%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN060+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:38:05 AM UTC 2025
% Result : Theorem 0.11s 0.36s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SYN060+1 : TPTP v9.0.0. Released v2.0.0.
% 0.11/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n006.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 12:26:50 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.36 % SZS status Theorem
% 0.11/0.36 % SZS output start Proof
% 0.11/0.36 tff(big_g_type, type, (
% 0.11/0.36 big_g: $i > $o)).
% 0.11/0.36 tff(tptp_fun_X_0_type, type, (
% 0.11/0.36 tptp_fun_X_0: $i)).
% 0.11/0.36 tff(big_f_type, type, (
% 0.11/0.36 big_f: $i > $o)).
% 0.11/0.36 tff(big_h_type, type, (
% 0.11/0.36 big_h: $i > $o)).
% 0.11/0.36 tff(big_i_type, type, (
% 0.11/0.36 big_i: $i > $o)).
% 0.11/0.36 tff(1,plain,
% 0.11/0.36 ((~![X: $i] : big_i(X)) <=> (~![X: $i] : big_i(X))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(2,axiom,(~![X: $i] : big_i(X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel30')).
% 0.11/0.36 tff(3,plain,
% 0.11/0.36 (~![X: $i] : big_i(X)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.11/0.36 tff(4,plain,
% 0.11/0.36 (~![X: $i] : big_i(X)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[3, 1])).
% 0.11/0.36 tff(5,plain,
% 0.11/0.36 (~![X: $i] : big_i(X)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.11/0.36 tff(6,plain,
% 0.11/0.36 (~![X: $i] : big_i(X)),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.11/0.36 tff(7,plain,(
% 0.11/0.36 ~big_i(X!0)),
% 0.11/0.36 inference(skolemize,[status(sab)],[6])).
% 0.11/0.36 tff(8,plain,
% 0.11/0.36 (((~big_g(X!0)) | (~big_i(X!0))) | big_i(X!0)),
% 0.11/0.36 inference(tautology,[status(thm)],[])).
% 0.11/0.36 tff(9,plain,
% 0.11/0.36 ((~big_g(X!0)) | (~big_i(X!0))),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.11/0.36 tff(10,plain,
% 0.11/0.36 (^[X: $i] : refl(((~((~big_g(X)) | (~big_i(X)))) | (~((~big_f(X)) | (~big_h(X))))) <=> ((~((~big_g(X)) | (~big_i(X)))) | (~((~big_f(X)) | (~big_h(X))))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(11,plain,
% 0.11/0.36 (![X: $i] : ((~((~big_g(X)) | (~big_i(X)))) | (~((~big_f(X)) | (~big_h(X))))) <=> ![X: $i] : ((~((~big_g(X)) | (~big_i(X)))) | (~((~big_f(X)) | (~big_h(X)))))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[10])).
% 0.11/0.36 tff(12,plain,
% 0.11/0.36 (^[X: $i] : trans(monotonicity(rewrite((big_f(X) & big_h(X)) <=> (~((~big_f(X)) | (~big_h(X))))), (((~((~big_g(X)) | (~big_i(X)))) | (big_f(X) & big_h(X))) <=> ((~((~big_g(X)) | (~big_i(X)))) | (~((~big_f(X)) | (~big_h(X))))))), rewrite(((~((~big_g(X)) | (~big_i(X)))) | (~((~big_f(X)) | (~big_h(X))))) <=> ((~((~big_g(X)) | (~big_i(X)))) | (~((~big_f(X)) | (~big_h(X)))))), (((~((~big_g(X)) | (~big_i(X)))) | (big_f(X) & big_h(X))) <=> ((~((~big_g(X)) | (~big_i(X)))) | (~((~big_f(X)) | (~big_h(X)))))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(13,plain,
% 0.11/0.36 (![X: $i] : ((~((~big_g(X)) | (~big_i(X)))) | (big_f(X) & big_h(X))) <=> ![X: $i] : ((~((~big_g(X)) | (~big_i(X)))) | (~((~big_f(X)) | (~big_h(X)))))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[12])).
