%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN652-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 : Sat Jun 21 05:39:46 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN652-1 : TPTP v9.0.0. Released v2.5.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n015.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 12:39:41 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.20/0.38 % SZS status Unsatisfiable
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 tff(p4_type, type, (
% 0.20/0.38 p4: ( $i * $i ) > $o)).
% 0.20/0.38 tff(f15_type, type, (
% 0.20/0.38 f15: ( $i * $i ) > $i)).
% 0.20/0.38 tff(c34_type, type, (
% 0.20/0.38 c34: $i)).
% 0.20/0.38 tff(f17_type, type, (
% 0.20/0.38 f17: ( $i * $i ) > $i)).
% 0.20/0.38 tff(c31_type, type, (
% 0.20/0.38 c31: $i)).
% 0.20/0.38 tff(c36_type, type, (
% 0.20/0.38 c36: $i)).
% 0.20/0.38 tff(f5_type, type, (
% 0.20/0.38 f5: ( $i * $i ) > $i)).
% 0.20/0.38 tff(c32_type, type, (
% 0.20/0.38 c32: $i)).
% 0.20/0.38 tff(c35_type, type, (
% 0.20/0.38 c35: $i)).
% 0.20/0.38 tff(p14_type, type, (
% 0.20/0.38 p14: ( $i * $i ) > $o)).
% 0.20/0.38 tff(c33_type, type, (
% 0.20/0.38 c33: $i)).
% 0.20/0.38 tff(p27_type, type, (
% 0.20/0.38 p27: ( $i * $i ) > $o)).
% 0.20/0.38 tff(f8_type, type, (
% 0.20/0.38 f8: ( $i * $i ) > $i)).
% 0.20/0.38 tff(f10_type, type, (
% 0.20/0.38 f10: ( $i * $i ) > $i)).
% 0.20/0.38 tff(f13_type, type, (
% 0.20/0.38 f13: ( $i * $i ) > $i)).
% 0.20/0.38 tff(c30_type, type, (
% 0.20/0.38 c30: $i)).
% 0.20/0.38 tff(c29_type, type, (
% 0.20/0.38 c29: $i)).
% 0.20/0.38 tff(c28_type, type, (
% 0.20/0.38 c28: $i)).
% 0.20/0.38 tff(1,assumption,(~p4(c34, c34)), introduced(assumption)).
% 0.20/0.38 tff(2,plain,
% 0.20/0.38 (^[X53: $i] : refl(p4(X53, X53) <=> p4(X53, X53))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(3,plain,
% 0.20/0.38 (![X53: $i] : p4(X53, X53) <=> ![X53: $i] : p4(X53, X53)),
% 0.20/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.38 tff(4,plain,
% 0.20/0.38 (![X53: $i] : p4(X53, X53) <=> ![X53: $i] : p4(X53, X53)),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(5,axiom,(![X53: $i] : p4(X53, X53)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p4_5')).
% 0.20/0.38 tff(6,plain,
% 0.20/0.38 (![X53: $i] : p4(X53, X53)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.38 tff(7,plain,(
% 0.20/0.38 ![X53: $i] : p4(X53, X53)),
% 0.20/0.38 inference(skolemize,[status(sab)],[6])).
