%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN706-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:39:52 AM UTC 2025
% Result : Unsatisfiable 0.18s 0.50s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SYN706-1 : TPTP v9.0.0. Released v2.5.0.
% 0.11/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n006.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 12:40:05 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.18/0.50 % SZS status Unsatisfiable
% 0.18/0.50 % SZS output start Proof
% 0.18/0.50 tff(p37_type, type, (
% 0.18/0.50 p37: ( $i * $i ) > $o)).
% 0.18/0.50 tff(f38_type, type, (
% 0.18/0.50 f38: ( $i * $i ) > $i)).
% 0.18/0.50 tff(c58_type, type, (
% 0.18/0.50 c58: $i)).
% 0.18/0.50 tff(f40_type, type, (
% 0.18/0.50 f40: ( $i * $i ) > $i)).
% 0.18/0.50 tff(c50_type, type, (
% 0.18/0.50 c50: $i)).
% 0.18/0.50 tff(c59_type, type, (
% 0.18/0.50 c59: $i)).
% 0.18/0.50 tff(f8_type, type, (
% 0.18/0.50 f8: ( $i * $i ) > $i)).
% 0.18/0.50 tff(f11_type, type, (
% 0.18/0.50 f11: ( $i * $i ) > $i)).
% 0.18/0.50 tff(f14_type, type, (
% 0.18/0.50 f14: ( $i * $i ) > $i)).
% 0.18/0.50 tff(f35_type, type, (
% 0.18/0.50 f35: ( $i * $i ) > $i)).
% 0.18/0.50 tff(c61_type, type, (
% 0.18/0.50 c61: $i)).
% 0.18/0.50 tff(f17_type, type, (
% 0.18/0.50 f17: ( $i * $i ) > $i)).
% 0.18/0.50 tff(c55_type, type, (
% 0.18/0.50 c55: $i)).
% 0.18/0.50 tff(c54_type, type, (
% 0.18/0.50 c54: $i)).
% 0.18/0.50 tff(p7_type, type, (
% 0.18/0.50 p7: ( $i * $i ) > $o)).
% 0.18/0.50 tff(p36_type, type, (
% 0.18/0.50 p36: ( $i * $i ) > $o)).
% 0.18/0.50 tff(p3_type, type, (
% 0.18/0.50 p3: ( $i * $i ) > $o)).
% 0.18/0.50 tff(p39_type, type, (
% 0.18/0.50 p39: ( $i * $i ) > $o)).
% 0.18/0.50 tff(p48_type, type, (
% 0.18/0.50 p48: ( $i * $i ) > $o)).
% 0.18/0.50 tff(c60_type, type, (
% 0.18/0.50 c60: $i)).
% 0.18/0.50 tff(p46_type, type, (
% 0.18/0.50 p46: ( $i * $i ) > $o)).
% 0.18/0.50 tff(f5_type, type, (
% 0.18/0.50 f5: ( $i * $i ) > $i)).
% 0.18/0.50 tff(c49_type, type, (
% 0.18/0.50 c49: $i)).
% 0.18/0.50 tff(f23_type, type, (
% 0.18/0.50 f23: ( $i * $i ) > $i)).
% 0.18/0.50 tff(c53_type, type, (
% 0.18/0.50 c53: $i)).
% 0.18/0.50 tff(p45_type, type, (
% 0.18/0.50 p45: ( $i * $i ) > $o)).
% 0.18/0.50 tff(f20_type, type, (
% 0.18/0.50 f20: ( $i * $i ) > $i)).
% 0.18/0.50 tff(c52_type, type, (
% 0.18/0.50 c52: $i)).
% 0.18/0.50 tff(p47_type, type, (
% 0.18/0.50 p47: ( $i * $i ) > $o)).
% 0.18/0.50 tff(1,plain,
% 0.18/0.50 (^[X166: $i, X167: $i] : refl(p7(f8(f11(c54, f14(f17(c55, X166), f35(X167, X166))), X167), X167) <=> p7(f8(f11(c54, f14(f17(c55, X166), f35(X167, X166))), X167), X167))),
% 0.18/0.50 inference(bind,[status(th)],[])).
% 0.18/0.50 tff(2,plain,
% 0.18/0.50 (![X166: $i, X167: $i] : p7(f8(f11(c54, f14(f17(c55, X166), f35(X167, X166))), X167), X167) <=> ![X166: $i, X167: $i] : p7(f8(f11(c54, f14(f17(c55, X166), f35(X167, X166))), X167), X167)),
% 0.18/0.50 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.50 tff(3,plain,
% 0.18/0.50 (![X166: $i, X167: $i] : p7(f8(f11(c54, f14(f17(c55, X166), f35(X167, X166))), X167), X167) <=> ![X166: $i, X167: $i] : p7(f8(f11(c54, f14(f17(c55, X166), f35(X167, X166))), X167), X167)),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(4,axiom,(![X166: $i, X167: $i] : p7(f8(f11(c54, f14(f17(c55, X166), f35(X167, X166))), X167), X167)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p7_59')).
% 0.18/0.50 tff(5,plain,
% 0.18/0.50 (![X166: $i, X167: $i] : p7(f8(f11(c54, f14(f17(c55, X166), f35(X167, X166))), X167), X167)),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.18/0.50 tff(6,plain,(
% 0.18/0.50 ![X166: $i, X167: $i] : p7(f8(f11(c54, f14(f17(c55, X166), f35(X167, X166))), X167), X167)),
% 0.18/0.50 inference(skolemize,[status(sab)],[5])).
% 0.18/0.50 tff(7,plain,
% 0.18/0.50 (![X166: $i, X167: $i] : p7(f8(f11(c54, f14(f17(c55, X166), f35(X167, X166))), X167), X167)),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.18/0.50 tff(8,plain,
% 0.18/0.50 ((~![X166: $i, X167: $i] : p7(f8(f11(c54, f14(f17(c55, X166), f35(X167, X166))), X167), X167)) | p7(f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58), c58)),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(9,plain,
% 0.18/0.50 (p7(f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58), c58)),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.18/0.50 tff(10,assumption,(~p3(c50, c50)), introduced(assumption)).
% 0.18/0.50 tff(11,plain,
% 0.18/0.50 (^[X78: $i] : refl(p3(X78, X78) <=> p3(X78, X78))),
% 0.18/0.50 inference(bind,[status(th)],[])).
