%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN591-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:39:38 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SYN591-1 : TPTP v9.0.0. Released v2.5.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:38:35 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.41 % SZS status Unsatisfiable
% 0.19/0.41 % SZS output start Proof
% 0.19/0.41 tff(p3_type, type, (
% 0.19/0.41 p3: ( $i * $i ) > $o)).
% 0.19/0.41 tff(f4_type, type, (
% 0.19/0.41 f4: ( $i * $i ) > $i)).
% 0.19/0.41 tff(c17_type, type, (
% 0.19/0.41 c17: $i)).
% 0.19/0.41 tff(f6_type, type, (
% 0.19/0.41 f6: $i > $i)).
% 0.19/0.41 tff(c18_type, type, (
% 0.19/0.41 c18: $i)).
% 0.19/0.41 tff(f5_type, type, (
% 0.19/0.41 f5: $i > $i)).
% 0.19/0.41 tff(p2_type, type, (
% 0.19/0.41 p2: ( $i * $i ) > $o)).
% 0.19/0.41 tff(p12_type, type, (
% 0.19/0.41 p12: ( $i * $i ) > $o)).
% 0.19/0.41 tff(c14_type, type, (
% 0.19/0.41 c14: $i)).
% 0.19/0.41 tff(p7_type, type, (
% 0.19/0.41 p7: ( $i * $i ) > $o)).
% 0.19/0.41 tff(c13_type, type, (
% 0.19/0.41 c13: $i)).
% 0.19/0.41 tff(p11_type, type, (
% 0.19/0.41 p11: ( $i * $i ) > $o)).
% 0.19/0.41 tff(1,assumption,(~p2(f6(c18), f6(c18))), introduced(assumption)).
% 0.19/0.41 tff(2,plain,
% 0.19/0.41 (^[X15: $i] : refl(p2(X15, X15) <=> p2(X15, X15))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(3,plain,
% 0.19/0.41 (![X15: $i] : p2(X15, X15) <=> ![X15: $i] : p2(X15, X15)),
% 0.19/0.41 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.41 tff(4,plain,
% 0.19/0.41 (![X15: $i] : p2(X15, X15) <=> ![X15: $i] : p2(X15, X15)),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(5,axiom,(![X15: $i] : p2(X15, X15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_4')).
% 0.19/0.41 tff(6,plain,
% 0.19/0.41 (![X15: $i] : p2(X15, X15)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.19/0.41 tff(7,plain,(
% 0.19/0.41 ![X15: $i] : p2(X15, X15)),
% 0.19/0.41 inference(skolemize,[status(sab)],[6])).
% 0.19/0.41 tff(8,plain,
% 0.19/0.41 (![X15: $i] : p2(X15, X15)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.41 tff(9,plain,
% 0.19/0.41 ((~![X15: $i] : p2(X15, X15)) | p2(f6(c18), f6(c18))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(10,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.19/0.41 tff(11,plain,(p2(f6(c18), f6(c18))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(12,plain,
% 0.19/0.41 (^[X20: $i] : refl(((~p12(c14, f4(X20, c17))) | p2(f6(X20), f5(X20))) <=> ((~p12(c14, f4(X20, c17))) | p2(f6(X20), f5(X20))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(13,plain,
% 0.19/0.41 (![X20: $i] : ((~p12(c14, f4(X20, c17))) | p2(f6(X20), f5(X20))) <=> ![X20: $i] : ((~p12(c14, f4(X20, c17))) | p2(f6(X20), f5(X20)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[12])).
% 0.19/0.41 tff(14,plain,
% 0.19/0.41 (![X20: $i] : ((~p12(c14, f4(X20, c17))) | p2(f6(X20), f5(X20))) <=> ![X20: $i] : ((~p12(c14, f4(X20, c17))) | p2(f6(X20), f5(X20)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(15,plain,
% 0.19/0.41 (^[X20: $i] : rewrite((p2(f6(X20), f5(X20)) | (~p12(c14, f4(X20, c17)))) <=> ((~p12(c14, f4(X20, c17))) | p2(f6(X20), f5(X20))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(16,plain,
% 0.19/0.41 (![X20: $i] : (p2(f6(X20), f5(X20)) | (~p12(c14, f4(X20, c17)))) <=> ![X20: $i] : ((~p12(c14, f4(X20, c17))) | p2(f6(X20), f5(X20)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[15])).
