%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN672-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:39:48 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN672-1 : TPTP v9.0.0. Released v2.5.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n007.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 12:41:35 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.38 % SZS status Unsatisfiable
% 0.19/0.38 % SZS output start Proof
% 0.19/0.38 tff(p9_type, type, (
% 0.19/0.38 p9: ( $i * $i ) > $o)).
% 0.19/0.38 tff(f10_type, type, (
% 0.19/0.38 f10: ( $i * $i ) > $i)).
% 0.19/0.38 tff(f14_type, type, (
% 0.19/0.38 f14: ( $i * $i ) > $i)).
% 0.19/0.38 tff(c39_type, type, (
% 0.19/0.38 c39: $i)).
% 0.19/0.38 tff(c35_type, type, (
% 0.19/0.38 c35: $i)).
% 0.19/0.38 tff(f12_type, type, (
% 0.19/0.38 f12: ( $i * $i ) > $i)).
% 0.19/0.38 tff(c33_type, type, (
% 0.19/0.38 c33: $i)).
% 0.19/0.38 tff(c32_type, type, (
% 0.19/0.38 c32: $i)).
% 0.19/0.38 tff(f4_type, type, (
% 0.19/0.38 f4: ( $i * $i ) > $i)).
% 0.19/0.38 tff(c38_type, type, (
% 0.19/0.38 c38: $i)).
% 0.19/0.38 tff(f7_type, type, (
% 0.19/0.38 f7: ( $i * $i ) > $i)).
% 0.19/0.38 tff(c34_type, type, (
% 0.19/0.38 c34: $i)).
% 0.19/0.38 tff(p8_type, type, (
% 0.19/0.38 p8: ( $i * $i ) > $o)).
% 0.19/0.38 tff(p3_type, type, (
% 0.19/0.38 p3: ( $i * $i ) > $o)).
% 0.19/0.38 tff(p30_type, type, (
% 0.19/0.38 p30: ( $i * $i ) > $o)).
% 0.19/0.38 tff(c40_type, type, (
% 0.19/0.38 c40: $i)).
% 0.19/0.38 tff(p31_type, type, (
% 0.19/0.38 p31: ( $i * $i ) > $o)).
% 0.19/0.38 tff(f17_type, type, (
% 0.19/0.38 f17: ( $i * $i ) > $i)).
% 0.19/0.38 tff(c37_type, type, (
% 0.19/0.38 c37: $i)).
% 0.19/0.38 tff(f20_type, type, (
% 0.19/0.38 f20: ( $i * $i ) > $i)).
% 0.19/0.38 tff(c36_type, type, (
% 0.19/0.38 c36: $i)).
% 0.19/0.38 tff(p2_type, type, (
% 0.19/0.38 p2: ( $i * $i ) > $o)).
% 0.19/0.38 tff(1,assumption,(~p8(f12(c32, c33), f12(c32, c33))), introduced(assumption)).
% 0.19/0.38 tff(2,plain,
% 0.19/0.38 (^[X98: $i] : refl(p8(X98, X98) <=> p8(X98, X98))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(3,plain,
% 0.19/0.38 (![X98: $i] : p8(X98, X98) <=> ![X98: $i] : p8(X98, X98)),
% 0.19/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.38 tff(4,plain,
% 0.19/0.38 (![X98: $i] : p8(X98, X98) <=> ![X98: $i] : p8(X98, X98)),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(5,axiom,(![X98: $i] : p8(X98, X98)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p8_3')).
% 0.19/0.38 tff(6,plain,
% 0.19/0.38 (![X98: $i] : p8(X98, X98)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.19/0.38 tff(7,plain,(
% 0.19/0.38 ![X98: $i] : p8(X98, X98)),
% 0.19/0.38 inference(skolemize,[status(sab)],[6])).
% 0.19/0.38 tff(8,plain,
% 0.19/0.38 (![X98: $i] : p8(X98, X98)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.38 tff(9,plain,
% 0.19/0.38 ((~![X98: $i] : p8(X98, X98)) | p8(f12(c32, c33), f12(c32, c33))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(10,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.19/0.38 tff(11,plain,(p8(f12(c32, c33), f12(c32, c33))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.38 tff(12,plain,
% 0.19/0.38 (^[X77: $i, X78: $i] : refl(p3(f4(f7(c34, X77), f14(c38, X78)), f14(X77, X78)) <=> p3(f4(f7(c34, X77), f14(c38, X78)), f14(X77, X78)))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(13,plain,
% 0.19/0.38 (![X77: $i, X78: $i] : p3(f4(f7(c34, X77), f14(c38, X78)), f14(X77, X78)) <=> ![X77: $i, X78: $i] : p3(f4(f7(c34, X77), f14(c38, X78)), f14(X77, X78))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[12])).
% 0.19/0.38 tff(14,plain,
% 0.19/0.38 (![X77: $i, X78: $i] : p3(f4(f7(c34, X77), f14(c38, X78)), f14(X77, X78)) <=> ![X77: $i, X78: $i] : p3(f4(f7(c34, X77), f14(c38, X78)), f14(X77, X78))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(15,axiom,(![X77: $i, X78: $i] : p3(f4(f7(c34, X77), f14(c38, X78)), f14(X77, X78))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p3_37')).
% 0.19/0.38 tff(16,plain,
% 0.19/0.38 (![X77: $i, X78: $i] : p3(f4(f7(c34, X77), f14(c38, X78)), f14(X77, X78))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.19/0.38 tff(17,plain,(
% 0.19/0.38 ![X77: $i, X78: $i] : p3(f4(f7(c34, X77), f14(c38, X78)), f14(X77, X78))),
% 0.19/0.38 inference(skolemize,[status(sab)],[16])).
