%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN055+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 05:38:04 AM UTC 2025
% Result : Theorem 0.22s 0.38s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SYN055+1 : TPTP v9.0.0. Released v2.0.0.
% 0.04/0.13 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n012.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Jun 20 12:26:10 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.22/0.38 % SZS status Theorem
% 0.22/0.38 % SZS output start Proof
% 0.22/0.38 tff(big_r_type, type, (
% 0.22/0.38 big_r: $i > $o)).
% 0.22/0.38 tff(tptp_fun_X_0_type, type, (
% 0.22/0.38 tptp_fun_X_0: $i)).
% 0.22/0.38 tff(big_g_type, type, (
% 0.22/0.38 big_g: $i > $o)).
% 0.22/0.38 tff(big_f_type, type, (
% 0.22/0.38 big_f: $i > $o)).
% 0.22/0.38 tff(big_p_type, type, (
% 0.22/0.38 big_p: $i > $o)).
% 0.22/0.38 tff(1,plain,
% 0.22/0.38 (^[X: $i] : refl(((~big_p(X)) | (~((~big_g(X)) | (~big_f(X))))) <=> ((~big_p(X)) | (~((~big_g(X)) | (~big_f(X))))))),
% 0.22/0.38 inference(bind,[status(th)],[])).
% 0.22/0.38 tff(2,plain,
% 0.22/0.38 (![X: $i] : ((~big_p(X)) | (~((~big_g(X)) | (~big_f(X))))) <=> ![X: $i] : ((~big_p(X)) | (~((~big_g(X)) | (~big_f(X)))))),
% 0.22/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.22/0.38 tff(3,plain,
% 0.22/0.38 (^[X: $i] : rewrite(((~big_p(X)) | (big_g(X) & big_f(X))) <=> ((~big_p(X)) | (~((~big_g(X)) | (~big_f(X))))))),
% 0.22/0.38 inference(bind,[status(th)],[])).
% 0.22/0.38 tff(4,plain,
% 0.22/0.38 (![X: $i] : ((~big_p(X)) | (big_g(X) & big_f(X))) <=> ![X: $i] : ((~big_p(X)) | (~((~big_g(X)) | (~big_f(X)))))),
% 0.22/0.38 inference(quant_intro,[status(thm)],[3])).
% 0.22/0.38 tff(5,plain,
% 0.22/0.38 (![X: $i] : ((~big_p(X)) | (big_g(X) & big_f(X))) <=> ![X: $i] : ((~big_p(X)) | (big_g(X) & big_f(X)))),
% 0.22/0.38 inference(rewrite,[status(thm)],[])).
% 0.22/0.38 tff(6,plain,
% 0.22/0.38 (^[X: $i] : rewrite((big_p(X) => (big_g(X) & big_f(X))) <=> ((~big_p(X)) | (big_g(X) & big_f(X))))),
% 0.22/0.38 inference(bind,[status(th)],[])).
% 0.22/0.38 tff(7,plain,
% 0.22/0.38 (![X: $i] : (big_p(X) => (big_g(X) & big_f(X))) <=> ![X: $i] : ((~big_p(X)) | (big_g(X) & big_f(X)))),
% 0.22/0.38 inference(quant_intro,[status(thm)],[6])).
% 0.22/0.38 tff(8,axiom,(![X: $i] : (big_p(X) => (big_g(X) & big_f(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel25_3')).
% 0.22/0.38 tff(9,plain,
% 0.22/0.38 (![X: $i] : ((~big_p(X)) | (big_g(X) & big_f(X)))),
% 0.22/0.38 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.22/0.38 tff(10,plain,
% 0.22/0.38 (![X: $i] : ((~big_p(X)) | (big_g(X) & big_f(X)))),
% 0.22/0.38 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.22/0.38 tff(11,plain,(
% 0.22/0.38 ![X: $i] : ((~big_p(X)) | (big_g(X) & big_f(X)))),
% 0.22/0.38 inference(skolemize,[status(sab)],[10])).
