%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN078+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 05:38:11 AM UTC 2025
% Result : Theorem 0.11s 0.37s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN078+1 : TPTP v9.0.0. Released v2.0.0.
% 0.06/0.12 % 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 12:31:35 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.37 % SZS status Theorem
% 0.11/0.37 % SZS output start Proof
% 0.11/0.37 tff(big_p_type, type, (
% 0.11/0.37 big_p: $i > $o)).
% 0.11/0.37 tff(tptp_fun_U_2_type, type, (
% 0.11/0.37 tptp_fun_U_2: $i)).
% 0.11/0.37 tff(f_type, type, (
% 0.11/0.37 f: $i > $i)).
% 0.11/0.37 tff(tptp_fun_Y_1_type, type, (
% 0.11/0.37 tptp_fun_Y_1: $i)).
% 0.11/0.37 tff(tptp_fun_X_0_type, type, (
% 0.11/0.37 tptp_fun_X_0: $i)).
% 0.11/0.37 tff(1,assumption,(~(big_p(X!0) | (~big_p(Y!1)) | (~(X!0 = f(Y!1))))), introduced(assumption)).
% 0.11/0.37 tff(2,plain,
% 0.11/0.37 ((big_p(X!0) | (~big_p(Y!1)) | (~(X!0 = f(Y!1)))) | (X!0 = f(Y!1))),
% 0.11/0.37 inference(tautology,[status(thm)],[])).
% 0.11/0.37 tff(3,plain,
% 0.11/0.37 (X!0 = f(Y!1)),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.11/0.37 tff(4,plain,
% 0.11/0.37 ((big_p(X!0) | (~big_p(Y!1)) | (~(X!0 = f(Y!1)))) | (~big_p(X!0))),
% 0.11/0.37 inference(tautology,[status(thm)],[])).
% 0.11/0.37 tff(5,plain,
% 0.11/0.37 (~big_p(X!0)),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[4, 1])).
% 0.11/0.37 tff(6,assumption,(X!0 = f(Y!1)), introduced(assumption)).
% 0.11/0.37 tff(7,plain,
% 0.11/0.37 (f(Y!1) = X!0),
% 0.11/0.37 inference(symmetry,[status(thm)],[6])).
% 0.11/0.37 tff(8,plain,
% 0.11/0.37 (big_p(f(Y!1)) <=> big_p(X!0)),
% 0.11/0.37 inference(monotonicity,[status(thm)],[7])).
% 0.11/0.37 tff(9,plain,
% 0.11/0.37 (big_p(X!0) <=> big_p(f(Y!1))),
% 0.11/0.37 inference(symmetry,[status(thm)],[8])).
% 0.11/0.37 tff(10,plain,
% 0.11/0.37 ((~big_p(X!0)) <=> (~big_p(f(Y!1)))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[9])).
% 0.11/0.37 tff(11,assumption,(~big_p(X!0)), introduced(assumption)).
% 0.11/0.37 tff(12,plain,
% 0.11/0.37 (~big_p(f(Y!1))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.11/0.37 tff(13,assumption,(big_p(f(Y!1))), introduced(assumption)).
% 0.11/0.37 tff(14,plain,
% 0.11/0.37 ($false),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.11/0.37 tff(15,plain,((~big_p(f(Y!1))) | big_p(X!0) | (~(X!0 = f(Y!1)))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.37 tff(16,plain,
% 0.11/0.37 (~big_p(f(Y!1))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[15, 5, 3])).
% 0.11/0.37 tff(17,plain,
% 0.11/0.37 ((big_p(X!0) | (~big_p(Y!1)) | (~(X!0 = f(Y!1)))) | big_p(Y!1)),
% 0.11/0.37 inference(tautology,[status(thm)],[])).
% 0.11/0.37 tff(18,plain,
% 0.11/0.37 (big_p(Y!1)),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[17, 1])).
% 0.11/0.37 tff(19,assumption,(~big_p(f(Y!1))), introduced(assumption)).
