%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MGT082+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 8 06:24:12 AM UTC 2026
% Result : Theorem 0.13s 0.43s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT082+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.08/0.36 % Computer : n011.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 7 14:17:19 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.13/0.43 % SZS status Theorem
% 0.13/0.43 % SZS output start Proof
% 0.13/0.43 tff(v601_type, type, (
% 0.13/0.43 v601: $i)).
% 0.13/0.43 tff(v600_type, type, (
% 0.13/0.43 v600: $i)).
% 0.13/0.43 tff(tptp_fun_X_4_type, type, (
% 0.13/0.43 tptp_fun_X_4: $i)).
% 0.13/0.43 tff(leq_type, type, (
% 0.13/0.43 leq: ( $i * $i ) > $o)).
% 0.13/0.43 tff(in_closed_type, type, (
% 0.13/0.43 in_closed: ( $i * $i * $i ) > $o)).
% 0.13/0.43 tff(in_lopen_type, type, (
% 0.13/0.43 in_lopen: ( $i * $i * $i ) > $o)).
% 0.13/0.43 tff(v32_type, type, (
% 0.13/0.43 v32: $i)).
% 0.13/0.43 tff(v0_type, type, (
% 0.13/0.43 v0: $i)).
% 0.13/0.43 tff(tptp_fun_Z_2_type, type, (
% 0.13/0.43 tptp_fun_Z_2: $i)).
% 0.13/0.43 tff(v16_type, type, (
% 0.13/0.43 v16: $i)).
% 0.13/0.43 tff(in_open_type, type, (
% 0.13/0.43 in_open: ( $i * $i * $i ) > $o)).
% 0.13/0.43 tff(v500_type, type, (
% 0.13/0.43 v500: $i)).
% 0.13/0.43 tff(tptp_fun_Y_3_type, type, (
% 0.13/0.43 tptp_fun_Y_3: $i)).
% 0.13/0.43 tff(less_type, type, (
% 0.13/0.43 less: ( $i * $i ) > $o)).
% 0.13/0.43 tff(v300_type, type, (
% 0.13/0.43 v300: $i)).
% 0.13/0.43 tff(1,plain,
% 0.13/0.43 ((X!4 = v601) <=> (v601 = X!4)),
% 0.13/0.43 inference(commutativity,[status(thm)],[])).
% 0.13/0.43 tff(2,plain,
% 0.13/0.43 (^[X: $i, A: $i, B: $i] : refl((~(((~leq(A, X)) | (~leq(X, B))) <=> in_closed(X, A, B))) <=> (~(((~leq(A, X)) | (~leq(X, B))) <=> in_closed(X, A, B))))),
% 0.13/0.43 inference(bind,[status(th)],[])).
% 0.13/0.43 tff(3,plain,
% 0.13/0.43 (![X: $i, A: $i, B: $i] : (~(((~leq(A, X)) | (~leq(X, B))) <=> in_closed(X, A, B))) <=> ![X: $i, A: $i, B: $i] : (~(((~leq(A, X)) | (~leq(X, B))) <=> in_closed(X, A, B)))),
% 0.13/0.43 inference(quant_intro,[status(thm)],[2])).
% 0.13/0.43 tff(4,plain,
% 0.13/0.43 (^[X: $i, A: $i, B: $i] : trans(trans(monotonicity(rewrite((leq(A, X) & leq(X, B)) <=> (~((~leq(A, X)) | (~leq(X, B))))), ((in_closed(X, A, B) <=> (leq(A, X) & leq(X, B))) <=> (in_closed(X, A, B) <=> (~((~leq(A, X)) | (~leq(X, B))))))), rewrite((in_closed(X, A, B) <=> (~((~leq(A, X)) | (~leq(X, B))))) <=> (~(((~leq(A, X)) | (~leq(X, B))) <=> in_closed(X, A, B)))), ((in_closed(X, A, B) <=> (leq(A, X) & leq(X, B))) <=> (~(((~leq(A, X)) | (~leq(X, B))) <=> in_closed(X, A, B))))), rewrite((~(((~leq(A, X)) | (~leq(X, B))) <=> in_closed(X, A, B))) <=> (~(((~leq(A, X)) | (~leq(X, B))) <=> in_closed(X, A, B)))), ((in_closed(X, A, B) <=> (leq(A, X) & leq(X, B))) <=> (~(((~leq(A, X)) | (~leq(X, B))) <=> in_closed(X, A, B)))))),
% 0.13/0.43 inference(bind,[status(th)],[])).
