TSTP Solution File: SYN616-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN616-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 23:56:39 EDT 2022
% Result : Unsatisfiable 0.12s 0.32s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SYN616-1 : TPTP v8.1.0. Released v2.5.0.
% 0.00/0.08 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.07/0.26 % Computer : n016.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 300
% 0.07/0.26 % DateTime : Mon Sep 5 06:30:09 EDT 2022
% 0.07/0.26 % CPUTime :
% 0.07/0.27 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.07/0.27 Usage: tptp [options] [-file:]file
% 0.07/0.27 -h, -? prints this message.
% 0.07/0.27 -smt2 print SMT-LIB2 benchmark.
% 0.07/0.27 -m, -model generate model.
% 0.07/0.27 -p, -proof generate proof.
% 0.07/0.27 -c, -core generate unsat core of named formulas.
% 0.07/0.27 -st, -statistics display statistics.
% 0.07/0.27 -t:timeout set timeout (in second).
% 0.07/0.27 -smt2status display status in smt2 format instead of SZS.
% 0.07/0.27 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.07/0.27 -<param>:<value> configuration parameter and value.
% 0.07/0.27 -o:<output-file> file to place output in.
% 0.12/0.32 % SZS status Unsatisfiable
% 0.12/0.32 % SZS output start Proof
% 0.12/0.32 tff(p2_type, type, (
% 0.12/0.32 p2: ( $i * $i ) > $o)).
% 0.12/0.32 tff(c22_type, type, (
% 0.12/0.32 c22: $i)).
% 0.12/0.32 tff(f12_type, type, (
% 0.12/0.32 f12: ( $i * $i ) > $i)).
% 0.12/0.32 tff(c28_type, type, (
% 0.12/0.32 c28: $i)).
% 0.12/0.32 tff(f8_type, type, (
% 0.12/0.32 f8: ( $i * $i ) > $i)).
% 0.12/0.32 tff(f3_type, type, (
% 0.12/0.32 f3: $i > $i)).
% 0.12/0.32 tff(f5_type, type, (
% 0.12/0.32 f5: $i > $i)).
% 0.12/0.32 tff(c20_type, type, (
% 0.12/0.32 c20: $i)).
% 0.12/0.32 tff(c21_type, type, (
% 0.12/0.32 c21: $i)).
% 0.12/0.32 tff(c25_type, type, (
% 0.12/0.32 c25: $i)).
% 0.12/0.32 tff(f11_type, type, (
% 0.12/0.32 f11: ( $i * $i * $i ) > $i)).
% 0.12/0.32 tff(c24_type, type, (
% 0.12/0.32 c24: $i)).
% 0.12/0.32 tff(c23_type, type, (
% 0.12/0.32 c23: $i)).
% 0.12/0.32 tff(f7_type, type, (
% 0.12/0.32 f7: ( $i * $i ) > $i)).
% 0.12/0.32 tff(f6_type, type, (
% 0.12/0.32 f6: $i > $i)).
% 0.12/0.32 tff(p14_type, type, (
% 0.12/0.32 p14: ( $i * $i * $i ) > $o)).
% 0.12/0.32 tff(1,assumption,(~p2(f12(f8(c21, f3(f5(c20))), c25), f12(f8(c21, f3(f5(c20))), c28))), introduced(assumption)).
% 0.12/0.32 tff(2,plain,
% 0.12/0.32 (p2(f11(c23, c24, f3(f5(c20))), f8(c21, f3(f5(c20)))) <=> p2(f11(c23, c24, f3(f5(c20))), f8(c21, f3(f5(c20))))),
% 0.12/0.32 inference(rewrite,[status(thm)],[])).
% 0.12/0.32 tff(3,axiom,(p2(f11(c23, c24, f3(f5(c20))), f8(c21, f3(f5(c20))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_19')).
% 0.12/0.32 tff(4,plain,
% 0.12/0.32 (p2(f11(c23, c24, f3(f5(c20))), f8(c21, f3(f5(c20))))),
% 0.12/0.32 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.12/0.32 tff(5,plain,
% 0.12/0.32 (^[X31: $i, X32: $i, X33: $i] : refl(((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33)) <=> ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33)))),
% 0.12/0.32 inference(bind,[status(th)],[])).
% 0.12/0.32 tff(6,plain,
% 0.12/0.32 (![X31: $i, X32: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33)) <=> ![X31: $i, X32: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33))),
% 0.12/0.32 inference(quant_intro,[status(thm)],[5])).
% 0.12/0.32 tff(7,plain,
% 0.12/0.32 (![X31: $i, X32: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33)) <=> ![X31: $i, X32: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33))),
% 0.12/0.32 inference(rewrite,[status(thm)],[])).
% 0.12/0.32 tff(8,plain,
% 0.12/0.32 (^[X31: $i, X32: $i, X33: $i] : trans(monotonicity(rewrite((p2(X32, X33) | (~p2(X31, X32))) <=> ((~p2(X31, X32)) | p2(X32, X33))), (((p2(X32, X33) | (~p2(X31, X32))) | (~p2(X31, X33))) <=> (((~p2(X31, X32)) | p2(X32, X33)) | (~p2(X31, X33))))), rewrite((((~p2(X31, X32)) | p2(X32, X33)) | (~p2(X31, X33))) <=> ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33))), (((p2(X32, X33) | (~p2(X31, X32))) | (~p2(X31, X33))) <=> ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33))))),
% 0.12/0.32 inference(bind,[status(th)],[])).
