%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN717-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:39:54 AM UTC 2025
% Result : Unsatisfiable 0.18s 0.39s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SYN717-1 : TPTP v9.0.0. Released v2.5.0.
% 0.07/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n013.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 12:41:08 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.18/0.39 % SZS status Unsatisfiable
% 0.18/0.39 % SZS output start Proof
% 0.18/0.39 tff(p24_type, type, (
% 0.18/0.39 p24: ( $i * $i ) > $o)).
% 0.18/0.39 tff(f25_type, type, (
% 0.18/0.39 f25: ( $i * $i ) > $i)).
% 0.18/0.39 tff(c77_type, type, (
% 0.18/0.39 c77: $i)).
% 0.18/0.39 tff(c75_type, type, (
% 0.18/0.39 c75: $i)).
% 0.18/0.39 tff(c79_type, type, (
% 0.18/0.39 c79: $i)).
% 0.18/0.39 tff(p22_type, type, (
% 0.18/0.39 p22: ( $i * $i ) > $o)).
% 0.18/0.39 tff(p23_type, type, (
% 0.18/0.39 p23: ( $i * $i ) > $o)).
% 0.18/0.39 tff(p60_type, type, (
% 0.18/0.39 p60: ( $i * $i ) > $o)).
% 0.18/0.39 tff(f21_type, type, (
% 0.18/0.39 f21: ( $i * $i ) > $i)).
% 0.18/0.39 tff(c78_type, type, (
% 0.18/0.39 c78: $i)).
% 0.18/0.39 tff(c76_type, type, (
% 0.18/0.39 c76: $i)).
% 0.18/0.39 tff(p59_type, type, (
% 0.18/0.39 p59: ( $i * $i ) > $o)).
% 0.18/0.39 tff(c72_type, type, (
% 0.18/0.39 c72: $i)).
% 0.18/0.39 tff(f29_type, type, (
% 0.18/0.39 f29: ( $i * $i ) > $i)).
% 0.18/0.39 tff(f31_type, type, (
% 0.18/0.39 f31: ( $i * $i ) > $i)).
% 0.18/0.39 tff(f33_type, type, (
% 0.18/0.39 f33: ( $i * $i ) > $i)).
% 0.18/0.39 tff(c74_type, type, (
% 0.18/0.39 c74: $i)).
% 0.18/0.39 tff(c73_type, type, (
% 0.18/0.39 c73: $i)).
% 0.18/0.39 tff(p20_type, type, (
% 0.18/0.39 p20: ( $i * $i ) > $o)).
% 0.18/0.39 tff(p18_type, type, (
% 0.18/0.39 p18: ( $i * $i ) > $o)).
% 0.18/0.39 tff(p19_type, type, (
% 0.18/0.39 p19: ( $i * $i ) > $o)).
% 0.18/0.39 tff(1,assumption,(~p22(c75, c75)), introduced(assumption)).
% 0.18/0.39 tff(2,plain,
% 0.18/0.39 (^[X55: $i] : refl(p22(X55, X55) <=> p22(X55, X55))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(3,plain,
% 0.18/0.39 (![X55: $i] : p22(X55, X55) <=> ![X55: $i] : p22(X55, X55)),
% 0.18/0.39 inference(quant_intro,[status(thm)],[2])).
% 0.18/0.39 tff(4,plain,
% 0.18/0.39 (![X55: $i] : p22(X55, X55) <=> ![X55: $i] : p22(X55, X55)),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(5,axiom,(![X55: $i] : p22(X55, X55)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p22_28')).
% 0.18/0.39 tff(6,plain,
% 0.18/0.39 (![X55: $i] : p22(X55, X55)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.18/0.39 tff(7,plain,(
% 0.18/0.39 ![X55: $i] : p22(X55, X55)),
% 0.18/0.39 inference(skolemize,[status(sab)],[6])).
% 0.18/0.39 tff(8,plain,
% 0.18/0.39 (![X55: $i] : p22(X55, X55)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.18/0.39 tff(9,plain,
% 0.18/0.39 ((~![X55: $i] : p22(X55, X55)) | p22(c75, c75)),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(10,plain,
% 0.18/0.39 ($false),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.18/0.39 tff(11,plain,(p22(c75, c75)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.39 tff(12,plain,
% 0.18/0.39 (^[X68: $i, X70: $i, X69: $i, X71: $i] : refl(((~p23(X69, X71)) | (~p22(X68, X70)) | p24(f25(X68, X69), f25(X70, X71))) <=> ((~p23(X69, X71)) | (~p22(X68, X70)) | p24(f25(X68, X69), f25(X70, X71))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(13,plain,
% 0.18/0.39 (![X68: $i, X70: $i, X69: $i, X71: $i] : ((~p23(X69, X71)) | (~p22(X68, X70)) | p24(f25(X68, X69), f25(X70, X71))) <=> ![X68: $i, X70: $i, X69: $i, X71: $i] : ((~p23(X69, X71)) | (~p22(X68, X70)) | p24(f25(X68, X69), f25(X70, X71)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[12])).