% 0.20/0.38 tff(8,plain,
% 0.20/0.38 (![X53: $i] : p4(X53, X53)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.38 tff(9,plain,
% 0.20/0.38 ((~![X53: $i] : p4(X53, X53)) | p4(c34, c34)),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(10,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.20/0.38 tff(11,plain,(p4(c34, c34)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.38 tff(12,plain,
% 0.20/0.38 (^[X53: $i, X55: $i, X54: $i] : refl(((~p4(X53, X55)) | (~p4(X53, X54)) | p4(X54, X55)) <=> ((~p4(X53, X55)) | (~p4(X53, X54)) | p4(X54, X55)))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(13,plain,
% 0.20/0.38 (![X53: $i, X55: $i, X54: $i] : ((~p4(X53, X55)) | (~p4(X53, X54)) | p4(X54, X55)) <=> ![X53: $i, X55: $i, X54: $i] : ((~p4(X53, X55)) | (~p4(X53, X54)) | p4(X54, X55))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.38 tff(14,plain,
% 0.20/0.38 (![X53: $i, X55: $i, X54: $i] : ((~p4(X53, X55)) | (~p4(X53, X54)) | p4(X54, X55)) <=> ![X53: $i, X55: $i, X54: $i] : ((~p4(X53, X55)) | (~p4(X53, X54)) | p4(X54, X55))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(15,plain,
% 0.20/0.38 (^[X53: $i, X55: $i, X54: $i] : trans(monotonicity(rewrite((p4(X54, X55) | (~p4(X53, X54))) <=> ((~p4(X53, X54)) | p4(X54, X55))), (((p4(X54, X55) | (~p4(X53, X54))) | (~p4(X53, X55))) <=> (((~p4(X53, X54)) | p4(X54, X55)) | (~p4(X53, X55))))), rewrite((((~p4(X53, X54)) | p4(X54, X55)) | (~p4(X53, X55))) <=> ((~p4(X53, X55)) | (~p4(X53, X54)) | p4(X54, X55))), (((p4(X54, X55) | (~p4(X53, X54))) | (~p4(X53, X55))) <=> ((~p4(X53, X55)) | (~p4(X53, X54)) | p4(X54, X55))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(16,plain,
% 0.20/0.38 (![X53: $i, X55: $i, X54: $i] : ((p4(X54, X55) | (~p4(X53, X54))) | (~p4(X53, X55))) <=> ![X53: $i, X55: $i, X54: $i] : ((~p4(X53, X55)) | (~p4(X53, X54)) | p4(X54, X55))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[15])).
% 0.20/0.38 tff(17,axiom,(![X53: $i, X55: $i, X54: $i] : ((p4(X54, X55) | (~p4(X53, X54))) | (~p4(X53, X55)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p4_23')).
% 0.20/0.38 tff(18,plain,
% 0.20/0.38 (![X53: $i, X55: $i, X54: $i] : ((~p4(X53, X55)) | (~p4(X53, X54)) | p4(X54, X55))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.20/0.38 tff(19,plain,
% 0.20/0.38 (![X53: $i, X55: $i, X54: $i] : ((~p4(X53, X55)) | (~p4(X53, X54)) | p4(X54, X55))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.20/0.38 tff(20,plain,(
% 0.20/0.38 ![X53: $i, X55: $i, X54: $i] : ((~p4(X53, X55)) | (~p4(X53, X54)) | p4(X54, X55))),
% 0.20/0.38 inference(skolemize,[status(sab)],[19])).
% 0.20/0.38 tff(21,plain,
% 0.20/0.38 (![X53: $i, X55: $i, X54: $i] : ((~p4(X53, X55)) | (~p4(X53, X54)) | p4(X54, X55))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.20/0.38 tff(22,plain,
% 0.20/0.38 (p4(c34, f5(c35, c32)) <=> p4(c34, f5(c35, c32))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(23,axiom,(p4(c34, f5(c35, c32))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p4_16')).
% 0.20/0.38 tff(24,plain,
% 0.20/0.38 (p4(c34, f5(c35, c32))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.38 tff(25,plain,
% 0.20/0.38 (((~![X53: $i, X55: $i, X54: $i] : ((~p4(X53, X55)) | (~p4(X53, X54)) | p4(X54, X55))) | ((~p4(c34, c34)) | (~p4(c34, f5(c35, c32))) | p4(f5(c35, c32), c34))) <=> ((~![X53: $i, X55: $i, X54: $i] : ((~p4(X53, X55)) | (~p4(X53, X54)) | p4(X54, X55))) | (~p4(c34, c34)) | (~p4(c34, f5(c35, c32))) | p4(f5(c35, c32), c34))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(26,plain,
% 0.20/0.38 ((~![X53: $i, X55: $i, X54: $i] : ((~p4(X53, X55)) | (~p4(X53, X54)) | p4(X54, X55))) | ((~p4(c34, c34)) | (~p4(c34, f5(c35, c32))) | p4(f5(c35, c32), c34))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(27,plain,
% 0.20/0.38 ((~![X53: $i, X55: $i, X54: $i] : ((~p4(X53, X55)) | (~p4(X53, X54)) | p4(X54, X55))) | (~p4(c34, c34)) | (~p4(c34, f5(c35, c32))) | p4(f5(c35, c32), c34)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.20/0.38 tff(28,plain,
% 0.20/0.38 (p4(f5(c35, c32), c34)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[27, 24, 21, 11])).
