TSTP Solution File: SYN685-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN685-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 23:56:56 EDT 2022
% Result : Unsatisfiable 72.25s 46.77s
% Output : Proof 72.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN685-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n004.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 Sep 5 06:29:04 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.
% 72.25/46.77 % SZS status Unsatisfiable
% 72.25/46.77 % SZS output start Proof
% 72.25/46.77 tff(p2_type, type, (
% 72.25/46.77 p2: ( $i * $i ) > $o)).
% 72.25/46.77 tff(f11_type, type, (
% 72.25/46.77 f11: ( $i * $i ) > $i)).
% 72.25/46.77 tff(c34_type, type, (
% 72.25/46.77 c34: $i)).
% 72.25/46.77 tff(f4_type, type, (
% 72.25/46.77 f4: $i > $i)).
% 72.25/46.77 tff(c36_type, type, (
% 72.25/46.77 c36: $i)).
% 72.25/46.77 tff(c32_type, type, (
% 72.25/46.77 c32: $i)).
% 72.25/46.77 tff(p3_type, type, (
% 72.25/46.77 p3: ( $i * $i ) > $o)).
% 72.25/46.77 tff(p10_type, type, (
% 72.25/46.77 p10: ( $i * $i ) > $o)).
% 72.25/46.77 tff(p25_type, type, (
% 72.25/46.77 p25: ( $i * $i ) > $o)).
% 72.25/46.77 tff(c33_type, type, (
% 72.25/46.77 c33: $i)).
% 72.25/46.77 tff(f18_type, type, (
% 72.25/46.77 f18: ( $i * $i ) > $i)).
% 72.25/46.77 tff(f9_type, type, (
% 72.25/46.77 f9: $i > $i)).
% 72.25/46.77 tff(f17_type, type, (
% 72.25/46.77 f17: $i > $i)).
% 72.25/46.77 tff(c31_type, type, (
% 72.25/46.77 c31: $i)).
% 72.25/46.77 tff(1,plain,
% 72.25/46.77 (^[X83: $i] : refl(p3(X83, X83) <=> p3(X83, X83))),
% 72.25/46.77 inference(bind,[status(th)],[])).
% 72.25/46.77 tff(2,plain,
% 72.25/46.77 (![X83: $i] : p3(X83, X83) <=> ![X83: $i] : p3(X83, X83)),
% 72.25/46.77 inference(quant_intro,[status(thm)],[1])).
% 72.25/46.77 tff(3,plain,
% 72.25/46.77 (![X83: $i] : p3(X83, X83) <=> ![X83: $i] : p3(X83, X83)),
% 72.25/46.77 inference(rewrite,[status(thm)],[])).
% 72.25/46.77 tff(4,axiom,(![X83: $i] : p3(X83, X83)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3_5')).
% 72.25/46.77 tff(5,plain,
% 72.25/46.77 (![X83: $i] : p3(X83, X83)),
% 72.25/46.77 inference(modus_ponens,[status(thm)],[4, 3])).
% 72.25/46.77 tff(6,plain,(
% 72.25/46.77 ![X83: $i] : p3(X83, X83)),
% 72.25/46.77 inference(skolemize,[status(sab)],[5])).
% 72.25/46.77 tff(7,plain,
% 72.25/46.77 (![X83: $i] : p3(X83, X83)),
% 72.25/46.77 inference(modus_ponens,[status(thm)],[6, 2])).
% 72.25/46.77 tff(8,plain,
% 72.25/46.77 ((~![X83: $i] : p3(X83, X83)) | p3(f4(c36), f4(c36))),
% 72.25/46.77 inference(quant_inst,[status(thm)],[])).
% 72.25/46.77 tff(9,plain,
% 72.25/46.77 (p3(f4(c36), f4(c36))),
% 72.25/46.77 inference(unit_resolution,[status(thm)],[8, 7])).
% 72.25/46.77 tff(10,assumption,(~p10(c34, c34)), introduced(assumption)).
% 72.25/46.77 tff(11,plain,
% 72.25/46.77 (^[X0: $i] : refl(p10(X0, X0) <=> p10(X0, X0))),
% 72.25/46.77 inference(bind,[status(th)],[])).
% 72.25/46.77 tff(12,plain,
% 72.25/46.77 (![X0: $i] : p10(X0, X0) <=> ![X0: $i] : p10(X0, X0)),
% 72.25/46.77 inference(quant_intro,[status(thm)],[11])).
