f(f7(f9(f10(c2), f7(c1))), f5(f9(f10(c2), f7(c1))))),
% 29.31/19.54 inference(transitivity,[status(thm)],[23117, 23113])).
% 29.31/19.54 tff(23119,plain,
% 29.31/19.54 ((~big_f(c1, c1)) <=> (~big_f(f7(f9(f10(c2), f7(c1))), f5(f9(f10(c2), f7(c1)))))),
% 29.31/19.54 inference(monotonicity,[status(thm)],[23118])).
% 29.31/19.54 tff(23120,plain,
% 29.31/19.54 (~big_f(f7(f9(f10(c2), f7(c1))), f5(f9(f10(c2), f7(c1))))),
% 29.31/19.54 inference(modus_ponens,[status(thm)],[66, 23119])).
% 29.31/19.54 tff(23121,plain,
% 29.31/19.54 (f7(f9(c2, c2)) = f7(f9(f10(c2), f7(c1)))),
% 29.31/19.54 inference(symmetry,[status(thm)],[23051])).
% 29.31/19.54 tff(23122,plain,
% 29.31/19.54 ((f7(f9(c2, c2)) = f9(c2, c2)) <=> (f7(f9(f10(c2), f7(c1))) = c2)),
% 29.31/19.54 inference(monotonicity,[status(thm)],[23121, 23108])).
% 29.31/19.54 tff(23123,plain,
% 29.31/19.54 ((f7(f9(f10(c2), f7(c1))) = c2) <=> (f7(f9(c2, c2)) = f9(c2, c2))),
% 29.31/19.54 inference(symmetry,[status(thm)],[23122])).
% 29.31/19.54 tff(23124,plain,
% 29.31/19.54 ((f7(f9(f10(c2), f7(c1))) = c2) <=> (c1 = c2)),
% 29.31/19.54 inference(monotonicity,[status(thm)],[23115])).
% 29.31/19.54 tff(23125,plain,
% 29.31/19.54 ((f7(f9(f10(c2), f7(c1))) = c2) <=> (c2 = c1)),
% 29.31/19.54 inference(transitivity,[status(thm)],[23124, 1])).
% 29.31/19.54 tff(23126,plain,
% 29.31/19.54 ((c2 = c1) <=> (f7(f9(f10(c2), f7(c1))) = c2)),
% 29.31/19.54 inference(symmetry,[status(thm)],[23125])).
% 29.31/19.54 tff(23127,plain,
% 29.31/19.54 ((c2 = c1) <=> (f7(f9(f10(c2), f7(c1))) = f9(f10(c2), f7(c1)))),
% 29.31/19.54 inference(transitivity,[status(thm)],[23126, 23123, 23053])).
% 29.31/19.54 tff(23128,plain,
% 29.31/19.54 ((~(c2 = c1)) <=> (~(f7(f9(f10(c2), f7(c1))) = f9(f10(c2), f7(c1))))),
% 29.31/19.54 inference(monotonicity,[status(thm)],[23127])).
% 29.31/19.54 tff(23129,plain,
% 29.31/19.54 (~(f7(f9(f10(c2), f7(c1))) = f9(f10(c2), f7(c1)))),
% 29.31/19.54 inference(modus_ponens,[status(thm)],[75, 23128])).
% 29.31/19.54 tff(23130,plain,
% 29.31/19.54 (f9(c1, c2) = c2),
% 29.31/19.54 inference(unit_resolution,[status(thm)],[9000, 23129, 3762, 22, 23120, 12093])).
% 29.31/19.54 tff(23131,plain,
% 29.31/19.54 (big_f(f9(c1, c2), f10(c1)) <=> big_f(c2, c1)),
% 29.31/19.54 inference(monotonicity,[status(thm)],[23130, 3762])).
% 29.31/19.54 tff(23132,plain,
% 29.31/19.54 (big_f(c2, c1) <=> big_f(f9(c1, c2), f10(c1))),
% 29.31/19.54 inference(symmetry,[status(thm)],[23131])).
% 29.31/19.54 tff(23133,plain,
% 29.31/19.54 (big_f(f9(c1, c2), f10(c1))),
% 29.31/19.54 inference(modus_ponens,[status(thm)],[348, 23132])).
% 29.31/19.54 tff(23134,plain,
% 29.31/19.54 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((f7(c2) = c2) | (~(f10(c1) = c1)) | (~(c1 = f5(c2))) | big_f(f7(c2), c1) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (f7(c2) = c2) | (~(f10(c1) = c1)) | (~(c1 = f5(c2))) | big_f(f7(c2), c1) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2)))),
% 29.31/19.54 inference(rewrite,[status(thm)],[])).
% 29.31/19.54 tff(23135,plain,
% 29.31/19.54 (((~(f10(c1) = c1)) | (f7(c2) = c2) | big_f(f7(c2), c1) | (~(f9(c1, c2) = c2)) | (~big_f(f9(c1, c2), f10(c1))) | (~(c1 = f5(c2)))) <=> ((f7(c2) = c2) | (~(f10(c1) = c1)) | (~(c1 = f5(c2))) | big_f(f7(c2), c1) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2)))),
% 29.31/19.54 inference(rewrite,[status(thm)],[])).
% 29.31/19.54 tff(23136,plain,
% 29.31/19.54 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f7(c2) = c2) | big_f(f7(c2), c1) | (~(f9(c1, c2) = c2)) | (~big_f(f9(c1, c2), f10(c1))) | (~(c1 = f5(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((f7(c2) = c2) | (~(f10(c1) = c1)) | (~(c1 = f5(c2))) | big_f(f7(c2), c1) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2))))),
% 29.31/19.54 inference(monotonicity,[status(thm)],[23135])).
% 29.31/19.54 tff(23137,plain,
% 29.31/19.54 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f7(c2) = c2) | big_f(f7(c2), c1) | (~(f9(c1, c2) = c2)) | (~big_f(f9(c1, c2), f10(c1))) | (~(c1 = f5(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (f7(c2) = c2) | (~(f10(c1) = c1)) | (~(c1 = f5(c2))) | big_f(f7(c2), c1) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2)))),
% 29.31/19.54 inference(transitivity,[status(thm)],[23136, 23134])).
% 29.31/19.54 tff(23138,plain,
% 29.31/19.54 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f7(c2) = c2) | big_f(f7(c2), c1) | (~(f9(c1, c2) = c2)) | (~big_f(f9(c1, c2), f10(c1))) | (~(c1 = f5(c2))))),
% 29.31/19.54 inference(quant_inst,[status(thm)],[])).
% 29.31/19.54 tff(23139,plain,
% 29.31/19.54 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (f7(c2) = c2) | (~(f10(c1) = c1)) | (~(c1 = f5(c2))) | big_f(f7(c2), c1) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2))),
% 29.31/19.54 inference(modus_ponens,[status(thm)],[23138, 23137])).
% 29.31/19.54 tff(23140,plain,
% 29.31/19.54 ($false),
% 29.31/19.54 inference(unit_resolution,[status(thm)],[23139, 783, 3762, 17, 23133, 23130, 17867, 12093])).
% 29.31/19.54 tff(23141,plain,((~(f5(c2) = c1)) | (~(f10(c1) = c1)) | (f7(c2) = c2) | (~big_f(c2, c1)) | (~(f7(c1) = c2)) | (~(f10(c2) = c2)) | big_f(c1, c1) | big_f(c1, c2) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 29.31/19.54 tff(23142,plain,
% 29.31/19.54 (~(f5(c2) = c1)),
% 29.31/19.54 inference(unit_resolution,[status(thm)],[23141, 66, 3762, 348, 347, 122, 17, 27, 121])).
% 29.31/19.54 tff(23143,plain,
% 29.31/19.54 (f5(c2) = c2),
% 29.31/19.54 inference(unit_resolution,[status(thm)],[1547, 23142])).
% 29.31/19.54 tff(23144,plain,
% 29.31/19.54 (c2 = f5(c2)),
% 29.31/19.54 inference(unit_resolution,[status(thm)],[8113, 23143])).
% 29.31/19.54 tff(23145,plain,
% 29.31/19.54 (~big_f(f7(c2), c2)),
% 29.31/19.54 inference(unit_resolution,[status(thm)],[21127, 22, 27])).
% 29.31/19.54 tff(23146,plain,
% 29.31/19.54 (~(f9(c2, f9(f10(c2), f10(c2))) = c2)),
% 29.31/19.54 inference(unit_resolution,[status(thm)],[23066, 7873, 122])).
% 29.31/19.54 tff(23147,plain,
% 29.31/19.54 (f9(c2, f9(f10(c2), f10(c2))) = c1),
% 29.31/19.54 inference(unit_resolution,[status(thm)],[23082, 23146])).
% 29.31/19.54 tff(23148,plain,
% 29.31/19.54 (f9(c2, f9(c2, c2)) = c1),
% 29.31/19.54 inference(transitivity,[status(thm)],[1134, 23147])).
% 29.31/19.54 tff(23149,plain,
% 29.31/19.54 (big_f(f9(c2, f9(c2, c2)), f10(c2)) <=> big_f(c1, c2)),
% 29.31/19.54 inference(monotonicity,[status(thm)],[23148, 122])).
% 29.31/19.54 tff(23150,plain,
% 29.31/19.54 (big_f(c1, c2) <=> big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 29.31/19.54 inference(symmetry,[status(thm)],[23149])).
% 29.31/19.54 tff(23151,plain,
% 29.31/19.54 ((~big_f(c1, c2)) <=> (~big_f(f9(c2, f9(c2, c2)), f10(c2)))),
% 29.31/19.54 inference(monotonicity,[status(thm)],[23150])).
% 29.31/19.54 tff(23152,plain,
% 29.31/19.54 (~big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 29.31/19.54 inference(modus_ponens,[status(thm)],[27, 23151])).
% 29.31/19.54 tff(23153,plain,
% 29.31/19.54 ($false),
% 29.31/19.54 inference(unit_resolution,[status(thm)],[1146, 23152])).
% 29.31/19.54 tff(23154,plain,((~big_f(f9(c2, f9(c2, c2)), f10(c2))) | big_f(c1, c2) | (~(f10(c2) = c2)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 29.31/19.54 tff(23155,plain,
% 29.31/19.54 (~big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 29.31/19.54 inference(unit_resolution,[status(thm)],[23154, 27, 122, 121])).
% 29.31/19.54 tff(23156,plain,
% 29.31/19.54 ($false),
% 29.31/19.54 inference(unit_resolution,[status(thm)],[6019, 267, 122, 17, 5124, 1521, 3896, 4469])).
% 29.31/19.54 tff(23157,plain,(big_f(f9(c2, f9(c2, c2)), f10(c2)) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (f9(c2, f9(c2, c2)) = f9(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 29.31/19.54 tff(23158,plain,
% 29.31/19.54 (f9(c2, f9(c2, c2)) = f9(c2, c2)),
% 29.31/19.54 inference(unit_resolution,[status(thm)],[23157, 23144, 23155, 17, 23145, 122])).
% 29.31/19.54 tff(23159,plain,
% 29.31/19.54 (big_f(f9(c2, f9(c2, c2)), f10(c2)) <=> big_f(f9(c2, c2), c2)),
% 29.31/19.54 inference(monotonicity,[status(thm)],[23158, 122])).
% 29.31/19.54 tff(23160,plain,
% 29.31/19.54 (big_f(f9(c2, f9(c2, c2)), f10(c2)) <=> big_f(f9(c2, c2), f10(c2))),
% 29.31/19.54 inference(transitivity,[status(thm)],[23159, 130])).
% 29.31/19.54 tff(23161,plain,
% 29.31/19.54 ((~big_f(f9(c2, f9(c2, c2)), f10(c2))) <=> (~big_f(f9(c2, c2), f10(c2)))),
% 29.31/19.54 inference(monotonicity,[status(thm)],[23160])).
% 29.31/19.54 tff(23162,plain,
% 29.31/19.54 (~big_f(f9(c2, c2), f10(c2))),
% 29.31/19.54 inference(modus_ponens,[status(thm)],[23155, 23161])).
% 29.31/19.54 tff(23163,plain,
% 29.31/19.54 ((~(c2 = f5(c2))) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2))),
% 29.31/19.54 inference(unit_resolution,[status(thm)],[1527, 267, 122, 17, 23145])).
% 29.31/19.54 tff(23164,plain,
% 29.31/19.54 (f9(c2, c2) = c2),
% 29.31/19.54 inference(unit_resolution,[status(thm)],[23163, 23162, 23144])).
% 29.31/19.54 tff(23165,plain,
% 29.31/19.54 ((f7(f9(c2, c2)) = f9(c2, c2)) <=> (f7(f9(f10(c2), f7(c1))) = c2)),
% 29.31/19.54 inference(monotonicity,[status(thm)],[23121, 23164])).
% 29.31/19.54 tff(23166,plain,
% 29.31/19.54 ((f7(f9(f10(c2), f7(c1))) = c2) <=> (f7(f9(c2, c2)) = f9(c2, c2))),
% 29.31/19.54 inference(symmetry,[status(thm)],[23165])).
% 29.31/19.54 tff(23167,plain,
% 29.31/19.54 (f7(f9(c2, c2)) = f7(c2)),
% 29.31/19.54 inference(monotonicity,[status(thm)],[23164])).
% 29.31/19.54 tff(23168,plain,
% 29.31/19.54 (f7(f9(f10(c2), f7(c1))) = c1),
% 29.31/19.54 inference(transitivity,[status(thm)],[23051, 23167, 22])).
% 29.31/19.54 tff(23169,plain,
% 29.31/19.54 ((f7(f9(f10(c2), f7(c1))) = c2) <=> (c1 = c2)),
% 29.31/19.54 inference(monotonicity,[status(thm)],[23168])).
% 29.31/19.54 tff(23170,plain,
% 29.31/19.54 ((f7(f9(f10(c2), f7(c1))) = c2) <=> (c2 = c1)),
% 29.31/19.54 inference(transitivity,[status(thm)],[23169, 1])).
% 29.31/19.54 tff(23171,plain,
% 29.31/19.54 ((c2 = c1) <=> (f7(f9(f10(c2), f7(c1))) = c2)),
% 29.31/19.54 inference(symmetry,[status(thm)],[23170])).
% 29.31/19.54 tff(23172,plain,
% 29.31/19.54 ((c2 = c1) <=> (f7(f9(f10(c2), f7(c1))) = f9(f10(c2), f7(c1)))),
% 29.31/19.54 inference(transitivity,[status(thm)],[23171, 23166, 23053])).
% 29.31/19.54 tff(23173,plain,
% 29.31/19.54 ((~(c2 = c1)) <=> (~(f7(f9(f10(c2), f7(c1))) = f9(f10(c2), f7(c1))))),
% 29.31/19.54 inference(monotonicity,[status(thm)],[23172])).
% 29.31/19.54 tff(23174,plain,
% 29.31/19.54 (~(f7(f9(f10(c2), f7(c1))) = f9(f10(c2), f7(c1)))),
% 29.31/19.54 inference(modus_ponens,[status(thm)],[75, 23173])).
% 29.31/19.54 tff(23175,plain,
% 29.31/19.54 (f5(f9(c2, c2)) = f5(c2)),
% 29.31/19.54 inference(monotonicity,[status(thm)],[23164])).
% 29.31/19.54 tff(23176,plain,
% 29.31/19.54 (f5(f9(f10(c2), f7(c1))) = c2),
% 29.31/19.54 inference(transitivity,[status(thm)],[23110, 23175, 23143])).
% 29.31/19.54 tff(23177,plain,
% 29.31/19.54 (big_f(f7(f9(f10(c2), f7(c1))), f5(f9(f10(c2), f7(c1)))) <=> big_f(f7(f9(c2, c2)), c2)),
% 29.31/19.54 inference(monotonicity,[status(thm)],[23051, 23176])).
% 29.31/19.54 tff(23178,plain,
% 29.31/19.54 (big_f(f7(f9(c2, c2)), c2) <=> big_f(f7(f9(f10(c2), f7(c1))), f5(f9(f10(c2), f7(c1))))),
% 29.31/19.54 inference(symmetry,[status(thm)],[23177])).
% 29.31/19.54 tff(23179,plain,
% 29.31/19.54 (f7(f9(c2, c2)) = c1),
% 29.31/19.54 inference(transitivity,[status(thm)],[23167, 22])).
% 29.31/19.54 tff(23180,plain,
% 29.31/19.54 (big_f(f7(f9(c2, c2)), c2) <=> big_f(c1, c2)),
% 29.31/19.54 inference(monotonicity,[status(thm)],[23179])).
% 29.31/19.54 tff(23181,plain,
% 29.31/19.54 (big_f(c1, c2) <=> big_f(f7(f9(c2, c2)), c2)),
% 29.31/19.54 inference(symmetry,[status(thm)],[23180])).
% 29.31/19.54 tff(23182,plain,
% 29.31/19.54 (big_f(c1, c2) <=> big_f(f7(f9(f10(c2), f7(c1))), f5(f9(f10(c2), f7(c1))))),
% 29.31/19.54 inference(transitivity,[status(thm)],[23181, 23178])).
% 29.31/19.54 tff(23183,plain,
% 29.31/19.54 ((~big_f(c1, c2)) <=> (~big_f(f7(f9(f10(c2), f7(c1))), f5(f9(f10(c2), f7(c1)))))),
% 29.31/19.54 inference(monotonicity,[status(thm)],[23182])).
% 29.31/19.54 tff(23184,plain,
% 29.31/19.54 (~big_f(f7(f9(f10(c2), f7(c1))), f5(f9(f10(c2), f7(c1))))),
% 29.31/19.54 inference(modus_ponens,[status(thm)],[27, 23183])).
% 29.31/19.54 tff(23185,plain,
% 29.31/19.54 (f9(c1, c2) = c2),
% 29.31/19.54 inference(unit_resolution,[status(thm)],[9000, 12093, 3762, 22, 23184, 23174])).
% 29.31/19.54 tff(23186,plain,
% 29.31/19.54 (big_f(f9(c1, c2), f10(c1)) <=> big_f(c2, c1)),
% 29.31/19.54 inference(monotonicity,[status(thm)],[23185, 3762])).
% 29.31/19.54 tff(23187,plain,
% 29.31/19.54 (big_f(c2, c1) <=> big_f(f9(c1, c2), f10(c1))),
% 29.31/19.54 inference(symmetry,[status(thm)],[23186])).
% 29.31/19.54 tff(23188,plain,
% 29.31/19.54 (big_f(f9(c1, c2), f10(c1))),
% 29.31/19.54 inference(modus_ponens,[status(thm)],[348, 23187])).
% 29.31/19.54 tff(23189,plain,
% 29.31/19.54 (~big_f(f9(c1, c2), f10(c1))),
% 29.31/19.54 inference(unit_resolution,[status(thm)],[8204, 23185, 3762, 17, 23145, 23144])).
% 29.31/19.54 tff(23190,plain,
% 29.31/19.54 ($false),
% 29.31/19.54 inference(unit_resolution,[status(thm)],[23189, 23188])).
% 29.31/19.54 tff(23191,plain,(big_f(c1, c1) | (~big_f(c2, c1)) | (~(f10(c1) = c1)) | (f7(c2) = c2) | (~(f7(c1) = c2)) | (~(f10(c2) = c2)) | big_f(c1, c2) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 29.31/19.54 tff(23192,plain,
% 29.31/19.54 (f7(c2) = c2),
% 29.31/19.54 inference(unit_resolution,[status(thm)],[23191, 23035, 22733, 22980, 120, 122, 27, 121])).
% 29.31/19.54 tff(23193,plain,
% 29.31/19.54 (~big_f(f7(c2), f6(c2, c1))),
% 29.31/19.54 inference(unit_resolution,[status(thm)],[11642, 23192, 22733, 23035, 22980, 121, 115])).
% 29.31/19.54 tff(23194,plain,
% 29.31/19.54 (~(f5(c1) = c2)),
% 29.31/19.54 inference(modus_ponens,[status(thm)],[23048, 11786])).
% 29.31/19.54 tff(23195,plain,
% 29.31/19.54 (f5(c1) = c1),
% 29.31/19.54 inference(unit_resolution,[status(thm)],[1708, 23194])).
% 29.31/19.54 tff(23196,plain,
% 29.31/19.54 (f9(c2, c1) = c1),
% 29.31/19.54 inference(unit_resolution,[status(thm)],[11359, 23192, 115, 122, 121, 22980])).
% 29.31/19.54 tff(23197,plain,
% 29.31/19.54 (f2(c2) = f2(c3)),
% 29.31/19.54 inference(monotonicity,[status(thm)],[1344])).
% 29.31/19.54 tff(23198,plain,
% 29.31/19.54 (f2(c2) = c1),
% 29.31/19.54 inference(transitivity,[status(thm)],[23197, 1247])).
% 29.31/19.54 tff(23199,plain,
% 29.31/19.54 ((f6(c2, c1) = f2(c2)) <=> (f6(c2, c1) = c1)),
% 29.31/19.54 inference(monotonicity,[status(thm)],[23198])).
% 29.31/19.54 tff(23200,plain,
% 29.31/19.54 ((~(f6(c2, c1) = f2(c2))) <=> (~(f6(c2, c1) = c1))),
% 29.31/19.54 inference(monotonicity,[status(thm)],[23199])).
% 29.31/19.54 tff(23201,assumption,(~(f6(c2, c1) = f2(c2))), introduced(assumption)).
% 29.31/19.54 tff(23202,plain,
% 29.31/19.54 (~(f6(c2, c1) = c1)),
% 29.31/19.54 inference(modus_ponens,[status(thm)],[23201, 23200])).
% 29.31/19.54 tff(23203,plain,
% 29.31/19.54 (~(f9(c1, c2) = c2)),
% 29.31/19.54 inference(unit_resolution,[status(thm)],[11435, 23202, 3762, 77, 3197, 348])).
% 29.31/19.54 tff(23204,plain,
% 29.31/19.54 ((c2 = f2(c2)) <=> (c2 = c1)),
% 29.31/19.54 inference(monotonicity,[status(thm)],[23198])).
% 29.31/19.54 tff(23205,plain,
% 29.31/19.54 ((c2 = c1) <=> (c2 = f2(c2))),
% 29.31/19.54 inference(symmetry,[status(thm)],[23204])).
% 29.31/19.54 tff(23206,plain,
% 29.31/19.54 ((~(c2 = c1)) <=> (~(c2 = f2(c2)))),
% 29.31/19.54 inference(monotonicity,[status(thm)],[23205])).
% 29.31/19.54 tff(23207,plain,
% 29.31/19.54 (~(c2 = f2(c2))),
% 29.31/19.54 inference(modus_ponens,[status(thm)],[75, 23206])).
% 29.31/19.54 tff(23208,plain,
% 29.31/19.54 (f5(c1) = c1),
% 29.31/19.54 inference(transitivity,[status(thm)],[11571, 328])).
% 29.31/19.54 tff(23209,plain,
% 29.31/19.54 (f9(c2, f5(c1)) = f9(c2, c1)),
% 29.31/19.54 inference(monotonicity,[status(thm)],[23208])).
% 29.31/19.54 tff(23210,plain,
% 29.31/19.54 (f9(c2, f5(c1)) = c1),
% 29.31/19.54 inference(transitivity,[status(thm)],[23209, 736])).
% 29.31/19.54 tff(23211,plain,
% 29.31/19.54 (f6(c2, f9(c2, f5(c1))) = f6(c2, c1)),
% 29.31/19.54 inference(monotonicity,[status(thm)],[23210])).
% 29.31/19.54 tff(23212,plain,
% 29.31/19.54 ((f6(c2, f9(c2, f5(c1))) = c1) <=> (f6(c2, c1) = c1)),
% 29.31/19.54 inference(monotonicity,[status(thm)],[23211])).
% 29.31/19.54 tff(23213,plain,
% 29.31/19.54 ((f6(c2, c1) = c1) <=> (f6(c2, f9(c2, f5(c1))) = c1)),
% 29.31/19.54 inference(symmetry,[status(thm)],[23212])).
% 29.31/19.54 tff(23214,plain,
% 29.31/19.54 ((f6(c2, c1) = f2(c2)) <=> (f6(c2, f9(c2, f5(c1))) = c1)),
% 29.31/19.54 inference(transitivity,[status(thm)],[23199, 23213])).
% 29.31/19.54 tff(23215,plain,
% 29.31/19.54 ((~(f6(c2, c1) = f2(c2))) <=> (~(f6(c2, f9(c2, f5(c1))) = c1))),
% 29.31/19.54 inference(monotonicity,[status(thm)],[23214])).
% 29.31/19.54 tff(23216,plain,
% 29.31/19.54 (~(f6(c2, f9(c2, f5(c1))) = c1)),
% 29.31/19.54 inference(modus_ponens,[status(thm)],[23201, 23215])).
% 29.31/19.54 tff(23217,plain,
% 29.31/19.54 (f6(c2, f9(c2, f5(c1))) = c2),
% 29.31/19.54 inference(unit_resolution,[status(thm)],[7234, 23216])).
% 29.31/19.54 tff(23218,plain,
% 29.31/19.54 (f10(f2(c2)) = f10(c1)),
% 29.31/19.54 inference(monotonicity,[status(thm)],[1368])).
% 29.31/19.54 tff(23219,plain,
% 29.31/19.54 (f10(f2(c2)) = f2(c2)),
% 29.31/19.54 inference(transitivity,[status(thm)],[23218, 3762, 1367, 1221])).
% 29.31/19.54 tff(23220,plain,
% 29.31/19.54 (f9(f2(c2), c2) = f9(c1, c2)),
% 29.31/19.54 inference(monotonicity,[status(thm)],[1368])).
% 29.31/19.54 tff(23221,plain,
% 29.31/19.54 (f9(f2(c2), c2) = f2(c2)),
% 29.31/19.54 inference(transitivity,[status(thm)],[23220, 8169, 1367, 1221])).
% 29.31/19.54 tff(23222,plain,
% 29.31/19.54 ((f9(f2(c2), c2) = c2) <=> (f2(c2) = c2)),
% 29.31/19.54 inference(monotonicity,[status(thm)],[23221])).
% 29.31/19.54 tff(23223,plain,
% 29.31/19.54 ((f9(f2(c2), c2) = c2) <=> (c2 = f2(c2))),
% 29.31/19.54 inference(transitivity,[status(thm)],[23222, 1337])).
% 29.31/19.54 tff(23224,plain,
% 29.31/19.54 ((c2 = f2(c2)) <=> (f9(f2(c2), c2) = c2)),
% 29.31/19.54 inference(symmetry,[status(thm)],[23223])).
% 29.31/19.54 tff(23225,plain,
% 29.31/19.54 ((~(c2 = f2(c2))) <=> (~(f9(f2(c2), c2) = c2))),
% 29.31/19.54 inference(monotonicity,[status(thm)],[23224])).
% 29.31/19.54 tff(23226,plain,
% 29.31/19.54 (~(f9(f2(c2), c2) = c2)),
% 29.31/19.54 inference(modus_ponens,[status(thm)],[1342, 23225])).
% 29.31/19.54 tff(23227,plain,
% 29.31/19.54 (f10(f2(c2)) = c1),
% 29.31/19.54 inference(transitivity,[status(thm)],[23218, 3762])).
% 29.31/19.54 tff(23228,plain,
% 29.31/19.54 (f9(f2(c2), c2) = c1),
% 29.31/19.54 inference(transitivity,[status(thm)],[23220, 8169])).
% 29.31/19.54 tff(23229,plain,
% 29.31/19.54 (big_f(f9(f2(c2), c2), f10(f2(c2))) <=> big_f(c1, c1)),
% 29.31/19.54 inference(monotonicity,[status(thm)],[23228, 23227])).
% 29.31/19.54 tff(23230,plain,
% 29.31/19.54 (big_f(c1, c1) <=> big_f(f9(f2(c2), c2), f10(f2(c2)))),
% 29.31/19.54 inference(symmetry,[status(thm)],[23229])).
% 29.31/19.54 tff(23231,plain,
% 29.31/19.54 ((~big_f(c1, c1)) <=> (~big_f(f9(f2(c2), c2), f10(f2(c2))))),
% 29.31/19.54 inference(monotonicity,[status(thm)],[23230])).
% 29.31/19.54 tff(23232,plain,
% 29.31/19.54 (~big_f(f9(f2(c2), c2), f10(f2(c2)))),
% 29.31/19.54 inference(modus_ponens,[status(thm)],[66, 23231])).
% 29.31/19.54 tff(23233,assumption,(f6(c2, f9(c2, f5(c1))) = c2), introduced(assumption)).
% 29.31/19.54 tff(23234,plain,
% 29.31/19.54 (f9(c2, f5(c1)) = f9(f10(c2), f2(c3))),
% 29.31/19.54 inference(monotonicity,[status(thm)],[216, 2338])).
% 29.31/19.54 tff(23235,plain,
% 29.31/19.54 (f9(f10(c2), f2(c3)) = f9(c2, f5(c1))),
% 29.31/19.54 inference(symmetry,[status(thm)],[23234])).
% 29.31/19.54 tff(23236,plain,
% 29.31/19.54 (c1 = f9(c2, c1)),
% 29.31/19.54 inference(symmetry,[status(thm)],[736])).
% 29.31/19.54 tff(23237,plain,
% 29.31/19.54 (c1 = f9(c2, f5(c1))),
% 29.31/19.54 inference(transitivity,[status(thm)],[23236, 1249, 23235])).
% 29.31/19.54 tff(23238,plain,
% 29.31/19.54 (f6(c2, c1) = f6(c2, f9(c2, f5(c1)))),
% 29.31/19.54 inference(monotonicity,[status(thm)],[23237])).
% 29.31/19.54 tff(23239,plain,
% 29.31/19.54 (f6(c2, f2(c2)) = f6(c2, c1)),
% 29.31/19.54 inference(monotonicity,[status(thm)],[1368])).
% 29.31/19.54 tff(23240,plain,
% 29.31/19.54 (f6(c2, f2(c2)) = c2),
% 29.31/19.54 inference(transitivity,[status(thm)],[23239, 23238, 23233])).
% 29.31/19.54 tff(23241,plain,
% 29.31/19.54 ((f6(c2, f2(c2)) = f2(c2)) <=> (c2 = f2(c2))),
% 29.31/19.54 inference(monotonicity,[status(thm)],[23240])).
% 29.31/19.54 tff(23242,plain,
% 29.31/19.54 ((c2 = f2(c2)) <=> (f6(c2, f2(c2)) = f2(c2))),
% 29.31/19.54 inference(symmetry,[status(thm)],[23241])).
% 29.31/19.54 tff(23243,plain,
% 29.31/19.54 ((~(c2 = f2(c2))) <=> (~(f6(c2, f2(c2)) = f2(c2)))),
% 29.31/19.54 inference(monotonicity,[status(thm)],[23242])).
% 29.31/19.54 tff(23244,plain,
% 29.31/19.54 (~(f6(c2, f2(c2)) = f2(c2))),
% 29.31/19.54 inference(modus_ponens,[status(thm)],[1342, 23243])).
% 29.31/19.54 tff(23245,plain,
% 29.31/19.54 (big_f(f7(c2), f6(c2, f2(c2))) <=> big_f(c2, c2)),
% 29.31/19.54 inference(monotonicity,[status(thm)],[77, 23240])).
% 29.31/19.54 tff(23246,plain,
% 29.31/19.54 (big_f(c2, c2) <=> big_f(f7(c2), f6(c2, f2(c2)))),
% 29.31/19.54 inference(symmetry,[status(thm)],[23245])).
% 29.31/19.54 tff(23247,plain,
% 29.31/19.54 ((~big_f(c2, c2)) <=> (~big_f(f7(c2), f6(c2, f2(c2))))),
% 29.31/19.54 inference(monotonicity,[status(thm)],[23246])).
% 29.31/19.54 tff(23248,plain,
% 29.31/19.54 (~big_f(f7(c2), f6(c2, f2(c2)))),
% 29.31/19.54 inference(modus_ponens,[status(thm)],[121, 23247])).
% 29.31/19.54 tff(23249,plain,
% 29.31/19.54 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f7(c2) = c2)) | (f6(c2, f2(c2)) = f2(c2)) | big_f(f7(c2), f6(c2, f2(c2))) | big_f(f9(f2(c2), c2), f10(f2(c2))) | (f9(f2(c2), c2) = c2) | (~(f10(f2(c2)) = f2(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c2) = c2)) | (f6(c2, f2(c2)) = f2(c2)) | big_f(f7(c2), f6(c2, f2(c2))) | big_f(f9(f2(c2), c2), f10(f2(c2))) | (f9(f2(c2), c2) = c2) | (~(f10(f2(c2)) = f2(c2))))),
% 29.31/19.54 inference(rewrite,[status(thm)],[])).
% 29.31/19.54 tff(23250,plain,
% 29.31/19.54 (((~(f10(f2(c2)) = f2(c2))) | (f9(f2(c2), c2) = c2) | big_f(f9(f2(c2), c2), f10(f2(c2))) | (~(f7(c2) = c2)) | (f6(c2, f2(c2)) = f2(c2)) | big_f(f7(c2), f6(c2, f2(c2)))) <=> ((~(f7(c2) = c2)) | (f6(c2, f2(c2)) = f2(c2)) | big_f(f7(c2), f6(c2, f2(c2))) | big_f(f9(f2(c2), c2), f10(f2(c2))) | (f9(f2(c2), c2) = c2) | (~(f10(f2(c2)) = f2(c2))))),
% 29.31/19.54 inference(rewrite,[status(thm)],[])).
% 29.31/19.54 tff(23251,plain,
% 29.31/19.54 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(f2(c2)) = f2(c2))) | (f9(f2(c2), c2) = c2) | big_f(f9(f2(c2), c2), f10(f2(c2))) | (~(f7(c2) = c2)) | (f6(c2, f2(c2)) = f2(c2)) | big_f(f7(c2), f6(c2, f2(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f7(c2) = c2)) | (f6(c2, f2(c2)) = f2(c2)) | big_f(f7(c2), f6(c2, f2(c2))) | big_f(f9(f2(c2), c2), f10(f2(c2))) | (f9(f2(c2), c2) = c2) | (~(f10(f2(c2)) = f2(c2)))))),
% 29.31/19.54 inference(monotonicity,[status(thm)],[23250])).
% 29.31/19.54 tff(23252,plain,
% 29.31/19.54 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(f2(c2)) = f2(c2))) | (f9(f2(c2), c2) = c2) | big_f(f9(f2(c2), c2), f10(f2(c2))) | (~(f7(c2) = c2)) | (f6(c2, f2(c2)) = f2(c2)) | big_f(f7(c2), f6(c2, f2(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c2) = c2)) | (f6(c2, f2(c2)) = f2(c2)) | big_f(f7(c2), f6(c2, f2(c2))) | big_f(f9(f2(c2), c2), f10(f2(c2))) | (f9(f2(c2), c2) = c2) | (~(f10(f2(c2)) = f2(c2))))),
% 29.31/19.54 inference(transitivity,[status(thm)],[23251, 23249])).
% 29.31/19.54 tff(23253,plain,
% 29.31/19.54 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(f2(c2)) = f2(c2))) | (f9(f2(c2), c2) = c2) | big_f(f9(f2(c2), c2), f10(f2(c2))) | (~(f7(c2) = c2)) | (f6(c2, f2(c2)) = f2(c2)) | big_f(f7(c2), f6(c2, f2(c2))))),
% 29.31/19.54 inference(quant_inst,[status(thm)],[])).
% 29.31/19.54 tff(23254,plain,
% 29.31/19.54 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c2) = c2)) | (f6(c2, f2(c2)) = f2(c2)) | big_f(f7(c2), f6(c2, f2(c2))) | big_f(f9(f2(c2), c2), f10(f2(c2))) | (f9(f2(c2), c2) = c2) | (~(f10(f2(c2)) = f2(c2)))),
% 29.31/19.54 inference(modus_ponens,[status(thm)],[23253, 23252])).
% 29.31/19.54 tff(23255,plain,
% 29.31/19.54 ((f6(c2, f2(c2)) = f2(c2)) | big_f(f7(c2), f6(c2, f2(c2))) | big_f(f9(f2(c2), c2), f10(f2(c2))) | (f9(f2(c2), c2) = c2) | (~(f10(f2(c2)) = f2(c2)))),
% 29.31/19.54 inference(unit_resolution,[status(thm)],[23254, 2492, 77])).
% 29.31/19.54 tff(23256,plain,
% 29.31/19.54 ($false),
% 29.31/19.54 inference(unit_resolution,[status(thm)],[23255, 23248, 23244, 23232, 23226, 23219])).
% 29.31/19.54 tff(23257,plain,((~(f9(c1, c2) = c1)) | (~(f7(c2) = c2)) | big_f(c1, c1) | (~(f10(c1) = c1)) | (~(f2(c3) = c1)) | (~(c3 = c2)) | (c2 = f2(c2)) | big_f(c2, c2) | (~(f6(c2, f9(c2, f5(c1))) = c2)) | (~(f9(c2, c1) = c1)) | (~(f5(c1) = c1)) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.31/19.54 tff(23258,plain,
% 29.31/19.54 (~(f9(c1, c2) = c1)),
% 29.31/19.54 inference(unit_resolution,[status(thm)],[23257, 23217, 3762, 66, 77, 9300, 1247, 121, 23207, 736, 230, 122])).
% 29.31/19.54 tff(23259,plain,
% 29.31/19.54 ($false),
% 29.31/19.54 inference(unit_resolution,[status(thm)],[3791, 23258, 23203])).
% 29.31/19.54 tff(23260,plain,((f6(c2, c1) = f2(c2)) | (~(f10(c1) = c1)) | big_f(c1, c1) | (~(f7(c2) = c2)) | (~(f2(c3) = c1)) | big_f(c2, c2) | (~(f9(c2, c1) = c1)) | (~(f5(c1) = c1)) | (~(f10(c2) = c2)) | big_f(f7(c2), f6(c2, c1)) | (~big_f(c2, c1)) | (~(c2 = c3)) | (~(f5(f10(c1)) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.31/19.54 tff(23261,plain,
% 29.31/19.54 (f6(c2, c1) = f2(c2)),
% 29.31/19.54 inference(unit_resolution,[status(thm)],[23260, 23035, 22733, 23192, 23039, 121, 23196, 23195, 122, 23193, 22980, 22963, 23050])).
% 29.31/19.55 tff(23262,plain,
% 29.31/19.55 (f6(c2, c1) = c1),
% 29.31/19.55 inference(transitivity,[status(thm)],[23261, 23040, 23039])).
% 29.31/19.55 tff(23263,plain,
% 29.31/19.55 (big_f(c2, f6(c2, c1)) <=> big_f(c2, c1)),
% 29.31/19.55 inference(monotonicity,[status(thm)],[23262])).
% 29.31/19.55 tff(23264,plain,
% 29.31/19.55 (big_f(c2, c1) <=> big_f(c2, f6(c2, c1))),
% 29.31/19.55 inference(symmetry,[status(thm)],[23263])).
% 29.31/19.55 tff(23265,plain,
% 29.31/19.55 (big_f(c2, f6(c2, c1))),
% 29.31/19.55 inference(modus_ponens,[status(thm)],[22980, 23264])).
% 29.31/19.55 tff(23266,plain,
% 29.31/19.55 (big_f(f7(c2), f6(c2, c1)) <=> big_f(c2, f6(c2, c1))),
% 29.31/19.55 inference(monotonicity,[status(thm)],[23192])).
% 29.31/19.55 tff(23267,plain,
% 29.31/19.55 ((~big_f(f7(c2), f6(c2, c1))) <=> (~big_f(c2, f6(c2, c1)))),
% 29.31/19.55 inference(monotonicity,[status(thm)],[23266])).
% 29.31/19.55 tff(23268,plain,
% 29.31/19.55 (~big_f(c2, f6(c2, c1))),
% 29.31/19.55 inference(modus_ponens,[status(thm)],[23193, 23267])).
% 29.31/19.55 tff(23269,plain,
% 29.31/19.55 ($false),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[23268, 23265])).
% 29.31/19.55 tff(23270,plain,(big_f(c1, c2) | big_f(c2, c2) | (~(f10(c2) = c2)) | (f7(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.31/19.55 tff(23271,plain,
% 29.31/19.55 (big_f(c1, c2)),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[23270, 121, 122, 115])).
% 29.31/19.55 tff(23272,plain,
% 29.31/19.55 (big_f(f7(c2), c2)),
% 29.31/19.55 inference(modus_ponens,[status(thm)],[23271, 126])).
% 29.31/19.55 tff(23273,plain,
% 29.31/19.55 (~big_f(f7(c2), f7(c2))),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[15961, 23272, 122, 121, 17])).
% 29.31/19.55 tff(23274,plain,
% 29.31/19.55 (~big_f(c1, c1)),
% 29.31/19.55 inference(modus_ponens,[status(thm)],[23273, 124])).
% 29.31/19.55 tff(23275,plain,
% 29.31/19.55 (~(f7(c2) = f5(c2))),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[15985, 23272, 122, 121, 17, 23273])).
% 29.31/19.55 tff(23276,plain,
% 29.31/19.55 (~(f5(c2) = c1)),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[8394, 23275, 22])).
% 29.31/19.55 tff(23277,plain,
% 29.31/19.55 (f5(c2) = c2),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[1547, 23276])).
% 29.31/19.55 tff(23278,plain,
% 29.31/19.55 (c2 = f5(c2)),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[8113, 23277])).
% 29.31/19.55 tff(23279,plain,
% 29.31/19.55 (f7(c1) = f5(f7(c1))),
% 29.31/19.55 inference(modus_ponens,[status(thm)],[5124, 16039])).
% 29.31/19.55 tff(23280,plain,
% 29.31/19.55 ($false),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[20569, 23279])).
% 29.31/19.55 tff(23281,plain,((~(c2 = f5(c2))) | (f7(c1) = f5(f7(c1))) | (~(f7(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.31/19.55 tff(23282,plain,
% 29.31/19.55 (f7(c1) = f5(f7(c1))),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[23281, 23278, 120])).
% 29.31/19.55 tff(23283,plain,
% 29.31/19.55 (~(f5(c1) = c2)),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[10391, 23272, 122, 121, 115, 22])).
% 29.31/19.55 tff(23284,plain,
% 29.31/19.55 (f5(c1) = c1),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[1708, 23283])).
% 29.31/19.55 tff(23285,plain,
% 29.31/19.55 (big_f(f7(c1), c1)),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[22879, 23271, 122, 115, 121])).
% 29.31/19.55 tff(23286,plain,
% 29.31/19.55 ((f7(c2) = c3) <=> (f7(c2) = c2)),
% 29.31/19.55 inference(monotonicity,[status(thm)],[22967])).
% 29.31/19.55 tff(23287,plain,
% 29.31/19.55 ((f7(c2) = c2) <=> (f7(c2) = c3)),
% 29.31/19.55 inference(symmetry,[status(thm)],[23286])).
% 29.31/19.55 tff(23288,plain,
% 29.31/19.55 ((~(f7(c2) = c2)) <=> (~(f7(c2) = c3))),
% 29.31/19.55 inference(monotonicity,[status(thm)],[23287])).
% 29.31/19.55 tff(23289,plain,
% 29.31/19.55 (~(f7(c2) = c3)),
% 29.31/19.55 inference(modus_ponens,[status(thm)],[17, 23288])).
% 29.31/19.55 tff(23290,plain,
% 29.31/19.55 (big_f(c2, c1)),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[15738, 23285, 120])).
% 29.31/19.55 tff(23291,plain,
% 29.31/19.55 (big_f(c2, f7(c2))),
% 29.31/19.55 inference(modus_ponens,[status(thm)],[23290, 9312])).
% 29.31/19.55 tff(23292,plain,
% 29.31/19.55 ((c1 = c4) <=> (f7(c2) = c4)),
% 29.31/19.55 inference(symmetry,[status(thm)],[16687])).
% 29.31/19.55 tff(23293,plain,
% 29.31/19.55 (~big_f(f7(c2), c1)),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[17079, 23273, 22])).
% 29.31/19.55 tff(23294,plain,
% 29.31/19.55 (c2 = c4),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[9203, 23293, 121, 22975, 23272, 23289, 120, 17])).
% 29.31/19.55 tff(23295,plain,
% 29.31/19.55 (c4 = c2),
% 29.31/19.55 inference(symmetry,[status(thm)],[23294])).
% 29.31/19.55 tff(23296,plain,
% 29.31/19.55 ((c1 = c4) <=> (c1 = c2)),
% 29.31/19.55 inference(monotonicity,[status(thm)],[23295])).
% 29.31/19.55 tff(23297,plain,
% 29.31/19.55 ((c1 = c4) <=> (c2 = c1)),
% 29.31/19.55 inference(transitivity,[status(thm)],[23296, 1])).
% 29.31/19.55 tff(23298,plain,
% 29.31/19.55 ((c2 = c1) <=> (c1 = c4)),
% 29.31/19.55 inference(symmetry,[status(thm)],[23297])).
% 29.31/19.55 tff(23299,plain,
% 29.31/19.55 ((c2 = c1) <=> (f7(c2) = c4)),
% 29.31/19.55 inference(transitivity,[status(thm)],[23298, 23292])).
% 29.31/19.55 tff(23300,plain,
% 29.31/19.55 ((~(c2 = c1)) <=> (~(f7(c2) = c4))),
% 29.31/19.55 inference(monotonicity,[status(thm)],[23299])).
% 29.31/19.55 tff(23301,plain,
% 29.31/19.55 (~(f7(c2) = c4)),
% 29.31/19.55 inference(modus_ponens,[status(thm)],[75, 23300])).
% 29.31/19.55 tff(23302,plain,
% 29.31/19.55 (~(f3(c1, c2) = c2)),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[16240, 23301, 17, 23291, 23289, 23272, 23273])).
% 29.31/19.55 tff(23303,plain,
% 29.31/19.55 (~(f1(c2, c1) = c1)),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[16063, 16041, 230, 347, 16042, 12777])).
% 29.31/19.55 tff(23304,plain,
% 29.31/19.55 (f1(c2, c1) = c2),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[10113, 23303])).
% 29.31/19.55 tff(23305,plain,
% 29.31/19.55 (~(f1(f7(f7(c2)), c1) = c2)),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[20609, 16041, 292, 230, 16042, 347, 12777])).
% 29.31/19.55 tff(23306,plain,
% 29.31/19.55 (f1(f7(f7(c2)), c1) = c1),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[384, 23305])).
% 29.31/19.55 tff(23307,plain,
% 29.31/19.55 (big_f(f7(c1), f1(f7(c1), c1))),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[15864, 23306, 15735, 292])).
% 29.31/19.55 tff(23308,plain,
% 29.31/19.55 ($false),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[12197, 23307, 23304, 121, 347])).
% 29.31/19.55 tff(23309,plain,((c1 = f3(c1, c2)) | big_f(c2, c2) | (~(f7(c1) = c2)) | (~big_f(f7(c1), c1)) | (~(f7(c2) = c1)) | (~(f5(c1) = c1)) | (~(f7(c1) = f5(f7(c1)))) | (f3(c1, c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 29.31/19.55 tff(23310,plain,
% 29.31/19.55 (c1 = f3(c1, c2)),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[23309, 23302, 120, 23285, 22, 23284, 23282, 121])).
% 29.31/19.55 tff(23311,plain,
% 29.31/19.55 (big_f(c1, c1) <=> big_f(f3(c1, c2), c1)),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[13192, 23310])).
% 29.31/19.55 tff(23312,plain,
% 29.31/19.55 ((~(c2 = c1)) <=> (~(c1 = c4))),
% 29.31/19.55 inference(monotonicity,[status(thm)],[23298])).
% 29.31/19.55 tff(23313,plain,
% 29.31/19.55 (~(c1 = c4)),
% 29.31/19.55 inference(modus_ponens,[status(thm)],[75, 23312])).
% 29.31/19.55 tff(23314,assumption,(big_f(c1, c1) <=> big_f(f3(c1, c2), c1)), introduced(assumption)).
% 29.31/19.55 tff(23315,plain,
% 29.31/19.55 (~big_f(f3(c1, c2), c1)),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[13186, 66, 23314])).
% 29.31/19.55 tff(23316,plain,
% 29.31/19.55 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (c1 = c4) | (~big_f(c1, f1(c1, c2))) | (~(f1(c1, c2) = c2)) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (c1 = c4) | (~big_f(c1, f1(c1, c2))) | (~(f1(c1, c2) = c2)) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2))),
% 29.31/19.55 inference(rewrite,[status(thm)],[])).
% 29.31/19.55 tff(23317,plain,
% 29.31/19.55 (((c1 = c4) | (f3(c1, c2) = c2) | big_f(f3(c1, c2), c1) | (c1 = c3) | (~(f1(c1, c2) = c2)) | (~big_f(c1, f1(c1, c2)))) <=> ((c1 = c3) | (c1 = c4) | (~big_f(c1, f1(c1, c2))) | (~(f1(c1, c2) = c2)) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2))),
% 29.31/19.55 inference(rewrite,[status(thm)],[])).
% 29.31/19.55 tff(23318,plain,
% 29.31/19.55 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c4) | (f3(c1, c2) = c2) | big_f(f3(c1, c2), c1) | (c1 = c3) | (~(f1(c1, c2) = c2)) | (~big_f(c1, f1(c1, c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (c1 = c4) | (~big_f(c1, f1(c1, c2))) | (~(f1(c1, c2) = c2)) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2)))),
% 29.31/19.55 inference(monotonicity,[status(thm)],[23317])).
% 29.31/19.55 tff(23319,plain,
% 29.31/19.55 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c4) | (f3(c1, c2) = c2) | big_f(f3(c1, c2), c1) | (c1 = c3) | (~(f1(c1, c2) = c2)) | (~big_f(c1, f1(c1, c2))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (c1 = c4) | (~big_f(c1, f1(c1, c2))) | (~(f1(c1, c2) = c2)) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2))),
% 29.31/19.55 inference(transitivity,[status(thm)],[23318, 23316])).
% 29.31/19.55 tff(23320,plain,
% 29.31/19.55 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c4) | (f3(c1, c2) = c2) | big_f(f3(c1, c2), c1) | (c1 = c3) | (~(f1(c1, c2) = c2)) | (~big_f(c1, f1(c1, c2))))),
% 29.31/19.55 inference(quant_inst,[status(thm)],[])).
% 29.31/19.55 tff(23321,plain,
% 29.31/19.55 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (c1 = c4) | (~big_f(c1, f1(c1, c2))) | (~(f1(c1, c2) = c2)) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2)),
% 29.31/19.55 inference(modus_ponens,[status(thm)],[23320, 23319])).
% 29.31/19.55 tff(23322,plain,
% 29.31/19.55 ($false),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[23321, 904, 168, 482, 822, 13536, 13164, 12777])).
% 29.31/19.55 tff(23323,plain,((~(f1(c1, c2) = c2)) | (c1 = c3) | (c1 = c4) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2) | (~big_f(c1, c2))), inference(lemma,lemma(discharge,[]))).
% 29.31/19.55 tff(23324,plain,
% 29.31/19.55 (~(f1(c1, c2) = c2)),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[23323, 23315, 482, 168, 12777, 2865])).
% 29.31/19.55 tff(23325,plain,
% 29.31/19.55 (f1(c1, c2) = c1),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[841, 23324])).
% 29.31/19.55 tff(23326,plain,
% 29.31/19.55 (big_f(c1, f1(c1, c2)) <=> big_f(c1, c1)),
% 29.31/19.55 inference(monotonicity,[status(thm)],[23325])).
% 29.31/19.55 tff(23327,plain,
% 29.31/19.55 (big_f(c1, c1) <=> big_f(c1, f1(c1, c2))),
% 29.31/19.55 inference(symmetry,[status(thm)],[23326])).
% 29.31/19.55 tff(23328,plain,
% 29.31/19.55 ((~big_f(c1, c1)) <=> (~big_f(c1, f1(c1, c2)))),
% 29.31/19.55 inference(monotonicity,[status(thm)],[23327])).
% 29.31/19.55 tff(23329,plain,
% 29.31/19.55 (~big_f(c1, f1(c1, c2))),
% 29.31/19.55 inference(modus_ponens,[status(thm)],[66, 23328])).
% 29.31/19.55 tff(23330,plain,
% 29.31/19.55 ($false),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[16487, 1014, 168, 482, 23324, 23329, 23315, 12777])).
% 29.31/19.55 tff(23331,plain,(big_f(c1, c1) | (c1 = c3) | (c1 = c4) | (f3(c1, c2) = c2) | (~big_f(c1, c2)) | (~(big_f(c1, c1) <=> big_f(f3(c1, c2), c1)))), inference(lemma,lemma(discharge,[]))).
% 29.31/19.55 tff(23332,plain,
% 29.31/19.55 (big_f(c1, c1)),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[23331, 23313, 22975, 23302, 23271, 23311])).
% 29.31/19.55 tff(23333,plain,
% 29.31/19.55 ($false),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[23332, 23274])).
% 29.31/19.55 tff(23334,plain,((f7(c2) = c2) | big_f(c2, c2) | (~(f10(c2) = c2)) | (f7(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.31/19.55 tff(23335,plain,
% 29.31/19.55 (f7(c2) = c2),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[23334, 121, 122, 115])).
% 29.31/19.55 tff(23336,plain,
% 29.31/19.55 (f9(c2, c1) = c1),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[11359, 23335, 115, 122, 121, 23290])).
% 29.31/19.55 tff(23337,plain,
% 29.31/19.55 (big_f(f9(c2, c1), f10(c2)) <=> big_f(c1, c2)),
% 29.31/19.55 inference(monotonicity,[status(thm)],[23336, 122])).
% 29.31/19.55 tff(23338,plain,
% 29.31/19.55 (big_f(c1, c2) <=> big_f(f9(c2, c1), f10(c2))),
% 29.31/19.55 inference(symmetry,[status(thm)],[23337])).
% 29.31/19.55 tff(23339,plain,
% 29.31/19.55 (big_f(f9(c2, c1), f10(c2))),
% 29.31/19.55 inference(modus_ponens,[status(thm)],[23271, 23338])).
% 29.31/19.55 tff(23340,plain,
% 29.31/19.55 (c1 = f5(c1)),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[22948, 1190, 115, 122, 23336, 23339, 23285])).
% 29.31/19.55 tff(23341,plain,
% 29.31/19.55 (f5(c1) = c1),
% 29.31/19.55 inference(modus_ponens,[status(thm)],[23340, 128])).
% 29.31/19.55 tff(23342,plain,
% 29.31/19.55 (big_f(f7(c2), f6(c2, c1))),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[22958, 23341, 23271, 122, 23290, 23336, 23335])).
% 29.31/19.55 tff(23343,plain,
% 29.31/19.55 (f5(f10(c1)) = f5(c1)),
% 29.31/19.55 inference(monotonicity,[status(thm)],[22733])).
% 29.31/19.55 tff(23344,plain,
% 29.31/19.55 ((f5(f10(c1)) = c1) <=> (f5(c1) = c1)),
% 29.31/19.55 inference(monotonicity,[status(thm)],[23343])).
% 29.31/19.55 tff(23345,plain,
% 29.31/19.55 ((f5(c1) = c1) <=> (f5(f10(c1)) = c1)),
% 29.31/19.55 inference(symmetry,[status(thm)],[23344])).
% 29.31/19.55 tff(23346,plain,
% 29.31/19.55 ((c1 = f5(c1)) <=> (f5(f10(c1)) = c1)),
% 29.31/19.55 inference(transitivity,[status(thm)],[128, 23345])).
% 29.31/19.55 tff(23347,plain,
% 29.31/19.55 (f5(f10(c1)) = c1),
% 29.31/19.55 inference(modus_ponens,[status(thm)],[23340, 23346])).
% 29.31/19.55 tff(23348,plain,
% 29.31/19.55 (~(f6(f7(c2), f5(c1)) = c2)),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[11619, 23342, 22733, 121, 23335, 23347])).
% 29.31/19.55 tff(23349,plain,
% 29.31/19.55 (f6(f7(c2), f5(c1)) = c1),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[2978, 23348])).
% 29.31/19.55 tff(23350,plain,
% 29.31/19.55 (f6(c2, c1) = c1),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[13591, 23349, 23335, 23341])).
% 29.31/19.55 tff(23351,plain,
% 29.31/19.55 ($false),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[3097, 2378, 122, 23336, 23339, 23335, 23350, 23342])).
% 29.31/19.55 tff(23352,plain,(big_f(c2, c2) | (~(f10(c2) = c2)) | (f7(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.31/19.55 tff(23353,plain,
% 29.31/19.55 (~(f10(c2) = c2)),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[23352, 121, 115])).
% 29.31/19.55 tff(23354,plain,
% 29.31/19.55 (f10(c2) = c1),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[93, 23353])).
% 29.31/19.55 tff(23355,plain,
% 29.31/19.55 (f7(f10(c2)) = f7(c1)),
% 29.31/19.55 inference(monotonicity,[status(thm)],[23354])).
% 29.31/19.55 tff(23356,plain,
% 29.31/19.55 (f7(f10(c2)) = c2),
% 29.31/19.55 inference(transitivity,[status(thm)],[23355, 120])).
% 29.31/19.55 tff(23357,plain,
% 29.31/19.55 (big_f(f7(f10(c2)), f10(c2)) <=> big_f(c2, c1)),
% 29.31/19.55 inference(monotonicity,[status(thm)],[23356, 23354])).
% 29.31/19.55 tff(23358,plain,
% 29.31/19.55 (big_f(c2, c1) <=> big_f(f7(f10(c2)), f10(c2))),
% 29.31/19.55 inference(symmetry,[status(thm)],[23357])).
% 29.31/19.55 tff(23359,plain,
% 29.31/19.55 ((f8(f6(c2, f7(f4(c4)))) = c2) <=> (c2 = f8(f6(c2, f7(f4(c4)))))),
% 29.31/19.55 inference(commutativity,[status(thm)],[])).
% 29.31/19.55 tff(23360,plain,
% 29.31/19.55 ((c2 = f8(f6(c2, f7(f4(c4))))) <=> (f8(f6(c2, f7(f4(c4)))) = c2)),
% 29.31/19.55 inference(symmetry,[status(thm)],[23359])).
% 29.31/19.55 tff(23361,plain,
% 29.31/19.55 (c2 = f7(c2)),
% 29.31/19.55 inference(modus_ponens,[status(thm)],[77, 17312])).
% 29.31/19.55 tff(23362,plain,
% 29.31/19.55 ($false),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[11444, 2492, 3762, 77, 3198, 3197, 17944, 4236])).
% 29.31/19.55 tff(23363,plain,(big_f(f7(c2), f6(c2, c1)) | (~(f10(c1) = c1)) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f9(c1, c2), f10(c1)) | (f9(c1, c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 29.31/19.55 tff(23364,plain,
% 29.31/19.55 (big_f(f7(c2), f6(c2, c1))),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[23363, 3198, 77, 3762, 17944, 4236])).
% 29.31/19.55 tff(23365,plain,
% 29.31/19.55 (~(big_f(c2, c2) <=> big_f(f7(c2), f6(c2, c1)))),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[17315, 23364, 121])).
% 29.31/19.55 tff(23366,plain,
% 29.31/19.55 (~(c2 = f6(c2, c1))),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[17322, 23365, 23361])).
% 29.31/19.55 tff(23367,assumption,(f6(c2, f6(c2, c1)) = c1), introduced(assumption)).
% 29.31/19.55 tff(23368,plain,
% 29.31/19.55 (f6(c2, f6(c2, f6(c2, c1))) = f6(c2, c1)),
% 29.31/19.55 inference(monotonicity,[status(thm)],[23367])).
% 29.31/19.55 tff(23369,plain,
% 29.31/19.55 ((f6(c2, f6(c2, f6(c2, c1))) = c1) <=> (f6(c2, c1) = c1)),
% 29.31/19.55 inference(monotonicity,[status(thm)],[23368])).
% 29.31/19.55 tff(23370,plain,
% 29.31/19.55 ((f6(c2, c1) = c1) <=> (f6(c2, f6(c2, f6(c2, c1))) = c1)),
% 29.31/19.55 inference(symmetry,[status(thm)],[23369])).
% 29.31/19.55 tff(23371,plain,
% 29.31/19.55 ((~(f6(c2, c1) = c1)) <=> (~(f6(c2, f6(c2, f6(c2, c1))) = c1))),
% 29.31/19.55 inference(monotonicity,[status(thm)],[23370])).
% 29.31/19.55 tff(23372,plain,
% 29.31/19.55 (~(f6(c2, f6(c2, f6(c2, c1))) = c1)),
% 29.31/19.55 inference(modus_ponens,[status(thm)],[3198, 23371])).
% 29.31/19.55 tff(23373,plain,
% 29.31/19.55 ((f6(c2, c1) = c2) <=> (c2 = f6(c2, c1))),
% 29.31/19.55 inference(commutativity,[status(thm)],[])).
% 29.31/19.55 tff(23374,plain,
% 29.31/19.55 ((f6(c2, f6(c2, f6(c2, c1))) = c2) <=> (f6(c2, c1) = c2)),
% 29.31/19.55 inference(monotonicity,[status(thm)],[23368])).
% 29.31/19.55 tff(23375,plain,
% 29.31/19.55 ((f6(c2, f6(c2, f6(c2, c1))) = c2) <=> (c2 = f6(c2, c1))),
% 29.31/19.55 inference(transitivity,[status(thm)],[23374, 23373])).
% 29.31/19.55 tff(23376,plain,
% 29.31/19.55 ((c2 = f6(c2, c1)) <=> (f6(c2, f6(c2, f6(c2, c1))) = c2)),
% 29.31/19.55 inference(symmetry,[status(thm)],[23375])).
% 29.31/19.55 tff(23377,plain,
% 29.31/19.55 ((~(c2 = f6(c2, c1))) <=> (~(f6(c2, f6(c2, f6(c2, c1))) = c2))),
% 29.31/19.55 inference(monotonicity,[status(thm)],[23376])).
% 29.31/19.55 tff(23378,assumption,(~(c2 = f6(c2, c1))), introduced(assumption)).
% 29.31/19.55 tff(23379,plain,
% 29.31/19.55 (~(f6(c2, f6(c2, f6(c2, c1))) = c2)),
% 29.31/19.55 inference(modus_ponens,[status(thm)],[23378, 23377])).
% 29.31/19.55 tff(23380,plain,
% 29.31/19.55 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f6(c2, f6(c2, f6(c2, c1))) = c1) | (f6(c2, f6(c2, f6(c2, c1))) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f6(c2, f6(c2, f6(c2, c1))) = c1) | (f6(c2, f6(c2, f6(c2, c1))) = c2))),
% 29.31/19.55 inference(rewrite,[status(thm)],[])).
% 29.31/19.55 tff(23381,plain,
% 29.31/19.55 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f6(c2, f6(c2, f6(c2, c1))) = c1) | (f6(c2, f6(c2, f6(c2, c1))) = c2))),
% 29.31/19.55 inference(quant_inst,[status(thm)],[])).
% 29.31/19.55 tff(23382,plain,
% 29.31/19.55 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f6(c2, f6(c2, f6(c2, c1))) = c1) | (f6(c2, f6(c2, f6(c2, c1))) = c2)),
% 29.31/19.55 inference(modus_ponens,[status(thm)],[23381, 23380])).
% 29.31/19.55 tff(23383,plain,
% 29.31/19.55 ((f6(c2, f6(c2, f6(c2, c1))) = c1) | (f6(c2, f6(c2, f6(c2, c1))) = c2)),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[23382, 10])).
% 29.31/19.55 tff(23384,plain,
% 29.31/19.55 ($false),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[23383, 23379, 23372])).
% 29.31/19.55 tff(23385,plain,((~(f6(c2, f6(c2, c1)) = c1)) | (c2 = f6(c2, c1)) | (f6(c2, c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.31/19.55 tff(23386,plain,
% 29.31/19.55 (~(f6(c2, f6(c2, c1)) = c1)),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[23385, 23366, 3198])).
% 29.31/19.55 tff(23387,plain,
% 29.31/19.55 (f6(c2, f6(c2, c1)) = c2),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[14655, 23386])).
% 29.31/19.55 tff(23388,plain,
% 29.31/19.55 ((f6(c2, f6(c2, c1)) = f6(c2, c1)) <=> (c2 = f6(c2, c1))),
% 29.31/19.55 inference(monotonicity,[status(thm)],[23387])).
% 29.31/19.55 tff(23389,plain,
% 29.31/19.55 ((c2 = f6(c2, c1)) <=> (f6(c2, f6(c2, c1)) = f6(c2, c1))),
% 29.31/19.55 inference(symmetry,[status(thm)],[23388])).
% 29.31/19.55 tff(23390,plain,
% 29.31/19.55 ((~(c2 = f6(c2, c1))) <=> (~(f6(c2, f6(c2, c1)) = f6(c2, c1)))),
% 29.31/19.55 inference(monotonicity,[status(thm)],[23389])).
% 29.31/19.55 tff(23391,plain,
% 29.31/19.55 (~(f6(c2, f6(c2, c1)) = f6(c2, c1))),
% 29.31/19.55 inference(modus_ponens,[status(thm)],[23366, 23390])).
% 29.31/19.55 tff(23392,plain,
% 29.31/19.55 (big_f(c2, f6(c2, f6(c2, c1))) <=> big_f(c2, c2)),
% 29.31/19.55 inference(monotonicity,[status(thm)],[23387])).
% 29.31/19.55 tff(23393,plain,
% 29.31/19.55 (big_f(c2, c2) <=> big_f(c2, f6(c2, f6(c2, c1)))),
% 29.31/19.55 inference(symmetry,[status(thm)],[23392])).
% 29.31/19.55 tff(23394,plain,
% 29.31/19.55 (big_f(c2, c2) <=> big_f(f7(c2), f6(c2, f6(c2, c1)))),
% 29.31/19.55 inference(transitivity,[status(thm)],[23393, 14631])).
% 29.31/19.55 tff(23395,plain,
% 29.31/19.55 ((~big_f(c2, c2)) <=> (~big_f(f7(c2), f6(c2, f6(c2, c1))))),
% 29.31/19.55 inference(monotonicity,[status(thm)],[23394])).
% 29.31/19.55 tff(23396,plain,
% 29.31/19.55 (~big_f(f7(c2), f6(c2, f6(c2, c1)))),
% 29.31/19.55 inference(modus_ponens,[status(thm)],[121, 23395])).
% 29.31/19.55 tff(23397,plain,
% 29.31/19.55 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f7(c2) = c2)) | big_f(f7(c2), f6(c2, f6(c2, c1))) | (f6(c2, f6(c2, c1)) = f6(c2, c1)) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c2) = c2)) | big_f(f7(c2), f6(c2, f6(c2, c1))) | (f6(c2, f6(c2, c1)) = f6(c2, c1)) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)))),
% 29.31/19.55 inference(rewrite,[status(thm)],[])).
% 29.31/19.55 tff(23398,plain,
% 29.31/19.55 (((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (~(f7(c2) = c2)) | (f6(c2, f6(c2, c1)) = f6(c2, c1)) | big_f(f7(c2), f6(c2, f6(c2, c1)))) <=> ((~(f7(c2) = c2)) | big_f(f7(c2), f6(c2, f6(c2, c1))) | (f6(c2, f6(c2, c1)) = f6(c2, c1)) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)))),
% 29.31/19.55 inference(rewrite,[status(thm)],[])).
% 29.31/19.55 tff(23399,plain,
% 29.31/19.55 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (~(f7(c2) = c2)) | (f6(c2, f6(c2, c1)) = f6(c2, c1)) | big_f(f7(c2), f6(c2, f6(c2, c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f7(c2) = c2)) | big_f(f7(c2), f6(c2, f6(c2, c1))) | (f6(c2, f6(c2, c1)) = f6(c2, c1)) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1))))),
% 29.31/19.55 inference(monotonicity,[status(thm)],[23398])).
% 29.31/19.55 tff(23400,plain,
% 29.31/19.55 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (~(f7(c2) = c2)) | (f6(c2, f6(c2, c1)) = f6(c2, c1)) | big_f(f7(c2), f6(c2, f6(c2, c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c2) = c2)) | big_f(f7(c2), f6(c2, f6(c2, c1))) | (f6(c2, f6(c2, c1)) = f6(c2, c1)) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)))),
% 29.31/19.55 inference(transitivity,[status(thm)],[23399, 23397])).
% 29.31/19.55 tff(23401,plain,
% 29.31/19.55 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (~(f7(c2) = c2)) | (f6(c2, f6(c2, c1)) = f6(c2, c1)) | big_f(f7(c2), f6(c2, f6(c2, c1))))),
% 29.31/19.55 inference(quant_inst,[status(thm)],[])).
% 29.31/19.55 tff(23402,plain,
% 29.31/19.55 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c2) = c2)) | big_f(f7(c2), f6(c2, f6(c2, c1))) | (f6(c2, f6(c2, c1)) = f6(c2, c1)) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1))),
% 29.31/19.55 inference(modus_ponens,[status(thm)],[23401, 23400])).
% 29.31/19.55 tff(23403,plain,
% 29.31/19.55 ($false),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[23402, 2492, 3762, 77, 17944, 4236, 23396, 23391])).
% 29.31/19.55 tff(23404,plain,((f6(c2, c1) = c1) | (~(f10(c1) = c1)) | (~(f7(c2) = c2)) | big_f(f9(c1, c2), f10(c1)) | (f9(c1, c2) = c2) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 29.31/19.55 tff(23405,plain,
% 29.31/19.55 (f6(c2, c1) = c1),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[23404, 4236, 77, 17944, 3762, 121])).
% 29.31/19.55 tff(23406,plain,
% 29.31/19.55 (big_f(c2, f6(c2, c1)) <=> big_f(c2, c1)),
% 29.31/19.55 inference(monotonicity,[status(thm)],[23405])).
% 29.31/19.55 tff(23407,plain,
% 29.31/19.55 (big_f(c2, c1) <=> big_f(c2, f6(c2, c1))),
% 29.31/19.55 inference(symmetry,[status(thm)],[23406])).
% 29.31/19.55 tff(23408,plain,
% 29.31/19.55 (big_f(c2, c1) <=> big_f(f7(c2), f6(c2, c1))),
% 29.31/19.55 inference(transitivity,[status(thm)],[23407, 13581])).
% 29.31/19.55 tff(23409,plain,
% 29.31/19.55 (big_f(f7(c2), f6(c2, c1))),
% 29.31/19.55 inference(modus_ponens,[status(thm)],[348, 23408])).
% 29.31/19.55 tff(23410,plain,
% 29.31/19.55 (~big_f(f7(c2), f6(c2, c1))),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[11630, 23405, 3762, 66, 77, 4236])).
% 29.31/19.55 tff(23411,plain,
% 29.31/19.55 ($false),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[23410, 23409])).
% 29.31/19.55 tff(23412,plain,((f9(c1, c2) = c2) | (~big_f(c2, c1)) | (~(f7(c2) = c2)) | (~(f10(c1) = c1)) | big_f(c1, c1) | big_f(f9(c1, c2), f10(c1)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 29.31/19.55 tff(23413,plain,
% 29.31/19.55 (f9(c1, c2) = c2),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[23412, 17944, 77, 3762, 66, 348, 121])).
% 29.31/19.55 tff(23414,plain,
% 29.31/19.55 (big_f(f9(c1, c2), f10(c1)) <=> big_f(c2, c1)),
% 29.31/19.55 inference(monotonicity,[status(thm)],[23413, 3762])).
% 29.31/19.55 tff(23415,plain,
% 29.31/19.55 (big_f(c2, c1) <=> big_f(f9(c1, c2), f10(c1))),
% 29.31/19.55 inference(symmetry,[status(thm)],[23414])).
% 29.31/19.55 tff(23416,plain,
% 29.31/19.55 (big_f(f9(c1, c2), f10(c1))),
% 29.31/19.55 inference(modus_ponens,[status(thm)],[348, 23415])).
% 29.31/19.55 tff(23417,plain,
% 29.31/19.55 ($false),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[17944, 23416])).
% 29.31/19.55 tff(23418,plain,(big_f(f9(c1, c2), f10(c1)) | (~big_f(c2, c1)) | (~(f10(c1) = c1)) | (~(f7(c2) = c2)) | big_f(c1, c1) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 29.31/19.55 tff(23419,plain,
% 29.31/19.55 (big_f(f9(c1, c2), f10(c1))),
% 29.31/19.55 inference(unit_resolution,[status(thm)],[23418, 66, 3762, 77, 348, 121])).
% 29.31/19.55 tff(23420,plain,
% 29.31/19.55 (big_f(f9(c1, c2), f10(c1)) <=> big_f(c1, c1)),
% 29.31/19.55 inference(monotonicity,[status(thm)],[8169, 3762])).
% 29.31/19.55 tff(23421,plain,
% 29.31/19.55 (big_f(c1, c1) <=> big_f(f9(c1, c2), f10(c1))),
% 29.31/19.55 inference(symmetry,[status(thm)],[23420])).
% 29.31/19.55 tff(23422,plain,
% 29.31/19.55 ((~big_f(c1, c1)) <=> (~big_f(f9(c1, c2), f10(c1)))),
% 29.31/19.55 inference(monotonicity,[status(thm)],[23421])).
% 29.31/19.55 tff(23423,plain,
% 29.31/19.55 (~big_f(f9(c1, c2), f10(c1))),
% 29.31/19.56 inference(modus_ponens,[status(thm)],[66, 23422])).
% 29.31/19.56 tff(23424,plain,
% 29.31/19.56 ($false),
% 29.31/19.56 inference(unit_resolution,[status(thm)],[17888, 23423])).
% 29.31/19.56 tff(23425,plain,((~(f9(c1, c2) = c1)) | (~big_f(f9(c1, c2), f10(c1))) | big_f(c1, c1) | (~(f10(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.31/19.56 tff(23426,plain,
% 29.31/19.56 (~(f9(c1, c2) = c1)),
% 29.31/19.56 inference(unit_resolution,[status(thm)],[23425, 23419, 66, 3762])).
% 29.31/19.56 tff(23427,plain,
% 29.31/19.56 (f9(c1, c2) = c2),
% 29.31/19.56 inference(unit_resolution,[status(thm)],[3791, 23426])).
% 29.31/19.56 tff(23428,plain,
% 29.31/19.56 (big_f(f7(c2), f6(c2, c1))),
% 29.31/19.56 inference(unit_resolution,[status(thm)],[11435, 3198, 348, 3762, 77, 3764])).
% 29.31/19.56 tff(23429,plain,
% 29.31/19.56 (~(big_f(c2, c2) <=> big_f(f7(c2), f6(c2, c1)))),
% 29.31/19.56 inference(unit_resolution,[status(thm)],[17315, 23428, 121])).
% 29.31/19.56 tff(23430,plain,
% 29.31/19.56 (~(c2 = f6(c2, c1))),
% 29.31/19.56 inference(unit_resolution,[status(thm)],[17322, 23429, 23361])).
% 29.31/19.56 tff(23431,plain,
% 29.31/19.56 (~(f6(c2, f6(c2, c1)) = c1)),
% 29.31/19.56 inference(unit_resolution,[status(thm)],[23385, 23430, 3198])).
% 29.31/19.56 tff(23432,plain,
% 29.31/19.56 (f6(c2, f6(c2, c1)) = c2),
% 29.31/19.56 inference(unit_resolution,[status(thm)],[14655, 23431])).
% 29.31/19.56 tff(23433,plain,
% 29.31/19.56 ((f6(c2, f6(c2, c1)) = f6(c2, c1)) <=> (c2 = f6(c2, c1))),
% 29.31/19.56 inference(monotonicity,[status(thm)],[23432])).
% 29.31/19.56 tff(23434,plain,
% 29.31/19.56 ((c2 = f6(c2, c1)) <=> (f6(c2, f6(c2, c1)) = f6(c2, c1))),
% 29.31/19.56 inference(symmetry,[status(thm)],[23433])).
% 29.31/19.56 tff(23435,plain,
% 29.31/19.56 ((~(c2 = f6(c2, c1))) <=> (~(f6(c2, f6(c2, c1)) = f6(c2, c1)))),
% 29.31/19.56 inference(monotonicity,[status(thm)],[23434])).
% 29.31/19.56 tff(23436,plain,
% 29.31/19.56 (~(f6(c2, f6(c2, c1)) = f6(c2, c1))),
% 29.31/19.56 inference(modus_ponens,[status(thm)],[23430, 23435])).
% 29.31/19.56 tff(23437,plain,
% 29.31/19.56 (big_f(c2, f6(c2, f6(c2, c1))) <=> big_f(c2, c2)),
% 29.31/19.56 inference(monotonicity,[status(thm)],[23432])).
% 29.31/19.56 tff(23438,plain,
% 29.31/19.56 (big_f(c2, c2) <=> big_f(c2, f6(c2, f6(c2, c1)))),
% 29.31/19.56 inference(symmetry,[status(thm)],[23437])).
% 29.31/19.56 tff(23439,plain,
% 29.31/19.56 (big_f(c2, c2) <=> big_f(f7(c2), f6(c2, f6(c2, c1)))),
% 29.31/19.56 inference(transitivity,[status(thm)],[23438, 14631])).
% 29.31/19.56 tff(23440,plain,
% 29.31/19.56 ((~big_f(c2, c2)) <=> (~big_f(f7(c2), f6(c2, f6(c2, c1))))),
% 29.31/19.56 inference(monotonicity,[status(thm)],[23439])).
% 29.31/19.56 tff(23441,plain,
% 29.31/19.56 (~big_f(f7(c2), f6(c2, f6(c2, c1)))),
% 29.31/19.56 inference(modus_ponens,[status(thm)],[121, 23440])).
% 29.31/19.56 tff(23442,plain,
% 29.31/19.56 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f7(c2) = c2)) | big_f(f7(c2), f6(c2, f6(c2, c1))) | (f6(c2, f6(c2, c1)) = f6(c2, c1)) | (~(f10(c1) = c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f7(c2) = c2)) | big_f(f7(c2), f6(c2, f6(c2, c1))) | (f6(c2, f6(c2, c1)) = f6(c2, c1)) | (~(f10(c1) = c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2)))),
% 29.31/19.56 inference(rewrite,[status(thm)],[])).
% 29.31/19.56 tff(23443,plain,
% 29.31/19.56 (((~(f10(c1) = c1)) | (~(f7(c2) = c2)) | (f6(c2, f6(c2, c1)) = f6(c2, c1)) | big_f(f7(c2), f6(c2, f6(c2, c1))) | (~(f9(c1, c2) = c2)) | (~big_f(f9(c1, c2), f10(c1)))) <=> ((~(f7(c2) = c2)) | big_f(f7(c2), f6(c2, f6(c2, c1))) | (f6(c2, f6(c2, c1)) = f6(c2, c1)) | (~(f10(c1) = c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2)))),
% 29.31/19.56 inference(rewrite,[status(thm)],[])).
% 29.31/19.56 tff(23444,plain,
% 29.31/19.56 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c1) = c1)) | (~(f7(c2) = c2)) | (f6(c2, f6(c2, c1)) = f6(c2, c1)) | big_f(f7(c2), f6(c2, f6(c2, c1))) | (~(f9(c1, c2) = c2)) | (~big_f(f9(c1, c2), f10(c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f7(c2) = c2)) | big_f(f7(c2), f6(c2, f6(c2, c1))) | (f6(c2, f6(c2, c1)) = f6(c2, c1)) | (~(f10(c1) = c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2))))),
% 29.31/19.56 inference(monotonicity,[status(thm)],[23443])).
% 29.31/19.56 tff(23445,plain,
% 29.31/19.56 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c1) = c1)) | (~(f7(c2) = c2)) | (f6(c2, f6(c2, c1)) = f6(c2, c1)) | big_f(f7(c2), f6(c2, f6(c2, c1))) | (~(f9(c1, c2) = c2)) | (~big_f(f9(c1, c2), f10(c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f7(c2) = c2)) | big_f(f7(c2), f6(c2, f6(c2, c1))) | (f6(c2, f6(c2, c1)) = f6(c2, c1)) | (~(f10(c1) = c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2)))),
% 29.31/19.56 inference(transitivity,[status(thm)],[23444, 23442])).
% 29.31/19.56 tff(23446,plain,
% 29.31/19.56 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c1) = c1)) | (~(f7(c2) = c2)) | (f6(c2, f6(c2, c1)) = f6(c2, c1)) | big_f(f7(c2), f6(c2, f6(c2, c1))) | (~(f9(c1, c2) = c2)) | (~big_f(f9(c1, c2), f10(c1))))),
% 29.31/19.56 inference(quant_inst,[status(thm)],[])).
% 29.31/19.56 tff(23447,plain,
% 29.31/19.56 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f7(c2) = c2)) | big_f(f7(c2), f6(c2, f6(c2, c1))) | (f6(c2, f6(c2, c1)) = f6(c2, c1)) | (~(f10(c1) = c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2))),
% 29.31/19.56 inference(modus_ponens,[status(thm)],[23446, 23445])).
% 29.31/19.56 tff(23448,plain,
% 29.31/19.56 ($false),
% 29.31/19.56 inference(unit_resolution,[status(thm)],[23447, 2409, 3762, 77, 17888, 3764, 23441, 23436])).
% 29.31/19.56 tff(23449,plain,((f6(c2, c1) = c1) | (~(f10(c1) = c1)) | (~(f7(c2) = c2)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2)) | big_f(c2, c2) | (~big_f(c2, c1))), inference(lemma,lemma(discharge,[]))).
% 29.31/19.56 tff(23450,plain,
% 29.31/19.56 (f6(c2, c1) = c1),
% 29.31/19.56 inference(unit_resolution,[status(thm)],[23449, 23419, 77, 3762, 23427, 121, 348])).
% 29.31/19.56 tff(23451,plain,
% 29.31/19.56 (big_f(c2, f6(c2, c1)) <=> big_f(c2, c1)),
% 29.31/19.56 inference(monotonicity,[status(thm)],[23450])).
% 29.31/19.56 tff(23452,plain,
% 29.31/19.56 (big_f(c2, c1) <=> big_f(c2, f6(c2, c1))),
% 29.31/19.56 inference(symmetry,[status(thm)],[23451])).
% 29.31/19.56 tff(23453,plain,
% 29.31/19.56 (big_f(c2, c1) <=> big_f(f7(c2), f6(c2, c1))),
% 29.31/19.56 inference(transitivity,[status(thm)],[23452, 13581])).
% 29.31/19.56 tff(23454,plain,
% 29.31/19.56 (big_f(f7(c2), f6(c2, c1))),
% 29.31/19.56 inference(modus_ponens,[status(thm)],[348, 23453])).
% 29.31/19.56 tff(23455,plain,
% 29.31/19.56 ($false),
% 29.31/19.56 inference(unit_resolution,[status(thm)],[11640, 2378, 3762, 77, 23450, 23454, 23419, 23427])).
% 29.31/19.56 tff(23456,plain,(big_f(c1, c1) | (~(f10(c1) = c1)) | (~(f7(c2) = c2)) | (~big_f(c2, c1)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 29.31/19.56 tff(23457,plain,
% 29.31/19.56 (~big_f(c2, c1)),
% 29.31/19.56 inference(unit_resolution,[status(thm)],[23456, 121, 22733, 66, 77])).
% 29.31/19.56 tff(23458,plain,
% 29.31/19.56 (~big_f(f7(c1), c1)),
% 29.31/19.56 inference(unit_resolution,[status(thm)],[15738, 23457, 120])).
% 29.31/19.56 tff(23459,plain,
% 29.31/19.56 (big_f(c2, c2)),
% 29.31/19.56 inference(unit_resolution,[status(thm)],[23352, 122, 115])).
% 29.31/19.56 tff(23460,plain,
% 29.31/19.56 (f9(f10(c2), f4(c4)) = c2),
% 29.31/19.56 inference(unit_resolution,[status(thm)],[8065, 79, 122])).
% 29.31/19.56 tff(23461,plain,
% 29.31/19.56 (f9(c2, c2) = c2),
% 29.31/19.56 inference(unit_resolution,[status(thm)],[1606, 79, 23460, 122])).
% 29.31/19.56 tff(23462,plain,
% 29.31/19.56 (big_f(f9(c2, c2), c2) <=> big_f(c2, c2)),
% 29.31/19.56 inference(monotonicity,[status(thm)],[23461])).
% 29.31/19.56 tff(23463,plain,
% 29.31/19.56 (big_f(c2, c2) <=> big_f(f9(c2, c2), c2)),
% 29.31/19.56 inference(symmetry,[status(thm)],[23462])).
% 29.31/19.56 tff(23464,plain,
% 29.31/19.56 (big_f(c2, c2) <=> big_f(f9(c2, c2), f10(c2))),
% 29.31/19.56 inference(transitivity,[status(thm)],[23463, 130])).
% 29.31/19.56 tff(23465,plain,
% 29.31/19.56 (big_f(f9(c2, c2), f10(c2))),
% 29.31/19.56 inference(modus_ponens,[status(thm)],[1345, 23464])).
% 29.31/19.56 tff(23466,plain,
% 29.31/19.56 (~(f6(c2, f7(f4(c4))) = c1)),
% 29.31/19.56 inference(unit_resolution,[status(thm)],[14767, 79, 122, 347, 77, 1345])).
% 29.31/19.56 tff(23467,plain,
% 29.31/19.56 (f6(c2, f7(f4(c4))) = c2),
% 29.31/19.56 inference(unit_resolution,[status(thm)],[6601, 23466])).
% 29.31/19.56 tff(23468,plain,
% 29.31/19.56 (f6(c2, c2) = c2),
% 29.31/19.56 inference(transitivity,[status(thm)],[84, 23467])).
% 29.31/19.56 tff(23469,plain,
% 29.31/19.56 (big_f(f7(c2), f6(c2, c2)) <=> big_f(c2, c2)),
% 29.31/19.56 inference(monotonicity,[status(thm)],[77, 23468])).
% 29.31/19.56 tff(23470,plain,
% 29.31/19.56 (big_f(c2, c2) <=> big_f(f7(c2), f6(c2, c2))),
% 29.31/19.56 inference(symmetry,[status(thm)],[23469])).
% 29.31/19.56 tff(23471,plain,
% 29.31/19.56 (big_f(f7(c2), f6(c2, c2))),
% 29.31/19.56 inference(modus_ponens,[status(thm)],[1345, 23470])).
% 29.31/19.56 tff(23472,plain,
% 29.31/19.56 ($false),
% 29.31/19.56 inference(unit_resolution,[status(thm)],[2384, 2378, 122, 77, 23468, 23471, 23461, 23465])).
% 29.31/19.56 tff(23473,plain,((~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~big_f(c2, c2)) | (~(f7(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.31/19.56 tff(23474,plain,
% 29.31/19.56 (~(f4(c4) = c2)),
% 29.31/19.56 inference(unit_resolution,[status(thm)],[23473, 23459, 77, 122, 120])).
% 29.31/19.56 tff(23475,plain,
% 29.31/19.56 (f4(c4) = c1),
% 29.31/19.56 inference(unit_resolution,[status(thm)],[11750, 23474])).
% 29.31/19.56 tff(23476,plain,
% 29.31/19.56 (big_f(c2, c2)),
% 29.31/19.56 inference(unit_resolution,[status(thm)],[23352, 115, 122])).
% 29.31/19.56 tff(23477,plain,
% 29.31/19.56 (f4(c2) = c1),
% 29.31/19.56 inference(transitivity,[status(thm)],[434, 11752])).
% 29.31/19.56 tff(23478,plain,
% 29.31/19.56 ((c2 = f4(c2)) <=> (c2 = c1)),
% 29.31/19.56 inference(monotonicity,[status(thm)],[23477])).
% 29.31/19.56 tff(23479,plain,
% 29.31/19.56 ((c2 = c1) <=> (c2 = f4(c2))),
% 29.31/19.56 inference(symmetry,[status(thm)],[23478])).
% 29.31/19.56 tff(23480,plain,
% 29.31/19.56 ((~(c2 = c1)) <=> (~(c2 = f4(c2)))),
% 29.31/19.56 inference(monotonicity,[status(thm)],[23479])).
% 29.31/19.56 tff(23481,plain,
% 29.31/19.56 (~(c2 = f4(c2))),
% 29.31/19.56 inference(modus_ponens,[status(thm)],[75, 23480])).
% 29.31/19.56 tff(23482,plain,
% 29.31/19.56 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((f1(c1, c2) = c2) | (c1 = c3) | (~(c2 = c4)) | (c2 = f4(c2)) | big_f(c1, f1(c1, c2)) | (~big_f(c2, c2)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (f1(c1, c2) = c2) | (c1 = c3) | (~(c2 = c4)) | (c2 = f4(c2)) | big_f(c1, f1(c1, c2)) | (~big_f(c2, c2)))),
% 29.31/19.56 inference(rewrite,[status(thm)],[])).
% 29.31/19.56 tff(23483,plain,
% 29.31/19.56 (((c1 = c3) | (f1(c1, c2) = c2) | big_f(c1, f1(c1, c2)) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2))) <=> ((f1(c1, c2) = c2) | (c1 = c3) | (~(c2 = c4)) | (c2 = f4(c2)) | big_f(c1, f1(c1, c2)) | (~big_f(c2, c2)))),
% 29.31/19.56 inference(rewrite,[status(thm)],[])).
% 29.31/19.56 tff(23484,plain,
% 29.31/19.56 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c1 = c3) | (f1(c1, c2) = c2) | big_f(c1, f1(c1, c2)) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((f1(c1, c2) = c2) | (c1 = c3) | (~(c2 = c4)) | (c2 = f4(c2)) | big_f(c1, f1(c1, c2)) | (~big_f(c2, c2))))),
% 29.31/19.56 inference(monotonicity,[status(thm)],[23483])).
% 29.31/19.56 tff(23485,plain,
% 29.31/19.56 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c1 = c3) | (f1(c1, c2) = c2) | big_f(c1, f1(c1, c2)) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (f1(c1, c2) = c2) | (c1 = c3) | (~(c2 = c4)) | (c2 = f4(c2)) | big_f(c1, f1(c1, c2)) | (~big_f(c2, c2)))),
% 29.31/19.56 inference(transitivity,[status(thm)],[23484, 23482])).
% 29.31/19.56 tff(23486,plain,
% 29.31/19.56 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((c1 = c3) | (f1(c1, c2) = c2) | big_f(c1, f1(c1, c2)) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)))),
% 29.31/19.56 inference(quant_inst,[status(thm)],[])).
% 29.31/19.56 tff(23487,plain,
% 29.31/19.56 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (f1(c1, c2) = c2) | (c1 = c3) | (~(c2 = c4)) | (c2 = f4(c2)) | big_f(c1, f1(c1, c2)) | (~big_f(c2, c2))),
% 29.31/19.56 inference(modus_ponens,[status(thm)],[23486, 23485])).
% 29.31/19.56 tff(23488,plain,
% 29.31/19.56 ((~(c2 = c4)) | (c2 = f4(c2))),
% 29.31/19.56 inference(unit_resolution,[status(thm)],[23487, 525, 168, 1345, 1052, 13508])).
% 29.31/19.56 tff(23489,plain,
% 29.31/19.56 ($false),
% 29.31/19.56 inference(unit_resolution,[status(thm)],[23488, 23481, 432])).
% 29.31/19.56 tff(23490,plain,((~(c4 = c2)) | (c1 = c3) | (~big_f(c2, c2)) | (f1(c1, c2) = c2) | big_f(c1, f1(c1, c2)) | (~(f4(c4) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.31/19.56 tff(23491,plain,
% 29.31/19.56 (~(c4 = c2)),
% 29.31/19.56 inference(unit_resolution,[status(thm)],[23490, 1052, 1345, 168, 7524, 11752])).
% 29.31/19.56 tff(23492,plain,
% 29.31/19.56 (c4 = c1),
% 29.31/19.56 inference(unit_resolution,[status(thm)],[461, 23491])).
% 29.31/19.56 tff(23493,plain,
% 29.31/19.56 (c1 = c4),
% 29.31/19.56 inference(symmetry,[status(thm)],[23492])).
% 29.31/19.56 tff(23494,plain,
% 29.31/19.56 (f4(c1) = f4(c4)),
% 29.31/19.56 inference(monotonicity,[status(thm)],[23493])).
% 29.31/19.56 tff(23495,plain,
% 29.31/19.56 (f4(c4) = f4(c1)),
% 29.31/19.56 inference(symmetry,[status(thm)],[23494])).
% 29.31/19.56 tff(23496,plain,
% 29.31/19.56 (c1 = f4(c1)),
% 29.31/19.56 inference(transitivity,[status(thm)],[16651, 23495])).
% 29.31/19.56 tff(23497,plain,
% 29.31/19.56 (c1 = c4),
% 29.31/19.56 inference(unit_resolution,[status(thm)],[484, 23492])).
% 29.31/19.56 tff(23498,plain,
% 29.31/19.56 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f1(c1, c2) = c2) | (c1 = c3) | big_f(c1, f1(c1, c2)) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (f1(c1, c2) = c2) | (c1 = c3) | big_f(c1, f1(c1, c2)) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))))),
% 29.31/19.56 inference(rewrite,[status(thm)],[])).
% 29.31/19.56 tff(23499,plain,
% 29.31/19.56 (((c1 = c3) | (f1(c1, c2) = c2) | big_f(c1, f1(c1, c2)) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1)))) <=> ((f1(c1, c2) = c2) | (c1 = c3) | big_f(c1, f1(c1, c2)) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))))),
% 29.31/19.56 inference(rewrite,[status(thm)],[])).
% 29.31/19.56 tff(23500,plain,
% 29.31/19.56 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c1 = c3) | (f1(c1, c2) = c2) | big_f(c1, f1(c1, c2)) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f1(c1, c2) = c2) | (c1 = c3) | big_f(c1, f1(c1, c2)) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1)))))),
% 29.31/19.56 inference(monotonicity,[status(thm)],[23499])).
% 29.31/19.56 tff(23501,plain,
% 29.31/19.56 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c1 = c3) | (f1(c1, c2) = c2) | big_f(c1, f1(c1, c2)) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (f1(c1, c2) = c2) | (c1 = c3) | big_f(c1, f1(c1, c2)) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))))),
% 29.31/19.56 inference(transitivity,[status(thm)],[23500, 23498])).
% 29.31/19.56 tff(23502,plain,
% 29.31/19.56 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c1 = c3) | (f1(c1, c2) = c2) | big_f(c1, f1(c1, c2)) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))))),
% 29.31/19.56 inference(quant_inst,[status(thm)],[])).
% 29.31/19.56 tff(23503,plain,
% 29.31/19.56 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (f1(c1, c2) = c2) | (c1 = c3) | big_f(c1, f1(c1, c2)) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1)))),
% 29.31/19.56 inference(modus_ponens,[status(thm)],[23502, 23501])).
% 29.31/19.56 tff(23504,plain,
% 29.31/19.56 ($false),
% 29.31/19.56 inference(unit_resolution,[status(thm)],[23503, 402, 168, 23497, 1052, 7524, 23496, 66])).
% 29.31/19.56 tff(23505,plain,((f1(c1, c2) = c2) | (c1 = c3) | big_f(c1, c1) | (~(f4(c4) = c1)) | (~big_f(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 29.31/19.56 tff(23506,plain,
% 29.31/19.56 (f1(c1, c2) = c2),
% 29.31/19.56 inference(unit_resolution,[status(thm)],[23505, 66, 168, 11752, 23476])).
% 29.31/19.56 tff(23507,plain,
% 29.31/19.56 (big_f(c1, f1(c1, c2)) <=> big_f(c1, c2)),
% 29.31/19.56 inference(monotonicity,[status(thm)],[23506])).
% 29.31/19.56 tff(23508,plain,
% 29.31/19.56 (big_f(c1, c2) <=> big_f(c1, f1(c1, c2))),
% 29.31/19.56 inference(symmetry,[status(thm)],[23507])).
% 29.31/19.56 tff(23509,plain,
% 29.31/19.56 ((f7(f7(c2)) = c1) <=> (c2 = c1)),
% 29.31/19.56 inference(monotonicity,[status(thm)],[8406])).
% 29.31/19.56 tff(23510,plain,
% 29.31/19.56 ((c2 = c1) <=> (f7(f7(c2)) = c1)),
% 29.31/19.56 inference(symmetry,[status(thm)],[23509])).
% 29.31/19.56 tff(23511,plain,
% 29.31/19.56 ((c2 = c1) <=> (f7(f7(c2)) = f7(c2))),
% 29.31/19.56 inference(transitivity,[status(thm)],[23510, 21317])).
% 29.31/19.56 tff(23512,plain,
% 29.31/19.56 ((~(c2 = c1)) <=> (~(f7(f7(c2)) = f7(c2)))),
% 29.31/19.56 inference(monotonicity,[status(thm)],[23511])).
% 29.31/19.56 tff(23513,plain,
% 29.31/19.56 (~(f7(f7(c2)) = f7(c2))),
% 29.31/19.56 inference(modus_ponens,[status(thm)],[75, 23512])).
% 29.31/19.56 tff(23514,plain,
% 29.31/19.56 (~(f4(c4) = c2)),
% 29.31/19.56 inference(unit_resolution,[status(thm)],[10739, 17, 122])).
% 29.31/19.56 tff(23515,plain,
% 29.31/19.56 (f4(c4) = c1),
% 29.31/19.56 inference(unit_resolution,[status(thm)],[11750, 23514])).
% 29.31/19.56 tff(23516,plain,
% 29.31/19.56 (~(c3 = c1)),
% 29.31/19.56 inference(unit_resolution,[status(thm)],[11784, 23515, 66, 27])).
% 29.31/19.56 tff(23517,plain,
% 29.31/19.56 (c3 = c2),
% 29.31/19.56 inference(unit_resolution,[status(thm)],[180, 23516])).
% 29.31/19.56 tff(23518,plain,
% 29.31/19.56 (~big_f(f4(c4), c4)),
% 29.31/19.56 inference(unit_resolution,[status(thm)],[11772, 23515, 27, 66])).
% 29.31/19.56 tff(23519,plain,
% 29.31/19.56 (big_f(c3, f2(c3))),
% 29.31/19.56 inference(unit_resolution,[status(thm)],[1315, 23518])).
% 29.31/19.56 tff(23520,plain,
% 29.31/19.56 (big_f(c3, f2(c3)) <=> big_f(c2, c1)),
% 29.31/19.56 inference(monotonicity,[status(thm)],[67, 1247])).
% 29.31/19.56 tff(23521,plain,
% 29.31/19.56 (big_f(c2, c1) <=> big_f(c3, f2(c3))),
% 29.31/19.56 inference(symmetry,[status(thm)],[23520])).
% 29.31/19.56 tff(23522,plain,
% 29.31/19.56 ((~big_f(c2, c1)) <=> (~big_f(c3, f2(c3)))),
% 29.31/19.56 inference(monotonicity,[status(thm)],[23521])).
% 29.31/19.56 tff(23523,plain,
% 29.31/19.56 (~big_f(c3, f2(c3))),
% 29.31/19.56 inference(modus_ponens,[status(thm)],[2, 23522])).
% 29.31/19.56 tff(23524,plain,
% 29.31/19.56 ($false),
% 29.31/19.56 inference(unit_resolution,[status(thm)],[2274, 23523])).
% 29.31/19.56 tff(23525,plain,((~(f2(c3) = c1)) | (~big_f(c3, f2(c3))) | big_f(c2, c1) | (~(c3 = c2))), inference(lemma,lemma(discharge,[]))).
% 29.31/19.56 tff(23526,plain,
% 29.31/19.56 (~(f2(c3) = c1)),
% 29.31/19.56 inference(unit_resolution,[status(thm)],[23525, 2, 23519, 23517])).
% 29.31/19.56 tff(23527,plain,
% 29.31/19.56 (f2(c3) = c2),
% 29.31/19.56 inference(unit_resolution,[status(thm)],[1273, 23526])).
% 29.31/19.56 tff(23528,plain,
% 29.31/19.56 (c2 = f2(c2)),
% 29.31/19.56 inference(unit_resolution,[status(thm)],[4867, 23527, 23517])).
% 29.31/19.56 tff(23529,plain,
% 29.31/19.56 (~(f5(c2) = c2)),
% 29.31/19.56 inference(unit_resolution,[status(thm)],[17031, 2853, 122, 1345, 17, 1521, 67, 186])).
% 29.31/19.56 tff(23530,plain,
% 29.31/19.56 (f5(c2) = c1),
% 29.31/19.56 inference(unit_resolution,[status(thm)],[1547, 23529])).
% 29.31/19.56 tff(23531,plain,
% 29.31/19.56 (big_f(f7(c2), f5(c2)) <=> big_f(c1, c1)),
% 29.31/19.56 inference(monotonicity,[status(thm)],[22, 23530])).
% 29.31/19.56 tff(23532,plain,
% 29.31/19.56 (big_f(c1, c1) <=> big_f(f7(c2), f5(c2))),
% 29.31/19.56 inference(symmetry,[status(thm)],[23531])).
% 29.31/19.56 tff(23533,plain,
% 29.31/19.56 ((~big_f(c1, c1)) <=> (~big_f(f7(c2), f5(c2)))),
% 29.31/19.56 inference(monotonicity,[status(thm)],[23532])).
% 29.31/19.56 tff(23534,plain,
% 29.31/19.56 (~big_f(f7(c2), f5(c2))),
% 29.31/19.56 inference(modus_ponens,[status(thm)],[66, 23533])).
% 29.31/19.56 tff(23535,plain,
% 29.31/19.56 (f9(c2, c2) = c2),
% 29.31/19.56 inference(unit_resolution,[status(thm)],[17023, 23534, 122, 67, 17, 1521, 2853, 186])).
% 29.31/19.56 tff(23536,plain,
% 29.31/19.56 (big_f(f9(c2, c2), c2) <=> big_f(c2, c2)),
% 29.31/19.56 inference(monotonicity,[status(thm)],[23535])).
% 29.31/19.56 tff(23537,plain,
% 29.31/19.56 (big_f(c2, c2) <=> big_f(f9(c2, c2), c2)),
% 29.31/19.56 inference(symmetry,[status(thm)],[23536])).
% 29.31/19.56 tff(23538,plain,
% 29.31/19.56 (big_f(f9(c2, c2), c2)),
% 29.31/19.56 inference(modus_ponens,[status(thm)],[1345, 23537])).
% 29.31/19.56 tff(23539,plain,
% 29.31/19.56 (big_f(c1, c1) <=> big_f(f7(c2), f7(c2))),
% 29.31/19.56 inference(symmetry,[status(thm)],[123])).
% 29.31/19.56 tff(23540,plain,
% 29.31/19.56 ((~big_f(c1, c1)) <=> (~big_f(f7(c2), f7(c2)))),
% 29.31/19.56 inference(monotonicity,[status(thm)],[23539])).
% 29.31/19.56 tff(23541,plain,
% 29.31/19.56 (~big_f(f7(c2), f7(c2))),
% 29.31/19.56 inference(modus_ponens,[status(thm)],[66, 23540])).
% 29.31/19.56 tff(23542,plain,
% 29.31/19.56 (f7(c2) = f5(c2)),
% 29.31/19.56 inference(unit_resolution,[status(thm)],[8394, 23530, 22])).
% 29.31/19.56 tff(23543,plain,
% 29.31/19.56 (~big_f(f9(c2, c2), f10(c2))),
% 29.31/19.56 inference(unit_resolution,[status(thm)],[8386, 23535, 122, 17, 23542, 23541])).
% 29.31/19.56 tff(23544,plain,
% 29.31/19.56 (~big_f(f9(c2, c2), c2)),
% 29.31/19.56 inference(unit_resolution,[status(thm)],[6482, 23543, 122])).
% 29.31/19.56 tff(23545,plain,
% 29.31/19.56 ($false),
% 29.31/19.56 inference(unit_resolution,[status(thm)],[23544, 23538])).
% 29.31/19.56 tff(23546,plain,((~(c2 = f2(c2))) | (~big_f(c2, c2)) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~(c3 = c2)) | big_f(f7(c2), c2) | (~(f5(c1) = c2)) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 29.31/19.56 tff(23547,plain,
% 29.31/19.56 (~(f5(c1) = c2)),
% 29.31/19.56 inference(unit_resolution,[status(thm)],[23546, 23528, 122, 17, 23517, 23145, 23459, 66])).
% 29.31/19.56 tff(23548,plain,
% 29.31/19.56 (f5(c1) = c1),
% 29.31/19.56 inference(unit_resolution,[status(thm)],[1708, 23547])).
% 29.31/19.56 tff(23549,plain,
% 29.31/19.56 (c1 = f5(c1)),
% 29.31/19.56 inference(modus_ponens,[status(thm)],[23548, 192])).
% 29.31/19.56 tff(23550,plain,
% 29.31/19.56 (big_f(f7(c2), f5(c2)) <=> big_f(c1, c2)),
% 29.31/19.56 inference(monotonicity,[status(thm)],[22, 8109])).
% 29.31/19.56 tff(23551,plain,
% 29.31/19.56 (big_f(c1, c2) <=> big_f(f7(c2), f5(c2))),
% 29.31/19.56 inference(symmetry,[status(thm)],[23550])).
% 29.31/19.56 tff(23552,plain,
% 29.31/19.56 ((~big_f(c1, c2)) <=> (~big_f(f7(c2), f5(c2)))),
% 29.31/19.56 inference(monotonicity,[status(thm)],[23551])).
% 29.31/19.56 tff(23553,plain,
% 29.31/19.56 (~big_f(f7(c2), f5(c2))),
% 29.31/19.56 inference(modus_ponens,[status(thm)],[27, 23552])).
% 29.31/19.56 tff(23554,plain,
% 29.31/19.56 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((f7(c1) = c1) | (~(f10(c2) = c2)) | big_f(f7(c1), c1) | (~(c1 = f5(c1))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (f7(c1) = c1) | (~(f10(c2) = c2)) | big_f(f7(c1), c1) | (~(c1 = f5(c1))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))))),
% 29.31/19.56 inference(rewrite,[status(thm)],[])).
% 29.31/19.56 tff(23555,plain,
% 29.31/19.56 (((~(f10(c2) = c2)) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(c1 = f5(c1)))) <=> ((f7(c1) = c1) | (~(f10(c2) = c2)) | big_f(f7(c1), c1) | (~(c1 = f5(c1))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))))),
% 29.31/19.56 inference(rewrite,[status(thm)],[])).
% 29.31/19.56 tff(23556,plain,
% 29.31/19.56 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(c1 = f5(c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((f7(c1) = c1) | (~(f10(c2) = c2)) | big_f(f7(c1), c1) | (~(c1 = f5(c1))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2)))))),
% 29.31/19.56 inference(monotonicity,[status(thm)],[23555])).
% 29.31/19.56 tff(23557,plain,
% 29.31/19.56 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(c1 = f5(c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (f7(c1) = c1) | (~(f10(c2) = c2)) | big_f(f7(c1), c1) | (~(c1 = f5(c1))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))))),
% 29.31/19.57 inference(transitivity,[status(thm)],[23556, 23554])).
% 29.31/19.57 tff(23558,plain,
% 29.31/19.57 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c2) = c2)) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(c1 = f5(c1))))),
% 29.31/19.57 inference(quant_inst,[status(thm)],[])).
% 29.31/19.57 tff(23559,plain,
% 29.31/19.57 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (f7(c1) = c1) | (~(f10(c2) = c2)) | big_f(f7(c1), c1) | (~(c1 = f5(c1))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2)))),
% 29.31/19.57 inference(modus_ponens,[status(thm)],[23558, 23557])).
% 29.31/19.57 tff(23560,plain,
% 29.31/19.57 (~(f9(c2, f9(c2, c2)) = f9(c2, c2))),
% 29.31/19.57 inference(unit_resolution,[status(thm)],[23559, 783, 115, 122, 285, 11826, 1146])).
% 29.31/19.57 tff(23561,plain,
% 29.31/19.57 (f9(c2, c2) = f9(f10(c2), f2(c3))),
% 29.31/19.57 inference(monotonicity,[status(thm)],[216, 13016])).
% 29.31/19.57 tff(23562,plain,
% 29.31/19.57 (f9(f10(c2), f2(c3)) = f9(c2, c2)),
% 29.31/19.57 inference(symmetry,[status(thm)],[23561])).
% 29.31/19.57 tff(23563,plain,
% 29.31/19.57 ((f9(f10(c2), f2(c3)) = c2) <=> (f9(c2, c2) = c2)),
% 29.31/19.57 inference(monotonicity,[status(thm)],[23562])).
% 29.31/19.57 tff(23564,plain,
% 29.31/19.57 ((f9(c2, c2) = c2) <=> (f9(f10(c2), f2(c3)) = c2)),
% 29.31/19.57 inference(symmetry,[status(thm)],[23563])).
% 29.31/19.57 tff(23565,plain,
% 29.31/19.57 ((f9(c2, f9(c2, c2)) = f9(c2, c2)) <=> (f9(f10(c2), f2(c3)) = c2)),
% 29.31/19.57 inference(transitivity,[status(thm)],[23058, 23564])).
% 29.31/19.57 tff(23566,plain,
% 29.31/19.57 ((~(f9(c2, f9(c2, c2)) = f9(c2, c2))) <=> (~(f9(f10(c2), f2(c3)) = c2))),
% 29.31/19.57 inference(monotonicity,[status(thm)],[23565])).
% 29.31/19.57 tff(23567,plain,
% 29.31/19.57 (~(f9(f10(c2), f2(c3)) = c2)),
% 29.31/19.57 inference(modus_ponens,[status(thm)],[4469, 23566])).
% 29.31/19.57 tff(23568,plain,
% 29.31/19.57 (f9(f10(c2), f2(c3)) = c1),
% 29.31/19.57 inference(unit_resolution,[status(thm)],[1245, 23567])).
% 29.31/19.57 tff(23569,plain,
% 29.31/19.57 (f9(c2, c2) = c1),
% 29.31/19.57 inference(transitivity,[status(thm)],[23561, 23568])).
% 29.31/19.57 tff(23570,plain,
% 29.31/19.57 (big_f(f9(c2, c2), c2) <=> big_f(c1, c2)),
% 29.31/19.57 inference(monotonicity,[status(thm)],[23569])).
% 29.31/19.57 tff(23571,plain,
% 29.31/19.57 (big_f(c1, c2) <=> big_f(f9(c2, c2), c2)),
% 29.31/19.57 inference(symmetry,[status(thm)],[23570])).
% 29.31/19.57 tff(23572,plain,
% 29.31/19.57 ((~big_f(c1, c2)) <=> (~big_f(f9(c2, c2), c2))),
% 29.31/19.57 inference(monotonicity,[status(thm)],[23571])).
% 29.31/19.57 tff(23573,plain,
% 29.31/19.57 (~big_f(f9(c2, c2), c2)),
% 29.31/19.57 inference(modus_ponens,[status(thm)],[27, 23572])).
% 29.31/19.57 tff(23574,plain,
% 29.31/19.57 ((~(f9(c2, f9(c2, c2)) = f9(c2, c2))) <=> (~(f9(c2, c2) = c2))),
% 29.31/19.57 inference(monotonicity,[status(thm)],[23058])).
% 29.31/19.57 tff(23575,plain,
% 29.31/19.57 (~(f9(c2, c2) = c2)),
% 29.31/19.57 inference(modus_ponens,[status(thm)],[4469, 23574])).
% 29.31/19.57 tff(23576,plain,
% 29.31/19.57 (big_f(f9(c2, c2), c2)),
% 29.31/19.57 inference(unit_resolution,[status(thm)],[4860, 23575, 122, 17, 67, 11651, 4829])).
% 29.31/19.57 tff(23577,plain,
% 29.31/19.57 ($false),
% 29.31/19.57 inference(unit_resolution,[status(thm)],[23576, 23573])).
% 29.31/19.57 tff(23578,plain,((~(f9(c2, f9(f10(c2), f10(c2))) = c2)) | big_f(c1, c2) | (~(f2(c3) = c2)) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~(c3 = c2)) | big_f(f7(c2), f5(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 29.31/19.57 tff(23579,plain,
% 29.31/19.57 (~(f9(c2, f9(f10(c2), f10(c2))) = c2)),
% 29.31/19.57 inference(unit_resolution,[status(thm)],[23578, 23560, 1319, 122, 17, 67, 4829, 27])).
% 29.31/19.57 tff(23580,plain,
% 29.31/19.57 (f9(c2, f9(f10(c2), f10(c2))) = c1),
% 29.31/19.57 inference(unit_resolution,[status(thm)],[23082, 23579])).
% 29.31/19.57 tff(23581,plain,
% 29.31/19.57 (f9(c2, f9(c2, c2)) = c1),
% 29.31/19.57 inference(transitivity,[status(thm)],[1134, 23580])).
% 29.31/19.57 tff(23582,plain,
% 29.31/19.57 (big_f(f9(c2, f9(c2, c2)), f10(c2)) <=> big_f(c1, c2)),
% 29.31/19.57 inference(monotonicity,[status(thm)],[23581, 122])).
% 29.31/19.57 tff(23583,plain,
% 29.31/19.57 (big_f(c1, c2) <=> big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 29.31/19.57 inference(symmetry,[status(thm)],[23582])).
% 29.31/19.57 tff(23584,plain,
% 29.31/19.57 ((~big_f(c1, c2)) <=> (~big_f(f9(c2, f9(c2, c2)), f10(c2)))),
% 29.31/19.57 inference(monotonicity,[status(thm)],[23583])).
% 29.31/19.57 tff(23585,plain,
% 29.31/19.57 (~big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 29.31/19.57 inference(modus_ponens,[status(thm)],[27, 23584])).
% 29.31/19.57 tff(23586,plain,
% 29.31/19.57 ($false),
% 29.31/19.57 inference(unit_resolution,[status(thm)],[1146, 23585])).
% 29.31/19.57 tff(23587,plain,((~big_f(f9(c2, f9(c2, c2)), f10(c2))) | big_f(c1, c2) | (~(f10(c2) = c2)) | (~(f2(c3) = c2)) | (f7(c2) = c2) | (~(c3 = c2)) | big_f(f7(c2), f5(c2)) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(c1 = f5(c1)))), inference(lemma,lemma(discharge,[]))).
% 29.31/19.57 tff(23588,plain,
% 29.31/19.57 (~big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 29.31/19.57 inference(unit_resolution,[status(thm)],[23587, 23553, 122, 1319, 17, 67, 27, 115, 285, 11826])).
% 29.31/19.57 tff(23589,plain,
% 29.31/19.57 (~(big_f(c2, c2) <=> big_f(f9(c2, f9(c2, c2)), f10(c2)))),
% 29.31/19.57 inference(unit_resolution,[status(thm)],[6486, 23588, 23459])).
% 29.31/19.57 tff(23590,plain,
% 29.31/19.57 (~(c2 = f9(c2, f9(c2, c2)))),
% 29.31/19.57 inference(unit_resolution,[status(thm)],[5003, 23589, 4989])).
% 29.31/19.57 tff(23591,plain,
% 29.31/19.57 (~(f9(c2, f9(f10(c2), f10(c2))) = c2)),
% 29.31/19.57 inference(unit_resolution,[status(thm)],[23066, 23590, 122])).
% 29.31/19.57 tff(23592,plain,
% 29.31/19.57 (f9(c2, f9(f10(c2), f10(c2))) = c1),
% 29.31/19.57 inference(unit_resolution,[status(thm)],[23082, 23591])).
% 29.31/19.57 tff(23593,plain,
% 29.31/19.57 (f9(c2, f9(c2, c2)) = f9(c2, c2)),
% 29.31/19.57 inference(unit_resolution,[status(thm)],[23157, 23588, 23145, 17, 9020, 122])).
% 29.31/19.57 tff(23594,plain,
% 29.31/19.57 (f9(c2, c2) = f9(c2, f9(c2, c2))),
% 29.31/19.57 inference(symmetry,[status(thm)],[23593])).
% 29.31/19.57 tff(23595,plain,
% 29.31/19.57 (f9(c2, c2) = c1),
% 29.31/19.57 inference(transitivity,[status(thm)],[23594, 1134, 23592])).
% 29.31/19.57 tff(23596,plain,
% 29.31/19.57 ((f9(c2, c2) = c2) <=> (c1 = c2)),
% 29.31/19.57 inference(monotonicity,[status(thm)],[23595])).
% 29.31/19.57 tff(23597,plain,
% 29.31/19.57 ((f9(c2, c2) = c2) <=> (c2 = c1)),
% 29.31/19.57 inference(transitivity,[status(thm)],[23596, 1])).
% 29.31/19.57 tff(23598,plain,
% 29.31/19.57 ((c2 = c1) <=> (f9(c2, c2) = c2)),
% 29.31/19.57 inference(symmetry,[status(thm)],[23597])).
% 29.31/19.57 tff(23599,plain,
% 29.31/19.57 ((~(c2 = c1)) <=> (~(f9(c2, c2) = c2))),
% 29.31/19.57 inference(monotonicity,[status(thm)],[23598])).
% 29.31/19.57 tff(23600,plain,
% 29.31/19.57 (~(f9(c2, c2) = c2)),
% 29.31/19.57 inference(modus_ponens,[status(thm)],[75, 23599])).
% 29.31/19.57 tff(23601,plain,
% 29.31/19.57 (big_f(f9(c2, c2), c2) <=> big_f(c1, c2)),
% 29.31/19.57 inference(monotonicity,[status(thm)],[23595])).
% 29.31/19.57 tff(23602,plain,
% 29.31/19.57 (big_f(c1, c2) <=> big_f(f9(c2, c2), c2)),
% 29.31/19.57 inference(symmetry,[status(thm)],[23601])).
% 29.31/19.57 tff(23603,plain,
% 29.31/19.57 ((~big_f(c1, c2)) <=> (~big_f(f9(c2, c2), c2))),
% 29.31/19.57 inference(monotonicity,[status(thm)],[23602])).
% 29.31/19.57 tff(23604,plain,
% 29.31/19.57 (~big_f(f9(c2, c2), c2)),
% 29.31/19.57 inference(modus_ponens,[status(thm)],[27, 23603])).
% 29.31/19.57 tff(23605,plain,
% 29.31/19.57 ($false),
% 29.31/19.57 inference(unit_resolution,[status(thm)],[4860, 23604, 23600, 122, 17, 67, 11651, 23553])).
% 29.31/19.57 tff(23606,plain,((~(f5(c2) = c2)) | (~(f10(c2) = c2)) | (f7(c2) = c2) | (~(c3 = c2)) | big_f(c1, c2) | (~(f2(c3) = c2)) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(c1 = f5(c1)))), inference(lemma,lemma(discharge,[]))).
% 29.31/19.57 tff(23607,plain,
% 29.31/19.57 (~(f5(c2) = c2)),
% 29.31/19.57 inference(unit_resolution,[status(thm)],[23606, 23527, 17, 23517, 27, 122, 115, 17574, 23549])).
% 29.31/19.57 tff(23608,plain,
% 29.31/19.57 (f5(c2) = c1),
% 29.31/19.57 inference(unit_resolution,[status(thm)],[1547, 23607])).
% 29.31/19.57 tff(23609,plain,
% 29.31/19.57 (big_f(f7(c2), f5(c2)) <=> big_f(c1, c1)),
% 29.31/19.57 inference(monotonicity,[status(thm)],[22, 23608])).
% 29.31/19.57 tff(23610,plain,
% 29.31/19.57 (big_f(c1, c1) <=> big_f(f7(c2), f5(c2))),
% 29.31/19.57 inference(symmetry,[status(thm)],[23609])).
% 29.31/19.57 tff(23611,plain,
% 29.31/19.57 ((~big_f(c1, c1)) <=> (~big_f(f7(c2), f5(c2)))),
% 29.31/19.57 inference(monotonicity,[status(thm)],[23610])).
% 29.31/19.57 tff(23612,plain,
% 29.31/19.57 (~big_f(f7(c2), f5(c2))),
% 29.31/19.57 inference(modus_ponens,[status(thm)],[66, 23611])).
% 29.31/19.57 tff(23613,plain,
% 29.31/19.57 (~big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 29.31/19.57 inference(unit_resolution,[status(thm)],[23587, 23612, 122, 23527, 17, 23517, 27, 115, 17574, 23549])).
% 29.31/19.57 tff(23614,plain,
% 29.31/19.57 (~(big_f(c2, c2) <=> big_f(f9(c2, f9(c2, c2)), f10(c2)))),
% 29.31/19.57 inference(unit_resolution,[status(thm)],[6486, 23613, 23459])).
% 29.31/19.57 tff(23615,plain,
% 29.31/19.57 (~(c2 = f9(c2, f9(c2, c2)))),
% 29.31/19.57 inference(unit_resolution,[status(thm)],[5003, 23614, 4989])).
% 29.31/19.57 tff(23616,plain,
% 29.31/19.57 (~(f9(c2, f9(f10(c2), f10(c2))) = c2)),
% 29.31/19.57 inference(unit_resolution,[status(thm)],[23066, 23615, 122])).
% 29.31/19.57 tff(23617,plain,
% 29.31/19.57 (f9(c2, f9(f10(c2), f10(c2))) = c1),
% 29.31/19.57 inference(unit_resolution,[status(thm)],[23082, 23616])).
% 29.31/19.57 tff(23618,plain,
% 29.31/19.57 (c1 = f5(c2)),
% 29.31/19.57 inference(unit_resolution,[status(thm)],[8139, 23608])).
% 29.31/19.57 tff(23619,plain,
% 29.31/19.57 (f9(c2, f9(c2, c2)) = f9(c2, c2)),
% 29.31/19.57 inference(unit_resolution,[status(thm)],[23075, 267, 122, 17, 23618, 12093, 23613])).
% 29.31/19.57 tff(23620,plain,
% 29.31/19.57 (f9(c2, c2) = f9(c2, f9(c2, c2))),
% 29.31/19.57 inference(symmetry,[status(thm)],[23619])).
% 29.31/19.57 tff(23621,plain,
% 29.31/19.57 (f9(c2, c2) = c1),
% 29.31/19.57 inference(transitivity,[status(thm)],[23620, 1134, 23617])).
% 29.31/19.57 tff(23622,plain,
% 29.31/19.57 ((f9(c2, c2) = c2) <=> (c1 = c2)),
% 29.31/19.57 inference(monotonicity,[status(thm)],[23621])).
% 29.31/19.57 tff(23623,plain,
% 29.31/19.57 ((f9(c2, c2) = c2) <=> (c2 = c1)),
% 29.31/19.57 inference(transitivity,[status(thm)],[23622, 1])).
% 29.31/19.57 tff(23624,plain,
% 29.31/19.57 ((c2 = c1) <=> (f9(c2, c2) = c2)),
% 29.31/19.57 inference(symmetry,[status(thm)],[23623])).
% 29.31/19.57 tff(23625,plain,
% 29.31/19.57 ((~(c2 = c1)) <=> (~(f9(c2, c2) = c2))),
% 29.31/19.57 inference(monotonicity,[status(thm)],[23624])).
% 29.31/19.57 tff(23626,plain,
% 29.31/19.57 (~(f9(c2, c2) = c2)),
% 29.31/19.57 inference(modus_ponens,[status(thm)],[75, 23625])).
% 29.31/19.57 tff(23627,plain,
% 29.31/19.57 (big_f(f9(c2, c2), c2) <=> big_f(c1, c2)),
% 29.31/19.57 inference(monotonicity,[status(thm)],[23621])).
% 29.31/19.57 tff(23628,plain,
% 29.31/19.57 (big_f(c1, c2) <=> big_f(f9(c2, c2), c2)),
% 29.31/19.57 inference(symmetry,[status(thm)],[23627])).
% 29.31/19.57 tff(23629,plain,
% 29.31/19.57 ((~big_f(c1, c2)) <=> (~big_f(f9(c2, c2), c2))),
% 29.31/19.57 inference(monotonicity,[status(thm)],[23628])).
% 29.31/19.57 tff(23630,plain,
% 29.31/19.57 (~big_f(f9(c2, c2), c2)),
% 29.31/19.57 inference(modus_ponens,[status(thm)],[27, 23629])).
% 29.31/19.57 tff(23631,plain,
% 29.31/19.57 ($false),
% 29.31/19.57 inference(unit_resolution,[status(thm)],[4860, 23630, 23626, 122, 17, 23517, 23528, 23612])).
% 29.31/19.57 tff(23632,plain,(big_f(c2, c1) | (~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(c1, c2) | (f7(c1) = c1) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 29.31/19.57 tff(23633,plain,
% 29.31/19.57 (big_f(c2, c1)),
% 29.31/19.57 inference(unit_resolution,[status(thm)],[23632, 17, 122, 27, 115, 66])).
% 29.31/19.57 tff(23634,plain,
% 29.31/19.57 (big_f(f7(f7(c2)), f7(c2))),
% 29.31/19.57 inference(modus_ponens,[status(thm)],[23633, 8448])).
% 29.31/19.57 tff(23635,plain,
% 29.31/19.57 (f5(c1) = c1),
% 29.31/19.57 inference(unit_resolution,[status(thm)],[16558, 23634, 122, 23459, 22, 23145, 23513])).
% 29.31/19.57 tff(23636,plain,
% 29.31/19.57 ((c2 = f5(c1)) <=> (c2 = c1)),
% 29.31/19.57 inference(monotonicity,[status(thm)],[23635])).
% 29.31/19.57 tff(23637,plain,
% 29.31/19.57 ((c2 = c1) <=> (c2 = f5(c1))),
% 29.31/19.57 inference(symmetry,[status(thm)],[23636])).
% 29.31/19.57 tff(23638,plain,
% 29.31/19.57 ((~(c2 = c1)) <=> (~(c2 = f5(c1)))),
% 29.31/19.57 inference(monotonicity,[status(thm)],[23637])).
% 29.31/19.57 tff(23639,plain,
% 29.31/19.57 (~(c2 = f5(c1))),
% 29.31/19.57 inference(modus_ponens,[status(thm)],[75, 23638])).
% 29.31/19.57 tff(23640,plain,
% 29.31/19.57 (big_f(f7(c1), c2)),
% 29.31/19.57 inference(modus_ponens,[status(thm)],[23459, 1724])).
% 29.31/19.57 tff(23641,plain,
% 29.31/19.57 (~(big_f(c2, c2) <=> big_f(f9(c2, f9(c2, c2)), f10(c2)))),
% 29.31/19.57 inference(unit_resolution,[status(thm)],[6486, 3896, 23459])).
% 29.31/19.57 tff(23642,plain,
% 29.31/19.57 (~(c2 = f9(c2, f9(c2, c2)))),
% 29.31/19.57 inference(unit_resolution,[status(thm)],[5003, 23641, 4989])).
% 29.31/19.57 tff(23643,plain,
% 29.31/19.57 (~(f9(c2, f9(f10(c2), f10(c2))) = c2)),
% 29.31/19.57 inference(unit_resolution,[status(thm)],[23066, 23642, 122])).
% 29.31/19.57 tff(23644,plain,
% 29.31/19.57 (f9(c2, f9(f10(c2), f10(c2))) = c1),
% 29.31/19.57 inference(unit_resolution,[status(thm)],[23082, 23643])).
% 29.31/19.57 tff(23645,plain,
% 29.31/19.57 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((c2 = f5(c1)) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (~big_f(f7(c1), c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (c2 = f5(c1)) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (~big_f(f7(c1), c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)))),
% 29.31/19.57 inference(rewrite,[status(thm)],[])).
% 29.31/19.57 tff(23646,plain,
% 29.31/19.57 (((~(f10(c2) = c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2))) <=> ((c2 = f5(c1)) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (~big_f(f7(c1), c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)))),
% 29.31/19.57 inference(rewrite,[status(thm)],[])).
% 29.31/19.57 tff(23647,plain,
% 29.31/19.57 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((c2 = f5(c1)) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (~big_f(f7(c1), c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2))))),
% 29.31/19.57 inference(monotonicity,[status(thm)],[23646])).
% 29.31/19.57 tff(23648,plain,
% 29.31/19.57 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (c2 = f5(c1)) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (~big_f(f7(c1), c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)))),
% 29.31/19.57 inference(transitivity,[status(thm)],[23647, 23645])).
% 29.31/19.57 tff(23649,plain,
% 29.31/19.57 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c2) = c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)))),
% 29.31/19.57 inference(quant_inst,[status(thm)],[])).
% 29.31/19.57 tff(23650,plain,
% 29.31/19.57 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (c2 = f5(c1)) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (~big_f(f7(c1), c2)) | big_f(f9(c2, f9(c2, c2)), f10(c2)) | (f9(c2, f9(c2, c2)) = f9(c2, c2))),
% 29.31/19.57 inference(modus_ponens,[status(thm)],[23649, 23648])).
% 29.31/19.57 tff(23651,plain,
% 29.31/19.57 (f9(c2, f9(c2, c2)) = f9(c2, c2)),
% 29.31/19.57 inference(unit_resolution,[status(thm)],[23650, 676, 12775, 23640, 115, 122, 3896])).
% 29.31/19.57 tff(23652,plain,
% 29.31/19.57 (f9(c2, c2) = f9(c2, f9(c2, c2))),
% 29.31/19.57 inference(symmetry,[status(thm)],[23651])).
% 29.31/19.57 tff(23653,plain,
% 29.31/19.57 (f9(c2, c2) = c1),
% 29.31/19.57 inference(transitivity,[status(thm)],[23652, 1134, 23644])).
% 29.31/19.57 tff(23654,plain,
% 29.31/19.57 ((f9(c2, c2) = c2) <=> (c1 = c2)),
% 29.31/19.57 inference(monotonicity,[status(thm)],[23653])).
% 29.31/19.57 tff(23655,plain,
% 29.31/19.57 ((f9(c2, c2) = c2) <=> (c2 = c1)),
% 29.31/19.57 inference(transitivity,[status(thm)],[23654, 1])).
% 29.31/19.57 tff(23656,plain,
% 29.31/19.57 ((c2 = c1) <=> (f9(c2, c2) = c2)),
% 29.31/19.57 inference(symmetry,[status(thm)],[23655])).
% 29.31/19.57 tff(23657,plain,
% 29.31/19.57 ((~(c2 = c1)) <=> (~(f9(c2, c2) = c2))),
% 29.31/19.57 inference(monotonicity,[status(thm)],[23656])).
% 29.31/19.57 tff(23658,plain,
% 29.31/19.57 (~(f9(c2, c2) = c2)),
% 29.31/19.57 inference(modus_ponens,[status(thm)],[75, 23657])).
% 29.31/19.57 tff(23659,plain,
% 29.31/19.57 (big_f(f9(c2, c2), c2) <=> big_f(c1, c2)),
% 29.31/19.57 inference(monotonicity,[status(thm)],[23653])).
% 29.31/19.57 tff(23660,plain,
% 29.31/19.57 (big_f(c1, c2) <=> big_f(f9(c2, c2), c2)),
% 29.31/19.57 inference(symmetry,[status(thm)],[23659])).
% 29.31/19.57 tff(23661,plain,
% 29.31/19.57 (big_f(c1, c2) <=> big_f(f9(c2, c2), f10(c2))),
% 29.31/19.57 inference(transitivity,[status(thm)],[23660, 130])).
% 29.31/19.57 tff(23662,plain,
% 29.31/19.57 ((~big_f(c1, c2)) <=> (~big_f(f9(c2, c2), f10(c2)))),
% 29.31/19.57 inference(monotonicity,[status(thm)],[23661])).
% 29.31/19.57 tff(23663,plain,
% 29.31/19.57 (~big_f(f9(c2, c2), f10(c2))),
% 29.31/19.57 inference(modus_ponens,[status(thm)],[27, 23662])).
% 29.31/19.57 tff(23664,plain,
% 29.31/19.57 ($false),
% 29.31/19.57 inference(unit_resolution,[status(thm)],[17345, 23663, 23658, 122, 115, 23640, 12775])).
% 29.31/19.57 tff(23665,plain,(big_f(f9(c2, f9(c2, c2)), f10(c2)) | (~(f10(c2) = c2)) | (f7(c1) = c1) | (c2 = f5(c1)) | big_f(c1, c2)), inference(lemma,lemma(discharge,[]))).
% 29.39/19.57 tff(23666,plain,
% 29.39/19.57 (big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 29.39/19.57 inference(unit_resolution,[status(thm)],[23665, 23639, 115, 122, 27])).
% 29.39/19.57 tff(23667,assumption,(f9(c2, f9(f10(c2), f10(c2))) = c1), introduced(assumption)).
% 29.39/19.57 tff(23668,plain,
% 29.39/19.57 (f9(c2, f9(c2, c2)) = c1),
% 29.39/19.57 inference(transitivity,[status(thm)],[1134, 23667])).
% 29.39/19.57 tff(23669,plain,
% 29.39/19.57 (big_f(f9(c2, f9(c2, c2)), f10(c2)) <=> big_f(c1, c2)),
% 29.39/19.57 inference(monotonicity,[status(thm)],[23668, 122])).
% 29.39/19.57 tff(23670,plain,
% 29.39/19.57 (big_f(c1, c2) <=> big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 29.39/19.57 inference(symmetry,[status(thm)],[23669])).
% 29.39/19.57 tff(23671,plain,
% 29.39/19.57 ((~big_f(c1, c2)) <=> (~big_f(f9(c2, f9(c2, c2)), f10(c2)))),
% 29.39/19.57 inference(monotonicity,[status(thm)],[23670])).
% 29.39/19.57 tff(23672,plain,
% 29.39/19.57 (~big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 29.39/19.57 inference(modus_ponens,[status(thm)],[27, 23671])).
% 29.39/19.57 tff(23673,plain,
% 29.39/19.57 ($false),
% 29.39/19.57 inference(unit_resolution,[status(thm)],[1146, 23672])).
% 29.39/19.57 tff(23674,plain,((~(f9(c2, f9(f10(c2), f10(c2))) = c1)) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | big_f(c1, c2) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.39/19.57 tff(23675,plain,
% 29.39/19.57 (~(f9(c2, f9(f10(c2), f10(c2))) = c1)),
% 29.39/19.57 inference(unit_resolution,[status(thm)],[23674, 23666, 27, 122])).
% 29.39/19.57 tff(23676,plain,
% 29.39/19.57 (f9(c2, f9(f10(c2), f10(c2))) = c2),
% 29.39/19.57 inference(unit_resolution,[status(thm)],[23082, 23675])).
% 29.39/19.57 tff(23677,plain,
% 29.39/19.57 (big_f(f9(c2, f9(c2, c2)), c2) <=> big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 29.39/19.57 inference(monotonicity,[status(thm)],[216])).
% 29.39/19.57 tff(23678,plain,
% 29.39/19.57 (big_f(f9(c2, f9(c2, c2)), f10(c2)) <=> big_f(f9(c2, f9(c2, c2)), c2)),
% 29.39/19.57 inference(symmetry,[status(thm)],[23677])).
% 29.39/19.57 tff(23679,plain,
% 29.39/19.57 (big_f(f9(c2, f9(c2, c2)), c2)),
% 29.39/19.57 inference(modus_ponens,[status(thm)],[23666, 23678])).
% 29.39/19.57 tff(23680,assumption,(big_f(f9(c2, f9(c2, c2)), c2)), introduced(assumption)).
% 29.39/19.57 tff(23681,plain,
% 29.39/19.57 ((f9(c2, f9(c2, c2)) = c3) <=> (f9(c2, f9(c2, c2)) = c2)),
% 29.39/19.57 inference(monotonicity,[status(thm)],[67])).
% 29.39/19.57 tff(23682,plain,
% 29.39/19.57 ((f9(c2, f9(c2, c2)) = c3) <=> (c2 = f9(c2, f9(c2, c2)))),
% 29.39/19.57 inference(transitivity,[status(thm)],[23681, 5005])).
% 29.39/19.57 tff(23683,plain,
% 29.39/19.57 ((c2 = f9(c2, f9(c2, c2))) <=> (f9(c2, f9(c2, c2)) = c3)),
% 29.39/19.57 inference(symmetry,[status(thm)],[23682])).
% 29.39/19.57 tff(23684,plain,
% 29.39/19.57 (f9(c2, f9(c2, c2)) = c3),
% 29.39/19.57 inference(modus_ponens,[status(thm)],[23067, 23683])).
% 29.39/19.57 tff(23685,plain,
% 29.39/19.57 (f2(f9(c2, f9(c2, c2))) = f2(c2)),
% 29.39/19.57 inference(monotonicity,[status(thm)],[23056])).
% 29.39/19.57 tff(23686,plain,
% 29.39/19.57 ((c2 = f2(f9(c2, f9(c2, c2)))) <=> (c2 = f2(c2))),
% 29.39/19.57 inference(monotonicity,[status(thm)],[23685])).
% 29.39/19.57 tff(23687,plain,
% 29.39/19.57 ((c2 = f2(c2)) <=> (c2 = f2(f9(c2, f9(c2, c2))))),
% 29.39/19.57 inference(symmetry,[status(thm)],[23686])).
% 29.39/19.57 tff(23688,plain,
% 29.39/19.57 ((c2 = f2(c2)) <=> (c2 = c1)),
% 29.39/19.57 inference(monotonicity,[status(thm)],[1427])).
% 29.39/19.57 tff(23689,plain,
% 29.39/19.57 ((c2 = c1) <=> (c2 = f2(c2))),
% 29.39/19.57 inference(symmetry,[status(thm)],[23688])).
% 29.39/19.57 tff(23690,plain,
% 29.39/19.57 ((c2 = c1) <=> (c2 = f2(f9(c2, f9(c2, c2))))),
% 29.39/19.57 inference(transitivity,[status(thm)],[23689, 23687])).
% 29.39/19.57 tff(23691,plain,
% 29.39/19.57 ((~(c2 = c1)) <=> (~(c2 = f2(f9(c2, f9(c2, c2)))))),
% 29.39/19.57 inference(monotonicity,[status(thm)],[23690])).
% 29.39/19.57 tff(23692,plain,
% 29.39/19.57 (~(c2 = f2(f9(c2, f9(c2, c2))))),
% 29.39/19.57 inference(modus_ponens,[status(thm)],[75, 23691])).
% 29.39/19.57 tff(23693,plain,
% 29.39/19.57 ((~(c2 = c1)) <=> (~(c2 = f2(c2)))),
% 29.39/19.57 inference(monotonicity,[status(thm)],[23689])).
% 29.39/19.57 tff(23694,plain,
% 29.39/19.57 (~(c2 = f2(c2))),
% 29.39/19.57 inference(modus_ponens,[status(thm)],[75, 23693])).
% 29.39/19.57 tff(23695,plain,
% 29.39/19.57 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = f2(c2)) | (~(c1 = c4)) | (~big_f(c2, c1)) | (~big_f(c2, c2)) | (c2 = f4(c1)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = f2(c2)) | (~(c1 = c4)) | (~big_f(c2, c1)) | (~big_f(c2, c2)) | (c2 = f4(c1)))),
% 29.39/19.57 inference(rewrite,[status(thm)],[])).
% 29.39/19.57 tff(23696,plain,
% 29.39/19.57 (((~(c2 = c3)) | (~(c1 = c4)) | (c2 = f4(c1)) | (~big_f(c2, c1)) | (c2 = f2(c2)) | (~big_f(c2, c2))) <=> ((~(c2 = c3)) | (c2 = f2(c2)) | (~(c1 = c4)) | (~big_f(c2, c1)) | (~big_f(c2, c2)) | (c2 = f4(c1)))),
% 29.39/19.57 inference(rewrite,[status(thm)],[])).
% 29.39/19.57 tff(23697,plain,
% 29.39/19.57 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c1 = c4)) | (c2 = f4(c1)) | (~big_f(c2, c1)) | (c2 = f2(c2)) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = f2(c2)) | (~(c1 = c4)) | (~big_f(c2, c1)) | (~big_f(c2, c2)) | (c2 = f4(c1))))),
% 29.39/19.57 inference(monotonicity,[status(thm)],[23696])).
% 29.39/19.57 tff(23698,plain,
% 29.39/19.57 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c1 = c4)) | (c2 = f4(c1)) | (~big_f(c2, c1)) | (c2 = f2(c2)) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = f2(c2)) | (~(c1 = c4)) | (~big_f(c2, c1)) | (~big_f(c2, c2)) | (c2 = f4(c1)))),
% 29.39/19.57 inference(transitivity,[status(thm)],[23697, 23695])).
% 29.39/19.57 tff(23699,plain,
% 29.39/19.57 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c1 = c4)) | (c2 = f4(c1)) | (~big_f(c2, c1)) | (c2 = f2(c2)) | (~big_f(c2, c2)))),
% 29.39/19.57 inference(quant_inst,[status(thm)],[])).
% 29.39/19.57 tff(23700,plain,
% 29.39/19.57 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = f2(c2)) | (~(c1 = c4)) | (~big_f(c2, c1)) | (~big_f(c2, c2)) | (c2 = f4(c1))),
% 29.39/19.57 inference(modus_ponens,[status(thm)],[23699, 23698])).
% 29.39/19.57 tff(23701,plain,
% 29.39/19.57 ((c2 = f2(c2)) | (~(c1 = c4)) | (c2 = f4(c1))),
% 29.39/19.57 inference(unit_resolution,[status(thm)],[23700, 1355, 1345, 1344, 348])).
% 29.39/19.57 tff(23702,plain,
% 29.39/19.57 (c2 = f4(c1)),
% 29.39/19.57 inference(unit_resolution,[status(thm)],[23701, 11526, 1342])).
% 29.39/19.57 tff(23703,plain,
% 29.39/19.57 (c2 = c1),
% 29.39/19.57 inference(transitivity,[status(thm)],[23702, 19665, 11752])).
% 29.39/19.57 tff(23704,plain,
% 29.39/19.57 ($false),
% 29.39/19.57 inference(unit_resolution,[status(thm)],[75, 23703])).
% 29.39/19.57 tff(23705,plain,((~(c1 = c4)) | (~(f4(c4) = c1)) | (c2 = f2(c2)) | (~big_f(c2, c2)) | (~(c2 = c3)) | (~big_f(c2, c1))), inference(lemma,lemma(discharge,[]))).
% 29.39/19.57 tff(23706,plain,
% 29.39/19.57 (~(c1 = c4)),
% 29.39/19.57 inference(unit_resolution,[status(thm)],[23705, 23694, 11752, 1345, 1335, 348])).
% 29.39/19.57 tff(23707,plain,
% 29.39/19.57 (~(c4 = c1)),
% 29.39/19.57 inference(unit_resolution,[status(thm)],[484, 23706])).
% 29.39/19.57 tff(23708,plain,
% 29.39/19.57 (c4 = c2),
% 29.39/19.57 inference(unit_resolution,[status(thm)],[461, 23707])).
% 29.39/19.57 tff(23709,plain,
% 29.39/19.57 (c2 = c4),
% 29.39/19.57 inference(modus_ponens,[status(thm)],[23708, 159])).
% 29.39/19.57 tff(23710,plain,
% 29.39/19.57 (c2 = c4),
% 29.39/19.57 inference(symmetry,[status(thm)],[23708])).
% 29.39/19.57 tff(23711,plain,
% 29.39/19.57 (f4(c2) = f4(c4)),
% 29.39/19.57 inference(monotonicity,[status(thm)],[23710])).
% 29.39/19.57 tff(23712,plain,
% 29.39/19.57 (f4(c4) = f4(c2)),
% 29.39/19.57 inference(symmetry,[status(thm)],[23711])).
% 29.39/19.57 tff(23713,plain,
% 29.39/19.57 (c1 = f4(c2)),
% 29.39/19.57 inference(transitivity,[status(thm)],[16651, 23712])).
% 29.39/19.57 tff(23714,plain,
% 29.39/19.57 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c4)) | big_f(c1, c2) | (~(c1 = f4(c2))) | (c2 = f2(f9(c2, f9(c2, c2)))) | (~(f9(c2, f9(c2, c2)) = c3)) | (~big_f(f9(c2, f9(c2, c2)), c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c4)) | big_f(c1, c2) | (~(c1 = f4(c2))) | (c2 = f2(f9(c2, f9(c2, c2)))) | (~(f9(c2, f9(c2, c2)) = c3)) | (~big_f(f9(c2, f9(c2, c2)), c2)))),
% 29.39/19.57 inference(rewrite,[status(thm)],[])).
% 29.39/19.57 tff(23715,plain,
% 29.39/19.57 (((~(f9(c2, f9(c2, c2)) = c3)) | (~(c2 = c4)) | big_f(c1, c2) | (~(c1 = f4(c2))) | (c2 = f2(f9(c2, f9(c2, c2)))) | (~big_f(f9(c2, f9(c2, c2)), c2))) <=> ((~(c2 = c4)) | big_f(c1, c2) | (~(c1 = f4(c2))) | (c2 = f2(f9(c2, f9(c2, c2)))) | (~(f9(c2, f9(c2, c2)) = c3)) | (~big_f(f9(c2, f9(c2, c2)), c2)))),
% 29.39/19.58 inference(rewrite,[status(thm)],[])).
% 29.39/19.58 tff(23716,plain,
% 29.39/19.58 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c2, f9(c2, c2)) = c3)) | (~(c2 = c4)) | big_f(c1, c2) | (~(c1 = f4(c2))) | (c2 = f2(f9(c2, f9(c2, c2)))) | (~big_f(f9(c2, f9(c2, c2)), c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c4)) | big_f(c1, c2) | (~(c1 = f4(c2))) | (c2 = f2(f9(c2, f9(c2, c2)))) | (~(f9(c2, f9(c2, c2)) = c3)) | (~big_f(f9(c2, f9(c2, c2)), c2))))),
% 29.39/19.58 inference(monotonicity,[status(thm)],[23715])).
% 29.39/19.58 tff(23717,plain,
% 29.39/19.58 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c2, f9(c2, c2)) = c3)) | (~(c2 = c4)) | big_f(c1, c2) | (~(c1 = f4(c2))) | (c2 = f2(f9(c2, f9(c2, c2)))) | (~big_f(f9(c2, f9(c2, c2)), c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c4)) | big_f(c1, c2) | (~(c1 = f4(c2))) | (c2 = f2(f9(c2, f9(c2, c2)))) | (~(f9(c2, f9(c2, c2)) = c3)) | (~big_f(f9(c2, f9(c2, c2)), c2)))),
% 29.39/19.58 inference(transitivity,[status(thm)],[23716, 23714])).
% 29.39/19.58 tff(23718,plain,
% 29.39/19.58 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f9(c2, f9(c2, c2)) = c3)) | (~(c2 = c4)) | big_f(c1, c2) | (~(c1 = f4(c2))) | (c2 = f2(f9(c2, f9(c2, c2)))) | (~big_f(f9(c2, f9(c2, c2)), c2)))),
% 29.39/19.58 inference(quant_inst,[status(thm)],[])).
% 29.39/19.58 tff(23719,plain,
% 29.39/19.58 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c4)) | big_f(c1, c2) | (~(c1 = f4(c2))) | (c2 = f2(f9(c2, f9(c2, c2)))) | (~(f9(c2, f9(c2, c2)) = c3)) | (~big_f(f9(c2, f9(c2, c2)), c2))),
% 29.39/19.58 inference(modus_ponens,[status(thm)],[23718, 23717])).
% 29.39/19.58 tff(23720,plain,
% 29.39/19.58 ((~(c2 = c4)) | (~(c1 = f4(c2))) | (c2 = f2(f9(c2, f9(c2, c2)))) | (~(f9(c2, f9(c2, c2)) = c3)) | (~big_f(f9(c2, f9(c2, c2)), c2))),
% 29.39/19.58 inference(unit_resolution,[status(thm)],[23719, 5622, 27])).
% 29.39/19.58 tff(23721,plain,
% 29.39/19.58 ($false),
% 29.39/19.58 inference(unit_resolution,[status(thm)],[23720, 23713, 23709, 23692, 23684, 23680])).
% 29.39/19.58 tff(23722,plain,((~(f2(c3) = c1)) | (~big_f(f9(c2, f9(c2, c2)), c2)) | big_f(c1, c2) | (~(f4(c4) = c1)) | (~big_f(c2, c2)) | (~big_f(c2, c1)) | (~(c3 = c2)) | (~(f9(c2, f9(f10(c2), f10(c2))) = c2)) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.39/19.58 tff(23723,plain,
% 29.39/19.58 (~(f2(c3) = c1)),
% 29.39/19.58 inference(unit_resolution,[status(thm)],[23722, 23679, 27, 23515, 23459, 23633, 23517, 23676, 122])).
% 29.39/19.58 tff(23724,plain,
% 29.39/19.58 (f2(c3) = c2),
% 29.39/19.58 inference(unit_resolution,[status(thm)],[1273, 23723])).
% 29.39/19.58 tff(23725,plain,
% 29.39/19.58 (c2 = f2(c3)),
% 29.39/19.58 inference(symmetry,[status(thm)],[23724])).
% 29.39/19.58 tff(23726,plain,
% 29.39/19.58 (f9(c2, c2) = f9(f10(c2), f2(c3))),
% 29.39/19.58 inference(monotonicity,[status(thm)],[216, 23725])).
% 29.39/19.58 tff(23727,plain,
% 29.39/19.58 (f9(f10(c2), f2(c3)) = f9(c2, c2)),
% 29.39/19.58 inference(symmetry,[status(thm)],[23726])).
% 29.39/19.58 tff(23728,plain,
% 29.39/19.58 ((f9(f10(c2), f2(c3)) = c2) <=> (f9(c2, c2) = c2)),
% 29.39/19.58 inference(monotonicity,[status(thm)],[23727])).
% 29.39/19.58 tff(23729,plain,
% 29.39/19.58 ((f9(c2, c2) = c2) <=> (f9(f10(c2), f2(c3)) = c2)),
% 29.39/19.58 inference(symmetry,[status(thm)],[23728])).
% 29.39/19.58 tff(23730,plain,
% 29.39/19.58 ((~(f9(c2, c2) = c2)) <=> (~(f9(f10(c2), f2(c3)) = c2))),
% 29.39/19.58 inference(monotonicity,[status(thm)],[23729])).
% 29.39/19.58 tff(23731,plain,
% 29.39/19.58 (f9(c2, f9(c2, c2)) = c2),
% 29.39/19.58 inference(transitivity,[status(thm)],[1134, 23676])).
% 29.39/19.58 tff(23732,plain,
% 29.39/19.58 ((f9(c2, f9(c2, c2)) = f9(c2, c2)) <=> (c2 = f9(c2, c2))),
% 29.39/19.58 inference(monotonicity,[status(thm)],[23731])).
% 29.39/19.58 tff(23733,plain,
% 29.39/19.58 ((f9(c2, f9(c2, c2)) = f9(c2, c2)) <=> (f9(c2, c2) = c2)),
% 29.39/19.58 inference(transitivity,[status(thm)],[23732, 167])).
% 29.39/19.58 tff(23734,plain,
% 29.39/19.58 ((~(f9(c2, f9(c2, c2)) = f9(c2, c2))) <=> (~(f9(c2, c2) = c2))),
% 29.39/19.58 inference(monotonicity,[status(thm)],[23733])).
% 29.39/19.58 tff(23735,plain,
% 29.39/19.58 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((c2 = f5(c1)) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (~big_f(f7(c1), c2)) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (c2 = f5(c1)) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (~big_f(f7(c1), c2)) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))))),
% 29.39/19.58 inference(rewrite,[status(thm)],[])).
% 29.39/19.58 tff(23736,plain,
% 29.39/19.58 (((~(f10(c2) = c2)) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2)))) <=> ((c2 = f5(c1)) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (~big_f(f7(c1), c2)) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))))),
% 29.39/19.58 inference(rewrite,[status(thm)],[])).
% 29.39/19.58 tff(23737,plain,
% 29.39/19.58 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((c2 = f5(c1)) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (~big_f(f7(c1), c2)) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2)))))),
% 29.39/19.58 inference(monotonicity,[status(thm)],[23736])).
% 29.39/19.58 tff(23738,plain,
% 29.39/19.58 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (c2 = f5(c1)) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (~big_f(f7(c1), c2)) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))))),
% 29.39/19.58 inference(transitivity,[status(thm)],[23737, 23735])).
% 29.39/19.58 tff(23739,plain,
% 29.39/19.58 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2))) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))))),
% 29.39/19.58 inference(quant_inst,[status(thm)],[])).
% 29.39/19.58 tff(23740,plain,
% 29.39/19.58 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (c2 = f5(c1)) | (f7(c1) = c1) | (~(f10(c2) = c2)) | (~big_f(f7(c1), c2)) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2)))),
% 29.39/19.58 inference(modus_ponens,[status(thm)],[23739, 23738])).
% 29.39/19.58 tff(23741,plain,
% 29.39/19.58 (~(f9(c2, f9(c2, c2)) = f9(c2, c2))),
% 29.39/19.58 inference(unit_resolution,[status(thm)],[23740, 1190, 23639, 23640, 115, 122, 23666])).
% 29.39/19.58 tff(23742,plain,
% 29.39/19.58 (~(f9(c2, c2) = c2)),
% 29.39/19.58 inference(modus_ponens,[status(thm)],[23741, 23734])).
% 29.39/19.58 tff(23743,plain,
% 29.39/19.58 (~(f9(f10(c2), f2(c3)) = c2)),
% 29.39/19.58 inference(modus_ponens,[status(thm)],[23742, 23730])).
% 29.39/19.58 tff(23744,plain,
% 29.39/19.58 (f9(f10(c2), f2(c3)) = c1),
% 29.39/19.58 inference(unit_resolution,[status(thm)],[1245, 23743])).
% 29.39/19.58 tff(23745,plain,
% 29.39/19.58 (f9(c2, c2) = c1),
% 29.39/19.58 inference(transitivity,[status(thm)],[23726, 23744])).
% 29.39/19.58 tff(23746,plain,
% 29.39/19.58 (big_f(f9(c2, c2), c2) <=> big_f(c1, c2)),
% 29.39/19.58 inference(monotonicity,[status(thm)],[23745])).
% 29.39/19.58 tff(23747,plain,
% 29.39/19.58 (big_f(c1, c2) <=> big_f(f9(c2, c2), c2)),
% 29.39/19.58 inference(symmetry,[status(thm)],[23746])).
% 29.39/19.58 tff(23748,plain,
% 29.39/19.58 ((~big_f(c1, c2)) <=> (~big_f(f9(c2, c2), c2))),
% 29.39/19.58 inference(monotonicity,[status(thm)],[23747])).
% 29.39/19.58 tff(23749,plain,
% 29.39/19.58 (~big_f(f9(c2, c2), c2)),
% 29.39/19.58 inference(modus_ponens,[status(thm)],[27, 23748])).
% 29.39/19.58 tff(23750,plain,
% 29.39/19.58 (big_f(f9(c2, c2), f10(c2))),
% 29.39/19.58 inference(unit_resolution,[status(thm)],[17345, 23742, 122, 115, 23640, 23639])).
% 29.39/19.58 tff(23751,plain,
% 29.39/19.58 (big_f(f9(c2, c2), c2)),
% 29.39/19.58 inference(unit_resolution,[status(thm)],[3687, 23750, 122])).
% 29.39/19.58 tff(23752,plain,
% 29.39/19.58 ($false),
% 29.39/19.58 inference(unit_resolution,[status(thm)],[23751, 23749])).
% 29.39/19.58 tff(23753,plain,((f7(c2) = c2) | big_f(c1, c2) | (~(f10(c2) = c2)) | (f7(c1) = c1) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 29.39/19.58 tff(23754,plain,
% 29.39/19.58 (f7(c2) = c2),
% 29.39/19.58 inference(unit_resolution,[status(thm)],[23753, 66, 122, 115, 27])).
% 29.39/19.58 tff(23755,plain,
% 29.39/19.58 (~(f4(c4) = c2)),
% 29.39/19.58 inference(unit_resolution,[status(thm)],[23473, 23754, 122, 23459, 120])).
% 29.39/19.58 tff(23756,plain,
% 29.39/19.58 (f4(c4) = c1),
% 29.39/19.58 inference(unit_resolution,[status(thm)],[11750, 23755])).
% 29.39/19.58 tff(23757,plain,
% 29.39/19.58 (~big_f(f4(c4), c4)),
% 29.39/19.58 inference(unit_resolution,[status(thm)],[11772, 23756, 27, 66])).
% 29.39/19.58 tff(23758,plain,
% 29.39/19.58 (big_f(c3, f2(c3))),
% 29.39/19.58 inference(unit_resolution,[status(thm)],[1315, 23757])).
% 29.39/19.58 tff(23759,plain,
% 29.39/19.58 (f9(c2, f9(c2, c2)) = f9(c2, f9(f10(c2), f10(c2)))),
% 29.39/19.58 inference(symmetry,[status(thm)],[3822])).
% 29.39/19.58 tff(23760,plain,
% 29.39/19.58 (c2 = f5(c1)),
% 29.39/19.58 inference(unit_resolution,[status(thm)],[23665, 3896, 115, 122, 27])).
% 29.39/19.58 tff(23761,plain,
% 29.39/19.58 (f9(c2, c2) = f9(c2, f5(c1))),
% 29.39/19.58 inference(monotonicity,[status(thm)],[2908])).
% 29.39/19.58 tff(23762,plain,
% 29.39/19.58 (f9(c2, c2) = c1),
% 29.39/19.58 inference(transitivity,[status(thm)],[23761, 17374])).
% 29.39/19.58 tff(23763,plain,
% 29.39/19.58 (big_f(f9(c2, c2), c2) <=> big_f(c1, c2)),
% 29.39/19.58 inference(monotonicity,[status(thm)],[23762])).
% 29.39/19.58 tff(23764,plain,
% 29.39/19.58 (big_f(c1, c2) <=> big_f(f9(c2, c2), c2)),
% 29.39/19.58 inference(symmetry,[status(thm)],[23763])).
% 29.39/19.58 tff(23765,plain,
% 29.39/19.58 ((~big_f(c1, c2)) <=> (~big_f(f9(c2, c2), c2))),
% 29.39/19.58 inference(monotonicity,[status(thm)],[23764])).
% 29.39/19.58 tff(23766,plain,
% 29.39/19.58 (~big_f(f9(c2, c2), c2)),
% 29.39/19.58 inference(modus_ponens,[status(thm)],[27, 23765])).
% 29.39/19.58 tff(23767,plain,
% 29.39/19.58 (~(f4(c4) = c2)),
% 29.39/19.58 inference(unit_resolution,[status(thm)],[23473, 77, 122, 1345, 347])).
% 29.39/19.58 tff(23768,plain,
% 29.39/19.58 (f4(c4) = c1),
% 29.39/19.58 inference(unit_resolution,[status(thm)],[11750, 23767])).
% 29.39/19.58 tff(23769,plain,
% 29.39/19.58 (big_f(f9(c2, c2), f10(c2))),
% 29.39/19.58 inference(unit_resolution,[status(thm)],[17415, 1209, 122, 77, 23768, 347, 17372, 1345])).
% 29.39/19.58 tff(23770,plain,
% 29.39/19.58 (big_f(f9(c2, c2), c2)),
% 29.39/19.58 inference(unit_resolution,[status(thm)],[3687, 23769, 122])).
% 29.39/19.58 tff(23771,plain,
% 29.39/19.58 ($false),
% 29.39/19.58 inference(unit_resolution,[status(thm)],[23770, 23766])).
% 29.39/19.58 tff(23772,plain,((f9(c2, c2) = c2) | big_f(c1, c2) | (~(c2 = f5(c1))) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~(f7(c1) = c2)) | (~big_f(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 29.39/19.58 tff(23773,plain,
% 29.39/19.58 (f9(c2, c2) = c2),
% 29.39/19.58 inference(unit_resolution,[status(thm)],[23772, 23760, 27, 122, 77, 120, 23459])).
% 29.39/19.58 tff(23774,plain,
% 29.39/19.58 (f9(c2, f9(c2, c2)) = f9(c2, c2)),
% 29.39/19.58 inference(monotonicity,[status(thm)],[23773])).
% 29.39/19.58 tff(23775,plain,
% 29.39/19.58 (f9(c2, c2) = f9(c2, f9(c2, c2))),
% 29.39/19.58 inference(symmetry,[status(thm)],[23774])).
% 29.39/19.58 tff(23776,plain,
% 29.39/19.58 (c2 = f9(c2, c2)),
% 29.39/19.58 inference(symmetry,[status(thm)],[23773])).
% 29.39/19.58 tff(23777,plain,
% 29.39/19.58 (c2 = c1),
% 29.39/19.58 inference(transitivity,[status(thm)],[23776, 23775, 23759, 23644])).
% 29.39/19.58 tff(23778,plain,
% 29.39/19.58 ($false),
% 29.39/19.58 inference(unit_resolution,[status(thm)],[75, 23777])).
% 29.39/19.58 tff(23779,plain,(big_f(f9(c2, f9(c2, c2)), f10(c2)) | (~(f10(c2) = c2)) | big_f(c1, c2) | (~(f7(c2) = c2)) | (f7(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.39/19.58 tff(23780,plain,
% 29.39/19.58 (big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 29.39/19.58 inference(unit_resolution,[status(thm)],[23779, 23754, 27, 122, 115])).
% 29.39/19.58 tff(23781,plain,
% 29.39/19.58 (big_f(f9(c2, f9(c2, c2)), c2)),
% 29.39/19.58 inference(modus_ponens,[status(thm)],[23780, 23678])).
% 29.39/19.58 tff(23782,plain,
% 29.39/19.58 (~(c3 = c1)),
% 29.39/19.58 inference(unit_resolution,[status(thm)],[11784, 23756, 66, 27])).
% 29.39/19.58 tff(23783,plain,
% 29.39/19.58 (c3 = c2),
% 29.39/19.58 inference(unit_resolution,[status(thm)],[180, 23782])).
% 29.39/19.58 tff(23784,plain,
% 29.39/19.58 (~(f9(c2, f9(f10(c2), f10(c2))) = c1)),
% 29.39/19.58 inference(unit_resolution,[status(thm)],[23674, 23780, 27, 122])).
% 29.39/19.58 tff(23785,plain,
% 29.39/19.58 (f9(c2, f9(f10(c2), f10(c2))) = c2),
% 29.39/19.58 inference(unit_resolution,[status(thm)],[23082, 23784])).
% 29.39/19.58 tff(23786,plain,
% 29.39/19.58 (big_f(c2, c1)),
% 29.39/19.58 inference(unit_resolution,[status(thm)],[23525, 1247, 2274, 67])).
% 29.39/19.58 tff(23787,plain,
% 29.39/19.58 ($false),
% 29.39/19.58 inference(unit_resolution,[status(thm)],[23722, 23786, 1247, 27, 11752, 1345, 23055, 67, 23680, 122])).
% 29.39/19.58 tff(23788,plain,((~(f2(c3) = c1)) | big_f(c1, c2) | (~(f4(c4) = c1)) | (~big_f(c2, c2)) | (~(f9(c2, f9(f10(c2), f10(c2))) = c2)) | (~(c3 = c2)) | (~big_f(f9(c2, f9(c2, c2)), c2)) | (~(f10(c2) = c2)) | (~big_f(c3, f2(c3)))), inference(lemma,lemma(discharge,[]))).
% 29.39/19.58 tff(23789,plain,
% 29.39/19.58 (~(f2(c3) = c1)),
% 29.39/19.58 inference(unit_resolution,[status(thm)],[23788, 23756, 27, 23459, 23785, 23783, 23781, 122, 23758])).
% 29.39/19.58 tff(23790,plain,
% 29.39/19.58 (f2(c3) = c2),
% 29.39/19.58 inference(unit_resolution,[status(thm)],[1273, 23789])).
% 29.39/19.58 tff(23791,plain,
% 29.39/19.58 ((~(f9(c2, c2) = c2)) <=> (~(f9(f10(c2), f2(c3)) = c2))),
% 29.39/19.58 inference(monotonicity,[status(thm)],[23564])).
% 29.39/19.58 tff(23792,plain,
% 29.39/19.58 (~(f9(f10(c2), f2(c3)) = c2)),
% 29.39/19.58 inference(modus_ponens,[status(thm)],[1209, 23791])).
% 29.39/19.58 tff(23793,plain,
% 29.39/19.58 (f9(f10(c2), f2(c3)) = c1),
% 29.39/19.58 inference(unit_resolution,[status(thm)],[1245, 23792])).
% 29.39/19.58 tff(23794,plain,
% 29.39/19.58 (c1 = f9(f10(c2), f2(c3))),
% 29.39/19.58 inference(symmetry,[status(thm)],[23793])).
% 29.39/19.58 tff(23795,plain,
% 29.39/19.58 (c1 = f9(c2, c2)),
% 29.39/19.58 inference(transitivity,[status(thm)],[23794, 23562])).
% 29.39/19.58 tff(23796,plain,
% 29.39/19.58 (big_f(c1, c2) <=> big_f(f9(c2, c2), c2)),
% 29.39/19.58 inference(monotonicity,[status(thm)],[23795])).
% 29.39/19.58 tff(23797,plain,
% 29.39/19.58 (big_f(f9(c2, c2), c2) <=> big_f(c1, c2)),
% 29.39/19.58 inference(symmetry,[status(thm)],[23796])).
% 29.39/19.58 tff(23798,plain,
% 29.39/19.58 (big_f(c1, c2)),
% 29.39/19.58 inference(modus_ponens,[status(thm)],[2041, 23797])).
% 29.39/19.58 tff(23799,plain,
% 29.39/19.58 ($false),
% 29.39/19.58 inference(unit_resolution,[status(thm)],[27, 23798])).
% 29.39/19.58 tff(23800,plain,((~(f2(c3) = c2)) | big_f(c1, c2) | (~big_f(f9(c2, c2), c2)) | (~(f10(c2) = c2)) | (f9(c2, c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 29.39/19.58 tff(23801,plain,
% 29.39/19.58 (~big_f(f9(c2, c2), c2)),
% 29.39/19.58 inference(unit_resolution,[status(thm)],[23800, 1209, 27, 122, 1319])).
% 29.39/19.58 tff(23802,plain,
% 29.39/19.58 (~(c2 = f5(c1))),
% 29.39/19.58 inference(unit_resolution,[status(thm)],[23772, 1209, 27, 122, 77, 120, 23459])).
% 29.39/19.58 tff(23803,plain,
% 29.39/19.58 (big_f(f9(c2, c2), f10(c2))),
% 29.39/19.58 inference(unit_resolution,[status(thm)],[17345, 23802, 122, 115, 23640, 1209])).
% 29.39/19.58 tff(23804,plain,
% 29.39/19.58 ($false),
% 29.39/19.58 inference(unit_resolution,[status(thm)],[3687, 23803, 23801, 122])).
% 29.39/19.58 tff(23805,plain,((f9(c2, c2) = c2) | (~(f10(c2) = c2)) | (f7(c1) = c1) | big_f(c1, c2) | (~(f2(c3) = c2)) | (~(f7(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.39/19.58 tff(23806,plain,
% 29.39/19.58 (f9(c2, c2) = c2),
% 29.39/19.58 inference(unit_resolution,[status(thm)],[23805, 23790, 115, 27, 122, 23754])).
% 29.39/19.58 tff(23807,plain,
% 29.39/19.58 (big_f(f9(c2, c2), c2) <=> big_f(c2, c2)),
% 29.39/19.58 inference(monotonicity,[status(thm)],[23806])).
% 29.39/19.58 tff(23808,plain,
% 29.39/19.58 (big_f(c2, c2) <=> big_f(f9(c2, c2), c2)),
% 29.39/19.58 inference(symmetry,[status(thm)],[23807])).
% 29.39/19.58 tff(23809,plain,
% 29.39/19.58 (big_f(c2, c2) <=> big_f(f9(c2, c2), f10(c2))),
% 29.39/19.58 inference(transitivity,[status(thm)],[23808, 130])).
% 29.39/19.58 tff(23810,plain,
% 29.39/19.58 (big_f(f9(c2, c2), f10(c2))),
% 29.39/19.58 inference(modus_ponens,[status(thm)],[23459, 23809])).
% 29.39/19.58 tff(23811,plain,
% 29.39/19.58 (~(f6(f7(c2), c3) = c2)),
% 29.39/19.58 inference(unit_resolution,[status(thm)],[2386, 23810, 122, 23754, 23783, 23459, 23806])).
% 29.39/19.58 tff(23812,plain,
% 29.39/19.58 (f6(f7(c2), c3) = c1),
% 29.39/19.58 inference(unit_resolution,[status(thm)],[2391, 23811])).
% 29.39/19.58 tff(23813,plain,
% 29.39/19.58 (c2 = c3),
% 29.39/19.58 inference(symmetry,[status(thm)],[23783])).
% 29.39/19.58 tff(23814,plain,
% 29.39/19.58 (c2 = f7(c2)),
% 29.39/19.58 inference(symmetry,[status(thm)],[23754])).
% 29.39/19.58 tff(23815,plain,
% 29.39/19.58 (f6(c2, c2) = f6(f7(c2), c3)),
% 29.39/19.58 inference(monotonicity,[status(thm)],[23814, 23813])).
% 29.39/19.58 tff(23816,plain,
% 29.39/19.58 (f6(c2, c2) = c1),
% 29.39/19.58 inference(transitivity,[status(thm)],[23815, 23812])).
% 29.39/19.58 tff(23817,plain,
% 29.39/19.58 ((f6(c2, c2) = c2) <=> (c1 = c2)),
% 29.39/19.58 inference(monotonicity,[status(thm)],[23816])).
% 29.39/19.58 tff(23818,plain,
% 29.39/19.58 ((f6(c2, c2) = c2) <=> (c2 = c1)),
% 29.39/19.58 inference(transitivity,[status(thm)],[23817, 1])).
% 29.39/19.58 tff(23819,plain,
% 29.39/19.58 ((c2 = c1) <=> (f6(c2, c2) = c2)),
% 29.39/19.58 inference(symmetry,[status(thm)],[23818])).
% 29.39/19.58 tff(23820,plain,
% 29.39/19.58 ((~(c2 = c1)) <=> (~(f6(c2, c2) = c2))),
% 29.39/19.58 inference(monotonicity,[status(thm)],[23819])).
% 29.39/19.58 tff(23821,plain,
% 29.39/19.58 (~(f6(c2, c2) = c2)),
% 29.39/19.58 inference(modus_ponens,[status(thm)],[75, 23820])).
% 29.39/19.58 tff(23822,plain,
% 29.39/19.58 (big_f(f7(c2), f6(c2, c2))),
% 29.39/19.58 inference(unit_resolution,[status(thm)],[2412, 2409, 122, 23754, 23821, 23806, 23810])).
% 29.39/19.58 tff(23823,plain,
% 29.39/19.58 (f9(f10(c2), f2(c3)) = f9(c2, c2)),
% 29.39/19.58 inference(monotonicity,[status(thm)],[122, 23790])).
% 29.39/19.58 tff(23824,plain,
% 29.39/19.58 ((f9(f10(c2), f2(c3)) = c2) <=> (f9(c2, c2) = c2)),
% 29.39/19.58 inference(monotonicity,[status(thm)],[23823])).
% 29.39/19.58 tff(23825,plain,
% 29.39/19.58 ((f9(c2, c2) = c2) <=> (f9(f10(c2), f2(c3)) = c2)),
% 29.39/19.58 inference(symmetry,[status(thm)],[23824])).
% 29.39/19.58 tff(23826,plain,
% 29.39/19.58 (f9(f10(c2), f2(c3)) = c2),
% 29.39/19.58 inference(modus_ponens,[status(thm)],[23806, 23825])).
% 29.39/19.58 tff(23827,plain,
% 29.39/19.58 (f9(c2, f9(c2, c2)) = c2),
% 29.39/19.58 inference(transitivity,[status(thm)],[1134, 23785])).
% 29.39/19.58 tff(23828,plain,
% 29.39/19.58 ((f9(c2, f9(c2, c2)) = f9(c2, c2)) <=> (c2 = f9(c2, c2))),
% 29.39/19.58 inference(monotonicity,[status(thm)],[23827])).
% 29.39/19.58 tff(23829,plain,
% 29.39/19.58 ((f9(c2, f9(c2, c2)) = f9(c2, c2)) <=> (f9(c2, c2) = c2)),
% 29.39/19.58 inference(transitivity,[status(thm)],[23828, 167])).
% 29.39/19.58 tff(23830,plain,
% 29.39/19.58 ((f9(c2, c2) = c2) <=> (f9(c2, f9(c2, c2)) = f9(c2, c2))),
% 29.39/19.58 inference(symmetry,[status(thm)],[23829])).
% 29.39/19.58 tff(23831,plain,
% 29.39/19.58 (f9(c2, f9(c2, c2)) = f9(c2, c2)),
% 29.39/19.58 inference(modus_ponens,[status(thm)],[23806, 23830])).
% 29.39/19.58 tff(23832,plain,
% 29.39/19.58 ((c2 = f5(c1)) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2)))),
% 29.39/19.58 inference(unit_resolution,[status(thm)],[23740, 1190, 23640, 115, 122, 23780])).
% 29.39/19.58 tff(23833,plain,
% 29.39/19.58 (c2 = f5(c1)),
% 29.39/19.58 inference(unit_resolution,[status(thm)],[23832, 23831])).
% 29.39/19.58 tff(23834,plain,
% 29.39/19.58 (f5(c1) = c2),
% 29.39/19.58 inference(modus_ponens,[status(thm)],[23833, 8483])).
% 29.39/19.58 tff(23835,plain,
% 29.39/19.58 (f5(c1) = c2),
% 29.39/19.58 inference(symmetry,[status(thm)],[23833])).
% 29.39/19.58 tff(23836,plain,
% 29.39/19.58 (f6(f7(c2), f5(c1)) = f6(c2, c2)),
% 29.39/19.58 inference(monotonicity,[status(thm)],[23754, 23835])).
% 29.39/19.58 tff(23837,plain,
% 29.39/19.58 (f6(f7(c2), f5(c1)) = c1),
% 29.39/19.58 inference(transitivity,[status(thm)],[23836, 23815, 23812])).
% 29.39/19.58 tff(23838,plain,
% 29.39/19.58 (f9(c2, c2) = c2),
% 29.39/19.58 inference(transitivity,[status(thm)],[23561, 1230])).
% 29.39/19.58 tff(23839,plain,
% 29.39/19.58 (big_f(f9(c2, c2), f10(c2)) <=> big_f(c2, c2)),
% 29.39/19.58 inference(monotonicity,[status(thm)],[23838, 122])).
% 29.39/19.58 tff(23840,plain,
% 29.39/19.58 (big_f(c2, c2) <=> big_f(f9(c2, c2), f10(c2))),
% 29.39/19.58 inference(symmetry,[status(thm)],[23839])).
% 29.39/19.58 tff(23841,plain,
% 29.39/19.58 (big_f(f9(c2, c2), f10(c2))),
% 29.39/19.58 inference(modus_ponens,[status(thm)],[1345, 23840])).
% 29.39/19.58 tff(23842,plain,
% 29.39/19.58 (f9(c2, c2) = c2),
% 29.39/19.58 inference(modus_ponens,[status(thm)],[1230, 23563])).
% 29.39/19.58 tff(23843,plain,
% 29.39/19.58 ((f6(c2, c2) = f5(f6(c2, c2))) | (f7(f6(c2, c2)) = f6(c2, c2)) | (~big_f(f7(f6(c2, c2)), f6(c2, c2)))),
% 29.39/19.58 inference(unit_resolution,[status(thm)],[3316, 1190, 122, 23842, 23841])).
% 29.39/19.58 tff(23844,plain,
% 29.39/19.58 ($false),
% 29.39/19.58 inference(unit_resolution,[status(thm)],[23843, 3277, 3271, 3260])).
% 29.39/19.58 tff(23845,plain,((~(f9(f10(c2), f2(c3)) = c2)) | (~(f10(c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~(f7(c2) = c2)) | (~(f7(c1) = c2)) | (~(f6(f7(c2), f5(c1)) = c1)) | (~(f5(c1) = c2)) | (~big_f(c2, c2)) | (~(f2(c3) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.39/19.58 tff(23846,plain,
% 29.39/19.58 ($false),
% 29.39/19.58 inference(unit_resolution,[status(thm)],[23845, 23837, 23834, 120, 122, 23754, 23826, 23822, 23459, 23790])).
% 29.39/19.58 tff(23847,plain,(big_f(c1, c1) | (~(f10(c2) = c2)) | (f7(c1) = c1) | big_f(c1, c2)), inference(lemma,lemma(discharge,[]))).
% 29.39/19.58 tff(23848,plain,
% 29.39/19.58 (big_f(c1, c2)),
% 29.39/19.58 inference(unit_resolution,[status(thm)],[23847, 66, 115, 122])).
% 29.39/19.58 tff(23849,plain,
% 29.39/19.58 (big_f(c1, f1(c1, c2))),
% 29.39/19.58 inference(modus_ponens,[status(thm)],[23848, 23508])).
% 29.39/19.58 tff(23850,assumption,(big_f(c1, f1(c1, c2))), introduced(assumption)).
% 29.39/19.58 tff(23851,plain,
% 29.39/19.58 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (~big_f(c1, f1(c1, c2))) | (~(f1(c1, c2) = c2)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (~big_f(c1, f1(c1, c2))) | (~(f1(c1, c2) = c2)))),
% 29.39/19.58 inference(rewrite,[status(thm)],[])).
% 29.39/19.58 tff(23852,plain,
% 29.39/19.58 (((c1 = c3) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (~(f1(c1, c2) = c2)) | (~big_f(c1, f1(c1, c2)))) <=> ((c1 = c3) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (~big_f(c1, f1(c1, c2))) | (~(f1(c1, c2) = c2)))),
% 29.39/19.58 inference(rewrite,[status(thm)],[])).
% 29.39/19.58 tff(23853,plain,
% 29.39/19.58 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (~(f1(c1, c2) = c2)) | (~big_f(c1, f1(c1, c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (~big_f(c1, f1(c1, c2))) | (~(f1(c1, c2) = c2))))),
% 29.39/19.58 inference(monotonicity,[status(thm)],[23852])).
% 29.39/19.58 tff(23854,plain,
% 29.39/19.58 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (~(f1(c1, c2) = c2)) | (~big_f(c1, f1(c1, c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (~big_f(c1, f1(c1, c2))) | (~(f1(c1, c2) = c2)))),
% 29.39/19.58 inference(transitivity,[status(thm)],[23853, 23851])).
% 29.39/19.58 tff(23855,plain,
% 29.39/19.58 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (~(f1(c1, c2) = c2)) | (~big_f(c1, f1(c1, c2))))),
% 29.39/19.58 inference(quant_inst,[status(thm)],[])).
% 29.39/19.58 tff(23856,plain,
% 29.39/19.58 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (~big_f(c1, f1(c1, c2))) | (~(f1(c1, c2) = c2))),
% 29.39/19.58 inference(modus_ponens,[status(thm)],[23855, 23854])).
% 29.39/19.58 tff(23857,plain,
% 29.39/19.58 ((~(c1 = c4)) | (~(c1 = f4(c1)))),
% 29.39/19.58 inference(unit_resolution,[status(thm)],[23856, 447, 168, 822, 23850, 66])).
% 29.39/19.58 tff(23858,plain,
% 29.39/19.58 (~(c1 = f4(c1))),
% 29.39/19.58 inference(unit_resolution,[status(thm)],[23857, 564])).
% 29.39/19.58 tff(23859,plain,
% 29.39/19.58 ($false),
% 29.39/19.58 inference(unit_resolution,[status(thm)],[23858, 19825])).
% 29.39/19.58 tff(23860,plain,((~(c4 = c1)) | (~(f4(c4) = c1)) | (c1 = c3) | (~(f1(c1, c2) = c2)) | (~big_f(c1, f1(c1, c2))) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 29.39/19.58 tff(23861,plain,
% 29.39/19.58 (~(c4 = c1)),
% 29.39/19.58 inference(unit_resolution,[status(thm)],[23860, 23506, 168, 11752, 23849, 66])).
% 29.39/19.58 tff(23862,plain,
% 29.39/19.58 (c4 = c2),
% 29.39/19.58 inference(unit_resolution,[status(thm)],[461, 23861])).
% 29.39/19.58 tff(23863,plain,
% 29.39/19.58 (c2 = c4),
% 29.39/19.58 inference(modus_ponens,[status(thm)],[23862, 159])).
% 29.39/19.58 tff(23864,plain,
% 29.39/19.58 (c2 = c4),
% 29.39/19.58 inference(symmetry,[status(thm)],[23862])).
% 29.39/19.59 tff(23865,plain,
% 29.39/19.59 (f4(c2) = f4(c4)),
% 29.39/19.59 inference(monotonicity,[status(thm)],[23864])).
% 29.39/19.59 tff(23866,plain,
% 29.39/19.59 (f4(c2) = c1),
% 29.39/19.59 inference(transitivity,[status(thm)],[23865, 11752])).
% 29.39/19.59 tff(23867,plain,
% 29.39/19.59 ((c2 = f4(c2)) <=> (c2 = c1)),
% 29.39/19.59 inference(monotonicity,[status(thm)],[23866])).
% 29.39/19.59 tff(23868,plain,
% 29.39/19.59 ((c2 = c1) <=> (c2 = f4(c2))),
% 29.39/19.59 inference(symmetry,[status(thm)],[23867])).
% 29.39/19.59 tff(23869,plain,
% 29.39/19.59 ((~(c2 = c1)) <=> (~(c2 = f4(c2)))),
% 29.39/19.59 inference(monotonicity,[status(thm)],[23868])).
% 29.39/19.59 tff(23870,plain,
% 29.39/19.59 (~(c2 = f4(c2))),
% 29.39/19.59 inference(modus_ponens,[status(thm)],[75, 23869])).
% 29.39/19.59 tff(23871,plain,
% 29.39/19.59 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c1, f1(c1, c2))) | (~(f1(c1, c2) = c2)) | (~big_f(c2, c2)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c1, f1(c1, c2))) | (~(f1(c1, c2) = c2)) | (~big_f(c2, c2)))),
% 29.39/19.59 inference(rewrite,[status(thm)],[])).
% 29.39/19.59 tff(23872,plain,
% 29.39/19.59 (((c1 = c3) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)) | (~(f1(c1, c2) = c2)) | (~big_f(c1, f1(c1, c2)))) <=> ((c1 = c3) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c1, f1(c1, c2))) | (~(f1(c1, c2) = c2)) | (~big_f(c2, c2)))),
% 29.39/19.59 inference(rewrite,[status(thm)],[])).
% 29.39/19.59 tff(23873,plain,
% 29.39/19.59 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)) | (~(f1(c1, c2) = c2)) | (~big_f(c1, f1(c1, c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c1, f1(c1, c2))) | (~(f1(c1, c2) = c2)) | (~big_f(c2, c2))))),
% 29.39/19.59 inference(monotonicity,[status(thm)],[23872])).
% 29.39/19.59 tff(23874,plain,
% 29.39/19.59 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)) | (~(f1(c1, c2) = c2)) | (~big_f(c1, f1(c1, c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c1, f1(c1, c2))) | (~(f1(c1, c2) = c2)) | (~big_f(c2, c2)))),
% 29.39/19.59 inference(transitivity,[status(thm)],[23873, 23871])).
% 29.39/19.59 tff(23875,plain,
% 29.39/19.59 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)) | (~(f1(c1, c2) = c2)) | (~big_f(c1, f1(c1, c2))))),
% 29.39/19.59 inference(quant_inst,[status(thm)],[])).
% 29.39/19.59 tff(23876,plain,
% 29.39/19.59 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c1, f1(c1, c2))) | (~(f1(c1, c2) = c2)) | (~big_f(c2, c2))),
% 29.39/19.59 inference(modus_ponens,[status(thm)],[23875, 23874])).
% 29.39/19.59 tff(23877,plain,
% 29.39/19.59 ((~(c2 = c4)) | (c2 = f4(c2))),
% 29.39/19.59 inference(unit_resolution,[status(thm)],[23876, 553, 168, 23476, 23506, 23849])).
% 29.39/19.59 tff(23878,plain,
% 29.39/19.59 ($false),
% 29.39/19.59 inference(unit_resolution,[status(thm)],[23877, 23870, 23863])).
% 29.39/19.59 tff(23879,plain,(big_f(c1, c1) | (c1 = c3) | (~(f4(c4) = c1)) | (f7(c1) = c1) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.39/19.59 tff(23880,plain,
% 29.39/19.59 (c1 = c3),
% 29.39/19.59 inference(unit_resolution,[status(thm)],[23879, 23475, 66, 115, 122])).
% 29.39/19.59 tff(23881,plain,
% 29.39/19.59 (c3 = c1),
% 29.39/19.59 inference(symmetry,[status(thm)],[23880])).
% 29.39/19.59 tff(23882,plain,
% 29.39/19.59 ((c2 = c3) <=> (c2 = c1)),
% 29.39/19.59 inference(monotonicity,[status(thm)],[23881])).
% 29.39/19.59 tff(23883,plain,
% 29.39/19.59 ((c2 = c1) <=> (c2 = c3)),
% 29.39/19.59 inference(symmetry,[status(thm)],[23882])).
% 29.39/19.59 tff(23884,plain,
% 29.39/19.59 ((c2 = c1) <=> (f7(c1) = c3)),
% 29.39/19.59 inference(transitivity,[status(thm)],[23883, 12383])).
% 29.39/19.59 tff(23885,plain,
% 29.39/19.59 ((~(c2 = c1)) <=> (~(f7(c1) = c3))),
% 29.39/19.59 inference(monotonicity,[status(thm)],[23884])).
% 29.39/19.59 tff(23886,plain,
% 29.39/19.59 (~(f7(c1) = c3)),
% 29.39/19.59 inference(modus_ponens,[status(thm)],[75, 23885])).
% 29.39/19.59 tff(23887,plain,
% 29.39/19.59 ((~(c2 = c1)) <=> (~(c2 = c3))),
% 29.39/19.59 inference(monotonicity,[status(thm)],[23883])).
% 29.39/19.59 tff(23888,plain,
% 29.39/19.59 (~(c2 = c3)),
% 29.39/19.59 inference(modus_ponens,[status(thm)],[75, 23887])).
% 29.39/19.59 tff(23889,plain,
% 29.39/19.59 (~big_f(f9(c1, c2), f10(c1))),
% 29.39/19.59 inference(unit_resolution,[status(thm)],[23425, 4240, 66, 3762])).
% 29.39/19.59 tff(23890,plain,
% 29.39/19.59 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((c2 = f5(c1)) | (f7(c1) = c1) | (~big_f(f7(c1), c2)) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (c2 = f5(c1)) | (f7(c1) = c1) | (~big_f(f7(c1), c2)) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)))),
% 29.39/19.59 inference(rewrite,[status(thm)],[])).
% 29.39/19.59 tff(23891,plain,
% 29.39/19.59 (((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2))) <=> ((c2 = f5(c1)) | (f7(c1) = c1) | (~big_f(f7(c1), c2)) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)))),
% 29.39/19.59 inference(rewrite,[status(thm)],[])).
% 29.39/19.59 tff(23892,plain,
% 29.39/19.59 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((c2 = f5(c1)) | (f7(c1) = c1) | (~big_f(f7(c1), c2)) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1))))),
% 29.39/19.59 inference(monotonicity,[status(thm)],[23891])).
% 29.39/19.59 tff(23893,plain,
% 29.39/19.59 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (c2 = f5(c1)) | (f7(c1) = c1) | (~big_f(f7(c1), c2)) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)))),
% 29.39/19.59 inference(transitivity,[status(thm)],[23892, 23890])).
% 29.39/19.59 tff(23894,plain,
% 29.39/19.59 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)))),
% 29.39/19.59 inference(quant_inst,[status(thm)],[])).
% 29.39/19.59 tff(23895,plain,
% 29.39/19.59 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (c2 = f5(c1)) | (f7(c1) = c1) | (~big_f(f7(c1), c2)) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1))),
% 29.39/19.59 inference(modus_ponens,[status(thm)],[23894, 23893])).
% 29.39/19.59 tff(23896,plain,
% 29.39/19.59 ($false),
% 29.39/19.59 inference(unit_resolution,[status(thm)],[23895, 676, 12775, 12871, 115, 3762, 23889, 4236])).
% 29.39/19.59 tff(23897,plain,((f9(c1, c2) = c2) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)) | (f7(c1) = c1) | (~(f10(c1) = c1)) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 29.39/19.59 tff(23898,plain,
% 29.39/19.59 (f9(c1, c2) = c2),
% 29.39/19.59 inference(unit_resolution,[status(thm)],[23897, 12775, 115, 12871, 22733, 66])).
% 29.39/19.59 tff(23899,plain,
% 29.39/19.59 (big_f(f9(c1, c2), f10(c1)) <=> big_f(c2, c1)),
% 29.39/19.59 inference(monotonicity,[status(thm)],[23898, 22733])).
% 29.39/19.59 tff(23900,plain,
% 29.39/19.59 (big_f(c2, c1) <=> big_f(f9(c1, c2), f10(c1))),
% 29.39/19.59 inference(symmetry,[status(thm)],[23899])).
% 29.39/19.59 tff(23901,plain,
% 29.39/19.59 (big_f(f9(c1, c2), f10(c1))),
% 29.39/19.59 inference(modus_ponens,[status(thm)],[348, 23900])).
% 29.39/19.59 tff(23902,plain,
% 29.39/19.59 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((c2 = f5(c1)) | (f7(c1) = c1) | (~big_f(f7(c1), c2)) | (~(f10(c1) = c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (c2 = f5(c1)) | (f7(c1) = c1) | (~big_f(f7(c1), c2)) | (~(f10(c1) = c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2)))),
% 29.39/19.59 inference(rewrite,[status(thm)],[])).
% 29.39/19.59 tff(23903,plain,
% 29.39/19.59 (((~(f10(c1) = c1)) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)) | (~(f9(c1, c2) = c2)) | (~big_f(f9(c1, c2), f10(c1)))) <=> ((c2 = f5(c1)) | (f7(c1) = c1) | (~big_f(f7(c1), c2)) | (~(f10(c1) = c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2)))),
% 29.39/19.59 inference(rewrite,[status(thm)],[])).
% 29.39/19.59 tff(23904,plain,
% 29.39/19.59 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c1) = c1)) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)) | (~(f9(c1, c2) = c2)) | (~big_f(f9(c1, c2), f10(c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((c2 = f5(c1)) | (f7(c1) = c1) | (~big_f(f7(c1), c2)) | (~(f10(c1) = c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2))))),
% 29.39/19.59 inference(monotonicity,[status(thm)],[23903])).
% 29.39/19.59 tff(23905,plain,
% 29.39/19.59 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c1) = c1)) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)) | (~(f9(c1, c2) = c2)) | (~big_f(f9(c1, c2), f10(c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (c2 = f5(c1)) | (f7(c1) = c1) | (~big_f(f7(c1), c2)) | (~(f10(c1) = c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2)))),
% 29.39/19.59 inference(transitivity,[status(thm)],[23904, 23902])).
% 29.39/19.59 tff(23906,plain,
% 29.39/19.59 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c1) = c1)) | (f7(c1) = c1) | (c2 = f5(c1)) | (~big_f(f7(c1), c2)) | (~(f9(c1, c2) = c2)) | (~big_f(f9(c1, c2), f10(c1))))),
% 29.39/19.59 inference(quant_inst,[status(thm)],[])).
% 29.39/19.59 tff(23907,plain,
% 29.39/19.59 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (c2 = f5(c1)) | (f7(c1) = c1) | (~big_f(f7(c1), c2)) | (~(f10(c1) = c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2))),
% 29.39/19.59 inference(modus_ponens,[status(thm)],[23906, 23905])).
% 29.39/19.59 tff(23908,plain,
% 29.39/19.59 ($false),
% 29.39/19.59 inference(unit_resolution,[status(thm)],[23907, 1190, 12775, 12871, 115, 22733, 23901, 23898])).
% 29.39/19.59 tff(23909,plain,((c2 = f5(c1)) | (~big_f(f7(c1), c2)) | (f7(c1) = c1) | (~big_f(c2, c1)) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 29.39/19.59 tff(23910,plain,
% 29.39/19.59 (c2 = f5(c1)),
% 29.39/19.59 inference(unit_resolution,[status(thm)],[23909, 348, 115, 12871, 66])).
% 29.39/19.59 tff(23911,plain,
% 29.39/19.59 (f5(c1) = c2),
% 29.39/19.59 inference(symmetry,[status(thm)],[23910])).
% 29.39/19.59 tff(23912,plain,
% 29.39/19.59 ((f5(c1) = c1) <=> (c2 = c1)),
% 29.39/19.59 inference(monotonicity,[status(thm)],[23911])).
% 29.39/19.59 tff(23913,plain,
% 29.39/19.59 ((c2 = c1) <=> (f5(c1) = c1)),
% 29.39/19.59 inference(symmetry,[status(thm)],[23912])).
% 29.39/19.59 tff(23914,plain,
% 29.39/19.59 ((c2 = c1) <=> (c1 = f5(c1))),
% 29.39/19.59 inference(transitivity,[status(thm)],[23913, 192])).
% 29.39/19.59 tff(23915,plain,
% 29.39/19.59 ((~(c2 = c1)) <=> (~(c1 = f5(c1)))),
% 29.39/19.59 inference(monotonicity,[status(thm)],[23914])).
% 29.39/19.59 tff(23916,plain,
% 29.39/19.59 (~(c1 = f5(c1))),
% 29.39/19.59 inference(modus_ponens,[status(thm)],[75, 23915])).
% 29.39/19.59 tff(23917,plain,
% 29.39/19.59 (big_f(f7(c1), c1)),
% 29.39/19.59 inference(modus_ponens,[status(thm)],[348, 693])).
% 29.39/19.59 tff(23918,plain,
% 29.39/19.59 (big_f(f9(c1, c2), f10(c1))),
% 29.39/19.59 inference(unit_resolution,[status(thm)],[3807, 4236, 115, 22733, 15735, 3761])).
% 29.39/19.59 tff(23919,plain,
% 29.39/19.59 ($false),
% 29.39/19.59 inference(unit_resolution,[status(thm)],[23425, 23918, 4240, 66, 22733])).
% 29.39/19.59 tff(23920,plain,((f9(c1, c2) = c2) | big_f(c1, c1) | (f7(c1) = c1) | (~big_f(f7(c1), c1)) | (c1 = f5(c1))), inference(lemma,lemma(discharge,[]))).
% 29.39/19.59 tff(23921,plain,
% 29.39/19.59 (f9(c1, c2) = c2),
% 29.39/19.59 inference(unit_resolution,[status(thm)],[23920, 23917, 115, 66, 23916])).
% 29.39/19.59 tff(23922,plain,
% 29.39/19.59 (big_f(f9(c1, c2), f10(c1)) <=> big_f(c2, c1)),
% 29.39/19.59 inference(monotonicity,[status(thm)],[23921, 22733])).
% 29.39/19.59 tff(23923,plain,
% 29.39/19.59 (big_f(c2, c1) <=> big_f(f9(c1, c2), f10(c1))),
% 29.39/19.59 inference(symmetry,[status(thm)],[23922])).
% 29.39/19.59 tff(23924,plain,
% 29.39/19.59 (big_f(f9(c1, c2), f10(c1))),
% 29.39/19.59 inference(modus_ponens,[status(thm)],[348, 23923])).
% 29.39/19.59 tff(23925,plain,
% 29.39/19.59 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((f7(c1) = c1) | (~(f10(c1) = c1)) | (c1 = f5(c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2)) | (~big_f(f7(c1), c1)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (f7(c1) = c1) | (~(f10(c1) = c1)) | (c1 = f5(c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2)) | (~big_f(f7(c1), c1)))),
% 29.39/19.59 inference(rewrite,[status(thm)],[])).
% 29.39/19.59 tff(23926,plain,
% 29.39/19.59 (((~(f10(c1) = c1)) | (f7(c1) = c1) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)) | (~(f9(c1, c2) = c2)) | (~big_f(f9(c1, c2), f10(c1)))) <=> ((f7(c1) = c1) | (~(f10(c1) = c1)) | (c1 = f5(c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2)) | (~big_f(f7(c1), c1)))),
% 29.39/19.59 inference(rewrite,[status(thm)],[])).
% 29.39/19.59 tff(23927,plain,
% 29.39/19.59 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c1) = c1)) | (f7(c1) = c1) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)) | (~(f9(c1, c2) = c2)) | (~big_f(f9(c1, c2), f10(c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((f7(c1) = c1) | (~(f10(c1) = c1)) | (c1 = f5(c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2)) | (~big_f(f7(c1), c1))))),
% 29.39/19.59 inference(monotonicity,[status(thm)],[23926])).
% 29.39/19.59 tff(23928,plain,
% 29.39/19.59 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c1) = c1)) | (f7(c1) = c1) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)) | (~(f9(c1, c2) = c2)) | (~big_f(f9(c1, c2), f10(c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (f7(c1) = c1) | (~(f10(c1) = c1)) | (c1 = f5(c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2)) | (~big_f(f7(c1), c1)))),
% 29.39/19.59 inference(transitivity,[status(thm)],[23927, 23925])).
% 29.39/19.59 tff(23929,plain,
% 29.39/19.59 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c1) = c1)) | (f7(c1) = c1) | (c1 = f5(c1)) | (~big_f(f7(c1), c1)) | (~(f9(c1, c2) = c2)) | (~big_f(f9(c1, c2), f10(c1))))),
% 29.39/19.59 inference(quant_inst,[status(thm)],[])).
% 29.39/19.59 tff(23930,plain,
% 29.39/19.59 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (f7(c1) = c1) | (~(f10(c1) = c1)) | (c1 = f5(c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2)) | (~big_f(f7(c1), c1))),
% 29.39/19.59 inference(modus_ponens,[status(thm)],[23929, 23928])).
% 29.39/19.59 tff(23931,plain,
% 29.39/19.59 ($false),
% 29.39/19.59 inference(unit_resolution,[status(thm)],[23930, 1190, 115, 22733, 23917, 23916, 23924, 23921])).
% 29.39/19.59 tff(23932,plain,((~big_f(c2, c1)) | (f7(c1) = c1) | big_f(c1, c1) | (~big_f(f7(c1), c2))), inference(lemma,lemma(discharge,[]))).
% 29.39/19.59 tff(23933,plain,
% 29.39/19.59 (~big_f(c2, c1)),
% 29.39/19.59 inference(unit_resolution,[status(thm)],[23932, 12774, 115, 66])).
% 29.39/19.59 tff(23934,plain,
% 29.39/19.59 (~big_f(f7(c1), c1)),
% 29.39/19.59 inference(unit_resolution,[status(thm)],[15738, 23933, 120])).
% 29.39/19.59 tff(23935,plain,
% 29.39/19.59 (f1(f7(c1), f7(c1)) = f1(c2, c2)),
% 29.39/19.59 inference(monotonicity,[status(thm)],[120, 120])).
% 29.39/19.59 tff(23936,plain,
% 29.39/19.59 (f1(f7(c1), f7(c1)) = c1),
% 29.39/19.59 inference(transitivity,[status(thm)],[23935, 14884])).
% 29.39/19.59 tff(23937,plain,
% 29.39/19.59 ((f1(f7(c1), f7(c1)) = f7(c1)) <=> (c1 = f7(c1))),
% 29.39/19.59 inference(monotonicity,[status(thm)],[23936])).
% 29.39/19.59 tff(23938,plain,
% 29.39/19.59 ((f1(f7(c1), f7(c1)) = f7(c1)) <=> (f7(c1) = c1)),
% 29.39/19.59 inference(transitivity,[status(thm)],[23937, 14336])).
% 29.39/19.59 tff(23939,plain,
% 29.39/19.59 ((f7(c1) = c1) <=> (f1(f7(c1), f7(c1)) = f7(c1))),
% 29.39/19.59 inference(symmetry,[status(thm)],[23938])).
% 29.39/19.59 tff(23940,plain,
% 29.39/19.59 ((~(f7(c1) = c1)) <=> (~(f1(f7(c1), f7(c1)) = f7(c1)))),
% 29.39/19.59 inference(monotonicity,[status(thm)],[23939])).
% 29.39/19.59 tff(23941,plain,
% 29.39/19.59 (~(f1(f7(c1), f7(c1)) = f7(c1))),
% 29.39/19.59 inference(modus_ponens,[status(thm)],[115, 23940])).
% 29.39/19.59 tff(23942,plain,
% 29.39/19.59 (big_f(f7(c1), f1(f7(c1), f7(c1))) <=> big_f(f7(c1), c1)),
% 29.39/19.59 inference(monotonicity,[status(thm)],[23936])).
% 29.39/19.59 tff(23943,plain,
% 29.39/19.59 (big_f(f7(c1), c1) <=> big_f(f7(c1), f1(f7(c1), f7(c1)))),
% 29.39/19.59 inference(symmetry,[status(thm)],[23942])).
% 29.39/19.59 tff(23944,plain,
% 29.39/19.59 ((~big_f(f7(c1), c1)) <=> (~big_f(f7(c1), f1(f7(c1), f7(c1))))),
% 29.39/19.59 inference(monotonicity,[status(thm)],[23943])).
% 29.39/19.59 tff(23945,plain,
% 29.39/19.59 (~big_f(f7(c1), f1(f7(c1), f7(c1)))),
% 29.39/19.59 inference(modus_ponens,[status(thm)],[285, 23944])).
% 29.39/19.59 tff(23946,plain,
% 29.39/19.59 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f7(c1) = c3) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (f1(f7(c1), f7(c1)) = f7(c1)) | big_f(f7(c1), f1(f7(c1), f7(c1))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (f7(c1) = c3) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (f1(f7(c1), f7(c1)) = f7(c1)) | big_f(f7(c1), f1(f7(c1), f7(c1))))),
% 29.39/19.59 inference(rewrite,[status(thm)],[])).
% 29.39/19.59 tff(23947,plain,
% 29.39/19.59 (((f7(c1) = c3) | (f1(f7(c1), f7(c1)) = f7(c1)) | big_f(f7(c1), f1(f7(c1), f7(c1))) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1)))) <=> ((f7(c1) = c3) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (f1(f7(c1), f7(c1)) = f7(c1)) | big_f(f7(c1), f1(f7(c1), f7(c1))))),
% 29.39/19.59 inference(rewrite,[status(thm)],[])).
% 29.39/19.59 tff(23948,plain,
% 29.39/19.59 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f7(c1) = c3) | (f1(f7(c1), f7(c1)) = f7(c1)) | big_f(f7(c1), f1(f7(c1), f7(c1))) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f7(c1) = c3) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (f1(f7(c1), f7(c1)) = f7(c1)) | big_f(f7(c1), f1(f7(c1), f7(c1)))))),
% 29.39/19.59 inference(monotonicity,[status(thm)],[23947])).
% 29.39/19.59 tff(23949,plain,
% 29.39/19.59 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f7(c1) = c3) | (f1(f7(c1), f7(c1)) = f7(c1)) | big_f(f7(c1), f1(f7(c1), f7(c1))) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (f7(c1) = c3) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (f1(f7(c1), f7(c1)) = f7(c1)) | big_f(f7(c1), f1(f7(c1), f7(c1))))),
% 29.39/19.60 inference(transitivity,[status(thm)],[23948, 23946])).
% 29.39/19.60 tff(23950,plain,
% 29.39/19.60 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f7(c1) = c3) | (f1(f7(c1), f7(c1)) = f7(c1)) | big_f(f7(c1), f1(f7(c1), f7(c1))) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))))),
% 29.39/19.60 inference(quant_inst,[status(thm)],[])).
% 29.39/19.60 tff(23951,plain,
% 29.39/19.60 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (f7(c1) = c3) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (f1(f7(c1), f7(c1)) = f7(c1)) | big_f(f7(c1), f1(f7(c1), f7(c1)))),
% 29.39/19.60 inference(modus_ponens,[status(thm)],[23950, 23949])).
% 29.39/19.60 tff(23952,plain,
% 29.39/19.60 ((f1(f7(c1), f7(c1)) = f7(c1)) | big_f(f7(c1), f1(f7(c1), f7(c1)))),
% 29.39/19.60 inference(unit_resolution,[status(thm)],[23951, 402, 11526, 12165, 19844, 66])).
% 29.39/19.60 tff(23953,plain,
% 29.39/19.60 ($false),
% 29.39/19.60 inference(unit_resolution,[status(thm)],[23952, 23945, 23941])).
% 29.39/19.60 tff(23954,plain,((~(f1(c2, c2) = c1)) | (~(c1 = c4)) | (f7(c1) = c3) | (~(c1 = f4(c1))) | big_f(c1, c1) | big_f(f7(c1), c1) | (f7(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.39/19.60 tff(23955,plain,
% 29.39/19.60 (~(f1(c2, c2) = c1)),
% 29.39/19.60 inference(unit_resolution,[status(thm)],[23954, 19825, 12165, 564, 66, 23934, 115])).
% 29.39/19.60 tff(23956,plain,
% 29.39/19.60 (f1(c2, c2) = c2),
% 29.39/19.60 inference(unit_resolution,[status(thm)],[5270, 23955])).
% 29.39/19.60 tff(23957,plain,
% 29.39/19.60 (big_f(c2, f1(c2, c2)) <=> big_f(c2, c2)),
% 29.39/19.60 inference(monotonicity,[status(thm)],[23956])).
% 29.39/19.60 tff(23958,plain,
% 29.39/19.60 (big_f(c2, c2) <=> big_f(c2, f1(c2, c2))),
% 29.39/19.60 inference(symmetry,[status(thm)],[23957])).
% 29.39/19.60 tff(23959,plain,
% 29.39/19.60 (big_f(c2, f1(c2, c2))),
% 29.39/19.60 inference(modus_ponens,[status(thm)],[1345, 23958])).
% 29.39/19.60 tff(23960,plain,
% 29.39/19.60 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))),
% 29.39/19.60 inference(rewrite,[status(thm)],[])).
% 29.39/19.60 tff(23961,plain,
% 29.39/19.60 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))),
% 29.39/19.60 inference(quant_inst,[status(thm)],[])).
% 29.39/19.60 tff(23962,plain,
% 29.39/19.60 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2)))),
% 29.39/19.60 inference(modus_ponens,[status(thm)],[23961, 23960])).
% 29.39/19.60 tff(23963,plain,
% 29.39/19.60 ($false),
% 29.39/19.60 inference(unit_resolution,[status(thm)],[23962, 447, 564, 377, 23956, 23959, 19825, 66])).
% 29.39/19.60 tff(23964,plain,((~(c4 = c1)) | (c2 = c3) | big_f(c1, c1) | (~big_f(c2, c2)) | (f7(c1) = c3) | (f7(c1) = c1) | (~(f4(c4) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.39/19.60 tff(23965,plain,
% 29.39/19.60 (~(c4 = c1)),
% 29.39/19.60 inference(unit_resolution,[status(thm)],[23964, 23888, 66, 23459, 23886, 115, 23475])).
% 29.39/19.60 tff(23966,plain,
% 29.39/19.60 (c4 = c2),
% 29.39/19.60 inference(unit_resolution,[status(thm)],[461, 23965])).
% 29.39/19.60 tff(23967,plain,
% 29.39/19.60 (c2 = c4),
% 29.39/19.60 inference(modus_ponens,[status(thm)],[23966, 159])).
% 29.39/19.60 tff(23968,plain,
% 29.39/19.60 (big_f(f7(c2), c2)),
% 29.39/19.60 inference(modus_ponens,[status(thm)],[23459, 21531])).
% 29.39/19.60 tff(23969,plain,
% 29.39/19.60 (~big_f(c2, c1)),
% 29.39/19.60 inference(unit_resolution,[status(thm)],[23932, 23640, 115, 66])).
% 29.39/19.60 tff(23970,plain,
% 29.39/19.60 (c2 = c4),
% 29.39/19.60 inference(symmetry,[status(thm)],[23966])).
% 29.39/19.60 tff(23971,plain,
% 29.39/19.60 (f4(c2) = f4(c4)),
% 29.39/19.60 inference(monotonicity,[status(thm)],[23970])).
% 29.39/19.60 tff(23972,plain,
% 29.39/19.60 (f4(c2) = c1),
% 29.39/19.60 inference(transitivity,[status(thm)],[23971, 23475])).
% 29.39/19.60 tff(23973,plain,
% 29.39/19.60 ((c2 = f4(c2)) <=> (c2 = c1)),
% 29.39/19.60 inference(monotonicity,[status(thm)],[23972])).
% 29.39/19.60 tff(23974,plain,
% 29.39/19.60 ((c2 = c1) <=> (c2 = f4(c2))),
% 29.39/19.60 inference(symmetry,[status(thm)],[23973])).
% 29.39/19.60 tff(23975,plain,
% 29.39/19.60 ((c2 = c1) <=> (f7(c2) = f4(c2))),
% 29.39/19.60 inference(transitivity,[status(thm)],[23974, 21536])).
% 29.39/19.60 tff(23976,plain,
% 29.39/19.60 ((~(c2 = c1)) <=> (~(f7(c2) = f4(c2)))),
% 29.39/19.60 inference(monotonicity,[status(thm)],[23975])).
% 29.39/19.60 tff(23977,plain,
% 29.39/19.60 (~(f7(c2) = f4(c2))),
% 29.39/19.60 inference(modus_ponens,[status(thm)],[75, 23976])).
% 29.39/19.60 tff(23978,plain,
% 29.39/19.60 (f1(c2, c2) = c2),
% 29.39/19.60 inference(unit_resolution,[status(thm)],[9464, 23977, 23969, 23968, 23888, 23967])).
% 29.39/19.60 tff(23979,plain,
% 29.39/19.60 (big_f(c2, f1(c2, c2)) <=> big_f(c2, c2)),
% 29.39/19.60 inference(monotonicity,[status(thm)],[23978])).
% 29.39/19.60 tff(23980,plain,
% 29.39/19.60 (big_f(c2, c2) <=> big_f(c2, f1(c2, c2))),
% 29.39/19.60 inference(symmetry,[status(thm)],[23979])).
% 29.39/19.60 tff(23981,plain,
% 29.39/19.60 (big_f(c2, f1(c2, c2))),
% 29.39/19.60 inference(modus_ponens,[status(thm)],[23459, 23980])).
% 29.39/19.60 tff(23982,plain,
% 29.39/19.60 ((~(c2 = c1)) <=> (~(c2 = f4(c2)))),
% 29.39/19.60 inference(monotonicity,[status(thm)],[23974])).
% 29.39/19.60 tff(23983,plain,
% 29.39/19.60 (~(c2 = f4(c2))),
% 29.39/19.60 inference(modus_ponens,[status(thm)],[75, 23982])).
% 29.39/19.60 tff(23984,plain,
% 29.39/19.60 ($false),
% 29.39/19.60 inference(unit_resolution,[status(thm)],[16875, 553, 23967, 23983, 23459, 23888, 23978, 23981])).
% 29.39/19.60 tff(23985,plain,((~(f10(c2) = c2)) | (~(f7(c2) = c2)) | big_f(c1, c1) | (f7(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.39/19.60 tff(23986,plain,
% 29.39/19.60 (~(f10(c2) = c2)),
% 29.39/19.60 inference(unit_resolution,[status(thm)],[23985, 77, 66, 115])).
% 29.39/19.60 tff(23987,plain,
% 29.39/19.60 (f10(c2) = c1),
% 29.39/19.60 inference(unit_resolution,[status(thm)],[93, 23986])).
% 29.39/19.60 tff(23988,plain,
% 29.39/19.60 ((f7(c1) = f8(f7(c1))) <=> (c2 = f8(c2))),
% 29.39/19.60 inference(monotonicity,[status(thm)],[120, 12280])).
% 29.39/19.60 tff(23989,plain,
% 29.39/19.60 ((c2 = f8(c2)) <=> (f7(c1) = f8(f7(c1)))),
% 29.39/19.60 inference(symmetry,[status(thm)],[23988])).
% 29.39/19.60 tff(23990,plain,
% 29.39/19.60 ((~(c2 = f8(c2))) <=> (~(f7(c1) = f8(f7(c1))))),
% 29.39/19.60 inference(monotonicity,[status(thm)],[23989])).
% 29.39/19.60 tff(23991,plain,
% 29.39/19.60 (~big_f(f7(c1), f5(c1))),
% 29.39/19.60 inference(unit_resolution,[status(thm)],[8430, 23458, 120, 121])).
% 29.39/19.60 tff(23992,plain,
% 29.39/19.60 (big_f(c2, f10(c2)) <=> big_f(c2, c1)),
% 29.39/19.60 inference(monotonicity,[status(thm)],[23987])).
% 29.39/19.60 tff(23993,plain,
% 29.39/19.60 (big_f(c2, c1) <=> big_f(c2, f10(c2))),
% 29.39/19.60 inference(symmetry,[status(thm)],[23992])).
% 29.39/19.60 tff(23994,plain,
% 29.39/19.60 ((~big_f(c2, c1)) <=> (~big_f(c2, f10(c2)))),
% 29.39/19.60 inference(monotonicity,[status(thm)],[23993])).
% 29.39/19.60 tff(23995,plain,
% 29.39/19.60 (~big_f(c2, f10(c2))),
% 29.39/19.60 inference(modus_ponens,[status(thm)],[23457, 23994])).
% 29.39/19.60 tff(23996,plain,
% 29.39/19.60 (~(c2 = f8(c2))),
% 29.39/19.60 inference(unit_resolution,[status(thm)],[12015, 23995, 23991, 23986, 115])).
% 29.39/19.60 tff(23997,plain,
% 29.39/19.60 (~(f7(c1) = f8(f7(c1)))),
% 29.39/19.60 inference(modus_ponens,[status(thm)],[23996, 23990])).
% 29.39/19.60 tff(23998,plain,
% 29.39/19.60 ((f8(f9(f10(c2), f7(c1))) = c1) <=> (c1 = f8(f9(f10(c2), f7(c1))))),
% 29.39/19.60 inference(commutativity,[status(thm)],[])).
% 29.39/19.60 tff(23999,plain,
% 29.39/19.60 ((c1 = f8(f9(f10(c2), f7(c1)))) <=> (f8(f9(f10(c2), f7(c1))) = c1)),
% 29.39/19.60 inference(symmetry,[status(thm)],[23998])).
% 29.39/19.60 tff(24000,plain,
% 29.39/19.60 (f9(f10(c2), f7(c1)) = f9(c1, c2)),
% 29.39/19.60 inference(monotonicity,[status(thm)],[11819, 120])).
% 29.39/19.60 tff(24001,plain,
% 29.39/19.60 (f9(f10(c2), f7(c1)) = c1),
% 29.39/19.60 inference(transitivity,[status(thm)],[24000, 4240])).
% 29.39/19.60 tff(24002,plain,
% 29.39/19.60 ((f7(f9(f10(c2), f7(c1))) = f9(f10(c2), f7(c1))) <=> (f7(f9(f10(c2), f7(c1))) = c1)),
% 29.39/19.60 inference(monotonicity,[status(thm)],[24001])).
% 29.39/19.60 tff(24003,plain,
% 29.39/19.60 ((f7(f9(f10(c2), f7(c1))) = c1) <=> (f7(f9(f10(c2), f7(c1))) = f9(f10(c2), f7(c1)))),
% 29.39/19.60 inference(symmetry,[status(thm)],[24002])).
% 29.39/19.60 tff(24004,plain,
% 29.39/19.60 (f7(f9(f10(c2), f7(c1))) = f7(c1)),
% 29.39/19.60 inference(monotonicity,[status(thm)],[24001])).
% 29.39/19.60 tff(24005,plain,
% 29.39/19.60 ((f7(f9(f10(c2), f7(c1))) = c1) <=> (f7(c1) = c1)),
% 29.39/19.60 inference(monotonicity,[status(thm)],[24004])).
% 29.39/19.60 tff(24006,plain,
% 29.39/19.60 ((f7(c1) = c1) <=> (f7(f9(f10(c2), f7(c1))) = c1)),
% 29.39/19.60 inference(symmetry,[status(thm)],[24005])).
% 29.39/19.60 tff(24007,plain,
% 29.39/19.60 ((f7(c1) = c1) <=> (f7(f9(f10(c2), f7(c1))) = f9(f10(c2), f7(c1)))),
% 29.39/19.60 inference(transitivity,[status(thm)],[24006, 24003])).
% 29.39/19.60 tff(24008,plain,
% 29.39/19.60 ((~(f7(c1) = c1)) <=> (~(f7(f9(f10(c2), f7(c1))) = f9(f10(c2), f7(c1))))),
% 29.39/19.60 inference(monotonicity,[status(thm)],[24007])).
% 29.39/19.60 tff(24009,plain,
% 29.39/19.60 (~(f7(f9(f10(c2), f7(c1))) = f9(f10(c2), f7(c1)))),
% 29.39/19.60 inference(modus_ponens,[status(thm)],[115, 24008])).
% 29.39/19.60 tff(24010,plain,
% 29.39/19.60 (f5(f9(f10(c2), f7(c1))) = f5(c1)),
% 29.39/19.60 inference(monotonicity,[status(thm)],[24001])).
% 29.39/19.60 tff(24011,plain,
% 29.39/19.60 (f5(f9(f10(c2), f7(c1))) = c1),
% 29.39/19.60 inference(transitivity,[status(thm)],[24010, 230])).
% 29.39/19.60 tff(24012,plain,
% 29.39/19.60 (big_f(f7(f9(f10(c2), f7(c1))), f5(f9(f10(c2), f7(c1)))) <=> big_f(f7(c1), c1)),
% 29.39/19.60 inference(monotonicity,[status(thm)],[24004, 24011])).
% 29.39/19.60 tff(24013,plain,
% 29.39/19.60 (big_f(f7(c1), c1) <=> big_f(f7(f9(f10(c2), f7(c1))), f5(f9(f10(c2), f7(c1))))),
% 29.39/19.60 inference(symmetry,[status(thm)],[24012])).
% 29.39/19.60 tff(24014,plain,
% 29.39/19.60 ((~big_f(f7(c1), c1)) <=> (~big_f(f7(f9(f10(c2), f7(c1))), f5(f9(f10(c2), f7(c1)))))),
% 29.39/19.60 inference(monotonicity,[status(thm)],[24013])).
% 29.39/19.60 tff(24015,plain,
% 29.39/19.60 (~big_f(f7(f9(f10(c2), f7(c1))), f5(f9(f10(c2), f7(c1))))),
% 29.39/19.60 inference(modus_ponens,[status(thm)],[285, 24014])).
% 29.39/19.60 tff(24016,plain,
% 29.39/19.60 ($false),
% 29.39/19.60 inference(unit_resolution,[status(thm)],[8997, 24015, 24009, 3762, 4236, 23889])).
% 29.39/19.60 tff(24017,plain,((f9(c1, c2) = c2) | (~(f10(c1) = c1)) | big_f(f7(c1), c1) | (~(f5(c1) = c1)) | (~(f10(c2) = c1)) | (f7(c1) = c1) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 29.39/19.60 tff(24018,plain,
% 29.39/19.60 (f9(c1, c2) = c2),
% 29.39/19.60 inference(unit_resolution,[status(thm)],[24017, 230, 285, 3762, 11819, 115, 66])).
% 29.39/19.60 tff(24019,plain,
% 29.39/19.60 (f9(f10(c2), f7(c1)) = f7(c1)),
% 29.39/19.60 inference(transitivity,[status(thm)],[24000, 24018, 2778])).
% 29.39/19.60 tff(24020,plain,
% 29.39/19.60 (f8(f9(f10(c2), f7(c1))) = f8(f7(c1))),
% 29.39/19.60 inference(monotonicity,[status(thm)],[24019])).
% 29.39/19.60 tff(24021,plain,
% 29.39/19.60 ((c1 = f8(f9(f10(c2), f7(c1)))) <=> (c1 = f8(f7(c1)))),
% 29.39/19.60 inference(monotonicity,[status(thm)],[24020])).
% 29.39/19.60 tff(24022,plain,
% 29.39/19.60 ((c1 = f8(f7(c1))) <=> (c1 = f8(f9(f10(c2), f7(c1))))),
% 29.39/19.60 inference(symmetry,[status(thm)],[24021])).
% 29.39/19.60 tff(24023,plain,
% 29.39/19.60 ((c1 = f8(f7(c1))) <=> (f8(f9(f10(c2), f7(c1))) = c1)),
% 29.39/19.60 inference(transitivity,[status(thm)],[24022, 23999])).
% 29.39/19.60 tff(24024,plain,
% 29.39/19.60 ((~(c1 = f8(f7(c1)))) <=> (~(f8(f9(f10(c2), f7(c1))) = c1))),
% 29.39/19.60 inference(monotonicity,[status(thm)],[24023])).
% 29.39/19.60 tff(24025,plain,
% 29.39/19.60 (big_f(c1, f10(f7(c1))) <=> big_f(c1, c1)),
% 29.39/19.60 inference(monotonicity,[status(thm)],[17718])).
% 29.39/19.60 tff(24026,plain,
% 29.39/19.60 (big_f(c1, c1) <=> big_f(c1, f10(f7(c1)))),
% 29.39/19.60 inference(symmetry,[status(thm)],[24025])).
% 29.39/19.60 tff(24027,plain,
% 29.39/19.60 ((~big_f(c1, c1)) <=> (~big_f(c1, f10(f7(c1))))),
% 29.39/19.60 inference(monotonicity,[status(thm)],[24026])).
% 29.39/19.60 tff(24028,plain,
% 29.39/19.60 (~big_f(c1, f10(f7(c1)))),
% 29.39/19.60 inference(modus_ponens,[status(thm)],[66, 24027])).
% 29.39/19.60 tff(24029,plain,
% 29.39/19.60 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f7(c1) = c1) | big_f(f7(c1), c1) | (~(c1 = f5(c1))) | big_f(c1, f10(f7(c1))) | (f10(f7(c1)) = f7(c1)) | (~(c1 = f8(f7(c1)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(c1 = f5(c1))) | big_f(c1, f10(f7(c1))) | (f10(f7(c1)) = f7(c1)) | (~(c1 = f8(f7(c1)))))),
% 29.39/19.60 inference(rewrite,[status(thm)],[])).
% 29.39/19.60 tff(24030,plain,
% 29.39/19.60 (((~(c1 = f5(c1))) | (f10(f7(c1)) = f7(c1)) | big_f(c1, f10(f7(c1))) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(c1 = f8(f7(c1))))) <=> ((f7(c1) = c1) | big_f(f7(c1), c1) | (~(c1 = f5(c1))) | big_f(c1, f10(f7(c1))) | (f10(f7(c1)) = f7(c1)) | (~(c1 = f8(f7(c1)))))),
% 29.39/19.60 inference(rewrite,[status(thm)],[])).
% 29.39/19.60 tff(24031,plain,
% 29.39/19.60 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c1 = f5(c1))) | (f10(f7(c1)) = f7(c1)) | big_f(c1, f10(f7(c1))) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(c1 = f8(f7(c1)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f7(c1) = c1) | big_f(f7(c1), c1) | (~(c1 = f5(c1))) | big_f(c1, f10(f7(c1))) | (f10(f7(c1)) = f7(c1)) | (~(c1 = f8(f7(c1))))))),
% 29.39/19.60 inference(monotonicity,[status(thm)],[24030])).
% 29.39/19.60 tff(24032,plain,
% 29.39/19.60 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c1 = f5(c1))) | (f10(f7(c1)) = f7(c1)) | big_f(c1, f10(f7(c1))) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(c1 = f8(f7(c1)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(c1 = f5(c1))) | big_f(c1, f10(f7(c1))) | (f10(f7(c1)) = f7(c1)) | (~(c1 = f8(f7(c1)))))),
% 29.39/19.60 inference(transitivity,[status(thm)],[24031, 24029])).
% 29.39/19.60 tff(24033,plain,
% 29.39/19.60 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c1 = f5(c1))) | (f10(f7(c1)) = f7(c1)) | big_f(c1, f10(f7(c1))) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(c1 = f8(f7(c1)))))),
% 29.39/19.60 inference(quant_inst,[status(thm)],[])).
% 29.39/19.60 tff(24034,plain,
% 29.39/19.60 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(c1) = c1) | big_f(f7(c1), c1) | (~(c1 = f5(c1))) | big_f(c1, f10(f7(c1))) | (f10(f7(c1)) = f7(c1)) | (~(c1 = f8(f7(c1))))),
% 29.39/19.60 inference(modus_ponens,[status(thm)],[24033, 24032])).
% 29.39/19.60 tff(24035,plain,
% 29.39/19.60 ((~(c1 = f5(c1))) | (~(c1 = f8(f7(c1))))),
% 29.39/19.60 inference(unit_resolution,[status(thm)],[24034, 1745, 115, 285, 20254, 24028])).
% 29.39/19.60 tff(24036,plain,
% 29.39/19.60 (~(c1 = f8(f7(c1)))),
% 29.39/19.60 inference(unit_resolution,[status(thm)],[24035, 692])).
% 29.39/19.60 tff(24037,plain,
% 29.39/19.60 (~(f8(f9(f10(c2), f7(c1))) = c1)),
% 29.39/19.60 inference(modus_ponens,[status(thm)],[24036, 24024])).
% 29.39/19.60 tff(24038,plain,
% 29.39/19.60 ((f8(f7(c1)) = f7(c1)) <=> (f7(c1) = f8(f7(c1)))),
% 29.39/19.60 inference(commutativity,[status(thm)],[])).
% 29.39/19.60 tff(24039,plain,
% 29.39/19.60 ((f8(f9(f10(c2), f7(c1))) = c2) <=> (f8(f7(c1)) = f7(c1))),
% 29.39/19.60 inference(monotonicity,[status(thm)],[24020, 2778])).
% 29.39/19.60 tff(24040,plain,
% 29.39/19.60 ((f8(f9(f10(c2), f7(c1))) = c2) <=> (f7(c1) = f8(f7(c1)))),
% 29.39/19.60 inference(transitivity,[status(thm)],[24039, 24038])).
% 29.39/19.60 tff(24041,plain,
% 29.39/19.60 ((f7(c1) = f8(f7(c1))) <=> (f8(f9(f10(c2), f7(c1))) = c2)),
% 29.39/19.60 inference(symmetry,[status(thm)],[24040])).
% 29.39/19.60 tff(24042,plain,
% 29.39/19.60 ((~(f7(c1) = f8(f7(c1)))) <=> (~(f8(f9(f10(c2), f7(c1))) = c2))),
% 29.39/19.60 inference(monotonicity,[status(thm)],[24041])).
% 29.39/19.60 tff(24043,assumption,(~(f7(c1) = f8(f7(c1)))), introduced(assumption)).
% 29.39/19.60 tff(24044,plain,
% 29.39/19.60 (~(f8(f9(f10(c2), f7(c1))) = c2)),
% 29.39/19.60 inference(modus_ponens,[status(thm)],[24043, 24042])).
% 29.39/19.60 tff(24045,plain,
% 29.39/19.60 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f8(f9(f10(c2), f7(c1))) = c1) | (f8(f9(f10(c2), f7(c1))) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f8(f9(f10(c2), f7(c1))) = c1) | (f8(f9(f10(c2), f7(c1))) = c2))),
% 29.39/19.60 inference(rewrite,[status(thm)],[])).
% 29.39/19.60 tff(24046,plain,
% 29.39/19.60 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f8(f9(f10(c2), f7(c1))) = c1) | (f8(f9(f10(c2), f7(c1))) = c2))),
% 29.39/19.60 inference(quant_inst,[status(thm)],[])).
% 29.39/19.60 tff(24047,plain,
% 29.39/19.60 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f8(f9(f10(c2), f7(c1))) = c1) | (f8(f9(f10(c2), f7(c1))) = c2)),
% 29.39/19.60 inference(modus_ponens,[status(thm)],[24046, 24045])).
% 29.39/19.60 tff(24048,plain,
% 29.39/19.60 ((f8(f9(f10(c2), f7(c1))) = c1) | (f8(f9(f10(c2), f7(c1))) = c2)),
% 29.39/19.60 inference(unit_resolution,[status(thm)],[24047, 10])).
% 29.39/19.60 tff(24049,plain,
% 29.39/19.60 ($false),
% 29.39/19.60 inference(unit_resolution,[status(thm)],[24048, 24044, 24037])).
% 29.39/19.60 tff(24050,plain,((~(f5(c1) = c1)) | (f7(c1) = f8(f7(c1))) | (~(f10(c2) = c1)) | big_f(f7(c1), c1) | (~(f10(c1) = c1)) | (f7(c1) = c1) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 29.39/19.60 tff(24051,plain,
% 29.39/19.60 (~(f5(c1) = c1)),
% 29.39/19.60 inference(unit_resolution,[status(thm)],[24050, 23997, 23987, 23458, 22733, 115, 66])).
% 29.39/19.60 tff(24052,plain,
% 29.39/19.60 (f5(c1) = c2),
% 29.39/19.60 inference(unit_resolution,[status(thm)],[1708, 24051])).
% 29.39/19.60 tff(24053,plain,
% 29.39/19.60 ($false),
% 29.39/19.60 inference(unit_resolution,[status(thm)],[12775, 1727])).
% 29.39/19.60 tff(24054,plain,((~(f5(c1) = c2)) | (c2 = f5(c1))), inference(lemma,lemma(discharge,[]))).
% 29.39/19.60 tff(24055,plain,
% 29.39/19.60 (c2 = f5(c1)),
% 29.39/19.60 inference(unit_resolution,[status(thm)],[24054, 24052])).
% 29.39/19.60 tff(24056,plain,
% 29.39/19.60 (f7(c1) = f5(c1)),
% 29.39/19.60 inference(modus_ponens,[status(thm)],[24055, 14333])).
% 29.39/19.60 tff(24057,plain,
% 29.39/19.60 (f9(c1, c2) = c2),
% 29.39/19.60 inference(unit_resolution,[status(thm)],[11590, 2907, 115, 3762, 2908, 66])).
% 29.39/19.60 tff(24058,plain,
% 29.39/19.60 (f9(f10(c2), f7(c1)) = f7(c1)),
% 29.39/19.60 inference(transitivity,[status(thm)],[24000, 24057, 2778])).
% 29.39/19.60 tff(24059,plain,
% 29.39/19.60 (f8(f9(f10(c2), f7(c1))) = f8(f7(c1))),
% 29.39/19.60 inference(monotonicity,[status(thm)],[24058])).
% 29.39/19.60 tff(24060,plain,
% 29.39/19.60 ((c1 = f8(f9(f10(c2), f7(c1)))) <=> (c1 = f8(f7(c1)))),
% 29.39/19.60 inference(monotonicity,[status(thm)],[24059])).
% 29.39/19.60 tff(24061,plain,
% 29.39/19.60 ((c1 = f8(f7(c1))) <=> (c1 = f8(f9(f10(c2), f7(c1))))),
% 29.39/19.60 inference(symmetry,[status(thm)],[24060])).
% 29.39/19.60 tff(24062,plain,
% 29.39/19.60 ((c1 = f8(f7(c1))) <=> (f8(f9(f10(c2), f7(c1))) = c1)),
% 29.39/19.60 inference(transitivity,[status(thm)],[24061, 23999])).
% 29.39/19.60 tff(24063,plain,
% 29.39/19.60 ((~(c1 = f8(f7(c1)))) <=> (~(f8(f9(f10(c2), f7(c1))) = c1))),
% 29.39/19.60 inference(monotonicity,[status(thm)],[24062])).
% 29.39/19.60 tff(24064,plain,
% 29.39/19.60 (big_f(f7(c1), f7(c1)) <=> big_f(f7(c1), c2)),
% 29.39/19.60 inference(monotonicity,[status(thm)],[120])).
% 29.39/19.60 tff(24065,plain,
% 29.39/19.60 (big_f(f7(c1), c2) <=> big_f(f7(c1), f7(c1))),
% 29.39/19.60 inference(symmetry,[status(thm)],[24064])).
% 29.39/19.60 tff(24066,plain,
% 29.39/19.60 ((~big_f(f7(c1), c2)) <=> (~big_f(f7(c1), f7(c1)))),
% 29.39/19.60 inference(monotonicity,[status(thm)],[24065])).
% 29.39/19.60 tff(24067,plain,
% 29.39/19.60 (~big_f(f7(c1), f7(c1))),
% 29.39/19.60 inference(modus_ponens,[status(thm)],[2907, 24066])).
% 29.39/19.60 tff(24068,plain,
% 29.39/19.60 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f7(c1) = c1) | big_f(c1, f10(f7(c1))) | (f10(f7(c1)) = f7(c1)) | big_f(f7(c1), f7(c1)) | (~(f7(c1) = f5(c1))) | (~(c1 = f8(f7(c1)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(c1) = c1) | big_f(c1, f10(f7(c1))) | (f10(f7(c1)) = f7(c1)) | big_f(f7(c1), f7(c1)) | (~(f7(c1) = f5(c1))) | (~(c1 = f8(f7(c1)))))),
% 29.39/19.60 inference(rewrite,[status(thm)],[])).
% 29.39/19.60 tff(24069,plain,
% 29.39/19.60 (((~(f7(c1) = f5(c1))) | (f10(f7(c1)) = f7(c1)) | big_f(c1, f10(f7(c1))) | (f7(c1) = c1) | big_f(f7(c1), f7(c1)) | (~(c1 = f8(f7(c1))))) <=> ((f7(c1) = c1) | big_f(c1, f10(f7(c1))) | (f10(f7(c1)) = f7(c1)) | big_f(f7(c1), f7(c1)) | (~(f7(c1) = f5(c1))) | (~(c1 = f8(f7(c1)))))),
% 29.39/19.60 inference(rewrite,[status(thm)],[])).
% 29.39/19.60 tff(24070,plain,
% 29.39/19.60 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(f7(c1) = f5(c1))) | (f10(f7(c1)) = f7(c1)) | big_f(c1, f10(f7(c1))) | (f7(c1) = c1) | big_f(f7(c1), f7(c1)) | (~(c1 = f8(f7(c1)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f7(c1) = c1) | big_f(c1, f10(f7(c1))) | (f10(f7(c1)) = f7(c1)) | big_f(f7(c1), f7(c1)) | (~(f7(c1) = f5(c1))) | (~(c1 = f8(f7(c1))))))),
% 29.39/19.60 inference(monotonicity,[status(thm)],[24069])).
% 29.39/19.60 tff(24071,plain,
% 29.39/19.60 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(f7(c1) = f5(c1))) | (f10(f7(c1)) = f7(c1)) | big_f(c1, f10(f7(c1))) | (f7(c1) = c1) | big_f(f7(c1), f7(c1)) | (~(c1 = f8(f7(c1)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(c1) = c1) | big_f(c1, f10(f7(c1))) | (f10(f7(c1)) = f7(c1)) | big_f(f7(c1), f7(c1)) | (~(f7(c1) = f5(c1))) | (~(c1 = f8(f7(c1)))))),
% 29.39/19.60 inference(transitivity,[status(thm)],[24070, 24068])).
% 29.39/19.60 tff(24072,plain,
% 29.39/19.60 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(f7(c1) = f5(c1))) | (f10(f7(c1)) = f7(c1)) | big_f(c1, f10(f7(c1))) | (f7(c1) = c1) | big_f(f7(c1), f7(c1)) | (~(c1 = f8(f7(c1)))))),
% 29.39/19.60 inference(quant_inst,[status(thm)],[])).
% 29.39/19.60 tff(24073,plain,
% 29.39/19.60 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(c1) = c1) | big_f(c1, f10(f7(c1))) | (f10(f7(c1)) = f7(c1)) | big_f(f7(c1), f7(c1)) | (~(f7(c1) = f5(c1))) | (~(c1 = f8(f7(c1))))),
% 29.39/19.60 inference(modus_ponens,[status(thm)],[24072, 24071])).
% 29.39/19.60 tff(24074,plain,
% 29.39/19.60 (~(c1 = f8(f7(c1)))),
% 29.39/19.60 inference(unit_resolution,[status(thm)],[24073, 1745, 115, 14338, 20254, 24028, 24067])).
% 29.39/19.60 tff(24075,plain,
% 29.39/19.60 (~(f8(f9(f10(c2), f7(c1))) = c1)),
% 29.39/19.60 inference(modus_ponens,[status(thm)],[24074, 24063])).
% 29.39/19.60 tff(24076,plain,
% 29.39/19.60 ((f8(f9(f10(c2), f7(c1))) = c2) <=> (f8(f7(c1)) = f7(c1))),
% 29.39/19.60 inference(monotonicity,[status(thm)],[24059, 2778])).
% 29.39/19.60 tff(24077,plain,
% 29.39/19.60 ((f8(f9(f10(c2), f7(c1))) = c2) <=> (f7(c1) = f8(f7(c1)))),
% 29.39/19.60 inference(transitivity,[status(thm)],[24076, 24038])).
% 29.39/19.60 tff(24078,plain,
% 29.39/19.60 ((f7(c1) = f8(f7(c1))) <=> (f8(f9(f10(c2), f7(c1))) = c2)),
% 29.39/19.60 inference(symmetry,[status(thm)],[24077])).
% 29.39/19.60 tff(24079,plain,
% 29.39/19.60 ((~(f7(c1) = f8(f7(c1)))) <=> (~(f8(f9(f10(c2), f7(c1))) = c2))),
% 29.39/19.60 inference(monotonicity,[status(thm)],[24078])).
% 29.39/19.60 tff(24080,plain,
% 29.39/19.60 (~(f8(f9(f10(c2), f7(c1))) = c2)),
% 29.39/19.60 inference(modus_ponens,[status(thm)],[24043, 24079])).
% 29.39/19.60 tff(24081,plain,
% 29.39/19.60 (f8(f9(f10(c2), f7(c1))) = c1),
% 29.39/19.60 inference(unit_resolution,[status(thm)],[24048, 24080])).
% 29.39/19.60 tff(24082,plain,
% 29.39/19.60 ($false),
% 29.39/19.60 inference(unit_resolution,[status(thm)],[24081, 24075])).
% 29.39/19.60 tff(24083,plain,(big_f(f7(c1), c2) | (~(f10(c2) = c1)) | (f7(c1) = c1) | (~(f7(c1) = f5(c1))) | (f7(c1) = f8(f7(c1))) | (~(f10(c1) = c1)) | (~(c2 = f5(c1))) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 29.39/19.60 tff(24084,plain,
% 29.39/19.60 (~(f7(c1) = f5(c1))),
% 29.39/19.60 inference(unit_resolution,[status(thm)],[24083, 24055, 115, 23987, 1726, 22733, 23997, 66])).
% 29.39/19.60 tff(24085,plain,
% 29.39/19.60 ($false),
% 29.39/19.60 inference(unit_resolution,[status(thm)],[24084, 24056])).
% 29.39/19.60 tff(24086,plain,(big_f(c2, c2) | (f7(c1) = c1) | big_f(c1, c1) | (~(f7(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.39/19.60 tff(24087,plain,
% 29.39/19.60 (big_f(c2, c2)),
% 29.39/19.60 inference(unit_resolution,[status(thm)],[24086, 77, 66, 115])).
% 29.39/19.60 tff(24088,plain,
% 29.39/19.60 (big_f(f7(c1), c2)),
% 29.39/19.60 inference(modus_ponens,[status(thm)],[24087, 1724])).
% 29.39/19.60 tff(24089,plain,
% 29.39/19.60 (~big_f(c2, c1)),
% 29.39/19.60 inference(unit_resolution,[status(thm)],[23932, 24088, 115, 66])).
% 29.39/19.60 tff(24090,plain,
% 29.39/19.60 (~(c1 = f5(c1))),
% 29.39/19.60 inference(unit_resolution,[status(thm)],[13377, 79, 115, 77, 66, 23986, 24089])).
% 29.39/19.60 tff(24091,plain,
% 29.39/19.60 (~(f5(c1) = c1)),
% 29.39/19.60 inference(modus_ponens,[status(thm)],[24090, 2279])).
% 29.39/19.60 tff(24092,plain,
% 29.39/19.60 (f5(c1) = c2),
% 29.39/19.60 inference(unit_resolution,[status(thm)],[1708, 24091])).
% 29.39/19.60 tff(24093,plain,
% 29.39/19.60 (big_f(c1, f10(c2)) <=> big_f(c1, c1)),
% 29.39/19.60 inference(monotonicity,[status(thm)],[23987])).
% 29.39/19.60 tff(24094,plain,
% 29.39/19.60 (big_f(c1, c1) <=> big_f(c1, f10(c2))),
% 29.39/19.60 inference(symmetry,[status(thm)],[24093])).
% 29.39/19.60 tff(24095,plain,
% 29.39/19.60 ((~big_f(c1, c1)) <=> (~big_f(c1, f10(c2)))),
% 29.39/19.60 inference(monotonicity,[status(thm)],[24094])).
% 29.39/19.60 tff(24096,plain,
% 29.39/19.61 (~big_f(c1, f10(c2))),
% 29.39/19.61 inference(modus_ponens,[status(thm)],[66, 24095])).
% 29.39/19.61 tff(24097,plain,
% 29.39/19.61 (f6(c2, c2) = c1),
% 29.39/19.61 inference(transitivity,[status(thm)],[2258, 4049])).
% 29.39/19.61 tff(24098,plain,
% 29.39/19.61 (big_f(f7(c2), f6(c2, c2)) <=> big_f(c2, c1)),
% 29.39/19.61 inference(monotonicity,[status(thm)],[77, 24097])).
% 29.39/19.61 tff(24099,plain,
% 29.39/19.61 (big_f(c2, c1) <=> big_f(f7(c2), f6(c2, c2))),
% 29.39/19.61 inference(symmetry,[status(thm)],[24098])).
% 29.39/19.61 tff(24100,plain,
% 29.39/19.61 ((~big_f(c2, c1)) <=> (~big_f(f7(c2), f6(c2, c2)))),
% 29.39/19.61 inference(monotonicity,[status(thm)],[24099])).
% 29.39/19.61 tff(24101,plain,
% 29.39/19.61 (~big_f(f7(c2), f6(c2, c2))),
% 29.39/19.61 inference(modus_ponens,[status(thm)],[2, 24100])).
% 29.39/19.61 tff(24102,plain,
% 29.39/19.61 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | big_f(c1, f10(c2)) | (~(c1 = f8(c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | big_f(c1, f10(c2)) | (~(c1 = f8(c2))))),
% 29.39/19.61 inference(rewrite,[status(thm)],[])).
% 29.39/19.61 tff(24103,plain,
% 29.39/19.61 (((f10(c2) = c2) | big_f(c1, f10(c2)) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (~(c1 = f8(c2)))) <=> ((f10(c2) = c2) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | big_f(c1, f10(c2)) | (~(c1 = f8(c2))))),
% 29.39/19.61 inference(rewrite,[status(thm)],[])).
% 29.39/19.61 tff(24104,plain,
% 29.39/19.61 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | big_f(c1, f10(c2)) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (~(c1 = f8(c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | big_f(c1, f10(c2)) | (~(c1 = f8(c2)))))),
% 29.39/19.61 inference(monotonicity,[status(thm)],[24103])).
% 29.39/19.61 tff(24105,plain,
% 29.39/19.61 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | big_f(c1, f10(c2)) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (~(c1 = f8(c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | big_f(c1, f10(c2)) | (~(c1 = f8(c2))))),
% 29.39/19.61 inference(transitivity,[status(thm)],[24104, 24102])).
% 29.39/19.61 tff(24106,plain,
% 29.39/19.61 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | big_f(c1, f10(c2)) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (~(c1 = f8(c2))))),
% 29.39/19.61 inference(quant_inst,[status(thm)],[])).
% 29.39/19.61 tff(24107,plain,
% 29.39/19.61 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | big_f(c1, f10(c2)) | (~(c1 = f8(c2)))),
% 29.39/19.61 inference(modus_ponens,[status(thm)],[24106, 24105])).
% 29.39/19.61 tff(24108,plain,
% 29.39/19.61 (big_f(f7(c2), f6(c2, c2)) | (~(c1 = f8(c2)))),
% 29.39/19.61 inference(unit_resolution,[status(thm)],[24107, 2994, 89, 77, 2637, 12055])).
% 29.39/19.61 tff(24109,plain,
% 29.39/19.61 (~(c1 = f8(c2))),
% 29.39/19.61 inference(unit_resolution,[status(thm)],[24108, 24101])).
% 29.39/19.61 tff(24110,plain,
% 29.39/19.61 (~(f8(f7(f4(c4))) = c1)),
% 29.39/19.61 inference(modus_ponens,[status(thm)],[24109, 13365])).
% 29.39/19.61 tff(24111,plain,
% 29.39/19.61 ((~(c2 = f8(f7(f4(c4))))) <=> (~(f8(f7(f4(c4))) = c2))),
% 29.39/19.61 inference(monotonicity,[status(thm)],[106])).
% 29.39/19.61 tff(24112,plain,
% 29.39/19.61 ((f6(c2, f7(f4(c4))) = f7(f4(c4))) <=> (f6(c2, f7(f4(c4))) = c2)),
% 29.39/19.61 inference(monotonicity,[status(thm)],[2474])).
% 29.39/19.61 tff(24113,plain,
% 29.39/19.61 ((f6(c2, f7(f4(c4))) = c2) <=> (f6(c2, f7(f4(c4))) = f7(f4(c4)))),
% 29.39/19.61 inference(symmetry,[status(thm)],[24112])).
% 29.39/19.61 tff(24114,plain,
% 29.39/19.61 ((f6(c2, f7(f4(c4))) = c2) <=> (f6(c2, c2) = c2)),
% 29.39/19.61 inference(monotonicity,[status(thm)],[2475])).
% 29.39/19.61 tff(24115,plain,
% 29.39/19.61 ((f6(c2, c2) = c2) <=> (f6(c2, f7(f4(c4))) = c2)),
% 29.39/19.61 inference(symmetry,[status(thm)],[24114])).
% 29.39/19.61 tff(24116,plain,
% 29.39/19.61 ((f6(c2, c2) = c2) <=> (f6(c2, f7(f4(c4))) = f7(f4(c4)))),
% 29.39/19.61 inference(transitivity,[status(thm)],[24115, 24113])).
% 29.39/19.61 tff(24117,plain,
% 29.39/19.61 ((~(f6(c2, c2) = c2)) <=> (~(f6(c2, f7(f4(c4))) = f7(f4(c4))))),
% 29.39/19.61 inference(monotonicity,[status(thm)],[24116])).
% 29.39/19.61 tff(24118,plain,
% 29.39/19.61 (~(f6(c2, f7(f4(c4))) = f7(f4(c4)))),
% 29.39/19.61 inference(modus_ponens,[status(thm)],[2637, 24117])).
% 29.39/19.61 tff(24119,plain,
% 29.39/19.61 (f10(f7(c2)) = c1),
% 29.39/19.61 inference(transitivity,[status(thm)],[95, 94])).
% 29.39/19.61 tff(24120,plain,
% 29.39/19.61 ((f10(f7(c2)) = f7(c2)) <=> (c1 = c2)),
% 29.39/19.61 inference(monotonicity,[status(thm)],[24119, 77])).
% 29.39/19.61 tff(24121,plain,
% 29.39/19.61 ((f10(f7(c2)) = f7(c2)) <=> (c2 = c1)),
% 29.39/19.61 inference(transitivity,[status(thm)],[24120, 1])).
% 29.39/19.61 tff(24122,plain,
% 29.39/19.61 ((c2 = c1) <=> (f10(f7(c2)) = f7(c2))),
% 29.39/19.61 inference(symmetry,[status(thm)],[24121])).
% 29.39/19.61 tff(24123,plain,
% 29.39/19.61 ((c2 = c1) <=> (f10(f7(f4(c4))) = f7(f4(c4)))),
% 29.39/19.61 inference(transitivity,[status(thm)],[24122, 14129])).
% 29.39/19.61 tff(24124,plain,
% 29.39/19.61 ((~(c2 = c1)) <=> (~(f10(f7(f4(c4))) = f7(f4(c4))))),
% 29.39/19.61 inference(monotonicity,[status(thm)],[24123])).
% 29.39/19.61 tff(24125,plain,
% 29.39/19.61 (~(f10(f7(f4(c4))) = f7(f4(c4)))),
% 29.39/19.61 inference(modus_ponens,[status(thm)],[75, 24124])).
% 29.39/19.61 tff(24126,plain,
% 29.39/19.61 (big_f(c2, f10(f7(f4(c4)))) <=> big_f(c2, f10(f7(c2)))),
% 29.39/19.61 inference(monotonicity,[status(thm)],[12113])).
% 29.39/19.61 tff(24127,plain,
% 29.39/19.61 (big_f(c2, f10(f7(c2))) <=> big_f(c2, f10(f7(f4(c4))))),
% 29.39/19.61 inference(symmetry,[status(thm)],[24126])).
% 29.39/19.61 tff(24128,plain,
% 29.39/19.61 (big_f(c2, f10(f7(c2))) <=> big_f(c2, c1)),
% 29.39/19.61 inference(monotonicity,[status(thm)],[24119])).
% 29.39/19.61 tff(24129,plain,
% 29.39/19.61 (big_f(c2, c1) <=> big_f(c2, f10(f7(c2)))),
% 29.39/19.61 inference(symmetry,[status(thm)],[24128])).
% 29.39/19.61 tff(24130,plain,
% 29.39/19.61 (big_f(c2, c1) <=> big_f(c2, f10(f7(f4(c4))))),
% 29.39/19.61 inference(transitivity,[status(thm)],[24129, 24127])).
% 29.39/19.61 tff(24131,plain,
% 29.39/19.61 ((~big_f(c2, c1)) <=> (~big_f(c2, f10(f7(f4(c4)))))),
% 29.39/19.61 inference(monotonicity,[status(thm)],[24130])).
% 29.39/19.61 tff(24132,plain,
% 29.39/19.61 (~big_f(c2, f10(f7(f4(c4))))),
% 29.39/19.61 inference(modus_ponens,[status(thm)],[2, 24131])).
% 29.39/19.61 tff(24133,plain,
% 29.39/19.61 (big_f(f7(c2), f6(c2, c2)) <=> big_f(f7(c2), f6(c2, f7(f4(c4))))),
% 29.39/19.61 inference(symmetry,[status(thm)],[2476])).
% 29.39/19.61 tff(24134,plain,
% 29.39/19.61 (big_f(c2, c1) <=> big_f(f7(c2), f6(c2, f7(f4(c4))))),
% 29.39/19.61 inference(transitivity,[status(thm)],[24099, 24133])).
% 29.39/19.61 tff(24135,plain,
% 29.39/19.61 ((~big_f(c2, c1)) <=> (~big_f(f7(c2), f6(c2, f7(f4(c4)))))),
% 29.39/19.61 inference(monotonicity,[status(thm)],[24134])).
% 29.39/19.61 tff(24136,plain,
% 29.39/19.61 (~big_f(f7(c2), f6(c2, f7(f4(c4))))),
% 29.39/19.61 inference(modus_ponens,[status(thm)],[2, 24135])).
% 29.39/19.61 tff(24137,plain,
% 29.39/19.61 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((~(f7(c2) = c2)) | (f10(f7(f4(c4))) = f7(f4(c4))) | big_f(c2, f10(f7(f4(c4)))) | (f6(c2, f7(f4(c4))) = f7(f4(c4))) | big_f(f7(c2), f6(c2, f7(f4(c4)))) | (~(c2 = f8(f7(f4(c4))))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (~(f7(c2) = c2)) | (f10(f7(f4(c4))) = f7(f4(c4))) | big_f(c2, f10(f7(f4(c4)))) | (f6(c2, f7(f4(c4))) = f7(f4(c4))) | big_f(f7(c2), f6(c2, f7(f4(c4)))) | (~(c2 = f8(f7(f4(c4))))))),
% 29.39/19.61 inference(rewrite,[status(thm)],[])).
% 29.39/19.61 tff(24138,plain,
% 29.39/19.61 (((f10(f7(f4(c4))) = f7(f4(c4))) | big_f(c2, f10(f7(f4(c4)))) | (~(f7(c2) = c2)) | (f6(c2, f7(f4(c4))) = f7(f4(c4))) | big_f(f7(c2), f6(c2, f7(f4(c4)))) | (~(c2 = f8(f7(f4(c4)))))) <=> ((~(f7(c2) = c2)) | (f10(f7(f4(c4))) = f7(f4(c4))) | big_f(c2, f10(f7(f4(c4)))) | (f6(c2, f7(f4(c4))) = f7(f4(c4))) | big_f(f7(c2), f6(c2, f7(f4(c4)))) | (~(c2 = f8(f7(f4(c4))))))),
% 29.39/19.61 inference(rewrite,[status(thm)],[])).
% 29.39/19.61 tff(24139,plain,
% 29.39/19.61 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(f7(f4(c4))) = f7(f4(c4))) | big_f(c2, f10(f7(f4(c4)))) | (~(f7(c2) = c2)) | (f6(c2, f7(f4(c4))) = f7(f4(c4))) | big_f(f7(c2), f6(c2, f7(f4(c4)))) | (~(c2 = f8(f7(f4(c4))))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((~(f7(c2) = c2)) | (f10(f7(f4(c4))) = f7(f4(c4))) | big_f(c2, f10(f7(f4(c4)))) | (f6(c2, f7(f4(c4))) = f7(f4(c4))) | big_f(f7(c2), f6(c2, f7(f4(c4)))) | (~(c2 = f8(f7(f4(c4)))))))),
% 29.39/19.61 inference(monotonicity,[status(thm)],[24138])).
% 29.39/19.61 tff(24140,plain,
% 29.39/19.61 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(f7(f4(c4))) = f7(f4(c4))) | big_f(c2, f10(f7(f4(c4)))) | (~(f7(c2) = c2)) | (f6(c2, f7(f4(c4))) = f7(f4(c4))) | big_f(f7(c2), f6(c2, f7(f4(c4)))) | (~(c2 = f8(f7(f4(c4))))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (~(f7(c2) = c2)) | (f10(f7(f4(c4))) = f7(f4(c4))) | big_f(c2, f10(f7(f4(c4)))) | (f6(c2, f7(f4(c4))) = f7(f4(c4))) | big_f(f7(c2), f6(c2, f7(f4(c4)))) | (~(c2 = f8(f7(f4(c4))))))),
% 29.39/19.61 inference(transitivity,[status(thm)],[24139, 24137])).
% 29.39/19.61 tff(24141,plain,
% 29.39/19.61 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(f7(f4(c4))) = f7(f4(c4))) | big_f(c2, f10(f7(f4(c4)))) | (~(f7(c2) = c2)) | (f6(c2, f7(f4(c4))) = f7(f4(c4))) | big_f(f7(c2), f6(c2, f7(f4(c4)))) | (~(c2 = f8(f7(f4(c4))))))),
% 29.39/19.61 inference(quant_inst,[status(thm)],[])).
% 29.39/19.61 tff(24142,plain,
% 29.39/19.61 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (~(f7(c2) = c2)) | (f10(f7(f4(c4))) = f7(f4(c4))) | big_f(c2, f10(f7(f4(c4)))) | (f6(c2, f7(f4(c4))) = f7(f4(c4))) | big_f(f7(c2), f6(c2, f7(f4(c4)))) | (~(c2 = f8(f7(f4(c4)))))),
% 29.39/19.61 inference(modus_ponens,[status(thm)],[24141, 24140])).
% 29.39/19.61 tff(24143,plain,
% 29.39/19.61 ((~(f7(c2) = c2)) | (f10(f7(f4(c4))) = f7(f4(c4))) | big_f(c2, f10(f7(f4(c4)))) | (f6(c2, f7(f4(c4))) = f7(f4(c4))) | big_f(f7(c2), f6(c2, f7(f4(c4)))) | (~(c2 = f8(f7(f4(c4)))))),
% 29.39/19.61 inference(unit_resolution,[status(thm)],[24142, 2994])).
% 29.39/19.61 tff(24144,plain,
% 29.39/19.61 (~(c2 = f8(f7(f4(c4))))),
% 29.39/19.61 inference(unit_resolution,[status(thm)],[24143, 24136, 77, 24132, 24125, 24118])).
% 29.39/19.61 tff(24145,plain,
% 29.39/19.61 (~(f8(f7(f4(c4))) = c2)),
% 29.39/19.61 inference(modus_ponens,[status(thm)],[24144, 24111])).
% 29.39/19.61 tff(24146,plain,
% 29.39/19.61 ($false),
% 29.39/19.61 inference(unit_resolution,[status(thm)],[13371, 24145, 24110])).
% 29.39/19.61 tff(24147,plain,((f6(c2, c2) = c2) | (~(f7(c2) = c2)) | (~(f4(c4) = c2)) | (f10(c2) = c2) | big_f(c1, f10(c2)) | big_f(c2, c1) | (~(f5(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.39/19.61 tff(24148,plain,
% 29.39/19.61 (f6(c2, c2) = c2),
% 29.39/19.61 inference(unit_resolution,[status(thm)],[24147, 24092, 77, 23986, 24096, 24089, 79])).
% 29.39/19.61 tff(24149,plain,
% 29.39/19.61 (big_f(f7(c2), f6(c2, c2))),
% 29.39/19.61 inference(unit_resolution,[status(thm)],[2627, 24148, 77, 24087])).
% 29.39/19.61 tff(24150,plain,
% 29.39/19.61 (f6(c2, c2) = c1),
% 29.39/19.61 inference(transitivity,[status(thm)],[2258, 2947])).
% 29.39/19.61 tff(24151,plain,
% 29.39/19.61 (big_f(f7(c2), f6(c2, c2)) <=> big_f(c2, c1)),
% 29.39/19.61 inference(monotonicity,[status(thm)],[77, 24150])).
% 29.39/19.61 tff(24152,plain,
% 29.39/19.61 (big_f(c2, c1) <=> big_f(f7(c2), f6(c2, c2))),
% 29.39/19.61 inference(symmetry,[status(thm)],[24151])).
% 29.39/19.61 tff(24153,plain,
% 29.39/19.61 ((~big_f(c2, c1)) <=> (~big_f(f7(c2), f6(c2, c2)))),
% 29.39/19.61 inference(monotonicity,[status(thm)],[24152])).
% 29.39/19.61 tff(24154,plain,
% 29.39/19.61 (~big_f(f7(c2), f6(c2, c2))),
% 29.39/19.61 inference(modus_ponens,[status(thm)],[2, 24153])).
% 29.39/19.61 tff(24155,plain,
% 29.39/19.61 ($false),
% 29.39/19.61 inference(unit_resolution,[status(thm)],[2707, 24154])).
% 29.39/19.61 tff(24156,plain,((~(f6(f7(c2), f5(c1)) = c1)) | (~big_f(f7(c2), f6(c2, c2))) | big_f(c2, c1) | (~(f5(c1) = c2)) | (~(f7(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.39/19.61 tff(24157,plain,
% 29.39/19.61 (~(f6(f7(c2), f5(c1)) = c1)),
% 29.39/19.61 inference(unit_resolution,[status(thm)],[24156, 24149, 77, 24089, 24092])).
% 29.39/19.61 tff(24158,plain,
% 29.39/19.61 (f6(f7(c2), f5(c1)) = c2),
% 29.39/19.61 inference(unit_resolution,[status(thm)],[2978, 24157])).
% 29.39/19.61 tff(24159,plain,
% 29.39/19.61 (c2 = f5(c1)),
% 29.39/19.61 inference(symmetry,[status(thm)],[24092])).
% 29.39/19.61 tff(24160,plain,
% 29.39/19.61 (f6(c2, c2) = f6(f7(c2), f5(c1))),
% 29.39/19.61 inference(monotonicity,[status(thm)],[82, 24159])).
% 29.39/19.61 tff(24161,plain,
% 29.39/19.61 (f6(c2, f7(f4(c4))) = c2),
% 29.39/19.61 inference(transitivity,[status(thm)],[2475, 24160, 24158])).
% 29.39/19.61 tff(24162,plain,
% 29.39/19.61 (f8(f6(c2, f7(f4(c4)))) = f8(c2)),
% 29.39/19.61 inference(monotonicity,[status(thm)],[24161])).
% 29.39/19.61 tff(24163,plain,
% 29.39/19.61 ((c2 = f8(f6(c2, f7(f4(c4))))) <=> (c2 = f8(c2))),
% 29.39/19.61 inference(monotonicity,[status(thm)],[24162])).
% 29.39/19.61 tff(24164,plain,
% 29.39/19.61 ((c2 = f8(c2)) <=> (c2 = f8(f6(c2, f7(f4(c4)))))),
% 29.39/19.61 inference(symmetry,[status(thm)],[24163])).
% 29.39/19.61 tff(24165,plain,
% 29.39/19.61 ((c2 = f8(c2)) <=> (f8(f6(c2, f7(f4(c4)))) = c2)),
% 29.39/19.61 inference(transitivity,[status(thm)],[24164, 23360])).
% 29.39/19.61 tff(24166,plain,
% 29.39/19.61 ((~(c2 = f8(c2))) <=> (~(f8(f6(c2, f7(f4(c4)))) = c2))),
% 29.39/19.61 inference(monotonicity,[status(thm)],[24165])).
% 29.39/19.61 tff(24167,plain,
% 29.39/19.61 (~big_f(c2, f10(c2))),
% 29.39/19.61 inference(modus_ponens,[status(thm)],[24089, 23994])).
% 29.39/19.61 tff(24168,plain,
% 29.39/19.61 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (~(f7(c2) = c2)) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))),
% 29.39/19.61 inference(rewrite,[status(thm)],[])).
% 29.39/19.61 tff(24169,plain,
% 29.39/19.61 (((f10(c2) = c2) | big_f(c2, f10(c2)) | (~(f7(c2) = c2)) | (~(c2 = f8(c2))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2)))) <=> ((f10(c2) = c2) | (~(f7(c2) = c2)) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))),
% 29.39/19.61 inference(rewrite,[status(thm)],[])).
% 29.39/19.61 tff(24170,plain,
% 29.39/19.61 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | big_f(c2, f10(c2)) | (~(f7(c2) = c2)) | (~(c2 = f8(c2))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (~(f7(c2) = c2)) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2)))))),
% 29.39/19.61 inference(monotonicity,[status(thm)],[24169])).
% 29.39/19.61 tff(24171,plain,
% 29.39/19.61 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | big_f(c2, f10(c2)) | (~(f7(c2) = c2)) | (~(c2 = f8(c2))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))),
% 29.39/19.61 inference(transitivity,[status(thm)],[24170, 24168])).
% 29.39/19.61 tff(24172,plain,
% 29.39/19.61 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | big_f(c2, f10(c2)) | (~(f7(c2) = c2)) | (~(c2 = f8(c2))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))),
% 29.39/19.61 inference(quant_inst,[status(thm)],[])).
% 29.39/19.61 tff(24173,plain,
% 29.39/19.61 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2)))),
% 29.39/19.61 inference(modus_ponens,[status(thm)],[24172, 24171])).
% 29.39/19.61 tff(24174,plain,
% 29.39/19.61 (~(c2 = f8(c2))),
% 29.39/19.61 inference(unit_resolution,[status(thm)],[24173, 2963, 23986, 77, 24167, 24148, 24149])).
% 29.39/19.61 tff(24175,plain,
% 29.39/19.61 (~(f8(f6(c2, f7(f4(c4)))) = c2)),
% 29.39/19.61 inference(modus_ponens,[status(thm)],[24174, 24166])).
% 29.39/19.61 tff(24176,plain,
% 29.39/19.61 ((f8(f6(c2, f7(f4(c4)))) = c1) <=> (c1 = f8(f6(c2, f7(f4(c4)))))),
% 29.39/19.61 inference(commutativity,[status(thm)],[])).
% 29.39/19.61 tff(24177,plain,
% 29.39/19.61 ((c1 = f8(f6(c2, f7(f4(c4))))) <=> (f8(f6(c2, f7(f4(c4)))) = c1)),
% 29.39/19.61 inference(symmetry,[status(thm)],[24176])).
% 29.39/19.61 tff(24178,plain,
% 29.39/19.61 ((c1 = f8(f6(c2, f7(f4(c4))))) <=> (c1 = f8(c2))),
% 29.39/19.61 inference(monotonicity,[status(thm)],[24162])).
% 29.39/19.61 tff(24179,plain,
% 29.39/19.61 ((c1 = f8(c2)) <=> (c1 = f8(f6(c2, f7(f4(c4)))))),
% 29.39/19.61 inference(symmetry,[status(thm)],[24178])).
% 29.39/19.61 tff(24180,plain,
% 29.39/19.61 ((c1 = f8(c2)) <=> (f8(f6(c2, f7(f4(c4)))) = c1)),
% 29.39/19.61 inference(transitivity,[status(thm)],[24179, 24177])).
% 29.39/19.61 tff(24181,plain,
% 29.39/19.61 ((~(c1 = f8(c2))) <=> (~(f8(f6(c2, f7(f4(c4)))) = c1))),
% 29.39/19.61 inference(monotonicity,[status(thm)],[24180])).
% 29.39/19.61 tff(24182,plain,
% 29.39/19.61 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | big_f(c1, f10(c2)) | (~(c1 = f8(c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | big_f(c1, f10(c2)) | (~(c1 = f8(c2))))),
% 29.39/19.61 inference(rewrite,[status(thm)],[])).
% 29.39/19.61 tff(24183,plain,
% 29.39/19.61 (((f10(c2) = c2) | big_f(c1, f10(c2)) | (~(f7(c2) = c2)) | (~(c1 = f8(c2))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2)))) <=> ((f10(c2) = c2) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | big_f(c1, f10(c2)) | (~(c1 = f8(c2))))),
% 29.39/19.61 inference(rewrite,[status(thm)],[])).
% 29.39/19.61 tff(24184,plain,
% 29.39/19.61 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | big_f(c1, f10(c2)) | (~(f7(c2) = c2)) | (~(c1 = f8(c2))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | big_f(c1, f10(c2)) | (~(c1 = f8(c2)))))),
% 29.39/19.61 inference(monotonicity,[status(thm)],[24183])).
% 29.39/19.61 tff(24185,plain,
% 29.39/19.61 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | big_f(c1, f10(c2)) | (~(f7(c2) = c2)) | (~(c1 = f8(c2))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | big_f(c1, f10(c2)) | (~(c1 = f8(c2))))),
% 29.39/19.61 inference(transitivity,[status(thm)],[24184, 24182])).
% 29.39/19.61 tff(24186,plain,
% 29.39/19.61 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | big_f(c1, f10(c2)) | (~(f7(c2) = c2)) | (~(c1 = f8(c2))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))),
% 29.39/19.61 inference(quant_inst,[status(thm)],[])).
% 29.39/19.61 tff(24187,plain,
% 29.39/19.61 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | big_f(c1, f10(c2)) | (~(c1 = f8(c2)))),
% 29.39/19.61 inference(modus_ponens,[status(thm)],[24186, 24185])).
% 29.39/19.61 tff(24188,plain,
% 29.39/19.61 (~(c1 = f8(c2))),
% 29.39/19.61 inference(unit_resolution,[status(thm)],[24187, 2963, 23986, 77, 24148, 24149, 24096])).
% 29.39/19.61 tff(24189,plain,
% 29.39/19.61 (~(f8(f6(c2, f7(f4(c4)))) = c1)),
% 29.39/19.61 inference(modus_ponens,[status(thm)],[24188, 24181])).
% 29.39/19.61 tff(24190,plain,
% 29.39/19.61 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f8(f6(c2, f7(f4(c4)))) = c1) | (f8(f6(c2, f7(f4(c4)))) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f8(f6(c2, f7(f4(c4)))) = c1) | (f8(f6(c2, f7(f4(c4)))) = c2))),
% 29.39/19.61 inference(rewrite,[status(thm)],[])).
% 29.39/19.61 tff(24191,plain,
% 29.39/19.61 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f8(f6(c2, f7(f4(c4)))) = c1) | (f8(f6(c2, f7(f4(c4)))) = c2))),
% 29.39/19.61 inference(quant_inst,[status(thm)],[])).
% 29.39/19.61 tff(24192,plain,
% 29.39/19.61 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f8(f6(c2, f7(f4(c4)))) = c1) | (f8(f6(c2, f7(f4(c4)))) = c2)),
% 29.39/19.61 inference(modus_ponens,[status(thm)],[24191, 24190])).
% 29.39/19.61 tff(24193,plain,
% 29.39/19.61 ((f8(f6(c2, f7(f4(c4)))) = c1) | (f8(f6(c2, f7(f4(c4)))) = c2)),
% 29.39/19.61 inference(unit_resolution,[status(thm)],[24192, 10])).
% 29.39/19.61 tff(24194,plain,
% 29.39/19.61 ($false),
% 29.39/19.61 inference(unit_resolution,[status(thm)],[24193, 24189, 24175])).
% 29.39/19.61 tff(24195,plain,((~(f4(c4) = c2)) | (~(f7(c2) = c2)) | (f7(c1) = c1) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 29.39/19.61 tff(24196,plain,
% 29.39/19.61 (~(f4(c4) = c2)),
% 29.39/19.61 inference(unit_resolution,[status(thm)],[24195, 77, 115, 66])).
% 29.39/19.61 tff(24197,plain,
% 29.39/19.61 (f4(c4) = c1),
% 29.39/19.61 inference(unit_resolution,[status(thm)],[11750, 24196])).
% 29.39/19.61 tff(24198,plain,
% 29.39/19.61 (f7(f4(c4)) = f7(c1)),
% 29.39/19.61 inference(monotonicity,[status(thm)],[24197])).
% 29.39/19.61 tff(24199,plain,
% 29.39/19.61 (f7(c1) = f7(f4(c4))),
% 29.39/19.61 inference(symmetry,[status(thm)],[24198])).
% 29.39/19.61 tff(24200,plain,
% 29.39/19.61 (c2 = f7(f4(c4))),
% 29.39/19.61 inference(transitivity,[status(thm)],[2778, 24199])).
% 29.39/19.61 tff(24201,plain,
% 29.39/19.61 (f8(c2) = f8(f7(f4(c4)))),
% 29.39/19.61 inference(monotonicity,[status(thm)],[24200])).
% 29.39/19.61 tff(24202,plain,
% 29.39/19.61 (f8(f7(f4(c4))) = f8(c2)),
% 29.39/19.61 inference(symmetry,[status(thm)],[24201])).
% 29.39/19.61 tff(24203,plain,
% 29.39/19.61 (c1 = f8(c2)),
% 29.39/19.61 inference(modus_ponens,[status(thm)],[16268, 21568])).
% 29.39/19.61 tff(24204,plain,
% 29.39/19.61 (big_f(c1, f10(c2)) <=> big_f(c1, c1)),
% 29.39/19.61 inference(monotonicity,[status(thm)],[94])).
% 29.39/19.61 tff(24205,plain,
% 29.39/19.61 (big_f(c1, c1) <=> big_f(c1, f10(c2))),
% 29.39/19.61 inference(symmetry,[status(thm)],[24204])).
% 29.39/19.61 tff(24206,plain,
% 29.39/19.61 ((~big_f(c1, c1)) <=> (~big_f(c1, f10(c2)))),
% 29.39/19.61 inference(monotonicity,[status(thm)],[24205])).
% 29.39/19.61 tff(24207,plain,
% 29.39/19.61 (~big_f(c1, f10(c2))),
% 29.39/19.61 inference(modus_ponens,[status(thm)],[66, 24206])).
% 29.39/19.61 tff(24208,plain,
% 29.39/19.61 (big_f(f8(f7(f4(c4))), f10(c2)) <=> big_f(c1, c1)),
% 29.39/19.61 inference(monotonicity,[status(thm)],[16268, 94])).
% 29.39/19.61 tff(24209,plain,
% 29.39/19.61 (big_f(c1, c1) <=> big_f(f8(f7(f4(c4))), f10(c2))),
% 29.39/19.61 inference(symmetry,[status(thm)],[24208])).
% 29.39/19.61 tff(24210,plain,
% 29.39/19.61 ((~big_f(c1, c1)) <=> (~big_f(f8(f7(f4(c4))), f10(c2)))),
% 29.39/19.61 inference(monotonicity,[status(thm)],[24209])).
% 29.39/19.61 tff(24211,plain,
% 29.39/19.61 (~big_f(f8(f7(f4(c4))), f10(c2))),
% 29.39/19.61 inference(modus_ponens,[status(thm)],[66, 24210])).
% 29.39/19.61 tff(24212,assumption,(f8(f7(f4(c4))) = f8(c2)), introduced(assumption)).
% 29.39/19.61 tff(24213,assumption,(~big_f(f8(f7(f4(c4))), f10(c2))), introduced(assumption)).
% 29.39/19.61 tff(24214,plain,
% 29.39/19.61 (big_f(f7(c2), f6(c2, c2))),
% 29.39/19.61 inference(unit_resolution,[status(thm)],[2627, 2622, 1345, 77])).
% 29.39/19.61 tff(24215,plain,
% 29.39/19.61 ($false),
% 29.39/19.61 inference(unit_resolution,[status(thm)],[15287, 24214, 2622, 89, 77, 24213, 24212])).
% 29.39/19.61 tff(24216,plain,((~(f6(c2, c2) = c2)) | (f10(c2) = c2) | (~(f7(c2) = c2)) | big_f(f8(f7(f4(c4))), f10(c2)) | (~(f8(f7(f4(c4))) = f8(c2))) | (~big_f(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 29.39/19.61 tff(24217,plain,
% 29.39/19.61 (~(f6(c2, c2) = c2)),
% 29.39/19.61 inference(unit_resolution,[status(thm)],[24216, 24211, 77, 89, 16247, 1345])).
% 29.39/19.61 tff(24218,plain,
% 29.39/19.61 (~(f6(c2, f7(f4(c4))) = c2)),
% 29.39/19.61 inference(unit_resolution,[status(thm)],[17412, 24217, 347, 11752])).
% 29.39/19.61 tff(24219,plain,
% 29.39/19.61 (f6(c2, f7(f4(c4))) = c1),
% 29.39/19.61 inference(unit_resolution,[status(thm)],[6601, 24218])).
% 29.39/19.61 tff(24220,plain,
% 29.39/19.61 (f6(c2, c2) = c1),
% 29.39/19.61 inference(transitivity,[status(thm)],[21473, 24219])).
% 29.39/19.61 tff(24221,plain,
% 29.39/19.61 (big_f(f7(c2), f6(c2, c2)) <=> big_f(c2, c1)),
% 29.39/19.61 inference(monotonicity,[status(thm)],[77, 24220])).
% 29.39/19.61 tff(24222,plain,
% 29.39/19.61 (big_f(c2, c1) <=> big_f(f7(c2), f6(c2, c2))),
% 29.39/19.61 inference(symmetry,[status(thm)],[24221])).
% 29.39/19.61 tff(24223,plain,
% 29.39/19.61 ((~big_f(c2, c1)) <=> (~big_f(f7(c2), f6(c2, c2)))),
% 29.39/19.61 inference(monotonicity,[status(thm)],[24222])).
% 29.39/19.61 tff(24224,plain,
% 29.39/19.61 (~big_f(f7(c2), f6(c2, c2))),
% 29.39/19.61 inference(modus_ponens,[status(thm)],[2, 24223])).
% 29.39/19.61 tff(24225,plain,
% 29.39/19.61 ($false),
% 29.39/19.61 inference(unit_resolution,[status(thm)],[24107, 2994, 89, 77, 24217, 24224, 24207, 24203])).
% 29.39/19.61 tff(24226,plain,((~(f8(f7(f4(c4))) = c1)) | (f10(c2) = c2) | (~(f7(c2) = c2)) | big_f(c2, c1) | (~(f7(c1) = c2)) | (~(f4(c4) = c1)) | (~big_f(c2, c2)) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 29.39/19.61 tff(24227,plain,
% 29.39/19.61 (~(f8(f7(f4(c4))) = c1)),
% 29.39/19.61 inference(unit_resolution,[status(thm)],[24226, 23986, 77, 24089, 120, 24197, 24087, 66])).
% 29.39/19.61 tff(24228,plain,
% 29.39/19.61 (f8(f7(f4(c4))) = c2),
% 29.39/19.61 inference(unit_resolution,[status(thm)],[13371, 24227])).
% 29.39/19.61 tff(24229,plain,
% 29.39/19.61 (big_f(f8(f7(f4(c4))), f10(c2)) <=> big_f(c2, c1)),
% 29.39/19.61 inference(monotonicity,[status(thm)],[24228, 23987])).
% 29.39/19.61 tff(24230,plain,
% 29.39/19.61 (big_f(c2, c1) <=> big_f(f8(f7(f4(c4))), f10(c2))),
% 29.39/19.61 inference(symmetry,[status(thm)],[24229])).
% 29.39/19.61 tff(24231,plain,
% 29.39/19.61 ((~big_f(c2, c1)) <=> (~big_f(f8(f7(f4(c4))), f10(c2)))),
% 29.39/19.61 inference(monotonicity,[status(thm)],[24230])).
% 29.39/19.61 tff(24232,plain,
% 29.39/19.61 (~big_f(f8(f7(f4(c4))), f10(c2))),
% 29.39/19.61 inference(modus_ponens,[status(thm)],[24089, 24231])).
% 29.39/19.61 tff(24233,plain,
% 29.39/19.61 (~(f6(c2, c2) = c2)),
% 29.39/19.61 inference(unit_resolution,[status(thm)],[24216, 24232, 77, 23986, 24202, 24087])).
% 29.39/19.61 tff(24234,plain,
% 29.39/19.61 (~(f6(c2, f7(f4(c4))) = c2)),
% 29.39/19.61 inference(unit_resolution,[status(thm)],[17412, 24233, 120, 24197])).
% 29.39/19.61 tff(24235,plain,
% 29.39/19.61 (f6(c2, f7(f4(c4))) = c1),
% 29.39/19.61 inference(unit_resolution,[status(thm)],[6601, 24234])).
% 29.39/19.61 tff(24236,plain,
% 29.39/19.61 (f6(c2, c2) = f6(c2, f7(f4(c4)))),
% 29.39/19.61 inference(monotonicity,[status(thm)],[24200])).
% 29.39/19.61 tff(24237,plain,
% 29.39/19.61 (f6(c2, c2) = c1),
% 29.39/19.61 inference(transitivity,[status(thm)],[24236, 24235])).
% 29.39/19.61 tff(24238,plain,
% 29.39/19.61 (big_f(f7(c2), f6(c2, c2)) <=> big_f(c2, c1)),
% 29.39/19.61 inference(monotonicity,[status(thm)],[77, 24237])).
% 29.39/19.61 tff(24239,plain,
% 29.39/19.61 (big_f(c2, c1) <=> big_f(f7(c2), f6(c2, c2))),
% 29.39/19.61 inference(symmetry,[status(thm)],[24238])).
% 29.39/19.61 tff(24240,plain,
% 29.39/19.61 ((~big_f(c2, c1)) <=> (~big_f(f7(c2), f6(c2, c2)))),
% 29.39/19.61 inference(monotonicity,[status(thm)],[24239])).
% 29.39/19.61 tff(24241,plain,
% 29.39/19.61 (~big_f(f7(c2), f6(c2, c2))),
% 29.39/19.61 inference(modus_ponens,[status(thm)],[24089, 24240])).
% 29.39/19.61 tff(24242,plain,
% 29.39/19.61 (c2 = f8(c2)),
% 29.39/19.61 inference(unit_resolution,[status(thm)],[17582, 24228, 120, 24197])).
% 29.39/19.61 tff(24243,plain,
% 29.39/19.61 ($false),
% 29.39/19.61 inference(unit_resolution,[status(thm)],[14124, 2994, 23986, 77, 24167, 24242, 24233, 24241])).
% 29.39/19.61 tff(24244,plain,((~(f7(c2) = c2)) | big_f(c1, c1) | (f7(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.39/19.61 tff(24245,plain,
% 29.39/19.61 (~(f7(c2) = c2)),
% 29.39/19.61 inference(unit_resolution,[status(thm)],[24244, 66, 115])).
% 29.39/19.61 tff(24246,plain,
% 29.39/19.61 (f7(c1) = c1),
% 29.39/19.61 inference(unit_resolution,[status(thm)],[21431, 3, 17])).
% 29.39/19.61 tff(24247,plain,
% 29.39/19.61 (big_f(c1, c2) <=> big_f(c1, f10(c1))),
% 29.39/19.61 inference(monotonicity,[status(thm)],[5571])).
% 29.39/19.61 tff(24248,plain,
% 29.39/19.61 (~(c2 = f5(c2))),
% 29.39/19.61 inference(unit_resolution,[status(thm)],[21159, 13152])).
% 29.39/19.61 tff(24249,plain,
% 29.39/19.61 (~(f5(c2) = c2)),
% 29.39/19.62 inference(unit_resolution,[status(thm)],[8113, 24248])).
% 29.39/19.62 tff(24250,plain,
% 29.39/19.62 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | (f7(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (~(c1 = f5(c2))) | big_f(f7(c2), c1))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | (f7(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (~(c1 = f5(c2))) | big_f(f7(c2), c1))),
% 29.39/19.62 inference(rewrite,[status(thm)],[])).
% 29.39/19.62 tff(24251,plain,
% 29.39/19.62 (((~(c1 = f5(c2))) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), c1) | (~(c2 = f8(c2)))) <=> ((f10(c2) = c2) | (f7(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (~(c1 = f5(c2))) | big_f(f7(c2), c1))),
% 29.39/19.62 inference(rewrite,[status(thm)],[])).
% 29.39/19.62 tff(24252,plain,
% 29.39/19.62 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c1 = f5(c2))) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), c1) | (~(c2 = f8(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | (f7(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (~(c1 = f5(c2))) | big_f(f7(c2), c1)))),
% 29.39/19.62 inference(monotonicity,[status(thm)],[24251])).
% 29.39/19.62 tff(24253,plain,
% 29.39/19.62 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c1 = f5(c2))) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), c1) | (~(c2 = f8(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | (f7(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (~(c1 = f5(c2))) | big_f(f7(c2), c1))),
% 29.39/19.62 inference(transitivity,[status(thm)],[24252, 24250])).
% 29.39/19.62 tff(24254,plain,
% 29.39/19.62 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c1 = f5(c2))) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), c1) | (~(c2 = f8(c2))))),
% 29.39/19.62 inference(quant_inst,[status(thm)],[])).
% 29.39/19.62 tff(24255,plain,
% 29.39/19.62 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | (f7(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (~(c1 = f5(c2))) | big_f(f7(c2), c1)),
% 29.39/19.62 inference(modus_ponens,[status(thm)],[24254, 24253])).
% 29.39/19.62 tff(24256,plain,
% 29.39/19.62 ((~(c2 = f8(c2))) | (~(c1 = f5(c2)))),
% 29.39/19.62 inference(unit_resolution,[status(thm)],[24255, 1745, 89, 17, 15517, 333])).
% 29.39/19.62 tff(24257,plain,
% 29.39/19.62 (~(c1 = f5(c2))),
% 29.39/19.62 inference(unit_resolution,[status(thm)],[24256, 13152])).
% 29.39/19.62 tff(24258,plain,
% 29.39/19.62 (~(f5(c2) = c1)),
% 29.39/19.62 inference(unit_resolution,[status(thm)],[8139, 24257])).
% 29.39/19.62 tff(24259,plain,
% 29.39/19.62 ($false),
% 29.39/19.62 inference(unit_resolution,[status(thm)],[1547, 24258, 24249])).
% 29.39/19.62 tff(24260,plain,((~(c2 = f8(c2))) | (f10(c2) = c2) | (f7(c2) = c2) | big_f(c2, f10(c2)) | big_f(f7(c2), c1) | big_f(f7(c2), c2)), inference(lemma,lemma(discharge,[]))).
% 29.39/19.62 tff(24261,plain,
% 29.39/19.62 (~(c2 = f8(c2))),
% 29.39/19.62 inference(unit_resolution,[status(thm)],[24260, 21128, 89, 17, 15517, 12093])).
% 29.39/19.62 tff(24262,plain,
% 29.39/19.62 (~(f7(c2) = f8(c2))),
% 29.39/19.62 inference(unit_resolution,[status(thm)],[12706, 21128, 89, 17, 23541])).
% 29.39/19.62 tff(24263,plain,
% 29.39/19.62 ((f7(c2) = f8(c2)) <=> (c1 = f8(c2))),
% 29.39/19.62 inference(monotonicity,[status(thm)],[292])).
% 29.39/19.62 tff(24264,plain,
% 29.39/19.62 ((c1 = f8(c2)) <=> (f7(c2) = f8(c2))),
% 29.39/19.62 inference(symmetry,[status(thm)],[24263])).
% 29.39/19.62 tff(24265,plain,
% 29.39/19.62 ((f8(f10(c1)) = c1) <=> (f7(c2) = f8(c2))),
% 29.39/19.62 inference(transitivity,[status(thm)],[11996, 12674, 24264])).
% 29.39/19.62 tff(24266,plain,
% 29.39/19.62 ((c2 = f8(f10(c1))) <=> (f8(f10(c1)) = c2)),
% 29.39/19.62 inference(commutativity,[status(thm)],[])).
% 29.39/19.62 tff(24267,plain,
% 29.39/19.62 ((c2 = f8(c2)) <=> (c2 = f8(f10(c1)))),
% 29.39/19.62 inference(monotonicity,[status(thm)],[12670])).
% 29.39/19.62 tff(24268,plain,
% 29.39/19.62 ((c2 = f8(c2)) <=> (f8(f10(c1)) = c2)),
% 29.39/19.62 inference(transitivity,[status(thm)],[24267, 24266])).
% 29.39/19.62 tff(24269,plain,
% 29.39/19.62 ((~(c2 = f8(c2))) <=> (~(f8(f10(c1)) = c2))),
% 29.39/19.62 inference(monotonicity,[status(thm)],[24268])).
% 29.39/19.62 tff(24270,plain,
% 29.39/19.62 (~(f8(f10(c1)) = c2)),
% 29.39/19.62 inference(modus_ponens,[status(thm)],[12290, 24269])).
% 29.39/19.62 tff(24271,plain,
% 29.39/19.62 (f8(f10(c1)) = c1),
% 29.39/19.62 inference(unit_resolution,[status(thm)],[12021, 24270])).
% 29.39/19.62 tff(24272,plain,
% 29.39/19.62 (f7(c2) = f8(c2)),
% 29.39/19.62 inference(modus_ponens,[status(thm)],[24271, 24265])).
% 29.39/19.62 tff(24273,plain,
% 29.39/19.62 ($false),
% 29.39/19.62 inference(unit_resolution,[status(thm)],[21140, 24272])).
% 29.39/19.62 tff(24274,plain,((~(f10(c1) = c2)) | (f7(c2) = f8(c2)) | (~(f7(c2) = c1)) | (c2 = f8(c2))), inference(lemma,lemma(discharge,[]))).
% 29.39/19.62 tff(24275,plain,
% 29.39/19.62 (~(f10(c1) = c2)),
% 29.39/19.62 inference(unit_resolution,[status(thm)],[24274, 24262, 22, 24261])).
% 29.39/19.62 tff(24276,plain,
% 29.39/19.62 (f10(c1) = c1),
% 29.39/19.62 inference(unit_resolution,[status(thm)],[14, 24275])).
% 29.39/19.62 tff(24277,plain,
% 29.39/19.62 ((~(f7(c2) = f8(c2))) <=> (~(c1 = f8(c2)))),
% 29.39/19.62 inference(monotonicity,[status(thm)],[12676])).
% 29.39/19.62 tff(24278,plain,
% 29.39/19.62 (~(c1 = f8(c2))),
% 29.39/19.62 inference(modus_ponens,[status(thm)],[24262, 24277])).
% 29.39/19.62 tff(24279,assumption,(f6(c1, f8(c2)) = f8(c2)), introduced(assumption)).
% 29.39/19.62 tff(24280,plain,
% 29.39/19.62 ((f6(c1, f8(c2)) = c1) <=> (f8(c2) = c1)),
% 29.39/19.62 inference(monotonicity,[status(thm)],[24279])).
% 29.39/19.62 tff(24281,plain,
% 29.39/19.62 ((f6(c1, f8(c2)) = c1) <=> (c1 = f8(c2))),
% 29.39/19.62 inference(transitivity,[status(thm)],[24280, 13044])).
% 29.39/19.62 tff(24282,plain,
% 29.39/19.62 ((c1 = f8(c2)) <=> (f6(c1, f8(c2)) = c1)),
% 29.39/19.62 inference(symmetry,[status(thm)],[24281])).
% 29.39/19.62 tff(24283,plain,
% 29.39/19.62 ((~(c1 = f8(c2))) <=> (~(f6(c1, f8(c2)) = c1))),
% 29.39/19.62 inference(monotonicity,[status(thm)],[24282])).
% 29.39/19.62 tff(24284,assumption,(~(c1 = f8(c2))), introduced(assumption)).
% 29.39/19.62 tff(24285,plain,
% 29.39/19.62 (~(f6(c1, f8(c2)) = c1)),
% 29.39/19.62 inference(modus_ponens,[status(thm)],[24284, 24283])).
% 29.39/19.62 tff(24286,plain,
% 29.39/19.62 ((c2 = f6(c1, f8(c2))) <=> (f6(c1, f8(c2)) = c2)),
% 29.39/19.62 inference(commutativity,[status(thm)],[])).
% 29.39/19.62 tff(24287,plain,
% 29.39/19.62 (f8(c2) = f6(c1, f8(c2))),
% 29.39/19.62 inference(symmetry,[status(thm)],[24279])).
% 29.39/19.62 tff(24288,plain,
% 29.39/19.62 ((c2 = f8(c2)) <=> (c2 = f6(c1, f8(c2)))),
% 29.39/19.62 inference(monotonicity,[status(thm)],[24287])).
% 29.39/19.62 tff(24289,plain,
% 29.39/19.62 ((c2 = f8(c2)) <=> (f6(c1, f8(c2)) = c2)),
% 29.39/19.62 inference(transitivity,[status(thm)],[24288, 24286])).
% 29.39/19.62 tff(24290,plain,
% 29.39/19.62 ((~(c2 = f8(c2))) <=> (~(f6(c1, f8(c2)) = c2))),
% 29.39/19.62 inference(monotonicity,[status(thm)],[24289])).
% 29.39/19.62 tff(24291,plain,
% 29.39/19.62 (~(f6(c1, f8(c2)) = c2)),
% 29.39/19.62 inference(modus_ponens,[status(thm)],[12290, 24290])).
% 29.39/19.62 tff(24292,plain,
% 29.39/19.62 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f6(c1, f8(c2)) = c1) | (f6(c1, f8(c2)) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f6(c1, f8(c2)) = c1) | (f6(c1, f8(c2)) = c2))),
% 29.39/19.62 inference(rewrite,[status(thm)],[])).
% 29.39/19.62 tff(24293,plain,
% 29.39/19.62 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f6(c1, f8(c2)) = c1) | (f6(c1, f8(c2)) = c2))),
% 29.39/19.62 inference(quant_inst,[status(thm)],[])).
% 29.39/19.62 tff(24294,plain,
% 29.39/19.62 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f6(c1, f8(c2)) = c1) | (f6(c1, f8(c2)) = c2)),
% 29.39/19.62 inference(modus_ponens,[status(thm)],[24293, 24292])).
% 29.39/19.62 tff(24295,plain,
% 29.39/19.62 ((f6(c1, f8(c2)) = c1) | (f6(c1, f8(c2)) = c2)),
% 29.39/19.62 inference(unit_resolution,[status(thm)],[24294, 10])).
% 29.39/19.62 tff(24296,plain,
% 29.39/19.62 ($false),
% 29.39/19.62 inference(unit_resolution,[status(thm)],[24295, 24291, 24285])).
% 29.39/19.62 tff(24297,plain,((~(f6(c1, f8(c2)) = f8(c2))) | (c2 = f8(c2)) | (c1 = f8(c2))), inference(lemma,lemma(discharge,[]))).
% 29.39/19.62 tff(24298,plain,
% 29.39/19.62 (~(f6(c1, f8(c2)) = f8(c2))),
% 29.39/19.62 inference(unit_resolution,[status(thm)],[24297, 24261, 24278])).
% 29.39/19.62 tff(24299,plain,
% 29.39/19.62 ((f7(f10(c2)) = f10(c2)) <=> (c2 = c1)),
% 29.39/19.62 inference(monotonicity,[status(thm)],[17554, 94])).
% 29.39/19.62 tff(24300,plain,
% 29.39/19.62 ((c2 = c1) <=> (f7(f10(c2)) = f10(c2))),
% 29.39/19.62 inference(symmetry,[status(thm)],[24299])).
% 29.39/19.62 tff(24301,plain,
% 29.39/19.62 ((~(c2 = c1)) <=> (~(f7(f10(c2)) = f10(c2)))),
% 29.39/19.62 inference(monotonicity,[status(thm)],[24300])).
% 29.39/19.62 tff(24302,plain,
% 29.39/19.62 (~(f7(f10(c2)) = f10(c2))),
% 29.39/19.62 inference(modus_ponens,[status(thm)],[75, 24301])).
% 29.39/19.62 tff(24303,plain,
% 29.39/19.62 (~(c3 = c2)),
% 29.39/19.62 inference(unit_resolution,[status(thm)],[8259, 79, 121, 2])).
% 29.39/19.62 tff(24304,plain,
% 29.39/19.62 (c3 = c1),
% 29.39/19.62 inference(unit_resolution,[status(thm)],[180, 24303])).
% 29.39/19.62 tff(24305,plain,
% 29.39/19.62 (~big_f(f4(c4), c4)),
% 29.39/19.62 inference(unit_resolution,[status(thm)],[5036, 79, 121, 2])).
% 29.39/19.62 tff(24306,plain,
% 29.39/19.62 (big_f(c3, f2(c3))),
% 29.39/19.62 inference(unit_resolution,[status(thm)],[1315, 24305])).
% 29.39/19.62 tff(24307,plain,
% 29.39/19.62 (big_f(c1, f2(c1))),
% 29.39/19.62 inference(unit_resolution,[status(thm)],[8631, 24306, 24304])).
% 29.39/19.62 tff(24308,plain,
% 29.39/19.62 (~(f2(c3) = c1)),
% 29.39/19.62 inference(unit_resolution,[status(thm)],[10932, 24307, 66, 24304])).
% 29.39/19.62 tff(24309,plain,
% 29.39/19.62 (f2(c3) = c2),
% 29.39/19.62 inference(unit_resolution,[status(thm)],[1273, 24308])).
% 29.39/19.62 tff(24310,plain,
% 29.39/19.62 (big_f(c3, f2(c3)) <=> big_f(c1, c2)),
% 29.39/19.62 inference(monotonicity,[status(thm)],[24304, 24309])).
% 29.39/19.62 tff(24311,plain,
% 29.39/19.62 (big_f(c1, c2) <=> big_f(c3, f2(c3))),
% 29.39/19.62 inference(symmetry,[status(thm)],[24310])).
% 29.39/19.62 tff(24312,plain,
% 29.39/19.62 ((~big_f(c1, c2)) <=> (~big_f(c3, f2(c3)))),
% 29.39/19.62 inference(monotonicity,[status(thm)],[24311])).
% 29.39/19.62 tff(24313,plain,
% 29.39/19.62 (~big_f(c3, f2(c3))),
% 29.39/19.62 inference(modus_ponens,[status(thm)],[27, 24312])).
% 29.39/19.62 tff(24314,plain,
% 29.39/19.62 ($false),
% 29.39/19.62 inference(unit_resolution,[status(thm)],[24306, 24313])).
% 29.39/19.62 tff(24315,plain,((~(f4(c4) = c2)) | big_f(c1, c2) | big_f(c1, c1) | big_f(c2, c2) | big_f(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 29.39/19.62 tff(24316,plain,
% 29.39/19.62 (~(f4(c4) = c2)),
% 29.39/19.62 inference(unit_resolution,[status(thm)],[24315, 66, 27, 121, 2])).
% 29.39/19.62 tff(24317,plain,
% 29.39/19.62 (f4(c4) = c1),
% 29.39/19.62 inference(unit_resolution,[status(thm)],[11750, 24316])).
% 29.39/19.62 tff(24318,plain,
% 29.39/19.62 (~big_f(f4(c4), c4)),
% 29.39/19.62 inference(unit_resolution,[status(thm)],[11772, 24317, 27, 66])).
% 29.39/19.62 tff(24319,plain,
% 29.39/19.62 (big_f(c3, f2(c3))),
% 29.39/19.62 inference(unit_resolution,[status(thm)],[1315, 24318])).
% 29.39/19.62 tff(24320,plain,
% 29.39/19.62 (~(c3 = c1)),
% 29.39/19.62 inference(unit_resolution,[status(thm)],[11784, 24317, 66, 27])).
% 29.39/19.62 tff(24321,plain,
% 29.39/19.62 (c3 = c2),
% 29.39/19.62 inference(unit_resolution,[status(thm)],[180, 24320])).
% 29.39/19.62 tff(24322,plain,
% 29.39/19.62 ($false),
% 29.39/19.62 inference(unit_resolution,[status(thm)],[8256, 24321, 24319, 121, 2])).
% 29.39/19.62 tff(24323,plain,(big_f(c1, c1) | big_f(c2, c2) | big_f(c2, c1) | big_f(c1, c2)), inference(lemma,lemma(discharge,[]))).
% 29.39/19.62 tff(24324,plain,
% 29.39/19.62 (big_f(c2, c1)),
% 29.39/19.62 inference(unit_resolution,[status(thm)],[24323, 66, 27, 121])).
% 29.39/19.62 tff(24325,plain,
% 29.39/19.62 (big_f(c2, f10(c2))),
% 29.39/19.62 inference(modus_ponens,[status(thm)],[24324, 12069])).
% 29.39/19.62 tff(24326,plain,
% 29.39/19.62 (big_f(c2, c1)),
% 29.39/19.62 inference(unit_resolution,[status(thm)],[24323, 66, 121, 27])).
% 29.39/19.62 tff(24327,plain,
% 29.39/19.62 ($false),
% 29.39/19.62 inference(unit_resolution,[status(thm)],[23456, 24326, 66, 3762, 77, 121])).
% 29.39/19.62 tff(24328,plain,(big_f(c1, c1) | (~(f10(c1) = c1)) | (~(f7(c2) = c2)) | big_f(c2, c2) | big_f(c1, c2)), inference(lemma,lemma(discharge,[]))).
% 29.39/19.62 tff(24329,plain,
% 29.39/19.62 (~(f7(c2) = c2)),
% 29.39/19.62 inference(unit_resolution,[status(thm)],[24328, 66, 3762, 27, 121])).
% 29.39/19.62 tff(24330,plain,
% 29.39/19.62 (f7(c2) = c1),
% 29.39/19.62 inference(unit_resolution,[status(thm)],[21, 24329])).
% 29.39/19.62 tff(24331,plain,
% 29.39/19.62 (~big_f(f7(c2), c2)),
% 29.39/19.62 inference(unit_resolution,[status(thm)],[21127, 24330, 27])).
% 29.39/19.62 tff(24332,plain,
% 29.39/19.62 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f10(c2) = c2) | (f7(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(c1 = f5(c2))) | big_f(f7(c2), c1))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(c2) = c2) | (f7(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(c1 = f5(c2))) | big_f(f7(c2), c1))),
% 29.39/19.62 inference(rewrite,[status(thm)],[])).
% 29.39/19.62 tff(24333,plain,
% 29.39/19.62 (((~(c1 = f5(c2))) | (f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(c2) = c2) | big_f(f7(c2), c1)) <=> ((f10(c2) = c2) | (f7(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(c1 = f5(c2))) | big_f(f7(c2), c1))),
% 29.39/19.62 inference(rewrite,[status(thm)],[])).
% 29.39/19.62 tff(24334,plain,
% 29.39/19.62 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c1 = f5(c2))) | (f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(c2) = c2) | big_f(f7(c2), c1))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f10(c2) = c2) | (f7(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(c1 = f5(c2))) | big_f(f7(c2), c1)))),
% 29.39/19.62 inference(monotonicity,[status(thm)],[24333])).
% 29.39/19.62 tff(24335,plain,
% 29.39/19.62 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c1 = f5(c2))) | (f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(c2) = c2) | big_f(f7(c2), c1))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(c2) = c2) | (f7(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(c1 = f5(c2))) | big_f(f7(c2), c1))),
% 29.39/19.62 inference(transitivity,[status(thm)],[24334, 24332])).
% 29.39/19.62 tff(24336,plain,
% 29.39/19.62 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c1 = f5(c2))) | (f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(c2) = c2) | big_f(f7(c2), c1))),
% 29.39/19.62 inference(quant_inst,[status(thm)],[])).
% 29.39/19.62 tff(24337,plain,
% 29.39/19.62 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(c2) = c2) | (f7(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(c1 = f5(c2))) | big_f(f7(c2), c1)),
% 29.39/19.62 inference(modus_ponens,[status(thm)],[24336, 24335])).
% 29.39/19.62 tff(24338,plain,
% 29.39/19.62 ((c2 = f8(c2)) | (~(c1 = f5(c2)))),
% 29.39/19.62 inference(unit_resolution,[status(thm)],[24337, 705, 89, 17, 12291, 333])).
% 29.39/19.62 tff(24339,plain,
% 29.39/19.62 (c2 = f8(c2)),
% 29.39/19.62 inference(unit_resolution,[status(thm)],[24338, 23054])).
% 29.39/19.62 tff(24340,plain,
% 29.39/19.62 (f9(c1, c2) = c2),
% 29.39/19.62 inference(unit_resolution,[status(thm)],[8242, 23054, 3762, 17, 333, 17944])).
% 29.39/19.62 tff(24341,plain,
% 29.39/19.62 (f9(c1, c2) = f8(c2)),
% 29.39/19.62 inference(transitivity,[status(thm)],[24340, 24339])).
% 29.39/19.62 tff(24342,plain,
% 29.39/19.62 (f10(c2) = f10(c1)),
% 29.39/19.62 inference(transitivity,[status(thm)],[94, 11570])).
% 29.39/19.62 tff(24343,plain,
% 29.39/19.62 (big_f(f9(c1, c2), f10(c2)) <=> big_f(f9(c1, c2), f10(c1))),
% 29.39/19.62 inference(monotonicity,[status(thm)],[24342])).
% 29.39/19.62 tff(24344,plain,
% 29.39/19.62 (big_f(f9(c1, c2), f10(c1)) <=> big_f(f9(c1, c2), f10(c2))),
% 29.39/19.62 inference(symmetry,[status(thm)],[24343])).
% 29.39/19.62 tff(24345,plain,
% 29.39/19.62 ((~big_f(f9(c1, c2), f10(c1))) <=> (~big_f(f9(c1, c2), f10(c2)))),
% 29.39/19.62 inference(monotonicity,[status(thm)],[24344])).
% 29.39/19.62 tff(24346,plain,
% 29.39/19.62 (~big_f(f9(c1, c2), f10(c2))),
% 29.39/19.62 inference(modus_ponens,[status(thm)],[17944, 24345])).
% 29.39/19.62 tff(24347,plain,
% 29.39/19.62 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | (f7(c2) = c2) | (~(c1 = f5(c2))) | big_f(f7(c2), c1) | big_f(f9(c1, c2), f10(c2)) | (~(f9(c1, c2) = f8(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | (f7(c2) = c2) | (~(c1 = f5(c2))) | big_f(f7(c2), c1) | big_f(f9(c1, c2), f10(c2)) | (~(f9(c1, c2) = f8(c2))))),
% 29.39/19.62 inference(rewrite,[status(thm)],[])).
% 29.39/19.62 tff(24348,plain,
% 29.39/19.62 (((~(c1 = f5(c2))) | (f10(c2) = c2) | big_f(f9(c1, c2), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), c1) | (~(f9(c1, c2) = f8(c2)))) <=> ((f10(c2) = c2) | (f7(c2) = c2) | (~(c1 = f5(c2))) | big_f(f7(c2), c1) | big_f(f9(c1, c2), f10(c2)) | (~(f9(c1, c2) = f8(c2))))),
% 29.39/19.62 inference(rewrite,[status(thm)],[])).
% 29.39/19.62 tff(24349,plain,
% 29.39/19.62 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c1 = f5(c2))) | (f10(c2) = c2) | big_f(f9(c1, c2), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), c1) | (~(f9(c1, c2) = f8(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | (f7(c2) = c2) | (~(c1 = f5(c2))) | big_f(f7(c2), c1) | big_f(f9(c1, c2), f10(c2)) | (~(f9(c1, c2) = f8(c2)))))),
% 29.39/19.62 inference(monotonicity,[status(thm)],[24348])).
% 29.39/19.62 tff(24350,plain,
% 29.39/19.62 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c1 = f5(c2))) | (f10(c2) = c2) | big_f(f9(c1, c2), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), c1) | (~(f9(c1, c2) = f8(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | (f7(c2) = c2) | (~(c1 = f5(c2))) | big_f(f7(c2), c1) | big_f(f9(c1, c2), f10(c2)) | (~(f9(c1, c2) = f8(c2))))),
% 29.39/19.62 inference(transitivity,[status(thm)],[24349, 24347])).
% 29.39/19.62 tff(24351,plain,
% 29.39/19.62 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c1 = f5(c2))) | (f10(c2) = c2) | big_f(f9(c1, c2), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), c1) | (~(f9(c1, c2) = f8(c2))))),
% 29.39/19.62 inference(quant_inst,[status(thm)],[])).
% 29.39/19.62 tff(24352,plain,
% 29.39/19.62 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | (f7(c2) = c2) | (~(c1 = f5(c2))) | big_f(f7(c2), c1) | big_f(f9(c1, c2), f10(c2)) | (~(f9(c1, c2) = f8(c2)))),
% 29.39/19.62 inference(modus_ponens,[status(thm)],[24351, 24350])).
% 29.39/19.62 tff(24353,plain,
% 29.39/19.62 ((~(c1 = f5(c2))) | big_f(f9(c1, c2), f10(c2)) | (~(f9(c1, c2) = f8(c2)))),
% 29.39/19.62 inference(unit_resolution,[status(thm)],[24352, 1745, 89, 17, 333])).
% 29.39/19.62 tff(24354,plain,
% 29.39/19.62 (~(f9(c1, c2) = f8(c2))),
% 29.39/19.62 inference(unit_resolution,[status(thm)],[24353, 23054, 24346])).
% 29.39/19.62 tff(24355,plain,
% 29.39/19.62 ($false),
% 29.39/19.62 inference(unit_resolution,[status(thm)],[24354, 24341])).
% 29.39/19.62 tff(24356,plain,((~(c1 = f5(c2))) | (f10(c2) = c2) | (f7(c2) = c2) | big_f(f7(c2), c1) | (~(f10(c1) = c1)) | big_f(f9(c1, c2), f10(c1)) | (~big_f(c2, f10(c2)))), inference(lemma,lemma(discharge,[]))).
% 29.39/19.62 tff(24357,plain,
% 29.39/19.62 (~(c1 = f5(c2))),
% 29.39/19.62 inference(unit_resolution,[status(thm)],[24356, 17944, 17, 333, 3762, 89, 12291])).
% 29.39/19.62 tff(24358,plain,
% 29.39/19.62 (~(f5(c2) = c1)),
% 29.39/19.62 inference(unit_resolution,[status(thm)],[8139, 24357])).
% 29.39/19.62 tff(24359,plain,
% 29.39/19.62 (f5(c2) = c2),
% 29.39/19.62 inference(unit_resolution,[status(thm)],[1547, 24358])).
% 29.39/19.62 tff(24360,plain,
% 29.39/19.62 (c2 = f5(c2)),
% 29.39/19.62 inference(unit_resolution,[status(thm)],[8113, 24359])).
% 29.39/19.62 tff(24361,plain,
% 29.39/19.62 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f10(c2) = c2) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(c2) = c2) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))))),
% 29.39/19.62 inference(rewrite,[status(thm)],[])).
% 29.39/19.62 tff(24362,plain,
% 29.39/19.62 (((~(c2 = f5(c2))) | (f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(c2) = c2) | big_f(f7(c2), c2)) <=> ((f10(c2) = c2) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))))),
% 29.39/19.62 inference(rewrite,[status(thm)],[])).
% 29.39/19.62 tff(24363,plain,
% 29.39/19.62 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c2 = f5(c2))) | (f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(c2) = c2) | big_f(f7(c2), c2))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f10(c2) = c2) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2)))))),
% 29.39/19.62 inference(monotonicity,[status(thm)],[24362])).
% 29.39/19.62 tff(24364,plain,
% 29.39/19.62 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c2 = f5(c2))) | (f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(c2) = c2) | big_f(f7(c2), c2))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(c2) = c2) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))))),
% 29.39/19.62 inference(transitivity,[status(thm)],[24363, 24361])).
% 29.39/19.62 tff(24365,plain,
% 29.39/19.62 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c2 = f5(c2))) | (f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(c2) = c2) | big_f(f7(c2), c2))),
% 29.39/19.62 inference(quant_inst,[status(thm)],[])).
% 29.39/19.62 tff(24366,plain,
% 29.39/19.62 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(c2) = c2) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2)))),
% 29.39/19.62 inference(modus_ponens,[status(thm)],[24365, 24364])).
% 29.39/19.62 tff(24367,plain,
% 29.39/19.62 ((~(c2 = f5(c2))) | (c2 = f8(c2))),
% 29.39/19.62 inference(unit_resolution,[status(thm)],[24366, 705, 89, 17, 1521, 12291])).
% 29.39/19.62 tff(24368,plain,
% 29.39/19.62 (c2 = f8(c2)),
% 29.39/19.62 inference(unit_resolution,[status(thm)],[24367, 24360])).
% 29.39/19.62 tff(24369,plain,
% 29.39/19.62 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)))),
% 29.39/19.62 inference(rewrite,[status(thm)],[])).
% 29.39/19.62 tff(24370,plain,
% 29.39/19.62 (((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(c2 = f5(c2)))) <=> ((f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)))),
% 29.39/19.62 inference(rewrite,[status(thm)],[])).
% 29.39/19.62 tff(24371,plain,
% 29.39/19.62 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(c2 = f5(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1))))),
% 29.39/19.62 inference(monotonicity,[status(thm)],[24370])).
% 29.39/19.62 tff(24372,plain,
% 29.39/19.62 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(c2 = f5(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)))),
% 29.39/19.63 inference(transitivity,[status(thm)],[24371, 24369])).
% 29.39/19.63 tff(24373,plain,
% 29.39/19.63 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(c2 = f5(c2))))),
% 29.39/19.63 inference(quant_inst,[status(thm)],[])).
% 29.39/19.63 tff(24374,plain,
% 29.39/19.63 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1))),
% 29.39/19.63 inference(modus_ponens,[status(thm)],[24373, 24372])).
% 29.39/19.63 tff(24375,plain,
% 29.39/19.63 ((~(c2 = f5(c2))) | (f9(c1, c2) = c2)),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[24374, 267, 3762, 17, 1521, 17944])).
% 29.39/19.63 tff(24376,plain,
% 29.39/19.63 (f9(c1, c2) = c2),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[24375, 24360])).
% 29.39/19.63 tff(24377,plain,
% 29.39/19.63 (f9(c1, c2) = f8(c2)),
% 29.39/19.63 inference(transitivity,[status(thm)],[24376, 24368])).
% 29.39/19.63 tff(24378,plain,
% 29.39/19.63 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | big_f(f9(c1, c2), f10(c2)) | (~(f9(c1, c2) = f8(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | big_f(f9(c1, c2), f10(c2)) | (~(f9(c1, c2) = f8(c2))))),
% 29.39/19.63 inference(rewrite,[status(thm)],[])).
% 29.39/19.63 tff(24379,plain,
% 29.39/19.63 (((~(c2 = f5(c2))) | (f10(c2) = c2) | big_f(f9(c1, c2), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(f9(c1, c2) = f8(c2)))) <=> ((f10(c2) = c2) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | big_f(f9(c1, c2), f10(c2)) | (~(f9(c1, c2) = f8(c2))))),
% 29.39/19.63 inference(rewrite,[status(thm)],[])).
% 29.39/19.63 tff(24380,plain,
% 29.39/19.63 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c2 = f5(c2))) | (f10(c2) = c2) | big_f(f9(c1, c2), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(f9(c1, c2) = f8(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | big_f(f9(c1, c2), f10(c2)) | (~(f9(c1, c2) = f8(c2)))))),
% 29.39/19.63 inference(monotonicity,[status(thm)],[24379])).
% 29.39/19.63 tff(24381,plain,
% 29.39/19.63 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c2 = f5(c2))) | (f10(c2) = c2) | big_f(f9(c1, c2), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(f9(c1, c2) = f8(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | big_f(f9(c1, c2), f10(c2)) | (~(f9(c1, c2) = f8(c2))))),
% 29.39/19.63 inference(transitivity,[status(thm)],[24380, 24378])).
% 29.39/19.63 tff(24382,plain,
% 29.39/19.63 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c2 = f5(c2))) | (f10(c2) = c2) | big_f(f9(c1, c2), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(f9(c1, c2) = f8(c2))))),
% 29.39/19.63 inference(quant_inst,[status(thm)],[])).
% 29.39/19.63 tff(24383,plain,
% 29.39/19.63 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | big_f(f9(c1, c2), f10(c2)) | (~(f9(c1, c2) = f8(c2)))),
% 29.39/19.63 inference(modus_ponens,[status(thm)],[24382, 24381])).
% 29.39/19.63 tff(24384,plain,
% 29.39/19.63 ((~(c2 = f5(c2))) | big_f(f9(c1, c2), f10(c2)) | (~(f9(c1, c2) = f8(c2)))),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[24383, 1745, 89, 17, 1521])).
% 29.39/19.63 tff(24385,plain,
% 29.39/19.63 (~(f9(c1, c2) = f8(c2))),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[24384, 24360, 24346])).
% 29.39/19.63 tff(24386,plain,
% 29.39/19.63 ($false),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[24385, 24377])).
% 29.39/19.63 tff(24387,plain,(big_f(f9(c1, c2), f10(c1)) | (~(f10(c1) = c1)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (f10(c2) = c2) | (~big_f(c2, f10(c2))) | big_f(f7(c2), c1)), inference(lemma,lemma(discharge,[]))).
% 29.39/19.63 tff(24388,plain,
% 29.39/19.63 (big_f(f9(c1, c2), f10(c1))),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[24387, 12093, 17, 1521, 89, 12291, 3762])).
% 29.39/19.63 tff(24389,plain,
% 29.39/19.63 (~(f9(c1, c2) = c1)),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[23425, 24388, 66, 3762])).
% 29.39/19.63 tff(24390,plain,
% 29.39/19.63 (f9(c1, c2) = c2),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[3791, 24389])).
% 29.39/19.63 tff(24391,plain,
% 29.39/19.63 (~(c2 = f5(c2))),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[8204, 24390, 3762, 17, 1521, 24388])).
% 29.39/19.63 tff(24392,plain,
% 29.39/19.63 (~(f5(c2) = c2)),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[8113, 24391])).
% 29.39/19.63 tff(24393,plain,
% 29.39/19.63 ((~(c1 = f5(c2))) | (~(f9(c1, c2) = c2))),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[23139, 783, 3762, 17, 24388, 12093])).
% 29.39/19.63 tff(24394,plain,
% 29.39/19.63 (~(c1 = f5(c2))),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[24393, 24390])).
% 29.39/19.63 tff(24395,plain,
% 29.39/19.63 (~(f5(c2) = c1)),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[8139, 24394])).
% 29.39/19.63 tff(24396,plain,
% 29.39/19.63 ($false),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[1547, 24395, 24392])).
% 29.39/19.63 tff(24397,plain,(big_f(c1, c1) | (~(f10(c1) = c1)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (f10(c2) = c2) | (~big_f(c2, f10(c2)))), inference(lemma,lemma(discharge,[]))).
% 29.39/19.63 tff(24398,plain,
% 29.39/19.63 (~big_f(c2, f10(c2))),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[24397, 24331, 3762, 89, 66, 24329])).
% 29.39/19.63 tff(24399,plain,
% 29.39/19.63 ($false),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[24398, 24325])).
% 29.39/19.63 tff(24400,plain,(big_f(c1, c1) | (~(f10(c1) = c1)) | (f10(c2) = c2) | big_f(c1, c2) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 29.39/19.63 tff(24401,plain,
% 29.39/19.63 (big_f(c1, c1)),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[24400, 121, 89, 27, 22733])).
% 29.39/19.63 tff(24402,plain,
% 29.39/19.63 (big_f(c2, c1)),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[22765, 24401, 115, 1726])).
% 29.39/19.63 tff(24403,plain,
% 29.39/19.63 (~(f4(c4) = c2)),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[12437, 24401, 120, 27, 121, 89, 24402])).
% 29.39/19.63 tff(24404,plain,
% 29.39/19.63 (f4(c4) = c1),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[11750, 24403])).
% 29.39/19.63 tff(24405,plain,
% 29.39/19.63 (c2 = c3),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[22871, 24404, 115, 27, 121])).
% 29.39/19.63 tff(24406,plain,
% 29.39/19.63 (c3 = c2),
% 29.39/19.63 inference(symmetry,[status(thm)],[24405])).
% 29.39/19.63 tff(24407,plain,
% 29.39/19.63 ((c1 = c3) <=> (c1 = c2)),
% 29.39/19.63 inference(monotonicity,[status(thm)],[24406])).
% 29.39/19.63 tff(24408,plain,
% 29.39/19.63 ((c1 = c3) <=> (c2 = c1)),
% 29.39/19.63 inference(transitivity,[status(thm)],[24407, 1])).
% 29.39/19.63 tff(24409,plain,
% 29.39/19.63 ((c2 = c1) <=> (c1 = c3)),
% 29.39/19.63 inference(symmetry,[status(thm)],[24408])).
% 29.39/19.63 tff(24410,plain,
% 29.39/19.63 ((~(c2 = c1)) <=> (~(c1 = c3))),
% 29.39/19.63 inference(monotonicity,[status(thm)],[24409])).
% 29.39/19.63 tff(24411,plain,
% 29.39/19.63 (~(c1 = c3)),
% 29.39/19.63 inference(modus_ponens,[status(thm)],[75, 24410])).
% 29.39/19.63 tff(24412,plain,
% 29.39/19.63 ((f4(c4) = c3) <=> (c1 = c3)),
% 29.39/19.63 inference(monotonicity,[status(thm)],[24404])).
% 29.39/19.63 tff(24413,plain,
% 29.39/19.63 ((c1 = c3) <=> (f4(c4) = c3)),
% 29.39/19.63 inference(symmetry,[status(thm)],[24412])).
% 29.39/19.63 tff(24414,plain,
% 29.39/19.63 ((c2 = c1) <=> (f4(c4) = c3)),
% 29.39/19.63 inference(transitivity,[status(thm)],[24409, 24413])).
% 29.39/19.63 tff(24415,plain,
% 29.39/19.63 ((~(c2 = c1)) <=> (~(f4(c4) = c3))),
% 29.39/19.63 inference(monotonicity,[status(thm)],[24414])).
% 29.39/19.63 tff(24416,plain,
% 29.39/19.63 (~(f4(c4) = c3)),
% 29.39/19.63 inference(modus_ponens,[status(thm)],[75, 24415])).
% 29.39/19.63 tff(24417,plain,
% 29.39/19.63 ($false),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[23034, 24416, 24411, 27, 24402, 24401, 24404])).
% 29.39/19.63 tff(24418,plain,(big_f(c2, c2) | big_f(c1, c2) | (f7(c1) = c1) | (f10(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 29.39/19.63 tff(24419,plain,
% 29.39/19.63 (big_f(c2, c2)),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[24418, 89, 115, 27])).
% 29.39/19.63 tff(24420,plain,
% 29.39/19.63 (big_f(f7(c1), c2)),
% 29.39/19.63 inference(modus_ponens,[status(thm)],[24419, 1724])).
% 29.39/19.63 tff(24421,plain,
% 29.39/19.63 (~big_f(c2, c1)),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[23932, 66, 115, 24420])).
% 29.39/19.63 tff(24422,plain,
% 29.39/19.63 (~big_f(f7(c2), c1)),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[12570, 17, 1345, 377, 79, 2])).
% 29.39/19.63 tff(24423,plain,
% 29.39/19.63 (~big_f(f7(c2), f7(c2))),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[8374, 24422, 22])).
% 29.39/19.63 tff(24424,plain,
% 29.39/19.63 (~(f7(c2) = f8(c2))),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[12706, 24423, 89, 17, 23145])).
% 29.39/19.63 tff(24425,plain,
% 29.39/19.63 (~(c1 = f8(c2))),
% 29.39/19.63 inference(modus_ponens,[status(thm)],[24424, 24277])).
% 29.39/19.63 tff(24426,plain,
% 29.39/19.63 ($false),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[24374, 267, 3762, 17, 5124, 1521, 23889, 4236])).
% 29.39/19.63 tff(24427,plain,((f9(c1, c2) = c2) | (~(f10(c1) = c1)) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 29.39/19.63 tff(24428,plain,
% 29.39/19.63 (f9(c1, c2) = c2),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[24427, 5124, 17, 3762, 1521, 66])).
% 29.39/19.63 tff(24429,plain,
% 29.39/19.63 (f9(f10(c2), f7(c1)) = f9(c1, c2)),
% 29.39/19.63 inference(monotonicity,[status(thm)],[94, 347])).
% 29.39/19.63 tff(24430,plain,
% 29.39/19.63 (f9(f10(c2), f7(c1)) = c2),
% 29.39/19.63 inference(transitivity,[status(thm)],[24429, 24428])).
% 29.39/19.63 tff(24431,plain,
% 29.39/19.63 (f8(f9(f10(c2), f7(c1))) = f8(c2)),
% 29.39/19.63 inference(monotonicity,[status(thm)],[24430])).
% 29.39/19.63 tff(24432,plain,
% 29.39/19.63 ((c1 = f8(f9(f10(c2), f7(c1)))) <=> (c1 = f8(c2))),
% 29.39/19.63 inference(monotonicity,[status(thm)],[24431])).
% 29.39/19.63 tff(24433,plain,
% 29.39/19.63 ((c1 = f8(c2)) <=> (c1 = f8(f9(f10(c2), f7(c1))))),
% 29.39/19.63 inference(symmetry,[status(thm)],[24432])).
% 29.39/19.63 tff(24434,plain,
% 29.39/19.63 ((c1 = f8(c2)) <=> (f8(f9(f10(c2), f7(c1))) = c1)),
% 29.39/19.63 inference(transitivity,[status(thm)],[24433, 23999])).
% 29.39/19.63 tff(24435,plain,
% 29.39/19.63 ((~(c1 = f8(c2))) <=> (~(f8(f9(f10(c2), f7(c1))) = c1))),
% 29.39/19.63 inference(monotonicity,[status(thm)],[24434])).
% 29.39/19.63 tff(24436,plain,
% 29.39/19.63 (~(f8(f9(f10(c2), f7(c1))) = c1)),
% 29.39/19.63 inference(modus_ponens,[status(thm)],[24284, 24435])).
% 29.39/19.63 tff(24437,plain,
% 29.39/19.63 ((f8(f9(f10(c2), f7(c1))) = c2) <=> (f8(c2) = c2)),
% 29.39/19.63 inference(monotonicity,[status(thm)],[24431])).
% 29.39/19.63 tff(24438,plain,
% 29.39/19.63 ((f8(f9(f10(c2), f7(c1))) = c2) <=> (c2 = f8(c2))),
% 29.39/19.63 inference(transitivity,[status(thm)],[24437, 11998])).
% 29.39/19.63 tff(24439,plain,
% 29.39/19.63 ((c2 = f8(c2)) <=> (f8(f9(f10(c2), f7(c1))) = c2)),
% 29.39/19.63 inference(symmetry,[status(thm)],[24438])).
% 29.39/19.63 tff(24440,plain,
% 29.39/19.63 ((~(c2 = f8(c2))) <=> (~(f8(f9(f10(c2), f7(c1))) = c2))),
% 29.39/19.63 inference(monotonicity,[status(thm)],[24439])).
% 29.39/19.63 tff(24441,plain,
% 29.39/19.63 (~(c2 = f8(c2))),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[21159, 5124])).
% 29.39/19.63 tff(24442,plain,
% 29.39/19.63 (~(f8(f9(f10(c2), f7(c1))) = c2)),
% 29.39/19.63 inference(modus_ponens,[status(thm)],[24441, 24440])).
% 29.39/19.63 tff(24443,plain,
% 29.39/19.63 ($false),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[24048, 24442, 24436])).
% 29.39/19.63 tff(24444,plain,((~(c2 = f5(c2))) | (~(f7(c1) = c2)) | (c1 = f8(c2)) | (f10(c2) = c2) | (f7(c2) = c2) | big_f(f7(c2), c2) | big_f(c2, f10(c2)) | (~(f10(c1) = c1)) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 29.39/19.63 tff(24445,plain,
% 29.39/19.63 (~(c2 = f5(c2))),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[24444, 24425, 347, 89, 17, 23145, 12071, 3762, 66])).
% 29.39/19.63 tff(24446,plain,
% 29.39/19.63 (~(f5(c2) = c2)),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[8113, 24445])).
% 29.39/19.63 tff(24447,plain,
% 29.39/19.63 (f5(c2) = c1),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[1547, 24446])).
% 29.39/19.63 tff(24448,plain,
% 29.39/19.63 (c1 = f5(c2)),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[8139, 24447])).
% 29.39/19.63 tff(24449,plain,
% 29.39/19.63 (big_f(f9(c1, c2), f10(c1))),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[8242, 4236, 3762, 17, 333, 23054])).
% 29.39/19.63 tff(24450,plain,
% 29.39/19.63 ($false),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[23425, 24449, 4240, 66, 3762])).
% 29.39/19.63 tff(24451,plain,((f9(c1, c2) = c2) | big_f(c1, c1) | (~(f10(c1) = c1)) | (f7(c2) = c2) | big_f(f7(c2), c1) | (~(c1 = f5(c2)))), inference(lemma,lemma(discharge,[]))).
% 29.39/19.63 tff(24452,plain,
% 29.39/19.63 (f9(c1, c2) = c2),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[24451, 24448, 3762, 17, 66, 24422])).
% 29.39/19.63 tff(24453,plain,
% 29.39/19.63 (f9(f10(c2), f7(c1)) = c2),
% 29.39/19.63 inference(transitivity,[status(thm)],[24429, 24452])).
% 29.39/19.63 tff(24454,plain,
% 29.39/19.63 (f8(f9(f10(c2), f7(c1))) = f8(c2)),
% 29.39/19.63 inference(monotonicity,[status(thm)],[24453])).
% 29.39/19.63 tff(24455,plain,
% 29.39/19.63 ((c1 = f8(f9(f10(c2), f7(c1)))) <=> (c1 = f8(c2))),
% 29.39/19.63 inference(monotonicity,[status(thm)],[24454])).
% 29.39/19.63 tff(24456,plain,
% 29.39/19.63 ((c1 = f8(c2)) <=> (c1 = f8(f9(f10(c2), f7(c1))))),
% 29.39/19.63 inference(symmetry,[status(thm)],[24455])).
% 29.39/19.63 tff(24457,plain,
% 29.39/19.63 ((c1 = f8(c2)) <=> (f8(f9(f10(c2), f7(c1))) = c1)),
% 29.39/19.63 inference(transitivity,[status(thm)],[24456, 23999])).
% 29.39/19.63 tff(24458,plain,
% 29.39/19.63 ((~(c1 = f8(c2))) <=> (~(f8(f9(f10(c2), f7(c1))) = c1))),
% 29.39/19.63 inference(monotonicity,[status(thm)],[24457])).
% 29.39/19.63 tff(24459,plain,
% 29.39/19.63 (~(f8(f9(f10(c2), f7(c1))) = c1)),
% 29.39/19.63 inference(modus_ponens,[status(thm)],[24425, 24458])).
% 29.39/19.63 tff(24460,plain,
% 29.39/19.63 ((f8(f9(f10(c2), f7(c1))) = c2) <=> (f8(c2) = c2)),
% 29.39/19.63 inference(monotonicity,[status(thm)],[24454])).
% 29.39/19.63 tff(24461,plain,
% 29.39/19.63 ((f8(f9(f10(c2), f7(c1))) = c2) <=> (c2 = f8(c2))),
% 29.39/19.63 inference(transitivity,[status(thm)],[24460, 11998])).
% 29.39/19.63 tff(24462,plain,
% 29.39/19.63 ((c2 = f8(c2)) <=> (f8(f9(f10(c2), f7(c1))) = c2)),
% 29.39/19.63 inference(symmetry,[status(thm)],[24461])).
% 29.39/19.63 tff(24463,plain,
% 29.39/19.63 ((~(c2 = f8(c2))) <=> (~(f8(f9(f10(c2), f7(c1))) = c2))),
% 29.39/19.63 inference(monotonicity,[status(thm)],[24462])).
% 29.39/19.63 tff(24464,plain,
% 29.39/19.63 ((~(c2 = f8(c2))) | (~(c1 = f5(c2)))),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[24255, 1745, 89, 17, 12071, 24422])).
% 29.39/19.63 tff(24465,plain,
% 29.39/19.63 (~(c2 = f8(c2))),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[24464, 24448])).
% 29.39/19.63 tff(24466,plain,
% 29.39/19.63 (~(f8(f9(f10(c2), f7(c1))) = c2)),
% 29.39/19.63 inference(modus_ponens,[status(thm)],[24465, 24463])).
% 29.39/19.63 tff(24467,plain,
% 29.39/19.63 ($false),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[24048, 24466, 24459])).
% 29.39/19.63 tff(24468,plain,((f7(c2) = c2) | (~(f7(c1) = c2)) | (f10(c2) = c2) | (~(f10(c1) = c1)) | big_f(c1, c1) | big_f(c1, c2) | (~big_f(c2, c2)) | (c2 = c3) | (~(f4(c4) = c2)) | big_f(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 29.39/19.63 tff(24469,plain,
% 29.39/19.63 (f7(c2) = c2),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[24468, 2, 89, 22733, 66, 27, 24419, 377, 79, 120])).
% 29.39/19.63 tff(24470,plain,
% 29.39/19.63 (~(c1 = f5(c1))),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[13377, 24469, 115, 89, 66, 79, 2])).
% 29.39/19.63 tff(24471,plain,
% 29.39/19.63 (~(f5(c1) = c1)),
% 29.39/19.63 inference(modus_ponens,[status(thm)],[24470, 2279])).
% 29.39/19.63 tff(24472,plain,
% 29.39/19.63 (f5(c1) = c2),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[1708, 24471])).
% 29.39/19.63 tff(24473,plain,
% 29.39/19.63 (f6(c2, c2) = c2),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[24147, 24469, 79, 89, 24207, 2, 24472])).
% 29.39/19.63 tff(24474,plain,
% 29.39/19.63 (f7(f4(c4)) = c2),
% 29.39/19.63 inference(transitivity,[status(thm)],[80, 24469])).
% 29.39/19.63 tff(24475,plain,
% 29.39/19.63 (f6(c2, f7(f4(c4))) = f6(c2, c2)),
% 29.39/19.63 inference(monotonicity,[status(thm)],[24474])).
% 29.39/19.63 tff(24476,plain,
% 29.39/19.63 (f6(c2, f7(f4(c4))) = c2),
% 29.39/19.63 inference(transitivity,[status(thm)],[24475, 24473])).
% 29.39/19.63 tff(24477,plain,
% 29.39/19.63 (f8(f6(c2, f7(f4(c4)))) = f8(c2)),
% 29.39/19.63 inference(monotonicity,[status(thm)],[24476])).
% 29.39/19.63 tff(24478,plain,
% 29.39/19.63 ((c1 = f8(f6(c2, f7(f4(c4))))) <=> (c1 = f8(c2))),
% 29.39/19.63 inference(monotonicity,[status(thm)],[24477])).
% 29.39/19.63 tff(24479,plain,
% 29.39/19.63 ((c1 = f8(c2)) <=> (c1 = f8(f6(c2, f7(f4(c4)))))),
% 29.39/19.63 inference(symmetry,[status(thm)],[24478])).
% 29.39/19.63 tff(24480,plain,
% 29.39/19.63 ((c1 = f8(c2)) <=> (f8(f6(c2, f7(f4(c4)))) = c1)),
% 29.39/19.63 inference(transitivity,[status(thm)],[24479, 24177])).
% 29.39/19.63 tff(24481,plain,
% 29.39/19.63 ((~(c1 = f8(c2))) <=> (~(f8(f6(c2, f7(f4(c4)))) = c1))),
% 29.39/19.63 inference(monotonicity,[status(thm)],[24480])).
% 29.39/19.63 tff(24482,plain,
% 29.39/19.63 (big_f(f7(c2), f6(c2, c2))),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[2627, 24473, 24419, 24469])).
% 29.39/19.63 tff(24483,plain,
% 29.39/19.63 (~(c1 = f8(c2))),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[24187, 2963, 89, 24469, 24473, 24482, 24207])).
% 29.39/19.63 tff(24484,plain,
% 29.39/19.63 (~(f8(f6(c2, f7(f4(c4)))) = c1)),
% 29.39/19.63 inference(modus_ponens,[status(thm)],[24483, 24481])).
% 29.39/19.63 tff(24485,plain,
% 29.39/19.63 ((c2 = f8(f6(c2, f7(f4(c4))))) <=> (c2 = f8(c2))),
% 29.39/19.63 inference(monotonicity,[status(thm)],[24477])).
% 29.39/19.63 tff(24486,plain,
% 29.39/19.63 ((c2 = f8(c2)) <=> (c2 = f8(f6(c2, f7(f4(c4)))))),
% 29.39/19.63 inference(symmetry,[status(thm)],[24485])).
% 29.39/19.63 tff(24487,plain,
% 29.39/19.63 ((c2 = f8(c2)) <=> (f8(f6(c2, f7(f4(c4)))) = c2)),
% 29.39/19.63 inference(transitivity,[status(thm)],[24486, 23360])).
% 29.39/19.63 tff(24488,plain,
% 29.39/19.63 ((~(c2 = f8(c2))) <=> (~(f8(f6(c2, f7(f4(c4)))) = c2))),
% 29.39/19.63 inference(monotonicity,[status(thm)],[24487])).
% 29.39/19.63 tff(24489,plain,
% 29.39/19.63 (~(c2 = f8(c2))),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[24173, 2963, 89, 24469, 12071, 24473, 24482])).
% 29.39/19.63 tff(24490,plain,
% 29.39/19.63 (~(f8(f6(c2, f7(f4(c4)))) = c2)),
% 29.39/19.63 inference(modus_ponens,[status(thm)],[24489, 24488])).
% 29.39/19.63 tff(24491,plain,
% 29.39/19.63 ($false),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[24193, 24490, 24484])).
% 29.39/19.63 tff(24492,plain,(big_f(c2, c1) | (~(f4(c4) = c2)) | (f10(c2) = c2) | (f7(c1) = c1) | big_f(c1, c1) | big_f(c1, c2) | (c2 = c3)), inference(lemma,lemma(discharge,[]))).
% 29.39/19.63 tff(24493,plain,
% 29.39/19.63 (c2 = c3),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[24492, 79, 89, 115, 66, 27, 24421])).
% 29.39/19.63 tff(24494,plain,
% 29.39/19.63 (c3 = c2),
% 29.39/19.63 inference(modus_ponens,[status(thm)],[24493, 127])).
% 29.39/19.63 tff(24495,plain,
% 29.39/19.63 ((c1 = f8(c2)) <=> (f7(c2) = f8(c2))),
% 29.39/19.63 inference(symmetry,[status(thm)],[12676])).
% 29.39/19.63 tff(24496,plain,
% 29.39/19.63 ((~big_f(c1, c1)) <=> (~big_f(f7(c2), c1))),
% 29.39/19.63 inference(monotonicity,[status(thm)],[20219])).
% 29.39/19.63 tff(24497,plain,
% 29.39/19.63 (~big_f(f7(c2), c1)),
% 29.39/19.63 inference(modus_ponens,[status(thm)],[66, 24496])).
% 29.39/19.63 tff(24498,plain,
% 29.39/19.63 (~big_f(f7(c1), c1)),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[15738, 24421, 120])).
% 29.39/19.63 tff(24499,plain,
% 29.39/19.63 ($false),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[20429, 16987, 230, 115, 11752, 89, 292, 333])).
% 29.39/19.63 tff(24500,plain,((~(f5(c1) = c1)) | (f7(c1) = c1) | (~(f4(c4) = c1)) | (f10(c2) = c2) | (~(f7(c2) = c1)) | big_f(f7(c2), c1) | big_f(f7(c1), c1)), inference(lemma,lemma(discharge,[]))).
% 29.39/19.63 tff(24501,plain,
% 29.39/19.63 (~(f4(c4) = c1)),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[24500, 230, 115, 89, 24498, 292, 24497])).