% 0.12/0.32 tff(9,plain,
% 0.12/0.32 (![X31: $i, X32: $i, X33: $i] : ((p2(X32, X33) | (~p2(X31, X32))) | (~p2(X31, X33))) <=> ![X31: $i, X32: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33))),
% 0.12/0.32 inference(quant_intro,[status(thm)],[8])).
% 0.12/0.32 tff(10,axiom,(![X31: $i, X32: $i, X33: $i] : ((p2(X32, X33) | (~p2(X31, X32))) | (~p2(X31, X33)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_17')).
% 0.12/0.32 tff(11,plain,
% 0.12/0.32 (![X31: $i, X32: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33))),
% 0.12/0.32 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.12/0.32 tff(12,plain,
% 0.12/0.32 (![X31: $i, X32: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33))),
% 0.12/0.32 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.12/0.32 tff(13,plain,(
% 0.12/0.32 ![X31: $i, X32: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33))),
% 0.12/0.32 inference(skolemize,[status(sab)],[12])).
% 0.12/0.32 tff(14,plain,
% 0.12/0.32 (![X31: $i, X32: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33))),
% 0.12/0.32 inference(modus_ponens,[status(thm)],[13, 6])).
% 0.12/0.32 tff(15,plain,
% 0.12/0.32 (((~![X31: $i, X32: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33))) | ((~p2(f11(c23, c24, f3(f5(c20))), f8(c21, f3(f5(c20))))) | p2(f8(c21, f3(f5(c20))), f8(c21, f3(f5(c20)))))) <=> ((~![X31: $i, X32: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33))) | (~p2(f11(c23, c24, f3(f5(c20))), f8(c21, f3(f5(c20))))) | p2(f8(c21, f3(f5(c20))), f8(c21, f3(f5(c20)))))),
% 0.12/0.32 inference(rewrite,[status(thm)],[])).
% 0.12/0.32 tff(16,plain,
% 0.12/0.32 (((~p2(f11(c23, c24, f3(f5(c20))), f8(c21, f3(f5(c20))))) | (~p2(f11(c23, c24, f3(f5(c20))), f8(c21, f3(f5(c20))))) | p2(f8(c21, f3(f5(c20))), f8(c21, f3(f5(c20))))) <=> ((~p2(f11(c23, c24, f3(f5(c20))), f8(c21, f3(f5(c20))))) | p2(f8(c21, f3(f5(c20))), f8(c21, f3(f5(c20)))))),
% 0.12/0.32 inference(rewrite,[status(thm)],[])).
% 0.12/0.32 tff(17,plain,
% 0.12/0.32 (((~![X31: $i, X32: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33))) | ((~p2(f11(c23, c24, f3(f5(c20))), f8(c21, f3(f5(c20))))) | (~p2(f11(c23, c24, f3(f5(c20))), f8(c21, f3(f5(c20))))) | p2(f8(c21, f3(f5(c20))), f8(c21, f3(f5(c20)))))) <=> ((~![X31: $i, X32: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33))) | ((~p2(f11(c23, c24, f3(f5(c20))), f8(c21, f3(f5(c20))))) | p2(f8(c21, f3(f5(c20))), f8(c21, f3(f5(c20))))))),
% 0.12/0.32 inference(monotonicity,[status(thm)],[16])).
% 0.12/0.32 tff(18,plain,
% 0.12/0.32 (((~![X31: $i, X32: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33))) | ((~p2(f11(c23, c24, f3(f5(c20))), f8(c21, f3(f5(c20))))) | (~p2(f11(c23, c24, f3(f5(c20))), f8(c21, f3(f5(c20))))) | p2(f8(c21, f3(f5(c20))), f8(c21, f3(f5(c20)))))) <=> ((~![X31: $i, X32: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33))) | (~p2(f11(c23, c24, f3(f5(c20))), f8(c21, f3(f5(c20))))) | p2(f8(c21, f3(f5(c20))), f8(c21, f3(f5(c20)))))),
% 0.12/0.32 inference(transitivity,[status(thm)],[17, 15])).
% 0.12/0.32 tff(19,plain,
% 0.12/0.32 ((~![X31: $i, X32: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33))) | ((~p2(f11(c23, c24, f3(f5(c20))), f8(c21, f3(f5(c20))))) | (~p2(f11(c23, c24, f3(f5(c20))), f8(c21, f3(f5(c20))))) | p2(f8(c21, f3(f5(c20))), f8(c21, f3(f5(c20)))))),
% 0.12/0.32 inference(quant_inst,[status(thm)],[])).
% 0.12/0.32 tff(20,plain,
% 0.12/0.32 ((~![X31: $i, X32: $i, X33: $i] : ((~p2(X31, X33)) | (~p2(X31, X32)) | p2(X32, X33))) | (~p2(f11(c23, c24, f3(f5(c20))), f8(c21, f3(f5(c20))))) | p2(f8(c21, f3(f5(c20))), f8(c21, f3(f5(c20))))),
% 0.12/0.32 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.12/0.32 tff(21,plain,
% 0.12/0.32 (p2(f8(c21, f3(f5(c20))), f8(c21, f3(f5(c20))))),
% 0.12/0.32 inference(unit_resolution,[status(thm)],[20, 14, 4])).
% 0.12/0.32 tff(22,plain,
% 0.12/0.32 (^[X43: $i, X42: $i, X41: $i, X40: $i] : refl(((~p2(X41, X43)) | (~p2(X40, X42)) | p2(f12(X40, X41), f12(X42, X43))) <=> ((~p2(X41, X43)) | (~p2(X40, X42)) | p2(f12(X40, X41), f12(X42, X43))))),
% 0.12/0.32 inference(bind,[status(th)],[])).
