%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN713-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:39:53 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.45s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN713-1 : TPTP v9.0.0. Released v2.5.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:45:05 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.21/0.45 % SZS status Unsatisfiable
% 0.21/0.45 % SZS output start Proof
% 0.21/0.45 tff(p4_type, type, (
% 0.21/0.45 p4: ( $i * $i ) > $o)).
% 0.21/0.45 tff(f11_type, type, (
% 0.21/0.45 f11: ( $i * $i ) > $i)).
% 0.21/0.45 tff(f14_type, type, (
% 0.21/0.45 f14: ( $i * $i ) > $i)).
% 0.21/0.45 tff(f23_type, type, (
% 0.21/0.45 f23: ( $i * $i ) > $i)).
% 0.21/0.45 tff(c77_type, type, (
% 0.21/0.45 c77: $i)).
% 0.21/0.45 tff(c74_type, type, (
% 0.21/0.45 c74: $i)).
% 0.21/0.45 tff(f17_type, type, (
% 0.21/0.45 f17: ( $i * $i ) > $i)).
% 0.21/0.45 tff(c67_type, type, (
% 0.21/0.45 c67: $i)).
% 0.21/0.45 tff(c66_type, type, (
% 0.21/0.45 c66: $i)).
% 0.21/0.45 tff(c65_type, type, (
% 0.21/0.45 c65: $i)).
% 0.21/0.45 tff(c68_type, type, (
% 0.21/0.45 c68: $i)).
% 0.21/0.45 tff(p9_type, type, (
% 0.21/0.45 p9: ( $i * $i ) > $o)).
% 0.21/0.45 tff(p10_type, type, (
% 0.21/0.45 p10: ( $i * $i ) > $o)).
% 0.21/0.45 tff(p12_type, type, (
% 0.21/0.45 p12: ( $i * $i ) > $o)).
% 0.21/0.45 tff(p13_type, type, (
% 0.21/0.45 p13: ( $i * $i ) > $o)).
% 0.21/0.45 tff(p58_type, type, (
% 0.21/0.45 p58: ( $i * $i ) > $o)).
% 0.21/0.45 tff(f19_type, type, (
% 0.21/0.45 f19: ( $i * $i ) > $i)).
% 0.21/0.45 tff(f22_type, type, (
% 0.21/0.45 f22: ( $i * $i ) > $i)).
% 0.21/0.45 tff(c69_type, type, (
% 0.21/0.45 c69: $i)).
% 0.21/0.45 tff(c70_type, type, (
% 0.21/0.45 c70: $i)).
% 0.21/0.45 tff(f31_type, type, (
% 0.21/0.45 f31: ( $i * $i ) > $i)).
% 0.21/0.45 tff(f33_type, type, (
% 0.21/0.45 f33: ( $i * $i ) > $i)).
% 0.21/0.45 tff(c76_type, type, (
% 0.21/0.45 c76: $i)).
% 0.21/0.45 tff(c75_type, type, (
% 0.21/0.45 c75: $i)).
% 0.21/0.45 tff(p59_type, type, (
% 0.21/0.45 p59: ( $i * $i ) > $o)).
% 0.21/0.45 tff(f35_type, type, (
% 0.21/0.45 f35: ( $i * $i ) > $i)).
% 0.21/0.45 tff(c73_type, type, (
% 0.21/0.45 c73: $i)).
% 0.21/0.45 tff(f38_type, type, (
% 0.21/0.45 f38: ( $i * $i ) > $i)).
% 0.21/0.45 tff(c72_type, type, (
% 0.21/0.45 c72: $i)).
% 0.21/0.45 tff(p56_type, type, (
% 0.21/0.45 p56: ( $i * $i ) > $o)).
% 0.21/0.45 tff(c64_type, type, (
% 0.21/0.45 c64: $i)).
% 0.21/0.45 tff(p57_type, type, (
% 0.21/0.45 p57: ( $i * $i ) > $o)).
% 0.21/0.45 tff(f26_type, type, (
% 0.21/0.45 f26: ( $i * $i ) > $i)).
% 0.21/0.45 tff(f41_type, type, (
% 0.21/0.45 f41: ( $i * $i ) > $i)).
% 0.21/0.45 tff(c78_type, type, (
% 0.21/0.45 c78: $i)).
% 0.21/0.45 tff(f28_type, type, (
% 0.21/0.45 f28: ( $i * $i ) > $i)).
% 0.21/0.45 tff(c71_type, type, (
% 0.21/0.45 c71: $i)).
% 0.21/0.45 tff(p40_type, type, (
% 0.21/0.45 p40: ( $i * $i ) > $o)).
% 0.21/0.45 tff(1,assumption,(~p9(c65, c65)), introduced(assumption)).
% 0.21/0.45 tff(2,plain,
% 0.21/0.45 (^[X210: $i] : refl(p9(X210, X210) <=> p9(X210, X210))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(3,plain,
% 0.21/0.45 (![X210: $i] : p9(X210, X210) <=> ![X210: $i] : p9(X210, X210)),
% 0.21/0.45 inference(quant_intro,[status(thm)],[2])).
% 0.21/0.45 tff(4,plain,
% 0.21/0.45 (![X210: $i] : p9(X210, X210) <=> ![X210: $i] : p9(X210, X210)),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(5,axiom,(![X210: $i] : p9(X210, X210)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p9_2')).
% 0.21/0.45 tff(6,plain,
% 0.21/0.45 (![X210: $i] : p9(X210, X210)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.21/0.45 tff(7,plain,(
% 0.21/0.45 ![X210: $i] : p9(X210, X210)),
% 0.21/0.45 inference(skolemize,[status(sab)],[6])).
% 0.21/0.45 tff(8,plain,
% 0.21/0.45 (![X210: $i] : p9(X210, X210)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.21/0.45 tff(9,plain,
% 0.21/0.45 ((~![X210: $i] : p9(X210, X210)) | p9(c65, c65)),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(10,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.21/0.45 tff(11,plain,(p9(c65, c65)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.45 tff(12,assumption,(~p12(f17(c66, c67), f17(c66, c67))), introduced(assumption)).
