%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN406+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 0.13s 0.38s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYN406+1 : TPTP v9.0.0. Released v2.0.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n003.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 12:33:54 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.38 % SZS status Theorem
% 0.13/0.38 % SZS output start Proof
% 0.13/0.38 tff(g_type, type, (
% 0.13/0.38 g: $i > $o)).
% 0.13/0.38 tff(tptp_fun_Y_0_type, type, (
% 0.13/0.38 tptp_fun_Y_0: $i)).
% 0.13/0.38 tff(f_type, type, (
% 0.13/0.38 f: $i > $o)).
% 0.13/0.38 tff(h_type, type, (
% 0.13/0.38 h: $i > $o)).
% 0.13/0.38 tff(1,plain,
% 0.13/0.38 (?[Y: $i] : (f(Y) & h(Y)) <=> ?[Y: $i] : (f(Y) & h(Y))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(2,plain,
% 0.13/0.38 ((~((![X: $i] : (f(X) => g(X)) & ?[Y: $i] : (f(Y) & h(Y))) => ?[Z: $i] : (g(Z) & h(Z)))) <=> (~((~(![X: $i] : (g(X) | (~f(X))) & ?[Y: $i] : (f(Y) & h(Y)))) | ?[Z: $i] : (g(Z) & h(Z))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(3,axiom,(~((![X: $i] : (f(X) => g(X)) & ?[Y: $i] : (f(Y) & h(Y))) => ?[Z: $i] : (g(Z) & h(Z)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','kalish240')).
% 0.13/0.38 tff(4,plain,
% 0.13/0.38 (~((~(![X: $i] : (g(X) | (~f(X))) & ?[Y: $i] : (f(Y) & h(Y)))) | ?[Z: $i] : (g(Z) & h(Z)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.13/0.38 tff(5,plain,
% 0.13/0.38 (![X: $i] : (g(X) | (~f(X))) & ?[Y: $i] : (f(Y) & h(Y))),
% 0.13/0.38 inference(or_elim,[status(thm)],[4])).
% 0.13/0.38 tff(6,plain,
% 0.13/0.38 (?[Y: $i] : (f(Y) & h(Y))),
% 0.13/0.38 inference(and_elim,[status(thm)],[5])).
% 0.13/0.38 tff(7,plain,
% 0.13/0.38 (?[Y: $i] : (f(Y) & h(Y))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.13/0.38 tff(8,plain,(
% 0.13/0.38 f(Y!0) & h(Y!0)),
% 0.13/0.38 inference(skolemize,[status(sab)],[7])).
% 0.13/0.38 tff(9,plain,
% 0.13/0.38 (f(Y!0)),
% 0.13/0.38 inference(and_elim,[status(thm)],[8])).
% 0.13/0.38 tff(10,plain,
% 0.13/0.38 (^[X: $i] : refl((g(X) | (~f(X))) <=> (g(X) | (~f(X))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(11,plain,
% 0.13/0.38 (![X: $i] : (g(X) | (~f(X))) <=> ![X: $i] : (g(X) | (~f(X)))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[10])).
% 0.13/0.38 tff(12,plain,
% 0.13/0.38 (![X: $i] : (g(X) | (~f(X))) <=> ![X: $i] : (g(X) | (~f(X)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(13,plain,
% 0.13/0.38 (![X: $i] : (g(X) | (~f(X)))),
% 0.13/0.38 inference(and_elim,[status(thm)],[5])).
% 0.13/0.38 tff(14,plain,
% 0.13/0.38 (![X: $i] : (g(X) | (~f(X)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.13/0.38 tff(15,plain,(
% 0.13/0.38 ![X: $i] : (g(X) | (~f(X)))),
% 0.13/0.38 inference(skolemize,[status(sab)],[14])).
% 0.13/0.38 tff(16,plain,
% 0.13/0.38 (![X: $i] : (g(X) | (~f(X)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.13/0.38 tff(17,plain,
% 0.13/0.38 (((~![X: $i] : (g(X) | (~f(X)))) | (g(Y!0) | (~f(Y!0)))) <=> ((~![X: $i] : (g(X) | (~f(X)))) | g(Y!0) | (~f(Y!0)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(18,plain,
% 0.13/0.38 ((~![X: $i] : (g(X) | (~f(X)))) | (g(Y!0) | (~f(Y!0)))),
% 0.13/0.38 inference(quant_inst,[status(thm)],[])).