% 72.25/46.77 tff(13,plain,
% 72.25/46.77 (![X0: $i] : p10(X0, X0) <=> ![X0: $i] : p10(X0, X0)),
% 72.25/46.77 inference(rewrite,[status(thm)],[])).
% 72.25/46.77 tff(14,axiom,(![X0: $i] : p10(X0, X0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p10_2')).
% 72.25/46.77 tff(15,plain,
% 72.25/46.77 (![X0: $i] : p10(X0, X0)),
% 72.25/46.77 inference(modus_ponens,[status(thm)],[14, 13])).
% 72.25/46.77 tff(16,plain,(
% 72.25/46.77 ![X0: $i] : p10(X0, X0)),
% 72.25/46.77 inference(skolemize,[status(sab)],[15])).
% 72.25/46.77 tff(17,plain,
% 72.25/46.77 (![X0: $i] : p10(X0, X0)),
% 72.25/46.77 inference(modus_ponens,[status(thm)],[16, 12])).
% 72.25/46.77 tff(18,plain,
% 72.25/46.77 ((~![X0: $i] : p10(X0, X0)) | p10(c34, c34)),
% 72.25/46.77 inference(quant_inst,[status(thm)],[])).
% 72.25/46.77 tff(19,plain,
% 72.25/46.77 ($false),
% 72.25/46.77 inference(unit_resolution,[status(thm)],[18, 17, 10])).
% 72.25/46.77 tff(20,plain,(p10(c34, c34)), inference(lemma,lemma(discharge,[]))).
% 72.25/46.77 tff(21,plain,
% 72.25/46.77 (^[X31: $i, X32: $i, X34: $i, X33: $i] : refl(((~p10(X32, X34)) | (~p3(X31, X33)) | p2(f11(X31, X32), f11(X33, X34))) <=> ((~p10(X32, X34)) | (~p3(X31, X33)) | p2(f11(X31, X32), f11(X33, X34))))),
% 72.25/46.77 inference(bind,[status(th)],[])).
% 72.25/46.77 tff(22,plain,
% 72.25/46.77 (![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p10(X32, X34)) | (~p3(X31, X33)) | p2(f11(X31, X32), f11(X33, X34))) <=> ![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p10(X32, X34)) | (~p3(X31, X33)) | p2(f11(X31, X32), f11(X33, X34)))),
% 72.25/46.77 inference(quant_intro,[status(thm)],[21])).
% 72.25/46.77 tff(23,plain,
% 72.25/46.77 (![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p10(X32, X34)) | (~p3(X31, X33)) | p2(f11(X31, X32), f11(X33, X34))) <=> ![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p10(X32, X34)) | (~p3(X31, X33)) | p2(f11(X31, X32), f11(X33, X34)))),
% 72.25/46.77 inference(rewrite,[status(thm)],[])).
% 72.25/46.77 tff(24,plain,
% 72.25/46.77 (^[X31: $i, X32: $i, X34: $i, X33: $i] : trans(monotonicity(rewrite((p2(f11(X31, X32), f11(X33, X34)) | (~p10(X32, X34))) <=> ((~p10(X32, X34)) | p2(f11(X31, X32), f11(X33, X34)))), (((p2(f11(X31, X32), f11(X33, X34)) | (~p10(X32, X34))) | (~p3(X31, X33))) <=> (((~p10(X32, X34)) | p2(f11(X31, X32), f11(X33, X34))) | (~p3(X31, X33))))), rewrite((((~p10(X32, X34)) | p2(f11(X31, X32), f11(X33, X34))) | (~p3(X31, X33))) <=> ((~p10(X32, X34)) | (~p3(X31, X33)) | p2(f11(X31, X32), f11(X33, X34)))), (((p2(f11(X31, X32), f11(X33, X34)) | (~p10(X32, X34))) | (~p3(X31, X33))) <=> ((~p10(X32, X34)) | (~p3(X31, X33)) | p2(f11(X31, X32), f11(X33, X34)))))),
% 72.25/46.77 inference(bind,[status(th)],[])).
