TSTP Solution File: SYN619-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN619-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.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 0.13s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN619-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n002.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 06:21:48 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.13/0.40 % SZS status Unsatisfiable
% 0.13/0.40 % SZS output start Proof
% 0.13/0.40 tff(p2_type, type, (
% 0.13/0.40 p2: ( $i * $i ) > $o)).
% 0.13/0.40 tff(c20_type, type, (
% 0.13/0.40 c20: $i)).
% 0.13/0.40 tff(p17_type, type, (
% 0.13/0.40 p17: ( $i * $i ) > $o)).
% 0.13/0.40 tff(c21_type, type, (
% 0.13/0.40 c21: $i)).
% 0.13/0.40 tff(p8_type, type, (
% 0.13/0.40 p8: ( $i * $i ) > $o)).
% 0.13/0.40 tff(f9_type, type, (
% 0.13/0.40 f9: ( $i * $i ) > $i)).
% 0.13/0.40 tff(f11_type, type, (
% 0.13/0.40 f11: $i > $i)).
% 0.13/0.40 tff(f12_type, type, (
% 0.13/0.40 f12: $i > $i)).
% 0.13/0.40 tff(f7_type, type, (
% 0.13/0.40 f7: ( $i * $i ) > $i)).
% 0.13/0.40 tff(c23_type, type, (
% 0.13/0.40 c23: $i)).
% 0.13/0.40 tff(c22_type, type, (
% 0.13/0.40 c22: $i)).
% 0.13/0.40 tff(f13_type, type, (
% 0.13/0.40 f13: ( $i * $i ) > $i)).
% 0.13/0.40 tff(c24_type, type, (
% 0.13/0.40 c24: $i)).
% 0.13/0.40 tff(p18_type, type, (
% 0.13/0.40 p18: ( $i * $i ) > $o)).
% 0.13/0.40 tff(f6_type, type, (
% 0.13/0.40 f6: $i > $i)).
% 0.13/0.40 tff(c19_type, type, (
% 0.13/0.40 c19: $i)).
% 0.13/0.40 tff(f15_type, type, (
% 0.13/0.40 f15: $i > $i)).
% 0.13/0.40 tff(f3_type, type, (
% 0.13/0.40 f3: $i > $i)).
% 0.13/0.40 tff(c25_type, type, (
% 0.13/0.40 c25: $i)).
% 0.13/0.40 tff(f14_type, type, (
% 0.13/0.40 f14: $i > $i)).
% 0.13/0.40 tff(f16_type, type, (
% 0.13/0.40 f16: $i > $i)).
% 0.13/0.40 tff(1,assumption,(~p17(c21, c21)), introduced(assumption)).
% 0.13/0.40 tff(2,plain,
% 0.13/0.40 (^[X9: $i] : refl(p17(X9, X9) <=> p17(X9, X9))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(3,plain,
% 0.20/0.40 (![X9: $i] : p17(X9, X9) <=> ![X9: $i] : p17(X9, X9)),
% 0.20/0.40 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.40 tff(4,plain,
% 0.20/0.40 (![X9: $i] : p17(X9, X9) <=> ![X9: $i] : p17(X9, X9)),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(5,axiom,(![X9: $i] : p17(X9, X9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p17_6')).
% 0.20/0.40 tff(6,plain,
% 0.20/0.40 (![X9: $i] : p17(X9, X9)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.40 tff(7,plain,(
% 0.20/0.40 ![X9: $i] : p17(X9, X9)),
% 0.20/0.40 inference(skolemize,[status(sab)],[6])).
% 0.20/0.40 tff(8,plain,
% 0.20/0.40 (![X9: $i] : p17(X9, X9)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.40 tff(9,plain,
% 0.20/0.40 ((~![X9: $i] : p17(X9, X9)) | p17(c21, c21)),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(10,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.20/0.40 tff(11,plain,(p17(c21, c21)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(12,assumption,(~p18(c24, f6(c19))), introduced(assumption)).