% 0.20/0.38 tff(29,assumption,(~p14(f17(c36, c31), f17(c36, c31))), introduced(assumption)).
% 0.20/0.38 tff(30,plain,
% 0.20/0.38 (^[X6: $i] : refl(p14(X6, X6) <=> p14(X6, X6))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(31,plain,
% 0.20/0.38 (![X6: $i] : p14(X6, X6) <=> ![X6: $i] : p14(X6, X6)),
% 0.20/0.38 inference(quant_intro,[status(thm)],[30])).
% 0.20/0.38 tff(32,plain,
% 0.20/0.38 (![X6: $i] : p14(X6, X6) <=> ![X6: $i] : p14(X6, X6)),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(33,axiom,(![X6: $i] : p14(X6, X6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p14_14')).
% 0.20/0.38 tff(34,plain,
% 0.20/0.38 (![X6: $i] : p14(X6, X6)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.20/0.38 tff(35,plain,(
% 0.20/0.38 ![X6: $i] : p14(X6, X6)),
% 0.20/0.38 inference(skolemize,[status(sab)],[34])).
% 0.20/0.38 tff(36,plain,
% 0.20/0.38 (![X6: $i] : p14(X6, X6)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.20/0.38 tff(37,plain,
% 0.20/0.38 ((~![X6: $i] : p14(X6, X6)) | p14(f17(c36, c31), f17(c36, c31))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(38,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[37, 36, 29])).
% 0.20/0.38 tff(39,plain,(p14(f17(c36, c31), f17(c36, c31))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.38 tff(40,plain,
% 0.20/0.38 (^[X57: $i, X56: $i, X59: $i, X58: $i] : refl(((~p14(X56, X58)) | (~p4(X57, X59)) | p4(f15(X56, X57), f15(X58, X59))) <=> ((~p14(X56, X58)) | (~p4(X57, X59)) | p4(f15(X56, X57), f15(X58, X59))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(41,plain,
% 0.20/0.38 (![X57: $i, X56: $i, X59: $i, X58: $i] : ((~p14(X56, X58)) | (~p4(X57, X59)) | p4(f15(X56, X57), f15(X58, X59))) <=> ![X57: $i, X56: $i, X59: $i, X58: $i] : ((~p14(X56, X58)) | (~p4(X57, X59)) | p4(f15(X56, X57), f15(X58, X59)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[40])).
% 0.20/0.38 tff(42,plain,
% 0.20/0.38 (![X57: $i, X56: $i, X59: $i, X58: $i] : ((~p14(X56, X58)) | (~p4(X57, X59)) | p4(f15(X56, X57), f15(X58, X59))) <=> ![X57: $i, X56: $i, X59: $i, X58: $i] : ((~p14(X56, X58)) | (~p4(X57, X59)) | p4(f15(X56, X57), f15(X58, X59)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(43,plain,
% 0.20/0.38 (^[X57: $i, X56: $i, X59: $i, X58: $i] : trans(monotonicity(rewrite((p4(f15(X56, X57), f15(X58, X59)) | (~p14(X56, X58))) <=> ((~p14(X56, X58)) | p4(f15(X56, X57), f15(X58, X59)))), (((p4(f15(X56, X57), f15(X58, X59)) | (~p14(X56, X58))) | (~p4(X57, X59))) <=> (((~p14(X56, X58)) | p4(f15(X56, X57), f15(X58, X59))) | (~p4(X57, X59))))), rewrite((((~p14(X56, X58)) | p4(f15(X56, X57), f15(X58, X59))) | (~p4(X57, X59))) <=> ((~p14(X56, X58)) | (~p4(X57, X59)) | p4(f15(X56, X57), f15(X58, X59)))), (((p4(f15(X56, X57), f15(X58, X59)) | (~p14(X56, X58))) | (~p4(X57, X59))) <=> ((~p14(X56, X58)) | (~p4(X57, X59)) | p4(f15(X56, X57), f15(X58, X59)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(44,plain,
% 0.20/0.38 (![X57: $i, X56: $i, X59: $i, X58: $i] : ((p4(f15(X56, X57), f15(X58, X59)) | (~p14(X56, X58))) | (~p4(X57, X59))) <=> ![X57: $i, X56: $i, X59: $i, X58: $i] : ((~p14(X56, X58)) | (~p4(X57, X59)) | p4(f15(X56, X57), f15(X58, X59)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[43])).
