%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MGT083+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n026.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 0.40s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT083+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.07/0.33 % Computer : n026.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 14:20:59 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(less_type, type, (
% 0.13/0.40 less: ( $i * $i ) > $o)).
% 0.13/0.40 tff(v600_type, type, (
% 0.13/0.40 v600: $i)).
% 0.13/0.40 tff(tptp_fun_X_2_type, type, (
% 0.13/0.40 tptp_fun_X_2: $i)).
% 0.13/0.40 tff(v0_type, type, (
% 0.13/0.40 v0: $i)).
% 0.13/0.40 tff(in_open_type, type, (
% 0.13/0.40 in_open: ( $i * $i * $i ) > $o)).
% 0.13/0.40 tff(1,plain,
% 0.13/0.40 (^[X: $i, A: $i, B: $i] : refl((~(((~less(A, X)) | (~less(X, B))) <=> in_open(X, A, B))) <=> (~(((~less(A, X)) | (~less(X, B))) <=> in_open(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] : (~(((~less(A, X)) | (~less(X, B))) <=> in_open(X, A, B))) <=> ![X: $i, A: $i, B: $i] : (~(((~less(A, X)) | (~less(X, B))) <=> in_open(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) & less(X, B)) <=> (~((~less(A, X)) | (~less(X, B))))), ((in_open(X, A, B) <=> (less(A, X) & less(X, B))) <=> (in_open(X, A, B) <=> (~((~less(A, X)) | (~less(X, B))))))), rewrite((in_open(X, A, B) <=> (~((~less(A, X)) | (~less(X, B))))) <=> (~(((~less(A, X)) | (~less(X, B))) <=> in_open(X, A, B)))), ((in_open(X, A, B) <=> (less(A, X) & less(X, B))) <=> (~(((~less(A, X)) | (~less(X, B))) <=> in_open(X, A, B))))), rewrite((~(((~less(A, X)) | (~less(X, B))) <=> in_open(X, A, B))) <=> (~(((~less(A, X)) | (~less(X, B))) <=> in_open(X, A, B)))), ((in_open(X, A, B) <=> (less(A, X) & less(X, B))) <=> (~(((~less(A, X)) | (~less(X, B))) <=> in_open(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_open(X, A, B) <=> (less(A, X) & less(X, B))) <=> ![X: $i, A: $i, B: $i] : (~(((~less(A, X)) | (~less(X, B))) <=> in_open(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_open(X, A, B) <=> (less(A, X) & less(X, B))) <=> ![X: $i, A: $i, B: $i] : (in_open(X, A, B) <=> (less(A, X) & less(X, B)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(6,axiom,(![X: $i, A: $i, B: $i] : (in_open(X, A, B) <=> (less(A, X) & less(X, B)))), file('/export/starexec/sandbox/benchmark/Axioms/MGT002+2.ax','in_open')).
% 0.13/0.40 tff(7,plain,
% 0.13/0.40 (![X: $i, A: $i, B: $i] : (in_open(X, A, B) <=> (less(A, X) & less(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_open(X, A, B) <=> (less(A, X) & less(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] : (~(((~less(A, X)) | (~less(X, B))) <=> in_open(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] : (~(((~less(A, X)) | (~less(X, B))) <=> in_open(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] : (~(((~less(A, X)) | (~less(X, B))) <=> in_open(X, A, B)))) | (~(((~less(v0, X!2)) | (~less(X!2, v600))) <=> in_open(X!2, v0, v600)))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(12,plain,
% 0.13/0.40 (~(((~less(v0, X!2)) | (~less(X!2, v600))) <=> in_open(X!2, 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] : (in_open(X, v0, v600) & less(v600, X)) <=> ?[X: $i] : (in_open(X, v0, v600) & less(v600, X))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(14,plain,
% 0.13/0.40 ((~(~?[X: $i] : (in_open(X, v0, v600) & less(v600, X)))) <=> ?[X: $i] : (in_open(X, v0, v600) & less(v600, X))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(15,plain,
% 0.13/0.40 ((~?[X: $i] : (in_open(X, v0, v600) & less(v600, X))) <=> (~?[X: $i] : (in_open(X, v0, v600) & less(v600, X)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(16,plain,
% 0.13/0.40 ((~(~?[X: $i] : (in_open(X, v0, v600) & less(v600, X)))) <=> (~(~?[X: $i] : (in_open(X, v0, v600) & less(v600, X))))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[15])).