% 29.39/19.63 tff(24502,plain,
% 29.39/19.63 (f4(c4) = c2),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[11750, 24501])).
% 29.39/19.63 tff(24503,plain,
% 29.39/19.63 (c2 = c3),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[24492, 24502, 89, 115, 66, 27, 24421])).
% 29.39/19.63 tff(24504,plain,
% 29.39/19.63 (c3 = c2),
% 29.39/19.63 inference(modus_ponens,[status(thm)],[24503, 127])).
% 29.39/19.63 tff(24505,plain,
% 29.39/19.63 ($false),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[13073, 13811, 24504, 115, 89, 24421, 24207, 24502])).
% 29.39/19.63 tff(24506,plain,((~(f5(c1) = c1)) | (f7(c1) = c1) | (f10(c2) = c2) | big_f(c1, c1) | big_f(c1, c2) | (~(f7(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.39/19.63 tff(24507,plain,
% 29.39/19.63 (~(f5(c1) = c1)),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[24506, 22, 89, 66, 27, 115])).
% 29.39/19.63 tff(24508,plain,
% 29.39/19.63 (f5(c1) = c2),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[1708, 24507])).
% 29.39/19.63 tff(24509,plain,
% 29.39/19.63 (c2 = f5(c1)),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[24054, 24508])).
% 29.39/19.63 tff(24510,plain,
% 29.39/19.63 (c2 = f5(f7(c2))),
% 29.39/19.63 inference(modus_ponens,[status(thm)],[24509, 8602])).
% 29.39/19.63 tff(24511,plain,
% 29.39/19.63 (~(f4(c4) = c2)),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[24468, 377, 89, 3762, 66, 27, 1345, 2, 17, 347])).
% 29.39/19.63 tff(24512,plain,
% 29.39/19.63 (~(c2 = c4)),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[16877, 9314, 1345, 377, 17, 11752])).
% 29.39/19.63 tff(24513,plain,
% 29.39/19.63 (~(c4 = c2)),
% 29.39/19.63 inference(modus_ponens,[status(thm)],[24512, 8722])).
% 29.39/19.63 tff(24514,plain,
% 29.39/19.63 (c4 = c1),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[461, 24513])).
% 29.39/19.63 tff(24515,plain,
% 29.39/19.63 (big_f(c2, c4) <=> big_f(c2, c1)),
% 29.39/19.63 inference(monotonicity,[status(thm)],[24514])).
% 29.39/19.63 tff(24516,plain,
% 29.39/19.63 (big_f(c2, c1) <=> big_f(c2, c4)),
% 29.39/19.63 inference(symmetry,[status(thm)],[24515])).
% 29.39/19.63 tff(24517,plain,
% 29.39/19.63 ((~big_f(c2, c1)) <=> (~big_f(c2, c4))),
% 29.39/19.63 inference(monotonicity,[status(thm)],[24516])).
% 29.39/19.63 tff(24518,plain,
% 29.39/19.63 (~big_f(c2, c4)),
% 29.39/19.63 inference(modus_ponens,[status(thm)],[2, 24517])).
% 29.39/19.63 tff(24519,plain,
% 29.39/19.63 (big_f(f3(c2, c2), c2)),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[21029, 24512, 1345, 22, 9314, 377])).
% 29.39/19.63 tff(24520,plain,
% 29.39/19.63 (~(f3(f5(c1), f5(c1)) = c1)),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[17065, 24519, 22, 1521, 8686])).
% 29.39/19.63 tff(24521,plain,
% 29.39/19.63 (f3(f5(c1), f5(c1)) = c2),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[7625, 24520])).
% 29.39/19.63 tff(24522,plain,
% 29.39/19.63 (f5(f7(c2)) = c2),
% 29.39/19.63 inference(symmetry,[status(thm)],[8686])).
% 29.39/19.63 tff(24523,plain,
% 29.39/19.63 (f5(c1) = c2),
% 29.39/19.63 inference(transitivity,[status(thm)],[17055, 24522])).
% 29.39/19.63 tff(24524,plain,
% 29.39/19.63 (f3(f5(c1), f5(c1)) = f3(c2, c2)),
% 29.39/19.63 inference(monotonicity,[status(thm)],[24523, 24523])).
% 29.39/19.63 tff(24525,plain,
% 29.39/19.63 ((f3(f5(c1), f5(c1)) = c2) <=> (f3(c2, c2) = c2)),
% 29.39/19.63 inference(monotonicity,[status(thm)],[24524])).
% 29.39/19.63 tff(24526,plain,
% 29.39/19.63 (f3(c2, c2) = c2),
% 29.39/19.63 inference(modus_ponens,[status(thm)],[13005, 24525])).
% 29.39/19.63 tff(24527,plain,
% 29.39/19.63 ($false),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[12861, 24526])).
% 29.39/19.63 tff(24528,plain,((~(f3(f5(c1), f5(c1)) = c2)) | (f3(c2, c2) = c2) | (~(c2 = f5(f7(c2)))) | (~(f7(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.39/19.63 tff(24529,plain,
% 29.39/19.63 (f3(c2, c2) = c2),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[24528, 24521, 22, 8686])).
% 29.39/19.63 tff(24530,plain,
% 29.39/19.63 (big_f(c2, c4)),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[21039, 24529, 1345, 377, 24512, 24519])).
% 29.39/19.63 tff(24531,plain,
% 29.39/19.63 ($false),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[24530, 24518])).
% 29.39/19.63 tff(24532,plain,(big_f(c2, c1) | (~big_f(c2, c2)) | (c2 = c3) | (~(c2 = f5(f7(c2)))) | big_f(f7(c2), c2) | (f7(c2) = c2) | (~(f4(c4) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.39/19.63 tff(24533,plain,
% 29.39/19.63 (~(f4(c4) = c1)),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[24532, 377, 1345, 8686, 2, 17, 23145])).
% 29.39/19.63 tff(24534,plain,
% 29.39/19.63 ($false),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[11750, 24533, 24511])).
% 29.39/19.63 tff(24535,plain,((c2 = c3) | (~big_f(c2, c2)) | (~(c2 = f5(f7(c2)))) | big_f(c2, c1) | (f7(c2) = c2) | (f10(c2) = c2) | (~(f10(c1) = c1)) | big_f(c1, c1) | big_f(c1, c2) | (~(f7(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.39/19.63 tff(24536,plain,
% 29.39/19.63 (c2 = c3),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[24535, 24510, 24419, 24421, 17, 89, 22733, 66, 27, 120])).
% 29.39/19.63 tff(24537,plain,
% 29.39/19.63 (c3 = c2),
% 29.39/19.63 inference(symmetry,[status(thm)],[24536])).
% 29.39/19.63 tff(24538,plain,
% 29.39/19.63 (f8(c3) = f8(c2)),
% 29.39/19.63 inference(monotonicity,[status(thm)],[24537])).
% 29.39/19.63 tff(24539,plain,
% 29.39/19.63 ((f8(c3) = c1) <=> (f8(c2) = c1)),
% 29.39/19.63 inference(monotonicity,[status(thm)],[24538])).
% 29.39/19.63 tff(24540,plain,
% 29.39/19.63 ((f8(c3) = c1) <=> (c1 = f8(c2))),
% 29.39/19.63 inference(transitivity,[status(thm)],[24539, 13044])).
% 29.39/19.63 tff(24541,plain,
% 29.39/19.63 ((f8(c3) = c1) <=> (f7(c2) = f8(c2))),
% 29.39/19.63 inference(transitivity,[status(thm)],[24540, 24495])).
% 29.39/19.63 tff(24542,plain,
% 29.39/19.63 ((f8(c3) = c2) <=> (f8(c2) = c2)),
% 29.39/19.63 inference(monotonicity,[status(thm)],[24538])).
% 29.39/19.63 tff(24543,plain,
% 29.39/19.63 ((f8(c3) = c2) <=> (c2 = f8(c2))),
% 29.39/19.63 inference(transitivity,[status(thm)],[24542, 11998])).
% 29.39/19.63 tff(24544,plain,
% 29.39/19.63 ((c2 = f8(c2)) <=> (f8(c3) = c2)),
% 29.39/19.63 inference(symmetry,[status(thm)],[24543])).
% 29.39/19.63 tff(24545,plain,
% 29.39/19.63 ((~(c2 = f8(c2))) <=> (~(f8(c3) = c2))),
% 29.39/19.63 inference(monotonicity,[status(thm)],[24544])).
% 29.39/19.63 tff(24546,plain,
% 29.39/19.63 (~big_f(c2, f10(c2))),
% 29.39/19.63 inference(modus_ponens,[status(thm)],[24421, 12070])).
% 29.39/19.63 tff(24547,plain,
% 29.39/19.63 (~(c2 = f8(c2))),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[24260, 17, 89, 24546, 12093, 23145])).
% 29.39/19.63 tff(24548,plain,
% 29.39/19.63 (~(f8(c3) = c2)),
% 29.39/19.63 inference(modus_ponens,[status(thm)],[24547, 24545])).
% 29.39/19.63 tff(24549,plain,
% 29.39/19.63 (f8(c3) = c1),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[8569, 24548])).
% 29.39/19.63 tff(24550,plain,
% 29.39/19.63 (f7(c2) = f8(c2)),
% 29.39/19.63 inference(modus_ponens,[status(thm)],[24549, 24541])).
% 29.39/19.63 tff(24551,plain,
% 29.39/19.63 (~(f7(c2) = f8(c2))),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[12706, 23541, 89, 17, 23145])).
% 29.39/19.63 tff(24552,plain,
% 29.39/19.63 ($false),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[24551, 24550])).
% 29.39/19.63 tff(24553,plain,((f7(c2) = c2) | (f10(c2) = c2) | big_f(c1, c1) | big_f(c1, c2) | (f7(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.39/19.63 tff(24554,plain,
% 29.39/19.63 (f7(c2) = c2),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[24553, 66, 89, 27, 115])).
% 29.39/19.63 tff(24555,plain,
% 29.39/19.63 (~(c1 = f5(c1))),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[13373, 79, 115, 89, 24207, 24421, 24554])).
% 29.39/19.63 tff(24556,plain,
% 29.39/19.63 (~(f5(c1) = c1)),
% 29.39/19.63 inference(modus_ponens,[status(thm)],[24555, 2279])).
% 29.39/19.63 tff(24557,plain,
% 29.39/19.63 (f5(c1) = c2),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[1708, 24556])).
% 29.39/19.63 tff(24558,plain,
% 29.39/19.63 (f6(c2, c2) = c2),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[24147, 24557, 24421, 89, 24207, 24554, 79])).
% 29.39/19.63 tff(24559,plain,
% 29.39/19.63 (big_f(f7(c2), f6(c2, c2))),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[2627, 24558, 24419, 24554])).
% 29.39/19.63 tff(24560,plain,
% 29.39/19.63 (~(f6(f7(c2), c3) = c1)),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[2710, 24559, 24421, 24554, 24494])).
% 29.39/19.63 tff(24561,plain,
% 29.39/19.63 (f6(f7(c2), c3) = c2),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[2391, 24560])).
% 29.39/19.63 tff(24562,plain,
% 29.39/19.63 (c2 = f7(c2)),
% 29.39/19.63 inference(symmetry,[status(thm)],[24554])).
% 29.39/19.63 tff(24563,plain,
% 29.39/19.63 (f6(c2, c2) = f6(f7(c2), c3)),
% 29.39/19.63 inference(monotonicity,[status(thm)],[24562, 24493])).
% 29.39/19.63 tff(24564,plain,
% 29.39/19.63 (f7(f4(c4)) = c2),
% 29.39/19.63 inference(transitivity,[status(thm)],[80, 24554])).
% 29.39/19.63 tff(24565,plain,
% 29.39/19.63 (f6(c2, f7(f4(c4))) = f6(c2, c2)),
% 29.39/19.63 inference(monotonicity,[status(thm)],[24564])).
% 29.39/19.63 tff(24566,plain,
% 29.39/19.63 (f6(c2, f7(f4(c4))) = c2),
% 29.39/19.63 inference(transitivity,[status(thm)],[24565, 24563, 24561])).
% 29.39/19.63 tff(24567,plain,
% 29.39/19.63 (f8(f6(c2, f7(f4(c4)))) = f8(c2)),
% 29.39/19.63 inference(monotonicity,[status(thm)],[24566])).
% 29.39/19.63 tff(24568,plain,
% 29.39/19.63 ((c2 = f8(f6(c2, f7(f4(c4))))) <=> (c2 = f8(c2))),
% 29.39/19.63 inference(monotonicity,[status(thm)],[24567])).
% 29.39/19.63 tff(24569,plain,
% 29.39/19.63 ((c2 = f8(c2)) <=> (c2 = f8(f6(c2, f7(f4(c4)))))),
% 29.39/19.63 inference(symmetry,[status(thm)],[24568])).
% 29.39/19.63 tff(24570,plain,
% 29.39/19.63 ((c2 = f8(c2)) <=> (f8(f6(c2, f7(f4(c4)))) = c2)),
% 29.39/19.63 inference(transitivity,[status(thm)],[24569, 23360])).
% 29.39/19.63 tff(24571,plain,
% 29.39/19.63 ((~(c2 = f8(c2))) <=> (~(f8(f6(c2, f7(f4(c4)))) = c2))),
% 29.39/19.63 inference(monotonicity,[status(thm)],[24570])).
% 29.39/19.63 tff(24572,plain,
% 29.39/19.63 (~(c2 = f8(c2))),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[24173, 2963, 89, 24554, 24546, 24558, 24559])).
% 29.39/19.63 tff(24573,plain,
% 29.39/19.63 (~(f8(f6(c2, f7(f4(c4)))) = c2)),
% 29.39/19.63 inference(modus_ponens,[status(thm)],[24572, 24571])).
% 29.39/19.63 tff(24574,plain,
% 29.39/19.63 ((c1 = f8(f6(c2, f7(f4(c4))))) <=> (c1 = f8(c2))),
% 29.39/19.63 inference(monotonicity,[status(thm)],[24567])).
% 29.39/19.63 tff(24575,plain,
% 29.39/19.63 ((c1 = f8(c2)) <=> (c1 = f8(f6(c2, f7(f4(c4)))))),
% 29.39/19.63 inference(symmetry,[status(thm)],[24574])).
% 29.39/19.63 tff(24576,plain,
% 29.39/19.63 ((c1 = f8(c2)) <=> (f8(f6(c2, f7(f4(c4)))) = c1)),
% 29.39/19.63 inference(transitivity,[status(thm)],[24575, 24177])).
% 29.39/19.63 tff(24577,plain,
% 29.39/19.63 ((~(c1 = f8(c2))) <=> (~(f8(f6(c2, f7(f4(c4)))) = c1))),
% 29.39/19.63 inference(monotonicity,[status(thm)],[24576])).
% 29.39/19.63 tff(24578,plain,
% 29.39/19.63 (~(c1 = f8(c2))),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[24187, 2963, 89, 24554, 24558, 24559, 24207])).
% 29.39/19.63 tff(24579,plain,
% 29.39/19.63 (~(f8(f6(c2, f7(f4(c4)))) = c1)),
% 29.39/19.63 inference(modus_ponens,[status(thm)],[24578, 24577])).
% 29.39/19.63 tff(24580,plain,
% 29.39/19.63 ($false),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[24193, 24579, 24573])).
% 29.39/19.63 tff(24581,plain,((~(f4(c4) = c2)) | (f10(c2) = c2) | (f7(c1) = c1) | big_f(c1, c1) | big_f(c1, c2)), inference(lemma,lemma(discharge,[]))).
% 29.39/19.63 tff(24582,plain,
% 29.39/19.63 (~(f4(c4) = c2)),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[24581, 66, 115, 89, 27])).
% 29.39/19.63 tff(24583,plain,
% 29.39/19.63 (f4(c4) = c1),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[11750, 24582])).
% 29.39/19.63 tff(24584,plain,
% 29.39/19.63 (f7(f4(c4)) = f7(c1)),
% 29.39/19.63 inference(monotonicity,[status(thm)],[24583])).
% 29.39/19.63 tff(24585,plain,
% 29.39/19.63 (f7(f4(c4)) = c2),
% 29.39/19.63 inference(transitivity,[status(thm)],[24584, 120])).
% 29.39/19.63 tff(24586,plain,
% 29.39/19.63 (f8(f7(f4(c4))) = f8(c2)),
% 29.39/19.63 inference(monotonicity,[status(thm)],[24585])).
% 29.39/19.63 tff(24587,plain,
% 29.39/19.63 ((f8(f7(f4(c4))) = c1) <=> (f8(c2) = c1)),
% 29.39/19.63 inference(monotonicity,[status(thm)],[24586])).
% 29.39/19.63 tff(24588,plain,
% 29.39/19.63 ((f8(f7(f4(c4))) = c1) <=> (c1 = f8(c2))),
% 29.39/19.63 inference(transitivity,[status(thm)],[24587, 13044])).
% 29.39/19.63 tff(24589,plain,
% 29.39/19.63 ((c1 = f8(c2)) <=> (f8(f7(f4(c4))) = c1)),
% 29.39/19.63 inference(symmetry,[status(thm)],[24588])).
% 29.39/19.63 tff(24590,plain,
% 29.39/19.63 ((~(c1 = f8(c2))) <=> (~(f8(f7(f4(c4))) = c1))),
% 29.39/19.63 inference(monotonicity,[status(thm)],[24589])).
% 29.39/19.63 tff(24591,plain,
% 29.39/19.63 (big_f(f10(c2), f10(c2)) <=> big_f(c1, c1)),
% 29.39/19.63 inference(monotonicity,[status(thm)],[94, 94])).
% 29.39/19.63 tff(24592,plain,
% 29.39/19.63 (big_f(c1, c1) <=> big_f(f10(c2), f10(c2))),
% 29.39/19.63 inference(symmetry,[status(thm)],[24591])).
% 29.39/19.63 tff(24593,plain,
% 29.39/19.63 ((~big_f(c1, c1)) <=> (~big_f(f10(c2), f10(c2)))),
% 29.39/19.63 inference(monotonicity,[status(thm)],[24592])).
% 29.39/19.63 tff(24594,plain,
% 29.39/19.63 (~big_f(f10(c2), f10(c2))),
% 29.39/19.63 inference(modus_ponens,[status(thm)],[66, 24593])).
% 29.39/19.63 tff(24595,plain,
% 29.39/19.63 (~(c3 = c1)),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[11784, 24583, 27, 66])).
% 29.39/19.63 tff(24596,plain,
% 29.39/19.63 (c3 = c2),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[180, 24595])).
% 29.39/19.63 tff(24597,plain,
% 29.39/19.63 ((f8(f7(f4(c4))) = c1) <=> (f10(c2) = f8(c2))),
% 29.39/19.63 inference(transitivity,[status(thm)],[21137, 21566])).
% 29.39/19.63 tff(24598,plain,
% 29.39/19.63 (~(c2 = f8(c2))),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[21595, 2637, 89, 12071, 77, 67])).
% 29.39/19.63 tff(24599,plain,
% 29.39/19.63 (~(f8(f7(f4(c4))) = c2)),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[17582, 24598, 347, 11752])).
% 29.39/19.63 tff(24600,plain,
% 29.39/19.63 (f8(f7(f4(c4))) = c1),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[13371, 24599])).
% 29.39/19.63 tff(24601,plain,
% 29.39/19.63 (f10(c2) = f8(c2)),
% 29.39/19.63 inference(modus_ponens,[status(thm)],[24600, 24597])).
% 29.39/19.63 tff(24602,plain,
% 29.39/19.63 (~(f10(c2) = f8(c2))),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[21579, 2637, 89, 20783, 2, 77, 67])).
% 29.39/19.63 tff(24603,plain,
% 29.39/19.63 ($false),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[24602, 24601])).
% 29.39/19.63 tff(24604,plain,((f6(c2, c2) = c2) | (~(f7(c1) = c2)) | (~(f4(c4) = c1)) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (~(c3 = c2)) | big_f(f10(c2), f10(c2)) | big_f(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 29.39/19.63 tff(24605,plain,
% 29.39/19.63 (f6(c2, c2) = c2),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[24604, 24583, 120, 89, 24554, 24596, 24594, 24421])).
% 29.39/19.63 tff(24606,plain,
% 29.39/19.63 (big_f(f7(c2), f6(c2, c2))),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[2627, 24605, 24419, 24554])).
% 29.39/19.63 tff(24607,plain,
% 29.39/19.63 (~(c1 = f8(c2))),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[24187, 2963, 89, 24554, 24605, 24606, 24207])).
% 29.39/19.63 tff(24608,plain,
% 29.39/19.63 (~(f8(f7(f4(c4))) = c1)),
% 29.39/19.63 inference(modus_ponens,[status(thm)],[24607, 24590])).
% 29.39/19.63 tff(24609,plain,
% 29.39/19.63 (~(c2 = f8(c2))),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[24173, 2963, 89, 24554, 24546, 24605, 24606])).
% 29.39/19.63 tff(24610,plain,
% 29.39/19.63 (~(f8(f7(f4(c4))) = c2)),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[17582, 24609, 120, 24583])).
% 29.39/19.63 tff(24611,plain,
% 29.39/19.63 (f8(f7(f4(c4))) = c1),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[13371, 24610])).
% 29.39/19.63 tff(24612,plain,
% 29.39/19.63 ($false),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[24611, 24608])).
% 29.39/19.63 tff(24613,plain,(big_f(c1, c1) | (f10(c2) = c2) | big_f(c1, c2) | (f7(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.39/19.63 tff(24614,plain,
% 29.39/19.63 (big_f(c1, c1)),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[24613, 89, 27, 115])).
% 29.39/19.63 tff(24615,plain,
% 29.39/19.63 (big_f(f7(c2), c1)),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[20926, 22, 94, 24614])).
% 29.39/19.63 tff(24616,plain,
% 29.39/19.63 (big_f(f7(c2), f10(c2))),
% 29.39/19.63 inference(unit_resolution,[status(thm)],[21331, 24615, 94])).
% 29.39/19.63 tff(24617,plain,
% 29.39/19.63 (big_f(f7(f7(c2)), c2)),
% 29.39/19.63 inference(modus_ponens,[status(thm)],[24419, 8617])).
% 29.39/19.63 tff(24618,plain,
% 29.39/19.64 (~big_f(c2, c1)),
% 29.39/19.64 inference(unit_resolution,[status(thm)],[12536, 24617, 120, 89, 17, 24616])).
% 29.39/19.64 tff(24619,plain,
% 29.39/19.64 (~(f4(c4) = c2)),
% 29.39/19.64 inference(unit_resolution,[status(thm)],[12603, 24618, 27, 24419, 24614, 17])).
% 29.39/19.64 tff(24620,plain,
% 29.39/19.64 (f4(c4) = c1),
% 29.39/19.64 inference(unit_resolution,[status(thm)],[11750, 24619])).
% 29.39/19.64 tff(24621,plain,
% 29.39/19.64 (big_f(f9(c1, c1), c1)),
% 29.39/19.64 inference(unit_resolution,[status(thm)],[22759, 17574, 115, 4932, 11826])).
% 29.39/19.64 tff(24622,plain,
% 29.39/19.64 (big_f(f9(c1, c1), f10(c1))),
% 29.39/19.64 inference(unit_resolution,[status(thm)],[8716, 24621, 22733])).
% 29.39/19.64 tff(24623,plain,
% 29.39/19.64 (~(f9(c1, c1) = c2)),
% 29.39/19.64 inference(unit_resolution,[status(thm)],[10058, 24621, 2])).
% 29.39/19.64 tff(24624,plain,
% 29.39/19.64 (f9(c1, c1) = c1),
% 29.39/19.64 inference(unit_resolution,[status(thm)],[3939, 24623])).
% 29.39/19.64 tff(24625,plain,
% 29.39/19.64 ($false),
% 29.39/19.64 inference(unit_resolution,[status(thm)],[18656, 783, 115, 22733, 24624, 24622, 17574, 11826])).
% 29.39/19.64 tff(24626,plain,(big_f(c2, c1) | (f7(c1) = c1) | (~(c1 = f5(c1))) | (~big_f(c1, c1))), inference(lemma,lemma(discharge,[]))).
% 29.39/19.64 tff(24627,plain,
% 29.39/19.64 (~(c1 = f5(c1))),
% 29.39/19.64 inference(unit_resolution,[status(thm)],[24626, 24618, 115, 24614])).
% 29.39/19.64 tff(24628,plain,
% 29.39/19.64 (~(f5(c1) = c1)),
% 29.39/19.64 inference(modus_ponens,[status(thm)],[24627, 2279])).
% 29.39/19.64 tff(24629,plain,
% 29.39/19.64 (f5(c1) = c2),
% 29.39/19.64 inference(unit_resolution,[status(thm)],[1708, 24628])).
% 29.39/19.64 tff(24630,plain,
% 29.39/19.64 (c2 = f5(c1)),
% 29.39/19.64 inference(unit_resolution,[status(thm)],[24054, 24629])).
% 29.39/19.64 tff(24631,plain,
% 29.39/19.64 (c2 = f5(f7(c2))),
% 29.39/19.64 inference(modus_ponens,[status(thm)],[24630, 8602])).
% 29.39/19.64 tff(24632,plain,
% 29.39/19.64 (c2 = c3),
% 29.39/19.64 inference(unit_resolution,[status(thm)],[24532, 24631, 24419, 17, 24618, 24620, 23145])).
% 29.39/19.64 tff(24633,plain,
% 29.39/19.64 (c3 = c2),
% 29.39/19.64 inference(symmetry,[status(thm)],[24632])).
% 29.39/19.64 tff(24634,plain,
% 29.39/19.64 ((c1 = c3) <=> (c1 = c2)),
% 29.39/19.64 inference(monotonicity,[status(thm)],[24633])).
% 29.39/19.64 tff(24635,plain,
% 29.39/19.64 ((c1 = c3) <=> (c2 = c1)),
% 29.39/19.64 inference(transitivity,[status(thm)],[24634, 1])).
% 29.39/19.64 tff(24636,plain,
% 29.39/19.64 ((c2 = c1) <=> (c1 = c3)),
% 29.39/19.64 inference(symmetry,[status(thm)],[24635])).
% 29.39/19.64 tff(24637,plain,
% 29.39/19.64 ((c2 = c1) <=> (f7(c2) = c3)),
% 29.39/19.64 inference(transitivity,[status(thm)],[24636, 13076])).
% 29.39/19.64 tff(24638,plain,
% 29.39/19.64 ((~(c2 = c1)) <=> (~(f7(c2) = c3))),
% 29.39/19.64 inference(monotonicity,[status(thm)],[24637])).
% 29.39/19.64 tff(24639,plain,
% 29.39/19.64 (~(f7(c2) = c3)),
% 29.39/19.64 inference(modus_ponens,[status(thm)],[75, 24638])).
% 29.39/19.64 tff(24640,plain,
% 29.39/19.64 ((~(c2 = c1)) <=> (~(c1 = c3))),
% 29.39/19.64 inference(monotonicity,[status(thm)],[24636])).
% 29.39/19.64 tff(24641,plain,
% 29.39/19.64 (~(c1 = c3)),
% 29.39/19.64 inference(modus_ponens,[status(thm)],[75, 24640])).
% 29.39/19.64 tff(24642,plain,
% 29.39/19.64 (f3(c2, c2) = f3(f5(c1), f5(c1))),
% 29.39/19.64 inference(monotonicity,[status(thm)],[2908, 2908])).
% 29.39/19.64 tff(24643,plain,
% 29.39/19.64 (f3(c2, c2) = c1),
% 29.39/19.64 inference(transitivity,[status(thm)],[24642, 14337])).
% 29.39/19.64 tff(24644,plain,
% 29.39/19.64 ((f3(c2, c2) = c2) <=> (c1 = c2)),
% 29.39/19.64 inference(monotonicity,[status(thm)],[24643])).
% 29.39/19.64 tff(24645,plain,
% 29.39/19.64 ((f3(c2, c2) = c2) <=> (c2 = c1)),
% 29.39/19.64 inference(transitivity,[status(thm)],[24644, 1])).
% 29.39/19.64 tff(24646,plain,
% 29.39/19.64 ((c2 = c1) <=> (f3(c2, c2) = c2)),
% 29.39/19.64 inference(symmetry,[status(thm)],[24645])).
% 29.39/19.64 tff(24647,plain,
% 29.39/19.64 ((~(c2 = c1)) <=> (~(f3(c2, c2) = c2))),
% 29.39/19.64 inference(monotonicity,[status(thm)],[24646])).
% 29.39/19.64 tff(24648,plain,
% 29.39/19.64 (~(f3(c2, c2) = c2)),
% 29.39/19.64 inference(modus_ponens,[status(thm)],[75, 24647])).
% 29.39/19.64 tff(24649,plain,
% 29.39/19.64 (c2 = f5(f7(c2))),
% 29.39/19.64 inference(modus_ponens,[status(thm)],[2908, 10375])).
% 29.39/19.64 tff(24650,plain,
% 29.39/19.64 (~big_f(f7(c2), c2)),
% 29.39/19.64 inference(unit_resolution,[status(thm)],[21127, 292, 27])).
% 29.39/19.64 tff(24651,plain,
% 29.39/19.64 (~big_f(f3(c2, c2), c2)),
% 29.39/19.64 inference(unit_resolution,[status(thm)],[17065, 14337, 292, 24650, 24649])).
% 29.39/19.64 tff(24652,plain,
% 29.39/19.64 (f3(c2, c2) = c2),
% 29.39/19.64 inference(unit_resolution,[status(thm)],[21176, 24651, 168, 4932, 873, 27])).
% 29.39/19.64 tff(24653,plain,
% 29.39/19.64 ($false),
% 29.39/19.64 inference(unit_resolution,[status(thm)],[24652, 24648])).
% 29.39/19.64 tff(24654,plain,((~(f3(f5(c1), f5(c1)) = c1)) | (~(c2 = f5(c1))) | (c1 = c3) | (~big_f(c1, c1)) | (c2 = c4) | big_f(c1, c2) | (~(f7(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.39/19.64 tff(24655,plain,
% 29.39/19.64 (~(f3(f5(c1), f5(c1)) = c1)),
% 29.39/19.64 inference(unit_resolution,[status(thm)],[24654, 873, 168, 4932, 2908, 27, 292])).
% 29.39/19.64 tff(24656,plain,
% 29.39/19.64 (f3(f5(c1), f5(c1)) = c2),
% 29.39/19.64 inference(unit_resolution,[status(thm)],[7625, 24655])).
% 29.39/19.64 tff(24657,plain,
% 29.39/19.64 (f3(c2, c2) = c2),
% 29.39/19.64 inference(transitivity,[status(thm)],[24642, 24656])).
% 29.39/19.64 tff(24658,plain,
% 29.39/19.64 (big_f(f3(c2, c2), c2) <=> big_f(c2, c2)),
% 29.39/19.64 inference(monotonicity,[status(thm)],[24657])).
% 29.39/19.64 tff(24659,plain,
% 29.39/19.64 (big_f(c2, c2) <=> big_f(f3(c2, c2), c2)),
% 29.39/19.64 inference(symmetry,[status(thm)],[24658])).
% 29.39/19.64 tff(24660,plain,
% 29.39/19.64 (big_f(f3(c2, c2), c2)),
% 29.39/19.64 inference(modus_ponens,[status(thm)],[1345, 24659])).
% 29.39/19.64 tff(24661,plain,
% 29.39/19.64 (f3(c2, c2) = c2),
% 29.39/19.64 inference(unit_resolution,[status(thm)],[24528, 24656, 292, 24649])).
% 29.39/19.64 tff(24662,plain,
% 29.39/19.64 (f1(c1, c1) = c1),
% 29.39/19.64 inference(unit_resolution,[status(thm)],[17109, 24660, 9092, 873, 292, 24661, 27])).
% 29.39/19.64 tff(24663,plain,
% 29.39/19.64 (big_f(c1, f1(c1, c1))),
% 29.39/19.64 inference(unit_resolution,[status(thm)],[9678, 24662, 4932])).
% 29.39/19.64 tff(24664,plain,
% 29.39/19.64 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (c2 = c4) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (c2 = c4) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)))),
% 29.39/19.64 inference(rewrite,[status(thm)],[])).
% 29.39/19.64 tff(24665,plain,
% 29.39/19.64 (((c2 = c4) | (c1 = c3) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1)))) <=> ((c1 = c3) | (c2 = c4) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)))),
% 29.39/19.64 inference(rewrite,[status(thm)],[])).
% 29.39/19.64 tff(24666,plain,
% 29.39/19.64 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (c1 = c3) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (c2 = c4) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2))))),
% 29.39/19.64 inference(monotonicity,[status(thm)],[24665])).
% 29.39/19.64 tff(24667,plain,
% 29.39/19.64 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (c1 = c3) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (c2 = c4) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)))),
% 29.39/19.64 inference(transitivity,[status(thm)],[24666, 24664])).
% 29.39/19.64 tff(24668,plain,
% 29.39/19.64 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c4) | (c1 = c3) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))))),
% 29.39/19.64 inference(quant_inst,[status(thm)],[])).
% 29.39/19.64 tff(24669,plain,
% 29.39/19.64 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (c2 = c4) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2))),
% 29.39/19.64 inference(modus_ponens,[status(thm)],[24668, 24667])).
% 29.39/19.64 tff(24670,plain,
% 29.39/19.64 ($false),
% 29.39/19.64 inference(unit_resolution,[status(thm)],[24669, 933, 24662, 168, 24663, 873, 24661, 24660])).
% 29.39/19.64 tff(24671,plain,((c2 = c4) | (c1 = c3) | (~big_f(c1, c1)) | (f7(c2) = c3) | (~(f7(c2) = c1)) | big_f(c1, c2) | (~big_f(c2, c2)) | (~(c2 = f5(c1)))), inference(lemma,lemma(discharge,[]))).
% 29.39/19.64 tff(24672,plain,
% 29.39/19.64 (c2 = c4),
% 29.39/19.64 inference(unit_resolution,[status(thm)],[24671, 24639, 27, 24419, 24614, 24641, 22, 24630])).
% 29.39/19.64 tff(24673,plain,
% 29.39/19.64 (c4 = c2),
% 29.39/19.64 inference(modus_ponens,[status(thm)],[24672, 8721])).
% 29.39/19.64 tff(24674,plain,
% 29.39/19.64 (~big_f(c1, f1(c1, c1))),
% 29.39/19.64 inference(unit_resolution,[status(thm)],[23017, 24673, 27, 24620, 24641])).
% 29.39/19.64 tff(24675,plain,
% 29.39/19.64 (c4 = c2),
% 29.39/19.64 inference(symmetry,[status(thm)],[24672])).
% 29.39/19.64 tff(24676,plain,
% 29.39/19.64 ((c1 = c4) <=> (c1 = c2)),
% 29.39/19.64 inference(monotonicity,[status(thm)],[24675])).
% 29.39/19.64 tff(24677,plain,
% 29.39/19.64 ((c1 = c4) <=> (c2 = c1)),
% 29.39/19.64 inference(transitivity,[status(thm)],[24676, 1])).
% 29.39/19.64 tff(24678,plain,
% 29.39/19.64 ((c2 = c1) <=> (c1 = c4)),
% 29.39/19.64 inference(symmetry,[status(thm)],[24677])).
% 29.39/19.64 tff(24679,plain,
% 29.39/19.64 ((c2 = c1) <=> (f7(c2) = c4)),
% 29.39/19.64 inference(transitivity,[status(thm)],[24678, 23292])).
% 29.39/19.64 tff(24680,plain,
% 29.39/19.64 ((~(c2 = c1)) <=> (~(f7(c2) = c4))),
% 29.39/19.64 inference(monotonicity,[status(thm)],[24679])).
% 29.39/19.64 tff(24681,plain,
% 29.39/19.64 (~(f7(c2) = c4)),
% 29.39/19.64 inference(modus_ponens,[status(thm)],[75, 24680])).
% 29.39/19.64 tff(24682,plain,
% 29.39/19.64 ((~(c2 = c1)) <=> (~(c1 = c4))),
% 29.39/19.64 inference(monotonicity,[status(thm)],[24678])).
% 29.39/19.64 tff(24683,plain,
% 29.39/19.64 (~(c1 = c4)),
% 29.39/19.64 inference(modus_ponens,[status(thm)],[75, 24682])).
% 29.39/19.64 tff(24684,plain,
% 29.39/19.64 (f3(c1, c1) = c1),
% 29.39/19.64 inference(unit_resolution,[status(thm)],[9696, 24683, 17, 24614, 27, 24618, 24641, 24681, 24639])).
% 29.39/19.64 tff(24685,plain,
% 29.39/19.64 ($false),
% 29.39/19.64 inference(unit_resolution,[status(thm)],[9724, 24684, 24681, 24615, 22, 24674, 24639])).
% 29.39/19.64 tff(24686,plain,((f7(c2) = c2) | big_f(c1, c2) | (f7(c1) = c1) | (f10(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 29.39/19.64 tff(24687,plain,
% 29.39/19.64 (f7(c2) = c2),
% 29.39/19.64 inference(unit_resolution,[status(thm)],[24686, 89, 115, 27])).
% 29.39/19.64 tff(24688,plain,
% 29.39/19.64 (~(c1 = f5(c1))),
% 29.39/19.64 inference(unit_resolution,[status(thm)],[24626, 2, 115, 4932])).
% 29.39/19.64 tff(24689,plain,
% 29.39/19.64 (~(f5(c1) = c1)),
% 29.39/19.64 inference(modus_ponens,[status(thm)],[24688, 2279])).
% 29.39/19.64 tff(24690,plain,
% 29.39/19.64 (f5(c1) = c2),
% 29.39/19.64 inference(unit_resolution,[status(thm)],[1708, 24689])).
% 29.39/19.64 tff(24691,plain,
% 29.39/19.64 (~big_f(f9(c1, c1), c1)),
% 29.39/19.64 inference(unit_resolution,[status(thm)],[10058, 4071, 2])).
% 29.39/19.64 tff(24692,plain,
% 29.39/19.64 (~big_f(f9(c1, c1), f10(c1))),
% 29.39/19.64 inference(unit_resolution,[status(thm)],[10033, 24691, 3762])).
% 29.39/19.64 tff(24693,plain,
% 29.39/19.64 (big_f(f9(c1, f10(f10(c2))), f10(c1)) <=> big_f(f9(c1, c1), c1)),
% 29.39/19.64 inference(monotonicity,[status(thm)],[19277, 3762])).
% 29.39/19.64 tff(24694,plain,
% 29.39/19.64 (big_f(f9(c1, f10(f10(c2))), f10(c1)) <=> big_f(f9(c1, c1), f10(c1))),
% 29.39/19.64 inference(transitivity,[status(thm)],[24693, 3932])).
% 29.39/19.64 tff(24695,assumption,(big_f(f9(c1, f10(f10(c2))), f10(c1))), introduced(assumption)).
% 29.39/19.64 tff(24696,plain,
% 29.39/19.64 (big_f(f9(c1, c1), f10(c1))),
% 29.39/19.64 inference(modus_ponens,[status(thm)],[24695, 24694])).
% 29.39/19.64 tff(24697,plain,
% 29.39/19.64 ($false),
% 29.39/19.64 inference(unit_resolution,[status(thm)],[8712, 24696])).
% 29.39/19.64 tff(24698,plain,((~big_f(f9(c1, f10(f10(c2))), f10(c1))) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~(f10(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.39/19.64 tff(24699,plain,
% 29.39/19.64 (~big_f(f9(c1, f10(f10(c2))), f10(c1))),
% 29.39/19.64 inference(unit_resolution,[status(thm)],[24698, 24692, 3762, 11819])).
% 29.39/19.64 tff(24700,plain,
% 29.39/19.64 (~(f9(c1, f10(f10(c2))) = f10(f10(c2)))),
% 29.39/19.64 inference(modus_ponens,[status(thm)],[4070, 19280])).
% 29.39/19.64 tff(24701,plain,
% 29.39/19.64 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~(f10(c1) = c1)) | (f9(c1, f10(f10(c2))) = f10(f10(c2))) | big_f(f9(c1, f10(f10(c2))), f10(c1)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~(f10(c1) = c1)) | (f9(c1, f10(f10(c2))) = f10(f10(c2))) | big_f(f9(c1, f10(f10(c2))), f10(c1)))),
% 29.39/19.64 inference(rewrite,[status(thm)],[])).
% 29.39/19.64 tff(24702,plain,
% 29.39/19.64 (((~(f10(c1) = c1)) | (f9(c1, f10(f10(c2))) = f10(f10(c2))) | big_f(f9(c1, f10(f10(c2))), f10(c1)) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2)))) <=> ((~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~(f10(c1) = c1)) | (f9(c1, f10(f10(c2))) = f10(f10(c2))) | big_f(f9(c1, f10(f10(c2))), f10(c1)))),
% 29.39/19.64 inference(rewrite,[status(thm)],[])).
% 29.39/19.64 tff(24703,plain,
% 29.39/19.64 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (f9(c1, f10(f10(c2))) = f10(f10(c2))) | big_f(f9(c1, f10(f10(c2))), f10(c1)) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~(f10(c1) = c1)) | (f9(c1, f10(f10(c2))) = f10(f10(c2))) | big_f(f9(c1, f10(f10(c2))), f10(c1))))),
% 29.39/19.64 inference(monotonicity,[status(thm)],[24702])).
% 29.39/19.64 tff(24704,plain,
% 29.39/19.64 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (f9(c1, f10(f10(c2))) = f10(f10(c2))) | big_f(f9(c1, f10(f10(c2))), f10(c1)) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~(f10(c1) = c1)) | (f9(c1, f10(f10(c2))) = f10(f10(c2))) | big_f(f9(c1, f10(f10(c2))), f10(c1)))),
% 29.39/19.64 inference(transitivity,[status(thm)],[24703, 24701])).
% 29.39/19.64 tff(24705,plain,
% 29.39/19.64 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (f9(c1, f10(f10(c2))) = f10(f10(c2))) | big_f(f9(c1, f10(f10(c2))), f10(c1)) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))),
% 29.39/19.64 inference(quant_inst,[status(thm)],[])).
% 29.39/19.64 tff(24706,plain,
% 29.39/19.64 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~(f10(c1) = c1)) | (f9(c1, f10(f10(c2))) = f10(f10(c2))) | big_f(f9(c1, f10(f10(c2))), f10(c1))),
% 29.39/19.64 inference(modus_ponens,[status(thm)],[24705, 24704])).
% 29.39/19.64 tff(24707,plain,
% 29.39/19.64 ((~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~(f10(c1) = c1)) | (f9(c1, f10(f10(c2))) = f10(f10(c2))) | big_f(f9(c1, f10(f10(c2))), f10(c1))),
% 29.39/19.64 inference(unit_resolution,[status(thm)],[24706, 2534])).
% 29.39/19.64 tff(24708,plain,
% 29.39/19.64 ($false),
% 29.39/19.64 inference(unit_resolution,[status(thm)],[24707, 24214, 2622, 18604, 3762, 77, 18603])).
% 29.39/19.64 tff(24709,plain,((~(f6(c2, c2) = c2)) | (f9(c1, f10(f10(c2))) = f10(f10(c2))) | (~(f10(c1) = c1)) | (~(f7(c2) = c2)) | big_f(f9(c1, f10(f10(c2))), f10(c1)) | (~big_f(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 29.39/19.64 tff(24710,plain,
% 29.39/19.64 (~(f6(c2, c2) = c2)),
% 29.39/19.64 inference(unit_resolution,[status(thm)],[24709, 24700, 3762, 77, 24699, 1345])).
% 29.39/19.64 tff(24711,plain,
% 29.39/19.64 (~(f6(f7(c2), f5(c1)) = c2)),
% 29.39/19.64 inference(modus_ponens,[status(thm)],[24710, 4047])).
% 29.39/19.64 tff(24712,plain,
% 29.39/19.64 (f6(f7(c2), f5(c1)) = c1),
% 29.39/19.64 inference(unit_resolution,[status(thm)],[2978, 24711])).
% 29.39/19.64 tff(24713,plain,
% 29.39/19.64 (f6(c2, c2) = c1),
% 29.39/19.64 inference(transitivity,[status(thm)],[2258, 24712])).
% 29.39/19.64 tff(24714,plain,
% 29.39/19.64 (big_f(f7(c2), f6(c2, c2)) <=> big_f(c2, c1)),
% 29.39/19.64 inference(monotonicity,[status(thm)],[77, 24713])).
% 29.39/19.64 tff(24715,plain,
% 29.39/19.64 (big_f(c2, c1) <=> big_f(f7(c2), f6(c2, c2))),
% 29.39/19.64 inference(symmetry,[status(thm)],[24714])).
% 29.39/19.64 tff(24716,plain,
% 29.39/19.64 ((~big_f(c2, c1)) <=> (~big_f(f7(c2), f6(c2, c2)))),
% 29.39/19.64 inference(monotonicity,[status(thm)],[24715])).
% 29.39/19.64 tff(24717,plain,
% 29.39/19.64 (~big_f(f7(c2), f6(c2, c2))),
% 29.39/19.64 inference(modus_ponens,[status(thm)],[2, 24716])).
% 29.39/19.64 tff(24718,plain,
% 29.39/19.64 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)))),
% 29.39/19.64 inference(rewrite,[status(thm)],[])).
% 29.39/19.64 tff(24719,plain,
% 29.39/19.64 (((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2))) <=> ((~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)))),
% 29.39/19.64 inference(rewrite,[status(thm)],[])).
% 29.39/19.64 tff(24720,plain,
% 29.39/19.64 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1))))),
% 29.39/19.64 inference(monotonicity,[status(thm)],[24719])).
% 29.39/19.64 tff(24721,plain,
% 29.39/19.64 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)))),
% 29.39/19.64 inference(transitivity,[status(thm)],[24720, 24718])).
% 29.39/19.64 tff(24722,plain,
% 29.39/19.64 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)))),
% 29.39/19.64 inference(quant_inst,[status(thm)],[])).
% 29.39/19.64 tff(24723,plain,
% 29.39/19.64 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1))),
% 29.39/19.64 inference(modus_ponens,[status(thm)],[24722, 24721])).
% 29.39/19.64 tff(24724,plain,
% 29.39/19.64 (big_f(f7(c2), f6(c2, c2))),
% 29.39/19.64 inference(unit_resolution,[status(thm)],[24723, 2492, 3762, 77, 4070, 24692, 24710])).
% 29.39/19.64 tff(24725,plain,
% 29.39/19.64 ($false),
% 29.39/19.64 inference(unit_resolution,[status(thm)],[24724, 24717])).
% 29.39/19.64 tff(24726,plain,((f9(c1, c1) = c1) | big_f(c2, c1) | (~(f5(c1) = c2)) | (~(f7(c2) = c2)) | (~(f10(c1) = c1)) | (~big_f(c2, c2)) | (~(f10(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.39/19.64 tff(24727,plain,
% 29.39/19.64 (f9(c1, c1) = c1),
% 29.39/19.64 inference(unit_resolution,[status(thm)],[24726, 24690, 77, 2, 22733, 1345, 11819])).
% 29.39/19.64 tff(24728,plain,
% 29.39/19.64 (big_f(f9(c1, c1), c1)),
% 29.39/19.64 inference(unit_resolution,[status(thm)],[10938, 24727, 4932])).
% 29.39/19.64 tff(24729,plain,
% 29.39/19.64 (big_f(f9(c1, c1), f10(c1))),
% 29.39/19.64 inference(unit_resolution,[status(thm)],[8716, 24728, 22733])).
% 29.39/19.64 tff(24730,plain,
% 29.39/19.64 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))),
% 29.39/19.64 inference(rewrite,[status(thm)],[])).
% 29.39/19.64 tff(24731,plain,
% 29.39/19.64 (((~(f10(c1) = c1)) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1)))) <=> ((~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))),
% 29.39/19.64 inference(rewrite,[status(thm)],[])).
% 29.39/19.64 tff(24732,plain,
% 29.39/19.64 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c1) = c1)) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1)))))),
% 29.39/19.65 inference(monotonicity,[status(thm)],[24731])).
% 29.39/19.65 tff(24733,plain,
% 29.39/19.65 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c1) = c1)) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))),
% 29.39/19.65 inference(transitivity,[status(thm)],[24732, 24730])).
% 29.39/19.65 tff(24734,plain,
% 29.39/19.65 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c1) = c1)) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))),
% 29.39/19.65 inference(quant_inst,[status(thm)],[])).
% 29.39/19.65 tff(24735,plain,
% 29.39/19.65 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1)))),
% 29.39/19.65 inference(modus_ponens,[status(thm)],[24734, 24733])).
% 29.39/19.65 tff(24736,plain,
% 29.39/19.65 ($false),
% 29.39/19.65 inference(unit_resolution,[status(thm)],[24735, 2409, 3762, 77, 3949, 3948, 2628, 2621])).
% 29.39/19.65 tff(24737,plain,(big_f(f7(c2), f6(c2, c2)) | (~(f10(c1) = c1)) | (~(f7(c2) = c2)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~big_f(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 29.39/19.65 tff(24738,plain,
% 29.39/19.65 (big_f(f7(c2), f6(c2, c2))),
% 29.39/19.65 inference(unit_resolution,[status(thm)],[24737, 24729, 22733, 1345, 77, 24727])).
% 29.39/19.65 tff(24739,plain,
% 29.39/19.65 (c2 = f5(c1)),
% 29.39/19.65 inference(symmetry,[status(thm)],[24690])).
% 29.39/19.65 tff(24740,plain,
% 29.39/19.65 (f6(c2, c2) = f6(f7(c2), f5(c1))),
% 29.39/19.65 inference(monotonicity,[status(thm)],[82, 24739])).
% 29.39/19.65 tff(24741,plain,
% 29.39/19.65 ((f6(c2, c2) = c2) <=> (f6(f7(c2), f5(c1)) = c2)),
% 29.39/19.65 inference(monotonicity,[status(thm)],[24740])).
% 29.39/19.65 tff(24742,plain,
% 29.39/19.65 ((f6(f7(c2), f5(c1)) = c2) <=> (f6(c2, c2) = c2)),
% 29.39/19.65 inference(symmetry,[status(thm)],[24741])).
% 29.39/19.65 tff(24743,plain,
% 29.39/19.65 (~(f6(f7(c2), f5(c1)) = c1)),
% 29.39/19.65 inference(unit_resolution,[status(thm)],[24156, 24738, 2, 24690, 77])).
% 29.39/19.65 tff(24744,plain,
% 29.39/19.65 (f6(f7(c2), f5(c1)) = c2),
% 29.39/19.65 inference(unit_resolution,[status(thm)],[2978, 24743])).
% 29.39/19.65 tff(24745,plain,
% 29.39/19.65 (f6(c2, c2) = c2),
% 29.39/19.65 inference(modus_ponens,[status(thm)],[24744, 24742])).
% 29.39/19.65 tff(24746,plain,
% 29.39/19.65 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))),
% 29.39/19.65 inference(rewrite,[status(thm)],[])).
% 29.39/19.65 tff(24747,plain,
% 29.39/19.65 (((~(f10(c1) = c1)) | (~(f7(c2) = c2)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2)))) <=> ((~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))),
% 29.39/19.65 inference(rewrite,[status(thm)],[])).
% 29.39/19.65 tff(24748,plain,
% 29.39/19.65 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (~(f7(c2) = c2)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1)))))),
% 29.39/19.65 inference(monotonicity,[status(thm)],[24747])).
% 29.39/19.65 tff(24749,plain,
% 29.39/19.65 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (~(f7(c2) = c2)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))),
% 29.39/19.65 inference(transitivity,[status(thm)],[24748, 24746])).
% 29.39/19.65 tff(24750,plain,
% 29.39/19.65 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (~(f7(c2) = c2)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))),
% 29.39/19.65 inference(quant_inst,[status(thm)],[])).
% 29.39/19.65 tff(24751,plain,
% 29.39/19.65 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1)))),
% 29.39/19.65 inference(modus_ponens,[status(thm)],[24750, 24749])).
% 29.39/19.65 tff(24752,plain,
% 29.39/19.65 ($false),
% 29.39/19.65 inference(unit_resolution,[status(thm)],[24751, 2378, 22733, 77, 24727, 24729, 24745, 24738])).
% 29.39/19.65 tff(24753,plain,(big_f(c2, c1) | (~(f7(c2) = c2)) | (~big_f(c2, c2)) | (~big_f(c1, c1)) | (~(f10(c2) = c1)) | (f7(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.39/19.65 tff(24754,plain,
% 29.39/19.65 (big_f(c2, c1)),
% 29.39/19.65 inference(unit_resolution,[status(thm)],[24753, 24687, 24419, 24614, 94, 115])).
% 29.39/19.65 tff(24755,plain,
% 29.39/19.65 (big_f(c2, f10(c2))),
% 29.39/19.65 inference(modus_ponens,[status(thm)],[24754, 12069])).
% 29.39/19.65 tff(24756,plain,
% 29.39/19.65 (big_f(f7(f10(c2)), c2)),
% 29.39/19.65 inference(modus_ponens,[status(thm)],[24419, 17556])).
% 29.39/19.65 tff(24757,plain,
% 29.39/19.65 (big_f(f7(f10(c2)), f10(c2)) <=> big_f(c2, c1)),
% 29.39/19.65 inference(monotonicity,[status(thm)],[17554, 94])).
% 29.39/19.65 tff(24758,plain,
% 29.39/19.65 (big_f(c2, c1) <=> big_f(f7(f10(c2)), f10(c2))),
% 29.39/19.65 inference(symmetry,[status(thm)],[24757])).
% 29.39/19.65 tff(24759,plain,
% 29.39/19.65 (big_f(f7(f10(c2)), f10(c2))),
% 29.39/19.65 inference(modus_ponens,[status(thm)],[24754, 24758])).
% 29.39/19.65 tff(24760,plain,
% 29.39/19.65 (c2 = f8(c2)),
% 29.39/19.65 inference(unit_resolution,[status(thm)],[21713, 24759, 89, 24756, 24755, 24302])).
% 29.39/19.65 tff(24761,plain,
% 29.39/19.65 (f8(c2) = c2),
% 29.39/19.65 inference(symmetry,[status(thm)],[24760])).
% 29.39/19.65 tff(24762,plain,
% 29.39/19.65 ((c1 = f8(c2)) <=> (c1 = c2)),
% 29.39/19.65 inference(monotonicity,[status(thm)],[24761])).
% 29.39/19.65 tff(24763,plain,
% 29.39/19.65 ((c1 = f8(c2)) <=> (c2 = c1)),
% 29.39/19.65 inference(transitivity,[status(thm)],[24762, 1])).
% 29.39/19.65 tff(24764,plain,
% 29.39/19.65 ((c2 = c1) <=> (c1 = f8(c2))),
% 29.39/19.65 inference(symmetry,[status(thm)],[24763])).
% 29.39/19.65 tff(24765,plain,
% 29.39/19.65 ((c2 = c1) <=> (f10(c2) = f8(c2))),
% 29.39/19.65 inference(transitivity,[status(thm)],[24764, 21566])).
% 29.39/19.65 tff(24766,plain,
% 29.39/19.65 ((~(c2 = c1)) <=> (~(f10(c2) = f8(c2)))),
% 29.39/19.65 inference(monotonicity,[status(thm)],[24765])).
% 29.39/19.65 tff(24767,plain,
% 29.39/19.65 (~(f10(c2) = f8(c2))),
% 29.39/19.65 inference(modus_ponens,[status(thm)],[75, 24766])).
% 29.39/19.65 tff(24768,plain,
% 29.39/19.65 (big_f(f10(c2), f10(c2))),
% 29.39/19.65 inference(unit_resolution,[status(thm)],[21743, 24614, 94])).
% 29.39/19.65 tff(24769,plain,
% 29.39/19.65 (f10(c2) = f8(c2)),
% 29.39/19.65 inference(unit_resolution,[status(thm)],[21739, 24759, 89, 24756, 24768, 24302])).
% 29.39/19.65 tff(24770,plain,
% 29.39/19.65 ($false),
% 29.39/19.65 inference(unit_resolution,[status(thm)],[24769, 24767])).
% 29.39/19.65 tff(24771,plain,((f10(c2) = c2) | (f7(c1) = c1) | big_f(c1, c2)), inference(lemma,lemma(discharge,[]))).
% 29.39/19.65 tff(24772,plain,
% 29.39/19.65 (f7(c1) = c1),
% 29.39/19.65 inference(unit_resolution,[status(thm)],[24771, 27, 89])).
% 29.39/19.65 tff(24773,plain,
% 29.39/19.65 (big_f(f7(c1), f6(c1, f8(c2))) <=> big_f(c1, f6(c1, f8(c2)))),
% 29.39/19.65 inference(monotonicity,[status(thm)],[24772])).
% 29.39/19.65 tff(24774,plain,
% 29.39/19.65 (big_f(c1, f6(c1, f8(c2))) <=> big_f(f7(c1), f6(c1, f8(c2)))),
% 29.39/19.65 inference(symmetry,[status(thm)],[24773])).
% 29.39/19.65 tff(24775,plain,
% 29.39/19.65 ((~big_f(c1, f6(c1, f8(c2)))) <=> (~big_f(f7(c1), f6(c1, f8(c2))))),
% 29.39/19.65 inference(monotonicity,[status(thm)],[24774])).
% 29.39/19.65 tff(24776,assumption,(big_f(c1, f6(c1, f8(c2)))), introduced(assumption)).
% 29.39/19.65 tff(24777,assumption,(f6(c1, f8(c2)) = c1), introduced(assumption)).
% 29.39/19.65 tff(24778,plain,
% 29.39/19.65 (big_f(c1, f6(c1, f8(c2))) <=> big_f(c1, c1)),
% 29.39/19.65 inference(monotonicity,[status(thm)],[24777])).
% 29.39/19.65 tff(24779,plain,
% 29.39/19.65 (big_f(c1, c1) <=> big_f(c1, f6(c1, f8(c2)))),
% 29.39/19.65 inference(symmetry,[status(thm)],[24778])).
% 29.39/19.65 tff(24780,plain,
% 29.39/19.65 ((~big_f(c1, c1)) <=> (~big_f(c1, f6(c1, f8(c2))))),
% 29.39/19.65 inference(monotonicity,[status(thm)],[24779])).
% 29.39/19.65 tff(24781,plain,
% 29.39/19.65 (~big_f(c1, f6(c1, f8(c2)))),
% 29.39/19.65 inference(modus_ponens,[status(thm)],[66, 24780])).
% 29.39/19.65 tff(24782,plain,
% 29.39/19.65 ($false),
% 29.39/19.65 inference(unit_resolution,[status(thm)],[24776, 24781])).
% 29.39/19.65 tff(24783,plain,((~(f6(c1, f8(c2)) = c1)) | (~big_f(c1, f6(c1, f8(c2)))) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 29.39/19.65 tff(24784,plain,
% 29.39/19.65 (~(f6(c1, f8(c2)) = c1)),
% 29.39/19.65 inference(unit_resolution,[status(thm)],[24783, 24776, 66])).
% 29.39/19.65 tff(24785,plain,
% 29.39/19.65 (f6(c1, f8(c2)) = c2),
% 29.39/19.65 inference(unit_resolution,[status(thm)],[24295, 24784])).
% 29.39/19.65 tff(24786,plain,
% 29.39/19.65 (big_f(c1, f6(c1, f8(c2))) <=> big_f(c1, c2)),
% 29.39/19.65 inference(monotonicity,[status(thm)],[24785])).
% 29.39/19.65 tff(24787,plain,
% 29.39/19.65 (big_f(c1, c2) <=> big_f(c1, f6(c1, f8(c2)))),
% 29.39/19.65 inference(symmetry,[status(thm)],[24786])).
% 29.39/19.65 tff(24788,plain,
% 29.39/19.65 ((~big_f(c1, c2)) <=> (~big_f(c1, f6(c1, f8(c2))))),
% 29.39/19.65 inference(monotonicity,[status(thm)],[24787])).
% 29.39/19.65 tff(24789,plain,
% 29.39/19.65 (~big_f(c1, f6(c1, f8(c2)))),
% 29.39/19.65 inference(modus_ponens,[status(thm)],[27, 24788])).
% 29.39/19.65 tff(24790,plain,
% 29.39/19.65 ($false),
% 29.39/19.65 inference(unit_resolution,[status(thm)],[24776, 24789])).
% 29.39/19.65 tff(24791,plain,((~big_f(c1, f6(c1, f8(c2)))) | big_f(c1, c2) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 29.39/19.65 tff(24792,plain,
% 29.39/19.65 (~big_f(c1, f6(c1, f8(c2)))),
% 29.39/19.65 inference(unit_resolution,[status(thm)],[24791, 27, 66])).
% 29.39/19.65 tff(24793,plain,
% 29.39/19.65 (~big_f(f7(c1), f6(c1, f8(c2)))),
% 29.39/19.65 inference(modus_ponens,[status(thm)],[24792, 24775])).
% 29.39/19.65 tff(24794,assumption,(~big_f(f9(c1, f8(c2)), f10(c2))), introduced(assumption)).
% 29.39/19.65 tff(24795,plain,
% 29.39/19.65 (f10(c1) = f10(c2)),
% 29.39/19.65 inference(transitivity,[status(thm)],[3762, 12231])).
% 29.39/19.65 tff(24796,plain,
% 29.39/19.65 (big_f(f9(c1, f8(c2)), f10(c1)) <=> big_f(f9(c1, f8(c2)), f10(c2))),
% 29.39/19.65 inference(monotonicity,[status(thm)],[24795])).
% 29.39/19.65 tff(24797,assumption,(big_f(f9(c1, f8(c2)), f10(c1))), introduced(assumption)).
% 29.39/19.65 tff(24798,plain,
% 29.39/19.65 (big_f(f9(c1, f8(c2)), f10(c2))),
% 29.39/19.65 inference(modus_ponens,[status(thm)],[24797, 24796])).
% 29.39/19.65 tff(24799,plain,
% 29.39/19.65 ($false),
% 29.39/19.65 inference(unit_resolution,[status(thm)],[24794, 24798])).
% 29.39/19.65 tff(24800,plain,((~big_f(f9(c1, f8(c2)), f10(c1))) | big_f(f9(c1, f8(c2)), f10(c2)) | (~(f10(c1) = c1)) | (~(f10(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.39/19.65 tff(24801,plain,
% 29.39/19.65 (~big_f(f9(c1, f8(c2)), f10(c1))),
% 29.39/19.65 inference(unit_resolution,[status(thm)],[24800, 24794, 3762, 94])).
% 29.39/19.65 tff(24802,plain,
% 29.39/19.65 (f9(c1, f8(c2)) = f8(c2)),
% 29.39/19.65 inference(unit_resolution,[status(thm)],[20111, 24801, 3762, 4234, 20099, 20098])).
% 29.39/19.65 tff(24803,plain,
% 29.39/19.65 (f8(c2) = f9(c1, f8(c2))),
% 29.39/19.65 inference(symmetry,[status(thm)],[24802])).
% 29.39/19.65 tff(24804,plain,
% 29.39/19.65 (big_f(f8(c2), f10(c2)) <=> big_f(f9(c1, f8(c2)), f10(c2))),
% 29.39/19.65 inference(monotonicity,[status(thm)],[24803])).
% 29.39/19.65 tff(24805,plain,
% 29.39/19.65 (big_f(f9(c1, f8(c2)), f10(c2)) <=> big_f(f8(c2), f10(c2))),
% 29.39/19.65 inference(symmetry,[status(thm)],[24804])).
% 29.39/19.65 tff(24806,plain,
% 29.39/19.65 ((~big_f(f9(c1, f8(c2)), f10(c2))) <=> (~big_f(f8(c2), f10(c2)))),
% 29.39/19.65 inference(monotonicity,[status(thm)],[24805])).
% 29.39/19.65 tff(24807,plain,
% 29.39/19.65 (~big_f(f8(c2), f10(c2))),
% 29.39/19.65 inference(modus_ponens,[status(thm)],[24794, 24806])).
% 29.39/19.65 tff(24808,plain,
% 29.39/19.65 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | big_f(f7(c1), f6(c1, f8(c2))) | (~(f7(c1) = c1)) | (f6(c1, f8(c2)) = f8(c2)) | big_f(f8(c2), f10(c2)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | big_f(f7(c1), f6(c1, f8(c2))) | (~(f7(c1) = c1)) | (f6(c1, f8(c2)) = f8(c2)) | big_f(f8(c2), f10(c2)))),
% 29.39/19.65 inference(rewrite,[status(thm)],[])).
% 29.39/19.65 tff(24809,plain,
% 29.39/19.65 (((f10(c2) = c2) | big_f(f8(c2), f10(c2)) | (~(f7(c1) = c1)) | (f6(c1, f8(c2)) = f8(c2)) | big_f(f7(c1), f6(c1, f8(c2))) | $false) <=> ((f10(c2) = c2) | big_f(f7(c1), f6(c1, f8(c2))) | (~(f7(c1) = c1)) | (f6(c1, f8(c2)) = f8(c2)) | big_f(f8(c2), f10(c2)))),
% 29.39/19.65 inference(rewrite,[status(thm)],[])).
% 29.39/19.65 tff(24810,plain,
% 29.39/19.65 ((f8(c2) = f8(c2)) <=> $true),
% 29.39/19.65 inference(rewrite,[status(thm)],[])).
% 29.39/19.65 tff(24811,plain,
% 29.39/19.65 ((~(f8(c2) = f8(c2))) <=> (~$true)),
% 29.39/19.65 inference(monotonicity,[status(thm)],[24810])).
% 29.39/19.65 tff(24812,plain,
% 29.39/19.65 ((~(f8(c2) = f8(c2))) <=> $false),
% 29.39/19.65 inference(transitivity,[status(thm)],[24811, 270])).
% 29.39/19.65 tff(24813,plain,
% 29.39/19.65 (((f10(c2) = c2) | big_f(f8(c2), f10(c2)) | (~(f7(c1) = c1)) | (f6(c1, f8(c2)) = f8(c2)) | big_f(f7(c1), f6(c1, f8(c2))) | (~(f8(c2) = f8(c2)))) <=> ((f10(c2) = c2) | big_f(f8(c2), f10(c2)) | (~(f7(c1) = c1)) | (f6(c1, f8(c2)) = f8(c2)) | big_f(f7(c1), f6(c1, f8(c2))) | $false)),
% 29.39/19.65 inference(monotonicity,[status(thm)],[24812])).
% 29.39/19.65 tff(24814,plain,
% 29.39/19.65 (((f10(c2) = c2) | big_f(f8(c2), f10(c2)) | (~(f7(c1) = c1)) | (f6(c1, f8(c2)) = f8(c2)) | big_f(f7(c1), f6(c1, f8(c2))) | (~(f8(c2) = f8(c2)))) <=> ((f10(c2) = c2) | big_f(f7(c1), f6(c1, f8(c2))) | (~(f7(c1) = c1)) | (f6(c1, f8(c2)) = f8(c2)) | big_f(f8(c2), f10(c2)))),
% 29.39/19.65 inference(transitivity,[status(thm)],[24813, 24809])).
% 29.39/19.65 tff(24815,plain,
% 29.39/19.65 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | big_f(f8(c2), f10(c2)) | (~(f7(c1) = c1)) | (f6(c1, f8(c2)) = f8(c2)) | big_f(f7(c1), f6(c1, f8(c2))) | (~(f8(c2) = f8(c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | big_f(f7(c1), f6(c1, f8(c2))) | (~(f7(c1) = c1)) | (f6(c1, f8(c2)) = f8(c2)) | big_f(f8(c2), f10(c2))))),
% 29.39/19.65 inference(monotonicity,[status(thm)],[24814])).
% 29.39/19.65 tff(24816,plain,
% 29.39/19.65 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | big_f(f8(c2), f10(c2)) | (~(f7(c1) = c1)) | (f6(c1, f8(c2)) = f8(c2)) | big_f(f7(c1), f6(c1, f8(c2))) | (~(f8(c2) = f8(c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | big_f(f7(c1), f6(c1, f8(c2))) | (~(f7(c1) = c1)) | (f6(c1, f8(c2)) = f8(c2)) | big_f(f8(c2), f10(c2)))),
% 29.39/19.65 inference(transitivity,[status(thm)],[24815, 24808])).
% 29.39/19.65 tff(24817,plain,
% 29.39/19.65 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | big_f(f8(c2), f10(c2)) | (~(f7(c1) = c1)) | (f6(c1, f8(c2)) = f8(c2)) | big_f(f7(c1), f6(c1, f8(c2))) | (~(f8(c2) = f8(c2))))),
% 29.39/19.65 inference(quant_inst,[status(thm)],[])).
% 29.39/19.65 tff(24818,plain,
% 29.39/19.65 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | big_f(f7(c1), f6(c1, f8(c2))) | (~(f7(c1) = c1)) | (f6(c1, f8(c2)) = f8(c2)) | big_f(f8(c2), f10(c2))),
% 29.39/19.65 inference(modus_ponens,[status(thm)],[24817, 24816])).
% 29.39/19.65 tff(24819,plain,
% 29.39/19.65 (big_f(f8(c2), f10(c2))),
% 29.39/19.65 inference(unit_resolution,[status(thm)],[24818, 2994, 4234, 89, 20098, 20099])).
% 29.39/19.65 tff(24820,plain,
% 29.39/19.65 ($false),
% 29.39/19.65 inference(unit_resolution,[status(thm)],[24819, 24807])).
% 29.39/19.65 tff(24821,plain,(big_f(f9(c1, f8(c2)), f10(c2)) | (~(f7(c1) = c1)) | (f10(c2) = c2) | big_f(f7(c1), f6(c1, f8(c2))) | (f6(c1, f8(c2)) = f8(c2)) | (~(f10(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.39/19.65 tff(24822,plain,
% 29.39/19.65 (big_f(f9(c1, f8(c2)), f10(c2))),
% 29.39/19.65 inference(unit_resolution,[status(thm)],[24821, 24772, 89, 24793, 24298, 24276])).
% 29.39/19.65 tff(24823,assumption,(big_f(f9(c1, f8(c2)), f10(c2))), introduced(assumption)).
% 29.39/19.65 tff(24824,plain,
% 29.39/19.65 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f10(c2) = c2) | (f7(c2) = c2) | (~(c1 = f5(c2))) | big_f(f7(c2), c1) | (f9(c1, f8(c2)) = f8(c2)) | (~big_f(f9(c1, f8(c2)), f10(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(c2) = c2) | (f7(c2) = c2) | (~(c1 = f5(c2))) | big_f(f7(c2), c1) | (f9(c1, f8(c2)) = f8(c2)) | (~big_f(f9(c1, f8(c2)), f10(c2))))),
% 29.39/19.65 inference(rewrite,[status(thm)],[])).
% 29.39/19.65 tff(24825,plain,
% 29.39/19.65 (((~(c1 = f5(c2))) | (f10(c2) = c2) | (f9(c1, f8(c2)) = f8(c2)) | (~big_f(f9(c1, f8(c2)), f10(c2))) | (f7(c2) = c2) | big_f(f7(c2), c1)) <=> ((f10(c2) = c2) | (f7(c2) = c2) | (~(c1 = f5(c2))) | big_f(f7(c2), c1) | (f9(c1, f8(c2)) = f8(c2)) | (~big_f(f9(c1, f8(c2)), f10(c2))))),
% 29.39/19.65 inference(rewrite,[status(thm)],[])).
% 29.39/19.65 tff(24826,plain,
% 29.39/19.65 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c1 = f5(c2))) | (f10(c2) = c2) | (f9(c1, f8(c2)) = f8(c2)) | (~big_f(f9(c1, f8(c2)), f10(c2))) | (f7(c2) = c2) | big_f(f7(c2), c1))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f10(c2) = c2) | (f7(c2) = c2) | (~(c1 = f5(c2))) | big_f(f7(c2), c1) | (f9(c1, f8(c2)) = f8(c2)) | (~big_f(f9(c1, f8(c2)), f10(c2)))))),
% 29.39/19.65 inference(monotonicity,[status(thm)],[24825])).
% 29.39/19.65 tff(24827,plain,
% 29.39/19.65 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c1 = f5(c2))) | (f10(c2) = c2) | (f9(c1, f8(c2)) = f8(c2)) | (~big_f(f9(c1, f8(c2)), f10(c2))) | (f7(c2) = c2) | big_f(f7(c2), c1))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(c2) = c2) | (f7(c2) = c2) | (~(c1 = f5(c2))) | big_f(f7(c2), c1) | (f9(c1, f8(c2)) = f8(c2)) | (~big_f(f9(c1, f8(c2)), f10(c2))))),
% 29.39/19.65 inference(transitivity,[status(thm)],[24826, 24824])).
% 29.39/19.65 tff(24828,plain,
% 29.39/19.65 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c1 = f5(c2))) | (f10(c2) = c2) | (f9(c1, f8(c2)) = f8(c2)) | (~big_f(f9(c1, f8(c2)), f10(c2))) | (f7(c2) = c2) | big_f(f7(c2), c1))),
% 29.39/19.65 inference(quant_inst,[status(thm)],[])).
% 29.39/19.65 tff(24829,plain,
% 29.39/19.65 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(c2) = c2) | (f7(c2) = c2) | (~(c1 = f5(c2))) | big_f(f7(c2), c1) | (f9(c1, f8(c2)) = f8(c2)) | (~big_f(f9(c1, f8(c2)), f10(c2)))),
% 29.39/19.65 inference(modus_ponens,[status(thm)],[24828, 24827])).
% 29.39/19.65 tff(24830,plain,
% 29.39/19.65 ((~(c1 = f5(c2))) | (f9(c1, f8(c2)) = f8(c2))),
% 29.39/19.65 inference(unit_resolution,[status(thm)],[24829, 705, 89, 17, 333, 24823])).
% 29.39/19.65 tff(24831,plain,
% 29.39/19.65 (~(c1 = f5(c2))),
% 29.39/19.65 inference(unit_resolution,[status(thm)],[24830, 17868])).
% 29.39/19.65 tff(24832,plain,
% 29.39/19.65 (~(f5(c2) = c1)),
% 29.39/19.65 inference(unit_resolution,[status(thm)],[8139, 24831])).
% 29.39/19.65 tff(24833,plain,
% 29.39/19.65 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f10(c2) = c2) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (f9(c1, f8(c2)) = f8(c2)) | (~big_f(f9(c1, f8(c2)), f10(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(c2) = c2) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (f9(c1, f8(c2)) = f8(c2)) | (~big_f(f9(c1, f8(c2)), f10(c2))))),
% 29.39/19.65 inference(rewrite,[status(thm)],[])).
% 29.39/19.65 tff(24834,plain,
% 29.39/19.65 (((~(c2 = f5(c2))) | (f10(c2) = c2) | (f9(c1, f8(c2)) = f8(c2)) | (~big_f(f9(c1, f8(c2)), f10(c2))) | (f7(c2) = c2) | big_f(f7(c2), c2)) <=> ((f10(c2) = c2) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (f9(c1, f8(c2)) = f8(c2)) | (~big_f(f9(c1, f8(c2)), f10(c2))))),
% 29.39/19.65 inference(rewrite,[status(thm)],[])).
% 29.39/19.65 tff(24835,plain,
% 29.39/19.65 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c2 = f5(c2))) | (f10(c2) = c2) | (f9(c1, f8(c2)) = f8(c2)) | (~big_f(f9(c1, f8(c2)), f10(c2))) | (f7(c2) = c2) | big_f(f7(c2), c2))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f10(c2) = c2) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (f9(c1, f8(c2)) = f8(c2)) | (~big_f(f9(c1, f8(c2)), f10(c2)))))),
% 29.39/19.65 inference(monotonicity,[status(thm)],[24834])).
% 29.39/19.65 tff(24836,plain,
% 29.39/19.65 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c2 = f5(c2))) | (f10(c2) = c2) | (f9(c1, f8(c2)) = f8(c2)) | (~big_f(f9(c1, f8(c2)), f10(c2))) | (f7(c2) = c2) | big_f(f7(c2), c2))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(c2) = c2) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (f9(c1, f8(c2)) = f8(c2)) | (~big_f(f9(c1, f8(c2)), f10(c2))))),
% 29.39/19.65 inference(transitivity,[status(thm)],[24835, 24833])).
% 29.39/19.65 tff(24837,plain,
% 29.39/19.65 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c2 = f5(c2))) | (f10(c2) = c2) | (f9(c1, f8(c2)) = f8(c2)) | (~big_f(f9(c1, f8(c2)), f10(c2))) | (f7(c2) = c2) | big_f(f7(c2), c2))),
% 29.39/19.66 inference(quant_inst,[status(thm)],[])).
% 29.39/19.66 tff(24838,plain,
% 29.39/19.66 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(c2) = c2) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (f9(c1, f8(c2)) = f8(c2)) | (~big_f(f9(c1, f8(c2)), f10(c2)))),
% 29.39/19.66 inference(modus_ponens,[status(thm)],[24837, 24836])).
% 29.39/19.66 tff(24839,plain,
% 29.39/19.66 ((~(c2 = f5(c2))) | (f9(c1, f8(c2)) = f8(c2))),
% 29.39/19.66 inference(unit_resolution,[status(thm)],[24838, 705, 89, 17, 1521, 24823])).
% 29.39/19.66 tff(24840,plain,
% 29.39/19.66 (~(c2 = f5(c2))),
% 29.39/19.66 inference(unit_resolution,[status(thm)],[24839, 17868])).
% 29.39/19.66 tff(24841,plain,
% 29.39/19.66 (~(f5(c2) = c2)),
% 29.39/19.66 inference(unit_resolution,[status(thm)],[8113, 24840])).
% 29.39/19.66 tff(24842,plain,
% 29.39/19.66 ($false),
% 29.39/19.66 inference(unit_resolution,[status(thm)],[1547, 24841, 24832])).
% 29.39/19.66 tff(24843,plain,((f9(c1, f8(c2)) = f8(c2)) | (f10(c2) = c2) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~big_f(f9(c1, f8(c2)), f10(c2))) | big_f(f7(c2), c1)), inference(lemma,lemma(discharge,[]))).
% 29.39/19.66 tff(24844,plain,
% 29.39/19.66 (f9(c1, f8(c2)) = f8(c2)),
% 29.39/19.66 inference(unit_resolution,[status(thm)],[24843, 24822, 17, 12093, 21128, 89])).
% 29.39/19.66 tff(24845,plain,
% 29.39/19.66 (f10(c1) = f10(c2)),
% 29.39/19.66 inference(transitivity,[status(thm)],[24276, 99])).
% 29.39/19.66 tff(24846,plain,
% 29.39/19.66 (big_f(f9(c1, f8(c2)), f10(c1)) <=> big_f(f9(c1, f8(c2)), f10(c2))),
% 29.39/19.66 inference(monotonicity,[status(thm)],[24845])).
% 29.39/19.66 tff(24847,plain,
% 29.39/19.66 (big_f(f9(c1, f8(c2)), f10(c2)) <=> big_f(f9(c1, f8(c2)), f10(c1))),
% 29.39/19.66 inference(symmetry,[status(thm)],[24846])).
% 29.39/19.66 tff(24848,plain,
% 29.39/19.66 (big_f(f9(c1, f8(c2)), f10(c1))),
% 29.39/19.66 inference(modus_ponens,[status(thm)],[24822, 24847])).
% 29.39/19.66 tff(24849,plain,
% 29.39/19.66 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c1) = c1)) | big_f(f7(c1), f6(c1, f8(c2))) | (~(f7(c1) = c1)) | (f6(c1, f8(c2)) = f8(c2)) | (~(f9(c1, f8(c2)) = f8(c2))) | (~big_f(f9(c1, f8(c2)), f10(c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c1) = c1)) | big_f(f7(c1), f6(c1, f8(c2))) | (~(f7(c1) = c1)) | (f6(c1, f8(c2)) = f8(c2)) | (~(f9(c1, f8(c2)) = f8(c2))) | (~big_f(f9(c1, f8(c2)), f10(c1))))),
% 29.39/19.66 inference(rewrite,[status(thm)],[])).
% 29.39/19.66 tff(24850,plain,
% 29.39/19.66 (((~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (f6(c1, f8(c2)) = f8(c2)) | big_f(f7(c1), f6(c1, f8(c2))) | (~(f9(c1, f8(c2)) = f8(c2))) | (~big_f(f9(c1, f8(c2)), f10(c1)))) <=> ((~(f10(c1) = c1)) | big_f(f7(c1), f6(c1, f8(c2))) | (~(f7(c1) = c1)) | (f6(c1, f8(c2)) = f8(c2)) | (~(f9(c1, f8(c2)) = f8(c2))) | (~big_f(f9(c1, f8(c2)), f10(c1))))),
% 29.39/19.66 inference(rewrite,[status(thm)],[])).
% 29.39/19.66 tff(24851,plain,
% 29.39/19.66 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (f6(c1, f8(c2)) = f8(c2)) | big_f(f7(c1), f6(c1, f8(c2))) | (~(f9(c1, f8(c2)) = f8(c2))) | (~big_f(f9(c1, f8(c2)), f10(c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c1) = c1)) | big_f(f7(c1), f6(c1, f8(c2))) | (~(f7(c1) = c1)) | (f6(c1, f8(c2)) = f8(c2)) | (~(f9(c1, f8(c2)) = f8(c2))) | (~big_f(f9(c1, f8(c2)), f10(c1)))))),
% 29.39/19.66 inference(monotonicity,[status(thm)],[24850])).
% 29.39/19.66 tff(24852,plain,
% 29.39/19.66 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (f6(c1, f8(c2)) = f8(c2)) | big_f(f7(c1), f6(c1, f8(c2))) | (~(f9(c1, f8(c2)) = f8(c2))) | (~big_f(f9(c1, f8(c2)), f10(c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c1) = c1)) | big_f(f7(c1), f6(c1, f8(c2))) | (~(f7(c1) = c1)) | (f6(c1, f8(c2)) = f8(c2)) | (~(f9(c1, f8(c2)) = f8(c2))) | (~big_f(f9(c1, f8(c2)), f10(c1))))),
% 29.39/19.66 inference(transitivity,[status(thm)],[24851, 24849])).
% 29.39/19.66 tff(24853,plain,
% 29.39/19.66 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (f6(c1, f8(c2)) = f8(c2)) | big_f(f7(c1), f6(c1, f8(c2))) | (~(f9(c1, f8(c2)) = f8(c2))) | (~big_f(f9(c1, f8(c2)), f10(c1))))),
% 29.39/19.66 inference(quant_inst,[status(thm)],[])).
% 29.39/19.66 tff(24854,plain,
% 29.39/19.66 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c1) = c1)) | big_f(f7(c1), f6(c1, f8(c2))) | (~(f7(c1) = c1)) | (f6(c1, f8(c2)) = f8(c2)) | (~(f9(c1, f8(c2)) = f8(c2))) | (~big_f(f9(c1, f8(c2)), f10(c1)))),
% 29.39/19.66 inference(modus_ponens,[status(thm)],[24853, 24852])).
% 29.39/19.66 tff(24855,plain,
% 29.39/19.66 ($false),
% 29.39/19.66 inference(unit_resolution,[status(thm)],[24854, 2409, 24772, 24276, 24793, 24298, 24848, 24844])).
% 29.39/19.66 tff(24856,plain,(big_f(c1, c2) | (f7(c2) = c2) | (f10(c2) = c2) | big_f(c1, c1) | big_f(c2, f10(c2))), inference(lemma,lemma(discharge,[]))).
% 29.39/19.66 tff(24857,plain,
% 29.39/19.66 (big_f(c1, c2)),
% 29.39/19.66 inference(unit_resolution,[status(thm)],[24856, 66, 89, 17, 12071])).
% 29.39/19.66 tff(24858,plain,
% 29.39/19.66 (big_f(c1, f10(c1))),
% 29.39/19.66 inference(modus_ponens,[status(thm)],[24857, 24247])).
% 29.39/19.66 tff(24859,assumption,(f8(f10(c1)) = c2), introduced(assumption)).
% 29.39/19.66 tff(24860,plain,
% 29.39/19.66 (f10(f10(c1)) = f10(c2)),
% 29.39/19.66 inference(monotonicity,[status(thm)],[15])).
% 29.39/19.66 tff(24861,plain,
% 29.39/19.66 (f10(f10(c1)) = c1),
% 29.39/19.66 inference(transitivity,[status(thm)],[24860, 94])).
% 29.39/19.66 tff(24862,plain,
% 29.39/19.66 (big_f(f10(c1), f10(f10(c1))) <=> big_f(c2, c1)),
% 29.39/19.66 inference(monotonicity,[status(thm)],[15, 24861])).
% 29.39/19.66 tff(24863,plain,
% 29.39/19.66 (big_f(c2, c1) <=> big_f(f10(c1), f10(f10(c1)))),
% 29.39/19.66 inference(symmetry,[status(thm)],[24862])).
% 29.39/19.66 tff(24864,plain,
% 29.39/19.66 ((~big_f(c2, c1)) <=> (~big_f(f10(c1), f10(f10(c1))))),
% 29.39/19.66 inference(monotonicity,[status(thm)],[24863])).
% 29.39/19.66 tff(24865,plain,
% 29.39/19.66 (~big_f(f10(c1), f10(f10(c1)))),
% 29.39/19.66 inference(modus_ponens,[status(thm)],[2, 24864])).
% 29.39/19.66 tff(24866,plain,
% 29.39/19.66 ((c2 = f6(c1, c2)) <=> (f6(c1, c2) = c2)),
% 29.39/19.66 inference(commutativity,[status(thm)],[])).
% 29.39/19.66 tff(24867,assumption,(~big_f(f10(c1), f10(f10(c1)))), introduced(assumption)).
% 29.39/19.66 tff(24868,plain,
% 29.39/19.66 (f8(c2) = f8(f10(c1))),
% 29.39/19.66 inference(monotonicity,[status(thm)],[5571])).
% 29.39/19.66 tff(24869,plain,
% 29.39/19.66 ((c2 = f8(c2)) <=> (c2 = f8(f10(c1)))),
% 29.39/19.66 inference(monotonicity,[status(thm)],[24868])).
% 29.39/19.66 tff(24870,plain,
% 29.39/19.66 ((c2 = f8(c2)) <=> (f8(f10(c1)) = c2)),
% 29.39/19.66 inference(transitivity,[status(thm)],[24869, 24266])).
% 29.39/19.66 tff(24871,plain,
% 29.39/19.66 ((f8(f10(c1)) = c2) <=> (c2 = f8(c2))),
% 29.39/19.66 inference(symmetry,[status(thm)],[24870])).
% 29.39/19.66 tff(24872,plain,
% 29.39/19.66 (c2 = f8(c2)),
% 29.39/19.66 inference(modus_ponens,[status(thm)],[24859, 24871])).
% 29.39/19.66 tff(24873,plain,
% 29.39/19.66 (f8(c2) = c2),
% 29.39/19.66 inference(transitivity,[status(thm)],[24868, 24859])).
% 29.39/19.66 tff(24874,plain,
% 29.39/19.66 ((f6(c1, f8(c2)) = f8(c2)) <=> (f6(c1, f8(c2)) = c2)),
% 29.39/19.66 inference(monotonicity,[status(thm)],[24873])).
% 29.39/19.66 tff(24875,plain,
% 29.39/19.66 ((f6(c1, f8(c2)) = c2) <=> (f6(c1, f8(c2)) = f8(c2))),
% 29.39/19.66 inference(symmetry,[status(thm)],[24874])).
% 29.39/19.66 tff(24876,plain,
% 29.39/19.66 (f6(c1, f8(c2)) = f6(c1, c2)),
% 29.39/19.66 inference(monotonicity,[status(thm)],[24873])).
% 29.39/19.66 tff(24877,plain,
% 29.39/19.66 ((f6(c1, f8(c2)) = c2) <=> (f6(c1, c2) = c2)),
% 29.39/19.66 inference(monotonicity,[status(thm)],[24876])).
% 29.39/19.66 tff(24878,plain,
% 29.39/19.66 ((f6(c1, c2) = c2) <=> (f6(c1, f8(c2)) = c2)),
% 29.39/19.66 inference(symmetry,[status(thm)],[24877])).
% 29.39/19.66 tff(24879,plain,
% 29.39/19.66 ((f10(c1) = f8(f10(c1))) <=> (c2 = f8(f10(c1)))),
% 29.39/19.66 inference(monotonicity,[status(thm)],[15])).
% 29.39/19.66 tff(24880,plain,
% 29.39/19.66 ((f10(c1) = f8(f10(c1))) <=> (f8(f10(c1)) = c2)),
% 29.39/19.66 inference(transitivity,[status(thm)],[24879, 24266])).
% 29.39/19.66 tff(24881,plain,
% 29.39/19.66 ((f8(f10(c1)) = c2) <=> (f10(c1) = f8(f10(c1)))),
% 29.39/19.66 inference(symmetry,[status(thm)],[24880])).
% 29.39/19.66 tff(24882,plain,
% 29.39/19.66 (f10(c1) = f8(f10(c1))),
% 29.39/19.66 inference(modus_ponens,[status(thm)],[24859, 24881])).
% 29.39/19.66 tff(24883,plain,
% 29.39/19.66 (big_f(f7(c1), f6(c1, f6(c1, c2))) <=> big_f(c1, c1)),
% 29.39/19.66 inference(monotonicity,[status(thm)],[4234, 29])).
% 29.39/19.66 tff(24884,plain,
% 29.39/19.66 (big_f(c1, c1) <=> big_f(f7(c1), f6(c1, f6(c1, c2)))),
% 29.39/19.66 inference(symmetry,[status(thm)],[24883])).
% 29.39/19.66 tff(24885,plain,
% 29.39/19.66 ((~big_f(c1, c1)) <=> (~big_f(f7(c1), f6(c1, f6(c1, c2))))),
% 29.39/19.66 inference(monotonicity,[status(thm)],[24884])).
% 29.39/19.66 tff(24886,plain,
% 29.39/19.66 (~big_f(f7(c1), f6(c1, f6(c1, c2)))),
% 29.39/19.66 inference(modus_ponens,[status(thm)],[66, 24885])).
% 29.39/19.66 tff(24887,plain,
% 29.39/19.66 ((f10(f10(c1)) = f10(c1)) <=> (c1 = f10(c1))),
% 29.39/19.66 inference(monotonicity,[status(thm)],[24861])).
% 29.39/19.66 tff(24888,plain,
% 29.39/19.66 ((f10(f10(c1)) = f10(c1)) <=> (f10(c1) = c1)),
% 29.39/19.66 inference(transitivity,[status(thm)],[24887, 18819])).
% 29.39/19.66 tff(24889,plain,
% 29.39/19.66 ((f10(c1) = c1) <=> (f10(f10(c1)) = f10(c1))),
% 29.39/19.66 inference(symmetry,[status(thm)],[24888])).
% 29.39/19.66 tff(24890,plain,
% 29.39/19.66 ((~(f10(c1) = c1)) <=> (~(f10(f10(c1)) = f10(c1)))),
% 29.39/19.66 inference(monotonicity,[status(thm)],[24889])).
% 29.39/19.66 tff(24891,plain,
% 29.39/19.66 (~(f10(f10(c1)) = f10(c1))),
% 29.39/19.66 inference(modus_ponens,[status(thm)],[3, 24890])).
% 29.39/19.66 tff(24892,plain,
% 29.39/19.66 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, f6(c1, c2))) | (f6(c1, f6(c1, c2)) = f6(c1, c2)) | big_f(f10(c1), f10(f10(c1))) | (~(f10(c1) = f8(f10(c1)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, f6(c1, c2))) | (f6(c1, f6(c1, c2)) = f6(c1, c2)) | big_f(f10(c1), f10(f10(c1))) | (~(f10(c1) = f8(f10(c1)))))),
% 29.39/19.66 inference(rewrite,[status(thm)],[])).
% 29.39/19.66 tff(24893,plain,
% 29.39/19.66 (((f10(f10(c1)) = f10(c1)) | big_f(f10(c1), f10(f10(c1))) | (~(f7(c1) = c1)) | (f6(c1, f6(c1, c2)) = f6(c1, c2)) | big_f(f7(c1), f6(c1, f6(c1, c2))) | (~(f10(c1) = f8(f10(c1))))) <=> ((f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, f6(c1, c2))) | (f6(c1, f6(c1, c2)) = f6(c1, c2)) | big_f(f10(c1), f10(f10(c1))) | (~(f10(c1) = f8(f10(c1)))))),
% 29.39/19.66 inference(rewrite,[status(thm)],[])).
% 29.39/19.66 tff(24894,plain,
% 29.39/19.66 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(f10(c1)) = f10(c1)) | big_f(f10(c1), f10(f10(c1))) | (~(f7(c1) = c1)) | (f6(c1, f6(c1, c2)) = f6(c1, c2)) | big_f(f7(c1), f6(c1, f6(c1, c2))) | (~(f10(c1) = f8(f10(c1)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, f6(c1, c2))) | (f6(c1, f6(c1, c2)) = f6(c1, c2)) | big_f(f10(c1), f10(f10(c1))) | (~(f10(c1) = f8(f10(c1))))))),
% 29.39/19.66 inference(monotonicity,[status(thm)],[24893])).
% 29.39/19.66 tff(24895,plain,
% 29.39/19.66 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(f10(c1)) = f10(c1)) | big_f(f10(c1), f10(f10(c1))) | (~(f7(c1) = c1)) | (f6(c1, f6(c1, c2)) = f6(c1, c2)) | big_f(f7(c1), f6(c1, f6(c1, c2))) | (~(f10(c1) = f8(f10(c1)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, f6(c1, c2))) | (f6(c1, f6(c1, c2)) = f6(c1, c2)) | big_f(f10(c1), f10(f10(c1))) | (~(f10(c1) = f8(f10(c1)))))),
% 29.39/19.66 inference(transitivity,[status(thm)],[24894, 24892])).
% 29.39/19.66 tff(24896,plain,
% 29.39/19.66 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(f10(c1)) = f10(c1)) | big_f(f10(c1), f10(f10(c1))) | (~(f7(c1) = c1)) | (f6(c1, f6(c1, c2)) = f6(c1, c2)) | big_f(f7(c1), f6(c1, f6(c1, c2))) | (~(f10(c1) = f8(f10(c1)))))),
% 29.39/19.66 inference(quant_inst,[status(thm)],[])).
% 29.39/19.66 tff(24897,plain,
% 29.39/19.66 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, f6(c1, c2))) | (f6(c1, f6(c1, c2)) = f6(c1, c2)) | big_f(f10(c1), f10(f10(c1))) | (~(f10(c1) = f8(f10(c1))))),
% 29.39/19.66 inference(modus_ponens,[status(thm)],[24896, 24895])).
% 29.39/19.66 tff(24898,plain,
% 29.39/19.66 (f6(c1, f6(c1, c2)) = f6(c1, c2)),
% 29.39/19.66 inference(unit_resolution,[status(thm)],[24897, 2994, 4234, 24891, 24886, 24867, 24882])).
% 29.39/19.66 tff(24899,plain,
% 29.39/19.66 (f6(c1, c2) = f6(c1, f6(c1, c2))),
% 29.39/19.66 inference(symmetry,[status(thm)],[24898])).
% 29.39/19.66 tff(24900,plain,
% 29.39/19.66 (f6(c1, c2) = c1),
% 29.39/19.66 inference(transitivity,[status(thm)],[24899, 29])).
% 29.39/19.66 tff(24901,plain,
% 29.39/19.66 ((f6(c1, c2) = c2) <=> (c1 = f10(c1))),
% 29.39/19.66 inference(monotonicity,[status(thm)],[24900, 5571])).
% 29.39/19.66 tff(24902,plain,
% 29.39/19.66 ((f6(c1, c2) = c2) <=> (f10(c1) = c1)),
% 29.39/19.66 inference(transitivity,[status(thm)],[24901, 18819])).
% 29.39/19.66 tff(24903,plain,
% 29.39/19.66 ((f10(c1) = c1) <=> (f6(c1, c2) = c2)),
% 29.39/19.66 inference(symmetry,[status(thm)],[24902])).
% 29.39/19.66 tff(24904,plain,
% 29.39/19.66 ((f10(c1) = c1) <=> (f6(c1, f8(c2)) = f8(c2))),
% 29.39/19.66 inference(transitivity,[status(thm)],[24903, 24878, 24875])).
% 29.39/19.66 tff(24905,plain,
% 29.39/19.66 ((~(f10(c1) = c1)) <=> (~(f6(c1, f8(c2)) = f8(c2)))),
% 29.39/19.66 inference(monotonicity,[status(thm)],[24904])).
% 29.39/19.66 tff(24906,plain,
% 29.39/19.66 (~(f6(c1, f8(c2)) = f8(c2))),
% 29.39/19.66 inference(modus_ponens,[status(thm)],[3, 24905])).
% 29.39/19.66 tff(24907,plain,
% 29.39/19.66 (big_f(c1, f6(c1, f8(c2))) <=> big_f(c1, f6(c1, c2))),
% 29.39/19.66 inference(monotonicity,[status(thm)],[24876])).
% 29.39/19.66 tff(24908,plain,
% 29.39/19.66 (big_f(c1, f6(c1, c2)) <=> big_f(c1, f6(c1, f8(c2)))),
% 29.39/19.66 inference(symmetry,[status(thm)],[24907])).
% 29.39/19.66 tff(24909,plain,
% 29.39/19.66 (big_f(c1, f6(c1, c2)) <=> big_f(c1, c1)),
% 29.39/19.66 inference(monotonicity,[status(thm)],[24900])).
% 29.39/19.66 tff(24910,plain,
% 29.39/19.66 (big_f(c1, c1) <=> big_f(c1, f6(c1, c2))),
% 29.39/19.66 inference(symmetry,[status(thm)],[24909])).
% 29.39/19.66 tff(24911,plain,
% 29.39/19.66 (big_f(c1, c1) <=> big_f(f7(c1), f6(c1, f8(c2)))),
% 29.39/19.66 inference(transitivity,[status(thm)],[24910, 24908, 20030])).
% 29.39/19.66 tff(24912,plain,
% 29.39/19.66 ((~big_f(c1, c1)) <=> (~big_f(f7(c1), f6(c1, f8(c2))))),
% 29.39/19.66 inference(monotonicity,[status(thm)],[24911])).
% 29.39/19.66 tff(24913,plain,
% 29.39/19.66 (~big_f(f7(c1), f6(c1, f8(c2)))),
% 29.39/19.66 inference(modus_ponens,[status(thm)],[66, 24912])).
% 29.39/19.66 tff(24914,plain,
% 29.39/19.66 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | big_f(f7(c1), f6(c1, f8(c2))) | (~(f7(c1) = c1)) | (f6(c1, f8(c2)) = f8(c2)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | big_f(f7(c1), f6(c1, f8(c2))) | (~(f7(c1) = c1)) | (f6(c1, f8(c2)) = f8(c2)))),
% 29.39/19.66 inference(rewrite,[status(thm)],[])).
% 29.39/19.66 tff(24915,plain,
% 29.39/19.66 (((f10(c2) = c2) | big_f(c2, f10(c2)) | (~(f7(c1) = c1)) | (f6(c1, f8(c2)) = f8(c2)) | big_f(f7(c1), f6(c1, f8(c2))) | (~(c2 = f8(c2)))) <=> ((f10(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | big_f(f7(c1), f6(c1, f8(c2))) | (~(f7(c1) = c1)) | (f6(c1, f8(c2)) = f8(c2)))),
% 29.39/19.66 inference(rewrite,[status(thm)],[])).
% 29.39/19.66 tff(24916,plain,
% 29.39/19.66 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | big_f(c2, f10(c2)) | (~(f7(c1) = c1)) | (f6(c1, f8(c2)) = f8(c2)) | big_f(f7(c1), f6(c1, f8(c2))) | (~(c2 = f8(c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | big_f(f7(c1), f6(c1, f8(c2))) | (~(f7(c1) = c1)) | (f6(c1, f8(c2)) = f8(c2))))),
% 29.39/19.66 inference(monotonicity,[status(thm)],[24915])).
% 29.39/19.66 tff(24917,plain,
% 29.39/19.66 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | big_f(c2, f10(c2)) | (~(f7(c1) = c1)) | (f6(c1, f8(c2)) = f8(c2)) | big_f(f7(c1), f6(c1, f8(c2))) | (~(c2 = f8(c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | big_f(f7(c1), f6(c1, f8(c2))) | (~(f7(c1) = c1)) | (f6(c1, f8(c2)) = f8(c2)))),
% 29.39/19.66 inference(transitivity,[status(thm)],[24916, 24914])).
% 29.39/19.66 tff(24918,plain,
% 29.39/19.66 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | big_f(c2, f10(c2)) | (~(f7(c1) = c1)) | (f6(c1, f8(c2)) = f8(c2)) | big_f(f7(c1), f6(c1, f8(c2))) | (~(c2 = f8(c2))))),
% 29.39/19.66 inference(quant_inst,[status(thm)],[])).
% 29.39/19.66 tff(24919,plain,
% 29.39/19.66 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | big_f(f7(c1), f6(c1, f8(c2))) | (~(f7(c1) = c1)) | (f6(c1, f8(c2)) = f8(c2))),
% 29.39/19.66 inference(modus_ponens,[status(thm)],[24918, 24917])).
% 29.39/19.66 tff(24920,plain,
% 29.39/19.66 ((f10(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | big_f(f7(c1), f6(c1, f8(c2))) | (~(f7(c1) = c1)) | (f6(c1, f8(c2)) = f8(c2))),
% 29.39/19.66 inference(unit_resolution,[status(thm)],[24919, 2994])).
% 29.39/19.66 tff(24921,plain,
% 29.39/19.66 ($false),
% 29.39/19.66 inference(unit_resolution,[status(thm)],[24920, 24913, 24906, 89, 4234, 15517, 24872])).
% 29.39/19.66 tff(24922,plain,((~(f6(c1, f6(c1, c2)) = c1)) | (f10(c2) = c2) | (~(f7(c1) = c1)) | big_f(c2, f10(c2)) | big_f(c1, c1) | (~(f8(f10(c1)) = c2)) | (f10(c1) = c1) | big_f(f10(c1), f10(f10(c1)))), inference(lemma,lemma(discharge,[]))).
% 29.39/19.66 tff(24923,plain,
% 29.39/19.66 (~(f6(c1, f6(c1, c2)) = c1)),
% 29.39/19.66 inference(unit_resolution,[status(thm)],[24922, 24859, 4234, 15517, 66, 89, 3, 24867])).
% 29.39/19.66 tff(24924,plain,
% 29.39/19.66 (f6(c1, f6(c1, c2)) = c2),
% 29.39/19.66 inference(unit_resolution,[status(thm)],[63, 24923])).
% 29.39/19.66 tff(24925,plain,
% 29.39/19.66 ((f6(c1, f6(c1, c2)) = f6(c1, c2)) <=> (c2 = f6(c1, c2))),
% 29.39/19.66 inference(monotonicity,[status(thm)],[24924])).
% 29.39/19.66 tff(24926,plain,
% 29.39/19.66 ((f6(c1, f6(c1, c2)) = f6(c1, c2)) <=> (f6(c1, c2) = c2)),
% 29.39/19.66 inference(transitivity,[status(thm)],[24925, 24866])).
% 29.39/19.66 tff(24927,plain,
% 29.39/19.66 ((~(f6(c1, f6(c1, c2)) = f6(c1, c2))) <=> (~(f6(c1, c2) = c2))),
% 29.39/19.66 inference(monotonicity,[status(thm)],[24926])).
% 29.39/19.66 tff(24928,plain,
% 29.39/19.66 (f6(c1, f6(c1, c2)) = f10(c1)),
% 29.39/19.66 inference(transitivity,[status(thm)],[24924, 5571])).
% 29.39/19.66 tff(24929,plain,
% 29.39/19.66 (big_f(f7(c1), f6(c1, f6(c1, c2))) <=> big_f(c1, f10(c1))),
% 29.39/19.66 inference(monotonicity,[status(thm)],[4234, 24928])).
% 29.39/19.66 tff(24930,plain,
% 29.39/19.66 (big_f(c1, f10(c1)) <=> big_f(f7(c1), f6(c1, f6(c1, c2)))),
% 29.39/19.66 inference(symmetry,[status(thm)],[24929])).
% 29.39/19.66 tff(24931,plain,
% 29.39/19.66 (big_f(f7(c1), f6(c1, f6(c1, c2)))),
% 29.39/19.66 inference(modus_ponens,[status(thm)],[3023, 24930])).
% 29.39/19.66 tff(24932,plain,
% 29.39/19.66 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))) | big_f(f10(c1), f10(f10(c1))) | (~(f10(c1) = f8(f10(c1)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))) | big_f(f10(c1), f10(f10(c1))) | (~(f10(c1) = f8(f10(c1)))))),
% 29.39/19.66 inference(rewrite,[status(thm)],[])).
% 29.39/19.66 tff(24933,plain,
% 29.39/19.66 (((f10(f10(c1)) = f10(c1)) | big_f(f10(c1), f10(f10(c1))) | (~(f7(c1) = c1)) | (~(f10(c1) = f8(f10(c1)))) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2))))) <=> ((f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))) | big_f(f10(c1), f10(f10(c1))) | (~(f10(c1) = f8(f10(c1)))))),
% 29.39/19.66 inference(rewrite,[status(thm)],[])).
% 29.39/19.66 tff(24934,plain,
% 29.39/19.66 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f10(c1)) = f10(c1)) | big_f(f10(c1), f10(f10(c1))) | (~(f7(c1) = c1)) | (~(f10(c1) = f8(f10(c1)))) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))) | big_f(f10(c1), f10(f10(c1))) | (~(f10(c1) = f8(f10(c1))))))),
% 29.39/19.66 inference(monotonicity,[status(thm)],[24933])).
% 29.39/19.66 tff(24935,plain,
% 29.39/19.66 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f10(c1)) = f10(c1)) | big_f(f10(c1), f10(f10(c1))) | (~(f7(c1) = c1)) | (~(f10(c1) = f8(f10(c1)))) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))) | big_f(f10(c1), f10(f10(c1))) | (~(f10(c1) = f8(f10(c1)))))),
% 29.39/19.66 inference(transitivity,[status(thm)],[24934, 24932])).
% 29.39/19.66 tff(24936,plain,
% 29.39/19.66 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f10(c1)) = f10(c1)) | big_f(f10(c1), f10(f10(c1))) | (~(f7(c1) = c1)) | (~(f10(c1) = f8(f10(c1)))) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))),
% 29.39/19.66 inference(quant_inst,[status(thm)],[])).
% 29.39/19.66 tff(24937,plain,
% 29.39/19.66 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))) | big_f(f10(c1), f10(f10(c1))) | (~(f10(c1) = f8(f10(c1))))),
% 29.39/19.66 inference(modus_ponens,[status(thm)],[24936, 24935])).
% 29.39/19.66 tff(24938,plain,
% 29.39/19.66 (~(f6(c1, f6(c1, c2)) = f6(c1, c2))),
% 29.39/19.66 inference(unit_resolution,[status(thm)],[24937, 2963, 4234, 24891, 24931, 24867, 24882])).
% 29.39/19.66 tff(24939,plain,
% 29.39/19.66 (~(f6(c1, c2) = c2)),
% 29.39/19.66 inference(modus_ponens,[status(thm)],[24938, 24927])).
% 29.39/19.66 tff(24940,plain,
% 29.39/19.66 (f6(c1, c2) = c1),
% 29.39/19.66 inference(unit_resolution,[status(thm)],[48, 24939])).
% 29.39/19.66 tff(24941,plain,
% 29.39/19.66 (big_f(c1, f6(c1, c2)) <=> big_f(c1, c1)),
% 29.39/19.66 inference(monotonicity,[status(thm)],[24940])).
% 29.39/19.66 tff(24942,plain,
% 29.39/19.66 (big_f(c1, c1) <=> big_f(c1, f6(c1, c2))),
% 29.39/19.66 inference(symmetry,[status(thm)],[24941])).
% 29.39/19.66 tff(24943,plain,
% 29.39/19.66 ((~big_f(c1, c1)) <=> (~big_f(c1, f6(c1, c2)))),
% 29.39/19.66 inference(monotonicity,[status(thm)],[24942])).
% 29.39/19.66 tff(24944,plain,
% 29.39/19.66 (~big_f(c1, f6(c1, c2))),
% 29.39/19.66 inference(modus_ponens,[status(thm)],[66, 24943])).
% 29.39/19.66 tff(24945,plain,
% 29.39/19.66 (big_f(f7(c1), f6(c1, f8(c2))) <=> big_f(c1, f6(c1, c2))),
% 29.39/19.66 inference(transitivity,[status(thm)],[20029, 24907])).
% 29.39/19.67 tff(24946,plain,
% 29.39/19.67 ((f6(c1, f6(c1, c2)) = f6(c1, c2)) <=> (f6(c1, f8(c2)) = f8(c2))),
% 29.39/19.67 inference(transitivity,[status(thm)],[24926, 24878, 24875])).
% 29.39/19.67 tff(24947,plain,
% 29.39/19.67 ((~(f6(c1, f6(c1, c2)) = f6(c1, c2))) <=> (~(f6(c1, f8(c2)) = f8(c2)))),
% 29.39/19.67 inference(monotonicity,[status(thm)],[24946])).
% 29.39/19.67 tff(24948,plain,
% 29.39/19.67 (~(f6(c1, f8(c2)) = f8(c2))),
% 29.39/19.67 inference(modus_ponens,[status(thm)],[24938, 24947])).
% 29.39/19.67 tff(24949,plain,
% 29.39/19.67 (big_f(f7(c1), f6(c1, f8(c2)))),
% 29.39/19.67 inference(unit_resolution,[status(thm)],[24920, 24948, 89, 4234, 15517, 24872])).
% 29.39/19.67 tff(24950,plain,
% 29.39/19.67 (big_f(c1, f6(c1, c2))),
% 29.39/19.67 inference(modus_ponens,[status(thm)],[24949, 24945])).
% 29.39/19.67 tff(24951,plain,
% 29.39/19.67 ($false),
% 29.39/19.67 inference(unit_resolution,[status(thm)],[24950, 24944])).
% 29.39/19.67 tff(24952,plain,((~(f8(f10(c1)) = c2)) | big_f(c1, c1) | (~(f7(c1) = c1)) | (f10(c2) = c2) | big_f(c2, f10(c2)) | big_f(f10(c1), f10(f10(c1))) | (~big_f(c1, f10(c1))) | (f10(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.39/19.67 tff(24953,plain,
% 29.39/19.67 ($false),
% 29.39/19.67 inference(unit_resolution,[status(thm)],[24952, 12071, 24865, 4234, 89, 24859, 66, 3023, 3])).
% 29.39/19.67 tff(24954,plain,(big_f(c2, c1) | (~(f7(c1) = c1)) | (f10(c2) = c2) | (~(f8(f10(c1)) = c2)) | big_f(c1, c1) | (~big_f(c1, f10(c1))) | (f10(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.39/19.67 tff(24955,plain,
% 29.39/19.67 (~(f8(f10(c1)) = c2)),
% 29.39/19.67 inference(unit_resolution,[status(thm)],[24954, 24858, 89, 2, 66, 24246, 3])).
% 29.39/19.67 tff(24956,plain,
% 29.39/19.67 (f8(f10(c1)) = c1),
% 29.39/19.67 inference(unit_resolution,[status(thm)],[12021, 24955])).
% 29.39/19.67 tff(24957,plain,
% 29.39/19.67 (c1 = f8(f10(c1))),
% 29.39/19.67 inference(modus_ponens,[status(thm)],[24956, 11996])).
% 29.39/19.67 tff(24958,plain,
% 29.39/19.67 (big_f(c1, f10(f10(c1))) <=> big_f(c1, c1)),
% 29.39/19.67 inference(monotonicity,[status(thm)],[24861])).
% 29.39/19.67 tff(24959,plain,
% 29.39/19.67 (big_f(c1, c1) <=> big_f(c1, f10(f10(c1)))),
% 29.39/19.67 inference(symmetry,[status(thm)],[24958])).
% 29.39/19.67 tff(24960,plain,
% 29.39/19.67 ((~big_f(c1, c1)) <=> (~big_f(c1, f10(f10(c1))))),
% 29.39/19.67 inference(monotonicity,[status(thm)],[24959])).
% 29.39/19.67 tff(24961,plain,
% 29.39/19.67 (~big_f(c1, f10(f10(c1)))),
% 29.39/19.67 inference(modus_ponens,[status(thm)],[66, 24960])).
% 29.39/19.67 tff(24962,plain,
% 29.39/19.67 (big_f(f7(f10(c1)), f10(c1)) <=> big_f(c1, f10(c1))),
% 29.39/19.67 inference(monotonicity,[status(thm)],[18820])).
% 29.39/19.67 tff(24963,plain,
% 29.39/19.67 (big_f(c1, f10(c1)) <=> big_f(f7(f10(c1)), f10(c1))),
% 29.39/19.67 inference(symmetry,[status(thm)],[24962])).
% 29.39/19.67 tff(24964,plain,
% 29.39/19.67 (big_f(f7(f10(c1)), f10(c1))),
% 29.39/19.67 inference(modus_ponens,[status(thm)],[24858, 24963])).
% 29.39/19.67 tff(24965,assumption,(~big_f(c1, f10(f10(c1)))), introduced(assumption)).
% 29.39/19.67 tff(24966,assumption,(c1 = f8(f10(c1))), introduced(assumption)).
% 29.39/19.67 tff(24967,assumption,(big_f(f7(f10(c1)), f10(c1))), introduced(assumption)).
% 29.39/19.67 tff(24968,assumption,(~(f10(f10(c1)) = f10(c1))), introduced(assumption)).
% 29.39/19.67 tff(24969,plain,
% 29.39/19.67 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | big_f(c1, f10(f10(c1))) | (f10(c1) = f5(f10(c1))) | (~(c1 = f8(f10(c1)))) | (~big_f(f7(f10(c1)), f10(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | (f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | big_f(c1, f10(f10(c1))) | (f10(c1) = f5(f10(c1))) | (~(c1 = f8(f10(c1)))) | (~big_f(f7(f10(c1)), f10(c1))))),
% 29.39/19.67 inference(rewrite,[status(thm)],[])).
% 29.39/19.67 tff(24970,plain,
% 29.39/19.67 (((f10(f10(c1)) = f10(c1)) | big_f(c1, f10(f10(c1))) | (f7(f10(c1)) = f10(c1)) | (f10(c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f10(c1))) | (~(c1 = f8(f10(c1))))) <=> ((f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | big_f(c1, f10(f10(c1))) | (f10(c1) = f5(f10(c1))) | (~(c1 = f8(f10(c1)))) | (~big_f(f7(f10(c1)), f10(c1))))),
% 29.39/19.67 inference(rewrite,[status(thm)],[])).
% 29.39/19.67 tff(24971,plain,
% 29.39/19.67 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(f10(c1)) = f10(c1)) | big_f(c1, f10(f10(c1))) | (f7(f10(c1)) = f10(c1)) | (f10(c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f10(c1))) | (~(c1 = f8(f10(c1)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | big_f(c1, f10(f10(c1))) | (f10(c1) = f5(f10(c1))) | (~(c1 = f8(f10(c1)))) | (~big_f(f7(f10(c1)), f10(c1)))))),
% 29.39/19.67 inference(monotonicity,[status(thm)],[24970])).
% 29.39/19.67 tff(24972,plain,
% 29.39/19.67 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(f10(c1)) = f10(c1)) | big_f(c1, f10(f10(c1))) | (f7(f10(c1)) = f10(c1)) | (f10(c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f10(c1))) | (~(c1 = f8(f10(c1)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | (f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | big_f(c1, f10(f10(c1))) | (f10(c1) = f5(f10(c1))) | (~(c1 = f8(f10(c1)))) | (~big_f(f7(f10(c1)), f10(c1))))),
% 29.39/19.67 inference(transitivity,[status(thm)],[24971, 24969])).
% 29.39/19.67 tff(24973,plain,
% 29.39/19.67 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(f10(c1)) = f10(c1)) | big_f(c1, f10(f10(c1))) | (f7(f10(c1)) = f10(c1)) | (f10(c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f10(c1))) | (~(c1 = f8(f10(c1)))))),
% 29.39/19.67 inference(quant_inst,[status(thm)],[])).
% 29.39/19.67 tff(24974,plain,
% 29.39/19.67 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | (f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | big_f(c1, f10(f10(c1))) | (f10(c1) = f5(f10(c1))) | (~(c1 = f8(f10(c1)))) | (~big_f(f7(f10(c1)), f10(c1)))),
% 29.39/19.67 inference(modus_ponens,[status(thm)],[24973, 24972])).
% 29.39/19.67 tff(24975,plain,
% 29.39/19.67 (big_f(c1, f10(f10(c1))) | (f10(c1) = f5(f10(c1))) | (~(c1 = f8(f10(c1))))),
% 29.39/19.67 inference(unit_resolution,[status(thm)],[24974, 2795, 24968, 297, 24967])).
% 29.39/19.67 tff(24976,plain,
% 29.39/19.67 (f10(c1) = f5(f10(c1))),
% 29.39/19.67 inference(unit_resolution,[status(thm)],[24975, 24966, 24965])).
% 29.39/19.67 tff(24977,plain,
% 29.39/19.67 (f5(f10(c1)) = f10(c1)),
% 29.39/19.67 inference(symmetry,[status(thm)],[24976])).
% 29.39/19.67 tff(24978,plain,
% 29.39/19.67 (big_f(f7(f10(c1)), f6(c1, f6(c1, c2))) <=> big_f(f7(c1), f6(c1, f6(c1, c2)))),
% 29.39/19.67 inference(monotonicity,[status(thm)],[6346])).
% 29.39/19.67 tff(24979,plain,
% 29.39/19.67 (big_f(f7(c1), f6(c1, f6(c1, c2))) <=> big_f(f7(f10(c1)), f6(c1, f6(c1, c2)))),
% 29.39/19.67 inference(symmetry,[status(thm)],[24978])).
% 29.39/19.67 tff(24980,assumption,(f10(c1) = f5(f10(c1))), introduced(assumption)).
% 29.39/19.67 tff(24981,plain,
% 29.39/19.67 (f5(f10(c1)) = f10(c1)),
% 29.39/19.67 inference(symmetry,[status(thm)],[24980])).
% 29.39/19.67 tff(24982,plain,
% 29.39/19.67 (f5(f10(c1)) = c2),
% 29.39/19.67 inference(transitivity,[status(thm)],[24981, 16])).
% 29.39/19.67 tff(24983,plain,
% 29.39/19.67 ((f6(c1, f6(c1, c2)) = f5(f10(c1))) <=> (f6(c1, f6(c1, c2)) = c2)),
% 29.39/19.67 inference(monotonicity,[status(thm)],[24982])).
% 29.39/19.67 tff(24984,plain,
% 29.39/19.67 ((f6(c1, f6(c1, c2)) = c2) <=> (f6(c1, f6(c1, c2)) = f5(f10(c1)))),
% 29.39/19.67 inference(symmetry,[status(thm)],[24983])).
% 29.39/19.67 tff(24985,assumption,(~big_f(f7(c1), f6(c1, f6(c1, c2)))), introduced(assumption)).
% 29.39/19.67 tff(24986,plain,
% 29.39/19.67 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | big_f(c1, f10(f10(c1))) | (~(c1 = f8(f10(c1)))) | big_f(f7(c1), f6(c1, f6(c1, c2))) | (f6(c1, f6(c1, c2)) = f6(c1, c2)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | big_f(c1, f10(f10(c1))) | (~(c1 = f8(f10(c1)))) | big_f(f7(c1), f6(c1, f6(c1, c2))) | (f6(c1, f6(c1, c2)) = f6(c1, c2)))),
% 29.39/19.67 inference(rewrite,[status(thm)],[])).
% 29.39/19.67 tff(24987,plain,
% 29.39/19.67 (((f10(f10(c1)) = f10(c1)) | big_f(c1, f10(f10(c1))) | (~(f7(c1) = c1)) | (f6(c1, f6(c1, c2)) = f6(c1, c2)) | big_f(f7(c1), f6(c1, f6(c1, c2))) | (~(c1 = f8(f10(c1))))) <=> ((f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | big_f(c1, f10(f10(c1))) | (~(c1 = f8(f10(c1)))) | big_f(f7(c1), f6(c1, f6(c1, c2))) | (f6(c1, f6(c1, c2)) = f6(c1, c2)))),
% 29.39/19.67 inference(rewrite,[status(thm)],[])).
% 29.39/19.67 tff(24988,plain,
% 29.39/19.67 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(f10(c1)) = f10(c1)) | big_f(c1, f10(f10(c1))) | (~(f7(c1) = c1)) | (f6(c1, f6(c1, c2)) = f6(c1, c2)) | big_f(f7(c1), f6(c1, f6(c1, c2))) | (~(c1 = f8(f10(c1)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | big_f(c1, f10(f10(c1))) | (~(c1 = f8(f10(c1)))) | big_f(f7(c1), f6(c1, f6(c1, c2))) | (f6(c1, f6(c1, c2)) = f6(c1, c2))))),
% 29.39/19.67 inference(monotonicity,[status(thm)],[24987])).
% 29.39/19.67 tff(24989,plain,
% 29.39/19.67 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(f10(c1)) = f10(c1)) | big_f(c1, f10(f10(c1))) | (~(f7(c1) = c1)) | (f6(c1, f6(c1, c2)) = f6(c1, c2)) | big_f(f7(c1), f6(c1, f6(c1, c2))) | (~(c1 = f8(f10(c1)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | big_f(c1, f10(f10(c1))) | (~(c1 = f8(f10(c1)))) | big_f(f7(c1), f6(c1, f6(c1, c2))) | (f6(c1, f6(c1, c2)) = f6(c1, c2)))),
% 29.39/19.67 inference(transitivity,[status(thm)],[24988, 24986])).
% 29.39/19.67 tff(24990,plain,
% 29.39/19.67 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(f10(c1)) = f10(c1)) | big_f(c1, f10(f10(c1))) | (~(f7(c1) = c1)) | (f6(c1, f6(c1, c2)) = f6(c1, c2)) | big_f(f7(c1), f6(c1, f6(c1, c2))) | (~(c1 = f8(f10(c1)))))),
% 29.39/19.67 inference(quant_inst,[status(thm)],[])).
% 29.39/19.67 tff(24991,plain,
% 29.39/19.67 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | big_f(c1, f10(f10(c1))) | (~(c1 = f8(f10(c1)))) | big_f(f7(c1), f6(c1, f6(c1, c2))) | (f6(c1, f6(c1, c2)) = f6(c1, c2))),
% 29.39/19.67 inference(modus_ponens,[status(thm)],[24990, 24989])).
% 29.39/19.67 tff(24992,plain,
% 29.39/19.67 (f6(c1, f6(c1, c2)) = f6(c1, c2)),
% 29.39/19.67 inference(unit_resolution,[status(thm)],[24991, 2994, 4234, 24968, 24966, 24985, 24965])).
% 29.39/19.67 tff(24993,plain,
% 29.39/19.67 (f6(c1, c2) = f6(c1, f6(c1, c2))),
% 29.39/19.67 inference(symmetry,[status(thm)],[24992])).
% 29.39/19.67 tff(24994,plain,
% 29.39/19.67 ((f6(c1, c2) = c2) <=> (f6(c1, f6(c1, c2)) = c2)),
% 29.39/19.67 inference(monotonicity,[status(thm)],[24993])).
% 29.39/19.67 tff(24995,plain,
% 29.39/19.67 (f6(c1, f10(c1)) = f6(c1, c2)),
% 29.39/19.67 inference(monotonicity,[status(thm)],[16])).
% 29.39/19.67 tff(24996,plain,
% 29.39/19.67 ((f6(c1, f10(c1)) = f10(c1)) <=> (f6(c1, c2) = c2)),
% 29.39/19.67 inference(monotonicity,[status(thm)],[24995, 16])).
% 29.39/19.67 tff(24997,plain,
% 29.39/19.67 ((f6(c1, f10(c1)) = f10(c1)) <=> (f6(c1, f6(c1, c2)) = f5(f10(c1)))),
% 29.39/19.67 inference(transitivity,[status(thm)],[24996, 24994, 24984])).
% 29.39/19.67 tff(24998,plain,
% 29.39/19.67 (big_f(f7(c1), f6(c1, f10(c1))) <=> big_f(c1, f6(c1, c2))),
% 29.39/19.67 inference(monotonicity,[status(thm)],[4234, 24995])).
% 29.39/19.67 tff(24999,plain,
% 29.39/19.67 (big_f(c1, f6(c1, c2)) <=> big_f(f7(c1), f6(c1, f10(c1)))),
% 29.39/19.67 inference(symmetry,[status(thm)],[24998])).
% 29.39/19.67 tff(25000,plain,
% 29.39/19.67 ((~big_f(c1, f6(c1, c2))) <=> (~big_f(f7(c1), f6(c1, f10(c1))))),
% 29.39/19.67 inference(monotonicity,[status(thm)],[24999])).
% 29.39/19.67 tff(25001,plain,
% 29.39/19.67 (big_f(f7(c1), f6(c1, f6(c1, c2))) <=> big_f(c1, f6(c1, c2))),
% 29.39/19.67 inference(monotonicity,[status(thm)],[4234, 24992])).
% 29.39/19.67 tff(25002,plain,
% 29.39/19.67 ((~big_f(f7(c1), f6(c1, f6(c1, c2)))) <=> (~big_f(c1, f6(c1, c2)))),
% 29.39/19.67 inference(monotonicity,[status(thm)],[25001])).
% 29.49/19.67 tff(25003,plain,
% 29.49/19.67 (~big_f(c1, f6(c1, c2))),
% 29.49/19.67 inference(modus_ponens,[status(thm)],[24985, 25002])).
% 29.49/19.67 tff(25004,plain,
% 29.49/19.67 (~big_f(f7(c1), f6(c1, f10(c1)))),
% 29.49/19.67 inference(modus_ponens,[status(thm)],[25003, 25000])).
% 29.49/19.67 tff(25005,plain,
% 29.49/19.67 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | big_f(c1, f10(f10(c1))) | (~(c1 = f8(f10(c1)))) | big_f(f7(c1), f6(c1, f10(c1))) | (f6(c1, f10(c1)) = f10(c1)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | big_f(c1, f10(f10(c1))) | (~(c1 = f8(f10(c1)))) | big_f(f7(c1), f6(c1, f10(c1))) | (f6(c1, f10(c1)) = f10(c1)))),
% 29.49/19.67 inference(rewrite,[status(thm)],[])).
% 29.49/19.67 tff(25006,plain,
% 29.49/19.67 (((f10(f10(c1)) = f10(c1)) | big_f(c1, f10(f10(c1))) | (~(f7(c1) = c1)) | (f6(c1, f10(c1)) = f10(c1)) | big_f(f7(c1), f6(c1, f10(c1))) | (~(c1 = f8(f10(c1))))) <=> ((f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | big_f(c1, f10(f10(c1))) | (~(c1 = f8(f10(c1)))) | big_f(f7(c1), f6(c1, f10(c1))) | (f6(c1, f10(c1)) = f10(c1)))),
% 29.49/19.67 inference(rewrite,[status(thm)],[])).
% 29.49/19.67 tff(25007,plain,
% 29.49/19.67 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(f10(c1)) = f10(c1)) | big_f(c1, f10(f10(c1))) | (~(f7(c1) = c1)) | (f6(c1, f10(c1)) = f10(c1)) | big_f(f7(c1), f6(c1, f10(c1))) | (~(c1 = f8(f10(c1)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | big_f(c1, f10(f10(c1))) | (~(c1 = f8(f10(c1)))) | big_f(f7(c1), f6(c1, f10(c1))) | (f6(c1, f10(c1)) = f10(c1))))),
% 29.49/19.67 inference(monotonicity,[status(thm)],[25006])).
% 29.49/19.67 tff(25008,plain,
% 29.49/19.67 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(f10(c1)) = f10(c1)) | big_f(c1, f10(f10(c1))) | (~(f7(c1) = c1)) | (f6(c1, f10(c1)) = f10(c1)) | big_f(f7(c1), f6(c1, f10(c1))) | (~(c1 = f8(f10(c1)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | big_f(c1, f10(f10(c1))) | (~(c1 = f8(f10(c1)))) | big_f(f7(c1), f6(c1, f10(c1))) | (f6(c1, f10(c1)) = f10(c1)))),
% 29.49/19.67 inference(transitivity,[status(thm)],[25007, 25005])).
% 29.49/19.67 tff(25009,plain,
% 29.49/19.67 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(f10(c1)) = f10(c1)) | big_f(c1, f10(f10(c1))) | (~(f7(c1) = c1)) | (f6(c1, f10(c1)) = f10(c1)) | big_f(f7(c1), f6(c1, f10(c1))) | (~(c1 = f8(f10(c1)))))),
% 29.49/19.67 inference(quant_inst,[status(thm)],[])).
% 29.49/19.67 tff(25010,plain,
% 29.49/19.67 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | big_f(c1, f10(f10(c1))) | (~(c1 = f8(f10(c1)))) | big_f(f7(c1), f6(c1, f10(c1))) | (f6(c1, f10(c1)) = f10(c1))),
% 29.49/19.67 inference(modus_ponens,[status(thm)],[25009, 25008])).
% 29.49/19.67 tff(25011,plain,
% 29.49/19.67 (big_f(f7(c1), f6(c1, f10(c1))) | (f6(c1, f10(c1)) = f10(c1))),
% 29.49/19.67 inference(unit_resolution,[status(thm)],[25010, 2994, 4234, 24968, 24966, 24965])).
% 29.49/19.67 tff(25012,plain,
% 29.49/19.67 (f6(c1, f10(c1)) = f10(c1)),
% 29.49/19.67 inference(unit_resolution,[status(thm)],[25011, 25004])).
% 29.49/19.67 tff(25013,plain,
% 29.49/19.67 (f6(c1, f6(c1, c2)) = f5(f10(c1))),
% 29.49/19.67 inference(modus_ponens,[status(thm)],[25012, 24997])).
% 29.49/19.67 tff(25014,plain,
% 29.49/19.67 ((~big_f(f7(c1), f6(c1, f6(c1, c2)))) <=> (~big_f(f7(f10(c1)), f6(c1, f6(c1, c2))))),
% 29.49/19.67 inference(monotonicity,[status(thm)],[24979])).
% 29.49/19.67 tff(25015,plain,
% 29.49/19.67 (~big_f(f7(f10(c1)), f6(c1, f6(c1, c2)))),
% 29.49/19.67 inference(modus_ponens,[status(thm)],[24985, 25014])).
% 29.49/19.67 tff(25016,plain,
% 29.49/19.67 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | big_f(c1, f10(f10(c1))) | (~(c1 = f8(f10(c1)))) | (~(f6(c1, f6(c1, c2)) = f5(f10(c1)))) | big_f(f7(f10(c1)), f6(c1, f6(c1, c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | big_f(c1, f10(f10(c1))) | (~(c1 = f8(f10(c1)))) | (~(f6(c1, f6(c1, c2)) = f5(f10(c1)))) | big_f(f7(f10(c1)), f6(c1, f6(c1, c2))))),
% 29.49/19.67 inference(rewrite,[status(thm)],[])).
% 29.49/19.67 tff(25017,plain,
% 29.49/19.67 (((~(f6(c1, f6(c1, c2)) = f5(f10(c1)))) | (f10(f10(c1)) = f10(c1)) | big_f(c1, f10(f10(c1))) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), f6(c1, f6(c1, c2))) | (~(c1 = f8(f10(c1))))) <=> ((f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | big_f(c1, f10(f10(c1))) | (~(c1 = f8(f10(c1)))) | (~(f6(c1, f6(c1, c2)) = f5(f10(c1)))) | big_f(f7(f10(c1)), f6(c1, f6(c1, c2))))),
% 29.49/19.67 inference(rewrite,[status(thm)],[])).
% 29.49/19.67 tff(25018,plain,
% 29.49/19.67 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(f6(c1, f6(c1, c2)) = f5(f10(c1)))) | (f10(f10(c1)) = f10(c1)) | big_f(c1, f10(f10(c1))) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), f6(c1, f6(c1, c2))) | (~(c1 = f8(f10(c1)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | big_f(c1, f10(f10(c1))) | (~(c1 = f8(f10(c1)))) | (~(f6(c1, f6(c1, c2)) = f5(f10(c1)))) | big_f(f7(f10(c1)), f6(c1, f6(c1, c2)))))),
% 29.49/19.67 inference(monotonicity,[status(thm)],[25017])).
% 29.49/19.67 tff(25019,plain,
% 29.49/19.67 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(f6(c1, f6(c1, c2)) = f5(f10(c1)))) | (f10(f10(c1)) = f10(c1)) | big_f(c1, f10(f10(c1))) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), f6(c1, f6(c1, c2))) | (~(c1 = f8(f10(c1)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | big_f(c1, f10(f10(c1))) | (~(c1 = f8(f10(c1)))) | (~(f6(c1, f6(c1, c2)) = f5(f10(c1)))) | big_f(f7(f10(c1)), f6(c1, f6(c1, c2))))),
% 29.49/19.67 inference(transitivity,[status(thm)],[25018, 25016])).
% 29.49/19.67 tff(25020,plain,
% 29.49/19.67 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(f6(c1, f6(c1, c2)) = f5(f10(c1)))) | (f10(f10(c1)) = f10(c1)) | big_f(c1, f10(f10(c1))) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), f6(c1, f6(c1, c2))) | (~(c1 = f8(f10(c1)))))),
% 29.49/19.67 inference(quant_inst,[status(thm)],[])).
% 29.49/19.67 tff(25021,plain,
% 29.49/19.67 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | big_f(c1, f10(f10(c1))) | (~(c1 = f8(f10(c1)))) | (~(f6(c1, f6(c1, c2)) = f5(f10(c1)))) | big_f(f7(f10(c1)), f6(c1, f6(c1, c2)))),
% 29.49/19.67 inference(modus_ponens,[status(thm)],[25020, 25019])).
% 29.49/19.67 tff(25022,plain,
% 29.49/19.67 ((~(f6(c1, f6(c1, c2)) = f5(f10(c1)))) | big_f(f7(f10(c1)), f6(c1, f6(c1, c2)))),
% 29.49/19.67 inference(unit_resolution,[status(thm)],[25021, 1745, 24968, 297, 24966, 24965])).
% 29.49/19.67 tff(25023,plain,
% 29.49/19.67 (~(f6(c1, f6(c1, c2)) = f5(f10(c1)))),
% 29.49/19.67 inference(unit_resolution,[status(thm)],[25022, 25015])).
% 29.49/19.67 tff(25024,plain,
% 29.49/19.67 ($false),
% 29.49/19.67 inference(unit_resolution,[status(thm)],[25023, 25013])).
% 29.49/19.68 tff(25025,plain,(big_f(f7(c1), f6(c1, f6(c1, c2))) | (~(f10(c1) = c2)) | (~(f10(c1) = f5(f10(c1)))) | (~(f7(c1) = c1)) | (f10(f10(c1)) = f10(c1)) | (~(c1 = f8(f10(c1)))) | big_f(c1, f10(f10(c1))) | (f7(f10(c1)) = f10(c1)) | (~(f7(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.49/19.68 tff(25026,plain,
% 29.49/19.68 (big_f(f7(c1), f6(c1, f6(c1, c2)))),
% 29.49/19.68 inference(unit_resolution,[status(thm)],[25025, 24976, 16, 4234, 24968, 24966, 24965, 297, 292])).
% 29.49/19.68 tff(25027,plain,
% 29.49/19.68 (big_f(f7(f10(c1)), f6(c1, f6(c1, c2)))),
% 29.49/19.68 inference(modus_ponens,[status(thm)],[25026, 24979])).
% 29.49/19.68 tff(25028,plain,
% 29.49/19.68 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | big_f(c1, f10(f10(c1))) | (~(c1 = f8(f10(c1)))) | (f6(c1, f6(c1, c2)) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, f6(c1, c2)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | (f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | big_f(c1, f10(f10(c1))) | (~(c1 = f8(f10(c1)))) | (f6(c1, f6(c1, c2)) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, f6(c1, c2)))))),
% 29.49/19.68 inference(rewrite,[status(thm)],[])).
% 29.49/19.68 tff(25029,plain,
% 29.49/19.68 (((f10(f10(c1)) = f10(c1)) | big_f(c1, f10(f10(c1))) | (f7(f10(c1)) = f10(c1)) | (f6(c1, f6(c1, c2)) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, f6(c1, c2)))) | (~(c1 = f8(f10(c1))))) <=> ((f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | big_f(c1, f10(f10(c1))) | (~(c1 = f8(f10(c1)))) | (f6(c1, f6(c1, c2)) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, f6(c1, c2)))))),
% 29.49/19.68 inference(rewrite,[status(thm)],[])).
% 29.49/19.68 tff(25030,plain,
% 29.49/19.68 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(f10(c1)) = f10(c1)) | big_f(c1, f10(f10(c1))) | (f7(f10(c1)) = f10(c1)) | (f6(c1, f6(c1, c2)) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, f6(c1, c2)))) | (~(c1 = f8(f10(c1)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | big_f(c1, f10(f10(c1))) | (~(c1 = f8(f10(c1)))) | (f6(c1, f6(c1, c2)) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, f6(c1, c2))))))),
% 29.49/19.68 inference(monotonicity,[status(thm)],[25029])).
% 29.49/19.68 tff(25031,plain,
% 29.49/19.68 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(f10(c1)) = f10(c1)) | big_f(c1, f10(f10(c1))) | (f7(f10(c1)) = f10(c1)) | (f6(c1, f6(c1, c2)) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, f6(c1, c2)))) | (~(c1 = f8(f10(c1)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | (f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | big_f(c1, f10(f10(c1))) | (~(c1 = f8(f10(c1)))) | (f6(c1, f6(c1, c2)) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, f6(c1, c2)))))),
% 29.49/19.68 inference(transitivity,[status(thm)],[25030, 25028])).
% 29.49/19.68 tff(25032,plain,
% 29.49/19.68 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(f10(c1)) = f10(c1)) | big_f(c1, f10(f10(c1))) | (f7(f10(c1)) = f10(c1)) | (f6(c1, f6(c1, c2)) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, f6(c1, c2)))) | (~(c1 = f8(f10(c1)))))),
% 29.49/19.68 inference(quant_inst,[status(thm)],[])).
% 29.49/19.68 tff(25033,plain,
% 29.49/19.68 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | (f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | big_f(c1, f10(f10(c1))) | (~(c1 = f8(f10(c1)))) | (f6(c1, f6(c1, c2)) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, f6(c1, c2))))),
% 29.49/19.68 inference(modus_ponens,[status(thm)],[25032, 25031])).
% 29.49/19.68 tff(25034,plain,
% 29.49/19.68 ((f6(c1, f6(c1, c2)) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, f6(c1, c2))))),
% 29.49/19.68 inference(unit_resolution,[status(thm)],[25033, 2795, 24968, 297, 24966, 24965])).
% 29.49/19.68 tff(25035,plain,
% 29.49/19.68 (f6(c1, f6(c1, c2)) = f5(f10(c1))),
% 29.49/19.68 inference(unit_resolution,[status(thm)],[25034, 25027])).
% 29.49/19.68 tff(25036,plain,
% 29.49/19.68 (f6(c1, f6(c1, c2)) = c2),
% 29.49/19.68 inference(transitivity,[status(thm)],[25035, 24977, 16])).
% 29.49/19.68 tff(25037,plain,
% 29.49/19.68 ((f6(c1, f6(c1, c2)) = f6(c1, c2)) <=> (c2 = f6(c1, c2))),
% 29.49/19.68 inference(monotonicity,[status(thm)],[25036])).
% 29.49/19.68 tff(25038,plain,
% 29.49/19.68 ((f6(c1, f6(c1, c2)) = f6(c1, c2)) <=> (f6(c1, c2) = c2)),
% 29.49/19.68 inference(transitivity,[status(thm)],[25037, 24866])).
% 29.49/19.68 tff(25039,plain,
% 29.49/19.68 ((~(f6(c1, f6(c1, c2)) = f6(c1, c2))) <=> (~(f6(c1, c2) = c2))),
% 29.49/19.68 inference(monotonicity,[status(thm)],[25038])).
% 29.49/19.68 tff(25040,plain,
% 29.49/19.68 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | big_f(c1, f10(f10(c1))) | (~(c1 = f8(f10(c1)))) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | big_f(c1, f10(f10(c1))) | (~(c1 = f8(f10(c1)))) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))),
% 29.49/19.68 inference(rewrite,[status(thm)],[])).
% 29.49/19.68 tff(25041,plain,
% 29.49/19.68 (((f10(f10(c1)) = f10(c1)) | big_f(c1, f10(f10(c1))) | (~(f7(c1) = c1)) | (~(c1 = f8(f10(c1)))) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2))))) <=> ((f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | big_f(c1, f10(f10(c1))) | (~(c1 = f8(f10(c1)))) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))),
% 29.49/19.68 inference(rewrite,[status(thm)],[])).
% 29.49/19.68 tff(25042,plain,
% 29.49/19.68 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f10(c1)) = f10(c1)) | big_f(c1, f10(f10(c1))) | (~(f7(c1) = c1)) | (~(c1 = f8(f10(c1)))) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | big_f(c1, f10(f10(c1))) | (~(c1 = f8(f10(c1)))) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2))))))),
% 29.49/19.68 inference(monotonicity,[status(thm)],[25041])).
% 29.49/19.68 tff(25043,plain,
% 29.49/19.68 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f10(c1)) = f10(c1)) | big_f(c1, f10(f10(c1))) | (~(f7(c1) = c1)) | (~(c1 = f8(f10(c1)))) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | big_f(c1, f10(f10(c1))) | (~(c1 = f8(f10(c1)))) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))),
% 29.49/19.68 inference(transitivity,[status(thm)],[25042, 25040])).
% 29.49/19.68 tff(25044,plain,
% 29.49/19.68 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f10(c1)) = f10(c1)) | big_f(c1, f10(f10(c1))) | (~(f7(c1) = c1)) | (~(c1 = f8(f10(c1)))) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))),
% 29.49/19.68 inference(quant_inst,[status(thm)],[])).
% 29.49/19.68 tff(25045,plain,
% 29.49/19.68 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | big_f(c1, f10(f10(c1))) | (~(c1 = f8(f10(c1)))) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2))))),
% 29.49/19.68 inference(modus_ponens,[status(thm)],[25044, 25043])).
% 29.49/19.68 tff(25046,plain,
% 29.49/19.68 (~(f6(c1, f6(c1, c2)) = f6(c1, c2))),
% 29.49/19.68 inference(unit_resolution,[status(thm)],[25045, 2963, 4234, 24968, 24966, 25026, 24965])).
% 29.49/19.68 tff(25047,plain,
% 29.49/19.68 (~(f6(c1, c2) = c2)),
% 29.49/19.68 inference(modus_ponens,[status(thm)],[25046, 25039])).
% 29.49/19.68 tff(25048,plain,
% 29.49/19.68 (f6(c1, c2) = c1),
% 29.49/19.68 inference(unit_resolution,[status(thm)],[48, 25047])).
% 29.49/19.68 tff(25049,plain,
% 29.49/19.68 (big_f(c1, f6(c1, c2)) <=> big_f(c1, c1)),
% 29.49/19.68 inference(monotonicity,[status(thm)],[25048])).
% 29.49/19.68 tff(25050,plain,
% 29.49/19.68 (big_f(c1, c1) <=> big_f(c1, f6(c1, c2))),
% 29.49/19.68 inference(symmetry,[status(thm)],[25049])).
% 29.49/19.68 tff(25051,plain,
% 29.49/19.68 ((~big_f(c1, c1)) <=> (~big_f(c1, f6(c1, c2)))),
% 29.49/19.68 inference(monotonicity,[status(thm)],[25050])).
% 29.49/19.68 tff(25052,plain,
% 29.49/19.68 (~big_f(c1, f6(c1, c2))),
% 29.49/19.68 inference(modus_ponens,[status(thm)],[66, 25051])).
% 29.49/19.68 tff(25053,plain,
% 29.49/19.68 ((f6(c1, c2) = c2) <=> (f6(c1, f10(c1)) = f10(c1))),
% 29.49/19.68 inference(symmetry,[status(thm)],[24996])).
% 29.49/19.68 tff(25054,plain,
% 29.49/19.68 ((f6(c1, f6(c1, c2)) = f6(c1, c2)) <=> (f6(c1, f10(c1)) = f10(c1))),
% 29.49/19.68 inference(transitivity,[status(thm)],[25038, 25053])).
% 29.49/19.68 tff(25055,plain,
% 29.49/19.68 ((~(f6(c1, f6(c1, c2)) = f6(c1, c2))) <=> (~(f6(c1, f10(c1)) = f10(c1)))),
% 29.49/19.68 inference(monotonicity,[status(thm)],[25054])).
% 29.49/19.68 tff(25056,plain,
% 29.49/19.68 (~(f6(c1, f10(c1)) = f10(c1))),
% 29.49/19.68 inference(modus_ponens,[status(thm)],[25046, 25055])).
% 29.49/19.68 tff(25057,plain,
% 29.49/19.68 (big_f(f7(c1), f6(c1, f10(c1)))),
% 29.49/19.68 inference(unit_resolution,[status(thm)],[25011, 25056])).
% 29.49/19.68 tff(25058,plain,
% 29.49/19.68 (big_f(c1, f6(c1, c2))),
% 29.49/19.68 inference(modus_ponens,[status(thm)],[25057, 24998])).
% 29.49/19.68 tff(25059,plain,
% 29.49/19.68 ($false),
% 29.49/19.68 inference(unit_resolution,[status(thm)],[25058, 25052])).
% 29.49/19.68 tff(25060,plain,((~(c1 = f8(f10(c1)))) | big_f(c1, c1) | (~(f10(c1) = c2)) | (~(f7(c1) = c1)) | (f10(f10(c1)) = f10(c1)) | big_f(c1, f10(f10(c1))) | (f7(f10(c1)) = f10(c1)) | (~(f7(c2) = c1)) | (~big_f(f7(f10(c1)), f10(c1)))), inference(lemma,lemma(discharge,[]))).
% 29.49/19.68 tff(25061,plain,
% 29.49/19.68 (~(c1 = f8(f10(c1)))),
% 29.49/19.68 inference(unit_resolution,[status(thm)],[25060, 24964, 15, 24246, 24891, 24961, 18825, 22, 66])).
% 29.49/19.68 tff(25062,plain,
% 29.49/19.68 ($false),
% 29.49/19.68 inference(unit_resolution,[status(thm)],[25061, 24957])).
% 29.49/19.68 tff(25063,plain,((f10(c1) = c1) | big_f(c1, c1) | (f10(c2) = c2) | big_f(c2, c1) | (f7(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 29.49/19.68 tff(25064,plain,
% 29.49/19.68 (f10(c1) = c1),
% 29.49/19.68 inference(unit_resolution,[status(thm)],[25063, 66, 89, 2, 17])).
% 29.49/19.68 tff(25065,plain,
% 29.49/19.68 (~big_f(f7(c1), c1)),
% 29.49/19.68 inference(unit_resolution,[status(thm)],[15738, 120, 2])).
% 29.49/19.68 tff(25066,plain,
% 29.49/19.68 ((~(c2 = f8(c2))) <=> (~(f7(c1) = f8(f7(c1))))),
% 29.49/19.68 inference(monotonicity,[status(thm)],[17704])).
% 29.49/19.68 tff(25067,plain,
% 29.49/19.68 (big_f(c2, c2) <=> big_f(f7(c1), f7(c1))),
% 29.49/19.68 inference(monotonicity,[status(thm)],[2778, 2778])).
% 29.49/19.68 tff(25068,plain,
% 29.49/19.68 (big_f(f7(c1), f7(c1)) <=> big_f(c2, c2)),
% 29.49/19.68 inference(symmetry,[status(thm)],[25067])).
% 29.49/19.68 tff(25069,plain,
% 29.49/19.68 (big_f(f7(c1), c2) <=> big_f(c2, c2)),
% 29.49/19.68 inference(transitivity,[status(thm)],[24065, 25068])).
% 29.49/19.68 tff(25070,plain,
% 29.49/19.68 ((~big_f(f7(c1), c2)) <=> (~big_f(c2, c2))),
% 29.49/19.68 inference(monotonicity,[status(thm)],[25069])).
% 29.49/19.68 tff(25071,plain,
% 29.49/19.68 (big_f(c2, c2)),
% 29.49/19.68 inference(modus_ponens,[status(thm)],[12871, 25069])).
% 29.49/19.68 tff(25072,plain,
% 29.49/19.68 (big_f(f7(c1), f7(c1))),
% 29.49/19.68 inference(modus_ponens,[status(thm)],[12871, 24065])).
% 29.49/19.68 tff(25073,plain,
% 29.49/19.68 ((c2 = c3) <=> (f7(c1) = c3)),
% 29.49/19.68 inference(monotonicity,[status(thm)],[2778])).
% 29.49/19.68 tff(25074,plain,
% 29.49/19.68 ((f7(c1) = c3) <=> (c2 = c3)),
% 29.49/19.68 inference(symmetry,[status(thm)],[25073])).
% 29.49/19.68 tff(25075,plain,
% 29.49/19.68 (~(c3 = c2)),
% 29.49/19.68 inference(unit_resolution,[status(thm)],[9397, 79, 17, 2, 333, 1180])).
% 29.49/19.68 tff(25076,plain,
% 29.49/19.68 (c3 = c1),
% 29.49/19.68 inference(unit_resolution,[status(thm)],[180, 25075])).
% 29.49/19.68 tff(25077,plain,
% 29.49/19.68 ((f7(c1) = c3) <=> (f7(c1) = c1)),
% 29.49/19.68 inference(monotonicity,[status(thm)],[25076])).
% 29.49/19.68 tff(25078,plain,
% 29.49/19.68 ((f7(c1) = c1) <=> (f7(c1) = c3)),
% 29.49/19.68 inference(symmetry,[status(thm)],[25077])).
% 29.49/19.68 tff(25079,plain,
% 29.49/19.68 ((f7(c1) = c1) <=> (c2 = c3)),
% 29.49/19.68 inference(transitivity,[status(thm)],[25078, 25074])).
% 29.49/19.68 tff(25080,plain,
% 29.49/19.68 ((~(f7(c1) = c1)) <=> (~(c2 = c3))),
% 29.49/19.68 inference(monotonicity,[status(thm)],[25079])).
% 29.49/19.68 tff(25081,plain,
% 29.49/19.68 (~(c2 = c3)),
% 29.49/19.68 inference(modus_ponens,[status(thm)],[115, 25080])).
% 29.49/19.68 tff(25082,plain,
% 29.49/19.68 (~(c4 = c1)),
% 29.49/19.68 inference(unit_resolution,[status(thm)],[9437, 25081, 1345, 22, 2, 79, 9314])).
% 29.49/19.68 tff(25083,plain,
% 29.49/19.68 (c4 = c2),
% 29.49/19.68 inference(unit_resolution,[status(thm)],[461, 25082])).
% 29.49/19.68 tff(25084,plain,
% 29.49/19.68 (c2 = c4),
% 29.49/19.68 inference(modus_ponens,[status(thm)],[25083, 159])).
% 29.49/19.68 tff(25085,plain,
% 29.49/19.68 (f4(c2) = f4(f7(c1))),
% 29.49/19.68 inference(monotonicity,[status(thm)],[2778])).
% 29.49/19.68 tff(25086,plain,
% 29.49/19.68 ((c1 = f4(c2)) <=> (c1 = f4(f7(c1)))),
% 29.49/19.68 inference(monotonicity,[status(thm)],[25085])).
% 29.49/19.68 tff(25087,plain,
% 29.49/19.68 ((c1 = f4(f7(c1))) <=> (c1 = f4(c2))),
% 29.49/19.68 inference(symmetry,[status(thm)],[25086])).
% 29.49/19.68 tff(25088,plain,
% 29.49/19.68 (c2 = c4),
% 29.49/19.68 inference(symmetry,[status(thm)],[25083])).
% 29.49/19.68 tff(25089,plain,
% 29.49/19.68 (f7(c1) = c4),
% 29.49/19.68 inference(transitivity,[status(thm)],[120, 25088])).
% 29.49/19.68 tff(25090,plain,
% 29.49/19.68 (f4(f7(c1)) = f4(c4)),
% 29.49/19.68 inference(monotonicity,[status(thm)],[25089])).
% 29.49/19.68 tff(25091,plain,
% 29.49/19.68 (f4(f7(c1)) = f7(c1)),
% 29.49/19.68 inference(transitivity,[status(thm)],[25090, 79, 2778])).
% 29.49/19.68 tff(25092,plain,
% 29.49/19.68 ((c1 = f4(f7(c1))) <=> (c1 = f7(c1))),
% 29.49/19.68 inference(monotonicity,[status(thm)],[25091])).
% 29.49/19.68 tff(25093,plain,
% 29.49/19.68 ((c1 = f4(f7(c1))) <=> (f7(c1) = c1)),
% 29.49/19.68 inference(transitivity,[status(thm)],[25092, 14336])).
% 29.49/19.68 tff(25094,plain,
% 29.49/19.68 ((f7(c1) = c1) <=> (c1 = f4(f7(c1)))),
% 29.49/19.68 inference(symmetry,[status(thm)],[25093])).
% 29.49/19.68 tff(25095,plain,
% 29.49/19.68 ((f7(c1) = c1) <=> (f7(c2) = f4(c2))),
% 29.49/19.68 inference(transitivity,[status(thm)],[25094, 25087, 9302])).
% 29.49/19.68 tff(25096,plain,
% 29.49/19.68 ((~(f7(c1) = c1)) <=> (~(f7(c2) = f4(c2)))),
% 29.49/19.68 inference(monotonicity,[status(thm)],[25095])).
% 29.49/19.68 tff(25097,plain,
% 29.49/19.68 (~(f7(c2) = f4(c2))),
% 29.49/19.68 inference(modus_ponens,[status(thm)],[115, 25096])).
% 29.49/19.68 tff(25098,plain,
% 29.49/19.68 (f1(c2, c2) = c2),
% 29.49/19.68 inference(unit_resolution,[status(thm)],[9464, 25097, 2, 1180, 25081, 25084])).
% 29.49/19.68 tff(25099,plain,
% 29.49/19.68 (f1(f7(c1), f7(c1)) = f7(c1)),
% 29.49/19.68 inference(transitivity,[status(thm)],[23935, 25098, 2778])).
% 29.49/19.68 tff(25100,plain,
% 29.49/19.68 (big_f(f7(c1), f1(f7(c1), f7(c1))) <=> big_f(f7(c1), f7(c1))),
% 29.49/19.68 inference(monotonicity,[status(thm)],[25099])).
% 29.49/19.68 tff(25101,plain,
% 29.49/19.68 (big_f(f7(c1), f7(c1)) <=> big_f(f7(c1), f1(f7(c1), f7(c1)))),
% 29.49/19.68 inference(symmetry,[status(thm)],[25100])).
% 29.49/19.68 tff(25102,assumption,(big_f(f7(c1), f7(c1))), introduced(assumption)).
% 29.49/19.68 tff(25103,plain,
% 29.49/19.68 (big_f(f7(c1), f1(f7(c1), f7(c1)))),
% 29.49/19.68 inference(modus_ponens,[status(thm)],[25102, 25101])).
% 29.49/19.68 tff(25104,plain,
% 29.49/19.68 ((~(f7(c1) = c1)) <=> (~(c1 = f4(f7(c1))))),
% 29.49/19.68 inference(monotonicity,[status(thm)],[25094])).
% 29.49/19.68 tff(25105,plain,
% 29.49/19.68 (~(c1 = f4(f7(c1)))),
% 29.49/19.68 inference(modus_ponens,[status(thm)],[115, 25104])).
% 29.49/19.68 tff(25106,plain,
% 29.49/19.68 ((~(f7(c1) = c1)) <=> (~(f7(c1) = c3))),
% 29.49/19.68 inference(monotonicity,[status(thm)],[25078])).
% 29.49/19.68 tff(25107,plain,
% 29.49/19.68 (~(f7(c1) = c3)),
% 29.49/19.68 inference(modus_ponens,[status(thm)],[115, 25106])).
% 29.49/19.68 tff(25108,plain,
% 29.49/19.68 (f7(c1) = c4),
% 29.49/19.68 inference(unit_resolution,[status(thm)],[19869, 25083, 120])).
% 29.49/19.68 tff(25109,plain,
% 29.49/19.68 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c1) = c3) | (~(f7(c1) = c4)) | (~big_f(c1, f7(c1))) | (c1 = f4(f7(c1))) | (~(f1(f7(c1), f7(c1)) = f7(c1))) | (~big_f(f7(c1), f1(f7(c1), f7(c1)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (f7(c1) = c3) | (~(f7(c1) = c4)) | (~big_f(c1, f7(c1))) | (c1 = f4(f7(c1))) | (~(f1(f7(c1), f7(c1)) = f7(c1))) | (~big_f(f7(c1), f1(f7(c1), f7(c1)))))),
% 29.49/19.68 inference(rewrite,[status(thm)],[])).
% 29.49/19.68 tff(25110,plain,
% 29.49/19.68 (((f7(c1) = c3) | (~(f7(c1) = c4)) | (c1 = f4(f7(c1))) | (~big_f(c1, f7(c1))) | (~(f1(f7(c1), f7(c1)) = f7(c1))) | (~big_f(f7(c1), f1(f7(c1), f7(c1))))) <=> ((f7(c1) = c3) | (~(f7(c1) = c4)) | (~big_f(c1, f7(c1))) | (c1 = f4(f7(c1))) | (~(f1(f7(c1), f7(c1)) = f7(c1))) | (~big_f(f7(c1), f1(f7(c1), f7(c1)))))),
% 29.49/19.68 inference(rewrite,[status(thm)],[])).
% 29.49/19.68 tff(25111,plain,
% 29.49/19.68 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c1) = c3) | (~(f7(c1) = c4)) | (c1 = f4(f7(c1))) | (~big_f(c1, f7(c1))) | (~(f1(f7(c1), f7(c1)) = f7(c1))) | (~big_f(f7(c1), f1(f7(c1), f7(c1)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c1) = c3) | (~(f7(c1) = c4)) | (~big_f(c1, f7(c1))) | (c1 = f4(f7(c1))) | (~(f1(f7(c1), f7(c1)) = f7(c1))) | (~big_f(f7(c1), f1(f7(c1), f7(c1))))))),
% 29.49/19.68 inference(monotonicity,[status(thm)],[25110])).
% 29.49/19.68 tff(25112,plain,
% 29.49/19.68 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c1) = c3) | (~(f7(c1) = c4)) | (c1 = f4(f7(c1))) | (~big_f(c1, f7(c1))) | (~(f1(f7(c1), f7(c1)) = f7(c1))) | (~big_f(f7(c1), f1(f7(c1), f7(c1)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (f7(c1) = c3) | (~(f7(c1) = c4)) | (~big_f(c1, f7(c1))) | (c1 = f4(f7(c1))) | (~(f1(f7(c1), f7(c1)) = f7(c1))) | (~big_f(f7(c1), f1(f7(c1), f7(c1)))))),
% 29.49/19.68 inference(transitivity,[status(thm)],[25111, 25109])).
% 29.49/19.68 tff(25113,plain,
% 29.49/19.68 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c1) = c3) | (~(f7(c1) = c4)) | (c1 = f4(f7(c1))) | (~big_f(c1, f7(c1))) | (~(f1(f7(c1), f7(c1)) = f7(c1))) | (~big_f(f7(c1), f1(f7(c1), f7(c1)))))),
% 29.49/19.68 inference(quant_inst,[status(thm)],[])).
% 29.49/19.68 tff(25114,plain,
% 29.49/19.68 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (f7(c1) = c3) | (~(f7(c1) = c4)) | (~big_f(c1, f7(c1))) | (c1 = f4(f7(c1))) | (~(f1(f7(c1), f7(c1)) = f7(c1))) | (~big_f(f7(c1), f1(f7(c1), f7(c1))))),
% 29.49/19.68 inference(modus_ponens,[status(thm)],[25113, 25112])).
% 29.49/19.68 tff(25115,plain,
% 29.49/19.68 ((~(f1(f7(c1), f7(c1)) = f7(c1))) | (~big_f(f7(c1), f1(f7(c1), f7(c1))))),
% 29.49/19.68 inference(unit_resolution,[status(thm)],[25114, 553, 25108, 25107, 11909, 25105])).
% 29.49/19.68 tff(25116,plain,
% 29.49/19.68 ($false),
% 29.49/19.68 inference(unit_resolution,[status(thm)],[25115, 25103, 25099])).
% 29.49/19.68 tff(25117,plain,((~(f4(c4) = c2)) | (~big_f(c1, f7(c1))) | (~big_f(f7(c1), f7(c1))) | big_f(c2, c1) | (~big_f(f7(c2), c2)) | (f7(c1) = c1) | (~big_f(c2, c2)) | (f7(c2) = c2) | big_f(f7(c2), c1)), inference(lemma,lemma(discharge,[]))).
% 29.49/19.68 tff(25118,plain,
% 29.49/19.68 (~(f4(c4) = c2)),
% 29.49/19.68 inference(unit_resolution,[status(thm)],[25117, 25072, 17601, 2, 12167, 115, 25071, 17, 12093])).
% 29.49/19.68 tff(25119,plain,
% 29.49/19.68 (f4(c4) = c1),
% 29.49/19.68 inference(unit_resolution,[status(thm)],[11750, 25118])).
% 29.49/19.68 tff(25120,plain,
% 29.49/19.68 ((f7(c1) = c1) <=> (c2 = c3)),
% 29.49/19.68 inference(transitivity,[status(thm)],[20483, 25074])).
% 29.49/19.68 tff(25121,plain,
% 29.49/19.68 ((~(f7(c1) = c1)) <=> (~(c2 = c3))),
% 29.49/19.68 inference(monotonicity,[status(thm)],[25120])).
% 29.49/19.68 tff(25122,plain,
% 29.49/19.68 (~(c2 = c3)),
% 29.49/19.68 inference(modus_ponens,[status(thm)],[115, 25121])).
% 29.49/19.68 tff(25123,plain,
% 29.49/19.68 (~(c2 = c4)),
% 29.49/19.68 inference(unit_resolution,[status(thm)],[16877, 25122, 9331, 1345, 11752, 17])).
% 29.49/19.68 tff(25124,plain,
% 29.49/19.68 (~(c4 = c2)),
% 29.49/19.68 inference(modus_ponens,[status(thm)],[25123, 8722])).
% 29.49/19.68 tff(25125,plain,
% 29.49/19.68 (c4 = c1),
% 29.49/19.68 inference(unit_resolution,[status(thm)],[461, 25124])).
% 29.49/19.68 tff(25126,plain,
% 29.49/19.68 (c1 = c4),
% 29.49/19.68 inference(unit_resolution,[status(thm)],[484, 25125])).
% 29.49/19.68 tff(25127,plain,
% 29.49/19.68 (c1 = c4),
% 29.49/19.68 inference(symmetry,[status(thm)],[25125])).
% 29.49/19.68 tff(25128,plain,
% 29.49/19.68 (f4(c1) = f4(c4)),
% 29.49/19.68 inference(monotonicity,[status(thm)],[25127])).
% 29.49/19.68 tff(25129,plain,
% 29.49/19.68 (f4(c4) = f4(c1)),
% 29.49/19.68 inference(symmetry,[status(thm)],[25128])).
% 29.49/19.68 tff(25130,plain,
% 29.49/19.68 (c1 = f4(c1)),
% 29.49/19.68 inference(transitivity,[status(thm)],[16651, 25129])).
% 29.49/19.68 tff(25131,plain,
% 29.49/19.68 (~(f1(c2, c2) = c1)),
% 29.49/19.68 inference(unit_resolution,[status(thm)],[23954, 25130, 20485, 25126, 66, 285, 115])).
% 29.49/19.68 tff(25132,plain,
% 29.49/19.68 (f1(c2, c2) = c2),
% 29.49/19.68 inference(unit_resolution,[status(thm)],[5270, 25131])).
% 29.49/19.68 tff(25133,plain,
% 29.49/19.68 (f1(f7(c1), f7(c1)) = f7(c1)),
% 29.49/19.68 inference(transitivity,[status(thm)],[23935, 25132, 2778])).
% 29.49/19.68 tff(25134,plain,
% 29.49/19.68 (big_f(f7(c1), f1(f7(c1), f7(c1))) <=> big_f(f7(c1), f7(c1))),
% 29.49/19.68 inference(monotonicity,[status(thm)],[25133])).
% 29.49/19.68 tff(25135,plain,
% 29.49/19.68 (big_f(f7(c1), f7(c1)) <=> big_f(f7(c1), f1(f7(c1), f7(c1)))),
% 29.49/19.68 inference(symmetry,[status(thm)],[25134])).
% 29.49/19.68 tff(25136,plain,
% 29.49/19.68 (big_f(f7(c1), f1(f7(c1), f7(c1)))),
% 29.49/19.68 inference(modus_ponens,[status(thm)],[25102, 25135])).
% 29.49/19.68 tff(25137,plain,
% 29.49/19.68 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c1) = c3) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (~(f1(f7(c1), f7(c1)) = f7(c1))) | (~big_f(f7(c1), f1(f7(c1), f7(c1)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (f7(c1) = c3) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (~(f1(f7(c1), f7(c1)) = f7(c1))) | (~big_f(f7(c1), f1(f7(c1), f7(c1)))))),
% 29.49/19.68 inference(rewrite,[status(thm)],[])).
% 29.49/19.68 tff(25138,plain,
% 29.49/19.68 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f7(c1) = c3) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (~(f1(f7(c1), f7(c1)) = f7(c1))) | (~big_f(f7(c1), f1(f7(c1), f7(c1)))))),
% 29.49/19.68 inference(quant_inst,[status(thm)],[])).
% 29.49/19.68 tff(25139,plain,
% 29.49/19.68 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (f7(c1) = c3) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (~(f1(f7(c1), f7(c1)) = f7(c1))) | (~big_f(f7(c1), f1(f7(c1), f7(c1))))),
% 29.49/19.68 inference(modus_ponens,[status(thm)],[25138, 25137])).
% 29.49/19.68 tff(25140,plain,
% 29.49/19.68 ((~(f1(f7(c1), f7(c1)) = f7(c1))) | (~big_f(f7(c1), f1(f7(c1), f7(c1))))),
% 29.49/19.68 inference(unit_resolution,[status(thm)],[25139, 447, 25126, 20485, 25130, 66])).
% 29.49/19.68 tff(25141,plain,
% 29.49/19.68 ($false),
% 29.49/19.68 inference(unit_resolution,[status(thm)],[25140, 25136, 25133])).
% 29.49/19.68 tff(25142,plain,((~(c3 = c1)) | big_f(c1, c1) | (~big_f(f7(c1), f7(c1))) | big_f(f7(c1), c1) | (f7(c1) = c1) | (~(f4(c4) = c1)) | big_f(c2, f7(c2)) | (~big_f(c2, c2)) | (f7(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 29.49/19.68 tff(25143,plain,
% 29.49/19.68 (~(c3 = c1)),
% 29.49/19.68 inference(unit_resolution,[status(thm)],[25142, 25072, 66, 25065, 115, 25119, 9314, 25071, 17])).
% 29.49/19.68 tff(25144,plain,
% 29.49/19.68 (~(c1 = c3)),
% 29.49/19.68 inference(modus_ponens,[status(thm)],[25143, 648])).
% 29.49/19.68 tff(25145,plain,
% 29.49/19.68 (f1(c1, c2) = c2),
% 29.49/19.68 inference(unit_resolution,[status(thm)],[23505, 25144, 66, 25071, 25119])).
% 29.49/19.68 tff(25146,plain,
% 29.49/19.68 ((c3 = c1) <=> (f7(c2) = c3)),
% 29.49/19.68 inference(transitivity,[status(thm)],[68, 13076])).
% 29.49/19.68 tff(25147,plain,
% 29.49/19.68 ((~(c3 = c1)) <=> (~(f7(c2) = c3))),
% 29.49/19.68 inference(monotonicity,[status(thm)],[25146])).
% 29.49/19.68 tff(25148,plain,
% 29.49/19.68 (~(f7(c2) = c3)),
% 29.49/19.68 inference(modus_ponens,[status(thm)],[25143, 25147])).
% 29.49/19.68 tff(25149,plain,
% 29.49/19.68 (big_f(f4(c4), c4)),
% 29.49/19.68 inference(unit_resolution,[status(thm)],[21246, 25145, 2865, 25144])).
% 29.49/19.68 tff(25150,plain,
% 29.49/19.68 (~(c4 = c1)),
% 29.49/19.68 inference(unit_resolution,[status(thm)],[17136, 25149, 22, 23541, 25119])).
% 29.49/19.68 tff(25151,plain,
% 29.49/19.68 (c4 = c2),
% 29.49/19.68 inference(unit_resolution,[status(thm)],[461, 25150])).
% 29.49/19.68 tff(25152,plain,
% 29.49/19.68 (c2 = c4),
% 29.49/19.68 inference(modus_ponens,[status(thm)],[25151, 159])).
% 29.49/19.68 tff(25153,plain,
% 29.49/19.68 (c2 = c4),
% 29.49/19.68 inference(symmetry,[status(thm)],[25151])).
% 29.49/19.68 tff(25154,plain,
% 29.49/19.68 (f7(c1) = c4),
% 29.49/19.68 inference(transitivity,[status(thm)],[120, 25153])).
% 29.49/19.68 tff(25155,plain,
% 29.49/19.68 (f4(f7(c1)) = f4(c4)),
% 29.49/19.68 inference(monotonicity,[status(thm)],[25154])).
% 29.49/19.68 tff(25156,plain,
% 29.49/19.68 (f4(c2) = c1),
% 29.49/19.68 inference(transitivity,[status(thm)],[25085, 25155, 25119])).
% 29.49/19.68 tff(25157,plain,
% 29.49/19.68 ((c2 = f4(c2)) <=> (f7(c1) = c1)),
% 29.49/19.68 inference(monotonicity,[status(thm)],[2778, 25156])).
% 29.49/19.68 tff(25158,plain,
% 29.49/19.68 ((f7(c1) = c1) <=> (c2 = f4(c2))),
% 29.49/19.68 inference(symmetry,[status(thm)],[25157])).
% 29.49/19.68 tff(25159,plain,
% 29.49/19.68 ((~(f7(c1) = c1)) <=> (~(c2 = f4(c2)))),
% 29.49/19.68 inference(monotonicity,[status(thm)],[25158])).
% 29.49/19.68 tff(25160,plain,
% 29.49/19.68 (~(c2 = f4(c2))),
% 29.49/19.68 inference(modus_ponens,[status(thm)],[115, 25159])).
% 29.49/19.68 tff(25161,plain,
% 29.49/19.68 ($false),
% 29.49/19.68 inference(unit_resolution,[status(thm)],[17200, 25160, 25152, 12167, 22, 25071, 25148, 25145])).
% 29.49/19.68 tff(25162,plain,((~big_f(f7(c1), c2)) | (f7(c1) = c1) | (~big_f(c1, c2)) | big_f(c1, c1) | (f7(c2) = c2) | big_f(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 29.49/19.68 tff(25163,plain,
% 29.49/19.68 (~big_f(f7(c1), c2)),
% 29.49/19.68 inference(unit_resolution,[status(thm)],[25162, 115, 24857, 66, 17, 2])).
% 29.49/19.68 tff(25164,plain,
% 29.49/19.68 (~big_f(c2, c2)),
% 29.49/19.68 inference(modus_ponens,[status(thm)],[25163, 25070])).
% 29.49/19.68 tff(25165,plain,
% 29.49/19.68 (~big_f(f7(c1), f5(c1))),
% 29.49/19.68 inference(unit_resolution,[status(thm)],[8430, 25164, 120, 25065])).
% 29.49/19.68 tff(25166,plain,
% 29.49/19.68 (~(c2 = f8(c2))),
% 29.49/19.68 inference(unit_resolution,[status(thm)],[12015, 25165, 12071, 89, 115])).
% 29.49/19.68 tff(25167,plain,
% 29.49/19.68 (~(f7(c1) = f8(f7(c1)))),
% 29.49/19.68 inference(modus_ponens,[status(thm)],[25166, 25066])).
% 29.49/19.68 tff(25168,plain,
% 29.49/19.68 (~(f5(c1) = c1)),
% 29.49/19.68 inference(unit_resolution,[status(thm)],[24050, 25167, 94, 25065, 25064, 115, 66])).
% 29.49/19.68 tff(25169,plain,
% 29.49/19.68 (f5(c1) = c2),
% 29.49/19.68 inference(unit_resolution,[status(thm)],[1708, 25168])).
% 29.49/19.68 tff(25170,plain,
% 29.49/19.68 (c2 = f5(c1)),
% 29.49/19.68 inference(symmetry,[status(thm)],[25169])).
% 29.49/19.68 tff(25171,plain,
% 29.49/19.68 (f7(c1) = f5(c1)),
% 29.49/19.68 inference(transitivity,[status(thm)],[120, 25170])).
% 29.49/19.68 tff(25172,plain,
% 29.49/19.68 (c2 = f5(c1)),
% 29.49/19.68 inference(unit_resolution,[status(thm)],[24054, 25169])).
% 29.49/19.69 tff(25173,plain,
% 29.49/19.69 (~(f7(c1) = f5(c1))),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[24083, 25172, 115, 94, 25163, 25064, 25167, 66])).
% 29.49/19.69 tff(25174,plain,
% 29.49/19.69 ($false),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[25173, 25171])).
% 29.49/19.69 tff(25175,plain,((f7(c1) = c1) | big_f(c1, c1) | (f10(c2) = c2) | (f7(c2) = c2) | big_f(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 29.49/19.69 tff(25176,plain,
% 29.49/19.69 (big_f(c2, c1)),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[25175, 23353, 115, 66, 24245])).
% 29.49/19.69 tff(25177,plain,
% 29.49/19.69 (~big_f(f7(c1), c2)),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[23932, 25176, 115, 66])).
% 29.49/19.69 tff(25178,plain,
% 29.49/19.69 (~(c2 = f5(c1))),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[11602, 25177, 115, 22733, 66, 25176])).
% 29.49/19.69 tff(25179,plain,
% 29.49/19.69 (~(f5(c1) = c2)),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[24054, 25178])).
% 29.49/19.69 tff(25180,plain,
% 29.49/19.69 (f5(c1) = c1),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[1708, 25179])).
% 29.49/19.69 tff(25181,plain,
% 29.49/19.69 (f7(c2) = c1),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[21, 24245])).
% 29.49/19.69 tff(25182,plain,
% 29.49/19.69 (big_f(f7(c2), f7(c2)) <=> big_f(c1, c1)),
% 29.49/19.69 inference(monotonicity,[status(thm)],[25181, 25181])).
% 29.49/19.69 tff(25183,plain,
% 29.49/19.69 (big_f(c1, c1) <=> big_f(f7(c2), f7(c2))),
% 29.49/19.69 inference(symmetry,[status(thm)],[25182])).
% 29.49/19.69 tff(25184,plain,
% 29.49/19.69 ((~big_f(c1, c1)) <=> (~big_f(f7(c2), f7(c2)))),
% 29.49/19.69 inference(monotonicity,[status(thm)],[25183])).
% 29.49/19.69 tff(25185,plain,
% 29.49/19.69 (~big_f(f7(c2), f7(c2))),
% 29.49/19.69 inference(modus_ponens,[status(thm)],[66, 25184])).
% 29.49/19.69 tff(25186,plain,
% 29.49/19.69 ((f7(c2) = c3) <=> (c1 = c3)),
% 29.49/19.69 inference(monotonicity,[status(thm)],[25181])).
% 29.49/19.69 tff(25187,plain,
% 29.49/19.69 ((c1 = c3) <=> (f7(c2) = c3)),
% 29.49/19.69 inference(symmetry,[status(thm)],[25186])).
% 29.49/19.69 tff(25188,plain,
% 29.49/19.69 (big_f(c1, c2)),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[24400, 121, 23353, 66, 22733])).
% 29.49/19.69 tff(25189,plain,
% 29.49/19.69 (~(c3 = c2)),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[13626, 79, 2865, 89, 347, 66, 121])).
% 29.49/19.69 tff(25190,plain,
% 29.49/19.69 (c3 = c1),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[180, 25189])).
% 29.49/19.69 tff(25191,plain,
% 29.49/19.69 ((c2 = c3) <=> (c2 = c1)),
% 29.49/19.69 inference(monotonicity,[status(thm)],[25190])).
% 29.49/19.69 tff(25192,plain,
% 29.49/19.69 ((c2 = c1) <=> (c2 = c3)),
% 29.49/19.69 inference(symmetry,[status(thm)],[25191])).
% 29.49/19.69 tff(25193,plain,
% 29.49/19.69 ((~(c2 = c1)) <=> (~(c2 = c3))),
% 29.49/19.69 inference(monotonicity,[status(thm)],[25192])).
% 29.49/19.69 tff(25194,plain,
% 29.49/19.69 (~(c2 = c3)),
% 29.49/19.69 inference(modus_ponens,[status(thm)],[75, 25193])).
% 29.49/19.69 tff(25195,plain,
% 29.49/19.69 ((c2 = c1) <=> (f7(c1) = c3)),
% 29.49/19.69 inference(transitivity,[status(thm)],[25192, 1002])).
% 29.49/19.69 tff(25196,plain,
% 29.49/19.69 ((~(c2 = c1)) <=> (~(f7(c1) = c3))),
% 29.49/19.69 inference(monotonicity,[status(thm)],[25195])).
% 29.49/19.69 tff(25197,plain,
% 29.49/19.69 (~(f7(c1) = c3)),
% 29.49/19.69 inference(modus_ponens,[status(thm)],[75, 25196])).
% 29.49/19.69 tff(25198,plain,
% 29.49/19.69 ((c2 = c1) <=> (f7(f7(c2)) = c3)),
% 29.49/19.69 inference(transitivity,[status(thm)],[25192, 8810])).
% 29.49/19.69 tff(25199,plain,
% 29.49/19.69 ((~(c2 = c1)) <=> (~(f7(f7(c2)) = c3))),
% 29.49/19.69 inference(monotonicity,[status(thm)],[25198])).
% 29.49/19.69 tff(25200,plain,
% 29.49/19.69 (~(f7(f7(c2)) = c3)),
% 29.49/19.69 inference(modus_ponens,[status(thm)],[75, 25199])).
% 29.49/19.69 tff(25201,plain,
% 29.49/19.69 (~(c2 = c4)),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[8754, 25194, 347, 348, 79, 25200, 22, 121])).
% 29.49/19.69 tff(25202,plain,
% 29.49/19.69 ($false),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[12226, 25201, 25197, 347, 348, 17, 25194, 2865, 121])).
% 29.49/19.69 tff(25203,plain,((~(f4(c4) = c2)) | (~(f7(c1) = c2)) | (~big_f(c2, c1)) | (f7(c2) = c2) | (~big_f(c1, c2)) | big_f(c2, c2) | (f10(c2) = c2) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 29.49/19.69 tff(25204,plain,
% 29.49/19.69 (~(f4(c4) = c2)),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[25203, 25176, 120, 24245, 25188, 121, 23353, 66])).
% 29.49/19.69 tff(25205,plain,
% 29.49/19.69 (f4(c4) = c1),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[11750, 25204])).
% 29.49/19.69 tff(25206,plain,
% 29.49/19.69 (~(c3 = c1)),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[20729, 25205, 115, 24245, 66, 121, 23353])).
% 29.49/19.69 tff(25207,plain,
% 29.49/19.69 (c3 = c2),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[180, 25206])).
% 29.49/19.69 tff(25208,plain,
% 29.49/19.69 ((c1 = c3) <=> (c1 = c2)),
% 29.49/19.69 inference(monotonicity,[status(thm)],[25207])).
% 29.49/19.69 tff(25209,plain,
% 29.49/19.69 ((c1 = c3) <=> (c2 = c1)),
% 29.49/19.69 inference(transitivity,[status(thm)],[25208, 1])).
% 29.49/19.69 tff(25210,plain,
% 29.49/19.69 ((c2 = c1) <=> (c1 = c3)),
% 29.49/19.69 inference(symmetry,[status(thm)],[25209])).
% 29.49/19.69 tff(25211,plain,
% 29.49/19.69 ((c2 = c1) <=> (f7(c2) = c3)),
% 29.49/19.69 inference(transitivity,[status(thm)],[25210, 25187])).
% 29.49/19.69 tff(25212,plain,
% 29.49/19.69 ((~(c2 = c1)) <=> (~(f7(c2) = c3))),
% 29.49/19.69 inference(monotonicity,[status(thm)],[25211])).
% 29.49/19.69 tff(25213,plain,
% 29.49/19.69 (~(f7(c2) = c3)),
% 29.49/19.69 inference(modus_ponens,[status(thm)],[75, 25212])).
% 29.49/19.69 tff(25214,plain,
% 29.49/19.69 (big_f(f7(c2), c2) <=> big_f(c1, c2)),
% 29.49/19.69 inference(monotonicity,[status(thm)],[25181])).
% 29.49/19.69 tff(25215,plain,
% 29.49/19.69 (big_f(c1, c2) <=> big_f(f7(c2), c2)),
% 29.49/19.69 inference(symmetry,[status(thm)],[25214])).
% 29.49/19.69 tff(25216,plain,
% 29.49/19.69 (big_f(f7(c2), c2)),
% 29.49/19.69 inference(modus_ponens,[status(thm)],[25188, 25215])).
% 29.49/19.69 tff(25217,plain,
% 29.49/19.69 (big_f(f7(f7(c2)), f7(c2)) <=> big_f(c2, c1)),
% 29.49/19.69 inference(monotonicity,[status(thm)],[363, 292])).
% 29.49/19.69 tff(25218,plain,
% 29.49/19.69 ((~big_f(f7(f7(c2)), f7(c2))) <=> (~big_f(c2, c1))),
% 29.49/19.69 inference(monotonicity,[status(thm)],[25217])).
% 29.49/19.69 tff(25219,plain,
% 29.49/19.69 (~big_f(c2, c1)),
% 29.49/19.69 inference(modus_ponens,[status(thm)],[8452, 25218])).
% 29.49/19.69 tff(25220,plain,
% 29.49/19.69 ($false),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[348, 25219])).
% 29.49/19.69 tff(25221,plain,((~big_f(c2, c1)) | big_f(f7(f7(c2)), f7(c2)) | (~(f7(c2) = c1)) | (~(f7(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.49/19.69 tff(25222,plain,
% 29.49/19.69 (big_f(f7(f7(c2)), f7(c2))),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[25221, 25176, 120, 25181])).
% 29.49/19.69 tff(25223,plain,
% 29.49/19.69 (big_f(c2, f7(c2))),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[15941, 25222, 120, 25181])).
% 29.49/19.69 tff(25224,plain,
% 29.49/19.69 ((f7(c2) = c4) <=> (c1 = c4)),
% 29.49/19.69 inference(monotonicity,[status(thm)],[25181])).
% 29.49/19.69 tff(25225,plain,
% 29.49/19.69 ((c1 = c4) <=> (f7(c2) = c4)),
% 29.49/19.69 inference(symmetry,[status(thm)],[25224])).
% 29.49/19.69 tff(25226,plain,
% 29.49/19.69 ((~(c2 = c1)) <=> (~(c1 = c3))),
% 29.49/19.69 inference(monotonicity,[status(thm)],[25210])).
% 29.49/19.69 tff(25227,plain,
% 29.49/19.69 (~(c1 = c3)),
% 29.49/19.69 inference(modus_ponens,[status(thm)],[75, 25226])).
% 29.49/19.69 tff(25228,plain,
% 29.49/19.69 (big_f(f7(c2), c1) <=> big_f(c1, c1)),
% 29.49/19.69 inference(monotonicity,[status(thm)],[25181])).
% 29.49/19.69 tff(25229,plain,
% 29.49/19.69 (big_f(c1, c1) <=> big_f(f7(c2), c1)),
% 29.49/19.69 inference(symmetry,[status(thm)],[25228])).
% 29.49/19.69 tff(25230,plain,
% 29.49/19.69 ((~big_f(c1, c1)) <=> (~big_f(f7(c2), c1))),
% 29.49/19.69 inference(monotonicity,[status(thm)],[25229])).
% 29.49/19.69 tff(25231,plain,
% 29.49/19.69 (~big_f(f7(c2), c1)),
% 29.49/19.69 inference(modus_ponens,[status(thm)],[66, 25230])).
% 29.49/19.69 tff(25232,plain,
% 29.49/19.69 (c2 = c4),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[9203, 25213, 120, 121, 25216, 25231, 25227, 24245])).
% 29.49/19.69 tff(25233,plain,
% 29.49/19.69 (c4 = c2),
% 29.49/19.69 inference(symmetry,[status(thm)],[25232])).
% 29.49/19.69 tff(25234,plain,
% 29.49/19.69 ((c1 = c4) <=> (c1 = c2)),
% 29.49/19.69 inference(monotonicity,[status(thm)],[25233])).
% 29.49/19.69 tff(25235,plain,
% 29.49/19.69 ((c1 = c4) <=> (c2 = c1)),
% 29.49/19.69 inference(transitivity,[status(thm)],[25234, 1])).
% 29.49/19.69 tff(25236,plain,
% 29.49/19.69 ((c2 = c1) <=> (c1 = c4)),
% 29.49/19.69 inference(symmetry,[status(thm)],[25235])).
% 29.49/19.69 tff(25237,plain,
% 29.49/19.69 ((c2 = c1) <=> (f7(c2) = c4)),
% 29.49/19.69 inference(transitivity,[status(thm)],[25236, 25225])).
% 29.49/19.69 tff(25238,plain,
% 29.49/19.69 ((~(c2 = c1)) <=> (~(f7(c2) = c4))),
% 29.49/19.69 inference(monotonicity,[status(thm)],[25237])).
% 29.49/19.69 tff(25239,plain,
% 29.49/19.69 (~(f7(c2) = c4)),
% 29.49/19.69 inference(modus_ponens,[status(thm)],[75, 25238])).
% 29.49/19.69 tff(25240,plain,
% 29.49/19.69 (~(f3(c1, c2) = c2)),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[16240, 25239, 24245, 25223, 25216, 25213, 25185])).
% 29.49/19.69 tff(25241,plain,
% 29.49/19.69 (f1(f7(f7(c2)), c1) = f1(c2, c1)),
% 29.49/19.69 inference(monotonicity,[status(thm)],[363])).
% 29.49/19.69 tff(25242,plain,
% 29.49/19.69 ((f1(f7(f7(c2)), c1) = c2) <=> (f1(c2, c1) = c2)),
% 29.49/19.69 inference(monotonicity,[status(thm)],[25241])).
% 29.49/19.69 tff(25243,plain,
% 29.49/19.69 ((f1(c2, c1) = c2) <=> (f1(f7(f7(c2)), c1) = c2)),
% 29.49/19.69 inference(symmetry,[status(thm)],[25242])).
% 29.49/19.69 tff(25244,plain,
% 29.49/19.69 (f1(f7(f7(c2)), c1) = c2),
% 29.49/19.69 inference(modus_ponens,[status(thm)],[23304, 25243])).
% 29.49/19.69 tff(25245,plain,
% 29.49/19.69 ($false),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[23305, 25244])).
% 29.49/19.69 tff(25246,plain,((c1 = f3(c1, c2)) | (~(f7(c1) = c2)) | (~(f7(c2) = c1)) | (~(f5(c1) = c1)) | (~(f7(c1) = f5(f7(c1)))) | (f3(c1, c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 29.49/19.69 tff(25247,plain,
% 29.49/19.69 (~(f7(c1) = f5(f7(c1)))),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[25246, 12777, 292, 230, 347, 16041])).
% 29.49/19.69 tff(25248,plain,
% 29.49/19.69 (~(c2 = f5(c2))),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[23281, 25247, 347])).
% 29.49/19.69 tff(25249,plain,
% 29.49/19.69 (~(f5(c2) = c2)),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[8113, 25248])).
% 29.49/19.69 tff(25250,plain,
% 29.49/19.69 (f5(c2) = c1),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[1547, 25249])).
% 29.49/19.69 tff(25251,plain,
% 29.49/19.69 (c1 = f5(c2)),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[8139, 25250])).
% 29.49/19.69 tff(25252,plain,
% 29.49/19.69 ((f5(f10(c1)) = c1) <=> (f5(c1) = c1)),
% 29.49/19.69 inference(monotonicity,[status(thm)],[4152])).
% 29.49/19.69 tff(25253,plain,
% 29.49/19.69 ((f5(c1) = c1) <=> (f5(f10(c1)) = c1)),
% 29.49/19.69 inference(symmetry,[status(thm)],[25252])).
% 29.49/19.69 tff(25254,plain,
% 29.49/19.69 ((c1 = f5(c1)) <=> (f5(f10(c1)) = c1)),
% 29.49/19.69 inference(transitivity,[status(thm)],[128, 25253])).
% 29.49/19.69 tff(25255,plain,
% 29.49/19.69 (f5(f10(c1)) = c1),
% 29.49/19.69 inference(modus_ponens,[status(thm)],[11826, 25254])).
% 29.49/19.69 tff(25256,plain,
% 29.49/19.69 (f1(f5(c2), f5(c1)) = f1(c1, c1)),
% 29.49/19.69 inference(monotonicity,[status(thm)],[1569, 23208])).
% 29.49/19.69 tff(25257,plain,
% 29.49/19.69 (f1(f5(c2), f5(c1)) = c1),
% 29.49/19.69 inference(transitivity,[status(thm)],[25256, 624])).
% 29.49/19.69 tff(25258,plain,
% 29.49/19.69 (f3(f1(f5(c2), f5(c1)), c2) = f3(c1, c2)),
% 29.49/19.69 inference(monotonicity,[status(thm)],[25257])).
% 29.49/19.69 tff(25259,plain,
% 29.49/19.69 ((f3(f1(f5(c2), f5(c1)), c2) = c2) <=> (f3(c1, c2) = c2)),
% 29.49/19.69 inference(monotonicity,[status(thm)],[25258])).
% 29.49/19.69 tff(25260,plain,
% 29.49/19.69 ((f3(c1, c2) = c2) <=> (f3(f1(f5(c2), f5(c1)), c2) = c2)),
% 29.49/19.69 inference(symmetry,[status(thm)],[25259])).
% 29.49/19.69 tff(25261,plain,
% 29.49/19.69 ((~(f3(c1, c2) = c2)) <=> (~(f3(f1(f5(c2), f5(c1)), c2) = c2))),
% 29.49/19.69 inference(monotonicity,[status(thm)],[25260])).
% 29.49/19.69 tff(25262,plain,
% 29.49/19.69 (~(f3(f1(f5(c2), f5(c1)), c2) = c2)),
% 29.49/19.69 inference(modus_ponens,[status(thm)],[12777, 25261])).
% 29.49/19.69 tff(25263,plain,
% 29.49/19.69 ((f3(f1(f5(c2), f5(c1)), c2) = c1) <=> (f3(c1, c2) = c1)),
% 29.49/19.69 inference(monotonicity,[status(thm)],[25258])).
% 29.49/19.69 tff(25264,plain,
% 29.49/19.69 ((f3(f1(f5(c2), f5(c1)), c2) = c1) <=> (c1 = f3(c1, c2))),
% 29.49/19.69 inference(transitivity,[status(thm)],[25263, 13151])).
% 29.49/19.69 tff(25265,plain,
% 29.49/19.69 ((c1 = f3(c1, c2)) <=> (f3(f1(f5(c2), f5(c1)), c2) = c1)),
% 29.49/19.69 inference(symmetry,[status(thm)],[25264])).
% 29.49/19.69 tff(25266,plain,
% 29.49/19.69 ((~(c1 = f3(c1, c2))) <=> (~(f3(f1(f5(c2), f5(c1)), c2) = c1))),
% 29.49/19.69 inference(monotonicity,[status(thm)],[25265])).
% 29.49/19.69 tff(25267,plain,
% 29.49/19.69 (~(f3(f1(f5(c2), f5(c1)), c2) = c1)),
% 29.49/19.69 inference(modus_ponens,[status(thm)],[16041, 25266])).
% 29.49/19.69 tff(25268,plain,
% 29.49/19.69 ($false),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[16061, 25267, 25262])).
% 29.49/19.69 tff(25269,plain,((~(f5(c2) = c1)) | (c1 = f3(c1, c2)) | (~(f1(c1, c1) = c1)) | (~(f5(f10(c1)) = c1)) | (~(f10(c1) = c1)) | (f3(c1, c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 29.49/19.69 tff(25270,plain,
% 29.49/19.69 (~(f1(c1, c1) = c1)),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[25269, 16041, 1569, 25255, 3762, 12777])).
% 29.49/19.69 tff(25271,plain,
% 29.49/19.69 (f1(c1, c1) = c2),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[601, 25270])).
% 29.49/19.69 tff(25272,plain,
% 29.49/19.69 (f5(c1) = c1),
% 29.49/19.69 inference(symmetry,[status(thm)],[11826])).
% 29.49/19.69 tff(25273,plain,
% 29.49/19.69 (f5(c2) = c1),
% 29.49/19.69 inference(symmetry,[status(thm)],[23054])).
% 29.49/19.69 tff(25274,plain,
% 29.49/19.69 (f1(f5(c2), f5(c1)) = f1(c1, c1)),
% 29.49/19.69 inference(monotonicity,[status(thm)],[25273, 25272])).
% 29.49/19.69 tff(25275,plain,
% 29.49/19.69 (f1(f5(c2), f5(c1)) = c2),
% 29.49/19.69 inference(transitivity,[status(thm)],[25274, 25271])).
% 29.49/19.69 tff(25276,plain,
% 29.49/19.69 (f3(c1, f1(f5(c2), f5(c1))) = f3(c1, c2)),
% 29.49/19.69 inference(monotonicity,[status(thm)],[25275])).
% 29.49/19.69 tff(25277,plain,
% 29.49/19.69 ((f3(c1, f1(f5(c2), f5(c1))) = c1) <=> (f3(c1, c2) = c1)),
% 29.49/19.69 inference(monotonicity,[status(thm)],[25276])).
% 29.49/19.69 tff(25278,plain,
% 29.49/19.69 ((f3(c1, f1(f5(c2), f5(c1))) = c1) <=> (c1 = f3(c1, c2))),
% 29.49/19.69 inference(transitivity,[status(thm)],[25277, 13151])).
% 29.49/19.69 tff(25279,plain,
% 29.49/19.69 ((c1 = f3(c1, c2)) <=> (f3(c1, f1(f5(c2), f5(c1))) = c1)),
% 29.49/19.69 inference(symmetry,[status(thm)],[25278])).
% 29.49/19.69 tff(25280,plain,
% 29.49/19.69 ((~(c1 = f3(c1, c2))) <=> (~(f3(c1, f1(f5(c2), f5(c1))) = c1))),
% 29.49/19.69 inference(monotonicity,[status(thm)],[25279])).
% 29.49/19.69 tff(25281,plain,
% 29.49/19.69 (~(f3(c1, f1(f5(c2), f5(c1))) = c1)),
% 29.49/19.69 inference(modus_ponens,[status(thm)],[16041, 25280])).
% 29.49/19.69 tff(25282,plain,
% 29.49/19.69 ((f3(c1, f1(f5(c2), f5(c1))) = c2) <=> (f3(c1, c2) = c2)),
% 29.49/19.69 inference(monotonicity,[status(thm)],[25276])).
% 29.49/19.69 tff(25283,plain,
% 29.49/19.69 ((f3(c1, c2) = c2) <=> (f3(c1, f1(f5(c2), f5(c1))) = c2)),
% 29.49/19.69 inference(symmetry,[status(thm)],[25282])).
% 29.49/19.69 tff(25284,plain,
% 29.49/19.69 ((~(f3(c1, c2) = c2)) <=> (~(f3(c1, f1(f5(c2), f5(c1))) = c2))),
% 29.49/19.69 inference(monotonicity,[status(thm)],[25283])).
% 29.49/19.69 tff(25285,plain,
% 29.49/19.69 (~(f3(c1, f1(f5(c2), f5(c1))) = c2)),
% 29.49/19.69 inference(modus_ponens,[status(thm)],[12777, 25284])).
% 29.49/19.69 tff(25286,plain,
% 29.49/19.69 ($false),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[16082, 25285, 25281])).
% 29.49/19.69 tff(25287,plain,((c1 = f3(c1, c2)) | (f3(c1, c2) = c2) | (~(c1 = f5(c1))) | (~(c1 = f5(c2))) | (~(f5(c2) = c1)) | (~(f10(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.49/19.69 tff(25288,plain,
% 29.49/19.69 ($false),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[25287, 25251, 25250, 692, 12777, 16041, 3762])).
% 29.49/19.69 tff(25289,plain,((f3(c1, c2) = c2) | (c1 = f3(c1, c2)) | (~(f10(c1) = c1)) | (~(f7(c1) = c2)) | (~(f7(c2) = c1)) | (~(f5(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.49/19.69 tff(25290,plain,
% 29.49/19.69 (c1 = f3(c1, c2)),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[25289, 25240, 22733, 120, 25181, 25180])).
% 29.49/19.69 tff(25291,plain,
% 29.49/19.69 ((~(c2 = c1)) <=> (~(c1 = c4))),
% 29.49/19.69 inference(monotonicity,[status(thm)],[25236])).
% 29.49/19.69 tff(25292,plain,
% 29.49/19.69 (~(c1 = c4)),
% 29.49/19.69 inference(modus_ponens,[status(thm)],[75, 25291])).
% 29.49/19.69 tff(25293,plain,
% 29.49/19.69 (~(big_f(c1, c1) <=> big_f(f3(c1, c2), c1))),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[23331, 25240, 66, 25188, 25227, 25292])).
% 29.49/19.69 tff(25294,plain,
% 29.49/19.69 ($false),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[13192, 25293, 25290])).
% 29.49/19.69 tff(25295,plain,(big_f(c2, c2) | big_f(c1, c1) | (f7(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.49/19.69 tff(25296,plain,
% 29.49/19.69 (big_f(c2, c2)),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[25295, 66, 115])).
% 29.49/19.69 tff(25297,plain,
% 29.49/19.69 (big_f(f7(c1), c2)),
% 29.49/19.69 inference(modus_ponens,[status(thm)],[25296, 1724])).
% 29.49/19.69 tff(25298,plain,
% 29.49/19.69 (~big_f(c2, c1)),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[23932, 25297, 115, 66])).
% 29.49/19.69 tff(25299,plain,
% 29.49/19.69 (f10(c2) = c2),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[25175, 25298, 115, 66, 24245])).
% 29.49/19.69 tff(25300,plain,
% 29.49/19.69 (~big_f(c1, c2)),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[25162, 25298, 115, 66, 24245, 25297])).
% 29.49/19.69 tff(25301,plain,
% 29.49/19.69 ($false),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[23847, 25300, 25299, 115, 66])).
% 29.49/19.69 tff(25302,plain,(big_f(c1, c1) | (f7(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.49/19.69 tff(25303,plain,
% 29.49/19.69 (big_f(c1, c1)),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[25302, 115])).
% 29.49/19.69 tff(25304,plain,
% 29.49/19.69 (big_f(c2, c1)),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[22765, 1726, 25303, 115])).
% 29.49/19.69 tff(25305,plain,
% 29.49/19.69 (big_f(f7(f10(c2)), f10(c2))),
% 29.49/19.69 inference(modus_ponens,[status(thm)],[25304, 23358])).
% 29.49/19.69 tff(25306,plain,
% 29.49/19.69 ((f7(f10(c2)) = f10(c2)) <=> (c2 = c1)),
% 29.49/19.69 inference(monotonicity,[status(thm)],[23356, 23354])).
% 29.49/19.69 tff(25307,plain,
% 29.49/19.69 ((c2 = c1) <=> (f7(f10(c2)) = f10(c2))),
% 29.49/19.69 inference(symmetry,[status(thm)],[25306])).
% 29.49/19.69 tff(25308,plain,
% 29.49/19.69 ((~(c2 = c1)) <=> (~(f7(f10(c2)) = f10(c2)))),
% 29.49/19.69 inference(monotonicity,[status(thm)],[25307])).
% 29.49/19.69 tff(25309,plain,
% 29.49/19.69 (~(f7(f10(c2)) = f10(c2))),
% 29.49/19.69 inference(modus_ponens,[status(thm)],[75, 25308])).
% 29.49/19.69 tff(25310,plain,
% 29.49/19.69 (big_f(c2, f10(c2)) <=> big_f(c2, c1)),
% 29.49/19.69 inference(monotonicity,[status(thm)],[23354])).
% 29.49/19.69 tff(25311,plain,
% 29.49/19.69 (big_f(c2, c1) <=> big_f(c2, f10(c2))),
% 29.49/19.69 inference(symmetry,[status(thm)],[25310])).
% 29.49/19.69 tff(25312,plain,
% 29.49/19.69 (big_f(c2, f10(c2))),
% 29.49/19.69 inference(modus_ponens,[status(thm)],[25304, 25311])).
% 29.49/19.69 tff(25313,plain,
% 29.49/19.69 (big_f(c1, c2)),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[24418, 121, 23353, 115])).
% 29.49/19.69 tff(25314,plain,
% 29.49/19.69 (big_f(f7(c2), c1)),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[20926, 22, 25303, 94])).
% 29.49/19.69 tff(25315,plain,
% 29.49/19.69 ($false),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[20479, 17573, 12167, 12291, 89, 17, 25314, 115])).
% 29.49/19.69 tff(25316,plain,((f7(c2) = c2) | (~big_f(c2, f10(c2))) | (f10(c2) = c2) | (f7(c1) = c1) | (~big_f(c1, c2))), inference(lemma,lemma(discharge,[]))).
% 29.49/19.69 tff(25317,plain,
% 29.49/19.69 (f7(c2) = c2),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[25316, 25312, 23353, 115, 25313])).
% 29.49/19.69 tff(25318,plain,
% 29.49/19.69 (c2 = f8(c2)),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[22110, 25317, 25312, 25309, 121, 25305, 23353])).
% 29.49/19.69 tff(25319,plain,
% 29.49/19.69 (f8(c2) = c2),
% 29.49/19.69 inference(symmetry,[status(thm)],[25318])).
% 29.49/19.69 tff(25320,plain,
% 29.49/19.69 ((c1 = f8(c2)) <=> (c1 = c2)),
% 29.49/19.69 inference(monotonicity,[status(thm)],[25319])).
% 29.49/19.69 tff(25321,plain,
% 29.49/19.69 ((c1 = f8(c2)) <=> (c2 = c1)),
% 29.49/19.69 inference(transitivity,[status(thm)],[25320, 1])).
% 29.49/19.69 tff(25322,plain,
% 29.49/19.69 ((c2 = c1) <=> (c1 = f8(c2))),
% 29.49/19.69 inference(symmetry,[status(thm)],[25321])).
% 29.49/19.69 tff(25323,plain,
% 29.49/19.69 ((~(c2 = c1)) <=> (~(c1 = f8(c2)))),
% 29.49/19.69 inference(monotonicity,[status(thm)],[25322])).
% 29.49/19.69 tff(25324,plain,
% 29.49/19.69 (~(c1 = f8(c2))),
% 29.49/19.69 inference(modus_ponens,[status(thm)],[75, 25323])).
% 29.49/19.69 tff(25325,plain,
% 29.49/19.69 (big_f(c1, f10(c2)) <=> big_f(c1, c1)),
% 29.49/19.69 inference(monotonicity,[status(thm)],[23354])).
% 29.49/19.69 tff(25326,plain,
% 29.49/19.69 (big_f(c1, c1) <=> big_f(c1, f10(c2))),
% 29.49/19.69 inference(symmetry,[status(thm)],[25325])).
% 29.49/19.69 tff(25327,plain,
% 29.49/19.69 (big_f(c1, f10(c2))),
% 29.49/19.69 inference(modus_ponens,[status(thm)],[25303, 25326])).
% 29.49/19.69 tff(25328,plain,
% 29.49/19.69 (big_f(f7(c2), f6(c2, c1)) <=> big_f(c2, f6(c2, c1))),
% 29.49/19.69 inference(monotonicity,[status(thm)],[25317])).
% 29.49/19.69 tff(25329,plain,
% 29.49/19.69 (big_f(c2, f6(c2, c1)) <=> big_f(f7(c2), f6(c2, c1))),
% 29.49/19.69 inference(symmetry,[status(thm)],[25328])).
% 29.49/19.69 tff(25330,plain,
% 29.49/19.69 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))))),
% 29.49/19.69 inference(rewrite,[status(thm)],[])).
% 29.49/19.69 tff(25331,plain,
% 29.49/19.69 (((~(c2 = f5(c1))) | (f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (f7(c1) = c1) | big_f(f7(c1), c2)) <=> ((~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))))),
% 29.49/19.69 inference(rewrite,[status(thm)],[])).
% 29.49/19.69 tff(25332,plain,
% 29.49/19.69 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c2 = f5(c1))) | (f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (f7(c1) = c1) | big_f(f7(c1), c2))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2)))))),
% 29.49/19.69 inference(monotonicity,[status(thm)],[25331])).
% 29.49/19.69 tff(25333,plain,
% 29.49/19.69 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c2 = f5(c1))) | (f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (f7(c1) = c1) | big_f(f7(c1), c2))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))))),
% 29.49/19.69 inference(transitivity,[status(thm)],[25332, 25330])).
% 29.49/19.69 tff(25334,plain,
% 29.49/19.69 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c2 = f5(c1))) | (f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (f7(c1) = c1) | big_f(f7(c1), c2))),
% 29.49/19.69 inference(quant_inst,[status(thm)],[])).
% 29.49/19.69 tff(25335,plain,
% 29.49/19.69 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (~(c2 = f5(c1))) | big_f(f7(c1), c2) | (f7(c1) = c1) | (f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2)))),
% 29.49/19.69 inference(modus_ponens,[status(thm)],[25334, 25333])).
% 29.49/19.69 tff(25336,plain,
% 29.49/19.69 ((~(c2 = f5(c1))) | (c1 = f8(c2))),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[25335, 705, 1726, 115, 23353, 25327])).
% 29.49/19.69 tff(25337,plain,
% 29.49/19.69 (~(c2 = f5(c1))),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[25336, 25324])).
% 29.49/19.69 tff(25338,plain,
% 29.49/19.69 (~(f5(c1) = c2)),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[24054, 25337])).
% 29.49/19.69 tff(25339,plain,
% 29.49/19.69 (f5(c1) = c1),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[1708, 25338])).
% 29.49/19.69 tff(25340,plain,
% 29.49/19.69 ((f10(c2) = f8(c2)) <=> (c1 = f8(c2))),
% 29.49/19.69 inference(monotonicity,[status(thm)],[23354])).
% 29.49/19.69 tff(25341,plain,
% 29.49/19.69 ((c1 = f8(c2)) <=> (f10(c2) = f8(c2))),
% 29.49/19.69 inference(symmetry,[status(thm)],[25340])).
% 29.49/19.69 tff(25342,plain,
% 29.49/19.69 ((c2 = c1) <=> (f10(c2) = f8(c2))),
% 29.49/19.69 inference(transitivity,[status(thm)],[25322, 25341])).
% 29.49/19.69 tff(25343,plain,
% 29.49/19.69 ((~(c2 = c1)) <=> (~(f10(c2) = f8(c2)))),
% 29.49/19.69 inference(monotonicity,[status(thm)],[25342])).
% 29.49/19.69 tff(25344,plain,
% 29.49/19.69 (~(f10(c2) = f8(c2))),
% 29.49/19.69 inference(modus_ponens,[status(thm)],[75, 25343])).
% 29.49/19.69 tff(25345,plain,
% 29.49/19.69 (big_f(f10(c2), f10(c2))),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[21743, 23354, 25303])).
% 29.49/19.69 tff(25346,plain,
% 29.49/19.69 (f10(c2) = f5(f10(c2))),
% 29.49/19.69 inference(modus_ponens,[status(thm)],[230, 21048])).
% 29.49/19.69 tff(25347,plain,
% 29.49/19.69 ($false),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[22691, 25346])).
% 29.49/19.69 tff(25348,plain,((~(f5(c1) = c1)) | (f10(c2) = f5(f10(c2))) | (~(f10(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.49/19.69 tff(25349,plain,
% 29.49/19.69 (f10(c2) = f5(f10(c2))),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[25348, 25339, 23354])).
% 29.49/19.69 tff(25350,plain,
% 29.49/19.69 (~(f6(f7(c2), f5(c1)) = c2)),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[22576, 25349, 25317, 25345, 25344, 121, 23353])).
% 29.49/19.69 tff(25351,plain,
% 29.49/19.69 (f6(f7(c2), f5(c1)) = c1),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[2978, 25350])).
% 29.49/19.69 tff(25352,plain,
% 29.49/19.69 (f6(c2, c1) = c1),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[13591, 25351, 25317, 25339])).
% 29.49/19.69 tff(25353,plain,
% 29.49/19.69 (big_f(c2, f6(c2, c1)) <=> big_f(c2, c1)),
% 29.49/19.69 inference(monotonicity,[status(thm)],[25352])).
% 29.49/19.69 tff(25354,plain,
% 29.49/19.69 (big_f(c2, c1) <=> big_f(c2, f6(c2, c1))),
% 29.49/19.69 inference(symmetry,[status(thm)],[25353])).
% 29.49/19.69 tff(25355,plain,
% 29.49/19.69 (big_f(c2, c1) <=> big_f(f7(c2), f6(c2, c1))),
% 29.49/19.69 inference(transitivity,[status(thm)],[25354, 25329])).
% 29.49/19.69 tff(25356,plain,
% 29.49/19.69 (big_f(f7(c2), f6(c2, c1))),
% 29.49/19.69 inference(modus_ponens,[status(thm)],[25304, 25355])).
% 29.49/19.69 tff(25357,plain,
% 29.49/19.69 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (~big_f(f7(c2), f6(c2, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (~big_f(f7(c2), f6(c2, c1))))),
% 29.49/19.69 inference(rewrite,[status(thm)],[])).
% 29.49/19.69 tff(25358,plain,
% 29.49/19.69 (((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1)))) <=> ((f10(c2) = c2) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (~big_f(f7(c2), f6(c2, c1))))),
% 29.49/19.69 inference(rewrite,[status(thm)],[])).
% 29.49/19.69 tff(25359,plain,
% 29.49/19.69 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (~big_f(f7(c2), f6(c2, c1)))))),
% 29.49/19.69 inference(monotonicity,[status(thm)],[25358])).
% 29.49/19.69 tff(25360,plain,
% 29.49/19.69 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (~big_f(f7(c2), f6(c2, c1))))),
% 29.49/19.69 inference(transitivity,[status(thm)],[25359, 25357])).
% 29.49/19.69 tff(25361,plain,
% 29.49/19.69 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1))))),
% 29.49/19.69 inference(quant_inst,[status(thm)],[])).
% 29.49/19.69 tff(25362,plain,
% 29.49/19.69 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (~big_f(f7(c2), f6(c2, c1)))),
% 29.49/19.69 inference(modus_ponens,[status(thm)],[25361, 25360])).
% 29.49/19.69 tff(25363,plain,
% 29.49/19.69 ($false),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[25362, 2730, 23353, 25317, 25352, 25356, 25327, 25324])).
% 29.49/19.69 tff(25364,plain,(big_f(c2, c2) | (f7(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.49/19.69 tff(25365,plain,
% 29.49/19.69 (big_f(c2, c2)),
% 29.49/19.69 inference(unit_resolution,[status(thm)],[25364, 115])).
% 29.49/19.69 tff(25366,plain,
% 29.49/19.70 (big_f(c1, c2)),
% 29.49/19.70 inference(unit_resolution,[status(thm)],[24771, 89, 115])).
% 29.49/19.70 tff(25367,plain,
% 29.49/19.70 (big_f(f9(c1, c1), c1)),
% 29.49/19.70 inference(unit_resolution,[status(thm)],[10938, 4932, 3949])).
% 29.49/19.70 tff(25368,plain,
% 29.49/19.70 (big_f(f9(c1, c1), f10(c1))),
% 29.49/19.70 inference(unit_resolution,[status(thm)],[8716, 25367, 3762])).
% 29.49/19.70 tff(25369,plain,
% 29.49/19.70 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((f7(c2) = c2) | (~big_f(f7(c2), c1)) | (~(f10(c1) = c1)) | (c1 = f5(c2)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (f7(c2) = c2) | (~big_f(f7(c2), c1)) | (~(f10(c1) = c1)) | (c1 = f5(c2)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))),
% 29.49/19.70 inference(rewrite,[status(thm)],[])).
% 29.49/19.70 tff(25370,plain,
% 29.49/19.70 (((~(f10(c1) = c1)) | (f7(c2) = c2) | (c1 = f5(c2)) | (~big_f(f7(c2), c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1)))) <=> ((f7(c2) = c2) | (~big_f(f7(c2), c1)) | (~(f10(c1) = c1)) | (c1 = f5(c2)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))),
% 29.49/19.70 inference(rewrite,[status(thm)],[])).
% 29.49/19.70 tff(25371,plain,
% 29.49/19.70 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c1) = c1)) | (f7(c2) = c2) | (c1 = f5(c2)) | (~big_f(f7(c2), c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((f7(c2) = c2) | (~big_f(f7(c2), c1)) | (~(f10(c1) = c1)) | (c1 = f5(c2)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1)))))),
% 29.49/19.70 inference(monotonicity,[status(thm)],[25370])).
% 29.49/19.70 tff(25372,plain,
% 29.49/19.70 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c1) = c1)) | (f7(c2) = c2) | (c1 = f5(c2)) | (~big_f(f7(c2), c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (f7(c2) = c2) | (~big_f(f7(c2), c1)) | (~(f10(c1) = c1)) | (c1 = f5(c2)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))),
% 29.49/19.70 inference(transitivity,[status(thm)],[25371, 25369])).
% 29.49/19.70 tff(25373,plain,
% 29.49/19.70 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c1) = c1)) | (f7(c2) = c2) | (c1 = f5(c2)) | (~big_f(f7(c2), c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))),
% 29.49/19.70 inference(quant_inst,[status(thm)],[])).
% 29.49/19.70 tff(25374,plain,
% 29.49/19.70 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (f7(c2) = c2) | (~big_f(f7(c2), c1)) | (~(f10(c1) = c1)) | (c1 = f5(c2)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1)))),
% 29.49/19.70 inference(modus_ponens,[status(thm)],[25373, 25372])).
% 29.49/19.70 tff(25375,plain,
% 29.49/19.70 (c1 = f5(c2)),
% 29.49/19.70 inference(unit_resolution,[status(thm)],[25374, 1190, 3762, 17, 3949, 25368, 17698])).
% 29.49/19.70 tff(25376,plain,
% 29.49/19.70 (f5(c2) = c1),
% 29.49/19.70 inference(symmetry,[status(thm)],[25375])).
% 29.49/19.70 tff(25377,plain,
% 29.49/19.70 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((f7(c2) = c2) | (c2 = f5(c2)) | (~(f10(c1) = c1)) | (~big_f(f7(c2), c2)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (f7(c2) = c2) | (c2 = f5(c2)) | (~(f10(c1) = c1)) | (~big_f(f7(c2), c2)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))),
% 29.49/19.70 inference(rewrite,[status(thm)],[])).
% 29.49/19.70 tff(25378,plain,
% 29.49/19.70 (((~(f10(c1) = c1)) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1)))) <=> ((f7(c2) = c2) | (c2 = f5(c2)) | (~(f10(c1) = c1)) | (~big_f(f7(c2), c2)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))),
% 29.49/19.70 inference(rewrite,[status(thm)],[])).
% 29.49/19.70 tff(25379,plain,
% 29.49/19.70 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c1) = c1)) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((f7(c2) = c2) | (c2 = f5(c2)) | (~(f10(c1) = c1)) | (~big_f(f7(c2), c2)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1)))))),
% 29.49/19.70 inference(monotonicity,[status(thm)],[25378])).
% 29.49/19.70 tff(25380,plain,
% 29.49/19.70 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c1) = c1)) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (f7(c2) = c2) | (c2 = f5(c2)) | (~(f10(c1) = c1)) | (~big_f(f7(c2), c2)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))),
% 29.49/19.70 inference(transitivity,[status(thm)],[25379, 25377])).
% 29.49/19.70 tff(25381,plain,
% 29.49/19.70 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c1) = c1)) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))),
% 29.49/19.70 inference(quant_inst,[status(thm)],[])).
% 29.49/19.70 tff(25382,plain,
% 29.49/19.70 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (f7(c2) = c2) | (c2 = f5(c2)) | (~(f10(c1) = c1)) | (~big_f(f7(c2), c2)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1)))),
% 29.49/19.70 inference(modus_ponens,[status(thm)],[25381, 25380])).
% 29.49/19.70 tff(25383,plain,
% 29.49/19.70 (c2 = f5(c2)),
% 29.49/19.70 inference(unit_resolution,[status(thm)],[25382, 1190, 3762, 17, 12167, 3949, 25368])).
% 29.49/19.70 tff(25384,plain,
% 29.49/19.70 (c2 = c1),
% 29.49/19.70 inference(transitivity,[status(thm)],[25383, 25376])).
% 29.49/19.70 tff(25385,plain,
% 29.49/19.70 ($false),
% 29.49/19.70 inference(unit_resolution,[status(thm)],[75, 25384])).
% 29.49/19.70 tff(25386,plain,((f7(c2) = c2) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(c1, c1)) | (~big_f(c1, c2))), inference(lemma,lemma(discharge,[]))).
% 29.49/19.70 tff(25387,plain,
% 29.49/19.70 (~(f9(c1, c1) = c1)),
% 29.49/19.70 inference(unit_resolution,[status(thm)],[25386, 25366, 25303, 22733, 17])).
% 29.49/19.70 tff(25388,plain,
% 29.49/19.70 (f9(c1, c1) = c2),
% 29.49/19.70 inference(unit_resolution,[status(thm)],[3939, 25387])).
% 29.49/19.70 tff(25389,plain,
% 29.49/19.70 (big_f(f7(f7(c2)), c2)),
% 29.49/19.70 inference(modus_ponens,[status(thm)],[25365, 8617])).
% 29.49/19.70 tff(25390,plain,
% 29.49/19.70 (big_f(f7(c2), c1)),
% 29.49/19.70 inference(modus_ponens,[status(thm)],[25303, 12091])).
% 29.49/19.70 tff(25391,plain,
% 29.49/19.70 (big_f(f7(c2), f10(c2))),
% 29.49/19.70 inference(unit_resolution,[status(thm)],[21331, 94, 25390])).
% 29.49/19.70 tff(25392,plain,
% 29.49/19.70 (~big_f(c2, c1)),
% 29.49/19.70 inference(unit_resolution,[status(thm)],[12536, 25391, 120, 25389, 17, 89])).
% 29.49/19.70 tff(25393,plain,
% 29.49/19.70 (~big_f(f9(c1, c1), c1)),
% 29.49/19.70 inference(unit_resolution,[status(thm)],[10058, 25392, 25388])).
% 29.49/19.70 tff(25394,plain,
% 29.49/19.70 (~big_f(f9(c1, c1), f10(c1))),
% 29.49/19.70 inference(unit_resolution,[status(thm)],[10033, 25393, 22733])).
% 29.49/19.70 tff(25395,plain,
% 29.49/19.70 (f7(f9(c1, c1)) = f7(c2)),
% 29.49/19.70 inference(monotonicity,[status(thm)],[25388])).
% 29.49/19.70 tff(25396,plain,
% 29.49/19.70 (f7(f9(c1, c1)) = c1),
% 29.49/19.70 inference(transitivity,[status(thm)],[25395, 22])).
% 29.49/19.70 tff(25397,plain,
% 29.49/19.70 ((f7(f9(c1, c1)) = f9(c1, c1)) <=> (c1 = c2)),
% 29.49/19.70 inference(monotonicity,[status(thm)],[25396, 25388])).
% 29.49/19.70 tff(25398,plain,
% 29.49/19.70 ((f7(f9(c1, c1)) = f9(c1, c1)) <=> (c2 = c1)),
% 29.49/19.70 inference(transitivity,[status(thm)],[25397, 1])).
% 29.49/19.70 tff(25399,plain,
% 29.49/19.70 ((c2 = c1) <=> (f7(f9(c1, c1)) = f9(c1, c1))),
% 29.49/19.70 inference(symmetry,[status(thm)],[25398])).
% 29.49/19.70 tff(25400,plain,
% 29.49/19.70 ((~(c2 = c1)) <=> (~(f7(f9(c1, c1)) = f9(c1, c1)))),
% 29.49/19.70 inference(monotonicity,[status(thm)],[25399])).
% 29.49/19.70 tff(25401,plain,
% 29.49/19.70 (~(f7(f9(c1, c1)) = f9(c1, c1))),
% 29.49/19.70 inference(modus_ponens,[status(thm)],[75, 25400])).
% 29.49/19.70 tff(25402,plain,
% 29.49/19.70 (big_f(f7(f9(c1, c1)), c1) <=> big_f(c1, c1)),
% 29.49/19.70 inference(monotonicity,[status(thm)],[25396])).
% 29.49/19.70 tff(25403,plain,
% 29.49/19.70 (big_f(c1, c1) <=> big_f(f7(f9(c1, c1)), c1)),
% 29.49/19.70 inference(symmetry,[status(thm)],[25402])).
% 29.49/19.70 tff(25404,plain,
% 29.49/19.70 (big_f(f7(f9(c1, c1)), c1)),
% 29.49/19.70 inference(modus_ponens,[status(thm)],[25303, 25403])).
% 29.49/19.70 tff(25405,plain,
% 29.49/19.70 (big_f(f7(f9(c1, c1)), f9(c1, c1)) <=> big_f(c1, c2)),
% 29.49/19.70 inference(monotonicity,[status(thm)],[25396, 25388])).
% 29.49/19.70 tff(25406,plain,
% 29.49/19.70 (big_f(c1, c2) <=> big_f(f7(f9(c1, c1)), f9(c1, c1))),
% 29.49/19.70 inference(symmetry,[status(thm)],[25405])).
% 29.49/19.70 tff(25407,plain,
% 29.49/19.70 (big_f(f7(f9(c1, c1)), f9(c1, c1))),
% 29.49/19.70 inference(modus_ponens,[status(thm)],[25366, 25406])).
% 29.49/19.70 tff(25408,plain,
% 29.49/19.70 ($false),
% 29.49/19.70 inference(unit_resolution,[status(thm)],[20184, 25407, 25404, 22733, 25387, 25401, 25394])).
% 29.49/19.70 tff(25409,plain,((f10(c2) = c2) | (f7(c2) = c2) | (f7(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.49/19.70 tff(25410,plain,
% 29.49/19.70 (f10(c2) = c2),
% 29.49/19.70 inference(unit_resolution,[status(thm)],[25409, 17, 115])).
% 29.49/19.70 tff(25411,plain,
% 29.49/19.70 (~(f4(c4) = c2)),
% 29.49/19.70 inference(unit_resolution,[status(thm)],[10739, 25410, 17])).
% 29.49/19.70 tff(25412,plain,
% 29.49/19.70 (f4(c4) = c1),
% 29.49/19.70 inference(unit_resolution,[status(thm)],[11750, 25411])).
% 29.49/19.70 tff(25413,plain,
% 29.49/19.70 (c2 = f10(c2)),
% 29.49/19.70 inference(symmetry,[status(thm)],[25410])).
% 29.49/19.70 tff(25414,plain,
% 29.49/19.70 (f9(c2, c2) = f9(f10(c2), f7(c1))),
% 29.49/19.70 inference(monotonicity,[status(thm)],[25413, 2778])).
% 29.49/19.70 tff(25415,plain,
% 29.49/19.70 (f9(f10(c2), f7(c1)) = f9(c2, c2)),
% 29.49/19.70 inference(symmetry,[status(thm)],[25414])).
% 29.49/19.70 tff(25416,plain,
% 29.49/19.70 ((f9(f10(c2), f7(c1)) = c2) <=> (f9(c2, c2) = c2)),
% 29.49/19.70 inference(monotonicity,[status(thm)],[25415])).
% 29.49/19.70 tff(25417,plain,
% 29.49/19.70 ((f9(c2, c2) = c2) <=> (f9(f10(c2), f7(c1)) = c2)),
% 29.49/19.70 inference(symmetry,[status(thm)],[25416])).
% 29.49/19.70 tff(25418,plain,
% 29.49/19.70 (c2 = f5(f7(c2))),
% 29.49/19.70 inference(modus_ponens,[status(thm)],[2908, 8602])).
% 29.49/19.70 tff(25419,plain,
% 29.49/19.70 ((f7(f7(c2)) = c1) <=> (c2 = c1)),
% 29.49/19.70 inference(monotonicity,[status(thm)],[8808])).
% 29.49/19.70 tff(25420,plain,
% 29.49/19.70 ((c2 = c1) <=> (f7(f7(c2)) = c1)),
% 29.49/19.70 inference(symmetry,[status(thm)],[25419])).
% 29.49/19.70 tff(25421,plain,
% 29.49/19.70 ((c2 = c1) <=> (f7(f7(c2)) = f7(c2))),
% 29.49/19.70 inference(transitivity,[status(thm)],[25420, 21317])).
% 29.49/19.70 tff(25422,plain,
% 29.49/19.70 ((~(c2 = c1)) <=> (~(f7(f7(c2)) = f7(c2)))),
% 29.49/19.70 inference(monotonicity,[status(thm)],[25421])).
% 29.49/19.70 tff(25423,plain,
% 29.49/19.70 (~(f7(f7(c2)) = f7(c2))),
% 29.49/19.70 inference(modus_ponens,[status(thm)],[75, 25422])).
% 29.49/19.70 tff(25424,plain,
% 29.49/19.70 ((f5(c1) = c1) <=> (c2 = c1)),
% 29.49/19.70 inference(monotonicity,[status(thm)],[17375])).
% 29.49/19.70 tff(25425,plain,
% 29.49/19.70 ((c2 = c1) <=> (f5(c1) = c1)),
% 29.49/19.70 inference(symmetry,[status(thm)],[25424])).
% 29.49/19.70 tff(25426,plain,
% 29.49/19.70 ((~(c2 = c1)) <=> (~(f5(c1) = c1))),
% 29.49/19.70 inference(monotonicity,[status(thm)],[25425])).
% 29.49/19.70 tff(25427,plain,
% 29.49/19.70 (~(f5(c1) = c1)),
% 29.49/19.70 inference(modus_ponens,[status(thm)],[75, 25426])).
% 29.49/19.70 tff(25428,plain,
% 29.49/19.70 (~big_f(f7(f7(c2)), f7(c2))),
% 29.49/19.70 inference(unit_resolution,[status(thm)],[16558, 25427, 122, 1345, 22, 23145, 25423])).
% 29.49/19.70 tff(25429,plain,
% 29.49/19.70 (~big_f(c2, c1)),
% 29.49/19.70 inference(unit_resolution,[status(thm)],[25221, 25428, 22, 347])).
% 29.49/19.70 tff(25430,plain,
% 29.49/19.70 (c2 = c3),
% 29.49/19.70 inference(unit_resolution,[status(thm)],[24532, 25429, 1345, 25418, 23145, 17, 23515])).
% 29.49/19.70 tff(25431,plain,
% 29.49/19.70 (c3 = c2),
% 29.49/19.70 inference(symmetry,[status(thm)],[25430])).
% 29.49/19.70 tff(25432,plain,
% 29.49/19.70 ((c1 = c3) <=> (c1 = c2)),
% 29.49/19.70 inference(monotonicity,[status(thm)],[25431])).
% 29.49/19.70 tff(25433,plain,
% 29.49/19.70 ((c1 = c3) <=> (c2 = c1)),
% 29.49/19.70 inference(transitivity,[status(thm)],[25432, 1])).
% 29.49/19.70 tff(25434,plain,
% 29.49/19.70 ((c2 = c1) <=> (c1 = c3)),
% 29.49/19.70 inference(symmetry,[status(thm)],[25433])).
% 29.49/19.70 tff(25435,plain,
% 29.49/19.70 ((c2 = c1) <=> (f7(c2) = c3)),
% 29.49/19.70 inference(transitivity,[status(thm)],[25434, 13076])).
% 29.49/19.70 tff(25436,plain,
% 29.49/19.70 ((~(c2 = c1)) <=> (~(f7(c2) = c3))),
% 29.49/19.70 inference(monotonicity,[status(thm)],[25435])).
% 29.49/19.70 tff(25437,plain,
% 29.49/19.70 (~(f7(c2) = c3)),
% 29.49/19.70 inference(modus_ponens,[status(thm)],[75, 25436])).
% 29.49/19.70 tff(25438,plain,
% 29.49/19.70 ((~(c2 = c1)) <=> (~(c1 = c3))),
% 29.49/19.70 inference(monotonicity,[status(thm)],[25434])).
% 29.49/19.70 tff(25439,plain,
% 29.49/19.70 (~(c1 = c3)),
% 29.49/19.70 inference(modus_ponens,[status(thm)],[75, 25438])).
% 29.49/19.70 tff(25440,plain,
% 29.49/19.70 (c2 = c4),
% 29.49/19.70 inference(unit_resolution,[status(thm)],[24671, 25439, 4932, 25437, 22, 27, 1345, 2908])).
% 29.49/19.70 tff(25441,plain,
% 29.49/19.70 (c4 = c2),
% 29.49/19.70 inference(modus_ponens,[status(thm)],[25440, 8721])).
% 29.49/19.70 tff(25442,plain,
% 29.49/19.70 (~big_f(c1, f1(c1, c1))),
% 29.49/19.70 inference(unit_resolution,[status(thm)],[23017, 25441, 27, 25439, 23515])).
% 29.49/19.70 tff(25443,plain,
% 29.49/19.70 (c4 = c2),
% 29.49/19.70 inference(symmetry,[status(thm)],[25440])).
% 29.49/19.70 tff(25444,plain,
% 29.49/19.70 ((c1 = c4) <=> (c1 = c2)),
% 29.49/19.70 inference(monotonicity,[status(thm)],[25443])).
% 29.49/19.70 tff(25445,plain,
% 29.49/19.70 ((c1 = c4) <=> (c2 = c1)),
% 29.49/19.70 inference(transitivity,[status(thm)],[25444, 1])).
% 29.49/19.70 tff(25446,plain,
% 29.49/19.70 ((c2 = c1) <=> (c1 = c4)),
% 29.49/19.70 inference(symmetry,[status(thm)],[25445])).
% 29.49/19.70 tff(25447,plain,
% 29.49/19.70 ((c2 = c1) <=> (f7(c2) = c4)),
% 29.49/19.70 inference(transitivity,[status(thm)],[25446, 23292])).
% 29.49/19.70 tff(25448,plain,
% 29.49/19.70 ((~(c2 = c1)) <=> (~(f7(c2) = c4))),
% 29.49/19.70 inference(monotonicity,[status(thm)],[25447])).
% 29.49/19.70 tff(25449,plain,
% 29.49/19.70 (~(f7(c2) = c4)),
% 29.49/19.70 inference(modus_ponens,[status(thm)],[75, 25448])).
% 29.49/19.70 tff(25450,plain,
% 29.49/19.70 ((~(c2 = c1)) <=> (~(c1 = c4))),
% 29.49/19.70 inference(monotonicity,[status(thm)],[25446])).
% 29.49/19.70 tff(25451,plain,
% 29.49/19.70 (~(c1 = c4)),
% 29.49/19.70 inference(modus_ponens,[status(thm)],[75, 25450])).
% 29.49/19.70 tff(25452,plain,
% 29.49/19.70 (f3(c1, c1) = c1),
% 29.49/19.70 inference(unit_resolution,[status(thm)],[9696, 25451, 4932, 17, 27, 25429, 25439, 25449, 25437])).
% 29.49/19.70 tff(25453,plain,
% 29.49/19.70 ($false),
% 29.49/19.70 inference(unit_resolution,[status(thm)],[9724, 25452, 25449, 22, 17698, 25442, 25437])).
% 29.49/19.70 tff(25454,plain,((~(c2 = f5(c1))) | (~big_f(c1, c1)) | (f7(c2) = c2) | big_f(c1, c2) | (~big_f(c2, c2)) | (~(f7(c1) = c2)) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.49/19.70 tff(25455,plain,
% 29.49/19.70 (~(c2 = f5(c1))),
% 29.49/19.70 inference(unit_resolution,[status(thm)],[25454, 27, 25303, 17, 25365, 120, 25410])).
% 29.49/19.70 tff(25456,plain,
% 29.49/19.70 (big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 29.49/19.70 inference(unit_resolution,[status(thm)],[23665, 25455, 115, 25410, 27])).
% 29.49/19.70 tff(25457,plain,
% 29.49/19.70 (~(f9(c2, f9(f10(c2), f10(c2))) = c1)),
% 29.49/19.70 inference(unit_resolution,[status(thm)],[23674, 25456, 25410, 27])).
% 29.49/19.70 tff(25458,plain,
% 29.49/19.70 (f9(c2, f9(f10(c2), f10(c2))) = c2),
% 29.49/19.70 inference(unit_resolution,[status(thm)],[23082, 25457])).
% 29.49/19.70 tff(25459,plain,
% 29.49/19.70 (f9(f10(c2), f10(c2)) = f9(c2, c2)),
% 29.49/19.70 inference(monotonicity,[status(thm)],[25410, 25410])).
% 29.49/19.70 tff(25460,plain,
% 29.49/19.70 (f9(c2, c2) = f9(f10(c2), f10(c2))),
% 29.49/19.70 inference(symmetry,[status(thm)],[25459])).
% 29.49/19.70 tff(25461,plain,
% 29.49/19.70 (f9(c2, f9(c2, c2)) = f9(c2, f9(f10(c2), f10(c2)))),
% 29.49/19.70 inference(monotonicity,[status(thm)],[25460])).
% 29.49/19.70 tff(25462,plain,
% 29.49/19.70 (f9(c2, f9(c2, c2)) = c2),
% 29.49/19.70 inference(transitivity,[status(thm)],[25461, 25458])).
% 29.49/19.70 tff(25463,plain,
% 29.49/19.70 ((f9(c2, f9(c2, c2)) = f9(c2, c2)) <=> (c2 = f9(c2, c2))),
% 29.49/19.70 inference(monotonicity,[status(thm)],[25462])).
% 29.49/19.70 tff(25464,plain,
% 29.49/19.70 ((f9(c2, f9(c2, c2)) = f9(c2, c2)) <=> (f9(c2, c2) = c2)),
% 29.49/19.70 inference(transitivity,[status(thm)],[25463, 167])).
% 29.49/19.70 tff(25465,plain,
% 29.49/19.70 ((f9(c2, f9(c2, c2)) = f9(c2, c2)) <=> (f9(f10(c2), f7(c1)) = c2)),
% 29.49/19.70 inference(transitivity,[status(thm)],[25464, 25417])).
% 29.49/19.70 tff(25466,plain,
% 29.49/19.70 ((~(f9(c2, f9(c2, c2)) = f9(c2, c2))) <=> (~(f9(f10(c2), f7(c1)) = c2))),
% 29.49/19.70 inference(monotonicity,[status(thm)],[25465])).
% 29.49/19.70 tff(25467,plain,
% 29.49/19.70 (big_f(f7(c1), c2)),
% 29.49/19.70 inference(modus_ponens,[status(thm)],[25365, 1724])).
% 29.49/19.70 tff(25468,plain,
% 29.49/19.70 (~(f9(c2, f9(c2, c2)) = f9(c2, c2))),
% 29.49/19.70 inference(unit_resolution,[status(thm)],[23740, 1190, 25455, 25467, 115, 25410, 25456])).
% 29.49/19.70 tff(25469,plain,
% 29.49/19.70 (~(f9(f10(c2), f7(c1)) = c2)),
% 29.49/19.70 inference(modus_ponens,[status(thm)],[25468, 25466])).
% 29.49/19.70 tff(25470,plain,
% 29.49/19.70 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f9(f10(c2), f7(c1)) = c1) | (f9(f10(c2), f7(c1)) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f9(f10(c2), f7(c1)) = c1) | (f9(f10(c2), f7(c1)) = c2))),
% 29.49/19.70 inference(rewrite,[status(thm)],[])).
% 29.49/19.70 tff(25471,plain,
% 29.49/19.70 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f9(f10(c2), f7(c1)) = c1) | (f9(f10(c2), f7(c1)) = c2))),
% 29.49/19.70 inference(quant_inst,[status(thm)],[])).
% 29.49/19.70 tff(25472,plain,
% 29.49/19.70 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f9(f10(c2), f7(c1)) = c1) | (f9(f10(c2), f7(c1)) = c2)),
% 29.49/19.70 inference(modus_ponens,[status(thm)],[25471, 25470])).
% 29.49/19.70 tff(25473,plain,
% 29.49/19.70 ((f9(f10(c2), f7(c1)) = c1) | (f9(f10(c2), f7(c1)) = c2)),
% 29.49/19.70 inference(unit_resolution,[status(thm)],[25472, 10])).
% 29.49/19.70 tff(25474,plain,
% 29.49/19.70 (f9(f10(c2), f7(c1)) = c1),
% 29.49/19.70 inference(unit_resolution,[status(thm)],[25473, 25469])).
% 29.49/19.70 tff(25475,plain,
% 29.49/19.70 (f9(c2, c2) = c1),
% 29.49/19.70 inference(transitivity,[status(thm)],[25414, 25474])).
% 29.49/19.70 tff(25476,plain,
% 29.49/19.70 (big_f(f9(c2, c2), c2) <=> big_f(c1, c2)),
% 29.49/19.70 inference(monotonicity,[status(thm)],[25475])).
% 29.49/19.70 tff(25477,plain,
% 29.49/19.70 (big_f(c1, c2) <=> big_f(f9(c2, c2), c2)),
% 29.49/19.70 inference(symmetry,[status(thm)],[25476])).
% 29.49/19.70 tff(25478,plain,
% 29.49/19.70 ((~big_f(c1, c2)) <=> (~big_f(f9(c2, c2), c2))),
% 29.49/19.70 inference(monotonicity,[status(thm)],[25477])).
% 29.49/19.70 tff(25479,plain,
% 29.49/19.70 (~big_f(f9(c2, c2), c2)),
% 29.49/19.70 inference(modus_ponens,[status(thm)],[27, 25478])).
% 29.49/19.70 tff(25480,plain,
% 29.49/19.70 ((~(f9(c2, f9(c2, c2)) = f9(c2, c2))) <=> (~(f9(c2, c2) = c2))),
% 29.49/19.70 inference(monotonicity,[status(thm)],[25464])).
% 29.49/19.70 tff(25481,plain,
% 29.49/19.70 (~(f9(c2, c2) = c2)),
% 29.49/19.70 inference(modus_ponens,[status(thm)],[25468, 25480])).
% 29.49/19.70 tff(25482,plain,
% 29.49/19.70 (big_f(f9(c2, c2), f10(c2))),
% 29.49/19.70 inference(unit_resolution,[status(thm)],[17345, 25481, 115, 25410, 25467, 25455])).
% 29.49/19.70 tff(25483,plain,
% 29.49/19.70 (big_f(f9(c2, c2), c2)),
% 29.49/19.70 inference(unit_resolution,[status(thm)],[3687, 25482, 25410])).
% 29.49/19.70 tff(25484,plain,
% 29.49/19.70 ($false),
% 29.49/19.70 inference(unit_resolution,[status(thm)],[25483, 25479])).
% 29.49/19.70 tff(25485,plain,(big_f(c1, c2) | (f7(c1) = c1) | (f7(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 29.49/19.70 tff(25486,plain,
% 29.49/19.70 (big_f(c1, c2)),
% 29.49/19.70 inference(unit_resolution,[status(thm)],[25485, 17, 115])).
% 29.49/19.70 tff(25487,plain,
% 29.49/19.70 (~(c1 = f5(c1))),
% 29.49/19.70 inference(unit_resolution,[status(thm)],[24626, 2, 25303, 115])).
% 29.49/19.70 tff(25488,plain,
% 29.49/19.70 (~(f5(c1) = c1)),
% 29.49/19.70 inference(modus_ponens,[status(thm)],[25487, 2279])).
% 29.49/19.70 tff(25489,plain,
% 29.49/19.70 (f5(c1) = c2),
% 29.49/19.70 inference(unit_resolution,[status(thm)],[1708, 25488])).
% 29.49/19.70 tff(25490,plain,
% 29.49/19.70 (c2 = f5(c1)),
% 29.49/19.70 inference(unit_resolution,[status(thm)],[24054, 25489])).
% 29.49/19.70 tff(25491,plain,
% 29.49/19.70 (big_f(c1, c2)),
% 29.49/19.70 inference(unit_resolution,[status(thm)],[25454, 25490, 25303, 17, 25365, 120, 25410])).
% 29.49/19.70 tff(25492,plain,
% 29.49/19.70 (~(f9(c1, c1) = c1)),
% 29.49/19.70 inference(unit_resolution,[status(thm)],[25386, 25491, 25303, 22733, 17])).
% 29.49/19.70 tff(25493,plain,
% 29.49/19.70 (f9(c1, c1) = c2),
% 29.49/19.70 inference(unit_resolution,[status(thm)],[3939, 25492])).
% 29.49/19.70 tff(25494,plain,
% 29.49/19.70 (~big_f(f9(c1, c1), c1)),
% 29.49/19.70 inference(unit_resolution,[status(thm)],[10058, 25493, 2])).
% 29.49/19.70 tff(25495,plain,
% 29.49/19.70 (~big_f(f9(c1, c1), f10(c1))),
% 29.49/19.70 inference(unit_resolution,[status(thm)],[10033, 25494, 22733])).
% 29.49/19.70 tff(25496,plain,
% 29.49/19.70 (f7(f9(c1, c1)) = f7(c2)),
% 29.49/19.70 inference(monotonicity,[status(thm)],[25493])).
% 29.49/19.70 tff(25497,plain,
% 29.49/19.70 (f7(f9(c1, c1)) = c1),
% 29.49/19.70 inference(transitivity,[status(thm)],[25496, 22])).
% 29.49/19.70 tff(25498,plain,
% 29.49/19.70 ((f7(f9(c1, c1)) = f9(c1, c1)) <=> (c1 = c2)),
% 29.49/19.70 inference(monotonicity,[status(thm)],[25497, 25493])).
% 29.49/19.70 tff(25499,plain,
% 29.49/19.70 ((f7(f9(c1, c1)) = f9(c1, c1)) <=> (c2 = c1)),
% 29.49/19.70 inference(transitivity,[status(thm)],[25498, 1])).
% 29.49/19.70 tff(25500,plain,
% 29.49/19.70 ((c2 = c1) <=> (f7(f9(c1, c1)) = f9(c1, c1))),
% 29.49/19.70 inference(symmetry,[status(thm)],[25499])).
% 29.49/19.70 tff(25501,plain,
% 29.49/19.70 ((~(c2 = c1)) <=> (~(f7(f9(c1, c1)) = f9(c1, c1)))),
% 29.49/19.70 inference(monotonicity,[status(thm)],[25500])).
% 29.49/19.70 tff(25502,plain,
% 29.49/19.70 (~(f7(f9(c1, c1)) = f9(c1, c1))),
% 29.49/19.70 inference(modus_ponens,[status(thm)],[75, 25501])).
% 29.49/19.70 tff(25503,plain,
% 29.49/19.70 (big_f(f7(f9(c1, c1)), c1) <=> big_f(c1, c1)),
% 29.49/19.70 inference(monotonicity,[status(thm)],[25497])).
% 29.49/19.70 tff(25504,plain,
% 29.49/19.70 (big_f(c1, c1) <=> big_f(f7(f9(c1, c1)), c1)),
% 29.49/19.70 inference(symmetry,[status(thm)],[25503])).
% 29.49/19.70 tff(25505,plain,
% 29.49/19.70 (big_f(f7(f9(c1, c1)), c1)),
% 29.49/19.70 inference(modus_ponens,[status(thm)],[25303, 25504])).
% 29.49/19.70 tff(25506,plain,
% 29.49/19.70 (big_f(f7(f9(c1, c1)), f9(c1, c1)) <=> big_f(c1, c2)),
% 29.49/19.70 inference(monotonicity,[status(thm)],[25497, 25493])).
% 29.49/19.70 tff(25507,plain,
% 29.49/19.70 (big_f(c1, c2) <=> big_f(f7(f9(c1, c1)), f9(c1, c1))),
% 29.49/19.70 inference(symmetry,[status(thm)],[25506])).
% 29.49/19.70 tff(25508,plain,
% 29.49/19.70 (big_f(f7(f9(c1, c1)), f9(c1, c1))),
% 29.49/19.70 inference(modus_ponens,[status(thm)],[25491, 25507])).
% 29.49/19.70 tff(25509,plain,
% 29.49/19.70 ($false),
% 29.49/19.70 inference(unit_resolution,[status(thm)],[20184, 25508, 25505, 22733, 25492, 25502, 25495])).
% 29.49/19.70 tff(25510,plain,(big_f(c2, c1) | (f7(c2) = c2) | (f7(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.49/19.70 tff(25511,plain,
% 29.49/19.70 (big_f(c2, c1)),
% 29.49/19.70 inference(unit_resolution,[status(thm)],[25510, 17, 115])).
% 29.49/19.70 tff(25512,plain,
% 29.49/19.70 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c1 = c4)) | (c1 = f2(c2)) | (~big_f(c2, c1)) | (c2 = f4(c1)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (~(c1 = c4)) | (c1 = f2(c2)) | (~big_f(c2, c1)) | (c2 = f4(c1)))),
% 29.49/19.70 inference(rewrite,[status(thm)],[])).
% 29.49/19.70 tff(25513,plain,
% 29.49/19.70 (((~(c2 = c3)) | (~(c1 = c4)) | (c2 = f4(c1)) | (~big_f(c2, c1)) | (c1 = f2(c2)) | (~big_f(c2, c1))) <=> ((~(c2 = c3)) | (~(c1 = c4)) | (c1 = f2(c2)) | (~big_f(c2, c1)) | (c2 = f4(c1)))),
% 29.49/19.70 inference(rewrite,[status(thm)],[])).
% 29.49/19.70 tff(25514,plain,
% 29.49/19.70 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c1 = c4)) | (c2 = f4(c1)) | (~big_f(c2, c1)) | (c1 = f2(c2)) | (~big_f(c2, c1)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c1 = c4)) | (c1 = f2(c2)) | (~big_f(c2, c1)) | (c2 = f4(c1))))),
% 29.49/19.70 inference(monotonicity,[status(thm)],[25513])).
% 29.49/19.70 tff(25515,plain,
% 29.49/19.70 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c1 = c4)) | (c2 = f4(c1)) | (~big_f(c2, c1)) | (c1 = f2(c2)) | (~big_f(c2, c1)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (~(c1 = c4)) | (c1 = f2(c2)) | (~big_f(c2, c1)) | (c2 = f4(c1)))),
% 29.49/19.70 inference(transitivity,[status(thm)],[25514, 25512])).
% 29.49/19.70 tff(25516,plain,
% 29.49/19.70 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c1 = c4)) | (c2 = f4(c1)) | (~big_f(c2, c1)) | (c1 = f2(c2)) | (~big_f(c2, c1)))),
% 29.49/19.70 inference(quant_inst,[status(thm)],[])).
% 29.49/19.70 tff(25517,plain,
% 29.49/19.70 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (~(c1 = c4)) | (c1 = f2(c2)) | (~big_f(c2, c1)) | (c2 = f4(c1))),
% 29.49/19.70 inference(modus_ponens,[status(thm)],[25516, 25515])).
% 29.49/19.70 tff(25518,plain,
% 29.49/19.70 ((~(c2 = c3)) | (~(c1 = c4)) | (c1 = f2(c2)) | (c2 = f4(c1))),
% 29.49/19.70 inference(unit_resolution,[status(thm)],[25517, 1355, 348])).
% 29.49/19.70 tff(25519,plain,
% 29.49/19.70 (c1 = f2(c2)),
% 29.49/19.70 inference(unit_resolution,[status(thm)],[25518, 1344, 11526, 22771])).
% 29.49/19.70 tff(25520,plain,
% 29.49/19.70 (f2(c2) = c1),
% 29.49/19.70 inference(symmetry,[status(thm)],[25519])).
% 29.49/19.71 tff(25521,plain,
% 29.49/19.71 (c2 = f2(c2)),
% 29.49/19.71 inference(unit_resolution,[status(thm)],[23705, 1344, 1345, 348, 11752, 11526])).
% 29.49/19.71 tff(25522,plain,
% 29.49/19.71 (c2 = c1),
% 29.49/19.71 inference(transitivity,[status(thm)],[25521, 25520])).
% 29.49/19.71 tff(25523,plain,
% 29.49/19.71 ($false),
% 29.49/19.71 inference(unit_resolution,[status(thm)],[75, 25522])).
% 29.49/19.71 tff(25524,plain,((~(c2 = c3)) | (~(c1 = c4)) | (c2 = f4(c1)) | (~big_f(c2, c1)) | (~big_f(c2, c2)) | (~(f4(c4) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.49/19.71 tff(25525,plain,
% 29.49/19.71 (~(c2 = c3)),
% 29.49/19.71 inference(unit_resolution,[status(thm)],[25524, 564, 22770, 348, 1345, 11752])).
% 29.49/19.71 tff(25526,plain,
% 29.49/19.71 (~(c3 = c2)),
% 29.49/19.71 inference(modus_ponens,[status(thm)],[25525, 9745])).
% 29.49/19.71 tff(25527,plain,
% 29.49/19.71 (c3 = c1),
% 29.49/19.71 inference(unit_resolution,[status(thm)],[180, 25526])).
% 29.49/19.71 tff(25528,plain,
% 29.49/19.71 (c1 = c3),
% 29.49/19.71 inference(unit_resolution,[status(thm)],[175, 25527])).
% 29.49/19.71 tff(25529,plain,
% 29.49/19.71 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c1 = f2(c1)) | (~(c1 = c4)) | (~big_f(c1, c1)) | (~big_f(c2, c1)) | (c2 = f4(c1)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c1 = c3)) | (c1 = f2(c1)) | (~(c1 = c4)) | (~big_f(c1, c1)) | (~big_f(c2, c1)) | (c2 = f4(c1)))),
% 29.49/19.71 inference(rewrite,[status(thm)],[])).
% 29.49/19.71 tff(25530,plain,
% 29.49/19.71 (((~(c1 = c3)) | (~(c1 = c4)) | (c2 = f4(c1)) | (~big_f(c2, c1)) | (c1 = f2(c1)) | (~big_f(c1, c1))) <=> ((~(c1 = c3)) | (c1 = f2(c1)) | (~(c1 = c4)) | (~big_f(c1, c1)) | (~big_f(c2, c1)) | (c2 = f4(c1)))),
% 29.49/19.71 inference(rewrite,[status(thm)],[])).
% 29.49/19.71 tff(25531,plain,
% 29.49/19.71 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (~(c1 = c4)) | (c2 = f4(c1)) | (~big_f(c2, c1)) | (c1 = f2(c1)) | (~big_f(c1, c1)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c1 = f2(c1)) | (~(c1 = c4)) | (~big_f(c1, c1)) | (~big_f(c2, c1)) | (c2 = f4(c1))))),
% 29.49/19.71 inference(monotonicity,[status(thm)],[25530])).
% 29.49/19.71 tff(25532,plain,
% 29.49/19.71 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (~(c1 = c4)) | (c2 = f4(c1)) | (~big_f(c2, c1)) | (c1 = f2(c1)) | (~big_f(c1, c1)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c1 = c3)) | (c1 = f2(c1)) | (~(c1 = c4)) | (~big_f(c1, c1)) | (~big_f(c2, c1)) | (c2 = f4(c1)))),
% 29.49/19.71 inference(transitivity,[status(thm)],[25531, 25529])).
% 29.49/19.71 tff(25533,plain,
% 29.49/19.71 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (~(c1 = c4)) | (c2 = f4(c1)) | (~big_f(c2, c1)) | (c1 = f2(c1)) | (~big_f(c1, c1)))),
% 29.49/19.71 inference(quant_inst,[status(thm)],[])).
% 29.49/19.71 tff(25534,plain,
% 29.49/19.71 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c1 = c3)) | (c1 = f2(c1)) | (~(c1 = c4)) | (~big_f(c1, c1)) | (~big_f(c2, c1)) | (c2 = f4(c1))),
% 29.49/19.71 inference(modus_ponens,[status(thm)],[25533, 25532])).
% 29.49/19.71 tff(25535,plain,
% 29.49/19.71 ((~(c1 = c3)) | (c1 = f2(c1)) | (~(c1 = c4)) | (c2 = f4(c1))),
% 29.49/19.71 inference(unit_resolution,[status(thm)],[25534, 1355, 348, 4932])).
% 29.49/19.71 tff(25536,plain,
% 29.49/19.71 (c1 = f2(c1)),
% 29.49/19.71 inference(unit_resolution,[status(thm)],[25535, 25528, 564, 22770])).
% 29.49/19.71 tff(25537,plain,
% 29.49/19.71 (f2(c1) = c1),
% 29.49/19.71 inference(symmetry,[status(thm)],[25536])).
% 29.49/19.71 tff(25538,plain,
% 29.49/19.71 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (~(c1 = c4)) | (~big_f(c1, c2)) | (c2 = f2(c1)) | (~big_f(c2, c1)) | (c2 = f4(c1)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c1 = c3)) | (~(c1 = c4)) | (~big_f(c1, c2)) | (c2 = f2(c1)) | (~big_f(c2, c1)) | (c2 = f4(c1)))),
% 29.49/19.71 inference(rewrite,[status(thm)],[])).
% 29.49/19.71 tff(25539,plain,
% 29.49/19.71 (((~(c1 = c3)) | (~(c1 = c4)) | (c2 = f4(c1)) | (~big_f(c2, c1)) | (c2 = f2(c1)) | (~big_f(c1, c2))) <=> ((~(c1 = c3)) | (~(c1 = c4)) | (~big_f(c1, c2)) | (c2 = f2(c1)) | (~big_f(c2, c1)) | (c2 = f4(c1)))),
% 29.49/19.71 inference(rewrite,[status(thm)],[])).
% 29.49/19.71 tff(25540,plain,
% 29.49/19.71 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (~(c1 = c4)) | (c2 = f4(c1)) | (~big_f(c2, c1)) | (c2 = f2(c1)) | (~big_f(c1, c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (~(c1 = c4)) | (~big_f(c1, c2)) | (c2 = f2(c1)) | (~big_f(c2, c1)) | (c2 = f4(c1))))),
% 29.49/19.71 inference(monotonicity,[status(thm)],[25539])).
% 29.49/19.71 tff(25541,plain,
% 29.49/19.71 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (~(c1 = c4)) | (c2 = f4(c1)) | (~big_f(c2, c1)) | (c2 = f2(c1)) | (~big_f(c1, c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c1 = c3)) | (~(c1 = c4)) | (~big_f(c1, c2)) | (c2 = f2(c1)) | (~big_f(c2, c1)) | (c2 = f4(c1)))),
% 29.49/19.71 inference(transitivity,[status(thm)],[25540, 25538])).
% 29.49/19.71 tff(25542,plain,
% 29.49/19.71 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (~(c1 = c4)) | (c2 = f4(c1)) | (~big_f(c2, c1)) | (c2 = f2(c1)) | (~big_f(c1, c2)))),
% 29.49/19.71 inference(quant_inst,[status(thm)],[])).
% 29.49/19.71 tff(25543,plain,
% 29.49/19.71 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c1 = c3)) | (~(c1 = c4)) | (~big_f(c1, c2)) | (c2 = f2(c1)) | (~big_f(c2, c1)) | (c2 = f4(c1))),
% 29.49/19.71 inference(modus_ponens,[status(thm)],[25542, 25541])).
% 29.49/19.71 tff(25544,plain,
% 29.49/19.71 ((~(c1 = c3)) | (~(c1 = c4)) | (c2 = f2(c1)) | (c2 = f4(c1))),
% 29.49/19.71 inference(unit_resolution,[status(thm)],[25543, 1355, 2865, 348])).
% 29.49/19.71 tff(25545,plain,
% 29.49/19.71 (c2 = f2(c1)),
% 29.49/19.71 inference(unit_resolution,[status(thm)],[25544, 25528, 564, 22770])).
% 29.49/19.71 tff(25546,plain,
% 29.49/19.71 (c2 = c1),
% 29.49/19.71 inference(transitivity,[status(thm)],[25545, 25537])).
% 29.49/19.71 tff(25547,plain,
% 29.49/19.71 ($false),
% 29.49/19.71 inference(unit_resolution,[status(thm)],[75, 25546])).
% 29.49/19.71 tff(25548,plain,((~(c4 = c1)) | (~big_f(c2, c1)) | (~big_f(c1, c1)) | (~big_f(c1, c2)) | (~big_f(c2, c2)) | (~(f4(c4) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.49/19.71 tff(25549,plain,
% 29.49/19.71 (~(c4 = c1)),
% 29.49/19.71 inference(unit_resolution,[status(thm)],[25548, 25511, 25303, 25486, 25365, 25412])).
% 29.49/19.71 tff(25550,plain,
% 29.49/19.71 (c4 = c2),
% 29.49/19.71 inference(unit_resolution,[status(thm)],[461, 25549])).
% 29.49/19.71 tff(25551,plain,
% 29.49/19.71 (c2 = c4),
% 29.49/19.71 inference(symmetry,[status(thm)],[25550])).
% 29.49/19.71 tff(25552,plain,
% 29.49/19.71 (f4(c2) = f4(c4)),
% 29.49/19.71 inference(monotonicity,[status(thm)],[25551])).
% 29.49/19.71 tff(25553,plain,
% 29.49/19.71 (f4(c2) = c1),
% 29.49/19.71 inference(transitivity,[status(thm)],[25552, 25412])).
% 29.49/19.71 tff(25554,plain,
% 29.49/19.71 ((c2 = f4(c2)) <=> (c2 = c1)),
% 29.49/19.71 inference(monotonicity,[status(thm)],[25553])).
% 29.49/19.71 tff(25555,plain,
% 29.49/19.71 ((c2 = c1) <=> (c2 = f4(c2))),
% 29.49/19.71 inference(symmetry,[status(thm)],[25554])).
% 29.49/19.71 tff(25556,plain,
% 29.49/19.71 ((~(c2 = c1)) <=> (~(c2 = f4(c2)))),
% 29.49/19.71 inference(monotonicity,[status(thm)],[25555])).
% 29.49/19.71 tff(25557,plain,
% 29.49/19.71 (~(c2 = f4(c2))),
% 29.49/19.71 inference(modus_ponens,[status(thm)],[75, 25556])).
% 29.49/19.71 tff(25558,plain,
% 29.49/19.71 (c2 = c4),
% 29.49/19.71 inference(modus_ponens,[status(thm)],[25550, 159])).
% 29.49/19.71 tff(25559,plain,
% 29.49/19.71 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c4)) | (c2 = f4(c2)) | (~(c1 = c3)) | (c1 = f2(c1)) | (~big_f(c1, c1)) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c4)) | (c2 = f4(c2)) | (~(c1 = c3)) | (c1 = f2(c1)) | (~big_f(c1, c1)) | (~big_f(c2, c2)))),
% 29.52/19.71 inference(rewrite,[status(thm)],[])).
% 29.52/19.71 tff(25560,plain,
% 29.52/19.71 (((~(c1 = c3)) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)) | (c1 = f2(c1)) | (~big_f(c1, c1))) <=> ((~(c2 = c4)) | (c2 = f4(c2)) | (~(c1 = c3)) | (c1 = f2(c1)) | (~big_f(c1, c1)) | (~big_f(c2, c2)))),
% 29.52/19.71 inference(rewrite,[status(thm)],[])).
% 29.52/19.71 tff(25561,plain,
% 29.52/19.71 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)) | (c1 = f2(c1)) | (~big_f(c1, c1)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c4)) | (c2 = f4(c2)) | (~(c1 = c3)) | (c1 = f2(c1)) | (~big_f(c1, c1)) | (~big_f(c2, c2))))),
% 29.52/19.71 inference(monotonicity,[status(thm)],[25560])).
% 29.52/19.71 tff(25562,plain,
% 29.52/19.71 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)) | (c1 = f2(c1)) | (~big_f(c1, c1)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c4)) | (c2 = f4(c2)) | (~(c1 = c3)) | (c1 = f2(c1)) | (~big_f(c1, c1)) | (~big_f(c2, c2)))),
% 29.52/19.71 inference(transitivity,[status(thm)],[25561, 25559])).
% 29.52/19.71 tff(25563,plain,
% 29.52/19.71 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)) | (c1 = f2(c1)) | (~big_f(c1, c1)))),
% 29.52/19.71 inference(quant_inst,[status(thm)],[])).
% 29.52/19.71 tff(25564,plain,
% 29.52/19.71 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c4)) | (c2 = f4(c2)) | (~(c1 = c3)) | (c1 = f2(c1)) | (~big_f(c1, c1)) | (~big_f(c2, c2))),
% 29.52/19.71 inference(modus_ponens,[status(thm)],[25563, 25562])).
% 29.52/19.71 tff(25565,plain,
% 29.52/19.71 ((~(c2 = c4)) | (c2 = f4(c2)) | (~(c1 = c3)) | (c1 = f2(c1))),
% 29.52/19.71 inference(unit_resolution,[status(thm)],[25564, 1355, 1345, 4932])).
% 29.52/19.71 tff(25566,plain,
% 29.52/19.71 (c1 = f2(c1)),
% 29.52/19.71 inference(unit_resolution,[status(thm)],[25565, 5080, 631, 16857])).
% 29.52/19.71 tff(25567,plain,
% 29.52/19.71 (f2(c1) = c1),
% 29.52/19.71 inference(symmetry,[status(thm)],[25566])).
% 29.52/19.71 tff(25568,plain,
% 29.52/19.71 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c4)) | (c2 = f4(c2)) | (~(c1 = c3)) | (~big_f(c1, c2)) | (c2 = f2(c1)) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c4)) | (c2 = f4(c2)) | (~(c1 = c3)) | (~big_f(c1, c2)) | (c2 = f2(c1)) | (~big_f(c2, c2)))),
% 29.52/19.71 inference(rewrite,[status(thm)],[])).
% 29.52/19.71 tff(25569,plain,
% 29.52/19.71 (((~(c1 = c3)) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)) | (c2 = f2(c1)) | (~big_f(c1, c2))) <=> ((~(c2 = c4)) | (c2 = f4(c2)) | (~(c1 = c3)) | (~big_f(c1, c2)) | (c2 = f2(c1)) | (~big_f(c2, c2)))),
% 29.52/19.71 inference(rewrite,[status(thm)],[])).
% 29.52/19.71 tff(25570,plain,
% 29.52/19.71 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)) | (c2 = f2(c1)) | (~big_f(c1, c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c4)) | (c2 = f4(c2)) | (~(c1 = c3)) | (~big_f(c1, c2)) | (c2 = f2(c1)) | (~big_f(c2, c2))))),
% 29.52/19.71 inference(monotonicity,[status(thm)],[25569])).
% 29.52/19.71 tff(25571,plain,
% 29.52/19.71 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)) | (c2 = f2(c1)) | (~big_f(c1, c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c4)) | (c2 = f4(c2)) | (~(c1 = c3)) | (~big_f(c1, c2)) | (c2 = f2(c1)) | (~big_f(c2, c2)))),
% 29.52/19.71 inference(transitivity,[status(thm)],[25570, 25568])).
% 29.52/19.71 tff(25572,plain,
% 29.52/19.71 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)) | (c2 = f2(c1)) | (~big_f(c1, c2)))),
% 29.52/19.71 inference(quant_inst,[status(thm)],[])).
% 29.52/19.71 tff(25573,plain,
% 29.52/19.71 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c4)) | (c2 = f4(c2)) | (~(c1 = c3)) | (~big_f(c1, c2)) | (c2 = f2(c1)) | (~big_f(c2, c2))),
% 29.52/19.71 inference(modus_ponens,[status(thm)],[25572, 25571])).
% 29.52/19.71 tff(25574,plain,
% 29.52/19.71 ((~(c2 = c4)) | (c2 = f4(c2)) | (~(c1 = c3)) | (c2 = f2(c1))),
% 29.52/19.71 inference(unit_resolution,[status(thm)],[25573, 1355, 1345, 2865])).
% 29.52/19.71 tff(25575,plain,
% 29.52/19.71 (c2 = f2(c1)),
% 29.52/19.71 inference(unit_resolution,[status(thm)],[25574, 5080, 16857, 631])).
% 29.52/19.71 tff(25576,plain,
% 29.52/19.71 (c2 = c1),
% 29.52/19.71 inference(transitivity,[status(thm)],[25575, 25567])).
% 29.52/19.71 tff(25577,plain,
% 29.52/19.71 ($false),
% 29.52/19.71 inference(unit_resolution,[status(thm)],[75, 25576])).
% 29.52/19.71 tff(25578,plain,((~(c1 = c3)) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)) | (~big_f(c1, c1)) | (~big_f(c1, c2))), inference(lemma,lemma(discharge,[]))).
% 29.52/19.71 tff(25579,plain,
% 29.52/19.71 (~(c1 = c3)),
% 29.52/19.71 inference(unit_resolution,[status(thm)],[25578, 25558, 25557, 25365, 25303, 25486])).
% 29.52/19.71 tff(25580,plain,
% 29.52/19.71 (~(c3 = c1)),
% 29.52/19.71 inference(unit_resolution,[status(thm)],[175, 25579])).
% 29.52/19.71 tff(25581,plain,
% 29.52/19.71 (c3 = c2),
% 29.52/19.71 inference(unit_resolution,[status(thm)],[180, 25580])).
% 29.52/19.71 tff(25582,plain,
% 29.52/19.71 (c2 = c3),
% 29.52/19.71 inference(modus_ponens,[status(thm)],[25581, 78])).
% 29.52/19.71 tff(25583,plain,
% 29.52/19.71 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c2 = c4)) | (c2 = f4(c2)) | (c1 = f2(c2)) | (~big_f(c2, c1)) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (~(c2 = c4)) | (c2 = f4(c2)) | (c1 = f2(c2)) | (~big_f(c2, c1)) | (~big_f(c2, c2)))),
% 29.52/19.71 inference(rewrite,[status(thm)],[])).
% 29.52/19.71 tff(25584,plain,
% 29.52/19.71 (((~(c2 = c3)) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)) | (c1 = f2(c2)) | (~big_f(c2, c1))) <=> ((~(c2 = c3)) | (~(c2 = c4)) | (c2 = f4(c2)) | (c1 = f2(c2)) | (~big_f(c2, c1)) | (~big_f(c2, c2)))),
% 29.52/19.71 inference(rewrite,[status(thm)],[])).
% 29.52/19.71 tff(25585,plain,
% 29.52/19.71 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)) | (c1 = f2(c2)) | (~big_f(c2, c1)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c2 = c4)) | (c2 = f4(c2)) | (c1 = f2(c2)) | (~big_f(c2, c1)) | (~big_f(c2, c2))))),
% 29.52/19.71 inference(monotonicity,[status(thm)],[25584])).
% 29.52/19.71 tff(25586,plain,
% 29.52/19.71 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)) | (c1 = f2(c2)) | (~big_f(c2, c1)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (~(c2 = c4)) | (c2 = f4(c2)) | (c1 = f2(c2)) | (~big_f(c2, c1)) | (~big_f(c2, c2)))),
% 29.52/19.71 inference(transitivity,[status(thm)],[25585, 25583])).
% 29.52/19.71 tff(25587,plain,
% 29.52/19.71 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)) | (c1 = f2(c2)) | (~big_f(c2, c1)))),
% 29.52/19.71 inference(quant_inst,[status(thm)],[])).
% 29.52/19.71 tff(25588,plain,
% 29.52/19.71 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (~(c2 = c4)) | (c2 = f4(c2)) | (c1 = f2(c2)) | (~big_f(c2, c1)) | (~big_f(c2, c2))),
% 29.52/19.71 inference(modus_ponens,[status(thm)],[25587, 25586])).
% 29.52/19.71 tff(25589,plain,
% 29.52/19.71 ((~(c2 = c3)) | (~(c2 = c4)) | (c2 = f4(c2)) | (c1 = f2(c2))),
% 29.52/19.71 inference(unit_resolution,[status(thm)],[25588, 1355, 25365, 25511])).
% 29.52/19.71 tff(25590,plain,
% 29.52/19.71 (c1 = f2(c2)),
% 29.52/19.71 inference(unit_resolution,[status(thm)],[25589, 25582, 25558, 25557])).
% 29.52/19.71 tff(25591,plain,
% 29.52/19.71 (f2(c2) = c1),
% 29.52/19.71 inference(symmetry,[status(thm)],[25590])).
% 29.52/19.71 tff(25592,plain,
% 29.52/19.71 ((~(c2 = c3)) | (~(c2 = c4)) | (c2 = f4(c2)) | (c2 = f2(c2))),
% 29.52/19.71 inference(unit_resolution,[status(thm)],[17172, 1355, 25365])).
% 29.52/19.71 tff(25593,plain,
% 29.52/19.71 (c2 = f2(c2)),
% 29.52/19.71 inference(unit_resolution,[status(thm)],[25592, 25582, 25558, 25557])).
% 29.52/19.71 tff(25594,plain,
% 29.52/19.71 (c2 = c1),
% 29.52/19.71 inference(transitivity,[status(thm)],[25593, 25591])).
% 29.52/19.71 tff(25595,plain,
% 29.52/19.71 ($false),
% 29.52/19.71 inference(unit_resolution,[status(thm)],[75, 25594])).
% 29.52/19.71 tff(25596,plain,((f7(c2) = c2) | (f7(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.52/19.71 tff(25597,plain,
% 29.52/19.71 (f7(c2) = c2),
% 29.52/19.71 inference(unit_resolution,[status(thm)],[25596, 115])).
% 29.52/19.71 tff(25598,plain,
% 29.52/19.71 (f9(c2, f5(c1)) = f9(c2, c2)),
% 29.52/19.71 inference(monotonicity,[status(thm)],[25489])).
% 29.52/19.71 tff(25599,plain,
% 29.52/19.71 (~(f10(c2) = c1)),
% 29.52/19.71 inference(unit_resolution,[status(thm)],[24753, 2, 25303, 25365, 25597, 115])).
% 29.52/19.71 tff(25600,plain,
% 29.52/19.71 (f10(c2) = c2),
% 29.52/19.71 inference(unit_resolution,[status(thm)],[93, 25599])).
% 29.52/19.71 tff(25601,plain,
% 29.52/19.71 (big_f(f9(c2, c2), c2) <=> big_f(c2, c2)),
% 29.52/19.71 inference(monotonicity,[status(thm)],[1572])).
% 29.52/19.71 tff(25602,plain,
% 29.52/19.71 (big_f(c2, c2) <=> big_f(f9(c2, c2), c2)),
% 29.52/19.71 inference(symmetry,[status(thm)],[25601])).
% 29.52/19.71 tff(25603,plain,
% 29.52/19.71 (big_f(c2, c2) <=> big_f(f9(c2, c2), f10(c2))),
% 29.52/19.71 inference(transitivity,[status(thm)],[25602, 130])).
% 29.52/19.71 tff(25604,plain,
% 29.52/19.71 (big_f(f9(c2, c2), f10(c2))),
% 29.52/19.71 inference(modus_ponens,[status(thm)],[1345, 25603])).
% 29.52/19.71 tff(25605,plain,
% 29.52/19.71 (~(f4(c4) = c2)),
% 29.52/19.71 inference(unit_resolution,[status(thm)],[23473, 122, 77, 1345, 347])).
% 29.52/19.71 tff(25606,plain,
% 29.52/19.71 (f4(c4) = c1),
% 29.52/19.71 inference(unit_resolution,[status(thm)],[11750, 25605])).
% 29.52/19.71 tff(25607,plain,
% 29.52/19.71 (f6(c2, c2) = c2),
% 29.52/19.71 inference(unit_resolution,[status(thm)],[17491, 25604, 2, 122, 77, 1572, 347, 25606])).
% 29.52/19.71 tff(25608,plain,
% 29.52/19.71 (big_f(f7(c2), f6(c2, c2))),
% 29.52/19.71 inference(unit_resolution,[status(thm)],[2627, 25607, 77, 1345])).
% 29.52/19.71 tff(25609,plain,
% 29.52/19.71 ($false),
% 29.52/19.71 inference(unit_resolution,[status(thm)],[2384, 2378, 122, 77, 25607, 25608, 1572, 25604])).
% 29.52/19.71 tff(25610,plain,((~(f9(c2, c2) = c2)) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~big_f(c2, c2)) | big_f(c2, c1) | (~(f7(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.52/19.71 tff(25611,plain,
% 29.52/19.71 (~(f9(c2, c2) = c2)),
% 29.52/19.71 inference(unit_resolution,[status(thm)],[25610, 25600, 25597, 25365, 2, 120])).
% 29.52/19.71 tff(25612,plain,
% 29.52/19.71 (~(f9(c2, f5(c1)) = c2)),
% 29.52/19.71 inference(unit_resolution,[status(thm)],[17013, 25611, 25489])).
% 29.52/19.71 tff(25613,plain,
% 29.52/19.71 (f9(c2, f5(c1)) = c1),
% 29.52/19.71 inference(unit_resolution,[status(thm)],[16529, 25612])).
% 29.52/19.71 tff(25614,plain,
% 29.52/19.71 (c1 = f9(c2, f5(c1))),
% 29.52/19.71 inference(symmetry,[status(thm)],[25613])).
% 29.52/19.71 tff(25615,plain,
% 29.52/19.71 (f9(c2, c2) = f9(c2, f5(c1))),
% 29.52/19.71 inference(symmetry,[status(thm)],[25598])).
% 29.52/19.71 tff(25616,plain,
% 29.52/19.71 (f9(c2, c2) = c1),
% 29.52/19.71 inference(transitivity,[status(thm)],[25615, 25613])).
% 29.52/19.71 tff(25617,plain,
% 29.52/19.71 (f10(f9(c2, c2)) = f10(c1)),
% 29.52/19.71 inference(monotonicity,[status(thm)],[25616])).
% 29.52/19.71 tff(25618,plain,
% 29.52/19.71 (f10(f9(c2, c2)) = f9(c2, c2)),
% 29.52/19.71 inference(transitivity,[status(thm)],[25617, 22733, 25614, 25598])).
% 29.52/19.71 tff(25619,plain,
% 29.52/19.71 (big_f(c2, f9(c2, c2)) <=> big_f(c2, c1)),
% 29.52/19.71 inference(monotonicity,[status(thm)],[25616])).
% 29.52/19.71 tff(25620,plain,
% 29.52/19.71 (big_f(c2, c1) <=> big_f(c2, f9(c2, c2))),
% 29.52/19.71 inference(symmetry,[status(thm)],[25619])).
% 29.52/19.71 tff(25621,plain,
% 29.52/19.71 ((~big_f(c2, c1)) <=> (~big_f(c2, f9(c2, c2)))),
% 29.52/19.71 inference(monotonicity,[status(thm)],[25620])).
% 29.52/19.71 tff(25622,plain,
% 29.52/19.71 (~big_f(c2, f9(c2, c2))),
% 29.52/19.71 inference(modus_ponens,[status(thm)],[2, 25621])).
% 29.52/19.71 tff(25623,plain,
% 29.52/19.71 (~(f4(c4) = c2)),
% 29.52/19.71 inference(unit_resolution,[status(thm)],[23473, 25600, 25597, 25365, 120])).
% 29.52/19.71 tff(25624,plain,
% 29.52/19.71 (f4(c4) = c1),
% 29.52/19.71 inference(unit_resolution,[status(thm)],[11750, 25623])).
% 29.52/19.71 tff(25625,plain,
% 29.52/19.71 (f6(c2, c2) = f9(c2, c2)),
% 29.52/19.71 inference(transitivity,[status(thm)],[21473, 17484, 17425, 7218])).
% 29.52/19.71 tff(25626,plain,
% 29.52/19.71 (big_f(f7(c2), f6(c2, c2)) <=> big_f(c2, f9(c2, c2))),
% 29.52/19.71 inference(monotonicity,[status(thm)],[77, 25625])).
% 29.52/19.71 tff(25627,plain,
% 29.52/19.71 (big_f(c2, f9(c2, c2)) <=> big_f(f7(c2), f6(c2, c2))),
% 29.52/19.71 inference(symmetry,[status(thm)],[25626])).
% 29.52/19.71 tff(25628,plain,
% 29.52/19.71 ((~big_f(c2, f9(c2, c2))) <=> (~big_f(f7(c2), f6(c2, c2)))),
% 29.52/19.71 inference(monotonicity,[status(thm)],[25627])).
% 29.52/19.71 tff(25629,plain,
% 29.52/19.71 (~big_f(f7(c2), f6(c2, c2))),
% 29.52/19.71 inference(modus_ponens,[status(thm)],[2040, 25628])).
% 29.52/19.71 tff(25630,plain,
% 29.52/19.71 (f9(c2, c2) = c1),
% 29.52/19.71 inference(transitivity,[status(thm)],[7219, 17424])).
% 29.52/19.71 tff(25631,plain,
% 29.52/19.71 (f10(f9(c2, c2)) = f10(c1)),
% 29.52/19.71 inference(monotonicity,[status(thm)],[25630])).
% 29.52/19.71 tff(25632,plain,
% 29.52/19.71 (f10(f9(c2, c2)) = f9(c2, c2)),
% 29.52/19.71 inference(transitivity,[status(thm)],[25631, 3762, 17425, 7218])).
% 29.52/19.71 tff(25633,plain,
% 29.52/19.71 (f9(f9(c2, c2), f9(c2, c2)) = f9(c1, c1)),
% 29.52/19.71 inference(monotonicity,[status(thm)],[25630, 25630])).
% 29.52/19.71 tff(25634,plain,
% 29.52/19.71 (f9(f9(c2, c2), f9(c2, c2)) = c2),
% 29.52/19.71 inference(transitivity,[status(thm)],[25633, 4071])).
% 29.52/19.71 tff(25635,plain,
% 29.52/19.71 (big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))) <=> big_f(c2, f9(c2, c2))),
% 29.52/19.71 inference(monotonicity,[status(thm)],[25634, 25632])).
% 29.52/19.71 tff(25636,plain,
% 29.52/19.71 (big_f(c2, f9(c2, c2)) <=> big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))),
% 29.52/19.71 inference(symmetry,[status(thm)],[25635])).
% 29.52/19.71 tff(25637,plain,
% 29.52/19.71 ((~big_f(c2, f9(c2, c2))) <=> (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))))),
% 29.52/19.71 inference(monotonicity,[status(thm)],[25636])).
% 29.52/19.71 tff(25638,plain,
% 29.52/19.71 (~big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))),
% 29.52/19.71 inference(modus_ponens,[status(thm)],[2040, 25637])).
% 29.52/19.71 tff(25639,plain,
% 29.52/19.71 (c1 = f9(c2, c2)),
% 29.52/19.71 inference(transitivity,[status(thm)],[17425, 7218])).
% 29.52/19.71 tff(25640,plain,
% 29.52/19.71 (f9(c1, c1) = f9(f9(c2, c2), f9(c2, c2))),
% 29.52/19.71 inference(symmetry,[status(thm)],[25633])).
% 29.52/19.71 tff(25641,plain,
% 29.52/19.71 ((f9(c1, c1) = c1) <=> (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))),
% 29.52/19.71 inference(monotonicity,[status(thm)],[25640, 25639])).
% 29.52/19.71 tff(25642,plain,
% 29.52/19.71 ((~(f9(c1, c1) = c1)) <=> (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)))),
% 29.52/19.71 inference(monotonicity,[status(thm)],[25641])).
% 29.52/19.71 tff(25643,plain,
% 29.52/19.71 (~(f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2))),
% 29.52/19.71 inference(modus_ponens,[status(thm)],[4070, 25642])).
% 29.52/19.71 tff(25644,plain,
% 29.52/19.71 ($false),
% 29.52/19.71 inference(unit_resolution,[status(thm)],[4042, 2492, 77, 2637, 2621, 25632, 25643, 25638])).
% 29.52/19.71 tff(25645,plain,((f9(c1, c1) = c1) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | big_f(c2, f9(c2, c2)) | (~(f10(c1) = c1)) | (~(f9(c2, f5(c1)) = c1)) | (~(f5(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.52/19.71 tff(25646,plain,
% 29.52/19.71 (f9(c1, c1) = c1),
% 29.52/19.71 inference(unit_resolution,[status(thm)],[25645, 2637, 77, 25629, 2040, 3762, 17424, 186])).
% 29.52/19.71 tff(25647,plain,
% 29.52/19.71 (big_f(f9(c1, c1), c1)),
% 29.52/19.71 inference(unit_resolution,[status(thm)],[10938, 25646, 4932])).
% 29.52/19.71 tff(25648,plain,
% 29.52/19.71 (~big_f(f9(c1, c1), f10(c1))),
% 29.52/19.72 inference(unit_resolution,[status(thm)],[24737, 25646, 3762, 77, 1345, 25629])).
% 29.52/19.72 tff(25649,plain,
% 29.52/19.72 ($false),
% 29.52/19.72 inference(unit_resolution,[status(thm)],[8716, 25648, 25647, 3762])).
% 29.52/19.72 tff(25650,plain,((f6(c2, c2) = c2) | (~(f10(c1) = c1)) | (~(f7(c2) = c2)) | (~big_f(c2, c2)) | (~big_f(c1, c1)) | big_f(c2, f9(c2, c2)) | (~(f9(c2, f5(c1)) = c1)) | (~(f5(c1) = c2)) | (~(f7(c1) = c2)) | (~(f4(c4) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.52/19.72 tff(25651,plain,
% 29.52/19.72 (f6(c2, c2) = c2),
% 29.52/19.72 inference(unit_resolution,[status(thm)],[25650, 25622, 25597, 25365, 25303, 22733, 25613, 25489, 120, 25624])).
% 29.52/19.72 tff(25652,plain,
% 29.52/19.72 (big_f(f7(c2), f6(c2, c2))),
% 29.52/19.72 inference(unit_resolution,[status(thm)],[2627, 25651, 25597, 25365])).
% 29.52/19.72 tff(25653,plain,
% 29.52/19.72 ($false),
% 29.52/19.72 inference(unit_resolution,[status(thm)],[4063, 2534, 77, 2622, 2707, 25632, 25643, 25638])).
% 29.52/19.72 tff(25654,plain,((f9(c1, c1) = c1) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | big_f(c2, f9(c2, c2)) | (~(f10(c1) = c1)) | (~(f9(c2, f5(c1)) = c1)) | (~(f5(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.52/19.72 tff(25655,plain,
% 29.52/19.72 (f9(c1, c1) = c1),
% 29.52/19.72 inference(unit_resolution,[status(thm)],[25654, 25651, 25597, 25652, 25622, 22733, 25613, 25489])).
% 29.52/19.72 tff(25656,plain,
% 29.52/19.72 (f9(f9(c2, c2), f9(c2, c2)) = f9(c1, c1)),
% 29.52/19.72 inference(monotonicity,[status(thm)],[25616, 25616])).
% 29.52/19.72 tff(25657,plain,
% 29.52/19.72 (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)),
% 29.52/19.72 inference(transitivity,[status(thm)],[25656, 25655, 25614, 25598])).
% 29.52/19.72 tff(25658,plain,
% 29.52/19.72 (big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2))) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 29.52/19.72 inference(monotonicity,[status(thm)],[25657, 25618])).
% 29.52/19.72 tff(25659,plain,
% 29.52/19.72 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))),
% 29.52/19.72 inference(symmetry,[status(thm)],[25658])).
% 29.52/19.72 tff(25660,plain,
% 29.52/19.72 (big_f(f9(c2, c2), f9(c2, c2)) <=> big_f(c1, c1)),
% 29.52/19.72 inference(monotonicity,[status(thm)],[25616, 25616])).
% 29.52/19.72 tff(25661,plain,
% 29.52/19.72 (big_f(c1, c1) <=> big_f(f9(c2, c2), f9(c2, c2))),
% 29.52/19.72 inference(symmetry,[status(thm)],[25660])).
% 29.52/19.72 tff(25662,plain,
% 29.52/19.72 (big_f(f9(c2, c2), f9(c2, c2))),
% 29.52/19.72 inference(modus_ponens,[status(thm)],[25303, 25661])).
% 29.52/19.72 tff(25663,plain,
% 29.52/19.72 (big_f(f9(f9(c2, c2), f9(c2, c2)), f10(f9(c2, c2)))),
% 29.52/19.72 inference(modus_ponens,[status(thm)],[25662, 25659])).
% 29.52/19.72 tff(25664,plain,
% 29.52/19.72 (f9(c2, c2) = c1),
% 29.52/19.72 inference(transitivity,[status(thm)],[16520, 17424])).
% 29.52/19.72 tff(25665,plain,
% 29.52/19.72 (f9(f9(c2, c2), f9(c2, c2)) = f9(c1, c1)),
% 29.52/19.72 inference(monotonicity,[status(thm)],[25664, 25664])).
% 29.52/19.72 tff(25666,plain,
% 29.52/19.72 (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)),
% 29.52/19.72 inference(transitivity,[status(thm)],[25665, 3949, 17425, 16521])).
% 29.52/19.72 tff(25667,plain,
% 29.52/19.72 ($false),
% 29.52/19.72 inference(unit_resolution,[status(thm)],[4036, 25666])).
% 29.52/19.72 tff(25668,plain,((~(f9(c2, f5(c1)) = c1)) | (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | (~(f9(c1, c1) = c1)) | (~(f5(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.52/19.72 tff(25669,plain,
% 29.52/19.72 (~(f9(c2, f5(c1)) = c1)),
% 29.52/19.72 inference(unit_resolution,[status(thm)],[25668, 4036, 3949, 186])).
% 29.52/19.72 tff(25670,plain,
% 29.52/19.72 (f9(c2, f5(c1)) = c2),
% 29.52/19.72 inference(unit_resolution,[status(thm)],[16529, 25669])).
% 29.52/19.72 tff(25671,plain,
% 29.52/19.72 (f9(c2, c2) = c2),
% 29.52/19.72 inference(transitivity,[status(thm)],[16520, 25670])).
% 29.52/19.72 tff(25672,plain,
% 29.52/19.72 (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)),
% 29.52/19.72 inference(monotonicity,[status(thm)],[25671, 25671])).
% 29.52/19.72 tff(25673,plain,
% 29.52/19.72 ($false),
% 29.52/19.72 inference(unit_resolution,[status(thm)],[4036, 25672])).
% 29.52/19.72 tff(25674,plain,((f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)) | (~(f5(c1) = c2)) | (~(f9(c1, c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.52/19.72 tff(25675,plain,
% 29.52/19.72 (f9(f9(c2, c2), f9(c2, c2)) = f9(c2, c2)),
% 29.52/19.72 inference(unit_resolution,[status(thm)],[25674, 25655, 25489])).
% 29.52/19.72 tff(25676,plain,
% 29.52/19.72 ($false),
% 29.52/19.72 inference(unit_resolution,[status(thm)],[3986, 2378, 25597, 25651, 25652, 25618, 25675, 25663])).
% 29.52/19.72 tff(25677,plain,(big_f(c2, c1) | (f7(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.52/19.72 tff(25678,plain,
% 29.52/19.72 (big_f(c2, c1)),
% 29.52/19.72 inference(unit_resolution,[status(thm)],[25677, 115])).
% 29.52/19.72 tff(25679,plain,
% 29.52/19.72 ((f7(f10(c2)) = f10(c2)) <=> (c2 = c1)),
% 29.52/19.72 inference(monotonicity,[status(thm)],[21867, 94])).
% 29.52/19.72 tff(25680,plain,
% 29.52/19.72 ((c2 = c1) <=> (f7(f10(c2)) = f10(c2))),
% 29.52/19.72 inference(symmetry,[status(thm)],[25679])).
% 29.52/19.72 tff(25681,plain,
% 29.52/19.72 ((~(c2 = c1)) <=> (~(f7(f10(c2)) = f10(c2)))),
% 29.52/19.72 inference(monotonicity,[status(thm)],[25680])).
% 29.52/19.72 tff(25682,plain,
% 29.52/19.72 (~(f7(f10(c2)) = f10(c2))),
% 29.52/19.72 inference(modus_ponens,[status(thm)],[75, 25681])).
% 29.52/19.72 tff(25683,plain,
% 29.52/19.72 (big_f(c2, f10(c2))),
% 29.52/19.72 inference(modus_ponens,[status(thm)],[348, 12069])).
% 29.52/19.72 tff(25684,plain,
% 29.52/19.72 (big_f(f7(f10(c2)), c2)),
% 29.52/19.72 inference(modus_ponens,[status(thm)],[1345, 21869])).
% 29.52/19.72 tff(25685,plain,
% 29.52/19.72 (big_f(f7(f10(c2)), f10(c2)) <=> big_f(c2, c1)),
% 29.52/19.72 inference(monotonicity,[status(thm)],[21867, 94])).
% 29.52/19.72 tff(25686,plain,
% 29.52/19.72 (big_f(c2, c1) <=> big_f(f7(f10(c2)), f10(c2))),
% 29.52/19.72 inference(symmetry,[status(thm)],[25685])).
% 29.52/19.72 tff(25687,plain,
% 29.52/19.72 (big_f(f7(f10(c2)), f10(c2))),
% 29.52/19.72 inference(modus_ponens,[status(thm)],[348, 25686])).
% 29.52/19.72 tff(25688,plain,
% 29.52/19.72 (c2 = f8(c2)),
% 29.52/19.72 inference(unit_resolution,[status(thm)],[21713, 25687, 89, 25684, 25683, 25682])).
% 29.52/19.72 tff(25689,plain,
% 29.52/19.72 (f8(c2) = c2),
% 29.52/19.72 inference(symmetry,[status(thm)],[25688])).
% 29.52/19.72 tff(25690,plain,
% 29.52/19.72 ((c1 = f8(c2)) <=> (c1 = c2)),
% 29.52/19.72 inference(monotonicity,[status(thm)],[25689])).
% 29.52/19.72 tff(25691,plain,
% 29.52/19.72 ((c1 = f8(c2)) <=> (c2 = c1)),
% 29.52/19.72 inference(transitivity,[status(thm)],[25690, 1])).
% 29.52/19.72 tff(25692,plain,
% 29.52/19.72 ((c2 = c1) <=> (c1 = f8(c2))),
% 29.52/19.72 inference(symmetry,[status(thm)],[25691])).
% 29.52/19.72 tff(25693,plain,
% 29.52/19.72 ((c2 = c1) <=> (f10(c2) = f8(c2))),
% 29.52/19.72 inference(transitivity,[status(thm)],[25692, 21566])).
% 29.52/19.72 tff(25694,plain,
% 29.52/19.72 ((~(c2 = c1)) <=> (~(f10(c2) = f8(c2)))),
% 29.52/19.72 inference(monotonicity,[status(thm)],[25693])).
% 29.52/19.72 tff(25695,plain,
% 29.52/19.72 (~(f10(c2) = f8(c2))),
% 29.52/19.72 inference(modus_ponens,[status(thm)],[75, 25694])).
% 29.52/19.72 tff(25696,plain,
% 29.52/19.72 (big_f(f10(c2), f10(c2))),
% 29.52/19.72 inference(unit_resolution,[status(thm)],[21743, 94, 4932])).
% 29.52/19.72 tff(25697,plain,
% 29.52/19.72 (f10(c2) = f8(c2)),
% 29.52/19.72 inference(unit_resolution,[status(thm)],[21739, 25687, 89, 25684, 25696, 25682])).
% 29.52/19.72 tff(25698,plain,
% 29.52/19.72 ($false),
% 29.52/19.72 inference(unit_resolution,[status(thm)],[25697, 25695])).
% 29.52/19.72 tff(25699,plain,((f10(c2) = c2) | (~big_f(c2, c1)) | (~(f7(c1) = c2)) | (~big_f(c2, c2)) | (~big_f(c1, c1))), inference(lemma,lemma(discharge,[]))).
% 29.52/19.72 tff(25700,plain,
% 29.52/19.72 (f10(c2) = c2),
% 29.52/19.72 inference(unit_resolution,[status(thm)],[25699, 25678, 120, 25365, 25303])).
% 29.52/19.72 tff(25701,plain,
% 29.52/19.72 (~(f4(c4) = c2)),
% 29.52/19.72 inference(unit_resolution,[status(thm)],[23473, 25700, 25597, 25365, 120])).
% 29.52/19.72 tff(25702,plain,
% 29.52/19.72 (f4(c4) = c1),
% 29.52/19.72 inference(unit_resolution,[status(thm)],[11750, 25701])).
% 29.52/19.72 tff(25703,plain,
% 29.52/19.72 (big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 29.52/19.72 inference(unit_resolution,[status(thm)],[23779, 27, 115, 25597, 25700])).
% 29.52/19.72 tff(25704,plain,
% 29.52/19.72 (f9(c2, f9(f10(c2), f10(c2))) = f9(c2, f9(c2, c2))),
% 29.52/19.72 inference(symmetry,[status(thm)],[1134])).
% 29.52/19.72 tff(25705,plain,
% 29.52/19.72 (big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2)) <=> big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 29.52/19.72 inference(monotonicity,[status(thm)],[25704])).
% 29.52/19.72 tff(25706,plain,
% 29.52/19.72 ((~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2))) <=> (~big_f(f9(c2, f9(c2, c2)), f10(c2)))),
% 29.52/19.72 inference(monotonicity,[status(thm)],[25705])).
% 29.52/19.72 tff(25707,assumption,(~big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2))), introduced(assumption)).
% 29.52/19.72 tff(25708,plain,
% 29.52/19.72 (~big_f(f9(c2, f9(c2, c2)), f10(c2))),
% 29.52/19.72 inference(modus_ponens,[status(thm)],[25707, 25706])).
% 29.52/19.72 tff(25709,plain,
% 29.52/19.72 ($false),
% 29.52/19.72 inference(unit_resolution,[status(thm)],[1146, 25708])).
% 29.52/19.72 tff(25710,plain,(big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2)) | (~big_f(f9(c2, f9(c2, c2)), f10(c2))) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.52/19.72 tff(25711,plain,
% 29.52/19.72 (big_f(f9(c2, f9(f10(c2), f10(c2))), f10(c2))),
% 29.52/19.72 inference(unit_resolution,[status(thm)],[25710, 25703, 25700])).
% 29.52/19.72 tff(25712,plain,
% 29.52/19.72 (big_f(f7(c1), f10(c1)) <=> big_f(c2, f10(c1))),
% 29.52/19.72 inference(monotonicity,[status(thm)],[120])).
% 29.52/19.72 tff(25713,plain,
% 29.52/19.72 (big_f(c2, f10(c1)) <=> big_f(f7(c1), f10(c1))),
% 29.52/19.72 inference(symmetry,[status(thm)],[25712])).
% 29.52/19.72 tff(25714,plain,
% 29.52/19.72 (big_f(c2, f10(c1)) <=> big_f(c2, c1)),
% 29.52/19.72 inference(monotonicity,[status(thm)],[22733])).
% 29.52/19.72 tff(25715,plain,
% 29.52/19.72 (big_f(c2, c1) <=> big_f(c2, f10(c1))),
% 29.52/19.72 inference(symmetry,[status(thm)],[25714])).
% 29.52/19.72 tff(25716,plain,
% 29.52/19.72 (big_f(c2, c1) <=> big_f(f7(c1), f10(c1))),
% 29.52/19.72 inference(transitivity,[status(thm)],[25715, 25713])).
% 29.52/19.72 tff(25717,plain,
% 29.52/19.72 (big_f(f7(c1), f10(c1))),
% 29.52/19.72 inference(modus_ponens,[status(thm)],[25678, 25716])).
% 29.52/19.72 tff(25718,plain,
% 29.52/19.72 (f9(f10(c2), f10(c2)) = f9(c2, c2)),
% 29.52/19.72 inference(monotonicity,[status(thm)],[25700, 25700])).
% 29.52/19.72 tff(25719,plain,
% 29.52/19.72 (f9(c2, c2) = f9(f10(c2), f10(c2))),
% 29.52/19.72 inference(symmetry,[status(thm)],[25718])).
% 29.52/19.72 tff(25720,plain,
% 29.52/19.72 (f9(c2, f9(c2, c2)) = f9(c2, f9(f10(c2), f10(c2)))),
% 29.52/19.72 inference(monotonicity,[status(thm)],[25719])).
% 29.52/19.72 tff(25721,plain,
% 29.52/19.72 (f9(c2, f9(f10(c2), f10(c2))) = f9(c2, f9(c2, c2))),
% 29.52/19.72 inference(symmetry,[status(thm)],[25720])).
% 29.52/19.72 tff(25722,plain,
% 29.52/19.72 ((f9(c2, f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2))) <=> (f9(c2, f9(c2, c2)) = f9(c2, c2))),
% 29.52/19.72 inference(monotonicity,[status(thm)],[25721, 25718])).
% 29.52/19.72 tff(25723,plain,
% 29.52/19.72 ((f9(c2, f9(c2, c2)) = f9(c2, c2)) <=> (f9(c2, f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))),
% 29.52/19.72 inference(symmetry,[status(thm)],[25722])).
% 29.52/19.72 tff(25724,plain,
% 29.52/19.72 (~(f9(c2, f9(f10(c2), f10(c2))) = c1)),
% 29.52/19.72 inference(unit_resolution,[status(thm)],[23674, 25703, 25700, 27])).
% 29.52/19.72 tff(25725,plain,
% 29.52/19.72 (f9(c2, f9(f10(c2), f10(c2))) = c2),
% 29.52/19.72 inference(unit_resolution,[status(thm)],[23082, 25724])).
% 29.52/19.72 tff(25726,plain,
% 29.52/19.72 (f9(c2, f9(c2, c2)) = c2),
% 29.52/19.72 inference(transitivity,[status(thm)],[25720, 25725])).
% 29.52/19.72 tff(25727,plain,
% 29.52/19.72 ((f9(c2, f9(c2, c2)) = f9(c2, c2)) <=> (c2 = f9(c2, c2))),
% 29.52/19.72 inference(monotonicity,[status(thm)],[25726])).
% 29.52/19.72 tff(25728,plain,
% 29.52/19.72 ((f9(c2, f9(c2, c2)) = f9(c2, c2)) <=> (f9(c2, c2) = c2)),
% 29.52/19.72 inference(transitivity,[status(thm)],[25727, 167])).
% 29.52/19.72 tff(25729,plain,
% 29.52/19.72 ((f9(c2, c2) = c2) <=> (f9(c2, f9(c2, c2)) = f9(c2, c2))),
% 29.52/19.72 inference(symmetry,[status(thm)],[25728])).
% 29.52/19.72 tff(25730,plain,
% 29.52/19.72 ((f9(c2, c2) = c2) <=> (f9(c2, f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))),
% 29.52/19.72 inference(transitivity,[status(thm)],[25729, 25723])).
% 29.52/19.72 tff(25731,plain,
% 29.52/19.72 (c2 = f10(c2)),
% 29.52/19.72 inference(symmetry,[status(thm)],[25700])).
% 29.52/19.72 tff(25732,plain,
% 29.52/19.72 (f9(c2, c2) = f9(f10(c2), f7(c1))),
% 29.52/19.72 inference(monotonicity,[status(thm)],[25731, 2778])).
% 29.52/19.72 tff(25733,plain,
% 29.52/19.72 (f9(f10(c2), f7(c1)) = f9(c2, c2)),
% 29.52/19.72 inference(symmetry,[status(thm)],[25732])).
% 29.52/19.72 tff(25734,plain,
% 29.52/19.72 ((f9(f10(c2), f7(c1)) = c2) <=> (f9(c2, c2) = c2)),
% 29.52/19.72 inference(monotonicity,[status(thm)],[25733])).
% 29.52/19.72 tff(25735,plain,
% 29.52/19.72 ((f9(c2, c2) = c2) <=> (f9(f10(c2), f7(c1)) = c2)),
% 29.52/19.72 inference(symmetry,[status(thm)],[25734])).
% 29.52/19.72 tff(25736,plain,
% 29.52/19.72 ((f9(c2, f9(c2, c2)) = f9(c2, c2)) <=> (f9(f10(c2), f7(c1)) = c2)),
% 29.52/19.72 inference(transitivity,[status(thm)],[25728, 25735])).
% 29.52/19.72 tff(25737,plain,
% 29.52/19.72 ((~(f9(c2, f9(c2, c2)) = f9(c2, c2))) <=> (~(f9(f10(c2), f7(c1)) = c2))),
% 29.52/19.72 inference(monotonicity,[status(thm)],[25736])).
% 29.52/19.72 tff(25738,plain,
% 29.52/19.72 ((c2 = f5(c1)) | (~(f9(c2, f9(c2, c2)) = f9(c2, c2)))),
% 29.52/19.72 inference(unit_resolution,[status(thm)],[23740, 1190, 25467, 115, 25700, 25703])).
% 29.52/19.72 tff(25739,plain,
% 29.52/19.72 (~(f9(c2, f9(c2, c2)) = f9(c2, c2))),
% 29.52/19.72 inference(unit_resolution,[status(thm)],[25738, 12775])).
% 29.52/19.72 tff(25740,plain,
% 29.52/19.72 (~(f9(f10(c2), f7(c1)) = c2)),
% 29.52/19.72 inference(modus_ponens,[status(thm)],[25739, 25737])).
% 29.52/19.72 tff(25741,plain,
% 29.52/19.72 (f9(f10(c2), f7(c1)) = c1),
% 29.52/19.72 inference(unit_resolution,[status(thm)],[25473, 25740])).
% 29.52/19.72 tff(25742,plain,
% 29.52/19.72 (f9(c2, c2) = c1),
% 29.52/19.72 inference(transitivity,[status(thm)],[25732, 25741])).
% 29.52/19.72 tff(25743,plain,
% 29.52/19.72 (big_f(f9(c2, c2), c2) <=> big_f(c1, c2)),
% 29.52/19.72 inference(monotonicity,[status(thm)],[25742])).
% 29.52/19.72 tff(25744,plain,
% 29.52/19.72 (big_f(c1, c2) <=> big_f(f9(c2, c2), c2)),
% 29.52/19.72 inference(symmetry,[status(thm)],[25743])).
% 29.52/19.72 tff(25745,plain,
% 29.52/19.72 ((~big_f(c1, c2)) <=> (~big_f(f9(c2, c2), c2))),
% 29.52/19.72 inference(monotonicity,[status(thm)],[25744])).
% 29.52/19.72 tff(25746,plain,
% 29.52/19.72 (~big_f(f9(c2, c2), c2)),
% 29.52/19.72 inference(modus_ponens,[status(thm)],[27, 25745])).
% 29.52/19.72 tff(25747,plain,
% 29.52/19.72 ((~(f9(c2, f9(c2, c2)) = f9(c2, c2))) <=> (~(f9(c2, c2) = c2))),
% 29.52/19.72 inference(monotonicity,[status(thm)],[25728])).
% 29.52/19.72 tff(25748,plain,
% 29.52/19.72 (~(f9(c2, c2) = c2)),
% 29.52/19.72 inference(modus_ponens,[status(thm)],[25739, 25747])).
% 29.52/19.72 tff(25749,plain,
% 29.52/19.72 ((c2 = f5(c1)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2))),
% 29.52/19.72 inference(unit_resolution,[status(thm)],[17343, 676, 25467, 115, 25700])).
% 29.52/19.72 tff(25750,plain,
% 29.52/19.72 (big_f(f9(c2, c2), f10(c2))),
% 29.52/19.72 inference(unit_resolution,[status(thm)],[25749, 25748, 12775])).
% 29.52/19.72 tff(25751,plain,
% 29.52/19.72 (big_f(f9(c2, c2), c2)),
% 29.52/19.72 inference(unit_resolution,[status(thm)],[3687, 25750, 25700])).
% 29.52/19.72 tff(25752,plain,
% 29.52/19.72 ($false),
% 29.52/19.72 inference(unit_resolution,[status(thm)],[25751, 25746])).
% 29.52/19.72 tff(25753,plain,((c2 = f5(c1)) | big_f(c1, c2) | (f7(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.52/19.72 tff(25754,plain,
% 29.52/19.72 (c2 = f5(c1)),
% 29.52/19.72 inference(unit_resolution,[status(thm)],[25753, 27, 115])).
% 29.52/19.72 tff(25755,plain,
% 29.52/19.72 (f9(c2, c2) = c2),
% 29.52/19.72 inference(unit_resolution,[status(thm)],[23772, 25754, 25597, 25700, 27, 120, 25365])).
% 29.52/19.72 tff(25756,plain,
% 29.52/19.72 (f9(c2, f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2))),
% 29.52/19.72 inference(modus_ponens,[status(thm)],[25755, 25730])).
% 29.52/19.72 tff(25757,plain,
% 29.52/19.72 ((f10(c1) = f5(c1)) <=> (c1 = f5(c1))),
% 29.52/19.72 inference(monotonicity,[status(thm)],[22733])).
% 29.52/19.72 tff(25758,plain,
% 29.52/19.72 ((f10(c1) = f5(c1)) <=> (f5(c1) = c1)),
% 29.52/19.72 inference(transitivity,[status(thm)],[25757, 128])).
% 29.52/19.72 tff(25759,plain,
% 29.52/19.72 ((f5(c1) = c1) <=> (f10(c1) = f5(c1))),
% 29.52/19.72 inference(symmetry,[status(thm)],[25758])).
% 29.52/19.72 tff(25760,plain,
% 29.52/19.72 (f5(c1) = c2),
% 29.52/19.72 inference(symmetry,[status(thm)],[25754])).
% 29.52/19.72 tff(25761,plain,
% 29.52/19.72 ((f5(c1) = c1) <=> (c2 = c1)),
% 29.52/19.72 inference(monotonicity,[status(thm)],[25760])).
% 29.52/19.72 tff(25762,plain,
% 29.52/19.72 ((c2 = c1) <=> (f5(c1) = c1)),
% 29.52/19.72 inference(symmetry,[status(thm)],[25761])).
% 29.52/19.72 tff(25763,plain,
% 29.52/19.72 ((c2 = c1) <=> (f10(c1) = f5(c1))),
% 29.52/19.72 inference(transitivity,[status(thm)],[25762, 25759])).
% 29.52/19.72 tff(25764,plain,
% 29.52/19.72 ((~(c2 = c1)) <=> (~(f10(c1) = f5(c1)))),
% 29.52/19.72 inference(monotonicity,[status(thm)],[25763])).
% 29.52/19.72 tff(25765,plain,
% 29.52/19.72 (~(f10(c1) = f5(c1))),
% 29.52/19.72 inference(modus_ponens,[status(thm)],[75, 25764])).
% 29.52/19.72 tff(25766,plain,
% 29.52/19.72 ($false),
% 29.52/19.72 inference(unit_resolution,[status(thm)],[3907, 25765, 25756, 25717, 25700, 25711, 115])).
% 29.52/19.72 tff(25767,plain,(big_f(c1, c2) | (f7(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.52/19.72 tff(25768,plain,
% 29.52/19.72 (big_f(c1, c2)),
% 29.52/19.72 inference(unit_resolution,[status(thm)],[25767, 115])).
% 29.52/19.72 tff(25769,plain,
% 29.52/19.72 (~(c4 = c1)),
% 29.52/19.72 inference(unit_resolution,[status(thm)],[25548, 25768, 25303, 25678, 25365, 25702])).
% 29.52/19.72 tff(25770,plain,
% 29.52/19.72 (c4 = c2),
% 29.52/19.72 inference(unit_resolution,[status(thm)],[461, 25769])).
% 29.52/19.72 tff(25771,plain,
% 29.52/19.72 (c2 = c4),
% 29.52/19.72 inference(symmetry,[status(thm)],[25770])).
% 29.52/19.72 tff(25772,plain,
% 29.52/19.72 (f4(c2) = f4(c4)),
% 29.52/19.72 inference(monotonicity,[status(thm)],[25771])).
% 29.52/19.72 tff(25773,plain,
% 29.52/19.72 (f4(c4) = f4(c2)),
% 29.52/19.72 inference(symmetry,[status(thm)],[25772])).
% 29.52/19.72 tff(25774,plain,
% 29.52/19.72 (c1 = f4(c4)),
% 29.52/19.72 inference(symmetry,[status(thm)],[25702])).
% 29.52/19.72 tff(25775,plain,
% 29.52/19.72 (f4(c2) = c1),
% 29.52/19.72 inference(transitivity,[status(thm)],[25772, 25702])).
% 29.52/19.72 tff(25776,plain,
% 29.52/19.72 ((c2 = f4(c2)) <=> (c2 = c1)),
% 29.52/19.72 inference(monotonicity,[status(thm)],[25775])).
% 29.52/19.72 tff(25777,plain,
% 29.52/19.72 ((c2 = c1) <=> (c2 = f4(c2))),
% 29.52/19.72 inference(symmetry,[status(thm)],[25776])).
% 29.52/19.72 tff(25778,plain,
% 29.52/19.72 ((~(c2 = c1)) <=> (~(c2 = f4(c2)))),
% 29.52/19.72 inference(monotonicity,[status(thm)],[25777])).
% 29.52/19.72 tff(25779,plain,
% 29.52/19.72 (~(c2 = f4(c2))),
% 29.52/19.72 inference(modus_ponens,[status(thm)],[75, 25778])).
% 29.52/19.72 tff(25780,plain,
% 29.52/19.72 (c2 = c4),
% 29.52/19.72 inference(modus_ponens,[status(thm)],[25770, 159])).
% 29.52/19.72 tff(25781,plain,
% 29.52/19.72 (~(c1 = c3)),
% 29.52/19.72 inference(unit_resolution,[status(thm)],[25578, 25779, 25780, 25365, 25303, 25768])).
% 29.52/19.72 tff(25782,plain,
% 29.52/19.72 (~(c3 = c1)),
% 29.52/19.72 inference(unit_resolution,[status(thm)],[175, 25781])).
% 29.52/19.72 tff(25783,plain,
% 29.52/19.72 (c3 = c2),
% 29.52/19.72 inference(unit_resolution,[status(thm)],[180, 25782])).
% 29.52/19.72 tff(25784,plain,
% 29.52/19.72 (c2 = c3),
% 29.52/19.72 inference(modus_ponens,[status(thm)],[25783, 78])).
% 29.52/19.72 tff(25785,plain,
% 29.52/19.72 ((~(c2 = c3)) | (~(c2 = c4)) | (c2 = f4(c2)) | (c1 = f2(c2))),
% 29.52/19.72 inference(unit_resolution,[status(thm)],[25588, 1355, 25365, 25678])).
% 29.52/19.72 tff(25786,plain,
% 29.52/19.72 (c1 = f2(c2)),
% 29.52/19.72 inference(unit_resolution,[status(thm)],[25785, 25784, 25780, 25779])).
% 29.52/19.72 tff(25787,plain,
% 29.52/19.72 (f2(c2) = c1),
% 29.52/19.72 inference(symmetry,[status(thm)],[25786])).
% 29.52/19.72 tff(25788,plain,
% 29.52/19.72 (c2 = f2(c2)),
% 29.52/19.72 inference(unit_resolution,[status(thm)],[25592, 25784, 25780, 25779])).
% 29.52/19.72 tff(25789,plain,
% 29.52/19.72 (c2 = f4(c2)),
% 29.52/19.72 inference(transitivity,[status(thm)],[25788, 25787, 25774, 25773])).
% 29.52/19.72 tff(25790,plain,
% 29.52/19.72 ($false),
% 29.52/19.72 inference(unit_resolution,[status(thm)],[25779, 25789])).
% 29.52/19.72 tff(25791,plain,(f7(c1) = c1), inference(lemma,lemma(discharge,[]))).
% 29.52/19.72 tff(25792,plain,
% 29.52/19.72 (big_f(f7(c1), f6(c1, c2)) <=> big_f(c1, f6(c1, c2))),
% 29.52/19.72 inference(monotonicity,[status(thm)],[25791])).
% 29.52/19.72 tff(25793,plain,
% 29.52/19.72 (big_f(c1, f6(c1, c2)) <=> big_f(f7(c1), f6(c1, c2))),
% 29.52/19.72 inference(symmetry,[status(thm)],[25792])).
% 29.52/19.72 tff(25794,plain,
% 29.52/19.72 (big_f(c1, f6(c1, c2)) <=> big_f(c1, c1)),
% 29.52/19.72 inference(monotonicity,[status(thm)],[4262])).
% 29.52/19.72 tff(25795,plain,
% 29.52/19.72 (big_f(c1, c1) <=> big_f(c1, f6(c1, c2))),
% 29.52/19.72 inference(symmetry,[status(thm)],[25794])).
% 29.52/19.72 tff(25796,plain,
% 29.52/19.72 (big_f(c1, c1) <=> big_f(f7(c1), f6(c1, c2))),
% 29.52/19.72 inference(transitivity,[status(thm)],[25795, 25793])).
% 29.52/19.72 tff(25797,plain,
% 29.52/19.72 ((~big_f(c1, c1)) <=> (~big_f(f7(c1), f6(c1, c2)))),
% 29.52/19.72 inference(monotonicity,[status(thm)],[25796])).
% 29.52/19.72 tff(25798,plain,
% 29.52/19.72 (~big_f(f7(c1), f6(c1, c2))),
% 29.52/19.72 inference(modus_ponens,[status(thm)],[66, 25797])).
% 29.52/19.72 tff(25799,plain,
% 29.52/19.72 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2))),
% 29.52/19.72 inference(rewrite,[status(thm)],[])).
% 29.52/19.72 tff(25800,plain,
% 29.52/19.72 (((f10(c2) = c2) | big_f(c2, f10(c2)) | (~(f7(c1) = c1)) | (f6(c1, c2) = c2) | big_f(f7(c1), f6(c1, c2)) | (~(c2 = f8(c2)))) <=> ((f10(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2))),
% 29.52/19.72 inference(rewrite,[status(thm)],[])).
% 29.52/19.72 tff(25801,plain,
% 29.52/19.72 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | big_f(c2, f10(c2)) | (~(f7(c1) = c1)) | (f6(c1, c2) = c2) | big_f(f7(c1), f6(c1, c2)) | (~(c2 = f8(c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2)))),
% 29.52/19.72 inference(monotonicity,[status(thm)],[25800])).
% 29.52/19.72 tff(25802,plain,
% 29.52/19.72 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | big_f(c2, f10(c2)) | (~(f7(c1) = c1)) | (f6(c1, c2) = c2) | big_f(f7(c1), f6(c1, c2)) | (~(c2 = f8(c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2))),
% 29.52/19.72 inference(transitivity,[status(thm)],[25801, 25799])).
% 29.52/19.72 tff(25803,plain,
% 29.52/19.72 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | big_f(c2, f10(c2)) | (~(f7(c1) = c1)) | (f6(c1, c2) = c2) | big_f(f7(c1), f6(c1, c2)) | (~(c2 = f8(c2))))),
% 29.52/19.72 inference(quant_inst,[status(thm)],[])).
% 29.52/19.72 tff(25804,plain,
% 29.52/19.72 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2)),
% 29.52/19.72 inference(modus_ponens,[status(thm)],[25803, 25802])).
% 29.52/19.72 tff(25805,plain,
% 29.52/19.72 (~(c2 = f8(c2))),
% 29.52/19.72 inference(unit_resolution,[status(thm)],[25804, 2994, 25791, 89, 15517, 25798, 114])).
% 29.52/19.72 tff(25806,plain,
% 29.52/19.72 (~(f8(f7(f4(c4))) = c2)),
% 29.52/19.72 inference(modus_ponens,[status(thm)],[25805, 113])).
% 29.52/19.72 tff(25807,plain,
% 29.52/19.72 (f8(c2) = f8(f7(f4(c4)))),
% 29.52/19.72 inference(transitivity,[status(thm)],[110, 108])).
% 29.52/19.72 tff(25808,plain,
% 29.52/19.72 ((c1 = f8(c2)) <=> (c1 = f8(f7(f4(c4))))),
% 29.52/19.72 inference(monotonicity,[status(thm)],[25807])).
% 29.52/19.72 tff(25809,plain,
% 29.52/19.72 ((c1 = f8(c2)) <=> (f8(f7(f4(c4))) = c1)),
% 29.52/19.72 inference(transitivity,[status(thm)],[25808, 8517])).
% 29.52/19.72 tff(25810,plain,
% 29.52/19.72 ((~(c1 = f8(c2))) <=> (~(f8(f7(f4(c4))) = c1))),
% 29.52/19.72 inference(monotonicity,[status(thm)],[25809])).
% 29.52/19.72 tff(25811,plain,
% 29.52/19.72 (f10(c2) = f10(f7(f4(c4)))),
% 29.52/19.72 inference(transitivity,[status(thm)],[96, 12114])).
% 29.52/19.72 tff(25812,plain,
% 29.52/19.72 (big_f(c1, f10(c2)) <=> big_f(c1, f10(f7(f4(c4))))),
% 29.52/19.72 inference(monotonicity,[status(thm)],[25811])).
% 29.52/19.72 tff(25813,plain,
% 29.52/19.72 (big_f(c1, f10(f7(f4(c4)))) <=> big_f(c1, f10(c2))),
% 29.52/19.72 inference(symmetry,[status(thm)],[25812])).
% 29.52/19.72 tff(25814,plain,
% 29.52/19.72 (f10(f7(f4(c4))) = c1),
% 29.52/19.72 inference(transitivity,[status(thm)],[12113, 95, 94])).
% 29.52/19.72 tff(25815,plain,
% 29.52/19.72 (big_f(c1, f10(f7(f4(c4)))) <=> big_f(c1, c1)),
% 29.52/19.72 inference(monotonicity,[status(thm)],[25814])).
% 29.52/19.72 tff(25816,plain,
% 29.52/19.72 (big_f(c1, c1) <=> big_f(c1, f10(f7(f4(c4))))),
% 29.52/19.72 inference(symmetry,[status(thm)],[25815])).
% 29.52/19.72 tff(25817,plain,
% 29.52/19.72 (big_f(c1, c1) <=> big_f(c1, f10(c2))),
% 29.52/19.72 inference(transitivity,[status(thm)],[25816, 25813])).
% 29.52/19.72 tff(25818,plain,
% 29.52/19.72 ((~big_f(c1, c1)) <=> (~big_f(c1, f10(c2)))),
% 29.52/19.72 inference(monotonicity,[status(thm)],[25817])).
% 29.52/19.72 tff(25819,plain,
% 29.52/19.72 (~big_f(c1, f10(c2))),
% 29.52/19.72 inference(modus_ponens,[status(thm)],[66, 25818])).
% 29.52/19.72 tff(25820,plain,
% 29.52/19.72 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | big_f(c1, f10(c2)) | (~(c1 = f8(c2))) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | big_f(c1, f10(c2)) | (~(c1 = f8(c2))) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2))),
% 29.52/19.72 inference(rewrite,[status(thm)],[])).
% 29.52/19.72 tff(25821,plain,
% 29.52/19.72 (((f10(c2) = c2) | big_f(c1, f10(c2)) | (~(f7(c1) = c1)) | (f6(c1, c2) = c2) | big_f(f7(c1), f6(c1, c2)) | (~(c1 = f8(c2)))) <=> ((f10(c2) = c2) | big_f(c1, f10(c2)) | (~(c1 = f8(c2))) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2))),
% 29.52/19.72 inference(rewrite,[status(thm)],[])).
% 29.52/19.72 tff(25822,plain,
% 29.52/19.72 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | big_f(c1, f10(c2)) | (~(f7(c1) = c1)) | (f6(c1, c2) = c2) | big_f(f7(c1), f6(c1, c2)) | (~(c1 = f8(c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | big_f(c1, f10(c2)) | (~(c1 = f8(c2))) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2)))),
% 29.52/19.72 inference(monotonicity,[status(thm)],[25821])).
% 29.52/19.72 tff(25823,plain,
% 29.52/19.72 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | big_f(c1, f10(c2)) | (~(f7(c1) = c1)) | (f6(c1, c2) = c2) | big_f(f7(c1), f6(c1, c2)) | (~(c1 = f8(c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | big_f(c1, f10(c2)) | (~(c1 = f8(c2))) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2))),
% 29.52/19.72 inference(transitivity,[status(thm)],[25822, 25820])).
% 29.52/19.72 tff(25824,plain,
% 29.52/19.72 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | big_f(c1, f10(c2)) | (~(f7(c1) = c1)) | (f6(c1, c2) = c2) | big_f(f7(c1), f6(c1, c2)) | (~(c1 = f8(c2))))),
% 29.52/19.72 inference(quant_inst,[status(thm)],[])).
% 29.52/19.72 tff(25825,plain,
% 29.52/19.72 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | big_f(c1, f10(c2)) | (~(c1 = f8(c2))) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2)),
% 29.52/19.72 inference(modus_ponens,[status(thm)],[25824, 25823])).
% 29.52/19.72 tff(25826,plain,
% 29.52/19.72 (~(c1 = f8(c2))),
% 29.52/19.72 inference(unit_resolution,[status(thm)],[25825, 2994, 25791, 89, 25798, 114, 25819])).
% 29.52/19.72 tff(25827,plain,
% 29.52/19.72 (~(f8(f7(f4(c4))) = c1)),
% 29.52/19.72 inference(modus_ponens,[status(thm)],[25826, 25810])).
% 29.52/19.72 tff(25828,plain,
% 29.52/19.72 ($false),
% 29.52/19.72 inference(unit_resolution,[status(thm)],[13371, 25827, 25806])).
% 29.52/19.72 tff(25829,plain,((f6(c1, c2) = c2) | (~(f4(c4) = c2)) | (~(f7(c2) = c2)) | (f10(c2) = c2) | big_f(c2, f10(c2)) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 29.52/19.72 tff(25830,plain,
% 29.52/19.72 (f6(c1, c2) = c2),
% 29.52/19.72 inference(unit_resolution,[status(thm)],[25829, 89, 77, 79, 104, 66])).
% 29.52/19.72 tff(25831,plain,
% 29.52/19.72 (f10(f6(c1, c2)) = f10(c2)),
% 29.52/19.72 inference(monotonicity,[status(thm)],[25830])).
% 29.52/19.72 tff(25832,plain,
% 29.52/19.72 (f10(f6(c1, c2)) = c1),
% 29.52/19.72 inference(transitivity,[status(thm)],[25831, 94])).
% 29.52/19.72 tff(25833,plain,
% 29.52/19.72 (big_f(c1, f10(f6(c1, c2))) <=> big_f(c1, c1)),
% 29.52/19.72 inference(monotonicity,[status(thm)],[25832])).
% 29.52/19.72 tff(25834,plain,
% 29.52/19.72 (big_f(c1, c1) <=> big_f(c1, f10(f6(c1, c2)))),
% 29.52/19.72 inference(symmetry,[status(thm)],[25833])).
% 29.52/19.72 tff(25835,plain,
% 29.52/19.72 ((~big_f(c1, c1)) <=> (~big_f(c1, f10(f6(c1, c2))))),
% 29.52/19.72 inference(monotonicity,[status(thm)],[25834])).
% 29.52/19.72 tff(25836,plain,
% 29.52/19.72 (~big_f(c1, f10(f6(c1, c2)))),
% 29.52/19.72 inference(modus_ponens,[status(thm)],[66, 25835])).
% 29.52/19.72 tff(25837,plain,
% 29.52/19.72 (f8(f6(c1, c2)) = f8(c2)),
% 29.52/19.72 inference(monotonicity,[status(thm)],[36])).
% 29.52/19.72 tff(25838,plain,
% 29.52/19.72 (f8(f6(c1, c2)) = f8(f7(f4(c4)))),
% 29.52/19.72 inference(transitivity,[status(thm)],[25837, 110, 108])).
% 29.52/19.72 tff(25839,plain,
% 29.52/19.72 ((c1 = f8(f6(c1, c2))) <=> (c1 = f8(f7(f4(c4))))),
% 29.52/19.72 inference(monotonicity,[status(thm)],[25838])).
% 29.52/19.72 tff(25840,plain,
% 29.52/19.72 ((c1 = f8(f6(c1, c2))) <=> (f8(f7(f4(c4))) = c1)),
% 29.52/19.72 inference(transitivity,[status(thm)],[25839, 8517])).
% 29.52/19.72 tff(25841,plain,
% 29.52/19.72 ((~(c1 = f8(f6(c1, c2)))) <=> (~(f8(f7(f4(c4))) = c1))),
% 29.52/19.72 inference(monotonicity,[status(thm)],[25840])).
% 29.52/19.72 tff(25842,plain,
% 29.52/19.72 (f10(f6(c1, c2)) = f10(c2)),
% 29.52/19.72 inference(monotonicity,[status(thm)],[36])).
% 29.52/19.72 tff(25843,plain,
% 29.52/19.72 (f10(f6(c1, c2)) = c1),
% 29.52/19.72 inference(transitivity,[status(thm)],[25842, 94])).
% 29.52/19.72 tff(25844,plain,
% 29.52/19.72 ((f10(f6(c1, c2)) = f6(c1, c2)) <=> (c1 = c2)),
% 29.52/19.72 inference(monotonicity,[status(thm)],[25843, 36])).
% 29.52/19.72 tff(25845,plain,
% 29.52/19.72 ((f10(f6(c1, c2)) = f6(c1, c2)) <=> (c2 = c1)),
% 29.52/19.72 inference(transitivity,[status(thm)],[25844, 1])).
% 29.52/19.72 tff(25846,plain,
% 29.52/19.72 ((c2 = c1) <=> (f10(f6(c1, c2)) = f6(c1, c2))),
% 29.52/19.72 inference(symmetry,[status(thm)],[25845])).
% 29.52/19.72 tff(25847,plain,
% 29.52/19.72 ((~(c2 = c1)) <=> (~(f10(f6(c1, c2)) = f6(c1, c2)))),
% 29.52/19.72 inference(monotonicity,[status(thm)],[25846])).
% 29.52/19.72 tff(25848,plain,
% 29.52/19.72 (~(f10(f6(c1, c2)) = f6(c1, c2))),
% 29.52/19.72 inference(modus_ponens,[status(thm)],[75, 25847])).
% 29.52/19.72 tff(25849,plain,
% 29.52/19.72 (f6(c1, f6(c1, c2)) = f6(c1, c2)),
% 29.52/19.72 inference(unit_resolution,[status(thm)],[43, 36])).
% 29.52/19.72 tff(25850,assumption,(~big_f(c1, f10(f6(c1, c2)))), introduced(assumption)).
% 29.52/19.72 tff(25851,plain,
% 29.52/19.72 (big_f(f7(c1), f6(c1, f6(c1, c2))) <=> big_f(c1, c2)),
% 29.52/19.72 inference(monotonicity,[status(thm)],[25791, 40])).
% 29.52/19.73 tff(25852,plain,
% 29.52/19.73 (big_f(c1, c2) <=> big_f(f7(c1), f6(c1, f6(c1, c2)))),
% 29.52/19.73 inference(symmetry,[status(thm)],[25851])).
% 29.52/19.73 tff(25853,plain,
% 29.52/19.73 (big_f(f7(c1), f6(c1, f6(c1, c2)))),
% 29.52/19.73 inference(modus_ponens,[status(thm)],[2865, 25852])).
% 29.52/19.73 tff(25854,plain,
% 29.52/19.73 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (big_f(c1, f10(f6(c1, c2))) | (~(f7(c1) = c1)) | (f10(f6(c1, c2)) = f6(c1, c2)) | (~(c1 = f8(f6(c1, c2)))) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | big_f(c1, f10(f6(c1, c2))) | (~(f7(c1) = c1)) | (f10(f6(c1, c2)) = f6(c1, c2)) | (~(c1 = f8(f6(c1, c2)))) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))),
% 29.52/19.73 inference(rewrite,[status(thm)],[])).
% 29.52/19.73 tff(25855,plain,
% 29.52/19.73 (((f10(f6(c1, c2)) = f6(c1, c2)) | big_f(c1, f10(f6(c1, c2))) | (~(f7(c1) = c1)) | (~(c1 = f8(f6(c1, c2)))) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2))))) <=> (big_f(c1, f10(f6(c1, c2))) | (~(f7(c1) = c1)) | (f10(f6(c1, c2)) = f6(c1, c2)) | (~(c1 = f8(f6(c1, c2)))) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))),
% 29.52/19.73 inference(rewrite,[status(thm)],[])).
% 29.52/19.73 tff(25856,plain,
% 29.52/19.73 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f6(c1, c2)) = f6(c1, c2)) | big_f(c1, f10(f6(c1, c2))) | (~(f7(c1) = c1)) | (~(c1 = f8(f6(c1, c2)))) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (big_f(c1, f10(f6(c1, c2))) | (~(f7(c1) = c1)) | (f10(f6(c1, c2)) = f6(c1, c2)) | (~(c1 = f8(f6(c1, c2)))) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2))))))),
% 29.52/19.73 inference(monotonicity,[status(thm)],[25855])).
% 29.52/19.73 tff(25857,plain,
% 29.52/19.73 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f6(c1, c2)) = f6(c1, c2)) | big_f(c1, f10(f6(c1, c2))) | (~(f7(c1) = c1)) | (~(c1 = f8(f6(c1, c2)))) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | big_f(c1, f10(f6(c1, c2))) | (~(f7(c1) = c1)) | (f10(f6(c1, c2)) = f6(c1, c2)) | (~(c1 = f8(f6(c1, c2)))) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))),
% 29.52/19.73 inference(transitivity,[status(thm)],[25856, 25854])).
% 29.52/19.73 tff(25858,plain,
% 29.52/19.73 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f6(c1, c2)) = f6(c1, c2)) | big_f(c1, f10(f6(c1, c2))) | (~(f7(c1) = c1)) | (~(c1 = f8(f6(c1, c2)))) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))),
% 29.52/19.73 inference(quant_inst,[status(thm)],[])).
% 29.52/19.73 tff(25859,plain,
% 29.52/19.73 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | big_f(c1, f10(f6(c1, c2))) | (~(f7(c1) = c1)) | (f10(f6(c1, c2)) = f6(c1, c2)) | (~(c1 = f8(f6(c1, c2)))) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2))))),
% 29.52/19.73 inference(modus_ponens,[status(thm)],[25858, 25857])).
% 29.52/19.73 tff(25860,plain,
% 29.52/19.73 (big_f(c1, f10(f6(c1, c2))) | (~(f7(c1) = c1)) | (f10(f6(c1, c2)) = f6(c1, c2)) | (~(c1 = f8(f6(c1, c2)))) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2))))),
% 29.52/19.73 inference(unit_resolution,[status(thm)],[25859, 2963])).
% 29.52/19.73 tff(25861,plain,
% 29.52/19.73 (big_f(c1, f10(f6(c1, c2))) | (f10(f6(c1, c2)) = f6(c1, c2)) | (~(c1 = f8(f6(c1, c2)))) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2))))),
% 29.52/19.73 inference(unit_resolution,[status(thm)],[25860, 25791])).
% 29.52/19.73 tff(25862,plain,
% 29.52/19.73 (~(c1 = f8(f6(c1, c2)))),
% 29.52/19.73 inference(unit_resolution,[status(thm)],[25861, 25853, 25850, 25849, 25848])).
% 29.52/19.73 tff(25863,plain,
% 29.52/19.73 (~(f8(f7(f4(c4))) = c1)),
% 29.52/19.73 inference(modus_ponens,[status(thm)],[25862, 25841])).
% 29.52/19.73 tff(25864,plain,
% 29.52/19.73 (big_f(c1, c2) <=> big_f(f7(c1), f6(c1, c2))),
% 29.52/19.73 inference(transitivity,[status(thm)],[11066, 25793])).
% 29.52/19.73 tff(25865,plain,
% 29.52/19.73 (big_f(f7(c1), f6(c1, c2))),
% 29.52/19.73 inference(modus_ponens,[status(thm)],[2865, 25864])).
% 29.52/19.73 tff(25866,plain,
% 29.52/19.73 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)))),
% 29.52/19.73 inference(rewrite,[status(thm)],[])).
% 29.52/19.73 tff(25867,plain,
% 29.52/19.73 (((f10(c2) = c2) | big_f(c2, f10(c2)) | (~(f7(c1) = c1)) | (~(c2 = f8(c2))) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2)))) <=> ((f10(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)))),
% 29.52/19.73 inference(rewrite,[status(thm)],[])).
% 29.52/19.73 tff(25868,plain,
% 29.52/19.73 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | big_f(c2, f10(c2)) | (~(f7(c1) = c1)) | (~(c2 = f8(c2))) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2))))),
% 29.52/19.73 inference(monotonicity,[status(thm)],[25867])).
% 29.52/19.73 tff(25869,plain,
% 29.52/19.73 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | big_f(c2, f10(c2)) | (~(f7(c1) = c1)) | (~(c2 = f8(c2))) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)))),
% 29.52/19.73 inference(transitivity,[status(thm)],[25868, 25866])).
% 29.52/19.73 tff(25870,plain,
% 29.52/19.73 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | big_f(c2, f10(c2)) | (~(f7(c1) = c1)) | (~(c2 = f8(c2))) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2))))),
% 29.52/19.73 inference(quant_inst,[status(thm)],[])).
% 29.52/19.73 tff(25871,plain,
% 29.52/19.73 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2))),
% 29.52/19.73 inference(modus_ponens,[status(thm)],[25870, 25869])).
% 29.52/19.73 tff(25872,plain,
% 29.52/19.73 ((~(c2 = f8(c2))) | (~big_f(f7(c1), f6(c1, c2)))),
% 29.52/19.73 inference(unit_resolution,[status(thm)],[25871, 2963, 25791, 89, 15517, 36])).
% 29.52/19.73 tff(25873,plain,
% 29.52/19.73 (~(c2 = f8(c2))),
% 29.52/19.73 inference(unit_resolution,[status(thm)],[25872, 25865])).
% 29.52/19.73 tff(25874,plain,
% 29.52/19.73 (~(f8(f7(f4(c4))) = c2)),
% 29.52/19.73 inference(modus_ponens,[status(thm)],[25873, 113])).
% 29.52/19.73 tff(25875,plain,
% 29.52/19.73 ($false),
% 29.52/19.73 inference(unit_resolution,[status(thm)],[13371, 25874, 25863])).
% 29.52/19.73 tff(25876,plain,((~big_f(c1, c2)) | (~(f4(c4) = c2)) | (~(f7(c2) = c2)) | (~(f6(c1, c2) = c2)) | (f10(c2) = c2) | big_f(c2, f10(c2)) | big_f(c1, f10(f6(c1, c2)))), inference(lemma,lemma(discharge,[]))).
% 29.52/19.73 tff(25877,plain,
% 29.52/19.73 (~big_f(c1, c2)),
% 29.52/19.73 inference(unit_resolution,[status(thm)],[25876, 25830, 77, 79, 89, 104, 25836])).
% 29.52/19.73 tff(25878,plain,
% 29.52/19.73 (big_f(c2, c2)),
% 29.52/19.73 inference(unit_resolution,[status(thm)],[24323, 25877, 2, 66])).
% 29.52/19.73 tff(25879,plain,
% 29.52/19.73 (f8(f7(c2)) = f8(c2)),
% 29.52/19.73 inference(symmetry,[status(thm)],[110])).
% 29.52/19.73 tff(25880,plain,
% 29.52/19.73 (f8(f7(f4(c4))) = f8(c2)),
% 29.52/19.73 inference(transitivity,[status(thm)],[15256, 25879])).
% 29.52/19.73 tff(25881,plain,
% 29.52/19.73 (big_f(f8(f7(f4(c4))), f10(c2)) <=> big_f(f8(f7(f4(c4))), f10(f7(f4(c4))))),
% 29.52/19.73 inference(monotonicity,[status(thm)],[25811])).
% 29.52/19.73 tff(25882,plain,
% 29.52/19.73 (big_f(f8(f7(f4(c4))), f10(f7(f4(c4)))) <=> big_f(f8(f7(f4(c4))), f10(c2))),
% 29.52/19.73 inference(symmetry,[status(thm)],[25881])).
% 29.52/19.73 tff(25883,plain,
% 29.52/19.73 (big_f(f8(f7(f4(c4))), f10(f7(f4(c4)))) <=> big_f(c1, c1)),
% 29.52/19.73 inference(monotonicity,[status(thm)],[16268, 25814])).
% 29.52/19.73 tff(25884,plain,
% 29.52/19.73 (big_f(c1, c1) <=> big_f(f8(f7(f4(c4))), f10(f7(f4(c4))))),
% 29.52/19.73 inference(symmetry,[status(thm)],[25883])).
