%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN377+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:38:56 AM UTC 2025
% Result : Theorem 0.13s 0.38s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SYN377+1 : TPTP v9.0.0. Released v2.0.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 12:33:24 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.38 % SZS status Theorem
% 0.13/0.38 % SZS output start Proof
% 0.13/0.38 tff(big_p_type, type, (
% 0.13/0.38 big_p: $i > $o)).
% 0.13/0.38 tff(tptp_fun_Y_0_type, type, (
% 0.13/0.38 tptp_fun_Y_0: $i)).
% 0.13/0.38 tff(tptp_fun_X_1_type, type, (
% 0.13/0.38 tptp_fun_X_1: $i)).
% 0.13/0.38 tff(tptp_fun_X_2_type, type, (
% 0.13/0.38 tptp_fun_X_2: $i)).
% 0.13/0.38 tff(1,assumption,(~![Y: $i] : big_p(Y)), introduced(assumption)).
% 0.13/0.38 tff(2,assumption,(~(![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y))), introduced(assumption)).
% 0.13/0.38 tff(3,plain,
% 0.13/0.38 ((![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y)) | (~![Y: $i] : big_p(Y))),
% 0.13/0.38 inference(tautology,[status(thm)],[])).
% 0.13/0.38 tff(4,plain,
% 0.13/0.38 (~![Y: $i] : big_p(Y)),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[3, 2])).
% 0.13/0.38 tff(5,plain,
% 0.13/0.38 (((~(big_p(X!2) | (~big_p(Y!0)))) | (~(![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y)))) | (![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y))),
% 0.13/0.38 inference(tautology,[status(thm)],[])).
% 0.13/0.38 tff(6,plain,
% 0.13/0.38 ((~(big_p(X!2) | (~big_p(Y!0)))) | (~(![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y)))),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[5, 2])).
% 0.13/0.38 tff(7,plain,
% 0.13/0.38 ((![X: $i] : (~((~(big_p(X) | (~big_p(Y!0)))) | (~((~big_p(X)) | ![Y: $i] : big_p(Y))))) | (~((~(big_p(X!2) | (~big_p(Y!0)))) | (~(![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y)))))) <=> (![X: $i] : (~((~(big_p(X) | (~big_p(Y!0)))) | (~((~big_p(X)) | ![Y: $i] : big_p(Y))))) | (~((~(big_p(X!2) | (~big_p(Y!0)))) | (~(![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y))))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(8,plain,
% 0.13/0.38 ((~((~(![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y))) | (~(big_p(X!2) | (~big_p(Y!0)))))) <=> (~((~(big_p(X!2) | (~big_p(Y!0)))) | (~(![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y)))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(9,plain,
% 0.13/0.38 (^[X: $i] : rewrite((~((~((~big_p(X)) | ![Y: $i] : big_p(Y))) | (~(big_p(X) | (~big_p(Y!0)))))) <=> (~((~(big_p(X) | (~big_p(Y!0)))) | (~((~big_p(X)) | ![Y: $i] : big_p(Y))))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(10,plain,
% 0.13/0.38 (![X: $i] : (~((~((~big_p(X)) | ![Y: $i] : big_p(Y))) | (~(big_p(X) | (~big_p(Y!0)))))) <=> ![X: $i] : (~((~(big_p(X) | (~big_p(Y!0)))) | (~((~big_p(X)) | ![Y: $i] : big_p(Y)))))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[9])).
% 0.13/0.38 tff(11,plain,
% 0.13/0.38 ((![X: $i] : (~((~((~big_p(X)) | ![Y: $i] : big_p(Y))) | (~(big_p(X) | (~big_p(Y!0)))))) | (~((~(![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y))) | (~(big_p(X!2) | (~big_p(Y!0))))))) <=> (![X: $i] : (~((~(big_p(X) | (~big_p(Y!0)))) | (~((~big_p(X)) | ![Y: $i] : big_p(Y))))) | (~((~(big_p(X!2) | (~big_p(Y!0)))) | (~(![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y))))))),
% 0.13/0.38 inference(monotonicity,[status(thm)],[10, 8])).
% 0.13/0.38 tff(12,plain,
% 0.13/0.38 ((![X: $i] : (~((~((~big_p(X)) | ![Y: $i] : big_p(Y))) | (~(big_p(X) | (~big_p(Y!0)))))) | (~((~(![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y))) | (~(big_p(X!2) | (~big_p(Y!0))))))) <=> (![X: $i] : (~((~(big_p(X) | (~big_p(Y!0)))) | (~((~big_p(X)) | ![Y: $i] : big_p(Y))))) | (~((~(big_p(X!2) | (~big_p(Y!0)))) | (~(![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y))))))),
% 0.13/0.38 inference(transitivity,[status(thm)],[11, 7])).
