%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN662-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:39:47 AM UTC 2025
% Result : Unsatisfiable 0.13s 0.40s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYN662-1 : TPTP v9.0.0. Released v2.5.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n003.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 : Fri Jun 20 12:40:09 EDT 2025
% 0.13/0.34 % CPUTime :
% 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(f11_type, type, (
% 0.13/0.40 f11: ( $i * $i ) > $i)).
% 0.13/0.40 tff(c34_type, type, (
% 0.13/0.40 c34: $i)).
% 0.13/0.40 tff(f4_type, type, (
% 0.13/0.40 f4: $i > $i)).
% 0.13/0.40 tff(c33_type, type, (
% 0.13/0.40 c33: $i)).
% 0.13/0.40 tff(c32_type, type, (
% 0.13/0.40 c32: $i)).
% 0.13/0.40 tff(p10_type, type, (
% 0.13/0.40 p10: ( $i * $i ) > $o)).
% 0.13/0.40 tff(p3_type, type, (
% 0.13/0.40 p3: ( $i * $i ) > $o)).
% 0.13/0.40 tff(p25_type, type, (
% 0.13/0.40 p25: ( $i * $i ) > $o)).
% 0.13/0.40 tff(c36_type, type, (
% 0.13/0.40 c36: $i)).
% 0.13/0.40 tff(f16_type, type, (
% 0.13/0.40 f16: ( $i * $i ) > $i)).
% 0.13/0.40 tff(f9_type, type, (
% 0.13/0.40 f9: $i > $i)).
% 0.13/0.40 tff(f17_type, type, (
% 0.13/0.40 f17: $i > $i)).
% 0.13/0.40 tff(c31_type, type, (
% 0.13/0.40 c31: $i)).
% 0.13/0.40 tff(1,assumption,(~p10(c34, c34)), introduced(assumption)).
% 0.13/0.40 tff(2,plain,
% 0.13/0.40 (^[X0: $i] : refl(p10(X0, X0) <=> p10(X0, X0))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(3,plain,
% 0.13/0.40 (![X0: $i] : p10(X0, X0) <=> ![X0: $i] : p10(X0, X0)),
% 0.13/0.40 inference(quant_intro,[status(thm)],[2])).
% 0.13/0.40 tff(4,plain,
% 0.13/0.40 (![X0: $i] : p10(X0, X0) <=> ![X0: $i] : p10(X0, X0)),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(5,axiom,(![X0: $i] : p10(X0, X0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p10_2')).
% 0.13/0.40 tff(6,plain,
% 0.13/0.40 (![X0: $i] : p10(X0, X0)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.13/0.40 tff(7,plain,(
% 0.13/0.40 ![X0: $i] : p10(X0, X0)),
% 0.13/0.40 inference(skolemize,[status(sab)],[6])).
% 0.13/0.40 tff(8,plain,
% 0.13/0.40 (![X0: $i] : p10(X0, X0)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.13/0.40 tff(9,plain,
% 0.13/0.40 ((~![X0: $i] : p10(X0, X0)) | p10(c34, c34)),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(10,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.13/0.40 tff(11,plain,(p10(c34, c34)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.40 tff(12,assumption,(~p3(f4(c33), f4(c33))), introduced(assumption)).
% 0.13/0.40 tff(13,plain,
% 0.13/0.40 (^[X83: $i] : refl(p3(X83, X83) <=> p3(X83, X83))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(14,plain,
% 0.13/0.40 (![X83: $i] : p3(X83, X83) <=> ![X83: $i] : p3(X83, X83)),
% 0.13/0.40 inference(quant_intro,[status(thm)],[13])).
% 0.13/0.40 tff(15,plain,
% 0.13/0.40 (![X83: $i] : p3(X83, X83) <=> ![X83: $i] : p3(X83, X83)),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(16,axiom,(![X83: $i] : p3(X83, X83)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3_5')).
% 0.13/0.40 tff(17,plain,
% 0.13/0.40 (![X83: $i] : p3(X83, X83)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.13/0.40 tff(18,plain,(
% 0.13/0.40 ![X83: $i] : p3(X83, X83)),
% 0.13/0.40 inference(skolemize,[status(sab)],[17])).
