%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN407+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 0.18s 0.36s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.11 % Problem : SYN407+1 : TPTP v9.0.0. Released v2.0.0.
% 0.12/0.11 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n014.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
% 0.12/0.32 % DateTime : Fri Jun 20 12:33:54 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.18/0.36 % SZS status Theorem
% 0.18/0.36 % SZS output start Proof
% 0.18/0.36 tff(h_type, type, (
% 0.18/0.36 h: $i > $o)).
% 0.18/0.36 tff(tptp_fun_Y_0_type, type, (
% 0.18/0.36 tptp_fun_Y_0: $i)).
% 0.18/0.36 tff(f_type, type, (
% 0.18/0.36 f: $i > $o)).
% 0.18/0.36 tff(g_type, type, (
% 0.18/0.36 g: $i > $o)).
% 0.18/0.36 tff(1,plain,
% 0.18/0.36 ((~![Y: $i] : (g(Y) | (~f(Y)))) <=> (~![Y: $i] : (g(Y) | (~f(Y))))),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(2,plain,
% 0.18/0.36 ((~(![X: $i] : (f(X) => (g(X) | h(X))) => (![Y: $i] : (f(Y) => g(Y)) | ?[Z: $i] : (f(Z) & h(Z))))) <=> (~(?[Z: $i] : (f(Z) & h(Z)) | ![Y: $i] : (g(Y) | (~f(Y))) | (~![X: $i] : (h(X) | g(X) | (~f(X))))))),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(3,axiom,(~(![X: $i] : (f(X) => (g(X) | h(X))) => (![Y: $i] : (f(Y) => g(Y)) | ?[Z: $i] : (f(Z) & h(Z))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','kalish241')).
% 0.18/0.36 tff(4,plain,
% 0.18/0.36 (~(?[Z: $i] : (f(Z) & h(Z)) | ![Y: $i] : (g(Y) | (~f(Y))) | (~![X: $i] : (h(X) | g(X) | (~f(X)))))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.18/0.36 tff(5,plain,
% 0.18/0.36 (~![Y: $i] : (g(Y) | (~f(Y)))),
% 0.18/0.36 inference(or_elim,[status(thm)],[4])).
% 0.18/0.36 tff(6,plain,
% 0.18/0.36 (~![Y: $i] : (g(Y) | (~f(Y)))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.18/0.36 tff(7,plain,
% 0.18/0.36 (~![Y: $i] : (g(Y) | (~f(Y)))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.18/0.36 tff(8,plain,
% 0.18/0.36 (~![Y: $i] : (g(Y) | (~f(Y)))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.18/0.36 tff(9,plain,(
% 0.18/0.36 ~(g(Y!0) | (~f(Y!0)))),
% 0.18/0.36 inference(skolemize,[status(sab)],[8])).
% 0.18/0.36 tff(10,plain,
% 0.18/0.36 (f(Y!0)),
% 0.18/0.36 inference(or_elim,[status(thm)],[9])).
% 0.18/0.36 tff(11,plain,
% 0.18/0.36 (^[Z: $i] : refl(((~f(Z)) | (~h(Z))) <=> ((~f(Z)) | (~h(Z))))),
% 0.18/0.36 inference(bind,[status(th)],[])).
% 0.18/0.36 tff(12,plain,
% 0.18/0.36 (![Z: $i] : ((~f(Z)) | (~h(Z))) <=> ![Z: $i] : ((~f(Z)) | (~h(Z)))),
% 0.18/0.36 inference(quant_intro,[status(thm)],[11])).
% 0.18/0.36 tff(13,plain,
% 0.18/0.36 (^[Z: $i] : trans(monotonicity(rewrite((f(Z) & h(Z)) <=> (~((~f(Z)) | (~h(Z))))), ((~(f(Z) & h(Z))) <=> (~(~((~f(Z)) | (~h(Z))))))), rewrite((~(~((~f(Z)) | (~h(Z))))) <=> ((~f(Z)) | (~h(Z)))), ((~(f(Z) & h(Z))) <=> ((~f(Z)) | (~h(Z)))))),
% 0.18/0.36 inference(bind,[status(th)],[])).
% 0.18/0.36 tff(14,plain,
% 0.18/0.36 (![Z: $i] : (~(f(Z) & h(Z))) <=> ![Z: $i] : ((~f(Z)) | (~h(Z)))),
% 0.18/0.36 inference(quant_intro,[status(thm)],[13])).
% 0.18/0.36 tff(15,plain,
% 0.18/0.36 ((~?[Z: $i] : (f(Z) & h(Z))) <=> (~?[Z: $i] : (f(Z) & h(Z)))),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(16,plain,
% 0.18/0.36 (~?[Z: $i] : (f(Z) & h(Z))),
% 0.18/0.36 inference(or_elim,[status(thm)],[4])).
% 0.18/0.36 tff(17,plain,
% 0.18/0.36 (~?[Z: $i] : (f(Z) & h(Z))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.18/0.36 tff(18,plain,
% 0.18/0.36 (~?[Z: $i] : (f(Z) & h(Z))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[17, 15])).
% 0.18/0.36 tff(19,plain,
% 0.18/0.36 (~?[Z: $i] : (f(Z) & h(Z))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[18, 15])).
% 0.18/0.36 tff(20,plain,
% 0.18/0.36 (^[Z: $i] : refl($oeq((~(f(Z) & h(Z))), (~(f(Z) & h(Z)))))),
% 0.18/0.36 inference(bind,[status(th)],[])).