% 0.18/0.50 tff(12,plain,
% 0.18/0.50 (![X78: $i] : p3(X78, X78) <=> ![X78: $i] : p3(X78, X78)),
% 0.18/0.50 inference(quant_intro,[status(thm)],[11])).
% 0.18/0.50 tff(13,plain,
% 0.18/0.50 (![X78: $i] : p3(X78, X78) <=> ![X78: $i] : p3(X78, X78)),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(14,axiom,(![X78: $i] : p3(X78, X78)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p3_13')).
% 0.18/0.50 tff(15,plain,
% 0.18/0.50 (![X78: $i] : p3(X78, X78)),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.18/0.50 tff(16,plain,(
% 0.18/0.50 ![X78: $i] : p3(X78, X78)),
% 0.18/0.50 inference(skolemize,[status(sab)],[15])).
% 0.18/0.50 tff(17,plain,
% 0.18/0.50 (![X78: $i] : p3(X78, X78)),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.18/0.50 tff(18,plain,
% 0.18/0.50 ((~![X78: $i] : p3(X78, X78)) | p3(c50, c50)),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(19,plain,
% 0.18/0.50 ($false),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[18, 17, 10])).
% 0.18/0.51 tff(20,plain,(p3(c50, c50)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.51 tff(21,assumption,(~p39(c59, c59)), introduced(assumption)).
% 0.18/0.51 tff(22,plain,
% 0.18/0.51 (^[X102: $i] : refl(p39(X102, X102) <=> p39(X102, X102))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(23,plain,
% 0.18/0.51 (![X102: $i] : p39(X102, X102) <=> ![X102: $i] : p39(X102, X102)),
% 0.18/0.51 inference(quant_intro,[status(thm)],[22])).
% 0.18/0.51 tff(24,plain,
% 0.18/0.51 (![X102: $i] : p39(X102, X102) <=> ![X102: $i] : p39(X102, X102)),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(25,axiom,(![X102: $i] : p39(X102, X102)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p39_9')).
% 0.18/0.51 tff(26,plain,
% 0.18/0.51 (![X102: $i] : p39(X102, X102)),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.18/0.51 tff(27,plain,(
% 0.18/0.51 ![X102: $i] : p39(X102, X102)),
% 0.18/0.51 inference(skolemize,[status(sab)],[26])).
% 0.18/0.51 tff(28,plain,
% 0.18/0.51 (![X102: $i] : p39(X102, X102)),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.18/0.51 tff(29,plain,
% 0.18/0.51 ((~![X102: $i] : p39(X102, X102)) | p39(c59, c59)),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(30,plain,
% 0.18/0.51 ($false),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[29, 28, 21])).
% 0.18/0.51 tff(31,plain,(p39(c59, c59)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.51 tff(32,plain,
% 0.18/0.51 (^[X93: $i, X94: $i, X91: $i, X92: $i] : refl(((~p39(X91, X93)) | (~p3(X92, X94)) | p36(f40(X91, X92), f40(X93, X94))) <=> ((~p39(X91, X93)) | (~p3(X92, X94)) | p36(f40(X91, X92), f40(X93, X94))))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(33,plain,
% 0.18/0.51 (![X93: $i, X94: $i, X91: $i, X92: $i] : ((~p39(X91, X93)) | (~p3(X92, X94)) | p36(f40(X91, X92), f40(X93, X94))) <=> ![X93: $i, X94: $i, X91: $i, X92: $i] : ((~p39(X91, X93)) | (~p3(X92, X94)) | p36(f40(X91, X92), f40(X93, X94)))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[32])).
% 0.18/0.51 tff(34,plain,
% 0.18/0.51 (![X93: $i, X94: $i, X91: $i, X92: $i] : ((~p39(X91, X93)) | (~p3(X92, X94)) | p36(f40(X91, X92), f40(X93, X94))) <=> ![X93: $i, X94: $i, X91: $i, X92: $i] : ((~p39(X91, X93)) | (~p3(X92, X94)) | p36(f40(X91, X92), f40(X93, X94)))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(35,plain,
% 0.18/0.51 (^[X93: $i, X94: $i, X91: $i, X92: $i] : trans(monotonicity(rewrite((p36(f40(X91, X92), f40(X93, X94)) | (~p3(X92, X94))) <=> ((~p3(X92, X94)) | p36(f40(X91, X92), f40(X93, X94)))), (((p36(f40(X91, X92), f40(X93, X94)) | (~p3(X92, X94))) | (~p39(X91, X93))) <=> (((~p3(X92, X94)) | p36(f40(X91, X92), f40(X93, X94))) | (~p39(X91, X93))))), rewrite((((~p3(X92, X94)) | p36(f40(X91, X92), f40(X93, X94))) | (~p39(X91, X93))) <=> ((~p39(X91, X93)) | (~p3(X92, X94)) | p36(f40(X91, X92), f40(X93, X94)))), (((p36(f40(X91, X92), f40(X93, X94)) | (~p3(X92, X94))) | (~p39(X91, X93))) <=> ((~p39(X91, X93)) | (~p3(X92, X94)) | p36(f40(X91, X92), f40(X93, X94)))))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(36,plain,
% 0.18/0.51 (![X93: $i, X94: $i, X91: $i, X92: $i] : ((p36(f40(X91, X92), f40(X93, X94)) | (~p3(X92, X94))) | (~p39(X91, X93))) <=> ![X93: $i, X94: $i, X91: $i, X92: $i] : ((~p39(X91, X93)) | (~p3(X92, X94)) | p36(f40(X91, X92), f40(X93, X94)))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[35])).
% 0.18/0.51 tff(37,axiom,(![X93: $i, X94: $i, X91: $i, X92: $i] : ((p36(f40(X91, X92), f40(X93, X94)) | (~p3(X92, X94))) | (~p39(X91, X93)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p36_68')).
% 0.18/0.51 tff(38,plain,
% 0.18/0.51 (![X93: $i, X94: $i, X91: $i, X92: $i] : ((~p39(X91, X93)) | (~p3(X92, X94)) | p36(f40(X91, X92), f40(X93, X94)))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.18/0.51 tff(39,plain,
% 0.18/0.51 (![X93: $i, X94: $i, X91: $i, X92: $i] : ((~p39(X91, X93)) | (~p3(X92, X94)) | p36(f40(X91, X92), f40(X93, X94)))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.18/0.51 tff(40,plain,(
% 0.18/0.51 ![X93: $i, X94: $i, X91: $i, X92: $i] : ((~p39(X91, X93)) | (~p3(X92, X94)) | p36(f40(X91, X92), f40(X93, X94)))),
% 0.18/0.51 inference(skolemize,[status(sab)],[39])).