% 0.13/0.40 tff(19,plain,
% 0.13/0.40 (![X83: $i] : p3(X83, X83)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.13/0.40 tff(20,plain,
% 0.13/0.40 ((~![X83: $i] : p3(X83, X83)) | p3(f4(c33), f4(c33))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(21,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[20, 19, 12])).
% 0.13/0.40 tff(22,plain,(p3(f4(c33), f4(c33))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.40 tff(23,plain,
% 0.13/0.40 (^[X39: $i, X38: $i, X41: $i, X40: $i] : refl(((~p3(X38, X40)) | (~p10(X39, X41)) | p2(f11(X38, X39), f11(X40, X41))) <=> ((~p3(X38, X40)) | (~p10(X39, X41)) | p2(f11(X38, X39), f11(X40, X41))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(24,plain,
% 0.13/0.40 (![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p3(X38, X40)) | (~p10(X39, X41)) | p2(f11(X38, X39), f11(X40, X41))) <=> ![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p3(X38, X40)) | (~p10(X39, X41)) | p2(f11(X38, X39), f11(X40, X41)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[23])).
% 0.13/0.40 tff(25,plain,
% 0.13/0.40 (![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p3(X38, X40)) | (~p10(X39, X41)) | p2(f11(X38, X39), f11(X40, X41))) <=> ![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p3(X38, X40)) | (~p10(X39, X41)) | p2(f11(X38, X39), f11(X40, X41)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(26,plain,
% 0.13/0.40 (^[X39: $i, X38: $i, X41: $i, X40: $i] : trans(monotonicity(rewrite((p2(f11(X38, X39), f11(X40, X41)) | (~p10(X39, X41))) <=> ((~p10(X39, X41)) | p2(f11(X38, X39), f11(X40, X41)))), (((p2(f11(X38, X39), f11(X40, X41)) | (~p10(X39, X41))) | (~p3(X38, X40))) <=> (((~p10(X39, X41)) | p2(f11(X38, X39), f11(X40, X41))) | (~p3(X38, X40))))), rewrite((((~p10(X39, X41)) | p2(f11(X38, X39), f11(X40, X41))) | (~p3(X38, X40))) <=> ((~p3(X38, X40)) | (~p10(X39, X41)) | p2(f11(X38, X39), f11(X40, X41)))), (((p2(f11(X38, X39), f11(X40, X41)) | (~p10(X39, X41))) | (~p3(X38, X40))) <=> ((~p3(X38, X40)) | (~p10(X39, X41)) | p2(f11(X38, X39), f11(X40, X41)))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(27,plain,
% 0.13/0.40 (![X39: $i, X38: $i, X41: $i, X40: $i] : ((p2(f11(X38, X39), f11(X40, X41)) | (~p10(X39, X41))) | (~p3(X38, X40))) <=> ![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p3(X38, X40)) | (~p10(X39, X41)) | p2(f11(X38, X39), f11(X40, X41)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[26])).
% 0.13/0.40 tff(28,axiom,(![X39: $i, X38: $i, X41: $i, X40: $i] : ((p2(f11(X38, X39), f11(X40, X41)) | (~p10(X39, X41))) | (~p3(X38, X40)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_47')).
% 0.13/0.40 tff(29,plain,
% 0.13/0.40 (![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p3(X38, X40)) | (~p10(X39, X41)) | p2(f11(X38, X39), f11(X40, X41)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.13/0.40 tff(30,plain,
% 0.13/0.40 (![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p3(X38, X40)) | (~p10(X39, X41)) | p2(f11(X38, X39), f11(X40, X41)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.13/0.40 tff(31,plain,(
% 0.13/0.40 ![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p3(X38, X40)) | (~p10(X39, X41)) | p2(f11(X38, X39), f11(X40, X41)))),
% 0.13/0.40 inference(skolemize,[status(sab)],[30])).