% 0.22/0.38 tff(12,plain,
% 0.22/0.38 (![X: $i] : ((~big_p(X)) | (~((~big_g(X)) | (~big_f(X)))))),
% 0.22/0.38 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.22/0.38 tff(13,plain,
% 0.22/0.38 (![X: $i] : ((~big_p(X)) | (~((~big_g(X)) | (~big_f(X)))))),
% 0.22/0.38 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.22/0.38 tff(14,plain,
% 0.22/0.38 (?[X: $i] : big_p(X) <=> ?[X: $i] : big_p(X)),
% 0.22/0.38 inference(rewrite,[status(thm)],[])).
% 0.22/0.38 tff(15,axiom,(?[X: $i] : big_p(X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel25_1')).
% 0.22/0.38 tff(16,plain,
% 0.22/0.38 (?[X: $i] : big_p(X)),
% 0.22/0.38 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.22/0.38 tff(17,plain,(
% 0.22/0.38 big_p(X!0)),
% 0.22/0.38 inference(skolemize,[status(sab)],[16])).
% 0.22/0.38 tff(18,plain,
% 0.22/0.38 (((~![X: $i] : ((~big_p(X)) | (~((~big_g(X)) | (~big_f(X)))))) | ((~big_p(X!0)) | (~((~big_g(X!0)) | (~big_f(X!0)))))) <=> ((~![X: $i] : ((~big_p(X)) | (~((~big_g(X)) | (~big_f(X)))))) | (~big_p(X!0)) | (~((~big_g(X!0)) | (~big_f(X!0)))))),
% 0.22/0.38 inference(rewrite,[status(thm)],[])).
% 0.22/0.38 tff(19,plain,
% 0.22/0.38 ((~![X: $i] : ((~big_p(X)) | (~((~big_g(X)) | (~big_f(X)))))) | ((~big_p(X!0)) | (~((~big_g(X!0)) | (~big_f(X!0)))))),
% 0.22/0.38 inference(quant_inst,[status(thm)],[])).
% 0.22/0.38 tff(20,plain,
% 0.22/0.38 ((~![X: $i] : ((~big_p(X)) | (~((~big_g(X)) | (~big_f(X)))))) | (~big_p(X!0)) | (~((~big_g(X!0)) | (~big_f(X!0))))),
% 0.22/0.38 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.22/0.38 tff(21,plain,
% 0.22/0.38 (~((~big_g(X!0)) | (~big_f(X!0)))),
% 0.22/0.38 inference(unit_resolution,[status(thm)],[20, 17, 13])).
% 0.22/0.38 tff(22,plain,
% 0.22/0.38 (((~big_g(X!0)) | (~big_f(X!0))) | big_g(X!0)),
% 0.22/0.38 inference(tautology,[status(thm)],[])).
% 0.22/0.38 tff(23,plain,
% 0.22/0.38 (big_g(X!0)),
% 0.22/0.38 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.22/0.38 tff(24,plain,
% 0.22/0.38 ((big_g(X!0) | (~big_r(X!0))) | (~big_g(X!0))),
% 0.22/0.38 inference(tautology,[status(thm)],[])).
% 0.22/0.38 tff(25,plain,
% 0.22/0.38 (big_g(X!0) | (~big_r(X!0))),
% 0.22/0.38 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.22/0.38 tff(26,plain,
% 0.22/0.38 (((~big_g(X!0)) | (~big_f(X!0))) | big_f(X!0)),
% 0.22/0.38 inference(tautology,[status(thm)],[])).
% 0.22/0.38 tff(27,plain,
% 0.22/0.38 (big_f(X!0)),
% 0.22/0.38 inference(unit_resolution,[status(thm)],[26, 21])).
% 0.22/0.38 tff(28,plain,
% 0.22/0.38 (^[X: $i] : refl(((~big_f(X)) | (~(big_g(X) | (~big_r(X))))) <=> ((~big_f(X)) | (~(big_g(X) | (~big_r(X))))))),
% 0.22/0.38 inference(bind,[status(th)],[])).
% 0.22/0.38 tff(29,plain,
% 0.22/0.38 (![X: $i] : ((~big_f(X)) | (~(big_g(X) | (~big_r(X))))) <=> ![X: $i] : ((~big_f(X)) | (~(big_g(X) | (~big_r(X)))))),
% 0.22/0.38 inference(quant_intro,[status(thm)],[28])).
% 0.22/0.38 tff(30,plain,
% 0.22/0.38 (^[X: $i] : rewrite(((~big_f(X)) | ((~big_g(X)) & big_r(X))) <=> ((~big_f(X)) | (~(big_g(X) | (~big_r(X))))))),
% 0.22/0.38 inference(bind,[status(th)],[])).
