%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN375+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:38:55 AM UTC 2025
% Result : Theorem 0.19s 0.36s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYN375+1 : TPTP v9.0.0. Released v2.0.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n013.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:33:23 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.36 % SZS status Theorem
% 0.19/0.36 % SZS output start Proof
% 0.19/0.36 tff(big_p_type, type, (
% 0.19/0.36 big_p: $i > $o)).
% 0.19/0.36 tff(tptp_fun_X_1_type, type, (
% 0.19/0.36 tptp_fun_X_1: $i)).
% 0.19/0.36 tff(tptp_fun_Y_0_type, type, (
% 0.19/0.36 tptp_fun_Y_0: $i)).
% 0.19/0.36 tff(tptp_fun_X_2_type, type, (
% 0.19/0.36 tptp_fun_X_2: $i)).
% 0.19/0.36 tff(1,assumption,(~big_p(X!1)), introduced(assumption)).
% 0.19/0.36 tff(2,assumption,(~big_p(Y!0)), introduced(assumption)).
% 0.19/0.36 tff(3,plain,
% 0.19/0.36 ((~(big_p(X!1) | big_p(Y!0))) | big_p(X!1) | big_p(Y!0)),
% 0.19/0.36 inference(tautology,[status(thm)],[])).
% 0.19/0.36 tff(4,plain,
% 0.19/0.36 (~(big_p(X!1) | big_p(Y!0))),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[3, 2, 1])).
% 0.19/0.36 tff(5,plain,
% 0.19/0.36 (((~(big_p(X!1) | big_p(Y!0))) | (~((~big_p(X!1)) | ![Y: $i] : (~big_p(Y))))) | (big_p(X!1) | big_p(Y!0))),
% 0.19/0.36 inference(tautology,[status(thm)],[])).
% 0.19/0.36 tff(6,plain,
% 0.19/0.36 ((~(big_p(X!1) | big_p(Y!0))) | (~((~big_p(X!1)) | ![Y: $i] : (~big_p(Y))))),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[5, 4])).
% 0.19/0.36 tff(7,plain,
% 0.19/0.36 (((~((~(big_p(X!1) | big_p(Y!0))) | (~((~big_p(X!1)) | ![Y: $i] : (~big_p(Y)))))) | (~((~(![X: $i] : big_p(X) | big_p(Y!0))) | (~((~big_p(X!2)) | ![Y: $i] : (~big_p(Y))))))) <=> ((~((~(big_p(X!1) | big_p(Y!0))) | (~((~big_p(X!1)) | ![Y: $i] : (~big_p(Y)))))) | (~((~(big_p(Y!0) | ![X: $i] : big_p(X))) | (~((~big_p(X!2)) | ![Y: $i] : (~big_p(Y)))))))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(8,plain,
% 0.19/0.36 (((~((~(big_p(X!1) | big_p(Y!0))) | (~((~big_p(X!1)) | ![Y: $i] : (~big_p(Y)))))) | (~((~(![X: $i] : big_p(X) | big_p(Y!0))) | (~((~big_p(X!2)) | ![Y: $i] : (~big_p(Y))))))) <=> ((~((~(big_p(X!1) | big_p(Y!0))) | (~((~big_p(X!1)) | ![Y: $i] : (~big_p(Y)))))) | (~((~(![X: $i] : big_p(X) | big_p(Y!0))) | (~((~big_p(X!2)) | ![Y: $i] : (~big_p(Y)))))))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(9,plain,
