TSTP Solution File: ALG012-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ALG012-1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.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 : Tue Sep 6 16:07:01 EDT 2022
% Result : Unsatisfiable 0.20s 0.45s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ALG012-1 : TPTP v8.1.0. Released v2.7.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 29 13:03:49 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.45 % SZS status Unsatisfiable
% 0.20/0.45 % SZS output start Proof
% 0.20/0.45 tff(c_type, type, (
% 0.20/0.45 c: $i > $o)).
% 0.20/0.45 tff(f_type, type, (
% 0.20/0.45 f: ( $i * $i ) > $i)).
% 0.20/0.45 tff(a1_type, type, (
% 0.20/0.45 a1: $i)).
% 0.20/0.45 tff(d2_type, type, (
% 0.20/0.45 d2: $i > $o)).
% 0.20/0.45 tff(d1_type, type, (
% 0.20/0.45 d1: $i > $o)).
% 0.20/0.45 tff(1,plain,
% 0.20/0.45 (^[Z: $i, Y: $i, X: $i] : refl((f(X, f(Y, Z)) = f(f(X, Y), Z)) <=> (f(X, f(Y, Z)) = f(f(X, Y), Z)))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(2,plain,
% 0.20/0.45 (![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z)) <=> ![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.45 tff(3,plain,
% 0.20/0.45 (![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z)) <=> ![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(4,axiom,(![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','f_is_associative')).
% 0.20/0.45 tff(5,plain,
% 0.20/0.45 (![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.45 tff(6,plain,(
% 0.20/0.45 ![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))),
% 0.20/0.45 inference(skolemize,[status(sab)],[5])).
% 0.20/0.45 tff(7,plain,
% 0.20/0.45 (![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.45 tff(8,plain,
% 0.20/0.45 ((~![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))) | (f(f(f(f(a1, a1), a1), a1), f(a1, a1)) = f(f(f(f(f(a1, a1), a1), a1), a1), a1))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(9,plain,
% 0.20/0.45 (f(f(f(f(a1, a1), a1), a1), f(a1, a1)) = f(f(f(f(f(a1, a1), a1), a1), a1), a1)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.45 tff(10,plain,
% 0.20/0.45 ((~![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))) | (f(f(f(a1, a1), a1), f(a1, f(a1, a1))) = f(f(f(f(a1, a1), a1), a1), f(a1, a1)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(11,plain,
% 0.20/0.45 (f(f(f(a1, a1), a1), f(a1, f(a1, a1))) = f(f(f(f(a1, a1), a1), a1), f(a1, a1))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[10, 7])).
% 0.20/0.45 tff(12,plain,
% 0.20/0.45 ((~![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))) | (f(a1, f(a1, a1)) = f(f(a1, a1), a1))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(13,plain,
% 0.20/0.45 (f(a1, f(a1, a1)) = f(f(a1, a1), a1)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[12, 7])).
% 0.20/0.45 tff(14,plain,
% 0.20/0.45 (f(f(a1, a1), a1) = f(a1, f(a1, a1))),
% 0.20/0.45 inference(symmetry,[status(thm)],[13])).
% 0.20/0.45 tff(15,plain,
% 0.20/0.45 (f(f(f(a1, a1), a1), f(f(a1, a1), a1)) = f(f(f(a1, a1), a1), f(a1, f(a1, a1)))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[14])).
% 0.20/0.45 tff(16,plain,
% 0.20/0.45 (f(f(f(a1, a1), a1), f(f(a1, a1), a1)) = f(f(f(f(f(a1, a1), a1), a1), a1), a1)),
% 0.20/0.45 inference(transitivity,[status(thm)],[15, 11, 9])).
% 0.20/0.45 tff(17,plain,
% 0.20/0.45 (c(f(f(f(a1, a1), a1), f(f(a1, a1), a1))) <=> c(f(f(f(f(f(a1, a1), a1), a1), a1), a1))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[16])).
% 0.20/0.45 tff(18,assumption,(d1(f(f(a1, a1), a1))), introduced(assumption)).
% 0.20/0.45 tff(19,plain,
% 0.20/0.45 (^[Y: $i, X: $i] : refl(((~d1(X)) | (~d1(Y)) | c(f(X, Y))) <=> ((~d1(X)) | (~d1(Y)) | c(f(X, Y))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(20,plain,
% 0.20/0.45 (![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y))) <=> ![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[19])).
% 0.20/0.45 tff(21,plain,
% 0.20/0.45 (![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y))) <=> ![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(22,plain,
% 0.20/0.45 (^[Y: $i, X: $i] : rewrite(((c(f(X, Y)) | (~d1(X))) | (~d1(Y))) <=> ((~d1(X)) | (~d1(Y)) | c(f(X, Y))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(23,plain,
% 0.20/0.45 (![Y: $i, X: $i] : ((c(f(X, Y)) | (~d1(X))) | (~d1(Y))) <=> ![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[22])).
% 0.20/0.45 tff(24,axiom,(![Y: $i, X: $i] : ((c(f(X, Y)) | (~d1(X))) | (~d1(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conjecture_2')).
% 0.20/0.45 tff(25,plain,
% 0.20/0.45 (![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.20/0.45 tff(26,plain,
% 0.20/0.45 (![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.20/0.45 tff(27,plain,(
% 0.20/0.45 ![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[26])).
% 0.20/0.45 tff(28,plain,
% 0.20/0.45 (![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.20/0.45 tff(29,plain,
% 0.20/0.45 (((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | ((~d1(f(f(a1, a1), a1))) | c(f(f(f(a1, a1), a1), f(f(a1, a1), a1))))) <=> ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | (~d1(f(f(a1, a1), a1))) | c(f(f(f(a1, a1), a1), f(f(a1, a1), a1))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(30,plain,
% 0.20/0.45 (((~d1(f(f(a1, a1), a1))) | (~d1(f(f(a1, a1), a1))) | c(f(f(f(a1, a1), a1), f(f(a1, a1), a1)))) <=> ((~d1(f(f(a1, a1), a1))) | c(f(f(f(a1, a1), a1), f(f(a1, a1), a1))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(31,plain,
% 0.20/0.45 (((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | ((~d1(f(f(a1, a1), a1))) | (~d1(f(f(a1, a1), a1))) | c(f(f(f(a1, a1), a1), f(f(a1, a1), a1))))) <=> ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | ((~d1(f(f(a1, a1), a1))) | c(f(f(f(a1, a1), a1), f(f(a1, a1), a1)))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[30])).
% 0.20/0.45 tff(32,plain,
% 0.20/0.45 (((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | ((~d1(f(f(a1, a1), a1))) | (~d1(f(f(a1, a1), a1))) | c(f(f(f(a1, a1), a1), f(f(a1, a1), a1))))) <=> ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | (~d1(f(f(a1, a1), a1))) | c(f(f(f(a1, a1), a1), f(f(a1, a1), a1))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[31, 29])).
% 0.20/0.45 tff(33,plain,
% 0.20/0.45 ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | ((~d1(f(f(a1, a1), a1))) | (~d1(f(f(a1, a1), a1))) | c(f(f(f(a1, a1), a1), f(f(a1, a1), a1))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(34,plain,
% 0.20/0.45 ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | (~d1(f(f(a1, a1), a1))) | c(f(f(f(a1, a1), a1), f(f(a1, a1), a1)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.20/0.45 tff(35,plain,
% 0.20/0.45 ((~d1(f(f(a1, a1), a1))) | c(f(f(f(a1, a1), a1), f(f(a1, a1), a1)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[34, 28])).
% 0.20/0.45 tff(36,plain,
% 0.20/0.45 (c(f(f(f(a1, a1), a1), f(f(a1, a1), a1)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[35, 18])).
% 0.20/0.45 tff(37,plain,
% 0.20/0.45 (c(f(f(f(f(f(a1, a1), a1), a1), a1), a1))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[36, 17])).
% 0.20/0.45 tff(38,plain,
% 0.20/0.45 (f(f(f(f(f(a1, a1), a1), a1), a1), a1) = f(f(f(f(a1, a1), a1), a1), f(a1, a1))),
% 0.20/0.45 inference(symmetry,[status(thm)],[9])).
% 0.20/0.45 tff(39,plain,
% 0.20/0.45 (f(f(f(f(f(f(a1, a1), a1), a1), a1), a1), a1) = f(f(f(f(f(a1, a1), a1), a1), f(a1, a1)), a1)),
% 0.20/0.45 inference(monotonicity,[status(thm)],[38])).
% 0.20/0.45 tff(40,plain,
% 0.20/0.45 (f(f(f(f(f(a1, a1), a1), a1), f(a1, a1)), a1) = f(f(f(f(f(f(a1, a1), a1), a1), a1), a1), a1)),
% 0.20/0.45 inference(symmetry,[status(thm)],[39])).
% 0.20/0.45 tff(41,plain,
% 0.20/0.45 (d2(f(f(f(f(f(a1, a1), a1), a1), f(a1, a1)), a1)) <=> d2(f(f(f(f(f(f(a1, a1), a1), a1), a1), a1), a1))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[40])).
% 0.20/0.45 tff(42,plain,
% 0.20/0.45 ((~d2(f(f(f(f(f(a1, a1), a1), a1), f(a1, a1)), a1))) <=> (~d2(f(f(f(f(f(f(a1, a1), a1), a1), a1), a1), a1)))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[41])).
% 0.20/0.45 tff(43,plain,
% 0.20/0.45 ((~![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))) | (f(f(f(f(a1, a1), a1), a1), f(f(a1, a1), a1)) = f(f(f(f(f(a1, a1), a1), a1), f(a1, a1)), a1))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(44,plain,
% 0.20/0.45 (f(f(f(f(a1, a1), a1), a1), f(f(a1, a1), a1)) = f(f(f(f(f(a1, a1), a1), a1), f(a1, a1)), a1)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[43, 7])).
% 0.20/0.45 tff(45,plain,
% 0.20/0.45 (f(f(f(f(f(a1, a1), a1), a1), f(a1, a1)), a1) = f(f(f(f(a1, a1), a1), a1), f(f(a1, a1), a1))),
% 0.20/0.45 inference(symmetry,[status(thm)],[44])).
% 0.20/0.45 tff(46,plain,
% 0.20/0.45 (c(f(f(f(f(f(a1, a1), a1), a1), f(a1, a1)), a1)) <=> c(f(f(f(f(a1, a1), a1), a1), f(f(a1, a1), a1)))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[45])).
% 0.20/0.45 tff(47,plain,
% 0.20/0.45 (c(f(f(f(f(a1, a1), a1), a1), f(f(a1, a1), a1))) <=> c(f(f(f(f(f(a1, a1), a1), a1), f(a1, a1)), a1))),
% 0.20/0.45 inference(symmetry,[status(thm)],[46])).