% 0.21/0.45 tff(13,plain,
% 0.21/0.45 (^[X7: $i] : refl(p12(X7, X7) <=> p12(X7, X7))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(14,plain,
% 0.21/0.45 (![X7: $i] : p12(X7, X7) <=> ![X7: $i] : p12(X7, X7)),
% 0.21/0.45 inference(quant_intro,[status(thm)],[13])).
% 0.21/0.45 tff(15,plain,
% 0.21/0.45 (![X7: $i] : p12(X7, X7) <=> ![X7: $i] : p12(X7, X7)),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(16,axiom,(![X7: $i] : p12(X7, X7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p12_34')).
% 0.21/0.45 tff(17,plain,
% 0.21/0.45 (![X7: $i] : p12(X7, X7)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.21/0.45 tff(18,plain,(
% 0.21/0.45 ![X7: $i] : p12(X7, X7)),
% 0.21/0.45 inference(skolemize,[status(sab)],[17])).
% 0.21/0.45 tff(19,plain,
% 0.21/0.45 (![X7: $i] : p12(X7, X7)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.21/0.45 tff(20,plain,
% 0.21/0.45 ((~![X7: $i] : p12(X7, X7)) | p12(f17(c66, c67), f17(c66, c67))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(21,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[20, 19, 12])).
% 0.21/0.45 tff(22,plain,(p12(f17(c66, c67), f17(c66, c67))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.45 tff(23,assumption,(~p13(c68, f23(c74, c77))), introduced(assumption)).
% 0.21/0.45 tff(24,plain,
% 0.21/0.45 (^[X17: $i, X18: $i] : refl(((~p59(f38(c72, X18), f35(c73, X17))) | p58(f31(f33(c75, c76), f23(c69, X18)), f19(f22(c70, c69), X17)) | p13(X17, f23(c74, X18))) <=> ((~p59(f38(c72, X18), f35(c73, X17))) | p58(f31(f33(c75, c76), f23(c69, X18)), f19(f22(c70, c69), X17)) | p13(X17, f23(c74, X18))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(25,plain,
% 0.21/0.45 (![X17: $i, X18: $i] : ((~p59(f38(c72, X18), f35(c73, X17))) | p58(f31(f33(c75, c76), f23(c69, X18)), f19(f22(c70, c69), X17)) | p13(X17, f23(c74, X18))) <=> ![X17: $i, X18: $i] : ((~p59(f38(c72, X18), f35(c73, X17))) | p58(f31(f33(c75, c76), f23(c69, X18)), f19(f22(c70, c69), X17)) | p13(X17, f23(c74, X18)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[24])).
% 0.21/0.45 tff(26,plain,
% 0.21/0.45 (![X17: $i, X18: $i] : ((~p59(f38(c72, X18), f35(c73, X17))) | p58(f31(f33(c75, c76), f23(c69, X18)), f19(f22(c70, c69), X17)) | p13(X17, f23(c74, X18))) <=> ![X17: $i, X18: $i] : ((~p59(f38(c72, X18), f35(c73, X17))) | p58(f31(f33(c75, c76), f23(c69, X18)), f19(f22(c70, c69), X17)) | p13(X17, f23(c74, X18)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(27,plain,
% 0.21/0.45 (^[X17: $i, X18: $i] : rewrite(((p13(X17, f23(c74, X18)) | p58(f31(f33(c75, c76), f23(c69, X18)), f19(f22(c70, c69), X17))) | (~p59(f38(c72, X18), f35(c73, X17)))) <=> ((~p59(f38(c72, X18), f35(c73, X17))) | p58(f31(f33(c75, c76), f23(c69, X18)), f19(f22(c70, c69), X17)) | p13(X17, f23(c74, X18))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(28,plain,
% 0.21/0.45 (![X17: $i, X18: $i] : ((p13(X17, f23(c74, X18)) | p58(f31(f33(c75, c76), f23(c69, X18)), f19(f22(c70, c69), X17))) | (~p59(f38(c72, X18), f35(c73, X17)))) <=> ![X17: $i, X18: $i] : ((~p59(f38(c72, X18), f35(c73, X17))) | p58(f31(f33(c75, c76), f23(c69, X18)), f19(f22(c70, c69), X17)) | p13(X17, f23(c74, X18)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[27])).
% 0.21/0.45 tff(29,axiom,(![X17: $i, X18: $i] : ((p13(X17, f23(c74, X18)) | p58(f31(f33(c75, c76), f23(c69, X18)), f19(f22(c70, c69), X17))) | (~p59(f38(c72, X18), f35(c73, X17))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p13_105')).
% 0.21/0.45 tff(30,plain,
% 0.21/0.45 (![X17: $i, X18: $i] : ((~p59(f38(c72, X18), f35(c73, X17))) | p58(f31(f33(c75, c76), f23(c69, X18)), f19(f22(c70, c69), X17)) | p13(X17, f23(c74, X18)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.21/0.45 tff(31,plain,
% 0.21/0.45 (![X17: $i, X18: $i] : ((~p59(f38(c72, X18), f35(c73, X17))) | p58(f31(f33(c75, c76), f23(c69, X18)), f19(f22(c70, c69), X17)) | p13(X17, f23(c74, X18)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.21/0.45 tff(32,plain,(
% 0.21/0.45 ![X17: $i, X18: $i] : ((~p59(f38(c72, X18), f35(c73, X17))) | p58(f31(f33(c75, c76), f23(c69, X18)), f19(f22(c70, c69), X17)) | p13(X17, f23(c74, X18)))),
% 0.21/0.45 inference(skolemize,[status(sab)],[31])).
% 0.21/0.45 tff(33,plain,
% 0.21/0.45 (![X17: $i, X18: $i] : ((~p59(f38(c72, X18), f35(c73, X17))) | p58(f31(f33(c75, c76), f23(c69, X18)), f19(f22(c70, c69), X17)) | p13(X17, f23(c74, X18)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.21/0.45 tff(34,plain,
% 0.21/0.45 ((~p58(f31(f33(c75, c76), f23(c69, c77)), f19(f22(c70, c69), c68))) <=> (~p58(f31(f33(c75, c76), f23(c69, c77)), f19(f22(c70, c69), c68)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(35,axiom,(~p58(f31(f33(c75, c76), f23(c69, c77)), f19(f22(c70, c69), c68))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_p58_80')).