% 0.20/0.40 tff(13,plain,
% 0.20/0.40 (^[X12: $i] : refl(((~p18(X12, f6(c25))) | p18(X12, f6(c19)) | p17(f3(c21), f15(X12))) <=> ((~p18(X12, f6(c25))) | p18(X12, f6(c19)) | p17(f3(c21), f15(X12))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(14,plain,
% 0.20/0.40 (![X12: $i] : ((~p18(X12, f6(c25))) | p18(X12, f6(c19)) | p17(f3(c21), f15(X12))) <=> ![X12: $i] : ((~p18(X12, f6(c25))) | p18(X12, f6(c19)) | p17(f3(c21), f15(X12)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.40 tff(15,plain,
% 0.20/0.40 (![X12: $i] : ((~p18(X12, f6(c25))) | p18(X12, f6(c19)) | p17(f3(c21), f15(X12))) <=> ![X12: $i] : ((~p18(X12, f6(c25))) | p18(X12, f6(c19)) | p17(f3(c21), f15(X12)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(16,plain,
% 0.20/0.40 (^[X12: $i] : trans(monotonicity(rewrite((p18(X12, f6(c19)) | p17(f3(c21), f15(X12))) <=> (p18(X12, f6(c19)) | p17(f3(c21), f15(X12)))), (((p18(X12, f6(c19)) | p17(f3(c21), f15(X12))) | (~p18(X12, f6(c25)))) <=> ((p18(X12, f6(c19)) | p17(f3(c21), f15(X12))) | (~p18(X12, f6(c25)))))), rewrite(((p18(X12, f6(c19)) | p17(f3(c21), f15(X12))) | (~p18(X12, f6(c25)))) <=> ((~p18(X12, f6(c25))) | p18(X12, f6(c19)) | p17(f3(c21), f15(X12)))), (((p18(X12, f6(c19)) | p17(f3(c21), f15(X12))) | (~p18(X12, f6(c25)))) <=> ((~p18(X12, f6(c25))) | p18(X12, f6(c19)) | p17(f3(c21), f15(X12)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(17,plain,
% 0.20/0.40 (![X12: $i] : ((p18(X12, f6(c19)) | p17(f3(c21), f15(X12))) | (~p18(X12, f6(c25)))) <=> ![X12: $i] : ((~p18(X12, f6(c25))) | p18(X12, f6(c19)) | p17(f3(c21), f15(X12)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[16])).
% 0.20/0.40 tff(18,axiom,(![X12: $i] : ((p18(X12, f6(c19)) | p17(f3(c21), f15(X12))) | (~p18(X12, f6(c25))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p18_27')).
% 0.20/0.40 tff(19,plain,
% 0.20/0.40 (![X12: $i] : ((~p18(X12, f6(c25))) | p18(X12, f6(c19)) | p17(f3(c21), f15(X12)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.20/0.40 tff(20,plain,
% 0.20/0.40 (![X12: $i] : ((~p18(X12, f6(c25))) | p18(X12, f6(c19)) | p17(f3(c21), f15(X12)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.20/0.40 tff(21,plain,(
% 0.20/0.40 ![X12: $i] : ((~p18(X12, f6(c25))) | p18(X12, f6(c19)) | p17(f3(c21), f15(X12)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[20])).
% 0.20/0.41 tff(22,plain,
% 0.20/0.41 (![X12: $i] : ((~p18(X12, f6(c25))) | p18(X12, f6(c19)) | p17(f3(c21), f15(X12)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.20/0.41 tff(23,plain,
% 0.20/0.41 (p18(c24, f6(c25)) <=> p18(c24, f6(c25))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(24,axiom,(p18(c24, f6(c25))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p18_7')).
% 0.20/0.41 tff(25,plain,
% 0.20/0.41 (p18(c24, f6(c25))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.20/0.41 tff(26,plain,
% 0.20/0.41 (((~![X12: $i] : ((~p18(X12, f6(c25))) | p18(X12, f6(c19)) | p17(f3(c21), f15(X12)))) | ((~p18(c24, f6(c25))) | p18(c24, f6(c19)) | p17(f3(c21), f15(c24)))) <=> ((~![X12: $i] : ((~p18(X12, f6(c25))) | p18(X12, f6(c19)) | p17(f3(c21), f15(X12)))) | (~p18(c24, f6(c25))) | p18(c24, f6(c19)) | p17(f3(c21), f15(c24)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(27,plain,
% 0.20/0.41 ((~![X12: $i] : ((~p18(X12, f6(c25))) | p18(X12, f6(c19)) | p17(f3(c21), f15(X12)))) | ((~p18(c24, f6(c25))) | p18(c24, f6(c19)) | p17(f3(c21), f15(c24)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(28,plain,
% 0.20/0.41 ((~![X12: $i] : ((~p18(X12, f6(c25))) | p18(X12, f6(c19)) | p17(f3(c21), f15(X12)))) | (~p18(c24, f6(c25))) | p18(c24, f6(c19)) | p17(f3(c21), f15(c24))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.20/0.41 tff(29,plain,
% 0.20/0.41 (p18(c24, f6(c19)) | p17(f3(c21), f15(c24))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[28, 25, 22])).
% 0.20/0.41 tff(30,plain,
% 0.20/0.41 (p17(f3(c21), f15(c24))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[29, 12])).
% 0.20/0.41 tff(31,plain,
% 0.20/0.41 (^[X11: $i, X10: $i] : refl(((~p17(f3(X10), X11)) | p17(X10, X11)) <=> ((~p17(f3(X10), X11)) | p17(X10, X11)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(32,plain,
% 0.20/0.41 (![X11: $i, X10: $i] : ((~p17(f3(X10), X11)) | p17(X10, X11)) <=> ![X11: $i, X10: $i] : ((~p17(f3(X10), X11)) | p17(X10, X11))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[31])).
% 0.20/0.41 tff(33,plain,
% 0.20/0.41 (![X11: $i, X10: $i] : ((~p17(f3(X10), X11)) | p17(X10, X11)) <=> ![X11: $i, X10: $i] : ((~p17(f3(X10), X11)) | p17(X10, X11))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(34,plain,
% 0.20/0.41 (^[X11: $i, X10: $i] : rewrite((p17(X10, X11) | (~p17(f3(X10), X11))) <=> ((~p17(f3(X10), X11)) | p17(X10, X11)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(35,plain,
% 0.20/0.41 (![X11: $i, X10: $i] : (p17(X10, X11) | (~p17(f3(X10), X11))) <=> ![X11: $i, X10: $i] : ((~p17(f3(X10), X11)) | p17(X10, X11))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[34])).
