%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN695-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:39:51 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN695-1 : TPTP v9.0.0. Released v2.5.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n009.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 12:39:33 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.20/0.39 % SZS status Unsatisfiable
% 0.20/0.39 % SZS output start Proof
% 0.20/0.39 tff(p2_type, type, (
% 0.20/0.39 p2: ( $i * $i ) > $o)).
% 0.20/0.39 tff(f11_type, type, (
% 0.20/0.39 f11: ( $i * $i ) > $i)).
% 0.20/0.39 tff(c43_type, type, (
% 0.20/0.39 c43: $i)).
% 0.20/0.39 tff(f4_type, type, (
% 0.20/0.39 f4: $i > $i)).
% 0.20/0.39 tff(f23_type, type, (
% 0.20/0.39 f23: ( $i * $i ) > $i)).
% 0.20/0.39 tff(f9_type, type, (
% 0.20/0.39 f9: $i > $i)).
% 0.20/0.39 tff(f20_type, type, (
% 0.20/0.39 f20: $i > $i)).
% 0.20/0.39 tff(c37_type, type, (
% 0.20/0.39 c37: $i)).
% 0.20/0.39 tff(c44_type, type, (
% 0.20/0.39 c44: $i)).
% 0.20/0.39 tff(c45_type, type, (
% 0.20/0.39 c45: $i)).
% 0.20/0.39 tff(p10_type, type, (
% 0.20/0.39 p10: ( $i * $i ) > $o)).
% 0.20/0.39 tff(p31_type, type, (
% 0.20/0.39 p31: ( $i * $i ) > $o)).
% 0.20/0.39 tff(c42_type, type, (
% 0.20/0.39 c42: $i)).
% 0.20/0.39 tff(f5_type, type, (
% 0.20/0.39 f5: $i > $i)).
% 0.20/0.39 tff(p3_type, type, (
% 0.20/0.39 p3: ( $i * $i ) > $o)).
% 0.20/0.39 tff(1,plain,
% 0.20/0.39 (^[X0: $i] : refl(((~p31(f11(f4(f5(c42)), X0), f11(f4(c42), X0))) | p10(X0, c43)) <=> ((~p31(f11(f4(f5(c42)), X0), f11(f4(c42), X0))) | p10(X0, c43)))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(2,plain,
% 0.20/0.39 (![X0: $i] : ((~p31(f11(f4(f5(c42)), X0), f11(f4(c42), X0))) | p10(X0, c43)) <=> ![X0: $i] : ((~p31(f11(f4(f5(c42)), X0), f11(f4(c42), X0))) | p10(X0, c43))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.39 tff(3,plain,
% 0.20/0.39 (![X0: $i] : ((~p31(f11(f4(f5(c42)), X0), f11(f4(c42), X0))) | p10(X0, c43)) <=> ![X0: $i] : ((~p31(f11(f4(f5(c42)), X0), f11(f4(c42), X0))) | p10(X0, c43))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(4,plain,
% 0.20/0.39 (^[X0: $i] : rewrite((p10(X0, c43) | (~p31(f11(f4(f5(c42)), X0), f11(f4(c42), X0)))) <=> ((~p31(f11(f4(f5(c42)), X0), f11(f4(c42), X0))) | p10(X0, c43)))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(5,plain,
% 0.20/0.39 (![X0: $i] : (p10(X0, c43) | (~p31(f11(f4(f5(c42)), X0), f11(f4(c42), X0)))) <=> ![X0: $i] : ((~p31(f11(f4(f5(c42)), X0), f11(f4(c42), X0))) | p10(X0, c43))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.39 tff(6,axiom,(![X0: $i] : (p10(X0, c43) | (~p31(f11(f4(f5(c42)), X0), f11(f4(c42), X0))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p10_57')).
% 0.20/0.39 tff(7,plain,
% 0.20/0.39 (![X0: $i] : ((~p31(f11(f4(f5(c42)), X0), f11(f4(c42), X0))) | p10(X0, c43))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.20/0.39 tff(8,plain,
% 0.20/0.39 (![X0: $i] : ((~p31(f11(f4(f5(c42)), X0), f11(f4(c42), X0))) | p10(X0, c43))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.39 tff(9,plain,(
% 0.20/0.39 ![X0: $i] : ((~p31(f11(f4(f5(c42)), X0), f11(f4(c42), X0))) | p10(X0, c43))),
% 0.20/0.39 inference(skolemize,[status(sab)],[8])).