% 0.21/0.45 tff(36,plain,
% 0.21/0.45 (~p58(f31(f33(c75, c76), f23(c69, c77)), f19(f22(c70, c69), c68))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.21/0.45 tff(37,plain,
% 0.21/0.45 (p59(f38(c72, c77), f35(c73, c68)) <=> p59(f38(c72, c77), f35(c73, c68))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(38,axiom,(p59(f38(c72, c77), f35(c73, c68))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p59_35')).
% 0.21/0.45 tff(39,plain,
% 0.21/0.45 (p59(f38(c72, c77), f35(c73, c68))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.21/0.45 tff(40,plain,
% 0.21/0.45 (((~![X17: $i, X18: $i] : ((~p59(f38(c72, X18), f35(c73, X17))) | p58(f31(f33(c75, c76), f23(c69, X18)), f19(f22(c70, c69), X17)) | p13(X17, f23(c74, X18)))) | (p58(f31(f33(c75, c76), f23(c69, c77)), f19(f22(c70, c69), c68)) | p13(c68, f23(c74, c77)) | (~p59(f38(c72, c77), f35(c73, c68))))) <=> ((~![X17: $i, X18: $i] : ((~p59(f38(c72, X18), f35(c73, X17))) | p58(f31(f33(c75, c76), f23(c69, X18)), f19(f22(c70, c69), X17)) | p13(X17, f23(c74, X18)))) | p58(f31(f33(c75, c76), f23(c69, c77)), f19(f22(c70, c69), c68)) | p13(c68, f23(c74, c77)) | (~p59(f38(c72, c77), f35(c73, c68))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(41,plain,
% 0.21/0.45 (((~p59(f38(c72, c77), f35(c73, c68))) | p58(f31(f33(c75, c76), f23(c69, c77)), f19(f22(c70, c69), c68)) | p13(c68, f23(c74, c77))) <=> (p58(f31(f33(c75, c76), f23(c69, c77)), f19(f22(c70, c69), c68)) | p13(c68, f23(c74, c77)) | (~p59(f38(c72, c77), f35(c73, c68))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(42,plain,
% 0.21/0.45 (((~![X17: $i, X18: $i] : ((~p59(f38(c72, X18), f35(c73, X17))) | p58(f31(f33(c75, c76), f23(c69, X18)), f19(f22(c70, c69), X17)) | p13(X17, f23(c74, X18)))) | ((~p59(f38(c72, c77), f35(c73, c68))) | p58(f31(f33(c75, c76), f23(c69, c77)), f19(f22(c70, c69), c68)) | p13(c68, f23(c74, c77)))) <=> ((~![X17: $i, X18: $i] : ((~p59(f38(c72, X18), f35(c73, X17))) | p58(f31(f33(c75, c76), f23(c69, X18)), f19(f22(c70, c69), X17)) | p13(X17, f23(c74, X18)))) | (p58(f31(f33(c75, c76), f23(c69, c77)), f19(f22(c70, c69), c68)) | p13(c68, f23(c74, c77)) | (~p59(f38(c72, c77), f35(c73, c68)))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[41])).
% 0.21/0.45 tff(43,plain,
% 0.21/0.45 (((~![X17: $i, X18: $i] : ((~p59(f38(c72, X18), f35(c73, X17))) | p58(f31(f33(c75, c76), f23(c69, X18)), f19(f22(c70, c69), X17)) | p13(X17, f23(c74, X18)))) | ((~p59(f38(c72, c77), f35(c73, c68))) | p58(f31(f33(c75, c76), f23(c69, c77)), f19(f22(c70, c69), c68)) | p13(c68, f23(c74, c77)))) <=> ((~![X17: $i, X18: $i] : ((~p59(f38(c72, X18), f35(c73, X17))) | p58(f31(f33(c75, c76), f23(c69, X18)), f19(f22(c70, c69), X17)) | p13(X17, f23(c74, X18)))) | p58(f31(f33(c75, c76), f23(c69, c77)), f19(f22(c70, c69), c68)) | p13(c68, f23(c74, c77)) | (~p59(f38(c72, c77), f35(c73, c68))))),
% 0.21/0.45 inference(transitivity,[status(thm)],[42, 40])).
% 0.21/0.45 tff(44,plain,
% 0.21/0.45 ((~![X17: $i, X18: $i] : ((~p59(f38(c72, X18), f35(c73, X17))) | p58(f31(f33(c75, c76), f23(c69, X18)), f19(f22(c70, c69), X17)) | p13(X17, f23(c74, X18)))) | ((~p59(f38(c72, c77), f35(c73, c68))) | p58(f31(f33(c75, c76), f23(c69, c77)), f19(f22(c70, c69), c68)) | p13(c68, f23(c74, c77)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(45,plain,
% 0.21/0.45 ((~![X17: $i, X18: $i] : ((~p59(f38(c72, X18), f35(c73, X17))) | p58(f31(f33(c75, c76), f23(c69, X18)), f19(f22(c70, c69), X17)) | p13(X17, f23(c74, X18)))) | p58(f31(f33(c75, c76), f23(c69, c77)), f19(f22(c70, c69), c68)) | p13(c68, f23(c74, c77)) | (~p59(f38(c72, c77), f35(c73, c68)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.21/0.45 tff(46,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[45, 39, 36, 33, 23])).
% 0.21/0.45 tff(47,plain,(p13(c68, f23(c74, c77))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.45 tff(48,plain,
% 0.21/0.45 (^[X6: $i, X4: $i, X3: $i, X5: $i] : refl(((~p12(X3, X5)) | (~p13(X4, X6)) | p10(f14(X3, X4), f14(X5, X6))) <=> ((~p12(X3, X5)) | (~p13(X4, X6)) | p10(f14(X3, X4), f14(X5, X6))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(49,plain,
% 0.21/0.45 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p12(X3, X5)) | (~p13(X4, X6)) | p10(f14(X3, X4), f14(X5, X6))) <=> ![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p12(X3, X5)) | (~p13(X4, X6)) | p10(f14(X3, X4), f14(X5, X6)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[48])).