% 0.18/0.51 tff(41,plain,
% 0.18/0.51 (![X93: $i, X94: $i, X91: $i, X92: $i] : ((~p39(X91, X93)) | (~p3(X92, X94)) | p36(f40(X91, X92), f40(X93, X94)))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.18/0.51 tff(42,plain,
% 0.18/0.51 (((~![X93: $i, X94: $i, X91: $i, X92: $i] : ((~p39(X91, X93)) | (~p3(X92, X94)) | p36(f40(X91, X92), f40(X93, X94)))) | ((~p3(c50, c50)) | p36(f40(c59, c50), f40(c59, c50)) | (~p39(c59, c59)))) <=> ((~![X93: $i, X94: $i, X91: $i, X92: $i] : ((~p39(X91, X93)) | (~p3(X92, X94)) | p36(f40(X91, X92), f40(X93, X94)))) | (~p3(c50, c50)) | p36(f40(c59, c50), f40(c59, c50)) | (~p39(c59, c59)))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(43,plain,
% 0.18/0.51 (((~p39(c59, c59)) | (~p3(c50, c50)) | p36(f40(c59, c50), f40(c59, c50))) <=> ((~p3(c50, c50)) | p36(f40(c59, c50), f40(c59, c50)) | (~p39(c59, c59)))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(44,plain,
% 0.18/0.51 (((~![X93: $i, X94: $i, X91: $i, X92: $i] : ((~p39(X91, X93)) | (~p3(X92, X94)) | p36(f40(X91, X92), f40(X93, X94)))) | ((~p39(c59, c59)) | (~p3(c50, c50)) | p36(f40(c59, c50), f40(c59, c50)))) <=> ((~![X93: $i, X94: $i, X91: $i, X92: $i] : ((~p39(X91, X93)) | (~p3(X92, X94)) | p36(f40(X91, X92), f40(X93, X94)))) | ((~p3(c50, c50)) | p36(f40(c59, c50), f40(c59, c50)) | (~p39(c59, c59))))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[43])).
% 0.18/0.51 tff(45,plain,
% 0.18/0.51 (((~![X93: $i, X94: $i, X91: $i, X92: $i] : ((~p39(X91, X93)) | (~p3(X92, X94)) | p36(f40(X91, X92), f40(X93, X94)))) | ((~p39(c59, c59)) | (~p3(c50, c50)) | p36(f40(c59, c50), f40(c59, c50)))) <=> ((~![X93: $i, X94: $i, X91: $i, X92: $i] : ((~p39(X91, X93)) | (~p3(X92, X94)) | p36(f40(X91, X92), f40(X93, X94)))) | (~p3(c50, c50)) | p36(f40(c59, c50), f40(c59, c50)) | (~p39(c59, c59)))),
% 0.18/0.51 inference(transitivity,[status(thm)],[44, 42])).
% 0.18/0.51 tff(46,plain,
% 0.18/0.51 ((~![X93: $i, X94: $i, X91: $i, X92: $i] : ((~p39(X91, X93)) | (~p3(X92, X94)) | p36(f40(X91, X92), f40(X93, X94)))) | ((~p39(c59, c59)) | (~p3(c50, c50)) | p36(f40(c59, c50), f40(c59, c50)))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(47,plain,
% 0.18/0.51 ((~![X93: $i, X94: $i, X91: $i, X92: $i] : ((~p39(X91, X93)) | (~p3(X92, X94)) | p36(f40(X91, X92), f40(X93, X94)))) | (~p3(c50, c50)) | p36(f40(c59, c50), f40(c59, c50)) | (~p39(c59, c59))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.18/0.51 tff(48,plain,
% 0.18/0.51 ((~p3(c50, c50)) | p36(f40(c59, c50), f40(c59, c50)) | (~p39(c59, c59))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[47, 41])).
% 0.18/0.51 tff(49,plain,
% 0.18/0.51 (p36(f40(c59, c50), f40(c59, c50))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[48, 31, 20])).
% 0.18/0.51 tff(50,plain,
% 0.18/0.51 (^[X99: $i, X100: $i, X98: $i, X101: $i] : refl(((~p7(X99, X101)) | (~p36(X98, X100)) | p37(f38(X98, X99), f38(X100, X101))) <=> ((~p7(X99, X101)) | (~p36(X98, X100)) | p37(f38(X98, X99), f38(X100, X101))))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(51,plain,
% 0.18/0.51 (![X99: $i, X100: $i, X98: $i, X101: $i] : ((~p7(X99, X101)) | (~p36(X98, X100)) | p37(f38(X98, X99), f38(X100, X101))) <=> ![X99: $i, X100: $i, X98: $i, X101: $i] : ((~p7(X99, X101)) | (~p36(X98, X100)) | p37(f38(X98, X99), f38(X100, X101)))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[50])).
% 0.18/0.51 tff(52,plain,
% 0.18/0.51 (![X99: $i, X100: $i, X98: $i, X101: $i] : ((~p7(X99, X101)) | (~p36(X98, X100)) | p37(f38(X98, X99), f38(X100, X101))) <=> ![X99: $i, X100: $i, X98: $i, X101: $i] : ((~p7(X99, X101)) | (~p36(X98, X100)) | p37(f38(X98, X99), f38(X100, X101)))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(53,plain,
% 0.18/0.51 (^[X99: $i, X100: $i, X98: $i, X101: $i] : trans(monotonicity(rewrite((p37(f38(X98, X99), f38(X100, X101)) | (~p36(X98, X100))) <=> ((~p36(X98, X100)) | p37(f38(X98, X99), f38(X100, X101)))), (((p37(f38(X98, X99), f38(X100, X101)) | (~p36(X98, X100))) | (~p7(X99, X101))) <=> (((~p36(X98, X100)) | p37(f38(X98, X99), f38(X100, X101))) | (~p7(X99, X101))))), rewrite((((~p36(X98, X100)) | p37(f38(X98, X99), f38(X100, X101))) | (~p7(X99, X101))) <=> ((~p7(X99, X101)) | (~p36(X98, X100)) | p37(f38(X98, X99), f38(X100, X101)))), (((p37(f38(X98, X99), f38(X100, X101)) | (~p36(X98, X100))) | (~p7(X99, X101))) <=> ((~p7(X99, X101)) | (~p36(X98, X100)) | p37(f38(X98, X99), f38(X100, X101)))))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(54,plain,
% 0.18/0.51 (![X99: $i, X100: $i, X98: $i, X101: $i] : ((p37(f38(X98, X99), f38(X100, X101)) | (~p36(X98, X100))) | (~p7(X99, X101))) <=> ![X99: $i, X100: $i, X98: $i, X101: $i] : ((~p7(X99, X101)) | (~p36(X98, X100)) | p37(f38(X98, X99), f38(X100, X101)))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[53])).