% 0.20/0.39 tff(10,plain,
% 0.20/0.39 (![X0: $i] : ((~p31(f11(f4(f5(c42)), X0), f11(f4(c42), X0))) | p10(X0, c43))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.20/0.39 tff(11,plain,
% 0.20/0.39 (p31(f11(f4(f5(c42)), c43), f11(f4(c42), c43)) <=> p31(f11(f4(f5(c42)), c43), f11(f4(c42), c43))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(12,axiom,(p31(f11(f4(f5(c42)), c43), f11(f4(c42), c43))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p31_45')).
% 0.20/0.39 tff(13,plain,
% 0.20/0.39 (p31(f11(f4(f5(c42)), c43), f11(f4(c42), c43))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.20/0.39 tff(14,plain,
% 0.20/0.39 (((~![X0: $i] : ((~p31(f11(f4(f5(c42)), X0), f11(f4(c42), X0))) | p10(X0, c43))) | ((~p31(f11(f4(f5(c42)), c43), f11(f4(c42), c43))) | p10(c43, c43))) <=> ((~![X0: $i] : ((~p31(f11(f4(f5(c42)), X0), f11(f4(c42), X0))) | p10(X0, c43))) | (~p31(f11(f4(f5(c42)), c43), f11(f4(c42), c43))) | p10(c43, c43))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(15,plain,
% 0.20/0.39 ((~![X0: $i] : ((~p31(f11(f4(f5(c42)), X0), f11(f4(c42), X0))) | p10(X0, c43))) | ((~p31(f11(f4(f5(c42)), c43), f11(f4(c42), c43))) | p10(c43, c43))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(16,plain,
% 0.20/0.39 ((~![X0: $i] : ((~p31(f11(f4(f5(c42)), X0), f11(f4(c42), X0))) | p10(X0, c43))) | (~p31(f11(f4(f5(c42)), c43), f11(f4(c42), c43))) | p10(c43, c43)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.20/0.39 tff(17,plain,
% 0.20/0.39 (p10(c43, c43)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[16, 13, 10])).
% 0.20/0.39 tff(18,plain,
% 0.20/0.39 (^[X91: $i, X92: $i] : refl(((~p2(X91, X92)) | p3(f4(X91), f4(X92))) <=> ((~p2(X91, X92)) | p3(f4(X91), f4(X92))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(19,plain,
% 0.20/0.39 (![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92))) <=> ![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[18])).
% 0.20/0.39 tff(20,plain,
% 0.20/0.39 (![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92))) <=> ![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(21,plain,
% 0.20/0.39 (^[X91: $i, X92: $i] : rewrite((p3(f4(X91), f4(X92)) | (~p2(X91, X92))) <=> ((~p2(X91, X92)) | p3(f4(X91), f4(X92))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(22,plain,
% 0.20/0.39 (![X91: $i, X92: $i] : (p3(f4(X91), f4(X92)) | (~p2(X91, X92))) <=> ![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[21])).
% 0.20/0.39 tff(23,axiom,(![X91: $i, X92: $i] : (p3(f4(X91), f4(X92)) | (~p2(X91, X92)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p3_30')).
% 0.20/0.39 tff(24,plain,
% 0.20/0.39 (![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.39 tff(25,plain,
% 0.20/0.39 (![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.20/0.39 tff(26,plain,(
% 0.20/0.39 ![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[25])).
% 0.20/0.39 tff(27,plain,
% 0.20/0.39 (![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.20/0.39 tff(28,plain,
% 0.20/0.39 (p2(c44, c45) <=> p2(c44, c45)),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(29,axiom,(p2(c44, c45)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_18')).
% 0.20/0.39 tff(30,plain,
% 0.20/0.39 (p2(c44, c45)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.20/0.39 tff(31,plain,
% 0.20/0.39 (((~![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92)))) | ((~p2(c44, c45)) | p3(f4(c44), f4(c45)))) <=> ((~![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92)))) | (~p2(c44, c45)) | p3(f4(c44), f4(c45)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(32,plain,
% 0.20/0.39 ((~![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92)))) | ((~p2(c44, c45)) | p3(f4(c44), f4(c45)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(33,plain,
% 0.20/0.39 ((~![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92)))) | (~p2(c44, c45)) | p3(f4(c44), f4(c45))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.20/0.39 tff(34,plain,
% 0.20/0.39 (p3(f4(c44), f4(c45))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[33, 30, 27])).
% 0.20/0.39 tff(35,plain,
% 0.20/0.39 (^[X47: $i, X49: $i, X46: $i, X48: $i] : refl(((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49))) <=> ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(36,plain,
% 0.20/0.39 (![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49))) <=> ![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[35])).