% 0.12/0.32 tff(23,plain,
% 0.12/0.32 (![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p2(X41, X43)) | (~p2(X40, X42)) | p2(f12(X40, X41), f12(X42, X43))) <=> ![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p2(X41, X43)) | (~p2(X40, X42)) | p2(f12(X40, X41), f12(X42, X43)))),
% 0.12/0.32 inference(quant_intro,[status(thm)],[22])).
% 0.12/0.32 tff(24,plain,
% 0.12/0.32 (![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p2(X41, X43)) | (~p2(X40, X42)) | p2(f12(X40, X41), f12(X42, X43))) <=> ![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p2(X41, X43)) | (~p2(X40, X42)) | p2(f12(X40, X41), f12(X42, X43)))),
% 0.12/0.32 inference(rewrite,[status(thm)],[])).
% 0.12/0.32 tff(25,plain,
% 0.12/0.32 (^[X43: $i, X42: $i, X41: $i, X40: $i] : trans(monotonicity(rewrite((p2(f12(X40, X41), f12(X42, X43)) | (~p2(X40, X42))) <=> ((~p2(X40, X42)) | p2(f12(X40, X41), f12(X42, X43)))), (((p2(f12(X40, X41), f12(X42, X43)) | (~p2(X40, X42))) | (~p2(X41, X43))) <=> (((~p2(X40, X42)) | p2(f12(X40, X41), f12(X42, X43))) | (~p2(X41, X43))))), rewrite((((~p2(X40, X42)) | p2(f12(X40, X41), f12(X42, X43))) | (~p2(X41, X43))) <=> ((~p2(X41, X43)) | (~p2(X40, X42)) | p2(f12(X40, X41), f12(X42, X43)))), (((p2(f12(X40, X41), f12(X42, X43)) | (~p2(X40, X42))) | (~p2(X41, X43))) <=> ((~p2(X41, X43)) | (~p2(X40, X42)) | p2(f12(X40, X41), f12(X42, X43)))))),
% 0.12/0.32 inference(bind,[status(th)],[])).
% 0.12/0.32 tff(26,plain,
% 0.12/0.32 (![X43: $i, X42: $i, X41: $i, X40: $i] : ((p2(f12(X40, X41), f12(X42, X43)) | (~p2(X40, X42))) | (~p2(X41, X43))) <=> ![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p2(X41, X43)) | (~p2(X40, X42)) | p2(f12(X40, X41), f12(X42, X43)))),
% 0.12/0.32 inference(quant_intro,[status(thm)],[25])).
% 0.12/0.32 tff(27,axiom,(![X43: $i, X42: $i, X41: $i, X40: $i] : ((p2(f12(X40, X41), f12(X42, X43)) | (~p2(X40, X42))) | (~p2(X41, X43)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_27')).
% 0.12/0.32 tff(28,plain,
% 0.12/0.32 (![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p2(X41, X43)) | (~p2(X40, X42)) | p2(f12(X40, X41), f12(X42, X43)))),
% 0.12/0.32 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.12/0.32 tff(29,plain,
% 0.12/0.32 (![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p2(X41, X43)) | (~p2(X40, X42)) | p2(f12(X40, X41), f12(X42, X43)))),
% 0.12/0.32 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.12/0.32 tff(30,plain,(
% 0.12/0.32 ![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p2(X41, X43)) | (~p2(X40, X42)) | p2(f12(X40, X41), f12(X42, X43)))),
% 0.12/0.32 inference(skolemize,[status(sab)],[29])).
% 0.12/0.32 tff(31,plain,
% 0.12/0.32 (![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p2(X41, X43)) | (~p2(X40, X42)) | p2(f12(X40, X41), f12(X42, X43)))),
% 0.12/0.32 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.12/0.32 tff(32,plain,
% 0.12/0.32 (p2(c25, c28) <=> p2(c25, c28)),
% 0.12/0.32 inference(rewrite,[status(thm)],[])).
% 0.12/0.32 tff(33,axiom,(p2(c25, c28)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_7')).
% 0.12/0.32 tff(34,plain,
% 0.12/0.32 (p2(c25, c28)),
% 0.12/0.32 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.12/0.32 tff(35,plain,
% 0.12/0.32 (((~![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p2(X41, X43)) | (~p2(X40, X42)) | p2(f12(X40, X41), f12(X42, X43)))) | ((~p2(c25, c28)) | (~p2(f8(c21, f3(f5(c20))), f8(c21, f3(f5(c20))))) | p2(f12(f8(c21, f3(f5(c20))), c25), f12(f8(c21, f3(f5(c20))), c28)))) <=> ((~![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p2(X41, X43)) | (~p2(X40, X42)) | p2(f12(X40, X41), f12(X42, X43)))) | (~p2(c25, c28)) | (~p2(f8(c21, f3(f5(c20))), f8(c21, f3(f5(c20))))) | p2(f12(f8(c21, f3(f5(c20))), c25), f12(f8(c21, f3(f5(c20))), c28)))),
% 0.12/0.32 inference(rewrite,[status(thm)],[])).
% 0.12/0.32 tff(36,plain,
% 0.12/0.32 ((~![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p2(X41, X43)) | (~p2(X40, X42)) | p2(f12(X40, X41), f12(X42, X43)))) | ((~p2(c25, c28)) | (~p2(f8(c21, f3(f5(c20))), f8(c21, f3(f5(c20))))) | p2(f12(f8(c21, f3(f5(c20))), c25), f12(f8(c21, f3(f5(c20))), c28)))),
% 0.12/0.32 inference(quant_inst,[status(thm)],[])).
