%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN694-1 : 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 05:39:51 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN694-1 : TPTP v9.0.0. Released v2.5.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n015.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 12:39:56 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.20/0.41 % SZS status Unsatisfiable
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 tff(p2_type, type, (
% 0.20/0.41 p2: ( $i * $i ) > $o)).
% 0.20/0.41 tff(f11_type, type, (
% 0.20/0.41 f11: ( $i * $i ) > $i)).
% 0.20/0.41 tff(c43_type, type, (
% 0.20/0.41 c43: $i)).
% 0.20/0.41 tff(f4_type, type, (
% 0.20/0.41 f4: $i > $i)).
% 0.20/0.41 tff(f23_type, type, (
% 0.20/0.41 f23: ( $i * $i ) > $i)).
% 0.20/0.41 tff(f9_type, type, (
% 0.20/0.41 f9: $i > $i)).
% 0.20/0.41 tff(f20_type, type, (
% 0.20/0.41 f20: $i > $i)).
% 0.20/0.41 tff(c37_type, type, (
% 0.20/0.41 c37: $i)).
% 0.20/0.41 tff(c44_type, type, (
% 0.20/0.41 c44: $i)).
% 0.20/0.41 tff(c45_type, type, (
% 0.20/0.41 c45: $i)).
% 0.20/0.41 tff(p10_type, type, (
% 0.20/0.41 p10: ( $i * $i ) > $o)).
% 0.20/0.41 tff(p31_type, type, (
% 0.20/0.41 p31: ( $i * $i ) > $o)).
% 0.20/0.41 tff(c42_type, type, (
% 0.20/0.41 c42: $i)).
% 0.20/0.41 tff(f5_type, type, (
% 0.20/0.41 f5: $i > $i)).
% 0.20/0.41 tff(p3_type, type, (
% 0.20/0.41 p3: ( $i * $i ) > $o)).
% 0.20/0.41 tff(1,plain,
% 0.20/0.41 (^[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)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(2,plain,
% 0.20/0.41 (![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))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.42 tff(3,plain,
% 0.20/0.42 (![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))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(4,plain,
% 0.20/0.42 (^[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)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(5,plain,
% 0.20/0.42 (![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))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.42 tff(6,axiom,(![X0: $i] : (p10(X0, c43) | (~p31(f11(f4(f5(c42)), X0), f11(f4(c42), X0))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p10_57')).
% 0.20/0.42 tff(7,plain,
% 0.20/0.42 (![X0: $i] : ((~p31(f11(f4(f5(c42)), X0), f11(f4(c42), X0))) | p10(X0, c43))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.20/0.42 tff(8,plain,
% 0.20/0.42 (![X0: $i] : ((~p31(f11(f4(f5(c42)), X0), f11(f4(c42), X0))) | p10(X0, c43))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.42 tff(9,plain,(
% 0.20/0.42 ![X0: $i] : ((~p31(f11(f4(f5(c42)), X0), f11(f4(c42), X0))) | p10(X0, c43))),
% 0.20/0.42 inference(skolemize,[status(sab)],[8])).
% 0.20/0.42 tff(10,plain,
% 0.20/0.42 (![X0: $i] : ((~p31(f11(f4(f5(c42)), X0), f11(f4(c42), X0))) | p10(X0, c43))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.20/0.42 tff(11,plain,
% 0.20/0.42 (p31(f11(f4(f5(c42)), c43), f11(f4(c42), c43)) <=> p31(f11(f4(f5(c42)), c43), f11(f4(c42), c43))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(12,axiom,(p31(f11(f4(f5(c42)), c43), f11(f4(c42), c43))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p31_46')).
% 0.20/0.42 tff(13,plain,
% 0.20/0.42 (p31(f11(f4(f5(c42)), c43), f11(f4(c42), c43))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.20/0.42 tff(14,plain,
% 0.20/0.42 (((~![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))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(15,plain,
% 0.20/0.42 ((~![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))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(16,plain,
% 0.20/0.42 ((~![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)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.20/0.42 tff(17,plain,
% 0.20/0.42 (p10(c43, c43)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[16, 13, 10])).