% 0.20/0.38 tff(45,axiom,(![X57: $i, X56: $i, X59: $i, X58: $i] : ((p4(f15(X56, X57), f15(X58, X59)) | (~p14(X56, X58))) | (~p4(X57, X59)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p4_41')).
% 0.20/0.38 tff(46,plain,
% 0.20/0.38 (![X57: $i, X56: $i, X59: $i, X58: $i] : ((~p14(X56, X58)) | (~p4(X57, X59)) | p4(f15(X56, X57), f15(X58, X59)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.20/0.38 tff(47,plain,
% 0.20/0.38 (![X57: $i, X56: $i, X59: $i, X58: $i] : ((~p14(X56, X58)) | (~p4(X57, X59)) | p4(f15(X56, X57), f15(X58, X59)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.20/0.38 tff(48,plain,(
% 0.20/0.38 ![X57: $i, X56: $i, X59: $i, X58: $i] : ((~p14(X56, X58)) | (~p4(X57, X59)) | p4(f15(X56, X57), f15(X58, X59)))),
% 0.20/0.38 inference(skolemize,[status(sab)],[47])).
% 0.20/0.38 tff(49,plain,
% 0.20/0.38 (![X57: $i, X56: $i, X59: $i, X58: $i] : ((~p14(X56, X58)) | (~p4(X57, X59)) | p4(f15(X56, X57), f15(X58, X59)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[48, 41])).
% 0.20/0.38 tff(50,plain,
% 0.20/0.38 (((~![X57: $i, X56: $i, X59: $i, X58: $i] : ((~p14(X56, X58)) | (~p4(X57, X59)) | p4(f15(X56, X57), f15(X58, X59)))) | ((~p14(f17(c36, c31), f17(c36, c31))) | (~p4(f5(c35, c32), c34)) | p4(f15(f17(c36, c31), f5(c35, c32)), f15(f17(c36, c31), c34)))) <=> ((~![X57: $i, X56: $i, X59: $i, X58: $i] : ((~p14(X56, X58)) | (~p4(X57, X59)) | p4(f15(X56, X57), f15(X58, X59)))) | (~p14(f17(c36, c31), f17(c36, c31))) | (~p4(f5(c35, c32), c34)) | p4(f15(f17(c36, c31), f5(c35, c32)), f15(f17(c36, c31), c34)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(51,plain,
% 0.20/0.38 ((~![X57: $i, X56: $i, X59: $i, X58: $i] : ((~p14(X56, X58)) | (~p4(X57, X59)) | p4(f15(X56, X57), f15(X58, X59)))) | ((~p14(f17(c36, c31), f17(c36, c31))) | (~p4(f5(c35, c32), c34)) | p4(f15(f17(c36, c31), f5(c35, c32)), f15(f17(c36, c31), c34)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(52,plain,
% 0.20/0.38 ((~![X57: $i, X56: $i, X59: $i, X58: $i] : ((~p14(X56, X58)) | (~p4(X57, X59)) | p4(f15(X56, X57), f15(X58, X59)))) | (~p14(f17(c36, c31), f17(c36, c31))) | (~p4(f5(c35, c32), c34)) | p4(f15(f17(c36, c31), f5(c35, c32)), f15(f17(c36, c31), c34))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.20/0.38 tff(53,plain,
% 0.20/0.38 ((~p14(f17(c36, c31), f17(c36, c31))) | (~p4(f5(c35, c32), c34)) | p4(f15(f17(c36, c31), f5(c35, c32)), f15(f17(c36, c31), c34))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[52, 49])).
% 0.20/0.38 tff(54,plain,
% 0.20/0.38 (p4(f15(f17(c36, c31), f5(c35, c32)), f15(f17(c36, c31), c34))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[53, 39, 28])).