% 0.13/0.40 tff(32,plain,
% 0.13/0.40 (![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p3(X38, X40)) | (~p10(X39, X41)) | p2(f11(X38, X39), f11(X40, X41)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.13/0.40 tff(33,plain,
% 0.13/0.40 (((~![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p3(X38, X40)) | (~p10(X39, X41)) | p2(f11(X38, X39), f11(X40, X41)))) | ((~p10(c34, c34)) | (~p3(f4(c33), f4(c33))) | p2(f11(f4(c33), c34), f11(f4(c33), c34)))) <=> ((~![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p3(X38, X40)) | (~p10(X39, X41)) | p2(f11(X38, X39), f11(X40, X41)))) | (~p10(c34, c34)) | (~p3(f4(c33), f4(c33))) | p2(f11(f4(c33), c34), f11(f4(c33), c34)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(34,plain,
% 0.13/0.40 (((~p3(f4(c33), f4(c33))) | (~p10(c34, c34)) | p2(f11(f4(c33), c34), f11(f4(c33), c34))) <=> ((~p10(c34, c34)) | (~p3(f4(c33), f4(c33))) | p2(f11(f4(c33), c34), f11(f4(c33), c34)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(35,plain,
% 0.13/0.40 (((~![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p3(X38, X40)) | (~p10(X39, X41)) | p2(f11(X38, X39), f11(X40, X41)))) | ((~p3(f4(c33), f4(c33))) | (~p10(c34, c34)) | p2(f11(f4(c33), c34), f11(f4(c33), c34)))) <=> ((~![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p3(X38, X40)) | (~p10(X39, X41)) | p2(f11(X38, X39), f11(X40, X41)))) | ((~p10(c34, c34)) | (~p3(f4(c33), f4(c33))) | p2(f11(f4(c33), c34), f11(f4(c33), c34))))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[34])).
% 0.13/0.40 tff(36,plain,
% 0.13/0.40 (((~![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p3(X38, X40)) | (~p10(X39, X41)) | p2(f11(X38, X39), f11(X40, X41)))) | ((~p3(f4(c33), f4(c33))) | (~p10(c34, c34)) | p2(f11(f4(c33), c34), f11(f4(c33), c34)))) <=> ((~![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p3(X38, X40)) | (~p10(X39, X41)) | p2(f11(X38, X39), f11(X40, X41)))) | (~p10(c34, c34)) | (~p3(f4(c33), f4(c33))) | p2(f11(f4(c33), c34), f11(f4(c33), c34)))),
% 0.13/0.40 inference(transitivity,[status(thm)],[35, 33])).
% 0.13/0.40 tff(37,plain,
% 0.13/0.40 ((~![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p3(X38, X40)) | (~p10(X39, X41)) | p2(f11(X38, X39), f11(X40, X41)))) | ((~p3(f4(c33), f4(c33))) | (~p10(c34, c34)) | p2(f11(f4(c33), c34), f11(f4(c33), c34)))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(38,plain,
% 0.13/0.40 ((~![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p3(X38, X40)) | (~p10(X39, X41)) | p2(f11(X38, X39), f11(X40, X41)))) | (~p10(c34, c34)) | (~p3(f4(c33), f4(c33))) | p2(f11(f4(c33), c34), f11(f4(c33), c34))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.13/0.40 tff(39,plain,
% 0.13/0.40 ((~p10(c34, c34)) | (~p3(f4(c33), f4(c33))) | p2(f11(f4(c33), c34), f11(f4(c33), c34))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[38, 32])).
% 0.13/0.40 tff(40,plain,
% 0.13/0.40 (p2(f11(f4(c33), c34), f11(f4(c33), c34))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[39, 22, 11])).
% 0.13/0.40 tff(41,plain,
% 0.13/0.40 (^[X43: $i] : refl(((~p25(c32, X43)) | p2(f11(f4(X43), c34), f11(f4(c32), c34)) | (~p25(X43, c36))) <=> ((~p25(c32, X43)) | p2(f11(f4(X43), c34), f11(f4(c32), c34)) | (~p25(X43, c36))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(42,plain,
% 0.13/0.41 (![X43: $i] : ((~p25(c32, X43)) | p2(f11(f4(X43), c34), f11(f4(c32), c34)) | (~p25(X43, c36))) <=> ![X43: $i] : ((~p25(c32, X43)) | p2(f11(f4(X43), c34), f11(f4(c32), c34)) | (~p25(X43, c36)))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[41])).