% 72.25/46.77 tff(25,plain,
% 72.25/46.77 (![X31: $i, X32: $i, X34: $i, X33: $i] : ((p2(f11(X31, X32), f11(X33, X34)) | (~p10(X32, X34))) | (~p3(X31, X33))) <=> ![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p10(X32, X34)) | (~p3(X31, X33)) | p2(f11(X31, X32), f11(X33, X34)))),
% 72.25/46.77 inference(quant_intro,[status(thm)],[24])).
% 72.25/46.77 tff(26,axiom,(![X31: $i, X32: $i, X34: $i, X33: $i] : ((p2(f11(X31, X32), f11(X33, X34)) | (~p10(X32, X34))) | (~p3(X31, X33)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_47')).
% 72.25/46.77 tff(27,plain,
% 72.25/46.77 (![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p10(X32, X34)) | (~p3(X31, X33)) | p2(f11(X31, X32), f11(X33, X34)))),
% 72.25/46.77 inference(modus_ponens,[status(thm)],[26, 25])).
% 72.25/46.77 tff(28,plain,
% 72.25/46.77 (![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p10(X32, X34)) | (~p3(X31, X33)) | p2(f11(X31, X32), f11(X33, X34)))),
% 72.25/46.77 inference(modus_ponens,[status(thm)],[27, 23])).
% 72.25/46.77 tff(29,plain,(
% 72.25/46.77 ![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p10(X32, X34)) | (~p3(X31, X33)) | p2(f11(X31, X32), f11(X33, X34)))),
% 72.25/46.77 inference(skolemize,[status(sab)],[28])).
% 72.25/46.77 tff(30,plain,
% 72.25/46.77 (![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p10(X32, X34)) | (~p3(X31, X33)) | p2(f11(X31, X32), f11(X33, X34)))),
% 72.25/46.77 inference(modus_ponens,[status(thm)],[29, 22])).
% 72.25/46.77 tff(31,plain,
% 72.25/46.77 (((~![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p10(X32, X34)) | (~p3(X31, X33)) | p2(f11(X31, X32), f11(X33, X34)))) | ((~p10(c34, c34)) | (~p3(f4(c36), f4(c36))) | p2(f11(f4(c36), c34), f11(f4(c36), c34)))) <=> ((~![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p10(X32, X34)) | (~p3(X31, X33)) | p2(f11(X31, X32), f11(X33, X34)))) | (~p10(c34, c34)) | (~p3(f4(c36), f4(c36))) | p2(f11(f4(c36), c34), f11(f4(c36), c34)))),
% 72.25/46.77 inference(rewrite,[status(thm)],[])).
% 72.25/46.77 tff(32,plain,
% 72.25/46.77 ((~![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p10(X32, X34)) | (~p3(X31, X33)) | p2(f11(X31, X32), f11(X33, X34)))) | ((~p10(c34, c34)) | (~p3(f4(c36), f4(c36))) | p2(f11(f4(c36), c34), f11(f4(c36), c34)))),
% 72.25/46.77 inference(quant_inst,[status(thm)],[])).
% 72.25/46.77 tff(33,plain,
% 72.25/46.77 ((~![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p10(X32, X34)) | (~p3(X31, X33)) | p2(f11(X31, X32), f11(X33, X34)))) | (~p10(c34, c34)) | (~p3(f4(c36), f4(c36))) | p2(f11(f4(c36), c34), f11(f4(c36), c34))),
% 72.25/46.77 inference(modus_ponens,[status(thm)],[32, 31])).
% 72.25/46.77 tff(34,plain,
% 72.25/46.77 (p2(f11(f4(c36), c34), f11(f4(c36), c34))),
% 72.25/46.77 inference(unit_resolution,[status(thm)],[33, 30, 20, 9])).
% 72.25/46.77 tff(35,plain,
% 72.25/46.77 (^[X35: $i] : refl(((~p25(c32, X35)) | (~p25(X35, c33)) | p2(f11(f4(X35), c34), f11(f4(c32), c34))) <=> ((~p25(c32, X35)) | (~p25(X35, c33)) | p2(f11(f4(X35), c34), f11(f4(c32), c34))))),
% 72.25/46.77 inference(bind,[status(th)],[])).
% 72.25/46.77 tff(36,plain,
% 72.25/46.77 (![X35: $i] : ((~p25(c32, X35)) | (~p25(X35, c33)) | p2(f11(f4(X35), c34), f11(f4(c32), c34))) <=> ![X35: $i] : ((~p25(c32, X35)) | (~p25(X35, c33)) | p2(f11(f4(X35), c34), f11(f4(c32), c34)))),
% 72.25/46.77 inference(quant_intro,[status(thm)],[35])).
