%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MGT076+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% 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 : 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 0.14s 0.41s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT076+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.09/0.34 % Computer : n014.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Mon Sep 7 14:12:28 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.14/0.41 % SZS status Theorem
% 0.14/0.41 % SZS output start Proof
% 0.14/0.41 tff(leq_type, type, (
% 0.14/0.41 leq: ( $i * $i ) > $o)).
% 0.14/0.41 tff(v800_type, type, (
% 0.14/0.41 v800: $i)).
% 0.14/0.41 tff(v400_type, type, (
% 0.14/0.41 v400: $i)).
% 0.14/0.41 tff(less_type, type, (
% 0.14/0.41 less: ( $i * $i ) > $o)).
% 0.14/0.41 tff(tptp_fun_X_2_type, type, (
% 0.14/0.41 tptp_fun_X_2: $i)).
% 0.14/0.41 tff(1,plain,
% 0.14/0.41 (less(v400, v800) <=> less(v400, v800)),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(2,axiom,(less(v400, v800)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ord_v400_v800')).
% 0.14/0.41 tff(3,plain,
% 0.14/0.41 (less(v400, v800)),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.14/0.41 tff(4,plain,
% 0.14/0.41 (^[X: $i, Y: $i] : refl(((~less(X, Y)) | leq(X, Y)) <=> ((~less(X, Y)) | leq(X, Y)))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(5,plain,
% 0.14/0.41 (![X: $i, Y: $i] : ((~less(X, Y)) | leq(X, Y)) <=> ![X: $i, Y: $i] : ((~less(X, Y)) | leq(X, Y))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[4])).
% 0.14/0.41 tff(6,plain,
% 0.14/0.41 (![X: $i, Y: $i] : ((~less(X, Y)) | leq(X, Y)) <=> ![X: $i, Y: $i] : ((~less(X, Y)) | leq(X, Y))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(7,plain,
% 0.14/0.41 (^[X: $i, Y: $i] : rewrite((less(X, Y) => leq(X, Y)) <=> ((~less(X, Y)) | leq(X, Y)))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(8,plain,
% 0.14/0.41 (![X: $i, Y: $i] : (less(X, Y) => leq(X, Y)) <=> ![X: $i, Y: $i] : ((~less(X, Y)) | leq(X, Y))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[7])).
% 0.14/0.41 tff(9,axiom,(![X: $i, Y: $i] : (less(X, Y) => leq(X, Y))), file('/export/starexec/sandbox2/benchmark/Axioms/MGT002+0.ax','less_implies_leq')).
% 0.14/0.41 tff(10,plain,
% 0.14/0.41 (![X: $i, Y: $i] : ((~less(X, Y)) | leq(X, Y))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.14/0.41 tff(11,plain,
% 0.14/0.41 (![X: $i, Y: $i] : ((~less(X, Y)) | leq(X, Y))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.14/0.41 tff(12,plain,(
% 0.14/0.41 ![X: $i, Y: $i] : ((~less(X, Y)) | leq(X, Y))),
% 0.14/0.41 inference(skolemize,[status(sab)],[11])).
% 0.14/0.41 tff(13,plain,
% 0.14/0.41 (![X: $i, Y: $i] : ((~less(X, Y)) | leq(X, Y))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.14/0.41 tff(14,plain,
% 0.14/0.41 (((~![X: $i, Y: $i] : ((~less(X, Y)) | leq(X, Y))) | ((~less(v400, v800)) | leq(v400, v800))) <=> ((~![X: $i, Y: $i] : ((~less(X, Y)) | leq(X, Y))) | (~less(v400, v800)) | leq(v400, v800))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(15,plain,
% 0.14/0.41 ((~![X: $i, Y: $i] : ((~less(X, Y)) | leq(X, Y))) | ((~less(v400, v800)) | leq(v400, v800))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(16,plain,
% 0.14/0.41 ((~![X: $i, Y: $i] : ((~less(X, Y)) | leq(X, Y))) | (~less(v400, v800)) | leq(v400, v800)),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.14/0.41 tff(17,plain,
% 0.14/0.41 (leq(v400, v800)),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[16, 13, 3])).
% 0.14/0.41 tff(18,plain,
% 0.14/0.41 ((~![X: $i] : ((~leq(v800, X)) | leq(v400, X))) <=> (~![X: $i] : ((~leq(v800, X)) | leq(v400, X)))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(19,plain,
% 0.14/0.41 ((~![X: $i] : (leq(v800, X) => leq(v400, X))) <=> (~![X: $i] : ((~leq(v800, X)) | leq(v400, X)))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(20,axiom,(~![X: $i] : (leq(v800, X) => leq(v400, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','odrl311')).