% 0.20/0.41 tff(36,axiom,(![X11: $i, X10: $i] : (p17(X10, X11) | (~p17(f3(X10), X11)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p17_9')).
% 0.20/0.41 tff(37,plain,
% 0.20/0.41 (![X11: $i, X10: $i] : ((~p17(f3(X10), X11)) | p17(X10, X11))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.20/0.41 tff(38,plain,
% 0.20/0.41 (![X11: $i, X10: $i] : ((~p17(f3(X10), X11)) | p17(X10, X11))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.20/0.41 tff(39,plain,(
% 0.20/0.41 ![X11: $i, X10: $i] : ((~p17(f3(X10), X11)) | p17(X10, X11))),
% 0.20/0.41 inference(skolemize,[status(sab)],[38])).
% 0.20/0.41 tff(40,plain,
% 0.20/0.41 (![X11: $i, X10: $i] : ((~p17(f3(X10), X11)) | p17(X10, X11))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.20/0.41 tff(41,plain,
% 0.20/0.41 (((~![X11: $i, X10: $i] : ((~p17(f3(X10), X11)) | p17(X10, X11))) | ((~p17(f3(c21), f15(c24))) | p17(c21, f15(c24)))) <=> ((~![X11: $i, X10: $i] : ((~p17(f3(X10), X11)) | p17(X10, X11))) | (~p17(f3(c21), f15(c24))) | p17(c21, f15(c24)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(42,plain,
% 0.20/0.41 ((~![X11: $i, X10: $i] : ((~p17(f3(X10), X11)) | p17(X10, X11))) | ((~p17(f3(c21), f15(c24))) | p17(c21, f15(c24)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(43,plain,
% 0.20/0.41 ((~![X11: $i, X10: $i] : ((~p17(f3(X10), X11)) | p17(X10, X11))) | (~p17(f3(c21), f15(c24))) | p17(c21, f15(c24))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.41 tff(44,plain,
% 0.20/0.41 (p17(c21, f15(c24))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[43, 40, 30])).
% 0.20/0.41 tff(45,plain,
% 0.20/0.41 (^[X12: $i] : refl(((~p18(X12, f6(c25))) | p2(f14(X12), c20) | p18(X12, f6(c19))) <=> ((~p18(X12, f6(c25))) | p2(f14(X12), c20) | p18(X12, f6(c19))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(46,plain,
% 0.20/0.41 (![X12: $i] : ((~p18(X12, f6(c25))) | p2(f14(X12), c20) | p18(X12, f6(c19))) <=> ![X12: $i] : ((~p18(X12, f6(c25))) | p2(f14(X12), c20) | p18(X12, f6(c19)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[45])).
% 0.20/0.41 tff(47,plain,
% 0.20/0.41 (![X12: $i] : ((~p18(X12, f6(c25))) | p2(f14(X12), c20) | p18(X12, f6(c19))) <=> ![X12: $i] : ((~p18(X12, f6(c25))) | p2(f14(X12), c20) | p18(X12, f6(c19)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(48,plain,
% 0.20/0.41 (^[X12: $i] : rewrite(((p18(X12, f6(c19)) | p2(f14(X12), c20)) | (~p18(X12, f6(c25)))) <=> ((~p18(X12, f6(c25))) | p2(f14(X12), c20) | p18(X12, f6(c19))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(49,plain,
% 0.20/0.41 (![X12: $i] : ((p18(X12, f6(c19)) | p2(f14(X12), c20)) | (~p18(X12, f6(c25)))) <=> ![X12: $i] : ((~p18(X12, f6(c25))) | p2(f14(X12), c20) | p18(X12, f6(c19)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[48])).
% 0.20/0.41 tff(50,axiom,(![X12: $i] : ((p18(X12, f6(c19)) | p2(f14(X12), c20)) | (~p18(X12, f6(c25))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p18_24')).
% 0.20/0.41 tff(51,plain,
% 0.20/0.41 (![X12: $i] : ((~p18(X12, f6(c25))) | p2(f14(X12), c20) | p18(X12, f6(c19)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.20/0.41 tff(52,plain,
% 0.20/0.41 (![X12: $i] : ((~p18(X12, f6(c25))) | p2(f14(X12), c20) | p18(X12, f6(c19)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.20/0.41 tff(53,plain,(
% 0.20/0.41 ![X12: $i] : ((~p18(X12, f6(c25))) | p2(f14(X12), c20) | p18(X12, f6(c19)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[52])).
