%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN618-1 : 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 05:39:42 AM UTC 2025
% Result : Unsatisfiable 0.18s 0.38s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN618-1 : TPTP v9.0.0. Released v2.5.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.33 % CPULimit : 300
% 0.18/0.33 % WCLimit : 300
% 0.18/0.33 % DateTime : Fri Jun 20 12:39:26 EDT 2025
% 0.18/0.33 % CPUTime :
% 0.18/0.38 % SZS status Unsatisfiable
% 0.18/0.38 % SZS output start Proof
% 0.18/0.38 tff(p5_type, type, (
% 0.18/0.38 p5: ( $i * $i ) > $o)).
% 0.18/0.38 tff(f8_type, type, (
% 0.18/0.38 f8: ( $i * $i ) > $i)).
% 0.18/0.38 tff(c20_type, type, (
% 0.18/0.38 c20: $i)).
% 0.18/0.38 tff(f3_type, type, (
% 0.18/0.38 f3: $i > $i)).
% 0.18/0.38 tff(c16_type, type, (
% 0.18/0.38 c16: $i)).
% 0.18/0.38 tff(c23_type, type, (
% 0.18/0.38 c23: $i)).
% 0.18/0.38 tff(f6_type, type, (
% 0.18/0.38 f6: $i > $i)).
% 0.18/0.38 tff(f7_type, type, (
% 0.18/0.38 f7: $i > $i)).
% 0.18/0.38 tff(c22_type, type, (
% 0.18/0.38 c22: $i)).
% 0.18/0.38 tff(c17_type, type, (
% 0.18/0.38 c17: $i)).
% 0.18/0.38 tff(p2_type, type, (
% 0.18/0.38 p2: ( $i * $i ) > $o)).
% 0.18/0.38 tff(p13_type, type, (
% 0.18/0.38 p13: ( $i * $i ) > $o)).
% 0.18/0.38 tff(c21_type, type, (
% 0.18/0.38 c21: $i)).
% 0.18/0.38 tff(c19_type, type, (
% 0.18/0.38 c19: $i)).
% 0.18/0.38 tff(1,assumption,(~p2(c17, c17)), introduced(assumption)).
% 0.18/0.38 tff(2,plain,
% 0.18/0.38 (^[X24: $i] : refl(p2(X24, X24) <=> p2(X24, X24))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(3,plain,
% 0.18/0.38 (![X24: $i] : p2(X24, X24) <=> ![X24: $i] : p2(X24, X24)),
% 0.18/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.18/0.38 tff(4,plain,
% 0.18/0.38 (![X24: $i] : p2(X24, X24) <=> ![X24: $i] : p2(X24, X24)),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(5,axiom,(![X24: $i] : p2(X24, X24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_5')).
% 0.18/0.38 tff(6,plain,
% 0.18/0.38 (![X24: $i] : p2(X24, X24)),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.18/0.38 tff(7,plain,(
% 0.18/0.38 ![X24: $i] : p2(X24, X24)),
% 0.18/0.38 inference(skolemize,[status(sab)],[6])).
% 0.18/0.38 tff(8,plain,
% 0.18/0.38 (![X24: $i] : p2(X24, X24)),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.18/0.38 tff(9,plain,
% 0.18/0.38 ((~![X24: $i] : p2(X24, X24)) | p2(c17, c17)),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(10,plain,
% 0.18/0.38 ($false),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.18/0.38 tff(11,plain,(p2(c17, c17)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.38 tff(12,plain,
% 0.18/0.38 (^[X25: $i, X24: $i, X26: $i] : refl(((~p2(X24, X26)) | (~p2(X24, X25)) | p2(X25, X26)) <=> ((~p2(X24, X26)) | (~p2(X24, X25)) | p2(X25, X26)))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(13,plain,
% 0.18/0.38 (![X25: $i, X24: $i, X26: $i] : ((~p2(X24, X26)) | (~p2(X24, X25)) | p2(X25, X26)) <=> ![X25: $i, X24: $i, X26: $i] : ((~p2(X24, X26)) | (~p2(X24, X25)) | p2(X25, X26))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[12])).