% 0.20/0.45 tff(48,plain,
% 0.20/0.46 (f(f(f(f(a1, a1), a1), a1), f(a1, f(a1, a1))) = f(f(f(f(a1, a1), a1), a1), f(f(a1, a1), a1))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[13])).
% 0.20/0.46 tff(49,plain,
% 0.20/0.46 ((~![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))) | (f(f(f(f(a1, a1), a1), a1), f(a1, f(a1, a1))) = f(f(f(f(f(a1, a1), a1), a1), a1), f(a1, a1)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(50,plain,
% 0.20/0.46 (f(f(f(f(a1, a1), a1), a1), f(a1, f(a1, a1))) = f(f(f(f(f(a1, a1), a1), a1), a1), f(a1, a1))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[49, 7])).
% 0.20/0.46 tff(51,plain,
% 0.20/0.46 (f(f(f(f(f(a1, a1), a1), a1), a1), f(a1, a1)) = f(f(f(f(a1, a1), a1), a1), f(a1, f(a1, a1)))),
% 0.20/0.46 inference(symmetry,[status(thm)],[50])).
% 0.20/0.46 tff(52,plain,
% 0.20/0.46 (f(f(f(f(f(a1, a1), a1), a1), a1), f(a1, a1)) = f(f(f(f(a1, a1), a1), a1), f(f(a1, a1), a1))),
% 0.20/0.46 inference(transitivity,[status(thm)],[51, 48])).
% 0.20/0.46 tff(53,plain,
% 0.20/0.46 (c(f(f(f(f(f(a1, a1), a1), a1), a1), f(a1, a1))) <=> c(f(f(f(f(a1, a1), a1), a1), f(f(a1, a1), a1)))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[52])).
% 0.20/0.46 tff(54,plain,
% 0.20/0.46 (c(f(f(f(f(f(a1, a1), a1), a1), a1), f(a1, a1))) <=> c(f(f(f(f(f(a1, a1), a1), a1), f(a1, a1)), a1))),
% 0.20/0.46 inference(transitivity,[status(thm)],[53, 47])).
% 0.20/0.46 tff(55,plain,
% 0.20/0.46 ((~![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))) | (f(f(a1, a1), f(a1, a1)) = f(f(f(a1, a1), a1), a1))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(56,plain,
% 0.20/0.46 (f(f(a1, a1), f(a1, a1)) = f(f(f(a1, a1), a1), a1)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[55, 7])).
% 0.20/0.46 tff(57,plain,
% 0.20/0.46 ((~![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))) | (f(a1, f(a1, f(a1, a1))) = f(f(a1, a1), f(a1, a1)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(58,plain,
% 0.20/0.46 (f(a1, f(a1, f(a1, a1))) = f(f(a1, a1), f(a1, a1))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[57, 7])).
% 0.20/0.46 tff(59,plain,
% 0.20/0.46 (f(a1, f(f(a1, a1), a1)) = f(a1, f(a1, f(a1, a1)))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[14])).
% 0.20/0.46 tff(60,plain,
% 0.20/0.46 (f(a1, f(f(a1, a1), a1)) = f(f(f(a1, a1), a1), a1)),
% 0.20/0.46 inference(transitivity,[status(thm)],[59, 58, 56])).
% 0.20/0.46 tff(61,plain,
% 0.20/0.46 (f(f(f(f(a1, a1), a1), a1), f(a1, f(f(a1, a1), a1))) = f(f(f(f(a1, a1), a1), a1), f(f(f(a1, a1), a1), a1))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[60])).
% 0.20/0.46 tff(62,plain,
% 0.20/0.46 ((~![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))) | (f(f(f(f(a1, a1), a1), a1), f(a1, f(f(a1, a1), a1))) = f(f(f(f(f(a1, a1), a1), a1), a1), f(f(a1, a1), a1)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(63,plain,
% 0.20/0.46 (f(f(f(f(a1, a1), a1), a1), f(a1, f(f(a1, a1), a1))) = f(f(f(f(f(a1, a1), a1), a1), a1), f(f(a1, a1), a1))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[62, 7])).
% 0.20/0.46 tff(64,plain,
% 0.20/0.46 (f(f(f(f(f(a1, a1), a1), a1), a1), f(f(a1, a1), a1)) = f(f(f(f(a1, a1), a1), a1), f(a1, f(f(a1, a1), a1)))),
% 0.20/0.46 inference(symmetry,[status(thm)],[63])).
% 0.20/0.46 tff(65,plain,
% 0.20/0.46 (f(f(f(f(f(a1, a1), a1), a1), a1), f(f(a1, a1), a1)) = f(f(f(f(a1, a1), a1), a1), f(f(f(a1, a1), a1), a1))),
% 0.20/0.46 inference(transitivity,[status(thm)],[64, 61])).
% 0.20/0.46 tff(66,plain,
% 0.20/0.46 (c(f(f(f(f(f(a1, a1), a1), a1), a1), f(f(a1, a1), a1))) <=> c(f(f(f(f(a1, a1), a1), a1), f(f(f(a1, a1), a1), a1)))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[65])).
% 0.20/0.46 tff(67,plain,
% 0.20/0.46 (c(f(f(f(f(a1, a1), a1), a1), f(f(f(a1, a1), a1), a1))) <=> c(f(f(f(f(f(a1, a1), a1), a1), a1), f(f(a1, a1), a1)))),
% 0.20/0.46 inference(symmetry,[status(thm)],[66])).
% 0.20/0.46 tff(68,plain,
% 0.20/0.46 ((~c(f(f(f(f(a1, a1), a1), a1), f(f(f(a1, a1), a1), a1)))) <=> (~c(f(f(f(f(f(a1, a1), a1), a1), a1), f(f(a1, a1), a1))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[67])).
% 0.20/0.46 tff(69,assumption,(c(f(f(f(f(a1, a1), a1), a1), f(f(f(a1, a1), a1), a1)))), introduced(assumption)).
% 0.20/0.46 tff(70,plain,
% 0.20/0.46 (^[X: $i] : refl(((~c(X)) | (~d2(X))) <=> ((~c(X)) | (~d2(X))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(71,plain,
% 0.20/0.46 (![X: $i] : ((~c(X)) | (~d2(X))) <=> ![X: $i] : ((~c(X)) | (~d2(X)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[70])).
% 0.20/0.46 tff(72,plain,
% 0.20/0.46 (![X: $i] : ((~c(X)) | (~d2(X))) <=> ![X: $i] : ((~c(X)) | (~d2(X)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(73,axiom,(![X: $i] : ((~c(X)) | (~d2(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','partitions_exclusive_c_d2')).
% 0.20/0.46 tff(74,plain,
% 0.20/0.46 (![X: $i] : ((~c(X)) | (~d2(X)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.20/0.46 tff(75,plain,(
% 0.20/0.46 ![X: $i] : ((~c(X)) | (~d2(X)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[74])).
% 0.20/0.46 tff(76,plain,
% 0.20/0.46 (![X: $i] : ((~c(X)) | (~d2(X)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.20/0.46 tff(77,plain,
% 0.20/0.46 (((~![X: $i] : ((~c(X)) | (~d2(X)))) | ((~c(f(f(f(f(a1, a1), a1), a1), f(f(f(a1, a1), a1), a1)))) | (~d2(f(f(f(f(a1, a1), a1), a1), f(f(f(a1, a1), a1), a1)))))) <=> ((~![X: $i] : ((~c(X)) | (~d2(X)))) | (~c(f(f(f(f(a1, a1), a1), a1), f(f(f(a1, a1), a1), a1)))) | (~d2(f(f(f(f(a1, a1), a1), a1), f(f(f(a1, a1), a1), a1)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(78,plain,
% 0.20/0.46 ((~![X: $i] : ((~c(X)) | (~d2(X)))) | ((~c(f(f(f(f(a1, a1), a1), a1), f(f(f(a1, a1), a1), a1)))) | (~d2(f(f(f(f(a1, a1), a1), a1), f(f(f(a1, a1), a1), a1)))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(79,plain,
% 0.20/0.46 ((~![X: $i] : ((~c(X)) | (~d2(X)))) | (~c(f(f(f(f(a1, a1), a1), a1), f(f(f(a1, a1), a1), a1)))) | (~d2(f(f(f(f(a1, a1), a1), a1), f(f(f(a1, a1), a1), a1))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.20/0.46 tff(80,plain,
% 0.20/0.46 (~d2(f(f(f(f(a1, a1), a1), a1), f(f(f(a1, a1), a1), a1)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[79, 76, 69])).
% 0.20/0.46 tff(81,plain,
% 0.20/0.46 (^[X: $i] : refl(((~c(X)) | (~d1(X))) <=> ((~c(X)) | (~d1(X))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(82,plain,
% 0.20/0.46 (![X: $i] : ((~c(X)) | (~d1(X))) <=> ![X: $i] : ((~c(X)) | (~d1(X)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[81])).
% 0.20/0.46 tff(83,plain,
% 0.20/0.46 (![X: $i] : ((~c(X)) | (~d1(X))) <=> ![X: $i] : ((~c(X)) | (~d1(X)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(84,axiom,(![X: $i] : ((~c(X)) | (~d1(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','partitions_exclusive_c_d1')).
% 0.20/0.46 tff(85,plain,
% 0.20/0.46 (![X: $i] : ((~c(X)) | (~d1(X)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.20/0.46 tff(86,plain,(
% 0.20/0.46 ![X: $i] : ((~c(X)) | (~d1(X)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[85])).
% 0.20/0.46 tff(87,plain,
% 0.20/0.46 (![X: $i] : ((~c(X)) | (~d1(X)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.20/0.46 tff(88,plain,
% 0.20/0.46 (((~![X: $i] : ((~c(X)) | (~d1(X)))) | ((~c(f(f(f(f(a1, a1), a1), a1), f(f(f(a1, a1), a1), a1)))) | (~d1(f(f(f(f(a1, a1), a1), a1), f(f(f(a1, a1), a1), a1)))))) <=> ((~![X: $i] : ((~c(X)) | (~d1(X)))) | (~c(f(f(f(f(a1, a1), a1), a1), f(f(f(a1, a1), a1), a1)))) | (~d1(f(f(f(f(a1, a1), a1), a1), f(f(f(a1, a1), a1), a1)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(89,plain,
% 0.20/0.46 ((~![X: $i] : ((~c(X)) | (~d1(X)))) | ((~c(f(f(f(f(a1, a1), a1), a1), f(f(f(a1, a1), a1), a1)))) | (~d1(f(f(f(f(a1, a1), a1), a1), f(f(f(a1, a1), a1), a1)))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(90,plain,
% 0.20/0.46 ((~![X: $i] : ((~c(X)) | (~d1(X)))) | (~c(f(f(f(f(a1, a1), a1), a1), f(f(f(a1, a1), a1), a1)))) | (~d1(f(f(f(f(a1, a1), a1), a1), f(f(f(a1, a1), a1), a1))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.20/0.46 tff(91,plain,
% 0.20/0.46 (~d1(f(f(f(f(a1, a1), a1), a1), f(f(f(a1, a1), a1), a1)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[90, 87, 69])).