% 0.12/0.32 tff(37,plain,
% 0.12/0.32 ((~![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p2(X41, X43)) | (~p2(X40, X42)) | p2(f12(X40, X41), f12(X42, X43)))) | (~p2(c25, c28)) | (~p2(f8(c21, f3(f5(c20))), f8(c21, f3(f5(c20))))) | p2(f12(f8(c21, f3(f5(c20))), c25), f12(f8(c21, f3(f5(c20))), c28))),
% 0.12/0.32 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.12/0.32 tff(38,plain,
% 0.12/0.32 ($false),
% 0.12/0.32 inference(unit_resolution,[status(thm)],[37, 34, 31, 21, 1])).
% 0.12/0.32 tff(39,plain,(p2(f12(f8(c21, f3(f5(c20))), c25), f12(f8(c21, f3(f5(c20))), c28))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.32 tff(40,assumption,(~p2(f3(f5(c20)), f3(f5(c20)))), introduced(assumption)).
% 0.12/0.32 tff(41,plain,
% 0.12/0.32 (^[X31: $i] : refl(p2(X31, X31) <=> p2(X31, X31))),
% 0.12/0.32 inference(bind,[status(th)],[])).
% 0.12/0.32 tff(42,plain,
% 0.12/0.32 (![X31: $i] : p2(X31, X31) <=> ![X31: $i] : p2(X31, X31)),
% 0.12/0.32 inference(quant_intro,[status(thm)],[41])).
% 0.12/0.32 tff(43,plain,
% 0.12/0.32 (![X31: $i] : p2(X31, X31) <=> ![X31: $i] : p2(X31, X31)),
% 0.12/0.32 inference(rewrite,[status(thm)],[])).
% 0.12/0.32 tff(44,axiom,(![X31: $i] : p2(X31, X31)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_4')).
% 0.12/0.32 tff(45,plain,
% 0.12/0.32 (![X31: $i] : p2(X31, X31)),
% 0.12/0.32 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.12/0.32 tff(46,plain,(
% 0.12/0.32 ![X31: $i] : p2(X31, X31)),
% 0.12/0.32 inference(skolemize,[status(sab)],[45])).
% 0.12/0.32 tff(47,plain,
% 0.12/0.32 (![X31: $i] : p2(X31, X31)),
% 0.12/0.32 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.12/0.32 tff(48,plain,
% 0.12/0.32 ((~![X31: $i] : p2(X31, X31)) | p2(f3(f5(c20)), f3(f5(c20)))),
% 0.12/0.32 inference(quant_inst,[status(thm)],[])).
% 0.12/0.32 tff(49,plain,
% 0.12/0.32 ($false),
% 0.12/0.32 inference(unit_resolution,[status(thm)],[48, 47, 40])).
% 0.12/0.32 tff(50,plain,(p2(f3(f5(c20)), f3(f5(c20)))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.32 tff(51,assumption,(~p2(f6(c21), f6(c21))), introduced(assumption)).
% 0.12/0.32 tff(52,plain,
% 0.12/0.32 ((~![X31: $i] : p2(X31, X31)) | p2(f6(c21), f6(c21))),
% 0.12/0.32 inference(quant_inst,[status(thm)],[])).
% 0.12/0.32 tff(53,plain,
% 0.12/0.32 ($false),
% 0.12/0.32 inference(unit_resolution,[status(thm)],[52, 47, 51])).
% 0.12/0.32 tff(54,plain,(p2(f6(c21), f6(c21))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.32 tff(55,plain,
% 0.12/0.32 (^[X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : refl(((~p2(X10, X7)) | (~p2(X11, X8)) | (~p14(X10, X11, X12)) | (~p2(X12, X9)) | p14(X7, X8, X9)) <=> ((~p2(X10, X7)) | (~p2(X11, X8)) | (~p14(X10, X11, X12)) | (~p2(X12, X9)) | p14(X7, X8, X9)))),
% 0.12/0.32 inference(bind,[status(th)],[])).
% 0.12/0.33 tff(56,plain,
% 0.12/0.33 (![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X7)) | (~p2(X11, X8)) | (~p14(X10, X11, X12)) | (~p2(X12, X9)) | p14(X7, X8, X9)) <=> ![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X7)) | (~p2(X11, X8)) | (~p14(X10, X11, X12)) | (~p2(X12, X9)) | p14(X7, X8, X9))),
% 0.12/0.33 inference(quant_intro,[status(thm)],[55])).
% 0.12/0.33 tff(57,plain,
% 0.12/0.33 (![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X7)) | (~p2(X11, X8)) | (~p14(X10, X11, X12)) | (~p2(X12, X9)) | p14(X7, X8, X9)) <=> ![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X7)) | (~p2(X11, X8)) | (~p14(X10, X11, X12)) | (~p2(X12, X9)) | p14(X7, X8, X9))),
% 0.12/0.33 inference(rewrite,[status(thm)],[])).