% 0.18/0.51 tff(55,axiom,(![X99: $i, X100: $i, X98: $i, X101: $i] : ((p37(f38(X98, X99), f38(X100, X101)) | (~p36(X98, X100))) | (~p7(X99, X101)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p37_67')).
% 0.18/0.51 tff(56,plain,
% 0.18/0.51 (![X99: $i, X100: $i, X98: $i, X101: $i] : ((~p7(X99, X101)) | (~p36(X98, X100)) | p37(f38(X98, X99), f38(X100, X101)))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.18/0.51 tff(57,plain,
% 0.18/0.51 (![X99: $i, X100: $i, X98: $i, X101: $i] : ((~p7(X99, X101)) | (~p36(X98, X100)) | p37(f38(X98, X99), f38(X100, X101)))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.18/0.51 tff(58,plain,(
% 0.18/0.51 ![X99: $i, X100: $i, X98: $i, X101: $i] : ((~p7(X99, X101)) | (~p36(X98, X100)) | p37(f38(X98, X99), f38(X100, X101)))),
% 0.18/0.51 inference(skolemize,[status(sab)],[57])).
% 0.18/0.51 tff(59,plain,
% 0.18/0.51 (![X99: $i, X100: $i, X98: $i, X101: $i] : ((~p7(X99, X101)) | (~p36(X98, X100)) | p37(f38(X98, X99), f38(X100, X101)))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.18/0.51 tff(60,plain,
% 0.18/0.51 (((~![X99: $i, X100: $i, X98: $i, X101: $i] : ((~p7(X99, X101)) | (~p36(X98, X100)) | p37(f38(X98, X99), f38(X100, X101)))) | ((~p36(f40(c59, c50), f40(c59, c50))) | p37(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)), f38(f40(c59, c50), c58)) | (~p7(f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58), c58)))) <=> ((~![X99: $i, X100: $i, X98: $i, X101: $i] : ((~p7(X99, X101)) | (~p36(X98, X100)) | p37(f38(X98, X99), f38(X100, X101)))) | (~p36(f40(c59, c50), f40(c59, c50))) | p37(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)), f38(f40(c59, c50), c58)) | (~p7(f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58), c58)))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(61,plain,
% 0.18/0.51 (((~p7(f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58), c58)) | (~p36(f40(c59, c50), f40(c59, c50))) | p37(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)), f38(f40(c59, c50), c58))) <=> ((~p36(f40(c59, c50), f40(c59, c50))) | p37(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)), f38(f40(c59, c50), c58)) | (~p7(f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58), c58)))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(62,plain,
% 0.18/0.51 (((~![X99: $i, X100: $i, X98: $i, X101: $i] : ((~p7(X99, X101)) | (~p36(X98, X100)) | p37(f38(X98, X99), f38(X100, X101)))) | ((~p7(f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58), c58)) | (~p36(f40(c59, c50), f40(c59, c50))) | p37(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)), f38(f40(c59, c50), c58)))) <=> ((~![X99: $i, X100: $i, X98: $i, X101: $i] : ((~p7(X99, X101)) | (~p36(X98, X100)) | p37(f38(X98, X99), f38(X100, X101)))) | ((~p36(f40(c59, c50), f40(c59, c50))) | p37(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)), f38(f40(c59, c50), c58)) | (~p7(f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58), c58))))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[61])).
% 0.18/0.51 tff(63,plain,
% 0.18/0.51 (((~![X99: $i, X100: $i, X98: $i, X101: $i] : ((~p7(X99, X101)) | (~p36(X98, X100)) | p37(f38(X98, X99), f38(X100, X101)))) | ((~p7(f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58), c58)) | (~p36(f40(c59, c50), f40(c59, c50))) | p37(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)), f38(f40(c59, c50), c58)))) <=> ((~![X99: $i, X100: $i, X98: $i, X101: $i] : ((~p7(X99, X101)) | (~p36(X98, X100)) | p37(f38(X98, X99), f38(X100, X101)))) | (~p36(f40(c59, c50), f40(c59, c50))) | p37(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)), f38(f40(c59, c50), c58)) | (~p7(f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58), c58)))),
% 0.18/0.51 inference(transitivity,[status(thm)],[62, 60])).
% 0.18/0.51 tff(64,plain,
% 0.18/0.51 ((~![X99: $i, X100: $i, X98: $i, X101: $i] : ((~p7(X99, X101)) | (~p36(X98, X100)) | p37(f38(X98, X99), f38(X100, X101)))) | ((~p7(f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58), c58)) | (~p36(f40(c59, c50), f40(c59, c50))) | p37(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)), f38(f40(c59, c50), c58)))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(65,plain,
% 0.18/0.51 ((~![X99: $i, X100: $i, X98: $i, X101: $i] : ((~p7(X99, X101)) | (~p36(X98, X100)) | p37(f38(X98, X99), f38(X100, X101)))) | (~p36(f40(c59, c50), f40(c59, c50))) | p37(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)), f38(f40(c59, c50), c58)) | (~p7(f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58), c58))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.18/0.51 tff(66,plain,
% 0.18/0.51 (p37(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)), f38(f40(c59, c50), c58))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[65, 59, 49, 9])).
