%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN063+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:38:06 AM UTC 2025
% Result : Theorem 0.20s 0.38s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN063+1 : TPTP v9.0.0. Released v2.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 12:27:47 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.38 % SZS status Theorem
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 tff(big_p_type, type, (
% 0.20/0.38 big_p: $i > $o)).
% 0.20/0.38 tff(tptp_fun_X_0_type, type, (
% 0.20/0.38 tptp_fun_X_0: $i)).
% 0.20/0.38 tff(b_type, type, (
% 0.20/0.38 b: $i)).
% 0.20/0.38 tff(c_type, type, (
% 0.20/0.38 c: $i)).
% 0.20/0.38 tff(a_type, type, (
% 0.20/0.38 a: $i)).
% 0.20/0.38 tff(tptp_fun_X1_1_type, type, (
% 0.20/0.38 tptp_fun_X1_1: $i)).
% 0.20/0.38 tff(1,assumption,(~big_p(c)), introduced(assumption)).
% 0.20/0.38 tff(2,assumption,(~big_p(a)), introduced(assumption)).
% 0.20/0.38 tff(3,plain,
% 0.20/0.38 (((~big_p(a)) | big_p(c) | (~(big_p(b) | (~big_p(X!0))))) | big_p(a)),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(4,plain,
% 0.20/0.38 ((~big_p(a)) | big_p(c) | (~(big_p(b) | (~big_p(X!0))))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[3, 2])).
% 0.20/0.38 tff(5,plain,
% 0.20/0.38 (((~big_p(a)) | big_p(c) | (~big_p(b))) | big_p(a)),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(6,plain,
% 0.20/0.38 ((~big_p(a)) | big_p(c) | (~big_p(b))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[5, 2])).
% 0.20/0.38 tff(7,plain,
% 0.20/0.38 (((~big_p(a)) | big_p(c) | big_p(X1!1)) | big_p(a)),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(8,plain,
% 0.20/0.38 ((~big_p(a)) | big_p(c) | big_p(X1!1)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[7, 2])).
% 0.20/0.38 tff(9,plain,
% 0.20/0.38 (((~((~big_p(a)) | big_p(c) | (~(big_p(b) | (~big_p(X!0)))))) | ((~((~big_p(a)) | big_p(c) | big_p(X1!1))) | (~((~big_p(a)) | big_p(c) | (~big_p(b)))))) <=> ((~((~big_p(a)) | big_p(c) | (~big_p(b)))) | (~((~big_p(a)) | big_p(c) | big_p(X1!1))) | (~((~big_p(a)) | big_p(c) | (~(big_p(b) | (~big_p(X!0)))))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(10,plain,
% 0.20/0.38 ((~(~((~((~big_p(a)) | big_p(c) | big_p(X1!1))) | (~((~big_p(a)) | big_p(c) | (~big_p(b))))))) <=> ((~((~big_p(a)) | big_p(c) | big_p(X1!1))) | (~((~big_p(a)) | big_p(c) | (~big_p(b)))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(11,plain,
% 0.20/0.38 ((((~big_p(a)) | big_p(c) | big_p(X1!1)) & ((~big_p(a)) | big_p(c) | (~big_p(b)))) <=> (~((~((~big_p(a)) | big_p(c) | big_p(X1!1))) | (~((~big_p(a)) | big_p(c) | (~big_p(b))))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(12,plain,
% 0.20/0.38 (((~big_p(a)) | big_p(c) | (~big_p(b))) <=> ((~big_p(a)) | big_p(c) | (~big_p(b)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(13,plain,
% 0.20/0.38 (((~big_p(a)) | big_p(c) | big_p(X1!1)) <=> ((~big_p(a)) | big_p(c) | big_p(X1!1))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(14,plain,
% 0.20/0.38 ((((~big_p(a)) | big_p(c) | big_p(X1!1)) & ((~big_p(a)) | big_p(c) | (~big_p(b)))) <=> (((~big_p(a)) | big_p(c) | big_p(X1!1)) & ((~big_p(a)) | big_p(c) | (~big_p(b))))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[13, 12])).