% 29.52/19.73 tff(25885,plain,
% 29.52/19.73 (big_f(c1, c1) <=> big_f(f8(f7(f4(c4))), f10(c2))),
% 29.52/19.73 inference(transitivity,[status(thm)],[25884, 25882])).
% 29.52/19.73 tff(25886,plain,
% 29.52/19.73 ((~big_f(c1, c1)) <=> (~big_f(f8(f7(f4(c4))), f10(c2)))),
% 29.52/19.73 inference(monotonicity,[status(thm)],[25885])).
% 29.52/19.73 tff(25887,plain,
% 29.52/19.73 (~big_f(f8(f7(f4(c4))), f10(c2))),
% 29.52/19.73 inference(modus_ponens,[status(thm)],[66, 25886])).
% 29.52/19.73 tff(25888,plain,
% 29.52/19.73 (~(f6(c2, c2) = c2)),
% 29.52/19.73 inference(unit_resolution,[status(thm)],[24216, 25887, 77, 89, 25880, 25878])).
% 29.52/19.73 tff(25889,plain,
% 29.52/19.73 (~(f6(c2, f7(f4(c4))) = c2)),
% 29.52/19.73 inference(modus_ponens,[status(thm)],[25888, 88])).
% 29.52/19.73 tff(25890,plain,
% 29.52/19.73 (f6(c2, f7(f4(c4))) = c1),
% 29.52/19.73 inference(unit_resolution,[status(thm)],[6601, 25889])).
% 29.52/19.73 tff(25891,plain,
% 29.52/19.73 (f6(c2, c2) = c1),
% 29.52/19.73 inference(transitivity,[status(thm)],[84, 25890])).
% 29.52/19.73 tff(25892,plain,
% 29.52/19.73 (big_f(f7(c2), f6(c2, c2)) <=> big_f(c2, c1)),
% 29.52/19.73 inference(monotonicity,[status(thm)],[77, 25891])).
% 29.52/19.73 tff(25893,plain,
% 29.52/19.73 (big_f(c2, c1) <=> big_f(f7(c2), f6(c2, c2))),
% 29.52/19.73 inference(symmetry,[status(thm)],[25892])).
% 29.52/19.73 tff(25894,plain,
% 29.52/19.73 ((~big_f(c2, c1)) <=> (~big_f(f7(c2), f6(c2, c2)))),
% 29.52/19.73 inference(monotonicity,[status(thm)],[25893])).
% 29.52/19.73 tff(25895,plain,
% 29.52/19.73 (~big_f(f7(c2), f6(c2, c2))),
% 29.52/19.73 inference(modus_ponens,[status(thm)],[2, 25894])).
% 29.52/19.73 tff(25896,plain,
% 29.52/19.73 (f8(c2) = f8(f7(f4(c4)))),
% 29.52/19.73 inference(transitivity,[status(thm)],[110, 8536])).
% 29.52/19.73 tff(25897,plain,
% 29.52/19.73 ((c1 = f8(c2)) <=> (c1 = f8(f7(f4(c4))))),
% 29.52/19.73 inference(monotonicity,[status(thm)],[25896])).
% 29.52/19.73 tff(25898,plain,
% 29.52/19.73 ((c1 = f8(c2)) <=> (f8(f7(f4(c4))) = c1)),
% 29.52/19.73 inference(transitivity,[status(thm)],[25897, 8517])).
% 29.52/19.73 tff(25899,plain,
% 29.52/19.73 ((f8(f7(f4(c4))) = c1) <=> (c1 = f8(c2))),
% 29.52/19.73 inference(symmetry,[status(thm)],[25898])).
% 29.52/19.73 tff(25900,plain,
% 29.52/19.73 (c1 = f8(c2)),
% 29.52/19.73 inference(modus_ponens,[status(thm)],[16268, 25899])).
% 29.52/19.73 tff(25901,plain,
% 29.52/19.73 (big_f(f7(c2), f6(c2, c2))),
% 29.52/19.73 inference(unit_resolution,[status(thm)],[24107, 2994, 89, 77, 25888, 25819, 25900])).
% 29.52/19.73 tff(25902,plain,
% 29.52/19.73 ($false),
% 29.52/19.73 inference(unit_resolution,[status(thm)],[25901, 25895])).
% 29.52/19.73 tff(25903,plain,((~(f8(f7(f4(c4))) = c1)) | big_f(c2, c1) | (~(f7(c2) = c2)) | (~(f4(c4) = c2)) | (f10(c2) = c2) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 29.52/19.73 tff(25904,plain,
% 29.52/19.73 (~(f8(f7(f4(c4))) = c1)),
% 29.52/19.73 inference(unit_resolution,[status(thm)],[25903, 89, 77, 79, 2, 66])).
% 29.52/19.73 tff(25905,plain,
% 29.52/19.73 (f8(f7(f4(c4))) = c2),
% 29.52/19.73 inference(unit_resolution,[status(thm)],[13371, 25904])).
% 29.52/19.73 tff(25906,plain,
% 29.52/19.73 (big_f(f8(f7(f4(c4))), f10(f7(f4(c4)))) <=> big_f(c2, c1)),
% 29.52/19.73 inference(monotonicity,[status(thm)],[25905, 25814])).
% 29.52/19.73 tff(25907,plain,
% 29.52/19.73 (big_f(c2, c1) <=> big_f(f8(f7(f4(c4))), f10(f7(f4(c4))))),
% 29.52/19.73 inference(symmetry,[status(thm)],[25906])).
% 29.52/19.73 tff(25908,plain,
% 29.52/19.73 (big_f(c2, c1) <=> big_f(f8(f7(f4(c4))), f10(c2))),
% 29.52/19.73 inference(transitivity,[status(thm)],[25907, 25882])).
% 29.52/19.73 tff(25909,plain,
% 29.52/19.73 ((~big_f(c2, c1)) <=> (~big_f(f8(f7(f4(c4))), f10(c2)))),
% 29.52/19.73 inference(monotonicity,[status(thm)],[25908])).
% 29.52/19.73 tff(25910,plain,
% 29.52/19.73 (~big_f(f8(f7(f4(c4))), f10(c2))),
% 29.52/19.73 inference(modus_ponens,[status(thm)],[2, 25909])).
% 29.52/19.73 tff(25911,plain,
% 29.52/19.73 (~(f6(c2, c2) = c2)),
% 29.52/19.73 inference(unit_resolution,[status(thm)],[24216, 25910, 77, 89, 25880, 25878])).
% 29.52/19.73 tff(25912,plain,
% 29.52/19.73 (~(f6(c2, f7(f4(c4))) = c2)),
% 29.52/19.73 inference(modus_ponens,[status(thm)],[25911, 88])).
% 29.52/19.73 tff(25913,plain,
% 29.52/19.73 (f6(c2, f7(f4(c4))) = c1),
% 29.52/19.73 inference(unit_resolution,[status(thm)],[6601, 25912])).
% 29.52/19.73 tff(25914,plain,
% 29.52/19.73 (f6(c2, c2) = c1),
% 29.52/19.73 inference(transitivity,[status(thm)],[84, 25913])).
% 29.52/19.73 tff(25915,plain,
% 29.52/19.73 (big_f(f7(c2), f6(c2, c2)) <=> big_f(c2, c1)),
% 29.52/19.73 inference(monotonicity,[status(thm)],[77, 25914])).
% 29.52/19.73 tff(25916,plain,
% 29.52/19.73 (big_f(c2, c1) <=> big_f(f7(c2), f6(c2, c2))),
% 29.52/19.73 inference(symmetry,[status(thm)],[25915])).
% 29.52/19.73 tff(25917,plain,
% 29.52/19.73 ((~big_f(c2, c1)) <=> (~big_f(f7(c2), f6(c2, c2)))),
% 29.52/19.73 inference(monotonicity,[status(thm)],[25916])).
% 29.52/19.73 tff(25918,plain,
% 29.52/19.73 (~big_f(f7(c2), f6(c2, c2))),
% 29.52/19.73 inference(modus_ponens,[status(thm)],[2, 25917])).
% 29.52/19.73 tff(25919,plain,
% 29.52/19.73 ((c2 = f8(f7(c2))) <=> (c2 = f8(c2))),
% 29.52/19.73 inference(symmetry,[status(thm)],[111])).
% 29.52/19.73 tff(25920,plain,
% 29.52/19.73 ((c2 = f8(f7(f4(c4)))) <=> (c2 = f8(f7(c2)))),
% 29.52/19.73 inference(symmetry,[status(thm)],[8537])).
% 29.52/19.73 tff(25921,plain,
% 29.52/19.73 ((f8(f7(f4(c4))) = c2) <=> (c2 = f8(c2))),
% 29.52/19.73 inference(transitivity,[status(thm)],[105, 25920, 25919])).
% 29.52/19.73 tff(25922,plain,
% 29.52/19.73 (c2 = f8(c2)),
% 29.52/19.73 inference(modus_ponens,[status(thm)],[25905, 25921])).
% 29.52/19.73 tff(25923,plain,
% 29.52/19.73 (big_f(f7(c2), f6(c2, c2))),
% 29.52/19.73 inference(unit_resolution,[status(thm)],[14124, 2994, 89, 77, 104, 25922, 25911])).
% 29.52/19.73 tff(25924,plain,
% 29.52/19.73 ($false),
% 29.52/19.73 inference(unit_resolution,[status(thm)],[25923, 25918])).
% 29.52/19.73 tff(25925,plain,((f10(c2) = c2) | big_f(c2, c1) | (~(f7(c2) = c2)) | (~(f4(c4) = c2)) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 29.52/19.73 tff(25926,plain,
% 29.52/19.73 (f10(c2) = c2),
% 29.52/19.73 inference(unit_resolution,[status(thm)],[25925, 2, 77, 79, 66])).
% 29.52/19.73 tff(25927,plain,
% 29.52/19.73 (big_f(f9(c2, c2), f10(c2)) <=> big_f(f9(c2, c2), c2)),
% 29.52/19.73 inference(monotonicity,[status(thm)],[25926])).
% 29.52/19.73 tff(25928,plain,
% 29.52/19.73 (big_f(f9(c2, c2), c2) <=> big_f(f9(c2, c2), f10(c2))),
% 29.52/19.73 inference(symmetry,[status(thm)],[25927])).
% 29.52/19.73 tff(25929,plain,
% 29.52/19.73 (f9(f10(c2), f4(c4)) = c2),
% 29.52/19.73 inference(unit_resolution,[status(thm)],[8065, 25926, 79])).
% 29.52/19.73 tff(25930,plain,
% 29.52/19.73 (f9(c2, c2) = c2),
% 29.52/19.73 inference(unit_resolution,[status(thm)],[1606, 25926, 79, 25929])).
% 29.52/19.73 tff(25931,plain,
% 29.52/19.73 (big_f(f9(c2, c2), c2) <=> big_f(c2, c2)),
% 29.52/19.73 inference(monotonicity,[status(thm)],[25930])).
% 29.52/19.73 tff(25932,plain,
% 29.52/19.73 (big_f(c2, c2) <=> big_f(f9(c2, c2), c2)),
% 29.52/19.73 inference(symmetry,[status(thm)],[25931])).
% 29.52/19.73 tff(25933,plain,
% 29.52/19.73 (big_f(c2, c2) <=> big_f(f9(c2, c2), f10(c2))),
% 29.52/19.73 inference(transitivity,[status(thm)],[25932, 25928])).
% 29.52/19.73 tff(25934,plain,
% 29.52/19.73 (big_f(c2, c2)),
% 29.52/19.73 inference(unit_resolution,[status(thm)],[11331, 25926, 79, 2])).
% 29.52/19.73 tff(25935,plain,
% 29.52/19.73 (big_f(f9(c2, c2), f10(c2))),
% 29.52/19.73 inference(modus_ponens,[status(thm)],[25934, 25933])).
% 29.52/19.73 tff(25936,plain,
% 29.52/19.73 ((~(f6(c2, c2) = c2)) <=> (~(f6(c2, f7(f4(c4))) = c2))),
% 29.52/19.73 inference(monotonicity,[status(thm)],[24115])).
% 29.52/19.73 tff(25937,plain,
% 29.52/19.73 (~(f6(c2, f7(f4(c4))) = c2)),
% 29.52/19.73 inference(modus_ponens,[status(thm)],[2637, 25936])).
% 29.52/19.73 tff(25938,plain,
% 29.52/19.73 (f6(c2, f7(f4(c4))) = c1),
% 29.52/19.73 inference(unit_resolution,[status(thm)],[6601, 25937])).
% 29.52/19.73 tff(25939,plain,
% 29.52/19.73 (c1 = f6(c2, f7(f4(c4)))),
% 29.52/19.73 inference(symmetry,[status(thm)],[25938])).
% 29.52/19.73 tff(25940,plain,
% 29.52/19.73 (c1 = f6(c2, c2)),
% 29.52/19.73 inference(transitivity,[status(thm)],[25939, 2475])).
% 29.52/19.73 tff(25941,plain,
% 29.52/19.73 (big_f(c2, c1) <=> big_f(f7(c2), f6(c2, c2))),
% 29.52/19.73 inference(monotonicity,[status(thm)],[82, 25940])).
% 29.52/19.73 tff(25942,plain,
% 29.52/19.73 (big_f(f7(c2), f6(c2, c2)) <=> big_f(c2, c1)),
% 29.52/19.73 inference(symmetry,[status(thm)],[25941])).
% 29.52/19.73 tff(25943,plain,
% 29.52/19.73 (big_f(c2, c2)),
% 29.52/19.73 inference(unit_resolution,[status(thm)],[11331, 122, 79, 2])).
% 29.52/19.73 tff(25944,plain,
% 29.52/19.73 (big_f(f7(c2), f6(c2, c2))),
% 29.52/19.73 inference(unit_resolution,[status(thm)],[2639, 2637, 79, 77, 25943, 8066, 122])).
% 29.52/19.73 tff(25945,plain,
% 29.52/19.73 (big_f(c2, c1)),
% 29.52/19.73 inference(modus_ponens,[status(thm)],[25944, 25942])).
% 29.52/19.73 tff(25946,plain,
% 29.52/19.73 ($false),
% 29.52/19.73 inference(unit_resolution,[status(thm)],[2, 25945])).
% 29.52/19.73 tff(25947,plain,((f6(c2, c2) = c2) | big_f(c2, c1) | (~(f7(c2) = c2)) | (~(f4(c4) = c2)) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.52/19.73 tff(25948,plain,
% 29.52/19.73 (f6(c2, c2) = c2),
% 29.52/19.73 inference(unit_resolution,[status(thm)],[25947, 2, 77, 79, 25926])).
% 29.52/19.73 tff(25949,plain,
% 29.52/19.73 (big_f(f7(c2), f6(c2, c2))),
% 29.52/19.73 inference(unit_resolution,[status(thm)],[2627, 25948, 77, 25934])).
% 29.52/19.73 tff(25950,plain,
% 29.52/19.73 ($false),
% 29.52/19.73 inference(unit_resolution,[status(thm)],[2384, 2378, 25926, 77, 25948, 25949, 25930, 25935])).
% 29.52/19.73 tff(25951,plain,(big_f(c2, c1) | (~(f7(c2) = c2)) | (~(f4(c4) = c2)) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 29.52/19.73 tff(25952,plain,
% 29.52/19.73 (big_f(c2, c1)),
% 29.52/19.73 inference(unit_resolution,[status(thm)],[25951, 77, 79, 66])).
% 29.52/19.73 tff(25953,plain,
% 29.52/19.73 (~(f10(c1) = c1)),
% 29.52/19.73 inference(unit_resolution,[status(thm)],[23456, 121, 66, 77, 348])).
% 29.52/19.73 tff(25954,plain,
% 29.52/19.73 (f10(c1) = c2),
% 29.52/19.73 inference(unit_resolution,[status(thm)],[14, 25953])).
% 29.52/19.73 tff(25955,plain,
% 29.52/19.73 (big_f(c1, f10(c1)) <=> big_f(c1, c2)),
% 29.52/19.73 inference(monotonicity,[status(thm)],[25954])).
% 29.52/19.73 tff(25956,plain,
% 29.52/19.73 (big_f(c1, c2) <=> big_f(c1, f10(c1))),
% 29.52/19.73 inference(symmetry,[status(thm)],[25955])).
% 29.52/19.73 tff(25957,plain,
% 29.52/19.73 ((~big_f(c1, c2)) <=> (~big_f(c1, f10(c1)))),
% 29.52/19.73 inference(monotonicity,[status(thm)],[25956])).
% 29.52/19.73 tff(25958,plain,
% 29.52/19.73 (~big_f(c1, f10(c1))),
% 29.52/19.73 inference(modus_ponens,[status(thm)],[27, 25957])).
% 29.52/19.73 tff(25959,plain,
% 29.52/19.73 (f6(f10(c1), c1) = f6(c2, c1)),
% 29.52/19.73 inference(monotonicity,[status(thm)],[15])).
% 29.52/19.73 tff(25960,plain,
% 29.52/19.73 (f7(f10(c1)) = c2),
% 29.52/19.73 inference(transitivity,[status(thm)],[219, 77])).
% 29.52/19.73 tff(25961,plain,
% 29.52/19.73 (big_f(f7(f10(c1)), f6(f10(c1), c1)) <=> big_f(c2, f6(c2, c1))),
% 29.52/19.73 inference(monotonicity,[status(thm)],[25960, 25959])).
% 29.52/19.73 tff(25962,plain,
% 29.52/19.73 (big_f(f7(f10(c1)), f6(f10(c1), c1)) <=> big_f(f7(c2), f6(c2, c1))),
% 29.52/19.73 inference(transitivity,[status(thm)],[25961, 13581])).
% 29.52/19.73 tff(25963,plain,
% 29.52/19.73 ((f6(f10(c1), c1) = c1) <=> (f6(c2, c1) = c1)),
% 29.52/19.73 inference(monotonicity,[status(thm)],[25959])).
% 29.52/19.73 tff(25964,plain,
% 29.52/19.73 ((f6(c2, c1) = c1) <=> (f6(f10(c1), c1) = c1)),
% 29.52/19.73 inference(symmetry,[status(thm)],[25963])).
% 29.52/19.73 tff(25965,plain,
% 29.52/19.73 ((~(f6(c2, c1) = c1)) <=> (~(f6(f10(c1), c1) = c1))),
% 29.52/19.73 inference(monotonicity,[status(thm)],[25964])).
% 29.52/19.73 tff(25966,plain,
% 29.52/19.73 (~(f6(f10(c1), c1) = c1)),
% 29.52/19.73 inference(modus_ponens,[status(thm)],[3198, 25965])).
% 29.52/19.73 tff(25967,plain,
% 29.52/19.73 (f7(f10(c1)) = f10(c1)),
% 29.52/19.73 inference(modus_ponens,[status(thm)],[77, 221])).
% 29.52/19.73 tff(25968,plain,
% 29.52/19.73 (~(c2 = f8(c1))),
% 29.52/19.73 inference(unit_resolution,[status(thm)],[3001, 3197, 3, 3198, 2946, 77])).
% 29.52/19.73 tff(25969,plain,
% 29.52/19.73 (~(f8(c1) = c2)),
% 29.52/19.73 inference(unit_resolution,[status(thm)],[1675, 25968])).
% 29.52/19.73 tff(25970,plain,
% 29.52/19.73 (f8(c1) = c1),
% 29.52/19.73 inference(unit_resolution,[status(thm)],[1680, 25969])).
% 29.52/19.73 tff(25971,plain,
% 29.52/19.73 (c1 = f8(c1)),
% 29.52/19.73 inference(unit_resolution,[status(thm)],[9808, 25970])).
% 29.52/19.73 tff(25972,plain,
% 29.52/19.73 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | big_f(f7(f10(c1)), f6(f10(c1), c1)) | (f6(f10(c1), c1) = c1))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | big_f(f7(f10(c1)), f6(f10(c1), c1)) | (f6(f10(c1), c1) = c1))),
% 29.52/19.73 inference(rewrite,[status(thm)],[])).
% 29.55/19.73 tff(25973,plain,
% 29.55/19.73 (((f10(c1) = c1) | big_f(c1, f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | (f6(f10(c1), c1) = c1) | big_f(f7(f10(c1)), f6(f10(c1), c1)) | (~(c1 = f8(c1)))) <=> ((f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | big_f(f7(f10(c1)), f6(f10(c1), c1)) | (f6(f10(c1), c1) = c1))),
% 29.55/19.73 inference(rewrite,[status(thm)],[])).
% 29.55/19.73 tff(25974,plain,
% 29.55/19.73 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | big_f(c1, f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | (f6(f10(c1), c1) = c1) | big_f(f7(f10(c1)), f6(f10(c1), c1)) | (~(c1 = f8(c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | big_f(f7(f10(c1)), f6(f10(c1), c1)) | (f6(f10(c1), c1) = c1)))),
% 29.55/19.73 inference(monotonicity,[status(thm)],[25973])).
% 29.55/19.73 tff(25975,plain,
% 29.55/19.73 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | big_f(c1, f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | (f6(f10(c1), c1) = c1) | big_f(f7(f10(c1)), f6(f10(c1), c1)) | (~(c1 = f8(c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | big_f(f7(f10(c1)), f6(f10(c1), c1)) | (f6(f10(c1), c1) = c1))),
% 29.55/19.73 inference(transitivity,[status(thm)],[25974, 25972])).
% 29.55/19.73 tff(25976,plain,
% 29.55/19.73 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | big_f(c1, f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | (f6(f10(c1), c1) = c1) | big_f(f7(f10(c1)), f6(f10(c1), c1)) | (~(c1 = f8(c1))))),
% 29.55/19.73 inference(quant_inst,[status(thm)],[])).
% 29.55/19.73 tff(25977,plain,
% 29.55/19.73 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | big_f(f7(f10(c1)), f6(f10(c1), c1)) | (f6(f10(c1), c1) = c1)),
% 29.55/19.73 inference(modus_ponens,[status(thm)],[25976, 25975])).
% 29.55/19.73 tff(25978,plain,
% 29.55/19.73 (big_f(f7(f10(c1)), f6(f10(c1), c1)) | (f6(f10(c1), c1) = c1)),
% 29.55/19.73 inference(unit_resolution,[status(thm)],[25977, 2994, 3, 25971, 3030, 25967])).
% 29.55/19.73 tff(25979,plain,
% 29.55/19.73 (big_f(f7(f10(c1)), f6(f10(c1), c1))),
% 29.55/19.73 inference(unit_resolution,[status(thm)],[25978, 25966])).
% 29.55/19.73 tff(25980,plain,
% 29.55/19.73 (big_f(f7(c2), f6(c2, c1))),
% 29.55/19.73 inference(modus_ponens,[status(thm)],[25979, 25962])).
% 29.55/19.73 tff(25981,plain,
% 29.55/19.73 ($false),
% 29.55/19.73 inference(unit_resolution,[status(thm)],[3197, 25980])).
% 29.55/19.73 tff(25982,plain,(big_f(f7(c2), f6(c2, c1)) | (~(f7(c2) = c2)) | (f10(c1) = c1) | big_f(c1, f10(c1)) | (f6(c2, c1) = c1) | big_f(c2, f10(c1))), inference(lemma,lemma(discharge,[]))).
% 29.55/19.73 tff(25983,plain,
% 29.55/19.73 (big_f(f7(c2), f6(c2, c1))),
% 29.55/19.73 inference(unit_resolution,[status(thm)],[25982, 77, 3, 3030, 3198, 8451])).
% 29.55/19.73 tff(25984,plain,
% 29.55/19.73 (~(big_f(c2, c2) <=> big_f(f7(c2), f6(c2, c1)))),
% 29.55/19.73 inference(unit_resolution,[status(thm)],[17315, 25983, 121])).
% 29.55/19.73 tff(25985,plain,
% 29.55/19.73 (~(c2 = f6(c2, c1))),
% 29.55/19.73 inference(unit_resolution,[status(thm)],[17322, 25984, 23361])).
% 29.55/19.73 tff(25986,plain,
% 29.55/19.73 (~(f6(c2, f6(c2, c1)) = c1)),
% 29.55/19.73 inference(unit_resolution,[status(thm)],[23385, 25985, 3198])).
% 29.55/19.73 tff(25987,plain,
% 29.55/19.73 (f6(c2, f6(c2, c1)) = c2),
% 29.55/19.73 inference(unit_resolution,[status(thm)],[14655, 25986])).
% 29.55/19.73 tff(25988,plain,
% 29.55/19.73 (f6(f10(c1), f6(c2, c1)) = f6(c2, f6(c2, c1))),
% 29.55/19.73 inference(monotonicity,[status(thm)],[15])).
% 29.55/19.73 tff(25989,plain,
% 29.55/19.73 (f6(f10(c1), f6(c2, c1)) = c2),
% 29.55/19.73 inference(transitivity,[status(thm)],[25988, 25987])).
% 29.55/19.74 tff(25990,plain,
% 29.55/19.74 ((f6(f10(c1), f6(c2, c1)) = f6(c2, c1)) <=> (c2 = f6(c2, c1))),
% 29.55/19.74 inference(monotonicity,[status(thm)],[25989])).
% 29.55/19.74 tff(25991,plain,
% 29.55/19.74 ((c2 = f6(c2, c1)) <=> (f6(f10(c1), f6(c2, c1)) = f6(c2, c1))),
% 29.55/19.74 inference(symmetry,[status(thm)],[25990])).
% 29.55/19.74 tff(25992,plain,
% 29.55/19.74 ((~(c2 = f6(c2, c1))) <=> (~(f6(f10(c1), f6(c2, c1)) = f6(c2, c1)))),
% 29.55/19.74 inference(monotonicity,[status(thm)],[25991])).
% 29.55/19.74 tff(25993,plain,
% 29.55/19.74 (~(f6(f10(c1), f6(c2, c1)) = f6(c2, c1))),
% 29.55/19.74 inference(modus_ponens,[status(thm)],[25985, 25992])).
% 29.55/19.74 tff(25994,plain,
% 29.55/19.74 (f6(f10(c1), f6(c2, c1)) = f10(c1)),
% 29.55/19.74 inference(transitivity,[status(thm)],[25988, 25987, 5571])).
% 29.55/19.74 tff(25995,plain,
% 29.55/19.74 (f7(f10(c1)) = f10(c1)),
% 29.55/19.74 inference(transitivity,[status(thm)],[219, 77, 5571])).
% 29.55/19.74 tff(25996,plain,
% 29.55/19.74 (big_f(f7(f10(c1)), f6(f10(c1), f6(c2, c1))) <=> big_f(f10(c1), f10(c1))),
% 29.55/19.74 inference(monotonicity,[status(thm)],[25995, 25994])).
% 29.55/19.74 tff(25997,plain,
% 29.55/19.74 (big_f(f10(c1), f10(c1)) <=> big_f(f7(f10(c1)), f6(f10(c1), f6(c2, c1)))),
% 29.55/19.74 inference(symmetry,[status(thm)],[25996])).
% 29.55/19.74 tff(25998,plain,
% 29.55/19.74 ((~big_f(f10(c1), f10(c1))) <=> (~big_f(f7(f10(c1)), f6(f10(c1), f6(c2, c1))))),
% 29.55/19.74 inference(monotonicity,[status(thm)],[25997])).
% 29.55/19.74 tff(25999,plain,
% 29.55/19.74 (big_f(c2, c2) <=> big_f(f10(c1), f10(c1))),
% 29.55/19.74 inference(monotonicity,[status(thm)],[5571, 5571])).
% 29.55/19.74 tff(26000,plain,
% 29.55/19.74 ((~big_f(c2, c2)) <=> (~big_f(f10(c1), f10(c1)))),
% 29.55/19.74 inference(monotonicity,[status(thm)],[25999])).
% 29.55/19.74 tff(26001,plain,
% 29.55/19.74 (~big_f(f10(c1), f10(c1))),
% 29.55/19.74 inference(modus_ponens,[status(thm)],[121, 26000])).
% 29.55/19.74 tff(26002,plain,
% 29.55/19.74 (~big_f(f7(f10(c1)), f6(f10(c1), f6(c2, c1)))),
% 29.55/19.74 inference(modus_ponens,[status(thm)],[26001, 25998])).
% 29.55/19.74 tff(26003,plain,
% 29.55/19.74 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | big_f(f7(f10(c1)), f6(f10(c1), f6(c2, c1))) | (f6(f10(c1), f6(c2, c1)) = f6(c2, c1)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | big_f(f7(f10(c1)), f6(f10(c1), f6(c2, c1))) | (f6(f10(c1), f6(c2, c1)) = f6(c2, c1)))),
% 29.55/19.74 inference(rewrite,[status(thm)],[])).
% 29.55/19.74 tff(26004,plain,
% 29.55/19.74 (((f10(c1) = c1) | big_f(c1, f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | (f6(f10(c1), f6(c2, c1)) = f6(c2, c1)) | big_f(f7(f10(c1)), f6(f10(c1), f6(c2, c1))) | (~(c1 = f8(c1)))) <=> ((f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | big_f(f7(f10(c1)), f6(f10(c1), f6(c2, c1))) | (f6(f10(c1), f6(c2, c1)) = f6(c2, c1)))),
% 29.55/19.74 inference(rewrite,[status(thm)],[])).
% 29.55/19.74 tff(26005,plain,
% 29.55/19.74 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | big_f(c1, f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | (f6(f10(c1), f6(c2, c1)) = f6(c2, c1)) | big_f(f7(f10(c1)), f6(f10(c1), f6(c2, c1))) | (~(c1 = f8(c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | big_f(f7(f10(c1)), f6(f10(c1), f6(c2, c1))) | (f6(f10(c1), f6(c2, c1)) = f6(c2, c1))))),
% 29.55/19.74 inference(monotonicity,[status(thm)],[26004])).
% 29.55/19.74 tff(26006,plain,
% 29.55/19.74 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | big_f(c1, f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | (f6(f10(c1), f6(c2, c1)) = f6(c2, c1)) | big_f(f7(f10(c1)), f6(f10(c1), f6(c2, c1))) | (~(c1 = f8(c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | big_f(f7(f10(c1)), f6(f10(c1), f6(c2, c1))) | (f6(f10(c1), f6(c2, c1)) = f6(c2, c1)))),
% 29.55/19.74 inference(transitivity,[status(thm)],[26005, 26003])).
% 29.55/19.74 tff(26007,plain,
% 29.55/19.74 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | big_f(c1, f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | (f6(f10(c1), f6(c2, c1)) = f6(c2, c1)) | big_f(f7(f10(c1)), f6(f10(c1), f6(c2, c1))) | (~(c1 = f8(c1))))),
% 29.55/19.74 inference(quant_inst,[status(thm)],[])).
% 29.55/19.74 tff(26008,plain,
% 29.55/19.74 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | big_f(f7(f10(c1)), f6(f10(c1), f6(c2, c1))) | (f6(f10(c1), f6(c2, c1)) = f6(c2, c1))),
% 29.55/19.74 inference(modus_ponens,[status(thm)],[26007, 26006])).
% 29.55/19.74 tff(26009,plain,
% 29.55/19.74 ((~(c1 = f8(c1))) | big_f(f7(f10(c1)), f6(f10(c1), f6(c2, c1))) | (f6(f10(c1), f6(c2, c1)) = f6(c2, c1))),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[26008, 2994, 3, 3030, 25967])).
% 29.55/19.74 tff(26010,plain,
% 29.55/19.74 (~(c1 = f8(c1))),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[26009, 26002, 25993])).
% 29.55/19.74 tff(26011,plain,
% 29.55/19.74 (~(f8(c1) = c1)),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[9808, 26010])).
% 29.55/19.74 tff(26012,plain,
% 29.55/19.74 (f8(c1) = c2),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[1680, 26011])).
% 29.55/19.74 tff(26013,plain,
% 29.55/19.74 (c2 = f8(c1)),
% 29.55/19.74 inference(symmetry,[status(thm)],[26012])).
% 29.55/19.74 tff(26014,plain,
% 29.55/19.74 (f10(c1) = f8(c1)),
% 29.55/19.74 inference(transitivity,[status(thm)],[15, 26013])).
% 29.55/19.74 tff(26015,plain,
% 29.55/19.74 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | (~(f7(f10(c1)) = f10(c1))) | big_f(f10(c1), f10(c1)) | (~(f10(c1) = f8(c1))) | big_f(f7(f10(c1)), f6(f10(c1), f6(c2, c1))) | (f6(f10(c1), f6(c2, c1)) = f6(c2, c1)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (f10(c1) = c1) | (~(f7(f10(c1)) = f10(c1))) | big_f(f10(c1), f10(c1)) | (~(f10(c1) = f8(c1))) | big_f(f7(f10(c1)), f6(f10(c1), f6(c2, c1))) | (f6(f10(c1), f6(c2, c1)) = f6(c2, c1)))),
% 29.55/19.74 inference(rewrite,[status(thm)],[])).
% 29.55/19.74 tff(26016,plain,
% 29.55/19.74 (((f10(c1) = c1) | big_f(f10(c1), f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | (f6(f10(c1), f6(c2, c1)) = f6(c2, c1)) | big_f(f7(f10(c1)), f6(f10(c1), f6(c2, c1))) | (~(f10(c1) = f8(c1)))) <=> ((f10(c1) = c1) | (~(f7(f10(c1)) = f10(c1))) | big_f(f10(c1), f10(c1)) | (~(f10(c1) = f8(c1))) | big_f(f7(f10(c1)), f6(f10(c1), f6(c2, c1))) | (f6(f10(c1), f6(c2, c1)) = f6(c2, c1)))),
% 29.55/19.74 inference(rewrite,[status(thm)],[])).
% 29.55/19.74 tff(26017,plain,
% 29.55/19.74 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | big_f(f10(c1), f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | (f6(f10(c1), f6(c2, c1)) = f6(c2, c1)) | big_f(f7(f10(c1)), f6(f10(c1), f6(c2, c1))) | (~(f10(c1) = f8(c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | (~(f7(f10(c1)) = f10(c1))) | big_f(f10(c1), f10(c1)) | (~(f10(c1) = f8(c1))) | big_f(f7(f10(c1)), f6(f10(c1), f6(c2, c1))) | (f6(f10(c1), f6(c2, c1)) = f6(c2, c1))))),
% 29.55/19.74 inference(monotonicity,[status(thm)],[26016])).
% 29.55/19.74 tff(26018,plain,
% 29.55/19.74 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | big_f(f10(c1), f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | (f6(f10(c1), f6(c2, c1)) = f6(c2, c1)) | big_f(f7(f10(c1)), f6(f10(c1), f6(c2, c1))) | (~(f10(c1) = f8(c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (f10(c1) = c1) | (~(f7(f10(c1)) = f10(c1))) | big_f(f10(c1), f10(c1)) | (~(f10(c1) = f8(c1))) | big_f(f7(f10(c1)), f6(f10(c1), f6(c2, c1))) | (f6(f10(c1), f6(c2, c1)) = f6(c2, c1)))),
% 29.55/19.74 inference(transitivity,[status(thm)],[26017, 26015])).
% 29.55/19.74 tff(26019,plain,
% 29.55/19.74 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | big_f(f10(c1), f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | (f6(f10(c1), f6(c2, c1)) = f6(c2, c1)) | big_f(f7(f10(c1)), f6(f10(c1), f6(c2, c1))) | (~(f10(c1) = f8(c1))))),
% 29.55/19.74 inference(quant_inst,[status(thm)],[])).
% 29.55/19.74 tff(26020,plain,
% 29.55/19.74 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(X8 = f8(X7))))) | (f10(c1) = c1) | (~(f7(f10(c1)) = f10(c1))) | big_f(f10(c1), f10(c1)) | (~(f10(c1) = f8(c1))) | big_f(f7(f10(c1)), f6(f10(c1), f6(c2, c1))) | (f6(f10(c1), f6(c2, c1)) = f6(c2, c1))),
% 29.55/19.74 inference(modus_ponens,[status(thm)],[26019, 26018])).
% 29.55/19.74 tff(26021,plain,
% 29.55/19.74 ((~(f10(c1) = f8(c1))) | big_f(f7(f10(c1)), f6(f10(c1), f6(c2, c1))) | (f6(f10(c1), f6(c2, c1)) = f6(c2, c1))),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[26020, 2994, 3, 25967, 26001])).
% 29.55/19.74 tff(26022,plain,
% 29.55/19.74 (~(f10(c1) = f8(c1))),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[26021, 26002, 25993])).
% 29.55/19.74 tff(26023,plain,
% 29.55/19.74 ($false),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[26022, 26014])).
% 29.55/19.74 tff(26024,plain,((~(f7(c2) = c2)) | (f10(c1) = c1) | big_f(c1, f10(c1)) | (f6(c2, c1) = c1) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 29.55/19.74 tff(26025,plain,
% 29.55/19.74 (f6(c2, c1) = c1),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[26024, 25958, 77, 121, 25953])).
% 29.55/19.74 tff(26026,plain,
% 29.55/19.74 (big_f(c2, f6(c2, c1)) <=> big_f(c2, c1)),
% 29.55/19.74 inference(monotonicity,[status(thm)],[26025])).
% 29.55/19.74 tff(26027,plain,
% 29.55/19.74 (big_f(c2, c1) <=> big_f(c2, f6(c2, c1))),
% 29.55/19.74 inference(symmetry,[status(thm)],[26026])).
% 29.55/19.74 tff(26028,plain,
% 29.55/19.74 (big_f(c2, c1) <=> big_f(f7(c2), f6(c2, c1))),
% 29.55/19.74 inference(transitivity,[status(thm)],[26027, 13581])).
% 29.55/19.74 tff(26029,plain,
% 29.55/19.74 (big_f(f7(c2), f6(c2, c1))),
% 29.55/19.74 inference(modus_ponens,[status(thm)],[348, 26028])).
% 29.55/19.74 tff(26030,plain,
% 29.55/19.74 (~big_f(c2, f10(c1))),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[6125, 25954, 121])).
% 29.55/19.74 tff(26031,plain,
% 29.55/19.74 (~(c2 = f8(c1))),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[11412, 2963, 26030, 25953, 77, 26025, 26029])).
% 29.55/19.74 tff(26032,plain,
% 29.55/19.74 (~(f8(c1) = c2)),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[1675, 26031])).
% 29.55/19.74 tff(26033,plain,
% 29.55/19.74 (~(c1 = f8(c1))),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[3064, 2963, 25953, 77, 26025, 26029, 25958])).
% 29.55/19.74 tff(26034,plain,
% 29.55/19.74 (~(f8(c1) = c1)),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[9808, 26033])).
% 29.55/19.74 tff(26035,plain,
% 29.55/19.74 ($false),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[1680, 26034, 26032])).
% 29.55/19.74 tff(26036,plain,(big_f(c2, c2) | (~(f7(c2) = c2)) | (~big_f(c2, c1)) | big_f(c1, c2) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 29.55/19.74 tff(26037,plain,
% 29.55/19.74 (big_f(c2, c2)),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[26036, 27, 25952, 77, 66])).
% 29.55/19.74 tff(26038,plain,
% 29.55/19.74 (big_f(f3(c1, c2), c1)),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[13184, 12777, 1345, 1344, 348, 482])).
% 29.55/19.74 tff(26039,plain,
% 29.55/19.74 (~(big_f(c1, c1) <=> big_f(f3(c1, c2), c1))),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[13186, 26038, 66])).
% 29.55/19.74 tff(26040,plain,
% 29.55/19.74 (~(c1 = f3(c1, c2))),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[13192, 26039])).
% 29.55/19.74 tff(26041,plain,
% 29.55/19.74 (f3(c1, f1(f5(c2), f5(c1))) = f3(c1, c2)),
% 29.55/19.74 inference(monotonicity,[status(thm)],[5131])).
% 29.55/19.74 tff(26042,plain,
% 29.55/19.74 ((f3(c1, f1(f5(c2), f5(c1))) = c1) <=> (f3(c1, c2) = c1)),
% 29.55/19.74 inference(monotonicity,[status(thm)],[26041])).
% 29.55/19.74 tff(26043,plain,
% 29.55/19.74 ((f3(c1, f1(f5(c2), f5(c1))) = c1) <=> (c1 = f3(c1, c2))),
% 29.55/19.74 inference(transitivity,[status(thm)],[26042, 13151])).
% 29.55/19.74 tff(26044,plain,
% 29.55/19.74 ((c1 = f3(c1, c2)) <=> (f3(c1, f1(f5(c2), f5(c1))) = c1)),
% 29.55/19.74 inference(symmetry,[status(thm)],[26043])).
% 29.55/19.74 tff(26045,plain,
% 29.55/19.74 ((~(c1 = f3(c1, c2))) <=> (~(f3(c1, f1(f5(c2), f5(c1))) = c1))),
% 29.55/19.74 inference(monotonicity,[status(thm)],[26044])).
% 29.55/19.74 tff(26046,plain,
% 29.55/19.74 (~(f3(c1, f1(f5(c2), f5(c1))) = c1)),
% 29.55/19.74 inference(modus_ponens,[status(thm)],[16041, 26045])).
% 29.55/19.74 tff(26047,plain,
% 29.55/19.74 ((f3(c1, f1(f5(c2), f5(c1))) = c2) <=> (f3(c1, c2) = c2)),
% 29.55/19.74 inference(monotonicity,[status(thm)],[26041])).
% 29.55/19.74 tff(26048,plain,
% 29.55/19.74 ((f3(c1, c2) = c2) <=> (f3(c1, f1(f5(c2), f5(c1))) = c2)),
% 29.55/19.74 inference(symmetry,[status(thm)],[26047])).
% 29.55/19.74 tff(26049,plain,
% 29.55/19.74 ((~(f3(c1, c2) = c2)) <=> (~(f3(c1, f1(f5(c2), f5(c1))) = c2))),
% 29.55/19.74 inference(monotonicity,[status(thm)],[26048])).
% 29.55/19.74 tff(26050,plain,
% 29.55/19.74 (~(f3(c1, f1(f5(c2), f5(c1))) = c2)),
% 29.55/19.74 inference(modus_ponens,[status(thm)],[12777, 26049])).
% 29.55/19.74 tff(26051,plain,
% 29.55/19.74 ($false),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[16082, 26050, 26046])).
% 29.55/19.74 tff(26052,plain,((~(f1(f5(c2), f5(c1)) = c2)) | (f3(c1, c2) = c2) | (c1 = f3(c1, c2))), inference(lemma,lemma(discharge,[]))).
% 29.55/19.74 tff(26053,plain,
% 29.55/19.74 (~(f1(f5(c2), f5(c1)) = c2)),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[26052, 12777, 26040])).
% 29.55/19.74 tff(26054,plain,
% 29.55/19.74 (f1(f5(c2), f5(c1)) = c1),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[5191, 26053])).
% 29.55/19.74 tff(26055,plain,
% 29.55/19.74 (f3(f1(f5(c2), f5(c1)), c2) = f3(c1, c2)),
% 29.55/19.74 inference(monotonicity,[status(thm)],[26054])).
% 29.55/19.74 tff(26056,plain,
% 29.55/19.74 ((f3(f1(f5(c2), f5(c1)), c2) = c2) <=> (f3(c1, c2) = c2)),
% 29.55/19.74 inference(monotonicity,[status(thm)],[26055])).
% 29.55/19.74 tff(26057,plain,
% 29.55/19.74 ((f3(c1, c2) = c2) <=> (f3(f1(f5(c2), f5(c1)), c2) = c2)),
% 29.55/19.74 inference(symmetry,[status(thm)],[26056])).
% 29.55/19.74 tff(26058,plain,
% 29.55/19.74 ((~(f3(c1, c2) = c2)) <=> (~(f3(f1(f5(c2), f5(c1)), c2) = c2))),
% 29.55/19.74 inference(monotonicity,[status(thm)],[26057])).
% 29.55/19.74 tff(26059,plain,
% 29.55/19.74 (~(f3(f1(f5(c2), f5(c1)), c2) = c2)),
% 29.55/19.74 inference(modus_ponens,[status(thm)],[12777, 26058])).
% 29.55/19.74 tff(26060,plain,
% 29.55/19.74 ((f3(f1(f5(c2), f5(c1)), c2) = c1) <=> (f3(c1, c2) = c1)),
% 29.55/19.74 inference(monotonicity,[status(thm)],[26055])).
% 29.55/19.74 tff(26061,plain,
% 29.55/19.74 ((f3(f1(f5(c2), f5(c1)), c2) = c1) <=> (c1 = f3(c1, c2))),
% 29.55/19.74 inference(transitivity,[status(thm)],[26060, 13151])).
% 29.55/19.74 tff(26062,plain,
% 29.55/19.74 ((c1 = f3(c1, c2)) <=> (f3(f1(f5(c2), f5(c1)), c2) = c1)),
% 29.55/19.74 inference(symmetry,[status(thm)],[26061])).
% 29.55/19.74 tff(26063,plain,
% 29.55/19.74 ((~(c1 = f3(c1, c2))) <=> (~(f3(f1(f5(c2), f5(c1)), c2) = c1))),
% 29.55/19.74 inference(monotonicity,[status(thm)],[26062])).
% 29.55/19.74 tff(26064,plain,
% 29.55/19.74 (~(f3(f1(f5(c2), f5(c1)), c2) = c1)),
% 29.55/19.74 inference(modus_ponens,[status(thm)],[26040, 26063])).
% 29.55/19.74 tff(26065,plain,
% 29.55/19.74 ($false),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[16061, 26064, 26059])).
% 29.55/19.74 tff(26066,plain,((f3(c1, c2) = c2) | big_f(c1, c1) | (~big_f(c2, c2)) | (~(c2 = c3)) | (~big_f(c2, c1)) | (c1 = c4)), inference(lemma,lemma(discharge,[]))).
% 29.55/19.74 tff(26067,plain,
% 29.55/19.74 (f3(c1, c2) = c2),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[26066, 1344, 1345, 66, 348, 482])).
% 29.55/19.74 tff(26068,plain,
% 29.55/19.74 (big_f(f3(c1, c2), c1) <=> big_f(c2, c1)),
% 29.55/19.74 inference(monotonicity,[status(thm)],[16111])).
% 29.55/19.74 tff(26069,plain,
% 29.55/19.74 (big_f(c2, c1) <=> big_f(f3(c1, c2), c1)),
% 29.55/19.74 inference(symmetry,[status(thm)],[26068])).
% 29.55/19.74 tff(26070,plain,
% 29.55/19.74 (big_f(f3(c1, c2), c1)),
% 29.55/19.74 inference(modus_ponens,[status(thm)],[348, 26069])).
% 29.55/19.74 tff(26071,plain,
% 29.55/19.74 ($false),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[13164, 26070])).
% 29.55/19.74 tff(26072,plain,((~(f3(c1, c2) = c2)) | big_f(f3(c1, c2), c1) | (~big_f(c2, c1))), inference(lemma,lemma(discharge,[]))).
% 29.55/19.74 tff(26073,plain,
% 29.55/19.74 (big_f(f3(c1, c2), c1)),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[26072, 26067, 348])).
% 29.55/19.74 tff(26074,plain,
% 29.55/19.74 (c1 = f2(c2)),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[13205, 7051, 482, 1344, 26073, 26067, 348])).
% 29.55/19.74 tff(26075,plain,
% 29.55/19.74 (f2(c2) = c1),
% 29.55/19.74 inference(symmetry,[status(thm)],[26074])).
% 29.55/19.74 tff(26076,plain,
% 29.55/19.74 (c2 = f2(c2)),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[13213, 7051, 482, 1345, 1344, 26073, 26067])).
% 29.55/19.74 tff(26077,plain,
% 29.55/19.74 (c2 = c1),
% 29.55/19.74 inference(transitivity,[status(thm)],[26076, 26075])).
% 29.55/19.74 tff(26078,plain,
% 29.55/19.74 ($false),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[75, 26077])).
% 29.55/19.74 tff(26079,plain,((~(c2 = c3)) | (c1 = c4) | (~big_f(c2, c1)) | (~big_f(c2, c2)) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 29.55/19.74 tff(26080,plain,
% 29.55/19.74 (~(c2 = c3)),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[26079, 482, 348, 1345, 66])).
% 29.55/19.74 tff(26081,plain,
% 29.55/19.74 (~(c3 = c2)),
% 29.55/19.74 inference(modus_ponens,[status(thm)],[26080, 9745])).
% 29.55/19.74 tff(26082,plain,
% 29.55/19.74 (c3 = c1),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[180, 26081])).
% 29.55/19.74 tff(26083,plain,
% 29.55/19.74 (big_f(f3(c1, c2), c1)),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[26072, 16111, 348])).
% 29.55/19.74 tff(26084,plain,
% 29.55/19.74 (~(c2 = f2(c1))),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[12849, 1398, 5611, 482, 27, 26083, 16111])).
% 29.55/19.74 tff(26085,plain,
% 29.55/19.74 (~(f2(c3) = c2)),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[12823, 26084, 172])).
% 29.55/19.74 tff(26086,plain,
% 29.55/19.74 (~(c1 = f2(c1))),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[12812, 1398, 5611, 482, 26083, 16111, 66])).
% 29.55/19.74 tff(26087,plain,
% 29.55/19.74 (~(f2(c3) = c1)),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[6771, 26086, 172])).
% 29.55/19.74 tff(26088,plain,
% 29.55/19.74 ($false),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[1273, 26087, 26085])).
% 29.55/19.74 tff(26089,plain,((~(f3(c1, c2) = c2)) | (~(c3 = c1)) | (c1 = c4) | big_f(c1, c1) | big_f(c1, c2) | (~big_f(c2, c1))), inference(lemma,lemma(discharge,[]))).
% 29.55/19.74 tff(26090,plain,
% 29.55/19.74 (~(f3(c1, c2) = c2)),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[26089, 26082, 27, 66, 482, 348])).
% 29.55/19.74 tff(26091,plain,
% 29.55/19.74 (~(f3(c1, c2) = c2)),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[26072, 13164, 348])).
% 29.55/19.74 tff(26092,plain,
% 29.55/19.74 ($false),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[12800, 1459, 5080, 482, 13164, 26091, 6632, 66])).
% 29.55/19.74 tff(26093,plain,(big_f(f3(c1, c2), c1) | (~(c1 = c3)) | (c1 = c4) | (~(c1 = f2(c1))) | big_f(c1, c1) | (~big_f(c2, c1))), inference(lemma,lemma(discharge,[]))).
% 29.55/19.74 tff(26094,plain,
% 29.55/19.74 (~(c1 = f2(c1))),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[26093, 13164, 482, 5611, 66, 348])).
% 29.55/19.74 tff(26095,plain,
% 29.55/19.74 (~(f2(c3) = c1)),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[6771, 26094, 172])).
% 29.55/19.74 tff(26096,plain,
% 29.55/19.74 (~(f3(c1, c2) = c2)),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[26089, 172, 27, 66, 482, 348])).
% 29.55/19.74 tff(26097,plain,
% 29.55/19.74 ($false),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[12837, 1459, 5080, 482, 12831, 27, 13164, 12777])).
% 29.55/19.74 tff(26098,plain,(big_f(c1, c2) | (~(c1 = c3)) | (c1 = c4) | (~(c2 = f2(c1))) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 29.55/19.74 tff(26099,plain,
% 29.55/19.74 (~(c2 = f2(c1))),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[26098, 13164, 27, 482, 5611, 26096])).
% 29.55/19.74 tff(26100,plain,
% 29.55/19.74 (~(f2(c3) = c2)),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[12823, 26099, 172])).
% 29.55/19.74 tff(26101,plain,
% 29.55/19.74 ($false),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[1273, 26100, 26095])).
% 29.55/19.74 tff(26102,plain,(big_f(f3(c1, c2), c1) | (~(c3 = c1)) | big_f(c1, c2) | (c1 = c4) | big_f(c1, c1) | (~big_f(c2, c1))), inference(lemma,lemma(discharge,[]))).
% 29.55/19.74 tff(26103,plain,
% 29.55/19.74 (big_f(f3(c1, c2), c1)),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[26102, 26082, 27, 482, 66, 348])).
% 29.55/19.74 tff(26104,plain,
% 29.55/19.74 (~(big_f(c1, c1) <=> big_f(f3(c1, c2), c1))),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[13186, 26103, 66])).
% 29.55/19.74 tff(26105,plain,
% 29.55/19.74 (~(c1 = f3(c1, c2))),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[13192, 26104])).
% 29.55/19.74 tff(26106,plain,
% 29.55/19.74 (~(f1(f5(c2), f5(c1)) = c2)),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[26052, 26105, 26090])).
% 29.55/19.74 tff(26107,plain,
% 29.55/19.74 (f1(f5(c2), f5(c1)) = c1),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[5191, 26106])).
% 29.55/19.74 tff(26108,plain,
% 29.55/19.74 (f3(f1(f5(c2), f5(c1)), c2) = f3(c1, c2)),
% 29.55/19.74 inference(monotonicity,[status(thm)],[26107])).
% 29.55/19.74 tff(26109,plain,
% 29.55/19.74 (f3(c1, c2) = f3(f1(f5(c2), f5(c1)), c2)),
% 29.55/19.74 inference(symmetry,[status(thm)],[26108])).
% 29.55/19.74 tff(26110,plain,
% 29.55/19.74 ((f3(c1, c2) = c2) <=> (f3(f1(f5(c2), f5(c1)), c2) = c2)),
% 29.55/19.74 inference(monotonicity,[status(thm)],[26109])).
% 29.55/19.74 tff(26111,plain,
% 29.55/19.74 ((~(f3(c1, c2) = c2)) <=> (~(f3(f1(f5(c2), f5(c1)), c2) = c2))),
% 29.55/19.74 inference(monotonicity,[status(thm)],[26110])).
% 29.55/19.74 tff(26112,plain,
% 29.55/19.74 (~(f3(f1(f5(c2), f5(c1)), c2) = c2)),
% 29.55/19.74 inference(modus_ponens,[status(thm)],[26090, 26111])).
% 29.55/19.74 tff(26113,plain,
% 29.55/19.74 ((c1 = f3(f1(f5(c2), f5(c1)), c2)) <=> (f3(f1(f5(c2), f5(c1)), c2) = c1)),
% 29.55/19.74 inference(commutativity,[status(thm)],[])).
% 29.55/19.74 tff(26114,plain,
% 29.55/19.74 ((c1 = f3(c1, c2)) <=> (c1 = f3(f1(f5(c2), f5(c1)), c2))),
% 29.55/19.74 inference(monotonicity,[status(thm)],[26109])).
% 29.55/19.74 tff(26115,plain,
% 29.55/19.74 ((c1 = f3(c1, c2)) <=> (f3(f1(f5(c2), f5(c1)), c2) = c1)),
% 29.55/19.74 inference(transitivity,[status(thm)],[26114, 26113])).
% 29.55/19.74 tff(26116,plain,
% 29.55/19.74 ((~(c1 = f3(c1, c2))) <=> (~(f3(f1(f5(c2), f5(c1)), c2) = c1))),
% 29.55/19.74 inference(monotonicity,[status(thm)],[26115])).
% 29.55/19.74 tff(26117,plain,
% 29.55/19.74 (~(f3(f1(f5(c2), f5(c1)), c2) = c1)),
% 29.55/19.74 inference(modus_ponens,[status(thm)],[26105, 26116])).
% 29.55/19.74 tff(26118,plain,
% 29.55/19.74 ($false),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[16061, 26117, 26112])).
% 29.55/19.74 tff(26119,plain,((c1 = c4) | big_f(c1, c1) | big_f(c1, c2) | (~big_f(c2, c1)) | (~big_f(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 29.55/19.74 tff(26120,plain,
% 29.55/19.74 (c1 = c4),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[26119, 27, 66, 25952, 26037])).
% 29.55/19.74 tff(26121,plain,
% 29.55/19.74 (c4 = c1),
% 29.55/19.74 inference(symmetry,[status(thm)],[26120])).
% 29.55/19.74 tff(26122,plain,
% 29.55/19.74 ((c2 = c4) <=> (c2 = c1)),
% 29.55/19.74 inference(monotonicity,[status(thm)],[26121])).
% 29.55/19.74 tff(26123,plain,
% 29.55/19.74 ((c2 = c1) <=> (c2 = c4)),
% 29.55/19.74 inference(symmetry,[status(thm)],[26122])).
% 29.55/19.74 tff(26124,plain,
% 29.55/19.74 ((~(c2 = c1)) <=> (~(c2 = c4))),
% 29.55/19.74 inference(monotonicity,[status(thm)],[26123])).
% 29.55/19.74 tff(26125,plain,
% 29.55/19.74 (~(c2 = c4)),
% 29.55/19.74 inference(modus_ponens,[status(thm)],[75, 26124])).
% 29.55/19.74 tff(26126,plain,
% 29.55/19.74 (big_f(f3(c2, c2), c2)),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[14309, 172, 66, 873, 1345, 27])).
% 29.55/19.74 tff(26127,plain,
% 29.55/19.74 (~(f3(f7(f4(c4)), f4(c4)) = c1)),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[15359, 26126, 27, 79, 77])).
% 29.55/19.74 tff(26128,plain,
% 29.55/19.74 (f3(f7(f4(c4)), f4(c4)) = c2),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[7693, 26127])).
% 29.55/19.74 tff(26129,plain,
% 29.55/19.74 (f3(c2, c2) = c2),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[15367, 26128, 79, 77])).
% 29.55/19.74 tff(26130,plain,
% 29.55/19.74 (~(c2 = f2(c1))),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[12931, 1398, 5611, 873, 27, 26129, 26126])).
% 29.55/19.74 tff(26131,plain,
% 29.55/19.74 (~(f2(c3) = c2)),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[12823, 26130, 172])).
% 29.55/19.74 tff(26132,plain,
% 29.55/19.74 (~(c1 = f2(c1))),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[12923, 1398, 5611, 873, 66, 26129, 26126])).
% 29.55/19.74 tff(26133,plain,
% 29.55/19.74 (~(f2(c3) = c1)),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[6771, 26132, 172])).
% 29.55/19.74 tff(26134,plain,
% 29.55/19.74 ($false),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[1273, 26133, 26131])).
% 29.55/19.74 tff(26135,plain,((~(c3 = c1)) | (c2 = c4) | big_f(c1, c1) | big_f(c1, c2) | (~(f4(c4) = c2)) | (~(f7(c2) = c2)) | (~big_f(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 29.55/19.74 tff(26136,plain,
% 29.55/19.74 (~(c3 = c1)),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[26135, 26125, 66, 27, 79, 77, 26037])).
% 29.55/19.74 tff(26137,plain,
% 29.55/19.74 (c3 = c2),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[180, 26136])).
% 29.55/19.74 tff(26138,plain,
% 29.55/19.74 (c2 = c3),
% 29.55/19.74 inference(modus_ponens,[status(thm)],[26137, 78])).
% 29.55/19.74 tff(26139,plain,
% 29.55/19.74 (big_f(f3(c2, c2), c2)),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[13236, 1344, 1345, 348, 873])).
% 29.55/19.74 tff(26140,plain,
% 29.55/19.74 (~(f3(f7(f4(c4)), f4(c4)) = c1)),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[15359, 27, 26139, 79, 77])).
% 29.55/19.74 tff(26141,plain,
% 29.55/19.74 (f3(f7(f4(c4)), f4(c4)) = c2),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[7693, 26140])).
% 29.55/19.74 tff(26142,plain,
% 29.55/19.74 (f3(c2, c2) = c2),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[15367, 26141, 79, 77])).
% 29.55/19.74 tff(26143,plain,
% 29.55/19.74 ((c1 = f2(c2)) | (~(f3(c2, c2) = c2))),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[13120, 7051, 873, 1344, 348, 26139])).
% 29.55/19.74 tff(26144,plain,
% 29.55/19.74 (c1 = f2(c2)),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[26143, 26142])).
% 29.55/19.74 tff(26145,plain,
% 29.55/19.74 (f2(c2) = c1),
% 29.55/19.74 inference(symmetry,[status(thm)],[26144])).
% 29.55/19.74 tff(26146,plain,
% 29.55/19.74 (c2 = f2(c2)),
% 29.55/19.74 inference(unit_resolution,[status(thm)],[15433, 27, 79, 1345, 873, 77, 1344, 348])).
% 29.55/19.75 tff(26147,plain,
% 29.55/19.75 (c2 = c1),
% 29.55/19.75 inference(transitivity,[status(thm)],[26146, 26145])).
% 29.55/19.75 tff(26148,plain,
% 29.55/19.75 ($false),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[75, 26147])).
% 29.55/19.75 tff(26149,plain,(big_f(c1, c2) | (c2 = c4) | (~(c2 = c3)) | (~big_f(c2, c1)) | (~(f4(c4) = c2)) | (~(f7(c2) = c2)) | (~big_f(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 29.55/19.75 tff(26150,plain,
% 29.55/19.75 (~(c2 = c3)),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[26149, 26125, 27, 25952, 79, 77, 26037])).
% 29.55/19.75 tff(26151,plain,
% 29.55/19.75 ($false),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[26150, 26138])).
% 29.55/19.75 tff(26152,plain,(big_f(c1, c2) | (~(f4(c4) = c2)) | (~(f7(c2) = c2)) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 29.55/19.75 tff(26153,plain,
% 29.55/19.75 (~(f4(c4) = c2)),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[26152, 77, 27, 66])).
% 29.55/19.75 tff(26154,plain,
% 29.55/19.75 (f4(c4) = c1),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[11750, 26153])).
% 29.55/19.75 tff(26155,plain,
% 29.55/19.75 (~big_f(f4(c4), c4)),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[11772, 26154, 66, 27])).
% 29.55/19.75 tff(26156,plain,
% 29.55/19.75 (big_f(c3, f2(c3))),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[1315, 26155])).
% 29.55/19.75 tff(26157,plain,
% 29.55/19.75 (~(f2(c3) = c1)),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[23525, 2, 67, 26156])).
% 29.55/19.75 tff(26158,plain,
% 29.55/19.75 (f2(c3) = c2),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[1273, 26157])).
% 29.55/19.75 tff(26159,plain,
% 29.55/19.75 (big_f(c2, c2)),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[24323, 2, 27, 66])).
% 29.55/19.75 tff(26160,plain,
% 29.55/19.75 (f6(c2, c2) = c2),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[2716, 2362, 67, 77])).
% 29.55/19.75 tff(26161,plain,
% 29.55/19.75 (big_f(f7(c2), f6(c2, c2))),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[2627, 26160, 77, 1345])).
% 29.55/19.75 tff(26162,plain,
% 29.55/19.75 (big_f(f9(c2, c2), f10(c2))),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[2750, 26161, 77, 122, 1345, 26160])).
% 29.55/19.75 tff(26163,plain,
% 29.55/19.75 (big_f(f9(c2, c2), c2)),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[3687, 26162, 122])).
% 29.55/19.75 tff(26164,plain,
% 29.55/19.75 (~(f9(c2, c2) = c2)),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[2386, 26162, 67, 77, 1345, 122, 2362])).
% 29.55/19.75 tff(26165,plain,
% 29.55/19.75 ($false),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[23800, 26164, 26163, 1319, 27, 122])).
% 29.55/19.75 tff(26166,plain,((~(f6(f7(c2), c3) = c2)) | (~(f2(c3) = c2)) | big_f(c1, c2) | (~(f10(c2) = c2)) | (~(c3 = c2)) | (~(f7(c2) = c2)) | (~big_f(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 29.55/19.75 tff(26167,plain,
% 29.55/19.75 (~(f6(f7(c2), c3) = c2)),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[26166, 122, 27, 1319, 67, 77, 1345])).
% 29.55/19.75 tff(26168,plain,
% 29.55/19.75 (f6(f7(c2), c3) = c1),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[2391, 26167])).
% 29.55/19.75 tff(26169,plain,
% 29.55/19.75 (~big_f(f7(c2), f6(c2, c2))),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[2710, 26168, 77, 67, 2])).
% 29.55/19.75 tff(26170,plain,
% 29.55/19.75 (~big_f(f9(c2, c2), c2)),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[23800, 1209, 1319, 27, 122])).
% 29.55/19.75 tff(26171,plain,
% 29.55/19.75 (big_f(f9(c2, c2), f10(c2))),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[5485, 1209, 1345, 122, 77, 2621])).
% 29.55/19.75 tff(26172,plain,
% 29.55/19.75 ($false),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[3687, 26171, 26170, 122])).
% 29.55/19.75 tff(26173,plain,((f9(c2, c2) = c2) | (~(f10(c2) = c2)) | (~big_f(c2, c2)) | (~(f7(c2) = c2)) | big_f(f7(c2), f6(c2, c2)) | (~(f2(c3) = c2)) | big_f(c1, c2)), inference(lemma,lemma(discharge,[]))).
% 29.55/19.75 tff(26174,plain,
% 29.55/19.75 (f9(c2, c2) = c2),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[26173, 122, 1345, 77, 26169, 1319, 27])).
% 29.55/19.75 tff(26175,plain,
% 29.55/19.75 (big_f(f9(c2, c2), c2) <=> big_f(c2, c2)),
% 29.55/19.75 inference(monotonicity,[status(thm)],[26174])).
% 29.55/19.75 tff(26176,plain,
% 29.55/19.75 (big_f(c2, c2) <=> big_f(f9(c2, c2), c2)),
% 29.55/19.75 inference(symmetry,[status(thm)],[26175])).
% 29.55/19.75 tff(26177,plain,
% 29.55/19.75 (big_f(c2, c2) <=> big_f(f9(c2, c2), f10(c2))),
% 29.55/19.75 inference(transitivity,[status(thm)],[26176, 130])).
% 29.55/19.75 tff(26178,plain,
% 29.55/19.75 (big_f(f9(c2, c2), f10(c2))),
% 29.55/19.75 inference(modus_ponens,[status(thm)],[1345, 26177])).
% 29.55/19.75 tff(26179,plain,
% 29.55/19.75 (~(f6(c2, c2) = c2)),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[2627, 26169, 77, 1345])).
% 29.55/19.75 tff(26180,plain,
% 29.55/19.75 ($false),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[2412, 2409, 122, 77, 26179, 26169, 26174, 26178])).
% 29.55/19.75 tff(26181,plain,((~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~big_f(c2, c2)) | (~(f2(c3) = c2)) | big_f(c1, c2) | (~(c3 = c2)) | big_f(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 29.55/19.75 tff(26182,plain,
% 29.55/19.75 (~(f10(c2) = c2)),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[26181, 26159, 77, 26158, 27, 67, 2])).
% 29.55/19.75 tff(26183,plain,
% 29.55/19.75 (f10(c2) = c1),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[93, 26182])).
% 29.55/19.75 tff(26184,plain,
% 29.55/19.75 ((f10(c2) = f8(c2)) <=> (c1 = f8(c2))),
% 29.55/19.75 inference(monotonicity,[status(thm)],[26183])).
% 29.55/19.75 tff(26185,plain,
% 29.55/19.75 ((c1 = f8(c2)) <=> (f10(c2) = f8(c2))),
% 29.55/19.75 inference(symmetry,[status(thm)],[26184])).
% 29.55/19.75 tff(26186,plain,
% 29.55/19.75 (c1 = f10(c2)),
% 29.55/19.75 inference(symmetry,[status(thm)],[26183])).
% 29.55/19.75 tff(26187,plain,
% 29.55/19.75 (big_f(c2, c1) <=> big_f(c2, f10(c2))),
% 29.55/19.75 inference(monotonicity,[status(thm)],[26186])).
% 29.55/19.75 tff(26188,plain,
% 29.55/19.75 ((~big_f(c2, c1)) <=> (~big_f(c2, f10(c2)))),
% 29.55/19.75 inference(monotonicity,[status(thm)],[26187])).
% 29.55/19.75 tff(26189,plain,
% 29.55/19.75 (~big_f(c2, f10(c2))),
% 29.55/19.75 inference(modus_ponens,[status(thm)],[2, 26188])).
% 29.55/19.75 tff(26190,plain,
% 29.55/19.75 (big_f(c1, f10(c2)) <=> big_f(c1, c1)),
% 29.55/19.75 inference(monotonicity,[status(thm)],[26183])).
% 29.55/19.75 tff(26191,plain,
% 29.55/19.75 (big_f(c1, c1) <=> big_f(c1, f10(c2))),
% 29.55/19.75 inference(symmetry,[status(thm)],[26190])).
% 29.55/19.75 tff(26192,plain,
% 29.55/19.75 ((~big_f(c1, c1)) <=> (~big_f(c1, f10(c2)))),
% 29.55/19.75 inference(monotonicity,[status(thm)],[26191])).
% 29.55/19.75 tff(26193,plain,
% 29.55/19.75 (~big_f(c1, f10(c2))),
% 29.55/19.75 inference(modus_ponens,[status(thm)],[66, 26192])).
% 29.55/19.75 tff(26194,plain,
% 29.55/19.75 (big_f(f7(c2), f6(c2, c2))),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[2627, 2622, 77, 1345])).
% 29.55/19.75 tff(26195,plain,
% 29.55/19.75 (~(c2 = f8(c2))),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[24173, 2963, 89, 77, 15517, 2622, 26194])).
% 29.55/19.75 tff(26196,plain,
% 29.55/19.75 (~(c1 = f8(c2))),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[24187, 2963, 89, 77, 2622, 26194, 12055])).
% 29.55/19.75 tff(26197,plain,
% 29.55/19.75 (~(f8(c3) = c1)),
% 29.55/19.75 inference(modus_ponens,[status(thm)],[24284, 13049])).
% 29.55/19.75 tff(26198,plain,
% 29.55/19.75 ((c2 = f8(c2)) <=> (c2 = f8(c3))),
% 29.55/19.75 inference(monotonicity,[status(thm)],[20761])).
% 29.55/19.75 tff(26199,plain,
% 29.55/19.75 ((c2 = f8(c2)) <=> (f8(c3) = c2)),
% 29.55/19.75 inference(transitivity,[status(thm)],[26198, 208])).
% 29.55/19.75 tff(26200,plain,
% 29.55/19.75 ((~(c2 = f8(c2))) <=> (~(f8(c3) = c2))),
% 29.55/19.75 inference(monotonicity,[status(thm)],[26199])).
% 29.55/19.75 tff(26201,plain,
% 29.55/19.75 (~(f8(c3) = c2)),
% 29.55/19.75 inference(modus_ponens,[status(thm)],[12290, 26200])).
% 29.55/19.75 tff(26202,plain,
% 29.55/19.75 ($false),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[8569, 26201, 26197])).
% 29.55/19.75 tff(26203,plain,((~(c3 = c2)) | (c2 = f8(c2)) | (c1 = f8(c2))), inference(lemma,lemma(discharge,[]))).
% 29.55/19.75 tff(26204,plain,
% 29.55/19.75 ($false),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[26203, 26196, 26195, 67])).
% 29.55/19.75 tff(26205,plain,((~(f6(c2, c2) = c2)) | (~(c3 = c2)) | (f10(c2) = c2) | (~(f7(c2) = c2)) | big_f(c1, f10(c2)) | big_f(c2, f10(c2)) | (~big_f(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 29.55/19.75 tff(26206,plain,
% 29.55/19.75 (~(f6(c2, c2) = c2)),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[26205, 26189, 77, 26182, 26193, 67, 26159])).
% 29.55/19.75 tff(26207,plain,
% 29.55/19.75 (~(c2 = f8(c2))),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[21595, 26206, 67, 26182, 77, 26189])).
% 29.55/19.75 tff(26208,plain,
% 29.55/19.75 (c1 = f8(c2)),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[26203, 26207, 67])).
% 29.55/19.75 tff(26209,plain,
% 29.55/19.75 (f10(c2) = f8(c2)),
% 29.55/19.75 inference(modus_ponens,[status(thm)],[26208, 26185])).
% 29.55/19.75 tff(26210,plain,
% 29.55/19.75 (big_f(f10(c2), f10(c2)) <=> big_f(c1, c1)),
% 29.55/19.75 inference(monotonicity,[status(thm)],[26183, 26183])).
% 29.55/19.75 tff(26211,plain,
% 29.55/19.75 (big_f(c1, c1) <=> big_f(f10(c2), f10(c2))),
% 29.55/19.75 inference(symmetry,[status(thm)],[26210])).
% 29.55/19.75 tff(26212,plain,
% 29.55/19.75 ((~big_f(c1, c1)) <=> (~big_f(f10(c2), f10(c2)))),
% 29.55/19.75 inference(monotonicity,[status(thm)],[26211])).
% 29.55/19.75 tff(26213,plain,
% 29.55/19.75 (~big_f(f10(c2), f10(c2))),
% 29.55/19.75 inference(modus_ponens,[status(thm)],[66, 26212])).
% 29.55/19.75 tff(26214,plain,
% 29.55/19.75 (~(f10(c2) = f8(c2))),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[21579, 26206, 67, 26182, 2, 77, 26213])).
% 29.55/19.75 tff(26215,plain,
% 29.55/19.75 ($false),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[26214, 26209])).
% 29.55/19.75 tff(26216,plain,(big_f(c2, c1) | (~(c3 = c2)) | (~(f7(c2) = c2)) | big_f(c1, c1) | big_f(c1, c2)), inference(lemma,lemma(discharge,[]))).
% 29.55/19.75 tff(26217,plain,
% 29.55/19.75 (big_f(c2, c1)),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[26216, 77, 67, 66, 27])).
% 29.55/19.75 tff(26218,plain,
% 29.55/19.75 (big_f(c2, c2)),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[26036, 26217, 27, 77, 66])).
% 29.55/19.75 tff(26219,plain,
% 29.55/19.75 (c1 = c4),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[26079, 26217, 1335, 26218, 66])).
% 29.55/19.75 tff(26220,plain,
% 29.55/19.75 (c4 = c1),
% 29.55/19.75 inference(symmetry,[status(thm)],[26219])).
% 29.55/19.75 tff(26221,plain,
% 29.55/19.75 (f4(c4) = f4(c1)),
% 29.55/19.75 inference(monotonicity,[status(thm)],[26220])).
% 29.55/19.75 tff(26222,plain,
% 29.55/19.75 (f4(c1) = f4(c4)),
% 29.55/19.75 inference(symmetry,[status(thm)],[26221])).
% 29.55/19.75 tff(26223,plain,
% 29.55/19.75 (c2 = f4(c1)),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[25524, 26217, 1335, 26218, 26219, 26154])).
% 29.55/19.75 tff(26224,plain,
% 29.55/19.75 (c2 = c1),
% 29.55/19.75 inference(transitivity,[status(thm)],[26223, 26222, 26154])).
% 29.55/19.75 tff(26225,plain,
% 29.55/19.75 ($false),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[75, 26224])).
% 29.55/19.75 tff(26226,plain,((~(f7(c2) = c2)) | big_f(c1, c1) | big_f(c1, c2) | (~(c3 = c2))), inference(lemma,lemma(discharge,[]))).
% 29.55/19.75 tff(26227,plain,
% 29.55/19.75 (~(f7(c2) = c2)),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[26226, 66, 27, 67])).
% 29.55/19.75 tff(26228,plain,
% 29.55/19.75 (big_f(c2, f10(c2))),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[24856, 27, 66, 17, 89])).
% 29.55/19.75 tff(26229,plain,
% 29.55/19.75 (~(f10(c1) = c1)),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[24397, 21128, 66, 26228, 89, 17])).
% 29.55/19.75 tff(26230,plain,
% 29.55/19.75 (f10(c1) = c2),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[14, 26229])).
% 29.55/19.75 tff(26231,plain,
% 29.55/19.75 (f5(f10(c1)) = f5(c2)),
% 29.55/19.75 inference(monotonicity,[status(thm)],[26230])).
% 29.55/19.75 tff(26232,plain,
% 29.55/19.75 ((c1 = f5(f10(c1))) <=> (c1 = f5(c2))),
% 29.55/19.75 inference(monotonicity,[status(thm)],[26231])).
% 29.55/19.75 tff(26233,plain,
% 29.55/19.75 ((c1 = f5(f10(c1))) <=> (f5(c2) = c1)),
% 29.55/19.75 inference(transitivity,[status(thm)],[26232, 1531])).
% 29.55/19.75 tff(26234,plain,
% 29.55/19.75 ((f5(c2) = c1) <=> (c1 = f5(f10(c1)))),
% 29.55/19.75 inference(symmetry,[status(thm)],[26233])).
% 29.55/19.75 tff(26235,plain,
% 29.55/19.75 (~(c1 = f8(c1))),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[12260, 26229, 17, 94, 27, 12093])).
% 29.55/19.75 tff(26236,plain,
% 29.55/19.75 (~(f8(c1) = c1)),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[9808, 26235])).
% 29.55/19.75 tff(26237,plain,
% 29.55/19.75 (f8(c1) = c2),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[1680, 26236])).
% 29.55/19.75 tff(26238,plain,
% 29.55/19.75 ((f3(c2, c2) = f8(c1)) <=> (f3(c2, c2) = c2)),
% 29.55/19.75 inference(monotonicity,[status(thm)],[26237])).
% 29.55/19.75 tff(26239,plain,
% 29.55/19.75 ((f3(c2, c2) = c2) <=> (f3(c2, c2) = f8(c1))),
% 29.55/19.75 inference(symmetry,[status(thm)],[26238])).
% 29.55/19.75 tff(26240,plain,
% 29.55/19.75 (f3(f10(c1), f10(c1)) = f3(c2, c2)),
% 29.55/19.75 inference(monotonicity,[status(thm)],[26230, 26230])).
% 29.55/19.75 tff(26241,plain,
% 29.55/19.75 ((f3(f10(c1), f10(c1)) = f10(c1)) <=> (f3(c2, c2) = c2)),
% 29.55/19.75 inference(monotonicity,[status(thm)],[26240, 26230])).
% 29.55/19.75 tff(26242,plain,
% 29.55/19.75 ((f3(f10(c1), f10(c1)) = f10(c1)) <=> (f3(c2, c2) = f8(c1))),
% 29.55/19.75 inference(transitivity,[status(thm)],[26241, 26239])).
% 29.55/19.75 tff(26243,plain,
% 29.55/19.75 ((~(f3(f10(c1), f10(c1)) = f10(c1))) <=> (~(f3(c2, c2) = f8(c1)))),
% 29.55/19.75 inference(monotonicity,[status(thm)],[26242])).
% 29.55/19.75 tff(26244,plain,
% 29.55/19.75 (c2 = f10(c1)),
% 29.55/19.75 inference(symmetry,[status(thm)],[26230])).
% 29.55/19.75 tff(26245,plain,
% 29.55/19.75 (big_f(c1, c2) <=> big_f(c1, f10(c1))),
% 29.55/19.75 inference(monotonicity,[status(thm)],[26244])).
% 29.55/19.75 tff(26246,plain,
% 29.55/19.75 ((~big_f(c1, c2)) <=> (~big_f(c1, f10(c1)))),
% 29.55/19.75 inference(monotonicity,[status(thm)],[26245])).
% 29.55/19.75 tff(26247,plain,
% 29.55/19.75 (~big_f(c1, f10(c1))),
% 29.55/19.75 inference(modus_ponens,[status(thm)],[27, 26246])).
% 29.55/19.75 tff(26248,plain,
% 29.55/19.75 (big_f(f3(f10(c1), f10(c1)), f10(c1)) <=> big_f(f3(c2, c2), f10(c1))),
% 29.55/19.75 inference(monotonicity,[status(thm)],[26240])).
% 29.55/19.75 tff(26249,plain,
% 29.55/19.75 (big_f(f3(c2, c2), f10(c1)) <=> big_f(f3(f10(c1), f10(c1)), f10(c1))),
% 29.55/19.75 inference(symmetry,[status(thm)],[26248])).
% 29.55/19.75 tff(26250,plain,
% 29.55/19.75 (big_f(c1, c1)),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[24323, 2, 121, 27])).
% 29.55/19.75 tff(26251,plain,
% 29.55/19.75 (big_f(c1, f10(c2))),
% 29.55/19.75 inference(modus_ponens,[status(thm)],[26250, 24205])).
% 29.55/19.75 tff(26252,plain,
% 29.55/19.75 (~big_f(c2, c4)),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[6521, 79, 24305])).
% 29.55/19.75 tff(26253,plain,
% 29.55/19.75 ((f7(f7(c2)) = c3) <=> (f7(f7(c2)) = c1)),
% 29.55/19.75 inference(monotonicity,[status(thm)],[172])).
% 29.55/19.75 tff(26254,plain,
% 29.55/19.75 ((f7(f7(c2)) = c1) <=> (f7(f7(c2)) = c3)),
% 29.55/19.75 inference(symmetry,[status(thm)],[26253])).
% 29.55/19.75 tff(26255,plain,
% 29.55/19.75 ((f7(f7(c2)) = c1) <=> (c2 = c1)),
% 29.55/19.75 inference(monotonicity,[status(thm)],[5429])).
% 29.55/19.75 tff(26256,plain,
% 29.55/19.75 ((c2 = c1) <=> (f7(f7(c2)) = c1)),
% 29.55/19.75 inference(symmetry,[status(thm)],[26255])).
% 29.55/19.75 tff(26257,plain,
% 29.55/19.75 ((c2 = c1) <=> (f7(f7(c2)) = c3)),
% 29.55/19.75 inference(transitivity,[status(thm)],[26256, 26254])).
% 29.55/19.75 tff(26258,plain,
% 29.55/19.75 ((~(c2 = c1)) <=> (~(f7(f7(c2)) = c3))),
% 29.55/19.75 inference(monotonicity,[status(thm)],[26257])).
% 29.55/19.75 tff(26259,plain,
% 29.55/19.75 (~(f7(f7(c2)) = c3)),
% 29.55/19.75 inference(modus_ponens,[status(thm)],[75, 26258])).
% 29.55/19.75 tff(26260,plain,
% 29.55/19.75 (f1(f7(f7(c2)), c1) = c1),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[5433, 26259, 121, 379, 77])).
% 29.55/19.75 tff(26261,plain,
% 29.55/19.75 ((f1(c2, c1) = c3) <=> (f1(c2, c1) = c1)),
% 29.55/19.75 inference(monotonicity,[status(thm)],[172])).
% 29.55/19.75 tff(26262,plain,
% 29.55/19.75 ((f1(c2, c1) = c1) <=> (f1(c2, c1) = c3)),
% 29.55/19.75 inference(symmetry,[status(thm)],[26261])).
% 29.55/19.75 tff(26263,plain,
% 29.55/19.75 ((f1(f7(f7(c2)), c1) = c1) <=> (f1(c2, c1) = c3)),
% 29.55/19.75 inference(transitivity,[status(thm)],[11482, 26262])).
% 29.55/19.75 tff(26264,plain,
% 29.55/19.75 (f1(c2, c1) = c3),
% 29.55/19.75 inference(modus_ponens,[status(thm)],[26260, 26263])).
% 29.55/19.75 tff(26265,plain,
% 29.55/19.75 (f10(c1) = c1),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[11240, 26264, 4234, 4932, 121, 3865, 10089, 77, 26260])).
% 29.55/19.75 tff(26266,plain,
% 29.55/19.75 (f6(c1, c1) = c1),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[11298, 26260, 4234, 77, 172, 121, 2, 4932, 3865, 10089])).
% 29.55/19.75 tff(26267,plain,
% 29.55/19.75 (big_f(f7(c1), f6(c1, c1))),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[11304, 26266, 4234, 4932])).
% 29.55/19.75 tff(26268,plain,
% 29.55/19.75 (~(f9(c1, c1) = c1)),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[11325, 26265, 77, 4932, 26260, 4234, 26266])).
% 29.55/19.75 tff(26269,plain,
% 29.55/19.75 (big_f(f9(c1, c1), f10(c1))),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[10042, 26268, 26266, 26267, 26265, 4234])).
% 29.55/19.75 tff(26270,plain,
% 29.55/19.75 (f9(c1, c1) = c2),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[3939, 26268])).
% 29.55/19.75 tff(26271,plain,
% 29.55/19.75 (~big_f(f9(c1, c1), c1)),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[10058, 26270, 2])).
% 29.55/19.75 tff(26272,plain,
% 29.55/19.75 ($false),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[10033, 26271, 26269, 26265])).
% 29.55/19.75 tff(26273,plain,((~(f7(c2) = c2)) | big_f(c2, c1) | (~(f7(c1) = c1)) | (~big_f(c1, c1)) | big_f(c2, c2) | big_f(c2, c4) | (~(c2 = f4(c4))) | (~(c3 = c1)) | big_f(f4(c4), c4)), inference(lemma,lemma(discharge,[]))).
% 29.55/19.75 tff(26274,plain,
% 29.55/19.75 (~(f7(c2) = c2)),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[26273, 26252, 4234, 26250, 121, 2, 2602, 24304, 24305])).
% 29.55/19.75 tff(26275,plain,
% 29.55/19.75 (f7(c2) = c1),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[21, 26274])).
% 29.55/19.75 tff(26276,plain,
% 29.55/19.75 (~big_f(f7(c2), c2)),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[21127, 26275, 27])).
% 29.55/19.75 tff(26277,plain,
% 29.55/19.75 (big_f(f7(c2), c1)),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[20926, 26275, 11819, 26250])).
% 29.55/19.75 tff(26278,plain,
% 29.55/19.75 ($false),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[10081, 26277, 26276, 4234, 2, 79, 26274, 121])).
% 29.55/19.75 tff(26279,plain,((~(f4(c4) = c2)) | (~(f7(c1) = c1)) | big_f(c2, c1) | big_f(c2, c2) | (~(f10(c2) = c1)) | big_f(c1, c2)), inference(lemma,lemma(discharge,[]))).
% 29.55/19.75 tff(26280,plain,
% 29.55/19.75 (~(f4(c4) = c2)),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[26279, 2, 4234, 121, 11819, 27])).
% 29.55/19.75 tff(26281,plain,
% 29.55/19.75 (f4(c4) = c1),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[11750, 26280])).
% 29.55/19.75 tff(26282,plain,
% 29.55/19.75 (f7(f4(c4)) = f7(c1)),
% 29.55/19.75 inference(monotonicity,[status(thm)],[26281])).
% 29.55/19.75 tff(26283,plain,
% 29.55/19.75 (f7(f4(c4)) = c1),
% 29.55/19.75 inference(transitivity,[status(thm)],[26282, 4234])).
% 29.55/19.75 tff(26284,plain,
% 29.55/19.75 (big_f(f7(f4(c4)), c2) <=> big_f(c1, c2)),
% 29.55/19.75 inference(monotonicity,[status(thm)],[26283])).
% 29.55/19.75 tff(26285,plain,
% 29.55/19.75 (big_f(c1, c2) <=> big_f(f7(f4(c4)), c2)),
% 29.55/19.75 inference(symmetry,[status(thm)],[26284])).
% 29.55/19.75 tff(26286,plain,
% 29.55/19.75 ((~big_f(c1, c2)) <=> (~big_f(f7(f4(c4)), c2))),
% 29.55/19.75 inference(monotonicity,[status(thm)],[26285])).
% 29.55/19.75 tff(26287,plain,
% 29.55/19.75 (~big_f(f7(f4(c4)), c2)),
% 29.55/19.75 inference(modus_ponens,[status(thm)],[27, 26286])).
% 29.55/19.75 tff(26288,plain,
% 29.55/19.75 (big_f(f7(c2), c1)),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[20926, 22, 11819, 26250])).
% 29.55/19.75 tff(26289,plain,
% 29.55/19.75 (~big_f(f8(c1), f10(c1))),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[15724, 15, 22, 121, 23145])).
% 29.55/19.75 tff(26290,plain,
% 29.55/19.75 (~(c2 = f5(c2))),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[8107, 26289, 17, 23145, 3])).
% 29.55/19.75 tff(26291,plain,
% 29.55/19.75 (~(f5(c2) = c2)),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[8113, 26290])).
% 29.55/19.75 tff(26292,plain,
% 29.55/19.75 (f5(c2) = c1),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[1547, 26291])).
% 29.55/19.75 tff(26293,plain,
% 29.55/19.75 ((f6(c1, c1) = f5(c2)) <=> (f6(c1, c1) = c1)),
% 29.55/19.75 inference(monotonicity,[status(thm)],[26292])).
% 29.55/19.75 tff(26294,plain,
% 29.55/19.75 ((f6(c1, c1) = c1) <=> (f6(c1, c1) = f5(c2))),
% 29.55/19.75 inference(symmetry,[status(thm)],[26293])).
% 29.55/19.75 tff(26295,plain,
% 29.55/19.75 (f5(f10(c1)) = c1),
% 29.55/19.75 inference(transitivity,[status(thm)],[9888, 26292])).
% 29.55/19.75 tff(26296,plain,
% 29.55/19.75 ((f6(c1, c1) = f5(f10(c1))) <=> (f6(c1, c1) = c1)),
% 29.55/19.75 inference(monotonicity,[status(thm)],[26295])).
% 29.55/19.75 tff(26297,plain,
% 29.55/19.75 ((f6(c1, c1) = f5(f10(c1))) <=> (f6(c1, c1) = f5(c2))),
% 29.55/19.75 inference(transitivity,[status(thm)],[26296, 26294])).
% 29.55/19.75 tff(26298,plain,
% 29.55/19.75 ((~big_f(c2, c2)) <=> (~big_f(f10(c1), f10(c1)))),
% 29.55/19.75 inference(monotonicity,[status(thm)],[18939])).
% 29.55/19.75 tff(26299,plain,
% 29.55/19.75 (~big_f(f10(c1), f10(c1))),
% 29.55/19.75 inference(modus_ponens,[status(thm)],[121, 26298])).
% 29.55/19.75 tff(26300,plain,
% 29.55/19.75 (big_f(f7(c1), f6(c1, c1))),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[9826, 15821, 4234, 22, 338, 8451, 3])).
% 29.55/19.75 tff(26301,plain,
% 29.55/19.75 (big_f(f7(f10(c1)), f6(c1, c1))),
% 29.55/19.75 inference(modus_ponens,[status(thm)],[26300, 18802])).
% 29.55/19.75 tff(26302,plain,
% 29.55/19.75 ((f6(c1, c1) = f5(c2)) <=> (f6(c1, c1) = c1)),
% 29.55/19.75 inference(monotonicity,[status(thm)],[1569])).
% 29.55/19.75 tff(26303,plain,
% 29.55/19.75 ((f6(c1, c1) = c1) <=> (f6(c1, c1) = f5(c2))),
% 29.55/19.75 inference(symmetry,[status(thm)],[26302])).
% 29.55/19.75 tff(26304,plain,
% 29.55/19.75 (f5(f10(c1)) = c1),
% 29.55/19.75 inference(transitivity,[status(thm)],[9888, 1569])).
% 29.55/19.75 tff(26305,plain,
% 29.55/19.75 ((f6(c1, c1) = f5(f10(c1))) <=> (f6(c1, c1) = c1)),
% 29.55/19.75 inference(monotonicity,[status(thm)],[26304])).
% 29.55/19.75 tff(26306,plain,
% 29.55/19.75 ((f6(c1, c1) = f5(f10(c1))) <=> (f6(c1, c1) = f5(c2))),
% 29.55/19.75 inference(transitivity,[status(thm)],[26305, 26303])).
% 29.55/19.75 tff(26307,plain,
% 29.55/19.75 (f7(f10(c1)) = f7(c1)),
% 29.55/19.75 inference(transitivity,[status(thm)],[219, 292, 5544])).
% 29.55/19.75 tff(26308,plain,
% 29.55/19.75 (big_f(f7(f10(c1)), f6(c1, c1)) <=> big_f(f7(c1), f6(c1, c1))),
% 29.55/19.75 inference(monotonicity,[status(thm)],[26307])).
% 29.55/19.75 tff(26309,plain,
% 29.55/19.75 (big_f(f7(c1), f6(c1, c1)) <=> big_f(f7(f10(c1)), f6(c1, c1))),
% 29.55/19.75 inference(symmetry,[status(thm)],[26308])).
% 29.55/19.75 tff(26310,plain,
% 29.55/19.75 (big_f(f7(f10(c1)), f6(c1, c1))),
% 29.55/19.75 inference(modus_ponens,[status(thm)],[5964, 26309])).
% 29.55/19.75 tff(26311,plain,
% 29.55/19.75 (f7(f10(c1)) = c1),
% 29.55/19.75 inference(transitivity,[status(thm)],[219, 292])).
% 29.55/19.75 tff(26312,plain,
% 29.55/19.75 ((f7(f10(c1)) = f10(c1)) <=> (c1 = f10(c1))),
% 29.55/19.75 inference(monotonicity,[status(thm)],[26311])).
% 29.55/19.75 tff(26313,plain,
% 29.55/19.75 ((f7(f10(c1)) = f10(c1)) <=> (f10(c1) = c1)),
% 29.55/19.75 inference(transitivity,[status(thm)],[26312, 18819])).
% 29.55/19.75 tff(26314,plain,
% 29.55/19.75 ((f10(c1) = c1) <=> (f7(f10(c1)) = f10(c1))),
% 29.55/19.75 inference(symmetry,[status(thm)],[26313])).
% 29.55/19.75 tff(26315,plain,
% 29.55/19.75 ((~(f10(c1) = c1)) <=> (~(f7(f10(c1)) = f10(c1)))),
% 29.55/19.75 inference(monotonicity,[status(thm)],[26314])).
% 29.55/19.75 tff(26316,plain,
% 29.55/19.75 (~(f7(f10(c1)) = f10(c1))),
% 29.55/19.75 inference(modus_ponens,[status(thm)],[3, 26315])).
% 29.55/19.75 tff(26317,plain,
% 29.55/19.75 ((~(c1 = f8(c1))) | (f6(c1, c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, c1)))),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[18840, 2795, 3, 3030, 26316])).
% 29.55/19.75 tff(26318,plain,
% 29.55/19.75 (f6(c1, c1) = f5(f10(c1))),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[26317, 3031, 26310])).
% 29.55/19.75 tff(26319,plain,
% 29.55/19.75 (f6(c1, c1) = f5(c2)),
% 29.55/19.75 inference(modus_ponens,[status(thm)],[26318, 26306])).
% 29.55/19.75 tff(26320,plain,
% 29.55/19.75 (f7(c2) = f5(c2)),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[8394, 1569, 292])).
% 29.55/19.75 tff(26321,plain,
% 29.55/19.75 ((~(c1 = f8(c1))) | (~(f6(c1, c1) = c1))),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[18583, 2963, 4234, 3, 3030, 5964])).
% 29.55/19.75 tff(26322,plain,
% 29.55/19.75 (~(f6(c1, c1) = c1)),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[26321, 3031])).
% 29.55/19.75 tff(26323,plain,
% 29.55/19.75 (~(f6(c1, c1) = f5(c2))),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[10715, 26322, 292, 26320])).
% 29.55/19.75 tff(26324,plain,
% 29.55/19.75 ($false),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[26323, 26319])).
% 29.55/19.75 tff(26325,plain,((~(c1 = f8(c1))) | (~(f5(c2) = c1)) | (~(f7(c2) = c1)) | (~(f7(c1) = c1)) | (f10(c1) = c1) | big_f(c1, f10(c1)) | (~big_f(f7(c1), f6(c1, c1)))), inference(lemma,lemma(discharge,[]))).
% 29.55/19.75 tff(26326,plain,
% 29.55/19.75 (~(c1 = f8(c1))),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[26325, 26292, 22, 4234, 3, 15821, 26300])).
% 29.55/19.75 tff(26327,plain,
% 29.55/19.75 (~(f8(c1) = c1)),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[9808, 26326])).
% 29.55/19.75 tff(26328,plain,
% 29.55/19.75 (f8(c1) = c2),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[1680, 26327])).
% 29.55/19.75 tff(26329,plain,
% 29.55/19.75 (c2 = f8(c1)),
% 29.55/19.75 inference(symmetry,[status(thm)],[26328])).
% 29.55/19.75 tff(26330,plain,
% 29.55/19.75 (f10(c1) = f8(c1)),
% 29.55/19.75 inference(transitivity,[status(thm)],[15, 26329])).
% 29.55/19.75 tff(26331,plain,
% 29.55/19.75 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | (f7(f10(c1)) = f10(c1)) | (f6(c1, c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, c1))) | big_f(f10(c1), f10(c1)) | (~(f10(c1) = f8(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | (f10(c1) = c1) | (f7(f10(c1)) = f10(c1)) | (f6(c1, c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, c1))) | big_f(f10(c1), f10(c1)) | (~(f10(c1) = f8(c1))))),
% 29.55/19.75 inference(rewrite,[status(thm)],[])).
% 29.55/19.75 tff(26332,plain,
% 29.55/19.75 (((f10(c1) = c1) | big_f(f10(c1), f10(c1)) | (f7(f10(c1)) = f10(c1)) | (f6(c1, c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, c1))) | (~(f10(c1) = f8(c1)))) <=> ((f10(c1) = c1) | (f7(f10(c1)) = f10(c1)) | (f6(c1, c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, c1))) | big_f(f10(c1), f10(c1)) | (~(f10(c1) = f8(c1))))),
% 29.55/19.75 inference(rewrite,[status(thm)],[])).
% 29.55/19.75 tff(26333,plain,
% 29.55/19.75 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | big_f(f10(c1), f10(c1)) | (f7(f10(c1)) = f10(c1)) | (f6(c1, c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, c1))) | (~(f10(c1) = f8(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | (f7(f10(c1)) = f10(c1)) | (f6(c1, c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, c1))) | big_f(f10(c1), f10(c1)) | (~(f10(c1) = f8(c1)))))),
% 29.55/19.75 inference(monotonicity,[status(thm)],[26332])).
% 29.55/19.75 tff(26334,plain,
% 29.55/19.75 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | big_f(f10(c1), f10(c1)) | (f7(f10(c1)) = f10(c1)) | (f6(c1, c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, c1))) | (~(f10(c1) = f8(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | (f10(c1) = c1) | (f7(f10(c1)) = f10(c1)) | (f6(c1, c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, c1))) | big_f(f10(c1), f10(c1)) | (~(f10(c1) = f8(c1))))),
% 29.55/19.75 inference(transitivity,[status(thm)],[26333, 26331])).
% 29.55/19.75 tff(26335,plain,
% 29.55/19.75 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | ((f10(c1) = c1) | big_f(f10(c1), f10(c1)) | (f7(f10(c1)) = f10(c1)) | (f6(c1, c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, c1))) | (~(f10(c1) = f8(c1))))),
% 29.55/19.75 inference(quant_inst,[status(thm)],[])).
% 29.55/19.75 tff(26336,plain,
% 29.55/19.75 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(X8 = f8(X7))))) | (f10(c1) = c1) | (f7(f10(c1)) = f10(c1)) | (f6(c1, c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, c1))) | big_f(f10(c1), f10(c1)) | (~(f10(c1) = f8(c1)))),
% 29.55/19.75 inference(modus_ponens,[status(thm)],[26335, 26334])).
% 29.55/19.75 tff(26337,plain,
% 29.55/19.75 ((f6(c1, c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, c1))) | big_f(f10(c1), f10(c1)) | (~(f10(c1) = f8(c1)))),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[26336, 2795, 3, 18825])).
% 29.55/19.75 tff(26338,plain,
% 29.55/19.75 (f6(c1, c1) = f5(f10(c1))),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[26337, 26330, 26301, 26299])).
% 29.55/19.75 tff(26339,plain,
% 29.55/19.75 (f6(c1, c1) = f5(c2)),
% 29.55/19.75 inference(modus_ponens,[status(thm)],[26338, 26297])).
% 29.55/19.75 tff(26340,plain,
% 29.55/19.75 (f7(c2) = f5(c2)),
% 29.55/19.75 inference(unit_resolution,[status(thm)],[8394, 26292, 22])).
% 29.55/19.75 tff(26341,plain,
% 29.55/19.75 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | big_f(f10(c1), f10(c1)) | (~(f10(c1) = f8(c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | big_f(f10(c1), f10(c1)) | (~(f10(c1) = f8(c1))))),
% 29.55/19.75 inference(rewrite,[status(thm)],[])).
% 29.55/19.75 tff(26342,plain,
% 29.55/19.75 (((f10(c1) = c1) | big_f(f10(c1), f10(c1)) | (~(f7(c1) = c1)) | (~(f10(c1) = f8(c1))) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1)))) <=> ((f10(c1) = c1) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | big_f(f10(c1), f10(c1)) | (~(f10(c1) = f8(c1))))),
% 29.55/19.75 inference(rewrite,[status(thm)],[])).
% 29.55/19.75 tff(26343,plain,
% 29.55/19.75 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | big_f(f10(c1), f10(c1)) | (~(f7(c1) = c1)) | (~(f10(c1) = f8(c1))) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | big_f(f10(c1), f10(c1)) | (~(f10(c1) = f8(c1)))))),
% 29.55/19.75 inference(monotonicity,[status(thm)],[26342])).
% 29.55/19.75 tff(26344,plain,
% 29.55/19.75 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | big_f(f10(c1), f10(c1)) | (~(f7(c1) = c1)) | (~(f10(c1) = f8(c1))) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | big_f(f10(c1), f10(c1)) | (~(f10(c1) = f8(c1))))),
% 29.55/19.75 inference(transitivity,[status(thm)],[26343, 26341])).
% 29.55/19.75 tff(26345,plain,
% 29.55/19.75 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | big_f(f10(c1), f10(c1)) | (~(f7(c1) = c1)) | (~(f10(c1) = f8(c1))) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))),
% 29.55/19.75 inference(quant_inst,[status(thm)],[])).
% 29.55/19.75 tff(26346,plain,
% 29.55/19.75 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | big_f(f10(c1), f10(c1)) | (~(f10(c1) = f8(c1)))),
% 29.55/19.75 inference(modus_ponens,[status(thm)],[26345, 26344])).
% 29.55/19.75 tff(26347,plain,
% 29.55/19.75 ((~(f6(c1, c1) = c1)) | big_f(f10(c1), f10(c1)) | (~(f10(c1) = f8(c1)))),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[26346, 2963, 4234, 3, 26300])).
% 29.55/19.76 tff(26348,plain,
% 29.55/19.76 (~(f6(c1, c1) = c1)),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[26347, 26330, 26299])).
% 29.55/19.76 tff(26349,plain,
% 29.55/19.76 (~(f6(c1, c1) = f5(c2))),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[10715, 26348, 22, 26340])).
% 29.55/19.76 tff(26350,plain,
% 29.55/19.76 ($false),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[26349, 26339])).
% 29.55/19.76 tff(26351,plain,((f10(c1) = c1) | (~(f7(c1) = c1)) | big_f(c2, c2) | (~big_f(f7(c2), c1)) | big_f(c1, c2) | (f7(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 29.55/19.76 tff(26352,plain,
% 29.55/19.76 (f10(c1) = c1),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[26351, 26288, 121, 4234, 27, 17])).
% 29.55/19.76 tff(26353,plain,
% 29.55/19.76 (~(f9(c1, c1) = c1)),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[9972, 65, 4234, 292, 3762, 338, 19047])).
% 29.55/19.76 tff(26354,plain,
% 29.55/19.76 (~(f9(f10(c2), f4(c4)) = c1)),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[19829, 26353, 11752, 11819])).
% 29.55/19.76 tff(26355,plain,
% 29.55/19.76 (f9(f10(c2), f4(c4)) = c2),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[146, 26354])).
% 29.55/19.76 tff(26356,plain,
% 29.55/19.76 (f9(f10(c2), f10(c2)) = c2),
% 29.55/19.76 inference(transitivity,[status(thm)],[17769, 17727, 26355])).
% 29.55/19.76 tff(26357,plain,
% 29.55/19.76 (f10(f9(f10(c2), f10(c2))) = f10(c2)),
% 29.55/19.76 inference(monotonicity,[status(thm)],[26356])).
% 29.55/19.76 tff(26358,plain,
% 29.55/19.76 (f10(f9(c1, c1)) = f10(f9(f10(c2), f10(c2)))),
% 29.55/19.76 inference(monotonicity,[status(thm)],[17870])).
% 29.55/19.76 tff(26359,plain,
% 29.55/19.76 (f10(f9(c1, c1)) = f10(c1)),
% 29.55/19.76 inference(transitivity,[status(thm)],[26358, 26357, 11819, 11570])).
% 29.55/19.76 tff(26360,plain,
% 29.55/19.76 (big_f(f9(c1, c1), f10(f9(c1, c1))) <=> big_f(f9(c1, c1), f10(c1))),
% 29.55/19.76 inference(monotonicity,[status(thm)],[26359])).
% 29.55/19.76 tff(26361,plain,
% 29.55/19.76 (big_f(f9(c1, c1), f10(c1)) <=> big_f(f9(c1, c1), f10(f9(c1, c1)))),
% 29.55/19.76 inference(symmetry,[status(thm)],[26360])).
% 29.55/19.76 tff(26362,plain,
% 29.55/19.76 (big_f(f9(c1, c1), f10(f9(c1, c1)))),
% 29.55/19.76 inference(modus_ponens,[status(thm)],[19047, 26361])).
% 29.55/19.76 tff(26363,plain,
% 29.55/19.76 (f10(f9(c1, c1)) = c1),
% 29.55/19.76 inference(transitivity,[status(thm)],[26358, 26357, 11819])).
% 29.55/19.76 tff(26364,plain,
% 29.55/19.76 (big_f(c1, f10(f9(c1, c1))) <=> big_f(f7(c2), c1)),
% 29.55/19.76 inference(monotonicity,[status(thm)],[342, 26363])).
% 29.55/19.76 tff(26365,plain,
% 29.55/19.76 (big_f(f7(c2), c1) <=> big_f(c1, f10(f9(c1, c1)))),
% 29.55/19.76 inference(symmetry,[status(thm)],[26364])).
% 29.55/19.76 tff(26366,plain,
% 29.55/19.76 (big_f(c1, f10(f9(c1, c1)))),
% 29.55/19.76 inference(modus_ponens,[status(thm)],[338, 26365])).
% 29.55/19.76 tff(26367,plain,
% 29.55/19.76 ((f10(f9(c1, c1)) = f9(c1, c1)) <=> (c1 = f9(c1, c1))),
% 29.55/19.76 inference(monotonicity,[status(thm)],[26363])).
% 29.55/19.76 tff(26368,plain,
% 29.55/19.76 ((f10(f9(c1, c1)) = f9(c1, c1)) <=> (f9(c1, c1) = c1)),
% 29.55/19.76 inference(transitivity,[status(thm)],[26367, 17725])).
% 29.55/19.76 tff(26369,plain,
% 29.55/19.76 ((f9(c1, c1) = c1) <=> (f10(f9(c1, c1)) = f9(c1, c1))),
% 29.55/19.76 inference(symmetry,[status(thm)],[26368])).
% 29.55/19.76 tff(26370,plain,
% 29.55/19.76 ((~(f9(c1, c1) = c1)) <=> (~(f10(f9(c1, c1)) = f9(c1, c1)))),
% 29.55/19.76 inference(monotonicity,[status(thm)],[26369])).
% 29.55/19.76 tff(26371,plain,
% 29.55/19.76 (~(f10(f9(c1, c1)) = f9(c1, c1))),
% 29.55/19.76 inference(modus_ponens,[status(thm)],[26353, 26370])).
% 29.55/19.76 tff(26372,plain,
% 29.55/19.76 (f6(c1, c1) = c1),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[19458, 26353, 4234, 65, 26371, 26366, 26362])).
% 29.55/19.76 tff(26373,plain,
% 29.55/19.76 (f6(c1, f5(c1)) = f6(c1, c1)),
% 29.55/19.76 inference(monotonicity,[status(thm)],[230])).
% 29.55/19.76 tff(26374,plain,
% 29.55/19.76 (f6(c1, f5(c1)) = c1),
% 29.55/19.76 inference(transitivity,[status(thm)],[26373, 26372])).
% 29.55/19.76 tff(26375,plain,
% 29.55/19.76 (big_f(f7(c1), f6(c1, f5(c1))) <=> big_f(f7(c2), c1)),
% 29.55/19.76 inference(monotonicity,[status(thm)],[8286, 26374])).
% 29.55/19.76 tff(26376,plain,
% 29.55/19.76 (big_f(f7(c2), c1) <=> big_f(f7(c1), f6(c1, f5(c1)))),
% 29.55/19.76 inference(symmetry,[status(thm)],[26375])).
% 29.55/19.76 tff(26377,plain,
% 29.55/19.76 (big_f(f7(c1), f6(c1, f5(c1)))),
% 29.55/19.76 inference(modus_ponens,[status(thm)],[338, 26376])).
% 29.55/19.76 tff(26378,plain,
% 29.55/19.76 (f6(c1, c1) = f6(c1, f5(c1))),
% 29.55/19.76 inference(symmetry,[status(thm)],[26373])).
% 29.55/19.76 tff(26379,plain,
% 29.55/19.76 (big_f(f7(c1), f6(c1, c1)) <=> big_f(f7(c1), f6(c1, f5(c1)))),
% 29.55/19.76 inference(monotonicity,[status(thm)],[26378])).
% 29.55/19.76 tff(26380,plain,
% 29.55/19.76 ((~big_f(f7(c1), f6(c1, c1))) <=> (~big_f(f7(c1), f6(c1, f5(c1))))),
% 29.55/19.76 inference(monotonicity,[status(thm)],[26379])).
% 29.55/19.76 tff(26381,plain,
% 29.55/19.76 (~big_f(f7(c1), f6(c1, f5(c1)))),
% 29.55/19.76 inference(modus_ponens,[status(thm)],[65, 26380])).
% 29.55/19.76 tff(26382,plain,
% 29.55/19.76 ($false),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[26381, 26377])).
% 29.55/19.76 tff(26383,plain,(big_f(f7(c1), f6(c1, c1)) | (~big_f(f7(c2), c1)) | (~(f5(c1) = c1)) | (~(f7(c1) = c1)) | (~(f7(c2) = c1)) | (~(f10(c1) = c1)) | (~(f10(c2) = c1)) | (~(f4(c4) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.55/19.76 tff(26384,plain,
% 29.55/19.76 (big_f(f7(c1), f6(c1, c1))),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[26383, 230, 4234, 11819, 338, 292, 3762, 11752])).
% 29.55/19.76 tff(26385,plain,
% 29.55/19.76 (f6(f7(c2), f5(c1)) = f6(c1, f5(c1))),
% 29.55/19.76 inference(monotonicity,[status(thm)],[292])).
% 29.55/19.76 tff(26386,plain,
% 29.55/19.76 (f6(c1, f5(c1)) = f6(f7(c2), f5(c1))),
% 29.55/19.76 inference(symmetry,[status(thm)],[26385])).
% 29.55/19.76 tff(26387,plain,
% 29.55/19.76 (f6(c1, c1) = c2),
% 29.55/19.76 inference(transitivity,[status(thm)],[26378, 26386, 3032])).
% 29.55/19.76 tff(26388,plain,
% 29.55/19.76 (big_f(f7(c1), f6(c1, c1)) <=> big_f(c1, c2)),
% 29.55/19.76 inference(monotonicity,[status(thm)],[4234, 26387])).
% 29.55/19.76 tff(26389,plain,
% 29.55/19.76 (big_f(c1, c2) <=> big_f(f7(c1), f6(c1, c1))),
% 29.55/19.76 inference(symmetry,[status(thm)],[26388])).
% 29.55/19.76 tff(26390,plain,
% 29.55/19.76 ((~big_f(c1, c2)) <=> (~big_f(f7(c1), f6(c1, c1)))),
% 29.55/19.76 inference(monotonicity,[status(thm)],[26389])).
% 29.55/19.76 tff(26391,plain,
% 29.55/19.76 (~big_f(f7(c1), f6(c1, c1))),
% 29.55/19.76 inference(modus_ponens,[status(thm)],[27, 26390])).
% 29.55/19.76 tff(26392,plain,
% 29.55/19.76 ($false),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[5964, 26391])).
% 29.55/19.76 tff(26393,plain,((~(f6(f7(c2), f5(c1)) = c2)) | (~big_f(f7(c1), f6(c1, c1))) | big_f(c1, c2) | (~(f5(c1) = c1)) | (~(f7(c2) = c1)) | (~(f7(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.55/19.76 tff(26394,plain,
% 29.55/19.76 (~(f6(f7(c2), f5(c1)) = c2)),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[26393, 26384, 27, 230, 292, 4234])).
% 29.55/19.76 tff(26395,plain,
% 29.55/19.76 (f6(f7(c2), f5(c1)) = c1),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[2978, 26394])).
% 29.55/19.76 tff(26396,plain,
% 29.55/19.76 (f6(c1, c1) = f6(c1, f5(c1))),
% 29.55/19.76 inference(monotonicity,[status(thm)],[2941])).
% 29.55/19.76 tff(26397,plain,
% 29.55/19.76 (f6(c1, c1) = f6(f7(c2), f5(c1))),
% 29.55/19.76 inference(transitivity,[status(thm)],[26396, 26386])).
% 29.55/19.76 tff(26398,plain,
% 29.55/19.76 ((f6(c1, c1) = c1) <=> (f6(f7(c2), f5(c1)) = c1)),
% 29.55/19.76 inference(monotonicity,[status(thm)],[26397])).
% 29.55/19.76 tff(26399,plain,
% 29.55/19.76 ((f6(f7(c2), f5(c1)) = c1) <=> (f6(c1, c1) = c1)),
% 29.55/19.76 inference(symmetry,[status(thm)],[26398])).
% 29.55/19.76 tff(26400,plain,
% 29.55/19.76 (f6(c1, c1) = c1),
% 29.55/19.76 inference(modus_ponens,[status(thm)],[2947, 26399])).
% 29.55/19.76 tff(26401,plain,
% 29.55/19.76 ($false),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[28, 26400])).
% 29.55/19.76 tff(26402,plain,((~(f6(f7(c2), f5(c1)) = c1)) | (f6(c1, c1) = c1) | (~(f5(c1) = c1)) | (~(f7(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.55/19.76 tff(26403,plain,
% 29.55/19.76 (f6(c1, c1) = c1),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[26402, 26395, 292, 230])).
% 29.55/19.76 tff(26404,plain,
% 29.55/19.76 (big_f(f9(c1, c1), f10(c1))),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[19043, 148, 292, 3762, 338, 11752, 11819])).
% 29.55/19.76 tff(26405,plain,
% 29.55/19.76 (f9(c1, c1) = c1),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[19829, 148, 11752, 11819])).
% 29.55/19.76 tff(26406,plain,
% 29.55/19.76 ($false),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[18907, 2378, 4234, 3762, 26405, 26404, 5964, 10030])).
% 29.55/19.76 tff(26407,plain,((~(f9(f10(c2), f4(c4)) = c1)) | (~(f7(c1) = c1)) | (~(f10(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (~(f7(c2) = c1)) | (~big_f(f7(c2), c1)) | (~(f4(c4) = c1)) | (~(f10(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.55/19.76 tff(26408,plain,
% 29.55/19.76 (~(f9(f10(c2), f4(c4)) = c1)),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[26407, 26403, 4234, 11752, 338, 292, 3762, 26384, 11819])).
% 29.55/19.76 tff(26409,plain,
% 29.55/19.76 (f9(f10(c2), f4(c4)) = c2),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[146, 26408])).
% 29.55/19.76 tff(26410,plain,
% 29.55/19.76 (big_f(f9(c1, c1), c1)),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[10051, 26403, 292, 3762, 26384, 4234, 338])).
% 29.55/19.76 tff(26411,plain,
% 29.55/19.76 (big_f(f9(c1, c1), f10(c1))),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[8716, 26410, 3762])).
% 29.55/19.76 tff(26412,plain,
% 29.55/19.76 ($false),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[19082, 26411, 26409, 11819, 11752, 2, 3762])).
% 29.55/19.76 tff(26413,plain,((~(f5(c1) = c1)) | (~(f10(c2) = c1)) | (~(f4(c4) = c1)) | big_f(c2, c1) | (~(f10(c1) = c1)) | (~(f7(c2) = c1)) | (~(f7(c1) = c1)) | (~big_f(f7(c2), c1)) | big_f(c1, c2)), inference(lemma,lemma(discharge,[]))).
% 29.55/19.76 tff(26414,plain,
% 29.55/19.76 (~(f5(c1) = c1)),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[26413, 26352, 26281, 2, 11819, 22, 4234, 26288, 27])).
% 29.55/19.76 tff(26415,plain,
% 29.55/19.76 (f7(f5(c1)) = f7(c2)),
% 29.55/19.76 inference(monotonicity,[status(thm)],[16519])).
% 29.55/19.76 tff(26416,plain,
% 29.55/19.76 (f7(f5(c1)) = c1),
% 29.55/19.76 inference(transitivity,[status(thm)],[26415, 22])).
% 29.55/19.76 tff(26417,plain,
% 29.55/19.76 ((f7(f5(c1)) = f5(c1)) <=> (c1 = f5(c1))),
% 29.55/19.76 inference(monotonicity,[status(thm)],[26416])).
% 29.55/19.76 tff(26418,plain,
% 29.55/19.76 ((f7(f5(c1)) = f5(c1)) <=> (f5(c1) = c1)),
% 29.55/19.76 inference(transitivity,[status(thm)],[26417, 128])).
% 29.55/19.76 tff(26419,plain,
% 29.55/19.76 ((f5(c1) = c1) <=> (f7(f5(c1)) = f5(c1))),
% 29.55/19.76 inference(symmetry,[status(thm)],[26418])).
% 29.55/19.76 tff(26420,plain,
% 29.55/19.76 ((~(f5(c1) = c1)) <=> (~(f7(f5(c1)) = f5(c1)))),
% 29.55/19.76 inference(monotonicity,[status(thm)],[26419])).
% 29.55/19.76 tff(26421,plain,
% 29.55/19.76 (~(f7(f5(c1)) = f5(c1))),
% 29.55/19.76 inference(modus_ponens,[status(thm)],[16518, 26420])).
% 29.55/19.76 tff(26422,plain,
% 29.55/19.76 (f5(f5(c1)) = f5(c2)),
% 29.55/19.76 inference(monotonicity,[status(thm)],[16519])).
% 29.55/19.76 tff(26423,plain,
% 29.55/19.76 (f5(c2) = f5(f5(c1))),
% 29.55/19.76 inference(symmetry,[status(thm)],[26422])).
% 29.55/19.76 tff(26424,plain,
% 29.55/19.76 (f5(c1) = f5(f5(c1))),
% 29.55/19.76 inference(transitivity,[status(thm)],[16519, 10481, 26423])).
% 29.55/19.76 tff(26425,plain,
% 29.55/19.76 (big_f(f7(f5(c1)), f5(c1)) <=> big_f(c1, f5(c1))),
% 29.55/19.76 inference(monotonicity,[status(thm)],[26416])).
% 29.55/19.76 tff(26426,plain,
% 29.55/19.76 (big_f(c1, f5(c1)) <=> big_f(f7(f5(c1)), f5(c1))),
% 29.55/19.76 inference(symmetry,[status(thm)],[26425])).
% 29.55/19.76 tff(26427,plain,
% 29.55/19.76 ((~big_f(c1, f5(c1))) <=> (~big_f(f7(f5(c1)), f5(c1)))),
% 29.55/19.76 inference(monotonicity,[status(thm)],[26426])).
% 29.55/19.76 tff(26428,plain,
% 29.55/19.76 (~big_f(f7(c1), f5(c1))),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[18267, 16519, 11752, 18265])).
% 29.55/19.76 tff(26429,plain,
% 29.55/19.76 (~big_f(c1, f5(c1))),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[18887, 26428, 4234])).
% 29.55/19.76 tff(26430,plain,
% 29.55/19.76 (~big_f(f7(f5(c1)), f5(c1))),
% 29.55/19.76 inference(modus_ponens,[status(thm)],[26429, 26427])).
% 29.55/19.76 tff(26431,plain,
% 29.55/19.76 (~(f9(f10(c2), f4(c4)) = c2)),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[20203, 16519, 11819, 11752, 121, 17, 3762])).
% 29.55/19.76 tff(26432,plain,
% 29.55/19.76 (f9(f10(c2), f4(c4)) = c1),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[146, 26431])).
% 29.55/19.76 tff(26433,plain,
% 29.55/19.76 (big_f(f9(c1, c1), f10(c1))),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[19043, 26432, 11819, 11752, 338, 22, 3762])).
% 29.55/19.76 tff(26434,plain,
% 29.55/19.76 (f9(c1, c1) = c1),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[19829, 26432, 11819, 11752])).
% 29.55/19.76 tff(26435,plain,
% 29.55/19.76 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(f5(c1) = f5(f5(c1)))) | big_f(f7(f5(c1)), f5(c1)) | (f7(f5(c1)) = f5(c1)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(f5(c1) = f5(f5(c1)))) | big_f(f7(f5(c1)), f5(c1)) | (f7(f5(c1)) = f5(c1)))),
% 29.55/19.76 inference(rewrite,[status(thm)],[])).
% 29.55/19.76 tff(26436,plain,
% 29.55/19.76 (((~(f10(c1) = c1)) | (f7(f5(c1)) = f5(c1)) | big_f(f7(f5(c1)), f5(c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(f5(c1) = f5(f5(c1))))) <=> ((~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(f5(c1) = f5(f5(c1)))) | big_f(f7(f5(c1)), f5(c1)) | (f7(f5(c1)) = f5(c1)))),
% 29.55/19.76 inference(rewrite,[status(thm)],[])).
% 29.55/19.76 tff(26437,plain,
% 29.55/19.76 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f7(f5(c1)) = f5(c1)) | big_f(f7(f5(c1)), f5(c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(f5(c1) = f5(f5(c1)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(f5(c1) = f5(f5(c1)))) | big_f(f7(f5(c1)), f5(c1)) | (f7(f5(c1)) = f5(c1))))),
% 29.55/19.76 inference(monotonicity,[status(thm)],[26436])).
% 29.55/19.76 tff(26438,plain,
% 29.55/19.76 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f7(f5(c1)) = f5(c1)) | big_f(f7(f5(c1)), f5(c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(f5(c1) = f5(f5(c1)))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(f5(c1) = f5(f5(c1)))) | big_f(f7(f5(c1)), f5(c1)) | (f7(f5(c1)) = f5(c1)))),
% 29.55/19.76 inference(transitivity,[status(thm)],[26437, 26435])).
% 29.55/19.76 tff(26439,plain,
% 29.55/19.76 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f7(f5(c1)) = f5(c1)) | big_f(f7(f5(c1)), f5(c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(f5(c1) = f5(f5(c1)))))),
% 29.55/19.76 inference(quant_inst,[status(thm)],[])).
% 29.55/19.76 tff(26440,plain,
% 29.55/19.76 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(f5(c1) = f5(f5(c1)))) | big_f(f7(f5(c1)), f5(c1)) | (f7(f5(c1)) = f5(c1))),
% 29.55/19.76 inference(modus_ponens,[status(thm)],[26439, 26438])).
% 29.55/19.76 tff(26441,plain,
% 29.55/19.76 ((~(f5(c1) = f5(f5(c1)))) | big_f(f7(f5(c1)), f5(c1)) | (f7(f5(c1)) = f5(c1))),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[26440, 783, 3762, 26434, 26433])).
% 29.55/19.76 tff(26442,plain,
% 29.55/19.76 ($false),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[26441, 26430, 26424, 26421])).
% 29.55/19.76 tff(26443,plain,((f5(c1) = c1) | (~(f10(c1) = c1)) | (~(f5(c2) = c2)) | (~(f10(c2) = c1)) | (~(f4(c4) = c1)) | (~big_f(f7(c2), c1)) | (~(f7(c1) = c1)) | big_f(c2, c2) | (f7(c2) = c2) | big_f(f7(f4(c4)), c2)), inference(lemma,lemma(discharge,[]))).
% 29.55/19.76 tff(26444,plain,
% 29.55/19.76 (~(f5(c2) = c2)),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[26443, 26414, 26352, 11819, 26281, 26288, 4234, 121, 17, 26287])).
% 29.55/19.76 tff(26445,plain,
% 29.55/19.76 (f5(c2) = c1),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[1547, 26444])).
% 29.55/19.76 tff(26446,plain,
% 29.55/19.76 (f5(c1) = c2),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[1708, 26414])).
% 29.55/19.76 tff(26447,plain,
% 29.55/19.76 (f5(f5(c1)) = f5(c2)),
% 29.55/19.76 inference(monotonicity,[status(thm)],[26446])).
% 29.55/19.76 tff(26448,plain,
% 29.55/19.76 (f5(f5(c1)) = c1),
% 29.55/19.76 inference(transitivity,[status(thm)],[26447, 26445])).
% 29.55/19.76 tff(26449,plain,
% 29.55/19.76 ((f6(c1, c1) = f5(f5(c1))) <=> (f6(c1, c1) = c1)),
% 29.55/19.76 inference(monotonicity,[status(thm)],[26448])).
% 29.55/19.76 tff(26450,plain,
% 29.55/19.76 ((f6(c1, c1) = c1) <=> (f6(c1, c1) = f5(f5(c1)))),
% 29.55/19.76 inference(symmetry,[status(thm)],[26449])).
% 29.55/19.76 tff(26451,plain,
% 29.55/19.76 ((~(f6(c1, c1) = c1)) <=> (~(f6(c1, c1) = f5(f5(c1))))),
% 29.55/19.76 inference(monotonicity,[status(thm)],[26450])).
% 29.55/19.76 tff(26452,plain,
% 29.55/19.76 (~(f9(f10(c2), f4(c4)) = c2)),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[20203, 26446, 11819, 26281, 121, 17, 26352])).
% 29.55/19.76 tff(26453,plain,
% 29.55/19.76 (f9(f10(c2), f4(c4)) = c1),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[146, 26452])).
% 29.55/19.76 tff(26454,plain,
% 29.55/19.76 (f9(c1, c1) = c1),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[19829, 26453, 11819, 26281])).
% 29.55/19.76 tff(26455,plain,
% 29.55/19.76 (big_f(f7(c1), f6(c1, c1))),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[9976, 26454, 4234, 26288, 22, 26352])).
% 29.55/19.76 tff(26456,plain,
% 29.55/19.76 (~(f6(c1, c1) = c1)),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[26407, 26455, 4234, 26281, 26288, 22, 26352, 26453, 11819])).
% 29.55/19.76 tff(26457,plain,
% 29.55/19.76 (~(f6(c1, c1) = f5(f5(c1)))),
% 29.55/19.76 inference(modus_ponens,[status(thm)],[26456, 26451])).
% 29.55/19.76 tff(26458,plain,
% 29.55/19.76 (f7(f5(c1)) = f7(c2)),
% 29.55/19.76 inference(monotonicity,[status(thm)],[26446])).
% 29.55/19.76 tff(26459,plain,
% 29.55/19.76 (f7(f5(c1)) = c1),
% 29.55/19.76 inference(transitivity,[status(thm)],[26458, 22])).
% 29.55/19.76 tff(26460,plain,
% 29.55/19.76 ((f7(f5(c1)) = f5(c1)) <=> (c1 = f5(c1))),
% 29.55/19.76 inference(monotonicity,[status(thm)],[26459])).
% 29.55/19.76 tff(26461,plain,
% 29.55/19.76 ((f7(f5(c1)) = f5(c1)) <=> (f5(c1) = c1)),
% 29.55/19.76 inference(transitivity,[status(thm)],[26460, 128])).
% 29.55/19.76 tff(26462,plain,
% 29.55/19.76 ((f5(c1) = c1) <=> (f7(f5(c1)) = f5(c1))),
% 29.55/19.76 inference(symmetry,[status(thm)],[26461])).
% 29.55/19.76 tff(26463,plain,
% 29.55/19.76 ((~(f5(c1) = c1)) <=> (~(f7(f5(c1)) = f5(c1)))),
% 29.55/19.76 inference(monotonicity,[status(thm)],[26462])).
% 29.55/19.76 tff(26464,plain,
% 29.55/19.76 (~(f7(f5(c1)) = f5(c1))),
% 29.55/19.76 inference(modus_ponens,[status(thm)],[26414, 26463])).
% 29.55/19.76 tff(26465,plain,
% 29.55/19.76 (f7(f5(c1)) = f7(c1)),
% 29.55/19.76 inference(transitivity,[status(thm)],[26458, 22, 5544])).
% 29.55/19.76 tff(26466,plain,
% 29.55/19.76 (big_f(f7(f5(c1)), f6(c1, c1)) <=> big_f(f7(c1), f6(c1, c1))),
% 29.55/19.76 inference(monotonicity,[status(thm)],[26465])).
% 29.55/19.76 tff(26467,plain,
% 29.55/19.76 (big_f(f7(c1), f6(c1, c1)) <=> big_f(f7(f5(c1)), f6(c1, c1))),
% 29.55/19.76 inference(symmetry,[status(thm)],[26466])).
% 29.55/19.76 tff(26468,plain,
% 29.55/19.76 (big_f(f7(f5(c1)), f6(c1, c1))),
% 29.55/19.76 inference(modus_ponens,[status(thm)],[26455, 26467])).
% 29.55/19.76 tff(26469,plain,
% 29.55/19.76 (big_f(f9(c1, c1), f10(c1))),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[19043, 26453, 11819, 26281, 26288, 22, 26352])).
% 29.55/19.76 tff(26470,plain,
% 29.55/19.76 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (f7(f5(c1)) = f5(c1)) | (~big_f(f7(f5(c1)), f6(c1, c1))) | (f6(c1, c1) = f5(f5(c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (f7(f5(c1)) = f5(c1)) | (~big_f(f7(f5(c1)), f6(c1, c1))) | (f6(c1, c1) = f5(f5(c1))))),
% 29.55/19.76 inference(rewrite,[status(thm)],[])).
% 29.55/19.76 tff(26471,plain,
% 29.55/19.76 (((~(f10(c1) = c1)) | (f7(f5(c1)) = f5(c1)) | (f6(c1, c1) = f5(f5(c1))) | (~big_f(f7(f5(c1)), f6(c1, c1))) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1)))) <=> ((~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (f7(f5(c1)) = f5(c1)) | (~big_f(f7(f5(c1)), f6(c1, c1))) | (f6(c1, c1) = f5(f5(c1))))),
% 29.55/19.76 inference(rewrite,[status(thm)],[])).
% 29.55/19.76 tff(26472,plain,
% 29.55/19.76 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c1) = c1)) | (f7(f5(c1)) = f5(c1)) | (f6(c1, c1) = f5(f5(c1))) | (~big_f(f7(f5(c1)), f6(c1, c1))) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (f7(f5(c1)) = f5(c1)) | (~big_f(f7(f5(c1)), f6(c1, c1))) | (f6(c1, c1) = f5(f5(c1)))))),
% 29.55/19.76 inference(monotonicity,[status(thm)],[26471])).
% 29.55/19.76 tff(26473,plain,
% 29.55/19.76 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c1) = c1)) | (f7(f5(c1)) = f5(c1)) | (f6(c1, c1) = f5(f5(c1))) | (~big_f(f7(f5(c1)), f6(c1, c1))) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (f7(f5(c1)) = f5(c1)) | (~big_f(f7(f5(c1)), f6(c1, c1))) | (f6(c1, c1) = f5(f5(c1))))),
% 29.55/19.76 inference(transitivity,[status(thm)],[26472, 26470])).
% 29.55/19.76 tff(26474,plain,
% 29.55/19.76 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c1) = c1)) | (f7(f5(c1)) = f5(c1)) | (f6(c1, c1) = f5(f5(c1))) | (~big_f(f7(f5(c1)), f6(c1, c1))) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))),
% 29.55/19.76 inference(quant_inst,[status(thm)],[])).
% 29.55/19.76 tff(26475,plain,
% 29.55/19.76 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (f7(f5(c1)) = f5(c1)) | (~big_f(f7(f5(c1)), f6(c1, c1))) | (f6(c1, c1) = f5(f5(c1)))),
% 29.55/19.76 inference(modus_ponens,[status(thm)],[26474, 26473])).
% 29.55/19.76 tff(26476,plain,
% 29.55/19.76 ((f7(f5(c1)) = f5(c1)) | (~big_f(f7(f5(c1)), f6(c1, c1))) | (f6(c1, c1) = f5(f5(c1)))),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[26475, 1190, 26352, 26454, 26469])).
% 29.55/19.76 tff(26477,plain,
% 29.55/19.76 ($false),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[26476, 26468, 26464, 26457])).
% 29.55/19.76 tff(26478,plain,((f7(c2) = c2) | (~(f7(c1) = c1)) | (~(f10(c2) = c1)) | big_f(c2, c2) | big_f(c2, c1) | big_f(c1, c2)), inference(lemma,lemma(discharge,[]))).
% 29.55/19.76 tff(26479,plain,
% 29.55/19.76 (f7(c2) = c2),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[26478, 2, 94, 121, 4234, 27])).
% 29.55/19.76 tff(26480,plain,
% 29.55/19.76 (big_f(f7(c2), f6(c2, c1)) <=> big_f(c2, f6(c2, c1))),
% 29.55/19.76 inference(monotonicity,[status(thm)],[26479])).
% 29.55/19.76 tff(26481,plain,
% 29.55/19.76 (big_f(c2, f6(c2, c1)) <=> big_f(f7(c2), f6(c2, c1))),
% 29.55/19.76 inference(symmetry,[status(thm)],[26480])).
% 29.55/19.76 tff(26482,plain,
% 29.55/19.76 (~(f4(c4) = c2)),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[26279, 2, 4234, 121, 94, 27])).
% 29.55/19.76 tff(26483,plain,
% 29.55/19.76 (f4(c4) = c1),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[11750, 26482])).
% 29.55/19.76 tff(26484,plain,
% 29.55/19.76 ((~big_f(c1, c2)) <=> (~big_f(c1, f10(c1)))),
% 29.55/19.76 inference(monotonicity,[status(thm)],[24247])).
% 29.55/19.76 tff(26485,plain,
% 29.55/19.76 (~big_f(c1, f10(c1))),
% 29.55/19.76 inference(modus_ponens,[status(thm)],[27, 26484])).
% 29.55/19.76 tff(26486,plain,
% 29.55/19.76 (~(f6(c1, c1) = c1)),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[11304, 65, 4234, 4932])).
% 29.55/19.76 tff(26487,plain,
% 29.55/19.76 ($false),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[9820, 26486, 65, 4234, 3, 2946, 3030])).
% 29.55/19.76 tff(26488,plain,(big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f10(c1) = c1) | big_f(c2, f10(c1)) | big_f(c1, f10(c1)) | (~big_f(c1, c1))), inference(lemma,lemma(discharge,[]))).
% 29.55/19.76 tff(26489,plain,
% 29.55/19.76 (big_f(f7(c1), f6(c1, c1))),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[26488, 3, 4234, 8451, 26485, 4932])).
% 29.55/19.76 tff(26490,plain,
% 29.55/19.76 (c1 = f7(f4(c4))),
% 29.55/19.76 inference(transitivity,[status(thm)],[5544, 16244])).
% 29.55/19.76 tff(26491,plain,
% 29.55/19.76 (f6(c2, c1) = f6(c2, f7(f4(c4)))),
% 29.55/19.76 inference(monotonicity,[status(thm)],[26490])).
% 29.55/19.76 tff(26492,plain,
% 29.55/19.76 (f6(c2, f7(f4(c4))) = f6(c2, c1)),
% 29.55/19.76 inference(symmetry,[status(thm)],[26491])).
% 29.55/19.76 tff(26493,plain,
% 29.55/19.76 ((f6(c2, f7(f4(c4))) = c1) <=> (f6(c2, c1) = c1)),
% 29.55/19.76 inference(monotonicity,[status(thm)],[26492])).
% 29.55/19.76 tff(26494,plain,
% 29.55/19.76 ((f6(c2, c1) = c1) <=> (f6(c2, f7(f4(c4))) = c1)),
% 29.55/19.76 inference(symmetry,[status(thm)],[26493])).
% 29.55/19.76 tff(26495,plain,
% 29.55/19.76 ((~(f6(c2, c1) = c1)) <=> (~(f6(c2, f7(f4(c4))) = c1))),
% 29.55/19.76 inference(monotonicity,[status(thm)],[26494])).
% 29.55/19.76 tff(26496,plain,
% 29.55/19.76 (~(f6(c2, f7(f4(c4))) = c1)),
% 29.55/19.76 inference(modus_ponens,[status(thm)],[3198, 26495])).
% 29.55/19.76 tff(26497,plain,
% 29.55/19.76 (f6(c2, f7(f4(c4))) = c2),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[6601, 26496])).
% 29.55/19.76 tff(26498,plain,
% 29.55/19.76 (f6(c2, c1) = f10(c1)),
% 29.55/19.76 inference(transitivity,[status(thm)],[26491, 26497, 5571])).
% 29.55/19.76 tff(26499,plain,
% 29.55/19.76 (big_f(c2, f6(c2, c1)) <=> big_f(f10(c1), f10(c1))),
% 29.55/19.76 inference(monotonicity,[status(thm)],[5571, 26498])).
% 29.55/19.76 tff(26500,plain,
% 29.55/19.76 (big_f(f10(c1), f10(c1)) <=> big_f(c2, f6(c2, c1))),
% 29.55/19.76 inference(symmetry,[status(thm)],[26499])).
% 29.55/19.76 tff(26501,plain,
% 29.55/19.76 (big_f(f10(c1), f10(c1)) <=> big_f(f7(c2), f6(c2, c1))),
% 29.55/19.76 inference(transitivity,[status(thm)],[26500, 13581])).
% 29.55/19.76 tff(26502,plain,
% 29.55/19.76 ((~big_f(f10(c1), f10(c1))) <=> (~big_f(f7(c2), f6(c2, c1)))),
% 29.55/19.76 inference(monotonicity,[status(thm)],[26501])).
% 29.55/19.76 tff(26503,assumption,(~big_f(f10(c1), f10(c1))), introduced(assumption)).
% 29.55/19.76 tff(26504,plain,
% 29.55/19.76 (~big_f(f7(c2), f6(c2, c1))),
% 29.55/19.76 inference(modus_ponens,[status(thm)],[26503, 26502])).
% 29.55/19.76 tff(26505,plain,
% 29.55/19.76 (~(c2 = f8(c1))),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[3001, 26504, 77, 3, 2946, 3198])).
% 29.55/19.76 tff(26506,plain,
% 29.55/19.76 (~(f8(c1) = c2)),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[1675, 26505])).
% 29.55/19.76 tff(26507,plain,
% 29.55/19.76 (f6(f10(c1), c1) = f10(c1)),
% 29.55/19.76 inference(transitivity,[status(thm)],[25959, 26491, 26497, 5571])).
% 29.55/19.76 tff(26508,plain,
% 29.55/19.76 ((f6(f10(c1), c1) = c1) <=> (f10(c1) = c1)),
% 29.55/19.76 inference(monotonicity,[status(thm)],[26507])).
% 29.55/19.76 tff(26509,plain,
% 29.55/19.76 ((f10(c1) = c1) <=> (f6(f10(c1), c1) = c1)),
% 29.55/19.76 inference(symmetry,[status(thm)],[26508])).
% 29.55/19.76 tff(26510,plain,
% 29.55/19.76 ((~(f10(c1) = c1)) <=> (~(f6(f10(c1), c1) = c1))),
% 29.55/19.76 inference(monotonicity,[status(thm)],[26509])).
% 29.55/19.76 tff(26511,plain,
% 29.55/19.76 (~(f6(f10(c1), c1) = c1)),
% 29.55/19.76 inference(modus_ponens,[status(thm)],[3, 26510])).
% 29.55/19.76 tff(26512,plain,
% 29.55/19.76 (big_f(f7(f10(c1)), f6(f10(c1), c1)) <=> big_f(f10(c1), f10(c1))),
% 29.55/19.76 inference(monotonicity,[status(thm)],[25995, 26507])).
% 29.55/19.76 tff(26513,plain,
% 29.55/19.76 (big_f(f10(c1), f10(c1)) <=> big_f(f7(f10(c1)), f6(f10(c1), c1))),
% 29.55/19.76 inference(symmetry,[status(thm)],[26512])).
% 29.55/19.76 tff(26514,plain,
% 29.55/19.76 ((~big_f(f10(c1), f10(c1))) <=> (~big_f(f7(f10(c1)), f6(f10(c1), c1)))),
% 29.55/19.76 inference(monotonicity,[status(thm)],[26513])).
% 29.55/19.76 tff(26515,plain,
% 29.55/19.76 (~big_f(f7(f10(c1)), f6(f10(c1), c1))),
% 29.55/19.76 inference(modus_ponens,[status(thm)],[26503, 26514])).
% 29.55/19.76 tff(26516,plain,
% 29.55/19.76 ((~(c1 = f8(c1))) | big_f(f7(f10(c1)), f6(f10(c1), c1)) | (f6(f10(c1), c1) = c1)),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[25977, 2994, 3, 3030, 25995])).
% 29.55/19.76 tff(26517,plain,
% 29.55/19.76 (~(c1 = f8(c1))),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[26516, 26515, 26511])).
% 29.55/19.76 tff(26518,plain,
% 29.55/19.76 (~(f8(c1) = c1)),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[9808, 26517])).
% 29.55/19.76 tff(26519,plain,
% 29.55/19.76 ($false),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[1680, 26518, 26506])).
% 29.55/19.76 tff(26520,plain,((f6(c2, c1) = c1) | (f10(c1) = c1) | big_f(c1, f10(c1)) | (~(f7(c2) = c2)) | big_f(c2, f10(c1)) | (~(f7(c1) = c1)) | (~(f4(c4) = c1)) | big_f(f10(c1), f10(c1))), inference(lemma,lemma(discharge,[]))).
% 29.55/19.76 tff(26521,plain,
% 29.55/19.76 (f6(c2, c1) = c1),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[26520, 3, 26485, 77, 8451, 4234, 11752, 26299])).
% 29.55/19.76 tff(26522,plain,
% 29.55/19.76 (c1 = f6(c2, c1)),
% 29.55/19.76 inference(symmetry,[status(thm)],[3079])).
% 29.55/19.76 tff(26523,plain,
% 29.55/19.76 (f6(c1, c1) = f6(c1, f6(c2, c1))),
% 29.55/19.76 inference(monotonicity,[status(thm)],[26522])).
% 29.55/19.76 tff(26524,plain,
% 29.55/19.76 ((f6(c1, c1) = c1) <=> (f6(c1, f6(c2, c1)) = c1)),
% 29.55/19.76 inference(monotonicity,[status(thm)],[26523])).
% 29.55/19.76 tff(26525,plain,
% 29.55/19.76 ((~(f6(c1, c1) = c1)) <=> (~(f6(c1, f6(c2, c1)) = c1))),
% 29.55/19.76 inference(monotonicity,[status(thm)],[26524])).
% 29.55/19.76 tff(26526,plain,
% 29.55/19.76 (~(f6(c1, f6(c2, c1)) = c1)),
% 29.55/19.76 inference(modus_ponens,[status(thm)],[28, 26525])).
% 29.55/19.76 tff(26527,plain,
% 29.55/19.76 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f6(c1, f6(c2, c1)) = c1) | (f6(c1, f6(c2, c1)) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f6(c1, f6(c2, c1)) = c1) | (f6(c1, f6(c2, c1)) = c2))),
% 29.55/19.76 inference(rewrite,[status(thm)],[])).
% 29.55/19.76 tff(26528,plain,
% 29.55/19.76 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f6(c1, f6(c2, c1)) = c1) | (f6(c1, f6(c2, c1)) = c2))),
% 29.55/19.76 inference(quant_inst,[status(thm)],[])).
% 29.55/19.76 tff(26529,plain,
% 29.55/19.76 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f6(c1, f6(c2, c1)) = c1) | (f6(c1, f6(c2, c1)) = c2)),
% 29.55/19.76 inference(modus_ponens,[status(thm)],[26528, 26527])).
% 29.55/19.76 tff(26530,plain,
% 29.55/19.76 ((f6(c1, f6(c2, c1)) = c1) | (f6(c1, f6(c2, c1)) = c2)),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[26529, 10])).
% 29.55/19.76 tff(26531,plain,
% 29.55/19.76 (f6(c1, f6(c2, c1)) = c2),
% 29.55/19.76 inference(unit_resolution,[status(thm)],[26530, 26526])).
% 29.55/19.76 tff(26532,plain,
% 29.55/19.76 (f6(c1, f6(c2, c1)) = f10(c1)),
% 29.55/19.76 inference(transitivity,[status(thm)],[26531, 293])).
% 29.55/19.76 tff(26533,plain,
% 29.55/19.76 (big_f(f7(c1), f6(c1, f6(c2, c1))) <=> big_f(c1, f10(c1))),
% 29.55/19.76 inference(monotonicity,[status(thm)],[4234, 26532])).
% 29.55/19.77 tff(26534,plain,
% 29.55/19.77 (big_f(c1, f10(c1)) <=> big_f(f7(c1), f6(c1, f6(c2, c1)))),
% 29.55/19.77 inference(symmetry,[status(thm)],[26533])).
% 29.55/19.77 tff(26535,plain,
% 29.55/19.77 ((~big_f(c1, f10(c1))) <=> (~big_f(f7(c1), f6(c1, f6(c2, c1))))),
% 29.55/19.77 inference(monotonicity,[status(thm)],[26534])).
% 29.55/19.77 tff(26536,plain,
% 29.55/19.77 (~big_f(f7(c1), f6(c1, f6(c2, c1)))),
% 29.55/19.77 inference(modus_ponens,[status(thm)],[3030, 26535])).
% 29.55/19.77 tff(26537,plain,
% 29.55/19.77 (big_f(f7(c1), f6(c1, c1)) <=> big_f(f7(c1), f6(c1, f6(c2, c1)))),
% 29.55/19.77 inference(monotonicity,[status(thm)],[26523])).
% 29.55/19.77 tff(26538,plain,
% 29.55/19.77 (big_f(f7(c1), f6(c1, f6(c2, c1)))),
% 29.55/19.77 inference(modus_ponens,[status(thm)],[5964, 26537])).
% 29.55/19.77 tff(26539,plain,
% 29.55/19.77 ($false),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[26538, 26536])).
% 29.55/19.77 tff(26540,plain,((~(f6(c2, c1) = c1)) | big_f(c1, f10(c1)) | (~(f10(c1) = c2)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | (~big_f(f7(c1), f6(c1, c1)))), inference(lemma,lemma(discharge,[]))).
% 29.55/19.77 tff(26541,plain,
% 29.55/19.77 (f6(c1, c1) = c1),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[26540, 26521, 15, 4234, 26485, 26489])).
% 29.55/19.77 tff(26542,plain,
% 29.55/19.77 ((~(c1 = f8(c1))) | (~(f6(c1, c1) = c1))),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[18583, 2963, 4234, 3, 26485, 26489])).
% 29.55/19.77 tff(26543,plain,
% 29.55/19.77 (~(c1 = f8(c1))),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[26542, 26541])).
% 29.55/19.77 tff(26544,plain,
% 29.55/19.77 (~(f8(c1) = c1)),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[9808, 26543])).
% 29.55/19.77 tff(26545,plain,
% 29.55/19.77 (f8(c1) = c2),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[1680, 26544])).
% 29.55/19.77 tff(26546,plain,
% 29.55/19.77 (c2 = f8(c1)),
% 29.55/19.77 inference(symmetry,[status(thm)],[26545])).
% 29.55/19.77 tff(26547,plain,
% 29.55/19.77 (f10(c1) = f8(c1)),
% 29.55/19.77 inference(transitivity,[status(thm)],[15, 26546])).
% 29.55/19.77 tff(26548,plain,
% 29.55/19.77 ((~(f6(c1, c1) = c1)) | (~(f10(c1) = f8(c1)))),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[26346, 2963, 4234, 3, 26489, 26299])).
% 29.55/19.77 tff(26549,plain,
% 29.55/19.77 (~(f10(c1) = f8(c1))),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[26548, 26541])).
% 29.55/19.77 tff(26550,plain,
% 29.55/19.77 ($false),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[26549, 26547])).
% 29.55/19.77 tff(26551,plain,((f10(c1) = c1) | (~(f7(c1) = c1)) | (~(f7(c2) = c2)) | (~(f4(c4) = c1)) | (~big_f(c1, c1)) | big_f(c1, c2) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 29.55/19.77 tff(26552,plain,
% 29.55/19.77 (f10(c1) = c1),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[26551, 26479, 4234, 26483, 26250, 27, 121])).
% 29.55/19.77 tff(26553,plain,
% 29.55/19.77 (~(f9(c1, c1) = c1)),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[11249, 65, 4234, 3762, 28, 4932])).
% 29.55/19.77 tff(26554,plain,
% 29.55/19.77 (f9(c1, c1) = c2),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[3939, 26553])).
% 29.55/19.77 tff(26555,plain,
% 29.55/19.77 (~big_f(f9(c1, c1), c1)),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[10058, 26554, 2])).
% 29.55/19.77 tff(26556,plain,
% 29.55/19.77 (~big_f(f9(c1, c1), f10(c1))),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[10033, 26555, 3762])).
% 29.55/19.77 tff(26557,plain,
% 29.55/19.77 ($false),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[9987, 2492, 4234, 3762, 26553, 26556, 65, 28])).
% 29.55/19.77 tff(26558,plain,(big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (~(f10(c1) = c1)) | (f6(c1, c1) = c1) | big_f(c2, c1) | (~big_f(c1, c1))), inference(lemma,lemma(discharge,[]))).
% 29.55/19.77 tff(26559,plain,
% 29.55/19.77 (big_f(f7(c1), f6(c1, c1))),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[26558, 28, 26552, 4234, 2, 26250])).
% 29.55/19.77 tff(26560,plain,
% 29.55/19.77 (big_f(f7(c1), f6(c1, f6(c2, c1))) <=> big_f(c1, c2)),
% 29.55/19.77 inference(monotonicity,[status(thm)],[4234, 26531])).
% 29.55/19.77 tff(26561,plain,
% 29.55/19.77 (big_f(c1, c2) <=> big_f(f7(c1), f6(c1, f6(c2, c1)))),
% 29.55/19.77 inference(symmetry,[status(thm)],[26560])).
% 29.55/19.77 tff(26562,plain,
% 29.55/19.77 ((~big_f(c1, c2)) <=> (~big_f(f7(c1), f6(c1, f6(c2, c1))))),
% 29.55/19.77 inference(monotonicity,[status(thm)],[26561])).
% 29.55/19.77 tff(26563,plain,
% 29.55/19.77 (~big_f(f7(c1), f6(c1, f6(c2, c1)))),
% 29.55/19.77 inference(modus_ponens,[status(thm)],[27, 26562])).
% 29.55/19.77 tff(26564,plain,
% 29.55/19.77 ($false),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[26538, 26563])).
% 29.55/19.77 tff(26565,plain,((~(f6(c2, c1) = c1)) | big_f(c1, c2) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | (~big_f(f7(c1), f6(c1, c1)))), inference(lemma,lemma(discharge,[]))).
% 29.55/19.77 tff(26566,plain,
% 29.55/19.77 (~(f6(c2, c1) = c1)),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[26565, 28, 4234, 27, 26559])).
% 29.55/19.77 tff(26567,plain,
% 29.55/19.77 (f7(f4(c4)) = c1),
% 29.55/19.77 inference(transitivity,[status(thm)],[16243, 4234])).
% 29.55/19.77 tff(26568,plain,
% 29.55/19.77 (f6(c2, f7(f4(c4))) = f6(c2, c1)),
% 29.55/19.77 inference(monotonicity,[status(thm)],[26567])).
% 29.55/19.77 tff(26569,plain,
% 29.55/19.77 ((f6(c2, f7(f4(c4))) = c1) <=> (f6(c2, c1) = c1)),
% 29.55/19.77 inference(monotonicity,[status(thm)],[26568])).
% 29.55/19.77 tff(26570,plain,
% 29.55/19.77 (f6(c2, c1) = c1),
% 29.55/19.77 inference(modus_ponens,[status(thm)],[6634, 26569])).
% 29.55/19.77 tff(26571,plain,
% 29.55/19.77 ($false),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[3198, 26570])).
% 29.55/19.77 tff(26572,plain,((~(f6(c2, f7(f4(c4))) = c1)) | (f6(c2, c1) = c1) | (~(f7(c1) = c1)) | (~(f4(c4) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.55/19.77 tff(26573,plain,
% 29.55/19.77 (~(f6(c2, f7(f4(c4))) = c1)),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[26572, 26566, 4234, 26483])).
% 29.55/19.77 tff(26574,plain,
% 29.55/19.77 (f6(c2, f7(f4(c4))) = c2),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[6601, 26573])).
% 29.55/19.77 tff(26575,plain,
% 29.55/19.77 (f7(f4(c4)) = f7(c1)),
% 29.55/19.77 inference(monotonicity,[status(thm)],[26483])).
% 29.55/19.77 tff(26576,plain,
% 29.55/19.77 (f7(c1) = f7(f4(c4))),
% 29.55/19.77 inference(symmetry,[status(thm)],[26575])).
% 29.55/19.77 tff(26577,plain,
% 29.55/19.77 (c1 = f7(f4(c4))),
% 29.55/19.77 inference(transitivity,[status(thm)],[5544, 26576])).
% 29.55/19.77 tff(26578,plain,
% 29.55/19.77 (f6(c2, c1) = f6(c2, f7(f4(c4)))),
% 29.55/19.77 inference(monotonicity,[status(thm)],[26577])).
% 29.55/19.77 tff(26579,plain,
% 29.55/19.77 (f6(c2, c1) = c2),
% 29.55/19.77 inference(transitivity,[status(thm)],[26578, 26574])).
% 29.55/19.77 tff(26580,plain,
% 29.55/19.77 (big_f(c2, f6(c2, c1)) <=> big_f(c2, c2)),
% 29.55/19.77 inference(monotonicity,[status(thm)],[26579])).
% 29.55/19.77 tff(26581,plain,
% 29.55/19.77 (big_f(c2, c2) <=> big_f(c2, f6(c2, c1))),
% 29.55/19.77 inference(symmetry,[status(thm)],[26580])).
% 29.55/19.77 tff(26582,plain,
% 29.55/19.77 (big_f(c2, c2) <=> big_f(f7(c2), f6(c2, c1))),
% 29.55/19.77 inference(transitivity,[status(thm)],[26581, 26481])).
% 29.55/19.77 tff(26583,plain,
% 29.55/19.77 ((~big_f(c2, c2)) <=> (~big_f(f7(c2), f6(c2, c1)))),
% 29.55/19.77 inference(monotonicity,[status(thm)],[26582])).
% 29.55/19.77 tff(26584,plain,
% 29.55/19.77 (~big_f(f7(c2), f6(c2, c1))),
% 29.55/19.77 inference(modus_ponens,[status(thm)],[121, 26583])).
% 29.55/19.77 tff(26585,plain,
% 29.55/19.77 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))))),
% 29.55/19.77 inference(rewrite,[status(thm)],[])).
% 29.55/19.77 tff(26586,plain,
% 29.55/19.77 (((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1))) <=> ((f10(c2) = c2) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))))),
% 29.55/19.77 inference(rewrite,[status(thm)],[])).
% 29.55/19.77 tff(26587,plain,
% 29.55/19.77 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (c1 = f8(c2)) | (~big_f(c1, f10(c2)))))),
% 29.55/19.77 inference(monotonicity,[status(thm)],[26586])).
% 29.55/19.77 tff(26588,plain,
% 29.55/19.77 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))))),
% 29.55/19.77 inference(transitivity,[status(thm)],[26587, 26585])).
% 29.55/19.77 tff(26589,plain,
% 29.55/19.77 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)))),
% 29.55/19.77 inference(quant_inst,[status(thm)],[])).
% 29.55/19.77 tff(26590,plain,
% 29.55/19.77 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (c1 = f8(c2)) | (~big_f(c1, f10(c2)))),
% 29.55/19.77 inference(modus_ponens,[status(thm)],[26589, 26588])).
% 29.55/19.77 tff(26591,plain,
% 29.55/19.77 (c1 = f8(c2)),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[26590, 2662, 89, 26479, 26566, 26584, 26251])).
% 29.55/19.77 tff(26592,plain,
% 29.55/19.77 (f6(c1, c1) = f6(c1, f8(c2))),
% 29.55/19.77 inference(monotonicity,[status(thm)],[26591])).
% 29.55/19.77 tff(26593,plain,
% 29.55/19.77 ((f6(c1, c1) = c1) <=> (f6(c1, f8(c2)) = c1)),
% 29.55/19.77 inference(monotonicity,[status(thm)],[26592])).
% 29.55/19.77 tff(26594,plain,
% 29.55/19.77 ((~(f6(c1, c1) = c1)) <=> (~(f6(c1, f8(c2)) = c1))),
% 29.55/19.77 inference(monotonicity,[status(thm)],[26593])).
% 29.55/19.77 tff(26595,plain,
% 29.55/19.77 (~(f6(c1, f8(c2)) = c1)),
% 29.55/19.77 inference(modus_ponens,[status(thm)],[28, 26594])).
% 29.55/19.77 tff(26596,plain,
% 29.55/19.77 (f6(c1, f8(c2)) = c2),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[24295, 26595])).
% 29.55/19.77 tff(26597,plain,
% 29.55/19.77 (f6(c1, c1) = c2),
% 29.55/19.77 inference(transitivity,[status(thm)],[26592, 26596])).
% 29.55/19.77 tff(26598,plain,
% 29.55/19.77 (big_f(f7(c1), f6(c1, c1)) <=> big_f(c1, c2)),
% 29.55/19.77 inference(monotonicity,[status(thm)],[4234, 26597])).
% 29.55/19.77 tff(26599,plain,
% 29.55/19.77 (big_f(c1, c2) <=> big_f(f7(c1), f6(c1, c1))),
% 29.55/19.77 inference(symmetry,[status(thm)],[26598])).
% 29.55/19.77 tff(26600,plain,
% 29.55/19.77 ((~big_f(c1, c2)) <=> (~big_f(f7(c1), f6(c1, c1)))),
% 29.55/19.77 inference(monotonicity,[status(thm)],[26599])).
% 29.55/19.77 tff(26601,plain,
% 29.55/19.77 (~big_f(f7(c1), f6(c1, c1))),
% 29.55/19.77 inference(modus_ponens,[status(thm)],[27, 26600])).
% 29.55/19.77 tff(26602,plain,
% 29.55/19.77 ($false),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[26559, 26601])).
% 29.55/19.77 tff(26603,plain,((f6(c1, c1) = c1) | big_f(c1, c2) | (~(f7(c1) = c1)) | (f10(c2) = c2) | big_f(c2, c2) | big_f(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 29.55/19.77 tff(26604,plain,
% 29.55/19.77 (f6(c1, c1) = c1),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[26603, 2, 4234, 89, 121, 27])).
% 29.55/19.77 tff(26605,plain,
% 29.55/19.77 (big_f(f7(c1), f6(c1, c1))),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[11304, 26604, 4234, 26250])).
% 29.55/19.77 tff(26606,plain,
% 29.55/19.77 (big_f(f9(c1, c1), f10(c1))),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[10042, 4070, 10030, 5964, 3762, 4234])).
% 29.55/19.77 tff(26607,plain,
% 29.55/19.77 ($false),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[10033, 24691, 26606, 3762])).
% 29.55/19.77 tff(26608,plain,((f9(c1, c1) = c1) | (~(f10(c1) = c1)) | big_f(c2, c1) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f7(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.55/19.77 tff(26609,plain,
% 29.55/19.77 (f9(c1, c1) = c1),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[26608, 26552, 2, 26604, 26605, 4234])).
% 29.55/19.77 tff(26610,plain,
% 29.55/19.77 (big_f(f9(c1, c1), c1)),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[10938, 26609, 26250])).
% 29.55/19.77 tff(26611,plain,
% 29.55/19.77 (big_f(f9(c1, c1), f10(c1))),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[8716, 26610, 26552])).
% 29.55/19.77 tff(26612,plain,
% 29.55/19.77 ($false),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[18907, 2378, 4234, 26552, 26609, 26611, 26605, 26604])).
% 29.55/19.77 tff(26613,plain,(big_f(c2, c1) | (~(f7(c1) = c1)) | (f10(c2) = c2) | big_f(c2, c2) | big_f(c1, c2)), inference(lemma,lemma(discharge,[]))).
% 29.55/19.77 tff(26614,plain,
% 29.55/19.77 (big_f(c2, c1)),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[26613, 27, 89, 121, 4234])).
% 29.55/19.77 tff(26615,plain,
% 29.55/19.77 (~big_f(f7(c2), c1)),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[26351, 17, 121, 4234, 27, 3])).
% 29.55/19.77 tff(26616,plain,
% 29.55/19.77 (~(c1 = f8(c1))),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[12260, 26615, 11819, 27, 17, 3])).
% 29.55/19.77 tff(26617,plain,
% 29.55/19.77 (~(f8(c1) = c1)),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[9808, 26616])).
% 29.55/19.77 tff(26618,plain,
% 29.55/19.77 (f8(c1) = c2),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[1680, 26617])).
% 29.55/19.77 tff(26619,plain,
% 29.55/19.77 (c2 = f8(c1)),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[1675, 26618])).
% 29.55/19.77 tff(26620,plain,
% 29.55/19.77 (f7(c2) = f7(f10(c1))),
% 29.55/19.77 inference(symmetry,[status(thm)],[219])).
% 29.55/19.77 tff(26621,plain,
% 29.55/19.77 ((f7(c2) = c2) <=> (f7(f10(c1)) = f10(c1))),
% 29.55/19.77 inference(monotonicity,[status(thm)],[26620, 5571])).
% 29.55/19.77 tff(26622,plain,
% 29.55/19.77 ((~(f7(c2) = c2)) <=> (~(f7(f10(c1)) = f10(c1)))),
% 29.55/19.77 inference(monotonicity,[status(thm)],[26621])).
% 29.55/19.77 tff(26623,plain,
% 29.55/19.77 (~(f7(f10(c1)) = f10(c1))),
% 29.55/19.77 inference(modus_ponens,[status(thm)],[17, 26622])).
% 29.55/19.77 tff(26624,plain,
% 29.55/19.77 (~big_f(f8(c1), f10(c1))),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[15724, 22, 15, 121, 23145])).
% 29.55/19.77 tff(26625,plain,
% 29.55/19.77 (~(c2 = f5(c2))),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[8107, 26624, 3, 17, 23145])).
% 29.55/19.77 tff(26626,plain,
% 29.55/19.77 (~(f5(c2) = c2)),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[8113, 26625])).
% 29.55/19.77 tff(26627,plain,
% 29.55/19.77 (f5(c2) = c1),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[1547, 26626])).
% 29.55/19.77 tff(26628,plain,
% 29.55/19.77 (f5(f10(c1)) = c1),
% 29.55/19.77 inference(transitivity,[status(thm)],[9888, 26627])).
% 29.55/19.77 tff(26629,plain,
% 29.55/19.77 (big_f(f7(f10(c1)), f5(f10(c1))) <=> big_f(c1, c1)),
% 29.55/19.77 inference(monotonicity,[status(thm)],[18820, 26628])).
% 29.55/19.77 tff(26630,plain,
% 29.55/19.77 (big_f(c1, c1) <=> big_f(f7(f10(c1)), f5(f10(c1)))),
% 29.55/19.77 inference(symmetry,[status(thm)],[26629])).
% 29.55/19.77 tff(26631,plain,
% 29.55/19.77 ((~big_f(c1, c1)) <=> (~big_f(f7(f10(c1)), f5(f10(c1))))),
% 29.55/19.77 inference(monotonicity,[status(thm)],[26630])).
% 29.55/19.77 tff(26632,plain,
% 29.55/19.77 (~big_f(f7(f10(c1)), f5(f10(c1)))),
% 29.55/19.77 inference(modus_ponens,[status(thm)],[66, 26631])).
% 29.55/19.77 tff(26633,plain,
% 29.55/19.77 ($false),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[15818, 26632, 26623, 3, 8451, 26619])).
% 29.55/19.77 tff(26634,plain,((f7(c2) = c2) | (f10(c1) = c1) | big_f(c1, c1) | (~(f10(c2) = c1)) | big_f(c1, c2) | big_f(c2, c2) | (~(f7(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.55/19.77 tff(26635,plain,
% 29.55/19.77 (big_f(c1, c1)),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[26634, 17, 3, 11819, 27, 121, 4234])).
% 29.55/19.77 tff(26636,plain,
% 29.55/19.77 ($false),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[20926, 26635, 26615, 11819, 22])).
% 29.55/19.77 tff(26637,plain,((f7(c2) = c2) | (~(f10(c2) = c1)) | (f10(c1) = c1) | big_f(c1, c2) | big_f(c2, c2) | (~(f7(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.55/19.77 tff(26638,plain,
% 29.55/19.77 (f7(c2) = c2),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[26637, 3, 11819, 27, 121, 4234])).
% 29.55/19.77 tff(26639,plain,
% 29.55/19.77 (f6(c2, c1) = c1),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[26024, 26638, 26485, 3, 121])).
% 29.55/19.77 tff(26640,plain,
% 29.55/19.77 ((f6(c2, f6(c2, c1)) = f6(c2, c1)) <=> (f6(c2, f6(c2, c1)) = c1)),
% 29.55/19.77 inference(monotonicity,[status(thm)],[26639])).
% 29.55/19.77 tff(26641,plain,
% 29.55/19.77 ((f6(c2, f6(c2, c1)) = c1) <=> (f6(c2, f6(c2, c1)) = f6(c2, c1))),
% 29.55/19.77 inference(symmetry,[status(thm)],[26640])).
% 29.55/19.77 tff(26642,plain,
% 29.55/19.77 (f6(c2, f6(c2, c1)) = f6(c2, c1)),
% 29.55/19.77 inference(monotonicity,[status(thm)],[26639])).
% 29.55/19.77 tff(26643,plain,
% 29.55/19.77 (f6(c2, f6(c2, c1)) = c1),
% 29.55/19.77 inference(transitivity,[status(thm)],[26642, 26639])).
% 29.55/19.77 tff(26644,plain,
% 29.55/19.77 (f6(c2, f6(c2, c1)) = f6(c2, c1)),
% 29.55/19.77 inference(modus_ponens,[status(thm)],[26643, 26641])).
% 29.55/19.77 tff(26645,plain,
% 29.55/19.77 (big_f(f7(c2), f6(c2, f6(c2, c1))) <=> big_f(c2, f6(c2, f6(c2, c1)))),
% 29.55/19.77 inference(monotonicity,[status(thm)],[26638])).
% 29.55/19.77 tff(26646,plain,
% 29.55/19.77 (big_f(c2, f6(c2, f6(c2, c1))) <=> big_f(f7(c2), f6(c2, f6(c2, c1)))),
% 29.55/19.77 inference(symmetry,[status(thm)],[26645])).
% 29.55/19.77 tff(26647,plain,
% 29.55/19.77 (big_f(c2, f6(c2, f6(c2, c1))) <=> big_f(c2, c1)),
% 29.55/19.77 inference(monotonicity,[status(thm)],[26643])).
% 29.55/19.77 tff(26648,plain,
% 29.55/19.77 (big_f(c2, c1) <=> big_f(c2, f6(c2, f6(c2, c1)))),
% 29.55/19.77 inference(symmetry,[status(thm)],[26647])).
% 29.55/19.77 tff(26649,plain,
% 29.55/19.77 (big_f(c2, c1) <=> big_f(f7(c2), f6(c2, f6(c2, c1)))),
% 29.55/19.77 inference(transitivity,[status(thm)],[26648, 26646])).
% 29.55/19.77 tff(26650,plain,
% 29.55/19.77 (big_f(f7(c2), f6(c2, f6(c2, c1)))),
% 29.55/19.77 inference(modus_ponens,[status(thm)],[348, 26649])).
% 29.55/19.77 tff(26651,plain,
% 29.55/19.77 (~(c2 = f8(c1))),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[2970, 26650, 26638, 3, 8451, 26644])).
% 29.55/19.77 tff(26652,plain,
% 29.55/19.77 (~(f8(c1) = c2)),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[1675, 26651])).
% 29.55/19.77 tff(26653,plain,
% 29.55/19.77 (f8(c1) = c1),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[1680, 26652])).
% 29.55/19.77 tff(26654,plain,
% 29.55/19.77 (c1 = f8(c1)),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[9808, 26653])).
% 29.55/19.77 tff(26655,plain,
% 29.55/19.77 (f6(f10(c1), c1) = c1),
% 29.55/19.77 inference(transitivity,[status(thm)],[25959, 26639])).
% 29.55/19.77 tff(26656,plain,
% 29.55/19.77 (f7(f10(c1)) = c2),
% 29.55/19.77 inference(transitivity,[status(thm)],[219, 26638])).
% 29.55/19.77 tff(26657,plain,
% 29.55/19.77 (big_f(f7(f10(c1)), f6(f10(c1), c1)) <=> big_f(c2, c1)),
% 29.55/19.77 inference(monotonicity,[status(thm)],[26656, 26655])).
% 29.55/19.77 tff(26658,plain,
% 29.55/19.77 (big_f(c2, c1) <=> big_f(f7(f10(c1)), f6(f10(c1), c1))),
% 29.55/19.77 inference(symmetry,[status(thm)],[26657])).
% 29.55/19.77 tff(26659,plain,
% 29.55/19.77 (big_f(f7(f10(c1)), f6(f10(c1), c1))),
% 29.55/19.77 inference(modus_ponens,[status(thm)],[348, 26658])).
% 29.55/19.77 tff(26660,plain,
% 29.55/19.77 (f7(f10(c1)) = f10(c1)),
% 29.55/19.77 inference(modus_ponens,[status(thm)],[26638, 221])).
% 29.55/19.77 tff(26661,plain,
% 29.55/19.77 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | (~big_f(f7(f10(c1)), f6(f10(c1), c1))) | (~(f6(f10(c1), c1) = c1)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | (~big_f(f7(f10(c1)), f6(f10(c1), c1))) | (~(f6(f10(c1), c1) = c1)))),
% 29.55/19.77 inference(rewrite,[status(thm)],[])).
% 29.55/19.77 tff(26662,plain,
% 29.55/19.77 (((f10(c1) = c1) | big_f(c1, f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | (~(c1 = f8(c1))) | (~(f6(f10(c1), c1) = c1)) | (~big_f(f7(f10(c1)), f6(f10(c1), c1)))) <=> ((f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | (~big_f(f7(f10(c1)), f6(f10(c1), c1))) | (~(f6(f10(c1), c1) = c1)))),
% 29.55/19.77 inference(rewrite,[status(thm)],[])).
% 29.55/19.77 tff(26663,plain,
% 29.55/19.77 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | big_f(c1, f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | (~(c1 = f8(c1))) | (~(f6(f10(c1), c1) = c1)) | (~big_f(f7(f10(c1)), f6(f10(c1), c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | (~big_f(f7(f10(c1)), f6(f10(c1), c1))) | (~(f6(f10(c1), c1) = c1))))),
% 29.55/19.77 inference(monotonicity,[status(thm)],[26662])).
% 29.55/19.77 tff(26664,plain,
% 29.55/19.77 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | big_f(c1, f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | (~(c1 = f8(c1))) | (~(f6(f10(c1), c1) = c1)) | (~big_f(f7(f10(c1)), f6(f10(c1), c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | (~big_f(f7(f10(c1)), f6(f10(c1), c1))) | (~(f6(f10(c1), c1) = c1)))),
% 29.55/19.77 inference(transitivity,[status(thm)],[26663, 26661])).
% 29.55/19.77 tff(26665,plain,
% 29.55/19.77 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | big_f(c1, f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | (~(c1 = f8(c1))) | (~(f6(f10(c1), c1) = c1)) | (~big_f(f7(f10(c1)), f6(f10(c1), c1))))),
% 29.55/19.77 inference(quant_inst,[status(thm)],[])).
% 29.55/19.77 tff(26666,plain,
% 29.55/19.77 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | (~big_f(f7(f10(c1)), f6(f10(c1), c1))) | (~(f6(f10(c1), c1) = c1))),
% 29.55/19.77 inference(modus_ponens,[status(thm)],[26665, 26664])).
% 29.55/19.77 tff(26667,plain,
% 29.55/19.77 ((~(c1 = f8(c1))) | (~big_f(f7(f10(c1)), f6(f10(c1), c1))) | (~(f6(f10(c1), c1) = c1))),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[26666, 2963, 3, 26485, 26660])).
% 29.55/19.77 tff(26668,plain,
% 29.55/19.77 ($false),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[26667, 26659, 26655, 26654])).
% 29.55/19.77 tff(26669,plain,((f10(c1) = c1) | (~big_f(c2, c1)) | big_f(c2, c2) | (~(f10(c2) = c1)) | big_f(c1, c2) | (~(f7(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.55/19.77 tff(26670,plain,
% 29.55/19.77 (f10(c1) = c1),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[26669, 26614, 121, 94, 27, 4234])).
% 29.55/19.77 tff(26671,plain,
% 29.55/19.77 (big_f(f7(c2), c1)),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[8245, 79, 3762, 17, 1521, 348])).
% 29.55/19.77 tff(26672,plain,
% 29.55/19.77 ($false),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[10195, 26671, 79, 4234, 121, 17, 1521])).
% 29.55/19.77 tff(26673,plain,((~(f4(c4) = c2)) | (~(f7(c1) = c1)) | big_f(c2, c2) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(f10(c1) = c1)) | (~big_f(c2, c1))), inference(lemma,lemma(discharge,[]))).
% 29.55/19.77 tff(26674,plain,
% 29.55/19.77 (~(f4(c4) = c2)),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[26673, 17, 121, 4234, 23145, 26670, 26614])).
% 29.55/19.77 tff(26675,plain,
% 29.55/19.77 (f4(c4) = c1),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[11750, 26674])).
% 29.55/19.77 tff(26676,plain,
% 29.55/19.77 (big_f(c2, f10(c2))),
% 29.55/19.77 inference(modus_ponens,[status(thm)],[26614, 12069])).
% 29.55/19.77 tff(26677,plain,
% 29.55/19.77 (big_f(c1, c1)),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[24397, 17, 26670, 23145, 89, 26676])).
% 29.55/19.77 tff(26678,plain,
% 29.55/19.77 (big_f(f7(c2), c1)),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[20926, 26677, 94, 22])).
% 29.55/19.77 tff(26679,plain,
% 29.55/19.77 (~(f9(c1, c1) = c1)),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[9976, 65, 4234, 338, 22, 3762])).
% 29.55/19.77 tff(26680,plain,
% 29.55/19.77 (~(f9(f10(c2), f4(c4)) = c1)),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[19829, 26679, 11819, 11752])).
% 29.55/19.77 tff(26681,plain,
% 29.55/19.77 (~(f5(c1) = c1)),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[26383, 65, 4234, 11819, 338, 22, 3762, 11752])).
% 29.55/19.77 tff(26682,plain,
% 29.55/19.77 (f5(c1) = c2),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[1708, 26681])).
% 29.55/19.77 tff(26683,plain,
% 29.55/19.77 (~(f9(f10(c2), f4(c4)) = c2)),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[20203, 26682, 11819, 17, 121, 11752, 3762])).
% 29.55/19.77 tff(26684,plain,
% 29.55/19.77 ($false),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[146, 26683, 26680])).
% 29.55/19.77 tff(26685,plain,(big_f(f7(c1), f6(c1, c1)) | (~(f10(c2) = c1)) | (f7(c2) = c2) | big_f(c2, c2) | (~(f4(c4) = c1)) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~big_f(f7(c2), c1))), inference(lemma,lemma(discharge,[]))).
% 29.55/19.77 tff(26686,plain,
% 29.55/19.77 (big_f(f7(c1), f6(c1, c1))),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[26685, 26678, 17, 121, 94, 26670, 4234, 26675])).
% 29.55/19.77 tff(26687,plain,
% 29.55/19.77 (~(f4(c4) = c2)),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[8245, 12093, 3762, 17, 1521, 348])).
% 29.55/19.77 tff(26688,plain,
% 29.55/19.77 (f4(c4) = c1),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[11750, 26687])).
% 29.55/19.77 tff(26689,plain,
% 29.55/19.77 (~(f6(c2, f7(f4(c4))) = c1)),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[26572, 26688, 4234, 3198])).
% 29.55/19.77 tff(26690,plain,
% 29.55/19.77 (f6(c2, f7(f4(c4))) = c2),
% 29.55/19.77 inference(unit_resolution,[status(thm)],[6601, 26689])).
% 29.55/19.77 tff(26691,plain,
% 29.55/19.77 (c2 = f6(c2, f7(f4(c4)))),
% 29.55/19.77 inference(symmetry,[status(thm)],[26690])).
% 29.55/19.77 tff(26692,plain,
% 29.55/19.77 (f8(c2) = f8(f6(c2, f7(f4(c4))))),
% 29.55/19.77 inference(monotonicity,[status(thm)],[26691])).
% 29.55/19.77 tff(26693,plain,
% 29.55/19.77 (f8(f6(c2, f7(f4(c4)))) = f8(c2)),
% 29.55/19.77 inference(symmetry,[status(thm)],[26692])).
% 29.55/19.77 tff(26694,plain,
% 29.55/19.77 (f7(f6(c2, f7(f4(c4)))) = f7(c2)),
% 29.55/19.77 inference(monotonicity,[status(thm)],[26690])).
% 29.55/19.77 tff(26695,plain,
% 29.55/19.77 (f7(f6(c2, f7(f4(c4)))) = c1),
% 29.55/19.77 inference(transitivity,[status(thm)],[26694, 22])).
% 29.55/19.77 tff(26696,plain,
% 29.55/19.77 (big_f(f7(f6(c2, f7(f4(c4)))), c1) <=> big_f(c1, c1)),
% 29.55/19.77 inference(monotonicity,[status(thm)],[26695])).
% 29.55/19.77 tff(26697,plain,
% 29.55/19.77 (big_f(c1, c1) <=> big_f(f7(f6(c2, f7(f4(c4)))), c1)),
% 29.55/19.77 inference(symmetry,[status(thm)],[26696])).
% 29.55/19.77 tff(26698,plain,
% 29.55/19.77 ((~big_f(c1, c1)) <=> (~big_f(f7(f6(c2, f7(f4(c4)))), c1))),
% 29.55/19.77 inference(monotonicity,[status(thm)],[26697])).
% 29.55/19.77 tff(26699,plain,
% 29.55/19.77 (~big_f(f7(f6(c2, f7(f4(c4)))), c1)),
% 29.55/19.77 inference(modus_ponens,[status(thm)],[66, 26698])).
% 29.55/19.77 tff(26700,plain,
% 29.55/19.77 (f10(f6(c2, f7(f4(c4)))) = f10(c2)),
% 29.55/19.77 inference(monotonicity,[status(thm)],[26690])).
% 29.55/19.77 tff(26701,plain,
% 29.55/19.77 (f10(f6(c2, f7(f4(c4)))) = c1),
% 29.55/19.77 inference(transitivity,[status(thm)],[26700, 94])).
% 29.55/19.77 tff(26702,plain,
% 29.55/19.77 (big_f(c2, f10(f6(c2, f7(f4(c4))))) <=> big_f(c2, c1)),
% 29.55/19.77 inference(monotonicity,[status(thm)],[26701])).
% 29.55/19.77 tff(26703,plain,
% 29.55/19.77 (big_f(c2, c1) <=> big_f(c2, f10(f6(c2, f7(f4(c4)))))),
% 29.55/19.77 inference(symmetry,[status(thm)],[26702])).
% 29.55/19.77 tff(26704,plain,
% 29.55/19.77 (big_f(c2, f10(f6(c2, f7(f4(c4)))))),
% 29.55/19.77 inference(modus_ponens,[status(thm)],[348, 26703])).
% 29.55/19.77 tff(26705,plain,
% 29.55/19.77 (f8(f6(c2, f7(f4(c4)))) = f8(c2)),
% 29.55/19.77 inference(monotonicity,[status(thm)],[17409])).
% 29.55/19.77 tff(26706,plain,
% 29.55/19.77 (f8(c2) = f8(f6(c2, f7(f4(c4))))),
% 29.55/19.77 inference(symmetry,[status(thm)],[26705])).
% 29.55/19.77 tff(26707,plain,
% 29.55/19.77 ((c2 = f8(c2)) <=> (c2 = f8(f6(c2, f7(f4(c4)))))),
% 29.55/19.77 inference(monotonicity,[status(thm)],[26706])).
% 29.55/19.77 tff(26708,plain,
% 29.55/19.77 (f5(f6(c2, f7(f4(c4)))) = f5(c2)),
% 29.55/19.77 inference(monotonicity,[status(thm)],[17409])).
% 29.55/19.77 tff(26709,plain,
% 29.55/19.77 ((c1 = f5(f6(c2, f7(f4(c4))))) <=> (c1 = f5(c2))),
% 29.55/19.77 inference(monotonicity,[status(thm)],[26708])).
% 29.55/19.77 tff(26710,plain,
% 29.55/19.77 ((c1 = f5(f6(c2, f7(f4(c4))))) <=> (f5(c2) = c1)),
% 29.55/19.77 inference(transitivity,[status(thm)],[26709, 1531])).
% 29.55/19.77 tff(26711,plain,
% 29.55/19.77 ((~(c1 = f5(f6(c2, f7(f4(c4)))))) <=> (~(f5(c2) = c1))),
% 29.55/19.77 inference(monotonicity,[status(thm)],[26710])).
% 29.55/19.77 tff(26712,assumption,(~big_f(f7(f6(c2, f7(f4(c4)))), c1)), introduced(assumption)).
% 29.55/19.77 tff(26713,plain,
% 29.55/19.77 (f7(f6(c2, f7(f4(c4)))) = f7(c2)),
% 29.55/19.77 inference(monotonicity,[status(thm)],[17409])).
% 29.55/19.77 tff(26714,plain,
% 29.55/19.77 (f7(f6(c2, f7(f4(c4)))) = c1),
% 29.55/19.77 inference(transitivity,[status(thm)],[26713, 22])).
% 29.55/19.77 tff(26715,plain,
% 29.55/19.77 ((f7(f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4)))) <=> (c1 = c2)),
% 29.55/19.77 inference(monotonicity,[status(thm)],[26714, 17409])).
% 29.55/19.77 tff(26716,plain,
% 29.55/19.77 ((f7(f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4)))) <=> (c2 = c1)),
% 29.55/19.77 inference(transitivity,[status(thm)],[26715, 1])).
% 29.55/19.77 tff(26717,plain,
% 29.55/19.77 ((c2 = c1) <=> (f7(f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4))))),
% 29.55/19.77 inference(symmetry,[status(thm)],[26716])).
% 29.55/19.77 tff(26718,plain,
% 29.55/19.77 ((~(c2 = c1)) <=> (~(f7(f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4)))))),
% 29.55/19.77 inference(monotonicity,[status(thm)],[26717])).
% 29.55/19.77 tff(26719,plain,
% 29.55/19.77 (~(f7(f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4))))),
% 29.55/19.77 inference(modus_ponens,[status(thm)],[75, 26718])).
% 29.55/19.77 tff(26720,plain,
% 29.55/19.77 (f10(f6(c2, f7(f4(c4)))) = f10(c2)),
% 29.55/19.77 inference(monotonicity,[status(thm)],[17409])).
% 29.55/19.77 tff(26721,plain,
% 29.55/19.77 (f10(f6(c2, f7(f4(c4)))) = c1),
% 29.55/19.77 inference(transitivity,[status(thm)],[26720, 94])).
% 29.55/19.77 tff(26722,plain,
% 29.55/19.77 ((f10(f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4)))) <=> (c1 = c2)),
% 29.55/19.77 inference(monotonicity,[status(thm)],[26721, 17409])).
% 29.55/19.77 tff(26723,plain,
% 29.55/19.77 ((f10(f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4)))) <=> (c2 = c1)),
% 29.55/19.77 inference(transitivity,[status(thm)],[26722, 1])).
% 29.55/19.77 tff(26724,plain,
% 29.55/19.77 ((c2 = c1) <=> (f10(f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4))))),
% 29.55/19.77 inference(symmetry,[status(thm)],[26723])).
% 29.55/19.77 tff(26725,plain,
% 29.55/19.77 ((~(c2 = c1)) <=> (~(f10(f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4)))))),
% 29.55/19.77 inference(monotonicity,[status(thm)],[26724])).
% 29.55/19.77 tff(26726,plain,
% 29.55/19.77 (~(f10(f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4))))),
% 29.55/19.77 inference(modus_ponens,[status(thm)],[75, 26725])).
% 29.55/19.77 tff(26727,assumption,(big_f(c2, f10(f6(c2, f7(f4(c4)))))), introduced(assumption)).
% 29.55/19.77 tff(26728,assumption,(~(c2 = f8(f6(c2, f7(f4(c4)))))), introduced(assumption)).
% 29.55/19.77 tff(26729,plain,
% 29.55/19.77 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f10(f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4)))) | (~(c1 = f5(f6(c2, f7(f4(c4)))))) | (c2 = f8(f6(c2, f7(f4(c4))))) | (~big_f(c2, f10(f6(c2, f7(f4(c4)))))) | (f7(f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4)))) | big_f(f7(f6(c2, f7(f4(c4)))), c1))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4)))) | (~(c1 = f5(f6(c2, f7(f4(c4)))))) | (c2 = f8(f6(c2, f7(f4(c4))))) | (~big_f(c2, f10(f6(c2, f7(f4(c4)))))) | (f7(f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4)))) | big_f(f7(f6(c2, f7(f4(c4)))), c1))),
% 29.55/19.78 inference(rewrite,[status(thm)],[])).
% 29.55/19.78 tff(26730,plain,
% 29.55/19.78 (((~(c1 = f5(f6(c2, f7(f4(c4)))))) | (f10(f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4)))) | (c2 = f8(f6(c2, f7(f4(c4))))) | (~big_f(c2, f10(f6(c2, f7(f4(c4)))))) | (f7(f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4)))) | big_f(f7(f6(c2, f7(f4(c4)))), c1)) <=> ((f10(f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4)))) | (~(c1 = f5(f6(c2, f7(f4(c4)))))) | (c2 = f8(f6(c2, f7(f4(c4))))) | (~big_f(c2, f10(f6(c2, f7(f4(c4)))))) | (f7(f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4)))) | big_f(f7(f6(c2, f7(f4(c4)))), c1))),
% 29.55/19.78 inference(rewrite,[status(thm)],[])).
% 29.55/19.78 tff(26731,plain,
% 29.55/19.78 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c1 = f5(f6(c2, f7(f4(c4)))))) | (f10(f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4)))) | (c2 = f8(f6(c2, f7(f4(c4))))) | (~big_f(c2, f10(f6(c2, f7(f4(c4)))))) | (f7(f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4)))) | big_f(f7(f6(c2, f7(f4(c4)))), c1))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f10(f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4)))) | (~(c1 = f5(f6(c2, f7(f4(c4)))))) | (c2 = f8(f6(c2, f7(f4(c4))))) | (~big_f(c2, f10(f6(c2, f7(f4(c4)))))) | (f7(f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4)))) | big_f(f7(f6(c2, f7(f4(c4)))), c1)))),
% 29.55/19.78 inference(monotonicity,[status(thm)],[26730])).
% 29.55/19.78 tff(26732,plain,
% 29.55/19.78 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c1 = f5(f6(c2, f7(f4(c4)))))) | (f10(f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4)))) | (c2 = f8(f6(c2, f7(f4(c4))))) | (~big_f(c2, f10(f6(c2, f7(f4(c4)))))) | (f7(f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4)))) | big_f(f7(f6(c2, f7(f4(c4)))), c1))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4)))) | (~(c1 = f5(f6(c2, f7(f4(c4)))))) | (c2 = f8(f6(c2, f7(f4(c4))))) | (~big_f(c2, f10(f6(c2, f7(f4(c4)))))) | (f7(f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4)))) | big_f(f7(f6(c2, f7(f4(c4)))), c1))),
% 29.55/19.78 inference(transitivity,[status(thm)],[26731, 26729])).
% 29.55/19.78 tff(26733,plain,
% 29.55/19.78 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c1 = f5(f6(c2, f7(f4(c4)))))) | (f10(f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4)))) | (c2 = f8(f6(c2, f7(f4(c4))))) | (~big_f(c2, f10(f6(c2, f7(f4(c4)))))) | (f7(f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4)))) | big_f(f7(f6(c2, f7(f4(c4)))), c1))),
% 29.55/19.78 inference(quant_inst,[status(thm)],[])).
% 29.55/19.78 tff(26734,plain,
% 29.55/19.78 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4)))) | (~(c1 = f5(f6(c2, f7(f4(c4)))))) | (c2 = f8(f6(c2, f7(f4(c4))))) | (~big_f(c2, f10(f6(c2, f7(f4(c4)))))) | (f7(f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4)))) | big_f(f7(f6(c2, f7(f4(c4)))), c1)),
% 29.55/19.78 inference(modus_ponens,[status(thm)],[26733, 26732])).
% 29.55/19.78 tff(26735,plain,
% 29.55/19.78 ((f10(f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4)))) | (~(c1 = f5(f6(c2, f7(f4(c4)))))) | (c2 = f8(f6(c2, f7(f4(c4))))) | (~big_f(c2, f10(f6(c2, f7(f4(c4)))))) | (f7(f6(c2, f7(f4(c4)))) = f6(c2, f7(f4(c4)))) | big_f(f7(f6(c2, f7(f4(c4)))), c1)),
% 29.55/19.78 inference(unit_resolution,[status(thm)],[26734, 705])).
% 29.55/19.78 tff(26736,plain,
% 29.55/19.78 (~(c1 = f5(f6(c2, f7(f4(c4)))))),
% 29.55/19.78 inference(unit_resolution,[status(thm)],[26735, 26728, 26727, 26726, 26719, 26712])).
% 29.55/19.78 tff(26737,plain,
% 29.55/19.78 (~(f5(c2) = c1)),
% 29.55/19.78 inference(modus_ponens,[status(thm)],[26736, 26711])).
% 29.55/19.78 tff(26738,plain,
% 29.55/19.78 (f5(c2) = c2),
% 29.55/19.78 inference(unit_resolution,[status(thm)],[1547, 26737])).
% 29.55/19.78 tff(26739,plain,
% 29.55/19.78 (c2 = f5(c2)),
% 29.55/19.78 inference(unit_resolution,[status(thm)],[8113, 26738])).
% 29.55/19.78 tff(26740,plain,
% 29.55/19.78 (c2 = f8(c2)),
% 29.55/19.78 inference(unit_resolution,[status(thm)],[24367, 26739])).
% 29.55/19.78 tff(26741,plain,
% 29.55/19.78 (c2 = f8(f6(c2, f7(f4(c4))))),
% 29.55/19.78 inference(modus_ponens,[status(thm)],[26740, 26707])).
% 29.55/19.78 tff(26742,plain,
% 29.55/19.78 ($false),
% 29.55/19.78 inference(unit_resolution,[status(thm)],[26728, 26741])).
% 29.55/19.78 tff(26743,plain,((c2 = f8(f6(c2, f7(f4(c4))))) | (~(f6(c2, f7(f4(c4))) = c2)) | (f10(c2) = c2) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~big_f(c2, f10(c2))) | (~big_f(c2, f10(f6(c2, f7(f4(c4)))))) | big_f(f7(f6(c2, f7(f4(c4)))), c1)), inference(lemma,lemma(discharge,[]))).
% 29.55/19.78 tff(26744,plain,
% 29.55/19.78 (c2 = f8(f6(c2, f7(f4(c4))))),
% 29.55/19.78 inference(unit_resolution,[status(thm)],[26743, 26690, 89, 17, 1521, 25683, 26704, 26699])).
% 29.55/19.78 tff(26745,plain,
% 29.55/19.78 (c2 = f8(c2)),
% 29.55/19.78 inference(transitivity,[status(thm)],[26744, 26693])).
% 29.55/19.78 tff(26746,plain,
% 29.55/19.78 (f9(c1, c2) = f9(c1, f8(c2))),
% 29.55/19.78 inference(monotonicity,[status(thm)],[26745])).
% 29.55/19.78 tff(26747,plain,
% 29.55/19.78 (big_f(f9(c1, c2), f10(c1)) <=> big_f(f9(c1, f8(c2)), f10(c1))),
% 29.55/19.78 inference(monotonicity,[status(thm)],[26746])).
% 29.55/19.78 tff(26748,plain,
% 29.55/19.78 (big_f(f9(c1, f8(c2)), f10(c1)) <=> big_f(f9(c1, c2), f10(c1))),
% 29.55/19.78 inference(symmetry,[status(thm)],[26747])).
% 29.55/19.78 tff(26749,plain,
% 29.55/19.78 (c2 = f6(c2, f7(f4(c4)))),
% 29.55/19.78 inference(symmetry,[status(thm)],[17409])).
% 29.55/19.78 tff(26750,plain,
% 29.55/19.78 (f8(c2) = f8(f6(c2, f7(f4(c4))))),
% 29.55/19.78 inference(monotonicity,[status(thm)],[26749])).
% 29.55/19.78 tff(26751,plain,
% 29.55/19.78 (f8(f6(c2, f7(f4(c4)))) = f8(c2)),
% 29.55/19.78 inference(symmetry,[status(thm)],[26750])).
% 29.55/19.78 tff(26752,assumption,(c2 = f8(f6(c2, f7(f4(c4))))), introduced(assumption)).
% 29.55/19.78 tff(26753,plain,
% 29.55/19.78 (c2 = f8(c2)),
% 29.55/19.78 inference(transitivity,[status(thm)],[26752, 26751])).
% 29.55/19.78 tff(26754,plain,
% 29.55/19.78 (f9(c1, c2) = f9(c1, f8(c2))),
% 29.55/19.78 inference(monotonicity,[status(thm)],[26753])).
% 29.55/19.78 tff(26755,plain,
% 29.55/19.78 ((f9(c1, c2) = c2) <=> (f9(c1, f8(c2)) = f8(c2))),
% 29.55/19.78 inference(monotonicity,[status(thm)],[26754, 26753])).
% 29.55/19.78 tff(26756,assumption,(~big_f(f9(c1, f8(c2)), f10(c1))), introduced(assumption)).
% 29.55/19.78 tff(26757,plain,
% 29.55/19.78 (f8(f6(c2, f7(f4(c4)))) = c2),
% 29.55/19.78 inference(symmetry,[status(thm)],[26752])).
% 29.55/19.78 tff(26758,plain,
% 29.55/19.78 (f8(c2) = c2),
% 29.55/19.78 inference(transitivity,[status(thm)],[26750, 26757])).
% 29.55/19.78 tff(26759,plain,
% 29.55/19.78 (f9(c1, f8(c2)) = f9(c1, c2)),
% 29.55/19.78 inference(monotonicity,[status(thm)],[26758])).
% 29.55/19.78 tff(26760,plain,
% 29.55/19.78 (f9(c1, c2) = f9(c1, f8(c2))),
% 29.55/19.78 inference(symmetry,[status(thm)],[26759])).
% 29.55/19.78 tff(26761,plain,
% 29.55/19.78 (big_f(f9(c1, c2), f10(c1)) <=> big_f(f9(c1, f8(c2)), f10(c1))),
% 29.55/19.78 inference(monotonicity,[status(thm)],[26760])).
% 29.55/19.78 tff(26762,plain,
% 29.55/19.78 (big_f(f9(c1, f8(c2)), f10(c1))),
% 29.55/19.78 inference(modus_ponens,[status(thm)],[17888, 26761])).
% 29.55/19.78 tff(26763,plain,
% 29.55/19.78 ($false),
% 29.55/19.78 inference(unit_resolution,[status(thm)],[26756, 26762])).
% 29.55/19.78 tff(26764,plain,((~big_f(f9(c1, c2), f10(c1))) | big_f(f9(c1, f8(c2)), f10(c1)) | (~(c2 = f8(f6(c2, f7(f4(c4)))))) | (~(f6(c2, f7(f4(c4))) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.55/19.78 tff(26765,plain,
% 29.55/19.78 (~big_f(f9(c1, c2), f10(c1))),
% 29.55/19.78 inference(unit_resolution,[status(thm)],[26764, 26756, 26752, 17409])).
% 29.55/19.78 tff(26766,plain,
% 29.55/19.78 (big_f(f9(c1, f8(c2)), f10(c2)) <=> big_f(f9(c1, f8(c2)), f10(c1))),
% 29.55/19.78 inference(monotonicity,[status(thm)],[24342])).
% 29.55/19.78 tff(26767,plain,
% 29.55/19.78 (big_f(f9(c1, f8(c2)), f10(c1)) <=> big_f(f9(c1, f8(c2)), f10(c2))),
% 29.55/19.78 inference(symmetry,[status(thm)],[26766])).
% 29.55/19.78 tff(26768,plain,
% 29.55/19.78 ((~big_f(f9(c1, f8(c2)), f10(c1))) <=> (~big_f(f9(c1, f8(c2)), f10(c2)))),
% 29.55/19.78 inference(monotonicity,[status(thm)],[26767])).
% 29.55/19.78 tff(26769,plain,
% 29.55/19.78 (~big_f(f9(c1, f8(c2)), f10(c2))),
% 29.55/19.78 inference(modus_ponens,[status(thm)],[26756, 26768])).
% 29.55/19.78 tff(26770,plain,
% 29.55/19.78 (f9(c1, f8(c2)) = f8(c2)),
% 29.55/19.78 inference(modus_ponens,[status(thm)],[24340, 26755])).
% 29.55/19.78 tff(26771,plain,
% 29.55/19.78 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | (f7(c2) = c2) | (~(c1 = f5(c2))) | big_f(f7(c2), c1) | (~(f9(c1, f8(c2)) = f8(c2))) | big_f(f9(c1, f8(c2)), f10(c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | (f7(c2) = c2) | (~(c1 = f5(c2))) | big_f(f7(c2), c1) | (~(f9(c1, f8(c2)) = f8(c2))) | big_f(f9(c1, f8(c2)), f10(c2)))),
% 29.55/19.78 inference(rewrite,[status(thm)],[])).
% 29.55/19.78 tff(26772,plain,
% 29.55/19.78 (((~(c1 = f5(c2))) | (f10(c2) = c2) | big_f(f9(c1, f8(c2)), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), c1) | (~(f9(c1, f8(c2)) = f8(c2)))) <=> ((f10(c2) = c2) | (f7(c2) = c2) | (~(c1 = f5(c2))) | big_f(f7(c2), c1) | (~(f9(c1, f8(c2)) = f8(c2))) | big_f(f9(c1, f8(c2)), f10(c2)))),
% 29.55/19.78 inference(rewrite,[status(thm)],[])).
% 29.55/19.78 tff(26773,plain,
% 29.55/19.78 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c1 = f5(c2))) | (f10(c2) = c2) | big_f(f9(c1, f8(c2)), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), c1) | (~(f9(c1, f8(c2)) = f8(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | (f7(c2) = c2) | (~(c1 = f5(c2))) | big_f(f7(c2), c1) | (~(f9(c1, f8(c2)) = f8(c2))) | big_f(f9(c1, f8(c2)), f10(c2))))),
% 29.55/19.78 inference(monotonicity,[status(thm)],[26772])).
% 29.55/19.78 tff(26774,plain,
% 29.55/19.78 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c1 = f5(c2))) | (f10(c2) = c2) | big_f(f9(c1, f8(c2)), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), c1) | (~(f9(c1, f8(c2)) = f8(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | (f7(c2) = c2) | (~(c1 = f5(c2))) | big_f(f7(c2), c1) | (~(f9(c1, f8(c2)) = f8(c2))) | big_f(f9(c1, f8(c2)), f10(c2)))),
% 29.55/19.78 inference(transitivity,[status(thm)],[26773, 26771])).
% 29.55/19.78 tff(26775,plain,
% 29.55/19.78 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c1 = f5(c2))) | (f10(c2) = c2) | big_f(f9(c1, f8(c2)), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), c1) | (~(f9(c1, f8(c2)) = f8(c2))))),
% 29.55/19.78 inference(quant_inst,[status(thm)],[])).
% 29.55/19.78 tff(26776,plain,
% 29.55/19.78 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | (f7(c2) = c2) | (~(c1 = f5(c2))) | big_f(f7(c2), c1) | (~(f9(c1, f8(c2)) = f8(c2))) | big_f(f9(c1, f8(c2)), f10(c2))),
% 29.55/19.78 inference(modus_ponens,[status(thm)],[26775, 26774])).
% 29.55/19.78 tff(26777,plain,
% 29.55/19.78 ((~(c1 = f5(c2))) | (~(f9(c1, f8(c2)) = f8(c2))) | big_f(f9(c1, f8(c2)), f10(c2))),
% 29.55/19.78 inference(unit_resolution,[status(thm)],[26776, 1745, 89, 17, 333])).
% 29.55/19.78 tff(26778,plain,
% 29.55/19.78 (~(f9(c1, f8(c2)) = f8(c2))),
% 29.55/19.78 inference(unit_resolution,[status(thm)],[26777, 23054, 24794])).
% 29.55/19.78 tff(26779,plain,
% 29.55/19.78 ($false),
% 29.55/19.78 inference(unit_resolution,[status(thm)],[26778, 26770])).
% 29.55/19.78 tff(26780,plain,((~(c1 = f5(c2))) | (~(c2 = f8(f6(c2, f7(f4(c4)))))) | (~(f6(c2, f7(f4(c4))) = c2)) | big_f(f9(c1, f8(c2)), f10(c2)) | (f10(c2) = c2) | (f7(c2) = c2) | big_f(f7(c2), c1) | (~(f10(c1) = c1)) | big_f(f9(c1, c2), f10(c1))), inference(lemma,lemma(discharge,[]))).
% 29.55/19.78 tff(26781,plain,
% 29.55/19.78 (~(c1 = f5(c2))),
% 29.55/19.78 inference(unit_resolution,[status(thm)],[26780, 26769, 17409, 26752, 89, 17, 333, 3762, 26765])).
% 29.55/19.78 tff(26782,plain,
% 29.55/19.78 (~(f5(c2) = c1)),
% 29.55/19.78 inference(unit_resolution,[status(thm)],[8139, 26781])).
% 29.55/19.78 tff(26783,plain,
% 29.55/19.78 (f5(c2) = c2),
% 29.55/19.78 inference(unit_resolution,[status(thm)],[1547, 26782])).
% 29.55/19.78 tff(26784,plain,
% 29.55/19.78 (c2 = f5(c2)),
% 29.55/19.78 inference(unit_resolution,[status(thm)],[8113, 26783])).
% 29.55/19.78 tff(26785,plain,
% 29.55/19.78 ((~(c2 = f5(c2))) | (f9(c1, c2) = c2)),
% 29.55/19.78 inference(unit_resolution,[status(thm)],[24374, 267, 3762, 17, 1521, 26765])).
% 29.55/19.78 tff(26786,plain,
% 29.55/19.78 (f9(c1, c2) = c2),
% 29.55/19.78 inference(unit_resolution,[status(thm)],[26785, 26784])).
% 29.55/19.78 tff(26787,plain,
% 29.55/19.78 (f9(c1, f8(c2)) = f8(c2)),
% 29.55/19.78 inference(modus_ponens,[status(thm)],[26786, 26755])).
% 29.55/19.78 tff(26788,plain,
% 29.55/19.78 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (~(f9(c1, f8(c2)) = f8(c2))) | big_f(f9(c1, f8(c2)), f10(c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (~(f9(c1, f8(c2)) = f8(c2))) | big_f(f9(c1, f8(c2)), f10(c2)))),
% 29.55/19.78 inference(rewrite,[status(thm)],[])).
% 29.55/19.78 tff(26789,plain,
% 29.55/19.78 (((~(c2 = f5(c2))) | (f10(c2) = c2) | big_f(f9(c1, f8(c2)), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(f9(c1, f8(c2)) = f8(c2)))) <=> ((f10(c2) = c2) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (~(f9(c1, f8(c2)) = f8(c2))) | big_f(f9(c1, f8(c2)), f10(c2)))),
% 29.55/19.78 inference(rewrite,[status(thm)],[])).
% 29.55/19.78 tff(26790,plain,
% 29.55/19.78 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c2 = f5(c2))) | (f10(c2) = c2) | big_f(f9(c1, f8(c2)), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(f9(c1, f8(c2)) = f8(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((f10(c2) = c2) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (~(f9(c1, f8(c2)) = f8(c2))) | big_f(f9(c1, f8(c2)), f10(c2))))),
% 29.55/19.78 inference(monotonicity,[status(thm)],[26789])).
% 29.55/19.78 tff(26791,plain,
% 29.55/19.78 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c2 = f5(c2))) | (f10(c2) = c2) | big_f(f9(c1, f8(c2)), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(f9(c1, f8(c2)) = f8(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (~(f9(c1, f8(c2)) = f8(c2))) | big_f(f9(c1, f8(c2)), f10(c2)))),
% 29.55/19.78 inference(transitivity,[status(thm)],[26790, 26788])).
% 29.55/19.78 tff(26792,plain,
% 29.55/19.78 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | ((~(c2 = f5(c2))) | (f10(c2) = c2) | big_f(f9(c1, f8(c2)), f10(c2)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(f9(c1, f8(c2)) = f8(c2))))),
% 29.55/19.78 inference(quant_inst,[status(thm)],[])).
% 29.55/19.78 tff(26793,plain,
% 29.55/19.78 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | big_f(X8, f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X8 = f8(X7))))) | (f10(c2) = c2) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (~(f9(c1, f8(c2)) = f8(c2))) | big_f(f9(c1, f8(c2)), f10(c2))),
% 29.55/19.78 inference(modus_ponens,[status(thm)],[26792, 26791])).
% 29.55/19.78 tff(26794,plain,
% 29.55/19.78 ((~(c2 = f5(c2))) | (~(f9(c1, f8(c2)) = f8(c2))) | big_f(f9(c1, f8(c2)), f10(c2))),
% 29.55/19.78 inference(unit_resolution,[status(thm)],[26793, 1745, 89, 17, 1521])).
% 29.55/19.78 tff(26795,plain,
% 29.55/19.78 (~(f9(c1, f8(c2)) = f8(c2))),
% 29.55/19.78 inference(unit_resolution,[status(thm)],[26794, 26784, 26769])).
% 29.55/19.78 tff(26796,plain,
% 29.55/19.78 ($false),
% 29.55/19.78 inference(unit_resolution,[status(thm)],[26795, 26787])).
% 29.55/19.78 tff(26797,plain,(big_f(f9(c1, f8(c2)), f10(c1)) | (~(c2 = f8(f6(c2, f7(f4(c4)))))) | (~(f6(c2, f7(f4(c4))) = c2)) | (~(f10(c1) = c1)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (f10(c2) = c2) | big_f(f7(c2), c1)), inference(lemma,lemma(discharge,[]))).
% 29.55/19.78 tff(26798,plain,
% 29.55/19.78 (big_f(f9(c1, f8(c2)), f10(c1))),
% 29.55/19.78 inference(unit_resolution,[status(thm)],[26797, 26744, 26690, 3762, 17, 1521, 89, 12093])).
% 29.55/19.78 tff(26799,plain,
% 29.55/19.78 (big_f(f9(c1, c2), f10(c1))),
% 29.55/19.78 inference(modus_ponens,[status(thm)],[26798, 26748])).
% 29.55/19.78 tff(26800,plain,
% 29.55/19.78 ((f9(c1, c2) = c2) <=> (f9(c1, f8(c2)) = f8(c2))),
% 29.55/19.78 inference(monotonicity,[status(thm)],[26746, 26745])).
% 29.55/19.78 tff(26801,plain,
% 29.55/19.78 ((f9(c1, f8(c2)) = f8(c2)) <=> (f9(c1, c2) = c2)),
% 29.55/19.78 inference(symmetry,[status(thm)],[26800])).
% 29.55/19.78 tff(26802,plain,
% 29.55/19.78 (big_f(f9(c1, f8(c2)), f10(c2))),
% 29.55/19.78 inference(modus_ponens,[status(thm)],[26798, 26767])).
% 29.55/19.78 tff(26803,plain,
% 29.55/19.78 (f9(c1, f8(c2)) = f8(c2)),
% 29.55/19.78 inference(unit_resolution,[status(thm)],[24843, 26802, 17, 1521, 89, 12093])).
% 29.55/19.78 tff(26804,plain,
% 29.55/19.78 (f9(c1, c2) = c2),
% 29.55/19.78 inference(modus_ponens,[status(thm)],[26803, 26801])).
% 29.55/19.78 tff(26805,plain,
% 29.55/19.78 (~(c2 = f5(c2))),
% 29.55/19.78 inference(unit_resolution,[status(thm)],[8204, 26804, 3762, 17, 1521, 26799])).
% 29.55/19.78 tff(26806,plain,
% 29.55/19.78 (~(f5(c2) = c2)),
% 29.55/19.78 inference(unit_resolution,[status(thm)],[8113, 26805])).
% 29.55/19.78 tff(26807,plain,
% 29.55/19.78 ((~(c1 = f5(c2))) | (~(f9(c1, c2) = c2))),
% 29.55/19.78 inference(unit_resolution,[status(thm)],[23139, 783, 3762, 17, 26799, 12093])).
% 29.55/19.78 tff(26808,plain,
% 29.55/19.78 (~(c1 = f5(c2))),
% 29.55/19.78 inference(unit_resolution,[status(thm)],[26807, 26804])).
% 29.55/19.78 tff(26809,plain,
% 29.55/19.78 (~(f5(c2) = c1)),
% 29.55/19.78 inference(unit_resolution,[status(thm)],[8139, 26808])).
% 29.55/19.78 tff(26810,plain,
% 29.55/19.78 ($false),
% 29.55/19.78 inference(unit_resolution,[status(thm)],[1547, 26809, 26806])).
% 29.55/19.78 tff(26811,plain,(big_f(c1, c1) | (~(f10(c1) = c1)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (f10(c2) = c2) | (~big_f(c2, c1)) | (~(f7(c1) = c1)) | (f6(c2, c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.55/19.78 tff(26812,plain,
% 29.55/19.78 (big_f(c1, c1)),
% 29.55/19.78 inference(unit_resolution,[status(thm)],[26811, 3198, 17, 1521, 89, 348, 4234, 3762])).
% 29.55/19.78 tff(26813,plain,
% 29.55/19.78 (big_f(f7(c2), c1)),
% 29.55/19.78 inference(unit_resolution,[status(thm)],[20926, 26812, 94, 22])).
% 29.55/19.78 tff(26814,plain,
% 29.55/19.78 (~(f4(c4) = c2)),
% 29.55/19.78 inference(unit_resolution,[status(thm)],[10334, 26813, 17, 121, 1521, 348])).
% 29.55/19.78 tff(26815,plain,
% 29.55/19.78 (f4(c4) = c1),
% 29.55/19.78 inference(unit_resolution,[status(thm)],[11750, 26814])).
% 29.55/19.78 tff(26816,plain,
% 29.55/19.78 (~(f6(c2, f7(f4(c4))) = c1)),
% 29.55/19.78 inference(unit_resolution,[status(thm)],[26572, 26815, 4234, 3198])).
% 29.55/19.78 tff(26817,plain,
% 29.55/19.78 (f6(c2, f7(f4(c4))) = c2),
% 29.55/19.78 inference(unit_resolution,[status(thm)],[6601, 26816])).
% 29.55/19.78 tff(26818,plain,
% 29.55/19.78 (f7(f4(c4)) = f7(c1)),
% 29.55/19.78 inference(monotonicity,[status(thm)],[26815])).
% 29.55/19.78 tff(26819,plain,
% 29.55/19.78 (f7(f4(c4)) = c1),
% 29.55/19.78 inference(transitivity,[status(thm)],[26818, 4234])).
% 29.55/19.78 tff(26820,plain,
% 29.55/19.78 (f6(c2, f7(f4(c4))) = f6(c2, c1)),
% 29.55/19.78 inference(monotonicity,[status(thm)],[26819])).
% 29.55/19.78 tff(26821,plain,
% 29.55/19.78 (f6(c2, c1) = f6(c2, f7(f4(c4)))),
% 29.55/19.78 inference(symmetry,[status(thm)],[26820])).
% 29.55/19.78 tff(26822,plain,
% 29.55/19.78 (f6(c2, c1) = c2),
% 29.55/19.78 inference(transitivity,[status(thm)],[26821, 26817])).
% 29.55/19.78 tff(26823,plain,
% 29.55/19.78 (f7(f6(c2, c1)) = f7(c2)),
% 29.55/19.78 inference(monotonicity,[status(thm)],[26822])).
% 29.55/19.78 tff(26824,plain,
% 29.55/19.78 (f7(f6(c2, c1)) = f7(c1)),
% 29.55/19.78 inference(transitivity,[status(thm)],[26823, 22, 5544])).
% 29.55/19.78 tff(26825,plain,
% 29.55/19.78 (big_f(f7(f6(c2, c1)), f6(c1, c1)) <=> big_f(f7(c1), f6(c1, c1))),
% 29.55/19.78 inference(monotonicity,[status(thm)],[26824])).
% 29.55/19.78 tff(26826,plain,
% 29.55/19.78 (big_f(f7(c1), f6(c1, c1)) <=> big_f(f7(f6(c2, c1)), f6(c1, c1))),
% 29.55/19.78 inference(symmetry,[status(thm)],[26825])).
% 29.55/19.78 tff(26827,plain,
% 29.55/19.78 (big_f(f7(c1), f6(c1, c1))),
% 29.55/19.78 inference(unit_resolution,[status(thm)],[26685, 26815, 17, 121, 94, 3762, 4234, 26813])).
% 29.55/19.78 tff(26828,plain,
% 29.55/19.78 (big_f(f7(f6(c2, c1)), f6(c1, c1))),
% 29.55/19.78 inference(modus_ponens,[status(thm)],[26827, 26826])).
% 29.55/19.78 tff(26829,plain,
% 29.55/19.78 (c2 = f6(c2, f7(f4(c4)))),
% 29.55/19.78 inference(symmetry,[status(thm)],[26817])).
% 29.55/19.78 tff(26830,plain,
% 29.55/19.78 (c2 = f6(c2, c1)),
% 29.55/19.78 inference(transitivity,[status(thm)],[26829, 26820])).
% 29.55/19.78 tff(26831,plain,
% 29.55/19.78 (f5(c2) = f5(f6(c2, c1))),
% 29.55/19.78 inference(monotonicity,[status(thm)],[26830])).
% 29.55/19.78 tff(26832,plain,
% 29.55/19.78 (f5(f6(c2, c1)) = f5(c2)),
% 29.55/19.78 inference(symmetry,[status(thm)],[26831])).
% 29.55/19.78 tff(26833,plain,
% 29.55/19.78 ((f6(c1, c1) = f5(f6(c2, c1))) <=> (f6(c1, c1) = f5(c2))),
% 29.55/19.78 inference(monotonicity,[status(thm)],[26832])).
% 29.55/19.78 tff(26834,plain,
% 29.55/19.78 ((f6(c1, c1) = f5(c2)) <=> (f6(c1, c1) = f5(f6(c2, c1)))),
% 29.55/19.78 inference(symmetry,[status(thm)],[26833])).
% 29.55/19.78 tff(26835,plain,
% 29.55/19.78 (f10(f6(c2, c1)) = f10(c2)),
% 29.55/19.78 inference(monotonicity,[status(thm)],[26822])).
% 29.55/19.78 tff(26836,plain,
% 29.55/19.78 (f10(f6(c2, c1)) = c1),
% 29.55/19.78 inference(transitivity,[status(thm)],[26835, 94])).
% 29.55/19.78 tff(26837,plain,
% 29.55/19.78 (big_f(c1, f10(f6(c2, c1))) <=> big_f(c1, c1)),
% 29.55/19.78 inference(monotonicity,[status(thm)],[26836])).
% 29.55/19.78 tff(26838,plain,
% 29.55/19.78 (big_f(c1, c1) <=> big_f(c1, f10(f6(c2, c1)))),
% 29.55/19.78 inference(symmetry,[status(thm)],[26837])).
% 29.55/19.78 tff(26839,plain,
% 29.55/19.78 (big_f(c1, f10(f6(c2, c1)))),
% 29.55/19.78 inference(modus_ponens,[status(thm)],[26812, 26838])).
% 29.55/19.78 tff(26840,plain,
% 29.55/19.78 (f7(f6(c2, c1)) = c1),
% 29.55/19.78 inference(transitivity,[status(thm)],[26823, 22])).
% 29.55/19.78 tff(26841,plain,
% 29.55/19.78 (big_f(f7(f6(c2, c1)), c1) <=> big_f(c1, c1)),
% 29.55/19.78 inference(monotonicity,[status(thm)],[26840])).
% 29.55/19.78 tff(26842,plain,
% 29.55/19.78 (big_f(c1, c1) <=> big_f(f7(f6(c2, c1)), c1)),
% 29.55/19.78 inference(symmetry,[status(thm)],[26841])).
% 29.55/19.78 tff(26843,plain,
% 29.55/19.78 (big_f(f7(f6(c2, c1)), c1)),
% 29.55/19.78 inference(modus_ponens,[status(thm)],[26812, 26842])).
% 29.55/19.78 tff(26844,plain,
% 29.55/19.78 ((f10(f6(c2, c1)) = f6(c2, c1)) <=> (c1 = f6(c2, c1))),
% 29.55/19.78 inference(monotonicity,[status(thm)],[26836])).
% 29.55/19.78 tff(26845,plain,
% 29.55/19.78 ((f10(f6(c2, c1)) = f6(c2, c1)) <=> (f6(c2, c1) = c1)),
% 29.55/19.78 inference(transitivity,[status(thm)],[26844, 14624])).
% 29.55/19.78 tff(26846,plain,
% 29.55/19.78 ((f6(c2, c1) = c1) <=> (f10(f6(c2, c1)) = f6(c2, c1))),
% 29.55/19.78 inference(symmetry,[status(thm)],[26845])).
% 29.55/19.78 tff(26847,plain,
% 29.55/19.78 ((~(f6(c2, c1) = c1)) <=> (~(f10(f6(c2, c1)) = f6(c2, c1)))),
% 29.55/19.78 inference(monotonicity,[status(thm)],[26846])).
% 29.55/19.78 tff(26848,plain,
% 29.55/19.78 (~(f10(f6(c2, c1)) = f6(c2, c1))),
% 29.55/19.78 inference(modus_ponens,[status(thm)],[3198, 26847])).
% 29.55/19.78 tff(26849,plain,
% 29.55/19.78 (f8(c2) = f8(f6(c2, c1))),
% 29.55/19.78 inference(monotonicity,[status(thm)],[26830])).
% 29.55/19.78 tff(26850,plain,
% 29.55/19.78 (f8(f6(c2, c1)) = f8(c2)),
% 29.55/19.78 inference(symmetry,[status(thm)],[26849])).
% 29.55/19.78 tff(26851,plain,
% 29.55/19.78 ((c1 = f8(f6(c2, c1))) <=> (c1 = f8(c2))),
% 29.55/19.78 inference(monotonicity,[status(thm)],[26850])).
% 29.55/19.78 tff(26852,plain,
% 29.55/19.78 ((c1 = f8(c2)) <=> (c1 = f8(f6(c2, c1)))),
% 29.55/19.78 inference(symmetry,[status(thm)],[26851])).
% 29.55/19.78 tff(26853,plain,
% 29.55/19.78 (big_f(f6(c2, c1), f10(f6(c2, c1))) <=> big_f(c2, c1)),
% 29.55/19.78 inference(monotonicity,[status(thm)],[26822, 26836])).
% 29.55/19.78 tff(26854,plain,
% 29.55/19.78 (big_f(c2, c1) <=> big_f(f6(c2, c1), f10(f6(c2, c1)))),
% 29.55/19.78 inference(symmetry,[status(thm)],[26853])).
% 29.55/19.78 tff(26855,plain,
% 29.55/19.78 (big_f(f6(c2, c1), f10(f6(c2, c1)))),
% 29.55/19.78 inference(modus_ponens,[status(thm)],[348, 26854])).
% 29.55/19.78 tff(26856,plain,
% 29.55/19.78 ((f7(f6(c2, c1)) = f6(c2, c1)) <=> (c1 = f6(c2, c1))),
% 29.55/19.78 inference(monotonicity,[status(thm)],[26840])).
% 29.55/19.78 tff(26857,plain,
% 29.55/19.78 ((f7(f6(c2, c1)) = f6(c2, c1)) <=> (f6(c2, c1) = c1)),
% 29.55/19.78 inference(transitivity,[status(thm)],[26856, 14624])).
% 29.55/19.78 tff(26858,plain,
% 29.55/19.78 ((f6(c2, c1) = c1) <=> (f7(f6(c2, c1)) = f6(c2, c1))),
% 29.55/19.78 inference(symmetry,[status(thm)],[26857])).
% 29.55/19.78 tff(26859,plain,
% 29.55/19.78 ((~(f6(c2, c1) = c1)) <=> (~(f7(f6(c2, c1)) = f6(c2, c1)))),
% 29.55/19.78 inference(monotonicity,[status(thm)],[26858])).
% 29.55/19.78 tff(26860,plain,
% 29.55/19.78 (~(f7(f6(c2, c1)) = f6(c2, c1))),
% 29.55/19.78 inference(modus_ponens,[status(thm)],[3198, 26859])).
% 29.55/19.78 tff(26861,plain,
% 29.55/19.78 (f6(c2, c1) = f6(c2, f7(f4(c4)))),
% 29.55/19.78 inference(symmetry,[status(thm)],[26568])).
% 29.55/19.78 tff(26862,plain,
% 29.55/19.78 (f6(c2, c1) = c2),
% 29.55/19.78 inference(transitivity,[status(thm)],[26861, 17409])).
% 29.55/19.78 tff(26863,plain,
% 29.55/19.78 (f7(f6(c2, c1)) = f7(c2)),
% 29.55/19.78 inference(monotonicity,[status(thm)],[26862])).
% 29.55/19.78 tff(26864,plain,
% 29.55/19.78 (f7(f6(c2, c1)) = f7(c1)),
% 29.55/19.78 inference(transitivity,[status(thm)],[26863, 292, 5544])).
% 29.55/19.78 tff(26865,plain,
% 29.55/19.78 (big_f(f7(f6(c2, c1)), f6(c1, c1)) <=> big_f(f7(c1), f6(c1, c1))),
% 29.55/19.78 inference(monotonicity,[status(thm)],[26864])).
% 29.55/19.78 tff(26866,plain,
% 29.55/19.78 (big_f(f7(c1), f6(c1, c1)) <=> big_f(f7(f6(c2, c1)), f6(c1, c1))),
% 29.55/19.79 inference(symmetry,[status(thm)],[26865])).
% 29.55/19.79 tff(26867,plain,
% 29.55/19.79 (big_f(f7(f6(c2, c1)), f6(c1, c1))),
% 29.55/19.79 inference(modus_ponens,[status(thm)],[5964, 26866])).
% 29.55/19.79 tff(26868,assumption,(big_f(f7(f6(c2, c1)), c1)), introduced(assumption)).
% 29.55/19.79 tff(26869,assumption,(big_f(f6(c2, c1), f10(f6(c2, c1)))), introduced(assumption)).
% 29.55/19.79 tff(26870,assumption,(~(f10(f6(c2, c1)) = f6(c2, c1))), introduced(assumption)).
% 29.55/19.79 tff(26871,assumption,(~(f6(c2, c1) = f8(f6(c2, c1)))), introduced(assumption)).
% 29.55/19.79 tff(26872,assumption,(~(f7(f6(c2, c1)) = f6(c2, c1))), introduced(assumption)).
% 29.55/19.79 tff(26873,plain,
% 29.55/19.79 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(f6(c2, c1)) = f6(c2, c1)) | (c1 = f5(f6(c2, c1))) | (f10(f6(c2, c1)) = f6(c2, c1)) | (~big_f(f6(c2, c1), f10(f6(c2, c1)))) | (f6(c2, c1) = f8(f6(c2, c1))) | (~big_f(f7(f6(c2, c1)), c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(f6(c2, c1)) = f6(c2, c1)) | (c1 = f5(f6(c2, c1))) | (f10(f6(c2, c1)) = f6(c2, c1)) | (~big_f(f6(c2, c1), f10(f6(c2, c1)))) | (f6(c2, c1) = f8(f6(c2, c1))) | (~big_f(f7(f6(c2, c1)), c1)))),
% 29.55/19.79 inference(rewrite,[status(thm)],[])).
% 29.55/19.79 tff(26874,plain,
% 29.55/19.79 (((f10(f6(c2, c1)) = f6(c2, c1)) | (f6(c2, c1) = f8(f6(c2, c1))) | (~big_f(f6(c2, c1), f10(f6(c2, c1)))) | (f7(f6(c2, c1)) = f6(c2, c1)) | (c1 = f5(f6(c2, c1))) | (~big_f(f7(f6(c2, c1)), c1))) <=> ((f7(f6(c2, c1)) = f6(c2, c1)) | (c1 = f5(f6(c2, c1))) | (f10(f6(c2, c1)) = f6(c2, c1)) | (~big_f(f6(c2, c1), f10(f6(c2, c1)))) | (f6(c2, c1) = f8(f6(c2, c1))) | (~big_f(f7(f6(c2, c1)), c1)))),
% 29.55/19.79 inference(rewrite,[status(thm)],[])).
% 29.55/19.79 tff(26875,plain,
% 29.55/19.79 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f6(c2, c1)) = f6(c2, c1)) | (f6(c2, c1) = f8(f6(c2, c1))) | (~big_f(f6(c2, c1), f10(f6(c2, c1)))) | (f7(f6(c2, c1)) = f6(c2, c1)) | (c1 = f5(f6(c2, c1))) | (~big_f(f7(f6(c2, c1)), c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(f6(c2, c1)) = f6(c2, c1)) | (c1 = f5(f6(c2, c1))) | (f10(f6(c2, c1)) = f6(c2, c1)) | (~big_f(f6(c2, c1), f10(f6(c2, c1)))) | (f6(c2, c1) = f8(f6(c2, c1))) | (~big_f(f7(f6(c2, c1)), c1))))),
% 29.55/19.79 inference(monotonicity,[status(thm)],[26874])).
% 29.55/19.79 tff(26876,plain,
% 29.55/19.79 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f6(c2, c1)) = f6(c2, c1)) | (f6(c2, c1) = f8(f6(c2, c1))) | (~big_f(f6(c2, c1), f10(f6(c2, c1)))) | (f7(f6(c2, c1)) = f6(c2, c1)) | (c1 = f5(f6(c2, c1))) | (~big_f(f7(f6(c2, c1)), c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(f6(c2, c1)) = f6(c2, c1)) | (c1 = f5(f6(c2, c1))) | (f10(f6(c2, c1)) = f6(c2, c1)) | (~big_f(f6(c2, c1), f10(f6(c2, c1)))) | (f6(c2, c1) = f8(f6(c2, c1))) | (~big_f(f7(f6(c2, c1)), c1)))),
% 29.55/19.79 inference(transitivity,[status(thm)],[26875, 26873])).
% 29.55/19.79 tff(26877,plain,
% 29.55/19.79 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f6(c2, c1)) = f6(c2, c1)) | (f6(c2, c1) = f8(f6(c2, c1))) | (~big_f(f6(c2, c1), f10(f6(c2, c1)))) | (f7(f6(c2, c1)) = f6(c2, c1)) | (c1 = f5(f6(c2, c1))) | (~big_f(f7(f6(c2, c1)), c1)))),
% 29.55/19.79 inference(quant_inst,[status(thm)],[])).
% 29.55/19.79 tff(26878,plain,
% 29.55/19.79 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(f6(c2, c1)) = f6(c2, c1)) | (c1 = f5(f6(c2, c1))) | (f10(f6(c2, c1)) = f6(c2, c1)) | (~big_f(f6(c2, c1), f10(f6(c2, c1)))) | (f6(c2, c1) = f8(f6(c2, c1))) | (~big_f(f7(f6(c2, c1)), c1))),
% 29.55/19.79 inference(modus_ponens,[status(thm)],[26877, 26876])).
% 29.55/19.79 tff(26879,plain,
% 29.55/19.79 ((c1 = f5(f6(c2, c1))) | (f10(f6(c2, c1)) = f6(c2, c1)) | (~big_f(f6(c2, c1), f10(f6(c2, c1)))) | (f6(c2, c1) = f8(f6(c2, c1))) | (~big_f(f7(f6(c2, c1)), c1))),
% 29.55/19.79 inference(unit_resolution,[status(thm)],[26878, 1659, 26872])).
% 29.55/19.79 tff(26880,plain,
% 29.55/19.79 (c1 = f5(f6(c2, c1))),
% 29.55/19.79 inference(unit_resolution,[status(thm)],[26879, 26871, 26870, 26869, 26868])).
% 29.55/19.79 tff(26881,plain,
% 29.55/19.79 (f5(f6(c2, c1)) = c1),
% 29.55/19.79 inference(symmetry,[status(thm)],[26880])).
% 29.55/19.79 tff(26882,plain,
% 29.55/19.79 ((f6(c1, c1) = f5(f6(c2, c1))) <=> (f6(c1, c1) = c1)),
% 29.55/19.79 inference(monotonicity,[status(thm)],[26881])).
% 29.55/19.79 tff(26883,plain,
% 29.55/19.79 ((f6(c1, c1) = c1) <=> (f6(c1, c1) = f5(f6(c2, c1)))),
% 29.55/19.79 inference(symmetry,[status(thm)],[26882])).
% 29.55/19.79 tff(26884,plain,
% 29.55/19.79 ((~(f6(c1, c1) = c1)) <=> (~(f6(c1, c1) = f5(f6(c2, c1))))),
% 29.55/19.79 inference(monotonicity,[status(thm)],[26883])).
% 29.55/19.79 tff(26885,plain,
% 29.55/19.79 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (f10(f6(c2, c1)) = f6(c2, c1)) | (~big_f(f6(c2, c1), f10(f6(c2, c1)))) | (f6(c2, c1) = f8(f6(c2, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (f10(f6(c2, c1)) = f6(c2, c1)) | (~big_f(f6(c2, c1), f10(f6(c2, c1)))) | (f6(c2, c1) = f8(f6(c2, c1))))),
% 29.55/19.79 inference(rewrite,[status(thm)],[])).
% 29.55/19.79 tff(26886,plain,
% 29.55/19.79 (((f10(f6(c2, c1)) = f6(c2, c1)) | (f6(c2, c1) = f8(f6(c2, c1))) | (~big_f(f6(c2, c1), f10(f6(c2, c1)))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1)))) <=> ((~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (f10(f6(c2, c1)) = f6(c2, c1)) | (~big_f(f6(c2, c1), f10(f6(c2, c1)))) | (f6(c2, c1) = f8(f6(c2, c1))))),
% 29.55/19.79 inference(rewrite,[status(thm)],[])).
% 29.55/19.79 tff(26887,plain,
% 29.55/19.79 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f6(c2, c1)) = f6(c2, c1)) | (f6(c2, c1) = f8(f6(c2, c1))) | (~big_f(f6(c2, c1), f10(f6(c2, c1)))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (f10(f6(c2, c1)) = f6(c2, c1)) | (~big_f(f6(c2, c1), f10(f6(c2, c1)))) | (f6(c2, c1) = f8(f6(c2, c1)))))),
% 29.55/19.79 inference(monotonicity,[status(thm)],[26886])).
% 29.55/19.79 tff(26888,plain,
% 29.55/19.79 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f6(c2, c1)) = f6(c2, c1)) | (f6(c2, c1) = f8(f6(c2, c1))) | (~big_f(f6(c2, c1), f10(f6(c2, c1)))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (f10(f6(c2, c1)) = f6(c2, c1)) | (~big_f(f6(c2, c1), f10(f6(c2, c1)))) | (f6(c2, c1) = f8(f6(c2, c1))))),
% 29.55/19.79 inference(transitivity,[status(thm)],[26887, 26885])).
% 29.55/19.79 tff(26889,plain,
% 29.55/19.79 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f6(c2, c1)) = f6(c2, c1)) | (f6(c2, c1) = f8(f6(c2, c1))) | (~big_f(f6(c2, c1), f10(f6(c2, c1)))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))),
% 29.55/19.79 inference(quant_inst,[status(thm)],[])).
% 29.55/19.79 tff(26890,plain,
% 29.55/19.79 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (f10(f6(c2, c1)) = f6(c2, c1)) | (~big_f(f6(c2, c1), f10(f6(c2, c1)))) | (f6(c2, c1) = f8(f6(c2, c1)))),
% 29.55/19.79 inference(modus_ponens,[status(thm)],[26889, 26888])).
% 29.55/19.79 tff(26891,plain,
% 29.55/19.79 (~(f6(c1, c1) = c1)),
% 29.55/19.79 inference(unit_resolution,[status(thm)],[26890, 2730, 4234, 5964, 26870, 26869, 26871])).
% 29.55/19.79 tff(26892,plain,
% 29.55/19.79 (~(f6(c1, c1) = f5(f6(c2, c1)))),
% 29.55/19.79 inference(modus_ponens,[status(thm)],[26891, 26884])).
% 29.55/19.79 tff(26893,plain,
% 29.55/19.79 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(f6(c2, c1)) = f6(c2, c1)) | (f10(f6(c2, c1)) = f6(c2, c1)) | (~big_f(f6(c2, c1), f10(f6(c2, c1)))) | (f6(c2, c1) = f8(f6(c2, c1))) | (~big_f(f7(f6(c2, c1)), f6(c1, c1))) | (f6(c1, c1) = f5(f6(c2, c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(f6(c2, c1)) = f6(c2, c1)) | (f10(f6(c2, c1)) = f6(c2, c1)) | (~big_f(f6(c2, c1), f10(f6(c2, c1)))) | (f6(c2, c1) = f8(f6(c2, c1))) | (~big_f(f7(f6(c2, c1)), f6(c1, c1))) | (f6(c1, c1) = f5(f6(c2, c1))))),
% 29.55/19.79 inference(rewrite,[status(thm)],[])).
% 29.55/19.79 tff(26894,plain,
% 29.55/19.79 (((f10(f6(c2, c1)) = f6(c2, c1)) | (f6(c2, c1) = f8(f6(c2, c1))) | (~big_f(f6(c2, c1), f10(f6(c2, c1)))) | (f7(f6(c2, c1)) = f6(c2, c1)) | (f6(c1, c1) = f5(f6(c2, c1))) | (~big_f(f7(f6(c2, c1)), f6(c1, c1)))) <=> ((f7(f6(c2, c1)) = f6(c2, c1)) | (f10(f6(c2, c1)) = f6(c2, c1)) | (~big_f(f6(c2, c1), f10(f6(c2, c1)))) | (f6(c2, c1) = f8(f6(c2, c1))) | (~big_f(f7(f6(c2, c1)), f6(c1, c1))) | (f6(c1, c1) = f5(f6(c2, c1))))),
% 29.55/19.79 inference(rewrite,[status(thm)],[])).
% 29.55/19.79 tff(26895,plain,
% 29.55/19.79 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f6(c2, c1)) = f6(c2, c1)) | (f6(c2, c1) = f8(f6(c2, c1))) | (~big_f(f6(c2, c1), f10(f6(c2, c1)))) | (f7(f6(c2, c1)) = f6(c2, c1)) | (f6(c1, c1) = f5(f6(c2, c1))) | (~big_f(f7(f6(c2, c1)), f6(c1, c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(f6(c2, c1)) = f6(c2, c1)) | (f10(f6(c2, c1)) = f6(c2, c1)) | (~big_f(f6(c2, c1), f10(f6(c2, c1)))) | (f6(c2, c1) = f8(f6(c2, c1))) | (~big_f(f7(f6(c2, c1)), f6(c1, c1))) | (f6(c1, c1) = f5(f6(c2, c1)))))),
% 29.55/19.79 inference(monotonicity,[status(thm)],[26894])).
% 29.55/19.79 tff(26896,plain,
% 29.55/19.79 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f6(c2, c1)) = f6(c2, c1)) | (f6(c2, c1) = f8(f6(c2, c1))) | (~big_f(f6(c2, c1), f10(f6(c2, c1)))) | (f7(f6(c2, c1)) = f6(c2, c1)) | (f6(c1, c1) = f5(f6(c2, c1))) | (~big_f(f7(f6(c2, c1)), f6(c1, c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(f6(c2, c1)) = f6(c2, c1)) | (f10(f6(c2, c1)) = f6(c2, c1)) | (~big_f(f6(c2, c1), f10(f6(c2, c1)))) | (f6(c2, c1) = f8(f6(c2, c1))) | (~big_f(f7(f6(c2, c1)), f6(c1, c1))) | (f6(c1, c1) = f5(f6(c2, c1))))),
% 29.55/19.79 inference(transitivity,[status(thm)],[26895, 26893])).
% 29.55/19.79 tff(26897,plain,
% 29.55/19.79 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f6(c2, c1)) = f6(c2, c1)) | (f6(c2, c1) = f8(f6(c2, c1))) | (~big_f(f6(c2, c1), f10(f6(c2, c1)))) | (f7(f6(c2, c1)) = f6(c2, c1)) | (f6(c1, c1) = f5(f6(c2, c1))) | (~big_f(f7(f6(c2, c1)), f6(c1, c1))))),
% 29.55/19.79 inference(quant_inst,[status(thm)],[])).
% 29.55/19.79 tff(26898,plain,
% 29.55/19.79 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(f6(c2, c1)) = f6(c2, c1)) | (f10(f6(c2, c1)) = f6(c2, c1)) | (~big_f(f6(c2, c1), f10(f6(c2, c1)))) | (f6(c2, c1) = f8(f6(c2, c1))) | (~big_f(f7(f6(c2, c1)), f6(c1, c1))) | (f6(c1, c1) = f5(f6(c2, c1)))),
% 29.55/19.79 inference(modus_ponens,[status(thm)],[26897, 26896])).
% 29.55/19.79 tff(26899,plain,
% 29.55/19.79 ((~big_f(f7(f6(c2, c1)), f6(c1, c1))) | (f6(c1, c1) = f5(f6(c2, c1)))),
% 29.55/19.79 inference(unit_resolution,[status(thm)],[26898, 1659, 26872, 26870, 26869, 26871])).
% 29.55/19.79 tff(26900,plain,
% 29.55/19.79 ($false),
% 29.55/19.79 inference(unit_resolution,[status(thm)],[26899, 26892, 26867])).
% 29.55/19.79 tff(26901,plain,((f6(c2, c1) = f8(f6(c2, c1))) | (f7(f6(c2, c1)) = f6(c2, c1)) | (f10(f6(c2, c1)) = f6(c2, c1)) | (~big_f(f6(c2, c1), f10(f6(c2, c1)))) | (~big_f(f7(c1), f6(c1, c1))) | (~(f7(c1) = c1)) | (~(f7(c2) = c1)) | (~(f6(c2, f7(f4(c4))) = c2)) | (~(f4(c4) = c1)) | (~big_f(f7(f6(c2, c1)), c1))), inference(lemma,lemma(discharge,[]))).
% 29.55/19.79 tff(26902,plain,
% 29.55/19.79 (f6(c2, c1) = f8(f6(c2, c1))),
% 29.55/19.79 inference(unit_resolution,[status(thm)],[26901, 26860, 26848, 26855, 26827, 4234, 22, 26817, 26815, 26843])).
% 29.55/19.79 tff(26903,plain,
% 29.55/19.79 (f8(f6(c2, c1)) = f6(c2, c1)),
% 29.55/19.79 inference(symmetry,[status(thm)],[26902])).
% 29.55/19.79 tff(26904,plain,
% 29.55/19.79 (f8(c2) = f6(c2, c1)),
% 29.55/19.79 inference(transitivity,[status(thm)],[26849, 26903])).
% 29.55/19.79 tff(26905,plain,
% 29.55/19.79 ((c1 = f8(c2)) <=> (c1 = f6(c2, c1))),
% 29.55/19.79 inference(monotonicity,[status(thm)],[26904])).
% 29.55/19.79 tff(26906,plain,
% 29.55/19.79 ((c1 = f8(c2)) <=> (f6(c2, c1) = c1)),
% 29.55/19.79 inference(transitivity,[status(thm)],[26905, 14624])).
% 29.55/19.79 tff(26907,plain,
% 29.55/19.79 ((f6(c2, c1) = c1) <=> (c1 = f8(c2))),
% 29.55/19.79 inference(symmetry,[status(thm)],[26906])).
% 29.55/19.79 tff(26908,plain,
% 29.55/19.79 ((f6(c2, c1) = c1) <=> (c1 = f8(f6(c2, c1)))),
% 29.55/19.79 inference(transitivity,[status(thm)],[26907, 26852])).
% 29.55/19.79 tff(26909,plain,
% 29.55/19.79 ((~(f6(c2, c1) = c1)) <=> (~(c1 = f8(f6(c2, c1))))),
% 29.55/19.79 inference(monotonicity,[status(thm)],[26908])).
% 29.55/19.79 tff(26910,plain,
% 29.55/19.79 (~(c1 = f8(f6(c2, c1)))),
% 29.55/19.79 inference(modus_ponens,[status(thm)],[3198, 26909])).
% 29.55/19.79 tff(26911,plain,
% 29.55/19.79 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(f6(c2, c1)) = f6(c2, c1)) | (c1 = f8(f6(c2, c1))) | (c1 = f5(f6(c2, c1))) | (f10(f6(c2, c1)) = f6(c2, c1)) | (~big_f(f7(f6(c2, c1)), c1)) | (~big_f(c1, f10(f6(c2, c1)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(f6(c2, c1)) = f6(c2, c1)) | (c1 = f8(f6(c2, c1))) | (c1 = f5(f6(c2, c1))) | (f10(f6(c2, c1)) = f6(c2, c1)) | (~big_f(f7(f6(c2, c1)), c1)) | (~big_f(c1, f10(f6(c2, c1)))))),
% 29.55/19.79 inference(rewrite,[status(thm)],[])).
% 29.55/19.79 tff(26912,plain,
% 29.55/19.79 (((f10(f6(c2, c1)) = f6(c2, c1)) | (c1 = f8(f6(c2, c1))) | (~big_f(c1, f10(f6(c2, c1)))) | (f7(f6(c2, c1)) = f6(c2, c1)) | (c1 = f5(f6(c2, c1))) | (~big_f(f7(f6(c2, c1)), c1))) <=> ((f7(f6(c2, c1)) = f6(c2, c1)) | (c1 = f8(f6(c2, c1))) | (c1 = f5(f6(c2, c1))) | (f10(f6(c2, c1)) = f6(c2, c1)) | (~big_f(f7(f6(c2, c1)), c1)) | (~big_f(c1, f10(f6(c2, c1)))))),
% 29.55/19.79 inference(rewrite,[status(thm)],[])).
% 29.55/19.79 tff(26913,plain,
% 29.55/19.79 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f6(c2, c1)) = f6(c2, c1)) | (c1 = f8(f6(c2, c1))) | (~big_f(c1, f10(f6(c2, c1)))) | (f7(f6(c2, c1)) = f6(c2, c1)) | (c1 = f5(f6(c2, c1))) | (~big_f(f7(f6(c2, c1)), c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(f6(c2, c1)) = f6(c2, c1)) | (c1 = f8(f6(c2, c1))) | (c1 = f5(f6(c2, c1))) | (f10(f6(c2, c1)) = f6(c2, c1)) | (~big_f(f7(f6(c2, c1)), c1)) | (~big_f(c1, f10(f6(c2, c1))))))),
% 29.55/19.79 inference(monotonicity,[status(thm)],[26912])).
% 29.55/19.79 tff(26914,plain,
% 29.55/19.79 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f6(c2, c1)) = f6(c2, c1)) | (c1 = f8(f6(c2, c1))) | (~big_f(c1, f10(f6(c2, c1)))) | (f7(f6(c2, c1)) = f6(c2, c1)) | (c1 = f5(f6(c2, c1))) | (~big_f(f7(f6(c2, c1)), c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(f6(c2, c1)) = f6(c2, c1)) | (c1 = f8(f6(c2, c1))) | (c1 = f5(f6(c2, c1))) | (f10(f6(c2, c1)) = f6(c2, c1)) | (~big_f(f7(f6(c2, c1)), c1)) | (~big_f(c1, f10(f6(c2, c1)))))),
% 29.55/19.80 inference(transitivity,[status(thm)],[26913, 26911])).
% 29.55/19.80 tff(26915,plain,
% 29.55/19.80 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f6(c2, c1)) = f6(c2, c1)) | (c1 = f8(f6(c2, c1))) | (~big_f(c1, f10(f6(c2, c1)))) | (f7(f6(c2, c1)) = f6(c2, c1)) | (c1 = f5(f6(c2, c1))) | (~big_f(f7(f6(c2, c1)), c1)))),
% 29.55/19.80 inference(quant_inst,[status(thm)],[])).
% 29.55/19.80 tff(26916,plain,
% 29.55/19.80 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(f6(c2, c1)) = f6(c2, c1)) | (c1 = f8(f6(c2, c1))) | (c1 = f5(f6(c2, c1))) | (f10(f6(c2, c1)) = f6(c2, c1)) | (~big_f(f7(f6(c2, c1)), c1)) | (~big_f(c1, f10(f6(c2, c1))))),
% 29.55/19.80 inference(modus_ponens,[status(thm)],[26915, 26914])).
% 29.55/19.80 tff(26917,plain,
% 29.55/19.80 ((c1 = f8(f6(c2, c1))) | (c1 = f5(f6(c2, c1))) | (f10(f6(c2, c1)) = f6(c2, c1)) | (~big_f(f7(f6(c2, c1)), c1)) | (~big_f(c1, f10(f6(c2, c1))))),
% 29.55/19.80 inference(unit_resolution,[status(thm)],[26916, 1659, 26860])).
% 29.55/19.80 tff(26918,plain,
% 29.55/19.80 (c1 = f5(f6(c2, c1))),
% 29.55/19.80 inference(unit_resolution,[status(thm)],[26917, 26910, 26848, 26843, 26839])).
% 29.55/19.80 tff(26919,plain,
% 29.55/19.80 (f5(f6(c2, c1)) = c1),
% 29.55/19.80 inference(symmetry,[status(thm)],[26918])).
% 29.55/19.80 tff(26920,plain,
% 29.55/19.80 (f5(c2) = c1),
% 29.55/19.80 inference(transitivity,[status(thm)],[26831, 26919])).
% 29.55/19.80 tff(26921,plain,
% 29.55/19.80 ((f6(c1, c1) = f5(c2)) <=> (f6(c1, c1) = c1)),
% 29.55/19.80 inference(monotonicity,[status(thm)],[26920])).
% 29.55/19.80 tff(26922,plain,
% 29.55/19.80 ((f6(c1, c1) = c1) <=> (f6(c1, c1) = f5(c2))),
% 29.55/19.80 inference(symmetry,[status(thm)],[26921])).
% 29.55/19.80 tff(26923,plain,
% 29.55/19.80 ((f6(c1, c1) = c1) <=> (f6(c1, c1) = f5(f6(c2, c1)))),
% 29.55/19.80 inference(transitivity,[status(thm)],[26922, 26834])).
% 29.55/19.80 tff(26924,plain,
% 29.55/19.80 ((~(f6(c1, c1) = c1)) <=> (~(f6(c1, c1) = f5(f6(c2, c1))))),
% 29.55/19.80 inference(monotonicity,[status(thm)],[26923])).
% 29.55/19.80 tff(26925,plain,
% 29.55/19.80 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (c1 = f8(f6(c2, c1))) | (f10(f6(c2, c1)) = f6(c2, c1)) | (~big_f(c1, f10(f6(c2, c1)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (c1 = f8(f6(c2, c1))) | (f10(f6(c2, c1)) = f6(c2, c1)) | (~big_f(c1, f10(f6(c2, c1)))))),
% 29.55/19.80 inference(rewrite,[status(thm)],[])).
% 29.55/19.80 tff(26926,plain,
% 29.55/19.80 (((f10(f6(c2, c1)) = f6(c2, c1)) | (c1 = f8(f6(c2, c1))) | (~big_f(c1, f10(f6(c2, c1)))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1)))) <=> ((~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (c1 = f8(f6(c2, c1))) | (f10(f6(c2, c1)) = f6(c2, c1)) | (~big_f(c1, f10(f6(c2, c1)))))),
% 29.55/19.80 inference(rewrite,[status(thm)],[])).
% 29.55/19.80 tff(26927,plain,
% 29.55/19.80 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f6(c2, c1)) = f6(c2, c1)) | (c1 = f8(f6(c2, c1))) | (~big_f(c1, f10(f6(c2, c1)))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (c1 = f8(f6(c2, c1))) | (f10(f6(c2, c1)) = f6(c2, c1)) | (~big_f(c1, f10(f6(c2, c1))))))),
% 29.61/19.80 inference(monotonicity,[status(thm)],[26926])).
% 29.61/19.80 tff(26928,plain,
% 29.61/19.80 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f6(c2, c1)) = f6(c2, c1)) | (c1 = f8(f6(c2, c1))) | (~big_f(c1, f10(f6(c2, c1)))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (c1 = f8(f6(c2, c1))) | (f10(f6(c2, c1)) = f6(c2, c1)) | (~big_f(c1, f10(f6(c2, c1)))))),
% 29.61/19.80 inference(transitivity,[status(thm)],[26927, 26925])).
% 29.61/19.80 tff(26929,plain,
% 29.61/19.80 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f6(c2, c1)) = f6(c2, c1)) | (c1 = f8(f6(c2, c1))) | (~big_f(c1, f10(f6(c2, c1)))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))),
% 29.61/19.80 inference(quant_inst,[status(thm)],[])).
% 29.61/19.80 tff(26930,plain,
% 29.61/19.80 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (c1 = f8(f6(c2, c1))) | (f10(f6(c2, c1)) = f6(c2, c1)) | (~big_f(c1, f10(f6(c2, c1))))),
% 29.61/19.80 inference(modus_ponens,[status(thm)],[26929, 26928])).
% 29.61/19.80 tff(26931,plain,
% 29.61/19.80 (~(f6(c1, c1) = c1)),
% 29.61/19.80 inference(unit_resolution,[status(thm)],[26930, 2730, 4234, 26827, 26848, 26910, 26839])).
% 29.61/19.80 tff(26932,plain,
% 29.61/19.80 (~(f6(c1, c1) = f5(f6(c2, c1)))),
% 29.61/19.80 inference(modus_ponens,[status(thm)],[26931, 26924])).
% 29.61/19.80 tff(26933,plain,
% 29.61/19.80 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(f6(c2, c1)) = f6(c2, c1)) | (c1 = f8(f6(c2, c1))) | (f10(f6(c2, c1)) = f6(c2, c1)) | (~big_f(c1, f10(f6(c2, c1)))) | (~big_f(f7(f6(c2, c1)), f6(c1, c1))) | (f6(c1, c1) = f5(f6(c2, c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(f6(c2, c1)) = f6(c2, c1)) | (c1 = f8(f6(c2, c1))) | (f10(f6(c2, c1)) = f6(c2, c1)) | (~big_f(c1, f10(f6(c2, c1)))) | (~big_f(f7(f6(c2, c1)), f6(c1, c1))) | (f6(c1, c1) = f5(f6(c2, c1))))),
% 29.61/19.80 inference(rewrite,[status(thm)],[])).
% 29.61/19.80 tff(26934,plain,
% 29.61/19.80 (((f10(f6(c2, c1)) = f6(c2, c1)) | (c1 = f8(f6(c2, c1))) | (~big_f(c1, f10(f6(c2, c1)))) | (f7(f6(c2, c1)) = f6(c2, c1)) | (f6(c1, c1) = f5(f6(c2, c1))) | (~big_f(f7(f6(c2, c1)), f6(c1, c1)))) <=> ((f7(f6(c2, c1)) = f6(c2, c1)) | (c1 = f8(f6(c2, c1))) | (f10(f6(c2, c1)) = f6(c2, c1)) | (~big_f(c1, f10(f6(c2, c1)))) | (~big_f(f7(f6(c2, c1)), f6(c1, c1))) | (f6(c1, c1) = f5(f6(c2, c1))))),
% 29.61/19.80 inference(rewrite,[status(thm)],[])).
% 29.61/19.80 tff(26935,plain,
% 29.61/19.80 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f6(c2, c1)) = f6(c2, c1)) | (c1 = f8(f6(c2, c1))) | (~big_f(c1, f10(f6(c2, c1)))) | (f7(f6(c2, c1)) = f6(c2, c1)) | (f6(c1, c1) = f5(f6(c2, c1))) | (~big_f(f7(f6(c2, c1)), f6(c1, c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(f6(c2, c1)) = f6(c2, c1)) | (c1 = f8(f6(c2, c1))) | (f10(f6(c2, c1)) = f6(c2, c1)) | (~big_f(c1, f10(f6(c2, c1)))) | (~big_f(f7(f6(c2, c1)), f6(c1, c1))) | (f6(c1, c1) = f5(f6(c2, c1)))))),
% 29.61/19.80 inference(monotonicity,[status(thm)],[26934])).
% 29.61/19.80 tff(26936,plain,
% 29.61/19.80 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f6(c2, c1)) = f6(c2, c1)) | (c1 = f8(f6(c2, c1))) | (~big_f(c1, f10(f6(c2, c1)))) | (f7(f6(c2, c1)) = f6(c2, c1)) | (f6(c1, c1) = f5(f6(c2, c1))) | (~big_f(f7(f6(c2, c1)), f6(c1, c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(f6(c2, c1)) = f6(c2, c1)) | (c1 = f8(f6(c2, c1))) | (f10(f6(c2, c1)) = f6(c2, c1)) | (~big_f(c1, f10(f6(c2, c1)))) | (~big_f(f7(f6(c2, c1)), f6(c1, c1))) | (f6(c1, c1) = f5(f6(c2, c1))))),
% 29.61/19.80 inference(transitivity,[status(thm)],[26935, 26933])).
% 29.61/19.80 tff(26937,plain,
% 29.61/19.80 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f6(c2, c1)) = f6(c2, c1)) | (c1 = f8(f6(c2, c1))) | (~big_f(c1, f10(f6(c2, c1)))) | (f7(f6(c2, c1)) = f6(c2, c1)) | (f6(c1, c1) = f5(f6(c2, c1))) | (~big_f(f7(f6(c2, c1)), f6(c1, c1))))),
% 29.61/19.80 inference(quant_inst,[status(thm)],[])).
% 29.61/19.80 tff(26938,plain,
% 29.61/19.80 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(f6(c2, c1)) = f6(c2, c1)) | (c1 = f8(f6(c2, c1))) | (f10(f6(c2, c1)) = f6(c2, c1)) | (~big_f(c1, f10(f6(c2, c1)))) | (~big_f(f7(f6(c2, c1)), f6(c1, c1))) | (f6(c1, c1) = f5(f6(c2, c1)))),
% 29.61/19.80 inference(modus_ponens,[status(thm)],[26937, 26936])).
% 29.61/19.80 tff(26939,plain,
% 29.61/19.80 ((~big_f(f7(f6(c2, c1)), f6(c1, c1))) | (f6(c1, c1) = f5(f6(c2, c1)))),
% 29.61/19.80 inference(unit_resolution,[status(thm)],[26938, 1659, 26860, 26848, 26910, 26839])).
% 29.61/19.80 tff(26940,plain,
% 29.61/19.80 ($false),
% 29.61/19.80 inference(unit_resolution,[status(thm)],[26939, 26932, 26828])).
% 29.61/19.80 tff(26941,plain,((f6(c2, c1) = c1) | (~(f7(c1) = c1)) | (f7(c2) = c2) | big_f(c2, c2) | (~(f10(c1) = c1)) | (~big_f(c2, c1)) | big_f(f7(c2), c2) | (f10(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 29.61/19.80 tff(26942,plain,
% 29.61/19.80 (f6(c2, c1) = c1),
% 29.61/19.80 inference(unit_resolution,[status(thm)],[26941, 17, 4234, 121, 26670, 26614, 23145, 89])).
% 29.61/19.80 tff(26943,plain,
% 29.61/19.80 (f6(c1, c1) = c1),
% 29.61/19.80 inference(unit_resolution,[status(thm)],[26565, 26686, 4234, 27, 26942])).
% 29.61/19.80 tff(26944,plain,
% 29.61/19.80 (~(f9(f10(c2), f4(c4)) = c1)),
% 29.61/19.80 inference(unit_resolution,[status(thm)],[26407, 26943, 4234, 26678, 26675, 22, 26670, 26686, 94])).
% 29.61/19.80 tff(26945,plain,
% 29.61/19.80 (f9(f10(c2), f4(c4)) = c2),
% 29.61/19.80 inference(unit_resolution,[status(thm)],[146, 26944])).
% 29.61/19.80 tff(26946,plain,
% 29.61/19.80 (f9(f10(c2), f4(c4)) = f9(c1, c1)),
% 29.61/19.80 inference(monotonicity,[status(thm)],[94, 26675])).
% 29.61/19.80 tff(26947,plain,
% 29.61/19.80 (f9(c1, c1) = f9(f10(c2), f4(c4))),
% 29.61/19.80 inference(symmetry,[status(thm)],[26946])).
% 29.61/19.80 tff(26948,plain,
% 29.61/19.80 (f9(c1, c1) = c2),
% 29.61/19.80 inference(transitivity,[status(thm)],[26947, 26945])).
% 29.61/19.80 tff(26949,plain,
% 29.61/19.80 (f7(f9(c1, c1)) = f7(c2)),
% 29.61/19.80 inference(monotonicity,[status(thm)],[26948])).
% 29.61/19.80 tff(26950,plain,
% 29.61/19.80 (f7(f9(c1, c1)) = c1),
% 29.61/19.80 inference(transitivity,[status(thm)],[26949, 22])).
% 29.61/19.80 tff(26951,plain,
% 29.61/19.80 ((f7(f9(c1, c1)) = f9(c1, c1)) <=> (c1 = f9(c1, c1))),
% 29.61/19.80 inference(monotonicity,[status(thm)],[26950])).
% 29.61/19.80 tff(26952,plain,
% 29.61/19.80 ((f7(f9(c1, c1)) = f9(c1, c1)) <=> (f9(c1, c1) = c1)),
% 29.61/19.80 inference(transitivity,[status(thm)],[26951, 17725])).
% 29.61/19.80 tff(26953,plain,
% 29.61/19.80 ((f9(c1, c1) = c1) <=> (f7(f9(c1, c1)) = f9(c1, c1))),
% 29.61/19.80 inference(symmetry,[status(thm)],[26952])).
% 29.61/19.80 tff(26954,plain,
% 29.61/19.80 ((~(f9(c1, c1) = c1)) <=> (~(f7(f9(c1, c1)) = f9(c1, c1)))),
% 29.61/19.80 inference(monotonicity,[status(thm)],[26953])).
% 29.61/19.80 tff(26955,plain,
% 29.61/19.80 ((f9(c1, c1) = c1) <=> (c2 = c1)),
% 29.61/19.80 inference(monotonicity,[status(thm)],[26948])).
% 29.61/19.80 tff(26956,plain,
% 29.61/19.80 ((c2 = c1) <=> (f9(c1, c1) = c1)),
% 29.61/19.80 inference(symmetry,[status(thm)],[26955])).
% 29.61/19.80 tff(26957,plain,
% 29.61/19.80 ((~(c2 = c1)) <=> (~(f9(c1, c1) = c1))),
% 29.61/19.80 inference(monotonicity,[status(thm)],[26956])).
% 29.61/19.80 tff(26958,plain,
% 29.61/19.80 (~(f9(c1, c1) = c1)),
% 29.61/19.80 inference(modus_ponens,[status(thm)],[75, 26957])).
% 29.61/19.80 tff(26959,plain,
% 29.61/19.80 (~(f7(f9(c1, c1)) = f9(c1, c1))),
% 29.61/19.80 inference(modus_ponens,[status(thm)],[26958, 26954])).
% 29.61/19.80 tff(26960,plain,
% 29.61/19.80 (big_f(f9(c1, c1), c1)),
% 29.61/19.80 inference(modus_ponens,[status(thm)],[348, 10054])).
% 29.61/19.80 tff(26961,plain,
% 29.61/19.80 ($false),
% 29.61/19.80 inference(unit_resolution,[status(thm)],[10020, 26960])).
% 29.61/19.80 tff(26962,plain,((~(f9(c1, c1) = c2)) | big_f(f9(c1, c1), c1) | (~big_f(c2, c1))), inference(lemma,lemma(discharge,[]))).
% 29.61/19.80 tff(26963,plain,
% 29.61/19.80 (~(f9(c1, c1) = c2)),
% 29.61/19.80 inference(unit_resolution,[status(thm)],[26962, 10020, 348])).
% 29.61/19.80 tff(26964,plain,
% 29.61/19.80 (f9(c1, c1) = c1),
% 29.61/19.80 inference(unit_resolution,[status(thm)],[3939, 26963])).
% 29.61/19.80 tff(26965,plain,
% 29.61/19.80 ($false),
% 29.61/19.80 inference(unit_resolution,[status(thm)],[10049, 26964, 10029, 292])).
% 29.61/19.80 tff(26966,plain,(big_f(f9(c1, c1), c1) | (~(f7(c2) = c1)) | (~big_f(f7(c2), c1)) | (~big_f(c2, c1))), inference(lemma,lemma(discharge,[]))).
% 29.61/19.80 tff(26967,plain,
% 29.61/19.80 (big_f(f9(c1, c1), c1)),
% 29.61/19.80 inference(unit_resolution,[status(thm)],[26966, 26678, 26614, 22])).
% 29.61/19.80 tff(26968,plain,
% 29.61/19.80 (~(f5(c1) = c2)),
% 29.61/19.80 inference(unit_resolution,[status(thm)],[20203, 26945, 94, 17, 121, 26675, 26670])).
% 29.61/19.80 tff(26969,plain,
% 29.61/19.80 (f5(c1) = c1),
% 29.61/19.80 inference(unit_resolution,[status(thm)],[1708, 26968])).
% 29.61/19.80 tff(26970,plain,
% 29.61/19.80 (big_f(c1, f10(c1)) <=> big_f(f7(c2), c1)),
% 29.61/19.80 inference(monotonicity,[status(thm)],[125, 3762])).
% 29.61/19.80 tff(26971,plain,
% 29.61/19.80 (f2(c3) = c1),
% 29.61/19.80 inference(unit_resolution,[status(thm)],[19091, 172, 27, 17, 94, 11752])).
% 29.61/19.80 tff(26972,plain,
% 29.61/19.80 (~big_f(c3, f2(c3))),
% 29.61/19.80 inference(unit_resolution,[status(thm)],[8267, 3030, 3762, 172, 1247])).
% 29.61/19.80 tff(26973,plain,
% 29.61/19.80 (big_f(f4(c4), c4)),
% 29.61/19.80 inference(unit_resolution,[status(thm)],[1315, 26972])).
% 29.61/19.80 tff(26974,plain,
% 29.61/19.80 (~(c1 = c4)),
% 29.61/19.80 inference(unit_resolution,[status(thm)],[18234, 26973, 19650, 3030, 11819, 11752])).
% 29.61/19.80 tff(26975,plain,
% 29.61/19.80 (~(c4 = c1)),
% 29.61/19.80 inference(unit_resolution,[status(thm)],[484, 26974])).
% 29.61/19.80 tff(26976,plain,
% 29.61/19.80 (c4 = c2),
% 29.61/19.80 inference(unit_resolution,[status(thm)],[461, 26975])).
% 29.61/19.80 tff(26977,plain,
% 29.61/19.80 (big_f(f4(c4), c4) <=> big_f(c1, c2)),
% 29.61/19.80 inference(monotonicity,[status(thm)],[11752, 26976])).
% 29.61/19.80 tff(26978,plain,
% 29.61/19.80 (big_f(c1, c2) <=> big_f(f4(c4), c4)),
% 29.61/19.80 inference(symmetry,[status(thm)],[26977])).
% 29.61/19.80 tff(26979,plain,
% 29.61/19.80 ((~big_f(c1, c2)) <=> (~big_f(f4(c4), c4))),
% 29.61/19.80 inference(monotonicity,[status(thm)],[26978])).
% 29.61/19.80 tff(26980,plain,
% 29.61/19.80 (~big_f(f4(c4), c4)),
% 29.61/19.80 inference(modus_ponens,[status(thm)],[27, 26979])).
% 29.61/19.80 tff(26981,plain,
% 29.61/19.80 ($false),
% 29.61/19.80 inference(unit_resolution,[status(thm)],[26973, 26980])).
% 29.61/19.80 tff(26982,plain,(big_f(c1, f10(c1)) | big_f(c1, c2) | (~(f4(c4) = c1)) | (~(f10(c2) = c1)) | (~(f10(c1) = c1)) | (~(c3 = c1)) | (~(f2(c3) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.61/19.80 tff(26983,plain,
% 29.61/19.80 (big_f(c1, f10(c1))),
% 29.61/19.80 inference(unit_resolution,[status(thm)],[26982, 172, 11752, 94, 3762, 27, 26971])).
% 29.61/19.80 tff(26984,plain,
% 29.61/19.80 (big_f(f7(c2), c1)),
% 29.61/19.80 inference(modus_ponens,[status(thm)],[26983, 26970])).
% 29.61/19.80 tff(26985,plain,
% 29.61/19.80 (big_f(f7(c1), f6(c1, c1))),
% 29.61/19.80 inference(unit_resolution,[status(thm)],[26383, 26984, 230, 4234, 22, 3762, 94, 11752])).
% 29.61/19.80 tff(26986,plain,
% 29.61/19.80 (big_f(f7(c1), f6(c1, f5(c1)))),
% 29.61/19.80 inference(modus_ponens,[status(thm)],[26985, 26379])).
% 29.61/19.80 tff(26987,plain,
% 29.61/19.80 (c2 = f6(c1, f5(c1))),
% 29.61/19.80 inference(transitivity,[status(thm)],[6728, 18491, 26378])).
% 29.61/19.80 tff(26988,plain,
% 29.61/19.80 (big_f(c1, c2) <=> big_f(f7(c1), f6(c1, f5(c1)))),
% 29.61/19.80 inference(monotonicity,[status(thm)],[5544, 26987])).
% 29.61/19.80 tff(26989,plain,
% 29.61/19.80 (big_f(f7(c1), f6(c1, f5(c1))) <=> big_f(c1, c2)),
% 29.61/19.80 inference(symmetry,[status(thm)],[26988])).
% 29.61/19.80 tff(26990,assumption,(big_f(f7(c1), f6(c1, f5(c1)))), introduced(assumption)).
% 29.61/19.80 tff(26991,plain,
% 29.61/19.80 (big_f(c1, c2)),
% 29.61/19.80 inference(modus_ponens,[status(thm)],[26990, 26989])).
% 29.61/19.80 tff(26992,plain,
% 29.61/19.80 ($false),
% 29.61/19.80 inference(unit_resolution,[status(thm)],[27, 26991])).
% 29.61/19.80 tff(26993,plain,((~(f6(f7(c2), c3) = c2)) | big_f(c1, c2) | (~big_f(f7(c1), f6(c1, f5(c1)))) | (~(c3 = c1)) | (~(f7(c2) = c1)) | (~(f5(c1) = c1)) | (~(f7(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.61/19.80 tff(26994,plain,
% 29.61/19.80 (~(f6(f7(c2), c3) = c2)),
% 29.61/19.80 inference(unit_resolution,[status(thm)],[26993, 26986, 27, 172, 22, 230, 4234])).
% 29.61/19.80 tff(26995,plain,
% 29.61/19.80 (f6(f7(c2), c3) = c1),
% 29.61/19.80 inference(unit_resolution,[status(thm)],[2391, 26994])).
% 29.61/19.80 tff(26996,plain,
% 29.61/19.80 (f6(c1, c1) = c1),
% 29.61/19.80 inference(unit_resolution,[status(thm)],[10018, 26995, 172, 22])).
% 29.61/19.80 tff(26997,plain,
% 29.61/19.80 (big_f(c1, f10(c2)) <=> big_f(f7(c2), c1)),
% 29.61/19.80 inference(monotonicity,[status(thm)],[125, 94])).
% 29.61/19.80 tff(26998,plain,
% 29.61/19.80 (big_f(f7(c2), c1) <=> big_f(c1, f10(c2))),
% 29.61/19.80 inference(symmetry,[status(thm)],[26997])).
% 29.61/19.80 tff(26999,plain,
% 29.61/19.80 (big_f(c1, f10(c2))),
% 29.61/19.80 inference(modus_ponens,[status(thm)],[26984, 26998])).
% 29.61/19.80 tff(27000,plain,
% 29.61/19.80 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (c1 = f8(c2)) | (~(f7(c1) = c1)) | (~big_f(c1, f10(c2))) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (c1 = f8(c2)) | (~(f7(c1) = c1)) | (~big_f(c1, f10(c2))) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)))),
% 29.61/19.80 inference(rewrite,[status(thm)],[])).
% 29.61/19.80 tff(27001,plain,
% 29.61/19.80 (((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1)))) <=> ((f10(c2) = c2) | (c1 = f8(c2)) | (~(f7(c1) = c1)) | (~big_f(c1, f10(c2))) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)))),
% 29.61/19.80 inference(rewrite,[status(thm)],[])).
% 29.61/19.80 tff(27002,plain,
% 29.61/19.80 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (c1 = f8(c2)) | (~(f7(c1) = c1)) | (~big_f(c1, f10(c2))) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1))))),
% 29.61/19.80 inference(monotonicity,[status(thm)],[27001])).
% 29.61/19.80 tff(27003,plain,
% 29.61/19.80 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (c1 = f8(c2)) | (~(f7(c1) = c1)) | (~big_f(c1, f10(c2))) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)))),
% 29.61/19.80 inference(transitivity,[status(thm)],[27002, 27000])).
% 29.61/19.80 tff(27004,plain,
% 29.61/19.80 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))),
% 29.61/19.80 inference(quant_inst,[status(thm)],[])).
% 29.61/19.80 tff(27005,plain,
% 29.61/19.80 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (c1 = f8(c2)) | (~(f7(c1) = c1)) | (~big_f(c1, f10(c2))) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1))),
% 29.61/19.80 inference(modus_ponens,[status(thm)],[27004, 27003])).
% 29.61/19.80 tff(27006,plain,
% 29.61/19.80 ((c1 = f8(c2)) | (~(f6(c1, c1) = c1))),
% 29.61/19.80 inference(unit_resolution,[status(thm)],[27005, 2730, 4234, 89, 26985, 26999])).
% 29.61/19.80 tff(27007,plain,
% 29.61/19.80 (c1 = f8(c2)),
% 29.61/19.80 inference(unit_resolution,[status(thm)],[27006, 26996])).
% 29.61/19.80 tff(27008,plain,
% 29.61/19.80 (f8(c2) = c1),
% 29.61/19.80 inference(symmetry,[status(thm)],[27007])).
% 29.61/19.80 tff(27009,plain,
% 29.61/19.80 (~(f9(f10(c2), f4(c4)) = c1)),
% 29.61/19.80 inference(unit_resolution,[status(thm)],[26407, 26996, 3762, 4234, 26985, 22, 26984, 11752, 94])).
% 29.61/19.80 tff(27010,plain,
% 29.61/19.80 (f9(f10(c2), f4(c4)) = c2),
% 29.61/19.80 inference(unit_resolution,[status(thm)],[146, 27009])).
% 29.61/19.80 tff(27011,plain,
% 29.61/19.80 (f9(f10(c2), f4(c4)) = f9(c1, c1)),
% 29.61/19.80 inference(monotonicity,[status(thm)],[94, 11752])).
% 29.61/19.80 tff(27012,plain,
% 29.61/19.80 (f9(c1, c1) = f9(f10(c2), f4(c4))),
% 29.61/19.80 inference(symmetry,[status(thm)],[27011])).
% 29.61/19.80 tff(27013,plain,
% 29.61/19.80 (f9(f10(c2), f10(c2)) = f9(c1, c1)),
% 29.61/19.80 inference(monotonicity,[status(thm)],[94, 94])).
% 29.61/19.80 tff(27014,plain,
% 29.61/19.80 (f9(f10(c2), f10(c2)) = c2),
% 29.61/19.80 inference(transitivity,[status(thm)],[27013, 27012, 27010])).
% 29.61/19.80 tff(27015,plain,
% 29.61/19.80 (f8(f9(f10(c2), f10(c2))) = f8(c2)),
% 29.61/19.80 inference(monotonicity,[status(thm)],[27014])).
% 29.61/19.80 tff(27016,plain,
% 29.61/19.80 (f9(c1, c1) = f9(f10(c2), f10(c2))),
% 29.61/19.80 inference(symmetry,[status(thm)],[27013])).
% 29.61/19.80 tff(27017,plain,
% 29.61/19.80 (f8(f9(c1, c1)) = f8(f9(f10(c2), f10(c2)))),
% 29.61/19.80 inference(monotonicity,[status(thm)],[27016])).
% 29.61/19.80 tff(27018,plain,
% 29.61/19.80 (f10(f9(c1, c1)) = f10(f9(f10(c2), f10(c2)))),
% 29.61/19.80 inference(monotonicity,[status(thm)],[27016])).
% 29.61/19.80 tff(27019,plain,
% 29.61/19.80 (big_f(f9(c1, c1), f10(f9(c1, c1))) <=> big_f(f9(f10(c2), f10(c2)), f10(f9(f10(c2), f10(c2))))),
% 29.61/19.80 inference(monotonicity,[status(thm)],[27016, 27018])).
% 29.61/19.80 tff(27020,plain,
% 29.61/19.80 (big_f(f9(f10(c2), f10(c2)), f10(f9(f10(c2), f10(c2)))) <=> big_f(f9(c1, c1), f10(f9(c1, c1)))),
% 29.61/19.80 inference(symmetry,[status(thm)],[27019])).
% 29.61/19.80 tff(27021,plain,
% 29.61/19.80 (f10(f9(f10(c2), f10(c2))) = f10(c2)),
% 29.61/19.80 inference(monotonicity,[status(thm)],[27014])).
% 29.61/19.80 tff(27022,plain,
% 29.61/19.80 (f10(f9(f10(c2), f10(c2))) = f10(c1)),
% 29.61/19.80 inference(transitivity,[status(thm)],[27021, 94, 11570])).
% 29.61/19.80 tff(27023,plain,
% 29.61/19.80 (big_f(f9(f10(c2), f10(c2)), f10(f9(f10(c2), f10(c2)))) <=> big_f(f9(c1, c1), f10(c1))),
% 29.61/19.80 inference(monotonicity,[status(thm)],[27013, 27022])).
% 29.61/19.80 tff(27024,plain,
% 29.61/19.80 (big_f(f9(c1, c1), f10(c1)) <=> big_f(f9(f10(c2), f10(c2)), f10(f9(f10(c2), f10(c2))))),
% 29.61/19.80 inference(symmetry,[status(thm)],[27023])).
% 29.61/19.80 tff(27025,plain,
% 29.61/19.80 (big_f(f9(c1, c1), f10(c1)) <=> big_f(f9(c1, c1), f10(f9(c1, c1)))),
% 29.61/19.80 inference(transitivity,[status(thm)],[27024, 27020])).
% 29.61/19.80 tff(27026,plain,
% 29.61/19.80 (f9(c1, c1) = c2),
% 29.61/19.80 inference(transitivity,[status(thm)],[27012, 27010])).
% 29.61/19.80 tff(27027,plain,
% 29.61/19.80 ((f9(c1, c1) = c1) <=> (c2 = c1)),
% 29.61/19.80 inference(monotonicity,[status(thm)],[27026])).
% 29.61/19.80 tff(27028,plain,
% 29.61/19.80 ((c2 = c1) <=> (f9(c1, c1) = c1)),
% 29.61/19.80 inference(symmetry,[status(thm)],[27027])).
% 29.61/19.80 tff(27029,plain,
% 29.61/19.80 ((~(c2 = c1)) <=> (~(f9(c1, c1) = c1))),
% 29.61/19.80 inference(monotonicity,[status(thm)],[27028])).
% 29.61/19.80 tff(27030,plain,
% 29.61/19.80 (~(f9(c1, c1) = c1)),
% 29.61/19.80 inference(modus_ponens,[status(thm)],[75, 27029])).
% 29.61/19.80 tff(27031,plain,
% 29.61/19.80 (big_f(f9(c1, c1), f10(c1))),
% 29.61/19.80 inference(unit_resolution,[status(thm)],[10040, 2534, 4234, 3762, 27030, 26985, 26996])).
% 29.61/19.80 tff(27032,plain,
% 29.61/19.80 (big_f(f9(c1, c1), f10(f9(c1, c1)))),
% 29.61/19.80 inference(modus_ponens,[status(thm)],[27031, 27025])).
% 29.61/19.80 tff(27033,plain,
% 29.61/19.80 ((f10(f9(c1, c1)) = f9(c1, c1)) <=> (f10(f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))),
% 29.61/19.80 inference(monotonicity,[status(thm)],[27018, 27016])).
% 29.61/19.80 tff(27034,plain,
% 29.61/19.80 ((f10(f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2))) <=> (f10(f9(c1, c1)) = f9(c1, c1))),
% 29.61/19.80 inference(symmetry,[status(thm)],[27033])).
% 29.61/19.80 tff(27035,plain,
% 29.61/19.80 (f10(f9(f10(c2), f10(c2))) = c1),
% 29.61/19.80 inference(transitivity,[status(thm)],[27021, 94])).
% 29.61/19.80 tff(27036,plain,
% 29.61/19.80 ((f10(f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2))) <=> (c1 = f9(c1, c1))),
% 29.61/19.80 inference(monotonicity,[status(thm)],[27035, 27013])).
% 29.61/19.80 tff(27037,plain,
% 29.61/19.80 ((f10(f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2))) <=> (f9(c1, c1) = c1)),
% 29.61/19.80 inference(transitivity,[status(thm)],[27036, 17725])).
% 29.61/19.80 tff(27038,plain,
% 29.61/19.80 ((f9(c1, c1) = c1) <=> (f10(f9(f10(c2), f10(c2))) = f9(f10(c2), f10(c2)))),
% 29.61/19.80 inference(symmetry,[status(thm)],[27037])).
% 29.61/19.80 tff(27039,plain,
% 29.61/19.80 ((f9(c1, c1) = c1) <=> (f10(f9(c1, c1)) = f9(c1, c1))),
% 29.61/19.80 inference(transitivity,[status(thm)],[27038, 27034])).
% 29.61/19.80 tff(27040,plain,
% 29.61/19.80 ((~(f9(c1, c1) = c1)) <=> (~(f10(f9(c1, c1)) = f9(c1, c1)))),
% 29.61/19.81 inference(monotonicity,[status(thm)],[27039])).
% 29.61/19.81 tff(27041,plain,
% 29.61/19.81 (~(f10(f9(c1, c1)) = f9(c1, c1))),
% 29.61/19.81 inference(modus_ponens,[status(thm)],[27030, 27040])).
% 29.61/19.81 tff(27042,plain,
% 29.61/19.81 (f9(c1, c1) = f8(f9(c1, c1))),
% 29.61/19.81 inference(unit_resolution,[status(thm)],[19481, 2730, 4234, 26985, 26996, 27041, 27032])).
% 29.61/19.81 tff(27043,plain,
% 29.61/19.81 (f9(c1, c1) = c1),
% 29.61/19.81 inference(transitivity,[status(thm)],[27042, 27017, 27015, 27008])).
% 29.61/19.81 tff(27044,plain,
% 29.61/19.81 ($false),
% 29.61/19.81 inference(unit_resolution,[status(thm)],[27030, 27043])).
% 29.61/19.81 tff(27045,plain,((~(c3 = c1)) | (~(f4(c4) = c1)) | (~(f7(c1) = c1)) | (~(f10(c1) = c1)) | (f10(c2) = c2) | big_f(c1, c2) | (~(f5(c1) = c1)) | (f7(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 29.61/19.81 tff(27046,plain,
% 29.61/19.81 (~(c3 = c1)),
% 29.61/19.81 inference(unit_resolution,[status(thm)],[27045, 26969, 4234, 27, 89, 26675, 26670, 17])).
% 29.61/19.81 tff(27047,plain,
% 29.61/19.81 (c3 = c2),
% 29.61/19.81 inference(unit_resolution,[status(thm)],[180, 27046])).
% 29.61/19.81 tff(27048,plain,
% 29.61/19.81 (f7(f9(c1, c1)) = f9(c1, c1)),
% 29.61/19.81 inference(unit_resolution,[status(thm)],[18147, 27047, 94, 22, 26678, 26675, 26945, 26967])).
% 29.61/19.81 tff(27049,plain,
% 29.61/19.81 ($false),
% 29.61/19.81 inference(unit_resolution,[status(thm)],[27048, 26959])).
% 29.61/19.81 tff(27050,plain,((f7(c2) = c2) | (~(f7(c1) = c1)) | big_f(c1, c2) | (f10(c2) = c2) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 29.61/19.81 tff(27051,plain,
% 29.61/19.81 ((f7(c2) = c2) | big_f(c1, c2) | (f10(c2) = c2) | big_f(c2, c2)),
% 29.61/19.81 inference(unit_resolution,[status(thm)],[27050, 25791])).
% 29.61/19.81 tff(27052,plain,
% 29.61/19.81 (big_f(c2, c2)),
% 29.61/19.81 inference(unit_resolution,[status(thm)],[27051, 27, 89, 17])).
% 29.61/19.81 tff(27053,plain,
% 29.61/19.81 ((c2 = c4) <=> (f10(c1) = c4)),
% 29.61/19.81 inference(monotonicity,[status(thm)],[26244])).
% 29.61/19.81 tff(27054,plain,
% 29.61/19.81 ((f10(c1) = c4) <=> (c2 = c4)),
% 29.61/19.81 inference(symmetry,[status(thm)],[27053])).
% 29.61/19.81 tff(27055,plain,
% 29.61/19.81 (big_f(c2, c1)),
% 29.61/19.81 inference(unit_resolution,[status(thm)],[25063, 26229, 66, 17, 89])).
% 29.61/19.81 tff(27056,plain,
% 29.61/19.81 (c1 = c3),
% 29.61/19.81 inference(unit_resolution,[status(thm)],[175, 26082])).
% 29.61/19.81 tff(27057,plain,
% 29.61/19.81 (~(c1 = f2(c1))),
% 29.61/19.81 inference(unit_resolution,[status(thm)],[26093, 13164, 482, 27056, 66, 348])).
% 29.61/19.81 tff(27058,plain,
% 29.61/19.81 (~(f2(c3) = c1)),
% 29.61/19.81 inference(unit_resolution,[status(thm)],[6771, 27057, 26082])).
% 29.61/19.81 tff(27059,plain,
% 29.61/19.81 (f2(c3) = c2),
% 29.61/19.81 inference(unit_resolution,[status(thm)],[1273, 27058])).
% 29.61/19.81 tff(27060,plain,
% 29.61/19.81 (c2 = f2(c1)),
% 29.61/19.81 inference(unit_resolution,[status(thm)],[12823, 27059, 26082])).
% 29.61/19.81 tff(27061,plain,
% 29.61/19.81 (big_f(c1, c2)),
% 29.61/19.81 inference(unit_resolution,[status(thm)],[26098, 27060, 482, 27056, 13164, 12777])).
% 29.61/19.81 tff(27062,plain,
% 29.61/19.81 (c2 = f2(c1)),
% 29.61/19.81 inference(unit_resolution,[status(thm)],[12823, 1319, 172])).
% 29.61/19.81 tff(27063,plain,
% 29.61/19.81 (f2(c1) = c2),
% 29.61/19.81 inference(symmetry,[status(thm)],[27062])).
% 29.61/19.81 tff(27064,plain,
% 29.61/19.81 (big_f(c1, f2(c1)) <=> big_f(c1, c2)),
% 29.61/19.81 inference(monotonicity,[status(thm)],[27063])).
% 29.61/19.81 tff(27065,plain,
% 29.61/19.81 (big_f(c1, c2) <=> big_f(c1, f2(c1))),
% 29.61/19.81 inference(symmetry,[status(thm)],[27064])).
% 29.61/19.81 tff(27066,plain,
% 29.61/19.81 (big_f(c1, f2(c1))),
% 29.61/19.81 inference(modus_ponens,[status(thm)],[2865, 27065])).
% 29.61/19.81 tff(27067,plain,
% 29.61/19.81 (f2(c1) = f10(c1)),
% 29.61/19.81 inference(transitivity,[status(thm)],[5586, 1319, 293])).
% 29.61/19.81 tff(27068,plain,
% 29.61/19.81 (big_f(c1, f2(c1)) <=> big_f(c1, f10(c1))),
% 29.61/19.81 inference(monotonicity,[status(thm)],[27067])).
% 29.61/19.81 tff(27069,plain,
% 29.61/19.81 (big_f(c1, f10(c1)) <=> big_f(c1, f2(c1))),
% 29.61/19.81 inference(symmetry,[status(thm)],[27068])).
% 29.61/19.81 tff(27070,plain,
% 29.61/19.81 ((~big_f(c1, f10(c1))) <=> (~big_f(c1, f2(c1)))),
% 29.61/19.81 inference(monotonicity,[status(thm)],[27069])).
% 29.61/19.81 tff(27071,plain,
% 29.61/19.81 (~big_f(c1, f2(c1))),
% 29.61/19.81 inference(modus_ponens,[status(thm)],[3030, 27070])).
% 29.61/19.81 tff(27072,plain,
% 29.61/19.81 ($false),
% 29.61/19.81 inference(unit_resolution,[status(thm)],[6546, 27071])).
% 29.61/19.81 tff(27073,plain,((~(f2(c3) = c2)) | (~big_f(c1, f2(c1))) | big_f(c1, f10(c1)) | (~(f10(c1) = c2)) | (~(c3 = c1))), inference(lemma,lemma(discharge,[]))).
% 29.61/19.81 tff(27074,plain,
% 29.61/19.81 (big_f(c1, f10(c1))),
% 29.61/19.81 inference(unit_resolution,[status(thm)],[27073, 15, 172, 6546, 1319])).
% 29.61/19.81 tff(27075,plain,
% 29.61/19.81 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2))),
% 29.61/19.81 inference(rewrite,[status(thm)],[])).
% 29.61/19.81 tff(27076,plain,
% 29.61/19.81 (((f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f7(c1) = c1)) | (f6(c1, c2) = c2) | big_f(f7(c1), f6(c1, c2))) <=> ((f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2))),
% 29.61/19.81 inference(rewrite,[status(thm)],[])).
% 29.61/19.81 tff(27077,plain,
% 29.61/19.81 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f7(c1) = c1)) | (f6(c1, c2) = c2) | big_f(f7(c1), f6(c1, c2)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2)))),
% 29.61/19.81 inference(monotonicity,[status(thm)],[27076])).
% 29.61/19.81 tff(27078,plain,
% 29.61/19.81 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f7(c1) = c1)) | (f6(c1, c2) = c2) | big_f(f7(c1), f6(c1, c2)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2))),
% 29.61/19.81 inference(transitivity,[status(thm)],[27077, 27075])).
% 29.61/19.81 tff(27079,plain,
% 29.61/19.81 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f7(c1) = c1)) | (f6(c1, c2) = c2) | big_f(f7(c1), f6(c1, c2)))),
% 29.61/19.81 inference(quant_inst,[status(thm)],[])).
% 29.61/19.81 tff(27080,plain,
% 29.61/19.81 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2)),
% 29.61/19.81 inference(modus_ponens,[status(thm)],[27079, 27078])).
% 29.61/19.81 tff(27081,plain,
% 29.61/19.81 (c1 = f8(c1)),
% 29.61/19.81 inference(unit_resolution,[status(thm)],[27080, 2662, 25791, 3, 27074, 5714, 114])).
% 29.61/19.81 tff(27082,plain,
% 29.61/19.81 (f8(c1) = c1),
% 29.61/19.81 inference(symmetry,[status(thm)],[27081])).
% 29.61/19.81 tff(27083,plain,
% 29.61/19.81 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (c2 = f8(c1)) | (~(f7(c1) = c1)) | (~big_f(c2, f10(c1))) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c1) = c1) | (c2 = f8(c1)) | (~(f7(c1) = c1)) | (~big_f(c2, f10(c1))) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2))),
% 29.61/19.81 inference(rewrite,[status(thm)],[])).
% 29.61/19.81 tff(27084,plain,
% 29.61/19.81 (((f10(c1) = c1) | (c2 = f8(c1)) | (~big_f(c2, f10(c1))) | (~(f7(c1) = c1)) | (f6(c1, c2) = c2) | big_f(f7(c1), f6(c1, c2))) <=> ((f10(c1) = c1) | (c2 = f8(c1)) | (~(f7(c1) = c1)) | (~big_f(c2, f10(c1))) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2))),
% 29.61/19.81 inference(rewrite,[status(thm)],[])).
% 29.61/19.81 tff(27085,plain,
% 29.61/19.81 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (c2 = f8(c1)) | (~big_f(c2, f10(c1))) | (~(f7(c1) = c1)) | (f6(c1, c2) = c2) | big_f(f7(c1), f6(c1, c2)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (c2 = f8(c1)) | (~(f7(c1) = c1)) | (~big_f(c2, f10(c1))) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2)))),
% 29.61/19.81 inference(monotonicity,[status(thm)],[27084])).
% 29.61/19.81 tff(27086,plain,
% 29.61/19.81 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (c2 = f8(c1)) | (~big_f(c2, f10(c1))) | (~(f7(c1) = c1)) | (f6(c1, c2) = c2) | big_f(f7(c1), f6(c1, c2)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c1) = c1) | (c2 = f8(c1)) | (~(f7(c1) = c1)) | (~big_f(c2, f10(c1))) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2))),
% 29.61/19.81 inference(transitivity,[status(thm)],[27085, 27083])).
% 29.61/19.81 tff(27087,plain,
% 29.61/19.81 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (c2 = f8(c1)) | (~big_f(c2, f10(c1))) | (~(f7(c1) = c1)) | (f6(c1, c2) = c2) | big_f(f7(c1), f6(c1, c2)))),
% 29.61/19.81 inference(quant_inst,[status(thm)],[])).
% 29.61/19.81 tff(27088,plain,
% 29.61/19.81 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c1) = c1) | (c2 = f8(c1)) | (~(f7(c1) = c1)) | (~big_f(c2, f10(c1))) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2)),
% 29.61/19.81 inference(modus_ponens,[status(thm)],[27087, 27086])).
% 29.61/19.81 tff(27089,plain,
% 29.61/19.81 (c2 = f8(c1)),
% 29.61/19.81 inference(unit_resolution,[status(thm)],[27088, 2662, 25791, 3332, 3, 5714, 114])).
% 29.61/19.81 tff(27090,plain,
% 29.61/19.81 (c2 = c1),
% 29.61/19.81 inference(transitivity,[status(thm)],[27089, 27082])).
% 29.61/19.81 tff(27091,plain,
% 29.61/19.81 ($false),
% 29.61/19.81 inference(unit_resolution,[status(thm)],[75, 27090])).
% 29.61/19.81 tff(27092,plain,((f10(c1) = c1) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2) | (~big_f(c2, c2)) | (~(c3 = c1)) | (~big_f(c1, f2(c1))) | (~(f2(c3) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.61/19.81 tff(27093,plain,
% 29.61/19.81 (f10(c1) = c1),
% 29.61/19.81 inference(unit_resolution,[status(thm)],[27092, 25798, 114, 1345, 172, 27066, 1319])).
% 29.61/19.81 tff(27094,plain,
% 29.61/19.81 (big_f(c1, f6(c1, c2)) <=> big_f(f7(c1), f6(c1, c2))),
% 29.61/19.81 inference(symmetry,[status(thm)],[11068])).
% 29.61/19.81 tff(27095,plain,
% 29.61/19.81 (big_f(c1, c1) <=> big_f(f7(c1), f6(c1, c2))),
% 29.61/19.81 inference(transitivity,[status(thm)],[25795, 27094])).
% 29.61/19.81 tff(27096,plain,
% 29.61/19.81 ((~big_f(c1, c1)) <=> (~big_f(f7(c1), f6(c1, c2)))),
% 29.61/19.81 inference(monotonicity,[status(thm)],[27095])).
% 29.61/19.81 tff(27097,plain,
% 29.61/19.81 (~big_f(f7(c1), f6(c1, c2))),
% 29.61/19.81 inference(modus_ponens,[status(thm)],[66, 27096])).
% 29.61/19.81 tff(27098,plain,
% 29.61/19.81 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2))),
% 29.61/19.81 inference(rewrite,[status(thm)],[])).
% 29.61/19.81 tff(27099,plain,
% 29.61/19.81 (((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (~(f7(c1) = c1)) | (f6(c1, c2) = c2) | big_f(f7(c1), f6(c1, c2))) <=> ((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2))),
% 29.61/19.81 inference(rewrite,[status(thm)],[])).
% 29.61/19.81 tff(27100,plain,
% 29.61/19.81 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (~(f7(c1) = c1)) | (f6(c1, c2) = c2) | big_f(f7(c1), f6(c1, c2)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2)))),
% 29.61/19.81 inference(monotonicity,[status(thm)],[27099])).
% 29.61/19.81 tff(27101,plain,
% 29.61/19.81 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (~(f7(c1) = c1)) | (f6(c1, c2) = c2) | big_f(f7(c1), f6(c1, c2)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2))),
% 29.61/19.81 inference(transitivity,[status(thm)],[27100, 27098])).
% 29.61/19.81 tff(27102,plain,
% 29.61/19.81 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (~(f7(c1) = c1)) | (f6(c1, c2) = c2) | big_f(f7(c1), f6(c1, c2)))),
% 29.61/19.81 inference(quant_inst,[status(thm)],[])).
% 29.61/19.81 tff(27103,plain,
% 29.61/19.81 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2)),
% 29.61/19.81 inference(modus_ponens,[status(thm)],[27102, 27101])).
% 29.61/19.81 tff(27104,plain,
% 29.61/19.81 ($false),
% 29.61/19.81 inference(unit_resolution,[status(thm)],[27103, 2492, 4234, 3762, 23889, 4236, 27097, 114])).
% 29.61/19.81 tff(27105,plain,((f6(c1, c2) = c2) | (~(f7(c1) = c1)) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 29.61/19.81 tff(27106,plain,
% 29.61/19.81 (f6(c1, c2) = c2),
% 29.61/19.81 inference(unit_resolution,[status(thm)],[27105, 4236, 3762, 4234, 66])).
% 29.61/19.81 tff(27107,plain,
% 29.61/19.81 (big_f(c1, f6(c1, c2)) <=> big_f(c1, c2)),
% 29.61/19.81 inference(monotonicity,[status(thm)],[27106])).
% 29.61/19.81 tff(27108,plain,
% 29.61/19.81 (big_f(c1, c2) <=> big_f(c1, f6(c1, c2))),
% 29.61/19.81 inference(symmetry,[status(thm)],[27107])).
% 29.61/19.81 tff(27109,plain,
% 29.61/19.81 (big_f(c1, c2) <=> big_f(f7(c1), f6(c1, c2))),
% 29.61/19.81 inference(transitivity,[status(thm)],[27108, 27094])).
% 29.61/19.81 tff(27110,plain,
% 29.61/19.81 (big_f(f7(c1), f6(c1, c2))),
% 29.61/19.81 inference(modus_ponens,[status(thm)],[2865, 27109])).
% 29.61/19.81 tff(27111,plain,
% 29.61/19.81 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)))),
% 29.61/19.81 inference(rewrite,[status(thm)],[])).
% 29.61/19.81 tff(27112,plain,
% 29.61/19.81 (((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (~(f7(c1) = c1)) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2)))) <=> ((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)))),
% 29.61/19.81 inference(rewrite,[status(thm)],[])).
% 29.61/19.81 tff(27113,plain,
% 29.61/19.81 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (~(f7(c1) = c1)) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2))))),
% 29.61/19.81 inference(monotonicity,[status(thm)],[27112])).
% 29.61/19.81 tff(27114,plain,
% 29.61/19.81 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (~(f7(c1) = c1)) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)))),
% 29.61/19.81 inference(transitivity,[status(thm)],[27113, 27111])).
% 29.61/19.81 tff(27115,plain,
% 29.61/19.81 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (~(f7(c1) = c1)) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2))))),
% 29.61/19.81 inference(quant_inst,[status(thm)],[])).
% 29.61/19.81 tff(27116,plain,
% 29.61/19.81 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(f9(c1, c2), f10(c1)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2))),
% 29.61/19.81 inference(modus_ponens,[status(thm)],[27115, 27114])).
% 29.61/19.81 tff(27117,plain,
% 29.61/19.81 ($false),
% 29.61/19.81 inference(unit_resolution,[status(thm)],[27116, 2534, 4234, 3762, 23889, 4236, 27110, 27106])).
% 29.61/19.81 tff(27118,plain,((f9(c1, c2) = c2) | (~(f7(c1) = c1)) | (~(f10(c1) = c1)) | (~big_f(c1, c2)) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 29.61/19.81 tff(27119,plain,
% 29.61/19.81 ((f9(c1, c2) = c2) | (~(f10(c1) = c1)) | (~big_f(c1, c2)) | big_f(c1, c1)),
% 29.61/19.81 inference(unit_resolution,[status(thm)],[27118, 25791])).
% 29.61/19.81 tff(27120,plain,
% 29.61/19.81 (f9(c1, c2) = c2),
% 29.61/19.81 inference(unit_resolution,[status(thm)],[27119, 27093, 2865, 66])).
% 29.61/19.81 tff(27121,plain,
% 29.61/19.81 (f10(c1) = f10(c2)),
% 29.61/19.81 inference(transitivity,[status(thm)],[27093, 99])).
% 29.61/19.81 tff(27122,plain,
% 29.61/19.81 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2))),
% 29.61/19.81 inference(rewrite,[status(thm)],[])).
% 29.61/19.81 tff(27123,plain,
% 29.61/19.81 (((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c1) = c1)) | (f6(c1, c2) = c2) | big_f(f7(c1), f6(c1, c2))) <=> ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2))),
% 29.61/19.81 inference(rewrite,[status(thm)],[])).
% 29.61/19.81 tff(27124,plain,
% 29.61/19.81 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c1) = c1)) | (f6(c1, c2) = c2) | big_f(f7(c1), f6(c1, c2)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2)))),
% 29.61/19.82 inference(monotonicity,[status(thm)],[27123])).
% 29.61/19.82 tff(27125,plain,
% 29.61/19.82 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c1) = c1)) | (f6(c1, c2) = c2) | big_f(f7(c1), f6(c1, c2)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2))),
% 29.61/19.82 inference(transitivity,[status(thm)],[27124, 27122])).
% 29.61/19.82 tff(27126,plain,
% 29.61/19.82 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c1) = c1)) | (f6(c1, c2) = c2) | big_f(f7(c1), f6(c1, c2)))),
% 29.61/19.82 inference(quant_inst,[status(thm)],[])).
% 29.61/19.82 tff(27127,plain,
% 29.61/19.82 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2)),
% 29.61/19.82 inference(modus_ponens,[status(thm)],[27126, 27125])).
% 29.61/19.82 tff(27128,plain,
% 29.61/19.82 (c2 = f8(c2)),
% 29.61/19.82 inference(unit_resolution,[status(thm)],[27127, 2662, 25791, 89, 12291, 25798, 114])).
% 29.61/19.82 tff(27129,plain,
% 29.61/19.82 (f8(c2) = c2),
% 29.61/19.82 inference(symmetry,[status(thm)],[27128])).
% 29.61/19.82 tff(27130,plain,
% 29.61/19.82 (f9(c1, f8(c2)) = f9(c1, c2)),
% 29.61/19.82 inference(monotonicity,[status(thm)],[27129])).
% 29.61/19.82 tff(27131,plain,
% 29.61/19.82 (f9(c1, c2) = f9(c1, f8(c2))),
% 29.61/19.82 inference(symmetry,[status(thm)],[27130])).
% 29.61/19.82 tff(27132,plain,
% 29.61/19.82 (big_f(f9(c1, c2), f10(c1)) <=> big_f(f9(c1, f8(c2)), f10(c2))),
% 29.61/19.82 inference(monotonicity,[status(thm)],[27131, 27121])).
% 29.61/19.82 tff(27133,plain,
% 29.61/19.82 (big_f(f9(c1, f8(c2)), f10(c2)) <=> big_f(f9(c1, c2), f10(c1))),
% 29.61/19.82 inference(symmetry,[status(thm)],[27132])).
% 29.61/19.82 tff(27134,plain,
% 29.61/19.82 ((f6(c1, f8(c2)) = f8(c2)) <=> (f6(c1, f8(c2)) = c2)),
% 29.61/19.82 inference(monotonicity,[status(thm)],[27129])).
% 29.61/19.82 tff(27135,plain,
% 29.61/19.82 ((f6(c1, f8(c2)) = c2) <=> (f6(c1, f8(c2)) = f8(c2))),
% 29.61/19.82 inference(symmetry,[status(thm)],[27134])).
% 29.61/19.82 tff(27136,plain,
% 29.61/19.82 (f6(c1, f8(c2)) = f6(c1, c2)),
% 29.61/19.82 inference(monotonicity,[status(thm)],[27129])).
% 29.61/19.82 tff(27137,plain,
% 29.61/19.82 (f6(c1, f8(c2)) = c1),
% 29.61/19.82 inference(transitivity,[status(thm)],[27136, 4262])).
% 29.61/19.82 tff(27138,plain,
% 29.61/19.82 ((f6(c1, f8(c2)) = c2) <=> (c1 = c2)),
% 29.61/19.82 inference(monotonicity,[status(thm)],[27137])).
% 29.61/19.82 tff(27139,plain,
% 29.61/19.82 ((f6(c1, f8(c2)) = c2) <=> (c2 = c1)),
% 29.61/19.82 inference(transitivity,[status(thm)],[27138, 1])).
% 29.61/19.82 tff(27140,plain,
% 29.61/19.82 ((c2 = c1) <=> (f6(c1, f8(c2)) = c2)),
% 29.61/19.82 inference(symmetry,[status(thm)],[27139])).
% 29.61/19.82 tff(27141,plain,
% 29.61/19.82 ((c2 = c1) <=> (f6(c1, f8(c2)) = f8(c2))),
% 29.61/19.82 inference(transitivity,[status(thm)],[27140, 27135])).
% 29.61/19.82 tff(27142,plain,
% 29.61/19.82 ((~(c2 = c1)) <=> (~(f6(c1, f8(c2)) = f8(c2)))),
% 29.61/19.82 inference(monotonicity,[status(thm)],[27141])).
% 29.61/19.82 tff(27143,plain,
% 29.61/19.82 (~(f6(c1, f8(c2)) = f8(c2))),
% 29.61/19.82 inference(modus_ponens,[status(thm)],[75, 27142])).
% 29.61/19.82 tff(27144,plain,
% 29.61/19.82 (big_f(f7(c1), f6(c1, f8(c2))) <=> big_f(c1, f6(c1, f8(c2)))),
% 29.61/19.82 inference(monotonicity,[status(thm)],[25791])).
% 29.61/19.82 tff(27145,plain,
% 29.61/19.82 (big_f(c1, f6(c1, f8(c2))) <=> big_f(f7(c1), f6(c1, f8(c2)))),
% 29.61/19.82 inference(symmetry,[status(thm)],[27144])).
% 29.61/19.82 tff(27146,plain,
% 29.61/19.82 (big_f(c1, f6(c1, f8(c2))) <=> big_f(c1, c1)),
% 29.61/19.82 inference(monotonicity,[status(thm)],[27137])).
% 29.61/19.82 tff(27147,plain,
% 29.61/19.82 (big_f(c1, c1) <=> big_f(c1, f6(c1, f8(c2)))),
% 29.61/19.82 inference(symmetry,[status(thm)],[27146])).
% 29.61/19.82 tff(27148,plain,
% 29.61/19.82 (big_f(c1, c1) <=> big_f(f7(c1), f6(c1, f8(c2)))),
% 29.61/19.82 inference(transitivity,[status(thm)],[27147, 27145])).
% 29.61/19.82 tff(27149,plain,
% 29.61/19.82 ((~big_f(c1, c1)) <=> (~big_f(f7(c1), f6(c1, f8(c2))))),
% 29.61/19.82 inference(monotonicity,[status(thm)],[27148])).
% 29.61/19.82 tff(27150,plain,
% 29.61/19.82 (~big_f(f7(c1), f6(c1, f8(c2)))),
% 29.61/19.82 inference(modus_ponens,[status(thm)],[66, 27149])).
% 29.61/19.82 tff(27151,plain,
% 29.61/19.82 (big_f(f9(c1, f8(c2)), f10(c2)) | (f10(c2) = c2) | big_f(f7(c1), f6(c1, f8(c2))) | (f6(c1, f8(c2)) = f8(c2)) | (~(f10(c1) = c1))),
% 29.61/19.82 inference(unit_resolution,[status(thm)],[24821, 25791])).
% 29.61/19.82 tff(27152,plain,
% 29.61/19.82 (big_f(f9(c1, f8(c2)), f10(c2))),
% 29.61/19.82 inference(unit_resolution,[status(thm)],[27151, 27093, 89, 27150, 27143])).
% 29.61/19.82 tff(27153,plain,
% 29.61/19.82 (big_f(f9(c1, c2), f10(c1))),
% 29.61/19.82 inference(modus_ponens,[status(thm)],[27152, 27133])).
% 29.61/19.82 tff(27154,plain,
% 29.61/19.82 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c1) = c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2)) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c1) = c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2)) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2))),
% 29.61/19.82 inference(rewrite,[status(thm)],[])).
% 29.61/19.82 tff(27155,plain,
% 29.61/19.82 (((~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (f6(c1, c2) = c2) | big_f(f7(c1), f6(c1, c2)) | (~(f9(c1, c2) = c2)) | (~big_f(f9(c1, c2), f10(c1)))) <=> ((~(f10(c1) = c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2)) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2))),
% 29.61/19.82 inference(rewrite,[status(thm)],[])).
% 29.61/19.82 tff(27156,plain,
% 29.61/19.82 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (f6(c1, c2) = c2) | big_f(f7(c1), f6(c1, c2)) | (~(f9(c1, c2) = c2)) | (~big_f(f9(c1, c2), f10(c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c1) = c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2)) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2)))),
% 29.61/19.82 inference(monotonicity,[status(thm)],[27155])).
% 29.61/19.82 tff(27157,plain,
% 29.61/19.82 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (f6(c1, c2) = c2) | big_f(f7(c1), f6(c1, c2)) | (~(f9(c1, c2) = c2)) | (~big_f(f9(c1, c2), f10(c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c1) = c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2)) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2))),
% 29.61/19.82 inference(transitivity,[status(thm)],[27156, 27154])).
% 29.61/19.82 tff(27158,plain,
% 29.61/19.82 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (f6(c1, c2) = c2) | big_f(f7(c1), f6(c1, c2)) | (~(f9(c1, c2) = c2)) | (~big_f(f9(c1, c2), f10(c1))))),
% 29.61/19.82 inference(quant_inst,[status(thm)],[])).
% 29.61/19.82 tff(27159,plain,
% 29.61/19.82 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c1) = c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2)) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2)),
% 29.61/19.82 inference(modus_ponens,[status(thm)],[27158, 27157])).
% 29.61/19.82 tff(27160,plain,
% 29.61/19.82 ($false),
% 29.61/19.82 inference(unit_resolution,[status(thm)],[27159, 2409, 25791, 27093, 27153, 27120, 25798, 114])).
% 29.61/19.82 tff(27161,plain,((f6(c1, c2) = c2) | (f10(c2) = c2) | (~big_f(c1, c2)) | big_f(c1, c1) | (~big_f(c2, c2)) | (~(c3 = c1)) | (~(f2(c3) = c2)) | (~big_f(c2, f10(c2)))), inference(lemma,lemma(discharge,[]))).
% 29.61/19.82 tff(27162,plain,
% 29.61/19.82 (f6(c1, c2) = c2),
% 29.61/19.82 inference(unit_resolution,[status(thm)],[27161, 27061, 89, 66, 1345, 26082, 27059, 12291])).
% 29.61/19.82 tff(27163,plain,
% 29.61/19.82 (big_f(c1, f6(c1, c2)) <=> big_f(c1, c2)),
% 29.61/19.82 inference(monotonicity,[status(thm)],[27162])).
% 29.61/19.82 tff(27164,plain,
% 29.61/19.82 (big_f(c1, c2) <=> big_f(c1, f6(c1, c2))),
% 29.61/19.82 inference(symmetry,[status(thm)],[27163])).
% 29.61/19.82 tff(27165,plain,
% 29.61/19.82 (big_f(c1, c2) <=> big_f(f7(c1), f6(c1, c2))),
% 29.61/19.82 inference(transitivity,[status(thm)],[27164, 25793])).
% 29.61/19.82 tff(27166,plain,
% 29.61/19.82 (big_f(f7(c1), f6(c1, c2))),
% 29.61/19.82 inference(modus_ponens,[status(thm)],[27061, 27165])).
% 29.61/19.82 tff(27167,plain,
% 29.61/19.82 (c1 = c3),
% 29.61/19.82 inference(symmetry,[status(thm)],[26082])).
% 29.61/19.82 tff(27168,plain,
% 29.61/19.82 (f2(c1) = f2(c3)),
% 29.61/19.82 inference(monotonicity,[status(thm)],[27167])).
% 29.61/19.82 tff(27169,plain,
% 29.61/19.82 (f2(c1) = c2),
% 29.61/19.82 inference(transitivity,[status(thm)],[27168, 27059])).
% 29.61/19.82 tff(27170,plain,
% 29.61/19.82 (big_f(c1, f2(c1)) <=> big_f(c1, c2)),
% 29.61/19.82 inference(monotonicity,[status(thm)],[27169])).
% 29.61/19.82 tff(27171,plain,
% 29.61/19.82 (big_f(c1, c2) <=> big_f(c1, f2(c1))),
% 29.61/19.82 inference(symmetry,[status(thm)],[27170])).
% 29.61/19.82 tff(27172,plain,
% 29.61/19.82 (big_f(c1, f2(c1))),
% 29.61/19.82 inference(modus_ponens,[status(thm)],[27061, 27171])).
% 29.61/19.82 tff(27173,plain,
% 29.61/19.82 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)))),
% 29.61/19.82 inference(rewrite,[status(thm)],[])).
% 29.61/19.82 tff(27174,plain,
% 29.61/19.82 (((f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f7(c1) = c1)) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2)))) <=> ((f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)))),
% 29.61/19.82 inference(rewrite,[status(thm)],[])).
% 29.61/19.82 tff(27175,plain,
% 29.61/19.82 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f7(c1) = c1)) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2))))),
% 29.61/19.82 inference(monotonicity,[status(thm)],[27174])).
% 29.61/19.82 tff(27176,plain,
% 29.61/19.82 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f7(c1) = c1)) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)))),
% 29.61/19.82 inference(transitivity,[status(thm)],[27175, 27173])).
% 29.61/19.82 tff(27177,plain,
% 29.61/19.82 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f7(c1) = c1)) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2))))),
% 29.61/19.82 inference(quant_inst,[status(thm)],[])).
% 29.61/19.82 tff(27178,plain,
% 29.61/19.82 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2))),
% 29.61/19.82 inference(modus_ponens,[status(thm)],[27177, 27176])).
% 29.61/19.82 tff(27179,plain,
% 29.61/19.82 (c1 = f8(c1)),
% 29.61/19.82 inference(unit_resolution,[status(thm)],[27178, 2730, 25791, 3, 27074, 6215, 36])).
% 29.61/19.82 tff(27180,plain,
% 29.61/19.82 (f8(c1) = c1),
% 29.61/19.82 inference(symmetry,[status(thm)],[27179])).
% 29.61/19.82 tff(27181,plain,
% 29.61/19.82 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (c2 = f8(c1)) | (~(f7(c1) = c1)) | (~big_f(c2, f10(c1))) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (c2 = f8(c1)) | (~(f7(c1) = c1)) | (~big_f(c2, f10(c1))) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)))),
% 29.61/19.82 inference(rewrite,[status(thm)],[])).
% 29.61/19.82 tff(27182,plain,
% 29.61/19.82 (((f10(c1) = c1) | (c2 = f8(c1)) | (~big_f(c2, f10(c1))) | (~(f7(c1) = c1)) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2)))) <=> ((f10(c1) = c1) | (c2 = f8(c1)) | (~(f7(c1) = c1)) | (~big_f(c2, f10(c1))) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)))),
% 29.61/19.82 inference(rewrite,[status(thm)],[])).
% 29.61/19.82 tff(27183,plain,
% 29.61/19.82 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (c2 = f8(c1)) | (~big_f(c2, f10(c1))) | (~(f7(c1) = c1)) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (c2 = f8(c1)) | (~(f7(c1) = c1)) | (~big_f(c2, f10(c1))) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2))))),
% 29.61/19.82 inference(monotonicity,[status(thm)],[27182])).
% 29.61/19.82 tff(27184,plain,
% 29.61/19.82 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (c2 = f8(c1)) | (~big_f(c2, f10(c1))) | (~(f7(c1) = c1)) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (c2 = f8(c1)) | (~(f7(c1) = c1)) | (~big_f(c2, f10(c1))) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)))),
% 29.61/19.82 inference(transitivity,[status(thm)],[27183, 27181])).
% 29.61/19.82 tff(27185,plain,
% 29.61/19.82 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (c2 = f8(c1)) | (~big_f(c2, f10(c1))) | (~(f7(c1) = c1)) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2))))),
% 29.61/19.82 inference(quant_inst,[status(thm)],[])).
% 29.61/19.82 tff(27186,plain,
% 29.61/19.82 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (c2 = f8(c1)) | (~(f7(c1) = c1)) | (~big_f(c2, f10(c1))) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2))),
% 29.61/19.82 inference(modus_ponens,[status(thm)],[27185, 27184])).
% 29.61/19.82 tff(27187,plain,
% 29.61/19.82 (c2 = f8(c1)),
% 29.61/19.82 inference(unit_resolution,[status(thm)],[27186, 2730, 25791, 3332, 3, 6215, 36])).
% 29.61/19.82 tff(27188,plain,
% 29.61/19.82 (c2 = c1),
% 29.61/19.82 inference(transitivity,[status(thm)],[27187, 27180])).
% 29.61/19.82 tff(27189,plain,
% 29.61/19.82 ($false),
% 29.61/19.82 inference(unit_resolution,[status(thm)],[75, 27188])).
% 29.61/19.82 tff(27190,plain,((f10(c1) = c1) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)) | (~big_f(c2, c2)) | (~(c3 = c1)) | (~big_f(c1, f2(c1))) | (~(f2(c3) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.61/19.82 tff(27191,plain,
% 29.61/19.82 (f10(c1) = c1),
% 29.61/19.82 inference(unit_resolution,[status(thm)],[27190, 27166, 27162, 1345, 26082, 27172, 27059])).
% 29.61/19.82 tff(27192,plain,
% 29.61/19.82 (f9(c1, c2) = c2),
% 29.61/19.82 inference(unit_resolution,[status(thm)],[27119, 27191, 27061, 66])).
% 29.61/19.82 tff(27193,plain,
% 29.61/19.82 (big_f(f9(c1, c2), f10(c1)) <=> big_f(c2, c1)),
% 29.61/19.82 inference(monotonicity,[status(thm)],[27192, 27191])).
% 29.61/19.82 tff(27194,plain,
% 29.61/19.82 (big_f(c2, c1) <=> big_f(f9(c1, c2), f10(c1))),
% 29.61/19.82 inference(symmetry,[status(thm)],[27193])).
% 29.61/19.82 tff(27195,plain,
% 29.61/19.82 (big_f(f9(c1, c2), f10(c1))),
% 29.61/19.82 inference(modus_ponens,[status(thm)],[348, 27194])).
% 29.61/19.82 tff(27196,plain,
% 29.61/19.82 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c1) = c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)))),
% 29.61/19.82 inference(rewrite,[status(thm)],[])).
% 29.61/19.82 tff(27197,plain,
% 29.61/19.82 (((~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~(f9(c1, c2) = c2)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2)))) <=> ((~(f10(c1) = c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)))),
% 29.61/19.82 inference(rewrite,[status(thm)],[])).
% 29.61/19.82 tff(27198,plain,
% 29.61/19.82 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~(f9(c1, c2) = c2)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2))))),
% 29.61/19.82 inference(monotonicity,[status(thm)],[27197])).
% 29.61/19.82 tff(27199,plain,
% 29.61/19.82 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~(f9(c1, c2) = c2)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c1) = c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)))),
% 29.61/19.82 inference(transitivity,[status(thm)],[27198, 27196])).
% 29.61/19.82 tff(27200,plain,
% 29.61/19.82 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~(f9(c1, c2) = c2)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2))))),
% 29.61/19.82 inference(quant_inst,[status(thm)],[])).
% 29.61/19.82 tff(27201,plain,
% 29.61/19.82 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c1) = c1)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f9(c1, c2) = c2)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2))),
% 29.61/19.82 inference(modus_ponens,[status(thm)],[27200, 27199])).
% 29.61/19.82 tff(27202,plain,
% 29.61/19.82 ($false),
% 29.61/19.82 inference(unit_resolution,[status(thm)],[27201, 2378, 25791, 27191, 27195, 27192, 27166, 27162])).
% 29.61/19.82 tff(27203,plain,(big_f(f3(c1, c2), c1) | (~big_f(c2, c1)) | big_f(c1, c1) | (~big_f(c2, c2)) | (f10(c2) = c2) | (~big_f(c2, f10(c2))) | (c1 = c4) | (f3(c1, c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 29.61/19.82 tff(27204,plain,
% 29.61/19.82 (big_f(f3(c1, c2), c1)),
% 29.61/19.82 inference(unit_resolution,[status(thm)],[27203, 12777, 66, 1345, 89, 12291, 482, 348])).
% 29.61/19.82 tff(27205,plain,
% 29.61/19.82 (~(big_f(c1, c1) <=> big_f(f3(c1, c2), c1))),
% 29.61/19.82 inference(unit_resolution,[status(thm)],[13186, 27204, 66])).
% 29.61/19.82 tff(27206,plain,
% 29.61/19.82 (~(c1 = f3(c1, c2))),
% 29.61/19.82 inference(unit_resolution,[status(thm)],[13192, 27205])).
% 29.61/19.82 tff(27207,plain,
% 29.61/19.82 (~(f1(f5(c2), f5(c1)) = c2)),
% 29.61/19.82 inference(unit_resolution,[status(thm)],[26052, 27206, 12777])).
% 29.61/19.82 tff(27208,plain,
% 29.61/19.82 (f1(f5(c2), f5(c1)) = c1),
% 29.61/19.82 inference(unit_resolution,[status(thm)],[5191, 27207])).
% 29.61/19.82 tff(27209,plain,
% 29.61/19.82 (f3(f1(f5(c2), f5(c1)), c2) = f3(c1, c2)),
% 29.61/19.82 inference(monotonicity,[status(thm)],[27208])).
% 29.61/19.82 tff(27210,plain,
% 29.61/19.82 ((f3(f1(f5(c2), f5(c1)), c2) = c2) <=> (f3(c1, c2) = c2)),
% 29.61/19.82 inference(monotonicity,[status(thm)],[27209])).
% 29.61/19.82 tff(27211,plain,
% 29.61/19.82 ((f3(c1, c2) = c2) <=> (f3(f1(f5(c2), f5(c1)), c2) = c2)),
% 29.61/19.82 inference(symmetry,[status(thm)],[27210])).
% 29.61/19.82 tff(27212,plain,
% 29.61/19.82 ((~(f3(c1, c2) = c2)) <=> (~(f3(f1(f5(c2), f5(c1)), c2) = c2))),
% 29.61/19.82 inference(monotonicity,[status(thm)],[27211])).
% 29.61/19.82 tff(27213,plain,
% 29.61/19.82 (~(f3(f1(f5(c2), f5(c1)), c2) = c2)),
% 29.61/19.82 inference(modus_ponens,[status(thm)],[12777, 27212])).
% 29.61/19.82 tff(27214,plain,
% 29.61/19.82 (f3(c1, c2) = f3(f1(f5(c2), f5(c1)), c2)),
% 29.61/19.82 inference(symmetry,[status(thm)],[27209])).
% 29.61/19.82 tff(27215,plain,
% 29.61/19.82 ((c1 = f3(c1, c2)) <=> (c1 = f3(f1(f5(c2), f5(c1)), c2))),
% 29.61/19.82 inference(monotonicity,[status(thm)],[27214])).
% 29.61/19.82 tff(27216,plain,
% 29.61/19.82 ((c1 = f3(c1, c2)) <=> (f3(f1(f5(c2), f5(c1)), c2) = c1)),
% 29.61/19.82 inference(transitivity,[status(thm)],[27215, 26113])).
% 29.61/19.82 tff(27217,plain,
% 29.61/19.82 ((~(c1 = f3(c1, c2))) <=> (~(f3(f1(f5(c2), f5(c1)), c2) = c1))),
% 29.61/19.82 inference(monotonicity,[status(thm)],[27216])).
% 29.61/19.82 tff(27218,plain,
% 29.61/19.82 (~(f3(f1(f5(c2), f5(c1)), c2) = c1)),
% 29.61/19.82 inference(modus_ponens,[status(thm)],[27206, 27217])).
% 29.61/19.82 tff(27219,plain,
% 29.61/19.82 ($false),
% 29.61/19.82 inference(unit_resolution,[status(thm)],[16061, 27218, 27213])).
% 29.61/19.82 tff(27220,plain,((f3(c1, c2) = c2) | big_f(c1, c1) | (~big_f(c2, c2)) | (f10(c2) = c2) | (~big_f(c2, f10(c2))) | (c1 = c4) | (~big_f(c2, c1))), inference(lemma,lemma(discharge,[]))).
% 29.61/19.82 tff(27221,plain,
% 29.61/19.82 (f3(c1, c2) = c2),
% 29.61/19.82 inference(unit_resolution,[status(thm)],[27220, 482, 1345, 89, 12291, 66, 348])).
% 29.61/19.82 tff(27222,plain,
% 29.61/19.82 (big_f(c1, c2)),
% 29.61/19.82 inference(unit_resolution,[status(thm)],[26089, 27221, 482, 66, 26082, 348])).
% 29.61/19.82 tff(27223,plain,
% 29.61/19.82 (big_f(f3(c1, c2), c1)),
% 29.61/19.82 inference(unit_resolution,[status(thm)],[26072, 27221, 348])).
% 29.61/19.82 tff(27224,plain,
% 29.61/19.82 (~(c1 = f2(c1))),
% 29.61/19.82 inference(unit_resolution,[status(thm)],[12812, 1398, 27056, 482, 27223, 27221, 66])).
% 29.61/19.82 tff(27225,plain,
% 29.61/19.82 (~(f2(c3) = c1)),
% 29.61/19.82 inference(unit_resolution,[status(thm)],[6771, 27224, 26082])).
% 29.61/19.82 tff(27226,plain,
% 29.61/19.82 (f2(c3) = c2),
% 29.61/19.82 inference(unit_resolution,[status(thm)],[1273, 27225])).
% 29.61/19.82 tff(27227,plain,
% 29.61/19.82 (f6(c1, c2) = c2),
% 29.61/19.82 inference(unit_resolution,[status(thm)],[27161, 27226, 89, 66, 1345, 26082, 27222, 12291])).
% 29.61/19.82 tff(27228,plain,
% 29.61/19.82 (big_f(c1, f6(c1, c2)) <=> big_f(c1, c2)),
% 29.61/19.82 inference(monotonicity,[status(thm)],[27227])).
% 29.61/19.82 tff(27229,plain,
% 29.61/19.82 (big_f(c1, c2) <=> big_f(c1, f6(c1, c2))),
% 29.61/19.83 inference(symmetry,[status(thm)],[27228])).
% 29.61/19.83 tff(27230,plain,
% 29.61/19.83 (big_f(c1, c2) <=> big_f(f7(c1), f6(c1, c2))),
% 29.61/19.83 inference(transitivity,[status(thm)],[27229, 25793])).
% 29.61/19.83 tff(27231,plain,
% 29.61/19.83 (big_f(f7(c1), f6(c1, c2))),
% 29.61/19.83 inference(modus_ponens,[status(thm)],[27222, 27230])).
% 29.61/19.83 tff(27232,plain,
% 29.61/19.83 (big_f(c3, c2) <=> big_f(c1, c2)),
% 29.61/19.83 inference(monotonicity,[status(thm)],[26082])).
% 29.61/19.83 tff(27233,plain,
% 29.61/19.83 (big_f(c1, c2) <=> big_f(c3, c2)),
% 29.61/19.83 inference(symmetry,[status(thm)],[27232])).
% 29.61/19.83 tff(27234,plain,
% 29.61/19.83 (big_f(c3, c2)),
% 29.61/19.83 inference(modus_ponens,[status(thm)],[27222, 27233])).
% 29.61/19.83 tff(27235,plain,
% 29.61/19.83 (big_f(c3, f2(c3))),
% 29.61/19.83 inference(unit_resolution,[status(thm)],[1325, 27226, 27234])).
% 29.61/19.83 tff(27236,plain,
% 29.61/19.83 (big_f(c1, f2(c1))),
% 29.61/19.83 inference(unit_resolution,[status(thm)],[8631, 27235, 26082])).
% 29.61/19.83 tff(27237,plain,
% 29.61/19.83 (f10(c1) = c1),
% 29.61/19.83 inference(unit_resolution,[status(thm)],[27190, 27231, 27227, 1345, 26082, 27236, 27226])).
% 29.61/19.83 tff(27238,plain,
% 29.61/19.83 (f9(c1, c2) = c2),
% 29.61/19.83 inference(unit_resolution,[status(thm)],[27119, 27237, 27222, 66])).
% 29.61/19.83 tff(27239,plain,
% 29.61/19.83 (big_f(f9(c1, c2), f10(c1)) <=> big_f(c2, c1)),
% 29.61/19.83 inference(monotonicity,[status(thm)],[27238, 27237])).
% 29.61/19.83 tff(27240,plain,
% 29.61/19.83 (big_f(c2, c1) <=> big_f(f9(c1, c2), f10(c1))),
% 29.61/19.83 inference(symmetry,[status(thm)],[27239])).
% 29.61/19.83 tff(27241,plain,
% 29.61/19.83 (big_f(f9(c1, c2), f10(c1))),
% 29.61/19.83 inference(modus_ponens,[status(thm)],[348, 27240])).
% 29.61/19.83 tff(27242,plain,
% 29.61/19.83 ($false),
% 29.61/19.83 inference(unit_resolution,[status(thm)],[27201, 2378, 25791, 27237, 27241, 27238, 27231, 27227])).
% 29.61/19.83 tff(27243,plain,((c1 = c4) | (~big_f(c2, c1)) | big_f(c1, c1) | (~big_f(c2, c2)) | (f10(c2) = c2) | (~big_f(c2, f10(c2)))), inference(lemma,lemma(discharge,[]))).
% 29.61/19.83 tff(27244,plain,
% 29.61/19.83 (c1 = c4),
% 29.61/19.83 inference(unit_resolution,[status(thm)],[27243, 27055, 66, 89, 27052, 26228])).
% 29.61/19.83 tff(27245,plain,
% 29.61/19.83 (c4 = c1),
% 29.61/19.83 inference(symmetry,[status(thm)],[27244])).
% 29.61/19.83 tff(27246,plain,
% 29.61/19.83 ((f10(c1) = c4) <=> (f10(c1) = c1)),
% 29.61/19.83 inference(monotonicity,[status(thm)],[27245])).
% 29.61/19.83 tff(27247,plain,
% 29.61/19.83 ((f10(c1) = c1) <=> (f10(c1) = c4)),
% 29.61/19.83 inference(symmetry,[status(thm)],[27246])).
% 29.61/19.83 tff(27248,plain,
% 29.61/19.83 ((f10(c1) = c1) <=> (c2 = c4)),
% 29.61/19.83 inference(transitivity,[status(thm)],[27247, 27054])).
% 29.61/19.83 tff(27249,plain,
% 29.61/19.83 ((~(f10(c1) = c1)) <=> (~(c2 = c4))),
% 29.61/19.83 inference(monotonicity,[status(thm)],[27248])).
% 29.61/19.83 tff(27250,plain,
% 29.61/19.83 (~(c2 = c4)),
% 29.61/19.83 inference(modus_ponens,[status(thm)],[26229, 27249])).
% 29.61/19.83 tff(27251,plain,
% 29.61/19.83 ((~(f10(c1) = c1)) <=> (~(f10(c1) = c4))),
% 29.61/19.83 inference(monotonicity,[status(thm)],[27247])).
% 29.61/19.83 tff(27252,plain,
% 29.61/19.83 (~(f10(c1) = c4)),
% 29.61/19.83 inference(modus_ponens,[status(thm)],[26229, 27251])).
% 29.61/19.83 tff(27253,plain,
% 29.61/19.83 (~(f7(c2) = f8(c2))),
% 29.61/19.83 inference(unit_resolution,[status(thm)],[12706, 21128, 17, 89, 23541])).
% 29.61/19.83 tff(27254,plain,
% 29.61/19.83 (c2 = f8(c2)),
% 29.61/19.83 inference(unit_resolution,[status(thm)],[24274, 26230, 22, 27253])).
% 29.61/19.83 tff(27255,plain,
% 29.61/19.83 (f7(f10(c1)) = f7(c2)),
% 29.61/19.83 inference(monotonicity,[status(thm)],[26230])).
% 29.61/19.83 tff(27256,plain,
% 29.61/19.83 (f7(f10(c1)) = c1),
% 29.61/19.83 inference(transitivity,[status(thm)],[27255, 22])).
% 29.61/19.83 tff(27257,plain,
% 29.61/19.83 (big_f(f7(f10(c1)), f10(c1)) <=> big_f(c1, f10(c1))),
% 29.61/19.83 inference(monotonicity,[status(thm)],[27256])).
% 29.61/19.83 tff(27258,plain,
% 29.61/19.83 (big_f(c1, f10(c1)) <=> big_f(f7(f10(c1)), f10(c1))),
% 29.61/19.83 inference(symmetry,[status(thm)],[27257])).
% 29.61/19.83 tff(27259,plain,
% 29.61/19.83 ((~big_f(c1, f10(c1))) <=> (~big_f(f7(f10(c1)), f10(c1)))),
% 29.61/19.83 inference(monotonicity,[status(thm)],[27258])).
% 29.61/19.83 tff(27260,plain,
% 29.61/19.83 (~big_f(f7(f10(c1)), f10(c1))),
% 29.61/19.83 inference(modus_ponens,[status(thm)],[26247, 27259])).
% 29.61/19.83 tff(27261,plain,
% 29.61/19.83 ((c1 = f5(f10(c1))) <=> (c1 = f5(c2))),
% 29.61/19.83 inference(monotonicity,[status(thm)],[9888])).
% 29.61/19.83 tff(27262,plain,
% 29.61/19.83 ((c1 = f5(f10(c1))) <=> (f5(c2) = c1)),
% 29.61/19.83 inference(transitivity,[status(thm)],[27261, 1531])).
% 29.61/19.83 tff(27263,plain,
% 29.61/19.83 ((f5(c2) = c1) <=> (c1 = f5(f10(c1)))),
% 29.61/19.83 inference(symmetry,[status(thm)],[27262])).
% 29.61/19.83 tff(27264,plain,
% 29.61/19.83 (big_f(f3(f10(f10(c2)), f8(c3)), f10(c1)) <=> big_f(f3(f10(f10(c2)), f8(c3)), f10(f10(c2)))),
% 29.61/19.83 inference(monotonicity,[status(thm)],[17779])).
% 29.61/19.83 tff(27265,plain,
% 29.61/19.83 (big_f(f3(f10(f10(c2)), f8(c3)), f10(f10(c2))) <=> big_f(f3(f10(f10(c2)), f8(c3)), f10(c1))),
% 29.61/19.83 inference(symmetry,[status(thm)],[27264])).
% 29.61/19.83 tff(27266,plain,
% 29.61/19.83 (c3 = f10(c1)),
% 29.61/19.83 inference(transitivity,[status(thm)],[67, 5571])).
% 29.61/19.83 tff(27267,plain,
% 29.61/19.83 (f8(c3) = f8(f10(c1))),
% 29.61/19.83 inference(monotonicity,[status(thm)],[27266])).
% 29.61/19.83 tff(27268,plain,
% 29.61/19.83 (f8(f10(c1)) = f8(c3)),
% 29.61/19.83 inference(symmetry,[status(thm)],[27267])).
% 29.61/19.83 tff(27269,plain,
% 29.61/19.83 (c2 = f8(c3)),
% 29.61/19.83 inference(transitivity,[status(thm)],[13152, 13830, 27268])).
% 29.61/19.83 tff(27270,plain,
% 29.61/19.83 (c2 = f10(f10(c2))),
% 29.61/19.83 inference(transitivity,[status(thm)],[5571, 17779])).
% 29.61/19.83 tff(27271,plain,
% 29.61/19.83 (f3(c2, c2) = f3(f10(f10(c2)), f8(c3))),
% 29.61/19.83 inference(monotonicity,[status(thm)],[27270, 27269])).
% 29.61/19.83 tff(27272,plain,
% 29.61/19.83 (f3(f10(f10(c2)), f8(c3)) = f3(c2, c2)),
% 29.61/19.83 inference(symmetry,[status(thm)],[27271])).
% 29.61/19.83 tff(27273,plain,
% 29.61/19.83 (big_f(f3(f10(f10(c2)), f8(c3)), f10(f10(c2))) <=> big_f(f3(c2, c2), f10(c1))),
% 29.61/19.83 inference(monotonicity,[status(thm)],[27272, 11844])).
% 29.61/19.83 tff(27274,plain,
% 29.61/19.83 (big_f(f3(c2, c2), f10(c1)) <=> big_f(f3(f10(f10(c2)), f8(c3)), f10(f10(c2)))),
% 29.61/19.83 inference(symmetry,[status(thm)],[27273])).
% 29.61/19.83 tff(27275,plain,
% 29.61/19.83 (big_f(f3(c2, c2), c2)),
% 29.61/19.83 inference(unit_resolution,[status(thm)],[13236, 1335, 1345, 348, 873])).
% 29.61/19.83 tff(27276,plain,
% 29.61/19.83 (big_f(f3(c2, c2), f10(c1)) <=> big_f(f3(c2, c2), c2)),
% 29.61/19.83 inference(monotonicity,[status(thm)],[16])).
% 29.61/19.83 tff(27277,plain,
% 29.61/19.83 ((~big_f(f3(c2, c2), f10(c1))) <=> (~big_f(f3(c2, c2), c2))),
% 29.61/19.83 inference(monotonicity,[status(thm)],[27276])).
% 29.61/19.83 tff(27278,assumption,(~big_f(f3(c2, c2), f10(c1))), introduced(assumption)).
% 29.61/19.83 tff(27279,plain,
% 29.61/19.83 (~big_f(f3(c2, c2), c2)),
% 29.61/19.83 inference(modus_ponens,[status(thm)],[27278, 27277])).
% 29.61/19.83 tff(27280,plain,
% 29.61/19.83 ($false),
% 29.61/19.83 inference(unit_resolution,[status(thm)],[15356, 27279])).
% 29.61/19.83 tff(27281,plain,(big_f(f3(c2, c2), f10(c1)) | (~big_f(f3(c2, c2), c2)) | (~(f10(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.61/19.83 tff(27282,plain,
% 29.61/19.83 (big_f(f3(c2, c2), f10(c1))),
% 29.61/19.83 inference(unit_resolution,[status(thm)],[27281, 27275, 15])).
% 29.61/19.83 tff(27283,plain,
% 29.61/19.83 (big_f(f3(f10(f10(c2)), f8(c3)), f10(f10(c2)))),
% 29.61/19.83 inference(modus_ponens,[status(thm)],[27282, 27274])).
% 29.61/19.83 tff(27284,plain,
% 29.61/19.83 (big_f(f3(f10(f10(c2)), f8(c3)), f10(c1))),
% 29.61/19.83 inference(modus_ponens,[status(thm)],[27283, 27265])).
% 29.61/19.83 tff(27285,plain,
% 29.61/19.83 (f8(c1) = f8(c3)),
% 29.61/19.83 inference(transitivity,[status(thm)],[1671, 13152, 13830, 27268])).
% 29.61/19.83 tff(27286,plain,
% 29.61/19.83 ((f3(f10(f10(c2)), f8(c3)) = f8(c1)) <=> (f3(f10(f10(c2)), f8(c3)) = f8(c3))),
% 29.61/19.83 inference(monotonicity,[status(thm)],[27285])).
% 29.61/19.83 tff(27287,plain,
% 29.61/19.83 ((f3(f10(f10(c2)), f8(c3)) = f8(c3)) <=> (f3(f10(f10(c2)), f8(c3)) = f8(c1))),
% 29.61/19.83 inference(symmetry,[status(thm)],[27286])).
