%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN628-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:39:43 AM UTC 2025
% Result : Unsatisfiable 0.22s 0.39s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SYN628-1 : TPTP v9.0.0. Released v2.5.0.
% 0.04/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n011.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 12:39:11 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.22/0.39 % SZS status Unsatisfiable
% 0.22/0.39 % SZS output start Proof
% 0.22/0.39 tff(p9_type, type, (
% 0.22/0.39 p9: ( $i * $i ) > $o)).
% 0.22/0.39 tff(f10_type, type, (
% 0.22/0.39 f10: ( $i * $i ) > $i)).
% 0.22/0.39 tff(f11_type, type, (
% 0.22/0.39 f11: $i > $i)).
% 0.22/0.39 tff(f12_type, type, (
% 0.22/0.39 f12: $i > $i)).
% 0.22/0.39 tff(f13_type, type, (
% 0.22/0.39 f13: $i > $i)).
% 0.22/0.39 tff(f14_type, type, (
% 0.22/0.39 f14: $i > $i)).
% 0.22/0.39 tff(c29_type, type, (
% 0.22/0.39 c29: $i)).
% 0.22/0.39 tff(f15_type, type, (
% 0.22/0.39 f15: ( $i * $i ) > $i)).
% 0.22/0.39 tff(c22_type, type, (
% 0.22/0.39 c22: $i)).
% 0.22/0.39 tff(f7_type, type, (
% 0.22/0.39 f7: ( $i * $i ) > $i)).
% 0.22/0.39 tff(f8_type, type, (
% 0.22/0.39 f8: ( $i * $i ) > $i)).
% 0.22/0.39 tff(c25_type, type, (
% 0.22/0.39 c25: $i)).
% 0.22/0.39 tff(c24_type, type, (
% 0.22/0.39 c24: $i)).
% 0.22/0.39 tff(c23_type, type, (
% 0.22/0.39 c23: $i)).
% 0.22/0.39 tff(c28_type, type, (
% 0.22/0.39 c28: $i)).
% 0.22/0.39 tff(p5_type, type, (
% 0.22/0.39 p5: ( $i * $i ) > $o)).
% 0.22/0.39 tff(p2_type, type, (
% 0.22/0.39 p2: ( $i * $i ) > $o)).
% 0.22/0.39 tff(f16_type, type, (
% 0.22/0.39 f16: $i > $i)).
% 0.22/0.39 tff(f17_type, type, (
% 0.22/0.39 f17: ( $i * $i ) > $i)).
% 0.22/0.39 tff(c27_type, type, (
% 0.22/0.39 c27: $i)).
% 0.22/0.39 tff(p20_type, type, (
% 0.22/0.39 p20: ( $i * $i ) > $o)).
% 0.22/0.39 tff(1,assumption,(~p5(f14(c29), f14(c29))), introduced(assumption)).
% 0.22/0.39 tff(2,plain,
% 0.22/0.39 (^[X24: $i] : refl(p5(X24, X24) <=> p5(X24, X24))),
% 0.22/0.39 inference(bind,[status(th)],[])).
% 0.22/0.39 tff(3,plain,
% 0.22/0.39 (![X24: $i] : p5(X24, X24) <=> ![X24: $i] : p5(X24, X24)),
% 0.22/0.39 inference(quant_intro,[status(thm)],[2])).
% 0.22/0.39 tff(4,plain,
% 0.22/0.39 (![X24: $i] : p5(X24, X24) <=> ![X24: $i] : p5(X24, X24)),
% 0.22/0.39 inference(rewrite,[status(thm)],[])).
% 0.22/0.39 tff(5,axiom,(![X24: $i] : p5(X24, X24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p5_4')).
% 0.22/0.39 tff(6,plain,
% 0.22/0.39 (![X24: $i] : p5(X24, X24)),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.22/0.39 tff(7,plain,(
% 0.22/0.39 ![X24: $i] : p5(X24, X24)),
% 0.22/0.39 inference(skolemize,[status(sab)],[6])).
% 0.22/0.39 tff(8,plain,
% 0.22/0.39 (![X24: $i] : p5(X24, X24)),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.22/0.39 tff(9,plain,
% 0.22/0.39 ((~![X24: $i] : p5(X24, X24)) | p5(f14(c29), f14(c29))),
% 0.22/0.39 inference(quant_inst,[status(thm)],[])).
% 0.22/0.39 tff(10,plain,
% 0.22/0.39 ($false),
% 0.22/0.39 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.22/0.39 tff(11,plain,(p5(f14(c29), f14(c29))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.39 tff(12,plain,
% 0.22/0.39 (^[X30: $i, X29: $i] : refl(((~p5(X29, X30)) | p5(f13(X29), f13(X30))) <=> ((~p5(X29, X30)) | p5(f13(X29), f13(X30))))),
% 0.22/0.39 inference(bind,[status(th)],[])).
% 0.22/0.39 tff(13,plain,
% 0.22/0.39 (![X30: $i, X29: $i] : ((~p5(X29, X30)) | p5(f13(X29), f13(X30))) <=> ![X30: $i, X29: $i] : ((~p5(X29, X30)) | p5(f13(X29), f13(X30)))),
% 0.22/0.39 inference(quant_intro,[status(thm)],[12])).
% 0.22/0.39 tff(14,plain,
% 0.22/0.39 (![X30: $i, X29: $i] : ((~p5(X29, X30)) | p5(f13(X29), f13(X30))) <=> ![X30: $i, X29: $i] : ((~p5(X29, X30)) | p5(f13(X29), f13(X30)))),
% 0.22/0.39 inference(rewrite,[status(thm)],[])).
% 0.22/0.39 tff(15,plain,
% 0.22/0.39 (^[X30: $i, X29: $i] : rewrite((p5(f13(X29), f13(X30)) | (~p5(X29, X30))) <=> ((~p5(X29, X30)) | p5(f13(X29), f13(X30))))),
% 0.22/0.39 inference(bind,[status(th)],[])).
% 0.22/0.39 tff(16,plain,
% 0.22/0.39 (![X30: $i, X29: $i] : (p5(f13(X29), f13(X30)) | (~p5(X29, X30))) <=> ![X30: $i, X29: $i] : ((~p5(X29, X30)) | p5(f13(X29), f13(X30)))),
% 0.22/0.39 inference(quant_intro,[status(thm)],[15])).
% 0.22/0.39 tff(17,axiom,(![X30: $i, X29: $i] : (p5(f13(X29), f13(X30)) | (~p5(X29, X30)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p5_16')).
% 0.22/0.39 tff(18,plain,
% 0.22/0.39 (![X30: $i, X29: $i] : ((~p5(X29, X30)) | p5(f13(X29), f13(X30)))),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.22/0.39 tff(19,plain,
% 0.22/0.39 (![X30: $i, X29: $i] : ((~p5(X29, X30)) | p5(f13(X29), f13(X30)))),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.22/0.39 tff(20,plain,(
% 0.22/0.39 ![X30: $i, X29: $i] : ((~p5(X29, X30)) | p5(f13(X29), f13(X30)))),
% 0.22/0.39 inference(skolemize,[status(sab)],[19])).
