%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN607-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:39:40 AM UTC 2025
% Result : Unsatisfiable 0.11s 0.38s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SYN607-1 : TPTP v9.0.0. Released v2.5.0.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n012.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 12:38:25 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.38 % SZS status Unsatisfiable
% 0.11/0.38 % SZS output start Proof
% 0.11/0.38 tff(p2_type, type, (
% 0.11/0.38 p2: ( $i * $i ) > $o)).
% 0.11/0.38 tff(f9_type, type, (
% 0.11/0.38 f9: $i > $i)).
% 0.11/0.38 tff(f10_type, type, (
% 0.11/0.38 f10: ( $i * $i ) > $i)).
% 0.11/0.38 tff(f12_type, type, (
% 0.11/0.38 f12: ( $i * $i ) > $i)).
% 0.11/0.38 tff(c21_type, type, (
% 0.11/0.38 c21: $i)).
% 0.11/0.38 tff(f15_type, type, (
% 0.11/0.38 f15: $i > $i)).
% 0.11/0.38 tff(c22_type, type, (
% 0.11/0.38 c22: $i)).
% 0.11/0.38 tff(f14_type, type, (
% 0.11/0.38 f14: ( $i * $i ) > $i)).
% 0.11/0.38 tff(c19_type, type, (
% 0.11/0.38 c19: $i)).
% 0.11/0.38 tff(f4_type, type, (
% 0.11/0.38 f4: $i > $i)).
% 0.11/0.38 tff(p3_type, type, (
% 0.11/0.38 p3: ( $i * $i ) > $o)).
% 0.11/0.38 tff(f6_type, type, (
% 0.11/0.38 f6: $i > $i)).
% 0.11/0.38 tff(f7_type, type, (
% 0.11/0.38 f7: $i > $i)).
% 0.11/0.38 tff(f8_type, type, (
% 0.11/0.38 f8: $i > $i)).
% 0.11/0.38 tff(c20_type, type, (
% 0.11/0.38 c20: $i)).
% 0.11/0.38 tff(p5_type, type, (
% 0.11/0.38 p5: ( $i * $i ) > $o)).
% 0.11/0.38 tff(p17_type, type, (
% 0.11/0.38 p17: ( $i * $i ) > $o)).
% 0.11/0.38 tff(1,assumption,(~p3(f12(f15(c22), c21), f12(f15(c22), c21))), introduced(assumption)).
% 0.11/0.38 tff(2,plain,
% 0.11/0.38 (^[X18: $i] : refl(p3(X18, X18) <=> p3(X18, X18))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(3,plain,
% 0.11/0.38 (![X18: $i] : p3(X18, X18) <=> ![X18: $i] : p3(X18, X18)),
% 0.11/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.11/0.38 tff(4,plain,
% 0.11/0.38 (![X18: $i] : p3(X18, X18) <=> ![X18: $i] : p3(X18, X18)),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(5,axiom,(![X18: $i] : p3(X18, X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3_4')).
% 0.11/0.38 tff(6,plain,
% 0.11/0.38 (![X18: $i] : p3(X18, X18)),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.11/0.38 tff(7,plain,(
% 0.11/0.38 ![X18: $i] : p3(X18, X18)),
% 0.11/0.38 inference(skolemize,[status(sab)],[6])).
% 0.11/0.38 tff(8,plain,
% 0.11/0.38 (![X18: $i] : p3(X18, X18)),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.11/0.38 tff(9,plain,
% 0.11/0.38 ((~![X18: $i] : p3(X18, X18)) | p3(f12(f15(c22), c21), f12(f15(c22), c21))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(10,plain,
% 0.11/0.38 ($false),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.11/0.38 tff(11,plain,(p3(f12(f15(c22), c21), f12(f15(c22), c21))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.38 tff(12,assumption,(~p3(f14(f4(f9(c19)), c19), f14(f4(f9(c19)), c19))), introduced(assumption)).
% 0.11/0.38 tff(13,plain,
% 0.11/0.38 ((~![X18: $i] : p3(X18, X18)) | p3(f14(f4(f9(c19)), c19), f14(f4(f9(c19)), c19))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(14,plain,
% 0.11/0.38 ($false),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[13, 8, 12])).
% 0.11/0.38 tff(15,plain,(p3(f14(f4(f9(c19)), c19), f14(f4(f9(c19)), c19))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.38 tff(16,plain,
% 0.11/0.38 (^[X22: $i, X21: $i, X23: $i, X24: $i] : refl(((~p3(X21, X23)) | (~p3(X22, X24)) | p3(f10(X21, X22), f10(X23, X24))) <=> ((~p3(X21, X23)) | (~p3(X22, X24)) | p3(f10(X21, X22), f10(X23, X24))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(17,plain,
% 0.11/0.38 (![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X21, X23)) | (~p3(X22, X24)) | p3(f10(X21, X22), f10(X23, X24))) <=> ![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X21, X23)) | (~p3(X22, X24)) | p3(f10(X21, X22), f10(X23, X24)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[16])).
% 0.11/0.38 tff(18,plain,
% 0.11/0.38 (![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X21, X23)) | (~p3(X22, X24)) | p3(f10(X21, X22), f10(X23, X24))) <=> ![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X21, X23)) | (~p3(X22, X24)) | p3(f10(X21, X22), f10(X23, X24)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(19,plain,
% 0.11/0.38 (^[X22: $i, X21: $i, X23: $i, X24: $i] : trans(monotonicity(rewrite((p3(f10(X21, X22), f10(X23, X24)) | (~p3(X21, X23))) <=> ((~p3(X21, X23)) | p3(f10(X21, X22), f10(X23, X24)))), (((p3(f10(X21, X22), f10(X23, X24)) | (~p3(X21, X23))) | (~p3(X22, X24))) <=> (((~p3(X21, X23)) | p3(f10(X21, X22), f10(X23, X24))) | (~p3(X22, X24))))), rewrite((((~p3(X21, X23)) | p3(f10(X21, X22), f10(X23, X24))) | (~p3(X22, X24))) <=> ((~p3(X21, X23)) | (~p3(X22, X24)) | p3(f10(X21, X22), f10(X23, X24)))), (((p3(f10(X21, X22), f10(X23, X24)) | (~p3(X21, X23))) | (~p3(X22, X24))) <=> ((~p3(X21, X23)) | (~p3(X22, X24)) | p3(f10(X21, X22), f10(X23, X24)))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(20,plain,
% 0.11/0.38 (![X22: $i, X21: $i, X23: $i, X24: $i] : ((p3(f10(X21, X22), f10(X23, X24)) | (~p3(X21, X23))) | (~p3(X22, X24))) <=> ![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X21, X23)) | (~p3(X22, X24)) | p3(f10(X21, X22), f10(X23, X24)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[19])).