% 0.22/0.38 tff(31,plain,
% 0.22/0.38 (![X: $i] : ((~big_f(X)) | ((~big_g(X)) & big_r(X))) <=> ![X: $i] : ((~big_f(X)) | (~(big_g(X) | (~big_r(X)))))),
% 0.22/0.38 inference(quant_intro,[status(thm)],[30])).
% 0.22/0.38 tff(32,plain,
% 0.22/0.38 (![X: $i] : ((~big_f(X)) | ((~big_g(X)) & big_r(X))) <=> ![X: $i] : ((~big_f(X)) | ((~big_g(X)) & big_r(X)))),
% 0.22/0.38 inference(rewrite,[status(thm)],[])).
% 0.22/0.38 tff(33,plain,
% 0.22/0.38 (^[X: $i] : rewrite((big_f(X) => ((~big_g(X)) & big_r(X))) <=> ((~big_f(X)) | ((~big_g(X)) & big_r(X))))),
% 0.22/0.38 inference(bind,[status(th)],[])).
% 0.22/0.38 tff(34,plain,
% 0.22/0.38 (![X: $i] : (big_f(X) => ((~big_g(X)) & big_r(X))) <=> ![X: $i] : ((~big_f(X)) | ((~big_g(X)) & big_r(X)))),
% 0.22/0.38 inference(quant_intro,[status(thm)],[33])).
% 0.22/0.38 tff(35,axiom,(![X: $i] : (big_f(X) => ((~big_g(X)) & big_r(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel25_2')).
% 0.22/0.38 tff(36,plain,
% 0.22/0.38 (![X: $i] : ((~big_f(X)) | ((~big_g(X)) & big_r(X)))),
% 0.22/0.38 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.22/0.38 tff(37,plain,
% 0.22/0.38 (![X: $i] : ((~big_f(X)) | ((~big_g(X)) & big_r(X)))),
% 0.22/0.38 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.22/0.38 tff(38,plain,(
% 0.22/0.38 ![X: $i] : ((~big_f(X)) | ((~big_g(X)) & big_r(X)))),
% 0.22/0.38 inference(skolemize,[status(sab)],[37])).
% 0.22/0.38 tff(39,plain,
% 0.22/0.38 (![X: $i] : ((~big_f(X)) | (~(big_g(X) | (~big_r(X)))))),
% 0.22/0.38 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.22/0.38 tff(40,plain,
% 0.22/0.38 (![X: $i] : ((~big_f(X)) | (~(big_g(X) | (~big_r(X)))))),
% 0.22/0.38 inference(modus_ponens,[status(thm)],[39, 29])).
% 0.22/0.38 tff(41,plain,
% 0.22/0.38 (((~![X: $i] : ((~big_f(X)) | (~(big_g(X) | (~big_r(X)))))) | ((~big_f(X!0)) | (~(big_g(X!0) | (~big_r(X!0)))))) <=> ((~![X: $i] : ((~big_f(X)) | (~(big_g(X) | (~big_r(X)))))) | (~big_f(X!0)) | (~(big_g(X!0) | (~big_r(X!0)))))),
% 0.22/0.38 inference(rewrite,[status(thm)],[])).
% 0.22/0.38 tff(42,plain,
% 0.22/0.38 ((~![X: $i] : ((~big_f(X)) | (~(big_g(X) | (~big_r(X)))))) | ((~big_f(X!0)) | (~(big_g(X!0) | (~big_r(X!0)))))),
% 0.22/0.38 inference(quant_inst,[status(thm)],[])).
% 0.22/0.38 tff(43,plain,
% 0.22/0.38 ((~![X: $i] : ((~big_f(X)) | (~(big_g(X) | (~big_r(X)))))) | (~big_f(X!0)) | (~(big_g(X!0) | (~big_r(X!0))))),
% 0.22/0.38 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.22/0.38 tff(44,plain,
% 0.22/0.38 ($false),
% 0.22/0.38 inference(unit_resolution,[status(thm)],[43, 40, 27, 25])).
% 0.22/0.38 % SZS output end Proof
% 0.22/0.39 % E exiting
%------------------------------------------------------------------------------