% 0.18/0.36 tff(21,plain,(
% 0.18/0.36 ![Z: $i] : (~(f(Z) & h(Z)))),
% 0.18/0.36 inference(nnf-neg,[status(sab)],[19, 20])).
% 0.18/0.36 tff(22,plain,
% 0.18/0.36 (![Z: $i] : ((~f(Z)) | (~h(Z)))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.18/0.36 tff(23,plain,
% 0.18/0.36 (![Z: $i] : ((~f(Z)) | (~h(Z)))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[22, 12])).
% 0.18/0.36 tff(24,plain,
% 0.18/0.36 (((~![Z: $i] : ((~f(Z)) | (~h(Z)))) | ((~f(Y!0)) | (~h(Y!0)))) <=> ((~![Z: $i] : ((~f(Z)) | (~h(Z)))) | (~f(Y!0)) | (~h(Y!0)))),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(25,plain,
% 0.18/0.36 ((~![Z: $i] : ((~f(Z)) | (~h(Z)))) | ((~f(Y!0)) | (~h(Y!0)))),
% 0.18/0.36 inference(quant_inst,[status(thm)],[])).
% 0.18/0.36 tff(26,plain,
% 0.18/0.36 ((~![Z: $i] : ((~f(Z)) | (~h(Z)))) | (~f(Y!0)) | (~h(Y!0))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.18/0.36 tff(27,plain,
% 0.18/0.36 (~h(Y!0)),
% 0.18/0.36 inference(unit_resolution,[status(thm)],[26, 23, 10])).
% 0.18/0.36 tff(28,plain,
% 0.18/0.36 (^[X: $i] : refl((h(X) | g(X) | (~f(X))) <=> (h(X) | g(X) | (~f(X))))),
% 0.18/0.36 inference(bind,[status(th)],[])).
% 0.18/0.36 tff(29,plain,
% 0.18/0.36 (![X: $i] : (h(X) | g(X) | (~f(X))) <=> ![X: $i] : (h(X) | g(X) | (~f(X)))),
% 0.18/0.36 inference(quant_intro,[status(thm)],[28])).
% 0.18/0.36 tff(30,plain,
% 0.18/0.36 (![X: $i] : (h(X) | g(X) | (~f(X))) <=> ![X: $i] : (h(X) | g(X) | (~f(X)))),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(31,plain,
% 0.18/0.36 (![X: $i] : (h(X) | g(X) | (~f(X)))),
% 0.18/0.36 inference(or_elim,[status(thm)],[4])).
% 0.18/0.36 tff(32,plain,
% 0.18/0.36 (![X: $i] : (h(X) | g(X) | (~f(X)))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.18/0.36 tff(33,plain,(
% 0.18/0.36 ![X: $i] : (h(X) | g(X) | (~f(X)))),
% 0.18/0.36 inference(skolemize,[status(sab)],[32])).
% 0.18/0.36 tff(34,plain,
% 0.18/0.36 (![X: $i] : (h(X) | g(X) | (~f(X)))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.18/0.36 tff(35,plain,
% 0.18/0.36 (~g(Y!0)),
% 0.18/0.36 inference(or_elim,[status(thm)],[9])).
% 0.18/0.36 tff(36,plain,
% 0.18/0.36 (((~![X: $i] : (h(X) | g(X) | (~f(X)))) | (g(Y!0) | (~f(Y!0)) | h(Y!0))) <=> ((~![X: $i] : (h(X) | g(X) | (~f(X)))) | g(Y!0) | (~f(Y!0)) | h(Y!0))),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(37,plain,
% 0.18/0.36 ((h(Y!0) | g(Y!0) | (~f(Y!0))) <=> (g(Y!0) | (~f(Y!0)) | h(Y!0))),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(38,plain,
% 0.18/0.36 (((~![X: $i] : (h(X) | g(X) | (~f(X)))) | (h(Y!0) | g(Y!0) | (~f(Y!0)))) <=> ((~![X: $i] : (h(X) | g(X) | (~f(X)))) | (g(Y!0) | (~f(Y!0)) | h(Y!0)))),
% 0.18/0.36 inference(monotonicity,[status(thm)],[37])).
% 0.18/0.36 tff(39,plain,
% 0.18/0.36 (((~![X: $i] : (h(X) | g(X) | (~f(X)))) | (h(Y!0) | g(Y!0) | (~f(Y!0)))) <=> ((~![X: $i] : (h(X) | g(X) | (~f(X)))) | g(Y!0) | (~f(Y!0)) | h(Y!0))),
% 0.18/0.36 inference(transitivity,[status(thm)],[38, 36])).
% 0.18/0.36 tff(40,plain,
% 0.18/0.36 ((~![X: $i] : (h(X) | g(X) | (~f(X)))) | (h(Y!0) | g(Y!0) | (~f(Y!0)))),
% 0.18/0.36 inference(quant_inst,[status(thm)],[])).
% 0.18/0.36 tff(41,plain,
% 0.18/0.36 ((~![X: $i] : (h(X) | g(X) | (~f(X)))) | g(Y!0) | (~f(Y!0)) | h(Y!0)),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.18/0.36 tff(42,plain,
% 0.18/0.36 ($false),
% 0.18/0.36 inference(unit_resolution,[status(thm)],[41, 35, 10, 34, 27])).
% 0.18/0.36 % SZS output end Proof
% 0.18/0.36 % E exiting
%------------------------------------------------------------------------------