% 0.20/0.42 tff(18,plain,
% 0.20/0.42 (^[X91: $i, X92: $i] : refl(((~p2(X91, X92)) | p3(f4(X91), f4(X92))) <=> ((~p2(X91, X92)) | p3(f4(X91), f4(X92))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(19,plain,
% 0.20/0.42 (![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92))) <=> ![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[18])).
% 0.20/0.42 tff(20,plain,
% 0.20/0.42 (![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92))) <=> ![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(21,plain,
% 0.20/0.42 (^[X91: $i, X92: $i] : rewrite((p3(f4(X91), f4(X92)) | (~p2(X91, X92))) <=> ((~p2(X91, X92)) | p3(f4(X91), f4(X92))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(22,plain,
% 0.20/0.42 (![X91: $i, X92: $i] : (p3(f4(X91), f4(X92)) | (~p2(X91, X92))) <=> ![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[21])).
% 0.20/0.42 tff(23,axiom,(![X91: $i, X92: $i] : (p3(f4(X91), f4(X92)) | (~p2(X91, X92)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3_36')).
% 0.20/0.42 tff(24,plain,
% 0.20/0.42 (![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.42 tff(25,plain,
% 0.20/0.42 (![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.20/0.42 tff(26,plain,(
% 0.20/0.42 ![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[25])).
% 0.20/0.42 tff(27,plain,
% 0.20/0.42 (![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.20/0.42 tff(28,plain,
% 0.20/0.42 (p2(c44, c45) <=> p2(c44, c45)),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(29,axiom,(p2(c44, c45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_18')).
% 0.20/0.42 tff(30,plain,
% 0.20/0.42 (p2(c44, c45)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.20/0.42 tff(31,plain,
% 0.20/0.42 (((~![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)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(32,plain,
% 0.20/0.42 ((~![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92)))) | ((~p2(c44, c45)) | p3(f4(c44), f4(c45)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(33,plain,
% 0.20/0.42 ((~![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92)))) | (~p2(c44, c45)) | p3(f4(c44), f4(c45))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.20/0.42 tff(34,plain,
% 0.20/0.42 (p3(f4(c44), f4(c45))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[33, 30, 27])).
% 0.20/0.42 tff(35,plain,
% 0.20/0.42 (^[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))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(36,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[35])).
% 0.20/0.42 tff(37,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(38,plain,
% 0.20/0.42 (^[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)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(39,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[38])).
% 0.20/0.42 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/sandbox2/benchmark/theBenchmark.p','p2_61')).
% 0.20/0.42 tff(41,plain,
% 0.20/0.42 (![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.20/0.42 tff(42,plain,
% 0.20/0.42 (![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.20/0.42 tff(43,plain,(
% 0.20/0.42 ![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[42])).
% 0.20/0.42 tff(44,plain,
% 0.20/0.42 (![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.20/0.42 tff(45,plain,
% 0.20/0.42 (((~![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)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(46,plain,
% 0.20/0.42 (((~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)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(47,plain,
% 0.20/0.42 (((~![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))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[46])).
% 0.20/0.42 tff(48,plain,
% 0.20/0.42 (((~![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)))),
% 0.20/0.42 inference(transitivity,[status(thm)],[47, 45])).
% 0.20/0.42 tff(49,plain,
% 0.20/0.42 ((~![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)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(50,plain,
% 0.20/0.42 ((~![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))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.20/0.42 tff(51,plain,
% 0.20/0.42 (p2(f11(f4(c44), c43), f11(f4(c45), c43))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[50, 44, 34, 17])).
% 0.20/0.42 tff(52,assumption,(~p2(c37, c37)), introduced(assumption)).
% 0.20/0.42 tff(53,plain,
% 0.20/0.42 (^[X43: $i] : refl(p2(X43, X43) <=> p2(X43, X43))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(54,plain,
% 0.20/0.42 (![X43: $i] : p2(X43, X43) <=> ![X43: $i] : p2(X43, X43)),
% 0.20/0.42 inference(quant_intro,[status(thm)],[53])).