% 0.19/0.41 tff(17,axiom,(![X20: $i] : (p2(f6(X20), f5(X20)) | (~p12(c14, f4(X20, c17))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_22')).
% 0.19/0.41 tff(18,plain,
% 0.19/0.41 (![X20: $i] : ((~p12(c14, f4(X20, c17))) | p2(f6(X20), f5(X20)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.19/0.41 tff(19,plain,
% 0.19/0.41 (![X20: $i] : ((~p12(c14, f4(X20, c17))) | p2(f6(X20), f5(X20)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.19/0.41 tff(20,plain,(
% 0.19/0.41 ![X20: $i] : ((~p12(c14, f4(X20, c17))) | p2(f6(X20), f5(X20)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[19])).
% 0.19/0.41 tff(21,plain,
% 0.19/0.41 (![X20: $i] : ((~p12(c14, f4(X20, c17))) | p2(f6(X20), f5(X20)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.19/0.41 tff(22,plain,
% 0.19/0.41 (p12(c14, f4(c18, c17)) <=> p12(c14, f4(c18, c17))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(23,axiom,(p12(c14, f4(c18, c17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p12_11')).
% 0.19/0.41 tff(24,plain,
% 0.19/0.41 (p12(c14, f4(c18, c17))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.19/0.41 tff(25,plain,
% 0.19/0.41 (((~![X20: $i] : ((~p12(c14, f4(X20, c17))) | p2(f6(X20), f5(X20)))) | ((~p12(c14, f4(c18, c17))) | p2(f6(c18), f5(c18)))) <=> ((~![X20: $i] : ((~p12(c14, f4(X20, c17))) | p2(f6(X20), f5(X20)))) | (~p12(c14, f4(c18, c17))) | p2(f6(c18), f5(c18)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(26,plain,
% 0.19/0.41 ((~![X20: $i] : ((~p12(c14, f4(X20, c17))) | p2(f6(X20), f5(X20)))) | ((~p12(c14, f4(c18, c17))) | p2(f6(c18), f5(c18)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(27,plain,
% 0.19/0.41 ((~![X20: $i] : ((~p12(c14, f4(X20, c17))) | p2(f6(X20), f5(X20)))) | (~p12(c14, f4(c18, c17))) | p2(f6(c18), f5(c18))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.19/0.41 tff(28,plain,
% 0.19/0.41 (p2(f6(c18), f5(c18))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[27, 24, 21])).
% 0.19/0.41 tff(29,plain,
% 0.19/0.41 (^[X17: $i, X16: $i, X15: $i] : refl(((~p2(X15, X16)) | (~p2(X15, X17)) | p2(X16, X17)) <=> ((~p2(X15, X16)) | (~p2(X15, X17)) | p2(X16, X17)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(30,plain,
% 0.19/0.41 (![X17: $i, X16: $i, X15: $i] : ((~p2(X15, X16)) | (~p2(X15, X17)) | p2(X16, X17)) <=> ![X17: $i, X16: $i, X15: $i] : ((~p2(X15, X16)) | (~p2(X15, X17)) | p2(X16, X17))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[29])).
% 0.19/0.41 tff(31,plain,
% 0.19/0.41 (![X17: $i, X16: $i, X15: $i] : ((~p2(X15, X16)) | (~p2(X15, X17)) | p2(X16, X17)) <=> ![X17: $i, X16: $i, X15: $i] : ((~p2(X15, X16)) | (~p2(X15, X17)) | p2(X16, X17))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(32,plain,
% 0.19/0.41 (^[X17: $i, X16: $i, X15: $i] : trans(monotonicity(rewrite((p2(X16, X17) | (~p2(X15, X16))) <=> ((~p2(X15, X16)) | p2(X16, X17))), (((p2(X16, X17) | (~p2(X15, X16))) | (~p2(X15, X17))) <=> (((~p2(X15, X16)) | p2(X16, X17)) | (~p2(X15, X17))))), rewrite((((~p2(X15, X16)) | p2(X16, X17)) | (~p2(X15, X17))) <=> ((~p2(X15, X16)) | (~p2(X15, X17)) | p2(X16, X17))), (((p2(X16, X17) | (~p2(X15, X16))) | (~p2(X15, X17))) <=> ((~p2(X15, X16)) | (~p2(X15, X17)) | p2(X16, X17))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(33,plain,
% 0.19/0.41 (![X17: $i, X16: $i, X15: $i] : ((p2(X16, X17) | (~p2(X15, X16))) | (~p2(X15, X17))) <=> ![X17: $i, X16: $i, X15: $i] : ((~p2(X15, X16)) | (~p2(X15, X17)) | p2(X16, X17))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[32])).