% 0.22/0.39 tff(21,plain,
% 0.22/0.39 (![X30: $i, X29: $i] : ((~p5(X29, X30)) | p5(f13(X29), f13(X30)))),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.22/0.39 tff(22,plain,
% 0.22/0.39 (((~![X30: $i, X29: $i] : ((~p5(X29, X30)) | p5(f13(X29), f13(X30)))) | ((~p5(f14(c29), f14(c29))) | p5(f13(f14(c29)), f13(f14(c29))))) <=> ((~![X30: $i, X29: $i] : ((~p5(X29, X30)) | p5(f13(X29), f13(X30)))) | (~p5(f14(c29), f14(c29))) | p5(f13(f14(c29)), f13(f14(c29))))),
% 0.22/0.39 inference(rewrite,[status(thm)],[])).
% 0.22/0.39 tff(23,plain,
% 0.22/0.39 ((~![X30: $i, X29: $i] : ((~p5(X29, X30)) | p5(f13(X29), f13(X30)))) | ((~p5(f14(c29), f14(c29))) | p5(f13(f14(c29)), f13(f14(c29))))),
% 0.22/0.39 inference(quant_inst,[status(thm)],[])).
% 0.22/0.39 tff(24,plain,
% 0.22/0.39 ((~![X30: $i, X29: $i] : ((~p5(X29, X30)) | p5(f13(X29), f13(X30)))) | (~p5(f14(c29), f14(c29))) | p5(f13(f14(c29)), f13(f14(c29)))),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.22/0.39 tff(25,plain,
% 0.22/0.39 ((~p5(f14(c29), f14(c29))) | p5(f13(f14(c29)), f13(f14(c29)))),
% 0.22/0.39 inference(unit_resolution,[status(thm)],[24, 21])).
% 0.22/0.39 tff(26,plain,
% 0.22/0.39 (p5(f13(f14(c29)), f13(f14(c29)))),
% 0.22/0.39 inference(unit_resolution,[status(thm)],[25, 11])).
% 0.22/0.39 tff(27,plain,
% 0.22/0.39 (^[X27: $i, X28: $i] : refl(((~p5(X27, X28)) | p5(f12(X27), f12(X28))) <=> ((~p5(X27, X28)) | p5(f12(X27), f12(X28))))),
% 0.22/0.39 inference(bind,[status(th)],[])).
% 0.22/0.39 tff(28,plain,
% 0.22/0.39 (![X27: $i, X28: $i] : ((~p5(X27, X28)) | p5(f12(X27), f12(X28))) <=> ![X27: $i, X28: $i] : ((~p5(X27, X28)) | p5(f12(X27), f12(X28)))),
% 0.22/0.39 inference(quant_intro,[status(thm)],[27])).
% 0.22/0.39 tff(29,plain,
% 0.22/0.39 (![X27: $i, X28: $i] : ((~p5(X27, X28)) | p5(f12(X27), f12(X28))) <=> ![X27: $i, X28: $i] : ((~p5(X27, X28)) | p5(f12(X27), f12(X28)))),
% 0.22/0.39 inference(rewrite,[status(thm)],[])).
% 0.22/0.39 tff(30,plain,
% 0.22/0.39 (^[X27: $i, X28: $i] : rewrite((p5(f12(X27), f12(X28)) | (~p5(X27, X28))) <=> ((~p5(X27, X28)) | p5(f12(X27), f12(X28))))),
% 0.22/0.39 inference(bind,[status(th)],[])).
% 0.22/0.39 tff(31,plain,
% 0.22/0.39 (![X27: $i, X28: $i] : (p5(f12(X27), f12(X28)) | (~p5(X27, X28))) <=> ![X27: $i, X28: $i] : ((~p5(X27, X28)) | p5(f12(X27), f12(X28)))),
% 0.22/0.39 inference(quant_intro,[status(thm)],[30])).
% 0.22/0.39 tff(32,axiom,(![X27: $i, X28: $i] : (p5(f12(X27), f12(X28)) | (~p5(X27, X28)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p5_15')).
% 0.22/0.39 tff(33,plain,
% 0.22/0.39 (![X27: $i, X28: $i] : ((~p5(X27, X28)) | p5(f12(X27), f12(X28)))),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.22/0.39 tff(34,plain,
% 0.22/0.39 (![X27: $i, X28: $i] : ((~p5(X27, X28)) | p5(f12(X27), f12(X28)))),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.22/0.39 tff(35,plain,(
% 0.22/0.39 ![X27: $i, X28: $i] : ((~p5(X27, X28)) | p5(f12(X27), f12(X28)))),
% 0.22/0.39 inference(skolemize,[status(sab)],[34])).
% 0.22/0.39 tff(36,plain,
% 0.22/0.39 (![X27: $i, X28: $i] : ((~p5(X27, X28)) | p5(f12(X27), f12(X28)))),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.22/0.39 tff(37,plain,
% 0.22/0.39 (((~![X27: $i, X28: $i] : ((~p5(X27, X28)) | p5(f12(X27), f12(X28)))) | ((~p5(f13(f14(c29)), f13(f14(c29)))) | p5(f12(f13(f14(c29))), f12(f13(f14(c29)))))) <=> ((~![X27: $i, X28: $i] : ((~p5(X27, X28)) | p5(f12(X27), f12(X28)))) | (~p5(f13(f14(c29)), f13(f14(c29)))) | p5(f12(f13(f14(c29))), f12(f13(f14(c29)))))),
% 0.22/0.39 inference(rewrite,[status(thm)],[])).
% 0.22/0.39 tff(38,plain,
% 0.22/0.39 ((~![X27: $i, X28: $i] : ((~p5(X27, X28)) | p5(f12(X27), f12(X28)))) | ((~p5(f13(f14(c29)), f13(f14(c29)))) | p5(f12(f13(f14(c29))), f12(f13(f14(c29)))))),
% 0.22/0.39 inference(quant_inst,[status(thm)],[])).
% 0.22/0.39 tff(39,plain,
% 0.22/0.39 ((~![X27: $i, X28: $i] : ((~p5(X27, X28)) | p5(f12(X27), f12(X28)))) | (~p5(f13(f14(c29)), f13(f14(c29)))) | p5(f12(f13(f14(c29))), f12(f13(f14(c29))))),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.22/0.39 tff(40,plain,
% 0.22/0.39 ((~p5(f13(f14(c29)), f13(f14(c29)))) | p5(f12(f13(f14(c29))), f12(f13(f14(c29))))),
% 0.22/0.39 inference(unit_resolution,[status(thm)],[39, 36])).
% 0.22/0.39 tff(41,plain,
% 0.22/0.39 (p5(f12(f13(f14(c29))), f12(f13(f14(c29))))),
% 0.22/0.39 inference(unit_resolution,[status(thm)],[40, 26])).
% 0.22/0.39 tff(42,plain,
% 0.22/0.39 (^[X47: $i, X48: $i] : refl(((~p5(X47, X48)) | p9(f11(X47), f11(X48))) <=> ((~p5(X47, X48)) | p9(f11(X47), f11(X48))))),
% 0.22/0.39 inference(bind,[status(th)],[])).
