%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN405+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 05:39:00 AM UTC 2025
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SYN405+1 : TPTP v9.0.0. Released v2.0.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:38:05 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(f_type, type, (
% 0.12/0.37 f: $i > $o)).
% 0.12/0.37 tff(tptp_fun_Y_0_type, type, (
% 0.12/0.37 tptp_fun_Y_0: $i)).
% 0.12/0.37 tff(g_type, type, (
% 0.12/0.37 g: $i > $o)).
% 0.12/0.37 tff(1,plain,
% 0.12/0.37 (^[Z: $i] : refl(((~f(Z)) | (~g(Z))) <=> ((~f(Z)) | (~g(Z))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 (![Z: $i] : ((~f(Z)) | (~g(Z))) <=> ![Z: $i] : ((~f(Z)) | (~g(Z)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.37 tff(3,plain,
% 0.12/0.37 (^[Z: $i] : trans(monotonicity(rewrite((f(Z) & g(Z)) <=> (~((~f(Z)) | (~g(Z))))), ((~(f(Z) & g(Z))) <=> (~(~((~f(Z)) | (~g(Z))))))), rewrite((~(~((~f(Z)) | (~g(Z))))) <=> ((~f(Z)) | (~g(Z)))), ((~(f(Z) & g(Z))) <=> ((~f(Z)) | (~g(Z)))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(4,plain,
% 0.12/0.37 (![Z: $i] : (~(f(Z) & g(Z))) <=> ![Z: $i] : ((~f(Z)) | (~g(Z)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.37 tff(5,plain,
% 0.12/0.37 ((~?[Z: $i] : (f(Z) & g(Z))) <=> (~?[Z: $i] : (f(Z) & g(Z)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(6,plain,
% 0.12/0.37 ((~((![X: $i] : f(X) & ?[Y: $i] : g(Y)) => ?[Z: $i] : (f(Z) & g(Z)))) <=> (~((~(![X: $i] : f(X) & ?[Y: $i] : g(Y))) | ?[Z: $i] : (f(Z) & g(Z))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(7,axiom,(~((![X: $i] : f(X) & ?[Y: $i] : g(Y)) => ?[Z: $i] : (f(Z) & g(Z)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','kalish239')).
% 0.12/0.37 tff(8,plain,
% 0.12/0.37 (~((~(![X: $i] : f(X) & ?[Y: $i] : g(Y))) | ?[Z: $i] : (f(Z) & g(Z)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 (~?[Z: $i] : (f(Z) & g(Z))),
% 0.12/0.37 inference(or_elim,[status(thm)],[8])).
% 0.12/0.37 tff(10,plain,
% 0.12/0.37 (~?[Z: $i] : (f(Z) & g(Z))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.12/0.37 tff(11,plain,
% 0.12/0.37 (~?[Z: $i] : (f(Z) & g(Z))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.12/0.37 tff(12,plain,
% 0.12/0.37 (~?[Z: $i] : (f(Z) & g(Z))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[11, 5])).
% 0.12/0.37 tff(13,plain,
% 0.12/0.37 (^[Z: $i] : refl($oeq((~(f(Z) & g(Z))), (~(f(Z) & g(Z)))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(14,plain,(
% 0.12/0.37 ![Z: $i] : (~(f(Z) & g(Z)))),
% 0.12/0.37 inference(nnf-neg,[status(sab)],[12, 13])).
% 0.12/0.37 tff(15,plain,
% 0.12/0.37 (![Z: $i] : ((~f(Z)) | (~g(Z)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[14, 4])).
% 0.12/0.37 tff(16,plain,
% 0.12/0.37 (![Z: $i] : ((~f(Z)) | (~g(Z)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[15, 2])).
% 0.12/0.37 tff(17,plain,
% 0.12/0.37 (?[Y: $i] : g(Y) <=> ?[Y: $i] : g(Y)),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(18,plain,
% 0.12/0.37 (![X: $i] : f(X) & ?[Y: $i] : g(Y)),
% 0.12/0.37 inference(or_elim,[status(thm)],[8])).
% 0.12/0.37 tff(19,plain,
% 0.12/0.37 (?[Y: $i] : g(Y)),
% 0.12/0.37 inference(and_elim,[status(thm)],[18])).
% 0.12/0.37 tff(20,plain,
% 0.12/0.37 (?[Y: $i] : g(Y)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[19, 17])).
% 0.12/0.37 tff(21,plain,(
% 0.12/0.37 g(Y!0)),
% 0.12/0.37 inference(skolemize,[status(sab)],[20])).
% 0.12/0.37 tff(22,plain,
% 0.12/0.37 (((~![Z: $i] : ((~f(Z)) | (~g(Z)))) | ((~f(Y!0)) | (~g(Y!0)))) <=> ((~![Z: $i] : ((~f(Z)) | (~g(Z)))) | (~f(Y!0)) | (~g(Y!0)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(23,plain,
% 0.12/0.37 ((~![Z: $i] : ((~f(Z)) | (~g(Z)))) | ((~f(Y!0)) | (~g(Y!0)))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(24,plain,
% 0.12/0.37 ((~![Z: $i] : ((~f(Z)) | (~g(Z)))) | (~f(Y!0)) | (~g(Y!0))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.12/0.37 tff(25,plain,
% 0.12/0.37 (~f(Y!0)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[24, 21, 16])).
% 0.12/0.37 tff(26,plain,
% 0.12/0.37 (^[X: $i] : refl(f(X) <=> f(X))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(27,plain,
% 0.12/0.37 (![X: $i] : f(X) <=> ![X: $i] : f(X)),
% 0.12/0.37 inference(quant_intro,[status(thm)],[26])).
% 0.12/0.37 tff(28,plain,
% 0.12/0.37 (![X: $i] : f(X) <=> ![X: $i] : f(X)),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(29,plain,
% 0.12/0.37 (![X: $i] : f(X)),
% 0.12/0.37 inference(and_elim,[status(thm)],[18])).
% 0.12/0.37 tff(30,plain,
% 0.12/0.37 (![X: $i] : f(X)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.12/0.37 tff(31,plain,(
% 0.12/0.37 ![X: $i] : f(X)),
% 0.12/0.37 inference(skolemize,[status(sab)],[30])).
% 0.12/0.37 tff(32,plain,
% 0.12/0.37 (![X: $i] : f(X)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.12/0.37 tff(33,plain,
% 0.12/0.37 ((~![X: $i] : f(X)) | f(Y!0)),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(34,plain,
% 0.12/0.37 ($false),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[33, 32, 25])).
% 0.12/0.37 % SZS output end Proof
% 0.12/0.37 % E exiting
%------------------------------------------------------------------------------