% 0.13/0.43 tff(5,plain,
% 0.13/0.43 (![X: $i, A: $i, B: $i] : (in_closed(X, A, B) <=> (leq(A, X) & leq(X, B))) <=> ![X: $i, A: $i, B: $i] : (~(((~leq(A, X)) | (~leq(X, B))) <=> in_closed(X, A, B)))),
% 0.13/0.43 inference(quant_intro,[status(thm)],[4])).
% 0.13/0.43 tff(6,plain,
% 0.13/0.43 (![X: $i, A: $i, B: $i] : (in_closed(X, A, B) <=> (leq(A, X) & leq(X, B))) <=> ![X: $i, A: $i, B: $i] : (in_closed(X, A, B) <=> (leq(A, X) & leq(X, B)))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(7,axiom,(![X: $i, A: $i, B: $i] : (in_closed(X, A, B) <=> (leq(A, X) & leq(X, B)))), file('/export/starexec/sandbox2/benchmark/Axioms/MGT002+2.ax','in_closed')).
% 0.13/0.43 tff(8,plain,
% 0.13/0.43 (![X: $i, A: $i, B: $i] : (in_closed(X, A, B) <=> (leq(A, X) & leq(X, B)))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.13/0.43 tff(9,plain,(
% 0.13/0.43 ![X: $i, A: $i, B: $i] : (in_closed(X, A, B) <=> (leq(A, X) & leq(X, B)))),
% 0.13/0.43 inference(skolemize,[status(sab)],[8])).
% 0.13/0.43 tff(10,plain,
% 0.13/0.43 (![X: $i, A: $i, B: $i] : (~(((~leq(A, X)) | (~leq(X, B))) <=> in_closed(X, A, B)))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.13/0.43 tff(11,plain,
% 0.13/0.43 (![X: $i, A: $i, B: $i] : (~(((~leq(A, X)) | (~leq(X, B))) <=> in_closed(X, A, B)))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.13/0.43 tff(12,plain,
% 0.13/0.43 ((~![X: $i, A: $i, B: $i] : (~(((~leq(A, X)) | (~leq(X, B))) <=> in_closed(X, A, B)))) | (~(((~leq(v600, X!4)) | (~leq(X!4, v600))) <=> in_closed(X!4, v600, v600)))),
% 0.13/0.43 inference(quant_inst,[status(thm)],[])).