% 0.18/0.39 tff(14,plain,
% 0.18/0.39 (![X68: $i, X70: $i, X69: $i, X71: $i] : ((~p23(X69, X71)) | (~p22(X68, X70)) | p24(f25(X68, X69), f25(X70, X71))) <=> ![X68: $i, X70: $i, X69: $i, X71: $i] : ((~p23(X69, X71)) | (~p22(X68, X70)) | p24(f25(X68, X69), f25(X70, X71)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(15,plain,
% 0.18/0.39 (^[X68: $i, X70: $i, X69: $i, X71: $i] : trans(monotonicity(rewrite((p24(f25(X68, X69), f25(X70, X71)) | (~p22(X68, X70))) <=> ((~p22(X68, X70)) | p24(f25(X68, X69), f25(X70, X71)))), (((p24(f25(X68, X69), f25(X70, X71)) | (~p22(X68, X70))) | (~p23(X69, X71))) <=> (((~p22(X68, X70)) | p24(f25(X68, X69), f25(X70, X71))) | (~p23(X69, X71))))), rewrite((((~p22(X68, X70)) | p24(f25(X68, X69), f25(X70, X71))) | (~p23(X69, X71))) <=> ((~p23(X69, X71)) | (~p22(X68, X70)) | p24(f25(X68, X69), f25(X70, X71)))), (((p24(f25(X68, X69), f25(X70, X71)) | (~p22(X68, X70))) | (~p23(X69, X71))) <=> ((~p23(X69, X71)) | (~p22(X68, X70)) | p24(f25(X68, X69), f25(X70, X71)))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(16,plain,
% 0.18/0.39 (![X68: $i, X70: $i, X69: $i, X71: $i] : ((p24(f25(X68, X69), f25(X70, X71)) | (~p22(X68, X70))) | (~p23(X69, X71))) <=> ![X68: $i, X70: $i, X69: $i, X71: $i] : ((~p23(X69, X71)) | (~p22(X68, X70)) | p24(f25(X68, X69), f25(X70, X71)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[15])).
% 0.18/0.39 tff(17,axiom,(![X68: $i, X70: $i, X69: $i, X71: $i] : ((p24(f25(X68, X69), f25(X70, X71)) | (~p22(X68, X70))) | (~p23(X69, X71)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p24_94')).
% 0.18/0.39 tff(18,plain,
% 0.18/0.39 (![X68: $i, X70: $i, X69: $i, X71: $i] : ((~p23(X69, X71)) | (~p22(X68, X70)) | p24(f25(X68, X69), f25(X70, X71)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.18/0.39 tff(19,plain,
% 0.18/0.39 (![X68: $i, X70: $i, X69: $i, X71: $i] : ((~p23(X69, X71)) | (~p22(X68, X70)) | p24(f25(X68, X69), f25(X70, X71)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.18/0.39 tff(20,plain,(
% 0.18/0.39 ![X68: $i, X70: $i, X69: $i, X71: $i] : ((~p23(X69, X71)) | (~p22(X68, X70)) | p24(f25(X68, X69), f25(X70, X71)))),
% 0.18/0.39 inference(skolemize,[status(sab)],[19])).
% 0.18/0.39 tff(21,plain,
% 0.18/0.39 (![X68: $i, X70: $i, X69: $i, X71: $i] : ((~p23(X69, X71)) | (~p22(X68, X70)) | p24(f25(X68, X69), f25(X70, X71)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.18/0.39 tff(22,plain,
% 0.18/0.39 (p23(c79, c77) <=> p23(c79, c77)),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(23,axiom,(p23(c79, c77)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p23_36')).
% 0.18/0.39 tff(24,plain,
% 0.18/0.39 (p23(c79, c77)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.18/0.39 tff(25,plain,
% 0.18/0.39 (((~![X68: $i, X70: $i, X69: $i, X71: $i] : ((~p23(X69, X71)) | (~p22(X68, X70)) | p24(f25(X68, X69), f25(X70, X71)))) | ((~p23(c79, c77)) | (~p22(c75, c75)) | p24(f25(c75, c79), f25(c75, c77)))) <=> ((~![X68: $i, X70: $i, X69: $i, X71: $i] : ((~p23(X69, X71)) | (~p22(X68, X70)) | p24(f25(X68, X69), f25(X70, X71)))) | (~p23(c79, c77)) | (~p22(c75, c75)) | p24(f25(c75, c79), f25(c75, c77)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(26,plain,
% 0.18/0.39 ((~![X68: $i, X70: $i, X69: $i, X71: $i] : ((~p23(X69, X71)) | (~p22(X68, X70)) | p24(f25(X68, X69), f25(X70, X71)))) | ((~p23(c79, c77)) | (~p22(c75, c75)) | p24(f25(c75, c79), f25(c75, c77)))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(27,plain,
% 0.18/0.39 ((~![X68: $i, X70: $i, X69: $i, X71: $i] : ((~p23(X69, X71)) | (~p22(X68, X70)) | p24(f25(X68, X69), f25(X70, X71)))) | (~p23(c79, c77)) | (~p22(c75, c75)) | p24(f25(c75, c79), f25(c75, c77))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.18/0.39 tff(28,plain,
% 0.18/0.39 ((~p22(c75, c75)) | p24(f25(c75, c79), f25(c75, c77))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[27, 24, 21])).