% 0.18/0.39 tff(21,axiom,(![X22: $i, X21: $i, X23: $i, X24: $i] : ((p3(f10(X21, X22), f10(X23, X24)) | (~p3(X21, X23))) | (~p3(X22, X24)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3_24')).
% 0.18/0.39 tff(22,plain,
% 0.18/0.39 (![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X21, X23)) | (~p3(X22, X24)) | p3(f10(X21, X22), f10(X23, X24)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.18/0.39 tff(23,plain,
% 0.18/0.39 (![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X21, X23)) | (~p3(X22, X24)) | p3(f10(X21, X22), f10(X23, X24)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.18/0.39 tff(24,plain,(
% 0.18/0.39 ![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X21, X23)) | (~p3(X22, X24)) | p3(f10(X21, X22), f10(X23, X24)))),
% 0.18/0.39 inference(skolemize,[status(sab)],[23])).
% 0.18/0.39 tff(25,plain,
% 0.18/0.39 (![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X21, X23)) | (~p3(X22, X24)) | p3(f10(X21, X22), f10(X23, X24)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.18/0.39 tff(26,plain,
% 0.18/0.39 (((~![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X21, X23)) | (~p3(X22, X24)) | p3(f10(X21, X22), f10(X23, X24)))) | ((~p3(f14(f4(f9(c19)), c19), f14(f4(f9(c19)), c19))) | (~p3(f12(f15(c22), c21), f12(f15(c22), c21))) | p3(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21)), f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))))) <=> ((~![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X21, X23)) | (~p3(X22, X24)) | p3(f10(X21, X22), f10(X23, X24)))) | (~p3(f14(f4(f9(c19)), c19), f14(f4(f9(c19)), c19))) | (~p3(f12(f15(c22), c21), f12(f15(c22), c21))) | p3(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21)), f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(27,plain,
% 0.18/0.39 ((~![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X21, X23)) | (~p3(X22, X24)) | p3(f10(X21, X22), f10(X23, X24)))) | ((~p3(f14(f4(f9(c19)), c19), f14(f4(f9(c19)), c19))) | (~p3(f12(f15(c22), c21), f12(f15(c22), c21))) | p3(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21)), f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(28,plain,
% 0.18/0.39 ((~![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X21, X23)) | (~p3(X22, X24)) | p3(f10(X21, X22), f10(X23, X24)))) | (~p3(f14(f4(f9(c19)), c19), f14(f4(f9(c19)), c19))) | (~p3(f12(f15(c22), c21), f12(f15(c22), c21))) | p3(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21)), f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.18/0.39 tff(29,plain,
% 0.18/0.39 ((~p3(f14(f4(f9(c19)), c19), f14(f4(f9(c19)), c19))) | (~p3(f12(f15(c22), c21), f12(f15(c22), c21))) | p3(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21)), f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21)))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[28, 25])).
% 0.18/0.39 tff(30,plain,
% 0.18/0.39 ((~p3(f12(f15(c22), c21), f12(f15(c22), c21))) | p3(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21)), f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21)))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[29, 15])).
% 0.18/0.39 tff(31,plain,
% 0.18/0.39 (p3(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21)), f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21)))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[30, 11])).
% 0.18/0.39 tff(32,plain,
% 0.18/0.39 (^[X17: $i, X16: $i] : refl(((~p3(X16, X17)) | p2(f9(X16), f9(X17))) <=> ((~p3(X16, X17)) | p2(f9(X16), f9(X17))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(33,plain,
% 0.18/0.39 (![X17: $i, X16: $i] : ((~p3(X16, X17)) | p2(f9(X16), f9(X17))) <=> ![X17: $i, X16: $i] : ((~p3(X16, X17)) | p2(f9(X16), f9(X17)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[32])).
% 0.18/0.39 tff(34,plain,
% 0.18/0.39 (![X17: $i, X16: $i] : ((~p3(X16, X17)) | p2(f9(X16), f9(X17))) <=> ![X17: $i, X16: $i] : ((~p3(X16, X17)) | p2(f9(X16), f9(X17)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(35,plain,
% 0.18/0.39 (^[X17: $i, X16: $i] : rewrite((p2(f9(X16), f9(X17)) | (~p3(X16, X17))) <=> ((~p3(X16, X17)) | p2(f9(X16), f9(X17))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(36,plain,
% 0.18/0.39 (![X17: $i, X16: $i] : (p2(f9(X16), f9(X17)) | (~p3(X16, X17))) <=> ![X17: $i, X16: $i] : ((~p3(X16, X17)) | p2(f9(X16), f9(X17)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[35])).
% 0.18/0.39 tff(37,axiom,(![X17: $i, X16: $i] : (p2(f9(X16), f9(X17)) | (~p3(X16, X17)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_12')).
% 0.18/0.39 tff(38,plain,
% 0.18/0.39 (![X17: $i, X16: $i] : ((~p3(X16, X17)) | p2(f9(X16), f9(X17)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.18/0.39 tff(39,plain,
% 0.18/0.39 (![X17: $i, X16: $i] : ((~p3(X16, X17)) | p2(f9(X16), f9(X17)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.18/0.39 tff(40,plain,(
% 0.18/0.39 ![X17: $i, X16: $i] : ((~p3(X16, X17)) | p2(f9(X16), f9(X17)))),
% 0.18/0.39 inference(skolemize,[status(sab)],[39])).