% 0.22/0.39 tff(43,plain,
% 0.22/0.39 (![X47: $i, X48: $i] : ((~p5(X47, X48)) | p9(f11(X47), f11(X48))) <=> ![X47: $i, X48: $i] : ((~p5(X47, X48)) | p9(f11(X47), f11(X48)))),
% 0.22/0.39 inference(quant_intro,[status(thm)],[42])).
% 0.22/0.39 tff(44,plain,
% 0.22/0.39 (![X47: $i, X48: $i] : ((~p5(X47, X48)) | p9(f11(X47), f11(X48))) <=> ![X47: $i, X48: $i] : ((~p5(X47, X48)) | p9(f11(X47), f11(X48)))),
% 0.22/0.39 inference(rewrite,[status(thm)],[])).
% 0.22/0.39 tff(45,plain,
% 0.22/0.39 (^[X47: $i, X48: $i] : rewrite((p9(f11(X47), f11(X48)) | (~p5(X47, X48))) <=> ((~p5(X47, X48)) | p9(f11(X47), f11(X48))))),
% 0.22/0.39 inference(bind,[status(th)],[])).
% 0.22/0.39 tff(46,plain,
% 0.22/0.39 (![X47: $i, X48: $i] : (p9(f11(X47), f11(X48)) | (~p5(X47, X48))) <=> ![X47: $i, X48: $i] : ((~p5(X47, X48)) | p9(f11(X47), f11(X48)))),
% 0.22/0.39 inference(quant_intro,[status(thm)],[45])).
% 0.22/0.39 tff(47,axiom,(![X47: $i, X48: $i] : (p9(f11(X47), f11(X48)) | (~p5(X47, X48)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p9_18')).
% 0.22/0.39 tff(48,plain,
% 0.22/0.39 (![X47: $i, X48: $i] : ((~p5(X47, X48)) | p9(f11(X47), f11(X48)))),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.22/0.39 tff(49,plain,
% 0.22/0.39 (![X47: $i, X48: $i] : ((~p5(X47, X48)) | p9(f11(X47), f11(X48)))),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.22/0.39 tff(50,plain,(
% 0.22/0.39 ![X47: $i, X48: $i] : ((~p5(X47, X48)) | p9(f11(X47), f11(X48)))),
% 0.22/0.39 inference(skolemize,[status(sab)],[49])).
% 0.22/0.39 tff(51,plain,
% 0.22/0.39 (![X47: $i, X48: $i] : ((~p5(X47, X48)) | p9(f11(X47), f11(X48)))),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.22/0.39 tff(52,plain,
% 0.22/0.39 (((~![X47: $i, X48: $i] : ((~p5(X47, X48)) | p9(f11(X47), f11(X48)))) | ((~p5(f12(f13(f14(c29))), f12(f13(f14(c29))))) | p9(f11(f12(f13(f14(c29)))), f11(f12(f13(f14(c29))))))) <=> ((~![X47: $i, X48: $i] : ((~p5(X47, X48)) | p9(f11(X47), f11(X48)))) | (~p5(f12(f13(f14(c29))), f12(f13(f14(c29))))) | p9(f11(f12(f13(f14(c29)))), f11(f12(f13(f14(c29))))))),
% 0.22/0.39 inference(rewrite,[status(thm)],[])).
% 0.22/0.39 tff(53,plain,
% 0.22/0.39 ((~![X47: $i, X48: $i] : ((~p5(X47, X48)) | p9(f11(X47), f11(X48)))) | ((~p5(f12(f13(f14(c29))), f12(f13(f14(c29))))) | p9(f11(f12(f13(f14(c29)))), f11(f12(f13(f14(c29))))))),
% 0.22/0.39 inference(quant_inst,[status(thm)],[])).
% 0.22/0.39 tff(54,plain,
% 0.22/0.39 ((~![X47: $i, X48: $i] : ((~p5(X47, X48)) | p9(f11(X47), f11(X48)))) | (~p5(f12(f13(f14(c29))), f12(f13(f14(c29))))) | p9(f11(f12(f13(f14(c29)))), f11(f12(f13(f14(c29)))))),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.22/0.39 tff(55,plain,
% 0.22/0.39 (p9(f11(f12(f13(f14(c29)))), f11(f12(f13(f14(c29)))))),
% 0.22/0.39 inference(unit_resolution,[status(thm)],[54, 51, 41])).
% 0.22/0.39 tff(56,assumption,(~p2(f7(c23, f8(c24, c25)), f7(c23, f8(c24, c25)))), introduced(assumption)).
% 0.22/0.39 tff(57,plain,
% 0.22/0.39 (^[X4: $i] : refl(p2(X4, X4) <=> p2(X4, X4))),
% 0.22/0.39 inference(bind,[status(th)],[])).
% 0.22/0.39 tff(58,plain,
% 0.22/0.39 (![X4: $i] : p2(X4, X4) <=> ![X4: $i] : p2(X4, X4)),
% 0.22/0.39 inference(quant_intro,[status(thm)],[57])).
% 0.22/0.39 tff(59,plain,
% 0.22/0.39 (![X4: $i] : p2(X4, X4) <=> ![X4: $i] : p2(X4, X4)),
% 0.22/0.39 inference(rewrite,[status(thm)],[])).
% 0.22/0.39 tff(60,axiom,(![X4: $i] : p2(X4, X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_1')).
% 0.22/0.39 tff(61,plain,
% 0.22/0.39 (![X4: $i] : p2(X4, X4)),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.22/0.39 tff(62,plain,(
% 0.22/0.39 ![X4: $i] : p2(X4, X4)),
% 0.22/0.39 inference(skolemize,[status(sab)],[61])).
% 0.22/0.39 tff(63,plain,
% 0.22/0.39 (![X4: $i] : p2(X4, X4)),
% 0.22/0.39 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.22/0.39 tff(64,plain,
% 0.22/0.39 ((~![X4: $i] : p2(X4, X4)) | p2(f7(c23, f8(c24, c25)), f7(c23, f8(c24, c25)))),
% 0.22/0.39 inference(quant_inst,[status(thm)],[])).
% 0.22/0.39 tff(65,plain,
% 0.22/0.39 ($false),
% 0.22/0.39 inference(unit_resolution,[status(thm)],[64, 63, 56])).
% 0.22/0.39 tff(66,plain,(p2(f7(c23, f8(c24, c25)), f7(c23, f8(c24, c25)))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.39 tff(67,plain,
% 0.22/0.39 (^[X49: $i, X52: $i, X51: $i, X50: $i] : refl(((~p9(X50, X52)) | (~p2(X49, X51)) | p9(f15(X49, X50), f15(X51, X52))) <=> ((~p9(X50, X52)) | (~p2(X49, X51)) | p9(f15(X49, X50), f15(X51, X52))))),
% 0.22/0.39 inference(bind,[status(th)],[])).
% 0.22/0.39 tff(68,plain,
% 0.22/0.39 (![X49: $i, X52: $i, X51: $i, X50: $i] : ((~p9(X50, X52)) | (~p2(X49, X51)) | p9(f15(X49, X50), f15(X51, X52))) <=> ![X49: $i, X52: $i, X51: $i, X50: $i] : ((~p9(X50, X52)) | (~p2(X49, X51)) | p9(f15(X49, X50), f15(X51, X52)))),
% 0.22/0.39 inference(quant_intro,[status(thm)],[67])).
