%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MGT078+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n019.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 06:24:11 AM UTC 2026
% Result : Theorem 0.13s 0.40s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT078+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% 0.00/0.02 % Command : run_E %s %d THM
% 0.07/0.33 % Computer : n019.cluster.edu
% 0.07/0.33 % Model : x86_64 x86_64
% 0.07/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.33 % Memory : 8046.5625MB
% 0.07/0.33 % OS : Linux 6.8.0-71-generic
% 0.07/0.33 % CPULimit : 300
% 0.07/0.33 % WCLimit : 300
% 0.07/0.33 % DateTime : Mon Sep 7 14:14:39 UTC 2026
% 0.07/0.33 % CPUTime :
% 0.13/0.40 % SZS status Theorem
% 0.13/0.40 % SZS output start Proof
% 0.13/0.40 tff(leq_type, type, (
% 0.13/0.40 leq: ( $i * $i ) > $o)).
% 0.13/0.40 tff(v600_type, type, (
% 0.13/0.40 v600: $i)).
% 0.13/0.40 tff(v1200_type, type, (
% 0.13/0.40 v1200: $i)).
% 0.13/0.40 tff(tptp_fun_X_4_type, type, (
% 0.13/0.40 tptp_fun_X_4: $i)).
% 0.13/0.40 tff(less_type, type, (
% 0.13/0.40 less: ( $i * $i ) > $o)).
% 0.13/0.40 tff(v0_type, type, (
% 0.13/0.40 v0: $i)).
% 0.13/0.40 tff(in_lopen_type, type, (
% 0.13/0.40 in_lopen: ( $i * $i * $i ) > $o)).
% 0.13/0.40 tff(tptp_fun_Z_2_type, type, (
% 0.13/0.40 tptp_fun_Z_2: $i)).
% 0.13/0.40 tff(v8_type, type, (
% 0.13/0.40 v8: $i)).
% 0.13/0.40 tff(v32_type, type, (
% 0.13/0.40 v32: $i)).
% 0.13/0.40 tff(tptp_fun_Y_3_type, type, (
% 0.13/0.40 tptp_fun_Y_3: $i)).
% 0.13/0.40 tff(v200_type, type, (
% 0.13/0.40 v200: $i)).
% 0.13/0.40 tff(v800_type, type, (
% 0.13/0.40 v800: $i)).
% 0.13/0.40 tff(1,plain,
% 0.13/0.40 (^[X: $i, A: $i, B: $i] : refl((~(((~leq(X, B)) | (~less(A, X))) <=> in_lopen(X, A, B))) <=> (~(((~leq(X, B)) | (~less(A, X))) <=> in_lopen(X, A, B))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(2,plain,
% 0.13/0.40 (![X: $i, A: $i, B: $i] : (~(((~leq(X, B)) | (~less(A, X))) <=> in_lopen(X, A, B))) <=> ![X: $i, A: $i, B: $i] : (~(((~leq(X, B)) | (~less(A, X))) <=> in_lopen(X, A, B)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.40 tff(3,plain,
% 0.13/0.40 (^[X: $i, A: $i, B: $i] : trans(trans(monotonicity(rewrite((less(A, X) & leq(X, B)) <=> (~((~leq(X, B)) | (~less(A, X))))), ((in_lopen(X, A, B) <=> (less(A, X) & leq(X, B))) <=> (in_lopen(X, A, B) <=> (~((~leq(X, B)) | (~less(A, X))))))), rewrite((in_lopen(X, A, B) <=> (~((~leq(X, B)) | (~less(A, X))))) <=> (~(((~leq(X, B)) | (~less(A, X))) <=> in_lopen(X, A, B)))), ((in_lopen(X, A, B) <=> (less(A, X) & leq(X, B))) <=> (~(((~leq(X, B)) | (~less(A, X))) <=> in_lopen(X, A, B))))), rewrite((~(((~leq(X, B)) | (~less(A, X))) <=> in_lopen(X, A, B))) <=> (~(((~leq(X, B)) | (~less(A, X))) <=> in_lopen(X, A, B)))), ((in_lopen(X, A, B) <=> (less(A, X) & leq(X, B))) <=> (~(((~leq(X, B)) | (~less(A, X))) <=> in_lopen(X, A, B)))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(4,plain,
% 0.13/0.40 (![X: $i, A: $i, B: $i] : (in_lopen(X, A, B) <=> (less(A, X) & leq(X, B))) <=> ![X: $i, A: $i, B: $i] : (~(((~leq(X, B)) | (~less(A, X))) <=> in_lopen(X, A, B)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[3])).