% 0.18/0.39 tff(41,plain,
% 0.18/0.39 (![X17: $i, X16: $i] : ((~p3(X16, X17)) | p2(f9(X16), f9(X17)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.18/0.39 tff(42,plain,
% 0.18/0.39 (((~![X17: $i, X16: $i] : ((~p3(X16, X17)) | p2(f9(X16), f9(X17)))) | ((~p3(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21)), f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21)))) | p2(f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))), f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21)))))) <=> ((~![X17: $i, X16: $i] : ((~p3(X16, X17)) | p2(f9(X16), f9(X17)))) | (~p3(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21)), f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21)))) | p2(f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))), f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21)))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(43,plain,
% 0.18/0.39 ((~![X17: $i, X16: $i] : ((~p3(X16, X17)) | p2(f9(X16), f9(X17)))) | ((~p3(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21)), f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21)))) | p2(f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))), f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21)))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(44,plain,
% 0.18/0.39 ((~![X17: $i, X16: $i] : ((~p3(X16, X17)) | p2(f9(X16), f9(X17)))) | (~p3(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21)), f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21)))) | p2(f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))), f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.18/0.39 tff(45,plain,
% 0.18/0.39 (p2(f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))), f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[44, 41, 31])).
% 0.18/0.39 tff(46,plain,
% 0.18/0.39 (p3(f12(f15(c22), c21), f15(c22)) <=> p3(f12(f15(c22), c21), f15(c22))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(47,axiom,(p3(f12(f15(c22), c21), f15(c22))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3_8')).
% 0.18/0.39 tff(48,plain,
% 0.18/0.39 (p3(f12(f15(c22), c21), f15(c22))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.18/0.39 tff(49,plain,
% 0.18/0.39 (((~![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X21, X23)) | (~p3(X22, X24)) | p3(f10(X21, X22), f10(X23, X24)))) | ((~p3(f12(f15(c22), c21), f15(c22))) | (~p3(f14(f4(f9(c19)), c19), f14(f4(f9(c19)), c19))) | p3(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21)), f10(f14(f4(f9(c19)), c19), f15(c22))))) <=> ((~![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X21, X23)) | (~p3(X22, X24)) | p3(f10(X21, X22), f10(X23, X24)))) | (~p3(f12(f15(c22), c21), f15(c22))) | (~p3(f14(f4(f9(c19)), c19), f14(f4(f9(c19)), c19))) | p3(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21)), f10(f14(f4(f9(c19)), c19), f15(c22))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(50,plain,
% 0.18/0.39 (((~p3(f14(f4(f9(c19)), c19), f14(f4(f9(c19)), c19))) | (~p3(f12(f15(c22), c21), f15(c22))) | p3(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21)), f10(f14(f4(f9(c19)), c19), f15(c22)))) <=> ((~p3(f12(f15(c22), c21), f15(c22))) | (~p3(f14(f4(f9(c19)), c19), f14(f4(f9(c19)), c19))) | p3(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21)), f10(f14(f4(f9(c19)), c19), f15(c22))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(51,plain,
% 0.18/0.39 (((~![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X21, X23)) | (~p3(X22, X24)) | p3(f10(X21, X22), f10(X23, X24)))) | ((~p3(f14(f4(f9(c19)), c19), f14(f4(f9(c19)), c19))) | (~p3(f12(f15(c22), c21), f15(c22))) | p3(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21)), f10(f14(f4(f9(c19)), c19), f15(c22))))) <=> ((~![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X21, X23)) | (~p3(X22, X24)) | p3(f10(X21, X22), f10(X23, X24)))) | ((~p3(f12(f15(c22), c21), f15(c22))) | (~p3(f14(f4(f9(c19)), c19), f14(f4(f9(c19)), c19))) | p3(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21)), f10(f14(f4(f9(c19)), c19), f15(c22)))))),
% 0.18/0.39 inference(monotonicity,[status(thm)],[50])).
% 0.18/0.39 tff(52,plain,
% 0.18/0.39 (((~![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X21, X23)) | (~p3(X22, X24)) | p3(f10(X21, X22), f10(X23, X24)))) | ((~p3(f14(f4(f9(c19)), c19), f14(f4(f9(c19)), c19))) | (~p3(f12(f15(c22), c21), f15(c22))) | p3(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21)), f10(f14(f4(f9(c19)), c19), f15(c22))))) <=> ((~![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X21, X23)) | (~p3(X22, X24)) | p3(f10(X21, X22), f10(X23, X24)))) | (~p3(f12(f15(c22), c21), f15(c22))) | (~p3(f14(f4(f9(c19)), c19), f14(f4(f9(c19)), c19))) | p3(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21)), f10(f14(f4(f9(c19)), c19), f15(c22))))),
% 0.18/0.39 inference(transitivity,[status(thm)],[51, 49])).
% 0.18/0.39 tff(53,plain,
% 0.18/0.39 ((~![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X21, X23)) | (~p3(X22, X24)) | p3(f10(X21, X22), f10(X23, X24)))) | ((~p3(f14(f4(f9(c19)), c19), f14(f4(f9(c19)), c19))) | (~p3(f12(f15(c22), c21), f15(c22))) | p3(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21)), f10(f14(f4(f9(c19)), c19), f15(c22))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(54,plain,
% 0.18/0.39 ((~![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X21, X23)) | (~p3(X22, X24)) | p3(f10(X21, X22), f10(X23, X24)))) | (~p3(f12(f15(c22), c21), f15(c22))) | (~p3(f14(f4(f9(c19)), c19), f14(f4(f9(c19)), c19))) | p3(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21)), f10(f14(f4(f9(c19)), c19), f15(c22)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.18/0.39 tff(55,plain,
% 0.18/0.39 ((~p3(f14(f4(f9(c19)), c19), f14(f4(f9(c19)), c19))) | p3(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21)), f10(f14(f4(f9(c19)), c19), f15(c22)))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[54, 48, 25])).