% 0.20/0.46 tff(92,plain,
% 0.20/0.46 (f(f(f(a1, a1), a1), a1) = f(f(a1, a1), f(a1, a1))),
% 0.20/0.46 inference(symmetry,[status(thm)],[56])).
% 0.20/0.46 tff(93,plain,
% 0.20/0.46 (c(f(f(f(a1, a1), a1), a1)) <=> c(f(f(a1, a1), f(a1, a1)))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[92])).
% 0.20/0.46 tff(94,plain,
% 0.20/0.46 (c(f(f(a1, a1), f(a1, a1))) <=> c(f(f(f(a1, a1), a1), a1))),
% 0.20/0.46 inference(symmetry,[status(thm)],[93])).
% 0.20/0.46 tff(95,assumption,(~c(f(f(a1, a1), f(a1, a1)))), introduced(assumption)).
% 0.20/0.46 tff(96,plain,
% 0.20/0.46 (^[Y: $i, X: $i] : refl(((~d2(X)) | c(f(X, Y)) | (~d2(Y))) <=> ((~d2(X)) | c(f(X, Y)) | (~d2(Y))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(97,plain,
% 0.20/0.46 (![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y))) <=> ![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[96])).
% 0.20/0.46 tff(98,plain,
% 0.20/0.46 (![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y))) <=> ![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(99,plain,
% 0.20/0.46 (^[Y: $i, X: $i] : rewrite(((c(f(X, Y)) | (~d2(X))) | (~d2(Y))) <=> ((~d2(X)) | c(f(X, Y)) | (~d2(Y))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(100,plain,
% 0.20/0.46 (![Y: $i, X: $i] : ((c(f(X, Y)) | (~d2(X))) | (~d2(Y))) <=> ![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[99])).
% 0.20/0.46 tff(101,axiom,(![Y: $i, X: $i] : ((c(f(X, Y)) | (~d2(X))) | (~d2(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conjecture_3')).
% 0.20/0.46 tff(102,plain,
% 0.20/0.46 (![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.20/0.46 tff(103,plain,
% 0.20/0.46 (![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.20/0.46 tff(104,plain,(
% 0.20/0.46 ![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[103])).
% 0.20/0.46 tff(105,plain,
% 0.20/0.46 (![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[104, 97])).
% 0.20/0.46 tff(106,plain,
% 0.20/0.46 (((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(f(a1, a1))) | c(f(f(a1, a1), f(a1, a1))))) <=> ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | (~d2(f(a1, a1))) | c(f(f(a1, a1), f(a1, a1))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(107,plain,
% 0.20/0.46 (((~d2(f(a1, a1))) | c(f(f(a1, a1), f(a1, a1))) | (~d2(f(a1, a1)))) <=> ((~d2(f(a1, a1))) | c(f(f(a1, a1), f(a1, a1))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(108,plain,
% 0.20/0.46 (((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(f(a1, a1))) | c(f(f(a1, a1), f(a1, a1))) | (~d2(f(a1, a1))))) <=> ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(f(a1, a1))) | c(f(f(a1, a1), f(a1, a1)))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[107])).
% 0.20/0.46 tff(109,plain,
% 0.20/0.46 (((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(f(a1, a1))) | c(f(f(a1, a1), f(a1, a1))) | (~d2(f(a1, a1))))) <=> ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | (~d2(f(a1, a1))) | c(f(f(a1, a1), f(a1, a1))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[108, 106])).
% 0.20/0.46 tff(110,plain,
% 0.20/0.46 ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(f(a1, a1))) | c(f(f(a1, a1), f(a1, a1))) | (~d2(f(a1, a1))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(111,plain,
% 0.20/0.46 ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | (~d2(f(a1, a1))) | c(f(f(a1, a1), f(a1, a1)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.20/0.46 tff(112,plain,
% 0.20/0.46 ((~d2(f(a1, a1))) | c(f(f(a1, a1), f(a1, a1)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[111, 105])).
% 0.20/0.46 tff(113,plain,
% 0.20/0.46 (~d2(f(a1, a1))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[112, 95])).
% 0.20/0.46 tff(114,plain,
% 0.20/0.46 (((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | ((~d1(f(a1, a1))) | c(f(f(a1, a1), f(a1, a1))))) <=> ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | (~d1(f(a1, a1))) | c(f(f(a1, a1), f(a1, a1))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(115,plain,
% 0.20/0.46 (((~d1(f(a1, a1))) | (~d1(f(a1, a1))) | c(f(f(a1, a1), f(a1, a1)))) <=> ((~d1(f(a1, a1))) | c(f(f(a1, a1), f(a1, a1))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(116,plain,
% 0.20/0.46 (((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | ((~d1(f(a1, a1))) | (~d1(f(a1, a1))) | c(f(f(a1, a1), f(a1, a1))))) <=> ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | ((~d1(f(a1, a1))) | c(f(f(a1, a1), f(a1, a1)))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[115])).
% 0.20/0.46 tff(117,plain,
% 0.20/0.46 (((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | ((~d1(f(a1, a1))) | (~d1(f(a1, a1))) | c(f(f(a1, a1), f(a1, a1))))) <=> ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | (~d1(f(a1, a1))) | c(f(f(a1, a1), f(a1, a1))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[116, 114])).
% 0.20/0.46 tff(118,plain,
% 0.20/0.46 ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | ((~d1(f(a1, a1))) | (~d1(f(a1, a1))) | c(f(f(a1, a1), f(a1, a1))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(119,plain,
% 0.20/0.46 ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | (~d1(f(a1, a1))) | c(f(f(a1, a1), f(a1, a1)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.20/0.47 tff(120,plain,
% 0.20/0.47 ((~d1(f(a1, a1))) | c(f(f(a1, a1), f(a1, a1)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[119, 28])).
% 0.20/0.47 tff(121,plain,
% 0.20/0.47 (~d1(f(a1, a1))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[120, 95])).
% 0.20/0.47 tff(122,plain,
% 0.20/0.47 (^[Y: $i, X: $i] : refl(((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y))) <=> ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(123,plain,
% 0.20/0.47 (![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y))) <=> ![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[122])).
% 0.20/0.47 tff(124,plain,
% 0.20/0.47 (![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y))) <=> ![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(125,plain,
% 0.20/0.47 (^[Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((d2(f(X, Y)) | d1(f(X, Y))) <=> (d1(f(X, Y)) | d2(f(X, Y)))), (((d2(f(X, Y)) | d1(f(X, Y))) | (~c(X))) <=> ((d1(f(X, Y)) | d2(f(X, Y))) | (~c(X))))), rewrite(((d1(f(X, Y)) | d2(f(X, Y))) | (~c(X))) <=> ((~c(X)) | d1(f(X, Y)) | d2(f(X, Y)))), (((d2(f(X, Y)) | d1(f(X, Y))) | (~c(X))) <=> ((~c(X)) | d1(f(X, Y)) | d2(f(X, Y))))), ((((d2(f(X, Y)) | d1(f(X, Y))) | (~c(X))) | (~c(Y))) <=> (((~c(X)) | d1(f(X, Y)) | d2(f(X, Y))) | (~c(Y))))), rewrite((((~c(X)) | d1(f(X, Y)) | d2(f(X, Y))) | (~c(Y))) <=> ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))), ((((d2(f(X, Y)) | d1(f(X, Y))) | (~c(X))) | (~c(Y))) <=> ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(126,plain,
% 0.20/0.47 (![Y: $i, X: $i] : (((d2(f(X, Y)) | d1(f(X, Y))) | (~c(X))) | (~c(Y))) <=> ![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[125])).
% 0.20/0.47 tff(127,axiom,(![Y: $i, X: $i] : (((d2(f(X, Y)) | d1(f(X, Y))) | (~c(X))) | (~c(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conjecture_1')).
% 0.20/0.47 tff(128,plain,
% 0.20/0.47 (![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.20/0.47 tff(129,plain,
% 0.20/0.47 (![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[128, 124])).
% 0.20/0.47 tff(130,plain,(
% 0.20/0.47 ![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))),
% 0.20/0.47 inference(skolemize,[status(sab)],[129])).
% 0.20/0.47 tff(131,plain,
% 0.20/0.47 (![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[130, 123])).
% 0.20/0.47 tff(132,plain,
% 0.20/0.47 (c(a1) <=> c(a1)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(133,axiom,(c(a1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','partition_c_not_empty')).
% 0.20/0.47 tff(134,plain,
% 0.20/0.47 (c(a1)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.20/0.47 tff(135,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(a1)) | d1(f(a1, a1)) | d2(f(a1, a1)))) <=> ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | (~c(a1)) | d1(f(a1, a1)) | d2(f(a1, a1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(136,plain,
% 0.20/0.47 (((~c(a1)) | (~c(a1)) | d1(f(a1, a1)) | d2(f(a1, a1))) <=> ((~c(a1)) | d1(f(a1, a1)) | d2(f(a1, a1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(137,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(a1)) | (~c(a1)) | d1(f(a1, a1)) | d2(f(a1, a1)))) <=> ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(a1)) | d1(f(a1, a1)) | d2(f(a1, a1))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[136])).
% 0.20/0.47 tff(138,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(a1)) | (~c(a1)) | d1(f(a1, a1)) | d2(f(a1, a1)))) <=> ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | (~c(a1)) | d1(f(a1, a1)) | d2(f(a1, a1)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[137, 135])).
% 0.20/0.47 tff(139,plain,
% 0.20/0.47 ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(a1)) | (~c(a1)) | d1(f(a1, a1)) | d2(f(a1, a1)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(140,plain,
% 0.20/0.47 ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | (~c(a1)) | d1(f(a1, a1)) | d2(f(a1, a1))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.20/0.47 tff(141,plain,
% 0.20/0.47 (d1(f(a1, a1)) | d2(f(a1, a1))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[140, 134, 131])).
% 0.20/0.47 tff(142,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[141, 121, 113])).