% 0.11/0.37 tff(20,assumption,(big_p(Y!1)), introduced(assumption)).
% 0.11/0.37 tff(21,assumption,(![U: $i] : (big_p(f(U)) | (~big_p(U)))), introduced(assumption)).
% 0.11/0.37 tff(22,plain,
% 0.11/0.37 (((~![U: $i] : (big_p(f(U)) | (~big_p(U)))) | (big_p(f(Y!1)) | (~big_p(Y!1)))) <=> ((~![U: $i] : (big_p(f(U)) | (~big_p(U)))) | big_p(f(Y!1)) | (~big_p(Y!1)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(23,plain,
% 0.11/0.37 ((~![U: $i] : (big_p(f(U)) | (~big_p(U)))) | (big_p(f(Y!1)) | (~big_p(Y!1)))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(24,plain,
% 0.11/0.37 ((~![U: $i] : (big_p(f(U)) | (~big_p(U)))) | big_p(f(Y!1)) | (~big_p(Y!1))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.11/0.37 tff(25,plain,
% 0.11/0.37 ($false),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[24, 21, 20, 19])).
% 0.11/0.37 tff(26,plain,((~![U: $i] : (big_p(f(U)) | (~big_p(U)))) | (~big_p(Y!1)) | big_p(f(Y!1))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.37 tff(27,plain,
% 0.11/0.37 (~![U: $i] : (big_p(f(U)) | (~big_p(U)))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[26, 18, 16])).
% 0.11/0.37 tff(28,plain,
% 0.11/0.37 ((![U: $i] : (big_p(f(U)) | (~big_p(U))) | ![X: $i] : (big_p(X) | ![Y: $i] : ((~big_p(Y)) | (~(X = f(Y)))))) <=> (![U: $i] : (big_p(f(U)) | (~big_p(U))) | ![X: $i] : (big_p(X) | ![Y: $i] : ((~big_p(Y)) | (~(X = f(Y))))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(29,plain,
% 0.11/0.37 ((![U: $i] : (big_p(f(U)) | (~big_p(U))) | ![X: $i] : (big_p(X) | ![Y: $i] : (~(big_p(Y) & (X = f(Y)))))) <=> (![U: $i] : (big_p(f(U)) | (~big_p(U))) | ![X: $i] : (big_p(X) | ![Y: $i] : ((~big_p(Y)) | (~(X = f(Y))))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(30,plain,
% 0.11/0.37 (((![X: $i] : (big_p(X) | ![Y: $i] : (~(big_p(Y) & (X = f(Y))))) | ![U: $i] : (big_p(f(U)) | (~big_p(U)))) & (((~big_p(X!0)) & (big_p(Y!1) & (X!0 = f(Y!1)))) | (~(big_p(f(U!2)) | (~big_p(U!2)))))) <=> ((![U: $i] : (big_p(f(U)) | (~big_p(U))) | ![X: $i] : (big_p(X) | ![Y: $i] : (~(big_p(Y) & (X = f(Y)))))) & ((~(big_p(f(U!2)) | (~big_p(U!2)))) | ((~big_p(X!0)) & big_p(Y!1) & (X!0 = f(Y!1)))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(31,plain,
% 0.11/0.37 ((~(![X: $i] : (big_p(X) | (~?[Y: $i] : (big_p(Y) & (X = f(Y))))) <=> ![U: $i] : (big_p(f(U)) | (~big_p(U))))) <=> (~(![X: $i] : (big_p(X) | (~?[Y: $i] : (big_p(Y) & (X = f(Y))))) <=> ![U: $i] : (big_p(f(U)) | (~big_p(U)))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(32,plain,
% 0.11/0.38 ((![X: $i] : (big_p(X) | (~?[Y: $i] : (big_p(Y) & (X = f(Y))))) <=> ![U: $i] : (big_p(f(U)) | (~big_p(U)))) <=> (![X: $i] : (big_p(X) | (~?[Y: $i] : (big_p(Y) & (X = f(Y))))) <=> ![U: $i] : (big_p(f(U)) | (~big_p(U))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(33,plain,
% 0.11/0.38 ((~(![X: $i] : (big_p(X) | (~?[Y: $i] : (big_p(Y) & (X = f(Y))))) <=> ![U: $i] : (big_p(f(U)) | (~big_p(U))))) <=> (~(![X: $i] : (big_p(X) | (~?[Y: $i] : (big_p(Y) & (X = f(Y))))) <=> ![U: $i] : (big_p(f(U)) | (~big_p(U)))))),
% 0.11/0.38 inference(monotonicity,[status(thm)],[32])).