% 0.20/0.38 tff(15,plain,
% 0.20/0.38 ((((~big_p(a)) | big_p(c) | big_p(X1!1)) & ((~big_p(a)) | big_p(c) | (~big_p(b)))) <=> (~((~((~big_p(a)) | big_p(c) | big_p(X1!1))) | (~((~big_p(a)) | big_p(c) | (~big_p(b))))))),
% 0.20/0.38 inference(transitivity,[status(thm)],[14, 11])).
% 0.20/0.38 tff(16,plain,
% 0.20/0.38 ((~(((~big_p(a)) | big_p(c) | big_p(X1!1)) & ((~big_p(a)) | big_p(c) | (~big_p(b))))) <=> (~(~((~((~big_p(a)) | big_p(c) | big_p(X1!1))) | (~((~big_p(a)) | big_p(c) | (~big_p(b)))))))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[15])).
% 0.20/0.38 tff(17,plain,
% 0.20/0.38 ((~(((~big_p(a)) | big_p(c) | big_p(X1!1)) & ((~big_p(a)) | big_p(c) | (~big_p(b))))) <=> ((~((~big_p(a)) | big_p(c) | big_p(X1!1))) | (~((~big_p(a)) | big_p(c) | (~big_p(b)))))),
% 0.20/0.38 inference(transitivity,[status(thm)],[16, 10])).
% 0.20/0.38 tff(18,plain,
% 0.20/0.38 ((~(big_p(c) | (~(big_p(a) & (big_p(b) | (~big_p(X!0))))))) <=> (~((~big_p(a)) | big_p(c) | (~(big_p(b) | (~big_p(X!0))))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(19,plain,
% 0.20/0.38 (((~(big_p(c) | (~(big_p(a) & (big_p(b) | (~big_p(X!0))))))) | (~(((~big_p(a)) | big_p(c) | big_p(X1!1)) & ((~big_p(a)) | big_p(c) | (~big_p(b)))))) <=> ((~((~big_p(a)) | big_p(c) | (~(big_p(b) | (~big_p(X!0)))))) | ((~((~big_p(a)) | big_p(c) | big_p(X1!1))) | (~((~big_p(a)) | big_p(c) | (~big_p(b))))))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[18, 17])).
% 0.20/0.38 tff(20,plain,
% 0.20/0.38 (((~(big_p(c) | (~(big_p(a) & (big_p(b) | (~big_p(X!0))))))) | (~(((~big_p(a)) | big_p(c) | big_p(X1!1)) & ((~big_p(a)) | big_p(c) | (~big_p(b)))))) <=> ((~((~big_p(a)) | big_p(c) | (~big_p(b)))) | (~((~big_p(a)) | big_p(c) | big_p(X1!1))) | (~((~big_p(a)) | big_p(c) | (~(big_p(b) | (~big_p(X!0)))))))),
% 0.20/0.38 inference(transitivity,[status(thm)],[19, 9])).