% 0.13/0.41 tff(43,plain,
% 0.13/0.41 (![X43: $i] : ((~p25(c32, X43)) | p2(f11(f4(X43), c34), f11(f4(c32), c34)) | (~p25(X43, c36))) <=> ![X43: $i] : ((~p25(c32, X43)) | p2(f11(f4(X43), c34), f11(f4(c32), c34)) | (~p25(X43, c36)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(44,plain,
% 0.13/0.41 (^[X43: $i] : trans(monotonicity(rewrite((p2(f11(f4(X43), c34), f11(f4(c32), c34)) | (~p25(X43, c36))) <=> (p2(f11(f4(X43), c34), f11(f4(c32), c34)) | (~p25(X43, c36)))), (((p2(f11(f4(X43), c34), f11(f4(c32), c34)) | (~p25(X43, c36))) | (~p25(c32, X43))) <=> ((p2(f11(f4(X43), c34), f11(f4(c32), c34)) | (~p25(X43, c36))) | (~p25(c32, X43))))), rewrite(((p2(f11(f4(X43), c34), f11(f4(c32), c34)) | (~p25(X43, c36))) | (~p25(c32, X43))) <=> ((~p25(c32, X43)) | p2(f11(f4(X43), c34), f11(f4(c32), c34)) | (~p25(X43, c36)))), (((p2(f11(f4(X43), c34), f11(f4(c32), c34)) | (~p25(X43, c36))) | (~p25(c32, X43))) <=> ((~p25(c32, X43)) | p2(f11(f4(X43), c34), f11(f4(c32), c34)) | (~p25(X43, c36)))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(45,plain,
% 0.13/0.41 (![X43: $i] : ((p2(f11(f4(X43), c34), f11(f4(c32), c34)) | (~p25(X43, c36))) | (~p25(c32, X43))) <=> ![X43: $i] : ((~p25(c32, X43)) | p2(f11(f4(X43), c34), f11(f4(c32), c34)) | (~p25(X43, c36)))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[44])).
% 0.13/0.41 tff(46,axiom,(![X43: $i] : ((p2(f11(f4(X43), c34), f11(f4(c32), c34)) | (~p25(X43, c36))) | (~p25(c32, X43)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_50')).
% 0.13/0.41 tff(47,plain,
% 0.13/0.41 (![X43: $i] : ((~p25(c32, X43)) | p2(f11(f4(X43), c34), f11(f4(c32), c34)) | (~p25(X43, c36)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.13/0.41 tff(48,plain,
% 0.13/0.41 (![X43: $i] : ((~p25(c32, X43)) | p2(f11(f4(X43), c34), f11(f4(c32), c34)) | (~p25(X43, c36)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.13/0.41 tff(49,plain,(
% 0.13/0.41 ![X43: $i] : ((~p25(c32, X43)) | p2(f11(f4(X43), c34), f11(f4(c32), c34)) | (~p25(X43, c36)))),
% 0.13/0.41 inference(skolemize,[status(sab)],[48])).
% 0.13/0.41 tff(50,plain,
% 0.13/0.41 (![X43: $i] : ((~p25(c32, X43)) | p2(f11(f4(X43), c34), f11(f4(c32), c34)) | (~p25(X43, c36)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.13/0.41 tff(51,plain,
% 0.13/0.41 (p25(c32, c33) <=> p25(c32, c33)),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(52,axiom,(p25(c32, c33)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p25_12')).
% 0.13/0.41 tff(53,plain,
% 0.13/0.41 (p25(c32, c33)),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.13/0.41 tff(54,plain,
% 0.13/0.41 (p25(c33, c36) <=> p25(c33, c36)),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(55,axiom,(p25(c33, c36)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p25_11')).