% 0.20/0.41 tff(54,plain,
% 0.20/0.41 (![X12: $i] : ((~p18(X12, f6(c25))) | p2(f14(X12), c20) | p18(X12, f6(c19)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.20/0.41 tff(55,plain,
% 0.20/0.41 (((~![X12: $i] : ((~p18(X12, f6(c25))) | p2(f14(X12), c20) | p18(X12, f6(c19)))) | ((~p18(c24, f6(c25))) | p18(c24, f6(c19)) | p2(f14(c24), c20))) <=> ((~![X12: $i] : ((~p18(X12, f6(c25))) | p2(f14(X12), c20) | p18(X12, f6(c19)))) | (~p18(c24, f6(c25))) | p18(c24, f6(c19)) | p2(f14(c24), c20))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(56,plain,
% 0.20/0.41 (((~p18(c24, f6(c25))) | p2(f14(c24), c20) | p18(c24, f6(c19))) <=> ((~p18(c24, f6(c25))) | p18(c24, f6(c19)) | p2(f14(c24), c20))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(57,plain,
% 0.20/0.41 (((~![X12: $i] : ((~p18(X12, f6(c25))) | p2(f14(X12), c20) | p18(X12, f6(c19)))) | ((~p18(c24, f6(c25))) | p2(f14(c24), c20) | p18(c24, f6(c19)))) <=> ((~![X12: $i] : ((~p18(X12, f6(c25))) | p2(f14(X12), c20) | p18(X12, f6(c19)))) | ((~p18(c24, f6(c25))) | p18(c24, f6(c19)) | p2(f14(c24), c20)))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[56])).
% 0.20/0.41 tff(58,plain,
% 0.20/0.41 (((~![X12: $i] : ((~p18(X12, f6(c25))) | p2(f14(X12), c20) | p18(X12, f6(c19)))) | ((~p18(c24, f6(c25))) | p2(f14(c24), c20) | p18(c24, f6(c19)))) <=> ((~![X12: $i] : ((~p18(X12, f6(c25))) | p2(f14(X12), c20) | p18(X12, f6(c19)))) | (~p18(c24, f6(c25))) | p18(c24, f6(c19)) | p2(f14(c24), c20))),
% 0.20/0.41 inference(transitivity,[status(thm)],[57, 55])).
% 0.20/0.41 tff(59,plain,
% 0.20/0.41 ((~![X12: $i] : ((~p18(X12, f6(c25))) | p2(f14(X12), c20) | p18(X12, f6(c19)))) | ((~p18(c24, f6(c25))) | p2(f14(c24), c20) | p18(c24, f6(c19)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(60,plain,
% 0.20/0.41 ((~![X12: $i] : ((~p18(X12, f6(c25))) | p2(f14(X12), c20) | p18(X12, f6(c19)))) | (~p18(c24, f6(c25))) | p18(c24, f6(c19)) | p2(f14(c24), c20)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.20/0.41 tff(61,plain,
% 0.20/0.41 (p18(c24, f6(c19)) | p2(f14(c24), c20)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[60, 25, 54])).
% 0.20/0.41 tff(62,plain,
% 0.20/0.41 (p2(f14(c24), c20)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[61, 12])).
% 0.20/0.41 tff(63,plain,
% 0.20/0.41 (^[X12: $i] : refl(((~p18(X12, f6(c25))) | p18(X12, f6(c19)) | p8(X12, f9(f13(f14(X12), f15(X12)), f16(X12)))) <=> ((~p18(X12, f6(c25))) | p18(X12, f6(c19)) | p8(X12, f9(f13(f14(X12), f15(X12)), f16(X12)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(64,plain,
% 0.20/0.41 (![X12: $i] : ((~p18(X12, f6(c25))) | p18(X12, f6(c19)) | p8(X12, f9(f13(f14(X12), f15(X12)), f16(X12)))) <=> ![X12: $i] : ((~p18(X12, f6(c25))) | p18(X12, f6(c19)) | p8(X12, f9(f13(f14(X12), f15(X12)), f16(X12))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[63])).
% 0.20/0.41 tff(65,plain,
% 0.20/0.41 (![X12: $i] : ((~p18(X12, f6(c25))) | p18(X12, f6(c19)) | p8(X12, f9(f13(f14(X12), f15(X12)), f16(X12)))) <=> ![X12: $i] : ((~p18(X12, f6(c25))) | p18(X12, f6(c19)) | p8(X12, f9(f13(f14(X12), f15(X12)), f16(X12))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(66,plain,
% 0.20/0.41 (^[X12: $i] : rewrite(((p18(X12, f6(c19)) | p8(X12, f9(f13(f14(X12), f15(X12)), f16(X12)))) | (~p18(X12, f6(c25)))) <=> ((~p18(X12, f6(c25))) | p18(X12, f6(c19)) | p8(X12, f9(f13(f14(X12), f15(X12)), f16(X12)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(67,plain,
% 0.20/0.41 (![X12: $i] : ((p18(X12, f6(c19)) | p8(X12, f9(f13(f14(X12), f15(X12)), f16(X12)))) | (~p18(X12, f6(c25)))) <=> ![X12: $i] : ((~p18(X12, f6(c25))) | p18(X12, f6(c19)) | p8(X12, f9(f13(f14(X12), f15(X12)), f16(X12))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[66])).
% 0.20/0.41 tff(68,axiom,(![X12: $i] : ((p18(X12, f6(c19)) | p8(X12, f9(f13(f14(X12), f15(X12)), f16(X12)))) | (~p18(X12, f6(c25))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p18_33')).