% 0.18/0.38 tff(14,plain,
% 0.18/0.38 (![X25: $i, X24: $i, X26: $i] : ((~p2(X24, X26)) | (~p2(X24, X25)) | p2(X25, X26)) <=> ![X25: $i, X24: $i, X26: $i] : ((~p2(X24, X26)) | (~p2(X24, X25)) | p2(X25, X26))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(15,plain,
% 0.18/0.38 (^[X25: $i, X24: $i, X26: $i] : trans(monotonicity(rewrite((p2(X25, X26) | (~p2(X24, X25))) <=> ((~p2(X24, X25)) | p2(X25, X26))), (((p2(X25, X26) | (~p2(X24, X25))) | (~p2(X24, X26))) <=> (((~p2(X24, X25)) | p2(X25, X26)) | (~p2(X24, X26))))), rewrite((((~p2(X24, X25)) | p2(X25, X26)) | (~p2(X24, X26))) <=> ((~p2(X24, X26)) | (~p2(X24, X25)) | p2(X25, X26))), (((p2(X25, X26) | (~p2(X24, X25))) | (~p2(X24, X26))) <=> ((~p2(X24, X26)) | (~p2(X24, X25)) | p2(X25, X26))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(16,plain,
% 0.18/0.38 (![X25: $i, X24: $i, X26: $i] : ((p2(X25, X26) | (~p2(X24, X25))) | (~p2(X24, X26))) <=> ![X25: $i, X24: $i, X26: $i] : ((~p2(X24, X26)) | (~p2(X24, X25)) | p2(X25, X26))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[15])).
% 0.18/0.38 tff(17,axiom,(![X25: $i, X24: $i, X26: $i] : ((p2(X25, X26) | (~p2(X24, X25))) | (~p2(X24, X26)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_24')).
% 0.18/0.38 tff(18,plain,
% 0.18/0.38 (![X25: $i, X24: $i, X26: $i] : ((~p2(X24, X26)) | (~p2(X24, X25)) | p2(X25, X26))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.18/0.38 tff(19,plain,
% 0.18/0.38 (![X25: $i, X24: $i, X26: $i] : ((~p2(X24, X26)) | (~p2(X24, X25)) | p2(X25, X26))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.18/0.38 tff(20,plain,(
% 0.18/0.38 ![X25: $i, X24: $i, X26: $i] : ((~p2(X24, X26)) | (~p2(X24, X25)) | p2(X25, X26))),
% 0.18/0.38 inference(skolemize,[status(sab)],[19])).
% 0.18/0.38 tff(21,plain,
% 0.18/0.38 (![X25: $i, X24: $i, X26: $i] : ((~p2(X24, X26)) | (~p2(X24, X25)) | p2(X25, X26))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.18/0.38 tff(22,plain,
% 0.18/0.38 (p2(c17, f3(c16)) <=> p2(c17, f3(c16))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(23,axiom,(p2(c17, f3(c16))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_12')).
% 0.18/0.38 tff(24,plain,
% 0.18/0.38 (p2(c17, f3(c16))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.18/0.38 tff(25,plain,
% 0.18/0.38 (((~![X25: $i, X24: $i, X26: $i] : ((~p2(X24, X26)) | (~p2(X24, X25)) | p2(X25, X26))) | ((~p2(c17, c17)) | (~p2(c17, f3(c16))) | p2(f3(c16), c17))) <=> ((~![X25: $i, X24: $i, X26: $i] : ((~p2(X24, X26)) | (~p2(X24, X25)) | p2(X25, X26))) | (~p2(c17, c17)) | (~p2(c17, f3(c16))) | p2(f3(c16), c17))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(26,plain,
% 0.18/0.38 ((~![X25: $i, X24: $i, X26: $i] : ((~p2(X24, X26)) | (~p2(X24, X25)) | p2(X25, X26))) | ((~p2(c17, c17)) | (~p2(c17, f3(c16))) | p2(f3(c16), c17))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(27,plain,
% 0.18/0.38 ((~![X25: $i, X24: $i, X26: $i] : ((~p2(X24, X26)) | (~p2(X24, X25)) | p2(X25, X26))) | (~p2(c17, c17)) | (~p2(c17, f3(c16))) | p2(f3(c16), c17)),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.18/0.38 tff(28,plain,
% 0.18/0.38 (p2(f3(c16), c17)),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[27, 24, 21, 11])).
% 0.18/0.38 tff(29,assumption,(~p5(c23, c23)), introduced(assumption)).
% 0.18/0.38 tff(30,plain,
% 0.18/0.38 (^[X34: $i] : refl(p5(X34, X34) <=> p5(X34, X34))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(31,plain,
% 0.18/0.38 (![X34: $i] : p5(X34, X34) <=> ![X34: $i] : p5(X34, X34)),
% 0.18/0.38 inference(quant_intro,[status(thm)],[30])).