% 0.13/0.41 tff(56,plain,
% 0.13/0.41 (p25(c33, c36)),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.13/0.41 tff(57,plain,
% 0.13/0.41 (((~![X43: $i] : ((~p25(c32, X43)) | p2(f11(f4(X43), c34), f11(f4(c32), c34)) | (~p25(X43, c36)))) | (p2(f11(f4(c33), c34), f11(f4(c32), c34)) | (~p25(c32, c33)) | (~p25(c33, c36)))) <=> ((~![X43: $i] : ((~p25(c32, X43)) | p2(f11(f4(X43), c34), f11(f4(c32), c34)) | (~p25(X43, c36)))) | p2(f11(f4(c33), c34), f11(f4(c32), c34)) | (~p25(c32, c33)) | (~p25(c33, c36)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(58,plain,
% 0.13/0.41 (((~p25(c32, c33)) | p2(f11(f4(c33), c34), f11(f4(c32), c34)) | (~p25(c33, c36))) <=> (p2(f11(f4(c33), c34), f11(f4(c32), c34)) | (~p25(c32, c33)) | (~p25(c33, c36)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(59,plain,
% 0.13/0.41 (((~![X43: $i] : ((~p25(c32, X43)) | p2(f11(f4(X43), c34), f11(f4(c32), c34)) | (~p25(X43, c36)))) | ((~p25(c32, c33)) | p2(f11(f4(c33), c34), f11(f4(c32), c34)) | (~p25(c33, c36)))) <=> ((~![X43: $i] : ((~p25(c32, X43)) | p2(f11(f4(X43), c34), f11(f4(c32), c34)) | (~p25(X43, c36)))) | (p2(f11(f4(c33), c34), f11(f4(c32), c34)) | (~p25(c32, c33)) | (~p25(c33, c36))))),
% 0.22/0.41 inference(monotonicity,[status(thm)],[58])).
% 0.22/0.41 tff(60,plain,
% 0.22/0.41 (((~![X43: $i] : ((~p25(c32, X43)) | p2(f11(f4(X43), c34), f11(f4(c32), c34)) | (~p25(X43, c36)))) | ((~p25(c32, c33)) | p2(f11(f4(c33), c34), f11(f4(c32), c34)) | (~p25(c33, c36)))) <=> ((~![X43: $i] : ((~p25(c32, X43)) | p2(f11(f4(X43), c34), f11(f4(c32), c34)) | (~p25(X43, c36)))) | p2(f11(f4(c33), c34), f11(f4(c32), c34)) | (~p25(c32, c33)) | (~p25(c33, c36)))),
% 0.22/0.41 inference(transitivity,[status(thm)],[59, 57])).
% 0.22/0.41 tff(61,plain,
% 0.22/0.41 ((~![X43: $i] : ((~p25(c32, X43)) | p2(f11(f4(X43), c34), f11(f4(c32), c34)) | (~p25(X43, c36)))) | ((~p25(c32, c33)) | p2(f11(f4(c33), c34), f11(f4(c32), c34)) | (~p25(c33, c36)))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(62,plain,
% 0.22/0.41 ((~![X43: $i] : ((~p25(c32, X43)) | p2(f11(f4(X43), c34), f11(f4(c32), c34)) | (~p25(X43, c36)))) | p2(f11(f4(c33), c34), f11(f4(c32), c34)) | (~p25(c32, c33)) | (~p25(c33, c36))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.22/0.41 tff(63,plain,
% 0.22/0.41 (p2(f11(f4(c33), c34), f11(f4(c32), c34))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[62, 56, 53, 50])).
% 0.22/0.41 tff(64,plain,
% 0.22/0.41 (^[X37: $i, X35: $i, X36: $i] : refl(((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37)) <=> ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37)))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(65,plain,
% 0.22/0.41 (![X37: $i, X35: $i, X36: $i] : ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37)) <=> ![X37: $i, X35: $i, X36: $i] : ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[64])).
