%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN061+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 05:38:06 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
% 0.07/0.12 % Problem : SYN061+1 : TPTP v9.0.0. Released v2.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:27:05 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(big_j_type, type, (
% 0.12/0.36 big_j: $i > $o)).
% 0.12/0.36 tff(tptp_fun_X_0_type, type, (
% 0.12/0.36 tptp_fun_X_0: $i)).
% 0.12/0.36 tff(big_i_type, type, (
% 0.12/0.36 big_i: $i > $o)).
% 0.12/0.36 tff(big_f_type, type, (
% 0.12/0.36 big_f: $i > $o)).
% 0.12/0.36 tff(big_h_type, type, (
% 0.12/0.36 big_h: $i > $o)).
% 0.12/0.36 tff(big_g_type, type, (
% 0.12/0.36 big_g: $i > $o)).
% 0.12/0.36 tff(1,plain,
% 0.12/0.36 (^[X: $i] : refl(((~big_i(X)) | (~big_j(X))) <=> ((~big_i(X)) | (~big_j(X))))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(2,plain,
% 0.12/0.36 (![X: $i] : ((~big_i(X)) | (~big_j(X))) <=> ![X: $i] : ((~big_i(X)) | (~big_j(X)))),
% 0.12/0.36 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.36 tff(3,plain,
% 0.12/0.36 (^[X: $i] : trans(monotonicity(rewrite((big_i(X) & big_j(X)) <=> (~((~big_i(X)) | (~big_j(X))))), ((~(big_i(X) & big_j(X))) <=> (~(~((~big_i(X)) | (~big_j(X))))))), rewrite((~(~((~big_i(X)) | (~big_j(X))))) <=> ((~big_i(X)) | (~big_j(X)))), ((~(big_i(X) & big_j(X))) <=> ((~big_i(X)) | (~big_j(X)))))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(4,plain,
% 0.12/0.36 (![X: $i] : (~(big_i(X) & big_j(X))) <=> ![X: $i] : ((~big_i(X)) | (~big_j(X)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.37 tff(5,plain,
% 0.12/0.37 ((~?[X: $i] : (big_i(X) & big_j(X))) <=> (~?[X: $i] : (big_i(X) & big_j(X)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(6,axiom,(~?[X: $i] : (big_i(X) & big_j(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel31')).
% 0.12/0.37 tff(7,plain,
% 0.12/0.37 (~?[X: $i] : (big_i(X) & big_j(X))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.12/0.37 tff(8,plain,
% 0.12/0.37 (~?[X: $i] : (big_i(X) & big_j(X))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[7, 5])).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 (~?[X: $i] : (big_i(X) & big_j(X))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.12/0.37 tff(10,plain,
% 0.12/0.37 (~?[X: $i] : (big_i(X) & big_j(X))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.12/0.37 tff(11,plain,
% 0.12/0.37 (^[X: $i] : refl($oeq((~(big_i(X) & big_j(X))), (~(big_i(X) & big_j(X)))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(12,plain,(
% 0.12/0.37 ![X: $i] : (~(big_i(X) & big_j(X)))),
% 0.12/0.37 inference(nnf-neg,[status(sab)],[10, 11])).
% 0.12/0.37 tff(13,plain,
% 0.12/0.37 (![X: $i] : ((~big_i(X)) | (~big_j(X)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[12, 4])).
% 0.12/0.37 tff(14,plain,
% 0.12/0.37 (![X: $i] : ((~big_i(X)) | (~big_j(X)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[13, 2])).
% 0.12/0.37 tff(15,plain,
% 0.12/0.37 (?[X: $i] : (big_i(X) & big_f(X)) <=> ?[X: $i] : (big_i(X) & big_f(X))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(16,axiom,(?[X: $i] : (big_i(X) & big_f(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel31_2')).
% 0.12/0.37 tff(17,plain,
% 0.12/0.37 (?[X: $i] : (big_i(X) & big_f(X))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.12/0.37 tff(18,plain,(
% 0.12/0.37 big_i(X!0) & big_f(X!0)),
% 0.12/0.37 inference(skolemize,[status(sab)],[17])).