% 0.21/0.45 tff(50,plain,
% 0.21/0.45 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p12(X3, X5)) | (~p13(X4, X6)) | p10(f14(X3, X4), f14(X5, X6))) <=> ![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p12(X3, X5)) | (~p13(X4, X6)) | p10(f14(X3, X4), f14(X5, X6)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(51,plain,
% 0.21/0.45 (^[X6: $i, X4: $i, X3: $i, X5: $i] : trans(monotonicity(rewrite((p10(f14(X3, X4), f14(X5, X6)) | (~p12(X3, X5))) <=> ((~p12(X3, X5)) | p10(f14(X3, X4), f14(X5, X6)))), (((p10(f14(X3, X4), f14(X5, X6)) | (~p12(X3, X5))) | (~p13(X4, X6))) <=> (((~p12(X3, X5)) | p10(f14(X3, X4), f14(X5, X6))) | (~p13(X4, X6))))), rewrite((((~p12(X3, X5)) | p10(f14(X3, X4), f14(X5, X6))) | (~p13(X4, X6))) <=> ((~p12(X3, X5)) | (~p13(X4, X6)) | p10(f14(X3, X4), f14(X5, X6)))), (((p10(f14(X3, X4), f14(X5, X6)) | (~p12(X3, X5))) | (~p13(X4, X6))) <=> ((~p12(X3, X5)) | (~p13(X4, X6)) | p10(f14(X3, X4), f14(X5, X6)))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(52,plain,
% 0.21/0.46 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((p10(f14(X3, X4), f14(X5, X6)) | (~p12(X3, X5))) | (~p13(X4, X6))) <=> ![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p12(X3, X5)) | (~p13(X4, X6)) | p10(f14(X3, X4), f14(X5, X6)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[51])).
% 0.21/0.46 tff(53,axiom,(![X6: $i, X4: $i, X3: $i, X5: $i] : ((p10(f14(X3, X4), f14(X5, X6)) | (~p12(X3, X5))) | (~p13(X4, X6)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p10_81')).
% 0.21/0.46 tff(54,plain,
% 0.21/0.46 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p12(X3, X5)) | (~p13(X4, X6)) | p10(f14(X3, X4), f14(X5, X6)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.21/0.46 tff(55,plain,
% 0.21/0.46 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p12(X3, X5)) | (~p13(X4, X6)) | p10(f14(X3, X4), f14(X5, X6)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.21/0.46 tff(56,plain,(
% 0.21/0.46 ![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p12(X3, X5)) | (~p13(X4, X6)) | p10(f14(X3, X4), f14(X5, X6)))),
% 0.21/0.46 inference(skolemize,[status(sab)],[55])).
% 0.21/0.46 tff(57,plain,
% 0.21/0.46 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p12(X3, X5)) | (~p13(X4, X6)) | p10(f14(X3, X4), f14(X5, X6)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[56, 49])).
% 0.21/0.46 tff(58,plain,
% 0.21/0.46 (((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p12(X3, X5)) | (~p13(X4, X6)) | p10(f14(X3, X4), f14(X5, X6)))) | ((~p12(f17(c66, c67), f17(c66, c67))) | (~p13(c68, f23(c74, c77))) | p10(f14(f17(c66, c67), c68), f14(f17(c66, c67), f23(c74, c77))))) <=> ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p12(X3, X5)) | (~p13(X4, X6)) | p10(f14(X3, X4), f14(X5, X6)))) | (~p12(f17(c66, c67), f17(c66, c67))) | (~p13(c68, f23(c74, c77))) | p10(f14(f17(c66, c67), c68), f14(f17(c66, c67), f23(c74, c77))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(59,plain,
% 0.21/0.46 ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p12(X3, X5)) | (~p13(X4, X6)) | p10(f14(X3, X4), f14(X5, X6)))) | ((~p12(f17(c66, c67), f17(c66, c67))) | (~p13(c68, f23(c74, c77))) | p10(f14(f17(c66, c67), c68), f14(f17(c66, c67), f23(c74, c77))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(60,plain,
% 0.21/0.46 ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p12(X3, X5)) | (~p13(X4, X6)) | p10(f14(X3, X4), f14(X5, X6)))) | (~p12(f17(c66, c67), f17(c66, c67))) | (~p13(c68, f23(c74, c77))) | p10(f14(f17(c66, c67), c68), f14(f17(c66, c67), f23(c74, c77)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.21/0.46 tff(61,plain,
% 0.21/0.46 ((~p12(f17(c66, c67), f17(c66, c67))) | (~p13(c68, f23(c74, c77))) | p10(f14(f17(c66, c67), c68), f14(f17(c66, c67), f23(c74, c77)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[60, 57])).
% 0.21/0.46 tff(62,plain,
% 0.21/0.46 (p10(f14(f17(c66, c67), c68), f14(f17(c66, c67), f23(c74, c77)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[61, 47, 22])).
% 0.21/0.46 tff(63,plain,
% 0.21/0.46 (^[X122: $i, X124: $i, X121: $i, X123: $i] : refl(((~p9(X121, X123)) | (~p10(X122, X124)) | p4(f11(X121, X122), f11(X123, X124))) <=> ((~p9(X121, X123)) | (~p10(X122, X124)) | p4(f11(X121, X122), f11(X123, X124))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(64,plain,
% 0.21/0.46 (![X122: $i, X124: $i, X121: $i, X123: $i] : ((~p9(X121, X123)) | (~p10(X122, X124)) | p4(f11(X121, X122), f11(X123, X124))) <=> ![X122: $i, X124: $i, X121: $i, X123: $i] : ((~p9(X121, X123)) | (~p10(X122, X124)) | p4(f11(X121, X122), f11(X123, X124)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[63])).