% 0.20/0.38 tff(55,plain,
% 0.20/0.38 (^[X60: $i, X61: $i] : refl(p4(f15(f17(c36, X60), f5(c35, X61)), f5(X60, X61)) <=> p4(f15(f17(c36, X60), f5(c35, X61)), f5(X60, X61)))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(56,plain,
% 0.20/0.38 (![X60: $i, X61: $i] : p4(f15(f17(c36, X60), f5(c35, X61)), f5(X60, X61)) <=> ![X60: $i, X61: $i] : p4(f15(f17(c36, X60), f5(c35, X61)), f5(X60, X61))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[55])).
% 0.20/0.38 tff(57,plain,
% 0.20/0.38 (![X60: $i, X61: $i] : p4(f15(f17(c36, X60), f5(c35, X61)), f5(X60, X61)) <=> ![X60: $i, X61: $i] : p4(f15(f17(c36, X60), f5(c35, X61)), f5(X60, X61))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(58,axiom,(![X60: $i, X61: $i] : p4(f15(f17(c36, X60), f5(c35, X61)), f5(X60, X61))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p4_34')).
% 0.20/0.38 tff(59,plain,
% 0.20/0.38 (![X60: $i, X61: $i] : p4(f15(f17(c36, X60), f5(c35, X61)), f5(X60, X61))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.20/0.38 tff(60,plain,(
% 0.20/0.38 ![X60: $i, X61: $i] : p4(f15(f17(c36, X60), f5(c35, X61)), f5(X60, X61))),
% 0.20/0.38 inference(skolemize,[status(sab)],[59])).
% 0.20/0.38 tff(61,plain,
% 0.20/0.38 (![X60: $i, X61: $i] : p4(f15(f17(c36, X60), f5(c35, X61)), f5(X60, X61))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.20/0.38 tff(62,plain,
% 0.20/0.38 ((~![X60: $i, X61: $i] : p4(f15(f17(c36, X60), f5(c35, X61)), f5(X60, X61))) | p4(f15(f17(c36, c31), f5(c35, c32)), f5(c31, c32))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(63,plain,
% 0.20/0.38 (p4(f15(f17(c36, c31), f5(c35, c32)), f5(c31, c32))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.20/0.39 tff(64,plain,
% 0.20/0.39 (((~![X53: $i, X55: $i, X54: $i] : ((~p4(X53, X55)) | (~p4(X53, X54)) | p4(X54, X55))) | ((~p4(f15(f17(c36, c31), f5(c35, c32)), f5(c31, c32))) | (~p4(f15(f17(c36, c31), f5(c35, c32)), f15(f17(c36, c31), c34))) | p4(f5(c31, c32), f15(f17(c36, c31), c34)))) <=> ((~![X53: $i, X55: $i, X54: $i] : ((~p4(X53, X55)) | (~p4(X53, X54)) | p4(X54, X55))) | (~p4(f15(f17(c36, c31), f5(c35, c32)), f5(c31, c32))) | (~p4(f15(f17(c36, c31), f5(c35, c32)), f15(f17(c36, c31), c34))) | p4(f5(c31, c32), f15(f17(c36, c31), c34)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(65,plain,
% 0.20/0.39 (((~p4(f15(f17(c36, c31), f5(c35, c32)), f15(f17(c36, c31), c34))) | (~p4(f15(f17(c36, c31), f5(c35, c32)), f5(c31, c32))) | p4(f5(c31, c32), f15(f17(c36, c31), c34))) <=> ((~p4(f15(f17(c36, c31), f5(c35, c32)), f5(c31, c32))) | (~p4(f15(f17(c36, c31), f5(c35, c32)), f15(f17(c36, c31), c34))) | p4(f5(c31, c32), f15(f17(c36, c31), c34)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(66,plain,
% 0.20/0.39 (((~![X53: $i, X55: $i, X54: $i] : ((~p4(X53, X55)) | (~p4(X53, X54)) | p4(X54, X55))) | ((~p4(f15(f17(c36, c31), f5(c35, c32)), f15(f17(c36, c31), c34))) | (~p4(f15(f17(c36, c31), f5(c35, c32)), f5(c31, c32))) | p4(f5(c31, c32), f15(f17(c36, c31), c34)))) <=> ((~![X53: $i, X55: $i, X54: $i] : ((~p4(X53, X55)) | (~p4(X53, X54)) | p4(X54, X55))) | ((~p4(f15(f17(c36, c31), f5(c35, c32)), f5(c31, c32))) | (~p4(f15(f17(c36, c31), f5(c35, c32)), f15(f17(c36, c31), c34))) | p4(f5(c31, c32), f15(f17(c36, c31), c34))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[65])).