% 0.19/0.38 tff(18,plain,
% 0.19/0.38 (![X77: $i, X78: $i] : p3(f4(f7(c34, X77), f14(c38, X78)), f14(X77, X78))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.19/0.38 tff(19,plain,
% 0.19/0.38 ((~![X77: $i, X78: $i] : p3(f4(f7(c34, X77), f14(c38, X78)), f14(X77, X78))) | p3(f4(f7(c34, c35), f14(c38, c39)), f14(c35, c39))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(20,plain,
% 0.19/0.38 (p3(f4(f7(c34, c35), f14(c38, c39)), f14(c35, c39))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.19/0.38 tff(21,plain,
% 0.19/0.38 (^[X110: $i, X111: $i, X109: $i, X108: $i] : refl(((~p8(X108, X110)) | (~p3(X109, X111)) | p9(f10(X108, X109), f10(X110, X111))) <=> ((~p8(X108, X110)) | (~p3(X109, X111)) | p9(f10(X108, X109), f10(X110, X111))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(22,plain,
% 0.19/0.38 (![X110: $i, X111: $i, X109: $i, X108: $i] : ((~p8(X108, X110)) | (~p3(X109, X111)) | p9(f10(X108, X109), f10(X110, X111))) <=> ![X110: $i, X111: $i, X109: $i, X108: $i] : ((~p8(X108, X110)) | (~p3(X109, X111)) | p9(f10(X108, X109), f10(X110, X111)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[21])).
% 0.19/0.38 tff(23,plain,
% 0.19/0.38 (![X110: $i, X111: $i, X109: $i, X108: $i] : ((~p8(X108, X110)) | (~p3(X109, X111)) | p9(f10(X108, X109), f10(X110, X111))) <=> ![X110: $i, X111: $i, X109: $i, X108: $i] : ((~p8(X108, X110)) | (~p3(X109, X111)) | p9(f10(X108, X109), f10(X110, X111)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(24,plain,
% 0.19/0.38 (^[X110: $i, X111: $i, X109: $i, X108: $i] : trans(monotonicity(rewrite((p9(f10(X108, X109), f10(X110, X111)) | (~p3(X109, X111))) <=> ((~p3(X109, X111)) | p9(f10(X108, X109), f10(X110, X111)))), (((p9(f10(X108, X109), f10(X110, X111)) | (~p3(X109, X111))) | (~p8(X108, X110))) <=> (((~p3(X109, X111)) | p9(f10(X108, X109), f10(X110, X111))) | (~p8(X108, X110))))), rewrite((((~p3(X109, X111)) | p9(f10(X108, X109), f10(X110, X111))) | (~p8(X108, X110))) <=> ((~p8(X108, X110)) | (~p3(X109, X111)) | p9(f10(X108, X109), f10(X110, X111)))), (((p9(f10(X108, X109), f10(X110, X111)) | (~p3(X109, X111))) | (~p8(X108, X110))) <=> ((~p8(X108, X110)) | (~p3(X109, X111)) | p9(f10(X108, X109), f10(X110, X111)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(25,plain,
% 0.19/0.38 (![X110: $i, X111: $i, X109: $i, X108: $i] : ((p9(f10(X108, X109), f10(X110, X111)) | (~p3(X109, X111))) | (~p8(X108, X110))) <=> ![X110: $i, X111: $i, X109: $i, X108: $i] : ((~p8(X108, X110)) | (~p3(X109, X111)) | p9(f10(X108, X109), f10(X110, X111)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[24])).
% 0.19/0.38 tff(26,axiom,(![X110: $i, X111: $i, X109: $i, X108: $i] : ((p9(f10(X108, X109), f10(X110, X111)) | (~p3(X109, X111))) | (~p8(X108, X110)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p9_42')).
% 0.19/0.38 tff(27,plain,
% 0.19/0.38 (![X110: $i, X111: $i, X109: $i, X108: $i] : ((~p8(X108, X110)) | (~p3(X109, X111)) | p9(f10(X108, X109), f10(X110, X111)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.19/0.38 tff(28,plain,
% 0.19/0.38 (![X110: $i, X111: $i, X109: $i, X108: $i] : ((~p8(X108, X110)) | (~p3(X109, X111)) | p9(f10(X108, X109), f10(X110, X111)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.19/0.38 tff(29,plain,(
% 0.19/0.38 ![X110: $i, X111: $i, X109: $i, X108: $i] : ((~p8(X108, X110)) | (~p3(X109, X111)) | p9(f10(X108, X109), f10(X110, X111)))),
% 0.19/0.38 inference(skolemize,[status(sab)],[28])).
% 0.19/0.38 tff(30,plain,
% 0.19/0.38 (![X110: $i, X111: $i, X109: $i, X108: $i] : ((~p8(X108, X110)) | (~p3(X109, X111)) | p9(f10(X108, X109), f10(X110, X111)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.19/0.38 tff(31,plain,
% 0.19/0.38 (((~![X110: $i, X111: $i, X109: $i, X108: $i] : ((~p8(X108, X110)) | (~p3(X109, X111)) | p9(f10(X108, X109), f10(X110, X111)))) | ((~p8(f12(c32, c33), f12(c32, c33))) | (~p3(f4(f7(c34, c35), f14(c38, c39)), f14(c35, c39))) | p9(f10(f12(c32, c33), f4(f7(c34, c35), f14(c38, c39))), f10(f12(c32, c33), f14(c35, c39))))) <=> ((~![X110: $i, X111: $i, X109: $i, X108: $i] : ((~p8(X108, X110)) | (~p3(X109, X111)) | p9(f10(X108, X109), f10(X110, X111)))) | (~p8(f12(c32, c33), f12(c32, c33))) | (~p3(f4(f7(c34, c35), f14(c38, c39)), f14(c35, c39))) | p9(f10(f12(c32, c33), f4(f7(c34, c35), f14(c38, c39))), f10(f12(c32, c33), f14(c35, c39))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(32,plain,
% 0.19/0.38 ((~![X110: $i, X111: $i, X109: $i, X108: $i] : ((~p8(X108, X110)) | (~p3(X109, X111)) | p9(f10(X108, X109), f10(X110, X111)))) | ((~p8(f12(c32, c33), f12(c32, c33))) | (~p3(f4(f7(c34, c35), f14(c38, c39)), f14(c35, c39))) | p9(f10(f12(c32, c33), f4(f7(c34, c35), f14(c38, c39))), f10(f12(c32, c33), f14(c35, c39))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(33,plain,
% 0.19/0.38 ((~![X110: $i, X111: $i, X109: $i, X108: $i] : ((~p8(X108, X110)) | (~p3(X109, X111)) | p9(f10(X108, X109), f10(X110, X111)))) | (~p8(f12(c32, c33), f12(c32, c33))) | (~p3(f4(f7(c34, c35), f14(c38, c39)), f14(c35, c39))) | p9(f10(f12(c32, c33), f4(f7(c34, c35), f14(c38, c39))), f10(f12(c32, c33), f14(c35, c39)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.19/0.38 tff(34,plain,
% 0.19/0.38 ((~p8(f12(c32, c33), f12(c32, c33))) | p9(f10(f12(c32, c33), f4(f7(c34, c35), f14(c38, c39))), f10(f12(c32, c33), f14(c35, c39)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[33, 30, 20])).