% 0.22/0.39 tff(69,plain,
% 0.22/0.39 (![X49: $i, X52: $i, X51: $i, X50: $i] : ((~p9(X50, X52)) | (~p2(X49, X51)) | p9(f15(X49, X50), f15(X51, X52))) <=> ![X49: $i, X52: $i, X51: $i, X50: $i] : ((~p9(X50, X52)) | (~p2(X49, X51)) | p9(f15(X49, X50), f15(X51, X52)))),
% 0.22/0.39 inference(rewrite,[status(thm)],[])).
% 0.22/0.39 tff(70,plain,
% 0.22/0.39 (^[X49: $i, X52: $i, X51: $i, X50: $i] : trans(monotonicity(rewrite((p9(f15(X49, X50), f15(X51, X52)) | (~p2(X49, X51))) <=> ((~p2(X49, X51)) | p9(f15(X49, X50), f15(X51, X52)))), (((p9(f15(X49, X50), f15(X51, X52)) | (~p2(X49, X51))) | (~p9(X50, X52))) <=> (((~p2(X49, X51)) | p9(f15(X49, X50), f15(X51, X52))) | (~p9(X50, X52))))), rewrite((((~p2(X49, X51)) | p9(f15(X49, X50), f15(X51, X52))) | (~p9(X50, X52))) <=> ((~p9(X50, X52)) | (~p2(X49, X51)) | p9(f15(X49, X50), f15(X51, X52)))), (((p9(f15(X49, X50), f15(X51, X52)) | (~p2(X49, X51))) | (~p9(X50, X52))) <=> ((~p9(X50, X52)) | (~p2(X49, X51)) | p9(f15(X49, X50), f15(X51, X52)))))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(71,plain,
% 0.22/0.40 (![X49: $i, X52: $i, X51: $i, X50: $i] : ((p9(f15(X49, X50), f15(X51, X52)) | (~p2(X49, X51))) | (~p9(X50, X52))) <=> ![X49: $i, X52: $i, X51: $i, X50: $i] : ((~p9(X50, X52)) | (~p2(X49, X51)) | p9(f15(X49, X50), f15(X51, X52)))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[70])).
% 0.22/0.40 tff(72,axiom,(![X49: $i, X52: $i, X51: $i, X50: $i] : ((p9(f15(X49, X50), f15(X51, X52)) | (~p2(X49, X51))) | (~p9(X50, X52)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p9_30')).
% 0.22/0.40 tff(73,plain,
% 0.22/0.40 (![X49: $i, X52: $i, X51: $i, X50: $i] : ((~p9(X50, X52)) | (~p2(X49, X51)) | p9(f15(X49, X50), f15(X51, X52)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.22/0.40 tff(74,plain,
% 0.22/0.40 (![X49: $i, X52: $i, X51: $i, X50: $i] : ((~p9(X50, X52)) | (~p2(X49, X51)) | p9(f15(X49, X50), f15(X51, X52)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.22/0.40 tff(75,plain,(
% 0.22/0.40 ![X49: $i, X52: $i, X51: $i, X50: $i] : ((~p9(X50, X52)) | (~p2(X49, X51)) | p9(f15(X49, X50), f15(X51, X52)))),
% 0.22/0.40 inference(skolemize,[status(sab)],[74])).
% 0.22/0.40 tff(76,plain,
% 0.22/0.40 (![X49: $i, X52: $i, X51: $i, X50: $i] : ((~p9(X50, X52)) | (~p2(X49, X51)) | p9(f15(X49, X50), f15(X51, X52)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[75, 68])).
% 0.22/0.40 tff(77,plain,
% 0.22/0.40 (p9(c28, c22) <=> p9(c28, c22)),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(78,axiom,(p9(c28, c22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p9_6')).
% 0.22/0.40 tff(79,plain,
% 0.22/0.40 (p9(c28, c22)),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.22/0.40 tff(80,plain,
% 0.22/0.40 (((~![X49: $i, X52: $i, X51: $i, X50: $i] : ((~p9(X50, X52)) | (~p2(X49, X51)) | p9(f15(X49, X50), f15(X51, X52)))) | ((~p9(c28, c22)) | (~p2(f7(c23, f8(c24, c25)), f7(c23, f8(c24, c25)))) | p9(f15(f7(c23, f8(c24, c25)), c28), f15(f7(c23, f8(c24, c25)), c22)))) <=> ((~![X49: $i, X52: $i, X51: $i, X50: $i] : ((~p9(X50, X52)) | (~p2(X49, X51)) | p9(f15(X49, X50), f15(X51, X52)))) | (~p9(c28, c22)) | (~p2(f7(c23, f8(c24, c25)), f7(c23, f8(c24, c25)))) | p9(f15(f7(c23, f8(c24, c25)), c28), f15(f7(c23, f8(c24, c25)), c22)))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(81,plain,
% 0.22/0.40 ((~![X49: $i, X52: $i, X51: $i, X50: $i] : ((~p9(X50, X52)) | (~p2(X49, X51)) | p9(f15(X49, X50), f15(X51, X52)))) | ((~p9(c28, c22)) | (~p2(f7(c23, f8(c24, c25)), f7(c23, f8(c24, c25)))) | p9(f15(f7(c23, f8(c24, c25)), c28), f15(f7(c23, f8(c24, c25)), c22)))),
% 0.22/0.40 inference(quant_inst,[status(thm)],[])).
% 0.22/0.40 tff(82,plain,
% 0.22/0.40 ((~![X49: $i, X52: $i, X51: $i, X50: $i] : ((~p9(X50, X52)) | (~p2(X49, X51)) | p9(f15(X49, X50), f15(X51, X52)))) | (~p9(c28, c22)) | (~p2(f7(c23, f8(c24, c25)), f7(c23, f8(c24, c25)))) | p9(f15(f7(c23, f8(c24, c25)), c28), f15(f7(c23, f8(c24, c25)), c22))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.22/0.40 tff(83,plain,
% 0.22/0.40 ((~p2(f7(c23, f8(c24, c25)), f7(c23, f8(c24, c25)))) | p9(f15(f7(c23, f8(c24, c25)), c28), f15(f7(c23, f8(c24, c25)), c22))),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[82, 79, 76])).
% 0.22/0.40 tff(84,plain,
% 0.22/0.40 (p9(f15(f7(c23, f8(c24, c25)), c28), f15(f7(c23, f8(c24, c25)), c22))),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[83, 66])).
% 0.22/0.40 tff(85,plain,
% 0.22/0.40 (^[X43: $i, X45: $i, X46: $i, X44: $i] : refl(((~p9(X44, X46)) | (~p9(X43, X45)) | p9(f10(X43, X44), f10(X45, X46))) <=> ((~p9(X44, X46)) | (~p9(X43, X45)) | p9(f10(X43, X44), f10(X45, X46))))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(86,plain,
% 0.22/0.40 (![X43: $i, X45: $i, X46: $i, X44: $i] : ((~p9(X44, X46)) | (~p9(X43, X45)) | p9(f10(X43, X44), f10(X45, X46))) <=> ![X43: $i, X45: $i, X46: $i, X44: $i] : ((~p9(X44, X46)) | (~p9(X43, X45)) | p9(f10(X43, X44), f10(X45, X46)))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[85])).