% 72.25/46.77 tff(37,plain,
% 72.25/46.77 (![X35: $i] : ((~p25(c32, X35)) | (~p25(X35, c33)) | p2(f11(f4(X35), c34), f11(f4(c32), c34))) <=> ![X35: $i] : ((~p25(c32, X35)) | (~p25(X35, c33)) | p2(f11(f4(X35), c34), f11(f4(c32), c34)))),
% 72.25/46.77 inference(rewrite,[status(thm)],[])).
% 72.25/46.77 tff(38,plain,
% 72.25/46.77 (^[X35: $i] : trans(monotonicity(rewrite((p2(f11(f4(X35), c34), f11(f4(c32), c34)) | (~p25(X35, c33))) <=> ((~p25(X35, c33)) | p2(f11(f4(X35), c34), f11(f4(c32), c34)))), (((p2(f11(f4(X35), c34), f11(f4(c32), c34)) | (~p25(X35, c33))) | (~p25(c32, X35))) <=> (((~p25(X35, c33)) | p2(f11(f4(X35), c34), f11(f4(c32), c34))) | (~p25(c32, X35))))), rewrite((((~p25(X35, c33)) | p2(f11(f4(X35), c34), f11(f4(c32), c34))) | (~p25(c32, X35))) <=> ((~p25(c32, X35)) | (~p25(X35, c33)) | p2(f11(f4(X35), c34), f11(f4(c32), c34)))), (((p2(f11(f4(X35), c34), f11(f4(c32), c34)) | (~p25(X35, c33))) | (~p25(c32, X35))) <=> ((~p25(c32, X35)) | (~p25(X35, c33)) | p2(f11(f4(X35), c34), f11(f4(c32), c34)))))),
% 72.25/46.77 inference(bind,[status(th)],[])).
% 72.25/46.77 tff(39,plain,
% 72.25/46.77 (![X35: $i] : ((p2(f11(f4(X35), c34), f11(f4(c32), c34)) | (~p25(X35, c33))) | (~p25(c32, X35))) <=> ![X35: $i] : ((~p25(c32, X35)) | (~p25(X35, c33)) | p2(f11(f4(X35), c34), f11(f4(c32), c34)))),
% 72.25/46.77 inference(quant_intro,[status(thm)],[38])).
% 72.25/46.77 tff(40,axiom,(![X35: $i] : ((p2(f11(f4(X35), c34), f11(f4(c32), c34)) | (~p25(X35, c33))) | (~p25(c32, X35)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_50')).
% 72.25/46.77 tff(41,plain,
% 72.25/46.77 (![X35: $i] : ((~p25(c32, X35)) | (~p25(X35, c33)) | p2(f11(f4(X35), c34), f11(f4(c32), c34)))),
% 72.25/46.77 inference(modus_ponens,[status(thm)],[40, 39])).
% 72.25/46.77 tff(42,plain,
% 72.25/46.77 (![X35: $i] : ((~p25(c32, X35)) | (~p25(X35, c33)) | p2(f11(f4(X35), c34), f11(f4(c32), c34)))),
% 72.25/46.77 inference(modus_ponens,[status(thm)],[41, 37])).
% 72.25/46.77 tff(43,plain,(
% 72.25/46.77 ![X35: $i] : ((~p25(c32, X35)) | (~p25(X35, c33)) | p2(f11(f4(X35), c34), f11(f4(c32), c34)))),
% 72.25/46.77 inference(skolemize,[status(sab)],[42])).
% 72.25/46.77 tff(44,plain,
% 72.25/46.77 (![X35: $i] : ((~p25(c32, X35)) | (~p25(X35, c33)) | p2(f11(f4(X35), c34), f11(f4(c32), c34)))),
% 72.25/46.77 inference(modus_ponens,[status(thm)],[43, 36])).
% 72.25/46.77 tff(45,plain,
% 72.25/46.77 (p25(c32, c36) <=> p25(c32, c36)),
% 72.25/46.77 inference(rewrite,[status(thm)],[])).
% 72.25/46.77 tff(46,axiom,(p25(c32, c36)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p25_13')).
% 72.25/46.77 tff(47,plain,
% 72.25/46.77 (p25(c32, c36)),
% 72.25/46.77 inference(modus_ponens,[status(thm)],[46, 45])).