% 0.18/0.38 tff(32,plain,
% 0.18/0.38 (![X34: $i] : p5(X34, X34) <=> ![X34: $i] : p5(X34, X34)),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(33,axiom,(![X34: $i] : p5(X34, X34)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p5_3')).
% 0.18/0.38 tff(34,plain,
% 0.18/0.38 (![X34: $i] : p5(X34, X34)),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.18/0.38 tff(35,plain,(
% 0.18/0.38 ![X34: $i] : p5(X34, X34)),
% 0.18/0.38 inference(skolemize,[status(sab)],[34])).
% 0.18/0.38 tff(36,plain,
% 0.18/0.38 (![X34: $i] : p5(X34, X34)),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.18/0.38 tff(37,plain,
% 0.18/0.38 ((~![X34: $i] : p5(X34, X34)) | p5(c23, c23)),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(38,plain,
% 0.18/0.38 ($false),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[37, 36, 29])).
% 0.18/0.38 tff(39,plain,(p5(c23, c23)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.38 tff(40,plain,
% 0.18/0.38 (^[X43: $i, X42: $i, X41: $i, X40: $i] : refl(((~p5(X41, X43)) | (~p2(X40, X42)) | p5(f8(X40, X41), f8(X42, X43))) <=> ((~p5(X41, X43)) | (~p2(X40, X42)) | p5(f8(X40, X41), f8(X42, X43))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(41,plain,
% 0.18/0.38 (![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p5(X41, X43)) | (~p2(X40, X42)) | p5(f8(X40, X41), f8(X42, X43))) <=> ![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p5(X41, X43)) | (~p2(X40, X42)) | p5(f8(X40, X41), f8(X42, X43)))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[40])).
% 0.18/0.38 tff(42,plain,
% 0.18/0.38 (![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p5(X41, X43)) | (~p2(X40, X42)) | p5(f8(X40, X41), f8(X42, X43))) <=> ![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p5(X41, X43)) | (~p2(X40, X42)) | p5(f8(X40, X41), f8(X42, X43)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(43,plain,
% 0.18/0.38 (^[X43: $i, X42: $i, X41: $i, X40: $i] : trans(monotonicity(rewrite((p5(f8(X40, X41), f8(X42, X43)) | (~p2(X40, X42))) <=> ((~p2(X40, X42)) | p5(f8(X40, X41), f8(X42, X43)))), (((p5(f8(X40, X41), f8(X42, X43)) | (~p2(X40, X42))) | (~p5(X41, X43))) <=> (((~p2(X40, X42)) | p5(f8(X40, X41), f8(X42, X43))) | (~p5(X41, X43))))), rewrite((((~p2(X40, X42)) | p5(f8(X40, X41), f8(X42, X43))) | (~p5(X41, X43))) <=> ((~p5(X41, X43)) | (~p2(X40, X42)) | p5(f8(X40, X41), f8(X42, X43)))), (((p5(f8(X40, X41), f8(X42, X43)) | (~p2(X40, X42))) | (~p5(X41, X43))) <=> ((~p5(X41, X43)) | (~p2(X40, X42)) | p5(f8(X40, X41), f8(X42, X43)))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(44,plain,
% 0.18/0.38 (![X43: $i, X42: $i, X41: $i, X40: $i] : ((p5(f8(X40, X41), f8(X42, X43)) | (~p2(X40, X42))) | (~p5(X41, X43))) <=> ![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p5(X41, X43)) | (~p2(X40, X42)) | p5(f8(X40, X41), f8(X42, X43)))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[43])).
% 0.18/0.38 tff(45,axiom,(![X43: $i, X42: $i, X41: $i, X40: $i] : ((p5(f8(X40, X41), f8(X42, X43)) | (~p2(X40, X42))) | (~p5(X41, X43)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p5_30')).
% 0.18/0.38 tff(46,plain,
% 0.18/0.38 (![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p5(X41, X43)) | (~p2(X40, X42)) | p5(f8(X40, X41), f8(X42, X43)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.18/0.39 tff(47,plain,
% 0.18/0.39 (![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p5(X41, X43)) | (~p2(X40, X42)) | p5(f8(X40, X41), f8(X42, X43)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.18/0.39 tff(48,plain,(
% 0.18/0.39 ![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p5(X41, X43)) | (~p2(X40, X42)) | p5(f8(X40, X41), f8(X42, X43)))),
% 0.18/0.39 inference(skolemize,[status(sab)],[47])).