% 0.22/0.41 tff(66,plain,
% 0.22/0.41 (![X37: $i, X35: $i, X36: $i] : ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37)) <=> ![X37: $i, X35: $i, X36: $i] : ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(67,plain,
% 0.22/0.41 (^[X37: $i, X35: $i, X36: $i] : trans(monotonicity(rewrite((p2(X36, X37) | (~p2(X35, X36))) <=> ((~p2(X35, X36)) | p2(X36, X37))), (((p2(X36, X37) | (~p2(X35, X36))) | (~p2(X35, X37))) <=> (((~p2(X35, X36)) | p2(X36, X37)) | (~p2(X35, X37))))), rewrite((((~p2(X35, X36)) | p2(X36, X37)) | (~p2(X35, X37))) <=> ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37))), (((p2(X36, X37) | (~p2(X35, X36))) | (~p2(X35, X37))) <=> ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(68,plain,
% 0.22/0.41 (![X37: $i, X35: $i, X36: $i] : ((p2(X36, X37) | (~p2(X35, X36))) | (~p2(X35, X37))) <=> ![X37: $i, X35: $i, X36: $i] : ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[67])).
% 0.22/0.41 tff(69,axiom,(![X37: $i, X35: $i, X36: $i] : ((p2(X36, X37) | (~p2(X35, X36))) | (~p2(X35, X37)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_30')).
% 0.22/0.41 tff(70,plain,
% 0.22/0.41 (![X37: $i, X35: $i, X36: $i] : ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.22/0.41 tff(71,plain,
% 0.22/0.41 (![X37: $i, X35: $i, X36: $i] : ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.22/0.41 tff(72,plain,(
% 0.22/0.41 ![X37: $i, X35: $i, X36: $i] : ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37))),
% 0.22/0.41 inference(skolemize,[status(sab)],[71])).
% 0.22/0.41 tff(73,plain,
% 0.22/0.41 (![X37: $i, X35: $i, X36: $i] : ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[72, 65])).
% 0.22/0.41 tff(74,plain,
% 0.22/0.41 (((~![X37: $i, X35: $i, X36: $i] : ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37))) | (p2(f11(f4(c32), c34), f11(f4(c33), c34)) | (~p2(f11(f4(c33), c34), f11(f4(c32), c34))) | (~p2(f11(f4(c33), c34), f11(f4(c33), c34))))) <=> ((~![X37: $i, X35: $i, X36: $i] : ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37))) | p2(f11(f4(c32), c34), f11(f4(c33), c34)) | (~p2(f11(f4(c33), c34), f11(f4(c32), c34))) | (~p2(f11(f4(c33), c34), f11(f4(c33), c34))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(75,plain,
% 0.22/0.41 (((~p2(f11(f4(c33), c34), f11(f4(c33), c34))) | (~p2(f11(f4(c33), c34), f11(f4(c32), c34))) | p2(f11(f4(c32), c34), f11(f4(c33), c34))) <=> (p2(f11(f4(c32), c34), f11(f4(c33), c34)) | (~p2(f11(f4(c33), c34), f11(f4(c32), c34))) | (~p2(f11(f4(c33), c34), f11(f4(c33), c34))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(76,plain,
% 0.22/0.41 (((~![X37: $i, X35: $i, X36: $i] : ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37))) | ((~p2(f11(f4(c33), c34), f11(f4(c33), c34))) | (~p2(f11(f4(c33), c34), f11(f4(c32), c34))) | p2(f11(f4(c32), c34), f11(f4(c33), c34)))) <=> ((~![X37: $i, X35: $i, X36: $i] : ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37))) | (p2(f11(f4(c32), c34), f11(f4(c33), c34)) | (~p2(f11(f4(c33), c34), f11(f4(c32), c34))) | (~p2(f11(f4(c33), c34), f11(f4(c33), c34)))))),
% 0.22/0.41 inference(monotonicity,[status(thm)],[75])).