% 0.21/0.46 tff(65,plain,
% 0.21/0.46 (![X122: $i, X124: $i, X121: $i, X123: $i] : ((~p9(X121, X123)) | (~p10(X122, X124)) | p4(f11(X121, X122), f11(X123, X124))) <=> ![X122: $i, X124: $i, X121: $i, X123: $i] : ((~p9(X121, X123)) | (~p10(X122, X124)) | p4(f11(X121, X122), f11(X123, X124)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(66,plain,
% 0.21/0.46 (^[X122: $i, X124: $i, X121: $i, X123: $i] : trans(monotonicity(rewrite((p4(f11(X121, X122), f11(X123, X124)) | (~p10(X122, X124))) <=> ((~p10(X122, X124)) | p4(f11(X121, X122), f11(X123, X124)))), (((p4(f11(X121, X122), f11(X123, X124)) | (~p10(X122, X124))) | (~p9(X121, X123))) <=> (((~p10(X122, X124)) | p4(f11(X121, X122), f11(X123, X124))) | (~p9(X121, X123))))), rewrite((((~p10(X122, X124)) | p4(f11(X121, X122), f11(X123, X124))) | (~p9(X121, X123))) <=> ((~p9(X121, X123)) | (~p10(X122, X124)) | p4(f11(X121, X122), f11(X123, X124)))), (((p4(f11(X121, X122), f11(X123, X124)) | (~p10(X122, X124))) | (~p9(X121, X123))) <=> ((~p9(X121, X123)) | (~p10(X122, X124)) | p4(f11(X121, X122), f11(X123, X124)))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(67,plain,
% 0.21/0.46 (![X122: $i, X124: $i, X121: $i, X123: $i] : ((p4(f11(X121, X122), f11(X123, X124)) | (~p10(X122, X124))) | (~p9(X121, X123))) <=> ![X122: $i, X124: $i, X121: $i, X123: $i] : ((~p9(X121, X123)) | (~p10(X122, X124)) | p4(f11(X121, X122), f11(X123, X124)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[66])).
% 0.21/0.46 tff(68,axiom,(![X122: $i, X124: $i, X121: $i, X123: $i] : ((p4(f11(X121, X122), f11(X123, X124)) | (~p10(X122, X124))) | (~p9(X121, X123)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p4_87')).
% 0.21/0.46 tff(69,plain,
% 0.21/0.46 (![X122: $i, X124: $i, X121: $i, X123: $i] : ((~p9(X121, X123)) | (~p10(X122, X124)) | p4(f11(X121, X122), f11(X123, X124)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.21/0.46 tff(70,plain,
% 0.21/0.46 (![X122: $i, X124: $i, X121: $i, X123: $i] : ((~p9(X121, X123)) | (~p10(X122, X124)) | p4(f11(X121, X122), f11(X123, X124)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.21/0.46 tff(71,plain,(
% 0.21/0.46 ![X122: $i, X124: $i, X121: $i, X123: $i] : ((~p9(X121, X123)) | (~p10(X122, X124)) | p4(f11(X121, X122), f11(X123, X124)))),
% 0.21/0.46 inference(skolemize,[status(sab)],[70])).
% 0.21/0.46 tff(72,plain,
% 0.21/0.46 (![X122: $i, X124: $i, X121: $i, X123: $i] : ((~p9(X121, X123)) | (~p10(X122, X124)) | p4(f11(X121, X122), f11(X123, X124)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.21/0.46 tff(73,plain,
% 0.21/0.46 (((~![X122: $i, X124: $i, X121: $i, X123: $i] : ((~p9(X121, X123)) | (~p10(X122, X124)) | p4(f11(X121, X122), f11(X123, X124)))) | ((~p9(c65, c65)) | (~p10(f14(f17(c66, c67), c68), f14(f17(c66, c67), f23(c74, c77)))) | p4(f11(c65, f14(f17(c66, c67), c68)), f11(c65, f14(f17(c66, c67), f23(c74, c77)))))) <=> ((~![X122: $i, X124: $i, X121: $i, X123: $i] : ((~p9(X121, X123)) | (~p10(X122, X124)) | p4(f11(X121, X122), f11(X123, X124)))) | (~p9(c65, c65)) | (~p10(f14(f17(c66, c67), c68), f14(f17(c66, c67), f23(c74, c77)))) | p4(f11(c65, f14(f17(c66, c67), c68)), f11(c65, f14(f17(c66, c67), f23(c74, c77)))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(74,plain,
% 0.21/0.46 ((~![X122: $i, X124: $i, X121: $i, X123: $i] : ((~p9(X121, X123)) | (~p10(X122, X124)) | p4(f11(X121, X122), f11(X123, X124)))) | ((~p9(c65, c65)) | (~p10(f14(f17(c66, c67), c68), f14(f17(c66, c67), f23(c74, c77)))) | p4(f11(c65, f14(f17(c66, c67), c68)), f11(c65, f14(f17(c66, c67), f23(c74, c77)))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(75,plain,
% 0.21/0.46 ((~![X122: $i, X124: $i, X121: $i, X123: $i] : ((~p9(X121, X123)) | (~p10(X122, X124)) | p4(f11(X121, X122), f11(X123, X124)))) | (~p9(c65, c65)) | (~p10(f14(f17(c66, c67), c68), f14(f17(c66, c67), f23(c74, c77)))) | p4(f11(c65, f14(f17(c66, c67), c68)), f11(c65, f14(f17(c66, c67), f23(c74, c77))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.21/0.46 tff(76,plain,
% 0.21/0.46 ((~p9(c65, c65)) | (~p10(f14(f17(c66, c67), c68), f14(f17(c66, c67), f23(c74, c77)))) | p4(f11(c65, f14(f17(c66, c67), c68)), f11(c65, f14(f17(c66, c67), f23(c74, c77))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[75, 72])).
% 0.21/0.46 tff(77,plain,
% 0.21/0.46 (p4(f11(c65, f14(f17(c66, c67), c68)), f11(c65, f14(f17(c66, c67), f23(c74, c77))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[76, 62, 11])).
% 0.21/0.46 tff(78,plain,
% 0.21/0.46 (^[X188: $i, X186: $i, X187: $i] : refl(((~p57(f26(X186, X187), X188)) | p57(f26(f28(c71, X186), X187), X188)) <=> ((~p57(f26(X186, X187), X188)) | p57(f26(f28(c71, X186), X187), X188)))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(79,plain,
% 0.21/0.46 (![X188: $i, X186: $i, X187: $i] : ((~p57(f26(X186, X187), X188)) | p57(f26(f28(c71, X186), X187), X188)) <=> ![X188: $i, X186: $i, X187: $i] : ((~p57(f26(X186, X187), X188)) | p57(f26(f28(c71, X186), X187), X188))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[78])).