% 0.19/0.41 tff(34,axiom,(![X17: $i, X16: $i, X15: $i] : ((p2(X16, X17) | (~p2(X15, X16))) | (~p2(X15, X17)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_20')).
% 0.19/0.41 tff(35,plain,
% 0.19/0.41 (![X17: $i, X16: $i, X15: $i] : ((~p2(X15, X16)) | (~p2(X15, X17)) | p2(X16, X17))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.19/0.41 tff(36,plain,
% 0.19/0.41 (![X17: $i, X16: $i, X15: $i] : ((~p2(X15, X16)) | (~p2(X15, X17)) | p2(X16, X17))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.19/0.41 tff(37,plain,(
% 0.19/0.41 ![X17: $i, X16: $i, X15: $i] : ((~p2(X15, X16)) | (~p2(X15, X17)) | p2(X16, X17))),
% 0.19/0.41 inference(skolemize,[status(sab)],[36])).
% 0.19/0.41 tff(38,plain,
% 0.19/0.41 (![X17: $i, X16: $i, X15: $i] : ((~p2(X15, X16)) | (~p2(X15, X17)) | p2(X16, X17))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.19/0.41 tff(39,plain,
% 0.19/0.41 (((~![X17: $i, X16: $i, X15: $i] : ((~p2(X15, X16)) | (~p2(X15, X17)) | p2(X16, X17))) | ((~p2(f6(c18), f5(c18))) | (~p2(f6(c18), f6(c18))) | p2(f5(c18), f6(c18)))) <=> ((~![X17: $i, X16: $i, X15: $i] : ((~p2(X15, X16)) | (~p2(X15, X17)) | p2(X16, X17))) | (~p2(f6(c18), f5(c18))) | (~p2(f6(c18), f6(c18))) | p2(f5(c18), f6(c18)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(40,plain,
% 0.19/0.41 ((~![X17: $i, X16: $i, X15: $i] : ((~p2(X15, X16)) | (~p2(X15, X17)) | p2(X16, X17))) | ((~p2(f6(c18), f5(c18))) | (~p2(f6(c18), f6(c18))) | p2(f5(c18), f6(c18)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(41,plain,
% 0.19/0.41 ((~![X17: $i, X16: $i, X15: $i] : ((~p2(X15, X16)) | (~p2(X15, X17)) | p2(X16, X17))) | (~p2(f6(c18), f5(c18))) | (~p2(f6(c18), f6(c18))) | p2(f5(c18), f6(c18))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.19/0.41 tff(42,plain,
% 0.19/0.41 (p2(f5(c18), f6(c18))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[41, 38, 28, 11])).
% 0.19/0.41 tff(43,assumption,(~p2(c17, c17)), introduced(assumption)).
% 0.19/0.41 tff(44,plain,
% 0.19/0.41 ((~![X15: $i] : p2(X15, X15)) | p2(c17, c17)),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(45,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[44, 8, 43])).
% 0.19/0.41 tff(46,plain,(p2(c17, c17)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(47,plain,
% 0.19/0.41 (^[X27: $i, X29: $i, X28: $i, X26: $i] : refl(((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29))) <=> ((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(48,plain,
% 0.19/0.42 (![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29))) <=> ![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[47])).