% 0.22/0.40 tff(87,plain,
% 0.22/0.40 (![X43: $i, X45: $i, X46: $i, X44: $i] : ((~p9(X44, X46)) | (~p9(X43, X45)) | p9(f10(X43, X44), f10(X45, X46))) <=> ![X43: $i, X45: $i, X46: $i, X44: $i] : ((~p9(X44, X46)) | (~p9(X43, X45)) | p9(f10(X43, X44), f10(X45, X46)))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(88,plain,
% 0.22/0.40 (^[X43: $i, X45: $i, X46: $i, X44: $i] : trans(monotonicity(rewrite((p9(f10(X43, X44), f10(X45, X46)) | (~p9(X43, X45))) <=> ((~p9(X43, X45)) | p9(f10(X43, X44), f10(X45, X46)))), (((p9(f10(X43, X44), f10(X45, X46)) | (~p9(X43, X45))) | (~p9(X44, X46))) <=> (((~p9(X43, X45)) | p9(f10(X43, X44), f10(X45, X46))) | (~p9(X44, X46))))), rewrite((((~p9(X43, X45)) | p9(f10(X43, X44), f10(X45, X46))) | (~p9(X44, X46))) <=> ((~p9(X44, X46)) | (~p9(X43, X45)) | p9(f10(X43, X44), f10(X45, X46)))), (((p9(f10(X43, X44), f10(X45, X46)) | (~p9(X43, X45))) | (~p9(X44, X46))) <=> ((~p9(X44, X46)) | (~p9(X43, X45)) | p9(f10(X43, X44), f10(X45, X46)))))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(89,plain,
% 0.22/0.40 (![X43: $i, X45: $i, X46: $i, X44: $i] : ((p9(f10(X43, X44), f10(X45, X46)) | (~p9(X43, X45))) | (~p9(X44, X46))) <=> ![X43: $i, X45: $i, X46: $i, X44: $i] : ((~p9(X44, X46)) | (~p9(X43, X45)) | p9(f10(X43, X44), f10(X45, X46)))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[88])).
% 0.22/0.40 tff(90,axiom,(![X43: $i, X45: $i, X46: $i, X44: $i] : ((p9(f10(X43, X44), f10(X45, X46)) | (~p9(X43, X45))) | (~p9(X44, X46)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p9_31')).
% 0.22/0.40 tff(91,plain,
% 0.22/0.40 (![X43: $i, X45: $i, X46: $i, X44: $i] : ((~p9(X44, X46)) | (~p9(X43, X45)) | p9(f10(X43, X44), f10(X45, X46)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.22/0.40 tff(92,plain,
% 0.22/0.40 (![X43: $i, X45: $i, X46: $i, X44: $i] : ((~p9(X44, X46)) | (~p9(X43, X45)) | p9(f10(X43, X44), f10(X45, X46)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[91, 87])).
% 0.22/0.40 tff(93,plain,(
% 0.22/0.40 ![X43: $i, X45: $i, X46: $i, X44: $i] : ((~p9(X44, X46)) | (~p9(X43, X45)) | p9(f10(X43, X44), f10(X45, X46)))),
% 0.22/0.40 inference(skolemize,[status(sab)],[92])).
% 0.22/0.40 tff(94,plain,
% 0.22/0.40 (![X43: $i, X45: $i, X46: $i, X44: $i] : ((~p9(X44, X46)) | (~p9(X43, X45)) | p9(f10(X43, X44), f10(X45, X46)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[93, 86])).
% 0.22/0.40 tff(95,plain,
% 0.22/0.40 (((~![X43: $i, X45: $i, X46: $i, X44: $i] : ((~p9(X44, X46)) | (~p9(X43, X45)) | p9(f10(X43, X44), f10(X45, X46)))) | ((~p9(f11(f12(f13(f14(c29)))), f11(f12(f13(f14(c29)))))) | (~p9(f15(f7(c23, f8(c24, c25)), c28), f15(f7(c23, f8(c24, c25)), c22))) | p9(f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29))))), f10(f15(f7(c23, f8(c24, c25)), c22), f11(f12(f13(f14(c29)))))))) <=> ((~![X43: $i, X45: $i, X46: $i, X44: $i] : ((~p9(X44, X46)) | (~p9(X43, X45)) | p9(f10(X43, X44), f10(X45, X46)))) | (~p9(f11(f12(f13(f14(c29)))), f11(f12(f13(f14(c29)))))) | (~p9(f15(f7(c23, f8(c24, c25)), c28), f15(f7(c23, f8(c24, c25)), c22))) | p9(f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29))))), f10(f15(f7(c23, f8(c24, c25)), c22), f11(f12(f13(f14(c29)))))))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(96,plain,
% 0.22/0.40 ((~![X43: $i, X45: $i, X46: $i, X44: $i] : ((~p9(X44, X46)) | (~p9(X43, X45)) | p9(f10(X43, X44), f10(X45, X46)))) | ((~p9(f11(f12(f13(f14(c29)))), f11(f12(f13(f14(c29)))))) | (~p9(f15(f7(c23, f8(c24, c25)), c28), f15(f7(c23, f8(c24, c25)), c22))) | p9(f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29))))), f10(f15(f7(c23, f8(c24, c25)), c22), f11(f12(f13(f14(c29)))))))),
% 0.22/0.40 inference(quant_inst,[status(thm)],[])).
% 0.22/0.40 tff(97,plain,
% 0.22/0.40 ((~![X43: $i, X45: $i, X46: $i, X44: $i] : ((~p9(X44, X46)) | (~p9(X43, X45)) | p9(f10(X43, X44), f10(X45, X46)))) | (~p9(f11(f12(f13(f14(c29)))), f11(f12(f13(f14(c29)))))) | (~p9(f15(f7(c23, f8(c24, c25)), c28), f15(f7(c23, f8(c24, c25)), c22))) | p9(f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29))))), f10(f15(f7(c23, f8(c24, c25)), c22), f11(f12(f13(f14(c29))))))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.22/0.40 tff(98,plain,
% 0.22/0.40 ((~p9(f11(f12(f13(f14(c29)))), f11(f12(f13(f14(c29)))))) | (~p9(f15(f7(c23, f8(c24, c25)), c28), f15(f7(c23, f8(c24, c25)), c22))) | p9(f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29))))), f10(f15(f7(c23, f8(c24, c25)), c22), f11(f12(f13(f14(c29))))))),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[97, 94])).
% 0.22/0.40 tff(99,plain,
% 0.22/0.40 (p9(f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29))))), f10(f15(f7(c23, f8(c24, c25)), c22), f11(f12(f13(f14(c29))))))),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[98, 84, 55])).
% 0.22/0.40 tff(100,assumption,(~p9(c27, c27)), introduced(assumption)).
% 0.22/0.40 tff(101,plain,
% 0.22/0.40 (^[X40: $i] : refl(p9(X40, X40) <=> p9(X40, X40))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(102,plain,
% 0.22/0.40 (![X40: $i] : p9(X40, X40) <=> ![X40: $i] : p9(X40, X40)),
% 0.22/0.40 inference(quant_intro,[status(thm)],[101])).