% 0.18/0.39 tff(56,plain,
% 0.18/0.39 (p3(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21)), f10(f14(f4(f9(c19)), c19), f15(c22)))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[55, 15])).
% 0.18/0.39 tff(57,plain,
% 0.18/0.39 (((~![X17: $i, X16: $i] : ((~p3(X16, X17)) | p2(f9(X16), f9(X17)))) | ((~p3(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21)), f10(f14(f4(f9(c19)), c19), f15(c22)))) | p2(f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))), f9(f10(f14(f4(f9(c19)), c19), f15(c22)))))) <=> ((~![X17: $i, X16: $i] : ((~p3(X16, X17)) | p2(f9(X16), f9(X17)))) | (~p3(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21)), f10(f14(f4(f9(c19)), c19), f15(c22)))) | p2(f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))), f9(f10(f14(f4(f9(c19)), c19), f15(c22)))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(58,plain,
% 0.18/0.39 ((~![X17: $i, X16: $i] : ((~p3(X16, X17)) | p2(f9(X16), f9(X17)))) | ((~p3(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21)), f10(f14(f4(f9(c19)), c19), f15(c22)))) | p2(f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))), f9(f10(f14(f4(f9(c19)), c19), f15(c22)))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(59,plain,
% 0.18/0.39 ((~![X17: $i, X16: $i] : ((~p3(X16, X17)) | p2(f9(X16), f9(X17)))) | (~p3(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21)), f10(f14(f4(f9(c19)), c19), f15(c22)))) | p2(f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))), f9(f10(f14(f4(f9(c19)), c19), f15(c22))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.18/0.39 tff(60,plain,
% 0.18/0.39 (p2(f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))), f9(f10(f14(f4(f9(c19)), c19), f15(c22))))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[59, 41, 56])).
% 0.18/0.39 tff(61,plain,
% 0.18/0.39 (^[X12: $i, X11: $i, X13: $i] : refl(((~p2(X11, X13)) | (~p2(X11, X12)) | p2(X12, X13)) <=> ((~p2(X11, X13)) | (~p2(X11, X12)) | p2(X12, X13)))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(62,plain,
% 0.18/0.39 (![X12: $i, X11: $i, X13: $i] : ((~p2(X11, X13)) | (~p2(X11, X12)) | p2(X12, X13)) <=> ![X12: $i, X11: $i, X13: $i] : ((~p2(X11, X13)) | (~p2(X11, X12)) | p2(X12, X13))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[61])).
% 0.18/0.39 tff(63,plain,
% 0.18/0.39 (![X12: $i, X11: $i, X13: $i] : ((~p2(X11, X13)) | (~p2(X11, X12)) | p2(X12, X13)) <=> ![X12: $i, X11: $i, X13: $i] : ((~p2(X11, X13)) | (~p2(X11, X12)) | p2(X12, X13))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(64,plain,
% 0.18/0.40 (^[X12: $i, X11: $i, X13: $i] : trans(monotonicity(rewrite((p2(X12, X13) | (~p2(X11, X12))) <=> ((~p2(X11, X12)) | p2(X12, X13))), (((p2(X12, X13) | (~p2(X11, X12))) | (~p2(X11, X13))) <=> (((~p2(X11, X12)) | p2(X12, X13)) | (~p2(X11, X13))))), rewrite((((~p2(X11, X12)) | p2(X12, X13)) | (~p2(X11, X13))) <=> ((~p2(X11, X13)) | (~p2(X11, X12)) | p2(X12, X13))), (((p2(X12, X13) | (~p2(X11, X12))) | (~p2(X11, X13))) <=> ((~p2(X11, X13)) | (~p2(X11, X12)) | p2(X12, X13))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(65,plain,
% 0.18/0.40 (![X12: $i, X11: $i, X13: $i] : ((p2(X12, X13) | (~p2(X11, X12))) | (~p2(X11, X13))) <=> ![X12: $i, X11: $i, X13: $i] : ((~p2(X11, X13)) | (~p2(X11, X12)) | p2(X12, X13))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[64])).
% 0.18/0.40 tff(66,axiom,(![X12: $i, X11: $i, X13: $i] : ((p2(X12, X13) | (~p2(X11, X12))) | (~p2(X11, X13)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_17')).
% 0.18/0.40 tff(67,plain,
% 0.18/0.40 (![X12: $i, X11: $i, X13: $i] : ((~p2(X11, X13)) | (~p2(X11, X12)) | p2(X12, X13))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.18/0.40 tff(68,plain,
% 0.18/0.40 (![X12: $i, X11: $i, X13: $i] : ((~p2(X11, X13)) | (~p2(X11, X12)) | p2(X12, X13))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.18/0.40 tff(69,plain,(
% 0.18/0.40 ![X12: $i, X11: $i, X13: $i] : ((~p2(X11, X13)) | (~p2(X11, X12)) | p2(X12, X13))),
% 0.18/0.40 inference(skolemize,[status(sab)],[68])).
% 0.18/0.40 tff(70,plain,
% 0.18/0.40 (![X12: $i, X11: $i, X13: $i] : ((~p2(X11, X13)) | (~p2(X11, X12)) | p2(X12, X13))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[69, 62])).