% 0.18/0.39 tff(29,plain,
% 0.18/0.39 (p24(f25(c75, c79), f25(c75, c77))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[28, 11])).
% 0.18/0.39 tff(30,plain,
% 0.18/0.39 (^[X212: $i, X210: $i, X211: $i, X209: $i] : refl(((~p59(f29(c73, f31(f33(c74, X209), X210)), c72)) | (~p59(f29(c73, f31(f33(c74, X211), X212)), c72)) | (~p60(f25(c75, X209), f21(c76, X212)))) <=> ((~p59(f29(c73, f31(f33(c74, X209), X210)), c72)) | (~p59(f29(c73, f31(f33(c74, X211), X212)), c72)) | (~p60(f25(c75, X209), f21(c76, X212)))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(31,plain,
% 0.18/0.39 (![X212: $i, X210: $i, X211: $i, X209: $i] : ((~p59(f29(c73, f31(f33(c74, X209), X210)), c72)) | (~p59(f29(c73, f31(f33(c74, X211), X212)), c72)) | (~p60(f25(c75, X209), f21(c76, X212)))) <=> ![X212: $i, X210: $i, X211: $i, X209: $i] : ((~p59(f29(c73, f31(f33(c74, X209), X210)), c72)) | (~p59(f29(c73, f31(f33(c74, X211), X212)), c72)) | (~p60(f25(c75, X209), f21(c76, X212))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[30])).
% 0.18/0.39 tff(32,plain,
% 0.18/0.39 (![X212: $i, X210: $i, X211: $i, X209: $i] : ((~p59(f29(c73, f31(f33(c74, X209), X210)), c72)) | (~p59(f29(c73, f31(f33(c74, X211), X212)), c72)) | (~p60(f25(c75, X209), f21(c76, X212)))) <=> ![X212: $i, X210: $i, X211: $i, X209: $i] : ((~p59(f29(c73, f31(f33(c74, X209), X210)), c72)) | (~p59(f29(c73, f31(f33(c74, X211), X212)), c72)) | (~p60(f25(c75, X209), f21(c76, X212))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(33,plain,
% 0.18/0.39 (^[X212: $i, X210: $i, X211: $i, X209: $i] : rewrite((((~p60(f25(c75, X209), f21(c76, X212))) | (~p59(f29(c73, f31(f33(c74, X211), X212)), c72))) | (~p59(f29(c73, f31(f33(c74, X209), X210)), c72))) <=> ((~p59(f29(c73, f31(f33(c74, X209), X210)), c72)) | (~p59(f29(c73, f31(f33(c74, X211), X212)), c72)) | (~p60(f25(c75, X209), f21(c76, X212)))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(34,plain,
% 0.18/0.39 (![X212: $i, X210: $i, X211: $i, X209: $i] : (((~p60(f25(c75, X209), f21(c76, X212))) | (~p59(f29(c73, f31(f33(c74, X211), X212)), c72))) | (~p59(f29(c73, f31(f33(c74, X209), X210)), c72))) <=> ![X212: $i, X210: $i, X211: $i, X209: $i] : ((~p59(f29(c73, f31(f33(c74, X209), X210)), c72)) | (~p59(f29(c73, f31(f33(c74, X211), X212)), c72)) | (~p60(f25(c75, X209), f21(c76, X212))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[33])).
% 0.18/0.40 tff(35,axiom,(![X212: $i, X210: $i, X211: $i, X209: $i] : (((~p60(f25(c75, X209), f21(c76, X212))) | (~p59(f29(c73, f31(f33(c74, X211), X212)), c72))) | (~p59(f29(c73, f31(f33(c74, X209), X210)), c72)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_p60_107')).
% 0.18/0.40 tff(36,plain,
% 0.18/0.40 (![X212: $i, X210: $i, X211: $i, X209: $i] : ((~p59(f29(c73, f31(f33(c74, X209), X210)), c72)) | (~p59(f29(c73, f31(f33(c74, X211), X212)), c72)) | (~p60(f25(c75, X209), f21(c76, X212))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.18/0.40 tff(37,plain,
% 0.18/0.40 (![X212: $i, X210: $i, X211: $i, X209: $i] : ((~p59(f29(c73, f31(f33(c74, X209), X210)), c72)) | (~p59(f29(c73, f31(f33(c74, X211), X212)), c72)) | (~p60(f25(c75, X209), f21(c76, X212))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.18/0.40 tff(38,plain,(
% 0.18/0.40 ![X212: $i, X210: $i, X211: $i, X209: $i] : ((~p59(f29(c73, f31(f33(c74, X209), X210)), c72)) | (~p59(f29(c73, f31(f33(c74, X211), X212)), c72)) | (~p60(f25(c75, X209), f21(c76, X212))))),
% 0.18/0.40 inference(skolemize,[status(sab)],[37])).