% 0.19/0.42 tff(49,plain,
% 0.19/0.42 (![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29))) <=> ![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(50,plain,
% 0.19/0.42 (^[X27: $i, X29: $i, X28: $i, X26: $i] : trans(monotonicity(rewrite((p3(f4(X26, X27), f4(X28, X29)) | (~p2(X26, X28))) <=> ((~p2(X26, X28)) | p3(f4(X26, X27), f4(X28, X29)))), (((p3(f4(X26, X27), f4(X28, X29)) | (~p2(X26, X28))) | (~p2(X27, X29))) <=> (((~p2(X26, X28)) | p3(f4(X26, X27), f4(X28, X29))) | (~p2(X27, X29))))), rewrite((((~p2(X26, X28)) | p3(f4(X26, X27), f4(X28, X29))) | (~p2(X27, X29))) <=> ((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29)))), (((p3(f4(X26, X27), f4(X28, X29)) | (~p2(X26, X28))) | (~p2(X27, X29))) <=> ((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(51,plain,
% 0.19/0.42 (![X27: $i, X29: $i, X28: $i, X26: $i] : ((p3(f4(X26, X27), f4(X28, X29)) | (~p2(X26, X28))) | (~p2(X27, X29))) <=> ![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[50])).
% 0.19/0.42 tff(52,axiom,(![X27: $i, X29: $i, X28: $i, X26: $i] : ((p3(f4(X26, X27), f4(X28, X29)) | (~p2(X26, X28))) | (~p2(X27, X29)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3_26')).
% 0.19/0.42 tff(53,plain,
% 0.19/0.42 (![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.19/0.42 tff(54,plain,
% 0.19/0.42 (![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.19/0.42 tff(55,plain,(
% 0.19/0.42 ![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[54])).
% 0.19/0.42 tff(56,plain,
% 0.19/0.42 (![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.19/0.42 tff(57,plain,
% 0.19/0.42 (((~![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29)))) | ((~p2(c17, c17)) | (~p2(f5(c18), f6(c18))) | p3(f4(f5(c18), c17), f4(f6(c18), c17)))) <=> ((~![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29)))) | (~p2(c17, c17)) | (~p2(f5(c18), f6(c18))) | p3(f4(f5(c18), c17), f4(f6(c18), c17)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(58,plain,
% 0.19/0.42 (((~p2(f5(c18), f6(c18))) | (~p2(c17, c17)) | p3(f4(f5(c18), c17), f4(f6(c18), c17))) <=> ((~p2(c17, c17)) | (~p2(f5(c18), f6(c18))) | p3(f4(f5(c18), c17), f4(f6(c18), c17)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(59,plain,
% 0.19/0.42 (((~![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29)))) | ((~p2(f5(c18), f6(c18))) | (~p2(c17, c17)) | p3(f4(f5(c18), c17), f4(f6(c18), c17)))) <=> ((~![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29)))) | ((~p2(c17, c17)) | (~p2(f5(c18), f6(c18))) | p3(f4(f5(c18), c17), f4(f6(c18), c17))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[58])).
% 0.19/0.42 tff(60,plain,
% 0.19/0.42 (((~![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29)))) | ((~p2(f5(c18), f6(c18))) | (~p2(c17, c17)) | p3(f4(f5(c18), c17), f4(f6(c18), c17)))) <=> ((~![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29)))) | (~p2(c17, c17)) | (~p2(f5(c18), f6(c18))) | p3(f4(f5(c18), c17), f4(f6(c18), c17)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[59, 57])).
% 0.19/0.42 tff(61,plain,
% 0.19/0.42 ((~![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29)))) | ((~p2(f5(c18), f6(c18))) | (~p2(c17, c17)) | p3(f4(f5(c18), c17), f4(f6(c18), c17)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(62,plain,
% 0.19/0.42 ((~![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29)))) | (~p2(c17, c17)) | (~p2(f5(c18), f6(c18))) | p3(f4(f5(c18), c17), f4(f6(c18), c17))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.19/0.42 tff(63,plain,
% 0.19/0.42 (p3(f4(f5(c18), c17), f4(f6(c18), c17))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[62, 56, 46, 42])).
% 0.19/0.42 tff(64,assumption,(~p7(c13, c13)), introduced(assumption)).
% 0.19/0.42 tff(65,plain,
% 0.19/0.42 (^[X30: $i] : refl(p7(X30, X30) <=> p7(X30, X30))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(66,plain,
% 0.19/0.42 (![X30: $i] : p7(X30, X30) <=> ![X30: $i] : p7(X30, X30)),
% 0.19/0.42 inference(quant_intro,[status(thm)],[65])).