% 0.20/0.41 tff(69,plain,
% 0.20/0.41 (![X12: $i] : ((~p18(X12, f6(c25))) | p18(X12, f6(c19)) | p8(X12, f9(f13(f14(X12), f15(X12)), f16(X12))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.20/0.41 tff(70,plain,
% 0.20/0.41 (![X12: $i] : ((~p18(X12, f6(c25))) | p18(X12, f6(c19)) | p8(X12, f9(f13(f14(X12), f15(X12)), f16(X12))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.20/0.41 tff(71,plain,(
% 0.20/0.41 ![X12: $i] : ((~p18(X12, f6(c25))) | p18(X12, f6(c19)) | p8(X12, f9(f13(f14(X12), f15(X12)), f16(X12))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[70])).
% 0.20/0.41 tff(72,plain,
% 0.20/0.41 (![X12: $i] : ((~p18(X12, f6(c25))) | p18(X12, f6(c19)) | p8(X12, f9(f13(f14(X12), f15(X12)), f16(X12))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.20/0.41 tff(73,plain,
% 0.20/0.41 (((~![X12: $i] : ((~p18(X12, f6(c25))) | p18(X12, f6(c19)) | p8(X12, f9(f13(f14(X12), f15(X12)), f16(X12))))) | ((~p18(c24, f6(c25))) | p18(c24, f6(c19)) | p8(c24, f9(f13(f14(c24), f15(c24)), f16(c24))))) <=> ((~![X12: $i] : ((~p18(X12, f6(c25))) | p18(X12, f6(c19)) | p8(X12, f9(f13(f14(X12), f15(X12)), f16(X12))))) | (~p18(c24, f6(c25))) | p18(c24, f6(c19)) | p8(c24, f9(f13(f14(c24), f15(c24)), f16(c24))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(74,plain,
% 0.20/0.41 ((~![X12: $i] : ((~p18(X12, f6(c25))) | p18(X12, f6(c19)) | p8(X12, f9(f13(f14(X12), f15(X12)), f16(X12))))) | ((~p18(c24, f6(c25))) | p18(c24, f6(c19)) | p8(c24, f9(f13(f14(c24), f15(c24)), f16(c24))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(75,plain,
% 0.20/0.41 ((~![X12: $i] : ((~p18(X12, f6(c25))) | p18(X12, f6(c19)) | p8(X12, f9(f13(f14(X12), f15(X12)), f16(X12))))) | (~p18(c24, f6(c25))) | p18(c24, f6(c19)) | p8(c24, f9(f13(f14(c24), f15(c24)), f16(c24)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.20/0.41 tff(76,plain,
% 0.20/0.41 (p18(c24, f6(c19)) | p8(c24, f9(f13(f14(c24), f15(c24)), f16(c24)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[75, 25, 72])).
% 0.20/0.41 tff(77,plain,
% 0.20/0.41 (p8(c24, f9(f13(f14(c24), f15(c24)), f16(c24)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[76, 12])).
% 0.20/0.41 tff(78,plain,
% 0.20/0.41 (^[X59: $i, X60: $i, X58: $i] : refl(((~p8(c24, f9(f13(X59, X58), X60))) | (~p17(c21, X58)) | (~p2(X59, c20))) <=> ((~p8(c24, f9(f13(X59, X58), X60))) | (~p17(c21, X58)) | (~p2(X59, c20))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(79,plain,
% 0.20/0.41 (![X59: $i, X60: $i, X58: $i] : ((~p8(c24, f9(f13(X59, X58), X60))) | (~p17(c21, X58)) | (~p2(X59, c20))) <=> ![X59: $i, X60: $i, X58: $i] : ((~p8(c24, f9(f13(X59, X58), X60))) | (~p17(c21, X58)) | (~p2(X59, c20)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[78])).
% 0.20/0.41 tff(80,plain,
% 0.20/0.41 (![X59: $i, X60: $i, X58: $i] : ((~p8(c24, f9(f13(X59, X58), X60))) | (~p17(c21, X58)) | (~p2(X59, c20))) <=> ![X59: $i, X60: $i, X58: $i] : ((~p8(c24, f9(f13(X59, X58), X60))) | (~p17(c21, X58)) | (~p2(X59, c20)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(81,plain,
% 0.20/0.41 (^[X59: $i, X60: $i, X58: $i] : trans(monotonicity(rewrite(((~p2(X59, c20)) | (~p17(c21, X58))) <=> ((~p17(c21, X58)) | (~p2(X59, c20)))), ((((~p2(X59, c20)) | (~p17(c21, X58))) | (~p8(c24, f9(f13(X59, X58), X60)))) <=> (((~p17(c21, X58)) | (~p2(X59, c20))) | (~p8(c24, f9(f13(X59, X58), X60)))))), rewrite((((~p17(c21, X58)) | (~p2(X59, c20))) | (~p8(c24, f9(f13(X59, X58), X60)))) <=> ((~p8(c24, f9(f13(X59, X58), X60))) | (~p17(c21, X58)) | (~p2(X59, c20)))), ((((~p2(X59, c20)) | (~p17(c21, X58))) | (~p8(c24, f9(f13(X59, X58), X60)))) <=> ((~p8(c24, f9(f13(X59, X58), X60))) | (~p17(c21, X58)) | (~p2(X59, c20)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(82,plain,
% 0.20/0.42 (![X59: $i, X60: $i, X58: $i] : (((~p2(X59, c20)) | (~p17(c21, X58))) | (~p8(c24, f9(f13(X59, X58), X60)))) <=> ![X59: $i, X60: $i, X58: $i] : ((~p8(c24, f9(f13(X59, X58), X60))) | (~p17(c21, X58)) | (~p2(X59, c20)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[81])).
