%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN592-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 0.18s 0.43s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : SYN592-1 : TPTP v9.0.0. Released v2.5.0.
% 0.05/0.10 % Command : run_E %s %d THM
% 0.11/0.31 % Computer : n014.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Fri Jun 20 12:38:24 EDT 2025
% 0.16/0.31 % CPUTime :
% 0.18/0.43 % SZS status Unsatisfiable
% 0.18/0.43 % SZS output start Proof
% 0.18/0.43 tff(p3_type, type, (
% 0.18/0.43 p3: ( $i * $i ) > $o)).
% 0.18/0.43 tff(f4_type, type, (
% 0.18/0.43 f4: ( $i * $i ) > $i)).
% 0.18/0.43 tff(c17_type, type, (
% 0.18/0.43 c17: $i)).
% 0.18/0.43 tff(f5_type, type, (
% 0.18/0.43 f5: $i > $i)).
% 0.18/0.43 tff(c18_type, type, (
% 0.18/0.43 c18: $i)).
% 0.18/0.43 tff(f6_type, type, (
% 0.18/0.43 f6: $i > $i)).
% 0.18/0.43 tff(p2_type, type, (
% 0.18/0.43 p2: ( $i * $i ) > $o)).
% 0.18/0.43 tff(p12_type, type, (
% 0.18/0.43 p12: ( $i * $i ) > $o)).
% 0.18/0.43 tff(c14_type, type, (
% 0.18/0.43 c14: $i)).
% 0.18/0.43 tff(p7_type, type, (
% 0.18/0.43 p7: ( $i * $i ) > $o)).
% 0.18/0.43 tff(c13_type, type, (
% 0.18/0.43 c13: $i)).
% 0.18/0.43 tff(p11_type, type, (
% 0.18/0.43 p11: ( $i * $i ) > $o)).
% 0.18/0.43 tff(1,plain,
% 0.18/0.43 (^[X20: $i] : refl(((~p12(c14, f4(X20, c17))) | p2(f6(X20), f5(X20))) <=> ((~p12(c14, f4(X20, c17))) | p2(f6(X20), f5(X20))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(2,plain,
% 0.18/0.43 (![X20: $i] : ((~p12(c14, f4(X20, c17))) | p2(f6(X20), f5(X20))) <=> ![X20: $i] : ((~p12(c14, f4(X20, c17))) | p2(f6(X20), f5(X20)))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.43 tff(3,plain,
% 0.18/0.43 (![X20: $i] : ((~p12(c14, f4(X20, c17))) | p2(f6(X20), f5(X20))) <=> ![X20: $i] : ((~p12(c14, f4(X20, c17))) | p2(f6(X20), f5(X20)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(4,plain,
% 0.18/0.43 (^[X20: $i] : rewrite((p2(f6(X20), f5(X20)) | (~p12(c14, f4(X20, c17)))) <=> ((~p12(c14, f4(X20, c17))) | p2(f6(X20), f5(X20))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(5,plain,
% 0.18/0.43 (![X20: $i] : (p2(f6(X20), f5(X20)) | (~p12(c14, f4(X20, c17)))) <=> ![X20: $i] : ((~p12(c14, f4(X20, c17))) | p2(f6(X20), f5(X20)))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[4])).
% 0.18/0.43 tff(6,axiom,(![X20: $i] : (p2(f6(X20), f5(X20)) | (~p12(c14, f4(X20, c17))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_22')).
% 0.18/0.43 tff(7,plain,
% 0.18/0.43 (![X20: $i] : ((~p12(c14, f4(X20, c17))) | p2(f6(X20), f5(X20)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.18/0.43 tff(8,plain,
% 0.18/0.43 (![X20: $i] : ((~p12(c14, f4(X20, c17))) | p2(f6(X20), f5(X20)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.18/0.43 tff(9,plain,(
% 0.18/0.43 ![X20: $i] : ((~p12(c14, f4(X20, c17))) | p2(f6(X20), f5(X20)))),
% 0.18/0.43 inference(skolemize,[status(sab)],[8])).