% 0.19/0.42 tff(67,plain,
% 0.19/0.42 (![X30: $i] : p7(X30, X30) <=> ![X30: $i] : p7(X30, X30)),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(68,axiom,(![X30: $i] : p7(X30, X30)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p7_3')).
% 0.19/0.42 tff(69,plain,
% 0.19/0.42 (![X30: $i] : p7(X30, X30)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.19/0.42 tff(70,plain,(
% 0.19/0.42 ![X30: $i] : p7(X30, X30)),
% 0.19/0.42 inference(skolemize,[status(sab)],[69])).
% 0.19/0.42 tff(71,plain,
% 0.19/0.42 (![X30: $i] : p7(X30, X30)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.19/0.42 tff(72,plain,
% 0.19/0.42 ((~![X30: $i] : p7(X30, X30)) | p7(c13, c13)),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(73,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[72, 71, 64])).
% 0.19/0.42 tff(74,plain,(p7(c13, c13)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(75,assumption,(~p3(f4(c17, f5(c18)), f4(c17, f6(c18)))), introduced(assumption)).
% 0.19/0.42 tff(76,plain,
% 0.19/0.42 (((~![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29)))) | ((~p2(c17, c17)) | (~p2(f5(c18), f6(c18))) | p3(f4(c17, f5(c18)), f4(c17, f6(c18))))) <=> ((~![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29)))) | (~p2(c17, c17)) | (~p2(f5(c18), f6(c18))) | p3(f4(c17, f5(c18)), f4(c17, f6(c18))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(77,plain,
% 0.19/0.42 ((~![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29)))) | ((~p2(c17, c17)) | (~p2(f5(c18), f6(c18))) | p3(f4(c17, f5(c18)), f4(c17, f6(c18))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(78,plain,
% 0.19/0.42 ((~![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29)))) | (~p2(c17, c17)) | (~p2(f5(c18), f6(c18))) | p3(f4(c17, f5(c18)), f4(c17, f6(c18)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.19/0.42 tff(79,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[78, 56, 46, 42, 75])).
% 0.19/0.42 tff(80,plain,(p3(f4(c17, f5(c18)), f4(c17, f6(c18)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(81,plain,
% 0.19/0.42 (^[X6: $i, X7: $i, X5: $i, X8: $i] : refl(((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6)) <=> ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6)))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(82,plain,
% 0.19/0.42 (![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6)) <=> ![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[81])).
% 0.19/0.42 tff(83,plain,
% 0.19/0.42 (![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6)) <=> ![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(84,plain,
% 0.19/0.42 (^[X6: $i, X7: $i, X5: $i, X8: $i] : trans(monotonicity(trans(monotonicity(rewrite((p11(X5, X6) | (~p3(X8, X6))) <=> ((~p3(X8, X6)) | p11(X5, X6))), (((p11(X5, X6) | (~p3(X8, X6))) | (~p7(X7, X5))) <=> (((~p3(X8, X6)) | p11(X5, X6)) | (~p7(X7, X5))))), rewrite((((~p3(X8, X6)) | p11(X5, X6)) | (~p7(X7, X5))) <=> ((~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))), (((p11(X5, X6) | (~p3(X8, X6))) | (~p7(X7, X5))) <=> ((~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6)))), ((((p11(X5, X6) | (~p3(X8, X6))) | (~p7(X7, X5))) | (~p11(X7, X8))) <=> (((~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6)) | (~p11(X7, X8))))), rewrite((((~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6)) | (~p11(X7, X8))) <=> ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))), ((((p11(X5, X6) | (~p3(X8, X6))) | (~p7(X7, X5))) | (~p11(X7, X8))) <=> ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(85,plain,
% 0.19/0.42 (![X6: $i, X7: $i, X5: $i, X8: $i] : (((p11(X5, X6) | (~p3(X8, X6))) | (~p7(X7, X5))) | (~p11(X7, X8))) <=> ![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[84])).
% 0.19/0.42 tff(86,axiom,(![X6: $i, X7: $i, X5: $i, X8: $i] : (((p11(X5, X6) | (~p3(X8, X6))) | (~p7(X7, X5))) | (~p11(X7, X8)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p11_25')).