% 0.20/0.42 tff(55,plain,
% 0.20/0.42 (![X43: $i] : p2(X43, X43) <=> ![X43: $i] : p2(X43, X43)),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(56,axiom,(![X43: $i] : p2(X43, X43)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_12')).
% 0.20/0.42 tff(57,plain,
% 0.20/0.42 (![X43: $i] : p2(X43, X43)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.20/0.42 tff(58,plain,(
% 0.20/0.42 ![X43: $i] : p2(X43, X43)),
% 0.20/0.42 inference(skolemize,[status(sab)],[57])).
% 0.20/0.42 tff(59,plain,
% 0.20/0.42 (![X43: $i] : p2(X43, X43)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.20/0.42 tff(60,plain,
% 0.20/0.42 ((~![X43: $i] : p2(X43, X43)) | p2(c37, c37)),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(61,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[60, 59, 52])).
% 0.20/0.42 tff(62,plain,(p2(c37, c37)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(63,plain,
% 0.20/0.42 (^[X57: $i, X56: $i] : refl(((~p2(X56, X57)) | p2(f20(X56), f20(X57))) <=> ((~p2(X56, X57)) | p2(f20(X56), f20(X57))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(64,plain,
% 0.20/0.42 (![X57: $i, X56: $i] : ((~p2(X56, X57)) | p2(f20(X56), f20(X57))) <=> ![X57: $i, X56: $i] : ((~p2(X56, X57)) | p2(f20(X56), f20(X57)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[63])).
% 0.20/0.42 tff(65,plain,
% 0.20/0.42 (![X57: $i, X56: $i] : ((~p2(X56, X57)) | p2(f20(X56), f20(X57))) <=> ![X57: $i, X56: $i] : ((~p2(X56, X57)) | p2(f20(X56), f20(X57)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(66,plain,
% 0.20/0.42 (^[X57: $i, X56: $i] : rewrite((p2(f20(X56), f20(X57)) | (~p2(X56, X57))) <=> ((~p2(X56, X57)) | p2(f20(X56), f20(X57))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(67,plain,
% 0.20/0.42 (![X57: $i, X56: $i] : (p2(f20(X56), f20(X57)) | (~p2(X56, X57))) <=> ![X57: $i, X56: $i] : ((~p2(X56, X57)) | p2(f20(X56), f20(X57)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[66])).
% 0.20/0.42 tff(68,axiom,(![X57: $i, X56: $i] : (p2(f20(X56), f20(X57)) | (~p2(X56, X57)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_32')).
% 0.20/0.42 tff(69,plain,
% 0.20/0.42 (![X57: $i, X56: $i] : ((~p2(X56, X57)) | p2(f20(X56), f20(X57)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.20/0.42 tff(70,plain,
% 0.20/0.42 (![X57: $i, X56: $i] : ((~p2(X56, X57)) | p2(f20(X56), f20(X57)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.20/0.42 tff(71,plain,(
% 0.20/0.42 ![X57: $i, X56: $i] : ((~p2(X56, X57)) | p2(f20(X56), f20(X57)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[70])).
% 0.20/0.42 tff(72,plain,
% 0.20/0.42 (![X57: $i, X56: $i] : ((~p2(X56, X57)) | p2(f20(X56), f20(X57)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.20/0.42 tff(73,plain,
% 0.20/0.42 (((~![X57: $i, X56: $i] : ((~p2(X56, X57)) | p2(f20(X56), f20(X57)))) | ((~p2(c37, c37)) | p2(f20(c37), f20(c37)))) <=> ((~![X57: $i, X56: $i] : ((~p2(X56, X57)) | p2(f20(X56), f20(X57)))) | (~p2(c37, c37)) | p2(f20(c37), f20(c37)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(74,plain,
% 0.20/0.42 ((~![X57: $i, X56: $i] : ((~p2(X56, X57)) | p2(f20(X56), f20(X57)))) | ((~p2(c37, c37)) | p2(f20(c37), f20(c37)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(75,plain,
% 0.20/0.42 ((~![X57: $i, X56: $i] : ((~p2(X56, X57)) | p2(f20(X56), f20(X57)))) | (~p2(c37, c37)) | p2(f20(c37), f20(c37))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.20/0.42 tff(76,plain,
% 0.20/0.42 ((~p2(c37, c37)) | p2(f20(c37), f20(c37))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[75, 72])).