% 0.18/0.43 tff(10,plain,
% 0.18/0.43 (![X20: $i] : ((~p12(c14, f4(X20, c17))) | p2(f6(X20), f5(X20)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.18/0.43 tff(11,plain,
% 0.18/0.43 (p12(c14, f4(c18, c17)) <=> p12(c14, f4(c18, c17))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(12,axiom,(p12(c14, f4(c18, c17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p12_11')).
% 0.18/0.43 tff(13,plain,
% 0.18/0.43 (p12(c14, f4(c18, c17))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.18/0.43 tff(14,plain,
% 0.18/0.43 (((~![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)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(15,plain,
% 0.18/0.43 ((~![X20: $i] : ((~p12(c14, f4(X20, c17))) | p2(f6(X20), f5(X20)))) | ((~p12(c14, f4(c18, c17))) | p2(f6(c18), f5(c18)))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(16,plain,
% 0.18/0.43 ((~![X20: $i] : ((~p12(c14, f4(X20, c17))) | p2(f6(X20), f5(X20)))) | (~p12(c14, f4(c18, c17))) | p2(f6(c18), f5(c18))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.18/0.43 tff(17,plain,
% 0.18/0.43 (p2(f6(c18), f5(c18))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[16, 13, 10])).
% 0.18/0.43 tff(18,assumption,(~p2(c17, c17)), introduced(assumption)).
% 0.18/0.43 tff(19,plain,
% 0.18/0.43 (^[X15: $i] : refl(p2(X15, X15) <=> p2(X15, X15))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(20,plain,
% 0.18/0.43 (![X15: $i] : p2(X15, X15) <=> ![X15: $i] : p2(X15, X15)),
% 0.18/0.43 inference(quant_intro,[status(thm)],[19])).
% 0.18/0.43 tff(21,plain,
% 0.18/0.43 (![X15: $i] : p2(X15, X15) <=> ![X15: $i] : p2(X15, X15)),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(22,axiom,(![X15: $i] : p2(X15, X15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_4')).
% 0.18/0.43 tff(23,plain,
% 0.18/0.43 (![X15: $i] : p2(X15, X15)),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.18/0.43 tff(24,plain,(
% 0.18/0.43 ![X15: $i] : p2(X15, X15)),
% 0.18/0.43 inference(skolemize,[status(sab)],[23])).
% 0.18/0.43 tff(25,plain,
% 0.18/0.43 (![X15: $i] : p2(X15, X15)),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.18/0.44 tff(26,plain,
% 0.18/0.44 ((~![X15: $i] : p2(X15, X15)) | p2(c17, c17)),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(27,plain,
% 0.18/0.44 ($false),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[26, 25, 18])).
% 0.18/0.44 tff(28,plain,(p2(c17, c17)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.44 tff(29,plain,
% 0.18/0.44 (^[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))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(30,plain,
% 0.18/0.44 (![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)))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[29])).
% 0.18/0.44 tff(31,plain,
% 0.18/0.44 (![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)))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(32,plain,
% 0.18/0.44 (^[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)))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(33,plain,
% 0.18/0.44 (![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)))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[32])).
% 0.18/0.44 tff(34,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')).
% 0.18/0.44 tff(35,plain,
% 0.18/0.44 (![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.18/0.44 tff(36,plain,
% 0.18/0.44 (![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.18/0.44 tff(37,plain,(
% 0.18/0.44 ![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29)))),
% 0.18/0.44 inference(skolemize,[status(sab)],[36])).