% 0.13/0.43 tff(13,plain,
% 0.13/0.43 (~(((~leq(v600, X!4)) | (~leq(X!4, v600))) <=> in_closed(X!4, v600, v600))),
% 0.13/0.43 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.13/0.43 tff(14,plain,
% 0.13/0.43 (?[X: $i, Y: $i, Z: $i] : (in_closed(X, v600, v600) & in_closed(X, v601, v601) & less(v300, Y) & in_open(Y, v0, v500) & leq(v16, Z) & in_lopen(Z, v0, v32)) <=> ?[X: $i, Y: $i, Z: $i] : (in_closed(X, v600, v600) & in_closed(X, v601, v601) & less(v300, Y) & in_open(Y, v0, v500) & leq(v16, Z) & in_lopen(Z, v0, v32))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(15,plain,
% 0.13/0.43 ((~(~?[X: $i, Y: $i, Z: $i] : (in_closed(X, v600, v600) & in_closed(X, v601, v601) & less(v300, Y) & in_open(Y, v0, v500) & leq(v16, Z) & in_lopen(Z, v0, v32)))) <=> ?[X: $i, Y: $i, Z: $i] : (in_closed(X, v600, v600) & in_closed(X, v601, v601) & less(v300, Y) & in_open(Y, v0, v500) & leq(v16, Z) & in_lopen(Z, v0, v32))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(16,plain,
% 0.13/0.43 ((~?[X: $i, Y: $i, Z: $i] : (((((in_closed(X, v600, v600) & in_closed(X, v601, v601)) & less(v300, Y)) & in_open(Y, v0, v500)) & leq(v16, Z)) & in_lopen(Z, v0, v32))) <=> (~?[X: $i, Y: $i, Z: $i] : (in_closed(X, v600, v600) & in_closed(X, v601, v601) & less(v300, Y) & in_open(Y, v0, v500) & leq(v16, Z) & in_lopen(Z, v0, v32)))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(17,plain,
% 0.13/0.43 ((~(~?[X: $i, Y: $i, Z: $i] : (((((in_closed(X, v600, v600) & in_closed(X, v601, v601)) & less(v300, Y)) & in_open(Y, v0, v500)) & leq(v16, Z)) & in_lopen(Z, v0, v32)))) <=> (~(~?[X: $i, Y: $i, Z: $i] : (in_closed(X, v600, v600) & in_closed(X, v601, v601) & less(v300, Y) & in_open(Y, v0, v500) & leq(v16, Z) & in_lopen(Z, v0, v32))))),
% 0.13/0.43 inference(monotonicity,[status(thm)],[16])).
% 0.13/0.43 tff(18,plain,
% 0.13/0.43 ((~(~?[X: $i, Y: $i, Z: $i] : (((((in_closed(X, v600, v600) & in_closed(X, v601, v601)) & less(v300, Y)) & in_open(Y, v0, v500)) & leq(v16, Z)) & in_lopen(Z, v0, v32)))) <=> ?[X: $i, Y: $i, Z: $i] : (in_closed(X, v600, v600) & in_closed(X, v601, v601) & less(v300, Y) & in_open(Y, v0, v500) & leq(v16, Z) & in_lopen(Z, v0, v32))),
% 0.13/0.43 inference(transitivity,[status(thm)],[17, 15])).
% 0.13/0.43 tff(19,axiom,(~(~?[X: $i, Y: $i, Z: $i] : (((((in_closed(X, v600, v600) & in_closed(X, v601, v601)) & less(v300, Y)) & in_open(Y, v0, v500)) & leq(v16, Z)) & in_lopen(Z, v0, v32)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','odrl411')).
% 0.13/0.43 tff(20,plain,
% 0.13/0.43 (?[X: $i, Y: $i, Z: $i] : (in_closed(X, v600, v600) & in_closed(X, v601, v601) & less(v300, Y) & in_open(Y, v0, v500) & leq(v16, Z) & in_lopen(Z, v0, v32))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.13/0.43 tff(21,plain,
% 0.13/0.43 (?[X: $i, Y: $i, Z: $i] : (in_closed(X, v600, v600) & in_closed(X, v601, v601) & less(v300, Y) & in_open(Y, v0, v500) & leq(v16, Z) & in_lopen(Z, v0, v32))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[20, 14])).
% 0.13/0.43 tff(22,plain,(
% 0.13/0.43 in_closed(X!4, v600, v600) & in_closed(X!4, v601, v601) & less(v300, Y!3) & in_open(Y!3, v0, v500) & leq(v16, Z!2) & in_lopen(Z!2, v0, v32)),
% 0.13/0.43 inference(skolemize,[status(sab)],[21])).
% 0.13/0.43 tff(23,plain,
% 0.13/0.43 (in_closed(X!4, v600, v600)),
% 0.13/0.43 inference(and_elim,[status(thm)],[22])).
