%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN700-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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
% 0.06/0.12 % Problem : SYN700-1 : TPTP v9.0.0. Released v2.5.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n010.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Jun 20 12:42:12 EDT 2025
% 0.13/0.33 % 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(c46_type, type, (
% 0.20/0.41 c46: $i)).
% 0.20/0.41 tff(p10_type, type, (
% 0.20/0.41 p10: ( $i * $i ) > $o)).
% 0.20/0.41 tff(p3_type, type, (
% 0.20/0.41 p3: ( $i * $i ) > $o)).
% 0.20/0.41 tff(1,assumption,(~p10(c43, c43)), introduced(assumption)).
% 0.20/0.41 tff(2,plain,
% 0.20/0.41 (^[X5: $i] : refl(p10(X5, X5) <=> p10(X5, X5))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(3,plain,
% 0.20/0.41 (![X5: $i] : p10(X5, X5) <=> ![X5: $i] : p10(X5, X5)),
% 0.20/0.41 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.41 tff(4,plain,
% 0.20/0.41 (![X5: $i] : p10(X5, X5) <=> ![X5: $i] : p10(X5, X5)),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(5,axiom,(![X5: $i] : p10(X5, X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p10_7')).
% 0.20/0.41 tff(6,plain,
% 0.20/0.41 (![X5: $i] : p10(X5, X5)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.41 tff(7,plain,(
% 0.20/0.41 ![X5: $i] : p10(X5, X5)),
% 0.20/0.41 inference(skolemize,[status(sab)],[6])).
% 0.20/0.41 tff(8,plain,
% 0.20/0.41 (![X5: $i] : p10(X5, X5)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.41 tff(9,plain,
% 0.20/0.41 ((~![X5: $i] : p10(X5, X5)) | p10(c43, c43)),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(10,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.20/0.41 tff(11,plain,(p10(c43, c43)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(12,plain,
% 0.20/0.41 (^[X91: $i, X92: $i] : refl(((~p2(X91, X92)) | p3(f4(X91), f4(X92))) <=> ((~p2(X91, X92)) | p3(f4(X91), f4(X92))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(13,plain,
% 0.20/0.41 (![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92))) <=> ![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.41 tff(14,plain,
% 0.20/0.41 (![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92))) <=> ![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(15,plain,
% 0.20/0.41 (^[X91: $i, X92: $i] : rewrite((p3(f4(X91), f4(X92)) | (~p2(X91, X92))) <=> ((~p2(X91, X92)) | p3(f4(X91), f4(X92))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(16,plain,
% 0.20/0.41 (![X91: $i, X92: $i] : (p3(f4(X91), f4(X92)) | (~p2(X91, X92))) <=> ![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[15])).
% 0.20/0.41 tff(17,axiom,(![X91: $i, X92: $i] : (p3(f4(X91), f4(X92)) | (~p2(X91, X92)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3_37')).
% 0.20/0.41 tff(18,plain,
% 0.20/0.41 (![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.20/0.41 tff(19,plain,
% 0.20/0.41 (![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.20/0.41 tff(20,plain,(
% 0.20/0.41 ![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[19])).
% 0.20/0.41 tff(21,plain,
% 0.20/0.41 (![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.20/0.41 tff(22,plain,
% 0.20/0.41 (p2(c44, c46) <=> p2(c44, c46)),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(23,axiom,(p2(c44, c46)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_16')).
% 0.20/0.41 tff(24,plain,
% 0.20/0.41 (p2(c44, c46)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.41 tff(25,plain,
% 0.20/0.41 (((~![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92)))) | ((~p2(c44, c46)) | p3(f4(c44), f4(c46)))) <=> ((~![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92)))) | (~p2(c44, c46)) | p3(f4(c44), f4(c46)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(26,plain,
% 0.20/0.41 ((~![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92)))) | ((~p2(c44, c46)) | p3(f4(c44), f4(c46)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(27,plain,
% 0.20/0.41 ((~![X91: $i, X92: $i] : ((~p2(X91, X92)) | p3(f4(X91), f4(X92)))) | (~p2(c44, c46)) | p3(f4(c44), f4(c46))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.20/0.41 tff(28,plain,
% 0.20/0.41 (p3(f4(c44), f4(c46))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[27, 24, 21])).
% 0.20/0.41 tff(29,plain,
% 0.20/0.41 (^[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))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(30,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[29])).
% 0.20/0.41 tff(31,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(32,plain,
% 0.20/0.41 (^[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)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(33,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[32])).
% 0.20/0.41 tff(34,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_62')).
% 0.20/0.41 tff(35,plain,
% 0.20/0.41 (![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.20/0.41 tff(36,plain,
% 0.20/0.41 (![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.20/0.41 tff(37,plain,(
% 0.20/0.41 ![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[36])).