% 0.20/0.47 tff(143,plain,(c(f(f(a1, a1), f(a1, a1)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(144,plain,
% 0.20/0.47 (c(f(f(f(a1, a1), a1), a1))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[143, 94])).
% 0.20/0.47 tff(145,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(f(f(a1, a1), a1), a1))) | d1(f(f(f(f(a1, a1), a1), a1), f(f(f(a1, a1), a1), a1))) | d2(f(f(f(f(a1, a1), a1), a1), f(f(f(a1, a1), a1), a1))))) <=> ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | (~c(f(f(f(a1, a1), a1), a1))) | d1(f(f(f(f(a1, a1), a1), a1), f(f(f(a1, a1), a1), a1))) | d2(f(f(f(f(a1, a1), a1), a1), f(f(f(a1, a1), a1), a1))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(146,plain,
% 0.20/0.47 (((~c(f(f(f(a1, a1), a1), a1))) | (~c(f(f(f(a1, a1), a1), a1))) | d1(f(f(f(f(a1, a1), a1), a1), f(f(f(a1, a1), a1), a1))) | d2(f(f(f(f(a1, a1), a1), a1), f(f(f(a1, a1), a1), a1)))) <=> ((~c(f(f(f(a1, a1), a1), a1))) | d1(f(f(f(f(a1, a1), a1), a1), f(f(f(a1, a1), a1), a1))) | d2(f(f(f(f(a1, a1), a1), a1), f(f(f(a1, a1), a1), a1))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(147,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(f(f(a1, a1), a1), a1))) | (~c(f(f(f(a1, a1), a1), a1))) | d1(f(f(f(f(a1, a1), a1), a1), f(f(f(a1, a1), a1), a1))) | d2(f(f(f(f(a1, a1), a1), a1), f(f(f(a1, a1), a1), a1))))) <=> ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(f(f(a1, a1), a1), a1))) | d1(f(f(f(f(a1, a1), a1), a1), f(f(f(a1, a1), a1), a1))) | d2(f(f(f(f(a1, a1), a1), a1), f(f(f(a1, a1), a1), a1)))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[146])).
% 0.20/0.47 tff(148,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(f(f(a1, a1), a1), a1))) | (~c(f(f(f(a1, a1), a1), a1))) | d1(f(f(f(f(a1, a1), a1), a1), f(f(f(a1, a1), a1), a1))) | d2(f(f(f(f(a1, a1), a1), a1), f(f(f(a1, a1), a1), a1))))) <=> ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | (~c(f(f(f(a1, a1), a1), a1))) | d1(f(f(f(f(a1, a1), a1), a1), f(f(f(a1, a1), a1), a1))) | d2(f(f(f(f(a1, a1), a1), a1), f(f(f(a1, a1), a1), a1))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[147, 145])).
% 0.20/0.47 tff(149,plain,
% 0.20/0.47 ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(f(f(a1, a1), a1), a1))) | (~c(f(f(f(a1, a1), a1), a1))) | d1(f(f(f(f(a1, a1), a1), a1), f(f(f(a1, a1), a1), a1))) | d2(f(f(f(f(a1, a1), a1), a1), f(f(f(a1, a1), a1), a1))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(150,plain,
% 0.20/0.47 ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | (~c(f(f(f(a1, a1), a1), a1))) | d1(f(f(f(f(a1, a1), a1), a1), f(f(f(a1, a1), a1), a1))) | d2(f(f(f(f(a1, a1), a1), a1), f(f(f(a1, a1), a1), a1)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.20/0.47 tff(151,plain,
% 0.20/0.47 ((~c(f(f(f(a1, a1), a1), a1))) | d1(f(f(f(f(a1, a1), a1), a1), f(f(f(a1, a1), a1), a1))) | d2(f(f(f(f(a1, a1), a1), a1), f(f(f(a1, a1), a1), a1)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[150, 131])).
% 0.20/0.47 tff(152,plain,
% 0.20/0.47 (d1(f(f(f(f(a1, a1), a1), a1), f(f(f(a1, a1), a1), a1))) | d2(f(f(f(f(a1, a1), a1), a1), f(f(f(a1, a1), a1), a1)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[151, 144])).
% 0.20/0.47 tff(153,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[152, 91, 80])).
% 0.20/0.47 tff(154,plain,(~c(f(f(f(f(a1, a1), a1), a1), f(f(f(a1, a1), a1), a1)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(155,plain,
% 0.20/0.47 (~c(f(f(f(f(f(a1, a1), a1), a1), a1), f(f(a1, a1), a1)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[154, 68])).
% 0.20/0.47 tff(156,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | ((~d1(f(f(a1, a1), a1))) | (~d1(f(f(f(f(a1, a1), a1), a1), a1))) | c(f(f(f(f(f(a1, a1), a1), a1), a1), f(f(a1, a1), a1))))) <=> ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | (~d1(f(f(a1, a1), a1))) | (~d1(f(f(f(f(a1, a1), a1), a1), a1))) | c(f(f(f(f(f(a1, a1), a1), a1), a1), f(f(a1, a1), a1))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(157,plain,
% 0.20/0.47 (((~d1(f(f(f(f(a1, a1), a1), a1), a1))) | (~d1(f(f(a1, a1), a1))) | c(f(f(f(f(f(a1, a1), a1), a1), a1), f(f(a1, a1), a1)))) <=> ((~d1(f(f(a1, a1), a1))) | (~d1(f(f(f(f(a1, a1), a1), a1), a1))) | c(f(f(f(f(f(a1, a1), a1), a1), a1), f(f(a1, a1), a1))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(158,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | ((~d1(f(f(f(f(a1, a1), a1), a1), a1))) | (~d1(f(f(a1, a1), a1))) | c(f(f(f(f(f(a1, a1), a1), a1), a1), f(f(a1, a1), a1))))) <=> ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | ((~d1(f(f(a1, a1), a1))) | (~d1(f(f(f(f(a1, a1), a1), a1), a1))) | c(f(f(f(f(f(a1, a1), a1), a1), a1), f(f(a1, a1), a1)))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[157])).
% 0.20/0.47 tff(159,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | ((~d1(f(f(f(f(a1, a1), a1), a1), a1))) | (~d1(f(f(a1, a1), a1))) | c(f(f(f(f(f(a1, a1), a1), a1), a1), f(f(a1, a1), a1))))) <=> ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | (~d1(f(f(a1, a1), a1))) | (~d1(f(f(f(f(a1, a1), a1), a1), a1))) | c(f(f(f(f(f(a1, a1), a1), a1), a1), f(f(a1, a1), a1))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[158, 156])).
% 0.20/0.47 tff(160,plain,
% 0.20/0.47 ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | ((~d1(f(f(f(f(a1, a1), a1), a1), a1))) | (~d1(f(f(a1, a1), a1))) | c(f(f(f(f(f(a1, a1), a1), a1), a1), f(f(a1, a1), a1))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(161,plain,
% 0.20/0.47 ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | (~d1(f(f(a1, a1), a1))) | (~d1(f(f(f(f(a1, a1), a1), a1), a1))) | c(f(f(f(f(f(a1, a1), a1), a1), a1), f(f(a1, a1), a1)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.20/0.47 tff(162,plain,
% 0.20/0.47 ((~d1(f(f(a1, a1), a1))) | (~d1(f(f(f(f(a1, a1), a1), a1), a1))) | c(f(f(f(f(f(a1, a1), a1), a1), a1), f(f(a1, a1), a1)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[161, 28])).
% 0.20/0.47 tff(163,plain,
% 0.20/0.47 ((~d1(f(f(a1, a1), a1))) | (~d1(f(f(f(f(a1, a1), a1), a1), a1)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[162, 155])).
% 0.20/0.47 tff(164,plain,
% 0.20/0.47 (~d1(f(f(f(f(a1, a1), a1), a1), a1))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[163, 18])).
% 0.20/0.47 tff(165,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(a1)) | (~c(f(f(f(a1, a1), a1), a1))) | d1(f(f(f(f(a1, a1), a1), a1), a1)) | d2(f(f(f(f(a1, a1), a1), a1), a1)))) <=> ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | (~c(a1)) | (~c(f(f(f(a1, a1), a1), a1))) | d1(f(f(f(f(a1, a1), a1), a1), a1)) | d2(f(f(f(f(a1, a1), a1), a1), a1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(166,plain,
% 0.20/0.47 (((~c(f(f(f(a1, a1), a1), a1))) | (~c(a1)) | d1(f(f(f(f(a1, a1), a1), a1), a1)) | d2(f(f(f(f(a1, a1), a1), a1), a1))) <=> ((~c(a1)) | (~c(f(f(f(a1, a1), a1), a1))) | d1(f(f(f(f(a1, a1), a1), a1), a1)) | d2(f(f(f(f(a1, a1), a1), a1), a1)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(167,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(f(f(a1, a1), a1), a1))) | (~c(a1)) | d1(f(f(f(f(a1, a1), a1), a1), a1)) | d2(f(f(f(f(a1, a1), a1), a1), a1)))) <=> ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(a1)) | (~c(f(f(f(a1, a1), a1), a1))) | d1(f(f(f(f(a1, a1), a1), a1), a1)) | d2(f(f(f(f(a1, a1), a1), a1), a1))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[166])).
% 0.20/0.47 tff(168,plain,
% 0.20/0.47 (((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(f(f(a1, a1), a1), a1))) | (~c(a1)) | d1(f(f(f(f(a1, a1), a1), a1), a1)) | d2(f(f(f(f(a1, a1), a1), a1), a1)))) <=> ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | (~c(a1)) | (~c(f(f(f(a1, a1), a1), a1))) | d1(f(f(f(f(a1, a1), a1), a1), a1)) | d2(f(f(f(f(a1, a1), a1), a1), a1)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[167, 165])).
% 0.20/0.48 tff(169,plain,
% 0.20/0.48 ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(f(f(a1, a1), a1), a1))) | (~c(a1)) | d1(f(f(f(f(a1, a1), a1), a1), a1)) | d2(f(f(f(f(a1, a1), a1), a1), a1)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(170,plain,
% 0.20/0.48 ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | (~c(a1)) | (~c(f(f(f(a1, a1), a1), a1))) | d1(f(f(f(f(a1, a1), a1), a1), a1)) | d2(f(f(f(f(a1, a1), a1), a1), a1))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.20/0.48 tff(171,plain,
% 0.20/0.48 ((~c(f(f(f(a1, a1), a1), a1))) | d1(f(f(f(f(a1, a1), a1), a1), a1)) | d2(f(f(f(f(a1, a1), a1), a1), a1))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[170, 134, 131])).
