%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN317+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:38:44 AM UTC 2025
% Result : Theorem 0.11s 0.36s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SYN317+1 : TPTP v9.0.0. Released v2.0.0.
% 0.10/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n005.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 12:30:20 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.36 % SZS status Theorem
% 0.11/0.36 % SZS output start Proof
% 0.11/0.36 tff(big_f_type, type, (
% 0.11/0.36 big_f: $i > $o)).
% 0.11/0.36 tff(tptp_fun_X_2_type, type, (
% 0.11/0.36 tptp_fun_X_2: $i)).
% 0.11/0.36 tff(big_g_type, type, (
% 0.11/0.36 big_g: $i > $o)).
% 0.11/0.36 tff(tptp_fun_X_0_type, type, (
% 0.11/0.36 tptp_fun_X_0: $i)).
% 0.11/0.36 tff(tptp_fun_Y_1_type, type, (
% 0.11/0.36 tptp_fun_Y_1: $i)).
% 0.11/0.36 tff(1,assumption,(~big_g(X!0)), introduced(assumption)).
% 0.11/0.36 tff(2,assumption,(![X: $i, Y: $i] : (~(big_g(Y) | (~big_f(X))))), introduced(assumption)).
% 0.11/0.36 tff(3,plain,
% 0.11/0.36 ((~![X: $i, Y: $i] : (~(big_g(Y) | (~big_f(X))))) | (~(big_g(X!2) | (~big_f(X!2))))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(4,plain,
% 0.11/0.36 (~(big_g(X!2) | (~big_f(X!2)))),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[3, 2])).
% 0.11/0.36 tff(5,plain,
% 0.11/0.36 ((big_g(X!2) | (~big_f(X!2))) | big_f(X!2)),
% 0.11/0.36 inference(tautology,[status(thm)],[])).
% 0.11/0.36 tff(6,plain,
% 0.11/0.36 (big_f(X!2)),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[5, 4])).
% 0.11/0.36 tff(7,assumption,(big_g(X!2) | (~big_f(X!0))), introduced(assumption)).
% 0.11/0.36 tff(8,plain,
% 0.11/0.36 ((~![X: $i, Y: $i] : (~(big_g(Y) | (~big_f(X))))) | (~(big_g(X!2) | (~big_f(X!0))))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(9,plain,
% 0.11/0.36 ($false),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[8, 2, 7])).
% 0.11/0.36 tff(10,plain,((~(big_g(X!2) | (~big_f(X!0)))) | (~![X: $i, Y: $i] : (~(big_g(Y) | (~big_f(X)))))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.36 tff(11,plain,
% 0.11/0.36 (~(big_g(X!2) | (~big_f(X!0)))),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[10, 2])).
% 0.11/0.36 tff(12,plain,
% 0.11/0.36 ((big_g(X!2) | (~big_f(X!0))) | big_f(X!0)),
% 0.11/0.36 inference(tautology,[status(thm)],[])).
% 0.11/0.36 tff(13,plain,
% 0.11/0.36 (big_f(X!0)),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.11/0.36 tff(14,plain,
% 0.11/0.36 ((((big_g(X!0) | (~big_f(X!0))) | (big_g(Y!1) | (~big_f(X!2)))) & (![X: $i] : (~(big_g(X) | (~big_f(X)))) | ![X: $i, Y: $i] : (~(big_g(Y) | (~big_f(X)))))) <=> ((big_g(X!0) | (~big_f(X!0)) | big_g(Y!1) | (~big_f(X!2))) & (![X: $i] : (~(big_g(X) | (~big_f(X)))) | ![X: $i, Y: $i] : (~(big_g(Y) | (~big_f(X))))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(15,plain,
% 0.11/0.36 ((~(?[X: $i] : (big_g(X) | (~big_f(X))) <=> ?[X: $i, Y: $i] : (big_g(Y) | (~big_f(X))))) <=> (~(?[X: $i] : (big_g(X) | (~big_f(X))) <=> ?[X: $i, Y: $i] : (big_g(Y) | (~big_f(X)))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(16,plain,
% 0.11/0.36 ((?[X: $i] : (big_g(X) | (~big_f(X))) <=> ?[X: $i, Y: $i] : (big_g(Y) | (~big_f(X)))) <=> (?[X: $i] : (big_g(X) | (~big_f(X))) <=> ?[X: $i, Y: $i] : (big_g(Y) | (~big_f(X))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(17,plain,
% 0.11/0.36 ((~(?[X: $i] : (big_g(X) | (~big_f(X))) <=> ?[X: $i, Y: $i] : (big_g(Y) | (~big_f(X))))) <=> (~(?[X: $i] : (big_g(X) | (~big_f(X))) <=> ?[X: $i, Y: $i] : (big_g(Y) | (~big_f(X)))))),
% 0.11/0.36 inference(monotonicity,[status(thm)],[16])).