% 0.18/0.40 tff(39,plain,
% 0.18/0.40 (![X212: $i, X210: $i, X211: $i, X209: $i] : ((~p59(f29(c73, f31(f33(c74, X209), X210)), c72)) | (~p59(f29(c73, f31(f33(c74, X211), X212)), c72)) | (~p60(f25(c75, X209), f21(c76, X212))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.18/0.40 tff(40,plain,
% 0.18/0.40 (p59(f29(c73, f31(f33(c74, c77), c78)), c72) <=> p59(f29(c73, f31(f33(c74, c77), c78)), c72)),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(41,axiom,(p59(f29(c73, f31(f33(c74, c77), c78)), c72)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p59_44')).
% 0.18/0.40 tff(42,plain,
% 0.18/0.40 (p59(f29(c73, f31(f33(c74, c77), c78)), c72)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.18/0.40 tff(43,plain,
% 0.18/0.40 (((~![X212: $i, X210: $i, X211: $i, X209: $i] : ((~p59(f29(c73, f31(f33(c74, X209), X210)), c72)) | (~p59(f29(c73, f31(f33(c74, X211), X212)), c72)) | (~p60(f25(c75, X209), f21(c76, X212))))) | ((~p59(f29(c73, f31(f33(c74, c77), c78)), c72)) | (~p60(f25(c75, c77), f21(c76, c78))))) <=> ((~![X212: $i, X210: $i, X211: $i, X209: $i] : ((~p59(f29(c73, f31(f33(c74, X209), X210)), c72)) | (~p59(f29(c73, f31(f33(c74, X211), X212)), c72)) | (~p60(f25(c75, X209), f21(c76, X212))))) | (~p59(f29(c73, f31(f33(c74, c77), c78)), c72)) | (~p60(f25(c75, c77), f21(c76, c78))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(44,plain,
% 0.18/0.40 (((~p59(f29(c73, f31(f33(c74, c77), c78)), c72)) | (~p59(f29(c73, f31(f33(c74, c77), c78)), c72)) | (~p60(f25(c75, c77), f21(c76, c78)))) <=> ((~p59(f29(c73, f31(f33(c74, c77), c78)), c72)) | (~p60(f25(c75, c77), f21(c76, c78))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(45,plain,
% 0.18/0.40 (((~![X212: $i, X210: $i, X211: $i, X209: $i] : ((~p59(f29(c73, f31(f33(c74, X209), X210)), c72)) | (~p59(f29(c73, f31(f33(c74, X211), X212)), c72)) | (~p60(f25(c75, X209), f21(c76, X212))))) | ((~p59(f29(c73, f31(f33(c74, c77), c78)), c72)) | (~p59(f29(c73, f31(f33(c74, c77), c78)), c72)) | (~p60(f25(c75, c77), f21(c76, c78))))) <=> ((~![X212: $i, X210: $i, X211: $i, X209: $i] : ((~p59(f29(c73, f31(f33(c74, X209), X210)), c72)) | (~p59(f29(c73, f31(f33(c74, X211), X212)), c72)) | (~p60(f25(c75, X209), f21(c76, X212))))) | ((~p59(f29(c73, f31(f33(c74, c77), c78)), c72)) | (~p60(f25(c75, c77), f21(c76, c78)))))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[44])).
% 0.18/0.40 tff(46,plain,
% 0.18/0.40 (((~![X212: $i, X210: $i, X211: $i, X209: $i] : ((~p59(f29(c73, f31(f33(c74, X209), X210)), c72)) | (~p59(f29(c73, f31(f33(c74, X211), X212)), c72)) | (~p60(f25(c75, X209), f21(c76, X212))))) | ((~p59(f29(c73, f31(f33(c74, c77), c78)), c72)) | (~p59(f29(c73, f31(f33(c74, c77), c78)), c72)) | (~p60(f25(c75, c77), f21(c76, c78))))) <=> ((~![X212: $i, X210: $i, X211: $i, X209: $i] : ((~p59(f29(c73, f31(f33(c74, X209), X210)), c72)) | (~p59(f29(c73, f31(f33(c74, X211), X212)), c72)) | (~p60(f25(c75, X209), f21(c76, X212))))) | (~p59(f29(c73, f31(f33(c74, c77), c78)), c72)) | (~p60(f25(c75, c77), f21(c76, c78))))),
% 0.18/0.40 inference(transitivity,[status(thm)],[45, 43])).