% 0.20/0.48 tff(172,plain,
% 0.20/0.48 (d1(f(f(f(f(a1, a1), a1), a1), a1)) | d2(f(f(f(f(a1, a1), a1), a1), a1))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[171, 144])).
% 0.20/0.48 tff(173,plain,
% 0.20/0.48 (d2(f(f(f(f(a1, a1), a1), a1), a1))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[172, 164])).
% 0.20/0.48 tff(174,plain,
% 0.20/0.48 (f(f(f(a1, a1), f(a1, a1)), a1) = f(f(f(f(a1, a1), a1), a1), a1)),
% 0.20/0.48 inference(monotonicity,[status(thm)],[56])).
% 0.20/0.48 tff(175,plain,
% 0.20/0.48 ((~![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))) | (f(f(a1, a1), f(f(a1, a1), a1)) = f(f(f(a1, a1), f(a1, a1)), a1))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(176,plain,
% 0.20/0.48 (f(f(a1, a1), f(f(a1, a1), a1)) = f(f(f(a1, a1), f(a1, a1)), a1)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[175, 7])).
% 0.20/0.48 tff(177,plain,
% 0.20/0.48 (f(f(a1, a1), f(f(a1, a1), a1)) = f(f(f(f(a1, a1), a1), a1), a1)),
% 0.20/0.48 inference(transitivity,[status(thm)],[176, 174])).
% 0.20/0.48 tff(178,plain,
% 0.20/0.48 (c(f(f(a1, a1), f(f(a1, a1), a1))) <=> c(f(f(f(f(a1, a1), a1), a1), a1))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[177])).
% 0.20/0.48 tff(179,plain,
% 0.20/0.48 (c(f(f(f(f(a1, a1), a1), a1), a1)) <=> c(f(f(a1, a1), f(f(a1, a1), a1)))),
% 0.20/0.48 inference(symmetry,[status(thm)],[178])).
% 0.20/0.48 tff(180,plain,
% 0.20/0.48 ((~c(f(f(f(f(a1, a1), a1), a1), a1))) <=> (~c(f(f(a1, a1), f(f(a1, a1), a1))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[179])).
% 0.20/0.48 tff(181,assumption,(c(f(f(f(a1, a1), a1), a1))), introduced(assumption)).
% 0.20/0.48 tff(182,assumption,(c(f(f(f(f(a1, a1), a1), a1), a1))), introduced(assumption)).
% 0.20/0.48 tff(183,plain,
% 0.20/0.48 (((~![X: $i] : ((~c(X)) | (~d2(X)))) | ((~c(f(f(f(f(a1, a1), a1), a1), a1))) | (~d2(f(f(f(f(a1, a1), a1), a1), a1))))) <=> ((~![X: $i] : ((~c(X)) | (~d2(X)))) | (~c(f(f(f(f(a1, a1), a1), a1), a1))) | (~d2(f(f(f(f(a1, a1), a1), a1), a1))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(184,plain,
% 0.20/0.48 ((~![X: $i] : ((~c(X)) | (~d2(X)))) | ((~c(f(f(f(f(a1, a1), a1), a1), a1))) | (~d2(f(f(f(f(a1, a1), a1), a1), a1))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(185,plain,
% 0.20/0.48 ((~![X: $i] : ((~c(X)) | (~d2(X)))) | (~c(f(f(f(f(a1, a1), a1), a1), a1))) | (~d2(f(f(f(f(a1, a1), a1), a1), a1)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.20/0.48 tff(186,plain,
% 0.20/0.48 (~d2(f(f(f(f(a1, a1), a1), a1), a1))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[185, 76, 182])).
% 0.20/0.48 tff(187,plain,
% 0.20/0.48 (((~![X: $i] : ((~c(X)) | (~d1(X)))) | ((~c(f(f(f(f(a1, a1), a1), a1), a1))) | (~d1(f(f(f(f(a1, a1), a1), a1), a1))))) <=> ((~![X: $i] : ((~c(X)) | (~d1(X)))) | (~c(f(f(f(f(a1, a1), a1), a1), a1))) | (~d1(f(f(f(f(a1, a1), a1), a1), a1))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(188,plain,
% 0.20/0.48 ((~![X: $i] : ((~c(X)) | (~d1(X)))) | ((~c(f(f(f(f(a1, a1), a1), a1), a1))) | (~d1(f(f(f(f(a1, a1), a1), a1), a1))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(189,plain,
% 0.20/0.48 ((~![X: $i] : ((~c(X)) | (~d1(X)))) | (~c(f(f(f(f(a1, a1), a1), a1), a1))) | (~d1(f(f(f(f(a1, a1), a1), a1), a1)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.20/0.48 tff(190,plain,
% 0.20/0.48 (~d1(f(f(f(f(a1, a1), a1), a1), a1))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[189, 87, 182])).
% 0.20/0.48 tff(191,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[171, 190, 186, 181])).
% 0.20/0.48 tff(192,plain,((~c(f(f(f(f(a1, a1), a1), a1), a1))) | (~c(f(f(f(a1, a1), a1), a1)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(193,plain,
% 0.20/0.48 (~c(f(f(f(f(a1, a1), a1), a1), a1))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[192, 144])).
% 0.20/0.48 tff(194,plain,
% 0.20/0.48 (~c(f(f(a1, a1), f(f(a1, a1), a1)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[193, 180])).
% 0.20/0.48 tff(195,plain,
% 0.20/0.48 (((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | ((~d1(f(a1, a1))) | (~d1(f(f(a1, a1), a1))) | c(f(f(a1, a1), f(f(a1, a1), a1))))) <=> ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | (~d1(f(a1, a1))) | (~d1(f(f(a1, a1), a1))) | c(f(f(a1, a1), f(f(a1, a1), a1))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(196,plain,
% 0.20/0.48 ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | ((~d1(f(a1, a1))) | (~d1(f(f(a1, a1), a1))) | c(f(f(a1, a1), f(f(a1, a1), a1))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(197,plain,
% 0.20/0.48 ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | (~d1(f(a1, a1))) | (~d1(f(f(a1, a1), a1))) | c(f(f(a1, a1), f(f(a1, a1), a1)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.20/0.48 tff(198,plain,
% 0.20/0.48 ((~d1(f(a1, a1))) | (~d1(f(f(a1, a1), a1))) | c(f(f(a1, a1), f(f(a1, a1), a1)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[197, 28])).
% 0.20/0.48 tff(199,plain,
% 0.20/0.48 ((~d1(f(a1, a1))) | (~d1(f(f(a1, a1), a1)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[198, 194])).
% 0.20/0.48 tff(200,plain,
% 0.20/0.48 (~d1(f(a1, a1))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[199, 18])).
% 0.20/0.48 tff(201,plain,
% 0.20/0.48 (d2(f(a1, a1))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[141, 200])).
% 0.20/0.48 tff(202,plain,
% 0.20/0.48 (((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(f(a1, a1))) | (~d2(f(f(f(f(a1, a1), a1), a1), a1))) | c(f(f(f(f(f(a1, a1), a1), a1), a1), f(a1, a1))))) <=> ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | (~d2(f(a1, a1))) | (~d2(f(f(f(f(a1, a1), a1), a1), a1))) | c(f(f(f(f(f(a1, a1), a1), a1), a1), f(a1, a1))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(203,plain,
% 0.20/0.48 (((~d2(f(f(f(f(a1, a1), a1), a1), a1))) | c(f(f(f(f(f(a1, a1), a1), a1), a1), f(a1, a1))) | (~d2(f(a1, a1)))) <=> ((~d2(f(a1, a1))) | (~d2(f(f(f(f(a1, a1), a1), a1), a1))) | c(f(f(f(f(f(a1, a1), a1), a1), a1), f(a1, a1))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(204,plain,
% 0.20/0.48 (((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(f(f(f(f(a1, a1), a1), a1), a1))) | c(f(f(f(f(f(a1, a1), a1), a1), a1), f(a1, a1))) | (~d2(f(a1, a1))))) <=> ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(f(a1, a1))) | (~d2(f(f(f(f(a1, a1), a1), a1), a1))) | c(f(f(f(f(f(a1, a1), a1), a1), a1), f(a1, a1)))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[203])).
% 0.20/0.48 tff(205,plain,
% 0.20/0.48 (((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(f(f(f(f(a1, a1), a1), a1), a1))) | c(f(f(f(f(f(a1, a1), a1), a1), a1), f(a1, a1))) | (~d2(f(a1, a1))))) <=> ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | (~d2(f(a1, a1))) | (~d2(f(f(f(f(a1, a1), a1), a1), a1))) | c(f(f(f(f(f(a1, a1), a1), a1), a1), f(a1, a1))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[204, 202])).
% 0.20/0.48 tff(206,plain,
% 0.20/0.48 ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(f(f(f(f(a1, a1), a1), a1), a1))) | c(f(f(f(f(f(a1, a1), a1), a1), a1), f(a1, a1))) | (~d2(f(a1, a1))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(207,plain,
% 0.20/0.48 ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | (~d2(f(a1, a1))) | (~d2(f(f(f(f(a1, a1), a1), a1), a1))) | c(f(f(f(f(f(a1, a1), a1), a1), a1), f(a1, a1)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[206, 205])).
% 0.20/0.48 tff(208,plain,
% 0.20/0.48 ((~d2(f(a1, a1))) | (~d2(f(f(f(f(a1, a1), a1), a1), a1))) | c(f(f(f(f(f(a1, a1), a1), a1), a1), f(a1, a1)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[207, 105])).
% 0.20/0.48 tff(209,plain,
% 0.20/0.48 (c(f(f(f(f(f(a1, a1), a1), a1), a1), f(a1, a1)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[208, 201, 173])).
% 0.20/0.48 tff(210,plain,
% 0.20/0.48 (c(f(f(f(f(f(a1, a1), a1), a1), f(a1, a1)), a1))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[209, 54])).
% 0.20/0.48 tff(211,plain,
% 0.20/0.48 (((~![X: $i] : ((~c(X)) | (~d2(X)))) | ((~c(f(f(f(f(f(a1, a1), a1), a1), f(a1, a1)), a1))) | (~d2(f(f(f(f(f(a1, a1), a1), a1), f(a1, a1)), a1))))) <=> ((~![X: $i] : ((~c(X)) | (~d2(X)))) | (~c(f(f(f(f(f(a1, a1), a1), a1), f(a1, a1)), a1))) | (~d2(f(f(f(f(f(a1, a1), a1), a1), f(a1, a1)), a1))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(212,plain,
% 0.20/0.48 ((~![X: $i] : ((~c(X)) | (~d2(X)))) | ((~c(f(f(f(f(f(a1, a1), a1), a1), f(a1, a1)), a1))) | (~d2(f(f(f(f(f(a1, a1), a1), a1), f(a1, a1)), a1))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(213,plain,
% 0.20/0.48 ((~![X: $i] : ((~c(X)) | (~d2(X)))) | (~c(f(f(f(f(f(a1, a1), a1), a1), f(a1, a1)), a1))) | (~d2(f(f(f(f(f(a1, a1), a1), a1), f(a1, a1)), a1)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.20/0.48 tff(214,plain,
% 0.20/0.48 (~d2(f(f(f(f(f(a1, a1), a1), a1), f(a1, a1)), a1))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[213, 76, 210])).