% 0.18/0.44 tff(38,plain,
% 0.18/0.44 (![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.18/0.44 tff(39,plain,
% 0.18/0.44 (((~![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(f6(c18), f5(c18))) | p3(f4(f6(c18), c17), f4(f5(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(f6(c18), f5(c18))) | p3(f4(f6(c18), c17), f4(f5(c18), c17)))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(40,plain,
% 0.18/0.44 (((~p2(f6(c18), f5(c18))) | (~p2(c17, c17)) | p3(f4(f6(c18), c17), f4(f5(c18), c17))) <=> ((~p2(c17, c17)) | (~p2(f6(c18), f5(c18))) | p3(f4(f6(c18), c17), f4(f5(c18), c17)))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(41,plain,
% 0.18/0.44 (((~![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29)))) | ((~p2(f6(c18), f5(c18))) | (~p2(c17, c17)) | p3(f4(f6(c18), c17), f4(f5(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(f6(c18), f5(c18))) | p3(f4(f6(c18), c17), f4(f5(c18), c17))))),
% 0.18/0.44 inference(monotonicity,[status(thm)],[40])).
% 0.18/0.44 tff(42,plain,
% 0.18/0.44 (((~![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29)))) | ((~p2(f6(c18), f5(c18))) | (~p2(c17, c17)) | p3(f4(f6(c18), c17), f4(f5(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(f6(c18), f5(c18))) | p3(f4(f6(c18), c17), f4(f5(c18), c17)))),
% 0.18/0.44 inference(transitivity,[status(thm)],[41, 39])).
% 0.18/0.44 tff(43,plain,
% 0.18/0.44 ((~![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29)))) | ((~p2(f6(c18), f5(c18))) | (~p2(c17, c17)) | p3(f4(f6(c18), c17), f4(f5(c18), c17)))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(44,plain,
% 0.18/0.44 ((~![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(f6(c18), f5(c18))) | p3(f4(f6(c18), c17), f4(f5(c18), c17))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.18/0.44 tff(45,plain,
% 0.18/0.44 (p3(f4(f6(c18), c17), f4(f5(c18), c17))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[44, 38, 28, 17])).
% 0.18/0.44 tff(46,assumption,(~p7(c13, c13)), introduced(assumption)).
% 0.18/0.44 tff(47,plain,
% 0.18/0.44 (^[X30: $i] : refl(p7(X30, X30) <=> p7(X30, X30))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(48,plain,
% 0.18/0.44 (![X30: $i] : p7(X30, X30) <=> ![X30: $i] : p7(X30, X30)),
% 0.18/0.44 inference(quant_intro,[status(thm)],[47])).
% 0.18/0.44 tff(49,plain,
% 0.18/0.44 (![X30: $i] : p7(X30, X30) <=> ![X30: $i] : p7(X30, X30)),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(50,axiom,(![X30: $i] : p7(X30, X30)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p7_3')).
% 0.18/0.44 tff(51,plain,
% 0.18/0.44 (![X30: $i] : p7(X30, X30)),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.18/0.44 tff(52,plain,(
% 0.18/0.44 ![X30: $i] : p7(X30, X30)),
% 0.18/0.44 inference(skolemize,[status(sab)],[51])).
% 0.18/0.44 tff(53,plain,
% 0.18/0.44 (![X30: $i] : p7(X30, X30)),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.18/0.44 tff(54,plain,
% 0.18/0.44 ((~![X30: $i] : p7(X30, X30)) | p7(c13, c13)),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(55,plain,
% 0.18/0.44 ($false),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[54, 53, 46])).
% 0.18/0.44 tff(56,plain,(p7(c13, c13)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.44 tff(57,plain,
% 0.18/0.44 (((~![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(f6(c18), f5(c18))) | p3(f4(c17, f6(c18)), f4(c17, f5(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(f6(c18), f5(c18))) | p3(f4(c17, f6(c18)), f4(c17, f5(c18))))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(58,plain,
% 0.18/0.44 ((~![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(f6(c18), f5(c18))) | p3(f4(c17, f6(c18)), f4(c17, f5(c18))))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(59,plain,
% 0.18/0.44 ((~![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(f6(c18), f5(c18))) | p3(f4(c17, f6(c18)), f4(c17, f5(c18)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.18/0.44 tff(60,plain,
% 0.18/0.44 (p3(f4(c17, f6(c18)), f4(c17, f5(c18)))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[59, 38, 28, 17])).
% 0.18/0.44 tff(61,assumption,(p11(c13, f4(c17, f6(c18)))), introduced(assumption)).