% 0.18/0.40 tff(47,plain,
% 0.18/0.40 ((~![X212: $i, X210: $i, X211: $i, X209: $i] : ((~p59(f29(c73, f31(f33(c74, X209), X210)), c72)) | (~p59(f29(c73, f31(f33(c74, X211), X212)), c72)) | (~p60(f25(c75, X209), f21(c76, X212))))) | ((~p59(f29(c73, f31(f33(c74, c77), c78)), c72)) | (~p59(f29(c73, f31(f33(c74, c77), c78)), c72)) | (~p60(f25(c75, c77), f21(c76, c78))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(48,plain,
% 0.18/0.40 ((~![X212: $i, X210: $i, X211: $i, X209: $i] : ((~p59(f29(c73, f31(f33(c74, X209), X210)), c72)) | (~p59(f29(c73, f31(f33(c74, X211), X212)), c72)) | (~p60(f25(c75, X209), f21(c76, X212))))) | (~p59(f29(c73, f31(f33(c74, c77), c78)), c72)) | (~p60(f25(c75, c77), f21(c76, c78)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.18/0.40 tff(49,plain,
% 0.18/0.40 (~p60(f25(c75, c77), f21(c76, c78))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[48, 42, 39])).
% 0.18/0.40 tff(50,assumption,(~p18(c76, c76)), introduced(assumption)).
% 0.18/0.40 tff(51,plain,
% 0.18/0.40 (^[X24: $i] : refl(p18(X24, X24) <=> p18(X24, X24))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(52,plain,
% 0.18/0.40 (![X24: $i] : p18(X24, X24) <=> ![X24: $i] : p18(X24, X24)),
% 0.18/0.40 inference(quant_intro,[status(thm)],[51])).
% 0.18/0.40 tff(53,plain,
% 0.18/0.40 (![X24: $i] : p18(X24, X24) <=> ![X24: $i] : p18(X24, X24)),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(54,axiom,(![X24: $i] : p18(X24, X24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p18_32')).
% 0.18/0.40 tff(55,plain,
% 0.18/0.40 (![X24: $i] : p18(X24, X24)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.18/0.40 tff(56,plain,(
% 0.18/0.40 ![X24: $i] : p18(X24, X24)),
% 0.18/0.40 inference(skolemize,[status(sab)],[55])).
% 0.18/0.40 tff(57,plain,
% 0.18/0.40 (![X24: $i] : p18(X24, X24)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.18/0.40 tff(58,plain,
% 0.18/0.40 ((~![X24: $i] : p18(X24, X24)) | p18(c76, c76)),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(59,plain,
% 0.18/0.40 ($false),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[58, 57, 50])).
% 0.18/0.40 tff(60,plain,(p18(c76, c76)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.40 tff(61,assumption,(~p19(c78, c78)), introduced(assumption)).
% 0.18/0.40 tff(62,plain,
% 0.18/0.40 (^[X27: $i] : refl(p19(X27, X27) <=> p19(X27, X27))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(63,plain,
% 0.18/0.40 (![X27: $i] : p19(X27, X27) <=> ![X27: $i] : p19(X27, X27)),
% 0.18/0.40 inference(quant_intro,[status(thm)],[62])).
% 0.18/0.40 tff(64,plain,
% 0.18/0.40 (![X27: $i] : p19(X27, X27) <=> ![X27: $i] : p19(X27, X27)),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(65,axiom,(![X27: $i] : p19(X27, X27)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p19_31')).
% 0.18/0.40 tff(66,plain,
% 0.18/0.40 (![X27: $i] : p19(X27, X27)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.18/0.40 tff(67,plain,(
% 0.18/0.40 ![X27: $i] : p19(X27, X27)),
% 0.18/0.40 inference(skolemize,[status(sab)],[66])).
% 0.18/0.40 tff(68,plain,
% 0.18/0.40 (![X27: $i] : p19(X27, X27)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.18/0.40 tff(69,plain,
% 0.18/0.40 ((~![X27: $i] : p19(X27, X27)) | p19(c78, c78)),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(70,plain,
% 0.18/0.40 ($false),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[69, 68, 61])).
% 0.18/0.40 tff(71,plain,(p19(c78, c78)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.40 tff(72,plain,
% 0.18/0.40 (^[X53: $i, X52: $i, X51: $i, X54: $i] : refl(((~p19(X52, X54)) | (~p18(X51, X53)) | p20(f21(X51, X52), f21(X53, X54))) <=> ((~p19(X52, X54)) | (~p18(X51, X53)) | p20(f21(X51, X52), f21(X53, X54))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(73,plain,
% 0.18/0.40 (![X53: $i, X52: $i, X51: $i, X54: $i] : ((~p19(X52, X54)) | (~p18(X51, X53)) | p20(f21(X51, X52), f21(X53, X54))) <=> ![X53: $i, X52: $i, X51: $i, X54: $i] : ((~p19(X52, X54)) | (~p18(X51, X53)) | p20(f21(X51, X52), f21(X53, X54)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[72])).
