%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN409+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:39:00 AM UTC 2025
% Result : Theorem 0.20s 0.37s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN409+1 : TPTP v9.0.0. Released v2.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n001.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 12:37:50 EDT 2025
% 0.11/0.34 % CPUTime :
% 0.20/0.37 % SZS status Theorem
% 0.20/0.37 % SZS output start Proof
% 0.20/0.37 tff(f_type, type, (
% 0.20/0.37 f: $i > $o)).
% 0.20/0.37 tff(tptp_fun_Z_1_type, type, (
% 0.20/0.37 tptp_fun_Z_1: $i)).
% 0.20/0.37 tff(tptp_fun_Y_2_type, type, (
% 0.20/0.37 tptp_fun_Y_2: $i)).
% 0.20/0.37 tff(tptp_fun_X_0_type, type, (
% 0.20/0.37 tptp_fun_X_0: $i)).
% 0.20/0.37 tff(1,assumption,(~f(Y!2)), introduced(assumption)).
% 0.20/0.37 tff(2,assumption,(![Y: $i, Z: $i] : (~((~f(Y)) | (~f(Z))))), introduced(assumption)).
% 0.20/0.37 tff(3,assumption,((~f(X!0)) | (~f(Y!2))), introduced(assumption)).
% 0.20/0.37 tff(4,plain,
% 0.20/0.37 (((~![Y: $i, Z: $i] : (~((~f(Y)) | (~f(Z))))) | (~((~f(X!0)) | (~f(Y!2))))) <=> ((~![Y: $i, Z: $i] : (~((~f(Y)) | (~f(Z))))) | (~((~f(X!0)) | (~f(Y!2)))))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(5,plain,
% 0.20/0.37 ((~((~f(Y!2)) | (~f(X!0)))) <=> (~((~f(X!0)) | (~f(Y!2))))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(6,plain,
% 0.20/0.37 (((~![Y: $i, Z: $i] : (~((~f(Y)) | (~f(Z))))) | (~((~f(Y!2)) | (~f(X!0))))) <=> ((~![Y: $i, Z: $i] : (~((~f(Y)) | (~f(Z))))) | (~((~f(X!0)) | (~f(Y!2)))))),
% 0.20/0.37 inference(monotonicity,[status(thm)],[5])).
% 0.20/0.37 tff(7,plain,
% 0.20/0.37 (((~![Y: $i, Z: $i] : (~((~f(Y)) | (~f(Z))))) | (~((~f(Y!2)) | (~f(X!0))))) <=> ((~![Y: $i, Z: $i] : (~((~f(Y)) | (~f(Z))))) | (~((~f(X!0)) | (~f(Y!2)))))),
% 0.20/0.37 inference(transitivity,[status(thm)],[6, 4])).
% 0.20/0.37 tff(8,plain,
% 0.20/0.37 ((~![Y: $i, Z: $i] : (~((~f(Y)) | (~f(Z))))) | (~((~f(Y!2)) | (~f(X!0))))),
% 0.20/0.37 inference(quant_inst,[status(thm)],[])).
% 0.20/0.37 tff(9,plain,
% 0.20/0.37 ((~![Y: $i, Z: $i] : (~((~f(Y)) | (~f(Z))))) | (~((~f(X!0)) | (~f(Y!2))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.20/0.37 tff(10,plain,
% 0.20/0.37 ($false),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[9, 2, 3])).
% 0.20/0.37 tff(11,plain,((~((~f(X!0)) | (~f(Y!2)))) | (~![Y: $i, Z: $i] : (~((~f(Y)) | (~f(Z)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.37 tff(12,plain,
% 0.20/0.37 (~((~f(X!0)) | (~f(Y!2)))),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[11, 2])).
% 0.20/0.37 tff(13,plain,
% 0.20/0.37 (((~f(X!0)) | (~f(Y!2))) | f(Y!2)),
% 0.20/0.37 inference(tautology,[status(thm)],[])).
% 0.20/0.37 tff(14,plain,
% 0.20/0.37 (f(Y!2)),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.20/0.37 tff(15,assumption,(~f(X!0)), introduced(assumption)).
% 0.20/0.37 tff(16,assumption,(![X: $i] : f(X)), introduced(assumption)).
% 0.20/0.37 tff(17,plain,
% 0.20/0.37 ((~![X: $i] : f(X)) | f(X!0)),
% 0.20/0.37 inference(quant_inst,[status(thm)],[])).
% 0.20/0.37 tff(18,plain,
% 0.20/0.37 ($false),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[17, 16, 15])).
% 0.20/0.37 tff(19,plain,((~![X: $i] : f(X)) | f(X!0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.37 tff(20,plain,
% 0.20/0.37 (~![X: $i] : f(X)),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[19, 15])).