% 0.13/0.40 tff(17,plain,
% 0.13/0.40 ((~(~?[X: $i] : (in_open(X, v0, v600) & less(v600, X)))) <=> ?[X: $i] : (in_open(X, v0, v600) & less(v600, X))),
% 0.13/0.40 inference(transitivity,[status(thm)],[16, 14])).
% 0.13/0.40 tff(18,axiom,(~(~?[X: $i] : (in_open(X, v0, v600) & less(v600, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','odrl423')).
% 0.13/0.40 tff(19,plain,
% 0.13/0.40 (?[X: $i] : (in_open(X, v0, v600) & less(v600, X))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.13/0.40 tff(20,plain,
% 0.13/0.40 (?[X: $i] : (in_open(X, v0, v600) & less(v600, X))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[19, 13])).
% 0.13/0.40 tff(21,plain,(
% 0.13/0.40 in_open(X!2, v0, v600) & less(v600, X!2)),
% 0.13/0.40 inference(skolemize,[status(sab)],[20])).
% 0.13/0.40 tff(22,plain,
% 0.13/0.40 (in_open(X!2, v0, v600)),
% 0.13/0.40 inference(and_elim,[status(thm)],[21])).
% 0.13/0.40 tff(23,plain,
% 0.13/0.40 ((((~less(v0, X!2)) | (~less(X!2, v600))) <=> in_open(X!2, v0, v600)) | (~((~less(v0, X!2)) | (~less(X!2, v600)))) | (~in_open(X!2, v0, v600))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(24,plain,
% 0.13/0.40 ((((~less(v0, X!2)) | (~less(X!2, v600))) <=> in_open(X!2, v0, v600)) | (~((~less(v0, X!2)) | (~less(X!2, v600))))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.13/0.40 tff(25,plain,
% 0.13/0.40 (~((~less(v0, X!2)) | (~less(X!2, v600)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[24, 12])).
% 0.13/0.40 tff(26,plain,
% 0.13/0.40 (((~less(v0, X!2)) | (~less(X!2, v600))) | less(X!2, v600)),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(27,plain,
% 0.13/0.40 (less(X!2, v600)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.13/0.40 tff(28,plain,
% 0.13/0.40 (less(v600, X!2)),
% 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] : (less(X, Z) | (~less(Y, Z)) | (~less(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (less(X, Z) | (~less(Y, Z)) | (~less(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((less(X, Y) & less(Y, Z)) <=> (~((~less(Y, Z)) | (~less(X, Y))))), ((~(less(X, Y) & less(Y, Z))) <=> (~(~((~less(Y, Z)) | (~less(X, Y))))))), rewrite((~(~((~less(Y, Z)) | (~less(X, Y))))) <=> ((~less(Y, Z)) | (~less(X, Y)))), ((~(less(X, Y) & less(Y, Z))) <=> ((~less(Y, Z)) | (~less(X, Y))))), (((~(less(X, Y) & less(Y, Z))) | less(X, Z)) <=> (((~less(Y, Z)) | (~less(X, Y))) | less(X, Z)))), rewrite((((~less(Y, Z)) | (~less(X, Y))) | less(X, Z)) <=> (less(X, Z) | (~less(Y, Z)) | (~less(X, Y)))), (((~(less(X, Y) & less(Y, Z))) | less(X, Z)) <=> (less(X, Z) | (~less(Y, Z)) | (~less(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] : ((~(less(X, Y) & less(Y, Z))) | less(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : (less(X, Z) | (~less(Y, Z)) | (~less(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] : ((~(less(X, Y) & less(Y, Z))) | less(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(less(X, Y) & less(Y, Z))) | less(X, Z))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(33,plain,
% 0.13/0.40 (^[X: $i, Y: $i, Z: $i] : rewrite(((less(X, Y) & less(Y, Z)) => less(X, Z)) <=> ((~(less(X, Y) & less(Y, Z))) | less(X, Z)))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(34,plain,
% 0.13/0.40 (![X: $i, Y: $i, Z: $i] : ((less(X, Y) & less(Y, Z)) => less(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(less(X, Y) & less(Y, Z))) | less(X, Z))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[33])).
% 0.13/0.40 tff(35,axiom,(![X: $i, Y: $i, Z: $i] : ((less(X, Y) & less(Y, Z)) => less(X, Z))), file('/export/starexec/sandbox/benchmark/Axioms/MGT002+0.ax','transitive')).