% 0.20/0.39 tff(67,plain,
% 0.20/0.39 (((~![X53: $i, X55: $i, X54: $i] : ((~p4(X53, X55)) | (~p4(X53, X54)) | p4(X54, X55))) | ((~p4(f15(f17(c36, c31), f5(c35, c32)), f15(f17(c36, c31), c34))) | (~p4(f15(f17(c36, c31), f5(c35, c32)), f5(c31, c32))) | p4(f5(c31, c32), f15(f17(c36, c31), c34)))) <=> ((~![X53: $i, X55: $i, X54: $i] : ((~p4(X53, X55)) | (~p4(X53, X54)) | p4(X54, X55))) | (~p4(f15(f17(c36, c31), f5(c35, c32)), f5(c31, c32))) | (~p4(f15(f17(c36, c31), f5(c35, c32)), f15(f17(c36, c31), c34))) | p4(f5(c31, c32), f15(f17(c36, c31), c34)))),
% 0.20/0.39 inference(transitivity,[status(thm)],[66, 64])).
% 0.20/0.39 tff(68,plain,
% 0.20/0.39 ((~![X53: $i, X55: $i, X54: $i] : ((~p4(X53, X55)) | (~p4(X53, X54)) | p4(X54, X55))) | ((~p4(f15(f17(c36, c31), f5(c35, c32)), f15(f17(c36, c31), c34))) | (~p4(f15(f17(c36, c31), f5(c35, c32)), f5(c31, c32))) | p4(f5(c31, c32), f15(f17(c36, c31), c34)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(69,plain,
% 0.20/0.39 ((~![X53: $i, X55: $i, X54: $i] : ((~p4(X53, X55)) | (~p4(X53, X54)) | p4(X54, X55))) | (~p4(f15(f17(c36, c31), f5(c35, c32)), f5(c31, c32))) | (~p4(f15(f17(c36, c31), f5(c35, c32)), f15(f17(c36, c31), c34))) | p4(f5(c31, c32), f15(f17(c36, c31), c34))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.20/0.39 tff(70,plain,
% 0.20/0.39 (p4(f5(c31, c32), f15(f17(c36, c31), c34))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[69, 21, 63, 54])).
% 0.20/0.39 tff(71,plain,
% 0.20/0.39 (^[X73: $i, X74: $i] : refl(((~p27(f8(f10(c28, f13(c29, c30)), X73), X74)) | p4(f5(c31, X73), f5(c31, X74))) <=> ((~p27(f8(f10(c28, f13(c29, c30)), X73), X74)) | p4(f5(c31, X73), f5(c31, X74))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(72,plain,
% 0.20/0.39 (![X73: $i, X74: $i] : ((~p27(f8(f10(c28, f13(c29, c30)), X73), X74)) | p4(f5(c31, X73), f5(c31, X74))) <=> ![X73: $i, X74: $i] : ((~p27(f8(f10(c28, f13(c29, c30)), X73), X74)) | p4(f5(c31, X73), f5(c31, X74)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[71])).
% 0.20/0.39 tff(73,plain,
% 0.20/0.39 (![X73: $i, X74: $i] : ((~p27(f8(f10(c28, f13(c29, c30)), X73), X74)) | p4(f5(c31, X73), f5(c31, X74))) <=> ![X73: $i, X74: $i] : ((~p27(f8(f10(c28, f13(c29, c30)), X73), X74)) | p4(f5(c31, X73), f5(c31, X74)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(74,plain,
% 0.20/0.39 (^[X73: $i, X74: $i] : rewrite((p4(f5(c31, X73), f5(c31, X74)) | (~p27(f8(f10(c28, f13(c29, c30)), X73), X74))) <=> ((~p27(f8(f10(c28, f13(c29, c30)), X73), X74)) | p4(f5(c31, X73), f5(c31, X74))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(75,plain,
% 0.20/0.39 (![X73: $i, X74: $i] : (p4(f5(c31, X73), f5(c31, X74)) | (~p27(f8(f10(c28, f13(c29, c30)), X73), X74))) <=> ![X73: $i, X74: $i] : ((~p27(f8(f10(c28, f13(c29, c30)), X73), X74)) | p4(f5(c31, X73), f5(c31, X74)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[74])).