% 0.11/0.38 tff(34,plain,
% 0.11/0.38 ((~(![X: $i] : (big_p(X) | (~?[Y: $i] : (big_p(Y) & (X = f(Y))))) <=> ![U: $i] : (big_p(f(U)) | (~big_p(U))))) <=> (~(![X: $i] : (big_p(X) | (~?[Y: $i] : (big_p(Y) & (X = f(Y))))) <=> ![U: $i] : (big_p(f(U)) | (~big_p(U)))))),
% 0.11/0.38 inference(transitivity,[status(thm)],[33, 31])).
% 0.11/0.38 tff(35,plain,
% 0.11/0.38 ((![X: $i] : (?[Y: $i] : (big_p(Y) & (X = f(Y))) => big_p(X)) <=> ![U: $i] : (big_p(U) => big_p(f(U)))) <=> (![X: $i] : (big_p(X) | (~?[Y: $i] : (big_p(Y) & (X = f(Y))))) <=> ![U: $i] : (big_p(f(U)) | (~big_p(U))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(36,plain,
% 0.11/0.38 ((~(![X: $i] : (?[Y: $i] : (big_p(Y) & (X = f(Y))) => big_p(X)) <=> ![U: $i] : (big_p(U) => big_p(f(U))))) <=> (~(![X: $i] : (big_p(X) | (~?[Y: $i] : (big_p(Y) & (X = f(Y))))) <=> ![U: $i] : (big_p(f(U)) | (~big_p(U)))))),
% 0.11/0.38 inference(monotonicity,[status(thm)],[35])).
% 0.11/0.38 tff(37,plain,
% 0.11/0.38 ((~(![X: $i] : (?[Y: $i] : (big_p(Y) & (X = f(Y))) => big_p(X)) <=> ![U: $i] : (big_p(U) => big_p(f(U))))) <=> (~(![X: $i] : (big_p(X) | (~?[Y: $i] : (big_p(Y) & (X = f(Y))))) <=> ![U: $i] : (big_p(f(U)) | (~big_p(U)))))),
% 0.11/0.38 inference(transitivity,[status(thm)],[36, 31])).
% 0.11/0.38 tff(38,axiom,(~(![X: $i] : (?[Y: $i] : (big_p(Y) & (X = f(Y))) => big_p(X)) <=> ![U: $i] : (big_p(U) => big_p(f(U))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel56')).
% 0.11/0.38 tff(39,plain,
% 0.11/0.38 (~(![X: $i] : (big_p(X) | (~?[Y: $i] : (big_p(Y) & (X = f(Y))))) <=> ![U: $i] : (big_p(f(U)) | (~big_p(U))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.11/0.38 tff(40,plain,
% 0.11/0.38 (~(![X: $i] : (big_p(X) | (~?[Y: $i] : (big_p(Y) & (X = f(Y))))) <=> ![U: $i] : (big_p(f(U)) | (~big_p(U))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[39, 34])).
% 0.11/0.38 tff(41,plain,
% 0.11/0.38 (~(![X: $i] : (big_p(X) | (~?[Y: $i] : (big_p(Y) & (X = f(Y))))) <=> ![U: $i] : (big_p(f(U)) | (~big_p(U))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[40, 31])).