% 0.18/0.51 tff(67,plain,
% 0.18/0.51 (^[X142: $i, X137: $i, X136: $i] : refl(((~p45(f20(c52, X136), X137)) | p46(f23(c53, f35(X137, X142)), f5(c49, X136))) <=> ((~p45(f20(c52, X136), X137)) | p46(f23(c53, f35(X137, X142)), f5(c49, X136))))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(68,plain,
% 0.18/0.51 (![X142: $i, X137: $i, X136: $i] : ((~p45(f20(c52, X136), X137)) | p46(f23(c53, f35(X137, X142)), f5(c49, X136))) <=> ![X142: $i, X137: $i, X136: $i] : ((~p45(f20(c52, X136), X137)) | p46(f23(c53, f35(X137, X142)), f5(c49, X136)))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[67])).
% 0.18/0.51 tff(69,plain,
% 0.18/0.51 (![X142: $i, X137: $i, X136: $i] : ((~p45(f20(c52, X136), X137)) | p46(f23(c53, f35(X137, X142)), f5(c49, X136))) <=> ![X142: $i, X137: $i, X136: $i] : ((~p45(f20(c52, X136), X137)) | p46(f23(c53, f35(X137, X142)), f5(c49, X136)))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(70,plain,
% 0.18/0.51 (^[X142: $i, X137: $i, X136: $i] : rewrite((p46(f23(c53, f35(X137, X142)), f5(c49, X136)) | (~p45(f20(c52, X136), X137))) <=> ((~p45(f20(c52, X136), X137)) | p46(f23(c53, f35(X137, X142)), f5(c49, X136))))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(71,plain,
% 0.18/0.51 (![X142: $i, X137: $i, X136: $i] : (p46(f23(c53, f35(X137, X142)), f5(c49, X136)) | (~p45(f20(c52, X136), X137))) <=> ![X142: $i, X137: $i, X136: $i] : ((~p45(f20(c52, X136), X137)) | p46(f23(c53, f35(X137, X142)), f5(c49, X136)))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[70])).
% 0.18/0.51 tff(72,axiom,(![X142: $i, X137: $i, X136: $i] : (p46(f23(c53, f35(X137, X142)), f5(c49, X136)) | (~p45(f20(c52, X136), X137)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p46_78')).
% 0.18/0.51 tff(73,plain,
% 0.18/0.51 (![X142: $i, X137: $i, X136: $i] : ((~p45(f20(c52, X136), X137)) | p46(f23(c53, f35(X137, X142)), f5(c49, X136)))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.18/0.51 tff(74,plain,
% 0.18/0.51 (![X142: $i, X137: $i, X136: $i] : ((~p45(f20(c52, X136), X137)) | p46(f23(c53, f35(X137, X142)), f5(c49, X136)))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.18/0.51 tff(75,plain,(
% 0.18/0.51 ![X142: $i, X137: $i, X136: $i] : ((~p45(f20(c52, X136), X137)) | p46(f23(c53, f35(X137, X142)), f5(c49, X136)))),
% 0.18/0.51 inference(skolemize,[status(sab)],[74])).
% 0.18/0.51 tff(76,plain,
% 0.18/0.51 (![X142: $i, X137: $i, X136: $i] : ((~p45(f20(c52, X136), X137)) | p46(f23(c53, f35(X137, X142)), f5(c49, X136)))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[75, 68])).
% 0.18/0.51 tff(77,plain,
% 0.18/0.51 (p45(f20(c52, c50), c58) <=> p45(f20(c52, c50), c58)),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(78,axiom,(p45(f20(c52, c50), c58)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p45_27')).
% 0.18/0.51 tff(79,plain,
% 0.18/0.51 (p45(f20(c52, c50), c58)),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.18/0.51 tff(80,plain,
% 0.18/0.51 (((~![X142: $i, X137: $i, X136: $i] : ((~p45(f20(c52, X136), X137)) | p46(f23(c53, f35(X137, X142)), f5(c49, X136)))) | ((~p45(f20(c52, c50), c58)) | p46(f23(c53, f35(c58, c61)), f5(c49, c50)))) <=> ((~![X142: $i, X137: $i, X136: $i] : ((~p45(f20(c52, X136), X137)) | p46(f23(c53, f35(X137, X142)), f5(c49, X136)))) | (~p45(f20(c52, c50), c58)) | p46(f23(c53, f35(c58, c61)), f5(c49, c50)))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(81,plain,
% 0.18/0.51 ((~![X142: $i, X137: $i, X136: $i] : ((~p45(f20(c52, X136), X137)) | p46(f23(c53, f35(X137, X142)), f5(c49, X136)))) | ((~p45(f20(c52, c50), c58)) | p46(f23(c53, f35(c58, c61)), f5(c49, c50)))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.52 tff(82,plain,
% 0.18/0.52 ((~![X142: $i, X137: $i, X136: $i] : ((~p45(f20(c52, X136), X137)) | p46(f23(c53, f35(X137, X142)), f5(c49, X136)))) | (~p45(f20(c52, c50), c58)) | p46(f23(c53, f35(c58, c61)), f5(c49, c50))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.18/0.52 tff(83,plain,
% 0.18/0.52 (p46(f23(c53, f35(c58, c61)), f5(c49, c50))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[82, 79, 76])).
% 0.18/0.52 tff(84,plain,
% 0.18/0.52 (^[X150: $i, X151: $i] : refl(((~p46(f23(c53, X150), f5(c49, c50))) | (~p45(f20(c52, c50), X151)) | p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), X150)), X151)), c60)) <=> ((~p46(f23(c53, X150), f5(c49, c50))) | (~p45(f20(c52, c50), X151)) | p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), X150)), X151)), c60)))),
% 0.18/0.52 inference(bind,[status(th)],[])).
% 0.18/0.52 tff(85,plain,
% 0.18/0.52 (![X150: $i, X151: $i] : ((~p46(f23(c53, X150), f5(c49, c50))) | (~p45(f20(c52, c50), X151)) | p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), X150)), X151)), c60)) <=> ![X150: $i, X151: $i] : ((~p46(f23(c53, X150), f5(c49, c50))) | (~p45(f20(c52, c50), X151)) | p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), X150)), X151)), c60))),
% 0.18/0.52 inference(quant_intro,[status(thm)],[84])).