% 0.19/0.39 tff(35,plain,
% 0.19/0.39 (p9(f10(f12(c32, c33), f4(f7(c34, c35), f14(c38, c39))), f10(f12(c32, c33), f14(c35, c39)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[34, 11])).
% 0.19/0.39 tff(36,plain,
% 0.19/0.39 (^[X60: $i, X61: $i] : refl(((~p31(f20(c36, X61), f17(c37, X60))) | p30(f10(f12(c32, c33), f14(c38, X61)), X60) | p3(X60, f14(c38, X61))) <=> ((~p31(f20(c36, X61), f17(c37, X60))) | p30(f10(f12(c32, c33), f14(c38, X61)), X60) | p3(X60, f14(c38, X61))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(37,plain,
% 0.19/0.39 (![X60: $i, X61: $i] : ((~p31(f20(c36, X61), f17(c37, X60))) | p30(f10(f12(c32, c33), f14(c38, X61)), X60) | p3(X60, f14(c38, X61))) <=> ![X60: $i, X61: $i] : ((~p31(f20(c36, X61), f17(c37, X60))) | p30(f10(f12(c32, c33), f14(c38, X61)), X60) | p3(X60, f14(c38, X61)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[36])).
% 0.19/0.39 tff(38,plain,
% 0.19/0.39 (![X60: $i, X61: $i] : ((~p31(f20(c36, X61), f17(c37, X60))) | p30(f10(f12(c32, c33), f14(c38, X61)), X60) | p3(X60, f14(c38, X61))) <=> ![X60: $i, X61: $i] : ((~p31(f20(c36, X61), f17(c37, X60))) | p30(f10(f12(c32, c33), f14(c38, X61)), X60) | p3(X60, f14(c38, X61)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(39,plain,
% 0.19/0.39 (^[X60: $i, X61: $i] : rewrite(((p3(X60, f14(c38, X61)) | p30(f10(f12(c32, c33), f14(c38, X61)), X60)) | (~p31(f20(c36, X61), f17(c37, X60)))) <=> ((~p31(f20(c36, X61), f17(c37, X60))) | p30(f10(f12(c32, c33), f14(c38, X61)), X60) | p3(X60, f14(c38, X61))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(40,plain,
% 0.19/0.39 (![X60: $i, X61: $i] : ((p3(X60, f14(c38, X61)) | p30(f10(f12(c32, c33), f14(c38, X61)), X60)) | (~p31(f20(c36, X61), f17(c37, X60)))) <=> ![X60: $i, X61: $i] : ((~p31(f20(c36, X61), f17(c37, X60))) | p30(f10(f12(c32, c33), f14(c38, X61)), X60) | p3(X60, f14(c38, X61)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[39])).
% 0.19/0.39 tff(41,axiom,(![X60: $i, X61: $i] : ((p3(X60, f14(c38, X61)) | p30(f10(f12(c32, c33), f14(c38, X61)), X60)) | (~p31(f20(c36, X61), f17(c37, X60))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p3_53')).
% 0.19/0.39 tff(42,plain,
% 0.19/0.39 (![X60: $i, X61: $i] : ((~p31(f20(c36, X61), f17(c37, X60))) | p30(f10(f12(c32, c33), f14(c38, X61)), X60) | p3(X60, f14(c38, X61)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.19/0.39 tff(43,plain,
% 0.19/0.39 (![X60: $i, X61: $i] : ((~p31(f20(c36, X61), f17(c37, X60))) | p30(f10(f12(c32, c33), f14(c38, X61)), X60) | p3(X60, f14(c38, X61)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.19/0.39 tff(44,plain,(
% 0.19/0.39 ![X60: $i, X61: $i] : ((~p31(f20(c36, X61), f17(c37, X60))) | p30(f10(f12(c32, c33), f14(c38, X61)), X60) | p3(X60, f14(c38, X61)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[43])).
% 0.19/0.39 tff(45,plain,
% 0.19/0.39 (![X60: $i, X61: $i] : ((~p31(f20(c36, X61), f17(c37, X60))) | p30(f10(f12(c32, c33), f14(c38, X61)), X60) | p3(X60, f14(c38, X61)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.19/0.39 tff(46,plain,
% 0.19/0.39 (p31(f20(c36, c39), f17(c37, c40)) <=> p31(f20(c36, c39), f17(c37, c40))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(47,axiom,(p31(f20(c36, c39), f17(c37, c40))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p31_19')).
% 0.19/0.39 tff(48,plain,
% 0.19/0.39 (p31(f20(c36, c39), f17(c37, c40))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.19/0.39 tff(49,plain,
% 0.19/0.39 ((~p3(c40, f14(c38, c39))) <=> (~p3(c40, f14(c38, c39)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(50,axiom,(~p3(c40, f14(c38, c39))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_p3_18')).
