%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN408+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 05:39:00 AM UTC 2025
% Result : Theorem 0.12s 0.36s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN408+1 : TPTP v9.0.0. Released v2.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n005.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:33:35 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.36 % SZS status Theorem
% 0.12/0.36 % SZS output start Proof
% 0.12/0.36 tff(f_type, type, (
% 0.12/0.36 f: $i > $o)).
% 0.12/0.36 tff(tptp_fun_Y_0_type, type, (
% 0.12/0.36 tptp_fun_Y_0: $i)).
% 0.12/0.36 tff(g_type, type, (
% 0.12/0.36 g: $i > $o)).
% 0.12/0.36 tff(1,plain,
% 0.12/0.36 ((~![Y: $i] : (g(Y) | (~f(Y)))) <=> (~![Y: $i] : (g(Y) | (~f(Y))))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(2,plain,
% 0.12/0.36 ((~((~?[X: $i] : f(X)) => ![Y: $i] : (f(Y) => g(Y)))) <=> (~(?[X: $i] : f(X) | ![Y: $i] : (g(Y) | (~f(Y)))))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(3,axiom,(~((~?[X: $i] : f(X)) => ![Y: $i] : (f(Y) => g(Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','kalish244')).
% 0.12/0.36 tff(4,plain,
% 0.12/0.36 (~(?[X: $i] : f(X) | ![Y: $i] : (g(Y) | (~f(Y))))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.12/0.36 tff(5,plain,
% 0.12/0.36 (~![Y: $i] : (g(Y) | (~f(Y)))),
% 0.12/0.36 inference(or_elim,[status(thm)],[4])).
% 0.12/0.36 tff(6,plain,
% 0.12/0.36 (~![Y: $i] : (g(Y) | (~f(Y)))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.12/0.36 tff(7,plain,
% 0.12/0.36 (~![Y: $i] : (g(Y) | (~f(Y)))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.12/0.36 tff(8,plain,
% 0.12/0.36 (~![Y: $i] : (g(Y) | (~f(Y)))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.12/0.36 tff(9,plain,(
% 0.12/0.36 ~(g(Y!0) | (~f(Y!0)))),
% 0.12/0.36 inference(skolemize,[status(sab)],[8])).
% 0.12/0.36 tff(10,plain,
% 0.12/0.36 (f(Y!0)),
% 0.12/0.36 inference(or_elim,[status(thm)],[9])).
% 0.12/0.36 tff(11,plain,
% 0.12/0.36 (^[X: $i] : refl((~f(X)) <=> (~f(X)))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(12,plain,
% 0.12/0.36 (![X: $i] : (~f(X)) <=> ![X: $i] : (~f(X))),
% 0.12/0.36 inference(quant_intro,[status(thm)],[11])).
% 0.12/0.36 tff(13,plain,
% 0.12/0.36 ((~?[X: $i] : f(X)) <=> (~?[X: $i] : f(X))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(14,plain,
% 0.12/0.36 (~?[X: $i] : f(X)),
% 0.12/0.36 inference(or_elim,[status(thm)],[4])).
% 0.12/0.36 tff(15,plain,
% 0.12/0.36 (~?[X: $i] : f(X)),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.12/0.36 tff(16,plain,
% 0.12/0.36 (~?[X: $i] : f(X)),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[15, 13])).
% 0.12/0.36 tff(17,plain,
% 0.12/0.36 (~?[X: $i] : f(X)),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[16, 13])).
% 0.12/0.36 tff(18,plain,
% 0.12/0.36 (^[X: $i] : refl($oeq((~f(X)), (~f(X))))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(19,plain,(
% 0.12/0.36 ![X: $i] : (~f(X))),
% 0.12/0.36 inference(nnf-neg,[status(sab)],[17, 18])).
% 0.12/0.36 tff(20,plain,
% 0.12/0.36 (![X: $i] : (~f(X))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.12/0.36 tff(21,plain,
% 0.12/0.36 ((~![X: $i] : (~f(X))) | (~f(Y!0))),
% 0.12/0.36 inference(quant_inst,[status(thm)],[])).
% 0.12/0.36 tff(22,plain,
% 0.12/0.36 ($false),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[21, 20, 10])).
% 0.12/0.36 % SZS output end Proof
% 0.20/0.36 % E exiting
%------------------------------------------------------------------------------