% 72.25/46.77 tff(48,plain,
% 72.25/46.77 (p25(c36, c33) <=> p25(c36, c33)),
% 72.25/46.77 inference(rewrite,[status(thm)],[])).
% 72.25/46.77 tff(49,axiom,(p25(c36, c33)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p25_11')).
% 72.25/46.77 tff(50,plain,
% 72.25/46.77 (p25(c36, c33)),
% 72.25/46.77 inference(modus_ponens,[status(thm)],[49, 48])).
% 72.25/46.77 tff(51,plain,
% 72.25/46.77 (((~![X35: $i] : ((~p25(c32, X35)) | (~p25(X35, c33)) | p2(f11(f4(X35), c34), f11(f4(c32), c34)))) | ((~p25(c32, c36)) | (~p25(c36, c33)) | p2(f11(f4(c36), c34), f11(f4(c32), c34)))) <=> ((~![X35: $i] : ((~p25(c32, X35)) | (~p25(X35, c33)) | p2(f11(f4(X35), c34), f11(f4(c32), c34)))) | (~p25(c32, c36)) | (~p25(c36, c33)) | p2(f11(f4(c36), c34), f11(f4(c32), c34)))),
% 72.25/46.77 inference(rewrite,[status(thm)],[])).
% 72.25/46.77 tff(52,plain,
% 72.25/46.77 ((~![X35: $i] : ((~p25(c32, X35)) | (~p25(X35, c33)) | p2(f11(f4(X35), c34), f11(f4(c32), c34)))) | ((~p25(c32, c36)) | (~p25(c36, c33)) | p2(f11(f4(c36), c34), f11(f4(c32), c34)))),
% 72.25/46.77 inference(quant_inst,[status(thm)],[])).
% 72.25/46.77 tff(53,plain,
% 72.25/46.77 ((~![X35: $i] : ((~p25(c32, X35)) | (~p25(X35, c33)) | p2(f11(f4(X35), c34), f11(f4(c32), c34)))) | (~p25(c32, c36)) | (~p25(c36, c33)) | p2(f11(f4(c36), c34), f11(f4(c32), c34))),
% 72.25/46.77 inference(modus_ponens,[status(thm)],[52, 51])).
% 72.25/46.77 tff(54,plain,
% 72.25/46.77 (p2(f11(f4(c36), c34), f11(f4(c32), c34))),
% 72.25/46.77 inference(unit_resolution,[status(thm)],[53, 50, 47, 44])).
% 72.25/46.77 tff(55,plain,
% 72.25/46.77 (^[X30: $i, X29: $i, X28: $i] : refl(((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30)) <=> ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30)))),
% 72.25/46.77 inference(bind,[status(th)],[])).
% 72.25/46.77 tff(56,plain,
% 72.25/46.77 (![X30: $i, X29: $i, X28: $i] : ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30)) <=> ![X30: $i, X29: $i, X28: $i] : ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30))),
% 72.25/46.77 inference(quant_intro,[status(thm)],[55])).
% 72.25/46.77 tff(57,plain,
% 72.25/46.77 (![X30: $i, X29: $i, X28: $i] : ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30)) <=> ![X30: $i, X29: $i, X28: $i] : ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30))),
% 72.25/46.77 inference(rewrite,[status(thm)],[])).
% 72.25/46.77 tff(58,plain,
% 72.25/46.77 (^[X30: $i, X29: $i, X28: $i] : trans(monotonicity(rewrite((p2(X29, X30) | (~p2(X28, X29))) <=> ((~p2(X28, X29)) | p2(X29, X30))), (((p2(X29, X30) | (~p2(X28, X29))) | (~p2(X28, X30))) <=> (((~p2(X28, X29)) | p2(X29, X30)) | (~p2(X28, X30))))), rewrite((((~p2(X28, X29)) | p2(X29, X30)) | (~p2(X28, X30))) <=> ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30))), (((p2(X29, X30) | (~p2(X28, X29))) | (~p2(X28, X30))) <=> ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30))))),
% 72.25/46.77 inference(bind,[status(th)],[])).
% 72.25/46.77 tff(59,plain,
% 72.25/46.77 (![X30: $i, X29: $i, X28: $i] : ((p2(X29, X30) | (~p2(X28, X29))) | (~p2(X28, X30))) <=> ![X30: $i, X29: $i, X28: $i] : ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30))),
% 72.25/46.77 inference(quant_intro,[status(thm)],[58])).