% 0.13/0.43 tff(24,plain,
% 0.13/0.43 ((((~leq(v600, X!4)) | (~leq(X!4, v600))) <=> in_closed(X!4, v600, v600)) | (~((~leq(v600, X!4)) | (~leq(X!4, v600)))) | (~in_closed(X!4, v600, v600))),
% 0.13/0.43 inference(tautology,[status(thm)],[])).
% 0.13/0.43 tff(25,plain,
% 0.13/0.43 ((((~leq(v600, X!4)) | (~leq(X!4, v600))) <=> in_closed(X!4, v600, v600)) | (~((~leq(v600, X!4)) | (~leq(X!4, v600))))),
% 0.13/0.43 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.13/0.43 tff(26,plain,
% 0.13/0.43 (~((~leq(v600, X!4)) | (~leq(X!4, v600)))),
% 0.13/0.43 inference(unit_resolution,[status(thm)],[25, 13])).
% 0.13/0.43 tff(27,plain,
% 0.13/0.43 (((~leq(v600, X!4)) | (~leq(X!4, v600))) | leq(X!4, v600)),
% 0.13/0.43 inference(tautology,[status(thm)],[])).
% 0.13/0.43 tff(28,plain,
% 0.13/0.43 (leq(X!4, v600)),
% 0.13/0.43 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.13/0.43 tff(29,plain,
% 0.13/0.43 (((~leq(v600, X!4)) | (~leq(X!4, v600))) | leq(v600, X!4)),
% 0.13/0.43 inference(tautology,[status(thm)],[])).
% 0.13/0.43 tff(30,plain,
% 0.13/0.43 (leq(v600, X!4)),
% 0.13/0.43 inference(unit_resolution,[status(thm)],[29, 26])).
% 0.13/0.43 tff(31,plain,
% 0.13/0.43 (![X: $i, Y: $i] : ((X = Y) | (~leq(X, Y)) | (~leq(Y, X))) <=> ![X: $i, Y: $i] : ((X = Y) | (~leq(X, Y)) | (~leq(Y, X)))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(32,plain,
% 0.13/0.43 (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(X, Y) & leq(Y, X)) <=> (~((~leq(X, Y)) | (~leq(Y, X))))), ((~(leq(X, Y) & leq(Y, X))) <=> (~(~((~leq(X, Y)) | (~leq(Y, X))))))), rewrite((~(~((~leq(X, Y)) | (~leq(Y, X))))) <=> ((~leq(X, Y)) | (~leq(Y, X)))), ((~(leq(X, Y) & leq(Y, X))) <=> ((~leq(X, Y)) | (~leq(Y, X))))), (((~(leq(X, Y) & leq(Y, X))) | (X = Y)) <=> (((~leq(X, Y)) | (~leq(Y, X))) | (X = Y)))), rewrite((((~leq(X, Y)) | (~leq(Y, X))) | (X = Y)) <=> ((X = Y) | (~leq(X, Y)) | (~leq(Y, X)))), (((~(leq(X, Y) & leq(Y, X))) | (X = Y)) <=> ((X = Y) | (~leq(X, Y)) | (~leq(Y, X)))))),
% 0.13/0.43 inference(bind,[status(th)],[])).
% 0.13/0.43 tff(33,plain,
% 0.13/0.43 (![X: $i, Y: $i] : ((~(leq(X, Y) & leq(Y, X))) | (X = Y)) <=> ![X: $i, Y: $i] : ((X = Y) | (~leq(X, Y)) | (~leq(Y, X)))),
% 0.13/0.43 inference(quant_intro,[status(thm)],[32])).
% 0.13/0.43 tff(34,plain,
% 0.13/0.43 (![X: $i, Y: $i] : ((~(leq(X, Y) & leq(Y, X))) | (X = Y)) <=> ![X: $i, Y: $i] : ((~(leq(X, Y) & leq(Y, X))) | (X = Y))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(35,plain,
% 0.13/0.43 (^[X: $i, Y: $i] : rewrite(((leq(X, Y) & leq(Y, X)) => (X = Y)) <=> ((~(leq(X, Y) & leq(Y, X))) | (X = Y)))),
% 0.13/0.43 inference(bind,[status(th)],[])).