% 0.13/0.40 tff(5,plain,
% 0.13/0.40 (![X: $i, A: $i, B: $i] : (in_lopen(X, A, B) <=> (less(A, X) & leq(X, B))) <=> ![X: $i, A: $i, B: $i] : (in_lopen(X, A, B) <=> (less(A, X) & leq(X, B)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(6,axiom,(![X: $i, A: $i, B: $i] : (in_lopen(X, A, B) <=> (less(A, X) & leq(X, B)))), file('/export/starexec/sandbox/benchmark/Axioms/MGT002+2.ax','in_lopen')).
% 0.13/0.40 tff(7,plain,
% 0.13/0.40 (![X: $i, A: $i, B: $i] : (in_lopen(X, A, B) <=> (less(A, X) & leq(X, B)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.13/0.40 tff(8,plain,(
% 0.13/0.40 ![X: $i, A: $i, B: $i] : (in_lopen(X, A, B) <=> (less(A, X) & leq(X, B)))),
% 0.13/0.40 inference(skolemize,[status(sab)],[7])).
% 0.13/0.40 tff(9,plain,
% 0.13/0.40 (![X: $i, A: $i, B: $i] : (~(((~leq(X, B)) | (~less(A, X))) <=> in_lopen(X, A, B)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.13/0.40 tff(10,plain,
% 0.13/0.40 (![X: $i, A: $i, B: $i] : (~(((~leq(X, B)) | (~less(A, X))) <=> in_lopen(X, A, B)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.13/0.40 tff(11,plain,
% 0.13/0.40 ((~![X: $i, A: $i, B: $i] : (~(((~leq(X, B)) | (~less(A, X))) <=> in_lopen(X, A, B)))) | (~(((~leq(X!4, v600)) | (~less(v0, X!4))) <=> in_lopen(X!4, v0, v600)))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(12,plain,
% 0.13/0.40 (~(((~leq(X!4, v600)) | (~less(v0, X!4))) <=> in_lopen(X!4, v0, v600))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.13/0.40 tff(13,plain,
% 0.13/0.40 (?[X: $i, Y: $i, Z: $i] : (in_lopen(X, v0, v600) & leq(v1200, X) & in_lopen(Y, v0, v800) & leq(v200, Y) & in_lopen(Z, v0, v32) & leq(v8, Z)) <=> ?[X: $i, Y: $i, Z: $i] : (in_lopen(X, v0, v600) & leq(v1200, X) & in_lopen(Y, v0, v800) & leq(v200, Y) & in_lopen(Z, v0, v32) & leq(v8, Z))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(14,plain,
% 0.13/0.40 ((~(~?[X: $i, Y: $i, Z: $i] : (in_lopen(X, v0, v600) & leq(v1200, X) & in_lopen(Y, v0, v800) & leq(v200, Y) & in_lopen(Z, v0, v32) & leq(v8, Z)))) <=> ?[X: $i, Y: $i, Z: $i] : (in_lopen(X, v0, v600) & leq(v1200, X) & in_lopen(Y, v0, v800) & leq(v200, Y) & in_lopen(Z, v0, v32) & leq(v8, Z))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(15,plain,
% 0.13/0.40 ((~?[X: $i, Y: $i, Z: $i] : (((((in_lopen(X, v0, v600) & leq(v1200, X)) & in_lopen(Y, v0, v800)) & leq(v200, Y)) & in_lopen(Z, v0, v32)) & leq(v8, Z))) <=> (~?[X: $i, Y: $i, Z: $i] : (in_lopen(X, v0, v600) & leq(v1200, X) & in_lopen(Y, v0, v800) & leq(v200, Y) & in_lopen(Z, v0, v32) & leq(v8, Z)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(16,plain,
% 0.13/0.40 ((~(~?[X: $i, Y: $i, Z: $i] : (((((in_lopen(X, v0, v600) & leq(v1200, X)) & in_lopen(Y, v0, v800)) & leq(v200, Y)) & in_lopen(Z, v0, v32)) & leq(v8, Z)))) <=> (~(~?[X: $i, Y: $i, Z: $i] : (in_lopen(X, v0, v600) & leq(v1200, X) & in_lopen(Y, v0, v800) & leq(v200, Y) & in_lopen(Z, v0, v32) & leq(v8, Z))))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[15])).