% 0.21/0.46 tff(80,plain,
% 0.21/0.46 (![X188: $i, X186: $i, X187: $i] : ((~p57(f26(X186, X187), X188)) | p57(f26(f28(c71, X186), X187), X188)) <=> ![X188: $i, X186: $i, X187: $i] : ((~p57(f26(X186, X187), X188)) | p57(f26(f28(c71, X186), X187), X188))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(81,plain,
% 0.21/0.46 (^[X188: $i, X186: $i, X187: $i] : rewrite((p57(f26(f28(c71, X186), X187), X188) | (~p57(f26(X186, X187), X188))) <=> ((~p57(f26(X186, X187), X188)) | p57(f26(f28(c71, X186), X187), X188)))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(82,plain,
% 0.21/0.46 (![X188: $i, X186: $i, X187: $i] : (p57(f26(f28(c71, X186), X187), X188) | (~p57(f26(X186, X187), X188))) <=> ![X188: $i, X186: $i, X187: $i] : ((~p57(f26(X186, X187), X188)) | p57(f26(f28(c71, X186), X187), X188))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[81])).
% 0.21/0.46 tff(83,axiom,(![X188: $i, X186: $i, X187: $i] : (p57(f26(f28(c71, X186), X187), X188) | (~p57(f26(X186, X187), X188)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p57_74')).
% 0.21/0.46 tff(84,plain,
% 0.21/0.46 (![X188: $i, X186: $i, X187: $i] : ((~p57(f26(X186, X187), X188)) | p57(f26(f28(c71, X186), X187), X188))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.21/0.46 tff(85,plain,
% 0.21/0.46 (![X188: $i, X186: $i, X187: $i] : ((~p57(f26(X186, X187), X188)) | p57(f26(f28(c71, X186), X187), X188))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.21/0.46 tff(86,plain,(
% 0.21/0.46 ![X188: $i, X186: $i, X187: $i] : ((~p57(f26(X186, X187), X188)) | p57(f26(f28(c71, X186), X187), X188))),
% 0.21/0.46 inference(skolemize,[status(sab)],[85])).
% 0.21/0.46 tff(87,plain,
% 0.21/0.46 (![X188: $i, X186: $i, X187: $i] : ((~p57(f26(X186, X187), X188)) | p57(f26(f28(c71, X186), X187), X188))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[86, 79])).
% 0.21/0.46 tff(88,plain,
% 0.21/0.46 ((~p57(f26(f28(c71, f41(c78, c64)), c67), c77)) <=> (~p57(f26(f28(c71, f41(c78, c64)), c67), c77))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(89,axiom,(~p57(f26(f28(c71, f41(c78, c64)), c67), c77)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_p57_39')).
% 0.21/0.46 tff(90,plain,
% 0.21/0.46 (~p57(f26(f28(c71, f41(c78, c64)), c67), c77)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.21/0.46 tff(91,plain,
% 0.21/0.46 (((~![X188: $i, X186: $i, X187: $i] : ((~p57(f26(X186, X187), X188)) | p57(f26(f28(c71, X186), X187), X188))) | ((~p57(f26(f41(c78, c64), c67), c77)) | p57(f26(f28(c71, f41(c78, c64)), c67), c77))) <=> ((~![X188: $i, X186: $i, X187: $i] : ((~p57(f26(X186, X187), X188)) | p57(f26(f28(c71, X186), X187), X188))) | (~p57(f26(f41(c78, c64), c67), c77)) | p57(f26(f28(c71, f41(c78, c64)), c67), c77))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(92,plain,
% 0.21/0.46 ((~![X188: $i, X186: $i, X187: $i] : ((~p57(f26(X186, X187), X188)) | p57(f26(f28(c71, X186), X187), X188))) | ((~p57(f26(f41(c78, c64), c67), c77)) | p57(f26(f28(c71, f41(c78, c64)), c67), c77))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(93,plain,
% 0.21/0.46 ((~![X188: $i, X186: $i, X187: $i] : ((~p57(f26(X186, X187), X188)) | p57(f26(f28(c71, X186), X187), X188))) | (~p57(f26(f41(c78, c64), c67), c77)) | p57(f26(f28(c71, f41(c78, c64)), c67), c77)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.21/0.46 tff(94,plain,
% 0.21/0.46 (~p57(f26(f41(c78, c64), c67), c77)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[93, 90, 87])).
% 0.21/0.46 tff(95,plain,
% 0.21/0.46 (^[X179: $i, X181: $i, X180: $i] : refl(((~p56(f11(c65, f14(f17(c66, X179), f23(c74, X180))), X181)) | p57(f26(f41(c78, X181), X179), X180)) <=> ((~p56(f11(c65, f14(f17(c66, X179), f23(c74, X180))), X181)) | p57(f26(f41(c78, X181), X179), X180)))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(96,plain,
% 0.21/0.46 (![X179: $i, X181: $i, X180: $i] : ((~p56(f11(c65, f14(f17(c66, X179), f23(c74, X180))), X181)) | p57(f26(f41(c78, X181), X179), X180)) <=> ![X179: $i, X181: $i, X180: $i] : ((~p56(f11(c65, f14(f17(c66, X179), f23(c74, X180))), X181)) | p57(f26(f41(c78, X181), X179), X180))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[95])).
% 0.21/0.46 tff(97,plain,
% 0.21/0.46 (![X179: $i, X181: $i, X180: $i] : ((~p56(f11(c65, f14(f17(c66, X179), f23(c74, X180))), X181)) | p57(f26(f41(c78, X181), X179), X180)) <=> ![X179: $i, X181: $i, X180: $i] : ((~p56(f11(c65, f14(f17(c66, X179), f23(c74, X180))), X181)) | p57(f26(f41(c78, X181), X179), X180))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(98,plain,
% 0.21/0.47 (^[X179: $i, X181: $i, X180: $i] : rewrite((p57(f26(f41(c78, X181), X179), X180) | (~p56(f11(c65, f14(f17(c66, X179), f23(c74, X180))), X181))) <=> ((~p56(f11(c65, f14(f17(c66, X179), f23(c74, X180))), X181)) | p57(f26(f41(c78, X181), X179), X180)))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(99,plain,
% 0.21/0.47 (![X179: $i, X181: $i, X180: $i] : (p57(f26(f41(c78, X181), X179), X180) | (~p56(f11(c65, f14(f17(c66, X179), f23(c74, X180))), X181))) <=> ![X179: $i, X181: $i, X180: $i] : ((~p56(f11(c65, f14(f17(c66, X179), f23(c74, X180))), X181)) | p57(f26(f41(c78, X181), X179), X180))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[98])).