% 0.20/0.38 tff(21,plain,
% 0.20/0.38 (((![X: $i] : (big_p(c) | (~(big_p(a) & (big_p(b) | (~big_p(X)))))) | ![X1: $i] : (((~big_p(a)) | big_p(c) | big_p(X1)) & ((~big_p(a)) | big_p(c) | (~big_p(b))))) & ((~(big_p(c) | (~(big_p(a) & (big_p(b) | (~big_p(X!0))))))) | (~(((~big_p(a)) | big_p(c) | big_p(X1!1)) & ((~big_p(a)) | big_p(c) | (~big_p(b))))))) <=> ((![X: $i] : (big_p(c) | (~(big_p(a) & (big_p(b) | (~big_p(X)))))) | ![X1: $i] : (((~big_p(a)) | big_p(c) | big_p(X1)) & ((~big_p(a)) | big_p(c) | (~big_p(b))))) & ((~(big_p(c) | (~(big_p(a) & (big_p(b) | (~big_p(X!0))))))) | (~(((~big_p(a)) | big_p(c) | big_p(X1!1)) & ((~big_p(a)) | big_p(c) | (~big_p(b)))))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(22,plain,
% 0.20/0.38 ((~(![X: $i] : (big_p(c) | (~(big_p(a) & (big_p(b) | (~big_p(X)))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(c) | big_p(X1)) & ((~big_p(a)) | big_p(c) | (~big_p(b)))))) <=> (~(![X: $i] : (big_p(c) | (~(big_p(a) & (big_p(b) | (~big_p(X)))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(c) | big_p(X1)) & ((~big_p(a)) | big_p(c) | (~big_p(b))))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(23,plain,
% 0.20/0.38 ((![X: $i] : (big_p(c) | (~(big_p(a) & (big_p(b) | (~big_p(X)))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(c) | big_p(X1)) & ((~big_p(a)) | big_p(c) | (~big_p(b))))) <=> (![X: $i] : (big_p(c) | (~(big_p(a) & (big_p(b) | (~big_p(X)))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(c) | big_p(X1)) & ((~big_p(a)) | big_p(c) | (~big_p(b)))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(24,plain,
% 0.20/0.38 ((~(![X: $i] : (big_p(c) | (~(big_p(a) & (big_p(b) | (~big_p(X)))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(c) | big_p(X1)) & ((~big_p(a)) | big_p(c) | (~big_p(b)))))) <=> (~(![X: $i] : (big_p(c) | (~(big_p(a) & (big_p(b) | (~big_p(X)))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(c) | big_p(X1)) & ((~big_p(a)) | big_p(c) | (~big_p(b))))))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[23])).
% 0.20/0.38 tff(25,plain,
% 0.20/0.38 ((~(![X: $i] : (big_p(c) | (~(big_p(a) & (big_p(b) | (~big_p(X)))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(c) | big_p(X1)) & ((~big_p(a)) | big_p(c) | (~big_p(b)))))) <=> (~(![X: $i] : (big_p(c) | (~(big_p(a) & (big_p(b) | (~big_p(X)))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(c) | big_p(X1)) & ((~big_p(a)) | big_p(c) | (~big_p(b))))))),
% 0.20/0.38 inference(transitivity,[status(thm)],[24, 22])).
% 0.20/0.38 tff(26,plain,
% 0.20/0.38 ((![X: $i] : ((big_p(a) & (big_p(X) => big_p(b))) => big_p(c)) <=> ![X1: $i] : ((((~big_p(a)) | big_p(X1)) | big_p(c)) & (((~big_p(a)) | (~big_p(b))) | big_p(c)))) <=> (![X: $i] : (big_p(c) | (~(big_p(a) & (big_p(b) | (~big_p(X)))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(c) | big_p(X1)) & ((~big_p(a)) | big_p(c) | (~big_p(b)))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(27,plain,
% 0.20/0.38 ((~(![X: $i] : ((big_p(a) & (big_p(X) => big_p(b))) => big_p(c)) <=> ![X1: $i] : ((((~big_p(a)) | big_p(X1)) | big_p(c)) & (((~big_p(a)) | (~big_p(b))) | big_p(c))))) <=> (~(![X: $i] : (big_p(c) | (~(big_p(a) & (big_p(b) | (~big_p(X)))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(c) | big_p(X1)) & ((~big_p(a)) | big_p(c) | (~big_p(b))))))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[26])).
% 0.20/0.38 tff(28,plain,
% 0.20/0.38 ((~(![X: $i] : ((big_p(a) & (big_p(X) => big_p(b))) => big_p(c)) <=> ![X1: $i] : ((((~big_p(a)) | big_p(X1)) | big_p(c)) & (((~big_p(a)) | (~big_p(b))) | big_p(c))))) <=> (~(![X: $i] : (big_p(c) | (~(big_p(a) & (big_p(b) | (~big_p(X)))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(c) | big_p(X1)) & ((~big_p(a)) | big_p(c) | (~big_p(b))))))),
% 0.20/0.38 inference(transitivity,[status(thm)],[27, 22])).