% 0.20/0.39 tff(37,plain,
% 0.20/0.39 (![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49))) <=> ![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(38,plain,
% 0.20/0.39 (^[X47: $i, X49: $i, X46: $i, X48: $i] : trans(monotonicity(rewrite((p2(f11(X46, X47), f11(X48, X49)) | (~p10(X47, X49))) <=> ((~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49)))), (((p2(f11(X46, X47), f11(X48, X49)) | (~p10(X47, X49))) | (~p3(X46, X48))) <=> (((~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49))) | (~p3(X46, X48))))), rewrite((((~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49))) | (~p3(X46, X48))) <=> ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49)))), (((p2(f11(X46, X47), f11(X48, X49)) | (~p10(X47, X49))) | (~p3(X46, X48))) <=> ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(39,plain,
% 0.20/0.39 (![X47: $i, X49: $i, X46: $i, X48: $i] : ((p2(f11(X46, X47), f11(X48, X49)) | (~p10(X47, X49))) | (~p3(X46, X48))) <=> ![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[38])).
% 0.20/0.39 tff(40,axiom,(![X47: $i, X49: $i, X46: $i, X48: $i] : ((p2(f11(X46, X47), f11(X48, X49)) | (~p10(X47, X49))) | (~p3(X46, X48)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_61')).
% 0.20/0.39 tff(41,plain,
% 0.20/0.39 (![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.20/0.39 tff(42,plain,
% 0.20/0.39 (![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.20/0.39 tff(43,plain,(
% 0.20/0.39 ![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[42])).
% 0.20/0.39 tff(44,plain,
% 0.20/0.39 (![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.20/0.39 tff(45,plain,
% 0.20/0.39 (((~![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49)))) | ((~p10(c43, c43)) | (~p3(f4(c44), f4(c45))) | p2(f11(f4(c44), c43), f11(f4(c45), c43)))) <=> ((~![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49)))) | (~p10(c43, c43)) | (~p3(f4(c44), f4(c45))) | p2(f11(f4(c44), c43), f11(f4(c45), c43)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(46,plain,
% 0.20/0.39 (((~p3(f4(c44), f4(c45))) | (~p10(c43, c43)) | p2(f11(f4(c44), c43), f11(f4(c45), c43))) <=> ((~p10(c43, c43)) | (~p3(f4(c44), f4(c45))) | p2(f11(f4(c44), c43), f11(f4(c45), c43)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(47,plain,
% 0.20/0.39 (((~![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49)))) | ((~p3(f4(c44), f4(c45))) | (~p10(c43, c43)) | p2(f11(f4(c44), c43), f11(f4(c45), c43)))) <=> ((~![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49)))) | ((~p10(c43, c43)) | (~p3(f4(c44), f4(c45))) | p2(f11(f4(c44), c43), f11(f4(c45), c43))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[46])).
% 0.20/0.39 tff(48,plain,
% 0.20/0.39 (((~![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49)))) | ((~p3(f4(c44), f4(c45))) | (~p10(c43, c43)) | p2(f11(f4(c44), c43), f11(f4(c45), c43)))) <=> ((~![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49)))) | (~p10(c43, c43)) | (~p3(f4(c44), f4(c45))) | p2(f11(f4(c44), c43), f11(f4(c45), c43)))),
% 0.20/0.39 inference(transitivity,[status(thm)],[47, 45])).
% 0.20/0.39 tff(49,plain,
% 0.20/0.39 ((~![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49)))) | ((~p3(f4(c44), f4(c45))) | (~p10(c43, c43)) | p2(f11(f4(c44), c43), f11(f4(c45), c43)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(50,plain,
% 0.20/0.39 ((~![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49)))) | (~p10(c43, c43)) | (~p3(f4(c44), f4(c45))) | p2(f11(f4(c44), c43), f11(f4(c45), c43))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.20/0.39 tff(51,plain,
% 0.20/0.39 (p2(f11(f4(c44), c43), f11(f4(c45), c43))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[50, 44, 34, 17])).
% 0.20/0.39 tff(52,assumption,(~p3(f4(f23(c44, f9(f20(c37)))), f4(f23(c44, f9(f20(c37)))))), introduced(assumption)).
% 0.20/0.39 tff(53,plain,
% 0.20/0.39 (^[X88: $i] : refl(p3(X88, X88) <=> p3(X88, X88))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(54,plain,
% 0.20/0.39 (![X88: $i] : p3(X88, X88) <=> ![X88: $i] : p3(X88, X88)),
% 0.20/0.39 inference(quant_intro,[status(thm)],[53])).