% 0.12/0.33 tff(58,plain,
% 0.12/0.33 (^[X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((p14(X7, X8, X9) | (~p2(X12, X9))) <=> ((~p2(X12, X9)) | p14(X7, X8, X9))), (((p14(X7, X8, X9) | (~p2(X12, X9))) | (~p2(X11, X8))) <=> (((~p2(X12, X9)) | p14(X7, X8, X9)) | (~p2(X11, X8))))), rewrite((((~p2(X12, X9)) | p14(X7, X8, X9)) | (~p2(X11, X8))) <=> ((~p2(X11, X8)) | (~p2(X12, X9)) | p14(X7, X8, X9))), (((p14(X7, X8, X9) | (~p2(X12, X9))) | (~p2(X11, X8))) <=> ((~p2(X11, X8)) | (~p2(X12, X9)) | p14(X7, X8, X9)))), ((((p14(X7, X8, X9) | (~p2(X12, X9))) | (~p2(X11, X8))) | (~p2(X10, X7))) <=> (((~p2(X11, X8)) | (~p2(X12, X9)) | p14(X7, X8, X9)) | (~p2(X10, X7))))), rewrite((((~p2(X11, X8)) | (~p2(X12, X9)) | p14(X7, X8, X9)) | (~p2(X10, X7))) <=> ((~p2(X10, X7)) | (~p2(X11, X8)) | (~p2(X12, X9)) | p14(X7, X8, X9))), ((((p14(X7, X8, X9) | (~p2(X12, X9))) | (~p2(X11, X8))) | (~p2(X10, X7))) <=> ((~p2(X10, X7)) | (~p2(X11, X8)) | (~p2(X12, X9)) | p14(X7, X8, X9)))), (((((p14(X7, X8, X9) | (~p2(X12, X9))) | (~p2(X11, X8))) | (~p2(X10, X7))) | (~p14(X10, X11, X12))) <=> (((~p2(X10, X7)) | (~p2(X11, X8)) | (~p2(X12, X9)) | p14(X7, X8, X9)) | (~p14(X10, X11, X12))))), rewrite((((~p2(X10, X7)) | (~p2(X11, X8)) | (~p2(X12, X9)) | p14(X7, X8, X9)) | (~p14(X10, X11, X12))) <=> ((~p2(X10, X7)) | (~p2(X11, X8)) | (~p14(X10, X11, X12)) | (~p2(X12, X9)) | p14(X7, X8, X9))), (((((p14(X7, X8, X9) | (~p2(X12, X9))) | (~p2(X11, X8))) | (~p2(X10, X7))) | (~p14(X10, X11, X12))) <=> ((~p2(X10, X7)) | (~p2(X11, X8)) | (~p14(X10, X11, X12)) | (~p2(X12, X9)) | p14(X7, X8, X9))))),
% 0.12/0.33 inference(bind,[status(th)],[])).
% 0.12/0.33 tff(59,plain,
% 0.12/0.33 (![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((((p14(X7, X8, X9) | (~p2(X12, X9))) | (~p2(X11, X8))) | (~p2(X10, X7))) | (~p14(X10, X11, X12))) <=> ![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X7)) | (~p2(X11, X8)) | (~p14(X10, X11, X12)) | (~p2(X12, X9)) | p14(X7, X8, X9))),
% 0.12/0.33 inference(quant_intro,[status(thm)],[58])).
% 0.12/0.33 tff(60,axiom,(![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((((p14(X7, X8, X9) | (~p2(X12, X9))) | (~p2(X11, X8))) | (~p2(X10, X7))) | (~p14(X10, X11, X12)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p14_31')).
% 0.12/0.33 tff(61,plain,
% 0.12/0.33 (![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X7)) | (~p2(X11, X8)) | (~p14(X10, X11, X12)) | (~p2(X12, X9)) | p14(X7, X8, X9))),
% 0.12/0.33 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.12/0.33 tff(62,plain,
% 0.12/0.33 (![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X7)) | (~p2(X11, X8)) | (~p14(X10, X11, X12)) | (~p2(X12, X9)) | p14(X7, X8, X9))),
% 0.12/0.33 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.12/0.33 tff(63,plain,(
% 0.12/0.33 ![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X7)) | (~p2(X11, X8)) | (~p14(X10, X11, X12)) | (~p2(X12, X9)) | p14(X7, X8, X9))),
% 0.12/0.33 inference(skolemize,[status(sab)],[62])).
% 0.12/0.33 tff(64,plain,
% 0.12/0.33 (![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X7)) | (~p2(X11, X8)) | (~p14(X10, X11, X12)) | (~p2(X12, X9)) | p14(X7, X8, X9))),
% 0.12/0.33 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.12/0.33 tff(65,plain,
% 0.12/0.33 ((~p14(f7(c22, f12(f8(c21, f3(f5(c20))), c28)), f3(f5(c20)), f6(c21))) <=> (~p14(f7(c22, f12(f8(c21, f3(f5(c20))), c28)), f3(f5(c20)), f6(c21)))),
% 0.12/0.33 inference(rewrite,[status(thm)],[])).
% 0.12/0.33 tff(66,axiom,(~p14(f7(c22, f12(f8(c21, f3(f5(c20))), c28)), f3(f5(c20)), f6(c21))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_p14_30')).
% 0.12/0.33 tff(67,plain,
% 0.12/0.33 (~p14(f7(c22, f12(f8(c21, f3(f5(c20))), c28)), f3(f5(c20)), f6(c21))),
% 0.12/0.33 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.12/0.33 tff(68,plain,
% 0.12/0.33 (p14(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f3(f5(c20)), f6(c21)) <=> p14(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f3(f5(c20)), f6(c21))),
% 0.12/0.33 inference(rewrite,[status(thm)],[])).
% 0.12/0.33 tff(69,axiom,(p14(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f3(f5(c20)), f6(c21))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p14_29')).