% 0.20/0.48 tff(215,plain,
% 0.20/0.48 (~d2(f(f(f(f(f(f(a1, a1), a1), a1), a1), a1), a1))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[214, 42])).
% 0.20/0.48 tff(216,plain,
% 0.20/0.48 (d1(f(f(f(f(f(a1, a1), a1), a1), f(a1, a1)), a1)) <=> d1(f(f(f(f(f(f(a1, a1), a1), a1), a1), a1), a1))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[40])).
% 0.20/0.48 tff(217,plain,
% 0.20/0.48 ((~d1(f(f(f(f(f(a1, a1), a1), a1), f(a1, a1)), a1))) <=> (~d1(f(f(f(f(f(f(a1, a1), a1), a1), a1), a1), a1)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[216])).
% 0.20/0.48 tff(218,plain,
% 0.20/0.48 (((~![X: $i] : ((~c(X)) | (~d1(X)))) | ((~c(f(f(f(f(f(a1, a1), a1), a1), f(a1, a1)), a1))) | (~d1(f(f(f(f(f(a1, a1), a1), a1), f(a1, a1)), a1))))) <=> ((~![X: $i] : ((~c(X)) | (~d1(X)))) | (~c(f(f(f(f(f(a1, a1), a1), a1), f(a1, a1)), a1))) | (~d1(f(f(f(f(f(a1, a1), a1), a1), f(a1, a1)), a1))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(219,plain,
% 0.20/0.48 ((~![X: $i] : ((~c(X)) | (~d1(X)))) | ((~c(f(f(f(f(f(a1, a1), a1), a1), f(a1, a1)), a1))) | (~d1(f(f(f(f(f(a1, a1), a1), a1), f(a1, a1)), a1))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(220,plain,
% 0.20/0.48 ((~![X: $i] : ((~c(X)) | (~d1(X)))) | (~c(f(f(f(f(f(a1, a1), a1), a1), f(a1, a1)), a1))) | (~d1(f(f(f(f(f(a1, a1), a1), a1), f(a1, a1)), a1)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.20/0.48 tff(221,plain,
% 0.20/0.48 (~d1(f(f(f(f(f(a1, a1), a1), a1), f(a1, a1)), a1))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[220, 87, 210])).
% 0.20/0.48 tff(222,plain,
% 0.20/0.48 (~d1(f(f(f(f(f(f(a1, a1), a1), a1), a1), a1), a1))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[221, 217])).
% 0.20/0.48 tff(223,plain,
% 0.20/0.48 (((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(a1)) | (~c(f(f(f(f(f(a1, a1), a1), a1), a1), a1))) | d1(f(f(f(f(f(f(a1, a1), a1), a1), a1), a1), a1)) | d2(f(f(f(f(f(f(a1, a1), a1), a1), a1), a1), a1)))) <=> ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | (~c(a1)) | (~c(f(f(f(f(f(a1, a1), a1), a1), a1), a1))) | d1(f(f(f(f(f(f(a1, a1), a1), a1), a1), a1), a1)) | d2(f(f(f(f(f(f(a1, a1), a1), a1), a1), a1), a1)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(224,plain,
% 0.20/0.48 (((~c(f(f(f(f(f(a1, a1), a1), a1), a1), a1))) | (~c(a1)) | d1(f(f(f(f(f(f(a1, a1), a1), a1), a1), a1), a1)) | d2(f(f(f(f(f(f(a1, a1), a1), a1), a1), a1), a1))) <=> ((~c(a1)) | (~c(f(f(f(f(f(a1, a1), a1), a1), a1), a1))) | d1(f(f(f(f(f(f(a1, a1), a1), a1), a1), a1), a1)) | d2(f(f(f(f(f(f(a1, a1), a1), a1), a1), a1), a1)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(225,plain,
% 0.20/0.48 (((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(f(f(f(f(a1, a1), a1), a1), a1), a1))) | (~c(a1)) | d1(f(f(f(f(f(f(a1, a1), a1), a1), a1), a1), a1)) | d2(f(f(f(f(f(f(a1, a1), a1), a1), a1), a1), a1)))) <=> ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(a1)) | (~c(f(f(f(f(f(a1, a1), a1), a1), a1), a1))) | d1(f(f(f(f(f(f(a1, a1), a1), a1), a1), a1), a1)) | d2(f(f(f(f(f(f(a1, a1), a1), a1), a1), a1), a1))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[224])).
% 0.20/0.48 tff(226,plain,
% 0.20/0.48 (((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(f(f(f(f(a1, a1), a1), a1), a1), a1))) | (~c(a1)) | d1(f(f(f(f(f(f(a1, a1), a1), a1), a1), a1), a1)) | d2(f(f(f(f(f(f(a1, a1), a1), a1), a1), a1), a1)))) <=> ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | (~c(a1)) | (~c(f(f(f(f(f(a1, a1), a1), a1), a1), a1))) | d1(f(f(f(f(f(f(a1, a1), a1), a1), a1), a1), a1)) | d2(f(f(f(f(f(f(a1, a1), a1), a1), a1), a1), a1)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[225, 223])).
% 0.20/0.49 tff(227,plain,
% 0.20/0.49 ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(f(f(f(f(a1, a1), a1), a1), a1), a1))) | (~c(a1)) | d1(f(f(f(f(f(f(a1, a1), a1), a1), a1), a1), a1)) | d2(f(f(f(f(f(f(a1, a1), a1), a1), a1), a1), a1)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(228,plain,
% 0.20/0.49 ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | (~c(a1)) | (~c(f(f(f(f(f(a1, a1), a1), a1), a1), a1))) | d1(f(f(f(f(f(f(a1, a1), a1), a1), a1), a1), a1)) | d2(f(f(f(f(f(f(a1, a1), a1), a1), a1), a1), a1))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[227, 226])).
% 0.20/0.49 tff(229,plain,
% 0.20/0.49 ((~c(f(f(f(f(f(a1, a1), a1), a1), a1), a1))) | d1(f(f(f(f(f(f(a1, a1), a1), a1), a1), a1), a1)) | d2(f(f(f(f(f(f(a1, a1), a1), a1), a1), a1), a1))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[228, 134, 131])).
% 0.20/0.49 tff(230,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[229, 222, 215, 37])).
% 0.20/0.49 tff(231,plain,(~d1(f(f(a1, a1), a1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(232,plain,
% 0.20/0.49 (((~![X: $i] : ((~c(X)) | (~d2(X)))) | ((~c(f(f(f(a1, a1), a1), a1))) | (~d2(f(f(f(a1, a1), a1), a1))))) <=> ((~![X: $i] : ((~c(X)) | (~d2(X)))) | (~c(f(f(f(a1, a1), a1), a1))) | (~d2(f(f(f(a1, a1), a1), a1))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(233,plain,
% 0.20/0.49 ((~![X: $i] : ((~c(X)) | (~d2(X)))) | ((~c(f(f(f(a1, a1), a1), a1))) | (~d2(f(f(f(a1, a1), a1), a1))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(234,plain,
% 0.20/0.49 ((~![X: $i] : ((~c(X)) | (~d2(X)))) | (~c(f(f(f(a1, a1), a1), a1))) | (~d2(f(f(f(a1, a1), a1), a1)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[233, 232])).
% 0.20/0.49 tff(235,plain,
% 0.20/0.49 (~d2(f(f(f(a1, a1), a1), a1))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[234, 76, 144])).
% 0.20/0.49 tff(236,plain,
% 0.20/0.49 (((~![X: $i] : ((~c(X)) | (~d1(X)))) | ((~c(f(f(f(a1, a1), a1), a1))) | (~d1(f(f(f(a1, a1), a1), a1))))) <=> ((~![X: $i] : ((~c(X)) | (~d1(X)))) | (~c(f(f(f(a1, a1), a1), a1))) | (~d1(f(f(f(a1, a1), a1), a1))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(237,plain,
% 0.20/0.49 ((~![X: $i] : ((~c(X)) | (~d1(X)))) | ((~c(f(f(f(a1, a1), a1), a1))) | (~d1(f(f(f(a1, a1), a1), a1))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(238,plain,
% 0.20/0.49 ((~![X: $i] : ((~c(X)) | (~d1(X)))) | (~c(f(f(f(a1, a1), a1), a1))) | (~d1(f(f(f(a1, a1), a1), a1)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[237, 236])).
% 0.20/0.49 tff(239,plain,
% 0.20/0.49 (~d1(f(f(f(a1, a1), a1), a1))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[238, 87, 144])).
% 0.20/0.49 tff(240,plain,
% 0.20/0.49 (((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(a1)) | d1(f(f(f(a1, a1), a1), a1)) | (~c(f(f(a1, a1), a1))) | d2(f(f(f(a1, a1), a1), a1)))) <=> ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | (~c(a1)) | d1(f(f(f(a1, a1), a1), a1)) | (~c(f(f(a1, a1), a1))) | d2(f(f(f(a1, a1), a1), a1)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(241,plain,
% 0.20/0.49 (((~c(f(f(a1, a1), a1))) | (~c(a1)) | d1(f(f(f(a1, a1), a1), a1)) | d2(f(f(f(a1, a1), a1), a1))) <=> ((~c(a1)) | d1(f(f(f(a1, a1), a1), a1)) | (~c(f(f(a1, a1), a1))) | d2(f(f(f(a1, a1), a1), a1)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(242,plain,
% 0.20/0.49 (((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(f(a1, a1), a1))) | (~c(a1)) | d1(f(f(f(a1, a1), a1), a1)) | d2(f(f(f(a1, a1), a1), a1)))) <=> ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(a1)) | d1(f(f(f(a1, a1), a1), a1)) | (~c(f(f(a1, a1), a1))) | d2(f(f(f(a1, a1), a1), a1))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[241])).
% 0.20/0.49 tff(243,plain,
% 0.20/0.49 (((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(f(a1, a1), a1))) | (~c(a1)) | d1(f(f(f(a1, a1), a1), a1)) | d2(f(f(f(a1, a1), a1), a1)))) <=> ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | (~c(a1)) | d1(f(f(f(a1, a1), a1), a1)) | (~c(f(f(a1, a1), a1))) | d2(f(f(f(a1, a1), a1), a1)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[242, 240])).