% 0.19/0.39 tff(51,plain,
% 0.19/0.39 (~p3(c40, f14(c38, c39))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.19/0.39 tff(52,plain,
% 0.19/0.39 (((~![X60: $i, X61: $i] : ((~p31(f20(c36, X61), f17(c37, X60))) | p30(f10(f12(c32, c33), f14(c38, X61)), X60) | p3(X60, f14(c38, X61)))) | (p3(c40, f14(c38, c39)) | (~p31(f20(c36, c39), f17(c37, c40))) | p30(f10(f12(c32, c33), f14(c38, c39)), c40))) <=> ((~![X60: $i, X61: $i] : ((~p31(f20(c36, X61), f17(c37, X60))) | p30(f10(f12(c32, c33), f14(c38, X61)), X60) | p3(X60, f14(c38, X61)))) | p3(c40, f14(c38, c39)) | (~p31(f20(c36, c39), f17(c37, c40))) | p30(f10(f12(c32, c33), f14(c38, c39)), c40))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(53,plain,
% 0.19/0.39 (((~p31(f20(c36, c39), f17(c37, c40))) | p30(f10(f12(c32, c33), f14(c38, c39)), c40) | p3(c40, f14(c38, c39))) <=> (p3(c40, f14(c38, c39)) | (~p31(f20(c36, c39), f17(c37, c40))) | p30(f10(f12(c32, c33), f14(c38, c39)), c40))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(54,plain,
% 0.19/0.39 (((~![X60: $i, X61: $i] : ((~p31(f20(c36, X61), f17(c37, X60))) | p30(f10(f12(c32, c33), f14(c38, X61)), X60) | p3(X60, f14(c38, X61)))) | ((~p31(f20(c36, c39), f17(c37, c40))) | p30(f10(f12(c32, c33), f14(c38, c39)), c40) | p3(c40, f14(c38, c39)))) <=> ((~![X60: $i, X61: $i] : ((~p31(f20(c36, X61), f17(c37, X60))) | p30(f10(f12(c32, c33), f14(c38, X61)), X60) | p3(X60, f14(c38, X61)))) | (p3(c40, f14(c38, c39)) | (~p31(f20(c36, c39), f17(c37, c40))) | p30(f10(f12(c32, c33), f14(c38, c39)), c40)))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[53])).
% 0.19/0.39 tff(55,plain,
% 0.19/0.39 (((~![X60: $i, X61: $i] : ((~p31(f20(c36, X61), f17(c37, X60))) | p30(f10(f12(c32, c33), f14(c38, X61)), X60) | p3(X60, f14(c38, X61)))) | ((~p31(f20(c36, c39), f17(c37, c40))) | p30(f10(f12(c32, c33), f14(c38, c39)), c40) | p3(c40, f14(c38, c39)))) <=> ((~![X60: $i, X61: $i] : ((~p31(f20(c36, X61), f17(c37, X60))) | p30(f10(f12(c32, c33), f14(c38, X61)), X60) | p3(X60, f14(c38, X61)))) | p3(c40, f14(c38, c39)) | (~p31(f20(c36, c39), f17(c37, c40))) | p30(f10(f12(c32, c33), f14(c38, c39)), c40))),
% 0.19/0.39 inference(transitivity,[status(thm)],[54, 52])).
% 0.19/0.39 tff(56,plain,
% 0.19/0.39 ((~![X60: $i, X61: $i] : ((~p31(f20(c36, X61), f17(c37, X60))) | p30(f10(f12(c32, c33), f14(c38, X61)), X60) | p3(X60, f14(c38, X61)))) | ((~p31(f20(c36, c39), f17(c37, c40))) | p30(f10(f12(c32, c33), f14(c38, c39)), c40) | p3(c40, f14(c38, c39)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(57,plain,
% 0.19/0.39 ((~![X60: $i, X61: $i] : ((~p31(f20(c36, X61), f17(c37, X60))) | p30(f10(f12(c32, c33), f14(c38, X61)), X60) | p3(X60, f14(c38, X61)))) | p3(c40, f14(c38, c39)) | (~p31(f20(c36, c39), f17(c37, c40))) | p30(f10(f12(c32, c33), f14(c38, c39)), c40)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.19/0.39 tff(58,plain,
% 0.19/0.39 (p30(f10(f12(c32, c33), f14(c38, c39)), c40)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[57, 51, 48, 45])).
% 0.19/0.39 tff(59,plain,
% 0.19/0.39 (^[X87: $i, X86: $i] : refl(((~p30(f10(f12(c32, c33), X86), X87)) | p30(f10(f12(c32, c33), f4(f7(c34, c35), X86)), f4(f7(c34, c35), X87))) <=> ((~p30(f10(f12(c32, c33), X86), X87)) | p30(f10(f12(c32, c33), f4(f7(c34, c35), X86)), f4(f7(c34, c35), X87))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(60,plain,
% 0.19/0.39 (![X87: $i, X86: $i] : ((~p30(f10(f12(c32, c33), X86), X87)) | p30(f10(f12(c32, c33), f4(f7(c34, c35), X86)), f4(f7(c34, c35), X87))) <=> ![X87: $i, X86: $i] : ((~p30(f10(f12(c32, c33), X86), X87)) | p30(f10(f12(c32, c33), f4(f7(c34, c35), X86)), f4(f7(c34, c35), X87)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[59])).
% 0.19/0.39 tff(61,plain,
% 0.19/0.39 (![X87: $i, X86: $i] : ((~p30(f10(f12(c32, c33), X86), X87)) | p30(f10(f12(c32, c33), f4(f7(c34, c35), X86)), f4(f7(c34, c35), X87))) <=> ![X87: $i, X86: $i] : ((~p30(f10(f12(c32, c33), X86), X87)) | p30(f10(f12(c32, c33), f4(f7(c34, c35), X86)), f4(f7(c34, c35), X87)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(62,plain,
% 0.19/0.39 (^[X87: $i, X86: $i] : rewrite((p30(f10(f12(c32, c33), f4(f7(c34, c35), X86)), f4(f7(c34, c35), X87)) | (~p30(f10(f12(c32, c33), X86), X87))) <=> ((~p30(f10(f12(c32, c33), X86), X87)) | p30(f10(f12(c32, c33), f4(f7(c34, c35), X86)), f4(f7(c34, c35), X87))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(63,plain,
% 0.19/0.39 (![X87: $i, X86: $i] : (p30(f10(f12(c32, c33), f4(f7(c34, c35), X86)), f4(f7(c34, c35), X87)) | (~p30(f10(f12(c32, c33), X86), X87))) <=> ![X87: $i, X86: $i] : ((~p30(f10(f12(c32, c33), X86), X87)) | p30(f10(f12(c32, c33), f4(f7(c34, c35), X86)), f4(f7(c34, c35), X87)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[62])).
% 0.19/0.39 tff(64,axiom,(![X87: $i, X86: $i] : (p30(f10(f12(c32, c33), f4(f7(c34, c35), X86)), f4(f7(c34, c35), X87)) | (~p30(f10(f12(c32, c33), X86), X87)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p30_54')).