% 0.18/0.40 tff(74,plain,
% 0.18/0.40 (![X53: $i, X52: $i, X51: $i, X54: $i] : ((~p19(X52, X54)) | (~p18(X51, X53)) | p20(f21(X51, X52), f21(X53, X54))) <=> ![X53: $i, X52: $i, X51: $i, X54: $i] : ((~p19(X52, X54)) | (~p18(X51, X53)) | p20(f21(X51, X52), f21(X53, X54)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(75,plain,
% 0.18/0.40 (^[X53: $i, X52: $i, X51: $i, X54: $i] : trans(monotonicity(rewrite((p20(f21(X51, X52), f21(X53, X54)) | (~p18(X51, X53))) <=> ((~p18(X51, X53)) | p20(f21(X51, X52), f21(X53, X54)))), (((p20(f21(X51, X52), f21(X53, X54)) | (~p18(X51, X53))) | (~p19(X52, X54))) <=> (((~p18(X51, X53)) | p20(f21(X51, X52), f21(X53, X54))) | (~p19(X52, X54))))), rewrite((((~p18(X51, X53)) | p20(f21(X51, X52), f21(X53, X54))) | (~p19(X52, X54))) <=> ((~p19(X52, X54)) | (~p18(X51, X53)) | p20(f21(X51, X52), f21(X53, X54)))), (((p20(f21(X51, X52), f21(X53, X54)) | (~p18(X51, X53))) | (~p19(X52, X54))) <=> ((~p19(X52, X54)) | (~p18(X51, X53)) | p20(f21(X51, X52), f21(X53, X54)))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(76,plain,
% 0.18/0.40 (![X53: $i, X52: $i, X51: $i, X54: $i] : ((p20(f21(X51, X52), f21(X53, X54)) | (~p18(X51, X53))) | (~p19(X52, X54))) <=> ![X53: $i, X52: $i, X51: $i, X54: $i] : ((~p19(X52, X54)) | (~p18(X51, X53)) | p20(f21(X51, X52), f21(X53, X54)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[75])).
% 0.18/0.40 tff(77,axiom,(![X53: $i, X52: $i, X51: $i, X54: $i] : ((p20(f21(X51, X52), f21(X53, X54)) | (~p18(X51, X53))) | (~p19(X52, X54)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p20_92')).
% 0.18/0.40 tff(78,plain,
% 0.18/0.40 (![X53: $i, X52: $i, X51: $i, X54: $i] : ((~p19(X52, X54)) | (~p18(X51, X53)) | p20(f21(X51, X52), f21(X53, X54)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.18/0.40 tff(79,plain,
% 0.18/0.40 (![X53: $i, X52: $i, X51: $i, X54: $i] : ((~p19(X52, X54)) | (~p18(X51, X53)) | p20(f21(X51, X52), f21(X53, X54)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.18/0.40 tff(80,plain,(
% 0.18/0.40 ![X53: $i, X52: $i, X51: $i, X54: $i] : ((~p19(X52, X54)) | (~p18(X51, X53)) | p20(f21(X51, X52), f21(X53, X54)))),
% 0.18/0.40 inference(skolemize,[status(sab)],[79])).
% 0.18/0.40 tff(81,plain,
% 0.18/0.40 (![X53: $i, X52: $i, X51: $i, X54: $i] : ((~p19(X52, X54)) | (~p18(X51, X53)) | p20(f21(X51, X52), f21(X53, X54)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.18/0.40 tff(82,plain,
% 0.18/0.40 (((~![X53: $i, X52: $i, X51: $i, X54: $i] : ((~p19(X52, X54)) | (~p18(X51, X53)) | p20(f21(X51, X52), f21(X53, X54)))) | ((~p19(c78, c78)) | (~p18(c76, c76)) | p20(f21(c76, c78), f21(c76, c78)))) <=> ((~![X53: $i, X52: $i, X51: $i, X54: $i] : ((~p19(X52, X54)) | (~p18(X51, X53)) | p20(f21(X51, X52), f21(X53, X54)))) | (~p19(c78, c78)) | (~p18(c76, c76)) | p20(f21(c76, c78), f21(c76, c78)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(83,plain,
% 0.18/0.40 ((~![X53: $i, X52: $i, X51: $i, X54: $i] : ((~p19(X52, X54)) | (~p18(X51, X53)) | p20(f21(X51, X52), f21(X53, X54)))) | ((~p19(c78, c78)) | (~p18(c76, c76)) | p20(f21(c76, c78), f21(c76, c78)))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(84,plain,
% 0.18/0.40 ((~![X53: $i, X52: $i, X51: $i, X54: $i] : ((~p19(X52, X54)) | (~p18(X51, X53)) | p20(f21(X51, X52), f21(X53, X54)))) | (~p19(c78, c78)) | (~p18(c76, c76)) | p20(f21(c76, c78), f21(c76, c78))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.18/0.40 tff(85,plain,
% 0.18/0.40 ((~p19(c78, c78)) | (~p18(c76, c76)) | p20(f21(c76, c78), f21(c76, c78))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[84, 81])).
% 0.18/0.40 tff(86,plain,
% 0.18/0.40 ((~p18(c76, c76)) | p20(f21(c76, c78), f21(c76, c78))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[85, 71])).
% 0.18/0.40 tff(87,plain,
% 0.18/0.40 (p20(f21(c76, c78), f21(c76, c78))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[86, 60])).