% 0.21/0.47 tff(100,axiom,(![X179: $i, X181: $i, X180: $i] : (p57(f26(f41(c78, X181), X179), X180) | (~p56(f11(c65, f14(f17(c66, X179), f23(c74, X180))), X181)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p57_101')).
% 0.21/0.47 tff(101,plain,
% 0.21/0.47 (![X179: $i, X181: $i, X180: $i] : ((~p56(f11(c65, f14(f17(c66, X179), f23(c74, X180))), X181)) | p57(f26(f41(c78, X181), X179), X180))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.21/0.47 tff(102,plain,
% 0.21/0.47 (![X179: $i, X181: $i, X180: $i] : ((~p56(f11(c65, f14(f17(c66, X179), f23(c74, X180))), X181)) | p57(f26(f41(c78, X181), X179), X180))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[101, 97])).
% 0.21/0.47 tff(103,plain,(
% 0.21/0.47 ![X179: $i, X181: $i, X180: $i] : ((~p56(f11(c65, f14(f17(c66, X179), f23(c74, X180))), X181)) | p57(f26(f41(c78, X181), X179), X180))),
% 0.21/0.47 inference(skolemize,[status(sab)],[102])).
% 0.21/0.47 tff(104,plain,
% 0.21/0.47 (![X179: $i, X181: $i, X180: $i] : ((~p56(f11(c65, f14(f17(c66, X179), f23(c74, X180))), X181)) | p57(f26(f41(c78, X181), X179), X180))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[103, 96])).
% 0.21/0.47 tff(105,plain,
% 0.21/0.47 (((~![X179: $i, X181: $i, X180: $i] : ((~p56(f11(c65, f14(f17(c66, X179), f23(c74, X180))), X181)) | p57(f26(f41(c78, X181), X179), X180))) | ((~p56(f11(c65, f14(f17(c66, c67), f23(c74, c77))), c64)) | p57(f26(f41(c78, c64), c67), c77))) <=> ((~![X179: $i, X181: $i, X180: $i] : ((~p56(f11(c65, f14(f17(c66, X179), f23(c74, X180))), X181)) | p57(f26(f41(c78, X181), X179), X180))) | (~p56(f11(c65, f14(f17(c66, c67), f23(c74, c77))), c64)) | p57(f26(f41(c78, c64), c67), c77))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(106,plain,
% 0.21/0.47 ((~![X179: $i, X181: $i, X180: $i] : ((~p56(f11(c65, f14(f17(c66, X179), f23(c74, X180))), X181)) | p57(f26(f41(c78, X181), X179), X180))) | ((~p56(f11(c65, f14(f17(c66, c67), f23(c74, c77))), c64)) | p57(f26(f41(c78, c64), c67), c77))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(107,plain,
% 0.21/0.47 ((~![X179: $i, X181: $i, X180: $i] : ((~p56(f11(c65, f14(f17(c66, X179), f23(c74, X180))), X181)) | p57(f26(f41(c78, X181), X179), X180))) | (~p56(f11(c65, f14(f17(c66, c67), f23(c74, c77))), c64)) | p57(f26(f41(c78, c64), c67), c77)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.21/0.47 tff(108,plain,
% 0.21/0.47 (~p56(f11(c65, f14(f17(c66, c67), f23(c74, c77))), c64)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[107, 104, 94])).
% 0.21/0.47 tff(109,plain,
% 0.21/0.47 (^[X129: $i] : refl(p40(X129, X129) <=> p40(X129, X129))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(110,plain,
% 0.21/0.47 (![X129: $i] : p40(X129, X129) <=> ![X129: $i] : p40(X129, X129)),
% 0.21/0.47 inference(quant_intro,[status(thm)],[109])).
% 0.21/0.47 tff(111,plain,
% 0.21/0.47 (![X129: $i] : p40(X129, X129) <=> ![X129: $i] : p40(X129, X129)),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(112,axiom,(![X129: $i] : p40(X129, X129)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p40_14')).
% 0.21/0.47 tff(113,plain,
% 0.21/0.47 (![X129: $i] : p40(X129, X129)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.21/0.47 tff(114,plain,(
% 0.21/0.47 ![X129: $i] : p40(X129, X129)),
% 0.21/0.47 inference(skolemize,[status(sab)],[113])).
% 0.21/0.47 tff(115,plain,
% 0.21/0.47 (![X129: $i] : p40(X129, X129)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[114, 110])).
% 0.21/0.47 tff(116,plain,
% 0.21/0.47 ((~![X129: $i] : p40(X129, X129)) | p40(c64, c64)),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(117,plain,
% 0.21/0.47 (p40(c64, c64)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[116, 115])).
% 0.21/0.47 tff(118,plain,
% 0.21/0.47 (^[X175: $i, X176: $i, X178: $i, X177: $i] : refl(((~p40(X178, X176)) | (~p4(X177, X175)) | (~p56(X177, X178)) | p56(X175, X176)) <=> ((~p40(X178, X176)) | (~p4(X177, X175)) | (~p56(X177, X178)) | p56(X175, X176)))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(119,plain,
% 0.21/0.47 (![X175: $i, X176: $i, X178: $i, X177: $i] : ((~p40(X178, X176)) | (~p4(X177, X175)) | (~p56(X177, X178)) | p56(X175, X176)) <=> ![X175: $i, X176: $i, X178: $i, X177: $i] : ((~p40(X178, X176)) | (~p4(X177, X175)) | (~p56(X177, X178)) | p56(X175, X176))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[118])).