% 0.20/0.42 tff(83,axiom,(![X59: $i, X60: $i, X58: $i] : (((~p2(X59, c20)) | (~p17(c21, X58))) | (~p8(c24, f9(f13(X59, X58), X60))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_p2_32')).
% 0.20/0.42 tff(84,plain,
% 0.20/0.42 (![X59: $i, X60: $i, X58: $i] : ((~p8(c24, f9(f13(X59, X58), X60))) | (~p17(c21, X58)) | (~p2(X59, c20)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.20/0.42 tff(85,plain,
% 0.20/0.42 (![X59: $i, X60: $i, X58: $i] : ((~p8(c24, f9(f13(X59, X58), X60))) | (~p17(c21, X58)) | (~p2(X59, c20)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.20/0.42 tff(86,plain,(
% 0.20/0.42 ![X59: $i, X60: $i, X58: $i] : ((~p8(c24, f9(f13(X59, X58), X60))) | (~p17(c21, X58)) | (~p2(X59, c20)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[85])).
% 0.20/0.42 tff(87,plain,
% 0.20/0.42 (![X59: $i, X60: $i, X58: $i] : ((~p8(c24, f9(f13(X59, X58), X60))) | (~p17(c21, X58)) | (~p2(X59, c20)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[86, 79])).
% 0.20/0.42 tff(88,plain,
% 0.20/0.42 (((~![X59: $i, X60: $i, X58: $i] : ((~p8(c24, f9(f13(X59, X58), X60))) | (~p17(c21, X58)) | (~p2(X59, c20)))) | ((~p8(c24, f9(f13(f14(c24), f15(c24)), f16(c24)))) | (~p17(c21, f15(c24))) | (~p2(f14(c24), c20)))) <=> ((~![X59: $i, X60: $i, X58: $i] : ((~p8(c24, f9(f13(X59, X58), X60))) | (~p17(c21, X58)) | (~p2(X59, c20)))) | (~p8(c24, f9(f13(f14(c24), f15(c24)), f16(c24)))) | (~p17(c21, f15(c24))) | (~p2(f14(c24), c20)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(89,plain,
% 0.20/0.42 ((~![X59: $i, X60: $i, X58: $i] : ((~p8(c24, f9(f13(X59, X58), X60))) | (~p17(c21, X58)) | (~p2(X59, c20)))) | ((~p8(c24, f9(f13(f14(c24), f15(c24)), f16(c24)))) | (~p17(c21, f15(c24))) | (~p2(f14(c24), c20)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(90,plain,
% 0.20/0.42 ((~![X59: $i, X60: $i, X58: $i] : ((~p8(c24, f9(f13(X59, X58), X60))) | (~p17(c21, X58)) | (~p2(X59, c20)))) | (~p8(c24, f9(f13(f14(c24), f15(c24)), f16(c24)))) | (~p17(c21, f15(c24))) | (~p2(f14(c24), c20))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.20/0.42 tff(91,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[90, 87, 77, 62, 44])).
% 0.20/0.42 tff(92,plain,(p18(c24, f6(c19))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(93,plain,
% 0.20/0.42 (^[X17: $i] : refl(((~p18(X17, f6(c19))) | p8(X17, f9(f13(c20, c21), f11(f12(f7(c22, c23))))) | p18(X17, f6(f7(c22, c23)))) <=> ((~p18(X17, f6(c19))) | p8(X17, f9(f13(c20, c21), f11(f12(f7(c22, c23))))) | p18(X17, f6(f7(c22, c23)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(94,plain,
% 0.20/0.42 (![X17: $i] : ((~p18(X17, f6(c19))) | p8(X17, f9(f13(c20, c21), f11(f12(f7(c22, c23))))) | p18(X17, f6(f7(c22, c23)))) <=> ![X17: $i] : ((~p18(X17, f6(c19))) | p8(X17, f9(f13(c20, c21), f11(f12(f7(c22, c23))))) | p18(X17, f6(f7(c22, c23))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[93])).