% 0.19/0.40 tff(65,plain,
% 0.19/0.40 (![X87: $i, X86: $i] : ((~p30(f10(f12(c32, c33), X86), X87)) | p30(f10(f12(c32, c33), f4(f7(c34, c35), X86)), f4(f7(c34, c35), X87)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.19/0.40 tff(66,plain,
% 0.19/0.40 (![X87: $i, X86: $i] : ((~p30(f10(f12(c32, c33), X86), X87)) | p30(f10(f12(c32, c33), f4(f7(c34, c35), X86)), f4(f7(c34, c35), X87)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.19/0.40 tff(67,plain,(
% 0.19/0.40 ![X87: $i, X86: $i] : ((~p30(f10(f12(c32, c33), X86), X87)) | p30(f10(f12(c32, c33), f4(f7(c34, c35), X86)), f4(f7(c34, c35), X87)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[66])).
% 0.19/0.40 tff(68,plain,
% 0.19/0.40 (![X87: $i, X86: $i] : ((~p30(f10(f12(c32, c33), X86), X87)) | p30(f10(f12(c32, c33), f4(f7(c34, c35), X86)), f4(f7(c34, c35), X87)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[67, 60])).
% 0.19/0.40 tff(69,plain,
% 0.19/0.40 (((~![X87: $i, X86: $i] : ((~p30(f10(f12(c32, c33), X86), X87)) | p30(f10(f12(c32, c33), f4(f7(c34, c35), X86)), f4(f7(c34, c35), X87)))) | ((~p30(f10(f12(c32, c33), f14(c38, c39)), c40)) | p30(f10(f12(c32, c33), f4(f7(c34, c35), f14(c38, c39))), f4(f7(c34, c35), c40)))) <=> ((~![X87: $i, X86: $i] : ((~p30(f10(f12(c32, c33), X86), X87)) | p30(f10(f12(c32, c33), f4(f7(c34, c35), X86)), f4(f7(c34, c35), X87)))) | (~p30(f10(f12(c32, c33), f14(c38, c39)), c40)) | p30(f10(f12(c32, c33), f4(f7(c34, c35), f14(c38, c39))), f4(f7(c34, c35), c40)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(70,plain,
% 0.19/0.40 ((~![X87: $i, X86: $i] : ((~p30(f10(f12(c32, c33), X86), X87)) | p30(f10(f12(c32, c33), f4(f7(c34, c35), X86)), f4(f7(c34, c35), X87)))) | ((~p30(f10(f12(c32, c33), f14(c38, c39)), c40)) | p30(f10(f12(c32, c33), f4(f7(c34, c35), f14(c38, c39))), f4(f7(c34, c35), c40)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(71,plain,
% 0.19/0.40 ((~![X87: $i, X86: $i] : ((~p30(f10(f12(c32, c33), X86), X87)) | p30(f10(f12(c32, c33), f4(f7(c34, c35), X86)), f4(f7(c34, c35), X87)))) | (~p30(f10(f12(c32, c33), f14(c38, c39)), c40)) | p30(f10(f12(c32, c33), f4(f7(c34, c35), f14(c38, c39))), f4(f7(c34, c35), c40))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.19/0.40 tff(72,plain,
% 0.19/0.40 (p30(f10(f12(c32, c33), f4(f7(c34, c35), f14(c38, c39))), f4(f7(c34, c35), c40))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[71, 68, 58])).
% 0.19/0.40 tff(73,assumption,(~p2(f7(c34, c35), f7(c34, c35))), introduced(assumption)).
% 0.19/0.40 tff(74,plain,
% 0.19/0.40 (^[X26: $i] : refl(p2(X26, X26) <=> p2(X26, X26))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(75,plain,
% 0.19/0.40 (![X26: $i] : p2(X26, X26) <=> ![X26: $i] : p2(X26, X26)),
% 0.19/0.40 inference(quant_intro,[status(thm)],[74])).
% 0.19/0.40 tff(76,plain,
% 0.19/0.40 (![X26: $i] : p2(X26, X26) <=> ![X26: $i] : p2(X26, X26)),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(77,axiom,(![X26: $i] : p2(X26, X26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_12')).
% 0.19/0.40 tff(78,plain,
% 0.19/0.40 (![X26: $i] : p2(X26, X26)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.19/0.40 tff(79,plain,(
% 0.19/0.40 ![X26: $i] : p2(X26, X26)),
% 0.19/0.40 inference(skolemize,[status(sab)],[78])).
% 0.19/0.40 tff(80,plain,
% 0.19/0.40 (![X26: $i] : p2(X26, X26)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.19/0.40 tff(81,plain,
% 0.19/0.40 ((~![X26: $i] : p2(X26, X26)) | p2(f7(c34, c35), f7(c34, c35))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(82,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[81, 80, 73])).
% 0.19/0.40 tff(83,plain,(p2(f7(c34, c35), f7(c34, c35))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(84,assumption,(~p3(c40, c40)), introduced(assumption)).
% 0.19/0.40 tff(85,plain,
% 0.19/0.40 (^[X62: $i] : refl(p3(X62, X62) <=> p3(X62, X62))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(86,plain,
% 0.19/0.40 (![X62: $i] : p3(X62, X62) <=> ![X62: $i] : p3(X62, X62)),
% 0.19/0.40 inference(quant_intro,[status(thm)],[85])).
% 0.19/0.40 tff(87,plain,
% 0.19/0.40 (![X62: $i] : p3(X62, X62) <=> ![X62: $i] : p3(X62, X62)),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(88,axiom,(![X62: $i] : p3(X62, X62)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p3_6')).
% 0.19/0.40 tff(89,plain,
% 0.19/0.40 (![X62: $i] : p3(X62, X62)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.19/0.40 tff(90,plain,(
% 0.19/0.40 ![X62: $i] : p3(X62, X62)),
% 0.19/0.40 inference(skolemize,[status(sab)],[89])).
% 0.19/0.40 tff(91,plain,
% 0.19/0.40 (![X62: $i] : p3(X62, X62)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.19/0.40 tff(92,plain,
% 0.19/0.40 ((~![X62: $i] : p3(X62, X62)) | p3(c40, c40)),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(93,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[92, 91, 84])).