% 0.13/0.38 tff(13,plain,
% 0.13/0.38 ((![X: $i] : (~((~((~big_p(X)) | ![Y: $i] : big_p(Y))) | (~(big_p(X) | (~big_p(Y!0)))))) | (~((~(![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y))) | (~(big_p(X!2) | (~big_p(Y!0))))))) <=> (![X: $i] : (~((~((~big_p(X)) | ![Y: $i] : big_p(Y))) | (~(big_p(X) | (~big_p(Y!0)))))) | (~((~(![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y))) | (~(big_p(X!2) | (~big_p(Y!0)))))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(14,plain,
% 0.13/0.38 ((![X: $i] : (~((~((~big_p(X)) | ![Y: $i] : big_p(Y))) | (~(big_p(X) | (~big_p(Y!0)))))) | (~((~(![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y))) | (~(big_p(X!2) | (~big_p(Y!0))))))) <=> (![X: $i] : (~((~((~big_p(X)) | ![Y: $i] : big_p(Y))) | (~(big_p(X) | (~big_p(Y!0)))))) | (~((~(![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y))) | (~(big_p(X!2) | (~big_p(Y!0)))))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(15,plain,
% 0.13/0.38 (((![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y)) & (big_p(X!2) | (~big_p(Y!0)))) <=> (~((~(![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y))) | (~(big_p(X!2) | (~big_p(Y!0))))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(16,plain,
% 0.13/0.39 ((![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y)) <=> (![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(17,plain,
% 0.13/0.39 (((![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y)) & (big_p(X!2) | (~big_p(Y!0)))) <=> ((![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y)) & (big_p(X!2) | (~big_p(Y!0))))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[16])).
% 0.13/0.39 tff(18,plain,
% 0.13/0.39 (((![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y)) & (big_p(X!2) | (~big_p(Y!0)))) <=> (~((~(![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y))) | (~(big_p(X!2) | (~big_p(Y!0))))))),
% 0.13/0.39 inference(transitivity,[status(thm)],[17, 15])).
% 0.13/0.39 tff(19,plain,
% 0.13/0.39 (^[X: $i] : trans(monotonicity(rewrite(((~big_p(X)) | ![Y: $i] : big_p(Y)) <=> ((~big_p(X)) | ![Y: $i] : big_p(Y))), ((((~big_p(X)) | ![Y: $i] : big_p(Y)) & (big_p(X) | (~big_p(Y!0)))) <=> (((~big_p(X)) | ![Y: $i] : big_p(Y)) & (big_p(X) | (~big_p(Y!0)))))), rewrite((((~big_p(X)) | ![Y: $i] : big_p(Y)) & (big_p(X) | (~big_p(Y!0)))) <=> (~((~((~big_p(X)) | ![Y: $i] : big_p(Y))) | (~(big_p(X) | (~big_p(Y!0))))))), ((((~big_p(X)) | ![Y: $i] : big_p(Y)) & (big_p(X) | (~big_p(Y!0)))) <=> (~((~((~big_p(X)) | ![Y: $i] : big_p(Y))) | (~(big_p(X) | (~big_p(Y!0))))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(20,plain,
% 0.13/0.39 (![X: $i] : (((~big_p(X)) | ![Y: $i] : big_p(Y)) & (big_p(X) | (~big_p(Y!0)))) <=> ![X: $i] : (~((~((~big_p(X)) | ![Y: $i] : big_p(Y))) | (~(big_p(X) | (~big_p(Y!0))))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[19])).
% 0.13/0.39 tff(21,plain,
% 0.13/0.39 ((![X: $i] : (((~big_p(X)) | ![Y: $i] : big_p(Y)) & (big_p(X) | (~big_p(Y!0)))) | ((![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y)) & (big_p(X!2) | (~big_p(Y!0))))) <=> (![X: $i] : (~((~((~big_p(X)) | ![Y: $i] : big_p(Y))) | (~(big_p(X) | (~big_p(Y!0)))))) | (~((~(![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y))) | (~(big_p(X!2) | (~big_p(Y!0)))))))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[20, 18])).
% 0.13/0.39 tff(22,plain,
% 0.13/0.39 ((![X: $i] : (((~big_p(X)) | ![Y: $i] : big_p(Y)) & (big_p(X) | (~big_p(Y!0)))) | ((![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y)) & (big_p(X!2) | (~big_p(Y!0))))) <=> (![X: $i] : (~((~((~big_p(X)) | ![Y: $i] : big_p(Y))) | (~(big_p(X) | (~big_p(Y!0)))))) | (~((~(![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y))) | (~(big_p(X!2) | (~big_p(Y!0)))))))),
% 0.13/0.39 inference(transitivity,[status(thm)],[21, 14])).