% 0.18/0.52 tff(86,plain,
% 0.18/0.52 (![X150: $i, X151: $i] : ((~p46(f23(c53, X150), f5(c49, c50))) | (~p45(f20(c52, c50), X151)) | p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), X150)), X151)), c60)) <=> ![X150: $i, X151: $i] : ((~p46(f23(c53, X150), f5(c49, c50))) | (~p45(f20(c52, c50), X151)) | p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), X150)), X151)), c60))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(87,plain,
% 0.18/0.52 (^[X150: $i, X151: $i] : trans(monotonicity(rewrite((p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), X150)), X151)), c60) | (~p45(f20(c52, c50), X151))) <=> ((~p45(f20(c52, c50), X151)) | p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), X150)), X151)), c60))), (((p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), X150)), X151)), c60) | (~p45(f20(c52, c50), X151))) | (~p46(f23(c53, X150), f5(c49, c50)))) <=> (((~p45(f20(c52, c50), X151)) | p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), X150)), X151)), c60)) | (~p46(f23(c53, X150), f5(c49, c50)))))), rewrite((((~p45(f20(c52, c50), X151)) | p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), X150)), X151)), c60)) | (~p46(f23(c53, X150), f5(c49, c50)))) <=> ((~p46(f23(c53, X150), f5(c49, c50))) | (~p45(f20(c52, c50), X151)) | p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), X150)), X151)), c60))), (((p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), X150)), X151)), c60) | (~p45(f20(c52, c50), X151))) | (~p46(f23(c53, X150), f5(c49, c50)))) <=> ((~p46(f23(c53, X150), f5(c49, c50))) | (~p45(f20(c52, c50), X151)) | p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), X150)), X151)), c60))))),
% 0.18/0.52 inference(bind,[status(th)],[])).
% 0.18/0.52 tff(88,plain,
% 0.18/0.52 (![X150: $i, X151: $i] : ((p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), X150)), X151)), c60) | (~p45(f20(c52, c50), X151))) | (~p46(f23(c53, X150), f5(c49, c50)))) <=> ![X150: $i, X151: $i] : ((~p46(f23(c53, X150), f5(c49, c50))) | (~p45(f20(c52, c50), X151)) | p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), X150)), X151)), c60))),
% 0.18/0.52 inference(quant_intro,[status(thm)],[87])).
% 0.18/0.52 tff(89,axiom,(![X150: $i, X151: $i] : ((p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), X150)), X151)), c60) | (~p45(f20(c52, c50), X151))) | (~p46(f23(c53, X150), f5(c49, c50))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p48_81')).
% 0.18/0.52 tff(90,plain,
% 0.18/0.52 (![X150: $i, X151: $i] : ((~p46(f23(c53, X150), f5(c49, c50))) | (~p45(f20(c52, c50), X151)) | p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), X150)), X151)), c60))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.18/0.52 tff(91,plain,
% 0.18/0.52 (![X150: $i, X151: $i] : ((~p46(f23(c53, X150), f5(c49, c50))) | (~p45(f20(c52, c50), X151)) | p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), X150)), X151)), c60))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.18/0.52 tff(92,plain,(
% 0.18/0.52 ![X150: $i, X151: $i] : ((~p46(f23(c53, X150), f5(c49, c50))) | (~p45(f20(c52, c50), X151)) | p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), X150)), X151)), c60))),
% 0.18/0.52 inference(skolemize,[status(sab)],[91])).
% 0.18/0.52 tff(93,plain,
% 0.18/0.52 (![X150: $i, X151: $i] : ((~p46(f23(c53, X150), f5(c49, c50))) | (~p45(f20(c52, c50), X151)) | p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), X150)), X151)), c60))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[92, 85])).
% 0.18/0.52 tff(94,plain,
% 0.18/0.52 (((~![X150: $i, X151: $i] : ((~p46(f23(c53, X150), f5(c49, c50))) | (~p45(f20(c52, c50), X151)) | p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), X150)), X151)), c60))) | ((~p45(f20(c52, c50), c58)) | (~p46(f23(c53, f35(c58, c61)), f5(c49, c50))) | p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)), c60))) <=> ((~![X150: $i, X151: $i] : ((~p46(f23(c53, X150), f5(c49, c50))) | (~p45(f20(c52, c50), X151)) | p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), X150)), X151)), c60))) | (~p45(f20(c52, c50), c58)) | (~p46(f23(c53, f35(c58, c61)), f5(c49, c50))) | p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)), c60))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(95,plain,
% 0.18/0.52 (((~p46(f23(c53, f35(c58, c61)), f5(c49, c50))) | (~p45(f20(c52, c50), c58)) | p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)), c60)) <=> ((~p45(f20(c52, c50), c58)) | (~p46(f23(c53, f35(c58, c61)), f5(c49, c50))) | p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)), c60))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(96,plain,
% 0.18/0.52 (((~![X150: $i, X151: $i] : ((~p46(f23(c53, X150), f5(c49, c50))) | (~p45(f20(c52, c50), X151)) | p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), X150)), X151)), c60))) | ((~p46(f23(c53, f35(c58, c61)), f5(c49, c50))) | (~p45(f20(c52, c50), c58)) | p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)), c60))) <=> ((~![X150: $i, X151: $i] : ((~p46(f23(c53, X150), f5(c49, c50))) | (~p45(f20(c52, c50), X151)) | p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), X150)), X151)), c60))) | ((~p45(f20(c52, c50), c58)) | (~p46(f23(c53, f35(c58, c61)), f5(c49, c50))) | p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)), c60)))),
% 0.18/0.52 inference(monotonicity,[status(thm)],[95])).
% 0.18/0.52 tff(97,plain,
% 0.18/0.52 (((~![X150: $i, X151: $i] : ((~p46(f23(c53, X150), f5(c49, c50))) | (~p45(f20(c52, c50), X151)) | p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), X150)), X151)), c60))) | ((~p46(f23(c53, f35(c58, c61)), f5(c49, c50))) | (~p45(f20(c52, c50), c58)) | p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)), c60))) <=> ((~![X150: $i, X151: $i] : ((~p46(f23(c53, X150), f5(c49, c50))) | (~p45(f20(c52, c50), X151)) | p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), X150)), X151)), c60))) | (~p45(f20(c52, c50), c58)) | (~p46(f23(c53, f35(c58, c61)), f5(c49, c50))) | p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)), c60))),
% 0.18/0.52 inference(transitivity,[status(thm)],[96, 94])).