% 0.20/0.39 tff(76,axiom,(![X73: $i, X74: $i] : (p4(f5(c31, X73), f5(c31, X74)) | (~p27(f8(f10(c28, f13(c29, c30)), X73), X74)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p4_46')).
% 0.20/0.39 tff(77,plain,
% 0.20/0.39 (![X73: $i, X74: $i] : ((~p27(f8(f10(c28, f13(c29, c30)), X73), X74)) | p4(f5(c31, X73), f5(c31, X74)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.20/0.39 tff(78,plain,
% 0.20/0.39 (![X73: $i, X74: $i] : ((~p27(f8(f10(c28, f13(c29, c30)), X73), X74)) | p4(f5(c31, X73), f5(c31, X74)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[77, 73])).
% 0.20/0.39 tff(79,plain,(
% 0.20/0.39 ![X73: $i, X74: $i] : ((~p27(f8(f10(c28, f13(c29, c30)), X73), X74)) | p4(f5(c31, X73), f5(c31, X74)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[78])).
% 0.20/0.39 tff(80,plain,
% 0.20/0.39 (![X73: $i, X74: $i] : ((~p27(f8(f10(c28, f13(c29, c30)), X73), X74)) | p4(f5(c31, X73), f5(c31, X74)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[79, 72])).
% 0.20/0.39 tff(81,plain,
% 0.20/0.39 (p27(f8(f10(c28, f13(c29, c30)), c32), c33) <=> p27(f8(f10(c28, f13(c29, c30)), c32), c33)),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(82,axiom,(p27(f8(f10(c28, f13(c29, c30)), c32), c33)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p27_17')).
% 0.20/0.39 tff(83,plain,
% 0.20/0.39 (p27(f8(f10(c28, f13(c29, c30)), c32), c33)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.20/0.39 tff(84,plain,
% 0.20/0.39 (((~![X73: $i, X74: $i] : ((~p27(f8(f10(c28, f13(c29, c30)), X73), X74)) | p4(f5(c31, X73), f5(c31, X74)))) | ((~p27(f8(f10(c28, f13(c29, c30)), c32), c33)) | p4(f5(c31, c32), f5(c31, c33)))) <=> ((~![X73: $i, X74: $i] : ((~p27(f8(f10(c28, f13(c29, c30)), X73), X74)) | p4(f5(c31, X73), f5(c31, X74)))) | (~p27(f8(f10(c28, f13(c29, c30)), c32), c33)) | p4(f5(c31, c32), f5(c31, c33)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(85,plain,
% 0.20/0.39 ((~![X73: $i, X74: $i] : ((~p27(f8(f10(c28, f13(c29, c30)), X73), X74)) | p4(f5(c31, X73), f5(c31, X74)))) | ((~p27(f8(f10(c28, f13(c29, c30)), c32), c33)) | p4(f5(c31, c32), f5(c31, c33)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(86,plain,
% 0.20/0.39 ((~![X73: $i, X74: $i] : ((~p27(f8(f10(c28, f13(c29, c30)), X73), X74)) | p4(f5(c31, X73), f5(c31, X74)))) | (~p27(f8(f10(c28, f13(c29, c30)), c32), c33)) | p4(f5(c31, c32), f5(c31, c33))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.20/0.39 tff(87,plain,
% 0.20/0.39 (p4(f5(c31, c32), f5(c31, c33))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[86, 83, 80])).
% 0.20/0.39 tff(88,plain,
% 0.20/0.39 ((~p4(f5(c31, c33), f15(f17(c36, c31), c34))) <=> (~p4(f5(c31, c33), f15(f17(c36, c31), c34)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(89,axiom,(~p4(f5(c31, c33), f15(f17(c36, c31), c34))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_p4_18')).