% 72.25/46.77 tff(60,axiom,(![X30: $i, X29: $i, X28: $i] : ((p2(X29, X30) | (~p2(X28, X29))) | (~p2(X28, X30)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_31')).
% 72.25/46.78 tff(61,plain,
% 72.25/46.78 (![X30: $i, X29: $i, X28: $i] : ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30))),
% 72.25/46.78 inference(modus_ponens,[status(thm)],[60, 59])).
% 72.25/46.78 tff(62,plain,
% 72.25/46.78 (![X30: $i, X29: $i, X28: $i] : ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30))),
% 72.25/46.78 inference(modus_ponens,[status(thm)],[61, 57])).
% 72.25/46.78 tff(63,plain,(
% 72.25/46.78 ![X30: $i, X29: $i, X28: $i] : ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30))),
% 72.25/46.78 inference(skolemize,[status(sab)],[62])).
% 72.25/46.78 tff(64,plain,
% 72.25/46.78 (![X30: $i, X29: $i, X28: $i] : ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30))),
% 72.25/46.78 inference(modus_ponens,[status(thm)],[63, 56])).
% 72.25/46.78 tff(65,plain,
% 72.25/46.78 (((~![X30: $i, X29: $i, X28: $i] : ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30))) | ((~p2(f11(f4(c36), c34), f11(f4(c32), c34))) | (~p2(f11(f4(c36), c34), f11(f4(c36), c34))) | p2(f11(f4(c32), c34), f11(f4(c36), c34)))) <=> ((~![X30: $i, X29: $i, X28: $i] : ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30))) | (~p2(f11(f4(c36), c34), f11(f4(c32), c34))) | (~p2(f11(f4(c36), c34), f11(f4(c36), c34))) | p2(f11(f4(c32), c34), f11(f4(c36), c34)))),
% 72.25/46.78 inference(rewrite,[status(thm)],[])).
% 72.25/46.78 tff(66,plain,
% 72.25/46.78 ((~![X30: $i, X29: $i, X28: $i] : ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30))) | ((~p2(f11(f4(c36), c34), f11(f4(c32), c34))) | (~p2(f11(f4(c36), c34), f11(f4(c36), c34))) | p2(f11(f4(c32), c34), f11(f4(c36), c34)))),
% 72.25/46.78 inference(quant_inst,[status(thm)],[])).
% 72.25/46.78 tff(67,plain,
% 72.25/46.78 ((~![X30: $i, X29: $i, X28: $i] : ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30))) | (~p2(f11(f4(c36), c34), f11(f4(c32), c34))) | (~p2(f11(f4(c36), c34), f11(f4(c36), c34))) | p2(f11(f4(c32), c34), f11(f4(c36), c34))),
% 72.25/46.78 inference(modus_ponens,[status(thm)],[66, 65])).
% 72.25/46.78 tff(68,plain,
% 72.25/46.78 (p2(f11(f4(c32), c34), f11(f4(c36), c34))),
% 72.25/46.78 inference(unit_resolution,[status(thm)],[67, 64, 54, 34])).
% 72.25/46.78 tff(69,plain,
% 72.25/46.78 (^[X96: $i] : refl((~p2(X96, f18(X96, f9(f17(c31))))) <=> (~p2(X96, f18(X96, f9(f17(c31))))))),
% 72.25/46.78 inference(bind,[status(th)],[])).
% 72.25/46.78 tff(70,plain,
% 72.25/46.78 (![X96: $i] : (~p2(X96, f18(X96, f9(f17(c31))))) <=> ![X96: $i] : (~p2(X96, f18(X96, f9(f17(c31)))))),
% 72.25/46.78 inference(quant_intro,[status(thm)],[69])).
% 72.25/46.78 tff(71,plain,
% 72.25/46.78 (![X96: $i] : (~p2(X96, f18(X96, f9(f17(c31))))) <=> ![X96: $i] : (~p2(X96, f18(X96, f9(f17(c31)))))),
% 72.25/46.78 inference(rewrite,[status(thm)],[])).
% 72.25/46.78 tff(72,axiom,(![X96: $i] : (~p2(X96, f18(X96, f9(f17(c31)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_p2_19')).
