%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN395+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:38:58 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
% 0.11/0.12 % Problem : SYN395+1 : TPTP v9.0.0. Released v2.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n012.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 12:32:10 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(g_type, type, (
% 0.12/0.37 g: $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(f_type, type, (
% 0.12/0.37 f: $i > $o)).
% 0.12/0.37 tff(1,plain,
% 0.12/0.37 (^[X: $i] : refl((g(X) | (~f(X))) <=> (g(X) | (~f(X))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 (![X: $i] : (g(X) | (~f(X))) <=> ![X: $i] : (g(X) | (~f(X)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.37 tff(3,plain,
% 0.12/0.37 (![X: $i] : (g(X) | (~f(X))) <=> ![X: $i] : (g(X) | (~f(X)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(4,plain,
% 0.12/0.37 ((~(![X: $i] : (f(X) => g(X)) => (?[Y: $i] : f(Y) => ?[Z: $i] : g(Z)))) <=> (~(?[Z: $i] : g(Z) | (~?[Y: $i] : f(Y)) | (~![X: $i] : (g(X) | (~f(X))))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(5,axiom,(~(![X: $i] : (f(X) => g(X)) => (?[Y: $i] : f(Y) => ?[Z: $i] : g(Z)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','kalish202')).
% 0.12/0.37 tff(6,plain,
% 0.12/0.37 (~(?[Z: $i] : g(Z) | (~?[Y: $i] : f(Y)) | (~![X: $i] : (g(X) | (~f(X)))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.12/0.37 tff(7,plain,
% 0.12/0.37 (![X: $i] : (g(X) | (~f(X)))),
% 0.12/0.37 inference(or_elim,[status(thm)],[6])).
% 0.12/0.37 tff(8,plain,
% 0.12/0.37 (![X: $i] : (g(X) | (~f(X)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.12/0.37 tff(9,plain,(
% 0.12/0.37 ![X: $i] : (g(X) | (~f(X)))),
% 0.12/0.37 inference(skolemize,[status(sab)],[8])).
% 0.12/0.37 tff(10,plain,
% 0.12/0.37 (![X: $i] : (g(X) | (~f(X)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.12/0.37 tff(11,plain,
% 0.12/0.37 (?[Y: $i] : f(Y) <=> ?[Y: $i] : f(Y)),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(12,plain,
% 0.12/0.37 (?[Y: $i] : f(Y)),
% 0.12/0.37 inference(or_elim,[status(thm)],[6])).
% 0.12/0.37 tff(13,plain,
% 0.12/0.37 (?[Y: $i] : f(Y)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.12/0.37 tff(14,plain,(
% 0.12/0.37 f(Y!0)),
% 0.12/0.37 inference(skolemize,[status(sab)],[13])).
% 0.12/0.37 tff(15,plain,
% 0.12/0.37 (((~![X: $i] : (g(X) | (~f(X)))) | (g(Y!0) | (~f(Y!0)))) <=> ((~![X: $i] : (g(X) | (~f(X)))) | g(Y!0) | (~f(Y!0)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(16,plain,
% 0.12/0.37 ((~![X: $i] : (g(X) | (~f(X)))) | (g(Y!0) | (~f(Y!0)))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(17,plain,
% 0.12/0.37 ((~![X: $i] : (g(X) | (~f(X)))) | g(Y!0) | (~f(Y!0))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.12/0.37 tff(18,plain,
% 0.12/0.37 (g(Y!0)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[17, 14, 10])).
% 0.12/0.37 tff(19,plain,
% 0.12/0.37 (^[Z: $i] : refl((~g(Z)) <=> (~g(Z)))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(20,plain,
% 0.12/0.37 (![Z: $i] : (~g(Z)) <=> ![Z: $i] : (~g(Z))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[19])).
% 0.12/0.37 tff(21,plain,
% 0.12/0.37 ((~?[Z: $i] : g(Z)) <=> (~?[Z: $i] : g(Z))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(22,plain,
% 0.12/0.37 (~?[Z: $i] : g(Z)),
% 0.12/0.37 inference(or_elim,[status(thm)],[6])).
% 0.12/0.37 tff(23,plain,
% 0.12/0.37 (~?[Z: $i] : g(Z)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.12/0.37 tff(24,plain,
% 0.12/0.37 (~?[Z: $i] : g(Z)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[23, 21])).
% 0.12/0.37 tff(25,plain,
% 0.12/0.37 (~?[Z: $i] : g(Z)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.12/0.37 tff(26,plain,
% 0.12/0.37 (^[Z: $i] : refl($oeq((~g(Z)), (~g(Z))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(27,plain,(
% 0.12/0.37 ![Z: $i] : (~g(Z))),
% 0.12/0.37 inference(nnf-neg,[status(sab)],[25, 26])).
% 0.12/0.37 tff(28,plain,
% 0.12/0.37 (![Z: $i] : (~g(Z))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.12/0.37 tff(29,plain,
% 0.12/0.37 ((~![Z: $i] : (~g(Z))) | (~g(Y!0))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(30,plain,
% 0.12/0.37 ($false),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[29, 28, 18])).
% 0.12/0.37 % SZS output end Proof
% 0.12/0.37 % E exiting
%------------------------------------------------------------------------------