% 0.13/0.39 tff(23,plain,
% 0.13/0.39 (((![X: $i] : (((~big_p(X)) | ![Y: $i] : big_p(Y)) & (big_p(X) | (~big_p(Y!0)))) | ((![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y)) & (big_p(X!2) | (~big_p(Y!0))))) & (((big_p(X!1) | ![Y: $i] : big_p(Y)) & ((~big_p(X!1)) | (~big_p(Y!0)))) | ((big_p(X!2) | ![Y: $i] : big_p(Y)) & (![X: $i] : (~big_p(X)) | (~big_p(Y!0)))))) <=> ((![X: $i] : (((~big_p(X)) | ![Y: $i] : big_p(Y)) & (big_p(X) | (~big_p(Y!0)))) | ((![X: $i] : (~big_p(X)) | ![Y: $i] : big_p(Y)) & (big_p(X!2) | (~big_p(Y!0))))) & (((big_p(X!1) | ![Y: $i] : big_p(Y)) & ((~big_p(X!1)) | (~big_p(Y!0)))) | ((big_p(X!2) | ![Y: $i] : big_p(Y)) & ((~big_p(Y!0)) | ![X: $i] : (~big_p(X))))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(24,plain,
% 0.13/0.39 ((~(![X: $i] : (big_p(X) <=> ![Y: $i] : big_p(Y)) <=> (?[X: $i] : big_p(X) <=> ![Y: $i] : big_p(Y)))) <=> (~(![X: $i] : (big_p(X) <=> ![Y: $i] : big_p(Y)) <=> (?[X: $i] : big_p(X) <=> ![Y: $i] : big_p(Y))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(25,plain,
% 0.13/0.39 ((![X: $i] : (big_p(X) <=> ![Y: $i] : big_p(Y)) <=> (?[X: $i] : big_p(X) <=> ![Y: $i] : big_p(Y))) <=> (![X: $i] : (big_p(X) <=> ![Y: $i] : big_p(Y)) <=> (?[X: $i] : big_p(X) <=> ![Y: $i] : big_p(Y)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(26,plain,
% 0.13/0.39 ((~(![X: $i] : (big_p(X) <=> ![Y: $i] : big_p(Y)) <=> (?[X: $i] : big_p(X) <=> ![Y: $i] : big_p(Y)))) <=> (~(![X: $i] : (big_p(X) <=> ![Y: $i] : big_p(Y)) <=> (?[X: $i] : big_p(X) <=> ![Y: $i] : big_p(Y))))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[25])).
% 0.13/0.39 tff(27,plain,
% 0.13/0.39 ((~(![X: $i] : (big_p(X) <=> ![Y: $i] : big_p(Y)) <=> (?[X: $i] : big_p(X) <=> ![Y: $i] : big_p(Y)))) <=> (~(![X: $i] : (big_p(X) <=> ![Y: $i] : big_p(Y)) <=> (?[X: $i] : big_p(X) <=> ![Y: $i] : big_p(Y))))),
% 0.13/0.39 inference(transitivity,[status(thm)],[26, 24])).
% 0.13/0.39 tff(28,axiom,(~(![X: $i] : (big_p(X) <=> ![Y: $i] : big_p(Y)) <=> (?[X: $i] : big_p(X) <=> ![Y: $i] : big_p(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','x2128')).
% 0.13/0.39 tff(29,plain,
% 0.13/0.39 (~(![X: $i] : (big_p(X) <=> ![Y: $i] : big_p(Y)) <=> (?[X: $i] : big_p(X) <=> ![Y: $i] : big_p(Y)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.13/0.39 tff(30,plain,
% 0.13/0.39 (~(![X: $i] : (big_p(X) <=> ![Y: $i] : big_p(Y)) <=> (?[X: $i] : big_p(X) <=> ![Y: $i] : big_p(Y)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[29, 27])).
% 0.13/0.39 tff(31,plain,
% 0.13/0.39 (~(![X: $i] : (big_p(X) <=> ![Y: $i] : big_p(Y)) <=> (?[X: $i] : big_p(X) <=> ![Y: $i] : big_p(Y)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[30, 24])).