% 0.18/0.40 tff(71,plain,
% 0.18/0.40 (((~![X12: $i, X11: $i, X13: $i] : ((~p2(X11, X13)) | (~p2(X11, X12)) | p2(X12, X13))) | ((~p2(f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))), f9(f10(f14(f4(f9(c19)), c19), f15(c22))))) | (~p2(f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))), f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))))) | p2(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21)))))) <=> ((~![X12: $i, X11: $i, X13: $i] : ((~p2(X11, X13)) | (~p2(X11, X12)) | p2(X12, X13))) | (~p2(f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))), f9(f10(f14(f4(f9(c19)), c19), f15(c22))))) | (~p2(f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))), f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))))) | p2(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21)))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(72,plain,
% 0.18/0.40 (((~p2(f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))), f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))))) | (~p2(f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))), f9(f10(f14(f4(f9(c19)), c19), f15(c22))))) | p2(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))))) <=> ((~p2(f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))), f9(f10(f14(f4(f9(c19)), c19), f15(c22))))) | (~p2(f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))), f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))))) | p2(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21)))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(73,plain,
% 0.18/0.40 (((~![X12: $i, X11: $i, X13: $i] : ((~p2(X11, X13)) | (~p2(X11, X12)) | p2(X12, X13))) | ((~p2(f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))), f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))))) | (~p2(f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))), f9(f10(f14(f4(f9(c19)), c19), f15(c22))))) | p2(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21)))))) <=> ((~![X12: $i, X11: $i, X13: $i] : ((~p2(X11, X13)) | (~p2(X11, X12)) | p2(X12, X13))) | ((~p2(f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))), f9(f10(f14(f4(f9(c19)), c19), f15(c22))))) | (~p2(f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))), f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))))) | p2(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))))))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[72])).
% 0.18/0.40 tff(74,plain,
% 0.18/0.40 (((~![X12: $i, X11: $i, X13: $i] : ((~p2(X11, X13)) | (~p2(X11, X12)) | p2(X12, X13))) | ((~p2(f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))), f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))))) | (~p2(f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))), f9(f10(f14(f4(f9(c19)), c19), f15(c22))))) | p2(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21)))))) <=> ((~![X12: $i, X11: $i, X13: $i] : ((~p2(X11, X13)) | (~p2(X11, X12)) | p2(X12, X13))) | (~p2(f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))), f9(f10(f14(f4(f9(c19)), c19), f15(c22))))) | (~p2(f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))), f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))))) | p2(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21)))))),
% 0.18/0.40 inference(transitivity,[status(thm)],[73, 71])).
% 0.18/0.40 tff(75,plain,
% 0.18/0.40 ((~![X12: $i, X11: $i, X13: $i] : ((~p2(X11, X13)) | (~p2(X11, X12)) | p2(X12, X13))) | ((~p2(f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))), f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))))) | (~p2(f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))), f9(f10(f14(f4(f9(c19)), c19), f15(c22))))) | p2(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21)))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(76,plain,
% 0.18/0.40 ((~![X12: $i, X11: $i, X13: $i] : ((~p2(X11, X13)) | (~p2(X11, X12)) | p2(X12, X13))) | (~p2(f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))), f9(f10(f14(f4(f9(c19)), c19), f15(c22))))) | (~p2(f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))), f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))))) | p2(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.18/0.40 tff(77,plain,
% 0.18/0.40 (p2(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[76, 70, 60, 45])).
% 0.18/0.40 tff(78,assumption,(~p5(f8(c20), f8(c20))), introduced(assumption)).
% 0.18/0.40 tff(79,plain,
% 0.18/0.40 (^[X43: $i] : refl(p5(X43, X43) <=> p5(X43, X43))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(80,plain,
% 0.18/0.40 (![X43: $i] : p5(X43, X43) <=> ![X43: $i] : p5(X43, X43)),
% 0.18/0.40 inference(quant_intro,[status(thm)],[79])).
% 0.18/0.40 tff(81,plain,
% 0.18/0.40 (![X43: $i] : p5(X43, X43) <=> ![X43: $i] : p5(X43, X43)),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(82,axiom,(![X43: $i] : p5(X43, X43)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p5_3')).
% 0.18/0.40 tff(83,plain,
% 0.18/0.40 (![X43: $i] : p5(X43, X43)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.18/0.40 tff(84,plain,(
% 0.18/0.40 ![X43: $i] : p5(X43, X43)),
% 0.18/0.40 inference(skolemize,[status(sab)],[83])).
% 0.18/0.40 tff(85,plain,
% 0.18/0.40 (![X43: $i] : p5(X43, X43)),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.18/0.40 tff(86,plain,
% 0.18/0.40 ((~![X43: $i] : p5(X43, X43)) | p5(f8(c20), f8(c20))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(87,plain,
% 0.18/0.40 ($false),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[86, 85, 78])).
% 0.18/0.40 tff(88,plain,(p5(f8(c20), f8(c20))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.40 tff(89,plain,
% 0.18/0.40 (^[X47: $i, X46: $i] : refl(((~p5(X46, X47)) | p5(f7(X46), f7(X47))) <=> ((~p5(X46, X47)) | p5(f7(X46), f7(X47))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(90,plain,
% 0.18/0.40 (![X47: $i, X46: $i] : ((~p5(X46, X47)) | p5(f7(X46), f7(X47))) <=> ![X47: $i, X46: $i] : ((~p5(X46, X47)) | p5(f7(X46), f7(X47)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[89])).
% 0.18/0.40 tff(91,plain,
% 0.18/0.40 (![X47: $i, X46: $i] : ((~p5(X46, X47)) | p5(f7(X46), f7(X47))) <=> ![X47: $i, X46: $i] : ((~p5(X46, X47)) | p5(f7(X46), f7(X47)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(92,plain,
% 0.18/0.40 (^[X47: $i, X46: $i] : rewrite((p5(f7(X46), f7(X47)) | (~p5(X46, X47))) <=> ((~p5(X46, X47)) | p5(f7(X46), f7(X47))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(93,plain,
% 0.18/0.40 (![X47: $i, X46: $i] : (p5(f7(X46), f7(X47)) | (~p5(X46, X47))) <=> ![X47: $i, X46: $i] : ((~p5(X46, X47)) | p5(f7(X46), f7(X47)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[92])).
% 0.18/0.40 tff(94,axiom,(![X47: $i, X46: $i] : (p5(f7(X46), f7(X47)) | (~p5(X46, X47)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p5_16')).
% 0.18/0.40 tff(95,plain,
% 0.18/0.40 (![X47: $i, X46: $i] : ((~p5(X46, X47)) | p5(f7(X46), f7(X47)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.18/0.40 tff(96,plain,
% 0.18/0.40 (![X47: $i, X46: $i] : ((~p5(X46, X47)) | p5(f7(X46), f7(X47)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.18/0.40 tff(97,plain,(
% 0.18/0.40 ![X47: $i, X46: $i] : ((~p5(X46, X47)) | p5(f7(X46), f7(X47)))),
% 0.18/0.40 inference(skolemize,[status(sab)],[96])).