% 29.61/19.83 tff(27288,plain,
% 29.61/19.83 (f10(c1) = f8(c3)),
% 29.61/19.83 inference(transitivity,[status(thm)],[15, 13152, 13830, 27268])).
% 29.61/19.83 tff(27289,plain,
% 29.61/19.83 (f3(f10(c1), f10(c1)) = f3(c2, c2)),
% 29.61/19.83 inference(monotonicity,[status(thm)],[15, 15])).
% 29.61/19.83 tff(27290,plain,
% 29.61/19.83 (f3(f10(c1), f10(c1)) = f3(f10(f10(c2)), f8(c3))),
% 29.61/19.83 inference(transitivity,[status(thm)],[27289, 27271])).
% 29.61/19.83 tff(27291,plain,
% 29.61/19.83 ((f3(f10(c1), f10(c1)) = f10(c1)) <=> (f3(f10(f10(c2)), f8(c3)) = f8(c3))),
% 29.61/19.83 inference(monotonicity,[status(thm)],[27290, 27288])).
% 29.61/19.83 tff(27292,plain,
% 29.61/19.83 ((f3(f10(c1), f10(c1)) = f10(c1)) <=> (f3(f10(f10(c2)), f8(c3)) = f8(c1))),
% 29.61/19.83 inference(transitivity,[status(thm)],[27291, 27287])).
% 29.61/19.83 tff(27293,plain,
% 29.61/19.83 ((~(f3(f10(c1), f10(c1)) = f10(c1))) <=> (~(f3(f10(f10(c2)), f8(c3)) = f8(c1)))),
% 29.61/19.83 inference(monotonicity,[status(thm)],[27292])).
% 29.61/19.83 tff(27294,plain,
% 29.61/19.83 (big_f(f10(c1), f10(c1))),
% 29.61/19.83 inference(modus_ponens,[status(thm)],[1345, 25999])).
% 29.61/19.83 tff(27295,plain,
% 29.61/19.83 (big_f(f10(c1), c1) <=> big_f(c2, c1)),
% 29.61/19.83 inference(monotonicity,[status(thm)],[15])).
% 29.61/19.83 tff(27296,plain,
% 29.61/19.83 (big_f(c2, c1) <=> big_f(f10(c1), c1)),
% 29.61/19.83 inference(symmetry,[status(thm)],[27295])).
% 29.61/19.83 tff(27297,plain,
% 29.61/19.83 (big_f(f10(c1), c1)),
% 29.61/19.83 inference(modus_ponens,[status(thm)],[348, 27296])).
% 29.61/19.83 tff(27298,plain,
% 29.61/19.83 ((f10(c1) = c3) <=> (c2 = c3)),
% 29.61/19.83 inference(monotonicity,[status(thm)],[15])).
% 29.61/19.83 tff(27299,plain,
% 29.61/19.83 ((c2 = c3) <=> (f10(c1) = c3)),
% 29.61/19.83 inference(symmetry,[status(thm)],[27298])).
% 29.61/19.83 tff(27300,plain,
% 29.61/19.83 ((c3 = c2) <=> (f10(c1) = c3)),
% 29.61/19.83 inference(transitivity,[status(thm)],[78, 27299])).
% 29.61/19.83 tff(27301,plain,
% 29.61/19.83 (f10(c1) = c3),
% 29.61/19.83 inference(modus_ponens,[status(thm)],[67, 27300])).
% 29.61/19.83 tff(27302,plain,
% 29.61/19.83 (big_f(f3(f10(c1), f10(c1)), f10(c1)) <=> big_f(f3(f10(f10(c2)), f8(c3)), f10(f10(c2)))),
% 29.61/19.83 inference(monotonicity,[status(thm)],[27290, 17779])).
% 29.61/19.83 tff(27303,plain,
% 29.61/19.83 (big_f(f3(f10(f10(c2)), f8(c3)), f10(f10(c2))) <=> big_f(f3(f10(c1), f10(c1)), f10(c1))),
% 29.61/19.83 inference(symmetry,[status(thm)],[27302])).
% 29.61/19.83 tff(27304,plain,
% 29.61/19.83 (big_f(f3(f10(c1), f10(c1)), f10(c1))),
% 29.61/19.83 inference(modus_ponens,[status(thm)],[27283, 27303])).
% 29.61/19.83 tff(27305,assumption,(big_f(f3(f10(c1), f10(c1)), f10(c1))), introduced(assumption)).
% 29.61/19.83 tff(27306,assumption,(f3(f10(c1), f10(c1)) = f10(c1)), introduced(assumption)).
% 29.61/19.83 tff(27307,assumption,(big_f(f10(c1), c1)), introduced(assumption)).
% 29.61/19.83 tff(27308,assumption,(f10(c1) = c3), introduced(assumption)).
% 29.61/19.83 tff(27309,plain,
% 29.61/19.83 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((f10(c1) = c4) | (~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))) | (~big_f(f10(c1), c1)) | (~(f10(c1) = c3)) | (c1 = f2(f10(c1))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (f10(c1) = c4) | (~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))) | (~big_f(f10(c1), c1)) | (~(f10(c1) = c3)) | (c1 = f2(f10(c1))))),
% 29.61/19.83 inference(rewrite,[status(thm)],[])).
% 29.61/19.83 tff(27310,plain,
% 29.61/19.83 (((~(f10(c1) = c3)) | (f10(c1) = c4) | (~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))) | (c1 = f2(f10(c1))) | (~big_f(f10(c1), c1))) <=> ((f10(c1) = c4) | (~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))) | (~big_f(f10(c1), c1)) | (~(f10(c1) = c3)) | (c1 = f2(f10(c1))))),
% 29.61/19.83 inference(rewrite,[status(thm)],[])).
% 29.61/19.83 tff(27311,plain,
% 29.61/19.83 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f10(c1) = c3)) | (f10(c1) = c4) | (~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))) | (c1 = f2(f10(c1))) | (~big_f(f10(c1), c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((f10(c1) = c4) | (~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))) | (~big_f(f10(c1), c1)) | (~(f10(c1) = c3)) | (c1 = f2(f10(c1)))))),
% 29.61/19.83 inference(monotonicity,[status(thm)],[27310])).
% 29.61/19.83 tff(27312,plain,
% 29.61/19.83 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f10(c1) = c3)) | (f10(c1) = c4) | (~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))) | (c1 = f2(f10(c1))) | (~big_f(f10(c1), c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (f10(c1) = c4) | (~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))) | (~big_f(f10(c1), c1)) | (~(f10(c1) = c3)) | (c1 = f2(f10(c1))))),
% 29.61/19.83 inference(transitivity,[status(thm)],[27311, 27309])).
% 29.61/19.83 tff(27313,plain,
% 29.61/19.83 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f10(c1) = c3)) | (f10(c1) = c4) | (~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))) | (c1 = f2(f10(c1))) | (~big_f(f10(c1), c1)))),
% 29.61/19.83 inference(quant_inst,[status(thm)],[])).
% 29.61/19.83 tff(27314,plain,
% 29.61/19.83 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (f10(c1) = c4) | (~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))) | (~big_f(f10(c1), c1)) | (~(f10(c1) = c3)) | (c1 = f2(f10(c1)))),
% 29.61/19.83 inference(modus_ponens,[status(thm)],[27313, 27312])).
% 29.61/19.83 tff(27315,plain,
% 29.61/19.83 ((~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))) | (c1 = f2(f10(c1)))),
% 29.61/19.83 inference(unit_resolution,[status(thm)],[27314, 7051, 1046, 27308, 27307])).
% 29.61/19.83 tff(27316,plain,
% 29.61/19.83 (c1 = f2(f10(c1))),
% 29.61/19.83 inference(unit_resolution,[status(thm)],[27315, 27306, 27305])).
% 29.61/19.83 tff(27317,plain,
% 29.61/19.83 (f2(f10(c1)) = c1),
% 29.61/19.83 inference(symmetry,[status(thm)],[27316])).
% 29.61/19.83 tff(27318,assumption,(big_f(f10(c1), f10(c1))), introduced(assumption)).
% 29.61/19.83 tff(27319,plain,
% 29.61/19.83 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((f10(c1) = c4) | (~big_f(f10(c1), f10(c1))) | (~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))) | (~(f10(c1) = c3)) | (f10(c1) = f2(f10(c1))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (f10(c1) = c4) | (~big_f(f10(c1), f10(c1))) | (~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))) | (~(f10(c1) = c3)) | (f10(c1) = f2(f10(c1))))),
% 29.61/19.83 inference(rewrite,[status(thm)],[])).
% 29.61/19.83 tff(27320,plain,
% 29.61/19.83 (((~(f10(c1) = c3)) | (f10(c1) = c4) | (~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))) | (f10(c1) = f2(f10(c1))) | (~big_f(f10(c1), f10(c1)))) <=> ((f10(c1) = c4) | (~big_f(f10(c1), f10(c1))) | (~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))) | (~(f10(c1) = c3)) | (f10(c1) = f2(f10(c1))))),
% 29.61/19.83 inference(rewrite,[status(thm)],[])).
% 29.61/19.83 tff(27321,plain,
% 29.61/19.83 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f10(c1) = c3)) | (f10(c1) = c4) | (~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))) | (f10(c1) = f2(f10(c1))) | (~big_f(f10(c1), f10(c1))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((f10(c1) = c4) | (~big_f(f10(c1), f10(c1))) | (~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))) | (~(f10(c1) = c3)) | (f10(c1) = f2(f10(c1)))))),
% 29.61/19.83 inference(monotonicity,[status(thm)],[27320])).
% 29.61/19.83 tff(27322,plain,
% 29.61/19.83 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f10(c1) = c3)) | (f10(c1) = c4) | (~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))) | (f10(c1) = f2(f10(c1))) | (~big_f(f10(c1), f10(c1))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (f10(c1) = c4) | (~big_f(f10(c1), f10(c1))) | (~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))) | (~(f10(c1) = c3)) | (f10(c1) = f2(f10(c1))))),
% 29.61/19.83 inference(transitivity,[status(thm)],[27321, 27319])).
% 29.61/19.83 tff(27323,plain,
% 29.61/19.83 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f10(c1) = c3)) | (f10(c1) = c4) | (~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))) | (f10(c1) = f2(f10(c1))) | (~big_f(f10(c1), f10(c1))))),
% 29.61/19.83 inference(quant_inst,[status(thm)],[])).
% 29.61/19.83 tff(27324,plain,
% 29.61/19.83 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (f10(c1) = c4) | (~big_f(f10(c1), f10(c1))) | (~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))) | (~(f10(c1) = c3)) | (f10(c1) = f2(f10(c1)))),
% 29.61/19.83 inference(modus_ponens,[status(thm)],[27323, 27322])).
% 29.61/19.83 tff(27325,plain,
% 29.61/19.83 ((~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))) | (f10(c1) = f2(f10(c1)))),
% 29.61/19.83 inference(unit_resolution,[status(thm)],[27324, 7051, 1046, 27308, 27318])).
% 29.61/19.83 tff(27326,plain,
% 29.61/19.83 (f10(c1) = f2(f10(c1))),
% 29.61/19.83 inference(unit_resolution,[status(thm)],[27325, 27306, 27305])).
% 29.61/19.83 tff(27327,plain,
% 29.61/19.83 (f10(c1) = c1),
% 29.61/19.83 inference(transitivity,[status(thm)],[27326, 27317])).
% 29.61/19.83 tff(27328,plain,
% 29.61/19.83 ($false),
% 29.61/19.83 inference(unit_resolution,[status(thm)],[3, 27327])).
% 29.61/19.83 tff(27329,plain,((~(f3(f10(c1), f10(c1)) = f10(c1))) | (f10(c1) = c1) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))) | (f10(c1) = c4) | (~(f10(c1) = c3)) | (~big_f(f10(c1), c1)) | (~big_f(f10(c1), f10(c1)))), inference(lemma,lemma(discharge,[]))).
% 29.61/19.83 tff(27330,plain,
% 29.61/19.83 (~(f3(f10(c1), f10(c1)) = f10(c1))),
% 29.61/19.83 inference(unit_resolution,[status(thm)],[27329, 27304, 3, 1046, 27301, 27297, 27294])).
% 29.61/19.83 tff(27331,plain,
% 29.61/19.83 (~(f3(f10(f10(c2)), f8(c3)) = f8(c1))),
% 29.61/19.83 inference(modus_ponens,[status(thm)],[27330, 27293])).
% 29.61/19.83 tff(27332,assumption,(~big_f(f7(f10(c1)), f10(c1))), introduced(assumption)).
% 29.61/19.83 tff(27333,plain,
% 29.61/19.83 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f10(c1) = c1) | (f7(f10(c1)) = f10(c1)) | (~(f10(c1) = f5(f10(c1)))) | big_f(f7(f10(c1)), f10(c1)) | (~big_f(f3(f10(f10(c2)), f8(c3)), f10(c1))) | (f3(f10(f10(c2)), f8(c3)) = f8(c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(c1) = c1) | (f7(f10(c1)) = f10(c1)) | (~(f10(c1) = f5(f10(c1)))) | big_f(f7(f10(c1)), f10(c1)) | (~big_f(f3(f10(f10(c2)), f8(c3)), f10(c1))) | (f3(f10(f10(c2)), f8(c3)) = f8(c1)))),
% 29.61/19.83 inference(rewrite,[status(thm)],[])).
% 29.61/19.83 tff(27334,plain,
% 29.61/19.83 (((~(f10(c1) = f5(f10(c1)))) | (f10(c1) = c1) | (f3(f10(f10(c2)), f8(c3)) = f8(c1)) | (~big_f(f3(f10(f10(c2)), f8(c3)), f10(c1))) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), f10(c1))) <=> ((f10(c1) = c1) | (f7(f10(c1)) = f10(c1)) | (~(f10(c1) = f5(f10(c1)))) | big_f(f7(f10(c1)), f10(c1)) | (~big_f(f3(f10(f10(c2)), f8(c3)), f10(c1))) | (f3(f10(f10(c2)), f8(c3)) = f8(c1)))),
% 29.61/19.83 inference(rewrite,[status(thm)],[])).
% 29.61/19.83 tff(27335,plain,
% 29.61/19.83 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(f10(c1) = f5(f10(c1)))) | (f10(c1) = c1) | (f3(f10(f10(c2)), f8(c3)) = f8(c1)) | (~big_f(f3(f10(f10(c2)), f8(c3)), f10(c1))) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), f10(c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f10(c1) = c1) | (f7(f10(c1)) = f10(c1)) | (~(f10(c1) = f5(f10(c1)))) | big_f(f7(f10(c1)), f10(c1)) | (~big_f(f3(f10(f10(c2)), f8(c3)), f10(c1))) | (f3(f10(f10(c2)), f8(c3)) = f8(c1))))),
% 29.61/19.83 inference(monotonicity,[status(thm)],[27334])).
% 29.61/19.83 tff(27336,plain,
% 29.61/19.83 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(f10(c1) = f5(f10(c1)))) | (f10(c1) = c1) | (f3(f10(f10(c2)), f8(c3)) = f8(c1)) | (~big_f(f3(f10(f10(c2)), f8(c3)), f10(c1))) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), f10(c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(c1) = c1) | (f7(f10(c1)) = f10(c1)) | (~(f10(c1) = f5(f10(c1)))) | big_f(f7(f10(c1)), f10(c1)) | (~big_f(f3(f10(f10(c2)), f8(c3)), f10(c1))) | (f3(f10(f10(c2)), f8(c3)) = f8(c1)))),
% 29.61/19.83 inference(transitivity,[status(thm)],[27335, 27333])).
% 29.61/19.83 tff(27337,plain,
% 29.61/19.83 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(f10(c1) = f5(f10(c1)))) | (f10(c1) = c1) | (f3(f10(f10(c2)), f8(c3)) = f8(c1)) | (~big_f(f3(f10(f10(c2)), f8(c3)), f10(c1))) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), f10(c1)))),
% 29.61/19.83 inference(quant_inst,[status(thm)],[])).
% 29.61/19.83 tff(27338,plain,
% 29.61/19.83 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(c1) = c1) | (f7(f10(c1)) = f10(c1)) | (~(f10(c1) = f5(f10(c1)))) | big_f(f7(f10(c1)), f10(c1)) | (~big_f(f3(f10(f10(c2)), f8(c3)), f10(c1))) | (f3(f10(f10(c2)), f8(c3)) = f8(c1))),
% 29.61/19.83 inference(modus_ponens,[status(thm)],[27337, 27336])).
% 29.61/19.83 tff(27339,plain,
% 29.61/19.83 ((~(f10(c1) = f5(f10(c1)))) | (~big_f(f3(f10(f10(c2)), f8(c3)), f10(c1))) | (f3(f10(f10(c2)), f8(c3)) = f8(c1))),
% 29.61/19.83 inference(unit_resolution,[status(thm)],[27338, 705, 3, 26316, 27332])).
% 29.61/19.83 tff(27340,plain,
% 29.61/19.83 (~(f10(c1) = f5(f10(c1)))),
% 29.61/19.83 inference(unit_resolution,[status(thm)],[27339, 27331, 27284])).
% 29.61/19.83 tff(27341,plain,
% 29.61/19.83 ((f10(c1) = f5(f10(c1))) <=> (c2 = f5(f10(c1)))),
% 29.61/19.83 inference(monotonicity,[status(thm)],[16])).
% 29.61/19.83 tff(27342,plain,
% 29.61/19.83 ((c2 = f5(f10(c1))) <=> (f10(c1) = f5(f10(c1)))),
% 29.61/19.83 inference(symmetry,[status(thm)],[27341])).
% 29.61/19.83 tff(27343,plain,
% 29.61/19.83 ((c2 = f5(c2)) <=> (c2 = f5(f10(c1)))),
% 29.61/19.83 inference(monotonicity,[status(thm)],[294])).
% 29.61/19.83 tff(27344,plain,
% 29.61/19.83 ((f5(c2) = c2) <=> (f10(c1) = f5(f10(c1)))),
% 29.61/19.83 inference(transitivity,[status(thm)],[1279, 27343, 27342])).
% 29.61/19.83 tff(27345,plain,
% 29.61/19.83 (f10(c1) = f5(f10(c1))),
% 29.61/19.83 inference(modus_ponens,[status(thm)],[8109, 27344])).
% 29.61/19.83 tff(27346,assumption,(~(f10(c1) = f5(f10(c1)))), introduced(assumption)).
% 29.61/19.83 tff(27347,plain,
% 29.61/19.83 ($false),
% 29.61/19.83 inference(unit_resolution,[status(thm)],[27346, 27345])).
% 29.61/19.83 tff(27348,plain,((~(f5(c2) = c2)) | (f10(c1) = f5(f10(c1))) | (~(f10(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.61/19.83 tff(27349,plain,
% 29.61/19.83 (~(f5(c2) = c2)),
% 29.61/19.83 inference(unit_resolution,[status(thm)],[27348, 27340, 15])).
% 29.61/19.83 tff(27350,plain,
% 29.61/19.83 (f5(c2) = c1),
% 29.61/19.83 inference(unit_resolution,[status(thm)],[1547, 27349])).
% 29.61/19.83 tff(27351,plain,
% 29.61/19.83 (c1 = f5(f10(c1))),
% 29.61/19.83 inference(modus_ponens,[status(thm)],[27350, 27263])).
% 29.61/19.83 tff(27352,plain,
% 29.61/19.83 (big_f(f7(f10(c1)), c1) <=> big_f(c1, c1)),
% 29.61/19.83 inference(monotonicity,[status(thm)],[26311])).
% 29.61/19.83 tff(27353,plain,
% 29.61/19.83 (big_f(c1, c1) <=> big_f(f7(f10(c1)), c1)),
% 29.61/19.83 inference(symmetry,[status(thm)],[27352])).
% 29.61/19.83 tff(27354,plain,
% 29.61/19.83 ((~big_f(c1, c1)) <=> (~big_f(f7(f10(c1)), c1))),
% 29.61/19.83 inference(monotonicity,[status(thm)],[27353])).
% 29.61/19.83 tff(27355,plain,
% 29.61/19.83 (~big_f(f7(f10(c1)), c1)),
% 29.61/19.83 inference(modus_ponens,[status(thm)],[66, 27354])).
% 29.61/19.83 tff(27356,plain,
% 29.61/19.83 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f10(c1) = c1) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), c1) | (~(c1 = f5(f10(c1)))) | (~big_f(f3(f10(f10(c2)), f8(c3)), f10(c1))) | (f3(f10(f10(c2)), f8(c3)) = f8(c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(c1) = c1) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), c1) | (~(c1 = f5(f10(c1)))) | (~big_f(f3(f10(f10(c2)), f8(c3)), f10(c1))) | (f3(f10(f10(c2)), f8(c3)) = f8(c1)))),
% 29.61/19.83 inference(rewrite,[status(thm)],[])).
% 29.61/19.83 tff(27357,plain,
% 29.61/19.83 (((~(c1 = f5(f10(c1)))) | (f10(c1) = c1) | (f3(f10(f10(c2)), f8(c3)) = f8(c1)) | (~big_f(f3(f10(f10(c2)), f8(c3)), f10(c1))) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), c1)) <=> ((f10(c1) = c1) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), c1) | (~(c1 = f5(f10(c1)))) | (~big_f(f3(f10(f10(c2)), f8(c3)), f10(c1))) | (f3(f10(f10(c2)), f8(c3)) = f8(c1)))),
% 29.61/19.83 inference(rewrite,[status(thm)],[])).
% 29.61/19.83 tff(27358,plain,
% 29.61/19.83 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c1 = f5(f10(c1)))) | (f10(c1) = c1) | (f3(f10(f10(c2)), f8(c3)) = f8(c1)) | (~big_f(f3(f10(f10(c2)), f8(c3)), f10(c1))) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), c1))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f10(c1) = c1) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), c1) | (~(c1 = f5(f10(c1)))) | (~big_f(f3(f10(f10(c2)), f8(c3)), f10(c1))) | (f3(f10(f10(c2)), f8(c3)) = f8(c1))))),
% 29.61/19.84 inference(monotonicity,[status(thm)],[27357])).
% 29.61/19.84 tff(27359,plain,
% 29.61/19.84 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c1 = f5(f10(c1)))) | (f10(c1) = c1) | (f3(f10(f10(c2)), f8(c3)) = f8(c1)) | (~big_f(f3(f10(f10(c2)), f8(c3)), f10(c1))) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), c1))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(c1) = c1) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), c1) | (~(c1 = f5(f10(c1)))) | (~big_f(f3(f10(f10(c2)), f8(c3)), f10(c1))) | (f3(f10(f10(c2)), f8(c3)) = f8(c1)))),
% 29.61/19.84 inference(transitivity,[status(thm)],[27358, 27356])).
% 29.61/19.84 tff(27360,plain,
% 29.61/19.84 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c1 = f5(f10(c1)))) | (f10(c1) = c1) | (f3(f10(f10(c2)), f8(c3)) = f8(c1)) | (~big_f(f3(f10(f10(c2)), f8(c3)), f10(c1))) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), c1))),
% 29.61/19.84 inference(quant_inst,[status(thm)],[])).
% 29.61/19.84 tff(27361,plain,
% 29.61/19.84 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(c1) = c1) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), c1) | (~(c1 = f5(f10(c1)))) | (~big_f(f3(f10(f10(c2)), f8(c3)), f10(c1))) | (f3(f10(f10(c2)), f8(c3)) = f8(c1))),
% 29.61/19.84 inference(modus_ponens,[status(thm)],[27360, 27359])).
% 29.61/19.84 tff(27362,plain,
% 29.61/19.84 (big_f(f7(f10(c1)), c1) | (~(c1 = f5(f10(c1)))) | (~big_f(f3(f10(f10(c2)), f8(c3)), f10(c1))) | (f3(f10(f10(c2)), f8(c3)) = f8(c1))),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[27361, 705, 3, 26316])).
% 29.61/19.84 tff(27363,plain,
% 29.61/19.84 (~(c1 = f5(f10(c1)))),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[27362, 27331, 27355, 27284])).
% 29.61/19.84 tff(27364,plain,
% 29.61/19.84 ($false),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[27363, 27351])).
% 29.61/19.84 tff(27365,plain,((~(c3 = c2)) | (f10(c1) = c1) | big_f(f7(f10(c1)), f10(c1)) | (~(f8(c1) = c2)) | (~(c2 = f8(c2))) | (~(f10(c2) = c1)) | (f10(c1) = c4) | big_f(c1, c1) | (~(f7(c2) = c1)) | (~big_f(c2, c2)) | (~big_f(c2, c1)) | (c2 = c4)), inference(lemma,lemma(discharge,[]))).
% 29.61/19.84 tff(27366,plain,
% 29.61/19.84 (~(c3 = c2)),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[27365, 26229, 27260, 26237, 27254, 94, 27252, 66, 22, 27052, 27055, 27250])).
% 29.61/19.84 tff(27367,plain,
% 29.61/19.84 (c3 = c1),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[180, 27366])).
% 29.61/19.84 tff(27368,plain,
% 29.61/19.84 (big_f(f3(c2, c2), c2)),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[14309, 27367, 66, 27250, 27052, 27])).
% 29.61/19.84 tff(27369,plain,
% 29.61/19.84 (big_f(f3(c2, c2), f10(c1))),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[27281, 27368, 26230])).
% 29.61/19.84 tff(27370,plain,
% 29.61/19.84 (big_f(f3(f10(c1), f10(c1)), f10(c1))),
% 29.61/19.84 inference(modus_ponens,[status(thm)],[27369, 26249])).
% 29.61/19.84 tff(27371,plain,
% 29.61/19.84 ((f10(c1) = f2(c1)) <=> (c2 = f2(c1))),
% 29.61/19.84 inference(monotonicity,[status(thm)],[16])).
% 29.61/19.84 tff(27372,plain,
% 29.61/19.84 ((~(f10(c1) = f2(c1))) <=> (~(c2 = f2(c1)))),
% 29.61/19.84 inference(monotonicity,[status(thm)],[27371])).
% 29.61/19.84 tff(27373,plain,
% 29.61/19.84 ((~(f10(c1) = f2(c1))) | (~(f3(f10(c1), f10(c1)) = f10(c1)))),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[13023, 1398, 5611, 3030, 1046, 27305])).
% 29.61/19.84 tff(27374,plain,
% 29.61/19.84 (~(f10(c1) = f2(c1))),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[27373, 27306])).
% 29.61/19.84 tff(27375,plain,
% 29.61/19.84 (~(c2 = f2(c1))),
% 29.61/19.84 inference(modus_ponens,[status(thm)],[27374, 27372])).
% 29.61/19.84 tff(27376,plain,
% 29.61/19.84 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(c1 = f2(c1))) | big_f(c1, c1) | (f10(c1) = c4) | (~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (~(c1 = c3)) | (~(c1 = f2(c1))) | big_f(c1, c1) | (f10(c1) = c4) | (~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))))),
% 29.61/19.84 inference(rewrite,[status(thm)],[])).
% 29.61/19.84 tff(27377,plain,
% 29.61/19.84 (((~(c1 = c3)) | (~(c1 = f2(c1))) | (f10(c1) = c4) | (~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))) | big_f(c1, c1)) <=> ((~(c1 = c3)) | (~(c1 = f2(c1))) | big_f(c1, c1) | (f10(c1) = c4) | (~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))))),
% 29.61/19.84 inference(rewrite,[status(thm)],[])).
% 29.61/19.84 tff(27378,plain,
% 29.61/19.84 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(c1 = f2(c1))) | (f10(c1) = c4) | (~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))) | big_f(c1, c1))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(c1 = f2(c1))) | big_f(c1, c1) | (f10(c1) = c4) | (~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1)))))),
% 29.61/19.84 inference(monotonicity,[status(thm)],[27377])).
% 29.61/19.84 tff(27379,plain,
% 29.61/19.84 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(c1 = f2(c1))) | (f10(c1) = c4) | (~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))) | big_f(c1, c1))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (~(c1 = c3)) | (~(c1 = f2(c1))) | big_f(c1, c1) | (f10(c1) = c4) | (~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))))),
% 29.61/19.84 inference(transitivity,[status(thm)],[27378, 27376])).
% 29.61/19.84 tff(27380,plain,
% 29.61/19.84 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(c1 = f2(c1))) | (f10(c1) = c4) | (~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))) | big_f(c1, c1))),
% 29.61/19.84 inference(quant_inst,[status(thm)],[])).
% 29.61/19.84 tff(27381,plain,
% 29.61/19.84 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (~(c1 = c3)) | (~(c1 = f2(c1))) | big_f(c1, c1) | (f10(c1) = c4) | (~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1)))),
% 29.61/19.84 inference(modus_ponens,[status(thm)],[27380, 27379])).
% 29.61/19.84 tff(27382,plain,
% 29.61/19.84 ((~(c1 = f2(c1))) | (~(f3(f10(c1), f10(c1)) = f10(c1)))),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[27381, 1398, 5611, 1046, 66, 27305])).
% 29.61/19.84 tff(27383,plain,
% 29.61/19.84 (~(c1 = f2(c1))),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[27382, 27306])).
% 29.61/19.84 tff(27384,plain,
% 29.61/19.84 (~(f2(c3) = c1)),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[6771, 27383, 172])).
% 29.61/19.84 tff(27385,plain,
% 29.61/19.84 (f2(c3) = c2),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[1273, 27384])).
% 29.61/19.84 tff(27386,plain,
% 29.61/19.84 (c2 = f2(c1)),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[12823, 27385, 172])).
% 29.61/19.84 tff(27387,plain,
% 29.61/19.84 ($false),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[27386, 27375])).
% 29.61/19.84 tff(27388,plain,((~(f3(f10(c1), f10(c1)) = f10(c1))) | (~(f10(c1) = c2)) | (~(c3 = c1)) | (f10(c1) = c4) | big_f(c1, c1) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))) | big_f(c1, f10(c1))), inference(lemma,lemma(discharge,[]))).
% 29.61/19.84 tff(27389,plain,
% 29.61/19.84 (~(f3(f10(c1), f10(c1)) = f10(c1))),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[27388, 26230, 27367, 27252, 66, 27370, 26247])).
% 29.61/19.84 tff(27390,plain,
% 29.61/19.84 (~(f3(c2, c2) = f8(c1))),
% 29.61/19.84 inference(modus_ponens,[status(thm)],[27389, 26243])).
% 29.61/19.84 tff(27391,plain,
% 29.61/19.84 ((f7(f10(c1)) = f10(c1)) <=> (c1 = f10(c1))),
% 29.61/19.84 inference(monotonicity,[status(thm)],[27256])).
% 29.61/19.84 tff(27392,plain,
% 29.61/19.84 ((f7(f10(c1)) = f10(c1)) <=> (f10(c1) = c1)),
% 29.61/19.84 inference(transitivity,[status(thm)],[27391, 18819])).
% 29.61/19.84 tff(27393,plain,
% 29.61/19.84 ((f10(c1) = c1) <=> (f7(f10(c1)) = f10(c1))),
% 29.61/19.84 inference(symmetry,[status(thm)],[27392])).
% 29.61/19.84 tff(27394,plain,
% 29.61/19.84 ((~(f10(c1) = c1)) <=> (~(f7(f10(c1)) = f10(c1)))),
% 29.61/19.84 inference(monotonicity,[status(thm)],[27393])).
% 29.61/19.84 tff(27395,plain,
% 29.61/19.84 (~(f7(f10(c1)) = f10(c1))),
% 29.61/19.84 inference(modus_ponens,[status(thm)],[26229, 27394])).
% 29.61/19.84 tff(27396,plain,
% 29.61/19.84 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f10(c1) = c1) | (f7(f10(c1)) = f10(c1)) | (~(f10(c1) = f5(f10(c1)))) | big_f(f7(f10(c1)), f10(c1)) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(c1) = c1) | (f7(f10(c1)) = f10(c1)) | (~(f10(c1) = f5(f10(c1)))) | big_f(f7(f10(c1)), f10(c1)) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1))))),
% 29.61/19.84 inference(rewrite,[status(thm)],[])).
% 29.61/19.84 tff(27397,plain,
% 29.61/19.84 (((~(f10(c1) = f5(f10(c1)))) | (f10(c1) = c1) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1))) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), f10(c1))) <=> ((f10(c1) = c1) | (f7(f10(c1)) = f10(c1)) | (~(f10(c1) = f5(f10(c1)))) | big_f(f7(f10(c1)), f10(c1)) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1))))),
% 29.61/19.84 inference(rewrite,[status(thm)],[])).
% 29.61/19.84 tff(27398,plain,
% 29.61/19.84 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(f10(c1) = f5(f10(c1)))) | (f10(c1) = c1) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1))) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), f10(c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f10(c1) = c1) | (f7(f10(c1)) = f10(c1)) | (~(f10(c1) = f5(f10(c1)))) | big_f(f7(f10(c1)), f10(c1)) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1)))))),
% 29.61/19.84 inference(monotonicity,[status(thm)],[27397])).
% 29.61/19.84 tff(27399,plain,
% 29.61/19.84 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(f10(c1) = f5(f10(c1)))) | (f10(c1) = c1) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1))) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), f10(c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(c1) = c1) | (f7(f10(c1)) = f10(c1)) | (~(f10(c1) = f5(f10(c1)))) | big_f(f7(f10(c1)), f10(c1)) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1))))),
% 29.61/19.84 inference(transitivity,[status(thm)],[27398, 27396])).
% 29.61/19.84 tff(27400,plain,
% 29.61/19.84 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(f10(c1) = f5(f10(c1)))) | (f10(c1) = c1) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1))) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), f10(c1)))),
% 29.61/19.84 inference(quant_inst,[status(thm)],[])).
% 29.61/19.84 tff(27401,plain,
% 29.61/19.84 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(c1) = c1) | (f7(f10(c1)) = f10(c1)) | (~(f10(c1) = f5(f10(c1)))) | big_f(f7(f10(c1)), f10(c1)) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1)))),
% 29.61/19.84 inference(modus_ponens,[status(thm)],[27400, 27399])).
% 29.61/19.84 tff(27402,plain,
% 29.61/19.84 ((~(f10(c1) = f5(f10(c1)))) | (f3(c2, c2) = f8(c1))),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[27401, 705, 26229, 27395, 27369, 27260])).
% 29.61/19.84 tff(27403,plain,
% 29.61/19.84 (~(f10(c1) = f5(f10(c1)))),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[27402, 27390])).
% 29.61/19.84 tff(27404,plain,
% 29.61/19.84 (~(f5(c2) = c2)),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[27348, 27403, 26230])).
% 29.61/19.84 tff(27405,plain,
% 29.61/19.84 (f5(c2) = c1),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[1547, 27404])).
% 29.61/19.84 tff(27406,plain,
% 29.61/19.84 (c1 = f5(f10(c1))),
% 29.61/19.84 inference(modus_ponens,[status(thm)],[27405, 26234])).
% 29.61/19.84 tff(27407,plain,
% 29.61/19.84 (big_f(f7(f10(c1)), c1) <=> big_f(c1, c1)),
% 29.61/19.84 inference(monotonicity,[status(thm)],[27256])).
% 29.61/19.84 tff(27408,plain,
% 29.61/19.84 (big_f(c1, c1) <=> big_f(f7(f10(c1)), c1)),
% 29.61/19.84 inference(symmetry,[status(thm)],[27407])).
% 29.61/19.84 tff(27409,plain,
% 29.61/19.84 ((~big_f(c1, c1)) <=> (~big_f(f7(f10(c1)), c1))),
% 29.61/19.84 inference(monotonicity,[status(thm)],[27408])).
% 29.61/19.84 tff(27410,plain,
% 29.61/19.84 (~big_f(f7(f10(c1)), c1)),
% 29.61/19.84 inference(modus_ponens,[status(thm)],[66, 27409])).
% 29.61/19.84 tff(27411,plain,
% 29.61/19.84 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f10(c1) = c1) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), c1) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1))) | (~(c1 = f5(f10(c1)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(c1) = c1) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), c1) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1))) | (~(c1 = f5(f10(c1)))))),
% 29.61/19.84 inference(rewrite,[status(thm)],[])).
% 29.61/19.84 tff(27412,plain,
% 29.61/19.84 (((~(c1 = f5(f10(c1)))) | (f10(c1) = c1) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1))) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), c1)) <=> ((f10(c1) = c1) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), c1) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1))) | (~(c1 = f5(f10(c1)))))),
% 29.61/19.84 inference(rewrite,[status(thm)],[])).
% 29.61/19.84 tff(27413,plain,
% 29.61/19.84 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c1 = f5(f10(c1)))) | (f10(c1) = c1) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1))) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), c1))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f10(c1) = c1) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), c1) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1))) | (~(c1 = f5(f10(c1))))))),
% 29.61/19.84 inference(monotonicity,[status(thm)],[27412])).
% 29.61/19.84 tff(27414,plain,
% 29.61/19.84 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c1 = f5(f10(c1)))) | (f10(c1) = c1) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1))) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), c1))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(c1) = c1) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), c1) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1))) | (~(c1 = f5(f10(c1)))))),
% 29.61/19.84 inference(transitivity,[status(thm)],[27413, 27411])).
% 29.61/19.84 tff(27415,plain,
% 29.61/19.84 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c1 = f5(f10(c1)))) | (f10(c1) = c1) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1))) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), c1))),
% 29.61/19.84 inference(quant_inst,[status(thm)],[])).
% 29.61/19.84 tff(27416,plain,
% 29.61/19.84 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(c1) = c1) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), c1) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1))) | (~(c1 = f5(f10(c1))))),
% 29.61/19.84 inference(modus_ponens,[status(thm)],[27415, 27414])).
% 29.61/19.84 tff(27417,plain,
% 29.61/19.84 (big_f(f7(f10(c1)), c1) | (f3(c2, c2) = f8(c1)) | (~(c1 = f5(f10(c1))))),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[27416, 705, 26229, 27395, 27369])).
% 29.61/19.84 tff(27418,plain,
% 29.61/19.84 (~(c1 = f5(f10(c1)))),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[27417, 27390, 27410])).
% 29.61/19.84 tff(27419,plain,
% 29.61/19.84 ($false),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[27418, 27406])).
% 29.61/19.84 tff(27420,plain,(big_f(c1, c2) | big_f(c1, c1) | (f10(c2) = c2) | (f7(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 29.61/19.84 tff(27421,plain,
% 29.61/19.84 (f10(c2) = c2),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[27420, 26227, 27, 66])).
% 29.61/19.84 tff(27422,plain,
% 29.61/19.84 (big_f(f9(c2, c2), f10(c2)) <=> big_f(f9(c2, c2), c2)),
% 29.61/19.84 inference(monotonicity,[status(thm)],[27421])).
% 29.61/19.84 tff(27423,plain,
% 29.61/19.84 (big_f(f9(c2, c2), c2) <=> big_f(f9(c2, c2), f10(c2))),
% 29.61/19.84 inference(symmetry,[status(thm)],[27422])).
% 29.61/19.84 tff(27424,plain,
% 29.61/19.84 (f7(c2) = c1),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[21, 26227])).
% 29.61/19.84 tff(27425,plain,
% 29.61/19.84 (big_f(f7(c2), c1) <=> big_f(c1, c1)),
% 29.61/19.84 inference(monotonicity,[status(thm)],[27424])).
% 29.61/19.84 tff(27426,plain,
% 29.61/19.84 (big_f(c1, c1) <=> big_f(f7(c2), c1)),
% 29.61/19.84 inference(symmetry,[status(thm)],[27425])).
% 29.61/19.84 tff(27427,plain,
% 29.61/19.84 ((~big_f(c1, c1)) <=> (~big_f(f7(c2), c1))),
% 29.61/19.84 inference(monotonicity,[status(thm)],[27426])).
% 29.61/19.84 tff(27428,plain,
% 29.61/19.84 (~big_f(f7(c2), c1)),
% 29.61/19.84 inference(modus_ponens,[status(thm)],[66, 27427])).
% 29.61/19.84 tff(27429,plain,
% 29.61/19.84 (big_f(c2, c1)),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[24323, 121, 27, 66])).
% 29.61/19.84 tff(27430,plain,
% 29.61/19.84 (big_f(f9(c1, c2), f10(c1)) <=> big_f(c2, c1)),
% 29.61/19.84 inference(monotonicity,[status(thm)],[24428, 3762])).
% 29.61/19.84 tff(27431,plain,
% 29.61/19.84 (big_f(c2, c1) <=> big_f(f9(c1, c2), f10(c1))),
% 29.61/19.84 inference(symmetry,[status(thm)],[27430])).
% 29.61/19.84 tff(27432,plain,
% 29.61/19.84 (big_f(f9(c1, c2), f10(c1))),
% 29.61/19.84 inference(modus_ponens,[status(thm)],[348, 27431])).
% 29.61/19.84 tff(27433,plain,
% 29.61/19.84 (~big_f(f9(c1, c2), f10(c1))),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[8204, 24428, 3762, 17, 1521, 5124])).
% 29.61/19.84 tff(27434,plain,
% 29.61/19.84 ($false),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[27433, 27432])).
% 29.61/19.84 tff(27435,plain,((~(c2 = f5(c2))) | (~big_f(c2, c1)) | (~(f10(c1) = c1)) | (f7(c2) = c2) | big_f(f7(c2), c2) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 29.61/19.84 tff(27436,plain,
% 29.61/19.84 (~(f10(c1) = c1)),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[27435, 5124, 66, 17, 1521, 348])).
% 29.61/19.84 tff(27437,plain,
% 29.61/19.84 (f10(c1) = c2),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[14, 27436])).
% 29.61/19.84 tff(27438,plain,
% 29.61/19.84 (big_f(f8(c1), f10(c1))),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[8107, 27436, 17, 5124, 1521])).
% 29.61/19.84 tff(27439,plain,
% 29.61/19.84 ($false),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[15724, 27438, 27437, 22, 1521, 121])).
% 29.61/19.84 tff(27440,plain,((~(c2 = f5(c2))) | big_f(f7(c2), c2) | big_f(c2, c2) | (f7(c2) = c2) | big_f(c1, c1) | (~big_f(c2, c1))), inference(lemma,lemma(discharge,[]))).
% 29.61/19.84 tff(27441,plain,
% 29.61/19.84 (~(c2 = f5(c2))),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[27440, 121, 23145, 17, 66, 27429])).
% 29.61/19.84 tff(27442,plain,
% 29.61/19.84 (~(f5(c2) = c2)),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[8113, 27441])).
% 29.61/19.84 tff(27443,plain,
% 29.61/19.84 (f5(c2) = c1),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[1547, 27442])).
% 29.61/19.84 tff(27444,plain,
% 29.61/19.84 (c1 = f5(c2)),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[8139, 27443])).
% 29.61/19.84 tff(27445,plain,
% 29.61/19.84 (~(c2 = f8(c1))),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[12137, 1745, 8451, 3, 17, 23054, 333])).
% 29.61/19.84 tff(27446,plain,
% 29.61/19.84 (~(f8(c1) = c2)),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[1675, 27445])).
% 29.61/19.84 tff(27447,plain,
% 29.61/19.84 (~(c1 = f8(c1))),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[12149, 1745, 3, 17, 15821, 23054, 333])).
% 29.61/19.84 tff(27448,plain,
% 29.61/19.84 (~(f8(c1) = c1)),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[9808, 27447])).
% 29.61/19.84 tff(27449,plain,
% 29.61/19.84 ($false),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[1680, 27448, 27446])).
% 29.61/19.84 tff(27450,plain,((f10(c1) = c1) | (f7(c2) = c2) | (~(c1 = f5(c2))) | big_f(f7(c2), c1) | big_f(c1, c2) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 29.61/19.84 tff(27451,plain,
% 29.61/19.84 (f10(c1) = c1),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[27450, 27444, 17, 12093, 27, 121])).
% 29.61/19.84 tff(27452,plain,
% 29.61/19.84 (~(c2 = f5(c2))),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[24427, 4236, 17, 3762, 1521, 66])).
% 29.61/19.84 tff(27453,plain,
% 29.61/19.84 (~(f5(c2) = c2)),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[8113, 27452])).
% 29.61/19.84 tff(27454,plain,
% 29.61/19.84 (~(c1 = f5(c2))),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[24451, 4236, 3762, 17, 66, 12093])).
% 29.61/19.84 tff(27455,plain,
% 29.61/19.84 (~(f5(c2) = c1)),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[8139, 27454])).
% 29.61/19.84 tff(27456,plain,
% 29.61/19.84 ($false),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[1547, 27455, 27453])).
% 29.61/19.84 tff(27457,plain,((f9(c1, c2) = c2) | (~(f10(c1) = c1)) | (f7(c2) = c2) | big_f(c1, c1) | big_f(f7(c2), c2)), inference(lemma,lemma(discharge,[]))).
% 29.61/19.84 tff(27458,plain,
% 29.61/19.84 (f9(c1, c2) = c2),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[27457, 27451, 66, 17, 23145])).
% 29.61/19.84 tff(27459,plain,
% 29.61/19.84 (big_f(f9(c1, c2), f10(c1)) <=> big_f(c2, c1)),
% 29.61/19.84 inference(monotonicity,[status(thm)],[27458, 27451])).
% 29.61/19.84 tff(27460,plain,
% 29.61/19.84 (big_f(c2, c1) <=> big_f(f9(c1, c2), f10(c1))),
% 29.61/19.84 inference(symmetry,[status(thm)],[27459])).
% 29.61/19.84 tff(27461,plain,
% 29.61/19.84 (big_f(f9(c1, c2), f10(c1))),
% 29.61/19.84 inference(modus_ponens,[status(thm)],[27429, 27460])).
% 29.61/19.84 tff(27462,plain,
% 29.61/19.84 ($false),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[23139, 783, 27451, 17, 27461, 27458, 27444, 12093])).
% 29.61/19.84 tff(27463,plain,(big_f(c2, c2) | (f7(c2) = c2) | big_f(c1, c1) | big_f(c1, c2)), inference(lemma,lemma(discharge,[]))).
% 29.61/19.84 tff(27464,plain,
% 29.61/19.84 (big_f(c2, c2)),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[27463, 26227, 66, 27])).
% 29.61/19.84 tff(27465,plain,
% 29.61/19.84 (big_f(f9(c2, c2), c2)),
% 29.61/19.84 inference(modus_ponens,[status(thm)],[1345, 25602])).
% 29.61/19.84 tff(27466,plain,
% 29.61/19.84 (big_f(f7(c2), c1) | (~(f10(c2) = c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f7(c2) = c2)),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[9277, 25791])).
% 29.61/19.84 tff(27467,plain,
% 29.61/19.84 (~big_f(f9(c2, c2), f10(c2))),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[27466, 1572, 122, 17, 333])).
% 29.61/19.84 tff(27468,plain,
% 29.61/19.84 (~big_f(f9(c2, c2), c2)),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[6482, 27467, 122])).
% 29.61/19.84 tff(27469,plain,
% 29.61/19.84 ($false),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[27468, 27465])).
% 29.61/19.84 tff(27470,plain,((~(f9(c2, c2) = c2)) | (~big_f(c2, c2)) | (~(f10(c2) = c2)) | (f7(c2) = c2) | big_f(f7(c2), c1)), inference(lemma,lemma(discharge,[]))).
% 29.61/19.84 tff(27471,plain,
% 29.61/19.84 (~(f9(c2, c2) = c2)),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[27470, 27464, 27421, 26227, 27428])).
% 29.61/19.84 tff(27472,plain,
% 29.61/19.84 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f9(c2, c2) = c1) | (f9(c2, c2) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f9(c2, c2) = c1) | (f9(c2, c2) = c2))),
% 29.61/19.84 inference(rewrite,[status(thm)],[])).
% 29.61/19.84 tff(27473,plain,
% 29.61/19.84 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f9(c2, c2) = c1) | (f9(c2, c2) = c2))),
% 29.61/19.84 inference(quant_inst,[status(thm)],[])).
% 29.61/19.84 tff(27474,plain,
% 29.61/19.84 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f9(c2, c2) = c1) | (f9(c2, c2) = c2)),
% 29.61/19.84 inference(modus_ponens,[status(thm)],[27473, 27472])).
% 29.61/19.84 tff(27475,plain,
% 29.61/19.84 ((f9(c2, c2) = c1) | (f9(c2, c2) = c2)),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[27474, 10])).
% 29.61/19.84 tff(27476,plain,
% 29.61/19.84 (f9(c2, c2) = c1),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[27475, 27471])).
% 29.61/19.84 tff(27477,plain,
% 29.61/19.84 (big_f(f9(c2, c2), c2) <=> big_f(c1, c2)),
% 29.61/19.84 inference(monotonicity,[status(thm)],[27476])).
% 29.61/19.84 tff(27478,plain,
% 29.61/19.84 (big_f(c1, c2) <=> big_f(f9(c2, c2), c2)),
% 29.61/19.84 inference(symmetry,[status(thm)],[27477])).
% 29.61/19.84 tff(27479,plain,
% 29.61/19.84 (big_f(c1, c2) <=> big_f(f9(c2, c2), f10(c2))),
% 29.61/19.84 inference(transitivity,[status(thm)],[27478, 27423])).
% 29.61/19.84 tff(27480,plain,
% 29.61/19.84 ((~big_f(c1, c2)) <=> (~big_f(f9(c2, c2), f10(c2)))),
% 29.61/19.84 inference(monotonicity,[status(thm)],[27479])).
% 29.61/19.84 tff(27481,plain,
% 29.61/19.84 (~big_f(f9(c2, c2), f10(c2))),
% 29.61/19.84 inference(modus_ponens,[status(thm)],[27, 27480])).
% 29.61/19.84 tff(27482,plain,
% 29.61/19.84 (~(c1 = f5(c2))),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[23101, 267, 27421, 26227, 27428, 27471, 27481])).
% 29.61/19.84 tff(27483,plain,
% 29.61/19.84 (~(f5(c2) = c1)),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[8139, 27482])).
% 29.61/19.84 tff(27484,plain,
% 29.61/19.84 (~big_f(f7(c2), c2)),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[21127, 27424, 27])).
% 29.61/19.84 tff(27485,plain,
% 29.61/19.84 (~(c2 = f5(c2))),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[1527, 267, 27421, 26227, 27484, 27471, 27481])).
% 29.61/19.84 tff(27486,plain,
% 29.61/19.84 (~(f5(c2) = c2)),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[8113, 27485])).
% 29.61/19.84 tff(27487,plain,
% 29.61/19.84 ($false),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[1547, 27486, 27483])).
% 29.61/19.84 tff(27488,plain,(big_f(c1, c1) | big_f(c1, c2) | (~(c3 = c2))), inference(lemma,lemma(discharge,[]))).
% 29.61/19.84 tff(27489,plain,
% 29.61/19.84 (big_f(c1, c1)),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[27488, 67, 27])).
% 29.61/19.84 tff(27490,assumption,(f6(c1, f6(c1, c2)) = c2), introduced(assumption)).
% 29.61/19.84 tff(27491,plain,
% 29.61/19.84 (~(c4 = c1)),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[11545, 27, 168, 79, 4932])).
% 29.61/19.84 tff(27492,plain,
% 29.61/19.84 (c4 = c2),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[461, 27491])).
% 29.61/19.84 tff(27493,plain,
% 29.61/19.84 (c2 = c4),
% 29.61/19.84 inference(symmetry,[status(thm)],[27492])).
% 29.61/19.84 tff(27494,plain,
% 29.61/19.84 (f4(c2) = f4(c4)),
% 29.61/19.84 inference(monotonicity,[status(thm)],[27493])).
% 29.61/19.84 tff(27495,plain,
% 29.61/19.84 (f4(c4) = f4(c2)),
% 29.61/19.84 inference(symmetry,[status(thm)],[27494])).
% 29.61/19.84 tff(27496,plain,
% 29.61/19.84 (c2 = f4(c2)),
% 29.61/19.84 inference(transitivity,[status(thm)],[436, 27495])).
% 29.61/19.84 tff(27497,plain,
% 29.61/19.84 (c2 = c4),
% 29.61/19.84 inference(modus_ponens,[status(thm)],[27492, 159])).
% 29.61/19.84 tff(27498,plain,
% 29.61/19.84 (f1(c1, c1) = c1),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[9763, 27496, 121, 27, 27497, 168])).
% 29.61/19.84 tff(27499,plain,
% 29.61/19.84 (big_f(c1, f1(c1, c1))),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[9678, 27498, 4932])).
% 29.61/19.84 tff(27500,plain,
% 29.61/19.84 ($false),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[11560, 447, 27498, 168, 27499, 27497, 27496, 121])).
% 29.61/19.84 tff(27501,plain,(big_f(c1, c2) | (c1 = c3) | big_f(c2, c2) | (~big_f(c1, c1)) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.61/19.84 tff(27502,plain,
% 29.61/19.84 (~(f4(c4) = c2)),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[27501, 121, 76, 27489, 27])).
% 29.61/19.84 tff(27503,plain,
% 29.61/19.84 (f4(c4) = c1),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[11750, 27502])).
% 29.61/19.84 tff(27504,plain,
% 29.61/19.84 ((f4(c4) = c3) <=> (f4(c4) = c2)),
% 29.61/19.84 inference(monotonicity,[status(thm)],[67])).
% 29.61/19.84 tff(27505,plain,
% 29.61/19.84 ((f4(c4) = c3) <=> (c2 = f4(c4))),
% 29.61/19.84 inference(transitivity,[status(thm)],[27504, 2601])).
% 29.61/19.84 tff(27506,plain,
% 29.61/19.84 ((c2 = f4(c4)) <=> (f4(c4) = c3)),
% 29.61/19.84 inference(symmetry,[status(thm)],[27505])).
% 29.61/19.84 tff(27507,plain,
% 29.61/19.84 ((c2 = f4(c4)) <=> (c2 = c1)),
% 29.61/19.84 inference(monotonicity,[status(thm)],[27503])).
% 29.61/19.84 tff(27508,plain,
% 29.61/19.84 ((c2 = c1) <=> (c2 = f4(c4))),
% 29.61/19.84 inference(symmetry,[status(thm)],[27507])).
% 29.61/19.84 tff(27509,plain,
% 29.61/19.84 ((c2 = c1) <=> (f4(c4) = c3)),
% 29.61/19.84 inference(transitivity,[status(thm)],[27508, 27506])).
% 29.61/19.84 tff(27510,plain,
% 29.61/19.84 ((~(c2 = c1)) <=> (~(f4(c4) = c3))),
% 29.61/19.84 inference(monotonicity,[status(thm)],[27509])).
% 29.61/19.84 tff(27511,plain,
% 29.61/19.84 (~(f4(c4) = c3)),
% 29.61/19.84 inference(modus_ponens,[status(thm)],[75, 27510])).
% 29.61/19.84 tff(27512,plain,
% 29.61/19.84 (~big_f(c2, c1)),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[23034, 27511, 76, 27, 27489, 27503])).
% 29.61/19.84 tff(27513,plain,
% 29.61/19.84 ((c1 = c4) <=> (c1 = c2)),
% 29.61/19.84 inference(monotonicity,[status(thm)],[431])).
% 29.61/19.84 tff(27514,plain,
% 29.61/19.84 ((c1 = c4) <=> (c2 = c1)),
% 29.61/19.84 inference(transitivity,[status(thm)],[27513, 1])).
% 29.61/19.84 tff(27515,plain,
% 29.61/19.84 ((c2 = c1) <=> (c1 = c4)),
% 29.61/19.84 inference(symmetry,[status(thm)],[27514])).
% 29.61/19.84 tff(27516,plain,
% 29.61/19.84 ((~(c2 = c1)) <=> (~(c1 = c4))),
% 29.61/19.84 inference(monotonicity,[status(thm)],[27515])).
% 29.61/19.84 tff(27517,plain,
% 29.61/19.84 (~(c1 = c4)),
% 29.61/19.84 inference(modus_ponens,[status(thm)],[75, 27516])).
% 29.61/19.84 tff(27518,plain,
% 29.61/19.84 (big_f(f3(c1, c1), c1)),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[1482, 1431, 1286, 482, 67])).
% 29.61/19.84 tff(27519,plain,
% 29.61/19.84 ($false),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[27518, 9672])).
% 29.61/19.84 tff(27520,plain,((f3(c1, c1) = c1) | big_f(c2, c1) | big_f(c3, f2(c3)) | (c1 = c4) | (~(c3 = c2))), inference(lemma,lemma(discharge,[]))).
% 29.61/19.84 tff(27521,plain,
% 29.61/19.84 (f3(c1, c1) = c1),
% 29.61/19.84 inference(unit_resolution,[status(thm)],[27520, 27517, 8257, 2, 67])).
% 29.61/19.84 tff(27522,plain,
% 29.61/19.84 (big_f(f3(c1, c1), c1) <=> big_f(c1, c1)),
% 29.61/19.85 inference(monotonicity,[status(thm)],[27521])).
% 29.61/19.85 tff(27523,plain,
% 29.61/19.85 (big_f(c1, c1) <=> big_f(f3(c1, c1), c1)),
% 29.61/19.85 inference(symmetry,[status(thm)],[27522])).
% 29.61/19.85 tff(27524,plain,
% 29.61/19.85 (big_f(f3(c1, c1), c1)),
% 29.61/19.85 inference(modus_ponens,[status(thm)],[4932, 27523])).
% 29.61/19.85 tff(27525,plain,
% 29.61/19.85 (~(f2(c3) = c1)),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[1424, 27524, 8257, 431, 67])).
% 29.61/19.85 tff(27526,plain,
% 29.61/19.85 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (c1 = c4) | (~big_f(f3(c1, c1), c1)) | (~(f3(c1, c1) = c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (c1 = c4) | (~big_f(f3(c1, c1), c1)) | (~(f3(c1, c1) = c1)))),
% 29.61/19.85 inference(rewrite,[status(thm)],[])).
% 29.61/19.85 tff(27527,plain,
% 29.61/19.85 (((~(c2 = c3)) | (~(c2 = f2(c2))) | (c1 = c4) | (~(f3(c1, c1) = c1)) | (~big_f(f3(c1, c1), c1)) | big_f(c2, c2)) <=> ((~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (c1 = c4) | (~big_f(f3(c1, c1), c1)) | (~(f3(c1, c1) = c1)))),
% 29.61/19.85 inference(rewrite,[status(thm)],[])).
% 29.61/19.85 tff(27528,plain,
% 29.61/19.85 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | (c1 = c4) | (~(f3(c1, c1) = c1)) | (~big_f(f3(c1, c1), c1)) | big_f(c2, c2))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (c1 = c4) | (~big_f(f3(c1, c1), c1)) | (~(f3(c1, c1) = c1))))),
% 29.61/19.85 inference(monotonicity,[status(thm)],[27527])).
% 29.61/19.85 tff(27529,plain,
% 29.61/19.85 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | (c1 = c4) | (~(f3(c1, c1) = c1)) | (~big_f(f3(c1, c1), c1)) | big_f(c2, c2))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (c1 = c4) | (~big_f(f3(c1, c1), c1)) | (~(f3(c1, c1) = c1)))),
% 29.61/19.85 inference(transitivity,[status(thm)],[27528, 27526])).
% 29.61/19.85 tff(27530,plain,
% 29.61/19.85 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | (c1 = c4) | (~(f3(c1, c1) = c1)) | (~big_f(f3(c1, c1), c1)) | big_f(c2, c2))),
% 29.61/19.85 inference(quant_inst,[status(thm)],[])).
% 29.61/19.85 tff(27531,plain,
% 29.61/19.85 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (c1 = c4) | (~big_f(f3(c1, c1), c1)) | (~(f3(c1, c1) = c1))),
% 29.61/19.85 inference(modus_ponens,[status(thm)],[27530, 27529])).
% 29.61/19.85 tff(27532,plain,
% 29.61/19.85 (~(c2 = f2(c2))),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[27531, 1398, 27524, 27521, 27517, 121, 1335])).
% 29.61/19.85 tff(27533,plain,
% 29.61/19.85 (~(f2(c3) = c2)),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[4867, 27532, 67])).
% 29.61/19.85 tff(27534,plain,
% 29.61/19.85 ($false),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[1273, 27533, 27525])).
% 29.61/19.85 tff(27535,plain,((~(c4 = c2)) | (~(c3 = c2)) | big_f(c2, c2) | (~big_f(c1, c1)) | big_f(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 29.61/19.85 tff(27536,plain,
% 29.61/19.85 (~(c4 = c2)),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[27535, 27512, 27489, 121, 67])).
% 29.61/19.85 tff(27537,plain,
% 29.61/19.85 (c4 = c1),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[461, 27536])).
% 29.61/19.85 tff(27538,plain,
% 29.61/19.85 (~big_f(c3, f2(c3))),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[8256, 27512, 67, 121])).
% 29.61/19.85 tff(27539,plain,
% 29.61/19.85 (big_f(f4(c4), c4)),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[1315, 27538])).
% 29.61/19.85 tff(27540,plain,
% 29.61/19.85 (~(f4(c4) = c2)),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[27501, 121, 168, 4932, 27])).
% 29.61/19.85 tff(27541,plain,
% 29.61/19.85 (f4(c4) = c1),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[11750, 27540])).
% 29.61/19.85 tff(27542,plain,
% 29.61/19.85 (big_f(f7(c2), f7(c2))),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[17136, 22, 27541, 474, 480])).
% 29.61/19.85 tff(27543,plain,
% 29.61/19.85 (big_f(f7(c2), c1)),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[8374, 27542, 22])).
% 29.61/19.85 tff(27544,plain,
% 29.61/19.85 ((f10(c1) = c1) | big_f(c2, c2) | (~big_f(f7(c2), c1)) | big_f(c1, c2) | (f7(c2) = c2)),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[26351, 25791])).
% 29.61/19.85 tff(27545,plain,
% 29.61/19.85 (f10(c1) = c1),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[27544, 27543, 17, 27, 121])).
% 29.61/19.85 tff(27546,plain,
% 29.61/19.85 (~big_f(c2, c1)),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[23034, 18059, 168, 27, 4932, 27541])).
% 29.61/19.85 tff(27547,plain,
% 29.61/19.85 (~big_f(f4(c4), c4)),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[11772, 66, 27, 11752])).
% 29.61/19.85 tff(27548,plain,
% 29.61/19.85 (f1(f4(c4), c1) = c1),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[18077, 22986, 18059, 379])).
% 29.61/19.85 tff(27549,plain,
% 29.61/19.85 (f1(c1, c1) = c1),
% 29.61/19.85 inference(modus_ponens,[status(thm)],[27548, 18065])).
% 29.61/19.85 tff(27550,plain,
% 29.61/19.85 ($false),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[9710, 27549])).
% 29.61/19.85 tff(27551,plain,((f1(c1, c1) = c1) | (~(f4(c4) = c1)) | (f4(c4) = c3) | big_f(f4(c4), c4) | big_f(c1, c2)), inference(lemma,lemma(discharge,[]))).
% 29.61/19.85 tff(27552,plain,
% 29.61/19.85 (f1(c1, c1) = c1),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[27551, 27547, 11752, 18059, 27])).
% 29.61/19.85 tff(27553,plain,
% 29.61/19.85 (f1(f9(c1, c1), c1) = f1(c1, c1)),
% 29.61/19.85 inference(monotonicity,[status(thm)],[3949])).
% 29.61/19.85 tff(27554,plain,
% 29.61/19.85 ((f1(f9(c1, c1), c1) = c1) <=> (f1(c1, c1) = c1)),
% 29.61/19.85 inference(monotonicity,[status(thm)],[27553])).
% 29.61/19.85 tff(27555,plain,
% 29.61/19.85 ((f1(c1, c1) = c1) <=> (f1(f9(c1, c1), c1) = c1)),
% 29.61/19.85 inference(symmetry,[status(thm)],[27554])).
% 29.61/19.85 tff(27556,plain,
% 29.61/19.85 (f1(f9(c1, c1), c1) = c1),
% 29.61/19.85 inference(modus_ponens,[status(thm)],[624, 27555])).
% 29.61/19.85 tff(27557,plain,
% 29.61/19.85 ($false),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[19685, 27556])).
% 29.61/19.85 tff(27558,plain,((~(f1(c1, c1) = c1)) | (f1(f9(c1, c1), c1) = c1) | (~(f9(c1, c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.61/19.85 tff(27559,plain,
% 29.61/19.85 (f1(f9(c1, c1), c1) = c1),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[27558, 27552, 3949])).
% 29.61/19.85 tff(27560,plain,
% 29.61/19.85 (big_f(f9(c1, c1), f1(f9(c1, c1), c1)) <=> big_f(c1, f1(c1, c1))),
% 29.61/19.85 inference(monotonicity,[status(thm)],[3949, 27553])).
% 29.61/19.85 tff(27561,plain,
% 29.61/19.85 (big_f(c1, f1(c1, c1)) <=> big_f(f9(c1, c1), f1(f9(c1, c1), c1))),
% 29.61/19.85 inference(symmetry,[status(thm)],[27560])).
% 29.61/19.85 tff(27562,plain,
% 29.61/19.85 (big_f(c1, f1(c1, c1)) <=> big_f(c1, c1)),
% 29.61/19.85 inference(monotonicity,[status(thm)],[27552])).
% 29.61/19.85 tff(27563,plain,
% 29.61/19.85 (big_f(c1, c1) <=> big_f(c1, f1(c1, c1))),
% 29.61/19.85 inference(symmetry,[status(thm)],[27562])).
% 29.61/19.85 tff(27564,plain,
% 29.61/19.85 (big_f(c1, c1) <=> big_f(f9(c1, c1), f1(f9(c1, c1), c1))),
% 29.61/19.85 inference(transitivity,[status(thm)],[27563, 27561])).
% 29.61/19.85 tff(27565,plain,
% 29.61/19.85 ((~big_f(c1, c1)) <=> (~big_f(f9(c1, c1), f1(f9(c1, c1), c1)))),
% 29.61/19.85 inference(monotonicity,[status(thm)],[27564])).
% 29.61/19.85 tff(27566,plain,
% 29.61/19.85 (~big_f(f9(c1, c1), f1(f9(c1, c1), c1))),
% 29.61/19.85 inference(modus_ponens,[status(thm)],[66, 27565])).
% 29.61/19.85 tff(27567,plain,
% 29.61/19.85 (~big_f(f9(c1, c1), c1)),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[10153, 27566, 27559])).
% 29.61/19.85 tff(27568,plain,
% 29.61/19.85 (~big_f(f7(c2), c1)),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[26966, 27567, 22, 24326])).
% 29.61/19.85 tff(27569,plain,
% 29.61/19.85 (~(c2 = f5(c2))),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[27435, 24326, 3762, 17, 23145, 66])).
% 29.61/19.85 tff(27570,plain,
% 29.61/19.85 (~(f5(c2) = c2)),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[8113, 27569])).
% 29.61/19.85 tff(27571,plain,
% 29.61/19.85 (f5(c2) = c1),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[1547, 27570])).
% 29.61/19.85 tff(27572,plain,
% 29.61/19.85 (c1 = f5(c2)),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[8139, 27571])).
% 29.61/19.85 tff(27573,plain,
% 29.61/19.85 (f9(c1, c2) = c2),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[24451, 66, 3762, 17, 27568, 27572])).
% 29.61/19.85 tff(27574,plain,
% 29.61/19.85 (big_f(f9(c1, c2), f10(c1)) <=> big_f(c2, c1)),
% 29.61/19.85 inference(monotonicity,[status(thm)],[27573, 3762])).
% 29.61/19.85 tff(27575,plain,
% 29.61/19.85 (big_f(c2, c1) <=> big_f(f9(c1, c2), f10(c1))),
% 29.61/19.85 inference(symmetry,[status(thm)],[27574])).
% 29.61/19.85 tff(27576,plain,
% 29.61/19.85 (big_f(f9(c1, c2), f10(c1))),
% 29.61/19.85 inference(modus_ponens,[status(thm)],[24326, 27575])).
% 29.61/19.85 tff(27577,plain,
% 29.61/19.85 ($false),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[23139, 783, 3762, 17, 27576, 27573, 27572, 27568])).
% 29.61/19.85 tff(27578,plain,(big_f(c1, c1) | (~(f10(c1) = c1)) | (f7(c2) = c2) | (~(f9(c1, c1) = c1)) | (~(f4(c4) = c1)) | (f4(c4) = c3) | big_f(c1, c2) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 29.61/19.85 tff(27579,plain,
% 29.61/19.85 (big_f(c1, c1)),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[27578, 17, 3762, 3949, 11752, 18059, 27, 121])).
% 29.61/19.85 tff(27580,plain,
% 29.61/19.85 (big_f(f9(c1, c1), c1)),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[10938, 27579, 3949])).
% 29.61/19.85 tff(27581,plain,
% 29.61/19.85 (big_f(f9(c1, c1), f10(c1))),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[8716, 27580, 3762])).
% 29.61/19.85 tff(27582,plain,
% 29.61/19.85 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))),
% 29.61/19.85 inference(rewrite,[status(thm)],[])).
% 29.61/19.85 tff(27583,plain,
% 29.61/19.85 (((~(f10(c1) = c1)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(c2 = f5(c2)))) <=> ((f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))),
% 29.61/19.85 inference(rewrite,[status(thm)],[])).
% 29.61/19.85 tff(27584,plain,
% 29.61/19.85 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(c2 = f5(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1)))))),
% 29.61/19.85 inference(monotonicity,[status(thm)],[27583])).
% 29.61/19.85 tff(27585,plain,
% 29.61/19.85 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(c2 = f5(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))),
% 29.61/19.85 inference(transitivity,[status(thm)],[27584, 27582])).
% 29.61/19.85 tff(27586,plain,
% 29.61/19.85 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(c2 = f5(c2))))),
% 29.61/19.85 inference(quant_inst,[status(thm)],[])).
% 29.61/19.85 tff(27587,plain,
% 29.61/19.85 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(X5 = f5(X4))))) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1)))),
% 29.61/19.85 inference(modus_ponens,[status(thm)],[27586, 27585])).
% 29.61/19.85 tff(27588,plain,
% 29.61/19.85 ((~(c2 = f5(c2))) | (~big_f(f9(c1, c1), f10(c1)))),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[27587, 783, 3762, 17, 23145, 3949])).
% 29.61/19.85 tff(27589,plain,
% 29.61/19.85 (~(c2 = f5(c2))),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[27588, 27581])).
% 29.61/19.85 tff(27590,plain,
% 29.61/19.85 (~(f5(c2) = c2)),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[8113, 27589])).
% 29.61/19.85 tff(27591,plain,
% 29.61/19.85 (f5(c2) = c1),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[1547, 27590])).
% 29.61/19.85 tff(27592,plain,
% 29.61/19.85 (f7(c2) = f5(c2)),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[8394, 27591, 22])).
% 29.61/19.85 tff(27593,plain,
% 29.61/19.85 (big_f(f7(c2), f6(c1, c1)) <=> big_f(c1, f6(c1, c1))),
% 29.61/19.85 inference(monotonicity,[status(thm)],[22])).
% 29.61/19.85 tff(27594,plain,
% 29.61/19.85 (big_f(c1, f6(c1, c1)) <=> big_f(f7(c2), f6(c1, c1))),
% 29.61/19.85 inference(symmetry,[status(thm)],[27593])).
% 29.61/19.85 tff(27595,plain,
% 29.61/19.85 (big_f(c1, f6(c1, c1)) <=> big_f(f7(c1), f6(c1, c1))),
% 29.61/19.85 inference(monotonicity,[status(thm)],[5544])).
% 29.61/19.85 tff(27596,plain,
% 29.61/19.85 (big_f(f7(c1), f6(c1, c1)) <=> big_f(c1, f6(c1, c1))),
% 29.61/19.85 inference(symmetry,[status(thm)],[27595])).
% 29.61/19.85 tff(27597,plain,
% 29.61/19.85 (big_f(f7(c1), f6(c1, c1)) <=> big_f(f7(c2), f6(c1, c1))),
% 29.61/19.85 inference(transitivity,[status(thm)],[27596, 27594])).
% 29.61/19.85 tff(27598,plain,
% 29.61/19.85 (~big_f(c2, c1)),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[23034, 27579, 168, 18059, 27, 11752])).
% 29.61/19.85 tff(27599,plain,
% 29.61/19.85 (~big_f(c3, f2(c3))),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[8256, 27598, 121, 181])).
% 29.61/19.85 tff(27600,plain,
% 29.61/19.85 (big_f(f4(c4), c4)),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[1315, 27599])).
% 29.61/19.85 tff(27601,plain,
% 29.61/19.85 (~(c4 = c2)),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[11764, 27600, 11752, 27])).
% 29.61/19.85 tff(27602,plain,
% 29.61/19.85 (c4 = c1),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[461, 27601])).
% 29.61/19.85 tff(27603,plain,
% 29.61/19.85 (big_f(f7(c2), f7(c2))),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[17136, 27602, 11752, 22, 27600])).
% 29.61/19.85 tff(27604,plain,
% 29.61/19.85 (big_f(f7(c2), c1)),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[8374, 27603, 22])).
% 29.61/19.85 tff(27605,plain,
% 29.61/19.85 (big_f(f7(c1), f6(c1, c1))),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[9976, 27604, 3949, 4234, 22, 3762])).
% 29.61/19.85 tff(27606,plain,
% 29.61/19.85 (big_f(f7(c2), f6(c1, c1))),
% 29.61/19.85 inference(modus_ponens,[status(thm)],[27605, 27597])).
% 29.61/19.85 tff(27607,plain,
% 29.61/19.85 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((f7(c2) = c2) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (f7(c2) = c2) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))))),
% 29.61/19.85 inference(rewrite,[status(thm)],[])).
% 29.61/19.85 tff(27608,plain,
% 29.61/19.85 (((~(f10(c1) = c1)) | (f7(c2) = c2) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1)))) <=> ((f7(c2) = c2) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))))),
% 29.61/19.85 inference(rewrite,[status(thm)],[])).
% 29.61/19.85 tff(27609,plain,
% 29.61/19.85 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c1) = c1)) | (f7(c2) = c2) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((f7(c2) = c2) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1)))))),
% 29.61/19.85 inference(monotonicity,[status(thm)],[27608])).
% 29.61/19.85 tff(27610,plain,
% 29.61/19.85 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c1) = c1)) | (f7(c2) = c2) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (f7(c2) = c2) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))))),
% 29.61/19.85 inference(transitivity,[status(thm)],[27609, 27607])).
% 29.61/19.85 tff(27611,plain,
% 29.61/19.85 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c1) = c1)) | (f7(c2) = c2) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))))),
% 29.61/19.85 inference(quant_inst,[status(thm)],[])).
% 29.61/19.85 tff(27612,plain,
% 29.61/19.85 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (f7(c2) = c2) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1)))),
% 29.61/19.85 inference(modus_ponens,[status(thm)],[27611, 27610])).
% 29.61/19.85 tff(27613,plain,
% 29.61/19.85 (f6(c1, c1) = f5(c2)),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[27612, 1190, 3762, 17, 3949, 27581, 27606])).
% 29.61/19.85 tff(27614,plain,
% 29.61/19.85 (~(f6(c1, c1) = c1)),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[18907, 2378, 4234, 3762, 3949, 27581, 27605])).
% 29.61/19.85 tff(27615,plain,
% 29.61/19.85 ($false),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[10715, 27614, 27613, 22, 27592])).
% 29.61/19.85 tff(27616,plain,((f7(c2) = c2) | (~(f7(c1) = c1)) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~(f4(c4) = c1)) | big_f(c1, c2) | big_f(c2, c2) | (c1 = c3) | (f4(c4) = c3)), inference(lemma,lemma(discharge,[]))).
% 29.61/19.85 tff(27617,plain,
% 29.61/19.85 (f7(c2) = c2),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[27616, 27, 3762, 3949, 11752, 4234, 121, 168, 18059])).
% 29.61/19.85 tff(27618,plain,
% 29.61/19.85 (big_f(c1, c1)),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[24328, 27617, 3762, 121, 27])).
% 29.61/19.85 tff(27619,plain,
% 29.61/19.85 (~big_f(c2, c1)),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[23034, 27618, 168, 18059, 27, 11752])).
% 29.61/19.85 tff(27620,plain,
% 29.61/19.85 (f6(c2, f4(c4)) = f6(c2, c1)),
% 29.61/19.85 inference(monotonicity,[status(thm)],[11752])).
% 29.61/19.85 tff(27621,plain,
% 29.61/19.85 ((f6(c2, f4(c4)) = f4(c4)) <=> (f6(c2, c1) = c1)),
% 29.61/19.85 inference(monotonicity,[status(thm)],[27620, 11752])).
% 29.61/19.85 tff(27622,plain,
% 29.61/19.85 (~(f6(c2, f7(f4(c4))) = c1)),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[26572, 3198, 4234, 11752])).
% 29.61/19.85 tff(27623,plain,
% 29.61/19.85 (f6(c2, f7(f4(c4))) = c2),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[6601, 27622])).
% 29.61/19.85 tff(27624,plain,
% 29.61/19.85 (f6(c2, c1) = c2),
% 29.61/19.85 inference(transitivity,[status(thm)],[26491, 27623])).
% 29.61/19.85 tff(27625,plain,
% 29.61/19.85 (big_f(c2, f6(c2, c1)) <=> big_f(c2, c2)),
% 29.61/19.85 inference(monotonicity,[status(thm)],[27624])).
% 29.61/19.85 tff(27626,plain,
% 29.61/19.85 (big_f(c2, c2) <=> big_f(c2, f6(c2, c1))),
% 29.61/19.85 inference(symmetry,[status(thm)],[27625])).
% 29.61/19.85 tff(27627,plain,
% 29.61/19.85 (big_f(c2, c2) <=> big_f(f7(c2), f6(c2, c1))),
% 29.61/19.85 inference(transitivity,[status(thm)],[27626, 13581])).
% 29.61/19.85 tff(27628,plain,
% 29.61/19.85 ((~big_f(c2, c2)) <=> (~big_f(f7(c2), f6(c2, c1)))),
% 29.61/19.85 inference(monotonicity,[status(thm)],[27627])).
% 29.61/19.85 tff(27629,plain,
% 29.61/19.85 (~big_f(f7(c2), f6(c2, c1))),
% 29.61/19.85 inference(modus_ponens,[status(thm)],[121, 27628])).
% 29.61/19.85 tff(27630,plain,
% 29.61/19.85 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)))),
% 29.61/19.85 inference(rewrite,[status(thm)],[])).
% 29.61/19.85 tff(27631,plain,
% 29.61/19.85 (((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1))) <=> ((~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)))),
% 29.61/19.85 inference(rewrite,[status(thm)],[])).
% 29.61/19.85 tff(27632,plain,
% 29.61/19.85 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1))))),
% 29.61/19.85 inference(monotonicity,[status(thm)],[27631])).
% 29.61/19.85 tff(27633,plain,
% 29.61/19.85 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)))),
% 29.61/19.85 inference(transitivity,[status(thm)],[27632, 27630])).
% 29.61/19.85 tff(27634,plain,
% 29.61/19.85 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)))),
% 29.61/19.85 inference(quant_inst,[status(thm)],[])).
% 29.61/19.85 tff(27635,plain,
% 29.61/19.85 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1))),
% 29.61/19.85 inference(modus_ponens,[status(thm)],[27634, 27633])).
% 29.61/19.85 tff(27636,plain,
% 29.61/19.85 ($false),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[27635, 2492, 3762, 77, 3198, 3197, 4070, 8712])).
% 29.61/19.85 tff(27637,plain,((f6(c2, c1) = c1) | (~(f10(c1) = c1)) | (~(f7(c2) = c2)) | big_f(f7(c2), f6(c2, c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1))), inference(lemma,lemma(discharge,[]))).
% 29.61/19.85 tff(27638,plain,
% 29.61/19.85 (big_f(f9(c1, c1), f10(c1))),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[27637, 4070, 77, 3762, 3198, 3197])).
% 29.61/19.85 tff(27639,plain,
% 29.61/19.85 ($false),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[10033, 24691, 27638, 3762])).
% 29.61/19.85 tff(27640,plain,((f9(c1, c1) = c1) | (~(f10(c1) = c1)) | big_f(c2, c1) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1))), inference(lemma,lemma(discharge,[]))).
% 29.61/19.85 tff(27641,plain,
% 29.61/19.85 (f9(c1, c1) = c1),
% 29.61/19.85 inference(unit_resolution,[status(thm)],[27640, 3198, 2, 77, 3762, 27629])).
% 29.61/19.85 tff(27642,plain,
% 29.61/19.85 (big_f(f7(c2), f6(c2, f4(c4))) <=> big_f(f7(c2), f6(c2, c1))),
% 29.61/19.85 inference(monotonicity,[status(thm)],[27620])).
% 29.61/19.85 tff(27643,plain,
% 29.61/19.85 (big_f(f7(c2), f6(c2, c1)) <=> big_f(f7(c2), f6(c2, f4(c4)))),
% 29.61/19.85 inference(symmetry,[status(thm)],[27642])).
% 29.61/19.85 tff(27644,plain,
% 29.61/19.85 (big_f(c2, c2) <=> big_f(f7(c2), f6(c2, f4(c4)))),
% 29.61/19.85 inference(transitivity,[status(thm)],[27626, 13581, 27643])).
% 29.61/19.85 tff(27645,plain,
% 29.61/19.85 ((~big_f(c2, c2)) <=> (~big_f(f7(c2), f6(c2, f4(c4))))),
% 29.61/19.86 inference(monotonicity,[status(thm)],[27644])).
% 29.61/19.86 tff(27646,plain,
% 29.61/19.86 (~big_f(f7(c2), f6(c2, f4(c4)))),
% 29.61/19.86 inference(modus_ponens,[status(thm)],[121, 27645])).
% 29.61/19.86 tff(27647,plain,
% 29.61/19.86 (big_f(f9(c1, c1), c1)),
% 29.61/19.86 inference(unit_resolution,[status(thm)],[10938, 27641, 4932])).
% 29.61/19.86 tff(27648,plain,
% 29.61/19.86 (big_f(f9(c1, c1), f10(c1))),
% 29.61/19.86 inference(unit_resolution,[status(thm)],[8716, 27647, 3762])).
% 29.61/19.86 tff(27649,plain,
% 29.61/19.86 (f6(c2, f4(c4)) = f4(c4)),
% 29.61/19.86 inference(unit_resolution,[status(thm)],[3961, 27648, 77, 3762, 27646, 27641])).
% 29.61/19.86 tff(27650,plain,
% 29.61/19.86 (f6(c2, c1) = c1),
% 29.61/19.86 inference(modus_ponens,[status(thm)],[27649, 27621])).
% 29.61/19.86 tff(27651,plain,
% 29.61/19.86 ($false),
% 29.61/19.86 inference(unit_resolution,[status(thm)],[3198, 27650])).
% 29.61/19.86 tff(27652,plain,((f6(c2, c1) = c1) | (~(f4(c4) = c1)) | (~(f7(c2) = c2)) | (~(f10(c1) = c1)) | (~big_f(c1, c1)) | big_f(c2, c1) | big_f(c2, c2) | (~(f7(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.61/19.86 tff(27653,plain,
% 29.61/19.86 (f6(c2, c1) = c1),
% 29.61/19.86 inference(unit_resolution,[status(thm)],[27652, 27618, 121, 3762, 11752, 27617, 27619, 4234])).
% 29.61/19.86 tff(27654,plain,
% 29.61/19.86 (f6(c1, c1) = c1),
% 29.61/19.86 inference(unit_resolution,[status(thm)],[26558, 65, 3762, 4234, 2, 4932])).
% 29.61/19.86 tff(27655,plain,
% 29.61/19.86 ($false),
% 29.61/19.86 inference(unit_resolution,[status(thm)],[11304, 27654, 65, 4234, 4932])).
% 29.61/19.86 tff(27656,plain,(big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (~big_f(c1, c1)) | (~(f10(c1) = c1)) | big_f(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 29.61/19.86 tff(27657,plain,
% 29.61/19.86 (big_f(f7(c1), f6(c1, c1))),
% 29.61/19.86 inference(unit_resolution,[status(thm)],[27656, 27618, 4234, 3762, 27619])).
% 29.61/19.86 tff(27658,plain,
% 29.61/19.86 (f6(c1, c1) = c1),
% 29.61/19.86 inference(unit_resolution,[status(thm)],[26565, 27657, 4234, 27, 27653])).
% 29.61/19.86 tff(27659,plain,
% 29.61/19.86 (big_f(f9(c1, c1), c1)),
% 29.61/19.86 inference(unit_resolution,[status(thm)],[10938, 27618, 3949])).
% 29.61/19.86 tff(27660,plain,
% 29.61/19.86 (big_f(f9(c1, c1), f10(c1))),
% 29.61/19.86 inference(unit_resolution,[status(thm)],[8716, 27659, 3762])).
% 29.61/19.86 tff(27661,plain,
% 29.61/19.86 ($false),
% 29.61/19.86 inference(unit_resolution,[status(thm)],[18907, 2378, 4234, 3762, 3949, 27660, 27657, 27658])).
% 29.61/19.86 tff(27662,plain,(big_f(c1, c2) | (~(f7(c1) = c1)) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | big_f(c2, c2) | (~(f4(c4) = c1)) | (c1 = c3) | (f4(c4) = c3)), inference(lemma,lemma(discharge,[]))).
% 29.61/19.86 tff(27663,plain,
% 29.61/19.86 (big_f(c1, c2) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | big_f(c2, c2) | (~(f4(c4) = c1)) | (c1 = c3) | (f4(c4) = c3)),
% 29.61/19.86 inference(unit_resolution,[status(thm)],[27662, 25791])).
% 29.61/19.86 tff(27664,plain,
% 29.61/19.86 (~(f9(c1, c1) = c1)),
% 29.61/19.86 inference(unit_resolution,[status(thm)],[27663, 27545, 27, 121, 27541, 168, 18059])).
% 29.61/19.86 tff(27665,plain,
% 29.61/19.86 (f9(c1, c1) = c2),
% 29.61/19.86 inference(unit_resolution,[status(thm)],[3939, 27664])).
% 29.61/19.86 tff(27666,plain,
% 29.61/19.86 (~big_f(f9(c1, c1), c1)),
% 29.61/19.86 inference(unit_resolution,[status(thm)],[10058, 27665, 27546])).
% 29.61/19.86 tff(27667,plain,
% 29.61/19.86 (~big_f(f9(c1, c1), f10(c1))),
% 29.61/19.86 inference(unit_resolution,[status(thm)],[10033, 27666, 27545])).
% 29.61/19.86 tff(27668,plain,
% 29.61/19.86 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)))),
% 29.61/19.86 inference(rewrite,[status(thm)],[])).
% 29.61/19.86 tff(27669,plain,
% 29.61/19.86 (((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(c2 = f5(c2)))) <=> ((f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)))),
% 29.61/19.86 inference(rewrite,[status(thm)],[])).
% 29.61/19.86 tff(27670,plain,
% 29.61/19.86 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(c2 = f5(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1))))),
% 29.67/19.86 inference(monotonicity,[status(thm)],[27669])).
% 29.67/19.86 tff(27671,plain,
% 29.67/19.86 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(c2 = f5(c2))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)))),
% 29.67/19.86 inference(transitivity,[status(thm)],[27670, 27668])).
% 29.67/19.86 tff(27672,plain,
% 29.67/19.86 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~(c2 = f5(c2))))),
% 29.67/19.86 inference(quant_inst,[status(thm)],[])).
% 29.67/19.86 tff(27673,plain,
% 29.67/19.86 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | big_f(f7(X4), X5) | (~(X5 = f5(X4))))) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1))),
% 29.67/19.86 inference(modus_ponens,[status(thm)],[27672, 27671])).
% 29.67/19.86 tff(27674,plain,
% 29.67/19.86 (~(c2 = f5(c2))),
% 29.67/19.86 inference(unit_resolution,[status(thm)],[27673, 267, 27545, 17, 23145, 27664, 27667])).
% 29.67/19.86 tff(27675,plain,
% 29.67/19.86 (~(f5(c2) = c2)),
% 29.67/19.86 inference(unit_resolution,[status(thm)],[8113, 27674])).
% 29.67/19.86 tff(27676,plain,
% 29.67/19.86 (big_f(f7(c1), f6(c1, c1)) | (~big_f(c1, c1)) | (~(f10(c1) = c1)) | big_f(c2, c1)),
% 29.67/19.86 inference(unit_resolution,[status(thm)],[27656, 25791])).
% 29.67/19.86 tff(27677,plain,
% 29.67/19.86 (big_f(f7(c1), f6(c1, c1))),
% 29.67/19.86 inference(unit_resolution,[status(thm)],[27676, 27545, 4932, 27546])).
% 29.67/19.86 tff(27678,plain,
% 29.67/19.86 ((f9(c1, c1) = c1) | (~(f10(c1) = c1)) | big_f(c2, c1) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1)))),
% 29.67/19.86 inference(unit_resolution,[status(thm)],[26608, 25791])).
% 29.67/19.86 tff(27679,plain,
% 29.67/19.86 (~(f6(c1, c1) = c1)),
% 29.67/19.86 inference(unit_resolution,[status(thm)],[27678, 27677, 27546, 27664, 27545])).
% 29.67/19.86 tff(27680,plain,
% 29.67/19.86 (big_f(f7(c1), f6(c1, c1)) <=> big_f(c1, f6(c1, c1))),
% 29.67/19.86 inference(monotonicity,[status(thm)],[25791])).
% 29.67/19.86 tff(27681,plain,
% 29.67/19.86 (big_f(c1, f6(c1, c1))),
% 29.67/19.86 inference(modus_ponens,[status(thm)],[27677, 27680])).
% 29.67/19.86 tff(27682,plain,
% 29.67/19.86 (big_f(f7(c2), f6(c1, c1))),
% 29.67/19.86 inference(modus_ponens,[status(thm)],[27681, 27594])).
% 29.67/19.86 tff(27683,plain,
% 29.67/19.86 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(c2) = c2) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c2) = c2) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))))),
% 29.67/19.86 inference(rewrite,[status(thm)],[])).
% 29.67/19.86 tff(27684,plain,
% 29.67/19.86 (((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(c2) = c2) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1)))) <=> ((f7(c2) = c2) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))))),
% 29.67/19.86 inference(rewrite,[status(thm)],[])).
% 29.67/19.86 tff(27685,plain,
% 29.67/19.86 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(c2) = c2) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(c2) = c2) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1)))))),
% 29.67/19.86 inference(monotonicity,[status(thm)],[27684])).
% 29.67/19.86 tff(27686,plain,
% 29.67/19.86 (((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(c2) = c2) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))))) <=> ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c2) = c2) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))))),
% 29.67/19.86 inference(transitivity,[status(thm)],[27685, 27683])).
% 29.67/19.86 tff(27687,plain,
% 29.67/19.86 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (f7(c2) = c2) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))))),
% 29.67/19.86 inference(quant_inst,[status(thm)],[])).
% 29.67/19.86 tff(27688,plain,
% 29.67/19.86 ((~![X9: $i, X4: $i, X7: $i, X5: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(c2) = c2) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1)))),
% 29.67/19.86 inference(modus_ponens,[status(thm)],[27687, 27686])).
% 29.67/19.86 tff(27689,plain,
% 29.67/19.86 (f6(c1, c1) = f5(c2)),
% 29.67/19.86 inference(unit_resolution,[status(thm)],[27688, 676, 27545, 17, 27664, 27667, 27682])).
% 29.67/19.86 tff(27690,plain,
% 29.67/19.86 (~(f7(c2) = f5(c2))),
% 29.67/19.86 inference(unit_resolution,[status(thm)],[10715, 27689, 22, 27679])).
% 29.67/19.86 tff(27691,plain,
% 29.67/19.86 (~(f5(c2) = c1)),
% 29.67/19.86 inference(unit_resolution,[status(thm)],[8394, 27690, 22])).
% 29.67/19.86 tff(27692,plain,
% 29.67/19.86 ($false),
% 29.67/19.86 inference(unit_resolution,[status(thm)],[1547, 27691, 27675])).
% 29.67/19.86 tff(27693,plain,((f7(c2) = c2) | (~big_f(c1, c1)) | big_f(c1, c2) | big_f(c2, c2) | (c1 = c3) | (f4(c4) = c3) | (~big_f(f4(c4), c4)) | (~(c4 = c1))), inference(lemma,lemma(discharge,[]))).
% 29.67/19.86 tff(27694,plain,
% 29.67/19.86 (f7(c2) = c2),
% 29.67/19.86 inference(unit_resolution,[status(thm)],[27693, 121, 27, 27489, 76, 27511, 27539, 27537])).
% 29.67/19.86 tff(27695,plain,
% 29.67/19.86 ((f10(c1) = c1) | (~(f7(c2) = c2)) | (~(f4(c4) = c1)) | (~big_f(c1, c1)) | big_f(c1, c2) | big_f(c2, c2)),
% 29.67/19.86 inference(unit_resolution,[status(thm)],[26551, 25791])).
% 29.67/19.86 tff(27696,plain,
% 29.67/19.86 (f10(c1) = c1),
% 29.67/19.86 inference(unit_resolution,[status(thm)],[27695, 27694, 27489, 27503, 27, 121])).
% 29.67/19.86 tff(27697,plain,
% 29.67/19.86 (big_f(f7(c1), f6(c1, c1))),
% 29.67/19.86 inference(unit_resolution,[status(thm)],[27676, 27696, 27489, 27512])).
% 29.67/19.86 tff(27698,plain,
% 29.67/19.86 ((f6(c2, c1) = c1) | (~(f4(c4) = c1)) | (~(f7(c2) = c2)) | (~(f10(c1) = c1)) | (~big_f(c1, c1)) | big_f(c2, c1) | big_f(c2, c2)),
% 29.67/19.86 inference(unit_resolution,[status(thm)],[27652, 25791])).
% 29.67/19.86 tff(27699,plain,
% 29.67/19.86 (f6(c2, c1) = c1),
% 29.67/19.86 inference(unit_resolution,[status(thm)],[27698, 27696, 121, 27503, 27512, 27694, 27489])).
% 29.67/19.86 tff(27700,plain,
% 29.67/19.86 (~(f9(c1, c1) = c1)),
% 29.67/19.86 inference(unit_resolution,[status(thm)],[27663, 27696, 27, 121, 27503, 76, 27511])).
% 29.67/19.86 tff(27701,plain,
% 29.67/19.86 (~(f6(c1, c1) = c1)),
% 29.67/19.86 inference(unit_resolution,[status(thm)],[27678, 27697, 27512, 27700, 27696])).
% 29.67/19.86 tff(27702,plain,
% 29.67/19.86 ((~(f6(c2, c1) = c1)) | big_f(c1, c2) | (f6(c1, c1) = c1) | (~big_f(f7(c1), f6(c1, c1)))),
% 29.67/19.86 inference(unit_resolution,[status(thm)],[26565, 25791])).
% 29.67/19.86 tff(27703,plain,
% 29.67/19.86 ($false),
% 29.67/19.86 inference(unit_resolution,[status(thm)],[27702, 27701, 27699, 27, 27697])).
% 29.67/19.86 tff(27704,plain,(big_f(c2, c2) | big_f(c1, c2) | (~(c3 = c2))), inference(lemma,lemma(discharge,[]))).
% 29.67/19.86 tff(27705,plain,
% 29.67/19.86 (big_f(c2, c2)),
% 29.67/19.86 inference(unit_resolution,[status(thm)],[27704, 67, 27])).
% 29.67/19.86 tff(27706,plain,
% 29.67/19.86 (~(f4(c4) = c2)),
% 29.67/19.86 inference(unit_resolution,[status(thm)],[12603, 2, 27, 27489, 27705, 17])).
% 29.67/19.86 tff(27707,plain,
% 29.67/19.86 (f4(c4) = c1),
% 29.67/19.86 inference(unit_resolution,[status(thm)],[11750, 27706])).
% 29.67/19.86 tff(27708,plain,
% 29.67/19.86 ((c2 = f4(c4)) <=> (c2 = c1)),
% 29.67/19.86 inference(monotonicity,[status(thm)],[27707])).
% 29.67/19.86 tff(27709,plain,
% 29.67/19.86 ((c2 = c1) <=> (c2 = f4(c4))),
% 29.67/19.86 inference(symmetry,[status(thm)],[27708])).
% 29.67/19.86 tff(27710,plain,
% 29.67/19.86 ((c2 = c1) <=> (f4(c4) = c3)),
% 29.67/19.86 inference(transitivity,[status(thm)],[27709, 27506])).
% 29.67/19.86 tff(27711,plain,
% 29.67/19.86 ((~(c2 = c1)) <=> (~(f4(c4) = c3))),
% 29.67/19.86 inference(monotonicity,[status(thm)],[27710])).
% 29.67/19.86 tff(27712,plain,
% 29.67/19.86 (~(f4(c4) = c3)),
% 29.67/19.86 inference(modus_ponens,[status(thm)],[75, 27711])).
% 29.67/19.86 tff(27713,plain,
% 29.67/19.86 (~big_f(f4(c4), c4)),
% 29.67/19.86 inference(unit_resolution,[status(thm)],[11764, 431, 27, 11752])).
% 29.67/19.86 tff(27714,plain,
% 29.67/19.86 (~big_f(c1, f1(c1, c1))),
% 29.67/19.86 inference(unit_resolution,[status(thm)],[23017, 431, 27, 11752, 168])).
% 29.67/19.86 tff(27715,plain,
% 29.67/19.86 (~(f1(c1, c1) = c1)),
% 29.67/19.86 inference(unit_resolution,[status(thm)],[9678, 27714, 4932])).
% 29.67/19.86 tff(27716,plain,
% 29.67/19.86 ($false),
% 29.67/19.86 inference(unit_resolution,[status(thm)],[27551, 27715, 27713, 11752, 18059, 27])).
% 29.67/19.86 tff(27717,plain,((~(c4 = c2)) | (~(f4(c4) = c1)) | (f4(c4) = c3) | big_f(c1, c2) | (~big_f(c1, c1)) | (c1 = c3)), inference(lemma,lemma(discharge,[]))).
% 29.67/19.86 tff(27718,plain,
% 29.67/19.86 (~(c4 = c2)),
% 29.67/19.86 inference(unit_resolution,[status(thm)],[27717, 27707, 27712, 27, 27489, 76])).
% 29.67/19.86 tff(27719,plain,
% 29.67/19.86 (c4 = c1),
% 29.67/19.86 inference(unit_resolution,[status(thm)],[461, 27718])).
% 29.67/19.86 tff(27720,plain,
% 29.67/19.86 ((c2 = c4) <=> (c2 = c1)),
% 29.67/19.86 inference(monotonicity,[status(thm)],[27719])).
% 29.67/19.86 tff(27721,plain,
% 29.67/19.86 ((c2 = c1) <=> (c2 = c4)),
% 29.67/19.86 inference(symmetry,[status(thm)],[27720])).
% 29.67/19.86 tff(27722,plain,
% 29.67/19.86 ((~(c2 = c1)) <=> (~(c2 = c4))),
% 29.67/19.86 inference(monotonicity,[status(thm)],[27721])).
% 29.67/19.86 tff(27723,plain,
% 29.67/19.86 (~(c2 = c4)),
% 29.67/19.86 inference(modus_ponens,[status(thm)],[75, 27722])).
% 29.67/19.86 tff(27724,plain,
% 29.67/19.86 (~(c2 = f5(c1))),
% 29.67/19.86 inference(unit_resolution,[status(thm)],[24671, 27723, 76, 27489, 27, 27705, 22, 9306])).
% 29.67/19.86 tff(27725,plain,
% 29.67/19.86 (~(f5(c1) = c2)),
% 29.67/19.86 inference(unit_resolution,[status(thm)],[24054, 27724])).
% 29.67/19.86 tff(27726,plain,
% 29.67/19.86 (f5(c1) = c1),
% 29.67/19.86 inference(unit_resolution,[status(thm)],[1708, 27725])).
% 29.67/19.86 tff(27727,plain,
% 29.67/19.86 ((c2 = c4) <=> (c2 = c1)),
% 29.67/19.86 inference(monotonicity,[status(thm)],[480])).
% 29.67/19.86 tff(27728,plain,
% 29.67/19.86 ((c2 = c1) <=> (c2 = c4)),
% 29.67/19.86 inference(symmetry,[status(thm)],[27727])).
% 29.67/19.86 tff(27729,plain,
% 29.67/19.86 ((~(c2 = c1)) <=> (~(c2 = c4))),
% 29.67/19.86 inference(monotonicity,[status(thm)],[27728])).
% 29.67/19.86 tff(27730,plain,
% 29.67/19.86 (~(c2 = c4)),
% 29.67/19.86 inference(modus_ponens,[status(thm)],[75, 27729])).
% 29.67/19.86 tff(27731,plain,
% 29.67/19.86 (~(c2 = f5(c1))),
% 29.67/19.86 inference(unit_resolution,[status(thm)],[24671, 27730, 168, 4932, 27, 1345, 292, 9092])).
% 29.67/19.86 tff(27732,plain,
% 29.67/19.86 (~(f5(c1) = c2)),
% 29.67/19.86 inference(unit_resolution,[status(thm)],[24054, 27731])).
% 29.67/19.86 tff(27733,plain,
% 29.67/19.86 (f5(c1) = c1),
% 29.67/19.86 inference(unit_resolution,[status(thm)],[1708, 27732])).
% 29.67/19.86 tff(27734,plain,
% 29.67/19.86 (f3(c2, c2) = f3(f10(c1), f10(c1))),
% 29.67/19.86 inference(monotonicity,[status(thm)],[5571, 5571])).
% 29.67/19.86 tff(27735,plain,
% 29.67/19.86 ((f3(c2, c2) = c2) <=> (f3(f10(c1), f10(c1)) = f10(c1))),
% 29.67/19.86 inference(monotonicity,[status(thm)],[27734, 5571])).
% 29.67/19.86 tff(27736,plain,
% 29.67/19.86 ((f3(f10(c1), f10(c1)) = f10(c1)) <=> (f3(c2, c2) = c2)),
% 29.67/19.86 inference(symmetry,[status(thm)],[27735])).
% 29.67/19.86 tff(27737,plain,
% 29.67/19.86 ((f8(c1) = f10(c1)) <=> (f10(c1) = f8(c1))),
% 29.67/19.86 inference(commutativity,[status(thm)],[])).
% 29.67/19.86 tff(27738,plain,
% 29.67/19.86 (f3(f10(c1), f10(c1)) = f3(c2, c2)),
% 29.67/19.86 inference(symmetry,[status(thm)],[27734])).
% 29.67/19.86 tff(27739,plain,
% 29.67/19.86 (big_f(f3(f10(c1), f10(c1)), f10(c1)) <=> big_f(f3(c2, c2), f10(c1))),
% 29.67/19.86 inference(monotonicity,[status(thm)],[27738])).
% 29.67/19.86 tff(27740,plain,
% 29.67/19.86 (big_f(f3(c2, c2), f10(c1)) <=> big_f(f3(f10(c1), f10(c1)), f10(c1))),
% 29.67/19.86 inference(symmetry,[status(thm)],[27739])).
% 29.67/19.86 tff(27741,plain,
% 29.67/19.86 (big_f(f3(c2, c2), c2)),
% 29.67/19.86 inference(unit_resolution,[status(thm)],[21176, 12861, 27, 168, 4932, 873])).
% 29.67/19.86 tff(27742,plain,
% 29.67/19.86 (big_f(f3(c2, c2), f10(c1))),
% 29.67/19.86 inference(unit_resolution,[status(thm)],[27281, 27741, 15])).
% 29.67/19.86 tff(27743,plain,
% 29.67/19.86 (big_f(f3(f10(c1), f10(c1)), f10(c1))),
% 29.67/19.86 inference(modus_ponens,[status(thm)],[27742, 27740])).
% 29.67/19.86 tff(27744,plain,
% 29.67/19.86 (~(f6(f7(c2), f5(c1)) = c1)),
% 29.67/19.86 inference(unit_resolution,[status(thm)],[26402, 28, 292, 230])).
% 29.67/19.86 tff(27745,plain,
% 29.67/19.86 (f6(f7(c2), f5(c1)) = c2),
% 29.67/19.86 inference(unit_resolution,[status(thm)],[2978, 27744])).
% 29.67/19.86 tff(27746,plain,
% 29.67/19.86 ((~(f6(f7(c2), f5(c1)) = c2)) | (~big_f(f7(c1), f6(c1, c1))) | big_f(c1, c2) | (~(f5(c1) = c1)) | (~(f7(c2) = c1))),
% 29.67/19.86 inference(unit_resolution,[status(thm)],[26393, 25791])).
% 29.67/19.86 tff(27747,plain,
% 29.67/19.86 (~big_f(f7(c1), f6(c1, c1))),
% 29.67/19.86 inference(unit_resolution,[status(thm)],[27746, 27745, 27, 292, 230])).
% 29.67/19.86 tff(27748,plain,
% 29.67/19.86 ((f6(c1, c1) = c1) | (f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | big_f(f7(c1), f6(c1, c1))),
% 29.67/19.86 inference(unit_resolution,[status(thm)],[9803, 25791])).
% 29.67/19.86 tff(27749,plain,
% 29.67/19.86 (~(c1 = f8(c1))),
% 29.67/19.86 inference(unit_resolution,[status(thm)],[27748, 27747, 3, 15821, 28])).
% 29.67/19.86 tff(27750,assumption,(big_f(f3(c2, c2), f10(c1))), introduced(assumption)).
% 29.67/19.86 tff(27751,plain,
% 29.67/19.86 ((f3(c2, c2) = f8(c1)) <=> (f3(c2, c2) = c2)),
% 29.67/19.86 inference(monotonicity,[status(thm)],[1671])).
% 29.67/19.86 tff(27752,plain,
% 29.67/19.86 ((f3(c2, c2) = c2) <=> (f3(c2, c2) = f8(c1))),
% 29.67/19.86 inference(symmetry,[status(thm)],[27751])).
% 29.67/19.86 tff(27753,plain,
% 29.67/19.86 ((~(f3(c2, c2) = c2)) <=> (~(f3(c2, c2) = f8(c1)))),
% 29.67/19.86 inference(monotonicity,[status(thm)],[27752])).
% 29.67/19.86 tff(27754,plain,
% 29.67/19.86 (~(f3(c2, c2) = f8(c1))),
% 29.67/19.86 inference(modus_ponens,[status(thm)],[12861, 27753])).
% 29.67/19.86 tff(27755,plain,
% 29.67/19.86 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c1) = c1) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1))))),
% 29.67/19.86 inference(rewrite,[status(thm)],[])).
% 29.67/19.86 tff(27756,plain,
% 29.67/19.86 (((f10(c1) = c1) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1))) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1))) <=> ((f10(c1) = c1) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1))))),
% 29.67/19.86 inference(rewrite,[status(thm)],[])).
% 29.67/19.86 tff(27757,plain,
% 29.67/19.86 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1))) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1)))))),
% 29.67/19.86 inference(monotonicity,[status(thm)],[27756])).
% 29.67/19.86 tff(27758,plain,
% 29.67/19.86 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1))) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c1) = c1) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1))))),
% 29.67/19.86 inference(transitivity,[status(thm)],[27757, 27755])).
% 29.67/19.86 tff(27759,plain,
% 29.67/19.86 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1))) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1)))),
% 29.67/19.86 inference(quant_inst,[status(thm)],[])).
% 29.67/19.86 tff(27760,plain,
% 29.67/19.86 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c1) = c1) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1)))),
% 29.67/19.86 inference(modus_ponens,[status(thm)],[27759, 27758])).
% 29.67/19.86 tff(27761,plain,
% 29.67/19.86 ($false),
% 29.67/19.86 inference(unit_resolution,[status(thm)],[27760, 2662, 4234, 3, 65, 28, 27750, 27754])).
% 29.67/19.86 tff(27762,plain,((~big_f(f3(c2, c2), f10(c1))) | (~(f7(c1) = c1)) | (f10(c1) = c1) | big_f(f7(c1), f6(c1, c1)) | (f6(c1, c1) = c1) | (f3(c2, c2) = c2) | (~(f8(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.67/19.86 tff(27763,plain,
% 29.67/19.86 ((~big_f(f3(c2, c2), f10(c1))) | (f10(c1) = c1) | big_f(f7(c1), f6(c1, c1)) | (f6(c1, c1) = c1) | (f3(c2, c2) = c2) | (~(f8(c1) = c2))),
% 29.67/19.86 inference(unit_resolution,[status(thm)],[27762, 25791])).
% 29.67/19.86 tff(27764,plain,
% 29.67/19.86 (~(f8(c1) = c2)),
% 29.67/19.86 inference(unit_resolution,[status(thm)],[27763, 27747, 3, 12861, 28, 27750])).
% 29.67/19.86 tff(27765,plain,
% 29.67/19.86 (f8(c1) = c1),
% 29.67/19.86 inference(unit_resolution,[status(thm)],[1680, 27764])).
% 29.67/19.86 tff(27766,plain,
% 29.67/19.86 ($false),
% 29.67/19.86 inference(unit_resolution,[status(thm)],[9808, 27765, 27749])).
% 29.67/19.86 tff(27767,plain,((f6(c1, c1) = c1) | (f10(c1) = c1) | (f3(c2, c2) = c2) | (~big_f(f3(c2, c2), f10(c1))) | big_f(c1, c2) | (~(f7(c2) = c1)) | (~(f5(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.67/19.86 tff(27768,plain,
% 29.67/19.86 (f6(c1, c1) = c1),
% 29.67/19.86 inference(unit_resolution,[status(thm)],[27767, 27742, 3, 12861, 27, 292, 230])).
% 29.67/19.86 tff(27769,plain,
% 29.67/19.86 (big_f(f7(c1), f6(c1, c1)) | (~big_f(c1, c1)) | (~(f6(c1, c1) = c1))),
% 29.67/19.86 inference(unit_resolution,[status(thm)],[11304, 25791])).
% 29.67/19.86 tff(27770,plain,
% 29.67/19.86 (big_f(f7(c1), f6(c1, c1))),
% 29.67/19.86 inference(unit_resolution,[status(thm)],[27769, 27768, 4932])).
% 29.67/19.86 tff(27771,plain,
% 29.67/19.86 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))) | (f3(f10(c1), f10(c1)) = f8(c1)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))) | (f3(f10(c1), f10(c1)) = f8(c1)))),
% 29.67/19.86 inference(rewrite,[status(thm)],[])).
% 29.67/19.86 tff(27772,plain,
% 29.67/19.86 (((f10(c1) = c1) | (f3(f10(c1), f10(c1)) = f8(c1)) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1)))) <=> ((f10(c1) = c1) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))) | (f3(f10(c1), f10(c1)) = f8(c1)))),
% 29.67/19.86 inference(rewrite,[status(thm)],[])).
% 29.67/19.86 tff(27773,plain,
% 29.67/19.86 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (f3(f10(c1), f10(c1)) = f8(c1)) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))) | (f3(f10(c1), f10(c1)) = f8(c1))))),
% 29.67/19.87 inference(monotonicity,[status(thm)],[27772])).
% 29.67/19.87 tff(27774,plain,
% 29.67/19.87 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (f3(f10(c1), f10(c1)) = f8(c1)) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))) | (f3(f10(c1), f10(c1)) = f8(c1)))),
% 29.67/19.87 inference(transitivity,[status(thm)],[27773, 27771])).
% 29.67/19.87 tff(27775,plain,
% 29.67/19.87 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (f3(f10(c1), f10(c1)) = f8(c1)) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))),
% 29.67/19.87 inference(quant_inst,[status(thm)],[])).
% 29.67/19.87 tff(27776,plain,
% 29.67/19.87 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))) | (f3(f10(c1), f10(c1)) = f8(c1))),
% 29.67/19.87 inference(modus_ponens,[status(thm)],[27775, 27774])).
% 29.67/19.87 tff(27777,plain,
% 29.67/19.87 (f3(f10(c1), f10(c1)) = f8(c1)),
% 29.67/19.87 inference(unit_resolution,[status(thm)],[27776, 2730, 25791, 3, 27770, 27768, 27743])).
% 29.67/19.87 tff(27778,plain,
% 29.67/19.87 ((f3(f10(c1), f10(c1)) = f10(c1)) <=> (f8(c1) = f10(c1))),
% 29.67/19.87 inference(monotonicity,[status(thm)],[27777])).
% 29.67/19.87 tff(27779,plain,
% 29.67/19.87 ((f3(f10(c1), f10(c1)) = f10(c1)) <=> (f10(c1) = f8(c1))),
% 29.67/19.87 inference(transitivity,[status(thm)],[27778, 27737])).
% 29.67/19.87 tff(27780,plain,
% 29.67/19.87 ((f10(c1) = f8(c1)) <=> (f3(f10(c1), f10(c1)) = f10(c1))),
% 29.67/19.87 inference(symmetry,[status(thm)],[27779])).
% 29.67/19.87 tff(27781,plain,
% 29.67/19.87 ((f10(c1) = f8(c1)) <=> (f3(c2, c2) = c2)),
% 29.67/19.87 inference(transitivity,[status(thm)],[27780, 27736])).
% 29.67/19.87 tff(27782,plain,
% 29.67/19.87 (f10(c1) = f8(c1)),
% 29.67/19.87 inference(unit_resolution,[status(thm)],[19009, 2730, 25791, 3, 27770, 27768, 27318])).
% 29.67/19.87 tff(27783,plain,
% 29.67/19.87 (f3(c2, c2) = c2),
% 29.67/19.87 inference(modus_ponens,[status(thm)],[27782, 27781])).
% 29.67/19.87 tff(27784,plain,
% 29.67/19.87 ($false),
% 29.67/19.87 inference(unit_resolution,[status(thm)],[12861, 27783])).
% 29.67/19.87 tff(27785,plain,((f3(c2, c2) = c2) | (f10(c1) = c1) | (~big_f(f10(c1), f10(c1))) | (~big_f(c1, c1)) | big_f(c1, c2) | (~(f7(c2) = c1)) | (~(f5(c1) = c1)) | (c1 = c3) | (c2 = c4)), inference(lemma,lemma(discharge,[]))).
% 29.67/19.87 tff(27786,plain,
% 29.67/19.87 (f3(c2, c2) = c2),
% 29.67/19.87 inference(unit_resolution,[status(thm)],[27785, 3, 18940, 4932, 27, 292, 27733, 168, 27730])).
% 29.67/19.87 tff(27787,plain,
% 29.67/19.87 (f3(f10(c1), f10(c1)) = f10(c1)),
% 29.67/19.87 inference(transitivity,[status(thm)],[27289, 27786, 5571])).
% 29.67/19.87 tff(27788,plain,
% 29.67/19.87 (big_f(f3(f10(c1), f10(c1)), f10(c1)) <=> big_f(f10(c1), f10(c1))),
% 29.67/19.87 inference(monotonicity,[status(thm)],[27787])).
% 29.67/19.87 tff(27789,plain,
% 29.67/19.87 (big_f(f10(c1), f10(c1)) <=> big_f(f3(f10(c1), f10(c1)), f10(c1))),
% 29.67/19.87 inference(symmetry,[status(thm)],[27788])).
% 29.67/19.87 tff(27790,plain,
% 29.67/19.87 (big_f(f3(f10(c1), f10(c1)), f10(c1))),
% 29.67/19.87 inference(modus_ponens,[status(thm)],[18940, 27789])).
% 29.67/19.87 tff(27791,plain,
% 29.67/19.87 (f3(c2, c2) = f3(f10(c1), f10(c1))),
% 29.67/19.87 inference(symmetry,[status(thm)],[27289])).
% 29.67/19.87 tff(27792,plain,
% 29.67/19.87 ((f3(c2, c2) = c2) <=> (f3(f10(c1), f10(c1)) = f10(c1))),
% 29.67/19.87 inference(monotonicity,[status(thm)],[27791, 5571])).
% 29.67/19.87 tff(27793,plain,
% 29.67/19.87 (f3(f10(c1), f10(c1)) = f10(c1)),
% 29.67/19.87 inference(modus_ponens,[status(thm)],[27786, 27792])).
% 29.67/19.87 tff(27794,plain,
% 29.67/19.87 (big_f(f4(c4), c4) <=> big_f(c1, c1)),
% 29.67/19.87 inference(monotonicity,[status(thm)],[11752, 17112])).
% 29.67/19.87 tff(27795,plain,
% 29.67/19.87 (big_f(c1, c1) <=> big_f(f4(c4), c4)),
% 29.67/19.87 inference(symmetry,[status(thm)],[27794])).
% 29.67/19.87 tff(27796,plain,
% 29.67/19.87 (big_f(f4(c4), c4)),
% 29.67/19.87 inference(modus_ponens,[status(thm)],[4932, 27795])).
% 29.67/19.87 tff(27797,plain,
% 29.67/19.87 ($false),
% 29.67/19.87 inference(unit_resolution,[status(thm)],[379, 27796])).
% 29.67/19.87 tff(27798,plain,((~(c1 = c4)) | big_f(f4(c4), c4) | (~big_f(c1, c1)) | (~(f4(c4) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.67/19.87 tff(27799,plain,
% 29.67/19.87 (big_f(f4(c4), c4)),
% 29.67/19.87 inference(unit_resolution,[status(thm)],[27798, 564, 4932, 11752])).
% 29.67/19.87 tff(27800,plain,
% 29.67/19.87 (big_f(f3(c2, c2), c2) <=> big_f(f3(c2, c2), f10(c1))),
% 29.67/19.87 inference(monotonicity,[status(thm)],[5571])).
% 29.67/19.87 tff(27801,plain,
% 29.67/19.87 (big_f(f3(c2, c2), f10(c1)) <=> big_f(f3(c2, c2), c2)),
% 29.67/19.87 inference(symmetry,[status(thm)],[27800])).
% 29.67/19.87 tff(27802,plain,
% 29.67/19.87 (big_f(f3(c2, c2), f10(c1)) <=> big_f(f3(f10(c1), f10(c1)), f10(c1))),
% 29.67/19.87 inference(monotonicity,[status(thm)],[27791])).
% 29.67/19.87 tff(27803,plain,
% 29.67/19.87 (big_f(f3(f10(c1), f10(c1)), f10(c1)) <=> big_f(f3(c2, c2), f10(c1))),
% 29.67/19.87 inference(symmetry,[status(thm)],[27802])).
% 29.67/19.87 tff(27804,plain,
% 29.67/19.87 (big_f(f10(c1), f10(c1)) <=> big_f(f3(c2, c2), c2)),
% 29.67/19.87 inference(transitivity,[status(thm)],[27789, 27803, 27801])).
% 29.67/19.87 tff(27805,plain,
% 29.67/19.87 (big_f(f3(c2, c2), c2)),
% 29.67/19.87 inference(modus_ponens,[status(thm)],[18940, 27804])).
% 29.67/19.87 tff(27806,plain,
% 29.67/19.87 (f1(c1, c1) = c1),
% 29.67/19.87 inference(unit_resolution,[status(thm)],[17109, 27805, 27730, 27, 292, 9092, 27786])).
% 29.67/19.87 tff(27807,plain,
% 29.67/19.87 (big_f(c1, f1(c1, c1))),
% 29.67/19.87 inference(unit_resolution,[status(thm)],[17119, 27806, 11752, 27799, 564])).
% 29.67/19.87 tff(27808,plain,
% 29.67/19.87 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))) | (f10(c1) = c4) | (~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))) | (f10(c1) = c4) | (~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))))),
% 29.67/19.87 inference(rewrite,[status(thm)],[])).
% 29.67/19.87 tff(27809,plain,
% 29.67/19.87 (((f10(c1) = c4) | (c1 = c3) | (~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1)))) <=> ((c1 = c3) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))) | (f10(c1) = c4) | (~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))))),
% 29.67/19.87 inference(rewrite,[status(thm)],[])).
% 29.67/19.87 tff(27810,plain,
% 29.67/19.87 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f10(c1) = c4) | (c1 = c3) | (~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))) | (f10(c1) = c4) | (~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1)))))),
% 29.67/19.87 inference(monotonicity,[status(thm)],[27809])).
% 29.67/19.87 tff(27811,plain,
% 29.67/19.87 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f10(c1) = c4) | (c1 = c3) | (~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))) | (f10(c1) = c4) | (~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))))),
% 29.67/19.87 inference(transitivity,[status(thm)],[27810, 27808])).
% 29.67/19.87 tff(27812,plain,
% 29.67/19.87 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f10(c1) = c4) | (c1 = c3) | (~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1))) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))))),
% 29.67/19.87 inference(quant_inst,[status(thm)],[])).
% 29.67/19.87 tff(27813,plain,
% 29.67/19.87 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (~(f1(c1, c1) = c1)) | (~big_f(c1, f1(c1, c1))) | (f10(c1) = c4) | (~(f3(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f3(f10(c1), f10(c1)), f10(c1)))),
% 29.67/19.87 inference(modus_ponens,[status(thm)],[27812, 27811])).
% 29.67/19.87 tff(27814,plain,
% 29.67/19.87 ($false),
% 29.67/19.87 inference(unit_resolution,[status(thm)],[27813, 933, 27806, 168, 27807, 18947, 27793, 27790])).
% 29.67/19.87 tff(27815,plain,((f10(c1) = c1) | (c1 = c3) | (~(f4(c4) = c1)) | big_f(c1, c2) | (~(f7(c2) = c1)) | (f7(c2) = c3) | (~big_f(c1, c1)) | (~big_f(c2, c2)) | (~(c4 = c1))), inference(lemma,lemma(discharge,[]))).
% 29.67/19.87 tff(27816,plain,
% 29.67/19.87 (f10(c1) = c1),
% 29.67/19.87 inference(unit_resolution,[status(thm)],[27815, 27707, 76, 27, 22, 9306, 27489, 27705, 27719])).
% 29.67/19.87 tff(27817,plain,
% 29.67/19.87 (big_f(f7(c1), f6(c1, c1))),
% 29.67/19.87 inference(unit_resolution,[status(thm)],[27676, 27816, 27489, 2])).
% 29.67/19.87 tff(27818,plain,
% 29.67/19.87 (~(f6(f7(c2), f5(c1)) = c2)),
% 29.67/19.87 inference(unit_resolution,[status(thm)],[27746, 27817, 27, 22, 27726])).
% 29.67/19.87 tff(27819,plain,
% 29.67/19.87 (f6(f7(c2), f5(c1)) = c1),
% 29.67/19.87 inference(unit_resolution,[status(thm)],[2978, 27818])).
% 29.67/19.87 tff(27820,plain,
% 29.67/19.87 (f6(c1, c1) = c1),
% 29.67/19.87 inference(unit_resolution,[status(thm)],[26402, 27819, 22, 27726])).
% 29.67/19.87 tff(27821,plain,
% 29.67/19.87 (big_f(f7(c2), c1)),
% 29.67/19.87 inference(modus_ponens,[status(thm)],[27489, 12091])).
% 29.67/19.87 tff(27822,plain,
% 29.67/19.87 (big_f(f9(c1, c1), c1) | (~(f7(c2) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f10(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c2), c1))),
% 29.67/19.87 inference(unit_resolution,[status(thm)],[10051, 25791])).
% 29.67/19.87 tff(27823,plain,
% 29.67/19.87 (big_f(f9(c1, c1), c1)),
% 29.67/19.87 inference(unit_resolution,[status(thm)],[27822, 27820, 22, 27821, 27816, 27817])).
% 29.67/19.87 tff(27824,plain,
% 29.67/19.87 (big_f(f9(c1, c1), f10(c1))),
% 29.67/19.87 inference(unit_resolution,[status(thm)],[8716, 27823, 27816])).
% 29.67/19.87 tff(27825,plain,
% 29.67/19.87 (f9(c1, c1) = c1),
% 29.67/19.87 inference(unit_resolution,[status(thm)],[27678, 27820, 2, 27816, 27817])).
% 29.67/19.87 tff(27826,plain,
% 29.67/19.87 ($false),
% 29.67/19.87 inference(unit_resolution,[status(thm)],[18907, 2378, 25791, 27816, 27825, 27824, 27817, 27820])).
% 29.67/19.87 tff(27827,plain,(big_f(c2, c1) | big_f(c1, c2) | (~(c3 = c2)) | (f7(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 29.67/19.87 tff(27828,plain,
% 29.67/19.87 (big_f(c2, c1)),
% 29.67/19.87 inference(unit_resolution,[status(thm)],[27827, 17, 67, 27])).
% 29.67/19.87 tff(27829,plain,
% 29.67/19.87 ((c2 = f4(c4)) <=> (f4(c4) = c2)),
% 29.67/19.87 inference(symmetry,[status(thm)],[2601])).
% 29.67/19.87 tff(27830,plain,
% 29.67/19.87 ((f4(c4) = c3) <=> (f4(c4) = c2)),
% 29.67/19.87 inference(transitivity,[status(thm)],[27505, 27829])).
% 29.67/19.87 tff(27831,assumption,(~(f4(c4) = c2)), introduced(assumption)).
% 29.67/19.87 tff(27832,plain,
% 29.67/19.87 (f4(c4) = c1),
% 29.67/19.87 inference(unit_resolution,[status(thm)],[11750, 27831])).
% 29.67/19.87 tff(27833,plain,
% 29.67/19.87 (f4(c4) = c3),
% 29.67/19.87 inference(unit_resolution,[status(thm)],[23034, 27832, 76, 27, 27489, 348])).
% 29.67/19.87 tff(27834,plain,
% 29.67/19.87 (f4(c4) = c2),
% 29.67/19.87 inference(modus_ponens,[status(thm)],[27833, 27830])).
% 29.67/19.87 tff(27835,plain,
% 29.67/19.87 ($false),
% 29.67/19.87 inference(unit_resolution,[status(thm)],[27831, 27834])).
% 29.67/19.87 tff(27836,plain,((f4(c4) = c2) | (~(c3 = c2)) | big_f(c1, c2) | (~big_f(c2, c1))), inference(lemma,lemma(discharge,[]))).
% 29.67/19.87 tff(27837,plain,
% 29.67/19.87 (f4(c4) = c2),
% 29.67/19.87 inference(unit_resolution,[status(thm)],[27836, 27828, 27, 67])).
% 29.67/19.87 tff(27838,plain,
% 29.67/19.87 (~(f10(c2) = c2)),
% 29.67/19.87 inference(unit_resolution,[status(thm)],[10739, 27837, 17])).
% 29.67/19.87 tff(27839,plain,
% 29.67/19.87 (f10(c2) = c1),
% 29.67/19.87 inference(unit_resolution,[status(thm)],[93, 27838])).
% 29.67/19.87 tff(27840,plain,
% 29.67/19.87 (big_f(c1, f10(c2)) <=> big_f(c1, c1)),
% 29.67/19.87 inference(monotonicity,[status(thm)],[27839])).
% 29.67/19.87 tff(27841,plain,
% 29.67/19.87 (big_f(c1, c1) <=> big_f(c1, f10(c2))),
% 29.67/19.87 inference(symmetry,[status(thm)],[27840])).
% 29.67/19.87 tff(27842,plain,
% 29.67/19.87 (big_f(c1, f10(c2))),
% 29.67/19.87 inference(modus_ponens,[status(thm)],[27489, 27841])).
% 29.67/19.87 tff(27843,plain,
% 29.67/19.87 (big_f(f9(c1, c1), f10(c2)) <=> big_f(f9(c1, c1), c1)),
% 29.67/19.87 inference(monotonicity,[status(thm)],[27839])).
% 29.67/19.87 tff(27844,plain,
% 29.67/19.87 (big_f(f9(c1, c1), c1) <=> big_f(f9(c1, c1), f10(c2))),
% 29.67/19.87 inference(symmetry,[status(thm)],[27843])).
% 29.67/19.87 tff(27845,plain,
% 29.67/19.87 (big_f(f9(c1, c1), c1)),
% 29.67/19.87 inference(unit_resolution,[status(thm)],[26966, 27828, 22, 27821])).
% 29.67/19.87 tff(27846,plain,
% 29.67/19.87 (big_f(f9(c1, c1), f10(c2))),
% 29.67/19.87 inference(modus_ponens,[status(thm)],[27845, 27844])).
% 29.67/19.87 tff(27847,plain,
% 29.67/19.87 (big_f(f7(f10(c1)), f10(c1)) <=> big_f(f7(f10(c1)), c2)),
% 29.67/19.87 inference(monotonicity,[status(thm)],[15])).
% 29.67/19.87 tff(27848,plain,
% 29.67/19.87 (big_f(f7(f10(c1)), c2) <=> big_f(f7(f10(c1)), f10(c1))),
% 29.67/19.87 inference(symmetry,[status(thm)],[27847])).
% 29.67/19.87 tff(27849,plain,
% 29.67/19.87 (big_f(f7(f10(c1)), c2) <=> big_f(c1, c2)),
% 29.67/19.87 inference(monotonicity,[status(thm)],[26311])).
% 29.67/19.87 tff(27850,plain,
% 29.67/19.87 (big_f(c1, c2) <=> big_f(f7(f10(c1)), c2)),
% 29.67/19.87 inference(symmetry,[status(thm)],[27849])).
% 29.67/19.87 tff(27851,plain,
% 29.67/19.87 (big_f(c1, c2) <=> big_f(f7(f10(c1)), f10(c1))),
% 29.67/19.87 inference(transitivity,[status(thm)],[27850, 27848])).
% 29.67/19.87 tff(27852,plain,
% 29.67/19.87 ((~big_f(c1, c2)) <=> (~big_f(f7(f10(c1)), f10(c1)))),
% 29.67/19.87 inference(monotonicity,[status(thm)],[27851])).
% 29.67/19.87 tff(27853,plain,
% 29.67/19.87 (~big_f(f7(f10(c1)), f10(c1))),
% 29.67/19.87 inference(modus_ponens,[status(thm)],[27, 27852])).
% 29.67/19.87 tff(27854,plain,
% 29.67/19.87 (big_f(c1, f10(f10(c1))) <=> big_f(c1, f10(c2))),
% 29.67/19.87 inference(monotonicity,[status(thm)],[24860])).
% 29.67/19.87 tff(27855,plain,
% 29.67/19.87 (big_f(c1, f10(c2)) <=> big_f(c1, f10(f10(c1)))),
% 29.67/19.87 inference(symmetry,[status(thm)],[27854])).
% 29.67/19.87 tff(27856,plain,
% 29.67/19.87 (big_f(c1, c1) <=> big_f(c1, f10(f10(c1)))),
% 29.67/19.87 inference(transitivity,[status(thm)],[24205, 27855])).
% 29.67/19.87 tff(27857,plain,
% 29.67/19.87 (big_f(c1, f10(f10(c1)))),
% 29.67/19.87 inference(modus_ponens,[status(thm)],[4932, 27856])).
% 29.67/19.87 tff(27858,plain,
% 29.67/19.87 (big_f(f10(c1), f10(f10(c1))) <=> big_f(c2, f10(c2))),
% 29.67/19.87 inference(monotonicity,[status(thm)],[15, 24860])).
% 29.67/19.87 tff(27859,plain,
% 29.67/19.87 (big_f(c2, f10(c2)) <=> big_f(f10(c1), f10(f10(c1)))),
% 29.67/19.87 inference(symmetry,[status(thm)],[27858])).
% 29.67/19.87 tff(27860,plain,
% 29.67/19.87 (big_f(c2, f10(c2)) <=> big_f(f10(c1), c1)),
% 29.67/19.87 inference(monotonicity,[status(thm)],[5571, 94])).
% 29.67/19.87 tff(27861,plain,
% 29.67/19.87 (big_f(f10(c1), c1) <=> big_f(c2, f10(c2))),
% 29.67/19.87 inference(symmetry,[status(thm)],[27860])).
% 29.67/19.87 tff(27862,plain,
% 29.67/19.87 (big_f(f10(c1), c1) <=> big_f(f10(c1), f10(f10(c1)))),
% 29.67/19.87 inference(transitivity,[status(thm)],[27861, 27859])).
% 29.67/19.87 tff(27863,plain,
% 29.67/19.87 (big_f(f10(c1), f10(f10(c1)))),
% 29.67/19.87 inference(modus_ponens,[status(thm)],[27307, 27862])).
% 29.67/19.87 tff(27864,plain,
% 29.67/19.87 ((f10(f10(c1)) = f10(c1)) <=> (f10(c2) = c2)),
% 29.67/19.87 inference(monotonicity,[status(thm)],[24860, 15])).
% 29.67/19.87 tff(27865,plain,
% 29.67/19.87 ((f10(c2) = c2) <=> (f10(f10(c1)) = f10(c1))),
% 29.67/19.87 inference(symmetry,[status(thm)],[27864])).
% 29.67/19.87 tff(27866,plain,
% 29.67/19.87 ((~(f10(c2) = c2)) <=> (~(f10(f10(c1)) = f10(c1)))),
% 29.67/19.87 inference(monotonicity,[status(thm)],[27865])).
% 29.67/19.87 tff(27867,plain,
% 29.67/19.87 (~(f10(f10(c1)) = f10(c1))),
% 29.67/19.87 inference(modus_ponens,[status(thm)],[89, 27866])).
% 29.67/19.87 tff(27868,plain,
% 29.67/19.87 (f5(f10(c1)) = f5(c2)),
% 29.67/19.87 inference(symmetry,[status(thm)],[12253])).
% 29.67/19.87 tff(27869,plain,
% 29.67/19.87 ((f6(c1, c1) = f5(f10(c1))) <=> (f6(c1, c1) = f5(c2))),
% 29.67/19.87 inference(monotonicity,[status(thm)],[27868])).
% 29.67/19.87 tff(27870,plain,
% 29.67/19.87 (big_f(f7(f10(c1)), f6(c1, c1)) <=> big_f(c1, f6(c1, c1))),
% 29.67/19.87 inference(monotonicity,[status(thm)],[26311])).
% 29.67/19.87 tff(27871,plain,
% 29.67/19.87 (big_f(c1, f6(c1, c1)) <=> big_f(f7(f10(c1)), f6(c1, c1))),
% 29.67/19.87 inference(symmetry,[status(thm)],[27870])).
% 29.67/19.87 tff(27872,assumption,(big_f(c1, f10(f10(c1)))), introduced(assumption)).
% 29.67/19.87 tff(27873,assumption,(big_f(f10(c1), f10(f10(c1)))), introduced(assumption)).
% 29.67/19.87 tff(27874,plain,
% 29.67/19.87 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f10(c1)) = f10(c1)) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(f10(c1)) = f10(c1)) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))))),
% 29.67/19.87 inference(rewrite,[status(thm)],[])).
% 29.67/19.87 tff(27875,plain,
% 29.67/19.87 (((f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1))) <=> ((f10(f10(c1)) = f10(c1)) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))))),
% 29.67/19.87 inference(rewrite,[status(thm)],[])).
% 29.67/19.87 tff(27876,plain,
% 29.67/19.87 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f10(c1)) = f10(c1)) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1))))))),
% 29.67/19.87 inference(monotonicity,[status(thm)],[27875])).
% 29.67/19.87 tff(27877,plain,
% 29.67/19.87 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(f10(c1)) = f10(c1)) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))))),
% 29.67/19.87 inference(transitivity,[status(thm)],[27876, 27874])).
% 29.67/19.87 tff(27878,plain,
% 29.67/19.87 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1)))),
% 29.67/19.87 inference(quant_inst,[status(thm)],[])).
% 29.67/19.87 tff(27879,plain,
% 29.67/19.87 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(f10(c1)) = f10(c1)) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1))))),
% 29.67/19.87 inference(modus_ponens,[status(thm)],[27878, 27877])).
% 29.67/19.87 tff(27880,plain,
% 29.67/19.87 (c1 = f8(f10(c1))),
% 29.67/19.87 inference(unit_resolution,[status(thm)],[27879, 2662, 25791, 24968, 65, 28, 27872])).
% 29.67/19.87 tff(27881,plain,
% 29.67/19.87 (f8(f10(c1)) = c1),
% 29.67/19.87 inference(symmetry,[status(thm)],[27880])).
% 29.67/19.87 tff(27882,assumption,(f10(c1) = f8(f10(c1))), introduced(assumption)).
% 29.67/19.87 tff(27883,plain,
% 29.67/19.87 (f10(c1) = c1),
% 29.67/19.87 inference(transitivity,[status(thm)],[27882, 27881])).
% 29.67/19.87 tff(27884,plain,
% 29.67/19.87 ($false),
% 29.67/19.87 inference(unit_resolution,[status(thm)],[3, 27883])).
% 29.67/19.87 tff(27885,plain,((~(f10(c1) = f8(f10(c1)))) | (f10(c1) = c1) | (f10(f10(c1)) = f10(c1)) | big_f(f7(c1), f6(c1, c1)) | (f6(c1, c1) = c1) | (~big_f(c1, f10(f10(c1))))), inference(lemma,lemma(discharge,[]))).
% 29.67/19.87 tff(27886,plain,
% 29.67/19.87 (~(f10(c1) = f8(f10(c1)))),
% 29.67/19.87 inference(unit_resolution,[status(thm)],[27885, 65, 24968, 3, 28, 27872])).
% 29.67/19.87 tff(27887,plain,
% 29.67/19.87 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f10(c1)) = f10(c1)) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | (f10(c1) = f8(f10(c1))) | (~big_f(f10(c1), f10(f10(c1)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(f10(c1)) = f10(c1)) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | (f10(c1) = f8(f10(c1))) | (~big_f(f10(c1), f10(f10(c1)))))),
% 29.67/19.87 inference(rewrite,[status(thm)],[])).
% 29.67/19.87 tff(27888,plain,
% 29.67/19.87 (((f10(f10(c1)) = f10(c1)) | (f10(c1) = f8(f10(c1))) | (~big_f(f10(c1), f10(f10(c1)))) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1))) <=> ((f10(f10(c1)) = f10(c1)) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | (f10(c1) = f8(f10(c1))) | (~big_f(f10(c1), f10(f10(c1)))))),
% 29.67/19.87 inference(rewrite,[status(thm)],[])).
% 29.67/19.87 tff(27889,plain,
% 29.67/19.87 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f10(c1)) = f10(c1)) | (f10(c1) = f8(f10(c1))) | (~big_f(f10(c1), f10(f10(c1)))) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f10(c1)) = f10(c1)) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | (f10(c1) = f8(f10(c1))) | (~big_f(f10(c1), f10(f10(c1))))))),
% 29.67/19.87 inference(monotonicity,[status(thm)],[27888])).
% 29.67/19.87 tff(27890,plain,
% 29.67/19.87 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f10(c1)) = f10(c1)) | (f10(c1) = f8(f10(c1))) | (~big_f(f10(c1), f10(f10(c1)))) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(f10(c1)) = f10(c1)) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | (f10(c1) = f8(f10(c1))) | (~big_f(f10(c1), f10(f10(c1)))))),
% 29.67/19.87 inference(transitivity,[status(thm)],[27889, 27887])).
% 29.67/19.87 tff(27891,plain,
% 29.67/19.87 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f10(c1)) = f10(c1)) | (f10(c1) = f8(f10(c1))) | (~big_f(f10(c1), f10(f10(c1)))) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1)))),
% 29.67/19.87 inference(quant_inst,[status(thm)],[])).
% 29.67/19.87 tff(27892,plain,
% 29.67/19.87 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(f10(c1)) = f10(c1)) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | (f10(c1) = f8(f10(c1))) | (~big_f(f10(c1), f10(f10(c1))))),
% 29.67/19.87 inference(modus_ponens,[status(thm)],[27891, 27890])).
% 29.67/19.87 tff(27893,plain,
% 29.67/19.87 ($false),
% 29.67/19.87 inference(unit_resolution,[status(thm)],[27892, 2662, 25791, 24968, 65, 28, 27873, 27886])).
% 29.67/19.87 tff(27894,plain,(big_f(f7(c1), f6(c1, c1)) | (f10(f10(c1)) = f10(c1)) | (f6(c1, c1) = c1) | (~big_f(f10(c1), f10(f10(c1)))) | (f10(c1) = c1) | (~big_f(c1, f10(f10(c1))))), inference(lemma,lemma(discharge,[]))).
% 29.67/19.87 tff(27895,plain,
% 29.67/19.87 (big_f(f7(c1), f6(c1, c1))),
% 29.67/19.87 inference(unit_resolution,[status(thm)],[27894, 28, 24968, 27873, 3, 27872])).
% 29.67/19.87 tff(27896,plain,
% 29.67/19.87 (big_f(c1, f6(c1, c1))),
% 29.67/19.87 inference(modus_ponens,[status(thm)],[27895, 27680])).
% 29.67/19.87 tff(27897,plain,
% 29.67/19.87 (big_f(f7(f10(c1)), f6(c1, c1))),
% 29.67/19.87 inference(modus_ponens,[status(thm)],[27896, 27871])).
% 29.67/19.87 tff(27898,plain,
% 29.67/19.87 (f8(f10(c1)) = f8(c2)),
% 29.67/19.87 inference(symmetry,[status(thm)],[24868])).
% 29.67/19.87 tff(27899,plain,
% 29.67/19.87 ((f10(c1) = f8(f10(c1))) <=> (c2 = f8(c2))),
% 29.67/19.88 inference(monotonicity,[status(thm)],[15, 27898])).
% 29.67/19.88 tff(27900,plain,
% 29.67/19.88 ((c2 = f8(c2)) <=> (f10(c1) = f8(f10(c1)))),
% 29.67/19.88 inference(symmetry,[status(thm)],[27899])).
% 29.67/19.88 tff(27901,plain,
% 29.67/19.88 ((f6(c1, c1) = f5(f10(c1))) <=> (f6(c1, c1) = f5(c2))),
% 29.67/19.88 inference(monotonicity,[status(thm)],[295])).
% 29.67/19.88 tff(27902,assumption,(big_f(f7(f10(c1)), f6(c1, c1))), introduced(assumption)).
% 29.67/19.88 tff(27903,assumption,(~(c1 = f8(f10(c1)))), introduced(assumption)).
% 29.67/19.88 tff(27904,plain,
% 29.67/19.88 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (f6(c1, c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (f6(c1, c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, c1))))),
% 29.67/19.88 inference(rewrite,[status(thm)],[])).
% 29.67/19.88 tff(27905,plain,
% 29.67/19.88 (((f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (f7(f10(c1)) = f10(c1)) | (f6(c1, c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, c1)))) <=> ((f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (f6(c1, c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, c1))))),
% 29.67/19.88 inference(rewrite,[status(thm)],[])).
% 29.67/19.88 tff(27906,plain,
% 29.67/19.88 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (f7(f10(c1)) = f10(c1)) | (f6(c1, c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (f6(c1, c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, c1)))))),
% 29.67/19.88 inference(monotonicity,[status(thm)],[27905])).
% 29.67/19.88 tff(27907,plain,
% 29.67/19.88 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (f7(f10(c1)) = f10(c1)) | (f6(c1, c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (f6(c1, c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, c1))))),
% 29.67/19.88 inference(transitivity,[status(thm)],[27906, 27904])).
% 29.67/19.88 tff(27908,plain,
% 29.67/19.88 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (f7(f10(c1)) = f10(c1)) | (f6(c1, c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, c1))))),
% 29.67/19.88 inference(quant_inst,[status(thm)],[])).
% 29.67/19.88 tff(27909,plain,
% 29.67/19.88 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (f6(c1, c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, c1)))),
% 29.67/19.88 inference(modus_ponens,[status(thm)],[27908, 27907])).
% 29.67/19.88 tff(27910,plain,
% 29.67/19.88 ((c1 = f8(f10(c1))) | (f6(c1, c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, c1)))),
% 29.67/19.88 inference(unit_resolution,[status(thm)],[27909, 1659, 24968, 297, 27872])).
% 29.67/19.88 tff(27911,plain,
% 29.67/19.88 (f6(c1, c1) = f5(f10(c1))),
% 29.67/19.88 inference(unit_resolution,[status(thm)],[27910, 27903, 27902])).
% 29.67/19.88 tff(27912,plain,
% 29.67/19.88 (f6(c1, c1) = f5(c2)),
% 29.67/19.88 inference(modus_ponens,[status(thm)],[27911, 27901])).
% 29.67/19.88 tff(27913,plain,
% 29.67/19.88 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~(f10(c1) = f5(f10(c1)))) | big_f(f7(f10(c1)), f10(c1)) | (~big_f(c1, f10(f10(c1)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~(f10(c1) = f5(f10(c1)))) | big_f(f7(f10(c1)), f10(c1)) | (~big_f(c1, f10(f10(c1)))))),
% 29.67/19.88 inference(rewrite,[status(thm)],[])).
% 29.67/19.88 tff(27914,plain,
% 29.67/19.88 (((~(f10(c1) = f5(f10(c1)))) | (f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), f10(c1))) <=> ((f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~(f10(c1) = f5(f10(c1)))) | big_f(f7(f10(c1)), f10(c1)) | (~big_f(c1, f10(f10(c1)))))),
% 29.67/19.88 inference(rewrite,[status(thm)],[])).
% 29.67/19.88 tff(27915,plain,
% 29.67/19.88 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(f10(c1) = f5(f10(c1)))) | (f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), f10(c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~(f10(c1) = f5(f10(c1)))) | big_f(f7(f10(c1)), f10(c1)) | (~big_f(c1, f10(f10(c1))))))),
% 29.67/19.88 inference(monotonicity,[status(thm)],[27914])).
% 29.67/19.88 tff(27916,plain,
% 29.67/19.88 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(f10(c1) = f5(f10(c1)))) | (f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), f10(c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~(f10(c1) = f5(f10(c1)))) | big_f(f7(f10(c1)), f10(c1)) | (~big_f(c1, f10(f10(c1)))))),
% 29.67/19.88 inference(transitivity,[status(thm)],[27915, 27913])).
% 29.67/19.88 tff(27917,plain,
% 29.67/19.88 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(f10(c1) = f5(f10(c1)))) | (f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), f10(c1)))),
% 29.67/19.88 inference(quant_inst,[status(thm)],[])).
% 29.67/19.88 tff(27918,plain,
% 29.67/19.88 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~(f10(c1) = f5(f10(c1)))) | big_f(f7(f10(c1)), f10(c1)) | (~big_f(c1, f10(f10(c1))))),
% 29.67/19.88 inference(modus_ponens,[status(thm)],[27917, 27916])).
% 29.67/19.88 tff(27919,plain,
% 29.67/19.88 ((c1 = f8(f10(c1))) | (~(f10(c1) = f5(f10(c1))))),
% 29.67/19.88 inference(unit_resolution,[status(thm)],[27918, 705, 24968, 297, 27872, 27332])).
% 29.67/19.88 tff(27920,plain,
% 29.67/19.88 (~(f10(c1) = f5(f10(c1)))),
% 29.67/19.88 inference(unit_resolution,[status(thm)],[27919, 27903])).
% 29.67/19.88 tff(27921,plain,
% 29.67/19.88 (~(f5(c2) = c2)),
% 29.67/19.88 inference(unit_resolution,[status(thm)],[27348, 27920, 16])).
% 29.67/19.88 tff(27922,plain,
% 29.67/19.88 (f5(c2) = c1),
% 29.67/19.88 inference(unit_resolution,[status(thm)],[1547, 27921])).
% 29.67/19.88 tff(27923,plain,
% 29.67/19.88 (f7(c2) = f5(c2)),
% 29.67/19.88 inference(unit_resolution,[status(thm)],[8394, 27922, 292])).
% 29.67/19.88 tff(27924,plain,
% 29.67/19.88 (~(f6(c1, c1) = f5(c2))),
% 29.67/19.88 inference(unit_resolution,[status(thm)],[10715, 27923, 292, 28])).
% 29.67/19.88 tff(27925,plain,
% 29.67/19.88 ($false),
% 29.67/19.88 inference(unit_resolution,[status(thm)],[27924, 27912])).
% 29.67/19.88 tff(27926,plain,((c1 = f8(f10(c1))) | (~(f10(c1) = c2)) | (~(f7(c2) = c1)) | (f6(c1, c1) = c1) | (~big_f(f7(f10(c1)), f6(c1, c1))) | (f10(f10(c1)) = f10(c1)) | (f7(f10(c1)) = f10(c1)) | (~big_f(c1, f10(f10(c1)))) | big_f(f7(f10(c1)), f10(c1))), inference(lemma,lemma(discharge,[]))).
% 29.67/19.88 tff(27927,plain,
% 29.67/19.88 (c1 = f8(f10(c1))),
% 29.67/19.88 inference(unit_resolution,[status(thm)],[27926, 28, 292, 15, 27897, 24968, 26316, 27872, 27332])).
% 29.67/19.88 tff(27928,plain,
% 29.67/19.88 (f8(f10(c1)) = c1),
% 29.67/19.88 inference(symmetry,[status(thm)],[27927])).
% 29.67/19.88 tff(27929,plain,
% 29.67/19.88 (f8(c2) = c1),
% 29.67/19.88 inference(transitivity,[status(thm)],[24868, 27928])).
% 29.67/19.88 tff(27930,plain,
% 29.67/19.88 ((c2 = f8(c2)) <=> (f10(c1) = c1)),
% 29.67/19.88 inference(monotonicity,[status(thm)],[5571, 27929])).
% 29.67/19.88 tff(27931,plain,
% 29.67/19.88 ((f10(c1) = c1) <=> (c2 = f8(c2))),
% 29.67/19.88 inference(symmetry,[status(thm)],[27930])).
% 29.67/19.88 tff(27932,plain,
% 29.67/19.88 ((f10(c1) = c1) <=> (f10(c1) = f8(f10(c1)))),
% 29.67/19.88 inference(transitivity,[status(thm)],[27931, 27900])).
% 29.67/19.88 tff(27933,plain,
% 29.67/19.88 ((~(f10(c1) = c1)) <=> (~(f10(c1) = f8(f10(c1))))),
% 29.67/19.88 inference(monotonicity,[status(thm)],[27932])).
% 29.67/19.88 tff(27934,plain,
% 29.67/19.88 (~(f10(c1) = f8(f10(c1)))),
% 29.67/19.88 inference(modus_ponens,[status(thm)],[3, 27933])).
% 29.67/19.88 tff(27935,plain,
% 29.67/19.88 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | (f6(c1, c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, c1))) | (f10(c1) = f8(f10(c1))) | (~big_f(f10(c1), f10(f10(c1)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | (f6(c1, c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, c1))) | (f10(c1) = f8(f10(c1))) | (~big_f(f10(c1), f10(f10(c1)))))),
% 29.67/19.88 inference(rewrite,[status(thm)],[])).
% 29.67/19.88 tff(27936,plain,
% 29.67/19.88 (((f10(f10(c1)) = f10(c1)) | (f10(c1) = f8(f10(c1))) | (~big_f(f10(c1), f10(f10(c1)))) | (f7(f10(c1)) = f10(c1)) | (f6(c1, c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, c1)))) <=> ((f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | (f6(c1, c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, c1))) | (f10(c1) = f8(f10(c1))) | (~big_f(f10(c1), f10(f10(c1)))))),
% 29.67/19.88 inference(rewrite,[status(thm)],[])).
% 29.67/19.88 tff(27937,plain,
% 29.67/19.88 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f10(c1)) = f10(c1)) | (f10(c1) = f8(f10(c1))) | (~big_f(f10(c1), f10(f10(c1)))) | (f7(f10(c1)) = f10(c1)) | (f6(c1, c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | (f6(c1, c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, c1))) | (f10(c1) = f8(f10(c1))) | (~big_f(f10(c1), f10(f10(c1))))))),
% 29.67/19.88 inference(monotonicity,[status(thm)],[27936])).
% 29.67/19.88 tff(27938,plain,
% 29.67/19.88 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f10(c1)) = f10(c1)) | (f10(c1) = f8(f10(c1))) | (~big_f(f10(c1), f10(f10(c1)))) | (f7(f10(c1)) = f10(c1)) | (f6(c1, c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | (f6(c1, c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, c1))) | (f10(c1) = f8(f10(c1))) | (~big_f(f10(c1), f10(f10(c1)))))),
% 29.67/19.88 inference(transitivity,[status(thm)],[27937, 27935])).
% 29.67/19.88 tff(27939,plain,
% 29.67/19.88 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f10(c1)) = f10(c1)) | (f10(c1) = f8(f10(c1))) | (~big_f(f10(c1), f10(f10(c1)))) | (f7(f10(c1)) = f10(c1)) | (f6(c1, c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, c1))))),
% 29.67/19.88 inference(quant_inst,[status(thm)],[])).
% 29.67/19.88 tff(27940,plain,
% 29.67/19.88 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | (f6(c1, c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, c1))) | (f10(c1) = f8(f10(c1))) | (~big_f(f10(c1), f10(f10(c1))))),
% 29.67/19.88 inference(modus_ponens,[status(thm)],[27939, 27938])).
% 29.67/19.88 tff(27941,plain,
% 29.67/19.88 ((f6(c1, c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f6(c1, c1))) | (f10(c1) = f8(f10(c1)))),
% 29.67/19.88 inference(unit_resolution,[status(thm)],[27940, 1659, 24968, 26316, 27873])).
% 29.67/19.88 tff(27942,plain,
% 29.67/19.88 (f6(c1, c1) = f5(f10(c1))),
% 29.67/19.88 inference(unit_resolution,[status(thm)],[27941, 27934, 27897])).
% 29.67/19.88 tff(27943,plain,
% 29.67/19.88 (f6(c1, c1) = f5(c2)),
% 29.67/19.88 inference(modus_ponens,[status(thm)],[27942, 27869])).
% 29.67/19.88 tff(27944,plain,
% 29.67/19.88 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | (~(f10(c1) = f5(f10(c1)))) | big_f(f7(f10(c1)), f10(c1)) | (f10(c1) = f8(f10(c1))) | (~big_f(f10(c1), f10(f10(c1)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | (~(f10(c1) = f5(f10(c1)))) | big_f(f7(f10(c1)), f10(c1)) | (f10(c1) = f8(f10(c1))) | (~big_f(f10(c1), f10(f10(c1)))))),
% 29.67/19.88 inference(rewrite,[status(thm)],[])).
% 29.67/19.88 tff(27945,plain,
% 29.67/19.88 (((~(f10(c1) = f5(f10(c1)))) | (f10(f10(c1)) = f10(c1)) | (f10(c1) = f8(f10(c1))) | (~big_f(f10(c1), f10(f10(c1)))) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), f10(c1))) <=> ((f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | (~(f10(c1) = f5(f10(c1)))) | big_f(f7(f10(c1)), f10(c1)) | (f10(c1) = f8(f10(c1))) | (~big_f(f10(c1), f10(f10(c1)))))),
% 29.67/19.88 inference(rewrite,[status(thm)],[])).
% 29.67/19.88 tff(27946,plain,
% 29.67/19.88 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(f10(c1) = f5(f10(c1)))) | (f10(f10(c1)) = f10(c1)) | (f10(c1) = f8(f10(c1))) | (~big_f(f10(c1), f10(f10(c1)))) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), f10(c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | (~(f10(c1) = f5(f10(c1)))) | big_f(f7(f10(c1)), f10(c1)) | (f10(c1) = f8(f10(c1))) | (~big_f(f10(c1), f10(f10(c1))))))),
% 29.67/19.88 inference(monotonicity,[status(thm)],[27945])).
% 29.67/19.88 tff(27947,plain,
% 29.67/19.88 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(f10(c1) = f5(f10(c1)))) | (f10(f10(c1)) = f10(c1)) | (f10(c1) = f8(f10(c1))) | (~big_f(f10(c1), f10(f10(c1)))) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), f10(c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | (~(f10(c1) = f5(f10(c1)))) | big_f(f7(f10(c1)), f10(c1)) | (f10(c1) = f8(f10(c1))) | (~big_f(f10(c1), f10(f10(c1)))))),
% 29.67/19.88 inference(transitivity,[status(thm)],[27946, 27944])).
% 29.67/19.88 tff(27948,plain,
% 29.67/19.88 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(f10(c1) = f5(f10(c1)))) | (f10(f10(c1)) = f10(c1)) | (f10(c1) = f8(f10(c1))) | (~big_f(f10(c1), f10(f10(c1)))) | (f7(f10(c1)) = f10(c1)) | big_f(f7(f10(c1)), f10(c1)))),
% 29.67/19.88 inference(quant_inst,[status(thm)],[])).
% 29.67/19.88 tff(27949,plain,
% 29.67/19.88 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | (~(f10(c1) = f5(f10(c1)))) | big_f(f7(f10(c1)), f10(c1)) | (f10(c1) = f8(f10(c1))) | (~big_f(f10(c1), f10(f10(c1))))),
% 29.67/19.88 inference(modus_ponens,[status(thm)],[27948, 27947])).
% 29.67/19.88 tff(27950,plain,
% 29.67/19.88 ((~(f10(c1) = f5(f10(c1)))) | (f10(c1) = f8(f10(c1)))),
% 29.67/19.88 inference(unit_resolution,[status(thm)],[27949, 705, 24968, 26316, 27873, 27332])).
% 29.67/19.88 tff(27951,plain,
% 29.67/19.88 (~(f10(c1) = f5(f10(c1)))),
% 29.67/19.88 inference(unit_resolution,[status(thm)],[27950, 27934])).
% 29.67/19.88 tff(27952,plain,
% 29.67/19.88 (~(f5(c2) = c2)),
% 29.67/19.88 inference(unit_resolution,[status(thm)],[27348, 27951, 15])).
% 29.67/19.88 tff(27953,plain,
% 29.67/19.88 (f5(c2) = c1),
% 29.67/19.88 inference(unit_resolution,[status(thm)],[1547, 27952])).
% 29.67/19.88 tff(27954,plain,
% 29.67/19.88 (f7(c2) = f5(c2)),
% 29.67/19.88 inference(unit_resolution,[status(thm)],[8394, 27953, 292])).
% 29.67/19.88 tff(27955,plain,
% 29.67/19.88 (~(f6(c1, c1) = f5(c2))),
% 29.67/19.88 inference(unit_resolution,[status(thm)],[10715, 27954, 292, 28])).
% 29.67/19.88 tff(27956,plain,
% 29.67/19.88 ($false),
% 29.67/19.88 inference(unit_resolution,[status(thm)],[27955, 27943])).
% 29.67/19.88 tff(27957,plain,((f6(c1, c1) = c1) | (~(f7(c2) = c1)) | (f10(f10(c1)) = f10(c1)) | (~big_f(f10(c1), f10(f10(c1)))) | big_f(f7(f10(c1)), f10(c1)) | (f10(c1) = c1) | (~big_f(c1, f10(f10(c1))))), inference(lemma,lemma(discharge,[]))).
% 29.67/19.88 tff(27958,plain,
% 29.67/19.88 (f6(c1, c1) = c1),
% 29.67/19.88 inference(unit_resolution,[status(thm)],[27957, 27867, 292, 27863, 27332, 3, 27857])).
% 29.67/19.88 tff(27959,plain,
% 29.67/19.88 (big_f(f7(c1), f6(c1, c1))),
% 29.67/19.88 inference(unit_resolution,[status(thm)],[27769, 27958, 4932])).
% 29.67/19.88 tff(27960,plain,
% 29.67/19.88 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))))),
% 29.67/19.88 inference(rewrite,[status(thm)],[])).
% 29.67/19.88 tff(27961,plain,
% 29.67/19.88 (((f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1)))) <=> ((f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))))),
% 29.67/19.88 inference(rewrite,[status(thm)],[])).
% 29.67/19.88 tff(27962,plain,
% 29.67/19.88 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1))))))),
% 29.67/19.88 inference(monotonicity,[status(thm)],[27961])).
% 29.67/19.88 tff(27963,plain,
% 29.67/19.88 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))))),
% 29.67/19.88 inference(transitivity,[status(thm)],[27962, 27960])).
% 29.67/19.88 tff(27964,plain,
% 29.67/19.88 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))),
% 29.67/19.88 inference(quant_inst,[status(thm)],[])).
% 29.67/19.88 tff(27965,plain,
% 29.67/19.88 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1))))),
% 29.67/19.88 inference(modus_ponens,[status(thm)],[27964, 27963])).
% 29.67/19.88 tff(27966,plain,
% 29.67/19.88 (c1 = f8(f10(c1))),
% 29.67/19.88 inference(unit_resolution,[status(thm)],[27965, 2730, 25791, 27867, 27959, 27958, 27857])).
% 29.67/19.88 tff(27967,plain,
% 29.67/19.88 (f8(f10(c1)) = c1),
% 29.67/19.88 inference(symmetry,[status(thm)],[27966])).
% 29.67/19.88 tff(27968,plain,
% 29.67/19.88 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (f10(c1) = f8(f10(c1))) | (~big_f(f10(c1), f10(f10(c1)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (f10(c1) = f8(f10(c1))) | (~big_f(f10(c1), f10(f10(c1)))))),
% 29.67/19.88 inference(rewrite,[status(thm)],[])).
% 29.67/19.88 tff(27969,plain,
% 29.67/19.88 (((f10(f10(c1)) = f10(c1)) | (f10(c1) = f8(f10(c1))) | (~big_f(f10(c1), f10(f10(c1)))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1)))) <=> ((f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (f10(c1) = f8(f10(c1))) | (~big_f(f10(c1), f10(f10(c1)))))),
% 29.67/19.88 inference(rewrite,[status(thm)],[])).
% 29.67/19.88 tff(27970,plain,
% 29.67/19.88 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f10(c1)) = f10(c1)) | (f10(c1) = f8(f10(c1))) | (~big_f(f10(c1), f10(f10(c1)))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (f10(c1) = f8(f10(c1))) | (~big_f(f10(c1), f10(f10(c1))))))),
% 29.67/19.88 inference(monotonicity,[status(thm)],[27969])).
% 29.67/19.88 tff(27971,plain,
% 29.67/19.88 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f10(c1)) = f10(c1)) | (f10(c1) = f8(f10(c1))) | (~big_f(f10(c1), f10(f10(c1)))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (f10(c1) = f8(f10(c1))) | (~big_f(f10(c1), f10(f10(c1)))))),
% 29.67/19.88 inference(transitivity,[status(thm)],[27970, 27968])).
% 29.67/19.88 tff(27972,plain,
% 29.67/19.88 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f10(c1)) = f10(c1)) | (f10(c1) = f8(f10(c1))) | (~big_f(f10(c1), f10(f10(c1)))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))),
% 29.67/19.89 inference(quant_inst,[status(thm)],[])).
% 29.67/19.89 tff(27973,plain,
% 29.67/19.89 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (f10(c1) = f8(f10(c1))) | (~big_f(f10(c1), f10(f10(c1))))),
% 29.67/19.89 inference(modus_ponens,[status(thm)],[27972, 27971])).
% 29.67/19.89 tff(27974,plain,
% 29.67/19.89 (f10(c1) = f8(f10(c1))),
% 29.67/19.89 inference(unit_resolution,[status(thm)],[27973, 2730, 25791, 27867, 27959, 27958, 27863])).
% 29.67/19.89 tff(27975,plain,
% 29.67/19.89 (f10(c1) = c1),
% 29.67/19.89 inference(transitivity,[status(thm)],[27974, 27967])).
% 29.67/19.89 tff(27976,plain,
% 29.67/19.89 ($false),
% 29.67/19.89 inference(unit_resolution,[status(thm)],[3, 27975])).
% 29.67/19.89 tff(27977,plain,((f10(c2) = c2) | (f10(c1) = c1) | (~big_f(c1, c1)) | (~(f7(c2) = c1)) | big_f(f7(f10(c1)), f10(c1)) | (~big_f(f10(c1), c1))), inference(lemma,lemma(discharge,[]))).
% 29.67/19.89 tff(27978,plain,
% 29.67/19.89 ($false),
% 29.67/19.89 inference(unit_resolution,[status(thm)],[27977, 27853, 27297, 4932, 292, 89, 3])).
% 29.67/19.89 tff(27979,plain,((f10(c1) = c1) | (~big_f(c1, c1)) | (~(f7(c2) = c1)) | (f10(c2) = c2) | big_f(c1, c2) | (~big_f(c2, c1))), inference(lemma,lemma(discharge,[]))).
% 29.67/19.89 tff(27980,plain,
% 29.67/19.89 (f10(c1) = c1),
% 29.67/19.89 inference(unit_resolution,[status(thm)],[27979, 22, 27489, 27838, 27, 27828])).
% 29.67/19.89 tff(27981,plain,
% 29.67/19.89 (big_f(f9(c1, c1), f10(c1))),
% 29.67/19.89 inference(unit_resolution,[status(thm)],[8716, 27980, 27845])).
% 29.67/19.89 tff(27982,assumption,(big_f(c1, f10(c2))), introduced(assumption)).
% 29.67/19.89 tff(27983,plain,
% 29.67/19.89 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f10(c2) = c2) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(c2) = c2) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))))),
% 29.67/19.89 inference(rewrite,[status(thm)],[])).
% 29.67/19.89 tff(27984,plain,
% 29.67/19.89 (((~(c2 = f5(c2))) | (f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (f7(c2) = c2) | big_f(f7(c2), c2)) <=> ((f10(c2) = c2) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))))),
% 29.67/19.89 inference(rewrite,[status(thm)],[])).
% 29.67/19.89 tff(27985,plain,
% 29.67/19.89 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c2 = f5(c2))) | (f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (f7(c2) = c2) | big_f(f7(c2), c2))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f10(c2) = c2) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2)))))),
% 29.67/19.89 inference(monotonicity,[status(thm)],[27984])).
% 29.67/19.89 tff(27986,plain,
% 29.67/19.89 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c2 = f5(c2))) | (f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (f7(c2) = c2) | big_f(f7(c2), c2))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(c2) = c2) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))))),
% 29.67/19.89 inference(transitivity,[status(thm)],[27985, 27983])).
% 29.67/19.89 tff(27987,plain,
% 29.67/19.89 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c2 = f5(c2))) | (f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (f7(c2) = c2) | big_f(f7(c2), c2))),
% 29.67/19.89 inference(quant_inst,[status(thm)],[])).
% 29.67/19.89 tff(27988,plain,
% 29.67/19.89 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(c2) = c2) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2)))),
% 29.67/19.89 inference(modus_ponens,[status(thm)],[27987, 27986])).
% 29.67/19.89 tff(27989,plain,
% 29.67/19.89 ((~(c2 = f5(c2))) | (c1 = f8(c2))),
% 29.67/19.89 inference(unit_resolution,[status(thm)],[27988, 705, 89, 17, 1521, 27982])).
% 29.67/19.89 tff(27990,plain,
% 29.67/19.89 (c1 = f8(c2)),
% 29.67/19.89 inference(unit_resolution,[status(thm)],[27989, 5124])).
% 29.67/19.89 tff(27991,plain,
% 29.67/19.89 (f8(c2) = c1),
% 29.67/19.89 inference(symmetry,[status(thm)],[27990])).
% 29.67/19.89 tff(27992,assumption,(big_f(f9(c1, c1), f10(c2))), introduced(assumption)).
% 29.67/19.89 tff(27993,plain,
% 29.67/19.89 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f10(c2) = c2) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (f9(c1, c1) = f8(c2)) | (~big_f(f9(c1, c1), f10(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(c2) = c2) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (f9(c1, c1) = f8(c2)) | (~big_f(f9(c1, c1), f10(c2))))),
% 29.67/19.89 inference(rewrite,[status(thm)],[])).
% 29.67/19.89 tff(27994,plain,
% 29.67/19.89 (((~(c2 = f5(c2))) | (f10(c2) = c2) | (f9(c1, c1) = f8(c2)) | (~big_f(f9(c1, c1), f10(c2))) | (f7(c2) = c2) | big_f(f7(c2), c2)) <=> ((f10(c2) = c2) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (f9(c1, c1) = f8(c2)) | (~big_f(f9(c1, c1), f10(c2))))),
% 29.67/19.89 inference(rewrite,[status(thm)],[])).
% 29.67/19.89 tff(27995,plain,
% 29.67/19.89 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c2 = f5(c2))) | (f10(c2) = c2) | (f9(c1, c1) = f8(c2)) | (~big_f(f9(c1, c1), f10(c2))) | (f7(c2) = c2) | big_f(f7(c2), c2))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((f10(c2) = c2) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (f9(c1, c1) = f8(c2)) | (~big_f(f9(c1, c1), f10(c2)))))),
% 29.67/19.89 inference(monotonicity,[status(thm)],[27994])).
% 29.67/19.89 tff(27996,plain,
% 29.67/19.89 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c2 = f5(c2))) | (f10(c2) = c2) | (f9(c1, c1) = f8(c2)) | (~big_f(f9(c1, c1), f10(c2))) | (f7(c2) = c2) | big_f(f7(c2), c2))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(c2) = c2) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (f9(c1, c1) = f8(c2)) | (~big_f(f9(c1, c1), f10(c2))))),
% 29.67/19.89 inference(transitivity,[status(thm)],[27995, 27993])).
% 29.67/19.89 tff(27997,plain,
% 29.67/19.89 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | ((~(c2 = f5(c2))) | (f10(c2) = c2) | (f9(c1, c1) = f8(c2)) | (~big_f(f9(c1, c1), f10(c2))) | (f7(c2) = c2) | big_f(f7(c2), c2))),
% 29.67/19.89 inference(quant_inst,[status(thm)],[])).
% 29.67/19.89 tff(27998,plain,
% 29.67/19.89 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((~(X5 = f5(X4))) | (f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | big_f(f7(X4), X5))) | (f10(c2) = c2) | (f7(c2) = c2) | (~(c2 = f5(c2))) | big_f(f7(c2), c2) | (f9(c1, c1) = f8(c2)) | (~big_f(f9(c1, c1), f10(c2)))),
% 29.67/19.89 inference(modus_ponens,[status(thm)],[27997, 27996])).
% 29.67/19.89 tff(27999,plain,
% 29.67/19.89 ((~(c2 = f5(c2))) | (f9(c1, c1) = f8(c2)) | (~big_f(f9(c1, c1), f10(c2)))),
% 29.67/19.89 inference(unit_resolution,[status(thm)],[27998, 705, 89, 17, 1521])).
% 29.67/19.89 tff(28000,plain,
% 29.67/19.89 (f9(c1, c1) = f8(c2)),
% 29.67/19.89 inference(unit_resolution,[status(thm)],[27999, 5124, 27992])).
% 29.67/19.89 tff(28001,plain,
% 29.67/19.89 (f9(c1, c1) = c1),
% 29.67/19.89 inference(transitivity,[status(thm)],[28000, 27991])).
% 29.67/19.89 tff(28002,plain,
% 29.67/19.89 ((~(c2 = f5(c2))) | (~(f9(c1, c1) = c1))),
% 29.67/19.89 inference(unit_resolution,[status(thm)],[27587, 783, 3762, 17, 1521, 3948])).
% 29.67/19.89 tff(28003,plain,
% 29.67/19.89 (~(f9(c1, c1) = c1)),
% 29.67/19.89 inference(unit_resolution,[status(thm)],[28002, 5124])).
% 29.67/19.89 tff(28004,plain,
% 29.67/19.89 ($false),
% 29.67/19.89 inference(unit_resolution,[status(thm)],[28003, 28001])).
% 29.67/19.89 tff(28005,plain,((~(c2 = f5(c2))) | (~(f10(c1) = c1)) | (f7(c2) = c2) | big_f(f7(c2), c2) | (~big_f(f9(c1, c1), f10(c1))) | (~big_f(f9(c1, c1), f10(c2))) | (f10(c2) = c2) | (~big_f(c1, f10(c2)))), inference(lemma,lemma(discharge,[]))).
% 29.67/19.89 tff(28006,plain,
% 29.67/19.89 (~(c2 = f5(c2))),
% 29.67/19.89 inference(unit_resolution,[status(thm)],[28005, 27980, 17, 23145, 27981, 27846, 27838, 27842])).
% 29.67/19.89 tff(28007,plain,
% 29.67/19.89 (~(f5(c2) = c2)),
% 29.67/19.89 inference(unit_resolution,[status(thm)],[8113, 28006])).
% 29.67/19.89 tff(28008,plain,
% 29.67/19.89 (f5(c2) = c1),
% 29.67/19.89 inference(unit_resolution,[status(thm)],[1547, 28007])).
% 29.67/19.89 tff(28009,plain,
% 29.67/19.89 (f7(c2) = f5(c2)),
% 29.67/19.89 inference(unit_resolution,[status(thm)],[8394, 28008, 22])).
% 29.67/19.89 tff(28010,plain,
% 29.67/19.89 (big_f(c1, f6(c1, c1)) <=> big_f(f7(c1), f6(c1, c1))),
% 29.67/19.89 inference(symmetry,[status(thm)],[27680])).
% 29.67/19.89 tff(28011,plain,
% 29.67/19.89 (big_f(f7(c2), f6(c1, c1)) <=> big_f(f7(c1), f6(c1, c1))),
% 29.67/19.89 inference(transitivity,[status(thm)],[27593, 28010])).
% 29.67/19.89 tff(28012,plain,
% 29.67/19.89 ((~big_f(f7(c2), f6(c1, c1))) <=> (~big_f(f7(c1), f6(c1, c1)))),
% 29.67/19.89 inference(monotonicity,[status(thm)],[28011])).
% 29.67/19.89 tff(28013,plain,
% 29.67/19.89 (big_f(f9(c1, c1), c1)),
% 29.67/19.89 inference(unit_resolution,[status(thm)],[26966, 348, 22, 17698])).
% 29.67/19.89 tff(28014,plain,
% 29.67/19.89 (big_f(f9(c1, c1), f10(c1))),
% 29.67/19.89 inference(unit_resolution,[status(thm)],[8716, 3762, 28013])).
% 29.67/19.89 tff(28015,plain,
% 29.67/19.89 (big_f(c1, f10(c2))),
% 29.67/19.89 inference(modus_ponens,[status(thm)],[4932, 24205])).
% 29.67/19.89 tff(28016,plain,
% 29.67/19.89 (big_f(f9(c1, c1), f10(c2)) <=> big_f(f9(c1, c1), c1)),
% 29.67/19.89 inference(monotonicity,[status(thm)],[94])).
% 29.67/19.89 tff(28017,plain,
% 29.67/19.89 (big_f(f9(c1, c1), c1) <=> big_f(f9(c1, c1), f10(c2))),
% 29.67/19.89 inference(symmetry,[status(thm)],[28016])).
% 29.67/19.89 tff(28018,plain,
% 29.67/19.89 (big_f(f9(c1, c1), f10(c2))),
% 29.67/19.89 inference(modus_ponens,[status(thm)],[28013, 28017])).
% 29.67/19.89 tff(28019,plain,
% 29.67/19.89 (~(f6(c1, c1) = f5(c2))),
% 29.67/19.89 inference(unit_resolution,[status(thm)],[10715, 28, 22, 8378])).
% 29.67/19.89 tff(28020,assumption,(~(f6(c1, c1) = f5(c2))), introduced(assumption)).
% 29.67/19.89 tff(28021,assumption,(big_f(f7(c2), f6(c1, c1))), introduced(assumption)).
% 29.67/19.89 tff(28022,plain,
% 29.67/19.89 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f7(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (f7(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))))),
% 29.67/19.89 inference(rewrite,[status(thm)],[])).
% 29.67/19.89 tff(28023,plain,
% 29.67/19.89 (((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (f7(c2) = c2) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1)))) <=> ((f10(c2) = c2) | (f7(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))))),
% 29.67/19.89 inference(rewrite,[status(thm)],[])).
% 29.67/19.89 tff(28024,plain,
% 29.67/19.89 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (f7(c2) = c2) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f7(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1)))))),
% 29.67/19.89 inference(monotonicity,[status(thm)],[28023])).
% 29.67/19.89 tff(28025,plain,
% 29.67/19.89 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (f7(c2) = c2) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (f7(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))))),
% 29.67/19.89 inference(transitivity,[status(thm)],[28024, 28022])).
% 29.67/19.89 tff(28026,plain,
% 29.67/19.89 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (f7(c2) = c2) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))))),
% 29.67/19.89 inference(quant_inst,[status(thm)],[])).
% 29.67/19.89 tff(28027,plain,
% 29.67/19.89 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (f7(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1)))),
% 29.67/19.89 inference(modus_ponens,[status(thm)],[28026, 28025])).
% 29.67/19.89 tff(28028,plain,
% 29.67/19.89 ((c1 = f8(c2)) | (f6(c1, c1) = f5(c2))),
% 29.67/19.89 inference(unit_resolution,[status(thm)],[28027, 1659, 89, 17, 27982, 28021])).
% 29.67/19.89 tff(28029,plain,
% 29.67/19.89 (c1 = f8(c2)),
% 29.67/19.89 inference(unit_resolution,[status(thm)],[28028, 28020])).
% 29.67/19.89 tff(28030,plain,
% 29.67/19.89 (f8(c2) = c1),
% 29.67/19.89 inference(symmetry,[status(thm)],[28029])).
% 29.67/19.89 tff(28031,plain,
% 29.67/19.89 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f7(c2) = c2) | (f9(c1, c1) = f8(c2)) | (~big_f(f9(c1, c1), f10(c2))) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (f7(c2) = c2) | (f9(c1, c1) = f8(c2)) | (~big_f(f9(c1, c1), f10(c2))) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))))),
% 29.67/19.89 inference(rewrite,[status(thm)],[])).
% 29.67/19.89 tff(28032,plain,
% 29.67/19.89 (((f10(c2) = c2) | (f9(c1, c1) = f8(c2)) | (~big_f(f9(c1, c1), f10(c2))) | (f7(c2) = c2) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1)))) <=> ((f10(c2) = c2) | (f7(c2) = c2) | (f9(c1, c1) = f8(c2)) | (~big_f(f9(c1, c1), f10(c2))) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))))),
% 29.67/19.89 inference(rewrite,[status(thm)],[])).
% 29.67/19.89 tff(28033,plain,
% 29.67/19.89 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f9(c1, c1) = f8(c2)) | (~big_f(f9(c1, c1), f10(c2))) | (f7(c2) = c2) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f7(c2) = c2) | (f9(c1, c1) = f8(c2)) | (~big_f(f9(c1, c1), f10(c2))) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1)))))),
% 29.67/19.89 inference(monotonicity,[status(thm)],[28032])).
% 29.67/19.89 tff(28034,plain,
% 29.67/19.89 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f9(c1, c1) = f8(c2)) | (~big_f(f9(c1, c1), f10(c2))) | (f7(c2) = c2) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (f7(c2) = c2) | (f9(c1, c1) = f8(c2)) | (~big_f(f9(c1, c1), f10(c2))) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))))),
% 29.67/19.89 inference(transitivity,[status(thm)],[28033, 28031])).
% 29.67/19.89 tff(28035,plain,
% 29.67/19.89 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f9(c1, c1) = f8(c2)) | (~big_f(f9(c1, c1), f10(c2))) | (f7(c2) = c2) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))))),
% 29.67/19.89 inference(quant_inst,[status(thm)],[])).
% 29.67/19.89 tff(28036,plain,
% 29.67/19.89 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (f7(c2) = c2) | (f9(c1, c1) = f8(c2)) | (~big_f(f9(c1, c1), f10(c2))) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1)))),
% 29.67/19.89 inference(modus_ponens,[status(thm)],[28035, 28034])).
% 29.67/19.89 tff(28037,plain,
% 29.67/19.89 ((f9(c1, c1) = f8(c2)) | (f6(c1, c1) = f5(c2))),
% 29.67/19.89 inference(unit_resolution,[status(thm)],[28036, 1659, 89, 17, 28021, 27992])).
% 29.67/19.89 tff(28038,plain,
% 29.67/19.89 (f9(c1, c1) = f8(c2)),
% 29.67/19.89 inference(unit_resolution,[status(thm)],[28037, 28020])).
% 29.67/19.89 tff(28039,plain,
% 29.67/19.89 (f9(c1, c1) = c1),
% 29.67/19.89 inference(transitivity,[status(thm)],[28038, 28030])).
% 29.67/19.89 tff(28040,plain,
% 29.67/19.89 ((~(f9(c1, c1) = c1)) | (f6(c1, c1) = f5(c2))),
% 29.67/19.89 inference(unit_resolution,[status(thm)],[27612, 1190, 3762, 17, 3948, 28021])).
% 29.67/19.89 tff(28041,plain,
% 29.67/19.89 (~(f9(c1, c1) = c1)),
% 29.67/19.89 inference(unit_resolution,[status(thm)],[28040, 28020])).
% 29.67/19.89 tff(28042,plain,
% 29.67/19.89 ($false),
% 29.67/19.89 inference(unit_resolution,[status(thm)],[28041, 28039])).
% 29.67/19.89 tff(28043,plain,((f6(c1, c1) = f5(c2)) | (f10(c2) = c2) | (f7(c2) = c2) | (~big_f(f7(c2), f6(c1, c1))) | (~big_f(f9(c1, c1), f10(c2))) | (~big_f(c1, f10(c2))) | (~(f10(c1) = c1)) | (~big_f(f9(c1, c1), f10(c1)))), inference(lemma,lemma(discharge,[]))).
% 29.67/19.89 tff(28044,plain,
% 29.67/19.89 (~big_f(f7(c2), f6(c1, c1))),
% 29.67/19.89 inference(unit_resolution,[status(thm)],[28043, 28019, 17, 89, 28018, 28015, 3762, 28014])).
% 29.67/19.89 tff(28045,plain,
% 29.67/19.89 (~big_f(f7(c1), f6(c1, c1))),
% 29.67/19.89 inference(modus_ponens,[status(thm)],[28044, 28012])).
% 29.67/19.89 tff(28046,plain,
% 29.67/19.89 (f10(f9(f10(c2), f10(c2))) = f10(f9(c1, c1))),
% 29.67/19.89 inference(monotonicity,[status(thm)],[17769])).
% 29.67/19.89 tff(28047,plain,
% 29.67/19.89 (f10(f9(c1, c1)) = f10(f9(f10(c2), f10(c2)))),
% 29.67/19.89 inference(symmetry,[status(thm)],[28046])).
% 29.67/19.89 tff(28048,plain,
% 29.67/19.89 ((~(f9(c1, c1) = c1)) | (~big_f(f7(c2), c1)) | (~(f7(c2) = c1)) | (~(f10(c1) = c1)) | big_f(f7(c1), f6(c1, c1))),
% 29.67/19.89 inference(unit_resolution,[status(thm)],[9976, 25791])).
% 29.67/19.89 tff(28049,plain,
% 29.67/19.89 (~(f9(c1, c1) = c1)),
% 29.67/19.89 inference(unit_resolution,[status(thm)],[28048, 65, 292, 20220, 3762])).
% 29.67/19.89 tff(28050,plain,
% 29.67/19.89 (f9(c1, c1) = c2),
% 29.67/19.89 inference(unit_resolution,[status(thm)],[3939, 28049])).
% 29.67/19.89 tff(28051,plain,
% 29.67/19.89 (big_f(f9(c1, c1), f10(f9(c1, c1))) <=> big_f(c2, f10(f9(f10(c2), f10(c2))))),
% 29.67/19.89 inference(monotonicity,[status(thm)],[28050, 28047])).
% 29.67/19.89 tff(28052,plain,
% 29.67/19.89 (big_f(c2, f10(f9(f10(c2), f10(c2)))) <=> big_f(f9(c1, c1), f10(f9(c1, c1)))),
% 29.67/19.89 inference(symmetry,[status(thm)],[28051])).
% 29.67/19.89 tff(28053,plain,
% 29.67/19.89 (f10(f9(c1, c1)) = f10(c2)),
% 29.67/19.89 inference(monotonicity,[status(thm)],[28050])).
% 29.67/19.89 tff(28054,plain,
% 29.67/19.89 (f10(f9(f10(c2), f10(c2))) = c1),
% 29.67/19.89 inference(transitivity,[status(thm)],[28046, 28053, 11819])).
% 29.67/19.89 tff(28055,plain,
% 29.67/19.89 (big_f(c2, f10(f9(f10(c2), f10(c2)))) <=> big_f(c2, c1)),
% 29.67/19.89 inference(monotonicity,[status(thm)],[28054])).
% 29.67/19.89 tff(28056,plain,
% 29.67/19.89 (big_f(c2, c1) <=> big_f(c2, f10(f9(f10(c2), f10(c2))))),
% 29.67/19.89 inference(symmetry,[status(thm)],[28055])).
% 29.67/19.89 tff(28057,plain,
% 29.67/19.89 (big_f(c2, c1) <=> big_f(f9(c1, c1), f10(f9(c1, c1)))),
% 29.67/19.89 inference(transitivity,[status(thm)],[28056, 28052])).
% 29.67/19.89 tff(28058,plain,
% 29.67/19.89 (big_f(f9(c1, c1), f10(f9(c1, c1)))),
% 29.67/19.89 inference(modus_ponens,[status(thm)],[348, 28057])).
% 29.67/19.89 tff(28059,plain,
% 29.67/19.89 (f10(f9(c1, c1)) = c1),
% 29.67/19.89 inference(transitivity,[status(thm)],[28053, 11819])).
% 29.67/19.89 tff(28060,plain,
% 29.67/19.89 (big_f(c1, f10(f9(c1, c1))) <=> big_f(c1, c1)),
% 29.67/19.89 inference(monotonicity,[status(thm)],[28059])).
% 29.67/19.89 tff(28061,plain,
% 29.67/19.89 (big_f(c1, c1) <=> big_f(c1, f10(f9(c1, c1)))),
% 29.67/19.89 inference(symmetry,[status(thm)],[28060])).
% 29.67/19.89 tff(28062,plain,
% 29.67/19.89 (big_f(c1, f10(f9(c1, c1)))),
% 29.67/19.89 inference(modus_ponens,[status(thm)],[4932, 28061])).
% 29.67/19.89 tff(28063,plain,
% 29.67/19.89 (f9(f10(c2), f7(c1)) = f9(c1, c1)),
% 29.67/19.89 inference(monotonicity,[status(thm)],[11819, 25791])).
% 29.67/19.89 tff(28064,plain,
% 29.67/19.90 (f10(f9(f10(c2), f7(c1))) = f10(f9(c1, c1))),
% 29.67/19.90 inference(monotonicity,[status(thm)],[28063])).
% 29.67/19.90 tff(28065,plain,
% 29.67/19.90 (f10(f9(c1, c1)) = f10(f9(f10(c2), f7(c1)))),
% 29.67/19.90 inference(symmetry,[status(thm)],[28064])).
% 29.67/19.90 tff(28066,plain,
% 29.67/19.90 ((f10(f9(c1, c1)) = f9(c1, c1)) <=> (f10(f9(f10(c2), f7(c1))) = c2)),
% 29.67/19.90 inference(monotonicity,[status(thm)],[28065, 28050])).
% 29.67/19.90 tff(28067,plain,
% 29.67/19.90 ((f10(f9(f10(c2), f7(c1))) = c2) <=> (f10(f9(c1, c1)) = f9(c1, c1))),
% 29.67/19.90 inference(symmetry,[status(thm)],[28066])).
% 29.67/19.90 tff(28068,plain,
% 29.67/19.90 (f10(f9(f10(c2), f7(c1))) = c1),
% 29.67/19.90 inference(transitivity,[status(thm)],[28064, 28053, 11819])).
% 29.67/19.90 tff(28069,plain,
% 29.67/19.90 ((f10(f9(f10(c2), f7(c1))) = c2) <=> (c1 = c2)),
% 29.67/19.90 inference(monotonicity,[status(thm)],[28068])).
% 29.67/19.90 tff(28070,plain,
% 29.67/19.90 ((f10(f9(f10(c2), f7(c1))) = c2) <=> (c2 = c1)),
% 29.67/19.90 inference(transitivity,[status(thm)],[28069, 1])).
% 29.67/19.90 tff(28071,plain,
% 29.67/19.90 ((c2 = c1) <=> (f10(f9(f10(c2), f7(c1))) = c2)),
% 29.67/19.90 inference(symmetry,[status(thm)],[28070])).
% 29.67/19.90 tff(28072,plain,
% 29.67/19.90 ((c2 = c1) <=> (f10(f9(c1, c1)) = f9(c1, c1))),
% 29.67/19.90 inference(transitivity,[status(thm)],[28071, 28067])).
% 29.67/19.90 tff(28073,plain,
% 29.67/19.90 ((~(c2 = c1)) <=> (~(f10(f9(c1, c1)) = f9(c1, c1)))),
% 29.67/19.90 inference(monotonicity,[status(thm)],[28072])).
% 29.67/19.90 tff(28074,plain,
% 29.67/19.90 (~(f10(f9(c1, c1)) = f9(c1, c1))),
% 29.67/19.90 inference(modus_ponens,[status(thm)],[75, 28073])).
% 29.67/19.90 tff(28075,plain,
% 29.67/19.90 ((f6(c1, c1) = c1) | (f9(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1)) | (f10(f9(c1, c1)) = f9(c1, c1)) | (~big_f(c1, f10(f9(c1, c1)))) | (~big_f(f9(c1, c1), f10(f9(c1, c1))))),
% 29.67/19.90 inference(unit_resolution,[status(thm)],[19458, 25791])).
% 29.67/19.90 tff(28076,plain,
% 29.67/19.90 ($false),
% 29.67/19.90 inference(unit_resolution,[status(thm)],[28075, 28074, 28062, 65, 28049, 28058, 28])).
% 29.67/19.90 tff(28077,plain,(big_f(f7(c1), f6(c1, c1)) | (f6(c1, c1) = c1) | (~big_f(c2, c1)) | (~(f10(c2) = c1)) | (~big_f(c1, c1)) | (~(f7(c2) = c1)) | (~(f10(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.67/19.90 tff(28078,plain,
% 29.67/19.90 (big_f(f7(c1), f6(c1, c1))),
% 29.67/19.90 inference(unit_resolution,[status(thm)],[28077, 28, 348, 94, 4932, 22, 3762])).
% 29.67/19.90 tff(28079,plain,
% 29.67/19.90 ($false),
% 29.67/19.90 inference(unit_resolution,[status(thm)],[28078, 28045])).
% 29.67/19.90 tff(28080,plain,((f6(c1, c1) = c1) | (f7(c2) = c2) | (f10(c2) = c2) | (~(f10(c1) = c1)) | (~(f7(c2) = f5(c2))) | (~big_f(c2, c1)) | (~big_f(c1, c1))), inference(lemma,lemma(discharge,[]))).
% 29.67/19.90 tff(28081,plain,
% 29.67/19.90 (f6(c1, c1) = c1),
% 29.67/19.90 inference(unit_resolution,[status(thm)],[28080, 17, 27838, 27980, 28009, 27828, 27489])).
% 29.67/19.90 tff(28082,plain,
% 29.67/19.90 (big_f(f7(c1), f6(c1, c1))),
% 29.67/19.90 inference(unit_resolution,[status(thm)],[27769, 28081, 27489])).
% 29.67/19.90 tff(28083,plain,
% 29.67/19.90 (c1 = f8(c2)),
% 29.67/19.90 inference(unit_resolution,[status(thm)],[27005, 2730, 25791, 27838, 28082, 28081, 27842])).
% 29.67/19.90 tff(28084,plain,
% 29.67/19.90 (f8(c2) = c1),
% 29.67/19.90 inference(symmetry,[status(thm)],[28083])).
% 29.67/19.90 tff(28085,plain,
% 29.67/19.90 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (~(f7(c1) = c1)) | (f9(c1, c1) = f8(c2)) | (~big_f(f9(c1, c1), f10(c2))) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (~(f7(c1) = c1)) | (f9(c1, c1) = f8(c2)) | (~big_f(f9(c1, c1), f10(c2))) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)))),
% 29.67/19.90 inference(rewrite,[status(thm)],[])).
% 29.67/19.90 tff(28086,plain,
% 29.67/19.90 (((f10(c2) = c2) | (f9(c1, c1) = f8(c2)) | (~big_f(f9(c1, c1), f10(c2))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1)))) <=> ((f10(c2) = c2) | (~(f7(c1) = c1)) | (f9(c1, c1) = f8(c2)) | (~big_f(f9(c1, c1), f10(c2))) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)))),
% 29.67/19.90 inference(rewrite,[status(thm)],[])).
% 29.67/19.90 tff(28087,plain,
% 29.67/19.90 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (f9(c1, c1) = f8(c2)) | (~big_f(f9(c1, c1), f10(c2))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (~(f7(c1) = c1)) | (f9(c1, c1) = f8(c2)) | (~big_f(f9(c1, c1), f10(c2))) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1))))),
% 29.67/19.90 inference(monotonicity,[status(thm)],[28086])).
% 29.67/19.90 tff(28088,plain,
% 29.67/19.90 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (f9(c1, c1) = f8(c2)) | (~big_f(f9(c1, c1), f10(c2))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (~(f7(c1) = c1)) | (f9(c1, c1) = f8(c2)) | (~big_f(f9(c1, c1), f10(c2))) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)))),
% 29.67/19.90 inference(transitivity,[status(thm)],[28087, 28085])).
% 29.67/19.90 tff(28089,plain,
% 29.67/19.90 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (f9(c1, c1) = f8(c2)) | (~big_f(f9(c1, c1), f10(c2))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))),
% 29.67/19.90 inference(quant_inst,[status(thm)],[])).
% 29.67/19.90 tff(28090,plain,
% 29.67/19.90 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (~(f7(c1) = c1)) | (f9(c1, c1) = f8(c2)) | (~big_f(f9(c1, c1), f10(c2))) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1))),
% 29.67/19.90 inference(modus_ponens,[status(thm)],[28089, 28088])).
% 29.67/19.90 tff(28091,plain,
% 29.67/19.90 (f9(c1, c1) = f8(c2)),
% 29.67/19.90 inference(unit_resolution,[status(thm)],[28090, 2730, 25791, 27838, 28082, 28081, 27846])).
% 29.67/19.90 tff(28092,plain,
% 29.67/19.90 (f9(c1, c1) = c1),
% 29.67/19.90 inference(transitivity,[status(thm)],[28091, 28084])).
% 29.67/19.90 tff(28093,plain,
% 29.67/19.90 (~(f9(c1, c1) = c1)),
% 29.67/19.90 inference(unit_resolution,[status(thm)],[18907, 2378, 25791, 27980, 27981, 28082, 28081])).
% 29.67/19.90 tff(28094,plain,
% 29.67/19.90 ($false),
% 29.67/19.90 inference(unit_resolution,[status(thm)],[28093, 28092])).
% 29.67/19.90 tff(28095,plain,((f7(c2) = c2) | big_f(c1, c2) | (~(c3 = c2))), inference(lemma,lemma(discharge,[]))).
% 29.67/19.90 tff(28096,plain,
% 29.67/19.90 (f7(c2) = c2),
% 29.67/19.90 inference(unit_resolution,[status(thm)],[28095, 67, 27])).
% 29.67/19.90 tff(28097,plain,
% 29.67/19.90 (big_f(c1, f10(c2))),
% 29.67/19.90 inference(modus_ponens,[status(thm)],[27489, 24205])).
% 29.67/19.90 tff(28098,plain,
% 29.67/19.90 (big_f(f10(c2), c2) <=> big_f(c1, c2)),
% 29.67/19.90 inference(monotonicity,[status(thm)],[94])).
% 29.67/19.90 tff(28099,plain,
% 29.67/19.90 (big_f(c1, c2) <=> big_f(f10(c2), c2)),
% 29.67/19.90 inference(symmetry,[status(thm)],[28098])).
% 29.67/19.90 tff(28100,plain,
% 29.67/19.90 ((~big_f(c1, c2)) <=> (~big_f(f10(c2), c2))),
% 29.67/19.90 inference(monotonicity,[status(thm)],[28099])).
% 29.67/19.90 tff(28101,plain,
% 29.67/19.90 (~big_f(f10(c2), c2)),
% 29.67/19.90 inference(modus_ponens,[status(thm)],[27, 28100])).
% 29.67/19.90 tff(28102,plain,
% 29.67/19.90 ((f2(c3) = c1) <=> (f2(c2) = c1)),
% 29.67/19.90 inference(monotonicity,[status(thm)],[2265])).
% 29.67/19.90 tff(28103,plain,
% 29.67/19.90 ((f2(c3) = c1) <=> (c1 = f2(c2))),
% 29.67/19.90 inference(transitivity,[status(thm)],[28102, 1220])).
% 29.67/19.90 tff(28104,plain,
% 29.67/19.90 (big_f(c2, c1) <=> big_f(f10(c1), f10(f10(c1)))),
% 29.67/19.90 inference(transitivity,[status(thm)],[15252, 27859])).
% 29.67/19.90 tff(28105,plain,
% 29.67/19.90 (f6(f10(c2), f10(c2)) = f6(c1, c1)),
% 29.67/19.90 inference(monotonicity,[status(thm)],[94, 94])).
% 29.67/19.90 tff(28106,plain,
% 29.67/19.90 ((f6(f10(c2), f10(c2)) = f10(c2)) <=> (f6(c1, c1) = c1)),
% 29.67/19.90 inference(monotonicity,[status(thm)],[28105, 94])).
% 29.67/19.90 tff(28107,plain,
% 29.67/19.90 ((f6(c1, c1) = c1) <=> (f6(f10(c2), f10(c2)) = f10(c2))),
% 29.67/19.90 inference(symmetry,[status(thm)],[28106])).
% 29.67/19.90 tff(28108,plain,
% 29.67/19.90 ((~(f6(c1, c1) = c1)) <=> (~(f6(f10(c2), f10(c2)) = f10(c2)))),
% 29.67/19.90 inference(monotonicity,[status(thm)],[28107])).
% 29.67/19.90 tff(28109,plain,
% 29.67/19.90 (~(f6(f10(c2), f10(c2)) = f10(c2))),
% 29.67/19.90 inference(modus_ponens,[status(thm)],[28, 28108])).
% 29.67/19.90 tff(28110,plain,
% 29.67/19.90 (f7(f10(c2)) = c1),
% 29.67/19.90 inference(transitivity,[status(thm)],[17553, 25791])).
% 29.67/19.90 tff(28111,plain,
% 29.67/19.90 (big_f(f7(f10(c2)), f6(f10(c2), f10(c2))) <=> big_f(c1, f6(c1, c1))),
% 29.67/19.90 inference(monotonicity,[status(thm)],[28110, 28105])).
% 29.67/19.90 tff(28112,plain,
% 29.67/19.90 (big_f(c1, f6(c1, c1)) <=> big_f(f7(f10(c2)), f6(f10(c2), f10(c2)))),
% 29.67/19.90 inference(symmetry,[status(thm)],[28111])).
% 29.67/19.90 tff(28113,plain,
% 29.67/19.90 ((~big_f(c1, f6(c1, c1))) <=> (~big_f(f7(f10(c2)), f6(f10(c2), f10(c2))))),
% 29.67/19.90 inference(monotonicity,[status(thm)],[28112])).
% 29.67/19.90 tff(28114,plain,
% 29.67/19.90 ((~big_f(f7(c1), f6(c1, c1))) <=> (~big_f(c1, f6(c1, c1)))),
% 29.67/19.90 inference(monotonicity,[status(thm)],[27680])).
% 29.67/19.90 tff(28115,plain,
% 29.67/19.90 (~big_f(c1, f6(c1, c1))),
% 29.67/19.90 inference(modus_ponens,[status(thm)],[65, 28114])).
% 29.67/19.90 tff(28116,plain,
% 29.67/19.90 (~big_f(f7(f10(c2)), f6(f10(c2), f10(c2)))),
% 29.67/19.90 inference(modus_ponens,[status(thm)],[28115, 28113])).
% 29.67/19.90 tff(28117,plain,
% 29.67/19.90 (f7(f10(c2)) = f10(c2)),
% 29.67/19.90 inference(transitivity,[status(thm)],[17553, 25791, 99])).
% 29.67/19.90 tff(28118,plain,
% 29.67/19.90 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (~(f7(f10(c2)) = f10(c2))) | big_f(f7(f10(c2)), f6(f10(c2), f10(c2))) | (f6(f10(c2), f10(c2)) = f10(c2)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c2) = c2) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (~(f7(f10(c2)) = f10(c2))) | big_f(f7(f10(c2)), f6(f10(c2), f10(c2))) | (f6(f10(c2), f10(c2)) = f10(c2)))),
% 29.67/19.90 inference(rewrite,[status(thm)],[])).
% 29.67/19.90 tff(28119,plain,
% 29.67/19.90 (((f10(c2) = c2) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (~(f7(f10(c2)) = f10(c2))) | (f6(f10(c2), f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), f6(f10(c2), f10(c2)))) <=> ((f10(c2) = c2) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (~(f7(f10(c2)) = f10(c2))) | big_f(f7(f10(c2)), f6(f10(c2), f10(c2))) | (f6(f10(c2), f10(c2)) = f10(c2)))),
% 29.67/19.90 inference(rewrite,[status(thm)],[])).
% 29.67/19.90 tff(28120,plain,
% 29.67/19.90 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (~(f7(f10(c2)) = f10(c2))) | (f6(f10(c2), f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), f6(f10(c2), f10(c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (~(f7(f10(c2)) = f10(c2))) | big_f(f7(f10(c2)), f6(f10(c2), f10(c2))) | (f6(f10(c2), f10(c2)) = f10(c2))))),
% 29.67/19.90 inference(monotonicity,[status(thm)],[28119])).
% 29.67/19.90 tff(28121,plain,
% 29.67/19.90 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (~(f7(f10(c2)) = f10(c2))) | (f6(f10(c2), f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), f6(f10(c2), f10(c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c2) = c2) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (~(f7(f10(c2)) = f10(c2))) | big_f(f7(f10(c2)), f6(f10(c2), f10(c2))) | (f6(f10(c2), f10(c2)) = f10(c2)))),
% 29.67/19.90 inference(transitivity,[status(thm)],[28120, 28118])).
% 29.67/19.90 tff(28122,plain,
% 29.67/19.90 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (~(f7(f10(c2)) = f10(c2))) | (f6(f10(c2), f10(c2)) = f10(c2)) | big_f(f7(f10(c2)), f6(f10(c2), f10(c2))))),
% 29.67/19.90 inference(quant_inst,[status(thm)],[])).
% 29.67/19.90 tff(28123,plain,
% 29.67/19.90 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c2) = c2) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (~(f7(f10(c2)) = f10(c2))) | big_f(f7(f10(c2)), f6(f10(c2), f10(c2))) | (f6(f10(c2), f10(c2)) = f10(c2))),
% 29.67/19.90 inference(modus_ponens,[status(thm)],[28122, 28121])).
% 29.67/19.90 tff(28124,plain,
% 29.67/19.90 ((f10(c2) = f8(c2)) | big_f(f7(f10(c2)), f6(f10(c2), f10(c2))) | (f6(f10(c2), f10(c2)) = f10(c2))),
% 29.67/19.90 inference(unit_resolution,[status(thm)],[28123, 2662, 89, 28117, 25696])).
% 29.67/19.90 tff(28125,plain,
% 29.67/19.90 (f10(c2) = f8(c2)),
% 29.67/19.90 inference(unit_resolution,[status(thm)],[28124, 28116, 28109])).
% 29.67/19.90 tff(28126,plain,
% 29.67/19.90 (~(f3(c2, c2) = c2)),
% 29.67/19.90 inference(unit_resolution,[status(thm)],[21636, 873, 89, 1345, 27, 15667, 25696])).
% 29.67/19.90 tff(28127,plain,
% 29.67/19.90 (big_f(f3(c2, c2), c2)),
% 29.67/19.90 inference(unit_resolution,[status(thm)],[21176, 873, 27, 168, 4932, 28126])).
% 29.67/19.90 tff(28128,plain,
% 29.67/19.90 (~(c1 = f8(c1))),
% 29.67/19.90 inference(unit_resolution,[status(thm)],[27748, 65, 3, 26485, 28])).
% 29.67/19.90 tff(28129,plain,
% 29.67/19.90 (~(f8(c1) = c1)),
% 29.67/19.90 inference(unit_resolution,[status(thm)],[9808, 28128])).
% 29.67/19.90 tff(28130,plain,
% 29.67/19.90 (f8(c1) = c2),
% 29.67/19.90 inference(unit_resolution,[status(thm)],[1680, 28129])).
% 29.67/19.90 tff(28131,plain,
% 29.67/19.90 (~big_f(f3(c2, c2), f10(c1))),
% 29.67/19.90 inference(unit_resolution,[status(thm)],[27763, 28126, 3, 28, 65, 28130])).
% 29.67/19.90 tff(28132,plain,
% 29.67/19.90 ($false),
% 29.67/19.90 inference(unit_resolution,[status(thm)],[27281, 28131, 28127, 15])).
% 29.67/19.90 tff(28133,plain,((c2 = c4) | (f10(c1) = c1) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1)) | big_f(c1, c2) | (c1 = c3) | (~big_f(c1, c1)) | (f10(c2) = c2) | (~big_f(c2, c2)) | (f10(c2) = c3)), inference(lemma,lemma(discharge,[]))).
% 29.67/19.90 tff(28134,plain,
% 29.67/19.90 (c2 = c4),
% 29.67/19.90 inference(unit_resolution,[status(thm)],[28133, 65, 28, 3, 27, 168, 4932, 89, 1345, 15667])).
% 29.67/19.90 tff(28135,plain,
% 29.67/19.90 ((f4(c2) = c1) <=> (c1 = f4(c2))),
% 29.67/19.90 inference(commutativity,[status(thm)],[])).
% 29.67/19.90 tff(28136,plain,
% 29.67/19.90 (f4(c4) = f4(c2)),
% 29.67/19.90 inference(monotonicity,[status(thm)],[8728])).
% 29.67/19.90 tff(28137,plain,
% 29.67/19.90 ((f4(c4) = c1) <=> (f4(c2) = c1)),
% 29.67/19.90 inference(monotonicity,[status(thm)],[28136])).
% 29.67/19.90 tff(28138,plain,
% 29.67/19.90 ((f4(c4) = c1) <=> (c1 = f4(c2))),
% 29.67/19.90 inference(transitivity,[status(thm)],[28137, 28135])).
% 29.67/19.90 tff(28139,plain,
% 29.67/19.90 (c1 = f4(c2)),
% 29.67/19.90 inference(modus_ponens,[status(thm)],[11752, 28138])).
% 29.67/19.90 tff(28140,plain,
% 29.67/19.90 (~big_f(c1, f1(c1, c1))),
% 29.67/19.90 inference(unit_resolution,[status(thm)],[23017, 11752, 27, 13657, 168])).
% 29.67/19.90 tff(28141,plain,
% 29.67/19.90 (~(f1(c1, c1) = c1)),
% 29.67/19.90 inference(unit_resolution,[status(thm)],[9678, 28140, 4932])).
% 29.67/19.90 tff(28142,plain,
% 29.67/19.90 (~big_f(c1, f1(c1, c1))),
% 29.67/19.90 inference(unit_resolution,[status(thm)],[23015, 631, 168, 27, 18123])).
% 29.67/19.90 tff(28143,plain,
% 29.67/19.90 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f1(c1, c1) = c1) | (c1 = c3) | (~(c2 = c4)) | big_f(c1, f1(c1, c1)) | big_f(c1, c2) | (~(c1 = f4(c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (f1(c1, c1) = c1) | (c1 = c3) | (~(c2 = c4)) | big_f(c1, f1(c1, c1)) | big_f(c1, c2) | (~(c1 = f4(c2))))),
% 29.67/19.90 inference(rewrite,[status(thm)],[])).
% 29.67/19.90 tff(28144,plain,
% 29.67/19.90 (((c1 = c3) | (f1(c1, c1) = c1) | big_f(c1, f1(c1, c1)) | (~(c2 = c4)) | big_f(c1, c2) | (~(c1 = f4(c2)))) <=> ((f1(c1, c1) = c1) | (c1 = c3) | (~(c2 = c4)) | big_f(c1, f1(c1, c1)) | big_f(c1, c2) | (~(c1 = f4(c2))))),
% 29.67/19.90 inference(rewrite,[status(thm)],[])).
% 29.67/19.90 tff(28145,plain,
% 29.67/19.90 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c1 = c3) | (f1(c1, c1) = c1) | big_f(c1, f1(c1, c1)) | (~(c2 = c4)) | big_f(c1, c2) | (~(c1 = f4(c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f1(c1, c1) = c1) | (c1 = c3) | (~(c2 = c4)) | big_f(c1, f1(c1, c1)) | big_f(c1, c2) | (~(c1 = f4(c2)))))),
% 29.67/19.90 inference(monotonicity,[status(thm)],[28144])).
% 29.67/19.90 tff(28146,plain,
% 29.67/19.90 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c1 = c3) | (f1(c1, c1) = c1) | big_f(c1, f1(c1, c1)) | (~(c2 = c4)) | big_f(c1, c2) | (~(c1 = f4(c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (f1(c1, c1) = c1) | (c1 = c3) | (~(c2 = c4)) | big_f(c1, f1(c1, c1)) | big_f(c1, c2) | (~(c1 = f4(c2))))),
% 29.67/19.90 inference(transitivity,[status(thm)],[28145, 28143])).
% 29.67/19.90 tff(28147,plain,
% 29.67/19.90 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c1 = c3) | (f1(c1, c1) = c1) | big_f(c1, f1(c1, c1)) | (~(c2 = c4)) | big_f(c1, c2) | (~(c1 = f4(c2))))),
% 29.67/19.90 inference(quant_inst,[status(thm)],[])).
% 29.67/19.90 tff(28148,plain,
% 29.67/19.90 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (f1(c1, c1) = c1) | (c1 = c3) | (~(c2 = c4)) | big_f(c1, f1(c1, c1)) | big_f(c1, c2) | (~(c1 = f4(c2)))),
% 29.67/19.90 inference(modus_ponens,[status(thm)],[28147, 28146])).
% 29.67/19.90 tff(28149,plain,
% 29.67/19.90 ($false),
% 29.67/19.90 inference(unit_resolution,[status(thm)],[28148, 402, 9710, 168, 28142, 631, 27, 18123])).
% 29.67/19.90 tff(28150,plain,((f1(c1, c1) = c1) | (c1 = c3) | (~(c2 = c4)) | big_f(c1, c2) | (~(c1 = f4(c2)))), inference(lemma,lemma(discharge,[]))).
% 29.67/19.90 tff(28151,plain,
% 29.67/19.90 (~(c1 = f4(c2))),
% 29.67/19.90 inference(unit_resolution,[status(thm)],[28150, 28141, 27, 168, 631])).
% 29.67/19.90 tff(28152,plain,
% 29.67/19.90 ($false),
% 29.67/19.90 inference(unit_resolution,[status(thm)],[28151, 28139])).
% 29.67/19.90 tff(28153,plain,((~(f4(c4) = c1)) | (~(c2 = c4)) | big_f(c1, c2) | (c1 = c3) | (~big_f(c1, c1))), inference(lemma,lemma(discharge,[]))).
% 29.67/19.90 tff(28154,plain,
% 29.67/19.90 (~(f4(c4) = c1)),
% 29.67/19.90 inference(unit_resolution,[status(thm)],[28153, 28134, 27, 168, 4932])).
% 29.67/19.90 tff(28155,plain,
% 29.67/19.90 (f4(c4) = c2),
% 29.67/19.90 inference(unit_resolution,[status(thm)],[11750, 28154])).
% 29.67/19.90 tff(28156,plain,
% 29.67/19.90 (big_f(c2, c1)),
% 29.67/19.90 inference(unit_resolution,[status(thm)],[15688, 28155, 4932, 89, 1345, 28125, 27])).
% 29.67/19.90 tff(28157,plain,
% 29.67/19.90 (big_f(f10(c1), f10(f10(c1)))),
% 29.67/19.90 inference(modus_ponens,[status(thm)],[28156, 28104])).
% 29.67/19.90 tff(28158,plain,
% 29.67/19.90 (big_f(c1, f10(c2)) <=> big_f(f10(c2), f10(c2))),
% 29.67/19.90 inference(monotonicity,[status(thm)],[99])).
% 29.67/19.90 tff(28159,plain,
% 29.67/19.90 (big_f(f10(c2), f10(c2)) <=> big_f(c1, f10(c2))),
% 29.67/19.90 inference(symmetry,[status(thm)],[28158])).
% 29.67/19.90 tff(28160,plain,
% 29.67/19.90 (big_f(f10(c2), f10(c2)) <=> big_f(c1, f10(f10(c1)))),
% 29.67/19.90 inference(transitivity,[status(thm)],[28159, 27855])).
% 29.67/19.90 tff(28161,plain,
% 29.67/19.90 (big_f(c1, f10(f10(c1)))),
% 29.67/19.90 inference(modus_ponens,[status(thm)],[25696, 28160])).
% 29.67/19.90 tff(28162,plain,
% 29.67/19.90 (~big_f(f10(c1), f10(f10(c1)))),
% 29.67/19.90 inference(unit_resolution,[status(thm)],[27894, 65, 27867, 28, 3, 28161])).
% 29.67/19.90 tff(28163,plain,
% 29.67/19.90 ($false),
% 29.67/19.90 inference(unit_resolution,[status(thm)],[28162, 28157])).
% 29.67/19.90 tff(28164,plain,(big_f(f7(c1), f6(c1, c1)) | (~big_f(c1, c1)) | (f10(c2) = c2) | (~big_f(c2, c2)) | big_f(c1, c2) | (c1 = c3) | (f6(c1, c1) = c1) | (f10(c1) = c1) | (f10(c2) = c3)), inference(lemma,lemma(discharge,[]))).
% 29.67/19.90 tff(28165,plain,
% 29.67/19.90 (big_f(f7(c1), f6(c1, c1))),
% 29.67/19.90 inference(unit_resolution,[status(thm)],[28164, 28, 89, 27705, 27, 76, 27489, 3, 12420])).
% 29.67/19.90 tff(28166,plain,
% 29.67/19.90 (big_f(c1, f6(c1, c1))),
% 29.67/19.90 inference(modus_ponens,[status(thm)],[5964, 27680])).
% 29.67/19.90 tff(28167,assumption,(~big_f(c1, f6(c1, c1))), introduced(assumption)).
% 29.67/19.90 tff(28168,plain,
% 29.67/19.90 ($false),
% 29.67/19.90 inference(unit_resolution,[status(thm)],[28167, 28166])).
% 29.67/19.90 tff(28169,plain,(big_f(c1, f6(c1, c1)) | (~big_f(f7(c1), f6(c1, c1)))), inference(lemma,lemma(discharge,[]))).
% 29.67/19.90 tff(28170,plain,
% 29.67/19.90 (big_f(c1, f6(c1, c1))),
% 29.67/19.90 inference(unit_resolution,[status(thm)],[28169, 28165])).
% 29.67/19.90 tff(28171,assumption,(c1 = f8(c2)), introduced(assumption)).
% 29.67/19.90 tff(28172,plain,
% 29.67/19.90 (f6(c1, c1) = f6(c1, f8(c2))),
% 29.67/19.90 inference(monotonicity,[status(thm)],[28171])).
% 29.67/19.90 tff(28173,plain,
% 29.67/19.90 (f6(c1, f8(c2)) = f6(c1, c1)),
% 29.67/19.90 inference(symmetry,[status(thm)],[28172])).
% 29.67/19.90 tff(28174,plain,
% 29.67/19.90 ((f6(c1, f8(c2)) = c1) <=> (f6(c1, c1) = c1)),
% 29.67/19.90 inference(monotonicity,[status(thm)],[28173])).
% 29.67/19.90 tff(28175,plain,
% 29.67/19.90 ((f6(c1, c1) = c1) <=> (f6(c1, f8(c2)) = c1)),
% 29.67/19.90 inference(symmetry,[status(thm)],[28174])).
% 29.67/19.90 tff(28176,plain,
% 29.67/19.90 ((~(f6(c1, c1) = c1)) <=> (~(f6(c1, f8(c2)) = c1))),
% 29.67/19.90 inference(monotonicity,[status(thm)],[28175])).
% 29.67/19.90 tff(28177,plain,
% 29.67/19.90 (~(f6(c1, f8(c2)) = c1)),
% 29.67/19.90 inference(modus_ponens,[status(thm)],[28, 28176])).
% 29.67/19.90 tff(28178,plain,
% 29.67/19.90 (f6(c1, f8(c2)) = c2),
% 29.67/19.90 inference(unit_resolution,[status(thm)],[24295, 28177])).
% 29.67/19.90 tff(28179,plain,
% 29.67/19.90 (f6(c1, c1) = c2),
% 29.67/19.90 inference(transitivity,[status(thm)],[28172, 28178])).
% 29.67/19.90 tff(28180,plain,
% 29.67/19.90 (big_f(c1, f6(c1, c1)) <=> big_f(f10(c2), c2)),
% 29.67/19.90 inference(monotonicity,[status(thm)],[12231, 28179])).
% 29.67/19.90 tff(28181,plain,
% 29.67/19.90 (big_f(f10(c2), c2) <=> big_f(c1, f6(c1, c1))),
% 29.67/19.90 inference(symmetry,[status(thm)],[28180])).
% 29.67/19.90 tff(28182,plain,
% 29.67/19.90 ((~big_f(f10(c2), c2)) <=> (~big_f(c1, f6(c1, c1)))),
% 29.67/19.90 inference(monotonicity,[status(thm)],[28181])).
% 29.67/19.90 tff(28183,assumption,(~big_f(f10(c2), c2)), introduced(assumption)).
% 29.67/19.90 tff(28184,plain,
% 29.67/19.90 (~big_f(c1, f6(c1, c1))),
% 29.67/19.90 inference(modus_ponens,[status(thm)],[28183, 28182])).
% 29.67/19.90 tff(28185,assumption,(big_f(c1, f6(c1, c1))), introduced(assumption)).
% 29.67/19.90 tff(28186,plain,
% 29.67/19.90 ($false),
% 29.67/19.90 inference(unit_resolution,[status(thm)],[28185, 28184])).
% 29.67/19.90 tff(28187,plain,((~(c1 = f8(c2))) | (~big_f(c1, f6(c1, c1))) | big_f(f10(c2), c2) | (~(f10(c2) = c1)) | (f6(c1, c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.67/19.90 tff(28188,plain,
% 29.67/19.90 (~(c1 = f8(c2))),
% 29.67/19.90 inference(unit_resolution,[status(thm)],[28187, 28170, 28101, 94, 28])).
% 29.67/19.90 tff(28189,plain,
% 29.67/19.90 (c2 = f8(c2)),
% 29.67/19.90 inference(unit_resolution,[status(thm)],[26203, 28188, 67])).
% 29.67/19.90 tff(28190,plain,
% 29.67/19.90 (f6(c2, c2) = c2),
% 29.67/19.90 inference(unit_resolution,[status(thm)],[21595, 13152, 67, 77, 89, 15517])).
% 29.67/19.90 tff(28191,plain,
% 29.67/19.90 (big_f(f7(c2), f6(c2, c2))),
% 29.67/19.90 inference(unit_resolution,[status(thm)],[2627, 28190, 77, 1345])).
% 29.67/19.90 tff(28192,plain,
% 29.67/19.90 ($false),
% 29.67/19.90 inference(unit_resolution,[status(thm)],[24173, 2963, 89, 77, 15517, 13152, 28190, 28191])).
% 29.67/19.90 tff(28193,plain,((~(c2 = f8(c2))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | big_f(c2, f10(c2)) | (~big_f(c2, c2)) | (~(c3 = c2))), inference(lemma,lemma(discharge,[]))).
% 29.67/19.90 tff(28194,plain,
% 29.67/19.90 (big_f(c2, f10(c2))),
% 29.67/19.90 inference(unit_resolution,[status(thm)],[28193, 28189, 28096, 89, 27705, 67])).
% 29.67/19.90 tff(28195,plain,
% 29.67/19.90 (big_f(c2, c1)),
% 29.67/19.90 inference(modus_ponens,[status(thm)],[28194, 15253])).
% 29.67/19.90 tff(28196,plain,
% 29.67/19.90 (f4(c4) = c2),
% 29.67/19.90 inference(unit_resolution,[status(thm)],[27836, 28195, 27, 67])).
% 29.67/19.90 tff(28197,plain,
% 29.67/19.90 (c2 = c4),
% 29.67/19.90 inference(unit_resolution,[status(thm)],[26149, 28195, 27, 1335, 28096, 28196, 27705])).
% 29.67/19.90 tff(28198,plain,
% 29.67/19.90 (c4 = c2),
% 29.67/19.90 inference(symmetry,[status(thm)],[28197])).
% 29.67/19.90 tff(28199,plain,
% 29.67/19.90 (f3(c1, c2) = f3(f10(c2), c2)),
% 29.67/19.90 inference(monotonicity,[status(thm)],[99])).
% 29.67/19.90 tff(28200,plain,
% 29.67/19.90 (f3(f10(c2), c2) = f3(c1, c2)),
% 29.67/19.90 inference(symmetry,[status(thm)],[28199])).
% 29.67/19.90 tff(28201,plain,
% 29.67/19.90 (c2 = f8(c3)),
% 29.67/19.90 inference(transitivity,[status(thm)],[28189, 20761])).
% 29.67/19.90 tff(28202,plain,
% 29.67/19.90 (f3(f10(c2), c2) = f3(f10(c2), f8(c3))),
% 29.67/19.90 inference(monotonicity,[status(thm)],[28201])).
% 29.67/19.90 tff(28203,plain,
% 29.67/19.90 (f3(f10(c2), f8(c3)) = f3(f10(c2), c2)),
% 29.67/19.90 inference(symmetry,[status(thm)],[28202])).
% 29.67/19.90 tff(28204,plain,
% 29.67/19.90 ((f10(c2) = c4) <=> (f10(c2) = c2)),
% 29.67/19.90 inference(monotonicity,[status(thm)],[28198])).
% 29.67/19.90 tff(28205,plain,
% 29.67/19.90 ((f10(c2) = c2) <=> (f10(c2) = c4)),
% 29.67/19.90 inference(symmetry,[status(thm)],[28204])).
% 29.67/19.90 tff(28206,plain,
% 29.67/19.90 ((~(f10(c2) = c2)) <=> (~(f10(c2) = c4))),
% 29.67/19.90 inference(monotonicity,[status(thm)],[28205])).
% 29.67/19.90 tff(28207,plain,
% 29.67/19.90 (~(f10(c2) = c4)),
% 29.67/19.90 inference(modus_ponens,[status(thm)],[89, 28206])).
% 29.67/19.90 tff(28208,plain,
% 29.67/19.90 (f3(f10(c2), c2) = f3(f10(c2), f8(c3))),
% 29.67/19.90 inference(monotonicity,[status(thm)],[20762])).
% 29.67/19.90 tff(28209,plain,
% 29.67/19.90 (f3(f10(c2), c2) = f3(c1, f8(c3))),
% 29.67/19.90 inference(transitivity,[status(thm)],[28208, 20765])).
% 29.67/19.90 tff(28210,plain,
% 29.67/19.90 ((f3(f10(c2), c2) = c2) <=> (f3(c1, f8(c3)) = c2)),
% 29.67/19.90 inference(monotonicity,[status(thm)],[28209])).
% 29.67/19.90 tff(28211,plain,
% 29.67/19.90 ((f3(c1, f8(c3)) = c2) <=> (f3(f10(c2), c2) = c2)),
% 29.67/19.90 inference(symmetry,[status(thm)],[28210])).
% 29.67/19.90 tff(28212,plain,
% 29.67/19.90 (f3(f10(c2), c2) = c2),
% 29.67/19.90 inference(modus_ponens,[status(thm)],[12781, 28211])).
% 29.67/19.90 tff(28213,plain,
% 29.67/19.90 (f3(f10(c2), c2) = c2),
% 29.67/19.90 inference(transitivity,[status(thm)],[28208, 20765, 12781])).
% 29.67/19.90 tff(28214,plain,
% 29.67/19.90 (big_f(f3(f10(c2), c2), f10(c2)) <=> big_f(c2, f10(c2))),
% 29.67/19.90 inference(monotonicity,[status(thm)],[28213])).
% 29.67/19.90 tff(28215,plain,
% 29.67/19.90 (big_f(c2, f10(c2)) <=> big_f(f3(f10(c2), c2), f10(c2))),
% 29.67/19.90 inference(symmetry,[status(thm)],[28214])).
% 29.67/19.90 tff(28216,plain,
% 29.67/19.90 (big_f(f3(f10(c2), c2), f10(c2))),
% 29.67/19.90 inference(modus_ponens,[status(thm)],[12291, 28215])).
% 29.67/19.90 tff(28217,plain,
% 29.67/19.90 (c2 = f2(c2)),
% 29.67/19.90 inference(unit_resolution,[status(thm)],[15453, 7051, 1345, 1335, 15519, 28216, 28212])).
% 29.67/19.90 tff(28218,plain,
% 29.67/19.90 (f2(c2) = c2),
% 29.67/19.90 inference(symmetry,[status(thm)],[28217])).
% 29.67/19.90 tff(28219,plain,
% 29.67/19.90 (f10(c2) = f2(c2)),
% 29.67/19.90 inference(unit_resolution,[status(thm)],[15420, 7051, 1335, 15519, 12291, 28216, 28212])).
% 29.67/19.90 tff(28220,plain,
% 29.67/19.90 (f10(c2) = c2),
% 29.67/19.90 inference(transitivity,[status(thm)],[28219, 28218])).
% 29.67/19.90 tff(28221,plain,
% 29.67/19.90 ($false),
% 29.67/19.90 inference(unit_resolution,[status(thm)],[89, 28220])).
% 29.67/19.90 tff(28222,plain,((~(f3(c1, f8(c3)) = c2)) | (f10(c2) = c2) | (f10(c2) = c4) | (~big_f(c2, f10(c2))) | (~big_f(c2, c2)) | (~(c2 = f8(c2))) | (~(c3 = c2))), inference(lemma,lemma(discharge,[]))).
% 29.67/19.90 tff(28223,plain,
% 29.67/19.90 (~(f3(c1, f8(c3)) = c2)),
% 29.67/19.90 inference(unit_resolution,[status(thm)],[28222, 28207, 89, 28194, 27705, 28189, 67])).
% 29.67/19.90 tff(28224,plain,
% 29.67/19.90 (f3(c1, f8(c3)) = c1),
% 29.67/19.90 inference(unit_resolution,[status(thm)],[7123, 28223])).
% 29.67/19.90 tff(28225,plain,
% 29.67/19.90 (c1 = f3(c1, f8(c3))),
% 29.67/19.90 inference(symmetry,[status(thm)],[28224])).
% 29.67/19.90 tff(28226,plain,
% 29.67/19.90 (c1 = f3(c1, c2)),
% 29.67/19.90 inference(transitivity,[status(thm)],[28225, 20766, 28203, 28200])).
% 29.67/19.90 tff(28227,plain,
% 29.67/19.90 (f6(c1, c1) = f6(c1, f3(c1, c2))),
% 29.67/19.90 inference(monotonicity,[status(thm)],[28226])).
% 29.67/19.90 tff(28228,plain,
% 29.67/19.90 ((f6(c1, c1) = c4) <=> (f6(c1, f3(c1, c2)) = c2)),
% 29.67/19.90 inference(monotonicity,[status(thm)],[28227, 28198])).
% 29.67/19.90 tff(28229,plain,
% 29.67/19.90 (f3(c1, c2) = f3(f10(c2), c2)),
% 29.67/19.90 inference(monotonicity,[status(thm)],[12231])).
% 29.67/19.90 tff(28230,plain,
% 29.67/19.90 (f3(c1, c2) = c1),
% 29.67/19.90 inference(transitivity,[status(thm)],[28229, 28208, 22188, 16414])).
% 29.67/19.90 tff(28231,plain,
% 29.67/19.90 (f6(c1, f3(c1, c2)) = f6(c1, c1)),
% 29.67/19.90 inference(monotonicity,[status(thm)],[28230])).
% 29.67/19.90 tff(28232,plain,
% 29.67/19.90 ((f6(c1, f3(c1, c2)) = c1) <=> (f6(c1, c1) = c1)),
% 29.67/19.90 inference(monotonicity,[status(thm)],[28231])).
% 29.67/19.90 tff(28233,plain,
% 29.67/19.90 ((f6(c1, c1) = c1) <=> (f6(c1, f3(c1, c2)) = c1)),
% 29.67/19.90 inference(symmetry,[status(thm)],[28232])).
% 29.67/19.91 tff(28234,plain,
% 29.67/19.91 ((~(f6(c1, c1) = c1)) <=> (~(f6(c1, f3(c1, c2)) = c1))),
% 29.67/19.91 inference(monotonicity,[status(thm)],[28233])).
% 29.67/19.91 tff(28235,plain,
% 29.67/19.91 (~(f6(c1, f3(c1, c2)) = c1)),
% 29.67/19.91 inference(modus_ponens,[status(thm)],[28, 28234])).
% 29.67/19.91 tff(28236,plain,
% 29.67/19.91 (f6(c1, c1) = f6(c1, f3(c1, c2))),
% 29.67/19.91 inference(symmetry,[status(thm)],[28231])).
% 29.67/19.91 tff(28237,plain,
% 29.67/19.91 ((f6(c1, c1) = c4) <=> (f6(c1, f3(c1, c2)) = c2)),
% 29.67/19.91 inference(monotonicity,[status(thm)],[28236, 8728])).
% 29.67/19.91 tff(28238,plain,
% 29.67/19.91 ((~(f6(c1, c1) = c4)) <=> (~(f6(c1, f3(c1, c2)) = c2))),
% 29.67/19.91 inference(monotonicity,[status(thm)],[28237])).
% 29.67/19.91 tff(28239,assumption,(~(f6(c1, c1) = c4)), introduced(assumption)).
% 29.67/19.91 tff(28240,plain,
% 29.67/19.91 (~(f6(c1, f3(c1, c2)) = c2)),
% 29.67/19.91 inference(modus_ponens,[status(thm)],[28239, 28238])).
% 29.67/19.91 tff(28241,plain,
% 29.67/19.91 ($false),
% 29.67/19.91 inference(unit_resolution,[status(thm)],[6690, 28240, 28235])).
% 29.67/19.91 tff(28242,plain,((~(f3(c1, f8(c3)) = c1)) | (f6(c1, c1) = c4) | (~(c2 = c4)) | (~(c2 = f8(c2))) | (~(c3 = c2)) | (~(f10(c2) = c1)) | (f6(c1, c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.67/19.91 tff(28243,plain,
% 29.67/19.91 (f6(c1, c1) = c4),
% 29.67/19.91 inference(unit_resolution,[status(thm)],[28242, 28224, 28197, 28189, 67, 94, 28])).
% 29.67/19.91 tff(28244,plain,
% 29.67/19.91 (f6(c1, f3(c1, c2)) = c2),
% 29.67/19.91 inference(modus_ponens,[status(thm)],[28243, 28228])).
% 29.67/19.91 tff(28245,plain,
% 29.67/19.91 (f6(c1, c1) = c2),
% 29.67/19.91 inference(transitivity,[status(thm)],[28227, 28244])).
% 29.67/19.91 tff(28246,plain,
% 29.67/19.91 (big_f(c1, f6(c1, c1)) <=> big_f(f10(c2), c2)),
% 29.67/19.91 inference(monotonicity,[status(thm)],[99, 28245])).
% 29.67/19.91 tff(28247,plain,
% 29.67/19.91 (big_f(f10(c2), c2) <=> big_f(c1, f6(c1, c1))),
% 29.67/19.91 inference(symmetry,[status(thm)],[28246])).
% 29.67/19.91 tff(28248,plain,
% 29.67/19.91 ((~big_f(f10(c2), c2)) <=> (~big_f(c1, f6(c1, c1)))),
% 29.67/19.91 inference(monotonicity,[status(thm)],[28247])).
% 29.67/19.91 tff(28249,plain,
% 29.67/19.91 (~big_f(c1, f6(c1, c1))),
% 29.67/19.91 inference(modus_ponens,[status(thm)],[28101, 28248])).
% 29.67/19.91 tff(28250,plain,
% 29.67/19.91 ($false),
% 29.67/19.91 inference(unit_resolution,[status(thm)],[28170, 28249])).
% 29.67/19.91 tff(28251,plain,((f6(c1, c1) = c1) | (~(c3 = c2)) | (f10(c2) = c2) | big_f(c1, c2) | (f10(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.67/19.91 tff(28252,plain,
% 29.67/19.91 (f6(c1, c1) = c1),
% 29.67/19.91 inference(unit_resolution,[status(thm)],[28251, 89, 67, 27, 3])).
% 29.67/19.91 tff(28253,plain,
% 29.67/19.91 (f6(f10(c2), f10(c2)) = f10(c2)),
% 29.67/19.91 inference(transitivity,[status(thm)],[28105, 28252, 99])).
% 29.67/19.91 tff(28254,plain,
% 29.67/19.91 (big_f(f7(f10(c2)), f6(f10(c2), f10(c2))) <=> big_f(f10(c2), f10(c2))),
% 29.67/19.91 inference(monotonicity,[status(thm)],[28117, 28253])).
% 29.67/19.91 tff(28255,plain,
% 29.67/19.91 (big_f(f10(c2), f10(c2)) <=> big_f(f7(f10(c2)), f6(f10(c2), f10(c2)))),
% 29.67/19.91 inference(symmetry,[status(thm)],[28254])).
% 29.67/19.91 tff(28256,plain,
% 29.67/19.91 (big_f(f10(c2), f10(c2))),
% 29.67/19.91 inference(unit_resolution,[status(thm)],[21743, 94, 27489])).
% 29.67/19.91 tff(28257,plain,
% 29.67/19.91 (big_f(f7(f10(c2)), f6(f10(c2), f10(c2)))),
% 29.67/19.91 inference(modus_ponens,[status(thm)],[28256, 28255])).
% 29.67/19.91 tff(28258,plain,
% 29.67/19.91 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (~(f7(f10(c2)) = f10(c2))) | (~(f6(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f7(f10(c2)), f6(f10(c2), f10(c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (~(f7(f10(c2)) = f10(c2))) | (~(f6(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f7(f10(c2)), f6(f10(c2), f10(c2)))))),
% 29.67/19.91 inference(rewrite,[status(thm)],[])).
% 29.67/19.91 tff(28259,plain,
% 29.67/19.91 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (~(f7(f10(c2)) = f10(c2))) | (~(f6(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f7(f10(c2)), f6(f10(c2), f10(c2)))))),
% 29.67/19.91 inference(quant_inst,[status(thm)],[])).
% 29.67/19.91 tff(28260,plain,
% 29.67/19.91 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (f10(c2) = f8(c2)) | (~big_f(f10(c2), f10(c2))) | (~(f7(f10(c2)) = f10(c2))) | (~(f6(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f7(f10(c2)), f6(f10(c2), f10(c2))))),
% 29.67/19.91 inference(modus_ponens,[status(thm)],[28259, 28258])).
% 29.67/19.91 tff(28261,plain,
% 29.67/19.91 ((f10(c2) = f8(c2)) | (~(f6(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f7(f10(c2)), f6(f10(c2), f10(c2))))),
% 29.67/19.91 inference(unit_resolution,[status(thm)],[28260, 2730, 89, 28117, 28256])).
% 29.67/19.91 tff(28262,plain,
% 29.67/19.91 (f10(c2) = f8(c2)),
% 29.67/19.91 inference(unit_resolution,[status(thm)],[28261, 28253, 28257])).
% 29.67/19.91 tff(28263,plain,
% 29.67/19.91 (f8(c2) = f10(c2)),
% 29.67/19.91 inference(symmetry,[status(thm)],[28262])).
% 29.67/19.91 tff(28264,plain,
% 29.67/19.91 ((c2 = f8(c2)) <=> (c2 = f10(c2))),
% 29.67/19.91 inference(monotonicity,[status(thm)],[28263])).
% 29.67/19.91 tff(28265,plain,
% 29.67/19.91 ((c2 = f8(c2)) <=> (f10(c2) = c2)),
% 29.67/19.91 inference(transitivity,[status(thm)],[28264, 4987])).
% 29.67/19.91 tff(28266,plain,
% 29.67/19.91 ((f10(c2) = c2) <=> (c2 = f8(c2))),
% 29.67/19.91 inference(symmetry,[status(thm)],[28265])).
% 29.67/19.91 tff(28267,plain,
% 29.67/19.91 ((~(f10(c2) = c2)) <=> (~(c2 = f8(c2)))),
% 29.67/19.91 inference(monotonicity,[status(thm)],[28266])).
% 29.67/19.91 tff(28268,plain,
% 29.67/19.91 (~(c2 = f8(c2))),
% 29.67/19.91 inference(modus_ponens,[status(thm)],[89, 28267])).
% 29.67/19.91 tff(28269,assumption,(big_f(f7(f10(c2)), f6(f10(c2), f10(c2)))), introduced(assumption)).
% 29.67/19.91 tff(28270,assumption,(f6(f10(c2), f10(c2)) = f10(c2)), introduced(assumption)).
% 29.67/19.91 tff(28271,plain,
% 29.67/19.91 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f10(c2)) = f10(c2)) | (c2 = f8(f10(c2))) | (~big_f(c2, f10(f10(c2)))) | (~(f7(f10(c2)) = f10(c2))) | (~(f6(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f7(f10(c2)), f6(f10(c2), f10(c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(f10(c2)) = f10(c2)) | (c2 = f8(f10(c2))) | (~big_f(c2, f10(f10(c2)))) | (~(f7(f10(c2)) = f10(c2))) | (~(f6(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f7(f10(c2)), f6(f10(c2), f10(c2)))))),
% 29.67/19.91 inference(rewrite,[status(thm)],[])).
% 29.67/19.91 tff(28272,plain,
% 29.67/19.91 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f10(c2)) = f10(c2)) | (c2 = f8(f10(c2))) | (~big_f(c2, f10(f10(c2)))) | (~(f7(f10(c2)) = f10(c2))) | (~(f6(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f7(f10(c2)), f6(f10(c2), f10(c2)))))),
% 29.67/19.91 inference(quant_inst,[status(thm)],[])).
% 29.67/19.91 tff(28273,plain,
% 29.67/19.91 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(f10(c2)) = f10(c2)) | (c2 = f8(f10(c2))) | (~big_f(c2, f10(f10(c2)))) | (~(f7(f10(c2)) = f10(c2))) | (~(f6(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f7(f10(c2)), f6(f10(c2), f10(c2))))),
% 29.67/19.91 inference(modus_ponens,[status(thm)],[28272, 28271])).
% 29.67/19.91 tff(28274,plain,
% 29.67/19.91 ((c2 = f8(f10(c2))) | (~(f6(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f7(f10(c2)), f6(f10(c2), f10(c2))))),
% 29.67/19.91 inference(unit_resolution,[status(thm)],[28273, 2730, 15308, 21613, 28117])).
% 29.67/19.91 tff(28275,plain,
% 29.67/19.91 (c2 = f8(f10(c2))),
% 29.67/19.91 inference(unit_resolution,[status(thm)],[28274, 28270, 28269])).
% 29.67/19.91 tff(28276,plain,
% 29.67/19.91 (f8(f10(c2)) = c2),
% 29.67/19.91 inference(symmetry,[status(thm)],[28275])).
% 29.67/19.91 tff(28277,plain,
% 29.67/19.91 (big_f(f3(c2, c2), f10(c1))),
% 29.67/19.91 inference(unit_resolution,[status(thm)],[27281, 28127, 16])).
% 29.67/19.91 tff(28278,plain,
% 29.67/19.91 (big_f(f3(c2, c2), c2) <=> big_f(f3(c2, c2), f10(c1))),
% 29.67/19.91 inference(symmetry,[status(thm)],[27276])).
% 29.67/19.91 tff(28279,plain,
% 29.67/19.91 (big_f(f3(c2, c2), f10(f10(c2))) <=> big_f(f3(c2, c2), f10(c1))),
% 29.67/19.91 inference(transitivity,[status(thm)],[21201, 28278])).
% 29.67/19.91 tff(28280,plain,
% 29.67/19.91 ((~big_f(f3(c2, c2), f10(f10(c2)))) <=> (~big_f(f3(c2, c2), f10(c1)))),
% 29.67/19.91 inference(monotonicity,[status(thm)],[28279])).
% 29.67/19.91 tff(28281,assumption,(~big_f(f3(c2, c2), f10(f10(c2)))), introduced(assumption)).
% 29.67/19.91 tff(28282,plain,
% 29.67/19.91 (~big_f(f3(c2, c2), f10(c1))),
% 29.67/19.91 inference(modus_ponens,[status(thm)],[28281, 28280])).
% 29.67/19.91 tff(28283,plain,
% 29.67/19.91 ($false),
% 29.67/19.91 inference(unit_resolution,[status(thm)],[27750, 28282])).
% 29.67/19.91 tff(28284,plain,(big_f(f3(c2, c2), f10(f10(c2))) | (~big_f(f3(c2, c2), f10(c1))) | (~(f10(c1) = c2)) | (~(f10(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.67/19.91 tff(28285,plain,
% 29.67/19.91 (big_f(f3(c2, c2), f10(f10(c2)))),
% 29.67/19.91 inference(unit_resolution,[status(thm)],[28284, 28277, 94, 16])).
% 29.67/19.91 tff(28286,plain,
% 29.67/19.91 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f10(c2)) = f10(c2)) | (~(f7(f10(c2)) = f10(c2))) | (f3(c2, c2) = f8(f10(c2))) | (~big_f(f3(c2, c2), f10(f10(c2)))) | (~(f6(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f7(f10(c2)), f6(f10(c2), f10(c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(f10(c2)) = f10(c2)) | (~(f7(f10(c2)) = f10(c2))) | (f3(c2, c2) = f8(f10(c2))) | (~big_f(f3(c2, c2), f10(f10(c2)))) | (~(f6(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f7(f10(c2)), f6(f10(c2), f10(c2)))))),
% 29.67/19.91 inference(rewrite,[status(thm)],[])).
% 29.67/19.91 tff(28287,plain,
% 29.67/19.91 (((f10(f10(c2)) = f10(c2)) | (f3(c2, c2) = f8(f10(c2))) | (~big_f(f3(c2, c2), f10(f10(c2)))) | (~(f7(f10(c2)) = f10(c2))) | (~(f6(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f7(f10(c2)), f6(f10(c2), f10(c2))))) <=> ((f10(f10(c2)) = f10(c2)) | (~(f7(f10(c2)) = f10(c2))) | (f3(c2, c2) = f8(f10(c2))) | (~big_f(f3(c2, c2), f10(f10(c2)))) | (~(f6(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f7(f10(c2)), f6(f10(c2), f10(c2)))))),
% 29.67/19.91 inference(rewrite,[status(thm)],[])).
% 29.67/19.91 tff(28288,plain,
% 29.67/19.91 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f10(c2)) = f10(c2)) | (f3(c2, c2) = f8(f10(c2))) | (~big_f(f3(c2, c2), f10(f10(c2)))) | (~(f7(f10(c2)) = f10(c2))) | (~(f6(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f7(f10(c2)), f6(f10(c2), f10(c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f10(c2)) = f10(c2)) | (~(f7(f10(c2)) = f10(c2))) | (f3(c2, c2) = f8(f10(c2))) | (~big_f(f3(c2, c2), f10(f10(c2)))) | (~(f6(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f7(f10(c2)), f6(f10(c2), f10(c2))))))),
% 29.67/19.91 inference(monotonicity,[status(thm)],[28287])).
% 29.67/19.91 tff(28289,plain,
% 29.67/19.91 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f10(c2)) = f10(c2)) | (f3(c2, c2) = f8(f10(c2))) | (~big_f(f3(c2, c2), f10(f10(c2)))) | (~(f7(f10(c2)) = f10(c2))) | (~(f6(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f7(f10(c2)), f6(f10(c2), f10(c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(f10(c2)) = f10(c2)) | (~(f7(f10(c2)) = f10(c2))) | (f3(c2, c2) = f8(f10(c2))) | (~big_f(f3(c2, c2), f10(f10(c2)))) | (~(f6(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f7(f10(c2)), f6(f10(c2), f10(c2)))))),
% 29.67/19.91 inference(transitivity,[status(thm)],[28288, 28286])).
% 29.67/19.91 tff(28290,plain,
% 29.67/19.91 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f10(c2)) = f10(c2)) | (f3(c2, c2) = f8(f10(c2))) | (~big_f(f3(c2, c2), f10(f10(c2)))) | (~(f7(f10(c2)) = f10(c2))) | (~(f6(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f7(f10(c2)), f6(f10(c2), f10(c2)))))),
% 29.67/19.91 inference(quant_inst,[status(thm)],[])).
% 29.67/19.91 tff(28291,plain,
% 29.67/19.91 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(f10(c2)) = f10(c2)) | (~(f7(f10(c2)) = f10(c2))) | (f3(c2, c2) = f8(f10(c2))) | (~big_f(f3(c2, c2), f10(f10(c2)))) | (~(f6(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f7(f10(c2)), f6(f10(c2), f10(c2))))),
% 29.67/19.91 inference(modus_ponens,[status(thm)],[28290, 28289])).
% 29.67/19.91 tff(28292,plain,
% 29.67/19.91 (f3(c2, c2) = f8(f10(c2))),
% 29.67/19.91 inference(unit_resolution,[status(thm)],[28291, 2730, 15308, 28117, 28285, 28270, 28269])).
% 29.67/19.91 tff(28293,plain,
% 29.67/19.91 (f3(c2, c2) = c2),
% 29.67/19.91 inference(transitivity,[status(thm)],[28292, 28276])).
% 29.67/19.91 tff(28294,plain,
% 29.67/19.91 ($false),
% 29.67/19.91 inference(unit_resolution,[status(thm)],[28126, 28293])).
% 29.67/19.91 tff(28295,plain,((c2 = c4) | (~(f6(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f7(f10(c2)), f6(f10(c2), f10(c2)))) | (~(f10(c1) = c2)) | big_f(c1, c2) | (c1 = c3) | (~big_f(c1, c1)) | (f10(c2) = c2) | (~big_f(c2, c2)) | (f10(c2) = c3)), inference(lemma,lemma(discharge,[]))).
% 29.67/19.91 tff(28296,plain,
% 29.67/19.91 (c2 = c4),
% 29.67/19.91 inference(unit_resolution,[status(thm)],[28295, 28253, 28257, 15, 27, 76, 27489, 89, 27705, 12420])).
% 29.67/19.91 tff(28297,plain,
% 29.67/19.91 (~(f4(c4) = c1)),
% 29.67/19.91 inference(unit_resolution,[status(thm)],[28153, 28296, 27, 76, 27489])).
% 29.67/19.91 tff(28298,plain,
% 29.67/19.91 (f4(c4) = c2),
% 29.67/19.91 inference(unit_resolution,[status(thm)],[11750, 28297])).
% 29.67/19.91 tff(28299,plain,
% 29.67/19.91 (big_f(c2, c1)),
% 29.67/19.91 inference(unit_resolution,[status(thm)],[15688, 28298, 27489, 89, 27705, 28262, 27])).
% 29.67/19.91 tff(28300,plain,
% 29.67/19.91 (big_f(c2, f10(c2))),
% 29.67/19.91 inference(modus_ponens,[status(thm)],[28299, 15252])).
% 29.67/19.91 tff(28301,plain,
% 29.67/19.91 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(f10(c2)) = f10(c2))) | (~(f6(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f7(f10(c2)), f6(f10(c2), f10(c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(f10(c2)) = f10(c2))) | (~(f6(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f7(f10(c2)), f6(f10(c2), f10(c2)))))),
% 29.67/19.91 inference(rewrite,[status(thm)],[])).
% 29.67/19.91 tff(28302,plain,
% 29.67/19.91 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(f10(c2)) = f10(c2))) | (~(f6(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f7(f10(c2)), f6(f10(c2), f10(c2)))))),
% 29.67/19.91 inference(quant_inst,[status(thm)],[])).
% 29.67/19.91 tff(28303,plain,
% 29.67/19.91 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(f10(c2)) = f10(c2))) | (~(f6(f10(c2), f10(c2)) = f10(c2))) | (~big_f(f7(f10(c2)), f6(f10(c2), f10(c2))))),
% 29.67/19.91 inference(modus_ponens,[status(thm)],[28302, 28301])).
% 29.67/19.91 tff(28304,plain,
% 29.67/19.91 ($false),
% 29.67/19.91 inference(unit_resolution,[status(thm)],[28303, 2730, 89, 28300, 28268, 28117, 28253, 28257])).
% 29.67/19.91 tff(28305,plain,((f10(c2) = c2) | big_f(c1, c2) | (~(c3 = c2)) | (f10(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.67/19.91 tff(28306,plain,
% 29.67/19.91 (f10(c2) = c2),
% 29.67/19.91 inference(unit_resolution,[status(thm)],[28305, 3, 67, 27])).
% 29.67/19.91 tff(28307,plain,
% 29.67/19.91 (~(f4(c4) = c2)),
% 29.67/19.91 inference(unit_resolution,[status(thm)],[11545, 9094, 27489, 27, 76])).
% 29.67/19.91 tff(28308,plain,
% 29.67/19.91 (~big_f(c2, c1)),
% 29.67/19.91 inference(unit_resolution,[status(thm)],[27836, 28307, 27, 67])).
% 29.67/19.91 tff(28309,plain,
% 29.67/19.91 (~(f2(c3) = c2)),
% 29.67/19.91 inference(unit_resolution,[status(thm)],[26181, 28308, 27705, 28096, 27, 67, 28306])).
% 29.67/19.91 tff(28310,plain,
% 29.67/19.91 (f2(c3) = c1),
% 29.67/19.91 inference(unit_resolution,[status(thm)],[1273, 28309])).
% 29.67/19.91 tff(28311,plain,
% 29.67/19.91 (c1 = f2(c2)),
% 29.67/19.91 inference(modus_ponens,[status(thm)],[28310, 28103])).
% 29.67/19.91 tff(28312,assumption,(c1 = f2(c2)), introduced(assumption)).
% 29.67/19.91 tff(28313,plain,
% 29.67/19.91 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (c2 = c4) | big_f(c2, c1) | (~(c1 = f2(c2))) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (~(c2 = c3)) | (c2 = c4) | big_f(c2, c1) | (~(c1 = f2(c2))) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)))),
% 29.67/19.91 inference(rewrite,[status(thm)],[])).
% 29.67/19.91 tff(28314,plain,
% 29.67/19.91 (((~(c2 = c3)) | (~(c1 = f2(c2))) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | big_f(c2, c1)) <=> ((~(c2 = c3)) | (c2 = c4) | big_f(c2, c1) | (~(c1 = f2(c2))) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)))),
% 29.67/19.91 inference(rewrite,[status(thm)],[])).
% 29.67/19.91 tff(28315,plain,
% 29.67/19.91 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c1 = f2(c2))) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | big_f(c2, c1))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (c2 = c4) | big_f(c2, c1) | (~(c1 = f2(c2))) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2))))),
% 29.67/19.91 inference(monotonicity,[status(thm)],[28314])).
% 29.67/19.91 tff(28316,plain,
% 29.67/19.91 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c1 = f2(c2))) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | big_f(c2, c1))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (~(c2 = c3)) | (c2 = c4) | big_f(c2, c1) | (~(c1 = f2(c2))) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)))),
% 29.67/19.91 inference(transitivity,[status(thm)],[28315, 28313])).
% 29.67/19.91 tff(28317,plain,
% 29.67/19.91 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c1 = f2(c2))) | (c2 = c4) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2)) | big_f(c2, c1))),
% 29.67/19.91 inference(quant_inst,[status(thm)],[])).
% 29.67/19.91 tff(28318,plain,
% 29.67/19.91 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (~(c2 = c3)) | (c2 = c4) | big_f(c2, c1) | (~(c1 = f2(c2))) | (~(f3(c2, c2) = c2)) | (~big_f(f3(c2, c2), c2))),
% 29.67/19.91 inference(modus_ponens,[status(thm)],[28317, 28316])).
% 29.67/19.91 tff(28319,plain,
% 29.67/19.91 ($false),
% 29.67/19.91 inference(unit_resolution,[status(thm)],[28318, 1398, 873, 1344, 2, 28312, 7387, 21618])).
% 29.67/19.91 tff(28320,plain,((~(f3(c2, c2) = c2)) | (c2 = c4) | (~(c2 = c3)) | big_f(c2, c1) | (~(c1 = f2(c2))) | (~big_f(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 29.67/19.91 tff(28321,plain,
% 29.67/19.91 (~(f3(c2, c2) = c2)),
% 29.67/19.91 inference(unit_resolution,[status(thm)],[28320, 873, 1335, 28308, 28311, 27705])).
% 29.67/19.91 tff(28322,plain,
% 29.67/19.91 (big_f(f3(c2, c2), c2)),
% 29.67/19.91 inference(unit_resolution,[status(thm)],[21176, 28321, 27, 76, 27489, 873])).
% 29.67/19.91 tff(28323,plain,
% 29.67/19.91 (c2 = f6(c1, f6(c1, c2))),
% 29.67/19.91 inference(symmetry,[status(thm)],[27490])).
% 29.67/19.91 tff(28324,plain,
% 29.67/19.91 (f3(c2, c2) = f3(c2, f6(c1, f6(c1, c2)))),
% 29.67/19.91 inference(monotonicity,[status(thm)],[28323])).
% 29.67/19.91 tff(28325,plain,
% 29.67/19.91 (f3(c2, f6(c1, f6(c1, c2))) = f3(c2, c2)),
% 29.67/19.91 inference(symmetry,[status(thm)],[28324])).
% 29.67/19.91 tff(28326,plain,
% 29.67/19.91 ((f3(c2, f6(c1, f6(c1, c2))) = c2) <=> (f3(c2, c2) = c2)),
% 29.67/19.91 inference(monotonicity,[status(thm)],[28325])).
% 29.67/19.91 tff(28327,plain,
% 29.67/19.91 ((f3(c2, c2) = c2) <=> (f3(c2, f6(c1, f6(c1, c2))) = c2)),
% 29.67/19.91 inference(symmetry,[status(thm)],[28326])).
% 29.67/19.91 tff(28328,plain,
% 29.67/19.91 ((~(f3(c2, c2) = c2)) <=> (~(f3(c2, f6(c1, f6(c1, c2))) = c2))),
% 29.67/19.91 inference(monotonicity,[status(thm)],[28327])).
% 29.67/19.91 tff(28329,plain,
% 29.67/19.91 (~(f3(c2, f6(c1, f6(c1, c2))) = c2)),
% 29.67/19.91 inference(modus_ponens,[status(thm)],[12861, 28328])).
% 29.67/19.91 tff(28330,plain,
% 29.67/19.91 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f3(c2, f6(c1, f6(c1, c2))) = c1) | (f3(c2, f6(c1, f6(c1, c2))) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f3(c2, f6(c1, f6(c1, c2))) = c1) | (f3(c2, f6(c1, f6(c1, c2))) = c2))),
% 29.67/19.91 inference(rewrite,[status(thm)],[])).
% 29.67/19.91 tff(28331,plain,
% 29.67/19.91 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f3(c2, f6(c1, f6(c1, c2))) = c1) | (f3(c2, f6(c1, f6(c1, c2))) = c2))),
% 29.67/19.91 inference(quant_inst,[status(thm)],[])).
% 29.67/19.91 tff(28332,plain,
% 29.67/19.91 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f3(c2, f6(c1, f6(c1, c2))) = c1) | (f3(c2, f6(c1, f6(c1, c2))) = c2)),
% 29.67/19.91 inference(modus_ponens,[status(thm)],[28331, 28330])).
% 29.67/19.91 tff(28333,plain,
% 29.67/19.91 ((f3(c2, f6(c1, f6(c1, c2))) = c1) | (f3(c2, f6(c1, f6(c1, c2))) = c2)),
% 29.67/19.92 inference(unit_resolution,[status(thm)],[28332, 10])).
% 29.67/19.92 tff(28334,plain,
% 29.67/19.92 (f3(c2, f6(c1, f6(c1, c2))) = c1),
% 29.67/19.92 inference(unit_resolution,[status(thm)],[28333, 28329])).
% 29.67/19.92 tff(28335,plain,
% 29.67/19.92 (f3(c2, c2) = c1),
% 29.67/19.92 inference(transitivity,[status(thm)],[28324, 28334])).
% 29.67/19.92 tff(28336,plain,
% 29.67/19.92 (big_f(f3(c2, c2), c2) <=> big_f(c1, c2)),
% 29.67/19.92 inference(monotonicity,[status(thm)],[28335])).
% 29.67/19.92 tff(28337,plain,
% 29.67/19.92 (big_f(c1, c2) <=> big_f(f3(c2, c2), c2)),
% 29.67/19.92 inference(symmetry,[status(thm)],[28336])).
% 29.67/19.92 tff(28338,plain,
% 29.67/19.92 ((~big_f(c1, c2)) <=> (~big_f(f3(c2, c2), c2))),
% 29.67/19.92 inference(monotonicity,[status(thm)],[28337])).
% 29.67/19.92 tff(28339,plain,
% 29.67/19.92 (~big_f(f3(c2, c2), c2)),
% 29.67/19.92 inference(modus_ponens,[status(thm)],[27, 28338])).
% 29.67/19.92 tff(28340,plain,
% 29.67/19.92 ($false),
% 29.67/19.92 inference(unit_resolution,[status(thm)],[15356, 28339])).
% 29.67/19.92 tff(28341,plain,((~(f6(c1, f6(c1, c2)) = c2)) | (~big_f(f3(c2, c2), c2)) | big_f(c1, c2) | (f3(c2, c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 29.67/19.92 tff(28342,plain,
% 29.67/19.92 (~(f6(c1, f6(c1, c2)) = c2)),
% 29.67/19.92 inference(unit_resolution,[status(thm)],[28341, 28322, 27, 28321])).
% 29.67/19.92 tff(28343,plain,
% 29.67/19.92 (f6(c1, f6(c1, c2)) = c1),
% 29.67/19.92 inference(unit_resolution,[status(thm)],[63, 28342])).
% 29.67/19.92 tff(28344,plain,
% 29.67/19.92 ((f6(c1, f6(c1, c2)) = f6(c1, c2)) <=> (c1 = f6(c1, c2))),
% 29.67/19.92 inference(monotonicity,[status(thm)],[28343])).
% 29.67/19.92 tff(28345,plain,
% 29.67/19.92 ((f6(c1, f6(c1, c2)) = f6(c1, c2)) <=> (f6(c1, c2) = c1)),
% 29.67/19.92 inference(transitivity,[status(thm)],[28344, 30])).
% 29.67/19.92 tff(28346,plain,
% 29.67/19.92 ((~(f6(c1, f6(c1, c2)) = f6(c1, c2))) <=> (~(f6(c1, c2) = c1))),
% 29.67/19.92 inference(monotonicity,[status(thm)],[28345])).
% 29.67/19.92 tff(28347,plain,
% 29.67/19.92 ((f6(c1, c2) = c1) <=> (f6(c1, f6(c1, c2)) = f6(c1, c2))),
% 29.67/19.92 inference(symmetry,[status(thm)],[32])).
% 29.67/19.92 tff(28348,plain,
% 29.67/19.92 (big_f(f7(c1), f6(c1, f6(c1, c2))) <=> big_f(c1, c1)),
% 29.67/19.92 inference(monotonicity,[status(thm)],[25791, 29])).
% 29.67/19.92 tff(28349,plain,
% 29.67/19.92 (big_f(c1, c1) <=> big_f(f7(c1), f6(c1, f6(c1, c2)))),
% 29.67/19.92 inference(symmetry,[status(thm)],[28348])).
% 29.67/19.92 tff(28350,plain,
% 29.67/19.92 (big_f(f7(c1), f6(c1, f6(c1, c2)))),
% 29.67/19.92 inference(modus_ponens,[status(thm)],[4932, 28349])).
% 29.67/19.92 tff(28351,plain,
% 29.67/19.92 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))),
% 29.67/19.92 inference(rewrite,[status(thm)],[])).
% 29.67/19.92 tff(28352,plain,
% 29.67/19.92 (((f10(c1) = c1) | big_f(c1, f10(c1)) | (~(f7(c1) = c1)) | (~(c1 = f8(c1))) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2))))) <=> ((f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))),
% 29.67/19.92 inference(rewrite,[status(thm)],[])).
% 29.67/19.92 tff(28353,plain,
% 29.67/19.92 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | big_f(c1, f10(c1)) | (~(f7(c1) = c1)) | (~(c1 = f8(c1))) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2))))))),
% 29.67/19.92 inference(monotonicity,[status(thm)],[28352])).
% 29.67/19.92 tff(28354,plain,
% 29.67/19.92 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | big_f(c1, f10(c1)) | (~(f7(c1) = c1)) | (~(c1 = f8(c1))) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))),
% 29.67/19.92 inference(transitivity,[status(thm)],[28353, 28351])).
% 29.67/19.92 tff(28355,plain,
% 29.67/19.92 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | big_f(c1, f10(c1)) | (~(f7(c1) = c1)) | (~(c1 = f8(c1))) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))),
% 29.67/19.92 inference(quant_inst,[status(thm)],[])).
% 29.67/19.92 tff(28356,plain,
% 29.67/19.92 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2))))),
% 29.67/19.92 inference(modus_ponens,[status(thm)],[28355, 28354])).
% 29.67/19.92 tff(28357,plain,
% 29.67/19.92 ((~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2))))),
% 29.67/19.92 inference(unit_resolution,[status(thm)],[28356, 2963, 25791, 3, 3031, 3030])).
% 29.67/19.92 tff(28358,plain,
% 29.67/19.92 (~(f6(c1, f6(c1, c2)) = f6(c1, c2))),
% 29.67/19.92 inference(unit_resolution,[status(thm)],[28357, 28350])).
% 29.67/19.92 tff(28359,plain,
% 29.67/19.92 (~(f6(c1, c2) = c2)),
% 29.67/19.92 inference(unit_resolution,[status(thm)],[43, 28358])).
% 29.67/19.92 tff(28360,plain,
% 29.67/19.92 (f6(c1, c2) = c1),
% 29.67/19.92 inference(unit_resolution,[status(thm)],[48, 28359])).
% 29.67/19.92 tff(28361,plain,
% 29.67/19.92 (f6(c1, f6(c1, c2)) = f6(c1, c2)),
% 29.67/19.92 inference(modus_ponens,[status(thm)],[28360, 28347])).
% 29.67/19.92 tff(28362,plain,
% 29.67/19.92 ($false),
% 29.67/19.92 inference(unit_resolution,[status(thm)],[28358, 28361])).
% 29.67/19.92 tff(28363,plain,((~(f6(c1, f6(c1, c2)) = c1)) | (f10(c1) = c1) | (~(c1 = f8(c1))) | big_f(c1, f10(c1)) | (~big_f(c1, c1))), inference(lemma,lemma(discharge,[]))).
% 29.67/19.92 tff(28364,plain,
% 29.67/19.92 (~(c1 = f8(c1))),
% 29.67/19.92 inference(unit_resolution,[status(thm)],[28363, 28343, 3, 26485, 27489])).
% 29.67/19.92 tff(28365,plain,
% 29.67/19.92 (~(f8(c1) = c1)),
% 29.67/19.92 inference(unit_resolution,[status(thm)],[9808, 28364])).
% 29.67/19.92 tff(28366,plain,
% 29.67/19.92 (f8(c1) = c2),
% 29.67/19.92 inference(unit_resolution,[status(thm)],[1680, 28365])).
% 29.67/19.92 tff(28367,plain,
% 29.67/19.92 ((f3(c2, c2) = f8(c1)) <=> (f3(c2, c2) = c2)),
% 29.67/19.92 inference(monotonicity,[status(thm)],[28366])).
% 29.67/19.92 tff(28368,plain,
% 29.67/19.92 ((f3(c2, c2) = c2) <=> (f3(c2, c2) = f8(c1))),
% 29.67/19.92 inference(symmetry,[status(thm)],[28367])).
% 29.67/19.92 tff(28369,plain,
% 29.67/19.92 ((~(f3(c2, c2) = c2)) <=> (~(f3(c2, c2) = f8(c1)))),
% 29.67/19.92 inference(monotonicity,[status(thm)],[28368])).
% 29.67/19.92 tff(28370,plain,
% 29.67/19.92 (~(f3(c2, c2) = f8(c1))),
% 29.67/19.92 inference(modus_ponens,[status(thm)],[28321, 28369])).
% 29.67/19.92 tff(28371,plain,
% 29.67/19.92 (big_f(f3(c2, c2), f10(c1))),
% 29.67/19.92 inference(unit_resolution,[status(thm)],[27281, 28322, 15])).
% 29.67/19.92 tff(28372,plain,
% 29.67/19.92 (big_f(f7(c1), f6(c1, f6(c1, c2))) <=> big_f(c1, c1)),
% 29.67/19.92 inference(monotonicity,[status(thm)],[25791, 28343])).
% 29.67/19.92 tff(28373,plain,
% 29.67/19.92 (big_f(c1, c1) <=> big_f(f7(c1), f6(c1, f6(c1, c2)))),
% 29.67/19.92 inference(symmetry,[status(thm)],[28372])).
% 29.67/19.92 tff(28374,plain,
% 29.67/19.92 (big_f(f7(c1), f6(c1, f6(c1, c2)))),
% 29.67/19.92 inference(modus_ponens,[status(thm)],[27489, 28373])).
% 29.67/19.92 tff(28375,plain,
% 29.67/19.92 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1))))),
% 29.67/19.92 inference(rewrite,[status(thm)],[])).
% 29.67/19.92 tff(28376,plain,
% 29.67/19.92 (((f10(c1) = c1) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1))) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2))))) <=> ((f10(c1) = c1) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1))))),
% 29.67/19.92 inference(rewrite,[status(thm)],[])).
% 29.67/19.92 tff(28377,plain,
% 29.67/19.92 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1))) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1)))))),
% 29.67/19.92 inference(monotonicity,[status(thm)],[28376])).
% 29.67/19.92 tff(28378,plain,
% 29.67/19.92 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1))) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1))))),
% 29.67/19.92 inference(transitivity,[status(thm)],[28377, 28375])).
% 29.67/19.92 tff(28379,plain,
% 29.67/19.92 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1))) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))),
% 29.67/19.92 inference(quant_inst,[status(thm)],[])).
% 29.67/19.92 tff(28380,plain,
% 29.67/19.92 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1)))),
% 29.67/19.92 inference(modus_ponens,[status(thm)],[28379, 28378])).
% 29.67/19.92 tff(28381,plain,
% 29.67/19.92 (~(f6(c1, f6(c1, c2)) = f6(c1, c2))),
% 29.67/19.92 inference(unit_resolution,[status(thm)],[28380, 2730, 25791, 3, 28374, 28371, 28370])).
% 29.67/19.92 tff(28382,plain,
% 29.67/19.92 (~(f6(c1, c2) = c1)),
% 29.67/19.92 inference(modus_ponens,[status(thm)],[28381, 28346])).
% 29.67/19.92 tff(28383,plain,
% 29.67/19.92 (~(f6(c1, c2) = c2)),
% 29.67/19.92 inference(unit_resolution,[status(thm)],[43, 28381])).
% 29.67/19.92 tff(28384,plain,
% 29.67/19.92 (f6(c1, c2) = c1),
% 29.67/19.92 inference(unit_resolution,[status(thm)],[48, 28383])).
% 29.67/19.92 tff(28385,plain,
% 29.67/19.92 ($false),
% 29.67/19.92 inference(unit_resolution,[status(thm)],[28384, 28382])).
% 29.67/19.92 tff(28386,plain,((c2 = c4) | (f10(c1) = c1) | big_f(c1, c2) | (~(c3 = c2))), inference(lemma,lemma(discharge,[]))).
% 29.67/19.92 tff(28387,plain,
% 29.67/19.92 (c2 = c4),
% 29.67/19.92 inference(unit_resolution,[status(thm)],[28386, 3, 27, 67])).
% 29.67/19.92 tff(28388,plain,
% 29.67/19.92 (~(f4(c4) = c1)),
% 29.67/19.92 inference(unit_resolution,[status(thm)],[28153, 28387, 27, 76, 27489])).
% 29.67/19.92 tff(28389,plain,
% 29.67/19.92 (f4(c4) = c2),
% 29.67/19.92 inference(unit_resolution,[status(thm)],[11750, 28388])).
% 29.67/19.92 tff(28390,plain,
% 29.67/19.92 (~(c4 = c1)),
% 29.67/19.92 inference(unit_resolution,[status(thm)],[11545, 28389, 27489, 27, 76])).
% 29.67/19.92 tff(28391,plain,
% 29.67/19.92 (c4 = c2),
% 29.67/19.92 inference(unit_resolution,[status(thm)],[461, 28390])).
% 29.67/19.92 tff(28392,plain,
% 29.67/19.92 (f9(f10(c2), f4(c4)) = c2),
% 29.67/19.92 inference(unit_resolution,[status(thm)],[8065, 28389, 28306])).
% 29.67/19.92 tff(28393,plain,
% 29.67/19.92 (f9(c2, c2) = c2),
% 29.67/19.92 inference(unit_resolution,[status(thm)],[1606, 28389, 28306, 28392])).
% 29.67/19.92 tff(28394,plain,
% 29.67/19.92 (big_f(f9(c2, c2), f10(c2)) <=> big_f(f9(c2, c2), c2)),
% 29.67/19.92 inference(monotonicity,[status(thm)],[28306])).
% 29.67/19.92 tff(28395,plain,
% 29.67/19.92 (big_f(f9(c2, c2), c2) <=> big_f(f9(c2, c2), f10(c2))),
% 29.67/19.92 inference(symmetry,[status(thm)],[28394])).
% 29.67/19.92 tff(28396,plain,
% 29.67/19.92 (big_f(f9(c2, c2), c2) <=> big_f(c2, c2)),
% 29.67/19.92 inference(monotonicity,[status(thm)],[28393])).
% 29.67/19.92 tff(28397,plain,
% 29.67/19.92 (big_f(c2, c2) <=> big_f(f9(c2, c2), c2)),
% 29.67/19.92 inference(symmetry,[status(thm)],[28396])).
% 29.67/19.92 tff(28398,plain,
% 29.67/19.92 (big_f(c2, c2) <=> big_f(f9(c2, c2), f10(c2))),
% 29.67/19.92 inference(transitivity,[status(thm)],[28397, 28395])).
% 29.67/19.92 tff(28399,plain,
% 29.67/19.92 (big_f(f9(c2, c2), f10(c2))),
% 29.67/19.92 inference(modus_ponens,[status(thm)],[27705, 28398])).
% 29.67/19.92 tff(28400,plain,
% 29.67/19.92 (~(f6(f7(c2), c3) = c2)),
% 29.67/19.92 inference(unit_resolution,[status(thm)],[2386, 28399, 67, 28096, 27705, 28306, 28393])).
% 29.67/19.92 tff(28401,plain,
% 29.67/19.92 (~(f6(f7(c2), c3) = c4)),
% 29.67/19.92 inference(unit_resolution,[status(thm)],[3995, 28400, 28391])).
% 29.67/19.92 tff(28402,plain,
% 29.67/19.92 (f6(f7(c2), c3) = c1),
% 29.67/19.92 inference(unit_resolution,[status(thm)],[2391, 28400])).
% 29.67/19.92 tff(28403,plain,
% 29.67/19.92 (c2 = f7(c2)),
% 29.67/19.92 inference(symmetry,[status(thm)],[28096])).
% 29.67/19.92 tff(28404,plain,
% 29.67/19.92 (f6(c2, c2) = f6(f7(c2), c3)),
% 29.67/19.92 inference(monotonicity,[status(thm)],[28403, 69])).
% 29.67/19.92 tff(28405,plain,
% 29.67/19.92 (f6(c2, c2) = c1),
% 29.67/19.92 inference(transitivity,[status(thm)],[28404, 28402])).
% 29.67/19.92 tff(28406,plain,
% 29.67/19.92 (big_f(f6(c2, c2), f6(c2, c2)) <=> big_f(c1, c1)),
% 29.67/19.92 inference(monotonicity,[status(thm)],[28405, 28405])).
% 29.67/19.92 tff(28407,plain,
% 29.67/19.92 (big_f(c1, c1) <=> big_f(f6(c2, c2), f6(c2, c2))),
% 29.67/19.92 inference(symmetry,[status(thm)],[28406])).
% 29.67/19.92 tff(28408,plain,
% 29.67/19.92 (big_f(f6(c2, c2), f6(c2, c2))),
% 29.67/19.92 inference(modus_ponens,[status(thm)],[27489, 28407])).
% 29.67/19.92 tff(28409,plain,
% 29.67/19.92 (f6(c2, c2) = f6(f7(c2), c3)),
% 29.67/19.92 inference(symmetry,[status(thm)],[2466])).
% 29.67/19.92 tff(28410,plain,
% 29.67/19.92 (f6(c2, c2) = c1),
% 29.67/19.92 inference(transitivity,[status(thm)],[28409, 2702])).
% 29.67/19.92 tff(28411,plain,
% 29.67/19.92 (f6(f6(c2, c2), f6(c1, c2)) = f6(c1, f6(c1, c2))),
% 29.67/19.92 inference(monotonicity,[status(thm)],[28410])).
% 29.67/19.92 tff(28412,plain,
% 29.67/19.92 (f6(f6(c2, c2), f6(c1, c2)) = c1),
% 29.67/19.92 inference(transitivity,[status(thm)],[28411, 29])).
% 29.67/19.92 tff(28413,plain,
% 29.67/19.92 ((f6(f6(c2, c2), f6(c1, c2)) = f6(c1, c2)) <=> (c1 = f6(c1, c2))),
% 29.67/19.92 inference(monotonicity,[status(thm)],[28412])).
% 29.67/19.92 tff(28414,plain,
% 29.67/19.92 ((f6(f6(c2, c2), f6(c1, c2)) = f6(c1, c2)) <=> (f6(c1, c2) = c1)),
% 29.67/19.92 inference(transitivity,[status(thm)],[28413, 30])).
% 29.67/19.92 tff(28415,plain,
% 29.67/19.92 ((~(f6(f6(c2, c2), f6(c1, c2)) = f6(c1, c2))) <=> (~(f6(c1, c2) = c1))),
% 29.67/19.92 inference(monotonicity,[status(thm)],[28414])).
% 29.67/19.92 tff(28416,plain,
% 29.67/19.92 (f6(f6(c2, c2), f6(c1, c2)) = f6(c2, c2)),
% 29.67/19.92 inference(transitivity,[status(thm)],[28411, 29, 2703, 2466])).
% 29.67/19.92 tff(28417,plain,
% 29.67/19.92 (f7(f6(c2, c2)) = f7(c1)),
% 29.67/19.92 inference(monotonicity,[status(thm)],[28410])).
% 29.67/19.92 tff(28418,plain,
% 29.67/19.92 (f7(f6(c2, c2)) = f6(c2, c2)),
% 29.67/19.92 inference(transitivity,[status(thm)],[28417, 25791, 2703, 2466])).
% 29.67/19.92 tff(28419,plain,
% 29.67/19.92 (big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f6(c1, c2))) <=> big_f(f6(c2, c2), f6(c2, c2))),
% 29.67/19.92 inference(monotonicity,[status(thm)],[28418, 28416])).
% 29.67/19.92 tff(28420,plain,
% 29.67/19.92 (big_f(f6(c2, c2), f6(c2, c2)) <=> big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f6(c1, c2)))),
% 29.67/19.92 inference(symmetry,[status(thm)],[28419])).
% 29.67/19.92 tff(28421,plain,
% 29.67/19.92 (big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f6(c1, c2)))),
% 29.67/19.92 inference(modus_ponens,[status(thm)],[14865, 28420])).
% 29.67/19.92 tff(28422,plain,
% 29.67/19.92 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f7(f6(c2, c2)) = f6(c2, c2))) | (~(f6(f6(c2, c2), f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f6(c1, c2)))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f7(f6(c2, c2)) = f6(c2, c2))) | (~(f6(f6(c2, c2), f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f6(c1, c2)))))),
% 29.67/19.92 inference(rewrite,[status(thm)],[])).
% 29.67/19.92 tff(28423,plain,
% 29.67/19.92 (((~(f10(c2) = c2)) | (~(f7(f6(c2, c2)) = f6(c2, c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f6(f6(c2, c2), f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f6(c1, c2))))) <=> ((~(f10(c2) = c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f7(f6(c2, c2)) = f6(c2, c2))) | (~(f6(f6(c2, c2), f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f6(c1, c2)))))),
% 29.67/19.92 inference(rewrite,[status(thm)],[])).
% 29.67/19.92 tff(28424,plain,
% 29.67/19.92 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(f6(c2, c2)) = f6(c2, c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f6(f6(c2, c2), f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f6(c1, c2)))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f7(f6(c2, c2)) = f6(c2, c2))) | (~(f6(f6(c2, c2), f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f6(c1, c2))))))),
% 29.67/19.92 inference(monotonicity,[status(thm)],[28423])).
% 29.67/19.92 tff(28425,plain,
% 29.67/19.92 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(f6(c2, c2)) = f6(c2, c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f6(f6(c2, c2), f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f6(c1, c2)))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f7(f6(c2, c2)) = f6(c2, c2))) | (~(f6(f6(c2, c2), f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f6(c1, c2)))))),
% 29.67/19.92 inference(transitivity,[status(thm)],[28424, 28422])).
% 29.67/19.92 tff(28426,plain,
% 29.67/19.92 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(f6(c2, c2)) = f6(c2, c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f6(f6(c2, c2), f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f6(c1, c2)))))),
% 29.67/19.92 inference(quant_inst,[status(thm)],[])).
% 29.67/19.92 tff(28427,plain,
% 29.67/19.92 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f7(f6(c2, c2)) = f6(c2, c2))) | (~(f6(f6(c2, c2), f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f6(c1, c2))))),
% 29.67/19.92 inference(modus_ponens,[status(thm)],[28426, 28425])).
% 29.67/19.92 tff(28428,plain,
% 29.67/19.92 ((~(f6(f6(c2, c2), f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f6(c1, c2))))),
% 29.67/19.92 inference(unit_resolution,[status(thm)],[28427, 2378, 122, 1572, 690, 28418])).
% 29.67/19.92 tff(28429,plain,
% 29.67/19.92 (~(f6(f6(c2, c2), f6(c1, c2)) = f6(c1, c2))),
% 29.67/19.92 inference(unit_resolution,[status(thm)],[28428, 28421])).
% 29.67/19.92 tff(28430,plain,
% 29.67/19.92 (~(f6(c1, c2) = c1)),
% 29.67/19.92 inference(modus_ponens,[status(thm)],[28429, 28415])).
% 29.67/19.92 tff(28431,plain,
% 29.67/19.92 ((f6(f6(c2, c2), f6(c1, c2)) = f6(c1, c2)) <=> (f6(c1, f6(c1, c2)) = f6(c1, c2))),
% 29.67/19.92 inference(transitivity,[status(thm)],[28414, 28347])).
% 29.67/19.92 tff(28432,plain,
% 29.67/19.92 ((~(f6(f6(c2, c2), f6(c1, c2)) = f6(c1, c2))) <=> (~(f6(c1, f6(c1, c2)) = f6(c1, c2)))),
% 29.67/19.92 inference(monotonicity,[status(thm)],[28431])).
% 29.67/19.92 tff(28433,plain,
% 29.67/19.92 (~(f6(c1, f6(c1, c2)) = f6(c1, c2))),
% 29.67/19.92 inference(modus_ponens,[status(thm)],[28429, 28432])).
% 29.67/19.92 tff(28434,plain,
% 29.67/19.92 (~(f6(c1, c2) = c2)),
% 29.67/19.92 inference(unit_resolution,[status(thm)],[43, 28433])).
% 29.67/19.92 tff(28435,plain,
% 29.67/19.92 ($false),
% 29.67/19.92 inference(unit_resolution,[status(thm)],[48, 28434, 28430])).
% 29.67/19.92 tff(28436,plain,((~(f6(c1, f6(c1, c2)) = c1)) | (~(f6(f7(c2), c3) = c1)) | (~(c3 = c2)) | (~(f7(c2) = c2)) | (~(f10(c2) = c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~big_f(f6(c2, c2), f6(c2, c2)))), inference(lemma,lemma(discharge,[]))).
% 29.67/19.92 tff(28437,plain,
% 29.67/19.92 (~(f6(c1, f6(c1, c2)) = c1)),
% 29.67/19.92 inference(unit_resolution,[status(thm)],[28436, 28402, 67, 28096, 28306, 28393, 28399, 28408])).
% 29.67/19.92 tff(28438,plain,
% 29.67/19.92 (f6(c1, f6(c1, c2)) = c2),
% 29.67/19.92 inference(unit_resolution,[status(thm)],[63, 28437])).
% 29.67/19.92 tff(28439,plain,
% 29.67/19.92 (f6(f6(c2, c2), f6(c1, c2)) = f6(c1, f6(c1, c2))),
% 29.67/19.92 inference(monotonicity,[status(thm)],[28405])).
% 29.67/19.92 tff(28440,plain,
% 29.67/19.92 (f6(f6(c2, c2), f6(c1, c2)) = c2),
% 29.67/19.92 inference(transitivity,[status(thm)],[28439, 28438])).
% 29.67/19.92 tff(28441,plain,
% 29.67/19.92 (f7(f6(c2, c2)) = f7(c1)),
% 29.67/19.92 inference(monotonicity,[status(thm)],[28405])).
% 29.67/19.92 tff(28442,plain,
% 29.67/19.92 (f7(f6(c2, c2)) = c1),
% 29.67/19.92 inference(transitivity,[status(thm)],[28441, 25791])).
% 29.67/19.92 tff(28443,plain,
% 29.67/19.92 (big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f6(c1, c2))) <=> big_f(c1, c2)),
% 29.67/19.92 inference(monotonicity,[status(thm)],[28442, 28440])).
% 29.67/19.92 tff(28444,plain,
% 29.67/19.92 (big_f(c1, c2) <=> big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f6(c1, c2)))),
% 29.67/19.92 inference(symmetry,[status(thm)],[28443])).
% 29.67/19.92 tff(28445,plain,
% 29.67/19.92 ((~big_f(c1, c2)) <=> (~big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f6(c1, c2))))),
% 29.67/19.92 inference(monotonicity,[status(thm)],[28444])).
% 29.67/19.92 tff(28446,plain,
% 29.67/19.92 (~big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f6(c1, c2)))),
% 29.67/19.92 inference(modus_ponens,[status(thm)],[27, 28445])).
% 29.67/19.92 tff(28447,plain,
% 29.67/19.92 (f6(f7(c2), c3) = f6(c2, c2)),
% 29.67/19.92 inference(symmetry,[status(thm)],[28404])).
% 29.67/19.92 tff(28448,plain,
% 29.67/19.92 (c1 = f6(f7(c2), c3)),
% 29.67/19.92 inference(symmetry,[status(thm)],[28402])).
% 29.67/19.92 tff(28449,plain,
% 29.67/19.92 (f7(f6(c2, c2)) = f6(c2, c2)),
% 29.67/19.92 inference(transitivity,[status(thm)],[28441, 25791, 28448, 28447])).
% 29.67/19.92 tff(28450,plain,
% 29.67/19.92 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f7(f6(c2, c2)) = f6(c2, c2))) | big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f6(c1, c2))) | (f6(f6(c2, c2), f6(c1, c2)) = f6(c1, c2)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f7(f6(c2, c2)) = f6(c2, c2))) | big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f6(c1, c2))) | (f6(f6(c2, c2), f6(c1, c2)) = f6(c1, c2)))),
% 29.67/19.92 inference(rewrite,[status(thm)],[])).
% 29.67/19.92 tff(28451,plain,
% 29.67/19.92 (((~(f10(c2) = c2)) | (~(f7(f6(c2, c2)) = f6(c2, c2))) | (f6(f6(c2, c2), f6(c1, c2)) = f6(c1, c2)) | big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f6(c1, c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2)))) <=> ((~(f10(c2) = c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f7(f6(c2, c2)) = f6(c2, c2))) | big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f6(c1, c2))) | (f6(f6(c2, c2), f6(c1, c2)) = f6(c1, c2)))),
% 29.67/19.92 inference(rewrite,[status(thm)],[])).
% 29.67/19.92 tff(28452,plain,
% 29.67/19.92 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(f6(c2, c2)) = f6(c2, c2))) | (f6(f6(c2, c2), f6(c1, c2)) = f6(c1, c2)) | big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f6(c1, c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f7(f6(c2, c2)) = f6(c2, c2))) | big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f6(c1, c2))) | (f6(f6(c2, c2), f6(c1, c2)) = f6(c1, c2))))),
% 29.67/19.93 inference(monotonicity,[status(thm)],[28451])).
% 29.67/19.93 tff(28453,plain,
% 29.67/19.93 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(f6(c2, c2)) = f6(c2, c2))) | (f6(f6(c2, c2), f6(c1, c2)) = f6(c1, c2)) | big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f6(c1, c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f7(f6(c2, c2)) = f6(c2, c2))) | big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f6(c1, c2))) | (f6(f6(c2, c2), f6(c1, c2)) = f6(c1, c2)))),
% 29.67/19.93 inference(transitivity,[status(thm)],[28452, 28450])).
% 29.67/19.93 tff(28454,plain,
% 29.67/19.93 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(f6(c2, c2)) = f6(c2, c2))) | (f6(f6(c2, c2), f6(c1, c2)) = f6(c1, c2)) | big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f6(c1, c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))),
% 29.67/19.93 inference(quant_inst,[status(thm)],[])).
% 29.67/19.93 tff(28455,plain,
% 29.67/19.93 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f7(f6(c2, c2)) = f6(c2, c2))) | big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f6(c1, c2))) | (f6(f6(c2, c2), f6(c1, c2)) = f6(c1, c2))),
% 29.67/19.93 inference(modus_ponens,[status(thm)],[28454, 28453])).
% 29.67/19.93 tff(28456,plain,
% 29.67/19.93 (big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f6(c1, c2))) | (f6(f6(c2, c2), f6(c1, c2)) = f6(c1, c2))),
% 29.67/19.93 inference(unit_resolution,[status(thm)],[28455, 2409, 28306, 28393, 28399, 28449])).
% 29.67/19.93 tff(28457,plain,
% 29.67/19.93 (f6(f6(c2, c2), f6(c1, c2)) = f6(c1, c2)),
% 29.67/19.93 inference(unit_resolution,[status(thm)],[28456, 28446])).
% 29.67/19.93 tff(28458,plain,
% 29.67/19.93 (big_f(f7(c2), f6(c2, c2))),
% 29.67/19.93 inference(unit_resolution,[status(thm)],[2700, 28389, 28306, 15, 28096, 27705])).
% 29.67/19.93 tff(28459,plain,
% 29.67/19.93 (~(f6(c2, c2) = c2)),
% 29.67/19.93 inference(unit_resolution,[status(thm)],[2384, 2378, 28306, 28096, 28458, 28393, 28399])).
% 29.67/19.93 tff(28460,plain,
% 29.67/19.93 (~(f6(c1, f6(c1, c2)) = c1)),
% 29.67/19.93 inference(unit_resolution,[status(thm)],[28436, 2702, 67, 77, 122, 1572, 690, 14865])).
% 29.67/19.93 tff(28461,plain,
% 29.67/19.93 (f6(c1, f6(c1, c2)) = c2),
% 29.67/19.93 inference(unit_resolution,[status(thm)],[63, 28460])).
% 29.67/19.93 tff(28462,plain,
% 29.67/19.93 (f6(c2, c2) = c1),
% 29.67/19.93 inference(transitivity,[status(thm)],[2360, 2702])).
% 29.67/19.93 tff(28463,plain,
% 29.67/19.93 (f6(f6(c2, c2), f6(c1, c2)) = f6(c1, f6(c1, c2))),
% 29.67/19.93 inference(monotonicity,[status(thm)],[28462])).
% 29.67/19.93 tff(28464,assumption,(f6(f6(c2, c2), f6(c1, c2)) = f6(c1, c2)), introduced(assumption)).
% 29.67/19.93 tff(28465,plain,
% 29.67/19.93 (f6(c1, c2) = f6(f6(c2, c2), f6(c1, c2))),
% 29.67/19.93 inference(symmetry,[status(thm)],[28464])).
% 29.67/19.93 tff(28466,plain,
% 29.67/19.93 (f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)) = f6(c1, f3(c1, c2))),
% 29.67/19.93 inference(monotonicity,[status(thm)],[28462, 7517])).
% 29.67/19.93 tff(28467,plain,
% 29.67/19.93 (f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)) = c1),
% 29.67/19.93 inference(transitivity,[status(thm)],[28466, 6647])).
% 29.67/19.93 tff(28468,plain,
% 29.67/19.93 ((f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)) = f3(f6(f7(c2), c3), c2)) <=> (c1 = f3(f6(f7(c2), c3), c2))),
% 29.67/19.93 inference(monotonicity,[status(thm)],[28467])).
% 29.67/19.93 tff(28469,plain,
% 29.67/19.93 ((f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)) = f3(f6(f7(c2), c3), c2)) <=> (f3(f6(f7(c2), c3), c2) = c1)),
% 29.67/19.93 inference(transitivity,[status(thm)],[28468, 22473])).
% 29.67/19.93 tff(28470,plain,
% 29.67/19.93 ((~(f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)) = f3(f6(f7(c2), c3), c2))) <=> (~(f3(f6(f7(c2), c3), c2) = c1))),
% 29.67/19.93 inference(monotonicity,[status(thm)],[28469])).
% 29.67/19.93 tff(28471,plain,
% 29.67/19.93 (f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)) = f6(c2, c2)),
% 29.67/19.93 inference(transitivity,[status(thm)],[28466, 6647, 2703, 2361])).
% 29.67/19.93 tff(28472,plain,
% 29.67/19.93 (f7(f6(c2, c2)) = f7(c1)),
% 29.67/19.93 inference(monotonicity,[status(thm)],[28462])).
% 29.67/19.93 tff(28473,plain,
% 29.67/19.93 (f7(f6(c2, c2)) = f6(c2, c2)),
% 29.67/19.93 inference(transitivity,[status(thm)],[28472, 25791, 2703, 2361])).
% 29.67/19.93 tff(28474,plain,
% 29.67/19.93 (big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f3(f6(f7(c2), c3), c2))) <=> big_f(f6(c2, c2), f6(c2, c2))),
% 29.67/19.93 inference(monotonicity,[status(thm)],[28473, 28471])).
% 29.67/19.93 tff(28475,plain,
% 29.67/19.93 (big_f(f6(c2, c2), f6(c2, c2)) <=> big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)))),
% 29.67/19.93 inference(symmetry,[status(thm)],[28474])).
% 29.67/19.93 tff(28476,plain,
% 29.67/19.93 (big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)))),
% 29.67/19.93 inference(modus_ponens,[status(thm)],[14865, 28475])).
% 29.67/19.93 tff(28477,plain,
% 29.67/19.93 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f7(f6(c2, c2)) = f6(c2, c2))) | (~(f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)) = f3(f6(f7(c2), c3), c2))) | (~big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f7(f6(c2, c2)) = f6(c2, c2))) | (~(f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)) = f3(f6(f7(c2), c3), c2))) | (~big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)))))),
% 29.67/19.93 inference(rewrite,[status(thm)],[])).
% 29.67/19.93 tff(28478,plain,
% 29.67/19.93 (((~(f10(c2) = c2)) | (~(f7(f6(c2, c2)) = f6(c2, c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)) = f3(f6(f7(c2), c3), c2))) | (~big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f3(f6(f7(c2), c3), c2))))) <=> ((~(f10(c2) = c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f7(f6(c2, c2)) = f6(c2, c2))) | (~(f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)) = f3(f6(f7(c2), c3), c2))) | (~big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)))))),
% 29.67/19.93 inference(rewrite,[status(thm)],[])).
% 29.67/19.93 tff(28479,plain,
% 29.67/19.93 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(f6(c2, c2)) = f6(c2, c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)) = f3(f6(f7(c2), c3), c2))) | (~big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f7(f6(c2, c2)) = f6(c2, c2))) | (~(f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)) = f3(f6(f7(c2), c3), c2))) | (~big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f3(f6(f7(c2), c3), c2))))))),
% 29.67/19.93 inference(monotonicity,[status(thm)],[28478])).
% 29.67/19.93 tff(28480,plain,
% 29.67/19.93 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(f6(c2, c2)) = f6(c2, c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)) = f3(f6(f7(c2), c3), c2))) | (~big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f7(f6(c2, c2)) = f6(c2, c2))) | (~(f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)) = f3(f6(f7(c2), c3), c2))) | (~big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)))))),
% 29.67/19.93 inference(transitivity,[status(thm)],[28479, 28477])).
% 29.67/19.93 tff(28481,plain,
% 29.67/19.93 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(f6(c2, c2)) = f6(c2, c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)) = f3(f6(f7(c2), c3), c2))) | (~big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)))))),
% 29.67/19.93 inference(quant_inst,[status(thm)],[])).
% 29.67/19.93 tff(28482,plain,
% 29.67/19.93 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f7(f6(c2, c2)) = f6(c2, c2))) | (~(f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)) = f3(f6(f7(c2), c3), c2))) | (~big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f3(f6(f7(c2), c3), c2))))),
% 29.67/19.93 inference(modus_ponens,[status(thm)],[28481, 28480])).
% 29.67/19.93 tff(28483,plain,
% 29.67/19.93 ((~(f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)) = f3(f6(f7(c2), c3), c2))) | (~big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f3(f6(f7(c2), c3), c2))))),
% 29.67/19.93 inference(unit_resolution,[status(thm)],[28482, 2378, 122, 1572, 690, 28473])).
% 29.67/19.93 tff(28484,plain,
% 29.67/19.93 (~(f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)) = f3(f6(f7(c2), c3), c2))),
% 29.67/19.93 inference(unit_resolution,[status(thm)],[28483, 28476])).
% 29.67/19.93 tff(28485,plain,
% 29.67/19.93 (~(f3(f6(f7(c2), c3), c2) = c1)),
% 29.67/19.93 inference(modus_ponens,[status(thm)],[28484, 28470])).
% 29.67/19.93 tff(28486,plain,
% 29.67/19.93 (f3(f6(f7(c2), c3), c2) = c2),
% 29.67/19.93 inference(unit_resolution,[status(thm)],[6749, 28485])).
% 29.67/19.93 tff(28487,plain,
% 29.67/19.93 (f3(c1, c2) = c2),
% 29.67/19.93 inference(transitivity,[status(thm)],[7512, 28486])).
% 29.67/19.93 tff(28488,plain,
% 29.67/19.93 (f6(c1, f3(c1, c2)) = f6(c1, c2)),
% 29.67/19.93 inference(monotonicity,[status(thm)],[28487])).
% 29.67/19.93 tff(28489,plain,
% 29.67/19.93 (f6(c2, c2) = c2),
% 29.67/19.93 inference(transitivity,[status(thm)],[2360, 2702, 7127, 28488, 28465, 28463, 28461])).
% 29.67/19.93 tff(28490,plain,
% 29.67/19.93 ($false),
% 29.67/19.93 inference(unit_resolution,[status(thm)],[2637, 28489])).
% 29.67/19.93 tff(28491,plain,((~(f6(c1, f3(c1, c2)) = c1)) | (f6(c2, c2) = c2) | (~(f6(f7(c2), c3) = c1)) | (~(f6(f6(c2, c2), f6(c1, c2)) = f6(c1, c2))) | (~(c3 = c2)) | (~(f7(c2) = c2)) | (~(f10(c2) = c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~big_f(f6(c2, c2), f6(c2, c2)))), inference(lemma,lemma(discharge,[]))).
% 29.67/19.93 tff(28492,plain,
% 29.67/19.93 (~(f6(c1, f3(c1, c2)) = c1)),
% 29.67/19.93 inference(unit_resolution,[status(thm)],[28491, 28459, 28402, 28457, 67, 28096, 28306, 28393, 28399, 28408])).
% 29.67/19.93 tff(28493,plain,
% 29.67/19.93 (f6(c1, f3(c1, c2)) = c2),
% 29.67/19.93 inference(unit_resolution,[status(thm)],[6690, 28492])).
% 29.67/19.93 tff(28494,plain,
% 29.67/19.93 (f3(c1, c2) = f3(f6(f7(c2), c3), c2)),
% 29.67/19.93 inference(monotonicity,[status(thm)],[28448])).
% 29.67/19.93 tff(28495,plain,
% 29.67/19.93 (f3(f6(f7(c2), c3), c2) = f3(c1, c2)),
% 29.67/19.93 inference(symmetry,[status(thm)],[28494])).
% 29.67/19.93 tff(28496,plain,
% 29.67/19.93 (f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)) = f6(c1, f3(c1, c2))),
% 29.67/19.93 inference(monotonicity,[status(thm)],[28405, 28495])).
% 29.67/19.93 tff(28497,plain,
% 29.67/19.93 (f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)) = c2),
% 29.67/19.93 inference(transitivity,[status(thm)],[28496, 28493])).
% 29.67/19.93 tff(28498,plain,
% 29.67/19.93 ((f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)) = f3(f6(f7(c2), c3), c2)) <=> (c2 = f3(f6(f7(c2), c3), c2))),
% 29.67/19.93 inference(monotonicity,[status(thm)],[28497])).
% 29.67/19.93 tff(28499,plain,
% 29.67/19.93 ((f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)) = f3(f6(f7(c2), c3), c2)) <=> (f3(f6(f7(c2), c3), c2) = c2)),
% 29.67/19.93 inference(transitivity,[status(thm)],[28498, 7297])).
% 29.67/19.93 tff(28500,plain,
% 29.67/19.93 (big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f3(f6(f7(c2), c3), c2))) <=> big_f(c1, c2)),
% 29.67/19.93 inference(monotonicity,[status(thm)],[28442, 28497])).
% 29.67/19.93 tff(28501,plain,
% 29.67/19.93 (big_f(c1, c2) <=> big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)))),
% 29.67/19.93 inference(symmetry,[status(thm)],[28500])).
% 29.67/19.93 tff(28502,plain,
% 29.67/19.93 ((~big_f(c1, c2)) <=> (~big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f3(f6(f7(c2), c3), c2))))),
% 29.67/19.93 inference(monotonicity,[status(thm)],[28501])).
% 29.67/19.93 tff(28503,plain,
% 29.67/19.93 (~big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)))),
% 29.67/19.93 inference(modus_ponens,[status(thm)],[27, 28502])).
% 29.67/19.93 tff(28504,plain,
% 29.67/19.93 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f7(f6(c2, c2)) = f6(c2, c2))) | (f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)) = f3(f6(f7(c2), c3), c2)) | big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f3(f6(f7(c2), c3), c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f7(f6(c2, c2)) = f6(c2, c2))) | (f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)) = f3(f6(f7(c2), c3), c2)) | big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f3(f6(f7(c2), c3), c2))))),
% 29.67/19.93 inference(rewrite,[status(thm)],[])).
% 29.67/19.93 tff(28505,plain,
% 29.67/19.93 (((~(f10(c2) = c2)) | (~(f7(f6(c2, c2)) = f6(c2, c2))) | (f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)) = f3(f6(f7(c2), c3), c2)) | big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f3(f6(f7(c2), c3), c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2)))) <=> ((~(f10(c2) = c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f7(f6(c2, c2)) = f6(c2, c2))) | (f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)) = f3(f6(f7(c2), c3), c2)) | big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f3(f6(f7(c2), c3), c2))))),
% 29.67/19.93 inference(rewrite,[status(thm)],[])).
% 29.67/19.93 tff(28506,plain,
% 29.67/19.93 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(f6(c2, c2)) = f6(c2, c2))) | (f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)) = f3(f6(f7(c2), c3), c2)) | big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f3(f6(f7(c2), c3), c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f7(f6(c2, c2)) = f6(c2, c2))) | (f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)) = f3(f6(f7(c2), c3), c2)) | big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)))))),
% 29.67/19.93 inference(monotonicity,[status(thm)],[28505])).
% 29.67/19.93 tff(28507,plain,
% 29.67/19.93 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(f6(c2, c2)) = f6(c2, c2))) | (f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)) = f3(f6(f7(c2), c3), c2)) | big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f3(f6(f7(c2), c3), c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f7(f6(c2, c2)) = f6(c2, c2))) | (f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)) = f3(f6(f7(c2), c3), c2)) | big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f3(f6(f7(c2), c3), c2))))),
% 29.67/19.93 inference(transitivity,[status(thm)],[28506, 28504])).
% 29.67/19.93 tff(28508,plain,
% 29.67/19.93 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(f6(c2, c2)) = f6(c2, c2))) | (f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)) = f3(f6(f7(c2), c3), c2)) | big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f3(f6(f7(c2), c3), c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))),
% 29.67/19.94 inference(quant_inst,[status(thm)],[])).
% 29.67/19.94 tff(28509,plain,
% 29.67/19.94 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f7(f6(c2, c2)) = f6(c2, c2))) | (f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)) = f3(f6(f7(c2), c3), c2)) | big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)))),
% 29.67/19.94 inference(modus_ponens,[status(thm)],[28508, 28507])).
% 29.67/19.94 tff(28510,plain,
% 29.67/19.94 ((f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)) = f3(f6(f7(c2), c3), c2)) | big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)))),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[28509, 2409, 28306, 28393, 28399, 28449])).
% 29.67/19.94 tff(28511,plain,
% 29.67/19.94 (f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)) = f3(f6(f7(c2), c3), c2)),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[28510, 28503])).
% 29.67/19.94 tff(28512,plain,
% 29.67/19.94 (f3(f6(f7(c2), c3), c2) = c2),
% 29.67/19.94 inference(modus_ponens,[status(thm)],[28511, 28499])).
% 29.67/19.94 tff(28513,plain,
% 29.67/19.94 (f3(f6(f7(c2), c3), c2) = f6(f6(c2, c2), f3(f6(f7(c2), c3), c2))),
% 29.67/19.94 inference(symmetry,[status(thm)],[28511])).
% 29.67/19.94 tff(28514,plain,
% 29.67/19.94 (f3(f6(f7(c2), c3), c2) = f7(c2)),
% 29.67/19.94 inference(transitivity,[status(thm)],[28513, 28496, 28493, 28403])).
% 29.67/19.94 tff(28515,plain,
% 29.67/19.94 (big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3)) <=> big_f(f7(c2), f6(c2, c2))),
% 29.67/19.94 inference(monotonicity,[status(thm)],[28514, 28447])).
% 29.67/19.94 tff(28516,plain,
% 29.67/19.94 (big_f(f7(c2), f6(c2, c2)) <=> big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))),
% 29.67/19.94 inference(symmetry,[status(thm)],[28515])).
% 29.67/19.94 tff(28517,plain,
% 29.67/19.94 (big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))),
% 29.67/19.94 inference(modus_ponens,[status(thm)],[28458, 28516])).
% 29.67/19.94 tff(28518,plain,
% 29.67/19.94 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = f2(c2)) | (f6(f7(c2), c3) = c4) | (~big_f(c2, c2)) | (~big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))) | (~(f3(f6(f7(c2), c3), c2) = c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = f2(c2)) | (f6(f7(c2), c3) = c4) | (~big_f(c2, c2)) | (~big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))) | (~(f3(f6(f7(c2), c3), c2) = c2)))),
% 29.67/19.94 inference(rewrite,[status(thm)],[])).
% 29.67/19.94 tff(28519,plain,
% 29.67/19.94 (((~(c2 = c3)) | (f6(f7(c2), c3) = c4) | (~(f3(f6(f7(c2), c3), c2) = c2)) | (~big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))) | (c2 = f2(c2)) | (~big_f(c2, c2))) <=> ((~(c2 = c3)) | (c2 = f2(c2)) | (f6(f7(c2), c3) = c4) | (~big_f(c2, c2)) | (~big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))) | (~(f3(f6(f7(c2), c3), c2) = c2)))),
% 29.67/19.94 inference(rewrite,[status(thm)],[])).
% 29.67/19.94 tff(28520,plain,
% 29.67/19.94 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f6(f7(c2), c3) = c4) | (~(f3(f6(f7(c2), c3), c2) = c2)) | (~big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))) | (c2 = f2(c2)) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = f2(c2)) | (f6(f7(c2), c3) = c4) | (~big_f(c2, c2)) | (~big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))) | (~(f3(f6(f7(c2), c3), c2) = c2))))),
% 29.67/19.94 inference(monotonicity,[status(thm)],[28519])).
% 29.67/19.94 tff(28521,plain,
% 29.67/19.94 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f6(f7(c2), c3) = c4) | (~(f3(f6(f7(c2), c3), c2) = c2)) | (~big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))) | (c2 = f2(c2)) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = f2(c2)) | (f6(f7(c2), c3) = c4) | (~big_f(c2, c2)) | (~big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))) | (~(f3(f6(f7(c2), c3), c2) = c2)))),
% 29.67/19.94 inference(transitivity,[status(thm)],[28520, 28518])).
% 29.67/19.94 tff(28522,plain,
% 29.67/19.94 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f6(f7(c2), c3) = c4) | (~(f3(f6(f7(c2), c3), c2) = c2)) | (~big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))) | (c2 = f2(c2)) | (~big_f(c2, c2)))),
% 29.67/19.94 inference(quant_inst,[status(thm)],[])).
% 29.67/19.94 tff(28523,plain,
% 29.67/19.94 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = f2(c2)) | (f6(f7(c2), c3) = c4) | (~big_f(c2, c2)) | (~big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))) | (~(f3(f6(f7(c2), c3), c2) = c2))),
% 29.67/19.94 inference(modus_ponens,[status(thm)],[28522, 28521])).
% 29.67/19.94 tff(28524,plain,
% 29.67/19.94 ((~(c2 = c3)) | (c2 = f2(c2)) | (f6(f7(c2), c3) = c4) | (~big_f(c2, c2)) | (~big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))) | (~(f3(f6(f7(c2), c3), c2) = c2))),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[28523, 7051])).
% 29.67/19.94 tff(28525,plain,
% 29.67/19.94 (c2 = f2(c2)),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[28524, 28517, 27705, 1335, 28512, 28401])).
% 29.67/19.94 tff(28526,plain,
% 29.67/19.94 (f2(c2) = c2),
% 29.67/19.94 inference(symmetry,[status(thm)],[28525])).
% 29.67/19.94 tff(28527,plain,
% 29.67/19.94 (big_f(f7(c2), f6(c2, f4(c4)))),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[14036, 28458, 28389])).
% 29.67/19.94 tff(28528,plain,
% 29.67/19.94 (big_f(c2, f6(f7(c2), c3))),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[14585, 28527, 67, 28389, 28096])).
% 29.67/19.94 tff(28529,plain,
% 29.67/19.94 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f6(f7(c2), c3) = c4) | (f6(f7(c2), c3) = f2(c2)) | (~big_f(c2, f6(f7(c2), c3))) | (~big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))) | (~(f3(f6(f7(c2), c3), c2) = c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (f6(f7(c2), c3) = c4) | (f6(f7(c2), c3) = f2(c2)) | (~big_f(c2, f6(f7(c2), c3))) | (~big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))) | (~(f3(f6(f7(c2), c3), c2) = c2)))),
% 29.67/19.94 inference(rewrite,[status(thm)],[])).
% 29.67/19.94 tff(28530,plain,
% 29.67/19.94 (((~(c2 = c3)) | (f6(f7(c2), c3) = c4) | (~(f3(f6(f7(c2), c3), c2) = c2)) | (~big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))) | (f6(f7(c2), c3) = f2(c2)) | (~big_f(c2, f6(f7(c2), c3)))) <=> ((~(c2 = c3)) | (f6(f7(c2), c3) = c4) | (f6(f7(c2), c3) = f2(c2)) | (~big_f(c2, f6(f7(c2), c3))) | (~big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))) | (~(f3(f6(f7(c2), c3), c2) = c2)))),
% 29.67/19.94 inference(rewrite,[status(thm)],[])).
% 29.67/19.94 tff(28531,plain,
% 29.67/19.94 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f6(f7(c2), c3) = c4) | (~(f3(f6(f7(c2), c3), c2) = c2)) | (~big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))) | (f6(f7(c2), c3) = f2(c2)) | (~big_f(c2, f6(f7(c2), c3))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f6(f7(c2), c3) = c4) | (f6(f7(c2), c3) = f2(c2)) | (~big_f(c2, f6(f7(c2), c3))) | (~big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))) | (~(f3(f6(f7(c2), c3), c2) = c2))))),
% 29.67/19.94 inference(monotonicity,[status(thm)],[28530])).
% 29.67/19.94 tff(28532,plain,
% 29.67/19.94 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f6(f7(c2), c3) = c4) | (~(f3(f6(f7(c2), c3), c2) = c2)) | (~big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))) | (f6(f7(c2), c3) = f2(c2)) | (~big_f(c2, f6(f7(c2), c3))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (f6(f7(c2), c3) = c4) | (f6(f7(c2), c3) = f2(c2)) | (~big_f(c2, f6(f7(c2), c3))) | (~big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))) | (~(f3(f6(f7(c2), c3), c2) = c2)))),
% 29.67/19.94 inference(transitivity,[status(thm)],[28531, 28529])).
% 29.67/19.94 tff(28533,plain,
% 29.67/19.94 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (f6(f7(c2), c3) = c4) | (~(f3(f6(f7(c2), c3), c2) = c2)) | (~big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))) | (f6(f7(c2), c3) = f2(c2)) | (~big_f(c2, f6(f7(c2), c3))))),
% 29.67/19.94 inference(quant_inst,[status(thm)],[])).
% 29.67/19.94 tff(28534,plain,
% 29.67/19.94 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (f6(f7(c2), c3) = c4) | (f6(f7(c2), c3) = f2(c2)) | (~big_f(c2, f6(f7(c2), c3))) | (~big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))) | (~(f3(f6(f7(c2), c3), c2) = c2))),
% 29.67/19.94 inference(modus_ponens,[status(thm)],[28533, 28532])).
% 29.67/19.94 tff(28535,plain,
% 29.67/19.94 ((~(c2 = c3)) | (f6(f7(c2), c3) = c4) | (f6(f7(c2), c3) = f2(c2)) | (~big_f(c2, f6(f7(c2), c3))) | (~big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))) | (~(f3(f6(f7(c2), c3), c2) = c2))),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[28534, 7051])).
% 29.67/19.94 tff(28536,plain,
% 29.67/19.94 (f6(f7(c2), c3) = f2(c2)),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[28535, 28517, 1335, 28528, 28401, 28512])).
% 29.67/19.94 tff(28537,plain,
% 29.67/19.94 (f6(c2, c2) = c2),
% 29.67/19.94 inference(transitivity,[status(thm)],[28404, 28536, 28526])).
% 29.67/19.94 tff(28538,plain,
% 29.67/19.94 ($false),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[28459, 28537])).
% 29.67/19.94 tff(28539,plain,((f10(c1) = c1) | (~(c3 = c2)) | big_f(c1, c2)), inference(lemma,lemma(discharge,[]))).
% 29.67/19.94 tff(28540,plain,
% 29.67/19.94 (f10(c1) = c1),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[28539, 67, 27])).
% 29.67/19.94 tff(28541,plain,
% 29.67/19.94 (big_f(f7(c1), f6(c1, c1))),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[27676, 2, 4932, 3762])).
% 29.67/19.94 tff(28542,plain,
% 29.67/19.94 (big_f(c1, f6(c1, c1))),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[28169, 28541])).
% 29.67/19.94 tff(28543,plain,
% 29.67/19.94 (~(c2 = f8(c2))),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[28193, 15473, 77, 89, 1345, 67])).
% 29.67/19.94 tff(28544,plain,
% 29.67/19.94 (c1 = f8(c2)),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[26203, 28543, 67])).
% 29.67/19.94 tff(28545,plain,
% 29.67/19.94 (f6(c1, c1) = c1),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[28187, 28544, 28183, 94, 28542])).
% 29.67/19.94 tff(28546,plain,
% 29.67/19.94 (f9(c1, c1) = c1),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[27678, 28545, 3762, 2, 28541])).
% 29.67/19.94 tff(28547,plain,
% 29.67/19.94 (big_f(f9(c1, c1), c1)),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[10938, 28546, 4932])).
% 29.67/19.94 tff(28548,plain,
% 29.67/19.94 (big_f(f9(c1, c1), f10(c1))),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[8716, 28547, 3762])).
% 29.67/19.94 tff(28549,plain,
% 29.67/19.94 (big_f(f7(c2), f6(c2, c2))),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[24737, 28548, 77, 1345, 3762, 28546])).
% 29.67/19.94 tff(28550,plain,
% 29.67/19.94 (~big_f(f7(c2), f6(c2, c2))),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[7213, 2637, 67, 2, 77])).
% 29.67/19.94 tff(28551,plain,
% 29.67/19.94 ($false),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[24735, 2409, 3762, 77, 3949, 3948, 2637, 28550])).
% 29.67/19.94 tff(28552,plain,((f6(c2, c2) = c2) | (~(f10(c1) = c1)) | (~(f7(c2) = c2)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(c3 = c2)) | big_f(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 29.67/19.94 tff(28553,plain,
% 29.67/19.94 (f6(c2, c2) = c2),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[28552, 28548, 77, 2, 67, 28546, 3762])).
% 29.67/19.94 tff(28554,plain,
% 29.67/19.94 ($false),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[24751, 2378, 3762, 77, 28546, 28548, 28553, 28549])).
% 29.67/19.94 tff(28555,plain,(big_f(c2, c1) | (~(f10(c1) = c1)) | (~(f7(c2) = c2)) | (~big_f(c2, c2)) | (~(c3 = c2)) | (~big_f(c1, c1)) | big_f(f10(c2), c2) | (f10(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 29.67/19.94 tff(28556,plain,
% 29.67/19.94 (big_f(c2, c1)),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[28555, 28101, 28096, 27705, 67, 27489, 28540, 89])).
% 29.67/19.94 tff(28557,plain,
% 29.67/19.94 ((~(f9(c1, c1) = c1)) | (~(f10(c1) = c1)) | big_f(f7(c1), f6(c1, c1)) | (f6(c1, c1) = c1) | (~big_f(c1, c1))),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[11249, 25791])).
% 29.67/19.94 tff(28558,plain,
% 29.67/19.94 (~(f9(c1, c1) = c1)),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[28557, 65, 4932, 3762, 28])).
% 29.67/19.94 tff(28559,plain,
% 29.67/19.94 (f9(c1, c1) = c2),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[3939, 28558])).
% 29.67/19.94 tff(28560,plain,
% 29.67/19.94 (big_f(f9(c1, c1), f10(f9(c1, c1))) <=> big_f(c2, f10(f9(f10(c2), f10(c2))))),
% 29.67/19.94 inference(monotonicity,[status(thm)],[28559, 28047])).
% 29.67/19.94 tff(28561,plain,
% 29.67/19.94 (big_f(c2, f10(f9(f10(c2), f10(c2)))) <=> big_f(f9(c1, c1), f10(f9(c1, c1)))),
% 29.67/19.94 inference(symmetry,[status(thm)],[28560])).
% 29.67/19.94 tff(28562,plain,
% 29.67/19.94 (f10(f9(c1, c1)) = f10(c2)),
% 29.67/19.94 inference(monotonicity,[status(thm)],[28559])).
% 29.67/19.94 tff(28563,plain,
% 29.67/19.94 (f10(f9(f10(c2), f10(c2))) = c1),
% 29.67/19.94 inference(transitivity,[status(thm)],[28046, 28562, 11819])).
% 29.67/19.94 tff(28564,plain,
% 29.67/19.94 (big_f(c2, f10(f9(f10(c2), f10(c2)))) <=> big_f(c2, c1)),
% 29.67/19.94 inference(monotonicity,[status(thm)],[28563])).
% 29.67/19.94 tff(28565,plain,
% 29.67/19.94 (big_f(c2, c1) <=> big_f(c2, f10(f9(f10(c2), f10(c2))))),
% 29.67/19.94 inference(symmetry,[status(thm)],[28564])).
% 29.67/19.94 tff(28566,plain,
% 29.67/19.94 (big_f(c2, c1) <=> big_f(f9(c1, c1), f10(f9(c1, c1)))),
% 29.67/19.94 inference(transitivity,[status(thm)],[28565, 28561])).
% 29.67/19.94 tff(28567,plain,
% 29.67/19.94 (big_f(f9(c1, c1), f10(f9(c1, c1)))),
% 29.67/19.94 inference(modus_ponens,[status(thm)],[348, 28566])).
% 29.67/19.94 tff(28568,plain,
% 29.67/19.94 (f10(f9(c1, c1)) = c1),
% 29.67/19.94 inference(transitivity,[status(thm)],[28562, 11819])).
% 29.67/19.94 tff(28569,plain,
% 29.67/19.94 (big_f(c1, f10(f9(c1, c1))) <=> big_f(c1, c1)),
% 29.67/19.94 inference(monotonicity,[status(thm)],[28568])).
% 29.67/19.94 tff(28570,plain,
% 29.67/19.94 (big_f(c1, c1) <=> big_f(c1, f10(f9(c1, c1)))),
% 29.67/19.94 inference(symmetry,[status(thm)],[28569])).
% 29.67/19.94 tff(28571,plain,
% 29.67/19.94 (big_f(c1, f10(f9(c1, c1)))),
% 29.67/19.94 inference(modus_ponens,[status(thm)],[4932, 28570])).
% 29.67/19.94 tff(28572,plain,
% 29.67/19.94 ((f10(f9(c1, c1)) = f9(c1, c1)) <=> (f10(f9(f10(c2), f7(c1))) = c2)),
% 29.67/19.94 inference(monotonicity,[status(thm)],[28065, 28559])).
% 29.67/19.94 tff(28573,plain,
% 29.67/19.94 ((f10(f9(f10(c2), f7(c1))) = c2) <=> (f10(f9(c1, c1)) = f9(c1, c1))),
% 29.67/19.94 inference(symmetry,[status(thm)],[28572])).
% 29.67/19.94 tff(28574,plain,
% 29.67/19.94 (f10(f9(f10(c2), f7(c1))) = c1),
% 29.67/19.94 inference(transitivity,[status(thm)],[28064, 28562, 11819])).
% 29.67/19.94 tff(28575,plain,
% 29.67/19.94 ((f10(f9(f10(c2), f7(c1))) = c2) <=> (c1 = c2)),
% 29.67/19.94 inference(monotonicity,[status(thm)],[28574])).
% 29.67/19.94 tff(28576,plain,
% 29.67/19.94 ((f10(f9(f10(c2), f7(c1))) = c2) <=> (c2 = c1)),
% 29.67/19.94 inference(transitivity,[status(thm)],[28575, 1])).
% 29.67/19.94 tff(28577,plain,
% 29.67/19.94 ((c2 = c1) <=> (f10(f9(f10(c2), f7(c1))) = c2)),
% 29.67/19.94 inference(symmetry,[status(thm)],[28576])).
% 29.67/19.94 tff(28578,plain,
% 29.67/19.94 ((c2 = c1) <=> (f10(f9(c1, c1)) = f9(c1, c1))),
% 29.67/19.94 inference(transitivity,[status(thm)],[28577, 28573])).
% 29.67/19.94 tff(28579,plain,
% 29.67/19.94 ((~(c2 = c1)) <=> (~(f10(f9(c1, c1)) = f9(c1, c1)))),
% 29.67/19.94 inference(monotonicity,[status(thm)],[28578])).
% 29.67/19.94 tff(28580,plain,
% 29.67/19.94 (~(f10(f9(c1, c1)) = f9(c1, c1))),
% 29.67/19.94 inference(modus_ponens,[status(thm)],[75, 28579])).
% 29.67/19.94 tff(28581,plain,
% 29.67/19.94 ($false),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[28075, 28580, 28571, 65, 28558, 28567, 28])).
% 29.67/19.94 tff(28582,plain,(big_f(f7(c1), f6(c1, c1)) | (f6(c1, c1) = c1) | (~big_f(c2, c1)) | (~(f10(c2) = c1)) | (~big_f(c1, c1)) | (~(f10(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.67/19.94 tff(28583,plain,
% 29.67/19.94 (big_f(f7(c1), f6(c1, c1))),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[28582, 28, 28556, 94, 27489, 28540])).
% 29.67/19.94 tff(28584,plain,
% 29.67/19.94 (big_f(c1, f6(c1, c1))),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[28169, 28583])).
% 29.67/19.94 tff(28585,plain,
% 29.67/19.94 (~(c1 = f8(c2))),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[28187, 28584, 28101, 94, 28])).
% 29.67/19.94 tff(28586,plain,
% 29.67/19.94 (c2 = f8(c2)),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[26203, 28585, 67])).
% 29.67/19.94 tff(28587,plain,
% 29.67/19.94 (c2 = f8(c3)),
% 29.67/19.94 inference(transitivity,[status(thm)],[28586, 20761])).
% 29.67/19.94 tff(28588,plain,
% 29.67/19.94 (f3(c1, c2) = f3(c1, f8(c3))),
% 29.67/19.94 inference(monotonicity,[status(thm)],[28587])).
% 29.67/19.94 tff(28589,plain,
% 29.67/19.94 (f3(c1, f8(c3)) = f3(c1, c2)),
% 29.67/19.94 inference(symmetry,[status(thm)],[28588])).
% 29.67/19.94 tff(28590,plain,
% 29.67/19.94 ((f10(c2) = c4) <=> (c1 = c4)),
% 29.67/19.94 inference(monotonicity,[status(thm)],[94])).
% 29.67/19.94 tff(28591,plain,
% 29.67/19.94 ((c1 = c4) <=> (f10(c2) = c4)),
% 29.67/19.94 inference(symmetry,[status(thm)],[28590])).
% 29.67/19.94 tff(28592,plain,
% 29.67/19.94 (f4(c4) = c2),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[27836, 28556, 27, 67])).
% 29.67/19.94 tff(28593,plain,
% 29.67/19.94 (c2 = c4),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[26149, 28592, 27, 1335, 28096, 28556, 27705])).
% 29.67/19.94 tff(28594,plain,
% 29.67/19.94 (c4 = c2),
% 29.67/19.94 inference(symmetry,[status(thm)],[28593])).
% 29.67/19.94 tff(28595,plain,
% 29.67/19.94 ((c1 = c4) <=> (c1 = c2)),
% 29.67/19.94 inference(monotonicity,[status(thm)],[28594])).
% 29.67/19.94 tff(28596,plain,
% 29.67/19.94 ((c1 = c4) <=> (c2 = c1)),
% 29.67/19.94 inference(transitivity,[status(thm)],[28595, 1])).
% 29.67/19.94 tff(28597,plain,
% 29.67/19.94 ((c2 = c1) <=> (c1 = c4)),
% 29.67/19.94 inference(symmetry,[status(thm)],[28596])).
% 29.67/19.94 tff(28598,plain,
% 29.67/19.94 ((c2 = c1) <=> (f10(c2) = c4)),
% 29.67/19.94 inference(transitivity,[status(thm)],[28597, 28591])).
% 29.67/19.94 tff(28599,plain,
% 29.67/19.94 ((~(c2 = c1)) <=> (~(f10(c2) = c4))),
% 29.67/19.94 inference(monotonicity,[status(thm)],[28598])).
% 29.67/19.94 tff(28600,plain,
% 29.67/19.94 (~(f10(c2) = c4)),
% 29.67/19.94 inference(modus_ponens,[status(thm)],[75, 28599])).
% 29.67/19.94 tff(28601,plain,
% 29.67/19.94 (big_f(c2, f10(c2))),
% 29.67/19.94 inference(modus_ponens,[status(thm)],[28556, 15252])).
% 29.67/19.94 tff(28602,plain,
% 29.67/19.94 (~(f3(c1, f8(c3)) = c2)),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[28222, 28586, 89, 28601, 27705, 28600, 67])).
% 29.67/19.94 tff(28603,plain,
% 29.67/19.94 (f3(c1, f8(c3)) = c1),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[7123, 28602])).
% 29.67/19.94 tff(28604,plain,
% 29.67/19.94 (c1 = f3(c1, f8(c3))),
% 29.67/19.94 inference(symmetry,[status(thm)],[28603])).
% 29.67/19.94 tff(28605,plain,
% 29.67/19.94 (c1 = f3(c1, c2)),
% 29.67/19.94 inference(transitivity,[status(thm)],[28604, 28589])).
% 29.67/19.94 tff(28606,plain,
% 29.67/19.94 (f6(c1, c1) = f6(c1, f3(c1, c2))),
% 29.67/19.94 inference(monotonicity,[status(thm)],[28605])).
% 29.67/19.94 tff(28607,plain,
% 29.67/19.94 (f6(c1, f3(c1, c2)) = f6(c1, c1)),
% 29.67/19.94 inference(symmetry,[status(thm)],[28606])).
% 29.67/19.94 tff(28608,plain,
% 29.67/19.94 ((f6(c1, c1) = c4) <=> (f6(c1, f3(c1, c2)) = c2)),
% 29.67/19.94 inference(monotonicity,[status(thm)],[28606, 28594])).
% 29.67/19.94 tff(28609,plain,
% 29.67/19.94 (f6(c1, c1) = c4),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[28242, 28603, 28593, 28, 67, 94, 28586])).
% 29.67/19.94 tff(28610,plain,
% 29.67/19.94 (f6(c1, f3(c1, c2)) = c2),
% 29.67/19.94 inference(modus_ponens,[status(thm)],[28609, 28608])).
% 29.67/19.94 tff(28611,plain,
% 29.67/19.94 (c2 = f6(c1, f3(c1, c2))),
% 29.67/19.94 inference(symmetry,[status(thm)],[28610])).
% 29.67/19.94 tff(28612,plain,
% 29.67/19.94 (c2 = f6(c1, c1)),
% 29.67/19.94 inference(transitivity,[status(thm)],[28611, 28607])).
% 29.67/19.94 tff(28613,plain,
% 29.67/19.94 (big_f(c1, c2) <=> big_f(c1, f6(c1, c1))),
% 29.67/19.94 inference(monotonicity,[status(thm)],[28612])).
% 29.67/19.94 tff(28614,plain,
% 29.67/19.94 (big_f(c1, f6(c1, c1)) <=> big_f(c1, c2)),
% 29.67/19.94 inference(symmetry,[status(thm)],[28613])).
% 29.67/19.94 tff(28615,plain,
% 29.67/19.94 (big_f(c1, c2)),
% 29.67/19.94 inference(modus_ponens,[status(thm)],[28584, 28614])).
% 29.67/19.94 tff(28616,plain,
% 29.67/19.94 ($false),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[27, 28615])).
% 29.67/19.94 tff(28617,plain,((f6(c1, c1) = c1) | big_f(c1, c2) | (~(c3 = c2)) | (f10(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 29.67/19.94 tff(28618,plain,
% 29.67/19.94 (f6(c1, c1) = c1),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[28617, 89, 67, 27])).
% 29.67/19.94 tff(28619,plain,
% 29.67/19.94 (big_f(f7(c1), f6(c1, c1))),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[27769, 28618, 27489])).
% 29.67/19.94 tff(28620,plain,
% 29.67/19.94 (c1 = f8(c2)),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[27005, 2730, 25791, 89, 28619, 28618, 28097])).
% 29.67/19.94 tff(28621,plain,
% 29.67/19.94 (f8(c2) = c1),
% 29.67/19.94 inference(symmetry,[status(thm)],[28620])).
% 29.67/19.94 tff(28622,plain,
% 29.67/19.94 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)))),
% 29.67/19.94 inference(rewrite,[status(thm)],[])).
% 29.67/19.94 tff(28623,plain,
% 29.67/19.94 (((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1)))) <=> ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)))),
% 29.67/19.94 inference(rewrite,[status(thm)],[])).
% 29.67/19.94 tff(28624,plain,
% 29.67/19.94 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1))))),
% 29.67/19.94 inference(monotonicity,[status(thm)],[28623])).
% 29.67/19.94 tff(28625,plain,
% 29.67/19.94 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)))),
% 29.67/19.94 inference(transitivity,[status(thm)],[28624, 28622])).
% 29.67/19.94 tff(28626,plain,
% 29.67/19.94 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))),
% 29.67/19.94 inference(quant_inst,[status(thm)],[])).
% 29.67/19.94 tff(28627,plain,
% 29.67/19.94 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1))),
% 29.67/19.94 inference(modus_ponens,[status(thm)],[28626, 28625])).
% 29.67/19.94 tff(28628,plain,
% 29.67/19.94 (c2 = f8(c2)),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[28627, 2730, 25791, 89, 28601, 28619, 28618])).
% 29.67/19.94 tff(28629,plain,
% 29.67/19.94 (c2 = c1),
% 29.67/19.94 inference(transitivity,[status(thm)],[28628, 28621])).
% 29.67/19.94 tff(28630,plain,
% 29.67/19.94 ($false),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[75, 28629])).
% 29.67/19.94 tff(28631,plain,((f10(c2) = c2) | (~(c3 = c2)) | big_f(c1, c2)), inference(lemma,lemma(discharge,[]))).
% 29.67/19.94 tff(28632,plain,
% 29.67/19.94 (f10(c2) = c2),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[28631, 67, 27])).
% 29.67/19.94 tff(28633,plain,
% 29.67/19.94 (~(f2(c3) = c2)),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[26181, 2, 27705, 28096, 27, 67, 28632])).
% 29.67/19.94 tff(28634,plain,
% 29.67/19.94 (f2(c3) = c1),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[1273, 28633])).
% 29.67/19.94 tff(28635,plain,
% 29.67/19.94 (c1 = f2(c2)),
% 29.67/19.94 inference(modus_ponens,[status(thm)],[28634, 28103])).
% 29.67/19.94 tff(28636,plain,
% 29.67/19.94 (~(f3(c2, c2) = c2)),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[28320, 873, 1344, 2, 28312, 1345])).
% 29.67/19.94 tff(28637,plain,
% 29.67/19.94 (big_f(f3(c2, c2), c2)),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[21176, 28636, 27, 168, 4932, 873])).
% 29.67/19.94 tff(28638,plain,
% 29.67/19.94 ($false),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[28341, 28637, 28636, 27, 27490])).
% 29.67/19.94 tff(28639,plain,((c2 = c4) | big_f(c1, c2) | (~(f6(c1, f6(c1, c2)) = c2)) | (c1 = c3) | (~big_f(c1, c1)) | (~(c2 = c3)) | big_f(c2, c1) | (~(c1 = f2(c2))) | (~big_f(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 29.67/19.94 tff(28640,plain,
% 29.67/19.94 (c2 = c4),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[28639, 2, 27490, 76, 27489, 1335, 27, 28635, 27705])).
% 29.67/19.94 tff(28641,plain,
% 29.67/19.94 (~(f4(c4) = c1)),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[28153, 28640, 27, 76, 27489])).
% 29.67/19.94 tff(28642,plain,
% 29.67/19.94 (f4(c4) = c2),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[11750, 28641])).
% 29.67/19.94 tff(28643,plain,
% 29.67/19.94 (f6(c2, c2) = c2),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[25947, 28642, 28096, 2, 28632])).
% 29.67/19.94 tff(28644,plain,
% 29.67/19.94 (big_f(f7(c2), f6(c2, c2))),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[2627, 28643, 28096, 27705])).
% 29.67/19.94 tff(28645,plain,
% 29.67/19.94 (~(f6(f7(c2), c3) = c1)),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[2710, 28644, 28096, 67, 2])).
% 29.67/19.94 tff(28646,plain,
% 29.67/19.94 (f9(f10(c2), f4(c4)) = c2),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[8065, 28642, 28632])).
% 29.67/19.94 tff(28647,plain,
% 29.67/19.94 (f9(c2, c2) = c2),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[1606, 28642, 28632, 28646])).
% 29.67/19.94 tff(28648,plain,
% 29.67/19.94 (big_f(f9(c2, c2), f10(c2))),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[2750, 28643, 28096, 28632, 27705, 28644])).
% 29.67/19.94 tff(28649,plain,
% 29.67/19.94 (~(f6(f7(c2), c3) = c2)),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[2386, 28648, 67, 28096, 27705, 28632, 28647])).
% 29.67/19.94 tff(28650,plain,
% 29.67/19.94 ($false),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[2391, 28649, 28645])).
% 29.67/19.94 tff(28651,plain,(big_f(c2, c1) | (~(c3 = c2)) | big_f(c1, c2) | (~(f6(c1, f6(c1, c2)) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.67/19.94 tff(28652,plain,
% 29.67/19.94 (big_f(c2, c1)),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[28651, 27490, 27, 67])).
% 29.67/19.94 tff(28653,plain,
% 29.67/19.94 (f4(c4) = c2),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[27836, 28652, 27, 67])).
% 29.67/19.94 tff(28654,plain,
% 29.67/19.94 (~(c4 = c1)),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[11545, 28653, 27489, 27, 76])).
% 29.67/19.94 tff(28655,plain,
% 29.67/19.94 (c4 = c2),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[461, 28654])).
% 29.67/19.94 tff(28656,plain,
% 29.67/19.94 (f9(f10(c2), f4(c4)) = c2),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[8065, 28653, 28632])).
% 29.67/19.94 tff(28657,plain,
% 29.67/19.94 (f9(c2, c2) = c2),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[1606, 28653, 28632, 28656])).
% 29.67/19.94 tff(28658,plain,
% 29.67/19.94 (big_f(f9(c2, c2), f10(c2)) <=> big_f(f9(c2, c2), c2)),
% 29.67/19.94 inference(monotonicity,[status(thm)],[28632])).
% 29.67/19.94 tff(28659,plain,
% 29.67/19.94 (big_f(f9(c2, c2), c2) <=> big_f(f9(c2, c2), f10(c2))),
% 29.67/19.94 inference(symmetry,[status(thm)],[28658])).
% 29.67/19.94 tff(28660,plain,
% 29.67/19.94 (big_f(f9(c2, c2), c2) <=> big_f(c2, c2)),
% 29.67/19.94 inference(monotonicity,[status(thm)],[28657])).
% 29.67/19.94 tff(28661,plain,
% 29.67/19.94 (big_f(c2, c2) <=> big_f(f9(c2, c2), c2)),
% 29.67/19.94 inference(symmetry,[status(thm)],[28660])).
% 29.67/19.94 tff(28662,plain,
% 29.67/19.94 (big_f(c2, c2) <=> big_f(f9(c2, c2), f10(c2))),
% 29.67/19.94 inference(transitivity,[status(thm)],[28661, 28659])).
% 29.67/19.94 tff(28663,plain,
% 29.67/19.94 (big_f(f9(c2, c2), f10(c2))),
% 29.67/19.94 inference(modus_ponens,[status(thm)],[27705, 28662])).
% 29.67/19.94 tff(28664,plain,
% 29.67/19.94 (~(f6(f7(c2), c3) = c2)),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[2386, 28663, 67, 28096, 27705, 28632, 28657])).
% 29.67/19.94 tff(28665,plain,
% 29.67/19.94 (~(f6(f7(c2), c3) = c4)),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[3995, 28664, 28655])).
% 29.67/19.94 tff(28666,plain,
% 29.67/19.94 (f6(f7(c2), c3) = c1),
% 29.67/19.94 inference(unit_resolution,[status(thm)],[2391, 28664])).
% 29.67/19.94 tff(28667,plain,
% 29.67/19.94 (f6(c2, c2) = c1),
% 29.67/19.94 inference(transitivity,[status(thm)],[28404, 28666])).
% 29.67/19.94 tff(28668,plain,
% 29.67/19.94 ((f6(c2, c2) = c2) <=> (c1 = c2)),
% 29.67/19.94 inference(monotonicity,[status(thm)],[28667])).
% 29.67/19.94 tff(28669,plain,
% 29.67/19.94 ((f6(c2, c2) = c2) <=> (c2 = c1)),
% 29.67/19.94 inference(transitivity,[status(thm)],[28668, 1])).
% 29.67/19.94 tff(28670,plain,
% 29.67/19.94 ((c2 = c1) <=> (f6(c2, c2) = c2)),
% 29.67/19.94 inference(symmetry,[status(thm)],[28669])).
% 29.67/19.94 tff(28671,plain,
% 29.67/19.94 ((~(c2 = c1)) <=> (~(f6(c2, c2) = c2))),
% 29.67/19.94 inference(monotonicity,[status(thm)],[28670])).
% 29.67/19.94 tff(28672,plain,
% 29.67/19.94 (~(f6(c2, c2) = c2)),
% 29.67/19.94 inference(modus_ponens,[status(thm)],[75, 28671])).
% 29.67/19.94 tff(28673,plain,
% 29.67/19.94 (big_f(f7(c1), f6(c1, f6(c1, c2))) <=> big_f(c1, c2)),
% 29.67/19.95 inference(monotonicity,[status(thm)],[25791, 27490])).
% 29.67/19.95 tff(28674,plain,
% 29.67/19.95 (big_f(c1, c2) <=> big_f(f7(c1), f6(c1, f6(c1, c2)))),
% 29.67/19.95 inference(symmetry,[status(thm)],[28673])).