% 0.11/0.38 tff(42,plain,
% 0.11/0.38 (~(![X: $i] : (big_p(X) | (~?[Y: $i] : (big_p(Y) & (X = f(Y))))) <=> ![U: $i] : (big_p(f(U)) | (~big_p(U))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.11/0.38 unexpected number of arguments: (let ((a!1 (lambda ((X $i))
% 0.11/0.38 (let ((a!1 (proof-bind (lambda ((Y $i))
% 0.11/0.38 (let ((a!1 (not (and (big_p Y)
% 0.11/0.38 (= X (f Y))))))
% 0.11/0.38 (refl (~ a!1 a!1))))))
% 0.11/0.38 (a!2 (exists ((Y $i)) (and (big_p Y) (= X (f Y)))))
% 0.11/0.38 (a!3 (forall ((Y $i)) (not (and (big_p Y) (= X (f Y)))))))
% 0.11/0.38 (monotonicity (refl (~ (big_p X) (big_p X)))
% 0.11/0.38 (nnf-neg a!1 (~ (not a!2) a!3))
% 0.11/0.38 (~ (or (big_p X) (not a!2)) (or (big_p X) a!3))))))
% 0.11/0.38 (a!2 (forall ((X $i))
% 0.11/0.38 (let ((a!1 (exists ((Y $i)) (and (big_p Y) (= X (f Y))))))
% 0.11/0.38 (or (big_p X) (not a!1)))))
% 0.11/0.38 (a!3 (forall ((X $i))
% 0.11/0.38 (let ((a!1 (forall ((Y $i)) (not (and (big_p Y) (= X (f Y)))))))
% 0.11/0.38 (or (big_p X) a!1))))
% 0.11/0.38 (a!4 (exists ((Y $i)) (and (big_p Y) (= X!0 (f Y)))))
% 0.11/0.38 (a!6 (refl (~ (not (big_p X!0)) (not (big_p X!0)))))
% 0.11/0.38 (a!9 (and (not (big_p X!0)) (and (big_p Y!1) (= X!0 (f Y!1)))))
% 0.11/0.38 (a!12 (forall ((U $i)) (or (big_p (f U)) (not (big_p U)))))
% 0.11/0.38 (a!14 (not (or (big_p (f U!2)) (not (big_p U!2))))))
% 0.11/0.38 (let ((a!5 (~ (not a!2) (not (or (big_p X!0) (not a!4)))))
% 0.11/0.38 (a!7 (~ a!4 (and (big_p Y!1) (= X!0 (f Y!1)))))
% 0.11/0.38 (a!8 (~ (not (not a!4)) (and (big_p Y!1) (= X!0 (f Y!1)))))
% 0.11/0.38 (a!10 (~ (not (or (big_p X!0) (not a!4))) a!9))
% 0.11/0.38 (a!13 (nnf-pos (proof-bind (lambda ((U $i))
% 0.11/0.38 (let ((a!1 (~ (or (big_p (f U))
% 0.11/0.38 (not (big_p U)))
% 0.11/0.38 (or (big_p (f U))
% 0.11/0.38 (not (big_p U))))))
% 0.11/0.38 (refl a!1))))
% 0.11/0.38 (~ a!12 a!12))))
% 0.11/0.38 (let ((a!11 (trans (sk a!5)
% 0.11/0.38 (nnf-neg a!6 (nnf-neg (sk a!7) a!8) a!10)
% 0.11/0.38 (~ (not a!2) a!9))))
% 0.11/0.38 (nnf-neg (nnf-pos (proof-bind a!1) (~ a!2 a!3))
% 0.11/0.38 a!11
% 0.11/0.38 a!13
% 0.11/0.38 (sk (~ (not a!12) a!14))
% 0.11/0.38 (~ (not (= a!2 a!12)) (and (or a!3 a!12) (or a!9 a!14)))))))
% 0.11/0.38 Proof display could not be completed: unexpected number of arguments
% 0.11/0.38 % E exiting
%------------------------------------------------------------------------------