% 0.18/0.39 tff(49,plain,
% 0.18/0.39 (![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p5(X41, X43)) | (~p2(X40, X42)) | p5(f8(X40, X41), f8(X42, X43)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[48, 41])).
% 0.18/0.39 tff(50,plain,
% 0.18/0.39 (((~![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p5(X41, X43)) | (~p2(X40, X42)) | p5(f8(X40, X41), f8(X42, X43)))) | ((~p5(c23, c23)) | (~p2(f3(c16), c17)) | p5(f8(f3(c16), c23), f8(c17, c23)))) <=> ((~![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p5(X41, X43)) | (~p2(X40, X42)) | p5(f8(X40, X41), f8(X42, X43)))) | (~p5(c23, c23)) | (~p2(f3(c16), c17)) | p5(f8(f3(c16), c23), f8(c17, c23)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(51,plain,
% 0.18/0.39 ((~![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p5(X41, X43)) | (~p2(X40, X42)) | p5(f8(X40, X41), f8(X42, X43)))) | ((~p5(c23, c23)) | (~p2(f3(c16), c17)) | p5(f8(f3(c16), c23), f8(c17, c23)))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(52,plain,
% 0.18/0.39 ((~![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p5(X41, X43)) | (~p2(X40, X42)) | p5(f8(X40, X41), f8(X42, X43)))) | (~p5(c23, c23)) | (~p2(f3(c16), c17)) | p5(f8(f3(c16), c23), f8(c17, c23))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.18/0.39 tff(53,plain,
% 0.18/0.39 (p5(f8(f3(c16), c23), f8(c17, c23))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[52, 49, 39, 28])).
% 0.18/0.39 tff(54,assumption,(~p5(f8(c17, c23), f6(f7(c22)))), introduced(assumption)).
% 0.18/0.39 tff(55,plain,
% 0.18/0.39 (^[X35: $i, X34: $i, X36: $i] : refl(((~p5(X34, X36)) | (~p5(X34, X35)) | p5(X35, X36)) <=> ((~p5(X34, X36)) | (~p5(X34, X35)) | p5(X35, X36)))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(56,plain,
% 0.18/0.39 (![X35: $i, X34: $i, X36: $i] : ((~p5(X34, X36)) | (~p5(X34, X35)) | p5(X35, X36)) <=> ![X35: $i, X34: $i, X36: $i] : ((~p5(X34, X36)) | (~p5(X34, X35)) | p5(X35, X36))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[55])).
% 0.18/0.39 tff(57,plain,
% 0.18/0.39 (![X35: $i, X34: $i, X36: $i] : ((~p5(X34, X36)) | (~p5(X34, X35)) | p5(X35, X36)) <=> ![X35: $i, X34: $i, X36: $i] : ((~p5(X34, X36)) | (~p5(X34, X35)) | p5(X35, X36))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(58,plain,
% 0.18/0.39 (^[X35: $i, X34: $i, X36: $i] : trans(monotonicity(rewrite((p5(X35, X36) | (~p5(X34, X35))) <=> ((~p5(X34, X35)) | p5(X35, X36))), (((p5(X35, X36) | (~p5(X34, X35))) | (~p5(X34, X36))) <=> (((~p5(X34, X35)) | p5(X35, X36)) | (~p5(X34, X36))))), rewrite((((~p5(X34, X35)) | p5(X35, X36)) | (~p5(X34, X36))) <=> ((~p5(X34, X36)) | (~p5(X34, X35)) | p5(X35, X36))), (((p5(X35, X36) | (~p5(X34, X35))) | (~p5(X34, X36))) <=> ((~p5(X34, X36)) | (~p5(X34, X35)) | p5(X35, X36))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(59,plain,
% 0.18/0.39 (![X35: $i, X34: $i, X36: $i] : ((p5(X35, X36) | (~p5(X34, X35))) | (~p5(X34, X36))) <=> ![X35: $i, X34: $i, X36: $i] : ((~p5(X34, X36)) | (~p5(X34, X35)) | p5(X35, X36))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[58])).
% 0.18/0.39 tff(60,axiom,(![X35: $i, X34: $i, X36: $i] : ((p5(X35, X36) | (~p5(X34, X35))) | (~p5(X34, X36)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p5_22')).