% 29.67/19.95 tff(28675,plain,
% 29.67/19.95 ((~big_f(c1, c2)) <=> (~big_f(f7(c1), f6(c1, f6(c1, c2))))),
% 29.67/19.95 inference(monotonicity,[status(thm)],[28674])).
% 29.67/19.95 tff(28676,plain,
% 29.67/19.95 (~big_f(f7(c1), f6(c1, f6(c1, c2)))),
% 29.67/19.95 inference(modus_ponens,[status(thm)],[27, 28675])).
% 29.67/19.95 tff(28677,plain,
% 29.67/19.95 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | big_f(f7(c1), f6(c1, f6(c1, c2))) | (f6(c1, f6(c1, c2)) = f6(c1, c2)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | big_f(f7(c1), f6(c1, f6(c1, c2))) | (f6(c1, f6(c1, c2)) = f6(c1, c2)))),
% 29.67/19.95 inference(rewrite,[status(thm)],[])).
% 29.67/19.95 tff(28678,plain,
% 29.67/19.95 (((~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (f6(c1, f6(c1, c2)) = f6(c1, c2)) | big_f(f7(c1), f6(c1, f6(c1, c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2)))) <=> ((~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | big_f(f7(c1), f6(c1, f6(c1, c2))) | (f6(c1, f6(c1, c2)) = f6(c1, c2)))),
% 29.67/19.95 inference(rewrite,[status(thm)],[])).
% 29.67/19.95 tff(28679,plain,
% 29.67/19.95 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (f6(c1, f6(c1, c2)) = f6(c1, c2)) | big_f(f7(c1), f6(c1, f6(c1, c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | big_f(f7(c1), f6(c1, f6(c1, c2))) | (f6(c1, f6(c1, c2)) = f6(c1, c2))))),
% 29.67/19.95 inference(monotonicity,[status(thm)],[28678])).
% 29.67/19.95 tff(28680,plain,
% 29.67/19.95 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (f6(c1, f6(c1, c2)) = f6(c1, c2)) | big_f(f7(c1), f6(c1, f6(c1, c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | big_f(f7(c1), f6(c1, f6(c1, c2))) | (f6(c1, f6(c1, c2)) = f6(c1, c2)))),
% 29.67/19.95 inference(transitivity,[status(thm)],[28679, 28677])).
% 29.67/19.95 tff(28681,plain,
% 29.67/19.95 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (f6(c1, f6(c1, c2)) = f6(c1, c2)) | big_f(f7(c1), f6(c1, f6(c1, c2))) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))),
% 29.67/19.95 inference(quant_inst,[status(thm)],[])).
% 29.67/19.95 tff(28682,plain,
% 29.67/19.95 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | big_f(f7(c1), f6(c1, f6(c1, c2))) | (f6(c1, f6(c1, c2)) = f6(c1, c2))),
% 29.67/19.95 inference(modus_ponens,[status(thm)],[28681, 28680])).
% 29.67/19.95 tff(28683,plain,
% 29.67/19.95 (f6(c1, f6(c1, c2)) = f6(c1, c2)),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[28682, 2409, 25791, 28632, 28657, 28663, 28676])).
% 29.67/19.95 tff(28684,plain,
% 29.67/19.95 (f6(c1, c2) = f6(c1, f6(c1, c2))),
% 29.67/19.95 inference(symmetry,[status(thm)],[28683])).
% 29.67/19.95 tff(28685,plain,
% 29.67/19.95 (f6(c1, c2) = c2),
% 29.67/19.95 inference(transitivity,[status(thm)],[28684, 27490])).
% 29.67/19.95 tff(28686,plain,
% 29.67/19.95 (f6(f6(c2, c2), f6(c1, c2)) = f6(c1, c2)),
% 29.67/19.95 inference(monotonicity,[status(thm)],[28667, 28685])).
% 29.67/19.95 tff(28687,plain,
% 29.67/19.95 (big_f(f6(c2, c2), f6(c2, c2)) <=> big_f(c1, c1)),
% 29.67/19.95 inference(monotonicity,[status(thm)],[28667, 28667])).
% 29.67/19.95 tff(28688,plain,
% 29.67/19.95 (big_f(c1, c1) <=> big_f(f6(c2, c2), f6(c2, c2))),
% 29.67/19.95 inference(symmetry,[status(thm)],[28687])).
% 29.67/19.95 tff(28689,plain,
% 29.67/19.95 (big_f(f6(c2, c2), f6(c2, c2))),
% 29.67/19.95 inference(modus_ponens,[status(thm)],[27489, 28688])).
% 29.67/19.95 tff(28690,plain,
% 29.67/19.95 (~(f6(c1, f3(c1, c2)) = c1)),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[28491, 28689, 28666, 28686, 67, 28096, 28632, 28657, 28663, 28672])).
% 29.67/19.95 tff(28691,plain,
% 29.67/19.95 (f6(c1, f3(c1, c2)) = c2),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[6690, 28690])).
% 29.67/19.95 tff(28692,plain,
% 29.67/19.95 (c1 = f6(f7(c2), c3)),
% 29.67/19.95 inference(symmetry,[status(thm)],[28666])).
% 29.67/19.95 tff(28693,plain,
% 29.67/19.95 (f3(c1, c2) = f3(f6(f7(c2), c3), c2)),
% 29.67/19.95 inference(monotonicity,[status(thm)],[28692])).
% 29.67/19.95 tff(28694,plain,
% 29.67/19.95 (f3(f6(f7(c2), c3), c2) = f3(c1, c2)),
% 29.67/19.95 inference(symmetry,[status(thm)],[28693])).
% 29.67/19.95 tff(28695,plain,
% 29.67/19.95 (f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)) = f6(c1, f3(c1, c2))),
% 29.67/19.95 inference(monotonicity,[status(thm)],[28667, 28694])).
% 29.67/19.95 tff(28696,plain,
% 29.67/19.95 (f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)) = c2),
% 29.67/19.95 inference(transitivity,[status(thm)],[28695, 28691])).
% 29.67/19.95 tff(28697,plain,
% 29.67/19.95 ((f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)) = f3(f6(f7(c2), c3), c2)) <=> (c2 = f3(f6(f7(c2), c3), c2))),
% 29.67/19.95 inference(monotonicity,[status(thm)],[28696])).
% 29.67/19.95 tff(28698,plain,
% 29.67/19.95 ((f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)) = f3(f6(f7(c2), c3), c2)) <=> (f3(f6(f7(c2), c3), c2) = c2)),
% 29.67/19.95 inference(transitivity,[status(thm)],[28697, 7297])).
% 29.67/19.95 tff(28699,plain,
% 29.67/19.95 (f7(f6(c2, c2)) = f7(c1)),
% 29.67/19.95 inference(monotonicity,[status(thm)],[28667])).
% 29.67/19.95 tff(28700,plain,
% 29.67/19.95 (f7(f6(c2, c2)) = c1),
% 29.67/19.95 inference(transitivity,[status(thm)],[28699, 25791])).
% 29.67/19.95 tff(28701,plain,
% 29.67/19.95 (big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f3(f6(f7(c2), c3), c2))) <=> big_f(c1, c2)),
% 29.67/19.95 inference(monotonicity,[status(thm)],[28700, 28696])).
% 29.67/19.95 tff(28702,plain,
% 29.67/19.95 (big_f(c1, c2) <=> big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)))),
% 29.67/19.95 inference(symmetry,[status(thm)],[28701])).
% 29.67/19.95 tff(28703,plain,
% 29.67/19.95 ((~big_f(c1, c2)) <=> (~big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f3(f6(f7(c2), c3), c2))))),
% 29.67/19.95 inference(monotonicity,[status(thm)],[28702])).
% 29.67/19.95 tff(28704,plain,
% 29.67/19.95 (~big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)))),
% 29.67/19.95 inference(modus_ponens,[status(thm)],[27, 28703])).
% 29.67/19.95 tff(28705,plain,
% 29.67/19.95 (f7(f6(c2, c2)) = f6(c2, c2)),
% 29.67/19.95 inference(transitivity,[status(thm)],[28699, 25791, 28692, 28447])).
% 29.67/19.95 tff(28706,plain,
% 29.67/19.95 ((f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)) = f3(f6(f7(c2), c3), c2)) | big_f(f7(f6(c2, c2)), f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)))),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[28509, 2409, 28632, 28657, 28663, 28705])).
% 29.67/19.95 tff(28707,plain,
% 29.67/19.95 (f6(f6(c2, c2), f3(f6(f7(c2), c3), c2)) = f3(f6(f7(c2), c3), c2)),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[28706, 28704])).
% 29.67/19.95 tff(28708,plain,
% 29.67/19.95 (f3(f6(f7(c2), c3), c2) = c2),
% 29.67/19.95 inference(modus_ponens,[status(thm)],[28707, 28698])).
% 29.67/19.95 tff(28709,plain,
% 29.67/19.95 (f3(f6(f7(c2), c3), c2) = f6(f6(c2, c2), f3(f6(f7(c2), c3), c2))),
% 29.67/19.95 inference(symmetry,[status(thm)],[28707])).
% 29.67/19.95 tff(28710,plain,
% 29.67/19.95 (f3(f6(f7(c2), c3), c2) = f7(c2)),
% 29.67/19.95 inference(transitivity,[status(thm)],[28709, 28695, 28691, 28403])).
% 29.67/19.95 tff(28711,plain,
% 29.67/19.95 (big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3)) <=> big_f(f7(c2), f6(c2, c2))),
% 29.67/19.95 inference(monotonicity,[status(thm)],[28710, 28447])).
% 29.67/19.95 tff(28712,plain,
% 29.67/19.95 (big_f(f7(c2), f6(c2, c2)) <=> big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))),
% 29.67/19.95 inference(symmetry,[status(thm)],[28711])).
% 29.67/19.95 tff(28713,plain,
% 29.67/19.95 ((~big_f(f7(c2), f6(c2, c2))) <=> (~big_f(c2, c1))),
% 29.67/19.95 inference(monotonicity,[status(thm)],[2706])).
% 29.67/19.95 tff(28714,plain,
% 29.67/19.95 (~big_f(c2, c1)),
% 29.67/19.95 inference(modus_ponens,[status(thm)],[2621, 28713])).
% 29.67/19.95 tff(28715,plain,
% 29.67/19.95 ($false),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[348, 28714])).
% 29.67/19.95 tff(28716,plain,((~(f6(f7(c2), c3) = c1)) | (~big_f(c2, c1)) | big_f(f7(c2), f6(c2, c2)) | (~(c3 = c2)) | (~(f7(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.67/19.95 tff(28717,plain,
% 29.67/19.95 (big_f(f7(c2), f6(c2, c2))),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[28716, 28666, 28096, 28652, 67])).
% 29.67/19.95 tff(28718,plain,
% 29.67/19.95 (big_f(f3(f6(f7(c2), c3), c2), f6(f7(c2), c3))),
% 29.67/19.95 inference(modus_ponens,[status(thm)],[28717, 28712])).
% 29.67/19.95 tff(28719,plain,
% 29.67/19.95 (c2 = f2(c2)),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[28524, 28718, 27705, 1335, 28708, 28665])).
% 29.67/19.95 tff(28720,plain,
% 29.67/19.95 (f2(c2) = c2),
% 29.67/19.95 inference(symmetry,[status(thm)],[28719])).
% 29.67/19.95 tff(28721,plain,
% 29.67/19.95 (big_f(f7(c2), f6(c2, f4(c4)))),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[14036, 28717, 28653])).
% 29.67/19.95 tff(28722,plain,
% 29.67/19.95 (big_f(c2, f6(f7(c2), c3))),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[14585, 28721, 67, 28653, 28096])).
% 29.67/19.95 tff(28723,plain,
% 29.67/19.95 (f6(f7(c2), c3) = f2(c2)),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[28535, 28718, 1335, 28722, 28665, 28708])).
% 29.67/19.95 tff(28724,plain,
% 29.67/19.95 (f6(c2, c2) = c2),
% 29.67/19.95 inference(transitivity,[status(thm)],[28404, 28723, 28720])).
% 29.67/19.95 tff(28725,plain,
% 29.67/19.95 ($false),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[28672, 28724])).
% 29.67/19.95 tff(28726,plain,((~(f6(c1, f6(c1, c2)) = c2)) | (~(c3 = c2)) | big_f(c1, c2)), inference(lemma,lemma(discharge,[]))).
% 29.67/19.95 tff(28727,plain,
% 29.67/19.95 (~(f6(c1, f6(c1, c2)) = c2)),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[28726, 67, 27])).
% 29.67/19.95 tff(28728,plain,
% 29.67/19.95 (f6(c1, f6(c1, c2)) = c1),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[63, 28727])).
% 29.67/19.95 tff(28729,plain,
% 29.67/19.95 (f6(c1, c1) = c1),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[58, 28728])).
% 29.67/19.95 tff(28730,plain,
% 29.67/19.95 (big_f(f7(c1), f6(c1, c1))),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[27769, 28729, 27489])).
% 29.67/19.95 tff(28731,plain,
% 29.67/19.95 (f9(c1, c1) = c1),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[27678, 2, 28540, 28729, 28730])).
% 29.67/19.95 tff(28732,plain,
% 29.67/19.95 (big_f(f9(c1, c1), c1)),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[10938, 28731, 27489])).
% 29.67/19.95 tff(28733,plain,
% 29.67/19.95 (big_f(f9(c1, c1), f10(c1))),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[8716, 28732, 28540])).
% 29.67/19.95 tff(28734,plain,
% 29.67/19.95 (big_f(f7(c2), f6(c2, c2))),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[24737, 28733, 28096, 27705, 28540, 28731])).
% 29.67/19.95 tff(28735,plain,
% 29.67/19.95 (f6(c2, c2) = c2),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[28552, 28733, 28096, 2, 67, 28731, 28540])).
% 29.67/19.95 tff(28736,plain,
% 29.67/19.95 (big_f(f9(c2, c2), f10(c2))),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[2750, 28735, 28096, 28632, 27705, 28734])).
% 29.67/19.95 tff(28737,plain,
% 29.67/19.95 (~(f6(f7(c2), c3) = c1)),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[2710, 28734, 28096, 67, 2])).
% 29.67/19.95 tff(28738,plain,
% 29.67/19.95 (f6(f7(c2), c3) = c2),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[2391, 28737])).
% 29.67/19.95 tff(28739,plain,
% 29.67/19.95 (~(f9(c2, c2) = c2)),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[2386, 28738, 67, 28096, 27705, 28632, 28736])).
% 29.67/19.95 tff(28740,plain,
% 29.67/19.95 (f9(c2, c2) = c1),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[27475, 28739])).
% 29.67/19.95 tff(28741,plain,
% 29.67/19.95 (big_f(f9(c2, c2), c2) <=> big_f(c1, c2)),
% 29.67/19.95 inference(monotonicity,[status(thm)],[28740])).
% 29.67/19.95 tff(28742,plain,
% 29.67/19.95 (big_f(c1, c2) <=> big_f(f9(c2, c2), c2)),
% 29.67/19.95 inference(symmetry,[status(thm)],[28741])).
% 29.67/19.95 tff(28743,plain,
% 29.67/19.95 ((~big_f(c1, c2)) <=> (~big_f(f9(c2, c2), c2))),
% 29.67/19.95 inference(monotonicity,[status(thm)],[28742])).
% 29.67/19.95 tff(28744,plain,
% 29.67/19.95 (~big_f(f9(c2, c2), c2)),
% 29.67/19.95 inference(modus_ponens,[status(thm)],[27, 28743])).
% 29.67/19.95 tff(28745,plain,
% 29.67/19.95 (big_f(f9(c2, c2), c2)),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[3687, 28736, 28632])).
% 29.67/19.95 tff(28746,plain,
% 29.67/19.95 ($false),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[28745, 28744])).
% 29.67/19.95 tff(28747,plain,(big_f(c2, c1) | big_f(c1, c2) | (~(c3 = c2))), inference(lemma,lemma(discharge,[]))).
% 29.67/19.95 tff(28748,plain,
% 29.67/19.95 (big_f(c2, c1)),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[28747, 67, 27])).
% 29.67/19.95 tff(28749,plain,
% 29.67/19.95 (f4(c4) = c2),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[27836, 28748, 27, 67])).
% 29.67/19.95 tff(28750,plain,
% 29.67/19.95 (c2 = c4),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[26149, 28749, 27, 1335, 28096, 28748, 27705])).
% 29.67/19.95 tff(28751,plain,
% 29.67/19.95 (c4 = c2),
% 29.67/19.95 inference(symmetry,[status(thm)],[28750])).
% 29.67/19.95 tff(28752,plain,
% 29.67/19.95 ((~(f9(c2, c2) = c4)) <=> (~(c2 = c4))),
% 29.67/19.95 inference(monotonicity,[status(thm)],[8821])).
% 29.67/19.95 tff(28753,plain,
% 29.67/19.95 (~(c2 = c4)),
% 29.67/19.95 inference(modus_ponens,[status(thm)],[1861, 28752])).
% 29.67/19.95 tff(28754,plain,
% 29.67/19.95 ($false),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[631, 28753])).
% 29.67/19.95 tff(28755,plain,((~(c2 = c4)) | (f9(c2, c2) = c4) | (~(f4(c4) = c2)) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.67/19.95 tff(28756,plain,
% 29.67/19.95 (f9(c2, c2) = c4),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[28755, 28749, 28632, 28750])).
% 29.67/19.95 tff(28757,plain,
% 29.67/19.95 (f9(c2, c2) = c2),
% 29.67/19.95 inference(transitivity,[status(thm)],[28756, 28751])).
% 29.67/19.95 tff(28758,plain,
% 29.67/19.95 (big_f(f9(c2, c2), c2) <=> big_f(c2, c2)),
% 29.67/19.95 inference(monotonicity,[status(thm)],[28757])).
% 29.67/19.95 tff(28759,plain,
% 29.67/19.95 (big_f(c2, c2) <=> big_f(f9(c2, c2), c2)),
% 29.67/19.95 inference(symmetry,[status(thm)],[28758])).
% 29.67/19.95 tff(28760,plain,
% 29.67/19.95 (big_f(c2, c2) <=> big_f(f9(c2, c2), f10(c2))),
% 29.67/19.95 inference(transitivity,[status(thm)],[28759, 28659])).
% 29.67/19.95 tff(28761,plain,
% 29.67/19.95 (big_f(f9(c2, c2), f10(c2))),
% 29.67/19.95 inference(modus_ponens,[status(thm)],[27705, 28760])).
% 29.67/19.95 tff(28762,plain,
% 29.67/19.95 (f9(f10(c2), f4(c4)) = c2),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[8065, 28749, 28632])).
% 29.67/19.95 tff(28763,plain,
% 29.67/19.95 (f9(c2, c2) = c2),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[1606, 28762, 28632, 28749])).
% 29.67/19.95 tff(28764,plain,
% 29.67/19.95 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)))),
% 29.67/19.95 inference(rewrite,[status(thm)],[])).
% 29.67/19.95 tff(28765,plain,
% 29.67/19.95 (((~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1)))) <=> ((~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)))),
% 29.67/19.95 inference(rewrite,[status(thm)],[])).
% 29.67/19.95 tff(28766,plain,
% 29.67/19.95 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1))))),
% 29.67/19.95 inference(monotonicity,[status(thm)],[28765])).
% 29.67/19.95 tff(28767,plain,
% 29.67/19.95 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)))),
% 29.67/19.95 inference(transitivity,[status(thm)],[28766, 28764])).
% 29.67/19.95 tff(28768,plain,
% 29.67/19.95 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))),
% 29.67/19.95 inference(quant_inst,[status(thm)],[])).
% 29.67/19.95 tff(28769,plain,
% 29.67/19.95 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1))),
% 29.67/19.95 inference(modus_ponens,[status(thm)],[28768, 28767])).
% 29.67/19.95 tff(28770,plain,
% 29.67/19.95 ($false),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[28769, 2378, 25791, 28632, 28763, 28761, 28730, 28729])).
% 29.67/19.95 tff(28771,plain,((~(c3 = c2)) | big_f(c1, c2)), inference(lemma,lemma(discharge,[]))).
% 29.67/19.95 tff(28772,plain,
% 29.67/19.95 (~(c3 = c2)),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[28771, 27])).
% 29.67/19.95 tff(28773,plain,
% 29.67/19.95 (c3 = c1),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[180, 28772])).
% 29.67/19.95 tff(28774,plain,
% 29.67/19.95 (~(f4(c4) = c1)),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[11784, 66, 27, 28773])).
% 29.67/19.95 tff(28775,plain,
% 29.67/19.95 (f4(c4) = c2),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[11750, 28774])).
% 29.67/19.95 tff(28776,plain,
% 29.67/19.95 (f7(c2) = c2),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[27050, 27, 4234, 89, 121])).
% 29.67/19.95 tff(28777,plain,
% 29.67/19.95 (big_f(c1, c1)),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[23456, 26670, 28776, 26614, 121])).
% 29.67/19.95 tff(28778,plain,
% 29.67/19.95 (big_f(c1, f10(c2))),
% 29.67/19.95 inference(modus_ponens,[status(thm)],[28777, 24205])).
% 29.67/19.95 tff(28779,plain,
% 29.67/19.95 (big_f(f7(c2), f6(c2, c1)) <=> big_f(c2, f6(c2, c1))),
% 29.67/19.95 inference(monotonicity,[status(thm)],[28776])).
% 29.67/19.95 tff(28780,plain,
% 29.67/19.95 (big_f(c2, f6(c2, c1)) <=> big_f(f7(c2), f6(c2, c1))),
% 29.67/19.95 inference(symmetry,[status(thm)],[28779])).
% 29.67/19.95 tff(28781,plain,
% 29.67/19.95 (~(c3 = c1)),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[11517, 79, 121, 348, 77, 4932])).
% 29.67/19.95 tff(28782,plain,
% 29.67/19.95 (c3 = c2),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[180, 28781])).
% 29.67/19.95 tff(28783,plain,
% 29.67/19.95 ((c1 = c3) <=> (c1 = c2)),
% 29.67/19.95 inference(monotonicity,[status(thm)],[28782])).
% 29.67/19.95 tff(28784,plain,
% 29.67/19.95 ((c1 = c3) <=> (c2 = c1)),
% 29.67/19.95 inference(transitivity,[status(thm)],[28783, 1])).
% 29.67/19.95 tff(28785,plain,
% 29.67/19.95 ((c2 = c1) <=> (c1 = c3)),
% 29.67/19.95 inference(symmetry,[status(thm)],[28784])).
% 29.67/19.95 tff(28786,plain,
% 29.67/19.95 ((~(c2 = c1)) <=> (~(c1 = c3))),
% 29.67/19.95 inference(monotonicity,[status(thm)],[28785])).
% 29.67/19.95 tff(28787,plain,
% 29.67/19.95 (~(c1 = c3)),
% 29.67/19.95 inference(modus_ponens,[status(thm)],[75, 28786])).
% 29.67/19.95 tff(28788,plain,
% 29.67/19.95 (~(c4 = c1)),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[11545, 28787, 27, 4932, 79])).
% 29.67/19.95 tff(28789,plain,
% 29.67/19.95 (c4 = c2),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[461, 28788])).
% 29.67/19.95 tff(28790,plain,
% 29.67/19.95 (c2 = c4),
% 29.67/19.95 inference(modus_ponens,[status(thm)],[28789, 159])).
% 29.67/19.95 tff(28791,plain,
% 29.67/19.95 (c2 = c4),
% 29.67/19.95 inference(symmetry,[status(thm)],[28789])).
% 29.67/19.95 tff(28792,plain,
% 29.67/19.95 (f4(c2) = f4(c4)),
% 29.67/19.95 inference(monotonicity,[status(thm)],[28791])).
% 29.67/19.95 tff(28793,plain,
% 29.67/19.95 (f4(c4) = f4(c2)),
% 29.67/19.95 inference(symmetry,[status(thm)],[28792])).
% 29.67/19.95 tff(28794,plain,
% 29.67/19.95 (c2 = f4(c2)),
% 29.67/19.95 inference(transitivity,[status(thm)],[436, 28793])).
% 29.67/19.95 tff(28795,plain,
% 29.67/19.95 ($false),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[12429, 28794, 28790, 121, 27, 28782, 4932, 89])).
% 29.67/19.95 tff(28796,plain,((~(f4(c4) = c2)) | big_f(c2, c2) | big_f(c1, c2) | (~big_f(c1, c1)) | (f10(c2) = c2) | (~big_f(c2, c1)) | (~(f7(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.67/19.95 tff(28797,plain,
% 29.67/19.95 (~(f4(c4) = c2)),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[28796, 27, 121, 28777, 89, 26614, 28776])).
% 29.67/19.95 tff(28798,plain,
% 29.67/19.95 (f4(c4) = c1),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[11750, 28797])).
% 29.67/19.95 tff(28799,plain,
% 29.67/19.95 (c1 = f8(c2)),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[26590, 2662, 89, 77, 3198, 27629, 27982])).
% 29.67/19.95 tff(28800,plain,
% 29.67/19.95 (f8(c2) = c1),
% 29.67/19.95 inference(symmetry,[status(thm)],[28799])).
% 29.67/19.95 tff(28801,plain,
% 29.67/19.95 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))))),
% 29.67/19.95 inference(rewrite,[status(thm)],[])).
% 29.67/19.95 tff(28802,plain,
% 29.67/19.95 (((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1))) <=> ((f10(c2) = c2) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))))),
% 29.67/19.95 inference(rewrite,[status(thm)],[])).
% 29.67/19.95 tff(28803,plain,
% 29.67/19.95 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (c2 = f8(c2)) | (~big_f(c2, f10(c2)))))),
% 29.67/19.95 inference(monotonicity,[status(thm)],[28802])).
% 29.67/19.95 tff(28804,plain,
% 29.67/19.95 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))))),
% 29.67/19.95 inference(transitivity,[status(thm)],[28803, 28801])).
% 29.67/19.95 tff(28805,plain,
% 29.67/19.95 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)))),
% 29.67/19.95 inference(quant_inst,[status(thm)],[])).
% 29.67/19.95 tff(28806,plain,
% 29.67/19.95 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | big_f(f7(c2), f6(c2, c1)) | (c2 = f8(c2)) | (~big_f(c2, f10(c2)))),
% 29.67/19.95 inference(modus_ponens,[status(thm)],[28805, 28804])).
% 29.67/19.95 tff(28807,plain,
% 29.67/19.95 (c2 = f8(c2)),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[28806, 2662, 89, 77, 3198, 27629, 12291])).
% 29.67/19.95 tff(28808,plain,
% 29.67/19.95 (c2 = c1),
% 29.67/19.95 inference(transitivity,[status(thm)],[28807, 28800])).
% 29.67/19.95 tff(28809,plain,
% 29.67/19.95 ($false),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[75, 28808])).
% 29.67/19.95 tff(28810,plain,((f6(c2, c1) = c1) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (~big_f(c1, f10(c2))) | (~big_f(c2, f10(c2))) | big_f(c2, c2) | (~(f7(c1) = c1)) | (~(f4(c4) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.67/19.95 tff(28811,plain,
% 29.67/19.95 (f6(c2, c1) = c1),
% 29.67/19.95 inference(unit_resolution,[status(thm)],[28810, 28776, 89, 28778, 26676, 121, 4234, 28798])).
% 29.67/19.95 tff(28812,plain,
% 29.67/19.95 (big_f(c2, f6(c2, c1)) <=> big_f(c2, c1)),
% 29.67/19.95 inference(monotonicity,[status(thm)],[28811])).
% 29.67/19.95 tff(28813,plain,
% 29.67/19.95 (big_f(c2, c1) <=> big_f(c2, f6(c2, c1))),
% 29.77/19.96 inference(symmetry,[status(thm)],[28812])).
% 29.77/19.96 tff(28814,plain,
% 29.77/19.96 (big_f(c2, c1) <=> big_f(f7(c2), f6(c2, c1))),
% 29.77/19.96 inference(transitivity,[status(thm)],[28813, 28780])).
% 29.77/19.96 tff(28815,plain,
% 29.77/19.96 (big_f(f7(c2), f6(c2, c1))),
% 29.77/19.96 inference(modus_ponens,[status(thm)],[26614, 28814])).
% 29.77/19.96 tff(28816,plain,
% 29.77/19.96 (c1 = f8(c2)),
% 29.77/19.96 inference(unit_resolution,[status(thm)],[25362, 2730, 89, 28776, 28811, 28815, 28778])).
% 29.77/19.96 tff(28817,plain,
% 29.77/19.96 (f8(c2) = c1),
% 29.77/19.96 inference(symmetry,[status(thm)],[28816])).
% 29.77/19.96 tff(28818,plain,
% 29.77/19.96 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (~(f7(c2) = c2)) | (c2 = f8(c2)) | (~(f6(c2, c1) = c1)) | (~big_f(c2, f10(c2))) | (~big_f(f7(c2), f6(c2, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (c2 = f8(c2)) | (~(f6(c2, c1) = c1)) | (~big_f(c2, f10(c2))) | (~big_f(f7(c2), f6(c2, c1))))),
% 29.77/19.96 inference(rewrite,[status(thm)],[])).
% 29.77/19.96 tff(28819,plain,
% 29.77/19.96 (((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1)))) <=> ((f10(c2) = c2) | (~(f7(c2) = c2)) | (c2 = f8(c2)) | (~(f6(c2, c1) = c1)) | (~big_f(c2, f10(c2))) | (~big_f(f7(c2), f6(c2, c1))))),
% 29.77/19.96 inference(rewrite,[status(thm)],[])).
% 29.77/19.96 tff(28820,plain,
% 29.77/19.96 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (~(f7(c2) = c2)) | (c2 = f8(c2)) | (~(f6(c2, c1) = c1)) | (~big_f(c2, f10(c2))) | (~big_f(f7(c2), f6(c2, c1)))))),
% 29.77/19.96 inference(monotonicity,[status(thm)],[28819])).
% 29.77/19.96 tff(28821,plain,
% 29.77/19.96 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (c2 = f8(c2)) | (~(f6(c2, c1) = c1)) | (~big_f(c2, f10(c2))) | (~big_f(f7(c2), f6(c2, c1))))),
% 29.77/19.96 inference(transitivity,[status(thm)],[28820, 28818])).
% 29.77/19.96 tff(28822,plain,
% 29.77/19.96 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1))))),
% 29.77/19.96 inference(quant_inst,[status(thm)],[])).
% 29.77/19.96 tff(28823,plain,
% 29.77/19.96 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (c2 = f8(c2)) | (~(f6(c2, c1) = c1)) | (~big_f(c2, f10(c2))) | (~big_f(f7(c2), f6(c2, c1)))),
% 29.77/19.96 inference(modus_ponens,[status(thm)],[28822, 28821])).
% 29.77/19.96 tff(28824,plain,
% 29.77/19.96 (c2 = f8(c2)),
% 29.77/19.96 inference(unit_resolution,[status(thm)],[28823, 2730, 89, 28776, 28811, 28815, 26676])).
% 29.77/19.96 tff(28825,plain,
% 29.77/19.96 (c2 = c1),
% 29.77/19.96 inference(transitivity,[status(thm)],[28824, 28817])).
% 29.77/19.96 tff(28826,plain,
% 29.77/19.96 ($false),
% 29.77/19.96 inference(unit_resolution,[status(thm)],[75, 28825])).
% 29.77/19.96 tff(28827,plain,(big_f(c1, c2) | (f10(c2) = c2) | big_f(c2, c2) | (~(f7(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.77/19.96 tff(28828,plain,
% 29.77/19.96 (big_f(c1, c2) | (f10(c2) = c2) | big_f(c2, c2)),
% 29.77/19.96 inference(unit_resolution,[status(thm)],[28827, 25791])).
% 29.77/19.96 tff(28829,plain,
% 29.77/19.96 (big_f(c1, c2)),
% 29.77/19.96 inference(unit_resolution,[status(thm)],[28828, 121, 89])).
% 29.77/19.96 tff(28830,plain,
% 29.77/19.96 (~(f10(c1) = c1)),
% 29.77/19.96 inference(unit_resolution,[status(thm)],[23456, 121, 66, 77, 25952])).
% 29.77/19.96 tff(28831,plain,
% 29.77/19.96 (f10(c1) = c2),
% 29.77/19.96 inference(unit_resolution,[status(thm)],[14, 28830])).
% 29.77/19.96 tff(28832,plain,
% 29.77/19.96 (c2 = f10(c1)),
% 29.77/19.96 inference(symmetry,[status(thm)],[28831])).
% 29.77/19.96 tff(28833,plain,
% 29.77/19.96 (big_f(c1, c2) <=> big_f(c1, f10(c1))),
% 29.77/19.96 inference(monotonicity,[status(thm)],[28832])).
% 29.77/19.96 tff(28834,plain,
% 29.77/19.96 (big_f(c1, f10(c1))),
% 29.77/19.96 inference(modus_ponens,[status(thm)],[2865, 28833])).
% 29.77/19.96 tff(28835,plain,
% 29.77/19.96 (c1 = f8(c1)),
% 29.77/19.96 inference(unit_resolution,[status(thm)],[27080, 2662, 25791, 28830, 28834, 25798, 114])).
% 29.77/19.96 tff(28836,plain,
% 29.77/19.96 (f8(c1) = c1),
% 29.77/19.96 inference(symmetry,[status(thm)],[28835])).
% 29.77/19.96 tff(28837,plain,
% 29.77/19.96 ((f3(c2, c1) = f8(c1)) <=> (f3(c2, c1) = c1)),
% 29.77/19.96 inference(monotonicity,[status(thm)],[28836])).
% 29.77/19.96 tff(28838,plain,
% 29.77/19.96 ((f3(c2, c1) = c1) <=> (f3(c2, c1) = f8(c1))),
% 29.77/19.96 inference(symmetry,[status(thm)],[28837])).
% 29.77/19.96 tff(28839,plain,
% 29.77/19.96 ((~(f3(c2, c1) = c1)) <=> (~(f3(c2, c1) = f8(c1)))),
% 29.77/19.96 inference(monotonicity,[status(thm)],[28838])).
% 29.77/19.96 tff(28840,plain,
% 29.77/19.96 (f6(c1, f10(c1)) = f6(c1, c2)),
% 29.77/19.96 inference(monotonicity,[status(thm)],[28831])).
% 29.77/19.96 tff(28841,plain,
% 29.77/19.96 (big_f(f7(c1), f6(c1, f10(c1))) <=> big_f(c1, f6(c1, c2))),
% 29.77/19.96 inference(monotonicity,[status(thm)],[25791, 28840])).
% 29.77/19.96 tff(28842,plain,
% 29.77/19.96 (big_f(c1, f6(c1, c2)) <=> big_f(f7(c1), f6(c1, f10(c1)))),
% 29.77/19.96 inference(symmetry,[status(thm)],[28841])).
% 29.77/19.96 tff(28843,plain,
% 29.77/19.96 (big_f(c1, c1) <=> big_f(f7(c1), f6(c1, f10(c1)))),
% 29.77/19.96 inference(transitivity,[status(thm)],[25795, 28842])).
% 29.77/19.96 tff(28844,plain,
% 29.77/19.96 ((~big_f(c1, c1)) <=> (~big_f(f7(c1), f6(c1, f10(c1))))),
% 29.77/19.96 inference(monotonicity,[status(thm)],[28843])).
% 29.77/19.96 tff(28845,plain,
% 29.77/19.96 (~big_f(f7(c1), f6(c1, f10(c1)))),
% 29.77/19.96 inference(modus_ponens,[status(thm)],[66, 28844])).
% 29.77/19.96 tff(28846,assumption,(f6(c1, f10(c1)) = f10(c1)), introduced(assumption)).
% 29.77/19.96 tff(28847,plain,
% 29.77/19.96 (f6(c1, c2) = c2),
% 29.77/19.96 inference(modus_ponens,[status(thm)],[28846, 24996])).
% 29.77/19.96 tff(28848,plain,
% 29.77/19.96 ($false),
% 29.77/19.96 inference(unit_resolution,[status(thm)],[114, 28847])).
% 29.77/19.96 tff(28849,plain,((~(f6(c1, f10(c1)) = f10(c1))) | (f6(c1, c2) = c2) | (~(f10(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.77/19.96 tff(28850,plain,
% 29.77/19.96 (~(f6(c1, f10(c1)) = f10(c1))),
% 29.77/19.96 inference(unit_resolution,[status(thm)],[28849, 114, 28831])).
% 29.77/19.96 tff(28851,plain,
% 29.77/19.96 (big_f(c1, f10(c1))),
% 29.77/19.96 inference(modus_ponens,[status(thm)],[2865, 24247])).
% 29.77/19.96 tff(28852,assumption,(~big_f(f7(c1), f6(c1, f10(c1)))), introduced(assumption)).
% 29.77/19.96 tff(28853,assumption,(~(f6(c1, f10(c1)) = f10(c1))), introduced(assumption)).
% 29.77/19.96 tff(28854,plain,
% 29.77/19.96 (~(c4 = c2)),
% 29.77/19.96 inference(unit_resolution,[status(thm)],[13490, 168, 121, 2865, 66, 79])).
% 29.77/19.96 tff(28855,plain,
% 29.77/19.96 (c4 = c1),
% 29.77/19.96 inference(unit_resolution,[status(thm)],[461, 28854])).
% 29.77/19.96 tff(28856,plain,
% 29.77/19.96 ((f10(c1) = c4) <=> (f10(c1) = c1)),
% 29.77/19.96 inference(monotonicity,[status(thm)],[28855])).
% 29.77/19.96 tff(28857,plain,
% 29.77/19.96 ((f10(c1) = c1) <=> (f10(c1) = c4)),
% 29.77/19.96 inference(symmetry,[status(thm)],[28856])).
% 29.77/19.96 tff(28858,plain,
% 29.77/19.96 ((~(f10(c1) = c1)) <=> (~(f10(c1) = c4))),
% 29.77/19.96 inference(monotonicity,[status(thm)],[28857])).
% 29.77/19.96 tff(28859,plain,
% 29.77/19.96 (~(f10(c1) = c4)),
% 29.77/19.96 inference(modus_ponens,[status(thm)],[3, 28858])).
% 29.77/19.96 tff(28860,plain,
% 29.77/19.96 (f1(c1, f10(c1)) = f1(c1, c2)),
% 29.77/19.96 inference(monotonicity,[status(thm)],[15])).
% 29.77/19.96 tff(28861,plain,
% 29.77/19.96 (f1(c1, f10(c1)) = c1),
% 29.77/19.96 inference(transitivity,[status(thm)],[28860, 1053])).
% 29.77/19.96 tff(28862,plain,
% 29.77/19.96 (big_f(c1, f1(c1, f10(c1))) <=> big_f(c1, c1)),
% 29.77/19.96 inference(monotonicity,[status(thm)],[28861])).
% 29.77/19.96 tff(28863,plain,
% 29.77/19.96 (big_f(c1, c1) <=> big_f(c1, f1(c1, f10(c1)))),
% 29.77/19.96 inference(symmetry,[status(thm)],[28862])).
% 29.77/19.96 tff(28864,plain,
% 29.77/19.96 ((~big_f(c1, c1)) <=> (~big_f(c1, f1(c1, f10(c1))))),
% 29.77/19.96 inference(monotonicity,[status(thm)],[28863])).
% 29.77/19.96 tff(28865,plain,
% 29.77/19.96 (~big_f(c1, f1(c1, f10(c1)))),
% 29.77/19.96 inference(modus_ponens,[status(thm)],[66, 28864])).
% 29.77/19.96 tff(28866,plain,
% 29.77/19.96 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, f10(c1))) | (f6(c1, f10(c1)) = f10(c1)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, f10(c1))) | (f6(c1, f10(c1)) = f10(c1)))),
% 29.77/19.96 inference(rewrite,[status(thm)],[])).
% 29.77/19.96 tff(28867,plain,
% 29.77/19.96 (((f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f7(c1) = c1)) | (f6(c1, f10(c1)) = f10(c1)) | big_f(f7(c1), f6(c1, f10(c1)))) <=> ((f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, f10(c1))) | (f6(c1, f10(c1)) = f10(c1)))),
% 29.77/19.96 inference(rewrite,[status(thm)],[])).
% 29.77/19.96 tff(28868,plain,
% 29.77/19.96 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f7(c1) = c1)) | (f6(c1, f10(c1)) = f10(c1)) | big_f(f7(c1), f6(c1, f10(c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, f10(c1))) | (f6(c1, f10(c1)) = f10(c1))))),
% 29.77/19.96 inference(monotonicity,[status(thm)],[28867])).
% 29.77/19.96 tff(28869,plain,
% 29.77/19.96 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f7(c1) = c1)) | (f6(c1, f10(c1)) = f10(c1)) | big_f(f7(c1), f6(c1, f10(c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, f10(c1))) | (f6(c1, f10(c1)) = f10(c1)))),
% 29.77/19.96 inference(transitivity,[status(thm)],[28868, 28866])).
% 29.77/19.96 tff(28870,plain,
% 29.77/19.96 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f7(c1) = c1)) | (f6(c1, f10(c1)) = f10(c1)) | big_f(f7(c1), f6(c1, f10(c1))))),
% 29.77/19.96 inference(quant_inst,[status(thm)],[])).
% 29.77/19.96 tff(28871,plain,
% 29.77/19.96 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, f10(c1))) | (f6(c1, f10(c1)) = f10(c1))),
% 29.77/19.96 inference(modus_ponens,[status(thm)],[28870, 28869])).
% 29.77/19.96 tff(28872,plain,
% 29.77/19.96 ((c1 = f8(c1)) | big_f(f7(c1), f6(c1, f10(c1))) | (f6(c1, f10(c1)) = f10(c1))),
% 29.77/19.96 inference(unit_resolution,[status(thm)],[28871, 2662, 4234, 3, 3023])).
% 29.77/19.96 tff(28873,plain,
% 29.77/19.96 (c1 = f8(c1)),
% 29.77/19.96 inference(unit_resolution,[status(thm)],[28872, 28853, 28852])).
% 29.77/19.96 tff(28874,plain,
% 29.77/19.96 (f8(c1) = c1),
% 29.77/19.96 inference(symmetry,[status(thm)],[28873])).
% 29.77/19.96 tff(28875,plain,
% 29.77/19.96 (f3(f10(c1), c1) = c1),
% 29.77/19.96 inference(unit_resolution,[status(thm)],[1069, 1061, 168, 1046, 13508, 1052])).
% 29.77/19.96 tff(28876,plain,
% 29.77/19.96 (big_f(f3(f10(c1), c1), f10(c1)) <=> big_f(c1, f10(c1))),
% 29.77/19.96 inference(monotonicity,[status(thm)],[28875])).
% 29.77/19.96 tff(28877,plain,
% 29.77/19.96 (big_f(c1, f10(c1)) <=> big_f(f3(f10(c1), c1), f10(c1))),
% 29.77/19.96 inference(symmetry,[status(thm)],[28876])).
% 29.77/19.96 tff(28878,plain,
% 29.77/19.96 (big_f(f3(f10(c1), c1), f10(c1))),
% 29.77/19.96 inference(modus_ponens,[status(thm)],[3023, 28877])).
% 29.77/19.96 tff(28879,plain,
% 29.77/19.96 ($false),
% 29.77/19.96 inference(unit_resolution,[status(thm)],[1061, 28878])).
% 29.77/19.96 tff(28880,plain,(big_f(f3(f10(c1), c1), f10(c1)) | (~big_f(c1, f10(c1))) | (c1 = c3) | (f10(c1) = c4) | big_f(c1, f1(c1, c2)) | (f1(c1, c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 29.77/19.96 tff(28881,plain,
% 29.77/19.96 (big_f(f3(f10(c1), c1), f10(c1))),
% 29.77/19.96 inference(unit_resolution,[status(thm)],[28880, 7524, 168, 1046, 3023, 1052])).
% 29.77/19.96 tff(28882,plain,
% 29.77/19.96 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (~(f7(c1) = c1)) | (~big_f(f3(f10(c1), c1), f10(c1))) | big_f(f7(c1), f6(c1, f10(c1))) | (f6(c1, f10(c1)) = f10(c1)) | (f3(f10(c1), c1) = f8(c1)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c1) = c1) | (~(f7(c1) = c1)) | (~big_f(f3(f10(c1), c1), f10(c1))) | big_f(f7(c1), f6(c1, f10(c1))) | (f6(c1, f10(c1)) = f10(c1)) | (f3(f10(c1), c1) = f8(c1)))),
% 29.77/19.96 inference(rewrite,[status(thm)],[])).
% 29.77/19.96 tff(28883,plain,
% 29.77/19.96 (((f10(c1) = c1) | (f3(f10(c1), c1) = f8(c1)) | (~big_f(f3(f10(c1), c1), f10(c1))) | (~(f7(c1) = c1)) | (f6(c1, f10(c1)) = f10(c1)) | big_f(f7(c1), f6(c1, f10(c1)))) <=> ((f10(c1) = c1) | (~(f7(c1) = c1)) | (~big_f(f3(f10(c1), c1), f10(c1))) | big_f(f7(c1), f6(c1, f10(c1))) | (f6(c1, f10(c1)) = f10(c1)) | (f3(f10(c1), c1) = f8(c1)))),
% 29.77/19.96 inference(rewrite,[status(thm)],[])).
% 29.77/19.96 tff(28884,plain,
% 29.77/19.96 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (f3(f10(c1), c1) = f8(c1)) | (~big_f(f3(f10(c1), c1), f10(c1))) | (~(f7(c1) = c1)) | (f6(c1, f10(c1)) = f10(c1)) | big_f(f7(c1), f6(c1, f10(c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (~(f7(c1) = c1)) | (~big_f(f3(f10(c1), c1), f10(c1))) | big_f(f7(c1), f6(c1, f10(c1))) | (f6(c1, f10(c1)) = f10(c1)) | (f3(f10(c1), c1) = f8(c1))))),
% 29.77/19.96 inference(monotonicity,[status(thm)],[28883])).
% 29.77/19.96 tff(28885,plain,
% 29.77/19.96 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (f3(f10(c1), c1) = f8(c1)) | (~big_f(f3(f10(c1), c1), f10(c1))) | (~(f7(c1) = c1)) | (f6(c1, f10(c1)) = f10(c1)) | big_f(f7(c1), f6(c1, f10(c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c1) = c1) | (~(f7(c1) = c1)) | (~big_f(f3(f10(c1), c1), f10(c1))) | big_f(f7(c1), f6(c1, f10(c1))) | (f6(c1, f10(c1)) = f10(c1)) | (f3(f10(c1), c1) = f8(c1)))),
% 29.77/19.96 inference(transitivity,[status(thm)],[28884, 28882])).
% 29.77/19.96 tff(28886,plain,
% 29.77/19.96 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (f3(f10(c1), c1) = f8(c1)) | (~big_f(f3(f10(c1), c1), f10(c1))) | (~(f7(c1) = c1)) | (f6(c1, f10(c1)) = f10(c1)) | big_f(f7(c1), f6(c1, f10(c1))))),
% 29.77/19.96 inference(quant_inst,[status(thm)],[])).
% 29.77/19.96 tff(28887,plain,
% 29.77/19.96 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c1) = c1) | (~(f7(c1) = c1)) | (~big_f(f3(f10(c1), c1), f10(c1))) | big_f(f7(c1), f6(c1, f10(c1))) | (f6(c1, f10(c1)) = f10(c1)) | (f3(f10(c1), c1) = f8(c1))),
% 29.77/19.96 inference(modus_ponens,[status(thm)],[28886, 28885])).
% 29.77/19.96 tff(28888,plain,
% 29.77/19.96 (f3(f10(c1), c1) = f8(c1)),
% 29.77/19.96 inference(unit_resolution,[status(thm)],[28887, 2662, 4234, 3, 28881, 28853, 28852])).
% 29.77/19.96 tff(28889,plain,
% 29.77/19.96 (f3(f10(c1), c1) = c1),
% 29.77/19.96 inference(transitivity,[status(thm)],[28888, 28874])).
% 29.77/19.96 tff(28890,plain,
% 29.77/19.96 ((f1(c1, f10(c1)) = f10(c1)) <=> (c1 = f10(c1))),
% 29.77/19.96 inference(monotonicity,[status(thm)],[28861])).
% 29.77/19.96 tff(28891,plain,
% 29.77/19.96 ((f1(c1, f10(c1)) = f10(c1)) <=> (f10(c1) = c1)),
% 29.77/19.96 inference(transitivity,[status(thm)],[28890, 18819])).
% 29.77/19.96 tff(28892,plain,
% 29.77/19.96 ((f10(c1) = c1) <=> (f1(c1, f10(c1)) = f10(c1))),
% 29.77/19.96 inference(symmetry,[status(thm)],[28891])).
% 29.77/19.96 tff(28893,plain,
% 29.77/19.96 ((~(f10(c1) = c1)) <=> (~(f1(c1, f10(c1)) = f10(c1)))),
% 29.77/19.96 inference(monotonicity,[status(thm)],[28892])).
% 29.77/19.96 tff(28894,plain,
% 29.77/19.96 (~(f1(c1, f10(c1)) = f10(c1))),
% 29.77/19.96 inference(modus_ponens,[status(thm)],[3, 28893])).
% 29.77/19.96 tff(28895,plain,
% 29.77/19.96 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c1 = c3) | (f10(c1) = c4) | (~big_f(f3(f10(c1), c1), f10(c1))) | (~(f3(f10(c1), c1) = c1)) | (f1(c1, f10(c1)) = f10(c1)) | big_f(c1, f1(c1, f10(c1))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c1 = c3) | (f10(c1) = c4) | (~big_f(f3(f10(c1), c1), f10(c1))) | (~(f3(f10(c1), c1) = c1)) | (f1(c1, f10(c1)) = f10(c1)) | big_f(c1, f1(c1, f10(c1))))),
% 29.77/19.96 inference(rewrite,[status(thm)],[])).
% 29.77/19.96 tff(28896,plain,
% 29.77/19.96 (((f10(c1) = c4) | (c1 = c3) | (f1(c1, f10(c1)) = f10(c1)) | big_f(c1, f1(c1, f10(c1))) | (~(f3(f10(c1), c1) = c1)) | (~big_f(f3(f10(c1), c1), f10(c1)))) <=> ((c1 = c3) | (f10(c1) = c4) | (~big_f(f3(f10(c1), c1), f10(c1))) | (~(f3(f10(c1), c1) = c1)) | (f1(c1, f10(c1)) = f10(c1)) | big_f(c1, f1(c1, f10(c1))))),
% 29.77/19.96 inference(rewrite,[status(thm)],[])).
% 29.77/19.96 tff(28897,plain,
% 29.77/19.96 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((f10(c1) = c4) | (c1 = c3) | (f1(c1, f10(c1)) = f10(c1)) | big_f(c1, f1(c1, f10(c1))) | (~(f3(f10(c1), c1) = c1)) | (~big_f(f3(f10(c1), c1), f10(c1))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c1 = c3) | (f10(c1) = c4) | (~big_f(f3(f10(c1), c1), f10(c1))) | (~(f3(f10(c1), c1) = c1)) | (f1(c1, f10(c1)) = f10(c1)) | big_f(c1, f1(c1, f10(c1)))))),
% 29.77/19.96 inference(monotonicity,[status(thm)],[28896])).
% 29.77/19.96 tff(28898,plain,
% 29.77/19.96 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((f10(c1) = c4) | (c1 = c3) | (f1(c1, f10(c1)) = f10(c1)) | big_f(c1, f1(c1, f10(c1))) | (~(f3(f10(c1), c1) = c1)) | (~big_f(f3(f10(c1), c1), f10(c1))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c1 = c3) | (f10(c1) = c4) | (~big_f(f3(f10(c1), c1), f10(c1))) | (~(f3(f10(c1), c1) = c1)) | (f1(c1, f10(c1)) = f10(c1)) | big_f(c1, f1(c1, f10(c1))))),
% 29.77/19.96 inference(transitivity,[status(thm)],[28897, 28895])).
% 29.77/19.96 tff(28899,plain,
% 29.77/19.96 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((f10(c1) = c4) | (c1 = c3) | (f1(c1, f10(c1)) = f10(c1)) | big_f(c1, f1(c1, f10(c1))) | (~(f3(f10(c1), c1) = c1)) | (~big_f(f3(f10(c1), c1), f10(c1))))),
% 29.77/19.96 inference(quant_inst,[status(thm)],[])).
% 29.77/19.96 tff(28900,plain,
% 29.77/19.96 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c1 = c3) | (f10(c1) = c4) | (~big_f(f3(f10(c1), c1), f10(c1))) | (~(f3(f10(c1), c1) = c1)) | (f1(c1, f10(c1)) = f10(c1)) | big_f(c1, f1(c1, f10(c1)))),
% 29.77/19.96 inference(modus_ponens,[status(thm)],[28899, 28898])).
% 29.77/19.96 tff(28901,plain,
% 29.77/19.96 ((~(f3(f10(c1), c1) = c1)) | (f1(c1, f10(c1)) = f10(c1)) | big_f(c1, f1(c1, f10(c1)))),
% 29.77/19.96 inference(unit_resolution,[status(thm)],[28900, 969, 168, 1046, 28881])).
% 29.77/19.97 tff(28902,plain,
% 29.77/19.97 ($false),
% 29.77/19.97 inference(unit_resolution,[status(thm)],[28901, 28894, 28889, 28865])).
% 29.77/19.97 tff(28903,plain,((f1(c1, c2) = c2) | (c1 = c3) | (f10(c1) = c4) | big_f(c1, c1) | (f10(c1) = c1) | (~(f7(c1) = c1)) | (f6(c1, f10(c1)) = f10(c1)) | big_f(f7(c1), f6(c1, f10(c1))) | (~big_f(c1, f10(c1)))), inference(lemma,lemma(discharge,[]))).
% 29.77/19.97 tff(28904,plain,
% 29.77/19.97 (f1(c1, c2) = c2),
% 29.77/19.97 inference(unit_resolution,[status(thm)],[28903, 168, 28859, 66, 3, 4234, 28853, 28852, 28851])).
% 29.77/19.97 tff(28905,plain,
% 29.77/19.97 (f1(c1, f10(c1)) = f10(c1)),
% 29.77/19.97 inference(transitivity,[status(thm)],[28860, 28904, 5571])).
% 29.77/19.97 tff(28906,plain,
% 29.77/19.97 (big_f(c1, f1(c1, f10(c1))) <=> big_f(c1, f10(c1))),
% 29.77/19.97 inference(monotonicity,[status(thm)],[28905])).
% 29.77/19.97 tff(28907,plain,
% 29.77/19.97 (big_f(c1, f10(c1)) <=> big_f(c1, f1(c1, f10(c1)))),
% 29.77/19.97 inference(symmetry,[status(thm)],[28906])).
% 29.77/19.97 tff(28908,plain,
% 29.77/19.97 (big_f(c1, f1(c1, f10(c1)))),
% 29.77/19.97 inference(modus_ponens,[status(thm)],[28851, 28907])).
% 29.77/19.97 tff(28909,plain,
% 29.77/19.97 (f1(c1, f10(c1)) = f1(c1, c2)),
% 29.77/19.97 inference(monotonicity,[status(thm)],[16])).
% 29.77/19.97 tff(28910,plain,
% 29.77/19.97 (f1(c1, f10(c1)) = f10(c1)),
% 29.77/19.97 inference(transitivity,[status(thm)],[28909, 822, 293])).
% 29.77/19.97 tff(28911,assumption,(~(f1(c1, f10(c1)) = f10(c1))), introduced(assumption)).
% 29.77/19.97 tff(28912,plain,
% 29.77/19.97 ($false),
% 29.77/19.97 inference(unit_resolution,[status(thm)],[28911, 28910])).
% 29.77/19.97 tff(28913,plain,((f1(c1, f10(c1)) = f10(c1)) | (~(f1(c1, c2) = c2)) | (~(f10(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.77/19.97 tff(28914,plain,
% 29.77/19.97 (f1(c1, f10(c1)) = f10(c1)),
% 29.77/19.97 inference(unit_resolution,[status(thm)],[28913, 28904, 15])).
% 29.77/19.97 tff(28915,plain,
% 29.77/19.97 (f1(c1, f10(c1)) = f10(c1)),
% 29.77/19.97 inference(unit_resolution,[status(thm)],[28913, 822, 15])).
% 29.77/19.97 tff(28916,assumption,(f1(c1, f10(c1)) = f10(c1)), introduced(assumption)).
% 29.77/19.97 tff(28917,plain,
% 29.77/19.97 (big_f(c1, f1(c1, f10(c1))) <=> big_f(c1, f10(c1))),
% 29.77/19.97 inference(monotonicity,[status(thm)],[28910])).
% 29.77/19.97 tff(28918,plain,
% 29.77/19.97 (big_f(c1, f10(c1)) <=> big_f(c1, f1(c1, f10(c1)))),
% 29.77/19.97 inference(symmetry,[status(thm)],[28917])).
% 29.77/19.97 tff(28919,plain,
% 29.77/19.97 (big_f(c1, f1(c1, f10(c1)))),
% 29.77/19.97 inference(modus_ponens,[status(thm)],[3023, 28918])).
% 29.77/19.97 tff(28920,plain,
% 29.77/19.97 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (f10(c1) = c4) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1)) | (~big_f(c1, f1(c1, f10(c1)))) | (~(f1(c1, f10(c1)) = f10(c1))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (f10(c1) = c4) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1)) | (~big_f(c1, f1(c1, f10(c1)))) | (~(f1(c1, f10(c1)) = f10(c1))))),
% 29.77/19.97 inference(rewrite,[status(thm)],[])).
% 29.77/19.97 tff(28921,plain,
% 29.77/19.97 (((f10(c1) = c4) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1)) | (c1 = c3) | (~(f1(c1, f10(c1)) = f10(c1))) | (~big_f(c1, f1(c1, f10(c1))))) <=> ((c1 = c3) | (f10(c1) = c4) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1)) | (~big_f(c1, f1(c1, f10(c1)))) | (~(f1(c1, f10(c1)) = f10(c1))))),
% 29.77/19.97 inference(rewrite,[status(thm)],[])).
% 29.77/19.97 tff(28922,plain,
% 29.77/19.97 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f10(c1) = c4) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1)) | (c1 = c3) | (~(f1(c1, f10(c1)) = f10(c1))) | (~big_f(c1, f1(c1, f10(c1)))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (f10(c1) = c4) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1)) | (~big_f(c1, f1(c1, f10(c1)))) | (~(f1(c1, f10(c1)) = f10(c1)))))),
% 29.77/19.97 inference(monotonicity,[status(thm)],[28921])).
% 29.77/19.97 tff(28923,plain,
% 29.77/19.97 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f10(c1) = c4) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1)) | (c1 = c3) | (~(f1(c1, f10(c1)) = f10(c1))) | (~big_f(c1, f1(c1, f10(c1)))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (f10(c1) = c4) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1)) | (~big_f(c1, f1(c1, f10(c1)))) | (~(f1(c1, f10(c1)) = f10(c1))))),
% 29.77/19.97 inference(transitivity,[status(thm)],[28922, 28920])).
% 29.77/19.97 tff(28924,plain,
% 29.77/19.97 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f10(c1) = c4) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1)) | (c1 = c3) | (~(f1(c1, f10(c1)) = f10(c1))) | (~big_f(c1, f1(c1, f10(c1)))))),
% 29.77/19.97 inference(quant_inst,[status(thm)],[])).
% 29.77/19.97 tff(28925,plain,
% 29.77/19.97 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (f10(c1) = c4) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1)) | (~big_f(c1, f1(c1, f10(c1)))) | (~(f1(c1, f10(c1)) = f10(c1)))),
% 29.77/19.97 inference(modus_ponens,[status(thm)],[28924, 28923])).
% 29.77/19.97 tff(28926,plain,
% 29.77/19.97 ((~big_f(c1, f1(c1, f10(c1)))) | (~(f1(c1, f10(c1)) = f10(c1)))),
% 29.77/19.97 inference(unit_resolution,[status(thm)],[28925, 904, 168, 1046, 1062, 1061])).
% 29.77/19.97 tff(28927,plain,
% 29.77/19.97 ($false),
% 29.77/19.97 inference(unit_resolution,[status(thm)],[28926, 28919, 28916])).
% 29.77/19.97 tff(28928,plain,((~(f1(c1, f10(c1)) = f10(c1))) | (c1 = c3) | (f10(c1) = c4) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1)) | (~big_f(c1, f10(c1))) | (~(f1(c1, c2) = c2)) | (~(f10(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.77/19.97 tff(28929,plain,
% 29.77/19.97 (big_f(f3(f10(c1), c1), f10(c1))),
% 29.77/19.97 inference(unit_resolution,[status(thm)],[28928, 1062, 1046, 28915, 168, 3023, 822, 15])).
% 29.77/19.97 tff(28930,plain,
% 29.77/19.97 (f3(f10(c1), c1) = f8(c1)),
% 29.77/19.97 inference(unit_resolution,[status(thm)],[28887, 2662, 4234, 3, 28929, 28853, 28852])).
% 29.77/19.97 tff(28931,plain,
% 29.77/19.97 (f3(f10(c1), c1) = c1),
% 29.77/19.97 inference(transitivity,[status(thm)],[28930, 28874])).
% 29.77/19.97 tff(28932,plain,
% 29.77/19.97 ($false),
% 29.77/19.97 inference(unit_resolution,[status(thm)],[1062, 28931])).
% 29.77/19.97 tff(28933,plain,((f3(f10(c1), c1) = c1) | (~(f7(c1) = c1)) | (f10(c1) = c1) | (f6(c1, f10(c1)) = f10(c1)) | big_f(f7(c1), f6(c1, f10(c1))) | (f10(c1) = c4) | (c1 = c3) | (~big_f(c1, f10(c1))) | (~(f1(c1, c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.77/19.97 tff(28934,plain,
% 29.77/19.97 (f3(f10(c1), c1) = c1),
% 29.77/19.97 inference(unit_resolution,[status(thm)],[28933, 28859, 3, 28853, 28852, 4234, 168, 28851, 28904])).
% 29.77/19.97 tff(28935,plain,
% 29.77/19.97 (big_f(f3(f10(c1), c1), f10(c1)) <=> big_f(c1, f10(c1))),
% 29.77/19.97 inference(monotonicity,[status(thm)],[28934])).
% 29.77/19.97 tff(28936,plain,
% 29.77/19.97 (big_f(c1, f10(c1)) <=> big_f(f3(f10(c1), c1), f10(c1))),
% 29.77/19.97 inference(symmetry,[status(thm)],[28935])).
% 29.77/19.97 tff(28937,plain,
% 29.77/19.97 (big_f(f3(f10(c1), c1), f10(c1))),
% 29.77/19.97 inference(modus_ponens,[status(thm)],[28851, 28936])).
% 29.77/19.97 tff(28938,plain,
% 29.77/19.97 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (f10(c1) = c4) | (~big_f(f3(f10(c1), c1), f10(c1))) | (~(f3(f10(c1), c1) = c1)) | (~big_f(c1, f1(c1, f10(c1)))) | (~(f1(c1, f10(c1)) = f10(c1))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (f10(c1) = c4) | (~big_f(f3(f10(c1), c1), f10(c1))) | (~(f3(f10(c1), c1) = c1)) | (~big_f(c1, f1(c1, f10(c1)))) | (~(f1(c1, f10(c1)) = f10(c1))))),
% 29.77/19.97 inference(rewrite,[status(thm)],[])).
% 29.77/19.97 tff(28939,plain,
% 29.77/19.97 (((f10(c1) = c4) | (c1 = c3) | (~(f3(f10(c1), c1) = c1)) | (~big_f(f3(f10(c1), c1), f10(c1))) | (~(f1(c1, f10(c1)) = f10(c1))) | (~big_f(c1, f1(c1, f10(c1))))) <=> ((c1 = c3) | (f10(c1) = c4) | (~big_f(f3(f10(c1), c1), f10(c1))) | (~(f3(f10(c1), c1) = c1)) | (~big_f(c1, f1(c1, f10(c1)))) | (~(f1(c1, f10(c1)) = f10(c1))))),
% 29.77/19.97 inference(rewrite,[status(thm)],[])).
% 29.77/19.97 tff(28940,plain,
% 29.77/19.97 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f10(c1) = c4) | (c1 = c3) | (~(f3(f10(c1), c1) = c1)) | (~big_f(f3(f10(c1), c1), f10(c1))) | (~(f1(c1, f10(c1)) = f10(c1))) | (~big_f(c1, f1(c1, f10(c1)))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (f10(c1) = c4) | (~big_f(f3(f10(c1), c1), f10(c1))) | (~(f3(f10(c1), c1) = c1)) | (~big_f(c1, f1(c1, f10(c1)))) | (~(f1(c1, f10(c1)) = f10(c1)))))),
% 29.77/19.97 inference(monotonicity,[status(thm)],[28939])).
% 29.77/19.97 tff(28941,plain,
% 29.77/19.97 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f10(c1) = c4) | (c1 = c3) | (~(f3(f10(c1), c1) = c1)) | (~big_f(f3(f10(c1), c1), f10(c1))) | (~(f1(c1, f10(c1)) = f10(c1))) | (~big_f(c1, f1(c1, f10(c1)))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (f10(c1) = c4) | (~big_f(f3(f10(c1), c1), f10(c1))) | (~(f3(f10(c1), c1) = c1)) | (~big_f(c1, f1(c1, f10(c1)))) | (~(f1(c1, f10(c1)) = f10(c1))))),
% 29.77/19.97 inference(transitivity,[status(thm)],[28940, 28938])).
% 29.77/19.97 tff(28942,plain,
% 29.77/19.97 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f10(c1) = c4) | (c1 = c3) | (~(f3(f10(c1), c1) = c1)) | (~big_f(f3(f10(c1), c1), f10(c1))) | (~(f1(c1, f10(c1)) = f10(c1))) | (~big_f(c1, f1(c1, f10(c1)))))),
% 29.77/19.97 inference(quant_inst,[status(thm)],[])).
% 29.77/19.97 tff(28943,plain,
% 29.77/19.97 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (f10(c1) = c4) | (~big_f(f3(f10(c1), c1), f10(c1))) | (~(f3(f10(c1), c1) = c1)) | (~big_f(c1, f1(c1, f10(c1)))) | (~(f1(c1, f10(c1)) = f10(c1)))),
% 29.77/19.97 inference(modus_ponens,[status(thm)],[28942, 28941])).
% 29.77/19.97 tff(28944,plain,
% 29.77/19.97 (~big_f(c1, f1(c1, f10(c1)))),
% 29.77/19.97 inference(unit_resolution,[status(thm)],[28943, 933, 168, 28859, 28934, 28937, 28914])).
% 29.77/19.97 tff(28945,plain,
% 29.77/19.97 ($false),
% 29.77/19.97 inference(unit_resolution,[status(thm)],[28944, 28908])).
% 29.77/19.97 tff(28946,plain,((c1 = c3) | (f10(c1) = c1) | (f6(c1, f10(c1)) = f10(c1)) | big_f(f7(c1), f6(c1, f10(c1))) | (~(f7(c1) = c1)) | big_f(c1, c1) | big_f(c2, c2) | (~big_f(c1, c2)) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.77/19.97 tff(28947,plain,
% 29.77/19.97 ((c1 = c3) | (f10(c1) = c1) | (f6(c1, f10(c1)) = f10(c1)) | big_f(f7(c1), f6(c1, f10(c1))) | big_f(c1, c1) | big_f(c2, c2) | (~big_f(c1, c2)) | (~(f4(c4) = c2))),
% 29.77/19.97 inference(unit_resolution,[status(thm)],[28946, 25791])).
% 29.77/19.97 tff(28948,plain,
% 29.77/19.97 (c1 = c3),
% 29.77/19.97 inference(unit_resolution,[status(thm)],[28947, 28850, 79, 28845, 66, 121, 2865, 28830])).
% 29.77/19.97 tff(28949,plain,
% 29.77/19.97 (c3 = c1),
% 29.77/19.97 inference(symmetry,[status(thm)],[28948])).
% 29.77/19.97 tff(28950,plain,
% 29.77/19.97 ((c2 = c3) <=> (c2 = c1)),
% 29.77/19.97 inference(monotonicity,[status(thm)],[28949])).
% 29.77/19.97 tff(28951,plain,
% 29.77/19.97 ((c2 = c1) <=> (c2 = c3)),
% 29.77/19.97 inference(symmetry,[status(thm)],[28950])).
% 29.77/19.97 tff(28952,plain,
% 29.77/19.97 ((c2 = c1) <=> (f7(f7(c2)) = c3)),
% 29.77/19.97 inference(transitivity,[status(thm)],[28951, 11448])).
% 29.77/19.97 tff(28953,plain,
% 29.77/19.97 ((~(c2 = c1)) <=> (~(f7(f7(c2)) = c3))),
% 29.77/19.97 inference(monotonicity,[status(thm)],[28952])).
% 29.77/19.97 tff(28954,plain,
% 29.77/19.97 (~(f7(f7(c2)) = c3)),
% 29.77/19.97 inference(modus_ponens,[status(thm)],[75, 28953])).
% 29.77/19.97 tff(28955,plain,
% 29.77/19.97 ((~(c2 = c1)) <=> (~(c2 = c3))),
% 29.77/19.97 inference(monotonicity,[status(thm)],[28951])).
% 29.77/19.97 tff(28956,plain,
% 29.77/19.97 (~(c2 = c3)),
% 29.77/19.97 inference(modus_ponens,[status(thm)],[75, 28955])).
% 29.77/19.97 tff(28957,plain,
% 29.77/19.97 (~big_f(f4(c4), c4)),
% 29.77/19.97 inference(unit_resolution,[status(thm)],[476, 431, 121, 79])).
% 29.77/19.97 tff(28958,plain,
% 29.77/19.97 (f1(f7(f7(c2)), c1) = c1),
% 29.77/19.97 inference(unit_resolution,[status(thm)],[5433, 28957, 77, 121, 378])).
% 29.77/19.97 tff(28959,plain,
% 29.77/19.97 (f1(c2, c1) = c1),
% 29.77/19.97 inference(modus_ponens,[status(thm)],[28958, 22862])).
% 29.77/19.97 tff(28960,plain,
% 29.77/19.97 (~big_f(c2, c4)),
% 29.77/19.97 inference(unit_resolution,[status(thm)],[6521, 28957, 79])).
% 29.77/19.97 tff(28961,plain,
% 29.77/19.97 (big_f(c2, f1(c2, c1))),
% 29.77/19.97 inference(unit_resolution,[status(thm)],[10105, 28960, 2602, 348, 377])).
% 29.77/19.97 tff(28962,plain,
% 29.77/19.97 (~(f1(c2, c1) = c1)),
% 29.77/19.97 inference(unit_resolution,[status(thm)],[11494, 28961, 121, 79, 377, 431])).
% 29.77/19.97 tff(28963,plain,
% 29.77/19.97 ($false),
% 29.77/19.97 inference(unit_resolution,[status(thm)],[28962, 28959])).
% 29.77/19.97 tff(28964,plain,((~(c4 = c2)) | (~(f7(c2) = c2)) | big_f(c2, c2) | (~(f4(c4) = c2)) | (c2 = c3) | (~big_f(c2, c1)) | (f7(f7(c2)) = c3)), inference(lemma,lemma(discharge,[]))).
% 29.77/19.97 tff(28965,plain,
% 29.77/19.97 (~(c4 = c2)),
% 29.77/19.97 inference(unit_resolution,[status(thm)],[28964, 28956, 121, 79, 77, 25952, 28954])).
% 29.77/19.97 tff(28966,plain,
% 29.77/19.97 (~(c2 = c4)),
% 29.77/19.97 inference(modus_ponens,[status(thm)],[28965, 797])).
% 29.77/19.97 tff(28967,plain,
% 29.77/19.97 (c1 = f8(c1)),
% 29.77/19.97 inference(unit_resolution,[status(thm)],[27080, 2662, 25791, 3, 28851, 5714, 114])).
% 29.77/19.97 tff(28968,plain,
% 29.77/19.97 (f8(c1) = c1),
% 29.77/19.97 inference(symmetry,[status(thm)],[28967])).
% 29.77/19.97 tff(28969,plain,
% 29.77/19.97 ((f3(c2, c1) = f8(c1)) <=> (f3(c2, c1) = c1)),
% 29.77/19.97 inference(monotonicity,[status(thm)],[28968])).
% 29.77/19.97 tff(28970,plain,
% 29.77/19.97 ((f3(c2, c1) = c1) <=> (f3(c2, c1) = f8(c1))),
% 29.77/19.97 inference(symmetry,[status(thm)],[28969])).
% 29.77/19.97 tff(28971,plain,
% 29.77/19.97 ((~(f3(c2, c1) = c1)) <=> (~(f3(c2, c1) = f8(c1)))),
% 29.77/19.97 inference(monotonicity,[status(thm)],[28970])).
% 29.77/19.97 tff(28972,plain,
% 29.77/19.97 (big_f(c2, f1(c2, c1)) <=> big_f(c2, c1)),
% 29.77/19.97 inference(monotonicity,[status(thm)],[11485])).
% 29.77/19.97 tff(28973,plain,
% 29.77/19.97 (big_f(c2, c1) <=> big_f(c2, f1(c2, c1))),
% 29.77/19.97 inference(symmetry,[status(thm)],[28972])).
% 29.77/19.97 tff(28974,plain,
% 29.77/19.97 (big_f(c2, f1(c2, c1))),
% 29.77/19.97 inference(modus_ponens,[status(thm)],[348, 28973])).
% 29.77/19.97 tff(28975,plain,
% 29.77/19.97 (f3(c2, c1) = c1),
% 29.77/19.97 inference(unit_resolution,[status(thm)],[12221, 904, 873, 377, 11485, 11484, 12175])).
% 29.77/19.97 tff(28976,plain,
% 29.77/19.97 (big_f(f3(c2, c1), c2) <=> big_f(c1, c2)),
% 29.77/19.97 inference(monotonicity,[status(thm)],[28975])).
% 29.77/19.97 tff(28977,plain,
% 29.77/19.97 (big_f(c1, c2) <=> big_f(f3(c2, c1), c2)),
% 29.77/19.97 inference(symmetry,[status(thm)],[28976])).
% 29.77/19.97 tff(28978,plain,
% 29.77/19.97 (big_f(f3(c2, c1), c2)),
% 29.77/19.97 inference(modus_ponens,[status(thm)],[2865, 28977])).
% 29.77/19.97 tff(28979,plain,
% 29.77/19.97 ($false),
% 29.77/19.97 inference(unit_resolution,[status(thm)],[12175, 28978])).
% 29.77/19.97 tff(28980,plain,(big_f(f3(c2, c1), c2) | (~big_f(c1, c2)) | (c2 = c4) | (c2 = c3) | (~(f1(c2, c1) = c1)) | (~big_f(c2, f1(c2, c1)))), inference(lemma,lemma(discharge,[]))).
% 29.77/19.97 tff(28981,plain,
% 29.77/19.97 (big_f(f3(c2, c1), c2)),
% 29.77/19.97 inference(unit_resolution,[status(thm)],[28980, 11485, 873, 377, 2865, 28974])).
% 29.77/19.97 tff(28982,plain,
% 29.77/19.97 ((c2 = c3) | (c2 = c4) | (~big_f(c2, f1(c2, c1))) | (~(f1(c2, c1) = c1)) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2))),
% 29.77/19.97 inference(unit_resolution,[status(thm)],[13428, 933])).
% 29.77/19.97 tff(28983,plain,
% 29.77/19.97 (~(f3(c2, c1) = c1)),
% 29.77/19.97 inference(unit_resolution,[status(thm)],[28982, 28981, 11485, 377, 873, 28974])).
% 29.77/19.97 tff(28984,plain,
% 29.77/19.97 (~(f3(c2, c1) = f8(c1))),
% 29.77/19.97 inference(modus_ponens,[status(thm)],[28983, 28971])).
% 29.77/19.97 tff(28985,plain,
% 29.77/19.97 (big_f(f3(c2, c1), f10(c1)) <=> big_f(f3(c2, c1), c2)),
% 29.77/19.97 inference(monotonicity,[status(thm)],[15])).
% 29.77/19.97 tff(28986,plain,
% 29.77/19.97 (big_f(f3(c2, c1), c2) <=> big_f(f3(c2, c1), f10(c1))),
% 29.77/19.97 inference(symmetry,[status(thm)],[28985])).
% 29.77/19.97 tff(28987,plain,
% 29.77/19.97 (big_f(f3(c2, c1), f10(c1))),
% 29.77/19.97 inference(modus_ponens,[status(thm)],[28981, 28986])).
% 29.77/19.97 tff(28988,plain,
% 29.77/19.97 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2) | (f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c1) = c1) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2) | (f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1))))),
% 29.77/19.97 inference(rewrite,[status(thm)],[])).
% 29.77/19.97 tff(28989,plain,
% 29.77/19.97 (((f10(c1) = c1) | (f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1))) | (~(f7(c1) = c1)) | (f6(c1, c2) = c2) | big_f(f7(c1), f6(c1, c2))) <=> ((f10(c1) = c1) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2) | (f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1))))),
% 29.77/19.97 inference(rewrite,[status(thm)],[])).
% 29.77/19.97 tff(28990,plain,
% 29.77/19.97 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1))) | (~(f7(c1) = c1)) | (f6(c1, c2) = c2) | big_f(f7(c1), f6(c1, c2)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2) | (f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1)))))),
% 29.77/19.97 inference(monotonicity,[status(thm)],[28989])).
% 29.77/19.97 tff(28991,plain,
% 29.77/19.97 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1))) | (~(f7(c1) = c1)) | (f6(c1, c2) = c2) | big_f(f7(c1), f6(c1, c2)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c1) = c1) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2) | (f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1))))),
% 29.77/19.97 inference(transitivity,[status(thm)],[28990, 28988])).
% 29.77/19.97 tff(28992,plain,
% 29.77/19.97 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1))) | (~(f7(c1) = c1)) | (f6(c1, c2) = c2) | big_f(f7(c1), f6(c1, c2)))),
% 29.77/19.97 inference(quant_inst,[status(thm)],[])).
% 29.77/19.97 tff(28993,plain,
% 29.77/19.97 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c1) = c1) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2) | (f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1)))),
% 29.77/19.97 inference(modus_ponens,[status(thm)],[28992, 28991])).
% 29.77/19.97 tff(28994,plain,
% 29.77/19.97 ((f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1)))),
% 29.77/19.97 inference(unit_resolution,[status(thm)],[28993, 2662, 25791, 3, 5714, 114])).
% 29.77/19.97 tff(28995,plain,
% 29.77/19.97 ($false),
% 29.77/19.97 inference(unit_resolution,[status(thm)],[28994, 28987, 28984])).
% 29.77/19.97 tff(28996,plain,((~(f1(c2, c1) = c1)) | (f10(c1) = c1) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2) | (c2 = c3) | (c2 = c4) | (~big_f(c1, c2)) | (~big_f(c2, c1))), inference(lemma,lemma(discharge,[]))).
% 29.77/19.97 tff(28997,plain,
% 29.77/19.97 (~(f1(c2, c1) = c1)),
% 29.77/19.97 inference(unit_resolution,[status(thm)],[28996, 25798, 28830, 114, 28956, 28966, 2865, 25952])).
% 29.77/19.97 tff(28998,plain,
% 29.77/19.97 (f1(c2, c1) = c2),
% 29.77/19.97 inference(unit_resolution,[status(thm)],[10113, 28997])).
% 29.77/19.97 tff(28999,plain,
% 29.77/19.97 (big_f(c2, f1(c2, c1)) <=> big_f(c2, c2)),
% 29.77/19.97 inference(monotonicity,[status(thm)],[28998])).
% 29.77/19.97 tff(29000,plain,
% 29.77/19.97 (big_f(c2, c2) <=> big_f(c2, f1(c2, c1))),
% 29.77/19.97 inference(symmetry,[status(thm)],[28999])).
% 29.77/19.97 tff(29001,plain,
% 29.77/19.97 ((~big_f(c2, c2)) <=> (~big_f(c2, f1(c2, c1)))),
% 29.77/19.97 inference(monotonicity,[status(thm)],[29000])).
% 29.77/19.97 tff(29002,plain,
% 29.77/19.97 (~big_f(c2, f1(c2, c1))),
% 29.77/19.97 inference(modus_ponens,[status(thm)],[121, 29001])).
% 29.77/19.97 tff(29003,assumption,(~(f3(c2, c1) = c1)), introduced(assumption)).
% 29.77/19.97 tff(29004,plain,
% 29.77/19.97 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c2 = c3) | (c2 = c4) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (c2 = c3) | (c2 = c4) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2))),
% 29.77/19.97 inference(rewrite,[status(thm)],[])).
% 29.77/19.97 tff(29005,plain,
% 29.77/19.97 (((c2 = c4) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2) | (c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1))) <=> ((c2 = c3) | (c2 = c4) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2))),
% 29.77/19.97 inference(rewrite,[status(thm)],[])).
% 29.77/19.97 tff(29006,plain,
% 29.77/19.97 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c2 = c4) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2) | (c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c2 = c3) | (c2 = c4) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2)))),
% 29.77/19.97 inference(monotonicity,[status(thm)],[29005])).
% 29.77/19.97 tff(29007,plain,
% 29.77/19.97 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c2 = c4) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2) | (c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (c2 = c3) | (c2 = c4) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2))),
% 29.77/19.97 inference(transitivity,[status(thm)],[29006, 29004])).
% 29.77/19.97 tff(29008,plain,
% 29.77/19.97 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c2 = c4) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2) | (c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)))),
% 29.77/19.97 inference(quant_inst,[status(thm)],[])).
% 29.77/19.97 tff(29009,plain,
% 29.77/19.97 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (c2 = c3) | (c2 = c4) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2)),
% 29.77/19.97 inference(modus_ponens,[status(thm)],[29008, 29007])).
% 29.77/19.97 tff(29010,plain,
% 29.77/19.97 ($false),
% 29.77/19.97 inference(unit_resolution,[status(thm)],[29009, 1014, 873, 377, 12187, 10090, 29003, 12175])).
% 29.77/19.97 tff(29011,plain,((f3(c2, c1) = c1) | (c2 = c4) | (c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | big_f(f3(c2, c1), c2)), inference(lemma,lemma(discharge,[]))).
% 29.77/19.97 tff(29012,plain,
% 29.77/19.97 (f3(c2, c1) = c1),
% 29.77/19.97 inference(unit_resolution,[status(thm)],[29011, 12175, 377, 12187, 10090, 873])).
% 29.77/19.97 tff(29013,plain,
% 29.77/19.97 (big_f(f3(c2, c1), c2) <=> big_f(c1, c2)),
% 29.77/19.97 inference(monotonicity,[status(thm)],[29012])).
% 29.77/19.97 tff(29014,plain,
% 29.77/19.97 (big_f(c1, c2) <=> big_f(f3(c2, c1), c2)),
% 29.77/19.97 inference(symmetry,[status(thm)],[29013])).
% 29.77/19.97 tff(29015,plain,
% 29.77/19.97 (big_f(f3(c2, c1), c2)),
% 29.77/19.97 inference(modus_ponens,[status(thm)],[2865, 29014])).
% 29.77/19.97 tff(29016,plain,
% 29.77/19.97 ($false),
% 29.77/19.97 inference(unit_resolution,[status(thm)],[12175, 29015])).
% 29.77/19.97 tff(29017,plain,(big_f(f3(c2, c1), c2) | (~big_f(c1, c2)) | (c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | (c2 = c4)), inference(lemma,lemma(discharge,[]))).
% 29.77/19.97 tff(29018,plain,
% 29.77/19.97 (big_f(f3(c2, c1), c2)),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[29017, 28956, 2865, 28997, 29002, 28966])).
% 29.77/19.98 tff(29019,plain,
% 29.77/19.98 (~(f3(c2, c1) = c1)),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[13416, 969, 28966, 28956, 28997, 29002, 29018])).
% 29.77/19.98 tff(29020,plain,
% 29.77/19.98 (~(f3(c2, c1) = f8(c1))),
% 29.77/19.98 inference(modus_ponens,[status(thm)],[29019, 28839])).
% 29.77/19.98 tff(29021,plain,
% 29.77/19.98 (big_f(f3(c2, c1), f10(c1)) <=> big_f(f3(c2, c1), c2)),
% 29.77/19.98 inference(monotonicity,[status(thm)],[28831])).
% 29.77/19.98 tff(29022,plain,
% 29.77/19.98 (big_f(f3(c2, c1), c2) <=> big_f(f3(c2, c1), f10(c1))),
% 29.77/19.98 inference(symmetry,[status(thm)],[29021])).
% 29.77/19.98 tff(29023,plain,
% 29.77/19.98 (big_f(f3(c2, c1), f10(c1))),
% 29.77/19.98 inference(modus_ponens,[status(thm)],[29018, 29022])).
% 29.77/19.98 tff(29024,plain,
% 29.77/19.98 ((f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1)))),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[28993, 2662, 25791, 28830, 25798, 114])).
% 29.77/19.98 tff(29025,plain,
% 29.77/19.98 ($false),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[29024, 29023, 29020])).
% 29.77/19.98 tff(29026,plain,((f6(c1, c2) = c2) | (~big_f(c1, c2)) | big_f(c2, c2) | (~(f4(c4) = c2)) | (~(f7(c2) = c2)) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 29.77/19.98 tff(29027,plain,
% 29.77/19.98 (f6(c1, c2) = c2),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[29026, 28829, 121, 79, 77, 66])).
% 29.77/19.98 tff(29028,plain,
% 29.77/19.98 ((~(c2 = c3)) <=> (~(f7(f7(c2)) = c3))),
% 29.77/19.98 inference(monotonicity,[status(thm)],[11448])).
% 29.77/19.98 tff(29029,plain,
% 29.77/19.98 (~(f7(f7(c2)) = c3)),
% 29.77/19.98 inference(modus_ponens,[status(thm)],[377, 29028])).
% 29.77/19.98 tff(29030,plain,
% 29.77/19.98 (~(c4 = c2)),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[28964, 29029, 121, 79, 77, 348, 377])).
% 29.77/19.98 tff(29031,plain,
% 29.77/19.98 (c4 = c1),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[461, 29030])).
% 29.77/19.98 tff(29032,plain,
% 29.77/19.98 ((c2 = c4) <=> (c2 = c1)),
% 29.77/19.98 inference(monotonicity,[status(thm)],[29031])).
% 29.77/19.98 tff(29033,plain,
% 29.77/19.98 ((c2 = c1) <=> (c2 = c4)),
% 29.77/19.98 inference(symmetry,[status(thm)],[29032])).
% 29.77/19.98 tff(29034,plain,
% 29.77/19.98 ((~(c2 = c1)) <=> (~(c2 = c4))),
% 29.77/19.98 inference(monotonicity,[status(thm)],[29033])).
% 29.77/19.98 tff(29035,plain,
% 29.77/19.98 (~(c2 = c4)),
% 29.77/19.98 inference(modus_ponens,[status(thm)],[75, 29034])).
% 29.77/19.98 tff(29036,plain,
% 29.77/19.98 (big_f(c2, f1(c2, c1))),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[29017, 12187, 2865, 377, 12175, 873])).
% 29.77/19.98 tff(29037,plain,
% 29.77/19.98 (big_f(f10(c1), f1(f10(c1), c1))),
% 29.77/19.98 inference(modus_ponens,[status(thm)],[29036, 8900])).
% 29.77/19.98 tff(29038,plain,
% 29.77/19.98 (f1(f10(c1), c1) = f10(c1)),
% 29.77/19.98 inference(transitivity,[status(thm)],[8887, 12189, 293])).
% 29.77/19.98 tff(29039,plain,
% 29.77/19.98 (big_f(f10(c1), f1(f10(c1), c1)) <=> big_f(f10(c1), f10(c1))),
% 29.77/19.98 inference(monotonicity,[status(thm)],[29038])).
% 29.77/19.98 tff(29040,plain,
% 29.77/19.98 (big_f(f10(c1), f10(c1)) <=> big_f(f10(c1), f1(f10(c1), c1))),
% 29.77/19.98 inference(symmetry,[status(thm)],[29039])).
% 29.77/19.98 tff(29041,plain,
% 29.77/19.98 ((~big_f(f10(c1), f10(c1))) <=> (~big_f(f10(c1), f1(f10(c1), c1)))),
% 29.77/19.98 inference(monotonicity,[status(thm)],[29040])).
% 29.77/19.98 tff(29042,plain,
% 29.77/19.98 (~big_f(f10(c1), f1(f10(c1), c1))),
% 29.77/19.98 inference(modus_ponens,[status(thm)],[26503, 29041])).
% 29.77/19.98 tff(29043,assumption,(big_f(f10(c1), f1(f10(c1), c1))), introduced(assumption)).
% 29.77/19.98 tff(29044,plain,
% 29.77/19.98 ($false),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[29043, 29042])).
% 29.77/19.98 tff(29045,plain,((~(f1(c2, c1) = c2)) | (~big_f(f10(c1), f1(f10(c1), c1))) | big_f(f10(c1), f10(c1)) | (~(f10(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.77/19.98 tff(29046,plain,
% 29.77/19.98 (~big_f(f10(c1), f1(f10(c1), c1))),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[29045, 12188, 16, 26503])).
% 29.77/19.98 tff(29047,plain,
% 29.77/19.98 ($false),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[29046, 29037])).
% 29.77/19.98 tff(29048,plain,((f1(c2, c1) = c1) | (~(f10(c1) = c2)) | big_f(f10(c1), f10(c1)) | (~big_f(c1, c2)) | (c2 = c3) | big_f(f3(c2, c1), c2) | (c2 = c4)), inference(lemma,lemma(discharge,[]))).
% 29.77/19.98 tff(29049,plain,
% 29.77/19.98 (f1(c2, c1) = c1),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[29048, 12175, 26503, 2865, 377, 16, 873])).
% 29.77/19.98 tff(29050,plain,
% 29.77/19.98 (big_f(c2, f1(c2, c1)) <=> big_f(c2, c1)),
% 29.77/19.98 inference(monotonicity,[status(thm)],[29049])).
% 29.77/19.98 tff(29051,plain,
% 29.77/19.98 (big_f(c2, c1) <=> big_f(c2, f1(c2, c1))),
% 29.77/19.98 inference(symmetry,[status(thm)],[29050])).
% 29.77/19.98 tff(29052,plain,
% 29.77/19.98 (big_f(c2, f1(c2, c1))),
% 29.77/19.98 inference(modus_ponens,[status(thm)],[348, 29051])).
% 29.77/19.98 tff(29053,plain,
% 29.77/19.98 (~big_f(c2, f1(c2, c1))),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[28980, 29049, 873, 377, 2865, 12175])).
% 29.77/19.98 tff(29054,plain,
% 29.77/19.98 ($false),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[29053, 29052])).
% 29.77/19.98 tff(29055,plain,(big_f(f3(c2, c1), c2) | (~big_f(c2, c1)) | (c2 = c4) | (c2 = c3) | (~big_f(c1, c2)) | big_f(f10(c1), f10(c1)) | (~(f10(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.77/19.98 tff(29056,plain,
% 29.77/19.98 (big_f(f3(c2, c1), c2)),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[29055, 29035, 348, 377, 2865, 26299, 15])).
% 29.77/19.98 tff(29057,plain,
% 29.77/19.98 (c1 = f8(c1)),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[27178, 2730, 25791, 3, 28851, 25865, 36])).
% 29.77/19.98 tff(29058,plain,
% 29.77/19.98 (f8(c1) = c1),
% 29.77/19.98 inference(symmetry,[status(thm)],[29057])).
% 29.77/19.98 tff(29059,plain,
% 29.77/19.98 ((f3(c2, c1) = f8(c1)) <=> (f3(c2, c1) = c1)),
% 29.77/19.98 inference(monotonicity,[status(thm)],[29058])).
% 29.77/19.98 tff(29060,plain,
% 29.77/19.98 (big_f(f3(c2, c1), f10(c1))),
% 29.77/19.98 inference(modus_ponens,[status(thm)],[29056, 28986])).
% 29.77/19.98 tff(29061,plain,
% 29.77/19.98 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)) | (f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)) | (f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1))))),
% 29.77/19.98 inference(rewrite,[status(thm)],[])).
% 29.77/19.98 tff(29062,plain,
% 29.77/19.98 (((f10(c1) = c1) | (f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1))) | (~(f7(c1) = c1)) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2)))) <=> ((f10(c1) = c1) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)) | (f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1))))),
% 29.77/19.98 inference(rewrite,[status(thm)],[])).
% 29.77/19.98 tff(29063,plain,
% 29.77/19.98 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1))) | (~(f7(c1) = c1)) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)) | (f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1)))))),
% 29.77/19.98 inference(monotonicity,[status(thm)],[29062])).
% 29.77/19.98 tff(29064,plain,
% 29.77/19.98 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1))) | (~(f7(c1) = c1)) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)) | (f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1))))),
% 29.77/19.98 inference(transitivity,[status(thm)],[29063, 29061])).
% 29.77/19.98 tff(29065,plain,
% 29.77/19.98 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1))) | (~(f7(c1) = c1)) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2))))),
% 29.77/19.98 inference(quant_inst,[status(thm)],[])).
% 29.77/19.98 tff(29066,plain,
% 29.77/19.98 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)) | (f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1)))),
% 29.77/19.98 inference(modus_ponens,[status(thm)],[29065, 29064])).
% 29.77/19.98 tff(29067,plain,
% 29.77/19.98 ((f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1)))),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[29066, 2730, 25791, 3, 25865, 36])).
% 29.77/19.98 tff(29068,plain,
% 29.77/19.98 (f3(c2, c1) = f8(c1)),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[29067, 29060])).
% 29.77/19.98 tff(29069,plain,
% 29.77/19.98 (f3(c2, c1) = c1),
% 29.77/19.98 inference(modus_ponens,[status(thm)],[29068, 29059])).
% 29.77/19.98 tff(29070,plain,
% 29.77/19.98 (big_f(c2, f1(c2, c1)) <=> big_f(c2, c2)),
% 29.77/19.98 inference(monotonicity,[status(thm)],[12188])).
% 29.77/19.98 tff(29071,plain,
% 29.77/19.98 (big_f(c2, c2) <=> big_f(c2, f1(c2, c1))),
% 29.77/19.98 inference(symmetry,[status(thm)],[29070])).
% 29.77/19.98 tff(29072,plain,
% 29.77/19.98 ((~big_f(c2, c2)) <=> (~big_f(c2, f1(c2, c1)))),
% 29.77/19.98 inference(monotonicity,[status(thm)],[29071])).
% 29.77/19.98 tff(29073,plain,
% 29.77/19.98 (~big_f(c2, f1(c2, c1))),
% 29.77/19.98 inference(modus_ponens,[status(thm)],[121, 29072])).
% 29.77/19.98 tff(29074,plain,
% 29.77/19.98 ($false),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[13416, 969, 873, 377, 12187, 29073, 13405, 13404])).
% 29.77/19.98 tff(29075,plain,((f1(c2, c1) = c1) | (c2 = c4) | (c2 = c3) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 29.77/19.98 tff(29076,plain,
% 29.77/19.98 (f1(c2, c1) = c1),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[29075, 29035, 377, 29069, 29056, 121])).
% 29.77/19.98 tff(29077,plain,
% 29.77/19.98 (big_f(c2, f1(c2, c1)) <=> big_f(c2, c1)),
% 29.77/19.98 inference(monotonicity,[status(thm)],[29076])).
% 29.77/19.98 tff(29078,plain,
% 29.77/19.98 (big_f(c2, c1) <=> big_f(c2, f1(c2, c1))),
% 29.77/19.98 inference(symmetry,[status(thm)],[29077])).
% 29.77/19.98 tff(29079,plain,
% 29.77/19.98 (big_f(c2, f1(c2, c1))),
% 29.77/19.98 inference(modus_ponens,[status(thm)],[348, 29078])).
% 29.77/19.98 tff(29080,plain,
% 29.77/19.98 (~big_f(c2, f1(c2, c1))),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[28982, 29076, 29056, 377, 29035, 29069])).
% 29.77/19.98 tff(29081,plain,
% 29.77/19.98 ($false),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[29080, 29079])).
% 29.77/19.98 tff(29082,plain,((c2 = c3) | (~big_f(c2, c1)) | big_f(c2, c2) | (f10(c1) = c1) | (~(f6(c1, c2) = c2)) | (~big_f(c1, c2)) | (~(f4(c4) = c2)) | (~(f7(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.77/19.98 tff(29083,plain,
% 29.77/19.98 (c2 = c3),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[29082, 121, 25952, 28830, 29027, 28829, 79, 77])).
% 29.77/19.98 tff(29084,plain,
% 29.77/19.98 (c3 = c2),
% 29.77/19.98 inference(symmetry,[status(thm)],[29083])).
% 29.77/19.98 tff(29085,plain,
% 29.77/19.98 ((c1 = c3) <=> (c1 = c2)),
% 29.77/19.98 inference(monotonicity,[status(thm)],[29084])).
% 29.77/19.98 tff(29086,plain,
% 29.77/19.98 ((c1 = c3) <=> (c2 = c1)),
% 29.77/19.98 inference(transitivity,[status(thm)],[29085, 1])).
% 29.77/19.98 tff(29087,plain,
% 29.77/19.98 ((c2 = c1) <=> (c1 = c3)),
% 29.77/19.98 inference(symmetry,[status(thm)],[29086])).
% 29.77/19.98 tff(29088,plain,
% 29.77/19.98 ((~(c2 = c1)) <=> (~(c1 = c3))),
% 29.77/19.98 inference(monotonicity,[status(thm)],[29087])).
% 29.77/19.98 tff(29089,plain,
% 29.77/19.98 (~(c1 = c3)),
% 29.77/19.98 inference(modus_ponens,[status(thm)],[75, 29088])).
% 29.77/19.98 tff(29090,plain,
% 29.77/19.98 (~(c4 = c2)),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[13490, 29089, 79, 121, 28829, 66])).
% 29.77/19.98 tff(29091,plain,
% 29.77/19.98 (c4 = c1),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[461, 29090])).
% 29.77/19.98 tff(29092,plain,
% 29.77/19.98 ((c2 = c4) <=> (c2 = c1)),
% 29.77/19.98 inference(monotonicity,[status(thm)],[29091])).
% 29.77/19.98 tff(29093,plain,
% 29.77/19.98 ((c2 = c1) <=> (c2 = c4)),
% 29.77/19.98 inference(symmetry,[status(thm)],[29092])).
% 29.77/19.98 tff(29094,plain,
% 29.77/19.98 ((~(c2 = c1)) <=> (~(c2 = c4))),
% 29.77/19.98 inference(monotonicity,[status(thm)],[29093])).
% 29.77/19.98 tff(29095,plain,
% 29.77/19.98 (~(c2 = c4)),
% 29.77/19.98 inference(modus_ponens,[status(thm)],[75, 29094])).
% 29.77/19.98 tff(29096,plain,
% 29.77/19.98 ($false),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[13922, 904, 168, 873, 822, 13536, 29003, 12175])).
% 29.77/19.98 tff(29097,plain,((~(f1(c1, c2) = c2)) | (c1 = c3) | (c2 = c4) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2) | (~big_f(c1, c2))), inference(lemma,lemma(discharge,[]))).
% 29.77/19.98 tff(29098,plain,
% 29.77/19.98 (~(f1(c1, c2) = c2)),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[29097, 29003, 873, 168, 12175, 2865])).
% 29.77/19.98 tff(29099,plain,
% 29.77/19.98 (f1(c1, c2) = c1),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[841, 29098])).
% 29.77/19.98 tff(29100,plain,
% 29.77/19.98 (big_f(c1, f1(c1, c2)) <=> big_f(c1, c1)),
% 29.77/19.98 inference(monotonicity,[status(thm)],[29099])).
% 29.77/19.98 tff(29101,plain,
% 29.77/19.98 (big_f(c1, c1) <=> big_f(c1, f1(c1, c2))),
% 29.77/19.98 inference(symmetry,[status(thm)],[29100])).
% 29.77/19.98 tff(29102,plain,
% 29.77/19.98 ((~big_f(c1, c1)) <=> (~big_f(c1, f1(c1, c2)))),
% 29.77/19.98 inference(monotonicity,[status(thm)],[29101])).
% 29.77/19.98 tff(29103,plain,
% 29.77/19.98 (~big_f(c1, f1(c1, c2))),
% 29.77/19.98 inference(modus_ponens,[status(thm)],[66, 29102])).
% 29.77/19.98 tff(29104,plain,
% 29.77/19.98 ($false),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[13514, 1014, 168, 873, 29098, 29103, 29003, 12175])).
% 29.77/19.98 tff(29105,plain,((f3(c2, c1) = c1) | (c1 = c3) | (c2 = c4) | big_f(f3(c2, c1), c2) | big_f(c1, c1) | (~big_f(c1, c2))), inference(lemma,lemma(discharge,[]))).
% 29.77/19.98 tff(29106,plain,
% 29.77/19.98 (f3(c2, c1) = c1),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[29105, 12175, 873, 168, 66, 2865])).
% 29.77/19.98 tff(29107,plain,
% 29.77/19.98 (big_f(f3(c2, c1), c2) <=> big_f(c1, c2)),
% 29.77/19.98 inference(monotonicity,[status(thm)],[29106])).
% 29.77/19.98 tff(29108,plain,
% 29.77/19.98 (big_f(c1, c2) <=> big_f(f3(c2, c1), c2)),
% 29.77/19.98 inference(symmetry,[status(thm)],[29107])).
% 29.77/19.98 tff(29109,plain,
% 29.77/19.98 (big_f(f3(c2, c1), c2)),
% 29.77/19.98 inference(modus_ponens,[status(thm)],[2865, 29108])).
% 29.77/19.98 tff(29110,plain,
% 29.77/19.98 ($false),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[12175, 29109])).
% 29.77/19.98 tff(29111,plain,(big_f(f3(c2, c1), c2) | (~big_f(c1, c2)) | (c2 = c4) | (c1 = c3) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 29.77/19.98 tff(29112,plain,
% 29.77/19.98 (big_f(f3(c2, c1), c2)),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[29111, 28829, 29095, 29089, 66])).
% 29.77/19.98 tff(29113,plain,
% 29.77/19.98 (big_f(c1, f6(c1, c2)) <=> big_f(c1, c2)),
% 29.77/19.98 inference(monotonicity,[status(thm)],[29027])).
% 29.77/19.98 tff(29114,plain,
% 29.77/19.98 (big_f(c1, c2) <=> big_f(c1, f6(c1, c2))),
% 29.77/19.98 inference(symmetry,[status(thm)],[29113])).
% 29.77/19.98 tff(29115,plain,
% 29.77/19.98 (big_f(c1, c2) <=> big_f(f7(c1), f6(c1, c2))),
% 29.77/19.98 inference(transitivity,[status(thm)],[29114, 25793])).
% 29.77/19.98 tff(29116,plain,
% 29.77/19.98 (big_f(f7(c1), f6(c1, c2))),
% 29.77/19.98 inference(modus_ponens,[status(thm)],[28829, 29115])).
% 29.77/19.98 tff(29117,plain,
% 29.77/19.98 (big_f(c1, f10(c1))),
% 29.77/19.98 inference(modus_ponens,[status(thm)],[28829, 28833])).
% 29.77/19.98 tff(29118,plain,
% 29.77/19.98 (c1 = f8(c1)),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[27178, 2730, 25791, 28830, 29117, 29116, 29027])).
% 29.77/19.98 tff(29119,plain,
% 29.77/19.98 (f8(c1) = c1),
% 29.77/19.98 inference(symmetry,[status(thm)],[29118])).
% 29.77/19.98 tff(29120,plain,
% 29.77/19.98 ((f3(c2, c1) = f8(c1)) <=> (f3(c2, c1) = c1)),
% 29.77/19.98 inference(monotonicity,[status(thm)],[29119])).
% 29.77/19.98 tff(29121,plain,
% 29.77/19.98 (big_f(f3(c2, c1), f10(c1))),
% 29.77/19.98 inference(modus_ponens,[status(thm)],[29112, 29022])).
% 29.77/19.98 tff(29122,plain,
% 29.77/19.98 ((f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1)))),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[29066, 2730, 25791, 28830, 29116, 29027])).
% 29.77/19.98 tff(29123,plain,
% 29.77/19.98 (f3(c2, c1) = f8(c1)),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[29122, 29121])).
% 29.77/19.98 tff(29124,plain,
% 29.77/19.98 (f3(c2, c1) = c1),
% 29.77/19.98 inference(modus_ponens,[status(thm)],[29123, 29120])).
% 29.77/19.98 tff(29125,plain,
% 29.77/19.98 ($false),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[13529, 969, 168, 873, 1052, 7524, 13405, 13404])).
% 29.77/19.98 tff(29126,plain,((f1(c1, c2) = c2) | (c1 = c3) | (c2 = c4) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 29.77/19.98 tff(29127,plain,
% 29.77/19.98 (f1(c1, c2) = c2),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[29126, 29089, 29095, 29124, 29112, 66])).
% 29.77/19.98 tff(29128,plain,
% 29.77/19.98 (big_f(c1, f1(c1, c2)) <=> big_f(c1, c2)),
% 29.77/19.98 inference(monotonicity,[status(thm)],[29127])).
% 29.77/19.98 tff(29129,plain,
% 29.77/19.98 (big_f(c1, c2) <=> big_f(c1, f1(c1, c2))),
% 29.77/19.98 inference(symmetry,[status(thm)],[29128])).
% 29.77/19.98 tff(29130,plain,
% 29.77/19.98 (big_f(c1, f1(c1, c2))),
% 29.77/19.98 inference(modus_ponens,[status(thm)],[28829, 29129])).
% 29.77/19.98 tff(29131,plain,
% 29.77/19.98 ($false),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[13542, 933, 29089, 29095, 29127, 29130, 29124, 29112])).
% 29.77/19.98 tff(29132,plain,(big_f(c2, c2) | big_f(c1, c1) | (~(f4(c4) = c2)) | (~(f7(c2) = c2)) | (f10(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 29.77/19.98 tff(29133,plain,
% 29.77/19.98 (big_f(c2, c2)),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[29132, 89, 79, 77, 66])).
% 29.77/19.98 tff(29134,plain,
% 29.77/19.98 (big_f(c2, f10(c2))),
% 29.77/19.98 inference(modus_ponens,[status(thm)],[25952, 102])).
% 29.77/19.98 tff(29135,plain,
% 29.77/19.98 (c1 = c4),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[27243, 29133, 66, 25952, 89, 29134])).
% 29.77/19.98 tff(29136,plain,
% 29.77/19.98 (c4 = c1),
% 29.77/19.98 inference(symmetry,[status(thm)],[29135])).
% 29.77/19.98 tff(29137,plain,
% 29.77/19.98 ((c2 = c4) <=> (c2 = c1)),
% 29.77/19.98 inference(monotonicity,[status(thm)],[29136])).
% 29.77/19.98 tff(29138,plain,
% 29.77/19.98 ((c2 = c1) <=> (c2 = c4)),
% 29.77/19.98 inference(symmetry,[status(thm)],[29137])).
% 29.77/19.98 tff(29139,plain,
% 29.77/19.98 ((~(c2 = c1)) <=> (~(c2 = c4))),
% 29.77/19.98 inference(monotonicity,[status(thm)],[29138])).
% 29.77/19.98 tff(29140,plain,
% 29.77/19.98 (~(c2 = c4)),
% 29.77/19.98 inference(modus_ponens,[status(thm)],[75, 29139])).
% 29.77/19.98 tff(29141,plain,
% 29.77/19.98 (big_f(c1, f10(c1))),
% 29.77/19.98 inference(modus_ponens,[status(thm)],[2865, 3350])).
% 29.77/19.98 tff(29142,plain,
% 29.77/19.98 (c1 = f8(c1)),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[27178, 2730, 25791, 3, 29141, 25865, 36])).
% 29.77/19.98 tff(29143,plain,
% 29.77/19.98 (f8(c1) = c1),
% 29.77/19.98 inference(symmetry,[status(thm)],[29142])).
% 29.77/19.98 tff(29144,plain,
% 29.77/19.98 (c2 = f8(c1)),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[27186, 2730, 25791, 3332, 3, 25865, 36])).
% 29.77/19.98 tff(29145,plain,
% 29.77/19.98 (c2 = c1),
% 29.77/19.98 inference(transitivity,[status(thm)],[29144, 29143])).
% 29.77/19.98 tff(29146,plain,
% 29.77/19.98 ($false),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[75, 29145])).
% 29.77/19.98 tff(29147,plain,((f10(c1) = c1) | (~(f6(c1, c2) = c2)) | (~big_f(c1, c2)) | (~big_f(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 29.77/19.98 tff(29148,plain,
% 29.77/19.98 (f10(c1) = c1),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[29147, 36, 2865, 1345])).
% 29.77/19.98 tff(29149,plain,
% 29.77/19.98 (f9(c1, c2) = c2),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[27119, 29148, 2865, 66])).
% 29.77/19.98 tff(29150,plain,
% 29.77/19.98 (f10(c1) = f10(c2)),
% 29.77/19.98 inference(transitivity,[status(thm)],[29148, 99])).
% 29.77/19.98 tff(29151,plain,
% 29.77/19.98 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)))),
% 29.77/19.98 inference(rewrite,[status(thm)],[])).
% 29.77/19.98 tff(29152,plain,
% 29.77/19.98 (((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c1) = c1)) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2)))) <=> ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)))),
% 29.77/19.98 inference(rewrite,[status(thm)],[])).
% 29.77/19.98 tff(29153,plain,
% 29.77/19.98 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c1) = c1)) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2))))),
% 29.77/19.98 inference(monotonicity,[status(thm)],[29152])).
% 29.77/19.98 tff(29154,plain,
% 29.77/19.98 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c1) = c1)) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)))),
% 29.77/19.98 inference(transitivity,[status(thm)],[29153, 29151])).
% 29.77/19.98 tff(29155,plain,
% 29.77/19.98 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c1) = c1)) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2))))),
% 29.77/19.98 inference(quant_inst,[status(thm)],[])).
% 29.77/19.98 tff(29156,plain,
% 29.77/19.98 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2))),
% 29.77/19.98 inference(modus_ponens,[status(thm)],[29155, 29154])).
% 29.77/19.98 tff(29157,plain,
% 29.77/19.98 (c2 = f8(c2)),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[29156, 2730, 25791, 89, 12291, 25865, 36])).
% 29.77/19.98 tff(29158,plain,
% 29.77/19.98 (f8(c2) = c2),
% 29.77/19.98 inference(symmetry,[status(thm)],[29157])).
% 29.77/19.98 tff(29159,plain,
% 29.77/19.98 (f9(c1, f8(c2)) = f9(c1, c2)),
% 29.77/19.98 inference(monotonicity,[status(thm)],[29158])).
% 29.77/19.98 tff(29160,plain,
% 29.77/19.98 (f9(c1, c2) = f9(c1, f8(c2))),
% 29.77/19.98 inference(symmetry,[status(thm)],[29159])).
% 29.77/19.98 tff(29161,plain,
% 29.77/19.98 (big_f(f9(c1, c2), f10(c1)) <=> big_f(f9(c1, f8(c2)), f10(c2))),
% 29.77/19.98 inference(monotonicity,[status(thm)],[29160, 29150])).
% 29.77/19.98 tff(29162,plain,
% 29.77/19.98 (big_f(f9(c1, f8(c2)), f10(c2)) <=> big_f(f9(c1, c2), f10(c1))),
% 29.77/19.98 inference(symmetry,[status(thm)],[29161])).
% 29.77/19.98 tff(29163,plain,
% 29.77/19.98 (f9(c1, f8(c2)) = c2),
% 29.77/19.98 inference(transitivity,[status(thm)],[29159, 29149])).
% 29.77/19.98 tff(29164,plain,
% 29.77/19.98 (big_f(f9(c1, f8(c2)), f10(c2)) <=> big_f(c2, c1)),
% 29.77/19.98 inference(monotonicity,[status(thm)],[29163, 94])).
% 29.77/19.98 tff(29165,plain,
% 29.77/19.98 (big_f(c2, c1) <=> big_f(f9(c1, f8(c2)), f10(c2))),
% 29.77/19.98 inference(symmetry,[status(thm)],[29164])).
% 29.77/19.98 tff(29166,plain,
% 29.77/19.98 (big_f(c2, c1) <=> big_f(f9(c1, c2), f10(c1))),
% 29.77/19.98 inference(transitivity,[status(thm)],[29165, 29162])).
% 29.77/19.98 tff(29167,plain,
% 29.77/19.98 (big_f(f9(c1, c2), f10(c1))),
% 29.77/19.98 inference(modus_ponens,[status(thm)],[348, 29166])).
% 29.77/19.98 tff(29168,plain,
% 29.77/19.98 ($false),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[27201, 2378, 25791, 29148, 29167, 29149, 25865, 36])).
% 29.77/19.98 tff(29169,plain,((~(f6(c1, c2) = c2)) | (~big_f(c2, c1)) | (~big_f(c1, c2)) | big_f(c1, c1) | (~big_f(c2, c2)) | (f10(c2) = c2) | (~big_f(c2, f10(c2)))), inference(lemma,lemma(discharge,[]))).
% 29.77/19.98 tff(29170,plain,
% 29.77/19.98 (~(f6(c1, c2) = c2)),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[29169, 2865, 348, 66, 1345, 89, 12291])).
% 29.77/19.98 tff(29171,plain,
% 29.77/19.98 (f6(c1, c2) = c1),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[48, 29170])).
% 29.77/19.98 tff(29172,plain,
% 29.77/19.98 (big_f(c1, f6(c1, c2)) <=> big_f(c1, c1)),
% 29.77/19.98 inference(monotonicity,[status(thm)],[29171])).
% 29.77/19.98 tff(29173,plain,
% 29.77/19.98 (big_f(c1, c1) <=> big_f(c1, f6(c1, c2))),
% 29.77/19.98 inference(symmetry,[status(thm)],[29172])).
% 29.77/19.98 tff(29174,plain,
% 29.77/19.98 (big_f(c1, c1) <=> big_f(f7(c1), f6(c1, c2))),
% 29.77/19.98 inference(transitivity,[status(thm)],[29173, 25793])).
% 29.77/19.98 tff(29175,plain,
% 29.77/19.98 ((~big_f(c1, c1)) <=> (~big_f(f7(c1), f6(c1, c2)))),
% 29.77/19.98 inference(monotonicity,[status(thm)],[29174])).
% 29.77/19.98 tff(29176,plain,
% 29.77/19.98 (~big_f(f7(c1), f6(c1, c2))),
% 29.77/19.98 inference(modus_ponens,[status(thm)],[66, 29175])).
% 29.77/19.98 tff(29177,plain,
% 29.77/19.98 (c2 = f8(c2)),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[27127, 2662, 25791, 89, 12291, 29176, 29170])).
% 29.77/19.98 tff(29178,plain,
% 29.77/19.98 (f8(c2) = c2),
% 29.77/19.98 inference(symmetry,[status(thm)],[29177])).
% 29.77/19.98 tff(29179,plain,
% 29.77/19.98 (f6(c1, f8(c2)) = f6(c1, c2)),
% 29.77/19.98 inference(monotonicity,[status(thm)],[29178])).
% 29.77/19.98 tff(29180,plain,
% 29.77/19.98 (f6(c1, f8(c2)) = c1),
% 29.77/19.98 inference(transitivity,[status(thm)],[29179, 29171])).
% 29.77/19.98 tff(29181,plain,
% 29.77/19.98 (big_f(c1, f6(c1, f8(c2))) <=> big_f(c1, c1)),
% 29.77/19.98 inference(monotonicity,[status(thm)],[29180])).
% 29.77/19.98 tff(29182,plain,
% 29.77/19.98 (big_f(c1, c1) <=> big_f(c1, f6(c1, f8(c2)))),
% 29.77/19.98 inference(symmetry,[status(thm)],[29181])).
% 29.77/19.98 tff(29183,plain,
% 29.77/19.98 (big_f(c1, c1) <=> big_f(f7(c1), f6(c1, f8(c2)))),
% 29.77/19.98 inference(transitivity,[status(thm)],[29182, 27145])).
% 29.77/19.98 tff(29184,plain,
% 29.77/19.98 ((~big_f(c1, c1)) <=> (~big_f(f7(c1), f6(c1, f8(c2))))),
% 29.77/19.98 inference(monotonicity,[status(thm)],[29183])).
% 29.77/19.98 tff(29185,plain,
% 29.77/19.98 (~big_f(f7(c1), f6(c1, f8(c2)))),
% 29.77/19.98 inference(modus_ponens,[status(thm)],[66, 29184])).
% 29.77/19.98 tff(29186,plain,
% 29.77/19.98 ($false),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[27088, 2662, 25791, 3332, 3, 1673, 5714, 114])).
% 29.77/19.98 tff(29187,plain,((f10(c1) = c1) | (c2 = f8(c1)) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2) | (~big_f(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 29.77/19.98 tff(29188,plain,
% 29.77/19.98 (f10(c1) = c1),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[29187, 25798, 1673, 114, 1345])).
% 29.77/19.98 tff(29189,plain,
% 29.77/19.98 ((f6(c1, c2) = c2) | (~(f10(c1) = c1)) | (f9(c1, c2) = c2) | big_f(c1, c1)),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[27105, 25791])).
% 29.77/19.98 tff(29190,plain,
% 29.77/19.98 (f9(c1, c2) = c2),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[29189, 29188, 114, 66])).
% 29.77/19.98 tff(29191,plain,
% 29.77/19.98 (f10(c1) = f10(c2)),
% 29.77/19.98 inference(transitivity,[status(thm)],[29188, 99])).
% 29.77/19.98 tff(29192,plain,
% 29.77/19.98 (big_f(f9(c1, c2), f10(c1)) <=> big_f(f9(c1, f8(c2)), f10(c2))),
% 29.77/19.98 inference(monotonicity,[status(thm)],[27131, 29191])).
% 29.77/19.98 tff(29193,plain,
% 29.77/19.98 (big_f(f9(c1, f8(c2)), f10(c2)) <=> big_f(f9(c1, c2), f10(c1))),
% 29.77/19.98 inference(symmetry,[status(thm)],[29192])).
% 29.77/19.98 tff(29194,plain,
% 29.77/19.98 (big_f(f9(c1, f8(c2)), f10(c2))),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[27151, 29188, 89, 20098, 27143])).
% 29.77/19.98 tff(29195,plain,
% 29.77/19.98 (big_f(f9(c1, c2), f10(c1))),
% 29.77/19.98 inference(modus_ponens,[status(thm)],[29194, 29193])).
% 29.77/19.98 tff(29196,plain,
% 29.77/19.98 ($false),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[27159, 2409, 25791, 29188, 29195, 29190, 25798, 114])).
% 29.77/19.98 tff(29197,plain,((f6(c1, c2) = c2) | (f10(c2) = c2) | big_f(f7(c1), f6(c1, f8(c2))) | big_f(c1, c1) | (c2 = f8(c1)) | (~big_f(c2, c2)) | (~big_f(c2, f10(c2)))), inference(lemma,lemma(discharge,[]))).
% 29.77/19.98 tff(29198,plain,
% 29.77/19.98 (c2 = f8(c1)),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[29197, 29185, 29170, 66, 89, 1345, 12291])).
% 29.77/19.98 tff(29199,plain,
% 29.77/19.98 (f8(c1) = c1),
% 29.77/19.98 inference(symmetry,[status(thm)],[3031])).
% 29.77/19.98 tff(29200,plain,
% 29.77/19.98 (c2 = c1),
% 29.77/19.98 inference(transitivity,[status(thm)],[1642, 29199])).
% 29.77/19.98 tff(29201,plain,
% 29.77/19.98 ($false),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[75, 29200])).
% 29.77/19.98 tff(29202,plain,((~(c1 = f8(c1))) | (~(c2 = f8(c1)))), inference(lemma,lemma(discharge,[]))).
% 29.77/19.98 tff(29203,plain,
% 29.77/19.98 (~(c1 = f8(c1))),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[29202, 29198])).
% 29.77/19.98 tff(29204,plain,
% 29.77/19.98 ($false),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[27080, 2662, 25791, 3, 9806, 28851, 5714, 114])).
% 29.77/19.98 tff(29205,plain,((f10(c1) = c1) | (c1 = f8(c1)) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2) | (~big_f(c1, c2))), inference(lemma,lemma(discharge,[]))).
% 29.77/19.98 tff(29206,plain,
% 29.77/19.98 (f10(c1) = c1),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[29205, 29203, 29176, 29170, 2865])).
% 29.77/19.98 tff(29207,plain,
% 29.77/19.98 (f9(c1, c2) = c2),
% 29.77/19.98 inference(unit_resolution,[status(thm)],[27119, 29206, 2865, 66])).
% 29.77/19.98 tff(29208,plain,
% 29.77/19.98 (f10(c1) = f10(c2)),
% 29.77/19.98 inference(transitivity,[status(thm)],[29206, 99])).
% 29.77/19.98 tff(29209,plain,
% 29.77/19.98 (f9(c1, f8(c2)) = f9(c1, c2)),
% 29.77/19.98 inference(monotonicity,[status(thm)],[29178])).
% 29.77/19.98 tff(29210,plain,
% 29.77/19.98 (f9(c1, c2) = f9(c1, f8(c2))),
% 29.77/19.98 inference(symmetry,[status(thm)],[29209])).
% 29.77/19.98 tff(29211,plain,
% 29.77/19.98 (big_f(f9(c1, c2), f10(c1)) <=> big_f(f9(c1, f8(c2)), f10(c2))),
% 29.77/19.98 inference(monotonicity,[status(thm)],[29210, 29208])).
% 29.77/19.98 tff(29212,plain,
% 29.77/19.98 (big_f(f9(c1, f8(c2)), f10(c2)) <=> big_f(f9(c1, c2), f10(c1))),
% 29.77/19.98 inference(symmetry,[status(thm)],[29211])).
% 29.77/19.98 tff(29213,plain,
% 29.77/19.98 ((f6(c1, f8(c2)) = f8(c2)) <=> (f6(c1, f8(c2)) = c2)),
% 29.77/19.98 inference(monotonicity,[status(thm)],[29178])).
% 29.77/19.98 tff(29214,plain,
% 29.77/19.98 ((f6(c1, f8(c2)) = c2) <=> (f6(c1, f8(c2)) = f8(c2))),
% 29.77/19.98 inference(symmetry,[status(thm)],[29213])).
% 29.77/19.98 tff(29215,plain,
% 29.77/19.98 ((f6(c1, f8(c2)) = c2) <=> (c1 = c2)),
% 29.77/19.98 inference(monotonicity,[status(thm)],[29180])).
% 29.77/19.98 tff(29216,plain,
% 29.77/19.98 ((f6(c1, f8(c2)) = c2) <=> (c2 = c1)),
% 29.77/19.98 inference(transitivity,[status(thm)],[29215, 1])).
% 29.77/19.98 tff(29217,plain,
% 29.77/19.98 ((c2 = c1) <=> (f6(c1, f8(c2)) = c2)),
% 29.77/19.98 inference(symmetry,[status(thm)],[29216])).
% 29.77/19.98 tff(29218,plain,
% 29.77/19.98 ((c2 = c1) <=> (f6(c1, f8(c2)) = f8(c2))),
% 29.77/19.98 inference(transitivity,[status(thm)],[29217, 29214])).
% 29.77/19.99 tff(29219,plain,
% 29.77/19.99 ((~(c2 = c1)) <=> (~(f6(c1, f8(c2)) = f8(c2)))),
% 29.77/19.99 inference(monotonicity,[status(thm)],[29218])).
% 29.77/19.99 tff(29220,plain,
% 29.77/19.99 (~(f6(c1, f8(c2)) = f8(c2))),
% 29.77/19.99 inference(modus_ponens,[status(thm)],[75, 29219])).
% 29.77/19.99 tff(29221,plain,
% 29.77/19.99 (big_f(f9(c1, f8(c2)), f10(c2))),
% 29.77/19.99 inference(unit_resolution,[status(thm)],[27151, 29206, 89, 29185, 29220])).
% 29.77/19.99 tff(29222,plain,
% 29.77/19.99 (big_f(f9(c1, c2), f10(c1))),
% 29.77/19.99 inference(modus_ponens,[status(thm)],[29221, 29212])).
% 29.77/19.99 tff(29223,plain,
% 29.77/19.99 ($false),
% 29.77/19.99 inference(unit_resolution,[status(thm)],[27159, 2409, 25791, 29206, 29222, 29207, 29176, 29170])).
% 29.77/19.99 tff(29224,plain,((~big_f(c1, c2)) | (f10(c2) = c2) | big_f(c1, c1) | (~big_f(c2, c2)) | (~big_f(c2, f10(c2))) | (~big_f(c2, c1))), inference(lemma,lemma(discharge,[]))).
% 29.77/19.99 tff(29225,plain,
% 29.77/19.99 (~big_f(c1, c2)),
% 29.77/19.99 inference(unit_resolution,[status(thm)],[29224, 89, 66, 29133, 29134, 25952])).
% 29.77/19.99 tff(29226,plain,
% 29.77/19.99 (~(c3 = c1)),
% 29.77/19.99 inference(unit_resolution,[status(thm)],[26135, 29225, 66, 29140, 79, 77, 29133])).
% 29.77/19.99 tff(29227,plain,
% 29.77/19.99 (c3 = c2),
% 29.77/19.99 inference(unit_resolution,[status(thm)],[180, 29226])).
% 29.77/19.99 tff(29228,plain,
% 29.77/19.99 (c2 = c3),
% 29.77/19.99 inference(modus_ponens,[status(thm)],[29227, 78])).
% 29.77/19.99 tff(29229,plain,
% 29.77/19.99 (~(c2 = c3)),
% 29.77/19.99 inference(unit_resolution,[status(thm)],[26149, 29225, 29140, 25952, 79, 77, 29133])).
% 29.77/19.99 tff(29230,plain,
% 29.77/19.99 ($false),
% 29.77/19.99 inference(unit_resolution,[status(thm)],[29229, 29228])).
% 29.77/19.99 tff(29231,plain,((f10(c2) = c2) | (~(f4(c4) = c2)) | (~(f7(c2) = c2)) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 29.77/19.99 tff(29232,plain,
% 29.77/19.99 (f10(c2) = c2),
% 29.77/19.99 inference(unit_resolution,[status(thm)],[29231, 77, 79, 66])).
% 29.77/19.99 tff(29233,plain,
% 29.77/19.99 (f9(f10(c2), f4(c4)) = c2),
% 29.77/19.99 inference(unit_resolution,[status(thm)],[8065, 29232, 79])).
% 29.77/19.99 tff(29234,plain,
% 29.77/19.99 (f9(c2, c2) = c2),
% 29.77/19.99 inference(unit_resolution,[status(thm)],[1606, 29232, 79, 29233])).
% 29.77/19.99 tff(29235,plain,
% 29.77/19.99 (big_f(f9(c2, c2), f10(c2)) <=> big_f(f9(c2, c2), c2)),
% 29.77/19.99 inference(monotonicity,[status(thm)],[29232])).
% 29.77/19.99 tff(29236,plain,
% 29.77/19.99 (big_f(f9(c2, c2), c2) <=> big_f(f9(c2, c2), f10(c2))),
% 29.77/19.99 inference(symmetry,[status(thm)],[29235])).
% 29.77/19.99 tff(29237,plain,
% 29.77/19.99 (big_f(f9(c2, c2), c2) <=> big_f(c2, c2)),
% 29.77/19.99 inference(monotonicity,[status(thm)],[29234])).
% 29.77/19.99 tff(29238,plain,
% 29.77/19.99 (big_f(c2, c2) <=> big_f(f9(c2, c2), c2)),
% 29.77/19.99 inference(symmetry,[status(thm)],[29237])).
% 29.77/19.99 tff(29239,plain,
% 29.77/19.99 (big_f(c2, c2) <=> big_f(f9(c2, c2), f10(c2))),
% 29.77/19.99 inference(transitivity,[status(thm)],[29238, 29236])).
% 29.77/19.99 tff(29240,plain,
% 29.77/19.99 (big_f(c1, c2)),
% 29.77/19.99 inference(unit_resolution,[status(thm)],[26152, 77, 79, 66])).
% 29.77/19.99 tff(29241,plain,
% 29.77/19.99 (~(f6(c1, c2) = c2)),
% 29.77/19.99 inference(unit_resolution,[status(thm)],[11072, 8282, 122, 4234, 2865, 1139])).
% 29.77/19.99 tff(29242,plain,
% 29.77/19.99 (f6(c1, c2) = c1),
% 29.77/19.99 inference(unit_resolution,[status(thm)],[48, 29241])).
% 29.77/19.99 tff(29243,plain,
% 29.77/19.99 (big_f(c1, f6(c1, c2)) <=> big_f(c1, c1)),
% 29.77/19.99 inference(monotonicity,[status(thm)],[29242])).
% 29.77/19.99 tff(29244,plain,
% 29.77/19.99 (big_f(c1, c1) <=> big_f(c1, f6(c1, c2))),
% 29.77/19.99 inference(symmetry,[status(thm)],[29243])).
% 29.77/19.99 tff(29245,plain,
% 29.77/19.99 (big_f(c1, c1) <=> big_f(f7(c1), f6(c1, c2))),
% 29.77/19.99 inference(transitivity,[status(thm)],[29244, 27094])).
% 29.77/19.99 tff(29246,plain,
% 29.77/19.99 ((~big_f(c1, c1)) <=> (~big_f(f7(c1), f6(c1, c2)))),
% 29.77/19.99 inference(monotonicity,[status(thm)],[29245])).
% 29.77/19.99 tff(29247,plain,
% 29.77/19.99 (~big_f(f7(c1), f6(c1, c2))),
% 29.77/19.99 inference(modus_ponens,[status(thm)],[66, 29246])).
% 29.77/19.99 tff(29248,plain,
% 29.77/19.99 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2))),
% 29.77/19.99 inference(rewrite,[status(thm)],[])).
% 29.77/19.99 tff(29249,plain,
% 29.77/19.99 (((~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (~(f7(c1) = c1)) | (f6(c1, c2) = c2) | big_f(f7(c1), f6(c1, c2))) <=> ((~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2))),
% 29.77/19.99 inference(rewrite,[status(thm)],[])).
% 29.77/19.99 tff(29250,plain,
% 29.77/19.99 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (~(f7(c1) = c1)) | (f6(c1, c2) = c2) | big_f(f7(c1), f6(c1, c2)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2)))),
% 29.77/19.99 inference(monotonicity,[status(thm)],[29249])).
% 29.77/19.99 tff(29251,plain,
% 29.77/19.99 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (~(f7(c1) = c1)) | (f6(c1, c2) = c2) | big_f(f7(c1), f6(c1, c2)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2))),
% 29.77/19.99 inference(transitivity,[status(thm)],[29250, 29248])).
% 29.77/19.99 tff(29252,plain,
% 29.77/19.99 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (~(f7(c1) = c1)) | (f6(c1, c2) = c2) | big_f(f7(c1), f6(c1, c2)))),
% 29.77/19.99 inference(quant_inst,[status(thm)],[])).
% 29.77/19.99 tff(29253,plain,
% 29.77/19.99 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2)),
% 29.77/19.99 inference(modus_ponens,[status(thm)],[29252, 29251])).
% 29.77/19.99 tff(29254,plain,
% 29.77/19.99 ($false),
% 29.77/19.99 inference(unit_resolution,[status(thm)],[29253, 2492, 4234, 122, 1139, 8282, 29247, 29241])).
% 29.77/19.99 tff(29255,plain,((f9(c2, c1) = c1) | (~(f7(c1) = c1)) | (~(f10(c2) = c2)) | big_f(c1, c1) | (~big_f(c1, c2)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 29.77/19.99 tff(29256,plain,
% 29.77/19.99 (f9(c2, c1) = c1),
% 29.77/19.99 inference(unit_resolution,[status(thm)],[29255, 66, 122, 4234, 2865, 121])).
% 29.77/19.99 tff(29257,plain,
% 29.77/19.99 (big_f(f9(c2, c1), f10(c2)) <=> big_f(c1, c2)),
% 29.77/19.99 inference(monotonicity,[status(thm)],[29256, 122])).
% 29.77/19.99 tff(29258,plain,
% 29.77/19.99 (big_f(c1, c2) <=> big_f(f9(c2, c1), f10(c2))),
% 29.77/19.99 inference(symmetry,[status(thm)],[29257])).
% 29.77/19.99 tff(29259,plain,
% 29.77/19.99 (big_f(f9(c2, c1), f10(c2))),
% 29.77/19.99 inference(modus_ponens,[status(thm)],[2865, 29258])).
% 29.77/19.99 tff(29260,plain,
% 29.77/19.99 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2))),
% 29.77/19.99 inference(rewrite,[status(thm)],[])).
% 29.77/19.99 tff(29261,plain,
% 29.77/19.99 (((~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (f6(c1, c2) = c2) | big_f(f7(c1), f6(c1, c2)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2)))) <=> ((~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2))),
% 29.77/19.99 inference(rewrite,[status(thm)],[])).
% 29.77/19.99 tff(29262,plain,
% 29.77/19.99 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (f6(c1, c2) = c2) | big_f(f7(c1), f6(c1, c2)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2)))),
% 29.77/19.99 inference(monotonicity,[status(thm)],[29261])).
% 29.77/19.99 tff(29263,plain,
% 29.77/19.99 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (f6(c1, c2) = c2) | big_f(f7(c1), f6(c1, c2)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2))),
% 29.77/19.99 inference(transitivity,[status(thm)],[29262, 29260])).
% 29.77/19.99 tff(29264,plain,
% 29.77/19.99 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (f6(c1, c2) = c2) | big_f(f7(c1), f6(c1, c2)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))))),
% 29.77/19.99 inference(quant_inst,[status(thm)],[])).
% 29.77/19.99 tff(29265,plain,
% 29.77/19.99 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2)),
% 29.77/19.99 inference(modus_ponens,[status(thm)],[29264, 29263])).
% 29.77/19.99 tff(29266,plain,
% 29.77/19.99 ($false),
% 29.77/19.99 inference(unit_resolution,[status(thm)],[29265, 2409, 4234, 122, 736, 3894, 27097, 114])).
% 29.77/19.99 tff(29267,plain,((f6(c1, c2) = c2) | (~(f7(c1) = c1)) | (~(f10(c2) = c2)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 29.77/19.99 tff(29268,plain,
% 29.77/19.99 (f6(c1, c2) = c2),
% 29.77/19.99 inference(unit_resolution,[status(thm)],[29267, 29256, 122, 4234, 29259, 66])).
% 29.77/19.99 tff(29269,plain,
% 29.77/19.99 (big_f(c1, f6(c1, c2)) <=> big_f(c1, c2)),
% 29.77/19.99 inference(monotonicity,[status(thm)],[29268])).
% 29.77/19.99 tff(29270,plain,
% 29.77/19.99 (big_f(c1, c2) <=> big_f(c1, f6(c1, c2))),
% 29.77/19.99 inference(symmetry,[status(thm)],[29269])).
% 29.77/19.99 tff(29271,plain,
% 29.77/19.99 (big_f(c1, f6(c1, c2))),
% 29.77/19.99 inference(modus_ponens,[status(thm)],[2865, 29270])).
% 29.77/19.99 tff(29272,plain,
% 29.77/19.99 (~big_f(f7(c1), f6(c1, c2))),
% 29.77/19.99 inference(unit_resolution,[status(thm)],[5827, 29268, 122, 4234, 29256, 29259])).
% 29.77/19.99 tff(29273,plain,
% 29.77/19.99 (~big_f(c1, f6(c1, c2))),
% 29.77/19.99 inference(modus_ponens,[status(thm)],[29272, 11069])).
% 29.77/19.99 tff(29274,plain,
% 29.77/19.99 ($false),
% 29.77/19.99 inference(unit_resolution,[status(thm)],[29273, 29271])).
% 29.77/19.99 tff(29275,plain,(big_f(c1, c1) | (~big_f(c1, c2)) | (~(f7(c1) = c1)) | (~(f10(c2) = c2)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 29.77/19.99 tff(29276,plain,
% 29.77/19.99 (big_f(c1, c1) | (~big_f(c1, c2)) | (~(f10(c2) = c2)) | big_f(c2, c2)),
% 29.77/19.99 inference(unit_resolution,[status(thm)],[29275, 25791])).
% 29.77/19.99 tff(29277,plain,
% 29.77/19.99 (big_f(c2, c2)),
% 29.77/19.99 inference(unit_resolution,[status(thm)],[29276, 29240, 66, 29232])).
% 29.77/19.99 tff(29278,plain,
% 29.77/19.99 (big_f(f9(c2, c2), f10(c2))),
% 29.77/19.99 inference(modus_ponens,[status(thm)],[29277, 29239])).
% 29.77/19.99 tff(29279,plain,
% 29.77/19.99 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2))),
% 29.77/19.99 inference(rewrite,[status(thm)],[])).
% 29.77/19.99 tff(29280,plain,
% 29.77/19.99 (((~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (f6(c1, c2) = c2) | big_f(f7(c1), f6(c1, c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2)))) <=> ((~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2))),
% 29.77/19.99 inference(rewrite,[status(thm)],[])).
% 29.77/19.99 tff(29281,plain,
% 29.77/19.99 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (f6(c1, c2) = c2) | big_f(f7(c1), f6(c1, c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2)))),
% 29.77/19.99 inference(monotonicity,[status(thm)],[29280])).
% 29.77/19.99 tff(29282,plain,
% 29.77/19.99 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (f6(c1, c2) = c2) | big_f(f7(c1), f6(c1, c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2))),
% 29.77/19.99 inference(transitivity,[status(thm)],[29281, 29279])).
% 29.77/19.99 tff(29283,plain,
% 29.77/19.99 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (f6(c1, c2) = c2) | big_f(f7(c1), f6(c1, c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))),
% 29.77/19.99 inference(quant_inst,[status(thm)],[])).
% 29.77/19.99 tff(29284,plain,
% 29.77/19.99 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2)),
% 29.77/19.99 inference(modus_ponens,[status(thm)],[29283, 29282])).
% 29.77/19.99 tff(29285,plain,
% 29.77/19.99 ($false),
% 29.77/19.99 inference(unit_resolution,[status(thm)],[29284, 2409, 25791, 122, 1572, 690, 25798, 114])).
% 29.77/19.99 tff(29286,plain,((f6(c1, c2) = c2) | (~(f10(c2) = c2)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 29.77/19.99 tff(29287,plain,
% 29.77/19.99 (f6(c1, c2) = c2),
% 29.77/19.99 inference(unit_resolution,[status(thm)],[29286, 29278, 29234, 29232, 66])).
% 29.77/19.99 tff(29288,plain,
% 29.77/19.99 (big_f(c1, f6(c1, c2)) <=> big_f(c1, c2)),
% 29.77/19.99 inference(monotonicity,[status(thm)],[29287])).
% 29.77/19.99 tff(29289,plain,
% 29.77/19.99 (big_f(c1, c2) <=> big_f(c1, f6(c1, c2))),
% 29.77/19.99 inference(symmetry,[status(thm)],[29288])).
% 29.77/19.99 tff(29290,plain,
% 29.77/19.99 (big_f(c1, c2) <=> big_f(f7(c1), f6(c1, c2))),
% 29.77/19.99 inference(transitivity,[status(thm)],[29289, 25793])).
% 29.77/19.99 tff(29291,plain,
% 29.77/19.99 (big_f(f7(c1), f6(c1, c2))),
% 29.77/19.99 inference(modus_ponens,[status(thm)],[29240, 29290])).
% 29.77/19.99 tff(29292,plain,
% 29.77/19.99 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)))),
% 29.77/19.99 inference(rewrite,[status(thm)],[])).
% 29.77/19.99 tff(29293,plain,
% 29.77/19.99 (((~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2)))) <=> ((~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)))),
% 29.77/19.99 inference(rewrite,[status(thm)],[])).
% 29.77/19.99 tff(29294,plain,
% 29.77/19.99 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2))))),
% 29.77/19.99 inference(monotonicity,[status(thm)],[29293])).
% 29.77/19.99 tff(29295,plain,
% 29.77/19.99 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)))),
% 29.77/19.99 inference(transitivity,[status(thm)],[29294, 29292])).
% 29.77/19.99 tff(29296,plain,
% 29.77/19.99 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2))))),
% 29.77/19.99 inference(quant_inst,[status(thm)],[])).
% 29.77/19.99 tff(29297,plain,
% 29.77/19.99 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2))),
% 29.77/19.99 inference(modus_ponens,[status(thm)],[29296, 29295])).
% 29.77/19.99 tff(29298,plain,
% 29.77/19.99 ($false),
% 29.77/19.99 inference(unit_resolution,[status(thm)],[29297, 2378, 25791, 29232, 29234, 29278, 29291, 29287])).
% 29.77/19.99 tff(29299,plain,((~(f7(c2) = c2)) | big_f(c1, c1) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.77/19.99 tff(29300,plain,
% 29.77/19.99 (~(f7(c2) = c2)),
% 29.77/19.99 inference(unit_resolution,[status(thm)],[29299, 28775, 66])).
% 29.77/19.99 tff(29301,plain,
% 29.77/19.99 (~(f10(c2) = c2)),
% 29.77/19.99 inference(unit_resolution,[status(thm)],[10739, 29300, 28775])).
% 29.77/19.99 tff(29302,plain,
% 29.77/19.99 ($false),
% 29.77/19.99 inference(unit_resolution,[status(thm)],[27420, 29301, 29300, 27, 66])).
% 29.77/19.99 tff(29303,plain,(big_f(c1, c1) | big_f(c1, c2)), inference(lemma,lemma(discharge,[]))).
% 29.77/19.99 tff(29304,plain,
% 29.77/19.99 (big_f(c1, c1)),
% 29.77/19.99 inference(unit_resolution,[status(thm)],[29303, 27])).
% 29.77/19.99 tff(29305,plain,
% 29.77/19.99 (~(f10(c1) = c1)),
% 29.77/19.99 inference(unit_resolution,[status(thm)],[27676, 2, 29304, 65])).
% 29.77/19.99 tff(29306,plain,
% 29.77/19.99 (f10(c1) = c2),
% 29.77/19.99 inference(unit_resolution,[status(thm)],[14, 29305])).
% 29.77/19.99 tff(29307,plain,
% 29.77/19.99 (big_f(c1, f10(c1)) <=> big_f(c1, c2)),
% 29.77/19.99 inference(monotonicity,[status(thm)],[29306])).
% 29.77/19.99 tff(29308,plain,
% 29.77/19.99 (big_f(c1, c2) <=> big_f(c1, f10(c1))),
% 29.77/19.99 inference(symmetry,[status(thm)],[29307])).
% 29.77/19.99 tff(29309,plain,
% 29.77/19.99 ((~big_f(c1, c2)) <=> (~big_f(c1, f10(c1)))),
% 29.77/19.99 inference(monotonicity,[status(thm)],[29308])).
% 29.77/19.99 tff(29310,plain,
% 29.77/19.99 (~big_f(c1, f10(c1))),
% 29.77/19.99 inference(modus_ponens,[status(thm)],[27, 29309])).
% 29.77/19.99 tff(29311,plain,
% 29.77/19.99 (big_f(f7(c1), f6(c1, c1)) | (f10(c1) = c1) | big_f(c2, f10(c1)) | big_f(c1, f10(c1)) | (~big_f(c1, c1))),
% 29.77/19.99 inference(unit_resolution,[status(thm)],[26488, 25791])).
% 29.77/19.99 tff(29312,plain,
% 29.77/19.99 (big_f(c2, f10(c1))),
% 29.77/19.99 inference(unit_resolution,[status(thm)],[29311, 29310, 29304, 65, 29305])).
% 29.77/19.99 tff(29313,plain,
% 29.77/19.99 (big_f(c2, c2)),
% 29.77/19.99 inference(unit_resolution,[status(thm)],[6125, 29312, 29306])).
% 29.77/19.99 tff(29314,plain,
% 29.77/19.99 (~(c2 = c3)),
% 29.77/19.99 inference(modus_ponens,[status(thm)],[28772, 10473])).
% 29.77/19.99 tff(29315,plain,
% 29.77/19.99 (big_f(c2, c4) <=> big_f(c2, c1)),
% 29.77/19.99 inference(monotonicity,[status(thm)],[9094])).
% 29.77/19.99 tff(29316,plain,
% 29.77/19.99 (big_f(c2, c1) <=> big_f(c2, c4)),
% 29.77/19.99 inference(symmetry,[status(thm)],[29315])).
% 29.77/19.99 tff(29317,plain,
% 29.77/19.99 ((~big_f(c2, c1)) <=> (~big_f(c2, c4))),
% 29.77/19.99 inference(monotonicity,[status(thm)],[29316])).
% 29.77/19.99 tff(29318,plain,
% 29.77/19.99 (~big_f(c2, c4)),
% 29.77/19.99 inference(modus_ponens,[status(thm)],[2, 29317])).
% 29.77/19.99 tff(29319,plain,
% 29.77/19.99 (big_f(f3(c2, c2), c2)),
% 29.77/19.99 inference(unit_resolution,[status(thm)],[21470, 29318, 29314, 1345, 873])).
% 29.77/19.99 tff(29320,plain,
% 29.77/19.99 (~(f3(c2, c2) = c2)),
% 29.77/19.99 inference(unit_resolution,[status(thm)],[21039, 29318, 29314, 1345, 873, 29319])).
% 29.77/19.99 tff(29321,plain,
% 29.77/19.99 ($false),
% 29.77/19.99 inference(unit_resolution,[status(thm)],[28341, 29320, 29319, 27, 27490])).
% 29.77/19.99 tff(29322,plain,((c2 = c4) | big_f(c1, c2) | (~(f6(c1, f6(c1, c2)) = c2)) | (~big_f(c2, c2)) | big_f(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 29.77/19.99 tff(29323,plain,
% 29.77/19.99 (c2 = c4),
% 29.77/19.99 inference(unit_resolution,[status(thm)],[29322, 29313, 27, 27490, 2])).
% 29.77/19.99 tff(29324,plain,
% 29.77/19.99 (big_f(c1, f10(c2))),
% 29.77/19.99 inference(modus_ponens,[status(thm)],[29304, 24205])).
% 29.77/19.99 tff(29325,plain,
% 29.77/19.99 (big_f(c2, c2)),
% 29.77/19.99 inference(unit_resolution,[status(thm)],[28828, 89, 27])).
% 29.77/19.99 tff(29326,plain,
% 29.77/19.99 (big_f(f7(c2), c1)),
% 29.77/19.99 inference(unit_resolution,[status(thm)],[20926, 22, 29304, 94])).
% 29.77/19.99 tff(29327,plain,
% 29.77/19.99 (~(f4(c4) = c2)),
% 29.77/19.99 inference(unit_resolution,[status(thm)],[12570, 2, 29314, 29326, 29325, 17])).
% 29.77/19.99 tff(29328,plain,
% 29.77/19.99 (f4(c4) = c1),
% 29.77/19.99 inference(unit_resolution,[status(thm)],[11750, 29327])).
% 29.81/19.99 tff(29329,plain,
% 29.81/19.99 (~(c2 = c4)),
% 29.81/19.99 inference(unit_resolution,[status(thm)],[16877, 9314, 29314, 29325, 29328, 17])).
% 29.81/19.99 tff(29330,plain,
% 29.81/19.99 (~(c4 = c2)),
% 29.81/19.99 inference(modus_ponens,[status(thm)],[29329, 8722])).
% 29.81/19.99 tff(29331,plain,
% 29.81/19.99 (c4 = c1),
% 29.81/19.99 inference(unit_resolution,[status(thm)],[461, 29330])).
% 29.81/19.99 tff(29332,plain,
% 29.81/19.99 (big_f(c2, c4) <=> big_f(c2, c1)),
% 29.81/19.99 inference(monotonicity,[status(thm)],[29331])).
% 29.81/19.99 tff(29333,plain,
% 29.81/19.99 (big_f(c2, c1) <=> big_f(c2, c4)),
% 29.81/19.99 inference(symmetry,[status(thm)],[29332])).
% 29.81/19.99 tff(29334,plain,
% 29.81/19.99 ((~big_f(c2, c1)) <=> (~big_f(c2, c4))),
% 29.81/19.99 inference(monotonicity,[status(thm)],[29333])).
% 29.81/19.99 tff(29335,plain,
% 29.81/19.99 (~big_f(c2, c4)),
% 29.81/19.99 inference(modus_ponens,[status(thm)],[2, 29334])).
% 29.81/19.99 tff(29336,plain,
% 29.81/19.99 (~(f5(c1) = c2)),
% 29.81/19.99 inference(unit_resolution,[status(thm)],[16765, 29335, 29314, 29325, 23145, 22, 29331, 29329])).
% 29.81/19.99 tff(29337,plain,
% 29.81/19.99 (f5(c1) = c1),
% 29.81/19.99 inference(unit_resolution,[status(thm)],[1708, 29336])).
% 29.81/19.99 tff(29338,plain,
% 29.81/20.00 ((~(c3 = c1)) | (~(f4(c4) = c1)) | (~(f10(c1) = c1)) | (f10(c2) = c2) | big_f(c1, c2) | (~(f5(c1) = c1)) | (f7(c2) = c2)),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[27045, 25791])).
% 29.81/20.00 tff(29339,plain,
% 29.81/20.00 (~(f10(c1) = c1)),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[29338, 29337, 27, 28773, 89, 29328, 17])).
% 29.81/20.00 tff(29340,plain,
% 29.81/20.00 (f10(c1) = c2),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[14, 29339])).
% 29.81/20.00 tff(29341,plain,
% 29.81/20.00 (c2 = f10(c1)),
% 29.81/20.00 inference(symmetry,[status(thm)],[29340])).
% 29.81/20.00 tff(29342,plain,
% 29.81/20.00 (big_f(c2, c2) <=> big_f(f10(c1), f10(c1))),
% 29.81/20.00 inference(monotonicity,[status(thm)],[29341, 29341])).
% 29.81/20.00 tff(29343,plain,
% 29.81/20.00 (big_f(f10(c1), f10(c1))),
% 29.81/20.00 inference(modus_ponens,[status(thm)],[29325, 29342])).
% 29.81/20.00 tff(29344,plain,
% 29.81/20.00 (big_f(f3(c2, c2), c2)),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[21029, 9314, 29314, 29325, 22, 29329])).
% 29.81/20.00 tff(29345,plain,
% 29.81/20.00 (~(f3(c2, c2) = c2)),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[21039, 29335, 29314, 29325, 29329, 29344])).
% 29.81/20.00 tff(29346,plain,
% 29.81/20.00 (~(f6(c1, f6(c1, c2)) = c2)),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[28341, 29345, 27, 29344])).
% 29.81/20.00 tff(29347,plain,
% 29.81/20.00 (f6(c1, f6(c1, c2)) = c1),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[63, 29346])).
% 29.81/20.00 tff(29348,plain,
% 29.81/20.00 (f6(c1, c1) = c1),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[58, 29347])).
% 29.81/20.00 tff(29349,plain,
% 29.81/20.00 (big_f(f7(c1), f6(c1, c1))),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[27769, 29348, 29304])).
% 29.81/20.00 tff(29350,plain,
% 29.81/20.00 (f10(c1) = f8(c1)),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[19009, 2730, 25791, 29339, 29349, 29348, 29343])).
% 29.81/20.00 tff(29351,plain,
% 29.81/20.00 (f8(c1) = f10(c1)),
% 29.81/20.00 inference(symmetry,[status(thm)],[29350])).
% 29.81/20.00 tff(29352,plain,
% 29.81/20.00 (f3(c2, c2) = f3(f10(c1), f10(c1))),
% 29.81/20.00 inference(monotonicity,[status(thm)],[29341, 29341])).
% 29.81/20.00 tff(29353,plain,
% 29.81/20.00 (f3(f10(c1), f10(c1)) = f3(c2, c2)),
% 29.81/20.00 inference(symmetry,[status(thm)],[29352])).
% 29.81/20.00 tff(29354,plain,
% 29.81/20.00 (big_f(f3(f10(c1), f10(c1)), f10(c1)) <=> big_f(f3(c2, c2), f10(c1))),
% 29.81/20.00 inference(monotonicity,[status(thm)],[29353])).
% 29.81/20.00 tff(29355,plain,
% 29.81/20.00 (big_f(f3(c2, c2), f10(c1)) <=> big_f(f3(f10(c1), f10(c1)), f10(c1))),
% 29.81/20.00 inference(symmetry,[status(thm)],[29354])).
% 29.81/20.00 tff(29356,plain,
% 29.81/20.00 (big_f(f3(c2, c2), f10(c1))),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[27281, 29340, 29344])).
% 29.81/20.00 tff(29357,plain,
% 29.81/20.00 (big_f(f3(f10(c1), f10(c1)), f10(c1))),
% 29.81/20.00 inference(modus_ponens,[status(thm)],[29356, 29355])).
% 29.81/20.00 tff(29358,plain,
% 29.81/20.00 (f3(f10(c1), f10(c1)) = f8(c1)),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[27776, 2730, 25791, 29339, 29349, 29348, 29357])).
% 29.81/20.00 tff(29359,plain,
% 29.81/20.00 (f3(f10(c1), f10(c1)) = f10(c1)),
% 29.81/20.00 inference(transitivity,[status(thm)],[29358, 29351])).
% 29.81/20.00 tff(29360,plain,
% 29.81/20.00 ((f3(c2, c2) = c2) <=> (f3(f10(c1), f10(c1)) = f10(c1))),
% 29.81/20.00 inference(monotonicity,[status(thm)],[29352, 29341])).
% 29.81/20.00 tff(29361,plain,
% 29.81/20.00 ((~(f3(c2, c2) = c2)) <=> (~(f3(f10(c1), f10(c1)) = f10(c1)))),
% 29.81/20.00 inference(monotonicity,[status(thm)],[29360])).
% 29.81/20.00 tff(29362,plain,
% 29.81/20.00 (~(f3(f10(c1), f10(c1)) = f10(c1))),
% 29.81/20.00 inference(modus_ponens,[status(thm)],[29345, 29361])).
% 29.81/20.00 tff(29363,plain,
% 29.81/20.00 ($false),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[29362, 29359])).
% 29.81/20.00 tff(29364,plain,(big_f(c2, c1) | big_f(c1, c2) | (f10(c2) = c2) | (f7(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 29.81/20.00 tff(29365,plain,
% 29.81/20.00 (big_f(c2, c1)),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[29364, 17, 89, 27])).
% 29.81/20.00 tff(29366,plain,
% 29.81/20.00 (f10(c1) = c1),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[27979, 29365, 29304, 89, 27, 22])).
% 29.81/20.00 tff(29367,plain,
% 29.81/20.00 (big_f(f7(c1), f6(c1, c1))),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[28582, 28, 11819, 348, 4932, 3762])).
% 29.81/20.00 tff(29368,plain,
% 29.81/20.00 ((~(f6(f7(c2), c3) = c2)) | (~big_f(f7(c1), f6(c1, c1))) | big_f(f7(c2), c2) | (~(c3 = c1)) | (~(f7(c2) = c1))),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[10009, 25791])).
% 29.81/20.00 tff(29369,plain,
% 29.81/20.00 (~(f6(f7(c2), c3) = c2)),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[29368, 29367, 172, 1521, 292])).
% 29.81/20.00 tff(29370,plain,
% 29.81/20.00 ($false),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[2391, 29369, 18948])).
% 29.81/20.00 tff(29371,plain,((f6(c1, c1) = c1) | (~(c3 = c1)) | big_f(f7(c2), c2) | (~(f7(c2) = c1)) | (~(f10(c2) = c1)) | (~big_f(c2, c1)) | (~big_f(c1, c1)) | (~(f10(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.81/20.00 tff(29372,plain,
% 29.81/20.00 (f6(c1, c1) = c1),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[29371, 23145, 28773, 22, 94, 29365, 29304, 29366])).
% 29.81/20.00 tff(29373,plain,
% 29.81/20.00 (big_f(f7(c1), f6(c1, c1))),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[27769, 29372, 29304])).
% 29.81/20.00 tff(29374,plain,
% 29.81/20.00 (c1 = f8(c2)),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[27005, 2730, 25791, 89, 29373, 29372, 29324])).
% 29.81/20.00 tff(29375,plain,
% 29.81/20.00 (f8(c2) = c1),
% 29.81/20.00 inference(symmetry,[status(thm)],[29374])).
% 29.81/20.00 tff(29376,plain,
% 29.81/20.00 (big_f(c2, f10(c2))),
% 29.81/20.00 inference(modus_ponens,[status(thm)],[29365, 12069])).
% 29.81/20.00 tff(29377,plain,
% 29.81/20.00 (c2 = f8(c2)),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[28627, 2730, 25791, 89, 29376, 29373, 29372])).
% 29.81/20.00 tff(29378,plain,
% 29.81/20.00 (big_f(f9(c1, c1), c1)),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[26966, 29365, 22, 29326])).
% 29.81/20.00 tff(29379,plain,
% 29.81/20.00 (big_f(f9(c1, c1), f10(c1))),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[8716, 29378, 29366])).
% 29.81/20.00 tff(29380,plain,
% 29.81/20.00 (~(f9(c1, c1) = c1)),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[18907, 2378, 25791, 29366, 29379, 29373, 29372])).
% 29.81/20.00 tff(29381,plain,
% 29.81/20.00 (f9(c1, c1) = c2),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[3939, 29380])).
% 29.81/20.00 tff(29382,plain,
% 29.81/20.00 (f9(c1, c1) = c1),
% 29.81/20.00 inference(transitivity,[status(thm)],[29381, 29377, 29375])).
% 29.81/20.00 tff(29383,plain,
% 29.81/20.00 ($false),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[29380, 29382])).
% 29.81/20.00 tff(29384,plain,((f7(c2) = c2) | (f10(c2) = c2) | big_f(c1, c2)), inference(lemma,lemma(discharge,[]))).
% 29.81/20.00 tff(29385,plain,
% 29.81/20.00 (f7(c2) = c2),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[29384, 89, 27])).
% 29.81/20.00 tff(29386,plain,
% 29.81/20.00 (big_f(f10(c2), f10(c2))),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[21743, 94, 29304])).
% 29.81/20.00 tff(29387,plain,
% 29.81/20.00 (~(f4(c4) = c2)),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[15584, 2, 29314, 89, 29325, 29386])).
% 29.81/20.00 tff(29388,plain,
% 29.81/20.00 (f4(c4) = c1),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[11750, 29387])).
% 29.81/20.00 tff(29389,plain,
% 29.81/20.00 (f4(c2) = c1),
% 29.81/20.00 inference(transitivity,[status(thm)],[8744, 11752])).
% 29.81/20.00 tff(29390,plain,
% 29.81/20.00 ((c2 = f4(c2)) <=> (c2 = c1)),
% 29.81/20.00 inference(monotonicity,[status(thm)],[29389])).
% 29.81/20.00 tff(29391,plain,
% 29.81/20.00 ((c2 = c1) <=> (c2 = f4(c2))),
% 29.81/20.00 inference(symmetry,[status(thm)],[29390])).
% 29.81/20.00 tff(29392,plain,
% 29.81/20.00 ((c2 = c1) <=> (f7(c2) = f4(c2))),
% 29.81/20.00 inference(transitivity,[status(thm)],[29391, 21536])).
% 29.81/20.00 tff(29393,plain,
% 29.81/20.00 ((~(c2 = c1)) <=> (~(f7(c2) = f4(c2)))),
% 29.81/20.00 inference(monotonicity,[status(thm)],[29392])).
% 29.81/20.00 tff(29394,plain,
% 29.81/20.00 (~(f7(c2) = f4(c2))),
% 29.81/20.00 inference(modus_ponens,[status(thm)],[75, 29393])).
% 29.81/20.00 tff(29395,plain,
% 29.81/20.00 (f1(c2, c2) = c2),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[9464, 29394, 29314, 21532, 2, 631])).
% 29.81/20.00 tff(29396,plain,
% 29.81/20.00 (big_f(c2, f1(c2, c2)) <=> big_f(c2, c2)),
% 29.81/20.00 inference(monotonicity,[status(thm)],[29395])).
% 29.81/20.00 tff(29397,plain,
% 29.81/20.00 (big_f(c2, c2) <=> big_f(c2, f1(c2, c2))),
% 29.81/20.00 inference(symmetry,[status(thm)],[29396])).
% 29.81/20.00 tff(29398,plain,
% 29.81/20.00 (big_f(c2, f1(c2, c2))),
% 29.81/20.00 inference(modus_ponens,[status(thm)],[1345, 29397])).
% 29.81/20.00 tff(29399,plain,
% 29.81/20.00 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c2 = c4)) | big_f(c1, c2) | (~(c1 = f4(c2))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(c2 = c4)) | big_f(c1, c2) | (~(c1 = f4(c2))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))),
% 29.81/20.00 inference(rewrite,[status(thm)],[])).
% 29.81/20.00 tff(29400,plain,
% 29.81/20.00 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c2 = c3) | (~(c2 = c4)) | big_f(c1, c2) | (~(c1 = f4(c2))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2))))),
% 29.81/20.00 inference(quant_inst,[status(thm)],[])).
% 29.81/20.00 tff(29401,plain,
% 29.81/20.00 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c2 = c3) | (~(c2 = c4)) | big_f(c1, c2) | (~(c1 = f4(c2))) | (~(f1(c2, c2) = c2)) | (~big_f(c2, f1(c2, c2)))),
% 29.81/20.00 inference(modus_ponens,[status(thm)],[29400, 29399])).
% 29.81/20.00 tff(29402,plain,
% 29.81/20.00 ($false),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[29401, 447, 631, 29314, 29395, 29398, 27, 21280])).
% 29.81/20.00 tff(29403,plain,((~(c2 = c4)) | big_f(c1, c2) | (~big_f(c2, c2)) | big_f(c2, c1) | (~(f4(c4) = c1)) | (~(f7(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.81/20.00 tff(29404,plain,
% 29.81/20.00 (~(c2 = c4)),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[29403, 2, 29325, 27, 29388, 29385])).
% 29.81/20.00 tff(29405,plain,
% 29.81/20.00 (~(f6(c1, f6(c1, c2)) = c2)),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[29322, 29404, 27, 29325, 2])).
% 29.81/20.00 tff(29406,plain,
% 29.81/20.00 (f6(c1, f6(c1, c2)) = c1),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[63, 29405])).
% 29.81/20.00 tff(29407,plain,
% 29.81/20.00 (big_f(f7(c1), f6(c1, f6(c1, c2))) <=> big_f(c1, c1)),
% 29.81/20.00 inference(monotonicity,[status(thm)],[25791, 29406])).
% 29.81/20.00 tff(29408,plain,
% 29.81/20.00 (big_f(c1, c1) <=> big_f(f7(c1), f6(c1, f6(c1, c2)))),
% 29.81/20.00 inference(symmetry,[status(thm)],[29407])).
% 29.81/20.00 tff(29409,plain,
% 29.81/20.00 (big_f(f7(c1), f6(c1, f6(c1, c2)))),
% 29.81/20.00 inference(modus_ponens,[status(thm)],[29304, 29408])).
% 29.81/20.00 tff(29410,plain,
% 29.81/20.00 (f6(c1, f6(c1, c2)) = f6(c1, c2)),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[51, 29406])).
% 29.81/20.00 tff(29411,plain,
% 29.81/20.00 ((~big_f(c2, c1)) <=> (~big_f(f10(c1), c1))),
% 29.81/20.00 inference(monotonicity,[status(thm)],[27296])).
% 29.81/20.00 tff(29412,plain,
% 29.81/20.00 (~big_f(f10(c1), c1)),
% 29.81/20.00 inference(modus_ponens,[status(thm)],[2, 29411])).
% 29.81/20.00 tff(29413,plain,
% 29.81/20.00 ((f10(c1) = c3) <=> (f10(c1) = c1)),
% 29.81/20.00 inference(monotonicity,[status(thm)],[28773])).
% 29.81/20.00 tff(29414,plain,
% 29.81/20.00 ((f10(c1) = c1) <=> (f10(c1) = c3)),
% 29.81/20.00 inference(symmetry,[status(thm)],[29413])).
% 29.81/20.00 tff(29415,plain,
% 29.81/20.00 ((~(f10(c1) = c1)) <=> (~(f10(c1) = c3))),
% 29.81/20.00 inference(monotonicity,[status(thm)],[29414])).
% 29.81/20.00 tff(29416,plain,
% 29.81/20.00 (~(f10(c1) = c3)),
% 29.81/20.00 inference(modus_ponens,[status(thm)],[3, 29415])).
% 29.81/20.00 tff(29417,plain,
% 29.81/20.00 ((c2 = f4(c2)) <=> (f10(c1) = c1)),
% 29.81/20.00 inference(monotonicity,[status(thm)],[5571, 29389])).
% 29.81/20.00 tff(29418,plain,
% 29.81/20.00 ((f10(c1) = c1) <=> (c2 = f4(c2))),
% 29.81/20.00 inference(symmetry,[status(thm)],[29417])).
% 29.81/20.00 tff(29419,plain,
% 29.81/20.00 ((f10(c1) = c1) <=> (f7(c2) = f4(c2))),
% 29.81/20.00 inference(transitivity,[status(thm)],[29418, 21536])).
% 29.81/20.00 tff(29420,plain,
% 29.81/20.00 ((~(f10(c1) = c1)) <=> (~(f7(c2) = f4(c2)))),
% 29.81/20.00 inference(monotonicity,[status(thm)],[29419])).
% 29.81/20.00 tff(29421,plain,
% 29.81/20.00 (~(f7(c2) = f4(c2))),
% 29.81/20.00 inference(modus_ponens,[status(thm)],[3, 29420])).
% 29.81/20.00 tff(29422,plain,
% 29.81/20.00 (f1(c2, c2) = c2),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[9464, 29421, 377, 1180, 2, 631])).
% 29.81/20.00 tff(29423,plain,
% 29.81/20.00 (f1(f10(c1), f10(c1)) = f1(c2, c2)),
% 29.81/20.00 inference(monotonicity,[status(thm)],[15, 15])).
% 29.81/20.00 tff(29424,plain,
% 29.81/20.00 (f1(f10(c1), f10(c1)) = f10(c1)),
% 29.81/20.00 inference(transitivity,[status(thm)],[29423, 29422, 5571])).
% 29.81/20.00 tff(29425,plain,
% 29.81/20.00 (big_f(f10(c1), f1(f10(c1), f10(c1))) <=> big_f(f10(c1), f10(c1))),
% 29.81/20.00 inference(monotonicity,[status(thm)],[29424])).
% 29.81/20.00 tff(29426,plain,
% 29.81/20.00 (big_f(f10(c1), f10(c1)) <=> big_f(f10(c1), f1(f10(c1), f10(c1)))),
% 29.81/20.00 inference(symmetry,[status(thm)],[29425])).
% 29.81/20.00 tff(29427,plain,
% 29.81/20.00 (big_f(f10(c1), f1(f10(c1), f10(c1)))),
% 29.81/20.00 inference(modus_ponens,[status(thm)],[27318, 29426])).
% 29.81/20.00 tff(29428,plain,
% 29.81/20.00 (f4(f10(c1)) = f4(c2)),
% 29.81/20.00 inference(monotonicity,[status(thm)],[15])).
% 29.81/20.00 tff(29429,plain,
% 29.81/20.00 ((f10(c1) = f4(f10(c1))) <=> (c2 = f4(c2))),
% 29.81/20.00 inference(monotonicity,[status(thm)],[15, 29428])).
% 29.81/20.00 tff(29430,plain,
% 29.81/20.00 ((c2 = f4(c2)) <=> (f10(c1) = f4(f10(c1)))),
% 29.81/20.00 inference(symmetry,[status(thm)],[29429])).
% 29.81/20.00 tff(29431,plain,
% 29.81/20.00 ((f10(c1) = c1) <=> (f10(c1) = f4(f10(c1)))),
% 29.81/20.00 inference(transitivity,[status(thm)],[29418, 29430])).
% 29.81/20.00 tff(29432,plain,
% 29.81/20.00 ((~(f10(c1) = c1)) <=> (~(f10(c1) = f4(f10(c1))))),
% 29.81/20.00 inference(monotonicity,[status(thm)],[29431])).
% 29.81/20.00 tff(29433,plain,
% 29.81/20.00 (~(f10(c1) = f4(f10(c1)))),
% 29.81/20.00 inference(modus_ponens,[status(thm)],[3, 29432])).
% 29.81/20.00 tff(29434,assumption,(~(f10(c1) = c3)), introduced(assumption)).
% 29.81/20.00 tff(29435,plain,
% 29.81/20.00 ((c2 = c4) <=> (f10(c1) = c4)),
% 29.81/20.00 inference(monotonicity,[status(thm)],[5571])).
% 29.81/20.00 tff(29436,plain,
% 29.81/20.00 (f10(c1) = c4),
% 29.81/20.00 inference(modus_ponens,[status(thm)],[631, 29435])).
% 29.81/20.00 tff(29437,plain,
% 29.81/20.00 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((~(f10(c1) = c4)) | (f10(c1) = c3) | (~big_f(f10(c1), f10(c1))) | (~(f1(f10(c1), f10(c1)) = f10(c1))) | (f10(c1) = f4(f10(c1))) | (~big_f(f10(c1), f1(f10(c1), f10(c1)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (~(f10(c1) = c4)) | (f10(c1) = c3) | (~big_f(f10(c1), f10(c1))) | (~(f1(f10(c1), f10(c1)) = f10(c1))) | (f10(c1) = f4(f10(c1))) | (~big_f(f10(c1), f1(f10(c1), f10(c1)))))),
% 29.81/20.00 inference(rewrite,[status(thm)],[])).
% 29.81/20.00 tff(29438,plain,
% 29.81/20.00 (((f10(c1) = c3) | (~(f10(c1) = c4)) | (f10(c1) = f4(f10(c1))) | (~big_f(f10(c1), f10(c1))) | (~(f1(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f10(c1), f1(f10(c1), f10(c1))))) <=> ((~(f10(c1) = c4)) | (f10(c1) = c3) | (~big_f(f10(c1), f10(c1))) | (~(f1(f10(c1), f10(c1)) = f10(c1))) | (f10(c1) = f4(f10(c1))) | (~big_f(f10(c1), f1(f10(c1), f10(c1)))))),
% 29.81/20.00 inference(rewrite,[status(thm)],[])).
% 29.81/20.00 tff(29439,plain,
% 29.81/20.00 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f10(c1) = c3) | (~(f10(c1) = c4)) | (f10(c1) = f4(f10(c1))) | (~big_f(f10(c1), f10(c1))) | (~(f1(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f10(c1), f1(f10(c1), f10(c1)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((~(f10(c1) = c4)) | (f10(c1) = c3) | (~big_f(f10(c1), f10(c1))) | (~(f1(f10(c1), f10(c1)) = f10(c1))) | (f10(c1) = f4(f10(c1))) | (~big_f(f10(c1), f1(f10(c1), f10(c1))))))),
% 29.81/20.00 inference(monotonicity,[status(thm)],[29438])).
% 29.81/20.00 tff(29440,plain,
% 29.81/20.00 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f10(c1) = c3) | (~(f10(c1) = c4)) | (f10(c1) = f4(f10(c1))) | (~big_f(f10(c1), f10(c1))) | (~(f1(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f10(c1), f1(f10(c1), f10(c1)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (~(f10(c1) = c4)) | (f10(c1) = c3) | (~big_f(f10(c1), f10(c1))) | (~(f1(f10(c1), f10(c1)) = f10(c1))) | (f10(c1) = f4(f10(c1))) | (~big_f(f10(c1), f1(f10(c1), f10(c1)))))),
% 29.81/20.00 inference(transitivity,[status(thm)],[29439, 29437])).
% 29.81/20.00 tff(29441,plain,
% 29.81/20.00 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((f10(c1) = c3) | (~(f10(c1) = c4)) | (f10(c1) = f4(f10(c1))) | (~big_f(f10(c1), f10(c1))) | (~(f1(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f10(c1), f1(f10(c1), f10(c1)))))),
% 29.81/20.00 inference(quant_inst,[status(thm)],[])).
% 29.81/20.00 tff(29442,plain,
% 29.81/20.00 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (~(f10(c1) = c4)) | (f10(c1) = c3) | (~big_f(f10(c1), f10(c1))) | (~(f1(f10(c1), f10(c1)) = f10(c1))) | (f10(c1) = f4(f10(c1))) | (~big_f(f10(c1), f1(f10(c1), f10(c1))))),
% 29.81/20.00 inference(modus_ponens,[status(thm)],[29441, 29440])).
% 29.81/20.00 tff(29443,plain,
% 29.81/20.00 ((~(f1(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f10(c1), f1(f10(c1), f10(c1))))),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[29442, 553, 29436, 29434, 27318, 29433])).
% 29.81/20.00 tff(29444,plain,
% 29.81/20.00 ($false),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[29443, 29427, 29424])).
% 29.81/20.00 tff(29445,plain,((~(c2 = c4)) | (f10(c1) = c3) | (~big_f(f10(c1), f10(c1))) | (c2 = c3) | (~big_f(f7(c2), c2)) | big_f(c2, c1) | (f10(c1) = c1) | (~(f4(c4) = c1)) | (~(f7(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.81/20.00 tff(29446,plain,
% 29.81/20.00 (~(c2 = c4)),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[29445, 29416, 18940, 29314, 21532, 2, 3, 11752, 77])).
% 29.81/20.00 tff(29447,plain,
% 29.81/20.00 (big_f(c2, c4) <=> big_f(f10(c1), c1)),
% 29.81/20.00 inference(monotonicity,[status(thm)],[293, 9094])).
% 29.81/20.00 tff(29448,plain,
% 29.81/20.00 (big_f(f10(c1), c1) <=> big_f(c2, c4)),
% 29.81/20.00 inference(symmetry,[status(thm)],[29447])).
% 29.81/20.00 tff(29449,plain,
% 29.81/20.00 ((~big_f(f10(c1), c1)) <=> (~big_f(c2, c4))),
% 29.81/20.00 inference(monotonicity,[status(thm)],[29448])).
% 29.81/20.00 tff(29450,assumption,(~big_f(f10(c1), c1)), introduced(assumption)).
% 29.81/20.00 tff(29451,plain,
% 29.81/20.00 (~big_f(c2, c4)),
% 29.81/20.00 inference(modus_ponens,[status(thm)],[29450, 29449])).
% 29.81/20.00 tff(29452,plain,
% 29.81/20.00 (big_f(f3(c2, c2), c2)),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[21470, 29451, 29314, 1345, 873])).
% 29.81/20.00 tff(29453,plain,
% 29.81/20.00 (~(f3(c2, c2) = c2)),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[21039, 29451, 29314, 1345, 873, 29452])).
% 29.81/20.00 tff(29454,plain,
% 29.81/20.00 ($false),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[28341, 29453, 29452, 27, 27490])).
% 29.81/20.00 tff(29455,plain,((c2 = c4) | big_f(c1, c2) | (~(f6(c1, f6(c1, c2)) = c2)) | (~big_f(c2, c2)) | big_f(f10(c1), c1) | (~(f10(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.81/20.00 tff(29456,plain,
% 29.81/20.00 (~(f6(c1, f6(c1, c2)) = c2)),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[29455, 29446, 27, 1345, 29412, 15])).
% 29.81/20.00 tff(29457,plain,
% 29.81/20.00 (f6(c1, f6(c1, c2)) = c1),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[63, 29456])).
% 29.81/20.00 tff(29458,plain,
% 29.81/20.00 (~(c1 = f8(c1))),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[28363, 29457, 15821, 3, 29304])).
% 29.81/20.00 tff(29459,plain,
% 29.81/20.00 (~(f8(c1) = c1)),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[9808, 29458])).
% 29.81/20.00 tff(29460,plain,
% 29.81/20.00 (f8(c1) = c2),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[1680, 29459])).
% 29.81/20.00 tff(29461,plain,
% 29.81/20.00 ((f3(c2, c2) = f8(c1)) <=> (f3(c2, c2) = c2)),
% 29.81/20.00 inference(monotonicity,[status(thm)],[29460])).
% 29.81/20.00 tff(29462,plain,
% 29.81/20.00 (~(c4 = c2)),
% 29.81/20.00 inference(modus_ponens,[status(thm)],[29446, 8722])).
% 29.81/20.00 tff(29463,plain,
% 29.81/20.00 (c4 = c1),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[461, 29462])).
% 29.81/20.00 tff(29464,plain,
% 29.81/20.00 (big_f(c2, c4) <=> big_f(f10(c1), c1)),
% 29.81/20.00 inference(monotonicity,[status(thm)],[5571, 29463])).
% 29.81/20.00 tff(29465,plain,
% 29.81/20.00 (big_f(f10(c1), c1) <=> big_f(c2, c4)),
% 29.81/20.00 inference(symmetry,[status(thm)],[29464])).
% 29.81/20.00 tff(29466,plain,
% 29.81/20.00 ((~big_f(f10(c1), c1)) <=> (~big_f(c2, c4))),
% 29.81/20.00 inference(monotonicity,[status(thm)],[29465])).
% 29.81/20.00 tff(29467,plain,
% 29.81/20.00 (~big_f(c2, c4)),
% 29.81/20.00 inference(modus_ponens,[status(thm)],[29412, 29466])).
% 29.81/20.00 tff(29468,plain,
% 29.81/20.00 (big_f(f3(c2, c2), c2)),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[21470, 29467, 29314, 1345, 29446])).
% 29.81/20.00 tff(29469,plain,
% 29.81/20.00 (big_f(f3(c2, c2), f10(c1))),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[27281, 29468, 15])).
% 29.81/20.00 tff(29470,plain,
% 29.81/20.00 (f6(c1, c1) = c1),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[58, 29457])).
% 29.81/20.00 tff(29471,plain,
% 29.81/20.00 (big_f(f7(c1), f6(c1, c1))),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[27769, 29470, 29304])).
% 29.81/20.00 tff(29472,plain,
% 29.81/20.00 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1))))),
% 29.81/20.00 inference(rewrite,[status(thm)],[])).
% 29.81/20.00 tff(29473,plain,
% 29.81/20.00 (((f10(c1) = c1) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1)))) <=> ((f10(c1) = c1) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1))))),
% 29.81/20.00 inference(rewrite,[status(thm)],[])).
% 29.81/20.00 tff(29474,plain,
% 29.81/20.00 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1)))))),
% 29.81/20.00 inference(monotonicity,[status(thm)],[29473])).
% 29.81/20.00 tff(29475,plain,
% 29.81/20.00 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1))))),
% 29.81/20.00 inference(transitivity,[status(thm)],[29474, 29472])).
% 29.81/20.00 tff(29476,plain,
% 29.81/20.00 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))),
% 29.81/20.00 inference(quant_inst,[status(thm)],[])).
% 29.81/20.00 tff(29477,plain,
% 29.81/20.00 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (f3(c2, c2) = f8(c1)) | (~big_f(f3(c2, c2), f10(c1)))),
% 29.81/20.00 inference(modus_ponens,[status(thm)],[29476, 29475])).
% 29.81/20.00 tff(29478,plain,
% 29.81/20.00 (f3(c2, c2) = f8(c1)),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[29477, 2730, 25791, 3, 29471, 29470, 29469])).
% 29.81/20.00 tff(29479,plain,
% 29.81/20.00 (f3(c2, c2) = c2),
% 29.81/20.00 inference(modus_ponens,[status(thm)],[29478, 29461])).
% 29.81/20.00 tff(29480,plain,
% 29.81/20.00 (~(f3(c2, c2) = c2)),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[21039, 29467, 29314, 1345, 29446, 29468])).
% 29.81/20.00 tff(29481,plain,
% 29.81/20.00 ($false),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[29480, 29479])).
% 29.81/20.00 tff(29482,plain,((f10(c1) = c1) | (~big_f(c2, c2)) | big_f(c1, c2) | big_f(c2, c1) | (~(f4(c4) = c1)) | (~(f7(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.81/20.00 tff(29483,plain,
% 29.81/20.00 (f10(c1) = c1),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[29482, 2, 27, 29325, 29388, 29385])).
% 29.81/20.00 tff(29484,plain,
% 29.81/20.00 (big_f(f7(c1), f6(c1, c1))),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[27676, 29483, 29304, 2])).
% 29.81/20.00 tff(29485,plain,
% 29.81/20.00 (f6(c1, c1) = c1),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[58, 29406])).
% 29.81/20.00 tff(29486,plain,
% 29.81/20.00 (f9(c1, c1) = c1),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[27678, 29485, 2, 29483, 29484])).
% 29.81/20.00 tff(29487,plain,
% 29.81/20.00 (big_f(f9(c1, c1), c1)),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[10938, 29486, 29304])).
% 29.81/20.00 tff(29488,plain,
% 29.81/20.00 (big_f(f9(c1, c1), f10(c1))),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[8716, 29487, 29483])).
% 29.81/20.00 tff(29489,plain,
% 29.81/20.00 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))),
% 29.81/20.00 inference(rewrite,[status(thm)],[])).
% 29.81/20.00 tff(29490,plain,
% 29.81/20.00 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))),
% 29.81/20.00 inference(quant_inst,[status(thm)],[])).
% 29.81/20.00 tff(29491,plain,
% 29.81/20.00 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2))))),
% 29.81/20.00 inference(modus_ponens,[status(thm)],[29490, 29489])).
% 29.81/20.00 tff(29492,plain,
% 29.81/20.00 ($false),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[29491, 2378, 25791, 29483, 29486, 29488, 29410, 29409])).
% 29.81/20.00 tff(29493,plain,(big_f(c2, c1) | big_f(c1, c2) | (f10(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 29.81/20.00 tff(29494,plain,
% 29.81/20.00 (big_f(c2, c1)),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[29493, 89, 27])).
% 29.81/20.00 tff(29495,plain,
% 29.81/20.00 ((c1 = f8(c2)) <=> (c1 = f8(f10(c1)))),
% 29.81/20.00 inference(monotonicity,[status(thm)],[13830])).
% 29.81/20.00 tff(29496,plain,
% 29.81/20.00 (f10(f10(c1)) = c1),
% 29.81/20.00 inference(transitivity,[status(thm)],[24860, 11819])).
% 29.81/20.00 tff(29497,plain,
% 29.81/20.00 (big_f(c1, f10(f10(c1))) <=> big_f(c1, c1)),
% 29.81/20.00 inference(monotonicity,[status(thm)],[29496])).
% 29.81/20.00 tff(29498,plain,
% 29.81/20.00 (big_f(c1, c1) <=> big_f(c1, f10(f10(c1)))),
% 29.81/20.00 inference(symmetry,[status(thm)],[29497])).
% 29.81/20.00 tff(29499,plain,
% 29.81/20.00 (big_f(c1, f10(f10(c1)))),
% 29.81/20.00 inference(modus_ponens,[status(thm)],[29304, 29498])).
% 29.81/20.00 tff(29500,plain,
% 29.81/20.00 (big_f(f10(c1), f10(f10(c1))) <=> big_f(f10(c1), c1)),
% 29.81/20.00 inference(monotonicity,[status(thm)],[29496])).
% 29.81/20.00 tff(29501,plain,
% 29.81/20.00 (big_f(f10(c1), c1) <=> big_f(f10(c1), f10(f10(c1)))),
% 29.81/20.00 inference(symmetry,[status(thm)],[29500])).
% 29.81/20.00 tff(29502,plain,
% 29.81/20.00 (big_f(f10(c1), f10(f10(c1)))),
% 29.81/20.00 inference(modus_ponens,[status(thm)],[27297, 29501])).
% 29.81/20.00 tff(29503,plain,
% 29.81/20.00 ((f10(f10(c1)) = f10(c1)) <=> (c1 = f10(c1))),
% 29.81/20.00 inference(monotonicity,[status(thm)],[29496])).
% 29.81/20.00 tff(29504,plain,
% 29.81/20.00 ((f10(f10(c1)) = f10(c1)) <=> (f10(c1) = c1)),
% 29.81/20.00 inference(transitivity,[status(thm)],[29503, 18819])).
% 29.81/20.00 tff(29505,plain,
% 29.81/20.00 ((f10(c1) = c1) <=> (f10(f10(c1)) = f10(c1))),
% 29.81/20.00 inference(symmetry,[status(thm)],[29504])).
% 29.81/20.00 tff(29506,plain,
% 29.81/20.00 ((~(f10(c1) = c1)) <=> (~(f10(f10(c1)) = f10(c1)))),
% 29.81/20.00 inference(monotonicity,[status(thm)],[29505])).
% 29.81/20.00 tff(29507,plain,
% 29.81/20.00 (~(f10(f10(c1)) = f10(c1))),
% 29.81/20.00 inference(modus_ponens,[status(thm)],[3, 29506])).
% 29.81/20.00 tff(29508,plain,
% 29.81/20.00 (big_f(f7(c1), f6(c1, c1))),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[27769, 10030, 4932])).
% 29.81/20.00 tff(29509,plain,
% 29.81/20.00 (c1 = f8(f10(c1))),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[27965, 2730, 25791, 24968, 29508, 10030, 27872])).
% 29.81/20.00 tff(29510,plain,
% 29.81/20.00 (f8(f10(c1)) = c1),
% 29.81/20.00 inference(symmetry,[status(thm)],[29509])).
% 29.81/20.00 tff(29511,plain,
% 29.81/20.00 (f10(c1) = f8(f10(c1))),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[27973, 2730, 25791, 24968, 29508, 10030, 27873])).
% 29.81/20.00 tff(29512,plain,
% 29.81/20.00 (f10(c1) = c1),
% 29.81/20.00 inference(transitivity,[status(thm)],[29511, 29510])).
% 29.81/20.00 tff(29513,plain,
% 29.81/20.00 ($false),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[3, 29512])).
% 29.81/20.00 tff(29514,plain,((~(f6(c1, c1) = c1)) | (f10(c1) = c1) | (f10(f10(c1)) = f10(c1)) | (~big_f(c1, f10(f10(c1)))) | (~big_f(f10(c1), f10(f10(c1)))) | (~big_f(c1, c1))), inference(lemma,lemma(discharge,[]))).
% 29.81/20.00 tff(29515,plain,
% 29.81/20.00 (~(f6(c1, c1) = c1)),
% 29.81/20.00 inference(unit_resolution,[status(thm)],[29514, 3, 29507, 29499, 29502, 29304])).
% 29.81/20.01 tff(29516,plain,
% 29.81/20.01 (big_f(f7(c1), f6(c1, c1))),
% 29.81/20.01 inference(unit_resolution,[status(thm)],[27894, 29515, 29507, 29502, 3, 29499])).
% 29.81/20.01 tff(29517,plain,
% 29.81/20.01 (big_f(c1, f6(c1, c1))),
% 29.81/20.01 inference(unit_resolution,[status(thm)],[28169, 29516])).
% 29.81/20.01 tff(29518,plain,
% 29.81/20.01 (~(f6(c1, f6(c1, c2)) = c1)),
% 29.81/20.01 inference(unit_resolution,[status(thm)],[58, 29515])).
% 29.81/20.01 tff(29519,plain,
% 29.81/20.01 (f6(c1, f6(c1, c2)) = c2),
% 29.81/20.01 inference(unit_resolution,[status(thm)],[63, 29518])).
% 29.81/20.01 tff(29520,plain,
% 29.81/20.01 (f6(c1, c1) = f10(c1)),
% 29.81/20.01 inference(transitivity,[status(thm)],[6933, 27490, 293])).
% 29.81/20.01 tff(29521,plain,
% 29.81/20.01 (big_f(c1, f6(c1, c1)) <=> big_f(c1, f10(c1))),
% 29.81/20.01 inference(monotonicity,[status(thm)],[29520])).
% 29.81/20.01 tff(29522,plain,
% 29.81/20.01 (big_f(c1, f10(c1)) <=> big_f(c1, f6(c1, c1))),
% 29.81/20.01 inference(symmetry,[status(thm)],[29521])).
% 29.81/20.01 tff(29523,plain,
% 29.81/20.01 ((~big_f(c1, f10(c1))) <=> (~big_f(c1, f6(c1, c1)))),
% 29.81/20.01 inference(monotonicity,[status(thm)],[29522])).
% 29.81/20.01 tff(29524,plain,
% 29.81/20.01 (~big_f(c1, f6(c1, c1))),
% 29.81/20.01 inference(modus_ponens,[status(thm)],[3030, 29523])).
% 29.81/20.01 tff(29525,plain,
% 29.81/20.01 ($false),
% 29.81/20.01 inference(unit_resolution,[status(thm)],[28185, 29524])).
% 29.81/20.01 tff(29526,plain,((~(f6(c1, c2) = c1)) | (~big_f(c1, f6(c1, c1))) | big_f(c1, f10(c1)) | (~(f6(c1, f6(c1, c2)) = c2)) | (~(f10(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.81/20.01 tff(29527,plain,
% 29.81/20.01 (~(f6(c1, c2) = c1)),
% 29.81/20.01 inference(unit_resolution,[status(thm)],[29526, 29519, 15821, 29517, 15])).
% 29.81/20.01 tff(29528,plain,
% 29.81/20.01 (f6(c1, c2) = c2),
% 29.81/20.01 inference(unit_resolution,[status(thm)],[48, 29527])).
% 29.81/20.01 tff(29529,plain,
% 29.81/20.01 (f6(c1, c2) = f10(c1)),
% 29.81/20.01 inference(transitivity,[status(thm)],[29528, 5571])).
% 29.81/20.01 tff(29530,plain,
% 29.81/20.01 (f8(f6(c1, c2)) = f8(f10(c1))),
% 29.81/20.01 inference(monotonicity,[status(thm)],[29529])).
% 29.81/20.01 tff(29531,plain,
% 29.81/20.01 (f8(f6(c1, c2)) = f8(c2)),
% 29.81/20.01 inference(transitivity,[status(thm)],[29530, 13827])).
% 29.81/20.01 tff(29532,plain,
% 29.81/20.01 ((c1 = f8(f6(c1, c2))) <=> (c1 = f8(c2))),
% 29.81/20.01 inference(monotonicity,[status(thm)],[29531])).
% 29.81/20.01 tff(29533,plain,
% 29.81/20.01 ((c1 = f8(f6(c1, c2))) <=> (c1 = f8(f10(c1)))),
% 29.81/20.01 inference(transitivity,[status(thm)],[29532, 29495])).
% 29.81/20.01 tff(29534,plain,
% 29.81/20.01 ((~(c1 = f8(f6(c1, c2)))) <=> (~(c1 = f8(f10(c1))))),
% 29.81/20.01 inference(monotonicity,[status(thm)],[29533])).
% 29.81/20.01 tff(29535,plain,
% 29.81/20.01 ((c1 = f8(c2)) <=> (c1 = f8(f6(c1, c2)))),
% 29.81/20.01 inference(symmetry,[status(thm)],[29532])).
% 29.81/20.01 tff(29536,plain,
% 29.81/20.01 ((~(c1 = f8(c2))) <=> (~(c1 = f8(f6(c1, c2))))),
% 29.81/20.01 inference(monotonicity,[status(thm)],[29535])).
% 29.81/20.01 tff(29537,plain,
% 29.81/20.01 (big_f(f10(c2), c2) <=> big_f(c1, c2)),
% 29.81/20.01 inference(monotonicity,[status(thm)],[11819])).
% 29.81/20.01 tff(29538,plain,
% 29.81/20.01 (big_f(c1, c2) <=> big_f(f10(c2), c2)),
% 29.81/20.01 inference(symmetry,[status(thm)],[29537])).
% 29.81/20.01 tff(29539,plain,
% 29.81/20.01 ((~big_f(c1, c2)) <=> (~big_f(f10(c2), c2))),
% 29.81/20.01 inference(monotonicity,[status(thm)],[29538])).
% 29.81/20.01 tff(29540,plain,
% 29.81/20.01 (~big_f(f10(c2), c2)),
% 29.81/20.01 inference(modus_ponens,[status(thm)],[27, 29539])).
% 29.81/20.01 tff(29541,plain,
% 29.81/20.01 (~(c1 = f8(c2))),
% 29.81/20.01 inference(unit_resolution,[status(thm)],[28187, 29517, 29540, 11819, 29515])).
% 29.81/20.01 tff(29542,plain,
% 29.81/20.01 (~(c1 = f8(f6(c1, c2)))),
% 29.81/20.01 inference(modus_ponens,[status(thm)],[29541, 29536])).
% 29.81/20.01 tff(29543,plain,
% 29.81/20.01 (~(c1 = f8(f10(c1)))),
% 29.81/20.01 inference(modus_ponens,[status(thm)],[29542, 29534])).
% 29.81/20.01 tff(29544,plain,
% 29.81/20.01 (c1 = c3),
% 29.81/20.01 inference(unit_resolution,[status(thm)],[175, 28773])).
% 29.81/20.01 tff(29545,plain,
% 29.81/20.01 (big_f(c1, f6(c1, c1))),
% 29.81/20.01 inference(unit_resolution,[status(thm)],[28169, 27895])).
% 29.81/20.01 tff(29546,plain,
% 29.81/20.01 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c1 = f2(c1)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c1 = c3)) | (c1 = f2(c1)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)))),
% 29.81/20.01 inference(rewrite,[status(thm)],[])).
% 29.81/20.01 tff(29547,plain,
% 29.81/20.01 (((~(c1 = c3)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (c1 = f2(c1)) | (~big_f(c1, c1))) <=> ((~(c1 = c3)) | (c1 = f2(c1)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)))),
% 29.81/20.01 inference(rewrite,[status(thm)],[])).
% 29.81/20.01 tff(29548,plain,
% 29.81/20.01 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (c1 = f2(c1)) | (~big_f(c1, c1)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c1 = f2(c1)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1))))),
% 29.81/20.01 inference(monotonicity,[status(thm)],[29547])).
% 29.81/20.01 tff(29549,plain,
% 29.81/20.01 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (c1 = f2(c1)) | (~big_f(c1, c1)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c1 = c3)) | (c1 = f2(c1)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)))),
% 29.81/20.01 inference(transitivity,[status(thm)],[29548, 29546])).
% 29.81/20.01 tff(29550,plain,
% 29.81/20.01 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (c1 = f2(c1)) | (~big_f(c1, c1)))),
% 29.81/20.01 inference(quant_inst,[status(thm)],[])).
% 29.81/20.01 tff(29551,plain,
% 29.81/20.01 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c1 = c3)) | (c1 = f2(c1)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1))),
% 29.81/20.01 inference(modus_ponens,[status(thm)],[29550, 29549])).
% 29.81/20.01 tff(29552,plain,
% 29.81/20.01 ((c1 = f2(c1)) | (~(c1 = c4)) | (c1 = f4(c1))),
% 29.81/20.01 inference(unit_resolution,[status(thm)],[29551, 1355, 5080, 4932])).
% 29.81/20.01 tff(29553,plain,
% 29.81/20.01 (c1 = f2(c1)),
% 29.81/20.01 inference(unit_resolution,[status(thm)],[29552, 11525, 11526])).
% 29.81/20.01 tff(29554,plain,
% 29.81/20.01 (f2(c1) = c1),
% 29.81/20.01 inference(symmetry,[status(thm)],[29553])).
% 29.81/20.01 tff(29555,plain,
% 29.81/20.01 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (~big_f(c1, f6(c1, c1))) | (f6(c1, c1) = f2(c1)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c1 = c3)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (~big_f(c1, f6(c1, c1))) | (f6(c1, c1) = f2(c1)))),
% 29.81/20.01 inference(rewrite,[status(thm)],[])).
% 29.81/20.01 tff(29556,plain,
% 29.81/20.01 (((~(c1 = c3)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (f6(c1, c1) = f2(c1)) | (~big_f(c1, f6(c1, c1)))) <=> ((~(c1 = c3)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (~big_f(c1, f6(c1, c1))) | (f6(c1, c1) = f2(c1)))),
% 29.81/20.01 inference(rewrite,[status(thm)],[])).
% 29.81/20.01 tff(29557,plain,
% 29.81/20.01 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (f6(c1, c1) = f2(c1)) | (~big_f(c1, f6(c1, c1))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (~big_f(c1, f6(c1, c1))) | (f6(c1, c1) = f2(c1))))),
% 29.81/20.01 inference(monotonicity,[status(thm)],[29556])).
% 29.81/20.01 tff(29558,plain,
% 29.81/20.01 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (f6(c1, c1) = f2(c1)) | (~big_f(c1, f6(c1, c1))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c1 = c3)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (~big_f(c1, f6(c1, c1))) | (f6(c1, c1) = f2(c1)))),
% 29.81/20.01 inference(transitivity,[status(thm)],[29557, 29555])).
% 29.81/20.01 tff(29559,plain,
% 29.81/20.01 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (f6(c1, c1) = f2(c1)) | (~big_f(c1, f6(c1, c1))))),
% 29.81/20.01 inference(quant_inst,[status(thm)],[])).
% 29.81/20.01 tff(29560,plain,
% 29.81/20.01 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c1 = c3)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (~big_f(c1, f6(c1, c1))) | (f6(c1, c1) = f2(c1))),
% 29.81/20.01 inference(modus_ponens,[status(thm)],[29559, 29558])).
% 29.81/20.01 tff(29561,plain,
% 29.81/20.01 ((c1 = f4(c1)) | (f6(c1, c1) = f2(c1))),
% 29.81/20.01 inference(unit_resolution,[status(thm)],[29560, 1355, 5080, 11526, 4932, 28185])).
% 29.81/20.01 tff(29562,plain,
% 29.81/20.01 (f6(c1, c1) = f2(c1)),
% 29.81/20.01 inference(unit_resolution,[status(thm)],[29561, 11525])).
% 29.81/20.01 tff(29563,plain,
% 29.81/20.01 (f6(c1, c1) = c1),
% 29.81/20.01 inference(transitivity,[status(thm)],[29562, 29554])).
% 29.81/20.01 tff(29564,plain,
% 29.81/20.01 ($false),
% 29.81/20.01 inference(unit_resolution,[status(thm)],[28, 29563])).
% 29.81/20.01 tff(29565,plain,((c1 = f4(c1)) | (f6(c1, c1) = c1) | (~(c1 = c3)) | (~(c1 = c4)) | (~big_f(c1, c1)) | (~big_f(c1, f6(c1, c1)))), inference(lemma,lemma(discharge,[]))).
% 29.81/20.01 tff(29566,plain,
% 29.81/20.01 (c1 = f4(c1)),
% 29.81/20.01 inference(unit_resolution,[status(thm)],[29565, 28, 5080, 11526, 4932, 29545])).
% 29.81/20.01 tff(29567,plain,
% 29.81/20.01 (f4(c1) = c1),
% 29.81/20.01 inference(symmetry,[status(thm)],[29566])).
% 29.81/20.01 tff(29568,plain,
% 29.81/20.01 ((c2 = f4(c1)) <=> (f10(c1) = c1)),
% 29.81/20.01 inference(monotonicity,[status(thm)],[5571, 29567])).
% 29.81/20.01 tff(29569,plain,
% 29.81/20.01 ((f10(c1) = c1) <=> (c2 = f4(c1))),
% 29.81/20.01 inference(symmetry,[status(thm)],[29568])).
% 29.81/20.01 tff(29570,plain,
% 29.81/20.01 ((~(f10(c1) = c1)) <=> (~(c2 = f4(c1)))),
% 29.81/20.01 inference(monotonicity,[status(thm)],[29569])).
% 29.81/20.01 tff(29571,plain,
% 29.81/20.01 (~(c2 = f4(c1))),
% 29.81/20.01 inference(modus_ponens,[status(thm)],[3, 29570])).
% 29.81/20.01 tff(29572,plain,
% 29.81/20.01 ((c1 = f2(c1)) | (~(c1 = c4)) | (c2 = f4(c1))),
% 29.81/20.01 inference(unit_resolution,[status(thm)],[25534, 1355, 5080, 348, 4932])).
% 29.81/20.01 tff(29573,plain,
% 29.81/20.01 (c1 = f2(c1)),
% 29.81/20.01 inference(unit_resolution,[status(thm)],[29572, 29571, 11526])).
% 29.81/20.01 tff(29574,plain,
% 29.81/20.01 (f2(c1) = c1),
% 29.81/20.01 inference(symmetry,[status(thm)],[29573])).
% 29.81/20.01 tff(29575,plain,
% 29.81/20.01 ((f10(c1) = f4(c1)) <=> (c2 = f4(c1))),
% 29.81/20.01 inference(monotonicity,[status(thm)],[15])).
% 29.81/20.01 tff(29576,plain,
% 29.81/20.01 ((c2 = f4(c1)) <=> (f10(c1) = f4(c1))),
% 29.81/20.01 inference(symmetry,[status(thm)],[29575])).
% 29.81/20.01 tff(29577,plain,
% 29.81/20.01 ((f10(c1) = c1) <=> (f10(c1) = f4(c1))),
% 29.81/20.01 inference(transitivity,[status(thm)],[29569, 29576])).
% 29.81/20.01 tff(29578,plain,
% 29.81/20.01 ((~(f10(c1) = c1)) <=> (~(f10(c1) = f4(c1)))),
% 29.81/20.01 inference(monotonicity,[status(thm)],[29577])).
% 29.81/20.01 tff(29579,plain,
% 29.81/20.01 (~(f10(c1) = f4(c1))),
% 29.81/20.01 inference(modus_ponens,[status(thm)],[3, 29578])).
% 29.81/20.01 tff(29580,plain,
% 29.81/20.01 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (~(c1 = c4)) | (~big_f(c1, f6(c1, c1))) | (f6(c1, c1) = f2(c1)) | (~big_f(f10(c1), c1)) | (f10(c1) = f4(c1)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c1 = c3)) | (~(c1 = c4)) | (~big_f(c1, f6(c1, c1))) | (f6(c1, c1) = f2(c1)) | (~big_f(f10(c1), c1)) | (f10(c1) = f4(c1)))),
% 29.81/20.01 inference(rewrite,[status(thm)],[])).
% 29.81/20.01 tff(29581,plain,
% 29.81/20.01 (((~(c1 = c3)) | (~(c1 = c4)) | (f10(c1) = f4(c1)) | (~big_f(f10(c1), c1)) | (f6(c1, c1) = f2(c1)) | (~big_f(c1, f6(c1, c1)))) <=> ((~(c1 = c3)) | (~(c1 = c4)) | (~big_f(c1, f6(c1, c1))) | (f6(c1, c1) = f2(c1)) | (~big_f(f10(c1), c1)) | (f10(c1) = f4(c1)))),
% 29.81/20.01 inference(rewrite,[status(thm)],[])).
% 29.81/20.01 tff(29582,plain,
% 29.81/20.01 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (~(c1 = c4)) | (f10(c1) = f4(c1)) | (~big_f(f10(c1), c1)) | (f6(c1, c1) = f2(c1)) | (~big_f(c1, f6(c1, c1))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (~(c1 = c4)) | (~big_f(c1, f6(c1, c1))) | (f6(c1, c1) = f2(c1)) | (~big_f(f10(c1), c1)) | (f10(c1) = f4(c1))))),
% 29.81/20.01 inference(monotonicity,[status(thm)],[29581])).
% 29.81/20.01 tff(29583,plain,
% 29.81/20.01 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (~(c1 = c4)) | (f10(c1) = f4(c1)) | (~big_f(f10(c1), c1)) | (f6(c1, c1) = f2(c1)) | (~big_f(c1, f6(c1, c1))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c1 = c3)) | (~(c1 = c4)) | (~big_f(c1, f6(c1, c1))) | (f6(c1, c1) = f2(c1)) | (~big_f(f10(c1), c1)) | (f10(c1) = f4(c1)))),
% 29.81/20.01 inference(transitivity,[status(thm)],[29582, 29580])).
% 29.81/20.01 tff(29584,plain,
% 29.81/20.01 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (~(c1 = c4)) | (f10(c1) = f4(c1)) | (~big_f(f10(c1), c1)) | (f6(c1, c1) = f2(c1)) | (~big_f(c1, f6(c1, c1))))),
% 29.81/20.01 inference(quant_inst,[status(thm)],[])).
% 29.81/20.01 tff(29585,plain,
% 29.81/20.01 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c1 = c3)) | (~(c1 = c4)) | (~big_f(c1, f6(c1, c1))) | (f6(c1, c1) = f2(c1)) | (~big_f(f10(c1), c1)) | (f10(c1) = f4(c1))),
% 29.81/20.01 inference(modus_ponens,[status(thm)],[29584, 29583])).
% 29.81/20.01 tff(29586,plain,
% 29.81/20.01 ((f6(c1, c1) = f2(c1)) | (f10(c1) = f4(c1))),
% 29.81/20.01 inference(unit_resolution,[status(thm)],[29585, 1355, 5080, 11526, 29545, 27297])).
% 29.81/20.01 tff(29587,plain,
% 29.81/20.01 (f6(c1, c1) = f2(c1)),
% 29.81/20.01 inference(unit_resolution,[status(thm)],[29586, 29579])).
% 29.81/20.01 tff(29588,plain,
% 29.81/20.01 (f6(c1, c1) = c1),
% 29.81/20.01 inference(transitivity,[status(thm)],[29587, 29574])).
% 29.81/20.01 tff(29589,plain,
% 29.81/20.01 ($false),
% 29.81/20.01 inference(unit_resolution,[status(thm)],[28, 29588])).
% 29.81/20.01 tff(29590,plain,((f6(c1, c1) = c1) | (~(c1 = c3)) | (~(c1 = c4)) | (~big_f(c2, c1)) | (~big_f(c1, c1)) | (f10(c1) = c1) | (f10(f10(c1)) = f10(c1)) | (~big_f(f10(c1), f10(f10(c1)))) | (~big_f(c1, f10(f10(c1))))), inference(lemma,lemma(discharge,[]))).
% 29.81/20.01 tff(29591,plain,
% 29.81/20.01 (~(c1 = c4)),
% 29.81/20.01 inference(unit_resolution,[status(thm)],[29590, 29515, 29544, 348, 29304, 3, 29507, 29502, 29499])).
% 29.81/20.01 tff(29592,plain,
% 29.81/20.01 (~(f6(c1, c2) = c1)),
% 29.81/20.01 inference(unit_resolution,[status(thm)],[29526, 64, 3030, 28185, 15])).
% 29.81/20.01 tff(29593,plain,
% 29.81/20.01 (f6(c1, c2) = c2),
% 29.81/20.01 inference(unit_resolution,[status(thm)],[48, 29592])).
% 29.81/20.01 tff(29594,plain,
% 29.81/20.01 ((c2 = f2(c1)) <=> (c2 = f2(c3))),
% 29.81/20.01 inference(monotonicity,[status(thm)],[5586])).
% 29.81/20.01 tff(29595,plain,
% 29.81/20.01 ((f10(c1) = f2(c1)) <=> (f2(c3) = c2)),
% 29.81/20.01 inference(transitivity,[status(thm)],[27371, 29594, 3831])).
% 29.81/20.01 tff(29596,plain,
% 29.81/20.01 ((~(f10(c1) = f2(c1))) <=> (~(f2(c3) = c2))),
% 29.81/20.01 inference(monotonicity,[status(thm)],[29595])).
% 29.81/20.01 tff(29597,plain,
% 29.81/20.01 (f6(c1, f3(c1, c2)) = f10(c1)),
% 29.81/20.01 inference(transitivity,[status(thm)],[7021, 293])).
% 29.81/20.01 tff(29598,plain,
% 29.81/20.01 (big_f(f7(c1), f6(c1, f3(c1, c2))) <=> big_f(c1, f10(c1))),
% 29.81/20.01 inference(monotonicity,[status(thm)],[25791, 29597])).
% 29.81/20.01 tff(29599,plain,
% 29.81/20.01 (big_f(c1, f10(c1)) <=> big_f(f7(c1), f6(c1, f3(c1, c2)))),
% 29.81/20.01 inference(symmetry,[status(thm)],[29598])).
% 29.81/20.01 tff(29600,plain,
% 29.81/20.01 ((~big_f(c1, f10(c1))) <=> (~big_f(f7(c1), f6(c1, f3(c1, c2))))),
% 29.81/20.01 inference(monotonicity,[status(thm)],[29599])).
% 29.81/20.01 tff(29601,plain,
% 29.81/20.01 (~big_f(f7(c1), f6(c1, f3(c1, c2)))),
% 29.81/20.01 inference(modus_ponens,[status(thm)],[3030, 29600])).
% 29.81/20.01 tff(29602,plain,
% 29.81/20.01 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | (f6(c1, f3(c1, c2)) = f3(c1, c2)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | big_f(f7(c1), f6(c1, f3(c1, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | (f6(c1, f3(c1, c2)) = f3(c1, c2)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | big_f(f7(c1), f6(c1, f3(c1, c2))))),
% 29.81/20.01 inference(rewrite,[status(thm)],[])).
% 29.81/20.01 tff(29603,plain,
% 29.81/20.01 (((f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (~(f7(c1) = c1)) | (f6(c1, f3(c1, c2)) = f3(c1, c2)) | big_f(f7(c1), f6(c1, f3(c1, c2)))) <=> ((f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | (f6(c1, f3(c1, c2)) = f3(c1, c2)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | big_f(f7(c1), f6(c1, f3(c1, c2))))),
% 29.81/20.01 inference(rewrite,[status(thm)],[])).
% 29.81/20.01 tff(29604,plain,
% 29.81/20.01 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (~(f7(c1) = c1)) | (f6(c1, f3(c1, c2)) = f3(c1, c2)) | big_f(f7(c1), f6(c1, f3(c1, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | (f6(c1, f3(c1, c2)) = f3(c1, c2)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | big_f(f7(c1), f6(c1, f3(c1, c2)))))),
% 29.81/20.01 inference(monotonicity,[status(thm)],[29603])).
% 29.81/20.01 tff(29605,plain,
% 29.81/20.01 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (~(f7(c1) = c1)) | (f6(c1, f3(c1, c2)) = f3(c1, c2)) | big_f(f7(c1), f6(c1, f3(c1, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | (f6(c1, f3(c1, c2)) = f3(c1, c2)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | big_f(f7(c1), f6(c1, f3(c1, c2))))),
% 29.81/20.01 inference(transitivity,[status(thm)],[29604, 29602])).
% 29.81/20.01 tff(29606,plain,
% 29.81/20.01 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (~(f7(c1) = c1)) | (f6(c1, f3(c1, c2)) = f3(c1, c2)) | big_f(f7(c1), f6(c1, f3(c1, c2))))),
% 29.81/20.01 inference(quant_inst,[status(thm)],[])).
% 29.81/20.01 tff(29607,plain,
% 29.81/20.01 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | (f6(c1, f3(c1, c2)) = f3(c1, c2)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | big_f(f7(c1), f6(c1, f3(c1, c2)))),
% 29.81/20.01 inference(modus_ponens,[status(thm)],[29606, 29605])).
% 29.81/20.01 tff(29608,plain,
% 29.81/20.01 (f6(c1, f3(c1, c2)) = f3(c1, c2)),
% 29.81/20.01 inference(unit_resolution,[status(thm)],[29607, 2662, 25791, 24968, 27903, 29601, 27872])).
% 29.81/20.01 tff(29609,plain,
% 29.81/20.01 (f3(c1, f10(c1)) = f3(c1, c2)),
% 29.81/20.01 inference(monotonicity,[status(thm)],[16])).
% 29.81/20.01 tff(29610,plain,
% 29.81/20.01 ((f3(c1, f10(c1)) = f10(c1)) <=> (f3(c1, c2) = c2)),
% 29.81/20.01 inference(monotonicity,[status(thm)],[29609, 16])).
% 29.81/20.01 tff(29611,plain,
% 29.81/20.01 ((f3(c1, c2) = c2) <=> (f3(c1, f10(c1)) = f10(c1))),
% 29.81/20.01 inference(symmetry,[status(thm)],[29610])).
% 29.81/20.01 tff(29612,plain,
% 29.81/20.01 ((f6(c1, f3(c1, c2)) = f3(c1, c2)) <=> (f3(c1, f10(c1)) = f10(c1))),
% 29.81/20.01 inference(transitivity,[status(thm)],[7026, 29611])).
% 29.81/20.01 tff(29613,assumption,(f6(c1, f3(c1, c2)) = f3(c1, c2)), introduced(assumption)).
% 29.81/20.01 tff(29614,plain,
% 29.81/20.01 (f3(c1, f10(c1)) = f10(c1)),
% 29.81/20.01 inference(modus_ponens,[status(thm)],[29613, 29612])).
% 29.81/20.02 tff(29615,plain,
% 29.81/20.02 (big_f(f3(c1, f10(c1)), c1) <=> big_f(f3(c1, c2), c1)),
% 29.81/20.02 inference(monotonicity,[status(thm)],[29609])).
% 29.81/20.02 tff(29616,plain,
% 29.81/20.02 (big_f(f3(c1, c2), c1) <=> big_f(f3(c1, f10(c1)), c1)),
% 29.81/20.02 inference(symmetry,[status(thm)],[29615])).
% 29.81/20.02 tff(29617,plain,
% 29.81/20.02 (f3(c1, c2) = f6(c1, f3(c1, c2))),
% 29.81/20.02 inference(symmetry,[status(thm)],[29613])).
% 29.81/20.02 tff(29618,plain,
% 29.81/20.02 (f3(c1, c2) = f10(c1)),
% 29.81/20.02 inference(transitivity,[status(thm)],[29617, 7021, 293])).
% 29.81/20.02 tff(29619,plain,
% 29.81/20.02 (big_f(f3(c1, c2), c1) <=> big_f(f10(c1), c1)),
% 29.81/20.02 inference(monotonicity,[status(thm)],[29618])).
% 29.81/20.02 tff(29620,plain,
% 29.81/20.02 (big_f(f10(c1), c1) <=> big_f(f3(c1, c2), c1)),
% 29.81/20.02 inference(symmetry,[status(thm)],[29619])).
% 29.81/20.02 tff(29621,plain,
% 29.81/20.02 (big_f(f10(c1), c1) <=> big_f(f3(c1, f10(c1)), c1)),
% 29.81/20.02 inference(transitivity,[status(thm)],[29620, 29616])).
% 29.81/20.02 tff(29622,plain,
% 29.81/20.02 (big_f(f3(c1, f10(c1)), c1)),
% 29.81/20.02 inference(modus_ponens,[status(thm)],[27307, 29621])).
% 29.81/20.02 tff(29623,assumption,(f10(c1) = f2(c1)), introduced(assumption)).
% 29.81/20.02 tff(29624,plain,
% 29.81/20.02 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((c1 = c4) | (~(c1 = c3)) | (~(f10(c1) = f2(c1))) | big_f(c1, f10(c1)) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (c1 = c4) | (~(c1 = c3)) | (~(f10(c1) = f2(c1))) | big_f(c1, f10(c1)) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1)))),
% 29.81/20.02 inference(rewrite,[status(thm)],[])).
% 29.81/20.02 tff(29625,plain,
% 29.81/20.02 (((~(c1 = c3)) | (~(f10(c1) = f2(c1))) | (c1 = c4) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1)) | big_f(c1, f10(c1))) <=> ((c1 = c4) | (~(c1 = c3)) | (~(f10(c1) = f2(c1))) | big_f(c1, f10(c1)) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1)))),
% 29.81/20.02 inference(rewrite,[status(thm)],[])).
% 29.81/20.02 tff(29626,plain,
% 29.81/20.02 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(f10(c1) = f2(c1))) | (c1 = c4) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1)) | big_f(c1, f10(c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((c1 = c4) | (~(c1 = c3)) | (~(f10(c1) = f2(c1))) | big_f(c1, f10(c1)) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1))))),
% 29.81/20.02 inference(monotonicity,[status(thm)],[29625])).
% 29.81/20.02 tff(29627,plain,
% 29.81/20.02 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(f10(c1) = f2(c1))) | (c1 = c4) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1)) | big_f(c1, f10(c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (c1 = c4) | (~(c1 = c3)) | (~(f10(c1) = f2(c1))) | big_f(c1, f10(c1)) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1)))),
% 29.81/20.02 inference(transitivity,[status(thm)],[29626, 29624])).
% 29.81/20.02 tff(29628,plain,
% 29.81/20.02 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(f10(c1) = f2(c1))) | (c1 = c4) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1)) | big_f(c1, f10(c1)))),
% 29.81/20.02 inference(quant_inst,[status(thm)],[])).
% 29.81/20.02 tff(29629,plain,
% 29.81/20.02 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (c1 = c4) | (~(c1 = c3)) | (~(f10(c1) = f2(c1))) | big_f(c1, f10(c1)) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1))),
% 29.81/20.02 inference(modus_ponens,[status(thm)],[29628, 29627])).
% 29.81/20.02 tff(29630,plain,
% 29.81/20.02 ((~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1))),
% 29.81/20.02 inference(unit_resolution,[status(thm)],[29629, 1398, 5080, 482, 3030, 29623])).
% 29.81/20.02 tff(29631,plain,
% 29.81/20.02 ($false),
% 29.81/20.02 inference(unit_resolution,[status(thm)],[29630, 29622, 29614])).
% 29.81/20.02 tff(29632,plain,((~(f6(c1, f3(c1, c2)) = f3(c1, c2))) | (~(c1 = c3)) | (c1 = c4) | big_f(c1, f10(c1)) | (~(f10(c1) = f2(c1))) | (~big_f(f10(c1), c1)) | (~(f6(c1, f3(c1, c2)) = c2)) | (~(f10(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.81/20.02 tff(29633,plain,
% 29.81/20.02 (~(f10(c1) = f2(c1))),
% 29.81/20.02 inference(unit_resolution,[status(thm)],[29632, 29608, 482, 3030, 5611, 27307, 7021, 16])).
% 29.81/20.02 tff(29634,plain,
% 29.81/20.02 (~(f2(c3) = c2)),
% 29.81/20.02 inference(modus_ponens,[status(thm)],[29633, 29596])).
% 29.81/20.02 tff(29635,plain,
% 29.81/20.02 (f2(c3) = c1),
% 29.81/20.02 inference(unit_resolution,[status(thm)],[1273, 29634])).
% 29.81/20.02 tff(29636,plain,
% 29.81/20.02 (f3(c1, c2) = f6(c1, f3(c1, c2))),
% 29.81/20.02 inference(symmetry,[status(thm)],[29608])).
% 29.81/20.02 tff(29637,plain,
% 29.81/20.02 (f3(c1, f10(c1)) = f10(c1)),
% 29.81/20.02 inference(transitivity,[status(thm)],[29609, 29636, 7021, 293])).
% 29.81/20.02 tff(29638,plain,
% 29.81/20.02 (big_f(f3(c1, f10(c1)), c1) <=> big_f(f10(c1), c1)),
% 29.81/20.02 inference(monotonicity,[status(thm)],[29637])).
% 29.81/20.02 tff(29639,plain,
% 29.81/20.02 (big_f(f10(c1), c1) <=> big_f(f3(c1, f10(c1)), c1)),
% 29.81/20.02 inference(symmetry,[status(thm)],[29638])).
% 29.81/20.02 tff(29640,plain,
% 29.81/20.02 (big_f(f3(c1, f10(c1)), c1)),
% 29.81/20.02 inference(modus_ponens,[status(thm)],[27307, 29639])).
% 29.81/20.02 tff(29641,plain,
% 29.81/20.02 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((c1 = c4) | (~(c1 = c3)) | (~big_f(c1, f6(c1, c1))) | (f6(c1, c1) = f2(c1)) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (c1 = c4) | (~(c1 = c3)) | (~big_f(c1, f6(c1, c1))) | (f6(c1, c1) = f2(c1)) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1)))),
% 29.81/20.02 inference(rewrite,[status(thm)],[])).
% 29.81/20.02 tff(29642,plain,
% 29.81/20.02 (((~(c1 = c3)) | (c1 = c4) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1)) | (f6(c1, c1) = f2(c1)) | (~big_f(c1, f6(c1, c1)))) <=> ((c1 = c4) | (~(c1 = c3)) | (~big_f(c1, f6(c1, c1))) | (f6(c1, c1) = f2(c1)) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1)))),
% 29.81/20.02 inference(rewrite,[status(thm)],[])).
% 29.81/20.02 tff(29643,plain,
% 29.81/20.02 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c1 = c4) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1)) | (f6(c1, c1) = f2(c1)) | (~big_f(c1, f6(c1, c1))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((c1 = c4) | (~(c1 = c3)) | (~big_f(c1, f6(c1, c1))) | (f6(c1, c1) = f2(c1)) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1))))),
% 29.81/20.02 inference(monotonicity,[status(thm)],[29642])).
% 29.81/20.02 tff(29644,plain,
% 29.81/20.02 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c1 = c4) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1)) | (f6(c1, c1) = f2(c1)) | (~big_f(c1, f6(c1, c1))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (c1 = c4) | (~(c1 = c3)) | (~big_f(c1, f6(c1, c1))) | (f6(c1, c1) = f2(c1)) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1)))),
% 29.81/20.02 inference(transitivity,[status(thm)],[29643, 29641])).
% 29.81/20.02 tff(29645,plain,
% 29.81/20.02 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c1 = c4) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1)) | (f6(c1, c1) = f2(c1)) | (~big_f(c1, f6(c1, c1))))),
% 29.81/20.02 inference(quant_inst,[status(thm)],[])).
% 29.81/20.02 tff(29646,plain,
% 29.81/20.02 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (c1 = c4) | (~(c1 = c3)) | (~big_f(c1, f6(c1, c1))) | (f6(c1, c1) = f2(c1)) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1))),
% 29.81/20.02 inference(modus_ponens,[status(thm)],[29645, 29644])).
% 29.81/20.02 tff(29647,plain,
% 29.81/20.02 ((f6(c1, c1) = f2(c1)) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1))),
% 29.81/20.02 inference(unit_resolution,[status(thm)],[29646, 7051, 5611, 482, 28185])).
% 29.81/20.02 tff(29648,plain,
% 29.81/20.02 (f6(c1, c1) = f2(c1)),
% 29.81/20.02 inference(unit_resolution,[status(thm)],[29647, 29637, 29640])).
% 29.81/20.02 tff(29649,plain,
% 29.81/20.02 (f6(c1, c1) = c1),
% 29.81/20.02 inference(transitivity,[status(thm)],[29648, 5586, 29635])).
% 29.81/20.02 tff(29650,plain,
% 29.81/20.02 ($false),
% 29.81/20.02 inference(unit_resolution,[status(thm)],[28, 29649])).
% 29.81/20.02 tff(29651,plain,((~(f6(c1, f3(c1, c2)) = c2)) | (f6(c1, c1) = c1) | (~(c3 = c1)) | (c1 = c4) | (~big_f(c1, f6(c1, c1))) | (~big_f(f10(c1), c1)) | (~(f10(c1) = c2)) | big_f(c1, f10(c1)) | (f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1))))), inference(lemma,lemma(discharge,[]))).
% 29.81/20.02 tff(29652,plain,
% 29.81/20.02 (~(f6(c1, f3(c1, c2)) = c2)),
% 29.81/20.02 inference(unit_resolution,[status(thm)],[29651, 27903, 172, 482, 28185, 27307, 15, 3030, 24968, 28, 27872])).
% 29.81/20.02 tff(29653,plain,
% 29.81/20.02 (f6(c1, f3(c1, c2)) = c1),
% 29.81/20.02 inference(unit_resolution,[status(thm)],[6690, 29652])).
% 29.81/20.02 tff(29654,plain,
% 29.81/20.02 (f3(c1, c2) = f10(c1)),
% 29.81/20.02 inference(transitivity,[status(thm)],[16111, 5571])).
% 29.81/20.02 tff(29655,plain,
% 29.81/20.02 (f6(c1, f3(c1, c2)) = f6(c1, f10(c1))),
% 29.81/20.02 inference(monotonicity,[status(thm)],[29654])).
% 29.81/20.02 tff(29656,plain,
% 29.81/20.02 (f6(c1, f10(c1)) = f6(c1, f3(c1, c2))),
% 29.81/20.02 inference(symmetry,[status(thm)],[29655])).
% 29.81/20.02 tff(29657,plain,
% 29.81/20.02 (f6(c1, f10(c1)) = f6(c1, c2)),
% 29.81/20.02 inference(monotonicity,[status(thm)],[15])).
% 29.81/20.02 tff(29658,plain,
% 29.81/20.02 (f6(c1, c2) = f6(c1, f10(c1))),
% 29.81/20.02 inference(symmetry,[status(thm)],[29657])).
% 29.81/20.02 tff(29659,plain,
% 29.81/20.02 (c2 = f6(c1, c2)),
% 29.81/20.02 inference(symmetry,[status(thm)],[36])).
% 29.81/20.02 tff(29660,plain,
% 29.81/20.02 (f10(c1) = c1),
% 29.81/20.02 inference(transitivity,[status(thm)],[15, 29659, 29658, 29656, 6647])).
% 29.81/20.02 tff(29661,plain,
% 29.81/20.02 ($false),
% 29.81/20.02 inference(unit_resolution,[status(thm)],[3, 29660])).
% 29.81/20.02 tff(29662,plain,((~(f3(c1, c2) = c2)) | (f10(c1) = c1) | (~(f6(c1, f3(c1, c2)) = c1)) | (~(f6(c1, c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.81/20.02 tff(29663,plain,
% 29.81/20.02 (~(f3(c1, c2) = c2)),
% 29.81/20.02 inference(unit_resolution,[status(thm)],[29662, 29653, 3, 29593])).
% 29.81/20.02 tff(29664,plain,
% 29.81/20.02 ((f6(c1, f3(c1, c2)) = f3(c1, c2)) <=> (c1 = f3(c1, c2))),
% 29.81/20.02 inference(monotonicity,[status(thm)],[29653])).
% 29.81/20.02 tff(29665,plain,
% 29.81/20.02 ((~(f6(c1, f3(c1, c2)) = f3(c1, c2))) <=> (~(c1 = f3(c1, c2)))),
% 29.81/20.02 inference(monotonicity,[status(thm)],[29664])).
% 29.81/20.02 tff(29666,plain,
% 29.81/20.02 (big_f(f7(c1), f6(c1, f3(c1, c2))) <=> big_f(c1, c1)),
% 29.81/20.02 inference(monotonicity,[status(thm)],[25791, 29653])).
% 29.81/20.02 tff(29667,plain,
% 29.81/20.02 (big_f(c1, c1) <=> big_f(f7(c1), f6(c1, f3(c1, c2)))),
% 29.81/20.02 inference(symmetry,[status(thm)],[29666])).
% 29.81/20.02 tff(29668,plain,
% 29.81/20.02 (big_f(f7(c1), f6(c1, f3(c1, c2)))),
% 29.81/20.02 inference(modus_ponens,[status(thm)],[4932, 29667])).
% 29.81/20.02 tff(29669,plain,
% 29.81/20.02 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (~(f6(c1, f3(c1, c2)) = f3(c1, c2))) | (~big_f(f7(c1), f6(c1, f3(c1, c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (~(f6(c1, f3(c1, c2)) = f3(c1, c2))) | (~big_f(f7(c1), f6(c1, f3(c1, c2)))))),
% 29.81/20.02 inference(rewrite,[status(thm)],[])).
% 29.81/20.02 tff(29670,plain,
% 29.81/20.02 (((f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (~(f7(c1) = c1)) | (~(f6(c1, f3(c1, c2)) = f3(c1, c2))) | (~big_f(f7(c1), f6(c1, f3(c1, c2))))) <=> ((f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (~(f6(c1, f3(c1, c2)) = f3(c1, c2))) | (~big_f(f7(c1), f6(c1, f3(c1, c2)))))),
% 29.81/20.02 inference(rewrite,[status(thm)],[])).
% 29.81/20.02 tff(29671,plain,
% 29.81/20.02 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (~(f7(c1) = c1)) | (~(f6(c1, f3(c1, c2)) = f3(c1, c2))) | (~big_f(f7(c1), f6(c1, f3(c1, c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (~(f6(c1, f3(c1, c2)) = f3(c1, c2))) | (~big_f(f7(c1), f6(c1, f3(c1, c2))))))),
% 29.81/20.02 inference(monotonicity,[status(thm)],[29670])).
% 29.81/20.02 tff(29672,plain,
% 29.81/20.02 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (~(f7(c1) = c1)) | (~(f6(c1, f3(c1, c2)) = f3(c1, c2))) | (~big_f(f7(c1), f6(c1, f3(c1, c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (~(f6(c1, f3(c1, c2)) = f3(c1, c2))) | (~big_f(f7(c1), f6(c1, f3(c1, c2)))))),
% 29.81/20.02 inference(transitivity,[status(thm)],[29671, 29669])).
% 29.81/20.02 tff(29673,plain,
% 29.81/20.02 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (~(f7(c1) = c1)) | (~(f6(c1, f3(c1, c2)) = f3(c1, c2))) | (~big_f(f7(c1), f6(c1, f3(c1, c2)))))),
% 29.81/20.02 inference(quant_inst,[status(thm)],[])).
% 29.81/20.02 tff(29674,plain,
% 29.81/20.02 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (~(f6(c1, f3(c1, c2)) = f3(c1, c2))) | (~big_f(f7(c1), f6(c1, f3(c1, c2))))),
% 29.81/20.02 inference(modus_ponens,[status(thm)],[29673, 29672])).
% 29.81/20.02 tff(29675,plain,
% 29.81/20.02 (~(f6(c1, f3(c1, c2)) = f3(c1, c2))),
% 29.81/20.02 inference(unit_resolution,[status(thm)],[29674, 2730, 25791, 24968, 27903, 29668, 27872])).
% 29.81/20.02 tff(29676,plain,
% 29.81/20.02 (~(c1 = f3(c1, c2))),
% 29.81/20.02 inference(modus_ponens,[status(thm)],[29675, 29665])).
% 29.81/20.02 tff(29677,plain,
% 29.81/20.02 (~(f1(f5(c2), f5(c1)) = c2)),
% 29.81/20.02 inference(unit_resolution,[status(thm)],[26052, 29676, 29663])).
% 29.81/20.02 tff(29678,plain,
% 29.81/20.02 (f1(f5(c2), f5(c1)) = c1),
% 29.81/20.02 inference(unit_resolution,[status(thm)],[5191, 29677])).
% 29.81/20.02 tff(29679,plain,
% 29.81/20.02 (f3(f1(f5(c2), f5(c1)), c2) = f3(c1, c2)),
% 29.81/20.02 inference(monotonicity,[status(thm)],[29678])).
% 29.81/20.02 tff(29680,plain,
% 29.81/20.02 ((f3(f1(f5(c2), f5(c1)), c2) = c2) <=> (f3(c1, c2) = c2)),
% 29.81/20.02 inference(monotonicity,[status(thm)],[29679])).
% 29.81/20.02 tff(29681,plain,
% 29.81/20.02 ((f3(c1, c2) = c2) <=> (f3(f1(f5(c2), f5(c1)), c2) = c2)),
% 29.81/20.02 inference(symmetry,[status(thm)],[29680])).
% 29.81/20.02 tff(29682,plain,
% 29.81/20.02 ((~(f3(c1, c2) = c2)) <=> (~(f3(f1(f5(c2), f5(c1)), c2) = c2))),
% 29.81/20.02 inference(monotonicity,[status(thm)],[29681])).
% 29.81/20.02 tff(29683,plain,
% 29.81/20.02 (~(f3(f1(f5(c2), f5(c1)), c2) = c2)),
% 29.81/20.02 inference(modus_ponens,[status(thm)],[29663, 29682])).
% 29.81/20.02 tff(29684,plain,
% 29.81/20.02 ((f3(f1(f5(c2), f5(c1)), c2) = c1) <=> (f3(c1, c2) = c1)),
% 29.81/20.02 inference(monotonicity,[status(thm)],[29679])).
% 29.81/20.02 tff(29685,plain,
% 29.81/20.02 ((f3(f1(f5(c2), f5(c1)), c2) = c1) <=> (c1 = f3(c1, c2))),
% 29.81/20.02 inference(transitivity,[status(thm)],[29684, 13151])).
% 29.81/20.02 tff(29686,plain,
% 29.81/20.02 ((c1 = f3(c1, c2)) <=> (f3(f1(f5(c2), f5(c1)), c2) = c1)),
% 29.81/20.02 inference(symmetry,[status(thm)],[29685])).
% 29.81/20.02 tff(29687,plain,
% 29.81/20.02 ((~(c1 = f3(c1, c2))) <=> (~(f3(f1(f5(c2), f5(c1)), c2) = c1))),
% 29.81/20.02 inference(monotonicity,[status(thm)],[29686])).
% 29.81/20.02 tff(29688,plain,
% 29.81/20.02 (~(f3(f1(f5(c2), f5(c1)), c2) = c1)),
% 29.81/20.02 inference(modus_ponens,[status(thm)],[29676, 29687])).
% 29.81/20.02 tff(29689,plain,
% 29.81/20.02 ($false),
% 29.81/20.02 inference(unit_resolution,[status(thm)],[16061, 29688, 29683])).
% 29.81/20.02 tff(29690,plain,((c1 = f8(f10(c1))) | (f10(f10(c1)) = f10(c1)) | (~big_f(c1, f10(f10(c1)))) | (~big_f(c1, c1)) | (f10(c1) = c1) | (~(c3 = c1)) | (c1 = c4) | (~big_f(c1, f6(c1, c1))) | (~big_f(f10(c1), c1)) | big_f(c1, f10(c1)) | (f6(c1, c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.81/20.02 tff(29691,plain,
% 29.81/20.02 (c1 = f8(f10(c1))),
% 29.81/20.02 inference(unit_resolution,[status(thm)],[29690, 29507, 29499, 29304, 3, 28773, 29591, 29517, 27297, 15821, 29515])).
% 29.81/20.02 tff(29692,plain,
% 29.81/20.02 ($false),
% 29.81/20.02 inference(unit_resolution,[status(thm)],[29691, 29543])).
% 29.81/20.02 tff(29693,plain,((f10(c1) = c1) | (~(f10(c2) = c1)) | (~big_f(c2, c1)) | big_f(c1, c2)), inference(lemma,lemma(discharge,[]))).
% 29.81/20.02 tff(29694,plain,
% 29.81/20.02 (f10(c1) = c1),
% 29.81/20.02 inference(unit_resolution,[status(thm)],[29693, 94, 29494, 27])).
% 29.81/20.02 tff(29695,plain,
% 29.81/20.02 (big_f(f7(c1), f6(c1, c1))),
% 29.81/20.02 inference(unit_resolution,[status(thm)],[28582, 28, 94, 29494, 29304, 29694])).
% 29.81/20.02 tff(29696,plain,
% 29.81/20.02 (big_f(c1, f6(c1, c1))),
% 29.81/20.02 inference(unit_resolution,[status(thm)],[28169, 29695])).
% 29.81/20.02 tff(29697,plain,
% 29.81/20.02 (c1 = c3),
% 29.81/20.02 inference(symmetry,[status(thm)],[28773])).
% 29.81/20.02 tff(29698,plain,
% 29.81/20.02 (f2(c1) = f2(c3)),
% 29.81/20.02 inference(monotonicity,[status(thm)],[29697])).
% 29.81/20.02 tff(29699,plain,
% 29.81/20.02 (f2(c3) = f2(c1)),
% 29.81/20.02 inference(symmetry,[status(thm)],[29698])).
% 29.81/20.02 tff(29700,plain,
% 29.81/20.02 ((f2(c3) = c1) <=> (f2(c1) = c1)),
% 29.81/20.02 inference(monotonicity,[status(thm)],[29699])).
% 29.81/20.02 tff(29701,plain,
% 29.81/20.02 ((f2(c3) = c1) <=> (c1 = f2(c1))),
% 29.81/20.02 inference(transitivity,[status(thm)],[29700, 6764])).
% 29.81/20.02 tff(29702,plain,
% 29.81/20.02 ((c1 = f2(c1)) <=> (f2(c3) = c1)),
% 29.81/20.02 inference(symmetry,[status(thm)],[29701])).
% 29.81/20.02 tff(29703,assumption,(f6(c1, c1) = f2(c1)), introduced(assumption)).
% 29.81/20.02 tff(29704,plain,
% 29.81/20.02 ((f6(c1, c1) = c1) <=> (f2(c1) = c1)),
% 29.81/20.02 inference(monotonicity,[status(thm)],[29703])).
% 29.81/20.02 tff(29705,plain,
% 29.81/20.02 ((f6(c1, c1) = c1) <=> (c1 = f2(c1))),
% 29.81/20.02 inference(transitivity,[status(thm)],[29704, 6764])).
% 29.81/20.02 tff(29706,plain,
% 29.81/20.02 ((f6(c1, c1) = c1) <=> (f2(c3) = c1)),
% 29.81/20.02 inference(transitivity,[status(thm)],[29705, 29702])).
% 29.81/20.02 tff(29707,plain,
% 29.81/20.02 ((~(f6(c1, c1) = c1)) <=> (~(f2(c3) = c1))),
% 29.81/20.02 inference(monotonicity,[status(thm)],[29706])).
% 29.81/20.02 tff(29708,plain,
% 29.81/20.02 (~(f2(c3) = c1)),
% 29.81/20.02 inference(modus_ponens,[status(thm)],[28, 29707])).
% 29.81/20.02 tff(29709,plain,
% 29.81/20.02 (f2(c3) = c2),
% 29.81/20.02 inference(unit_resolution,[status(thm)],[1273, 29708])).
% 29.81/20.02 tff(29710,plain,
% 29.81/20.02 (f2(c1) = c2),
% 29.81/20.02 inference(transitivity,[status(thm)],[29698, 29709])).
% 29.81/20.02 tff(29711,plain,
% 29.81/20.02 (big_f(c1, f2(c1)) <=> big_f(c1, c2)),
% 29.81/20.02 inference(monotonicity,[status(thm)],[29710])).
% 29.81/20.02 tff(29712,plain,
% 29.81/20.02 (big_f(c1, c2) <=> big_f(c1, f2(c1))),
% 29.81/20.02 inference(symmetry,[status(thm)],[29711])).
% 29.81/20.02 tff(29713,plain,
% 29.81/20.02 ((~big_f(c1, c2)) <=> (~big_f(c1, f2(c1)))),
% 29.81/20.02 inference(monotonicity,[status(thm)],[29712])).
% 29.81/20.02 tff(29714,plain,
% 29.81/20.02 (~big_f(c1, f2(c1))),
% 29.81/20.02 inference(modus_ponens,[status(thm)],[27, 29713])).
% 29.81/20.02 tff(29715,plain,
% 29.81/20.02 (big_f(c1, f6(c1, c1)) <=> big_f(c1, f2(c1))),
% 29.81/20.02 inference(monotonicity,[status(thm)],[29703])).
% 29.81/20.02 tff(29716,plain,
% 29.81/20.02 (big_f(c1, f2(c1))),
% 29.81/20.02 inference(modus_ponens,[status(thm)],[28185, 29715])).
% 29.81/20.02 tff(29717,plain,
% 29.81/20.02 ($false),
% 29.81/20.02 inference(unit_resolution,[status(thm)],[29716, 29714])).
% 29.81/20.02 tff(29718,plain,((~(f6(c1, c1) = f2(c1))) | big_f(c1, c2) | (~big_f(c1, f6(c1, c1))) | (f6(c1, c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.81/20.02 tff(29719,plain,
% 29.81/20.02 (~(f6(c1, c1) = f2(c1))),
% 29.81/20.02 inference(unit_resolution,[status(thm)],[29718, 28185, 27, 28])).
% 29.81/20.02 tff(29720,plain,
% 29.81/20.02 (c1 = f4(c1)),
% 29.81/20.02 inference(unit_resolution,[status(thm)],[29565, 11526, 5080, 28, 4932, 28185])).
% 29.81/20.02 tff(29721,plain,
% 29.81/20.02 (f4(c1) = c1),
% 29.81/20.02 inference(symmetry,[status(thm)],[29720])).
% 29.81/20.02 tff(29722,plain,
% 29.81/20.02 ((c2 = f4(c1)) <=> (c2 = c1)),
% 29.81/20.02 inference(monotonicity,[status(thm)],[29721])).
% 29.81/20.02 tff(29723,plain,
% 29.81/20.02 ((c2 = c1) <=> (c2 = f4(c1))),
% 29.81/20.02 inference(symmetry,[status(thm)],[29722])).
% 29.81/20.02 tff(29724,plain,
% 29.81/20.02 ((~(c2 = c1)) <=> (~(c2 = f4(c1)))),
% 29.81/20.02 inference(monotonicity,[status(thm)],[29723])).
% 29.81/20.02 tff(29725,plain,
% 29.81/20.02 (~(c2 = f4(c1))),
% 29.81/20.02 inference(modus_ponens,[status(thm)],[75, 29724])).
% 29.81/20.02 tff(29726,plain,
% 29.81/20.02 (c1 = f2(c1)),
% 29.81/20.02 inference(unit_resolution,[status(thm)],[29572, 29725, 11526])).
% 29.81/20.02 tff(29727,plain,
% 29.81/20.02 (f2(c1) = c1),
% 29.81/20.02 inference(symmetry,[status(thm)],[29726])).
% 29.81/20.02 tff(29728,plain,
% 29.81/20.02 ((f6(c1, c1) = f2(c1)) <=> (f6(c1, c1) = c1)),
% 29.81/20.02 inference(monotonicity,[status(thm)],[29727])).
% 29.81/20.02 tff(29729,plain,
% 29.81/20.02 ((f6(c1, c1) = c1) <=> (f6(c1, c1) = f2(c1))),
% 29.81/20.02 inference(symmetry,[status(thm)],[29728])).
% 29.81/20.02 tff(29730,plain,
% 29.81/20.02 ((~(f6(c1, c1) = c1)) <=> (~(f6(c1, c1) = f2(c1)))),
% 29.81/20.02 inference(monotonicity,[status(thm)],[29729])).
% 29.81/20.02 tff(29731,plain,
% 29.81/20.02 (~(f6(c1, c1) = f2(c1))),
% 29.81/20.02 inference(modus_ponens,[status(thm)],[28, 29730])).
% 29.81/20.02 tff(29732,plain,
% 29.81/20.02 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (~(c1 = c4)) | (~big_f(c2, c1)) | (c2 = f4(c1)) | (~big_f(c1, f6(c1, c1))) | (f6(c1, c1) = f2(c1)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c1 = c3)) | (~(c1 = c4)) | (~big_f(c2, c1)) | (c2 = f4(c1)) | (~big_f(c1, f6(c1, c1))) | (f6(c1, c1) = f2(c1)))),
% 29.81/20.02 inference(rewrite,[status(thm)],[])).
% 29.81/20.02 tff(29733,plain,
% 29.81/20.02 (((~(c1 = c3)) | (~(c1 = c4)) | (c2 = f4(c1)) | (~big_f(c2, c1)) | (f6(c1, c1) = f2(c1)) | (~big_f(c1, f6(c1, c1)))) <=> ((~(c1 = c3)) | (~(c1 = c4)) | (~big_f(c2, c1)) | (c2 = f4(c1)) | (~big_f(c1, f6(c1, c1))) | (f6(c1, c1) = f2(c1)))),
% 29.81/20.02 inference(rewrite,[status(thm)],[])).
% 29.81/20.02 tff(29734,plain,
% 29.81/20.02 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (~(c1 = c4)) | (c2 = f4(c1)) | (~big_f(c2, c1)) | (f6(c1, c1) = f2(c1)) | (~big_f(c1, f6(c1, c1))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (~(c1 = c4)) | (~big_f(c2, c1)) | (c2 = f4(c1)) | (~big_f(c1, f6(c1, c1))) | (f6(c1, c1) = f2(c1))))),
% 29.81/20.02 inference(monotonicity,[status(thm)],[29733])).
% 29.81/20.02 tff(29735,plain,
% 29.81/20.02 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (~(c1 = c4)) | (c2 = f4(c1)) | (~big_f(c2, c1)) | (f6(c1, c1) = f2(c1)) | (~big_f(c1, f6(c1, c1))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c1 = c3)) | (~(c1 = c4)) | (~big_f(c2, c1)) | (c2 = f4(c1)) | (~big_f(c1, f6(c1, c1))) | (f6(c1, c1) = f2(c1)))),
% 29.81/20.02 inference(transitivity,[status(thm)],[29734, 29732])).
% 29.81/20.02 tff(29736,plain,
% 29.81/20.02 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (~(c1 = c4)) | (c2 = f4(c1)) | (~big_f(c2, c1)) | (f6(c1, c1) = f2(c1)) | (~big_f(c1, f6(c1, c1))))),
% 29.81/20.02 inference(quant_inst,[status(thm)],[])).
% 29.81/20.02 tff(29737,plain,
% 29.81/20.02 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c1 = c3)) | (~(c1 = c4)) | (~big_f(c2, c1)) | (c2 = f4(c1)) | (~big_f(c1, f6(c1, c1))) | (f6(c1, c1) = f2(c1))),
% 29.81/20.02 inference(modus_ponens,[status(thm)],[29736, 29735])).
% 29.81/20.03 tff(29738,plain,
% 29.81/20.03 ($false),
% 29.81/20.03 inference(unit_resolution,[status(thm)],[29737, 1355, 5080, 11526, 348, 29725, 28185, 29731])).
% 29.81/20.03 tff(29739,plain,((~(c1 = c4)) | (~(c1 = c3)) | (~big_f(c2, c1)) | (~big_f(c1, f6(c1, c1))) | (f6(c1, c1) = c1) | (~big_f(c1, c1))), inference(lemma,lemma(discharge,[]))).
% 29.81/20.03 tff(29740,plain,
% 29.81/20.03 (~(c1 = c4)),
% 29.81/20.03 inference(unit_resolution,[status(thm)],[29739, 28185, 348, 29544, 28, 29304])).
% 29.81/20.03 tff(29741,assumption,(~(f3(c1, f8(c3)) = c1)), introduced(assumption)).
% 29.81/20.03 tff(29742,plain,
% 29.81/20.03 (f3(c1, f8(c3)) = c2),
% 29.81/20.03 inference(unit_resolution,[status(thm)],[7123, 29741])).
% 29.81/20.03 tff(29743,plain,
% 29.81/20.03 (f8(c3) = f8(c1)),
% 29.81/20.03 inference(monotonicity,[status(thm)],[28773])).
% 29.81/20.03 tff(29744,plain,
% 29.81/20.03 (f8(c1) = f8(c3)),
% 29.81/20.03 inference(symmetry,[status(thm)],[29743])).
% 29.81/20.03 tff(29745,plain,
% 29.81/20.03 (f3(c1, f8(c1)) = f3(c1, f8(c3))),
% 29.81/20.03 inference(monotonicity,[status(thm)],[29744])).
% 29.81/20.03 tff(29746,plain,
% 29.81/20.03 (f3(c1, f8(c1)) = c2),
% 29.81/20.03 inference(transitivity,[status(thm)],[29745, 29742])).
% 29.81/20.03 tff(29747,plain,
% 29.81/20.03 ((f3(c1, f8(c1)) = f8(c1)) <=> (c2 = f8(c1))),
% 29.81/20.03 inference(monotonicity,[status(thm)],[29746])).
% 29.81/20.03 tff(29748,plain,
% 29.81/20.03 ((f3(c1, f8(c1)) = f8(c1)) <=> (f8(c1) = c2)),
% 29.81/20.03 inference(transitivity,[status(thm)],[29747, 2782])).
% 29.81/20.03 tff(29749,plain,
% 29.81/20.03 ((~(f3(c1, f8(c1)) = f8(c1))) <=> (~(f8(c1) = c2))),
% 29.81/20.03 inference(monotonicity,[status(thm)],[29748])).
% 29.81/20.03 tff(29750,plain,
% 29.81/20.03 (big_f(f3(c1, f8(c1)), c1) <=> big_f(c2, c1)),
% 29.81/20.03 inference(monotonicity,[status(thm)],[29746])).
% 29.81/20.03 tff(29751,plain,
% 29.81/20.03 (big_f(c2, c1) <=> big_f(f3(c1, f8(c1)), c1)),
% 29.81/20.03 inference(symmetry,[status(thm)],[29750])).
% 29.81/20.03 tff(29752,plain,
% 29.81/20.03 (big_f(f3(c1, f8(c1)), c1)),
% 29.81/20.03 inference(modus_ponens,[status(thm)],[348, 29751])).
% 29.81/20.03 tff(29753,plain,
% 29.81/20.03 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((c1 = c4) | (~(c1 = c3)) | (~(f3(c1, f8(c1)) = f8(c1))) | (~big_f(f3(c1, f8(c1)), c1)) | (~big_f(c1, f6(c1, c1))) | (f6(c1, c1) = f2(c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (c1 = c4) | (~(c1 = c3)) | (~(f3(c1, f8(c1)) = f8(c1))) | (~big_f(f3(c1, f8(c1)), c1)) | (~big_f(c1, f6(c1, c1))) | (f6(c1, c1) = f2(c1)))),
% 29.81/20.03 inference(rewrite,[status(thm)],[])).
% 29.81/20.03 tff(29754,plain,
% 29.81/20.03 (((~(c1 = c3)) | (c1 = c4) | (~(f3(c1, f8(c1)) = f8(c1))) | (~big_f(f3(c1, f8(c1)), c1)) | (f6(c1, c1) = f2(c1)) | (~big_f(c1, f6(c1, c1)))) <=> ((c1 = c4) | (~(c1 = c3)) | (~(f3(c1, f8(c1)) = f8(c1))) | (~big_f(f3(c1, f8(c1)), c1)) | (~big_f(c1, f6(c1, c1))) | (f6(c1, c1) = f2(c1)))),
% 29.81/20.03 inference(rewrite,[status(thm)],[])).
% 29.81/20.03 tff(29755,plain,
% 29.81/20.03 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c1 = c4) | (~(f3(c1, f8(c1)) = f8(c1))) | (~big_f(f3(c1, f8(c1)), c1)) | (f6(c1, c1) = f2(c1)) | (~big_f(c1, f6(c1, c1))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((c1 = c4) | (~(c1 = c3)) | (~(f3(c1, f8(c1)) = f8(c1))) | (~big_f(f3(c1, f8(c1)), c1)) | (~big_f(c1, f6(c1, c1))) | (f6(c1, c1) = f2(c1))))),
% 29.81/20.03 inference(monotonicity,[status(thm)],[29754])).
% 29.81/20.03 tff(29756,plain,
% 29.81/20.03 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c1 = c4) | (~(f3(c1, f8(c1)) = f8(c1))) | (~big_f(f3(c1, f8(c1)), c1)) | (f6(c1, c1) = f2(c1)) | (~big_f(c1, f6(c1, c1))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (c1 = c4) | (~(c1 = c3)) | (~(f3(c1, f8(c1)) = f8(c1))) | (~big_f(f3(c1, f8(c1)), c1)) | (~big_f(c1, f6(c1, c1))) | (f6(c1, c1) = f2(c1)))),
% 29.81/20.03 inference(transitivity,[status(thm)],[29755, 29753])).
% 29.81/20.03 tff(29757,plain,
% 29.81/20.03 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c1 = c4) | (~(f3(c1, f8(c1)) = f8(c1))) | (~big_f(f3(c1, f8(c1)), c1)) | (f6(c1, c1) = f2(c1)) | (~big_f(c1, f6(c1, c1))))),
% 29.81/20.03 inference(quant_inst,[status(thm)],[])).
% 29.81/20.03 tff(29758,plain,
% 29.81/20.03 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (c1 = c4) | (~(c1 = c3)) | (~(f3(c1, f8(c1)) = f8(c1))) | (~big_f(f3(c1, f8(c1)), c1)) | (~big_f(c1, f6(c1, c1))) | (f6(c1, c1) = f2(c1))),
% 29.81/20.03 inference(modus_ponens,[status(thm)],[29757, 29756])).
% 29.81/20.03 tff(29759,plain,
% 29.81/20.03 ((~(f3(c1, f8(c1)) = f8(c1))) | (~big_f(f3(c1, f8(c1)), c1))),
% 29.81/20.03 inference(unit_resolution,[status(thm)],[29758, 7051, 29544, 29740, 28185, 29719])).
% 29.81/20.03 tff(29760,plain,
% 29.81/20.03 (~(f3(c1, f8(c1)) = f8(c1))),
% 29.81/20.03 inference(unit_resolution,[status(thm)],[29759, 29752])).
% 29.81/20.03 tff(29761,plain,
% 29.81/20.03 (~(f8(c1) = c2)),
% 29.81/20.03 inference(modus_ponens,[status(thm)],[29760, 29749])).
% 29.81/20.03 tff(29762,plain,
% 29.81/20.03 (f8(c1) = c1),
% 29.81/20.03 inference(unit_resolution,[status(thm)],[1680, 29761])).
% 29.81/20.03 tff(29763,assumption,(~(f6(c1, c1) = f2(c1))), introduced(assumption)).
% 29.81/20.03 tff(29764,plain,
% 29.81/20.03 (c1 = f8(c3)),
% 29.81/20.03 inference(transitivity,[status(thm)],[3143, 12787])).
% 29.81/20.03 tff(29765,plain,
% 29.81/20.03 (f3(c1, c1) = f3(c1, f8(c3))),
% 29.81/20.03 inference(monotonicity,[status(thm)],[29764])).
% 29.81/20.03 tff(29766,plain,
% 29.81/20.03 (f3(c1, f8(c3)) = f3(c1, c1)),
% 29.81/20.03 inference(symmetry,[status(thm)],[29765])).
% 29.81/20.03 tff(29767,plain,
% 29.81/20.03 ((f3(c1, f8(c3)) = c1) <=> (f3(c1, c1) = c1)),
% 29.81/20.03 inference(monotonicity,[status(thm)],[29766])).
% 29.81/20.03 tff(29768,plain,
% 29.81/20.03 (f3(c1, c1) = c1),
% 29.81/20.03 inference(modus_ponens,[status(thm)],[16414, 29767])).
% 29.81/20.03 tff(29769,plain,
% 29.81/20.03 (f3(c1, c1) = c1),
% 29.81/20.03 inference(transitivity,[status(thm)],[29765, 16414])).
% 29.81/20.03 tff(29770,plain,
% 29.81/20.03 (big_f(f3(c1, c1), c1) <=> big_f(c1, c1)),
% 29.81/20.03 inference(monotonicity,[status(thm)],[29769])).
% 29.81/20.03 tff(29771,plain,
% 29.81/20.03 (big_f(c1, c1) <=> big_f(f3(c1, c1), c1)),
% 29.81/20.03 inference(symmetry,[status(thm)],[29770])).
% 29.81/20.03 tff(29772,plain,
% 29.81/20.03 (big_f(f3(c1, c1), c1)),
% 29.81/20.03 inference(modus_ponens,[status(thm)],[4932, 29771])).
% 29.81/20.03 tff(29773,plain,
% 29.81/20.03 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((c1 = c4) | (~(c1 = c3)) | (~big_f(f3(c1, c1), c1)) | (~(f3(c1, c1) = c1)) | (~big_f(c1, f6(c1, c1))) | (f6(c1, c1) = f2(c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (c1 = c4) | (~(c1 = c3)) | (~big_f(f3(c1, c1), c1)) | (~(f3(c1, c1) = c1)) | (~big_f(c1, f6(c1, c1))) | (f6(c1, c1) = f2(c1)))),
% 29.81/20.03 inference(rewrite,[status(thm)],[])).
% 29.81/20.03 tff(29774,plain,
% 29.81/20.03 (((~(c1 = c3)) | (c1 = c4) | (~(f3(c1, c1) = c1)) | (~big_f(f3(c1, c1), c1)) | (f6(c1, c1) = f2(c1)) | (~big_f(c1, f6(c1, c1)))) <=> ((c1 = c4) | (~(c1 = c3)) | (~big_f(f3(c1, c1), c1)) | (~(f3(c1, c1) = c1)) | (~big_f(c1, f6(c1, c1))) | (f6(c1, c1) = f2(c1)))),
% 29.81/20.03 inference(rewrite,[status(thm)],[])).
% 29.81/20.03 tff(29775,plain,
% 29.81/20.03 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c1 = c4) | (~(f3(c1, c1) = c1)) | (~big_f(f3(c1, c1), c1)) | (f6(c1, c1) = f2(c1)) | (~big_f(c1, f6(c1, c1))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((c1 = c4) | (~(c1 = c3)) | (~big_f(f3(c1, c1), c1)) | (~(f3(c1, c1) = c1)) | (~big_f(c1, f6(c1, c1))) | (f6(c1, c1) = f2(c1))))),
% 29.81/20.03 inference(monotonicity,[status(thm)],[29774])).
% 29.81/20.03 tff(29776,plain,
% 29.81/20.03 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c1 = c4) | (~(f3(c1, c1) = c1)) | (~big_f(f3(c1, c1), c1)) | (f6(c1, c1) = f2(c1)) | (~big_f(c1, f6(c1, c1))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (c1 = c4) | (~(c1 = c3)) | (~big_f(f3(c1, c1), c1)) | (~(f3(c1, c1) = c1)) | (~big_f(c1, f6(c1, c1))) | (f6(c1, c1) = f2(c1)))),
% 29.81/20.03 inference(transitivity,[status(thm)],[29775, 29773])).
% 29.81/20.03 tff(29777,plain,
% 29.81/20.03 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c1 = c4) | (~(f3(c1, c1) = c1)) | (~big_f(f3(c1, c1), c1)) | (f6(c1, c1) = f2(c1)) | (~big_f(c1, f6(c1, c1))))),
% 29.81/20.03 inference(quant_inst,[status(thm)],[])).
% 29.81/20.03 tff(29778,plain,
% 29.81/20.03 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (c1 = c4) | (~(c1 = c3)) | (~big_f(f3(c1, c1), c1)) | (~(f3(c1, c1) = c1)) | (~big_f(c1, f6(c1, c1))) | (f6(c1, c1) = f2(c1))),
% 29.81/20.03 inference(modus_ponens,[status(thm)],[29777, 29776])).
% 29.81/20.03 tff(29779,plain,
% 29.81/20.03 ($false),
% 29.81/20.03 inference(unit_resolution,[status(thm)],[29778, 7051, 29772, 5611, 29768, 482, 28185, 29763])).
% 29.81/20.03 tff(29780,plain,((~(f3(c1, f8(c3)) = c1)) | (c1 = c4) | (~big_f(c1, f6(c1, c1))) | (f6(c1, c1) = f2(c1)) | (~big_f(c1, c1)) | (~(f8(c1) = c1)) | (~(c3 = c1))), inference(lemma,lemma(discharge,[]))).
% 29.81/20.03 tff(29781,plain,
% 29.81/20.03 (~(f3(c1, f8(c3)) = c1)),
% 29.81/20.03 inference(unit_resolution,[status(thm)],[29780, 29763, 28185, 482, 4932, 3018, 172])).
% 29.81/20.03 tff(29782,plain,
% 29.81/20.03 (f3(c1, f8(c3)) = c2),
% 29.81/20.03 inference(unit_resolution,[status(thm)],[7123, 29781])).
% 29.81/20.03 tff(29783,plain,
% 29.81/20.03 ((f3(c1, f3(c1, f8(c3))) = c1) <=> (f3(c1, c2) = c1)),
% 29.81/20.03 inference(monotonicity,[status(thm)],[22195])).
% 29.81/20.03 tff(29784,plain,
% 29.81/20.03 ((f3(c1, f3(c1, f8(c3))) = c1) <=> (c1 = f3(c1, c2))),
% 29.81/20.03 inference(transitivity,[status(thm)],[29783, 13151])).
% 29.81/20.03 tff(29785,plain,
% 29.81/20.03 ((c1 = f3(c1, c2)) <=> (f3(c1, f3(c1, f8(c3))) = c1)),
% 29.81/20.03 inference(symmetry,[status(thm)],[29784])).
% 29.81/20.03 tff(29786,plain,
% 29.81/20.03 ((~(c1 = f3(c1, c2))) <=> (~(f3(c1, f3(c1, f8(c3))) = c1))),
% 29.81/20.03 inference(monotonicity,[status(thm)],[29785])).
% 29.81/20.03 tff(29787,plain,
% 29.81/20.03 (~(f3(c1, f3(c1, f8(c3))) = c1)),
% 29.81/20.03 inference(modus_ponens,[status(thm)],[16041, 29786])).
% 29.81/20.03 tff(29788,plain,
% 29.81/20.03 ((f3(c1, f3(c1, f8(c3))) = c2) <=> (f3(c1, c2) = c2)),
% 29.81/20.03 inference(monotonicity,[status(thm)],[22195])).
% 29.81/20.03 tff(29789,plain,
% 29.81/20.03 ((f3(c1, c2) = c2) <=> (f3(c1, f3(c1, f8(c3))) = c2)),
% 29.81/20.03 inference(symmetry,[status(thm)],[29788])).
% 29.81/20.03 tff(29790,plain,
% 29.81/20.03 ((~(f3(c1, c2) = c2)) <=> (~(f3(c1, f3(c1, f8(c3))) = c2))),
% 29.81/20.03 inference(monotonicity,[status(thm)],[29789])).
% 29.81/20.03 tff(29791,plain,
% 29.81/20.03 (~(f3(c1, f3(c1, f8(c3))) = c2)),
% 29.81/20.03 inference(modus_ponens,[status(thm)],[12777, 29790])).
% 29.81/20.03 tff(29792,plain,
% 29.81/20.03 ($false),
% 29.81/20.03 inference(unit_resolution,[status(thm)],[7157, 29791, 29787])).
% 29.81/20.03 tff(29793,plain,((~(f3(c1, f8(c3)) = c2)) | (f3(c1, c2) = c2) | (c1 = f3(c1, c2))), inference(lemma,lemma(discharge,[]))).
% 29.81/20.03 tff(29794,plain,
% 29.81/20.03 (f3(c1, c2) = c2),
% 29.81/20.03 inference(unit_resolution,[status(thm)],[29793, 29782, 16041])).
% 29.81/20.03 tff(29795,plain,
% 29.81/20.03 (big_f(f3(c1, c2), c1)),
% 29.81/20.03 inference(unit_resolution,[status(thm)],[26072, 29794, 348])).
% 29.81/20.03 tff(29796,plain,
% 29.81/20.03 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((c1 = c4) | (~(c1 = c3)) | (~big_f(f3(c1, c2), c1)) | (~(f3(c1, c2) = c2)) | (~big_f(c1, f6(c1, c1))) | (f6(c1, c1) = f2(c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (c1 = c4) | (~(c1 = c3)) | (~big_f(f3(c1, c2), c1)) | (~(f3(c1, c2) = c2)) | (~big_f(c1, f6(c1, c1))) | (f6(c1, c1) = f2(c1)))),
% 29.81/20.03 inference(rewrite,[status(thm)],[])).
% 29.81/20.03 tff(29797,plain,
% 29.81/20.03 (((~(c1 = c3)) | (c1 = c4) | (~(f3(c1, c2) = c2)) | (~big_f(f3(c1, c2), c1)) | (f6(c1, c1) = f2(c1)) | (~big_f(c1, f6(c1, c1)))) <=> ((c1 = c4) | (~(c1 = c3)) | (~big_f(f3(c1, c2), c1)) | (~(f3(c1, c2) = c2)) | (~big_f(c1, f6(c1, c1))) | (f6(c1, c1) = f2(c1)))),
% 29.81/20.03 inference(rewrite,[status(thm)],[])).
% 29.81/20.03 tff(29798,plain,
% 29.81/20.03 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c1 = c4) | (~(f3(c1, c2) = c2)) | (~big_f(f3(c1, c2), c1)) | (f6(c1, c1) = f2(c1)) | (~big_f(c1, f6(c1, c1))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((c1 = c4) | (~(c1 = c3)) | (~big_f(f3(c1, c2), c1)) | (~(f3(c1, c2) = c2)) | (~big_f(c1, f6(c1, c1))) | (f6(c1, c1) = f2(c1))))),
% 29.81/20.03 inference(monotonicity,[status(thm)],[29797])).
% 29.81/20.03 tff(29799,plain,
% 29.81/20.03 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c1 = c4) | (~(f3(c1, c2) = c2)) | (~big_f(f3(c1, c2), c1)) | (f6(c1, c1) = f2(c1)) | (~big_f(c1, f6(c1, c1))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (c1 = c4) | (~(c1 = c3)) | (~big_f(f3(c1, c2), c1)) | (~(f3(c1, c2) = c2)) | (~big_f(c1, f6(c1, c1))) | (f6(c1, c1) = f2(c1)))),
% 29.81/20.03 inference(transitivity,[status(thm)],[29798, 29796])).
% 29.81/20.03 tff(29800,plain,
% 29.81/20.03 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c1 = c4) | (~(f3(c1, c2) = c2)) | (~big_f(f3(c1, c2), c1)) | (f6(c1, c1) = f2(c1)) | (~big_f(c1, f6(c1, c1))))),
% 29.81/20.03 inference(quant_inst,[status(thm)],[])).
% 29.81/20.03 tff(29801,plain,
% 29.81/20.03 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (c1 = c4) | (~(c1 = c3)) | (~big_f(f3(c1, c2), c1)) | (~(f3(c1, c2) = c2)) | (~big_f(c1, f6(c1, c1))) | (f6(c1, c1) = f2(c1))),
% 29.81/20.03 inference(modus_ponens,[status(thm)],[29800, 29799])).
% 29.81/20.03 tff(29802,plain,
% 29.81/20.03 ((~big_f(f3(c1, c2), c1)) | (~(f3(c1, c2) = c2)) | (f6(c1, c1) = f2(c1))),
% 29.81/20.03 inference(unit_resolution,[status(thm)],[29801, 7051, 5611, 482, 28185])).
% 29.81/20.03 tff(29803,plain,
% 29.81/20.03 ($false),
% 29.81/20.03 inference(unit_resolution,[status(thm)],[29802, 29795, 29794, 29763])).
% 29.81/20.03 tff(29804,plain,((f6(c1, c1) = f2(c1)) | (c1 = c4) | (~big_f(c1, f6(c1, c1))) | (~big_f(c2, c1)) | (c1 = f3(c1, c2)) | (~big_f(c1, c1)) | (~(f8(c1) = c1)) | (~(c3 = c1))), inference(lemma,lemma(discharge,[]))).
% 29.81/20.03 tff(29805,plain,
% 29.81/20.03 (c1 = f3(c1, c2)),
% 29.81/20.03 inference(unit_resolution,[status(thm)],[29804, 29762, 28185, 348, 29740, 29304, 29719, 28773])).
% 29.81/20.03 tff(29806,plain,
% 29.81/20.03 (c1 = f8(c1)),
% 29.81/20.03 inference(unit_resolution,[status(thm)],[9808, 29762])).
% 29.81/20.03 tff(29807,plain,
% 29.81/20.03 ((f3(c1, f8(c3)) = c3) <=> (f3(c1, f8(c3)) = c1)),
% 29.81/20.03 inference(monotonicity,[status(thm)],[172])).
% 29.81/20.03 tff(29808,assumption,(f3(c1, f8(c3)) = c3), introduced(assumption)).
% 29.81/20.03 tff(29809,plain,
% 29.81/20.03 (f3(c1, f8(c3)) = c1),
% 29.81/20.03 inference(modus_ponens,[status(thm)],[29808, 29807])).
% 29.81/20.03 tff(29810,plain,
% 29.81/20.03 ($false),
% 29.81/20.03 inference(unit_resolution,[status(thm)],[29741, 29809])).
% 29.81/20.03 tff(29811,plain,((~(f3(c1, f8(c3)) = c3)) | (f3(c1, f8(c3)) = c1) | (~(c3 = c1))), inference(lemma,lemma(discharge,[]))).
% 29.81/20.03 tff(29812,plain,
% 29.81/20.03 (~(f3(c1, f8(c3)) = c3)),
% 29.81/20.03 inference(unit_resolution,[status(thm)],[29811, 29741, 28773])).
% 29.81/20.03 tff(29813,plain,
% 29.81/20.03 ((f3(c1, f8(c3)) = c1) <=> (f3(c1, f8(c3)) = c3)),
% 29.81/20.03 inference(symmetry,[status(thm)],[29807])).
% 29.81/20.03 tff(29814,plain,
% 29.81/20.03 (c1 = f8(c3)),
% 29.81/20.03 inference(transitivity,[status(thm)],[3031, 12787])).
% 29.81/20.03 tff(29815,plain,
% 29.81/20.03 (f3(c1, c1) = f3(c1, f8(c3))),
% 29.81/20.03 inference(monotonicity,[status(thm)],[29814])).
% 29.81/20.03 tff(29816,plain,
% 29.81/20.03 ((f3(c1, c1) = c1) <=> (f3(c1, f8(c3)) = c1)),
% 29.81/20.03 inference(monotonicity,[status(thm)],[29815])).
% 29.81/20.03 tff(29817,plain,
% 29.81/20.03 ((f3(c1, c1) = c1) <=> (f3(c1, f8(c3)) = c3)),
% 29.81/20.03 inference(transitivity,[status(thm)],[29816, 29813])).
% 29.81/20.03 tff(29818,plain,
% 29.81/20.03 (f3(c1, f8(c3)) = c3),
% 29.81/20.03 inference(modus_ponens,[status(thm)],[1938, 29817])).
% 29.81/20.03 tff(29819,assumption,(~(f3(c1, f8(c3)) = c3)), introduced(assumption)).
% 29.81/20.03 tff(29820,plain,
% 29.81/20.03 ($false),
% 29.81/20.03 inference(unit_resolution,[status(thm)],[29819, 29818])).
% 29.81/20.03 tff(29821,plain,((~(f3(c1, c1) = c1)) | (f3(c1, f8(c3)) = c3) | (~(c3 = c1)) | (~(c1 = f8(c1)))), inference(lemma,lemma(discharge,[]))).
% 29.81/20.03 tff(29822,plain,
% 29.81/20.03 (~(f3(c1, c1) = c1)),
% 29.81/20.03 inference(unit_resolution,[status(thm)],[29821, 29806, 28773, 29812])).
% 29.81/20.03 tff(29823,plain,
% 29.81/20.03 (f3(c1, c1) = c2),
% 29.81/20.03 inference(unit_resolution,[status(thm)],[1416, 29822])).
% 29.81/20.03 tff(29824,plain,
% 29.81/20.03 (f8(c3) = f8(c1)),
% 29.81/20.03 inference(monotonicity,[status(thm)],[5090])).
% 29.81/20.03 tff(29825,plain,
% 29.81/20.03 (f8(c3) = c1),
% 29.81/20.03 inference(transitivity,[status(thm)],[29824, 29199])).
% 29.81/20.03 tff(29826,plain,
% 29.81/20.03 (f3(c1, f8(c3)) = f3(c1, c1)),
% 29.81/20.03 inference(monotonicity,[status(thm)],[29825])).
% 29.81/20.03 tff(29827,plain,
% 29.81/20.03 (f3(c1, f8(c3)) = c2),
% 29.81/20.03 inference(transitivity,[status(thm)],[29826, 1441])).
% 29.81/20.03 tff(29828,plain,
% 29.81/20.03 (f3(c1, f3(c1, f8(c3))) = f3(c1, c2)),
% 29.81/20.03 inference(monotonicity,[status(thm)],[29827])).
% 29.81/20.03 tff(29829,plain,
% 29.81/20.03 ((f3(c1, f3(c1, f8(c3))) = c1) <=> (f3(c1, c2) = c1)),
% 29.81/20.03 inference(monotonicity,[status(thm)],[29828])).
% 29.81/20.03 tff(29830,plain,
% 29.81/20.03 ((f3(c1, f3(c1, f8(c3))) = c1) <=> (c1 = f3(c1, c2))),
% 29.81/20.03 inference(transitivity,[status(thm)],[29829, 13151])).
% 29.81/20.03 tff(29831,plain,
% 29.81/20.03 ((f3(c1, f3(c1, f8(c3))) = c3) <=> (f3(c1, f3(c1, f8(c3))) = c1)),
% 29.81/20.03 inference(monotonicity,[status(thm)],[5090])).
% 29.81/20.03 tff(29832,plain,
% 29.81/20.03 ((f3(c1, f3(c1, f8(c3))) = c3) <=> (c1 = f3(c1, c2))),
% 29.81/20.03 inference(transitivity,[status(thm)],[29831, 29830])).
% 29.81/20.03 tff(29833,plain,
% 29.81/20.03 ((~(f3(c1, f3(c1, f8(c3))) = c3)) <=> (~(c1 = f3(c1, c2)))),
% 29.81/20.03 inference(monotonicity,[status(thm)],[29832])).
% 29.81/20.03 tff(29834,assumption,(~(f3(c1, f3(c1, f8(c3))) = c3)), introduced(assumption)).
% 29.81/20.03 tff(29835,plain,
% 29.81/20.03 (~(c1 = f3(c1, c2))),
% 29.81/20.03 inference(modus_ponens,[status(thm)],[29834, 29833])).
% 29.81/20.03 tff(29836,plain,
% 29.81/20.03 ($false),
% 29.81/20.03 inference(unit_resolution,[status(thm)],[13189, 29835])).
% 29.81/20.03 tff(29837,plain,((f3(c1, f3(c1, f8(c3))) = c3) | (~(c1 = f3(c1, c2))) | (~(f3(c1, c1) = c2)) | (~(c1 = f8(c1))) | (~(c1 = c3))), inference(lemma,lemma(discharge,[]))).
% 29.81/20.03 tff(29838,plain,
% 29.81/20.03 (f3(c1, f3(c1, f8(c3))) = c3),
% 29.81/20.03 inference(unit_resolution,[status(thm)],[29837, 29823, 29544, 29806, 29805])).
% 29.81/20.03 tff(29839,plain,
% 29.81/20.03 (c2 = f3(c1, f8(c3))),
% 29.81/20.03 inference(symmetry,[status(thm)],[29742])).
% 29.81/20.03 tff(29840,plain,
% 29.81/20.03 (f3(c1, c2) = f3(c1, f3(c1, f8(c3)))),
% 29.81/20.03 inference(monotonicity,[status(thm)],[29839])).
% 29.81/20.03 tff(29841,plain,
% 29.81/20.03 (f3(c1, c2) = c1),
% 29.81/20.03 inference(transitivity,[status(thm)],[29840, 29838, 28773])).
% 29.81/20.03 tff(29842,plain,
% 29.81/20.03 (f6(c1, f3(c1, c2)) = f6(c1, c1)),
% 29.81/20.03 inference(monotonicity,[status(thm)],[29841])).
% 29.81/20.03 tff(29843,plain,
% 29.81/20.03 ((f6(c1, f3(c1, c2)) = c1) <=> (f6(c1, c1) = c1)),
% 29.81/20.03 inference(monotonicity,[status(thm)],[29842])).
% 29.81/20.03 tff(29844,plain,
% 29.81/20.03 ((f6(c1, c1) = c1) <=> (f6(c1, f3(c1, c2)) = c1)),
% 29.81/20.03 inference(symmetry,[status(thm)],[29843])).
% 29.81/20.03 tff(29845,plain,
% 29.81/20.03 ((~(f6(c1, c1) = c1)) <=> (~(f6(c1, f3(c1, c2)) = c1))),
% 29.81/20.03 inference(monotonicity,[status(thm)],[29844])).
% 29.81/20.03 tff(29846,plain,
% 29.81/20.03 (~(f6(c1, f3(c1, c2)) = c1)),
% 29.81/20.03 inference(modus_ponens,[status(thm)],[28, 29845])).
% 29.81/20.03 tff(29847,plain,
% 29.81/20.03 (big_f(f7(c1), f6(c1, f3(c1, c2))) <=> big_f(c1, f6(c1, c1))),
% 29.81/20.03 inference(monotonicity,[status(thm)],[25791, 29842])).
% 29.81/20.03 tff(29848,plain,
% 29.81/20.03 (big_f(c1, f6(c1, c1)) <=> big_f(f7(c1), f6(c1, f3(c1, c2)))),
% 29.81/20.03 inference(symmetry,[status(thm)],[29847])).
% 29.81/20.03 tff(29849,plain,
% 29.81/20.03 (big_f(f7(c1), f6(c1, f3(c1, c2)))),
% 29.81/20.03 inference(modus_ponens,[status(thm)],[28185, 29848])).
% 29.81/20.03 tff(29850,plain,
% 29.81/20.03 (big_f(f7(c1), f6(c1, f3(c1, c2))) <=> big_f(c1, c2)),
% 29.81/20.03 inference(monotonicity,[status(thm)],[25791, 7021])).
% 29.81/20.03 tff(29851,plain,
% 29.81/20.03 (big_f(c1, c2) <=> big_f(f7(c1), f6(c1, f3(c1, c2)))),
% 29.85/20.03 inference(symmetry,[status(thm)],[29850])).
% 29.85/20.03 tff(29852,plain,
% 29.85/20.03 ((~big_f(c1, c2)) <=> (~big_f(f7(c1), f6(c1, f3(c1, c2))))),
% 29.85/20.03 inference(monotonicity,[status(thm)],[29851])).
% 29.85/20.03 tff(29853,plain,
% 29.85/20.03 (~big_f(f7(c1), f6(c1, f3(c1, c2)))),
% 29.85/20.03 inference(modus_ponens,[status(thm)],[27, 29852])).
% 29.85/20.03 tff(29854,assumption,(big_f(f7(c1), f6(c1, f3(c1, c2)))), introduced(assumption)).
% 29.85/20.03 tff(29855,plain,
% 29.85/20.03 ($false),
% 29.85/20.03 inference(unit_resolution,[status(thm)],[29854, 29853])).
% 29.85/20.03 tff(29856,plain,((~(f6(c1, f3(c1, c2)) = c2)) | (~big_f(f7(c1), f6(c1, f3(c1, c2)))) | big_f(c1, c2)), inference(lemma,lemma(discharge,[]))).
% 29.85/20.03 tff(29857,plain,
% 29.85/20.03 (~(f6(c1, f3(c1, c2)) = c2)),
% 29.85/20.03 inference(unit_resolution,[status(thm)],[29856, 29849, 27])).
% 29.85/20.03 tff(29858,plain,
% 29.85/20.03 ($false),
% 29.85/20.03 inference(unit_resolution,[status(thm)],[6690, 29857, 29846])).
% 29.85/20.03 tff(29859,plain,((f3(c1, f8(c3)) = c1) | big_f(c1, c2) | (f6(c1, c1) = c1) | (~big_f(c1, f6(c1, c1))) | (~big_f(c2, c1))), inference(lemma,lemma(discharge,[]))).
% 29.85/20.03 tff(29860,plain,
% 29.85/20.03 (f3(c1, f8(c3)) = c1),
% 29.85/20.03 inference(unit_resolution,[status(thm)],[29859, 28, 27, 29696, 29494])).
% 29.85/20.03 tff(29861,plain,
% 29.85/20.03 (~(f6(c1, c1) = f2(c1))),
% 29.85/20.03 inference(unit_resolution,[status(thm)],[29718, 29696, 27, 28])).
% 29.85/20.03 tff(29862,plain,
% 29.85/20.03 (~(c1 = c4)),
% 29.85/20.03 inference(unit_resolution,[status(thm)],[29739, 29696, 29494, 29544, 28, 29304])).
% 29.85/20.03 tff(29863,plain,
% 29.85/20.03 (~(f8(c1) = c1)),
% 29.85/20.03 inference(unit_resolution,[status(thm)],[29780, 29860, 29696, 29862, 29304, 29861, 28773])).
% 29.85/20.03 tff(29864,plain,
% 29.85/20.03 (f8(c1) = c2),
% 29.85/20.03 inference(unit_resolution,[status(thm)],[1680, 29863])).
% 29.85/20.03 tff(29865,plain,
% 29.85/20.03 (f8(c3) = c2),
% 29.85/20.03 inference(transitivity,[status(thm)],[29743, 29864])).
% 29.85/20.03 tff(29866,plain,
% 29.85/20.03 (f3(c1, f8(c3)) = f3(c1, c2)),
% 29.85/20.03 inference(monotonicity,[status(thm)],[29865])).
% 29.85/20.03 tff(29867,plain,
% 29.85/20.03 (f3(c1, c2) = f3(c1, f8(c3))),
% 29.85/20.03 inference(symmetry,[status(thm)],[29866])).
% 29.85/20.03 tff(29868,plain,
% 29.85/20.03 (~(c1 = f8(c2))),
% 29.85/20.03 inference(unit_resolution,[status(thm)],[28187, 29696, 28101, 94, 28])).
% 29.85/20.03 tff(29869,plain,
% 29.85/20.03 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (c1 = f8(c2)) | (~(f7(c1) = c1)) | (~big_f(c1, f10(c2))) | big_f(f7(c1), f6(c1, f6(c1, c2))) | (f6(c1, f6(c1, c2)) = f6(c1, c2)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c2) = c2) | (c1 = f8(c2)) | (~(f7(c1) = c1)) | (~big_f(c1, f10(c2))) | big_f(f7(c1), f6(c1, f6(c1, c2))) | (f6(c1, f6(c1, c2)) = f6(c1, c2)))),
% 29.85/20.03 inference(rewrite,[status(thm)],[])).
% 29.85/20.03 tff(29870,plain,
% 29.85/20.03 (((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (~(f7(c1) = c1)) | (f6(c1, f6(c1, c2)) = f6(c1, c2)) | big_f(f7(c1), f6(c1, f6(c1, c2)))) <=> ((f10(c2) = c2) | (c1 = f8(c2)) | (~(f7(c1) = c1)) | (~big_f(c1, f10(c2))) | big_f(f7(c1), f6(c1, f6(c1, c2))) | (f6(c1, f6(c1, c2)) = f6(c1, c2)))),
% 29.85/20.03 inference(rewrite,[status(thm)],[])).
% 29.85/20.03 tff(29871,plain,
% 29.85/20.03 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (~(f7(c1) = c1)) | (f6(c1, f6(c1, c2)) = f6(c1, c2)) | big_f(f7(c1), f6(c1, f6(c1, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (c1 = f8(c2)) | (~(f7(c1) = c1)) | (~big_f(c1, f10(c2))) | big_f(f7(c1), f6(c1, f6(c1, c2))) | (f6(c1, f6(c1, c2)) = f6(c1, c2))))),
% 29.85/20.03 inference(monotonicity,[status(thm)],[29870])).
% 29.85/20.03 tff(29872,plain,
% 29.85/20.03 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (~(f7(c1) = c1)) | (f6(c1, f6(c1, c2)) = f6(c1, c2)) | big_f(f7(c1), f6(c1, f6(c1, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c2) = c2) | (c1 = f8(c2)) | (~(f7(c1) = c1)) | (~big_f(c1, f10(c2))) | big_f(f7(c1), f6(c1, f6(c1, c2))) | (f6(c1, f6(c1, c2)) = f6(c1, c2)))),
% 29.85/20.04 inference(transitivity,[status(thm)],[29871, 29869])).
% 29.85/20.04 tff(29873,plain,
% 29.85/20.04 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (~(f7(c1) = c1)) | (f6(c1, f6(c1, c2)) = f6(c1, c2)) | big_f(f7(c1), f6(c1, f6(c1, c2))))),
% 29.85/20.04 inference(quant_inst,[status(thm)],[])).
% 29.85/20.04 tff(29874,plain,
% 29.85/20.04 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c2) = c2) | (c1 = f8(c2)) | (~(f7(c1) = c1)) | (~big_f(c1, f10(c2))) | big_f(f7(c1), f6(c1, f6(c1, c2))) | (f6(c1, f6(c1, c2)) = f6(c1, c2))),
% 29.85/20.04 inference(modus_ponens,[status(thm)],[29873, 29872])).
% 29.85/20.04 tff(29875,plain,
% 29.85/20.04 (f6(c1, f6(c1, c2)) = f6(c1, c2)),
% 29.85/20.04 inference(unit_resolution,[status(thm)],[29874, 2662, 25791, 89, 28676, 29324, 24284])).
% 29.85/20.04 tff(29876,plain,
% 29.85/20.04 (f3(c1, c2) = f3(c1, f8(c3))),
% 29.85/20.04 inference(monotonicity,[status(thm)],[18339])).
% 29.85/20.04 tff(29877,plain,
% 29.85/20.04 ((c1 = f3(c1, c2)) <=> (c1 = f3(c1, f8(c3)))),
% 29.85/20.04 inference(monotonicity,[status(thm)],[29876])).
% 29.85/20.04 tff(29878,plain,
% 29.85/20.04 ((c1 = f3(c1, c2)) <=> (f3(c1, f8(c3)) = c1)),
% 29.85/20.04 inference(transitivity,[status(thm)],[29877, 7092])).
% 29.85/20.04 tff(29879,plain,
% 29.85/20.04 ((f6(c1, f3(c1, c2)) = f3(c1, c2)) <=> (c1 = f3(c1, c2))),
% 29.85/20.04 inference(monotonicity,[status(thm)],[6647])).
% 29.85/20.04 tff(29880,plain,
% 29.85/20.04 ((f6(c1, f3(c1, c2)) = f3(c1, c2)) <=> (f3(c1, f8(c3)) = c1)),
% 29.85/20.04 inference(transitivity,[status(thm)],[29879, 29878])).
% 29.85/20.04 tff(29881,plain,
% 29.85/20.04 ((~(f6(c1, f3(c1, c2)) = f3(c1, c2))) <=> (~(f3(c1, f8(c3)) = c1))),
% 29.85/20.04 inference(monotonicity,[status(thm)],[29880])).
% 29.85/20.04 tff(29882,plain,
% 29.85/20.04 (big_f(f7(c1), f6(c1, f3(c1, c2))) <=> big_f(c1, c1)),
% 29.85/20.04 inference(monotonicity,[status(thm)],[25791, 6647])).
% 29.85/20.04 tff(29883,plain,
% 29.85/20.04 (big_f(c1, c1) <=> big_f(f7(c1), f6(c1, f3(c1, c2)))),
% 29.85/20.04 inference(symmetry,[status(thm)],[29882])).
% 29.85/20.04 tff(29884,plain,
% 29.85/20.04 (big_f(f7(c1), f6(c1, f3(c1, c2)))),
% 29.85/20.04 inference(modus_ponens,[status(thm)],[4932, 29883])).
% 29.85/20.04 tff(29885,plain,
% 29.85/20.04 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (c1 = f8(c2)) | (~(f7(c1) = c1)) | (~big_f(c1, f10(c2))) | (~(f6(c1, f3(c1, c2)) = f3(c1, c2))) | (~big_f(f7(c1), f6(c1, f3(c1, c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (c1 = f8(c2)) | (~(f7(c1) = c1)) | (~big_f(c1, f10(c2))) | (~(f6(c1, f3(c1, c2)) = f3(c1, c2))) | (~big_f(f7(c1), f6(c1, f3(c1, c2)))))),
% 29.85/20.04 inference(rewrite,[status(thm)],[])).
% 29.85/20.04 tff(29886,plain,
% 29.85/20.04 (((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (~(f7(c1) = c1)) | (~(f6(c1, f3(c1, c2)) = f3(c1, c2))) | (~big_f(f7(c1), f6(c1, f3(c1, c2))))) <=> ((f10(c2) = c2) | (c1 = f8(c2)) | (~(f7(c1) = c1)) | (~big_f(c1, f10(c2))) | (~(f6(c1, f3(c1, c2)) = f3(c1, c2))) | (~big_f(f7(c1), f6(c1, f3(c1, c2)))))),
% 29.85/20.04 inference(rewrite,[status(thm)],[])).
% 29.85/20.04 tff(29887,plain,
% 29.85/20.04 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (~(f7(c1) = c1)) | (~(f6(c1, f3(c1, c2)) = f3(c1, c2))) | (~big_f(f7(c1), f6(c1, f3(c1, c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (c1 = f8(c2)) | (~(f7(c1) = c1)) | (~big_f(c1, f10(c2))) | (~(f6(c1, f3(c1, c2)) = f3(c1, c2))) | (~big_f(f7(c1), f6(c1, f3(c1, c2))))))),
% 29.85/20.04 inference(monotonicity,[status(thm)],[29886])).
% 29.85/20.04 tff(29888,plain,
% 29.85/20.04 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (~(f7(c1) = c1)) | (~(f6(c1, f3(c1, c2)) = f3(c1, c2))) | (~big_f(f7(c1), f6(c1, f3(c1, c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (c1 = f8(c2)) | (~(f7(c1) = c1)) | (~big_f(c1, f10(c2))) | (~(f6(c1, f3(c1, c2)) = f3(c1, c2))) | (~big_f(f7(c1), f6(c1, f3(c1, c2)))))),
% 29.85/20.04 inference(transitivity,[status(thm)],[29887, 29885])).
% 29.85/20.04 tff(29889,plain,
% 29.85/20.04 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (~(f7(c1) = c1)) | (~(f6(c1, f3(c1, c2)) = f3(c1, c2))) | (~big_f(f7(c1), f6(c1, f3(c1, c2)))))),
% 29.85/20.04 inference(quant_inst,[status(thm)],[])).
% 29.85/20.04 tff(29890,plain,
% 29.85/20.04 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (c1 = f8(c2)) | (~(f7(c1) = c1)) | (~big_f(c1, f10(c2))) | (~(f6(c1, f3(c1, c2)) = f3(c1, c2))) | (~big_f(f7(c1), f6(c1, f3(c1, c2))))),
% 29.85/20.04 inference(modus_ponens,[status(thm)],[29889, 29888])).
% 29.85/20.04 tff(29891,plain,
% 29.85/20.04 (~(f6(c1, f3(c1, c2)) = f3(c1, c2))),
% 29.85/20.04 inference(unit_resolution,[status(thm)],[29890, 2730, 25791, 89, 29884, 28015, 24284])).
% 29.85/20.04 tff(29892,plain,
% 29.85/20.04 (~(f3(c1, f8(c3)) = c1)),
% 29.85/20.04 inference(modus_ponens,[status(thm)],[29891, 29881])).
% 29.85/20.04 tff(29893,plain,
% 29.85/20.04 (f3(c1, f8(c3)) = c2),
% 29.85/20.04 inference(unit_resolution,[status(thm)],[7123, 29892])).
% 29.85/20.04 tff(29894,plain,
% 29.85/20.04 (f3(c1, c2) = c2),
% 29.85/20.04 inference(transitivity,[status(thm)],[29876, 29893])).
% 29.85/20.04 tff(29895,plain,
% 29.85/20.04 (f6(c1, f3(c1, c2)) = f6(c1, c2)),
% 29.85/20.04 inference(monotonicity,[status(thm)],[29894])).
% 29.85/20.04 tff(29896,plain,
% 29.85/20.04 (f6(c1, c2) = f6(c1, f3(c1, c2))),
% 29.85/20.04 inference(symmetry,[status(thm)],[29895])).
% 29.85/20.04 tff(29897,assumption,(f6(c1, f6(c1, c2)) = f6(c1, c2)), introduced(assumption)).
% 29.85/20.04 tff(29898,plain,
% 29.85/20.04 (c2 = c1),
% 29.85/20.04 inference(transitivity,[status(thm)],[28323, 29897, 29896, 6647])).
% 29.85/20.04 tff(29899,plain,
% 29.85/20.04 ($false),
% 29.85/20.04 inference(unit_resolution,[status(thm)],[75, 29898])).
% 29.85/20.04 tff(29900,plain,((~(f6(c1, f3(c1, c2)) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~(f6(c1, f6(c1, c2)) = c2)) | (~(f8(c1) = c2)) | (~(c3 = c1)) | (f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, c1))), inference(lemma,lemma(discharge,[]))).
% 29.85/20.04 tff(29901,plain,
% 29.85/20.04 (~(f6(c1, f3(c1, c2)) = c1)),
% 29.85/20.04 inference(unit_resolution,[status(thm)],[29900, 1671, 27490, 29875, 28773, 89, 24284, 29304])).
% 29.85/20.04 tff(29902,plain,
% 29.85/20.04 (f6(c1, f3(c1, c2)) = c2),
% 29.85/20.04 inference(unit_resolution,[status(thm)],[6690, 29901])).
% 29.85/20.04 tff(29903,plain,
% 29.85/20.04 (c2 = f8(c3)),
% 29.85/20.04 inference(transitivity,[status(thm)],[7098, 29744])).
% 29.85/20.04 tff(29904,plain,
% 29.85/20.04 (f3(c1, c2) = f3(c1, f8(c3))),
% 29.85/20.04 inference(monotonicity,[status(thm)],[29903])).
% 29.85/20.04 tff(29905,plain,
% 29.85/20.04 (f3(c1, f8(c3)) = f3(c1, c2)),
% 29.85/20.04 inference(symmetry,[status(thm)],[29904])).
% 29.85/20.04 tff(29906,plain,
% 29.85/20.04 ((f3(c1, c2) = c2) <=> (f3(c1, f8(c3)) = c2)),
% 29.85/20.04 inference(monotonicity,[status(thm)],[29904])).
% 29.85/20.04 tff(29907,plain,
% 29.85/20.04 ((~(f3(c1, c2) = c2)) <=> (~(f3(c1, f8(c3)) = c2))),
% 29.85/20.04 inference(monotonicity,[status(thm)],[29906])).
% 29.85/20.04 tff(29908,plain,
% 29.85/20.04 ((f6(c1, f3(c1, c2)) = f3(c1, c2)) <=> (c2 = f3(c1, c2))),
% 29.85/20.04 inference(monotonicity,[status(thm)],[29902])).
% 29.85/20.04 tff(29909,plain,
% 29.85/20.04 ((f6(c1, f3(c1, c2)) = f3(c1, c2)) <=> (f3(c1, c2) = c2)),
% 29.85/20.04 inference(transitivity,[status(thm)],[29908, 6643])).
% 29.85/20.04 tff(29910,plain,
% 29.85/20.04 ((~(f6(c1, f3(c1, c2)) = f3(c1, c2))) <=> (~(f3(c1, c2) = c2))),
% 29.85/20.04 inference(monotonicity,[status(thm)],[29909])).
% 29.85/20.04 tff(29911,assumption,(~(f6(c1, f3(c1, c2)) = f3(c1, c2))), introduced(assumption)).
% 29.85/20.04 tff(29912,plain,
% 29.85/20.04 (~(f3(c1, c2) = c2)),
% 29.85/20.04 inference(modus_ponens,[status(thm)],[29911, 29910])).
% 29.85/20.04 tff(29913,plain,
% 29.85/20.04 (~(f3(c1, f8(c3)) = c2)),
% 29.85/20.04 inference(modus_ponens,[status(thm)],[29912, 29907])).
% 29.85/20.04 tff(29914,plain,
% 29.85/20.04 (f3(c1, f8(c3)) = c1),
% 29.85/20.04 inference(unit_resolution,[status(thm)],[7123, 29913])).
% 29.85/20.04 tff(29915,plain,
% 29.85/20.04 (c1 = f3(c1, f8(c3))),
% 29.85/20.04 inference(symmetry,[status(thm)],[29914])).
% 29.85/20.04 tff(29916,plain,
% 29.85/20.04 (c1 = f3(c1, c2)),
% 29.85/20.04 inference(transitivity,[status(thm)],[29915, 29905])).
% 29.85/20.04 tff(29917,plain,
% 29.85/20.04 (f6(c1, c1) = f6(c1, f3(c1, c2))),
% 29.85/20.04 inference(monotonicity,[status(thm)],[29916])).
% 29.85/20.04 tff(29918,plain,
% 29.85/20.04 (f6(c1, c1) = c2),
% 29.85/20.04 inference(transitivity,[status(thm)],[29917, 29902])).
% 29.85/20.04 tff(29919,plain,
% 29.85/20.04 (big_f(c1, f6(c1, c1)) <=> big_f(c1, c2)),
% 29.85/20.04 inference(monotonicity,[status(thm)],[29918])).
% 29.85/20.04 tff(29920,plain,
% 29.85/20.04 (big_f(c1, c2) <=> big_f(c1, f6(c1, c1))),
% 29.85/20.04 inference(symmetry,[status(thm)],[29919])).
% 29.85/20.04 tff(29921,plain,
% 29.85/20.04 ((~big_f(c1, c2)) <=> (~big_f(c1, f6(c1, c1)))),
% 29.85/20.04 inference(monotonicity,[status(thm)],[29920])).
% 29.85/20.04 tff(29922,plain,
% 29.85/20.04 (~big_f(c1, f6(c1, c1))),
% 29.85/20.04 inference(modus_ponens,[status(thm)],[27, 29921])).
% 29.85/20.04 tff(29923,plain,
% 29.85/20.04 ($false),
% 29.85/20.04 inference(unit_resolution,[status(thm)],[28185, 29922])).
% 29.85/20.04 tff(29924,plain,((~(f8(c1) = c2)) | (~big_f(c1, f6(c1, c1))) | big_f(c1, c2) | (f6(c1, f3(c1, c2)) = f3(c1, c2)) | (~(f6(c1, f6(c1, c2)) = c2)) | (f10(c2) = c2) | (c1 = f8(c2))), inference(lemma,lemma(discharge,[]))).
% 29.85/20.04 tff(29925,plain,
% 29.85/20.04 (f6(c1, f3(c1, c2)) = f3(c1, c2)),
% 29.85/20.04 inference(unit_resolution,[status(thm)],[29924, 29864, 27, 29696, 64, 89, 29868])).
% 29.85/20.04 tff(29926,plain,
% 29.85/20.04 (big_f(f7(c1), f6(c1, f6(c1, c2))) <=> big_f(c1, c2)),
% 29.85/20.04 inference(monotonicity,[status(thm)],[25791, 64])).
% 29.85/20.04 tff(29927,plain,
% 29.85/20.04 (big_f(c1, c2) <=> big_f(f7(c1), f6(c1, f6(c1, c2)))),
% 29.85/20.04 inference(symmetry,[status(thm)],[29926])).
% 29.85/20.04 tff(29928,plain,
% 29.85/20.04 ((~big_f(c1, c2)) <=> (~big_f(f7(c1), f6(c1, f6(c1, c2))))),
% 29.85/20.04 inference(monotonicity,[status(thm)],[29927])).
% 29.85/20.04 tff(29929,plain,
% 29.85/20.04 (~big_f(f7(c1), f6(c1, f6(c1, c2)))),
% 29.85/20.04 inference(modus_ponens,[status(thm)],[27, 29928])).
% 29.85/20.04 tff(29930,plain,
% 29.85/20.04 (f6(c1, f6(c1, c2)) = f6(c1, c2)),
% 29.85/20.04 inference(unit_resolution,[status(thm)],[29874, 2662, 25791, 89, 29929, 29324, 29868])).
% 29.85/20.04 tff(29931,plain,
% 29.85/20.04 (~(f6(c1, f3(c1, c2)) = c1)),
% 29.85/20.04 inference(unit_resolution,[status(thm)],[29900, 29864, 64, 29930, 28773, 89, 29868, 29304])).
% 29.85/20.04 tff(29932,plain,
% 29.85/20.04 (f6(c1, f3(c1, c2)) = c2),
% 29.85/20.04 inference(unit_resolution,[status(thm)],[6690, 29931])).
% 29.85/20.04 tff(29933,plain,
% 29.85/20.04 (c2 = f6(c1, f3(c1, c2))),
% 29.85/20.04 inference(symmetry,[status(thm)],[29932])).
% 29.85/20.04 tff(29934,plain,
% 29.85/20.04 (c2 = c1),
% 29.85/20.04 inference(transitivity,[status(thm)],[29933, 29925, 29867, 29860])).
% 29.85/20.04 tff(29935,plain,
% 29.85/20.04 ($false),
% 29.85/20.04 inference(unit_resolution,[status(thm)],[75, 29934])).
% 29.85/20.04 tff(29936,plain,((f6(c1, c1) = c1) | big_f(c1, c2) | (f10(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 29.85/20.04 tff(29937,plain,
% 29.85/20.04 (f6(c1, c1) = c1),
% 29.85/20.04 inference(unit_resolution,[status(thm)],[29936, 89, 27])).
% 29.85/20.04 tff(29938,plain,
% 29.85/20.04 (big_f(f7(c1), f6(c1, c1))),
% 29.85/20.04 inference(unit_resolution,[status(thm)],[27769, 29937, 29304])).
% 29.85/20.04 tff(29939,plain,
% 29.85/20.04 (c1 = f8(c2)),
% 29.85/20.04 inference(unit_resolution,[status(thm)],[27005, 2730, 25791, 89, 29938, 29937, 29324])).
% 29.85/20.04 tff(29940,plain,
% 29.85/20.04 (f8(c2) = c1),
% 29.85/20.04 inference(symmetry,[status(thm)],[29939])).
% 29.85/20.04 tff(29941,plain,
% 29.85/20.04 (big_f(c2, f10(c2))),
% 29.85/20.04 inference(modus_ponens,[status(thm)],[29494, 12069])).
% 29.85/20.04 tff(29942,plain,
% 29.85/20.04 (c2 = f8(c2)),
% 29.85/20.04 inference(unit_resolution,[status(thm)],[28627, 2730, 25791, 89, 29941, 29938, 29937])).
% 29.85/20.04 tff(29943,plain,
% 29.85/20.04 (c2 = c1),
% 29.85/20.04 inference(transitivity,[status(thm)],[29942, 29940])).
% 29.85/20.04 tff(29944,plain,
% 29.85/20.04 ($false),
% 29.85/20.04 inference(unit_resolution,[status(thm)],[75, 29943])).
% 29.85/20.04 tff(29945,plain,((f10(c2) = c2) | big_f(c1, c2)), inference(lemma,lemma(discharge,[]))).
% 29.85/20.04 tff(29946,plain,
% 29.85/20.04 (f10(c2) = c2),
% 29.85/20.04 inference(unit_resolution,[status(thm)],[29945, 27])).
% 29.85/20.04 tff(29947,plain,
% 29.85/20.04 (~(f4(c4) = c2)),
% 29.85/20.04 inference(unit_resolution,[status(thm)],[10739, 17, 29946])).
% 29.85/20.04 tff(29948,plain,
% 29.85/20.04 (f4(c4) = c1),
% 29.85/20.04 inference(unit_resolution,[status(thm)],[11750, 29947])).
% 29.85/20.04 tff(29949,plain,
% 29.85/20.04 (f7(c2) = c4),
% 29.85/20.04 inference(unit_resolution,[status(thm)],[16679, 23145, 29314, 29948, 1345, 17, 2])).
% 29.85/20.04 tff(29950,plain,
% 29.85/20.04 ($false),
% 29.85/20.04 inference(unit_resolution,[status(thm)],[29949, 16349])).
% 29.85/20.04 tff(29951,plain,((f7(c2) = c2) | (~(c2 = c4)) | (~big_f(c2, c2)) | big_f(c2, c1) | big_f(c1, c2)), inference(lemma,lemma(discharge,[]))).
% 29.85/20.04 tff(29952,plain,
% 29.85/20.04 (f7(c2) = c2),
% 29.85/20.04 inference(unit_resolution,[status(thm)],[29951, 29323, 29313, 2, 27])).
% 29.85/20.04 tff(29953,plain,
% 29.85/20.04 (~(f4(c4) = c1)),
% 29.85/20.04 inference(unit_resolution,[status(thm)],[29482, 29952, 27, 2, 29305, 29313])).
% 29.85/20.04 tff(29954,plain,
% 29.85/20.04 (f4(c4) = c2),
% 29.85/20.04 inference(unit_resolution,[status(thm)],[11750, 29953])).
% 29.85/20.04 tff(29955,plain,
% 29.85/20.04 (big_f(f7(c2), f6(c2, c2))),
% 29.85/20.04 inference(unit_resolution,[status(thm)],[2700, 29954, 29946, 29306, 29952, 29313])).
% 29.85/20.04 tff(29956,plain,
% 29.85/20.04 (f6(c2, c2) = c2),
% 29.85/20.04 inference(unit_resolution,[status(thm)],[25947, 29954, 2, 29952, 29946])).
% 29.85/20.04 tff(29957,plain,
% 29.85/20.04 (big_f(f9(c2, c2), f10(c2))),
% 29.85/20.04 inference(unit_resolution,[status(thm)],[2750, 29956, 29952, 29946, 29313, 29955])).
% 29.85/20.04 tff(29958,plain,
% 29.85/20.04 (f9(f10(c2), f4(c4)) = c2),
% 29.85/20.04 inference(unit_resolution,[status(thm)],[8065, 29954, 29946])).
% 29.85/20.04 tff(29959,plain,
% 29.85/20.04 (f9(c2, c2) = c2),
% 29.85/20.04 inference(unit_resolution,[status(thm)],[1606, 29958, 29946, 29954])).
% 29.85/20.04 tff(29960,plain,
% 29.85/20.04 ($false),
% 29.85/20.04 inference(unit_resolution,[status(thm)],[2384, 2378, 29946, 29952, 29956, 29955, 29959, 29957])).
% 29.85/20.04 tff(29961,plain,(big_f(c2, c1) | big_f(c1, c2) | (~(f6(c1, f6(c1, c2)) = c2)) | big_f(f7(c1), f6(c1, c1))), inference(lemma,lemma(discharge,[]))).
% 29.85/20.04 tff(29962,plain,
% 29.85/20.04 (big_f(c2, c1)),
% 29.85/20.04 inference(unit_resolution,[status(thm)],[29961, 65, 64, 27])).
% 29.85/20.04 tff(29963,plain,
% 29.85/20.04 (f9(c2, c2) = c1),
% 29.85/20.04 inference(unit_resolution,[status(thm)],[27475, 1209])).
% 29.85/20.04 tff(29964,plain,
% 29.85/20.04 (big_f(f9(c2, c2), c2) <=> big_f(c1, c2)),
% 29.85/20.04 inference(monotonicity,[status(thm)],[29963])).
% 29.85/20.04 tff(29965,plain,
% 29.85/20.04 (big_f(c1, c2) <=> big_f(f9(c2, c2), c2)),
% 29.85/20.04 inference(symmetry,[status(thm)],[29964])).
% 29.85/20.04 tff(29966,plain,
% 29.85/20.04 ((~big_f(c1, c2)) <=> (~big_f(f9(c2, c2), c2))),
% 29.85/20.04 inference(monotonicity,[status(thm)],[29965])).
% 29.85/20.04 tff(29967,plain,
% 29.85/20.04 (~big_f(f9(c2, c2), c2)),
% 29.85/20.04 inference(modus_ponens,[status(thm)],[27, 29966])).
% 29.85/20.04 tff(29968,plain,
% 29.85/20.04 ((~(f10(c2) = c2)) | big_f(f7(c1), f6(c1, c1)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (f6(c1, c1) = c1)),
% 29.85/20.04 inference(unit_resolution,[status(thm)],[4650, 25791])).
% 29.85/20.04 tff(29969,plain,
% 29.85/20.04 (big_f(f9(c2, c2), f10(c2))),
% 29.85/20.04 inference(unit_resolution,[status(thm)],[29968, 1209, 29946, 28, 65])).
% 29.85/20.04 tff(29970,plain,
% 29.85/20.04 (big_f(f9(c2, c2), c2)),
% 29.85/20.04 inference(unit_resolution,[status(thm)],[3687, 29969, 29946])).
% 29.85/20.04 tff(29971,plain,
% 29.85/20.04 ($false),
% 29.85/20.04 inference(unit_resolution,[status(thm)],[29970, 29967])).
% 29.85/20.04 tff(29972,plain,((f9(c2, c2) = c2) | big_f(c1, c2) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1))), inference(lemma,lemma(discharge,[]))).
% 29.85/20.04 tff(29973,plain,
% 29.85/20.04 (f9(c2, c2) = c2),
% 29.85/20.04 inference(unit_resolution,[status(thm)],[29972, 65, 28, 27])).
% 29.85/20.04 tff(29974,plain,
% 29.85/20.04 (big_f(f9(c2, c2), c2) <=> big_f(c2, c2)),
% 29.85/20.04 inference(monotonicity,[status(thm)],[29973])).
% 29.85/20.04 tff(29975,plain,
% 29.85/20.04 (big_f(f9(c2, c2), f10(c2)) <=> big_f(f9(c2, c2), c2)),
% 29.85/20.04 inference(monotonicity,[status(thm)],[29946])).
% 29.85/20.04 tff(29976,plain,
% 29.85/20.04 (big_f(f9(c2, c2), f10(c2)) <=> big_f(c2, c2)),
% 29.85/20.04 inference(transitivity,[status(thm)],[29975, 29974])).
% 29.85/20.04 tff(29977,plain,
% 29.85/20.04 ((~big_f(f9(c2, c2), f10(c2))) <=> (~big_f(c2, c2))),
% 29.85/20.04 inference(monotonicity,[status(thm)],[29976])).
% 29.85/20.04 tff(29978,plain,
% 29.85/20.04 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f6(c1, c1) = c1))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f6(c1, c1) = c1))),
% 29.85/20.04 inference(rewrite,[status(thm)],[])).
% 29.85/20.04 tff(29979,plain,
% 29.85/20.04 (((~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2)))) <=> ((~(f10(c2) = c2)) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f6(c1, c1) = c1))),
% 29.85/20.04 inference(rewrite,[status(thm)],[])).
% 29.85/20.04 tff(29980,plain,
% 29.85/20.04 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f6(c1, c1) = c1)))),
% 29.85/20.04 inference(monotonicity,[status(thm)],[29979])).
% 29.85/20.04 tff(29981,plain,
% 29.85/20.04 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f6(c1, c1) = c1))),
% 29.85/20.04 inference(transitivity,[status(thm)],[29980, 29978])).
% 29.85/20.04 tff(29982,plain,
% 29.85/20.04 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (f6(c1, c1) = c1) | big_f(f7(c1), f6(c1, c1)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))))),
% 29.85/20.04 inference(quant_inst,[status(thm)],[])).
% 29.85/20.04 tff(29983,plain,
% 29.85/20.04 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c2) = c2)) | big_f(f7(c1), f6(c1, c1)) | (~(f7(c1) = c1)) | (~(f9(c2, c2) = c2)) | (~big_f(f9(c2, c2), f10(c2))) | (f6(c1, c1) = c1)),
% 29.85/20.04 inference(modus_ponens,[status(thm)],[29982, 29981])).
% 29.85/20.04 tff(29984,plain,
% 29.85/20.04 (~big_f(f9(c2, c2), f10(c2))),
% 29.85/20.04 inference(unit_resolution,[status(thm)],[29983, 2409, 25791, 29946, 29973, 65, 28])).
% 29.85/20.04 tff(29985,plain,
% 29.85/20.04 (~big_f(c2, c2)),
% 29.85/20.04 inference(modus_ponens,[status(thm)],[29984, 29977])).
% 29.85/20.04 tff(29986,plain,
% 29.85/20.04 (~(f7(c2) = c2)),
% 29.85/20.04 inference(unit_resolution,[status(thm)],[11517, 79, 172, 4932, 121, 348])).
% 29.85/20.04 tff(29987,plain,
% 29.85/20.04 ($false),
% 29.85/20.04 inference(unit_resolution,[status(thm)],[10739, 29986, 79, 122])).
% 29.85/20.04 tff(29988,plain,((~(f4(c4) = c2)) | (~(f10(c2) = c2)) | (~(c3 = c1)) | (~big_f(c1, c1)) | big_f(c2, c2) | (~big_f(c2, c1))), inference(lemma,lemma(discharge,[]))).
% 29.85/20.04 tff(29989,plain,
% 29.85/20.04 (~(f4(c4) = c2)),
% 29.85/20.04 inference(unit_resolution,[status(thm)],[29988, 29985, 28773, 29304, 29946, 29962])).
% 29.85/20.04 tff(29990,plain,
% 29.85/20.04 (f4(c4) = c1),
% 29.85/20.04 inference(unit_resolution,[status(thm)],[11750, 29989])).
% 29.85/20.04 tff(29991,plain,
% 29.85/20.04 ((f9(c1, c1) = c3) <=> (f9(c1, c1) = c1)),
% 29.85/20.04 inference(monotonicity,[status(thm)],[28773])).
% 29.85/20.04 tff(29992,plain,
% 29.85/20.04 ((f9(c1, c1) = c1) <=> (f9(c1, c1) = c3)),
% 29.85/20.04 inference(symmetry,[status(thm)],[29991])).
% 29.85/20.04 tff(29993,plain,
% 29.85/20.04 ((~(f9(c1, c1) = c1)) <=> (~(f9(c1, c1) = c3))),
% 29.85/20.04 inference(monotonicity,[status(thm)],[29992])).
% 29.85/20.04 tff(29994,plain,
% 29.85/20.04 (big_f(c1, f10(c1))),
% 29.85/20.04 inference(unit_resolution,[status(thm)],[29311, 8451, 29304, 65, 3])).
% 29.85/20.04 tff(29995,plain,
% 29.85/20.04 ($false),
% 29.85/20.04 inference(unit_resolution,[status(thm)],[29994, 15821])).
% 29.85/20.04 tff(29996,plain,((f10(c1) = c1) | big_f(c1, c2) | big_f(f7(c1), f6(c1, c1)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 29.85/20.04 tff(29997,plain,
% 29.85/20.04 (f10(c1) = c1),
% 29.85/20.04 inference(unit_resolution,[status(thm)],[29996, 65, 27, 29985])).
% 29.85/20.04 tff(29998,plain,
% 29.85/20.04 (~(f9(c1, c1) = c1)),
% 29.85/20.04 inference(unit_resolution,[status(thm)],[28557, 29997, 29304, 65, 28])).
% 29.85/20.04 tff(29999,plain,
% 29.85/20.04 (~(f9(c1, c1) = c3)),
% 29.85/20.04 inference(modus_ponens,[status(thm)],[29998, 29993])).
% 29.85/20.04 tff(30000,plain,
% 29.85/20.04 (f9(c1, c1) = c2),
% 29.85/20.04 inference(unit_resolution,[status(thm)],[3939, 29998])).
% 29.85/20.04 tff(30001,plain,
% 29.85/20.04 (big_f(f9(c1, c1), c1)),
% 29.85/20.04 inference(unit_resolution,[status(thm)],[26962, 30000, 29962])).
% 29.85/20.04 tff(30002,plain,
% 29.85/20.04 ((f4(c4) = c1) <=> (f4(c2) = c1)),
% 29.85/20.04 inference(monotonicity,[status(thm)],[435])).
% 29.85/20.04 tff(30003,plain,
% 29.85/20.04 ((f4(c4) = c1) <=> (c1 = f4(c2))),
% 29.85/20.04 inference(transitivity,[status(thm)],[30002, 28135])).
% 29.85/20.04 tff(30004,plain,
% 29.85/20.04 (c1 = f4(c2)),
% 29.85/20.04 inference(modus_ponens,[status(thm)],[11752, 30003])).
% 29.85/20.04 tff(30005,plain,
% 29.85/20.04 ((f9(c1, c1) = c4) <=> (c2 = c4)),
% 29.85/20.04 inference(monotonicity,[status(thm)],[4102])).
% 29.85/20.04 tff(30006,plain,
% 29.85/20.04 ((c2 = c4) <=> (f9(c1, c1) = c4)),
% 29.85/20.04 inference(symmetry,[status(thm)],[30005])).
% 29.85/20.04 tff(30007,plain,
% 29.85/20.04 ((c4 = c2) <=> (f9(c1, c1) = c4)),
% 29.85/20.04 inference(transitivity,[status(thm)],[159, 30006])).
% 29.85/20.04 tff(30008,plain,
% 29.85/20.04 (f9(c1, c1) = c4),
% 29.85/20.04 inference(modus_ponens,[status(thm)],[431, 30007])).
% 29.85/20.04 tff(30009,plain,
% 29.85/20.04 ($false),
% 29.85/20.04 inference(unit_resolution,[status(thm)],[3923, 30008])).
% 29.85/20.04 tff(30010,plain,((~(c4 = c2)) | (f9(c1, c1) = c4) | (~(f9(c1, c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.85/20.04 tff(30011,plain,
% 29.85/20.04 (f9(c1, c1) = c4),
% 29.85/20.04 inference(unit_resolution,[status(thm)],[30010, 431, 4102])).
% 29.85/20.04 tff(30012,plain,
% 29.85/20.04 (big_f(c1, f9(c1, c1)) <=> big_f(c1, c2)),
% 29.85/20.04 inference(monotonicity,[status(thm)],[4102])).
% 29.85/20.04 tff(30013,plain,
% 29.85/20.04 (big_f(c1, c2) <=> big_f(c1, f9(c1, c1))),
% 29.85/20.04 inference(symmetry,[status(thm)],[30012])).
% 29.85/20.04 tff(30014,plain,
% 29.85/20.04 ((~big_f(c1, c2)) <=> (~big_f(c1, f9(c1, c1)))),
% 29.85/20.04 inference(monotonicity,[status(thm)],[30013])).
% 29.85/20.04 tff(30015,plain,
% 29.85/20.04 (~big_f(c1, f9(c1, c1))),
% 29.85/20.04 inference(modus_ponens,[status(thm)],[27, 30014])).
% 29.85/20.04 tff(30016,plain,
% 29.85/20.04 (f4(f9(c1, c1)) = f4(c2)),
% 29.85/20.04 inference(monotonicity,[status(thm)],[4102])).
% 29.85/20.04 tff(30017,plain,
% 29.85/20.04 ((c1 = f4(f9(c1, c1))) <=> (c1 = f4(c2))),
% 29.85/20.04 inference(monotonicity,[status(thm)],[30016])).
% 29.85/20.04 tff(30018,plain,
% 29.85/20.04 ((c1 = f4(c2)) <=> (c1 = f4(f9(c1, c1)))),
% 29.85/20.04 inference(symmetry,[status(thm)],[30017])).
% 29.85/20.04 tff(30019,plain,
% 29.85/20.04 ((f4(c4) = c1) <=> (c1 = f4(f9(c1, c1)))),
% 29.85/20.04 inference(transitivity,[status(thm)],[30003, 30018])).
% 29.85/20.04 tff(30020,plain,
% 29.85/20.04 (c1 = f4(f9(c1, c1))),
% 29.85/20.04 inference(modus_ponens,[status(thm)],[11752, 30019])).
% 29.85/20.04 tff(30021,assumption,(c1 = f4(f9(c1, c1))), introduced(assumption)).
% 29.85/20.04 tff(30022,plain,
% 29.85/20.04 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f9(c1, c1) = c3) | (~(f9(c1, c1) = c4)) | (~(c1 = f4(f9(c1, c1)))) | big_f(c1, f9(c1, c1)) | (f1(f9(c1, c1), c1) = c1) | big_f(f9(c1, c1), f1(f9(c1, c1), c1)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (f9(c1, c1) = c3) | (~(f9(c1, c1) = c4)) | (~(c1 = f4(f9(c1, c1)))) | big_f(c1, f9(c1, c1)) | (f1(f9(c1, c1), c1) = c1) | big_f(f9(c1, c1), f1(f9(c1, c1), c1)))),
% 29.85/20.04 inference(rewrite,[status(thm)],[])).
% 29.85/20.04 tff(30023,plain,
% 29.85/20.04 (((f9(c1, c1) = c3) | (f1(f9(c1, c1), c1) = c1) | big_f(f9(c1, c1), f1(f9(c1, c1), c1)) | (~(f9(c1, c1) = c4)) | big_f(c1, f9(c1, c1)) | (~(c1 = f4(f9(c1, c1))))) <=> ((f9(c1, c1) = c3) | (~(f9(c1, c1) = c4)) | (~(c1 = f4(f9(c1, c1)))) | big_f(c1, f9(c1, c1)) | (f1(f9(c1, c1), c1) = c1) | big_f(f9(c1, c1), f1(f9(c1, c1), c1)))),
% 29.85/20.05 inference(rewrite,[status(thm)],[])).
% 29.85/20.05 tff(30024,plain,
% 29.85/20.05 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f9(c1, c1) = c3) | (f1(f9(c1, c1), c1) = c1) | big_f(f9(c1, c1), f1(f9(c1, c1), c1)) | (~(f9(c1, c1) = c4)) | big_f(c1, f9(c1, c1)) | (~(c1 = f4(f9(c1, c1)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f9(c1, c1) = c3) | (~(f9(c1, c1) = c4)) | (~(c1 = f4(f9(c1, c1)))) | big_f(c1, f9(c1, c1)) | (f1(f9(c1, c1), c1) = c1) | big_f(f9(c1, c1), f1(f9(c1, c1), c1))))),
% 29.85/20.05 inference(monotonicity,[status(thm)],[30023])).
% 29.85/20.05 tff(30025,plain,
% 29.85/20.05 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f9(c1, c1) = c3) | (f1(f9(c1, c1), c1) = c1) | big_f(f9(c1, c1), f1(f9(c1, c1), c1)) | (~(f9(c1, c1) = c4)) | big_f(c1, f9(c1, c1)) | (~(c1 = f4(f9(c1, c1)))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (f9(c1, c1) = c3) | (~(f9(c1, c1) = c4)) | (~(c1 = f4(f9(c1, c1)))) | big_f(c1, f9(c1, c1)) | (f1(f9(c1, c1), c1) = c1) | big_f(f9(c1, c1), f1(f9(c1, c1), c1)))),
% 29.85/20.05 inference(transitivity,[status(thm)],[30024, 30022])).
% 29.85/20.05 tff(30026,plain,
% 29.85/20.05 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f9(c1, c1) = c3) | (f1(f9(c1, c1), c1) = c1) | big_f(f9(c1, c1), f1(f9(c1, c1), c1)) | (~(f9(c1, c1) = c4)) | big_f(c1, f9(c1, c1)) | (~(c1 = f4(f9(c1, c1)))))),
% 29.85/20.05 inference(quant_inst,[status(thm)],[])).
% 29.85/20.05 tff(30027,plain,
% 29.85/20.05 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (f9(c1, c1) = c3) | (~(f9(c1, c1) = c4)) | (~(c1 = f4(f9(c1, c1)))) | big_f(c1, f9(c1, c1)) | (f1(f9(c1, c1), c1) = c1) | big_f(f9(c1, c1), f1(f9(c1, c1), c1))),
% 29.85/20.05 inference(modus_ponens,[status(thm)],[30026, 30025])).
% 29.85/20.05 tff(30028,plain,
% 29.85/20.05 ($false),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[30027, 402, 19621, 4068, 30021, 4686, 19685, 10151])).
% 29.85/20.05 tff(30029,plain,(big_f(c1, f9(c1, c1)) | (f9(c1, c1) = c3) | (~(f9(c1, c1) = c4)) | (~(c1 = f4(f9(c1, c1)))) | (f1(f9(c1, c1), c1) = c1) | big_f(f9(c1, c1), f1(f9(c1, c1), c1))), inference(lemma,lemma(discharge,[]))).
% 29.85/20.05 tff(30030,plain,
% 29.85/20.05 ($false),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[30029, 19684, 10151, 4686, 4068, 19621, 30021])).
% 29.85/20.05 tff(30031,plain,(big_f(f9(c1, c1), f1(f9(c1, c1), c1)) | big_f(c1, f9(c1, c1)) | (~(f9(c1, c1) = c4)) | (f9(c1, c1) = c3) | (~(c1 = f4(f9(c1, c1)))) | (~big_f(f9(c1, c1), c1))), inference(lemma,lemma(discharge,[]))).
% 29.85/20.05 tff(30032,plain,
% 29.85/20.05 (big_f(f9(c1, c1), f1(f9(c1, c1), c1))),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[30031, 30020, 8714, 30015, 19621, 30011])).
% 29.85/20.05 tff(30033,plain,
% 29.85/20.05 (big_f(c2, f1(c2, c1))),
% 29.85/20.05 inference(modus_ponens,[status(thm)],[30032, 10143])).
% 29.85/20.05 tff(30034,plain,
% 29.85/20.05 (~(f1(c2, c1) = c1)),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[22840, 447, 432, 29314, 30033, 27, 30004])).
% 29.85/20.05 tff(30035,plain,
% 29.85/20.05 (f1(c2, c1) = c2),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[10113, 30034])).
% 29.85/20.05 tff(30036,plain,
% 29.85/20.05 (big_f(c2, f1(c2, c1)) <=> big_f(c2, c2)),
% 29.85/20.05 inference(monotonicity,[status(thm)],[30035])).
% 29.85/20.05 tff(30037,plain,
% 29.85/20.05 (big_f(c2, c2) <=> big_f(c2, f1(c2, c1))),
% 29.85/20.05 inference(symmetry,[status(thm)],[30036])).
% 29.85/20.05 tff(30038,plain,
% 29.85/20.05 ((~big_f(c2, c2)) <=> (~big_f(c2, f1(c2, c1)))),
% 29.85/20.05 inference(monotonicity,[status(thm)],[30037])).
% 29.85/20.05 tff(30039,plain,
% 29.85/20.05 (~big_f(c2, f1(c2, c1))),
% 29.85/20.05 inference(modus_ponens,[status(thm)],[121, 30038])).
% 29.85/20.05 tff(30040,plain,
% 29.85/20.05 ($false),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[30033, 30039])).
% 29.85/20.05 tff(30041,plain,((~(f4(c4) = c1)) | big_f(c2, c2) | big_f(c1, c2) | (~(f9(c1, c1) = c2)) | (~big_f(f9(c1, c1), c1)) | (f9(c1, c1) = c3) | (~(c4 = c2))), inference(lemma,lemma(discharge,[]))).
% 29.85/20.05 tff(30042,plain,
% 29.85/20.05 (~(c4 = c2)),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[30041, 29990, 27, 30000, 30001, 29999, 29985])).
% 29.85/20.05 tff(30043,plain,
% 29.85/20.05 (c4 = c1),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[461, 30042])).
% 29.85/20.05 tff(30044,plain,
% 29.85/20.05 (c1 = c4),
% 29.85/20.05 inference(symmetry,[status(thm)],[30043])).
% 29.85/20.05 tff(30045,plain,
% 29.85/20.05 (f4(c1) = f4(c4)),
% 29.85/20.05 inference(monotonicity,[status(thm)],[30044])).
% 29.85/20.05 tff(30046,plain,
% 29.85/20.05 (f4(c1) = c1),
% 29.85/20.05 inference(transitivity,[status(thm)],[30045, 29990])).
% 29.85/20.05 tff(30047,plain,
% 29.85/20.05 ((c2 = f4(c1)) <=> (c2 = c1)),
% 29.85/20.05 inference(monotonicity,[status(thm)],[30046])).
% 29.85/20.05 tff(30048,plain,
% 29.85/20.05 ((c2 = c1) <=> (c2 = f4(c1))),
% 29.85/20.05 inference(symmetry,[status(thm)],[30047])).
% 29.85/20.05 tff(30049,plain,
% 29.85/20.05 ((~(c2 = c1)) <=> (~(c2 = f4(c1)))),
% 29.85/20.05 inference(monotonicity,[status(thm)],[30048])).
% 29.85/20.05 tff(30050,plain,
% 29.85/20.05 (~(c2 = f4(c1))),
% 29.85/20.05 inference(modus_ponens,[status(thm)],[75, 30049])).
% 29.85/20.05 tff(30051,plain,
% 29.85/20.05 (f1(f9(c1, c1), c1) = f1(c2, c1)),
% 29.85/20.05 inference(monotonicity,[status(thm)],[30000])).
% 29.85/20.05 tff(30052,plain,
% 29.85/20.05 (big_f(f9(c1, c1), f1(f9(c1, c1), c1)) <=> big_f(c2, f1(c2, c1))),
% 29.85/20.05 inference(monotonicity,[status(thm)],[30000, 30051])).
% 29.85/20.05 tff(30053,plain,
% 29.85/20.05 (c1 = c4),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[484, 30043])).
% 29.85/20.05 tff(30054,plain,
% 29.85/20.05 ((f9(c1, c1) = f4(c1)) <=> (c2 = f4(c1))),
% 29.85/20.05 inference(monotonicity,[status(thm)],[30000])).
% 29.85/20.05 tff(30055,plain,
% 29.85/20.05 ((c2 = f4(c1)) <=> (f9(c1, c1) = f4(c1))),
% 29.85/20.05 inference(symmetry,[status(thm)],[30054])).
% 29.85/20.05 tff(30056,plain,
% 29.85/20.05 ((c2 = c1) <=> (f9(c1, c1) = f4(c1))),
% 29.85/20.05 inference(transitivity,[status(thm)],[30048, 30055])).
% 29.85/20.05 tff(30057,plain,
% 29.85/20.05 ((~(c2 = c1)) <=> (~(f9(c1, c1) = f4(c1)))),
% 29.85/20.05 inference(monotonicity,[status(thm)],[30056])).
% 29.85/20.05 tff(30058,plain,
% 29.85/20.05 (~(f9(c1, c1) = f4(c1))),
% 29.85/20.05 inference(modus_ponens,[status(thm)],[75, 30057])).
% 29.85/20.05 tff(30059,plain,
% 29.85/20.05 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((~(c1 = c4)) | (f9(c1, c1) = c3) | (~big_f(f9(c1, c1), c1)) | (f9(c1, c1) = f4(c1)) | (f1(f9(c1, c1), c1) = c1) | big_f(f9(c1, c1), f1(f9(c1, c1), c1)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (~(c1 = c4)) | (f9(c1, c1) = c3) | (~big_f(f9(c1, c1), c1)) | (f9(c1, c1) = f4(c1)) | (f1(f9(c1, c1), c1) = c1) | big_f(f9(c1, c1), f1(f9(c1, c1), c1)))),
% 29.85/20.05 inference(rewrite,[status(thm)],[])).
% 29.85/20.05 tff(30060,plain,
% 29.85/20.05 (((f9(c1, c1) = c3) | (f1(f9(c1, c1), c1) = c1) | big_f(f9(c1, c1), f1(f9(c1, c1), c1)) | (~(c1 = c4)) | (f9(c1, c1) = f4(c1)) | (~big_f(f9(c1, c1), c1))) <=> ((~(c1 = c4)) | (f9(c1, c1) = c3) | (~big_f(f9(c1, c1), c1)) | (f9(c1, c1) = f4(c1)) | (f1(f9(c1, c1), c1) = c1) | big_f(f9(c1, c1), f1(f9(c1, c1), c1)))),
% 29.85/20.05 inference(rewrite,[status(thm)],[])).
% 29.85/20.05 tff(30061,plain,
% 29.85/20.05 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((f9(c1, c1) = c3) | (f1(f9(c1, c1), c1) = c1) | big_f(f9(c1, c1), f1(f9(c1, c1), c1)) | (~(c1 = c4)) | (f9(c1, c1) = f4(c1)) | (~big_f(f9(c1, c1), c1)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((~(c1 = c4)) | (f9(c1, c1) = c3) | (~big_f(f9(c1, c1), c1)) | (f9(c1, c1) = f4(c1)) | (f1(f9(c1, c1), c1) = c1) | big_f(f9(c1, c1), f1(f9(c1, c1), c1))))),
% 29.85/20.05 inference(monotonicity,[status(thm)],[30060])).
% 29.85/20.05 tff(30062,plain,
% 29.85/20.05 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((f9(c1, c1) = c3) | (f1(f9(c1, c1), c1) = c1) | big_f(f9(c1, c1), f1(f9(c1, c1), c1)) | (~(c1 = c4)) | (f9(c1, c1) = f4(c1)) | (~big_f(f9(c1, c1), c1)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (~(c1 = c4)) | (f9(c1, c1) = c3) | (~big_f(f9(c1, c1), c1)) | (f9(c1, c1) = f4(c1)) | (f1(f9(c1, c1), c1) = c1) | big_f(f9(c1, c1), f1(f9(c1, c1), c1)))),
% 29.85/20.05 inference(transitivity,[status(thm)],[30061, 30059])).
% 29.85/20.05 tff(30063,plain,
% 29.85/20.05 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | ((f9(c1, c1) = c3) | (f1(f9(c1, c1), c1) = c1) | big_f(f9(c1, c1), f1(f9(c1, c1), c1)) | (~(c1 = c4)) | (f9(c1, c1) = f4(c1)) | (~big_f(f9(c1, c1), c1)))),
% 29.85/20.05 inference(quant_inst,[status(thm)],[])).
% 29.85/20.05 tff(30064,plain,
% 29.85/20.05 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)))) | (~(c1 = c4)) | (f9(c1, c1) = c3) | (~big_f(f9(c1, c1), c1)) | (f9(c1, c1) = f4(c1)) | (f1(f9(c1, c1), c1) = c1) | big_f(f9(c1, c1), f1(f9(c1, c1), c1))),
% 29.85/20.05 inference(modus_ponens,[status(thm)],[30063, 30062])).
% 29.85/20.05 tff(30065,plain,
% 29.85/20.05 (f1(f9(c1, c1), c1) = c1),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[30064, 525, 11526, 19621, 8714, 18085, 10151])).
% 29.85/20.05 tff(30066,plain,
% 29.85/20.05 (big_f(f9(c1, c1), f1(f9(c1, c1), c1)) <=> big_f(f9(c1, c1), c1)),
% 29.85/20.05 inference(monotonicity,[status(thm)],[30065])).
% 29.85/20.05 tff(30067,plain,
% 29.85/20.05 (big_f(f9(c1, c1), c1) <=> big_f(f9(c1, c1), f1(f9(c1, c1), c1))),
% 29.85/20.05 inference(symmetry,[status(thm)],[30066])).
% 29.85/20.05 tff(30068,plain,
% 29.85/20.05 (big_f(f9(c1, c1), f1(f9(c1, c1), c1))),
% 29.85/20.05 inference(modus_ponens,[status(thm)],[8714, 30067])).
% 29.85/20.05 tff(30069,plain,
% 29.85/20.05 ($false),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[10151, 30068])).
% 29.85/20.05 tff(30070,plain,(big_f(f9(c1, c1), f1(f9(c1, c1), c1)) | (~big_f(f9(c1, c1), c1)) | (~(c1 = c4)) | (f9(c1, c1) = c3) | (f9(c1, c1) = f4(c1))), inference(lemma,lemma(discharge,[]))).
% 29.85/20.05 tff(30071,plain,
% 29.85/20.05 (big_f(f9(c1, c1), f1(f9(c1, c1), c1))),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[30070, 30058, 30001, 29999, 30053])).
% 29.85/20.05 tff(30072,plain,
% 29.85/20.05 (big_f(c2, f1(c2, c1))),
% 29.85/20.05 inference(modus_ponens,[status(thm)],[30071, 30052])).
% 29.85/20.05 tff(30073,plain,
% 29.85/20.05 (~(f1(c2, c1) = c1)),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[11512, 553, 30053, 29314, 30072, 29962, 30050])).
% 29.85/20.05 tff(30074,plain,
% 29.85/20.05 (f1(c2, c1) = c2),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[10113, 30073])).
% 29.85/20.05 tff(30075,plain,
% 29.85/20.05 (big_f(c2, f1(c2, c1)) <=> big_f(c2, c2)),
% 29.85/20.05 inference(monotonicity,[status(thm)],[30074])).
% 29.85/20.05 tff(30076,plain,
% 29.85/20.05 (big_f(c2, c2) <=> big_f(c2, f1(c2, c1))),
% 29.85/20.05 inference(symmetry,[status(thm)],[30075])).
% 29.85/20.05 tff(30077,plain,
% 29.85/20.05 ((~big_f(c2, c2)) <=> (~big_f(c2, f1(c2, c1)))),
% 29.85/20.05 inference(monotonicity,[status(thm)],[30076])).
% 29.85/20.05 tff(30078,plain,
% 29.85/20.05 (~big_f(c2, f1(c2, c1))),
% 29.85/20.05 inference(modus_ponens,[status(thm)],[29985, 30077])).
% 29.85/20.05 tff(30079,plain,
% 29.85/20.05 ($false),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[30072, 30078])).
% 29.85/20.05 tff(30080,plain,(big_f(f7(c1), f6(c1, c1)) | big_f(c1, c2) | (f6(c1, c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.85/20.05 tff(30081,plain,
% 29.85/20.05 (big_f(f7(c1), f6(c1, c1))),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[30080, 28, 27])).
% 29.85/20.05 tff(30082,plain,
% 29.85/20.05 (big_f(c1, f6(c1, c1))),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[28169, 30081])).
% 29.85/20.05 tff(30083,plain,
% 29.85/20.05 (~(f6(c2, c1) = c1)),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[27702, 30081, 27, 28])).
% 29.85/20.05 tff(30084,plain,
% 29.85/20.05 (~(f6(f7(c2), c3) = c1)),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[10018, 292, 28773, 28])).
% 29.85/20.05 tff(30085,plain,
% 29.85/20.05 (~(f6(f7(c2), c3) = c2)),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[29368, 24650, 28773, 30081, 292])).
% 29.85/20.05 tff(30086,plain,
% 29.85/20.05 ($false),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[2391, 30085, 30084])).
% 29.85/20.05 tff(30087,plain,((~(f7(c2) = c1)) | (f6(c1, c1) = c1) | big_f(c1, c2)), inference(lemma,lemma(discharge,[]))).