% 0.19/0.40 tff(94,plain,(p3(c40, c40)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(95,plain,
% 0.19/0.40 (^[X76: $i, X73: $i, X75: $i, X74: $i] : refl(((~p3(X74, X76)) | (~p2(X73, X75)) | p3(f4(X73, X74), f4(X75, X76))) <=> ((~p3(X74, X76)) | (~p2(X73, X75)) | p3(f4(X73, X74), f4(X75, X76))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(96,plain,
% 0.19/0.40 (![X76: $i, X73: $i, X75: $i, X74: $i] : ((~p3(X74, X76)) | (~p2(X73, X75)) | p3(f4(X73, X74), f4(X75, X76))) <=> ![X76: $i, X73: $i, X75: $i, X74: $i] : ((~p3(X74, X76)) | (~p2(X73, X75)) | p3(f4(X73, X74), f4(X75, X76)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[95])).
% 0.19/0.40 tff(97,plain,
% 0.19/0.40 (![X76: $i, X73: $i, X75: $i, X74: $i] : ((~p3(X74, X76)) | (~p2(X73, X75)) | p3(f4(X73, X74), f4(X75, X76))) <=> ![X76: $i, X73: $i, X75: $i, X74: $i] : ((~p3(X74, X76)) | (~p2(X73, X75)) | p3(f4(X73, X74), f4(X75, X76)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(98,plain,
% 0.19/0.40 (^[X76: $i, X73: $i, X75: $i, X74: $i] : trans(monotonicity(rewrite((p3(f4(X73, X74), f4(X75, X76)) | (~p2(X73, X75))) <=> ((~p2(X73, X75)) | p3(f4(X73, X74), f4(X75, X76)))), (((p3(f4(X73, X74), f4(X75, X76)) | (~p2(X73, X75))) | (~p3(X74, X76))) <=> (((~p2(X73, X75)) | p3(f4(X73, X74), f4(X75, X76))) | (~p3(X74, X76))))), rewrite((((~p2(X73, X75)) | p3(f4(X73, X74), f4(X75, X76))) | (~p3(X74, X76))) <=> ((~p3(X74, X76)) | (~p2(X73, X75)) | p3(f4(X73, X74), f4(X75, X76)))), (((p3(f4(X73, X74), f4(X75, X76)) | (~p2(X73, X75))) | (~p3(X74, X76))) <=> ((~p3(X74, X76)) | (~p2(X73, X75)) | p3(f4(X73, X74), f4(X75, X76)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(99,plain,
% 0.19/0.40 (![X76: $i, X73: $i, X75: $i, X74: $i] : ((p3(f4(X73, X74), f4(X75, X76)) | (~p2(X73, X75))) | (~p3(X74, X76))) <=> ![X76: $i, X73: $i, X75: $i, X74: $i] : ((~p3(X74, X76)) | (~p2(X73, X75)) | p3(f4(X73, X74), f4(X75, X76)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[98])).
% 0.19/0.40 tff(100,axiom,(![X76: $i, X73: $i, X75: $i, X74: $i] : ((p3(f4(X73, X74), f4(X75, X76)) | (~p2(X73, X75))) | (~p3(X74, X76)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p3_44')).
% 0.19/0.40 tff(101,plain,
% 0.19/0.40 (![X76: $i, X73: $i, X75: $i, X74: $i] : ((~p3(X74, X76)) | (~p2(X73, X75)) | p3(f4(X73, X74), f4(X75, X76)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.19/0.40 tff(102,plain,
% 0.19/0.40 (![X76: $i, X73: $i, X75: $i, X74: $i] : ((~p3(X74, X76)) | (~p2(X73, X75)) | p3(f4(X73, X74), f4(X75, X76)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[101, 97])).
% 0.19/0.40 tff(103,plain,(
% 0.19/0.40 ![X76: $i, X73: $i, X75: $i, X74: $i] : ((~p3(X74, X76)) | (~p2(X73, X75)) | p3(f4(X73, X74), f4(X75, X76)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[102])).
% 0.19/0.40 tff(104,plain,
% 0.19/0.40 (![X76: $i, X73: $i, X75: $i, X74: $i] : ((~p3(X74, X76)) | (~p2(X73, X75)) | p3(f4(X73, X74), f4(X75, X76)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[103, 96])).
% 0.19/0.40 tff(105,plain,
% 0.19/0.40 (((~![X76: $i, X73: $i, X75: $i, X74: $i] : ((~p3(X74, X76)) | (~p2(X73, X75)) | p3(f4(X73, X74), f4(X75, X76)))) | ((~p3(c40, c40)) | (~p2(f7(c34, c35), f7(c34, c35))) | p3(f4(f7(c34, c35), c40), f4(f7(c34, c35), c40)))) <=> ((~![X76: $i, X73: $i, X75: $i, X74: $i] : ((~p3(X74, X76)) | (~p2(X73, X75)) | p3(f4(X73, X74), f4(X75, X76)))) | (~p3(c40, c40)) | (~p2(f7(c34, c35), f7(c34, c35))) | p3(f4(f7(c34, c35), c40), f4(f7(c34, c35), c40)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(106,plain,
% 0.19/0.40 ((~![X76: $i, X73: $i, X75: $i, X74: $i] : ((~p3(X74, X76)) | (~p2(X73, X75)) | p3(f4(X73, X74), f4(X75, X76)))) | ((~p3(c40, c40)) | (~p2(f7(c34, c35), f7(c34, c35))) | p3(f4(f7(c34, c35), c40), f4(f7(c34, c35), c40)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(107,plain,
% 0.19/0.40 ((~![X76: $i, X73: $i, X75: $i, X74: $i] : ((~p3(X74, X76)) | (~p2(X73, X75)) | p3(f4(X73, X74), f4(X75, X76)))) | (~p3(c40, c40)) | (~p2(f7(c34, c35), f7(c34, c35))) | p3(f4(f7(c34, c35), c40), f4(f7(c34, c35), c40))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.19/0.40 tff(108,plain,
% 0.19/0.40 ((~p3(c40, c40)) | (~p2(f7(c34, c35), f7(c34, c35))) | p3(f4(f7(c34, c35), c40), f4(f7(c34, c35), c40))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[107, 104])).
% 0.19/0.40 tff(109,plain,
% 0.19/0.40 ((~p2(f7(c34, c35), f7(c34, c35))) | p3(f4(f7(c34, c35), c40), f4(f7(c34, c35), c40))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[108, 94])).
% 0.19/0.40 tff(110,plain,
% 0.19/0.40 (p3(f4(f7(c34, c35), c40), f4(f7(c34, c35), c40))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[109, 83])).