% 0.20/0.42 tff(95,plain,
% 0.20/0.42 (![X17: $i] : ((~p18(X17, f6(c19))) | p8(X17, f9(f13(c20, c21), f11(f12(f7(c22, c23))))) | p18(X17, f6(f7(c22, c23)))) <=> ![X17: $i] : ((~p18(X17, f6(c19))) | p8(X17, f9(f13(c20, c21), f11(f12(f7(c22, c23))))) | p18(X17, f6(f7(c22, c23))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(96,plain,
% 0.20/0.42 (^[X17: $i] : rewrite(((p18(X17, f6(f7(c22, c23))) | p8(X17, f9(f13(c20, c21), f11(f12(f7(c22, c23)))))) | (~p18(X17, f6(c19)))) <=> ((~p18(X17, f6(c19))) | p8(X17, f9(f13(c20, c21), f11(f12(f7(c22, c23))))) | p18(X17, f6(f7(c22, c23)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(97,plain,
% 0.20/0.42 (![X17: $i] : ((p18(X17, f6(f7(c22, c23))) | p8(X17, f9(f13(c20, c21), f11(f12(f7(c22, c23)))))) | (~p18(X17, f6(c19)))) <=> ![X17: $i] : ((~p18(X17, f6(c19))) | p8(X17, f9(f13(c20, c21), f11(f12(f7(c22, c23))))) | p18(X17, f6(f7(c22, c23))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[96])).
% 0.20/0.42 tff(98,axiom,(![X17: $i] : ((p18(X17, f6(f7(c22, c23))) | p8(X17, f9(f13(c20, c21), f11(f12(f7(c22, c23)))))) | (~p18(X17, f6(c19))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p18_34')).
% 0.20/0.42 tff(99,plain,
% 0.20/0.42 (![X17: $i] : ((~p18(X17, f6(c19))) | p8(X17, f9(f13(c20, c21), f11(f12(f7(c22, c23))))) | p18(X17, f6(f7(c22, c23))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.20/0.42 tff(100,plain,
% 0.20/0.42 (![X17: $i] : ((~p18(X17, f6(c19))) | p8(X17, f9(f13(c20, c21), f11(f12(f7(c22, c23))))) | p18(X17, f6(f7(c22, c23))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[99, 95])).
% 0.20/0.42 tff(101,plain,(
% 0.20/0.42 ![X17: $i] : ((~p18(X17, f6(c19))) | p8(X17, f9(f13(c20, c21), f11(f12(f7(c22, c23))))) | p18(X17, f6(f7(c22, c23))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[100])).
% 0.20/0.42 tff(102,plain,
% 0.20/0.42 (![X17: $i] : ((~p18(X17, f6(c19))) | p8(X17, f9(f13(c20, c21), f11(f12(f7(c22, c23))))) | p18(X17, f6(f7(c22, c23))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[101, 94])).
% 0.20/0.42 tff(103,plain,
% 0.20/0.42 ((~p18(c24, f6(f7(c22, c23)))) <=> (~p18(c24, f6(f7(c22, c23))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(104,axiom,(~p18(c24, f6(f7(c22, c23)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_p18_8')).
% 0.20/0.42 tff(105,plain,
% 0.20/0.42 (~p18(c24, f6(f7(c22, c23)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.20/0.42 tff(106,plain,
% 0.20/0.42 (((~![X17: $i] : ((~p18(X17, f6(c19))) | p8(X17, f9(f13(c20, c21), f11(f12(f7(c22, c23))))) | p18(X17, f6(f7(c22, c23))))) | (p18(c24, f6(f7(c22, c23))) | (~p18(c24, f6(c19))) | p8(c24, f9(f13(c20, c21), f11(f12(f7(c22, c23))))))) <=> ((~![X17: $i] : ((~p18(X17, f6(c19))) | p8(X17, f9(f13(c20, c21), f11(f12(f7(c22, c23))))) | p18(X17, f6(f7(c22, c23))))) | p18(c24, f6(f7(c22, c23))) | (~p18(c24, f6(c19))) | p8(c24, f9(f13(c20, c21), f11(f12(f7(c22, c23))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(107,plain,
% 0.20/0.42 (((~p18(c24, f6(c19))) | p8(c24, f9(f13(c20, c21), f11(f12(f7(c22, c23))))) | p18(c24, f6(f7(c22, c23)))) <=> (p18(c24, f6(f7(c22, c23))) | (~p18(c24, f6(c19))) | p8(c24, f9(f13(c20, c21), f11(f12(f7(c22, c23))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(108,plain,
% 0.20/0.42 (((~![X17: $i] : ((~p18(X17, f6(c19))) | p8(X17, f9(f13(c20, c21), f11(f12(f7(c22, c23))))) | p18(X17, f6(f7(c22, c23))))) | ((~p18(c24, f6(c19))) | p8(c24, f9(f13(c20, c21), f11(f12(f7(c22, c23))))) | p18(c24, f6(f7(c22, c23))))) <=> ((~![X17: $i] : ((~p18(X17, f6(c19))) | p8(X17, f9(f13(c20, c21), f11(f12(f7(c22, c23))))) | p18(X17, f6(f7(c22, c23))))) | (p18(c24, f6(f7(c22, c23))) | (~p18(c24, f6(c19))) | p8(c24, f9(f13(c20, c21), f11(f12(f7(c22, c23)))))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[107])).