% 0.18/0.39 tff(61,plain,
% 0.18/0.39 (![X35: $i, X34: $i, X36: $i] : ((~p5(X34, X36)) | (~p5(X34, X35)) | p5(X35, X36))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.18/0.39 tff(62,plain,
% 0.18/0.39 (![X35: $i, X34: $i, X36: $i] : ((~p5(X34, X36)) | (~p5(X34, X35)) | p5(X35, X36))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.18/0.39 tff(63,plain,(
% 0.18/0.39 ![X35: $i, X34: $i, X36: $i] : ((~p5(X34, X36)) | (~p5(X34, X35)) | p5(X35, X36))),
% 0.18/0.39 inference(skolemize,[status(sab)],[62])).
% 0.18/0.39 tff(64,plain,
% 0.18/0.39 (![X35: $i, X34: $i, X36: $i] : ((~p5(X34, X36)) | (~p5(X34, X35)) | p5(X35, X36))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.18/0.39 tff(65,plain,
% 0.18/0.39 (p5(f8(f3(c16), c23), f6(f7(c22))) <=> p5(f8(f3(c16), c23), f6(f7(c22)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(66,axiom,(p5(f8(f3(c16), c23), f6(f7(c22)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p5_16')).
% 0.18/0.39 tff(67,plain,
% 0.18/0.39 (p5(f8(f3(c16), c23), f6(f7(c22)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.18/0.39 tff(68,plain,
% 0.18/0.39 (((~![X35: $i, X34: $i, X36: $i] : ((~p5(X34, X36)) | (~p5(X34, X35)) | p5(X35, X36))) | ((~p5(f8(f3(c16), c23), f6(f7(c22)))) | (~p5(f8(f3(c16), c23), f8(c17, c23))) | p5(f8(c17, c23), f6(f7(c22))))) <=> ((~![X35: $i, X34: $i, X36: $i] : ((~p5(X34, X36)) | (~p5(X34, X35)) | p5(X35, X36))) | (~p5(f8(f3(c16), c23), f6(f7(c22)))) | (~p5(f8(f3(c16), c23), f8(c17, c23))) | p5(f8(c17, c23), f6(f7(c22))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(69,plain,
% 0.18/0.39 ((~![X35: $i, X34: $i, X36: $i] : ((~p5(X34, X36)) | (~p5(X34, X35)) | p5(X35, X36))) | ((~p5(f8(f3(c16), c23), f6(f7(c22)))) | (~p5(f8(f3(c16), c23), f8(c17, c23))) | p5(f8(c17, c23), f6(f7(c22))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(70,plain,
% 0.18/0.39 ((~![X35: $i, X34: $i, X36: $i] : ((~p5(X34, X36)) | (~p5(X34, X35)) | p5(X35, X36))) | (~p5(f8(f3(c16), c23), f6(f7(c22)))) | (~p5(f8(f3(c16), c23), f8(c17, c23))) | p5(f8(c17, c23), f6(f7(c22)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.18/0.39 tff(71,plain,
% 0.18/0.39 ($false),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[70, 67, 64, 54, 53])).
% 0.18/0.39 tff(72,plain,(p5(f8(c17, c23), f6(f7(c22)))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.39 tff(73,plain,
% 0.18/0.39 (^[X37: $i] : refl(((~p13(c19, X37)) | (~p13(X37, c21)) | p5(X37, c20) | (~p5(f8(c17, X37), f6(f7(c22))))) <=> ((~p13(c19, X37)) | (~p13(X37, c21)) | p5(X37, c20) | (~p5(f8(c17, X37), f6(f7(c22))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(74,plain,
% 0.18/0.39 (![X37: $i] : ((~p13(c19, X37)) | (~p13(X37, c21)) | p5(X37, c20) | (~p5(f8(c17, X37), f6(f7(c22))))) <=> ![X37: $i] : ((~p13(c19, X37)) | (~p13(X37, c21)) | p5(X37, c20) | (~p5(f8(c17, X37), f6(f7(c22)))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[73])).