% 0.20/0.42 tff(77,plain,
% 0.20/0.42 (p2(f20(c37), f20(c37))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[76, 62])).
% 0.20/0.42 tff(78,plain,
% 0.20/0.42 (^[X67: $i, X66: $i] : refl(((~p2(X66, X67)) | p2(f9(X66), f9(X67))) <=> ((~p2(X66, X67)) | p2(f9(X66), f9(X67))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(79,plain,
% 0.20/0.42 (![X67: $i, X66: $i] : ((~p2(X66, X67)) | p2(f9(X66), f9(X67))) <=> ![X67: $i, X66: $i] : ((~p2(X66, X67)) | p2(f9(X66), f9(X67)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[78])).
% 0.20/0.42 tff(80,plain,
% 0.20/0.42 (![X67: $i, X66: $i] : ((~p2(X66, X67)) | p2(f9(X66), f9(X67))) <=> ![X67: $i, X66: $i] : ((~p2(X66, X67)) | p2(f9(X66), f9(X67)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(81,plain,
% 0.20/0.42 (^[X67: $i, X66: $i] : rewrite((p2(f9(X66), f9(X67)) | (~p2(X66, X67))) <=> ((~p2(X66, X67)) | p2(f9(X66), f9(X67))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(82,plain,
% 0.20/0.42 (![X67: $i, X66: $i] : (p2(f9(X66), f9(X67)) | (~p2(X66, X67))) <=> ![X67: $i, X66: $i] : ((~p2(X66, X67)) | p2(f9(X66), f9(X67)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[81])).
% 0.20/0.42 tff(83,axiom,(![X67: $i, X66: $i] : (p2(f9(X66), f9(X67)) | (~p2(X66, X67)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_35')).
% 0.20/0.42 tff(84,plain,
% 0.20/0.42 (![X67: $i, X66: $i] : ((~p2(X66, X67)) | p2(f9(X66), f9(X67)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.20/0.42 tff(85,plain,
% 0.20/0.42 (![X67: $i, X66: $i] : ((~p2(X66, X67)) | p2(f9(X66), f9(X67)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.20/0.42 tff(86,plain,(
% 0.20/0.42 ![X67: $i, X66: $i] : ((~p2(X66, X67)) | p2(f9(X66), f9(X67)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[85])).
% 0.20/0.42 tff(87,plain,
% 0.20/0.42 (![X67: $i, X66: $i] : ((~p2(X66, X67)) | p2(f9(X66), f9(X67)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[86, 79])).
% 0.20/0.42 tff(88,plain,
% 0.20/0.42 (((~![X67: $i, X66: $i] : ((~p2(X66, X67)) | p2(f9(X66), f9(X67)))) | ((~p2(f20(c37), f20(c37))) | p2(f9(f20(c37)), f9(f20(c37))))) <=> ((~![X67: $i, X66: $i] : ((~p2(X66, X67)) | p2(f9(X66), f9(X67)))) | (~p2(f20(c37), f20(c37))) | p2(f9(f20(c37)), f9(f20(c37))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(89,plain,
% 0.20/0.42 ((~![X67: $i, X66: $i] : ((~p2(X66, X67)) | p2(f9(X66), f9(X67)))) | ((~p2(f20(c37), f20(c37))) | p2(f9(f20(c37)), f9(f20(c37))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(90,plain,
% 0.20/0.42 ((~![X67: $i, X66: $i] : ((~p2(X66, X67)) | p2(f9(X66), f9(X67)))) | (~p2(f20(c37), f20(c37))) | p2(f9(f20(c37)), f9(f20(c37)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.20/0.42 tff(91,plain,
% 0.20/0.42 ((~p2(f20(c37), f20(c37))) | p2(f9(f20(c37)), f9(f20(c37)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[90, 87])).