% 0.13/0.40 tff(17,plain,
% 0.13/0.40 ((~(~?[X: $i, Y: $i, Z: $i] : (((((in_lopen(X, v0, v600) & leq(v1200, X)) & in_lopen(Y, v0, v800)) & leq(v200, Y)) & in_lopen(Z, v0, v32)) & leq(v8, Z)))) <=> ?[X: $i, Y: $i, Z: $i] : (in_lopen(X, v0, v600) & leq(v1200, X) & in_lopen(Y, v0, v800) & leq(v200, Y) & in_lopen(Z, v0, v32) & leq(v8, Z))),
% 0.13/0.40 inference(transitivity,[status(thm)],[16, 14])).
% 0.13/0.40 tff(18,axiom,(~(~?[X: $i, Y: $i, Z: $i] : (((((in_lopen(X, v0, v600) & leq(v1200, X)) & in_lopen(Y, v0, v800)) & leq(v200, Y)) & in_lopen(Z, v0, v32)) & leq(v8, Z)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','odrl341')).
% 0.13/0.40 tff(19,plain,
% 0.13/0.40 (?[X: $i, Y: $i, Z: $i] : (in_lopen(X, v0, v600) & leq(v1200, X) & in_lopen(Y, v0, v800) & leq(v200, Y) & in_lopen(Z, v0, v32) & leq(v8, Z))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.13/0.40 tff(20,plain,
% 0.13/0.40 (?[X: $i, Y: $i, Z: $i] : (in_lopen(X, v0, v600) & leq(v1200, X) & in_lopen(Y, v0, v800) & leq(v200, Y) & in_lopen(Z, v0, v32) & leq(v8, Z))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[19, 13])).
% 0.13/0.40 tff(21,plain,(
% 0.13/0.40 in_lopen(X!4, v0, v600) & leq(v1200, X!4) & in_lopen(Y!3, v0, v800) & leq(v200, Y!3) & in_lopen(Z!2, v0, v32) & leq(v8, Z!2)),
% 0.13/0.40 inference(skolemize,[status(sab)],[20])).
% 0.13/0.40 tff(22,plain,
% 0.13/0.40 (in_lopen(X!4, v0, v600)),
% 0.13/0.40 inference(and_elim,[status(thm)],[21])).
% 0.13/0.40 tff(23,plain,
% 0.13/0.40 ((((~leq(X!4, v600)) | (~less(v0, X!4))) <=> in_lopen(X!4, v0, v600)) | (~((~leq(X!4, v600)) | (~less(v0, X!4)))) | (~in_lopen(X!4, v0, v600))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(24,plain,
% 0.13/0.40 ((((~leq(X!4, v600)) | (~less(v0, X!4))) <=> in_lopen(X!4, v0, v600)) | (~((~leq(X!4, v600)) | (~less(v0, X!4))))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.13/0.40 tff(25,plain,
% 0.13/0.40 (~((~leq(X!4, v600)) | (~less(v0, X!4)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[24, 12])).
% 0.13/0.40 tff(26,plain,
% 0.13/0.40 (((~leq(X!4, v600)) | (~less(v0, X!4))) | leq(X!4, v600)),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(27,plain,
% 0.13/0.40 (leq(X!4, v600)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.13/0.40 tff(28,plain,
% 0.13/0.40 (leq(v1200, X!4)),
% 0.13/0.40 inference(and_elim,[status(thm)],[21])).