% 0.20/0.39 tff(55,plain,
% 0.20/0.39 (![X88: $i] : p3(X88, X88) <=> ![X88: $i] : p3(X88, X88)),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(56,axiom,(![X88: $i] : p3(X88, X88)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p3_10')).
% 0.20/0.39 tff(57,plain,
% 0.20/0.39 (![X88: $i] : p3(X88, X88)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.20/0.40 tff(58,plain,(
% 0.20/0.40 ![X88: $i] : p3(X88, X88)),
% 0.20/0.40 inference(skolemize,[status(sab)],[57])).
% 0.20/0.40 tff(59,plain,
% 0.20/0.40 (![X88: $i] : p3(X88, X88)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.20/0.40 tff(60,plain,
% 0.20/0.40 ((~![X88: $i] : p3(X88, X88)) | p3(f4(f23(c44, f9(f20(c37)))), f4(f23(c44, f9(f20(c37)))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(61,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[60, 59, 52])).
% 0.20/0.40 tff(62,plain,(p3(f4(f23(c44, f9(f20(c37)))), f4(f23(c44, f9(f20(c37)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(63,plain,
% 0.20/0.40 (((~![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49)))) | ((~p10(c43, c43)) | (~p3(f4(f23(c44, f9(f20(c37)))), f4(f23(c44, f9(f20(c37)))))) | p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)))) <=> ((~![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49)))) | (~p10(c43, c43)) | (~p3(f4(f23(c44, f9(f20(c37)))), f4(f23(c44, f9(f20(c37)))))) | p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(64,plain,
% 0.20/0.40 (((~p3(f4(f23(c44, f9(f20(c37)))), f4(f23(c44, f9(f20(c37)))))) | (~p10(c43, c43)) | p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))) <=> ((~p10(c43, c43)) | (~p3(f4(f23(c44, f9(f20(c37)))), f4(f23(c44, f9(f20(c37)))))) | p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(65,plain,
% 0.20/0.40 (((~![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49)))) | ((~p3(f4(f23(c44, f9(f20(c37)))), f4(f23(c44, f9(f20(c37)))))) | (~p10(c43, c43)) | p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)))) <=> ((~![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49)))) | ((~p10(c43, c43)) | (~p3(f4(f23(c44, f9(f20(c37)))), f4(f23(c44, f9(f20(c37)))))) | p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[64])).
% 0.20/0.40 tff(66,plain,
% 0.20/0.40 (((~![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49)))) | ((~p3(f4(f23(c44, f9(f20(c37)))), f4(f23(c44, f9(f20(c37)))))) | (~p10(c43, c43)) | p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)))) <=> ((~![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49)))) | (~p10(c43, c43)) | (~p3(f4(f23(c44, f9(f20(c37)))), f4(f23(c44, f9(f20(c37)))))) | p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)))),
% 0.20/0.40 inference(transitivity,[status(thm)],[65, 63])).
% 0.20/0.40 tff(67,plain,
% 0.20/0.40 ((~![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49)))) | ((~p3(f4(f23(c44, f9(f20(c37)))), f4(f23(c44, f9(f20(c37)))))) | (~p10(c43, c43)) | p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(68,plain,
% 0.20/0.40 ((~![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49)))) | (~p10(c43, c43)) | (~p3(f4(f23(c44, f9(f20(c37)))), f4(f23(c44, f9(f20(c37)))))) | p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.20/0.40 tff(69,plain,
% 0.20/0.40 ((~p3(f4(f23(c44, f9(f20(c37)))), f4(f23(c44, f9(f20(c37)))))) | p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[68, 44, 17])).
% 0.20/0.40 tff(70,plain,
% 0.20/0.40 (p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[69, 62])).
% 0.20/0.40 tff(71,plain,
% 0.20/0.40 ((~p2(f11(f4(c45), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))) <=> (~p2(f11(f4(c45), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(72,axiom,(~p2(f11(f4(c45), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_p2_55')).
% 0.20/0.40 tff(73,plain,
% 0.20/0.40 (~p2(f11(f4(c45), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.20/0.40 tff(74,plain,
% 0.20/0.40 (^[X43: $i, X45: $i, X44: $i] : refl((p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44))) <=> (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(75,plain,
% 0.20/0.40 (![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44))) <=> ![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[74])).