% 0.18/0.44 tff(62,plain,
% 0.18/0.44 (^[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)))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(63,plain,
% 0.18/0.44 (![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))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[62])).
% 0.18/0.44 tff(64,plain,
% 0.18/0.44 (![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))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(65,plain,
% 0.18/0.44 (^[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))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(66,plain,
% 0.18/0.44 (![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))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[65])).
% 0.18/0.44 tff(67,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')).
% 0.18/0.44 tff(68,plain,
% 0.18/0.44 (![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.18/0.44 tff(69,plain,
% 0.18/0.44 (![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.18/0.44 tff(70,plain,(
% 0.18/0.44 ![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))),
% 0.18/0.44 inference(skolemize,[status(sab)],[69])).
% 0.18/0.44 tff(71,plain,
% 0.18/0.44 (![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.18/0.44 tff(72,plain,
% 0.18/0.44 ((~p11(c13, f4(c17, f5(c18)))) <=> (~p11(c13, f4(c17, f5(c18))))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(73,axiom,(~p11(c13, f4(c17, f5(c18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_p11_12')).
% 0.18/0.44 tff(74,plain,
% 0.18/0.44 (~p11(c13, f4(c17, f5(c18)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.18/0.44 tff(75,plain,
% 0.18/0.44 (((~![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))) | (~p3(f4(c17, f6(c18)), f4(c17, f5(c18)))) | (~p7(c13, c13)) | (~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, f5(c18))) | (~p3(f4(c17, f6(c18)), f4(c17, f5(c18)))) | (~p7(c13, c13)) | (~p11(c13, f4(c17, f6(c18)))))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(76,plain,
% 0.18/0.44 (((~p11(c13, f4(c17, f6(c18)))) | (~p7(c13, c13)) | (~p3(f4(c17, f6(c18)), f4(c17, f5(c18)))) | p11(c13, f4(c17, f5(c18)))) <=> (p11(c13, f4(c17, f5(c18))) | (~p3(f4(c17, f6(c18)), f4(c17, f5(c18)))) | (~p7(c13, c13)) | (~p11(c13, f4(c17, f6(c18)))))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(77,plain,
% 0.18/0.44 (((~![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)))) | (~p7(c13, c13)) | (~p3(f4(c17, f6(c18)), f4(c17, f5(c18)))) | p11(c13, f4(c17, f5(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, f5(c18))) | (~p3(f4(c17, f6(c18)), f4(c17, f5(c18)))) | (~p7(c13, c13)) | (~p11(c13, f4(c17, f6(c18))))))),
% 0.18/0.44 inference(monotonicity,[status(thm)],[76])).
% 0.18/0.44 tff(78,plain,
% 0.18/0.44 (((~![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)))) | (~p7(c13, c13)) | (~p3(f4(c17, f6(c18)), f4(c17, f5(c18)))) | p11(c13, f4(c17, f5(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, f5(c18))) | (~p3(f4(c17, f6(c18)), f4(c17, f5(c18)))) | (~p7(c13, c13)) | (~p11(c13, f4(c17, f6(c18)))))),
% 0.18/0.45 inference(transitivity,[status(thm)],[77, 75])).
% 0.18/0.45 tff(79,plain,
% 0.18/0.45 ((~![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)))) | (~p7(c13, c13)) | (~p3(f4(c17, f6(c18)), f4(c17, f5(c18)))) | p11(c13, f4(c17, f5(c18))))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(80,plain,
% 0.18/0.45 ((~![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))) | p11(c13, f4(c17, f5(c18))) | (~p3(f4(c17, f6(c18)), f4(c17, f5(c18)))) | (~p7(c13, c13)) | (~p11(c13, f4(c17, f6(c18))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.18/0.45 tff(81,plain,
% 0.18/0.45 ($false),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[80, 74, 71, 61, 60, 56])).