% 0.13/0.43 tff(36,plain,
% 0.13/0.43 (![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) => (X = Y)) <=> ![X: $i, Y: $i] : ((~(leq(X, Y) & leq(Y, X))) | (X = Y))),
% 0.13/0.43 inference(quant_intro,[status(thm)],[35])).
% 0.13/0.43 tff(37,axiom,(![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) => (X = Y))), file('/export/starexec/sandbox2/benchmark/Axioms/MGT002+0.ax','leq_antisym')).
% 0.13/0.43 tff(38,plain,
% 0.13/0.43 (![X: $i, Y: $i] : ((~(leq(X, Y) & leq(Y, X))) | (X = Y))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.13/0.43 tff(39,plain,
% 0.13/0.43 (![X: $i, Y: $i] : ((~(leq(X, Y) & leq(Y, X))) | (X = Y))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.13/0.43 tff(40,plain,(
% 0.13/0.43 ![X: $i, Y: $i] : ((~(leq(X, Y) & leq(Y, X))) | (X = Y))),
% 0.13/0.43 inference(skolemize,[status(sab)],[39])).
% 0.13/0.43 tff(41,plain,
% 0.13/0.43 (![X: $i, Y: $i] : ((X = Y) | (~leq(X, Y)) | (~leq(Y, X)))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.13/0.43 tff(42,plain,
% 0.13/0.43 (![X: $i, Y: $i] : ((X = Y) | (~leq(X, Y)) | (~leq(Y, X)))),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[41, 31])).
% 0.13/0.43 tff(43,plain,
% 0.13/0.43 (((~![X: $i, Y: $i] : ((X = Y) | (~leq(X, Y)) | (~leq(Y, X)))) | ((~leq(v600, X!4)) | (~leq(X!4, v600)) | (v600 = X!4))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~leq(X, Y)) | (~leq(Y, X)))) | (~leq(v600, X!4)) | (~leq(X!4, v600)) | (v600 = X!4))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(44,plain,
% 0.13/0.43 (((v600 = X!4) | (~leq(v600, X!4)) | (~leq(X!4, v600))) <=> ((~leq(v600, X!4)) | (~leq(X!4, v600)) | (v600 = X!4))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(45,plain,
% 0.13/0.43 (((~![X: $i, Y: $i] : ((X = Y) | (~leq(X, Y)) | (~leq(Y, X)))) | ((v600 = X!4) | (~leq(v600, X!4)) | (~leq(X!4, v600)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~leq(X, Y)) | (~leq(Y, X)))) | ((~leq(v600, X!4)) | (~leq(X!4, v600)) | (v600 = X!4)))),
% 0.13/0.43 inference(monotonicity,[status(thm)],[44])).
% 0.13/0.43 tff(46,plain,
% 0.13/0.43 (((~![X: $i, Y: $i] : ((X = Y) | (~leq(X, Y)) | (~leq(Y, X)))) | ((v600 = X!4) | (~leq(v600, X!4)) | (~leq(X!4, v600)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~leq(X, Y)) | (~leq(Y, X)))) | (~leq(v600, X!4)) | (~leq(X!4, v600)) | (v600 = X!4))),
% 0.13/0.43 inference(transitivity,[status(thm)],[45, 43])).
% 0.13/0.43 tff(47,plain,
% 0.13/0.43 ((~![X: $i, Y: $i] : ((X = Y) | (~leq(X, Y)) | (~leq(Y, X)))) | ((v600 = X!4) | (~leq(v600, X!4)) | (~leq(X!4, v600)))),
% 0.13/0.43 inference(quant_inst,[status(thm)],[])).