% 29.85/20.05 tff(30088,plain,
% 29.85/20.05 (~(f7(c2) = c1)),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[30087, 28, 27])).
% 29.85/20.05 tff(30089,plain,
% 29.85/20.05 (f7(c2) = c2),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[21, 30088])).
% 29.85/20.05 tff(30090,plain,
% 29.85/20.05 (~(f4(c4) = c2)),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[11331, 121, 29946, 2])).
% 29.85/20.05 tff(30091,plain,
% 29.85/20.05 (f4(c4) = c1),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[11750, 30090])).
% 29.85/20.05 tff(30092,plain,
% 29.85/20.05 (f10(c1) = c1),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[27695, 30091, 29304, 77, 27, 121])).
% 29.85/20.05 tff(30093,plain,
% 29.85/20.05 ($false),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[27698, 30092, 30091, 3198, 77, 2, 121, 29304])).
% 29.85/20.05 tff(30094,plain,(big_f(c2, c2) | (f6(c2, c1) = c1) | (~(f7(c2) = c2)) | big_f(c2, c1) | big_f(c1, c2)), inference(lemma,lemma(discharge,[]))).
% 29.85/20.05 tff(30095,plain,
% 29.85/20.05 (big_f(c2, c2)),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[30094, 2, 77, 3198, 27])).
% 29.85/20.05 tff(30096,plain,
% 29.85/20.05 (c2 = c4),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[29322, 30095, 27, 27490, 2])).
% 29.85/20.05 tff(30097,plain,
% 29.85/20.05 (~(f4(c4) = c1)),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[29403, 30095, 77, 27, 2, 30096])).
% 29.85/20.05 tff(30098,plain,
% 29.85/20.05 (f4(c4) = c2),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[11750, 30097])).
% 29.85/20.05 tff(30099,plain,
% 29.85/20.05 (f6(c2, c2) = c2),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[25947, 30098, 2, 77, 29946])).
% 29.85/20.05 tff(30100,plain,
% 29.85/20.05 (big_f(f7(c2), f6(c2, c2))),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[2627, 30099, 77, 30095])).
% 29.85/20.05 tff(30101,plain,
% 29.85/20.05 (big_f(f9(c2, c2), f10(c2))),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[2750, 30099, 77, 29946, 30095, 30100])).
% 29.85/20.05 tff(30102,plain,
% 29.85/20.05 (f9(f10(c2), f4(c4)) = c2),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[8065, 30098, 29946])).
% 29.85/20.05 tff(30103,plain,
% 29.85/20.05 (f9(c2, c2) = c2),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[1606, 30102, 29946, 30098])).
% 29.85/20.05 tff(30104,plain,
% 29.85/20.05 ($false),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[2384, 2378, 29946, 77, 30099, 30100, 30103, 30101])).
% 29.85/20.05 tff(30105,plain,(big_f(c2, c1) | (~(f7(c2) = c2)) | big_f(c1, c2) | (~(f6(c1, f6(c1, c2)) = c2)) | (f6(c2, c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.85/20.05 tff(30106,plain,
% 29.85/20.05 (big_f(c2, c1)),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[30105, 30089, 27, 64, 30083])).
% 29.85/20.05 tff(30107,plain,
% 29.85/20.05 (f3(c1, f8(c3)) = c1),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[29859, 30106, 27, 28, 30082])).
% 29.85/20.05 tff(30108,plain,
% 29.85/20.05 (~(f6(c1, c1) = f2(c1))),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[29718, 30082, 27, 28])).
% 29.85/20.05 tff(30109,plain,
% 29.85/20.05 (~(c1 = c4)),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[29739, 30106, 28, 29544, 30082, 29304])).
% 29.85/20.05 tff(30110,plain,
% 29.85/20.05 (~(f8(c1) = c1)),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[29780, 30107, 30082, 30109, 29304, 30108, 28773])).
% 29.85/20.05 tff(30111,plain,
% 29.85/20.05 (f8(c1) = c2),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[1680, 30110])).
% 29.85/20.05 tff(30112,plain,
% 29.85/20.05 (c2 = f8(c1)),
% 29.85/20.05 inference(symmetry,[status(thm)],[30111])).
% 29.85/20.05 tff(30113,plain,
% 29.85/20.05 (c2 = f8(c3)),
% 29.85/20.05 inference(transitivity,[status(thm)],[30112, 29744])).
% 29.85/20.05 tff(30114,plain,
% 29.85/20.05 (f3(c1, c2) = f3(c1, f8(c3))),
% 29.85/20.05 inference(monotonicity,[status(thm)],[30113])).
% 29.85/20.05 tff(30115,plain,
% 29.85/20.05 (f3(c1, c2) = c1),
% 29.85/20.05 inference(transitivity,[status(thm)],[30114, 30107])).
% 29.85/20.05 tff(30116,plain,
% 29.85/20.05 (f6(c1, f3(c1, c2)) = f6(c1, c1)),
% 29.85/20.05 inference(monotonicity,[status(thm)],[30115])).
% 29.85/20.05 tff(30117,plain,
% 29.85/20.05 (f6(c1, c1) = f6(c1, f3(c1, c2))),
% 29.85/20.05 inference(symmetry,[status(thm)],[30116])).
% 29.85/20.05 tff(30118,plain,
% 29.85/20.05 ((f6(c1, c1) = c1) <=> (f6(c1, f3(c1, c2)) = c1)),
% 29.85/20.05 inference(monotonicity,[status(thm)],[30117])).
% 29.85/20.05 tff(30119,plain,
% 29.85/20.05 ((~(f6(c1, c1) = c1)) <=> (~(f6(c1, f3(c1, c2)) = c1))),
% 29.85/20.05 inference(monotonicity,[status(thm)],[30118])).
% 29.85/20.05 tff(30120,plain,
% 29.85/20.05 (~(f6(c1, f3(c1, c2)) = c1)),
% 29.85/20.05 inference(modus_ponens,[status(thm)],[28, 30119])).
% 29.85/20.05 tff(30121,plain,
% 29.85/20.05 (big_f(f7(c1), f6(c1, f3(c1, c2))) <=> big_f(c1, f6(c1, c1))),
% 29.85/20.05 inference(monotonicity,[status(thm)],[25791, 30116])).
% 29.85/20.05 tff(30122,plain,
% 29.85/20.05 (big_f(c1, f6(c1, c1)) <=> big_f(f7(c1), f6(c1, f3(c1, c2)))),
% 29.85/20.05 inference(symmetry,[status(thm)],[30121])).
% 29.85/20.05 tff(30123,plain,
% 29.85/20.05 (big_f(f7(c1), f6(c1, f3(c1, c2)))),
% 29.85/20.05 inference(modus_ponens,[status(thm)],[30082, 30122])).
% 29.85/20.05 tff(30124,plain,
% 29.85/20.05 (~(f6(c1, f3(c1, c2)) = c2)),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[29856, 30123, 27])).
% 29.85/20.05 tff(30125,plain,
% 29.85/20.05 ($false),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[6690, 30124, 30120])).
% 29.85/20.05 tff(30126,plain,((f6(c1, c1) = c1) | big_f(c1, c2)), inference(lemma,lemma(discharge,[]))).
% 29.85/20.05 tff(30127,plain,
% 29.85/20.05 (f6(c1, c1) = c1),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[30126, 27])).
% 29.85/20.05 tff(30128,plain,
% 29.85/20.05 (big_f(f7(c1), f6(c1, c1))),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[27769, 30127, 29304])).
% 29.85/20.05 tff(30129,plain,
% 29.85/20.05 (big_f(f9(c2, c2), c2) <=> big_f(f9(c2, c2), f10(c2))),
% 29.85/20.05 inference(symmetry,[status(thm)],[29975])).
% 29.85/20.05 tff(30130,plain,
% 29.85/20.05 ((f1(c2, c1) = c2) <=> (c2 = f1(c2, c1))),
% 29.85/20.05 inference(symmetry,[status(thm)],[10784])).
% 29.85/20.05 tff(30131,plain,
% 29.85/20.05 (f9(c1, c1) = c1),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[27678, 3762, 10030, 2, 29508])).
% 29.85/20.05 tff(30132,plain,
% 29.85/20.05 (big_f(f9(c1, c1), c1)),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[10938, 30131, 4932])).
% 29.85/20.05 tff(30133,plain,
% 29.85/20.05 (big_f(f9(c1, c1), f10(c1))),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[8716, 30132, 3762])).
% 29.85/20.05 tff(30134,plain,
% 29.85/20.05 ($false),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[18907, 2378, 25791, 3762, 30131, 30133, 29508, 10030])).
% 29.85/20.05 tff(30135,plain,((~(f10(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(c1, c1)) | big_f(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 29.85/20.05 tff(30136,plain,
% 29.85/20.05 (~(f10(c1) = c1)),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[30135, 2, 29304, 30127])).
% 29.85/20.05 tff(30137,plain,
% 29.85/20.05 (f10(c1) = c2),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[14, 30136])).
% 29.85/20.05 tff(30138,plain,
% 29.85/20.05 (c2 = f10(c1)),
% 29.85/20.05 inference(symmetry,[status(thm)],[30137])).
% 29.85/20.05 tff(30139,plain,
% 29.85/20.05 (big_f(f7(c2), c1)),
% 29.85/20.05 inference(modus_ponens,[status(thm)],[29304, 12091])).
% 29.85/20.05 tff(30140,plain,
% 29.85/20.05 (f10(c1) = c1),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[27544, 30139, 121, 27, 17])).
% 29.85/20.05 tff(30141,plain,
% 29.85/20.05 (big_f(f9(c1, c1), c1)),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[27822, 30140, 22, 30139, 30127, 30128])).
% 29.85/20.05 tff(30142,plain,
% 29.85/20.05 (big_f(f9(c1, c1), f10(c1))),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[8716, 30141, 30140])).
% 29.85/20.05 tff(30143,plain,
% 29.85/20.05 (f9(c1, c1) = c1),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[27678, 30140, 30127, 2, 30128])).
% 29.85/20.05 tff(30144,plain,
% 29.85/20.05 ($false),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[18907, 2378, 25791, 30140, 30143, 30142, 30128, 30127])).
% 29.85/20.05 tff(30145,plain,((f7(c2) = c2) | big_f(c2, c1) | big_f(c2, c2) | big_f(c1, c2)), inference(lemma,lemma(discharge,[]))).
% 29.85/20.05 tff(30146,plain,
% 29.85/20.05 (f7(c2) = c2),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[30145, 121, 2, 27])).
% 29.85/20.05 tff(30147,plain,
% 29.85/20.05 ($false),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[27695, 30091, 30146, 29304, 30136, 27, 121])).
% 29.85/20.05 tff(30148,plain,(big_f(c2, c2) | big_f(c1, c2) | big_f(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 29.85/20.05 tff(30149,plain,
% 29.85/20.05 (big_f(c2, c2)),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[30148, 2, 27])).
% 29.85/20.05 tff(30150,plain,
% 29.85/20.05 (big_f(c1, f10(c1)) <=> big_f(c1, c2)),
% 29.85/20.05 inference(monotonicity,[status(thm)],[30137])).
% 29.85/20.05 tff(30151,plain,
% 29.85/20.05 (big_f(c1, c2) <=> big_f(c1, f10(c1))),
% 29.85/20.05 inference(symmetry,[status(thm)],[30150])).
% 29.85/20.05 tff(30152,plain,
% 29.85/20.05 ((~big_f(c1, c2)) <=> (~big_f(c1, f10(c1)))),
% 29.85/20.05 inference(monotonicity,[status(thm)],[30151])).
% 29.85/20.05 tff(30153,plain,
% 29.85/20.05 (~big_f(c1, f10(c1))),
% 29.85/20.05 inference(modus_ponens,[status(thm)],[27, 30152])).
% 29.85/20.05 tff(30154,plain,
% 29.85/20.05 (~(c1 = f8(c1))),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[18583, 2963, 25791, 30136, 30153, 30128, 30127])).
% 29.85/20.05 tff(30155,plain,
% 29.85/20.05 (~(f8(c1) = c1)),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[9808, 30154])).
% 29.85/20.05 tff(30156,plain,
% 29.85/20.05 (f8(c1) = c2),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[1680, 30155])).
% 29.85/20.05 tff(30157,plain,
% 29.85/20.05 ((f3(c2, c2) = f8(c1)) <=> (f3(c2, c2) = c2)),
% 29.85/20.05 inference(monotonicity,[status(thm)],[30156])).
% 29.85/20.05 tff(30158,plain,
% 29.85/20.05 (~(c2 = c4)),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[29951, 17, 2, 30149, 27])).
% 29.85/20.05 tff(30159,plain,
% 29.85/20.05 (big_f(c2, f7(c2)) <=> big_f(f10(c1), c1)),
% 29.85/20.05 inference(monotonicity,[status(thm)],[30138, 22])).
% 29.85/20.05 tff(30160,plain,
% 29.85/20.05 (big_f(f10(c1), c1) <=> big_f(c2, f7(c2))),
% 29.85/20.05 inference(symmetry,[status(thm)],[30159])).
% 29.85/20.05 tff(30161,plain,
% 29.85/20.05 ((~big_f(f10(c1), c1)) <=> (~big_f(c2, f7(c2)))),
% 29.85/20.05 inference(monotonicity,[status(thm)],[30160])).
% 29.85/20.05 tff(30162,plain,
% 29.85/20.05 (big_f(c2, c1) <=> big_f(f10(c1), c1)),
% 29.85/20.05 inference(monotonicity,[status(thm)],[30138])).
% 29.85/20.05 tff(30163,plain,
% 29.85/20.05 ((~big_f(c2, c1)) <=> (~big_f(f10(c1), c1))),
% 29.85/20.05 inference(monotonicity,[status(thm)],[30162])).
% 29.85/20.05 tff(30164,plain,
% 29.85/20.05 (~big_f(f10(c1), c1)),
% 29.85/20.05 inference(modus_ponens,[status(thm)],[2, 30163])).
% 29.85/20.05 tff(30165,plain,
% 29.85/20.05 (~big_f(c2, f7(c2))),
% 29.85/20.05 inference(modus_ponens,[status(thm)],[30164, 30161])).
% 29.85/20.05 tff(30166,plain,
% 29.85/20.05 (big_f(f3(c2, c2), c2)),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[21029, 30165, 29314, 30149, 22, 30158])).
% 29.85/20.05 tff(30167,plain,
% 29.85/20.05 (big_f(f3(c2, c2), f10(c1))),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[27281, 30166, 30137])).
% 29.85/20.05 tff(30168,plain,
% 29.85/20.05 (f3(c2, c2) = f8(c1)),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[29477, 2730, 25791, 30136, 30128, 30127, 30167])).
% 29.85/20.05 tff(30169,plain,
% 29.85/20.05 (f3(c2, c2) = c2),
% 29.85/20.05 inference(modus_ponens,[status(thm)],[30168, 30157])).
% 29.85/20.05 tff(30170,plain,
% 29.85/20.05 (f7(c2) = c4),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[16679, 29948, 29314, 2, 30149, 17, 23145])).
% 29.85/20.05 tff(30171,plain,
% 29.85/20.05 (c1 = c4),
% 29.85/20.05 inference(modus_ponens,[status(thm)],[30170, 16687])).
% 29.85/20.05 tff(30172,plain,
% 29.85/20.05 (c4 = c1),
% 29.85/20.05 inference(symmetry,[status(thm)],[30171])).
% 29.85/20.05 tff(30173,plain,
% 29.85/20.05 (big_f(c2, c4) <=> big_f(f10(c1), c1)),
% 29.85/20.05 inference(monotonicity,[status(thm)],[30138, 30172])).
% 29.85/20.05 tff(30174,plain,
% 29.85/20.05 (big_f(f10(c1), c1) <=> big_f(c2, c4)),
% 29.85/20.05 inference(symmetry,[status(thm)],[30173])).
% 29.85/20.05 tff(30175,plain,
% 29.85/20.05 ((~big_f(f10(c1), c1)) <=> (~big_f(c2, c4))),
% 29.85/20.05 inference(monotonicity,[status(thm)],[30174])).
% 29.85/20.05 tff(30176,plain,
% 29.85/20.05 (~big_f(c2, c4)),
% 29.85/20.05 inference(modus_ponens,[status(thm)],[30164, 30175])).
% 29.85/20.05 tff(30177,plain,
% 29.85/20.05 (~(f3(c2, c2) = c2)),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[21039, 30176, 29314, 30149, 30158, 30166])).
% 29.85/20.05 tff(30178,plain,
% 29.85/20.05 ($false),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[30177, 30169])).
% 29.85/20.05 tff(30179,plain,((f7(c2) = c2) | big_f(c2, c1) | big_f(c1, c2)), inference(lemma,lemma(discharge,[]))).
% 29.85/20.05 tff(30180,plain,
% 29.85/20.05 (f7(c2) = c2),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[30179, 2, 27])).
% 29.85/20.05 tff(30181,plain,
% 29.85/20.05 (~(f4(c4) = c1)),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[29482, 30180, 27, 30136, 2, 30149])).
% 29.85/20.05 tff(30182,plain,
% 29.85/20.05 (f4(c4) = c2),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[11750, 30181])).
% 29.85/20.05 tff(30183,plain,
% 29.85/20.05 (f9(f10(c2), f4(c4)) = c2),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[8065, 30182, 29946])).
% 29.85/20.05 tff(30184,plain,
% 29.85/20.05 (f9(c2, c2) = c2),
% 29.85/20.05 inference(unit_resolution,[status(thm)],[1606, 30183, 29946, 30182])).
% 29.85/20.05 tff(30185,plain,
% 29.85/20.05 (f9(f10(c1), f10(c1)) = f9(c2, c2)),
% 29.85/20.05 inference(monotonicity,[status(thm)],[30137, 30137])).
% 29.85/20.05 tff(30186,plain,
% 29.85/20.05 (f9(f10(c1), f10(c1)) = f10(c1)),
% 29.85/20.05 inference(transitivity,[status(thm)],[30185, 30184, 30138])).
% 29.85/20.05 tff(30187,plain,
% 29.85/20.05 (f10(f10(c1)) = f10(c2)),
% 29.85/20.05 inference(monotonicity,[status(thm)],[30137])).
% 29.85/20.05 tff(30188,plain,
% 29.85/20.05 (f10(f10(c1)) = f10(c1)),
% 29.85/20.05 inference(transitivity,[status(thm)],[30187, 29946, 30138])).
% 29.85/20.05 tff(30189,plain,
% 29.85/20.05 (big_f(f9(f10(c1), f10(c1)), f10(f10(c1))) <=> big_f(f10(c1), f10(c1))),
% 29.85/20.05 inference(monotonicity,[status(thm)],[30186, 30188])).
% 29.85/20.05 tff(30190,plain,
% 29.85/20.05 (big_f(f10(c1), f10(c1)) <=> big_f(f9(f10(c1), f10(c1)), f10(f10(c1)))),
% 29.85/20.05 inference(symmetry,[status(thm)],[30189])).
% 29.85/20.05 tff(30191,plain,
% 29.85/20.05 (big_f(f10(c1), f10(c1)) <=> big_f(c2, c2)),
% 29.85/20.05 inference(monotonicity,[status(thm)],[30137, 30137])).
% 29.85/20.05 tff(30192,plain,
% 29.85/20.05 (big_f(c2, c2) <=> big_f(f10(c1), f10(c1))),
% 29.85/20.05 inference(symmetry,[status(thm)],[30191])).
% 29.85/20.05 tff(30193,plain,
% 29.85/20.05 (big_f(f10(c1), f10(c1))),
% 29.85/20.05 inference(modus_ponens,[status(thm)],[30149, 30192])).
% 29.85/20.05 tff(30194,plain,
% 29.85/20.05 (big_f(f9(f10(c1), f10(c1)), f10(f10(c1)))),
% 29.85/20.05 inference(modus_ponens,[status(thm)],[30193, 30190])).
% 29.85/20.05 tff(30195,plain,
% 29.85/20.05 (f4(c4) = f10(c1)),
% 29.85/20.05 inference(transitivity,[status(thm)],[30182, 30138])).
% 29.85/20.05 tff(30196,plain,
% 29.85/20.05 (f7(f4(c4)) = f7(f10(c1))),
% 29.85/20.05 inference(monotonicity,[status(thm)],[30195])).
% 29.85/20.05 tff(30197,plain,
% 29.85/20.05 (f7(f10(c1)) = f7(f4(c4))),
% 29.85/20.06 inference(symmetry,[status(thm)],[30196])).
% 29.85/20.06 tff(30198,plain,
% 29.85/20.06 (f7(f10(c1)) = f7(c2)),
% 29.85/20.06 inference(monotonicity,[status(thm)],[30137])).
% 29.85/20.06 tff(30199,plain,
% 29.85/20.06 (f7(c2) = f7(f10(c1))),
% 29.85/20.06 inference(symmetry,[status(thm)],[30198])).
% 29.85/20.06 tff(30200,plain,
% 29.85/20.06 (c2 = f7(c2)),
% 29.85/20.06 inference(symmetry,[status(thm)],[30180])).
% 29.85/20.06 tff(30201,plain,
% 29.85/20.06 (c2 = f7(f4(c4))),
% 29.85/20.06 inference(transitivity,[status(thm)],[30200, 30199, 30197])).
% 29.85/20.06 tff(30202,plain,
% 29.85/20.06 (f6(c2, c2) = f6(c2, f7(f4(c4)))),
% 29.85/20.06 inference(monotonicity,[status(thm)],[30201])).
% 29.85/20.06 tff(30203,plain,
% 29.85/20.06 (f6(c2, f7(f4(c4))) = f6(c2, c2)),
% 29.85/20.06 inference(symmetry,[status(thm)],[30202])).
% 29.85/20.06 tff(30204,plain,
% 29.85/20.06 ((f6(c2, f7(f4(c4))) = c2) <=> (f6(c2, c2) = c2)),
% 29.85/20.06 inference(monotonicity,[status(thm)],[30203])).
% 29.85/20.06 tff(30205,plain,
% 29.85/20.06 ((f6(c2, c2) = c2) <=> (f6(c2, f7(f4(c4))) = c2)),
% 29.85/20.06 inference(symmetry,[status(thm)],[30204])).
% 29.85/20.06 tff(30206,plain,
% 29.85/20.06 (f6(c2, c2) = c2),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[25947, 30182, 2, 30180, 29946])).
% 29.85/20.06 tff(30207,plain,
% 29.85/20.06 (f6(c2, f7(f4(c4))) = c2),
% 29.85/20.06 inference(modus_ponens,[status(thm)],[30206, 30205])).
% 29.85/20.06 tff(30208,plain,
% 29.85/20.06 (f6(f10(c1), f10(c1)) = f6(c2, c2)),
% 29.85/20.06 inference(monotonicity,[status(thm)],[30137, 30137])).
% 29.85/20.06 tff(30209,plain,
% 29.85/20.06 (f6(f10(c1), f10(c1)) = f10(c1)),
% 29.85/20.06 inference(transitivity,[status(thm)],[30208, 30202, 30207, 30138])).
% 29.85/20.06 tff(30210,plain,
% 29.85/20.06 (f7(f10(c1)) = f10(c1)),
% 29.85/20.06 inference(transitivity,[status(thm)],[30198, 30180, 30138])).
% 29.85/20.06 tff(30211,plain,
% 29.85/20.06 (big_f(f7(f10(c1)), f6(f10(c1), f10(c1))) <=> big_f(f10(c1), f10(c1))),
% 29.85/20.06 inference(monotonicity,[status(thm)],[30210, 30209])).
% 29.85/20.06 tff(30212,plain,
% 29.85/20.06 (big_f(f10(c1), f10(c1)) <=> big_f(f7(f10(c1)), f6(f10(c1), f10(c1)))),
% 29.85/20.06 inference(symmetry,[status(thm)],[30211])).
% 29.85/20.06 tff(30213,plain,
% 29.85/20.06 (big_f(f7(f10(c1)), f6(f10(c1), f10(c1)))),
% 29.85/20.06 inference(modus_ponens,[status(thm)],[30193, 30212])).
% 29.85/20.06 tff(30214,plain,
% 29.85/20.06 ((f7(f10(c1)) = f10(c1)) <=> (f7(c2) = c2)),
% 29.85/20.06 inference(monotonicity,[status(thm)],[30198, 30137])).
% 29.85/20.06 tff(30215,plain,
% 29.85/20.06 ((f7(c2) = c2) <=> (f7(f10(c1)) = f10(c1))),
% 29.85/20.06 inference(symmetry,[status(thm)],[30214])).
% 29.85/20.06 tff(30216,plain,
% 29.85/20.06 (f7(f10(c1)) = f10(c1)),
% 29.85/20.06 inference(modus_ponens,[status(thm)],[30180, 30215])).
% 29.85/20.06 tff(30217,plain,
% 29.85/20.06 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(f10(c1)) = f10(c1))) | (~(f10(f10(c1)) = f10(c1))) | (~(f6(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f7(f10(c1)), f6(f10(c1), f10(c1)))) | (~big_f(f9(f10(c1), f10(c1)), f10(f10(c1)))) | (~(f9(f10(c1), f10(c1)) = f10(c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(f10(c1)) = f10(c1))) | (~(f10(f10(c1)) = f10(c1))) | (~(f6(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f7(f10(c1)), f6(f10(c1), f10(c1)))) | (~big_f(f9(f10(c1), f10(c1)), f10(f10(c1)))) | (~(f9(f10(c1), f10(c1)) = f10(c1))))),
% 29.85/20.06 inference(rewrite,[status(thm)],[])).
% 29.85/20.06 tff(30218,plain,
% 29.85/20.06 (((~(f10(f10(c1)) = f10(c1))) | (~(f7(f10(c1)) = f10(c1))) | (~(f9(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f9(f10(c1), f10(c1)), f10(f10(c1)))) | (~(f6(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f7(f10(c1)), f6(f10(c1), f10(c1))))) <=> ((~(f7(f10(c1)) = f10(c1))) | (~(f10(f10(c1)) = f10(c1))) | (~(f6(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f7(f10(c1)), f6(f10(c1), f10(c1)))) | (~big_f(f9(f10(c1), f10(c1)), f10(f10(c1)))) | (~(f9(f10(c1), f10(c1)) = f10(c1))))),
% 29.85/20.06 inference(rewrite,[status(thm)],[])).
% 29.85/20.06 tff(30219,plain,
% 29.85/20.06 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(f10(c1)) = f10(c1))) | (~(f7(f10(c1)) = f10(c1))) | (~(f9(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f9(f10(c1), f10(c1)), f10(f10(c1)))) | (~(f6(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f7(f10(c1)), f6(f10(c1), f10(c1)))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(f10(c1)) = f10(c1))) | (~(f10(f10(c1)) = f10(c1))) | (~(f6(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f7(f10(c1)), f6(f10(c1), f10(c1)))) | (~big_f(f9(f10(c1), f10(c1)), f10(f10(c1)))) | (~(f9(f10(c1), f10(c1)) = f10(c1)))))),
% 29.85/20.06 inference(monotonicity,[status(thm)],[30218])).
% 29.85/20.06 tff(30220,plain,
% 29.85/20.06 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(f10(c1)) = f10(c1))) | (~(f7(f10(c1)) = f10(c1))) | (~(f9(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f9(f10(c1), f10(c1)), f10(f10(c1)))) | (~(f6(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f7(f10(c1)), f6(f10(c1), f10(c1)))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(f10(c1)) = f10(c1))) | (~(f10(f10(c1)) = f10(c1))) | (~(f6(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f7(f10(c1)), f6(f10(c1), f10(c1)))) | (~big_f(f9(f10(c1), f10(c1)), f10(f10(c1)))) | (~(f9(f10(c1), f10(c1)) = f10(c1))))),
% 29.85/20.06 inference(transitivity,[status(thm)],[30219, 30217])).
% 29.85/20.06 tff(30221,plain,
% 29.85/20.06 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(f10(c1)) = f10(c1))) | (~(f7(f10(c1)) = f10(c1))) | (~(f9(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f9(f10(c1), f10(c1)), f10(f10(c1)))) | (~(f6(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f7(f10(c1)), f6(f10(c1), f10(c1)))))),
% 29.85/20.06 inference(quant_inst,[status(thm)],[])).
% 29.85/20.06 tff(30222,plain,
% 29.85/20.06 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(f10(c1)) = f10(c1))) | (~(f10(f10(c1)) = f10(c1))) | (~(f6(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f7(f10(c1)), f6(f10(c1), f10(c1)))) | (~big_f(f9(f10(c1), f10(c1)), f10(f10(c1)))) | (~(f9(f10(c1), f10(c1)) = f10(c1)))),
% 29.85/20.06 inference(modus_ponens,[status(thm)],[30221, 30220])).
% 29.85/20.06 tff(30223,plain,
% 29.85/20.06 ((~(f6(f10(c1), f10(c1)) = f10(c1))) | (~big_f(f7(f10(c1)), f6(f10(c1), f10(c1)))) | (~big_f(f9(f10(c1), f10(c1)), f10(f10(c1)))) | (~(f9(f10(c1), f10(c1)) = f10(c1)))),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[30222, 2378, 30188, 30216])).
% 29.85/20.06 tff(30224,plain,
% 29.85/20.06 ($false),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[30223, 30213, 30209, 30194, 30186])).
% 29.85/20.06 tff(30225,plain,(big_f(c2, c1) | big_f(c1, c2)), inference(lemma,lemma(discharge,[]))).
% 29.85/20.06 tff(30226,plain,
% 29.85/20.06 (big_f(c2, c1)),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[30225, 27])).
% 29.85/20.06 tff(30227,plain,
% 29.85/20.06 (~(f4(c4) = c2)),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[29988, 121, 28773, 29304, 29946, 30226])).
% 29.85/20.06 tff(30228,plain,
% 29.85/20.06 (f4(c4) = c1),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[11750, 30227])).
% 29.85/20.06 tff(30229,plain,
% 29.85/20.06 (~(f7(c2) = c2)),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[27695, 3, 29304, 121, 27, 30228])).
% 29.85/20.06 tff(30230,plain,
% 29.85/20.06 (f7(c2) = c1),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[21, 30229])).
% 29.85/20.06 tff(30231,plain,
% 29.85/20.06 (~big_f(f7(c2), c2)),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[21127, 30230, 27])).
% 29.85/20.06 tff(30232,plain,
% 29.85/20.06 (~big_f(f8(c1), f10(c1))),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[15724, 30231, 121, 15, 30230])).
% 29.85/20.06 tff(30233,plain,
% 29.85/20.06 (~(c2 = f5(c2))),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[8107, 30232, 30229, 3, 30231])).
% 29.85/20.06 tff(30234,plain,
% 29.85/20.06 (~big_f(f7(c2), c1)),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[27544, 30229, 121, 27, 3])).
% 29.85/20.06 tff(30235,plain,
% 29.85/20.06 (~(c1 = f5(c2))),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[27450, 30234, 30229, 121, 27, 3])).
% 29.85/20.06 tff(30236,plain,
% 29.85/20.06 (~(f5(c2) = c1)),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[8139, 30235])).
% 29.85/20.06 tff(30237,plain,
% 29.85/20.06 (f5(c2) = c2),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[1547, 30236])).
% 29.85/20.06 tff(30238,plain,
% 29.85/20.06 ($false),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[8113, 30237, 30233])).
% 29.85/20.06 tff(30239,plain,((f10(c1) = c1) | big_f(c2, c2) | big_f(c1, c2)), inference(lemma,lemma(discharge,[]))).
% 29.85/20.06 tff(30240,plain,
% 29.85/20.06 (f10(c1) = c1),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[30239, 121, 27])).
% 29.85/20.06 tff(30241,plain,
% 29.85/20.06 (big_f(f7(c2), c1)),
% 29.85/20.06 inference(modus_ponens,[status(thm)],[29304, 20219])).
% 29.85/20.06 tff(30242,plain,
% 29.85/20.06 (big_f(f9(c1, c1), c1)),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[26966, 30241, 30226, 292])).
% 29.85/20.06 tff(30243,plain,
% 29.85/20.06 (big_f(f9(c1, c1), f10(c1))),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[8716, 30242, 30240])).
% 29.85/20.06 tff(30244,plain,
% 29.85/20.06 (~(f9(c1, c1) = c1)),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[18907, 2378, 25791, 30240, 30243, 30128, 30127])).
% 29.85/20.06 tff(30245,plain,
% 29.85/20.06 (f9(c1, c1) = c2),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[3939, 30244])).
% 29.85/20.06 tff(30246,plain,
% 29.85/20.06 (~(f9(c1, c1) = c3)),
% 29.85/20.06 inference(modus_ponens,[status(thm)],[30244, 29993])).
% 29.85/20.06 tff(30247,plain,
% 29.85/20.06 (~(c4 = c2)),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[30041, 30246, 27, 30228, 30242, 30245, 121])).
% 29.85/20.06 tff(30248,plain,
% 29.85/20.06 (c4 = c1),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[461, 30247])).
% 29.85/20.06 tff(30249,plain,
% 29.85/20.06 (f7(c2) = c4),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[16645, 30248, 292])).
% 29.85/20.06 tff(30250,plain,
% 29.85/20.06 (big_f(c2, f7(c2)) <=> big_f(c2, c1)),
% 29.85/20.06 inference(monotonicity,[status(thm)],[292])).
% 29.85/20.06 tff(30251,plain,
% 29.85/20.06 (big_f(c2, c1) <=> big_f(c2, f7(c2))),
% 29.85/20.06 inference(symmetry,[status(thm)],[30250])).
% 29.85/20.06 tff(30252,plain,
% 29.85/20.06 (big_f(c2, f7(c2))),
% 29.85/20.06 inference(modus_ponens,[status(thm)],[30226, 30251])).
% 29.85/20.06 tff(30253,plain,
% 29.85/20.06 (c1 = c4),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[484, 30248])).
% 29.85/20.06 tff(30254,plain,
% 29.85/20.06 (f4(c1) = f4(c4)),
% 29.85/20.06 inference(monotonicity,[status(thm)],[30253])).
% 29.85/20.06 tff(30255,plain,
% 29.85/20.06 (f4(c1) = c1),
% 29.85/20.06 inference(transitivity,[status(thm)],[30254, 30228])).
% 29.85/20.06 tff(30256,plain,
% 29.85/20.06 ((c2 = f4(c1)) <=> (c2 = c1)),
% 29.85/20.06 inference(monotonicity,[status(thm)],[30255])).
% 29.85/20.06 tff(30257,plain,
% 29.85/20.06 ((c2 = c1) <=> (c2 = f4(c1))),
% 29.85/20.06 inference(symmetry,[status(thm)],[30256])).
% 29.85/20.06 tff(30258,plain,
% 29.85/20.06 ((c2 = c1) <=> (c2 = f4(f7(c2)))),
% 29.85/20.06 inference(transitivity,[status(thm)],[30257, 22794])).
% 29.85/20.06 tff(30259,plain,
% 29.85/20.06 ((~(c2 = c1)) <=> (~(c2 = f4(f7(c2))))),
% 29.85/20.06 inference(monotonicity,[status(thm)],[30258])).
% 29.85/20.06 tff(30260,plain,
% 29.85/20.06 (~(c2 = f4(f7(c2)))),
% 29.85/20.06 inference(modus_ponens,[status(thm)],[75, 30259])).
% 29.85/20.06 tff(30261,plain,
% 29.85/20.06 (~(f1(c2, c1) = c1)),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[15762, 30260, 292, 30252, 29314, 30249])).
% 29.85/20.06 tff(30262,plain,
% 29.85/20.06 (f1(c2, c1) = c2),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[10113, 30261])).
% 29.85/20.06 tff(30263,plain,
% 29.85/20.06 (big_f(c2, f1(c2, c1)) <=> big_f(c2, c2)),
% 29.85/20.06 inference(monotonicity,[status(thm)],[30262])).
% 29.85/20.06 tff(30264,plain,
% 29.85/20.06 (big_f(c2, c2) <=> big_f(c2, f1(c2, c1))),
% 29.85/20.06 inference(symmetry,[status(thm)],[30263])).
% 29.85/20.06 tff(30265,plain,
% 29.85/20.06 ((~big_f(c2, c2)) <=> (~big_f(c2, f1(c2, c1)))),
% 29.85/20.06 inference(monotonicity,[status(thm)],[30264])).
% 29.85/20.06 tff(30266,plain,
% 29.85/20.06 (~big_f(c2, f1(c2, c1))),
% 29.85/20.06 inference(modus_ponens,[status(thm)],[121, 30265])).
% 29.85/20.06 tff(30267,plain,
% 29.85/20.06 (f1(f9(c1, c1), c1) = f1(c2, c1)),
% 29.85/20.06 inference(monotonicity,[status(thm)],[30245])).
% 29.85/20.06 tff(30268,plain,
% 29.85/20.06 (big_f(f9(c1, c1), f1(f9(c1, c1), c1)) <=> big_f(c2, f1(c2, c1))),
% 29.85/20.06 inference(monotonicity,[status(thm)],[30245, 30267])).
% 29.85/20.06 tff(30269,plain,
% 29.85/20.06 ((f9(c1, c1) = f4(c1)) <=> (c2 = f4(c1))),
% 29.85/20.06 inference(monotonicity,[status(thm)],[30245])).
% 29.85/20.06 tff(30270,plain,
% 29.85/20.06 ((c2 = f4(c1)) <=> (f9(c1, c1) = f4(c1))),
% 29.85/20.06 inference(symmetry,[status(thm)],[30269])).
% 29.85/20.06 tff(30271,plain,
% 29.85/20.06 ((c2 = c1) <=> (f9(c1, c1) = f4(c1))),
% 29.85/20.06 inference(transitivity,[status(thm)],[30257, 30270])).
% 29.85/20.06 tff(30272,plain,
% 29.85/20.06 ((~(c2 = c1)) <=> (~(f9(c1, c1) = f4(c1)))),
% 29.85/20.06 inference(monotonicity,[status(thm)],[30271])).
% 29.85/20.06 tff(30273,plain,
% 29.85/20.06 (~(f9(c1, c1) = f4(c1))),
% 29.85/20.06 inference(modus_ponens,[status(thm)],[75, 30272])).
% 29.85/20.06 tff(30274,plain,
% 29.85/20.06 (big_f(f9(c1, c1), f1(f9(c1, c1), c1))),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[30070, 30273, 30242, 30246, 30253])).
% 29.85/20.06 tff(30275,plain,
% 29.85/20.06 (big_f(c2, f1(c2, c1))),
% 29.85/20.06 inference(modus_ponens,[status(thm)],[30274, 30268])).
% 29.85/20.06 tff(30276,plain,
% 29.85/20.06 ($false),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[30275, 30266])).
% 29.85/20.06 tff(30277,plain,((~(f7(c2) = c1)) | big_f(c2, c2) | big_f(c1, c2)), inference(lemma,lemma(discharge,[]))).
% 29.85/20.06 tff(30278,plain,
% 29.85/20.06 (~(f7(c2) = c1)),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[30277, 121, 27])).
% 29.85/20.06 tff(30279,plain,
% 29.85/20.06 (f7(c2) = c2),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[21, 30278])).
% 29.85/20.06 tff(30280,plain,
% 29.85/20.06 ((f7(f7(c2)) = c3) <=> (f7(f7(c2)) = c1)),
% 29.85/20.06 inference(monotonicity,[status(thm)],[28773])).
% 29.85/20.06 tff(30281,plain,
% 29.85/20.06 ((f7(f7(c2)) = c1) <=> (f7(f7(c2)) = c3)),
% 29.85/20.06 inference(symmetry,[status(thm)],[30280])).
% 29.85/20.06 tff(30282,plain,
% 29.85/20.06 (f7(f7(c2)) = f7(c2)),
% 29.85/20.06 inference(monotonicity,[status(thm)],[30279])).
% 29.85/20.06 tff(30283,plain,
% 29.85/20.06 (f7(f7(c2)) = c2),
% 29.85/20.06 inference(transitivity,[status(thm)],[30282, 30279])).
% 29.85/20.06 tff(30284,plain,
% 29.85/20.06 ((f7(f7(c2)) = c1) <=> (c2 = c1)),
% 29.85/20.06 inference(monotonicity,[status(thm)],[30283])).
% 29.85/20.06 tff(30285,plain,
% 29.85/20.06 ((c2 = c1) <=> (f7(f7(c2)) = c1)),
% 29.85/20.06 inference(symmetry,[status(thm)],[30284])).
% 29.85/20.06 tff(30286,plain,
% 29.85/20.06 ((c2 = c1) <=> (f7(f7(c2)) = c3)),
% 29.85/20.06 inference(transitivity,[status(thm)],[30285, 30281])).
% 29.85/20.06 tff(30287,plain,
% 29.85/20.06 ((~(c2 = c1)) <=> (~(f7(f7(c2)) = c3))),
% 29.85/20.06 inference(monotonicity,[status(thm)],[30286])).
% 29.85/20.06 tff(30288,plain,
% 29.85/20.06 (~(f7(f7(c2)) = c3)),
% 29.85/20.06 inference(modus_ponens,[status(thm)],[75, 30287])).
% 29.85/20.06 tff(30289,plain,
% 29.85/20.06 (~big_f(f4(c4), c4)),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[11764, 431, 27, 30228])).
% 29.85/20.06 tff(30290,plain,
% 29.85/20.06 (f1(f7(f7(c2)), c1) = c1),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[5433, 30289, 30288, 30279, 121])).
% 29.85/20.06 tff(30291,plain,
% 29.85/20.06 ((~(f9(c1, c1) = c1)) | (~big_f(c1, c1)) | (~(f6(c1, c1) = c1)) | (~(f1(f7(f7(c2)), c1) = c1)) | (~(f7(c2) = c2)) | (~(f10(c1) = c1))),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[11325, 25791])).
% 29.85/20.06 tff(30292,plain,
% 29.85/20.06 (~(f9(c1, c1) = c1)),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[30291, 30290, 29304, 30279, 30240, 30127])).
% 29.85/20.06 tff(30293,plain,
% 29.85/20.06 (f9(c1, c1) = c2),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[3939, 30292])).
% 29.85/20.06 tff(30294,plain,
% 29.85/20.06 (big_f(f9(c1, c1), c1)),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[26962, 30293, 30226])).
% 29.85/20.06 tff(30295,plain,
% 29.85/20.06 (f9(c1, c1) = c3),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[30041, 30294, 27, 30228, 431, 30293, 121])).
% 29.85/20.06 tff(30296,plain,
% 29.85/20.06 (f9(c1, c1) = c1),
% 29.85/20.06 inference(modus_ponens,[status(thm)],[30295, 29991])).
% 29.85/20.06 tff(30297,plain,
% 29.85/20.06 ($false),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[30292, 30296])).
% 29.85/20.06 tff(30298,plain,((~(c4 = c2)) | big_f(c1, c2) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 29.85/20.06 tff(30299,plain,
% 29.85/20.06 (~(c4 = c2)),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[30298, 121, 27])).
% 29.85/20.06 tff(30300,plain,
% 29.85/20.06 (c4 = c1),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[461, 30299])).
% 29.85/20.06 tff(30301,plain,
% 29.85/20.06 (c1 = c4),
% 29.85/20.06 inference(symmetry,[status(thm)],[30300])).
% 29.85/20.06 tff(30302,plain,
% 29.85/20.06 (f4(c1) = f4(c4)),
% 29.85/20.06 inference(monotonicity,[status(thm)],[30301])).
% 29.85/20.06 tff(30303,plain,
% 29.85/20.06 (f4(c1) = c1),
% 29.85/20.06 inference(transitivity,[status(thm)],[30302, 30228])).
% 29.85/20.06 tff(30304,plain,
% 29.85/20.06 ((c2 = f4(c1)) <=> (c2 = c1)),
% 29.85/20.06 inference(monotonicity,[status(thm)],[30303])).
% 29.85/20.06 tff(30305,plain,
% 29.85/20.06 ((c2 = c1) <=> (c2 = f4(c1))),
% 29.85/20.06 inference(symmetry,[status(thm)],[30304])).
% 29.85/20.06 tff(30306,plain,
% 29.85/20.06 ((~(c2 = c1)) <=> (~(c2 = f4(c1)))),
% 29.85/20.06 inference(monotonicity,[status(thm)],[30305])).
% 29.85/20.06 tff(30307,plain,
% 29.85/20.06 (~(c2 = f4(c1))),
% 29.85/20.06 inference(modus_ponens,[status(thm)],[75, 30306])).
% 29.85/20.06 tff(30308,plain,
% 29.85/20.06 ($false),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[3939, 26963, 22751])).
% 29.85/20.06 tff(30309,plain,(big_f(f9(c1, c1), c1) | (~big_f(c2, c1)) | (~big_f(c1, c1))), inference(lemma,lemma(discharge,[]))).
% 29.85/20.06 tff(30310,plain,
% 29.85/20.06 (big_f(f9(c1, c1), c1)),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[30309, 30226, 29304])).
% 29.85/20.06 tff(30311,plain,
% 29.85/20.06 (big_f(f9(c1, c1), f10(c1))),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[8716, 30240, 30310])).
% 29.85/20.06 tff(30312,plain,
% 29.85/20.06 (~(f9(c1, c1) = c1)),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[18907, 2378, 25791, 30240, 30311, 30128, 30127])).
% 29.85/20.06 tff(30313,plain,
% 29.85/20.06 (f9(c1, c1) = c2),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[3939, 30312])).
% 29.85/20.06 tff(30314,plain,
% 29.85/20.06 (f1(f9(c1, c1), c1) = f1(c2, c1)),
% 29.85/20.06 inference(monotonicity,[status(thm)],[30313])).
% 29.85/20.06 tff(30315,plain,
% 29.85/20.06 (big_f(f9(c1, c1), f1(f9(c1, c1), c1)) <=> big_f(c2, f1(c2, c1))),
% 29.85/20.06 inference(monotonicity,[status(thm)],[30313, 30314])).
% 29.85/20.06 tff(30316,plain,
% 29.85/20.06 (c1 = c4),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[484, 30300])).
% 29.85/20.06 tff(30317,plain,
% 29.85/20.06 (~(f9(c1, c1) = c3)),
% 29.85/20.06 inference(modus_ponens,[status(thm)],[30312, 29993])).
% 29.85/20.06 tff(30318,plain,
% 29.85/20.06 ((f9(c1, c1) = f4(c1)) <=> (f9(c1, c1) = c1)),
% 29.85/20.06 inference(monotonicity,[status(thm)],[30303])).
% 29.85/20.06 tff(30319,plain,
% 29.85/20.06 ((f9(c1, c1) = c1) <=> (f9(c1, c1) = f4(c1))),
% 29.85/20.06 inference(symmetry,[status(thm)],[30318])).
% 29.85/20.06 tff(30320,plain,
% 29.85/20.06 ((~(f9(c1, c1) = c1)) <=> (~(f9(c1, c1) = f4(c1)))),
% 29.85/20.06 inference(monotonicity,[status(thm)],[30319])).
% 29.85/20.06 tff(30321,plain,
% 29.85/20.06 (~(f9(c1, c1) = f4(c1))),
% 29.85/20.06 inference(modus_ponens,[status(thm)],[30312, 30320])).
% 29.85/20.06 tff(30322,plain,
% 29.85/20.06 (big_f(f9(c1, c1), f1(f9(c1, c1), c1))),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[30070, 30321, 30310, 30317, 30316])).
% 29.85/20.06 tff(30323,plain,
% 29.85/20.06 (big_f(c2, f1(c2, c1))),
% 29.85/20.06 inference(modus_ponens,[status(thm)],[30322, 30315])).
% 29.85/20.06 tff(30324,plain,
% 29.85/20.06 (~(f1(c2, c1) = c1)),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[11512, 553, 30316, 29314, 30323, 30226, 30307])).
% 29.85/20.06 tff(30325,plain,
% 29.85/20.06 (f1(c2, c1) = c2),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[10113, 30324])).
% 29.85/20.06 tff(30326,plain,
% 29.85/20.06 (c2 = f1(c2, c1)),
% 29.85/20.06 inference(modus_ponens,[status(thm)],[30325, 30130])).
% 29.85/20.06 tff(30327,plain,
% 29.85/20.06 ((~(big_f(c2, c2) <=> big_f(c2, f1(c2, c1)))) | big_f(c2, c2) | (~big_f(c2, f1(c2, c1)))),
% 29.85/20.06 inference(tautology,[status(thm)],[])).
% 29.85/20.06 tff(30328,plain,
% 29.85/20.06 (~(big_f(c2, c2) <=> big_f(c2, f1(c2, c1)))),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[30327, 30323, 121])).
% 29.85/20.06 tff(30329,assumption,(~(big_f(c2, c2) <=> big_f(c2, f1(c2, c1)))), introduced(assumption)).
% 29.85/20.06 tff(30330,assumption,(c2 = f1(c2, c1)), introduced(assumption)).
% 29.85/20.06 tff(30331,plain,
% 29.85/20.06 (big_f(c2, c2) <=> big_f(c2, f1(c2, c1))),
% 29.85/20.06 inference(monotonicity,[status(thm)],[30330])).
% 29.85/20.06 tff(30332,plain,
% 29.85/20.06 ($false),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[30331, 30329])).
% 29.85/20.06 tff(30333,plain,((~(c2 = f1(c2, c1))) | (big_f(c2, c2) <=> big_f(c2, f1(c2, c1)))), inference(lemma,lemma(discharge,[]))).
% 29.85/20.06 tff(30334,plain,
% 29.85/20.06 (~(c2 = f1(c2, c1))),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[30333, 30328])).
% 29.85/20.06 tff(30335,plain,
% 29.85/20.06 ($false),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[30334, 30326])).
% 29.85/20.06 tff(30336,plain,(big_f(c2, c2) | big_f(c1, c2)), inference(lemma,lemma(discharge,[]))).
% 29.85/20.06 tff(30337,plain,
% 29.85/20.06 (big_f(c2, c2)),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[30336, 27])).
% 29.85/20.06 tff(30338,plain,
% 29.85/20.06 ($false),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[28769, 2378, 25791, 122, 1572, 25604, 5964, 10030])).
% 29.85/20.06 tff(30339,plain,((~(f9(c2, c2) = c2)) | (~(f10(c2) = c2)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (~big_f(c2, c2))), inference(lemma,lemma(discharge,[]))).
% 29.85/20.06 tff(30340,plain,
% 29.85/20.06 (~(f9(c2, c2) = c2)),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[30339, 29946, 30128, 30127, 30337])).
% 29.85/20.06 tff(30341,plain,
% 29.85/20.06 (f9(c2, c2) = c1),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[27475, 30340])).
% 29.85/20.06 tff(30342,plain,
% 29.85/20.06 (big_f(f9(c2, c2), c2) <=> big_f(c1, c2)),
% 29.85/20.06 inference(monotonicity,[status(thm)],[30341])).
% 29.85/20.06 tff(30343,plain,
% 29.85/20.06 (big_f(c1, c2) <=> big_f(f9(c2, c2), c2)),
% 29.85/20.06 inference(symmetry,[status(thm)],[30342])).
% 29.85/20.06 tff(30344,plain,
% 29.85/20.06 (big_f(c1, c2) <=> big_f(f9(c2, c2), f10(c2))),
% 29.85/20.06 inference(transitivity,[status(thm)],[30343, 30129])).
% 29.85/20.06 tff(30345,plain,
% 29.85/20.06 ((~big_f(c1, c2)) <=> (~big_f(f9(c2, c2), f10(c2)))),
% 29.85/20.06 inference(monotonicity,[status(thm)],[30344])).
% 29.85/20.06 tff(30346,plain,
% 29.85/20.06 (~big_f(f9(c2, c2), f10(c2))),
% 29.85/20.06 inference(modus_ponens,[status(thm)],[27, 30345])).
% 29.85/20.06 tff(30347,plain,
% 29.85/20.06 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)))),
% 29.85/20.06 inference(rewrite,[status(thm)],[])).
% 29.85/20.06 tff(30348,plain,
% 29.85/20.06 (((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1)))) <=> ((~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)))),
% 29.85/20.06 inference(rewrite,[status(thm)],[])).
% 29.85/20.06 tff(30349,plain,
% 29.85/20.06 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1))))),
% 29.85/20.06 inference(monotonicity,[status(thm)],[30348])).
% 29.85/20.06 tff(30350,plain,
% 29.85/20.06 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)))),
% 29.85/20.06 inference(transitivity,[status(thm)],[30349, 30347])).
% 29.85/20.06 tff(30351,plain,
% 29.85/20.06 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))),
% 29.85/20.06 inference(quant_inst,[status(thm)],[])).
% 29.85/20.06 tff(30352,plain,
% 29.85/20.06 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (~(f7(c1) = c1)) | (f9(c2, c2) = c2) | big_f(f9(c2, c2), f10(c2)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1))),
% 29.85/20.06 inference(modus_ponens,[status(thm)],[30351, 30350])).
% 29.85/20.06 tff(30353,plain,
% 29.85/20.06 ($false),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[30352, 2534, 25791, 29946, 30340, 30346, 30128, 30127])).
% 29.85/20.06 tff(30354,plain,(big_f(c1, c2)), inference(lemma,lemma(discharge,[]))).
% 29.85/20.06 tff(30355,plain,
% 29.85/20.06 (big_f(f7(c2), f10(f7(c2)))),
% 29.85/20.06 inference(modus_ponens,[status(thm)],[30354, 26])).
% 29.85/20.06 tff(30356,plain,
% 29.85/20.06 (big_f(f7(c2), c2)),
% 29.85/20.06 inference(modus_ponens,[status(thm)],[30354, 12163])).
% 29.85/20.06 tff(30357,plain,
% 29.85/20.06 (f1(f10(c1), c1) = f1(c2, c1)),
% 29.85/20.06 inference(monotonicity,[status(thm)],[15])).
% 29.85/20.06 tff(30358,plain,
% 29.85/20.06 (f1(c2, c1) = f1(f10(c1), c1)),
% 29.85/20.06 inference(symmetry,[status(thm)],[30357])).
% 29.85/20.06 tff(30359,plain,
% 29.85/20.06 (big_f(c2, f1(c2, c1)) <=> big_f(f10(c1), f1(f10(c1), c1))),
% 29.85/20.06 inference(monotonicity,[status(thm)],[5571, 30358])).
% 29.85/20.06 tff(30360,plain,
% 29.85/20.06 (big_f(f10(c1), f1(f10(c1), c1)) <=> big_f(c2, f1(c2, c1))),
% 29.85/20.06 inference(symmetry,[status(thm)],[30359])).
% 29.85/20.06 tff(30361,plain,
% 29.85/20.06 ((~(c1 = f8(f10(c1)))) <=> (~(f8(f10(c1)) = c1))),
% 29.85/20.06 inference(monotonicity,[status(thm)],[12056])).
% 29.85/20.06 tff(30362,plain,
% 29.85/20.06 ((f10(c1) = c4) <=> (c2 = c4)),
% 29.85/20.06 inference(symmetry,[status(thm)],[29435])).
% 29.85/20.06 tff(30363,plain,
% 29.85/20.06 ((c2 = f8(c2)) <=> (f10(c1) = f8(f10(c1)))),
% 29.85/20.06 inference(monotonicity,[status(thm)],[5571, 24868])).
% 29.85/20.06 tff(30364,plain,
% 29.85/20.06 ((f10(c1) = f8(f10(c1))) <=> (c2 = f8(c2))),
% 29.85/20.06 inference(symmetry,[status(thm)],[30363])).
% 29.85/20.06 tff(30365,plain,
% 29.85/20.06 ((f8(f10(c1)) = f10(c1)) <=> (f10(c1) = f8(f10(c1)))),
% 29.85/20.06 inference(commutativity,[status(thm)],[])).
% 29.85/20.06 tff(30366,plain,
% 29.85/20.06 ((f8(f10(c1)) = c2) <=> (f8(f10(c1)) = f10(c1))),
% 29.85/20.06 inference(monotonicity,[status(thm)],[5571])).
% 29.85/20.06 tff(30367,plain,
% 29.85/20.06 ((f8(f10(c1)) = c2) <=> (f10(c1) = f8(f10(c1)))),
% 29.85/20.06 inference(transitivity,[status(thm)],[30366, 30365])).
% 29.85/20.06 tff(30368,plain,
% 29.85/20.06 ((f8(f10(c1)) = c2) <=> (c2 = f8(c2))),
% 29.85/20.06 inference(transitivity,[status(thm)],[30367, 30364])).
% 29.85/20.06 tff(30369,plain,
% 29.85/20.06 ((c1 = f8(f10(c1))) <=> (c1 = f8(c2))),
% 29.85/20.06 inference(monotonicity,[status(thm)],[27898])).
% 29.85/20.06 tff(30370,plain,
% 29.85/20.06 ((c1 = f8(c2)) <=> (c1 = f8(f10(c1)))),
% 29.85/20.06 inference(symmetry,[status(thm)],[30369])).
% 29.85/20.06 tff(30371,plain,
% 29.85/20.06 ((c1 = f8(c2)) <=> (f8(f10(c1)) = c1)),
% 29.85/20.06 inference(transitivity,[status(thm)],[30370, 12056])).
% 29.85/20.06 tff(30372,plain,
% 29.85/20.06 ((~(c1 = f8(c2))) <=> (~(f8(f10(c1)) = c1))),
% 29.85/20.06 inference(monotonicity,[status(thm)],[30371])).
% 29.85/20.06 tff(30373,assumption,(big_f(f7(c1), f6(c1, f6(c1, c2)))), introduced(assumption)).
% 29.85/20.06 tff(30374,plain,
% 29.85/20.06 (big_f(c1, c1) | (~(f10(c2) = c2)) | big_f(c2, c2)),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[29276, 30354])).
% 29.85/20.06 tff(30375,plain,
% 29.85/20.06 (~(f10(c2) = c2)),
% 29.85/20.06 inference(unit_resolution,[status(thm)],[30374, 121, 66])).
% 29.85/20.06 tff(30376,plain,
% 29.85/20.06 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | big_f(c1, f10(c2)) | (~(c1 = f8(c2))) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | big_f(c1, f10(c2)) | (~(c1 = f8(c2))) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))),
% 29.85/20.06 inference(rewrite,[status(thm)],[])).
% 29.85/20.06 tff(30377,plain,
% 29.85/20.06 (((f10(c2) = c2) | big_f(c1, f10(c2)) | (~(f7(c1) = c1)) | (~(c1 = f8(c2))) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2))))) <=> ((f10(c2) = c2) | big_f(c1, f10(c2)) | (~(c1 = f8(c2))) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))),
% 29.85/20.06 inference(rewrite,[status(thm)],[])).
% 29.85/20.06 tff(30378,plain,
% 29.85/20.06 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | big_f(c1, f10(c2)) | (~(f7(c1) = c1)) | (~(c1 = f8(c2))) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | big_f(c1, f10(c2)) | (~(c1 = f8(c2))) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2))))))),
% 29.85/20.06 inference(monotonicity,[status(thm)],[30377])).
% 29.85/20.06 tff(30379,plain,
% 29.85/20.06 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | big_f(c1, f10(c2)) | (~(f7(c1) = c1)) | (~(c1 = f8(c2))) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | big_f(c1, f10(c2)) | (~(c1 = f8(c2))) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))),
% 29.85/20.07 inference(transitivity,[status(thm)],[30378, 30376])).
% 29.85/20.07 tff(30380,plain,
% 29.85/20.07 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | big_f(c1, f10(c2)) | (~(f7(c1) = c1)) | (~(c1 = f8(c2))) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))),
% 29.85/20.07 inference(quant_inst,[status(thm)],[])).
% 29.85/20.07 tff(30381,plain,
% 29.85/20.07 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | big_f(c1, f10(c2)) | (~(c1 = f8(c2))) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2))))),
% 29.85/20.07 inference(modus_ponens,[status(thm)],[30380, 30379])).
% 29.85/20.07 tff(30382,plain,
% 29.85/20.07 ((~(c1 = f8(c2))) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2)))),
% 29.85/20.07 inference(unit_resolution,[status(thm)],[30381, 2963, 25791, 89, 30373, 24207])).
% 29.85/20.07 tff(30383,plain,
% 29.85/20.07 (~(f6(c1, f6(c1, c2)) = f6(c1, c2))),
% 29.85/20.07 inference(unit_resolution,[status(thm)],[30382, 28171])).
% 29.85/20.07 tff(30384,plain,
% 29.85/20.07 (~(f6(c1, c2) = c2)),
% 29.85/20.07 inference(unit_resolution,[status(thm)],[43, 30383])).
% 29.85/20.07 tff(30385,plain,
% 29.85/20.07 (f6(c1, c2) = c1),
% 29.85/20.07 inference(unit_resolution,[status(thm)],[48, 30384])).
% 29.85/20.07 tff(30386,plain,
% 29.85/20.07 (big_f(c1, f6(c1, c2)) <=> big_f(c1, c1)),
% 29.85/20.07 inference(monotonicity,[status(thm)],[30385])).
% 29.85/20.07 tff(30387,plain,
% 29.85/20.07 (big_f(c1, c1) <=> big_f(c1, f6(c1, c2))),
% 29.85/20.07 inference(symmetry,[status(thm)],[30386])).
% 29.85/20.07 tff(30388,plain,
% 29.85/20.07 ((~big_f(c1, c1)) <=> (~big_f(c1, f6(c1, c2)))),
% 29.85/20.07 inference(monotonicity,[status(thm)],[30387])).
% 29.85/20.07 tff(30389,plain,
% 29.85/20.07 (~big_f(c1, f6(c1, c2))),
% 29.85/20.07 inference(modus_ponens,[status(thm)],[66, 30388])).
% 29.85/20.07 tff(30390,plain,
% 29.85/20.07 ((~(c1 = f8(c2))) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2)),
% 29.85/20.07 inference(unit_resolution,[status(thm)],[25825, 2994, 25791, 89, 24207])).
% 29.85/20.07 tff(30391,plain,
% 29.85/20.07 (big_f(f7(c1), f6(c1, c2))),
% 29.85/20.07 inference(unit_resolution,[status(thm)],[30390, 30384, 28171])).
% 29.85/20.07 tff(30392,plain,
% 29.85/20.07 (big_f(c1, f6(c1, c2))),
% 29.85/20.07 inference(modus_ponens,[status(thm)],[30391, 25792])).
% 29.85/20.07 tff(30393,plain,
% 29.85/20.07 ($false),
% 29.85/20.07 inference(unit_resolution,[status(thm)],[30392, 30389])).
% 29.85/20.07 tff(30394,plain,((~(c1 = f8(c2))) | big_f(c1, c1) | (f10(c2) = c2) | (~big_f(f7(c1), f6(c1, f6(c1, c2))))), inference(lemma,lemma(discharge,[]))).
% 29.85/20.07 tff(30395,plain,
% 29.85/20.07 (~(c1 = f8(c2))),
% 29.85/20.07 inference(unit_resolution,[status(thm)],[30394, 30375, 66, 30373])).
% 29.85/20.07 tff(30396,plain,
% 29.85/20.07 (~(f8(f10(c1)) = c1)),
% 29.85/20.07 inference(modus_ponens,[status(thm)],[30395, 30372])).
% 29.85/20.07 tff(30397,plain,
% 29.85/20.07 (f8(f10(c1)) = c2),
% 29.85/20.07 inference(unit_resolution,[status(thm)],[12021, 30396])).
% 29.85/20.07 tff(30398,plain,
% 29.85/20.07 (c2 = f8(c2)),
% 29.85/20.07 inference(modus_ponens,[status(thm)],[30397, 30368])).
% 29.85/20.07 tff(30399,plain,
% 29.85/20.07 (f10(c2) = c1),
% 29.85/20.07 inference(unit_resolution,[status(thm)],[93, 30375])).
% 29.85/20.07 tff(30400,plain,
% 29.85/20.07 (big_f(c1, f10(c1))),
% 29.85/20.07 inference(modus_ponens,[status(thm)],[30354, 24247])).
% 29.85/20.07 tff(30401,plain,
% 29.85/20.07 (big_f(c2, c1) | (f10(c2) = c2) | (~(f8(f10(c1)) = c2)) | big_f(c1, c1) | (~big_f(c1, f10(c1))) | (f10(c1) = c1)),
% 29.85/20.07 inference(unit_resolution,[status(thm)],[24954, 25791])).
% 29.85/20.07 tff(30402,plain,
% 29.85/20.07 (~(f8(f10(c1)) = c2)),
% 29.85/20.07 inference(unit_resolution,[status(thm)],[30401, 30400, 66, 89, 2, 3])).
% 29.85/20.07 tff(30403,plain,
% 29.85/20.07 (f8(f10(c1)) = c1),
% 29.85/20.07 inference(unit_resolution,[status(thm)],[12021, 30402])).
% 29.85/20.07 tff(30404,plain,
% 29.85/20.07 (c1 = f8(f10(c1))),
% 29.85/20.07 inference(modus_ponens,[status(thm)],[30403, 11996])).
% 29.85/20.07 tff(30405,plain,
% 29.85/20.07 ((~(c1 = f8(f10(c1)))) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2)))),
% 29.85/20.07 inference(unit_resolution,[status(thm)],[25045, 2963, 25791, 24891, 30373, 24961])).
% 29.85/20.07 tff(30406,plain,
% 29.85/20.07 (~(f6(c1, f6(c1, c2)) = f6(c1, c2))),
% 29.85/20.07 inference(unit_resolution,[status(thm)],[30405, 30404])).
% 29.85/20.07 tff(30407,plain,
% 29.85/20.07 (~(f6(c1, c2) = c2)),
% 29.85/20.07 inference(unit_resolution,[status(thm)],[43, 30406])).
% 29.85/20.07 tff(30408,plain,
% 29.85/20.07 (f6(c1, c2) = c1),
% 29.85/20.07 inference(unit_resolution,[status(thm)],[48, 30407])).
% 29.85/20.07 tff(30409,plain,
% 29.85/20.07 (big_f(c1, f6(c1, c2)) <=> big_f(c1, c1)),
% 29.85/20.07 inference(monotonicity,[status(thm)],[30408])).
% 29.85/20.07 tff(30410,plain,
% 29.85/20.07 (big_f(c1, c1) <=> big_f(c1, f6(c1, c2))),
% 29.85/20.07 inference(symmetry,[status(thm)],[30409])).
% 29.85/20.07 tff(30411,plain,
% 29.85/20.07 ((~big_f(c1, c1)) <=> (~big_f(c1, f6(c1, c2)))),
% 29.85/20.07 inference(monotonicity,[status(thm)],[30410])).
% 29.85/20.07 tff(30412,plain,
% 29.85/20.07 (~big_f(c1, f6(c1, c2))),
% 29.85/20.07 inference(modus_ponens,[status(thm)],[66, 30411])).
% 29.85/20.07 tff(30413,plain,
% 29.85/20.07 (big_f(f7(c1), f6(c1, f10(c1))) <=> big_f(c1, f6(c1, c2))),
% 29.85/20.07 inference(monotonicity,[status(thm)],[25791, 29657])).
% 29.85/20.07 tff(30414,plain,
% 29.85/20.07 (~(f6(c1, f10(c1)) = f10(c1))),
% 29.85/20.07 inference(unit_resolution,[status(thm)],[28849, 30407, 15])).
% 29.85/20.07 tff(30415,plain,
% 29.85/20.07 ((~(c1 = f8(f10(c1)))) | big_f(f7(c1), f6(c1, f10(c1))) | (f6(c1, f10(c1)) = f10(c1))),
% 29.85/20.07 inference(unit_resolution,[status(thm)],[25010, 2994, 25791, 24891, 24961])).
% 29.85/20.07 tff(30416,plain,
% 29.85/20.07 (big_f(f7(c1), f6(c1, f10(c1)))),
% 29.85/20.07 inference(unit_resolution,[status(thm)],[30415, 30414, 30404])).
% 29.85/20.07 tff(30417,plain,
% 29.85/20.07 (big_f(c1, f6(c1, c2))),
% 29.85/20.07 inference(modus_ponens,[status(thm)],[30416, 30413])).
% 29.85/20.07 tff(30418,plain,
% 29.85/20.07 ($false),
% 29.85/20.07 inference(unit_resolution,[status(thm)],[30417, 30412])).
% 29.85/20.07 tff(30419,plain,((f10(c1) = c1) | big_f(c1, c1) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))) | (f10(c2) = c2) | big_f(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 29.85/20.07 tff(30420,plain,
% 29.85/20.07 (big_f(c2, c1)),
% 29.85/20.07 inference(unit_resolution,[status(thm)],[30419, 3, 30373, 30375, 66])).
% 29.85/20.07 tff(30421,assumption,(~(c3 = c1)), introduced(assumption)).
% 29.85/20.07 tff(30422,plain,
% 29.85/20.07 (c3 = c2),
% 29.85/20.07 inference(unit_resolution,[status(thm)],[180, 30421])).
% 29.85/20.07 tff(30423,plain,
% 29.85/20.07 (f3(f10(c2), f8(c3)) = f3(c1, c2)),
% 29.85/20.07 inference(monotonicity,[status(thm)],[11819, 13154])).
% 29.85/20.07 tff(30424,plain,
% 29.85/20.07 (f3(c1, f8(c3)) = f3(f10(c2), f8(c3))),
% 29.85/20.07 inference(monotonicity,[status(thm)],[12231])).
% 29.85/20.07 tff(30425,plain,
% 29.85/20.07 (f3(c1, f8(c3)) = f3(c1, c2)),
% 29.85/20.07 inference(transitivity,[status(thm)],[30424, 30423])).
% 29.85/20.07 tff(30426,plain,
% 29.85/20.07 ((f3(c1, f8(c3)) = c1) <=> (f3(c1, c2) = c1)),
% 29.85/20.07 inference(monotonicity,[status(thm)],[30425])).
% 29.85/20.07 tff(30427,plain,
% 29.85/20.07 ((f3(c1, f8(c3)) = c1) <=> (c1 = f3(c1, c2))),
% 29.85/20.07 inference(transitivity,[status(thm)],[30426, 13151])).
% 29.85/20.07 tff(30428,plain,
% 29.85/20.07 (~(f3(c1, f8(c3)) = c2)),
% 29.85/20.07 inference(unit_resolution,[status(thm)],[29793, 16041, 12777])).
% 29.85/20.07 tff(30429,plain,
% 29.85/20.07 (f3(c1, f8(c3)) = c1),
% 29.85/20.07 inference(unit_resolution,[status(thm)],[7123, 30428])).
% 29.85/20.07 tff(30430,plain,
% 29.85/20.07 (c1 = f3(c1, c2)),
% 29.85/20.07 inference(modus_ponens,[status(thm)],[30429, 30427])).
% 29.85/20.07 tff(30431,plain,
% 29.85/20.07 ($false),
% 29.85/20.07 inference(unit_resolution,[status(thm)],[16041, 30430])).
% 29.85/20.07 tff(30432,plain,((c1 = f3(c1, c2)) | (~(c2 = f8(c2))) | (~(c3 = c2)) | (~(f10(c2) = c1)) | (f3(c1, c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 29.85/20.07 tff(30433,plain,
% 29.85/20.07 (c1 = f3(c1, c2)),
% 29.85/20.07 inference(unit_resolution,[status(thm)],[30432, 12777, 67, 11819, 13152])).
% 29.85/20.07 tff(30434,plain,
% 29.85/20.07 (big_f(c1, c1) | (c1 = c3) | (c1 = c4) | (f3(c1, c2) = c2) | (~(big_f(c1, c1) <=> big_f(f3(c1, c2), c1)))),
% 29.85/20.07 inference(unit_resolution,[status(thm)],[23331, 30354])).
% 29.85/20.07 tff(30435,plain,
% 29.85/20.07 (~(big_f(c1, c1) <=> big_f(f3(c1, c2), c1))),
% 29.85/20.07 inference(unit_resolution,[status(thm)],[30434, 12777, 66, 482, 168])).
% 29.85/20.07 tff(30436,plain,
% 29.85/20.07 ($false),
% 29.85/20.07 inference(unit_resolution,[status(thm)],[13192, 30435, 30433])).
% 29.85/20.07 tff(30437,plain,((f3(c1, c2) = c2) | big_f(c1, c1) | (c1 = c4) | (c1 = c3) | (~(c3 = c2)) | (~(f10(c2) = c1)) | (~(c2 = f8(c2)))), inference(lemma,lemma(discharge,[]))).
% 29.85/20.07 tff(30438,plain,
% 29.85/20.07 (f3(c1, c2) = c2),
% 29.85/20.07 inference(unit_resolution,[status(thm)],[30437, 482, 66, 168, 67, 11819, 13152])).
% 29.85/20.07 tff(30439,plain,
% 29.85/20.07 (f3(c1, f10(c1)) = f10(c1)),
% 29.85/20.07 inference(transitivity,[status(thm)],[29609, 30438, 293])).
% 29.85/20.07 tff(30440,plain,
% 29.85/20.07 (big_f(f3(c1, f10(c1)), c1) <=> big_f(f10(c1), c1)),
% 29.85/20.07 inference(monotonicity,[status(thm)],[30439])).
% 29.85/20.07 tff(30441,plain,
% 29.85/20.07 (big_f(f10(c1), c1) <=> big_f(f3(c1, f10(c1)), c1)),
% 29.85/20.07 inference(symmetry,[status(thm)],[30440])).
% 29.85/20.07 tff(30442,plain,
% 29.85/20.07 (big_f(f3(c1, f10(c1)), c1)),
% 29.85/20.07 inference(modus_ponens,[status(thm)],[27307, 30441])).
% 29.85/20.07 tff(30443,plain,
% 29.85/20.07 (big_f(c1, c2) <=> big_f(c1, f10(c1))),
% 29.85/20.07 inference(monotonicity,[status(thm)],[293])).
% 29.85/20.07 tff(30444,plain,
% 29.85/20.07 (big_f(c1, f10(c1))),
% 29.85/20.07 inference(modus_ponens,[status(thm)],[30354, 30443])).
% 29.85/20.07 tff(30445,plain,
% 29.85/20.07 (big_f(c1, f1(c1, f10(c1)))),
% 29.85/20.07 inference(modus_ponens,[status(thm)],[30444, 28918])).
% 29.85/20.07 tff(30446,assumption,(big_f(f3(c1, f10(c1)), c1)), introduced(assumption)).
% 29.85/20.07 tff(30447,assumption,(f3(c1, f10(c1)) = f10(c1)), introduced(assumption)).
% 29.85/20.07 tff(30448,plain,
% 29.85/20.07 (f1(c1, f10(c1)) = f10(c1)),
% 29.85/20.07 inference(unit_resolution,[status(thm)],[28913, 822, 16])).
% 29.85/20.07 tff(30449,plain,
% 29.85/20.07 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (c1 = c4) | (~big_f(c1, f1(c1, f10(c1)))) | (~(f1(c1, f10(c1)) = f10(c1))) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (c1 = c4) | (~big_f(c1, f1(c1, f10(c1)))) | (~(f1(c1, f10(c1)) = f10(c1))) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1)))),
% 29.85/20.07 inference(rewrite,[status(thm)],[])).
% 29.85/20.07 tff(30450,plain,
% 29.85/20.07 (((c1 = c4) | (c1 = c3) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1)) | (~(f1(c1, f10(c1)) = f10(c1))) | (~big_f(c1, f1(c1, f10(c1))))) <=> ((c1 = c3) | (c1 = c4) | (~big_f(c1, f1(c1, f10(c1)))) | (~(f1(c1, f10(c1)) = f10(c1))) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1)))),
% 29.85/20.07 inference(rewrite,[status(thm)],[])).
% 29.85/20.07 tff(30451,plain,
% 29.85/20.07 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c4) | (c1 = c3) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1)) | (~(f1(c1, f10(c1)) = f10(c1))) | (~big_f(c1, f1(c1, f10(c1)))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c3) | (c1 = c4) | (~big_f(c1, f1(c1, f10(c1)))) | (~(f1(c1, f10(c1)) = f10(c1))) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1))))),
% 29.85/20.07 inference(monotonicity,[status(thm)],[30450])).
% 29.85/20.07 tff(30452,plain,
% 29.85/20.07 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c4) | (c1 = c3) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1)) | (~(f1(c1, f10(c1)) = f10(c1))) | (~big_f(c1, f1(c1, f10(c1)))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (c1 = c4) | (~big_f(c1, f1(c1, f10(c1)))) | (~(f1(c1, f10(c1)) = f10(c1))) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1)))),
% 29.85/20.07 inference(transitivity,[status(thm)],[30451, 30449])).
% 29.85/20.07 tff(30453,plain,
% 29.85/20.07 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c4) | (c1 = c3) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1)) | (~(f1(c1, f10(c1)) = f10(c1))) | (~big_f(c1, f1(c1, f10(c1)))))),
% 29.85/20.07 inference(quant_inst,[status(thm)],[])).
% 29.85/20.07 tff(30454,plain,
% 29.85/20.07 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c3) | (c1 = c4) | (~big_f(c1, f1(c1, f10(c1)))) | (~(f1(c1, f10(c1)) = f10(c1))) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1))),
% 29.85/20.07 inference(modus_ponens,[status(thm)],[30453, 30452])).
% 29.85/20.07 tff(30455,plain,
% 29.85/20.07 (~big_f(c1, f1(c1, f10(c1)))),
% 29.85/20.07 inference(unit_resolution,[status(thm)],[30454, 933, 168, 482, 30448, 30447, 30446])).
% 29.85/20.07 tff(30456,plain,
% 29.85/20.07 ($false),
% 29.85/20.07 inference(unit_resolution,[status(thm)],[30455, 30445])).
% 29.85/20.07 tff(30457,plain,((~(f1(c1, c2) = c2)) | (~(f10(c1) = c2)) | (c1 = c3) | (c1 = c4) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1))), inference(lemma,lemma(discharge,[]))).
% 29.85/20.07 tff(30458,plain,
% 29.85/20.07 (~(f1(c1, c2) = c2)),
% 29.85/20.07 inference(unit_resolution,[status(thm)],[30457, 482, 168, 16, 30439, 30442])).
% 29.85/20.07 tff(30459,plain,
% 29.85/20.07 (f1(c1, c2) = c1),
% 29.85/20.07 inference(unit_resolution,[status(thm)],[841, 30458])).
% 29.85/20.07 tff(30460,plain,
% 29.85/20.07 (f1(c1, f10(c1)) = c1),
% 29.85/20.07 inference(transitivity,[status(thm)],[28909, 30459])).
% 29.85/20.07 tff(30461,plain,
% 29.85/20.07 (big_f(c1, f1(c1, f10(c1))) <=> big_f(c1, c1)),
% 29.85/20.07 inference(monotonicity,[status(thm)],[30460])).
% 29.85/20.07 tff(30462,plain,
% 29.85/20.07 (big_f(c1, c1) <=> big_f(c1, f1(c1, f10(c1)))),
% 29.85/20.07 inference(symmetry,[status(thm)],[30461])).
% 29.85/20.07 tff(30463,plain,
% 29.85/20.07 ((~big_f(c1, c1)) <=> (~big_f(c1, f1(c1, f10(c1))))),
% 29.85/20.07 inference(monotonicity,[status(thm)],[30462])).
% 29.85/20.07 tff(30464,plain,
% 29.85/20.07 (~big_f(c1, f1(c1, f10(c1)))),
% 29.85/20.07 inference(modus_ponens,[status(thm)],[66, 30463])).
% 29.85/20.07 tff(30465,plain,
% 29.85/20.07 (f1(c1, c2) = f1(c1, f10(c1))),
% 29.85/20.07 inference(symmetry,[status(thm)],[28909])).
% 29.85/20.07 tff(30466,plain,
% 29.85/20.07 ((f1(c1, c2) = c2) <=> (f1(c1, f10(c1)) = f10(c1))),
% 29.85/20.07 inference(monotonicity,[status(thm)],[30465, 293])).
% 29.85/20.07 tff(30467,plain,
% 29.85/20.07 ((~(f1(c1, c2) = c2)) <=> (~(f1(c1, f10(c1)) = f10(c1)))),
% 29.85/20.07 inference(monotonicity,[status(thm)],[30466])).
% 29.85/20.07 tff(30468,plain,
% 29.85/20.07 (~(f1(c1, f10(c1)) = f10(c1))),
% 29.85/20.07 inference(modus_ponens,[status(thm)],[30458, 30467])).
% 29.85/20.07 tff(30469,plain,
% 29.85/20.07 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c1 = c3) | (c1 = c4) | (f1(c1, f10(c1)) = f10(c1)) | big_f(c1, f1(c1, f10(c1))) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c1 = c3) | (c1 = c4) | (f1(c1, f10(c1)) = f10(c1)) | big_f(c1, f1(c1, f10(c1))) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1)))),
% 29.85/20.07 inference(rewrite,[status(thm)],[])).
% 29.85/20.07 tff(30470,plain,
% 29.85/20.07 (((c1 = c4) | (c1 = c3) | (f1(c1, f10(c1)) = f10(c1)) | big_f(c1, f1(c1, f10(c1))) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1))) <=> ((c1 = c3) | (c1 = c4) | (f1(c1, f10(c1)) = f10(c1)) | big_f(c1, f1(c1, f10(c1))) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1)))),
% 29.85/20.07 inference(rewrite,[status(thm)],[])).
% 29.85/20.07 tff(30471,plain,
% 29.85/20.07 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c1 = c4) | (c1 = c3) | (f1(c1, f10(c1)) = f10(c1)) | big_f(c1, f1(c1, f10(c1))) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c1 = c3) | (c1 = c4) | (f1(c1, f10(c1)) = f10(c1)) | big_f(c1, f1(c1, f10(c1))) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1))))),
% 29.85/20.07 inference(monotonicity,[status(thm)],[30470])).
% 29.85/20.07 tff(30472,plain,
% 29.85/20.07 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c1 = c4) | (c1 = c3) | (f1(c1, f10(c1)) = f10(c1)) | big_f(c1, f1(c1, f10(c1))) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c1 = c3) | (c1 = c4) | (f1(c1, f10(c1)) = f10(c1)) | big_f(c1, f1(c1, f10(c1))) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1)))),
% 29.85/20.07 inference(transitivity,[status(thm)],[30471, 30469])).
% 29.85/20.07 tff(30473,plain,
% 29.85/20.07 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c1 = c4) | (c1 = c3) | (f1(c1, f10(c1)) = f10(c1)) | big_f(c1, f1(c1, f10(c1))) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1)))),
% 29.85/20.07 inference(quant_inst,[status(thm)],[])).
% 29.85/20.07 tff(30474,plain,
% 29.85/20.07 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c1 = c3) | (c1 = c4) | (f1(c1, f10(c1)) = f10(c1)) | big_f(c1, f1(c1, f10(c1))) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1))),
% 29.85/20.07 inference(modus_ponens,[status(thm)],[30473, 30472])).
% 29.85/20.07 tff(30475,plain,
% 29.85/20.07 (big_f(c1, f1(c1, f10(c1)))),
% 29.85/20.07 inference(unit_resolution,[status(thm)],[30474, 969, 168, 482, 30468, 30439, 30442])).
% 29.85/20.07 tff(30476,plain,
% 29.85/20.07 ($false),
% 29.85/20.07 inference(unit_resolution,[status(thm)],[30475, 30464])).
% 29.85/20.07 tff(30477,plain,((c1 = c4) | big_f(c1, c1) | (~(f10(c1) = c2)) | (c1 = c3) | (~big_f(f10(c1), c1)) | (~(c3 = c2)) | (~(f10(c2) = c1)) | (~(c2 = f8(c2)))), inference(lemma,lemma(discharge,[]))).
% 29.85/20.07 tff(30478,plain,
% 29.85/20.07 (c1 = c3),
% 29.85/20.07 inference(unit_resolution,[status(thm)],[30477, 30422, 16, 66, 27307, 482, 11819, 13152])).
% 29.85/20.07 tff(30479,plain,
% 29.85/20.07 (c3 = c1),
% 29.85/20.07 inference(modus_ponens,[status(thm)],[30478, 12387])).
% 29.85/20.07 tff(30480,plain,
% 29.85/20.07 ($false),
% 29.85/20.07 inference(unit_resolution,[status(thm)],[30421, 30479])).
% 29.85/20.07 tff(30481,plain,((c3 = c1) | (~(f10(c1) = c2)) | big_f(c1, c1) | (~big_f(f10(c1), c1)) | (c1 = c4) | (~(f10(c2) = c1)) | (~(c2 = f8(c2)))), inference(lemma,lemma(discharge,[]))).
% 29.85/20.07 tff(30482,plain,
% 29.85/20.07 (c3 = c1),
% 29.85/20.07 inference(unit_resolution,[status(thm)],[30481, 482, 66, 27297, 15, 11819, 13152])).
% 29.85/20.07 tff(30483,plain,
% 29.85/20.07 ((f10(c1) = c3) <=> (f10(c1) = c1)),
% 29.85/20.07 inference(monotonicity,[status(thm)],[30482])).
% 29.85/20.07 tff(30484,plain,
% 29.85/20.07 ((f10(c1) = c1) <=> (f10(c1) = c3)),
% 29.85/20.07 inference(symmetry,[status(thm)],[30483])).
% 29.85/20.07 tff(30485,plain,
% 29.85/20.07 ((~(f10(c1) = c1)) <=> (~(f10(c1) = c3))),
% 29.85/20.07 inference(monotonicity,[status(thm)],[30484])).
% 29.85/20.07 tff(30486,plain,
% 29.85/20.07 (~(f10(c1) = c3)),
% 29.85/20.07 inference(modus_ponens,[status(thm)],[3, 30485])).
% 29.85/20.07 tff(30487,plain,
% 29.85/20.07 ((c2 = c3) <=> (f10(c1) = c3)),
% 29.85/20.07 inference(monotonicity,[status(thm)],[5571])).
% 29.85/20.07 tff(30488,plain,
% 29.85/20.07 ((f10(c1) = c3) <=> (c2 = c3)),
% 29.85/20.07 inference(symmetry,[status(thm)],[30487])).
% 29.85/20.07 tff(30489,plain,
% 29.85/20.07 ((f10(c1) = c1) <=> (c2 = c3)),
% 29.85/20.07 inference(transitivity,[status(thm)],[30484, 30488])).
% 29.85/20.07 tff(30490,plain,
% 29.85/20.07 ((~(f10(c1) = c1)) <=> (~(c2 = c3))),
% 29.85/20.07 inference(monotonicity,[status(thm)],[30489])).
% 29.85/20.07 tff(30491,plain,
% 29.85/20.07 (~(c2 = c3)),
% 29.85/20.07 inference(modus_ponens,[status(thm)],[3, 30490])).
% 29.85/20.07 tff(30492,plain,
% 29.85/20.07 ((~big_f(f3(c1, c2), c1)) <=> (~big_f(f3(c1, f10(c1)), c1))),
% 29.85/20.07 inference(monotonicity,[status(thm)],[29616])).
% 29.85/20.07 tff(30493,plain,
% 29.85/20.07 (~big_f(f3(c1, f10(c1)), c1)),
% 29.85/20.07 inference(modus_ponens,[status(thm)],[13164, 30492])).
% 29.85/20.07 tff(30494,plain,
% 29.85/20.07 ((~(f3(c1, c2) = c2)) <=> (~(f3(c1, f10(c1)) = f10(c1)))),
% 29.85/20.07 inference(monotonicity,[status(thm)],[29611])).
% 29.85/20.07 tff(30495,plain,
% 29.85/20.07 (~(f3(c1, f10(c1)) = f10(c1))),
% 29.85/20.07 inference(modus_ponens,[status(thm)],[12777, 30494])).
% 29.85/20.07 tff(30496,assumption,(~big_f(f3(c1, f10(c1)), c1)), introduced(assumption)).
% 29.85/20.07 tff(30497,assumption,(~(f3(c1, f10(c1)) = f10(c1))), introduced(assumption)).
% 29.85/20.07 tff(30498,plain,
% 29.85/20.07 (f1(c2, c1) = f1(f10(c1), c1)),
% 29.85/20.07 inference(symmetry,[status(thm)],[8887])).
% 29.85/20.07 tff(30499,plain,
% 29.85/20.07 ((f1(c2, c1) = c1) <=> (f1(f10(c1), c1) = c1)),
% 29.85/20.07 inference(monotonicity,[status(thm)],[30498])).
% 29.85/20.07 tff(30500,plain,
% 29.85/20.07 ((~(f1(c2, c1) = c1)) <=> (~(f1(f10(c1), c1) = c1))),
% 29.85/20.07 inference(monotonicity,[status(thm)],[30499])).
% 29.85/20.07 tff(30501,plain,
% 29.85/20.07 (~(f1(f10(c1), c1) = c1)),
% 29.85/20.07 inference(modus_ponens,[status(thm)],[12187, 30500])).
% 29.85/20.07 tff(30502,plain,
% 29.85/20.07 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c1 = c4) | (f10(c1) = c3) | (f1(f10(c1), c1) = c1) | big_f(f10(c1), f1(f10(c1), c1)) | (f3(c1, f10(c1)) = f10(c1)) | big_f(f3(c1, f10(c1)), c1))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (c1 = c4) | (f10(c1) = c3) | (f1(f10(c1), c1) = c1) | big_f(f10(c1), f1(f10(c1), c1)) | (f3(c1, f10(c1)) = f10(c1)) | big_f(f3(c1, f10(c1)), c1))),
% 29.85/20.07 inference(rewrite,[status(thm)],[])).
% 29.85/20.07 tff(30503,plain,
% 29.85/20.07 (((c1 = c4) | (f3(c1, f10(c1)) = f10(c1)) | big_f(f3(c1, f10(c1)), c1) | (f10(c1) = c3) | (f1(f10(c1), c1) = c1) | big_f(f10(c1), f1(f10(c1), c1))) <=> ((c1 = c4) | (f10(c1) = c3) | (f1(f10(c1), c1) = c1) | big_f(f10(c1), f1(f10(c1), c1)) | (f3(c1, f10(c1)) = f10(c1)) | big_f(f3(c1, f10(c1)), c1))),
% 29.85/20.07 inference(rewrite,[status(thm)],[])).
% 29.85/20.07 tff(30504,plain,
% 29.85/20.07 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c1 = c4) | (f3(c1, f10(c1)) = f10(c1)) | big_f(f3(c1, f10(c1)), c1) | (f10(c1) = c3) | (f1(f10(c1), c1) = c1) | big_f(f10(c1), f1(f10(c1), c1)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c1 = c4) | (f10(c1) = c3) | (f1(f10(c1), c1) = c1) | big_f(f10(c1), f1(f10(c1), c1)) | (f3(c1, f10(c1)) = f10(c1)) | big_f(f3(c1, f10(c1)), c1)))),
% 29.85/20.07 inference(monotonicity,[status(thm)],[30503])).
% 29.85/20.07 tff(30505,plain,
% 29.85/20.07 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c1 = c4) | (f3(c1, f10(c1)) = f10(c1)) | big_f(f3(c1, f10(c1)), c1) | (f10(c1) = c3) | (f1(f10(c1), c1) = c1) | big_f(f10(c1), f1(f10(c1), c1)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (c1 = c4) | (f10(c1) = c3) | (f1(f10(c1), c1) = c1) | big_f(f10(c1), f1(f10(c1), c1)) | (f3(c1, f10(c1)) = f10(c1)) | big_f(f3(c1, f10(c1)), c1))),
% 29.85/20.07 inference(transitivity,[status(thm)],[30504, 30502])).
% 29.85/20.07 tff(30506,plain,
% 29.85/20.07 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | ((c1 = c4) | (f3(c1, f10(c1)) = f10(c1)) | big_f(f3(c1, f10(c1)), c1) | (f10(c1) = c3) | (f1(f10(c1), c1) = c1) | big_f(f10(c1), f1(f10(c1), c1)))),
% 29.85/20.07 inference(quant_inst,[status(thm)],[])).
% 29.85/20.07 tff(30507,plain,
% 29.85/20.07 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)))) | (c1 = c4) | (f10(c1) = c3) | (f1(f10(c1), c1) = c1) | big_f(f10(c1), f1(f10(c1), c1)) | (f3(c1, f10(c1)) = f10(c1)) | big_f(f3(c1, f10(c1)), c1)),
% 29.85/20.07 inference(modus_ponens,[status(thm)],[30506, 30505])).
% 29.85/20.07 tff(30508,plain,
% 29.85/20.07 ($false),
% 29.85/20.07 inference(unit_resolution,[status(thm)],[30507, 1014, 482, 29434, 30501, 29046, 30497, 30496])).
% 29.85/20.07 tff(30509,plain,((f1(c2, c1) = c1) | (c1 = c4) | (f10(c1) = c3) | (f3(c1, f10(c1)) = f10(c1)) | big_f(f3(c1, f10(c1)), c1) | (~(f10(c1) = c2)) | big_f(f10(c1), f10(c1))), inference(lemma,lemma(discharge,[]))).
% 29.85/20.07 tff(30510,plain,
% 29.85/20.07 (f1(c2, c1) = c1),
% 29.85/20.07 inference(unit_resolution,[status(thm)],[30509, 30495, 29434, 482, 30493, 16, 26503])).
% 29.85/20.07 tff(30511,plain,
% 29.85/20.07 (f1(f10(c1), c1) = c1),
% 29.85/20.07 inference(transitivity,[status(thm)],[8887, 30510])).
% 29.85/20.07 tff(30512,plain,
% 29.85/20.07 (big_f(f10(c1), f1(f10(c1), c1)) <=> big_f(f10(c1), c1)),
% 29.85/20.07 inference(monotonicity,[status(thm)],[30511])).
% 29.85/20.07 tff(30513,plain,
% 29.85/20.07 (big_f(f10(c1), c1) <=> big_f(f10(c1), f1(f10(c1), c1))),
% 29.85/20.08 inference(symmetry,[status(thm)],[30512])).
% 29.85/20.08 tff(30514,plain,
% 29.85/20.08 (big_f(f10(c1), f1(f10(c1), c1))),
% 29.85/20.08 inference(modus_ponens,[status(thm)],[27307, 30513])).
% 29.85/20.08 tff(30515,plain,
% 29.85/20.08 (big_f(c2, f1(c2, c1)) <=> big_f(f10(c1), f1(f10(c1), c1))),
% 29.85/20.08 inference(monotonicity,[status(thm)],[293, 30498])).
% 29.85/20.08 tff(30516,plain,
% 29.85/20.08 ((~big_f(c2, f1(c2, c1))) <=> (~big_f(f10(c1), f1(f10(c1), c1)))),
% 29.85/20.08 inference(monotonicity,[status(thm)],[30515])).
% 29.85/20.08 tff(30517,plain,
% 29.85/20.08 (~big_f(c2, f1(c2, c1))),
% 29.85/20.08 inference(unit_resolution,[status(thm)],[16144, 30510, 377, 482, 13164, 12777])).
% 29.85/20.08 tff(30518,plain,
% 29.85/20.08 (~big_f(f10(c1), f1(f10(c1), c1))),
% 29.85/20.08 inference(modus_ponens,[status(thm)],[30517, 30516])).
% 29.85/20.08 tff(30519,plain,
% 29.85/20.08 ($false),
% 29.85/20.08 inference(unit_resolution,[status(thm)],[30518, 30514])).
% 29.85/20.08 tff(30520,plain,(big_f(f3(c1, c2), c1) | (~big_f(f10(c1), c1)) | (~(f10(c1) = c2)) | (c2 = c3) | (c1 = c4) | (f3(c1, c2) = c2) | (f10(c1) = c3) | big_f(f10(c1), f10(c1))), inference(lemma,lemma(discharge,[]))).
% 29.85/20.08 tff(30521,plain,
% 29.85/20.08 (big_f(f3(c1, c2), c1)),
% 29.85/20.08 inference(unit_resolution,[status(thm)],[30520, 12777, 16, 377, 482, 27307, 29434, 26503])).
% 29.85/20.08 tff(30522,plain,
% 29.85/20.08 (~(big_f(c1, c1) <=> big_f(f3(c1, c2), c1))),
% 29.85/20.08 inference(unit_resolution,[status(thm)],[13186, 30521, 66])).
% 29.85/20.08 tff(30523,plain,
% 29.85/20.08 (~(c1 = f3(c1, c2))),
% 29.85/20.08 inference(unit_resolution,[status(thm)],[13192, 30522])).
% 29.85/20.08 tff(30524,plain,
% 29.85/20.08 (~(f1(f5(c2), f5(c1)) = c2)),
% 29.85/20.08 inference(unit_resolution,[status(thm)],[26052, 30523, 12777])).
% 29.85/20.08 tff(30525,plain,
% 29.85/20.08 (f1(f5(c2), f5(c1)) = c1),
% 29.85/20.08 inference(unit_resolution,[status(thm)],[5191, 30524])).
% 29.85/20.08 tff(30526,plain,
% 29.85/20.08 (f3(f1(f5(c2), f5(c1)), c2) = f3(c1, c2)),
% 29.85/20.08 inference(monotonicity,[status(thm)],[30525])).
% 29.85/20.08 tff(30527,plain,
% 29.85/20.08 ((f3(f1(f5(c2), f5(c1)), c2) = c2) <=> (f3(c1, c2) = c2)),
% 29.85/20.08 inference(monotonicity,[status(thm)],[30526])).
% 29.85/20.08 tff(30528,plain,
% 29.85/20.08 ((f3(c1, c2) = c2) <=> (f3(f1(f5(c2), f5(c1)), c2) = c2)),
% 29.85/20.08 inference(symmetry,[status(thm)],[30527])).
% 29.85/20.08 tff(30529,plain,
% 29.85/20.08 ((~(f3(c1, c2) = c2)) <=> (~(f3(f1(f5(c2), f5(c1)), c2) = c2))),
% 29.85/20.08 inference(monotonicity,[status(thm)],[30528])).
% 29.85/20.08 tff(30530,plain,
% 29.85/20.08 (~(f3(f1(f5(c2), f5(c1)), c2) = c2)),
% 29.85/20.08 inference(modus_ponens,[status(thm)],[12777, 30529])).
% 29.85/20.08 tff(30531,plain,
% 29.85/20.08 (f3(c1, c2) = f3(f1(f5(c2), f5(c1)), c2)),
% 29.85/20.08 inference(symmetry,[status(thm)],[30526])).
% 29.85/20.08 tff(30532,plain,
% 29.85/20.08 ((c1 = f3(c1, c2)) <=> (c1 = f3(f1(f5(c2), f5(c1)), c2))),
% 29.85/20.08 inference(monotonicity,[status(thm)],[30531])).
% 29.85/20.08 tff(30533,plain,
% 29.85/20.08 ((c1 = f3(c1, c2)) <=> (f3(f1(f5(c2), f5(c1)), c2) = c1)),
% 29.85/20.08 inference(transitivity,[status(thm)],[30532, 26113])).
% 29.85/20.08 tff(30534,plain,
% 29.85/20.08 ((~(c1 = f3(c1, c2))) <=> (~(f3(f1(f5(c2), f5(c1)), c2) = c1))),
% 29.85/20.08 inference(monotonicity,[status(thm)],[30533])).
% 29.85/20.08 tff(30535,plain,
% 29.85/20.08 (~(f3(f1(f5(c2), f5(c1)), c2) = c1)),
% 29.85/20.08 inference(modus_ponens,[status(thm)],[30523, 30534])).
% 29.85/20.08 tff(30536,plain,
% 29.85/20.08 ($false),
% 29.85/20.08 inference(unit_resolution,[status(thm)],[16061, 30535, 30530])).
% 29.85/20.08 tff(30537,plain,((f3(c1, c2) = c2) | big_f(c1, c1) | (~(f10(c1) = c2)) | (c2 = c3) | (c1 = c4) | (~big_f(f10(c1), c1)) | (f10(c1) = c3) | big_f(f10(c1), f10(c1))), inference(lemma,lemma(discharge,[]))).
% 29.85/20.08 tff(30538,plain,
% 29.85/20.08 (f3(c1, c2) = c2),
% 29.85/20.08 inference(unit_resolution,[status(thm)],[30537, 30491, 15, 66, 482, 27297, 30486, 26503])).
% 29.85/20.08 tff(30539,plain,
% 29.85/20.08 (big_f(f3(c1, c2), c1)),
% 29.85/20.08 inference(unit_resolution,[status(thm)],[26072, 30538, 348])).
% 29.85/20.08 tff(30540,plain,
% 29.85/20.08 ((~big_f(f3(c1, f10(c1)), c1)) <=> (~big_f(f3(c1, c2), c1))),
% 29.85/20.08 inference(monotonicity,[status(thm)],[29615])).
% 29.85/20.08 tff(30541,plain,
% 29.85/20.08 (~big_f(f3(c1, c2), c1)),
% 29.85/20.08 inference(modus_ponens,[status(thm)],[30496, 30540])).
% 29.85/20.08 tff(30542,plain,
% 29.85/20.08 ($false),
% 29.85/20.08 inference(unit_resolution,[status(thm)],[22442, 30541])).
% 29.85/20.08 tff(30543,plain,(big_f(f3(c1, f10(c1)), c1) | (~big_f(f3(c1, c2), c1)) | (~(f10(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.85/20.08 tff(30544,plain,
% 29.85/20.08 (big_f(f3(c1, f10(c1)), c1)),
% 29.85/20.08 inference(unit_resolution,[status(thm)],[30543, 30539, 15])).
% 29.85/20.08 tff(30545,plain,
% 29.85/20.08 (f3(c1, f10(c1)) = f3(c1, c2)),
% 29.85/20.08 inference(monotonicity,[status(thm)],[15])).
% 29.85/20.08 tff(30546,plain,
% 29.85/20.08 ((f3(c1, f10(c1)) = f10(c1)) <=> (f3(c1, c2) = c2)),
% 29.85/20.08 inference(monotonicity,[status(thm)],[30545, 15])).
% 29.85/20.08 tff(30547,plain,
% 29.85/20.08 ((f3(c1, c2) = c2) <=> (f3(c1, f10(c1)) = f10(c1))),
% 29.85/20.08 inference(symmetry,[status(thm)],[30546])).
% 29.85/20.08 tff(30548,plain,
% 29.85/20.08 (f3(c1, f10(c1)) = f10(c1)),
% 29.85/20.08 inference(modus_ponens,[status(thm)],[30538, 30547])).
% 29.85/20.08 tff(30549,plain,
% 29.85/20.08 (~big_f(f10(c1), f1(f10(c1), c1))),
% 29.85/20.08 inference(unit_resolution,[status(thm)],[29045, 12189, 15, 26503])).
% 29.85/20.08 tff(30550,plain,
% 29.85/20.08 (f1(f10(c1), c1) = f10(c1)),
% 29.85/20.08 inference(transitivity,[status(thm)],[30357, 12189, 5571])).
% 29.85/20.08 tff(30551,plain,
% 29.85/20.08 ((f1(f10(c1), c1) = c1) <=> (f10(c1) = c1)),
% 29.85/20.08 inference(monotonicity,[status(thm)],[30550])).
% 29.85/20.08 tff(30552,plain,
% 29.85/20.08 ((f10(c1) = c1) <=> (f1(f10(c1), c1) = c1)),
% 29.85/20.08 inference(symmetry,[status(thm)],[30551])).
% 29.85/20.08 tff(30553,plain,
% 29.85/20.08 ((~(f10(c1) = c1)) <=> (~(f1(f10(c1), c1) = c1))),
% 29.85/20.08 inference(monotonicity,[status(thm)],[30552])).
% 29.85/20.08 tff(30554,plain,
% 29.85/20.08 (~(f1(f10(c1), c1) = c1)),
% 29.85/20.08 inference(modus_ponens,[status(thm)],[3, 30553])).
% 29.85/20.08 tff(30555,plain,
% 29.85/20.08 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c1 = c4) | (f10(c1) = c3) | (f1(f10(c1), c1) = c1) | big_f(f10(c1), f1(f10(c1), c1)) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c1 = c4) | (f10(c1) = c3) | (f1(f10(c1), c1) = c1) | big_f(f10(c1), f1(f10(c1), c1)) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1)))),
% 29.85/20.08 inference(rewrite,[status(thm)],[])).
% 29.85/20.08 tff(30556,plain,
% 29.85/20.08 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | ((c1 = c4) | (f10(c1) = c3) | (f1(f10(c1), c1) = c1) | big_f(f10(c1), f1(f10(c1), c1)) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1)))),
% 29.85/20.08 inference(quant_inst,[status(thm)],[])).
% 29.85/20.08 tff(30557,plain,
% 29.85/20.08 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)))) | (c1 = c4) | (f10(c1) = c3) | (f1(f10(c1), c1) = c1) | big_f(f10(c1), f1(f10(c1), c1)) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1))),
% 29.85/20.08 inference(modus_ponens,[status(thm)],[30556, 30555])).
% 29.85/20.08 tff(30558,plain,
% 29.85/20.08 ($false),
% 29.85/20.08 inference(unit_resolution,[status(thm)],[30557, 969, 482, 29434, 30554, 30549, 30447, 30446])).
% 29.85/20.08 tff(30559,plain,((~(f1(c2, c1) = c2)) | (c1 = c4) | (f10(c1) = c3) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1)) | (f10(c1) = c1) | big_f(f10(c1), f10(c1))), inference(lemma,lemma(discharge,[]))).
% 29.85/20.08 tff(30560,plain,
% 29.85/20.08 (~(f1(c2, c1) = c2)),
% 29.85/20.08 inference(unit_resolution,[status(thm)],[30559, 482, 30486, 30548, 30544, 3, 26503])).
% 29.85/20.08 tff(30561,plain,
% 29.85/20.08 (f1(c2, c1) = c1),
% 29.85/20.08 inference(unit_resolution,[status(thm)],[10113, 30560])).
% 29.85/20.08 tff(30562,plain,
% 29.85/20.08 (f1(f10(c1), c1) = c1),
% 29.85/20.08 inference(transitivity,[status(thm)],[30357, 30561])).
% 29.85/20.08 tff(30563,plain,
% 29.85/20.08 (big_f(f10(c1), f1(f10(c1), c1)) <=> big_f(f10(c1), c1)),
% 29.85/20.08 inference(monotonicity,[status(thm)],[30562])).
% 29.85/20.08 tff(30564,plain,
% 29.85/20.08 (big_f(f10(c1), c1) <=> big_f(f10(c1), f1(f10(c1), c1))),
% 29.85/20.08 inference(symmetry,[status(thm)],[30563])).
% 29.85/20.08 tff(30565,plain,
% 29.85/20.08 (big_f(f10(c1), f1(f10(c1), c1))),
% 29.85/20.08 inference(modus_ponens,[status(thm)],[27297, 30564])).
% 29.85/20.08 tff(30566,plain,
% 29.85/20.08 ((f1(c2, c1) = c1) <=> (f1(f10(c1), c1) = c1)),
% 29.85/20.08 inference(monotonicity,[status(thm)],[30358])).
% 29.85/20.08 tff(30567,plain,
% 29.85/20.08 (f1(f10(c1), c1) = c1),
% 29.85/20.08 inference(modus_ponens,[status(thm)],[30561, 30566])).
% 29.85/20.08 tff(30568,plain,
% 29.85/20.08 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c4) | (f10(c1) = c3) | (~(f1(f10(c1), c1) = c1)) | (~big_f(f10(c1), f1(f10(c1), c1))) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1)))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c4) | (f10(c1) = c3) | (~(f1(f10(c1), c1) = c1)) | (~big_f(f10(c1), f1(f10(c1), c1))) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1)))),
% 29.85/20.08 inference(rewrite,[status(thm)],[])).
% 29.85/20.08 tff(30569,plain,
% 29.85/20.08 (((c1 = c4) | (f10(c1) = c3) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1)) | (~(f1(f10(c1), c1) = c1)) | (~big_f(f10(c1), f1(f10(c1), c1)))) <=> ((c1 = c4) | (f10(c1) = c3) | (~(f1(f10(c1), c1) = c1)) | (~big_f(f10(c1), f1(f10(c1), c1))) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1)))),
% 29.85/20.08 inference(rewrite,[status(thm)],[])).
% 29.85/20.08 tff(30570,plain,
% 29.85/20.08 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c4) | (f10(c1) = c3) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1)) | (~(f1(f10(c1), c1) = c1)) | (~big_f(f10(c1), f1(f10(c1), c1))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c4) | (f10(c1) = c3) | (~(f1(f10(c1), c1) = c1)) | (~big_f(f10(c1), f1(f10(c1), c1))) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1))))),
% 29.85/20.08 inference(monotonicity,[status(thm)],[30569])).
% 29.85/20.08 tff(30571,plain,
% 29.85/20.08 (((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c4) | (f10(c1) = c3) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1)) | (~(f1(f10(c1), c1) = c1)) | (~big_f(f10(c1), f1(f10(c1), c1))))) <=> ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c4) | (f10(c1) = c3) | (~(f1(f10(c1), c1) = c1)) | (~big_f(f10(c1), f1(f10(c1), c1))) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1)))),
% 29.85/20.08 inference(transitivity,[status(thm)],[30570, 30568])).
% 29.85/20.08 tff(30572,plain,
% 29.85/20.08 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | ((c1 = c4) | (f10(c1) = c3) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1)) | (~(f1(f10(c1), c1) = c1)) | (~big_f(f10(c1), f1(f10(c1), c1))))),
% 29.85/20.08 inference(quant_inst,[status(thm)],[])).
% 29.85/20.08 tff(30573,plain,
% 29.85/20.08 ((~![X11: $i, X13: $i, X10: $i, X2: $i] : ((X2 = c4) | (X10 = c3) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (~(f1(X10, X11) = X11)) | (~big_f(X10, f1(X10, X11))))) | (c1 = c4) | (f10(c1) = c3) | (~(f1(f10(c1), c1) = c1)) | (~big_f(f10(c1), f1(f10(c1), c1))) | (~(f3(c1, f10(c1)) = f10(c1))) | (~big_f(f3(c1, f10(c1)), c1))),
% 29.85/20.08 inference(modus_ponens,[status(thm)],[30572, 30571])).
% 29.85/20.08 tff(30574,plain,
% 29.85/20.08 ($false),
% 29.85/20.08 inference(unit_resolution,[status(thm)],[30573, 933, 482, 30486, 30567, 30565, 30548, 30544])).
% 29.85/20.08 tff(30575,plain,((c1 = c4) | (f10(c1) = c1) | big_f(f10(c1), f10(c1)) | (~big_f(c2, c1)) | big_f(c1, c1) | (~(f10(c2) = c1)) | (~(c2 = f8(c2)))), inference(lemma,lemma(discharge,[]))).
% 29.85/20.08 tff(30576,plain,
% 29.85/20.08 (c1 = c4),
% 29.85/20.08 inference(unit_resolution,[status(thm)],[30575, 3, 26001, 30420, 66, 30399, 30398])).
% 29.85/20.08 tff(30577,plain,
% 29.85/20.08 (c4 = c1),
% 29.85/20.08 inference(symmetry,[status(thm)],[30576])).
% 29.85/20.08 tff(30578,plain,
% 29.85/20.08 ((f10(c1) = c4) <=> (f10(c1) = c1)),
% 29.85/20.08 inference(monotonicity,[status(thm)],[30577])).
% 29.85/20.08 tff(30579,plain,
% 29.85/20.08 ((f10(c1) = c1) <=> (f10(c1) = c4)),
% 29.85/20.08 inference(symmetry,[status(thm)],[30578])).
% 29.85/20.08 tff(30580,plain,
% 29.85/20.08 ((f10(c1) = c1) <=> (c2 = c4)),
% 29.85/20.08 inference(transitivity,[status(thm)],[30579, 30362])).
% 29.85/20.08 tff(30581,plain,
% 29.85/20.08 ((~(f10(c1) = c1)) <=> (~(c2 = c4))),
% 29.85/20.08 inference(monotonicity,[status(thm)],[30580])).
% 29.85/20.08 tff(30582,plain,
% 29.85/20.08 (~(c2 = c4)),
% 29.85/20.08 inference(modus_ponens,[status(thm)],[3, 30581])).
% 29.85/20.08 tff(30583,plain,
% 29.85/20.08 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))),
% 29.85/20.08 inference(rewrite,[status(thm)],[])).
% 29.85/20.08 tff(30584,plain,
% 29.85/20.08 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))),
% 29.85/20.08 inference(quant_inst,[status(thm)],[])).
% 29.85/20.08 tff(30585,plain,
% 29.85/20.08 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2))))),
% 29.85/20.08 inference(modus_ponens,[status(thm)],[30584, 30583])).
% 29.85/20.08 tff(30586,plain,
% 29.85/20.08 ((c1 = f8(c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2)))),
% 29.85/20.08 inference(unit_resolution,[status(thm)],[30585, 2730, 25791, 3, 30400, 30373])).
% 29.85/20.08 tff(30587,plain,
% 29.85/20.08 (~(f6(c1, f6(c1, c2)) = f6(c1, c2))),
% 29.85/20.08 inference(unit_resolution,[status(thm)],[30586, 9806])).
% 29.85/20.08 tff(30588,plain,
% 29.85/20.08 (~(f6(c1, c2) = c2)),
% 29.85/20.08 inference(unit_resolution,[status(thm)],[43, 30587])).
% 29.85/20.08 tff(30589,plain,
% 29.85/20.08 (f6(c1, c2) = c1),
% 29.85/20.08 inference(unit_resolution,[status(thm)],[48, 30588])).
% 29.85/20.08 tff(30590,plain,
% 29.85/20.08 (big_f(c1, f6(c1, c2)) <=> big_f(c1, c1)),
% 29.85/20.08 inference(monotonicity,[status(thm)],[30589])).
% 29.85/20.08 tff(30591,plain,
% 29.85/20.08 (big_f(c1, c1) <=> big_f(c1, f6(c1, c2))),
% 29.85/20.08 inference(symmetry,[status(thm)],[30590])).
% 29.85/20.08 tff(30592,plain,
% 29.85/20.08 ((~big_f(c1, c1)) <=> (~big_f(c1, f6(c1, c2)))),
% 29.85/20.08 inference(monotonicity,[status(thm)],[30591])).
% 29.85/20.08 tff(30593,plain,
% 29.85/20.08 (~big_f(c1, f6(c1, c2))),
% 29.85/20.08 inference(modus_ponens,[status(thm)],[66, 30592])).
% 29.85/20.08 tff(30594,plain,
% 29.85/20.08 ((f10(c1) = c1) | (c1 = f8(c1)) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2)),
% 29.85/20.08 inference(unit_resolution,[status(thm)],[29205, 30354])).
% 29.85/20.08 tff(30595,plain,
% 29.85/20.08 (big_f(f7(c1), f6(c1, c2))),
% 29.85/20.08 inference(unit_resolution,[status(thm)],[30594, 30588, 3, 9806])).
% 29.85/20.08 tff(30596,plain,
% 29.85/20.08 (big_f(c1, f6(c1, c2))),
% 29.85/20.08 inference(modus_ponens,[status(thm)],[30595, 25792])).
% 29.85/20.08 tff(30597,plain,
% 29.85/20.08 ($false),
% 29.85/20.08 inference(unit_resolution,[status(thm)],[30596, 30593])).
% 29.85/20.08 tff(30598,plain,((c1 = f8(c1)) | big_f(c1, c1) | (f10(c1) = c1) | (~big_f(f7(c1), f6(c1, f6(c1, c2))))), inference(lemma,lemma(discharge,[]))).
% 29.85/20.08 tff(30599,plain,
% 29.85/20.08 (c1 = f8(c1)),
% 29.85/20.08 inference(unit_resolution,[status(thm)],[30598, 3, 66, 30373])).
% 29.85/20.08 tff(30600,plain,
% 29.85/20.08 (~(c2 = f8(c1))),
% 29.85/20.08 inference(unit_resolution,[status(thm)],[29202, 30599])).
% 29.85/20.08 tff(30601,plain,
% 29.85/20.08 (~(f8(c1) = c2)),
% 29.85/20.08 inference(unit_resolution,[status(thm)],[1675, 30600])).
% 29.85/20.08 tff(30602,plain,
% 29.85/20.08 (f8(c1) = c1),
% 29.85/20.08 inference(unit_resolution,[status(thm)],[1680, 30601])).
% 29.85/20.08 tff(30603,plain,
% 29.85/20.08 ((c1 = c3) <=> (c1 = f10(c1))),
% 29.85/20.08 inference(monotonicity,[status(thm)],[27266])).
% 29.85/20.08 tff(30604,plain,
% 29.85/20.08 ((c1 = c3) <=> (f10(c1) = c1)),
% 29.85/20.08 inference(transitivity,[status(thm)],[30603, 18819])).
% 29.85/20.08 tff(30605,plain,
% 29.85/20.08 ((f10(c1) = c1) <=> (c1 = c3)),
% 29.85/20.08 inference(symmetry,[status(thm)],[30604])).
% 29.85/20.08 tff(30606,plain,
% 29.85/20.08 ((~(f10(c1) = c1)) <=> (~(c1 = c3))),
% 29.85/20.08 inference(monotonicity,[status(thm)],[30605])).
% 29.85/20.08 tff(30607,plain,
% 29.85/20.08 (~(c1 = c3)),
% 29.85/20.08 inference(modus_ponens,[status(thm)],[3, 30606])).
% 29.85/20.08 tff(30608,plain,
% 29.85/20.08 (big_f(f10(c1), c1)),
% 29.85/20.08 inference(modus_ponens,[status(thm)],[30420, 27296])).
% 29.85/20.08 tff(30609,plain,
% 29.85/20.08 (c1 = c4),
% 29.85/20.08 inference(unit_resolution,[status(thm)],[30477, 30607, 15, 66, 30608, 67, 30399, 30398])).
% 29.85/20.08 tff(30610,plain,
% 29.85/20.08 (c4 = c1),
% 29.85/20.08 inference(symmetry,[status(thm)],[30609])).
% 29.85/20.08 tff(30611,plain,
% 29.85/20.08 ((~(c4 = c2)) | (c1 = c3) | big_f(c2, c2) | big_f(c1, c1) | (~(f4(c4) = c2))),
% 29.85/20.08 inference(unit_resolution,[status(thm)],[13490, 30354])).
% 29.85/20.08 tff(30612,plain,
% 29.85/20.08 (~(c4 = c2)),
% 29.85/20.08 inference(unit_resolution,[status(thm)],[30611, 79, 168, 121, 66])).
% 29.85/20.08 tff(30613,plain,
% 29.85/20.08 (c4 = c1),
% 29.85/20.08 inference(unit_resolution,[status(thm)],[461, 30612])).
% 29.85/20.08 tff(30614,plain,
% 29.85/20.08 ((f10(c1) = c4) <=> (f10(c1) = c1)),
% 29.85/20.08 inference(monotonicity,[status(thm)],[30613])).
% 29.85/20.08 tff(30615,plain,
% 29.85/20.08 ((f10(c1) = c1) <=> (f10(c1) = c4)),
% 29.85/20.08 inference(symmetry,[status(thm)],[30614])).
% 29.85/20.08 tff(30616,plain,
% 29.85/20.08 ((f10(c1) = c1) <=> (c2 = c4)),
% 29.85/20.08 inference(transitivity,[status(thm)],[30615, 30362])).
% 29.85/20.08 tff(30617,plain,
% 29.85/20.08 ((~(f10(c1) = c1)) <=> (~(c2 = c4))),
% 29.85/20.08 inference(monotonicity,[status(thm)],[30616])).
% 29.85/20.08 tff(30618,plain,
% 29.85/20.08 (~(c2 = c4)),
% 29.85/20.08 inference(modus_ponens,[status(thm)],[3, 30617])).
% 29.85/20.08 tff(30619,plain,
% 29.85/20.08 (big_f(f3(c2, c1), c2) | (c2 = c4) | (c1 = c3) | big_f(c1, c1)),
% 29.85/20.08 inference(unit_resolution,[status(thm)],[29111, 30354])).
% 29.85/20.08 tff(30620,plain,
% 29.85/20.08 (big_f(f3(c2, c1), c2)),
% 29.85/20.08 inference(unit_resolution,[status(thm)],[30619, 30618, 168, 66])).
% 29.85/20.08 tff(30621,plain,
% 29.85/20.08 ((f3(c2, c1) = f8(c1)) <=> (f3(c2, c1) = c1)),
% 29.85/20.08 inference(monotonicity,[status(thm)],[3018])).
% 29.85/20.08 tff(30622,plain,
% 29.85/20.08 (big_f(f3(c2, c1), f10(c1))),
% 29.85/20.08 inference(modus_ponens,[status(thm)],[30620, 28986])).
% 29.85/20.08 tff(30623,plain,
% 29.85/20.08 ((~big_f(c1, c1)) <=> (~big_f(c1, f6(c1, c2)))),
% 29.85/20.08 inference(monotonicity,[status(thm)],[25795])).
% 29.85/20.08 tff(30624,plain,
% 29.85/20.08 (~big_f(c1, f6(c1, c2))),
% 29.85/20.08 inference(modus_ponens,[status(thm)],[66, 30623])).
% 29.85/20.08 tff(30625,plain,
% 29.85/20.08 (~(f6(c1, f10(c1)) = f10(c1))),
% 29.85/20.08 inference(unit_resolution,[status(thm)],[28849, 114, 15])).
% 29.85/20.08 tff(30626,plain,
% 29.85/20.08 ((c1 = c3) | (f10(c1) = c1) | (f6(c1, f10(c1)) = f10(c1)) | big_f(f7(c1), f6(c1, f10(c1))) | big_f(c1, c1) | big_f(c2, c2) | (~(f4(c4) = c2))),
% 29.85/20.08 inference(unit_resolution,[status(thm)],[28947, 30354])).
% 29.85/20.08 tff(30627,plain,
% 29.85/20.08 (big_f(f7(c1), f6(c1, f10(c1)))),
% 29.85/20.08 inference(unit_resolution,[status(thm)],[30626, 30625, 121, 168, 66, 79, 3])).
% 29.85/20.08 tff(30628,plain,
% 29.85/20.08 (big_f(c1, f6(c1, c2))),
% 29.85/20.08 inference(modus_ponens,[status(thm)],[30627, 30413])).
% 29.85/20.08 tff(30629,plain,
% 29.85/20.08 ($false),
% 29.85/20.08 inference(unit_resolution,[status(thm)],[30628, 30624])).
% 29.85/20.08 tff(30630,plain,((f6(c1, c2) = c2) | big_f(c1, c1) | big_f(c2, c2) | (c1 = c3) | (~(f4(c4) = c2)) | (f10(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.85/20.08 tff(30631,plain,
% 29.85/20.08 (f6(c1, c2) = c2),
% 29.85/20.08 inference(unit_resolution,[status(thm)],[30630, 79, 121, 168, 66, 3])).
% 29.85/20.08 tff(30632,plain,
% 29.85/20.08 (f6(c1, f6(c1, c2)) = f6(c1, c2)),
% 29.85/20.08 inference(unit_resolution,[status(thm)],[43, 30631])).
% 29.85/20.08 tff(30633,plain,
% 29.85/20.08 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))) | (f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))) | (f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1))))),
% 29.85/20.08 inference(rewrite,[status(thm)],[])).
% 29.85/20.08 tff(30634,plain,
% 29.85/20.08 (((f10(c1) = c1) | (f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1))) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2))))) <=> ((f10(c1) = c1) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))) | (f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1))))),
% 29.85/20.08 inference(rewrite,[status(thm)],[])).
% 29.85/20.08 tff(30635,plain,
% 29.85/20.08 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1))) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))) | (f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1)))))),
% 29.85/20.08 inference(monotonicity,[status(thm)],[30634])).
% 29.85/20.08 tff(30636,plain,
% 29.85/20.08 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1))) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))) | (f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1))))),
% 29.85/20.08 inference(transitivity,[status(thm)],[30635, 30633])).
% 29.85/20.08 tff(30637,plain,
% 29.85/20.08 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1))) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))),
% 29.85/20.08 inference(quant_inst,[status(thm)],[])).
% 29.85/20.08 tff(30638,plain,
% 29.85/20.08 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))) | (f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1)))),
% 29.85/20.08 inference(modus_ponens,[status(thm)],[30637, 30636])).
% 29.85/20.08 tff(30639,plain,
% 29.85/20.08 ((~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1)))),
% 29.85/20.08 inference(unit_resolution,[status(thm)],[30638, 2730, 25791, 3, 30373])).
% 29.85/20.08 tff(30640,plain,
% 29.85/20.08 (f3(c2, c1) = f8(c1)),
% 29.85/20.08 inference(unit_resolution,[status(thm)],[30639, 30632, 30622])).
% 29.85/20.08 tff(30641,plain,
% 29.85/20.08 (f3(c2, c1) = c1),
% 29.85/20.08 inference(modus_ponens,[status(thm)],[30640, 30621])).
% 29.85/20.08 tff(30642,plain,
% 29.85/20.08 (f1(c1, c2) = c2),
% 29.85/20.08 inference(unit_resolution,[status(thm)],[29126, 30641, 30618, 30620, 168, 66])).
% 29.85/20.08 tff(30643,plain,
% 29.85/20.08 (f1(c1, f10(c1)) = f10(c1)),
% 29.85/20.08 inference(transitivity,[status(thm)],[28860, 30642, 5571])).
% 29.85/20.08 tff(30644,plain,
% 29.85/20.08 (big_f(c1, f1(c1, f10(c1))) <=> big_f(c1, f10(c1))),
% 29.85/20.08 inference(monotonicity,[status(thm)],[30643])).
% 29.85/20.08 tff(30645,plain,
% 29.85/20.08 (big_f(c1, f10(c1)) <=> big_f(c1, f1(c1, f10(c1)))),
% 29.85/20.08 inference(symmetry,[status(thm)],[30644])).
% 29.85/20.08 tff(30646,plain,
% 29.85/20.08 (big_f(c1, f1(c1, f10(c1)))),
% 29.85/20.08 inference(modus_ponens,[status(thm)],[30400, 30645])).
% 29.85/20.08 tff(30647,plain,
% 29.85/20.08 (f1(c1, f10(c1)) = f10(c1)),
% 29.85/20.08 inference(unit_resolution,[status(thm)],[28913, 30642, 15])).
% 29.85/20.08 tff(30648,plain,
% 29.85/20.08 (f3(f10(c1), c1) = f3(c2, c1)),
% 29.85/20.08 inference(monotonicity,[status(thm)],[15])).
% 29.85/20.08 tff(30649,plain,
% 29.85/20.08 (big_f(f3(f10(c1), c1), f10(c1)) <=> big_f(f3(c2, c1), c2)),
% 29.85/20.08 inference(monotonicity,[status(thm)],[30648, 15])).
% 29.85/20.08 tff(30650,plain,
% 29.85/20.08 (big_f(f3(c2, c1), c2) <=> big_f(f3(f10(c1), c1), f10(c1))),
% 29.85/20.08 inference(symmetry,[status(thm)],[30649])).
% 29.85/20.08 tff(30651,plain,
% 29.85/20.09 (big_f(f3(f10(c1), c1), f10(c1))),
% 29.85/20.09 inference(modus_ponens,[status(thm)],[30620, 30650])).
% 29.85/20.09 tff(30652,plain,
% 29.85/20.09 ((f3(f10(c1), c1) = c1) <=> (f3(c2, c1) = c1)),
% 29.85/20.09 inference(monotonicity,[status(thm)],[30648])).
% 29.85/20.09 tff(30653,plain,
% 29.85/20.09 ((f3(c2, c1) = c1) <=> (f3(f10(c1), c1) = c1)),
% 29.85/20.09 inference(symmetry,[status(thm)],[30652])).
% 29.85/20.09 tff(30654,plain,
% 29.85/20.09 ((f3(c2, c1) = f8(c1)) <=> (f3(f10(c1), c1) = c1)),
% 29.85/20.09 inference(transitivity,[status(thm)],[30621, 30653])).
% 29.85/20.09 tff(30655,plain,
% 29.85/20.09 (f3(f10(c1), c1) = c1),
% 29.85/20.09 inference(modus_ponens,[status(thm)],[30640, 30654])).
% 29.85/20.09 tff(30656,plain,
% 29.85/20.09 ((~(f10(c1) = c1)) <=> (~(f10(c1) = c4))),
% 29.85/20.09 inference(monotonicity,[status(thm)],[30615])).
% 29.85/20.09 tff(30657,plain,
% 29.85/20.09 (~(f10(c1) = c4)),
% 29.85/20.09 inference(modus_ponens,[status(thm)],[3, 30656])).
% 29.85/20.09 tff(30658,plain,
% 29.85/20.09 (~big_f(c1, f1(c1, f10(c1)))),
% 29.85/20.09 inference(unit_resolution,[status(thm)],[28943, 933, 168, 30657, 30655, 30651, 30647])).
% 29.85/20.09 tff(30659,plain,
% 29.85/20.09 ($false),
% 29.85/20.09 inference(unit_resolution,[status(thm)],[30658, 30646])).
% 29.85/20.09 tff(30660,plain,((~(f4(c4) = c2)) | (c1 = c3) | big_f(c1, c1) | (~(f8(c1) = c1)) | (f10(c1) = c1) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 29.85/20.09 tff(30661,plain,
% 29.85/20.09 (~(f4(c4) = c2)),
% 29.85/20.09 inference(unit_resolution,[status(thm)],[30660, 30607, 66, 3018, 3, 30373, 121])).
% 29.85/20.09 tff(30662,plain,
% 29.85/20.09 (f4(c4) = c1),
% 29.85/20.09 inference(unit_resolution,[status(thm)],[11750, 30661])).
% 29.85/20.09 tff(30663,plain,
% 29.85/20.09 (big_f(f4(c4), c4) <=> big_f(c1, c1)),
% 29.85/20.09 inference(monotonicity,[status(thm)],[30662, 30610])).
% 29.85/20.09 tff(30664,plain,
% 29.85/20.09 (big_f(c1, c1) <=> big_f(f4(c4), c4)),
% 29.85/20.09 inference(symmetry,[status(thm)],[30663])).
% 29.85/20.09 tff(30665,plain,
% 29.85/20.09 ((~big_f(c1, c1)) <=> (~big_f(f4(c4), c4))),
% 29.85/20.09 inference(monotonicity,[status(thm)],[30664])).
% 29.85/20.09 tff(30666,plain,
% 29.85/20.09 (~big_f(f4(c4), c4)),
% 29.85/20.09 inference(modus_ponens,[status(thm)],[66, 30665])).
% 29.85/20.09 tff(30667,plain,
% 29.85/20.09 ((~(f1(c1, c2) = c2)) | (c1 = c3) | big_f(f4(c4), c4)),
% 29.85/20.09 inference(unit_resolution,[status(thm)],[21246, 30354])).
% 29.85/20.09 tff(30668,plain,
% 29.85/20.09 (~(f1(c1, c2) = c2)),
% 29.85/20.09 inference(unit_resolution,[status(thm)],[30667, 30666, 30607])).
% 29.85/20.09 tff(30669,plain,
% 29.85/20.09 (f1(c1, c2) = c1),
% 29.85/20.09 inference(unit_resolution,[status(thm)],[841, 30668])).
% 29.85/20.09 tff(30670,plain,
% 29.85/20.09 (f1(c1, f10(c1)) = c1),
% 29.85/20.09 inference(transitivity,[status(thm)],[28860, 30669])).
% 29.85/20.09 tff(30671,plain,
% 29.85/20.09 (big_f(c1, f1(c1, f10(c1))) <=> big_f(c1, c1)),
% 29.85/20.09 inference(monotonicity,[status(thm)],[30670])).
% 29.85/20.09 tff(30672,plain,
% 29.85/20.09 (big_f(c1, c1) <=> big_f(c1, f1(c1, f10(c1)))),
% 29.85/20.09 inference(symmetry,[status(thm)],[30671])).
% 29.85/20.09 tff(30673,plain,
% 29.85/20.09 ((~big_f(c1, c1)) <=> (~big_f(c1, f1(c1, f10(c1))))),
% 29.85/20.09 inference(monotonicity,[status(thm)],[30672])).
% 29.85/20.09 tff(30674,plain,
% 29.85/20.09 (~big_f(c1, f1(c1, f10(c1)))),
% 29.85/20.09 inference(modus_ponens,[status(thm)],[66, 30673])).
% 29.85/20.09 tff(30675,plain,
% 29.85/20.09 (f1(c1, c2) = f1(c1, f10(c1))),
% 29.85/20.09 inference(symmetry,[status(thm)],[28860])).
% 29.85/20.09 tff(30676,plain,
% 29.85/20.09 ((f1(c1, c2) = c2) <=> (f1(c1, f10(c1)) = f10(c1))),
% 29.85/20.09 inference(monotonicity,[status(thm)],[30675, 5571])).
% 29.85/20.09 tff(30677,plain,
% 29.85/20.09 ((~(f1(c1, c2) = c2)) <=> (~(f1(c1, f10(c1)) = f10(c1)))),
% 29.85/20.09 inference(monotonicity,[status(thm)],[30676])).
% 29.85/20.09 tff(30678,plain,
% 29.85/20.09 (~(f1(c1, f10(c1)) = f10(c1))),
% 29.85/20.09 inference(modus_ponens,[status(thm)],[30668, 30677])).
% 29.85/20.09 tff(30679,plain,
% 29.85/20.09 (f4(c1) = f4(c4)),
% 29.85/20.09 inference(monotonicity,[status(thm)],[30609])).
% 29.85/20.09 tff(30680,plain,
% 29.85/20.09 (f4(c4) = f4(c1)),
% 29.85/20.09 inference(symmetry,[status(thm)],[30679])).
% 29.85/20.09 tff(30681,plain,
% 29.85/20.09 (c1 = f4(c4)),
% 29.85/20.09 inference(symmetry,[status(thm)],[30662])).
% 29.85/20.09 tff(30682,plain,
% 29.85/20.09 (c1 = f4(c1)),
% 29.85/20.09 inference(transitivity,[status(thm)],[30681, 30680])).
% 29.85/20.09 tff(30683,plain,
% 29.85/20.09 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c1 = c3) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (f1(c1, f10(c1)) = f10(c1)) | big_f(c1, f1(c1, f10(c1))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (c1 = c3) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (f1(c1, f10(c1)) = f10(c1)) | big_f(c1, f1(c1, f10(c1))))),
% 29.85/20.09 inference(rewrite,[status(thm)],[])).
% 29.85/20.09 tff(30684,plain,
% 29.85/20.09 (((c1 = c3) | (f1(c1, f10(c1)) = f10(c1)) | big_f(c1, f1(c1, f10(c1))) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1)))) <=> ((c1 = c3) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (f1(c1, f10(c1)) = f10(c1)) | big_f(c1, f1(c1, f10(c1))))),
% 29.85/20.09 inference(rewrite,[status(thm)],[])).
% 29.85/20.09 tff(30685,plain,
% 29.85/20.09 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c1 = c3) | (f1(c1, f10(c1)) = f10(c1)) | big_f(c1, f1(c1, f10(c1))) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c1 = c3) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (f1(c1, f10(c1)) = f10(c1)) | big_f(c1, f1(c1, f10(c1)))))),
% 29.85/20.09 inference(monotonicity,[status(thm)],[30684])).
% 29.85/20.09 tff(30686,plain,
% 29.85/20.09 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c1 = c3) | (f1(c1, f10(c1)) = f10(c1)) | big_f(c1, f1(c1, f10(c1))) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (c1 = c3) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (f1(c1, f10(c1)) = f10(c1)) | big_f(c1, f1(c1, f10(c1))))),
% 29.85/20.09 inference(transitivity,[status(thm)],[30685, 30683])).
% 29.85/20.09 tff(30687,plain,
% 29.85/20.09 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c1 = c3) | (f1(c1, f10(c1)) = f10(c1)) | big_f(c1, f1(c1, f10(c1))) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))))),
% 29.85/20.09 inference(quant_inst,[status(thm)],[])).
% 29.85/20.09 tff(30688,plain,
% 29.85/20.09 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (c1 = c3) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (f1(c1, f10(c1)) = f10(c1)) | big_f(c1, f1(c1, f10(c1)))),
% 29.85/20.09 inference(modus_ponens,[status(thm)],[30687, 30686])).
% 29.85/20.09 tff(30689,plain,
% 29.85/20.09 (big_f(c1, f1(c1, f10(c1)))),
% 29.85/20.09 inference(unit_resolution,[status(thm)],[30688, 402, 30607, 30609, 30682, 66, 30678])).
% 29.85/20.09 tff(30690,plain,
% 29.85/20.09 ($false),
% 29.85/20.09 inference(unit_resolution,[status(thm)],[30689, 30674])).
% 29.85/20.09 tff(30691,plain,((~(c3 = c2)) | big_f(c1, c1) | (~(f8(c1) = c1)) | (f10(c1) = c1) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 29.85/20.09 tff(30692,plain,
% 29.85/20.09 (~(c3 = c2)),
% 29.85/20.09 inference(unit_resolution,[status(thm)],[30691, 30602, 66, 3, 30373, 121])).
% 29.85/20.09 tff(30693,plain,
% 29.85/20.09 (c3 = c1),
% 29.85/20.09 inference(unit_resolution,[status(thm)],[180, 30692])).
% 29.85/20.09 tff(30694,plain,
% 29.85/20.09 ((f10(c1) = c3) <=> (f10(c1) = c1)),
% 29.85/20.09 inference(monotonicity,[status(thm)],[30693])).
% 29.85/20.09 tff(30695,plain,
% 29.85/20.09 ((f10(c1) = c1) <=> (f10(c1) = c3)),
% 29.85/20.09 inference(symmetry,[status(thm)],[30694])).
% 29.85/20.09 tff(30696,plain,
% 29.85/20.09 ((f10(c1) = c1) <=> (c2 = c3)),
% 29.85/20.09 inference(transitivity,[status(thm)],[30695, 30488])).
% 29.85/20.09 tff(30697,plain,
% 29.85/20.09 ((~(f10(c1) = c1)) <=> (~(c2 = c3))),
% 29.85/20.09 inference(monotonicity,[status(thm)],[30696])).
% 29.85/20.09 tff(30698,plain,
% 29.85/20.09 (~(c2 = c3)),
% 29.85/20.09 inference(modus_ponens,[status(thm)],[3, 30697])).
% 29.85/20.09 tff(30699,plain,
% 29.85/20.09 (big_f(f3(c2, c1), c2) | (~big_f(c2, c1)) | (c2 = c4) | (c2 = c3) | big_f(f10(c1), f10(c1)) | (~(f10(c1) = c2))),
% 29.85/20.09 inference(unit_resolution,[status(thm)],[29055, 30354])).
% 29.85/20.09 tff(30700,plain,
% 29.85/20.09 (big_f(f3(c2, c1), c2)),
% 29.85/20.09 inference(unit_resolution,[status(thm)],[30699, 30698, 30420, 26001, 15, 30582])).
% 29.85/20.09 tff(30701,plain,
% 29.85/20.09 (f8(c1) = c1),
% 29.85/20.09 inference(symmetry,[status(thm)],[30599])).
% 29.85/20.09 tff(30702,plain,
% 29.85/20.09 ((f3(c2, c1) = f8(c1)) <=> (f3(c2, c1) = c1)),
% 29.85/20.09 inference(monotonicity,[status(thm)],[30701])).
% 29.85/20.09 tff(30703,plain,
% 29.85/20.09 (big_f(f3(c2, c1), f10(c1))),
% 29.85/20.09 inference(modus_ponens,[status(thm)],[30700, 28986])).
% 29.85/20.09 tff(30704,assumption,(big_f(f3(c2, c1), f10(c1))), introduced(assumption)).
% 29.85/20.09 tff(30705,assumption,(~(f3(c2, c1) = f8(c1))), introduced(assumption)).
% 29.85/20.09 tff(30706,plain,
% 29.85/20.09 (~(f6(c1, f6(c1, c2)) = f6(c1, c2))),
% 29.85/20.09 inference(unit_resolution,[status(thm)],[30639, 30705, 30704])).
% 29.85/20.09 tff(30707,plain,
% 29.85/20.09 (~(f6(c1, c2) = c2)),
% 29.85/20.09 inference(unit_resolution,[status(thm)],[43, 30706])).
% 29.85/20.09 tff(30708,plain,
% 29.85/20.09 (f6(c1, c2) = c1),
% 29.85/20.09 inference(unit_resolution,[status(thm)],[48, 30707])).
% 29.85/20.09 tff(30709,plain,
% 29.85/20.09 (big_f(c1, f6(c1, c2)) <=> big_f(c1, c1)),
% 29.85/20.09 inference(monotonicity,[status(thm)],[30708])).
% 29.85/20.09 tff(30710,plain,
% 29.85/20.09 (big_f(c1, c1) <=> big_f(c1, f6(c1, c2))),
% 29.85/20.09 inference(symmetry,[status(thm)],[30709])).
% 29.85/20.09 tff(30711,plain,
% 29.85/20.09 ((~big_f(c1, c1)) <=> (~big_f(c1, f6(c1, c2)))),
% 29.85/20.09 inference(monotonicity,[status(thm)],[30710])).
% 29.85/20.09 tff(30712,plain,
% 29.85/20.09 (~big_f(c1, f6(c1, c2))),
% 29.85/20.09 inference(modus_ponens,[status(thm)],[66, 30711])).
% 29.85/20.09 tff(30713,plain,
% 29.85/20.09 (~(f6(c1, f10(c1)) = f10(c1))),
% 29.85/20.09 inference(unit_resolution,[status(thm)],[28849, 30707, 15])).
% 29.85/20.09 tff(30714,plain,
% 29.85/20.09 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, f10(c1))) | (f6(c1, f10(c1)) = f10(c1)) | (f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c1) = c1) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, f10(c1))) | (f6(c1, f10(c1)) = f10(c1)) | (f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1))))),
% 29.85/20.09 inference(rewrite,[status(thm)],[])).
% 29.85/20.09 tff(30715,plain,
% 29.85/20.09 (((f10(c1) = c1) | (f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1))) | (~(f7(c1) = c1)) | (f6(c1, f10(c1)) = f10(c1)) | big_f(f7(c1), f6(c1, f10(c1)))) <=> ((f10(c1) = c1) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, f10(c1))) | (f6(c1, f10(c1)) = f10(c1)) | (f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1))))),
% 29.85/20.09 inference(rewrite,[status(thm)],[])).
% 29.85/20.09 tff(30716,plain,
% 29.85/20.09 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1))) | (~(f7(c1) = c1)) | (f6(c1, f10(c1)) = f10(c1)) | big_f(f7(c1), f6(c1, f10(c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, f10(c1))) | (f6(c1, f10(c1)) = f10(c1)) | (f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1)))))),
% 29.85/20.09 inference(monotonicity,[status(thm)],[30715])).
% 29.85/20.09 tff(30717,plain,
% 29.85/20.09 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1))) | (~(f7(c1) = c1)) | (f6(c1, f10(c1)) = f10(c1)) | big_f(f7(c1), f6(c1, f10(c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c1) = c1) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, f10(c1))) | (f6(c1, f10(c1)) = f10(c1)) | (f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1))))),
% 29.85/20.09 inference(transitivity,[status(thm)],[30716, 30714])).
% 29.85/20.09 tff(30718,plain,
% 29.85/20.09 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1))) | (~(f7(c1) = c1)) | (f6(c1, f10(c1)) = f10(c1)) | big_f(f7(c1), f6(c1, f10(c1))))),
% 29.85/20.09 inference(quant_inst,[status(thm)],[])).
% 29.85/20.09 tff(30719,plain,
% 29.85/20.09 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c1) = c1) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, f10(c1))) | (f6(c1, f10(c1)) = f10(c1)) | (f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1)))),
% 29.85/20.09 inference(modus_ponens,[status(thm)],[30718, 30717])).
% 29.85/20.09 tff(30720,plain,
% 29.85/20.09 (big_f(f7(c1), f6(c1, f10(c1))) | (f6(c1, f10(c1)) = f10(c1)) | (f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1)))),
% 29.85/20.09 inference(unit_resolution,[status(thm)],[30719, 2662, 25791, 3])).
% 29.85/20.09 tff(30721,plain,
% 29.85/20.09 (big_f(f7(c1), f6(c1, f10(c1)))),
% 29.85/20.09 inference(unit_resolution,[status(thm)],[30720, 30713, 30705, 30704])).
% 29.85/20.09 tff(30722,plain,
% 29.85/20.09 (big_f(c1, f6(c1, c2))),
% 29.85/20.09 inference(modus_ponens,[status(thm)],[30721, 30413])).
% 29.85/20.09 tff(30723,plain,
% 29.85/20.09 ($false),
% 29.85/20.09 inference(unit_resolution,[status(thm)],[30722, 30712])).
% 29.85/20.09 tff(30724,plain,((f3(c2, c1) = f8(c1)) | big_f(c1, c1) | (~big_f(f3(c2, c1), f10(c1))) | (f10(c1) = c1) | (~big_f(f7(c1), f6(c1, f6(c1, c2))))), inference(lemma,lemma(discharge,[]))).
% 29.85/20.09 tff(30725,plain,
% 29.85/20.09 (f3(c2, c1) = f8(c1)),
% 29.85/20.09 inference(unit_resolution,[status(thm)],[30724, 30703, 66, 3, 30373])).
% 29.85/20.09 tff(30726,plain,
% 29.85/20.09 (f3(c2, c1) = c1),
% 29.85/20.09 inference(modus_ponens,[status(thm)],[30725, 30702])).
% 29.85/20.09 tff(30727,plain,
% 29.85/20.09 (f1(c2, c1) = c1),
% 29.85/20.09 inference(unit_resolution,[status(thm)],[29075, 30726, 30698, 30700, 30582, 121])).
% 29.85/20.09 tff(30728,plain,
% 29.85/20.09 (f1(f10(c1), c1) = c1),
% 29.85/20.09 inference(transitivity,[status(thm)],[30357, 30727])).
% 29.85/20.09 tff(30729,plain,
% 29.85/20.09 (big_f(f10(c1), f1(f10(c1), c1)) <=> big_f(f10(c1), c1)),
% 29.85/20.09 inference(monotonicity,[status(thm)],[30728])).
% 29.85/20.09 tff(30730,plain,
% 29.85/20.09 (big_f(f10(c1), c1) <=> big_f(f10(c1), f1(f10(c1), c1))),
% 29.85/20.09 inference(symmetry,[status(thm)],[30729])).
% 29.85/20.09 tff(30731,plain,
% 29.85/20.09 (big_f(f10(c1), f1(f10(c1), c1))),
% 29.85/20.09 inference(modus_ponens,[status(thm)],[30608, 30730])).
% 29.85/20.09 tff(30732,plain,
% 29.85/20.09 ((~big_f(c2, f1(c2, c1))) <=> (~big_f(f10(c1), f1(f10(c1), c1)))),
% 29.85/20.09 inference(monotonicity,[status(thm)],[30359])).
% 29.85/20.09 tff(30733,plain,
% 29.85/20.09 (~big_f(c2, f1(c2, c1))),
% 29.85/20.09 inference(unit_resolution,[status(thm)],[28982, 30727, 30700, 30726, 30582, 30698])).
% 29.85/20.09 tff(30734,plain,
% 29.85/20.09 (~big_f(f10(c1), f1(f10(c1), c1))),
% 29.85/20.09 inference(modus_ponens,[status(thm)],[30733, 30732])).
% 29.85/20.09 tff(30735,plain,
% 29.85/20.09 ($false),
% 29.85/20.09 inference(unit_resolution,[status(thm)],[30734, 30731])).
% 29.85/20.09 tff(30736,plain,((f10(c1) = c1) | big_f(c2, c2) | big_f(c1, c1) | (~big_f(f7(c1), f6(c1, f6(c1, c2))))), inference(lemma,lemma(discharge,[]))).
% 29.85/20.09 tff(30737,plain,
% 29.85/20.09 (~big_f(f7(c1), f6(c1, f6(c1, c2)))),
% 29.85/20.09 inference(unit_resolution,[status(thm)],[30736, 121, 66, 3])).
% 29.85/20.09 tff(30738,plain,
% 29.85/20.09 (big_f(f7(c1), f6(c1, f6(c1, c2)))),
% 29.85/20.09 inference(modus_ponens,[status(thm)],[30354, 25852])).
% 29.85/20.09 tff(30739,plain,
% 29.85/20.09 ($false),
% 29.85/20.09 inference(unit_resolution,[status(thm)],[24985, 30738])).
% 29.85/20.09 tff(30740,plain,((~(f6(c1, c2) = c2)) | big_f(f7(c1), f6(c1, f6(c1, c2)))), inference(lemma,lemma(discharge,[]))).
% 29.85/20.09 tff(30741,plain,
% 29.85/20.09 (~(f6(c1, c2) = c2)),
% 29.85/20.09 inference(unit_resolution,[status(thm)],[30740, 30737])).
% 29.85/20.09 tff(30742,plain,
% 29.85/20.09 (f6(c1, c2) = c1),
% 29.85/20.09 inference(unit_resolution,[status(thm)],[48, 30741])).
% 29.85/20.09 tff(30743,plain,
% 29.85/20.09 (f6(c1, f10(c1)) = c1),
% 29.85/20.09 inference(transitivity,[status(thm)],[29657, 30742])).
% 29.85/20.09 tff(30744,plain,
% 29.85/20.09 (big_f(f7(c1), f6(c1, f10(c1))) <=> big_f(c1, c1)),
% 29.85/20.09 inference(monotonicity,[status(thm)],[25791, 30743])).
% 29.85/20.09 tff(30745,plain,
% 29.85/20.09 (big_f(c1, c1) <=> big_f(f7(c1), f6(c1, f10(c1)))),
% 29.85/20.09 inference(symmetry,[status(thm)],[30744])).
% 29.85/20.09 tff(30746,plain,
% 29.85/20.09 ((~big_f(c1, c1)) <=> (~big_f(f7(c1), f6(c1, f10(c1))))),
% 29.85/20.09 inference(monotonicity,[status(thm)],[30745])).
% 29.85/20.09 tff(30747,plain,
% 29.85/20.09 (~big_f(f7(c1), f6(c1, f10(c1)))),
% 29.85/20.09 inference(modus_ponens,[status(thm)],[66, 30746])).
% 29.85/20.09 tff(30748,plain,
% 29.85/20.09 (~(f6(c1, f10(c1)) = f10(c1))),
% 29.85/20.09 inference(unit_resolution,[status(thm)],[28849, 30741, 15])).
% 29.85/20.09 tff(30749,plain,
% 29.85/20.09 (f10(f10(c1)) = c1),
% 29.85/20.09 inference(transitivity,[status(thm)],[24860, 30399])).
% 29.85/20.09 tff(30750,plain,
% 29.85/20.09 (big_f(c1, f10(f10(c1))) <=> big_f(c1, c1)),
% 29.85/20.09 inference(monotonicity,[status(thm)],[30749])).
% 29.85/20.09 tff(30751,plain,
% 29.85/20.09 (big_f(c1, c1) <=> big_f(c1, f10(f10(c1)))),
% 29.85/20.09 inference(symmetry,[status(thm)],[30750])).
% 29.85/20.09 tff(30752,plain,
% 29.85/20.09 ((~big_f(c1, c1)) <=> (~big_f(c1, f10(f10(c1))))),
% 29.85/20.09 inference(monotonicity,[status(thm)],[30751])).
% 29.85/20.09 tff(30753,plain,
% 29.85/20.09 (~big_f(c1, f10(f10(c1)))),
% 29.85/20.09 inference(modus_ponens,[status(thm)],[66, 30752])).
% 29.85/20.09 tff(30754,plain,
% 29.85/20.09 (f10(c2) = f10(f10(c1))),
% 29.85/20.09 inference(symmetry,[status(thm)],[24860])).
% 29.85/20.09 tff(30755,plain,
% 29.85/20.09 ((f10(c2) = c2) <=> (f10(f10(c1)) = f10(c1))),
% 29.85/20.09 inference(monotonicity,[status(thm)],[30754, 5571])).
% 29.85/20.09 tff(30756,plain,
% 29.85/20.09 ((~(f10(c2) = c2)) <=> (~(f10(f10(c1)) = f10(c1)))),
% 29.85/20.09 inference(monotonicity,[status(thm)],[30755])).
% 29.85/20.09 tff(30757,plain,
% 29.85/20.09 (~(f10(f10(c1)) = f10(c1))),
% 29.85/20.09 inference(modus_ponens,[status(thm)],[30375, 30756])).
% 29.85/20.09 tff(30758,plain,
% 29.85/20.09 (~(c1 = f8(f10(c1)))),
% 29.85/20.09 inference(unit_resolution,[status(thm)],[25010, 2994, 25791, 30757, 30753, 30748, 30747])).
% 29.85/20.09 tff(30759,plain,
% 29.85/20.09 (~(f8(f10(c1)) = c1)),
% 29.85/20.09 inference(modus_ponens,[status(thm)],[30758, 30361])).
% 29.85/20.09 tff(30760,plain,
% 29.85/20.09 (f8(f10(c1)) = c2),
% 29.85/20.09 inference(unit_resolution,[status(thm)],[12021, 30759])).
% 29.85/20.09 tff(30761,plain,
% 29.85/20.09 (c2 = c3),
% 29.85/20.09 inference(symmetry,[status(thm)],[30422])).
% 29.85/20.09 tff(30762,plain,
% 29.85/20.09 ((c2 = c1) <=> (c3 = c1)),
% 29.85/20.09 inference(monotonicity,[status(thm)],[30761])).
% 29.85/20.09 tff(30763,plain,
% 29.85/20.09 ((c2 = c1) <=> (c1 = c3)),
% 29.85/20.09 inference(transitivity,[status(thm)],[30762, 68])).
% 29.85/20.09 tff(30764,plain,
% 29.85/20.09 ((~(c2 = c1)) <=> (~(c1 = c3))),
% 29.85/20.09 inference(monotonicity,[status(thm)],[30763])).
% 29.85/20.09 tff(30765,plain,
% 29.85/20.09 (~(c1 = c3)),
% 29.85/20.09 inference(modus_ponens,[status(thm)],[75, 30764])).
% 29.85/20.09 tff(30766,plain,
% 29.85/20.09 (~(f7(c2) = c2)),
% 29.85/20.09 inference(unit_resolution,[status(thm)],[29299, 79, 66])).
% 29.85/20.09 tff(30767,plain,
% 29.85/20.09 ($false),
% 29.85/20.09 inference(unit_resolution,[status(thm)],[10739, 30766, 79, 122])).
% 29.85/20.09 tff(30768,plain,((~(f4(c4) = c2)) | (~(f10(c2) = c2)) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 29.85/20.09 tff(30769,plain,
% 29.85/20.09 (~(f10(c2) = c2)),
% 29.85/20.09 inference(unit_resolution,[status(thm)],[30768, 79, 66])).
% 29.85/20.09 tff(30770,plain,
% 29.85/20.09 (f7(c2) = c1),
% 29.85/20.09 inference(unit_resolution,[status(thm)],[21, 30766])).
% 29.85/20.09 tff(30771,plain,
% 29.85/20.09 (big_f(f7(c2), c2) <=> big_f(c1, c2)),
% 29.85/20.09 inference(monotonicity,[status(thm)],[30770])).
% 29.85/20.09 tff(30772,plain,
% 29.85/20.09 (big_f(c1, c2) <=> big_f(f7(c2), c2)),
% 29.85/20.09 inference(symmetry,[status(thm)],[30771])).
% 29.85/20.09 tff(30773,plain,
% 29.85/20.09 (big_f(f7(c2), c2)),
% 29.85/20.09 inference(modus_ponens,[status(thm)],[30354, 30772])).
% 29.85/20.09 tff(30774,plain,
% 29.85/20.09 (big_f(f7(c2), c1) <=> big_f(c1, c1)),
% 29.85/20.09 inference(monotonicity,[status(thm)],[30770])).
% 29.85/20.09 tff(30775,plain,
% 29.85/20.09 (big_f(c1, c1) <=> big_f(f7(c2), c1)),
% 29.85/20.09 inference(symmetry,[status(thm)],[30774])).
% 29.85/20.09 tff(30776,plain,
% 29.85/20.09 ((~big_f(c1, c1)) <=> (~big_f(f7(c2), c1))),
% 29.85/20.09 inference(monotonicity,[status(thm)],[30775])).
% 29.85/20.09 tff(30777,plain,
% 29.85/20.09 (~big_f(f7(c2), c1)),
% 29.85/20.09 inference(modus_ponens,[status(thm)],[66, 30776])).
% 29.85/20.09 tff(30778,plain,
% 29.85/20.09 (big_f(c2, c1)),
% 29.85/20.09 inference(unit_resolution,[status(thm)],[9397, 30777, 67, 79, 30766, 30773])).
% 29.85/20.09 tff(30779,plain,
% 29.85/20.09 (f10(c2) = c1),
% 29.85/20.09 inference(unit_resolution,[status(thm)],[93, 30769])).
% 29.85/20.09 tff(30780,plain,
% 29.85/20.09 (big_f(c2, f10(c2)) <=> big_f(c2, c1)),
% 29.85/20.09 inference(monotonicity,[status(thm)],[30779])).
% 29.85/20.09 tff(30781,plain,
% 29.85/20.09 (big_f(c2, c1) <=> big_f(c2, f10(c2))),
% 29.85/20.09 inference(symmetry,[status(thm)],[30780])).
% 29.85/20.09 tff(30782,plain,
% 29.85/20.09 (big_f(c2, f10(c2))),
% 29.85/20.09 inference(modus_ponens,[status(thm)],[30778, 30781])).
% 29.85/20.09 tff(30783,plain,
% 29.85/20.09 ((f10(c2) = c2) | big_f(c1, c1) | (~big_f(c2, c2)) | (~big_f(c2, f10(c2))) | (~big_f(c2, c1))),
% 29.85/20.09 inference(unit_resolution,[status(thm)],[29224, 30354])).
% 29.85/20.09 tff(30784,plain,
% 29.85/20.09 (~big_f(c2, c2)),
% 29.85/20.09 inference(unit_resolution,[status(thm)],[30783, 30782, 66, 30778, 30769])).
% 29.85/20.09 tff(30785,plain,
% 29.85/20.09 (big_f(c2, f10(c2))),
% 29.85/20.09 inference(modus_ponens,[status(thm)],[348, 30781])).
% 29.85/20.09 tff(30786,plain,
% 29.85/20.09 (~big_f(c2, c2)),
% 29.85/20.09 inference(unit_resolution,[status(thm)],[30783, 30785, 66, 348, 30769])).
% 29.85/20.09 tff(30787,plain,
% 29.85/20.09 (~(c4 = c2)),
% 29.85/20.09 inference(unit_resolution,[status(thm)],[30611, 30786, 168, 79, 66])).
% 29.85/20.09 tff(30788,plain,
% 29.85/20.09 (c4 = c1),
% 29.85/20.09 inference(unit_resolution,[status(thm)],[461, 30787])).
% 29.85/20.09 tff(30789,plain,
% 29.85/20.09 (f4(c4) = f4(c1)),
% 29.85/20.09 inference(monotonicity,[status(thm)],[30788])).
% 29.85/20.09 tff(30790,plain,
% 29.85/20.09 (f4(c1) = f4(c4)),
% 29.85/20.09 inference(symmetry,[status(thm)],[30789])).
% 29.85/20.09 tff(30791,plain,
% 29.85/20.09 (f4(c1) = c2),
% 29.85/20.09 inference(transitivity,[status(thm)],[30790, 79])).
% 29.85/20.09 tff(30792,plain,
% 29.85/20.09 (f6(c1, f4(c1)) = f6(c1, c2)),
% 29.85/20.09 inference(monotonicity,[status(thm)],[30791])).
% 29.85/20.09 tff(30793,plain,
% 29.85/20.09 (f6(c1, f4(c1)) = c1),
% 29.85/20.09 inference(transitivity,[status(thm)],[30792, 4262])).
% 29.85/20.09 tff(30794,plain,
% 29.85/20.09 (big_f(f7(c1), f6(c1, f4(c1))) <=> big_f(c1, c1)),
% 29.85/20.09 inference(monotonicity,[status(thm)],[25791, 30793])).
% 29.85/20.09 tff(30795,plain,
% 29.85/20.09 (big_f(c1, c1) <=> big_f(f7(c1), f6(c1, f4(c1)))),
% 29.85/20.09 inference(symmetry,[status(thm)],[30794])).
% 29.85/20.09 tff(30796,plain,
% 29.85/20.09 ((~big_f(c1, c1)) <=> (~big_f(f7(c1), f6(c1, f4(c1))))),
% 29.85/20.09 inference(monotonicity,[status(thm)],[30795])).
% 29.85/20.09 tff(30797,plain,
% 29.85/20.09 (~big_f(f7(c1), f6(c1, f4(c1)))),
% 29.85/20.09 inference(modus_ponens,[status(thm)],[66, 30796])).
% 29.85/20.09 tff(30798,plain,
% 29.85/20.09 ((f6(c1, f4(c1)) = f4(c1)) <=> (c1 = f4(c1))),
% 29.85/20.09 inference(monotonicity,[status(thm)],[30793])).
% 29.85/20.09 tff(30799,plain,
% 29.85/20.09 ((c1 = f4(c1)) <=> (f6(c1, f4(c1)) = f4(c1))),
% 29.85/20.09 inference(symmetry,[status(thm)],[30798])).
% 29.85/20.09 tff(30800,plain,
% 29.85/20.09 ((~(c1 = f4(c1))) <=> (~(f6(c1, f4(c1)) = f4(c1)))),
% 29.85/20.09 inference(monotonicity,[status(thm)],[30799])).
% 29.85/20.09 tff(30801,plain,
% 29.85/20.09 ((c1 = f4(c1)) <=> (c1 = c2)),
% 29.85/20.09 inference(monotonicity,[status(thm)],[30791])).
% 29.85/20.09 tff(30802,plain,
% 29.85/20.09 ((c1 = f4(c1)) <=> (c2 = c1)),
% 29.85/20.09 inference(transitivity,[status(thm)],[30801, 1])).
% 29.85/20.09 tff(30803,plain,
% 29.85/20.09 ((c2 = c1) <=> (c1 = f4(c1))),
% 29.85/20.09 inference(symmetry,[status(thm)],[30802])).
% 29.85/20.09 tff(30804,plain,
% 29.85/20.09 ((~(c2 = c1)) <=> (~(c1 = f4(c1)))),
% 29.85/20.09 inference(monotonicity,[status(thm)],[30803])).
% 29.85/20.09 tff(30805,plain,
% 29.85/20.09 (~(c1 = f4(c1))),
% 29.85/20.09 inference(modus_ponens,[status(thm)],[75, 30804])).
% 29.85/20.09 tff(30806,plain,
% 29.85/20.09 (~(f6(c1, f4(c1)) = f4(c1))),
% 29.85/20.09 inference(modus_ponens,[status(thm)],[30805, 30800])).
% 29.85/20.09 tff(30807,plain,
% 29.85/20.09 (f10(c1) = c1),
% 29.85/20.09 inference(unit_resolution,[status(thm)],[30630, 114, 168, 79, 66, 30786])).
% 29.85/20.09 tff(30808,plain,
% 29.85/20.09 ((f9(c1, c2) = c2) | (~(f10(c1) = c1)) | big_f(c1, c1)),
% 29.85/20.09 inference(unit_resolution,[status(thm)],[27119, 30354])).
% 29.85/20.09 tff(30809,plain,
% 29.85/20.09 (f9(c1, c2) = c2),
% 29.85/20.09 inference(unit_resolution,[status(thm)],[30808, 30807, 66])).
% 29.85/20.09 tff(30810,plain,
% 29.85/20.09 (f9(c1, f4(c1)) = f9(c1, c2)),
% 29.85/20.09 inference(monotonicity,[status(thm)],[30791])).
% 29.85/20.09 tff(30811,plain,
% 29.85/20.09 (f9(c1, f4(c1)) = f4(c1)),
% 29.85/20.09 inference(transitivity,[status(thm)],[30810, 30809, 436, 30789])).
% 29.85/20.09 tff(30812,plain,
% 29.85/20.09 (f9(c1, f4(c1)) = c2),
% 29.85/20.09 inference(transitivity,[status(thm)],[30810, 30809])).
% 29.85/20.09 tff(30813,plain,
% 29.85/20.09 (big_f(f9(c1, f4(c1)), f10(c1)) <=> big_f(c2, c1)),
% 29.85/20.09 inference(monotonicity,[status(thm)],[30812, 30807])).
% 29.85/20.09 tff(30814,plain,
% 29.85/20.09 (big_f(c2, c1) <=> big_f(f9(c1, f4(c1)), f10(c1))),
% 29.85/20.09 inference(symmetry,[status(thm)],[30813])).
% 29.85/20.09 tff(30815,plain,
% 29.85/20.09 (big_f(f9(c1, f4(c1)), f10(c1))),
% 29.85/20.09 inference(modus_ponens,[status(thm)],[348, 30814])).
% 29.85/20.09 tff(30816,plain,
% 29.85/20.09 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~big_f(f9(c1, f4(c1)), f10(c1))) | (~(f9(c1, f4(c1)) = f4(c1))) | (f6(c1, f4(c1)) = f4(c1)) | big_f(f7(c1), f6(c1, f4(c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~big_f(f9(c1, f4(c1)), f10(c1))) | (~(f9(c1, f4(c1)) = f4(c1))) | (f6(c1, f4(c1)) = f4(c1)) | big_f(f7(c1), f6(c1, f4(c1))))),
% 29.85/20.09 inference(rewrite,[status(thm)],[])).
% 29.85/20.09 tff(30817,plain,
% 29.85/20.09 (((~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (f6(c1, f4(c1)) = f4(c1)) | big_f(f7(c1), f6(c1, f4(c1))) | (~(f9(c1, f4(c1)) = f4(c1))) | (~big_f(f9(c1, f4(c1)), f10(c1)))) <=> ((~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~big_f(f9(c1, f4(c1)), f10(c1))) | (~(f9(c1, f4(c1)) = f4(c1))) | (f6(c1, f4(c1)) = f4(c1)) | big_f(f7(c1), f6(c1, f4(c1))))),
% 29.85/20.10 inference(rewrite,[status(thm)],[])).
% 29.85/20.10 tff(30818,plain,
% 29.85/20.10 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (f6(c1, f4(c1)) = f4(c1)) | big_f(f7(c1), f6(c1, f4(c1))) | (~(f9(c1, f4(c1)) = f4(c1))) | (~big_f(f9(c1, f4(c1)), f10(c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~big_f(f9(c1, f4(c1)), f10(c1))) | (~(f9(c1, f4(c1)) = f4(c1))) | (f6(c1, f4(c1)) = f4(c1)) | big_f(f7(c1), f6(c1, f4(c1)))))),
% 29.85/20.10 inference(monotonicity,[status(thm)],[30817])).
% 29.85/20.10 tff(30819,plain,
% 29.85/20.10 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (f6(c1, f4(c1)) = f4(c1)) | big_f(f7(c1), f6(c1, f4(c1))) | (~(f9(c1, f4(c1)) = f4(c1))) | (~big_f(f9(c1, f4(c1)), f10(c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~big_f(f9(c1, f4(c1)), f10(c1))) | (~(f9(c1, f4(c1)) = f4(c1))) | (f6(c1, f4(c1)) = f4(c1)) | big_f(f7(c1), f6(c1, f4(c1))))),
% 29.85/20.10 inference(transitivity,[status(thm)],[30818, 30816])).
% 29.85/20.10 tff(30820,plain,
% 29.85/20.10 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | ((~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (f6(c1, f4(c1)) = f4(c1)) | big_f(f7(c1), f6(c1, f4(c1))) | (~(f9(c1, f4(c1)) = f4(c1))) | (~big_f(f9(c1, f4(c1)), f10(c1))))),
% 29.85/20.10 inference(quant_inst,[status(thm)],[])).
% 29.85/20.10 tff(30821,plain,
% 29.85/20.10 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))))) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~big_f(f9(c1, f4(c1)), f10(c1))) | (~(f9(c1, f4(c1)) = f4(c1))) | (f6(c1, f4(c1)) = f4(c1)) | big_f(f7(c1), f6(c1, f4(c1)))),
% 29.85/20.10 inference(modus_ponens,[status(thm)],[30820, 30819])).
% 29.85/20.10 tff(30822,plain,
% 29.85/20.10 ((~big_f(f9(c1, f4(c1)), f10(c1))) | (~(f9(c1, f4(c1)) = f4(c1))) | (f6(c1, f4(c1)) = f4(c1)) | big_f(f7(c1), f6(c1, f4(c1)))),
% 29.85/20.10 inference(unit_resolution,[status(thm)],[30821, 2409, 25791, 30807])).
% 29.85/20.10 tff(30823,plain,
% 29.85/20.10 ($false),
% 29.85/20.10 inference(unit_resolution,[status(thm)],[30822, 30815, 30811, 30806, 30797])).
% 29.85/20.10 tff(30824,plain,((f6(c1, c2) = c2) | big_f(c1, c1) | (~(f4(c4) = c2)) | (~big_f(c2, c1)) | (c1 = c3)), inference(lemma,lemma(discharge,[]))).
% 29.85/20.10 tff(30825,plain,
% 29.85/20.10 (f6(c1, c2) = c2),
% 29.85/20.10 inference(unit_resolution,[status(thm)],[30824, 79, 66, 30778, 76])).
% 29.85/20.10 tff(30826,plain,
% 29.85/20.10 (big_f(f7(c1), f6(c1, f6(c1, c2)))),
% 29.85/20.10 inference(unit_resolution,[status(thm)],[30740, 30825])).
% 29.85/20.10 tff(30827,plain,
% 29.85/20.10 (f9(c1, c2) = c2),
% 29.85/20.10 inference(unit_resolution,[status(thm)],[30808, 3762, 66])).
% 29.85/20.10 tff(30828,plain,
% 29.85/20.10 (big_f(f9(c1, c2), f10(c1)) <=> big_f(c2, c1)),
% 29.85/20.10 inference(monotonicity,[status(thm)],[30827, 3762])).
% 29.85/20.10 tff(30829,plain,
% 29.85/20.10 (big_f(c2, c1) <=> big_f(f9(c1, c2), f10(c1))),
% 29.85/20.10 inference(symmetry,[status(thm)],[30828])).
% 29.85/20.10 tff(30830,plain,
% 29.85/20.10 (big_f(f9(c1, c2), f10(c1))),
% 29.85/20.10 inference(modus_ponens,[status(thm)],[348, 30829])).
% 29.85/20.10 tff(30831,plain,
% 29.85/20.10 ((f6(c1, c2) = c1) <=> (c1 = f6(c1, c2))),
% 29.85/20.10 inference(symmetry,[status(thm)],[30])).
% 29.85/20.10 tff(30832,plain,
% 29.85/20.10 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~(f9(c1, c2) = c2)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~(f9(c1, c2) = c2)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))),
% 29.91/20.10 inference(rewrite,[status(thm)],[])).
% 29.91/20.10 tff(30833,plain,
% 29.91/20.10 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~(f9(c1, c2) = c2)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))),
% 29.91/20.10 inference(quant_inst,[status(thm)],[])).
% 29.91/20.10 tff(30834,plain,
% 29.91/20.10 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~(f9(c1, c2) = c2)) | (~big_f(f9(c1, c2), f10(c1))) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2))))),
% 29.91/20.10 inference(modus_ponens,[status(thm)],[30833, 30832])).
% 29.91/20.10 tff(30835,plain,
% 29.91/20.10 ((~big_f(f9(c1, c2), f10(c1))) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2)))),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[30834, 2378, 25791, 3762, 30827, 30373])).
% 29.91/20.10 tff(30836,plain,
% 29.91/20.10 (~(f6(c1, f6(c1, c2)) = f6(c1, c2))),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[30835, 17888])).
% 29.91/20.10 tff(30837,plain,
% 29.91/20.10 (~(f6(c1, c2) = c2)),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[43, 30836])).
% 29.91/20.10 tff(30838,plain,
% 29.91/20.10 (f6(c1, c2) = c1),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[48, 30837])).
% 29.91/20.10 tff(30839,plain,
% 29.91/20.10 (c1 = f6(c1, c2)),
% 29.91/20.10 inference(modus_ponens,[status(thm)],[30838, 30831])).
% 29.91/20.10 tff(30840,plain,
% 29.91/20.10 (c1 = f7(c1)),
% 29.91/20.10 inference(symmetry,[status(thm)],[25791])).
% 29.91/20.10 tff(30841,plain,
% 29.91/20.10 ((~big_f(f9(c1, c2), f10(c1))) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2)),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[27159, 2409, 25791, 3762, 30827])).
% 29.91/20.10 tff(30842,plain,
% 29.91/20.10 (big_f(f7(c1), f6(c1, c2))),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[30841, 30837, 17888])).
% 29.91/20.10 tff(30843,plain,
% 29.91/20.10 ((~(big_f(c1, c1) <=> big_f(f7(c1), f6(c1, c2)))) | big_f(c1, c1) | (~big_f(f7(c1), f6(c1, c2)))),
% 29.91/20.10 inference(tautology,[status(thm)],[])).
% 29.91/20.10 tff(30844,plain,
% 29.91/20.10 ((~(big_f(c1, c1) <=> big_f(f7(c1), f6(c1, c2)))) | (~big_f(f7(c1), f6(c1, c2)))),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[30843, 66])).
% 29.91/20.10 tff(30845,plain,
% 29.91/20.10 (~(big_f(c1, c1) <=> big_f(f7(c1), f6(c1, c2)))),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[30844, 30842])).
% 29.91/20.10 tff(30846,assumption,(~(big_f(c1, c1) <=> big_f(f7(c1), f6(c1, c2)))), introduced(assumption)).
% 29.91/20.10 tff(30847,assumption,(c1 = f6(c1, c2)), introduced(assumption)).
% 29.91/20.10 tff(30848,assumption,(c1 = f7(c1)), introduced(assumption)).
% 29.91/20.10 tff(30849,plain,
% 29.91/20.10 (big_f(c1, c1) <=> big_f(f7(c1), f6(c1, c2))),
% 29.91/20.10 inference(monotonicity,[status(thm)],[30848, 30847])).
% 29.91/20.10 tff(30850,plain,
% 29.91/20.10 ($false),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[30849, 30846])).
% 29.91/20.10 tff(30851,plain,((~(c1 = f7(c1))) | (~(c1 = f6(c1, c2))) | (big_f(c1, c1) <=> big_f(f7(c1), f6(c1, c2)))), inference(lemma,lemma(discharge,[]))).
% 29.91/20.10 tff(30852,plain,
% 29.91/20.10 (~(c1 = f6(c1, c2))),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[30851, 30845, 30840])).
% 29.91/20.10 tff(30853,plain,
% 29.91/20.10 ($false),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[30852, 30839])).
% 29.91/20.10 tff(30854,plain,((~big_f(f9(c1, c2), f10(c1))) | big_f(c1, c1) | (~(f10(c1) = c1)) | (~big_f(f7(c1), f6(c1, f6(c1, c2))))), inference(lemma,lemma(discharge,[]))).
% 29.91/20.10 tff(30855,plain,
% 29.91/20.10 (~big_f(f9(c1, c2), f10(c1))),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[30854, 3762, 66, 30373])).
% 29.91/20.10 tff(30856,plain,
% 29.91/20.10 ($false),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[30855, 30830])).
% 29.91/20.10 tff(30857,plain,((~(f10(c1) = c1)) | (~big_f(c2, c1)) | big_f(c1, c1) | (~big_f(f7(c1), f6(c1, f6(c1, c2))))), inference(lemma,lemma(discharge,[]))).
% 29.91/20.10 tff(30858,plain,
% 29.91/20.10 (~(f10(c1) = c1)),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[30857, 30826, 66, 30778])).
% 29.91/20.10 tff(30859,plain,
% 29.91/20.10 ($false),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[30736, 30858, 30826, 66, 30784])).
% 29.91/20.10 tff(30860,plain,((~(f4(c4) = c2)) | big_f(c1, c1) | (~(c3 = c2))), inference(lemma,lemma(discharge,[]))).
% 29.91/20.10 tff(30861,plain,
% 29.91/20.10 (~(f4(c4) = c2)),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[30860, 30422, 66])).
% 29.91/20.10 tff(30862,plain,
% 29.91/20.10 (f4(c4) = c1),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[11750, 30861])).
% 29.91/20.10 tff(30863,plain,
% 29.91/20.10 (f1(c1, c2) = c2),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[23505, 168, 66, 1345, 11752])).
% 29.91/20.10 tff(30864,plain,
% 29.91/20.10 (big_f(c1, f1(c1, c2)) <=> big_f(c1, c2)),
% 29.91/20.10 inference(monotonicity,[status(thm)],[30863])).
% 29.91/20.10 tff(30865,plain,
% 29.91/20.10 (big_f(c1, c2) <=> big_f(c1, f1(c1, c2))),
% 29.91/20.10 inference(symmetry,[status(thm)],[30864])).
% 29.91/20.10 tff(30866,plain,
% 29.91/20.10 (big_f(c1, f1(c1, c2))),
% 29.91/20.10 inference(modus_ponens,[status(thm)],[30354, 30865])).
% 29.91/20.10 tff(30867,plain,
% 29.91/20.10 (~(c4 = c1)),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[23860, 30866, 66, 168, 11752, 30863])).
% 29.91/20.10 tff(30868,plain,
% 29.91/20.10 (c4 = c2),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[461, 30867])).
% 29.91/20.10 tff(30869,plain,
% 29.91/20.10 (c2 = c4),
% 29.91/20.10 inference(modus_ponens,[status(thm)],[30868, 159])).
% 29.91/20.10 tff(30870,plain,
% 29.91/20.10 (c2 = c4),
% 29.91/20.10 inference(symmetry,[status(thm)],[30868])).
% 29.91/20.10 tff(30871,plain,
% 29.91/20.10 (f4(c2) = f4(c4)),
% 29.91/20.10 inference(monotonicity,[status(thm)],[30870])).
% 29.91/20.10 tff(30872,plain,
% 29.91/20.10 (f4(c2) = c1),
% 29.91/20.10 inference(transitivity,[status(thm)],[30871, 11752])).
% 29.91/20.10 tff(30873,plain,
% 29.91/20.10 ((c2 = f4(c2)) <=> (c2 = c1)),
% 29.91/20.10 inference(monotonicity,[status(thm)],[30872])).
% 29.91/20.10 tff(30874,plain,
% 29.91/20.10 ((c2 = c1) <=> (c2 = f4(c2))),
% 29.91/20.10 inference(symmetry,[status(thm)],[30873])).
% 29.91/20.10 tff(30875,plain,
% 29.91/20.10 ((~(c2 = c1)) <=> (~(c2 = f4(c2)))),
% 29.91/20.10 inference(monotonicity,[status(thm)],[30874])).
% 29.91/20.10 tff(30876,plain,
% 29.91/20.10 (~(c2 = f4(c2))),
% 29.91/20.10 inference(modus_ponens,[status(thm)],[75, 30875])).
% 29.91/20.10 tff(30877,plain,
% 29.91/20.10 ((~(c2 = c4)) | (c2 = f4(c2))),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[23876, 553, 168, 1345, 30863, 30866])).
% 29.91/20.10 tff(30878,plain,
% 29.91/20.10 ($false),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[30877, 30876, 30869])).
% 29.91/20.10 tff(30879,plain,((c1 = c3) | (~big_f(c2, c2)) | (~(f4(c4) = c1)) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 29.91/20.10 tff(30880,plain,
% 29.91/20.10 (~big_f(c2, c2)),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[30879, 30862, 30765, 66])).
% 29.91/20.10 tff(30881,plain,
% 29.91/20.10 (~(f10(c2) = c2)),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[30374, 30880, 66])).
% 29.91/20.10 tff(30882,plain,
% 29.91/20.10 (f10(c2) = c1),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[93, 30881])).
% 29.91/20.10 tff(30883,plain,
% 29.91/20.10 (c1 = f10(c2)),
% 29.91/20.10 inference(symmetry,[status(thm)],[30882])).
% 29.91/20.10 tff(30884,plain,
% 29.91/20.10 (big_f(c2, c1) <=> big_f(c2, f10(c2))),
% 29.91/20.10 inference(monotonicity,[status(thm)],[30883])).
% 29.91/20.10 tff(30885,plain,
% 29.91/20.10 (big_f(c2, f10(c2)) <=> big_f(c2, c1)),
% 29.91/20.10 inference(symmetry,[status(thm)],[30884])).
% 29.91/20.10 tff(30886,plain,
% 29.91/20.10 (big_f(c1, f10(c2)) <=> big_f(c1, c1)),
% 29.91/20.10 inference(monotonicity,[status(thm)],[30882])).
% 29.91/20.10 tff(30887,plain,
% 29.91/20.10 (big_f(c1, c1) <=> big_f(c1, f10(c2))),
% 29.91/20.10 inference(symmetry,[status(thm)],[30886])).
% 29.91/20.10 tff(30888,plain,
% 29.91/20.10 ((~big_f(c1, c1)) <=> (~big_f(c1, f10(c2)))),
% 29.91/20.10 inference(monotonicity,[status(thm)],[30887])).
% 29.91/20.10 tff(30889,plain,
% 29.91/20.10 (~big_f(c1, f10(c2))),
% 29.91/20.10 inference(modus_ponens,[status(thm)],[66, 30888])).
% 29.91/20.10 tff(30890,plain,
% 29.91/20.10 (~(c1 = f8(c2))),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[25825, 2994, 25791, 30881, 25798, 114, 30889])).
% 29.91/20.10 tff(30891,plain,
% 29.91/20.10 (c2 = f8(c2)),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[26203, 30890, 30422])).
% 29.91/20.10 tff(30892,plain,
% 29.91/20.10 (f8(c2) = c2),
% 29.91/20.10 inference(symmetry,[status(thm)],[30891])).
% 29.91/20.10 tff(30893,plain,
% 29.91/20.10 (f9(c1, f8(c2)) = f9(c1, c2)),
% 29.91/20.10 inference(monotonicity,[status(thm)],[30892])).
% 29.91/20.10 tff(30894,plain,
% 29.91/20.10 ((f9(c1, f8(c2)) = f8(c2)) <=> (f9(c1, c2) = c2)),
% 29.91/20.10 inference(monotonicity,[status(thm)],[30893, 30892])).
% 29.91/20.10 tff(30895,plain,
% 29.91/20.10 ((f9(c1, c2) = c2) <=> (f9(c1, f8(c2)) = f8(c2))),
% 29.91/20.10 inference(symmetry,[status(thm)],[30894])).
% 29.91/20.10 tff(30896,plain,
% 29.91/20.10 (f6(c1, f8(c2)) = f6(c1, c2)),
% 29.91/20.10 inference(monotonicity,[status(thm)],[30892])).
% 29.91/20.10 tff(30897,plain,
% 29.91/20.10 (f10(c1) = f8(c2)),
% 29.91/20.10 inference(transitivity,[status(thm)],[15, 30891])).
% 29.91/20.10 tff(30898,plain,
% 29.91/20.10 (f6(c1, f10(c1)) = f6(c1, f8(c2))),
% 29.91/20.10 inference(monotonicity,[status(thm)],[30897])).
% 29.91/20.10 tff(30899,plain,
% 29.91/20.10 (f6(c1, f10(c1)) = c1),
% 29.91/20.10 inference(transitivity,[status(thm)],[30898, 30896, 4262])).
% 29.91/20.10 tff(30900,plain,
% 29.91/20.10 (big_f(f7(c1), f6(c1, f10(c1))) <=> big_f(c1, c1)),
% 29.91/20.10 inference(monotonicity,[status(thm)],[25791, 30899])).
% 29.91/20.10 tff(30901,plain,
% 29.91/20.10 (big_f(c1, c1) <=> big_f(f7(c1), f6(c1, f10(c1)))),
% 29.91/20.10 inference(symmetry,[status(thm)],[30900])).
% 29.91/20.10 tff(30902,plain,
% 29.91/20.10 ((~big_f(c1, c1)) <=> (~big_f(f7(c1), f6(c1, f10(c1))))),
% 29.91/20.10 inference(monotonicity,[status(thm)],[30901])).
% 29.91/20.10 tff(30903,plain,
% 29.91/20.10 (~big_f(f7(c1), f6(c1, f10(c1)))),
% 29.91/20.10 inference(modus_ponens,[status(thm)],[66, 30902])).
% 29.91/20.10 tff(30904,plain,
% 29.91/20.10 (~(f6(c1, f10(c1)) = f10(c1))),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[28849, 15, 114])).
% 29.91/20.10 tff(30905,plain,
% 29.91/20.10 (f10(c3) = f10(c2)),
% 29.91/20.10 inference(monotonicity,[status(thm)],[30422])).
% 29.91/20.10 tff(30906,plain,
% 29.91/20.10 (f10(c2) = f10(c3)),
% 29.91/20.10 inference(symmetry,[status(thm)],[30905])).
% 29.91/20.10 tff(30907,plain,
% 29.91/20.10 (c1 = f10(c3)),
% 29.91/20.10 inference(transitivity,[status(thm)],[30883, 30906])).
% 29.91/20.10 tff(30908,plain,
% 29.91/20.10 (f8(c3) = f8(c2)),
% 29.91/20.10 inference(monotonicity,[status(thm)],[30422])).
% 29.91/20.10 tff(30909,plain,
% 29.91/20.10 (f8(c2) = f8(c3)),
% 29.91/20.10 inference(symmetry,[status(thm)],[30908])).
% 29.91/20.10 tff(30910,plain,
% 29.91/20.10 (f10(c1) = f8(c3)),
% 29.91/20.10 inference(transitivity,[status(thm)],[15, 30891, 30909])).
% 29.91/20.10 tff(30911,plain,
% 29.91/20.10 (big_f(f10(c1), c1) <=> big_f(f8(c3), f10(c3))),
% 29.91/20.10 inference(monotonicity,[status(thm)],[30910, 30907])).
% 29.91/20.10 tff(30912,plain,
% 29.91/20.10 (big_f(f8(c3), f10(c3)) <=> big_f(f10(c1), c1)),
% 29.91/20.10 inference(symmetry,[status(thm)],[30911])).
% 29.91/20.10 tff(30913,plain,
% 29.91/20.10 (f10(c3) = c1),
% 29.91/20.10 inference(transitivity,[status(thm)],[30905, 30882])).
% 29.91/20.10 tff(30914,plain,
% 29.91/20.10 (f8(c3) = c2),
% 29.91/20.10 inference(transitivity,[status(thm)],[30908, 30892])).
% 29.91/20.10 tff(30915,plain,
% 29.91/20.10 (big_f(f8(c3), f10(c3)) <=> big_f(c2, c1)),
% 29.91/20.10 inference(monotonicity,[status(thm)],[30914, 30913])).
% 29.91/20.10 tff(30916,plain,
% 29.91/20.10 (big_f(c2, c1) <=> big_f(f8(c3), f10(c3))),
% 29.91/20.10 inference(symmetry,[status(thm)],[30915])).
% 29.91/20.10 tff(30917,plain,
% 29.91/20.10 (big_f(c2, f10(c2)) <=> big_f(f8(c3), f10(c3))),
% 29.91/20.10 inference(transitivity,[status(thm)],[30885, 30916])).
% 29.91/20.10 tff(30918,plain,
% 29.91/20.10 (f6(c1, f8(c2)) = c1),
% 29.91/20.10 inference(transitivity,[status(thm)],[30896, 4262])).
% 29.91/20.10 tff(30919,plain,
% 29.91/20.10 ((f6(c1, f8(c2)) = f8(c2)) <=> (c1 = f8(c2))),
% 29.91/20.10 inference(monotonicity,[status(thm)],[30918])).
% 29.91/20.10 tff(30920,plain,
% 29.91/20.10 ((c1 = f8(c2)) <=> (f6(c1, f8(c2)) = f8(c2))),
% 29.91/20.10 inference(symmetry,[status(thm)],[30919])).
% 29.91/20.10 tff(30921,plain,
% 29.91/20.10 ((~(c1 = f8(c2))) <=> (~(f6(c1, f8(c2)) = f8(c2)))),
% 29.91/20.10 inference(monotonicity,[status(thm)],[30920])).
% 29.91/20.10 tff(30922,plain,
% 29.91/20.10 (~(f6(c1, f8(c2)) = f8(c2))),
% 29.91/20.10 inference(modus_ponens,[status(thm)],[30890, 30921])).
% 29.91/20.10 tff(30923,plain,
% 29.91/20.10 (big_f(c1, f6(c1, f8(c2))) <=> big_f(c1, c1)),
% 29.91/20.10 inference(monotonicity,[status(thm)],[30918])).
% 29.91/20.10 tff(30924,plain,
% 29.91/20.10 (big_f(c1, c1) <=> big_f(c1, f6(c1, f8(c2)))),
% 29.91/20.10 inference(symmetry,[status(thm)],[30923])).
% 29.91/20.10 tff(30925,plain,
% 29.91/20.10 (big_f(c1, c1) <=> big_f(f7(c1), f6(c1, f8(c2)))),
% 29.91/20.10 inference(transitivity,[status(thm)],[30924, 27145])).
% 29.91/20.10 tff(30926,plain,
% 29.91/20.10 ((~big_f(c1, c1)) <=> (~big_f(f7(c1), f6(c1, f8(c2))))),
% 29.91/20.10 inference(monotonicity,[status(thm)],[30925])).
% 29.91/20.10 tff(30927,plain,
% 29.91/20.10 (~big_f(f7(c1), f6(c1, f8(c2)))),
% 29.91/20.10 inference(modus_ponens,[status(thm)],[66, 30926])).
% 29.91/20.10 tff(30928,plain,
% 29.91/20.10 ((f10(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | big_f(f7(c1), f6(c1, f8(c2))) | (f6(c1, f8(c2)) = f8(c2))),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[24920, 25791])).
% 29.91/20.10 tff(30929,plain,
% 29.91/20.10 (big_f(c2, f10(c2))),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[30928, 30927, 30881, 30891, 30922])).
% 29.91/20.10 tff(30930,plain,
% 29.91/20.10 (big_f(f8(c3), f10(c3))),
% 29.91/20.10 inference(modus_ponens,[status(thm)],[30929, 30917])).
% 29.91/20.10 tff(30931,plain,
% 29.91/20.10 (big_f(f10(c1), c1)),
% 29.91/20.10 inference(modus_ponens,[status(thm)],[30930, 30912])).
% 29.91/20.10 tff(30932,plain,
% 29.91/20.10 (c1 = c4),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[30481, 30931, 66, 30421, 15, 30882, 30891])).
% 29.91/20.10 tff(30933,plain,
% 29.91/20.10 (c4 = c1),
% 29.91/20.10 inference(symmetry,[status(thm)],[30932])).
% 29.91/20.10 tff(30934,plain,
% 29.91/20.10 ((f10(c1) = c4) <=> (f10(c1) = c1)),
% 29.91/20.10 inference(monotonicity,[status(thm)],[30933])).
% 29.91/20.10 tff(30935,plain,
% 29.91/20.10 ((f10(c1) = c1) <=> (f10(c1) = c4)),
% 29.91/20.10 inference(symmetry,[status(thm)],[30934])).
% 29.91/20.10 tff(30936,plain,
% 29.91/20.10 ((~(f10(c1) = c1)) <=> (~(f10(c1) = c4))),
% 29.91/20.10 inference(monotonicity,[status(thm)],[30935])).
% 29.91/20.10 tff(30937,plain,
% 29.91/20.10 (~(f10(c1) = c4)),
% 29.91/20.10 inference(modus_ponens,[status(thm)],[3, 30936])).
% 29.91/20.10 tff(30938,plain,
% 29.91/20.10 (big_f(f4(c4), c4) <=> big_f(c1, c1)),
% 29.91/20.10 inference(monotonicity,[status(thm)],[30862, 30933])).
% 29.91/20.10 tff(30939,plain,
% 29.91/20.10 (big_f(c1, c1) <=> big_f(f4(c4), c4)),
% 29.91/20.10 inference(symmetry,[status(thm)],[30938])).
% 29.91/20.10 tff(30940,plain,
% 29.91/20.10 ((~big_f(c1, c1)) <=> (~big_f(f4(c4), c4))),
% 29.91/20.10 inference(monotonicity,[status(thm)],[30939])).
% 29.91/20.10 tff(30941,plain,
% 29.91/20.10 (~big_f(f4(c4), c4)),
% 29.91/20.10 inference(modus_ponens,[status(thm)],[66, 30940])).
% 29.91/20.10 tff(30942,plain,
% 29.91/20.10 (~(f1(c1, c2) = c2)),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[30667, 30941, 30765])).
% 29.91/20.10 tff(30943,plain,
% 29.91/20.10 ((f1(c1, c2) = c2) | (c1 = c3) | (f10(c1) = c4) | big_f(c1, c1) | (f10(c1) = c1) | (f6(c1, f10(c1)) = f10(c1)) | big_f(f7(c1), f6(c1, f10(c1))) | (~big_f(c1, f10(c1)))),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[28903, 25791])).
% 29.91/20.10 tff(30944,plain,
% 29.91/20.10 ($false),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[30943, 30942, 30937, 66, 30765, 3, 30400, 30904, 30903])).
% 29.91/20.10 tff(30945,plain,((f10(c1) = c1) | big_f(c1, c1) | (c3 = c1) | (f6(c1, c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 29.91/20.10 tff(30946,plain,
% 29.91/20.10 (f10(c1) = c1),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[30945, 114, 30421, 66])).
% 29.91/20.10 tff(30947,plain,
% 29.91/20.10 (f9(c1, c2) = c2),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[30808, 30946, 66])).
% 29.91/20.10 tff(30948,plain,
% 29.91/20.10 (f9(c1, f8(c2)) = f8(c2)),
% 29.91/20.10 inference(modus_ponens,[status(thm)],[30947, 30895])).
% 29.91/20.10 tff(30949,plain,
% 29.91/20.10 (f10(c1) = f10(c2)),
% 29.91/20.10 inference(transitivity,[status(thm)],[30946, 30883])).
% 29.91/20.10 tff(30950,plain,
% 29.91/20.10 (big_f(f9(c1, f8(c2)), f10(c1)) <=> big_f(f9(c1, f8(c2)), f10(c2))),
% 29.91/20.10 inference(monotonicity,[status(thm)],[30949])).
% 29.91/20.10 tff(30951,plain,
% 29.91/20.10 (big_f(f9(c1, f8(c2)), f10(c2)) <=> big_f(f9(c1, f8(c2)), f10(c1))),
% 29.91/20.10 inference(symmetry,[status(thm)],[30950])).
% 29.91/20.10 tff(30952,plain,
% 29.91/20.10 (big_f(f9(c1, f8(c2)), f10(c2))),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[27151, 30946, 30927, 30881, 30922])).
% 29.91/20.10 tff(30953,plain,
% 29.91/20.10 (big_f(f9(c1, f8(c2)), f10(c1))),
% 29.91/20.10 inference(modus_ponens,[status(thm)],[30952, 30951])).
% 29.91/20.10 tff(30954,plain,
% 29.91/20.10 ($false),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[24854, 2409, 25791, 30946, 30927, 30922, 30953, 30948])).
% 29.91/20.10 tff(30955,plain,((f6(c1, c2) = c2) | big_f(c1, c1) | (c3 = c1)), inference(lemma,lemma(discharge,[]))).
% 29.91/20.10 tff(30956,plain,
% 29.91/20.10 (f6(c1, c2) = c2),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[30955, 30421, 66])).
% 29.91/20.10 tff(30957,plain,
% 29.91/20.10 (big_f(f7(c1), f6(c1, f6(c1, c2)))),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[30740, 30956])).
% 29.91/20.10 tff(30958,plain,
% 29.91/20.10 ((~(c1 = f8(c2))) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2)))),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[30381, 2963, 25791, 89, 30373, 12055])).
% 29.91/20.10 tff(30959,plain,
% 29.91/20.10 (~(c1 = f8(c2))),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[30958, 29897])).
% 29.91/20.10 tff(30960,plain,
% 29.91/20.10 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))),
% 29.91/20.10 inference(rewrite,[status(thm)],[])).
% 29.91/20.10 tff(30961,plain,
% 29.91/20.10 (((f10(c2) = c2) | big_f(c2, f10(c2)) | (~(f7(c1) = c1)) | (~(c2 = f8(c2))) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2))))) <=> ((f10(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))),
% 29.91/20.10 inference(rewrite,[status(thm)],[])).
% 29.91/20.10 tff(30962,plain,
% 29.91/20.10 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | big_f(c2, f10(c2)) | (~(f7(c1) = c1)) | (~(c2 = f8(c2))) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2))))))),
% 29.91/20.10 inference(monotonicity,[status(thm)],[30961])).
% 29.91/20.10 tff(30963,plain,
% 29.91/20.10 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | big_f(c2, f10(c2)) | (~(f7(c1) = c1)) | (~(c2 = f8(c2))) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))),
% 29.91/20.10 inference(transitivity,[status(thm)],[30962, 30960])).
% 29.91/20.10 tff(30964,plain,
% 29.91/20.10 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | big_f(c2, f10(c2)) | (~(f7(c1) = c1)) | (~(c2 = f8(c2))) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))),
% 29.91/20.10 inference(quant_inst,[status(thm)],[])).
% 29.91/20.10 tff(30965,plain,
% 29.91/20.10 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (~(c2 = f8(c2))) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2))))),
% 29.91/20.10 inference(modus_ponens,[status(thm)],[30964, 30963])).
% 29.91/20.10 tff(30966,plain,
% 29.91/20.10 ((~(c2 = f8(c2))) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2)))),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[30965, 2963, 25791, 89, 15517, 30373])).
% 29.91/20.10 tff(30967,plain,
% 29.91/20.10 (~(c2 = f8(c2))),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[30966, 29897])).
% 29.91/20.10 tff(30968,plain,
% 29.91/20.10 ($false),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[26203, 30967, 30959, 67])).
% 29.91/20.10 tff(30969,plain,((~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~(c3 = c2)) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))) | big_f(c1, f10(c2))), inference(lemma,lemma(discharge,[]))).
% 29.91/20.10 tff(30970,plain,
% 29.91/20.10 (~(f6(c1, f6(c1, c2)) = f6(c1, c2))),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[30969, 67, 89, 15517, 30373, 24207])).
% 29.91/20.10 tff(30971,plain,
% 29.91/20.10 (~(f6(c1, c2) = c2)),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[43, 30970])).
% 29.91/20.10 tff(30972,plain,
% 29.91/20.10 (f6(c1, c2) = c1),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[48, 30971])).
% 29.91/20.10 tff(30973,plain,
% 29.91/20.10 (big_f(c1, f6(c1, c2)) <=> big_f(c1, c1)),
% 29.91/20.10 inference(monotonicity,[status(thm)],[30972])).
% 29.91/20.10 tff(30974,plain,
% 29.91/20.10 (big_f(c1, c1) <=> big_f(c1, f6(c1, c2))),
% 29.91/20.10 inference(symmetry,[status(thm)],[30973])).
% 29.91/20.10 tff(30975,plain,
% 29.91/20.10 (big_f(c1, c1) <=> big_f(f7(c1), f6(c1, c2))),
% 29.91/20.10 inference(transitivity,[status(thm)],[30974, 25793])).
% 29.91/20.10 tff(30976,plain,
% 29.91/20.10 ((~big_f(c1, c1)) <=> (~big_f(f7(c1), f6(c1, c2)))),
% 29.91/20.10 inference(monotonicity,[status(thm)],[30975])).
% 29.91/20.10 tff(30977,plain,
% 29.91/20.10 (~big_f(f7(c1), f6(c1, c2))),
% 29.91/20.10 inference(modus_ponens,[status(thm)],[66, 30976])).
% 29.91/20.10 tff(30978,plain,
% 29.91/20.10 (~(c1 = f8(c2))),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[30390, 30977, 30971])).
% 29.91/20.10 tff(30979,plain,
% 29.91/20.10 ((~(c2 = f8(c2))) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2)),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[25804, 2994, 25791, 89, 15517])).
% 29.91/20.10 tff(30980,plain,
% 29.91/20.10 (~(c2 = f8(c2))),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[30979, 30977, 30971])).
% 29.91/20.10 tff(30981,plain,
% 29.91/20.10 ($false),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[26203, 30980, 30978, 67])).
% 29.91/20.10 tff(30982,plain,((~(c3 = c2)) | (f10(c2) = c2) | big_f(c2, f10(c2)) | big_f(c1, c1) | (~big_f(f7(c1), f6(c1, f6(c1, c2))))), inference(lemma,lemma(discharge,[]))).
% 29.91/20.10 tff(30983,plain,
% 29.91/20.10 (big_f(c2, f10(c2))),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[30982, 30957, 30422, 66, 30881])).
% 29.91/20.10 tff(30984,plain,
% 29.91/20.10 (big_f(c2, c1)),
% 29.91/20.10 inference(modus_ponens,[status(thm)],[30983, 30885])).
% 29.91/20.10 tff(30985,plain,
% 29.91/20.10 (f10(c1) = c1),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[30736, 30957, 66, 30880])).
% 29.91/20.10 tff(30986,plain,
% 29.91/20.10 (~big_f(c2, c1)),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[30857, 30985, 66, 30957])).
% 29.91/20.10 tff(30987,plain,
% 29.91/20.10 ($false),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[30986, 30984])).
% 29.91/20.10 tff(30988,plain,((c3 = c1) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 29.91/20.10 tff(30989,plain,
% 29.91/20.10 (c3 = c1),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[30988, 66])).
% 29.91/20.10 tff(30990,plain,
% 29.91/20.10 ((c2 = c3) <=> (c2 = c1)),
% 29.91/20.10 inference(monotonicity,[status(thm)],[30989])).
% 29.91/20.10 tff(30991,plain,
% 29.91/20.10 ((c2 = c1) <=> (c2 = c3)),
% 29.91/20.10 inference(symmetry,[status(thm)],[30990])).
% 29.91/20.10 tff(30992,plain,
% 29.91/20.10 ((~(c2 = c1)) <=> (~(c2 = c3))),
% 29.91/20.10 inference(monotonicity,[status(thm)],[30991])).
% 29.91/20.10 tff(30993,plain,
% 29.91/20.10 (~(c2 = c3)),
% 29.91/20.10 inference(modus_ponens,[status(thm)],[75, 30992])).
% 29.91/20.10 tff(30994,plain,
% 29.91/20.10 (big_f(c2, c1)),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[30401, 30760, 66, 30400, 30375, 3])).
% 29.91/20.10 tff(30995,plain,
% 29.91/20.10 ((f10(c1) = c3) <=> (f10(c1) = c1)),
% 29.91/20.10 inference(monotonicity,[status(thm)],[30989])).
% 29.91/20.10 tff(30996,plain,
% 29.91/20.10 ((f10(c1) = c1) <=> (f10(c1) = c3)),
% 29.91/20.10 inference(symmetry,[status(thm)],[30995])).
% 29.91/20.10 tff(30997,plain,
% 29.91/20.10 ((~(f10(c1) = c1)) <=> (~(f10(c1) = c3))),
% 29.91/20.10 inference(monotonicity,[status(thm)],[30996])).
% 29.91/20.10 tff(30998,plain,
% 29.91/20.10 (~(f10(c1) = c3)),
% 29.91/20.10 inference(modus_ponens,[status(thm)],[3, 30997])).
% 29.91/20.10 tff(30999,plain,
% 29.91/20.10 (big_f(f10(c1), f10(c1)) <=> big_f(c2, f10(c1))),
% 29.91/20.10 inference(monotonicity,[status(thm)],[15])).
% 29.91/20.10 tff(31000,plain,
% 29.91/20.10 (big_f(c2, c1)),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[25063, 30766, 66, 3, 30769])).
% 29.91/20.10 tff(31001,plain,
% 29.91/20.10 (big_f(c2, f10(c2)) <=> big_f(f10(c1), f10(f10(c1)))),
% 29.91/20.10 inference(monotonicity,[status(thm)],[5571, 30754])).
% 29.91/20.10 tff(31002,plain,
% 29.91/20.10 (big_f(f10(c1), f10(f10(c1))) <=> big_f(c2, f10(c2))),
% 29.91/20.10 inference(symmetry,[status(thm)],[31001])).
% 29.91/20.10 tff(31003,plain,
% 29.91/20.10 (f10(f10(c1)) = c1),
% 29.91/20.10 inference(transitivity,[status(thm)],[24860, 30779])).
% 29.91/20.10 tff(31004,plain,
% 29.91/20.10 (big_f(f10(c1), f10(f10(c1))) <=> big_f(f10(c1), c1)),
% 29.91/20.10 inference(monotonicity,[status(thm)],[31003])).
% 29.91/20.10 tff(31005,plain,
% 29.91/20.10 (big_f(f10(c1), c1) <=> big_f(f10(c1), f10(f10(c1)))),
% 29.91/20.10 inference(symmetry,[status(thm)],[31004])).
% 29.91/20.10 tff(31006,plain,
% 29.91/20.10 (big_f(f10(c1), c1) <=> big_f(c2, f10(c2))),
% 29.91/20.10 inference(transitivity,[status(thm)],[31005, 31002])).
% 29.91/20.10 tff(31007,plain,
% 29.91/20.10 (big_f(c2, c1) <=> big_f(f10(c1), c1)),
% 29.91/20.10 inference(monotonicity,[status(thm)],[5571])).
% 29.91/20.10 tff(31008,plain,
% 29.91/20.10 (big_f(f10(c1), c1)),
% 29.91/20.10 inference(modus_ponens,[status(thm)],[31000, 31007])).
% 29.91/20.10 tff(31009,plain,
% 29.91/20.10 (big_f(c2, f10(c2))),
% 29.91/20.10 inference(modus_ponens,[status(thm)],[31008, 31006])).
% 29.91/20.10 tff(31010,plain,
% 29.91/20.10 (~big_f(c2, c2)),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[30783, 31009, 66, 31000, 30769])).
% 29.91/20.10 tff(31011,plain,
% 29.91/20.10 (~big_f(f7(c1), f6(c1, f6(c1, c2)))),
% 29.91/20.10 inference(unit_resolution,[status(thm)],[30736, 31010, 66, 3])).
% 29.91/20.11 tff(31012,plain,
% 29.91/20.11 (~(f6(c1, c2) = c2)),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[30740, 31011])).
% 29.91/20.11 tff(31013,plain,
% 29.91/20.11 (f6(c1, c2) = c1),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[48, 31012])).
% 29.91/20.11 tff(31014,plain,
% 29.91/20.11 (big_f(f7(c1), f6(c1, f6(c1, c2)))),
% 29.91/20.11 inference(modus_ponens,[status(thm)],[30354, 29927])).
% 29.91/20.11 tff(31015,plain,
% 29.91/20.11 (big_f(c2, f10(c2)) <=> big_f(c2, c1)),
% 29.91/20.11 inference(monotonicity,[status(thm)],[30399])).
% 29.91/20.11 tff(31016,plain,
% 29.91/20.11 (big_f(c2, c1) <=> big_f(c2, f10(c2))),
% 29.91/20.11 inference(symmetry,[status(thm)],[31015])).
% 29.91/20.11 tff(31017,plain,
% 29.91/20.11 (f10(c1) = c1),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[30736, 121, 66, 31014])).
% 29.91/20.11 tff(31018,plain,
% 29.91/20.11 (f9(c1, c2) = c2),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[30808, 31017, 66])).
% 29.91/20.11 tff(31019,plain,
% 29.91/20.11 (big_f(f9(c1, c2), f10(c1)) <=> big_f(c2, c1)),
% 29.91/20.11 inference(monotonicity,[status(thm)],[31018, 31017])).
% 29.91/20.11 tff(31020,plain,
% 29.91/20.11 (big_f(f9(c1, c2), f10(c1)) <=> big_f(c2, f10(c2))),
% 29.91/20.11 inference(transitivity,[status(thm)],[31019, 31016])).
% 29.91/20.11 tff(31021,plain,
% 29.91/20.11 ((~big_f(f9(c1, c2), f10(c1))) <=> (~big_f(c2, f10(c2)))),
% 29.91/20.11 inference(monotonicity,[status(thm)],[31020])).
% 29.91/20.11 tff(31022,plain,
% 29.91/20.11 (~big_f(f9(c1, c2), f10(c1))),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[30854, 31017, 66, 31014])).
% 29.91/20.11 tff(31023,plain,
% 29.91/20.11 (~big_f(c2, f10(c2))),
% 29.91/20.11 inference(modus_ponens,[status(thm)],[31022, 31021])).
% 29.91/20.11 tff(31024,plain,
% 29.91/20.11 (~(f6(c1, f6(c1, c2)) = f6(c1, c2))),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[30966, 13152])).
% 29.91/20.11 tff(31025,plain,
% 29.91/20.11 (~(f6(c1, c2) = c2)),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[43, 31024])).
% 29.91/20.11 tff(31026,plain,
% 29.91/20.11 (f6(c1, c2) = c1),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[48, 31025])).
% 29.91/20.11 tff(31027,plain,
% 29.91/20.11 (big_f(c1, f6(c1, c2)) <=> big_f(c1, c1)),
% 29.91/20.11 inference(monotonicity,[status(thm)],[31026])).
% 29.91/20.11 tff(31028,plain,
% 29.91/20.11 (big_f(c1, c1) <=> big_f(c1, f6(c1, c2))),
% 29.91/20.11 inference(symmetry,[status(thm)],[31027])).
% 29.91/20.11 tff(31029,plain,
% 29.91/20.11 ((~big_f(c1, c1)) <=> (~big_f(c1, f6(c1, c2)))),
% 29.91/20.11 inference(monotonicity,[status(thm)],[31028])).
% 29.91/20.11 tff(31030,plain,
% 29.91/20.11 (~big_f(c1, f6(c1, c2))),
% 29.91/20.11 inference(modus_ponens,[status(thm)],[66, 31029])).
% 29.91/20.11 tff(31031,plain,
% 29.91/20.11 (big_f(f7(c1), f6(c1, c2))),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[30979, 31025, 13152])).
% 29.91/20.11 tff(31032,plain,
% 29.91/20.11 (big_f(c1, f6(c1, c2))),
% 29.91/20.11 inference(modus_ponens,[status(thm)],[31031, 25792])).
% 29.91/20.11 tff(31033,plain,
% 29.91/20.11 ($false),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[31032, 31030])).
% 29.91/20.11 tff(31034,plain,((~(c2 = f8(c2))) | big_f(c1, c1) | (f10(c2) = c2) | big_f(c2, f10(c2)) | (~big_f(f7(c1), f6(c1, f6(c1, c2))))), inference(lemma,lemma(discharge,[]))).
% 29.91/20.11 tff(31035,plain,
% 29.91/20.11 (~(c2 = f8(c2))),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[31034, 31023, 30375, 66, 31014])).
% 29.91/20.11 tff(31036,plain,
% 29.91/20.11 (~(c3 = c2)),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[30982, 31023, 30375, 66, 31014])).
% 29.91/20.11 tff(31037,plain,
% 29.91/20.11 (c3 = c1),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[180, 31036])).
% 29.91/20.11 tff(31038,plain,
% 29.91/20.11 (~(c1 = f8(c2))),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[30394, 30375, 66, 31014])).
% 29.91/20.11 tff(31039,plain,
% 29.91/20.11 (~(f6(f7(c2), c3) = c1)),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[10018, 30770, 28, 172])).
% 29.91/20.11 tff(31040,plain,
% 29.91/20.11 ((f8(f6(c1, f6(c2, c1))) = c1) <=> (c1 = f8(f6(c1, f6(c2, c1))))),
% 29.91/20.11 inference(commutativity,[status(thm)],[])).
% 29.91/20.11 tff(31041,plain,
% 29.91/20.11 ((c1 = f8(f6(c1, f6(c2, c1)))) <=> (f8(f6(c1, f6(c2, c1))) = c1)),
% 29.91/20.11 inference(symmetry,[status(thm)],[31040])).
% 29.91/20.11 tff(31042,plain,
% 29.91/20.11 (f6(c2, c1) = f6(c2, f7(f4(c4)))),
% 29.91/20.11 inference(monotonicity,[status(thm)],[8501])).
% 29.91/20.11 tff(31043,plain,
% 29.91/20.11 (f6(c2, f7(f4(c4))) = f6(c2, c1)),
% 29.91/20.11 inference(symmetry,[status(thm)],[31042])).
% 29.91/20.11 tff(31044,plain,
% 29.91/20.11 (c2 = f6(c2, c1)),
% 29.91/20.11 inference(transitivity,[status(thm)],[26749, 31043])).
% 29.91/20.11 tff(31045,plain,
% 29.91/20.11 (f8(c2) = f8(f6(c2, c1))),
% 29.91/20.11 inference(monotonicity,[status(thm)],[31044])).
% 29.91/20.11 tff(31046,plain,
% 29.91/20.11 (f8(f6(c2, c1)) = f8(c2)),
% 29.91/20.11 inference(symmetry,[status(thm)],[31045])).
% 29.91/20.11 tff(31047,plain,
% 29.91/20.11 (f8(f6(c2, c1)) = f8(f6(c2, f7(f4(c4))))),
% 29.91/20.11 inference(monotonicity,[status(thm)],[31042])).
% 29.91/20.11 tff(31048,plain,
% 29.91/20.11 (f8(f6(c2, f7(f4(c4)))) = f8(f6(c2, c1))),
% 29.91/20.11 inference(symmetry,[status(thm)],[31047])).
% 29.91/20.11 tff(31049,assumption,(f8(f6(c2, f7(f4(c4)))) = c2), introduced(assumption)).
% 29.91/20.11 tff(31050,plain,
% 29.91/20.11 (c2 = f8(f6(c2, f7(f4(c4))))),
% 29.91/20.11 inference(symmetry,[status(thm)],[31049])).
% 29.91/20.11 tff(31051,plain,
% 29.91/20.11 (c2 = f8(c2)),
% 29.91/20.11 inference(transitivity,[status(thm)],[31050, 31048, 31046])).
% 29.91/20.11 tff(31052,plain,
% 29.91/20.11 ($false),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[12290, 31051])).
% 29.91/20.11 tff(31053,plain,((~(f6(c2, f7(f4(c4))) = c2)) | (c2 = f8(c2)) | (~(f8(f6(c2, f7(f4(c4)))) = c2)) | (~(f7(c2) = c1)) | (~(f4(c4) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.91/20.11 tff(31054,plain,
% 29.91/20.11 (~(f8(f6(c2, f7(f4(c4)))) = c2)),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[31053, 17409, 79, 292, 12290])).
% 29.91/20.11 tff(31055,plain,
% 29.91/20.11 (f8(f6(c2, f7(f4(c4)))) = c1),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[24193, 31054])).
% 29.91/20.11 tff(31056,plain,
% 29.91/20.11 (c1 = f8(f6(c2, f7(f4(c4))))),
% 29.91/20.11 inference(symmetry,[status(thm)],[31055])).
% 29.91/20.11 tff(31057,plain,
% 29.91/20.11 (c1 = f8(c2)),
% 29.91/20.11 inference(transitivity,[status(thm)],[31056, 31048, 31046])).
% 29.91/20.11 tff(31058,plain,
% 29.91/20.11 ($false),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[24284, 31057])).
% 29.91/20.11 tff(31059,plain,((~(f6(c2, f7(f4(c4))) = c2)) | (c1 = f8(c2)) | (~(f7(c2) = c1)) | (~(f4(c4) = c2)) | (c2 = f8(c2))), inference(lemma,lemma(discharge,[]))).
% 29.91/20.11 tff(31060,plain,
% 29.91/20.11 (~(f6(c2, f7(f4(c4))) = c2)),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[31059, 12290, 292, 24284, 79])).
% 29.91/20.11 tff(31061,plain,
% 29.91/20.11 (f6(c2, f7(f4(c4))) = c1),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[6601, 31060])).
% 29.91/20.11 tff(31062,plain,
% 29.91/20.11 (f6(c2, c1) = c1),
% 29.91/20.11 inference(transitivity,[status(thm)],[31042, 31061])).
% 29.91/20.11 tff(31063,plain,
% 29.91/20.11 (f6(c1, f6(c2, c1)) = f6(c1, c1)),
% 29.91/20.11 inference(monotonicity,[status(thm)],[31062])).
% 29.91/20.11 tff(31064,plain,
% 29.91/20.11 (f6(c1, f6(c2, c1)) = c2),
% 29.91/20.11 inference(transitivity,[status(thm)],[31063, 5958, 2362])).
% 29.91/20.11 tff(31065,plain,
% 29.91/20.11 (f8(f6(c1, f6(c2, c1))) = f8(c2)),
% 29.91/20.11 inference(monotonicity,[status(thm)],[31064])).
% 29.91/20.11 tff(31066,plain,
% 29.91/20.11 ((c1 = f8(f6(c1, f6(c2, c1)))) <=> (c1 = f8(c2))),
% 29.91/20.11 inference(monotonicity,[status(thm)],[31065])).
% 29.91/20.11 tff(31067,plain,
% 29.91/20.11 ((c1 = f8(c2)) <=> (c1 = f8(f6(c1, f6(c2, c1))))),
% 29.91/20.11 inference(symmetry,[status(thm)],[31066])).
% 29.91/20.11 tff(31068,plain,
% 29.91/20.11 ((c1 = f8(c2)) <=> (f8(f6(c1, f6(c2, c1))) = c1)),
% 29.91/20.11 inference(transitivity,[status(thm)],[31067, 31041])).
% 29.91/20.11 tff(31069,plain,
% 29.91/20.11 ((~(c1 = f8(c2))) <=> (~(f8(f6(c1, f6(c2, c1))) = c1))),
% 29.91/20.11 inference(monotonicity,[status(thm)],[31068])).
% 29.91/20.11 tff(31070,plain,
% 29.91/20.11 (~(f8(f6(c1, f6(c2, c1))) = c1)),
% 29.91/20.11 inference(modus_ponens,[status(thm)],[24284, 31069])).
% 29.91/20.11 tff(31071,plain,
% 29.91/20.11 ((f8(f6(c1, f6(c2, c1))) = c2) <=> (f8(c2) = c2)),
% 29.91/20.11 inference(monotonicity,[status(thm)],[31065])).
% 29.91/20.11 tff(31072,plain,
% 29.91/20.11 ((f8(f6(c1, f6(c2, c1))) = c2) <=> (c2 = f8(c2))),
% 29.91/20.11 inference(transitivity,[status(thm)],[31071, 11998])).
% 29.91/20.11 tff(31073,plain,
% 29.91/20.11 ((c2 = f8(c2)) <=> (f8(f6(c1, f6(c2, c1))) = c2)),
% 29.91/20.11 inference(symmetry,[status(thm)],[31072])).
% 29.91/20.11 tff(31074,plain,
% 29.91/20.11 ((~(c2 = f8(c2))) <=> (~(f8(f6(c1, f6(c2, c1))) = c2))),
% 29.91/20.11 inference(monotonicity,[status(thm)],[31073])).
% 29.91/20.11 tff(31075,plain,
% 29.91/20.11 (~(f8(f6(c1, f6(c2, c1))) = c2)),
% 29.91/20.11 inference(modus_ponens,[status(thm)],[12290, 31074])).
% 29.91/20.11 tff(31076,plain,
% 29.91/20.11 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f8(f6(c1, f6(c2, c1))) = c1) | (f8(f6(c1, f6(c2, c1))) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f8(f6(c1, f6(c2, c1))) = c1) | (f8(f6(c1, f6(c2, c1))) = c2))),
% 29.91/20.11 inference(rewrite,[status(thm)],[])).
% 29.91/20.11 tff(31077,plain,
% 29.91/20.11 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f8(f6(c1, f6(c2, c1))) = c1) | (f8(f6(c1, f6(c2, c1))) = c2))),
% 29.91/20.11 inference(quant_inst,[status(thm)],[])).
% 29.91/20.11 tff(31078,plain,
% 29.91/20.11 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f8(f6(c1, f6(c2, c1))) = c1) | (f8(f6(c1, f6(c2, c1))) = c2)),
% 29.91/20.11 inference(modus_ponens,[status(thm)],[31077, 31076])).
% 29.91/20.11 tff(31079,plain,
% 29.91/20.11 ((f8(f6(c1, f6(c2, c1))) = c1) | (f8(f6(c1, f6(c2, c1))) = c2)),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[31078, 10])).
% 29.91/20.11 tff(31080,plain,
% 29.91/20.11 ($false),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[31079, 31075, 31070])).
% 29.91/20.11 tff(31081,plain,((c2 = f8(c2)) | (~(f6(f7(c2), c3) = c2)) | (~(c3 = c1)) | (~(f7(c2) = c1)) | (~(f4(c4) = c2)) | (c1 = f8(c2))), inference(lemma,lemma(discharge,[]))).
% 29.91/20.11 tff(31082,plain,
% 29.91/20.11 (~(f6(f7(c2), c3) = c2)),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[31081, 30770, 24284, 172, 12290, 79])).
% 29.91/20.11 tff(31083,plain,
% 29.91/20.11 ($false),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[2391, 31082, 31039])).
% 29.91/20.11 tff(31084,plain,((~(f4(c4) = c2)) | (c1 = f8(c2)) | (~(c3 = c1)) | (c2 = f8(c2)) | (f6(c1, c1) = c1) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 29.91/20.11 tff(31085,plain,
% 29.91/20.11 (~(f4(c4) = c2)),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[31084, 31038, 31037, 31035, 28, 66])).
% 29.91/20.11 tff(31086,plain,
% 29.91/20.11 (f4(c4) = c1),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[11750, 31085])).
% 29.91/20.11 tff(31087,plain,
% 29.91/20.11 ((f8(f6(c1, c1)) = c2) <=> (c2 = f8(f6(c1, c1)))),
% 29.91/20.11 inference(commutativity,[status(thm)],[])).
% 29.91/20.11 tff(31088,plain,
% 29.91/20.11 (~(c3 = c2)),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[26203, 24284, 12290])).
% 29.91/20.11 tff(31089,plain,
% 29.91/20.11 (c3 = c1),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[180, 31088])).
% 29.91/20.11 tff(31090,plain,
% 29.91/20.11 (c1 = c3),
% 29.91/20.11 inference(symmetry,[status(thm)],[31089])).
% 29.91/20.11 tff(31091,plain,
% 29.91/20.11 (f6(c2, c1) = f6(f7(c2), c3)),
% 29.91/20.11 inference(monotonicity,[status(thm)],[82, 31090])).
% 29.91/20.11 tff(31092,plain,
% 29.91/20.11 (f6(c2, c1) = c2),
% 29.91/20.11 inference(transitivity,[status(thm)],[31091, 2362])).
% 29.91/20.11 tff(31093,plain,
% 29.91/20.11 (f8(f6(c2, c1)) = f8(c2)),
% 29.91/20.11 inference(monotonicity,[status(thm)],[31092])).
% 29.91/20.11 tff(31094,plain,
% 29.91/20.11 (f7(f4(c4)) = c1),
% 29.91/20.11 inference(transitivity,[status(thm)],[16243, 25791])).
% 29.91/20.11 tff(31095,plain,
% 29.91/20.11 (f6(c2, f7(f4(c4))) = f6(c2, c1)),
% 29.91/20.11 inference(monotonicity,[status(thm)],[31094])).
% 29.91/20.11 tff(31096,plain,
% 29.91/20.11 (f8(f6(c2, f7(f4(c4)))) = f8(f6(c2, c1))),
% 29.91/20.11 inference(monotonicity,[status(thm)],[31095])).
% 29.91/20.11 tff(31097,plain,
% 29.91/20.11 (f8(f6(c2, f7(f4(c4)))) = f8(c2)),
% 29.91/20.11 inference(transitivity,[status(thm)],[31096, 31093])).
% 29.91/20.11 tff(31098,plain,
% 29.91/20.11 ((c2 = f8(f6(c2, f7(f4(c4))))) <=> (c2 = f8(c2))),
% 29.91/20.11 inference(monotonicity,[status(thm)],[31097])).
% 29.91/20.11 tff(31099,plain,
% 29.91/20.11 ((c2 = f8(c2)) <=> (c2 = f8(f6(c2, f7(f4(c4)))))),
% 29.91/20.11 inference(symmetry,[status(thm)],[31098])).
% 29.91/20.11 tff(31100,plain,
% 29.91/20.11 ((c2 = f8(c2)) <=> (f8(f6(c2, f7(f4(c4)))) = c2)),
% 29.91/20.11 inference(transitivity,[status(thm)],[31099, 23360])).
% 29.91/20.11 tff(31101,plain,
% 29.91/20.11 ((~(c2 = f8(c2))) <=> (~(f8(f6(c2, f7(f4(c4)))) = c2))),
% 29.91/20.11 inference(monotonicity,[status(thm)],[31100])).
% 29.91/20.11 tff(31102,plain,
% 29.91/20.11 (~(f8(f6(c2, f7(f4(c4)))) = c2)),
% 29.91/20.11 inference(modus_ponens,[status(thm)],[12290, 31101])).
% 29.91/20.11 tff(31103,plain,
% 29.91/20.11 ((c1 = f8(f6(c2, f7(f4(c4))))) <=> (c1 = f8(c2))),
% 29.91/20.11 inference(monotonicity,[status(thm)],[31097])).
% 29.91/20.11 tff(31104,plain,
% 29.91/20.11 ((c1 = f8(c2)) <=> (c1 = f8(f6(c2, f7(f4(c4)))))),
% 29.91/20.11 inference(symmetry,[status(thm)],[31103])).
% 29.91/20.11 tff(31105,plain,
% 29.91/20.11 ((c1 = f8(c2)) <=> (f8(f6(c2, f7(f4(c4)))) = c1)),
% 29.91/20.11 inference(transitivity,[status(thm)],[31104, 24177])).
% 29.91/20.11 tff(31106,plain,
% 29.91/20.11 ((~(c1 = f8(c2))) <=> (~(f8(f6(c2, f7(f4(c4)))) = c1))),
% 29.91/20.11 inference(monotonicity,[status(thm)],[31105])).
% 29.91/20.11 tff(31107,plain,
% 29.91/20.11 (~(f8(f6(c2, f7(f4(c4)))) = c1)),
% 29.91/20.11 inference(modus_ponens,[status(thm)],[24284, 31106])).
% 29.91/20.11 tff(31108,plain,
% 29.91/20.11 ($false),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[24193, 31107, 31102])).
% 29.91/20.11 tff(31109,plain,((~(f6(f7(c2), c3) = c2)) | (c1 = f8(c2)) | (~(f7(c2) = c2)) | (~(f4(c4) = c1)) | (c2 = f8(c2))), inference(lemma,lemma(discharge,[]))).
% 29.91/20.11 tff(31110,plain,
% 29.91/20.11 (~(f6(f7(c2), c3) = c2)),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[31109, 77, 24284, 12290, 11752])).
% 29.91/20.11 tff(31111,plain,
% 29.91/20.11 (f6(f7(c2), c3) = c1),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[2391, 31110])).
% 29.91/20.11 tff(31112,plain,
% 29.91/20.11 (c1 = f6(f7(c2), c3)),
% 29.91/20.11 inference(symmetry,[status(thm)],[31111])).
% 29.91/20.11 tff(31113,plain,
% 29.91/20.11 (c1 = f6(c2, c1)),
% 29.91/20.11 inference(transitivity,[status(thm)],[31112, 6169])).
% 29.91/20.11 tff(31114,plain,
% 29.91/20.11 (f6(c1, c1) = f6(c1, f6(c2, c1))),
% 29.91/20.11 inference(monotonicity,[status(thm)],[31113])).
% 29.91/20.11 tff(31115,plain,
% 29.91/20.11 (f6(c1, f6(c2, c1)) = f6(c1, c1)),
% 29.91/20.11 inference(symmetry,[status(thm)],[31114])).
% 29.91/20.11 tff(31116,plain,
% 29.91/20.11 (f8(f6(c1, f6(c2, c1))) = f8(f6(c1, c1))),
% 29.91/20.11 inference(monotonicity,[status(thm)],[31115])).
% 29.91/20.11 tff(31117,plain,
% 29.91/20.11 ((f8(f6(c1, f6(c2, c1))) = c2) <=> (f8(f6(c1, c1)) = c2)),
% 29.91/20.11 inference(monotonicity,[status(thm)],[31116])).
% 29.91/20.11 tff(31118,plain,
% 29.91/20.11 ((f8(f6(c1, f6(c2, c1))) = c2) <=> (c2 = f8(f6(c1, c1)))),
% 29.91/20.11 inference(transitivity,[status(thm)],[31117, 31087])).
% 29.91/20.11 tff(31119,plain,
% 29.91/20.11 ((c2 = f8(f6(c1, c1))) <=> (f8(f6(c1, f6(c2, c1))) = c2)),
% 29.91/20.11 inference(symmetry,[status(thm)],[31118])).
% 29.91/20.11 tff(31120,plain,
% 29.91/20.11 ((f6(c1, f6(c2, c1)) = c1) <=> (f6(c1, c1) = c1)),
% 29.91/20.11 inference(monotonicity,[status(thm)],[31115])).
% 29.91/20.11 tff(31121,plain,
% 29.91/20.11 ((f6(c1, c1) = c1) <=> (f6(c1, f6(c2, c1)) = c1)),
% 29.91/20.11 inference(symmetry,[status(thm)],[31120])).
% 29.91/20.11 tff(31122,plain,
% 29.91/20.11 ((~(f6(c1, c1) = c1)) <=> (~(f6(c1, f6(c2, c1)) = c1))),
% 29.91/20.11 inference(monotonicity,[status(thm)],[31121])).
% 29.91/20.11 tff(31123,plain,
% 29.91/20.11 (~(f6(c1, f6(c2, c1)) = c1)),
% 29.91/20.11 inference(modus_ponens,[status(thm)],[28, 31122])).
% 29.91/20.11 tff(31124,plain,
% 29.91/20.11 (f6(c1, f6(c2, c1)) = c2),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[26530, 31123])).
% 29.91/20.11 tff(31125,plain,
% 29.91/20.11 (f6(c1, c1) = c2),
% 29.91/20.11 inference(transitivity,[status(thm)],[31114, 31124])).
% 29.91/20.11 tff(31126,plain,
% 29.91/20.11 (f8(f6(c1, c1)) = f8(c2)),
% 29.91/20.11 inference(monotonicity,[status(thm)],[31125])).
% 29.91/20.11 tff(31127,plain,
% 29.91/20.11 ((c2 = f8(f6(c1, c1))) <=> (c2 = f8(c2))),
% 29.91/20.11 inference(monotonicity,[status(thm)],[31126])).
% 29.91/20.11 tff(31128,plain,
% 29.91/20.11 ((c2 = f8(c2)) <=> (c2 = f8(f6(c1, c1)))),
% 29.91/20.11 inference(symmetry,[status(thm)],[31127])).
% 29.91/20.11 tff(31129,plain,
% 29.91/20.11 ((c2 = f8(c2)) <=> (f8(f6(c1, f6(c2, c1))) = c2)),
% 29.91/20.11 inference(transitivity,[status(thm)],[31128, 31119])).
% 29.91/20.11 tff(31130,plain,
% 29.91/20.11 ((~(c2 = f8(c2))) <=> (~(f8(f6(c1, f6(c2, c1))) = c2))),
% 29.91/20.11 inference(monotonicity,[status(thm)],[31129])).
% 29.91/20.11 tff(31131,plain,
% 29.91/20.11 (~(f8(f6(c1, f6(c2, c1))) = c2)),
% 29.91/20.11 inference(modus_ponens,[status(thm)],[12290, 31130])).
% 29.91/20.11 tff(31132,plain,
% 29.91/20.11 (f8(f6(c1, f6(c2, c1))) = f8(c2)),
% 29.91/20.11 inference(transitivity,[status(thm)],[31116, 31126])).
% 29.91/20.11 tff(31133,plain,
% 29.91/20.11 ((c1 = f8(f6(c1, f6(c2, c1)))) <=> (c1 = f8(c2))),
% 29.91/20.11 inference(monotonicity,[status(thm)],[31132])).
% 29.91/20.11 tff(31134,plain,
% 29.91/20.11 ((c1 = f8(c2)) <=> (c1 = f8(f6(c1, f6(c2, c1))))),
% 29.91/20.11 inference(symmetry,[status(thm)],[31133])).
% 29.91/20.11 tff(31135,plain,
% 29.91/20.11 ((c1 = f8(c2)) <=> (f8(f6(c1, f6(c2, c1))) = c1)),
% 29.91/20.11 inference(transitivity,[status(thm)],[31134, 31041])).
% 29.91/20.11 tff(31136,plain,
% 29.91/20.11 ((~(c1 = f8(c2))) <=> (~(f8(f6(c1, f6(c2, c1))) = c1))),
% 29.91/20.11 inference(monotonicity,[status(thm)],[31135])).
% 29.91/20.11 tff(31137,plain,
% 29.91/20.11 (~(f8(f6(c1, f6(c2, c1))) = c1)),
% 29.91/20.11 inference(modus_ponens,[status(thm)],[24284, 31136])).
% 29.91/20.11 tff(31138,plain,
% 29.91/20.11 ($false),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[31079, 31137, 31131])).
% 29.91/20.11 tff(31139,plain,((~(f7(c2) = c2)) | (c1 = f8(c2)) | (~(c3 = c1)) | (c2 = f8(c2)) | (f6(c1, c1) = c1) | (~(f4(c4) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.91/20.11 tff(31140,plain,
% 29.91/20.11 (~(f7(c2) = c2)),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[31139, 31038, 31037, 31035, 28, 31086])).
% 29.91/20.11 tff(31141,plain,
% 29.91/20.11 (f7(c2) = c1),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[21, 31140])).
% 29.91/20.11 tff(31142,plain,
% 29.91/20.11 (~(f6(f7(c2), c3) = c1)),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[10018, 31141, 28, 31037])).
% 29.91/20.11 tff(31143,plain,
% 29.91/20.11 (f6(f7(c2), c3) = c2),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[2391, 31142])).
% 29.91/20.11 tff(31144,plain,
% 29.91/20.11 (c1 = f7(f4(c4))),
% 29.91/20.11 inference(transitivity,[status(thm)],[30840, 16244])).
% 29.91/20.11 tff(31145,plain,
% 29.91/20.11 (f6(c2, c1) = f6(c2, f7(f4(c4)))),
% 29.91/20.11 inference(monotonicity,[status(thm)],[31144])).
% 29.91/20.11 tff(31146,plain,
% 29.91/20.11 (f6(c2, f7(f4(c4))) = f6(c2, c1)),
% 29.91/20.11 inference(symmetry,[status(thm)],[31145])).
% 29.91/20.11 tff(31147,plain,
% 29.91/20.11 (f8(f6(c2, f7(f4(c4)))) = f8(f6(c2, c1))),
% 29.91/20.11 inference(monotonicity,[status(thm)],[31146])).
% 29.91/20.11 tff(31148,plain,
% 29.91/20.11 (f8(f6(c2, c1)) = f8(f6(c2, f7(f4(c4))))),
% 29.91/20.11 inference(symmetry,[status(thm)],[31147])).
% 29.91/20.11 tff(31149,plain,
% 29.91/20.11 (f6(c2, c1) = c2),
% 29.91/20.11 inference(transitivity,[status(thm)],[31145, 17409])).
% 29.91/20.11 tff(31150,plain,
% 29.91/20.11 (f8(f6(c2, c1)) = f8(c2)),
% 29.91/20.11 inference(monotonicity,[status(thm)],[31149])).
% 29.91/20.11 tff(31151,plain,
% 29.91/20.11 (f8(c2) = f8(f6(c2, c1))),
% 29.91/20.11 inference(symmetry,[status(thm)],[31150])).
% 29.91/20.11 tff(31152,plain,
% 29.91/20.11 (f8(c2) = f8(f6(c2, f7(f4(c4))))),
% 29.91/20.11 inference(transitivity,[status(thm)],[31151, 31148])).
% 29.91/20.11 tff(31153,plain,
% 29.91/20.11 ((c2 = f8(c2)) <=> (c2 = f8(f6(c2, f7(f4(c4)))))),
% 29.91/20.11 inference(monotonicity,[status(thm)],[31152])).
% 29.91/20.11 tff(31154,plain,
% 29.91/20.11 ((c2 = f8(c2)) <=> (f8(f6(c2, f7(f4(c4)))) = c2)),
% 29.91/20.11 inference(transitivity,[status(thm)],[31153, 23360])).
% 29.91/20.11 tff(31155,plain,
% 29.91/20.11 ((~(c2 = f8(c2))) <=> (~(f8(f6(c2, f7(f4(c4)))) = c2))),
% 29.91/20.11 inference(monotonicity,[status(thm)],[31154])).
% 29.91/20.11 tff(31156,plain,
% 29.91/20.11 (~(f8(f6(c2, f7(f4(c4)))) = c2)),
% 29.91/20.11 inference(modus_ponens,[status(thm)],[12290, 31155])).
% 29.91/20.11 tff(31157,plain,
% 29.91/20.11 (f8(f6(c2, f7(f4(c4)))) = f8(c2)),
% 29.91/20.11 inference(transitivity,[status(thm)],[31147, 31150])).
% 29.91/20.11 tff(31158,plain,
% 29.91/20.11 ((c1 = f8(f6(c2, f7(f4(c4))))) <=> (c1 = f8(c2))),
% 29.91/20.11 inference(monotonicity,[status(thm)],[31157])).
% 29.91/20.11 tff(31159,plain,
% 29.91/20.11 ((c1 = f8(c2)) <=> (c1 = f8(f6(c2, f7(f4(c4)))))),
% 29.91/20.11 inference(symmetry,[status(thm)],[31158])).
% 29.91/20.11 tff(31160,plain,
% 29.91/20.11 ((c1 = f8(c2)) <=> (f8(f6(c2, f7(f4(c4)))) = c1)),
% 29.91/20.11 inference(transitivity,[status(thm)],[31159, 24177])).
% 29.91/20.11 tff(31161,plain,
% 29.91/20.11 ((~(c1 = f8(c2))) <=> (~(f8(f6(c2, f7(f4(c4)))) = c1))),
% 29.91/20.11 inference(monotonicity,[status(thm)],[31160])).
% 29.91/20.11 tff(31162,plain,
% 29.91/20.11 (~(f8(f6(c2, f7(f4(c4)))) = c1)),
% 29.91/20.11 inference(modus_ponens,[status(thm)],[24284, 31161])).
% 29.91/20.11 tff(31163,plain,
% 29.91/20.11 ($false),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[24193, 31162, 31156])).
% 29.91/20.11 tff(31164,plain,((~(f6(c2, f7(f4(c4))) = c2)) | (c1 = f8(c2)) | (~(f4(c4) = c1)) | (c2 = f8(c2))), inference(lemma,lemma(discharge,[]))).
% 29.91/20.11 tff(31165,plain,
% 29.91/20.11 (~(f6(c2, f7(f4(c4))) = c2)),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[31164, 31038, 31086, 31035])).
% 29.91/20.11 tff(31166,plain,
% 29.91/20.11 (f6(c2, f7(f4(c4))) = c1),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[6601, 31165])).
% 29.91/20.11 tff(31167,plain,
% 29.91/20.11 (f6(c2, c1) = c1),
% 29.91/20.11 inference(transitivity,[status(thm)],[31145, 6634])).
% 29.91/20.11 tff(31168,plain,
% 29.91/20.11 (f6(c1, f6(c2, c1)) = f6(c1, c1)),
% 29.91/20.11 inference(monotonicity,[status(thm)],[31167])).
% 29.91/20.11 tff(31169,plain,
% 29.91/20.11 (f6(c1, c1) = f6(c1, f6(c2, c1))),
% 29.91/20.11 inference(symmetry,[status(thm)],[31168])).
% 29.91/20.11 tff(31170,plain,
% 29.91/20.11 (c2 = f6(c1, f6(c2, c1))),
% 29.91/20.11 inference(transitivity,[status(thm)],[6728, 18491, 31169])).
% 29.91/20.11 tff(31171,plain,
% 29.91/20.11 (f8(c2) = f8(f6(c1, f6(c2, c1)))),
% 29.91/20.11 inference(monotonicity,[status(thm)],[31170])).
% 29.91/20.11 tff(31172,plain,
% 29.91/20.11 (f8(f6(c1, f6(c2, c1))) = f8(c2)),
% 29.91/20.11 inference(symmetry,[status(thm)],[31171])).
% 29.91/20.11 tff(31173,assumption,(f8(f6(c1, f6(c2, c1))) = c2), introduced(assumption)).
% 29.91/20.11 tff(31174,plain,
% 29.91/20.11 (c2 = f8(f6(c1, f6(c2, c1)))),
% 29.91/20.11 inference(symmetry,[status(thm)],[31173])).
% 29.91/20.11 tff(31175,plain,
% 29.91/20.11 (c2 = f8(c2)),
% 29.91/20.11 inference(transitivity,[status(thm)],[31174, 31172])).
% 29.91/20.11 tff(31176,plain,
% 29.91/20.11 ($false),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[12290, 31175])).
% 29.91/20.11 tff(31177,plain,((~(f6(c2, f7(f4(c4))) = c1)) | (c2 = f8(c2)) | (~(f8(f6(c1, f6(c2, c1))) = c2)) | (~(f6(f7(c2), c3) = c2)) | (~(c3 = c1)) | (~(f7(c2) = c1)) | (~(f4(c4) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.91/20.11 tff(31178,plain,
% 29.91/20.11 (~(f8(f6(c1, f6(c2, c1))) = c2)),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[31177, 31166, 31035, 31143, 31037, 31141, 31086])).
% 29.91/20.11 tff(31179,assumption,(f8(f6(c1, f6(c2, c1))) = c1), introduced(assumption)).
% 29.91/20.11 tff(31180,plain,
% 29.91/20.11 (c1 = f8(f6(c1, f6(c2, c1)))),
% 29.91/20.11 inference(symmetry,[status(thm)],[31179])).
% 29.91/20.11 tff(31181,plain,
% 29.91/20.11 (c1 = f8(c2)),
% 29.91/20.11 inference(transitivity,[status(thm)],[31180, 31172])).
% 29.91/20.11 tff(31182,plain,
% 29.91/20.11 ($false),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[24284, 31181])).
% 29.91/20.11 tff(31183,plain,((~(f6(c2, f7(f4(c4))) = c1)) | (c1 = f8(c2)) | (~(f8(f6(c1, f6(c2, c1))) = c1)) | (~(f6(f7(c2), c3) = c2)) | (~(c3 = c1)) | (~(f7(c2) = c1)) | (~(f4(c4) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.91/20.11 tff(31184,plain,
% 29.91/20.11 (~(f8(f6(c1, f6(c2, c1))) = c1)),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[31183, 31166, 31038, 31143, 31037, 31141, 31086])).
% 29.91/20.11 tff(31185,plain,
% 29.91/20.11 ($false),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[31079, 31184, 31178])).
% 29.91/20.11 tff(31186,plain,(big_f(c2, c2) | (f6(c1, c1) = c1) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 29.91/20.11 tff(31187,plain,
% 29.91/20.11 (big_f(c2, c2)),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[31186, 28, 66])).
% 29.91/20.11 tff(31188,plain,
% 29.91/20.11 (c1 = c3),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[30879, 11752, 1345, 66])).
% 29.91/20.11 tff(31189,plain,
% 29.91/20.11 (c3 = c1),
% 29.91/20.11 inference(symmetry,[status(thm)],[31188])).
% 29.91/20.11 tff(31190,plain,
% 29.91/20.11 ((c2 = c3) <=> (c2 = c1)),
% 29.91/20.11 inference(monotonicity,[status(thm)],[31189])).
% 29.91/20.11 tff(31191,plain,
% 29.91/20.11 ((c2 = c1) <=> (c2 = c3)),
% 29.91/20.11 inference(symmetry,[status(thm)],[31190])).
% 29.91/20.11 tff(31192,plain,
% 29.91/20.11 ((~(c2 = c1)) <=> (~(c2 = c3))),
% 29.91/20.11 inference(monotonicity,[status(thm)],[31191])).
% 29.91/20.11 tff(31193,plain,
% 29.91/20.11 (~(c2 = c3)),
% 29.91/20.11 inference(modus_ponens,[status(thm)],[75, 31192])).
% 29.91/20.11 tff(31194,plain,
% 29.91/20.11 (c3 = c1),
% 29.91/20.11 inference(modus_ponens,[status(thm)],[31188, 12387])).
% 29.91/20.11 tff(31195,plain,
% 29.91/20.11 (big_f(f4(c4), c4) <=> big_f(c1, c1)),
% 29.91/20.11 inference(monotonicity,[status(thm)],[11752, 480])).
% 29.91/20.11 tff(31196,plain,
% 29.91/20.11 (big_f(c1, c1) <=> big_f(f4(c4), c4)),
% 29.91/20.11 inference(symmetry,[status(thm)],[31195])).
% 29.91/20.11 tff(31197,plain,
% 29.91/20.11 ((~big_f(c1, c1)) <=> (~big_f(f4(c4), c4))),
% 29.91/20.11 inference(monotonicity,[status(thm)],[31196])).
% 29.91/20.11 tff(31198,plain,
% 29.91/20.11 (~big_f(f4(c4), c4)),
% 29.91/20.11 inference(modus_ponens,[status(thm)],[66, 31197])).
% 29.91/20.11 tff(31199,plain,
% 29.91/20.11 (big_f(c3, f2(c3))),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[1315, 31198])).
% 29.91/20.11 tff(31200,plain,
% 29.91/20.11 (big_f(c1, f2(c1))),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[8631, 31199, 31194])).
% 29.91/20.11 tff(31201,plain,
% 29.91/20.11 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(c1 = f2(c1))) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))) | (~(c1 = c3)) | (~(c1 = f2(c1))) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))))),
% 29.91/20.11 inference(rewrite,[status(thm)],[])).
% 29.91/20.11 tff(31202,plain,
% 29.91/20.11 (((~(c1 = c3)) | (~(c1 = f2(c1))) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | big_f(c1, c1)) <=> ((~(c1 = c3)) | (~(c1 = f2(c1))) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))))),
% 29.91/20.11 inference(rewrite,[status(thm)],[])).
% 29.91/20.11 tff(31203,plain,
% 29.91/20.11 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(c1 = f2(c1))) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | big_f(c1, c1))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(c1 = f2(c1))) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1)))))),
% 29.91/20.11 inference(monotonicity,[status(thm)],[31202])).
% 29.91/20.11 tff(31204,plain,
% 29.91/20.11 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(c1 = f2(c1))) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | big_f(c1, c1))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))) | (~(c1 = c3)) | (~(c1 = f2(c1))) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))))),
% 29.91/20.11 inference(transitivity,[status(thm)],[31203, 31201])).
% 29.91/20.11 tff(31205,plain,
% 29.91/20.11 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(c1 = f2(c1))) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | big_f(c1, c1))),
% 29.91/20.11 inference(quant_inst,[status(thm)],[])).
% 29.91/20.11 tff(31206,plain,
% 29.91/20.11 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))) | big_f(X10, X12))) | (~(c1 = c3)) | (~(c1 = f2(c1))) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1)))),
% 29.91/20.11 inference(modus_ponens,[status(thm)],[31205, 31204])).
% 29.91/20.11 tff(31207,plain,
% 29.91/20.11 ((~(c1 = c3)) | (~(c1 = f2(c1))) | (~(c1 = c4)) | (~(c1 = f4(c1)))),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[31206, 1300, 66])).
% 29.91/20.11 tff(31208,plain,
% 29.91/20.11 (~(c1 = f2(c1))),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[31207, 19825, 31188, 564])).
% 29.91/20.11 tff(31209,plain,
% 29.91/20.11 (~(f2(c3) = c1)),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[6771, 31208, 31194])).
% 29.91/20.11 tff(31210,plain,
% 29.91/20.11 (f2(c3) = c2),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[1273, 31209])).
% 29.91/20.11 tff(31211,plain,
% 29.91/20.11 ((f10(c1) = c1) | (~(f6(c1, c2) = c2)) | (~big_f(c2, c2))),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[29147, 30354])).
% 29.91/20.11 tff(31212,plain,
% 29.91/20.11 (~(f6(c1, c2) = c2)),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[31211, 3, 1345])).
% 29.91/20.11 tff(31213,plain,
% 29.91/20.11 (f6(c1, c2) = c1),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[48, 31212])).
% 29.91/20.11 tff(31214,plain,
% 29.91/20.11 (c1 = f6(c1, c2)),
% 29.91/20.11 inference(modus_ponens,[status(thm)],[31213, 30831])).
% 29.91/20.11 tff(31215,plain,
% 29.91/20.11 (big_f(f7(c1), f6(c1, c2))),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[27092, 31212, 1345, 1319, 6546, 172, 3])).
% 29.91/20.11 tff(31216,plain,
% 29.91/20.11 (~(big_f(c1, c1) <=> big_f(f7(c1), f6(c1, c2)))),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[30844, 31215])).
% 29.91/20.11 tff(31217,plain,
% 29.91/20.11 (~(c1 = f6(c1, c2))),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[30851, 31216, 30840])).
% 29.91/20.11 tff(31218,plain,
% 29.91/20.11 ($false),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[31217, 31214])).
% 29.91/20.11 tff(31219,plain,((f10(c1) = c1) | big_f(c1, c1) | (~big_f(c2, c2)) | (~(f2(c3) = c2)) | (~big_f(c1, f2(c1))) | (~(c3 = c1))), inference(lemma,lemma(discharge,[]))).
% 29.91/20.11 tff(31220,plain,
% 29.91/20.11 (f10(c1) = c1),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[31219, 31210, 1345, 66, 31200, 31194])).
% 29.91/20.11 tff(31221,plain,
% 29.91/20.11 (~big_f(c2, c1)),
% 29.91/20.11 inference(unit_resolution,[status(thm)],[30857, 31220, 66, 30373])).
% 29.91/20.11 tff(31222,plain,
% 29.91/20.11 (~big_f(c2, c4)),
% 29.91/20.11 inference(modus_ponens,[status(thm)],[31221, 3835])).
% 29.91/20.11 tff(31223,plain,
% 29.91/20.11 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c2 = c3) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (c2 = c3) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2))),
% 29.91/20.11 inference(rewrite,[status(thm)],[])).
% 29.91/20.11 tff(31224,plain,
% 29.91/20.11 (((c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1)))) <=> ((c2 = c3) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2))),
% 29.91/20.11 inference(rewrite,[status(thm)],[])).
% 29.91/20.11 tff(31225,plain,
% 29.91/20.11 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c2 = c3) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2)))),
% 29.91/20.11 inference(monotonicity,[status(thm)],[31224])).
% 29.91/20.11 tff(31226,plain,
% 29.91/20.11 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (c2 = c3) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2))),
% 29.91/20.11 inference(transitivity,[status(thm)],[31225, 31223])).
% 29.91/20.11 tff(31227,plain,
% 29.91/20.11 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((c2 = c3) | (f1(c2, c2) = c2) | big_f(c2, f1(c2, c2)) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))))),
% 29.91/20.12 inference(quant_inst,[status(thm)],[])).
% 29.91/20.12 tff(31228,plain,
% 29.91/20.12 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (c2 = c3) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | big_f(c2, f1(c2, c2)) | (f1(c2, c2) = c2)),
% 29.91/20.12 inference(modus_ponens,[status(thm)],[31227, 31226])).
% 29.91/20.12 tff(31229,plain,
% 29.91/20.12 ($false),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[31228, 402, 564, 377, 1828, 14892, 19844, 66])).
% 29.91/20.12 tff(31230,plain,((f1(c2, c2) = c2) | (c2 = c3) | (~(c1 = f4(c1))) | big_f(c1, c1) | (~(c4 = c1)) | big_f(c2, c4)), inference(lemma,lemma(discharge,[]))).
% 29.91/20.12 tff(31231,plain,
% 29.91/20.12 (f1(c2, c2) = c2),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[31230, 19825, 31193, 66, 480, 31222])).
% 29.91/20.12 tff(31232,plain,
% 29.91/20.12 (big_f(c2, f1(c2, c2)) <=> big_f(c2, c2)),
% 29.91/20.12 inference(monotonicity,[status(thm)],[31231])).
% 29.91/20.12 tff(31233,plain,
% 29.91/20.12 (big_f(c2, c2) <=> big_f(c2, f1(c2, c2))),
% 29.91/20.12 inference(symmetry,[status(thm)],[31232])).
% 29.91/20.12 tff(31234,plain,
% 29.91/20.12 (big_f(c2, f1(c2, c2))),
% 29.91/20.12 inference(modus_ponens,[status(thm)],[1345, 31233])).
% 29.91/20.12 tff(31235,plain,
% 29.91/20.12 ($false),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[23962, 447, 564, 31193, 31231, 31234, 19825, 66])).
% 29.91/20.12 tff(31236,plain,((~(c4 = c1)) | big_f(c1, c1) | (~big_f(c2, c2)) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))) | (~(f4(c4) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.91/20.12 tff(31237,plain,
% 29.91/20.12 (~(c4 = c1)),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[31236, 11752, 1345, 30373, 66])).
% 29.91/20.12 tff(31238,plain,
% 29.91/20.12 (c4 = c2),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[461, 31237])).
% 29.91/20.12 tff(31239,plain,
% 29.91/20.12 (c2 = c4),
% 29.91/20.12 inference(symmetry,[status(thm)],[31238])).
% 29.91/20.12 tff(31240,plain,
% 29.91/20.12 (f4(c2) = f4(c4)),
% 29.91/20.12 inference(monotonicity,[status(thm)],[31239])).
% 29.91/20.12 tff(31241,plain,
% 29.91/20.12 (f4(c2) = c1),
% 29.91/20.12 inference(transitivity,[status(thm)],[31240, 11752])).
% 29.91/20.12 tff(31242,plain,
% 29.91/20.12 ((c2 = f4(c2)) <=> (c2 = c1)),
% 29.91/20.12 inference(monotonicity,[status(thm)],[31241])).
% 29.91/20.12 tff(31243,plain,
% 29.91/20.12 ((c2 = c1) <=> (c2 = f4(c2))),
% 29.91/20.12 inference(symmetry,[status(thm)],[31242])).
% 29.91/20.12 tff(31244,plain,
% 29.91/20.12 ((~(c2 = c1)) <=> (~(c2 = f4(c2)))),
% 29.91/20.12 inference(monotonicity,[status(thm)],[31243])).
% 29.91/20.12 tff(31245,plain,
% 29.91/20.12 (~(c2 = f4(c2))),
% 29.91/20.12 inference(modus_ponens,[status(thm)],[75, 31244])).
% 29.91/20.12 tff(31246,plain,
% 29.91/20.12 (c2 = c4),
% 29.91/20.12 inference(modus_ponens,[status(thm)],[31238, 159])).
% 29.91/20.12 tff(31247,plain,
% 29.91/20.12 ($false),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[16875, 553, 631, 16857, 1345, 377, 1908, 5263])).
% 29.91/20.12 tff(31248,plain,((~(f1(c2, c2) = c2)) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)) | (c2 = c3)), inference(lemma,lemma(discharge,[]))).
% 29.91/20.12 tff(31249,plain,
% 29.91/20.12 (~(f1(c2, c2) = c2)),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[31248, 31246, 31245, 1345, 31193])).
% 29.91/20.12 tff(31250,plain,
% 29.91/20.12 (f1(c2, c2) = c1),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[5270, 31249])).
% 29.91/20.12 tff(31251,plain,
% 29.91/20.12 (c1 = f1(c2, c2)),
% 29.91/20.12 inference(symmetry,[status(thm)],[31250])).
% 29.91/20.12 tff(31252,plain,
% 29.91/20.12 (big_f(c2, c1) <=> big_f(c2, f1(c2, c2))),
% 29.91/20.12 inference(monotonicity,[status(thm)],[31251])).
% 29.91/20.12 tff(31253,plain,
% 29.91/20.12 ((~big_f(c2, c1)) <=> (~big_f(c2, f1(c2, c2)))),
% 29.91/20.12 inference(monotonicity,[status(thm)],[31252])).
% 29.91/20.12 tff(31254,plain,
% 29.91/20.12 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | ((~(c2 = c4)) | (c2 = f4(c2)) | (~(c1 = c3)) | (~(c1 = f2(c1))) | big_f(c1, c1) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | (~(c2 = c4)) | (c2 = f4(c2)) | (~(c1 = c3)) | (~(c1 = f2(c1))) | big_f(c1, c1) | (~big_f(c2, c2)))),
% 29.91/20.12 inference(rewrite,[status(thm)],[])).
% 29.91/20.12 tff(31255,plain,
% 29.91/20.12 (((~(c1 = c3)) | (~(c1 = f2(c1))) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)) | big_f(c1, c1)) <=> ((~(c2 = c4)) | (c2 = f4(c2)) | (~(c1 = c3)) | (~(c1 = f2(c1))) | big_f(c1, c1) | (~big_f(c2, c2)))),
% 29.91/20.12 inference(rewrite,[status(thm)],[])).
% 29.91/20.12 tff(31256,plain,
% 29.91/20.12 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(c1 = f2(c1))) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)) | big_f(c1, c1))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | ((~(c2 = c4)) | (c2 = f4(c2)) | (~(c1 = c3)) | (~(c1 = f2(c1))) | big_f(c1, c1) | (~big_f(c2, c2))))),
% 29.91/20.12 inference(monotonicity,[status(thm)],[31255])).
% 29.91/20.12 tff(31257,plain,
% 29.91/20.12 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(c1 = f2(c1))) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)) | big_f(c1, c1))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | (~(c2 = c4)) | (c2 = f4(c2)) | (~(c1 = c3)) | (~(c1 = f2(c1))) | big_f(c1, c1) | (~big_f(c2, c2)))),
% 29.91/20.12 inference(transitivity,[status(thm)],[31256, 31254])).
% 29.91/20.12 tff(31258,plain,
% 29.91/20.12 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | ((~(c1 = c3)) | (~(c1 = f2(c1))) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)) | big_f(c1, c1))),
% 29.91/20.12 inference(quant_inst,[status(thm)],[])).
% 29.91/20.12 tff(31259,plain,
% 29.91/20.12 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | (~(c2 = c4)) | (c2 = f4(c2)) | (~(c1 = c3)) | (~(c1 = f2(c1))) | big_f(c1, c1) | (~big_f(c2, c2))),
% 29.91/20.12 inference(modus_ponens,[status(thm)],[31258, 31257])).
% 29.91/20.12 tff(31260,plain,
% 29.91/20.12 ((~(c2 = c4)) | (c2 = f4(c2)) | (~(c1 = c3)) | (~(c1 = f2(c1)))),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[31259, 11666, 1345, 66])).
% 29.91/20.12 tff(31261,plain,
% 29.91/20.12 (~(c1 = f2(c1))),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[31260, 31245, 31188, 31246])).
% 29.91/20.12 tff(31262,plain,
% 29.91/20.12 (~(f2(c3) = c1)),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[6771, 31261, 31194])).
% 29.91/20.12 tff(31263,plain,
% 29.91/20.12 (f2(c3) = c2),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[1273, 31262])).
% 29.91/20.12 tff(31264,plain,
% 29.91/20.12 (big_f(c3, c2) <=> big_f(c1, c2)),
% 29.91/20.12 inference(monotonicity,[status(thm)],[31189])).
% 29.91/20.12 tff(31265,plain,
% 29.91/20.12 (big_f(c1, c2) <=> big_f(c3, c2)),
% 29.91/20.12 inference(symmetry,[status(thm)],[31264])).
% 29.91/20.12 tff(31266,plain,
% 29.91/20.12 (big_f(c3, c2)),
% 29.91/20.12 inference(modus_ponens,[status(thm)],[30354, 31265])).
% 29.91/20.12 tff(31267,plain,
% 29.91/20.12 (big_f(c3, f2(c3))),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[1325, 31263, 31266])).
% 29.91/20.12 tff(31268,plain,
% 29.91/20.12 (big_f(c1, f2(c1))),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[8631, 31267, 31194])).
% 29.91/20.12 tff(31269,plain,
% 29.91/20.12 (f10(c1) = c1),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[31219, 31268, 1345, 66, 31263, 31194])).
% 29.91/20.12 tff(31270,plain,
% 29.91/20.12 (~big_f(c2, c1)),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[30857, 31269, 66, 30373])).
% 29.91/20.12 tff(31271,plain,
% 29.91/20.12 (~big_f(c2, f1(c2, c2))),
% 29.91/20.12 inference(modus_ponens,[status(thm)],[31270, 31253])).
% 29.91/20.12 tff(31272,plain,
% 29.91/20.12 ($false),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[16863, 525, 31246, 31245, 1345, 31193, 31249, 31271])).
% 29.91/20.12 tff(31273,plain,((~(f4(c4) = c1)) | (~big_f(c2, c2)) | big_f(c1, c1) | (~big_f(f7(c1), f6(c1, f6(c1, c2))))), inference(lemma,lemma(discharge,[]))).
% 29.91/20.12 tff(31274,plain,
% 29.91/20.12 (~(f4(c4) = c1)),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[31273, 31187, 66, 31014])).
% 29.91/20.12 tff(31275,plain,
% 29.91/20.12 (f4(c4) = c2),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[11750, 31274])).
% 29.91/20.12 tff(31276,plain,
% 29.91/20.12 (~(f10(c2) = c2)),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[30768, 31275, 66])).
% 29.91/20.12 tff(31277,plain,
% 29.91/20.12 (f10(c2) = c1),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[93, 31276])).
% 29.91/20.12 tff(31278,plain,
% 29.91/20.12 (big_f(c2, f10(c2)) <=> big_f(c2, c1)),
% 29.91/20.12 inference(monotonicity,[status(thm)],[31277])).
% 29.91/20.12 tff(31279,plain,
% 29.91/20.12 (big_f(c2, c1) <=> big_f(c2, f10(c2))),
% 29.91/20.12 inference(symmetry,[status(thm)],[31278])).
% 29.91/20.12 tff(31280,plain,
% 29.91/20.12 ((~big_f(c2, c1)) <=> (~big_f(c2, f10(c2)))),
% 29.91/20.12 inference(monotonicity,[status(thm)],[31279])).
% 29.91/20.12 tff(31281,plain,
% 29.91/20.12 (~(c1 = f8(c2))),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[30394, 31276, 66, 31014])).
% 29.91/20.12 tff(31282,plain,
% 29.91/20.12 (~(f4(c4) = c2)),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[31084, 31089, 24284, 12290, 28, 66])).
% 29.91/20.12 tff(31283,plain,
% 29.91/20.12 (f4(c4) = c1),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[11750, 31282])).
% 29.91/20.12 tff(31284,plain,
% 29.91/20.12 (~(f7(c2) = c2)),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[31139, 31283, 24284, 12290, 28, 31089])).
% 29.91/20.12 tff(31285,plain,
% 29.91/20.12 (f7(c2) = c1),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[21, 31284])).
% 29.91/20.12 tff(31286,plain,
% 29.91/20.12 (~(f6(c2, f7(f4(c4))) = c2)),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[31164, 31283, 24284, 12290])).
% 29.91/20.12 tff(31287,plain,
% 29.91/20.12 (f6(c2, f7(f4(c4))) = c1),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[6601, 31286])).
% 29.91/20.12 tff(31288,plain,
% 29.91/20.12 (~(f6(f7(c2), c3) = c1)),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[10018, 31285, 28, 31089])).
% 29.91/20.12 tff(31289,plain,
% 29.91/20.12 (f6(f7(c2), c3) = c2),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[2391, 31288])).
% 29.91/20.12 tff(31290,plain,
% 29.91/20.12 (~(f8(f6(c1, f6(c2, c1))) = c2)),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[31177, 31289, 12290, 31287, 31089, 31285, 31283])).
% 29.91/20.12 tff(31291,plain,
% 29.91/20.12 (~(f8(f6(c1, f6(c2, c1))) = c1)),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[31183, 31289, 24284, 31287, 31089, 31285, 31283])).
% 29.91/20.12 tff(31292,plain,
% 29.91/20.12 ($false),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[31079, 31291, 31290])).
% 29.91/20.12 tff(31293,plain,((c1 = f8(c2)) | (c2 = f8(c2)) | (f6(c1, c1) = c1) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 29.91/20.12 tff(31294,plain,
% 29.91/20.12 (c2 = f8(c2)),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[31293, 31281, 28, 66])).
% 29.91/20.12 tff(31295,plain,
% 29.91/20.12 (big_f(c2, f10(c2))),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[31034, 31294, 31276, 66, 31014])).
% 29.91/20.12 tff(31296,plain,
% 29.91/20.12 (~big_f(c2, c1)),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[30783, 31295, 66, 31187, 31276])).
% 29.91/20.12 tff(31297,plain,
% 29.91/20.12 (~big_f(c2, f10(c2))),
% 29.91/20.12 inference(modus_ponens,[status(thm)],[31296, 31280])).
% 29.91/20.12 tff(31298,plain,
% 29.91/20.12 ($false),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[31295, 31297])).
% 29.91/20.12 tff(31299,plain,((f6(c1, c1) = c1) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 29.91/20.12 tff(31300,plain,
% 29.91/20.12 (f6(c1, c1) = c1),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[31299, 66])).
% 29.91/20.12 tff(31301,plain,
% 29.91/20.12 (big_f(c1, f6(c1, c1)) <=> big_f(c1, c1)),
% 29.91/20.12 inference(monotonicity,[status(thm)],[31300])).
% 29.91/20.12 tff(31302,plain,
% 29.91/20.12 (big_f(c1, c1) <=> big_f(c1, f6(c1, c1))),
% 29.91/20.12 inference(symmetry,[status(thm)],[31301])).
% 29.91/20.12 tff(31303,plain,
% 29.91/20.12 (big_f(c1, c1) <=> big_f(f7(c1), f6(c1, c1))),
% 29.91/20.12 inference(transitivity,[status(thm)],[31302, 28010])).
% 29.91/20.12 tff(31304,plain,
% 29.91/20.12 ((~big_f(c1, c1)) <=> (~big_f(f7(c1), f6(c1, c1)))),
% 29.91/20.12 inference(monotonicity,[status(thm)],[31303])).
% 29.91/20.12 tff(31305,plain,
% 29.91/20.12 (~big_f(f7(c1), f6(c1, c1))),
% 29.91/20.12 inference(modus_ponens,[status(thm)],[66, 31304])).
% 29.91/20.12 tff(31306,plain,
% 29.91/20.12 (f6(c1, c1) = f10(c1)),
% 29.91/20.12 inference(transitivity,[status(thm)],[5958, 2362, 293])).
% 29.91/20.12 tff(31307,plain,
% 29.91/20.12 (big_f(f7(c1), f6(c1, c1)) <=> big_f(c1, f10(c1))),
% 29.91/20.12 inference(monotonicity,[status(thm)],[4234, 31306])).
% 29.91/20.12 tff(31308,plain,
% 29.91/20.12 (big_f(c1, f10(c1)) <=> big_f(f7(c1), f6(c1, c1))),
% 29.91/20.12 inference(symmetry,[status(thm)],[31307])).
% 29.91/20.12 tff(31309,plain,
% 29.91/20.12 (big_f(f7(c1), f6(c1, c1))),
% 29.91/20.12 inference(modus_ponens,[status(thm)],[3023, 31308])).
% 29.91/20.12 tff(31310,plain,
% 29.91/20.12 ($false),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[65, 31309])).
% 29.91/20.12 tff(31311,plain,((~(f6(f7(c2), c3) = c2)) | big_f(f7(c1), f6(c1, c1)) | (~big_f(c1, f10(c1))) | (~(f10(c1) = c2)) | (~(c3 = c1)) | (~(f7(c2) = c1)) | (~(f7(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.91/20.12 tff(31312,plain,
% 29.91/20.12 ((~(f6(f7(c2), c3) = c2)) | big_f(f7(c1), f6(c1, c1)) | (~big_f(c1, f10(c1))) | (~(f10(c1) = c2)) | (~(c3 = c1)) | (~(f7(c2) = c1))),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[31311, 25791])).
% 29.91/20.12 tff(31313,plain,
% 29.91/20.12 (~(f6(f7(c2), c3) = c2)),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[31312, 30770, 31305, 30989, 15, 30400])).
% 29.91/20.12 tff(31314,plain,
% 29.91/20.12 (f6(f7(c2), c3) = c1),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[2391, 31313])).
% 29.91/20.12 tff(31315,plain,
% 29.91/20.12 (~(c4 = c2)),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[10120, 31010, 30993, 31000, 30770, 79])).
% 29.91/20.12 tff(31316,plain,
% 29.91/20.12 (c4 = c1),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[461, 31315])).
% 29.91/20.12 tff(31317,plain,
% 29.91/20.12 ((f10(c1) = c4) <=> (f10(c1) = c1)),
% 29.91/20.12 inference(monotonicity,[status(thm)],[31316])).
% 29.91/20.12 tff(31318,plain,
% 29.91/20.12 ((f10(c1) = c1) <=> (f10(c1) = c4)),
% 29.91/20.12 inference(symmetry,[status(thm)],[31317])).
% 29.91/20.12 tff(31319,plain,
% 29.91/20.12 ((f10(c1) = c1) <=> (c2 = c4)),
% 29.91/20.12 inference(transitivity,[status(thm)],[31318, 30362])).
% 29.91/20.12 tff(31320,plain,
% 29.91/20.12 ((~(f10(c1) = c1)) <=> (~(c2 = c4))),
% 29.91/20.12 inference(monotonicity,[status(thm)],[31319])).
% 29.91/20.12 tff(31321,plain,
% 29.91/20.12 (~(c2 = c4)),
% 29.91/20.12 inference(modus_ponens,[status(thm)],[3, 31320])).
% 29.91/20.12 tff(31322,plain,
% 29.91/20.12 (big_f(c1, f6(c1, c2)) <=> big_f(f7(c1), f6(c1, f10(c1)))),
% 29.91/20.12 inference(monotonicity,[status(thm)],[30840, 29658])).
% 29.91/20.12 tff(31323,plain,
% 29.91/20.12 (big_f(f7(c1), f6(c1, f10(c1))) <=> big_f(c1, f6(c1, c2))),
% 29.91/20.12 inference(symmetry,[status(thm)],[31322])).
% 29.91/20.12 tff(31324,plain,
% 29.91/20.12 (f6(c1, f10(c1)) = c1),
% 29.91/20.12 inference(transitivity,[status(thm)],[29657, 31013])).
% 29.91/20.12 tff(31325,plain,
% 29.91/20.12 (big_f(f7(c1), f6(c1, f10(c1))) <=> big_f(c1, c1)),
% 29.91/20.12 inference(monotonicity,[status(thm)],[25791, 31324])).
% 29.91/20.12 tff(31326,plain,
% 29.91/20.12 (big_f(c1, c1) <=> big_f(f7(c1), f6(c1, f10(c1)))),
% 29.91/20.12 inference(symmetry,[status(thm)],[31325])).
% 29.91/20.12 tff(31327,plain,
% 29.91/20.12 (big_f(c1, c1) <=> big_f(f7(c1), f6(c1, c2))),
% 29.91/20.12 inference(transitivity,[status(thm)],[31326, 31323, 25793])).
% 29.91/20.12 tff(31328,plain,
% 29.91/20.12 ((~big_f(c1, c1)) <=> (~big_f(f7(c1), f6(c1, c2)))),
% 29.91/20.12 inference(monotonicity,[status(thm)],[31327])).
% 29.91/20.12 tff(31329,plain,
% 29.91/20.12 (~big_f(f7(c1), f6(c1, c2))),
% 29.91/20.12 inference(modus_ponens,[status(thm)],[66, 31328])).
% 29.91/20.12 tff(31330,plain,
% 29.91/20.12 ((~(f1(c2, c1) = c1)) | (f10(c1) = c1) | big_f(f7(c1), f6(c1, c2)) | (f6(c1, c2) = c2) | (c2 = c3) | (c2 = c4) | (~big_f(c2, c1))),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[28996, 30354])).
% 29.91/20.12 tff(31331,plain,
% 29.91/20.12 (~(f1(c2, c1) = c1)),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[31330, 31321, 30993, 3, 31012, 31329, 31000])).
% 29.91/20.12 tff(31332,plain,
% 29.91/20.12 (f1(c2, c1) = c2),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[10113, 31331])).
% 29.91/20.12 tff(31333,plain,
% 29.91/20.12 (c2 = f1(c2, c1)),
% 29.91/20.12 inference(modus_ponens,[status(thm)],[31332, 30130])).
% 29.91/20.12 tff(31334,plain,
% 29.91/20.12 (big_f(c2, c2) <=> big_f(c2, f1(c2, c1))),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[30333, 31333])).
% 29.91/20.12 tff(31335,plain,
% 29.91/20.12 (~big_f(c2, f1(c2, c1))),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[30327, 31334, 31010])).
% 29.91/20.12 tff(31336,plain,
% 29.91/20.12 (big_f(f3(c2, c1), c2) | (c2 = c3) | (f1(c2, c1) = c1) | big_f(c2, f1(c2, c1)) | (c2 = c4)),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[29017, 30354])).
% 29.91/20.12 tff(31337,plain,
% 29.91/20.12 (big_f(f3(c2, c1), c2)),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[31336, 31335, 30993, 31321, 31331])).
% 29.91/20.12 tff(31338,plain,
% 29.91/20.12 (~(f3(c2, c1) = c1)),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[29075, 31337, 30993, 31331, 31321, 31010])).
% 29.91/20.12 tff(31339,plain,
% 29.91/20.12 (f6(c1, f6(c1, c2)) = f6(c1, c1)),
% 29.91/20.12 inference(monotonicity,[status(thm)],[6931])).
% 29.91/20.12 tff(31340,plain,
% 29.91/20.12 (f6(c1, f6(c1, c2)) = c1),
% 29.91/20.12 inference(transitivity,[status(thm)],[31339, 5958, 2702])).
% 29.91/20.12 tff(31341,plain,
% 29.91/20.12 (f3(c2, f6(c1, f6(c1, c2))) = f3(c2, c1)),
% 29.91/20.12 inference(monotonicity,[status(thm)],[31340])).
% 29.91/20.12 tff(31342,plain,
% 29.91/20.12 ((f3(c2, f6(c1, f6(c1, c2))) = c1) <=> (f3(c2, c1) = c1)),
% 29.91/20.12 inference(monotonicity,[status(thm)],[31341])).
% 29.91/20.12 tff(31343,assumption,(f3(c2, f6(c1, f6(c1, c2))) = c1), introduced(assumption)).
% 29.91/20.12 tff(31344,plain,
% 29.91/20.12 (f3(c2, c1) = c1),
% 29.91/20.12 inference(modus_ponens,[status(thm)],[31343, 31342])).
% 29.91/20.12 tff(31345,plain,
% 29.91/20.12 ($false),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[29003, 31344])).
% 29.91/20.12 tff(31346,plain,((~(f3(c2, f6(c1, f6(c1, c2))) = c1)) | (f3(c2, c1) = c1) | (~(f6(f7(c2), c3) = c1)) | (~(c3 = c1)) | (~(f7(c2) = c1)) | (~(f6(c1, c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.91/20.12 tff(31347,plain,
% 29.91/20.12 (~(f3(c2, f6(c1, f6(c1, c2))) = c1)),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[31346, 31338, 30989, 30770, 31314, 31013])).
% 29.91/20.12 tff(31348,plain,
% 29.91/20.12 (f3(c2, f6(c1, f6(c1, c2))) = c2),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[28333, 31347])).
% 29.91/20.12 tff(31349,plain,
% 29.91/20.12 (big_f(c1, f10(c1)) <=> big_f(f7(c1), f6(c1, c1))),
% 29.91/20.12 inference(transitivity,[status(thm)],[29522, 28010])).
% 29.91/20.12 tff(31350,plain,
% 29.91/20.12 (big_f(f7(c1), f6(c1, c1))),
% 29.91/20.12 inference(modus_ponens,[status(thm)],[30444, 31349])).
% 29.91/20.12 tff(31351,plain,
% 29.91/20.12 ($false),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[65, 31350])).
% 29.91/20.12 tff(31352,plain,((~(f6(c1, c2) = c1)) | big_f(f7(c1), f6(c1, c1)) | (~(f6(c1, f6(c1, c2)) = c2)) | (~(f10(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.91/20.12 tff(31353,plain,
% 29.91/20.12 (~(f6(c1, f6(c1, c2)) = c2)),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[31352, 31013, 31305, 15])).
% 29.91/20.12 tff(31354,plain,
% 29.91/20.12 (f6(c1, f6(c1, c2)) = c1),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[63, 31353])).
% 29.91/20.12 tff(31355,plain,
% 29.91/20.12 (c1 = f6(c1, f6(c1, c2))),
% 29.91/20.12 inference(symmetry,[status(thm)],[31354])).
% 29.91/20.12 tff(31356,plain,
% 29.91/20.12 (f3(f10(c1), c1) = f3(c2, f6(c1, f6(c1, c2)))),
% 29.91/20.12 inference(monotonicity,[status(thm)],[15, 31355])).
% 29.91/20.12 tff(31357,plain,
% 29.91/20.12 (f3(f10(c1), c1) = f10(c1)),
% 29.91/20.12 inference(transitivity,[status(thm)],[31356, 31348, 5571])).
% 29.91/20.12 tff(31358,plain,
% 29.91/20.12 (big_f(f3(f10(c1), c1), f10(c1)) <=> big_f(f10(c1), f10(c1))),
% 29.91/20.12 inference(monotonicity,[status(thm)],[31357])).
% 29.91/20.12 tff(31359,plain,
% 29.91/20.12 (big_f(f3(f10(c1), c1), f10(c1)) <=> big_f(c2, f10(c1))),
% 29.91/20.12 inference(transitivity,[status(thm)],[31358, 30999])).
% 29.91/20.12 tff(31360,plain,
% 29.91/20.12 (f3(c2, c1) = f3(f10(c1), c1)),
% 29.91/20.12 inference(monotonicity,[status(thm)],[5571])).
% 29.91/20.12 tff(31361,plain,
% 29.91/20.12 (big_f(f3(c2, c1), f10(c1)) <=> big_f(f3(f10(c1), c1), f10(c1))),
% 29.91/20.12 inference(monotonicity,[status(thm)],[31360])).
% 29.91/20.12 tff(31362,plain,
% 29.91/20.12 (big_f(f3(c2, c1), c2) <=> big_f(f3(c2, c1), f10(c1))),
% 29.91/20.12 inference(monotonicity,[status(thm)],[5571])).
% 29.91/20.12 tff(31363,plain,
% 29.91/20.12 (big_f(f3(c2, c1), c2) <=> big_f(f3(f10(c1), c1), f10(c1))),
% 29.91/20.12 inference(transitivity,[status(thm)],[31362, 31361])).
% 29.91/20.12 tff(31364,plain,
% 29.91/20.12 (big_f(f3(f10(c1), c1), f10(c1))),
% 29.91/20.12 inference(modus_ponens,[status(thm)],[31337, 31363])).
% 29.91/20.12 tff(31365,plain,
% 29.91/20.12 (big_f(c2, f10(c1))),
% 29.91/20.12 inference(modus_ponens,[status(thm)],[31364, 31359])).
% 29.91/20.12 tff(31366,plain,
% 29.91/20.12 (~big_f(c2, f10(c1))),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[6125, 31010, 15])).
% 29.91/20.12 tff(31367,plain,
% 29.91/20.12 ($false),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[31366, 31365])).
% 29.91/20.12 tff(31368,plain,((~(f4(c4) = c2)) | (f10(c1) = c1) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 29.91/20.12 tff(31369,plain,
% 29.91/20.12 (~(f4(c4) = c2)),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[31368, 3, 66])).
% 29.91/20.12 tff(31370,plain,
% 29.91/20.12 (f4(c4) = c1),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[11750, 31369])).
% 29.91/20.12 tff(31371,plain,
% 29.91/20.12 (c1 = f4(c4)),
% 29.91/20.12 inference(symmetry,[status(thm)],[31370])).
% 29.91/20.12 tff(31372,plain,
% 29.91/20.12 (c1 = f4(c1)),
% 29.91/20.12 inference(transitivity,[status(thm)],[31371, 19666])).
% 29.91/20.12 tff(31373,plain,
% 29.91/20.12 (big_f(c1, c1) <=> big_f(f7(c1), f6(c1, c2))),
% 29.91/20.12 inference(transitivity,[status(thm)],[30745, 31323, 25793])).
% 29.91/20.12 tff(31374,plain,
% 29.91/20.12 ((~big_f(c1, c1)) <=> (~big_f(f7(c1), f6(c1, c2)))),
% 29.91/20.12 inference(monotonicity,[status(thm)],[31373])).
% 29.91/20.12 tff(31375,plain,
% 29.91/20.12 (~big_f(f7(c1), f6(c1, c2))),
% 29.91/20.12 inference(modus_ponens,[status(thm)],[66, 31374])).
% 29.91/20.12 tff(31376,plain,
% 29.91/20.12 ((f10(c1) = c4) <=> (f10(c1) = c1)),
% 29.91/20.12 inference(monotonicity,[status(thm)],[17112])).
% 29.91/20.12 tff(31377,plain,
% 29.91/20.12 ((f10(c1) = c1) <=> (f10(c1) = c4)),
% 29.91/20.12 inference(symmetry,[status(thm)],[31376])).
% 29.91/20.12 tff(31378,plain,
% 29.91/20.12 ((f10(c1) = c1) <=> (c2 = c4)),
% 29.91/20.12 inference(transitivity,[status(thm)],[31377, 30362])).
% 29.91/20.12 tff(31379,plain,
% 29.91/20.12 ((~(f10(c1) = c1)) <=> (~(c2 = c4))),
% 29.91/20.12 inference(monotonicity,[status(thm)],[31378])).
% 29.91/20.12 tff(31380,plain,
% 29.91/20.12 (~(c2 = c4)),
% 29.91/20.12 inference(modus_ponens,[status(thm)],[3, 31379])).
% 29.91/20.12 tff(31381,plain,
% 29.91/20.12 (~(f1(c2, c1) = c1)),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[31330, 31380, 30993, 3, 30741, 31375, 30994])).
% 29.91/20.12 tff(31382,plain,
% 29.91/20.12 (f1(c2, c1) = c2),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[10113, 31381])).
% 29.91/20.12 tff(31383,plain,
% 29.91/20.12 (c1 = c3),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[175, 30989])).
% 29.91/20.12 tff(31384,plain,
% 29.91/20.12 (~(c1 = f2(c1))),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[31207, 31372, 31383, 11526])).
% 29.91/20.12 tff(31385,plain,
% 29.91/20.12 (~(f2(c3) = c1)),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[6771, 31384, 30989])).
% 29.91/20.12 tff(31386,plain,
% 29.91/20.12 (f2(c3) = c2),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[1273, 31385])).
% 29.91/20.12 tff(31387,plain,
% 29.91/20.12 (f1(f2(c1), c1) = f1(c2, c1)),
% 29.91/20.12 inference(monotonicity,[status(thm)],[18545])).
% 29.91/20.12 tff(31388,plain,
% 29.91/20.12 (f1(f2(c1), c1) = c2),
% 29.91/20.12 inference(transitivity,[status(thm)],[31387, 12189])).
% 29.91/20.12 tff(31389,plain,
% 29.91/20.12 (big_f(f2(c1), f1(f2(c1), c1)) <=> big_f(c2, c2)),
% 29.91/20.12 inference(monotonicity,[status(thm)],[18545, 31388])).
% 29.91/20.12 tff(31390,plain,
% 29.91/20.12 (big_f(c2, c2) <=> big_f(f2(c1), f1(f2(c1), c1))),
% 29.91/20.12 inference(symmetry,[status(thm)],[31389])).
% 29.91/20.12 tff(31391,plain,
% 29.91/20.12 ((~big_f(c2, c2)) <=> (~big_f(f2(c1), f1(f2(c1), c1)))),
% 29.91/20.12 inference(monotonicity,[status(thm)],[31390])).
% 29.91/20.12 tff(31392,plain,
% 29.91/20.12 (~big_f(f2(c1), f1(f2(c1), c1))),
% 29.91/20.12 inference(modus_ponens,[status(thm)],[121, 31391])).
% 29.91/20.12 tff(31393,plain,
% 29.91/20.12 ((f2(c1) = c3) <=> (f2(c1) = c1)),
% 29.91/20.12 inference(monotonicity,[status(thm)],[172])).
% 29.91/20.12 tff(31394,plain,
% 29.91/20.12 ((f2(c1) = c3) <=> (c1 = f2(c1))),
% 29.91/20.12 inference(transitivity,[status(thm)],[31393, 6764])).
% 29.91/20.12 tff(31395,plain,
% 29.91/20.12 ((c1 = f2(c1)) <=> (f2(c1) = c3)),
% 29.91/20.12 inference(symmetry,[status(thm)],[31394])).
% 29.91/20.12 tff(31396,plain,
% 29.91/20.12 ((~(c1 = f2(c1))) <=> (~(f2(c1) = c3))),
% 29.91/20.12 inference(monotonicity,[status(thm)],[31395])).
% 29.91/20.12 tff(31397,plain,
% 29.91/20.12 ((c1 = f2(c1)) <=> (c1 = c2)),
% 29.91/20.12 inference(monotonicity,[status(thm)],[18545])).
% 29.91/20.12 tff(31398,plain,
% 29.91/20.12 ((c1 = f2(c1)) <=> (c2 = c1)),
% 29.91/20.12 inference(transitivity,[status(thm)],[31397, 1])).
% 29.91/20.12 tff(31399,plain,
% 29.91/20.12 ((c2 = c1) <=> (c1 = f2(c1))),
% 29.91/20.12 inference(symmetry,[status(thm)],[31398])).
% 29.91/20.12 tff(31400,plain,
% 29.91/20.12 ((~(c2 = c1)) <=> (~(c1 = f2(c1)))),
% 29.91/20.12 inference(monotonicity,[status(thm)],[31399])).
% 29.91/20.12 tff(31401,plain,
% 29.91/20.12 (~(c1 = f2(c1))),
% 29.91/20.12 inference(modus_ponens,[status(thm)],[75, 31400])).
% 29.91/20.12 tff(31402,plain,
% 29.91/20.12 (~(f2(c1) = c3)),
% 29.91/20.12 inference(modus_ponens,[status(thm)],[31401, 31396])).
% 29.91/20.12 tff(31403,plain,
% 29.91/20.12 (f1(f2(c1), c1) = f2(c1)),
% 29.91/20.12 inference(transitivity,[status(thm)],[31387, 12189, 13016, 6765])).
% 29.91/20.12 tff(31404,plain,
% 29.91/20.12 ((f1(f2(c1), c1) = c1) <=> (f2(c1) = c1)),
% 29.91/20.12 inference(monotonicity,[status(thm)],[31403])).
% 29.91/20.12 tff(31405,plain,
% 29.91/20.12 ((f1(f2(c1), c1) = c1) <=> (c1 = f2(c1))),
% 29.91/20.12 inference(transitivity,[status(thm)],[31404, 6764])).
% 29.91/20.12 tff(31406,plain,
% 29.91/20.12 ((c1 = f2(c1)) <=> (f1(f2(c1), c1) = c1)),
% 29.91/20.12 inference(symmetry,[status(thm)],[31405])).
% 29.91/20.12 tff(31407,plain,
% 29.91/20.12 ((~(c1 = f2(c1))) <=> (~(f1(f2(c1), c1) = c1))),
% 29.91/20.12 inference(monotonicity,[status(thm)],[31406])).
% 29.91/20.12 tff(31408,plain,
% 29.91/20.12 (~(f1(f2(c1), c1) = c1)),
% 29.91/20.12 inference(modus_ponens,[status(thm)],[31401, 31407])).
% 29.91/20.12 tff(31409,plain,
% 29.91/20.12 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (f1(f2(c1), c1) = c1) | (f2(c1) = c3) | big_f(f2(c1), f1(f2(c1), c1)))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (f1(f2(c1), c1) = c1) | (f2(c1) = c3) | big_f(f2(c1), f1(f2(c1), c1)))),
% 29.91/20.12 inference(rewrite,[status(thm)],[])).
% 29.91/20.12 tff(31410,plain,
% 29.91/20.12 (((f2(c1) = c3) | (f1(f2(c1), c1) = c1) | big_f(f2(c1), f1(f2(c1), c1)) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1)))) <=> ((~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (f1(f2(c1), c1) = c1) | (f2(c1) = c3) | big_f(f2(c1), f1(f2(c1), c1)))),
% 29.91/20.12 inference(rewrite,[status(thm)],[])).
% 29.91/20.12 tff(31411,plain,
% 29.91/20.12 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f2(c1) = c3) | (f1(f2(c1), c1) = c1) | big_f(f2(c1), f1(f2(c1), c1)) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (f1(f2(c1), c1) = c1) | (f2(c1) = c3) | big_f(f2(c1), f1(f2(c1), c1))))),
% 29.91/20.12 inference(monotonicity,[status(thm)],[31410])).
% 29.91/20.12 tff(31412,plain,
% 29.91/20.12 (((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f2(c1) = c3) | (f1(f2(c1), c1) = c1) | big_f(f2(c1), f1(f2(c1), c1)) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))))) <=> ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (f1(f2(c1), c1) = c1) | (f2(c1) = c3) | big_f(f2(c1), f1(f2(c1), c1)))),
% 29.91/20.12 inference(transitivity,[status(thm)],[31411, 31409])).
% 29.91/20.12 tff(31413,plain,
% 29.91/20.12 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | ((f2(c1) = c3) | (f1(f2(c1), c1) = c1) | big_f(f2(c1), f1(f2(c1), c1)) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))))),
% 29.91/20.12 inference(quant_inst,[status(thm)],[])).
% 29.91/20.12 tff(31414,plain,
% 29.91/20.12 ((~![X11: $i, X3: $i, X10: $i, X2: $i] : ((X10 = c3) | (f1(X10, X11) = X11) | big_f(X10, f1(X10, X11)) | (~(X2 = c4)) | big_f(X3, X2) | (~(X3 = f4(X2))))) | (~(c1 = c4)) | big_f(c1, c1) | (~(c1 = f4(c1))) | (f1(f2(c1), c1) = c1) | (f2(c1) = c3) | big_f(f2(c1), f1(f2(c1), c1))),
% 29.91/20.12 inference(modus_ponens,[status(thm)],[31413, 31412])).
% 29.91/20.12 tff(31415,plain,
% 29.91/20.12 ((f1(f2(c1), c1) = c1) | (f2(c1) = c3) | big_f(f2(c1), f1(f2(c1), c1))),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[31414, 402, 11526, 19844, 66])).
% 29.91/20.12 tff(31416,plain,
% 29.91/20.12 ($false),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[31415, 31408, 31402, 31392])).
% 29.91/20.12 tff(31417,plain,((~(f1(c2, c1) = c2)) | (~(c1 = c4)) | (~(c1 = f4(c1))) | big_f(c1, c1) | big_f(c2, c2) | (~(f2(c3) = c2)) | (~(c3 = c1))), inference(lemma,lemma(discharge,[]))).
% 29.91/20.12 tff(31418,plain,
% 29.91/20.12 ($false),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[31417, 31386, 31382, 121, 66, 11526, 31372, 30989])).
% 29.91/20.12 tff(31419,plain,((~(c1 = c4)) | big_f(c2, c2) | big_f(c1, c1) | (f10(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.91/20.12 tff(31420,plain,
% 29.91/20.12 (~(c1 = c4)),
% 29.91/20.12 inference(unit_resolution,[status(thm)],[31419, 121, 66, 3])).
% 29.91/20.12 tff(31421,plain,
% 29.91/20.12 (big_f(f10(c1), f1(f10(c1), c1)) <=> big_f(c2, f1(c2, c1))),
% 29.91/20.12 inference(symmetry,[status(thm)],[30515])).
% 29.91/20.12 tff(31422,plain,
% 29.91/20.12 (f1(f10(c1), c1) = c1),
% 29.91/20.12 inference(transitivity,[status(thm)],[8887, 11485])).
% 29.91/20.12 tff(31423,plain,
% 29.91/20.12 (big_f(f10(c1), f1(f10(c1), c1)) <=> big_f(f10(c1), c1)),
% 29.91/20.12 inference(monotonicity,[status(thm)],[31422])).
% 29.91/20.12 tff(31424,plain,
% 29.91/20.12 (big_f(f10(c1), c1) <=> big_f(f10(c1), f1(f10(c1), c1))),
% 29.91/20.12 inference(symmetry,[status(thm)],[31423])).
% 29.91/20.12 tff(31425,plain,
% 29.91/20.12 (big_f(f10(c1), c1) <=> big_f(c2, f1(c2, c1))),
% 29.91/20.12 inference(transitivity,[status(thm)],[31424, 31421])).
% 29.91/20.12 tff(31426,plain,
% 29.91/20.12 (big_f(c2, c1) <=> big_f(f10(c1), c1)),
% 29.91/20.12 inference(monotonicity,[status(thm)],[293])).
% 29.91/20.12 tff(31427,plain,
% 29.91/20.12 (big_f(f10(c1), c1)),
% 29.91/20.12 inference(modus_ponens,[status(thm)],[348, 31426])).
% 29.91/20.12 tff(31428,plain,
% 29.91/20.12 (big_f(c2, f1(c2, c1))),
% 29.91/20.12 inference(modus_ponens,[status(thm)],[31427, 31425])).
% 29.91/20.12 tff(31429,plain,
% 29.91/20.12 ((f3(c1, c2) = f8(f10(c1))) <=> (f3(c1, c2) = c2)),
% 29.91/20.12 inference(monotonicity,[status(thm)],[24859])).
% 29.91/20.12 tff(31430,plain,
% 29.91/20.12 ((f3(c1, c2) = c2) <=> (f3(c1, c2) = f8(f10(c1)))),
% 29.91/20.12 inference(symmetry,[status(thm)],[31429])).
% 29.91/20.12 tff(31431,plain,
% 29.91/20.12 ((~(f3(c1, c2) = c2)) <=> (~(f3(c1, c2) = f8(f10(c1))))),
% 29.91/20.12 inference(monotonicity,[status(thm)],[31430])).
% 29.91/20.12 tff(31432,plain,
% 29.91/20.12 (~(f3(c1, c2) = f8(f10(c1)))),
% 29.91/20.12 inference(modus_ponens,[status(thm)],[12777, 31431])).
% 29.91/20.12 tff(31433,plain,
% 29.91/20.12 (f10(f10(c1)) = f10(c2)),
% 29.91/20.12 inference(monotonicity,[status(thm)],[16])).
% 29.91/20.13 tff(31434,plain,
% 29.91/20.13 (f10(f10(c1)) = c1),
% 29.91/20.13 inference(transitivity,[status(thm)],[31433, 11819])).
% 29.91/20.13 tff(31435,plain,
% 29.91/20.13 (big_f(f3(c1, c2), f10(f10(c1))) <=> big_f(f3(c1, c2), c1)),
% 29.91/20.13 inference(monotonicity,[status(thm)],[31434])).
% 29.91/20.13 tff(31436,plain,
% 29.91/20.13 (big_f(f3(c1, c2), c1) <=> big_f(f3(c1, c2), f10(f10(c1)))),
% 29.91/20.13 inference(symmetry,[status(thm)],[31435])).
% 29.91/20.13 tff(31437,plain,
% 29.91/20.13 (big_f(f3(c1, c2), f10(f10(c1)))),
% 29.91/20.13 inference(modus_ponens,[status(thm)],[22442, 31436])).
% 29.91/20.13 tff(31438,plain,
% 29.91/20.13 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, f10(c1))) | (f6(c1, f10(c1)) = f10(c1)) | (f3(c1, c2) = f8(f10(c1))) | (~big_f(f3(c1, c2), f10(f10(c1)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, f10(c1))) | (f6(c1, f10(c1)) = f10(c1)) | (f3(c1, c2) = f8(f10(c1))) | (~big_f(f3(c1, c2), f10(f10(c1)))))),
% 29.91/20.13 inference(rewrite,[status(thm)],[])).
% 29.91/20.13 tff(31439,plain,
% 29.91/20.13 (((f10(f10(c1)) = f10(c1)) | (f3(c1, c2) = f8(f10(c1))) | (~big_f(f3(c1, c2), f10(f10(c1)))) | (~(f7(c1) = c1)) | (f6(c1, f10(c1)) = f10(c1)) | big_f(f7(c1), f6(c1, f10(c1)))) <=> ((f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, f10(c1))) | (f6(c1, f10(c1)) = f10(c1)) | (f3(c1, c2) = f8(f10(c1))) | (~big_f(f3(c1, c2), f10(f10(c1)))))),
% 29.91/20.13 inference(rewrite,[status(thm)],[])).
% 29.91/20.13 tff(31440,plain,
% 29.91/20.13 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f10(c1)) = f10(c1)) | (f3(c1, c2) = f8(f10(c1))) | (~big_f(f3(c1, c2), f10(f10(c1)))) | (~(f7(c1) = c1)) | (f6(c1, f10(c1)) = f10(c1)) | big_f(f7(c1), f6(c1, f10(c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, f10(c1))) | (f6(c1, f10(c1)) = f10(c1)) | (f3(c1, c2) = f8(f10(c1))) | (~big_f(f3(c1, c2), f10(f10(c1))))))),
% 29.91/20.13 inference(monotonicity,[status(thm)],[31439])).
% 29.91/20.13 tff(31441,plain,
% 29.91/20.13 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f10(c1)) = f10(c1)) | (f3(c1, c2) = f8(f10(c1))) | (~big_f(f3(c1, c2), f10(f10(c1)))) | (~(f7(c1) = c1)) | (f6(c1, f10(c1)) = f10(c1)) | big_f(f7(c1), f6(c1, f10(c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, f10(c1))) | (f6(c1, f10(c1)) = f10(c1)) | (f3(c1, c2) = f8(f10(c1))) | (~big_f(f3(c1, c2), f10(f10(c1)))))),
% 29.91/20.13 inference(transitivity,[status(thm)],[31440, 31438])).
% 29.91/20.13 tff(31442,plain,
% 29.91/20.13 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f10(c1)) = f10(c1)) | (f3(c1, c2) = f8(f10(c1))) | (~big_f(f3(c1, c2), f10(f10(c1)))) | (~(f7(c1) = c1)) | (f6(c1, f10(c1)) = f10(c1)) | big_f(f7(c1), f6(c1, f10(c1))))),
% 29.91/20.13 inference(quant_inst,[status(thm)],[])).
% 29.91/20.13 tff(31443,plain,
% 29.91/20.13 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(f10(c1)) = f10(c1)) | (~(f7(c1) = c1)) | big_f(f7(c1), f6(c1, f10(c1))) | (f6(c1, f10(c1)) = f10(c1)) | (f3(c1, c2) = f8(f10(c1))) | (~big_f(f3(c1, c2), f10(f10(c1))))),
% 29.91/20.13 inference(modus_ponens,[status(thm)],[31442, 31441])).
% 29.91/20.13 tff(31444,plain,
% 29.91/20.13 ((f3(c1, c2) = f8(f10(c1))) | (~big_f(f3(c1, c2), f10(f10(c1))))),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[31443, 2662, 25791, 24968, 28853, 28852])).
% 29.91/20.13 tff(31445,plain,
% 29.91/20.13 ($false),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[31444, 31437, 31432])).
% 29.91/20.13 tff(31446,plain,((~big_f(f3(c1, c2), c1)) | (f10(f10(c1)) = f10(c1)) | (f6(c1, f10(c1)) = f10(c1)) | big_f(f7(c1), f6(c1, f10(c1))) | (~(f10(c2) = c1)) | (~(f10(c1) = c2)) | (f3(c1, c2) = c2) | (~(f8(f10(c1)) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.91/20.13 tff(31447,plain,
% 29.91/20.13 (~big_f(f3(c1, c2), c1)),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[31446, 12777, 28852, 28853, 11819, 16, 24968, 24859])).
% 29.91/20.13 tff(31448,plain,
% 29.91/20.13 ($false),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[16144, 31447, 12777, 377, 482, 11485, 11484])).
% 29.91/20.13 tff(31449,plain,((f3(c1, c2) = c2) | (c2 = c3) | (c1 = c4) | (~(f1(c2, c1) = c1)) | (~big_f(c2, f1(c2, c1))) | big_f(f7(c1), f6(c1, f10(c1))) | (f6(c1, f10(c1)) = f10(c1)) | (~(f10(c2) = c1)) | (~(f10(c1) = c2)) | (f10(f10(c1)) = f10(c1)) | (~(f8(f10(c1)) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.91/20.13 tff(31450,plain,
% 29.91/20.13 (f3(c1, c2) = c2),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[31449, 11485, 482, 377, 31428, 28852, 28853, 11819, 16, 24968, 24859])).
% 29.91/20.13 tff(31451,plain,
% 29.91/20.13 (big_f(f3(c1, c2), c1)),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[26072, 31450, 348])).
% 29.91/20.13 tff(31452,plain,
% 29.91/20.13 (big_f(f3(c1, f10(c1)), c1)),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[30543, 31451, 16])).
% 29.91/20.13 tff(31453,plain,
% 29.91/20.13 (f3(c1, c2) = f3(c1, f10(c1))),
% 29.91/20.13 inference(symmetry,[status(thm)],[29609])).
% 29.91/20.13 tff(31454,plain,
% 29.91/20.13 ((f3(c1, c2) = c2) <=> (f3(c1, f10(c1)) = f10(c1))),
% 29.91/20.13 inference(monotonicity,[status(thm)],[31453, 293])).
% 29.91/20.13 tff(31455,plain,
% 29.91/20.13 (f3(c1, f10(c1)) = f10(c1)),
% 29.91/20.13 inference(modus_ponens,[status(thm)],[31450, 31454])).
% 29.91/20.13 tff(31456,plain,
% 29.91/20.13 (big_f(f10(c1), f1(f10(c1), c1))),
% 29.91/20.13 inference(modus_ponens,[status(thm)],[31427, 31424])).
% 29.91/20.13 tff(31457,plain,
% 29.91/20.13 (f1(f10(c1), c1) = c1),
% 29.91/20.13 inference(modus_ponens,[status(thm)],[11485, 30499])).
% 29.91/20.13 tff(31458,plain,
% 29.91/20.13 ($false),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[30573, 933, 482, 29434, 31457, 31456, 31455, 31452])).
% 29.91/20.13 tff(31459,plain,((~(f1(c2, c1) = c1)) | (c1 = c4) | (f10(c1) = c3) | (~(f10(c1) = c2)) | (~big_f(c2, c1)) | (c2 = c3) | big_f(f7(c1), f6(c1, f10(c1))) | (f6(c1, f10(c1)) = f10(c1)) | (~(f10(c2) = c1)) | (f10(f10(c1)) = f10(c1)) | (~(f8(f10(c1)) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.91/20.13 tff(31460,plain,
% 29.91/20.13 (~(f1(c2, c1) = c1)),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[31459, 31420, 30998, 15, 30994, 30993, 30747, 30748, 30399, 30757, 30760])).
% 29.91/20.13 tff(31461,plain,
% 29.91/20.13 (f1(c2, c1) = c2),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[10113, 31460])).
% 29.91/20.13 tff(31462,plain,
% 29.91/20.13 (f1(f10(c1), c1) = f10(c1)),
% 29.91/20.13 inference(transitivity,[status(thm)],[30357, 31461, 5571])).
% 29.91/20.13 tff(31463,plain,
% 29.91/20.13 (big_f(f10(c1), f1(f10(c1), c1)) <=> big_f(f10(c1), f10(c1))),
% 29.91/20.13 inference(monotonicity,[status(thm)],[31462])).
% 29.91/20.13 tff(31464,plain,
% 29.91/20.13 (big_f(f10(c1), f10(c1)) <=> big_f(f10(c1), f1(f10(c1), c1))),
% 29.91/20.13 inference(symmetry,[status(thm)],[31463])).
% 29.91/20.13 tff(31465,plain,
% 29.91/20.13 (big_f(f10(c1), f10(c1)) <=> big_f(c2, f1(c2, c1))),
% 29.91/20.13 inference(transitivity,[status(thm)],[31464, 30360])).
% 29.91/20.13 tff(31466,plain,
% 29.91/20.13 (c2 = f8(c2)),
% 29.91/20.13 inference(modus_ponens,[status(thm)],[30760, 30368])).
% 29.91/20.13 tff(31467,plain,
% 29.91/20.13 (big_f(f10(c1), f10(c1))),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[30575, 31420, 30399, 30994, 66, 3, 31466])).
% 29.91/20.13 tff(31468,plain,
% 29.91/20.13 (big_f(c2, f1(c2, c1))),
% 29.91/20.13 inference(modus_ponens,[status(thm)],[31467, 31465])).
% 29.91/20.13 tff(31469,plain,
% 29.91/20.13 (c2 = f1(c2, c1)),
% 29.91/20.13 inference(modus_ponens,[status(thm)],[31461, 30130])).
% 29.91/20.13 tff(31470,plain,
% 29.91/20.13 (big_f(c2, c2) <=> big_f(c2, f1(c2, c1))),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[30333, 31469])).
% 29.91/20.13 tff(31471,plain,
% 29.91/20.13 ($false),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[30327, 31470, 31468, 121])).
% 29.91/20.13 tff(31472,plain,(big_f(c2, c2) | big_f(c1, c1) | (f10(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.91/20.13 tff(31473,plain,
% 29.91/20.13 (big_f(c2, c2)),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[31472, 3, 66])).
% 29.91/20.13 tff(31474,plain,
% 29.91/20.13 (~(f6(c1, c2) = c2)),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[31211, 31473, 3])).
% 29.91/20.13 tff(31475,plain,
% 29.91/20.13 (f6(c1, c2) = c1),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[48, 31474])).
% 29.91/20.13 tff(31476,plain,
% 29.91/20.13 (f6(c1, f10(c1)) = c1),
% 29.91/20.13 inference(transitivity,[status(thm)],[29657, 31475])).
% 29.91/20.13 tff(31477,plain,
% 29.91/20.13 (big_f(f7(c1), f6(c1, f10(c1))) <=> big_f(c1, c1)),
% 29.91/20.13 inference(monotonicity,[status(thm)],[25791, 31476])).
% 29.91/20.13 tff(31478,plain,
% 29.91/20.13 (big_f(c1, c1) <=> big_f(f7(c1), f6(c1, f10(c1)))),
% 29.91/20.13 inference(symmetry,[status(thm)],[31477])).
% 29.91/20.13 tff(31479,plain,
% 29.91/20.13 ((~big_f(c1, c1)) <=> (~big_f(f7(c1), f6(c1, f10(c1))))),
% 29.91/20.13 inference(monotonicity,[status(thm)],[31478])).
% 29.91/20.13 tff(31480,plain,
% 29.91/20.13 (~big_f(f7(c1), f6(c1, f10(c1)))),
% 29.91/20.13 inference(modus_ponens,[status(thm)],[66, 31479])).
% 29.91/20.13 tff(31481,plain,
% 29.91/20.13 (~(f6(c1, f10(c1)) = f10(c1))),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[28849, 31474, 15])).
% 29.91/20.13 tff(31482,plain,
% 29.91/20.13 (c1 = f8(c1)),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[28871, 2662, 25791, 3, 30400, 31481, 31480])).
% 29.91/20.13 tff(31483,plain,
% 29.91/20.13 (big_f(c1, c1) <=> big_f(f7(c1), f6(c1, c2))),
% 29.91/20.13 inference(transitivity,[status(thm)],[31478, 31323, 25793])).
% 29.91/20.13 tff(31484,plain,
% 29.91/20.13 ((~big_f(c1, c1)) <=> (~big_f(f7(c1), f6(c1, c2)))),
% 29.91/20.13 inference(monotonicity,[status(thm)],[31483])).
% 29.91/20.13 tff(31485,plain,
% 29.91/20.13 (~big_f(f7(c1), f6(c1, c2))),
% 29.91/20.13 inference(modus_ponens,[status(thm)],[66, 31484])).
% 29.91/20.13 tff(31486,plain,
% 29.91/20.13 (c2 = f8(c1)),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[29187, 31485, 3, 31473, 31474])).
% 29.91/20.13 tff(31487,plain,
% 29.91/20.13 ($false),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[29202, 31486, 31482])).
% 29.91/20.13 tff(31488,plain,((f10(c1) = c1) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 29.91/20.13 tff(31489,plain,
% 29.91/20.13 (f10(c1) = c1),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[31488, 66])).
% 29.91/20.13 tff(31490,plain,
% 29.91/20.13 (~(f4(c4) = c2)),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[30768, 122, 66])).
% 29.91/20.13 tff(31491,plain,
% 29.91/20.13 (f4(c4) = c1),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[11750, 31490])).
% 29.91/20.13 tff(31492,plain,
% 29.91/20.13 (f9(c1, c2) = c2),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[30808, 66, 3762])).
% 29.91/20.13 tff(31493,plain,
% 29.91/20.13 (big_f(f9(c1, c2), f10(c1)) <=> big_f(c2, c1)),
% 29.91/20.13 inference(monotonicity,[status(thm)],[31492, 3762])).
% 29.91/20.13 tff(31494,plain,
% 29.91/20.13 ((~big_f(f9(c1, c2), f10(c1))) <=> (~big_f(c2, c1))),
% 29.91/20.13 inference(monotonicity,[status(thm)],[31493])).
% 29.91/20.13 tff(31495,plain,
% 29.91/20.13 (big_f(c2, c2)),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[30374, 122, 66])).
% 29.91/20.13 tff(31496,plain,
% 29.91/20.13 (~big_f(f7(c1), f6(c1, f6(c1, c2)))),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[31273, 31491, 66, 31495])).
% 29.91/20.13 tff(31497,plain,
% 29.91/20.13 (~(f6(c1, c2) = c2)),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[30740, 31496])).
% 29.91/20.13 tff(31498,plain,
% 29.91/20.13 (f6(c1, c2) = c1),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[48, 31497])).
% 29.91/20.13 tff(31499,plain,
% 29.91/20.13 (big_f(c1, f6(c1, c2)) <=> big_f(c1, c1)),
% 29.91/20.13 inference(monotonicity,[status(thm)],[31498])).
% 29.91/20.13 tff(31500,plain,
% 29.91/20.13 (big_f(c1, c1) <=> big_f(c1, f6(c1, c2))),
% 29.91/20.13 inference(symmetry,[status(thm)],[31499])).
% 29.91/20.13 tff(31501,plain,
% 29.91/20.13 (big_f(c1, c1) <=> big_f(f7(c1), f6(c1, c2))),
% 29.91/20.13 inference(transitivity,[status(thm)],[31500, 25793])).
% 29.91/20.13 tff(31502,plain,
% 29.91/20.13 ((~big_f(c1, c1)) <=> (~big_f(f7(c1), f6(c1, c2)))),
% 29.91/20.13 inference(monotonicity,[status(thm)],[31501])).
% 29.91/20.13 tff(31503,plain,
% 29.91/20.13 (~big_f(f7(c1), f6(c1, c2))),
% 29.91/20.13 inference(modus_ponens,[status(thm)],[66, 31502])).
% 29.91/20.13 tff(31504,plain,
% 29.91/20.13 (~big_f(f9(c1, c2), f10(c1))),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[27159, 2409, 25791, 3762, 31492, 31503, 31497])).
% 29.91/20.13 tff(31505,plain,
% 29.91/20.13 (~big_f(c2, c1)),
% 29.91/20.13 inference(modus_ponens,[status(thm)],[31504, 31494])).
% 29.91/20.13 tff(31506,plain,
% 29.91/20.13 (~(f1(c2, c2) = c2)),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[31248, 23481, 1345, 432, 377])).
% 29.91/20.13 tff(31507,plain,
% 29.91/20.13 (f1(c2, c2) = c1),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[5270, 31506])).
% 29.91/20.13 tff(31508,plain,
% 29.91/20.13 (big_f(c2, f1(c2, c2)) <=> big_f(c2, c1)),
% 29.91/20.13 inference(monotonicity,[status(thm)],[31507])).
% 29.91/20.13 tff(31509,plain,
% 29.91/20.13 (big_f(c2, c1) <=> big_f(c2, f1(c2, c2))),
% 29.91/20.13 inference(symmetry,[status(thm)],[31508])).
% 29.91/20.13 tff(31510,plain,
% 29.91/20.13 ((~big_f(c2, c1)) <=> (~big_f(c2, f1(c2, c2)))),
% 29.91/20.13 inference(monotonicity,[status(thm)],[31509])).
% 29.91/20.13 tff(31511,plain,
% 29.91/20.13 (~big_f(c2, f1(c2, c2))),
% 29.91/20.13 inference(modus_ponens,[status(thm)],[2, 31510])).
% 29.91/20.13 tff(31512,plain,
% 29.91/20.13 ($false),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[16863, 525, 432, 23481, 1345, 377, 31506, 31511])).
% 29.91/20.13 tff(31513,plain,((~(c4 = c2)) | (~big_f(c2, c2)) | (c2 = c3) | big_f(c2, c1) | (~(f4(c4) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.91/20.13 tff(31514,plain,
% 29.91/20.13 (~(c4 = c2)),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[31513, 31495, 30993, 31505, 31491])).
% 29.91/20.13 tff(31515,plain,
% 29.91/20.13 (c4 = c1),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[461, 31514])).
% 29.91/20.13 tff(31516,plain,
% 29.91/20.13 (c1 = c4),
% 29.91/20.13 inference(symmetry,[status(thm)],[31515])).
% 29.91/20.13 tff(31517,plain,
% 29.91/20.13 (f4(c1) = f4(c4)),
% 29.91/20.13 inference(monotonicity,[status(thm)],[31516])).
% 29.91/20.13 tff(31518,plain,
% 29.91/20.13 (f4(c4) = f4(c1)),
% 29.91/20.13 inference(symmetry,[status(thm)],[31517])).
% 29.91/20.13 tff(31519,plain,
% 29.91/20.13 (c1 = f4(c4)),
% 29.91/20.13 inference(symmetry,[status(thm)],[31491])).
% 29.91/20.13 tff(31520,plain,
% 29.91/20.13 (c1 = f4(c1)),
% 29.91/20.13 inference(transitivity,[status(thm)],[31519, 31518])).
% 29.91/20.13 tff(31521,plain,
% 29.91/20.13 (big_f(c2, c4) <=> big_f(c2, c1)),
% 29.91/20.13 inference(monotonicity,[status(thm)],[31515])).
% 29.91/20.13 tff(31522,plain,
% 29.91/20.13 (big_f(c2, c1) <=> big_f(c2, c4)),
% 29.91/20.13 inference(symmetry,[status(thm)],[31521])).
% 29.91/20.13 tff(31523,plain,
% 29.91/20.13 ((~big_f(c2, c1)) <=> (~big_f(c2, c4))),
% 29.91/20.13 inference(monotonicity,[status(thm)],[31522])).
% 29.91/20.13 tff(31524,plain,
% 29.91/20.13 (~big_f(c2, c4)),
% 29.91/20.13 inference(modus_ponens,[status(thm)],[31505, 31523])).
% 29.91/20.13 tff(31525,plain,
% 29.91/20.13 (f1(c2, c2) = c2),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[31230, 31524, 30993, 66, 31515, 31520])).
% 29.91/20.13 tff(31526,plain,
% 29.91/20.13 (big_f(c2, f1(c2, c2)) <=> big_f(c2, c2)),
% 29.91/20.13 inference(monotonicity,[status(thm)],[31525])).
% 29.91/20.13 tff(31527,plain,
% 29.91/20.13 (big_f(c2, c2) <=> big_f(c2, f1(c2, c2))),
% 29.91/20.13 inference(symmetry,[status(thm)],[31526])).
% 29.91/20.13 tff(31528,plain,
% 29.91/20.13 (big_f(c2, f1(c2, c2))),
% 29.91/20.13 inference(modus_ponens,[status(thm)],[31495, 31527])).
% 29.91/20.13 tff(31529,plain,
% 29.91/20.13 (c1 = c4),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[484, 31515])).
% 29.91/20.13 tff(31530,plain,
% 29.91/20.13 ($false),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[23962, 447, 31529, 30993, 31525, 31528, 31520, 66])).
% 29.91/20.13 tff(31531,plain,((~(f10(c2) = c2)) | big_f(c1, c1) | (~(f10(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.91/20.13 tff(31532,plain,
% 29.91/20.13 (~(f10(c2) = c2)),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[31531, 66, 3762])).
% 29.91/20.13 tff(31533,plain,
% 29.91/20.13 (f10(c2) = c1),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[93, 31532])).
% 29.91/20.13 tff(31534,plain,
% 29.91/20.13 (big_f(c2, f10(c2)) <=> big_f(c2, c1)),
% 29.91/20.13 inference(monotonicity,[status(thm)],[31533])).
% 29.91/20.13 tff(31535,plain,
% 29.91/20.13 (big_f(c2, c1) <=> big_f(c2, f10(c2))),
% 29.91/20.13 inference(symmetry,[status(thm)],[31534])).
% 29.91/20.13 tff(31536,plain,
% 29.91/20.13 (big_f(f9(c1, c2), f10(c1)) <=> big_f(c2, f10(c2))),
% 29.91/20.13 inference(transitivity,[status(thm)],[31493, 31535])).
% 29.91/20.13 tff(31537,plain,
% 29.91/20.13 ((~big_f(f9(c1, c2), f10(c1))) <=> (~big_f(c2, f10(c2)))),
% 29.91/20.13 inference(monotonicity,[status(thm)],[31536])).
% 29.91/20.13 tff(31538,plain,
% 29.91/20.13 (~big_f(f9(c1, c2), f10(c1))),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[27159, 2409, 25791, 3762, 31492, 25798, 114])).
% 29.91/20.13 tff(31539,plain,
% 29.91/20.13 (~big_f(c2, f10(c2))),
% 29.91/20.13 inference(modus_ponens,[status(thm)],[31538, 31537])).
% 29.91/20.13 tff(31540,plain,
% 29.91/20.13 (~(c2 = f8(c2))),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[25804, 2994, 25791, 31532, 31539, 25798, 114])).
% 29.91/20.13 tff(31541,plain,
% 29.91/20.13 (big_f(c1, f10(c2)) <=> big_f(c1, c1)),
% 29.91/20.13 inference(monotonicity,[status(thm)],[31533])).
% 29.91/20.13 tff(31542,plain,
% 29.91/20.13 (big_f(c1, c1) <=> big_f(c1, f10(c2))),
% 29.91/20.13 inference(symmetry,[status(thm)],[31541])).
% 29.91/20.13 tff(31543,plain,
% 29.91/20.13 ((~big_f(c1, c1)) <=> (~big_f(c1, f10(c2)))),
% 29.91/20.13 inference(monotonicity,[status(thm)],[31542])).
% 29.91/20.13 tff(31544,plain,
% 29.91/20.13 (~big_f(c1, f10(c2))),
% 29.91/20.13 inference(modus_ponens,[status(thm)],[66, 31543])).
% 29.91/20.13 tff(31545,plain,
% 29.91/20.13 (~(c1 = f8(c2))),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[25825, 2994, 25791, 31532, 25798, 114, 31544])).
% 29.91/20.13 tff(31546,plain,
% 29.91/20.13 ((c2 = f8(f3(c1, c2))) <=> (f8(f3(c1, c2)) = c2)),
% 29.91/20.13 inference(commutativity,[status(thm)],[])).
% 29.91/20.13 tff(31547,plain,
% 29.91/20.13 (c2 = f3(c1, c2)),
% 29.91/20.13 inference(symmetry,[status(thm)],[16111])).
% 29.91/20.13 tff(31548,plain,
% 29.91/20.13 (f8(c2) = f8(f3(c1, c2))),
% 29.91/20.13 inference(monotonicity,[status(thm)],[31547])).
% 29.91/20.13 tff(31549,plain,
% 29.91/20.13 ((c2 = f8(c2)) <=> (c2 = f8(f3(c1, c2)))),
% 29.91/20.13 inference(monotonicity,[status(thm)],[31548])).
% 29.91/20.13 tff(31550,plain,
% 29.91/20.13 ((c2 = f8(c2)) <=> (f8(f3(c1, c2)) = c2)),
% 29.91/20.13 inference(transitivity,[status(thm)],[31549, 31546])).
% 29.91/20.13 tff(31551,plain,
% 29.91/20.13 ((~(c2 = f8(c2))) <=> (~(f8(f3(c1, c2)) = c2))),
% 29.91/20.13 inference(monotonicity,[status(thm)],[31550])).
% 29.91/20.13 tff(31552,plain,
% 29.91/20.13 (~(f8(f3(c1, c2)) = c2)),
% 29.91/20.13 inference(modus_ponens,[status(thm)],[12290, 31551])).
% 29.91/20.13 tff(31553,plain,
% 29.91/20.13 ((f8(f3(c1, c2)) = c1) <=> (c1 = f8(f3(c1, c2)))),
% 29.91/20.13 inference(commutativity,[status(thm)],[])).
% 29.91/20.13 tff(31554,plain,
% 29.91/20.13 ((c1 = f8(f3(c1, c2))) <=> (f8(f3(c1, c2)) = c1)),
% 29.91/20.13 inference(symmetry,[status(thm)],[31553])).
% 29.91/20.13 tff(31555,plain,
% 29.91/20.13 (f8(f3(c1, c2)) = f8(c2)),
% 29.91/20.13 inference(symmetry,[status(thm)],[31548])).
% 29.91/20.13 tff(31556,plain,
% 29.91/20.13 ((c1 = f8(f3(c1, c2))) <=> (c1 = f8(c2))),
% 29.91/20.13 inference(monotonicity,[status(thm)],[31555])).
% 29.91/20.13 tff(31557,plain,
% 29.91/20.13 ((c1 = f8(c2)) <=> (c1 = f8(f3(c1, c2)))),
% 29.91/20.13 inference(symmetry,[status(thm)],[31556])).
% 29.91/20.13 tff(31558,plain,
% 29.91/20.13 ((c1 = f8(c2)) <=> (f8(f3(c1, c2)) = c1)),
% 29.91/20.13 inference(transitivity,[status(thm)],[31557, 31554])).
% 29.91/20.13 tff(31559,plain,
% 29.91/20.13 ((~(c1 = f8(c2))) <=> (~(f8(f3(c1, c2)) = c1))),
% 29.91/20.13 inference(monotonicity,[status(thm)],[31558])).
% 29.91/20.13 tff(31560,plain,
% 29.91/20.13 (~(f8(f3(c1, c2)) = c1)),
% 29.91/20.13 inference(modus_ponens,[status(thm)],[24284, 31559])).
% 29.91/20.13 tff(31561,plain,
% 29.91/20.13 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f8(f3(c1, c2)) = c1) | (f8(f3(c1, c2)) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f8(f3(c1, c2)) = c1) | (f8(f3(c1, c2)) = c2))),
% 29.91/20.13 inference(rewrite,[status(thm)],[])).
% 29.91/20.13 tff(31562,plain,
% 29.91/20.13 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f8(f3(c1, c2)) = c1) | (f8(f3(c1, c2)) = c2))),
% 29.91/20.13 inference(quant_inst,[status(thm)],[])).
% 29.91/20.13 tff(31563,plain,
% 29.91/20.13 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f8(f3(c1, c2)) = c1) | (f8(f3(c1, c2)) = c2)),
% 29.91/20.13 inference(modus_ponens,[status(thm)],[31562, 31561])).
% 29.91/20.13 tff(31564,plain,
% 29.91/20.13 ((f8(f3(c1, c2)) = c1) | (f8(f3(c1, c2)) = c2)),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[31563, 10])).
% 29.91/20.13 tff(31565,plain,
% 29.91/20.13 ($false),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[31564, 31560, 31552])).
% 29.91/20.13 tff(31566,plain,((~(f3(c1, c2) = c2)) | (c1 = f8(c2)) | (c2 = f8(c2))), inference(lemma,lemma(discharge,[]))).
% 29.91/20.13 tff(31567,plain,
% 29.91/20.13 (~(f3(c1, c2) = c2)),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[31566, 31545, 31540])).
% 29.91/20.13 tff(31568,plain,
% 29.91/20.13 (~(f1(f5(c2), f5(c1)) = c2)),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[26052, 16041, 12777])).
% 29.91/20.13 tff(31569,plain,
% 29.91/20.13 (f1(f5(c2), f5(c1)) = c1),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[5191, 31568])).
% 29.91/20.13 tff(31570,plain,
% 29.91/20.13 (f3(f1(f5(c2), f5(c1)), c2) = f3(c1, c2)),
% 29.91/20.13 inference(monotonicity,[status(thm)],[31569])).
% 29.91/20.13 tff(31571,plain,
% 29.91/20.13 ((f3(f1(f5(c2), f5(c1)), c2) = c2) <=> (f3(c1, c2) = c2)),
% 29.91/20.13 inference(monotonicity,[status(thm)],[31570])).
% 29.91/20.13 tff(31572,plain,
% 29.91/20.13 ((f3(c1, c2) = c2) <=> (f3(f1(f5(c2), f5(c1)), c2) = c2)),
% 29.91/20.13 inference(symmetry,[status(thm)],[31571])).
% 29.91/20.13 tff(31573,plain,
% 29.91/20.13 ((~(f3(c1, c2) = c2)) <=> (~(f3(f1(f5(c2), f5(c1)), c2) = c2))),
% 29.91/20.13 inference(monotonicity,[status(thm)],[31572])).
% 29.91/20.13 tff(31574,plain,
% 29.91/20.13 (~(f3(f1(f5(c2), f5(c1)), c2) = c2)),
% 29.91/20.13 inference(modus_ponens,[status(thm)],[12777, 31573])).
% 29.91/20.13 tff(31575,plain,
% 29.91/20.13 (f3(c1, c2) = f3(f1(f5(c2), f5(c1)), c2)),
% 29.91/20.13 inference(symmetry,[status(thm)],[31570])).
% 29.91/20.13 tff(31576,plain,
% 29.91/20.13 ((c1 = f3(c1, c2)) <=> (c1 = f3(f1(f5(c2), f5(c1)), c2))),
% 29.91/20.13 inference(monotonicity,[status(thm)],[31575])).
% 29.91/20.13 tff(31577,plain,
% 29.91/20.13 ((c1 = f3(c1, c2)) <=> (f3(f1(f5(c2), f5(c1)), c2) = c1)),
% 29.91/20.13 inference(transitivity,[status(thm)],[31576, 26113])).
% 29.91/20.13 tff(31578,plain,
% 29.91/20.13 ((~(c1 = f3(c1, c2))) <=> (~(f3(f1(f5(c2), f5(c1)), c2) = c1))),
% 29.91/20.13 inference(monotonicity,[status(thm)],[31577])).
% 29.91/20.13 tff(31579,plain,
% 29.91/20.13 (~(f3(f1(f5(c2), f5(c1)), c2) = c1)),
% 29.91/20.13 inference(modus_ponens,[status(thm)],[16041, 31578])).
% 29.91/20.13 tff(31580,plain,
% 29.91/20.13 ($false),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[16061, 31579, 31574])).
% 29.91/20.13 tff(31581,plain,((c1 = f3(c1, c2)) | (f3(c1, c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 29.91/20.13 tff(31582,plain,
% 29.91/20.13 (c1 = f3(c1, c2)),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[31581, 31567])).
% 29.91/20.13 tff(31583,plain,
% 29.91/20.13 (~(c1 = f8(c2))),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[25825, 2994, 25791, 89, 25798, 114, 24207])).
% 29.91/20.13 tff(31584,plain,
% 29.91/20.13 (big_f(f9(c1, c2), f10(c1)) <=> big_f(c2, f10(c2))),
% 29.91/20.13 inference(transitivity,[status(thm)],[31493, 12069])).
% 29.91/20.13 tff(31585,plain,
% 29.91/20.13 ((~big_f(f9(c1, c2), f10(c1))) <=> (~big_f(c2, f10(c2)))),
% 29.91/20.13 inference(monotonicity,[status(thm)],[31584])).
% 29.91/20.13 tff(31586,plain,
% 29.91/20.13 (~big_f(c2, f10(c2))),
% 29.91/20.13 inference(modus_ponens,[status(thm)],[31538, 31585])).
% 29.91/20.13 tff(31587,plain,
% 29.91/20.13 (~(c2 = f8(c2))),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[25804, 2994, 25791, 89, 31586, 25798, 114])).
% 29.91/20.13 tff(31588,plain,
% 29.91/20.13 (c1 = f3(c1, c2)),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[31581, 12777])).
% 29.91/20.13 tff(31589,plain,
% 29.91/20.13 (big_f(c1, c1) <=> big_f(f3(c1, c2), c1)),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[13192, 31588])).
% 29.91/20.13 tff(31590,plain,
% 29.91/20.13 (~big_f(f3(c1, c2), c1)),
% 29.91/20.13 inference(unit_resolution,[status(thm)],[13186, 31589, 66])).
% 29.91/20.13 tff(31591,plain,
% 29.91/20.13 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((c1 = c4) | (~(c1 = c3)) | (~big_f(c1, c2)) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2) | (c2 = f2(c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (c1 = c4) | (~(c1 = c3)) | (~big_f(c1, c2)) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2) | (c2 = f2(c1)))),
% 29.91/20.13 inference(rewrite,[status(thm)],[])).
% 29.91/20.13 tff(31592,plain,
% 29.91/20.13 (((~(c1 = c3)) | (c1 = c4) | (f3(c1, c2) = c2) | big_f(f3(c1, c2), c1) | (c2 = f2(c1)) | (~big_f(c1, c2))) <=> ((c1 = c4) | (~(c1 = c3)) | (~big_f(c1, c2)) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2) | (c2 = f2(c1)))),
% 29.91/20.13 inference(rewrite,[status(thm)],[])).
% 29.91/20.13 tff(31593,plain,
% 29.91/20.13 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c1 = c4) | (f3(c1, c2) = c2) | big_f(f3(c1, c2), c1) | (c2 = f2(c1)) | (~big_f(c1, c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((c1 = c4) | (~(c1 = c3)) | (~big_f(c1, c2)) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2) | (c2 = f2(c1))))),
% 29.91/20.13 inference(monotonicity,[status(thm)],[31592])).
% 29.91/20.13 tff(31594,plain,
% 29.91/20.13 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c1 = c4) | (f3(c1, c2) = c2) | big_f(f3(c1, c2), c1) | (c2 = f2(c1)) | (~big_f(c1, c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (c1 = c4) | (~(c1 = c3)) | (~big_f(c1, c2)) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2) | (c2 = f2(c1)))),
% 29.91/20.13 inference(transitivity,[status(thm)],[31593, 31591])).
% 29.91/20.13 tff(31595,plain,
% 29.91/20.13 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c1 = c4) | (f3(c1, c2) = c2) | big_f(f3(c1, c2), c1) | (c2 = f2(c1)) | (~big_f(c1, c2)))),
% 29.91/20.13 inference(quant_inst,[status(thm)],[])).
% 29.91/20.13 tff(31596,plain,
% 29.91/20.13 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (c1 = c4) | (~(c1 = c3)) | (~big_f(c1, c2)) | big_f(f3(c1, c2), c1) | (f3(c1, c2) = c2) | (c2 = f2(c1))),
% 29.91/20.13 inference(modus_ponens,[status(thm)],[31595, 31594])).
% 29.91/20.14 tff(31597,plain,
% 29.91/20.14 (c2 = f2(c1)),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[31596, 7352, 5080, 482, 30354, 31590, 12777])).
% 29.91/20.14 tff(31598,plain,
% 29.91/20.14 (f2(c1) = c2),
% 29.91/20.14 inference(symmetry,[status(thm)],[31597])).
% 29.91/20.14 tff(31599,plain,
% 29.91/20.14 (f3(c1, c2) = c1),
% 29.91/20.14 inference(symmetry,[status(thm)],[31588])).
% 29.91/20.14 tff(31600,plain,
% 29.91/20.14 (f2(f3(c1, c2)) = f2(c1)),
% 29.91/20.14 inference(monotonicity,[status(thm)],[31599])).
% 29.91/20.14 tff(31601,plain,
% 29.91/20.14 (f2(f3(c1, c2)) = c2),
% 29.91/20.14 inference(transitivity,[status(thm)],[31600, 31598])).
% 29.91/20.14 tff(31602,plain,
% 29.91/20.14 (f8(f2(f3(c1, c2))) = f8(c2)),
% 29.91/20.14 inference(monotonicity,[status(thm)],[31601])).
% 29.91/20.14 tff(31603,plain,
% 29.91/20.14 ((f8(f2(f3(c1, c2))) = c1) <=> (f8(c2) = c1)),
% 29.91/20.14 inference(monotonicity,[status(thm)],[31602])).
% 29.91/20.14 tff(31604,plain,
% 29.91/20.14 ((f8(f2(f3(c1, c2))) = c1) <=> (c1 = f8(c2))),
% 29.91/20.14 inference(transitivity,[status(thm)],[31603, 13044])).
% 29.91/20.14 tff(31605,plain,
% 29.91/20.14 ((c1 = f8(c2)) <=> (f8(f2(f3(c1, c2))) = c1)),
% 29.91/20.14 inference(symmetry,[status(thm)],[31604])).
% 29.91/20.14 tff(31606,plain,
% 29.91/20.14 ((~(c1 = f8(c2))) <=> (~(f8(f2(f3(c1, c2))) = c1))),
% 29.91/20.14 inference(monotonicity,[status(thm)],[31605])).
% 29.91/20.14 tff(31607,plain,
% 29.91/20.14 (~(f8(f2(f3(c1, c2))) = c1)),
% 29.91/20.14 inference(modus_ponens,[status(thm)],[24284, 31606])).
% 29.91/20.14 tff(31608,plain,
% 29.91/20.14 ((c2 = f8(f2(f3(c1, c2)))) <=> (f8(f2(f3(c1, c2))) = c2)),
% 29.91/20.14 inference(commutativity,[status(thm)],[])).
% 29.91/20.14 tff(31609,plain,
% 29.91/20.14 (f8(c2) = f8(f2(f3(c1, c2)))),
% 29.91/20.14 inference(symmetry,[status(thm)],[31602])).
% 29.91/20.14 tff(31610,plain,
% 29.91/20.14 ((c2 = f8(c2)) <=> (c2 = f8(f2(f3(c1, c2))))),
% 29.91/20.14 inference(monotonicity,[status(thm)],[31609])).
% 29.91/20.14 tff(31611,plain,
% 29.91/20.14 ((c2 = f8(c2)) <=> (f8(f2(f3(c1, c2))) = c2)),
% 29.91/20.14 inference(transitivity,[status(thm)],[31610, 31608])).
% 29.91/20.14 tff(31612,plain,
% 29.91/20.14 ((~(c2 = f8(c2))) <=> (~(f8(f2(f3(c1, c2))) = c2))),
% 29.91/20.14 inference(monotonicity,[status(thm)],[31611])).
% 29.91/20.14 tff(31613,plain,
% 29.91/20.14 (~(f8(f2(f3(c1, c2))) = c2)),
% 29.91/20.14 inference(modus_ponens,[status(thm)],[12290, 31612])).
% 29.91/20.14 tff(31614,plain,
% 29.91/20.14 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f8(f2(f3(c1, c2))) = c1) | (f8(f2(f3(c1, c2))) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f8(f2(f3(c1, c2))) = c1) | (f8(f2(f3(c1, c2))) = c2))),
% 29.91/20.14 inference(rewrite,[status(thm)],[])).
% 29.91/20.14 tff(31615,plain,
% 29.91/20.14 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f8(f2(f3(c1, c2))) = c1) | (f8(f2(f3(c1, c2))) = c2))),
% 29.91/20.14 inference(quant_inst,[status(thm)],[])).
% 29.91/20.14 tff(31616,plain,
% 29.91/20.14 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f8(f2(f3(c1, c2))) = c1) | (f8(f2(f3(c1, c2))) = c2)),
% 29.91/20.14 inference(modus_ponens,[status(thm)],[31615, 31614])).
% 29.91/20.14 tff(31617,plain,
% 29.91/20.14 ((f8(f2(f3(c1, c2))) = c1) | (f8(f2(f3(c1, c2))) = c2)),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[31616, 10])).
% 29.91/20.14 tff(31618,plain,
% 29.91/20.14 ($false),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[31617, 31613, 31607])).
% 29.91/20.14 tff(31619,plain,((f3(c1, c2) = c2) | (c2 = f8(c2)) | (c1 = f8(c2)) | (~(c1 = c3)) | (c1 = c4) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 29.91/20.14 tff(31620,plain,
% 29.91/20.14 (c1 = c4),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[31619, 31587, 31383, 12777, 31583, 66])).
% 29.91/20.14 tff(31621,plain,
% 29.91/20.14 (c4 = c1),
% 29.91/20.14 inference(modus_ponens,[status(thm)],[31620, 4135])).
% 29.91/20.14 tff(31622,plain,
% 29.91/20.14 (f2(c1) = c2),
% 29.91/20.14 inference(symmetry,[status(thm)],[12831])).