% 0.18/0.40 tff(98,plain,
% 0.18/0.40 (![X47: $i, X46: $i] : ((~p5(X46, X47)) | p5(f7(X46), f7(X47)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[97, 90])).
% 0.18/0.40 tff(99,plain,
% 0.18/0.40 (((~![X47: $i, X46: $i] : ((~p5(X46, X47)) | p5(f7(X46), f7(X47)))) | ((~p5(f8(c20), f8(c20))) | p5(f7(f8(c20)), f7(f8(c20))))) <=> ((~![X47: $i, X46: $i] : ((~p5(X46, X47)) | p5(f7(X46), f7(X47)))) | (~p5(f8(c20), f8(c20))) | p5(f7(f8(c20)), f7(f8(c20))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(100,plain,
% 0.18/0.40 ((~![X47: $i, X46: $i] : ((~p5(X46, X47)) | p5(f7(X46), f7(X47)))) | ((~p5(f8(c20), f8(c20))) | p5(f7(f8(c20)), f7(f8(c20))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(101,plain,
% 0.18/0.40 ((~![X47: $i, X46: $i] : ((~p5(X46, X47)) | p5(f7(X46), f7(X47)))) | (~p5(f8(c20), f8(c20))) | p5(f7(f8(c20)), f7(f8(c20)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.18/0.40 tff(102,plain,
% 0.18/0.40 ((~p5(f8(c20), f8(c20))) | p5(f7(f8(c20)), f7(f8(c20)))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[101, 98])).
% 0.18/0.40 tff(103,plain,
% 0.18/0.40 (p5(f7(f8(c20)), f7(f8(c20)))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[102, 88])).
% 0.18/0.40 tff(104,plain,
% 0.18/0.40 (^[X14: $i, X15: $i] : refl(((~p5(X14, X15)) | p2(f6(X14), f6(X15))) <=> ((~p5(X14, X15)) | p2(f6(X14), f6(X15))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(105,plain,
% 0.18/0.40 (![X14: $i, X15: $i] : ((~p5(X14, X15)) | p2(f6(X14), f6(X15))) <=> ![X14: $i, X15: $i] : ((~p5(X14, X15)) | p2(f6(X14), f6(X15)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[104])).
% 0.18/0.40 tff(106,plain,
% 0.18/0.40 (![X14: $i, X15: $i] : ((~p5(X14, X15)) | p2(f6(X14), f6(X15))) <=> ![X14: $i, X15: $i] : ((~p5(X14, X15)) | p2(f6(X14), f6(X15)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(107,plain,
% 0.18/0.40 (^[X14: $i, X15: $i] : rewrite((p2(f6(X14), f6(X15)) | (~p5(X14, X15))) <=> ((~p5(X14, X15)) | p2(f6(X14), f6(X15))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(108,plain,
% 0.18/0.40 (![X14: $i, X15: $i] : (p2(f6(X14), f6(X15)) | (~p5(X14, X15))) <=> ![X14: $i, X15: $i] : ((~p5(X14, X15)) | p2(f6(X14), f6(X15)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[107])).
% 0.18/0.40 tff(109,axiom,(![X14: $i, X15: $i] : (p2(f6(X14), f6(X15)) | (~p5(X14, X15)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_11')).
% 0.18/0.40 tff(110,plain,
% 0.18/0.40 (![X14: $i, X15: $i] : ((~p5(X14, X15)) | p2(f6(X14), f6(X15)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.18/0.40 tff(111,plain,
% 0.18/0.40 (![X14: $i, X15: $i] : ((~p5(X14, X15)) | p2(f6(X14), f6(X15)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[110, 106])).
% 0.18/0.40 tff(112,plain,(
% 0.18/0.40 ![X14: $i, X15: $i] : ((~p5(X14, X15)) | p2(f6(X14), f6(X15)))),
% 0.18/0.40 inference(skolemize,[status(sab)],[111])).
% 0.18/0.40 tff(113,plain,
% 0.18/0.40 (![X14: $i, X15: $i] : ((~p5(X14, X15)) | p2(f6(X14), f6(X15)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[112, 105])).
% 0.18/0.40 tff(114,plain,
% 0.18/0.40 (((~![X14: $i, X15: $i] : ((~p5(X14, X15)) | p2(f6(X14), f6(X15)))) | ((~p5(f7(f8(c20)), f7(f8(c20)))) | p2(f6(f7(f8(c20))), f6(f7(f8(c20)))))) <=> ((~![X14: $i, X15: $i] : ((~p5(X14, X15)) | p2(f6(X14), f6(X15)))) | (~p5(f7(f8(c20)), f7(f8(c20)))) | p2(f6(f7(f8(c20))), f6(f7(f8(c20)))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(115,plain,
% 0.18/0.40 ((~![X14: $i, X15: $i] : ((~p5(X14, X15)) | p2(f6(X14), f6(X15)))) | ((~p5(f7(f8(c20)), f7(f8(c20)))) | p2(f6(f7(f8(c20))), f6(f7(f8(c20)))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(116,plain,
% 0.18/0.40 ((~![X14: $i, X15: $i] : ((~p5(X14, X15)) | p2(f6(X14), f6(X15)))) | (~p5(f7(f8(c20)), f7(f8(c20)))) | p2(f6(f7(f8(c20))), f6(f7(f8(c20))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.18/0.40 tff(117,plain,
% 0.18/0.40 (p2(f6(f7(f8(c20))), f6(f7(f8(c20))))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[116, 113, 103])).