% 0.13/0.39 tff(32,plain,
% 0.13/0.39 (~(![X: $i] : (big_p(X) <=> ![Y: $i] : big_p(Y)) <=> (?[X: $i] : big_p(X) <=> ![Y: $i] : big_p(Y)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.13/0.39 unexpected number of arguments: (let ((a!1 (lambda ((X $i))
% 0.13/0.39 (let ((a!1 (refl (~ (not (big_p X)) (not (big_p X)))))
% 0.13/0.39 (a!2 (lambda ((Y $i)) (refl (~ (big_p Y) (big_p Y)))))
% 0.13/0.39 (a!3 (forall ((Y $i)) (big_p Y))))
% 0.13/0.39 (let ((a!4 (sk (~ (not a!3) (not (big_p Y!0)))))
% 0.13/0.39 (a!5 (and (or (not (big_p X)) a!3)
% 0.13/0.39 (or (big_p X) (not (big_p Y!0))))))
% 0.13/0.39 (nnf-pos (refl (~ (big_p X) (big_p X)))
% 0.13/0.39 a!1
% 0.13/0.39 (nnf-pos (proof-bind a!2) (~ a!3 a!3))
% 0.13/0.39 a!4
% 0.13/0.39 (~ (= (big_p X) a!3) a!5))))))
% 0.13/0.39 (a!2 (forall ((X $i))
% 0.13/0.39 (let ((a!1 (forall ((Y $i)) (big_p Y))))
% 0.13/0.39 (= (big_p X) a!1))))
% 0.13/0.39 (a!3 (forall ((X $i))
% 0.13/0.39 (let ((a!1 (forall ((Y $i)) (big_p Y))))
% 0.13/0.39 (and (or (not (big_p X)) a!1) (or (big_p X) (not (big_p Y!0)))))))
% 0.13/0.39 (a!4 (forall ((Y $i)) (big_p Y)))
% 0.13/0.39 (a!6 (refl (~ (not (big_p X!1)) (not (big_p X!1)))))
% 0.13/0.39 (a!7 (lambda ((Y $i)) (refl (~ (big_p Y) (big_p Y)))))
% 0.13/0.39 (a!12 (exists ((X $i)) (big_p X)))
% 0.13/0.39 (a!13 (lambda ((X $i)) (refl (~ (not (big_p X)) (not (big_p X))))))
% 0.13/0.39 (a!14 (forall ((X $i)) (not (big_p X)))))
% 0.13/0.39 (let ((a!5 (~ (not a!2) (not (= (big_p X!1) a!4))))
% 0.13/0.39 (a!8 (sk (~ (not a!4) (not (big_p Y!0)))))
% 0.13/0.39 (a!9 (and (or (big_p X!1) a!4) (or (not (big_p X!1)) (not (big_p Y!0)))))
% 0.13/0.39 (a!15 (and (or a!14 a!4) (or (big_p X!2) (not (big_p Y!0)))))
% 0.13/0.39 (a!17 (and (or (big_p X!2) a!4) (or a!14 (not (big_p Y!0))))))
% 0.13/0.39 (let ((a!10 (~ (not (= (big_p X!1) a!4)) a!9))
% 0.13/0.39 (a!16 (nnf-pos (sk (~ a!12 (big_p X!2)))
% 0.13/0.39 (nnf-neg (proof-bind a!13) (~ (not a!12) a!14))
% 0.13/0.39 (nnf-pos (proof-bind a!7) (~ a!4 a!4))
% 0.13/0.39 a!8
% 0.13/0.39 (~ (= a!12 a!4) a!15)))
% 0.13/0.39 (a!18 (nnf-neg (sk (~ a!12 (big_p X!2)))
% 0.13/0.39 (nnf-neg (proof-bind a!13) (~ (not a!12) a!14))
% 0.13/0.39 (nnf-pos (proof-bind a!7) (~ a!4 a!4))
% 0.13/0.39 a!8
% 0.13/0.39 (~ (not (= a!12 a!4)) a!17)))
% 0.13/0.39 (a!19 (~ (not (= a!2 (= a!12 a!4))) (and (or a!3 a!15) (or a!9 a!17)))))
% 0.13/0.39 (let ((a!11 (nnf-neg (refl (~ (big_p X!1) (big_p X!1)))
% 0.13/0.39 a!6
% 0.13/0.39 (nnf-pos (proof-bind a!7) (~ a!4 a!4))
% 0.13/0.39 a!8
% 0.13/0.39 a!10)))
% 0.13/0.39 (nnf-neg (nnf-pos (proof-bind a!1) (~ a!2 a!3))
% 0.13/0.39 (trans (sk a!5) a!11 (~ (not a!2) a!9))
% 0.13/0.39 a!16
% 0.13/0.39 a!18
% 0.13/0.39 a!19)))))
% 0.13/0.39 Proof display could not be completed: unexpected number of arguments
% 0.13/0.40 % E exiting
%------------------------------------------------------------------------------