% 0.18/0.39 tff(75,plain,
% 0.18/0.39 (![X37: $i] : ((~p13(c19, X37)) | (~p13(X37, c21)) | p5(X37, c20) | (~p5(f8(c17, X37), f6(f7(c22))))) <=> ![X37: $i] : ((~p13(c19, X37)) | (~p13(X37, c21)) | p5(X37, c20) | (~p5(f8(c17, X37), f6(f7(c22)))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(76,plain,
% 0.18/0.39 (^[X37: $i] : trans(monotonicity(trans(monotonicity(rewrite((p5(X37, c20) | (~p13(X37, c21))) <=> ((~p13(X37, c21)) | p5(X37, c20))), (((p5(X37, c20) | (~p13(X37, c21))) | (~p13(c19, X37))) <=> (((~p13(X37, c21)) | p5(X37, c20)) | (~p13(c19, X37))))), rewrite((((~p13(X37, c21)) | p5(X37, c20)) | (~p13(c19, X37))) <=> ((~p13(c19, X37)) | (~p13(X37, c21)) | p5(X37, c20))), (((p5(X37, c20) | (~p13(X37, c21))) | (~p13(c19, X37))) <=> ((~p13(c19, X37)) | (~p13(X37, c21)) | p5(X37, c20)))), ((((p5(X37, c20) | (~p13(X37, c21))) | (~p13(c19, X37))) | (~p5(f8(c17, X37), f6(f7(c22))))) <=> (((~p13(c19, X37)) | (~p13(X37, c21)) | p5(X37, c20)) | (~p5(f8(c17, X37), f6(f7(c22))))))), rewrite((((~p13(c19, X37)) | (~p13(X37, c21)) | p5(X37, c20)) | (~p5(f8(c17, X37), f6(f7(c22))))) <=> ((~p13(c19, X37)) | (~p13(X37, c21)) | p5(X37, c20) | (~p5(f8(c17, X37), f6(f7(c22)))))), ((((p5(X37, c20) | (~p13(X37, c21))) | (~p13(c19, X37))) | (~p5(f8(c17, X37), f6(f7(c22))))) <=> ((~p13(c19, X37)) | (~p13(X37, c21)) | p5(X37, c20) | (~p5(f8(c17, X37), f6(f7(c22)))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(77,plain,
% 0.18/0.39 (![X37: $i] : (((p5(X37, c20) | (~p13(X37, c21))) | (~p13(c19, X37))) | (~p5(f8(c17, X37), f6(f7(c22))))) <=> ![X37: $i] : ((~p13(c19, X37)) | (~p13(X37, c21)) | p5(X37, c20) | (~p5(f8(c17, X37), f6(f7(c22)))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[76])).
% 0.18/0.39 tff(78,axiom,(![X37: $i] : (((p5(X37, c20) | (~p13(X37, c21))) | (~p13(c19, X37))) | (~p5(f8(c17, X37), f6(f7(c22)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p5_31')).
% 0.18/0.39 tff(79,plain,
% 0.18/0.39 (![X37: $i] : ((~p13(c19, X37)) | (~p13(X37, c21)) | p5(X37, c20) | (~p5(f8(c17, X37), f6(f7(c22)))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.18/0.39 tff(80,plain,
% 0.18/0.39 (![X37: $i] : ((~p13(c19, X37)) | (~p13(X37, c21)) | p5(X37, c20) | (~p5(f8(c17, X37), f6(f7(c22)))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.18/0.39 tff(81,plain,(
% 0.18/0.39 ![X37: $i] : ((~p13(c19, X37)) | (~p13(X37, c21)) | p5(X37, c20) | (~p5(f8(c17, X37), f6(f7(c22)))))),
% 0.18/0.39 inference(skolemize,[status(sab)],[80])).
% 0.18/0.39 tff(82,plain,
% 0.18/0.39 (![X37: $i] : ((~p13(c19, X37)) | (~p13(X37, c21)) | p5(X37, c20) | (~p5(f8(c17, X37), f6(f7(c22)))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[81, 74])).
% 0.18/0.39 tff(83,plain,
% 0.18/0.39 (p13(c19, c23) <=> p13(c19, c23)),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(84,axiom,(p13(c19, c23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p13_9')).
% 0.18/0.39 tff(85,plain,
% 0.18/0.39 (p13(c19, c23)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.18/0.39 tff(86,plain,
% 0.18/0.39 (p13(c23, c21) <=> p13(c23, c21)),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(87,axiom,(p13(c23, c21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p13_8')).