% 0.12/0.33 tff(70,plain,
% 0.12/0.33 (p14(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f3(f5(c20)), f6(c21))),
% 0.12/0.33 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.12/0.33 tff(71,plain,
% 0.12/0.33 (((~![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X7)) | (~p2(X11, X8)) | (~p14(X10, X11, X12)) | (~p2(X12, X9)) | p14(X7, X8, X9))) | (p14(f7(c22, f12(f8(c21, f3(f5(c20))), c28)), f3(f5(c20)), f6(c21)) | (~p2(f3(f5(c20)), f3(f5(c20)))) | (~p2(f6(c21), f6(c21))) | (~p2(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f7(c22, f12(f8(c21, f3(f5(c20))), c28)))) | (~p14(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f3(f5(c20)), f6(c21))))) <=> ((~![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X7)) | (~p2(X11, X8)) | (~p14(X10, X11, X12)) | (~p2(X12, X9)) | p14(X7, X8, X9))) | p14(f7(c22, f12(f8(c21, f3(f5(c20))), c28)), f3(f5(c20)), f6(c21)) | (~p2(f3(f5(c20)), f3(f5(c20)))) | (~p2(f6(c21), f6(c21))) | (~p2(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f7(c22, f12(f8(c21, f3(f5(c20))), c28)))) | (~p14(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f3(f5(c20)), f6(c21))))),
% 0.12/0.33 inference(rewrite,[status(thm)],[])).
% 0.12/0.33 tff(72,plain,
% 0.12/0.33 (((~p2(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f7(c22, f12(f8(c21, f3(f5(c20))), c28)))) | (~p2(f3(f5(c20)), f3(f5(c20)))) | (~p14(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f3(f5(c20)), f6(c21))) | (~p2(f6(c21), f6(c21))) | p14(f7(c22, f12(f8(c21, f3(f5(c20))), c28)), f3(f5(c20)), f6(c21))) <=> (p14(f7(c22, f12(f8(c21, f3(f5(c20))), c28)), f3(f5(c20)), f6(c21)) | (~p2(f3(f5(c20)), f3(f5(c20)))) | (~p2(f6(c21), f6(c21))) | (~p2(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f7(c22, f12(f8(c21, f3(f5(c20))), c28)))) | (~p14(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f3(f5(c20)), f6(c21))))),
% 0.12/0.33 inference(rewrite,[status(thm)],[])).
% 0.12/0.33 tff(73,plain,
% 0.12/0.33 (((~![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X7)) | (~p2(X11, X8)) | (~p14(X10, X11, X12)) | (~p2(X12, X9)) | p14(X7, X8, X9))) | ((~p2(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f7(c22, f12(f8(c21, f3(f5(c20))), c28)))) | (~p2(f3(f5(c20)), f3(f5(c20)))) | (~p14(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f3(f5(c20)), f6(c21))) | (~p2(f6(c21), f6(c21))) | p14(f7(c22, f12(f8(c21, f3(f5(c20))), c28)), f3(f5(c20)), f6(c21)))) <=> ((~![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X7)) | (~p2(X11, X8)) | (~p14(X10, X11, X12)) | (~p2(X12, X9)) | p14(X7, X8, X9))) | (p14(f7(c22, f12(f8(c21, f3(f5(c20))), c28)), f3(f5(c20)), f6(c21)) | (~p2(f3(f5(c20)), f3(f5(c20)))) | (~p2(f6(c21), f6(c21))) | (~p2(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f7(c22, f12(f8(c21, f3(f5(c20))), c28)))) | (~p14(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f3(f5(c20)), f6(c21)))))),
% 0.12/0.33 inference(monotonicity,[status(thm)],[72])).
% 0.12/0.33 tff(74,plain,
% 0.12/0.33 (((~![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X7)) | (~p2(X11, X8)) | (~p14(X10, X11, X12)) | (~p2(X12, X9)) | p14(X7, X8, X9))) | ((~p2(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f7(c22, f12(f8(c21, f3(f5(c20))), c28)))) | (~p2(f3(f5(c20)), f3(f5(c20)))) | (~p14(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f3(f5(c20)), f6(c21))) | (~p2(f6(c21), f6(c21))) | p14(f7(c22, f12(f8(c21, f3(f5(c20))), c28)), f3(f5(c20)), f6(c21)))) <=> ((~![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X7)) | (~p2(X11, X8)) | (~p14(X10, X11, X12)) | (~p2(X12, X9)) | p14(X7, X8, X9))) | p14(f7(c22, f12(f8(c21, f3(f5(c20))), c28)), f3(f5(c20)), f6(c21)) | (~p2(f3(f5(c20)), f3(f5(c20)))) | (~p2(f6(c21), f6(c21))) | (~p2(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f7(c22, f12(f8(c21, f3(f5(c20))), c28)))) | (~p14(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f3(f5(c20)), f6(c21))))),
% 0.12/0.34 inference(transitivity,[status(thm)],[73, 71])).
% 0.12/0.34 tff(75,plain,
% 0.12/0.34 ((~![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X7)) | (~p2(X11, X8)) | (~p14(X10, X11, X12)) | (~p2(X12, X9)) | p14(X7, X8, X9))) | ((~p2(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f7(c22, f12(f8(c21, f3(f5(c20))), c28)))) | (~p2(f3(f5(c20)), f3(f5(c20)))) | (~p14(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f3(f5(c20)), f6(c21))) | (~p2(f6(c21), f6(c21))) | p14(f7(c22, f12(f8(c21, f3(f5(c20))), c28)), f3(f5(c20)), f6(c21)))),
% 0.12/0.34 inference(quant_inst,[status(thm)],[])).