% 0.20/0.37 tff(21,plain,
% 0.20/0.37 ((![X: $i] : f(X) | ![Y: $i, Z: $i] : (~((~f(Y)) | (~f(Z))))) <=> (![X: $i] : f(X) | ![Y: $i, Z: $i] : (~((~f(Y)) | (~f(Z)))))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(22,plain,
% 0.20/0.37 ((![X: $i] : f(X) | ![Y: $i, Z: $i] : (f(Y) & f(Z))) <=> (![X: $i] : f(X) | ![Y: $i, Z: $i] : (~((~f(Y)) | (~f(Z)))))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(23,plain,
% 0.20/0.37 ((![X: $i] : f(X) | ![Y: $i, Z: $i] : (f(Y) & f(Z))) <=> (![X: $i] : f(X) | ![Y: $i, Z: $i] : (f(Y) & f(Z)))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(24,plain,
% 0.20/0.37 (((![X: $i] : f(X) | ![Y: $i, Z: $i] : (f(Y) & f(Z))) & ((~f(X!0)) | (~(f(Y!2) & f(Z!1))))) <=> ((![X: $i] : f(X) | ![Y: $i, Z: $i] : (f(Y) & f(Z))) & ((~f(X!0)) | (~(f(Y!2) & f(Z!1)))))),
% 0.20/0.37 inference(monotonicity,[status(thm)],[23])).
% 0.20/0.37 tff(25,plain,
% 0.20/0.37 ((~(![X: $i] : f(X) <=> ![Y: $i, Z: $i] : (f(Y) & f(Z)))) <=> (~(![X: $i] : f(X) <=> ![Y: $i, Z: $i] : (f(Y) & f(Z))))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(26,plain,
% 0.20/0.37 ((![X: $i] : f(X) <=> ![Y: $i, Z: $i] : (f(Y) & f(Z))) <=> (![X: $i] : f(X) <=> ![Y: $i, Z: $i] : (f(Y) & f(Z)))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(27,plain,
% 0.20/0.37 ((~(![X: $i] : f(X) <=> ![Y: $i, Z: $i] : (f(Y) & f(Z)))) <=> (~(![X: $i] : f(X) <=> ![Y: $i, Z: $i] : (f(Y) & f(Z))))),
% 0.20/0.37 inference(monotonicity,[status(thm)],[26])).
% 0.20/0.37 tff(28,plain,
% 0.20/0.37 ((~(![X: $i] : f(X) <=> ![Y: $i, Z: $i] : (f(Y) & f(Z)))) <=> (~(![X: $i] : f(X) <=> ![Y: $i, Z: $i] : (f(Y) & f(Z))))),
% 0.20/0.37 inference(transitivity,[status(thm)],[27, 25])).
% 0.20/0.37 tff(29,axiom,(~(![X: $i] : f(X) <=> ![Y: $i, Z: $i] : (f(Y) & f(Z)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','kalish246')).
% 0.20/0.37 tff(30,plain,
% 0.20/0.37 (~(![X: $i] : f(X) <=> ![Y: $i, Z: $i] : (f(Y) & f(Z)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.20/0.37 tff(31,plain,
% 0.20/0.37 (~(![X: $i] : f(X) <=> ![Y: $i, Z: $i] : (f(Y) & f(Z)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[30, 28])).
% 0.20/0.37 tff(32,plain,
% 0.20/0.37 (~(![X: $i] : f(X) <=> ![Y: $i, Z: $i] : (f(Y) & f(Z)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[31, 25])).
% 0.20/0.37 tff(33,plain,
% 0.20/0.37 (~(![X: $i] : f(X) <=> ![Y: $i, Z: $i] : (f(Y) & f(Z)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.20/0.37 unexpected number of arguments: (let ((a!1 (lambda ((X $i)) (refl (~ (f X) (f X)))))
% 0.20/0.37 (a!2 (forall ((X $i)) (f X)))
% 0.20/0.37 (a!4 (lambda ((Y $i) (Z $i))
% 0.20/0.37 (refl (~ (and (f Y) (f Z)) (and (f Y) (f Z))))))
% 0.20/0.37 (a!5 (forall ((Y $i) (Z $i)) (and (f Y) (f Z))))
% 0.20/0.37 (a!7 (or (not (f X!0)) (not (and (f Y!2) (f Z!1))))))
% 0.20/0.37 (let ((a!3 (sk (~ (not a!2) (not (f X!0)))))
% 0.20/0.37 (a!6 (~ (not a!5) (not (and (f Y!2) (f Z!1))))))
% 0.20/0.37 (nnf-neg (nnf-pos (proof-bind a!1) (~ a!2 a!2))
% 0.20/0.37 a!3
% 0.20/0.37 (nnf-pos (proof-bind a!4) (~ a!5 a!5))
% 0.20/0.37 (sk a!6)
% 0.20/0.37 (~ (not (= a!2 a!5)) (and (or a!2 a!5) a!7)))))
% 0.20/0.37 Proof display could not be completed: unexpected number of arguments
% 0.20/0.38 % E exiting
%------------------------------------------------------------------------------