% 0.18/0.41 tff(118,plain,
% 0.18/0.41 (^[X50: $i] : refl((~p17(f9(f10(f14(f4(f9(c19)), c19), f12(X50, c21))), f6(f7(f8(c20))))) <=> (~p17(f9(f10(f14(f4(f9(c19)), c19), f12(X50, c21))), f6(f7(f8(c20))))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(119,plain,
% 0.18/0.41 (![X50: $i] : (~p17(f9(f10(f14(f4(f9(c19)), c19), f12(X50, c21))), f6(f7(f8(c20))))) <=> ![X50: $i] : (~p17(f9(f10(f14(f4(f9(c19)), c19), f12(X50, c21))), f6(f7(f8(c20)))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[118])).
% 0.18/0.41 tff(120,plain,
% 0.18/0.41 (![X50: $i] : (~p17(f9(f10(f14(f4(f9(c19)), c19), f12(X50, c21))), f6(f7(f8(c20))))) <=> ![X50: $i] : (~p17(f9(f10(f14(f4(f9(c19)), c19), f12(X50, c21))), f6(f7(f8(c20)))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(121,axiom,(![X50: $i] : (~p17(f9(f10(f14(f4(f9(c19)), c19), f12(X50, c21))), f6(f7(f8(c20)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_p17_29')).
% 0.18/0.41 tff(122,plain,
% 0.18/0.41 (![X50: $i] : (~p17(f9(f10(f14(f4(f9(c19)), c19), f12(X50, c21))), f6(f7(f8(c20)))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.18/0.41 tff(123,plain,(
% 0.18/0.41 ![X50: $i] : (~p17(f9(f10(f14(f4(f9(c19)), c19), f12(X50, c21))), f6(f7(f8(c20)))))),
% 0.18/0.41 inference(skolemize,[status(sab)],[122])).
% 0.18/0.41 tff(124,plain,
% 0.18/0.41 (![X50: $i] : (~p17(f9(f10(f14(f4(f9(c19)), c19), f12(X50, c21))), f6(f7(f8(c20)))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[123, 119])).
% 0.18/0.41 tff(125,plain,
% 0.18/0.41 ((~![X50: $i] : (~p17(f9(f10(f14(f4(f9(c19)), c19), f12(X50, c21))), f6(f7(f8(c20)))))) | (~p17(f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))), f6(f7(f8(c20)))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(126,plain,
% 0.18/0.41 (~p17(f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))), f6(f7(f8(c20))))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[125, 124])).
% 0.18/0.41 tff(127,plain,
% 0.18/0.41 (p17(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f6(f7(f8(c20)))) <=> p17(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f6(f7(f8(c20))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(128,axiom,(p17(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f6(f7(f8(c20))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p17_27')).
% 0.18/0.41 tff(129,plain,
% 0.18/0.41 (p17(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f6(f7(f8(c20))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.18/0.41 tff(130,plain,
% 0.18/0.41 (^[X4: $i, X3: $i, X2: $i, X5: $i] : refl(((~p17(X4, X5)) | (~p2(X5, X3)) | (~p2(X4, X2)) | p17(X2, X3)) <=> ((~p17(X4, X5)) | (~p2(X5, X3)) | (~p2(X4, X2)) | p17(X2, X3)))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(131,plain,
% 0.18/0.41 (![X4: $i, X3: $i, X2: $i, X5: $i] : ((~p17(X4, X5)) | (~p2(X5, X3)) | (~p2(X4, X2)) | p17(X2, X3)) <=> ![X4: $i, X3: $i, X2: $i, X5: $i] : ((~p17(X4, X5)) | (~p2(X5, X3)) | (~p2(X4, X2)) | p17(X2, X3))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[130])).
% 0.18/0.41 tff(132,plain,
% 0.18/0.41 (![X4: $i, X3: $i, X2: $i, X5: $i] : ((~p17(X4, X5)) | (~p2(X5, X3)) | (~p2(X4, X2)) | p17(X2, X3)) <=> ![X4: $i, X3: $i, X2: $i, X5: $i] : ((~p17(X4, X5)) | (~p2(X5, X3)) | (~p2(X4, X2)) | p17(X2, X3))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(133,plain,
% 0.18/0.41 (^[X4: $i, X3: $i, X2: $i, X5: $i] : trans(monotonicity(trans(monotonicity(rewrite((p17(X2, X3) | (~p2(X4, X2))) <=> ((~p2(X4, X2)) | p17(X2, X3))), (((p17(X2, X3) | (~p2(X4, X2))) | (~p2(X5, X3))) <=> (((~p2(X4, X2)) | p17(X2, X3)) | (~p2(X5, X3))))), rewrite((((~p2(X4, X2)) | p17(X2, X3)) | (~p2(X5, X3))) <=> ((~p2(X5, X3)) | (~p2(X4, X2)) | p17(X2, X3))), (((p17(X2, X3) | (~p2(X4, X2))) | (~p2(X5, X3))) <=> ((~p2(X5, X3)) | (~p2(X4, X2)) | p17(X2, X3)))), ((((p17(X2, X3) | (~p2(X4, X2))) | (~p2(X5, X3))) | (~p17(X4, X5))) <=> (((~p2(X5, X3)) | (~p2(X4, X2)) | p17(X2, X3)) | (~p17(X4, X5))))), rewrite((((~p2(X5, X3)) | (~p2(X4, X2)) | p17(X2, X3)) | (~p17(X4, X5))) <=> ((~p17(X4, X5)) | (~p2(X5, X3)) | (~p2(X4, X2)) | p17(X2, X3))), ((((p17(X2, X3) | (~p2(X4, X2))) | (~p2(X5, X3))) | (~p17(X4, X5))) <=> ((~p17(X4, X5)) | (~p2(X5, X3)) | (~p2(X4, X2)) | p17(X2, X3))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(134,plain,
% 0.18/0.41 (![X4: $i, X3: $i, X2: $i, X5: $i] : (((p17(X2, X3) | (~p2(X4, X2))) | (~p2(X5, X3))) | (~p17(X4, X5))) <=> ![X4: $i, X3: $i, X2: $i, X5: $i] : ((~p17(X4, X5)) | (~p2(X5, X3)) | (~p2(X4, X2)) | p17(X2, X3))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[133])).