% 0.18/0.45 tff(82,plain,(~p11(c13, f4(c17, f6(c18)))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.45 tff(83,plain,
% 0.18/0.45 (^[X9: $i] : refl(((~p12(c14, f4(X9, c17))) | p11(c13, f4(f6(X9), c17)) | p11(c13, f4(c17, f6(X9)))) <=> ((~p12(c14, f4(X9, c17))) | p11(c13, f4(f6(X9), c17)) | p11(c13, f4(c17, f6(X9)))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(84,plain,
% 0.18/0.45 (![X9: $i] : ((~p12(c14, f4(X9, c17))) | p11(c13, f4(f6(X9), c17)) | p11(c13, f4(c17, f6(X9)))) <=> ![X9: $i] : ((~p12(c14, f4(X9, c17))) | p11(c13, f4(f6(X9), c17)) | p11(c13, f4(c17, f6(X9))))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[83])).
% 0.18/0.45 tff(85,plain,
% 0.18/0.45 (![X9: $i] : ((~p12(c14, f4(X9, c17))) | p11(c13, f4(f6(X9), c17)) | p11(c13, f4(c17, f6(X9)))) <=> ![X9: $i] : ((~p12(c14, f4(X9, c17))) | p11(c13, f4(f6(X9), c17)) | p11(c13, f4(c17, f6(X9))))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(86,plain,
% 0.18/0.45 (^[X9: $i] : rewrite(((p11(c13, f4(c17, f6(X9))) | p11(c13, f4(f6(X9), c17))) | (~p12(c14, f4(X9, c17)))) <=> ((~p12(c14, f4(X9, c17))) | p11(c13, f4(f6(X9), c17)) | p11(c13, f4(c17, f6(X9)))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(87,plain,
% 0.18/0.45 (![X9: $i] : ((p11(c13, f4(c17, f6(X9))) | p11(c13, f4(f6(X9), c17))) | (~p12(c14, f4(X9, c17)))) <=> ![X9: $i] : ((~p12(c14, f4(X9, c17))) | p11(c13, f4(f6(X9), c17)) | p11(c13, f4(c17, f6(X9))))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[86])).
% 0.18/0.45 tff(88,axiom,(![X9: $i] : ((p11(c13, f4(c17, f6(X9))) | p11(c13, f4(f6(X9), c17))) | (~p12(c14, f4(X9, c17))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p11_27')).
% 0.18/0.45 tff(89,plain,
% 0.18/0.45 (![X9: $i] : ((~p12(c14, f4(X9, c17))) | p11(c13, f4(f6(X9), c17)) | p11(c13, f4(c17, f6(X9))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.18/0.45 tff(90,plain,
% 0.18/0.45 (![X9: $i] : ((~p12(c14, f4(X9, c17))) | p11(c13, f4(f6(X9), c17)) | p11(c13, f4(c17, f6(X9))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.18/0.45 tff(91,plain,(
% 0.18/0.45 ![X9: $i] : ((~p12(c14, f4(X9, c17))) | p11(c13, f4(f6(X9), c17)) | p11(c13, f4(c17, f6(X9))))),
% 0.18/0.45 inference(skolemize,[status(sab)],[90])).
% 0.18/0.45 tff(92,plain,
% 0.18/0.45 (![X9: $i] : ((~p12(c14, f4(X9, c17))) | p11(c13, f4(f6(X9), c17)) | p11(c13, f4(c17, f6(X9))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[91, 84])).