% 0.18/0.40 tff(88,plain,
% 0.18/0.40 (^[X188: $i, X189: $i, X186: $i, X187: $i] : refl(((~p20(X188, X187)) | (~p60(X189, X188)) | (~p24(X189, X186)) | p60(X186, X187)) <=> ((~p20(X188, X187)) | (~p60(X189, X188)) | (~p24(X189, X186)) | p60(X186, X187)))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(89,plain,
% 0.18/0.40 (![X188: $i, X189: $i, X186: $i, X187: $i] : ((~p20(X188, X187)) | (~p60(X189, X188)) | (~p24(X189, X186)) | p60(X186, X187)) <=> ![X188: $i, X189: $i, X186: $i, X187: $i] : ((~p20(X188, X187)) | (~p60(X189, X188)) | (~p24(X189, X186)) | p60(X186, X187))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[88])).
% 0.18/0.40 tff(90,plain,
% 0.18/0.40 (![X188: $i, X189: $i, X186: $i, X187: $i] : ((~p20(X188, X187)) | (~p60(X189, X188)) | (~p24(X189, X186)) | p60(X186, X187)) <=> ![X188: $i, X189: $i, X186: $i, X187: $i] : ((~p20(X188, X187)) | (~p60(X189, X188)) | (~p24(X189, X186)) | p60(X186, X187))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(91,plain,
% 0.18/0.40 (^[X188: $i, X189: $i, X186: $i, X187: $i] : trans(monotonicity(trans(monotonicity(rewrite((p60(X186, X187) | (~p24(X189, X186))) <=> ((~p24(X189, X186)) | p60(X186, X187))), (((p60(X186, X187) | (~p24(X189, X186))) | (~p60(X189, X188))) <=> (((~p24(X189, X186)) | p60(X186, X187)) | (~p60(X189, X188))))), rewrite((((~p24(X189, X186)) | p60(X186, X187)) | (~p60(X189, X188))) <=> ((~p60(X189, X188)) | (~p24(X189, X186)) | p60(X186, X187))), (((p60(X186, X187) | (~p24(X189, X186))) | (~p60(X189, X188))) <=> ((~p60(X189, X188)) | (~p24(X189, X186)) | p60(X186, X187)))), ((((p60(X186, X187) | (~p24(X189, X186))) | (~p60(X189, X188))) | (~p20(X188, X187))) <=> (((~p60(X189, X188)) | (~p24(X189, X186)) | p60(X186, X187)) | (~p20(X188, X187))))), rewrite((((~p60(X189, X188)) | (~p24(X189, X186)) | p60(X186, X187)) | (~p20(X188, X187))) <=> ((~p20(X188, X187)) | (~p60(X189, X188)) | (~p24(X189, X186)) | p60(X186, X187))), ((((p60(X186, X187) | (~p24(X189, X186))) | (~p60(X189, X188))) | (~p20(X188, X187))) <=> ((~p20(X188, X187)) | (~p60(X189, X188)) | (~p24(X189, X186)) | p60(X186, X187))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(92,plain,
% 0.18/0.40 (![X188: $i, X189: $i, X186: $i, X187: $i] : (((p60(X186, X187) | (~p24(X189, X186))) | (~p60(X189, X188))) | (~p20(X188, X187))) <=> ![X188: $i, X189: $i, X186: $i, X187: $i] : ((~p20(X188, X187)) | (~p60(X189, X188)) | (~p24(X189, X186)) | p60(X186, X187))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[91])).
% 0.18/0.40 tff(93,axiom,(![X188: $i, X189: $i, X186: $i, X187: $i] : (((p60(X186, X187) | (~p24(X189, X186))) | (~p60(X189, X188))) | (~p20(X188, X187)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p60_84')).
% 0.18/0.40 tff(94,plain,
% 0.18/0.40 (![X188: $i, X189: $i, X186: $i, X187: $i] : ((~p20(X188, X187)) | (~p60(X189, X188)) | (~p24(X189, X186)) | p60(X186, X187))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.18/0.40 tff(95,plain,
% 0.18/0.40 (![X188: $i, X189: $i, X186: $i, X187: $i] : ((~p20(X188, X187)) | (~p60(X189, X188)) | (~p24(X189, X186)) | p60(X186, X187))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[94, 90])).
% 0.18/0.40 tff(96,plain,(
% 0.18/0.40 ![X188: $i, X189: $i, X186: $i, X187: $i] : ((~p20(X188, X187)) | (~p60(X189, X188)) | (~p24(X189, X186)) | p60(X186, X187))),
% 0.18/0.40 inference(skolemize,[status(sab)],[95])).
% 0.18/0.40 tff(97,plain,
% 0.18/0.40 (![X188: $i, X189: $i, X186: $i, X187: $i] : ((~p20(X188, X187)) | (~p60(X189, X188)) | (~p24(X189, X186)) | p60(X186, X187))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[96, 89])).
% 0.18/0.40 tff(98,plain,
% 0.18/0.40 (p60(f25(c75, c79), f21(c76, c78)) <=> p60(f25(c75, c79), f21(c76, c78))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(99,axiom,(p60(f25(c75, c79), f21(c76, c78))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p60_42')).