% 0.22/0.40 tff(103,plain,
% 0.22/0.40 (![X40: $i] : p9(X40, X40) <=> ![X40: $i] : p9(X40, X40)),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(104,axiom,(![X40: $i] : p9(X40, X40)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p9_2')).
% 0.22/0.40 tff(105,plain,
% 0.22/0.40 (![X40: $i] : p9(X40, X40)),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.22/0.40 tff(106,plain,(
% 0.22/0.40 ![X40: $i] : p9(X40, X40)),
% 0.22/0.40 inference(skolemize,[status(sab)],[105])).
% 0.22/0.40 tff(107,plain,
% 0.22/0.40 (![X40: $i] : p9(X40, X40)),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[106, 102])).
% 0.22/0.40 tff(108,plain,
% 0.22/0.40 ((~![X40: $i] : p9(X40, X40)) | p9(c27, c27)),
% 0.22/0.40 inference(quant_inst,[status(thm)],[])).
% 0.22/0.40 tff(109,plain,
% 0.22/0.40 ($false),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[108, 107, 100])).
% 0.22/0.40 tff(110,plain,(p9(c27, c27)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.40 tff(111,plain,
% 0.22/0.40 (^[X57: $i, X56: $i, X55: $i, X58: $i] : refl(((~p9(X55, X57)) | (~p9(X56, X58)) | p9(f17(X55, X56), f17(X57, X58))) <=> ((~p9(X55, X57)) | (~p9(X56, X58)) | p9(f17(X55, X56), f17(X57, X58))))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(112,plain,
% 0.22/0.40 (![X57: $i, X56: $i, X55: $i, X58: $i] : ((~p9(X55, X57)) | (~p9(X56, X58)) | p9(f17(X55, X56), f17(X57, X58))) <=> ![X57: $i, X56: $i, X55: $i, X58: $i] : ((~p9(X55, X57)) | (~p9(X56, X58)) | p9(f17(X55, X56), f17(X57, X58)))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[111])).
% 0.22/0.40 tff(113,plain,
% 0.22/0.40 (![X57: $i, X56: $i, X55: $i, X58: $i] : ((~p9(X55, X57)) | (~p9(X56, X58)) | p9(f17(X55, X56), f17(X57, X58))) <=> ![X57: $i, X56: $i, X55: $i, X58: $i] : ((~p9(X55, X57)) | (~p9(X56, X58)) | p9(f17(X55, X56), f17(X57, X58)))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(114,plain,
% 0.22/0.40 (^[X57: $i, X56: $i, X55: $i, X58: $i] : trans(monotonicity(rewrite((p9(f17(X55, X56), f17(X57, X58)) | (~p9(X55, X57))) <=> ((~p9(X55, X57)) | p9(f17(X55, X56), f17(X57, X58)))), (((p9(f17(X55, X56), f17(X57, X58)) | (~p9(X55, X57))) | (~p9(X56, X58))) <=> (((~p9(X55, X57)) | p9(f17(X55, X56), f17(X57, X58))) | (~p9(X56, X58))))), rewrite((((~p9(X55, X57)) | p9(f17(X55, X56), f17(X57, X58))) | (~p9(X56, X58))) <=> ((~p9(X55, X57)) | (~p9(X56, X58)) | p9(f17(X55, X56), f17(X57, X58)))), (((p9(f17(X55, X56), f17(X57, X58)) | (~p9(X55, X57))) | (~p9(X56, X58))) <=> ((~p9(X55, X57)) | (~p9(X56, X58)) | p9(f17(X55, X56), f17(X57, X58)))))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(115,plain,
% 0.22/0.40 (![X57: $i, X56: $i, X55: $i, X58: $i] : ((p9(f17(X55, X56), f17(X57, X58)) | (~p9(X55, X57))) | (~p9(X56, X58))) <=> ![X57: $i, X56: $i, X55: $i, X58: $i] : ((~p9(X55, X57)) | (~p9(X56, X58)) | p9(f17(X55, X56), f17(X57, X58)))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[114])).
% 0.22/0.40 tff(116,axiom,(![X57: $i, X56: $i, X55: $i, X58: $i] : ((p9(f17(X55, X56), f17(X57, X58)) | (~p9(X55, X57))) | (~p9(X56, X58)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p9_29')).
% 0.22/0.40 tff(117,plain,
% 0.22/0.40 (![X57: $i, X56: $i, X55: $i, X58: $i] : ((~p9(X55, X57)) | (~p9(X56, X58)) | p9(f17(X55, X56), f17(X57, X58)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.22/0.40 tff(118,plain,
% 0.22/0.40 (![X57: $i, X56: $i, X55: $i, X58: $i] : ((~p9(X55, X57)) | (~p9(X56, X58)) | p9(f17(X55, X56), f17(X57, X58)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[117, 113])).
% 0.22/0.40 tff(119,plain,(
% 0.22/0.40 ![X57: $i, X56: $i, X55: $i, X58: $i] : ((~p9(X55, X57)) | (~p9(X56, X58)) | p9(f17(X55, X56), f17(X57, X58)))),
% 0.22/0.41 inference(skolemize,[status(sab)],[118])).
% 0.22/0.41 tff(120,plain,
% 0.22/0.41 (![X57: $i, X56: $i, X55: $i, X58: $i] : ((~p9(X55, X57)) | (~p9(X56, X58)) | p9(f17(X55, X56), f17(X57, X58)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[119, 112])).
% 0.22/0.41 tff(121,plain,
% 0.22/0.41 (((~![X57: $i, X56: $i, X55: $i, X58: $i] : ((~p9(X55, X57)) | (~p9(X56, X58)) | p9(f17(X55, X56), f17(X57, X58)))) | ((~p9(c28, c22)) | p9(f17(c28, c27), f17(c22, c27)) | (~p9(c27, c27)))) <=> ((~![X57: $i, X56: $i, X55: $i, X58: $i] : ((~p9(X55, X57)) | (~p9(X56, X58)) | p9(f17(X55, X56), f17(X57, X58)))) | (~p9(c28, c22)) | p9(f17(c28, c27), f17(c22, c27)) | (~p9(c27, c27)))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(122,plain,
% 0.22/0.41 (((~p9(c28, c22)) | (~p9(c27, c27)) | p9(f17(c28, c27), f17(c22, c27))) <=> ((~p9(c28, c22)) | p9(f17(c28, c27), f17(c22, c27)) | (~p9(c27, c27)))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(123,plain,
% 0.22/0.41 (((~![X57: $i, X56: $i, X55: $i, X58: $i] : ((~p9(X55, X57)) | (~p9(X56, X58)) | p9(f17(X55, X56), f17(X57, X58)))) | ((~p9(c28, c22)) | (~p9(c27, c27)) | p9(f17(c28, c27), f17(c22, c27)))) <=> ((~![X57: $i, X56: $i, X55: $i, X58: $i] : ((~p9(X55, X57)) | (~p9(X56, X58)) | p9(f17(X55, X56), f17(X57, X58)))) | ((~p9(c28, c22)) | p9(f17(c28, c27), f17(c22, c27)) | (~p9(c27, c27))))),
% 0.22/0.41 inference(monotonicity,[status(thm)],[122])).