% 0.19/0.42 tff(87,plain,
% 0.19/0.42 (![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.19/0.42 tff(88,plain,
% 0.19/0.42 (![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.19/0.42 tff(89,plain,(
% 0.19/0.42 ![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))),
% 0.19/0.42 inference(skolemize,[status(sab)],[88])).
% 0.19/0.42 tff(90,plain,
% 0.19/0.42 (![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[89, 82])).
% 0.19/0.42 tff(91,plain,
% 0.19/0.42 ((~p11(c13, f4(c17, f6(c18)))) <=> (~p11(c13, f4(c17, f6(c18))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(92,axiom,(~p11(c13, f4(c17, f6(c18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_p11_12')).
% 0.19/0.42 tff(93,plain,
% 0.19/0.42 (~p11(c13, f4(c17, f6(c18)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.19/0.42 tff(94,plain,
% 0.19/0.42 (((~![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))) | (p11(c13, f4(c17, f6(c18))) | (~p11(c13, f4(c17, f5(c18)))) | (~p3(f4(c17, f5(c18)), f4(c17, f6(c18)))) | (~p7(c13, c13)))) <=> ((~![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))) | p11(c13, f4(c17, f6(c18))) | (~p11(c13, f4(c17, f5(c18)))) | (~p3(f4(c17, f5(c18)), f4(c17, f6(c18)))) | (~p7(c13, c13)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(95,plain,
% 0.19/0.42 (((~p11(c13, f4(c17, f5(c18)))) | (~p7(c13, c13)) | (~p3(f4(c17, f5(c18)), f4(c17, f6(c18)))) | p11(c13, f4(c17, f6(c18)))) <=> (p11(c13, f4(c17, f6(c18))) | (~p11(c13, f4(c17, f5(c18)))) | (~p3(f4(c17, f5(c18)), f4(c17, f6(c18)))) | (~p7(c13, c13)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(96,plain,
% 0.19/0.42 (((~![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))) | ((~p11(c13, f4(c17, f5(c18)))) | (~p7(c13, c13)) | (~p3(f4(c17, f5(c18)), f4(c17, f6(c18)))) | p11(c13, f4(c17, f6(c18))))) <=> ((~![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))) | (p11(c13, f4(c17, f6(c18))) | (~p11(c13, f4(c17, f5(c18)))) | (~p3(f4(c17, f5(c18)), f4(c17, f6(c18)))) | (~p7(c13, c13))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[95])).
% 0.19/0.42 tff(97,plain,
% 0.19/0.42 (((~![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))) | ((~p11(c13, f4(c17, f5(c18)))) | (~p7(c13, c13)) | (~p3(f4(c17, f5(c18)), f4(c17, f6(c18)))) | p11(c13, f4(c17, f6(c18))))) <=> ((~![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))) | p11(c13, f4(c17, f6(c18))) | (~p11(c13, f4(c17, f5(c18)))) | (~p3(f4(c17, f5(c18)), f4(c17, f6(c18)))) | (~p7(c13, c13)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[96, 94])).
% 0.19/0.42 tff(98,plain,
% 0.19/0.42 ((~![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))) | ((~p11(c13, f4(c17, f5(c18)))) | (~p7(c13, c13)) | (~p3(f4(c17, f5(c18)), f4(c17, f6(c18)))) | p11(c13, f4(c17, f6(c18))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(99,plain,
% 0.19/0.43 ((~![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))) | p11(c13, f4(c17, f6(c18))) | (~p11(c13, f4(c17, f5(c18)))) | (~p3(f4(c17, f5(c18)), f4(c17, f6(c18)))) | (~p7(c13, c13))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.19/0.43 tff(100,plain,
% 0.19/0.43 ((~p11(c13, f4(c17, f5(c18)))) | (~p3(f4(c17, f5(c18)), f4(c17, f6(c18)))) | (~p7(c13, c13))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[99, 93, 90])).
% 0.19/0.43 tff(101,plain,
% 0.19/0.43 (~p11(c13, f4(c17, f5(c18)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[100, 80, 74])).