% 0.22/0.41 tff(77,plain,
% 0.22/0.41 (((~![X37: $i, X35: $i, X36: $i] : ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37))) | ((~p2(f11(f4(c33), c34), f11(f4(c33), c34))) | (~p2(f11(f4(c33), c34), f11(f4(c32), c34))) | p2(f11(f4(c32), c34), f11(f4(c33), c34)))) <=> ((~![X37: $i, X35: $i, X36: $i] : ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37))) | p2(f11(f4(c32), c34), f11(f4(c33), c34)) | (~p2(f11(f4(c33), c34), f11(f4(c32), c34))) | (~p2(f11(f4(c33), c34), f11(f4(c33), c34))))),
% 0.22/0.41 inference(transitivity,[status(thm)],[76, 74])).
% 0.22/0.41 tff(78,plain,
% 0.22/0.41 ((~![X37: $i, X35: $i, X36: $i] : ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37))) | ((~p2(f11(f4(c33), c34), f11(f4(c33), c34))) | (~p2(f11(f4(c33), c34), f11(f4(c32), c34))) | p2(f11(f4(c32), c34), f11(f4(c33), c34)))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(79,plain,
% 0.22/0.41 ((~![X37: $i, X35: $i, X36: $i] : ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37))) | p2(f11(f4(c32), c34), f11(f4(c33), c34)) | (~p2(f11(f4(c33), c34), f11(f4(c32), c34))) | (~p2(f11(f4(c33), c34), f11(f4(c33), c34)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.22/0.41 tff(80,plain,
% 0.22/0.41 (p2(f11(f4(c32), c34), f11(f4(c33), c34))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[79, 73, 63, 40])).
% 0.22/0.41 tff(81,plain,
% 0.22/0.41 (^[X96: $i] : refl((~p2(X96, f16(X96, f9(f17(c31))))) <=> (~p2(X96, f16(X96, f9(f17(c31))))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(82,plain,
% 0.22/0.41 (![X96: $i] : (~p2(X96, f16(X96, f9(f17(c31))))) <=> ![X96: $i] : (~p2(X96, f16(X96, f9(f17(c31)))))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[81])).
% 0.22/0.41 tff(83,plain,
% 0.22/0.41 (![X96: $i] : (~p2(X96, f16(X96, f9(f17(c31))))) <=> ![X96: $i] : (~p2(X96, f16(X96, f9(f17(c31)))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(84,axiom,(![X96: $i] : (~p2(X96, f16(X96, f9(f17(c31)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_p2_19')).
% 0.22/0.41 tff(85,plain,
% 0.22/0.41 (![X96: $i] : (~p2(X96, f16(X96, f9(f17(c31)))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.22/0.41 tff(86,plain,(
% 0.22/0.41 ![X96: $i] : (~p2(X96, f16(X96, f9(f17(c31)))))),
% 0.22/0.41 inference(skolemize,[status(sab)],[85])).
% 0.22/0.41 tff(87,plain,
% 0.22/0.41 (![X96: $i] : (~p2(X96, f16(X96, f9(f17(c31)))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.22/0.41 tff(88,plain,
% 0.22/0.41 ((~![X96: $i] : (~p2(X96, f16(X96, f9(f17(c31)))))) | (~p2(f11(f4(c33), c34), f16(f11(f4(c33), c34), f9(f17(c31)))))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(89,plain,
% 0.22/0.41 (~p2(f11(f4(c33), c34), f16(f11(f4(c33), c34), f9(f17(c31))))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.22/0.41 tff(90,plain,
% 0.22/0.41 (p2(f11(f4(c32), c34), f16(f11(f4(c33), c34), f9(f17(c31)))) <=> p2(f11(f4(c32), c34), f16(f11(f4(c33), c34), f9(f17(c31))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(91,axiom,(p2(f11(f4(c32), c34), f16(f11(f4(c33), c34), f9(f17(c31))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_39')).