% 0.20/0.41 tff(38,plain,
% 0.20/0.41 (![X47: $i, X49: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p10(X47, X49)) | p2(f11(X46, X47), f11(X48, X49)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.20/0.41 tff(39,plain,
% 0.20/0.41 (((~![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(c46))) | p2(f11(f4(c44), c43), f11(f4(c46), 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(c46))) | p2(f11(f4(c44), c43), f11(f4(c46), c43)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(40,plain,
% 0.20/0.41 (((~p3(f4(c44), f4(c46))) | (~p10(c43, c43)) | p2(f11(f4(c44), c43), f11(f4(c46), c43))) <=> ((~p10(c43, c43)) | (~p3(f4(c44), f4(c46))) | p2(f11(f4(c44), c43), f11(f4(c46), c43)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(41,plain,
% 0.20/0.41 (((~![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(c46))) | (~p10(c43, c43)) | p2(f11(f4(c44), c43), f11(f4(c46), 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(c46))) | p2(f11(f4(c44), c43), f11(f4(c46), c43))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[40])).
% 0.20/0.41 tff(42,plain,
% 0.20/0.41 (((~![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(c46))) | (~p10(c43, c43)) | p2(f11(f4(c44), c43), f11(f4(c46), 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(c46))) | p2(f11(f4(c44), c43), f11(f4(c46), c43)))),
% 0.20/0.41 inference(transitivity,[status(thm)],[41, 39])).
% 0.20/0.41 tff(43,plain,
% 0.20/0.41 ((~![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(c46))) | (~p10(c43, c43)) | p2(f11(f4(c44), c43), f11(f4(c46), c43)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(44,plain,
% 0.20/0.41 ((~![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(c46))) | p2(f11(f4(c44), c43), f11(f4(c46), c43))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.20/0.41 tff(45,plain,
% 0.20/0.41 ((~p10(c43, c43)) | p2(f11(f4(c44), c43), f11(f4(c46), c43))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[44, 38, 28])).
% 0.20/0.41 tff(46,plain,
% 0.20/0.41 (p2(f11(f4(c44), c43), f11(f4(c46), c43))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[45, 11])).
% 0.20/0.41 tff(47,assumption,(~p2(f9(f20(c37)), f9(f20(c37)))), introduced(assumption)).
% 0.20/0.41 tff(48,plain,
% 0.20/0.41 (^[X43: $i] : refl(p2(X43, X43) <=> p2(X43, X43))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(49,plain,
% 0.20/0.41 (![X43: $i] : p2(X43, X43) <=> ![X43: $i] : p2(X43, X43)),
% 0.20/0.41 inference(quant_intro,[status(thm)],[48])).
% 0.20/0.41 tff(50,plain,
% 0.20/0.41 (![X43: $i] : p2(X43, X43) <=> ![X43: $i] : p2(X43, X43)),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(51,axiom,(![X43: $i] : p2(X43, X43)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_12')).
% 0.20/0.41 tff(52,plain,
% 0.20/0.41 (![X43: $i] : p2(X43, X43)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.20/0.41 tff(53,plain,(
% 0.20/0.41 ![X43: $i] : p2(X43, X43)),
% 0.20/0.41 inference(skolemize,[status(sab)],[52])).
% 0.20/0.41 tff(54,plain,
% 0.20/0.41 (![X43: $i] : p2(X43, X43)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.20/0.41 tff(55,plain,
% 0.20/0.41 ((~![X43: $i] : p2(X43, X43)) | p2(f9(f20(c37)), f9(f20(c37)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(56,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[55, 54, 47])).
% 0.20/0.41 tff(57,plain,(p2(f9(f20(c37)), f9(f20(c37)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(58,assumption,(~p2(c44, c44)), introduced(assumption)).
% 0.20/0.41 tff(59,plain,
% 0.20/0.41 ((~![X43: $i] : p2(X43, X43)) | p2(c44, c44)),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(60,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[59, 54, 58])).
% 0.20/0.41 tff(61,plain,(p2(c44, c44)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(62,plain,
% 0.20/0.41 (^[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))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(63,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[62])).
% 0.20/0.41 tff(64,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(65,plain,
% 0.20/0.41 (^[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)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(66,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[65])).
% 0.20/0.42 tff(67,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_60')).
% 0.20/0.42 tff(68,plain,
% 0.20/0.42 (![X59: $i, X60: $i, X61: $i, X58: $i] : ((~p2(X59, X61)) | (~p2(X58, X60)) | p2(f23(X58, X59), f23(X60, X61)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.20/0.42 tff(69,plain,
% 0.20/0.42 (![X59: $i, X60: $i, X61: $i, X58: $i] : ((~p2(X59, X61)) | (~p2(X58, X60)) | p2(f23(X58, X59), f23(X60, X61)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.20/0.42 tff(70,plain,(
% 0.20/0.42 ![X59: $i, X60: $i, X61: $i, X58: $i] : ((~p2(X59, X61)) | (~p2(X58, X60)) | p2(f23(X58, X59), f23(X60, X61)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[69])).
% 0.20/0.42 tff(71,plain,
% 0.20/0.42 (![X59: $i, X60: $i, X61: $i, X58: $i] : ((~p2(X59, X61)) | (~p2(X58, X60)) | p2(f23(X58, X59), f23(X60, X61)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.20/0.42 tff(72,plain,
% 0.20/0.42 (((~![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)))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(73,plain,
% 0.20/0.42 ((~![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)))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(74,plain,
% 0.20/0.42 ((~![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))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.20/0.42 tff(75,plain,
% 0.20/0.42 ((~p2(f9(f20(c37)), f9(f20(c37)))) | (~p2(c44, c44)) | p2(f23(c44, f9(f20(c37))), f23(c44, f9(f20(c37))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[74, 71])).