% 0.20/0.49 tff(244,plain,
% 0.20/0.49 ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | ((~c(f(f(a1, a1), a1))) | (~c(a1)) | d1(f(f(f(a1, a1), a1), a1)) | d2(f(f(f(a1, a1), a1), a1)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(245,plain,
% 0.20/0.49 ((~![Y: $i, X: $i] : ((~c(X)) | (~c(Y)) | d1(f(X, Y)) | d2(f(X, Y)))) | (~c(a1)) | d1(f(f(f(a1, a1), a1), a1)) | (~c(f(f(a1, a1), a1))) | d2(f(f(f(a1, a1), a1), a1))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[244, 243])).
% 0.20/0.49 tff(246,plain,
% 0.20/0.49 (d1(f(f(f(a1, a1), a1), a1)) | (~c(f(f(a1, a1), a1))) | d2(f(f(f(a1, a1), a1), a1))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[245, 134, 131])).
% 0.20/0.49 tff(247,plain,
% 0.20/0.49 (~c(f(f(a1, a1), a1))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[246, 239, 235])).
% 0.20/0.49 tff(248,plain,
% 0.20/0.49 (^[X: $i] : refl((d2(X) | d1(X) | c(X)) <=> (d2(X) | d1(X) | c(X)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(249,plain,
% 0.20/0.49 (![X: $i] : (d2(X) | d1(X) | c(X)) <=> ![X: $i] : (d2(X) | d1(X) | c(X))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[248])).
% 0.20/0.49 tff(250,plain,
% 0.20/0.49 (![X: $i] : (d2(X) | d1(X) | c(X)) <=> ![X: $i] : (d2(X) | d1(X) | c(X))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(251,plain,
% 0.20/0.49 (^[X: $i] : rewrite(((c(X) | d1(X)) | d2(X)) <=> (d2(X) | d1(X) | c(X)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(252,plain,
% 0.20/0.49 (![X: $i] : ((c(X) | d1(X)) | d2(X)) <=> ![X: $i] : (d2(X) | d1(X) | c(X))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[251])).
% 0.20/0.49 tff(253,axiom,(![X: $i] : ((c(X) | d1(X)) | d2(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','partitions_union')).
% 0.20/0.49 tff(254,plain,
% 0.20/0.49 (![X: $i] : (d2(X) | d1(X) | c(X))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[253, 252])).
% 0.20/0.49 tff(255,plain,
% 0.20/0.49 (![X: $i] : (d2(X) | d1(X) | c(X))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[254, 250])).
% 0.20/0.49 tff(256,plain,(
% 0.20/0.49 ![X: $i] : (d2(X) | d1(X) | c(X))),
% 0.20/0.49 inference(skolemize,[status(sab)],[255])).
% 0.20/0.49 tff(257,plain,
% 0.20/0.49 (![X: $i] : (d2(X) | d1(X) | c(X))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[256, 249])).
% 0.20/0.49 tff(258,plain,
% 0.20/0.49 (((~![X: $i] : (d2(X) | d1(X) | c(X))) | (c(f(f(a1, a1), a1)) | d2(f(f(a1, a1), a1)) | d1(f(f(a1, a1), a1)))) <=> ((~![X: $i] : (d2(X) | d1(X) | c(X))) | c(f(f(a1, a1), a1)) | d2(f(f(a1, a1), a1)) | d1(f(f(a1, a1), a1)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(259,plain,
% 0.20/0.49 ((d2(f(f(a1, a1), a1)) | d1(f(f(a1, a1), a1)) | c(f(f(a1, a1), a1))) <=> (c(f(f(a1, a1), a1)) | d2(f(f(a1, a1), a1)) | d1(f(f(a1, a1), a1)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(260,plain,
% 0.20/0.49 (((~![X: $i] : (d2(X) | d1(X) | c(X))) | (d2(f(f(a1, a1), a1)) | d1(f(f(a1, a1), a1)) | c(f(f(a1, a1), a1)))) <=> ((~![X: $i] : (d2(X) | d1(X) | c(X))) | (c(f(f(a1, a1), a1)) | d2(f(f(a1, a1), a1)) | d1(f(f(a1, a1), a1))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[259])).
% 0.20/0.49 tff(261,plain,
% 0.20/0.49 (((~![X: $i] : (d2(X) | d1(X) | c(X))) | (d2(f(f(a1, a1), a1)) | d1(f(f(a1, a1), a1)) | c(f(f(a1, a1), a1)))) <=> ((~![X: $i] : (d2(X) | d1(X) | c(X))) | c(f(f(a1, a1), a1)) | d2(f(f(a1, a1), a1)) | d1(f(f(a1, a1), a1)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[260, 258])).
% 0.20/0.49 tff(262,plain,
% 0.20/0.49 ((~![X: $i] : (d2(X) | d1(X) | c(X))) | (d2(f(f(a1, a1), a1)) | d1(f(f(a1, a1), a1)) | c(f(f(a1, a1), a1)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(263,plain,
% 0.20/0.49 ((~![X: $i] : (d2(X) | d1(X) | c(X))) | c(f(f(a1, a1), a1)) | d2(f(f(a1, a1), a1)) | d1(f(f(a1, a1), a1))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[262, 261])).
% 0.20/0.49 tff(264,plain,
% 0.20/0.49 (d2(f(f(a1, a1), a1)) | d1(f(f(a1, a1), a1))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[263, 257, 247])).
% 0.20/0.49 tff(265,plain,
% 0.20/0.49 (d2(f(f(a1, a1), a1))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[264, 231])).
% 0.20/0.49 tff(266,plain,
% 0.20/0.49 (((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(f(f(a1, a1), a1))) | c(f(f(f(a1, a1), a1), f(f(a1, a1), a1))))) <=> ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | (~d2(f(f(a1, a1), a1))) | c(f(f(f(a1, a1), a1), f(f(a1, a1), a1))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(267,plain,
% 0.20/0.49 (((~d2(f(f(a1, a1), a1))) | c(f(f(f(a1, a1), a1), f(f(a1, a1), a1))) | (~d2(f(f(a1, a1), a1)))) <=> ((~d2(f(f(a1, a1), a1))) | c(f(f(f(a1, a1), a1), f(f(a1, a1), a1))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(268,plain,
% 0.20/0.49 (((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(f(f(a1, a1), a1))) | c(f(f(f(a1, a1), a1), f(f(a1, a1), a1))) | (~d2(f(f(a1, a1), a1))))) <=> ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(f(f(a1, a1), a1))) | c(f(f(f(a1, a1), a1), f(f(a1, a1), a1)))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[267])).
% 0.20/0.49 tff(269,plain,
% 0.20/0.49 (((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(f(f(a1, a1), a1))) | c(f(f(f(a1, a1), a1), f(f(a1, a1), a1))) | (~d2(f(f(a1, a1), a1))))) <=> ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | (~d2(f(f(a1, a1), a1))) | c(f(f(f(a1, a1), a1), f(f(a1, a1), a1))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[268, 266])).
% 0.20/0.49 tff(270,plain,
% 0.20/0.49 ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(f(f(a1, a1), a1))) | c(f(f(f(a1, a1), a1), f(f(a1, a1), a1))) | (~d2(f(f(a1, a1), a1))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(271,plain,
% 0.20/0.49 ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | (~d2(f(f(a1, a1), a1))) | c(f(f(f(a1, a1), a1), f(f(a1, a1), a1)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[270, 269])).
% 0.20/0.49 tff(272,plain,
% 0.20/0.49 ((~d2(f(f(a1, a1), a1))) | c(f(f(f(a1, a1), a1), f(f(a1, a1), a1)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[271, 105])).
% 0.20/0.49 tff(273,plain,
% 0.20/0.49 (c(f(f(f(a1, a1), a1), f(f(a1, a1), a1)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[272, 265])).
% 0.20/0.49 tff(274,plain,
% 0.20/0.49 (c(f(f(f(f(f(a1, a1), a1), a1), a1), a1))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[273, 17])).
% 0.20/0.49 tff(275,plain,
% 0.20/0.49 ((~![Z: $i, Y: $i, X: $i] : (f(X, f(Y, Z)) = f(f(X, Y), Z))) | (f(f(f(a1, a1), a1), f(a1, a1)) = f(f(f(f(a1, a1), a1), a1), a1))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(276,plain,
% 0.20/0.49 (f(f(f(a1, a1), a1), f(a1, a1)) = f(f(f(f(a1, a1), a1), a1), a1)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[275, 7])).
% 0.20/0.49 tff(277,plain,
% 0.20/0.49 (c(f(f(f(a1, a1), a1), f(a1, a1))) <=> c(f(f(f(f(a1, a1), a1), a1), a1))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[276])).
% 0.20/0.49 tff(278,plain,
% 0.20/0.49 (c(f(f(f(f(a1, a1), a1), a1), a1)) <=> c(f(f(f(a1, a1), a1), f(a1, a1)))),
% 0.20/0.49 inference(symmetry,[status(thm)],[277])).
% 0.20/0.49 tff(279,plain,
% 0.20/0.49 ((~c(f(f(f(f(a1, a1), a1), a1), a1))) <=> (~c(f(f(f(a1, a1), a1), f(a1, a1))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[278])).
% 0.20/0.49 tff(280,assumption,(~c(f(f(f(f(a1, a1), a1), a1), a1))), introduced(assumption)).
% 0.20/0.49 tff(281,plain,
% 0.20/0.49 (~c(f(f(f(a1, a1), a1), f(a1, a1)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[280, 279])).
% 0.20/0.49 tff(282,assumption,(d2(f(f(a1, a1), a1))), introduced(assumption)).
% 0.20/0.49 tff(283,assumption,(d2(f(a1, a1))), introduced(assumption)).
% 0.20/0.49 tff(284,plain,
% 0.20/0.49 (((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(f(a1, a1))) | (~d2(f(f(a1, a1), a1))) | c(f(f(f(a1, a1), a1), f(a1, a1))))) <=> ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | (~d2(f(a1, a1))) | (~d2(f(f(a1, a1), a1))) | c(f(f(f(a1, a1), a1), f(a1, a1))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(285,plain,
% 0.20/0.49 (((~d2(f(f(a1, a1), a1))) | c(f(f(f(a1, a1), a1), f(a1, a1))) | (~d2(f(a1, a1)))) <=> ((~d2(f(a1, a1))) | (~d2(f(f(a1, a1), a1))) | c(f(f(f(a1, a1), a1), f(a1, a1))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(286,plain,
% 0.20/0.49 (((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(f(f(a1, a1), a1))) | c(f(f(f(a1, a1), a1), f(a1, a1))) | (~d2(f(a1, a1))))) <=> ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(f(a1, a1))) | (~d2(f(f(a1, a1), a1))) | c(f(f(f(a1, a1), a1), f(a1, a1)))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[285])).