% 0.22/0.41 tff(92,plain,
% 0.22/0.41 (p2(f11(f4(c32), c34), f16(f11(f4(c33), c34), f9(f17(c31))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.22/0.41 tff(93,plain,
% 0.22/0.41 (((~![X37: $i, X35: $i, X36: $i] : ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37))) | ((~p2(f11(f4(c32), c34), f16(f11(f4(c33), c34), f9(f17(c31))))) | p2(f11(f4(c33), c34), f16(f11(f4(c33), c34), f9(f17(c31)))) | (~p2(f11(f4(c32), c34), f11(f4(c33), c34))))) <=> ((~![X37: $i, X35: $i, X36: $i] : ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37))) | (~p2(f11(f4(c32), c34), f16(f11(f4(c33), c34), f9(f17(c31))))) | p2(f11(f4(c33), c34), f16(f11(f4(c33), c34), f9(f17(c31)))) | (~p2(f11(f4(c32), c34), f11(f4(c33), c34))))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(94,plain,
% 0.22/0.42 (((~p2(f11(f4(c32), c34), f16(f11(f4(c33), c34), f9(f17(c31))))) | (~p2(f11(f4(c32), c34), f11(f4(c33), c34))) | p2(f11(f4(c33), c34), f16(f11(f4(c33), c34), f9(f17(c31))))) <=> ((~p2(f11(f4(c32), c34), f16(f11(f4(c33), c34), f9(f17(c31))))) | p2(f11(f4(c33), c34), f16(f11(f4(c33), c34), f9(f17(c31)))) | (~p2(f11(f4(c32), c34), f11(f4(c33), c34))))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(95,plain,
% 0.22/0.42 (((~![X37: $i, X35: $i, X36: $i] : ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37))) | ((~p2(f11(f4(c32), c34), f16(f11(f4(c33), c34), f9(f17(c31))))) | (~p2(f11(f4(c32), c34), f11(f4(c33), c34))) | p2(f11(f4(c33), c34), f16(f11(f4(c33), c34), f9(f17(c31)))))) <=> ((~![X37: $i, X35: $i, X36: $i] : ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37))) | ((~p2(f11(f4(c32), c34), f16(f11(f4(c33), c34), f9(f17(c31))))) | p2(f11(f4(c33), c34), f16(f11(f4(c33), c34), f9(f17(c31)))) | (~p2(f11(f4(c32), c34), f11(f4(c33), c34)))))),
% 0.22/0.42 inference(monotonicity,[status(thm)],[94])).
% 0.22/0.42 tff(96,plain,
% 0.22/0.42 (((~![X37: $i, X35: $i, X36: $i] : ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37))) | ((~p2(f11(f4(c32), c34), f16(f11(f4(c33), c34), f9(f17(c31))))) | (~p2(f11(f4(c32), c34), f11(f4(c33), c34))) | p2(f11(f4(c33), c34), f16(f11(f4(c33), c34), f9(f17(c31)))))) <=> ((~![X37: $i, X35: $i, X36: $i] : ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37))) | (~p2(f11(f4(c32), c34), f16(f11(f4(c33), c34), f9(f17(c31))))) | p2(f11(f4(c33), c34), f16(f11(f4(c33), c34), f9(f17(c31)))) | (~p2(f11(f4(c32), c34), f11(f4(c33), c34))))),
% 0.22/0.42 inference(transitivity,[status(thm)],[95, 93])).
% 0.22/0.42 tff(97,plain,
% 0.22/0.42 ((~![X37: $i, X35: $i, X36: $i] : ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37))) | ((~p2(f11(f4(c32), c34), f16(f11(f4(c33), c34), f9(f17(c31))))) | (~p2(f11(f4(c32), c34), f11(f4(c33), c34))) | p2(f11(f4(c33), c34), f16(f11(f4(c33), c34), f9(f17(c31)))))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(98,plain,
% 0.22/0.42 ((~![X37: $i, X35: $i, X36: $i] : ((~p2(X35, X37)) | (~p2(X35, X36)) | p2(X36, X37))) | (~p2(f11(f4(c32), c34), f16(f11(f4(c33), c34), f9(f17(c31))))) | p2(f11(f4(c33), c34), f16(f11(f4(c33), c34), f9(f17(c31)))) | (~p2(f11(f4(c32), c34), f11(f4(c33), c34)))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.22/0.42 tff(99,plain,
% 0.22/0.42 ($false),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[98, 73, 92, 89, 80])).
% 0.22/0.42 % SZS output end Proof
% 0.22/0.42 % E exiting
%------------------------------------------------------------------------------