% 0.18/0.45 tff(93,plain,
% 0.18/0.45 (((~![X9: $i] : ((~p12(c14, f4(X9, c17))) | p11(c13, f4(f6(X9), c17)) | p11(c13, f4(c17, f6(X9))))) | ((~p12(c14, f4(c18, c17))) | p11(c13, f4(f6(c18), c17)) | p11(c13, f4(c17, f6(c18))))) <=> ((~![X9: $i] : ((~p12(c14, f4(X9, c17))) | p11(c13, f4(f6(X9), c17)) | p11(c13, f4(c17, f6(X9))))) | (~p12(c14, f4(c18, c17))) | p11(c13, f4(f6(c18), c17)) | p11(c13, f4(c17, f6(c18))))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(94,plain,
% 0.18/0.45 ((~![X9: $i] : ((~p12(c14, f4(X9, c17))) | p11(c13, f4(f6(X9), c17)) | p11(c13, f4(c17, f6(X9))))) | ((~p12(c14, f4(c18, c17))) | p11(c13, f4(f6(c18), c17)) | p11(c13, f4(c17, f6(c18))))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(95,plain,
% 0.18/0.45 ((~![X9: $i] : ((~p12(c14, f4(X9, c17))) | p11(c13, f4(f6(X9), c17)) | p11(c13, f4(c17, f6(X9))))) | (~p12(c14, f4(c18, c17))) | p11(c13, f4(f6(c18), c17)) | p11(c13, f4(c17, f6(c18)))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.18/0.45 tff(96,plain,
% 0.18/0.45 (p11(c13, f4(f6(c18), c17)) | p11(c13, f4(c17, f6(c18)))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[95, 13, 92])).
% 0.18/0.45 tff(97,plain,
% 0.18/0.45 (p11(c13, f4(f6(c18), c17))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[96, 82])).
% 0.18/0.45 tff(98,plain,
% 0.18/0.45 ((~p11(c13, f4(f5(c18), c17))) <=> (~p11(c13, f4(f5(c18), c17)))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(99,axiom,(~p11(c13, f4(f5(c18), c17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_p11_13')).
% 0.18/0.45 tff(100,plain,
% 0.18/0.45 (~p11(c13, f4(f5(c18), c17))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.18/0.45 tff(101,plain,
% 0.18/0.45 (((~![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)) | (~p11(c13, f4(f6(c18), c17))) | (~p3(f4(f6(c18), c17), f4(f5(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(f5(c18), c17)) | (~p7(c13, c13)) | (~p11(c13, f4(f6(c18), c17))) | (~p3(f4(f6(c18), c17), f4(f5(c18), c17))))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(102,plain,
% 0.18/0.45 (((~p11(c13, f4(f6(c18), c17))) | (~p7(c13, c13)) | (~p3(f4(f6(c18), c17), f4(f5(c18), c17))) | p11(c13, f4(f5(c18), c17))) <=> (p11(c13, f4(f5(c18), c17)) | (~p7(c13, c13)) | (~p11(c13, f4(f6(c18), c17))) | (~p3(f4(f6(c18), c17), f4(f5(c18), c17))))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(103,plain,
% 0.18/0.45 (((~![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))) | (~p7(c13, c13)) | (~p3(f4(f6(c18), c17), f4(f5(c18), c17))) | p11(c13, f4(f5(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(f5(c18), c17)) | (~p7(c13, c13)) | (~p11(c13, f4(f6(c18), c17))) | (~p3(f4(f6(c18), c17), f4(f5(c18), c17)))))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[102])).
% 0.18/0.45 tff(104,plain,
% 0.18/0.45 (((~![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))) | (~p7(c13, c13)) | (~p3(f4(f6(c18), c17), f4(f5(c18), c17))) | p11(c13, f4(f5(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(f5(c18), c17)) | (~p7(c13, c13)) | (~p11(c13, f4(f6(c18), c17))) | (~p3(f4(f6(c18), c17), f4(f5(c18), c17))))),
% 0.18/0.45 inference(transitivity,[status(thm)],[103, 101])).
% 0.18/0.45 tff(105,plain,
% 0.18/0.45 ((~![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))) | (~p7(c13, c13)) | (~p3(f4(f6(c18), c17), f4(f5(c18), c17))) | p11(c13, f4(f5(c18), c17)))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(106,plain,
% 0.18/0.45 ((~![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))) | p11(c13, f4(f5(c18), c17)) | (~p7(c13, c13)) | (~p11(c13, f4(f6(c18), c17))) | (~p3(f4(f6(c18), c17), f4(f5(c18), c17)))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.18/0.45 tff(107,plain,
% 0.18/0.45 ($false),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[106, 100, 71, 97, 56, 45])).
% 0.18/0.45 % SZS output end Proof
% 0.18/0.45 % E exiting
%------------------------------------------------------------------------------