% 0.18/0.52 tff(98,plain,
% 0.18/0.52 ((~![X150: $i, X151: $i] : ((~p46(f23(c53, X150), f5(c49, c50))) | (~p45(f20(c52, c50), X151)) | p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), X150)), X151)), c60))) | ((~p46(f23(c53, f35(c58, c61)), f5(c49, c50))) | (~p45(f20(c52, c50), c58)) | p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)), c60))),
% 0.18/0.52 inference(quant_inst,[status(thm)],[])).
% 0.18/0.52 tff(99,plain,
% 0.18/0.52 ((~![X150: $i, X151: $i] : ((~p46(f23(c53, X150), f5(c49, c50))) | (~p45(f20(c52, c50), X151)) | p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), X150)), X151)), c60))) | (~p45(f20(c52, c50), c58)) | (~p46(f23(c53, f35(c58, c61)), f5(c49, c50))) | p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)), c60)),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.18/0.52 tff(100,plain,
% 0.18/0.52 ((~p46(f23(c53, f35(c58, c61)), f5(c49, c50))) | p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)), c60)),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[99, 79, 93])).
% 0.18/0.52 tff(101,plain,
% 0.18/0.52 (p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)), c60)),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[100, 83])).
% 0.18/0.52 tff(102,plain,
% 0.18/0.52 (^[X143: $i] : refl(p47(X143, X143) <=> p47(X143, X143))),
% 0.18/0.52 inference(bind,[status(th)],[])).
% 0.18/0.52 tff(103,plain,
% 0.18/0.52 (![X143: $i] : p47(X143, X143) <=> ![X143: $i] : p47(X143, X143)),
% 0.18/0.52 inference(quant_intro,[status(thm)],[102])).
% 0.18/0.52 tff(104,plain,
% 0.18/0.52 (![X143: $i] : p47(X143, X143) <=> ![X143: $i] : p47(X143, X143)),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(105,axiom,(![X143: $i] : p47(X143, X143)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p47_5')).
% 0.18/0.52 tff(106,plain,
% 0.18/0.52 (![X143: $i] : p47(X143, X143)),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.18/0.52 tff(107,plain,(
% 0.18/0.52 ![X143: $i] : p47(X143, X143)),
% 0.18/0.52 inference(skolemize,[status(sab)],[106])).
% 0.18/0.52 tff(108,plain,
% 0.18/0.52 (![X143: $i] : p47(X143, X143)),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.18/0.52 tff(109,plain,
% 0.18/0.52 ((~![X143: $i] : p47(X143, X143)) | p47(c60, c60)),
% 0.18/0.52 inference(quant_inst,[status(thm)],[])).
% 0.18/0.52 tff(110,plain,
% 0.18/0.52 (p47(c60, c60)),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[109, 108])).
% 0.18/0.52 tff(111,plain,
% 0.18/0.52 (^[X148: $i, X146: $i, X147: $i, X149: $i] : refl(((~p37(X148, X146)) | (~p48(X148, X149)) | (~p47(X149, X147)) | p48(X146, X147)) <=> ((~p37(X148, X146)) | (~p48(X148, X149)) | (~p47(X149, X147)) | p48(X146, X147)))),
% 0.18/0.52 inference(bind,[status(th)],[])).
% 0.18/0.52 tff(112,plain,
% 0.18/0.52 (![X148: $i, X146: $i, X147: $i, X149: $i] : ((~p37(X148, X146)) | (~p48(X148, X149)) | (~p47(X149, X147)) | p48(X146, X147)) <=> ![X148: $i, X146: $i, X147: $i, X149: $i] : ((~p37(X148, X146)) | (~p48(X148, X149)) | (~p47(X149, X147)) | p48(X146, X147))),
% 0.18/0.52 inference(quant_intro,[status(thm)],[111])).
% 0.18/0.52 tff(113,plain,
% 0.18/0.52 (![X148: $i, X146: $i, X147: $i, X149: $i] : ((~p37(X148, X146)) | (~p48(X148, X149)) | (~p47(X149, X147)) | p48(X146, X147)) <=> ![X148: $i, X146: $i, X147: $i, X149: $i] : ((~p37(X148, X146)) | (~p48(X148, X149)) | (~p47(X149, X147)) | p48(X146, X147))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(114,plain,
% 0.18/0.52 (^[X148: $i, X146: $i, X147: $i, X149: $i] : trans(monotonicity(trans(monotonicity(rewrite((p48(X146, X147) | (~p47(X149, X147))) <=> ((~p47(X149, X147)) | p48(X146, X147))), (((p48(X146, X147) | (~p47(X149, X147))) | (~p48(X148, X149))) <=> (((~p47(X149, X147)) | p48(X146, X147)) | (~p48(X148, X149))))), rewrite((((~p47(X149, X147)) | p48(X146, X147)) | (~p48(X148, X149))) <=> ((~p48(X148, X149)) | (~p47(X149, X147)) | p48(X146, X147))), (((p48(X146, X147) | (~p47(X149, X147))) | (~p48(X148, X149))) <=> ((~p48(X148, X149)) | (~p47(X149, X147)) | p48(X146, X147)))), ((((p48(X146, X147) | (~p47(X149, X147))) | (~p48(X148, X149))) | (~p37(X148, X146))) <=> (((~p48(X148, X149)) | (~p47(X149, X147)) | p48(X146, X147)) | (~p37(X148, X146))))), rewrite((((~p48(X148, X149)) | (~p47(X149, X147)) | p48(X146, X147)) | (~p37(X148, X146))) <=> ((~p37(X148, X146)) | (~p48(X148, X149)) | (~p47(X149, X147)) | p48(X146, X147))), ((((p48(X146, X147) | (~p47(X149, X147))) | (~p48(X148, X149))) | (~p37(X148, X146))) <=> ((~p37(X148, X146)) | (~p48(X148, X149)) | (~p47(X149, X147)) | p48(X146, X147))))),
% 0.18/0.52 inference(bind,[status(th)],[])).
% 0.18/0.52 tff(115,plain,
% 0.18/0.52 (![X148: $i, X146: $i, X147: $i, X149: $i] : (((p48(X146, X147) | (~p47(X149, X147))) | (~p48(X148, X149))) | (~p37(X148, X146))) <=> ![X148: $i, X146: $i, X147: $i, X149: $i] : ((~p37(X148, X146)) | (~p48(X148, X149)) | (~p47(X149, X147)) | p48(X146, X147))),
% 0.18/0.52 inference(quant_intro,[status(thm)],[114])).