% 0.13/0.43 tff(48,plain,
% 0.13/0.43 ((~![X: $i, Y: $i] : ((X = Y) | (~leq(X, Y)) | (~leq(Y, X)))) | (~leq(v600, X!4)) | (~leq(X!4, v600)) | (v600 = X!4)),
% 0.13/0.43 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.13/0.43 tff(49,plain,
% 0.13/0.43 (v600 = X!4),
% 0.13/0.43 inference(unit_resolution,[status(thm)],[48, 42, 30, 28])).
% 0.13/0.43 tff(50,plain,
% 0.13/0.43 ((v600 = v601) <=> (X!4 = v601)),
% 0.13/0.43 inference(monotonicity,[status(thm)],[49])).
% 0.13/0.43 tff(51,plain,
% 0.13/0.43 ((v600 = v601) <=> (v601 = X!4)),
% 0.13/0.43 inference(transitivity,[status(thm)],[50, 1])).
% 0.13/0.43 tff(52,plain,
% 0.13/0.43 ((v601 = X!4) <=> (v600 = v601)),
% 0.13/0.43 inference(symmetry,[status(thm)],[51])).
% 0.13/0.43 tff(53,plain,
% 0.13/0.43 ((~![X: $i, A: $i, B: $i] : (~(((~leq(A, X)) | (~leq(X, B))) <=> in_closed(X, A, B)))) | (~(((~leq(v601, X!4)) | (~leq(X!4, v601))) <=> in_closed(X!4, v601, v601)))),
% 0.13/0.43 inference(quant_inst,[status(thm)],[])).
% 0.13/0.43 tff(54,plain,
% 0.13/0.43 (~(((~leq(v601, X!4)) | (~leq(X!4, v601))) <=> in_closed(X!4, v601, v601))),
% 0.13/0.43 inference(unit_resolution,[status(thm)],[53, 11])).
% 0.13/0.43 tff(55,plain,
% 0.13/0.43 (in_closed(X!4, v601, v601)),
% 0.13/0.44 inference(and_elim,[status(thm)],[22])).
% 0.13/0.44 tff(56,plain,
% 0.13/0.44 ((((~leq(v601, X!4)) | (~leq(X!4, v601))) <=> in_closed(X!4, v601, v601)) | (~((~leq(v601, X!4)) | (~leq(X!4, v601)))) | (~in_closed(X!4, v601, v601))),
% 0.13/0.44 inference(tautology,[status(thm)],[])).
% 0.13/0.44 tff(57,plain,
% 0.13/0.44 ((((~leq(v601, X!4)) | (~leq(X!4, v601))) <=> in_closed(X!4, v601, v601)) | (~((~leq(v601, X!4)) | (~leq(X!4, v601))))),
% 0.13/0.44 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.13/0.44 tff(58,plain,
% 0.13/0.44 (~((~leq(v601, X!4)) | (~leq(X!4, v601)))),
% 0.13/0.44 inference(unit_resolution,[status(thm)],[57, 54])).
% 0.13/0.44 tff(59,plain,
% 0.13/0.44 (((~leq(v601, X!4)) | (~leq(X!4, v601))) | leq(X!4, v601)),
% 0.13/0.44 inference(tautology,[status(thm)],[])).
% 0.13/0.44 tff(60,plain,
% 0.13/0.44 (leq(X!4, v601)),
% 0.13/0.44 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.13/0.44 tff(61,plain,
% 0.13/0.44 (((~leq(v601, X!4)) | (~leq(X!4, v601))) | leq(v601, X!4)),
% 0.13/0.44 inference(tautology,[status(thm)],[])).
% 0.13/0.44 tff(62,plain,
% 0.13/0.44 (leq(v601, X!4)),
% 0.13/0.44 inference(unit_resolution,[status(thm)],[61, 58])).
