%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN084+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 05:38:12 AM UTC 2025
% Result : Theorem 0.21s 0.38s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SYN084+1 : TPTP v9.0.0. Released v2.0.0.
% 0.04/0.13 % 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 12:28:02 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.21/0.38 % SZS status Theorem
% 0.21/0.38 % SZS output start Proof
% 0.21/0.38 tff(big_p_type, type, (
% 0.21/0.38 big_p: $i > $o)).
% 0.21/0.38 tff(tptp_fun_X1_1_type, type, (
% 0.21/0.38 tptp_fun_X1_1: $i)).
% 0.21/0.38 tff(f_type, type, (
% 0.21/0.38 f: $i > $i)).
% 0.21/0.38 tff(a_type, type, (
% 0.21/0.38 a: $i)).
% 0.21/0.38 tff(tptp_fun_X_0_type, type, (
% 0.21/0.38 tptp_fun_X_0: $i)).
% 0.21/0.38 tff(1,assumption,(~((~big_p(a)) | big_p(f(f(X1!1))) | (~big_p(f(X1!1))))), introduced(assumption)).
% 0.21/0.38 tff(2,plain,
% 0.21/0.38 (((~big_p(a)) | big_p(f(f(X1!1))) | (~big_p(f(X1!1)))) | big_p(f(X1!1))),
% 0.21/0.38 inference(tautology,[status(thm)],[])).
% 0.21/0.38 tff(3,plain,
% 0.21/0.38 (big_p(f(X1!1))),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.21/0.38 tff(4,plain,
% 0.21/0.38 ((big_p(f(X1!1)) | (~big_p(X1!1))) | (~big_p(f(X1!1)))),
% 0.21/0.38 inference(tautology,[status(thm)],[])).
% 0.21/0.38 tff(5,plain,
% 0.21/0.38 (big_p(f(X1!1)) | (~big_p(X1!1))),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[4, 3])).
% 0.21/0.38 tff(6,plain,
% 0.21/0.38 (((~big_p(a)) | big_p(f(f(X1!1))) | (~big_p(f(X1!1)))) | (~big_p(f(f(X1!1))))),
% 0.21/0.38 inference(tautology,[status(thm)],[])).
% 0.21/0.38 tff(7,plain,
% 0.21/0.38 (~big_p(f(f(X1!1)))),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[6, 1])).
% 0.21/0.38 tff(8,assumption,(~big_p(a)), introduced(assumption)).
% 0.21/0.38 tff(9,plain,
% 0.21/0.38 (((~big_p(a)) | big_p(f(f(X1!1))) | big_p(X1!1)) | big_p(a)),
% 0.21/0.38 inference(tautology,[status(thm)],[])).
% 0.21/0.38 tff(10,plain,
% 0.21/0.38 ((~big_p(a)) | big_p(f(f(X1!1))) | big_p(X1!1)),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.21/0.38 tff(11,plain,
% 0.21/0.38 (((~big_p(a)) | big_p(f(f(X1!1))) | (~big_p(f(X1!1)))) | big_p(a)),
% 0.21/0.38 inference(tautology,[status(thm)],[])).
% 0.21/0.38 tff(12,plain,
% 0.21/0.38 ((~big_p(a)) | big_p(f(f(X1!1))) | (~big_p(f(X1!1)))),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[11, 8])).
% 0.21/0.38 tff(13,assumption,(~((~big_p(a)) | big_p(f(f(X!0))) | (~(big_p(f(X!0)) | (~big_p(X!0)))))), introduced(assumption)).
% 0.21/0.38 tff(14,plain,
% 0.21/0.38 (((~big_p(a)) | big_p(f(f(X!0))) | (~(big_p(f(X!0)) | (~big_p(X!0))))) | (big_p(f(X!0)) | (~big_p(X!0)))),
% 0.21/0.38 inference(tautology,[status(thm)],[])).