% 0.18/0.40 tff(100,plain,
% 0.18/0.40 (p60(f25(c75, c79), f21(c76, c78))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.18/0.40 tff(101,plain,
% 0.18/0.40 (((~![X188: $i, X189: $i, X186: $i, X187: $i] : ((~p20(X188, X187)) | (~p60(X189, X188)) | (~p24(X189, X186)) | p60(X186, X187))) | (p60(f25(c75, c77), f21(c76, c78)) | (~p20(f21(c76, c78), f21(c76, c78))) | (~p60(f25(c75, c79), f21(c76, c78))) | (~p24(f25(c75, c79), f25(c75, c77))))) <=> ((~![X188: $i, X189: $i, X186: $i, X187: $i] : ((~p20(X188, X187)) | (~p60(X189, X188)) | (~p24(X189, X186)) | p60(X186, X187))) | p60(f25(c75, c77), f21(c76, c78)) | (~p20(f21(c76, c78), f21(c76, c78))) | (~p60(f25(c75, c79), f21(c76, c78))) | (~p24(f25(c75, c79), f25(c75, c77))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(102,plain,
% 0.18/0.40 (((~p20(f21(c76, c78), f21(c76, c78))) | (~p60(f25(c75, c79), f21(c76, c78))) | (~p24(f25(c75, c79), f25(c75, c77))) | p60(f25(c75, c77), f21(c76, c78))) <=> (p60(f25(c75, c77), f21(c76, c78)) | (~p20(f21(c76, c78), f21(c76, c78))) | (~p60(f25(c75, c79), f21(c76, c78))) | (~p24(f25(c75, c79), f25(c75, c77))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(103,plain,
% 0.18/0.41 (((~![X188: $i, X189: $i, X186: $i, X187: $i] : ((~p20(X188, X187)) | (~p60(X189, X188)) | (~p24(X189, X186)) | p60(X186, X187))) | ((~p20(f21(c76, c78), f21(c76, c78))) | (~p60(f25(c75, c79), f21(c76, c78))) | (~p24(f25(c75, c79), f25(c75, c77))) | p60(f25(c75, c77), f21(c76, c78)))) <=> ((~![X188: $i, X189: $i, X186: $i, X187: $i] : ((~p20(X188, X187)) | (~p60(X189, X188)) | (~p24(X189, X186)) | p60(X186, X187))) | (p60(f25(c75, c77), f21(c76, c78)) | (~p20(f21(c76, c78), f21(c76, c78))) | (~p60(f25(c75, c79), f21(c76, c78))) | (~p24(f25(c75, c79), f25(c75, c77)))))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[102])).
% 0.18/0.41 tff(104,plain,
% 0.18/0.41 (((~![X188: $i, X189: $i, X186: $i, X187: $i] : ((~p20(X188, X187)) | (~p60(X189, X188)) | (~p24(X189, X186)) | p60(X186, X187))) | ((~p20(f21(c76, c78), f21(c76, c78))) | (~p60(f25(c75, c79), f21(c76, c78))) | (~p24(f25(c75, c79), f25(c75, c77))) | p60(f25(c75, c77), f21(c76, c78)))) <=> ((~![X188: $i, X189: $i, X186: $i, X187: $i] : ((~p20(X188, X187)) | (~p60(X189, X188)) | (~p24(X189, X186)) | p60(X186, X187))) | p60(f25(c75, c77), f21(c76, c78)) | (~p20(f21(c76, c78), f21(c76, c78))) | (~p60(f25(c75, c79), f21(c76, c78))) | (~p24(f25(c75, c79), f25(c75, c77))))),
% 0.18/0.41 inference(transitivity,[status(thm)],[103, 101])).
% 0.18/0.41 tff(105,plain,
% 0.18/0.41 ((~![X188: $i, X189: $i, X186: $i, X187: $i] : ((~p20(X188, X187)) | (~p60(X189, X188)) | (~p24(X189, X186)) | p60(X186, X187))) | ((~p20(f21(c76, c78), f21(c76, c78))) | (~p60(f25(c75, c79), f21(c76, c78))) | (~p24(f25(c75, c79), f25(c75, c77))) | p60(f25(c75, c77), f21(c76, c78)))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(106,plain,
% 0.18/0.41 ((~![X188: $i, X189: $i, X186: $i, X187: $i] : ((~p20(X188, X187)) | (~p60(X189, X188)) | (~p24(X189, X186)) | p60(X186, X187))) | p60(f25(c75, c77), f21(c76, c78)) | (~p20(f21(c76, c78), f21(c76, c78))) | (~p60(f25(c75, c79), f21(c76, c78))) | (~p24(f25(c75, c79), f25(c75, c77)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.18/0.41 tff(107,plain,
% 0.18/0.41 ($false),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[106, 100, 97, 87, 49, 29])).
% 0.18/0.41 % SZS output end Proof
% 0.18/0.41 % E exiting
%------------------------------------------------------------------------------