% 0.20/0.42 tff(92,plain,
% 0.20/0.42 (p2(f9(f20(c37)), f9(f20(c37)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[91, 77])).
% 0.20/0.42 tff(93,assumption,(~p2(c44, c44)), introduced(assumption)).
% 0.20/0.42 tff(94,plain,
% 0.20/0.42 ((~![X43: $i] : p2(X43, X43)) | p2(c44, c44)),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(95,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[94, 59, 93])).
% 0.20/0.42 tff(96,plain,(p2(c44, c44)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(97,plain,
% 0.20/0.42 (^[X59: $i, X60: $i, X61: $i, X58: $i] : refl(((~p2(X59, X61)) | (~p2(X58, X60)) | p2(f23(X58, X59), f23(X60, X61))) <=> ((~p2(X59, X61)) | (~p2(X58, X60)) | p2(f23(X58, X59), f23(X60, X61))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(98,plain,
% 0.20/0.43 (![X59: $i, X60: $i, X61: $i, X58: $i] : ((~p2(X59, X61)) | (~p2(X58, X60)) | p2(f23(X58, X59), f23(X60, X61))) <=> ![X59: $i, X60: $i, X61: $i, X58: $i] : ((~p2(X59, X61)) | (~p2(X58, X60)) | p2(f23(X58, X59), f23(X60, X61)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[97])).
% 0.20/0.43 tff(99,plain,
% 0.20/0.43 (![X59: $i, X60: $i, X61: $i, X58: $i] : ((~p2(X59, X61)) | (~p2(X58, X60)) | p2(f23(X58, X59), f23(X60, X61))) <=> ![X59: $i, X60: $i, X61: $i, X58: $i] : ((~p2(X59, X61)) | (~p2(X58, X60)) | p2(f23(X58, X59), f23(X60, X61)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(100,plain,
% 0.20/0.43 (^[X59: $i, X60: $i, X61: $i, X58: $i] : trans(monotonicity(rewrite((p2(f23(X58, X59), f23(X60, X61)) | (~p2(X58, X60))) <=> ((~p2(X58, X60)) | p2(f23(X58, X59), f23(X60, X61)))), (((p2(f23(X58, X59), f23(X60, X61)) | (~p2(X58, X60))) | (~p2(X59, X61))) <=> (((~p2(X58, X60)) | p2(f23(X58, X59), f23(X60, X61))) | (~p2(X59, X61))))), rewrite((((~p2(X58, X60)) | p2(f23(X58, X59), f23(X60, X61))) | (~p2(X59, X61))) <=> ((~p2(X59, X61)) | (~p2(X58, X60)) | p2(f23(X58, X59), f23(X60, X61)))), (((p2(f23(X58, X59), f23(X60, X61)) | (~p2(X58, X60))) | (~p2(X59, X61))) <=> ((~p2(X59, X61)) | (~p2(X58, X60)) | p2(f23(X58, X59), f23(X60, X61)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(101,plain,
% 0.20/0.43 (![X59: $i, X60: $i, X61: $i, X58: $i] : ((p2(f23(X58, X59), f23(X60, X61)) | (~p2(X58, X60))) | (~p2(X59, X61))) <=> ![X59: $i, X60: $i, X61: $i, X58: $i] : ((~p2(X59, X61)) | (~p2(X58, X60)) | p2(f23(X58, X59), f23(X60, X61)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[100])).
% 0.20/0.43 tff(102,axiom,(![X59: $i, X60: $i, X61: $i, X58: $i] : ((p2(f23(X58, X59), f23(X60, X61)) | (~p2(X58, X60))) | (~p2(X59, X61)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_59')).