% 0.20/0.49 tff(287,plain,
% 0.20/0.49 (((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(f(f(a1, a1), a1))) | c(f(f(f(a1, a1), a1), f(a1, a1))) | (~d2(f(a1, a1))))) <=> ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | (~d2(f(a1, a1))) | (~d2(f(f(a1, a1), a1))) | c(f(f(f(a1, a1), a1), f(a1, a1))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[286, 284])).
% 0.20/0.50 tff(288,plain,
% 0.20/0.50 ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(f(f(a1, a1), a1))) | c(f(f(f(a1, a1), a1), f(a1, a1))) | (~d2(f(a1, a1))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(289,plain,
% 0.20/0.50 ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | (~d2(f(a1, a1))) | (~d2(f(f(a1, a1), a1))) | c(f(f(f(a1, a1), a1), f(a1, a1)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[288, 287])).
% 0.20/0.50 tff(290,plain,
% 0.20/0.50 (c(f(f(f(a1, a1), a1), f(a1, a1)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[289, 105, 283, 282])).
% 0.20/0.50 tff(291,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[290, 281])).
% 0.20/0.50 tff(292,plain,(c(f(f(f(f(a1, a1), a1), a1), a1)) | (~d2(f(a1, a1))) | (~d2(f(f(a1, a1), a1)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(293,plain,
% 0.20/0.50 ((~d2(f(a1, a1))) | (~d2(f(f(a1, a1), a1)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[292, 193])).
% 0.20/0.50 tff(294,plain,
% 0.20/0.50 (~d2(f(a1, a1))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[293, 265])).
% 0.20/0.50 tff(295,plain,
% 0.20/0.50 (d1(f(a1, a1))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[141, 294])).
% 0.20/0.50 tff(296,assumption,(~c(f(f(f(f(a1, a1), a1), a1), f(f(f(a1, a1), a1), a1)))), introduced(assumption)).
% 0.20/0.50 tff(297,plain,
% 0.20/0.50 (~c(f(f(f(f(f(a1, a1), a1), a1), a1), f(f(a1, a1), a1)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[296, 68])).
% 0.20/0.50 tff(298,assumption,(d2(f(f(f(f(a1, a1), a1), a1), a1))), introduced(assumption)).
% 0.20/0.50 tff(299,plain,
% 0.20/0.50 (((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(f(f(a1, a1), a1))) | (~d2(f(f(f(f(a1, a1), a1), a1), a1))) | c(f(f(f(f(f(a1, a1), a1), a1), a1), f(f(a1, a1), a1))))) <=> ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | (~d2(f(f(a1, a1), a1))) | (~d2(f(f(f(f(a1, a1), a1), a1), a1))) | c(f(f(f(f(f(a1, a1), a1), a1), a1), f(f(a1, a1), a1))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(300,plain,
% 0.20/0.50 (((~d2(f(f(f(f(a1, a1), a1), a1), a1))) | c(f(f(f(f(f(a1, a1), a1), a1), a1), f(f(a1, a1), a1))) | (~d2(f(f(a1, a1), a1)))) <=> ((~d2(f(f(a1, a1), a1))) | (~d2(f(f(f(f(a1, a1), a1), a1), a1))) | c(f(f(f(f(f(a1, a1), a1), a1), a1), f(f(a1, a1), a1))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(301,plain,
% 0.20/0.50 (((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(f(f(f(f(a1, a1), a1), a1), a1))) | c(f(f(f(f(f(a1, a1), a1), a1), a1), f(f(a1, a1), a1))) | (~d2(f(f(a1, a1), a1))))) <=> ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(f(f(a1, a1), a1))) | (~d2(f(f(f(f(a1, a1), a1), a1), a1))) | c(f(f(f(f(f(a1, a1), a1), a1), a1), f(f(a1, a1), a1)))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[300])).
% 0.20/0.50 tff(302,plain,
% 0.20/0.50 (((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(f(f(f(f(a1, a1), a1), a1), a1))) | c(f(f(f(f(f(a1, a1), a1), a1), a1), f(f(a1, a1), a1))) | (~d2(f(f(a1, a1), a1))))) <=> ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | (~d2(f(f(a1, a1), a1))) | (~d2(f(f(f(f(a1, a1), a1), a1), a1))) | c(f(f(f(f(f(a1, a1), a1), a1), a1), f(f(a1, a1), a1))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[301, 299])).
% 0.20/0.50 tff(303,plain,
% 0.20/0.50 ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | ((~d2(f(f(f(f(a1, a1), a1), a1), a1))) | c(f(f(f(f(f(a1, a1), a1), a1), a1), f(f(a1, a1), a1))) | (~d2(f(f(a1, a1), a1))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(304,plain,
% 0.20/0.50 ((~![Y: $i, X: $i] : ((~d2(X)) | c(f(X, Y)) | (~d2(Y)))) | (~d2(f(f(a1, a1), a1))) | (~d2(f(f(f(f(a1, a1), a1), a1), a1))) | c(f(f(f(f(f(a1, a1), a1), a1), a1), f(f(a1, a1), a1)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[303, 302])).
% 0.20/0.50 tff(305,plain,
% 0.20/0.50 (c(f(f(f(f(f(a1, a1), a1), a1), a1), f(f(a1, a1), a1)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[304, 105, 282, 298])).
% 0.20/0.50 tff(306,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[305, 297])).
% 0.20/0.50 tff(307,plain,(c(f(f(f(f(a1, a1), a1), a1), f(f(f(a1, a1), a1), a1))) | (~d2(f(f(a1, a1), a1))) | (~d2(f(f(f(f(a1, a1), a1), a1), a1)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(308,plain,
% 0.20/0.50 ((~d2(f(f(a1, a1), a1))) | (~d2(f(f(f(f(a1, a1), a1), a1), a1)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[307, 154])).
% 0.20/0.50 tff(309,plain,
% 0.20/0.50 (~d2(f(f(f(f(a1, a1), a1), a1), a1))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[308, 265])).
% 0.20/0.50 tff(310,plain,
% 0.20/0.50 (d1(f(f(f(f(a1, a1), a1), a1), a1))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[172, 309])).
% 0.20/0.50 tff(311,plain,
% 0.20/0.50 (((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | ((~d1(f(a1, a1))) | (~d1(f(f(f(f(a1, a1), a1), a1), a1))) | c(f(f(f(f(f(a1, a1), a1), a1), a1), f(a1, a1))))) <=> ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | (~d1(f(a1, a1))) | (~d1(f(f(f(f(a1, a1), a1), a1), a1))) | c(f(f(f(f(f(a1, a1), a1), a1), a1), f(a1, a1))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(312,plain,
% 0.20/0.50 (((~d1(f(f(f(f(a1, a1), a1), a1), a1))) | (~d1(f(a1, a1))) | c(f(f(f(f(f(a1, a1), a1), a1), a1), f(a1, a1)))) <=> ((~d1(f(a1, a1))) | (~d1(f(f(f(f(a1, a1), a1), a1), a1))) | c(f(f(f(f(f(a1, a1), a1), a1), a1), f(a1, a1))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(313,plain,
% 0.20/0.50 (((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | ((~d1(f(f(f(f(a1, a1), a1), a1), a1))) | (~d1(f(a1, a1))) | c(f(f(f(f(f(a1, a1), a1), a1), a1), f(a1, a1))))) <=> ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | ((~d1(f(a1, a1))) | (~d1(f(f(f(f(a1, a1), a1), a1), a1))) | c(f(f(f(f(f(a1, a1), a1), a1), a1), f(a1, a1)))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[312])).
% 0.20/0.50 tff(314,plain,
% 0.20/0.50 (((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | ((~d1(f(f(f(f(a1, a1), a1), a1), a1))) | (~d1(f(a1, a1))) | c(f(f(f(f(f(a1, a1), a1), a1), a1), f(a1, a1))))) <=> ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | (~d1(f(a1, a1))) | (~d1(f(f(f(f(a1, a1), a1), a1), a1))) | c(f(f(f(f(f(a1, a1), a1), a1), a1), f(a1, a1))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[313, 311])).
% 0.20/0.50 tff(315,plain,
% 0.20/0.50 ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | ((~d1(f(f(f(f(a1, a1), a1), a1), a1))) | (~d1(f(a1, a1))) | c(f(f(f(f(f(a1, a1), a1), a1), a1), f(a1, a1))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(316,plain,
% 0.20/0.50 ((~![Y: $i, X: $i] : ((~d1(X)) | (~d1(Y)) | c(f(X, Y)))) | (~d1(f(a1, a1))) | (~d1(f(f(f(f(a1, a1), a1), a1), a1))) | c(f(f(f(f(f(a1, a1), a1), a1), a1), f(a1, a1)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[315, 314])).
% 0.20/0.50 tff(317,plain,
% 0.20/0.50 ((~d1(f(a1, a1))) | (~d1(f(f(f(f(a1, a1), a1), a1), a1))) | c(f(f(f(f(f(a1, a1), a1), a1), a1), f(a1, a1)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[316, 28])).
% 0.20/0.50 tff(318,plain,
% 0.20/0.50 (c(f(f(f(f(f(a1, a1), a1), a1), a1), f(a1, a1)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[317, 310, 295])).
% 0.20/0.50 tff(319,plain,
% 0.20/0.50 (c(f(f(f(f(f(a1, a1), a1), a1), f(a1, a1)), a1))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[318, 54])).
% 0.20/0.50 tff(320,plain,
% 0.20/0.50 (~d2(f(f(f(f(f(a1, a1), a1), a1), f(a1, a1)), a1))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[213, 76, 319])).
% 0.20/0.50 tff(321,plain,
% 0.20/0.50 (~d2(f(f(f(f(f(f(a1, a1), a1), a1), a1), a1), a1))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[320, 42])).
% 0.20/0.50 tff(322,plain,
% 0.20/0.50 (~d1(f(f(f(f(f(a1, a1), a1), a1), f(a1, a1)), a1))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[220, 87, 319])).
% 0.20/0.50 tff(323,plain,
% 0.20/0.50 (~d1(f(f(f(f(f(f(a1, a1), a1), a1), a1), a1), a1))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[322, 217])).
% 0.20/0.50 tff(324,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[229, 323, 321, 274])).
% 0.20/0.50 % SZS output end Proof
%------------------------------------------------------------------------------