% 0.11/0.36 tff(18,plain,
% 0.11/0.36 ((~(?[X: $i] : (big_g(X) | (~big_f(X))) <=> ?[X: $i, Y: $i] : (big_g(Y) | (~big_f(X))))) <=> (~(?[X: $i] : (big_g(X) | (~big_f(X))) <=> ?[X: $i, Y: $i] : (big_g(Y) | (~big_f(X)))))),
% 0.11/0.36 inference(transitivity,[status(thm)],[17, 15])).
% 0.11/0.36 tff(19,plain,
% 0.11/0.36 ((?[X: $i] : (big_f(X) => big_g(X)) <=> ?[X: $i, Y: $i] : (big_f(X) => big_g(Y))) <=> (?[X: $i] : (big_g(X) | (~big_f(X))) <=> ?[X: $i, Y: $i] : (big_g(Y) | (~big_f(X))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(20,plain,
% 0.11/0.36 ((~(?[X: $i] : (big_f(X) => big_g(X)) <=> ?[X: $i, Y: $i] : (big_f(X) => big_g(Y)))) <=> (~(?[X: $i] : (big_g(X) | (~big_f(X))) <=> ?[X: $i, Y: $i] : (big_g(Y) | (~big_f(X)))))),
% 0.11/0.36 inference(monotonicity,[status(thm)],[19])).
% 0.11/0.36 tff(21,plain,
% 0.11/0.36 ((~(?[X: $i] : (big_f(X) => big_g(X)) <=> ?[X: $i, Y: $i] : (big_f(X) => big_g(Y)))) <=> (~(?[X: $i] : (big_g(X) | (~big_f(X))) <=> ?[X: $i, Y: $i] : (big_g(Y) | (~big_f(X)))))),
% 0.11/0.36 inference(transitivity,[status(thm)],[20, 15])).
% 0.11/0.36 tff(22,axiom,(~(?[X: $i] : (big_f(X) => big_g(X)) <=> ?[X: $i, Y: $i] : (big_f(X) => big_g(Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','church_46_2_3')).
% 0.11/0.36 tff(23,plain,
% 0.11/0.36 (~(?[X: $i] : (big_g(X) | (~big_f(X))) <=> ?[X: $i, Y: $i] : (big_g(Y) | (~big_f(X))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.11/0.36 tff(24,plain,
% 0.11/0.36 (~(?[X: $i] : (big_g(X) | (~big_f(X))) <=> ?[X: $i, Y: $i] : (big_g(Y) | (~big_f(X))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[23, 18])).
% 0.11/0.36 tff(25,plain,
% 0.11/0.36 (~(?[X: $i] : (big_g(X) | (~big_f(X))) <=> ?[X: $i, Y: $i] : (big_g(Y) | (~big_f(X))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[24, 15])).
% 0.11/0.36 tff(26,plain,
% 0.11/0.36 (~(?[X: $i] : (big_g(X) | (~big_f(X))) <=> ?[X: $i, Y: $i] : (big_g(Y) | (~big_f(X))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.11/0.36 unexpected number of arguments: (let ((a!1 (exists ((X $i)) (or (big_g X) (not (big_f X)))))
% 0.11/0.36 (a!3 (proof-bind (lambda ((X $i))
% 0.11/0.36 (let ((a!1 (not (or (big_g X) (not (big_f X))))))
% 0.11/0.36 (refl (~ a!1 a!1))))))
% 0.11/0.36 (a!4 (forall ((X $i)) (not (or (big_g X) (not (big_f X))))))
% 0.11/0.36 (a!5 (exists ((X $i) (Y $i)) (or (big_g Y) (not (big_f X)))))
% 0.11/0.36 (a!7 (proof-bind (lambda ((X $i) (Y $i))
% 0.11/0.36 (let ((a!1 (not (or (big_g Y) (not (big_f X))))))
% 0.11/0.36 (refl (~ a!1 a!1))))))
% 0.11/0.36 (a!8 (forall ((X $i) (Y $i)) (not (or (big_g Y) (not (big_f X))))))
% 0.11/0.36 (a!9 (or (or (big_g X!0) (not (big_f X!0)))
% 0.11/0.36 (or (big_g Y!1) (not (big_f X!2))))))
% 0.11/0.36 (let ((a!2 (~ a!1 (or (big_g X!0) (not (big_f X!0)))))
% 0.11/0.36 (a!6 (~ a!5 (or (big_g Y!1) (not (big_f X!2))))))
% 0.11/0.36 (nnf-neg (sk a!2)
% 0.11/0.36 (nnf-neg a!3 (~ (not a!1) a!4))
% 0.11/0.36 (sk a!6)
% 0.11/0.36 (nnf-neg a!7 (~ (not a!5) a!8))
% 0.11/0.36 (~ (not (= a!1 a!5)) (and a!9 (or a!4 a!8))))))
% 0.11/0.36 Proof display could not be completed: unexpected number of arguments
% 0.11/0.37 % E exiting
%------------------------------------------------------------------------------