% 0.20/0.40 tff(76,plain,
% 0.20/0.40 (![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44))) <=> ![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(77,plain,
% 0.20/0.40 (^[X43: $i, X45: $i, X44: $i] : trans(monotonicity(rewrite((p2(X44, X45) | (~p2(X43, X44))) <=> (p2(X44, X45) | (~p2(X43, X44)))), (((p2(X44, X45) | (~p2(X43, X44))) | (~p2(X43, X45))) <=> ((p2(X44, X45) | (~p2(X43, X44))) | (~p2(X43, X45))))), rewrite(((p2(X44, X45) | (~p2(X43, X44))) | (~p2(X43, X45))) <=> (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))), (((p2(X44, X45) | (~p2(X43, X44))) | (~p2(X43, X45))) <=> (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(78,plain,
% 0.20/0.40 (![X43: $i, X45: $i, X44: $i] : ((p2(X44, X45) | (~p2(X43, X44))) | (~p2(X43, X45))) <=> ![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[77])).
% 0.20/0.40 tff(79,axiom,(![X43: $i, X45: $i, X44: $i] : ((p2(X44, X45) | (~p2(X43, X44))) | (~p2(X43, X45)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_41')).
% 0.20/0.40 tff(80,plain,
% 0.20/0.40 (![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.20/0.40 tff(81,plain,
% 0.20/0.40 (![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.20/0.40 tff(82,plain,(
% 0.20/0.40 ![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[81])).
% 0.20/0.40 tff(83,plain,
% 0.20/0.40 (![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[82, 75])).
% 0.20/0.40 tff(84,plain,
% 0.20/0.40 (((~![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))) | (p2(f11(f4(c45), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c45), c43))))) <=> ((~![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))) | p2(f11(f4(c45), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c45), c43))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(85,plain,
% 0.20/0.40 ((~![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))) | (p2(f11(f4(c45), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c45), c43))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(86,plain,
% 0.20/0.40 ((~![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))) | p2(f11(f4(c45), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c45), c43)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.20/0.40 tff(87,plain,
% 0.20/0.40 (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c45), c43))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[86, 83, 73, 70])).
% 0.20/0.40 tff(88,plain,
% 0.20/0.41 (((~![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))) | (p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c45), c43)) | (~p2(f11(f4(c44), c43), f11(f4(c45), c43))) | (~p2(f11(f4(c44), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))))) <=> ((~![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))) | p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c45), c43)) | (~p2(f11(f4(c44), c43), f11(f4(c45), c43))) | (~p2(f11(f4(c44), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(89,plain,
% 0.20/0.41 ((~![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))) | (p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c45), c43)) | (~p2(f11(f4(c44), c43), f11(f4(c45), c43))) | (~p2(f11(f4(c44), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(90,plain,
% 0.20/0.41 ((~![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))) | p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c45), c43)) | (~p2(f11(f4(c44), c43), f11(f4(c45), c43))) | (~p2(f11(f4(c44), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.20/0.41 tff(91,plain,
% 0.20/0.41 (~p2(f11(f4(c44), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[90, 83, 87, 51])).
% 0.20/0.41 tff(92,plain,
% 0.20/0.41 (p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c44), c43)) <=> p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c44), c43))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(93,axiom,(p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c44), c43))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_54')).
% 0.20/0.41 tff(94,plain,
% 0.20/0.41 (p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c44), c43))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.20/0.41 tff(95,plain,
% 0.20/0.41 (((~![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))) | ((~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c44), c43))) | p2(f11(f4(c44), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))))) <=> ((~![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c44), c43))) | p2(f11(f4(c44), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(96,plain,
% 0.20/0.41 ((p2(f11(f4(c44), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c44), c43)))) <=> ((~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c44), c43))) | p2(f11(f4(c44), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(97,plain,
% 0.20/0.41 (((~![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))) | (p2(f11(f4(c44), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c44), c43))))) <=> ((~![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))) | ((~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c44), c43))) | p2(f11(f4(c44), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[96])).
% 0.20/0.41 tff(98,plain,
% 0.20/0.41 (((~![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))) | (p2(f11(f4(c44), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c44), c43))))) <=> ((~![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c44), c43))) | p2(f11(f4(c44), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[97, 95])).
% 0.20/0.41 tff(99,plain,
% 0.20/0.41 ((~![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))) | (p2(f11(f4(c44), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c44), c43))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(100,plain,
% 0.20/0.41 ((~![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c44), c43))) | p2(f11(f4(c44), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.20/0.41 tff(101,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[100, 83, 94, 70, 91])).
% 0.20/0.41 % SZS output end Proof
% 0.20/0.41 % E exiting
%------------------------------------------------------------------------------