% 0.19/0.40 tff(111,plain,
% 0.19/0.40 ((~p30(f10(f12(c32, c33), f14(c35, c39)), f4(f7(c34, c35), c40))) <=> (~p30(f10(f12(c32, c33), f14(c35, c39)), f4(f7(c34, c35), c40)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(112,axiom,(~p30(f10(f12(c32, c33), f14(c35, c39)), f4(f7(c34, c35), c40))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_p30_40')).
% 0.19/0.40 tff(113,plain,
% 0.19/0.40 (~p30(f10(f12(c32, c33), f14(c35, c39)), f4(f7(c34, c35), c40))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.19/0.40 tff(114,plain,
% 0.19/0.40 (^[X82: $i, X83: $i, X85: $i, X84: $i] : refl(((~p3(X84, X83)) | (~p9(X85, X82)) | (~p30(X85, X84)) | p30(X82, X83)) <=> ((~p3(X84, X83)) | (~p9(X85, X82)) | (~p30(X85, X84)) | p30(X82, X83)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(115,plain,
% 0.19/0.40 (![X82: $i, X83: $i, X85: $i, X84: $i] : ((~p3(X84, X83)) | (~p9(X85, X82)) | (~p30(X85, X84)) | p30(X82, X83)) <=> ![X82: $i, X83: $i, X85: $i, X84: $i] : ((~p3(X84, X83)) | (~p9(X85, X82)) | (~p30(X85, X84)) | p30(X82, X83))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[114])).
% 0.19/0.40 tff(116,plain,
% 0.19/0.40 (![X82: $i, X83: $i, X85: $i, X84: $i] : ((~p3(X84, X83)) | (~p9(X85, X82)) | (~p30(X85, X84)) | p30(X82, X83)) <=> ![X82: $i, X83: $i, X85: $i, X84: $i] : ((~p3(X84, X83)) | (~p9(X85, X82)) | (~p30(X85, X84)) | p30(X82, X83))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(117,plain,
% 0.19/0.40 (^[X82: $i, X83: $i, X85: $i, X84: $i] : trans(monotonicity(trans(monotonicity(rewrite((p30(X82, X83) | (~p30(X85, X84))) <=> ((~p30(X85, X84)) | p30(X82, X83))), (((p30(X82, X83) | (~p30(X85, X84))) | (~p9(X85, X82))) <=> (((~p30(X85, X84)) | p30(X82, X83)) | (~p9(X85, X82))))), rewrite((((~p30(X85, X84)) | p30(X82, X83)) | (~p9(X85, X82))) <=> ((~p9(X85, X82)) | (~p30(X85, X84)) | p30(X82, X83))), (((p30(X82, X83) | (~p30(X85, X84))) | (~p9(X85, X82))) <=> ((~p9(X85, X82)) | (~p30(X85, X84)) | p30(X82, X83)))), ((((p30(X82, X83) | (~p30(X85, X84))) | (~p9(X85, X82))) | (~p3(X84, X83))) <=> (((~p9(X85, X82)) | (~p30(X85, X84)) | p30(X82, X83)) | (~p3(X84, X83))))), rewrite((((~p9(X85, X82)) | (~p30(X85, X84)) | p30(X82, X83)) | (~p3(X84, X83))) <=> ((~p3(X84, X83)) | (~p9(X85, X82)) | (~p30(X85, X84)) | p30(X82, X83))), ((((p30(X82, X83) | (~p30(X85, X84))) | (~p9(X85, X82))) | (~p3(X84, X83))) <=> ((~p3(X84, X83)) | (~p9(X85, X82)) | (~p30(X85, X84)) | p30(X82, X83))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(118,plain,
% 0.19/0.40 (![X82: $i, X83: $i, X85: $i, X84: $i] : (((p30(X82, X83) | (~p30(X85, X84))) | (~p9(X85, X82))) | (~p3(X84, X83))) <=> ![X82: $i, X83: $i, X85: $i, X84: $i] : ((~p3(X84, X83)) | (~p9(X85, X82)) | (~p30(X85, X84)) | p30(X82, X83))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[117])).
% 0.19/0.40 tff(119,axiom,(![X82: $i, X83: $i, X85: $i, X84: $i] : (((p30(X82, X83) | (~p30(X85, X84))) | (~p9(X85, X82))) | (~p3(X84, X83)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p30_39')).
% 0.19/0.40 tff(120,plain,
% 0.19/0.40 (![X82: $i, X83: $i, X85: $i, X84: $i] : ((~p3(X84, X83)) | (~p9(X85, X82)) | (~p30(X85, X84)) | p30(X82, X83))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.19/0.40 tff(121,plain,
% 0.19/0.40 (![X82: $i, X83: $i, X85: $i, X84: $i] : ((~p3(X84, X83)) | (~p9(X85, X82)) | (~p30(X85, X84)) | p30(X82, X83))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[120, 116])).
% 0.19/0.40 tff(122,plain,(
% 0.19/0.40 ![X82: $i, X83: $i, X85: $i, X84: $i] : ((~p3(X84, X83)) | (~p9(X85, X82)) | (~p30(X85, X84)) | p30(X82, X83))),
% 0.19/0.40 inference(skolemize,[status(sab)],[121])).
% 0.19/0.41 tff(123,plain,
% 0.19/0.41 (![X82: $i, X83: $i, X85: $i, X84: $i] : ((~p3(X84, X83)) | (~p9(X85, X82)) | (~p30(X85, X84)) | p30(X82, X83))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[122, 115])).