% 0.19/0.36 ((((big_p(X!1) | big_p(Y!0)) & ((~big_p(X!1)) | ![Y: $i] : (~big_p(Y)))) | ((![X: $i] : big_p(X) | big_p(Y!0)) & ((~big_p(X!2)) | ![Y: $i] : (~big_p(Y))))) <=> ((~((~(big_p(X!1) | big_p(Y!0))) | (~((~big_p(X!1)) | ![Y: $i] : (~big_p(Y)))))) | (~((~(![X: $i] : big_p(X) | big_p(Y!0))) | (~((~big_p(X!2)) | ![Y: $i] : (~big_p(Y)))))))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(10,plain,
% 0.19/0.36 (((![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))))) & (((big_p(X!1) | big_p(Y!0)) & ((~big_p(X!1)) | ![Y: $i] : (~big_p(Y)))) | ((![X: $i] : big_p(X) | big_p(Y!0)) & ((~big_p(X!2)) | ![Y: $i] : (~big_p(Y)))))) <=> ((![X: $i] : (((~big_p(X)) | big_p(Y!0)) & (big_p(X) | ![Y: $i] : (~big_p(Y)))) | ((big_p(Y!0) | (~big_p(X!2))) & (![X: $i] : big_p(X) | ![Y: $i] : (~big_p(Y))))) & (((big_p(X!1) | big_p(Y!0)) & ((~big_p(X!1)) | ![Y: $i] : (~big_p(Y)))) | ((![X: $i] : big_p(X) | big_p(Y!0)) & ((~big_p(X!2)) | ![Y: $i] : (~big_p(Y))))))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(11,plain,
% 0.19/0.36 ((~(![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))))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(12,plain,
% 0.19/0.36 ((![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)))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(13,plain,
% 0.19/0.36 ((~(![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))))),
% 0.19/0.36 inference(monotonicity,[status(thm)],[12])).
% 0.19/0.36 tff(14,plain,
% 0.19/0.36 ((~(![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))))),
% 0.19/0.36 inference(transitivity,[status(thm)],[13, 11])).
% 0.19/0.36 tff(15,axiom,(~(![X: $i] : (big_p(X) <=> ?[Y: $i] : big_p(Y)) <=> (![X: $i] : big_p(X) <=> ?[Y: $i] : big_p(Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','x2126')).
% 0.19/0.37 tff(16,plain,
% 0.19/0.37 (~(![X: $i] : (big_p(X) <=> ?[Y: $i] : big_p(Y)) <=> (![X: $i] : big_p(X) <=> ?[Y: $i] : big_p(Y)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.19/0.37 tff(17,plain,
% 0.19/0.37 (~(![X: $i] : (big_p(X) <=> ?[Y: $i] : big_p(Y)) <=> (![X: $i] : big_p(X) <=> ?[Y: $i] : big_p(Y)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[16, 14])).
% 0.19/0.37 tff(18,plain,
% 0.19/0.37 (~(![X: $i] : (big_p(X) <=> ?[Y: $i] : big_p(Y)) <=> (![X: $i] : big_p(X) <=> ?[Y: $i] : big_p(Y)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[17, 11])).
% 0.19/0.37 tff(19,plain,
% 0.19/0.37 (~(![X: $i] : (big_p(X) <=> ?[Y: $i] : big_p(Y)) <=> (![X: $i] : big_p(X) <=> ?[Y: $i] : big_p(Y)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.19/0.37 unexpected number of arguments: (let ((a!1 (lambda ((X $i))
% 0.19/0.37 (let ((a!1 (refl (~ (not (big_p X)) (not (big_p X)))))
% 0.19/0.37 (a!2 (exists ((Y $i)) (big_p Y)))