% 0.13/0.38 tff(19,plain,
% 0.13/0.38 ((~![X: $i] : (g(X) | (~f(X)))) | g(Y!0) | (~f(Y!0))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.13/0.38 tff(20,plain,
% 0.13/0.38 (g(Y!0)),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[19, 16, 9])).
% 0.13/0.38 tff(21,plain,
% 0.13/0.38 (^[Z: $i] : refl(((~g(Z)) | (~h(Z))) <=> ((~g(Z)) | (~h(Z))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(22,plain,
% 0.13/0.38 (![Z: $i] : ((~g(Z)) | (~h(Z))) <=> ![Z: $i] : ((~g(Z)) | (~h(Z)))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[21])).
% 0.13/0.38 tff(23,plain,
% 0.13/0.38 (^[Z: $i] : trans(monotonicity(rewrite((g(Z) & h(Z)) <=> (~((~g(Z)) | (~h(Z))))), ((~(g(Z) & h(Z))) <=> (~(~((~g(Z)) | (~h(Z))))))), rewrite((~(~((~g(Z)) | (~h(Z))))) <=> ((~g(Z)) | (~h(Z)))), ((~(g(Z) & h(Z))) <=> ((~g(Z)) | (~h(Z)))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(24,plain,
% 0.13/0.38 (![Z: $i] : (~(g(Z) & h(Z))) <=> ![Z: $i] : ((~g(Z)) | (~h(Z)))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[23])).
% 0.13/0.38 tff(25,plain,
% 0.13/0.38 ((~?[Z: $i] : (g(Z) & h(Z))) <=> (~?[Z: $i] : (g(Z) & h(Z)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(26,plain,
% 0.13/0.38 (~?[Z: $i] : (g(Z) & h(Z))),
% 0.13/0.38 inference(or_elim,[status(thm)],[4])).
% 0.13/0.38 tff(27,plain,
% 0.13/0.38 (~?[Z: $i] : (g(Z) & h(Z))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.13/0.38 tff(28,plain,
% 0.13/0.38 (~?[Z: $i] : (g(Z) & h(Z))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[27, 25])).
% 0.13/0.38 tff(29,plain,
% 0.13/0.38 (~?[Z: $i] : (g(Z) & h(Z))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[28, 25])).
% 0.13/0.38 tff(30,plain,
% 0.13/0.38 (^[Z: $i] : refl($oeq((~(g(Z) & h(Z))), (~(g(Z) & h(Z)))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(31,plain,(
% 0.13/0.38 ![Z: $i] : (~(g(Z) & h(Z)))),
% 0.13/0.38 inference(nnf-neg,[status(sab)],[29, 30])).
% 0.13/0.38 tff(32,plain,
% 0.13/0.38 (![Z: $i] : ((~g(Z)) | (~h(Z)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.13/0.38 tff(33,plain,
% 0.13/0.38 (![Z: $i] : ((~g(Z)) | (~h(Z)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[32, 22])).
% 0.13/0.38 tff(34,plain,
% 0.13/0.38 (h(Y!0)),
% 0.13/0.38 inference(and_elim,[status(thm)],[8])).
% 0.13/0.38 tff(35,plain,
% 0.13/0.38 (((~![Z: $i] : ((~g(Z)) | (~h(Z)))) | ((~g(Y!0)) | (~h(Y!0)))) <=> ((~![Z: $i] : ((~g(Z)) | (~h(Z)))) | (~g(Y!0)) | (~h(Y!0)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(36,plain,
% 0.13/0.38 ((~![Z: $i] : ((~g(Z)) | (~h(Z)))) | ((~g(Y!0)) | (~h(Y!0)))),
% 0.13/0.38 inference(quant_inst,[status(thm)],[])).
% 0.13/0.38 tff(37,plain,
% 0.13/0.38 ((~![Z: $i] : ((~g(Z)) | (~h(Z)))) | (~g(Y!0)) | (~h(Y!0))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.13/0.38 tff(38,plain,
% 0.13/0.38 ($false),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[37, 34, 33, 20])).
% 0.13/0.38 % SZS output end Proof
% 0.13/0.38 % E exiting
%------------------------------------------------------------------------------