% 0.13/0.40 tff(29,plain,
% 0.13/0.40 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(30,plain,
% 0.13/0.40 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(X, Y) & leq(Y, Z)) <=> (~((~leq(Y, Z)) | (~leq(X, Y))))), ((~(leq(X, Y) & leq(Y, Z))) <=> (~(~((~leq(Y, Z)) | (~leq(X, Y))))))), rewrite((~(~((~leq(Y, Z)) | (~leq(X, Y))))) <=> ((~leq(Y, Z)) | (~leq(X, Y)))), ((~(leq(X, Y) & leq(Y, Z))) <=> ((~leq(Y, Z)) | (~leq(X, Y))))), (((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> (((~leq(Y, Z)) | (~leq(X, Y))) | leq(X, Z)))), rewrite((((~leq(Y, Z)) | (~leq(X, Y))) | leq(X, Z)) <=> (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))), (((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(31,plain,
% 0.13/0.40 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[30])).
% 0.13/0.40 tff(32,plain,
% 0.13/0.40 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(33,plain,
% 0.13/0.41 (^[X: $i, Y: $i, Z: $i] : rewrite(((leq(X, Y) & leq(Y, Z)) => leq(X, Z)) <=> ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z)))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(34,plain,
% 0.13/0.41 (![X: $i, Y: $i, Z: $i] : ((leq(X, Y) & leq(Y, Z)) => leq(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[33])).
% 0.13/0.41 tff(35,axiom,(![X: $i, Y: $i, Z: $i] : ((leq(X, Y) & leq(Y, Z)) => leq(X, Z))), file('/export/starexec/sandbox/benchmark/Axioms/MGT002+0.ax','leq_trans')).
% 0.13/0.41 tff(36,plain,
% 0.13/0.41 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.13/0.41 tff(37,plain,
% 0.13/0.41 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.13/0.41 tff(38,plain,(
% 0.13/0.41 ![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.13/0.41 inference(skolemize,[status(sab)],[37])).
% 0.13/0.41 tff(39,plain,
% 0.13/0.41 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.13/0.41 tff(40,plain,
% 0.13/0.41 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[39, 29])).
% 0.13/0.41 tff(41,plain,
% 0.13/0.41 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | ((~leq(v1200, X!4)) | (~leq(X!4, v600)) | leq(v1200, v600))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(v1200, X!4)) | (~leq(X!4, v600)) | leq(v1200, v600))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(42,plain,
% 0.13/0.41 ((leq(v1200, v600) | (~leq(X!4, v600)) | (~leq(v1200, X!4))) <=> ((~leq(v1200, X!4)) | (~leq(X!4, v600)) | leq(v1200, v600))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(43,plain,
% 0.13/0.41 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(v1200, v600) | (~leq(X!4, v600)) | (~leq(v1200, X!4)))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | ((~leq(v1200, X!4)) | (~leq(X!4, v600)) | leq(v1200, v600)))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[42])).
% 0.13/0.41 tff(44,plain,
% 0.13/0.41 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(v1200, v600) | (~leq(X!4, v600)) | (~leq(v1200, X!4)))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(v1200, X!4)) | (~leq(X!4, v600)) | leq(v1200, v600))),
% 0.13/0.41 inference(transitivity,[status(thm)],[43, 41])).
% 0.13/0.41 tff(45,plain,
% 0.13/0.41 ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(v1200, v600) | (~leq(X!4, v600)) | (~leq(v1200, X!4)))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(46,plain,
% 0.13/0.41 ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(v1200, X!4)) | (~leq(X!4, v600)) | leq(v1200, v600)),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.13/0.41 tff(47,plain,
% 0.13/0.41 (leq(v1200, v600)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[46, 40, 28, 27])).
% 0.13/0.41 tff(48,plain,
% 0.13/0.41 (less(v600, v1200) <=> less(v600, v1200)),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(49,axiom,(less(v600, v1200)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ord_v600_v1200')).
% 0.13/0.41 tff(50,plain,
% 0.13/0.41 (less(v600, v1200)),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.13/0.41 tff(51,plain,
% 0.13/0.41 (^[X: $i, Y: $i] : refl(((~less(X, Y)) | leq(X, Y)) <=> ((~less(X, Y)) | leq(X, Y)))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(52,plain,
% 0.13/0.41 (![X: $i, Y: $i] : ((~less(X, Y)) | leq(X, Y)) <=> ![X: $i, Y: $i] : ((~less(X, Y)) | leq(X, Y))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[51])).