% 0.19/0.43 tff(102,plain,
% 0.19/0.43 (^[X9: $i] : refl(((~p12(c14, f4(X9, c17))) | p11(c13, f4(f5(X9), c17)) | p11(c13, f4(c17, f5(X9)))) <=> ((~p12(c14, f4(X9, c17))) | p11(c13, f4(f5(X9), c17)) | p11(c13, f4(c17, f5(X9)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(103,plain,
% 0.19/0.43 (![X9: $i] : ((~p12(c14, f4(X9, c17))) | p11(c13, f4(f5(X9), c17)) | p11(c13, f4(c17, f5(X9)))) <=> ![X9: $i] : ((~p12(c14, f4(X9, c17))) | p11(c13, f4(f5(X9), c17)) | p11(c13, f4(c17, f5(X9))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[102])).
% 0.19/0.43 tff(104,plain,
% 0.19/0.43 (![X9: $i] : ((~p12(c14, f4(X9, c17))) | p11(c13, f4(f5(X9), c17)) | p11(c13, f4(c17, f5(X9)))) <=> ![X9: $i] : ((~p12(c14, f4(X9, c17))) | p11(c13, f4(f5(X9), c17)) | p11(c13, f4(c17, f5(X9))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(105,plain,
% 0.19/0.43 (^[X9: $i] : rewrite(((p11(c13, f4(c17, f5(X9))) | p11(c13, f4(f5(X9), c17))) | (~p12(c14, f4(X9, c17)))) <=> ((~p12(c14, f4(X9, c17))) | p11(c13, f4(f5(X9), c17)) | p11(c13, f4(c17, f5(X9)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(106,plain,
% 0.19/0.43 (![X9: $i] : ((p11(c13, f4(c17, f5(X9))) | p11(c13, f4(f5(X9), c17))) | (~p12(c14, f4(X9, c17)))) <=> ![X9: $i] : ((~p12(c14, f4(X9, c17))) | p11(c13, f4(f5(X9), c17)) | p11(c13, f4(c17, f5(X9))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[105])).
% 0.19/0.43 tff(107,axiom,(![X9: $i] : ((p11(c13, f4(c17, f5(X9))) | p11(c13, f4(f5(X9), c17))) | (~p12(c14, f4(X9, c17))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p11_27')).
% 0.19/0.43 tff(108,plain,
% 0.19/0.43 (![X9: $i] : ((~p12(c14, f4(X9, c17))) | p11(c13, f4(f5(X9), c17)) | p11(c13, f4(c17, f5(X9))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.19/0.43 tff(109,plain,
% 0.19/0.43 (![X9: $i] : ((~p12(c14, f4(X9, c17))) | p11(c13, f4(f5(X9), c17)) | p11(c13, f4(c17, f5(X9))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[108, 104])).
% 0.19/0.43 tff(110,plain,(
% 0.19/0.43 ![X9: $i] : ((~p12(c14, f4(X9, c17))) | p11(c13, f4(f5(X9), c17)) | p11(c13, f4(c17, f5(X9))))),
% 0.19/0.43 inference(skolemize,[status(sab)],[109])).
% 0.19/0.43 tff(111,plain,
% 0.19/0.43 (![X9: $i] : ((~p12(c14, f4(X9, c17))) | p11(c13, f4(f5(X9), c17)) | p11(c13, f4(c17, f5(X9))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[110, 103])).
% 0.19/0.43 tff(112,plain,
% 0.19/0.43 (((~![X9: $i] : ((~p12(c14, f4(X9, c17))) | p11(c13, f4(f5(X9), c17)) | p11(c13, f4(c17, f5(X9))))) | ((~p12(c14, f4(c18, c17))) | p11(c13, f4(f5(c18), c17)) | p11(c13, f4(c17, f5(c18))))) <=> ((~![X9: $i] : ((~p12(c14, f4(X9, c17))) | p11(c13, f4(f5(X9), c17)) | p11(c13, f4(c17, f5(X9))))) | (~p12(c14, f4(c18, c17))) | p11(c13, f4(f5(c18), c17)) | p11(c13, f4(c17, f5(c18))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(113,plain,
% 0.19/0.43 ((~![X9: $i] : ((~p12(c14, f4(X9, c17))) | p11(c13, f4(f5(X9), c17)) | p11(c13, f4(c17, f5(X9))))) | ((~p12(c14, f4(c18, c17))) | p11(c13, f4(f5(c18), c17)) | p11(c13, f4(c17, f5(c18))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(114,plain,
% 0.19/0.43 ((~![X9: $i] : ((~p12(c14, f4(X9, c17))) | p11(c13, f4(f5(X9), c17)) | p11(c13, f4(c17, f5(X9))))) | (~p12(c14, f4(c18, c17))) | p11(c13, f4(f5(c18), c17)) | p11(c13, f4(c17, f5(c18)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.19/0.43 tff(115,plain,
% 0.19/0.43 (p11(c13, f4(f5(c18), c17)) | p11(c13, f4(c17, f5(c18)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[114, 24, 111])).