% 0.12/0.34 tff(76,plain,
% 0.12/0.34 ((~![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X7)) | (~p2(X11, X8)) | (~p14(X10, X11, X12)) | (~p2(X12, X9)) | p14(X7, X8, X9))) | p14(f7(c22, f12(f8(c21, f3(f5(c20))), c28)), f3(f5(c20)), f6(c21)) | (~p2(f3(f5(c20)), f3(f5(c20)))) | (~p2(f6(c21), f6(c21))) | (~p2(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f7(c22, f12(f8(c21, f3(f5(c20))), c28)))) | (~p14(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f3(f5(c20)), f6(c21)))),
% 0.12/0.34 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.12/0.34 tff(77,plain,
% 0.12/0.34 ((~p2(f3(f5(c20)), f3(f5(c20)))) | (~p2(f6(c21), f6(c21))) | (~p2(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f7(c22, f12(f8(c21, f3(f5(c20))), c28))))),
% 0.12/0.34 inference(unit_resolution,[status(thm)],[76, 70, 67, 64])).
% 0.12/0.34 tff(78,plain,
% 0.12/0.34 (~p2(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f7(c22, f12(f8(c21, f3(f5(c20))), c28)))),
% 0.12/0.34 inference(unit_resolution,[status(thm)],[77, 54, 50])).
% 0.12/0.34 tff(79,plain,
% 0.12/0.34 (^[X53: $i, X55: $i, X52: $i, X54: $i] : refl(((~p2(X53, X55)) | (~p2(X52, X54)) | p2(f7(X52, X53), f7(X54, X55))) <=> ((~p2(X53, X55)) | (~p2(X52, X54)) | p2(f7(X52, X53), f7(X54, X55))))),
% 0.12/0.34 inference(bind,[status(th)],[])).
% 0.12/0.34 tff(80,plain,
% 0.12/0.34 (![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p2(X53, X55)) | (~p2(X52, X54)) | p2(f7(X52, X53), f7(X54, X55))) <=> ![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p2(X53, X55)) | (~p2(X52, X54)) | p2(f7(X52, X53), f7(X54, X55)))),
% 0.12/0.34 inference(quant_intro,[status(thm)],[79])).
% 0.12/0.34 tff(81,plain,
% 0.12/0.34 (![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p2(X53, X55)) | (~p2(X52, X54)) | p2(f7(X52, X53), f7(X54, X55))) <=> ![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p2(X53, X55)) | (~p2(X52, X54)) | p2(f7(X52, X53), f7(X54, X55)))),
% 0.12/0.34 inference(rewrite,[status(thm)],[])).
% 0.12/0.34 tff(82,plain,
% 0.12/0.34 (^[X53: $i, X55: $i, X52: $i, X54: $i] : trans(monotonicity(rewrite((p2(f7(X52, X53), f7(X54, X55)) | (~p2(X53, X55))) <=> ((~p2(X53, X55)) | p2(f7(X52, X53), f7(X54, X55)))), (((p2(f7(X52, X53), f7(X54, X55)) | (~p2(X53, X55))) | (~p2(X52, X54))) <=> (((~p2(X53, X55)) | p2(f7(X52, X53), f7(X54, X55))) | (~p2(X52, X54))))), rewrite((((~p2(X53, X55)) | p2(f7(X52, X53), f7(X54, X55))) | (~p2(X52, X54))) <=> ((~p2(X53, X55)) | (~p2(X52, X54)) | p2(f7(X52, X53), f7(X54, X55)))), (((p2(f7(X52, X53), f7(X54, X55)) | (~p2(X53, X55))) | (~p2(X52, X54))) <=> ((~p2(X53, X55)) | (~p2(X52, X54)) | p2(f7(X52, X53), f7(X54, X55)))))),
% 0.12/0.34 inference(bind,[status(th)],[])).
% 0.12/0.34 tff(83,plain,
% 0.12/0.34 (![X53: $i, X55: $i, X52: $i, X54: $i] : ((p2(f7(X52, X53), f7(X54, X55)) | (~p2(X53, X55))) | (~p2(X52, X54))) <=> ![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p2(X53, X55)) | (~p2(X52, X54)) | p2(f7(X52, X53), f7(X54, X55)))),
% 0.12/0.34 inference(quant_intro,[status(thm)],[82])).
% 0.12/0.34 tff(84,axiom,(![X53: $i, X55: $i, X52: $i, X54: $i] : ((p2(f7(X52, X53), f7(X54, X55)) | (~p2(X53, X55))) | (~p2(X52, X54)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_28')).
% 0.12/0.34 tff(85,plain,
% 0.12/0.34 (![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p2(X53, X55)) | (~p2(X52, X54)) | p2(f7(X52, X53), f7(X54, X55)))),
% 0.12/0.34 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.12/0.34 tff(86,plain,
% 0.12/0.34 (![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p2(X53, X55)) | (~p2(X52, X54)) | p2(f7(X52, X53), f7(X54, X55)))),
% 0.12/0.34 inference(modus_ponens,[status(thm)],[85, 81])).
% 0.12/0.34 tff(87,plain,(
% 0.12/0.34 ![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p2(X53, X55)) | (~p2(X52, X54)) | p2(f7(X52, X53), f7(X54, X55)))),
% 0.12/0.34 inference(skolemize,[status(sab)],[86])).
% 0.12/0.34 tff(88,plain,
% 0.12/0.34 (![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p2(X53, X55)) | (~p2(X52, X54)) | p2(f7(X52, X53), f7(X54, X55)))),
% 0.12/0.34 inference(modus_ponens,[status(thm)],[87, 80])).