% 29.91/20.14 tff(31623,plain,
% 29.91/20.14 ((c1 = f3(c1, c2)) <=> (c1 = f3(f1(f5(c2), f5(c1)), c2))),
% 29.91/20.14 inference(monotonicity,[status(thm)],[16470])).
% 29.91/20.14 tff(31624,plain,
% 29.91/20.14 ((c1 = f3(c1, c2)) <=> (f3(f1(f5(c2), f5(c1)), c2) = c1)),
% 29.91/20.14 inference(transitivity,[status(thm)],[31623, 26113])).
% 29.91/20.14 tff(31625,plain,
% 29.91/20.14 (f3(f1(f5(c2), f5(c1)), c2) = c1),
% 29.91/20.14 inference(modus_ponens,[status(thm)],[13189, 31624])).
% 29.91/20.14 tff(31626,plain,
% 29.91/20.14 (f3(c1, c2) = c1),
% 29.91/20.14 inference(transitivity,[status(thm)],[16470, 31625])).
% 29.91/20.14 tff(31627,plain,
% 29.91/20.14 (f2(f3(c1, c2)) = f2(c1)),
% 29.91/20.14 inference(monotonicity,[status(thm)],[31626])).
% 29.91/20.14 tff(31628,plain,
% 29.91/20.14 (f2(f3(c1, c2)) = c2),
% 29.91/20.14 inference(transitivity,[status(thm)],[31627, 31622])).
% 29.91/20.14 tff(31629,plain,
% 29.91/20.14 (f8(f2(f3(c1, c2))) = f8(c2)),
% 29.91/20.14 inference(monotonicity,[status(thm)],[31628])).
% 29.91/20.14 tff(31630,plain,
% 29.91/20.14 ((f8(f2(f3(c1, c2))) = c1) <=> (f8(c2) = c1)),
% 29.91/20.14 inference(monotonicity,[status(thm)],[31629])).
% 29.91/20.14 tff(31631,plain,
% 29.91/20.14 ((f8(f2(f3(c1, c2))) = c1) <=> (c1 = f8(c2))),
% 29.91/20.14 inference(transitivity,[status(thm)],[31630, 13044])).
% 29.91/20.14 tff(31632,plain,
% 29.91/20.14 ((c1 = f8(c2)) <=> (f8(f2(f3(c1, c2))) = c1)),
% 29.91/20.14 inference(symmetry,[status(thm)],[31631])).
% 29.91/20.14 tff(31633,plain,
% 29.91/20.14 ((~(c1 = f8(c2))) <=> (~(f8(f2(f3(c1, c2))) = c1))),
% 29.91/20.14 inference(monotonicity,[status(thm)],[31632])).
% 29.91/20.14 tff(31634,plain,
% 29.91/20.14 (~(f8(f2(f3(c1, c2))) = c1)),
% 29.91/20.14 inference(modus_ponens,[status(thm)],[24284, 31633])).
% 29.91/20.14 tff(31635,plain,
% 29.91/20.14 ((f8(f2(f3(c1, c2))) = c2) <=> (f8(c2) = c2)),
% 29.91/20.14 inference(monotonicity,[status(thm)],[31629])).
% 29.91/20.14 tff(31636,plain,
% 29.91/20.14 ((f8(f2(f3(c1, c2))) = c2) <=> (c2 = f8(c2))),
% 29.91/20.14 inference(transitivity,[status(thm)],[31635, 11998])).
% 29.91/20.14 tff(31637,plain,
% 29.91/20.14 ((c2 = f8(c2)) <=> (f8(f2(f3(c1, c2))) = c2)),
% 29.91/20.14 inference(symmetry,[status(thm)],[31636])).
% 29.91/20.14 tff(31638,plain,
% 29.91/20.14 ((~(c2 = f8(c2))) <=> (~(f8(f2(f3(c1, c2))) = c2))),
% 29.91/20.14 inference(monotonicity,[status(thm)],[31637])).
% 29.91/20.14 tff(31639,plain,
% 29.91/20.14 (~(f8(f2(f3(c1, c2))) = c2)),
% 29.91/20.14 inference(modus_ponens,[status(thm)],[12290, 31638])).
% 29.91/20.14 tff(31640,plain,
% 29.91/20.14 ($false),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[31617, 31639, 31634])).
% 29.91/20.14 tff(31641,plain,((~(f1(f5(c2), f5(c1)) = c1)) | (c2 = f8(c2)) | (~(c2 = f2(c1))) | (c1 = f8(c2)) | (~(c1 = f3(c1, c2)))), inference(lemma,lemma(discharge,[]))).
% 29.91/20.14 tff(31642,plain,
% 29.91/20.14 (~(f1(f5(c2), f5(c1)) = c1)),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[31641, 13189, 12290, 24284, 27062])).
% 29.91/20.14 tff(31643,plain,
% 29.91/20.14 (f1(f5(c2), f5(c1)) = c2),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[5191, 31642])).
% 29.91/20.14 tff(31644,plain,
% 29.91/20.14 (c2 = f1(f5(c2), f5(c1))),
% 29.91/20.14 inference(symmetry,[status(thm)],[31643])).
% 29.91/20.14 tff(31645,plain,
% 29.91/20.14 (f3(c1, c2) = f3(c1, f1(f5(c2), f5(c1)))),
% 29.91/20.14 inference(monotonicity,[status(thm)],[31644])).
% 29.91/20.14 tff(31646,plain,
% 29.91/20.14 ((c1 = f3(c1, c2)) <=> (c1 = f3(c1, f1(f5(c2), f5(c1))))),
% 29.91/20.14 inference(monotonicity,[status(thm)],[31645])).
% 29.91/20.14 tff(31647,plain,
% 29.91/20.14 ((c1 = f3(c1, c2)) <=> (f3(c1, f1(f5(c2), f5(c1))) = c1)),
% 29.91/20.14 inference(transitivity,[status(thm)],[31646, 16034])).
% 29.91/20.14 tff(31648,plain,
% 29.91/20.14 (f3(c1, f1(f5(c2), f5(c1))) = c1),
% 29.91/20.14 inference(modus_ponens,[status(thm)],[13189, 31647])).
% 29.91/20.14 tff(31649,plain,
% 29.91/20.14 (f3(c1, c2) = c1),
% 29.91/20.14 inference(transitivity,[status(thm)],[31645, 31648])).
% 29.91/20.14 tff(31650,plain,
% 29.91/20.14 (f2(f3(c1, c2)) = f2(c1)),
% 29.91/20.14 inference(monotonicity,[status(thm)],[31649])).
% 29.91/20.14 tff(31651,plain,
% 29.91/20.14 (f2(f3(c1, c2)) = c2),
% 29.91/20.14 inference(transitivity,[status(thm)],[31650, 13678, 1319])).
% 29.91/20.14 tff(31652,plain,
% 29.91/20.14 (f8(f2(f3(c1, c2))) = f8(c2)),
% 29.91/20.14 inference(monotonicity,[status(thm)],[31651])).
% 29.91/20.14 tff(31653,plain,
% 29.91/20.14 ((f8(f2(f3(c1, c2))) = c1) <=> (f8(c2) = c1)),
% 29.91/20.14 inference(monotonicity,[status(thm)],[31652])).
% 29.91/20.14 tff(31654,plain,
% 29.91/20.14 ((f8(f2(f3(c1, c2))) = c1) <=> (c1 = f8(c2))),
% 29.91/20.14 inference(transitivity,[status(thm)],[31653, 13044])).
% 29.91/20.14 tff(31655,plain,
% 29.91/20.14 ((c1 = f8(c2)) <=> (f8(f2(f3(c1, c2))) = c1)),
% 29.91/20.14 inference(symmetry,[status(thm)],[31654])).
% 29.91/20.14 tff(31656,plain,
% 29.91/20.14 ((~(c1 = f8(c2))) <=> (~(f8(f2(f3(c1, c2))) = c1))),
% 29.91/20.14 inference(monotonicity,[status(thm)],[31655])).
% 29.91/20.14 tff(31657,plain,
% 29.91/20.14 (~(f8(f2(f3(c1, c2))) = c1)),
% 29.91/20.14 inference(modus_ponens,[status(thm)],[24284, 31656])).
% 29.91/20.14 tff(31658,plain,
% 29.91/20.14 ((f8(f2(f3(c1, c2))) = c2) <=> (f8(c2) = c2)),
% 29.91/20.14 inference(monotonicity,[status(thm)],[31652])).
% 29.91/20.14 tff(31659,plain,
% 29.91/20.14 ((f8(f2(f3(c1, c2))) = c2) <=> (c2 = f8(c2))),
% 29.91/20.14 inference(transitivity,[status(thm)],[31658, 11998])).
% 29.91/20.14 tff(31660,plain,
% 29.91/20.14 ((c2 = f8(c2)) <=> (f8(f2(f3(c1, c2))) = c2)),
% 29.91/20.14 inference(symmetry,[status(thm)],[31659])).
% 29.91/20.14 tff(31661,plain,
% 29.91/20.14 ((~(c2 = f8(c2))) <=> (~(f8(f2(f3(c1, c2))) = c2))),
% 29.91/20.14 inference(monotonicity,[status(thm)],[31660])).
% 29.91/20.14 tff(31662,plain,
% 29.91/20.14 (~(f8(f2(f3(c1, c2))) = c2)),
% 29.91/20.14 inference(modus_ponens,[status(thm)],[12290, 31661])).
% 29.91/20.14 tff(31663,plain,
% 29.91/20.14 ($false),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[31617, 31662, 31657])).
% 29.91/20.14 tff(31664,plain,((~(c1 = f3(c1, c2))) | (c2 = f8(c2)) | (~(f2(c3) = c2)) | (~(c3 = c1)) | (c1 = f8(c2))), inference(lemma,lemma(discharge,[]))).
% 29.91/20.14 tff(31665,plain,
% 29.91/20.14 (~(f2(c3) = c2)),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[31664, 31587, 30989, 13189, 31583])).
% 29.91/20.14 tff(31666,plain,
% 29.91/20.14 (f2(c3) = c1),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[1273, 31665])).
% 29.91/20.14 tff(31667,plain,
% 29.91/20.14 (~big_f(c3, f2(c3))),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[8267, 31666, 19649, 3762, 30989])).
% 29.91/20.14 tff(31668,plain,
% 29.91/20.14 (big_f(f4(c4), c4)),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[1315, 31667])).
% 29.91/20.14 tff(31669,plain,
% 29.91/20.14 (~big_f(c2, c1)),
% 29.91/20.14 inference(modus_ponens,[status(thm)],[31538, 31494])).
% 29.91/20.14 tff(31670,plain,
% 29.91/20.14 (f10(f10(c2)) = c1),
% 29.91/20.14 inference(transitivity,[status(thm)],[15299, 3762])).
% 29.91/20.14 tff(31671,plain,
% 29.91/20.14 (~(f4(c4) = c1)),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[18234, 31668, 19649, 94, 31620, 31670])).
% 29.91/20.14 tff(31672,plain,
% 29.91/20.14 (f4(c4) = c2),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[11750, 31671])).
% 29.91/20.14 tff(31673,plain,
% 29.91/20.14 (~(c4 = c1)),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[2221, 31672, 31669, 31668])).
% 29.91/20.14 tff(31674,plain,
% 29.91/20.14 ($false),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[31673, 31621])).
% 29.91/20.14 tff(31675,plain,((f6(c1, c2) = c2) | (~(f10(c1) = c1)) | (~(c1 = f3(c1, c2))) | (f3(c1, c2) = c2) | big_f(c1, c1) | (f10(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 29.91/20.14 tff(31676,plain,
% 29.91/20.14 ($false),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[31675, 31582, 31567, 3762, 31532, 66, 114])).
% 29.91/20.14 tff(31677,plain,((f6(c1, c2) = c2) | (~(f10(c1) = c1)) | big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 29.91/20.14 tff(31678,plain,
% 29.91/20.14 (f6(c1, c2) = c2),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[31677, 66, 3762])).
% 29.91/20.14 tff(31679,plain,
% 29.91/20.14 (big_f(c1, f6(c1, c2)) <=> big_f(c1, c2)),
% 29.91/20.14 inference(monotonicity,[status(thm)],[31678])).
% 29.91/20.14 tff(31680,plain,
% 29.91/20.14 (big_f(c1, c2) <=> big_f(c1, f6(c1, c2))),
% 29.91/20.14 inference(symmetry,[status(thm)],[31679])).
% 29.91/20.14 tff(31681,plain,
% 29.91/20.14 (big_f(c1, c2) <=> big_f(f7(c1), f6(c1, c2))),
% 29.91/20.14 inference(transitivity,[status(thm)],[31680, 25793])).
% 29.91/20.14 tff(31682,plain,
% 29.91/20.14 (big_f(f7(c1), f6(c1, c2))),
% 29.91/20.14 inference(modus_ponens,[status(thm)],[30354, 31681])).
% 29.91/20.14 tff(31683,plain,
% 29.91/20.14 ((~big_f(c2, c1)) <=> (~big_f(c2, f10(c2)))),
% 29.91/20.14 inference(monotonicity,[status(thm)],[31535])).
% 29.91/20.14 tff(31684,plain,
% 29.91/20.14 (big_f(f7(c1), f6(c1, f6(c1, c2)))),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[30740, 31678])).
% 29.91/20.14 tff(31685,plain,
% 29.91/20.14 (~big_f(c2, c1)),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[30857, 31684, 66, 3762])).
% 29.91/20.14 tff(31686,plain,
% 29.91/20.14 (~big_f(c2, f10(c2))),
% 29.91/20.14 inference(modus_ponens,[status(thm)],[31685, 31683])).
% 29.91/20.14 tff(31687,plain,
% 29.91/20.14 (~(c2 = f8(c2))),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[25871, 2963, 25791, 31532, 31686, 31682, 31678])).
% 29.91/20.14 tff(31688,plain,
% 29.91/20.14 (~(c1 = f8(c2))),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[30394, 31684, 66, 31532])).
% 29.91/20.14 tff(31689,plain,
% 29.91/20.14 (~(f3(c1, c2) = c2)),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[31566, 31687, 31688])).
% 29.91/20.14 tff(31690,plain,
% 29.91/20.14 (c1 = c4),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[31619, 31689, 31383, 31688, 31687, 66])).
% 29.91/20.14 tff(31691,plain,
% 29.91/20.14 (c4 = c1),
% 29.91/20.14 inference(modus_ponens,[status(thm)],[31690, 4135])).
% 29.91/20.14 tff(31692,plain,
% 29.91/20.14 (c1 = f3(c1, c2)),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[31581, 31689])).
% 29.91/20.14 tff(31693,plain,
% 29.91/20.14 (c1 = c4),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[31619, 24284, 31383, 12777, 12290, 66])).
% 29.91/20.14 tff(31694,plain,
% 29.91/20.14 (f4(c1) = f4(c4)),
% 29.91/20.14 inference(monotonicity,[status(thm)],[31693])).
% 29.91/20.14 tff(31695,plain,
% 29.91/20.14 (f4(c4) = f4(c1)),
% 29.91/20.14 inference(symmetry,[status(thm)],[31694])).
% 29.91/20.14 tff(31696,plain,
% 29.91/20.14 (c1 = f4(c1)),
% 29.91/20.14 inference(transitivity,[status(thm)],[16651, 31695])).
% 29.91/20.14 tff(31697,plain,
% 29.91/20.14 (~(f2(c3) = c2)),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[31664, 24284, 30989, 13189, 12290])).
% 29.91/20.14 tff(31698,plain,
% 29.91/20.14 (f2(c3) = c1),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[1273, 31697])).
% 29.91/20.14 tff(31699,plain,
% 29.91/20.14 (c1 = f2(c1)),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[6771, 31698, 30989])).
% 29.91/20.14 tff(31700,plain,
% 29.91/20.14 ((~(c1 = f2(c1))) | (~(c1 = c4)) | (~(c1 = f4(c1)))),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[31206, 1300, 31383, 66])).
% 29.91/20.14 tff(31701,plain,
% 29.91/20.14 (~(c1 = f4(c1))),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[31700, 31699, 31693])).
% 29.91/20.14 tff(31702,plain,
% 29.91/20.14 ($false),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[31701, 31696])).
% 29.91/20.14 tff(31703,plain,((c1 = f8(c2)) | (~(f4(c4) = c1)) | big_f(c1, c1) | (f3(c1, c2) = c2) | (c2 = f8(c2)) | (~(c1 = f3(c1, c2)))), inference(lemma,lemma(discharge,[]))).
% 29.91/20.14 tff(31704,plain,
% 29.91/20.14 (~(f4(c4) = c1)),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[31703, 31689, 66, 31688, 31687, 31692])).
% 29.91/20.14 tff(31705,plain,
% 29.91/20.14 (f4(c4) = c2),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[11750, 31704])).
% 29.91/20.14 tff(31706,plain,
% 29.91/20.14 (~(f2(c3) = c2)),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[31664, 31692, 30989, 31688, 31687])).
% 29.91/20.14 tff(31707,plain,
% 29.91/20.14 (f2(c3) = c1),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[1273, 31706])).
% 29.91/20.14 tff(31708,plain,
% 29.91/20.14 (~big_f(c3, f2(c3))),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[8267, 31707, 19649, 3762, 30989])).
% 29.91/20.14 tff(31709,plain,
% 29.91/20.14 (big_f(f4(c4), c4)),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[1315, 31708])).
% 29.91/20.14 tff(31710,plain,
% 29.91/20.14 (~(c4 = c1)),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[2221, 31709, 31685, 31705])).
% 29.91/20.14 tff(31711,plain,
% 29.91/20.14 ($false),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[31710, 31691])).
% 29.91/20.14 tff(31712,plain,(big_f(c1, c1) | (~(f10(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.91/20.14 tff(31713,plain,
% 29.91/20.14 ($false),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[31712, 31489, 66])).
% 29.91/20.14 tff(31714,plain,(big_f(c1, c1)), inference(lemma,lemma(discharge,[]))).
% 29.91/20.14 tff(31715,plain,
% 29.91/20.14 (big_f(f7(c2), f7(c2))),
% 29.91/20.14 inference(modus_ponens,[status(thm)],[31714, 23539])).
% 29.91/20.14 tff(31716,plain,
% 29.91/20.14 ((f10(f7(c2)) = f7(c2)) <=> (c2 = c1)),
% 29.91/20.14 inference(monotonicity,[status(thm)],[24, 22])).
% 29.91/20.14 tff(31717,plain,
% 29.91/20.14 ((c2 = c1) <=> (f10(f7(c2)) = f7(c2))),
% 29.91/20.14 inference(symmetry,[status(thm)],[31716])).
% 29.91/20.14 tff(31718,plain,
% 29.91/20.14 ((~(c2 = c1)) <=> (~(f10(f7(c2)) = f7(c2)))),
% 29.91/20.14 inference(monotonicity,[status(thm)],[31717])).
% 29.91/20.14 tff(31719,plain,
% 29.91/20.14 (~(f10(f7(c2)) = f7(c2))),
% 29.91/20.14 inference(modus_ponens,[status(thm)],[75, 31718])).
% 29.91/20.14 tff(31720,plain,
% 29.91/20.14 (big_f(f7(c2), c1)),
% 29.91/20.14 inference(modus_ponens,[status(thm)],[31714, 12091])).
% 29.91/20.14 tff(31721,plain,
% 29.91/20.14 (~(f10(c2) = c2)),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[15961, 31715, 30356, 121, 17])).
% 29.91/20.14 tff(31722,plain,
% 29.91/20.14 (f10(c2) = c1),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[93, 31721])).
% 29.91/20.14 tff(31723,plain,
% 29.91/20.14 (big_f(f7(c2), f10(c2))),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[21331, 31722, 31720])).
% 29.91/20.14 tff(31724,plain,
% 29.91/20.14 (big_f(c2, f10(c2)) <=> big_f(c2, c1)),
% 29.91/20.14 inference(monotonicity,[status(thm)],[31722])).
% 29.91/20.14 tff(31725,plain,
% 29.91/20.14 (big_f(c2, c1) <=> big_f(c2, f10(c2))),
% 29.91/20.14 inference(symmetry,[status(thm)],[31724])).
% 29.91/20.14 tff(31726,plain,
% 29.91/20.14 ((c2 = f2(c2)) <=> (f2(c2) = c2)),
% 29.91/20.14 inference(symmetry,[status(thm)],[1337])).
% 29.91/20.14 tff(31727,plain,
% 29.91/20.14 (f2(f10(c1)) = f2(c2)),
% 29.91/20.14 inference(monotonicity,[status(thm)],[15])).
% 29.91/20.14 tff(31728,plain,
% 29.91/20.14 ((f10(c1) = f2(f10(c1))) <=> (c2 = f2(c2))),
% 29.91/20.14 inference(monotonicity,[status(thm)],[15, 31727])).
% 29.91/20.14 tff(31729,plain,
% 29.91/20.14 ((f10(c1) = f2(f10(c1))) <=> (f2(c2) = c2)),
% 29.91/20.14 inference(transitivity,[status(thm)],[31728, 31726])).
% 29.91/20.14 tff(31730,plain,
% 29.91/20.14 ((~(f10(c1) = f2(f10(c1)))) <=> (~(f2(c2) = c2))),
% 29.91/20.14 inference(monotonicity,[status(thm)],[31729])).
% 29.91/20.14 tff(31731,plain,
% 29.91/20.14 (c2 = f3(c1, c1)),
% 29.91/20.14 inference(symmetry,[status(thm)],[1440])).
% 29.91/20.14 tff(31732,plain,
% 29.91/20.14 (f10(c1) = f3(c1, c1)),
% 29.91/20.14 inference(transitivity,[status(thm)],[15, 31731])).
% 29.91/20.14 tff(31733,plain,
% 29.91/20.14 (f3(f10(c1), c1) = f3(f3(c1, c1), c1)),
% 29.91/20.14 inference(monotonicity,[status(thm)],[31732])).
% 29.91/20.14 tff(31734,plain,
% 29.91/20.14 ((f3(f10(c1), c1) = c1) <=> (f3(f3(c1, c1), c1) = c1)),
% 29.91/20.14 inference(monotonicity,[status(thm)],[31733])).
% 29.91/20.14 tff(31735,plain,
% 29.91/20.14 ((f3(f3(c1, c1), c1) = c1) <=> (f3(f10(c1), c1) = c1)),
% 29.91/20.14 inference(symmetry,[status(thm)],[31734])).
% 29.91/20.14 tff(31736,plain,
% 29.91/20.14 (big_f(f7(c1), f6(c1, c2))),
% 29.91/20.14 inference(modus_ponens,[status(thm)],[30354, 25864])).
% 29.91/20.14 tff(31737,plain,
% 29.91/20.14 (big_f(f7(c1), f6(c1, f6(c1, c2)))),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[30740, 36])).
% 29.91/20.14 tff(31738,plain,
% 29.91/20.14 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))),
% 29.91/20.14 inference(rewrite,[status(thm)],[])).
% 29.91/20.14 tff(31739,plain,
% 29.91/20.14 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))))),
% 29.91/20.14 inference(quant_inst,[status(thm)],[])).
% 29.91/20.14 tff(31740,plain,
% 29.91/20.14 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2))))),
% 29.91/20.14 inference(modus_ponens,[status(thm)],[31739, 31738])).
% 29.91/20.14 tff(31741,plain,
% 29.91/20.14 ((~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2))))),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[31740, 2534])).
% 29.91/20.14 tff(31742,plain,
% 29.91/20.14 ((~(f10(c2) = c2)) | (f9(c2, c1) = c1) | big_f(f9(c2, c1), f10(c2)) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2))) | (~big_f(f7(c1), f6(c1, f6(c1, c2))))),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[31741, 25791])).
% 29.91/20.14 tff(31743,plain,
% 29.91/20.14 (big_f(f9(c2, c1), f10(c2))),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[31742, 1139, 122, 30373, 29897])).
% 29.91/20.14 tff(31744,plain,
% 29.91/20.14 (~(big_f(c2, c2) <=> big_f(f9(c2, c1), f10(c2)))),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[8436, 31743, 121])).
% 29.91/20.14 tff(31745,plain,
% 29.91/20.14 (~(c2 = f9(c2, c1))),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[8442, 31744, 4989])).
% 29.91/20.14 tff(31746,plain,
% 29.91/20.14 ($false),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[31745, 8434])).
% 29.91/20.14 tff(31747,plain,((f9(c2, c1) = c1) | big_f(c2, c2) | (~(f10(c2) = c2)) | (~big_f(f7(c1), f6(c1, f6(c1, c2)))) | (~(f6(c1, f6(c1, c2)) = f6(c1, c2)))), inference(lemma,lemma(discharge,[]))).
% 29.91/20.14 tff(31748,plain,
% 29.91/20.14 (f9(c2, c1) = c1),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[31747, 122, 31737, 25849, 121])).
% 29.91/20.14 tff(31749,plain,
% 29.91/20.14 (big_f(f9(c2, c1), f10(c2)) <=> big_f(c1, c2)),
% 29.91/20.14 inference(monotonicity,[status(thm)],[31748, 122])).
% 29.91/20.14 tff(31750,plain,
% 29.91/20.14 (big_f(c1, c2) <=> big_f(f9(c2, c1), f10(c2))),
% 29.91/20.14 inference(symmetry,[status(thm)],[31749])).
% 29.91/20.14 tff(31751,plain,
% 29.91/20.14 (big_f(f9(c2, c1), f10(c2))),
% 29.91/20.14 inference(modus_ponens,[status(thm)],[30354, 31750])).
% 29.91/20.14 tff(31752,plain,
% 29.91/20.14 ((~(f10(c2) = c2)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2))),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[5827, 25791])).
% 29.91/20.14 tff(31753,plain,
% 29.91/20.14 (~big_f(f9(c2, c1), f10(c2))),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[31752, 122, 31748, 36, 31736])).
% 29.91/20.14 tff(31754,plain,
% 29.91/20.14 ($false),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[31753, 31751])).
% 29.91/20.14 tff(31755,plain,((~(f10(c2) = c2)) | (~(f6(c1, c2) = c2)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 29.91/20.14 tff(31756,plain,
% 29.91/20.14 (~(f10(c2) = c2)),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[31755, 121, 36])).
% 29.91/20.14 tff(31757,plain,
% 29.91/20.14 (f10(c2) = c1),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[93, 31756])).
% 29.91/20.14 tff(31758,plain,
% 29.91/20.14 (big_f(c1, f10(c2)) <=> big_f(c1, c1)),
% 29.91/20.14 inference(monotonicity,[status(thm)],[31757])).
% 29.91/20.14 tff(31759,plain,
% 29.91/20.14 (big_f(c1, c1) <=> big_f(c1, f10(c2))),
% 29.91/20.14 inference(symmetry,[status(thm)],[31758])).
% 29.91/20.14 tff(31760,plain,
% 29.91/20.14 (big_f(c1, f10(c2))),
% 29.91/20.14 inference(modus_ponens,[status(thm)],[31714, 31759])).
% 29.91/20.14 tff(31761,plain,
% 29.91/20.14 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (c1 = f8(c2)) | (~(f7(c1) = c1)) | (~big_f(c1, f10(c2))) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (c1 = f8(c2)) | (~(f7(c1) = c1)) | (~big_f(c1, f10(c2))) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)))),
% 29.91/20.14 inference(rewrite,[status(thm)],[])).
% 29.91/20.14 tff(31762,plain,
% 29.91/20.14 (((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (~(f7(c1) = c1)) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2)))) <=> ((f10(c2) = c2) | (c1 = f8(c2)) | (~(f7(c1) = c1)) | (~big_f(c1, f10(c2))) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)))),
% 29.91/20.14 inference(rewrite,[status(thm)],[])).
% 29.91/20.14 tff(31763,plain,
% 29.91/20.14 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (~(f7(c1) = c1)) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (c1 = f8(c2)) | (~(f7(c1) = c1)) | (~big_f(c1, f10(c2))) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2))))),
% 29.91/20.14 inference(monotonicity,[status(thm)],[31762])).
% 29.91/20.14 tff(31764,plain,
% 29.91/20.14 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (~(f7(c1) = c1)) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (c1 = f8(c2)) | (~(f7(c1) = c1)) | (~big_f(c1, f10(c2))) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)))),
% 29.91/20.14 inference(transitivity,[status(thm)],[31763, 31761])).
% 29.91/20.14 tff(31765,plain,
% 29.91/20.14 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (~(f7(c1) = c1)) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2))))),
% 29.91/20.14 inference(quant_inst,[status(thm)],[])).
% 29.91/20.14 tff(31766,plain,
% 29.91/20.14 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (c1 = f8(c2)) | (~(f7(c1) = c1)) | (~big_f(c1, f10(c2))) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2))),
% 29.91/20.14 inference(modus_ponens,[status(thm)],[31765, 31764])).
% 29.91/20.14 tff(31767,plain,
% 29.91/20.14 (c1 = f8(c2)),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[31766, 2730, 25791, 31756, 31736, 36, 31760])).
% 29.91/20.14 tff(31768,plain,
% 29.91/20.14 (f8(c2) = c1),
% 29.91/20.14 inference(symmetry,[status(thm)],[31767])).
% 29.91/20.14 tff(31769,plain,
% 29.91/20.14 ((c2 = f8(c2)) <=> (c2 = c1)),
% 29.91/20.14 inference(monotonicity,[status(thm)],[31768])).
% 29.91/20.14 tff(31770,plain,
% 29.91/20.14 ((c2 = c1) <=> (c2 = f8(c2))),
% 29.91/20.14 inference(symmetry,[status(thm)],[31769])).
% 29.91/20.14 tff(31771,plain,
% 29.91/20.14 ((~(c2 = c1)) <=> (~(c2 = f8(c2)))),
% 29.91/20.14 inference(monotonicity,[status(thm)],[31770])).
% 29.91/20.14 tff(31772,plain,
% 29.91/20.14 (~(c2 = f8(c2))),
% 29.91/20.14 inference(modus_ponens,[status(thm)],[75, 31771])).
% 29.91/20.14 tff(31773,plain,
% 29.91/20.14 (big_f(c2, f10(c2)) <=> big_f(c2, c1)),
% 29.91/20.14 inference(monotonicity,[status(thm)],[31757])).
% 29.91/20.14 tff(31774,plain,
% 29.91/20.14 (big_f(c2, c1) <=> big_f(c2, f10(c2))),
% 29.91/20.14 inference(symmetry,[status(thm)],[31773])).
% 29.91/20.14 tff(31775,plain,
% 29.91/20.14 (f10(c2) = f10(c1)),
% 29.91/20.14 inference(transitivity,[status(thm)],[122, 5571])).
% 29.91/20.14 tff(31776,plain,
% 29.91/20.14 (~big_f(c2, c2)),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[31211, 36, 3])).
% 29.91/20.14 tff(31777,plain,
% 29.91/20.14 (f9(c2, c1) = c1),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[31747, 31776, 122, 31737, 25849])).
% 29.91/20.14 tff(31778,plain,
% 29.91/20.14 (big_f(f9(c2, c1), f10(c2)) <=> big_f(c1, f10(c1))),
% 29.91/20.14 inference(monotonicity,[status(thm)],[31777, 31775])).
% 29.91/20.14 tff(31779,plain,
% 29.91/20.14 (big_f(c1, f10(c1)) <=> big_f(f9(c2, c1), f10(c2))),
% 29.91/20.14 inference(symmetry,[status(thm)],[31778])).
% 29.91/20.14 tff(31780,plain,
% 29.91/20.14 (big_f(f9(c2, c1), f10(c2))),
% 29.91/20.14 inference(modus_ponens,[status(thm)],[30400, 31779])).
% 29.91/20.14 tff(31781,plain,
% 29.91/20.14 (f6(c1, f10(c1)) = f10(c1)),
% 29.91/20.14 inference(transitivity,[status(thm)],[29657, 36, 5571])).
% 29.91/20.14 tff(31782,plain,
% 29.91/20.14 (big_f(f7(c1), f6(c1, f10(c1))) <=> big_f(c1, f10(c1))),
% 29.91/20.14 inference(monotonicity,[status(thm)],[25791, 31781])).
% 29.91/20.14 tff(31783,plain,
% 29.91/20.14 (big_f(c1, f10(c1)) <=> big_f(f7(c1), f6(c1, f10(c1)))),
% 29.91/20.14 inference(symmetry,[status(thm)],[31782])).
% 29.91/20.14 tff(31784,plain,
% 29.91/20.14 (big_f(c1, f10(c1)) <=> big_f(f7(c1), f6(c1, c2))),
% 29.91/20.14 inference(transitivity,[status(thm)],[31783, 31323, 25793])).
% 29.91/20.14 tff(31785,plain,
% 29.91/20.14 (big_f(f7(c1), f6(c1, c2))),
% 29.91/20.14 inference(modus_ponens,[status(thm)],[30400, 31784])).
% 29.91/20.14 tff(31786,plain,
% 29.91/20.14 (~big_f(f9(c2, c1), f10(c2))),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[31752, 31777, 122, 36, 31785])).
% 29.91/20.14 tff(31787,plain,
% 29.91/20.14 ($false),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[31786, 31780])).
% 29.91/20.14 tff(31788,plain,((~(f6(c1, c2) = c2)) | (~(f10(c2) = c2)) | (f10(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.91/20.14 tff(31789,plain,
% 29.91/20.14 (~(f10(c2) = c2)),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[31788, 3, 36])).
% 29.91/20.14 tff(31790,plain,
% 29.91/20.14 (f10(c2) = c1),
% 29.91/20.14 inference(unit_resolution,[status(thm)],[93, 31789])).
% 29.91/20.14 tff(31791,plain,
% 29.91/20.14 (f6(f10(c2), c2) = f6(c1, c2)),
% 29.91/20.14 inference(monotonicity,[status(thm)],[31790])).
% 29.91/20.14 tff(31792,plain,
% 29.91/20.14 (f6(f10(c2), c2) = c2),
% 29.91/20.14 inference(transitivity,[status(thm)],[31791, 36])).
% 29.91/20.14 tff(31793,plain,
% 29.91/20.14 (c1 = f10(c2)),
% 29.91/20.14 inference(symmetry,[status(thm)],[31790])).
% 29.91/20.14 tff(31794,plain,
% 29.91/20.14 (f7(f10(c2)) = f7(c1)),
% 29.91/20.14 inference(monotonicity,[status(thm)],[31790])).
% 29.91/20.14 tff(31795,plain,
% 29.91/20.14 (f7(f10(c2)) = f10(c2)),
% 29.91/20.14 inference(transitivity,[status(thm)],[31794, 25791, 31793])).
% 29.91/20.14 tff(31796,plain,
% 29.91/20.14 (big_f(f7(f10(c2)), f6(f10(c2), c2)) <=> big_f(f10(c2), c2)),
% 29.91/20.14 inference(monotonicity,[status(thm)],[31795, 31792])).
% 29.91/20.14 tff(31797,plain,
% 29.91/20.14 (big_f(f10(c2), c2) <=> big_f(f7(f10(c2)), f6(f10(c2), c2))),
% 29.91/20.14 inference(symmetry,[status(thm)],[31796])).
% 29.91/20.14 tff(31798,plain,
% 29.91/20.14 (big_f(f10(c2), c2) <=> big_f(c1, c2)),
% 29.91/20.14 inference(monotonicity,[status(thm)],[31790])).
% 29.91/20.14 tff(31799,plain,
% 29.91/20.14 (big_f(c1, c2) <=> big_f(f10(c2), c2)),
% 29.91/20.14 inference(symmetry,[status(thm)],[31798])).
% 29.91/20.14 tff(31800,plain,
% 29.91/20.14 (big_f(f10(c2), c2)),
% 29.91/20.14 inference(modus_ponens,[status(thm)],[30354, 31799])).
% 29.91/20.14 tff(31801,plain,
% 29.91/20.14 (big_f(f7(f10(c2)), f6(f10(c2), c2))),
% 29.91/20.14 inference(modus_ponens,[status(thm)],[31800, 31797])).
% 29.91/20.14 tff(31802,plain,
% 29.91/20.14 (f6(c1, f6(c1, f6(c1, c2))) = f6(c1, c2)),
% 29.91/20.14 inference(monotonicity,[status(thm)],[40])).
% 29.91/20.14 tff(31803,plain,
% 29.91/20.14 (f6(c1, f6(c1, f6(c1, c2))) = c2),
% 29.91/20.14 inference(transitivity,[status(thm)],[31802, 36])).
% 29.91/20.14 tff(31804,plain,
% 29.91/20.14 (big_f(f7(c1), f6(c1, f6(c1, f6(c1, c2)))) <=> big_f(c1, c2)),
% 29.91/20.14 inference(monotonicity,[status(thm)],[25791, 31803])).
% 29.91/20.14 tff(31805,plain,
% 29.91/20.14 (big_f(c1, c2) <=> big_f(f7(c1), f6(c1, f6(c1, f6(c1, c2))))),
% 29.91/20.14 inference(symmetry,[status(thm)],[31804])).
% 29.91/20.14 tff(31806,plain,
% 29.91/20.14 (big_f(f7(c1), f6(c1, f6(c1, f6(c1, c2))))),
% 29.91/20.14 inference(modus_ponens,[status(thm)],[30354, 31805])).
% 29.91/20.14 tff(31807,plain,
% 29.91/20.14 (f6(c1, c2) = f6(c1, f6(c1, c2))),
% 29.91/20.14 inference(symmetry,[status(thm)],[39])).
% 29.91/20.14 tff(31808,plain,
% 29.91/20.14 (f6(c1, f6(c1, f6(c1, c2))) = f6(c1, f6(c1, c2))),
% 29.91/20.14 inference(transitivity,[status(thm)],[31802, 31807])).
% 29.91/20.14 tff(31809,plain,
% 29.91/20.14 (big_f(c1, f10(c2)) <=> big_f(f10(c2), f10(c2))),
% 29.91/20.14 inference(monotonicity,[status(thm)],[31793])).
% 29.91/20.14 tff(31810,plain,
% 29.91/20.14 (big_f(f10(c2), f10(c2)) <=> big_f(c1, f10(c2))),
% 29.91/20.14 inference(symmetry,[status(thm)],[31809])).
% 29.91/20.15 tff(31811,plain,
% 29.91/20.15 (big_f(f10(c2), f10(c2))),
% 29.91/20.15 inference(unit_resolution,[status(thm)],[21743, 31790, 31714])).
% 29.91/20.15 tff(31812,plain,
% 29.91/20.15 (big_f(c1, f10(c2))),
% 29.91/20.15 inference(modus_ponens,[status(thm)],[31811, 31810])).
% 29.91/20.15 tff(31813,plain,
% 29.91/20.15 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (c1 = f8(c2)) | (~(f7(c1) = c1)) | (~big_f(c1, f10(c2))) | (~big_f(f7(c1), f6(c1, f6(c1, f6(c1, c2))))) | (~(f6(c1, f6(c1, f6(c1, c2))) = f6(c1, f6(c1, c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (c1 = f8(c2)) | (~(f7(c1) = c1)) | (~big_f(c1, f10(c2))) | (~big_f(f7(c1), f6(c1, f6(c1, f6(c1, c2))))) | (~(f6(c1, f6(c1, f6(c1, c2))) = f6(c1, f6(c1, c2)))))),
% 29.91/20.15 inference(rewrite,[status(thm)],[])).
% 29.91/20.15 tff(31814,plain,
% 29.91/20.15 (((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, f6(c1, c2))) = f6(c1, f6(c1, c2)))) | (~big_f(f7(c1), f6(c1, f6(c1, f6(c1, c2)))))) <=> ((f10(c2) = c2) | (c1 = f8(c2)) | (~(f7(c1) = c1)) | (~big_f(c1, f10(c2))) | (~big_f(f7(c1), f6(c1, f6(c1, f6(c1, c2))))) | (~(f6(c1, f6(c1, f6(c1, c2))) = f6(c1, f6(c1, c2)))))),
% 29.91/20.15 inference(rewrite,[status(thm)],[])).
% 29.91/20.15 tff(31815,plain,
% 29.91/20.15 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, f6(c1, c2))) = f6(c1, f6(c1, c2)))) | (~big_f(f7(c1), f6(c1, f6(c1, f6(c1, c2))))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (c1 = f8(c2)) | (~(f7(c1) = c1)) | (~big_f(c1, f10(c2))) | (~big_f(f7(c1), f6(c1, f6(c1, f6(c1, c2))))) | (~(f6(c1, f6(c1, f6(c1, c2))) = f6(c1, f6(c1, c2))))))),
% 29.91/20.15 inference(monotonicity,[status(thm)],[31814])).
% 29.91/20.15 tff(31816,plain,
% 29.91/20.15 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, f6(c1, c2))) = f6(c1, f6(c1, c2)))) | (~big_f(f7(c1), f6(c1, f6(c1, f6(c1, c2))))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (c1 = f8(c2)) | (~(f7(c1) = c1)) | (~big_f(c1, f10(c2))) | (~big_f(f7(c1), f6(c1, f6(c1, f6(c1, c2))))) | (~(f6(c1, f6(c1, f6(c1, c2))) = f6(c1, f6(c1, c2)))))),
% 29.91/20.15 inference(transitivity,[status(thm)],[31815, 31813])).
% 29.91/20.15 tff(31817,plain,
% 29.91/20.15 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (~(f7(c1) = c1)) | (~(f6(c1, f6(c1, f6(c1, c2))) = f6(c1, f6(c1, c2)))) | (~big_f(f7(c1), f6(c1, f6(c1, f6(c1, c2))))))),
% 29.91/20.15 inference(quant_inst,[status(thm)],[])).
% 29.91/20.15 tff(31818,plain,
% 29.91/20.15 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (c1 = f8(c2)) | (~(f7(c1) = c1)) | (~big_f(c1, f10(c2))) | (~big_f(f7(c1), f6(c1, f6(c1, f6(c1, c2))))) | (~(f6(c1, f6(c1, f6(c1, c2))) = f6(c1, f6(c1, c2))))),
% 29.91/20.15 inference(modus_ponens,[status(thm)],[31817, 31816])).
% 29.91/20.15 tff(31819,plain,
% 29.91/20.15 ((f10(c2) = c2) | (c1 = f8(c2)) | (~(f7(c1) = c1)) | (~big_f(c1, f10(c2))) | (~big_f(f7(c1), f6(c1, f6(c1, f6(c1, c2))))) | (~(f6(c1, f6(c1, f6(c1, c2))) = f6(c1, f6(c1, c2))))),
% 29.91/20.15 inference(unit_resolution,[status(thm)],[31818, 2730])).
% 29.91/20.15 tff(31820,plain,
% 29.91/20.15 ((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (~big_f(f7(c1), f6(c1, f6(c1, f6(c1, c2))))) | (~(f6(c1, f6(c1, f6(c1, c2))) = f6(c1, f6(c1, c2))))),
% 29.91/20.15 inference(unit_resolution,[status(thm)],[31819, 25791])).
% 29.91/20.15 tff(31821,plain,
% 29.91/20.15 (c1 = f8(c2)),
% 29.91/20.15 inference(unit_resolution,[status(thm)],[31820, 31812, 31808, 31806, 31789])).
% 29.91/20.15 tff(31822,plain,
% 29.91/20.15 (f8(c2) = c1),
% 29.91/20.15 inference(symmetry,[status(thm)],[31821])).
% 29.91/20.15 tff(31823,plain,
% 29.91/20.15 (f8(c2) = f10(c2)),
% 29.91/20.15 inference(transitivity,[status(thm)],[31822, 31793])).
% 29.91/20.15 tff(31824,plain,
% 29.91/20.15 ((c2 = f8(c2)) <=> (c2 = f10(c2))),
% 29.91/20.15 inference(monotonicity,[status(thm)],[31823])).
% 29.91/20.15 tff(31825,plain,
% 29.91/20.15 ((c2 = f8(c2)) <=> (f10(c2) = c2)),
% 29.91/20.15 inference(transitivity,[status(thm)],[31824, 4987])).
% 29.91/20.15 tff(31826,plain,
% 29.91/20.15 ((f10(c2) = c2) <=> (c2 = f8(c2))),
% 29.91/20.15 inference(symmetry,[status(thm)],[31825])).
% 29.91/20.15 tff(31827,plain,
% 29.91/20.15 ((~(f10(c2) = c2)) <=> (~(c2 = f8(c2)))),
% 29.91/20.15 inference(monotonicity,[status(thm)],[31826])).
% 29.91/20.15 tff(31828,plain,
% 29.91/20.15 (~(c2 = f8(c2))),
% 29.91/20.15 inference(modus_ponens,[status(thm)],[31789, 31827])).
% 29.91/20.15 tff(31829,plain,
% 29.91/20.15 (big_f(c2, f10(c2)) <=> big_f(c2, c1)),
% 29.91/20.15 inference(monotonicity,[status(thm)],[31790])).
% 29.91/20.15 tff(31830,plain,
% 29.91/20.15 (big_f(c2, c1) <=> big_f(c2, f10(c2))),
% 29.91/20.15 inference(symmetry,[status(thm)],[31829])).
% 29.91/20.15 tff(31831,plain,
% 29.91/20.15 ((c1 = f2(f10(c1))) <=> (c1 = f2(c2))),
% 29.91/20.15 inference(monotonicity,[status(thm)],[31727])).
% 29.91/20.15 tff(31832,plain,
% 29.91/20.15 ((c1 = f2(c2)) <=> (c1 = f2(f10(c1)))),
% 29.91/20.15 inference(symmetry,[status(thm)],[31831])).
% 29.91/20.15 tff(31833,plain,
% 29.91/20.15 ((f6(c1, f6(c1, c2)) = c4) <=> (c2 = c4)),
% 29.91/20.15 inference(monotonicity,[status(thm)],[40])).
% 29.91/20.15 tff(31834,plain,
% 29.91/20.15 ((c2 = c4) <=> (f6(c1, f6(c1, c2)) = c4)),
% 29.91/20.15 inference(symmetry,[status(thm)],[31833])).
% 29.91/20.15 tff(31835,plain,
% 29.91/20.15 (~(c4 = c2)),
% 29.91/20.15 inference(unit_resolution,[status(thm)],[27535, 67, 31714, 121, 2])).
% 29.91/20.15 tff(31836,plain,
% 29.91/20.15 (c4 = c1),
% 29.91/20.15 inference(unit_resolution,[status(thm)],[461, 31835])).
% 29.91/20.15 tff(31837,plain,
% 29.91/20.15 (c1 = c4),
% 29.91/20.15 inference(unit_resolution,[status(thm)],[484, 31836])).
% 29.91/20.15 tff(31838,plain,
% 29.91/20.15 (c4 = c1),
% 29.91/20.15 inference(symmetry,[status(thm)],[31837])).
% 29.91/20.15 tff(31839,plain,
% 29.91/20.15 ((c2 = c4) <=> (c2 = c1)),
% 29.91/20.15 inference(monotonicity,[status(thm)],[31838])).
% 29.91/20.15 tff(31840,plain,
% 29.91/20.15 ((c2 = c1) <=> (c2 = c4)),
% 29.91/20.15 inference(symmetry,[status(thm)],[31839])).
% 29.91/20.15 tff(31841,plain,
% 29.91/20.15 ((c2 = c1) <=> (f6(c1, f6(c1, c2)) = c4)),
% 29.91/20.15 inference(transitivity,[status(thm)],[31840, 31834])).
% 29.91/20.15 tff(31842,plain,
% 29.91/20.15 ((~(c2 = c1)) <=> (~(f6(c1, f6(c1, c2)) = c4))),
% 29.91/20.15 inference(monotonicity,[status(thm)],[31841])).
% 29.91/20.15 tff(31843,plain,
% 29.91/20.15 (~(f6(c1, f6(c1, c2)) = c4)),
% 29.91/20.15 inference(modus_ponens,[status(thm)],[75, 31842])).
% 29.91/20.15 tff(31844,plain,
% 29.91/20.15 (f3(f6(c1, f6(c1, c2)), c1) = f3(c2, c1)),
% 29.91/20.15 inference(monotonicity,[status(thm)],[40])).
% 29.91/20.15 tff(31845,plain,
% 29.91/20.15 (big_f(f3(f6(c1, f6(c1, c2)), c1), f6(c1, f6(c1, c2))) <=> big_f(f3(c2, c1), c2)),
% 29.91/20.15 inference(monotonicity,[status(thm)],[31844, 40])).
% 29.91/20.15 tff(31846,plain,
% 29.91/20.15 (big_f(f3(c2, c1), c2) <=> big_f(f3(f6(c1, f6(c1, c2)), c1), f6(c1, f6(c1, c2)))),
% 29.91/20.15 inference(symmetry,[status(thm)],[31845])).
% 29.91/20.15 tff(31847,plain,
% 29.91/20.15 (big_f(c1, f10(c1))),
% 29.91/20.15 inference(modus_ponens,[status(thm)],[30354, 3350])).
% 29.91/20.15 tff(31848,plain,
% 29.91/20.15 (big_f(f7(c1), f6(c1, f10(c1)))),
% 29.91/20.15 inference(modus_ponens,[status(thm)],[31847, 31783])).
% 29.91/20.15 tff(31849,plain,
% 29.91/20.15 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, f6(c1, f6(c1, c2))))) | (~(f6(c1, f6(c1, f6(c1, c2))) = f6(c1, f6(c1, c2)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, f6(c1, f6(c1, c2))))) | (~(f6(c1, f6(c1, f6(c1, c2))) = f6(c1, f6(c1, c2)))))),
% 29.91/20.15 inference(rewrite,[status(thm)],[])).
% 29.91/20.15 tff(31850,plain,
% 29.91/20.15 (((f10(c1) = c1) | big_f(c2, f10(c1)) | (~(f7(c1) = c1)) | (~(c2 = f8(c1))) | (~(f6(c1, f6(c1, f6(c1, c2))) = f6(c1, f6(c1, c2)))) | (~big_f(f7(c1), f6(c1, f6(c1, f6(c1, c2)))))) <=> (big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, f6(c1, f6(c1, c2))))) | (~(f6(c1, f6(c1, f6(c1, c2))) = f6(c1, f6(c1, c2)))))),
% 29.91/20.15 inference(rewrite,[status(thm)],[])).
% 29.91/20.15 tff(31851,plain,
% 29.91/20.15 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | big_f(c2, f10(c1)) | (~(f7(c1) = c1)) | (~(c2 = f8(c1))) | (~(f6(c1, f6(c1, f6(c1, c2))) = f6(c1, f6(c1, c2)))) | (~big_f(f7(c1), f6(c1, f6(c1, f6(c1, c2))))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, f6(c1, f6(c1, c2))))) | (~(f6(c1, f6(c1, f6(c1, c2))) = f6(c1, f6(c1, c2))))))),
% 29.91/20.15 inference(monotonicity,[status(thm)],[31850])).
% 29.91/20.15 tff(31852,plain,
% 29.91/20.15 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | big_f(c2, f10(c1)) | (~(f7(c1) = c1)) | (~(c2 = f8(c1))) | (~(f6(c1, f6(c1, f6(c1, c2))) = f6(c1, f6(c1, c2)))) | (~big_f(f7(c1), f6(c1, f6(c1, f6(c1, c2))))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, f6(c1, f6(c1, c2))))) | (~(f6(c1, f6(c1, f6(c1, c2))) = f6(c1, f6(c1, c2)))))),
% 29.91/20.15 inference(transitivity,[status(thm)],[31851, 31849])).
% 29.91/20.15 tff(31853,plain,
% 29.91/20.15 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | big_f(c2, f10(c1)) | (~(f7(c1) = c1)) | (~(c2 = f8(c1))) | (~(f6(c1, f6(c1, f6(c1, c2))) = f6(c1, f6(c1, c2)))) | (~big_f(f7(c1), f6(c1, f6(c1, f6(c1, c2))))))),
% 29.91/20.15 inference(quant_inst,[status(thm)],[])).
% 29.91/20.15 tff(31854,plain,
% 29.91/20.15 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, f6(c1, f6(c1, c2))))) | (~(f6(c1, f6(c1, f6(c1, c2))) = f6(c1, f6(c1, c2))))),
% 29.91/20.15 inference(modus_ponens,[status(thm)],[31853, 31852])).
% 29.91/20.15 tff(31855,plain,
% 29.91/20.15 (big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, f6(c1, f6(c1, c2))))) | (~(f6(c1, f6(c1, f6(c1, c2))) = f6(c1, f6(c1, c2))))),
% 29.91/20.15 inference(unit_resolution,[status(thm)],[31854, 2963])).
% 29.91/20.15 tff(31856,plain,
% 29.91/20.15 (big_f(c2, f10(c1)) | (f10(c1) = c1) | (~(c2 = f8(c1))) | (~big_f(f7(c1), f6(c1, f6(c1, f6(c1, c2))))) | (~(f6(c1, f6(c1, f6(c1, c2))) = f6(c1, f6(c1, c2))))),
% 29.91/20.15 inference(unit_resolution,[status(thm)],[31855, 25791])).
% 29.91/20.15 tff(31857,plain,
% 29.91/20.15 (~(c2 = f8(c1))),
% 29.91/20.15 inference(unit_resolution,[status(thm)],[31856, 8451, 31808, 3, 31806])).
% 29.91/20.15 tff(31858,plain,
% 29.91/20.15 (~(f8(c1) = c2)),
% 29.91/20.15 inference(unit_resolution,[status(thm)],[1675, 31857])).
% 29.91/20.15 tff(31859,plain,
% 29.91/20.15 (f8(c1) = c1),
% 29.91/20.15 inference(unit_resolution,[status(thm)],[1680, 31858])).
% 29.91/20.15 tff(31860,plain,
% 29.91/20.15 ((~(c2 = c1)) <=> (~(c2 = c4))),
% 29.91/20.15 inference(monotonicity,[status(thm)],[31840])).
% 29.91/20.15 tff(31861,plain,
% 29.91/20.15 (~(c2 = c4)),
% 29.91/20.15 inference(modus_ponens,[status(thm)],[75, 31860])).
% 29.91/20.15 tff(31862,plain,
% 29.91/20.15 ((f10(c1) = c4) <=> (f10(c1) = c1)),
% 29.91/20.15 inference(monotonicity,[status(thm)],[31838])).
% 29.91/20.15 tff(31863,plain,
% 29.91/20.15 ((f10(c1) = c1) <=> (f10(c1) = c4)),
% 29.91/20.15 inference(symmetry,[status(thm)],[31862])).
% 29.91/20.15 tff(31864,plain,
% 29.91/20.15 ((~(f10(c1) = c1)) <=> (~(f10(c1) = c4))),
% 29.91/20.15 inference(monotonicity,[status(thm)],[31863])).
% 29.91/20.15 tff(31865,plain,
% 29.91/20.15 (~(f10(c1) = c4)),
% 29.91/20.15 inference(modus_ponens,[status(thm)],[3, 31864])).
% 29.91/20.15 tff(31866,plain,
% 29.91/20.15 ((~(f3(c2, c1) = f8(c1))) <=> (~(f3(c2, c1) = c1))),
% 29.91/20.15 inference(monotonicity,[status(thm)],[30621])).
% 29.91/20.15 tff(31867,plain,
% 29.91/20.15 ((~big_f(f3(c2, c1), c2)) <=> (~big_f(f3(c2, c1), f10(c1)))),
% 29.91/20.15 inference(monotonicity,[status(thm)],[28986])).
% 29.91/20.15 tff(31868,plain,
% 29.91/20.15 (~big_f(f3(c2, c1), f10(c1))),
% 29.91/20.15 inference(modus_ponens,[status(thm)],[12175, 31867])).
% 29.91/20.15 tff(31869,assumption,(big_f(f7(c1), f6(c1, f10(c1)))), introduced(assumption)).
% 29.91/20.15 tff(31870,plain,
% 29.91/20.15 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (~(f7(c1) = c1)) | (~(f6(c1, f10(c1)) = f10(c1))) | (~big_f(f7(c1), f6(c1, f10(c1)))) | big_f(f3(c2, c1), f10(c1)) | (~(f3(c2, c1) = f8(c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(f7(c1) = c1)) | (~(f6(c1, f10(c1)) = f10(c1))) | (~big_f(f7(c1), f6(c1, f10(c1)))) | big_f(f3(c2, c1), f10(c1)) | (~(f3(c2, c1) = f8(c1))))),
% 29.91/20.15 inference(rewrite,[status(thm)],[])).
% 29.91/20.15 tff(31871,plain,
% 29.91/20.15 (((f10(c1) = c1) | big_f(f3(c2, c1), f10(c1)) | (~(f7(c1) = c1)) | (~(f3(c2, c1) = f8(c1))) | (~(f6(c1, f10(c1)) = f10(c1))) | (~big_f(f7(c1), f6(c1, f10(c1))))) <=> ((f10(c1) = c1) | (~(f7(c1) = c1)) | (~(f6(c1, f10(c1)) = f10(c1))) | (~big_f(f7(c1), f6(c1, f10(c1)))) | big_f(f3(c2, c1), f10(c1)) | (~(f3(c2, c1) = f8(c1))))),
% 29.91/20.15 inference(rewrite,[status(thm)],[])).
% 29.91/20.15 tff(31872,plain,
% 29.91/20.15 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | big_f(f3(c2, c1), f10(c1)) | (~(f7(c1) = c1)) | (~(f3(c2, c1) = f8(c1))) | (~(f6(c1, f10(c1)) = f10(c1))) | (~big_f(f7(c1), f6(c1, f10(c1)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (~(f7(c1) = c1)) | (~(f6(c1, f10(c1)) = f10(c1))) | (~big_f(f7(c1), f6(c1, f10(c1)))) | big_f(f3(c2, c1), f10(c1)) | (~(f3(c2, c1) = f8(c1)))))),
% 29.91/20.15 inference(monotonicity,[status(thm)],[31871])).
% 29.91/20.15 tff(31873,plain,
% 29.91/20.15 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | big_f(f3(c2, c1), f10(c1)) | (~(f7(c1) = c1)) | (~(f3(c2, c1) = f8(c1))) | (~(f6(c1, f10(c1)) = f10(c1))) | (~big_f(f7(c1), f6(c1, f10(c1)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(f7(c1) = c1)) | (~(f6(c1, f10(c1)) = f10(c1))) | (~big_f(f7(c1), f6(c1, f10(c1)))) | big_f(f3(c2, c1), f10(c1)) | (~(f3(c2, c1) = f8(c1))))),
% 29.91/20.15 inference(transitivity,[status(thm)],[31872, 31870])).
% 29.91/20.15 tff(31874,plain,
% 29.91/20.15 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | big_f(f3(c2, c1), f10(c1)) | (~(f7(c1) = c1)) | (~(f3(c2, c1) = f8(c1))) | (~(f6(c1, f10(c1)) = f10(c1))) | (~big_f(f7(c1), f6(c1, f10(c1)))))),
% 29.91/20.15 inference(quant_inst,[status(thm)],[])).
% 29.91/20.15 tff(31875,plain,
% 29.91/20.15 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | big_f(X8, f10(X7)) | (~(f7(X4) = X4)) | (~(X8 = f8(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(f7(c1) = c1)) | (~(f6(c1, f10(c1)) = f10(c1))) | (~big_f(f7(c1), f6(c1, f10(c1)))) | big_f(f3(c2, c1), f10(c1)) | (~(f3(c2, c1) = f8(c1)))),
% 29.91/20.15 inference(modus_ponens,[status(thm)],[31874, 31873])).
% 29.91/20.15 tff(31876,plain,
% 29.91/20.15 (~(f3(c2, c1) = f8(c1))),
% 29.91/20.15 inference(unit_resolution,[status(thm)],[31875, 2963, 25791, 3, 28846, 31869, 31868])).
% 29.91/20.15 tff(31877,plain,
% 29.91/20.15 (~(f3(c2, c1) = c1)),
% 29.91/20.15 inference(modus_ponens,[status(thm)],[31876, 31866])).
% 29.91/20.15 tff(31878,plain,
% 29.91/20.15 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (c2 = c4) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (c2 = c4) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2))),
% 29.91/20.15 inference(rewrite,[status(thm)],[])).
% 29.91/20.15 tff(31879,plain,
% 29.91/20.15 (((~(c2 = c3)) | (~(c2 = f2(c2))) | (c2 = c4) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2) | big_f(c2, c2)) <=> ((~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (c2 = c4) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2))),
% 29.91/20.15 inference(rewrite,[status(thm)],[])).
% 29.91/20.15 tff(31880,plain,
% 29.91/20.15 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | (c2 = c4) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2) | big_f(c2, c2))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (c2 = c4) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2)))),
% 29.91/20.15 inference(monotonicity,[status(thm)],[31879])).
% 29.91/20.15 tff(31881,plain,
% 29.91/20.15 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | (c2 = c4) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2) | big_f(c2, c2))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (c2 = c4) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2))),
% 29.91/20.15 inference(transitivity,[status(thm)],[31880, 31878])).
% 29.91/20.15 tff(31882,plain,
% 29.91/20.15 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | (c2 = c4) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2) | big_f(c2, c2))),
% 29.91/20.15 inference(quant_inst,[status(thm)],[])).
% 29.91/20.15 tff(31883,plain,
% 29.91/20.15 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (c2 = c4) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2)),
% 29.91/20.15 inference(modus_ponens,[status(thm)],[31882, 31881])).
% 29.91/20.15 tff(31884,plain,
% 29.91/20.15 ($false),
% 29.91/20.15 inference(unit_resolution,[status(thm)],[31883, 1459, 873, 121, 1344, 2853, 29003, 12175])).
% 29.91/20.15 tff(31885,plain,((f3(c2, c1) = c1) | (c2 = c4) | big_f(c2, c2) | (~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(f3(c2, c1), c2)), inference(lemma,lemma(discharge,[]))).
% 29.91/20.15 tff(31886,plain,
% 29.91/20.15 (~(c2 = f2(c2))),
% 29.91/20.15 inference(unit_resolution,[status(thm)],[31885, 31877, 121, 1344, 12175, 873])).
% 29.91/20.15 tff(31887,assumption,(f2(c2) = c2), introduced(assumption)).
% 29.91/20.15 tff(31888,plain,
% 29.91/20.15 (c2 = f2(c2)),
% 29.91/20.15 inference(modus_ponens,[status(thm)],[31887, 1337])).
% 29.91/20.15 tff(31889,plain,
% 29.91/20.15 ($false),
% 29.91/20.15 inference(unit_resolution,[status(thm)],[1342, 31888])).
% 29.91/20.15 tff(31890,plain,((~(f2(c2) = c2)) | (c2 = f2(c2))), inference(lemma,lemma(discharge,[]))).
% 29.91/20.15 tff(31891,plain,
% 29.91/20.15 (~(f2(c2) = c2)),
% 29.91/20.15 inference(unit_resolution,[status(thm)],[31890, 31886])).
% 29.91/20.15 tff(31892,plain,
% 29.91/20.15 (big_f(f3(c2, c1), f10(c1)) <=> big_f(f3(c2, c1), c2)),
% 29.91/20.15 inference(monotonicity,[status(thm)],[16])).
% 29.91/20.15 tff(31893,plain,
% 29.91/20.15 (big_f(f3(f10(c1), c1), f10(c1)) <=> big_f(f3(c2, c1), f10(c1))),
% 29.91/20.15 inference(monotonicity,[status(thm)],[17656])).
% 29.91/20.16 tff(31894,plain,
% 29.91/20.16 (big_f(f3(f10(c1), c1), f10(c1)) <=> big_f(f3(c2, c1), c2)),
% 29.91/20.16 inference(transitivity,[status(thm)],[31893, 31892])).
% 29.91/20.16 tff(31895,assumption,(big_f(f3(f10(c1), c1), f10(c1))), introduced(assumption)).
% 29.91/20.16 tff(31896,plain,
% 29.91/20.16 (big_f(f3(c2, c1), c2)),
% 29.91/20.16 inference(modus_ponens,[status(thm)],[31895, 31894])).
% 29.91/20.16 tff(31897,plain,
% 29.91/20.16 ($false),
% 29.91/20.16 inference(unit_resolution,[status(thm)],[12175, 31896])).
% 29.91/20.16 tff(31898,plain,((~big_f(f3(f10(c1), c1), f10(c1))) | big_f(f3(c2, c1), c2) | (~(f10(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.91/20.16 tff(31899,plain,
% 29.91/20.16 (~big_f(f3(f10(c1), c1), f10(c1))),
% 29.91/20.16 inference(unit_resolution,[status(thm)],[31898, 12175, 15])).
% 29.91/20.16 tff(31900,plain,
% 29.91/20.16 ((~(f3(c2, c1) = f8(c1))) <=> (~(f3(f10(c1), c1) = c1))),
% 29.91/20.16 inference(monotonicity,[status(thm)],[30654])).
% 29.91/20.16 tff(31901,plain,
% 29.91/20.16 (~(f3(f10(c1), c1) = c1)),
% 29.91/20.16 inference(modus_ponens,[status(thm)],[31876, 31900])).
% 29.91/20.16 tff(31902,plain,
% 29.91/20.16 (~(c1 = f2(c2))),
% 29.91/20.16 inference(unit_resolution,[status(thm)],[17675, 31901, 1344, 2, 1046, 31899])).
% 29.91/20.16 tff(31903,assumption,(f2(c2) = c1), introduced(assumption)).
% 29.91/20.16 tff(31904,plain,
% 29.91/20.16 (c1 = f2(c2)),
% 29.91/20.16 inference(modus_ponens,[status(thm)],[31903, 1220])).
% 29.91/20.16 tff(31905,assumption,(~(c1 = f2(c2))), introduced(assumption)).
% 29.91/20.16 tff(31906,plain,
% 29.91/20.16 ($false),
% 29.91/20.16 inference(unit_resolution,[status(thm)],[31905, 31904])).
% 29.91/20.16 tff(31907,plain,((~(f2(c2) = c1)) | (c1 = f2(c2))), inference(lemma,lemma(discharge,[]))).
% 29.91/20.16 tff(31908,plain,
% 29.91/20.16 (~(f2(c2) = c1)),
% 29.91/20.16 inference(unit_resolution,[status(thm)],[31907, 31902])).
% 29.91/20.16 tff(31909,plain,
% 29.91/20.16 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f2(c2) = c1) | (f2(c2) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f2(c2) = c1) | (f2(c2) = c2))),
% 29.91/20.16 inference(rewrite,[status(thm)],[])).
% 29.91/20.16 tff(31910,plain,
% 29.91/20.16 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f2(c2) = c1) | (f2(c2) = c2))),
% 29.91/20.16 inference(quant_inst,[status(thm)],[])).
% 29.91/20.16 tff(31911,plain,
% 29.91/20.16 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f2(c2) = c1) | (f2(c2) = c2)),
% 29.91/20.16 inference(modus_ponens,[status(thm)],[31910, 31909])).
% 29.91/20.16 tff(31912,plain,
% 29.91/20.16 ((f2(c2) = c1) | (f2(c2) = c2)),
% 29.91/20.16 inference(unit_resolution,[status(thm)],[31911, 10])).
% 29.91/20.16 tff(31913,plain,
% 29.91/20.16 ($false),
% 29.91/20.16 inference(unit_resolution,[status(thm)],[31912, 31908, 31891])).
% 29.91/20.16 tff(31914,plain,(big_f(f3(c2, c1), c2) | (~(c2 = c3)) | big_f(c2, c1) | (f10(c1) = c4) | big_f(c2, c2) | (c2 = c4) | (~(f8(c1) = c1)) | (f10(c1) = c1) | (~(f6(c1, f10(c1)) = f10(c1))) | (~big_f(f7(c1), f6(c1, f10(c1))))), inference(lemma,lemma(discharge,[]))).
% 29.91/20.16 tff(31915,plain,
% 29.91/20.16 (big_f(f3(c2, c1), c2)),
% 29.91/20.16 inference(unit_resolution,[status(thm)],[31914, 31865, 2, 1335, 121, 31861, 31859, 3, 31781, 31848])).
% 29.91/20.16 tff(31916,plain,
% 29.91/20.16 (big_f(f3(f6(c1, f6(c1, c2)), c1), f6(c1, f6(c1, c2)))),
% 29.91/20.16 inference(modus_ponens,[status(thm)],[31915, 31846])).
% 29.91/20.16 tff(31917,plain,
% 29.91/20.16 ((f3(f6(c1, f6(c1, c2)), c1) = c1) <=> (f3(c2, c1) = c1)),
% 29.91/20.16 inference(monotonicity,[status(thm)],[31844])).
% 29.91/20.16 tff(31918,plain,
% 29.91/20.16 ((f3(c2, c1) = c1) <=> (f3(f6(c1, f6(c1, c2)), c1) = c1)),
% 29.91/20.16 inference(symmetry,[status(thm)],[31917])).
% 29.91/20.16 tff(31919,plain,
% 29.91/20.16 ((f3(c2, c1) = f8(c1)) <=> (f3(c2, c1) = c1)),
% 29.91/20.16 inference(monotonicity,[status(thm)],[31859])).
% 29.91/20.16 tff(31920,plain,
% 29.91/20.16 ((f3(c2, c1) = f8(c1)) <=> (f3(f6(c1, f6(c1, c2)), c1) = c1)),
% 29.91/20.16 inference(transitivity,[status(thm)],[31919, 31918])).
% 29.91/20.16 tff(31921,plain,
% 29.91/20.16 (big_f(f3(c2, c1), f10(c1))),
% 29.91/20.16 inference(modus_ponens,[status(thm)],[31915, 31362])).
% 29.91/20.16 tff(31922,plain,
% 29.91/20.16 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (~(f7(c1) = c1)) | (~(f6(c1, f10(c1)) = f10(c1))) | (~big_f(f7(c1), f6(c1, f10(c1)))) | (f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(f7(c1) = c1)) | (~(f6(c1, f10(c1)) = f10(c1))) | (~big_f(f7(c1), f6(c1, f10(c1)))) | (f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1))))),
% 29.97/20.16 inference(rewrite,[status(thm)],[])).
% 29.97/20.16 tff(31923,plain,
% 29.97/20.16 (((f10(c1) = c1) | (f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1))) | (~(f7(c1) = c1)) | (~(f6(c1, f10(c1)) = f10(c1))) | (~big_f(f7(c1), f6(c1, f10(c1))))) <=> ((f10(c1) = c1) | (~(f7(c1) = c1)) | (~(f6(c1, f10(c1)) = f10(c1))) | (~big_f(f7(c1), f6(c1, f10(c1)))) | (f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1))))),
% 29.97/20.16 inference(rewrite,[status(thm)],[])).
% 29.97/20.16 tff(31924,plain,
% 29.97/20.16 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1))) | (~(f7(c1) = c1)) | (~(f6(c1, f10(c1)) = f10(c1))) | (~big_f(f7(c1), f6(c1, f10(c1)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (~(f7(c1) = c1)) | (~(f6(c1, f10(c1)) = f10(c1))) | (~big_f(f7(c1), f6(c1, f10(c1)))) | (f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1)))))),
% 29.97/20.16 inference(monotonicity,[status(thm)],[31923])).
% 29.97/20.16 tff(31925,plain,
% 29.97/20.16 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1))) | (~(f7(c1) = c1)) | (~(f6(c1, f10(c1)) = f10(c1))) | (~big_f(f7(c1), f6(c1, f10(c1)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(f7(c1) = c1)) | (~(f6(c1, f10(c1)) = f10(c1))) | (~big_f(f7(c1), f6(c1, f10(c1)))) | (f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1))))),
% 29.97/20.16 inference(transitivity,[status(thm)],[31924, 31922])).
% 29.97/20.16 tff(31926,plain,
% 29.97/20.16 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1))) | (~(f7(c1) = c1)) | (~(f6(c1, f10(c1)) = f10(c1))) | (~big_f(f7(c1), f6(c1, f10(c1)))))),
% 29.97/20.16 inference(quant_inst,[status(thm)],[])).
% 29.97/20.16 tff(31927,plain,
% 29.97/20.16 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(f7(c1) = c1)) | (~(f6(c1, f10(c1)) = f10(c1))) | (~big_f(f7(c1), f6(c1, f10(c1)))) | (f3(c2, c1) = f8(c1)) | (~big_f(f3(c2, c1), f10(c1)))),
% 29.97/20.16 inference(modus_ponens,[status(thm)],[31926, 31925])).
% 29.97/20.16 tff(31928,plain,
% 29.97/20.16 (f3(c2, c1) = f8(c1)),
% 29.97/20.16 inference(unit_resolution,[status(thm)],[31927, 2730, 25791, 3, 31781, 31848, 31921])).
% 29.97/20.16 tff(31929,plain,
% 29.97/20.16 (f3(f6(c1, f6(c1, c2)), c1) = c1),
% 29.97/20.16 inference(modus_ponens,[status(thm)],[31928, 31920])).
% 29.97/20.16 tff(31930,plain,
% 29.97/20.16 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (~(f3(f6(c1, f6(c1, c2)), c1) = c1)) | (f6(c1, f6(c1, c2)) = c4) | (~big_f(f3(f6(c1, f6(c1, c2)), c1), f6(c1, f6(c1, c2)))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (~(f3(f6(c1, f6(c1, c2)), c1) = c1)) | (f6(c1, f6(c1, c2)) = c4) | (~big_f(f3(f6(c1, f6(c1, c2)), c1), f6(c1, f6(c1, c2)))))),
% 29.97/20.16 inference(rewrite,[status(thm)],[])).
% 29.97/20.16 tff(31931,plain,
% 29.97/20.16 (((~(c2 = c3)) | (~(c2 = f2(c2))) | (f6(c1, f6(c1, c2)) = c4) | (~(f3(f6(c1, f6(c1, c2)), c1) = c1)) | (~big_f(f3(f6(c1, f6(c1, c2)), c1), f6(c1, f6(c1, c2)))) | big_f(c2, c2)) <=> ((~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (~(f3(f6(c1, f6(c1, c2)), c1) = c1)) | (f6(c1, f6(c1, c2)) = c4) | (~big_f(f3(f6(c1, f6(c1, c2)), c1), f6(c1, f6(c1, c2)))))),
% 29.97/20.16 inference(rewrite,[status(thm)],[])).
% 29.97/20.16 tff(31932,plain,
% 29.97/20.16 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | (f6(c1, f6(c1, c2)) = c4) | (~(f3(f6(c1, f6(c1, c2)), c1) = c1)) | (~big_f(f3(f6(c1, f6(c1, c2)), c1), f6(c1, f6(c1, c2)))) | big_f(c2, c2))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (~(f3(f6(c1, f6(c1, c2)), c1) = c1)) | (f6(c1, f6(c1, c2)) = c4) | (~big_f(f3(f6(c1, f6(c1, c2)), c1), f6(c1, f6(c1, c2))))))),
% 29.97/20.16 inference(monotonicity,[status(thm)],[31931])).
% 29.97/20.16 tff(31933,plain,
% 29.97/20.16 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | (f6(c1, f6(c1, c2)) = c4) | (~(f3(f6(c1, f6(c1, c2)), c1) = c1)) | (~big_f(f3(f6(c1, f6(c1, c2)), c1), f6(c1, f6(c1, c2)))) | big_f(c2, c2))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (~(f3(f6(c1, f6(c1, c2)), c1) = c1)) | (f6(c1, f6(c1, c2)) = c4) | (~big_f(f3(f6(c1, f6(c1, c2)), c1), f6(c1, f6(c1, c2)))))),
% 29.97/20.16 inference(transitivity,[status(thm)],[31932, 31930])).
% 29.97/20.16 tff(31934,plain,
% 29.97/20.16 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | (f6(c1, f6(c1, c2)) = c4) | (~(f3(f6(c1, f6(c1, c2)), c1) = c1)) | (~big_f(f3(f6(c1, f6(c1, c2)), c1), f6(c1, f6(c1, c2)))) | big_f(c2, c2))),
% 29.97/20.16 inference(quant_inst,[status(thm)],[])).
% 29.97/20.16 tff(31935,plain,
% 29.97/20.16 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (~(f3(f6(c1, f6(c1, c2)), c1) = c1)) | (f6(c1, f6(c1, c2)) = c4) | (~big_f(f3(f6(c1, f6(c1, c2)), c1), f6(c1, f6(c1, c2))))),
% 29.97/20.16 inference(modus_ponens,[status(thm)],[31934, 31933])).
% 29.97/20.16 tff(31936,plain,
% 29.97/20.16 ((~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (~(f3(f6(c1, f6(c1, c2)), c1) = c1)) | (f6(c1, f6(c1, c2)) = c4) | (~big_f(f3(f6(c1, f6(c1, c2)), c1), f6(c1, f6(c1, c2))))),
% 29.97/20.16 inference(unit_resolution,[status(thm)],[31935, 1398])).
% 29.97/20.16 tff(31937,plain,
% 29.97/20.16 (~(c2 = f2(c2))),
% 29.97/20.16 inference(unit_resolution,[status(thm)],[31936, 31929, 121, 1335, 31916, 31843])).
% 29.97/20.16 tff(31938,plain,
% 29.97/20.16 (~(f2(c2) = c2)),
% 29.97/20.16 inference(unit_resolution,[status(thm)],[31890, 31937])).
% 29.97/20.16 tff(31939,plain,
% 29.97/20.16 (f2(c2) = c1),
% 29.97/20.16 inference(unit_resolution,[status(thm)],[31912, 31938])).
% 29.97/20.16 tff(31940,plain,
% 29.97/20.16 (c1 = f2(c2)),
% 29.97/20.16 inference(unit_resolution,[status(thm)],[31907, 31939])).
% 29.97/20.16 tff(31941,plain,
% 29.97/20.16 (c1 = f2(f10(c1))),
% 29.97/20.16 inference(modus_ponens,[status(thm)],[31940, 31832])).
% 29.97/20.16 tff(31942,plain,
% 29.97/20.16 ((f3(c2, c1) = f8(c1)) <=> (f3(f10(c1), c1) = c1)),
% 29.97/20.16 inference(transitivity,[status(thm)],[31919, 30653])).
% 29.97/20.16 tff(31943,plain,
% 29.97/20.16 (f3(f10(c1), c1) = c1),
% 29.97/20.16 inference(modus_ponens,[status(thm)],[31928, 31942])).
% 29.97/20.16 tff(31944,plain,
% 29.97/20.16 ((f10(c1) = c3) <=> (f10(c1) = c2)),
% 29.97/20.16 inference(monotonicity,[status(thm)],[67])).
% 29.97/20.16 tff(31945,plain,
% 29.97/20.16 ((f10(c1) = c2) <=> (f10(c1) = c3)),
% 29.97/20.16 inference(symmetry,[status(thm)],[31944])).
% 29.97/20.16 tff(31946,plain,
% 29.97/20.16 (f10(c1) = c3),
% 29.97/20.16 inference(modus_ponens,[status(thm)],[15, 31945])).
% 29.97/20.16 tff(31947,plain,
% 29.97/20.16 (big_f(f3(f10(c1), c1), f10(c1)) <=> big_f(f3(c2, c1), f10(c1))),
% 29.97/20.16 inference(monotonicity,[status(thm)],[30648])).
% 29.97/20.16 tff(31948,plain,
% 29.97/20.16 (big_f(f3(c2, c1), f10(c1)) <=> big_f(f3(f10(c1), c1), f10(c1))),
% 29.97/20.16 inference(symmetry,[status(thm)],[31947])).
% 29.97/20.16 tff(31949,plain,
% 29.97/20.16 (big_f(f3(c2, c1), c2) <=> big_f(f3(f10(c1), c1), f10(c1))),
% 29.97/20.16 inference(transitivity,[status(thm)],[31362, 31948])).
% 29.97/20.16 tff(31950,plain,
% 29.97/20.16 (big_f(f3(f10(c1), c1), f10(c1))),
% 29.97/20.16 inference(modus_ponens,[status(thm)],[31915, 31949])).
% 29.97/20.16 tff(31951,plain,
% 29.97/20.16 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((f10(c1) = c4) | (~big_f(f3(f10(c1), c1), f10(c1))) | (~(f3(f10(c1), c1) = c1)) | (~(f10(c1) = c3)) | big_f(f10(c1), c1) | (~(c1 = f2(f10(c1)))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (f10(c1) = c4) | (~big_f(f3(f10(c1), c1), f10(c1))) | (~(f3(f10(c1), c1) = c1)) | (~(f10(c1) = c3)) | big_f(f10(c1), c1) | (~(c1 = f2(f10(c1)))))),
% 29.97/20.16 inference(rewrite,[status(thm)],[])).
% 29.97/20.16 tff(31952,plain,
% 29.97/20.16 (((~(f10(c1) = c3)) | (~(c1 = f2(f10(c1)))) | (f10(c1) = c4) | (~(f3(f10(c1), c1) = c1)) | (~big_f(f3(f10(c1), c1), f10(c1))) | big_f(f10(c1), c1)) <=> ((f10(c1) = c4) | (~big_f(f3(f10(c1), c1), f10(c1))) | (~(f3(f10(c1), c1) = c1)) | (~(f10(c1) = c3)) | big_f(f10(c1), c1) | (~(c1 = f2(f10(c1)))))),
% 29.97/20.16 inference(rewrite,[status(thm)],[])).
% 29.97/20.16 tff(31953,plain,
% 29.97/20.16 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(f10(c1) = c3)) | (~(c1 = f2(f10(c1)))) | (f10(c1) = c4) | (~(f3(f10(c1), c1) = c1)) | (~big_f(f3(f10(c1), c1), f10(c1))) | big_f(f10(c1), c1))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((f10(c1) = c4) | (~big_f(f3(f10(c1), c1), f10(c1))) | (~(f3(f10(c1), c1) = c1)) | (~(f10(c1) = c3)) | big_f(f10(c1), c1) | (~(c1 = f2(f10(c1))))))),
% 29.97/20.16 inference(monotonicity,[status(thm)],[31952])).
% 29.97/20.16 tff(31954,plain,
% 29.97/20.16 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(f10(c1) = c3)) | (~(c1 = f2(f10(c1)))) | (f10(c1) = c4) | (~(f3(f10(c1), c1) = c1)) | (~big_f(f3(f10(c1), c1), f10(c1))) | big_f(f10(c1), c1))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (f10(c1) = c4) | (~big_f(f3(f10(c1), c1), f10(c1))) | (~(f3(f10(c1), c1) = c1)) | (~(f10(c1) = c3)) | big_f(f10(c1), c1) | (~(c1 = f2(f10(c1)))))),
% 29.97/20.16 inference(transitivity,[status(thm)],[31953, 31951])).
% 29.97/20.16 tff(31955,plain,
% 29.97/20.16 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(f10(c1) = c3)) | (~(c1 = f2(f10(c1)))) | (f10(c1) = c4) | (~(f3(f10(c1), c1) = c1)) | (~big_f(f3(f10(c1), c1), f10(c1))) | big_f(f10(c1), c1))),
% 29.97/20.16 inference(quant_inst,[status(thm)],[])).
% 29.97/20.16 tff(31956,plain,
% 29.97/20.16 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (f10(c1) = c4) | (~big_f(f3(f10(c1), c1), f10(c1))) | (~(f3(f10(c1), c1) = c1)) | (~(f10(c1) = c3)) | big_f(f10(c1), c1) | (~(c1 = f2(f10(c1))))),
% 29.97/20.16 inference(modus_ponens,[status(thm)],[31955, 31954])).
% 29.97/20.16 tff(31957,plain,
% 29.97/20.16 ((~(f3(f10(c1), c1) = c1)) | (~(c1 = f2(f10(c1))))),
% 29.97/20.16 inference(unit_resolution,[status(thm)],[31956, 1398, 31865, 31950, 31946, 29412])).
% 29.97/20.16 tff(31958,plain,
% 29.97/20.16 (~(c1 = f2(f10(c1)))),
% 29.97/20.16 inference(unit_resolution,[status(thm)],[31957, 31943])).
% 29.97/20.16 tff(31959,plain,
% 29.97/20.16 ($false),
% 29.97/20.16 inference(unit_resolution,[status(thm)],[31958, 31941])).
% 29.97/20.16 tff(31960,plain,((f10(c1) = c1) | big_f(c2, c2) | (~(f6(c1, c2) = c2)) | big_f(c2, c1) | (~(c3 = c2))), inference(lemma,lemma(discharge,[]))).
% 29.97/20.16 tff(31961,plain,
% 29.97/20.16 (~(c3 = c2)),
% 29.97/20.16 inference(unit_resolution,[status(thm)],[31960, 2, 36, 3, 121])).
% 29.97/20.16 tff(31962,plain,
% 29.97/20.16 (c3 = c1),
% 29.97/20.16 inference(unit_resolution,[status(thm)],[180, 31961])).
% 29.97/20.16 tff(31963,plain,
% 29.97/20.16 (c1 = c3),
% 29.97/20.16 inference(unit_resolution,[status(thm)],[175, 31962])).
% 29.97/20.16 tff(31964,plain,
% 29.97/20.16 ((~big_f(c2, c1)) <=> (~big_f(c2, f10(c2)))),
% 29.97/20.16 inference(monotonicity,[status(thm)],[31830])).
% 29.97/20.16 tff(31965,plain,
% 29.97/20.16 (~big_f(c2, f10(c2))),
% 29.97/20.16 inference(modus_ponens,[status(thm)],[2, 31964])).
% 29.97/20.16 tff(31966,plain,
% 29.97/20.16 (big_f(c2, f10(c2)) <=> big_f(f3(c1, c1), c1)),
% 29.97/20.16 inference(monotonicity,[status(thm)],[31731, 11819])).
% 29.97/20.16 tff(31967,plain,
% 29.97/20.16 (big_f(f3(c1, c1), c1) <=> big_f(c2, f10(c2))),
% 29.97/20.16 inference(symmetry,[status(thm)],[31966])).
% 29.97/20.16 tff(31968,plain,
% 29.97/20.16 ((c1 = c4) | (~(c1 = c3)) | (c1 = f2(c1))),
% 29.97/20.16 inference(unit_resolution,[status(thm)],[20233, 7352, 1430, 1431, 31714])).
% 29.97/20.16 tff(31969,plain,
% 29.97/20.16 (c1 = f2(c1)),
% 29.97/20.16 inference(unit_resolution,[status(thm)],[31968, 482, 5080])).
% 29.97/20.16 tff(31970,plain,
% 29.97/20.16 (f2(c1) = c1),
% 29.97/20.16 inference(symmetry,[status(thm)],[31969])).
% 29.97/20.16 tff(31971,plain,
% 29.97/20.16 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (big_f(f3(c1, c1), c1) | (f3(c1, c1) = c1) | (c1 = c4) | (~(c1 = c3)) | (~big_f(c1, c2)) | (c2 = f2(c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | big_f(f3(c1, c1), c1) | (f3(c1, c1) = c1) | (c1 = c4) | (~(c1 = c3)) | (~big_f(c1, c2)) | (c2 = f2(c1)))),
% 29.97/20.16 inference(rewrite,[status(thm)],[])).
% 29.97/20.16 tff(31972,plain,
% 29.97/20.16 (((~(c1 = c3)) | (c1 = c4) | (f3(c1, c1) = c1) | big_f(f3(c1, c1), c1) | (c2 = f2(c1)) | (~big_f(c1, c2))) <=> (big_f(f3(c1, c1), c1) | (f3(c1, c1) = c1) | (c1 = c4) | (~(c1 = c3)) | (~big_f(c1, c2)) | (c2 = f2(c1)))),
% 29.97/20.16 inference(rewrite,[status(thm)],[])).
% 29.97/20.16 tff(31973,plain,
% 29.97/20.16 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c1 = c4) | (f3(c1, c1) = c1) | big_f(f3(c1, c1), c1) | (c2 = f2(c1)) | (~big_f(c1, c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (big_f(f3(c1, c1), c1) | (f3(c1, c1) = c1) | (c1 = c4) | (~(c1 = c3)) | (~big_f(c1, c2)) | (c2 = f2(c1))))),
% 29.97/20.16 inference(monotonicity,[status(thm)],[31972])).
% 29.97/20.16 tff(31974,plain,
% 29.97/20.16 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c1 = c4) | (f3(c1, c1) = c1) | big_f(f3(c1, c1), c1) | (c2 = f2(c1)) | (~big_f(c1, c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | big_f(f3(c1, c1), c1) | (f3(c1, c1) = c1) | (c1 = c4) | (~(c1 = c3)) | (~big_f(c1, c2)) | (c2 = f2(c1)))),
% 29.97/20.16 inference(transitivity,[status(thm)],[31973, 31971])).
% 29.97/20.16 tff(31975,plain,
% 29.97/20.16 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c1 = c4) | (f3(c1, c1) = c1) | big_f(f3(c1, c1), c1) | (c2 = f2(c1)) | (~big_f(c1, c2)))),
% 29.97/20.16 inference(quant_inst,[status(thm)],[])).
% 29.97/20.16 tff(31976,plain,
% 29.97/20.16 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | big_f(f3(c1, c1), c1) | (f3(c1, c1) = c1) | (c1 = c4) | (~(c1 = c3)) | (~big_f(c1, c2)) | (c2 = f2(c1))),
% 29.97/20.16 inference(modus_ponens,[status(thm)],[31975, 31974])).
% 29.97/20.16 tff(31977,plain,
% 29.97/20.16 ((c1 = c4) | (~(c1 = c3)) | (c2 = f2(c1))),
% 29.97/20.16 inference(unit_resolution,[status(thm)],[31976, 7352, 1430, 1431, 30354])).
% 29.97/20.16 tff(31978,plain,
% 29.97/20.16 (c2 = f2(c1)),
% 29.97/20.16 inference(unit_resolution,[status(thm)],[31977, 482, 5080])).
% 29.97/20.16 tff(31979,plain,
% 29.97/20.16 (c2 = c1),
% 29.97/20.17 inference(transitivity,[status(thm)],[31978, 31970])).
% 29.97/20.17 tff(31980,plain,
% 29.97/20.17 ($false),
% 29.97/20.17 inference(unit_resolution,[status(thm)],[75, 31979])).
% 29.97/20.17 tff(31981,plain,((c1 = c4) | (~(c1 = c3)) | big_f(f3(c1, c1), c1) | (f3(c1, c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.97/20.17 tff(31982,plain,
% 29.97/20.17 (c1 = c4),
% 29.97/20.17 inference(unit_resolution,[status(thm)],[31981, 5080, 1430, 1431])).
% 29.97/20.17 tff(31983,plain,
% 29.97/20.17 (c4 = c1),
% 29.97/20.17 inference(symmetry,[status(thm)],[31982])).
% 29.97/20.17 tff(31984,plain,
% 29.97/20.17 ((c2 = c4) <=> (c2 = c1)),
% 29.97/20.17 inference(monotonicity,[status(thm)],[31983])).
% 29.97/20.17 tff(31985,plain,
% 29.97/20.17 ((c2 = c1) <=> (c2 = c4)),
% 29.97/20.17 inference(symmetry,[status(thm)],[31984])).
% 29.97/20.17 tff(31986,plain,
% 29.97/20.17 ((~(c2 = c1)) <=> (~(c2 = c4))),
% 29.97/20.17 inference(monotonicity,[status(thm)],[31985])).
% 29.97/20.17 tff(31987,plain,
% 29.97/20.17 (~(c2 = c4)),
% 29.97/20.17 inference(modus_ponens,[status(thm)],[75, 31986])).
% 29.97/20.17 tff(31988,assumption,(f3(f3(f7(c1), c1), c1) = c2), introduced(assumption)).
% 29.97/20.17 tff(31989,plain,
% 29.97/20.17 (f3(c2, c1) = f3(f6(c1, f6(c1, c2)), c1)),
% 29.97/20.17 inference(monotonicity,[status(thm)],[28323])).
% 29.97/20.17 tff(31990,plain,
% 29.97/20.17 (f3(f6(c1, f6(c1, c2)), c1) = f3(c2, c1)),
% 29.97/20.17 inference(symmetry,[status(thm)],[31989])).
% 29.97/20.17 tff(31991,plain,
% 29.97/20.17 (f6(c1, f6(c1, c2)) = f3(c1, c1)),
% 29.97/20.17 inference(transitivity,[status(thm)],[27490, 1442])).
% 29.97/20.17 tff(31992,plain,
% 29.97/20.17 (f3(f6(c1, f6(c1, c2)), c1) = f3(f3(c1, c1), c1)),
% 29.97/20.17 inference(monotonicity,[status(thm)],[31991])).
% 29.97/20.17 tff(31993,plain,
% 29.97/20.17 (f3(f3(c1, c1), c1) = f3(f6(c1, f6(c1, c2)), c1)),
% 29.97/20.17 inference(symmetry,[status(thm)],[31992])).
% 29.97/20.17 tff(31994,plain,
% 29.97/20.17 (f3(f7(c1), c1) = f3(c1, c1)),
% 29.97/20.17 inference(monotonicity,[status(thm)],[25791])).
% 29.97/20.17 tff(31995,plain,
% 29.97/20.17 (f3(c1, c1) = f3(f7(c1), c1)),
% 29.97/20.17 inference(symmetry,[status(thm)],[31994])).
% 29.97/20.17 tff(31996,plain,
% 29.97/20.17 (f3(f3(c1, c1), c1) = f3(f3(f7(c1), c1), c1)),
% 29.97/20.17 inference(monotonicity,[status(thm)],[31995])).
% 29.97/20.17 tff(31997,plain,
% 29.97/20.17 (f3(f3(f7(c1), c1), c1) = f3(f3(c1, c1), c1)),
% 29.97/20.17 inference(symmetry,[status(thm)],[31996])).
% 29.97/20.17 tff(31998,plain,
% 29.97/20.17 (c2 = f3(f3(f7(c1), c1), c1)),
% 29.97/20.17 inference(symmetry,[status(thm)],[31988])).
% 29.97/20.17 tff(31999,plain,
% 29.97/20.17 (c2 = f3(c2, c1)),
% 29.97/20.17 inference(transitivity,[status(thm)],[31998, 31997, 31993, 31990])).
% 29.97/20.17 tff(32000,assumption,(~(c2 = f3(c2, c1))), introduced(assumption)).
% 29.97/20.17 tff(32001,plain,
% 29.97/20.17 ($false),
% 29.97/20.17 inference(unit_resolution,[status(thm)],[32000, 31999])).
% 29.97/20.17 tff(32002,plain,((~(f3(c1, c1) = c2)) | (c2 = f3(c2, c1)) | (~(f3(f3(f7(c1), c1), c1) = c2)) | (~(f6(c1, f6(c1, c2)) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.97/20.17 tff(32003,plain,
% 29.97/20.17 (c2 = f3(c2, c1)),
% 29.97/20.17 inference(unit_resolution,[status(thm)],[32002, 31988, 27490, 1441])).
% 29.97/20.17 tff(32004,assumption,(~(big_f(c2, c2) <=> big_f(f3(c2, c1), c2))), introduced(assumption)).
% 29.97/20.17 tff(32005,assumption,(c2 = f3(c2, c1)), introduced(assumption)).
% 29.97/20.17 tff(32006,plain,
% 29.97/20.17 (big_f(c2, c2) <=> big_f(f3(c2, c1), c2)),
% 29.97/20.17 inference(monotonicity,[status(thm)],[32005])).
% 29.97/20.17 tff(32007,plain,
% 29.97/20.17 ($false),
% 29.97/20.17 inference(unit_resolution,[status(thm)],[32006, 32004])).
% 29.97/20.17 tff(32008,plain,((~(c2 = f3(c2, c1))) | (big_f(c2, c2) <=> big_f(f3(c2, c1), c2))), inference(lemma,lemma(discharge,[]))).
% 29.97/20.17 tff(32009,plain,
% 29.97/20.17 (big_f(c2, c2) <=> big_f(f3(c2, c1), c2)),
% 29.97/20.17 inference(unit_resolution,[status(thm)],[32008, 32003])).
% 29.97/20.17 tff(32010,plain,
% 29.97/20.17 ((~(big_f(c2, c2) <=> big_f(f3(c2, c1), c2))) | big_f(c2, c2) | (~big_f(f3(c2, c1), c2))),
% 29.97/20.17 inference(tautology,[status(thm)],[])).
% 29.97/20.17 tff(32011,plain,
% 29.97/20.17 (~big_f(f3(c2, c1), c2)),
% 29.97/20.17 inference(unit_resolution,[status(thm)],[32010, 32009, 121])).
% 29.97/20.17 tff(32012,plain,
% 29.97/20.17 (f3(c2, c1) = f3(f3(c1, c1), c1)),
% 29.97/20.17 inference(monotonicity,[status(thm)],[1442])).
% 29.97/20.17 tff(32013,plain,
% 29.97/20.17 (f3(c2, c1) = c2),
% 29.97/20.17 inference(transitivity,[status(thm)],[32012, 31996, 31988])).
% 29.97/20.17 tff(32014,plain,
% 29.97/20.17 ((f3(c2, c1) = c1) <=> (c2 = c1)),
% 29.97/20.17 inference(monotonicity,[status(thm)],[32013])).
% 29.97/20.17 tff(32015,plain,
% 29.97/20.17 ((c2 = c1) <=> (f3(c2, c1) = c1)),
% 29.97/20.17 inference(symmetry,[status(thm)],[32014])).
% 29.97/20.17 tff(32016,plain,
% 29.97/20.17 ((~(c2 = c1)) <=> (~(f3(c2, c1) = c1))),
% 29.97/20.17 inference(monotonicity,[status(thm)],[32015])).
% 29.97/20.17 tff(32017,plain,
% 29.97/20.17 (~(f3(c2, c1) = c1)),
% 29.97/20.17 inference(modus_ponens,[status(thm)],[75, 32016])).
% 29.97/20.17 tff(32018,plain,
% 29.97/20.17 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((c2 = c4) | (~(c1 = c3)) | (c1 = f2(c1)) | (~big_f(c1, c1)) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (c2 = c4) | (~(c1 = c3)) | (c1 = f2(c1)) | (~big_f(c1, c1)) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2))),
% 29.97/20.17 inference(rewrite,[status(thm)],[])).
% 29.97/20.17 tff(32019,plain,
% 29.97/20.17 (((~(c1 = c3)) | (c2 = c4) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2) | (c1 = f2(c1)) | (~big_f(c1, c1))) <=> ((c2 = c4) | (~(c1 = c3)) | (c1 = f2(c1)) | (~big_f(c1, c1)) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2))),
% 29.97/20.17 inference(rewrite,[status(thm)],[])).
% 29.97/20.17 tff(32020,plain,
% 29.97/20.17 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c2 = c4) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2) | (c1 = f2(c1)) | (~big_f(c1, c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((c2 = c4) | (~(c1 = c3)) | (c1 = f2(c1)) | (~big_f(c1, c1)) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2)))),
% 29.97/20.17 inference(monotonicity,[status(thm)],[32019])).
% 29.97/20.17 tff(32021,plain,
% 29.97/20.17 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c2 = c4) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2) | (c1 = f2(c1)) | (~big_f(c1, c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (c2 = c4) | (~(c1 = c3)) | (c1 = f2(c1)) | (~big_f(c1, c1)) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2))),
% 29.97/20.17 inference(transitivity,[status(thm)],[32020, 32018])).
% 29.97/20.17 tff(32022,plain,
% 29.97/20.17 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c2 = c4) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2) | (c1 = f2(c1)) | (~big_f(c1, c1)))),
% 29.97/20.17 inference(quant_inst,[status(thm)],[])).
% 29.97/20.17 tff(32023,plain,
% 29.97/20.17 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (c2 = c4) | (~(c1 = c3)) | (c1 = f2(c1)) | (~big_f(c1, c1)) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2)),
% 29.97/20.17 inference(modus_ponens,[status(thm)],[32022, 32021])).
% 29.97/20.17 tff(32024,plain,
% 29.97/20.17 (c1 = f2(c1)),
% 29.97/20.17 inference(unit_resolution,[status(thm)],[32023, 7352, 5080, 873, 32017, 32011, 31714])).
% 29.97/20.17 tff(32025,plain,
% 29.97/20.17 (f2(c1) = c1),
% 29.97/20.17 inference(symmetry,[status(thm)],[32024])).
% 29.97/20.17 tff(32026,plain,
% 29.97/20.17 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((c2 = c4) | (~(c1 = c3)) | (~big_f(c1, c2)) | (c2 = f2(c1)) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (c2 = c4) | (~(c1 = c3)) | (~big_f(c1, c2)) | (c2 = f2(c1)) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2))),
% 29.97/20.17 inference(rewrite,[status(thm)],[])).
% 29.97/20.17 tff(32027,plain,
% 29.97/20.17 (((~(c1 = c3)) | (c2 = c4) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2) | (c2 = f2(c1)) | (~big_f(c1, c2))) <=> ((c2 = c4) | (~(c1 = c3)) | (~big_f(c1, c2)) | (c2 = f2(c1)) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2))),
% 29.97/20.17 inference(rewrite,[status(thm)],[])).
% 29.97/20.17 tff(32028,plain,
% 29.97/20.17 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c2 = c4) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2) | (c2 = f2(c1)) | (~big_f(c1, c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((c2 = c4) | (~(c1 = c3)) | (~big_f(c1, c2)) | (c2 = f2(c1)) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2)))),
% 29.97/20.17 inference(monotonicity,[status(thm)],[32027])).
% 29.97/20.17 tff(32029,plain,
% 29.97/20.17 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c2 = c4) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2) | (c2 = f2(c1)) | (~big_f(c1, c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (c2 = c4) | (~(c1 = c3)) | (~big_f(c1, c2)) | (c2 = f2(c1)) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2))),
% 29.97/20.17 inference(transitivity,[status(thm)],[32028, 32026])).
% 29.97/20.17 tff(32030,plain,
% 29.97/20.17 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c2 = c4) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2) | (c2 = f2(c1)) | (~big_f(c1, c2)))),
% 29.97/20.17 inference(quant_inst,[status(thm)],[])).
% 29.97/20.17 tff(32031,plain,
% 29.97/20.17 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (c2 = c4) | (~(c1 = c3)) | (~big_f(c1, c2)) | (c2 = f2(c1)) | (f3(c2, c1) = c1) | big_f(f3(c2, c1), c2)),
% 29.97/20.17 inference(modus_ponens,[status(thm)],[32030, 32029])).
% 29.97/20.17 tff(32032,plain,
% 29.97/20.17 (c2 = f2(c1)),
% 29.97/20.17 inference(unit_resolution,[status(thm)],[32031, 7352, 5080, 873, 30354, 32017, 32011])).
% 29.97/20.17 tff(32033,plain,
% 29.97/20.17 (c2 = c1),
% 29.97/20.17 inference(transitivity,[status(thm)],[32032, 32025])).
% 29.97/20.17 tff(32034,plain,
% 29.97/20.17 ($false),
% 29.97/20.17 inference(unit_resolution,[status(thm)],[75, 32033])).
% 29.97/20.17 tff(32035,plain,((~(f3(f3(f7(c1), c1), c1) = c2)) | (~(c1 = c3)) | (c2 = c4) | (~(f3(c1, c1) = c2)) | big_f(c2, c2) | (~(f6(c1, f6(c1, c2)) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.97/20.17 tff(32036,plain,
% 29.97/20.17 (~(f3(f3(f7(c1), c1), c1) = c2)),
% 29.97/20.17 inference(unit_resolution,[status(thm)],[32035, 5080, 31987, 1440, 121, 27490])).
% 29.97/20.17 tff(32037,plain,
% 29.97/20.17 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f3(f3(f7(c1), c1), c1) = c1) | (f3(f3(f7(c1), c1), c1) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f3(f3(f7(c1), c1), c1) = c1) | (f3(f3(f7(c1), c1), c1) = c2))),
% 29.97/20.17 inference(rewrite,[status(thm)],[])).
% 29.97/20.17 tff(32038,plain,
% 29.97/20.17 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f3(f3(f7(c1), c1), c1) = c1) | (f3(f3(f7(c1), c1), c1) = c2))),
% 29.97/20.17 inference(quant_inst,[status(thm)],[])).
% 29.97/20.17 tff(32039,plain,
% 29.97/20.17 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f3(f3(f7(c1), c1), c1) = c1) | (f3(f3(f7(c1), c1), c1) = c2)),
% 29.97/20.17 inference(modus_ponens,[status(thm)],[32038, 32037])).
% 29.97/20.17 tff(32040,plain,
% 29.97/20.17 ((f3(f3(f7(c1), c1), c1) = c1) | (f3(f3(f7(c1), c1), c1) = c2)),
% 29.97/20.17 inference(unit_resolution,[status(thm)],[32039, 10])).
% 29.97/20.17 tff(32041,plain,
% 29.97/20.17 (f3(f3(f7(c1), c1), c1) = c1),
% 29.97/20.17 inference(unit_resolution,[status(thm)],[32040, 32036])).
% 29.97/20.17 tff(32042,plain,
% 29.97/20.17 (f3(c2, c1) = f3(f3(c1, c1), c1)),
% 29.97/20.17 inference(monotonicity,[status(thm)],[31731])).
% 29.97/20.17 tff(32043,plain,
% 29.97/20.17 (f3(c2, c1) = c1),
% 29.97/20.17 inference(transitivity,[status(thm)],[32042, 31996, 32041])).
% 29.97/20.17 tff(32044,plain,
% 29.97/20.17 (big_f(f3(c2, c1), c2) <=> big_f(c1, c2)),
% 29.97/20.17 inference(monotonicity,[status(thm)],[32043])).
% 29.97/20.17 tff(32045,plain,
% 29.97/20.17 (big_f(c1, c2) <=> big_f(f3(c2, c1), c2)),
% 29.97/20.17 inference(symmetry,[status(thm)],[32044])).
% 29.97/20.17 tff(32046,plain,
% 29.97/20.17 (big_f(f3(c2, c1), c2)),
% 29.97/20.17 inference(modus_ponens,[status(thm)],[30354, 32045])).
% 29.97/20.17 tff(32047,plain,
% 29.97/20.17 (f3(f3(c1, c1), c1) = f3(c2, c1)),
% 29.97/20.17 inference(monotonicity,[status(thm)],[1441])).
% 29.97/20.17 tff(32048,plain,
% 29.97/20.17 ((f3(f3(c1, c1), c1) = c1) <=> (f3(c2, c1) = c1)),
% 29.97/20.17 inference(monotonicity,[status(thm)],[32047])).
% 29.97/20.17 tff(32049,plain,
% 29.97/20.17 (f3(f3(f7(c1), c1), c1) = f3(f3(c1, c1), c1)),
% 29.97/20.17 inference(monotonicity,[status(thm)],[31994])).
% 29.97/20.17 tff(32050,plain,
% 29.97/20.17 ((f3(f3(f7(c1), c1), c1) = c1) <=> (f3(f3(c1, c1), c1) = c1)),
% 29.97/20.17 inference(monotonicity,[status(thm)],[32049])).
% 29.97/20.17 tff(32051,plain,
% 29.97/20.17 ((f3(f3(f7(c1), c1), c1) = c1) <=> (f3(c2, c1) = c1)),
% 29.97/20.17 inference(transitivity,[status(thm)],[32050, 32048])).
% 29.97/20.17 tff(32052,assumption,(f3(f3(f7(c1), c1), c1) = c1), introduced(assumption)).
% 29.97/20.17 tff(32053,plain,
% 29.97/20.17 (f3(c2, c1) = c1),
% 29.97/20.17 inference(modus_ponens,[status(thm)],[32052, 32051])).
% 29.97/20.17 tff(32054,plain,
% 29.97/20.17 ($false),
% 29.97/20.17 inference(unit_resolution,[status(thm)],[29003, 32053])).
% 29.97/20.17 tff(32055,plain,((~(f3(f3(f7(c1), c1), c1) = c1)) | (f3(c2, c1) = c1) | (~(f3(c1, c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.97/20.17 tff(32056,plain,
% 29.97/20.17 (f3(c2, c1) = c1),
% 29.97/20.17 inference(unit_resolution,[status(thm)],[32055, 32041, 1440])).
% 29.97/20.17 tff(32057,plain,
% 29.97/20.17 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((c2 = c4) | (~(c1 = c3)) | (c1 = f2(c1)) | (~big_f(c1, c1)) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (c2 = c4) | (~(c1 = c3)) | (c1 = f2(c1)) | (~big_f(c1, c1)) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)))),
% 29.97/20.17 inference(rewrite,[status(thm)],[])).
% 29.97/20.17 tff(32058,plain,
% 29.97/20.17 (((~(c1 = c3)) | (c2 = c4) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)) | (c1 = f2(c1)) | (~big_f(c1, c1))) <=> ((c2 = c4) | (~(c1 = c3)) | (c1 = f2(c1)) | (~big_f(c1, c1)) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)))),
% 29.97/20.17 inference(rewrite,[status(thm)],[])).
% 29.97/20.17 tff(32059,plain,
% 29.97/20.17 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c2 = c4) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)) | (c1 = f2(c1)) | (~big_f(c1, c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((c2 = c4) | (~(c1 = c3)) | (c1 = f2(c1)) | (~big_f(c1, c1)) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2))))),
% 29.97/20.17 inference(monotonicity,[status(thm)],[32058])).
% 29.97/20.17 tff(32060,plain,
% 29.97/20.17 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c2 = c4) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)) | (c1 = f2(c1)) | (~big_f(c1, c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (c2 = c4) | (~(c1 = c3)) | (c1 = f2(c1)) | (~big_f(c1, c1)) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)))),
% 29.97/20.17 inference(transitivity,[status(thm)],[32059, 32057])).
% 29.97/20.17 tff(32061,plain,
% 29.97/20.17 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c2 = c4) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)) | (c1 = f2(c1)) | (~big_f(c1, c1)))),
% 29.97/20.17 inference(quant_inst,[status(thm)],[])).
% 29.97/20.17 tff(32062,plain,
% 29.97/20.17 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (c2 = c4) | (~(c1 = c3)) | (c1 = f2(c1)) | (~big_f(c1, c1)) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2))),
% 29.97/20.17 inference(modus_ponens,[status(thm)],[32061, 32060])).
% 29.97/20.17 tff(32063,plain,
% 29.97/20.17 (c1 = f2(c1)),
% 29.97/20.17 inference(unit_resolution,[status(thm)],[32062, 7051, 5080, 31987, 32056, 32046, 31714])).
% 29.97/20.17 tff(32064,plain,
% 29.97/20.17 (f2(c1) = c1),
% 29.97/20.17 inference(symmetry,[status(thm)],[32063])).
% 29.97/20.17 tff(32065,plain,
% 29.97/20.17 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((c2 = c4) | (~(c1 = c3)) | (~big_f(c1, c2)) | (c2 = f2(c1)) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (c2 = c4) | (~(c1 = c3)) | (~big_f(c1, c2)) | (c2 = f2(c1)) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)))),
% 29.97/20.17 inference(rewrite,[status(thm)],[])).
% 29.97/20.17 tff(32066,plain,
% 29.97/20.17 (((~(c1 = c3)) | (c2 = c4) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)) | (c2 = f2(c1)) | (~big_f(c1, c2))) <=> ((c2 = c4) | (~(c1 = c3)) | (~big_f(c1, c2)) | (c2 = f2(c1)) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)))),
% 29.97/20.17 inference(rewrite,[status(thm)],[])).
% 29.97/20.17 tff(32067,plain,
% 29.97/20.17 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c2 = c4) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)) | (c2 = f2(c1)) | (~big_f(c1, c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((c2 = c4) | (~(c1 = c3)) | (~big_f(c1, c2)) | (c2 = f2(c1)) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2))))),
% 29.97/20.17 inference(monotonicity,[status(thm)],[32066])).
% 29.97/20.17 tff(32068,plain,
% 29.97/20.17 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c2 = c4) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)) | (c2 = f2(c1)) | (~big_f(c1, c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (c2 = c4) | (~(c1 = c3)) | (~big_f(c1, c2)) | (c2 = f2(c1)) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)))),
% 29.97/20.17 inference(transitivity,[status(thm)],[32067, 32065])).
% 29.97/20.17 tff(32069,plain,
% 29.97/20.17 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c2 = c4) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2)) | (c2 = f2(c1)) | (~big_f(c1, c2)))),
% 29.97/20.17 inference(quant_inst,[status(thm)],[])).
% 29.97/20.17 tff(32070,plain,
% 29.97/20.17 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (c2 = c4) | (~(c1 = c3)) | (~big_f(c1, c2)) | (c2 = f2(c1)) | (~(f3(c2, c1) = c1)) | (~big_f(f3(c2, c1), c2))),
% 29.97/20.17 inference(modus_ponens,[status(thm)],[32069, 32068])).
% 29.97/20.17 tff(32071,plain,
% 29.97/20.17 (c2 = f2(c1)),
% 29.97/20.17 inference(unit_resolution,[status(thm)],[32070, 7051, 5080, 31987, 30354, 32056, 32046])).
% 29.97/20.17 tff(32072,plain,
% 29.97/20.17 (c2 = c1),
% 29.97/20.17 inference(transitivity,[status(thm)],[32071, 32064])).
% 29.97/20.17 tff(32073,plain,
% 29.97/20.17 ($false),
% 29.97/20.17 inference(unit_resolution,[status(thm)],[75, 32072])).
% 29.97/20.17 tff(32074,plain,((~(c1 = c3)) | big_f(c2, c2) | (~(f6(c1, f6(c1, c2)) = c2)) | big_f(f3(c1, c1), c1) | (f3(c1, c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.97/20.17 tff(32075,plain,
% 29.97/20.17 (big_f(f3(c1, c1), c1)),
% 29.97/20.17 inference(unit_resolution,[status(thm)],[32074, 1431, 27490, 121, 5080])).
% 29.97/20.17 tff(32076,plain,
% 29.97/20.17 (big_f(c2, f10(c2))),
% 29.97/20.17 inference(modus_ponens,[status(thm)],[32075, 31967])).
% 29.97/20.17 tff(32077,plain,
% 29.97/20.17 ($false),
% 29.97/20.17 inference(unit_resolution,[status(thm)],[15517, 32076])).
% 29.97/20.17 tff(32078,plain,((f3(c1, c1) = c1) | big_f(c2, f10(c2)) | (~(f10(c2) = c1)) | (~(f6(c1, f6(c1, c2)) = c2)) | big_f(c2, c2) | (~(c1 = c3))), inference(lemma,lemma(discharge,[]))).
% 29.97/20.17 tff(32079,plain,
% 29.97/20.17 (f3(c1, c1) = c1),
% 29.97/20.17 inference(unit_resolution,[status(thm)],[32078, 31965, 31790, 40, 121, 31963])).
% 29.97/20.17 tff(32080,plain,
% 29.97/20.17 (f3(c1, c1) = f10(c2)),
% 29.97/20.17 inference(transitivity,[status(thm)],[32079, 31793])).
% 29.97/20.17 tff(32081,plain,
% 29.97/20.17 (big_f(f3(c1, c1), c1) <=> big_f(f10(c2), f10(c2))),
% 29.97/20.17 inference(monotonicity,[status(thm)],[32080, 31793])).
% 29.97/20.18 tff(32082,plain,
% 29.97/20.18 (big_f(f10(c2), f10(c2)) <=> big_f(f3(c1, c1), c1)),
% 29.97/20.18 inference(symmetry,[status(thm)],[32081])).
% 29.97/20.18 tff(32083,plain,
% 29.97/20.18 (big_f(f3(c1, c1), c1)),
% 29.97/20.18 inference(modus_ponens,[status(thm)],[31811, 32082])).
% 29.97/20.18 tff(32084,plain,
% 29.97/20.18 ((c1 = c4) | (~(c1 = c3)) | (c1 = f2(c1))),
% 29.97/20.18 inference(unit_resolution,[status(thm)],[7189, 7051, 1387, 1938, 31714])).
% 29.97/20.18 tff(32085,plain,
% 29.97/20.18 (c1 = f2(c1)),
% 29.97/20.18 inference(unit_resolution,[status(thm)],[32084, 482, 5080])).
% 29.97/20.18 tff(32086,plain,
% 29.97/20.18 (f2(c1) = c1),
% 29.97/20.18 inference(symmetry,[status(thm)],[32085])).
% 29.97/20.18 tff(32087,plain,
% 29.97/20.18 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((c1 = c4) | (~(c1 = c3)) | (~big_f(f3(c1, c1), c1)) | (~(f3(c1, c1) = c1)) | (f10(c1) = f2(c1)) | (~big_f(c1, f10(c1))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (c1 = c4) | (~(c1 = c3)) | (~big_f(f3(c1, c1), c1)) | (~(f3(c1, c1) = c1)) | (f10(c1) = f2(c1)) | (~big_f(c1, f10(c1))))),
% 29.97/20.18 inference(rewrite,[status(thm)],[])).
% 29.97/20.18 tff(32088,plain,
% 29.97/20.18 (((~(c1 = c3)) | (c1 = c4) | (~(f3(c1, c1) = c1)) | (~big_f(f3(c1, c1), c1)) | (f10(c1) = f2(c1)) | (~big_f(c1, f10(c1)))) <=> ((c1 = c4) | (~(c1 = c3)) | (~big_f(f3(c1, c1), c1)) | (~(f3(c1, c1) = c1)) | (f10(c1) = f2(c1)) | (~big_f(c1, f10(c1))))),
% 29.97/20.18 inference(rewrite,[status(thm)],[])).
% 29.97/20.18 tff(32089,plain,
% 29.97/20.18 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c1 = c4) | (~(f3(c1, c1) = c1)) | (~big_f(f3(c1, c1), c1)) | (f10(c1) = f2(c1)) | (~big_f(c1, f10(c1))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((c1 = c4) | (~(c1 = c3)) | (~big_f(f3(c1, c1), c1)) | (~(f3(c1, c1) = c1)) | (f10(c1) = f2(c1)) | (~big_f(c1, f10(c1)))))),
% 29.97/20.18 inference(monotonicity,[status(thm)],[32088])).
% 29.97/20.18 tff(32090,plain,
% 29.97/20.18 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c1 = c4) | (~(f3(c1, c1) = c1)) | (~big_f(f3(c1, c1), c1)) | (f10(c1) = f2(c1)) | (~big_f(c1, f10(c1))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (c1 = c4) | (~(c1 = c3)) | (~big_f(f3(c1, c1), c1)) | (~(f3(c1, c1) = c1)) | (f10(c1) = f2(c1)) | (~big_f(c1, f10(c1))))),
% 29.97/20.18 inference(transitivity,[status(thm)],[32089, 32087])).
% 29.97/20.18 tff(32091,plain,
% 29.97/20.18 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c1 = c4) | (~(f3(c1, c1) = c1)) | (~big_f(f3(c1, c1), c1)) | (f10(c1) = f2(c1)) | (~big_f(c1, f10(c1))))),
% 29.97/20.18 inference(quant_inst,[status(thm)],[])).
% 29.97/20.18 tff(32092,plain,
% 29.97/20.18 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (c1 = c4) | (~(c1 = c3)) | (~big_f(f3(c1, c1), c1)) | (~(f3(c1, c1) = c1)) | (f10(c1) = f2(c1)) | (~big_f(c1, f10(c1)))),
% 29.97/20.18 inference(modus_ponens,[status(thm)],[32091, 32090])).
% 29.97/20.18 tff(32093,plain,
% 29.97/20.18 ((c1 = c4) | (f10(c1) = f2(c1))),
% 29.97/20.18 inference(unit_resolution,[status(thm)],[32092, 7051, 1387, 5080, 1938, 31847])).
% 29.97/20.18 tff(32094,plain,
% 29.97/20.18 (f10(c1) = f2(c1)),
% 29.97/20.18 inference(unit_resolution,[status(thm)],[32093, 482])).
% 29.97/20.18 tff(32095,plain,
% 29.97/20.18 (f10(c1) = c1),
% 29.97/20.18 inference(transitivity,[status(thm)],[32094, 32086])).
% 29.97/20.18 tff(32096,plain,
% 29.97/20.18 ($false),
% 29.97/20.18 inference(unit_resolution,[status(thm)],[3, 32095])).
% 29.97/20.18 tff(32097,plain,((c1 = c4) | (f10(c1) = c1) | (~big_f(f3(c1, c1), c1)) | (~(c1 = c3)) | (~(f3(c1, c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.97/20.18 tff(32098,plain,
% 29.97/20.18 (c1 = c4),
% 29.97/20.18 inference(unit_resolution,[status(thm)],[32097, 3, 1387, 5611, 1938])).
% 29.97/20.18 tff(32099,plain,
% 29.97/20.18 (c4 = c1),
% 29.97/20.18 inference(symmetry,[status(thm)],[32098])).
% 29.97/20.18 tff(32100,plain,
% 29.97/20.18 ((f10(c1) = c4) <=> (f10(c1) = c1)),
% 29.97/20.18 inference(monotonicity,[status(thm)],[32099])).
% 29.97/20.18 tff(32101,plain,
% 29.97/20.18 ((f10(c1) = c1) <=> (f10(c1) = c4)),
% 29.97/20.18 inference(symmetry,[status(thm)],[32100])).
% 29.97/20.18 tff(32102,plain,
% 29.97/20.18 ((~(f10(c1) = c1)) <=> (~(f10(c1) = c4))),
% 29.97/20.18 inference(monotonicity,[status(thm)],[32101])).
% 29.97/20.18 tff(32103,plain,
% 29.97/20.18 (~(f10(c1) = c4)),
% 29.97/20.18 inference(modus_ponens,[status(thm)],[3, 32102])).
% 29.97/20.18 tff(32104,plain,
% 29.97/20.18 (big_f(f3(c2, c1), f10(c1)) <=> big_f(f3(c2, c1), c2)),
% 29.97/20.18 inference(symmetry,[status(thm)],[31362])).
% 29.97/20.18 tff(32105,plain,
% 29.97/20.18 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c1 = f2(c1)) | (f10(c1) = c4) | (~big_f(c1, c1)) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c1 = c3)) | (c1 = f2(c1)) | (f10(c1) = c4) | (~big_f(c1, c1)) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1)))),
% 29.97/20.18 inference(rewrite,[status(thm)],[])).
% 29.97/20.18 tff(32106,plain,
% 29.97/20.18 (((~(c1 = c3)) | (f10(c1) = c4) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1)) | (c1 = f2(c1)) | (~big_f(c1, c1))) <=> ((~(c1 = c3)) | (c1 = f2(c1)) | (f10(c1) = c4) | (~big_f(c1, c1)) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1)))),
% 29.97/20.18 inference(rewrite,[status(thm)],[])).
% 29.97/20.18 tff(32107,plain,
% 29.97/20.18 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (f10(c1) = c4) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1)) | (c1 = f2(c1)) | (~big_f(c1, c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c1 = f2(c1)) | (f10(c1) = c4) | (~big_f(c1, c1)) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1))))),
% 29.97/20.18 inference(monotonicity,[status(thm)],[32106])).
% 29.97/20.18 tff(32108,plain,
% 29.97/20.18 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (f10(c1) = c4) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1)) | (c1 = f2(c1)) | (~big_f(c1, c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c1 = c3)) | (c1 = f2(c1)) | (f10(c1) = c4) | (~big_f(c1, c1)) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1)))),
% 29.97/20.18 inference(transitivity,[status(thm)],[32107, 32105])).
% 29.97/20.18 tff(32109,plain,
% 29.97/20.18 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (f10(c1) = c4) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1)) | (c1 = f2(c1)) | (~big_f(c1, c1)))),
% 29.97/20.18 inference(quant_inst,[status(thm)],[])).
% 29.97/20.18 tff(32110,plain,
% 29.97/20.18 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c1 = c3)) | (c1 = f2(c1)) | (f10(c1) = c4) | (~big_f(c1, c1)) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1))),
% 29.97/20.18 inference(modus_ponens,[status(thm)],[32109, 32108])).
% 29.97/20.18 tff(32111,plain,
% 29.97/20.18 ((c1 = f2(c1)) | (f10(c1) = c4) | (f3(f10(c1), c1) = c1)),
% 29.97/20.18 inference(unit_resolution,[status(thm)],[32110, 7352, 5080, 1061, 31714])).
% 29.97/20.18 tff(32112,plain,
% 29.97/20.18 (c1 = f2(c1)),
% 29.97/20.18 inference(unit_resolution,[status(thm)],[32111, 1046, 1062])).
% 29.97/20.18 tff(32113,plain,
% 29.97/20.18 (f2(c1) = c1),
% 29.97/20.18 inference(symmetry,[status(thm)],[32112])).
% 29.97/20.18 tff(32114,plain,
% 29.97/20.18 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (f10(c1) = c4) | (f10(c1) = f2(c1)) | (~big_f(c1, f10(c1))) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c1 = c3)) | (f10(c1) = c4) | (f10(c1) = f2(c1)) | (~big_f(c1, f10(c1))) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1)))),
% 29.97/20.18 inference(rewrite,[status(thm)],[])).
% 29.97/20.18 tff(32115,plain,
% 29.97/20.18 (((~(c1 = c3)) | (f10(c1) = c4) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1)) | (f10(c1) = f2(c1)) | (~big_f(c1, f10(c1)))) <=> ((~(c1 = c3)) | (f10(c1) = c4) | (f10(c1) = f2(c1)) | (~big_f(c1, f10(c1))) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1)))),
% 29.97/20.18 inference(rewrite,[status(thm)],[])).
% 29.97/20.18 tff(32116,plain,
% 29.97/20.18 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (f10(c1) = c4) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1)) | (f10(c1) = f2(c1)) | (~big_f(c1, f10(c1))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (f10(c1) = c4) | (f10(c1) = f2(c1)) | (~big_f(c1, f10(c1))) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1))))),
% 29.97/20.18 inference(monotonicity,[status(thm)],[32115])).
% 29.97/20.18 tff(32117,plain,
% 29.97/20.18 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (f10(c1) = c4) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1)) | (f10(c1) = f2(c1)) | (~big_f(c1, f10(c1))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c1 = c3)) | (f10(c1) = c4) | (f10(c1) = f2(c1)) | (~big_f(c1, f10(c1))) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1)))),
% 29.97/20.18 inference(transitivity,[status(thm)],[32116, 32114])).
% 29.97/20.18 tff(32118,plain,
% 29.97/20.18 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (f10(c1) = c4) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1)) | (f10(c1) = f2(c1)) | (~big_f(c1, f10(c1))))),
% 29.97/20.18 inference(quant_inst,[status(thm)],[])).
% 29.97/20.18 tff(32119,plain,
% 29.97/20.18 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c1 = c3)) | (f10(c1) = c4) | (f10(c1) = f2(c1)) | (~big_f(c1, f10(c1))) | (f3(f10(c1), c1) = c1) | big_f(f3(f10(c1), c1), f10(c1))),
% 29.97/20.18 inference(modus_ponens,[status(thm)],[32118, 32117])).
% 29.97/20.18 tff(32120,plain,
% 29.97/20.18 ((f10(c1) = c4) | (f10(c1) = f2(c1)) | (f3(f10(c1), c1) = c1)),
% 29.97/20.18 inference(unit_resolution,[status(thm)],[32119, 7352, 5080, 31847, 1061])).
% 29.97/20.18 tff(32121,plain,
% 29.97/20.18 (f10(c1) = f2(c1)),
% 29.97/20.18 inference(unit_resolution,[status(thm)],[32120, 1046, 1062])).
% 29.97/20.18 tff(32122,plain,
% 29.97/20.18 (f10(c1) = c1),
% 29.97/20.18 inference(transitivity,[status(thm)],[32121, 32113])).
% 29.97/20.18 tff(32123,plain,
% 29.97/20.18 ($false),
% 29.97/20.18 inference(unit_resolution,[status(thm)],[3, 32122])).
% 29.97/20.18 tff(32124,plain,((f10(c1) = c4) | (f10(c1) = c1) | (f3(f10(c1), c1) = c1) | (~(c1 = c3)) | big_f(f3(f10(c1), c1), f10(c1))), inference(lemma,lemma(discharge,[]))).
% 29.97/20.18 tff(32125,plain,
% 29.97/20.18 (f3(f10(c1), c1) = c1),
% 29.97/20.18 inference(unit_resolution,[status(thm)],[32124, 31899, 3, 5080, 1046])).
% 29.97/20.18 tff(32126,plain,
% 29.97/20.18 (f3(c2, c1) = c1),
% 29.97/20.18 inference(transitivity,[status(thm)],[31360, 32125])).
% 29.97/20.18 tff(32127,plain,
% 29.97/20.18 (big_f(f3(c2, c1), f10(c1)) <=> big_f(c1, f10(c1))),
% 29.97/20.18 inference(monotonicity,[status(thm)],[32126])).
% 29.97/20.18 tff(32128,plain,
% 29.97/20.18 (big_f(c1, f10(c1)) <=> big_f(f3(c2, c1), f10(c1))),
% 29.97/20.18 inference(symmetry,[status(thm)],[32127])).
% 29.97/20.18 tff(32129,plain,
% 29.97/20.18 (big_f(c1, f10(c1)) <=> big_f(f3(c2, c1), c2)),
% 29.97/20.18 inference(transitivity,[status(thm)],[32128, 32104])).
% 29.97/20.18 tff(32130,plain,
% 29.97/20.18 (big_f(f3(c2, c1), c2)),
% 29.97/20.18 inference(modus_ponens,[status(thm)],[31847, 32129])).
% 29.97/20.18 tff(32131,plain,
% 29.97/20.18 ($false),
% 29.97/20.18 inference(unit_resolution,[status(thm)],[12175, 32130])).
% 29.97/20.18 tff(32132,plain,(big_f(f3(c2, c1), c2) | (f10(c1) = c1) | (~(c1 = c3)) | (f10(c1) = c4)), inference(lemma,lemma(discharge,[]))).
% 29.97/20.18 tff(32133,plain,
% 29.97/20.18 (big_f(f3(c2, c1), c2)),
% 29.97/20.18 inference(unit_resolution,[status(thm)],[32132, 3, 5611, 32103])).
% 29.97/20.18 tff(32134,plain,
% 29.97/20.18 (big_f(f3(c2, c1), f10(c1))),
% 29.97/20.18 inference(modus_ponens,[status(thm)],[32133, 31362])).
% 29.97/20.18 tff(32135,plain,
% 29.97/20.18 (f3(c2, c1) = f8(c1)),
% 29.97/20.18 inference(unit_resolution,[status(thm)],[31927, 2730, 25791, 3, 31781, 31848, 32134])).
% 29.97/20.18 tff(32136,plain,
% 29.97/20.18 (f3(f10(c1), c1) = c1),
% 29.97/20.18 inference(modus_ponens,[status(thm)],[32135, 31942])).
% 29.97/20.18 tff(32137,plain,
% 29.97/20.18 (big_f(f3(f10(c1), c1), f10(c1))),
% 29.97/20.18 inference(modus_ponens,[status(thm)],[32133, 31949])).
% 29.97/20.18 tff(32138,plain,
% 29.97/20.18 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c1 = f2(c1)) | (f10(c1) = c4) | (~big_f(c1, c1)) | (~big_f(f3(f10(c1), c1), f10(c1))) | (~(f3(f10(c1), c1) = c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c1 = c3)) | (c1 = f2(c1)) | (f10(c1) = c4) | (~big_f(c1, c1)) | (~big_f(f3(f10(c1), c1), f10(c1))) | (~(f3(f10(c1), c1) = c1)))),
% 29.97/20.18 inference(rewrite,[status(thm)],[])).
% 29.97/20.18 tff(32139,plain,
% 29.97/20.18 (((~(c1 = c3)) | (f10(c1) = c4) | (~(f3(f10(c1), c1) = c1)) | (~big_f(f3(f10(c1), c1), f10(c1))) | (c1 = f2(c1)) | (~big_f(c1, c1))) <=> ((~(c1 = c3)) | (c1 = f2(c1)) | (f10(c1) = c4) | (~big_f(c1, c1)) | (~big_f(f3(f10(c1), c1), f10(c1))) | (~(f3(f10(c1), c1) = c1)))),
% 29.97/20.18 inference(rewrite,[status(thm)],[])).
% 29.97/20.18 tff(32140,plain,
% 29.97/20.18 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (f10(c1) = c4) | (~(f3(f10(c1), c1) = c1)) | (~big_f(f3(f10(c1), c1), f10(c1))) | (c1 = f2(c1)) | (~big_f(c1, c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c1 = f2(c1)) | (f10(c1) = c4) | (~big_f(c1, c1)) | (~big_f(f3(f10(c1), c1), f10(c1))) | (~(f3(f10(c1), c1) = c1))))),
% 29.97/20.18 inference(monotonicity,[status(thm)],[32139])).
% 29.97/20.18 tff(32141,plain,
% 29.97/20.18 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (f10(c1) = c4) | (~(f3(f10(c1), c1) = c1)) | (~big_f(f3(f10(c1), c1), f10(c1))) | (c1 = f2(c1)) | (~big_f(c1, c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c1 = c3)) | (c1 = f2(c1)) | (f10(c1) = c4) | (~big_f(c1, c1)) | (~big_f(f3(f10(c1), c1), f10(c1))) | (~(f3(f10(c1), c1) = c1)))),
% 29.97/20.18 inference(transitivity,[status(thm)],[32140, 32138])).
% 29.97/20.18 tff(32142,plain,
% 29.97/20.18 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (f10(c1) = c4) | (~(f3(f10(c1), c1) = c1)) | (~big_f(f3(f10(c1), c1), f10(c1))) | (c1 = f2(c1)) | (~big_f(c1, c1)))),
% 29.97/20.18 inference(quant_inst,[status(thm)],[])).
% 29.97/20.18 tff(32143,plain,
% 29.97/20.18 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c1 = c3)) | (c1 = f2(c1)) | (f10(c1) = c4) | (~big_f(c1, c1)) | (~big_f(f3(f10(c1), c1), f10(c1))) | (~(f3(f10(c1), c1) = c1))),
% 29.97/20.18 inference(modus_ponens,[status(thm)],[32142, 32141])).
% 29.97/20.18 tff(32144,plain,
% 29.97/20.18 ((c1 = f2(c1)) | (~(f3(f10(c1), c1) = c1))),
% 29.97/20.18 inference(unit_resolution,[status(thm)],[32143, 7051, 5611, 32103, 32137, 31714])).
% 29.97/20.18 tff(32145,plain,
% 29.97/20.18 (c1 = f2(c1)),
% 29.97/20.18 inference(unit_resolution,[status(thm)],[32144, 32136])).
% 29.97/20.18 tff(32146,plain,
% 29.97/20.18 (f2(c1) = c1),
% 29.97/20.18 inference(symmetry,[status(thm)],[32145])).
% 29.97/20.18 tff(32147,plain,
% 29.97/20.18 (f3(c2, c1) = c1),
% 29.97/20.18 inference(transitivity,[status(thm)],[32135, 31859])).
% 29.97/20.18 tff(32148,plain,
% 29.97/20.18 (f2(f3(c2, c1)) = f2(c1)),
% 29.97/20.18 inference(monotonicity,[status(thm)],[32147])).
% 29.97/20.18 tff(32149,plain,
% 29.97/20.18 ((f3(c2, c1) = c3) <=> (f3(c2, c1) = c1)),
% 29.97/20.18 inference(monotonicity,[status(thm)],[172])).
% 29.97/20.18 tff(32150,plain,
% 29.97/20.18 ((f3(c2, c1) = c1) <=> (f3(c2, c1) = c3)),
% 29.97/20.18 inference(symmetry,[status(thm)],[32149])).
% 29.97/20.18 tff(32151,plain,
% 29.97/20.18 (f3(c2, c1) = c1),
% 29.97/20.18 inference(modus_ponens,[status(thm)],[32135, 31919])).
% 29.97/20.18 tff(32152,plain,
% 29.97/20.18 (f3(c2, c1) = c3),
% 29.97/20.18 inference(modus_ponens,[status(thm)],[32151, 32150])).
% 29.97/20.18 tff(32153,plain,
% 29.97/20.18 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((f10(c1) = c4) | (f10(c1) = f2(f3(c2, c1))) | (~big_f(f3(f10(c1), c1), f10(c1))) | (~(f3(f10(c1), c1) = c1)) | (~(f3(c2, c1) = c3)) | (~big_f(f3(c2, c1), f10(c1))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (f10(c1) = c4) | (f10(c1) = f2(f3(c2, c1))) | (~big_f(f3(f10(c1), c1), f10(c1))) | (~(f3(f10(c1), c1) = c1)) | (~(f3(c2, c1) = c3)) | (~big_f(f3(c2, c1), f10(c1))))),
% 29.97/20.18 inference(rewrite,[status(thm)],[])).
% 29.97/20.18 tff(32154,plain,
% 29.97/20.18 (((~(f3(c2, c1) = c3)) | (f10(c1) = c4) | (~(f3(f10(c1), c1) = c1)) | (~big_f(f3(f10(c1), c1), f10(c1))) | (f10(c1) = f2(f3(c2, c1))) | (~big_f(f3(c2, c1), f10(c1)))) <=> ((f10(c1) = c4) | (f10(c1) = f2(f3(c2, c1))) | (~big_f(f3(f10(c1), c1), f10(c1))) | (~(f3(f10(c1), c1) = c1)) | (~(f3(c2, c1) = c3)) | (~big_f(f3(c2, c1), f10(c1))))),
% 29.97/20.18 inference(rewrite,[status(thm)],[])).
% 29.97/20.18 tff(32155,plain,
% 29.97/20.18 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f3(c2, c1) = c3)) | (f10(c1) = c4) | (~(f3(f10(c1), c1) = c1)) | (~big_f(f3(f10(c1), c1), f10(c1))) | (f10(c1) = f2(f3(c2, c1))) | (~big_f(f3(c2, c1), f10(c1))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((f10(c1) = c4) | (f10(c1) = f2(f3(c2, c1))) | (~big_f(f3(f10(c1), c1), f10(c1))) | (~(f3(f10(c1), c1) = c1)) | (~(f3(c2, c1) = c3)) | (~big_f(f3(c2, c1), f10(c1)))))),
% 29.97/20.18 inference(monotonicity,[status(thm)],[32154])).
% 29.97/20.18 tff(32156,plain,
% 29.97/20.18 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f3(c2, c1) = c3)) | (f10(c1) = c4) | (~(f3(f10(c1), c1) = c1)) | (~big_f(f3(f10(c1), c1), f10(c1))) | (f10(c1) = f2(f3(c2, c1))) | (~big_f(f3(c2, c1), f10(c1))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (f10(c1) = c4) | (f10(c1) = f2(f3(c2, c1))) | (~big_f(f3(f10(c1), c1), f10(c1))) | (~(f3(f10(c1), c1) = c1)) | (~(f3(c2, c1) = c3)) | (~big_f(f3(c2, c1), f10(c1))))),
% 29.97/20.18 inference(transitivity,[status(thm)],[32155, 32153])).
% 29.97/20.18 tff(32157,plain,
% 29.97/20.18 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(f3(c2, c1) = c3)) | (f10(c1) = c4) | (~(f3(f10(c1), c1) = c1)) | (~big_f(f3(f10(c1), c1), f10(c1))) | (f10(c1) = f2(f3(c2, c1))) | (~big_f(f3(c2, c1), f10(c1))))),
% 29.97/20.18 inference(quant_inst,[status(thm)],[])).
% 29.97/20.18 tff(32158,plain,
% 29.97/20.18 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (f10(c1) = c4) | (f10(c1) = f2(f3(c2, c1))) | (~big_f(f3(f10(c1), c1), f10(c1))) | (~(f3(f10(c1), c1) = c1)) | (~(f3(c2, c1) = c3)) | (~big_f(f3(c2, c1), f10(c1)))),
% 29.97/20.18 inference(modus_ponens,[status(thm)],[32157, 32156])).
% 29.97/20.18 tff(32159,plain,
% 29.97/20.18 ((f10(c1) = f2(f3(c2, c1))) | (~(f3(f10(c1), c1) = c1)) | (~(f3(c2, c1) = c3))),
% 29.97/20.18 inference(unit_resolution,[status(thm)],[32158, 7051, 32103, 32137, 32134])).
% 29.97/20.18 tff(32160,plain,
% 29.97/20.18 (f10(c1) = f2(f3(c2, c1))),
% 29.97/20.18 inference(unit_resolution,[status(thm)],[32159, 32136, 32152])).
% 29.97/20.18 tff(32161,plain,
% 29.97/20.18 (f10(c1) = c1),
% 29.97/20.18 inference(transitivity,[status(thm)],[32160, 32148, 32146])).
% 29.97/20.18 tff(32162,plain,
% 29.97/20.18 ($false),
% 29.97/20.18 inference(unit_resolution,[status(thm)],[3, 32161])).
% 29.97/20.18 tff(32163,plain,((f10(c1) = c1) | (~(c3 = c1)) | (~big_f(f3(c1, c1), c1)) | (~(f3(c1, c1) = c1)) | (~(f6(c1, c2) = c2)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 29.97/20.18 tff(32164,plain,
% 29.97/20.18 (~big_f(f3(c1, c1), c1)),
% 29.97/20.18 inference(unit_resolution,[status(thm)],[32163, 32079, 3, 31962, 36, 121])).
% 29.97/20.18 tff(32165,plain,
% 29.97/20.18 ($false),
% 29.97/20.18 inference(unit_resolution,[status(thm)],[32164, 32083])).
% 29.97/20.18 tff(32166,plain,(big_f(c2, c1) | (f10(c1) = c1) | (~(f6(c1, c2) = c2)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 29.97/20.18 tff(32167,plain,
% 29.97/20.18 (big_f(c2, c1)),
% 29.97/20.18 inference(unit_resolution,[status(thm)],[32166, 3, 36, 121])).
% 29.97/20.18 tff(32168,plain,
% 29.97/20.18 (big_f(c2, f10(c2))),
% 29.97/20.18 inference(modus_ponens,[status(thm)],[32167, 31830])).
% 29.97/20.18 tff(32169,plain,
% 29.97/20.18 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(f10(c2)) = f10(c2))) | (~big_f(f7(f10(c2)), f6(f10(c2), c2))) | (~(f6(f10(c2), c2) = c2)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(f10(c2)) = f10(c2))) | (~big_f(f7(f10(c2)), f6(f10(c2), c2))) | (~(f6(f10(c2), c2) = c2)))),
% 29.97/20.18 inference(rewrite,[status(thm)],[])).
% 29.97/20.18 tff(32170,plain,
% 29.97/20.18 (((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(f10(c2)) = f10(c2))) | (~(f6(f10(c2), c2) = c2)) | (~big_f(f7(f10(c2)), f6(f10(c2), c2)))) <=> ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(f10(c2)) = f10(c2))) | (~big_f(f7(f10(c2)), f6(f10(c2), c2))) | (~(f6(f10(c2), c2) = c2)))),
% 29.97/20.18 inference(rewrite,[status(thm)],[])).
% 29.97/20.18 tff(32171,plain,
% 29.97/20.18 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(f10(c2)) = f10(c2))) | (~(f6(f10(c2), c2) = c2)) | (~big_f(f7(f10(c2)), f6(f10(c2), c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(f10(c2)) = f10(c2))) | (~big_f(f7(f10(c2)), f6(f10(c2), c2))) | (~(f6(f10(c2), c2) = c2))))),
% 29.97/20.18 inference(monotonicity,[status(thm)],[32170])).
% 29.97/20.18 tff(32172,plain,
% 29.97/20.18 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(f10(c2)) = f10(c2))) | (~(f6(f10(c2), c2) = c2)) | (~big_f(f7(f10(c2)), f6(f10(c2), c2))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(f10(c2)) = f10(c2))) | (~big_f(f7(f10(c2)), f6(f10(c2), c2))) | (~(f6(f10(c2), c2) = c2)))),
% 29.97/20.19 inference(transitivity,[status(thm)],[32171, 32169])).
% 29.97/20.19 tff(32173,plain,
% 29.97/20.19 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(f10(c2)) = f10(c2))) | (~(f6(f10(c2), c2) = c2)) | (~big_f(f7(f10(c2)), f6(f10(c2), c2))))),
% 29.97/20.19 inference(quant_inst,[status(thm)],[])).
% 29.97/20.19 tff(32174,plain,
% 29.97/20.19 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(f10(c2)) = f10(c2))) | (~big_f(f7(f10(c2)), f6(f10(c2), c2))) | (~(f6(f10(c2), c2) = c2))),
% 29.97/20.19 inference(modus_ponens,[status(thm)],[32173, 32172])).
% 29.97/20.19 tff(32175,plain,
% 29.97/20.19 ($false),
% 29.97/20.19 inference(unit_resolution,[status(thm)],[32174, 2730, 31789, 32168, 31828, 31795, 31801, 31792])).
% 29.97/20.19 tff(32176,plain,((f10(c1) = c1) | (~(f6(c1, c2) = c2)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 29.97/20.19 tff(32177,plain,
% 29.97/20.19 (f10(c1) = c1),
% 29.97/20.19 inference(unit_resolution,[status(thm)],[32176, 121, 36])).
% 29.97/20.19 tff(32178,plain,
% 29.97/20.19 (big_f(f9(c1, c1), c1)),
% 29.97/20.19 inference(unit_resolution,[status(thm)],[10938, 3949, 31714])).
% 29.97/20.19 tff(32179,plain,
% 29.97/20.19 (big_f(f9(c1, c1), f10(c1))),
% 29.97/20.19 inference(unit_resolution,[status(thm)],[8716, 32178, 3762])).
% 29.97/20.19 tff(32180,plain,
% 29.97/20.19 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)))),
% 29.97/20.19 inference(rewrite,[status(thm)],[])).
% 29.97/20.19 tff(32181,plain,
% 29.97/20.19 (((~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2)))) <=> ((~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)))),
% 29.97/20.19 inference(rewrite,[status(thm)],[])).
% 29.97/20.19 tff(32182,plain,
% 29.97/20.19 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2))))),
% 29.97/20.19 inference(monotonicity,[status(thm)],[32181])).
% 29.97/20.19 tff(32183,plain,
% 29.97/20.19 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)))),
% 29.97/20.19 inference(transitivity,[status(thm)],[32182, 32180])).
% 29.97/20.19 tff(32184,plain,
% 29.97/20.19 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2))))),
% 29.97/20.19 inference(quant_inst,[status(thm)],[])).
% 29.97/20.19 tff(32185,plain,
% 29.97/20.19 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2))),
% 29.97/20.19 inference(modus_ponens,[status(thm)],[32184, 32183])).
% 29.97/20.19 tff(32186,plain,
% 29.97/20.19 ($false),
% 29.97/20.19 inference(unit_resolution,[status(thm)],[32185, 2378, 25791, 3762, 3949, 32179, 31736, 36])).
% 29.97/20.19 tff(32187,plain,((~(f9(c1, c1) = c1)) | (~(f10(c1) = c1)) | (~(f6(c1, c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.97/20.19 tff(32188,plain,
% 29.97/20.19 (~(f9(c1, c1) = c1)),
% 29.97/20.19 inference(unit_resolution,[status(thm)],[32187, 32177, 36])).
% 29.97/20.19 tff(32189,plain,
% 29.97/20.19 (f9(c1, c1) = c2),
% 29.97/20.19 inference(unit_resolution,[status(thm)],[3939, 32188])).
% 29.97/20.19 tff(32190,plain,
% 29.97/20.19 (big_f(f9(c1, c1), c1) <=> big_f(c2, c1)),
% 29.97/20.19 inference(monotonicity,[status(thm)],[32189])).
% 29.97/20.19 tff(32191,plain,
% 29.97/20.19 (big_f(f9(c1, c1), f10(c1)) <=> big_f(f9(c1, c1), c1)),
% 29.97/20.19 inference(monotonicity,[status(thm)],[32177])).
% 29.97/20.19 tff(32192,plain,
% 29.97/20.19 (big_f(f9(c1, c1), f10(c1)) <=> big_f(c2, f10(c2))),
% 29.97/20.19 inference(transitivity,[status(thm)],[32191, 32190, 31774])).
% 29.97/20.19 tff(32193,plain,
% 29.97/20.19 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)))),
% 29.97/20.19 inference(rewrite,[status(thm)],[])).
% 29.97/20.19 tff(32194,plain,
% 29.97/20.19 (((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f7(c1) = c1)) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2)))) <=> ((f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)))),
% 29.97/20.19 inference(rewrite,[status(thm)],[])).
% 29.97/20.19 tff(32195,plain,
% 29.97/20.19 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f7(c1) = c1)) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2))))),
% 29.97/20.19 inference(monotonicity,[status(thm)],[32194])).
% 29.97/20.19 tff(32196,plain,
% 29.97/20.19 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f7(c1) = c1)) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2)))),
% 29.97/20.19 inference(transitivity,[status(thm)],[32195, 32193])).
% 29.97/20.19 tff(32197,plain,
% 29.97/20.19 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f7(c1) = c1)) | (~(f6(c1, c2) = c2)) | (~big_f(f7(c1), f6(c1, c2))))),
% 29.97/20.19 inference(quant_inst,[status(thm)],[])).
% 29.97/20.19 tff(32198,plain,
% 29.97/20.19 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c2))) | (~(f6(c1, c2) = c2))),
% 29.97/20.19 inference(modus_ponens,[status(thm)],[32197, 32196])).
% 29.97/20.19 tff(32199,plain,
% 29.97/20.19 (big_f(f9(c1, c1), f10(c1))),
% 29.97/20.19 inference(unit_resolution,[status(thm)],[32198, 2534, 25791, 32177, 32188, 31736, 36])).
% 29.97/20.19 tff(32200,plain,
% 29.97/20.19 (big_f(c2, f10(c2))),
% 29.97/20.19 inference(modus_ponens,[status(thm)],[32199, 32192])).
% 29.97/20.19 tff(32201,plain,
% 29.97/20.19 ($false),
% 29.97/20.19 inference(unit_resolution,[status(thm)],[29156, 2730, 25791, 31756, 32200, 31772, 31736, 36])).
% 29.97/20.19 tff(32202,plain,(big_f(c2, c2) | (~(f6(c1, c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.97/20.19 tff(32203,plain,
% 29.97/20.19 (big_f(c2, c2)),
% 29.97/20.19 inference(unit_resolution,[status(thm)],[32202, 36])).
% 29.97/20.19 tff(32204,plain,
% 29.97/20.19 (big_f(f9(c2, c2), f10(c2))),
% 29.97/20.19 inference(modus_ponens,[status(thm)],[32203, 25603])).
% 29.97/20.19 tff(32205,plain,
% 29.97/20.19 ($false),
% 29.97/20.19 inference(unit_resolution,[status(thm)],[29297, 2378, 25791, 122, 1572, 32204, 31736, 36])).
% 29.97/20.19 tff(32206,plain,((~(f9(c2, c2) = c2)) | (~(f10(c2) = c2)) | (~(f6(c1, c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.97/20.19 tff(32207,plain,
% 29.97/20.19 (~(f9(c2, c2) = c2)),
% 29.97/20.19 inference(unit_resolution,[status(thm)],[32206, 122, 36])).
% 29.97/20.19 tff(32208,plain,
% 29.97/20.19 (f10(c1) = c1),
% 29.97/20.19 inference(unit_resolution,[status(thm)],[31211, 32203, 36])).
% 29.97/20.19 tff(32209,plain,
% 29.97/20.19 (~(f9(c1, c1) = c1)),
% 29.97/20.19 inference(unit_resolution,[status(thm)],[32187, 32208, 36])).
% 29.97/20.19 tff(32210,plain,
% 29.97/20.19 (f9(c1, c1) = c2),
% 29.97/20.19 inference(unit_resolution,[status(thm)],[3939, 32209])).
% 29.97/20.19 tff(32211,plain,
% 29.97/20.19 (big_f(f9(c1, c1), f10(c1))),
% 29.97/20.19 inference(unit_resolution,[status(thm)],[32198, 2534, 25791, 32208, 32209, 31736, 36])).
% 29.97/20.19 tff(32212,plain,
% 29.97/20.19 (big_f(f9(c1, c1), c1)),
% 29.97/20.19 inference(unit_resolution,[status(thm)],[10033, 32211, 32208])).
% 29.97/20.19 tff(32213,plain,
% 29.97/20.19 (big_f(c2, c1)),
% 29.97/20.19 inference(unit_resolution,[status(thm)],[10058, 32212, 32210])).
% 29.97/20.19 tff(32214,plain,
% 29.97/20.19 ((~(c4 = c1)) | (~big_f(c2, c1)) | (~big_f(c1, c1)) | (~big_f(c2, c2)) | (~(f4(c4) = c1))),
% 29.97/20.19 inference(unit_resolution,[status(thm)],[25548, 30354])).
% 29.97/20.19 tff(32215,plain,
% 29.97/20.19 (~(c4 = c1)),
% 29.97/20.19 inference(unit_resolution,[status(thm)],[32214, 11752, 31714, 1345, 348])).
% 29.97/20.19 tff(32216,plain,
% 29.97/20.19 (c4 = c2),
% 29.97/20.19 inference(unit_resolution,[status(thm)],[461, 32215])).
% 29.97/20.19 tff(32217,plain,
% 29.97/20.19 (c2 = c4),
% 29.97/20.19 inference(symmetry,[status(thm)],[32216])).
% 29.97/20.19 tff(32218,plain,
% 29.97/20.19 (f4(c2) = f4(c4)),
% 29.97/20.19 inference(monotonicity,[status(thm)],[32217])).
% 29.97/20.19 tff(32219,plain,
% 29.97/20.19 (f4(c2) = c1),
% 29.97/20.19 inference(transitivity,[status(thm)],[32218, 11752])).
% 29.97/20.19 tff(32220,plain,
% 29.97/20.19 ((c2 = f4(c2)) <=> (c2 = c1)),
% 29.97/20.19 inference(monotonicity,[status(thm)],[32219])).
% 29.97/20.19 tff(32221,plain,
% 29.97/20.19 ((c2 = c1) <=> (c2 = f4(c2))),
% 29.97/20.19 inference(symmetry,[status(thm)],[32220])).
% 29.97/20.19 tff(32222,plain,
% 29.97/20.19 ((~(c2 = c1)) <=> (~(c2 = f4(c2)))),
% 29.97/20.19 inference(monotonicity,[status(thm)],[32221])).
% 29.97/20.19 tff(32223,plain,
% 29.97/20.19 (~(c2 = f4(c2))),
% 29.97/20.19 inference(modus_ponens,[status(thm)],[75, 32222])).
% 29.97/20.19 tff(32224,plain,
% 29.97/20.19 (c2 = c4),
% 29.97/20.19 inference(modus_ponens,[status(thm)],[32216, 159])).
% 29.97/20.19 tff(32225,plain,
% 29.97/20.19 ((~(c1 = c3)) | (~(c2 = c4)) | (c2 = f4(c2)) | (~big_f(c2, c2)) | (~big_f(c1, c1))),
% 29.97/20.19 inference(unit_resolution,[status(thm)],[25578, 30354])).
% 29.97/20.19 tff(32226,plain,
% 29.97/20.19 (~(c1 = c3)),
% 29.97/20.19 inference(unit_resolution,[status(thm)],[32225, 32223, 31714, 1345, 32224])).
% 29.97/20.19 tff(32227,plain,
% 29.97/20.19 (~(c3 = c1)),
% 29.97/20.19 inference(unit_resolution,[status(thm)],[175, 32226])).
% 29.97/20.19 tff(32228,plain,
% 29.97/20.19 (c3 = c2),
% 29.97/20.19 inference(unit_resolution,[status(thm)],[180, 32227])).
% 29.97/20.19 tff(32229,plain,
% 29.97/20.19 (c2 = c3),
% 29.97/20.19 inference(modus_ponens,[status(thm)],[32228, 78])).
% 29.97/20.19 tff(32230,plain,
% 29.97/20.19 ((~(c2 = c3)) | (~(c2 = c4)) | (c2 = f4(c2)) | (c1 = f2(c2))),
% 29.97/20.19 inference(unit_resolution,[status(thm)],[25588, 1355, 1345, 348])).
% 29.97/20.19 tff(32231,plain,
% 29.97/20.19 (c1 = f2(c2)),
% 29.97/20.19 inference(unit_resolution,[status(thm)],[32230, 32229, 32224, 32223])).
% 29.97/20.19 tff(32232,plain,
% 29.97/20.19 (f2(c2) = c1),
% 29.97/20.19 inference(symmetry,[status(thm)],[32231])).
% 29.97/20.19 tff(32233,plain,
% 29.97/20.19 (c2 = f2(c2)),
% 29.97/20.19 inference(unit_resolution,[status(thm)],[21374, 32229, 32224, 32223])).
% 29.97/20.19 tff(32234,plain,
% 29.97/20.19 (c2 = c1),
% 29.97/20.19 inference(transitivity,[status(thm)],[32233, 32232])).
% 29.97/20.19 tff(32235,plain,
% 29.97/20.19 ($false),
% 29.97/20.19 inference(unit_resolution,[status(thm)],[75, 32234])).
% 29.97/20.19 tff(32236,plain,((~(f4(c4) = c1)) | (~big_f(c2, c2)) | (~big_f(c2, c1))), inference(lemma,lemma(discharge,[]))).
% 29.97/20.19 tff(32237,plain,
% 29.97/20.19 (~(f4(c4) = c1)),
% 29.97/20.19 inference(unit_resolution,[status(thm)],[32236, 32203, 32213])).
% 29.97/20.19 tff(32238,plain,
% 29.97/20.19 (f4(c4) = c2),
% 29.97/20.19 inference(unit_resolution,[status(thm)],[11750, 32237])).
% 29.97/20.19 tff(32239,plain,
% 29.97/20.19 (f9(f10(c2), f4(c4)) = c2),
% 29.97/20.19 inference(unit_resolution,[status(thm)],[8065, 122, 32238])).
% 29.97/20.19 tff(32240,plain,
% 29.97/20.19 ($false),
% 29.97/20.19 inference(unit_resolution,[status(thm)],[1606, 32239, 122, 32238, 32207])).
% 29.97/20.19 tff(32241,plain,((~(f10(c2) = c2)) | (~(f6(c1, c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.97/20.19 tff(32242,plain,
% 29.97/20.19 (~(f10(c2) = c2)),
% 29.97/20.19 inference(unit_resolution,[status(thm)],[32241, 36])).
% 29.97/20.19 tff(32243,plain,
% 29.97/20.19 (f10(c2) = c1),
% 29.97/20.19 inference(unit_resolution,[status(thm)],[93, 32242])).
% 29.97/20.19 tff(32244,plain,
% 29.97/20.19 (big_f(c1, f10(c2)) <=> big_f(c1, c1)),
% 29.97/20.19 inference(monotonicity,[status(thm)],[32243])).
% 29.97/20.19 tff(32245,plain,
% 29.97/20.19 (big_f(c1, c1) <=> big_f(c1, f10(c2))),
% 29.97/20.19 inference(symmetry,[status(thm)],[32244])).
% 29.97/20.19 tff(32246,plain,
% 29.97/20.19 (big_f(c1, f10(c2))),
% 29.97/20.19 inference(modus_ponens,[status(thm)],[31714, 32245])).
% 29.97/20.19 tff(32247,plain,
% 29.97/20.19 (c1 = f8(c2)),
% 29.97/20.19 inference(unit_resolution,[status(thm)],[31766, 2730, 25791, 32242, 31736, 36, 32246])).
% 29.97/20.19 tff(32248,plain,
% 29.97/20.19 (f8(c2) = c1),
% 29.97/20.19 inference(symmetry,[status(thm)],[32247])).
% 29.97/20.19 tff(32249,plain,
% 29.97/20.19 (big_f(c2, f10(c2)) <=> big_f(c2, c1)),
% 29.97/20.19 inference(monotonicity,[status(thm)],[32243])).
% 29.97/20.19 tff(32250,plain,
% 29.97/20.19 (big_f(c2, c1) <=> big_f(c2, f10(c2))),
% 29.97/20.19 inference(symmetry,[status(thm)],[32249])).
% 29.97/20.19 tff(32251,plain,
% 29.97/20.19 (big_f(c2, f10(c2))),
% 29.97/20.19 inference(modus_ponens,[status(thm)],[32213, 32250])).
% 29.97/20.19 tff(32252,plain,
% 29.97/20.19 (c2 = f8(c2)),
% 29.97/20.19 inference(unit_resolution,[status(thm)],[29156, 2730, 25791, 32242, 32251, 31736, 36])).
% 29.97/20.19 tff(32253,plain,
% 29.97/20.19 (c2 = c1),
% 29.97/20.19 inference(transitivity,[status(thm)],[32252, 32248])).
% 29.97/20.19 tff(32254,plain,
% 29.97/20.19 ($false),
% 29.97/20.19 inference(unit_resolution,[status(thm)],[75, 32253])).
% 29.97/20.19 tff(32255,plain,(~(f6(c1, c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 29.97/20.19 tff(32256,plain,
% 29.97/20.19 (f6(c1, c2) = c1),
% 29.97/20.19 inference(unit_resolution,[status(thm)],[48, 32255])).
% 29.97/20.19 tff(32257,plain,
% 29.97/20.19 (~(f6(c1, f6(c1, c2)) = c2)),
% 29.97/20.19 inference(unit_resolution,[status(thm)],[31352, 65, 16, 6931])).
% 29.97/20.19 tff(32258,plain,
% 29.97/20.19 (~(f6(c1, c1) = c1)),
% 29.97/20.19 inference(unit_resolution,[status(thm)],[27769, 65, 4932])).
% 29.97/20.19 tff(32259,plain,
% 29.97/20.19 (~(f6(c1, f6(c1, c2)) = c1)),
% 29.97/20.19 inference(unit_resolution,[status(thm)],[58, 32258])).
% 29.97/20.19 tff(32260,plain,
% 29.97/20.19 ($false),
% 29.97/20.19 inference(unit_resolution,[status(thm)],[63, 32259, 32257])).
% 29.97/20.19 tff(32261,plain,(big_f(f7(c1), f6(c1, c1)) | (~(f10(c1) = c2)) | (~(f6(c1, c2) = c1)) | (~big_f(c1, c1))), inference(lemma,lemma(discharge,[]))).
% 29.97/20.19 tff(32262,plain,
% 29.97/20.19 (big_f(f7(c1), f6(c1, c1))),
% 29.97/20.19 inference(unit_resolution,[status(thm)],[32261, 15, 32256, 31714])).
% 29.97/20.19 tff(32263,plain,
% 29.97/20.19 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)))),
% 29.97/20.19 inference(rewrite,[status(thm)],[])).
% 29.97/20.19 tff(32264,plain,
% 29.97/20.19 (((f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1)))) <=> ((f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)))),
% 29.97/20.19 inference(rewrite,[status(thm)],[])).
% 29.97/20.19 tff(32265,plain,
% 29.97/20.19 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1))))),
% 29.97/20.19 inference(monotonicity,[status(thm)],[32264])).
% 29.97/20.19 tff(32266,plain,
% 29.97/20.19 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)))),
% 29.97/20.19 inference(transitivity,[status(thm)],[32265, 32263])).
% 29.97/20.19 tff(32267,plain,
% 29.97/20.19 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))),
% 29.97/20.19 inference(quant_inst,[status(thm)],[])).
% 29.97/20.19 tff(32268,plain,
% 29.97/20.19 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1))),
% 29.97/20.19 inference(modus_ponens,[status(thm)],[32267, 32266])).
% 29.97/20.19 tff(32269,plain,
% 29.97/20.19 ((c1 = f8(c1)) | (~(f6(c1, c1) = c1))),
% 29.97/20.19 inference(unit_resolution,[status(thm)],[32268, 2730, 25791, 3, 30400, 32262])).
% 29.97/20.19 tff(32270,plain,
% 29.97/20.19 (c1 = f8(c1)),
% 29.97/20.19 inference(unit_resolution,[status(thm)],[32269, 10030])).
% 29.97/20.19 tff(32271,plain,
% 29.97/20.19 (f8(c1) = c1),
% 29.97/20.19 inference(symmetry,[status(thm)],[32270])).
% 29.97/20.19 tff(32272,plain,
% 29.97/20.19 ((f3(f3(c1, c1), c1) = f8(c1)) <=> (f3(f3(c1, c1), c1) = c1)),
% 29.97/20.19 inference(monotonicity,[status(thm)],[32271])).
% 29.97/20.19 tff(32273,plain,
% 29.97/20.19 ((f3(f3(c1, c1), c1) = f8(c1)) <=> (f3(f10(c1), c1) = c1)),
% 29.97/20.19 inference(transitivity,[status(thm)],[32272, 31735])).
% 29.97/20.19 tff(32274,plain,
% 29.97/20.19 (big_f(f3(f3(c1, c1), c1), f10(c1)) <=> big_f(f3(f3(c1, c1), c1), f3(c1, c1))),
% 29.97/20.19 inference(monotonicity,[status(thm)],[31732])).
% 29.97/20.19 tff(32275,plain,
% 29.97/20.19 (big_f(f3(f3(c1, c1), c1), f3(c1, c1)) <=> big_f(f3(f3(c1, c1), c1), f10(c1))),
% 29.97/20.19 inference(symmetry,[status(thm)],[32274])).
% 29.97/20.19 tff(32276,plain,
% 29.97/20.19 (big_f(f3(f10(c1), c1), f10(c1)) <=> big_f(f3(f3(c1, c1), c1), f3(c1, c1))),
% 29.97/20.19 inference(monotonicity,[status(thm)],[31733, 31732])).
% 29.97/20.19 tff(32277,plain,
% 29.97/20.19 (big_f(f3(c2, c1), c2) <=> big_f(f3(f3(c1, c1), c1), f3(c1, c1))),
% 29.97/20.19 inference(transitivity,[status(thm)],[31362, 31361, 32276])).
% 29.97/20.19 tff(32278,plain,
% 29.97/20.19 ((c1 = f2(c2)) <=> (f2(c2) = c1)),
% 29.97/20.19 inference(symmetry,[status(thm)],[1220])).
% 29.97/20.19 tff(32279,plain,
% 29.97/20.19 ((c1 = f2(f10(c1))) <=> (f2(c2) = c1)),
% 29.97/20.19 inference(transitivity,[status(thm)],[31831, 32278])).
% 29.97/20.19 tff(32280,plain,
% 29.97/20.19 ((~(c1 = f2(f10(c1)))) <=> (~(f2(c2) = c1))),
% 29.97/20.19 inference(monotonicity,[status(thm)],[32279])).
% 29.97/20.19 tff(32281,plain,
% 29.97/20.19 (~big_f(c3, f2(c3))),
% 29.97/20.19 inference(unit_resolution,[status(thm)],[8256, 67, 121, 2])).
% 29.97/20.19 tff(32282,plain,
% 29.97/20.19 (c1 = c4),
% 29.97/20.19 inference(unit_resolution,[status(thm)],[27520, 32281, 1431, 2, 67])).
% 29.97/20.19 tff(32283,plain,
% 29.97/20.19 (c4 = c1),
% 29.97/20.19 inference(symmetry,[status(thm)],[32282])).
% 29.97/20.19 tff(32284,plain,
% 29.97/20.19 ((f10(c1) = c4) <=> (f10(c1) = c1)),
% 29.97/20.19 inference(monotonicity,[status(thm)],[32283])).
% 29.97/20.19 tff(32285,plain,
% 29.97/20.19 ((f10(c1) = c1) <=> (f10(c1) = c4)),
% 29.97/20.19 inference(symmetry,[status(thm)],[32284])).
% 29.97/20.19 tff(32286,plain,
% 29.97/20.19 ((~(f10(c1) = c1)) <=> (~(f10(c1) = c4))),
% 29.97/20.19 inference(monotonicity,[status(thm)],[32285])).
% 29.97/20.19 tff(32287,plain,
% 29.97/20.19 (~(f10(c1) = c4)),
% 29.97/20.19 inference(modus_ponens,[status(thm)],[3, 32286])).
% 29.97/20.19 tff(32288,plain,
% 29.97/20.19 ((f10(c1) = c1) <=> (c2 = c4)),
% 29.97/20.19 inference(transitivity,[status(thm)],[32285, 30362])).
% 29.97/20.19 tff(32289,plain,
% 29.97/20.19 ((~(f10(c1) = c1)) <=> (~(c2 = c4))),
% 29.97/20.19 inference(monotonicity,[status(thm)],[32288])).
% 29.97/20.19 tff(32290,plain,
% 29.97/20.19 (~(c2 = c4)),
% 29.97/20.19 inference(modus_ponens,[status(thm)],[3, 32289])).
% 29.97/20.19 tff(32291,plain,
% 29.97/20.19 (big_f(f3(c2, c1), c2) <=> big_f(f3(c2, c1), f10(c1))),
% 29.97/20.19 inference(monotonicity,[status(thm)],[293])).
% 29.97/20.19 tff(32292,plain,
% 29.97/20.19 (big_f(f3(c2, c1), f10(c1)) <=> big_f(f3(c2, c1), c2)),
% 29.97/20.19 inference(symmetry,[status(thm)],[32291])).
% 29.97/20.19 tff(32293,plain,
% 29.97/20.19 (f3(c2, c1) = f3(f10(c1), c1)),
% 29.97/20.19 inference(monotonicity,[status(thm)],[293])).
% 29.97/20.19 tff(32294,plain,
% 29.97/20.19 (big_f(f3(c2, c1), f10(c1)) <=> big_f(f3(f10(c1), c1), f10(c1))),
% 29.97/20.19 inference(monotonicity,[status(thm)],[32293])).
% 29.97/20.19 tff(32295,plain,
% 29.97/20.19 (big_f(f3(f10(c1), c1), f10(c1)) <=> big_f(f3(c2, c1), f10(c1))),
% 29.97/20.19 inference(symmetry,[status(thm)],[32294])).
% 29.97/20.19 tff(32296,plain,
% 29.97/20.19 (big_f(f3(f10(c1), c1), f10(c1)) <=> big_f(f3(c2, c1), c2)),
% 29.97/20.19 inference(transitivity,[status(thm)],[32295, 32292])).
% 29.97/20.19 tff(32297,plain,
% 29.97/20.19 ((~big_f(f3(f10(c1), c1), f10(c1))) <=> (~big_f(f3(c2, c1), c2))),
% 29.97/20.19 inference(monotonicity,[status(thm)],[32296])).
% 29.97/20.19 tff(32298,plain,
% 29.97/20.19 (~big_f(f3(c2, c1), c2)),
% 29.97/20.19 inference(modus_ponens,[status(thm)],[1061, 32297])).
% 29.97/20.19 tff(32299,plain,
% 29.97/20.19 (f10(c1) = f3(c1, c1)),
% 29.97/20.19 inference(transitivity,[status(thm)],[16, 1442])).
% 29.97/20.19 tff(32300,plain,
% 29.97/20.19 (f3(c1, c1) = f10(c1)),
% 29.97/20.19 inference(transitivity,[status(thm)],[1441, 293])).
% 29.97/20.19 tff(32301,plain,
% 29.97/20.19 (f3(f3(c1, c1), c1) = f3(f10(c1), c1)),
% 29.97/20.19 inference(monotonicity,[status(thm)],[32300])).
% 29.97/20.19 tff(32302,plain,
% 29.97/20.19 (f3(f10(c1), c1) = f3(f3(c1, c1), c1)),
% 29.97/20.19 inference(symmetry,[status(thm)],[32301])).
% 29.97/20.19 tff(32303,plain,
% 29.97/20.19 (big_f(f3(f10(c1), c1), f10(c1)) <=> big_f(f3(f3(c1, c1), c1), f3(c1, c1))),
% 29.97/20.19 inference(monotonicity,[status(thm)],[32302, 32299])).
% 29.97/20.19 tff(32304,plain,
% 29.97/20.19 (big_f(f3(f3(c1, c1), c1), f3(c1, c1)) <=> big_f(f3(f10(c1), c1), f10(c1))),
% 29.97/20.19 inference(symmetry,[status(thm)],[32303])).
% 29.97/20.19 tff(32305,assumption,(f3(f10(c1), c1) = c1), introduced(assumption)).
% 29.97/20.19 tff(32306,plain,
% 29.97/20.19 (f3(f3(c1, c1), c1) = c1),
% 29.97/20.19 inference(transitivity,[status(thm)],[32301, 32305])).
% 29.97/20.19 tff(32307,plain,
% 29.97/20.19 (big_f(f3(f3(c1, c1), c1), f3(c1, c1)) <=> big_f(c1, f10(c1))),
% 29.97/20.19 inference(monotonicity,[status(thm)],[32306, 32300])).
% 29.97/20.19 tff(32308,plain,
% 29.97/20.19 (big_f(c1, f10(c1)) <=> big_f(f3(f3(c1, c1), c1), f3(c1, c1))),
% 29.97/20.19 inference(symmetry,[status(thm)],[32307])).
% 29.97/20.19 tff(32309,plain,
% 29.97/20.19 (big_f(c1, f10(c1)) <=> big_f(f3(f10(c1), c1), f10(c1))),
% 29.97/20.19 inference(transitivity,[status(thm)],[32308, 32304])).
% 29.97/20.19 tff(32310,plain,
% 29.97/20.19 (big_f(f3(f10(c1), c1), f10(c1))),
% 29.97/20.19 inference(modus_ponens,[status(thm)],[30444, 32309])).
% 29.97/20.19 tff(32311,plain,
% 29.97/20.19 ($false),
% 29.97/20.19 inference(unit_resolution,[status(thm)],[1061, 32310])).
% 29.97/20.19 tff(32312,plain,((~(f3(f10(c1), c1) = c1)) | big_f(f3(f10(c1), c1), f10(c1)) | (~(f3(c1, c1) = c2)) | (~(f10(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.97/20.20 tff(32313,plain,
% 29.97/20.20 (~(f3(f10(c1), c1) = c1)),
% 29.97/20.20 inference(unit_resolution,[status(thm)],[32312, 1061, 1441, 16])).
% 29.97/20.20 tff(32314,plain,
% 29.97/20.20 ((f3(c2, c1) = c1) <=> (f3(f10(c1), c1) = c1)),
% 29.97/20.20 inference(monotonicity,[status(thm)],[32293])).
% 29.97/20.20 tff(32315,plain,
% 29.97/20.20 (~(c1 = f2(c2))),
% 29.97/20.20 inference(unit_resolution,[status(thm)],[17675, 1062, 2, 1344, 1046, 1061])).
% 29.97/20.20 tff(32316,plain,
% 29.97/20.20 (~(f2(c2) = c1)),
% 29.97/20.20 inference(unit_resolution,[status(thm)],[31907, 32315])).
% 29.97/20.20 tff(32317,plain,
% 29.97/20.20 (f2(c2) = c2),
% 29.97/20.20 inference(unit_resolution,[status(thm)],[31912, 32316])).
% 29.97/20.20 tff(32318,plain,
% 29.97/20.20 (c2 = f2(c2)),
% 29.97/20.20 inference(unit_resolution,[status(thm)],[31890, 32317])).
% 29.97/20.20 tff(32319,plain,
% 29.97/20.20 (f3(c2, c1) = c1),
% 29.97/20.20 inference(unit_resolution,[status(thm)],[31885, 32318, 121, 1344, 12175, 873])).
% 29.97/20.20 tff(32320,plain,
% 29.97/20.20 (f3(f10(c1), c1) = c1),
% 29.97/20.20 inference(modus_ponens,[status(thm)],[32319, 32314])).
% 29.97/20.20 tff(32321,plain,
% 29.97/20.20 ($false),
% 29.97/20.20 inference(unit_resolution,[status(thm)],[1062, 32320])).
% 29.97/20.20 tff(32322,plain,((f3(f10(c1), c1) = c1) | (~(f10(c1) = c2)) | big_f(c2, c2) | (~(c2 = c3)) | big_f(f3(c2, c1), c2) | (c2 = c4) | big_f(c2, c1) | (f10(c1) = c4) | big_f(f3(f10(c1), c1), f10(c1))), inference(lemma,lemma(discharge,[]))).
% 29.97/20.20 tff(32323,plain,
% 29.97/20.20 (big_f(f3(c2, c1), c2)),
% 29.97/20.20 inference(unit_resolution,[status(thm)],[32322, 32313, 121, 1344, 16, 873, 2, 1046, 1061])).
% 29.97/20.20 tff(32324,plain,
% 29.97/20.20 ($false),
% 29.97/20.20 inference(unit_resolution,[status(thm)],[32323, 32298])).
% 29.97/20.20 tff(32325,plain,(big_f(f3(f10(c1), c1), f10(c1)) | (~(f10(c1) = c2)) | big_f(c2, c2) | (~(c2 = c3)) | (c2 = c4) | big_f(c2, c1) | (f10(c1) = c4) | (~(f3(c1, c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.97/20.20 tff(32326,plain,
% 29.97/20.20 (big_f(f3(f10(c1), c1), f10(c1))),
% 29.97/20.20 inference(unit_resolution,[status(thm)],[32325, 1335, 121, 15, 32290, 2, 32287, 1440])).
% 29.97/20.20 tff(32327,plain,
% 29.97/20.20 (big_f(f3(f3(c1, c1), c1), f3(c1, c1))),
% 29.97/20.20 inference(modus_ponens,[status(thm)],[32326, 32276])).
% 29.97/20.20 tff(32328,plain,
% 29.97/20.20 (big_f(f3(f3(c1, c1), c1), f10(c1))),
% 29.97/20.20 inference(modus_ponens,[status(thm)],[32327, 32275])).
% 29.97/20.20 tff(32329,plain,
% 29.97/20.20 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (f3(f3(c1, c1), c1) = f8(c1)) | (~big_f(f3(f3(c1, c1), c1), f10(c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (f3(f3(c1, c1), c1) = f8(c1)) | (~big_f(f3(f3(c1, c1), c1), f10(c1))))),
% 29.97/20.20 inference(rewrite,[status(thm)],[])).
% 29.97/20.20 tff(32330,plain,
% 29.97/20.20 (((f10(c1) = c1) | (f3(f3(c1, c1), c1) = f8(c1)) | (~big_f(f3(f3(c1, c1), c1), f10(c1))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1)))) <=> ((f10(c1) = c1) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (f3(f3(c1, c1), c1) = f8(c1)) | (~big_f(f3(f3(c1, c1), c1), f10(c1))))),
% 29.97/20.20 inference(rewrite,[status(thm)],[])).
% 29.97/20.20 tff(32331,plain,
% 29.97/20.20 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (f3(f3(c1, c1), c1) = f8(c1)) | (~big_f(f3(f3(c1, c1), c1), f10(c1))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (f3(f3(c1, c1), c1) = f8(c1)) | (~big_f(f3(f3(c1, c1), c1), f10(c1)))))),
% 29.97/20.20 inference(monotonicity,[status(thm)],[32330])).
% 29.97/20.20 tff(32332,plain,
% 29.97/20.20 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (f3(f3(c1, c1), c1) = f8(c1)) | (~big_f(f3(f3(c1, c1), c1), f10(c1))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (f3(f3(c1, c1), c1) = f8(c1)) | (~big_f(f3(f3(c1, c1), c1), f10(c1))))),
% 29.97/20.20 inference(transitivity,[status(thm)],[32331, 32329])).
% 29.97/20.20 tff(32333,plain,
% 29.97/20.20 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (f3(f3(c1, c1), c1) = f8(c1)) | (~big_f(f3(f3(c1, c1), c1), f10(c1))) | (~(f7(c1) = c1)) | (~(f6(c1, c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))))),
% 29.97/20.20 inference(quant_inst,[status(thm)],[])).
% 29.97/20.20 tff(32334,plain,
% 29.97/20.20 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(f7(c1) = c1)) | (~big_f(f7(c1), f6(c1, c1))) | (~(f6(c1, c1) = c1)) | (f3(f3(c1, c1), c1) = f8(c1)) | (~big_f(f3(f3(c1, c1), c1), f10(c1)))),
% 29.97/20.20 inference(modus_ponens,[status(thm)],[32333, 32332])).
% 29.97/20.20 tff(32335,plain,
% 29.97/20.20 ((f3(f3(c1, c1), c1) = f8(c1)) | (~big_f(f3(f3(c1, c1), c1), f10(c1)))),
% 29.97/20.20 inference(unit_resolution,[status(thm)],[32334, 2730, 25791, 3, 32262, 10030])).
% 29.97/20.20 tff(32336,plain,
% 29.97/20.20 (f3(f3(c1, c1), c1) = f8(c1)),
% 29.97/20.20 inference(unit_resolution,[status(thm)],[32335, 32328])).
% 29.97/20.20 tff(32337,plain,
% 29.97/20.20 (f3(f10(c1), c1) = c1),
% 29.97/20.20 inference(modus_ponens,[status(thm)],[32336, 32273])).
% 29.97/20.20 tff(32338,plain,
% 29.97/20.20 ((~big_f(c2, c1)) <=> (~big_f(f10(c1), c1))),
% 29.97/20.20 inference(monotonicity,[status(thm)],[31007])).
% 29.97/20.20 tff(32339,plain,
% 29.97/20.20 (~big_f(f10(c1), c1)),
% 29.97/20.20 inference(modus_ponens,[status(thm)],[2, 32338])).
% 29.97/20.20 tff(32340,plain,
% 29.97/20.20 ((~(f3(f10(c1), c1) = c1)) | (~(c1 = f2(f10(c1))))),
% 29.97/20.20 inference(unit_resolution,[status(thm)],[31956, 1398, 32287, 32326, 27301, 32339])).
% 29.97/20.20 tff(32341,plain,
% 29.97/20.20 (~(c1 = f2(f10(c1)))),
% 29.97/20.20 inference(unit_resolution,[status(thm)],[32340, 32337])).
% 29.97/20.20 tff(32342,plain,
% 29.97/20.20 (~(f2(c2) = c1)),
% 29.97/20.20 inference(modus_ponens,[status(thm)],[32341, 32280])).
% 29.97/20.20 tff(32343,plain,
% 29.97/20.20 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((f10(c1) = c4) | big_f(f10(c1), f10(c1)) | (~big_f(f3(f10(c1), c1), f10(c1))) | (~(f3(f10(c1), c1) = c1)) | (~(f10(c1) = c3)) | (~(f10(c1) = f2(f10(c1)))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (f10(c1) = c4) | big_f(f10(c1), f10(c1)) | (~big_f(f3(f10(c1), c1), f10(c1))) | (~(f3(f10(c1), c1) = c1)) | (~(f10(c1) = c3)) | (~(f10(c1) = f2(f10(c1)))))),
% 29.97/20.20 inference(rewrite,[status(thm)],[])).
% 29.97/20.20 tff(32344,plain,
% 29.97/20.20 (((~(f10(c1) = c3)) | (~(f10(c1) = f2(f10(c1)))) | (f10(c1) = c4) | (~(f3(f10(c1), c1) = c1)) | (~big_f(f3(f10(c1), c1), f10(c1))) | big_f(f10(c1), f10(c1))) <=> ((f10(c1) = c4) | big_f(f10(c1), f10(c1)) | (~big_f(f3(f10(c1), c1), f10(c1))) | (~(f3(f10(c1), c1) = c1)) | (~(f10(c1) = c3)) | (~(f10(c1) = f2(f10(c1)))))),
% 29.97/20.20 inference(rewrite,[status(thm)],[])).
% 29.97/20.20 tff(32345,plain,
% 29.97/20.20 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(f10(c1) = c3)) | (~(f10(c1) = f2(f10(c1)))) | (f10(c1) = c4) | (~(f3(f10(c1), c1) = c1)) | (~big_f(f3(f10(c1), c1), f10(c1))) | big_f(f10(c1), f10(c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((f10(c1) = c4) | big_f(f10(c1), f10(c1)) | (~big_f(f3(f10(c1), c1), f10(c1))) | (~(f3(f10(c1), c1) = c1)) | (~(f10(c1) = c3)) | (~(f10(c1) = f2(f10(c1))))))),
% 29.97/20.20 inference(monotonicity,[status(thm)],[32344])).
% 29.97/20.20 tff(32346,plain,
% 29.97/20.20 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(f10(c1) = c3)) | (~(f10(c1) = f2(f10(c1)))) | (f10(c1) = c4) | (~(f3(f10(c1), c1) = c1)) | (~big_f(f3(f10(c1), c1), f10(c1))) | big_f(f10(c1), f10(c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (f10(c1) = c4) | big_f(f10(c1), f10(c1)) | (~big_f(f3(f10(c1), c1), f10(c1))) | (~(f3(f10(c1), c1) = c1)) | (~(f10(c1) = c3)) | (~(f10(c1) = f2(f10(c1)))))),
% 29.97/20.20 inference(transitivity,[status(thm)],[32345, 32343])).
% 29.97/20.20 tff(32347,plain,
% 29.97/20.20 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(f10(c1) = c3)) | (~(f10(c1) = f2(f10(c1)))) | (f10(c1) = c4) | (~(f3(f10(c1), c1) = c1)) | (~big_f(f3(f10(c1), c1), f10(c1))) | big_f(f10(c1), f10(c1)))),
% 29.97/20.20 inference(quant_inst,[status(thm)],[])).
% 29.97/20.20 tff(32348,plain,
% 29.97/20.20 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (f10(c1) = c4) | big_f(f10(c1), f10(c1)) | (~big_f(f3(f10(c1), c1), f10(c1))) | (~(f3(f10(c1), c1) = c1)) | (~(f10(c1) = c3)) | (~(f10(c1) = f2(f10(c1))))),
% 29.97/20.20 inference(modus_ponens,[status(thm)],[32347, 32346])).
% 29.97/20.20 tff(32349,plain,
% 29.97/20.20 ((~(f3(f10(c1), c1) = c1)) | (~(f10(c1) = f2(f10(c1))))),
% 29.97/20.20 inference(unit_resolution,[status(thm)],[32348, 1398, 32287, 32326, 27301, 26001])).
% 29.97/20.20 tff(32350,plain,
% 29.97/20.20 (~(f10(c1) = f2(f10(c1)))),
% 29.97/20.20 inference(unit_resolution,[status(thm)],[32349, 32337])).
% 29.97/20.20 tff(32351,plain,
% 29.97/20.20 (~(f2(c2) = c2)),
% 29.97/20.20 inference(modus_ponens,[status(thm)],[32350, 31730])).
% 29.97/20.20 tff(32352,plain,
% 29.97/20.20 ($false),
% 29.97/20.20 inference(unit_resolution,[status(thm)],[31912, 32351, 32342])).
% 29.97/20.20 tff(32353,plain,((~(c3 = c2)) | (f10(c1) = c1) | (~(f6(c1, c1) = c1)) | big_f(c2, c2) | big_f(c2, c1) | (f3(c1, c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.97/20.20 tff(32354,plain,
% 29.97/20.20 (~(c3 = c2)),
% 29.97/20.20 inference(unit_resolution,[status(thm)],[32353, 10030, 3, 121, 2, 1431])).
% 29.97/20.20 tff(32355,plain,
% 29.97/20.20 (c3 = c1),
% 29.97/20.20 inference(unit_resolution,[status(thm)],[180, 32354])).
% 29.97/20.20 tff(32356,plain,
% 29.97/20.20 (c1 = c3),
% 29.97/20.20 inference(unit_resolution,[status(thm)],[175, 32355])).
% 29.97/20.20 tff(32357,plain,
% 29.97/20.20 (big_f(f10(c1), c1) <=> big_f(f3(c1, c1), c1)),
% 29.97/20.20 inference(monotonicity,[status(thm)],[31732])).
% 29.97/20.20 tff(32358,plain,
% 29.97/20.20 ((~big_f(f10(c1), c1)) <=> (~big_f(f3(c1, c1), c1))),
% 29.97/20.20 inference(monotonicity,[status(thm)],[32357])).
% 29.97/20.20 tff(32359,plain,
% 29.97/20.20 (~big_f(f3(c1, c1), c1)),
% 29.97/20.20 inference(modus_ponens,[status(thm)],[32339, 32358])).
% 29.97/20.20 tff(32360,plain,
% 29.97/20.20 (c1 = c4),
% 29.97/20.20 inference(unit_resolution,[status(thm)],[31981, 32356, 32359, 1431])).
% 29.97/20.20 tff(32361,plain,
% 29.97/20.20 (c4 = c1),
% 29.97/20.20 inference(symmetry,[status(thm)],[32360])).
% 29.97/20.20 tff(32362,plain,
% 29.97/20.20 ((f10(c1) = c4) <=> (f10(c1) = c1)),
% 29.97/20.20 inference(monotonicity,[status(thm)],[32361])).
% 29.97/20.20 tff(32363,plain,
% 29.97/20.20 ((f10(c1) = c1) <=> (f10(c1) = c4)),
% 29.97/20.20 inference(symmetry,[status(thm)],[32362])).
% 29.97/20.20 tff(32364,plain,
% 29.97/20.20 ((~(f10(c1) = c1)) <=> (~(f10(c1) = c4))),
% 29.97/20.20 inference(monotonicity,[status(thm)],[32363])).
% 29.97/20.20 tff(32365,plain,
% 29.97/20.20 (~(f10(c1) = c4)),
% 29.97/20.20 inference(modus_ponens,[status(thm)],[3, 32364])).
% 29.97/20.20 tff(32366,plain,
% 29.97/20.20 (big_f(f3(c2, c1), c2)),
% 29.97/20.20 inference(unit_resolution,[status(thm)],[32132, 32365, 3, 32356])).
% 29.97/20.20 tff(32367,plain,
% 29.97/20.20 (big_f(f3(f3(c1, c1), c1), f3(c1, c1))),
% 29.97/20.20 inference(modus_ponens,[status(thm)],[32366, 32277])).
% 29.97/20.20 tff(32368,plain,
% 29.97/20.20 (big_f(f3(f3(c1, c1), c1), f10(c1))),
% 29.97/20.20 inference(modus_ponens,[status(thm)],[32367, 32275])).
% 29.97/20.20 tff(32369,plain,
% 29.97/20.20 (f3(f3(c1, c1), c1) = f8(c1)),
% 29.97/20.20 inference(unit_resolution,[status(thm)],[32335, 32368])).
% 29.97/20.20 tff(32370,plain,
% 29.97/20.20 (f3(f10(c1), c1) = c1),
% 29.97/20.20 inference(modus_ponens,[status(thm)],[32369, 32273])).
% 29.97/20.20 tff(32371,plain,
% 29.97/20.20 (big_f(f3(f10(c1), c1), f10(c1))),
% 29.97/20.20 inference(modus_ponens,[status(thm)],[32366, 31363])).
% 29.97/20.20 tff(32372,plain,
% 29.97/20.20 ((c1 = f2(c1)) | (~(f3(f10(c1), c1) = c1))),
% 29.97/20.20 inference(unit_resolution,[status(thm)],[32143, 7051, 32356, 32365, 32371, 31714])).
% 29.97/20.20 tff(32373,plain,
% 29.97/20.20 (c1 = f2(c1)),
% 29.97/20.20 inference(unit_resolution,[status(thm)],[32372, 32370])).
% 29.97/20.20 tff(32374,plain,
% 29.97/20.20 (f2(c1) = c1),
% 29.97/20.20 inference(symmetry,[status(thm)],[32373])).
% 29.97/20.20 tff(32375,plain,
% 29.97/20.20 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (f10(c1) = c4) | (f10(c1) = f2(c1)) | (~big_f(c1, f10(c1))) | (~big_f(f3(f10(c1), c1), f10(c1))) | (~(f3(f10(c1), c1) = c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c1 = c3)) | (f10(c1) = c4) | (f10(c1) = f2(c1)) | (~big_f(c1, f10(c1))) | (~big_f(f3(f10(c1), c1), f10(c1))) | (~(f3(f10(c1), c1) = c1)))),
% 29.97/20.20 inference(rewrite,[status(thm)],[])).
% 29.97/20.20 tff(32376,plain,
% 29.97/20.20 (((~(c1 = c3)) | (f10(c1) = c4) | (~(f3(f10(c1), c1) = c1)) | (~big_f(f3(f10(c1), c1), f10(c1))) | (f10(c1) = f2(c1)) | (~big_f(c1, f10(c1)))) <=> ((~(c1 = c3)) | (f10(c1) = c4) | (f10(c1) = f2(c1)) | (~big_f(c1, f10(c1))) | (~big_f(f3(f10(c1), c1), f10(c1))) | (~(f3(f10(c1), c1) = c1)))),
% 29.97/20.20 inference(rewrite,[status(thm)],[])).
% 29.97/20.20 tff(32377,plain,
% 29.97/20.20 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (f10(c1) = c4) | (~(f3(f10(c1), c1) = c1)) | (~big_f(f3(f10(c1), c1), f10(c1))) | (f10(c1) = f2(c1)) | (~big_f(c1, f10(c1))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (f10(c1) = c4) | (f10(c1) = f2(c1)) | (~big_f(c1, f10(c1))) | (~big_f(f3(f10(c1), c1), f10(c1))) | (~(f3(f10(c1), c1) = c1))))),
% 29.97/20.20 inference(monotonicity,[status(thm)],[32376])).
% 29.97/20.20 tff(32378,plain,
% 29.97/20.20 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (f10(c1) = c4) | (~(f3(f10(c1), c1) = c1)) | (~big_f(f3(f10(c1), c1), f10(c1))) | (f10(c1) = f2(c1)) | (~big_f(c1, f10(c1))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c1 = c3)) | (f10(c1) = c4) | (f10(c1) = f2(c1)) | (~big_f(c1, f10(c1))) | (~big_f(f3(f10(c1), c1), f10(c1))) | (~(f3(f10(c1), c1) = c1)))),
% 29.97/20.20 inference(transitivity,[status(thm)],[32377, 32375])).
% 29.97/20.20 tff(32379,plain,
% 29.97/20.20 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (f10(c1) = c4) | (~(f3(f10(c1), c1) = c1)) | (~big_f(f3(f10(c1), c1), f10(c1))) | (f10(c1) = f2(c1)) | (~big_f(c1, f10(c1))))),
% 29.97/20.20 inference(quant_inst,[status(thm)],[])).
% 29.97/20.20 tff(32380,plain,
% 29.97/20.20 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c1 = c3)) | (f10(c1) = c4) | (f10(c1) = f2(c1)) | (~big_f(c1, f10(c1))) | (~big_f(f3(f10(c1), c1), f10(c1))) | (~(f3(f10(c1), c1) = c1))),
% 29.97/20.20 inference(modus_ponens,[status(thm)],[32379, 32378])).
% 29.97/20.20 tff(32381,plain,
% 29.97/20.20 ((f10(c1) = f2(c1)) | (~(f3(f10(c1), c1) = c1))),
% 29.97/20.20 inference(unit_resolution,[status(thm)],[32380, 7051, 32356, 30400, 32365, 32371])).
% 29.97/20.20 tff(32382,plain,
% 29.97/20.20 (f10(c1) = f2(c1)),
% 29.97/20.20 inference(unit_resolution,[status(thm)],[32381, 32370])).
% 29.97/20.20 tff(32383,plain,
% 29.97/20.20 (f10(c1) = c1),
% 29.97/20.20 inference(transitivity,[status(thm)],[32382, 32374])).
% 29.97/20.20 tff(32384,plain,
% 29.97/20.20 ($false),
% 29.97/20.20 inference(unit_resolution,[status(thm)],[3, 32383])).
% 29.97/20.20 tff(32385,plain,((~(f6(c1, c1) = c1)) | (f10(c1) = c1) | (f3(c1, c1) = c1) | big_f(c2, c2) | big_f(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 29.97/20.20 tff(32386,plain,
% 29.97/20.20 (~(f6(c1, c1) = c1)),
% 29.97/20.20 inference(unit_resolution,[status(thm)],[32385, 1431, 3, 121, 2])).
% 29.97/20.20 tff(32387,plain,
% 29.97/20.20 (~(f6(c1, f6(c1, c2)) = c1)),
% 29.97/20.20 inference(unit_resolution,[status(thm)],[58, 32386])).
% 29.97/20.20 tff(32388,plain,
% 29.97/20.20 (f6(c1, f6(c1, c2)) = c2),
% 29.97/20.20 inference(unit_resolution,[status(thm)],[63, 32387])).
% 29.97/20.20 tff(32389,plain,
% 29.97/20.20 (c1 = f6(c1, c2)),
% 29.97/20.20 inference(symmetry,[status(thm)],[32256])).
% 29.97/20.20 tff(32390,plain,
% 29.97/20.20 (f6(c1, c1) = f6(c1, f6(c1, c2))),
% 29.97/20.20 inference(monotonicity,[status(thm)],[32389])).
% 29.97/20.20 tff(32391,plain,
% 29.97/20.20 (f6(c1, c1) = f10(c1)),
% 29.97/20.20 inference(transitivity,[status(thm)],[32390, 32388, 5571])).
% 29.97/20.20 tff(32392,plain,
% 29.97/20.20 (big_f(f6(c1, c1), c1) <=> big_f(f10(c1), c1)),
% 29.97/20.20 inference(monotonicity,[status(thm)],[32391])).
% 29.97/20.20 tff(32393,plain,
% 29.97/20.20 (big_f(f10(c1), c1) <=> big_f(f6(c1, c1), c1)),
% 29.97/20.20 inference(symmetry,[status(thm)],[32392])).
% 29.97/20.20 tff(32394,plain,
% 29.97/20.20 ((~big_f(f10(c1), c1)) <=> (~big_f(f6(c1, c1), c1))),
% 29.97/20.20 inference(monotonicity,[status(thm)],[32393])).
% 29.97/20.20 tff(32395,plain,
% 29.97/20.20 (~big_f(f6(c1, c1), c1)),
% 29.97/20.20 inference(modus_ponens,[status(thm)],[32339, 32394])).
% 29.97/20.20 tff(32396,plain,
% 29.97/20.20 (f10(c1) = f3(c1, c1)),
% 29.97/20.20 inference(transitivity,[status(thm)],[16, 31731])).
% 29.97/20.20 tff(32397,plain,
% 29.97/20.20 (big_f(f10(c1), c1) <=> big_f(f3(c1, c1), c1)),
% 29.97/20.20 inference(monotonicity,[status(thm)],[32396])).
% 29.97/20.20 tff(32398,plain,
% 29.97/20.20 (big_f(f3(c1, c1), c1) <=> big_f(f10(c1), c1)),
% 29.97/20.20 inference(symmetry,[status(thm)],[32397])).
% 29.97/20.20 tff(32399,plain,
% 29.97/20.20 (big_f(f10(c1), c1)),
% 29.97/20.20 inference(modus_ponens,[status(thm)],[32075, 32398])).
% 29.97/20.20 tff(32400,plain,
% 29.97/20.20 ($false),
% 29.97/20.20 inference(unit_resolution,[status(thm)],[29450, 32399])).
% 29.97/20.20 tff(32401,plain,((f3(c1, c1) = c1) | big_f(f10(c1), c1) | (~(f10(c1) = c2)) | (~(f6(c1, f6(c1, c2)) = c2)) | big_f(c2, c2) | (~(c1 = c3))), inference(lemma,lemma(discharge,[]))).
% 29.97/20.20 tff(32402,plain,
% 29.97/20.20 (~(c1 = c3)),
% 29.97/20.20 inference(unit_resolution,[status(thm)],[32401, 32388, 15, 32339, 121, 1431])).
% 29.97/20.20 tff(32403,plain,
% 29.97/20.20 (~(c3 = c1)),
% 29.97/20.20 inference(unit_resolution,[status(thm)],[175, 32402])).
% 29.97/20.20 tff(32404,plain,
% 29.97/20.20 (c3 = c2),
% 29.97/20.20 inference(unit_resolution,[status(thm)],[180, 32403])).
% 29.97/20.20 tff(32405,plain,
% 29.97/20.20 (~(c4 = c2)),
% 29.97/20.20 inference(unit_resolution,[status(thm)],[27535, 32404, 31714, 121, 2])).
% 29.97/20.20 tff(32406,plain,
% 29.97/20.20 (c4 = c1),
% 29.97/20.20 inference(unit_resolution,[status(thm)],[461, 32405])).
% 29.97/20.20 tff(32407,plain,
% 29.97/20.20 ((f6(c1, c1) = c3) <=> (f10(c1) = c3)),
% 29.97/20.20 inference(monotonicity,[status(thm)],[32391])).
% 29.97/20.20 tff(32408,plain,
% 29.97/20.20 ((f10(c1) = c3) <=> (f6(c1, c1) = c3)),
% 29.97/20.20 inference(symmetry,[status(thm)],[32407])).
% 29.97/20.20 tff(32409,plain,
% 29.97/20.20 (f10(c1) = c3),
% 29.97/20.20 inference(modus_ponens,[status(thm)],[32404, 27300])).
% 29.97/20.20 tff(32410,plain,
% 29.97/20.20 (f6(c1, c1) = c3),
% 29.97/20.20 inference(modus_ponens,[status(thm)],[32409, 32408])).
% 29.97/20.20 tff(32411,plain,
% 29.97/20.20 (c2 = c3),
% 29.97/20.20 inference(modus_ponens,[status(thm)],[32404, 78])).
% 29.97/20.20 tff(32412,plain,
% 29.97/20.20 (f6(c1, c1) = f6(c1, f6(c1, c2))),
% 29.97/20.20 inference(symmetry,[status(thm)],[31339])).
% 29.97/20.20 tff(32413,plain,
% 29.97/20.20 (f6(c1, c1) = c2),
% 29.97/20.20 inference(transitivity,[status(thm)],[32412, 64])).
% 29.97/20.20 tff(32414,plain,
% 29.97/20.20 (f2(f6(c1, c1)) = f2(c2)),
% 29.97/20.20 inference(monotonicity,[status(thm)],[32413])).
% 29.97/20.20 tff(32415,plain,
% 29.97/20.20 ((c1 = f2(f6(c1, c1))) <=> (c1 = f2(c2))),
% 29.97/20.20 inference(monotonicity,[status(thm)],[32414])).
% 29.97/20.20 tff(32416,plain,
% 29.97/20.20 ((c1 = f2(f6(c1, c1))) <=> (f2(c2) = c1)),
% 29.97/20.20 inference(transitivity,[status(thm)],[32415, 32278])).
% 29.97/20.20 tff(32417,plain,
% 29.97/20.20 ((~(c1 = f2(f6(c1, c1)))) <=> (~(f2(c2) = c1))),
% 29.97/20.20 inference(monotonicity,[status(thm)],[32416])).
% 29.97/20.20 tff(32418,plain,
% 29.97/20.20 (f3(f3(f7(c1), c1), c1) = c2),
% 29.97/20.20 inference(unit_resolution,[status(thm)],[32040, 9169])).
% 29.97/20.20 tff(32419,plain,
% 29.97/20.20 (f3(f3(c1, c1), c1) = f3(c1, c1)),
% 29.97/20.20 inference(monotonicity,[status(thm)],[1938])).
% 29.97/20.20 tff(32420,plain,
% 29.97/20.20 (f6(c1, c1) = c1),
% 29.97/20.20 inference(transitivity,[status(thm)],[6933, 64, 31998, 32049, 32419, 1938])).
% 29.97/20.20 tff(32421,plain,
% 29.97/20.20 ($false),
% 29.97/20.20 inference(unit_resolution,[status(thm)],[28, 32420])).
% 29.97/20.20 tff(32422,plain,((~(f3(c1, c1) = c1)) | (f6(c1, c1) = c1) | (~(f3(f3(f7(c1), c1), c1) = c2)) | (~(f6(c1, c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.97/20.20 tff(32423,plain,
% 29.97/20.20 (~(f3(c1, c1) = c1)),
% 29.97/20.20 inference(unit_resolution,[status(thm)],[32422, 32418, 28, 6931])).
% 29.97/20.20 tff(32424,plain,
% 29.97/20.20 ((f3(c1, c1) = c4) <=> (f3(c1, c1) = c1)),
% 29.97/20.20 inference(monotonicity,[status(thm)],[480])).
% 29.97/20.20 tff(32425,assumption,(f3(c1, c1) = c4), introduced(assumption)).
% 29.97/20.20 tff(32426,plain,
% 29.97/20.20 (f3(c1, c1) = c1),
% 29.97/20.20 inference(modus_ponens,[status(thm)],[32425, 32424])).
% 29.97/20.20 tff(32427,plain,
% 29.97/20.20 ($false),
% 29.97/20.20 inference(unit_resolution,[status(thm)],[1431, 32426])).
% 29.97/20.20 tff(32428,plain,((~(f3(c1, c1) = c4)) | (f3(c1, c1) = c1) | (~(c4 = c1))), inference(lemma,lemma(discharge,[]))).
% 29.97/20.20 tff(32429,plain,
% 29.97/20.20 (~(f3(c1, c1) = c4)),
% 29.97/20.20 inference(unit_resolution,[status(thm)],[32428, 32423, 480])).
% 29.97/20.20 tff(32430,plain,
% 29.97/20.20 (f3(c1, c1) = c2),
% 29.97/20.20 inference(unit_resolution,[status(thm)],[1416, 32423])).
% 29.97/20.20 tff(32431,plain,
% 29.97/20.20 (f3(f3(c1, c1), c1) = c2),
% 29.97/20.20 inference(transitivity,[status(thm)],[31996, 32418])).
% 29.97/20.20 tff(32432,plain,
% 29.97/20.20 (big_f(f3(f3(c1, c1), c1), f3(c1, c1)) <=> big_f(c2, c2)),
% 29.97/20.20 inference(monotonicity,[status(thm)],[32431, 32430])).
% 29.97/20.20 tff(32433,plain,
% 29.97/20.20 (big_f(c2, c2) <=> big_f(f3(f3(c1, c1), c1), f3(c1, c1))),
% 29.97/20.20 inference(symmetry,[status(thm)],[32432])).
% 29.97/20.20 tff(32434,plain,
% 29.97/20.20 ((~big_f(c2, c2)) <=> (~big_f(f3(f3(c1, c1), c1), f3(c1, c1)))),
% 29.97/20.20 inference(monotonicity,[status(thm)],[32433])).
% 29.97/20.20 tff(32435,plain,
% 29.97/20.20 (~big_f(f3(f3(c1, c1), c1), f3(c1, c1))),
% 29.97/20.20 inference(modus_ponens,[status(thm)],[121, 32434])).
% 29.97/20.20 tff(32436,assumption,(~big_f(f6(c1, c1), c1)), introduced(assumption)).
% 29.97/20.20 tff(32437,assumption,(f6(c1, c1) = c3), introduced(assumption)).
% 29.97/20.20 tff(32438,plain,
% 29.97/20.20 (c2 = f6(c1, f6(c1, c2))),
% 29.97/20.20 inference(symmetry,[status(thm)],[64])).
% 29.97/20.20 tff(32439,plain,
% 29.97/20.20 (f3(f3(c1, c1), c1) = f6(c1, c1)),
% 29.97/20.20 inference(transitivity,[status(thm)],[31996, 32418, 32438, 31339])).
% 29.97/20.20 tff(32440,plain,
% 29.97/20.20 ((f3(f3(c1, c1), c1) = c1) <=> (f6(c1, c1) = c1)),
% 29.97/20.20 inference(monotonicity,[status(thm)],[32439])).
% 29.97/20.20 tff(32441,plain,
% 29.97/20.20 ((f6(c1, c1) = c1) <=> (f3(f3(c1, c1), c1) = c1)),
% 29.97/20.20 inference(symmetry,[status(thm)],[32440])).
% 29.97/20.20 tff(32442,plain,
% 29.97/20.20 ((~(f6(c1, c1) = c1)) <=> (~(f3(f3(c1, c1), c1) = c1))),
% 29.97/20.20 inference(monotonicity,[status(thm)],[32441])).
% 29.97/20.20 tff(32443,plain,
% 29.97/20.20 (~(f3(f3(c1, c1), c1) = c1)),
% 29.97/20.20 inference(modus_ponens,[status(thm)],[28, 32442])).
% 29.97/20.20 tff(32444,plain,
% 29.97/20.20 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (big_f(f3(f3(c1, c1), c1), f3(c1, c1)) | (f3(f3(c1, c1), c1) = c1) | (f3(c1, c1) = c4) | (~(c1 = f2(f6(c1, c1)))) | (~(f6(c1, c1) = c3)) | big_f(f6(c1, c1), c1))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | big_f(f3(f3(c1, c1), c1), f3(c1, c1)) | (f3(f3(c1, c1), c1) = c1) | (f3(c1, c1) = c4) | (~(c1 = f2(f6(c1, c1)))) | (~(f6(c1, c1) = c3)) | big_f(f6(c1, c1), c1))),
% 29.97/20.20 inference(rewrite,[status(thm)],[])).
% 29.97/20.20 tff(32445,plain,
% 29.97/20.20 (((~(f6(c1, c1) = c3)) | (~(c1 = f2(f6(c1, c1)))) | (f3(c1, c1) = c4) | (f3(f3(c1, c1), c1) = c1) | big_f(f3(f3(c1, c1), c1), f3(c1, c1)) | big_f(f6(c1, c1), c1)) <=> (big_f(f3(f3(c1, c1), c1), f3(c1, c1)) | (f3(f3(c1, c1), c1) = c1) | (f3(c1, c1) = c4) | (~(c1 = f2(f6(c1, c1)))) | (~(f6(c1, c1) = c3)) | big_f(f6(c1, c1), c1))),
% 29.97/20.20 inference(rewrite,[status(thm)],[])).
% 29.97/20.20 tff(32446,plain,
% 29.97/20.20 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(f6(c1, c1) = c3)) | (~(c1 = f2(f6(c1, c1)))) | (f3(c1, c1) = c4) | (f3(f3(c1, c1), c1) = c1) | big_f(f3(f3(c1, c1), c1), f3(c1, c1)) | big_f(f6(c1, c1), c1))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (big_f(f3(f3(c1, c1), c1), f3(c1, c1)) | (f3(f3(c1, c1), c1) = c1) | (f3(c1, c1) = c4) | (~(c1 = f2(f6(c1, c1)))) | (~(f6(c1, c1) = c3)) | big_f(f6(c1, c1), c1)))),
% 29.97/20.21 inference(monotonicity,[status(thm)],[32445])).
% 29.97/20.21 tff(32447,plain,
% 29.97/20.21 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(f6(c1, c1) = c3)) | (~(c1 = f2(f6(c1, c1)))) | (f3(c1, c1) = c4) | (f3(f3(c1, c1), c1) = c1) | big_f(f3(f3(c1, c1), c1), f3(c1, c1)) | big_f(f6(c1, c1), c1))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | big_f(f3(f3(c1, c1), c1), f3(c1, c1)) | (f3(f3(c1, c1), c1) = c1) | (f3(c1, c1) = c4) | (~(c1 = f2(f6(c1, c1)))) | (~(f6(c1, c1) = c3)) | big_f(f6(c1, c1), c1))),
% 29.97/20.21 inference(transitivity,[status(thm)],[32446, 32444])).
% 29.97/20.21 tff(32448,plain,
% 29.97/20.21 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(f6(c1, c1) = c3)) | (~(c1 = f2(f6(c1, c1)))) | (f3(c1, c1) = c4) | (f3(f3(c1, c1), c1) = c1) | big_f(f3(f3(c1, c1), c1), f3(c1, c1)) | big_f(f6(c1, c1), c1))),
% 29.97/20.21 inference(quant_inst,[status(thm)],[])).
% 29.97/20.21 tff(32449,plain,
% 29.97/20.21 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | big_f(f3(f3(c1, c1), c1), f3(c1, c1)) | (f3(f3(c1, c1), c1) = c1) | (f3(c1, c1) = c4) | (~(c1 = f2(f6(c1, c1)))) | (~(f6(c1, c1) = c3)) | big_f(f6(c1, c1), c1)),
% 29.97/20.21 inference(modus_ponens,[status(thm)],[32448, 32447])).
% 29.97/20.21 tff(32450,plain,
% 29.97/20.21 (big_f(f3(f3(c1, c1), c1), f3(c1, c1)) | (f3(c1, c1) = c4) | (~(c1 = f2(f6(c1, c1))))),
% 29.97/20.21 inference(unit_resolution,[status(thm)],[32449, 1459, 32443, 32437, 32436])).
% 29.97/20.21 tff(32451,plain,
% 29.97/20.21 (~(c1 = f2(f6(c1, c1)))),
% 29.97/20.21 inference(unit_resolution,[status(thm)],[32450, 32435, 32429])).
% 29.97/20.21 tff(32452,plain,
% 29.97/20.21 (~(f2(c2) = c1)),
% 29.97/20.21 inference(modus_ponens,[status(thm)],[32451, 32417])).
% 29.97/20.21 tff(32453,plain,
% 29.97/20.21 ((f3(f7(c1), c1) = c4) <=> (f3(c1, c1) = c4)),
% 29.97/20.21 inference(monotonicity,[status(thm)],[31994])).
% 29.97/20.21 tff(32454,plain,
% 29.97/20.21 ((f3(c1, c1) = c4) <=> (f3(f7(c1), c1) = c4)),
% 29.97/20.21 inference(symmetry,[status(thm)],[32453])).
% 29.97/20.21 tff(32455,plain,
% 29.97/20.21 ((f3(c1, c1) = c1) <=> (f3(c1, c1) = c4)),
% 29.97/20.21 inference(symmetry,[status(thm)],[32424])).
% 29.97/20.21 tff(32456,plain,
% 29.97/20.21 ((f3(c1, c1) = c1) <=> (f3(f7(c1), c1) = c4)),
% 29.97/20.21 inference(transitivity,[status(thm)],[32455, 32454])).
% 29.97/20.21 tff(32457,plain,
% 29.97/20.21 ((~(f3(c1, c1) = c1)) <=> (~(f3(f7(c1), c1) = c4))),
% 29.97/20.21 inference(monotonicity,[status(thm)],[32456])).
% 29.97/20.21 tff(32458,plain,
% 29.97/20.21 (~(f3(f7(c1), c1) = c4)),
% 29.97/20.21 inference(modus_ponens,[status(thm)],[32423, 32457])).
% 29.97/20.21 tff(32459,plain,
% 29.97/20.21 (big_f(f3(f3(f7(c1), c1), c1), f3(f7(c1), c1)) <=> big_f(f3(f3(c1, c1), c1), f3(c1, c1))),
% 29.97/20.21 inference(monotonicity,[status(thm)],[31997, 31994])).
% 29.97/20.21 tff(32460,plain,
% 29.97/20.21 (big_f(f3(f3(c1, c1), c1), f3(c1, c1)) <=> big_f(f3(f3(f7(c1), c1), c1), f3(f7(c1), c1))),
% 29.97/20.21 inference(symmetry,[status(thm)],[32459])).
% 29.97/20.21 tff(32461,plain,
% 29.97/20.21 (big_f(c2, c2) <=> big_f(f3(f3(f7(c1), c1), c1), f3(f7(c1), c1))),
% 29.97/20.21 inference(transitivity,[status(thm)],[32433, 32460])).
% 29.97/20.21 tff(32462,plain,
% 29.97/20.21 ((~big_f(c2, c2)) <=> (~big_f(f3(f3(f7(c1), c1), c1), f3(f7(c1), c1)))),
% 29.97/20.21 inference(monotonicity,[status(thm)],[32461])).
% 29.97/20.21 tff(32463,plain,
% 29.97/20.21 (~big_f(f3(f3(f7(c1), c1), c1), f3(f7(c1), c1))),
% 29.97/20.21 inference(modus_ponens,[status(thm)],[121, 32462])).
% 29.97/20.21 tff(32464,plain,
% 29.97/20.21 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (f3(f3(f7(c1), c1), c1) = c1) | big_f(f3(f3(f7(c1), c1), c1), f3(f7(c1), c1)) | (f3(f7(c1), c1) = c4))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (f3(f3(f7(c1), c1), c1) = c1) | big_f(f3(f3(f7(c1), c1), c1), f3(f7(c1), c1)) | (f3(f7(c1), c1) = c4))),
% 29.97/20.21 inference(rewrite,[status(thm)],[])).
% 29.97/20.21 tff(32465,plain,
% 29.97/20.21 (((~(c2 = c3)) | (~(c2 = f2(c2))) | (f3(f7(c1), c1) = c4) | (f3(f3(f7(c1), c1), c1) = c1) | big_f(f3(f3(f7(c1), c1), c1), f3(f7(c1), c1)) | big_f(c2, c2)) <=> ((~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (f3(f3(f7(c1), c1), c1) = c1) | big_f(f3(f3(f7(c1), c1), c1), f3(f7(c1), c1)) | (f3(f7(c1), c1) = c4))),
% 29.97/20.21 inference(rewrite,[status(thm)],[])).
% 29.97/20.21 tff(32466,plain,
% 29.97/20.21 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | (f3(f7(c1), c1) = c4) | (f3(f3(f7(c1), c1), c1) = c1) | big_f(f3(f3(f7(c1), c1), c1), f3(f7(c1), c1)) | big_f(c2, c2))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (f3(f3(f7(c1), c1), c1) = c1) | big_f(f3(f3(f7(c1), c1), c1), f3(f7(c1), c1)) | (f3(f7(c1), c1) = c4)))),
% 29.97/20.21 inference(monotonicity,[status(thm)],[32465])).
% 29.97/20.21 tff(32467,plain,
% 29.97/20.21 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | (f3(f7(c1), c1) = c4) | (f3(f3(f7(c1), c1), c1) = c1) | big_f(f3(f3(f7(c1), c1), c1), f3(f7(c1), c1)) | big_f(c2, c2))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (f3(f3(f7(c1), c1), c1) = c1) | big_f(f3(f3(f7(c1), c1), c1), f3(f7(c1), c1)) | (f3(f7(c1), c1) = c4))),
% 29.97/20.21 inference(transitivity,[status(thm)],[32466, 32464])).
% 29.97/20.21 tff(32468,plain,
% 29.97/20.21 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | (f3(f7(c1), c1) = c4) | (f3(f3(f7(c1), c1), c1) = c1) | big_f(f3(f3(f7(c1), c1), c1), f3(f7(c1), c1)) | big_f(c2, c2))),
% 29.97/20.21 inference(quant_inst,[status(thm)],[])).
% 29.97/20.21 tff(32469,plain,
% 29.97/20.21 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (f3(f3(f7(c1), c1), c1) = c1) | big_f(f3(f3(f7(c1), c1), c1), f3(f7(c1), c1)) | (f3(f7(c1), c1) = c4)),
% 29.97/20.21 inference(modus_ponens,[status(thm)],[32468, 32467])).
% 29.97/20.21 tff(32470,plain,
% 29.97/20.21 ((~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (f3(f3(f7(c1), c1), c1) = c1) | big_f(f3(f3(f7(c1), c1), c1), f3(f7(c1), c1)) | (f3(f7(c1), c1) = c4)),
% 29.97/20.21 inference(unit_resolution,[status(thm)],[32469, 1459])).
% 29.97/20.21 tff(32471,plain,
% 29.97/20.21 (~(c2 = f2(c2))),
% 29.97/20.21 inference(unit_resolution,[status(thm)],[32470, 32463, 1344, 121, 9169, 32458])).
% 29.97/20.21 tff(32472,plain,
% 29.97/20.21 (~(f2(c2) = c2)),
% 29.97/20.21 inference(unit_resolution,[status(thm)],[31890, 32471])).
% 29.97/20.21 tff(32473,plain,
% 29.97/20.21 (f2(c2) = c1),
% 29.97/20.21 inference(unit_resolution,[status(thm)],[31912, 32472])).
% 29.97/20.21 tff(32474,plain,
% 29.97/20.21 ($false),
% 29.97/20.21 inference(unit_resolution,[status(thm)],[32473, 32452])).
% 29.97/20.21 tff(32475,plain,((f3(f3(f7(c1), c1), c1) = c1) | (~(f6(c1, c2) = c1)) | (~(c2 = c3)) | big_f(c2, c2) | (~(f6(c1, c1) = c3)) | big_f(f6(c1, c1), c1) | (~(c4 = c1)) | (f6(c1, c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.97/20.21 tff(32476,plain,
% 29.97/20.21 (f3(f3(f7(c1), c1), c1) = c1),
% 29.97/20.21 inference(unit_resolution,[status(thm)],[32475, 32411, 32256, 121, 32386, 32410, 32406, 32395])).
% 29.97/20.21 tff(32477,plain,
% 29.97/20.21 (big_f(c1, f6(c1, c1))),
% 29.97/20.21 inference(unit_resolution,[status(thm)],[28169, 32262])).
% 29.97/20.21 tff(32478,plain,
% 29.97/20.21 (f6(c1, f6(c1, c2)) = f6(c1, c1)),
% 29.97/20.21 inference(symmetry,[status(thm)],[32390])).
% 29.97/20.21 tff(32479,plain,
% 29.97/20.21 ((f6(c1, f6(c1, c2)) = c4) <=> (f6(c1, c1) = c4)),
% 29.97/20.21 inference(monotonicity,[status(thm)],[32478])).
% 29.97/20.21 tff(32480,plain,
% 29.97/20.21 ((f6(c1, c1) = c4) <=> (f6(c1, f6(c1, c2)) = c4)),
% 29.97/20.21 inference(symmetry,[status(thm)],[32479])).
% 29.97/20.21 tff(32481,plain,
% 29.97/20.21 ((f6(c1, c1) = c4) <=> (f10(c1) = c4)),
% 29.97/20.21 inference(monotonicity,[status(thm)],[32391])).
% 29.97/20.21 tff(32482,plain,
% 29.97/20.21 ((f10(c1) = c4) <=> (f6(c1, c1) = c4)),
% 29.97/20.21 inference(symmetry,[status(thm)],[32481])).
% 29.97/20.21 tff(32483,plain,
% 29.97/20.21 (~big_f(c3, f2(c3))),
% 29.97/20.21 inference(unit_resolution,[status(thm)],[8256, 32404, 121, 2])).
% 29.97/20.21 tff(32484,plain,
% 29.97/20.21 (c1 = c4),
% 29.97/20.21 inference(unit_resolution,[status(thm)],[27520, 32483, 1431, 2, 32404])).
% 29.97/20.21 tff(32485,plain,
% 29.97/20.21 (c4 = c1),
% 29.97/20.21 inference(symmetry,[status(thm)],[32484])).
% 29.97/20.21 tff(32486,plain,
% 29.97/20.21 ((f10(c1) = c4) <=> (f10(c1) = c1)),
% 29.97/20.21 inference(monotonicity,[status(thm)],[32485])).
% 29.97/20.21 tff(32487,plain,
% 29.97/20.21 ((f10(c1) = c1) <=> (f10(c1) = c4)),
% 29.97/20.21 inference(symmetry,[status(thm)],[32486])).
% 29.97/20.21 tff(32488,plain,
% 29.97/20.21 ((f10(c1) = c1) <=> (f6(c1, f6(c1, c2)) = c4)),
% 29.97/20.21 inference(transitivity,[status(thm)],[32487, 32482, 32480])).
% 29.97/20.21 tff(32489,plain,
% 29.97/20.21 ((~(f10(c1) = c1)) <=> (~(f6(c1, f6(c1, c2)) = c4))),
% 29.97/20.21 inference(monotonicity,[status(thm)],[32488])).
% 29.97/20.21 tff(32490,plain,
% 29.97/20.21 (~(f6(c1, f6(c1, c2)) = c4)),
% 29.97/20.21 inference(modus_ponens,[status(thm)],[3, 32489])).
% 29.97/20.21 tff(32491,plain,
% 29.97/20.21 (f6(c1, c1) = c2),
% 29.97/20.21 inference(transitivity,[status(thm)],[32412, 27490])).
% 29.97/20.21 tff(32492,plain,
% 29.97/20.21 (f2(f6(c1, c1)) = f2(c2)),
% 29.97/20.21 inference(monotonicity,[status(thm)],[32491])).
% 29.97/20.21 tff(32493,plain,
% 29.97/20.21 ((c1 = f2(f6(c1, c1))) <=> (c1 = f2(c2))),
% 29.97/20.21 inference(monotonicity,[status(thm)],[32492])).
% 29.97/20.21 tff(32494,plain,
% 29.97/20.21 ((c1 = f2(f6(c1, c1))) <=> (f2(c2) = c1)),
% 29.97/20.21 inference(transitivity,[status(thm)],[32493, 32278])).
% 29.97/20.21 tff(32495,plain,
% 29.97/20.21 ((~(c1 = f2(f6(c1, c1)))) <=> (~(f2(c2) = c1))),
% 29.97/20.21 inference(monotonicity,[status(thm)],[32494])).
% 29.97/20.21 tff(32496,plain,
% 29.97/20.21 (~(f3(c1, c1) = c4)),
% 29.97/20.21 inference(unit_resolution,[status(thm)],[32428, 1431, 480])).
% 29.97/20.21 tff(32497,plain,
% 29.97/20.21 (f3(c1, c1) = f6(c1, c1)),
% 29.97/20.21 inference(transitivity,[status(thm)],[1440, 28323, 31339])).
% 29.97/20.21 tff(32498,plain,
% 29.97/20.21 (f3(f3(c1, c1), c1) = c1),
% 29.97/20.21 inference(transitivity,[status(thm)],[31996, 32052])).
% 29.97/20.21 tff(32499,plain,
% 29.97/20.21 (big_f(f3(f3(c1, c1), c1), f3(c1, c1)) <=> big_f(c1, f6(c1, c1))),
% 29.97/20.21 inference(monotonicity,[status(thm)],[32498, 32497])).
% 29.97/20.21 tff(32500,plain,
% 29.97/20.21 (big_f(c1, f6(c1, c1)) <=> big_f(f3(f3(c1, c1), c1), f3(c1, c1))),
% 29.97/20.21 inference(symmetry,[status(thm)],[32499])).
% 29.97/20.21 tff(32501,plain,
% 29.97/20.21 (big_f(f3(f3(c1, c1), c1), f3(c1, c1))),
% 29.97/20.21 inference(modus_ponens,[status(thm)],[28185, 32500])).
% 29.97/20.21 tff(32502,plain,
% 29.97/20.21 ((f3(f3(f7(c1), c1), c1) = c1) <=> (f3(f3(c1, c1), c1) = c1)),
% 29.97/20.21 inference(monotonicity,[status(thm)],[31997])).
% 29.97/20.21 tff(32503,plain,
% 29.97/20.21 (f3(f3(c1, c1), c1) = c1),
% 29.97/20.21 inference(modus_ponens,[status(thm)],[32052, 32502])).
% 29.97/20.21 tff(32504,plain,
% 29.97/20.21 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((f3(c1, c1) = c4) | (~big_f(f3(f3(c1, c1), c1), f3(c1, c1))) | (~(f3(f3(c1, c1), c1) = c1)) | (~(c1 = f2(f6(c1, c1)))) | (~(f6(c1, c1) = c3)) | big_f(f6(c1, c1), c1))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (f3(c1, c1) = c4) | (~big_f(f3(f3(c1, c1), c1), f3(c1, c1))) | (~(f3(f3(c1, c1), c1) = c1)) | (~(c1 = f2(f6(c1, c1)))) | (~(f6(c1, c1) = c3)) | big_f(f6(c1, c1), c1))),
% 29.97/20.21 inference(rewrite,[status(thm)],[])).
% 29.97/20.21 tff(32505,plain,
% 29.97/20.21 (((~(f6(c1, c1) = c3)) | (~(c1 = f2(f6(c1, c1)))) | (f3(c1, c1) = c4) | (~(f3(f3(c1, c1), c1) = c1)) | (~big_f(f3(f3(c1, c1), c1), f3(c1, c1))) | big_f(f6(c1, c1), c1)) <=> ((f3(c1, c1) = c4) | (~big_f(f3(f3(c1, c1), c1), f3(c1, c1))) | (~(f3(f3(c1, c1), c1) = c1)) | (~(c1 = f2(f6(c1, c1)))) | (~(f6(c1, c1) = c3)) | big_f(f6(c1, c1), c1))),
% 29.97/20.21 inference(rewrite,[status(thm)],[])).
% 29.97/20.21 tff(32506,plain,
% 29.97/20.21 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(f6(c1, c1) = c3)) | (~(c1 = f2(f6(c1, c1)))) | (f3(c1, c1) = c4) | (~(f3(f3(c1, c1), c1) = c1)) | (~big_f(f3(f3(c1, c1), c1), f3(c1, c1))) | big_f(f6(c1, c1), c1))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((f3(c1, c1) = c4) | (~big_f(f3(f3(c1, c1), c1), f3(c1, c1))) | (~(f3(f3(c1, c1), c1) = c1)) | (~(c1 = f2(f6(c1, c1)))) | (~(f6(c1, c1) = c3)) | big_f(f6(c1, c1), c1)))),
% 29.97/20.21 inference(monotonicity,[status(thm)],[32505])).
% 29.97/20.21 tff(32507,plain,
% 29.97/20.21 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(f6(c1, c1) = c3)) | (~(c1 = f2(f6(c1, c1)))) | (f3(c1, c1) = c4) | (~(f3(f3(c1, c1), c1) = c1)) | (~big_f(f3(f3(c1, c1), c1), f3(c1, c1))) | big_f(f6(c1, c1), c1))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (f3(c1, c1) = c4) | (~big_f(f3(f3(c1, c1), c1), f3(c1, c1))) | (~(f3(f3(c1, c1), c1) = c1)) | (~(c1 = f2(f6(c1, c1)))) | (~(f6(c1, c1) = c3)) | big_f(f6(c1, c1), c1))),
% 29.97/20.21 inference(transitivity,[status(thm)],[32506, 32504])).
% 29.97/20.21 tff(32508,plain,
% 29.97/20.21 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(f6(c1, c1) = c3)) | (~(c1 = f2(f6(c1, c1)))) | (f3(c1, c1) = c4) | (~(f3(f3(c1, c1), c1) = c1)) | (~big_f(f3(f3(c1, c1), c1), f3(c1, c1))) | big_f(f6(c1, c1), c1))),
% 29.97/20.21 inference(quant_inst,[status(thm)],[])).
% 29.97/20.21 tff(32509,plain,
% 29.97/20.21 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (f3(c1, c1) = c4) | (~big_f(f3(f3(c1, c1), c1), f3(c1, c1))) | (~(f3(f3(c1, c1), c1) = c1)) | (~(c1 = f2(f6(c1, c1)))) | (~(f6(c1, c1) = c3)) | big_f(f6(c1, c1), c1)),
% 29.97/20.21 inference(modus_ponens,[status(thm)],[32508, 32507])).
% 29.97/20.21 tff(32510,plain,
% 29.97/20.21 ((f3(c1, c1) = c4) | (~big_f(f3(f3(c1, c1), c1), f3(c1, c1))) | (~(c1 = f2(f6(c1, c1))))),
% 29.97/20.21 inference(unit_resolution,[status(thm)],[32509, 1398, 32503, 32437, 32436])).
% 29.97/20.21 tff(32511,plain,
% 29.97/20.21 (~(c1 = f2(f6(c1, c1)))),
% 29.97/20.21 inference(unit_resolution,[status(thm)],[32510, 32501, 32496])).
% 29.97/20.21 tff(32512,plain,
% 29.97/20.21 (~(f2(c2) = c1)),
% 29.97/20.21 inference(modus_ponens,[status(thm)],[32511, 32495])).
% 29.97/20.21 tff(32513,assumption,(~(f6(c1, f6(c1, c2)) = c4)), introduced(assumption)).
% 29.97/20.21 tff(32514,plain,
% 29.97/20.21 (f3(c2, c1) = c1),
% 29.97/20.21 inference(unit_resolution,[status(thm)],[32055, 1440, 32052])).
% 29.97/20.21 tff(32515,plain,
% 29.97/20.21 (f3(f6(c1, f6(c1, c2)), c1) = f3(c2, c1)),
% 29.97/20.21 inference(monotonicity,[status(thm)],[27490])).
% 29.97/20.21 tff(32516,plain,
% 29.97/20.21 (f3(f6(c1, f6(c1, c2)), c1) = c1),
% 29.97/20.21 inference(transitivity,[status(thm)],[32515, 32514])).
% 29.97/20.21 tff(32517,plain,
% 29.97/20.21 (big_f(f3(f6(c1, f6(c1, c2)), c1), f6(c1, f6(c1, c2))) <=> big_f(c1, f6(c1, c1))),
% 29.97/20.21 inference(monotonicity,[status(thm)],[32516, 31339])).
% 29.97/20.21 tff(32518,plain,
% 29.97/20.21 (big_f(c1, f6(c1, c1)) <=> big_f(f3(f6(c1, f6(c1, c2)), c1), f6(c1, f6(c1, c2)))),
% 29.97/20.21 inference(symmetry,[status(thm)],[32517])).
% 29.97/20.21 tff(32519,plain,
% 29.97/20.21 (big_f(f3(f6(c1, f6(c1, c2)), c1), f6(c1, f6(c1, c2)))),
% 29.97/20.21 inference(modus_ponens,[status(thm)],[28185, 32518])).
% 29.97/20.21 tff(32520,plain,
% 29.97/20.21 (f3(c2, c1) = f3(f6(c1, f6(c1, c2)), c1)),
% 29.97/20.21 inference(symmetry,[status(thm)],[32515])).
% 29.97/20.21 tff(32521,plain,
% 29.97/20.21 ((f3(c2, c1) = c1) <=> (f3(f6(c1, f6(c1, c2)), c1) = c1)),
% 29.97/20.21 inference(monotonicity,[status(thm)],[32520])).
% 29.97/20.21 tff(32522,plain,
% 29.97/20.21 (f3(f6(c1, f6(c1, c2)), c1) = c1),
% 29.97/20.21 inference(modus_ponens,[status(thm)],[32514, 32521])).
% 29.97/20.21 tff(32523,plain,
% 29.97/20.21 (~(c2 = f2(c2))),
% 29.97/20.21 inference(unit_resolution,[status(thm)],[31936, 32522, 121, 1344, 32519, 32513])).
% 29.97/20.21 tff(32524,plain,
% 29.97/20.21 (~(f2(c2) = c2)),
% 29.97/20.21 inference(unit_resolution,[status(thm)],[31890, 32523])).
% 29.97/20.21 tff(32525,plain,
% 29.97/20.21 (f2(c2) = c1),
% 29.97/20.21 inference(unit_resolution,[status(thm)],[31912, 32524])).
% 29.97/20.21 tff(32526,plain,
% 29.97/20.21 ($false),
% 29.97/20.21 inference(unit_resolution,[status(thm)],[32525, 32512])).
% 29.97/20.21 tff(32527,plain,((f3(c1, c1) = c1) | (~(f6(c1, f6(c1, c2)) = c2)) | (~(f6(c1, c2) = c1)) | (~(f6(c1, c1) = c3)) | big_f(f6(c1, c1), c1) | big_f(c2, c2) | (~(c2 = c3)) | (f6(c1, f6(c1, c2)) = c4) | (~big_f(c1, f6(c1, c1))) | (~(f3(f3(f7(c1), c1), c1) = c1)) | (~(c4 = c1))), inference(lemma,lemma(discharge,[]))).
% 29.97/20.21 tff(32528,plain,
% 29.97/20.21 ($false),
% 29.97/20.21 inference(unit_resolution,[status(thm)],[32527, 32395, 32410, 32256, 1431, 32406, 121, 32411, 32490, 32477, 32476, 32388])).
% 29.97/20.21 tff(32529,plain,((f3(c1, c1) = c1) | big_f(c2, c2) | (f10(c1) = c1) | big_f(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 29.97/20.21 tff(32530,plain,
% 29.97/20.21 (f3(c1, c1) = c1),
% 29.97/20.21 inference(unit_resolution,[status(thm)],[32529, 2, 3, 121])).
% 29.97/20.21 tff(32531,plain,
% 29.97/20.21 (big_f(f3(c1, c1), c1) <=> big_f(c1, c1)),
% 29.97/20.21 inference(monotonicity,[status(thm)],[32530])).
% 29.97/20.21 tff(32532,plain,
% 29.97/20.21 (big_f(c1, c1) <=> big_f(f3(c1, c1), c1)),
% 29.97/20.21 inference(symmetry,[status(thm)],[32531])).
% 29.97/20.21 tff(32533,plain,
% 29.97/20.21 (big_f(f3(c1, c1), c1)),
% 29.97/20.21 inference(modus_ponens,[status(thm)],[31714, 32532])).
% 29.97/20.21 tff(32534,plain,
% 29.97/20.21 ((f10(c1) = c4) <=> (f10(c1) = c1)),
% 29.97/20.21 inference(monotonicity,[status(thm)],[31836])).
% 29.97/20.21 tff(32535,plain,
% 29.97/20.21 ((f10(c1) = c1) <=> (f10(c1) = c4)),
% 29.97/20.21 inference(symmetry,[status(thm)],[32534])).
% 29.97/20.21 tff(32536,plain,
% 29.97/20.21 ((~(f10(c1) = c1)) <=> (~(f10(c1) = c4))),
% 29.97/20.21 inference(monotonicity,[status(thm)],[32535])).
% 29.97/20.21 tff(32537,plain,
% 29.97/20.21 (~(f10(c1) = c4)),
% 29.97/20.21 inference(modus_ponens,[status(thm)],[3, 32536])).
% 29.97/20.21 tff(32538,plain,
% 29.97/20.21 (big_f(f3(f10(c1), c1), f10(c1)) <=> big_f(f3(c2, c1), f10(c1))),
% 29.97/20.21 inference(symmetry,[status(thm)],[31361])).
% 29.97/20.21 tff(32539,plain,
% 29.97/20.21 (big_f(f3(f10(c1), c1), f10(c1)) <=> big_f(f3(c2, c1), c2)),
% 29.97/20.21 inference(transitivity,[status(thm)],[32538, 32104])).
% 29.97/20.21 tff(32540,plain,
% 29.97/20.21 ((~big_f(f3(f10(c1), c1), f10(c1))) <=> (~big_f(f3(c2, c1), c2))),
% 29.97/20.21 inference(monotonicity,[status(thm)],[32539])).
% 29.97/20.21 tff(32541,plain,
% 29.97/20.21 (~big_f(f3(c2, c1), c2)),
% 29.97/20.21 inference(modus_ponens,[status(thm)],[1061, 32540])).
% 29.97/20.21 tff(32542,plain,
% 29.97/20.21 (big_f(f3(f10(c1), c1), f10(c1)) <=> big_f(c1, f10(c1))),
% 29.97/20.21 inference(monotonicity,[status(thm)],[32305])).
% 29.97/20.21 tff(32543,plain,
% 29.97/20.21 (big_f(c1, f10(c1)) <=> big_f(f3(f10(c1), c1), f10(c1))),
% 29.97/20.21 inference(symmetry,[status(thm)],[32542])).
% 29.97/20.21 tff(32544,plain,
% 29.97/20.21 (big_f(f3(f10(c1), c1), f10(c1))),
% 29.97/20.21 inference(modus_ponens,[status(thm)],[3023, 32543])).
% 29.97/20.21 tff(32545,plain,
% 29.97/20.21 ($false),
% 29.97/20.21 inference(unit_resolution,[status(thm)],[1061, 32544])).
% 29.97/20.21 tff(32546,plain,((~(f3(f10(c1), c1) = c1)) | big_f(f3(f10(c1), c1), f10(c1)) | (~big_f(c1, f10(c1)))), inference(lemma,lemma(discharge,[]))).
% 29.97/20.21 tff(32547,plain,
% 29.97/20.21 (~(f3(f10(c1), c1) = c1)),
% 29.97/20.21 inference(unit_resolution,[status(thm)],[32546, 1061, 30400])).
% 29.97/20.21 tff(32548,plain,
% 29.97/20.21 ((f10(c1) = c1) <=> (c2 = c4)),
% 29.97/20.21 inference(transitivity,[status(thm)],[32535, 30362])).
% 29.97/20.21 tff(32549,plain,
% 29.97/20.21 ((~(f10(c1) = c1)) <=> (~(c2 = c4))),
% 29.97/20.21 inference(monotonicity,[status(thm)],[32548])).
% 29.97/20.21 tff(32550,plain,
% 29.97/20.21 (~(c2 = c4)),
% 29.97/20.21 inference(modus_ponens,[status(thm)],[3, 32549])).
% 29.97/20.21 tff(32551,plain,
% 29.97/20.21 ($false),
% 29.97/20.21 inference(unit_resolution,[status(thm)],[32322, 32550, 1335, 121, 32547, 15, 32541, 2, 32537, 1061])).
% 29.97/20.21 tff(32552,plain,((~(c3 = c2)) | big_f(c2, c2) | big_f(c2, c1) | big_f(f3(f10(c1), c1), f10(c1)) | (f10(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.97/20.21 tff(32553,plain,
% 29.97/20.21 (~(c3 = c2)),
% 29.97/20.21 inference(unit_resolution,[status(thm)],[32552, 1061, 2, 121, 3])).
% 29.97/20.21 tff(32554,plain,
% 29.97/20.21 (c3 = c1),
% 29.97/20.21 inference(unit_resolution,[status(thm)],[180, 32553])).
% 29.97/20.21 tff(32555,plain,
% 29.97/20.21 (c1 = c3),
% 29.97/20.21 inference(unit_resolution,[status(thm)],[175, 32554])).
% 29.97/20.21 tff(32556,plain,
% 29.97/20.21 (c1 = c4),
% 29.97/20.21 inference(unit_resolution,[status(thm)],[32097, 32555, 3, 32533, 32530])).
% 29.97/20.21 tff(32557,plain,
% 29.97/20.21 (c4 = c1),
% 29.97/20.21 inference(symmetry,[status(thm)],[32556])).
% 29.97/20.21 tff(32558,plain,
% 29.97/20.21 (f10(c1) = c4),
% 29.97/20.21 inference(unit_resolution,[status(thm)],[32124, 32555, 3, 1061, 32547])).
% 29.97/20.21 tff(32559,plain,
% 29.97/20.21 (f10(c1) = c1),
% 29.97/20.21 inference(transitivity,[status(thm)],[32558, 32557])).
% 29.97/20.22 tff(32560,plain,
% 29.97/20.22 ($false),
% 29.97/20.22 inference(unit_resolution,[status(thm)],[3, 32559])).
% 29.97/20.22 tff(32561,plain,(big_f(f3(f10(c1), c1), f10(c1)) | (f10(c1) = c1) | big_f(c2, c1) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 29.97/20.22 tff(32562,plain,
% 29.97/20.22 (big_f(f3(f10(c1), c1), f10(c1))),
% 29.97/20.22 inference(unit_resolution,[status(thm)],[32561, 2, 3, 121])).
% 29.97/20.22 tff(32563,plain,
% 29.97/20.22 (c1 = c3),
% 29.97/20.22 inference(unit_resolution,[status(thm)],[175, 24304])).
% 29.97/20.22 tff(32564,plain,
% 29.97/20.22 (~big_f(c2, c4)),
% 29.97/20.22 inference(unit_resolution,[status(thm)],[6521, 24305, 79])).
% 29.97/20.22 tff(32565,plain,
% 29.97/20.22 ((c2 = c3) <=> (c2 = c1)),
% 29.97/20.22 inference(monotonicity,[status(thm)],[24304])).
% 29.97/20.22 tff(32566,plain,
% 29.97/20.22 ((c2 = c1) <=> (c2 = c3)),
% 29.97/20.22 inference(symmetry,[status(thm)],[32565])).
% 29.97/20.22 tff(32567,plain,
% 29.97/20.22 ((~(c2 = c1)) <=> (~(c2 = c3))),
% 29.97/20.22 inference(monotonicity,[status(thm)],[32566])).
% 29.97/20.22 tff(32568,plain,
% 29.97/20.22 (~(c2 = c3)),
% 29.97/20.22 inference(modus_ponens,[status(thm)],[75, 32567])).
% 29.97/20.22 tff(32569,plain,
% 29.97/20.22 (big_f(c2, f1(c2, c1))),
% 29.97/20.22 inference(unit_resolution,[status(thm)],[10099, 12187, 10089, 377, 3865])).
% 29.97/20.22 tff(32570,plain,
% 29.97/20.22 ($false),
% 29.97/20.22 inference(unit_resolution,[status(thm)],[32569, 29073])).
% 29.97/20.22 tff(32571,plain,((f1(c2, c1) = c1) | big_f(c2, c2) | (~(c2 = f4(c4))) | (c2 = c3) | big_f(c2, c4)), inference(lemma,lemma(discharge,[]))).
% 29.97/20.22 tff(32572,plain,
% 29.97/20.22 (f1(c2, c1) = c1),
% 29.97/20.22 inference(unit_resolution,[status(thm)],[32571, 2602, 32568, 32564, 121])).
% 29.97/20.22 tff(32573,plain,
% 29.97/20.22 (f1(c2, c1) = f1(f10(c1), c1)),
% 29.97/20.22 inference(monotonicity,[status(thm)],[293])).
% 29.97/20.22 tff(32574,plain,
% 29.97/20.22 ((f1(c2, c1) = c3) <=> (f1(f10(c1), c1) = c1)),
% 29.97/20.22 inference(monotonicity,[status(thm)],[32573, 5090])).
% 29.97/20.22 tff(32575,plain,
% 29.97/20.22 ((f1(f10(c1), c1) = c1) <=> (f1(c2, c1) = c3)),
% 29.97/20.22 inference(symmetry,[status(thm)],[32574])).
% 29.97/20.22 tff(32576,plain,
% 29.97/20.22 ((f1(c2, c1) = c1) <=> (f1(f10(c1), c1) = c1)),
% 29.97/20.22 inference(monotonicity,[status(thm)],[32573])).
% 29.97/20.22 tff(32577,plain,
% 29.97/20.22 ((f1(c2, c1) = c1) <=> (f1(c2, c1) = c3)),
% 29.97/20.22 inference(transitivity,[status(thm)],[32576, 32575])).
% 29.97/20.22 tff(32578,plain,
% 29.97/20.22 (f1(c2, c1) = c3),
% 29.97/20.22 inference(modus_ponens,[status(thm)],[11485, 32577])).
% 29.97/20.22 tff(32579,assumption,(~(f1(c2, c1) = c3)), introduced(assumption)).
% 29.97/20.22 tff(32580,plain,
% 29.97/20.22 ($false),
% 29.97/20.22 inference(unit_resolution,[status(thm)],[32579, 32578])).
% 29.97/20.22 tff(32581,plain,((~(f1(c2, c1) = c1)) | (f1(c2, c1) = c3) | (~(c1 = c3)) | (~(f10(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.97/20.22 tff(32582,plain,
% 29.97/20.22 (f1(c2, c1) = c3),
% 29.97/20.22 inference(unit_resolution,[status(thm)],[32581, 32572, 16, 32563])).
% 29.97/20.22 tff(32583,plain,
% 29.97/20.22 (big_f(f1(c2, c1), f1(c2, c1)) <=> big_f(c1, c1)),
% 29.97/20.22 inference(monotonicity,[status(thm)],[32572, 32572])).
% 29.97/20.22 tff(32584,plain,
% 29.97/20.22 (big_f(c1, c1) <=> big_f(f1(c2, c1), f1(c2, c1))),
% 29.97/20.22 inference(symmetry,[status(thm)],[32583])).
% 29.97/20.22 tff(32585,plain,
% 29.97/20.22 (big_f(f1(c2, c1), f1(c2, c1))),
% 29.97/20.22 inference(modus_ponens,[status(thm)],[31714, 32584])).
% 29.97/20.22 tff(32586,plain,
% 29.97/20.22 (big_f(f1(c2, c1), c2) <=> big_f(c1, c2)),
% 29.97/20.22 inference(monotonicity,[status(thm)],[32572])).
% 29.97/20.22 tff(32587,plain,
% 29.97/20.22 (big_f(c1, c2) <=> big_f(f1(c2, c1), c2)),
% 29.97/20.22 inference(symmetry,[status(thm)],[32586])).
% 29.97/20.22 tff(32588,plain,
% 29.97/20.22 (big_f(f1(c2, c1), c2)),
% 29.97/20.22 inference(modus_ponens,[status(thm)],[30354, 32587])).
% 29.97/20.22 tff(32589,plain,
% 29.97/20.22 ((f1(c2, c1) = c2) <=> (c1 = c2)),
% 29.97/20.22 inference(monotonicity,[status(thm)],[32572])).
% 29.97/20.22 tff(32590,plain,
% 29.97/20.22 ((f1(c2, c1) = c2) <=> (c2 = c1)),
% 29.97/20.22 inference(transitivity,[status(thm)],[32589, 1])).
% 29.97/20.22 tff(32591,plain,
% 29.97/20.22 ((c2 = c1) <=> (f1(c2, c1) = c2)),
% 29.97/20.22 inference(symmetry,[status(thm)],[32590])).
% 29.97/20.22 tff(32592,plain,
% 29.97/20.22 ((~(c2 = c1)) <=> (~(f1(c2, c1) = c2))),
% 29.97/20.22 inference(monotonicity,[status(thm)],[32591])).
% 29.97/20.22 tff(32593,plain,
% 29.97/20.22 (~(f1(c2, c1) = c2)),
% 29.97/20.22 inference(modus_ponens,[status(thm)],[75, 32592])).
% 29.97/20.22 tff(32594,plain,
% 29.97/20.22 (~(f1(c2, c1) = f2(f1(c2, c1)))),
% 29.97/20.22 inference(unit_resolution,[status(thm)],[11184, 32593, 2602, 32564, 32582, 32588])).
% 29.97/20.22 tff(32595,plain,
% 29.97/20.22 ($false),
% 29.97/20.22 inference(unit_resolution,[status(thm)],[11146, 32594, 32585, 32564, 2602, 32582])).
% 29.97/20.22 tff(32596,plain,((~(f4(c4) = c2)) | (~(f10(c1) = c2)) | big_f(c2, c2) | big_f(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 29.97/20.22 tff(32597,plain,
% 29.97/20.22 (~(f4(c4) = c2)),
% 29.97/20.22 inference(unit_resolution,[status(thm)],[32596, 2, 121, 15])).
% 29.97/20.22 tff(32598,plain,
% 29.97/20.22 (f4(c4) = c1),
% 29.97/20.22 inference(unit_resolution,[status(thm)],[11750, 32597])).
% 29.97/20.22 tff(32599,plain,
% 29.97/20.22 (f7(f4(c4)) = f7(c1)),
% 29.97/20.22 inference(monotonicity,[status(thm)],[32598])).
% 29.97/20.22 tff(32600,plain,
% 29.97/20.22 (f7(f4(c4)) = c1),
% 29.97/20.22 inference(transitivity,[status(thm)],[32599, 25791])).
% 29.97/20.22 tff(32601,plain,
% 29.97/20.22 (f3(f7(f4(c4)), f4(c4)) = f3(c1, c1)),
% 29.97/20.22 inference(monotonicity,[status(thm)],[32600, 32598])).
% 29.97/20.22 tff(32602,plain,
% 29.97/20.22 (f3(c1, c1) = f3(f7(f4(c4)), f4(c4))),
% 29.97/20.22 inference(symmetry,[status(thm)],[32601])).
% 29.97/20.22 tff(32603,plain,
% 29.97/20.22 (c1 = f3(c1, c1)),
% 29.97/20.22 inference(symmetry,[status(thm)],[32530])).
% 29.97/20.22 tff(32604,plain,
% 29.97/20.22 (c1 = f3(f7(f4(c4)), f4(c4))),
% 29.97/20.22 inference(transitivity,[status(thm)],[32603, 32602])).
% 29.97/20.22 tff(32605,plain,
% 29.97/20.22 (f3(f10(c1), c1) = f3(c2, f3(f7(f4(c4)), f4(c4)))),
% 29.97/20.22 inference(monotonicity,[status(thm)],[15, 32604])).
% 29.97/20.22 tff(32606,plain,
% 29.97/20.22 (f3(c2, f3(f7(f4(c4)), f4(c4))) = f3(f10(c1), c1)),
% 29.97/20.22 inference(symmetry,[status(thm)],[32605])).
% 29.97/20.22 tff(32607,plain,
% 29.97/20.22 ((f3(c2, f3(f7(f4(c4)), f4(c4))) = c1) <=> (f3(f10(c1), c1) = c1)),
% 29.97/20.22 inference(monotonicity,[status(thm)],[32606])).
% 29.97/20.22 tff(32608,plain,
% 29.97/20.22 (big_f(f3(c2, c1), c2)),
% 29.97/20.22 inference(unit_resolution,[status(thm)],[31898, 32562, 15])).
% 29.97/20.22 tff(32609,plain,
% 29.97/20.22 (~(big_f(c2, c2) <=> big_f(f3(c2, c1), c2))),
% 29.97/20.22 inference(unit_resolution,[status(thm)],[32010, 32608, 121])).
% 29.97/20.22 tff(32610,plain,
% 29.97/20.22 (~(c2 = f3(c2, c1))),
% 29.97/20.22 inference(unit_resolution,[status(thm)],[32008, 32609])).
% 29.97/20.22 tff(32611,plain,
% 29.97/20.22 ((f3(c2, c1) = c2) <=> (c2 = f3(c2, c1))),
% 29.97/20.22 inference(commutativity,[status(thm)],[])).
% 29.97/20.22 tff(32612,plain,
% 29.97/20.22 (f3(f10(c1), c1) = f3(c2, c1)),
% 29.97/20.22 inference(symmetry,[status(thm)],[32293])).
% 29.97/20.22 tff(32613,plain,
% 29.97/20.22 (f3(f7(f4(c4)), f4(c4)) = f3(c1, c1)),
% 29.97/20.22 inference(monotonicity,[status(thm)],[31094, 11752])).
% 29.97/20.22 tff(32614,plain,
% 29.97/20.22 (f3(f7(f4(c4)), f4(c4)) = c1),
% 29.97/20.22 inference(transitivity,[status(thm)],[32613, 1938])).
% 29.97/20.22 tff(32615,plain,
% 29.97/20.22 (f3(c2, f3(f7(f4(c4)), f4(c4))) = f3(f10(c1), c1)),
% 29.97/20.22 inference(monotonicity,[status(thm)],[293, 32614])).
% 29.97/20.22 tff(32616,plain,
% 29.97/20.22 (f3(c2, f3(f7(f4(c4)), f4(c4))) = f3(c2, c1)),
% 29.97/20.22 inference(transitivity,[status(thm)],[32615, 32612])).
% 29.97/20.22 tff(32617,plain,
% 29.97/20.22 ((f3(c2, f3(f7(f4(c4)), f4(c4))) = c2) <=> (f3(c2, c1) = c2)),
% 29.97/20.22 inference(monotonicity,[status(thm)],[32616])).
% 29.97/20.22 tff(32618,plain,
% 29.97/20.22 ((f3(c2, f3(f7(f4(c4)), f4(c4))) = c2) <=> (c2 = f3(c2, c1))),
% 29.97/20.22 inference(transitivity,[status(thm)],[32617, 32611])).
% 29.97/20.22 tff(32619,assumption,(f3(c2, f3(f7(f4(c4)), f4(c4))) = c2), introduced(assumption)).
% 29.97/20.22 tff(32620,plain,
% 29.97/20.22 (c2 = f3(c2, c1)),
% 29.97/20.22 inference(modus_ponens,[status(thm)],[32619, 32618])).
% 29.97/20.22 tff(32621,plain,
% 29.97/20.22 ($false),
% 29.97/20.22 inference(unit_resolution,[status(thm)],[32000, 32620])).
% 29.97/20.22 tff(32622,plain,((~(f3(c2, f3(f7(f4(c4)), f4(c4))) = c2)) | (c2 = f3(c2, c1)) | (~(f3(c1, c1) = c1)) | (~(f4(c4) = c1)) | (~(f10(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.97/20.22 tff(32623,plain,
% 29.97/20.22 (~(f3(c2, f3(f7(f4(c4)), f4(c4))) = c2)),
% 29.97/20.22 inference(unit_resolution,[status(thm)],[32622, 32610, 32530, 32598, 15])).
% 29.97/20.22 tff(32624,plain,
% 29.97/20.22 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f3(c2, f3(f7(f4(c4)), f4(c4))) = c1) | (f3(c2, f3(f7(f4(c4)), f4(c4))) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f3(c2, f3(f7(f4(c4)), f4(c4))) = c1) | (f3(c2, f3(f7(f4(c4)), f4(c4))) = c2))),
% 29.97/20.22 inference(rewrite,[status(thm)],[])).
% 29.97/20.22 tff(32625,plain,
% 29.97/20.22 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f3(c2, f3(f7(f4(c4)), f4(c4))) = c1) | (f3(c2, f3(f7(f4(c4)), f4(c4))) = c2))),
% 29.97/20.22 inference(quant_inst,[status(thm)],[])).
% 29.97/20.22 tff(32626,plain,
% 29.97/20.22 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f3(c2, f3(f7(f4(c4)), f4(c4))) = c1) | (f3(c2, f3(f7(f4(c4)), f4(c4))) = c2)),
% 29.97/20.22 inference(modus_ponens,[status(thm)],[32625, 32624])).
% 29.97/20.22 tff(32627,plain,
% 29.97/20.22 ((f3(c2, f3(f7(f4(c4)), f4(c4))) = c1) | (f3(c2, f3(f7(f4(c4)), f4(c4))) = c2)),
% 29.97/20.22 inference(unit_resolution,[status(thm)],[32626, 10])).
% 29.97/20.22 tff(32628,plain,
% 29.97/20.22 (f3(c2, f3(f7(f4(c4)), f4(c4))) = c1),
% 29.97/20.22 inference(unit_resolution,[status(thm)],[32627, 32623])).
% 29.97/20.22 tff(32629,plain,
% 29.97/20.22 (f3(f10(c1), c1) = c1),
% 29.97/20.22 inference(modus_ponens,[status(thm)],[32628, 32607])).
% 29.97/20.22 tff(32630,plain,
% 29.97/20.22 (big_f(f3(c1, c1), c1) <=> big_f(c1, c1)),
% 29.97/20.22 inference(monotonicity,[status(thm)],[1938])).
% 29.97/20.22 tff(32631,plain,
% 29.97/20.22 (big_f(c1, c1) <=> big_f(f3(c1, c1), c1)),
% 29.97/20.22 inference(symmetry,[status(thm)],[32630])).
% 29.97/20.22 tff(32632,plain,
% 29.97/20.22 (big_f(f3(c1, c1), c1)),
% 29.97/20.22 inference(modus_ponens,[status(thm)],[31714, 32631])).
% 29.97/20.22 tff(32633,plain,
% 29.97/20.22 (c1 = c4),
% 29.97/20.22 inference(unit_resolution,[status(thm)],[32097, 5080, 3, 32632, 1938])).
% 29.97/20.22 tff(32634,plain,
% 29.97/20.22 (c4 = c1),
% 29.97/20.22 inference(symmetry,[status(thm)],[32633])).
% 29.97/20.22 tff(32635,plain,
% 29.97/20.22 ((f10(c1) = c4) <=> (f10(c1) = c1)),
% 29.97/20.22 inference(monotonicity,[status(thm)],[32634])).
% 29.97/20.22 tff(32636,plain,
% 29.97/20.22 ((f10(c1) = c1) <=> (f10(c1) = c4)),
% 29.97/20.22 inference(symmetry,[status(thm)],[32635])).
% 29.97/20.22 tff(32637,plain,
% 29.97/20.22 ((~(f10(c1) = c1)) <=> (~(f10(c1) = c4))),
% 29.97/20.22 inference(monotonicity,[status(thm)],[32636])).
% 29.97/20.22 tff(32638,plain,
% 29.97/20.22 (~(f10(c1) = c4)),
% 29.97/20.22 inference(modus_ponens,[status(thm)],[3, 32637])).
% 29.97/20.22 tff(32639,plain,
% 29.97/20.22 ((~(c1 = c3)) | (c1 = f2(c1)) | (f10(c1) = c4)),
% 29.97/20.22 inference(unit_resolution,[status(thm)],[32143, 7051, 32305, 31895, 31714])).
% 29.97/20.22 tff(32640,plain,
% 29.97/20.22 (c1 = f2(c1)),
% 29.97/20.22 inference(unit_resolution,[status(thm)],[32639, 32638, 5080])).
% 29.97/20.22 tff(32641,plain,
% 29.97/20.22 (f2(c1) = c1),
% 29.97/20.22 inference(symmetry,[status(thm)],[32640])).
% 29.97/20.22 tff(32642,plain,
% 29.97/20.22 ((~(c1 = c3)) | (f10(c1) = c4) | (f10(c1) = f2(c1))),
% 29.97/20.22 inference(unit_resolution,[status(thm)],[32380, 7051, 30400, 32305, 31895])).
% 29.97/20.22 tff(32643,plain,
% 29.97/20.22 (f10(c1) = f2(c1)),
% 29.97/20.22 inference(unit_resolution,[status(thm)],[32642, 32638, 5080])).
% 29.97/20.22 tff(32644,plain,
% 29.97/20.22 (f10(c1) = c1),
% 29.97/20.22 inference(transitivity,[status(thm)],[32643, 32641])).
% 29.97/20.22 tff(32645,plain,
% 29.97/20.22 ($false),
% 29.97/20.22 inference(unit_resolution,[status(thm)],[3, 32644])).
% 29.97/20.22 tff(32646,plain,((~(c1 = c3)) | (f10(c1) = c1) | (~(f3(f10(c1), c1) = c1)) | (~big_f(f3(f10(c1), c1), f10(c1))) | (~(f3(c1, c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.97/20.22 tff(32647,plain,
% 29.97/20.22 (~(c1 = c3)),
% 29.97/20.22 inference(unit_resolution,[status(thm)],[32646, 32629, 3, 32562, 32530])).
% 29.97/20.22 tff(32648,plain,
% 29.97/20.22 (~(c3 = c1)),
% 29.97/20.22 inference(unit_resolution,[status(thm)],[175, 32647])).
% 29.97/20.22 tff(32649,plain,
% 29.97/20.22 (c3 = c2),
% 29.97/20.22 inference(unit_resolution,[status(thm)],[180, 32648])).
% 29.97/20.22 tff(32650,plain,
% 29.97/20.22 (f10(c1) = c3),
% 29.97/20.22 inference(modus_ponens,[status(thm)],[32649, 27300])).
% 29.97/20.22 tff(32651,plain,
% 29.97/20.22 (~(c4 = c2)),
% 29.97/20.22 inference(unit_resolution,[status(thm)],[27535, 32649, 31714, 121, 2])).
% 29.97/20.22 tff(32652,plain,
% 29.97/20.22 (c4 = c1),
% 29.97/20.22 inference(unit_resolution,[status(thm)],[461, 32651])).
% 29.97/20.22 tff(32653,plain,
% 29.97/20.22 ((f10(c1) = c4) <=> (f10(c1) = c1)),
% 29.97/20.22 inference(monotonicity,[status(thm)],[32652])).
% 29.97/20.22 tff(32654,plain,
% 29.97/20.22 ((f10(c1) = c1) <=> (f10(c1) = c4)),
% 29.97/20.22 inference(symmetry,[status(thm)],[32653])).
% 29.97/20.22 tff(32655,plain,
% 29.97/20.22 ((~(f10(c1) = c1)) <=> (~(f10(c1) = c4))),
% 29.97/20.22 inference(monotonicity,[status(thm)],[32654])).
% 29.97/20.22 tff(32656,plain,
% 29.97/20.22 (~(f10(c1) = c4)),
% 29.97/20.22 inference(modus_ponens,[status(thm)],[3, 32655])).
% 29.97/20.22 tff(32657,plain,
% 29.97/20.22 ((f10(c1) = c4) | (~(f10(c1) = c3)) | (~(f10(c1) = f2(f10(c1))))),
% 29.97/20.22 inference(unit_resolution,[status(thm)],[32348, 1398, 32629, 32562, 26001])).
% 29.97/20.22 tff(32658,plain,
% 29.97/20.22 (~(f10(c1) = f2(f10(c1)))),
% 29.97/20.22 inference(unit_resolution,[status(thm)],[32657, 32656, 32650])).
% 29.97/20.22 tff(32659,plain,
% 29.97/20.22 (~(f2(c2) = c2)),
% 29.97/20.22 inference(modus_ponens,[status(thm)],[32658, 31730])).
% 29.97/20.22 tff(32660,plain,
% 29.97/20.22 ((f10(c1) = c4) | (~(f10(c1) = c3)) | (~(c1 = f2(f10(c1))))),
% 29.97/20.22 inference(unit_resolution,[status(thm)],[31956, 1398, 32629, 32562, 32339])).
% 29.97/20.22 tff(32661,plain,
% 29.97/20.22 (~(c1 = f2(f10(c1)))),
% 29.97/20.22 inference(unit_resolution,[status(thm)],[32660, 32656, 32650])).
% 29.97/20.22 tff(32662,plain,
% 29.97/20.22 (~(f2(c2) = c1)),
% 29.97/20.22 inference(modus_ponens,[status(thm)],[32661, 32280])).
% 29.97/20.22 tff(32663,plain,
% 29.97/20.22 ($false),
% 29.97/20.22 inference(unit_resolution,[status(thm)],[31912, 32662, 32659])).
% 29.97/20.22 tff(32664,plain,(big_f(c2, c1) | (f10(c1) = c1) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 29.97/20.22 tff(32665,plain,
% 29.97/20.22 (big_f(c2, c1)),
% 29.97/20.22 inference(unit_resolution,[status(thm)],[32664, 3, 121])).
% 29.97/20.22 tff(32666,plain,
% 29.97/20.22 (big_f(f10(c1), c1)),
% 29.97/20.22 inference(modus_ponens,[status(thm)],[32665, 31007])).
% 29.97/20.22 tff(32667,plain,
% 29.97/20.22 (big_f(f10(c1), f10(f10(c1))) <=> big_f(f10(c1), c1)),
% 29.97/20.22 inference(monotonicity,[status(thm)],[24861])).
% 29.97/20.22 tff(32668,plain,
% 29.97/20.22 (big_f(f10(c1), c1) <=> big_f(f10(c1), f10(f10(c1)))),
% 29.97/20.22 inference(symmetry,[status(thm)],[32667])).
% 29.97/20.22 tff(32669,plain,
% 29.97/20.22 (big_f(f10(c1), c1) <=> big_f(c2, f10(c2))),
% 29.97/20.22 inference(transitivity,[status(thm)],[32668, 31002])).
% 29.97/20.22 tff(32670,plain,
% 29.97/20.22 (big_f(c2, f10(c2))),
% 29.97/20.22 inference(modus_ponens,[status(thm)],[32666, 32669])).
% 29.97/20.22 tff(32671,plain,
% 29.97/20.22 (big_f(f7(f10(c1)), c1) <=> big_f(c1, c1)),
% 29.97/20.22 inference(monotonicity,[status(thm)],[18820])).
% 29.97/20.22 tff(32672,plain,
% 29.97/20.22 (big_f(c1, c1) <=> big_f(f7(f10(c1)), c1)),
% 29.97/20.22 inference(symmetry,[status(thm)],[32671])).
% 29.97/20.22 tff(32673,plain,
% 29.97/20.22 (big_f(f7(f10(c1)), c1)),
% 29.97/20.22 inference(modus_ponens,[status(thm)],[31714, 32672])).
% 29.97/20.22 tff(32674,plain,
% 29.97/20.22 (big_f(f7(c2), c1)),
% 29.97/20.22 inference(unit_resolution,[status(thm)],[20926, 22, 31714, 94])).
% 29.97/20.22 tff(32675,plain,
% 29.97/20.22 (big_f(f7(c2), f10(c2))),
% 29.97/20.22 inference(unit_resolution,[status(thm)],[21331, 32674, 94])).
% 29.97/20.22 tff(32676,plain,
% 29.97/20.22 (big_f(f7(f10(c1)), f10(c1))),
% 29.97/20.22 inference(unit_resolution,[status(thm)],[27977, 22, 31714, 27307, 89, 3])).
% 29.97/20.22 tff(32677,plain,
% 29.97/20.22 (big_f(f7(c2), c2) <=> big_f(f7(f10(c1)), f10(c1))),
% 29.97/20.22 inference(monotonicity,[status(thm)],[6342, 293])).
% 29.97/20.22 tff(32678,plain,
% 29.97/20.22 ((~big_f(f7(c2), c2)) <=> (~big_f(f7(f10(c1)), f10(c1)))),
% 29.97/20.22 inference(monotonicity,[status(thm)],[32677])).
% 29.97/20.22 tff(32679,plain,
% 29.97/20.22 (~big_f(f7(f10(c1)), f10(c1))),
% 29.97/20.22 inference(modus_ponens,[status(thm)],[1521, 32678])).
% 29.97/20.22 tff(32680,plain,
% 29.97/20.22 ($false),
% 29.97/20.22 inference(unit_resolution,[status(thm)],[24967, 32679])).
% 29.97/20.22 tff(32681,plain,(big_f(f7(c2), c2) | (~big_f(f7(f10(c1)), f10(c1))) | (~(f10(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.97/20.22 tff(32682,plain,
% 29.97/20.22 (big_f(f7(c2), c2)),
% 29.97/20.22 inference(unit_resolution,[status(thm)],[32681, 32676, 15])).
% 29.97/20.22 tff(32683,plain,
% 29.97/20.22 (c2 = f8(c2)),
% 29.97/20.22 inference(unit_resolution,[status(thm)],[12312, 32682, 89, 12291, 17, 32675])).
% 29.97/20.22 tff(32684,plain,
% 29.97/20.22 (f8(c2) = c2),
% 29.97/20.22 inference(symmetry,[status(thm)],[32683])).
% 29.97/20.22 tff(32685,plain,
% 29.97/20.22 (f8(f10(c1)) = f10(c1)),
% 29.97/20.22 inference(transitivity,[status(thm)],[13827, 32684, 5571])).
% 29.97/20.22 tff(32686,plain,
% 29.97/20.22 ((c1 = f8(f10(c1))) <=> (c1 = f10(c1))),
% 29.97/20.22 inference(monotonicity,[status(thm)],[32685])).
% 29.97/20.22 tff(32687,plain,
% 29.97/20.22 ((c1 = f8(f10(c1))) <=> (f10(c1) = c1)),
% 29.97/20.22 inference(transitivity,[status(thm)],[32686, 18819])).
% 29.97/20.22 tff(32688,plain,
% 29.97/20.22 ((f10(c1) = c1) <=> (c1 = f8(f10(c1)))),
% 29.97/20.22 inference(symmetry,[status(thm)],[32687])).
% 29.97/20.22 tff(32689,plain,
% 29.97/20.22 ((~(f10(c1) = c1)) <=> (~(c1 = f8(f10(c1))))),
% 29.97/20.22 inference(monotonicity,[status(thm)],[32688])).
% 29.97/20.22 tff(32690,plain,
% 29.97/20.22 (~(c1 = f8(f10(c1)))),
% 29.97/20.22 inference(modus_ponens,[status(thm)],[3, 32689])).
% 29.97/20.22 tff(32691,plain,
% 29.97/20.22 (big_f(c1, f10(f10(c1)))),
% 29.97/20.22 inference(modus_ponens,[status(thm)],[31714, 24959])).
% 29.97/20.22 tff(32692,plain,
% 29.97/20.22 (~(f10(f10(c1)) = f10(c1))),
% 29.97/20.22 inference(modus_ponens,[status(thm)],[89, 30756])).
% 29.97/20.22 tff(32693,plain,
% 29.97/20.22 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (~big_f(f7(f10(c1)), c1)) | (c1 = f5(f10(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (~big_f(f7(f10(c1)), c1)) | (c1 = f5(f10(c1))))),
% 29.97/20.22 inference(rewrite,[status(thm)],[])).
% 29.97/20.22 tff(32694,plain,
% 29.97/20.22 (((f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (f7(f10(c1)) = f10(c1)) | (c1 = f5(f10(c1))) | (~big_f(f7(f10(c1)), c1))) <=> ((f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (~big_f(f7(f10(c1)), c1)) | (c1 = f5(f10(c1))))),
% 29.97/20.22 inference(rewrite,[status(thm)],[])).
% 29.97/20.22 tff(32695,plain,
% 29.97/20.22 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (f7(f10(c1)) = f10(c1)) | (c1 = f5(f10(c1))) | (~big_f(f7(f10(c1)), c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (~big_f(f7(f10(c1)), c1)) | (c1 = f5(f10(c1)))))),
% 29.97/20.22 inference(monotonicity,[status(thm)],[32694])).
% 29.97/20.22 tff(32696,plain,
% 29.97/20.22 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (f7(f10(c1)) = f10(c1)) | (c1 = f5(f10(c1))) | (~big_f(f7(f10(c1)), c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (~big_f(f7(f10(c1)), c1)) | (c1 = f5(f10(c1))))),
% 29.97/20.22 inference(transitivity,[status(thm)],[32695, 32693])).
% 29.97/20.22 tff(32697,plain,
% 29.97/20.22 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (f7(f10(c1)) = f10(c1)) | (c1 = f5(f10(c1))) | (~big_f(f7(f10(c1)), c1)))),
% 29.97/20.22 inference(quant_inst,[status(thm)],[])).
% 29.97/20.22 tff(32698,plain,
% 29.97/20.22 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (~big_f(f7(f10(c1)), c1)) | (c1 = f5(f10(c1)))),
% 29.97/20.22 inference(modus_ponens,[status(thm)],[32697, 32696])).
% 29.97/20.22 tff(32699,plain,
% 29.97/20.22 ((c1 = f8(f10(c1))) | (~big_f(f7(f10(c1)), c1)) | (c1 = f5(f10(c1)))),
% 29.97/20.22 inference(unit_resolution,[status(thm)],[32698, 1659, 32692, 26623, 32691])).
% 29.97/20.22 tff(32700,plain,
% 29.97/20.22 (c1 = f5(f10(c1))),
% 29.97/20.22 inference(unit_resolution,[status(thm)],[32699, 32690, 32673])).
% 29.97/20.22 tff(32701,plain,
% 29.97/20.22 (f5(f10(c1)) = c1),
% 29.97/20.22 inference(symmetry,[status(thm)],[32700])).
% 29.97/20.22 tff(32702,plain,
% 29.97/20.22 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (f10(c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f10(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (f10(c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f10(c1))))),
% 29.97/20.22 inference(rewrite,[status(thm)],[])).
% 29.97/20.22 tff(32703,plain,
% 29.97/20.22 (((f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (f7(f10(c1)) = f10(c1)) | (f10(c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f10(c1)))) <=> ((f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (f10(c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f10(c1))))),
% 29.97/20.22 inference(rewrite,[status(thm)],[])).
% 29.97/20.22 tff(32704,plain,
% 29.97/20.22 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (f7(f10(c1)) = f10(c1)) | (f10(c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f10(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (f10(c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f10(c1)))))),
% 29.97/20.22 inference(monotonicity,[status(thm)],[32703])).
% 29.97/20.22 tff(32705,plain,
% 29.97/20.22 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (f7(f10(c1)) = f10(c1)) | (f10(c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f10(c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (f10(c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f10(c1))))),
% 29.97/20.22 inference(transitivity,[status(thm)],[32704, 32702])).
% 29.97/20.22 tff(32706,plain,
% 29.97/20.22 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (f7(f10(c1)) = f10(c1)) | (f10(c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f10(c1))))),
% 29.97/20.22 inference(quant_inst,[status(thm)],[])).
% 29.97/20.22 tff(32707,plain,
% 29.97/20.22 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f7(f10(c1)) = f10(c1)) | (f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (f10(c1) = f5(f10(c1))) | (~big_f(f7(f10(c1)), f10(c1)))),
% 29.97/20.22 inference(modus_ponens,[status(thm)],[32706, 32705])).
% 29.97/20.22 tff(32708,plain,
% 29.97/20.22 ((c1 = f8(f10(c1))) | (f10(c1) = f5(f10(c1)))),
% 29.97/20.22 inference(unit_resolution,[status(thm)],[32707, 1659, 32692, 26623, 32691, 32676])).
% 29.97/20.22 tff(32709,plain,
% 29.97/20.22 (f10(c1) = f5(f10(c1))),
% 29.97/20.22 inference(unit_resolution,[status(thm)],[32708, 32690])).
% 29.97/20.22 tff(32710,plain,
% 29.97/20.22 (f10(c1) = c1),
% 29.97/20.22 inference(transitivity,[status(thm)],[32709, 32701])).
% 29.97/20.22 tff(32711,plain,
% 29.97/20.22 ($false),
% 29.97/20.22 inference(unit_resolution,[status(thm)],[3, 32710])).
% 29.97/20.22 tff(32712,plain,((f7(c2) = c2) | (f10(c1) = c1) | (f10(c2) = c2) | (~big_f(c2, f10(c2))) | (~big_f(f10(c1), c1))), inference(lemma,lemma(discharge,[]))).
% 29.97/20.22 tff(32713,plain,
% 29.97/20.22 (f7(c2) = c2),
% 29.97/20.22 inference(unit_resolution,[status(thm)],[32712, 32670, 3, 89, 32666])).
% 29.97/20.22 tff(32714,plain,
% 29.97/20.22 (big_f(c1, f10(c2)) <=> big_f(c1, f10(f10(c1)))),
% 29.97/20.22 inference(monotonicity,[status(thm)],[30754])).
% 29.97/20.22 tff(32715,plain,
% 29.97/20.22 (big_f(c1, f10(f10(c1))) <=> big_f(c1, f10(c2))),
% 29.97/20.22 inference(symmetry,[status(thm)],[32714])).
% 29.97/20.22 tff(32716,plain,
% 29.97/20.22 (big_f(c1, c1) <=> big_f(c1, f10(c2))),
% 29.97/20.22 inference(transitivity,[status(thm)],[24959, 32715])).
% 29.97/20.22 tff(32717,plain,
% 29.97/20.22 (big_f(c1, f10(c2))),
% 29.97/20.22 inference(modus_ponens,[status(thm)],[31714, 32716])).
% 29.97/20.22 tff(32718,plain,
% 29.97/20.22 (big_f(f10(c1), f10(f10(c1)))),
% 29.97/20.22 inference(modus_ponens,[status(thm)],[32666, 32668])).
% 29.97/20.22 tff(32719,plain,
% 29.97/20.22 (f6(f10(c1), c1) = c1),
% 29.97/20.22 inference(transitivity,[status(thm)],[25959, 3079])).
% 29.97/20.22 tff(32720,plain,
% 29.97/20.22 (big_f(f7(f10(c1)), f6(f10(c1), c1)) <=> big_f(f10(c1), c1)),
% 29.97/20.22 inference(monotonicity,[status(thm)],[25995, 32719])).
% 29.97/20.22 tff(32721,plain,
% 29.97/20.22 (big_f(f10(c1), c1) <=> big_f(f7(f10(c1)), f6(f10(c1), c1))),
% 29.97/20.22 inference(symmetry,[status(thm)],[32720])).
% 29.97/20.22 tff(32722,plain,
% 29.97/20.22 (big_f(f7(f10(c1)), f6(f10(c1), c1))),
% 29.97/20.22 inference(modus_ponens,[status(thm)],[27307, 32721])).
% 29.97/20.22 tff(32723,plain,
% 29.97/20.22 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f10(c1)) = f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (~big_f(f7(f10(c1)), f6(f10(c1), c1))) | (~(f6(f10(c1), c1) = c1)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(f10(c1)) = f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (~big_f(f7(f10(c1)), f6(f10(c1), c1))) | (~(f6(f10(c1), c1) = c1)))),
% 29.97/20.22 inference(rewrite,[status(thm)],[])).
% 29.97/20.22 tff(32724,plain,
% 29.97/20.22 (((f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (~(f7(f10(c1)) = f10(c1))) | (~(f6(f10(c1), c1) = c1)) | (~big_f(f7(f10(c1)), f6(f10(c1), c1)))) <=> ((f10(f10(c1)) = f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (~big_f(f7(f10(c1)), f6(f10(c1), c1))) | (~(f6(f10(c1), c1) = c1)))),
% 29.97/20.22 inference(rewrite,[status(thm)],[])).
% 29.97/20.22 tff(32725,plain,
% 29.97/20.22 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (~(f7(f10(c1)) = f10(c1))) | (~(f6(f10(c1), c1) = c1)) | (~big_f(f7(f10(c1)), f6(f10(c1), c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f10(c1)) = f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (~big_f(f7(f10(c1)), f6(f10(c1), c1))) | (~(f6(f10(c1), c1) = c1))))),
% 29.97/20.22 inference(monotonicity,[status(thm)],[32724])).
% 29.97/20.22 tff(32726,plain,
% 29.97/20.22 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (~(f7(f10(c1)) = f10(c1))) | (~(f6(f10(c1), c1) = c1)) | (~big_f(f7(f10(c1)), f6(f10(c1), c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(f10(c1)) = f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (~big_f(f7(f10(c1)), f6(f10(c1), c1))) | (~(f6(f10(c1), c1) = c1)))),
% 29.97/20.22 inference(transitivity,[status(thm)],[32725, 32723])).
% 29.97/20.22 tff(32727,plain,
% 29.97/20.22 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (~(f7(f10(c1)) = f10(c1))) | (~(f6(f10(c1), c1) = c1)) | (~big_f(f7(f10(c1)), f6(f10(c1), c1))))),
% 29.97/20.22 inference(quant_inst,[status(thm)],[])).
% 29.97/20.22 tff(32728,plain,
% 29.97/20.22 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(f10(c1)) = f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (~big_f(f7(f10(c1)), f6(f10(c1), c1))) | (~(f6(f10(c1), c1) = c1))),
% 29.97/20.22 inference(modus_ponens,[status(thm)],[32727, 32726])).
% 29.97/20.22 tff(32729,plain,
% 29.97/20.22 ((c1 = f8(f10(c1))) | (~big_f(f7(f10(c1)), f6(f10(c1), c1))) | (~(f6(f10(c1), c1) = c1))),
% 29.97/20.22 inference(unit_resolution,[status(thm)],[32728, 2730, 24968, 25967, 27872])).
% 29.97/20.22 tff(32730,plain,
% 29.97/20.22 (c1 = f8(f10(c1))),
% 29.97/20.22 inference(unit_resolution,[status(thm)],[32729, 32722, 32719])).
% 29.97/20.22 tff(32731,plain,
% 29.97/20.22 (f8(f10(c1)) = c1),
% 29.97/20.22 inference(symmetry,[status(thm)],[32730])).
% 29.97/20.22 tff(32732,plain,
% 29.97/20.22 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f10(c1)) = f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | (~big_f(f7(f10(c1)), f6(f10(c1), c1))) | (f10(c1) = f8(f10(c1))) | (~(f6(f10(c1), c1) = c1)) | (~big_f(f10(c1), f10(f10(c1)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(f10(c1)) = f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | (~big_f(f7(f10(c1)), f6(f10(c1), c1))) | (f10(c1) = f8(f10(c1))) | (~(f6(f10(c1), c1) = c1)) | (~big_f(f10(c1), f10(f10(c1)))))),
% 29.97/20.23 inference(rewrite,[status(thm)],[])).
% 29.97/20.23 tff(32733,plain,
% 29.97/20.23 (((f10(f10(c1)) = f10(c1)) | (f10(c1) = f8(f10(c1))) | (~big_f(f10(c1), f10(f10(c1)))) | (~(f7(f10(c1)) = f10(c1))) | (~(f6(f10(c1), c1) = c1)) | (~big_f(f7(f10(c1)), f6(f10(c1), c1)))) <=> ((f10(f10(c1)) = f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | (~big_f(f7(f10(c1)), f6(f10(c1), c1))) | (f10(c1) = f8(f10(c1))) | (~(f6(f10(c1), c1) = c1)) | (~big_f(f10(c1), f10(f10(c1)))))),
% 29.97/20.23 inference(rewrite,[status(thm)],[])).
% 29.97/20.23 tff(32734,plain,
% 29.97/20.23 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f10(c1)) = f10(c1)) | (f10(c1) = f8(f10(c1))) | (~big_f(f10(c1), f10(f10(c1)))) | (~(f7(f10(c1)) = f10(c1))) | (~(f6(f10(c1), c1) = c1)) | (~big_f(f7(f10(c1)), f6(f10(c1), c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f10(c1)) = f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | (~big_f(f7(f10(c1)), f6(f10(c1), c1))) | (f10(c1) = f8(f10(c1))) | (~(f6(f10(c1), c1) = c1)) | (~big_f(f10(c1), f10(f10(c1))))))),
% 29.97/20.23 inference(monotonicity,[status(thm)],[32733])).
% 29.97/20.23 tff(32735,plain,
% 29.97/20.23 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f10(c1)) = f10(c1)) | (f10(c1) = f8(f10(c1))) | (~big_f(f10(c1), f10(f10(c1)))) | (~(f7(f10(c1)) = f10(c1))) | (~(f6(f10(c1), c1) = c1)) | (~big_f(f7(f10(c1)), f6(f10(c1), c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(f10(c1)) = f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | (~big_f(f7(f10(c1)), f6(f10(c1), c1))) | (f10(c1) = f8(f10(c1))) | (~(f6(f10(c1), c1) = c1)) | (~big_f(f10(c1), f10(f10(c1)))))),
% 29.97/20.23 inference(transitivity,[status(thm)],[32734, 32732])).
% 29.97/20.23 tff(32736,plain,
% 29.97/20.23 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f10(c1)) = f10(c1)) | (f10(c1) = f8(f10(c1))) | (~big_f(f10(c1), f10(f10(c1)))) | (~(f7(f10(c1)) = f10(c1))) | (~(f6(f10(c1), c1) = c1)) | (~big_f(f7(f10(c1)), f6(f10(c1), c1))))),
% 29.97/20.23 inference(quant_inst,[status(thm)],[])).
% 29.97/20.23 tff(32737,plain,
% 29.97/20.23 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(f10(c1)) = f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | (~big_f(f7(f10(c1)), f6(f10(c1), c1))) | (f10(c1) = f8(f10(c1))) | (~(f6(f10(c1), c1) = c1)) | (~big_f(f10(c1), f10(f10(c1))))),
% 29.97/20.23 inference(modus_ponens,[status(thm)],[32736, 32735])).
% 29.97/20.23 tff(32738,plain,
% 29.97/20.23 ((~big_f(f7(f10(c1)), f6(f10(c1), c1))) | (f10(c1) = f8(f10(c1))) | (~(f6(f10(c1), c1) = c1))),
% 29.97/20.23 inference(unit_resolution,[status(thm)],[32737, 2730, 24968, 25967, 27873])).
% 29.97/20.23 tff(32739,plain,
% 29.97/20.23 (f10(c1) = f8(f10(c1))),
% 29.97/20.23 inference(unit_resolution,[status(thm)],[32738, 32722, 32719])).
% 29.97/20.23 tff(32740,plain,
% 29.97/20.23 (f10(c1) = c1),
% 29.97/20.23 inference(transitivity,[status(thm)],[32739, 32731])).
% 29.97/20.23 tff(32741,plain,
% 29.97/20.23 ($false),
% 29.97/20.23 inference(unit_resolution,[status(thm)],[3, 32740])).
% 29.97/20.23 tff(32742,plain,((~(f6(c2, c1) = c1)) | (f10(c1) = c1) | (f10(f10(c1)) = f10(c1)) | (~big_f(c1, f10(f10(c1)))) | (~big_f(f10(c1), f10(f10(c1)))) | (~big_f(f10(c1), c1)) | (~(f7(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.97/20.23 tff(32743,plain,
% 29.97/20.23 (~(f6(c2, c1) = c1)),
% 29.97/20.23 inference(unit_resolution,[status(thm)],[32742, 32692, 3, 32691, 32718, 32666, 32713])).
% 29.97/20.23 tff(32744,plain,
% 29.97/20.23 ((f6(c2, c1) = c1) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (~big_f(c1, f10(c2))) | (~big_f(c2, f10(c2))) | big_f(c2, c2) | (~(f4(c4) = c1))),
% 29.97/20.23 inference(unit_resolution,[status(thm)],[28810, 25791])).
% 29.97/20.23 tff(32745,plain,
% 29.97/20.23 (~(f4(c4) = c1)),
% 29.97/20.23 inference(unit_resolution,[status(thm)],[32744, 32743, 121, 89, 32670, 32717, 32713])).
% 29.97/20.23 tff(32746,plain,
% 29.97/20.23 (f4(c4) = c2),
% 29.97/20.23 inference(unit_resolution,[status(thm)],[11750, 32745])).
% 29.97/20.23 tff(32747,plain,
% 29.97/20.23 (f4(c4) = f10(c1)),
% 29.97/20.23 inference(transitivity,[status(thm)],[32746, 5571])).
% 29.97/20.23 tff(32748,plain,
% 29.97/20.23 (f7(f4(c4)) = f7(f10(c1))),
% 29.97/20.23 inference(monotonicity,[status(thm)],[32747])).
% 29.97/20.23 tff(32749,plain,
% 29.97/20.23 (f7(f4(c4)) = f10(c1)),
% 29.97/20.23 inference(transitivity,[status(thm)],[32748, 219, 32713, 5571])).
% 29.97/20.23 tff(32750,plain,
% 29.97/20.23 (f8(f7(f4(c4))) = f8(f10(c1))),
% 29.97/20.23 inference(monotonicity,[status(thm)],[32749])).
% 29.97/20.23 tff(32751,plain,
% 29.97/20.23 ((c2 = f8(f7(f4(c4)))) <=> (f10(c1) = f8(f10(c1)))),
% 29.97/20.23 inference(monotonicity,[status(thm)],[5571, 32750])).
% 29.97/20.23 tff(32752,plain,
% 29.97/20.23 ((f10(c1) = f8(f10(c1))) <=> (c2 = f8(f7(f4(c4))))),
% 29.97/20.23 inference(symmetry,[status(thm)],[32751])).
% 29.97/20.23 tff(32753,plain,
% 29.97/20.23 ((f10(c1) = f8(f10(c1))) <=> (f8(f7(f4(c4))) = c2)),
% 29.97/20.23 inference(transitivity,[status(thm)],[32752, 106])).
% 29.97/20.23 tff(32754,plain,
% 29.97/20.23 (~(f6(f10(c1), c1) = c1)),
% 29.97/20.23 inference(modus_ponens,[status(thm)],[32743, 25965])).
% 29.97/20.23 tff(32755,plain,
% 29.97/20.23 (f7(f10(c1)) = c2),
% 29.97/20.23 inference(transitivity,[status(thm)],[219, 32713])).
% 29.97/20.23 tff(32756,plain,
% 29.97/20.23 (big_f(f7(f10(c1)), f6(f10(c1), c1)) <=> big_f(c2, f6(c2, c1))),
% 29.97/20.23 inference(monotonicity,[status(thm)],[32755, 25959])).
% 29.97/20.23 tff(32757,plain,
% 29.97/20.23 (big_f(c2, f6(c2, c1)) <=> big_f(f7(f10(c1)), f6(f10(c1), c1))),
% 29.97/20.23 inference(symmetry,[status(thm)],[32756])).
% 29.97/20.23 tff(32758,plain,
% 29.97/20.23 ((~big_f(c2, f6(c2, c1))) <=> (~big_f(f7(f10(c1)), f6(f10(c1), c1)))),
% 29.97/20.23 inference(monotonicity,[status(thm)],[32757])).
% 29.97/20.23 tff(32759,plain,
% 29.97/20.23 (~(c3 = c1)),
% 29.97/20.23 inference(unit_resolution,[status(thm)],[11517, 32746, 31714, 32713, 121, 32665])).
% 29.97/20.23 tff(32760,plain,
% 29.97/20.23 (c3 = c2),
% 29.97/20.23 inference(unit_resolution,[status(thm)],[180, 32759])).
% 29.97/20.23 tff(32761,plain,
% 29.97/20.23 (~big_f(c2, f6(c2, c1))),
% 29.97/20.23 inference(unit_resolution,[status(thm)],[11706, 32760, 121, 431, 32746, 32743])).
% 29.97/20.23 tff(32762,plain,
% 29.97/20.23 (~big_f(f7(f10(c1)), f6(f10(c1), c1))),
% 29.97/20.23 inference(modus_ponens,[status(thm)],[32761, 32758])).
% 29.97/20.23 tff(32763,plain,
% 29.97/20.23 (f7(f10(c1)) = f10(c1)),
% 29.97/20.23 inference(modus_ponens,[status(thm)],[32713, 221])).
% 29.97/20.23 tff(32764,plain,
% 29.97/20.23 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f10(c1)) = f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | big_f(f7(f10(c1)), f6(f10(c1), c1)) | (f10(c1) = f8(f10(c1))) | (f6(f10(c1), c1) = c1) | (~big_f(f10(c1), f10(f10(c1)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(f10(c1)) = f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | big_f(f7(f10(c1)), f6(f10(c1), c1)) | (f10(c1) = f8(f10(c1))) | (f6(f10(c1), c1) = c1) | (~big_f(f10(c1), f10(f10(c1)))))),
% 29.97/20.23 inference(rewrite,[status(thm)],[])).
% 29.97/20.23 tff(32765,plain,
% 29.97/20.23 (((f10(f10(c1)) = f10(c1)) | (f10(c1) = f8(f10(c1))) | (~big_f(f10(c1), f10(f10(c1)))) | (~(f7(f10(c1)) = f10(c1))) | (f6(f10(c1), c1) = c1) | big_f(f7(f10(c1)), f6(f10(c1), c1))) <=> ((f10(f10(c1)) = f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | big_f(f7(f10(c1)), f6(f10(c1), c1)) | (f10(c1) = f8(f10(c1))) | (f6(f10(c1), c1) = c1) | (~big_f(f10(c1), f10(f10(c1)))))),
% 29.97/20.23 inference(rewrite,[status(thm)],[])).
% 29.97/20.23 tff(32766,plain,
% 29.97/20.23 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f10(c1)) = f10(c1)) | (f10(c1) = f8(f10(c1))) | (~big_f(f10(c1), f10(f10(c1)))) | (~(f7(f10(c1)) = f10(c1))) | (f6(f10(c1), c1) = c1) | big_f(f7(f10(c1)), f6(f10(c1), c1)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f10(c1)) = f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | big_f(f7(f10(c1)), f6(f10(c1), c1)) | (f10(c1) = f8(f10(c1))) | (f6(f10(c1), c1) = c1) | (~big_f(f10(c1), f10(f10(c1))))))),
% 29.97/20.23 inference(monotonicity,[status(thm)],[32765])).
% 29.97/20.23 tff(32767,plain,
% 29.97/20.23 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f10(c1)) = f10(c1)) | (f10(c1) = f8(f10(c1))) | (~big_f(f10(c1), f10(f10(c1)))) | (~(f7(f10(c1)) = f10(c1))) | (f6(f10(c1), c1) = c1) | big_f(f7(f10(c1)), f6(f10(c1), c1)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(f10(c1)) = f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | big_f(f7(f10(c1)), f6(f10(c1), c1)) | (f10(c1) = f8(f10(c1))) | (f6(f10(c1), c1) = c1) | (~big_f(f10(c1), f10(f10(c1)))))),
% 29.97/20.23 inference(transitivity,[status(thm)],[32766, 32764])).
% 29.97/20.23 tff(32768,plain,
% 29.97/20.23 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f10(c1)) = f10(c1)) | (f10(c1) = f8(f10(c1))) | (~big_f(f10(c1), f10(f10(c1)))) | (~(f7(f10(c1)) = f10(c1))) | (f6(f10(c1), c1) = c1) | big_f(f7(f10(c1)), f6(f10(c1), c1)))),
% 29.97/20.23 inference(quant_inst,[status(thm)],[])).
% 29.97/20.23 tff(32769,plain,
% 29.97/20.23 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(f10(c1)) = f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | big_f(f7(f10(c1)), f6(f10(c1), c1)) | (f10(c1) = f8(f10(c1))) | (f6(f10(c1), c1) = c1) | (~big_f(f10(c1), f10(f10(c1))))),
% 29.97/20.23 inference(modus_ponens,[status(thm)],[32768, 32767])).
% 29.97/20.23 tff(32770,plain,
% 29.97/20.23 (big_f(f7(f10(c1)), f6(f10(c1), c1)) | (f10(c1) = f8(f10(c1))) | (f6(f10(c1), c1) = c1)),
% 29.97/20.23 inference(unit_resolution,[status(thm)],[32769, 2662, 32692, 32763, 32718])).
% 29.97/20.23 tff(32771,plain,
% 29.97/20.23 (f10(c1) = f8(f10(c1))),
% 29.97/20.23 inference(unit_resolution,[status(thm)],[32770, 32762, 32754])).
% 29.97/20.23 tff(32772,plain,
% 29.97/20.23 (f8(f7(f4(c4))) = c2),
% 29.97/20.23 inference(modus_ponens,[status(thm)],[32771, 32753])).
% 29.97/20.23 tff(32773,plain,
% 29.97/20.23 (f10(f7(f4(c4))) = f10(f10(c1))),
% 29.97/20.23 inference(monotonicity,[status(thm)],[32749])).
% 29.97/20.23 tff(32774,plain,
% 29.97/20.23 (f10(f7(f4(c4))) = c1),
% 29.97/20.23 inference(transitivity,[status(thm)],[32773, 24860, 94])).
% 29.97/20.23 tff(32775,plain,
% 29.97/20.23 ((f10(f7(f4(c4))) = f7(f4(c4))) <=> (c1 = f10(c1))),
% 29.97/20.23 inference(monotonicity,[status(thm)],[32774, 32749])).
% 29.97/20.23 tff(32776,plain,
% 29.97/20.23 ((f10(f7(f4(c4))) = f7(f4(c4))) <=> (f10(c1) = c1)),
% 29.97/20.23 inference(transitivity,[status(thm)],[32775, 18819])).
% 29.97/20.23 tff(32777,plain,
% 29.97/20.23 ((f10(c1) = c1) <=> (f10(f7(f4(c4))) = f7(f4(c4)))),
% 29.97/20.23 inference(symmetry,[status(thm)],[32776])).
% 29.97/20.23 tff(32778,plain,
% 29.97/20.23 ((~(f10(c1) = c1)) <=> (~(f10(f7(f4(c4))) = f7(f4(c4))))),
% 29.97/20.23 inference(monotonicity,[status(thm)],[32777])).
% 29.97/20.23 tff(32779,plain,
% 29.97/20.23 (~(f10(f7(f4(c4))) = f7(f4(c4)))),
% 29.97/20.23 inference(modus_ponens,[status(thm)],[3, 32778])).
% 29.97/20.23 tff(32780,plain,
% 29.97/20.23 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f10(c1)) = f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | big_f(f7(f10(c1)), f6(f10(c1), c1)) | (f6(f10(c1), c1) = c1))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(f10(c1)) = f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | big_f(f7(f10(c1)), f6(f10(c1), c1)) | (f6(f10(c1), c1) = c1))),
% 29.97/20.23 inference(rewrite,[status(thm)],[])).
% 29.97/20.23 tff(32781,plain,
% 29.97/20.23 (((f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (~(f7(f10(c1)) = f10(c1))) | (f6(f10(c1), c1) = c1) | big_f(f7(f10(c1)), f6(f10(c1), c1))) <=> ((f10(f10(c1)) = f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | big_f(f7(f10(c1)), f6(f10(c1), c1)) | (f6(f10(c1), c1) = c1))),
% 29.97/20.23 inference(rewrite,[status(thm)],[])).
% 29.97/20.23 tff(32782,plain,
% 29.97/20.23 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (~(f7(f10(c1)) = f10(c1))) | (f6(f10(c1), c1) = c1) | big_f(f7(f10(c1)), f6(f10(c1), c1)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f10(c1)) = f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | big_f(f7(f10(c1)), f6(f10(c1), c1)) | (f6(f10(c1), c1) = c1)))),
% 29.97/20.23 inference(monotonicity,[status(thm)],[32781])).
% 29.97/20.23 tff(32783,plain,
% 29.97/20.23 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (~(f7(f10(c1)) = f10(c1))) | (f6(f10(c1), c1) = c1) | big_f(f7(f10(c1)), f6(f10(c1), c1)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(f10(c1)) = f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | big_f(f7(f10(c1)), f6(f10(c1), c1)) | (f6(f10(c1), c1) = c1))),
% 29.97/20.23 inference(transitivity,[status(thm)],[32782, 32780])).
% 29.97/20.23 tff(32784,plain,
% 29.97/20.23 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f10(c1)) = f10(c1)) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | (~(f7(f10(c1)) = f10(c1))) | (f6(f10(c1), c1) = c1) | big_f(f7(f10(c1)), f6(f10(c1), c1)))),
% 29.97/20.23 inference(quant_inst,[status(thm)],[])).
% 29.97/20.23 tff(32785,plain,
% 29.97/20.23 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(f10(c1)) = f10(c1)) | (~(f7(f10(c1)) = f10(c1))) | (c1 = f8(f10(c1))) | (~big_f(c1, f10(f10(c1)))) | big_f(f7(f10(c1)), f6(f10(c1), c1)) | (f6(f10(c1), c1) = c1)),
% 29.97/20.23 inference(modus_ponens,[status(thm)],[32784, 32783])).
% 29.97/20.23 tff(32786,plain,
% 29.97/20.23 ((c1 = f8(f10(c1))) | big_f(f7(f10(c1)), f6(f10(c1), c1)) | (f6(f10(c1), c1) = c1)),
% 29.97/20.23 inference(unit_resolution,[status(thm)],[32785, 2662, 32692, 32763, 32691])).
% 29.97/20.23 tff(32787,plain,
% 29.97/20.23 (c1 = f8(f10(c1))),
% 29.97/20.23 inference(unit_resolution,[status(thm)],[32786, 32762, 32754])).
% 29.97/20.23 tff(32788,plain,
% 29.97/20.23 (f4(c4) = f10(c1)),
% 29.97/20.23 inference(transitivity,[status(thm)],[79, 293])).
% 29.97/20.23 tff(32789,plain,
% 29.97/20.23 (f7(f4(c4)) = f7(f10(c1))),
% 29.97/20.23 inference(monotonicity,[status(thm)],[32788])).
% 29.97/20.23 tff(32790,plain,
% 29.97/20.23 (f7(f4(c4)) = f10(c1)),
% 29.97/20.23 inference(transitivity,[status(thm)],[32789, 232, 77, 293])).
% 29.97/20.23 tff(32791,plain,
% 29.97/20.23 (f10(f7(f4(c4))) = f10(f10(c1))),
% 29.97/20.23 inference(monotonicity,[status(thm)],[32790])).
% 29.97/20.23 tff(32792,plain,
% 29.97/20.23 (f10(f7(f4(c4))) = c1),
% 29.97/20.23 inference(transitivity,[status(thm)],[32791, 31433, 11819])).
% 29.97/20.23 tff(32793,plain,
% 29.97/20.23 ((f10(f7(f4(c4))) = f7(f4(c4))) <=> (c1 = f10(c1))),
% 29.97/20.23 inference(monotonicity,[status(thm)],[32792, 32790])).
% 29.97/20.23 tff(32794,plain,
% 29.97/20.23 ((f10(f7(f4(c4))) = f7(f4(c4))) <=> (f10(c1) = c1)),
% 29.97/20.23 inference(transitivity,[status(thm)],[32793, 18819])).
% 29.97/20.23 tff(32795,plain,
% 29.97/20.23 ((f10(c1) = c1) <=> (f10(f7(f4(c4))) = f7(f4(c4)))),
% 29.97/20.23 inference(symmetry,[status(thm)],[32794])).
% 29.97/20.23 tff(32796,plain,
% 29.97/20.23 (f7(f10(c1)) = f7(f4(c4))),
% 29.97/20.23 inference(symmetry,[status(thm)],[32789])).
% 29.97/20.23 tff(32797,plain,
% 29.97/20.23 (f10(c1) = f7(f4(c4))),
% 29.97/20.23 inference(transitivity,[status(thm)],[16, 82, 6342, 32796])).
% 29.97/20.23 tff(32798,plain,
% 29.97/20.23 (f8(f10(c1)) = f8(f7(f4(c4)))),
% 29.97/20.23 inference(monotonicity,[status(thm)],[32797])).
% 29.97/20.23 tff(32799,plain,
% 29.97/20.23 (f8(c2) = f10(c1)),
% 29.97/20.23 inference(transitivity,[status(thm)],[12670, 32798, 13856, 293])).
% 29.97/20.23 tff(32800,plain,
% 29.97/20.23 ((c1 = f8(c2)) <=> (c1 = f10(c1))),
% 29.97/20.23 inference(monotonicity,[status(thm)],[32799])).
% 29.97/20.23 tff(32801,plain,
% 29.97/20.23 ((c1 = f8(c2)) <=> (f10(c1) = c1)),
% 29.97/20.23 inference(transitivity,[status(thm)],[32800, 18819])).
% 29.97/20.23 tff(32802,plain,
% 29.97/20.23 ((c1 = f8(f10(c1))) <=> (f10(f7(f4(c4))) = f7(f4(c4)))),
% 29.97/20.23 inference(transitivity,[status(thm)],[12674, 32801, 32795])).
% 29.97/20.23 tff(32803,plain,
% 29.97/20.23 (f10(f7(f4(c4))) = f7(f4(c4))),
% 29.97/20.23 inference(modus_ponens,[status(thm)],[24966, 32802])).
% 29.97/20.23 tff(32804,assumption,(~(f10(f7(f4(c4))) = f7(f4(c4)))), introduced(assumption)).
% 29.97/20.23 tff(32805,plain,
% 29.97/20.23 ($false),
% 29.97/20.23 inference(unit_resolution,[status(thm)],[32804, 32803])).
% 29.97/20.23 tff(32806,plain,((~(c1 = f8(f10(c1)))) | (f10(f7(f4(c4))) = f7(f4(c4))) | (~(f8(f7(f4(c4))) = c2)) | (~(f10(c1) = c2)) | (~(f7(c2) = c2)) | (~(f4(c4) = c2)) | (~(f10(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.97/20.23 tff(32807,plain,
% 29.97/20.23 (~(f8(f7(f4(c4))) = c2)),
% 29.97/20.23 inference(unit_resolution,[status(thm)],[32806, 32787, 15, 32746, 32713, 32779, 94])).
% 29.97/20.23 tff(32808,plain,
% 29.97/20.23 ($false),
% 29.97/20.23 inference(unit_resolution,[status(thm)],[32807, 32772])).
% 29.97/20.23 tff(32809,plain,((f10(c2) = c2) | (f10(c1) = c1) | big_f(c2, c2) | (~(c4 = c2))), inference(lemma,lemma(discharge,[]))).
% 29.97/20.23 tff(32810,plain,
% 29.97/20.23 (f10(c2) = c2),
% 29.97/20.23 inference(unit_resolution,[status(thm)],[32809, 431, 121, 3])).
% 29.97/20.23 tff(32811,plain,
% 29.97/20.23 (big_f(f7(f10(c1)), f10(c1)) <=> big_f(f7(c2), c2)),
% 29.97/20.23 inference(symmetry,[status(thm)],[32677])).
% 29.97/20.23 tff(32812,plain,
% 29.97/20.23 (f7(f10(c1)) = c1),
% 29.97/20.23 inference(transitivity,[status(thm)],[232, 22])).
% 29.97/20.23 tff(32813,plain,
% 29.97/20.23 (big_f(f7(f10(c1)), f10(c1)) <=> big_f(c1, f10(c1))),
% 29.97/20.23 inference(monotonicity,[status(thm)],[32812])).
% 29.97/20.23 tff(32814,plain,
% 29.97/20.23 (big_f(c1, f10(c1)) <=> big_f(f7(f10(c1)), f10(c1))),
% 29.97/20.23 inference(symmetry,[status(thm)],[32813])).
% 29.97/20.23 tff(32815,plain,
% 29.97/20.23 (big_f(c1, f10(c1)) <=> big_f(f7(c2), c2)),
% 29.97/20.23 inference(transitivity,[status(thm)],[32814, 32811])).
% 29.97/20.23 tff(32816,plain,
% 29.97/20.23 (big_f(f7(c2), c2)),
% 29.97/20.23 inference(modus_ponens,[status(thm)],[30444, 32815])).
% 29.97/20.23 tff(32817,plain,
% 29.97/20.23 ($false),
% 29.97/20.23 inference(unit_resolution,[status(thm)],[15961, 31715, 32816, 122, 121, 17])).
% 29.97/20.23 tff(32818,plain,((f7(c2) = c2) | (~(f10(c2) = c2)) | big_f(c2, c2) | (~(f10(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.97/20.23 tff(32819,plain,
% 29.97/20.23 (f7(c2) = c2),
% 29.97/20.23 inference(unit_resolution,[status(thm)],[32818, 32810, 121, 15])).
% 29.97/20.23 tff(32820,plain,
% 29.97/20.23 (f9(f10(c1), c1) = f9(c2, c1)),
% 29.97/20.23 inference(monotonicity,[status(thm)],[15])).
% 29.97/20.23 tff(32821,plain,
% 29.97/20.23 ((f9(f10(c1), c1) = c1) <=> (f9(c2, c1) = c1)),
% 29.97/20.23 inference(monotonicity,[status(thm)],[32820])).
% 29.97/20.23 tff(32822,plain,
% 29.97/20.23 ((f9(c2, c1) = c1) <=> (f9(f10(c1), c1) = c1)),
% 29.97/20.23 inference(symmetry,[status(thm)],[32821])).
% 29.97/20.23 tff(32823,plain,
% 29.97/20.23 ((f6(c2, f6(c2, c1)) = f6(c2, c1)) <=> (f6(c2, f6(c2, c1)) = c1)),
% 29.97/20.23 inference(monotonicity,[status(thm)],[3079])).
% 29.97/20.23 tff(32824,plain,
% 29.97/20.23 ((f6(c2, f6(c2, c1)) = c1) <=> (f6(c2, f6(c2, c1)) = f6(c2, c1))),
% 29.97/20.23 inference(symmetry,[status(thm)],[32823])).
% 29.97/20.23 tff(32825,plain,
% 29.97/20.23 (f6(c2, f6(c2, c1)) = f6(c2, c1)),
% 29.97/20.23 inference(monotonicity,[status(thm)],[3079])).
% 29.97/20.23 tff(32826,plain,
% 29.97/20.23 (f6(c2, f6(c2, c1)) = c1),
% 29.97/20.23 inference(transitivity,[status(thm)],[32825, 3079])).
% 29.97/20.23 tff(32827,plain,
% 29.97/20.23 (f6(c2, f6(c2, c1)) = f6(c2, c1)),
% 29.97/20.23 inference(modus_ponens,[status(thm)],[32826, 32824])).
% 29.97/20.23 tff(32828,plain,
% 29.97/20.23 (big_f(c2, f6(c2, f6(c2, c1))) <=> big_f(f10(c1), c1)),
% 29.97/20.23 inference(monotonicity,[status(thm)],[5571, 32826])).
% 29.97/20.23 tff(32829,plain,
% 29.97/20.23 (big_f(f10(c1), c1) <=> big_f(c2, f6(c2, f6(c2, c1)))),
% 29.97/20.23 inference(symmetry,[status(thm)],[32828])).
% 29.97/20.23 tff(32830,plain,
% 29.97/20.23 (big_f(f10(c1), c1) <=> big_f(f7(c2), f6(c2, f6(c2, c1)))),
% 29.97/20.23 inference(transitivity,[status(thm)],[32829, 14631])).
% 29.97/20.23 tff(32831,plain,
% 29.97/20.23 (big_f(f7(c2), f6(c2, f6(c2, c1)))),
% 29.97/20.23 inference(modus_ponens,[status(thm)],[27307, 32830])).
% 29.97/20.23 tff(32832,plain,
% 29.97/20.23 (~(c2 = f8(c1))),
% 29.97/20.23 inference(unit_resolution,[status(thm)],[2970, 32831, 3, 32827, 2946, 77])).
% 29.97/20.23 tff(32833,plain,
% 29.97/20.23 (~(f8(c1) = c2)),
% 29.97/20.23 inference(unit_resolution,[status(thm)],[1675, 32832])).
% 29.97/20.23 tff(32834,plain,
% 29.97/20.23 (f8(c1) = c1),
% 29.97/20.23 inference(unit_resolution,[status(thm)],[1680, 32833])).
% 29.97/20.23 tff(32835,plain,
% 29.97/20.23 ((f9(c2, c1) = f8(c1)) <=> (f9(c2, c1) = c1)),
% 29.97/20.23 inference(monotonicity,[status(thm)],[32834])).
% 29.97/20.23 tff(32836,plain,
% 29.97/20.23 ((f9(c2, c1) = f8(c1)) <=> (f9(f10(c1), c1) = c1)),
% 29.97/20.23 inference(transitivity,[status(thm)],[32835, 32822])).
% 29.97/20.23 tff(32837,plain,
% 29.97/20.23 (big_f(c2, f6(c2, c1)) <=> big_f(f10(c1), c1)),
% 29.97/20.23 inference(monotonicity,[status(thm)],[5571, 3079])).
% 29.97/20.23 tff(32838,plain,
% 29.97/20.23 (big_f(f10(c1), c1) <=> big_f(c2, f6(c2, c1))),
% 29.97/20.23 inference(symmetry,[status(thm)],[32837])).
% 29.97/20.23 tff(32839,plain,
% 29.97/20.23 (big_f(f10(c1), c1) <=> big_f(f7(c2), f6(c2, c1))),
% 29.97/20.23 inference(transitivity,[status(thm)],[32838, 13581])).
% 29.97/20.23 tff(32840,plain,
% 29.97/20.23 (big_f(f7(c2), f6(c2, c1))),
% 29.97/20.23 inference(modus_ponens,[status(thm)],[27307, 32839])).
% 29.97/20.23 tff(32841,plain,
% 29.97/20.23 (big_f(f9(c2, c1), f10(c2)) | (~(f10(c2) = c2)) | (~(f7(c2) = c2)) | (~(f6(c2, c1) = c1)) | (~big_f(f7(c2), f6(c2, c1)))),
% 29.97/20.23 inference(unit_resolution,[status(thm)],[3090, 30354])).
% 29.97/20.23 tff(32842,plain,
% 29.97/20.23 (big_f(f9(c2, c1), f10(c2))),
% 29.97/20.23 inference(unit_resolution,[status(thm)],[32841, 32840, 122, 77, 3079])).
% 29.97/20.23 tff(32843,plain,
% 29.97/20.23 (big_f(f9(c2, c1), f10(c1))),
% 29.97/20.23 inference(modus_ponens,[status(thm)],[32842, 3101])).
% 29.97/20.23 tff(32844,plain,
% 29.97/20.23 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (~(f7(f10(c1)) = f10(c1))) | (f9(c2, c1) = f8(c1)) | (~big_f(f9(c2, c1), f10(c1))) | (~big_f(f7(f10(c1)), f6(f10(c1), c1))) | (~(f6(f10(c1), c1) = c1)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(f7(f10(c1)) = f10(c1))) | (f9(c2, c1) = f8(c1)) | (~big_f(f9(c2, c1), f10(c1))) | (~big_f(f7(f10(c1)), f6(f10(c1), c1))) | (~(f6(f10(c1), c1) = c1)))),
% 29.97/20.23 inference(rewrite,[status(thm)],[])).
% 29.97/20.23 tff(32845,plain,
% 29.97/20.23 (((f10(c1) = c1) | (f9(c2, c1) = f8(c1)) | (~big_f(f9(c2, c1), f10(c1))) | (~(f7(f10(c1)) = f10(c1))) | (~(f6(f10(c1), c1) = c1)) | (~big_f(f7(f10(c1)), f6(f10(c1), c1)))) <=> ((f10(c1) = c1) | (~(f7(f10(c1)) = f10(c1))) | (f9(c2, c1) = f8(c1)) | (~big_f(f9(c2, c1), f10(c1))) | (~big_f(f7(f10(c1)), f6(f10(c1), c1))) | (~(f6(f10(c1), c1) = c1)))),
% 29.97/20.23 inference(rewrite,[status(thm)],[])).
% 29.97/20.23 tff(32846,plain,
% 29.97/20.23 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (f9(c2, c1) = f8(c1)) | (~big_f(f9(c2, c1), f10(c1))) | (~(f7(f10(c1)) = f10(c1))) | (~(f6(f10(c1), c1) = c1)) | (~big_f(f7(f10(c1)), f6(f10(c1), c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (~(f7(f10(c1)) = f10(c1))) | (f9(c2, c1) = f8(c1)) | (~big_f(f9(c2, c1), f10(c1))) | (~big_f(f7(f10(c1)), f6(f10(c1), c1))) | (~(f6(f10(c1), c1) = c1))))),
% 29.97/20.23 inference(monotonicity,[status(thm)],[32845])).
% 29.97/20.23 tff(32847,plain,
% 29.97/20.23 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (f9(c2, c1) = f8(c1)) | (~big_f(f9(c2, c1), f10(c1))) | (~(f7(f10(c1)) = f10(c1))) | (~(f6(f10(c1), c1) = c1)) | (~big_f(f7(f10(c1)), f6(f10(c1), c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(f7(f10(c1)) = f10(c1))) | (f9(c2, c1) = f8(c1)) | (~big_f(f9(c2, c1), f10(c1))) | (~big_f(f7(f10(c1)), f6(f10(c1), c1))) | (~(f6(f10(c1), c1) = c1)))),
% 29.97/20.23 inference(transitivity,[status(thm)],[32846, 32844])).
% 29.97/20.23 tff(32848,plain,
% 29.97/20.23 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(c1) = c1) | (f9(c2, c1) = f8(c1)) | (~big_f(f9(c2, c1), f10(c1))) | (~(f7(f10(c1)) = f10(c1))) | (~(f6(f10(c1), c1) = c1)) | (~big_f(f7(f10(c1)), f6(f10(c1), c1))))),
% 29.97/20.24 inference(quant_inst,[status(thm)],[])).
% 29.97/20.24 tff(32849,plain,
% 29.97/20.24 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(c1) = c1) | (~(f7(f10(c1)) = f10(c1))) | (f9(c2, c1) = f8(c1)) | (~big_f(f9(c2, c1), f10(c1))) | (~big_f(f7(f10(c1)), f6(f10(c1), c1))) | (~(f6(f10(c1), c1) = c1))),
% 29.97/20.24 inference(modus_ponens,[status(thm)],[32848, 32847])).
% 29.97/20.24 tff(32850,plain,
% 29.97/20.24 ((f9(c2, c1) = f8(c1)) | (~big_f(f9(c2, c1), f10(c1)))),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[32849, 2730, 3, 25967, 32722, 32719])).
% 29.97/20.24 tff(32851,plain,
% 29.97/20.24 (f9(c2, c1) = f8(c1)),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[32850, 32843])).
% 29.97/20.24 tff(32852,plain,
% 29.97/20.24 (f9(f10(c1), c1) = c1),
% 29.97/20.24 inference(modus_ponens,[status(thm)],[32851, 32836])).
% 29.97/20.24 tff(32853,plain,
% 29.97/20.24 (big_f(f9(f10(c1), c1), f10(f10(c1))) <=> big_f(f9(c2, c1), f10(c2))),
% 29.97/20.24 inference(monotonicity,[status(thm)],[32820, 24860])).
% 29.97/20.24 tff(32854,plain,
% 29.97/20.24 (big_f(f9(c2, c1), f10(c2)) <=> big_f(f9(f10(c1), c1), f10(f10(c1)))),
% 29.97/20.24 inference(symmetry,[status(thm)],[32853])).
% 29.97/20.24 tff(32855,plain,
% 29.97/20.24 (big_f(f9(f10(c1), c1), f10(f10(c1)))),
% 29.97/20.24 inference(modus_ponens,[status(thm)],[32842, 32854])).
% 29.97/20.24 tff(32856,plain,
% 29.97/20.24 (f10(f10(c1)) = f10(c1)),
% 29.97/20.24 inference(modus_ponens,[status(thm)],[122, 27865])).
% 29.97/20.24 tff(32857,plain,
% 29.97/20.24 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(f10(c1)) = f10(c1))) | (~big_f(f7(f10(c1)), f6(f10(c1), c1))) | (~(f10(f10(c1)) = f10(c1))) | (~(f6(f10(c1), c1) = c1)) | (~big_f(f9(f10(c1), c1), f10(f10(c1)))) | (~(f9(f10(c1), c1) = c1)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(f10(c1)) = f10(c1))) | (~big_f(f7(f10(c1)), f6(f10(c1), c1))) | (~(f10(f10(c1)) = f10(c1))) | (~(f6(f10(c1), c1) = c1)) | (~big_f(f9(f10(c1), c1), f10(f10(c1)))) | (~(f9(f10(c1), c1) = c1)))),
% 29.97/20.24 inference(rewrite,[status(thm)],[])).
% 29.97/20.24 tff(32858,plain,
% 29.97/20.24 (((~(f10(f10(c1)) = f10(c1))) | (~(f7(f10(c1)) = f10(c1))) | (~(f9(f10(c1), c1) = c1)) | (~big_f(f9(f10(c1), c1), f10(f10(c1)))) | (~(f6(f10(c1), c1) = c1)) | (~big_f(f7(f10(c1)), f6(f10(c1), c1)))) <=> ((~(f7(f10(c1)) = f10(c1))) | (~big_f(f7(f10(c1)), f6(f10(c1), c1))) | (~(f10(f10(c1)) = f10(c1))) | (~(f6(f10(c1), c1) = c1)) | (~big_f(f9(f10(c1), c1), f10(f10(c1)))) | (~(f9(f10(c1), c1) = c1)))),
% 29.97/20.24 inference(rewrite,[status(thm)],[])).
% 29.97/20.24 tff(32859,plain,
% 29.97/20.24 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(f10(c1)) = f10(c1))) | (~(f7(f10(c1)) = f10(c1))) | (~(f9(f10(c1), c1) = c1)) | (~big_f(f9(f10(c1), c1), f10(f10(c1)))) | (~(f6(f10(c1), c1) = c1)) | (~big_f(f7(f10(c1)), f6(f10(c1), c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(f10(c1)) = f10(c1))) | (~big_f(f7(f10(c1)), f6(f10(c1), c1))) | (~(f10(f10(c1)) = f10(c1))) | (~(f6(f10(c1), c1) = c1)) | (~big_f(f9(f10(c1), c1), f10(f10(c1)))) | (~(f9(f10(c1), c1) = c1))))),
% 29.97/20.24 inference(monotonicity,[status(thm)],[32858])).
% 29.97/20.24 tff(32860,plain,
% 29.97/20.24 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(f10(c1)) = f10(c1))) | (~(f7(f10(c1)) = f10(c1))) | (~(f9(f10(c1), c1) = c1)) | (~big_f(f9(f10(c1), c1), f10(f10(c1)))) | (~(f6(f10(c1), c1) = c1)) | (~big_f(f7(f10(c1)), f6(f10(c1), c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(f10(c1)) = f10(c1))) | (~big_f(f7(f10(c1)), f6(f10(c1), c1))) | (~(f10(f10(c1)) = f10(c1))) | (~(f6(f10(c1), c1) = c1)) | (~big_f(f9(f10(c1), c1), f10(f10(c1)))) | (~(f9(f10(c1), c1) = c1)))),
% 29.97/20.24 inference(transitivity,[status(thm)],[32859, 32857])).
% 29.97/20.24 tff(32861,plain,
% 29.97/20.24 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(f10(c1)) = f10(c1))) | (~(f7(f10(c1)) = f10(c1))) | (~(f9(f10(c1), c1) = c1)) | (~big_f(f9(f10(c1), c1), f10(f10(c1)))) | (~(f6(f10(c1), c1) = c1)) | (~big_f(f7(f10(c1)), f6(f10(c1), c1))))),
% 29.97/20.24 inference(quant_inst,[status(thm)],[])).
% 29.97/20.24 tff(32862,plain,
% 29.97/20.24 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(f10(c1)) = f10(c1))) | (~big_f(f7(f10(c1)), f6(f10(c1), c1))) | (~(f10(f10(c1)) = f10(c1))) | (~(f6(f10(c1), c1) = c1)) | (~big_f(f9(f10(c1), c1), f10(f10(c1)))) | (~(f9(f10(c1), c1) = c1))),
% 29.97/20.24 inference(modus_ponens,[status(thm)],[32861, 32860])).
% 29.97/20.24 tff(32863,plain,
% 29.97/20.24 ((~big_f(f9(f10(c1), c1), f10(f10(c1)))) | (~(f9(f10(c1), c1) = c1))),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[32862, 2378, 32856, 25967, 32722, 32719])).
% 29.97/20.24 tff(32864,plain,
% 29.97/20.24 (~(f9(f10(c1), c1) = c1)),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[32863, 32855])).
% 29.97/20.24 tff(32865,plain,
% 29.97/20.24 ($false),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[32864, 32852])).
% 29.97/20.24 tff(32866,plain,((~(f6(c2, c1) = c1)) | (f10(c1) = c1) | (~(f10(c2) = c2)) | (~big_f(f10(c1), c1)) | (~(f7(c2) = c2)) | big_f(c2, f10(c1))), inference(lemma,lemma(discharge,[]))).
% 29.97/20.24 tff(32867,plain,
% 29.97/20.24 (~(f6(c2, c1) = c1)),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[32866, 32810, 3, 32666, 32819, 8451])).
% 29.97/20.24 tff(32868,plain,
% 29.97/20.24 (f7(c2) = c2),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[32818, 122, 121, 15])).
% 29.97/20.24 tff(32869,plain,
% 29.97/20.24 (big_f(f9(c2, c1), f10(c2))),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[11344, 1139, 77, 122, 348, 3197])).
% 29.97/20.24 tff(32870,plain,
% 29.97/20.24 (~(big_f(c2, c2) <=> big_f(f9(c2, c1), f10(c2)))),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[8436, 32869, 121])).
% 29.97/20.24 tff(32871,plain,
% 29.97/20.24 (~(c2 = f9(c2, c1))),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[8442, 32870, 4989])).
% 29.97/20.24 tff(32872,plain,
% 29.97/20.24 ($false),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[32871, 8434])).
% 29.97/20.24 tff(32873,plain,((f9(c2, c1) = c1) | big_f(c2, c2) | (~(f7(c2) = c2)) | (~(f10(c2) = c2)) | (~big_f(c2, c1)) | big_f(f7(c2), f6(c2, c1))), inference(lemma,lemma(discharge,[]))).
% 29.97/20.24 tff(32874,plain,
% 29.97/20.24 (f9(c2, c1) = c1),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[32873, 3197, 77, 122, 348, 121])).
% 29.97/20.24 tff(32875,plain,
% 29.97/20.24 (big_f(f9(c2, c1), f10(c2)) <=> big_f(c1, c2)),
% 29.97/20.24 inference(monotonicity,[status(thm)],[32874, 122])).
% 29.97/20.24 tff(32876,plain,
% 29.97/20.24 (big_f(f9(c2, c1), f10(c2)) <=> big_f(c1, f10(c1))),
% 29.97/20.24 inference(transitivity,[status(thm)],[32875, 3350])).
% 29.97/20.24 tff(32877,plain,
% 29.97/20.24 ((~big_f(f9(c2, c1), f10(c2))) <=> (~big_f(c1, f10(c1)))),
% 29.97/20.24 inference(monotonicity,[status(thm)],[32876])).
% 29.97/20.24 tff(32878,plain,
% 29.97/20.24 (~big_f(f9(c2, c1), f10(c2))),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[3225, 2409, 122, 32874, 77, 3198, 3197])).
% 29.97/20.24 tff(32879,plain,
% 29.97/20.24 (~big_f(c1, f10(c1))),
% 29.97/20.24 inference(modus_ponens,[status(thm)],[32878, 32877])).
% 29.97/20.24 tff(32880,plain,
% 29.97/20.24 (~(c2 = f8(c1))),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[3001, 3197, 77, 3, 8451, 3198])).
% 29.97/20.24 tff(32881,plain,
% 29.97/20.24 (~(f8(c1) = c2)),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[1675, 32880])).
% 29.97/20.24 tff(32882,plain,
% 29.97/20.24 (f8(c1) = c1),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[1680, 32881])).
% 29.97/20.24 tff(32883,plain,
% 29.97/20.24 (c1 = f8(c1)),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[9808, 32882])).
% 29.97/20.24 tff(32884,plain,
% 29.97/20.24 ($false),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[3047, 2994, 3, 77, 3198, 3197, 32883, 32879])).
% 29.97/20.24 tff(32885,plain,(big_f(f7(c2), f6(c2, c1)) | (f10(c1) = c1) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1) | (~(f10(c2) = c2)) | (~big_f(c2, c1)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 29.97/20.24 tff(32886,plain,
% 29.97/20.24 (big_f(f7(c2), f6(c2, c1))),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[32885, 3198, 121, 32665, 122, 32868, 3])).
% 29.97/20.24 tff(32887,plain,
% 29.97/20.24 ($false),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[17266, 32886, 3198, 121, 172, 32868])).
% 29.97/20.24 tff(32888,plain,((f6(c2, c1) = c1) | big_f(c2, c2) | (~(c3 = c1)) | (~(f10(c2) = c2)) | (f10(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.97/20.24 tff(32889,plain,
% 29.97/20.24 (~(c3 = c1)),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[32888, 32867, 121, 32810, 3])).
% 29.97/20.24 tff(32890,plain,
% 29.97/20.24 (c3 = c2),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[180, 32889])).
% 29.97/20.24 tff(32891,plain,
% 29.97/20.24 (big_f(f7(c2), f6(c2, c1)) <=> big_f(c2, f6(c2, c1))),
% 29.97/20.24 inference(monotonicity,[status(thm)],[32819])).
% 29.97/20.24 tff(32892,plain,
% 29.97/20.24 (big_f(f7(c2), f6(c2, c1))),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[32885, 32867, 121, 32665, 32810, 32819, 3])).
% 29.97/20.24 tff(32893,plain,
% 29.97/20.24 (big_f(c2, f6(c2, c1))),
% 29.97/20.24 inference(modus_ponens,[status(thm)],[32892, 32891])).
% 29.97/20.24 tff(32894,plain,
% 29.97/20.24 (~(f4(c4) = c2)),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[11706, 32893, 121, 431, 32890, 32867])).
% 29.97/20.24 tff(32895,plain,
% 29.97/20.24 (f4(c4) = c1),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[11750, 32894])).
% 29.97/20.24 tff(32896,plain,
% 29.97/20.24 ((~(f6(c2, f7(f4(c4))) = c1)) | (f6(c2, c1) = c1) | (~(f4(c4) = c1))),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[26572, 25791])).
% 29.97/20.24 tff(32897,plain,
% 29.97/20.24 (~(f6(c2, f7(f4(c4))) = c1)),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[32896, 32895, 32867])).
% 29.97/20.24 tff(32898,plain,
% 29.97/20.24 (f6(c2, f7(f4(c4))) = c2),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[6601, 32897])).
% 29.97/20.24 tff(32899,plain,
% 29.97/20.24 (f6(c2, f7(f4(c4))) = f10(c1)),
% 29.97/20.24 inference(transitivity,[status(thm)],[32898, 5571])).
% 29.97/20.24 tff(32900,plain,
% 29.97/20.24 (f7(c2) = f10(c1)),
% 29.97/20.24 inference(transitivity,[status(thm)],[32819, 5571])).
% 29.97/20.24 tff(32901,plain,
% 29.97/20.24 (big_f(f7(c2), f6(c2, f7(f4(c4)))) <=> big_f(f10(c1), f10(c1))),
% 29.97/20.24 inference(monotonicity,[status(thm)],[32900, 32899])).
% 29.97/20.24 tff(32902,plain,
% 29.97/20.24 (big_f(f10(c1), f10(c1)) <=> big_f(f7(c2), f6(c2, f7(f4(c4))))),
% 29.97/20.24 inference(symmetry,[status(thm)],[32901])).
% 29.97/20.24 tff(32903,plain,
% 29.97/20.24 ((~big_f(f10(c1), f10(c1))) <=> (~big_f(f7(c2), f6(c2, f7(f4(c4)))))),
% 29.97/20.24 inference(monotonicity,[status(thm)],[32902])).
% 29.97/20.24 tff(32904,plain,
% 29.97/20.24 (~big_f(f7(c2), f6(c2, f7(f4(c4))))),
% 29.97/20.24 inference(modus_ponens,[status(thm)],[26001, 32903])).
% 29.97/20.24 tff(32905,plain,
% 29.97/20.24 (big_f(f7(c2), f6(c2, f7(f4(c4)))) <=> big_f(f7(c2), f6(c2, c1))),
% 29.97/20.24 inference(monotonicity,[status(thm)],[26568])).
% 29.97/20.24 tff(32906,plain,
% 29.97/20.24 ((~big_f(f7(c2), f6(c2, f7(f4(c4))))) <=> (~big_f(f7(c2), f6(c2, c1)))),
% 29.97/20.24 inference(monotonicity,[status(thm)],[32905])).
% 29.97/20.24 tff(32907,assumption,(~big_f(f7(c2), f6(c2, f7(f4(c4))))), introduced(assumption)).
% 29.97/20.24 tff(32908,plain,
% 29.97/20.24 (~big_f(f7(c2), f6(c2, c1))),
% 29.97/20.24 inference(modus_ponens,[status(thm)],[32907, 32906])).
% 29.97/20.24 tff(32909,plain,
% 29.97/20.24 ($false),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[3078, 32908])).
% 29.97/20.24 tff(32910,plain,((~big_f(f7(c2), f6(c2, c1))) | big_f(f7(c2), f6(c2, f7(f4(c4)))) | (~(f7(c1) = c1)) | (~(f4(c4) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.97/20.24 tff(32911,plain,
% 29.97/20.24 ((~big_f(f7(c2), f6(c2, c1))) | big_f(f7(c2), f6(c2, f7(f4(c4)))) | (~(f4(c4) = c1))),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[32910, 25791])).
% 29.97/20.24 tff(32912,plain,
% 29.97/20.24 (big_f(f7(c2), f6(c2, f7(f4(c4))))),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[32911, 32895, 32892])).
% 29.97/20.24 tff(32913,plain,
% 29.97/20.24 ($false),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[32912, 32904])).
% 29.97/20.24 tff(32914,plain,((~(c4 = c2)) | big_f(c2, c2) | (f10(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.97/20.24 tff(32915,plain,
% 29.97/20.24 (~(c4 = c2)),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[32914, 3, 121])).
% 29.97/20.24 tff(32916,plain,
% 29.97/20.24 (c4 = c1),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[461, 32915])).
% 29.97/20.24 tff(32917,plain,
% 29.97/20.24 (big_f(f4(c4), c4)),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[27798, 23515, 31714, 564])).
% 29.97/20.24 tff(32918,plain,
% 29.97/20.24 (big_f(f7(c2), f7(c2))),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[17136, 22, 480, 11752, 474])).
% 29.97/20.24 tff(32919,plain,
% 29.97/20.24 (~big_f(f7(c2), c2)),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[15961, 32918, 122, 121, 17])).
% 29.97/20.24 tff(32920,plain,
% 29.97/20.24 ($false),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[32919, 32816])).
% 29.97/20.24 tff(32921,plain,((f7(c2) = c2) | (~(f10(c1) = c2)) | (~(f10(c2) = c2)) | big_f(c2, c2) | (~(c4 = c1)) | (~(f4(c4) = c1)) | (~big_f(f4(c4), c4))), inference(lemma,lemma(discharge,[]))).
% 29.97/20.24 tff(32922,plain,
% 29.97/20.24 ($false),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[32921, 32917, 23515, 480, 121, 16, 122, 17])).
% 29.97/20.24 tff(32923,plain,((f7(c2) = c2) | (~(c4 = c1)) | big_f(c2, c2) | (~(f10(c1) = c2)) | (~(f10(c2) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.97/20.24 tff(32924,plain,
% 29.97/20.24 (~(f10(c2) = c2)),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[32923, 17, 121, 15, 32916])).
% 29.97/20.24 tff(32925,plain,
% 29.97/20.24 (f10(c2) = c1),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[93, 32924])).
% 29.97/20.24 tff(32926,plain,
% 29.97/20.24 (f10(f10(c1)) = c1),
% 29.97/20.24 inference(transitivity,[status(thm)],[24860, 32925])).
% 29.97/20.24 tff(32927,plain,
% 29.97/20.24 (big_f(f10(c1), f10(f10(c1))) <=> big_f(f10(c1), c1)),
% 29.97/20.24 inference(monotonicity,[status(thm)],[32926])).
% 29.97/20.24 tff(32928,plain,
% 29.97/20.24 (big_f(f10(c1), c1) <=> big_f(f10(c1), f10(f10(c1)))),
% 29.97/20.24 inference(symmetry,[status(thm)],[32927])).
% 29.97/20.24 tff(32929,plain,
% 29.97/20.24 (big_f(f10(c1), f10(f10(c1)))),
% 29.97/20.24 inference(modus_ponens,[status(thm)],[32666, 32928])).
% 29.97/20.24 tff(32930,plain,
% 29.97/20.24 ((~big_f(c2, f10(c2))) <=> (~big_f(f10(c1), f10(f10(c1))))),
% 29.97/20.24 inference(monotonicity,[status(thm)],[31001])).
% 29.97/20.24 tff(32931,plain,
% 29.97/20.24 (~big_f(c2, f10(c2))),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[32712, 32924, 3, 17, 32666])).
% 29.97/20.24 tff(32932,plain,
% 29.97/20.24 (~big_f(f10(c1), f10(f10(c1)))),
% 29.97/20.24 inference(modus_ponens,[status(thm)],[32931, 32930])).