% 0.21/0.38 tff(15,plain,
% 0.21/0.38 (big_p(f(X!0)) | (~big_p(X!0))),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.21/0.38 tff(16,plain,
% 0.21/0.38 (((~big_p(a)) | big_p(f(f(X!0))) | (~(big_p(f(X!0)) | (~big_p(X!0))))) | (~big_p(f(f(X!0))))),
% 0.21/0.38 inference(tautology,[status(thm)],[])).
% 0.21/0.38 tff(17,plain,
% 0.21/0.38 (~big_p(f(f(X!0)))),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[16, 13])).
% 0.21/0.38 tff(18,plain,
% 0.21/0.38 (((~big_p(a)) | big_p(f(f(X!0))) | (~(big_p(f(X!0)) | (~big_p(X!0))))) | big_p(a)),
% 0.21/0.38 inference(tautology,[status(thm)],[])).
% 0.21/0.38 tff(19,plain,
% 0.21/0.38 (big_p(a)),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[18, 13])).
% 0.21/0.38 tff(20,assumption,(big_p(f(X!0)) | (~big_p(X!0))), introduced(assumption)).
% 0.21/0.38 tff(21,assumption,(~big_p(f(f(X!0)))), introduced(assumption)).
% 0.21/0.38 tff(22,assumption,(big_p(a)), introduced(assumption)).
% 0.21/0.38 tff(23,assumption,(![X: $i] : ((~big_p(a)) | big_p(f(f(X))) | (~(big_p(f(X)) | (~big_p(X)))))), introduced(assumption)).
% 0.21/0.38 tff(24,plain,
% 0.21/0.38 (((~![X: $i] : ((~big_p(a)) | big_p(f(f(X))) | (~(big_p(f(X)) | (~big_p(X)))))) | ((~big_p(a)) | big_p(f(f(X!0))) | (~(big_p(f(X!0)) | (~big_p(X!0)))))) <=> ((~![X: $i] : ((~big_p(a)) | big_p(f(f(X))) | (~(big_p(f(X)) | (~big_p(X)))))) | (~big_p(a)) | big_p(f(f(X!0))) | (~(big_p(f(X!0)) | (~big_p(X!0)))))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(25,plain,
% 0.21/0.38 ((~![X: $i] : ((~big_p(a)) | big_p(f(f(X))) | (~(big_p(f(X)) | (~big_p(X)))))) | ((~big_p(a)) | big_p(f(f(X!0))) | (~(big_p(f(X!0)) | (~big_p(X!0)))))),
% 0.21/0.38 inference(quant_inst,[status(thm)],[])).
% 0.21/0.38 tff(26,plain,
% 0.21/0.38 ((~![X: $i] : ((~big_p(a)) | big_p(f(f(X))) | (~(big_p(f(X)) | (~big_p(X)))))) | (~big_p(a)) | big_p(f(f(X!0))) | (~(big_p(f(X!0)) | (~big_p(X!0))))),
% 0.21/0.38 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.21/0.38 tff(27,plain,
% 0.21/0.38 ($false),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[26, 23, 22, 21, 20])).
% 0.21/0.38 tff(28,plain,((~![X: $i] : ((~big_p(a)) | big_p(f(f(X))) | (~(big_p(f(X)) | (~big_p(X)))))) | (~big_p(a)) | big_p(f(f(X!0))) | (~(big_p(f(X!0)) | (~big_p(X!0))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.38 tff(29,plain,
% 0.21/0.38 (~![X: $i] : ((~big_p(a)) | big_p(f(f(X))) | (~(big_p(f(X)) | (~big_p(X)))))),
% 0.21/0.38 inference(unit_resolution,[status(thm)],[28, 19, 17, 15])).