% 0.20/0.38 tff(29,axiom,(~(![X: $i] : ((big_p(a) & (big_p(X) => big_p(b))) => big_p(c)) <=> ![X1: $i] : ((((~big_p(a)) | big_p(X1)) | big_p(c)) & (((~big_p(a)) | (~big_p(b))) | big_p(c))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel33')).
% 0.20/0.38 tff(30,plain,
% 0.20/0.38 (~(![X: $i] : (big_p(c) | (~(big_p(a) & (big_p(b) | (~big_p(X)))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(c) | big_p(X1)) & ((~big_p(a)) | big_p(c) | (~big_p(b)))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.20/0.39 tff(31,plain,
% 0.20/0.39 (~(![X: $i] : (big_p(c) | (~(big_p(a) & (big_p(b) | (~big_p(X)))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(c) | big_p(X1)) & ((~big_p(a)) | big_p(c) | (~big_p(b)))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[30, 25])).
% 0.20/0.39 tff(32,plain,
% 0.20/0.39 (~(![X: $i] : (big_p(c) | (~(big_p(a) & (big_p(b) | (~big_p(X)))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(c) | big_p(X1)) & ((~big_p(a)) | big_p(c) | (~big_p(b)))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[31, 22])).
% 0.20/0.39 tff(33,plain,
% 0.20/0.39 (~(![X: $i] : (big_p(c) | (~(big_p(a) & (big_p(b) | (~big_p(X)))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(c) | big_p(X1)) & ((~big_p(a)) | big_p(c) | (~big_p(b)))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.20/0.39 unexpected number of arguments: (let ((a!1 (lambda ((X $i))
% 0.20/0.39 (let ((a!1 (and (big_p a) (or (big_p b) (not (big_p X))))))
% 0.20/0.39 (refl (~ (or (big_p c) (not a!1)) (or (big_p c) (not a!1)))))))
% 0.20/0.39 (a!2 (forall ((X $i))
% 0.20/0.39 (let ((a!1 (and (big_p a) (or (big_p b) (not (big_p X))))))
% 0.20/0.39 (or (big_p c) (not a!1)))))
% 0.20/0.39 (a!3 (and (big_p a) (or (big_p b) (not (big_p X!0)))))
% 0.20/0.39 (a!5 (proof-bind (lambda ((X1 $i))
% 0.20/0.39 (let ((a!1 (and (or (not (big_p a))
% 0.20/0.39 (big_p c)
% 0.20/0.39 (big_p X1))
% 0.20/0.39 (or (not (big_p a))
% 0.20/0.39 (big_p c)
% 0.20/0.39 (not (big_p b))))))
% 0.20/0.39 (refl (~ a!1 a!1))))))
% 0.20/0.39 (a!6 (forall ((X1 $i))
% 0.20/0.39 (and (or (not (big_p a)) (big_p c) (big_p X1))
% 0.20/0.39 (or (not (big_p a)) (big_p c) (not (big_p b))))))
% 0.20/0.39 (a!7 (and (or (not (big_p a)) (big_p c) (big_p X1!1))
% 0.20/0.39 (or (not (big_p a)) (big_p c) (not (big_p b))))))
% 0.20/0.39 (let ((a!4 (~ (not a!2) (not (or (big_p c) (not a!3)))))
% 0.20/0.39 (a!8 (or (not (or (big_p c) (not a!3))) (not a!7))))
% 0.20/0.39 (nnf-neg (nnf-pos (proof-bind a!1) (~ a!2 a!2))
% 0.20/0.39 (sk a!4)
% 0.20/0.39 (nnf-pos a!5 (~ a!6 a!6))
% 0.20/0.39 (sk (~ (not a!6) (not a!7)))
% 0.20/0.39 (~ (not (= a!2 a!6)) (and (or a!2 a!6) a!8)))))
% 0.20/0.39 Proof display could not be completed: unexpected number of arguments
% 0.20/0.39 % E exiting
%------------------------------------------------------------------------------