% 0.12/0.37 tff(19,plain,
% 0.12/0.37 (big_i(X!0)),
% 0.12/0.37 inference(and_elim,[status(thm)],[18])).
% 0.12/0.37 tff(20,plain,
% 0.12/0.37 (((~![X: $i] : ((~big_i(X)) | (~big_j(X)))) | ((~big_i(X!0)) | (~big_j(X!0)))) <=> ((~![X: $i] : ((~big_i(X)) | (~big_j(X)))) | (~big_i(X!0)) | (~big_j(X!0)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(21,plain,
% 0.12/0.37 ((~![X: $i] : ((~big_i(X)) | (~big_j(X)))) | ((~big_i(X!0)) | (~big_j(X!0)))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(22,plain,
% 0.12/0.37 ((~![X: $i] : ((~big_i(X)) | (~big_j(X)))) | (~big_i(X!0)) | (~big_j(X!0))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.12/0.37 tff(23,plain,
% 0.12/0.37 (~big_j(X!0)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[22, 19, 14])).
% 0.12/0.37 tff(24,plain,
% 0.12/0.37 (big_f(X!0)),
% 0.12/0.37 inference(and_elim,[status(thm)],[18])).
% 0.12/0.37 tff(25,plain,
% 0.12/0.37 (^[X: $i] : refl(((~big_f(X)) | (~(big_g(X) | big_h(X)))) <=> ((~big_f(X)) | (~(big_g(X) | big_h(X)))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(26,plain,
% 0.12/0.37 (![X: $i] : ((~big_f(X)) | (~(big_g(X) | big_h(X)))) <=> ![X: $i] : ((~big_f(X)) | (~(big_g(X) | big_h(X))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[25])).
% 0.12/0.37 tff(27,plain,
% 0.12/0.37 (^[X: $i] : trans(monotonicity(rewrite((big_f(X) & (big_g(X) | big_h(X))) <=> (~((~big_f(X)) | (~(big_g(X) | big_h(X)))))), ((~(big_f(X) & (big_g(X) | big_h(X)))) <=> (~(~((~big_f(X)) | (~(big_g(X) | big_h(X)))))))), rewrite((~(~((~big_f(X)) | (~(big_g(X) | big_h(X)))))) <=> ((~big_f(X)) | (~(big_g(X) | big_h(X))))), ((~(big_f(X) & (big_g(X) | big_h(X)))) <=> ((~big_f(X)) | (~(big_g(X) | big_h(X))))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(28,plain,
% 0.12/0.37 (![X: $i] : (~(big_f(X) & (big_g(X) | big_h(X)))) <=> ![X: $i] : ((~big_f(X)) | (~(big_g(X) | big_h(X))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[27])).
% 0.12/0.37 tff(29,plain,
% 0.12/0.37 ((~?[X: $i] : (big_f(X) & (big_g(X) | big_h(X)))) <=> (~?[X: $i] : (big_f(X) & (big_g(X) | big_h(X))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(30,axiom,(~?[X: $i] : (big_f(X) & (big_g(X) | big_h(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel31_1')).
% 0.12/0.37 tff(31,plain,
% 0.12/0.37 (~?[X: $i] : (big_f(X) & (big_g(X) | big_h(X)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.12/0.37 tff(32,plain,
% 0.12/0.37 (~?[X: $i] : (big_f(X) & (big_g(X) | big_h(X)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[31, 29])).
% 0.12/0.37 tff(33,plain,
% 0.12/0.37 (~?[X: $i] : (big_f(X) & (big_g(X) | big_h(X)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[32, 29])).
% 0.12/0.37 tff(34,plain,
% 0.12/0.37 (~?[X: $i] : (big_f(X) & (big_g(X) | big_h(X)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.12/0.37 tff(35,plain,
% 0.12/0.37 (^[X: $i] : refl($oeq((~(big_f(X) & (big_g(X) | big_h(X)))), (~(big_f(X) & (big_g(X) | big_h(X))))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(36,plain,(
% 0.12/0.37 ![X: $i] : (~(big_f(X) & (big_g(X) | big_h(X))))),
% 0.12/0.37 inference(nnf-neg,[status(sab)],[34, 35])).