% 0.13/0.41 tff(53,plain,
% 0.13/0.41 (![X: $i, Y: $i] : ((~less(X, Y)) | leq(X, Y)) <=> ![X: $i, Y: $i] : ((~less(X, Y)) | leq(X, Y))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(54,plain,
% 0.13/0.41 (^[X: $i, Y: $i] : rewrite((less(X, Y) => leq(X, Y)) <=> ((~less(X, Y)) | leq(X, Y)))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(55,plain,
% 0.13/0.41 (![X: $i, Y: $i] : (less(X, Y) => leq(X, Y)) <=> ![X: $i, Y: $i] : ((~less(X, Y)) | leq(X, Y))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[54])).
% 0.13/0.41 tff(56,axiom,(![X: $i, Y: $i] : (less(X, Y) => leq(X, Y))), file('/export/starexec/sandbox/benchmark/Axioms/MGT002+0.ax','less_implies_leq')).
% 0.13/0.41 tff(57,plain,
% 0.13/0.41 (![X: $i, Y: $i] : ((~less(X, Y)) | leq(X, Y))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.13/0.41 tff(58,plain,
% 0.13/0.41 (![X: $i, Y: $i] : ((~less(X, Y)) | leq(X, Y))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.13/0.41 tff(59,plain,(
% 0.13/0.41 ![X: $i, Y: $i] : ((~less(X, Y)) | leq(X, Y))),
% 0.13/0.41 inference(skolemize,[status(sab)],[58])).
% 0.13/0.41 tff(60,plain,
% 0.13/0.41 (![X: $i, Y: $i] : ((~less(X, Y)) | leq(X, Y))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.13/0.41 tff(61,plain,
% 0.13/0.41 (((~![X: $i, Y: $i] : ((~less(X, Y)) | leq(X, Y))) | ((~less(v600, v1200)) | leq(v600, v1200))) <=> ((~![X: $i, Y: $i] : ((~less(X, Y)) | leq(X, Y))) | (~less(v600, v1200)) | leq(v600, v1200))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(62,plain,
% 0.13/0.41 ((~![X: $i, Y: $i] : ((~less(X, Y)) | leq(X, Y))) | ((~less(v600, v1200)) | leq(v600, v1200))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(63,plain,
% 0.13/0.41 ((~![X: $i, Y: $i] : ((~less(X, Y)) | leq(X, Y))) | (~less(v600, v1200)) | leq(v600, v1200)),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.13/0.41 tff(64,plain,
% 0.13/0.41 (leq(v600, v1200)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[63, 60, 50])).
% 0.13/0.41 tff(65,plain,
% 0.13/0.41 ((~(v600 = v1200)) <=> (~(v600 = v1200))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(66,axiom,(((((((((((((((((((((~(v0 = v8)) & (~(v0 = v32))) & (~(v0 = v200))) & (~(v0 = v600))) & (~(v0 = v800))) & (~(v0 = v1200))) & (~(v8 = v32))) & (~(v8 = v200))) & (~(v8 = v600))) & (~(v8 = v800))) & (~(v8 = v1200))) & (~(v32 = v200))) & (~(v32 = v600))) & (~(v32 = v800))) & (~(v32 = v1200))) & (~(v200 = v600))) & (~(v200 = v800))) & (~(v200 = v1200))) & (~(v600 = v800))) & (~(v600 = v1200))) & (~(v800 = v1200))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','distinct')).
% 0.13/0.41 tff(67,plain,
% 0.13/0.41 ((((((((((((((((((((~(v0 = v8)) & (~(v0 = v32))) & (~(v0 = v200))) & (~(v0 = v600))) & (~(v0 = v800))) & (~(v0 = v1200))) & (~(v8 = v32))) & (~(v8 = v200))) & (~(v8 = v600))) & (~(v8 = v800))) & (~(v8 = v1200))) & (~(v32 = v200))) & (~(v32 = v600))) & (~(v32 = v800))) & (~(v32 = v1200))) & (~(v200 = v600))) & (~(v200 = v800))) & (~(v200 = v1200))) & (~(v600 = v800))) & (~(v600 = v1200))),
% 0.13/0.41 inference(and_elim,[status(thm)],[66])).