% 0.21/0.38 tff(30,plain,
% 0.21/0.38 ((![X: $i] : ((~big_p(a)) | big_p(f(f(X))) | (~(big_p(f(X)) | (~big_p(X))))) | ![X1: $i] : (~((~((~big_p(a)) | big_p(f(f(X1))) | big_p(X1))) | (~((~big_p(a)) | big_p(f(f(X1))) | (~big_p(f(X1)))))))) <=> (![X: $i] : ((~big_p(a)) | big_p(f(f(X))) | (~(big_p(f(X)) | (~big_p(X))))) | ![X1: $i] : (~((~((~big_p(a)) | big_p(f(f(X1))) | big_p(X1))) | (~((~big_p(a)) | big_p(f(f(X1))) | (~big_p(f(X1))))))))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(31,plain,
% 0.21/0.38 ((![X: $i] : (big_p(f(f(X))) | (~(big_p(a) & (big_p(f(X)) | (~big_p(X)))))) | ![X1: $i] : (((~big_p(a)) | big_p(f(f(X1))) | big_p(X1)) & ((~big_p(a)) | big_p(f(f(X1))) | (~big_p(f(X1)))))) <=> (![X: $i] : ((~big_p(a)) | big_p(f(f(X))) | (~(big_p(f(X)) | (~big_p(X))))) | ![X1: $i] : (~((~((~big_p(a)) | big_p(f(f(X1))) | big_p(X1))) | (~((~big_p(a)) | big_p(f(f(X1))) | (~big_p(f(X1))))))))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(32,plain,
% 0.21/0.38 (((![X: $i] : (big_p(f(f(X))) | (~(big_p(a) & (big_p(f(X)) | (~big_p(X)))))) | ![X1: $i] : (((~big_p(a)) | big_p(f(f(X1))) | big_p(X1)) & ((~big_p(a)) | big_p(f(f(X1))) | (~big_p(f(X1)))))) & ((~(big_p(f(f(X!0))) | (~(big_p(a) & (big_p(f(X!0)) | (~big_p(X!0))))))) | (~(((~big_p(a)) | big_p(f(f(X1!1))) | big_p(X1!1)) & ((~big_p(a)) | big_p(f(f(X1!1))) | (~big_p(f(X1!1)))))))) <=> ((![X: $i] : (big_p(f(f(X))) | (~(big_p(a) & (big_p(f(X)) | (~big_p(X)))))) | ![X1: $i] : (((~big_p(a)) | big_p(f(f(X1))) | big_p(X1)) & ((~big_p(a)) | big_p(f(f(X1))) | (~big_p(f(X1)))))) & ((~(big_p(f(f(X!0))) | (~(big_p(a) & (big_p(f(X!0)) | (~big_p(X!0))))))) | (~(((~big_p(a)) | big_p(f(f(X1!1))) | big_p(X1!1)) & ((~big_p(a)) | big_p(f(f(X1!1))) | (~big_p(f(X1!1))))))))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(33,plain,
% 0.21/0.38 ((~(![X: $i] : (big_p(f(f(X))) | (~(big_p(a) & (big_p(f(X)) | (~big_p(X)))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(f(f(X1))) | big_p(X1)) & ((~big_p(a)) | big_p(f(f(X1))) | (~big_p(f(X1))))))) <=> (~(![X: $i] : (big_p(f(f(X))) | (~(big_p(a) & (big_p(f(X)) | (~big_p(X)))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(f(f(X1))) | big_p(X1)) & ((~big_p(a)) | big_p(f(f(X1))) | (~big_p(f(X1)))))))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(34,plain,
% 0.21/0.38 ((![X: $i] : (big_p(f(f(X))) | (~(big_p(a) & (big_p(f(X)) | (~big_p(X)))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(f(f(X1))) | big_p(X1)) & ((~big_p(a)) | big_p(f(f(X1))) | (~big_p(f(X1)))))) <=> (![X: $i] : (big_p(f(f(X))) | (~(big_p(a) & (big_p(f(X)) | (~big_p(X)))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(f(f(X1))) | big_p(X1)) & ((~big_p(a)) | big_p(f(f(X1))) | (~big_p(f(X1))))))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(35,plain,
% 0.21/0.38 ((~(![X: $i] : (big_p(f(f(X))) | (~(big_p(a) & (big_p(f(X)) | (~big_p(X)))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(f(f(X1))) | big_p(X1)) & ((~big_p(a)) | big_p(f(f(X1))) | (~big_p(f(X1))))))) <=> (~(![X: $i] : (big_p(f(f(X))) | (~(big_p(a) & (big_p(f(X)) | (~big_p(X)))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(f(f(X1))) | big_p(X1)) & ((~big_p(a)) | big_p(f(f(X1))) | (~big_p(f(X1)))))))),
% 0.21/0.38 inference(monotonicity,[status(thm)],[34])).