% 0.12/0.37 tff(37,plain,
% 0.12/0.37 (![X: $i] : ((~big_f(X)) | (~(big_g(X) | big_h(X))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[36, 28])).
% 0.12/0.37 tff(38,plain,
% 0.12/0.37 (![X: $i] : ((~big_f(X)) | (~(big_g(X) | big_h(X))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[37, 26])).
% 0.12/0.37 tff(39,plain,
% 0.12/0.37 (((~![X: $i] : ((~big_f(X)) | (~(big_g(X) | big_h(X))))) | ((~big_f(X!0)) | (~(big_g(X!0) | big_h(X!0))))) <=> ((~![X: $i] : ((~big_f(X)) | (~(big_g(X) | big_h(X))))) | (~big_f(X!0)) | (~(big_g(X!0) | big_h(X!0))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(40,plain,
% 0.12/0.37 ((~![X: $i] : ((~big_f(X)) | (~(big_g(X) | big_h(X))))) | ((~big_f(X!0)) | (~(big_g(X!0) | big_h(X!0))))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(41,plain,
% 0.12/0.37 ((~![X: $i] : ((~big_f(X)) | (~(big_g(X) | big_h(X))))) | (~big_f(X!0)) | (~(big_g(X!0) | big_h(X!0)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.12/0.37 tff(42,plain,
% 0.12/0.37 (~(big_g(X!0) | big_h(X!0))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[41, 38, 24])).
% 0.12/0.37 tff(43,plain,
% 0.12/0.37 ((big_g(X!0) | big_h(X!0)) | (~big_h(X!0))),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(44,plain,
% 0.12/0.37 (~big_h(X!0)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.12/0.37 tff(45,plain,
% 0.12/0.37 (^[X: $i] : refl((big_h(X) | big_j(X)) <=> (big_h(X) | big_j(X)))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(46,plain,
% 0.12/0.37 (![X: $i] : (big_h(X) | big_j(X)) <=> ![X: $i] : (big_h(X) | big_j(X))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[45])).
% 0.12/0.37 tff(47,plain,
% 0.12/0.37 (![X: $i] : (big_h(X) | big_j(X)) <=> ![X: $i] : (big_h(X) | big_j(X))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(48,plain,
% 0.12/0.37 (^[X: $i] : rewrite(((~big_h(X)) => big_j(X)) <=> (big_h(X) | big_j(X)))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(49,plain,
% 0.12/0.37 (![X: $i] : ((~big_h(X)) => big_j(X)) <=> ![X: $i] : (big_h(X) | big_j(X))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[48])).
% 0.12/0.37 tff(50,axiom,(![X: $i] : ((~big_h(X)) => big_j(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel31_3')).
% 0.12/0.37 tff(51,plain,
% 0.12/0.37 (![X: $i] : (big_h(X) | big_j(X))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.12/0.37 tff(52,plain,
% 0.12/0.37 (![X: $i] : (big_h(X) | big_j(X))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.12/0.37 tff(53,plain,(
% 0.12/0.37 ![X: $i] : (big_h(X) | big_j(X))),
% 0.12/0.37 inference(skolemize,[status(sab)],[52])).
% 0.12/0.37 tff(54,plain,
% 0.12/0.37 (![X: $i] : (big_h(X) | big_j(X))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.12/0.37 tff(55,plain,
% 0.12/0.37 (((~![X: $i] : (big_h(X) | big_j(X))) | (big_h(X!0) | big_j(X!0))) <=> ((~![X: $i] : (big_h(X) | big_j(X))) | big_h(X!0) | big_j(X!0))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(56,plain,
% 0.12/0.37 ((~![X: $i] : (big_h(X) | big_j(X))) | (big_h(X!0) | big_j(X!0))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(57,plain,
% 0.12/0.37 ((~![X: $i] : (big_h(X) | big_j(X))) | big_h(X!0) | big_j(X!0)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.12/0.37 tff(58,plain,
% 0.12/0.37 ($false),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[57, 54, 44, 23])).
% 0.12/0.37 % SZS output end Proof
% 0.12/0.37 % E exiting
%------------------------------------------------------------------------------