% 0.18/0.39 tff(88,plain,
% 0.18/0.39 (p13(c23, c21)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.18/0.39 tff(89,plain,
% 0.18/0.39 (((~![X37: $i] : ((~p13(c19, X37)) | (~p13(X37, c21)) | p5(X37, c20) | (~p5(f8(c17, X37), f6(f7(c22)))))) | ((~p13(c19, c23)) | (~p13(c23, c21)) | p5(c23, c20) | (~p5(f8(c17, c23), f6(f7(c22)))))) <=> ((~![X37: $i] : ((~p13(c19, X37)) | (~p13(X37, c21)) | p5(X37, c20) | (~p5(f8(c17, X37), f6(f7(c22)))))) | (~p13(c19, c23)) | (~p13(c23, c21)) | p5(c23, c20) | (~p5(f8(c17, c23), f6(f7(c22)))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(90,plain,
% 0.18/0.39 ((~![X37: $i] : ((~p13(c19, X37)) | (~p13(X37, c21)) | p5(X37, c20) | (~p5(f8(c17, X37), f6(f7(c22)))))) | ((~p13(c19, c23)) | (~p13(c23, c21)) | p5(c23, c20) | (~p5(f8(c17, c23), f6(f7(c22)))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(91,plain,
% 0.18/0.39 ((~![X37: $i] : ((~p13(c19, X37)) | (~p13(X37, c21)) | p5(X37, c20) | (~p5(f8(c17, X37), f6(f7(c22)))))) | (~p13(c19, c23)) | (~p13(c23, c21)) | p5(c23, c20) | (~p5(f8(c17, c23), f6(f7(c22))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.18/0.39 tff(92,plain,
% 0.18/0.39 (p5(c23, c20) | (~p5(f8(c17, c23), f6(f7(c22))))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[91, 88, 85, 82])).
% 0.18/0.39 tff(93,plain,
% 0.18/0.39 (p5(c23, c20)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[92, 72])).
% 0.18/0.39 tff(94,plain,
% 0.18/0.39 (((~![X25: $i, X24: $i, X26: $i] : ((~p2(X24, X26)) | (~p2(X24, X25)) | p2(X25, X26))) | ((~p2(c17, f3(c16))) | p2(f3(c16), f3(c16)))) <=> ((~![X25: $i, X24: $i, X26: $i] : ((~p2(X24, X26)) | (~p2(X24, X25)) | p2(X25, X26))) | (~p2(c17, f3(c16))) | p2(f3(c16), f3(c16)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(95,plain,
% 0.18/0.39 (((~p2(c17, f3(c16))) | (~p2(c17, f3(c16))) | p2(f3(c16), f3(c16))) <=> ((~p2(c17, f3(c16))) | p2(f3(c16), f3(c16)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(96,plain,
% 0.18/0.39 (((~![X25: $i, X24: $i, X26: $i] : ((~p2(X24, X26)) | (~p2(X24, X25)) | p2(X25, X26))) | ((~p2(c17, f3(c16))) | (~p2(c17, f3(c16))) | p2(f3(c16), f3(c16)))) <=> ((~![X25: $i, X24: $i, X26: $i] : ((~p2(X24, X26)) | (~p2(X24, X25)) | p2(X25, X26))) | ((~p2(c17, f3(c16))) | p2(f3(c16), f3(c16))))),
% 0.18/0.39 inference(monotonicity,[status(thm)],[95])).
% 0.18/0.39 tff(97,plain,
% 0.18/0.39 (((~![X25: $i, X24: $i, X26: $i] : ((~p2(X24, X26)) | (~p2(X24, X25)) | p2(X25, X26))) | ((~p2(c17, f3(c16))) | (~p2(c17, f3(c16))) | p2(f3(c16), f3(c16)))) <=> ((~![X25: $i, X24: $i, X26: $i] : ((~p2(X24, X26)) | (~p2(X24, X25)) | p2(X25, X26))) | (~p2(c17, f3(c16))) | p2(f3(c16), f3(c16)))),
% 0.18/0.39 inference(transitivity,[status(thm)],[96, 94])).
% 0.18/0.39 tff(98,plain,
% 0.18/0.39 ((~![X25: $i, X24: $i, X26: $i] : ((~p2(X24, X26)) | (~p2(X24, X25)) | p2(X25, X26))) | ((~p2(c17, f3(c16))) | (~p2(c17, f3(c16))) | p2(f3(c16), f3(c16)))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(99,plain,
% 0.18/0.39 ((~![X25: $i, X24: $i, X26: $i] : ((~p2(X24, X26)) | (~p2(X24, X25)) | p2(X25, X26))) | (~p2(c17, f3(c16))) | p2(f3(c16), f3(c16))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.18/0.39 tff(100,plain,
% 0.18/0.39 (p2(f3(c16), f3(c16))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[99, 24, 21])).