% 0.20/0.43 tff(103,plain,
% 0.20/0.43 (![X59: $i, X60: $i, X61: $i, X58: $i] : ((~p2(X59, X61)) | (~p2(X58, X60)) | p2(f23(X58, X59), f23(X60, X61)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.20/0.43 tff(104,plain,
% 0.20/0.43 (![X59: $i, X60: $i, X61: $i, X58: $i] : ((~p2(X59, X61)) | (~p2(X58, X60)) | p2(f23(X58, X59), f23(X60, X61)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[103, 99])).
% 0.20/0.43 tff(105,plain,(
% 0.20/0.43 ![X59: $i, X60: $i, X61: $i, X58: $i] : ((~p2(X59, X61)) | (~p2(X58, X60)) | p2(f23(X58, X59), f23(X60, X61)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[104])).
% 0.20/0.43 tff(106,plain,
% 0.20/0.43 (![X59: $i, X60: $i, X61: $i, X58: $i] : ((~p2(X59, X61)) | (~p2(X58, X60)) | p2(f23(X58, X59), f23(X60, X61)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[105, 98])).
% 0.20/0.43 tff(107,plain,
% 0.20/0.43 (((~![X59: $i, X60: $i, X61: $i, X58: $i] : ((~p2(X59, X61)) | (~p2(X58, X60)) | p2(f23(X58, X59), f23(X60, X61)))) | ((~p2(f9(f20(c37)), f9(f20(c37)))) | (~p2(c44, c44)) | p2(f23(c44, f9(f20(c37))), f23(c44, f9(f20(c37)))))) <=> ((~![X59: $i, X60: $i, X61: $i, X58: $i] : ((~p2(X59, X61)) | (~p2(X58, X60)) | p2(f23(X58, X59), f23(X60, X61)))) | (~p2(f9(f20(c37)), f9(f20(c37)))) | (~p2(c44, c44)) | p2(f23(c44, f9(f20(c37))), f23(c44, f9(f20(c37)))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(108,plain,
% 0.20/0.43 ((~![X59: $i, X60: $i, X61: $i, X58: $i] : ((~p2(X59, X61)) | (~p2(X58, X60)) | p2(f23(X58, X59), f23(X60, X61)))) | ((~p2(f9(f20(c37)), f9(f20(c37)))) | (~p2(c44, c44)) | p2(f23(c44, f9(f20(c37))), f23(c44, f9(f20(c37)))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(109,plain,
% 0.20/0.43 ((~![X59: $i, X60: $i, X61: $i, X58: $i] : ((~p2(X59, X61)) | (~p2(X58, X60)) | p2(f23(X58, X59), f23(X60, X61)))) | (~p2(f9(f20(c37)), f9(f20(c37)))) | (~p2(c44, c44)) | p2(f23(c44, f9(f20(c37))), f23(c44, f9(f20(c37))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.20/0.43 tff(110,plain,
% 0.20/0.43 ((~p2(f9(f20(c37)), f9(f20(c37)))) | (~p2(c44, c44)) | p2(f23(c44, f9(f20(c37))), f23(c44, f9(f20(c37))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[109, 106])).
% 0.20/0.43 tff(111,plain,
% 0.20/0.43 (p2(f23(c44, f9(f20(c37))), f23(c44, f9(f20(c37))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[110, 96, 92])).
% 0.20/0.43 tff(112,plain,
% 0.20/0.43 (((~![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92)))) | ((~p2(f23(c44, f9(f20(c37))), f23(c44, f9(f20(c37))))) | p3(f4(f23(c44, f9(f20(c37)))), f4(f23(c44, f9(f20(c37))))))) <=> ((~![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92)))) | (~p2(f23(c44, f9(f20(c37))), f23(c44, f9(f20(c37))))) | p3(f4(f23(c44, f9(f20(c37)))), f4(f23(c44, f9(f20(c37))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(113,plain,
% 0.20/0.43 ((~![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92)))) | ((~p2(f23(c44, f9(f20(c37))), f23(c44, f9(f20(c37))))) | p3(f4(f23(c44, f9(f20(c37)))), f4(f23(c44, f9(f20(c37))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(114,plain,
% 0.20/0.43 ((~![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92)))) | (~p2(f23(c44, f9(f20(c37))), f23(c44, f9(f20(c37))))) | p3(f4(f23(c44, f9(f20(c37)))), f4(f23(c44, f9(f20(c37)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.20/0.43 tff(115,plain,
% 0.20/0.43 (p3(f4(f23(c44, f9(f20(c37)))), f4(f23(c44, f9(f20(c37)))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[114, 27, 111])).