% 0.13/0.41 tff(68,plain,
% 0.13/0.41 (~(v600 = v1200)),
% 0.13/0.41 inference(and_elim,[status(thm)],[67])).
% 0.13/0.41 tff(69,plain,
% 0.13/0.41 (~(v600 = v1200)),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[68, 65])).
% 0.13/0.41 tff(70,plain,
% 0.13/0.41 (![X: $i, Y: $i] : ((X = Y) | (~leq(X, Y)) | (~leq(Y, X))) <=> ![X: $i, Y: $i] : ((X = Y) | (~leq(X, Y)) | (~leq(Y, X)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(71,plain,
% 0.13/0.41 (^[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)))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(72,plain,
% 0.13/0.41 (![X: $i, Y: $i] : ((~(leq(X, Y) & leq(Y, X))) | (X = Y)) <=> ![X: $i, Y: $i] : ((X = Y) | (~leq(X, Y)) | (~leq(Y, X)))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[71])).
% 0.13/0.41 tff(73,plain,
% 0.13/0.41 (![X: $i, Y: $i] : ((~(leq(X, Y) & leq(Y, X))) | (X = Y)) <=> ![X: $i, Y: $i] : ((~(leq(X, Y) & leq(Y, X))) | (X = Y))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(74,plain,
% 0.13/0.41 (^[X: $i, Y: $i] : rewrite(((leq(X, Y) & leq(Y, X)) => (X = Y)) <=> ((~(leq(X, Y) & leq(Y, X))) | (X = Y)))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(75,plain,
% 0.13/0.41 (![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) => (X = Y)) <=> ![X: $i, Y: $i] : ((~(leq(X, Y) & leq(Y, X))) | (X = Y))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[74])).
% 0.13/0.41 tff(76,axiom,(![X: $i, Y: $i] : ((leq(X, Y) & leq(Y, X)) => (X = Y))), file('/export/starexec/sandbox/benchmark/Axioms/MGT002+0.ax','leq_antisym')).
% 0.13/0.41 tff(77,plain,
% 0.13/0.41 (![X: $i, Y: $i] : ((~(leq(X, Y) & leq(Y, X))) | (X = Y))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.13/0.41 tff(78,plain,
% 0.13/0.41 (![X: $i, Y: $i] : ((~(leq(X, Y) & leq(Y, X))) | (X = Y))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[77, 73])).
% 0.13/0.41 tff(79,plain,(
% 0.13/0.41 ![X: $i, Y: $i] : ((~(leq(X, Y) & leq(Y, X))) | (X = Y))),
% 0.13/0.41 inference(skolemize,[status(sab)],[78])).
% 0.13/0.41 tff(80,plain,
% 0.13/0.41 (![X: $i, Y: $i] : ((X = Y) | (~leq(X, Y)) | (~leq(Y, X)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[79, 72])).
% 0.13/0.41 tff(81,plain,
% 0.13/0.41 (![X: $i, Y: $i] : ((X = Y) | (~leq(X, Y)) | (~leq(Y, X)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[80, 70])).
% 0.13/0.41 tff(82,plain,
% 0.13/0.41 (((~![X: $i, Y: $i] : ((X = Y) | (~leq(X, Y)) | (~leq(Y, X)))) | ((v600 = v1200) | (~leq(v600, v1200)) | (~leq(v1200, v600)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~leq(X, Y)) | (~leq(Y, X)))) | (v600 = v1200) | (~leq(v600, v1200)) | (~leq(v1200, v600)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(83,plain,
% 0.13/0.41 ((~![X: $i, Y: $i] : ((X = Y) | (~leq(X, Y)) | (~leq(Y, X)))) | ((v600 = v1200) | (~leq(v600, v1200)) | (~leq(v1200, v600)))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(84,plain,
% 0.13/0.41 ((~![X: $i, Y: $i] : ((X = Y) | (~leq(X, Y)) | (~leq(Y, X)))) | (v600 = v1200) | (~leq(v600, v1200)) | (~leq(v1200, v600))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.13/0.41 tff(85,plain,
% 0.13/0.41 ($false),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[84, 81, 69, 64, 47])).
% 0.13/0.41 % SZS output end Proof
% 0.13/0.42 % E exiting
%------------------------------------------------------------------------------