% 0.21/0.38 tff(36,plain,
% 0.21/0.38 ((~(![X: $i] : (big_p(f(f(X))) | (~(big_p(a) & (big_p(f(X)) | (~big_p(X)))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(f(f(X1))) | big_p(X1)) & ((~big_p(a)) | big_p(f(f(X1))) | (~big_p(f(X1))))))) <=> (~(![X: $i] : (big_p(f(f(X))) | (~(big_p(a) & (big_p(f(X)) | (~big_p(X)))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(f(f(X1))) | big_p(X1)) & ((~big_p(a)) | big_p(f(f(X1))) | (~big_p(f(X1)))))))),
% 0.21/0.38 inference(transitivity,[status(thm)],[35, 33])).
% 0.21/0.38 tff(37,plain,
% 0.21/0.38 ((![X: $i] : ((big_p(a) & (big_p(X) => big_p(f(X)))) => big_p(f(f(X)))) <=> ![X1: $i] : ((((~big_p(a)) | big_p(X1)) | big_p(f(f(X1)))) & (((~big_p(a)) | (~big_p(f(X1)))) | big_p(f(f(X1)))))) <=> (![X: $i] : (big_p(f(f(X))) | (~(big_p(a) & (big_p(f(X)) | (~big_p(X)))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(f(f(X1))) | big_p(X1)) & ((~big_p(a)) | big_p(f(f(X1))) | (~big_p(f(X1))))))),
% 0.21/0.38 inference(rewrite,[status(thm)],[])).
% 0.21/0.38 tff(38,plain,
% 0.21/0.38 ((~(![X: $i] : ((big_p(a) & (big_p(X) => big_p(f(X)))) => big_p(f(f(X)))) <=> ![X1: $i] : ((((~big_p(a)) | big_p(X1)) | big_p(f(f(X1)))) & (((~big_p(a)) | (~big_p(f(X1)))) | big_p(f(f(X1))))))) <=> (~(![X: $i] : (big_p(f(f(X))) | (~(big_p(a) & (big_p(f(X)) | (~big_p(X)))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(f(f(X1))) | big_p(X1)) & ((~big_p(a)) | big_p(f(f(X1))) | (~big_p(f(X1)))))))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[37])).
% 0.21/0.39 tff(39,plain,
% 0.21/0.39 ((~(![X: $i] : ((big_p(a) & (big_p(X) => big_p(f(X)))) => big_p(f(f(X)))) <=> ![X1: $i] : ((((~big_p(a)) | big_p(X1)) | big_p(f(f(X1)))) & (((~big_p(a)) | (~big_p(f(X1)))) | big_p(f(f(X1))))))) <=> (~(![X: $i] : (big_p(f(f(X))) | (~(big_p(a) & (big_p(f(X)) | (~big_p(X)))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(f(f(X1))) | big_p(X1)) & ((~big_p(a)) | big_p(f(f(X1))) | (~big_p(f(X1)))))))),
% 0.21/0.39 inference(transitivity,[status(thm)],[38, 33])).
% 0.21/0.39 tff(40,axiom,(~(![X: $i] : ((big_p(a) & (big_p(X) => big_p(f(X)))) => big_p(f(f(X)))) <=> ![X1: $i] : ((((~big_p(a)) | big_p(X1)) | big_p(f(f(X1)))) & (((~big_p(a)) | (~big_p(f(X1)))) | big_p(f(f(X1))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel62')).