% 0.22/0.41 tff(124,plain,
% 0.22/0.41 (((~![X57: $i, X56: $i, X55: $i, X58: $i] : ((~p9(X55, X57)) | (~p9(X56, X58)) | p9(f17(X55, X56), f17(X57, X58)))) | ((~p9(c28, c22)) | (~p9(c27, c27)) | p9(f17(c28, c27), f17(c22, c27)))) <=> ((~![X57: $i, X56: $i, X55: $i, X58: $i] : ((~p9(X55, X57)) | (~p9(X56, X58)) | p9(f17(X55, X56), f17(X57, X58)))) | (~p9(c28, c22)) | p9(f17(c28, c27), f17(c22, c27)) | (~p9(c27, c27)))),
% 0.22/0.41 inference(transitivity,[status(thm)],[123, 121])).
% 0.22/0.41 tff(125,plain,
% 0.22/0.41 ((~![X57: $i, X56: $i, X55: $i, X58: $i] : ((~p9(X55, X57)) | (~p9(X56, X58)) | p9(f17(X55, X56), f17(X57, X58)))) | ((~p9(c28, c22)) | (~p9(c27, c27)) | p9(f17(c28, c27), f17(c22, c27)))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(126,plain,
% 0.22/0.41 ((~![X57: $i, X56: $i, X55: $i, X58: $i] : ((~p9(X55, X57)) | (~p9(X56, X58)) | p9(f17(X55, X56), f17(X57, X58)))) | (~p9(c28, c22)) | p9(f17(c28, c27), f17(c22, c27)) | (~p9(c27, c27))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.22/0.41 tff(127,plain,
% 0.22/0.41 (p9(f17(c28, c27), f17(c22, c27)) | (~p9(c27, c27))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[126, 79, 120])).
% 0.22/0.41 tff(128,plain,
% 0.22/0.41 (p9(f17(c28, c27), f17(c22, c27))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[127, 110])).
% 0.22/0.41 tff(129,plain,
% 0.22/0.41 (^[X53: $i, X54: $i] : refl(((~p9(X53, X54)) | p9(f16(X53), f16(X54))) <=> ((~p9(X53, X54)) | p9(f16(X53), f16(X54))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(130,plain,
% 0.22/0.41 (![X53: $i, X54: $i] : ((~p9(X53, X54)) | p9(f16(X53), f16(X54))) <=> ![X53: $i, X54: $i] : ((~p9(X53, X54)) | p9(f16(X53), f16(X54)))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[129])).
% 0.22/0.41 tff(131,plain,
% 0.22/0.41 (![X53: $i, X54: $i] : ((~p9(X53, X54)) | p9(f16(X53), f16(X54))) <=> ![X53: $i, X54: $i] : ((~p9(X53, X54)) | p9(f16(X53), f16(X54)))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(132,plain,
% 0.22/0.41 (^[X53: $i, X54: $i] : rewrite((p9(f16(X53), f16(X54)) | (~p9(X53, X54))) <=> ((~p9(X53, X54)) | p9(f16(X53), f16(X54))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(133,plain,
% 0.22/0.41 (![X53: $i, X54: $i] : (p9(f16(X53), f16(X54)) | (~p9(X53, X54))) <=> ![X53: $i, X54: $i] : ((~p9(X53, X54)) | p9(f16(X53), f16(X54)))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[132])).
% 0.22/0.41 tff(134,axiom,(![X53: $i, X54: $i] : (p9(f16(X53), f16(X54)) | (~p9(X53, X54)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p9_13')).
% 0.22/0.41 tff(135,plain,
% 0.22/0.41 (![X53: $i, X54: $i] : ((~p9(X53, X54)) | p9(f16(X53), f16(X54)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.22/0.41 tff(136,plain,
% 0.22/0.41 (![X53: $i, X54: $i] : ((~p9(X53, X54)) | p9(f16(X53), f16(X54)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[135, 131])).
% 0.22/0.41 tff(137,plain,(
% 0.22/0.41 ![X53: $i, X54: $i] : ((~p9(X53, X54)) | p9(f16(X53), f16(X54)))),
% 0.22/0.41 inference(skolemize,[status(sab)],[136])).
% 0.22/0.41 tff(138,plain,
% 0.22/0.41 (![X53: $i, X54: $i] : ((~p9(X53, X54)) | p9(f16(X53), f16(X54)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[137, 130])).
% 0.22/0.41 tff(139,plain,
% 0.22/0.41 (((~![X53: $i, X54: $i] : ((~p9(X53, X54)) | p9(f16(X53), f16(X54)))) | ((~p9(f17(c28, c27), f17(c22, c27))) | p9(f16(f17(c28, c27)), f16(f17(c22, c27))))) <=> ((~![X53: $i, X54: $i] : ((~p9(X53, X54)) | p9(f16(X53), f16(X54)))) | (~p9(f17(c28, c27), f17(c22, c27))) | p9(f16(f17(c28, c27)), f16(f17(c22, c27))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(140,plain,
% 0.22/0.41 ((~![X53: $i, X54: $i] : ((~p9(X53, X54)) | p9(f16(X53), f16(X54)))) | ((~p9(f17(c28, c27), f17(c22, c27))) | p9(f16(f17(c28, c27)), f16(f17(c22, c27))))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(141,plain,
% 0.22/0.41 ((~![X53: $i, X54: $i] : ((~p9(X53, X54)) | p9(f16(X53), f16(X54)))) | (~p9(f17(c28, c27), f17(c22, c27))) | p9(f16(f17(c28, c27)), f16(f17(c22, c27)))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.22/0.41 tff(142,plain,
% 0.22/0.41 ((~p9(f17(c28, c27), f17(c22, c27))) | p9(f16(f17(c28, c27)), f16(f17(c22, c27)))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[141, 138])).
% 0.22/0.41 tff(143,plain,
% 0.22/0.41 (p9(f16(f17(c28, c27)), f16(f17(c22, c27)))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[142, 128])).
% 0.22/0.41 tff(144,plain,
% 0.22/0.41 ((~p20(f16(f17(c22, c27)), f10(f15(f7(c23, f8(c24, c25)), c22), f11(f12(f13(f14(c29))))))) <=> (~p20(f16(f17(c22, c27)), f10(f15(f7(c23, f8(c24, c25)), c22), f11(f12(f13(f14(c29)))))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(145,axiom,(~p20(f16(f17(c22, c27)), f10(f15(f7(c23, f8(c24, c25)), c22), f11(f12(f13(f14(c29))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_p20_35')).
% 0.22/0.41 tff(146,plain,
% 0.22/0.41 (~p20(f16(f17(c22, c27)), f10(f15(f7(c23, f8(c24, c25)), c22), f11(f12(f13(f14(c29))))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.22/0.41 tff(147,plain,
% 0.22/0.41 (p20(f16(f17(c28, c27)), f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29)))))) <=> p20(f16(f17(c28, c27)), f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29))))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(148,axiom,(p20(f16(f17(c28, c27)), f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p20_34')).