% 72.25/46.78 tff(73,plain,
% 72.25/46.78 (![X96: $i] : (~p2(X96, f18(X96, f9(f17(c31)))))),
% 72.25/46.78 inference(modus_ponens,[status(thm)],[72, 71])).
% 72.25/46.78 tff(74,plain,(
% 72.25/46.78 ![X96: $i] : (~p2(X96, f18(X96, f9(f17(c31)))))),
% 72.25/46.78 inference(skolemize,[status(sab)],[73])).
% 72.25/46.78 tff(75,plain,
% 72.25/46.78 (![X96: $i] : (~p2(X96, f18(X96, f9(f17(c31)))))),
% 72.25/46.78 inference(modus_ponens,[status(thm)],[74, 70])).
% 72.25/46.78 tff(76,plain,
% 72.25/46.78 ((~![X96: $i] : (~p2(X96, f18(X96, f9(f17(c31)))))) | (~p2(f11(f4(c36), c34), f18(f11(f4(c36), c34), f9(f17(c31)))))),
% 72.25/46.78 inference(quant_inst,[status(thm)],[])).
% 72.25/46.78 tff(77,plain,
% 72.25/46.78 (~p2(f11(f4(c36), c34), f18(f11(f4(c36), c34), f9(f17(c31))))),
% 72.25/46.78 inference(unit_resolution,[status(thm)],[76, 75])).
% 72.25/46.78 tff(78,plain,
% 72.25/46.78 (p2(f11(f4(c32), c34), f18(f11(f4(c36), c34), f9(f17(c31)))) <=> p2(f11(f4(c32), c34), f18(f11(f4(c36), c34), f9(f17(c31))))),
% 72.25/46.78 inference(rewrite,[status(thm)],[])).
% 72.25/46.78 tff(79,axiom,(p2(f11(f4(c32), c34), f18(f11(f4(c36), c34), f9(f17(c31))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_40')).
% 72.25/46.78 tff(80,plain,
% 72.25/46.78 (p2(f11(f4(c32), c34), f18(f11(f4(c36), c34), f9(f17(c31))))),
% 72.25/46.78 inference(modus_ponens,[status(thm)],[79, 78])).
% 72.25/46.78 tff(81,plain,
% 72.25/46.78 (((~![X30: $i, X29: $i, X28: $i] : ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30))) | ((~p2(f11(f4(c32), c34), f11(f4(c36), c34))) | (~p2(f11(f4(c32), c34), f18(f11(f4(c36), c34), f9(f17(c31))))) | p2(f11(f4(c36), c34), f18(f11(f4(c36), c34), f9(f17(c31)))))) <=> ((~![X30: $i, X29: $i, X28: $i] : ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30))) | (~p2(f11(f4(c32), c34), f11(f4(c36), c34))) | (~p2(f11(f4(c32), c34), f18(f11(f4(c36), c34), f9(f17(c31))))) | p2(f11(f4(c36), c34), f18(f11(f4(c36), c34), f9(f17(c31)))))),
% 72.27/46.78 inference(rewrite,[status(thm)],[])).
% 72.27/46.78 tff(82,plain,
% 72.27/46.78 ((~![X30: $i, X29: $i, X28: $i] : ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30))) | ((~p2(f11(f4(c32), c34), f11(f4(c36), c34))) | (~p2(f11(f4(c32), c34), f18(f11(f4(c36), c34), f9(f17(c31))))) | p2(f11(f4(c36), c34), f18(f11(f4(c36), c34), f9(f17(c31)))))),
% 72.27/46.78 inference(quant_inst,[status(thm)],[])).
% 72.27/46.78 tff(83,plain,
% 72.27/46.78 ((~![X30: $i, X29: $i, X28: $i] : ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30))) | (~p2(f11(f4(c32), c34), f11(f4(c36), c34))) | (~p2(f11(f4(c32), c34), f18(f11(f4(c36), c34), f9(f17(c31))))) | p2(f11(f4(c36), c34), f18(f11(f4(c36), c34), f9(f17(c31))))),
% 72.27/46.78 inference(modus_ponens,[status(thm)],[82, 81])).
% 72.27/46.78 tff(84,plain,
% 72.27/46.78 ($false),
% 72.27/46.78 inference(unit_resolution,[status(thm)],[83, 64, 80, 77, 68])).
% 72.27/46.78 % SZS output end Proof
%------------------------------------------------------------------------------