% 0.21/0.47 tff(120,plain,
% 0.21/0.47 (![X175: $i, X176: $i, X178: $i, X177: $i] : ((~p40(X178, X176)) | (~p4(X177, X175)) | (~p56(X177, X178)) | p56(X175, X176)) <=> ![X175: $i, X176: $i, X178: $i, X177: $i] : ((~p40(X178, X176)) | (~p4(X177, X175)) | (~p56(X177, X178)) | p56(X175, X176))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(121,plain,
% 0.21/0.47 (^[X175: $i, X176: $i, X178: $i, X177: $i] : trans(monotonicity(trans(monotonicity(rewrite((p56(X175, X176) | (~p40(X178, X176))) <=> ((~p40(X178, X176)) | p56(X175, X176))), (((p56(X175, X176) | (~p40(X178, X176))) | (~p56(X177, X178))) <=> (((~p40(X178, X176)) | p56(X175, X176)) | (~p56(X177, X178))))), rewrite((((~p40(X178, X176)) | p56(X175, X176)) | (~p56(X177, X178))) <=> ((~p40(X178, X176)) | (~p56(X177, X178)) | p56(X175, X176))), (((p56(X175, X176) | (~p40(X178, X176))) | (~p56(X177, X178))) <=> ((~p40(X178, X176)) | (~p56(X177, X178)) | p56(X175, X176)))), ((((p56(X175, X176) | (~p40(X178, X176))) | (~p56(X177, X178))) | (~p4(X177, X175))) <=> (((~p40(X178, X176)) | (~p56(X177, X178)) | p56(X175, X176)) | (~p4(X177, X175))))), rewrite((((~p40(X178, X176)) | (~p56(X177, X178)) | p56(X175, X176)) | (~p4(X177, X175))) <=> ((~p40(X178, X176)) | (~p4(X177, X175)) | (~p56(X177, X178)) | p56(X175, X176))), ((((p56(X175, X176) | (~p40(X178, X176))) | (~p56(X177, X178))) | (~p4(X177, X175))) <=> ((~p40(X178, X176)) | (~p4(X177, X175)) | (~p56(X177, X178)) | p56(X175, X176))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(122,plain,
% 0.21/0.47 (![X175: $i, X176: $i, X178: $i, X177: $i] : (((p56(X175, X176) | (~p40(X178, X176))) | (~p56(X177, X178))) | (~p4(X177, X175))) <=> ![X175: $i, X176: $i, X178: $i, X177: $i] : ((~p40(X178, X176)) | (~p4(X177, X175)) | (~p56(X177, X178)) | p56(X175, X176))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[121])).
% 0.21/0.47 tff(123,axiom,(![X175: $i, X176: $i, X178: $i, X177: $i] : (((p56(X175, X176) | (~p40(X178, X176))) | (~p56(X177, X178))) | (~p4(X177, X175)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p56_76')).
% 0.21/0.47 tff(124,plain,
% 0.21/0.47 (![X175: $i, X176: $i, X178: $i, X177: $i] : ((~p40(X178, X176)) | (~p4(X177, X175)) | (~p56(X177, X178)) | p56(X175, X176))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.21/0.47 tff(125,plain,
% 0.21/0.47 (![X175: $i, X176: $i, X178: $i, X177: $i] : ((~p40(X178, X176)) | (~p4(X177, X175)) | (~p56(X177, X178)) | p56(X175, X176))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[124, 120])).
% 0.21/0.47 tff(126,plain,(
% 0.21/0.47 ![X175: $i, X176: $i, X178: $i, X177: $i] : ((~p40(X178, X176)) | (~p4(X177, X175)) | (~p56(X177, X178)) | p56(X175, X176))),
% 0.21/0.47 inference(skolemize,[status(sab)],[125])).
% 0.21/0.47 tff(127,plain,
% 0.21/0.47 (![X175: $i, X176: $i, X178: $i, X177: $i] : ((~p40(X178, X176)) | (~p4(X177, X175)) | (~p56(X177, X178)) | p56(X175, X176))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[126, 119])).
% 0.21/0.47 tff(128,plain,
% 0.21/0.47 (p56(f11(c65, f14(f17(c66, c67), c68)), c64) <=> p56(f11(c65, f14(f17(c66, c67), c68)), c64)),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(129,axiom,(p56(f11(c65, f14(f17(c66, c67), c68)), c64)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p56_38')).
% 0.21/0.47 tff(130,plain,
% 0.21/0.47 (p56(f11(c65, f14(f17(c66, c67), c68)), c64)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.21/0.47 tff(131,plain,
% 0.21/0.47 (((~![X175: $i, X176: $i, X178: $i, X177: $i] : ((~p40(X178, X176)) | (~p4(X177, X175)) | (~p56(X177, X178)) | p56(X175, X176))) | ((~p40(c64, c64)) | (~p4(f11(c65, f14(f17(c66, c67), c68)), f11(c65, f14(f17(c66, c67), f23(c74, c77))))) | (~p56(f11(c65, f14(f17(c66, c67), c68)), c64)) | p56(f11(c65, f14(f17(c66, c67), f23(c74, c77))), c64))) <=> ((~![X175: $i, X176: $i, X178: $i, X177: $i] : ((~p40(X178, X176)) | (~p4(X177, X175)) | (~p56(X177, X178)) | p56(X175, X176))) | (~p40(c64, c64)) | (~p4(f11(c65, f14(f17(c66, c67), c68)), f11(c65, f14(f17(c66, c67), f23(c74, c77))))) | (~p56(f11(c65, f14(f17(c66, c67), c68)), c64)) | p56(f11(c65, f14(f17(c66, c67), f23(c74, c77))), c64))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(132,plain,
% 0.21/0.47 ((~![X175: $i, X176: $i, X178: $i, X177: $i] : ((~p40(X178, X176)) | (~p4(X177, X175)) | (~p56(X177, X178)) | p56(X175, X176))) | ((~p40(c64, c64)) | (~p4(f11(c65, f14(f17(c66, c67), c68)), f11(c65, f14(f17(c66, c67), f23(c74, c77))))) | (~p56(f11(c65, f14(f17(c66, c67), c68)), c64)) | p56(f11(c65, f14(f17(c66, c67), f23(c74, c77))), c64))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(133,plain,
% 0.21/0.47 ((~![X175: $i, X176: $i, X178: $i, X177: $i] : ((~p40(X178, X176)) | (~p4(X177, X175)) | (~p56(X177, X178)) | p56(X175, X176))) | (~p40(c64, c64)) | (~p4(f11(c65, f14(f17(c66, c67), c68)), f11(c65, f14(f17(c66, c67), f23(c74, c77))))) | (~p56(f11(c65, f14(f17(c66, c67), c68)), c64)) | p56(f11(c65, f14(f17(c66, c67), f23(c74, c77))), c64)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.21/0.47 tff(134,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[133, 130, 127, 117, 108, 77])).
% 0.21/0.47 % SZS output end Proof
% 0.21/0.47 % E exiting
%------------------------------------------------------------------------------