% 0.20/0.39 tff(90,plain,
% 0.20/0.39 (~p4(f5(c31, c33), f15(f17(c36, c31), c34))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.20/0.39 tff(91,plain,
% 0.20/0.39 (((~![X53: $i, X55: $i, X54: $i] : ((~p4(X53, X55)) | (~p4(X53, X54)) | p4(X54, X55))) | (p4(f5(c31, c33), f15(f17(c36, c31), c34)) | (~p4(f5(c31, c32), f5(c31, c33))) | (~p4(f5(c31, c32), f15(f17(c36, c31), c34))))) <=> ((~![X53: $i, X55: $i, X54: $i] : ((~p4(X53, X55)) | (~p4(X53, X54)) | p4(X54, X55))) | p4(f5(c31, c33), f15(f17(c36, c31), c34)) | (~p4(f5(c31, c32), f5(c31, c33))) | (~p4(f5(c31, c32), f15(f17(c36, c31), c34))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(92,plain,
% 0.20/0.39 (((~p4(f5(c31, c32), f15(f17(c36, c31), c34))) | (~p4(f5(c31, c32), f5(c31, c33))) | p4(f5(c31, c33), f15(f17(c36, c31), c34))) <=> (p4(f5(c31, c33), f15(f17(c36, c31), c34)) | (~p4(f5(c31, c32), f5(c31, c33))) | (~p4(f5(c31, c32), f15(f17(c36, c31), c34))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(93,plain,
% 0.20/0.39 (((~![X53: $i, X55: $i, X54: $i] : ((~p4(X53, X55)) | (~p4(X53, X54)) | p4(X54, X55))) | ((~p4(f5(c31, c32), f15(f17(c36, c31), c34))) | (~p4(f5(c31, c32), f5(c31, c33))) | p4(f5(c31, c33), f15(f17(c36, c31), c34)))) <=> ((~![X53: $i, X55: $i, X54: $i] : ((~p4(X53, X55)) | (~p4(X53, X54)) | p4(X54, X55))) | (p4(f5(c31, c33), f15(f17(c36, c31), c34)) | (~p4(f5(c31, c32), f5(c31, c33))) | (~p4(f5(c31, c32), f15(f17(c36, c31), c34)))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[92])).
% 0.20/0.40 tff(94,plain,
% 0.20/0.40 (((~![X53: $i, X55: $i, X54: $i] : ((~p4(X53, X55)) | (~p4(X53, X54)) | p4(X54, X55))) | ((~p4(f5(c31, c32), f15(f17(c36, c31), c34))) | (~p4(f5(c31, c32), f5(c31, c33))) | p4(f5(c31, c33), f15(f17(c36, c31), c34)))) <=> ((~![X53: $i, X55: $i, X54: $i] : ((~p4(X53, X55)) | (~p4(X53, X54)) | p4(X54, X55))) | p4(f5(c31, c33), f15(f17(c36, c31), c34)) | (~p4(f5(c31, c32), f5(c31, c33))) | (~p4(f5(c31, c32), f15(f17(c36, c31), c34))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[93, 91])).
% 0.20/0.40 tff(95,plain,
% 0.20/0.40 ((~![X53: $i, X55: $i, X54: $i] : ((~p4(X53, X55)) | (~p4(X53, X54)) | p4(X54, X55))) | ((~p4(f5(c31, c32), f15(f17(c36, c31), c34))) | (~p4(f5(c31, c32), f5(c31, c33))) | p4(f5(c31, c33), f15(f17(c36, c31), c34)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(96,plain,
% 0.20/0.40 ((~![X53: $i, X55: $i, X54: $i] : ((~p4(X53, X55)) | (~p4(X53, X54)) | p4(X54, X55))) | p4(f5(c31, c33), f15(f17(c36, c31), c34)) | (~p4(f5(c31, c32), f5(c31, c33))) | (~p4(f5(c31, c32), f15(f17(c36, c31), c34)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.20/0.40 tff(97,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[96, 90, 21, 87, 70])).
% 0.20/0.40 % SZS output end Proof
% 0.20/0.40 % E exiting
%------------------------------------------------------------------------------