% 0.14/0.41 tff(21,plain,
% 0.14/0.41 (~![X: $i] : ((~leq(v800, X)) | leq(v400, X))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.14/0.41 tff(22,plain,
% 0.14/0.41 (~![X: $i] : ((~leq(v800, X)) | leq(v400, X))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[21, 18])).
% 0.14/0.41 tff(23,plain,
% 0.14/0.41 (~![X: $i] : ((~leq(v800, X)) | leq(v400, X))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.14/0.41 tff(24,plain,
% 0.14/0.41 (~![X: $i] : ((~leq(v800, X)) | leq(v400, X))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[23, 18])).
% 0.14/0.41 tff(25,plain,(
% 0.14/0.41 ~((~leq(v800, X!2)) | leq(v400, X!2))),
% 0.14/0.41 inference(skolemize,[status(sab)],[24])).
% 0.14/0.41 tff(26,plain,
% 0.14/0.41 (~leq(v400, X!2)),
% 0.14/0.41 inference(or_elim,[status(thm)],[25])).
% 0.14/0.41 tff(27,plain,
% 0.14/0.41 (leq(v800, X!2)),
% 0.14/0.41 inference(or_elim,[status(thm)],[25])).
% 0.14/0.41 tff(28,plain,
% 0.14/0.41 (![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)))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(29,plain,
% 0.14/0.41 (^[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)))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(30,plain,
% 0.14/0.42 (![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)))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[29])).
% 0.14/0.42 tff(31,plain,
% 0.14/0.42 (![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))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(32,plain,
% 0.14/0.42 (^[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)))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(33,plain,
% 0.14/0.42 (![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))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[32])).
% 0.14/0.42 tff(34,axiom,(![X: $i, Y: $i, Z: $i] : ((leq(X, Y) & leq(Y, Z)) => leq(X, Z))), file('/export/starexec/sandbox2/benchmark/Axioms/MGT002+0.ax','leq_trans')).
% 0.14/0.42 tff(35,plain,
% 0.14/0.42 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.14/0.42 tff(36,plain,
% 0.14/0.42 (![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.14/0.42 tff(37,plain,(
% 0.14/0.42 ![X: $i, Y: $i, Z: $i] : ((~(leq(X, Y) & leq(Y, Z))) | leq(X, Z))),
% 0.14/0.42 inference(skolemize,[status(sab)],[36])).
% 0.14/0.42 tff(38,plain,
% 0.14/0.42 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.14/0.42 tff(39,plain,
% 0.14/0.42 (![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[38, 28])).
% 0.14/0.42 tff(40,plain,
% 0.14/0.42 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | ((~leq(v800, X!2)) | leq(v400, X!2) | (~leq(v400, v800)))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(v800, X!2)) | leq(v400, X!2) | (~leq(v400, v800)))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(41,plain,
% 0.14/0.42 ((leq(v400, X!2) | (~leq(v800, X!2)) | (~leq(v400, v800))) <=> ((~leq(v800, X!2)) | leq(v400, X!2) | (~leq(v400, v800)))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(42,plain,
% 0.14/0.42 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(v400, X!2) | (~leq(v800, X!2)) | (~leq(v400, v800)))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | ((~leq(v800, X!2)) | leq(v400, X!2) | (~leq(v400, v800))))),
% 0.14/0.42 inference(monotonicity,[status(thm)],[41])).
% 0.14/0.42 tff(43,plain,
% 0.14/0.42 (((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(v400, X!2) | (~leq(v800, X!2)) | (~leq(v400, v800)))) <=> ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(v800, X!2)) | leq(v400, X!2) | (~leq(v400, v800)))),
% 0.14/0.42 inference(transitivity,[status(thm)],[42, 40])).
% 0.14/0.42 tff(44,plain,
% 0.14/0.42 ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (leq(v400, X!2) | (~leq(v800, X!2)) | (~leq(v400, v800)))),
% 0.14/0.42 inference(quant_inst,[status(thm)],[])).
% 0.14/0.42 tff(45,plain,
% 0.14/0.42 ((~![X: $i, Y: $i, Z: $i] : (leq(X, Z) | (~leq(Y, Z)) | (~leq(X, Y)))) | (~leq(v800, X!2)) | leq(v400, X!2) | (~leq(v400, v800))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.14/0.42 tff(46,plain,
% 0.14/0.42 ($false),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[45, 39, 27, 26, 17])).
% 0.14/0.42 % SZS output end Proof
% 0.14/0.42 % E exiting
%------------------------------------------------------------------------------