% 0.20/0.43 tff(116,plain,
% 0.20/0.43 (((~![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)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(117,plain,
% 0.20/0.43 (((~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)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(118,plain,
% 0.20/0.43 (((~![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))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[117])).
% 0.20/0.43 tff(119,plain,
% 0.20/0.43 (((~![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)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[118, 116])).
% 0.20/0.43 tff(120,plain,
% 0.20/0.43 ((~![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)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(121,plain,
% 0.20/0.43 ((~![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))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.20/0.43 tff(122,plain,
% 0.20/0.43 ((~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))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[121, 44, 17])).
% 0.20/0.43 tff(123,plain,
% 0.20/0.43 (p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[122, 115])).
% 0.20/0.43 tff(124,plain,
% 0.20/0.43 ((~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)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(125,axiom,(~p2(f11(f4(c45), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_p2_56')).
% 0.20/0.43 tff(126,plain,
% 0.20/0.43 (~p2(f11(f4(c45), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.20/0.43 tff(127,plain,
% 0.20/0.43 (^[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))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(128,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[127])).
% 0.20/0.43 tff(129,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(130,plain,
% 0.20/0.43 (^[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)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(131,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[130])).
% 0.20/0.44 tff(132,axiom,(![X43: $i, X45: $i, X44: $i] : ((p2(X44, X45) | (~p2(X43, X44))) | (~p2(X43, X45)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_42')).
% 0.20/0.44 tff(133,plain,
% 0.20/0.44 (![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.20/0.44 tff(134,plain,
% 0.20/0.44 (![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[133, 129])).
% 0.20/0.44 tff(135,plain,(
% 0.20/0.44 ![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[134])).
% 0.20/0.44 tff(136,plain,
% 0.20/0.44 (![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[135, 128])).
% 0.20/0.44 tff(137,plain,
% 0.20/0.44 (((~![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))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(138,plain,
% 0.20/0.44 ((~![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))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(139,plain,
% 0.20/0.44 ((~![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)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.20/0.44 tff(140,plain,
% 0.20/0.44 (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c45), c43))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[139, 136, 126, 123])).
% 0.20/0.44 tff(141,plain,
% 0.20/0.44 (((~![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))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(142,plain,
% 0.20/0.44 ((~![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))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(143,plain,
% 0.20/0.44 ((~![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)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.20/0.44 tff(144,plain,
% 0.20/0.44 (~p2(f11(f4(c44), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[143, 136, 140, 51])).
% 0.20/0.44 tff(145,plain,
% 0.20/0.44 (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))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(146,axiom,(p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c44), c43))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_55')).
% 0.20/0.44 tff(147,plain,
% 0.20/0.44 (p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c44), c43))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.20/0.44 tff(148,plain,
% 0.20/0.44 (((~![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))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(149,plain,
% 0.20/0.44 ((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))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(150,plain,
% 0.20/0.44 (((~![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)))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[149])).
% 0.20/0.44 tff(151,plain,
% 0.20/0.44 (((~![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))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[150, 148])).
% 0.20/0.44 tff(152,plain,
% 0.20/0.44 ((~![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))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(153,plain,
% 0.20/0.44 ((~![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c44), c43))) | p2(f11(f4(c44), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.20/0.44 tff(154,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[153, 136, 147, 123, 144])).
% 0.20/0.44 % SZS output end Proof
% 0.20/0.45 % E exiting
%------------------------------------------------------------------------------