% 0.11/0.36 tff(14,plain,
% 0.11/0.36 (![X: $i] : ((~((~big_g(X)) | (~big_i(X)))) | (big_f(X) & big_h(X))) <=> ![X: $i] : ((~((~big_g(X)) | (~big_i(X)))) | (big_f(X) & big_h(X)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(15,plain,
% 0.11/0.36 (^[X: $i] : trans(monotonicity(rewrite((big_g(X) => (~big_i(X))) <=> ((~big_g(X)) | (~big_i(X)))), (((big_g(X) => (~big_i(X))) => (big_f(X) & big_h(X))) <=> (((~big_g(X)) | (~big_i(X))) => (big_f(X) & big_h(X))))), rewrite((((~big_g(X)) | (~big_i(X))) => (big_f(X) & big_h(X))) <=> ((~((~big_g(X)) | (~big_i(X)))) | (big_f(X) & big_h(X)))), (((big_g(X) => (~big_i(X))) => (big_f(X) & big_h(X))) <=> ((~((~big_g(X)) | (~big_i(X)))) | (big_f(X) & big_h(X)))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(16,plain,
% 0.11/0.36 (![X: $i] : ((big_g(X) => (~big_i(X))) => (big_f(X) & big_h(X))) <=> ![X: $i] : ((~((~big_g(X)) | (~big_i(X)))) | (big_f(X) & big_h(X)))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[15])).
% 0.11/0.36 tff(17,axiom,(![X: $i] : ((big_g(X) => (~big_i(X))) => (big_f(X) & big_h(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel30_2')).
% 0.11/0.36 tff(18,plain,
% 0.11/0.36 (![X: $i] : ((~((~big_g(X)) | (~big_i(X)))) | (big_f(X) & big_h(X)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.11/0.36 tff(19,plain,
% 0.11/0.36 (![X: $i] : ((~((~big_g(X)) | (~big_i(X)))) | (big_f(X) & big_h(X)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.11/0.36 tff(20,plain,(
% 0.11/0.36 ![X: $i] : ((~((~big_g(X)) | (~big_i(X)))) | (big_f(X) & big_h(X)))),
% 0.11/0.36 inference(skolemize,[status(sab)],[19])).
% 0.11/0.36 tff(21,plain,
% 0.11/0.36 (![X: $i] : ((~((~big_g(X)) | (~big_i(X)))) | (~((~big_f(X)) | (~big_h(X)))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.11/0.36 tff(22,plain,
% 0.11/0.36 (![X: $i] : ((~((~big_g(X)) | (~big_i(X)))) | (~((~big_f(X)) | (~big_h(X)))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[21, 11])).
% 0.11/0.36 tff(23,plain,
% 0.11/0.36 (((~![X: $i] : ((~((~big_g(X)) | (~big_i(X)))) | (~((~big_f(X)) | (~big_h(X)))))) | ((~((~big_g(X!0)) | (~big_i(X!0)))) | (~((~big_f(X!0)) | (~big_h(X!0)))))) <=> ((~![X: $i] : ((~((~big_g(X)) | (~big_i(X)))) | (~((~big_f(X)) | (~big_h(X)))))) | (~((~big_g(X!0)) | (~big_i(X!0)))) | (~((~big_f(X!0)) | (~big_h(X!0)))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(24,plain,
% 0.11/0.36 ((~![X: $i] : ((~((~big_g(X)) | (~big_i(X)))) | (~((~big_f(X)) | (~big_h(X)))))) | ((~((~big_g(X!0)) | (~big_i(X!0)))) | (~((~big_f(X!0)) | (~big_h(X!0)))))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(25,plain,
% 0.11/0.36 ((~![X: $i] : ((~((~big_g(X)) | (~big_i(X)))) | (~((~big_f(X)) | (~big_h(X)))))) | (~((~big_g(X!0)) | (~big_i(X!0)))) | (~((~big_f(X!0)) | (~big_h(X!0))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.11/0.36 tff(26,plain,
% 0.11/0.36 (~((~big_f(X!0)) | (~big_h(X!0)))),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[25, 22, 9])).
% 0.11/0.36 tff(27,plain,
% 0.11/0.36 (((~big_f(X!0)) | (~big_h(X!0))) | big_f(X!0)),
% 0.11/0.36 inference(tautology,[status(thm)],[])).