% 29.97/20.24 tff(32933,plain,
% 29.97/20.24 ($false),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[32932, 32929])).
% 29.97/20.24 tff(32934,plain,((f7(c2) = c2) | (f10(c1) = c1) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 29.97/20.24 tff(32935,plain,
% 29.97/20.24 (f7(c2) = c2),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[32934, 3, 121])).
% 29.97/20.24 tff(32936,plain,
% 29.97/20.24 (~(f6(c1, c1) = c1)),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[29514, 32692, 32718, 3, 32691, 31714])).
% 29.97/20.24 tff(32937,plain,
% 29.97/20.24 (~(f6(c1, f6(c1, c2)) = c1)),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[58, 32936])).
% 29.97/20.24 tff(32938,plain,
% 29.97/20.24 (f6(c1, f6(c1, c2)) = c2),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[63, 32937])).
% 29.97/20.24 tff(32939,plain,
% 29.97/20.24 (c1 = c4),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[484, 32916])).
% 29.97/20.24 tff(32940,plain,
% 29.97/20.24 (~(c1 = c3)),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[29590, 32692, 31714, 32665, 32939, 32936, 3, 32718, 32691])).
% 29.97/20.24 tff(32941,plain,
% 29.97/20.24 (~(c3 = c1)),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[175, 32940])).
% 29.97/20.24 tff(32942,plain,
% 29.97/20.24 (c3 = c2),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[180, 32941])).
% 29.97/20.24 tff(32943,plain,
% 29.97/20.24 (~(f6(c2, c1) = c1)),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[32742, 32692, 3, 32691, 32718, 32666, 32935])).
% 29.97/20.24 tff(32944,plain,
% 29.97/20.24 (~(f4(c4) = c1)),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[32744, 32943, 121, 89, 32670, 32717, 32935])).
% 29.97/20.24 tff(32945,plain,
% 29.97/20.24 (f4(c4) = c2),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[11750, 32944])).
% 29.97/20.24 tff(32946,plain,
% 29.97/20.24 (f6(c1, c1) = f10(c1)),
% 29.97/20.24 inference(transitivity,[status(thm)],[32390, 27490, 293])).
% 29.97/20.24 tff(32947,plain,
% 29.97/20.24 (f7(f6(c1, c1)) = f7(f10(c1))),
% 29.97/20.24 inference(monotonicity,[status(thm)],[32946])).
% 29.97/20.24 tff(32948,plain,
% 29.97/20.24 (f7(f6(c1, c1)) = f7(c2)),
% 29.97/20.24 inference(transitivity,[status(thm)],[32947, 232])).
% 29.97/20.24 tff(32949,plain,
% 29.97/20.24 (big_f(f7(f6(c1, c1)), c1) <=> big_f(f7(c2), c1)),
% 29.97/20.24 inference(monotonicity,[status(thm)],[32948])).
% 29.97/20.24 tff(32950,plain,
% 29.97/20.24 (f7(f6(c1, f6(c1, c2))) = f7(f6(c1, c1))),
% 29.97/20.24 inference(monotonicity,[status(thm)],[32478])).
% 29.97/20.24 tff(32951,plain,
% 29.97/20.24 (big_f(f7(f6(c1, f6(c1, c2))), c1) <=> big_f(f7(f6(c1, c1)), c1)),
% 29.97/20.24 inference(monotonicity,[status(thm)],[32950])).
% 29.97/20.24 tff(32952,plain,
% 29.97/20.24 (big_f(f7(f6(c1, f6(c1, c2))), c1) <=> big_f(f7(c2), c1)),
% 29.97/20.24 inference(transitivity,[status(thm)],[32951, 32949])).
% 29.97/20.24 tff(32953,plain,
% 29.97/20.24 ((~big_f(f7(f6(c1, f6(c1, c2))), c1)) <=> (~big_f(f7(c2), c1))),
% 29.97/20.24 inference(monotonicity,[status(thm)],[32952])).
% 29.97/20.24 tff(32954,assumption,(~big_f(f7(f6(c1, f6(c1, c2))), c1)), introduced(assumption)).
% 29.97/20.24 tff(32955,plain,
% 29.97/20.24 (~big_f(f7(c2), c1)),
% 29.97/20.24 inference(modus_ponens,[status(thm)],[32954, 32953])).
% 29.97/20.24 tff(32956,plain,
% 29.97/20.24 ($false),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[338, 32955])).
% 29.97/20.24 tff(32957,plain,(big_f(f7(f6(c1, f6(c1, c2))), c1) | (~big_f(f7(c2), c1)) | (~(f10(c1) = c2)) | (~(f6(c1, f6(c1, c2)) = c2))), inference(lemma,lemma(discharge,[]))).
% 29.97/20.24 tff(32958,plain,
% 29.97/20.24 (big_f(f7(f6(c1, f6(c1, c2))), c1)),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[32957, 32674, 15, 27490])).
% 29.97/20.24 tff(32959,plain,
% 29.97/20.24 ((c1 = f8(f10(c1))) <=> (c1 = f8(c2))),
% 29.97/20.24 inference(symmetry,[status(thm)],[29495])).
% 29.97/20.24 tff(32960,plain,
% 29.97/20.24 ((f5(f10(c1)) = c1) <=> (f5(c2) = c1)),
% 29.97/20.24 inference(monotonicity,[status(thm)],[27868])).
% 29.97/20.24 tff(32961,plain,
% 29.97/20.24 ((c1 = f5(f10(c1))) <=> (f5(f10(c1)) = c1)),
% 29.97/20.24 inference(commutativity,[status(thm)],[])).
% 29.97/20.24 tff(32962,plain,
% 29.97/20.24 (f6(c1, c1) = f10(c1)),
% 29.97/20.24 inference(transitivity,[status(thm)],[32390, 27490, 5571])).
% 29.97/20.24 tff(32963,plain,
% 29.97/20.24 (f5(f6(c1, c1)) = f5(f10(c1))),
% 29.97/20.24 inference(monotonicity,[status(thm)],[32962])).
% 29.97/20.24 tff(32964,plain,
% 29.97/20.24 ((c1 = f5(f6(c1, c1))) <=> (c1 = f5(f10(c1)))),
% 29.97/20.24 inference(monotonicity,[status(thm)],[32963])).
% 29.97/20.24 tff(32965,plain,
% 29.97/20.24 ((c1 = f5(f6(c1, c1))) <=> (f5(f10(c1)) = c1)),
% 29.97/20.24 inference(transitivity,[status(thm)],[32964, 32961])).
% 29.97/20.24 tff(32966,plain,
% 29.97/20.24 (f5(f6(c1, f6(c1, c2))) = f5(f6(c1, c1))),
% 29.97/20.24 inference(monotonicity,[status(thm)],[32478])).
% 29.97/20.24 tff(32967,plain,
% 29.97/20.24 ((c1 = f5(f6(c1, f6(c1, c2)))) <=> (c1 = f5(f6(c1, c1)))),
% 29.97/20.24 inference(monotonicity,[status(thm)],[32966])).
% 29.97/20.24 tff(32968,plain,
% 29.97/20.24 ((c1 = f5(f6(c1, f6(c1, c2)))) <=> (f5(c2) = c1)),
% 29.97/20.24 inference(transitivity,[status(thm)],[32967, 32965, 32960])).
% 29.97/20.24 tff(32969,plain,
% 29.97/20.24 (big_f(f7(f6(c1, c1)), c1) <=> big_f(f7(f6(c1, f6(c1, c2))), c1)),
% 29.97/20.24 inference(symmetry,[status(thm)],[32951])).
% 29.97/20.24 tff(32970,plain,
% 29.97/20.24 (f7(f6(c1, c1)) = f7(f10(c1))),
% 29.97/20.24 inference(monotonicity,[status(thm)],[32962])).
% 29.97/20.24 tff(32971,plain,
% 29.97/20.24 (f7(f6(c1, c1)) = f7(c2)),
% 29.97/20.24 inference(transitivity,[status(thm)],[32970, 219])).
% 29.97/20.24 tff(32972,plain,
% 29.97/20.24 (big_f(f7(f6(c1, c1)), c1) <=> big_f(f7(c2), c1)),
% 29.97/20.24 inference(monotonicity,[status(thm)],[32971])).
% 29.97/20.24 tff(32973,plain,
% 29.97/20.24 (big_f(f7(c2), c1) <=> big_f(f7(f6(c1, c1)), c1)),
% 29.97/20.24 inference(symmetry,[status(thm)],[32972])).
% 29.97/20.24 tff(32974,plain,
% 29.97/20.24 (big_f(f7(c2), c1) <=> big_f(f7(f6(c1, f6(c1, c2))), c1)),
% 29.97/20.24 inference(transitivity,[status(thm)],[32973, 32969])).
% 29.97/20.24 tff(32975,plain,
% 29.97/20.24 (big_f(f7(f6(c1, f6(c1, c2))), c1)),
% 29.97/20.24 inference(modus_ponens,[status(thm)],[32674, 32974])).
% 29.97/20.24 tff(32976,plain,
% 29.97/20.24 ((f7(f6(c1, f6(c1, c2))) = f6(c1, f6(c1, c2))) <=> (f7(f6(c1, c1)) = f6(c1, c1))),
% 29.97/20.24 inference(monotonicity,[status(thm)],[32950, 32478])).
% 29.97/20.24 tff(32977,plain,
% 29.97/20.24 ((f7(f6(c1, c1)) = f6(c1, c1)) <=> (f7(f6(c1, f6(c1, c2))) = f6(c1, f6(c1, c2)))),
% 29.97/20.24 inference(symmetry,[status(thm)],[32976])).
% 29.97/20.24 tff(32978,plain,
% 29.97/20.24 ((f7(f6(c1, c1)) = f6(c1, c1)) <=> (f7(f10(c1)) = f10(c1))),
% 29.97/20.24 inference(monotonicity,[status(thm)],[32970, 32962])).
% 29.97/20.24 tff(32979,plain,
% 29.97/20.24 ((f7(f10(c1)) = f10(c1)) <=> (f7(f6(c1, c1)) = f6(c1, c1))),
% 29.97/20.24 inference(symmetry,[status(thm)],[32978])).
% 29.97/20.24 tff(32980,plain,
% 29.97/20.24 ((f7(c2) = c2) <=> (f7(f6(c1, f6(c1, c2))) = f6(c1, f6(c1, c2)))),
% 29.97/20.24 inference(transitivity,[status(thm)],[26621, 32979, 32977])).
% 29.97/20.24 tff(32981,plain,
% 29.97/20.24 ((~(f7(c2) = c2)) <=> (~(f7(f6(c1, f6(c1, c2))) = f6(c1, f6(c1, c2))))),
% 29.97/20.24 inference(monotonicity,[status(thm)],[32980])).
% 29.97/20.24 tff(32982,plain,
% 29.97/20.24 (~(f7(f6(c1, f6(c1, c2))) = f6(c1, f6(c1, c2)))),
% 29.97/20.24 inference(modus_ponens,[status(thm)],[17, 32981])).
% 29.97/20.24 tff(32983,plain,
% 29.97/20.24 ((f10(c1) = c1) | (f7(c2) = c2) | (~(f4(c4) = c2)) | big_f(f7(c2), c2) | big_f(c2, c2) | (~big_f(f7(c2), c1))),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[9951, 25791])).
% 29.97/20.24 tff(32984,plain,
% 29.97/20.24 (big_f(f7(c2), c2)),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[32983, 32674, 79, 121, 3, 17])).
% 29.97/20.24 tff(32985,plain,
% 29.97/20.24 (c2 = f8(c2)),
% 29.97/20.24 inference(unit_resolution,[status(thm)],[12312, 32675, 89, 12291, 17, 32984])).
% 29.97/20.24 tff(32986,plain,
% 29.97/20.24 (f8(c2) = c2),
% 29.97/20.24 inference(symmetry,[status(thm)],[32985])).
% 29.97/20.24 tff(32987,plain,
% 29.97/20.24 (f8(f10(c1)) = f10(c1)),
% 29.97/20.24 inference(transitivity,[status(thm)],[13827, 32986, 5571])).
% 29.97/20.24 tff(32988,plain,
% 29.97/20.24 ((c1 = f8(f10(c1))) <=> (c1 = f10(c1))),
% 29.97/20.24 inference(monotonicity,[status(thm)],[32987])).
% 29.97/20.24 tff(32989,plain,
% 29.97/20.24 ((c1 = f8(f10(c1))) <=> (f10(c1) = c1)),
% 29.97/20.24 inference(transitivity,[status(thm)],[32988, 18819])).
% 29.97/20.24 tff(32990,plain,
% 29.97/20.24 ((f10(c1) = c1) <=> (c1 = f8(f10(c1)))),
% 29.97/20.24 inference(symmetry,[status(thm)],[32989])).
% 29.97/20.24 tff(32991,plain,
% 29.97/20.24 ((f10(c1) = c1) <=> (c1 = f8(c2))),
% 29.97/20.24 inference(transitivity,[status(thm)],[32990, 32959])).
% 29.97/20.24 tff(32992,plain,
% 29.97/20.24 ((~(f10(c1) = c1)) <=> (~(c1 = f8(c2)))),
% 29.97/20.24 inference(monotonicity,[status(thm)],[32991])).
% 29.97/20.24 tff(32993,plain,
% 29.97/20.24 (~(c1 = f8(c2))),
% 29.97/20.24 inference(modus_ponens,[status(thm)],[3, 32992])).
% 29.97/20.24 tff(32994,plain,
% 29.97/20.24 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (~big_f(f7(f6(c1, f6(c1, c2))), c1)) | (f7(f6(c1, f6(c1, c2))) = f6(c1, f6(c1, c2))) | (c1 = f5(f6(c1, f6(c1, c2)))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (~big_f(f7(f6(c1, f6(c1, c2))), c1)) | (f7(f6(c1, f6(c1, c2))) = f6(c1, f6(c1, c2))) | (c1 = f5(f6(c1, f6(c1, c2)))))),
% 29.97/20.24 inference(rewrite,[status(thm)],[])).
% 29.97/20.24 tff(32995,plain,
% 29.97/20.24 (((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (f7(f6(c1, f6(c1, c2))) = f6(c1, f6(c1, c2))) | (c1 = f5(f6(c1, f6(c1, c2)))) | (~big_f(f7(f6(c1, f6(c1, c2))), c1))) <=> ((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (~big_f(f7(f6(c1, f6(c1, c2))), c1)) | (f7(f6(c1, f6(c1, c2))) = f6(c1, f6(c1, c2))) | (c1 = f5(f6(c1, f6(c1, c2)))))),
% 29.97/20.24 inference(rewrite,[status(thm)],[])).
% 29.97/20.24 tff(32996,plain,
% 29.97/20.24 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (f7(f6(c1, f6(c1, c2))) = f6(c1, f6(c1, c2))) | (c1 = f5(f6(c1, f6(c1, c2)))) | (~big_f(f7(f6(c1, f6(c1, c2))), c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (~big_f(f7(f6(c1, f6(c1, c2))), c1)) | (f7(f6(c1, f6(c1, c2))) = f6(c1, f6(c1, c2))) | (c1 = f5(f6(c1, f6(c1, c2))))))),
% 29.97/20.24 inference(monotonicity,[status(thm)],[32995])).
% 29.97/20.24 tff(32997,plain,
% 29.97/20.24 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (f7(f6(c1, f6(c1, c2))) = f6(c1, f6(c1, c2))) | (c1 = f5(f6(c1, f6(c1, c2)))) | (~big_f(f7(f6(c1, f6(c1, c2))), c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (~big_f(f7(f6(c1, f6(c1, c2))), c1)) | (f7(f6(c1, f6(c1, c2))) = f6(c1, f6(c1, c2))) | (c1 = f5(f6(c1, f6(c1, c2)))))),
% 29.97/20.24 inference(transitivity,[status(thm)],[32996, 32994])).
% 29.97/20.24 tff(32998,plain,
% 29.97/20.24 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (f7(f6(c1, f6(c1, c2))) = f6(c1, f6(c1, c2))) | (c1 = f5(f6(c1, f6(c1, c2)))) | (~big_f(f7(f6(c1, f6(c1, c2))), c1)))),
% 29.97/20.24 inference(quant_inst,[status(thm)],[])).
% 29.97/20.24 tff(32999,plain,
% 29.97/20.24 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (~big_f(f7(f6(c1, f6(c1, c2))), c1)) | (f7(f6(c1, f6(c1, c2))) = f6(c1, f6(c1, c2))) | (c1 = f5(f6(c1, f6(c1, c2))))),
% 29.97/20.25 inference(modus_ponens,[status(thm)],[32998, 32997])).
% 29.97/20.25 tff(33000,plain,
% 29.97/20.25 ((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (~big_f(f7(f6(c1, f6(c1, c2))), c1)) | (f7(f6(c1, f6(c1, c2))) = f6(c1, f6(c1, c2))) | (c1 = f5(f6(c1, f6(c1, c2))))),
% 29.97/20.25 inference(unit_resolution,[status(thm)],[32999, 1659])).
% 29.97/20.25 tff(33001,plain,
% 29.97/20.25 (c1 = f5(f6(c1, f6(c1, c2)))),
% 29.97/20.25 inference(unit_resolution,[status(thm)],[33000, 32993, 89, 32717, 32982, 32975])).
% 29.97/20.25 tff(33002,plain,
% 29.97/20.25 (f5(c2) = c1),
% 29.97/20.25 inference(modus_ponens,[status(thm)],[33001, 32968])).
% 29.97/20.25 tff(33003,assumption,(~(f8(c1) = c1)), introduced(assumption)).
% 29.97/20.25 tff(33004,plain,
% 29.97/20.25 (big_f(f7(c2), f6(c1, c1)) <=> big_f(f7(f10(c1)), f6(c1, c1))),
% 29.97/20.25 inference(monotonicity,[status(thm)],[26620])).
% 29.97/20.25 tff(33005,plain,
% 29.97/20.25 (big_f(f7(f10(c1)), f6(c1, c1)) <=> big_f(f7(c2), f6(c1, c1))),
% 29.97/20.25 inference(symmetry,[status(thm)],[33004])).
% 29.97/20.25 tff(33006,plain,
% 29.97/20.25 (big_f(f7(f10(c1)), f6(c1, c1)) <=> big_f(f7(f10(c1)), f10(c1))),
% 29.97/20.25 inference(monotonicity,[status(thm)],[32962])).
% 29.97/20.25 tff(33007,plain,
% 29.97/20.25 (big_f(f7(f10(c1)), f10(c1)) <=> big_f(f7(f10(c1)), f6(c1, c1))),
% 29.97/20.25 inference(symmetry,[status(thm)],[33006])).
% 29.97/20.25 tff(33008,plain,
% 29.97/20.25 (big_f(f7(f10(c1)), f10(c1)) <=> big_f(f7(c2), f6(c1, c1))),
% 29.97/20.25 inference(transitivity,[status(thm)],[33007, 33005])).
% 29.97/20.25 tff(33009,plain,
% 29.97/20.25 (big_f(f7(f10(c1)), f10(c1))),
% 29.97/20.25 inference(unit_resolution,[status(thm)],[27977, 22, 31714, 32666, 89, 3])).
% 29.97/20.25 tff(33010,plain,
% 29.97/20.25 (big_f(f7(c2), f6(c1, c1))),
% 29.97/20.25 inference(modus_ponens,[status(thm)],[33009, 33008])).
% 29.97/20.25 tff(33011,plain,
% 29.97/20.25 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f7(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (f7(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))))),
% 29.97/20.25 inference(rewrite,[status(thm)],[])).
% 29.97/20.25 tff(33012,plain,
% 29.97/20.25 (((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(c2) = c2) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1)))) <=> ((f10(c2) = c2) | (f7(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))))),
% 29.97/20.25 inference(rewrite,[status(thm)],[])).
% 29.97/20.25 tff(33013,plain,
% 29.97/20.25 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(c2) = c2) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f7(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1)))))),
% 29.97/20.25 inference(monotonicity,[status(thm)],[33012])).
% 29.97/20.25 tff(33014,plain,
% 29.97/20.25 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(c2) = c2) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (f7(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))))),
% 29.97/20.25 inference(transitivity,[status(thm)],[33013, 33011])).
% 29.97/20.25 tff(33015,plain,
% 29.97/20.25 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f7(c2) = c2) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1))))),
% 29.97/20.25 inference(quant_inst,[status(thm)],[])).
% 29.97/20.25 tff(33016,plain,
% 29.97/20.25 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (f7(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f6(c1, c1) = f5(c2)) | (~big_f(f7(c2), f6(c1, c1)))),
% 29.97/20.25 inference(modus_ponens,[status(thm)],[33015, 33014])).
% 29.97/20.25 tff(33017,plain,
% 29.97/20.25 ((c2 = f8(c2)) | (f6(c1, c1) = f5(c2))),
% 29.97/20.25 inference(unit_resolution,[status(thm)],[33016, 1659, 89, 17, 12291, 28021])).
% 29.97/20.25 tff(33018,plain,
% 29.97/20.25 (c2 = f8(c2)),
% 29.97/20.25 inference(unit_resolution,[status(thm)],[33017, 28020])).
% 29.97/20.25 tff(33019,plain,
% 29.97/20.25 (f8(c1) = c2),
% 29.97/20.25 inference(unit_resolution,[status(thm)],[1680, 33003])).
% 29.97/20.25 tff(33020,plain,
% 29.97/20.25 (f8(c1) = c1),
% 29.97/20.25 inference(transitivity,[status(thm)],[33019, 33018, 28030])).
% 29.97/20.25 tff(33021,plain,
% 29.97/20.25 ($false),
% 29.97/20.25 inference(unit_resolution,[status(thm)],[33003, 33020])).
% 29.97/20.25 tff(33022,plain,((f6(c1, c1) = f5(c2)) | (f8(c1) = c1) | (f10(c2) = c2) | (f7(c2) = c2) | (~big_f(c1, f10(c2))) | (~big_f(f7(c2), f6(c1, c1))) | (~big_f(c2, f10(c2)))), inference(lemma,lemma(discharge,[]))).
% 29.97/20.25 tff(33023,plain,
% 29.97/20.25 (f6(c1, c1) = f5(c2)),
% 29.97/20.25 inference(unit_resolution,[status(thm)],[33022, 33010, 89, 12291, 32717, 17, 33003])).
% 29.97/20.25 tff(33024,plain,
% 29.97/20.25 (~(f7(c2) = f5(c2))),
% 29.97/20.25 inference(unit_resolution,[status(thm)],[10715, 33023, 28, 22])).
% 29.97/20.25 tff(33025,plain,
% 29.97/20.25 (~(f5(c2) = c1)),
% 29.97/20.25 inference(unit_resolution,[status(thm)],[8394, 33024, 22])).
% 29.97/20.25 tff(33026,plain,
% 29.97/20.25 ($false),
% 29.97/20.25 inference(unit_resolution,[status(thm)],[33025, 33002])).
% 29.97/20.25 tff(33027,plain,((f7(c2) = c2) | (~(f6(c1, f6(c1, c2)) = c2)) | (f6(c1, c1) = c1) | (f10(c2) = c2) | (~big_f(c2, f10(c2))) | (f8(c1) = c1) | (f10(c1) = c1) | (~(f4(c4) = c2)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 29.97/20.25 tff(33028,plain,
% 29.97/20.25 (f8(c1) = c1),
% 29.97/20.25 inference(unit_resolution,[status(thm)],[33027, 17, 28, 89, 12291, 27490, 3, 79, 121])).
% 29.97/20.25 tff(33029,plain,
% 29.97/20.25 (big_f(f8(c1), f10(c1))),
% 29.97/20.25 inference(unit_resolution,[status(thm)],[3025, 33028, 30400])).
% 29.97/20.25 tff(33030,plain,
% 29.97/20.25 (big_f(f7(c2), c2)),
% 29.97/20.25 inference(unit_resolution,[status(thm)],[15716, 33028, 22, 33029, 15])).
% 29.97/20.25 tff(33031,plain,
% 29.97/20.25 (c2 = f8(c2)),
% 29.97/20.25 inference(unit_resolution,[status(thm)],[12312, 32675, 89, 12291, 17, 33030])).
% 29.97/20.25 tff(33032,plain,
% 29.97/20.25 (f8(c2) = c2),
% 29.97/20.25 inference(symmetry,[status(thm)],[33031])).
% 29.97/20.25 tff(33033,plain,
% 29.97/20.25 (f8(f10(c1)) = f10(c1)),
% 29.97/20.25 inference(transitivity,[status(thm)],[13827, 33032, 5571])).
% 29.97/20.25 tff(33034,plain,
% 29.97/20.25 ((c1 = f8(f10(c1))) <=> (c1 = f10(c1))),
% 29.97/20.25 inference(monotonicity,[status(thm)],[33033])).
% 29.97/20.25 tff(33035,plain,
% 29.97/20.25 ((c1 = f8(f10(c1))) <=> (f10(c1) = c1)),
% 29.97/20.25 inference(transitivity,[status(thm)],[33034, 18819])).
% 29.97/20.25 tff(33036,plain,
% 29.97/20.25 ((f10(c1) = c1) <=> (c1 = f8(f10(c1)))),
% 29.97/20.25 inference(symmetry,[status(thm)],[33035])).
% 29.97/20.25 tff(33037,plain,
% 29.97/20.25 ((f10(c1) = c1) <=> (c1 = f8(c2))),
% 29.97/20.25 inference(transitivity,[status(thm)],[33036, 32959])).
% 29.97/20.25 tff(33038,plain,
% 29.97/20.25 ((~(f10(c1) = c1)) <=> (~(c1 = f8(c2)))),
% 29.97/20.25 inference(monotonicity,[status(thm)],[33037])).
% 29.97/20.25 tff(33039,plain,
% 29.97/20.25 (~(c1 = f8(c2))),
% 29.97/20.25 inference(modus_ponens,[status(thm)],[3, 33038])).
% 29.97/20.25 tff(33040,plain,
% 29.97/20.25 (c1 = f5(f6(c1, f6(c1, c2)))),
% 29.97/20.25 inference(unit_resolution,[status(thm)],[33000, 32982, 89, 32717, 33039, 32958])).
% 29.97/20.25 tff(33041,plain,
% 29.97/20.25 (f5(f6(c1, f6(c1, c2))) = c1),
% 29.97/20.25 inference(symmetry,[status(thm)],[33040])).
% 29.97/20.25 tff(33042,plain,
% 29.97/20.25 (f5(f6(c1, c1)) = f5(f6(c1, f6(c1, c2)))),
% 29.97/20.25 inference(symmetry,[status(thm)],[32966])).
% 29.97/20.25 tff(33043,plain,
% 29.97/20.25 (f5(f10(c1)) = f5(f6(c1, c1))),
% 29.97/20.25 inference(symmetry,[status(thm)],[32963])).
% 29.97/20.25 tff(33044,plain,
% 29.97/20.25 ((~(f10(c1) = c1)) <=> (~(c1 = f8(f10(c1))))),
% 29.97/20.25 inference(monotonicity,[status(thm)],[33036])).
% 29.97/20.25 tff(33045,plain,
% 29.97/20.25 (~(c1 = f8(f10(c1)))),
% 29.97/20.25 inference(modus_ponens,[status(thm)],[3, 33044])).
% 29.97/20.25 tff(33046,plain,
% 29.97/20.25 (f10(c1) = f5(f10(c1))),
% 29.97/20.25 inference(unit_resolution,[status(thm)],[32707, 1659, 32692, 26623, 33045, 32691, 33009])).
% 29.97/20.25 tff(33047,plain,
% 29.97/20.25 (f10(c1) = c1),
% 29.97/20.25 inference(transitivity,[status(thm)],[33046, 33043, 33042, 33041])).
% 29.97/20.25 tff(33048,plain,
% 29.97/20.25 ($false),
% 29.97/20.25 inference(unit_resolution,[status(thm)],[3, 33047])).
% 29.97/20.25 tff(33049,plain,((f7(c2) = c2) | (f10(c1) = c1) | (~(f6(c1, f6(c1, c2)) = c2)) | (f10(c2) = c2) | (~big_f(c2, f10(c2))) | (f6(c1, c1) = c1) | (~(f4(c4) = c2)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 29.97/20.25 tff(33050,plain,
% 29.97/20.25 (f7(c2) = c2),
% 29.97/20.25 inference(unit_resolution,[status(thm)],[33049, 79, 27490, 89, 12291, 28, 3, 121])).
% 29.97/20.25 tff(33051,plain,
% 29.97/20.25 (f10(c2) = f8(c2)),
% 29.97/20.25 inference(unit_resolution,[status(thm)],[13744, 33050, 31714, 121, 1247, 79, 12291, 67, 89])).
% 29.97/20.25 tff(33052,plain,
% 29.97/20.25 ((f10(c2) = f8(c2)) <=> (c1 = f8(f10(c1)))),
% 29.97/20.25 inference(monotonicity,[status(thm)],[11819, 13830])).
% 29.97/20.25 tff(33053,plain,
% 29.97/20.25 ((c1 = f8(f10(c1))) <=> (f10(c2) = f8(c2))),
% 29.97/20.25 inference(symmetry,[status(thm)],[33052])).
% 29.97/20.25 tff(33054,plain,
% 29.97/20.25 (f8(f10(c1)) = f10(c1)),
% 29.97/20.25 inference(transitivity,[status(thm)],[13827, 13153, 5571])).
% 29.97/20.25 tff(33055,plain,
% 29.97/20.25 ((c1 = f8(f10(c1))) <=> (c1 = f10(c1))),
% 29.97/20.25 inference(monotonicity,[status(thm)],[33054])).
% 29.97/20.25 tff(33056,plain,
% 29.97/20.25 ((c1 = f8(f10(c1))) <=> (f10(c1) = c1)),
% 29.97/20.25 inference(transitivity,[status(thm)],[33055, 18819])).
% 29.97/20.25 tff(33057,plain,
% 29.97/20.25 ((f10(c1) = c1) <=> (c1 = f8(f10(c1)))),
% 29.97/20.25 inference(symmetry,[status(thm)],[33056])).
% 29.97/20.25 tff(33058,plain,
% 29.97/20.25 ((f10(c1) = c1) <=> (f10(c2) = f8(c2))),
% 29.97/20.25 inference(transitivity,[status(thm)],[33057, 33053])).
% 29.97/20.25 tff(33059,plain,
% 29.97/20.25 ((~(f10(c1) = c1)) <=> (~(f10(c2) = f8(c2)))),
% 29.97/20.25 inference(monotonicity,[status(thm)],[33058])).
% 29.97/20.25 tff(33060,plain,
% 29.97/20.25 (~(f10(c2) = f8(c2))),
% 29.97/20.25 inference(modus_ponens,[status(thm)],[3, 33059])).
% 29.97/20.25 tff(33061,plain,
% 29.97/20.25 ($false),
% 29.97/20.25 inference(unit_resolution,[status(thm)],[15586, 33060])).
% 29.97/20.25 tff(33062,plain,((~(c2 = f8(c2))) | (~(f10(c2) = f8(c2))) | (f10(c1) = c1) | (~(f10(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.97/20.25 tff(33063,plain,
% 29.97/20.25 (~(c2 = f8(c2))),
% 29.97/20.25 inference(unit_resolution,[status(thm)],[33062, 33051, 3, 94])).
% 29.97/20.25 tff(33064,plain,
% 29.97/20.25 (big_f(c2, f10(c2))),
% 29.97/20.25 inference(modus_ponens,[status(thm)],[348, 102])).
% 29.97/20.25 tff(33065,plain,
% 29.97/20.25 (~(f6(c2, f6(c2, c1)) = c2)),
% 29.97/20.25 inference(unit_resolution,[status(thm)],[14650, 12290, 77, 33064, 79, 121, 89, 6634])).
% 29.97/20.25 tff(33066,plain,
% 29.97/20.25 (f6(c2, f6(c2, c1)) = c1),
% 29.97/20.25 inference(unit_resolution,[status(thm)],[14655, 33065])).
% 29.97/20.25 tff(33067,plain,
% 29.97/20.25 (big_f(c2, f6(c2, f6(c2, c1))) <=> big_f(c2, c1)),
% 29.97/20.25 inference(monotonicity,[status(thm)],[33066])).
% 29.97/20.25 tff(33068,plain,
% 29.97/20.25 (big_f(c2, c1) <=> big_f(c2, f6(c2, f6(c2, c1)))),
% 29.97/20.25 inference(symmetry,[status(thm)],[33067])).
% 29.97/20.25 tff(33069,plain,
% 29.97/20.25 (big_f(c2, c1) <=> big_f(f7(c2), f6(c2, f6(c2, c1)))),
% 29.97/20.25 inference(transitivity,[status(thm)],[33068, 14631])).
% 29.97/20.25 tff(33070,plain,
% 29.97/20.25 (big_f(f7(c2), f6(c2, f6(c2, c1)))),
% 29.97/20.25 inference(modus_ponens,[status(thm)],[348, 33069])).
% 29.97/20.25 tff(33071,plain,
% 29.97/20.25 (~(f6(c2, f6(c2, c1)) = f6(c2, c1))),
% 29.97/20.25 inference(unit_resolution,[status(thm)],[14670, 2730, 89, 77, 33064, 12290, 33070])).
% 29.97/20.25 tff(33072,plain,
% 29.97/20.25 ((f6(c2, f6(c2, c1)) = f6(c2, c1)) <=> (c1 = f6(c2, c1))),
% 29.97/20.25 inference(monotonicity,[status(thm)],[23367])).
% 29.97/20.25 tff(33073,plain,
% 29.97/20.25 ((f6(c2, f6(c2, c1)) = f6(c2, c1)) <=> (f6(c2, c1) = c1)),
% 29.97/20.25 inference(transitivity,[status(thm)],[33072, 14624])).
% 29.97/20.25 tff(33074,plain,
% 29.97/20.25 ((f6(c2, c1) = c1) <=> (f6(c2, f6(c2, c1)) = f6(c2, c1))),
% 29.97/20.25 inference(symmetry,[status(thm)],[33073])).
% 29.97/20.25 tff(33075,plain,
% 29.97/20.25 ((f6(c2, f6(c2, f6(c2, c1))) = c1) <=> (f6(c2, f6(c2, c1)) = f6(c2, c1))),
% 29.97/20.25 inference(transitivity,[status(thm)],[23369, 33074])).
% 29.97/20.25 tff(33076,assumption,(f6(c2, f6(c2, f6(c2, c1))) = c1), introduced(assumption)).
% 29.97/20.25 tff(33077,plain,
% 29.97/20.25 (f6(c2, f6(c2, c1)) = f6(c2, c1)),
% 29.97/20.25 inference(modus_ponens,[status(thm)],[33076, 33075])).
% 29.97/20.25 tff(33078,assumption,(~(f6(c2, f6(c2, c1)) = f6(c2, c1))), introduced(assumption)).
% 29.97/20.25 tff(33079,plain,
% 29.97/20.25 ($false),
% 29.97/20.25 inference(unit_resolution,[status(thm)],[33078, 33077])).
% 29.97/20.25 tff(33080,plain,((~(f6(c2, f6(c2, f6(c2, c1))) = c1)) | (f6(c2, f6(c2, c1)) = f6(c2, c1)) | (~(f6(c2, f6(c2, c1)) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.97/20.25 tff(33081,plain,
% 29.97/20.25 (~(f6(c2, f6(c2, f6(c2, c1))) = c1)),
% 29.97/20.25 inference(unit_resolution,[status(thm)],[33080, 33071, 33066])).
% 29.97/20.25 tff(33082,assumption,(f6(c2, f6(c2, f6(c2, c1))) = c2), introduced(assumption)).
% 29.97/20.25 tff(33083,plain,
% 29.97/20.25 (big_f(f7(c2), f6(c2, f6(c2, f6(c2, c1)))) <=> big_f(c2, f6(c2, f6(c2, f6(c2, c1))))),
% 29.97/20.25 inference(monotonicity,[status(thm)],[77])).
% 29.97/20.25 tff(33084,plain,
% 29.97/20.25 (big_f(c2, f6(c2, f6(c2, f6(c2, c1)))) <=> big_f(f7(c2), f6(c2, f6(c2, f6(c2, c1))))),
% 29.97/20.25 inference(symmetry,[status(thm)],[33083])).
% 29.97/20.25 tff(33085,plain,
% 29.97/20.25 (big_f(c2, f6(c2, f6(c2, f6(c2, c1)))) <=> big_f(c2, c2)),
% 29.97/20.25 inference(monotonicity,[status(thm)],[33082])).
% 29.97/20.25 tff(33086,plain,
% 29.97/20.25 (big_f(c2, c2) <=> big_f(c2, f6(c2, f6(c2, f6(c2, c1))))),
% 29.97/20.25 inference(symmetry,[status(thm)],[33085])).
% 29.97/20.25 tff(33087,plain,
% 29.97/20.25 (big_f(c2, c2) <=> big_f(f7(c2), f6(c2, f6(c2, f6(c2, c1))))),
% 29.97/20.25 inference(transitivity,[status(thm)],[33086, 33084])).
% 29.97/20.25 tff(33088,plain,
% 29.97/20.25 ((~big_f(c2, c2)) <=> (~big_f(f7(c2), f6(c2, f6(c2, f6(c2, c1)))))),
% 29.97/20.25 inference(monotonicity,[status(thm)],[33087])).
% 29.97/20.25 tff(33089,plain,
% 29.97/20.25 (~big_f(f7(c2), f6(c2, f6(c2, f6(c2, c1))))),
% 29.97/20.25 inference(modus_ponens,[status(thm)],[121, 33088])).
% 29.97/20.25 tff(33090,plain,
% 29.97/20.25 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (~(f7(c2) = c2)) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f6(c2, f6(c2, f6(c2, c1))) = f6(c2, f6(c2, c1))) | big_f(f7(c2), f6(c2, f6(c2, f6(c2, c1)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f6(c2, f6(c2, f6(c2, c1))) = f6(c2, f6(c2, c1))) | big_f(f7(c2), f6(c2, f6(c2, f6(c2, c1)))))),
% 29.97/20.25 inference(rewrite,[status(thm)],[])).
% 29.97/20.25 tff(33091,plain,
% 29.97/20.25 (((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c2) = c2)) | (f6(c2, f6(c2, f6(c2, c1))) = f6(c2, f6(c2, c1))) | big_f(f7(c2), f6(c2, f6(c2, f6(c2, c1))))) <=> ((f10(c2) = c2) | (~(f7(c2) = c2)) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f6(c2, f6(c2, f6(c2, c1))) = f6(c2, f6(c2, c1))) | big_f(f7(c2), f6(c2, f6(c2, f6(c2, c1)))))),
% 29.97/20.25 inference(rewrite,[status(thm)],[])).
% 29.97/20.25 tff(33092,plain,
% 29.97/20.25 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c2) = c2)) | (f6(c2, f6(c2, f6(c2, c1))) = f6(c2, f6(c2, c1))) | big_f(f7(c2), f6(c2, f6(c2, f6(c2, c1)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (~(f7(c2) = c2)) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f6(c2, f6(c2, f6(c2, c1))) = f6(c2, f6(c2, c1))) | big_f(f7(c2), f6(c2, f6(c2, f6(c2, c1))))))),
% 29.97/20.25 inference(monotonicity,[status(thm)],[33091])).
% 29.97/20.25 tff(33093,plain,
% 29.97/20.25 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c2) = c2)) | (f6(c2, f6(c2, f6(c2, c1))) = f6(c2, f6(c2, c1))) | big_f(f7(c2), f6(c2, f6(c2, f6(c2, c1)))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f6(c2, f6(c2, f6(c2, c1))) = f6(c2, f6(c2, c1))) | big_f(f7(c2), f6(c2, f6(c2, f6(c2, c1)))))),
% 29.97/20.25 inference(transitivity,[status(thm)],[33092, 33090])).
% 29.97/20.25 tff(33094,plain,
% 29.97/20.25 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c2) = c2) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (~(f7(c2) = c2)) | (f6(c2, f6(c2, f6(c2, c1))) = f6(c2, f6(c2, c1))) | big_f(f7(c2), f6(c2, f6(c2, f6(c2, c1)))))),
% 29.97/20.25 inference(quant_inst,[status(thm)],[])).
% 29.97/20.25 tff(33095,plain,
% 29.97/20.25 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (c2 = f8(c2)) | (~big_f(c2, f10(c2))) | (f6(c2, f6(c2, f6(c2, c1))) = f6(c2, f6(c2, c1))) | big_f(f7(c2), f6(c2, f6(c2, f6(c2, c1))))),
% 29.97/20.25 inference(modus_ponens,[status(thm)],[33094, 33093])).
% 29.97/20.25 tff(33096,plain,
% 29.97/20.25 (f6(c2, f6(c2, f6(c2, c1))) = f6(c2, f6(c2, c1))),
% 29.97/20.25 inference(unit_resolution,[status(thm)],[33095, 2662, 89, 77, 12291, 12290, 33089])).
% 29.97/20.25 tff(33097,plain,
% 29.97/20.25 (f6(c2, f6(c2, c1)) = f6(c2, f6(c2, f6(c2, c1)))),
% 29.97/20.25 inference(symmetry,[status(thm)],[33096])).
% 29.97/20.25 tff(33098,plain,
% 29.97/20.25 (f6(c2, f6(c2, c1)) = c2),
% 29.97/20.25 inference(transitivity,[status(thm)],[33097, 33082])).
% 29.97/20.25 tff(33099,plain,
% 29.97/20.25 (big_f(c2, f6(c2, f6(c2, c1))) <=> big_f(c2, c2)),
% 29.97/20.25 inference(monotonicity,[status(thm)],[33098])).
% 29.97/20.25 tff(33100,plain,
% 29.97/20.25 (big_f(c2, c2) <=> big_f(c2, f6(c2, f6(c2, c1)))),
% 29.97/20.25 inference(symmetry,[status(thm)],[33099])).
% 29.97/20.25 tff(33101,plain,
% 29.97/20.25 ((~big_f(c2, c2)) <=> (~big_f(c2, f6(c2, f6(c2, c1))))),
% 29.97/20.25 inference(monotonicity,[status(thm)],[33100])).
% 29.97/20.25 tff(33102,plain,
% 29.97/20.25 (~big_f(c2, f6(c2, f6(c2, c1)))),
% 29.97/20.25 inference(modus_ponens,[status(thm)],[121, 33101])).
% 29.97/20.25 tff(33103,plain,
% 29.97/20.25 (big_f(f7(c2), f6(c2, f6(c2, c1)))),
% 29.97/20.25 inference(unit_resolution,[status(thm)],[14642, 2662, 89, 77, 12291, 12290, 33078])).
% 29.97/20.25 tff(33104,plain,
% 29.97/20.25 (big_f(c2, f6(c2, f6(c2, c1)))),
% 29.97/20.25 inference(modus_ponens,[status(thm)],[33103, 14630])).
% 29.97/20.25 tff(33105,plain,
% 29.97/20.25 ($false),
% 29.97/20.25 inference(unit_resolution,[status(thm)],[33104, 33102])).
% 29.97/20.25 tff(33106,plain,((~(f6(c2, f6(c2, f6(c2, c1))) = c2)) | big_f(c2, c2) | (~(f7(c2) = c2)) | (f10(c2) = c2) | (~big_f(c2, f10(c2))) | (c2 = f8(c2)) | (f6(c2, f6(c2, c1)) = f6(c2, c1))), inference(lemma,lemma(discharge,[]))).
% 29.97/20.25 tff(33107,plain,
% 29.97/20.25 (~(f6(c2, f6(c2, f6(c2, c1))) = c2)),
% 29.97/20.25 inference(unit_resolution,[status(thm)],[33106, 33071, 89, 33064, 77, 12290, 121])).
% 29.97/20.25 tff(33108,plain,
% 29.97/20.25 ($false),
% 29.97/20.25 inference(unit_resolution,[status(thm)],[23383, 33107, 33081])).
% 29.97/20.25 tff(33109,plain,((c2 = f8(c2)) | (f10(c2) = c2) | (~(f7(c2) = c2)) | big_f(c2, c2) | (~big_f(c2, c1)) | (~(f4(c4) = c2)) | (~(f6(c2, f7(f4(c4))) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.97/20.25 tff(33110,plain,
% 29.97/20.25 (~(f6(c2, f7(f4(c4))) = c1)),
% 29.97/20.25 inference(unit_resolution,[status(thm)],[33109, 33063, 79, 121, 33050, 32665, 89])).
% 29.97/20.25 tff(33111,plain,
% 29.97/20.25 (big_f(f10(c2), f10(c2))),
% 29.97/20.25 inference(unit_resolution,[status(thm)],[21743, 94, 31714])).
% 29.97/20.25 tff(33112,plain,
% 29.97/20.25 (f4(f10(c2)) = f4(c1)),
% 29.97/20.25 inference(monotonicity,[status(thm)],[94])).
% 29.97/20.25 tff(33113,plain,
% 29.97/20.25 ((f10(c2) = f4(f10(c2))) <=> (c1 = f4(c1))),
% 29.97/20.25 inference(monotonicity,[status(thm)],[94, 33112])).
% 29.97/20.25 tff(33114,plain,
% 29.97/20.25 ((c1 = f4(c1)) <=> (f10(c2) = f4(f10(c2)))),
% 29.97/20.25 inference(symmetry,[status(thm)],[33113])).
% 29.97/20.25 tff(33115,plain,
% 29.97/20.25 ((c1 = f4(c1)) <=> (f10(c2) = c2)),
% 29.97/20.25 inference(monotonicity,[status(thm)],[99, 569])).
% 29.97/20.25 tff(33116,plain,
% 29.97/20.25 ((f10(c2) = c2) <=> (c1 = f4(c1))),
% 29.97/20.25 inference(symmetry,[status(thm)],[33115])).
% 29.97/20.25 tff(33117,plain,
% 29.97/20.25 ((f10(c2) = c2) <=> (f10(c2) = f4(f10(c2)))),
% 29.97/20.25 inference(transitivity,[status(thm)],[33116, 33114])).
% 29.97/20.25 tff(33118,plain,
% 29.97/20.25 ((~(f10(c2) = c2)) <=> (~(f10(c2) = f4(f10(c2))))),
% 29.97/20.25 inference(monotonicity,[status(thm)],[33117])).
% 29.97/20.25 tff(33119,plain,
% 29.97/20.25 (~(f10(c2) = f4(f10(c2)))),
% 29.97/20.25 inference(modus_ponens,[status(thm)],[89, 33118])).
% 29.97/20.25 tff(33120,plain,
% 29.97/20.25 (f6(c2, c1) = f6(c2, f10(c2))),
% 29.97/20.25 inference(monotonicity,[status(thm)],[99])).
% 29.97/20.25 tff(33121,plain,
% 29.97/20.25 (f6(c2, f10(c2)) = f6(c2, c1)),
% 29.97/20.25 inference(symmetry,[status(thm)],[33120])).
% 29.97/20.25 tff(33122,plain,
% 29.97/20.25 ((f6(c2, f10(c2)) = f10(c2)) <=> (f6(c2, c1) = c1)),
% 29.97/20.25 inference(monotonicity,[status(thm)],[33121, 94])).
% 29.97/20.25 tff(33123,plain,
% 29.97/20.25 (big_f(f7(c2), f6(c2, f10(c2))) <=> big_f(c2, f6(c2, c1))),
% 29.97/20.25 inference(monotonicity,[status(thm)],[77, 33121])).
% 29.97/20.25 tff(33124,plain,
% 29.97/20.25 (big_f(c2, f6(c2, c1)) <=> big_f(f7(c2), f6(c2, f10(c2)))),
% 29.97/20.25 inference(symmetry,[status(thm)],[33123])).
% 29.97/20.25 tff(33125,plain,
% 29.97/20.25 ((~big_f(c2, f6(c2, c1))) <=> (~big_f(f7(c2), f6(c2, f10(c2))))),
% 29.97/20.25 inference(monotonicity,[status(thm)],[33124])).
% 29.97/20.25 tff(33126,plain,
% 29.97/20.25 (~(f6(c2, f6(c2, f6(c2, c1))) = c2)),
% 29.97/20.25 inference(unit_resolution,[status(thm)],[33106, 33078, 77, 89, 12291, 12290, 121])).
% 29.97/20.25 tff(33127,plain,
% 29.97/20.25 (f6(c2, f6(c2, f6(c2, c1))) = c1),
% 29.97/20.25 inference(unit_resolution,[status(thm)],[23383, 33126])).
% 29.97/20.25 tff(33128,plain,
% 29.97/20.25 (~(f6(c2, f6(c2, c1)) = c1)),
% 29.97/20.25 inference(unit_resolution,[status(thm)],[33080, 33127, 33078])).
% 29.97/20.25 tff(33129,plain,
% 29.97/20.25 (f6(c2, f6(c2, c1)) = c2),
% 29.97/20.25 inference(unit_resolution,[status(thm)],[14655, 33128])).
% 29.97/20.25 tff(33130,plain,
% 29.97/20.25 (f6(c2, f6(c2, f6(c2, c1))) = f6(c2, c2)),
% 29.97/20.25 inference(monotonicity,[status(thm)],[33129])).
% 29.97/20.25 tff(33131,plain,
% 29.97/20.25 (c1 = f6(c2, f6(c2, f6(c2, c1)))),
% 29.97/20.25 inference(symmetry,[status(thm)],[33127])).
% 29.97/20.25 tff(33132,plain,
% 29.97/20.25 (f10(c2) = c2),
% 29.97/20.25 inference(transitivity,[status(thm)],[94, 33131, 33130, 84, 17409])).
% 29.97/20.25 tff(33133,plain,
% 29.97/20.25 ($false),
% 29.97/20.25 inference(unit_resolution,[status(thm)],[89, 33132])).
% 29.97/20.25 tff(33134,plain,((f6(c2, f6(c2, c1)) = f6(c2, c1)) | (f10(c2) = c2) | (~(f6(c2, f7(f4(c4))) = c2)) | (~(f7(c2) = c2)) | (~(f4(c4) = c2)) | (~big_f(c2, f10(c2))) | (c2 = f8(c2)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 29.97/20.25 tff(33135,plain,
% 29.97/20.25 (f6(c2, f6(c2, c1)) = f6(c2, c1)),
% 29.97/20.25 inference(unit_resolution,[status(thm)],[33134, 12290, 17409, 77, 79, 12291, 89, 121])).
% 29.97/20.25 tff(33136,plain,
% 29.97/20.25 (big_f(c2, f6(c2, f6(c2, c1))) <=> big_f(c2, f6(c2, c1))),
% 29.97/20.25 inference(monotonicity,[status(thm)],[33135])).
% 29.97/20.25 tff(33137,plain,
% 29.97/20.25 (big_f(f7(c2), f6(c2, f6(c2, c1))) <=> big_f(c2, f6(c2, c1))),
% 29.97/20.25 inference(transitivity,[status(thm)],[14630, 33136])).
% 29.97/20.25 tff(33138,plain,
% 29.97/20.25 ((~big_f(f7(c2), f6(c2, f6(c2, c1)))) <=> (~big_f(c2, f6(c2, c1)))),
% 29.97/20.25 inference(monotonicity,[status(thm)],[33137])).
% 29.97/20.25 tff(33139,plain,
% 29.97/20.25 (~big_f(f7(c2), f6(c2, f6(c2, c1)))),
% 29.97/20.25 inference(unit_resolution,[status(thm)],[14670, 2730, 89, 77, 12291, 12290, 33135])).
% 29.97/20.25 tff(33140,plain,
% 29.97/20.25 (~big_f(c2, f6(c2, c1))),
% 29.97/20.25 inference(modus_ponens,[status(thm)],[33139, 33138])).
% 29.97/20.25 tff(33141,plain,
% 29.97/20.25 (~big_f(f7(c2), f6(c2, f10(c2)))),
% 29.97/20.25 inference(modus_ponens,[status(thm)],[33140, 33125])).
% 29.97/20.25 tff(33142,plain,
% 29.97/20.25 (f6(c2, f10(c2)) = f10(c2)),
% 29.97/20.25 inference(unit_resolution,[status(thm)],[13781, 33141])).
% 29.97/20.25 tff(33143,plain,
% 29.97/20.25 (f6(c2, c1) = c1),
% 29.97/20.25 inference(modus_ponens,[status(thm)],[33142, 33122])).
% 29.97/20.25 tff(33144,plain,
% 29.97/20.25 (f6(c2, c1) = f2(c2)),
% 29.97/20.25 inference(modus_ponens,[status(thm)],[33143, 11711])).
% 29.97/20.25 tff(33145,plain,
% 29.97/20.25 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(f10(c2) = c4)) | big_f(c2, f6(c2, c1)) | (~(f6(c2, c1) = f2(c2))) | (f10(c2) = f4(f10(c2))) | (~big_f(f10(c2), f10(c2))))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | (~(c2 = c3)) | (~(f10(c2) = c4)) | big_f(c2, f6(c2, c1)) | (~(f6(c2, c1) = f2(c2))) | (f10(c2) = f4(f10(c2))) | (~big_f(f10(c2), f10(c2))))),
% 29.97/20.25 inference(rewrite,[status(thm)],[])).
% 29.97/20.25 tff(33146,plain,
% 29.97/20.25 (((~(c2 = c3)) | (~(f6(c2, c1) = f2(c2))) | (~(f10(c2) = c4)) | (f10(c2) = f4(f10(c2))) | (~big_f(f10(c2), f10(c2))) | big_f(c2, f6(c2, c1))) <=> ((~(c2 = c3)) | (~(f10(c2) = c4)) | big_f(c2, f6(c2, c1)) | (~(f6(c2, c1) = f2(c2))) | (f10(c2) = f4(f10(c2))) | (~big_f(f10(c2), f10(c2))))),
% 29.97/20.25 inference(rewrite,[status(thm)],[])).
% 29.97/20.25 tff(33147,plain,
% 29.97/20.25 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(f6(c2, c1) = f2(c2))) | (~(f10(c2) = c4)) | (f10(c2) = f4(f10(c2))) | (~big_f(f10(c2), f10(c2))) | big_f(c2, f6(c2, c1)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(f10(c2) = c4)) | big_f(c2, f6(c2, c1)) | (~(f6(c2, c1) = f2(c2))) | (f10(c2) = f4(f10(c2))) | (~big_f(f10(c2), f10(c2)))))),
% 29.97/20.26 inference(monotonicity,[status(thm)],[33146])).
% 29.97/20.26 tff(33148,plain,
% 29.97/20.26 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(f6(c2, c1) = f2(c2))) | (~(f10(c2) = c4)) | (f10(c2) = f4(f10(c2))) | (~big_f(f10(c2), f10(c2))) | big_f(c2, f6(c2, c1)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | (~(c2 = c3)) | (~(f10(c2) = c4)) | big_f(c2, f6(c2, c1)) | (~(f6(c2, c1) = f2(c2))) | (f10(c2) = f4(f10(c2))) | (~big_f(f10(c2), f10(c2))))),
% 29.97/20.26 inference(transitivity,[status(thm)],[33147, 33145])).
% 29.97/20.26 tff(33149,plain,
% 29.97/20.26 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(f6(c2, c1) = f2(c2))) | (~(f10(c2) = c4)) | (f10(c2) = f4(f10(c2))) | (~big_f(f10(c2), f10(c2))) | big_f(c2, f6(c2, c1)))),
% 29.97/20.26 inference(quant_inst,[status(thm)],[])).
% 29.97/20.26 tff(33150,plain,
% 29.97/20.26 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | big_f(X10, X12))) | (~(c2 = c3)) | (~(f10(c2) = c4)) | big_f(c2, f6(c2, c1)) | (~(f6(c2, c1) = f2(c2))) | (f10(c2) = f4(f10(c2))) | (~big_f(f10(c2), f10(c2)))),
% 29.97/20.26 inference(modus_ponens,[status(thm)],[33149, 33148])).
% 29.97/20.26 tff(33151,plain,
% 29.97/20.26 (~(f6(c2, c1) = f2(c2))),
% 29.97/20.26 inference(unit_resolution,[status(thm)],[33150, 11666, 1335, 15484, 33140, 14686, 15483])).
% 29.97/20.26 tff(33152,plain,
% 29.97/20.26 ($false),
% 29.97/20.26 inference(unit_resolution,[status(thm)],[33151, 33144])).
% 29.97/20.26 tff(33153,plain,((c2 = f8(c2)) | (~(f2(c3) = c1)) | (~(c3 = c2)) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (~big_f(c2, f10(c2))) | (~(f10(c2) = c4)) | (~big_f(f10(c2), f10(c2))) | (f10(c2) = f4(f10(c2))) | (~(f6(c2, f7(f4(c4))) = c2)) | (~(f4(c4) = c2)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 29.97/20.26 tff(33154,plain,
% 29.97/20.26 ($false),
% 29.97/20.26 inference(unit_resolution,[status(thm)],[33153, 33119, 15476, 67, 89, 77, 12291, 1247, 14686, 12290, 17409, 79, 121])).
% 29.97/20.26 tff(33155,plain,((~(c4 = c1)) | (~(c3 = c2)) | (f10(c2) = c2) | (~(f7(c2) = c2)) | (~big_f(c2, f10(c2))) | (~(f2(c3) = c1)) | (~big_f(f10(c2), f10(c2))) | (c2 = f8(c2)) | (~(f6(c2, f7(f4(c4))) = c2)) | (~(f4(c4) = c2)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 29.97/20.26 tff(33156,plain,
% 29.97/20.26 (~(f6(c2, f7(f4(c4))) = c2)),
% 29.97/20.26 inference(unit_resolution,[status(thm)],[33155, 33063, 121, 480, 89, 33111, 12291, 1247, 33050, 79, 67])).
% 29.97/20.26 tff(33157,plain,
% 29.97/20.26 ($false),
% 29.97/20.26 inference(unit_resolution,[status(thm)],[6601, 33156, 33110])).
% 29.97/20.26 tff(33158,plain,((~(f4(c4) = c2)) | big_f(c2, c2) | (~(c4 = c1)) | (f10(c2) = c2) | (~big_f(c2, f10(c2))) | (~(f2(c3) = c1)) | (~(c3 = c2)) | (f10(c1) = c1) | (~(f6(c1, f6(c1, c2)) = c2)) | (f6(c1, c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.97/20.26 tff(33159,plain,
% 29.97/20.26 (~(f2(c3) = c1)),
% 29.97/20.26 inference(unit_resolution,[status(thm)],[33158, 32945, 32916, 121, 89, 32670, 32942, 3, 32938, 32936])).
% 29.97/20.26 tff(33160,plain,
% 29.97/20.26 (~(f2(c3) = c2)),
% 29.97/20.26 inference(unit_resolution,[status(thm)],[11686, 32945, 31714, 121, 32942, 32665])).
% 29.97/20.26 tff(33161,plain,
% 29.97/20.26 ($false),
% 29.97/20.26 inference(unit_resolution,[status(thm)],[1273, 33160, 33159])).
% 29.97/20.26 tff(33162,plain,((f10(c2) = c2) | big_f(c2, c2) | (f10(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.97/20.26 tff(33163,plain,
% 29.97/20.26 (f10(c2) = c2),
% 29.97/20.26 inference(unit_resolution,[status(thm)],[33162, 3, 121])).
% 29.97/20.26 tff(33164,plain,
% 29.97/20.26 (~(f6(c2, c1) = c1)),
% 29.97/20.26 inference(unit_resolution,[status(thm)],[32866, 33163, 3, 32666, 32935, 8451])).
% 29.97/20.26 tff(33165,plain,
% 29.97/20.26 (~(c3 = c1)),
% 29.97/20.26 inference(unit_resolution,[status(thm)],[32888, 33163, 121, 33164, 3])).
% 29.97/20.26 tff(33166,plain,
% 29.97/20.26 (c3 = c2),
% 29.97/20.26 inference(unit_resolution,[status(thm)],[180, 33165])).
% 29.97/20.26 tff(33167,plain,
% 29.97/20.26 (c2 = f7(c2)),
% 29.97/20.26 inference(modus_ponens,[status(thm)],[32935, 17312])).
% 29.97/20.26 tff(33168,plain,
% 29.97/20.26 (big_f(f7(c2), f6(c2, c1))),
% 29.97/20.26 inference(unit_resolution,[status(thm)],[32885, 33163, 121, 32665, 33164, 32935, 3])).
% 29.97/20.26 tff(33169,plain,
% 29.97/20.26 (~(big_f(c2, c2) <=> big_f(f7(c2), f6(c2, c1)))),
% 29.97/20.26 inference(unit_resolution,[status(thm)],[17315, 33168, 121])).
% 29.97/20.26 tff(33170,plain,
% 29.97/20.26 (~(c2 = f6(c2, c1))),
% 29.97/20.26 inference(unit_resolution,[status(thm)],[17322, 33169, 33167])).
% 29.97/20.26 tff(33171,plain,
% 29.97/20.26 ((f7(c1) = c1) <=> (f7(c1) = c4)),
% 29.97/20.26 inference(monotonicity,[status(thm)],[11526])).
% 29.97/20.26 tff(33172,plain,
% 29.97/20.26 (f7(c1) = c4),
% 29.97/20.26 inference(modus_ponens,[status(thm)],[4234, 33171])).
% 29.97/20.26 tff(33173,plain,
% 29.97/20.26 ($false),
% 29.97/20.26 inference(unit_resolution,[status(thm)],[1000, 33172])).
% 29.97/20.26 tff(33174,plain,((~(f7(c1) = c1)) | (f7(c1) = c4) | (~(c1 = c4))), inference(lemma,lemma(discharge,[]))).
% 29.97/20.26 tff(33175,plain,
% 29.97/20.26 ((f7(c1) = c4) | (~(c1 = c4))),
% 29.97/20.26 inference(unit_resolution,[status(thm)],[33174, 25791])).
% 29.97/20.26 tff(33176,plain,
% 29.97/20.26 (f7(c1) = c4),
% 29.97/20.26 inference(unit_resolution,[status(thm)],[33175, 11526])).
% 29.97/20.26 tff(33177,plain,
% 29.97/20.26 (f7(f4(c4)) = f4(c4)),
% 29.97/20.26 inference(unit_resolution,[status(thm)],[19880, 11752, 33176, 11526])).
% 29.97/20.26 tff(33178,plain,
% 29.97/20.26 (f4(c4) = f7(f4(c4))),
% 29.97/20.26 inference(symmetry,[status(thm)],[33177])).
% 29.97/20.26 tff(33179,plain,
% 29.97/20.26 (c1 = f7(f4(c4))),
% 29.97/20.26 inference(transitivity,[status(thm)],[16651, 33178])).
% 29.97/20.26 tff(33180,plain,
% 29.97/20.26 (f6(c2, c1) = f6(c2, f7(f4(c4)))),
% 29.97/20.26 inference(monotonicity,[status(thm)],[33179])).
% 29.97/20.26 tff(33181,plain,
% 29.97/20.26 (f6(c2, f7(f4(c4))) = f6(c2, c1)),
% 29.97/20.26 inference(symmetry,[status(thm)],[33180])).
% 29.97/20.26 tff(33182,plain,
% 29.97/20.26 (~(f6(c2, f7(f4(c4))) = c1)),
% 29.97/20.26 inference(unit_resolution,[status(thm)],[32896, 11752, 3198])).
% 29.97/20.26 tff(33183,plain,
% 29.97/20.26 (f6(c2, f7(f4(c4))) = c2),
% 29.97/20.26 inference(unit_resolution,[status(thm)],[6601, 33182])).
% 29.97/20.26 tff(33184,plain,
% 29.97/20.26 (c2 = f6(c2, f7(f4(c4)))),
% 29.97/20.26 inference(symmetry,[status(thm)],[33183])).
% 29.97/20.26 tff(33185,plain,
% 29.97/20.26 (c2 = f6(c2, c1)),
% 29.97/20.26 inference(transitivity,[status(thm)],[33184, 33181])).
% 29.97/20.26 tff(33186,plain,
% 29.97/20.26 ($false),
% 29.97/20.26 inference(unit_resolution,[status(thm)],[23378, 33185])).
% 29.97/20.26 tff(33187,plain,((~(f4(c4) = c1)) | (c2 = f6(c2, c1)) | (~(c1 = c4)) | (f6(c2, c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.97/20.26 tff(33188,plain,
% 29.97/20.26 (~(f4(c4) = c1)),
% 29.97/20.26 inference(unit_resolution,[status(thm)],[33187, 33170, 32939, 33164])).
% 29.97/20.26 tff(33189,plain,
% 29.97/20.26 (f4(c4) = c2),
% 29.97/20.26 inference(unit_resolution,[status(thm)],[11750, 33188])).
% 29.97/20.26 tff(33190,plain,
% 29.97/20.26 (big_f(f7(c2), f6(c2, c1)) <=> big_f(c2, f6(c2, c1))),
% 29.97/20.26 inference(symmetry,[status(thm)],[22951])).
% 29.97/20.26 tff(33191,plain,
% 29.97/20.26 (big_f(f7(c2), f6(c2, c1))),
% 29.97/20.26 inference(unit_resolution,[status(thm)],[32885, 3198, 121, 32665, 122, 77, 3])).
% 29.97/20.26 tff(33192,plain,
% 29.97/20.26 (big_f(c2, f6(c2, c1))),
% 29.97/20.26 inference(modus_ponens,[status(thm)],[33191, 33190])).
% 29.97/20.26 tff(33193,plain,
% 29.97/20.26 (~big_f(c2, f6(c2, c1))),
% 29.97/20.26 inference(unit_resolution,[status(thm)],[11730, 3198, 31714, 1247, 121, 79, 67])).
% 29.97/20.26 tff(33194,plain,
% 29.97/20.26 ($false),
% 29.97/20.26 inference(unit_resolution,[status(thm)],[33193, 33192])).
% 29.97/20.26 tff(33195,plain,((f6(c2, c1) = c1) | (~(f7(c2) = c2)) | (~(f2(c3) = c1)) | big_f(c2, c2) | (~(f4(c4) = c2)) | (~(c3 = c2)) | (~(f10(c2) = c2)) | (f10(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 29.97/20.26 tff(33196,plain,
% 29.97/20.26 (~(f2(c3) = c1)),
% 29.97/20.26 inference(unit_resolution,[status(thm)],[33195, 33189, 33163, 121, 32935, 33164, 33166, 3])).
% 29.97/20.26 tff(33197,plain,
% 29.97/20.26 (~(f2(c3) = c2)),
% 29.97/20.26 inference(unit_resolution,[status(thm)],[11686, 33189, 31714, 121, 33166, 32665])).
% 29.97/20.26 tff(33198,plain,
% 29.97/20.26 ($false),
% 29.97/20.26 inference(unit_resolution,[status(thm)],[1273, 33197, 33196])).
% 29.97/20.26 tff(33199,plain,((f10(c1) = c1) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 29.97/20.26 tff(33200,plain,
% 29.97/20.26 (f10(c1) = c1),
% 29.97/20.26 inference(unit_resolution,[status(thm)],[33199, 121])).
% 29.97/20.26 tff(33201,plain,
% 29.97/20.26 (big_f(c1, c1)),
% 29.97/20.26 inference(unit_resolution,[status(thm)],[31712, 3762])).
% 29.97/20.26 tff(33202,plain,
% 29.97/20.26 ((f7(c2) = c2) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(c1, c1))),
% 29.97/20.26 inference(unit_resolution,[status(thm)],[25386, 30354])).
% 29.97/20.26 tff(33203,plain,
% 29.97/20.26 (~(f9(c1, c1) = c1)),
% 29.97/20.26 inference(unit_resolution,[status(thm)],[33202, 17, 33201, 3762])).
% 29.97/20.26 tff(33204,plain,
% 29.97/20.26 (f9(c1, c1) = c2),
% 29.97/20.26 inference(unit_resolution,[status(thm)],[3939, 33203])).
% 29.97/20.26 tff(33205,plain,
% 29.97/20.26 (f7(f9(f10(c2), f7(c1))) = f7(f9(c1, c1))),
% 29.97/20.26 inference(monotonicity,[status(thm)],[28063])).
% 29.97/20.26 tff(33206,plain,
% 29.97/20.26 (f7(f9(c1, c1)) = f7(f9(f10(c2), f7(c1)))),
% 29.97/20.26 inference(symmetry,[status(thm)],[33205])).
% 29.97/20.26 tff(33207,plain,
% 29.97/20.26 ((f7(f9(c1, c1)) = f9(c1, c1)) <=> (f7(f9(f10(c2), f7(c1))) = c2)),
% 29.97/20.26 inference(monotonicity,[status(thm)],[33206, 33204])).
% 29.97/20.26 tff(33208,plain,
% 29.97/20.26 ((f7(f9(f10(c2), f7(c1))) = c2) <=> (f7(f9(c1, c1)) = f9(c1, c1))),
% 29.97/20.26 inference(symmetry,[status(thm)],[33207])).
% 29.97/20.26 tff(33209,plain,
% 29.97/20.26 ((c1 = f6(c1, c1)) <=> (f6(c1, c1) = c1)),
% 29.97/20.26 inference(commutativity,[status(thm)],[])).
% 29.97/20.26 tff(33210,plain,
% 29.97/20.26 (~(f6(c1, c1) = c1)),
% 29.97/20.26 inference(unit_resolution,[status(thm)],[30135, 2, 3762, 33201])).
% 29.97/20.26 tff(33211,plain,
% 29.97/20.26 (~(f6(c1, f6(c1, c2)) = c1)),
% 29.97/20.26 inference(unit_resolution,[status(thm)],[58, 33210])).
% 29.97/20.26 tff(33212,plain,
% 29.97/20.26 (f6(c1, f6(c1, c2)) = c2),
% 29.97/20.26 inference(unit_resolution,[status(thm)],[63, 33211])).
% 29.97/20.26 tff(33213,plain,
% 29.97/20.26 (c2 = f6(c1, f6(c1, c2))),
% 29.97/20.26 inference(symmetry,[status(thm)],[33212])).
% 29.97/20.26 tff(33214,plain,
% 29.97/20.26 (c2 = f6(c1, c1)),
% 29.97/20.26 inference(transitivity,[status(thm)],[33213, 31339])).
% 29.97/20.26 tff(33215,plain,
% 29.97/20.26 (f6(c1, c1) = c2),
% 29.97/20.26 inference(transitivity,[status(thm)],[32412, 33212])).
% 29.97/20.26 tff(33216,plain,
% 29.97/20.26 (f7(f6(c1, c1)) = f7(c2)),
% 29.97/20.26 inference(monotonicity,[status(thm)],[33215])).
% 29.97/20.26 tff(33217,plain,
% 29.97/20.26 (f9(c1, c1) = f6(c1, c1)),
% 29.97/20.26 inference(transitivity,[status(thm)],[33204, 33213, 31339])).
% 29.97/20.26 tff(33218,plain,
% 29.97/20.26 (f7(f9(c1, c1)) = f7(f6(c1, c1))),
% 29.97/20.26 inference(monotonicity,[status(thm)],[33217])).
% 29.97/20.26 tff(33219,plain,
% 29.97/20.26 (f7(f9(f10(c2), f7(c1))) = c1),
% 29.97/20.26 inference(transitivity,[status(thm)],[33205, 33218, 33216, 22])).
% 29.97/20.26 tff(33220,plain,
% 29.97/20.26 ((f7(f9(f10(c2), f7(c1))) = c2) <=> (c1 = f6(c1, c1))),
% 29.97/20.26 inference(monotonicity,[status(thm)],[33219, 33214])).
% 29.97/20.26 tff(33221,plain,
% 29.97/20.26 ((f7(f9(f10(c2), f7(c1))) = c2) <=> (f6(c1, c1) = c1)),
% 29.97/20.26 inference(transitivity,[status(thm)],[33220, 33209])).
% 29.97/20.26 tff(33222,plain,
% 29.97/20.26 ((f6(c1, c1) = c1) <=> (f7(f9(f10(c2), f7(c1))) = c2)),
% 29.97/20.26 inference(symmetry,[status(thm)],[33221])).
% 29.97/20.26 tff(33223,plain,
% 29.97/20.26 ((f6(c1, c1) = c1) <=> (f7(f9(c1, c1)) = f9(c1, c1))),
% 29.97/20.26 inference(transitivity,[status(thm)],[33222, 33208])).
% 29.97/20.26 tff(33224,plain,
% 29.97/20.26 ((~(f6(c1, c1) = c1)) <=> (~(f7(f9(c1, c1)) = f9(c1, c1)))),
% 29.97/20.26 inference(monotonicity,[status(thm)],[33223])).
% 29.97/20.26 tff(33225,plain,
% 29.97/20.26 (~(f7(f9(c1, c1)) = f9(c1, c1))),
% 29.97/20.26 inference(modus_ponens,[status(thm)],[33210, 33224])).
% 29.97/20.26 tff(33226,plain,
% 29.97/20.26 (~big_f(f9(c1, c1), c1)),
% 29.97/20.26 inference(unit_resolution,[status(thm)],[10058, 33204, 2])).
% 29.97/20.26 tff(33227,plain,
% 29.97/20.26 (~big_f(f9(c1, c1), f10(c1))),
% 29.97/20.26 inference(unit_resolution,[status(thm)],[10033, 33226, 3762])).
% 29.97/20.26 tff(33228,plain,
% 29.97/20.26 (f7(f9(c1, c1)) = c1),
% 29.97/20.26 inference(transitivity,[status(thm)],[33218, 33216, 22])).
% 29.97/20.26 tff(33229,plain,
% 29.97/20.26 (big_f(f7(f9(c1, c1)), c1) <=> big_f(c1, c1)),
% 29.97/20.26 inference(monotonicity,[status(thm)],[33228])).
% 29.97/20.26 tff(33230,plain,
% 29.97/20.26 (big_f(c1, c1) <=> big_f(f7(f9(c1, c1)), c1)),
% 29.97/20.26 inference(symmetry,[status(thm)],[33229])).
% 29.97/20.26 tff(33231,plain,
% 29.97/20.26 (big_f(f7(f9(c1, c1)), c1)),
% 29.97/20.26 inference(modus_ponens,[status(thm)],[33201, 33230])).
% 29.97/20.26 tff(33232,plain,
% 29.97/20.26 (big_f(f7(f9(c1, c1)), f9(c1, c1)) <=> big_f(f7(f9(c1, c1)), f6(c1, c1))),
% 29.97/20.26 inference(monotonicity,[status(thm)],[33217])).
% 29.97/20.26 tff(33233,plain,
% 29.97/20.26 (big_f(f7(f9(c1, c1)), f6(c1, c1)) <=> big_f(f7(f9(c1, c1)), f9(c1, c1))),
% 29.97/20.26 inference(symmetry,[status(thm)],[33232])).
% 29.97/20.26 tff(33234,plain,
% 29.97/20.26 (big_f(f7(f9(c1, c1)), f6(c1, c1)) <=> big_f(c1, f6(c1, c1))),
% 29.97/20.26 inference(monotonicity,[status(thm)],[33228])).
% 29.97/20.26 tff(33235,plain,
% 29.97/20.26 (big_f(c1, f6(c1, c1)) <=> big_f(f7(f9(c1, c1)), f6(c1, c1))),
% 29.97/20.26 inference(symmetry,[status(thm)],[33234])).
% 29.97/20.26 tff(33236,plain,
% 29.97/20.26 (big_f(c1, f6(c1, c1)) <=> big_f(f7(f9(c1, c1)), f9(c1, c1))),
% 29.97/20.26 inference(transitivity,[status(thm)],[33235, 33233])).
% 29.97/20.26 tff(33237,plain,
% 29.97/20.26 (big_f(f7(c1), f6(c1, c1))),
% 29.97/20.26 inference(unit_resolution,[status(thm)],[27676, 2, 3762, 33201])).
% 29.97/20.26 tff(33238,plain,
% 29.97/20.26 (big_f(c1, f6(c1, c1))),
% 29.97/20.26 inference(unit_resolution,[status(thm)],[28169, 33237])).
% 29.97/20.26 tff(33239,plain,
% 29.97/20.26 (big_f(f7(f9(c1, c1)), f9(c1, c1))),
% 29.97/20.26 inference(modus_ponens,[status(thm)],[33238, 33236])).
% 29.97/20.26 tff(33240,plain,
% 29.97/20.26 ($false),
% 29.97/20.26 inference(unit_resolution,[status(thm)],[20184, 33239, 33231, 3762, 33227, 33203, 33225])).
% 29.97/20.26 tff(33241,plain,((f7(c2) = c2) | (~(f10(c1) = c1)) | (~(f6(c1, c2) = c1)) | (~(f10(c2) = c1)) | big_f(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 29.97/20.26 tff(33242,plain,
% 29.97/20.26 (big_f(c2, c1)),
% 29.97/20.26 inference(unit_resolution,[status(thm)],[33241, 31722, 32256, 33200, 17])).
% 29.97/20.26 tff(33243,plain,
% 29.97/20.26 (big_f(c2, f10(c2))),
% 29.97/20.26 inference(modus_ponens,[status(thm)],[33242, 31725])).
% 29.97/20.26 tff(33244,plain,
% 29.97/20.26 (c2 = f8(c2)),
% 29.97/20.26 inference(unit_resolution,[status(thm)],[12312, 33243, 30356, 31721, 17, 31723])).
% 29.97/20.26 tff(33245,plain,
% 29.97/20.26 (f8(c2) = c2),
% 29.97/20.26 inference(symmetry,[status(thm)],[33244])).
% 29.97/20.26 tff(33246,plain,
% 29.97/20.26 ((c1 = f8(c2)) <=> (c1 = c2)),
% 29.97/20.26 inference(monotonicity,[status(thm)],[33245])).
% 29.97/20.26 tff(33247,plain,
% 29.97/20.26 ((c1 = f8(c2)) <=> (c2 = c1)),
% 29.97/20.26 inference(transitivity,[status(thm)],[33246, 1])).
% 29.97/20.26 tff(33248,plain,
% 29.97/20.26 ((c2 = c1) <=> (c1 = f8(c2))),
% 29.97/20.26 inference(symmetry,[status(thm)],[33247])).
% 29.97/20.26 tff(33249,plain,
% 29.97/20.26 ((~(c2 = c1)) <=> (~(c1 = f8(c2)))),
% 29.97/20.26 inference(monotonicity,[status(thm)],[33248])).
% 29.97/20.26 tff(33250,plain,
% 29.97/20.26 (~(c1 = f8(c2))),
% 29.97/20.26 inference(modus_ponens,[status(thm)],[75, 33249])).
% 29.97/20.26 tff(33251,plain,
% 29.97/20.26 (big_f(c1, f10(c2)) <=> big_f(c1, c1)),
% 29.97/20.26 inference(monotonicity,[status(thm)],[31722])).
% 29.97/20.26 tff(33252,plain,
% 29.97/20.26 (big_f(c1, c1) <=> big_f(c1, f10(c2))),
% 29.97/20.26 inference(symmetry,[status(thm)],[33251])).
% 29.97/20.26 tff(33253,plain,
% 29.97/20.26 (big_f(c1, f10(c2))),
% 29.97/20.26 inference(modus_ponens,[status(thm)],[31714, 33252])).
% 29.97/20.26 tff(33254,plain,
% 29.97/20.26 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f7(c2) = c2) | (c2 = f5(c2)) | (c1 = f8(c2)) | (~big_f(f7(c2), c2)) | (~big_f(c1, f10(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (f7(c2) = c2) | (c2 = f5(c2)) | (c1 = f8(c2)) | (~big_f(f7(c2), c2)) | (~big_f(c1, f10(c2))))),
% 29.97/20.26 inference(rewrite,[status(thm)],[])).
% 29.97/20.26 tff(33255,plain,
% 29.97/20.26 (((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2))) <=> ((f10(c2) = c2) | (f7(c2) = c2) | (c2 = f5(c2)) | (c1 = f8(c2)) | (~big_f(f7(c2), c2)) | (~big_f(c1, f10(c2))))),
% 29.97/20.26 inference(rewrite,[status(thm)],[])).
% 29.97/20.26 tff(33256,plain,
% 29.97/20.26 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f7(c2) = c2) | (c2 = f5(c2)) | (c1 = f8(c2)) | (~big_f(f7(c2), c2)) | (~big_f(c1, f10(c2)))))),
% 29.97/20.26 inference(monotonicity,[status(thm)],[33255])).
% 29.97/20.26 tff(33257,plain,
% 29.97/20.26 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (f7(c2) = c2) | (c2 = f5(c2)) | (c1 = f8(c2)) | (~big_f(f7(c2), c2)) | (~big_f(c1, f10(c2))))),
% 29.97/20.26 inference(transitivity,[status(thm)],[33256, 33254])).
% 29.97/20.26 tff(33258,plain,
% 29.97/20.26 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (f7(c2) = c2) | (c2 = f5(c2)) | (~big_f(f7(c2), c2)))),
% 29.97/20.26 inference(quant_inst,[status(thm)],[])).
% 29.97/20.26 tff(33259,plain,
% 29.97/20.26 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (f7(c2) = c2) | (c2 = f5(c2)) | (c1 = f8(c2)) | (~big_f(f7(c2), c2)) | (~big_f(c1, f10(c2)))),
% 29.97/20.26 inference(modus_ponens,[status(thm)],[33258, 33257])).
% 29.97/20.26 tff(33260,plain,
% 29.97/20.26 ((c2 = f5(c2)) | (c1 = f8(c2))),
% 29.97/20.26 inference(unit_resolution,[status(thm)],[33259, 1659, 31721, 17, 30356, 33253])).
% 29.97/20.26 tff(33261,plain,
% 29.97/20.26 (c2 = f5(c2)),
% 29.97/20.26 inference(unit_resolution,[status(thm)],[33260, 33250])).
% 29.97/20.26 tff(33262,plain,
% 29.97/20.26 (f5(c2) = c2),
% 29.97/20.26 inference(symmetry,[status(thm)],[33261])).
% 29.97/20.26 tff(33263,plain,
% 29.97/20.26 (big_f(f7(c2), f1(c1, c1)) <=> big_f(c1, f1(c1, c1))),
% 29.97/20.26 inference(monotonicity,[status(thm)],[22])).
% 29.97/20.26 tff(33264,plain,
% 29.97/20.26 (big_f(c1, f1(c1, c1)) <=> big_f(f7(c2), f1(c1, c1))),
% 29.97/20.26 inference(symmetry,[status(thm)],[33263])).
% 29.97/20.26 tff(33265,plain,
% 29.97/20.26 (big_f(c1, f1(c1, c1)) | (~big_f(c1, c1))),
% 29.97/20.26 inference(unit_resolution,[status(thm)],[20374, 30354])).
% 29.97/20.26 tff(33266,plain,
% 29.97/20.26 (big_f(c1, f1(c1, c1))),
% 29.97/20.26 inference(unit_resolution,[status(thm)],[33265, 31714])).
% 29.97/20.26 tff(33267,plain,
% 29.97/20.26 (big_f(f7(c2), f1(c1, c1))),
% 29.97/20.26 inference(modus_ponens,[status(thm)],[33266, 33264])).
% 29.97/20.26 tff(33268,plain,
% 29.97/20.26 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f7(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (f1(c1, c1) = f5(c2)) | (~big_f(f7(c2), f1(c1, c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (f7(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (f1(c1, c1) = f5(c2)) | (~big_f(f7(c2), f1(c1, c1))))),
% 29.97/20.26 inference(rewrite,[status(thm)],[])).
% 29.97/20.26 tff(33269,plain,
% 29.97/20.26 (((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (f7(c2) = c2) | (f1(c1, c1) = f5(c2)) | (~big_f(f7(c2), f1(c1, c1)))) <=> ((f10(c2) = c2) | (f7(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (f1(c1, c1) = f5(c2)) | (~big_f(f7(c2), f1(c1, c1))))),
% 29.97/20.26 inference(rewrite,[status(thm)],[])).
% 29.97/20.26 tff(33270,plain,
% 29.97/20.26 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (f7(c2) = c2) | (f1(c1, c1) = f5(c2)) | (~big_f(f7(c2), f1(c1, c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f7(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (f1(c1, c1) = f5(c2)) | (~big_f(f7(c2), f1(c1, c1)))))),
% 29.97/20.26 inference(monotonicity,[status(thm)],[33269])).
% 29.97/20.26 tff(33271,plain,
% 29.97/20.26 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (f7(c2) = c2) | (f1(c1, c1) = f5(c2)) | (~big_f(f7(c2), f1(c1, c1))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (f7(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (f1(c1, c1) = f5(c2)) | (~big_f(f7(c2), f1(c1, c1))))),
% 29.97/20.26 inference(transitivity,[status(thm)],[33270, 33268])).
% 29.97/20.26 tff(33272,plain,
% 29.97/20.26 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (f7(c2) = c2) | (f1(c1, c1) = f5(c2)) | (~big_f(f7(c2), f1(c1, c1))))),
% 29.97/20.26 inference(quant_inst,[status(thm)],[])).
% 29.97/20.26 tff(33273,plain,
% 29.97/20.26 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (f7(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (f1(c1, c1) = f5(c2)) | (~big_f(f7(c2), f1(c1, c1)))),
% 29.97/20.26 inference(modus_ponens,[status(thm)],[33272, 33271])).
% 29.97/20.26 tff(33274,plain,
% 29.97/20.26 ((c1 = f8(c2)) | (f1(c1, c1) = f5(c2))),
% 29.97/20.26 inference(unit_resolution,[status(thm)],[33273, 1659, 31721, 17, 33253, 33267])).
% 29.97/20.26 tff(33275,plain,
% 29.97/20.26 (f1(c1, c1) = f5(c2)),
% 29.97/20.26 inference(unit_resolution,[status(thm)],[33274, 33250])).
% 29.97/20.26 tff(33276,plain,
% 29.97/20.26 (f1(c1, c1) = c2),
% 29.97/20.26 inference(transitivity,[status(thm)],[33275, 33262])).
% 29.97/20.26 tff(33277,plain,
% 29.97/20.26 ((f1(c1, c1) = c1) <=> (c2 = c1)),
% 29.97/20.26 inference(monotonicity,[status(thm)],[33276])).
% 29.97/20.26 tff(33278,plain,
% 29.97/20.26 ((c2 = c1) <=> (f1(c1, c1) = c1)),
% 29.97/20.26 inference(symmetry,[status(thm)],[33277])).
% 29.97/20.26 tff(33279,plain,
% 29.97/20.26 ((~(c2 = c1)) <=> (~(f1(c1, c1) = c1))),
% 29.97/20.26 inference(monotonicity,[status(thm)],[33278])).
% 29.97/20.26 tff(33280,plain,
% 29.97/20.26 (~(f1(c1, c1) = c1)),
% 29.97/20.26 inference(modus_ponens,[status(thm)],[75, 33279])).
% 29.97/20.26 tff(33281,plain,
% 29.97/20.26 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f7(c2) = c2) | (~big_f(f7(c2), c1)) | (c1 = f8(c2)) | (c1 = f5(c2)) | (~big_f(c1, f10(c2))))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (f7(c2) = c2) | (~big_f(f7(c2), c1)) | (c1 = f8(c2)) | (c1 = f5(c2)) | (~big_f(c1, f10(c2))))),
% 29.97/20.26 inference(rewrite,[status(thm)],[])).
% 29.97/20.26 tff(33282,plain,
% 29.97/20.26 (((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (f7(c2) = c2) | (c1 = f5(c2)) | (~big_f(f7(c2), c1))) <=> ((f10(c2) = c2) | (f7(c2) = c2) | (~big_f(f7(c2), c1)) | (c1 = f8(c2)) | (c1 = f5(c2)) | (~big_f(c1, f10(c2))))),
% 29.97/20.26 inference(rewrite,[status(thm)],[])).
% 29.97/20.26 tff(33283,plain,
% 29.97/20.26 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (f7(c2) = c2) | (c1 = f5(c2)) | (~big_f(f7(c2), c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (f7(c2) = c2) | (~big_f(f7(c2), c1)) | (c1 = f8(c2)) | (c1 = f5(c2)) | (~big_f(c1, f10(c2)))))),
% 29.97/20.26 inference(monotonicity,[status(thm)],[33282])).
% 29.97/20.26 tff(33284,plain,
% 29.97/20.26 (((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (f7(c2) = c2) | (c1 = f5(c2)) | (~big_f(f7(c2), c1)))) <=> ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (f7(c2) = c2) | (~big_f(f7(c2), c1)) | (c1 = f8(c2)) | (c1 = f5(c2)) | (~big_f(c1, f10(c2))))),
% 29.97/20.26 inference(transitivity,[status(thm)],[33283, 33281])).
% 29.97/20.26 tff(33285,plain,
% 29.97/20.26 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | ((f10(c2) = c2) | (c1 = f8(c2)) | (~big_f(c1, f10(c2))) | (f7(c2) = c2) | (c1 = f5(c2)) | (~big_f(f7(c2), c1)))),
% 29.97/20.26 inference(quant_inst,[status(thm)],[])).
% 29.97/20.26 tff(33286,plain,
% 29.97/20.26 ((~![X4: $i, X7: $i, X5: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (f7(X4) = X4) | (X5 = f5(X4)) | (~big_f(f7(X4), X5)))) | (f10(c2) = c2) | (f7(c2) = c2) | (~big_f(f7(c2), c1)) | (c1 = f8(c2)) | (c1 = f5(c2)) | (~big_f(c1, f10(c2)))),
% 29.97/20.26 inference(modus_ponens,[status(thm)],[33285, 33284])).
% 29.97/20.27 tff(33287,plain,
% 29.97/20.27 ((c1 = f8(c2)) | (c1 = f5(c2))),
% 29.97/20.27 inference(unit_resolution,[status(thm)],[33286, 1659, 31721, 17, 31720, 33253])).
% 29.97/20.27 tff(33288,plain,
% 29.97/20.27 (c1 = f5(c2)),
% 29.97/20.27 inference(unit_resolution,[status(thm)],[33287, 33250])).
% 29.97/20.27 tff(33289,plain,
% 29.97/20.27 (f5(c2) = c1),
% 29.97/20.27 inference(symmetry,[status(thm)],[33288])).
% 29.97/20.27 tff(33290,plain,
% 29.97/20.27 (f1(c1, c1) = c1),
% 29.97/20.27 inference(transitivity,[status(thm)],[33275, 33289])).
% 29.97/20.27 tff(33291,plain,
% 29.97/20.27 ($false),
% 29.97/20.27 inference(unit_resolution,[status(thm)],[33290, 33280])).
% 29.97/20.27 tff(33292,plain,((f7(c2) = c2) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 29.97/20.27 tff(33293,plain,
% 29.97/20.27 (f7(c2) = c2),
% 29.97/20.27 inference(unit_resolution,[status(thm)],[33292, 121])).
% 29.97/20.27 tff(33294,plain,
% 29.97/20.27 (big_f(f7(c2), f6(c2, c1)) <=> big_f(c2, f6(c2, c1))),
% 29.97/20.27 inference(monotonicity,[status(thm)],[33293])).
% 29.97/20.27 tff(33295,plain,
% 29.97/20.27 (big_f(c2, f6(c2, c1)) <=> big_f(f7(c2), f6(c2, c1))),
% 29.97/20.27 inference(symmetry,[status(thm)],[33294])).
% 29.97/20.27 tff(33296,plain,
% 29.97/20.27 (~(f6(c1, c1) = c1)),
% 29.97/20.27 inference(unit_resolution,[status(thm)],[30135, 2, 33200, 31714])).
% 29.97/20.27 tff(33297,plain,
% 29.97/20.27 (~(f6(c1, f6(c1, c2)) = c1)),
% 29.97/20.27 inference(unit_resolution,[status(thm)],[58, 33296])).
% 29.97/20.27 tff(33298,plain,
% 29.97/20.27 (f6(c1, f6(c1, c2)) = c2),
% 29.97/20.27 inference(unit_resolution,[status(thm)],[63, 33297])).
% 29.97/20.27 tff(33299,plain,
% 29.97/20.27 (~(c4 = c2)),
% 29.97/20.27 inference(unit_resolution,[status(thm)],[27535, 67, 33201, 2, 121])).
% 29.97/20.27 tff(33300,plain,
% 29.97/20.27 (c4 = c1),
% 29.97/20.27 inference(unit_resolution,[status(thm)],[461, 33299])).
% 29.97/20.27 tff(33301,plain,
% 29.97/20.27 (big_f(f6(c1, c1), c1) <=> big_f(c2, c1)),
% 29.97/20.27 inference(monotonicity,[status(thm)],[33215])).
% 29.97/20.27 tff(33302,plain,
% 29.97/20.27 (big_f(c2, c1) <=> big_f(f6(c1, c1), c1)),
% 29.97/20.27 inference(symmetry,[status(thm)],[33301])).
% 29.97/20.27 tff(33303,plain,
% 29.97/20.27 ((~big_f(c2, c1)) <=> (~big_f(f6(c1, c1), c1))),
% 29.97/20.27 inference(monotonicity,[status(thm)],[33302])).
% 29.97/20.27 tff(33304,plain,
% 29.97/20.27 (~big_f(f6(c1, c1), c1)),
% 29.97/20.27 inference(modus_ponens,[status(thm)],[2, 33303])).
% 29.97/20.27 tff(33305,plain,
% 29.97/20.27 ((f6(c1, c1) = c3) <=> (f6(c1, f6(c1, c2)) = c3)),
% 29.97/20.27 inference(monotonicity,[status(thm)],[32412])).
% 29.97/20.27 tff(33306,plain,
% 29.97/20.27 ((f6(c1, f6(c1, c2)) = c3) <=> (f6(c1, c1) = c3)),
% 29.97/20.27 inference(symmetry,[status(thm)],[33305])).
% 29.97/20.27 tff(33307,plain,
% 29.97/20.27 ((c2 = c3) <=> (f6(c1, f6(c1, c2)) = c3)),
% 29.97/20.27 inference(monotonicity,[status(thm)],[33213])).
% 29.97/20.27 tff(33308,plain,
% 29.97/20.27 ((c3 = c2) <=> (f6(c1, c1) = c3)),
% 29.97/20.27 inference(transitivity,[status(thm)],[78, 33307, 33306])).
% 29.97/20.27 tff(33309,plain,
% 29.97/20.27 (f6(c1, c1) = c3),
% 29.97/20.27 inference(modus_ponens,[status(thm)],[67, 33308])).
% 29.97/20.27 tff(33310,plain,
% 29.97/20.27 (f3(f3(f7(c1), c1), c1) = c1),
% 29.97/20.27 inference(unit_resolution,[status(thm)],[32475, 1335, 6931, 121, 33309, 33304, 33300, 33210])).
% 29.97/20.27 tff(33311,plain,
% 29.97/20.27 ((f6(c1, f6(c1, c2)) = c4) <=> (f6(c1, c1) = c4)),
% 29.97/20.27 inference(monotonicity,[status(thm)],[31339])).
% 29.97/20.27 tff(33312,plain,
% 29.97/20.27 ((f6(c1, c1) = c4) <=> (f6(c1, f6(c1, c2)) = c4)),
% 29.97/20.27 inference(symmetry,[status(thm)],[33311])).
% 29.97/20.27 tff(33313,plain,
% 29.97/20.27 ((f6(c1, c1) = c4) <=> (f6(c1, c1) = c1)),
% 29.97/20.27 inference(monotonicity,[status(thm)],[33300])).
% 29.97/20.27 tff(33314,plain,
% 29.97/20.27 ((f6(c1, c1) = c1) <=> (f6(c1, c1) = c4)),
% 29.97/20.27 inference(symmetry,[status(thm)],[33313])).
% 29.97/20.27 tff(33315,plain,
% 29.97/20.27 ((f6(c1, c1) = c1) <=> (f6(c1, f6(c1, c2)) = c4)),
% 29.97/20.27 inference(transitivity,[status(thm)],[33314, 33312])).
% 29.97/20.27 tff(33316,plain,
% 29.97/20.27 ((~(f6(c1, c1) = c1)) <=> (~(f6(c1, f6(c1, c2)) = c4))),
% 29.97/20.27 inference(monotonicity,[status(thm)],[33315])).
% 29.97/20.27 tff(33317,plain,
% 29.97/20.27 (~(f6(c1, f6(c1, c2)) = c4)),
% 29.97/20.27 inference(modus_ponens,[status(thm)],[33210, 33316])).
% 29.97/20.27 tff(33318,plain,
% 29.97/20.27 (f3(c1, c1) = c1),
% 29.97/20.27 inference(unit_resolution,[status(thm)],[32527, 33309, 6931, 33212, 33304, 121, 1335, 33317, 33238, 33310, 33300])).
% 29.97/20.27 tff(33319,plain,
% 29.97/20.27 (f7(c2) = c2),
% 29.97/20.27 inference(unit_resolution,[status(thm)],[33241, 2, 6931, 11819, 3762])).
% 29.97/20.27 tff(33320,plain,
% 29.97/20.27 (big_f(c2, c2)),
% 29.97/20.27 inference(unit_resolution,[status(thm)],[8259, 79, 2, 67])).
% 29.97/20.27 tff(33321,plain,
% 29.97/20.27 (f6(f6(c1, c1), f6(c1, c1)) = f6(c2, c2)),
% 29.97/20.27 inference(monotonicity,[status(thm)],[32491, 32491])).
% 29.97/20.27 tff(33322,plain,
% 29.97/20.27 (f6(f6(c1, c1), f6(c1, c1)) = f6(c1, c1)),
% 29.97/20.27 inference(transitivity,[status(thm)],[33321, 2360, 2362, 28323, 31339])).
% 29.97/20.27 tff(33323,plain,
% 29.97/20.27 (f6(f6(c1, c1), f6(c1, c1)) = c2),
% 29.97/20.27 inference(transitivity,[status(thm)],[33321, 2360, 2362])).
% 29.97/20.27 tff(33324,plain,
% 29.97/20.27 (f7(f6(c1, c1)) = f7(c2)),
% 29.97/20.27 inference(monotonicity,[status(thm)],[32491])).
% 29.97/20.27 tff(33325,plain,
% 29.97/20.27 (f7(f6(c1, c1)) = c2),
% 29.97/20.27 inference(transitivity,[status(thm)],[33324, 77])).
% 29.97/20.27 tff(33326,plain,
% 29.97/20.27 (big_f(f7(f6(c1, c1)), f6(f6(c1, c1), f6(c1, c1))) <=> big_f(c2, c2)),
% 29.97/20.27 inference(monotonicity,[status(thm)],[33325, 33323])).
% 29.97/20.27 tff(33327,plain,
% 29.97/20.27 (big_f(c2, c2) <=> big_f(f7(f6(c1, c1)), f6(f6(c1, c1), f6(c1, c1)))),
% 29.97/20.27 inference(symmetry,[status(thm)],[33326])).
% 29.97/20.27 tff(33328,plain,
% 29.97/20.27 (big_f(f7(f6(c1, c1)), f6(f6(c1, c1), f6(c1, c1)))),
% 29.97/20.27 inference(modus_ponens,[status(thm)],[1345, 33327])).
% 29.97/20.27 tff(33329,plain,
% 29.97/20.27 (c2 = f6(c1, c1)),
% 29.97/20.27 inference(transitivity,[status(thm)],[28323, 31339])).
% 29.97/20.27 tff(33330,plain,
% 29.97/20.27 (f7(c2) = f7(f6(c1, c1))),
% 29.97/20.27 inference(symmetry,[status(thm)],[33324])).
% 29.97/20.27 tff(33331,plain,
% 29.97/20.27 ((f7(c2) = c2) <=> (f7(f6(c1, c1)) = f6(c1, c1))),
% 29.97/20.27 inference(monotonicity,[status(thm)],[33330, 33329])).
% 29.97/20.27 tff(33332,plain,
% 29.97/20.27 (f7(f6(c1, c1)) = f6(c1, c1)),
% 29.97/20.27 inference(modus_ponens,[status(thm)],[77, 33331])).
% 29.97/20.27 tff(33333,plain,
% 29.97/20.27 (big_f(f9(c1, c1), c1)),
% 29.97/20.27 inference(unit_resolution,[status(thm)],[10938, 3949, 33201])).
% 29.97/20.27 tff(33334,plain,
% 29.97/20.27 (big_f(f9(c1, c1), f10(c1))),
% 29.97/20.27 inference(unit_resolution,[status(thm)],[8716, 33333, 3762])).
% 29.97/20.27 tff(33335,plain,
% 29.97/20.27 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(f6(f6(c1, c1), f6(c1, c1)) = f6(c1, c1))) | (~(f7(f6(c1, c1)) = f6(c1, c1))) | (~big_f(f7(f6(c1, c1)), f6(f6(c1, c1), f6(c1, c1)))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(f6(f6(c1, c1), f6(c1, c1)) = f6(c1, c1))) | (~(f7(f6(c1, c1)) = f6(c1, c1))) | (~big_f(f7(f6(c1, c1)), f6(f6(c1, c1), f6(c1, c1)))))),
% 29.97/20.27 inference(rewrite,[status(thm)],[])).
% 29.97/20.27 tff(33336,plain,
% 29.97/20.27 (((~(f10(c1) = c1)) | (~(f7(f6(c1, c1)) = f6(c1, c1))) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(f6(f6(c1, c1), f6(c1, c1)) = f6(c1, c1))) | (~big_f(f7(f6(c1, c1)), f6(f6(c1, c1), f6(c1, c1))))) <=> ((~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(f6(f6(c1, c1), f6(c1, c1)) = f6(c1, c1))) | (~(f7(f6(c1, c1)) = f6(c1, c1))) | (~big_f(f7(f6(c1, c1)), f6(f6(c1, c1), f6(c1, c1)))))),
% 29.97/20.27 inference(rewrite,[status(thm)],[])).
% 29.97/20.27 tff(33337,plain,
% 29.97/20.27 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (~(f7(f6(c1, c1)) = f6(c1, c1))) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(f6(f6(c1, c1), f6(c1, c1)) = f6(c1, c1))) | (~big_f(f7(f6(c1, c1)), f6(f6(c1, c1), f6(c1, c1)))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(f6(f6(c1, c1), f6(c1, c1)) = f6(c1, c1))) | (~(f7(f6(c1, c1)) = f6(c1, c1))) | (~big_f(f7(f6(c1, c1)), f6(f6(c1, c1), f6(c1, c1))))))),
% 29.97/20.27 inference(monotonicity,[status(thm)],[33336])).
% 29.97/20.27 tff(33338,plain,
% 29.97/20.27 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (~(f7(f6(c1, c1)) = f6(c1, c1))) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(f6(f6(c1, c1), f6(c1, c1)) = f6(c1, c1))) | (~big_f(f7(f6(c1, c1)), f6(f6(c1, c1), f6(c1, c1)))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(f6(f6(c1, c1), f6(c1, c1)) = f6(c1, c1))) | (~(f7(f6(c1, c1)) = f6(c1, c1))) | (~big_f(f7(f6(c1, c1)), f6(f6(c1, c1), f6(c1, c1)))))),
% 29.97/20.27 inference(transitivity,[status(thm)],[33337, 33335])).
% 29.97/20.27 tff(33339,plain,
% 29.97/20.27 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (~(f7(f6(c1, c1)) = f6(c1, c1))) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(f6(f6(c1, c1), f6(c1, c1)) = f6(c1, c1))) | (~big_f(f7(f6(c1, c1)), f6(f6(c1, c1), f6(c1, c1)))))),
% 29.97/20.27 inference(quant_inst,[status(thm)],[])).
% 29.97/20.27 tff(33340,plain,
% 29.97/20.27 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (~(f7(X4) = X4)) | (~(f9(X7, X9) = X9)) | (~big_f(f9(X7, X9), f10(X7))) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1))) | (~(f6(f6(c1, c1), f6(c1, c1)) = f6(c1, c1))) | (~(f7(f6(c1, c1)) = f6(c1, c1))) | (~big_f(f7(f6(c1, c1)), f6(f6(c1, c1), f6(c1, c1))))),
% 29.97/20.27 inference(modus_ponens,[status(thm)],[33339, 33338])).
% 29.97/20.27 tff(33341,plain,
% 29.97/20.27 ((~(f6(f6(c1, c1), f6(c1, c1)) = f6(c1, c1))) | (~big_f(f7(f6(c1, c1)), f6(f6(c1, c1), f6(c1, c1))))),
% 29.97/20.27 inference(unit_resolution,[status(thm)],[33340, 2378, 3762, 3949, 33334, 33332])).
% 29.97/20.27 tff(33342,plain,
% 29.97/20.27 ($false),
% 29.97/20.27 inference(unit_resolution,[status(thm)],[33341, 33328, 33322])).
% 29.97/20.27 tff(33343,plain,((~(f9(c1, c1) = c1)) | (~(f10(c1) = c1)) | (~big_f(c2, c2)) | (~(f6(f7(c2), c3) = c2)) | (~(c3 = c2)) | (~(f7(c2) = c2)) | (~(f6(c1, f6(c1, c2)) = c2)) | (~(f6(c1, c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.97/20.27 tff(33344,plain,
% 29.97/20.27 (~(f9(c1, c1) = c1)),
% 29.97/20.27 inference(unit_resolution,[status(thm)],[33343, 2362, 1345, 3762, 67, 77, 33212, 6931])).
% 29.97/20.27 tff(33345,plain,
% 29.97/20.27 (~(f9(c1, f10(f10(c2))) = f10(f10(c2)))),
% 29.97/20.27 inference(modus_ponens,[status(thm)],[33344, 19280])).
% 29.97/20.27 tff(33346,plain,
% 29.97/20.27 (f9(c1, c1) = c2),
% 29.97/20.27 inference(unit_resolution,[status(thm)],[3939, 33344])).
% 29.97/20.27 tff(33347,plain,
% 29.97/20.27 (~big_f(f9(c1, c1), c1)),
% 29.97/20.27 inference(unit_resolution,[status(thm)],[10058, 33346, 2])).
% 29.97/20.27 tff(33348,plain,
% 29.97/20.27 (~big_f(f9(c1, c1), f10(c1))),
% 29.97/20.27 inference(unit_resolution,[status(thm)],[10033, 33347, 3762])).
% 29.97/20.27 tff(33349,plain,
% 29.97/20.27 (~big_f(f9(c1, f10(f10(c2))), f10(c1))),
% 29.97/20.27 inference(unit_resolution,[status(thm)],[24698, 33348, 3762, 11819])).
% 29.97/20.27 tff(33350,plain,
% 29.97/20.27 (f9(c1, f10(f10(c2))) = f10(f10(c2))),
% 29.97/20.27 inference(unit_resolution,[status(thm)],[24709, 33349, 3762, 77, 26160, 1345])).
% 29.97/20.27 tff(33351,plain,
% 29.97/20.27 ($false),
% 29.97/20.27 inference(unit_resolution,[status(thm)],[33350, 33345])).
% 29.97/20.27 tff(33352,plain,((~(f6(f7(c2), c3) = c2)) | (~(f10(c1) = c1)) | (~(f10(c2) = c1)) | (~(f7(c2) = c2)) | (~big_f(c2, c2)) | big_f(c2, c1) | (~(c3 = c2)) | (~(f6(c1, c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 29.97/20.27 tff(33353,plain,
% 29.97/20.27 (~(f6(f7(c2), c3) = c2)),
% 29.97/20.27 inference(unit_resolution,[status(thm)],[33352, 77, 11819, 3762, 33320, 2, 67, 6931])).
% 29.97/20.27 tff(33354,plain,
% 29.97/20.27 (f6(f7(c2), c3) = c1),
% 29.97/20.27 inference(unit_resolution,[status(thm)],[2391, 33353])).
% 29.97/20.27 tff(33355,plain,
% 29.97/20.27 (f6(f6(c1, c1), f6(c1, c1)) = f6(c2, c2)),
% 29.97/20.27 inference(monotonicity,[status(thm)],[33215, 33215])).
% 29.97/20.27 tff(33356,plain,
% 29.97/20.27 (f6(f6(c1, c1), f6(c1, c1)) = c1),
% 29.97/20.27 inference(transitivity,[status(thm)],[33355, 2360, 2702])).
% 29.97/20.27 tff(33357,plain,
% 29.97/20.27 ((f6(f6(c1, c1), f6(c1, c1)) = f6(c1, c1)) <=> (c1 = f6(c1, c1))),
% 29.97/20.27 inference(monotonicity,[status(thm)],[33356])).
% 29.97/20.27 tff(33358,plain,
% 29.97/20.27 ((f6(f6(c1, c1), f6(c1, c1)) = f6(c1, c1)) <=> (f6(c1, c1) = c1)),
% 29.97/20.27 inference(transitivity,[status(thm)],[33357, 33209])).
% 29.97/20.27 tff(33359,plain,
% 29.97/20.27 ((f6(c1, c1) = c1) <=> (f6(f6(c1, c1), f6(c1, c1)) = f6(c1, c1))),
% 29.97/20.27 inference(symmetry,[status(thm)],[33358])).
% 30.08/20.27 tff(33360,plain,
% 30.08/20.27 ((~(f6(c1, c1) = c1)) <=> (~(f6(f6(c1, c1), f6(c1, c1)) = f6(c1, c1)))),
% 30.08/20.27 inference(monotonicity,[status(thm)],[33359])).
% 30.08/20.27 tff(33361,plain,
% 30.08/20.27 (~(f6(f6(c1, c1), f6(c1, c1)) = f6(c1, c1))),
% 30.08/20.27 inference(modus_ponens,[status(thm)],[33210, 33360])).
% 30.08/20.27 tff(33362,plain,
% 30.08/20.27 (f7(f6(c1, c1)) = c2),
% 30.08/20.27 inference(transitivity,[status(thm)],[33216, 77])).
% 30.08/20.27 tff(33363,plain,
% 30.08/20.27 (big_f(f7(f6(c1, c1)), f6(f6(c1, c1), f6(c1, c1))) <=> big_f(c2, c1)),
% 30.08/20.27 inference(monotonicity,[status(thm)],[33362, 33356])).
% 30.08/20.27 tff(33364,plain,
% 30.08/20.27 (big_f(c2, c1) <=> big_f(f7(f6(c1, c1)), f6(f6(c1, c1), f6(c1, c1)))),
% 30.08/20.27 inference(symmetry,[status(thm)],[33363])).
% 30.08/20.27 tff(33365,plain,
% 30.08/20.27 ((~big_f(c2, c1)) <=> (~big_f(f7(f6(c1, c1)), f6(f6(c1, c1), f6(c1, c1))))),
% 30.08/20.27 inference(monotonicity,[status(thm)],[33364])).
% 30.08/20.27 tff(33366,plain,
% 30.08/20.27 (~big_f(f7(f6(c1, c1)), f6(f6(c1, c1), f6(c1, c1)))),
% 30.08/20.27 inference(modus_ponens,[status(thm)],[2, 33365])).
% 30.08/20.27 tff(33367,plain,
% 30.08/20.27 (f7(c2) = f7(f6(c1, c1))),
% 30.08/20.27 inference(symmetry,[status(thm)],[33216])).
% 30.08/20.27 tff(33368,plain,
% 30.08/20.27 ((f7(c2) = c2) <=> (f7(f6(c1, c1)) = f6(c1, c1))),
% 30.08/20.27 inference(monotonicity,[status(thm)],[33367, 33214])).
% 30.08/20.27 tff(33369,plain,
% 30.08/20.27 (f7(f6(c1, c1)) = f6(c1, c1)),
% 30.08/20.27 inference(modus_ponens,[status(thm)],[77, 33368])).
% 30.08/20.27 tff(33370,plain,
% 30.08/20.27 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~(f7(f6(c1, c1)) = f6(c1, c1))) | (f6(f6(c1, c1), f6(c1, c1)) = f6(c1, c1)) | big_f(f7(f6(c1, c1)), f6(f6(c1, c1), f6(c1, c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~(f7(f6(c1, c1)) = f6(c1, c1))) | (f6(f6(c1, c1), f6(c1, c1)) = f6(c1, c1)) | big_f(f7(f6(c1, c1)), f6(f6(c1, c1), f6(c1, c1))))),
% 30.08/20.27 inference(rewrite,[status(thm)],[])).
% 30.08/20.27 tff(33371,plain,
% 30.08/20.27 (((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f7(f6(c1, c1)) = f6(c1, c1))) | (f6(f6(c1, c1), f6(c1, c1)) = f6(c1, c1)) | big_f(f7(f6(c1, c1)), f6(f6(c1, c1), f6(c1, c1)))) <=> ((f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~(f7(f6(c1, c1)) = f6(c1, c1))) | (f6(f6(c1, c1), f6(c1, c1)) = f6(c1, c1)) | big_f(f7(f6(c1, c1)), f6(f6(c1, c1), f6(c1, c1))))),
% 30.08/20.27 inference(rewrite,[status(thm)],[])).
% 30.08/20.27 tff(33372,plain,
% 30.08/20.27 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f7(f6(c1, c1)) = f6(c1, c1))) | (f6(f6(c1, c1), f6(c1, c1)) = f6(c1, c1)) | big_f(f7(f6(c1, c1)), f6(f6(c1, c1), f6(c1, c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~(f7(f6(c1, c1)) = f6(c1, c1))) | (f6(f6(c1, c1), f6(c1, c1)) = f6(c1, c1)) | big_f(f7(f6(c1, c1)), f6(f6(c1, c1), f6(c1, c1)))))),
% 30.08/20.27 inference(monotonicity,[status(thm)],[33371])).
% 30.08/20.27 tff(33373,plain,
% 30.08/20.27 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f7(f6(c1, c1)) = f6(c1, c1))) | (f6(f6(c1, c1), f6(c1, c1)) = f6(c1, c1)) | big_f(f7(f6(c1, c1)), f6(f6(c1, c1), f6(c1, c1))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~(f7(f6(c1, c1)) = f6(c1, c1))) | (f6(f6(c1, c1), f6(c1, c1)) = f6(c1, c1)) | big_f(f7(f6(c1, c1)), f6(f6(c1, c1), f6(c1, c1))))),
% 30.08/20.27 inference(transitivity,[status(thm)],[33372, 33370])).
% 30.08/20.27 tff(33374,plain,
% 30.08/20.27 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f7(f6(c1, c1)) = f6(c1, c1))) | (f6(f6(c1, c1), f6(c1, c1)) = f6(c1, c1)) | big_f(f7(f6(c1, c1)), f6(f6(c1, c1), f6(c1, c1))))),
% 30.08/20.27 inference(quant_inst,[status(thm)],[])).
% 30.08/20.27 tff(33375,plain,
% 30.08/20.27 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)) | (~(f7(f6(c1, c1)) = f6(c1, c1))) | (f6(f6(c1, c1), f6(c1, c1)) = f6(c1, c1)) | big_f(f7(f6(c1, c1)), f6(f6(c1, c1), f6(c1, c1)))),
% 30.08/20.27 inference(modus_ponens,[status(thm)],[33374, 33373])).
% 30.08/20.27 tff(33376,plain,
% 30.08/20.27 ((f6(f6(c1, c1), f6(c1, c1)) = f6(c1, c1)) | big_f(f7(f6(c1, c1)), f6(f6(c1, c1), f6(c1, c1)))),
% 30.08/20.27 inference(unit_resolution,[status(thm)],[33375, 2492, 3762, 4070, 24692, 33369])).
% 30.08/20.27 tff(33377,plain,
% 30.08/20.27 ($false),
% 30.08/20.27 inference(unit_resolution,[status(thm)],[33376, 33366, 33361])).
% 30.08/20.27 tff(33378,plain,((f9(c1, c1) = c1) | (~(f10(c1) = c1)) | big_f(c2, c1) | (~(f6(f7(c2), c3) = c1)) | (~(c3 = c2)) | (~(f7(c2) = c2)) | (~(f6(c1, c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 30.08/20.27 tff(33379,plain,
% 30.08/20.27 (f9(c1, c1) = c1),
% 30.08/20.27 inference(unit_resolution,[status(thm)],[33378, 33354, 2, 3762, 67, 77, 6931])).
% 30.08/20.27 tff(33380,plain,
% 30.08/20.27 (big_f(f9(c1, c1), c1)),
% 30.08/20.27 inference(unit_resolution,[status(thm)],[10938, 33379, 33201])).
% 30.08/20.27 tff(33381,plain,
% 30.08/20.27 (~big_f(f7(c2), f6(c2, c2))),
% 30.08/20.27 inference(unit_resolution,[status(thm)],[2710, 33354, 77, 67, 2])).
% 30.08/20.27 tff(33382,plain,
% 30.08/20.27 (~big_f(f9(c1, c1), f10(c1))),
% 30.08/20.27 inference(unit_resolution,[status(thm)],[3965, 33379, 33320, 79, 3762, 77, 33381])).
% 30.08/20.27 tff(33383,plain,
% 30.08/20.27 ($false),
% 30.08/20.27 inference(unit_resolution,[status(thm)],[8716, 33382, 33380, 3762])).
% 30.08/20.27 tff(33384,plain,((~(f7(c2) = c2)) | (~(f10(c1) = c1)) | (~(f4(c4) = c2)) | big_f(c2, c1) | (~(c3 = c2)) | (~(f6(c1, c2) = c1)) | (~(f10(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 30.08/20.27 tff(33385,plain,
% 30.08/20.27 (~(f4(c4) = c2)),
% 30.08/20.27 inference(unit_resolution,[status(thm)],[33384, 67, 3762, 2, 33319, 6931, 11819])).
% 30.08/20.27 tff(33386,plain,
% 30.08/20.27 (f4(c4) = c1),
% 30.08/20.27 inference(unit_resolution,[status(thm)],[11750, 33385])).
% 30.08/20.27 tff(33387,plain,
% 30.08/20.27 (f6(c2, c1) = c1),
% 30.08/20.27 inference(unit_resolution,[status(thm)],[27698, 33386, 3762, 33201, 2, 33319, 121])).
% 30.08/20.27 tff(33388,plain,
% 30.08/20.27 (c1 = c4),
% 30.08/20.27 inference(unit_resolution,[status(thm)],[484, 33300])).
% 30.08/20.27 tff(33389,plain,
% 30.08/20.27 (f7(c1) = c4),
% 30.08/20.27 inference(unit_resolution,[status(thm)],[33175, 33388])).
% 30.08/20.27 tff(33390,plain,
% 30.08/20.27 (f7(f4(c4)) = f4(c4)),
% 30.08/20.27 inference(unit_resolution,[status(thm)],[19880, 33389, 33386, 33388])).
% 30.08/20.27 tff(33391,plain,
% 30.08/20.27 ((~(f6(c1, c1) = c1)) <=> (~(f6(c1, c1) = c4))),
% 30.08/20.27 inference(monotonicity,[status(thm)],[33314])).
% 30.08/20.27 tff(33392,plain,
% 30.08/20.27 (~(f6(c1, c1) = c4)),
% 30.08/20.27 inference(modus_ponens,[status(thm)],[33210, 33391])).
% 30.08/20.27 tff(33393,plain,
% 30.08/20.27 (f3(f6(c1, c1), c1) = f3(f6(c1, f6(c1, c2)), c1)),
% 30.08/20.27 inference(monotonicity,[status(thm)],[32412])).
% 30.08/20.27 tff(33394,plain,
% 30.08/20.27 (big_f(f3(f6(c1, c1), c1), f6(c1, c1)) <=> big_f(f3(f6(c1, f6(c1, c2)), c1), f6(c1, f6(c1, c2)))),
% 30.08/20.27 inference(monotonicity,[status(thm)],[33393, 32412])).
% 30.08/20.27 tff(33395,plain,
% 30.08/20.27 (big_f(f3(f6(c1, f6(c1, c2)), c1), f6(c1, f6(c1, c2))) <=> big_f(f3(f6(c1, c1), c1), f6(c1, c1))),
% 30.08/20.27 inference(symmetry,[status(thm)],[33394])).
% 30.08/20.27 tff(33396,assumption,(big_f(f3(f6(c1, f6(c1, c2)), c1), f6(c1, f6(c1, c2)))), introduced(assumption)).
% 30.08/20.27 tff(33397,plain,
% 30.08/20.27 (big_f(f3(f6(c1, c1), c1), f6(c1, c1))),
% 30.08/20.27 inference(modus_ponens,[status(thm)],[33396, 33395])).
% 30.08/20.27 tff(33398,plain,
% 30.08/20.27 ((f3(f6(c1, c1), c1) = c1) <=> (f3(f6(c1, f6(c1, c2)), c1) = c1)),
% 30.08/20.27 inference(monotonicity,[status(thm)],[33393])).
% 30.08/20.28 tff(33399,plain,
% 30.08/20.28 ((f3(f6(c1, f6(c1, c2)), c1) = c1) <=> (f3(f6(c1, c1), c1) = c1)),
% 30.08/20.28 inference(symmetry,[status(thm)],[33398])).
% 30.08/20.28 tff(33400,assumption,(f7(f4(c4)) = f4(c4)), introduced(assumption)).
% 30.08/20.28 tff(33401,plain,
% 30.08/20.28 (f7(f4(c4)) = c1),
% 30.08/20.28 inference(transitivity,[status(thm)],[33400, 11752])).
% 30.08/20.28 tff(33402,plain,
% 30.08/20.28 (f3(f7(f4(c4)), f4(c4)) = f3(c1, c1)),
% 30.08/20.28 inference(monotonicity,[status(thm)],[33401, 11752])).
% 30.08/20.28 tff(33403,plain,
% 30.08/20.28 (f3(c1, c1) = f3(f7(f4(c4)), f4(c4))),
% 30.08/20.28 inference(symmetry,[status(thm)],[33402])).
% 30.08/20.28 tff(33404,plain,
% 30.08/20.28 (c1 = f3(c1, c1)),
% 30.08/20.28 inference(symmetry,[status(thm)],[1938])).
% 30.08/20.28 tff(33405,plain,
% 30.08/20.28 (c1 = f3(f7(f4(c4)), f4(c4))),
% 30.08/20.28 inference(transitivity,[status(thm)],[33404, 33403])).
% 30.08/20.28 tff(33406,plain,
% 30.08/20.28 (f3(f6(c1, f6(c1, c2)), c1) = f3(c2, f3(f7(f4(c4)), f4(c4)))),
% 30.08/20.28 inference(monotonicity,[status(thm)],[27490, 33405])).
% 30.08/20.28 tff(33407,plain,
% 30.08/20.28 (f3(c2, f3(f7(f4(c4)), f4(c4))) = f3(f6(c1, f6(c1, c2)), c1)),
% 30.08/20.28 inference(symmetry,[status(thm)],[33406])).
% 30.08/20.28 tff(33408,plain,
% 30.08/20.28 ((f3(c2, f3(f7(f4(c4)), f4(c4))) = c1) <=> (f3(f6(c1, f6(c1, c2)), c1) = c1)),
% 30.08/20.28 inference(monotonicity,[status(thm)],[33407])).
% 30.08/20.28 tff(33409,plain,
% 30.08/20.28 ((f3(c2, f3(f7(f4(c4)), f4(c4))) = c1) <=> (f3(f6(c1, c1), c1) = c1)),
% 30.08/20.28 inference(transitivity,[status(thm)],[33408, 33399])).
% 30.08/20.28 tff(33410,plain,
% 30.08/20.28 (f3(c2, f3(f7(f4(c4)), f4(c4))) = f3(c2, c1)),
% 30.08/20.28 inference(transitivity,[status(thm)],[33407, 31990])).
% 30.08/20.28 tff(33411,plain,
% 30.08/20.28 ((f3(c2, f3(f7(f4(c4)), f4(c4))) = c2) <=> (f3(c2, c1) = c2)),
% 30.08/20.28 inference(monotonicity,[status(thm)],[33410])).
% 30.08/20.28 tff(33412,plain,
% 30.08/20.28 ((f3(c2, f3(f7(f4(c4)), f4(c4))) = c2) <=> (c2 = f3(c2, c1))),
% 30.08/20.28 inference(transitivity,[status(thm)],[33411, 32611])).
% 30.08/20.28 tff(33413,plain,
% 30.08/20.28 ((c2 = f3(c2, c1)) <=> (f3(c2, f3(f7(f4(c4)), f4(c4))) = c2)),
% 30.08/20.28 inference(symmetry,[status(thm)],[33412])).
% 30.08/20.28 tff(33414,plain,
% 30.08/20.28 ((f3(f6(c1, f6(c1, c2)), c1) = c3) <=> (f3(c2, c1) = c2)),
% 30.08/20.28 inference(monotonicity,[status(thm)],[31990, 67])).
% 30.08/20.28 tff(33415,plain,
% 30.08/20.28 ((f3(f6(c1, f6(c1, c2)), c1) = c3) <=> (c2 = f3(c2, c1))),
% 30.08/20.28 inference(transitivity,[status(thm)],[33414, 32611])).
% 30.08/20.28 tff(33416,plain,
% 30.08/20.28 ((f3(f6(c1, f6(c1, c2)), c1) = c3) <=> (f3(c2, f3(f7(f4(c4)), f4(c4))) = c2)),
% 30.08/20.28 inference(transitivity,[status(thm)],[33415, 33413])).
% 30.08/20.28 tff(33417,plain,
% 30.08/20.28 ((~(f3(f6(c1, f6(c1, c2)), c1) = c3)) <=> (~(f3(c2, f3(f7(f4(c4)), f4(c4))) = c2))),
% 30.08/20.28 inference(monotonicity,[status(thm)],[33416])).
% 30.08/20.28 tff(33418,plain,
% 30.08/20.28 ((c2 = f3(c2, c1)) <=> (f3(f6(c1, f6(c1, c2)), c1) = c3)),
% 30.08/20.28 inference(symmetry,[status(thm)],[33415])).
% 30.08/20.28 tff(33419,plain,
% 30.08/20.28 ((~(c2 = f3(c2, c1))) <=> (~(f3(f6(c1, f6(c1, c2)), c1) = c3))),
% 30.08/20.28 inference(monotonicity,[status(thm)],[33418])).
% 30.08/20.28 tff(33420,plain,
% 30.08/20.28 (big_f(f3(c2, c1), c2) <=> big_f(f3(f6(c1, f6(c1, c2)), c1), f6(c1, f6(c1, c2)))),
% 30.08/20.28 inference(monotonicity,[status(thm)],[31989, 28323])).
% 30.08/20.28 tff(33421,plain,
% 30.08/20.28 (big_f(f3(f6(c1, f6(c1, c2)), c1), f6(c1, f6(c1, c2))) <=> big_f(f3(c2, c1), c2)),
% 30.08/20.28 inference(symmetry,[status(thm)],[33420])).
% 30.08/20.28 tff(33422,plain,
% 30.08/20.28 (big_f(f3(c2, c1), c2)),
% 30.08/20.28 inference(modus_ponens,[status(thm)],[33396, 33421])).
% 30.08/20.28 tff(33423,plain,
% 30.08/20.28 ((~(big_f(c2, c2) <=> big_f(f3(c2, c1), c2))) | (~big_f(f3(c2, c1), c2))),
% 30.08/20.28 inference(unit_resolution,[status(thm)],[32010, 121])).
% 30.08/20.28 tff(33424,plain,
% 30.08/20.28 (~(big_f(c2, c2) <=> big_f(f3(c2, c1), c2))),
% 30.08/20.28 inference(unit_resolution,[status(thm)],[33423, 33422])).
% 30.08/20.28 tff(33425,plain,
% 30.08/20.28 (~(c2 = f3(c2, c1))),
% 30.08/20.28 inference(unit_resolution,[status(thm)],[32008, 33424])).
% 30.08/20.28 tff(33426,plain,
% 30.08/20.28 (~(f3(f6(c1, f6(c1, c2)), c1) = c3)),
% 30.08/20.28 inference(modus_ponens,[status(thm)],[33425, 33419])).
% 30.08/20.28 tff(33427,plain,
% 30.08/20.28 (~(f3(c2, f3(f7(f4(c4)), f4(c4))) = c2)),
% 30.08/20.28 inference(modus_ponens,[status(thm)],[33426, 33417])).
% 30.08/20.28 tff(33428,plain,
% 30.08/20.28 (f3(c2, f3(f7(f4(c4)), f4(c4))) = c1),
% 30.08/20.28 inference(unit_resolution,[status(thm)],[32627, 33427])).
% 30.08/20.28 tff(33429,plain,
% 30.08/20.28 (f3(f6(c1, c1), c1) = c1),
% 30.08/20.28 inference(modus_ponens,[status(thm)],[33428, 33409])).
% 30.08/20.28 tff(33430,plain,
% 30.08/20.28 ((c2 = c3) <=> (f6(c1, f6(c1, c2)) = c3)),
% 30.08/20.28 inference(monotonicity,[status(thm)],[28323])).
% 30.08/20.28 tff(33431,plain,
% 30.08/20.28 ((c3 = c2) <=> (f6(c1, c1) = c3)),
% 30.08/20.28 inference(transitivity,[status(thm)],[78, 33430, 33306])).
% 30.08/20.28 tff(33432,plain,
% 30.08/20.28 (f6(c1, c1) = c3),
% 30.08/20.28 inference(modus_ponens,[status(thm)],[67, 33431])).
% 30.08/20.28 tff(33433,plain,
% 30.08/20.28 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((f6(c1, c1) = c4) | (~(c1 = f2(f6(c1, c1)))) | (~(f6(c1, c1) = c3)) | (~big_f(f3(f6(c1, c1), c1), f6(c1, c1))) | (~(f3(f6(c1, c1), c1) = c1)) | big_f(f6(c1, c1), c1))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (f6(c1, c1) = c4) | (~(c1 = f2(f6(c1, c1)))) | (~(f6(c1, c1) = c3)) | (~big_f(f3(f6(c1, c1), c1), f6(c1, c1))) | (~(f3(f6(c1, c1), c1) = c1)) | big_f(f6(c1, c1), c1))),
% 30.08/20.28 inference(rewrite,[status(thm)],[])).
% 30.08/20.28 tff(33434,plain,
% 30.08/20.28 (((~(f6(c1, c1) = c3)) | (~(c1 = f2(f6(c1, c1)))) | (f6(c1, c1) = c4) | (~(f3(f6(c1, c1), c1) = c1)) | (~big_f(f3(f6(c1, c1), c1), f6(c1, c1))) | big_f(f6(c1, c1), c1)) <=> ((f6(c1, c1) = c4) | (~(c1 = f2(f6(c1, c1)))) | (~(f6(c1, c1) = c3)) | (~big_f(f3(f6(c1, c1), c1), f6(c1, c1))) | (~(f3(f6(c1, c1), c1) = c1)) | big_f(f6(c1, c1), c1))),
% 30.08/20.28 inference(rewrite,[status(thm)],[])).
% 30.08/20.28 tff(33435,plain,
% 30.08/20.28 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(f6(c1, c1) = c3)) | (~(c1 = f2(f6(c1, c1)))) | (f6(c1, c1) = c4) | (~(f3(f6(c1, c1), c1) = c1)) | (~big_f(f3(f6(c1, c1), c1), f6(c1, c1))) | big_f(f6(c1, c1), c1))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((f6(c1, c1) = c4) | (~(c1 = f2(f6(c1, c1)))) | (~(f6(c1, c1) = c3)) | (~big_f(f3(f6(c1, c1), c1), f6(c1, c1))) | (~(f3(f6(c1, c1), c1) = c1)) | big_f(f6(c1, c1), c1)))),
% 30.08/20.28 inference(monotonicity,[status(thm)],[33434])).
% 30.08/20.28 tff(33436,plain,
% 30.08/20.28 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(f6(c1, c1) = c3)) | (~(c1 = f2(f6(c1, c1)))) | (f6(c1, c1) = c4) | (~(f3(f6(c1, c1), c1) = c1)) | (~big_f(f3(f6(c1, c1), c1), f6(c1, c1))) | big_f(f6(c1, c1), c1))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (f6(c1, c1) = c4) | (~(c1 = f2(f6(c1, c1)))) | (~(f6(c1, c1) = c3)) | (~big_f(f3(f6(c1, c1), c1), f6(c1, c1))) | (~(f3(f6(c1, c1), c1) = c1)) | big_f(f6(c1, c1), c1))),
% 30.08/20.28 inference(transitivity,[status(thm)],[33435, 33433])).
% 30.08/20.28 tff(33437,plain,
% 30.08/20.28 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | ((~(f6(c1, c1) = c3)) | (~(c1 = f2(f6(c1, c1)))) | (f6(c1, c1) = c4) | (~(f3(f6(c1, c1), c1) = c1)) | (~big_f(f3(f6(c1, c1), c1), f6(c1, c1))) | big_f(f6(c1, c1), c1))),
% 30.08/20.28 inference(quant_inst,[status(thm)],[])).
% 30.08/20.28 tff(33438,plain,
% 30.08/20.28 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | big_f(X10, X12))) | (f6(c1, c1) = c4) | (~(c1 = f2(f6(c1, c1)))) | (~(f6(c1, c1) = c3)) | (~big_f(f3(f6(c1, c1), c1), f6(c1, c1))) | (~(f3(f6(c1, c1), c1) = c1)) | big_f(f6(c1, c1), c1)),
% 30.08/20.28 inference(modus_ponens,[status(thm)],[33437, 33436])).
% 30.08/20.28 tff(33439,plain,
% 30.08/20.28 ((~(c1 = f2(f6(c1, c1)))) | (~big_f(f3(f6(c1, c1), c1), f6(c1, c1))) | (~(f3(f6(c1, c1), c1) = c1))),
% 30.08/20.28 inference(unit_resolution,[status(thm)],[33438, 1398, 28239, 33432, 32436])).
% 30.08/20.28 tff(33440,plain,
% 30.08/20.28 (~(c1 = f2(f6(c1, c1)))),
% 30.08/20.28 inference(unit_resolution,[status(thm)],[33439, 33429, 33397])).
% 30.08/20.28 tff(33441,plain,
% 30.08/20.28 (~(f2(c2) = c1)),
% 30.08/20.28 inference(modus_ponens,[status(thm)],[33440, 32495])).
% 30.08/20.28 tff(33442,plain,
% 30.08/20.28 (f3(f6(c1, f6(c1, c2)), c1) = c1),
% 30.08/20.28 inference(modus_ponens,[status(thm)],[33428, 33408])).
% 30.08/20.28 tff(33443,plain,
% 30.08/20.28 (~(c2 = f2(c2))),
% 30.08/20.28 inference(unit_resolution,[status(thm)],[31936, 33442, 121, 1335, 33396, 32513])).
% 30.08/20.28 tff(33444,plain,
% 30.08/20.28 (~(f2(c2) = c2)),
% 30.08/20.28 inference(unit_resolution,[status(thm)],[31890, 33443])).
% 30.08/20.28 tff(33445,plain,
% 30.08/20.28 (f2(c2) = c1),
% 30.08/20.28 inference(unit_resolution,[status(thm)],[31912, 33444])).
% 30.08/20.28 tff(33446,plain,
% 30.08/20.28 ($false),
% 30.08/20.28 inference(unit_resolution,[status(thm)],[33445, 33441])).
% 30.08/20.28 tff(33447,plain,((~big_f(f3(f6(c1, f6(c1, c2)), c1), f6(c1, f6(c1, c2)))) | (~(f6(c1, f6(c1, c2)) = c2)) | (~(f6(c1, c2) = c1)) | (f6(c1, c1) = c4) | big_f(f6(c1, c1), c1) | big_f(c2, c2) | (f6(c1, f6(c1, c2)) = c4) | (~(f3(c1, c1) = c1)) | (~(f4(c4) = c1)) | (~(f7(f4(c4)) = f4(c4))) | (~(c3 = c2))), inference(lemma,lemma(discharge,[]))).
% 30.08/20.28 tff(33448,plain,
% 30.08/20.28 (~big_f(f3(f6(c1, f6(c1, c2)), c1), f6(c1, f6(c1, c2)))),
% 30.08/20.28 inference(unit_resolution,[status(thm)],[33447, 33392, 6931, 33212, 33304, 121, 33317, 33318, 33386, 33390, 67])).
% 30.08/20.28 tff(33449,assumption,(f3(c2, f3(f9(c2, c1), c1)) = c2), introduced(assumption)).
% 30.08/20.28 tff(33450,plain,
% 30.08/20.28 (f3(f6(c1, c1), f3(f9(c2, c1), c1)) = f3(c2, f3(f9(c2, c1), c1))),
% 30.08/20.28 inference(monotonicity,[status(thm)],[32413])).
% 30.08/20.28 tff(33451,plain,
% 30.08/20.28 (f3(f6(c1, c1), f3(f9(c2, c1), c1)) = c2),
% 30.08/20.28 inference(transitivity,[status(thm)],[33450, 33449])).
% 30.08/20.28 tff(33452,plain,
% 30.08/20.28 (big_f(f3(f6(c1, c1), f3(f9(c2, c1), c1)), f6(c1, c1)) <=> big_f(c2, c2)),
% 30.08/20.28 inference(monotonicity,[status(thm)],[33451, 32413])).
% 30.08/20.28 tff(33453,plain,
% 30.08/20.28 (big_f(c2, c2) <=> big_f(f3(f6(c1, c1), f3(f9(c2, c1), c1)), f6(c1, c1))),
% 30.08/20.28 inference(symmetry,[status(thm)],[33452])).
% 30.08/20.28 tff(33454,plain,
% 30.08/20.28 ((~big_f(c2, c2)) <=> (~big_f(f3(f6(c1, c1), f3(f9(c2, c1), c1)), f6(c1, c1)))),
% 30.08/20.28 inference(monotonicity,[status(thm)],[33453])).
% 30.08/20.28 tff(33455,plain,
% 30.08/20.28 (~big_f(f3(f6(c1, c1), f3(f9(c2, c1), c1)), f6(c1, c1))),
% 30.08/20.28 inference(modus_ponens,[status(thm)],[121, 33454])).
% 30.08/20.28 tff(33456,plain,
% 30.08/20.28 ((f3(f6(c1, c1), f3(f9(c2, c1), c1)) = f3(f9(c2, c1), c1)) <=> (f3(c2, f3(f9(c2, c1), c1)) = f3(f9(c2, c1), c1))),
% 30.08/20.28 inference(monotonicity,[status(thm)],[33450])).
% 30.08/20.28 tff(33457,plain,
% 30.08/20.28 ((f3(c2, f3(f9(c2, c1), c1)) = f3(f9(c2, c1), c1)) <=> (f3(f6(c1, c1), f3(f9(c2, c1), c1)) = f3(f9(c2, c1), c1))),
% 30.08/20.28 inference(symmetry,[status(thm)],[33456])).
% 30.08/20.28 tff(33458,plain,
% 30.08/20.28 (c2 = f6(c1, c1)),
% 30.08/20.28 inference(transitivity,[status(thm)],[32438, 31339])).
% 30.08/20.28 tff(33459,plain,
% 30.08/20.28 ((c2 = c4) <=> (f6(c1, c1) = c4)),
% 30.08/20.28 inference(monotonicity,[status(thm)],[33458])).
% 30.08/20.28 tff(33460,plain,
% 30.08/20.28 ((f6(c1, c1) = c4) <=> (c2 = c4)),
% 30.08/20.28 inference(symmetry,[status(thm)],[33459])).
% 30.08/20.28 tff(33461,plain,
% 30.08/20.28 ((f6(c1, c1) = c4) <=> (f6(c1, c1) = c1)),
% 30.08/20.28 inference(monotonicity,[status(thm)],[480])).
% 30.08/20.28 tff(33462,plain,
% 30.08/20.28 ((f6(c1, c1) = c1) <=> (f6(c1, c1) = c4)),
% 30.08/20.28 inference(symmetry,[status(thm)],[33461])).
% 30.08/20.28 tff(33463,plain,
% 30.08/20.28 ((f6(c1, c1) = c1) <=> (c2 = c4)),
% 30.08/20.28 inference(transitivity,[status(thm)],[33462, 33460])).
% 30.08/20.28 tff(33464,plain,
% 30.08/20.28 ((~(f6(c1, c1) = c1)) <=> (~(c2 = c4))),
% 30.08/20.28 inference(monotonicity,[status(thm)],[33463])).
% 30.08/20.28 tff(33465,plain,
% 30.08/20.28 (~(c2 = c4)),
% 30.08/20.28 inference(modus_ponens,[status(thm)],[28, 33464])).
% 30.08/20.28 tff(33466,assumption,(~big_f(f3(f6(c1, f6(c1, c2)), c1), f6(c1, f6(c1, c2)))), introduced(assumption)).
% 30.08/20.28 tff(33467,plain,
% 30.08/20.28 ((c1 = f2(c2)) <=> (c1 = f2(f6(c1, c1)))),
% 30.08/20.28 inference(symmetry,[status(thm)],[32493])).
% 30.08/20.28 tff(33468,plain,
% 30.08/20.28 ((~big_f(f3(f6(c1, f6(c1, c2)), c1), f6(c1, f6(c1, c2)))) <=> (~big_f(f3(c2, c1), c2))),
% 30.08/20.28 inference(monotonicity,[status(thm)],[33421])).
% 30.08/20.28 tff(33469,plain,
% 30.08/20.28 (~big_f(f3(c2, c1), c2)),
% 30.08/20.28 inference(modus_ponens,[status(thm)],[33466, 33468])).
% 30.08/20.28 tff(33470,assumption,(~(f3(f9(c2, c1), c1) = c1)), introduced(assumption)).
% 30.08/20.28 tff(33471,plain,
% 30.08/20.28 (f3(f9(c2, c1), c1) = f3(c1, c1)),
% 30.08/20.28 inference(monotonicity,[status(thm)],[736])).
% 30.08/20.28 tff(33472,plain,
% 30.08/20.28 (f3(f9(c2, c1), c1) = c1),
% 30.08/20.28 inference(transitivity,[status(thm)],[33471, 1938])).
% 30.08/20.28 tff(33473,plain,
% 30.08/20.28 ($false),
% 30.08/20.28 inference(unit_resolution,[status(thm)],[33470, 33472])).
% 30.08/20.28 tff(33474,plain,((~(f9(c2, c1) = c1)) | (f3(f9(c2, c1), c1) = c1) | (~(f3(c1, c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 30.08/20.28 tff(33475,plain,
% 30.08/20.28 (~(f9(c2, c1) = c1)),
% 30.08/20.28 inference(unit_resolution,[status(thm)],[33474, 33470, 1938])).
% 30.08/20.28 tff(33476,plain,
% 30.08/20.28 (f9(c2, c1) = c2),
% 30.08/20.28 inference(unit_resolution,[status(thm)],[3913, 33475])).
% 30.08/20.28 tff(33477,plain,
% 30.08/20.28 (f3(c2, c1) = c1),
% 30.08/20.28 inference(unit_resolution,[status(thm)],[31885, 12175, 121, 1344, 2853, 873])).
% 30.08/20.28 tff(33478,plain,
% 30.08/20.28 (f3(f9(c2, c1), c1) = f3(c2, c1)),
% 30.08/20.28 inference(monotonicity,[status(thm)],[5008])).
% 30.08/20.28 tff(33479,plain,
% 30.08/20.28 (f3(f9(c2, c1), c1) = c1),
% 30.08/20.28 inference(transitivity,[status(thm)],[33478, 33477])).
% 30.08/20.28 tff(33480,plain,
% 30.08/20.28 (big_f(f3(f9(c2, c1), c1), f9(c2, c1)) <=> big_f(c1, c2)),
% 30.08/20.28 inference(monotonicity,[status(thm)],[33479, 5008])).
% 30.08/20.28 tff(33481,plain,
% 30.08/20.28 (big_f(c1, c2) <=> big_f(f3(f9(c2, c1), c1), f9(c2, c1))),
% 30.08/20.28 inference(symmetry,[status(thm)],[33480])).
% 30.08/20.28 tff(33482,plain,
% 30.08/20.28 (big_f(f3(f9(c2, c1), c1), f9(c2, c1))),
% 30.08/20.28 inference(modus_ponens,[status(thm)],[2865, 33481])).
% 30.08/20.28 tff(33483,plain,
% 30.08/20.28 (f3(c2, c1) = f3(f9(c2, c1), c1)),
% 30.08/20.28 inference(symmetry,[status(thm)],[33478])).
% 30.08/20.28 tff(33484,plain,
% 30.08/20.28 (big_f(f3(c2, c1), c2) <=> big_f(f3(f9(c2, c1), c1), f9(c2, c1))),
% 30.08/20.28 inference(monotonicity,[status(thm)],[33483, 10395])).
% 30.08/20.28 tff(33485,plain,
% 30.08/20.28 ((~big_f(f3(c2, c1), c2)) <=> (~big_f(f3(f9(c2, c1), c1), f9(c2, c1)))),
% 30.08/20.28 inference(monotonicity,[status(thm)],[33484])).
% 30.08/20.28 tff(33486,plain,
% 30.08/20.28 (~big_f(f3(f9(c2, c1), c1), f9(c2, c1))),
% 30.08/20.28 inference(modus_ponens,[status(thm)],[12175, 33485])).
% 30.08/20.28 tff(33487,plain,
% 30.08/20.28 ($false),
% 30.08/20.28 inference(unit_resolution,[status(thm)],[33486, 33482])).
% 30.08/20.28 tff(33488,plain,(big_f(f3(c2, c1), c2) | (~big_f(c1, c2)) | (~(f9(c2, c1) = c2)) | big_f(c2, c2) | (~(c2 = c3)) | (~(c2 = f2(c2))) | (c2 = c4)), inference(lemma,lemma(discharge,[]))).
% 30.08/20.28 tff(33489,plain,
% 30.08/20.28 (big_f(f3(c2, c1), c2) | (~(f9(c2, c1) = c2)) | big_f(c2, c2) | (~(c2 = c3)) | (~(c2 = f2(c2))) | (c2 = c4)),
% 30.08/20.28 inference(unit_resolution,[status(thm)],[33488, 30354])).
% 30.08/20.28 tff(33490,plain,
% 30.08/20.28 (~(c2 = f2(c2))),
% 30.08/20.28 inference(unit_resolution,[status(thm)],[33489, 33476, 121, 1344, 33469, 873])).
% 30.08/20.28 tff(33491,plain,
% 30.08/20.28 (~(f2(c2) = c2)),
% 30.08/20.28 inference(unit_resolution,[status(thm)],[31890, 33490])).
% 30.08/20.28 tff(33492,plain,
% 30.08/20.28 (f2(c2) = c1),
% 30.08/20.28 inference(unit_resolution,[status(thm)],[31912, 33491])).
% 30.08/20.28 tff(33493,plain,
% 30.08/20.28 (c1 = f2(c2)),
% 30.08/20.28 inference(unit_resolution,[status(thm)],[31907, 33492])).
% 30.08/20.28 tff(33494,plain,
% 30.08/20.28 (c1 = f2(f6(c1, c1))),
% 30.08/20.28 inference(modus_ponens,[status(thm)],[33493, 33467])).
% 30.08/20.28 tff(33495,plain,
% 30.08/20.28 ((f9(c2, c1) = c4) <=> (f9(c2, c1) = c1)),
% 30.08/20.28 inference(monotonicity,[status(thm)],[480])).
% 30.08/20.28 tff(33496,plain,
% 30.08/20.28 ((f9(c2, c1) = c1) <=> (f9(c2, c1) = c4)),
% 30.08/20.28 inference(symmetry,[status(thm)],[33495])).
% 30.08/20.28 tff(33497,plain,
% 30.08/20.28 ((~(f9(c2, c1) = c1)) <=> (~(f9(c2, c1) = c4))),
% 30.08/20.28 inference(monotonicity,[status(thm)],[33496])).
% 30.08/20.28 tff(33498,plain,
% 30.08/20.28 (~(f9(c2, c1) = c4)),
% 30.08/20.28 inference(modus_ponens,[status(thm)],[33475, 33497])).
% 30.08/20.28 tff(33499,plain,
% 30.08/20.28 (f9(c2, c1) = f6(c1, f6(c1, c2))),
% 30.08/20.28 inference(transitivity,[status(thm)],[33476, 28323])).
% 30.08/20.28 tff(33500,plain,
% 30.08/20.28 (f3(f9(c2, c1), c1) = f3(f6(c1, f6(c1, c2)), c1)),
% 30.08/20.28 inference(monotonicity,[status(thm)],[33499])).
% 30.08/20.28 tff(33501,plain,
% 30.08/20.28 (big_f(f3(f9(c2, c1), c1), f9(c2, c1)) <=> big_f(f3(f6(c1, f6(c1, c2)), c1), f6(c1, f6(c1, c2)))),
% 30.08/20.28 inference(monotonicity,[status(thm)],[33500, 33499])).
% 30.08/20.28 tff(33502,plain,
% 30.08/20.28 (big_f(f3(f6(c1, f6(c1, c2)), c1), f6(c1, f6(c1, c2))) <=> big_f(f3(f9(c2, c1), c1), f9(c2, c1))),
% 30.08/20.28 inference(symmetry,[status(thm)],[33501])).
% 30.08/20.28 tff(33503,plain,
% 30.08/20.28 ((~big_f(f3(f6(c1, f6(c1, c2)), c1), f6(c1, f6(c1, c2)))) <=> (~big_f(f3(f9(c2, c1), c1), f9(c2, c1)))),
% 30.08/20.28 inference(monotonicity,[status(thm)],[33502])).
% 30.08/20.28 tff(33504,plain,
% 30.08/20.28 (~big_f(f3(f9(c2, c1), c1), f9(c2, c1))),
% 30.08/20.28 inference(modus_ponens,[status(thm)],[33466, 33503])).
% 30.08/20.28 tff(33505,plain,
% 30.08/20.28 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((f9(c2, c1) = c4) | big_f(f3(f9(c2, c1), c1), f9(c2, c1)) | (f3(f9(c2, c1), c1) = c1) | (~(c1 = f2(f6(c1, c1)))) | (~(f6(c1, c1) = c3)) | big_f(f6(c1, c1), c1))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (f9(c2, c1) = c4) | big_f(f3(f9(c2, c1), c1), f9(c2, c1)) | (f3(f9(c2, c1), c1) = c1) | (~(c1 = f2(f6(c1, c1)))) | (~(f6(c1, c1) = c3)) | big_f(f6(c1, c1), c1))),
% 30.08/20.28 inference(rewrite,[status(thm)],[])).
% 30.08/20.28 tff(33506,plain,
% 30.08/20.28 (((~(f6(c1, c1) = c3)) | (~(c1 = f2(f6(c1, c1)))) | (f9(c2, c1) = c4) | (f3(f9(c2, c1), c1) = c1) | big_f(f3(f9(c2, c1), c1), f9(c2, c1)) | big_f(f6(c1, c1), c1)) <=> ((f9(c2, c1) = c4) | big_f(f3(f9(c2, c1), c1), f9(c2, c1)) | (f3(f9(c2, c1), c1) = c1) | (~(c1 = f2(f6(c1, c1)))) | (~(f6(c1, c1) = c3)) | big_f(f6(c1, c1), c1))),
% 30.08/20.28 inference(rewrite,[status(thm)],[])).
% 30.08/20.28 tff(33507,plain,
% 30.08/20.28 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(f6(c1, c1) = c3)) | (~(c1 = f2(f6(c1, c1)))) | (f9(c2, c1) = c4) | (f3(f9(c2, c1), c1) = c1) | big_f(f3(f9(c2, c1), c1), f9(c2, c1)) | big_f(f6(c1, c1), c1))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((f9(c2, c1) = c4) | big_f(f3(f9(c2, c1), c1), f9(c2, c1)) | (f3(f9(c2, c1), c1) = c1) | (~(c1 = f2(f6(c1, c1)))) | (~(f6(c1, c1) = c3)) | big_f(f6(c1, c1), c1)))),
% 30.08/20.28 inference(monotonicity,[status(thm)],[33506])).
% 30.08/20.28 tff(33508,plain,
% 30.08/20.28 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(f6(c1, c1) = c3)) | (~(c1 = f2(f6(c1, c1)))) | (f9(c2, c1) = c4) | (f3(f9(c2, c1), c1) = c1) | big_f(f3(f9(c2, c1), c1), f9(c2, c1)) | big_f(f6(c1, c1), c1))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (f9(c2, c1) = c4) | big_f(f3(f9(c2, c1), c1), f9(c2, c1)) | (f3(f9(c2, c1), c1) = c1) | (~(c1 = f2(f6(c1, c1)))) | (~(f6(c1, c1) = c3)) | big_f(f6(c1, c1), c1))),
% 30.08/20.28 inference(transitivity,[status(thm)],[33507, 33505])).
% 30.08/20.28 tff(33509,plain,
% 30.08/20.28 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(f6(c1, c1) = c3)) | (~(c1 = f2(f6(c1, c1)))) | (f9(c2, c1) = c4) | (f3(f9(c2, c1), c1) = c1) | big_f(f3(f9(c2, c1), c1), f9(c2, c1)) | big_f(f6(c1, c1), c1))),
% 30.08/20.28 inference(quant_inst,[status(thm)],[])).
% 30.08/20.28 tff(33510,plain,
% 30.08/20.28 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (f9(c2, c1) = c4) | big_f(f3(f9(c2, c1), c1), f9(c2, c1)) | (f3(f9(c2, c1), c1) = c1) | (~(c1 = f2(f6(c1, c1)))) | (~(f6(c1, c1) = c3)) | big_f(f6(c1, c1), c1)),
% 30.08/20.28 inference(modus_ponens,[status(thm)],[33509, 33508])).
% 30.08/20.28 tff(33511,plain,
% 30.08/20.28 ((f9(c2, c1) = c4) | big_f(f3(f9(c2, c1), c1), f9(c2, c1)) | (f3(f9(c2, c1), c1) = c1) | (~(c1 = f2(f6(c1, c1))))),
% 30.08/20.28 inference(unit_resolution,[status(thm)],[33510, 1459, 32437, 32436])).
% 30.08/20.28 tff(33512,plain,
% 30.08/20.28 ($false),
% 30.08/20.28 inference(unit_resolution,[status(thm)],[33511, 33504, 33498, 33470, 33494])).
% 30.08/20.28 tff(33513,plain,((f3(f9(c2, c1), c1) = c1) | (~(f6(c1, c1) = c3)) | big_f(f6(c1, c1), c1) | big_f(f3(f6(c1, f6(c1, c2)), c1), f6(c1, f6(c1, c2))) | (~(f6(c1, f6(c1, c2)) = c2)) | (~(f6(c1, c2) = c1)) | (~(c4 = c1)) | big_f(c2, c2) | (~(c2 = c3)) | (c2 = c4) | (~(f3(c1, c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 30.08/20.28 tff(33514,plain,
% 30.08/20.28 (f3(f9(c2, c1), c1) = c1),
% 30.08/20.28 inference(unit_resolution,[status(thm)],[33513, 33466, 32436, 32437, 64, 6931, 480, 121, 1344, 33465, 1938])).
% 30.08/20.28 tff(33515,plain,
% 30.08/20.28 (f3(c2, f3(f9(c2, c1), c1)) = f6(c1, c1)),
% 30.08/20.28 inference(transitivity,[status(thm)],[33449, 32438, 31339])).
% 30.08/20.29 tff(33516,plain,
% 30.08/20.29 ((f3(c2, f3(f9(c2, c1), c1)) = f3(f9(c2, c1), c1)) <=> (f6(c1, c1) = c1)),
% 30.08/20.29 inference(monotonicity,[status(thm)],[33515, 33514])).
% 30.08/20.29 tff(33517,plain,
% 30.08/20.29 ((f6(c1, c1) = c1) <=> (f3(c2, f3(f9(c2, c1), c1)) = f3(f9(c2, c1), c1))),
% 30.08/20.29 inference(symmetry,[status(thm)],[33516])).
% 30.08/20.29 tff(33518,plain,
% 30.08/20.29 ((f6(c1, c1) = c1) <=> (f3(f6(c1, c1), f3(f9(c2, c1), c1)) = f3(f9(c2, c1), c1))),
% 30.08/20.29 inference(transitivity,[status(thm)],[33517, 33457])).
% 30.08/20.29 tff(33519,plain,
% 30.08/20.29 ((~(f6(c1, c1) = c1)) <=> (~(f3(f6(c1, c1), f3(f9(c2, c1), c1)) = f3(f9(c2, c1), c1)))),
% 30.08/20.29 inference(monotonicity,[status(thm)],[33518])).
% 30.08/20.29 tff(33520,plain,
% 30.08/20.29 (~(f3(f6(c1, c1), f3(f9(c2, c1), c1)) = f3(f9(c2, c1), c1))),
% 30.08/20.29 inference(modus_ponens,[status(thm)],[28, 33519])).
% 30.08/20.29 tff(33521,plain,
% 30.08/20.29 ((~(f6(c1, c1) = c1)) <=> (~(f6(c1, c1) = c4))),
% 30.08/20.29 inference(monotonicity,[status(thm)],[33462])).
% 30.08/20.29 tff(33522,plain,
% 30.08/20.29 (~(f6(c1, c1) = c4)),
% 30.08/20.29 inference(modus_ponens,[status(thm)],[28, 33521])).
% 30.08/20.29 tff(33523,plain,
% 30.08/20.29 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((f6(c1, c1) = c4) | (~(c1 = f2(f6(c1, c1)))) | (~(f6(c1, c1) = c3)) | (f3(f6(c1, c1), f3(f9(c2, c1), c1)) = f3(f9(c2, c1), c1)) | big_f(f3(f6(c1, c1), f3(f9(c2, c1), c1)), f6(c1, c1)) | big_f(f6(c1, c1), c1))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (f6(c1, c1) = c4) | (~(c1 = f2(f6(c1, c1)))) | (~(f6(c1, c1) = c3)) | (f3(f6(c1, c1), f3(f9(c2, c1), c1)) = f3(f9(c2, c1), c1)) | big_f(f3(f6(c1, c1), f3(f9(c2, c1), c1)), f6(c1, c1)) | big_f(f6(c1, c1), c1))),
% 30.08/20.29 inference(rewrite,[status(thm)],[])).
% 30.08/20.29 tff(33524,plain,
% 30.08/20.29 (((~(f6(c1, c1) = c3)) | (~(c1 = f2(f6(c1, c1)))) | (f6(c1, c1) = c4) | (f3(f6(c1, c1), f3(f9(c2, c1), c1)) = f3(f9(c2, c1), c1)) | big_f(f3(f6(c1, c1), f3(f9(c2, c1), c1)), f6(c1, c1)) | big_f(f6(c1, c1), c1)) <=> ((f6(c1, c1) = c4) | (~(c1 = f2(f6(c1, c1)))) | (~(f6(c1, c1) = c3)) | (f3(f6(c1, c1), f3(f9(c2, c1), c1)) = f3(f9(c2, c1), c1)) | big_f(f3(f6(c1, c1), f3(f9(c2, c1), c1)), f6(c1, c1)) | big_f(f6(c1, c1), c1))),
% 30.08/20.29 inference(rewrite,[status(thm)],[])).
% 30.08/20.29 tff(33525,plain,
% 30.08/20.29 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(f6(c1, c1) = c3)) | (~(c1 = f2(f6(c1, c1)))) | (f6(c1, c1) = c4) | (f3(f6(c1, c1), f3(f9(c2, c1), c1)) = f3(f9(c2, c1), c1)) | big_f(f3(f6(c1, c1), f3(f9(c2, c1), c1)), f6(c1, c1)) | big_f(f6(c1, c1), c1))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((f6(c1, c1) = c4) | (~(c1 = f2(f6(c1, c1)))) | (~(f6(c1, c1) = c3)) | (f3(f6(c1, c1), f3(f9(c2, c1), c1)) = f3(f9(c2, c1), c1)) | big_f(f3(f6(c1, c1), f3(f9(c2, c1), c1)), f6(c1, c1)) | big_f(f6(c1, c1), c1)))),
% 30.08/20.29 inference(monotonicity,[status(thm)],[33524])).
% 30.08/20.29 tff(33526,plain,
% 30.08/20.29 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(f6(c1, c1) = c3)) | (~(c1 = f2(f6(c1, c1)))) | (f6(c1, c1) = c4) | (f3(f6(c1, c1), f3(f9(c2, c1), c1)) = f3(f9(c2, c1), c1)) | big_f(f3(f6(c1, c1), f3(f9(c2, c1), c1)), f6(c1, c1)) | big_f(f6(c1, c1), c1))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (f6(c1, c1) = c4) | (~(c1 = f2(f6(c1, c1)))) | (~(f6(c1, c1) = c3)) | (f3(f6(c1, c1), f3(f9(c2, c1), c1)) = f3(f9(c2, c1), c1)) | big_f(f3(f6(c1, c1), f3(f9(c2, c1), c1)), f6(c1, c1)) | big_f(f6(c1, c1), c1))),
% 30.08/20.29 inference(transitivity,[status(thm)],[33525, 33523])).
% 30.08/20.29 tff(33527,plain,
% 30.08/20.29 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(f6(c1, c1) = c3)) | (~(c1 = f2(f6(c1, c1)))) | (f6(c1, c1) = c4) | (f3(f6(c1, c1), f3(f9(c2, c1), c1)) = f3(f9(c2, c1), c1)) | big_f(f3(f6(c1, c1), f3(f9(c2, c1), c1)), f6(c1, c1)) | big_f(f6(c1, c1), c1))),
% 30.08/20.29 inference(quant_inst,[status(thm)],[])).
% 30.08/20.29 tff(33528,plain,
% 30.08/20.29 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (f6(c1, c1) = c4) | (~(c1 = f2(f6(c1, c1)))) | (~(f6(c1, c1) = c3)) | (f3(f6(c1, c1), f3(f9(c2, c1), c1)) = f3(f9(c2, c1), c1)) | big_f(f3(f6(c1, c1), f3(f9(c2, c1), c1)), f6(c1, c1)) | big_f(f6(c1, c1), c1)),
% 30.08/20.29 inference(modus_ponens,[status(thm)],[33527, 33526])).
% 30.08/20.29 tff(33529,plain,
% 30.08/20.29 ((~(c1 = f2(f6(c1, c1)))) | (f3(f6(c1, c1), f3(f9(c2, c1), c1)) = f3(f9(c2, c1), c1)) | big_f(f3(f6(c1, c1), f3(f9(c2, c1), c1)), f6(c1, c1))),
% 30.08/20.29 inference(unit_resolution,[status(thm)],[33528, 1459, 33522, 32437, 32436])).
% 30.08/20.29 tff(33530,plain,
% 30.08/20.29 (~(c1 = f2(f6(c1, c1)))),
% 30.08/20.29 inference(unit_resolution,[status(thm)],[33529, 33520, 33455])).
% 30.08/20.29 tff(33531,plain,
% 30.08/20.29 (~(f2(c2) = c1)),
% 30.08/20.29 inference(modus_ponens,[status(thm)],[33530, 32417])).
% 30.08/20.29 tff(33532,plain,
% 30.08/20.29 (f6(c1, f6(c2, c1)) = f6(c1, c1)),
% 30.08/20.29 inference(monotonicity,[status(thm)],[3079])).
% 30.08/20.29 tff(33533,plain,
% 30.08/20.29 (f6(c1, f6(c2, c1)) = f6(c1, f6(c1, c2))),
% 30.08/20.29 inference(transitivity,[status(thm)],[33532, 32412])).
% 30.08/20.29 tff(33534,plain,
% 30.08/20.29 (f3(f6(c1, f6(c2, c1)), c1) = f3(f6(c1, f6(c1, c2)), c1)),
% 30.08/20.29 inference(monotonicity,[status(thm)],[33533])).
% 30.08/20.29 tff(33535,plain,
% 30.08/20.29 (big_f(f3(f6(c1, f6(c2, c1)), c1), f6(c1, f6(c2, c1))) <=> big_f(f3(f6(c1, f6(c1, c2)), c1), f6(c1, f6(c1, c2)))),
% 30.08/20.29 inference(monotonicity,[status(thm)],[33534, 33533])).
% 30.08/20.29 tff(33536,plain,
% 30.08/20.29 (big_f(f3(f6(c1, f6(c1, c2)), c1), f6(c1, f6(c1, c2))) <=> big_f(f3(f6(c1, f6(c2, c1)), c1), f6(c1, f6(c2, c1)))),
% 30.08/20.29 inference(symmetry,[status(thm)],[33535])).
% 30.08/20.29 tff(33537,plain,
% 30.08/20.29 ((~big_f(f3(f6(c1, f6(c1, c2)), c1), f6(c1, f6(c1, c2)))) <=> (~big_f(f3(f6(c1, f6(c2, c1)), c1), f6(c1, f6(c2, c1))))),
% 30.08/20.29 inference(monotonicity,[status(thm)],[33536])).
% 30.08/20.29 tff(33538,plain,
% 30.08/20.29 (~big_f(f3(f6(c1, f6(c2, c1)), c1), f6(c1, f6(c2, c1)))),
% 30.08/20.29 inference(modus_ponens,[status(thm)],[33466, 33537])).
% 30.08/20.29 tff(33539,plain,
% 30.08/20.29 ((f6(c1, f6(c2, c1)) = c4) <=> (f6(c1, f6(c2, c1)) = c1)),
% 30.08/20.29 inference(monotonicity,[status(thm)],[480])).
% 30.08/20.29 tff(33540,plain,
% 30.08/20.29 ((f6(c1, f6(c2, c1)) = c1) <=> (f6(c1, f6(c2, c1)) = c4)),
% 30.08/20.29 inference(symmetry,[status(thm)],[33539])).
% 30.08/20.29 tff(33541,plain,
% 30.08/20.29 ((f6(c1, f6(c2, c1)) = c1) <=> (f6(c1, c1) = c1)),
% 30.08/20.29 inference(monotonicity,[status(thm)],[33532])).
% 30.08/20.29 tff(33542,plain,
% 30.08/20.29 ((f6(c1, c1) = c1) <=> (f6(c1, f6(c2, c1)) = c1)),
% 30.08/20.29 inference(symmetry,[status(thm)],[33541])).
% 30.08/20.29 tff(33543,plain,
% 30.08/20.29 ((f6(c1, c1) = c1) <=> (f6(c1, f6(c2, c1)) = c4)),
% 30.08/20.29 inference(transitivity,[status(thm)],[33542, 33540])).
% 30.08/20.29 tff(33544,plain,
% 30.08/20.29 ((~(f6(c1, c1) = c1)) <=> (~(f6(c1, f6(c2, c1)) = c4))),
% 30.08/20.29 inference(monotonicity,[status(thm)],[33543])).
% 30.08/20.29 tff(33545,plain,
% 30.08/20.29 (~(f6(c1, f6(c2, c1)) = c4)),
% 30.08/20.29 inference(modus_ponens,[status(thm)],[28, 33544])).
% 30.08/20.29 tff(33546,plain,
% 30.08/20.29 ((f3(f6(c1, f6(c2, c1)), c1) = c1) <=> (f3(f6(c1, f6(c1, c2)), c1) = c1)),
% 30.08/20.29 inference(monotonicity,[status(thm)],[33534])).
% 30.08/20.29 tff(33547,plain,
% 30.08/20.29 ((f3(f6(c1, f6(c1, c2)), c1) = c1) <=> (f3(f6(c1, f6(c2, c1)), c1) = c1)),
% 30.08/20.29 inference(symmetry,[status(thm)],[33546])).
% 30.08/20.29 tff(33548,plain,
% 30.08/20.29 (c1 = f3(f9(c2, c1), c1)),
% 30.08/20.29 inference(symmetry,[status(thm)],[33514])).
% 30.08/20.29 tff(33549,plain,
% 30.08/20.29 (f3(f6(c1, f6(c1, c2)), c1) = f3(c2, f3(f9(c2, c1), c1))),
% 30.08/20.29 inference(monotonicity,[status(thm)],[64, 33548])).
% 30.08/20.29 tff(33550,plain,
% 30.08/20.29 (f3(f6(c1, f6(c1, c2)), c1) = f6(c1, c1)),
% 30.08/20.29 inference(transitivity,[status(thm)],[33549, 33449, 32438, 31339])).
% 30.08/20.29 tff(33551,plain,
% 30.08/20.29 ((f3(f6(c1, f6(c1, c2)), c1) = c1) <=> (f6(c1, c1) = c1)),
% 30.08/20.29 inference(monotonicity,[status(thm)],[33550])).
% 30.08/20.29 tff(33552,plain,
% 30.08/20.29 ((f6(c1, c1) = c1) <=> (f3(f6(c1, f6(c1, c2)), c1) = c1)),
% 30.08/20.29 inference(symmetry,[status(thm)],[33551])).
% 30.08/20.29 tff(33553,plain,
% 30.08/20.29 ((f6(c1, c1) = c1) <=> (f3(f6(c1, f6(c2, c1)), c1) = c1)),
% 30.08/20.29 inference(transitivity,[status(thm)],[33552, 33547])).
% 30.08/20.29 tff(33554,plain,
% 30.08/20.29 ((~(f6(c1, c1) = c1)) <=> (~(f3(f6(c1, f6(c2, c1)), c1) = c1))),
% 30.08/20.29 inference(monotonicity,[status(thm)],[33553])).
% 30.08/20.29 tff(33555,plain,
% 30.08/20.29 (~(f3(f6(c1, f6(c2, c1)), c1) = c1)),
% 30.08/20.29 inference(modus_ponens,[status(thm)],[28, 33554])).
% 30.08/20.29 tff(33556,plain,
% 30.08/20.29 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (f6(c1, f6(c2, c1)) = c4) | (f3(f6(c1, f6(c2, c1)), c1) = c1) | big_f(f3(f6(c1, f6(c2, c1)), c1), f6(c1, f6(c2, c1))))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (f6(c1, f6(c2, c1)) = c4) | (f3(f6(c1, f6(c2, c1)), c1) = c1) | big_f(f3(f6(c1, f6(c2, c1)), c1), f6(c1, f6(c2, c1))))),
% 30.08/20.29 inference(rewrite,[status(thm)],[])).
% 30.08/20.29 tff(33557,plain,
% 30.08/20.29 (((~(c2 = c3)) | (~(c2 = f2(c2))) | (f6(c1, f6(c2, c1)) = c4) | (f3(f6(c1, f6(c2, c1)), c1) = c1) | big_f(f3(f6(c1, f6(c2, c1)), c1), f6(c1, f6(c2, c1))) | big_f(c2, c2)) <=> ((~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (f6(c1, f6(c2, c1)) = c4) | (f3(f6(c1, f6(c2, c1)), c1) = c1) | big_f(f3(f6(c1, f6(c2, c1)), c1), f6(c1, f6(c2, c1))))),
% 30.08/20.29 inference(rewrite,[status(thm)],[])).
% 30.08/20.29 tff(33558,plain,
% 30.08/20.29 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | (f6(c1, f6(c2, c1)) = c4) | (f3(f6(c1, f6(c2, c1)), c1) = c1) | big_f(f3(f6(c1, f6(c2, c1)), c1), f6(c1, f6(c2, c1))) | big_f(c2, c2))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (f6(c1, f6(c2, c1)) = c4) | (f3(f6(c1, f6(c2, c1)), c1) = c1) | big_f(f3(f6(c1, f6(c2, c1)), c1), f6(c1, f6(c2, c1)))))),
% 30.08/20.29 inference(monotonicity,[status(thm)],[33557])).
% 30.08/20.29 tff(33559,plain,
% 30.08/20.29 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | (f6(c1, f6(c2, c1)) = c4) | (f3(f6(c1, f6(c2, c1)), c1) = c1) | big_f(f3(f6(c1, f6(c2, c1)), c1), f6(c1, f6(c2, c1))) | big_f(c2, c2))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (f6(c1, f6(c2, c1)) = c4) | (f3(f6(c1, f6(c2, c1)), c1) = c1) | big_f(f3(f6(c1, f6(c2, c1)), c1), f6(c1, f6(c2, c1))))),
% 30.08/20.29 inference(transitivity,[status(thm)],[33558, 33556])).
% 30.08/20.29 tff(33560,plain,
% 30.08/20.29 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | ((~(c2 = c3)) | (~(c2 = f2(c2))) | (f6(c1, f6(c2, c1)) = c4) | (f3(f6(c1, f6(c2, c1)), c1) = c1) | big_f(f3(f6(c1, f6(c2, c1)), c1), f6(c1, f6(c2, c1))) | big_f(c2, c2))),
% 30.08/20.29 inference(quant_inst,[status(thm)],[])).
% 30.08/20.29 tff(33561,plain,
% 30.08/20.29 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X12 = f2(X10))) | (X2 = c4) | (f3(X2, X13) = X13) | big_f(f3(X2, X13), X2) | big_f(X10, X12))) | (~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (f6(c1, f6(c2, c1)) = c4) | (f3(f6(c1, f6(c2, c1)), c1) = c1) | big_f(f3(f6(c1, f6(c2, c1)), c1), f6(c1, f6(c2, c1)))),
% 30.08/20.29 inference(modus_ponens,[status(thm)],[33560, 33559])).
% 30.08/20.29 tff(33562,plain,
% 30.08/20.29 ((~(c2 = c3)) | (~(c2 = f2(c2))) | big_f(c2, c2) | (f6(c1, f6(c2, c1)) = c4) | (f3(f6(c1, f6(c2, c1)), c1) = c1) | big_f(f3(f6(c1, f6(c2, c1)), c1), f6(c1, f6(c2, c1)))),
% 30.08/20.29 inference(unit_resolution,[status(thm)],[33561, 1459])).
% 30.08/20.29 tff(33563,plain,
% 30.08/20.29 (~(c2 = f2(c2))),
% 30.08/20.29 inference(unit_resolution,[status(thm)],[33562, 33555, 121, 1344, 33545, 33538])).
% 30.08/20.29 tff(33564,plain,
% 30.08/20.29 (~(f2(c2) = c2)),
% 30.08/20.29 inference(unit_resolution,[status(thm)],[31890, 33563])).
% 30.08/20.29 tff(33565,plain,
% 30.08/20.29 (f2(c2) = c1),
% 30.08/20.29 inference(unit_resolution,[status(thm)],[31912, 33564])).
% 30.08/20.29 tff(33566,plain,
% 30.08/20.29 ($false),
% 30.08/20.29 inference(unit_resolution,[status(thm)],[33565, 33531])).
% 30.08/20.29 tff(33567,plain,(big_f(f3(f6(c1, f6(c1, c2)), c1), f6(c1, f6(c1, c2))) | (~(f6(c1, c2) = c1)) | big_f(c2, c2) | (~(c2 = c3)) | (~(f6(c1, c1) = c3)) | big_f(f6(c1, c1), c1) | (f6(c1, c1) = c1) | (~(f3(c2, f3(f9(c2, c1), c1)) = c2)) | (~(f6(c2, c1) = c1)) | (~(c4 = c1)) | (~(f3(c1, c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 30.08/20.29 tff(33568,plain,
% 30.08/20.29 (~(f3(c2, f3(f9(c2, c1), c1)) = c2)),
% 30.08/20.29 inference(unit_resolution,[status(thm)],[33567, 33448, 121, 1335, 33309, 33304, 33210, 6931, 33387, 33300, 33318])).
% 30.08/20.29 tff(33569,plain,
% 30.08/20.29 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f3(c2, f3(f9(c2, c1), c1)) = c1) | (f3(c2, f3(f9(c2, c1), c1)) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f3(c2, f3(f9(c2, c1), c1)) = c1) | (f3(c2, f3(f9(c2, c1), c1)) = c2))),
% 30.08/20.29 inference(rewrite,[status(thm)],[])).
% 30.08/20.29 tff(33570,plain,
% 30.08/20.29 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f3(c2, f3(f9(c2, c1), c1)) = c1) | (f3(c2, f3(f9(c2, c1), c1)) = c2))),
% 30.08/20.29 inference(quant_inst,[status(thm)],[])).
% 30.08/20.29 tff(33571,plain,
% 30.08/20.29 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f3(c2, f3(f9(c2, c1), c1)) = c1) | (f3(c2, f3(f9(c2, c1), c1)) = c2)),
% 30.08/20.29 inference(modus_ponens,[status(thm)],[33570, 33569])).
% 30.08/20.29 tff(33572,plain,
% 30.08/20.29 ((f3(c2, f3(f9(c2, c1), c1)) = c1) | (f3(c2, f3(f9(c2, c1), c1)) = c2)),
% 30.08/20.29 inference(unit_resolution,[status(thm)],[33571, 10])).
% 30.08/20.29 tff(33573,plain,
% 30.08/20.29 (f3(c2, f3(f9(c2, c1), c1)) = c1),
% 30.08/20.29 inference(unit_resolution,[status(thm)],[33572, 33568])).
% 30.08/20.29 tff(33574,plain,
% 30.08/20.29 ((c2 = c4) <=> (f6(c1, c1) = c4)),
% 30.08/20.29 inference(monotonicity,[status(thm)],[33214])).
% 30.08/20.29 tff(33575,plain,
% 30.08/20.29 ((f6(c1, c1) = c4) <=> (c2 = c4)),
% 30.08/20.29 inference(symmetry,[status(thm)],[33574])).
% 30.08/20.29 tff(33576,plain,
% 30.08/20.29 ((f6(c1, c1) = c1) <=> (c2 = c4)),
% 30.08/20.29 inference(transitivity,[status(thm)],[33314, 33575])).
% 30.08/20.29 tff(33577,plain,
% 30.08/20.29 ((~(f6(c1, c1) = c1)) <=> (~(c2 = c4))),
% 30.08/20.29 inference(monotonicity,[status(thm)],[33576])).
% 30.08/20.29 tff(33578,plain,
% 30.08/20.29 (~(c2 = c4)),
% 30.08/20.29 inference(modus_ponens,[status(thm)],[33210, 33577])).
% 30.08/20.29 tff(33579,plain,
% 30.08/20.29 (f3(f9(c2, c1), c1) = c1),
% 30.08/20.29 inference(unit_resolution,[status(thm)],[33513, 33448, 33304, 33309, 33212, 6931, 33300, 121, 1335, 33578, 33318])).
% 30.08/20.29 tff(33580,plain,
% 30.08/20.29 (c1 = f3(f9(c2, c1), c1)),
% 30.08/20.29 inference(symmetry,[status(thm)],[33579])).
% 30.08/20.29 tff(33581,plain,
% 30.08/20.29 (f3(f6(c1, f6(c1, c2)), c1) = f3(c2, f3(f9(c2, c1), c1))),
% 30.08/20.29 inference(monotonicity,[status(thm)],[33212, 33580])).
% 30.08/20.29 tff(33582,plain,
% 30.08/20.29 (f3(f6(c1, f6(c1, c2)), c1) = c1),
% 30.08/20.29 inference(transitivity,[status(thm)],[33581, 33573])).
% 30.08/20.29 tff(33583,plain,
% 30.08/20.29 (big_f(f3(f6(c1, f6(c1, c2)), c1), f6(c1, f6(c1, c2))) <=> big_f(c1, f6(c1, c1))),
% 30.08/20.29 inference(monotonicity,[status(thm)],[33582, 31339])).
% 30.08/20.29 tff(33584,plain,
% 30.08/20.29 (big_f(c1, f6(c1, c1)) <=> big_f(f3(f6(c1, f6(c1, c2)), c1), f6(c1, f6(c1, c2)))),
% 30.08/20.29 inference(symmetry,[status(thm)],[33583])).
% 30.08/20.29 tff(33585,plain,
% 30.08/20.29 (big_f(f3(f6(c1, f6(c1, c2)), c1), f6(c1, f6(c1, c2)))),
% 30.08/20.29 inference(modus_ponens,[status(thm)],[33238, 33584])).
% 30.08/20.29 tff(33586,plain,
% 30.08/20.29 ($false),
% 30.08/20.29 inference(unit_resolution,[status(thm)],[33448, 33585])).
% 30.08/20.29 tff(33587,plain,((~(c3 = c2)) | (~(f6(c1, c2) = c1)) | big_f(c2, c2) | (~(f10(c1) = c1)) | big_f(c2, c1) | (~(f10(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 30.08/20.29 tff(33588,plain,
% 30.08/20.29 (~(c3 = c2)),
% 30.08/20.29 inference(unit_resolution,[status(thm)],[33587, 2, 32256, 121, 33200, 11819])).
% 30.08/20.29 tff(33589,plain,
% 30.08/20.29 (c3 = c1),
% 30.08/20.29 inference(unit_resolution,[status(thm)],[180, 33588])).
% 30.08/20.29 tff(33590,plain,
% 30.08/20.29 (c1 = c3),
% 30.08/20.29 inference(unit_resolution,[status(thm)],[175, 33589])).
% 30.08/20.29 tff(33591,plain,
% 30.08/20.29 (big_f(c2, f10(c2)) <=> big_f(c2, c1)),
% 30.08/20.29 inference(monotonicity,[status(thm)],[11819])).
% 30.08/20.29 tff(33592,plain,
% 30.08/20.29 (big_f(c2, c1) <=> big_f(c2, f10(c2))),
% 30.08/20.29 inference(symmetry,[status(thm)],[33591])).
% 30.08/20.29 tff(33593,plain,
% 30.08/20.29 ((~big_f(c2, c1)) <=> (~big_f(c2, f10(c2)))),
% 30.08/20.29 inference(monotonicity,[status(thm)],[33592])).
% 30.08/20.29 tff(33594,plain,
% 30.08/20.29 (~big_f(c2, f10(c2))),
% 30.08/20.29 inference(modus_ponens,[status(thm)],[2, 33593])).
% 30.08/20.29 tff(33595,plain,
% 30.08/20.29 (f3(c1, c1) = c1),
% 30.08/20.29 inference(unit_resolution,[status(thm)],[32078, 33594, 11819, 33590, 121, 33298])).
% 30.08/20.29 tff(33596,plain,
% 30.08/20.29 ((c2 = c3) <=> (c2 = c1)),
% 30.08/20.29 inference(monotonicity,[status(thm)],[33589])).
% 30.08/20.29 tff(33597,plain,
% 30.08/20.29 ((c2 = c1) <=> (c2 = c3)),
% 30.08/20.29 inference(symmetry,[status(thm)],[33596])).
% 30.08/20.29 tff(33598,plain,
% 30.08/20.29 ((~(c2 = c1)) <=> (~(c2 = c3))),
% 30.08/20.29 inference(monotonicity,[status(thm)],[33597])).
% 30.08/20.29 tff(33599,plain,
% 30.08/20.29 (~(c2 = c3)),
% 30.08/20.29 inference(modus_ponens,[status(thm)],[75, 33598])).
% 30.08/20.29 tff(33600,plain,
% 30.08/20.29 (f7(f7(c2)) = f7(c2)),
% 30.08/20.29 inference(monotonicity,[status(thm)],[33293])).
% 30.08/20.29 tff(33601,plain,
% 30.08/20.29 (f7(f7(c2)) = c2),
% 30.08/20.29 inference(transitivity,[status(thm)],[33600, 33293])).
% 30.08/20.29 tff(33602,plain,
% 30.08/20.29 ((f7(f7(c2)) = c3) <=> (c2 = c3)),
% 30.08/20.29 inference(monotonicity,[status(thm)],[33601])).
% 30.08/20.29 tff(33603,plain,
% 30.08/20.29 ((c2 = c3) <=> (f7(f7(c2)) = c3)),
% 30.08/20.29 inference(symmetry,[status(thm)],[33602])).
% 30.08/20.29 tff(33604,plain,
% 30.08/20.29 ((c2 = c1) <=> (f7(f7(c2)) = c3)),
% 30.08/20.29 inference(transitivity,[status(thm)],[33597, 33603])).
% 30.08/20.29 tff(33605,plain,
% 30.08/20.29 ((~(c2 = c1)) <=> (~(f7(f7(c2)) = c3))),
% 30.08/20.29 inference(monotonicity,[status(thm)],[33604])).
% 30.08/20.29 tff(33606,plain,
% 30.08/20.29 (~(f7(f7(c2)) = c3)),
% 30.08/20.29 inference(modus_ponens,[status(thm)],[75, 33605])).
% 30.08/20.29 tff(33607,plain,
% 30.08/20.29 (f1(f7(f7(c2)), c1) = c1),
% 30.08/20.29 inference(unit_resolution,[status(thm)],[11476, 79, 4932, 378, 377, 121, 77])).
% 30.08/20.29 tff(33608,plain,
% 30.08/20.29 (~big_f(f4(c4), c4)),
% 30.08/20.29 inference(unit_resolution,[status(thm)],[5036, 79, 2, 121])).
% 30.08/20.29 tff(33609,plain,
% 30.08/20.29 (~big_f(c2, c4)),
% 30.08/20.29 inference(unit_resolution,[status(thm)],[6521, 33608, 79])).
% 30.08/20.29 tff(33610,plain,
% 30.08/20.29 ((f6(c1, c1) = c1) | (~(f1(f7(f7(c2)), c1) = c1)) | (~(f7(c2) = c2)) | (~(c3 = c1)) | big_f(c2, c2) | big_f(c2, c1) | (~big_f(c1, c1)) | big_f(c2, c4) | (~(c2 = f4(c4)))),
% 30.08/20.29 inference(unit_resolution,[status(thm)],[11298, 25791])).
% 30.08/20.29 tff(33611,plain,
% 30.08/20.29 (~(c2 = f4(c4))),
% 30.08/20.29 inference(unit_resolution,[status(thm)],[33610, 33609, 4932, 77, 28, 2, 121, 172, 33607])).
% 30.08/20.29 tff(33612,plain,
% 30.08/20.29 ($false),
% 30.08/20.29 inference(unit_resolution,[status(thm)],[33611, 2602])).
% 30.08/20.29 tff(33613,plain,((~(f4(c4) = c2)) | (~big_f(c1, c1)) | (~(f7(c2) = c2)) | (f6(c1, c1) = c1) | big_f(c2, c1) | big_f(c2, c2) | (~(c3 = c1)) | (f7(f7(c2)) = c3) | (c2 = c3)), inference(lemma,lemma(discharge,[]))).
% 30.08/20.29 tff(33614,plain,
% 30.08/20.29 (~(f4(c4) = c2)),
% 30.08/20.29 inference(unit_resolution,[status(thm)],[33613, 33606, 121, 33293, 2, 31714, 33296, 33589, 33599])).
% 30.08/20.29 tff(33615,plain,
% 30.08/20.29 (f4(c4) = c1),
% 30.08/20.29 inference(unit_resolution,[status(thm)],[11750, 33614])).
% 30.08/20.29 tff(33616,plain,
% 30.08/20.29 (f7(f4(c4)) = f7(c1)),
% 30.08/20.29 inference(monotonicity,[status(thm)],[33615])).
% 30.08/20.29 tff(33617,plain,
% 30.08/20.29 (f7(f4(c4)) = c1),
% 30.08/20.29 inference(transitivity,[status(thm)],[33616, 25791])).
% 30.08/20.29 tff(33618,plain,
% 30.08/20.29 (f3(f7(f4(c4)), f4(c4)) = f3(c1, c1)),
% 30.08/20.29 inference(monotonicity,[status(thm)],[33617, 33615])).
% 30.08/20.29 tff(33619,plain,
% 30.08/20.29 (f3(f7(f4(c4)), f4(c4)) = c1),
% 30.08/20.29 inference(transitivity,[status(thm)],[33618, 33595])).
% 30.08/20.29 tff(33620,plain,
% 30.08/20.29 (f3(c2, f3(f7(f4(c4)), f4(c4))) = f3(c2, c1)),
% 30.08/20.29 inference(monotonicity,[status(thm)],[33619])).
% 30.08/20.29 tff(33621,plain,
% 30.08/20.29 ((f3(c2, f3(f7(f4(c4)), f4(c4))) = c2) <=> (f3(c2, c1) = c2)),
% 30.08/20.29 inference(monotonicity,[status(thm)],[33620])).
% 30.08/20.29 tff(33622,plain,
% 30.08/20.29 ((f3(c2, f3(f7(f4(c4)), f4(c4))) = c2) <=> (c2 = f3(c2, c1))),
% 30.08/20.29 inference(transitivity,[status(thm)],[33621, 32611])).
% 30.08/20.29 tff(33623,plain,
% 30.08/20.29 ((f3(c2, f3(f7(f4(c4)), f4(c4))) = c1) <=> (f3(c2, c1) = c1)),
% 30.08/20.29 inference(monotonicity,[status(thm)],[33620])).
% 30.08/20.29 tff(33624,plain,
% 30.08/20.29 ((f3(c2, c1) = c1) <=> (f3(c2, f3(f7(f4(c4)), f4(c4))) = c1)),
% 30.08/20.29 inference(symmetry,[status(thm)],[33623])).
% 30.08/20.29 tff(33625,plain,
% 30.08/20.29 ((~(f3(c2, c1) = c1)) <=> (~(f3(c2, f3(f7(f4(c4)), f4(c4))) = c1))),
% 30.08/20.29 inference(monotonicity,[status(thm)],[33624])).
% 30.08/20.29 tff(33626,plain,
% 30.08/20.29 (f3(c2, f3(f7(f4(c4)), f4(c4))) = f3(c2, c1)),
% 30.08/20.29 inference(monotonicity,[status(thm)],[32614])).
% 30.08/20.30 tff(33627,plain,
% 30.08/20.30 ((f3(c2, f3(f7(f4(c4)), f4(c4))) = c2) <=> (f3(c2, c1) = c2)),
% 30.08/20.30 inference(monotonicity,[status(thm)],[33626])).
% 30.08/20.30 tff(33628,plain,
% 30.08/20.30 ((f3(c2, f3(f7(f4(c4)), f4(c4))) = c2) <=> (c2 = f3(c2, c1))),
% 30.08/20.30 inference(transitivity,[status(thm)],[33627, 32611])).
% 30.08/20.30 tff(33629,plain,
% 30.08/20.30 ((f3(c2, f3(f7(f4(c4)), f4(c4))) = c1) <=> (f3(c2, c1) = c1)),
% 30.08/20.30 inference(monotonicity,[status(thm)],[33626])).
% 30.08/20.30 tff(33630,plain,
% 30.08/20.30 ((f3(c2, c1) = c1) <=> (f3(c2, f3(f7(f4(c4)), f4(c4))) = c1)),
% 30.08/20.30 inference(symmetry,[status(thm)],[33629])).
% 30.08/20.30 tff(33631,plain,
% 30.08/20.30 ((~(f3(c2, c1) = c1)) <=> (~(f3(c2, f3(f7(f4(c4)), f4(c4))) = c1))),
% 30.08/20.30 inference(monotonicity,[status(thm)],[33630])).
% 30.08/20.30 tff(33632,plain,
% 30.08/20.30 ((c1 = c4) | (c1 = f2(c1))),
% 30.08/20.30 inference(unit_resolution,[status(thm)],[7189, 7051, 32632, 5080, 1938, 31714])).
% 30.08/20.30 tff(33633,plain,
% 30.08/20.30 (c1 = f2(c1)),
% 30.08/20.30 inference(unit_resolution,[status(thm)],[33632, 482])).
% 30.08/20.30 tff(33634,plain,
% 30.08/20.30 (f2(c1) = c1),
% 30.08/20.30 inference(symmetry,[status(thm)],[33633])).
% 30.08/20.30 tff(33635,plain,
% 30.08/20.30 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((c1 = c4) | (~(c1 = c3)) | (~big_f(f3(c1, c1), c1)) | (~big_f(c1, c2)) | (~(f3(c1, c1) = c1)) | (c2 = f2(c1)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (c1 = c4) | (~(c1 = c3)) | (~big_f(f3(c1, c1), c1)) | (~big_f(c1, c2)) | (~(f3(c1, c1) = c1)) | (c2 = f2(c1)))),
% 30.08/20.30 inference(rewrite,[status(thm)],[])).
% 30.08/20.30 tff(33636,plain,
% 30.08/20.30 (((~(c1 = c3)) | (c1 = c4) | (~(f3(c1, c1) = c1)) | (~big_f(f3(c1, c1), c1)) | (c2 = f2(c1)) | (~big_f(c1, c2))) <=> ((c1 = c4) | (~(c1 = c3)) | (~big_f(f3(c1, c1), c1)) | (~big_f(c1, c2)) | (~(f3(c1, c1) = c1)) | (c2 = f2(c1)))),
% 30.08/20.30 inference(rewrite,[status(thm)],[])).
% 30.08/20.30 tff(33637,plain,
% 30.08/20.30 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c1 = c4) | (~(f3(c1, c1) = c1)) | (~big_f(f3(c1, c1), c1)) | (c2 = f2(c1)) | (~big_f(c1, c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((c1 = c4) | (~(c1 = c3)) | (~big_f(f3(c1, c1), c1)) | (~big_f(c1, c2)) | (~(f3(c1, c1) = c1)) | (c2 = f2(c1))))),
% 30.08/20.30 inference(monotonicity,[status(thm)],[33636])).
% 30.08/20.30 tff(33638,plain,
% 30.08/20.30 (((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c1 = c4) | (~(f3(c1, c1) = c1)) | (~big_f(f3(c1, c1), c1)) | (c2 = f2(c1)) | (~big_f(c1, c2)))) <=> ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (c1 = c4) | (~(c1 = c3)) | (~big_f(f3(c1, c1), c1)) | (~big_f(c1, c2)) | (~(f3(c1, c1) = c1)) | (c2 = f2(c1)))),
% 30.08/20.30 inference(transitivity,[status(thm)],[33637, 33635])).
% 30.08/20.30 tff(33639,plain,
% 30.08/20.30 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (c1 = c4) | (~(f3(c1, c1) = c1)) | (~big_f(f3(c1, c1), c1)) | (c2 = f2(c1)) | (~big_f(c1, c2)))),
% 30.08/20.30 inference(quant_inst,[status(thm)],[])).
% 30.08/20.30 tff(33640,plain,
% 30.08/20.30 ((~![X12: $i, X13: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (X2 = c4) | (~(f3(X2, X13) = X13)) | (~big_f(f3(X2, X13), X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (c1 = c4) | (~(c1 = c3)) | (~big_f(f3(c1, c1), c1)) | (~big_f(c1, c2)) | (~(f3(c1, c1) = c1)) | (c2 = f2(c1))),
% 30.08/20.30 inference(modus_ponens,[status(thm)],[33639, 33638])).
% 30.08/20.30 tff(33641,plain,
% 30.08/20.30 ((c1 = c4) | (c2 = f2(c1))),
% 30.08/20.30 inference(unit_resolution,[status(thm)],[33640, 7051, 32632, 5080, 1938, 30354])).
% 30.08/20.30 tff(33642,plain,
% 30.08/20.30 (c2 = f2(c1)),
% 30.08/20.30 inference(unit_resolution,[status(thm)],[33641, 482])).
% 30.08/20.30 tff(33643,plain,
% 30.08/20.30 (c2 = c1),
% 30.08/20.30 inference(transitivity,[status(thm)],[33642, 33634])).
% 30.08/20.30 tff(33644,plain,
% 30.08/20.30 ($false),
% 30.08/20.30 inference(unit_resolution,[status(thm)],[75, 33643])).
% 30.08/20.30 tff(33645,plain,((c1 = c4) | (~(c1 = c3)) | (~(f3(c1, c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 30.08/20.30 tff(33646,plain,
% 30.08/20.30 (c1 = c4),
% 30.08/20.30 inference(unit_resolution,[status(thm)],[33645, 5080, 1938])).
% 30.08/20.30 tff(33647,plain,
% 30.08/20.30 (c4 = c1),
% 30.08/20.30 inference(symmetry,[status(thm)],[33646])).
% 30.08/20.30 tff(33648,plain,
% 30.08/20.30 ((c2 = c4) <=> (c2 = c1)),
% 30.08/20.30 inference(monotonicity,[status(thm)],[33647])).
% 30.08/20.30 tff(33649,plain,
% 30.08/20.30 ((c2 = c1) <=> (c2 = c4)),
% 30.08/20.30 inference(symmetry,[status(thm)],[33648])).
% 30.08/20.30 tff(33650,plain,
% 30.08/20.30 ((~(c2 = c1)) <=> (~(c2 = c4))),
% 30.08/20.30 inference(monotonicity,[status(thm)],[33649])).
% 30.08/20.30 tff(33651,plain,
% 30.08/20.30 (~(c2 = c4)),
% 30.08/20.30 inference(modus_ponens,[status(thm)],[75, 33650])).
% 30.08/20.30 tff(33652,plain,
% 30.08/20.30 (f3(c2, c1) = c1),
% 30.08/20.30 inference(unit_resolution,[status(thm)],[32023, 7352, 5080, 873, 12175, 6769, 31714])).
% 30.08/20.30 tff(33653,plain,
% 30.08/20.30 (big_f(f3(c2, c1), c2) <=> big_f(c1, c2)),
% 30.08/20.30 inference(monotonicity,[status(thm)],[33652])).
% 30.08/20.30 tff(33654,plain,
% 30.08/20.30 (big_f(c1, c2) <=> big_f(f3(c2, c1), c2)),
% 30.08/20.30 inference(symmetry,[status(thm)],[33653])).
% 30.08/20.30 tff(33655,plain,
% 30.08/20.30 (big_f(f3(c2, c1), c2)),
% 30.08/20.30 inference(modus_ponens,[status(thm)],[30354, 33654])).
% 30.08/20.30 tff(33656,plain,
% 30.08/20.30 ($false),
% 30.08/20.30 inference(unit_resolution,[status(thm)],[12175, 33655])).
% 30.08/20.30 tff(33657,plain,(big_f(f3(c2, c1), c2) | (~(c1 = c3)) | (c2 = c4) | (c1 = f2(c1))), inference(lemma,lemma(discharge,[]))).
% 30.08/20.30 tff(33658,plain,
% 30.08/20.30 (big_f(f3(c2, c1), c2)),
% 30.08/20.30 inference(unit_resolution,[status(thm)],[33657, 6769, 33651, 5080])).
% 30.08/20.30 tff(33659,plain,
% 30.08/20.30 (~(f3(c2, c1) = c1)),
% 30.08/20.30 inference(unit_resolution,[status(thm)],[32062, 7051, 5080, 33651, 33658, 6769, 31714])).
% 30.08/20.30 tff(33660,plain,
% 30.08/20.30 (~(f3(c2, f3(f7(f4(c4)), f4(c4))) = c1)),
% 30.08/20.30 inference(modus_ponens,[status(thm)],[33659, 33631])).
% 30.08/20.30 tff(33661,plain,
% 30.08/20.30 (f3(c2, f3(f7(f4(c4)), f4(c4))) = c2),
% 30.08/20.30 inference(unit_resolution,[status(thm)],[32627, 33660])).
% 30.08/20.30 tff(33662,plain,
% 30.08/20.30 (c2 = f3(c2, c1)),
% 30.08/20.30 inference(modus_ponens,[status(thm)],[33661, 33628])).
% 30.08/20.30 tff(33663,plain,
% 30.08/20.30 (~(big_f(c2, c2) <=> big_f(f3(c2, c1), c2))),
% 30.08/20.30 inference(unit_resolution,[status(thm)],[32010, 33658, 121])).
% 30.08/20.30 tff(33664,plain,
% 30.08/20.30 (~(c2 = f3(c2, c1))),
% 30.08/20.30 inference(unit_resolution,[status(thm)],[32008, 33663])).
% 30.08/20.30 tff(33665,plain,
% 30.08/20.30 ($false),
% 30.08/20.30 inference(unit_resolution,[status(thm)],[33664, 33662])).
% 30.08/20.30 tff(33666,plain,((c1 = f2(c1)) | (~(f3(c1, c1) = c1)) | (~(f4(c4) = c1)) | (~(c1 = c3)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 30.08/20.30 tff(33667,plain,
% 30.08/20.30 (c1 = f2(c1)),
% 30.08/20.30 inference(unit_resolution,[status(thm)],[33666, 33595, 33615, 33590, 121])).
% 30.08/20.30 tff(33668,plain,
% 30.08/20.30 (f2(c1) = c1),
% 30.08/20.30 inference(symmetry,[status(thm)],[33667])).
% 30.08/20.30 tff(33669,plain,
% 30.08/20.30 ((c2 = f2(c1)) <=> (c2 = c1)),
% 30.08/20.30 inference(monotonicity,[status(thm)],[33668])).
% 30.08/20.30 tff(33670,plain,
% 30.08/20.30 ((c2 = c1) <=> (c2 = f2(c1))),
% 30.08/20.30 inference(symmetry,[status(thm)],[33669])).
% 30.08/20.30 tff(33671,plain,
% 30.08/20.30 ((~(c2 = c1)) <=> (~(c2 = f2(c1)))),
% 30.08/20.30 inference(monotonicity,[status(thm)],[33670])).
% 30.08/20.30 tff(33672,plain,
% 30.08/20.30 (~(c2 = f2(c1))),
% 30.08/20.30 inference(modus_ponens,[status(thm)],[75, 33671])).
% 30.08/20.30 tff(33673,plain,
% 30.08/20.30 (c1 = c4),
% 30.08/20.30 inference(unit_resolution,[status(thm)],[33645, 33590, 33595])).
% 30.08/20.30 tff(33674,plain,
% 30.08/20.30 (c4 = c1),
% 30.08/20.30 inference(symmetry,[status(thm)],[33673])).
% 30.08/20.30 tff(33675,plain,
% 30.08/20.30 ((c2 = c4) <=> (c2 = c1)),
% 30.08/20.30 inference(monotonicity,[status(thm)],[33674])).
% 30.08/20.30 tff(33676,plain,
% 30.08/20.30 ((c2 = c1) <=> (c2 = c4)),
% 30.08/20.30 inference(symmetry,[status(thm)],[33675])).
% 30.08/20.30 tff(33677,plain,
% 30.08/20.30 ((~(c2 = c1)) <=> (~(c2 = c4))),
% 30.08/20.30 inference(monotonicity,[status(thm)],[33676])).
% 30.08/20.30 tff(33678,plain,
% 30.08/20.30 (~(c2 = c4)),
% 30.08/20.30 inference(modus_ponens,[status(thm)],[75, 33677])).
% 30.08/20.30 tff(33679,plain,
% 30.08/20.30 (f3(c2, c1) = c1),
% 30.08/20.30 inference(unit_resolution,[status(thm)],[32031, 7352, 5080, 873, 12821, 30354, 12175])).
% 30.08/20.30 tff(33680,plain,
% 30.08/20.30 (big_f(f3(c2, c1), c2) <=> big_f(c1, c2)),
% 30.08/20.30 inference(monotonicity,[status(thm)],[33679])).
% 30.08/20.30 tff(33681,plain,
% 30.08/20.30 (big_f(c1, c2) <=> big_f(f3(c2, c1), c2)),
% 30.08/20.30 inference(symmetry,[status(thm)],[33680])).
% 30.08/20.30 tff(33682,plain,
% 30.08/20.30 (big_f(f3(c2, c1), c2)),
% 30.08/20.30 inference(modus_ponens,[status(thm)],[30354, 33681])).
% 30.08/20.30 tff(33683,plain,
% 30.08/20.30 ($false),
% 30.08/20.30 inference(unit_resolution,[status(thm)],[12175, 33682])).
% 30.08/20.30 tff(33684,plain,(big_f(f3(c2, c1), c2) | (~(c1 = c3)) | (c2 = c4) | (c2 = f2(c1))), inference(lemma,lemma(discharge,[]))).
% 30.08/20.30 tff(33685,plain,
% 30.08/20.30 (big_f(f3(c2, c1), c2)),
% 30.08/20.30 inference(unit_resolution,[status(thm)],[33684, 33590, 33678, 33672])).
% 30.08/20.30 tff(33686,plain,
% 30.08/20.30 (~(f3(c2, c1) = c1)),
% 30.08/20.30 inference(unit_resolution,[status(thm)],[32070, 7051, 33590, 33678, 33672, 30354, 33685])).
% 30.08/20.30 tff(33687,plain,
% 30.08/20.30 (~(f3(c2, f3(f7(f4(c4)), f4(c4))) = c1)),
% 30.08/20.30 inference(modus_ponens,[status(thm)],[33686, 33625])).
% 30.08/20.30 tff(33688,plain,
% 30.08/20.30 (f3(c2, f3(f7(f4(c4)), f4(c4))) = c2),
% 30.08/20.30 inference(unit_resolution,[status(thm)],[32627, 33687])).
% 30.08/20.30 tff(33689,plain,
% 30.08/20.30 (c2 = f3(c2, c1)),
% 30.08/20.30 inference(modus_ponens,[status(thm)],[33688, 33622])).
% 30.08/20.30 tff(33690,plain,
% 30.08/20.30 (~(big_f(c2, c2) <=> big_f(f3(c2, c1), c2))),
% 30.08/20.30 inference(unit_resolution,[status(thm)],[32010, 33685, 121])).
% 30.08/20.30 tff(33691,plain,
% 30.08/20.30 (~(c2 = f3(c2, c1))),
% 30.08/20.30 inference(unit_resolution,[status(thm)],[32008, 33690])).
% 30.08/20.30 tff(33692,plain,
% 30.08/20.30 ($false),
% 30.08/20.30 inference(unit_resolution,[status(thm)],[33691, 33689])).
% 30.08/20.30 tff(33693,plain,(big_f(c2, c1) | big_f(c2, c2) | (~(f10(c2) = c1))), inference(lemma,lemma(discharge,[]))).
% 30.08/20.30 tff(33694,plain,
% 30.08/20.30 (big_f(c2, c1)),
% 30.08/20.30 inference(unit_resolution,[status(thm)],[33693, 94, 121])).
% 30.08/20.30 tff(33695,plain,
% 30.08/20.30 (big_f(c2, f10(c2))),
% 30.08/20.30 inference(modus_ponens,[status(thm)],[33694, 12069])).
% 30.08/20.30 tff(33696,plain,
% 30.08/20.30 (big_f(c1, f10(c2))),
% 30.08/20.30 inference(modus_ponens,[status(thm)],[31714, 24205])).
% 30.08/20.30 tff(33697,plain,
% 30.08/20.30 (big_f(f7(c1), f6(c1, c1))),
% 30.08/20.30 inference(unit_resolution,[status(thm)],[27769, 10030, 31714])).
% 30.08/20.30 tff(33698,plain,
% 30.08/20.30 (c1 = f8(c2)),
% 30.08/20.30 inference(unit_resolution,[status(thm)],[27005, 2730, 25791, 89, 33697, 10030, 33696])).
% 30.08/20.30 tff(33699,plain,
% 30.08/20.30 (f8(c2) = c1),
% 30.08/20.30 inference(symmetry,[status(thm)],[33698])).
% 30.08/20.30 tff(33700,plain,
% 30.08/20.30 (c2 = f8(c2)),
% 30.08/20.30 inference(unit_resolution,[status(thm)],[28627, 2730, 25791, 89, 12291, 33697, 10030])).
% 30.08/20.30 tff(33701,plain,
% 30.08/20.30 (c2 = c1),
% 30.08/20.30 inference(transitivity,[status(thm)],[33700, 33699])).
% 30.08/20.30 tff(33702,plain,
% 30.08/20.30 ($false),
% 30.08/20.30 inference(unit_resolution,[status(thm)],[75, 33701])).
% 30.08/20.30 tff(33703,plain,((~(f6(c1, c1) = c1)) | (f10(c2) = c2) | (~big_f(c2, f10(c2)))), inference(lemma,lemma(discharge,[]))).
% 30.08/20.30 tff(33704,plain,
% 30.08/20.30 (~(f6(c1, c1) = c1)),
% 30.08/20.30 inference(unit_resolution,[status(thm)],[33703, 89, 33695])).
% 30.08/20.30 tff(33705,plain,
% 30.08/20.30 (~(f6(c1, f6(c1, c2)) = c1)),
% 30.08/20.30 inference(unit_resolution,[status(thm)],[58, 33704])).
% 30.08/20.30 tff(33706,plain,
% 30.08/20.30 (f6(c1, f6(c1, c2)) = c2),
% 30.08/20.30 inference(unit_resolution,[status(thm)],[63, 33705])).
% 30.08/20.30 tff(33707,plain,
% 30.08/20.30 (f6(c1, f6(c1, c2)) = f6(c1, c1)),
% 30.08/20.30 inference(monotonicity,[status(thm)],[32256])).
% 30.08/20.30 tff(33708,plain,
% 30.08/20.30 (f6(c1, c1) = f6(c1, f6(c1, c2))),
% 30.08/20.30 inference(symmetry,[status(thm)],[33707])).
% 30.08/20.30 tff(33709,plain,
% 30.08/20.30 (f6(c1, c1) = c2),
% 30.08/20.30 inference(transitivity,[status(thm)],[33708, 33706])).
% 30.08/20.30 tff(33710,plain,
% 30.08/20.30 (f10(f6(c1, c1)) = f10(c2)),
% 30.08/20.30 inference(monotonicity,[status(thm)],[33709])).
% 30.08/20.30 tff(33711,plain,
% 30.08/20.30 (f10(f6(c1, c1)) = c1),
% 30.08/20.30 inference(transitivity,[status(thm)],[33710, 94])).
% 30.08/20.30 tff(33712,plain,
% 30.08/20.30 (big_f(c1, f10(f6(c1, c1))) <=> big_f(c1, c1)),
% 30.08/20.30 inference(monotonicity,[status(thm)],[33711])).
% 30.08/20.30 tff(33713,plain,
% 30.08/20.30 (big_f(c1, c1) <=> big_f(c1, f10(f6(c1, c1)))),
% 30.08/20.30 inference(symmetry,[status(thm)],[33712])).
% 30.08/20.30 tff(33714,plain,
% 30.08/20.30 (big_f(c1, f10(f6(c1, c1)))),
% 30.08/20.30 inference(modus_ponens,[status(thm)],[31714, 33713])).
% 30.08/20.30 tff(33715,plain,
% 30.08/20.30 (f8(f6(c1, f6(c1, c2))) = f8(f6(c1, c1))),
% 30.08/20.30 inference(monotonicity,[status(thm)],[33707])).
% 30.08/20.30 tff(33716,plain,
% 30.08/20.30 (f8(f6(c1, c1)) = f8(f6(c1, f6(c1, c2)))),
% 30.08/20.30 inference(symmetry,[status(thm)],[33715])).
% 30.08/20.30 tff(33717,plain,
% 30.08/20.30 (f8(f6(c1, c1)) = f8(c2)),
% 30.08/20.30 inference(monotonicity,[status(thm)],[33709])).
% 30.08/20.30 tff(33718,plain,
% 30.08/20.30 (f8(c2) = f8(f6(c1, c1))),
% 30.08/20.30 inference(symmetry,[status(thm)],[33717])).
% 30.08/20.30 tff(33719,plain,
% 30.08/20.30 (f8(c2) = f8(f6(c1, f6(c1, c2)))),
% 30.08/20.30 inference(transitivity,[status(thm)],[33718, 33716])).
% 30.08/20.30 tff(33720,plain,
% 30.08/20.30 ((c1 = f8(c2)) <=> (c1 = f8(f6(c1, f6(c1, c2))))),
% 30.08/20.30 inference(monotonicity,[status(thm)],[33719])).
% 30.08/20.30 tff(33721,plain,
% 30.08/20.30 ((c1 = f8(f6(c1, f6(c1, c2)))) <=> (c1 = f8(c2))),
% 30.08/20.30 inference(symmetry,[status(thm)],[33720])).
% 30.08/20.30 tff(33722,plain,
% 30.08/20.30 (c2 = f6(c1, f6(c1, c2))),
% 30.08/20.30 inference(symmetry,[status(thm)],[33706])).
% 30.08/20.30 tff(33723,plain,
% 30.08/20.30 ((f10(f6(c1, c1)) = f6(c1, c1)) <=> (c1 = f6(c1, c1))),
% 30.08/20.30 inference(monotonicity,[status(thm)],[33711])).
% 30.08/20.30 tff(33724,plain,
% 30.08/20.30 ((f10(f6(c1, c1)) = f6(c1, c1)) <=> (f6(c1, c1) = c1)),
% 30.08/20.30 inference(transitivity,[status(thm)],[33723, 33209])).
% 30.08/20.30 tff(33725,plain,
% 30.08/20.30 ((f6(c1, c1) = c1) <=> (f10(f6(c1, c1)) = f6(c1, c1))),
% 30.08/20.30 inference(symmetry,[status(thm)],[33724])).
% 30.08/20.30 tff(33726,plain,
% 30.08/20.30 ((~(f6(c1, c1) = c1)) <=> (~(f10(f6(c1, c1)) = f6(c1, c1)))),
% 30.08/20.30 inference(monotonicity,[status(thm)],[33725])).
% 30.08/20.30 tff(33727,plain,
% 30.08/20.30 (~(f10(f6(c1, c1)) = f6(c1, c1))),
% 30.08/20.30 inference(modus_ponens,[status(thm)],[33704, 33726])).
% 30.08/20.30 tff(33728,plain,
% 30.08/20.30 (big_f(f6(c1, c1), c1) <=> big_f(c2, c1)),
% 30.08/20.30 inference(monotonicity,[status(thm)],[33709])).
% 30.08/20.30 tff(33729,plain,
% 30.08/20.30 (big_f(c2, c1) <=> big_f(f6(c1, c1), c1)),
% 30.08/20.30 inference(symmetry,[status(thm)],[33728])).
% 30.08/20.30 tff(33730,plain,
% 30.08/20.30 (big_f(f6(c1, c1), c1)),
% 30.08/20.30 inference(modus_ponens,[status(thm)],[33694, 33729])).
% 30.08/20.30 tff(33731,plain,
% 30.08/20.30 (f6(c1, c1) = c2),
% 30.08/20.30 inference(transitivity,[status(thm)],[33708, 27490])).
% 30.08/20.30 tff(33732,plain,
% 30.08/20.30 (f10(f6(c1, c1)) = f10(c2)),
% 30.08/20.30 inference(monotonicity,[status(thm)],[33731])).
% 30.08/20.30 tff(33733,plain,
% 30.08/20.30 (f10(f6(c1, c1)) = c1),
% 30.08/20.30 inference(transitivity,[status(thm)],[33732, 11819])).
% 30.08/20.30 tff(33734,plain,
% 30.08/20.30 (big_f(f6(c1, c1), f10(f6(c1, c1))) <=> big_f(f6(c1, c1), c1)),
% 30.08/20.30 inference(monotonicity,[status(thm)],[33733])).
% 30.08/20.30 tff(33735,plain,
% 30.08/20.30 (big_f(f6(c1, c1), c1) <=> big_f(f6(c1, c1), f10(f6(c1, c1)))),
% 30.08/20.30 inference(symmetry,[status(thm)],[33734])).
% 30.08/20.30 tff(33736,assumption,(big_f(f6(c1, c1), c1)), introduced(assumption)).
% 30.08/20.30 tff(33737,plain,
% 30.08/20.30 (big_f(f6(c1, c1), f10(f6(c1, c1)))),
% 30.08/20.30 inference(modus_ponens,[status(thm)],[33736, 33735])).
% 30.08/20.30 tff(33738,assumption,(~big_f(f6(c1, c1), f10(f6(c1, c1)))), introduced(assumption)).
% 30.08/20.30 tff(33739,plain,
% 30.08/20.30 ($false),
% 30.08/20.30 inference(unit_resolution,[status(thm)],[33738, 33737])).
% 30.08/20.30 tff(33740,plain,(big_f(f6(c1, c1), f10(f6(c1, c1))) | (~big_f(f6(c1, c1), c1)) | (~(f10(c2) = c1)) | (~(f6(c1, f6(c1, c2)) = c2))), inference(lemma,lemma(discharge,[]))).
% 30.08/20.30 tff(33741,plain,
% 30.08/20.30 (big_f(f6(c1, c1), f10(f6(c1, c1)))),
% 30.08/20.30 inference(unit_resolution,[status(thm)],[33740, 33730, 94, 33706])).
% 30.08/20.30 tff(33742,plain,
% 30.08/20.30 (~(f4(c4) = c1)),
% 30.08/20.30 inference(unit_resolution,[status(thm)],[32744, 3198, 121, 89, 33695, 33696, 33293])).
% 30.08/20.30 tff(33743,plain,
% 30.08/20.30 (f4(c4) = c2),
% 30.08/20.30 inference(unit_resolution,[status(thm)],[11750, 33742])).
% 30.08/20.30 tff(33744,plain,
% 30.08/20.30 (~(c3 = c1)),
% 30.08/20.30 inference(unit_resolution,[status(thm)],[11517, 33743, 31714, 33293, 121, 33694])).
% 30.08/20.30 tff(33745,plain,
% 30.08/20.30 (c3 = c2),
% 30.08/20.30 inference(unit_resolution,[status(thm)],[180, 33744])).
% 30.08/20.30 tff(33746,plain,
% 30.08/20.30 (~(f2(c3) = c2)),
% 30.08/20.30 inference(unit_resolution,[status(thm)],[11686, 33745, 31714, 121, 33743, 33694])).
% 30.08/20.30 tff(33747,plain,
% 30.08/20.30 (f2(c3) = c1),
% 30.08/20.30 inference(unit_resolution,[status(thm)],[1273, 33746])).
% 30.08/20.30 tff(33748,plain,
% 30.08/20.30 (~big_f(c2, f6(c2, c1))),
% 30.08/20.30 inference(unit_resolution,[status(thm)],[11730, 33747, 31714, 3198, 121, 33743, 33745])).
% 30.08/20.30 tff(33749,plain,
% 30.08/20.30 (f6(f6(c1, c1), c1) = f6(c2, c1)),
% 30.08/20.30 inference(monotonicity,[status(thm)],[33731])).
% 30.08/20.30 tff(33750,plain,
% 30.08/20.30 (f7(f6(c1, c1)) = f7(c2)),
% 30.08/20.30 inference(monotonicity,[status(thm)],[33731])).
% 30.08/20.30 tff(33751,plain,
% 30.08/20.30 (f7(f6(c1, c1)) = c2),
% 30.08/20.30 inference(transitivity,[status(thm)],[33750, 77])).
% 30.08/20.30 tff(33752,plain,
% 30.08/20.30 (big_f(f7(f6(c1, c1)), f6(f6(c1, c1), c1)) <=> big_f(c2, f6(c2, c1))),
% 30.08/20.30 inference(monotonicity,[status(thm)],[33751, 33749])).
% 30.08/20.30 tff(33753,plain,
% 30.08/20.30 (big_f(c2, f6(c2, c1)) <=> big_f(f7(f6(c1, c1)), f6(f6(c1, c1), c1))),
% 30.08/20.30 inference(symmetry,[status(thm)],[33752])).
% 30.08/20.30 tff(33754,plain,
% 30.08/20.30 ((~big_f(c2, f6(c2, c1))) <=> (~big_f(f7(f6(c1, c1)), f6(f6(c1, c1), c1)))),
% 30.08/20.30 inference(monotonicity,[status(thm)],[33753])).
% 30.08/20.30 tff(33755,assumption,(~big_f(c2, f6(c2, c1))), introduced(assumption)).
% 30.08/20.30 tff(33756,plain,
% 30.08/20.30 (~big_f(f7(f6(c1, c1)), f6(f6(c1, c1), c1))),
% 30.08/20.30 inference(modus_ponens,[status(thm)],[33755, 33754])).
% 30.08/20.30 tff(33757,assumption,(big_f(f6(c1, c1), f10(f6(c1, c1)))), introduced(assumption)).
% 30.08/20.30 tff(33758,plain,
% 30.08/20.30 ((f6(f6(c1, c1), c1) = c1) <=> (f6(c2, c1) = c1)),
% 30.08/20.30 inference(monotonicity,[status(thm)],[33749])).
% 30.08/20.30 tff(33759,plain,
% 30.08/20.30 ((f6(c2, c1) = c1) <=> (f6(f6(c1, c1), c1) = c1)),
% 30.08/20.30 inference(symmetry,[status(thm)],[33758])).
% 30.08/20.30 tff(33760,plain,
% 30.08/20.30 ((~(f6(c2, c1) = c1)) <=> (~(f6(f6(c1, c1), c1) = c1))),
% 30.08/20.30 inference(monotonicity,[status(thm)],[33759])).
% 30.08/20.30 tff(33761,plain,
% 30.08/20.30 (~(f6(f6(c1, c1), c1) = c1)),
% 30.08/20.30 inference(modus_ponens,[status(thm)],[3198, 33760])).
% 30.08/20.30 tff(33762,assumption,(~(f6(c1, c1) = f8(f6(c1, c1)))), introduced(assumption)).
% 30.08/20.30 tff(33763,plain,
% 30.08/20.30 (f7(f6(c1, c1)) = f6(c1, c1)),
% 30.08/20.30 inference(transitivity,[status(thm)],[33750, 77, 28323, 33707])).
% 30.08/20.30 tff(33764,assumption,(~(f10(f6(c1, c1)) = f6(c1, c1))), introduced(assumption)).
% 30.08/20.30 tff(33765,plain,
% 30.08/20.30 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f6(c1, c1)) = f6(c1, c1)) | (~(f7(f6(c1, c1)) = f6(c1, c1))) | (f6(c1, c1) = f8(f6(c1, c1))) | (~big_f(f6(c1, c1), f10(f6(c1, c1)))) | (f6(f6(c1, c1), c1) = c1) | big_f(f7(f6(c1, c1)), f6(f6(c1, c1), c1)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(f6(c1, c1)) = f6(c1, c1)) | (~(f7(f6(c1, c1)) = f6(c1, c1))) | (f6(c1, c1) = f8(f6(c1, c1))) | (~big_f(f6(c1, c1), f10(f6(c1, c1)))) | (f6(f6(c1, c1), c1) = c1) | big_f(f7(f6(c1, c1)), f6(f6(c1, c1), c1)))),
% 30.08/20.30 inference(rewrite,[status(thm)],[])).
% 30.08/20.30 tff(33766,plain,
% 30.08/20.30 (((f10(f6(c1, c1)) = f6(c1, c1)) | (f6(c1, c1) = f8(f6(c1, c1))) | (~big_f(f6(c1, c1), f10(f6(c1, c1)))) | (~(f7(f6(c1, c1)) = f6(c1, c1))) | (f6(f6(c1, c1), c1) = c1) | big_f(f7(f6(c1, c1)), f6(f6(c1, c1), c1))) <=> ((f10(f6(c1, c1)) = f6(c1, c1)) | (~(f7(f6(c1, c1)) = f6(c1, c1))) | (f6(c1, c1) = f8(f6(c1, c1))) | (~big_f(f6(c1, c1), f10(f6(c1, c1)))) | (f6(f6(c1, c1), c1) = c1) | big_f(f7(f6(c1, c1)), f6(f6(c1, c1), c1)))),
% 30.08/20.30 inference(rewrite,[status(thm)],[])).
% 30.08/20.30 tff(33767,plain,
% 30.08/20.30 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f6(c1, c1)) = f6(c1, c1)) | (f6(c1, c1) = f8(f6(c1, c1))) | (~big_f(f6(c1, c1), f10(f6(c1, c1)))) | (~(f7(f6(c1, c1)) = f6(c1, c1))) | (f6(f6(c1, c1), c1) = c1) | big_f(f7(f6(c1, c1)), f6(f6(c1, c1), c1)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f6(c1, c1)) = f6(c1, c1)) | (~(f7(f6(c1, c1)) = f6(c1, c1))) | (f6(c1, c1) = f8(f6(c1, c1))) | (~big_f(f6(c1, c1), f10(f6(c1, c1)))) | (f6(f6(c1, c1), c1) = c1) | big_f(f7(f6(c1, c1)), f6(f6(c1, c1), c1))))),
% 30.08/20.30 inference(monotonicity,[status(thm)],[33766])).
% 30.08/20.30 tff(33768,plain,
% 30.08/20.30 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f6(c1, c1)) = f6(c1, c1)) | (f6(c1, c1) = f8(f6(c1, c1))) | (~big_f(f6(c1, c1), f10(f6(c1, c1)))) | (~(f7(f6(c1, c1)) = f6(c1, c1))) | (f6(f6(c1, c1), c1) = c1) | big_f(f7(f6(c1, c1)), f6(f6(c1, c1), c1)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(f6(c1, c1)) = f6(c1, c1)) | (~(f7(f6(c1, c1)) = f6(c1, c1))) | (f6(c1, c1) = f8(f6(c1, c1))) | (~big_f(f6(c1, c1), f10(f6(c1, c1)))) | (f6(f6(c1, c1), c1) = c1) | big_f(f7(f6(c1, c1)), f6(f6(c1, c1), c1)))),
% 30.08/20.30 inference(transitivity,[status(thm)],[33767, 33765])).
% 30.08/20.30 tff(33769,plain,
% 30.08/20.30 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(f6(c1, c1)) = f6(c1, c1)) | (f6(c1, c1) = f8(f6(c1, c1))) | (~big_f(f6(c1, c1), f10(f6(c1, c1)))) | (~(f7(f6(c1, c1)) = f6(c1, c1))) | (f6(f6(c1, c1), c1) = c1) | big_f(f7(f6(c1, c1)), f6(f6(c1, c1), c1)))),
% 30.08/20.30 inference(quant_inst,[status(thm)],[])).
% 30.08/20.30 tff(33770,plain,
% 30.08/20.30 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(f6(c1, c1)) = f6(c1, c1)) | (~(f7(f6(c1, c1)) = f6(c1, c1))) | (f6(c1, c1) = f8(f6(c1, c1))) | (~big_f(f6(c1, c1), f10(f6(c1, c1)))) | (f6(f6(c1, c1), c1) = c1) | big_f(f7(f6(c1, c1)), f6(f6(c1, c1), c1))),
% 30.08/20.30 inference(modus_ponens,[status(thm)],[33769, 33768])).
% 30.08/20.30 tff(33771,plain,
% 30.08/20.30 ((~big_f(f6(c1, c1), f10(f6(c1, c1)))) | (f6(f6(c1, c1), c1) = c1) | big_f(f7(f6(c1, c1)), f6(f6(c1, c1), c1))),
% 30.08/20.30 inference(unit_resolution,[status(thm)],[33770, 2662, 33764, 33763, 33762])).
% 30.08/20.30 tff(33772,plain,
% 30.08/20.30 ($false),
% 30.08/20.30 inference(unit_resolution,[status(thm)],[33771, 33761, 33757, 33756])).
% 30.08/20.30 tff(33773,plain,((~big_f(f6(c1, c1), f10(f6(c1, c1)))) | (f10(f6(c1, c1)) = f6(c1, c1)) | (f6(c1, c1) = f8(f6(c1, c1))) | big_f(c2, f6(c2, c1)) | (~(f6(c1, f6(c1, c2)) = c2)) | (~(f7(c2) = c2)) | (f6(c2, c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 30.08/20.30 tff(33774,plain,
% 30.08/20.30 (f6(c1, c1) = f8(f6(c1, c1))),
% 30.08/20.30 inference(unit_resolution,[status(thm)],[33773, 33748, 33741, 3198, 33706, 33293, 33727])).
% 30.08/20.30 tff(33775,plain,
% 30.08/20.30 (c2 = f6(c1, c1)),
% 30.08/20.30 inference(transitivity,[status(thm)],[28323, 33707])).
% 30.08/20.30 tff(33776,plain,
% 30.08/20.30 (f8(c2) = f8(f6(c1, c1))),
% 30.08/20.30 inference(monotonicity,[status(thm)],[33775])).
% 30.08/20.30 tff(33777,plain,
% 30.08/20.30 (f8(f6(c1, c1)) = f8(c2)),
% 30.08/20.30 inference(symmetry,[status(thm)],[33776])).
% 30.08/20.30 tff(33778,plain,
% 30.08/20.30 ((c2 = f8(f6(c1, c1))) <=> (c2 = f8(c2))),
% 30.08/20.30 inference(monotonicity,[status(thm)],[33777])).
% 30.08/20.30 tff(33779,plain,
% 30.08/20.30 ((f6(c1, c1) = f8(f6(c1, c1))) <=> (c2 = f8(f6(c1, c1)))),
% 30.08/20.30 inference(monotonicity,[status(thm)],[33731])).
% 30.08/20.30 tff(33780,plain,
% 30.08/20.30 ((f6(c1, c1) = f8(f6(c1, c1))) <=> (c2 = f8(c2))),
% 30.08/20.30 inference(transitivity,[status(thm)],[33779, 33778])).
% 30.08/20.30 tff(33781,assumption,(f6(c1, c1) = f8(f6(c1, c1))), introduced(assumption)).
% 30.08/20.30 tff(33782,plain,
% 30.08/20.30 (c2 = f8(c2)),
% 30.08/20.30 inference(modus_ponens,[status(thm)],[33781, 33780])).
% 30.08/20.30 tff(33783,plain,
% 30.08/20.30 ($false),
% 30.08/20.30 inference(unit_resolution,[status(thm)],[12290, 33782])).
% 30.08/20.30 tff(33784,plain,((~(f6(c1, c1) = f8(f6(c1, c1)))) | (c2 = f8(c2)) | (~(f6(c1, f6(c1, c2)) = c2))), inference(lemma,lemma(discharge,[]))).
% 30.08/20.30 tff(33785,plain,
% 30.08/20.30 (c2 = f8(c2)),
% 30.08/20.30 inference(unit_resolution,[status(thm)],[33784, 33774, 33706])).
% 30.08/20.30 tff(33786,plain,
% 30.08/20.30 (f8(c2) = c2),
% 30.08/20.30 inference(symmetry,[status(thm)],[33785])).
% 30.08/20.30 tff(33787,plain,
% 30.08/20.30 (f8(f6(c1, f6(c1, c2))) = f6(c1, c1)),
% 30.08/20.30 inference(transitivity,[status(thm)],[33715, 33717, 33786, 33722, 33707])).
% 30.08/20.30 tff(33788,plain,
% 30.08/20.30 ((c1 = f8(f6(c1, f6(c1, c2)))) <=> (c1 = f6(c1, c1))),
% 30.08/20.30 inference(monotonicity,[status(thm)],[33787])).
% 30.08/20.30 tff(33789,plain,
% 30.08/20.30 ((c1 = f8(f6(c1, f6(c1, c2)))) <=> (f6(c1, c1) = c1)),
% 30.08/20.30 inference(transitivity,[status(thm)],[33788, 33209])).
% 30.08/20.30 tff(33790,plain,
% 30.08/20.30 ((f6(c1, c1) = c1) <=> (c1 = f8(f6(c1, f6(c1, c2))))),
% 30.08/20.30 inference(symmetry,[status(thm)],[33789])).
% 30.08/20.30 tff(33791,plain,
% 30.08/20.30 ((f6(c1, c1) = c1) <=> (f10(c2) = f8(c2))),
% 30.08/20.30 inference(transitivity,[status(thm)],[33790, 33721, 21566])).
% 30.08/20.30 tff(33792,plain,
% 30.08/20.30 ((~(f6(c1, c1) = c1)) <=> (~(f10(c2) = f8(c2)))),
% 30.08/20.30 inference(monotonicity,[status(thm)],[33791])).
% 30.08/20.30 tff(33793,plain,
% 30.08/20.30 (~(f10(c2) = f8(c2))),
% 30.08/20.30 inference(modus_ponens,[status(thm)],[33704, 33792])).
% 30.08/20.30 tff(33794,plain,
% 30.08/20.30 (f10(c2) = f8(c2)),
% 30.08/20.30 inference(unit_resolution,[status(thm)],[13744, 33747, 31714, 121, 33293, 33695, 33743, 33745, 89])).
% 30.08/20.31 tff(33795,plain,
% 30.08/20.31 ($false),
% 30.08/20.31 inference(unit_resolution,[status(thm)],[33794, 33793])).
% 30.08/20.31 tff(33796,plain,((f6(c2, c1) = c1) | big_f(c2, c2) | (f10(c2) = c2)), inference(lemma,lemma(discharge,[]))).
% 30.08/20.31 tff(33797,plain,
% 30.08/20.31 (f6(c2, c1) = c1),
% 30.08/20.31 inference(unit_resolution,[status(thm)],[33796, 89, 121])).
% 30.08/20.31 tff(33798,plain,
% 30.08/20.31 (f6(f6(c1, c1), c1) = f6(c2, c1)),
% 30.08/20.31 inference(monotonicity,[status(thm)],[33709])).
% 30.08/20.31 tff(33799,plain,
% 30.08/20.31 (f6(f6(c1, c1), c1) = c1),
% 30.08/20.31 inference(transitivity,[status(thm)],[33798, 33797])).
% 30.08/20.31 tff(33800,plain,
% 30.08/20.31 (f7(f6(c1, c1)) = f7(c2)),
% 30.08/20.31 inference(monotonicity,[status(thm)],[33709])).
% 30.08/20.31 tff(33801,plain,
% 30.08/20.31 (f7(f6(c1, c1)) = f6(c1, c1)),
% 30.08/20.31 inference(transitivity,[status(thm)],[33800, 33293, 33722, 33707])).
% 30.08/20.31 tff(33802,plain,
% 30.08/20.31 (big_f(f7(f6(c1, c1)), f6(f6(c1, c1), c1)) <=> big_f(f6(c1, c1), c1)),
% 30.08/20.31 inference(monotonicity,[status(thm)],[33801, 33799])).
% 30.08/20.31 tff(33803,plain,
% 30.08/20.31 (big_f(f6(c1, c1), c1) <=> big_f(f7(f6(c1, c1)), f6(f6(c1, c1), c1))),
% 30.08/20.31 inference(symmetry,[status(thm)],[33802])).
% 30.08/20.31 tff(33804,plain,
% 30.08/20.31 (big_f(f7(f6(c1, c1)), f6(f6(c1, c1), c1))),
% 30.08/20.31 inference(modus_ponens,[status(thm)],[33730, 33803])).
% 30.08/20.31 tff(33805,plain,
% 30.08/20.31 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f6(c1, c1)) = f6(c1, c1)) | (c1 = f8(f6(c1, c1))) | (~(f7(f6(c1, c1)) = f6(c1, c1))) | (~big_f(c1, f10(f6(c1, c1)))) | (~(f6(f6(c1, c1), c1) = c1)) | (~big_f(f7(f6(c1, c1)), f6(f6(c1, c1), c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(f6(c1, c1)) = f6(c1, c1)) | (c1 = f8(f6(c1, c1))) | (~(f7(f6(c1, c1)) = f6(c1, c1))) | (~big_f(c1, f10(f6(c1, c1)))) | (~(f6(f6(c1, c1), c1) = c1)) | (~big_f(f7(f6(c1, c1)), f6(f6(c1, c1), c1))))),
% 30.08/20.31 inference(rewrite,[status(thm)],[])).
% 30.08/20.31 tff(33806,plain,
% 30.08/20.31 (((f10(f6(c1, c1)) = f6(c1, c1)) | (c1 = f8(f6(c1, c1))) | (~big_f(c1, f10(f6(c1, c1)))) | (~(f7(f6(c1, c1)) = f6(c1, c1))) | (~(f6(f6(c1, c1), c1) = c1)) | (~big_f(f7(f6(c1, c1)), f6(f6(c1, c1), c1)))) <=> ((f10(f6(c1, c1)) = f6(c1, c1)) | (c1 = f8(f6(c1, c1))) | (~(f7(f6(c1, c1)) = f6(c1, c1))) | (~big_f(c1, f10(f6(c1, c1)))) | (~(f6(f6(c1, c1), c1) = c1)) | (~big_f(f7(f6(c1, c1)), f6(f6(c1, c1), c1))))),
% 30.08/20.31 inference(rewrite,[status(thm)],[])).
% 30.08/20.31 tff(33807,plain,
% 30.08/20.31 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f6(c1, c1)) = f6(c1, c1)) | (c1 = f8(f6(c1, c1))) | (~big_f(c1, f10(f6(c1, c1)))) | (~(f7(f6(c1, c1)) = f6(c1, c1))) | (~(f6(f6(c1, c1), c1) = c1)) | (~big_f(f7(f6(c1, c1)), f6(f6(c1, c1), c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f6(c1, c1)) = f6(c1, c1)) | (c1 = f8(f6(c1, c1))) | (~(f7(f6(c1, c1)) = f6(c1, c1))) | (~big_f(c1, f10(f6(c1, c1)))) | (~(f6(f6(c1, c1), c1) = c1)) | (~big_f(f7(f6(c1, c1)), f6(f6(c1, c1), c1)))))),
% 30.08/20.31 inference(monotonicity,[status(thm)],[33806])).
% 30.08/20.31 tff(33808,plain,
% 30.08/20.31 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f6(c1, c1)) = f6(c1, c1)) | (c1 = f8(f6(c1, c1))) | (~big_f(c1, f10(f6(c1, c1)))) | (~(f7(f6(c1, c1)) = f6(c1, c1))) | (~(f6(f6(c1, c1), c1) = c1)) | (~big_f(f7(f6(c1, c1)), f6(f6(c1, c1), c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(f6(c1, c1)) = f6(c1, c1)) | (c1 = f8(f6(c1, c1))) | (~(f7(f6(c1, c1)) = f6(c1, c1))) | (~big_f(c1, f10(f6(c1, c1)))) | (~(f6(f6(c1, c1), c1) = c1)) | (~big_f(f7(f6(c1, c1)), f6(f6(c1, c1), c1))))),
% 30.08/20.31 inference(transitivity,[status(thm)],[33807, 33805])).
% 30.12/20.31 tff(33809,plain,
% 30.12/20.31 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f6(c1, c1)) = f6(c1, c1)) | (c1 = f8(f6(c1, c1))) | (~big_f(c1, f10(f6(c1, c1)))) | (~(f7(f6(c1, c1)) = f6(c1, c1))) | (~(f6(f6(c1, c1), c1) = c1)) | (~big_f(f7(f6(c1, c1)), f6(f6(c1, c1), c1))))),
% 30.12/20.31 inference(quant_inst,[status(thm)],[])).
% 30.12/20.31 tff(33810,plain,
% 30.12/20.31 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(f6(c1, c1)) = f6(c1, c1)) | (c1 = f8(f6(c1, c1))) | (~(f7(f6(c1, c1)) = f6(c1, c1))) | (~big_f(c1, f10(f6(c1, c1)))) | (~(f6(f6(c1, c1), c1) = c1)) | (~big_f(f7(f6(c1, c1)), f6(f6(c1, c1), c1)))),
% 30.12/20.31 inference(modus_ponens,[status(thm)],[33809, 33808])).
% 30.12/20.31 tff(33811,plain,
% 30.12/20.31 ((c1 = f8(f6(c1, c1))) | (~big_f(c1, f10(f6(c1, c1)))) | (~(f6(f6(c1, c1), c1) = c1)) | (~big_f(f7(f6(c1, c1)), f6(f6(c1, c1), c1)))),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[33810, 2730, 33727, 33801])).
% 30.12/20.31 tff(33812,plain,
% 30.12/20.31 (c1 = f8(f6(c1, c1))),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[33811, 33804, 33799, 33714])).
% 30.12/20.31 tff(33813,plain,
% 30.12/20.31 (f8(f6(c1, c1)) = c1),
% 30.12/20.31 inference(symmetry,[status(thm)],[33812])).
% 30.12/20.31 tff(33814,plain,
% 30.12/20.31 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f6(c1, c1)) = f6(c1, c1)) | (~(f7(f6(c1, c1)) = f6(c1, c1))) | (f6(c1, c1) = f8(f6(c1, c1))) | (~big_f(f6(c1, c1), f10(f6(c1, c1)))) | (~(f6(f6(c1, c1), c1) = c1)) | (~big_f(f7(f6(c1, c1)), f6(f6(c1, c1), c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(f6(c1, c1)) = f6(c1, c1)) | (~(f7(f6(c1, c1)) = f6(c1, c1))) | (f6(c1, c1) = f8(f6(c1, c1))) | (~big_f(f6(c1, c1), f10(f6(c1, c1)))) | (~(f6(f6(c1, c1), c1) = c1)) | (~big_f(f7(f6(c1, c1)), f6(f6(c1, c1), c1))))),
% 30.12/20.31 inference(rewrite,[status(thm)],[])).
% 30.12/20.31 tff(33815,plain,
% 30.12/20.31 (((f10(f6(c1, c1)) = f6(c1, c1)) | (f6(c1, c1) = f8(f6(c1, c1))) | (~big_f(f6(c1, c1), f10(f6(c1, c1)))) | (~(f7(f6(c1, c1)) = f6(c1, c1))) | (~(f6(f6(c1, c1), c1) = c1)) | (~big_f(f7(f6(c1, c1)), f6(f6(c1, c1), c1)))) <=> ((f10(f6(c1, c1)) = f6(c1, c1)) | (~(f7(f6(c1, c1)) = f6(c1, c1))) | (f6(c1, c1) = f8(f6(c1, c1))) | (~big_f(f6(c1, c1), f10(f6(c1, c1)))) | (~(f6(f6(c1, c1), c1) = c1)) | (~big_f(f7(f6(c1, c1)), f6(f6(c1, c1), c1))))),
% 30.12/20.31 inference(rewrite,[status(thm)],[])).
% 30.12/20.31 tff(33816,plain,
% 30.12/20.31 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f6(c1, c1)) = f6(c1, c1)) | (f6(c1, c1) = f8(f6(c1, c1))) | (~big_f(f6(c1, c1), f10(f6(c1, c1)))) | (~(f7(f6(c1, c1)) = f6(c1, c1))) | (~(f6(f6(c1, c1), c1) = c1)) | (~big_f(f7(f6(c1, c1)), f6(f6(c1, c1), c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f6(c1, c1)) = f6(c1, c1)) | (~(f7(f6(c1, c1)) = f6(c1, c1))) | (f6(c1, c1) = f8(f6(c1, c1))) | (~big_f(f6(c1, c1), f10(f6(c1, c1)))) | (~(f6(f6(c1, c1), c1) = c1)) | (~big_f(f7(f6(c1, c1)), f6(f6(c1, c1), c1)))))),
% 30.12/20.31 inference(monotonicity,[status(thm)],[33815])).
% 30.12/20.31 tff(33817,plain,
% 30.12/20.31 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f6(c1, c1)) = f6(c1, c1)) | (f6(c1, c1) = f8(f6(c1, c1))) | (~big_f(f6(c1, c1), f10(f6(c1, c1)))) | (~(f7(f6(c1, c1)) = f6(c1, c1))) | (~(f6(f6(c1, c1), c1) = c1)) | (~big_f(f7(f6(c1, c1)), f6(f6(c1, c1), c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(f6(c1, c1)) = f6(c1, c1)) | (~(f7(f6(c1, c1)) = f6(c1, c1))) | (f6(c1, c1) = f8(f6(c1, c1))) | (~big_f(f6(c1, c1), f10(f6(c1, c1)))) | (~(f6(f6(c1, c1), c1) = c1)) | (~big_f(f7(f6(c1, c1)), f6(f6(c1, c1), c1))))),
% 30.12/20.31 inference(transitivity,[status(thm)],[33816, 33814])).
% 30.12/20.31 tff(33818,plain,
% 30.12/20.31 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((f10(f6(c1, c1)) = f6(c1, c1)) | (f6(c1, c1) = f8(f6(c1, c1))) | (~big_f(f6(c1, c1), f10(f6(c1, c1)))) | (~(f7(f6(c1, c1)) = f6(c1, c1))) | (~(f6(f6(c1, c1), c1) = c1)) | (~big_f(f7(f6(c1, c1)), f6(f6(c1, c1), c1))))),
% 30.12/20.31 inference(quant_inst,[status(thm)],[])).
% 30.12/20.31 tff(33819,plain,
% 30.12/20.31 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (f10(f6(c1, c1)) = f6(c1, c1)) | (~(f7(f6(c1, c1)) = f6(c1, c1))) | (f6(c1, c1) = f8(f6(c1, c1))) | (~big_f(f6(c1, c1), f10(f6(c1, c1)))) | (~(f6(f6(c1, c1), c1) = c1)) | (~big_f(f7(f6(c1, c1)), f6(f6(c1, c1), c1)))),
% 30.12/20.31 inference(modus_ponens,[status(thm)],[33818, 33817])).
% 30.12/20.31 tff(33820,plain,
% 30.12/20.31 ((f6(c1, c1) = f8(f6(c1, c1))) | (~(f6(f6(c1, c1), c1) = c1)) | (~big_f(f7(f6(c1, c1)), f6(f6(c1, c1), c1)))),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[33819, 2730, 33727, 33801, 33741])).
% 30.12/20.31 tff(33821,plain,
% 30.12/20.31 (f6(c1, c1) = f8(f6(c1, c1))),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[33820, 33799, 33804])).
% 30.12/20.31 tff(33822,plain,
% 30.12/20.31 (f6(c1, c1) = c1),
% 30.12/20.31 inference(transitivity,[status(thm)],[33821, 33813])).
% 30.12/20.31 tff(33823,plain,
% 30.12/20.31 ($false),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[33704, 33822])).
% 30.12/20.31 tff(33824,plain,((f10(c2) = c2) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 30.12/20.31 tff(33825,plain,
% 30.12/20.31 (f10(c2) = c2),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[33824, 121])).
% 30.12/20.31 tff(33826,plain,
% 30.12/20.31 (~(f4(c4) = c2)),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[11331, 2, 33825, 121])).
% 30.12/20.31 tff(33827,plain,
% 30.12/20.31 (~(f4(c4) = c1)),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[27698, 2, 121, 31714, 33200, 33293, 3198])).
% 30.12/20.31 tff(33828,plain,
% 30.12/20.31 ($false),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[11750, 33827, 33826])).
% 30.12/20.31 tff(33829,plain,(big_f(c2, c1) | big_f(c2, c2) | (f6(c2, c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 30.12/20.31 tff(33830,plain,
% 30.12/20.31 (big_f(c2, c1)),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[33829, 3198, 121])).
% 30.12/20.31 tff(33831,plain,
% 30.12/20.31 (f7(c2) = c2),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[10355, 79, 122, 121])).
% 30.12/20.31 tff(33832,plain,
% 30.12/20.31 (big_f(f7(c2), f6(c2, c1)) <=> big_f(c2, f6(c2, c1))),
% 30.12/20.31 inference(monotonicity,[status(thm)],[33831])).
% 30.12/20.31 tff(33833,plain,
% 30.12/20.31 (big_f(c2, c1)),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[11331, 79, 122, 121])).
% 30.12/20.31 tff(33834,plain,
% 30.12/20.31 (big_f(c1, c1)),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[23456, 33833, 3762, 33831, 121])).
% 30.12/20.31 tff(33835,plain,
% 30.12/20.31 (big_f(c1, c2)),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[27501, 33834, 121, 168, 79])).
% 30.12/20.31 tff(33836,plain,
% 30.12/20.31 (~(f2(c3) = c2)),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[11686, 33834, 121, 67, 79, 33833])).
% 30.12/20.31 tff(33837,plain,
% 30.12/20.31 (f2(c3) = c1),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[1273, 33836])).
% 30.12/20.31 tff(33838,plain,
% 30.12/20.31 (f9(c2, c1) = c1),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[1255, 1252, 122, 33837])).
% 30.12/20.31 tff(33839,plain,
% 30.12/20.31 (big_f(f7(c2), f6(c2, c1))),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[11568, 33838, 122, 3762, 79, 121])).
% 30.12/20.31 tff(33840,plain,
% 30.12/20.31 (big_f(c2, f6(c2, c1))),
% 30.12/20.31 inference(modus_ponens,[status(thm)],[33839, 33832])).
% 30.12/20.31 tff(33841,plain,
% 30.12/20.31 (c1 = f2(c3)),
% 30.12/20.31 inference(symmetry,[status(thm)],[33837])).
% 30.12/20.31 tff(33842,plain,
% 30.12/20.31 (f9(c2, c1) = f9(f10(c2), f2(c3))),
% 30.12/20.31 inference(monotonicity,[status(thm)],[216, 33841])).
% 30.12/20.31 tff(33843,plain,
% 30.12/20.31 (f9(c2, c1) = c1),
% 30.12/20.31 inference(transitivity,[status(thm)],[33842, 1252])).
% 30.12/20.31 tff(33844,plain,
% 30.12/20.31 (big_f(f9(c2, c1), f10(c2)) <=> big_f(c1, c2)),
% 30.12/20.31 inference(monotonicity,[status(thm)],[33843, 122])).
% 30.12/20.31 tff(33845,plain,
% 30.12/20.31 (big_f(c1, c2) <=> big_f(f9(c2, c1), f10(c2))),
% 30.12/20.31 inference(symmetry,[status(thm)],[33844])).
% 30.12/20.31 tff(33846,plain,
% 30.12/20.31 (big_f(f9(c2, c1), f10(c2))),
% 30.12/20.31 inference(modus_ponens,[status(thm)],[2865, 33845])).
% 30.12/20.31 tff(33847,plain,
% 30.12/20.31 (~(f6(c2, c1) = c1)),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[3097, 2378, 122, 33838, 33846, 33831, 33839])).
% 30.12/20.31 tff(33848,plain,
% 30.12/20.31 ($false),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[11730, 33847, 33840, 121, 33834, 33837, 79, 67])).
% 30.12/20.31 tff(33849,plain,((~(f9(f10(c2), f2(c3)) = c1)) | big_f(c2, c2) | (~(f4(c4) = c2)) | (~(c3 = c2)) | (~(f10(c2) = c2)) | (~big_f(c1, c2)) | (~(f10(c1) = c1))), inference(lemma,lemma(discharge,[]))).
% 30.12/20.31 tff(33850,plain,
% 30.12/20.31 (~(f9(f10(c2), f2(c3)) = c1)),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[33849, 79, 121, 181, 122, 33835, 3762])).
% 30.12/20.31 tff(33851,plain,
% 30.12/20.31 (f9(f10(c2), f2(c3)) = c2),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[1245, 33850])).
% 30.12/20.31 tff(33852,plain,
% 30.12/20.31 (~(f2(c3) = c2)),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[11686, 33834, 121, 181, 79, 33833])).
% 30.12/20.31 tff(33853,plain,
% 30.12/20.31 (f2(c3) = c1),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[1273, 33852])).
% 30.12/20.31 tff(33854,plain,
% 30.12/20.31 (c1 = f2(c3)),
% 30.12/20.31 inference(symmetry,[status(thm)],[33853])).
% 30.12/20.31 tff(33855,plain,
% 30.12/20.31 (f9(c2, c1) = f9(f10(c2), f2(c3))),
% 30.12/20.31 inference(monotonicity,[status(thm)],[216, 33854])).
% 30.12/20.31 tff(33856,plain,
% 30.12/20.31 (f9(c2, c1) = c2),
% 30.12/20.31 inference(transitivity,[status(thm)],[33855, 33851])).
% 30.12/20.31 tff(33857,plain,
% 30.12/20.31 (big_f(f9(c2, c1), f10(c2)) <=> big_f(c2, c2)),
% 30.12/20.31 inference(monotonicity,[status(thm)],[33856, 122])).
% 30.12/20.31 tff(33858,plain,
% 30.12/20.31 (big_f(c2, c2) <=> big_f(f9(c2, c1), f10(c2))),
% 30.12/20.31 inference(symmetry,[status(thm)],[33857])).
% 30.12/20.31 tff(33859,plain,
% 30.12/20.31 ((~big_f(c2, c2)) <=> (~big_f(f9(c2, c1), f10(c2)))),
% 30.12/20.31 inference(monotonicity,[status(thm)],[33858])).
% 30.12/20.31 tff(33860,plain,
% 30.12/20.31 (~big_f(f9(c2, c1), f10(c2))),
% 30.12/20.31 inference(modus_ponens,[status(thm)],[121, 33859])).
% 30.12/20.31 tff(33861,plain,
% 30.12/20.31 (f9(f10(c2), f2(c3)) = f9(c2, c1)),
% 30.12/20.31 inference(symmetry,[status(thm)],[33855])).
% 30.12/20.31 tff(33862,plain,
% 30.12/20.31 ((f9(f10(c2), f2(c3)) = c1) <=> (f9(c2, c1) = c1)),
% 30.12/20.31 inference(monotonicity,[status(thm)],[33861])).
% 30.12/20.31 tff(33863,plain,
% 30.12/20.31 ((~(f9(f10(c2), f2(c3)) = c1)) <=> (~(f9(c2, c1) = c1))),
% 30.12/20.31 inference(monotonicity,[status(thm)],[33862])).
% 30.12/20.31 tff(33864,plain,
% 30.12/20.31 (~(f9(c2, c1) = c1)),
% 30.12/20.31 inference(modus_ponens,[status(thm)],[33850, 33863])).
% 30.12/20.31 tff(33865,plain,
% 30.12/20.31 (big_f(f7(c2), f6(c2, c1))),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[11344, 33864, 122, 33831, 33833, 33860])).
% 30.12/20.31 tff(33866,plain,
% 30.12/20.31 (big_f(c2, f6(c2, c1))),
% 30.12/20.31 inference(modus_ponens,[status(thm)],[33865, 33832])).
% 30.12/20.31 tff(33867,plain,
% 30.12/20.31 (~(f6(c2, c1) = c1)),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[3090, 33860, 122, 33835, 33831, 33865])).
% 30.12/20.31 tff(33868,plain,
% 30.12/20.31 (~big_f(c2, f6(c2, c1))),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[11730, 33867, 121, 33834, 33853, 79, 181])).
% 30.12/20.31 tff(33869,plain,
% 30.12/20.31 ($false),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[33868, 33866])).
% 30.12/20.31 tff(33870,plain,((~(f4(c4) = c2)) | big_f(c2, c2) | (~(f10(c2) = c2)) | (~(f10(c1) = c1)) | (c1 = c3)), inference(lemma,lemma(discharge,[]))).
% 30.12/20.31 tff(33871,plain,
% 30.12/20.31 (c1 = c3),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[33870, 79, 121, 33200, 33825])).
% 30.12/20.31 tff(33872,plain,
% 30.12/20.31 (c3 = c1),
% 30.12/20.31 inference(modus_ponens,[status(thm)],[33871, 12387])).
% 30.12/20.31 tff(33873,plain,
% 30.12/20.31 (~(c3 = c1)),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[29988, 79, 31714, 121, 33825, 348])).
% 30.12/20.31 tff(33874,plain,
% 30.12/20.31 ($false),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[33873, 33872])).
% 30.12/20.31 tff(33875,plain,((~(f4(c4) = c2)) | big_f(c2, c2) | (~big_f(c2, c1))), inference(lemma,lemma(discharge,[]))).
% 30.12/20.31 tff(33876,plain,
% 30.12/20.31 (~(f4(c4) = c2)),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[33875, 33830, 121])).
% 30.12/20.31 tff(33877,plain,
% 30.12/20.31 (f4(c4) = c1),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[11750, 33876])).
% 30.12/20.31 tff(33878,plain,
% 30.12/20.31 (~(f6(c2, f7(f4(c4))) = c1)),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[32896, 33877, 3198])).
% 30.12/20.31 tff(33879,plain,
% 30.12/20.31 (f6(c2, f7(f4(c4))) = c2),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[6601, 33878])).
% 30.12/20.31 tff(33880,plain,
% 30.12/20.31 (f7(f4(c4)) = f7(c1)),
% 30.12/20.31 inference(monotonicity,[status(thm)],[33877])).
% 30.12/20.31 tff(33881,plain,
% 30.12/20.31 (f7(c1) = f7(f4(c4))),
% 30.12/20.31 inference(symmetry,[status(thm)],[33880])).
% 30.12/20.31 tff(33882,plain,
% 30.12/20.31 (c1 = f7(f4(c4))),
% 30.12/20.31 inference(transitivity,[status(thm)],[30840, 33881])).
% 30.12/20.31 tff(33883,plain,
% 30.12/20.31 (f6(c2, c1) = f6(c2, f7(f4(c4)))),
% 30.12/20.31 inference(monotonicity,[status(thm)],[33882])).
% 30.12/20.31 tff(33884,plain,
% 30.12/20.31 (f6(c2, c1) = c2),
% 30.12/20.31 inference(transitivity,[status(thm)],[33883, 33879])).
% 30.12/20.31 tff(33885,plain,
% 30.12/20.31 (big_f(c2, f6(c2, c1)) <=> big_f(c2, c2)),
% 30.12/20.31 inference(monotonicity,[status(thm)],[33884])).
% 30.12/20.31 tff(33886,plain,
% 30.12/20.31 (big_f(c2, c2) <=> big_f(c2, f6(c2, c1))),
% 30.12/20.31 inference(symmetry,[status(thm)],[33885])).
% 30.12/20.31 tff(33887,plain,
% 30.12/20.31 (big_f(c2, c2) <=> big_f(f7(c2), f6(c2, c1))),
% 30.12/20.31 inference(transitivity,[status(thm)],[33886, 33295])).
% 30.12/20.31 tff(33888,plain,
% 30.12/20.31 ((~big_f(c2, c2)) <=> (~big_f(f7(c2), f6(c2, c1)))),
% 30.12/20.31 inference(monotonicity,[status(thm)],[33887])).
% 30.12/20.31 tff(33889,plain,
% 30.12/20.31 (~big_f(f7(c2), f6(c2, c1))),
% 30.12/20.31 inference(modus_ponens,[status(thm)],[121, 33888])).
% 30.12/20.31 tff(33890,plain,
% 30.12/20.31 (f9(c2, c1) = c1),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[32873, 33889, 33825, 33830, 121, 33293])).
% 30.12/20.31 tff(33891,plain,
% 30.12/20.31 (big_f(f9(c2, c1), f10(c2)) <=> big_f(c1, c2)),
% 30.12/20.31 inference(monotonicity,[status(thm)],[33890, 33825])).
% 30.12/20.31 tff(33892,plain,
% 30.12/20.31 (big_f(c1, c2) <=> big_f(f9(c2, c1), f10(c2))),
% 30.12/20.31 inference(symmetry,[status(thm)],[33891])).
% 30.12/20.31 tff(33893,plain,
% 30.12/20.31 (big_f(f9(c2, c1), f10(c2))),
% 30.12/20.31 inference(modus_ponens,[status(thm)],[30354, 33892])).
% 30.12/20.31 tff(33894,plain,
% 30.12/20.31 ($false),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[3225, 2409, 122, 736, 3894, 77, 3198, 27629])).
% 30.12/20.31 tff(33895,plain,((f6(c2, c1) = c1) | (~(f10(c2) = c2)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))) | (~(f7(c2) = c2)) | big_f(c2, c2) | (~(f7(c1) = c1)) | (~(f4(c4) = c1))), inference(lemma,lemma(discharge,[]))).
% 30.12/20.31 tff(33896,plain,
% 30.12/20.31 ((f6(c2, c1) = c1) | (~(f10(c2) = c2)) | (~(f9(c2, c1) = c1)) | (~big_f(f9(c2, c1), f10(c2))) | (~(f7(c2) = c2)) | big_f(c2, c2) | (~(f4(c4) = c1))),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[33895, 25791])).
% 30.12/20.31 tff(33897,plain,
% 30.12/20.31 (~big_f(f9(c2, c1), f10(c2))),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[33896, 33890, 33825, 33293, 3198, 121, 33877])).
% 30.12/20.31 tff(33898,plain,
% 30.12/20.31 ($false),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[33897, 33893])).
% 30.12/20.31 tff(33899,plain,((f6(c2, c1) = c1) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 30.12/20.31 tff(33900,plain,
% 30.12/20.31 (f6(c2, c1) = c1),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[33899, 121])).
% 30.12/20.31 tff(33901,plain,
% 30.12/20.31 (big_f(c2, f6(c2, c1)) <=> big_f(c2, c1)),
% 30.12/20.31 inference(monotonicity,[status(thm)],[33900])).
% 30.12/20.31 tff(33902,plain,
% 30.12/20.31 (big_f(c2, c1) <=> big_f(c2, f6(c2, c1))),
% 30.12/20.31 inference(symmetry,[status(thm)],[33901])).
% 30.12/20.31 tff(33903,plain,
% 30.12/20.31 (big_f(c2, c1) <=> big_f(f7(c2), f6(c2, c1))),
% 30.12/20.31 inference(transitivity,[status(thm)],[33902, 33295])).
% 30.12/20.31 tff(33904,plain,
% 30.12/20.31 (big_f(f3(c1, c1), c1)),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[32074, 1431, 5080, 121, 33298])).
% 30.12/20.31 tff(33905,plain,
% 30.12/20.31 ($false),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[33904, 9672])).
% 30.12/20.31 tff(33906,plain,((f3(c1, c1) = c1) | big_f(c2, c1) | (~(c1 = c3)) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 30.12/20.31 tff(33907,plain,
% 30.12/20.31 (f3(c1, c1) = c1),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[33906, 5080, 2, 121])).
% 30.12/20.31 tff(33908,plain,
% 30.12/20.31 (f4(c4) = c1),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[11750, 33826])).
% 30.12/20.31 tff(33909,plain,
% 30.12/20.31 (f7(f4(c4)) = f7(c1)),
% 30.12/20.31 inference(monotonicity,[status(thm)],[33908])).
% 30.12/20.31 tff(33910,plain,
% 30.12/20.31 (f7(f4(c4)) = c1),
% 30.12/20.31 inference(transitivity,[status(thm)],[33909, 25791])).
% 30.12/20.31 tff(33911,plain,
% 30.12/20.31 (f3(f7(f4(c4)), f4(c4)) = f3(c1, c1)),
% 30.12/20.31 inference(monotonicity,[status(thm)],[33910, 33908])).
% 30.12/20.31 tff(33912,plain,
% 30.12/20.31 (f3(f7(f4(c4)), f4(c4)) = c1),
% 30.12/20.31 inference(transitivity,[status(thm)],[33911, 33907])).
% 30.12/20.31 tff(33913,plain,
% 30.12/20.31 (f3(c2, f3(f7(f4(c4)), f4(c4))) = f3(c2, c1)),
% 30.12/20.31 inference(monotonicity,[status(thm)],[33912])).
% 30.12/20.31 tff(33914,plain,
% 30.12/20.31 ((f3(c2, f3(f7(f4(c4)), f4(c4))) = c2) <=> (f3(c2, c1) = c2)),
% 30.12/20.31 inference(monotonicity,[status(thm)],[33913])).
% 30.12/20.31 tff(33915,plain,
% 30.12/20.31 ((f3(c2, f3(f7(f4(c4)), f4(c4))) = c2) <=> (c2 = f3(c2, c1))),
% 30.12/20.31 inference(transitivity,[status(thm)],[33914, 32611])).
% 30.12/20.31 tff(33916,plain,
% 30.12/20.31 (f3(c2, c1) = f3(c2, f3(f7(f4(c4)), f4(c4)))),
% 30.12/20.31 inference(symmetry,[status(thm)],[33913])).
% 30.12/20.31 tff(33917,plain,
% 30.12/20.31 (c2 = f6(c1, f6(c1, c2))),
% 30.12/20.31 inference(symmetry,[status(thm)],[33298])).
% 30.12/20.31 tff(33918,plain,
% 30.12/20.31 (f3(c2, c1) = f3(f6(c1, f6(c1, c2)), c1)),
% 30.12/20.31 inference(monotonicity,[status(thm)],[33917])).
% 30.12/20.31 tff(33919,plain,
% 30.12/20.31 (f3(f6(c1, f6(c1, c2)), c1) = f3(c2, c1)),
% 30.12/20.31 inference(symmetry,[status(thm)],[33918])).
% 30.12/20.31 tff(33920,plain,
% 30.12/20.31 (f3(f6(c1, f6(c1, c2)), c1) = f3(c2, f3(f7(f4(c4)), f4(c4)))),
% 30.12/20.31 inference(transitivity,[status(thm)],[33919, 33916])).
% 30.12/20.31 tff(33921,plain,
% 30.12/20.31 ((f3(f6(c1, f6(c1, c2)), c1) = c1) <=> (f3(c2, f3(f7(f4(c4)), f4(c4))) = c1)),
% 30.12/20.31 inference(monotonicity,[status(thm)],[33920])).
% 30.12/20.31 tff(33922,plain,
% 30.12/20.31 ((f3(c2, c1) = c1) <=> (f3(f6(c1, f6(c1, c2)), c1) = c1)),
% 30.12/20.31 inference(monotonicity,[status(thm)],[33918])).
% 30.12/20.31 tff(33923,plain,
% 30.12/20.31 ((f3(c2, c1) = c1) <=> (f3(c2, f3(f7(f4(c4)), f4(c4))) = c1)),
% 30.12/20.31 inference(transitivity,[status(thm)],[33922, 33921])).
% 30.12/20.31 tff(33924,plain,
% 30.12/20.31 ((~(f3(c2, c1) = c1)) <=> (~(f3(c2, f3(f7(f4(c4)), f4(c4))) = c1))),
% 30.12/20.31 inference(monotonicity,[status(thm)],[33923])).
% 30.12/20.31 tff(33925,plain,
% 30.12/20.31 (~(f3(c1, c1) = c1)),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[33645, 482, 5080])).
% 30.12/20.31 tff(33926,plain,
% 30.12/20.31 (f3(c1, c1) = c2),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[1416, 33925])).
% 30.12/20.31 tff(33927,plain,
% 30.12/20.31 (big_f(f3(c1, c1), c1) <=> big_f(c2, c1)),
% 30.12/20.31 inference(monotonicity,[status(thm)],[33926])).
% 30.12/20.31 tff(33928,plain,
% 30.12/20.31 (big_f(c2, c1) <=> big_f(f3(c1, c1), c1)),
% 30.12/20.31 inference(symmetry,[status(thm)],[33927])).
% 30.12/20.31 tff(33929,plain,
% 30.12/20.31 ((~big_f(c2, c1)) <=> (~big_f(f3(c1, c1), c1))),
% 30.12/20.31 inference(monotonicity,[status(thm)],[33928])).
% 30.12/20.31 tff(33930,plain,
% 30.12/20.31 (~big_f(f3(c1, c1), c1)),
% 30.12/20.31 inference(modus_ponens,[status(thm)],[2, 33929])).
% 30.12/20.31 tff(33931,plain,
% 30.12/20.31 (big_f(f3(c1, c1), c1)),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[31981, 482, 5080, 33925])).
% 30.12/20.31 tff(33932,plain,
% 30.12/20.31 ($false),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[33931, 33930])).
% 30.12/20.31 tff(33933,plain,((c1 = c4) | big_f(c2, c1) | (~(c1 = c3))), inference(lemma,lemma(discharge,[]))).
% 30.12/20.31 tff(33934,plain,
% 30.12/20.31 (c1 = c4),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[33933, 5080, 2])).
% 30.12/20.31 tff(33935,plain,
% 30.12/20.31 (c4 = c1),
% 30.12/20.31 inference(symmetry,[status(thm)],[33934])).
% 30.12/20.31 tff(33936,plain,
% 30.12/20.31 ((c2 = c4) <=> (c2 = c1)),
% 30.12/20.31 inference(monotonicity,[status(thm)],[33935])).
% 30.12/20.31 tff(33937,plain,
% 30.12/20.31 ((c2 = c1) <=> (c2 = c4)),
% 30.12/20.31 inference(symmetry,[status(thm)],[33936])).
% 30.12/20.31 tff(33938,plain,
% 30.12/20.31 ((~(c2 = c1)) <=> (~(c2 = c4))),
% 30.12/20.31 inference(monotonicity,[status(thm)],[33937])).
% 30.12/20.31 tff(33939,plain,
% 30.12/20.31 (~(c2 = c4)),
% 30.12/20.31 inference(modus_ponens,[status(thm)],[75, 33938])).
% 30.12/20.31 tff(33940,plain,
% 30.12/20.31 (c1 = f2(c1)),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[33666, 33907, 33908, 5080, 121])).
% 30.12/20.31 tff(33941,plain,
% 30.12/20.31 (f2(c1) = c1),
% 30.12/20.31 inference(symmetry,[status(thm)],[33940])).
% 30.12/20.31 tff(33942,plain,
% 30.12/20.31 ((c2 = f2(c1)) <=> (c2 = c1)),
% 30.12/20.31 inference(monotonicity,[status(thm)],[33941])).
% 30.12/20.31 tff(33943,plain,
% 30.12/20.31 ((c2 = c1) <=> (c2 = f2(c1))),
% 30.12/20.31 inference(symmetry,[status(thm)],[33942])).
% 30.12/20.31 tff(33944,plain,
% 30.12/20.31 ((~(c2 = c1)) <=> (~(c2 = f2(c1)))),
% 30.12/20.31 inference(monotonicity,[status(thm)],[33943])).
% 30.12/20.31 tff(33945,plain,
% 30.12/20.31 (~(c2 = f2(c1))),
% 30.12/20.31 inference(modus_ponens,[status(thm)],[75, 33944])).
% 30.12/20.31 tff(33946,plain,
% 30.12/20.31 (big_f(f3(c2, c1), c2)),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[33684, 33945, 5080, 33939])).
% 30.12/20.31 tff(33947,plain,
% 30.12/20.31 (~(f3(c2, c1) = c1)),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[32070, 7051, 5080, 33939, 33945, 30354, 33946])).
% 30.12/20.31 tff(33948,plain,
% 30.12/20.31 (~(f3(c2, f3(f7(f4(c4)), f4(c4))) = c1)),
% 30.12/20.31 inference(modus_ponens,[status(thm)],[33947, 33924])).
% 30.12/20.31 tff(33949,plain,
% 30.12/20.31 (f3(c2, f3(f7(f4(c4)), f4(c4))) = c2),
% 30.12/20.31 inference(unit_resolution,[status(thm)],[32627, 33948])).
% 30.12/20.31 tff(33950,plain,
% 30.12/20.31 (c2 = f3(c2, c1)),
% 30.12/20.31 inference(modus_ponens,[status(thm)],[33949, 33915])).
% 30.12/20.32 tff(33951,plain,
% 30.12/20.32 (~(big_f(c2, c2) <=> big_f(f3(c2, c1), c2))),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[32010, 33946, 121])).
% 30.12/20.32 tff(33952,plain,
% 30.12/20.32 (~(c2 = f3(c2, c1))),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[32008, 33951])).
% 30.12/20.32 tff(33953,plain,
% 30.12/20.32 ($false),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[33952, 33950])).
% 30.12/20.32 tff(33954,plain,((~(c1 = c3)) | big_f(c2, c2) | big_f(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 30.12/20.32 tff(33955,plain,
% 30.12/20.32 (~(c1 = c3)),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[33954, 2, 121])).
% 30.12/20.32 tff(33956,plain,
% 30.12/20.32 (~(c3 = c1)),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[175, 33955])).
% 30.12/20.32 tff(33957,plain,
% 30.12/20.32 (c3 = c2),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[180, 33956])).
% 30.12/20.32 tff(33958,plain,
% 30.12/20.32 (~(c4 = c2)),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[27535, 33957, 31714, 121, 2])).
% 30.12/20.32 tff(33959,plain,
% 30.12/20.32 (c4 = c1),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[461, 33958])).
% 30.12/20.32 tff(33960,plain,
% 30.12/20.32 (f6(c1, c1) = c2),
% 30.12/20.32 inference(transitivity,[status(thm)],[32390, 33298])).
% 30.12/20.32 tff(33961,plain,
% 30.12/20.32 ((f6(c1, c1) = c3) <=> (c2 = c3)),
% 30.12/20.32 inference(monotonicity,[status(thm)],[33960])).
% 30.12/20.32 tff(33962,plain,
% 30.12/20.32 ((c2 = c3) <=> (f6(c1, c1) = c3)),
% 30.12/20.32 inference(symmetry,[status(thm)],[33961])).
% 30.12/20.32 tff(33963,plain,
% 30.12/20.32 ((c3 = c2) <=> (f6(c1, c1) = c3)),
% 30.12/20.32 inference(transitivity,[status(thm)],[78, 33962])).
% 30.12/20.32 tff(33964,plain,
% 30.12/20.32 (f6(c1, c1) = c3),
% 30.12/20.32 inference(modus_ponens,[status(thm)],[33957, 33963])).
% 30.12/20.32 tff(33965,plain,
% 30.12/20.32 (big_f(f7(c1), f6(c1, c1))),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[27676, 2, 33200, 31714])).
% 30.12/20.32 tff(33966,plain,
% 30.12/20.32 (big_f(c1, f6(c1, c1))),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[28169, 33965])).
% 30.12/20.32 tff(33967,plain,
% 30.12/20.32 ((f6(c1, c1) = c4) <=> (c2 = c4)),
% 30.12/20.32 inference(monotonicity,[status(thm)],[33960])).
% 30.12/20.32 tff(33968,plain,
% 30.12/20.32 ((c2 = c4) <=> (f6(c1, c1) = c4)),
% 30.12/20.32 inference(symmetry,[status(thm)],[33967])).
% 30.12/20.32 tff(33969,plain,
% 30.12/20.32 ((c2 = c4) <=> (c2 = c1)),
% 30.12/20.32 inference(monotonicity,[status(thm)],[33959])).
% 30.12/20.32 tff(33970,plain,
% 30.12/20.32 ((c2 = c1) <=> (c2 = c4)),
% 30.12/20.32 inference(symmetry,[status(thm)],[33969])).
% 30.12/20.32 tff(33971,plain,
% 30.12/20.32 ((c2 = c1) <=> (f6(c1, f6(c1, c2)) = c4)),
% 30.12/20.32 inference(transitivity,[status(thm)],[33970, 33968, 32480])).
% 30.12/20.32 tff(33972,plain,
% 30.12/20.32 ((~(c2 = c1)) <=> (~(f6(c1, f6(c1, c2)) = c4))),
% 30.12/20.32 inference(monotonicity,[status(thm)],[33971])).
% 30.12/20.32 tff(33973,plain,
% 30.12/20.32 (~(f6(c1, f6(c1, c2)) = c4)),
% 30.12/20.32 inference(modus_ponens,[status(thm)],[75, 33972])).
% 30.12/20.32 tff(33974,plain,
% 30.12/20.32 (c2 = c3),
% 30.12/20.32 inference(modus_ponens,[status(thm)],[33957, 78])).
% 30.12/20.32 tff(33975,plain,
% 30.12/20.32 (big_f(f6(c1, c1), c1) <=> big_f(c2, c1)),
% 30.12/20.32 inference(monotonicity,[status(thm)],[33960])).
% 30.12/20.32 tff(33976,plain,
% 30.12/20.32 (big_f(c2, c1) <=> big_f(f6(c1, c1), c1)),
% 30.12/20.32 inference(symmetry,[status(thm)],[33975])).
% 30.12/20.32 tff(33977,plain,
% 30.12/20.32 ((~big_f(c2, c1)) <=> (~big_f(f6(c1, c1), c1))),
% 30.12/20.32 inference(monotonicity,[status(thm)],[33976])).
% 30.12/20.32 tff(33978,plain,
% 30.12/20.32 (~big_f(f6(c1, c1), c1)),
% 30.12/20.32 inference(modus_ponens,[status(thm)],[2, 33977])).
% 30.12/20.32 tff(33979,plain,
% 30.12/20.32 (f3(f3(f7(c1), c1), c1) = c1),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[32475, 33964, 32256, 121, 33978, 33974, 33959, 33296])).
% 30.12/20.32 tff(33980,plain,
% 30.12/20.32 (f3(c1, c1) = c1),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[32527, 33979, 32256, 33978, 33959, 121, 33974, 33973, 33966, 33964, 33298])).
% 30.12/20.32 tff(33981,plain,
% 30.12/20.32 (c1 = f4(c4)),
% 30.12/20.32 inference(symmetry,[status(thm)],[33908])).
% 30.12/20.32 tff(33982,plain,
% 30.12/20.32 (f7(f4(c4)) = f4(c4)),
% 30.12/20.32 inference(transitivity,[status(thm)],[33909, 25791, 33981])).
% 30.12/20.32 tff(33983,plain,
% 30.12/20.32 ((c2 = c1) <=> (f6(c1, c1) = c4)),
% 30.12/20.32 inference(transitivity,[status(thm)],[33970, 33968])).
% 30.12/20.32 tff(33984,plain,
% 30.12/20.32 ((~(c2 = c1)) <=> (~(f6(c1, c1) = c4))),
% 30.12/20.32 inference(monotonicity,[status(thm)],[33983])).
% 30.12/20.32 tff(33985,plain,
% 30.12/20.32 (~(f6(c1, c1) = c4)),
% 30.12/20.32 inference(modus_ponens,[status(thm)],[75, 33984])).
% 30.12/20.32 tff(33986,plain,
% 30.12/20.32 (~big_f(f3(f6(c1, f6(c1, c2)), c1), f6(c1, f6(c1, c2)))),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[33447, 33980, 32256, 33978, 33957, 121, 33973, 33985, 33908, 33982, 33298])).
% 30.12/20.32 tff(33987,plain,
% 30.12/20.32 (~(f3(c2, f3(f9(c2, c1), c1)) = c2)),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[33567, 33986, 121, 33900, 33978, 33974, 33296, 33964, 33980, 33959, 32256])).
% 30.12/20.32 tff(33988,plain,
% 30.12/20.32 (f3(c2, f3(f9(c2, c1), c1)) = c1),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[33572, 33987])).
% 30.12/20.32 tff(33989,plain,
% 30.12/20.32 ((~(c2 = c1)) <=> (~(c2 = c4))),
% 30.12/20.32 inference(monotonicity,[status(thm)],[33970])).
% 30.12/20.32 tff(33990,plain,
% 30.12/20.32 (~(c2 = c4)),
% 30.12/20.32 inference(modus_ponens,[status(thm)],[75, 33989])).
% 30.12/20.32 tff(33991,plain,
% 30.12/20.32 (f3(f9(c2, c1), c1) = c1),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[33513, 33986, 33978, 33974, 33298, 32256, 33959, 121, 33980, 33990, 33964])).
% 30.12/20.32 tff(33992,plain,
% 30.12/20.32 (c1 = f3(f9(c2, c1), c1)),
% 30.12/20.32 inference(symmetry,[status(thm)],[33991])).
% 30.12/20.32 tff(33993,plain,
% 30.12/20.32 (f3(c2, c1) = f3(c2, f3(f9(c2, c1), c1))),
% 30.12/20.32 inference(monotonicity,[status(thm)],[33992])).
% 30.12/20.32 tff(33994,plain,
% 30.12/20.32 (f3(f6(c1, f6(c1, c2)), c1) = f3(c2, c1)),
% 30.12/20.32 inference(monotonicity,[status(thm)],[33298])).
% 30.12/20.32 tff(33995,plain,
% 30.12/20.32 (f3(f6(c1, f6(c1, c2)), c1) = c1),
% 30.12/20.32 inference(transitivity,[status(thm)],[33994, 33993, 33988])).
% 30.12/20.32 tff(33996,plain,
% 30.12/20.32 (big_f(f3(f6(c1, f6(c1, c2)), c1), f6(c1, f6(c1, c2))) <=> big_f(c1, c2)),
% 30.12/20.32 inference(monotonicity,[status(thm)],[33995, 33298])).
% 30.12/20.32 tff(33997,plain,
% 30.12/20.32 (big_f(c1, c2) <=> big_f(f3(f6(c1, f6(c1, c2)), c1), f6(c1, f6(c1, c2)))),
% 30.12/20.32 inference(symmetry,[status(thm)],[33996])).
% 30.12/20.32 tff(33998,plain,
% 30.12/20.32 (big_f(f3(f6(c1, f6(c1, c2)), c1), f6(c1, f6(c1, c2)))),
% 30.12/20.32 inference(modus_ponens,[status(thm)],[30354, 33997])).
% 30.12/20.32 tff(33999,plain,
% 30.12/20.32 ($false),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[33986, 33998])).
% 30.12/20.32 tff(34000,plain,(big_f(c2, c1) | big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 30.12/20.32 tff(34001,plain,
% 30.12/20.32 (big_f(c2, c1)),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[34000, 121])).
% 30.12/20.32 tff(34002,plain,
% 30.12/20.32 (big_f(f7(c2), f6(c2, c1))),
% 30.12/20.32 inference(modus_ponens,[status(thm)],[34001, 33903])).
% 30.12/20.32 tff(34003,plain,
% 30.12/20.32 (big_f(f9(c2, c1), f10(c2))),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[32841, 34002, 33825, 33293, 33900])).
% 30.12/20.32 tff(34004,plain,
% 30.12/20.32 (~(f9(c2, c1) = c1)),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[3097, 2378, 33825, 34003, 33293, 33900, 34002])).
% 30.12/20.32 tff(34005,plain,
% 30.12/20.32 (f9(c2, c1) = c2),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[3913, 34004])).
% 30.12/20.32 tff(34006,plain,
% 30.12/20.32 (c2 = f9(c2, c1)),
% 30.12/20.32 inference(modus_ponens,[status(thm)],[34005, 8433])).
% 30.12/20.32 tff(34007,plain,
% 30.12/20.32 (c2 = f10(c2)),
% 30.12/20.32 inference(modus_ponens,[status(thm)],[33825, 4988])).
% 30.12/20.32 tff(34008,plain,
% 30.12/20.32 (~(big_f(c2, c2) <=> big_f(f9(c2, c1), f10(c2)))),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[8436, 34003, 121])).
% 30.12/20.32 tff(34009,plain,
% 30.12/20.32 (~(c2 = f9(c2, c1))),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[8442, 34008, 34007])).
% 30.12/20.32 tff(34010,plain,
% 30.12/20.32 ($false),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[34009, 34006])).
% 30.12/20.32 tff(34011,plain,(big_f(c2, c2)), inference(lemma,lemma(discharge,[]))).
% 30.12/20.32 tff(34012,plain,
% 30.12/20.32 (big_f(c2, f10(f7(c2)))),
% 30.12/20.32 inference(modus_ponens,[status(thm)],[34011, 12465])).
% 30.12/20.32 tff(34013,plain,
% 30.12/20.32 ($false),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[16899, 34012, 31719, 17, 31715, 30356, 30355])).
% 30.12/20.32 tff(34014,plain,((f7(c2) = c2) | (~(f10(c1) = c2))), inference(lemma,lemma(discharge,[]))).
% 30.12/20.32 tff(34015,plain,
% 30.12/20.32 (f7(c2) = c2),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[34014, 15])).
% 30.12/20.32 tff(34016,plain,
% 30.12/20.32 (big_f(f10(c1), f10(c1))),
% 30.12/20.32 inference(modus_ponens,[status(thm)],[34011, 18939])).
% 30.12/20.32 tff(34017,plain,
% 30.12/20.32 (big_f(f7(c1), f6(c1, c1)) | (~(f10(c1) = c2))),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[32261, 32256, 31714])).
% 30.12/20.32 tff(34018,plain,
% 30.12/20.32 (big_f(f7(c1), f6(c1, c1))),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[34017, 15])).
% 30.12/20.32 tff(34019,plain,
% 30.12/20.32 ((~(f6(c1, c1) = c1)) | (f10(c1) = f8(c1))),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[19009, 2730, 25791, 3, 34018, 34016])).
% 30.12/20.32 tff(34020,plain,
% 30.12/20.32 (f10(c1) = f8(c1)),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[34019, 10030])).
% 30.12/20.32 tff(34021,plain,
% 30.12/20.32 (f8(c1) = c2),
% 30.12/20.32 inference(modus_ponens,[status(thm)],[34020, 18972])).
% 30.12/20.32 tff(34022,plain,
% 30.12/20.32 ((c1 = f8(c1)) | (~(f6(c1, c1) = c1))),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[32268, 2730, 25791, 3, 30400, 34018])).
% 30.12/20.32 tff(34023,plain,
% 30.12/20.32 (c1 = f8(c1)),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[34022, 10030])).
% 30.12/20.32 tff(34024,plain,
% 30.12/20.32 (~(c2 = f8(c1))),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[29202, 34023])).
% 30.12/20.32 tff(34025,plain,
% 30.12/20.32 (~(f8(c1) = c2)),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[1675, 34024])).
% 30.12/20.32 tff(34026,plain,
% 30.12/20.32 ($false),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[34025, 34021])).
% 30.12/20.32 tff(34027,plain,((~(f6(c1, c1) = c1)) | (f10(c1) = c1)), inference(lemma,lemma(discharge,[]))).
% 30.12/20.32 tff(34028,plain,
% 30.12/20.32 (~(f6(c1, c1) = c1)),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[34027, 3])).
% 30.12/20.32 tff(34029,plain,
% 30.12/20.32 (~(f6(c1, f6(c1, c2)) = c1)),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[58, 34028])).
% 30.12/20.32 tff(34030,plain,
% 30.12/20.32 (f6(c1, f6(c1, c2)) = c2),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[63, 34029])).
% 30.12/20.32 tff(34031,plain,
% 30.12/20.32 (c2 = f6(c1, f6(c1, c2))),
% 30.12/20.32 inference(symmetry,[status(thm)],[34030])).
% 30.12/20.32 tff(34032,plain,
% 30.12/20.32 (f6(c2, c2) = f6(c2, f6(c1, f6(c1, c2)))),
% 30.12/20.32 inference(monotonicity,[status(thm)],[34031])).
% 30.12/20.32 tff(34033,plain,
% 30.12/20.32 (f6(c2, f6(c1, f6(c1, c2))) = f6(c2, c2)),
% 30.12/20.32 inference(symmetry,[status(thm)],[34032])).
% 30.12/20.32 tff(34034,plain,
% 30.12/20.32 ((f6(c2, f6(c1, f6(c1, c2))) = c2) <=> (f6(c2, c2) = c2)),
% 30.12/20.32 inference(monotonicity,[status(thm)],[34033])).
% 30.12/20.32 tff(34035,plain,
% 30.12/20.32 ((f6(c2, c2) = c2) <=> (f6(c2, f6(c1, f6(c1, c2))) = c2)),
% 30.12/20.32 inference(symmetry,[status(thm)],[34034])).
% 30.12/20.32 tff(34036,plain,
% 30.12/20.32 ((~(f6(c2, c2) = c2)) <=> (~(f6(c2, f6(c1, f6(c1, c2))) = c2))),
% 30.12/20.32 inference(monotonicity,[status(thm)],[34035])).
% 30.12/20.32 tff(34037,plain,
% 30.12/20.32 (~(f6(c2, f6(c1, f6(c1, c2))) = c2)),
% 30.12/20.32 inference(modus_ponens,[status(thm)],[2637, 34036])).
% 30.12/20.32 tff(34038,plain,
% 30.12/20.32 (((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f6(c2, f6(c1, f6(c1, c2))) = c1) | (f6(c2, f6(c1, f6(c1, c2))) = c2))) <=> ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f6(c2, f6(c1, f6(c1, c2))) = c1) | (f6(c2, f6(c1, f6(c1, c2))) = c2))),
% 30.12/20.32 inference(rewrite,[status(thm)],[])).
% 30.12/20.32 tff(34039,plain,
% 30.12/20.32 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | ((f6(c2, f6(c1, f6(c1, c2))) = c1) | (f6(c2, f6(c1, f6(c1, c2))) = c2))),
% 30.12/20.32 inference(quant_inst,[status(thm)],[])).
% 30.12/20.32 tff(34040,plain,
% 30.12/20.32 ((~![X1: $i] : ((X1 = c1) | (X1 = c2))) | (f6(c2, f6(c1, f6(c1, c2))) = c1) | (f6(c2, f6(c1, f6(c1, c2))) = c2)),
% 30.12/20.32 inference(modus_ponens,[status(thm)],[34039, 34038])).
% 30.12/20.32 tff(34041,plain,
% 30.12/20.32 ((f6(c2, f6(c1, f6(c1, c2))) = c1) | (f6(c2, f6(c1, f6(c1, c2))) = c2)),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[34040, 10])).
% 30.12/20.32 tff(34042,plain,
% 30.12/20.32 (f6(c2, f6(c1, f6(c1, c2))) = c1),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[34041, 34037])).
% 30.12/20.32 tff(34043,plain,
% 30.12/20.32 (f6(c2, c2) = c1),
% 30.12/20.32 inference(transitivity,[status(thm)],[34032, 34042])).
% 30.12/20.32 tff(34044,plain,
% 30.12/20.32 (big_f(f7(c2), f6(c2, c2)) <=> big_f(c2, c1)),
% 30.12/20.32 inference(monotonicity,[status(thm)],[34015, 34043])).
% 30.12/20.32 tff(34045,plain,
% 30.12/20.32 (big_f(c2, c1) <=> big_f(f7(c2), f6(c2, c2))),
% 30.12/20.32 inference(symmetry,[status(thm)],[34044])).
% 30.12/20.32 tff(34046,plain,
% 30.12/20.32 ((~big_f(c2, c1)) <=> (~big_f(f7(c2), f6(c2, c2)))),
% 30.12/20.32 inference(monotonicity,[status(thm)],[34045])).
% 30.12/20.32 tff(34047,plain,
% 30.12/20.32 (~big_f(f7(c2), f6(c2, c2))),
% 30.12/20.32 inference(modus_ponens,[status(thm)],[2, 34046])).
% 30.12/20.32 tff(34048,plain,
% 30.12/20.32 (big_f(c2, f10(c1))),
% 30.12/20.32 inference(modus_ponens,[status(thm)],[34011, 2719])).
% 30.12/20.32 tff(34049,plain,
% 30.12/20.32 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (c2 = f8(c1)) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (~big_f(c2, f10(c1))))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c1) = c1) | (c2 = f8(c1)) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (~big_f(c2, f10(c1))))),
% 30.12/20.32 inference(rewrite,[status(thm)],[])).
% 30.12/20.32 tff(34050,plain,
% 30.12/20.32 (((f10(c1) = c1) | (c2 = f8(c1)) | (~big_f(c2, f10(c1))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2))) <=> ((f10(c1) = c1) | (c2 = f8(c1)) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (~big_f(c2, f10(c1))))),
% 30.12/20.32 inference(rewrite,[status(thm)],[])).
% 30.12/20.32 tff(34051,plain,
% 30.12/20.32 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (c2 = f8(c1)) | (~big_f(c2, f10(c1))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (c2 = f8(c1)) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (~big_f(c2, f10(c1)))))),
% 30.12/20.32 inference(monotonicity,[status(thm)],[34050])).
% 30.12/20.32 tff(34052,plain,
% 30.12/20.32 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (c2 = f8(c1)) | (~big_f(c2, f10(c1))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c1) = c1) | (c2 = f8(c1)) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (~big_f(c2, f10(c1))))),
% 30.12/20.32 inference(transitivity,[status(thm)],[34051, 34049])).
% 30.12/20.32 tff(34053,plain,
% 30.12/20.32 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (c2 = f8(c1)) | (~big_f(c2, f10(c1))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)))),
% 30.12/20.32 inference(quant_inst,[status(thm)],[])).
% 30.12/20.32 tff(34054,plain,
% 30.12/20.32 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c1) = c1) | (c2 = f8(c1)) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | (~big_f(c2, f10(c1)))),
% 30.12/20.32 inference(modus_ponens,[status(thm)],[34053, 34052])).
% 30.12/20.32 tff(34055,plain,
% 30.12/20.32 ((c2 = f8(c1)) | big_f(f7(c2), f6(c2, c2))),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[34054, 2662, 34048, 3, 34015, 2637])).
% 30.12/20.32 tff(34056,plain,
% 30.12/20.32 (c2 = f8(c1)),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[34055, 34047])).
% 30.12/20.32 tff(34057,plain,
% 30.12/20.32 (big_f(c1, f6(c1, c1))),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[28169, 34018])).
% 30.12/20.32 tff(34058,plain,
% 30.12/20.32 ((~big_f(c1, f6(c1, c1))) | big_f(c1, f10(c1)) | (~(f6(c1, f6(c1, c2)) = c2)) | (~(f10(c1) = c2))),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[29526, 32256])).
% 30.12/20.32 tff(34059,plain,
% 30.12/20.32 (big_f(c1, f10(c1))),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[34058, 34030, 15, 34057])).
% 30.12/20.32 tff(34060,plain,
% 30.12/20.32 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (~(f7(c2) = c2)) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c1) = c1) | (~(f7(c2) = c2)) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)))),
% 30.12/20.32 inference(rewrite,[status(thm)],[])).
% 30.12/20.32 tff(34061,plain,
% 30.12/20.32 (((f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2))) <=> ((f10(c1) = c1) | (~(f7(c2) = c2)) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)))),
% 30.12/20.32 inference(rewrite,[status(thm)],[])).
% 30.12/20.32 tff(34062,plain,
% 30.12/20.32 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (~(f7(c2) = c2)) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2))))),
% 30.12/20.32 inference(monotonicity,[status(thm)],[34061])).
% 30.12/20.32 tff(34063,plain,
% 30.12/20.32 (((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)))) <=> ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c1) = c1) | (~(f7(c2) = c2)) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)))),
% 30.12/20.32 inference(transitivity,[status(thm)],[34062, 34060])).
% 30.12/20.32 tff(34064,plain,
% 30.12/20.32 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | ((f10(c1) = c1) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)))),
% 30.12/20.32 inference(quant_inst,[status(thm)],[])).
% 30.12/20.32 tff(34065,plain,
% 30.12/20.32 ((~![X6: $i, X4: $i, X7: $i, X8: $i] : ((f10(X7) = X7) | (X8 = f8(X7)) | (~big_f(X8, f10(X7))) | (~(f7(X4) = X4)) | (f6(X4, X6) = X6) | big_f(f7(X4), f6(X4, X6)))) | (f10(c1) = c1) | (~(f7(c2) = c2)) | (c1 = f8(c1)) | (~big_f(c1, f10(c1))) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2))),
% 30.12/20.32 inference(modus_ponens,[status(thm)],[34064, 34063])).
% 30.12/20.32 tff(34066,plain,
% 30.12/20.32 ((c1 = f8(c1)) | big_f(f7(c2), f6(c2, c2))),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[34065, 2662, 3, 34015, 34059, 2637])).
% 30.12/20.32 tff(34067,plain,
% 30.12/20.32 (c1 = f8(c1)),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[34066, 34047])).
% 30.12/20.32 tff(34068,plain,
% 30.12/20.32 ($false),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[29202, 34067, 34056])).
% 30.12/20.32 tff(34069,plain,((f6(c2, c2) = c2) | (f10(c1) = c1) | big_f(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 30.12/20.32 tff(34070,plain,
% 30.12/20.32 (f6(c2, c2) = c2),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[34069, 3, 2])).
% 30.12/20.32 tff(34071,plain,
% 30.12/20.32 ((~(f6(c2, c2) = c2)) | big_f(f7(c2), f6(c2, c2)) | (~(f7(c2) = c2))),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[2627, 34011])).
% 30.12/20.32 tff(34072,plain,
% 30.12/20.32 (big_f(f7(c2), f6(c2, c2))),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[34071, 34070, 34015])).
% 30.12/20.32 tff(34073,plain,
% 30.12/20.32 (c2 = f8(c1)),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[2736, 2730, 34048, 3, 34015, 34070, 34072])).
% 30.12/20.32 tff(34074,plain,
% 30.12/20.32 (c1 = f8(c1)),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[3373, 2730, 3, 34015, 34059, 34070, 34072])).
% 30.12/20.32 tff(34075,plain,
% 30.12/20.32 ($false),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[29202, 34074, 34073])).
% 30.12/20.32 tff(34076,plain,((f10(c1) = c1) | big_f(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 30.12/20.32 tff(34077,plain,
% 30.12/20.32 (f10(c1) = c1),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[34076, 2])).
% 30.12/20.32 tff(34078,plain,
% 30.12/20.32 ((f7(c2) = c2) | (~(f10(c1) = c1)) | (~(f9(c1, c1) = c1))),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[33202, 31714])).
% 30.12/20.32 tff(34079,plain,
% 30.12/20.32 (~(f9(c1, c1) = c1)),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[34078, 17, 34077])).
% 30.12/20.32 tff(34080,plain,
% 30.12/20.32 (f9(c1, c1) = c2),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[3939, 34079])).
% 30.12/20.32 tff(34081,plain,
% 30.12/20.32 (f7(f9(c1, c1)) = f7(c2)),
% 30.12/20.32 inference(monotonicity,[status(thm)],[34080])).
% 30.12/20.32 tff(34082,plain,
% 30.12/20.32 (f7(f9(c1, c1)) = c1),
% 30.12/20.32 inference(transitivity,[status(thm)],[34081, 22])).
% 30.12/20.32 tff(34083,plain,
% 30.12/20.32 ((f7(f9(c1, c1)) = f9(c1, c1)) <=> (c1 = c2)),
% 30.12/20.32 inference(monotonicity,[status(thm)],[34082, 34080])).
% 30.12/20.32 tff(34084,plain,
% 30.12/20.32 ((f7(f9(c1, c1)) = f9(c1, c1)) <=> (c2 = c1)),
% 30.12/20.32 inference(transitivity,[status(thm)],[34083, 1])).
% 30.12/20.32 tff(34085,plain,
% 30.12/20.32 ((c2 = c1) <=> (f7(f9(c1, c1)) = f9(c1, c1))),
% 30.12/20.32 inference(symmetry,[status(thm)],[34084])).
% 30.12/20.32 tff(34086,plain,
% 30.12/20.32 ((~(c2 = c1)) <=> (~(f7(f9(c1, c1)) = f9(c1, c1)))),
% 30.12/20.32 inference(monotonicity,[status(thm)],[34085])).
% 30.12/20.32 tff(34087,plain,
% 30.12/20.32 (~(f7(f9(c1, c1)) = f9(c1, c1))),
% 30.12/20.32 inference(modus_ponens,[status(thm)],[75, 34086])).
% 30.12/20.32 tff(34088,plain,
% 30.12/20.32 (~big_f(f9(c1, c1), c1)),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[10058, 34080, 2])).
% 30.12/20.32 tff(34089,plain,
% 30.12/20.32 (~big_f(f9(c1, c1), f10(c1))),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[10033, 34088, 34077])).
% 30.12/20.32 tff(34090,plain,
% 30.12/20.32 (big_f(f7(f9(c1, c1)), c1) <=> big_f(c1, c1)),
% 30.12/20.32 inference(monotonicity,[status(thm)],[34082])).
% 30.12/20.32 tff(34091,plain,
% 30.12/20.32 (big_f(c1, c1) <=> big_f(f7(f9(c1, c1)), c1)),
% 30.12/20.32 inference(symmetry,[status(thm)],[34090])).
% 30.12/20.32 tff(34092,plain,
% 30.12/20.32 (big_f(f7(f9(c1, c1)), c1)),
% 30.12/20.32 inference(modus_ponens,[status(thm)],[31714, 34091])).
% 30.12/20.32 tff(34093,plain,
% 30.12/20.32 ((~(f10(c1) = c1)) | (~(f6(c1, c1) = c1)) | big_f(c2, c1)),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[30135, 31714])).
% 30.12/20.32 tff(34094,plain,
% 30.12/20.32 (~(f6(c1, c1) = c1)),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[34093, 34077, 2])).
% 30.12/20.32 tff(34095,plain,
% 30.12/20.32 (~(f6(c1, f6(c1, c2)) = c1)),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[58, 34094])).
% 30.12/20.32 tff(34096,plain,
% 30.12/20.32 (f6(c1, f6(c1, c2)) = c2),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[63, 34095])).
% 30.12/20.32 tff(34097,plain,
% 30.12/20.32 (c2 = f6(c1, f6(c1, c2))),
% 30.12/20.32 inference(symmetry,[status(thm)],[34096])).
% 30.12/20.32 tff(34098,plain,
% 30.12/20.32 (f9(c1, c1) = f6(c1, c1)),
% 30.12/20.32 inference(transitivity,[status(thm)],[34080, 34097, 32478])).
% 30.12/20.32 tff(34099,plain,
% 30.12/20.32 (big_f(f7(f9(c1, c1)), f9(c1, c1)) <=> big_f(f7(f9(c1, c1)), f6(c1, c1))),
% 30.12/20.32 inference(monotonicity,[status(thm)],[34098])).
% 30.12/20.32 tff(34100,plain,
% 30.12/20.32 (big_f(f7(f9(c1, c1)), f6(c1, c1)) <=> big_f(f7(f9(c1, c1)), f9(c1, c1))),
% 30.12/20.32 inference(symmetry,[status(thm)],[34099])).
% 30.12/20.32 tff(34101,plain,
% 30.12/20.32 (f6(c1, c1) = c2),
% 30.12/20.32 inference(transitivity,[status(thm)],[32390, 34096])).
% 30.12/20.32 tff(34102,plain,
% 30.12/20.32 (big_f(f7(f9(c1, c1)), f6(c1, c1)) <=> big_f(c1, c2)),
% 30.12/20.32 inference(monotonicity,[status(thm)],[34082, 34101])).
% 30.12/20.32 tff(34103,plain,
% 30.12/20.32 (big_f(c1, c2) <=> big_f(f7(f9(c1, c1)), f6(c1, c1))),
% 30.12/20.32 inference(symmetry,[status(thm)],[34102])).
% 30.12/20.32 tff(34104,plain,
% 30.12/20.32 (big_f(c1, c2) <=> big_f(f7(f9(c1, c1)), f9(c1, c1))),
% 30.12/20.32 inference(transitivity,[status(thm)],[34103, 34100])).
% 30.12/20.32 tff(34105,plain,
% 30.12/20.32 (big_f(f7(f9(c1, c1)), f9(c1, c1))),
% 30.12/20.32 inference(modus_ponens,[status(thm)],[30354, 34104])).
% 30.12/20.32 tff(34106,plain,
% 30.12/20.32 ($false),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[20184, 34105, 34092, 34077, 34089, 34079, 34087])).
% 30.12/20.32 tff(34107,plain,((f7(c2) = c2) | big_f(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 30.12/20.32 tff(34108,plain,
% 30.12/20.32 (f7(c2) = c2),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[34107, 2])).
% 30.12/20.32 tff(34109,plain,
% 30.12/20.32 (f6(c2, c2) = f6(c2, f6(c1, f6(c1, c2)))),
% 30.12/20.32 inference(monotonicity,[status(thm)],[34097])).
% 30.12/20.32 tff(34110,plain,
% 30.12/20.32 (f6(c2, f6(c1, f6(c1, c2))) = f6(c2, c2)),
% 30.12/20.32 inference(symmetry,[status(thm)],[34109])).
% 30.12/20.32 tff(34111,plain,
% 30.12/20.32 ((f6(c2, f6(c1, f6(c1, c2))) = c2) <=> (f6(c2, c2) = c2)),
% 30.12/20.32 inference(monotonicity,[status(thm)],[34110])).
% 30.12/20.32 tff(34112,plain,
% 30.12/20.32 ((f6(c2, c2) = c2) <=> (f6(c2, f6(c1, f6(c1, c2))) = c2)),
% 30.12/20.32 inference(symmetry,[status(thm)],[34111])).
% 30.12/20.32 tff(34113,plain,
% 30.12/20.32 ((~(f6(c2, c2) = c2)) <=> (~(f6(c2, f6(c1, f6(c1, c2))) = c2))),
% 30.12/20.32 inference(monotonicity,[status(thm)],[34112])).
% 30.12/20.32 tff(34114,plain,
% 30.12/20.32 (~(f6(c2, f6(c1, f6(c1, c2))) = c2)),
% 30.12/20.32 inference(modus_ponens,[status(thm)],[2637, 34113])).
% 30.12/20.32 tff(34115,plain,
% 30.12/20.32 (f6(c2, f6(c1, f6(c1, c2))) = c1),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[34041, 34114])).
% 30.12/20.32 tff(34116,plain,
% 30.12/20.32 (f6(c2, c2) = c1),
% 30.12/20.32 inference(transitivity,[status(thm)],[34109, 34115])).
% 30.12/20.32 tff(34117,plain,
% 30.12/20.32 (big_f(f7(c2), f6(c2, c2)) <=> big_f(c2, c1)),
% 30.12/20.32 inference(monotonicity,[status(thm)],[34108, 34116])).
% 30.12/20.32 tff(34118,plain,
% 30.12/20.32 (big_f(c2, c1) <=> big_f(f7(c2), f6(c2, c2))),
% 30.12/20.32 inference(symmetry,[status(thm)],[34117])).
% 30.12/20.32 tff(34119,plain,
% 30.12/20.32 ((~big_f(c2, c1)) <=> (~big_f(f7(c2), f6(c2, c2)))),
% 30.12/20.32 inference(monotonicity,[status(thm)],[34118])).
% 30.12/20.32 tff(34120,plain,
% 30.12/20.32 (~big_f(f7(c2), f6(c2, c2))),
% 30.12/20.32 inference(modus_ponens,[status(thm)],[2, 34119])).
% 30.12/20.32 tff(34121,plain,
% 30.12/20.32 ($false),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[24723, 2492, 3762, 77, 4070, 24692, 2637, 2621])).
% 30.12/20.32 tff(34122,plain,((f9(c1, c1) = c1) | (~(f10(c1) = c1)) | (~(f7(c2) = c2)) | (f6(c2, c2) = c2) | big_f(f7(c2), f6(c2, c2)) | big_f(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 30.12/20.32 tff(34123,plain,
% 30.12/20.32 (f9(c1, c1) = c1),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[34122, 34120, 34077, 34108, 2637, 2])).
% 30.12/20.32 tff(34124,plain,
% 30.12/20.32 ((~(f9(c1, c1) = c1)) | big_f(f9(c1, c1), c1)),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[10938, 31714])).
% 30.12/20.32 tff(34125,plain,
% 30.12/20.32 (big_f(f9(c1, c1), c1)),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[34124, 34123])).
% 30.12/20.32 tff(34126,plain,
% 30.12/20.32 (big_f(f7(c2), f6(c2, c2)) | (~(f10(c1) = c1)) | (~(f7(c2) = c2)) | (~(f9(c1, c1) = c1)) | (~big_f(f9(c1, c1), f10(c1)))),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[24737, 34011])).
% 30.12/20.32 tff(34127,plain,
% 30.12/20.32 (~big_f(f9(c1, c1), f10(c1))),
% 30.12/20.32 inference(unit_resolution,[status(thm)],[34126, 34123, 34120, 34077, 34108])).
% 30.12/20.33 tff(34128,plain,
% 30.12/20.33 ($false),
% 30.12/20.33 inference(unit_resolution,[status(thm)],[8716, 34127, 34125, 34077])).
% 30.12/20.33 tff(34129,plain,((f6(c2, c2) = c2) | big_f(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 30.12/20.33 tff(34130,plain,
% 30.12/20.33 (f6(c2, c2) = c2),
% 30.12/20.33 inference(unit_resolution,[status(thm)],[34129, 2])).
% 30.12/20.33 tff(34131,plain,
% 30.12/20.33 (big_f(f7(c2), f6(c2, c2))),
% 30.12/20.33 inference(unit_resolution,[status(thm)],[34071, 34130, 34108])).
% 30.12/20.33 tff(34132,plain,
% 30.12/20.33 (~big_f(f9(c1, c1), f10(c1))),
% 30.12/20.33 inference(unit_resolution,[status(thm)],[10033, 24691, 34077])).
% 30.12/20.33 tff(34133,plain,
% 30.12/20.33 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)))),
% 30.12/20.33 inference(rewrite,[status(thm)],[])).
% 30.12/20.33 tff(34134,plain,
% 30.12/20.33 (((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2)))) <=> ((~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)))),
% 30.12/20.33 inference(rewrite,[status(thm)],[])).
% 30.12/20.33 tff(34135,plain,
% 30.12/20.33 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1))))),
% 30.12/20.33 inference(monotonicity,[status(thm)],[34134])).
% 30.12/20.33 tff(34136,plain,
% 30.12/20.33 (((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1)))),
% 30.12/20.33 inference(transitivity,[status(thm)],[34135, 34133])).
% 30.12/20.33 tff(34137,plain,
% 30.12/20.33 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | ((~(f10(c1) = c1)) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))))),
% 30.12/20.33 inference(quant_inst,[status(thm)],[])).
% 30.12/20.33 tff(34138,plain,
% 30.12/20.33 ((~![X9: $i, X6: $i, X4: $i, X7: $i] : ((~(f10(X7) = X7)) | (f9(X7, X9) = X9) | big_f(f9(X7, X9), f10(X7)) | (~(f7(X4) = X4)) | (~(f6(X4, X6) = X6)) | (~big_f(f7(X4), f6(X4, X6))))) | (~(f7(c2) = c2)) | (~(f6(c2, c2) = c2)) | (~big_f(f7(c2), f6(c2, c2))) | (f9(c1, c1) = c1) | big_f(f9(c1, c1), f10(c1)) | (~(f10(c1) = c1))),
% 30.12/20.33 inference(modus_ponens,[status(thm)],[34137, 34136])).
% 30.12/20.33 tff(34139,plain,
% 30.12/20.33 ($false),
% 30.12/20.33 inference(unit_resolution,[status(thm)],[34138, 2534, 34077, 34108, 4070, 34132, 34130, 34131])).
% 30.12/20.33 tff(34140,plain,((f9(c1, c1) = c1) | big_f(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 30.12/20.33 tff(34141,plain,
% 30.12/20.33 (f9(c1, c1) = c1),
% 30.12/20.33 inference(unit_resolution,[status(thm)],[34140, 2])).
% 30.12/20.33 tff(34142,plain,
% 30.12/20.33 (big_f(f9(c1, c1), c1)),
% 30.12/20.33 inference(unit_resolution,[status(thm)],[34124, 34141])).
% 30.12/20.33 tff(34143,plain,
% 30.12/20.33 (big_f(f9(c1, c1), f10(c1))),
% 30.12/20.33 inference(unit_resolution,[status(thm)],[8716, 34142, 34077])).
% 30.12/20.33 tff(34144,plain,
% 30.12/20.33 ($false),
% 30.12/20.33 inference(unit_resolution,[status(thm)],[24751, 2378, 34077, 34108, 34141, 34143, 34130, 34131])).
% 30.12/20.33 tff(34145,plain,(big_f(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 30.12/20.33 tff(34146,plain,
% 30.12/20.33 ((~(f4(c4) = c1)) | (~big_f(c2, c1))),
% 30.12/20.33 inference(unit_resolution,[status(thm)],[32236, 34011])).
% 30.12/20.33 tff(34147,plain,
% 30.12/20.33 (~(f4(c4) = c1)),
% 30.12/20.33 inference(unit_resolution,[status(thm)],[34146, 34145])).
% 30.12/20.33 tff(34148,plain,
% 30.12/20.33 (f4(c4) = c2),
% 30.12/20.33 inference(unit_resolution,[status(thm)],[11750, 34147])).
% 30.12/20.33 tff(34149,plain,
% 30.12/20.33 (f4(c2) = c2),
% 30.12/20.33 inference(transitivity,[status(thm)],[434, 34148])).
% 30.12/20.33 tff(34150,plain,
% 30.12/20.33 ((c1 = f4(c2)) <=> (c1 = c2)),
% 30.12/20.33 inference(monotonicity,[status(thm)],[34149])).
% 30.12/20.33 tff(34151,plain,
% 30.12/20.33 ((c1 = f4(c2)) <=> (c2 = c1)),
% 30.12/20.33 inference(transitivity,[status(thm)],[34150, 1])).
% 30.12/20.33 tff(34152,plain,
% 30.12/20.33 ((c2 = c1) <=> (c1 = f4(c2))),
% 30.12/20.33 inference(symmetry,[status(thm)],[34151])).
% 30.12/20.33 tff(34153,plain,
% 30.12/20.33 ((~(c2 = c1)) <=> (~(c1 = f4(c2)))),
% 30.12/20.33 inference(monotonicity,[status(thm)],[34152])).
% 30.12/20.33 tff(34154,plain,
% 30.12/20.33 (~(c1 = f4(c2))),
% 30.12/20.33 inference(modus_ponens,[status(thm)],[75, 34153])).
% 30.12/20.33 tff(34155,plain,
% 30.12/20.33 (f4(c1) = c2),
% 30.12/20.33 inference(transitivity,[status(thm)],[568, 34148])).
% 30.12/20.33 tff(34156,plain,
% 30.12/20.33 ((c1 = f4(c1)) <=> (c1 = c2)),
% 30.12/20.33 inference(monotonicity,[status(thm)],[34155])).
% 30.12/20.33 tff(34157,plain,
% 30.12/20.33 ((c1 = f4(c1)) <=> (c2 = c1)),
% 30.12/20.33 inference(transitivity,[status(thm)],[34156, 1])).
% 30.12/20.33 tff(34158,plain,
% 30.12/20.33 ((c2 = c1) <=> (c1 = f4(c1))),
% 30.12/20.33 inference(symmetry,[status(thm)],[34157])).
% 30.12/20.33 tff(34159,plain,
% 30.12/20.33 ((~(c2 = c1)) <=> (~(c1 = f4(c1)))),
% 30.12/20.33 inference(monotonicity,[status(thm)],[34158])).
% 30.12/20.33 tff(34160,plain,
% 30.12/20.33 (~(c1 = f4(c1))),
% 30.12/20.33 inference(modus_ponens,[status(thm)],[75, 34159])).
% 30.12/20.33 tff(34161,plain,
% 30.12/20.33 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (c1 = f2(c2)) | (~big_f(c2, c1)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (c1 = f2(c2)) | (~big_f(c2, c1)))),
% 30.12/20.33 inference(rewrite,[status(thm)],[])).
% 30.12/20.33 tff(34162,plain,
% 30.12/20.33 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (c1 = f2(c2)) | (~big_f(c2, c1)))),
% 30.12/20.33 inference(quant_inst,[status(thm)],[])).
% 30.12/20.33 tff(34163,plain,
% 30.12/20.33 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (c1 = f2(c2)) | (~big_f(c2, c1))),
% 30.12/20.33 inference(modus_ponens,[status(thm)],[34162, 34161])).
% 30.12/20.33 tff(34164,plain,
% 30.12/20.33 ((~(c2 = c3)) | (~(c1 = c4)) | (c1 = f4(c1)) | (c1 = f2(c2))),
% 30.12/20.33 inference(unit_resolution,[status(thm)],[34163, 1355, 34145, 31714])).
% 30.12/20.33 tff(34165,plain,
% 30.12/20.33 (c1 = f2(c2)),
% 30.12/20.33 inference(unit_resolution,[status(thm)],[34164, 34160, 1344, 564])).
% 30.12/20.33 tff(34166,plain,
% 30.12/20.33 (f2(c2) = c1),
% 30.12/20.33 inference(symmetry,[status(thm)],[34165])).
% 30.12/20.33 tff(34167,plain,
% 30.12/20.33 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = f2(c2)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = f2(c2)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (~big_f(c2, c2)))),
% 30.12/20.33 inference(rewrite,[status(thm)],[])).
% 30.12/20.33 tff(34168,plain,
% 30.12/20.33 (((~(c2 = c3)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (c2 = f2(c2)) | (~big_f(c2, c2))) <=> ((~(c2 = c3)) | (c2 = f2(c2)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (~big_f(c2, c2)))),
% 30.12/20.33 inference(rewrite,[status(thm)],[])).
% 30.12/20.33 tff(34169,plain,
% 30.12/20.33 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (c2 = f2(c2)) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (c2 = f2(c2)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (~big_f(c2, c2))))),
% 30.12/20.33 inference(monotonicity,[status(thm)],[34168])).
% 30.12/20.33 tff(34170,plain,
% 30.12/20.33 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (c2 = f2(c2)) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = f2(c2)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (~big_f(c2, c2)))),
% 30.12/20.33 inference(transitivity,[status(thm)],[34169, 34167])).
% 30.12/20.33 tff(34171,plain,
% 30.12/20.33 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (c2 = f2(c2)) | (~big_f(c2, c2)))),
% 30.12/20.33 inference(quant_inst,[status(thm)],[])).
% 30.12/20.33 tff(34172,plain,
% 30.12/20.33 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (c2 = f2(c2)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (~big_f(c2, c2))),
% 30.12/20.33 inference(modus_ponens,[status(thm)],[34171, 34170])).
% 30.12/20.33 tff(34173,plain,
% 30.12/20.33 ((~(c2 = c3)) | (c2 = f2(c2)) | (~(c1 = c4)) | (c1 = f4(c1))),
% 30.12/20.33 inference(unit_resolution,[status(thm)],[34172, 1355, 34011, 31714])).
% 30.12/20.33 tff(34174,plain,
% 30.12/20.33 (c2 = f2(c2)),
% 30.12/20.33 inference(unit_resolution,[status(thm)],[34173, 34160, 1344, 564])).
% 30.12/20.33 tff(34175,plain,
% 30.12/20.33 (c2 = c1),
% 30.12/20.33 inference(transitivity,[status(thm)],[34174, 34166])).
% 30.12/20.33 tff(34176,plain,
% 30.12/20.33 ($false),
% 30.12/20.33 inference(unit_resolution,[status(thm)],[75, 34175])).
% 30.12/20.33 tff(34177,plain,((~(c4 = c1)) | (~(c2 = c3))), inference(lemma,lemma(discharge,[]))).
% 30.12/20.33 tff(34178,plain,
% 30.12/20.33 (~(c4 = c1)),
% 30.12/20.33 inference(unit_resolution,[status(thm)],[34177, 1344])).
% 30.12/20.33 tff(34179,plain,
% 30.12/20.33 (c4 = c2),
% 30.12/20.33 inference(unit_resolution,[status(thm)],[461, 34178])).
% 30.12/20.33 tff(34180,plain,
% 30.12/20.33 (c2 = c4),
% 30.12/20.33 inference(modus_ponens,[status(thm)],[34179, 159])).
% 30.12/20.33 tff(34181,plain,
% 30.12/20.33 (c2 = c4),
% 30.12/20.33 inference(symmetry,[status(thm)],[34179])).
% 30.12/20.33 tff(34182,plain,
% 30.12/20.33 (f4(c2) = f4(c4)),
% 30.12/20.33 inference(monotonicity,[status(thm)],[34181])).
% 30.12/20.33 tff(34183,plain,
% 30.12/20.33 (f4(c2) = c2),
% 30.12/20.33 inference(transitivity,[status(thm)],[34182, 34148])).
% 30.12/20.33 tff(34184,plain,
% 30.12/20.33 ((c1 = f4(c2)) <=> (c1 = c2)),
% 30.12/20.33 inference(monotonicity,[status(thm)],[34183])).
% 30.12/20.33 tff(34185,plain,
% 30.12/20.33 ((c1 = f4(c2)) <=> (c2 = c1)),
% 30.12/20.33 inference(transitivity,[status(thm)],[34184, 1])).
% 30.12/20.33 tff(34186,plain,
% 30.12/20.33 ((c2 = c1) <=> (c1 = f4(c2))),
% 30.12/20.33 inference(symmetry,[status(thm)],[34185])).
% 30.12/20.33 tff(34187,plain,
% 30.12/20.33 ((~(c2 = c1)) <=> (~(c1 = f4(c2)))),
% 30.12/20.33 inference(monotonicity,[status(thm)],[34186])).
% 30.12/20.33 tff(34188,plain,
% 30.12/20.33 (~(c1 = f4(c2))),
% 30.12/20.33 inference(modus_ponens,[status(thm)],[75, 34187])).
% 30.12/20.33 tff(34189,plain,
% 30.12/20.33 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c2 = c4)) | (c1 = f4(c2)) | (~big_f(c1, c2)) | (c1 = f2(c2)) | (~big_f(c2, c1)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (~(c2 = c4)) | (c1 = f4(c2)) | (~big_f(c1, c2)) | (c1 = f2(c2)) | (~big_f(c2, c1)))),
% 30.12/20.33 inference(rewrite,[status(thm)],[])).
% 30.12/20.33 tff(34190,plain,
% 30.12/20.33 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c2 = c4)) | (c1 = f4(c2)) | (~big_f(c1, c2)) | (c1 = f2(c2)) | (~big_f(c2, c1)))),
% 30.12/20.33 inference(quant_inst,[status(thm)],[])).
% 30.12/20.33 tff(34191,plain,
% 30.12/20.33 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (~(c2 = c4)) | (c1 = f4(c2)) | (~big_f(c1, c2)) | (c1 = f2(c2)) | (~big_f(c2, c1))),
% 30.12/20.33 inference(modus_ponens,[status(thm)],[34190, 34189])).
% 30.12/20.33 tff(34192,plain,
% 30.12/20.33 ((~(c2 = c3)) | (~(c2 = c4)) | (c1 = f4(c2)) | (c1 = f2(c2))),
% 30.12/20.33 inference(unit_resolution,[status(thm)],[34191, 1355, 30354, 34145])).
% 30.12/20.33 tff(34193,plain,
% 30.12/20.33 (c1 = f2(c2)),
% 30.12/20.33 inference(unit_resolution,[status(thm)],[34192, 34188, 1344, 34180])).
% 30.12/20.33 tff(34194,plain,
% 30.12/20.33 (f2(c2) = c1),
% 30.12/20.33 inference(symmetry,[status(thm)],[34193])).
% 30.12/20.33 tff(34195,plain,
% 30.12/20.33 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c2 = c4)) | (c2 = f2(c2)) | (c1 = f4(c2)) | (~big_f(c1, c2)) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (~(c2 = c4)) | (c2 = f2(c2)) | (c1 = f4(c2)) | (~big_f(c1, c2)) | (~big_f(c2, c2)))),
% 30.12/20.33 inference(rewrite,[status(thm)],[])).
% 30.12/20.33 tff(34196,plain,
% 30.12/20.33 (((~(c2 = c3)) | (~(c2 = c4)) | (c1 = f4(c2)) | (~big_f(c1, c2)) | (c2 = f2(c2)) | (~big_f(c2, c2))) <=> ((~(c2 = c3)) | (~(c2 = c4)) | (c2 = f2(c2)) | (c1 = f4(c2)) | (~big_f(c1, c2)) | (~big_f(c2, c2)))),
% 30.12/20.33 inference(rewrite,[status(thm)],[])).
% 30.12/20.33 tff(34197,plain,
% 30.12/20.33 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c2 = c4)) | (c1 = f4(c2)) | (~big_f(c1, c2)) | (c2 = f2(c2)) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c2 = c4)) | (c2 = f2(c2)) | (c1 = f4(c2)) | (~big_f(c1, c2)) | (~big_f(c2, c2))))),
% 30.12/20.33 inference(monotonicity,[status(thm)],[34196])).
% 30.12/20.33 tff(34198,plain,
% 30.12/20.33 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c2 = c4)) | (c1 = f4(c2)) | (~big_f(c1, c2)) | (c2 = f2(c2)) | (~big_f(c2, c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (~(c2 = c4)) | (c2 = f2(c2)) | (c1 = f4(c2)) | (~big_f(c1, c2)) | (~big_f(c2, c2)))),
% 30.12/20.33 inference(transitivity,[status(thm)],[34197, 34195])).
% 30.12/20.33 tff(34199,plain,
% 30.12/20.33 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c3)) | (~(c2 = c4)) | (c1 = f4(c2)) | (~big_f(c1, c2)) | (c2 = f2(c2)) | (~big_f(c2, c2)))),
% 30.12/20.33 inference(quant_inst,[status(thm)],[])).
% 30.12/20.33 tff(34200,plain,
% 30.12/20.33 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c3)) | (~(c2 = c4)) | (c2 = f2(c2)) | (c1 = f4(c2)) | (~big_f(c1, c2)) | (~big_f(c2, c2))),
% 30.12/20.33 inference(modus_ponens,[status(thm)],[34199, 34198])).
% 30.12/20.33 tff(34201,plain,
% 30.12/20.33 ((~(c2 = c3)) | (~(c2 = c4)) | (c2 = f2(c2)) | (c1 = f4(c2))),
% 30.12/20.33 inference(unit_resolution,[status(thm)],[34200, 1355, 34011, 30354])).
% 30.12/20.33 tff(34202,plain,
% 30.12/20.33 (c2 = f2(c2)),
% 30.12/20.33 inference(unit_resolution,[status(thm)],[34201, 34180, 1344, 34188])).
% 30.12/20.33 tff(34203,plain,
% 30.12/20.33 (c2 = c1),
% 30.12/20.33 inference(transitivity,[status(thm)],[34202, 34194])).
% 30.12/20.33 tff(34204,plain,
% 30.12/20.33 ($false),
% 30.12/20.33 inference(unit_resolution,[status(thm)],[75, 34203])).
% 30.12/20.33 tff(34205,plain,(~(c2 = c3)), inference(lemma,lemma(discharge,[]))).
% 30.12/20.33 tff(34206,plain,
% 30.12/20.33 (~(c3 = c2)),
% 30.12/20.33 inference(modus_ponens,[status(thm)],[34205, 9745])).
% 30.12/20.33 tff(34207,plain,
% 30.12/20.33 (c3 = c1),
% 30.12/20.33 inference(unit_resolution,[status(thm)],[180, 34206])).
% 30.12/20.33 tff(34208,plain,
% 30.12/20.33 (c1 = c3),
% 30.12/20.33 inference(unit_resolution,[status(thm)],[175, 34207])).
% 30.12/20.33 tff(34209,plain,
% 30.12/20.33 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c4)) | (~(c1 = c3)) | (c1 = f2(c1)) | (c1 = f4(c2)) | (~big_f(c1, c2)) | (~big_f(c1, c1)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c4)) | (~(c1 = c3)) | (c1 = f2(c1)) | (c1 = f4(c2)) | (~big_f(c1, c2)) | (~big_f(c1, c1)))),
% 30.12/20.33 inference(rewrite,[status(thm)],[])).
% 30.12/20.33 tff(34210,plain,
% 30.12/20.33 (((~(c1 = c3)) | (~(c2 = c4)) | (c1 = f4(c2)) | (~big_f(c1, c2)) | (c1 = f2(c1)) | (~big_f(c1, c1))) <=> ((~(c2 = c4)) | (~(c1 = c3)) | (c1 = f2(c1)) | (c1 = f4(c2)) | (~big_f(c1, c2)) | (~big_f(c1, c1)))),
% 30.12/20.33 inference(rewrite,[status(thm)],[])).
% 30.12/20.33 tff(34211,plain,
% 30.12/20.33 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (~(c2 = c4)) | (c1 = f4(c2)) | (~big_f(c1, c2)) | (c1 = f2(c1)) | (~big_f(c1, c1)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c4)) | (~(c1 = c3)) | (c1 = f2(c1)) | (c1 = f4(c2)) | (~big_f(c1, c2)) | (~big_f(c1, c1))))),
% 30.12/20.33 inference(monotonicity,[status(thm)],[34210])).
% 30.12/20.33 tff(34212,plain,
% 30.12/20.33 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (~(c2 = c4)) | (c1 = f4(c2)) | (~big_f(c1, c2)) | (c1 = f2(c1)) | (~big_f(c1, c1)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c4)) | (~(c1 = c3)) | (c1 = f2(c1)) | (c1 = f4(c2)) | (~big_f(c1, c2)) | (~big_f(c1, c1)))),
% 30.12/20.33 inference(transitivity,[status(thm)],[34211, 34209])).
% 30.12/20.33 tff(34213,plain,
% 30.12/20.33 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (~(c2 = c4)) | (c1 = f4(c2)) | (~big_f(c1, c2)) | (c1 = f2(c1)) | (~big_f(c1, c1)))),
% 30.12/20.33 inference(quant_inst,[status(thm)],[])).
% 30.12/20.33 tff(34214,plain,
% 30.12/20.33 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c4)) | (~(c1 = c3)) | (c1 = f2(c1)) | (c1 = f4(c2)) | (~big_f(c1, c2)) | (~big_f(c1, c1))),
% 30.12/20.33 inference(modus_ponens,[status(thm)],[34213, 34212])).
% 30.12/20.33 tff(34215,plain,
% 30.12/20.33 ((~(c2 = c4)) | (~(c1 = c3)) | (c1 = f2(c1)) | (c1 = f4(c2))),
% 30.12/20.33 inference(unit_resolution,[status(thm)],[34214, 1355, 30354, 31714])).
% 30.12/20.33 tff(34216,plain,
% 30.12/20.33 (c1 = f2(c1)),
% 30.12/20.33 inference(unit_resolution,[status(thm)],[34215, 432, 34208, 34154])).
% 30.12/20.33 tff(34217,plain,
% 30.12/20.33 (f2(c1) = c1),
% 30.12/20.33 inference(symmetry,[status(thm)],[34216])).
% 30.12/20.33 tff(34218,plain,
% 30.12/20.33 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c4)) | (~(c1 = c3)) | (c1 = f4(c2)) | (~big_f(c1, c2)) | (c2 = f2(c1)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c4)) | (~(c1 = c3)) | (c1 = f4(c2)) | (~big_f(c1, c2)) | (c2 = f2(c1)))),
% 30.12/20.33 inference(rewrite,[status(thm)],[])).
% 30.12/20.33 tff(34219,plain,
% 30.12/20.33 (((~(c1 = c3)) | (~(c2 = c4)) | (c1 = f4(c2)) | (~big_f(c1, c2)) | (c2 = f2(c1)) | (~big_f(c1, c2))) <=> ((~(c2 = c4)) | (~(c1 = c3)) | (c1 = f4(c2)) | (~big_f(c1, c2)) | (c2 = f2(c1)))),
% 30.12/20.33 inference(rewrite,[status(thm)],[])).
% 30.12/20.33 tff(34220,plain,
% 30.12/20.33 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (~(c2 = c4)) | (c1 = f4(c2)) | (~big_f(c1, c2)) | (c2 = f2(c1)) | (~big_f(c1, c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c2 = c4)) | (~(c1 = c3)) | (c1 = f4(c2)) | (~big_f(c1, c2)) | (c2 = f2(c1))))),
% 30.12/20.33 inference(monotonicity,[status(thm)],[34219])).
% 30.12/20.33 tff(34221,plain,
% 30.12/20.33 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (~(c2 = c4)) | (c1 = f4(c2)) | (~big_f(c1, c2)) | (c2 = f2(c1)) | (~big_f(c1, c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c4)) | (~(c1 = c3)) | (c1 = f4(c2)) | (~big_f(c1, c2)) | (c2 = f2(c1)))),
% 30.12/20.33 inference(transitivity,[status(thm)],[34220, 34218])).
% 30.12/20.33 tff(34222,plain,
% 30.12/20.33 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (~(c2 = c4)) | (c1 = f4(c2)) | (~big_f(c1, c2)) | (c2 = f2(c1)) | (~big_f(c1, c2)))),
% 30.12/20.33 inference(quant_inst,[status(thm)],[])).
% 30.12/20.33 tff(34223,plain,
% 30.12/20.33 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c2 = c4)) | (~(c1 = c3)) | (c1 = f4(c2)) | (~big_f(c1, c2)) | (c2 = f2(c1))),
% 30.12/20.33 inference(modus_ponens,[status(thm)],[34222, 34221])).
% 30.12/20.33 tff(34224,plain,
% 30.12/20.33 ((~(c2 = c4)) | (~(c1 = c3)) | (c1 = f4(c2)) | (c2 = f2(c1))),
% 30.12/20.33 inference(unit_resolution,[status(thm)],[34223, 1355, 30354])).
% 30.12/20.33 tff(34225,plain,
% 30.12/20.33 (c2 = f2(c1)),
% 30.12/20.33 inference(unit_resolution,[status(thm)],[34224, 432, 34208, 34154])).
% 30.12/20.33 tff(34226,plain,
% 30.12/20.33 (c2 = c1),
% 30.12/20.33 inference(transitivity,[status(thm)],[34225, 34217])).
% 30.12/20.33 tff(34227,plain,
% 30.12/20.33 ($false),
% 30.12/20.33 inference(unit_resolution,[status(thm)],[75, 34226])).
% 30.12/20.33 tff(34228,plain,(~(c4 = c2)), inference(lemma,lemma(discharge,[]))).
% 30.12/20.33 tff(34229,plain,
% 30.12/20.33 (c4 = c1),
% 30.12/20.33 inference(unit_resolution,[status(thm)],[461, 34228])).
% 30.12/20.33 tff(34230,plain,
% 30.12/20.33 (c1 = c4),
% 30.12/20.33 inference(unit_resolution,[status(thm)],[484, 34229])).
% 30.12/20.33 tff(34231,plain,
% 30.12/20.33 (c1 = c4),
% 30.12/20.33 inference(symmetry,[status(thm)],[34229])).
% 30.12/20.33 tff(34232,plain,
% 30.12/20.33 (f4(c1) = f4(c4)),
% 30.12/20.33 inference(monotonicity,[status(thm)],[34231])).
% 30.12/20.33 tff(34233,plain,
% 30.12/20.33 (f4(c1) = c2),
% 30.12/20.33 inference(transitivity,[status(thm)],[34232, 34148])).
% 30.16/20.35 tff(34234,plain,
% 30.16/20.35 ((c1 = f4(c1)) <=> (c1 = c2)),
% 30.16/20.35 inference(monotonicity,[status(thm)],[34233])).
% 30.16/20.35 tff(34235,plain,
% 30.16/20.35 ((c1 = f4(c1)) <=> (c2 = c1)),
% 30.16/20.35 inference(transitivity,[status(thm)],[34234, 1])).
% 30.16/20.35 tff(34236,plain,
% 30.16/20.35 ((c2 = c1) <=> (c1 = f4(c1))),
% 30.16/20.35 inference(symmetry,[status(thm)],[34235])).
% 30.16/20.35 tff(34237,plain,
% 30.16/20.35 ((~(c2 = c1)) <=> (~(c1 = f4(c1)))),
% 30.16/20.35 inference(monotonicity,[status(thm)],[34236])).
% 30.16/20.35 tff(34238,plain,
% 30.16/20.35 (~(c1 = f4(c1))),
% 30.16/20.35 inference(modus_ponens,[status(thm)],[75, 34237])).
% 30.16/20.35 tff(34239,plain,
% 30.16/20.35 ((~(c1 = c3)) | (c1 = f2(c1)) | (~(c1 = c4)) | (c1 = f4(c1))),
% 30.16/20.35 inference(unit_resolution,[status(thm)],[29551, 1355, 31714])).
% 30.16/20.35 tff(34240,plain,
% 30.16/20.35 (c1 = f2(c1)),
% 30.16/20.35 inference(unit_resolution,[status(thm)],[34239, 34238, 34208, 34230])).
% 30.16/20.35 tff(34241,plain,
% 30.16/20.35 (f2(c1) = c1),
% 30.16/20.35 inference(symmetry,[status(thm)],[34240])).
% 30.16/20.35 tff(34242,plain,
% 30.16/20.35 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c2)) | (~big_f(c1, c1)) | (c2 = f2(c1)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c1 = c3)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c2)) | (~big_f(c1, c1)) | (c2 = f2(c1)))),
% 30.16/20.35 inference(rewrite,[status(thm)],[])).
% 30.16/20.35 tff(34243,plain,
% 30.16/20.35 (((~(c1 = c3)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (c2 = f2(c1)) | (~big_f(c1, c2))) <=> ((~(c1 = c3)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c2)) | (~big_f(c1, c1)) | (c2 = f2(c1)))),
% 30.16/20.35 inference(rewrite,[status(thm)],[])).
% 30.16/20.35 tff(34244,plain,
% 30.16/20.35 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (c2 = f2(c1)) | (~big_f(c1, c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c2)) | (~big_f(c1, c1)) | (c2 = f2(c1))))),
% 30.16/20.35 inference(monotonicity,[status(thm)],[34243])).
% 30.16/20.35 tff(34245,plain,
% 30.16/20.35 (((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (c2 = f2(c1)) | (~big_f(c1, c2)))) <=> ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c1 = c3)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c2)) | (~big_f(c1, c1)) | (c2 = f2(c1)))),
% 30.16/20.35 inference(transitivity,[status(thm)],[34244, 34242])).
% 30.16/20.35 tff(34246,plain,
% 30.16/20.35 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | ((~(c1 = c3)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c1)) | (c2 = f2(c1)) | (~big_f(c1, c2)))),
% 30.16/20.35 inference(quant_inst,[status(thm)],[])).
% 30.16/20.35 tff(34247,plain,
% 30.16/20.35 ((~![X12: $i, X3: $i, X10: $i, X2: $i] : ((~(X10 = c3)) | (~(X2 = c4)) | (X3 = f4(X2)) | (~big_f(X3, X2)) | (X12 = f2(X10)) | (~big_f(X10, X12)))) | (~(c1 = c3)) | (~(c1 = c4)) | (c1 = f4(c1)) | (~big_f(c1, c2)) | (~big_f(c1, c1)) | (c2 = f2(c1))),
% 30.16/20.35 inference(modus_ponens,[status(thm)],[34246, 34245])).
% 30.16/20.35 tff(34248,plain,
% 30.16/20.35 ((~(c1 = c3)) | (~(c1 = c4)) | (c1 = f4(c1)) | (c2 = f2(c1))),
% 30.16/20.35 inference(unit_resolution,[status(thm)],[34247, 1355, 30354, 31714])).
% 30.16/20.35 tff(34249,plain,
% 30.16/20.35 (c2 = f2(c1)),
% 30.16/20.35 inference(unit_resolution,[status(thm)],[34248, 34238, 34208, 34230])).
% 30.16/20.35 tff(34250,plain,
% 30.16/20.35 (c2 = c1),
% 30.16/20.35 inference(transitivity,[status(thm)],[34249, 34241])).
% 30.16/20.35 tff(34251,plain,
% 30.16/20.35 ($false),
% 30.16/20.35 inference(unit_resolution,[status(thm)],[75, 34250])).
% 30.16/20.35 % SZS output end Proof
%------------------------------------------------------------------------------