% 0.18/0.39 tff(101,plain,
% 0.18/0.39 (((~![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p5(X41, X43)) | (~p2(X40, X42)) | p5(f8(X40, X41), f8(X42, X43)))) | ((~p5(c23, c20)) | (~p2(f3(c16), f3(c16))) | p5(f8(f3(c16), c23), f8(f3(c16), c20)))) <=> ((~![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p5(X41, X43)) | (~p2(X40, X42)) | p5(f8(X40, X41), f8(X42, X43)))) | (~p5(c23, c20)) | (~p2(f3(c16), f3(c16))) | p5(f8(f3(c16), c23), f8(f3(c16), c20)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(102,plain,
% 0.18/0.40 ((~![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p5(X41, X43)) | (~p2(X40, X42)) | p5(f8(X40, X41), f8(X42, X43)))) | ((~p5(c23, c20)) | (~p2(f3(c16), f3(c16))) | p5(f8(f3(c16), c23), f8(f3(c16), c20)))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(103,plain,
% 0.18/0.40 ((~![X43: $i, X42: $i, X41: $i, X40: $i] : ((~p5(X41, X43)) | (~p2(X40, X42)) | p5(f8(X40, X41), f8(X42, X43)))) | (~p5(c23, c20)) | (~p2(f3(c16), f3(c16))) | p5(f8(f3(c16), c23), f8(f3(c16), c20))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.18/0.40 tff(104,plain,
% 0.18/0.40 ((~p5(c23, c20)) | p5(f8(f3(c16), c23), f8(f3(c16), c20))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[103, 49, 100])).
% 0.18/0.40 tff(105,plain,
% 0.18/0.40 (p5(f8(f3(c16), c23), f8(f3(c16), c20))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[104, 93])).
% 0.18/0.40 tff(106,plain,
% 0.18/0.40 ((~p5(f8(f3(c16), c20), f6(f7(c22)))) <=> (~p5(f8(f3(c16), c20), f6(f7(c22))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(107,axiom,(~p5(f8(f3(c16), c20), f6(f7(c22)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_p5_17')).
% 0.18/0.40 tff(108,plain,
% 0.18/0.40 (~p5(f8(f3(c16), c20), f6(f7(c22)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.18/0.40 tff(109,plain,
% 0.18/0.40 (((~![X35: $i, X34: $i, X36: $i] : ((~p5(X34, X36)) | (~p5(X34, X35)) | p5(X35, X36))) | ((~p5(f8(f3(c16), c23), f6(f7(c22)))) | (~p5(f8(f3(c16), c23), f8(f3(c16), c20))) | p5(f8(f3(c16), c20), f6(f7(c22))))) <=> ((~![X35: $i, X34: $i, X36: $i] : ((~p5(X34, X36)) | (~p5(X34, X35)) | p5(X35, X36))) | (~p5(f8(f3(c16), c23), f6(f7(c22)))) | (~p5(f8(f3(c16), c23), f8(f3(c16), c20))) | p5(f8(f3(c16), c20), f6(f7(c22))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(110,plain,
% 0.18/0.40 ((~![X35: $i, X34: $i, X36: $i] : ((~p5(X34, X36)) | (~p5(X34, X35)) | p5(X35, X36))) | ((~p5(f8(f3(c16), c23), f6(f7(c22)))) | (~p5(f8(f3(c16), c23), f8(f3(c16), c20))) | p5(f8(f3(c16), c20), f6(f7(c22))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(111,plain,
% 0.18/0.40 ((~![X35: $i, X34: $i, X36: $i] : ((~p5(X34, X36)) | (~p5(X34, X35)) | p5(X35, X36))) | (~p5(f8(f3(c16), c23), f6(f7(c22)))) | (~p5(f8(f3(c16), c23), f8(f3(c16), c20))) | p5(f8(f3(c16), c20), f6(f7(c22)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.18/0.40 tff(112,plain,
% 0.18/0.40 ($false),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[111, 67, 108, 64, 105])).
% 0.18/0.40 % SZS output end Proof
% 0.18/0.40 % E exiting
%------------------------------------------------------------------------------