% 0.19/0.43 tff(116,plain,
% 0.19/0.43 (p11(c13, f4(f5(c18), c17))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[115, 101])).
% 0.19/0.43 tff(117,plain,
% 0.19/0.43 ((~p11(c13, f4(f6(c18), c17))) <=> (~p11(c13, f4(f6(c18), c17)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(118,axiom,(~p11(c13, f4(f6(c18), c17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_p11_13')).
% 0.19/0.43 tff(119,plain,
% 0.19/0.43 (~p11(c13, f4(f6(c18), c17))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.19/0.43 tff(120,plain,
% 0.19/0.43 (((~![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))) | (p11(c13, f4(f6(c18), c17)) | (~p3(f4(f5(c18), c17), f4(f6(c18), c17))) | (~p11(c13, f4(f5(c18), c17))) | (~p7(c13, c13)))) <=> ((~![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))) | p11(c13, f4(f6(c18), c17)) | (~p3(f4(f5(c18), c17), f4(f6(c18), c17))) | (~p11(c13, f4(f5(c18), c17))) | (~p7(c13, c13)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(121,plain,
% 0.19/0.43 (((~p11(c13, f4(f5(c18), c17))) | (~p7(c13, c13)) | (~p3(f4(f5(c18), c17), f4(f6(c18), c17))) | p11(c13, f4(f6(c18), c17))) <=> (p11(c13, f4(f6(c18), c17)) | (~p3(f4(f5(c18), c17), f4(f6(c18), c17))) | (~p11(c13, f4(f5(c18), c17))) | (~p7(c13, c13)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(122,plain,
% 0.19/0.43 (((~![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))) | ((~p11(c13, f4(f5(c18), c17))) | (~p7(c13, c13)) | (~p3(f4(f5(c18), c17), f4(f6(c18), c17))) | p11(c13, f4(f6(c18), c17)))) <=> ((~![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))) | (p11(c13, f4(f6(c18), c17)) | (~p3(f4(f5(c18), c17), f4(f6(c18), c17))) | (~p11(c13, f4(f5(c18), c17))) | (~p7(c13, c13))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[121])).
% 0.19/0.43 tff(123,plain,
% 0.19/0.43 (((~![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))) | ((~p11(c13, f4(f5(c18), c17))) | (~p7(c13, c13)) | (~p3(f4(f5(c18), c17), f4(f6(c18), c17))) | p11(c13, f4(f6(c18), c17)))) <=> ((~![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))) | p11(c13, f4(f6(c18), c17)) | (~p3(f4(f5(c18), c17), f4(f6(c18), c17))) | (~p11(c13, f4(f5(c18), c17))) | (~p7(c13, c13)))),
% 0.19/0.43 inference(transitivity,[status(thm)],[122, 120])).
% 0.19/0.43 tff(124,plain,
% 0.19/0.43 ((~![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))) | ((~p11(c13, f4(f5(c18), c17))) | (~p7(c13, c13)) | (~p3(f4(f5(c18), c17), f4(f6(c18), c17))) | p11(c13, f4(f6(c18), c17)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(125,plain,
% 0.19/0.43 ((~![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))) | p11(c13, f4(f6(c18), c17)) | (~p3(f4(f5(c18), c17), f4(f6(c18), c17))) | (~p11(c13, f4(f5(c18), c17))) | (~p7(c13, c13))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.19/0.43 tff(126,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[125, 119, 90, 116, 74, 63])).
% 0.19/0.43 % SZS output end Proof
% 0.19/0.43 % E exiting
%------------------------------------------------------------------------------