% 0.21/0.39 tff(41,plain,
% 0.21/0.39 (~(![X: $i] : (big_p(f(f(X))) | (~(big_p(a) & (big_p(f(X)) | (~big_p(X)))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(f(f(X1))) | big_p(X1)) & ((~big_p(a)) | big_p(f(f(X1))) | (~big_p(f(X1))))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.21/0.39 tff(42,plain,
% 0.21/0.39 (~(![X: $i] : (big_p(f(f(X))) | (~(big_p(a) & (big_p(f(X)) | (~big_p(X)))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(f(f(X1))) | big_p(X1)) & ((~big_p(a)) | big_p(f(f(X1))) | (~big_p(f(X1))))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[41, 36])).
% 0.21/0.39 tff(43,plain,
% 0.21/0.39 (~(![X: $i] : (big_p(f(f(X))) | (~(big_p(a) & (big_p(f(X)) | (~big_p(X)))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(f(f(X1))) | big_p(X1)) & ((~big_p(a)) | big_p(f(f(X1))) | (~big_p(f(X1))))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[42, 33])).
% 0.21/0.39 tff(44,plain,
% 0.21/0.39 (~(![X: $i] : (big_p(f(f(X))) | (~(big_p(a) & (big_p(f(X)) | (~big_p(X)))))) <=> ![X1: $i] : (((~big_p(a)) | big_p(f(f(X1))) | big_p(X1)) & ((~big_p(a)) | big_p(f(f(X1))) | (~big_p(f(X1))))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.21/0.39 unexpected number of arguments: (let ((a!1 (proof-bind (lambda ((X $i))
% 0.21/0.39 (let ((a!1 (and (big_p a)
% 0.21/0.39 (or (big_p (f X)) (not (big_p X))))))
% 0.21/0.39 (let ((a!2 (or (big_p (f (f X))) (not a!1))))
% 0.21/0.39 (refl (~ a!2 a!2)))))))
% 0.21/0.39 (a!2 (forall ((X $i))
% 0.21/0.39 (let ((a!1 (and (big_p a) (or (big_p (f X)) (not (big_p X))))))
% 0.21/0.39 (or (big_p (f (f X))) (not a!1)))))
% 0.21/0.39 (a!3 (and (big_p a) (or (big_p (f X!0)) (not (big_p X!0)))))
% 0.21/0.39 (a!5 (lambda ((X1 $i))
% 0.21/0.39 (let ((a!1 (or (not (big_p a)) (big_p (f (f X1))) (big_p X1)))
% 0.21/0.39 (a!2 (or (not (big_p a))
% 0.21/0.39 (big_p (f (f X1)))
% 0.21/0.39 (not (big_p (f X1))))))
% 0.21/0.39 (refl (~ (and a!1 a!2) (and a!1 a!2))))))
% 0.21/0.39 (a!6 (forall ((X1 $i))
% 0.21/0.39 (let ((a!1 (or (not (big_p a)) (big_p (f (f X1))) (big_p X1)))
% 0.21/0.39 (a!2 (or (not (big_p a))
% 0.21/0.39 (big_p (f (f X1)))
% 0.21/0.39 (not (big_p (f X1))))))
% 0.21/0.39 (and a!1 a!2))))
% 0.21/0.39 (a!7 (or (not (big_p a)) (big_p (f (f X1!1))) (big_p X1!1)))
% 0.21/0.39 (a!8 (or (not (big_p a)) (big_p (f (f X1!1))) (not (big_p (f X1!1))))))
% 0.21/0.39 (let ((a!4 (or (big_p (f (f X!0))) (not a!3)))
% 0.21/0.39 (a!9 (sk (~ (not a!6) (not (and a!7 a!8))))))
% 0.21/0.39 (let ((a!10 (and (or a!2 a!6) (or (not a!4) (not (and a!7 a!8))))))
% 0.21/0.39 (nnf-neg (nnf-pos a!1 (~ a!2 a!2))
% 0.21/0.39 (sk (~ (not a!2) (not a!4)))
% 0.21/0.39 (nnf-pos (proof-bind a!5) (~ a!6 a!6))
% 0.21/0.39 a!9
% 0.21/0.39 (~ (not (= a!2 a!6)) a!10)))))
% 0.21/0.39 Proof display could not be completed: unexpected number of arguments
% 0.21/0.39 % E exiting
%------------------------------------------------------------------------------