% 0.20/0.42 tff(109,plain,
% 0.20/0.42 (((~![X17: $i] : ((~p18(X17, f6(c19))) | p8(X17, f9(f13(c20, c21), f11(f12(f7(c22, c23))))) | p18(X17, f6(f7(c22, c23))))) | ((~p18(c24, f6(c19))) | p8(c24, f9(f13(c20, c21), f11(f12(f7(c22, c23))))) | p18(c24, f6(f7(c22, c23))))) <=> ((~![X17: $i] : ((~p18(X17, f6(c19))) | p8(X17, f9(f13(c20, c21), f11(f12(f7(c22, c23))))) | p18(X17, f6(f7(c22, c23))))) | p18(c24, f6(f7(c22, c23))) | (~p18(c24, f6(c19))) | p8(c24, f9(f13(c20, c21), f11(f12(f7(c22, c23))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[108, 106])).
% 0.20/0.42 tff(110,plain,
% 0.20/0.42 ((~![X17: $i] : ((~p18(X17, f6(c19))) | p8(X17, f9(f13(c20, c21), f11(f12(f7(c22, c23))))) | p18(X17, f6(f7(c22, c23))))) | ((~p18(c24, f6(c19))) | p8(c24, f9(f13(c20, c21), f11(f12(f7(c22, c23))))) | p18(c24, f6(f7(c22, c23))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(111,plain,
% 0.20/0.42 ((~![X17: $i] : ((~p18(X17, f6(c19))) | p8(X17, f9(f13(c20, c21), f11(f12(f7(c22, c23))))) | p18(X17, f6(f7(c22, c23))))) | p18(c24, f6(f7(c22, c23))) | (~p18(c24, f6(c19))) | p8(c24, f9(f13(c20, c21), f11(f12(f7(c22, c23)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.20/0.43 tff(112,plain,
% 0.20/0.43 ((~p18(c24, f6(c19))) | p8(c24, f9(f13(c20, c21), f11(f12(f7(c22, c23)))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[111, 105, 102])).
% 0.20/0.43 tff(113,plain,
% 0.20/0.43 (p8(c24, f9(f13(c20, c21), f11(f12(f7(c22, c23)))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[112, 92])).
% 0.20/0.43 tff(114,plain,
% 0.20/0.43 (((~![X59: $i, X60: $i, X58: $i] : ((~p8(c24, f9(f13(X59, X58), X60))) | (~p17(c21, X58)) | (~p2(X59, c20)))) | ((~p8(c24, f9(f13(c20, c21), f11(f12(f7(c22, c23)))))) | (~p17(c21, c21)) | (~p2(c20, c20)))) <=> ((~![X59: $i, X60: $i, X58: $i] : ((~p8(c24, f9(f13(X59, X58), X60))) | (~p17(c21, X58)) | (~p2(X59, c20)))) | (~p8(c24, f9(f13(c20, c21), f11(f12(f7(c22, c23)))))) | (~p17(c21, c21)) | (~p2(c20, c20)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(115,plain,
% 0.20/0.43 ((~![X59: $i, X60: $i, X58: $i] : ((~p8(c24, f9(f13(X59, X58), X60))) | (~p17(c21, X58)) | (~p2(X59, c20)))) | ((~p8(c24, f9(f13(c20, c21), f11(f12(f7(c22, c23)))))) | (~p17(c21, c21)) | (~p2(c20, c20)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(116,plain,
% 0.20/0.43 ((~![X59: $i, X60: $i, X58: $i] : ((~p8(c24, f9(f13(X59, X58), X60))) | (~p17(c21, X58)) | (~p2(X59, c20)))) | (~p8(c24, f9(f13(c20, c21), f11(f12(f7(c22, c23)))))) | (~p17(c21, c21)) | (~p2(c20, c20))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.20/0.43 tff(117,plain,
% 0.20/0.43 ((~p17(c21, c21)) | (~p2(c20, c20))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[116, 87, 113])).
% 0.20/0.43 tff(118,plain,
% 0.20/0.43 (~p2(c20, c20)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[117, 11])).
% 0.20/0.43 tff(119,plain,
% 0.20/0.43 (^[X18: $i] : refl(p2(X18, X18) <=> p2(X18, X18))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(120,plain,
% 0.20/0.43 (![X18: $i] : p2(X18, X18) <=> ![X18: $i] : p2(X18, X18)),
% 0.20/0.43 inference(quant_intro,[status(thm)],[119])).
% 0.20/0.43 tff(121,plain,
% 0.20/0.43 (![X18: $i] : p2(X18, X18) <=> ![X18: $i] : p2(X18, X18)),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(122,axiom,(![X18: $i] : p2(X18, X18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_5')).
% 0.20/0.43 tff(123,plain,
% 0.20/0.43 (![X18: $i] : p2(X18, X18)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.20/0.43 tff(124,plain,(
% 0.20/0.43 ![X18: $i] : p2(X18, X18)),
% 0.20/0.43 inference(skolemize,[status(sab)],[123])).
% 0.20/0.43 tff(125,plain,
% 0.20/0.43 (![X18: $i] : p2(X18, X18)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[124, 120])).
% 0.20/0.43 tff(126,plain,
% 0.20/0.43 ((~![X18: $i] : p2(X18, X18)) | p2(c20, c20)),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(127,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[126, 125, 118])).
% 0.20/0.43 % SZS output end Proof
%------------------------------------------------------------------------------