% 0.13/0.44 tff(63,plain,
% 0.13/0.44 (((~![X: $i, Y: $i] : ((X = Y) | (~leq(X, Y)) | (~leq(Y, X)))) | ((~leq(v601, X!4)) | (~leq(X!4, v601)) | (v601 = X!4))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~leq(X, Y)) | (~leq(Y, X)))) | (~leq(v601, X!4)) | (~leq(X!4, v601)) | (v601 = X!4))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(64,plain,
% 0.13/0.44 (((v601 = X!4) | (~leq(v601, X!4)) | (~leq(X!4, v601))) <=> ((~leq(v601, X!4)) | (~leq(X!4, v601)) | (v601 = X!4))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(65,plain,
% 0.13/0.44 (((~![X: $i, Y: $i] : ((X = Y) | (~leq(X, Y)) | (~leq(Y, X)))) | ((v601 = X!4) | (~leq(v601, X!4)) | (~leq(X!4, v601)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~leq(X, Y)) | (~leq(Y, X)))) | ((~leq(v601, X!4)) | (~leq(X!4, v601)) | (v601 = X!4)))),
% 0.13/0.44 inference(monotonicity,[status(thm)],[64])).
% 0.13/0.44 tff(66,plain,
% 0.13/0.44 (((~![X: $i, Y: $i] : ((X = Y) | (~leq(X, Y)) | (~leq(Y, X)))) | ((v601 = X!4) | (~leq(v601, X!4)) | (~leq(X!4, v601)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~leq(X, Y)) | (~leq(Y, X)))) | (~leq(v601, X!4)) | (~leq(X!4, v601)) | (v601 = X!4))),
% 0.13/0.44 inference(transitivity,[status(thm)],[65, 63])).
% 0.13/0.44 tff(67,plain,
% 0.13/0.44 ((~![X: $i, Y: $i] : ((X = Y) | (~leq(X, Y)) | (~leq(Y, X)))) | ((v601 = X!4) | (~leq(v601, X!4)) | (~leq(X!4, v601)))),
% 0.13/0.44 inference(quant_inst,[status(thm)],[])).
% 0.13/0.44 tff(68,plain,
% 0.13/0.44 ((~![X: $i, Y: $i] : ((X = Y) | (~leq(X, Y)) | (~leq(Y, X)))) | (~leq(v601, X!4)) | (~leq(X!4, v601)) | (v601 = X!4)),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.13/0.44 tff(69,plain,
% 0.13/0.44 (v601 = X!4),
% 0.13/0.44 inference(unit_resolution,[status(thm)],[68, 42, 62, 60])).
% 0.13/0.44 tff(70,plain,
% 0.13/0.44 (v600 = v601),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[69, 52])).
% 0.13/0.44 tff(71,plain,
% 0.13/0.44 ((~(v600 = v601)) <=> (~(v600 = v601))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(72,axiom,(((((((((((((((((((((~(v0 = v16)) & (~(v0 = v32))) & (~(v0 = v300))) & (~(v0 = v500))) & (~(v0 = v600))) & (~(v0 = v601))) & (~(v16 = v32))) & (~(v16 = v300))) & (~(v16 = v500))) & (~(v16 = v600))) & (~(v16 = v601))) & (~(v32 = v300))) & (~(v32 = v500))) & (~(v32 = v600))) & (~(v32 = v601))) & (~(v300 = v500))) & (~(v300 = v600))) & (~(v300 = v601))) & (~(v500 = v600))) & (~(v500 = v601))) & (~(v600 = v601))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','distinct')).
% 0.13/0.44 tff(73,plain,
% 0.13/0.44 (~(v600 = v601)),
% 0.13/0.44 inference(and_elim,[status(thm)],[72])).
% 0.13/0.44 tff(74,plain,
% 0.13/0.44 (~(v600 = v601)),
% 0.13/0.44 inference(modus_ponens,[status(thm)],[73, 71])).
% 0.13/0.44 tff(75,plain,
% 0.13/0.44 ($false),
% 0.13/0.44 inference(unit_resolution,[status(thm)],[74, 70])).
% 0.13/0.44 % SZS output end Proof
% 0.13/0.44 % E exiting
%------------------------------------------------------------------------------