% 0.22/0.41 tff(149,plain,
% 0.22/0.41 (p20(f16(f17(c28, c27)), f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29))))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.22/0.41 tff(150,plain,
% 0.22/0.41 (^[X14: $i, X12: $i, X11: $i, X13: $i] : refl(((~p9(X13, X11)) | (~p20(X13, X14)) | (~p9(X14, X12)) | p20(X11, X12)) <=> ((~p9(X13, X11)) | (~p20(X13, X14)) | (~p9(X14, X12)) | p20(X11, X12)))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(151,plain,
% 0.22/0.41 (![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p9(X13, X11)) | (~p20(X13, X14)) | (~p9(X14, X12)) | p20(X11, X12)) <=> ![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p9(X13, X11)) | (~p20(X13, X14)) | (~p9(X14, X12)) | p20(X11, X12))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[150])).
% 0.22/0.41 tff(152,plain,
% 0.22/0.41 (![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p9(X13, X11)) | (~p20(X13, X14)) | (~p9(X14, X12)) | p20(X11, X12)) <=> ![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p9(X13, X11)) | (~p20(X13, X14)) | (~p9(X14, X12)) | p20(X11, X12))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(153,plain,
% 0.22/0.41 (^[X14: $i, X12: $i, X11: $i, X13: $i] : trans(monotonicity(trans(monotonicity(rewrite((p20(X11, X12) | (~p9(X13, X11))) <=> ((~p9(X13, X11)) | p20(X11, X12))), (((p20(X11, X12) | (~p9(X13, X11))) | (~p9(X14, X12))) <=> (((~p9(X13, X11)) | p20(X11, X12)) | (~p9(X14, X12))))), rewrite((((~p9(X13, X11)) | p20(X11, X12)) | (~p9(X14, X12))) <=> ((~p9(X13, X11)) | (~p9(X14, X12)) | p20(X11, X12))), (((p20(X11, X12) | (~p9(X13, X11))) | (~p9(X14, X12))) <=> ((~p9(X13, X11)) | (~p9(X14, X12)) | p20(X11, X12)))), ((((p20(X11, X12) | (~p9(X13, X11))) | (~p9(X14, X12))) | (~p20(X13, X14))) <=> (((~p9(X13, X11)) | (~p9(X14, X12)) | p20(X11, X12)) | (~p20(X13, X14))))), rewrite((((~p9(X13, X11)) | (~p9(X14, X12)) | p20(X11, X12)) | (~p20(X13, X14))) <=> ((~p9(X13, X11)) | (~p20(X13, X14)) | (~p9(X14, X12)) | p20(X11, X12))), ((((p20(X11, X12) | (~p9(X13, X11))) | (~p9(X14, X12))) | (~p20(X13, X14))) <=> ((~p9(X13, X11)) | (~p20(X13, X14)) | (~p9(X14, X12)) | p20(X11, X12))))),
% 0.22/0.41 inference(bind,[status(th)],[])).
% 0.22/0.41 tff(154,plain,
% 0.22/0.41 (![X14: $i, X12: $i, X11: $i, X13: $i] : (((p20(X11, X12) | (~p9(X13, X11))) | (~p9(X14, X12))) | (~p20(X13, X14))) <=> ![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p9(X13, X11)) | (~p20(X13, X14)) | (~p9(X14, X12)) | p20(X11, X12))),
% 0.22/0.41 inference(quant_intro,[status(thm)],[153])).
% 0.22/0.41 tff(155,axiom,(![X14: $i, X12: $i, X11: $i, X13: $i] : (((p20(X11, X12) | (~p9(X13, X11))) | (~p9(X14, X12))) | (~p20(X13, X14)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p20_26')).
% 0.22/0.41 tff(156,plain,
% 0.22/0.41 (![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p9(X13, X11)) | (~p20(X13, X14)) | (~p9(X14, X12)) | p20(X11, X12))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.22/0.41 tff(157,plain,
% 0.22/0.41 (![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p9(X13, X11)) | (~p20(X13, X14)) | (~p9(X14, X12)) | p20(X11, X12))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[156, 152])).
% 0.22/0.41 tff(158,plain,(
% 0.22/0.41 ![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p9(X13, X11)) | (~p20(X13, X14)) | (~p9(X14, X12)) | p20(X11, X12))),
% 0.22/0.41 inference(skolemize,[status(sab)],[157])).
% 0.22/0.41 tff(159,plain,
% 0.22/0.41 (![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p9(X13, X11)) | (~p20(X13, X14)) | (~p9(X14, X12)) | p20(X11, X12))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[158, 151])).
% 0.22/0.41 tff(160,plain,
% 0.22/0.41 (((~![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p9(X13, X11)) | (~p20(X13, X14)) | (~p9(X14, X12)) | p20(X11, X12))) | ((~p9(f16(f17(c28, c27)), f16(f17(c22, c27)))) | (~p20(f16(f17(c28, c27)), f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29))))))) | (~p9(f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29))))), f10(f15(f7(c23, f8(c24, c25)), c22), f11(f12(f13(f14(c29))))))) | p20(f16(f17(c22, c27)), f10(f15(f7(c23, f8(c24, c25)), c22), f11(f12(f13(f14(c29)))))))) <=> ((~![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p9(X13, X11)) | (~p20(X13, X14)) | (~p9(X14, X12)) | p20(X11, X12))) | (~p9(f16(f17(c28, c27)), f16(f17(c22, c27)))) | (~p20(f16(f17(c28, c27)), f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29))))))) | (~p9(f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29))))), f10(f15(f7(c23, f8(c24, c25)), c22), f11(f12(f13(f14(c29))))))) | p20(f16(f17(c22, c27)), f10(f15(f7(c23, f8(c24, c25)), c22), f11(f12(f13(f14(c29)))))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(161,plain,
% 0.22/0.41 ((~![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p9(X13, X11)) | (~p20(X13, X14)) | (~p9(X14, X12)) | p20(X11, X12))) | ((~p9(f16(f17(c28, c27)), f16(f17(c22, c27)))) | (~p20(f16(f17(c28, c27)), f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29))))))) | (~p9(f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29))))), f10(f15(f7(c23, f8(c24, c25)), c22), f11(f12(f13(f14(c29))))))) | p20(f16(f17(c22, c27)), f10(f15(f7(c23, f8(c24, c25)), c22), f11(f12(f13(f14(c29)))))))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(162,plain,
% 0.22/0.41 ((~![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p9(X13, X11)) | (~p20(X13, X14)) | (~p9(X14, X12)) | p20(X11, X12))) | (~p9(f16(f17(c28, c27)), f16(f17(c22, c27)))) | (~p20(f16(f17(c28, c27)), f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29))))))) | (~p9(f10(f15(f7(c23, f8(c24, c25)), c28), f11(f12(f13(f14(c29))))), f10(f15(f7(c23, f8(c24, c25)), c22), f11(f12(f13(f14(c29))))))) | p20(f16(f17(c22, c27)), f10(f15(f7(c23, f8(c24, c25)), c22), f11(f12(f13(f14(c29))))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.22/0.41 tff(163,plain,
% 0.22/0.41 ($false),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[162, 159, 149, 146, 143, 99])).
% 0.22/0.41 % SZS output end Proof
% 0.22/0.42 % E exiting
%------------------------------------------------------------------------------