% 0.18/0.41 tff(135,axiom,(![X4: $i, X3: $i, X2: $i, X5: $i] : (((p17(X2, X3) | (~p2(X4, X2))) | (~p2(X5, X3))) | (~p17(X4, X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p17_20')).
% 0.18/0.41 tff(136,plain,
% 0.18/0.41 (![X4: $i, X3: $i, X2: $i, X5: $i] : ((~p17(X4, X5)) | (~p2(X5, X3)) | (~p2(X4, X2)) | p17(X2, X3))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.18/0.41 tff(137,plain,
% 0.18/0.41 (![X4: $i, X3: $i, X2: $i, X5: $i] : ((~p17(X4, X5)) | (~p2(X5, X3)) | (~p2(X4, X2)) | p17(X2, X3))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[136, 132])).
% 0.18/0.41 tff(138,plain,(
% 0.18/0.41 ![X4: $i, X3: $i, X2: $i, X5: $i] : ((~p17(X4, X5)) | (~p2(X5, X3)) | (~p2(X4, X2)) | p17(X2, X3))),
% 0.18/0.41 inference(skolemize,[status(sab)],[137])).
% 0.18/0.41 tff(139,plain,
% 0.18/0.41 (![X4: $i, X3: $i, X2: $i, X5: $i] : ((~p17(X4, X5)) | (~p2(X5, X3)) | (~p2(X4, X2)) | p17(X2, X3))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[138, 131])).
% 0.18/0.41 tff(140,plain,
% 0.18/0.41 (((~![X4: $i, X3: $i, X2: $i, X5: $i] : ((~p17(X4, X5)) | (~p2(X5, X3)) | (~p2(X4, X2)) | p17(X2, X3))) | (p17(f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))), f6(f7(f8(c20)))) | (~p2(f6(f7(f8(c20))), f6(f7(f8(c20))))) | (~p17(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f6(f7(f8(c20))))) | (~p2(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))))))) <=> ((~![X4: $i, X3: $i, X2: $i, X5: $i] : ((~p17(X4, X5)) | (~p2(X5, X3)) | (~p2(X4, X2)) | p17(X2, X3))) | p17(f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))), f6(f7(f8(c20)))) | (~p2(f6(f7(f8(c20))), f6(f7(f8(c20))))) | (~p17(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f6(f7(f8(c20))))) | (~p2(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(141,plain,
% 0.18/0.41 (((~p17(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f6(f7(f8(c20))))) | (~p2(f6(f7(f8(c20))), f6(f7(f8(c20))))) | (~p2(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))))) | p17(f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))), f6(f7(f8(c20))))) <=> (p17(f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))), f6(f7(f8(c20)))) | (~p2(f6(f7(f8(c20))), f6(f7(f8(c20))))) | (~p17(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f6(f7(f8(c20))))) | (~p2(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(142,plain,
% 0.18/0.41 (((~![X4: $i, X3: $i, X2: $i, X5: $i] : ((~p17(X4, X5)) | (~p2(X5, X3)) | (~p2(X4, X2)) | p17(X2, X3))) | ((~p17(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f6(f7(f8(c20))))) | (~p2(f6(f7(f8(c20))), f6(f7(f8(c20))))) | (~p2(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))))) | p17(f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))), f6(f7(f8(c20)))))) <=> ((~![X4: $i, X3: $i, X2: $i, X5: $i] : ((~p17(X4, X5)) | (~p2(X5, X3)) | (~p2(X4, X2)) | p17(X2, X3))) | (p17(f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))), f6(f7(f8(c20)))) | (~p2(f6(f7(f8(c20))), f6(f7(f8(c20))))) | (~p17(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f6(f7(f8(c20))))) | (~p2(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21)))))))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[141])).
% 0.18/0.41 tff(143,plain,
% 0.18/0.41 (((~![X4: $i, X3: $i, X2: $i, X5: $i] : ((~p17(X4, X5)) | (~p2(X5, X3)) | (~p2(X4, X2)) | p17(X2, X3))) | ((~p17(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f6(f7(f8(c20))))) | (~p2(f6(f7(f8(c20))), f6(f7(f8(c20))))) | (~p2(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))))) | p17(f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))), f6(f7(f8(c20)))))) <=> ((~![X4: $i, X3: $i, X2: $i, X5: $i] : ((~p17(X4, X5)) | (~p2(X5, X3)) | (~p2(X4, X2)) | p17(X2, X3))) | p17(f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))), f6(f7(f8(c20)))) | (~p2(f6(f7(f8(c20))), f6(f7(f8(c20))))) | (~p17(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f6(f7(f8(c20))))) | (~p2(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))))))),
% 0.18/0.41 inference(transitivity,[status(thm)],[142, 140])).
% 0.18/0.41 tff(144,plain,
% 0.18/0.41 ((~![X4: $i, X3: $i, X2: $i, X5: $i] : ((~p17(X4, X5)) | (~p2(X5, X3)) | (~p2(X4, X2)) | p17(X2, X3))) | ((~p17(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f6(f7(f8(c20))))) | (~p2(f6(f7(f8(c20))), f6(f7(f8(c20))))) | (~p2(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))))) | p17(f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))), f6(f7(f8(c20)))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(145,plain,
% 0.18/0.41 ((~![X4: $i, X3: $i, X2: $i, X5: $i] : ((~p17(X4, X5)) | (~p2(X5, X3)) | (~p2(X4, X2)) | p17(X2, X3))) | p17(f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21))), f6(f7(f8(c20)))) | (~p2(f6(f7(f8(c20))), f6(f7(f8(c20))))) | (~p17(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f6(f7(f8(c20))))) | (~p2(f9(f10(f14(f4(f9(c19)), c19), f15(c22))), f9(f10(f14(f4(f9(c19)), c19), f12(f15(c22), c21)))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.18/0.41 tff(146,plain,
% 0.18/0.41 ($false),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[145, 139, 129, 126, 117, 77])).
% 0.18/0.41 % SZS output end Proof
% 0.18/0.42 % E exiting
%------------------------------------------------------------------------------