% 0.19/0.37 (a!3 (lambda ((Y $i))
% 0.19/0.37 (refl (~ (not (big_p Y)) (not (big_p Y))))))
% 0.19/0.37 (a!4 (forall ((Y $i)) (not (big_p Y)))))
% 0.19/0.37 (let ((a!5 (and (or (not (big_p X)) (big_p Y!0))
% 0.19/0.37 (or (big_p X) a!4))))
% 0.19/0.37 (nnf-pos (refl (~ (big_p X) (big_p X)))
% 0.19/0.37 a!1
% 0.19/0.37 (sk (~ a!2 (big_p Y!0)))
% 0.19/0.37 (nnf-neg (proof-bind a!3) (~ (not a!2) a!4))
% 0.19/0.37 (~ (= (big_p X) a!2) a!5))))))
% 0.19/0.37 (a!2 (forall ((X $i))
% 0.19/0.37 (let ((a!1 (exists ((Y $i)) (big_p Y))))
% 0.19/0.37 (= (big_p X) a!1))))
% 0.19/0.37 (a!3 (forall ((X $i))
% 0.19/0.37 (let ((a!1 (forall ((Y $i)) (not (big_p Y)))))
% 0.19/0.37 (and (or (not (big_p X)) (big_p Y!0)) (or (big_p X) a!1)))))
% 0.19/0.37 (a!4 (exists ((Y $i)) (big_p Y)))
% 0.19/0.37 (a!6 (refl (~ (not (big_p X!1)) (not (big_p X!1)))))
% 0.19/0.37 (a!7 (lambda ((Y $i)) (refl (~ (not (big_p Y)) (not (big_p Y))))))
% 0.19/0.37 (a!8 (forall ((Y $i)) (not (big_p Y))))
% 0.19/0.37 (a!12 (lambda ((X $i)) (refl (~ (big_p X) (big_p X)))))
% 0.19/0.37 (a!13 (forall ((X $i)) (big_p X))))
% 0.19/0.37 (let ((a!5 (~ (not a!2) (not (= (big_p X!1) a!4))))
% 0.19/0.37 (a!9 (and (or (big_p X!1) (big_p Y!0)) (or (not (big_p X!1)) a!8)))
% 0.19/0.37 (a!14 (sk (~ (not a!13) (not (big_p X!2)))))
% 0.19/0.37 (a!15 (and (or (not (big_p X!2)) (big_p Y!0)) (or a!13 a!8)))
% 0.19/0.37 (a!17 (and (or a!13 (big_p Y!0)) (or (not (big_p X!2)) a!8))))
% 0.19/0.37 (let ((a!10 (~ (not (= (big_p X!1) a!4)) a!9))
% 0.19/0.37 (a!16 (nnf-pos (nnf-pos (proof-bind a!12) (~ a!13 a!13))
% 0.19/0.37 a!14
% 0.19/0.37 (sk (~ a!4 (big_p Y!0)))
% 0.19/0.37 (nnf-neg (proof-bind a!7) (~ (not a!4) a!8))
% 0.19/0.37 (~ (= a!13 a!4) a!15)))
% 0.19/0.37 (a!18 (nnf-neg (nnf-pos (proof-bind a!12) (~ a!13 a!13))
% 0.19/0.37 a!14
% 0.19/0.37 (sk (~ a!4 (big_p Y!0)))
% 0.19/0.37 (nnf-neg (proof-bind a!7) (~ (not a!4) a!8))
% 0.19/0.37 (~ (not (= a!13 a!4)) a!17)))
% 0.19/0.37 (a!19 (~ (not (= a!2 (= a!13 a!4))) (and (or a!3 a!15) (or a!9 a!17)))))
% 0.19/0.37 (let ((a!11 (nnf-neg (refl (~ (big_p X!1) (big_p X!1)))
% 0.19/0.37 a!6
% 0.19/0.37 (sk (~ a!4 (big_p Y!0)))
% 0.19/0.37 (nnf-neg (proof-bind a!7) (~ (not a!4) a!8))
% 0.19/0.37 a!10)))
% 0.19/0.37 (nnf-neg (nnf-pos (proof-bind a!1) (~ a!2 a!3))
% 0.19/0.37 (trans (sk a!5) a!11 (~ (not a!2) a!9))
% 0.19/0.37 a!16
% 0.19/0.37 a!18
% 0.19/0.37 a!19)))))
% 0.19/0.37 Proof display could not be completed: unexpected number of arguments
% 0.19/0.37 % E exiting
%------------------------------------------------------------------------------