% 0.19/0.41 tff(124,plain,
% 0.19/0.41 (((~![X82: $i, X83: $i, X85: $i, X84: $i] : ((~p3(X84, X83)) | (~p9(X85, X82)) | (~p30(X85, X84)) | p30(X82, X83))) | (p30(f10(f12(c32, c33), f14(c35, c39)), f4(f7(c34, c35), c40)) | (~p9(f10(f12(c32, c33), f4(f7(c34, c35), f14(c38, c39))), f10(f12(c32, c33), f14(c35, c39)))) | (~p30(f10(f12(c32, c33), f4(f7(c34, c35), f14(c38, c39))), f4(f7(c34, c35), c40))) | (~p3(f4(f7(c34, c35), c40), f4(f7(c34, c35), c40))))) <=> ((~![X82: $i, X83: $i, X85: $i, X84: $i] : ((~p3(X84, X83)) | (~p9(X85, X82)) | (~p30(X85, X84)) | p30(X82, X83))) | p30(f10(f12(c32, c33), f14(c35, c39)), f4(f7(c34, c35), c40)) | (~p9(f10(f12(c32, c33), f4(f7(c34, c35), f14(c38, c39))), f10(f12(c32, c33), f14(c35, c39)))) | (~p30(f10(f12(c32, c33), f4(f7(c34, c35), f14(c38, c39))), f4(f7(c34, c35), c40))) | (~p3(f4(f7(c34, c35), c40), f4(f7(c34, c35), c40))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(125,plain,
% 0.19/0.41 (((~p3(f4(f7(c34, c35), c40), f4(f7(c34, c35), c40))) | (~p9(f10(f12(c32, c33), f4(f7(c34, c35), f14(c38, c39))), f10(f12(c32, c33), f14(c35, c39)))) | (~p30(f10(f12(c32, c33), f4(f7(c34, c35), f14(c38, c39))), f4(f7(c34, c35), c40))) | p30(f10(f12(c32, c33), f14(c35, c39)), f4(f7(c34, c35), c40))) <=> (p30(f10(f12(c32, c33), f14(c35, c39)), f4(f7(c34, c35), c40)) | (~p9(f10(f12(c32, c33), f4(f7(c34, c35), f14(c38, c39))), f10(f12(c32, c33), f14(c35, c39)))) | (~p30(f10(f12(c32, c33), f4(f7(c34, c35), f14(c38, c39))), f4(f7(c34, c35), c40))) | (~p3(f4(f7(c34, c35), c40), f4(f7(c34, c35), c40))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(126,plain,
% 0.19/0.41 (((~![X82: $i, X83: $i, X85: $i, X84: $i] : ((~p3(X84, X83)) | (~p9(X85, X82)) | (~p30(X85, X84)) | p30(X82, X83))) | ((~p3(f4(f7(c34, c35), c40), f4(f7(c34, c35), c40))) | (~p9(f10(f12(c32, c33), f4(f7(c34, c35), f14(c38, c39))), f10(f12(c32, c33), f14(c35, c39)))) | (~p30(f10(f12(c32, c33), f4(f7(c34, c35), f14(c38, c39))), f4(f7(c34, c35), c40))) | p30(f10(f12(c32, c33), f14(c35, c39)), f4(f7(c34, c35), c40)))) <=> ((~![X82: $i, X83: $i, X85: $i, X84: $i] : ((~p3(X84, X83)) | (~p9(X85, X82)) | (~p30(X85, X84)) | p30(X82, X83))) | (p30(f10(f12(c32, c33), f14(c35, c39)), f4(f7(c34, c35), c40)) | (~p9(f10(f12(c32, c33), f4(f7(c34, c35), f14(c38, c39))), f10(f12(c32, c33), f14(c35, c39)))) | (~p30(f10(f12(c32, c33), f4(f7(c34, c35), f14(c38, c39))), f4(f7(c34, c35), c40))) | (~p3(f4(f7(c34, c35), c40), f4(f7(c34, c35), c40)))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[125])).
% 0.19/0.41 tff(127,plain,
% 0.19/0.41 (((~![X82: $i, X83: $i, X85: $i, X84: $i] : ((~p3(X84, X83)) | (~p9(X85, X82)) | (~p30(X85, X84)) | p30(X82, X83))) | ((~p3(f4(f7(c34, c35), c40), f4(f7(c34, c35), c40))) | (~p9(f10(f12(c32, c33), f4(f7(c34, c35), f14(c38, c39))), f10(f12(c32, c33), f14(c35, c39)))) | (~p30(f10(f12(c32, c33), f4(f7(c34, c35), f14(c38, c39))), f4(f7(c34, c35), c40))) | p30(f10(f12(c32, c33), f14(c35, c39)), f4(f7(c34, c35), c40)))) <=> ((~![X82: $i, X83: $i, X85: $i, X84: $i] : ((~p3(X84, X83)) | (~p9(X85, X82)) | (~p30(X85, X84)) | p30(X82, X83))) | p30(f10(f12(c32, c33), f14(c35, c39)), f4(f7(c34, c35), c40)) | (~p9(f10(f12(c32, c33), f4(f7(c34, c35), f14(c38, c39))), f10(f12(c32, c33), f14(c35, c39)))) | (~p30(f10(f12(c32, c33), f4(f7(c34, c35), f14(c38, c39))), f4(f7(c34, c35), c40))) | (~p3(f4(f7(c34, c35), c40), f4(f7(c34, c35), c40))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[126, 124])).
% 0.19/0.41 tff(128,plain,
% 0.19/0.41 ((~![X82: $i, X83: $i, X85: $i, X84: $i] : ((~p3(X84, X83)) | (~p9(X85, X82)) | (~p30(X85, X84)) | p30(X82, X83))) | ((~p3(f4(f7(c34, c35), c40), f4(f7(c34, c35), c40))) | (~p9(f10(f12(c32, c33), f4(f7(c34, c35), f14(c38, c39))), f10(f12(c32, c33), f14(c35, c39)))) | (~p30(f10(f12(c32, c33), f4(f7(c34, c35), f14(c38, c39))), f4(f7(c34, c35), c40))) | p30(f10(f12(c32, c33), f14(c35, c39)), f4(f7(c34, c35), c40)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(129,plain,
% 0.19/0.41 ((~![X82: $i, X83: $i, X85: $i, X84: $i] : ((~p3(X84, X83)) | (~p9(X85, X82)) | (~p30(X85, X84)) | p30(X82, X83))) | p30(f10(f12(c32, c33), f14(c35, c39)), f4(f7(c34, c35), c40)) | (~p9(f10(f12(c32, c33), f4(f7(c34, c35), f14(c38, c39))), f10(f12(c32, c33), f14(c35, c39)))) | (~p30(f10(f12(c32, c33), f4(f7(c34, c35), f14(c38, c39))), f4(f7(c34, c35), c40))) | (~p3(f4(f7(c34, c35), c40), f4(f7(c34, c35), c40)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.19/0.41 tff(130,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[129, 123, 113, 110, 72, 35])).
% 0.19/0.41 % SZS output end Proof
% 0.19/0.41 % E exiting
%------------------------------------------------------------------------------