% 0.11/0.36 tff(28,plain,
% 0.11/0.36 (big_f(X!0)),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.11/0.36 tff(29,plain,
% 0.11/0.36 ((big_f(X!0) | big_g(X!0)) | (~big_f(X!0))),
% 0.11/0.36 inference(tautology,[status(thm)],[])).
% 0.11/0.36 tff(30,plain,
% 0.11/0.36 (big_f(X!0) | big_g(X!0)),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.11/0.36 tff(31,plain,
% 0.11/0.36 (((~big_f(X!0)) | (~big_h(X!0))) | big_h(X!0)),
% 0.11/0.36 inference(tautology,[status(thm)],[])).
% 0.11/0.36 tff(32,plain,
% 0.11/0.36 (big_h(X!0)),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[31, 26])).
% 0.11/0.36 tff(33,plain,
% 0.11/0.36 (^[X: $i] : refl(((~big_h(X)) | (~(big_f(X) | big_g(X)))) <=> ((~big_h(X)) | (~(big_f(X) | big_g(X)))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(34,plain,
% 0.11/0.36 (![X: $i] : ((~big_h(X)) | (~(big_f(X) | big_g(X)))) <=> ![X: $i] : ((~big_h(X)) | (~(big_f(X) | big_g(X))))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[33])).
% 0.11/0.36 tff(35,plain,
% 0.11/0.36 (![X: $i] : ((~big_h(X)) | (~(big_f(X) | big_g(X)))) <=> ![X: $i] : ((~big_h(X)) | (~(big_f(X) | big_g(X))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(36,plain,
% 0.11/0.36 (^[X: $i] : rewrite(((big_f(X) | big_g(X)) => (~big_h(X))) <=> ((~big_h(X)) | (~(big_f(X) | big_g(X)))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(37,plain,
% 0.11/0.36 (![X: $i] : ((big_f(X) | big_g(X)) => (~big_h(X))) <=> ![X: $i] : ((~big_h(X)) | (~(big_f(X) | big_g(X))))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[36])).
% 0.11/0.36 tff(38,axiom,(![X: $i] : ((big_f(X) | big_g(X)) => (~big_h(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel30_1')).
% 0.11/0.36 tff(39,plain,
% 0.11/0.36 (![X: $i] : ((~big_h(X)) | (~(big_f(X) | big_g(X))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.11/0.36 tff(40,plain,
% 0.11/0.36 (![X: $i] : ((~big_h(X)) | (~(big_f(X) | big_g(X))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.11/0.36 tff(41,plain,(
% 0.11/0.36 ![X: $i] : ((~big_h(X)) | (~(big_f(X) | big_g(X))))),
% 0.11/0.36 inference(skolemize,[status(sab)],[40])).
% 0.11/0.36 tff(42,plain,
% 0.11/0.36 (![X: $i] : ((~big_h(X)) | (~(big_f(X) | big_g(X))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.11/0.36 tff(43,plain,
% 0.11/0.36 (((~![X: $i] : ((~big_h(X)) | (~(big_f(X) | big_g(X))))) | ((~big_h(X!0)) | (~(big_f(X!0) | big_g(X!0))))) <=> ((~![X: $i] : ((~big_h(X)) | (~(big_f(X) | big_g(X))))) | (~big_h(X!0)) | (~(big_f(X!0) | big_g(X!0))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(44,plain,
% 0.11/0.36 ((~![X: $i] : ((~big_h(X)) | (~(big_f(X) | big_g(X))))) | ((~big_h(X!0)) | (~(big_f(X!0) | big_g(X!0))))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(45,plain,
% 0.11/0.36 ((~![X: $i] : ((~big_h(X)) | (~(big_f(X) | big_g(X))))) | (~big_h(X!0)) | (~(big_f(X!0) | big_g(X!0)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.11/0.36 tff(46,plain,
% 0.11/0.36 ($false),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[45, 42, 32, 30])).
% 0.11/0.36 % SZS output end Proof
% 0.11/0.36 % E exiting
%------------------------------------------------------------------------------