% 0.20/0.42 tff(76,plain,
% 0.20/0.42 (p2(f23(c44, f9(f20(c37))), f23(c44, f9(f20(c37))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[75, 61, 57])).
% 0.20/0.42 tff(77,plain,
% 0.20/0.42 (((~![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))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(78,plain,
% 0.20/0.42 ((~![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))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(79,plain,
% 0.20/0.42 ((~![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)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.20/0.42 tff(80,plain,
% 0.20/0.42 (p3(f4(f23(c44, f9(f20(c37)))), f4(f23(c44, f9(f20(c37)))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[79, 21, 76])).
% 0.20/0.42 tff(81,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(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)))) | (~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)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(82,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(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)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(83,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(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))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.20/0.42 tff(84,plain,
% 0.20/0.42 ((~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))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[83, 38])).
% 0.20/0.42 tff(85,plain,
% 0.20/0.42 (p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[84, 11, 80])).
% 0.20/0.42 tff(86,plain,
% 0.20/0.42 ((~p2(f11(f4(c46), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))) <=> (~p2(f11(f4(c46), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(87,axiom,(~p2(f11(f4(c46), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_p2_57')).
% 0.20/0.42 tff(88,plain,
% 0.20/0.42 (~p2(f11(f4(c46), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.20/0.42 tff(89,plain,
% 0.20/0.42 (^[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))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(90,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[89])).
% 0.20/0.42 tff(91,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(92,plain,
% 0.20/0.42 (^[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)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(93,plain,
% 0.20/0.42 (![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)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[92])).
% 0.20/0.42 tff(94,axiom,(![X43: $i, X45: $i, X44: $i] : ((p2(X44, X45) | (~p2(X43, X44))) | (~p2(X43, X45)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_43')).
% 0.20/0.42 tff(95,plain,
% 0.20/0.42 (![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.20/0.42 tff(96,plain,
% 0.20/0.42 (![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.20/0.42 tff(97,plain,(
% 0.20/0.42 ![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[96])).
% 0.20/0.42 tff(98,plain,
% 0.20/0.42 (![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[97, 90])).
% 0.20/0.42 tff(99,plain,
% 0.20/0.42 (((~![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))) | (p2(f11(f4(c46), 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(c46), c43))))) <=> ((~![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))) | p2(f11(f4(c46), 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(c46), c43))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(100,plain,
% 0.20/0.42 ((~![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))) | (p2(f11(f4(c46), 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(c46), c43))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(101,plain,
% 0.20/0.42 ((~![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))) | p2(f11(f4(c46), 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(c46), c43)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.20/0.42 tff(102,plain,
% 0.20/0.42 (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c46), c43))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[101, 98, 88, 85])).
% 0.20/0.42 tff(103,plain,
% 0.20/0.42 (((~![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(c46), c43)) | (~p2(f11(f4(c44), c43), f11(f4(c46), 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(c46), c43)) | (~p2(f11(f4(c44), c43), f11(f4(c46), c43))) | (~p2(f11(f4(c44), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(104,plain,
% 0.20/0.42 ((~![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(c46), c43)) | (~p2(f11(f4(c44), c43), f11(f4(c46), c43))) | (~p2(f11(f4(c44), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(105,plain,
% 0.20/0.42 ((~![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(c46), c43)) | (~p2(f11(f4(c44), c43), f11(f4(c46), c43))) | (~p2(f11(f4(c44), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.20/0.42 tff(106,plain,
% 0.20/0.42 (~p2(f11(f4(c44), c43), f11(f4(f23(c44, f9(f20(c37)))), c43))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[105, 98, 102, 46])).
% 0.20/0.42 tff(107,plain,
% 0.20/0.42 (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))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(108,axiom,(p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c44), c43))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_56')).
% 0.20/0.42 tff(109,plain,
% 0.20/0.42 (p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c44), c43))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.20/0.42 tff(110,plain,
% 0.20/0.42 (((~![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))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(111,plain,
% 0.20/0.43 ((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))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(112,plain,
% 0.20/0.43 (((~![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)))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[111])).
% 0.20/0.43 tff(113,plain,
% 0.20/0.43 (((~![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))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[112, 110])).
% 0.20/0.43 tff(114,plain,
% 0.20/0.43 ((~![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))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(115,plain,
% 0.20/0.43 ((~![X43: $i, X45: $i, X44: $i] : (p2(X44, X45) | (~p2(X43, X45)) | (~p2(X43, X44)))) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(c44), c43))) | p2(f11(f4(c44), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)) | (~p2(f11(f4(f23(c44, f9(f20(c37)))), c43), f11(f4(f23(c44, f9(f20(c37)))), c43)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.20/0.43 tff(116,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[115, 98, 109, 85, 106])).
% 0.20/0.43 % SZS output end Proof
% 0.20/0.43 % E exiting
%------------------------------------------------------------------------------