% 0.13/0.40 tff(36,plain,
% 0.13/0.40 (![X: $i, Y: $i, Z: $i] : ((~(less(X, Y) & less(Y, Z))) | less(X, Z))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.13/0.40 tff(37,plain,
% 0.13/0.40 (![X: $i, Y: $i, Z: $i] : ((~(less(X, Y) & less(Y, Z))) | less(X, Z))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.13/0.40 tff(38,plain,(
% 0.13/0.40 ![X: $i, Y: $i, Z: $i] : ((~(less(X, Y) & less(Y, Z))) | less(X, Z))),
% 0.13/0.40 inference(skolemize,[status(sab)],[37])).
% 0.13/0.40 tff(39,plain,
% 0.13/0.40 (![X: $i, Y: $i, Z: $i] : (less(X, Z) | (~less(Y, Z)) | (~less(X, Y)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.13/0.40 tff(40,plain,
% 0.13/0.40 (![X: $i, Y: $i, Z: $i] : (less(X, Z) | (~less(Y, Z)) | (~less(X, Y)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[39, 29])).
% 0.13/0.40 tff(41,plain,
% 0.13/0.40 (((~![X: $i, Y: $i, Z: $i] : (less(X, Z) | (~less(Y, Z)) | (~less(X, Y)))) | ((~less(v600, X!2)) | (~less(X!2, v600)) | less(v600, v600))) <=> ((~![X: $i, Y: $i, Z: $i] : (less(X, Z) | (~less(Y, Z)) | (~less(X, Y)))) | (~less(v600, X!2)) | (~less(X!2, v600)) | less(v600, v600))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(42,plain,
% 0.13/0.41 ((less(v600, v600) | (~less(X!2, v600)) | (~less(v600, X!2))) <=> ((~less(v600, X!2)) | (~less(X!2, v600)) | less(v600, 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] : (less(X, Z) | (~less(Y, Z)) | (~less(X, Y)))) | (less(v600, v600) | (~less(X!2, v600)) | (~less(v600, X!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (less(X, Z) | (~less(Y, Z)) | (~less(X, Y)))) | ((~less(v600, X!2)) | (~less(X!2, v600)) | less(v600, 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] : (less(X, Z) | (~less(Y, Z)) | (~less(X, Y)))) | (less(v600, v600) | (~less(X!2, v600)) | (~less(v600, X!2)))) <=> ((~![X: $i, Y: $i, Z: $i] : (less(X, Z) | (~less(Y, Z)) | (~less(X, Y)))) | (~less(v600, X!2)) | (~less(X!2, v600)) | less(v600, 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] : (less(X, Z) | (~less(Y, Z)) | (~less(X, Y)))) | (less(v600, v600) | (~less(X!2, v600)) | (~less(v600, X!2)))),
% 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] : (less(X, Z) | (~less(Y, Z)) | (~less(X, Y)))) | (~less(v600, X!2)) | (~less(X!2, v600)) | less(v600, v600)),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.13/0.41 tff(47,plain,
% 0.13/0.41 (less(v600, 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 (^[X: $i] : refl((~less(X, X)) <=> (~less(X, X)))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(49,plain,
% 0.13/0.41 (![X: $i] : (~less(X, X)) <=> ![X: $i] : (~less(X, X))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[48])).
% 0.13/0.41 tff(50,plain,
% 0.13/0.41 (![X: $i] : (~less(X, X)) <=> ![X: $i] : (~less(X, X))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(51,axiom,(![X: $i] : (~less(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/MGT002+0.ax','irreflexive')).
% 0.13/0.41 tff(52,plain,
% 0.13/0.41 (![X: $i] : (~less(X, X))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.13/0.41 tff(53,plain,(
% 0.13/0.41 ![X: $i] : (~less(X, X))),
% 0.13/0.41 inference(skolemize,[status(sab)],[52])).
% 0.13/0.41 tff(54,plain,
% 0.13/0.41 (![X: $i] : (~less(X, X))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.13/0.41 tff(55,plain,
% 0.13/0.41 ((~![X: $i] : (~less(X, X))) | (~less(v600, v600))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(56,plain,
% 0.13/0.41 ($false),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[55, 54, 47])).
% 0.13/0.41 % SZS output end Proof
% 0.13/0.41 % E exiting
%------------------------------------------------------------------------------