% 0.18/0.52 tff(116,axiom,(![X148: $i, X146: $i, X147: $i, X149: $i] : (((p48(X146, X147) | (~p47(X149, X147))) | (~p48(X148, X149))) | (~p37(X148, X146)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p48_57')).
% 0.18/0.52 tff(117,plain,
% 0.18/0.52 (![X148: $i, X146: $i, X147: $i, X149: $i] : ((~p37(X148, X146)) | (~p48(X148, X149)) | (~p47(X149, X147)) | p48(X146, X147))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.18/0.52 tff(118,plain,
% 0.18/0.52 (![X148: $i, X146: $i, X147: $i, X149: $i] : ((~p37(X148, X146)) | (~p48(X148, X149)) | (~p47(X149, X147)) | p48(X146, X147))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[117, 113])).
% 0.18/0.52 tff(119,plain,(
% 0.18/0.52 ![X148: $i, X146: $i, X147: $i, X149: $i] : ((~p37(X148, X146)) | (~p48(X148, X149)) | (~p47(X149, X147)) | p48(X146, X147))),
% 0.18/0.52 inference(skolemize,[status(sab)],[118])).
% 0.18/0.52 tff(120,plain,
% 0.18/0.52 (![X148: $i, X146: $i, X147: $i, X149: $i] : ((~p37(X148, X146)) | (~p48(X148, X149)) | (~p47(X149, X147)) | p48(X146, X147))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[119, 112])).
% 0.18/0.52 tff(121,plain,
% 0.18/0.52 ((~p48(f38(f40(c59, c50), c58), c60)) <=> (~p48(f38(f40(c59, c50), c58), c60))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(122,axiom,(~p48(f38(f40(c59, c50), c58), c60)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_p48_29')).
% 0.18/0.52 tff(123,plain,
% 0.18/0.52 (~p48(f38(f40(c59, c50), c58), c60)),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.18/0.52 tff(124,plain,
% 0.18/0.52 (((~![X148: $i, X146: $i, X147: $i, X149: $i] : ((~p37(X148, X146)) | (~p48(X148, X149)) | (~p47(X149, X147)) | p48(X146, X147))) | (p48(f38(f40(c59, c50), c58), c60) | (~p47(c60, c60)) | (~p37(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)), f38(f40(c59, c50), c58))) | (~p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)), c60)))) <=> ((~![X148: $i, X146: $i, X147: $i, X149: $i] : ((~p37(X148, X146)) | (~p48(X148, X149)) | (~p47(X149, X147)) | p48(X146, X147))) | p48(f38(f40(c59, c50), c58), c60) | (~p47(c60, c60)) | (~p37(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)), f38(f40(c59, c50), c58))) | (~p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)), c60)))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(125,plain,
% 0.18/0.52 (((~p37(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)), f38(f40(c59, c50), c58))) | (~p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)), c60)) | (~p47(c60, c60)) | p48(f38(f40(c59, c50), c58), c60)) <=> (p48(f38(f40(c59, c50), c58), c60) | (~p47(c60, c60)) | (~p37(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)), f38(f40(c59, c50), c58))) | (~p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)), c60)))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(126,plain,
% 0.18/0.52 (((~![X148: $i, X146: $i, X147: $i, X149: $i] : ((~p37(X148, X146)) | (~p48(X148, X149)) | (~p47(X149, X147)) | p48(X146, X147))) | ((~p37(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)), f38(f40(c59, c50), c58))) | (~p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)), c60)) | (~p47(c60, c60)) | p48(f38(f40(c59, c50), c58), c60))) <=> ((~![X148: $i, X146: $i, X147: $i, X149: $i] : ((~p37(X148, X146)) | (~p48(X148, X149)) | (~p47(X149, X147)) | p48(X146, X147))) | (p48(f38(f40(c59, c50), c58), c60) | (~p47(c60, c60)) | (~p37(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)), f38(f40(c59, c50), c58))) | (~p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)), c60))))),
% 0.18/0.52 inference(monotonicity,[status(thm)],[125])).
% 0.18/0.52 tff(127,plain,
% 0.18/0.52 (((~![X148: $i, X146: $i, X147: $i, X149: $i] : ((~p37(X148, X146)) | (~p48(X148, X149)) | (~p47(X149, X147)) | p48(X146, X147))) | ((~p37(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)), f38(f40(c59, c50), c58))) | (~p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)), c60)) | (~p47(c60, c60)) | p48(f38(f40(c59, c50), c58), c60))) <=> ((~![X148: $i, X146: $i, X147: $i, X149: $i] : ((~p37(X148, X146)) | (~p48(X148, X149)) | (~p47(X149, X147)) | p48(X146, X147))) | p48(f38(f40(c59, c50), c58), c60) | (~p47(c60, c60)) | (~p37(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)), f38(f40(c59, c50), c58))) | (~p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)), c60)))),
% 0.18/0.52 inference(transitivity,[status(thm)],[126, 124])).
% 0.18/0.52 tff(128,plain,
% 0.18/0.52 ((~![X148: $i, X146: $i, X147: $i, X149: $i] : ((~p37(X148, X146)) | (~p48(X148, X149)) | (~p47(X149, X147)) | p48(X146, X147))) | ((~p37(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)), f38(f40(c59, c50), c58))) | (~p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)), c60)) | (~p47(c60, c60)) | p48(f38(f40(c59, c50), c58), c60))),
% 0.18/0.53 inference(quant_inst,[status(thm)],[])).
% 0.18/0.53 tff(129,plain,
% 0.18/0.53 ((~![X148: $i, X146: $i, X147: $i, X149: $i] : ((~p37(X148, X146)) | (~p48(X148, X149)) | (~p47(X149, X147)) | p48(X146, X147))) | p48(f38(f40(c59, c50), c58), c60) | (~p47(c60, c60)) | (~p37(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)), f38(f40(c59, c50), c58))) | (~p48(f38(f40(c59, c50), f8(f11(c54, f14(f17(c55, c61), f35(c58, c61))), c58)), c60))),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.18/0.53 tff(130,plain,
% 0.18/0.53 ($false),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[129, 123, 120, 110, 101, 66])).
% 0.18/0.53 % SZS output end Proof
% 0.18/0.53 % E exiting
%------------------------------------------------------------------------------