% 0.12/0.34 tff(89,plain,
% 0.12/0.34 (((~![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p2(X53, X55)) | (~p2(X52, X54)) | p2(f7(X52, X53), f7(X54, X55)))) | (p2(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f7(c22, f12(f8(c21, f3(f5(c20))), c28))) | (~p2(c22, c22)) | (~p2(f12(f8(c21, f3(f5(c20))), c25), f12(f8(c21, f3(f5(c20))), c28))))) <=> ((~![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p2(X53, X55)) | (~p2(X52, X54)) | p2(f7(X52, X53), f7(X54, X55)))) | p2(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f7(c22, f12(f8(c21, f3(f5(c20))), c28))) | (~p2(c22, c22)) | (~p2(f12(f8(c21, f3(f5(c20))), c25), f12(f8(c21, f3(f5(c20))), c28))))),
% 0.12/0.34 inference(rewrite,[status(thm)],[])).
% 0.12/0.34 tff(90,plain,
% 0.12/0.34 (((~p2(f12(f8(c21, f3(f5(c20))), c25), f12(f8(c21, f3(f5(c20))), c28))) | (~p2(c22, c22)) | p2(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f7(c22, f12(f8(c21, f3(f5(c20))), c28)))) <=> (p2(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f7(c22, f12(f8(c21, f3(f5(c20))), c28))) | (~p2(c22, c22)) | (~p2(f12(f8(c21, f3(f5(c20))), c25), f12(f8(c21, f3(f5(c20))), c28))))),
% 0.12/0.34 inference(rewrite,[status(thm)],[])).
% 0.12/0.34 tff(91,plain,
% 0.12/0.34 (((~![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p2(X53, X55)) | (~p2(X52, X54)) | p2(f7(X52, X53), f7(X54, X55)))) | ((~p2(f12(f8(c21, f3(f5(c20))), c25), f12(f8(c21, f3(f5(c20))), c28))) | (~p2(c22, c22)) | p2(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f7(c22, f12(f8(c21, f3(f5(c20))), c28))))) <=> ((~![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p2(X53, X55)) | (~p2(X52, X54)) | p2(f7(X52, X53), f7(X54, X55)))) | (p2(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f7(c22, f12(f8(c21, f3(f5(c20))), c28))) | (~p2(c22, c22)) | (~p2(f12(f8(c21, f3(f5(c20))), c25), f12(f8(c21, f3(f5(c20))), c28)))))),
% 0.12/0.34 inference(monotonicity,[status(thm)],[90])).
% 0.12/0.34 tff(92,plain,
% 0.12/0.34 (((~![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p2(X53, X55)) | (~p2(X52, X54)) | p2(f7(X52, X53), f7(X54, X55)))) | ((~p2(f12(f8(c21, f3(f5(c20))), c25), f12(f8(c21, f3(f5(c20))), c28))) | (~p2(c22, c22)) | p2(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f7(c22, f12(f8(c21, f3(f5(c20))), c28))))) <=> ((~![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p2(X53, X55)) | (~p2(X52, X54)) | p2(f7(X52, X53), f7(X54, X55)))) | p2(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f7(c22, f12(f8(c21, f3(f5(c20))), c28))) | (~p2(c22, c22)) | (~p2(f12(f8(c21, f3(f5(c20))), c25), f12(f8(c21, f3(f5(c20))), c28))))),
% 0.12/0.34 inference(transitivity,[status(thm)],[91, 89])).
% 0.12/0.34 tff(93,plain,
% 0.12/0.34 ((~![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p2(X53, X55)) | (~p2(X52, X54)) | p2(f7(X52, X53), f7(X54, X55)))) | ((~p2(f12(f8(c21, f3(f5(c20))), c25), f12(f8(c21, f3(f5(c20))), c28))) | (~p2(c22, c22)) | p2(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f7(c22, f12(f8(c21, f3(f5(c20))), c28))))),
% 0.12/0.34 inference(quant_inst,[status(thm)],[])).
% 0.12/0.34 tff(94,plain,
% 0.12/0.34 ((~![X53: $i, X55: $i, X52: $i, X54: $i] : ((~p2(X53, X55)) | (~p2(X52, X54)) | p2(f7(X52, X53), f7(X54, X55)))) | p2(f7(c22, f12(f8(c21, f3(f5(c20))), c25)), f7(c22, f12(f8(c21, f3(f5(c20))), c28))) | (~p2(c22, c22)) | (~p2(f12(f8(c21, f3(f5(c20))), c25), f12(f8(c21, f3(f5(c20))), c28)))),
% 0.12/0.34 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.12/0.34 tff(95,plain,
% 0.12/0.34 ((~p2(c22, c22)) | (~p2(f12(f8(c21, f3(f5(c20))), c25), f12(f8(c21, f3(f5(c20))), c28)))),
% 0.12/0.34 inference(unit_resolution,[status(thm)],[94, 88, 78])).
% 0.12/0.34 tff(96,plain,
% 0.12/0.34 (~p2(c22, c22)),
% 0.12/0.34 inference(unit_resolution,[status(thm)],[95, 39])).
% 0.12/0.34 tff(97,plain,
% 0.12/0.34 ((~![X31: $i] : p2(X31, X31)) | p2(c22, c22)),
% 0.12/0.34 inference(quant_inst,[status(thm)],[])).
% 0.12/0.34 tff(98,plain,
% 0.12/0.34 ($false),
% 0.12/0.34 inference(unit_resolution,[status(thm)],[97, 47, 96])).
% 0.12/0.34 % SZS output end Proof
%------------------------------------------------------------------------------