%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN062+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 0.11s 0.36s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN062+1 : TPTP v9.0.0. Released v2.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n007.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 12:28:50 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.36 % SZS status Theorem
% 0.11/0.36 % SZS output start Proof
% 0.11/0.36 tff(big_h_type, type, (
% 0.11/0.36 big_h: $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_g_type, type, (
% 0.11/0.36 big_g: $i > $o)).
% 0.11/0.36 tff(big_k_type, type, (
% 0.11/0.36 big_k: $i > $o)).
% 0.11/0.36 tff(big_f_type, type, (
% 0.11/0.36 big_f: $i > $o)).
% 0.11/0.36 tff(big_j_type, type, (
% 0.11/0.36 big_j: $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_j(X) | (~(big_f(X) & big_k(X))))) <=> (~![X: $i] : (big_j(X) | (~(big_f(X) & big_k(X)))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(2,plain,
% 0.11/0.36 ((~![X: $i] : ((big_f(X) & big_k(X)) => big_j(X))) <=> (~![X: $i] : (big_j(X) | (~(big_f(X) & big_k(X)))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(3,axiom,(~![X: $i] : ((big_f(X) & big_k(X)) => big_j(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel32')).
% 0.11/0.36 tff(4,plain,
% 0.11/0.36 (~![X: $i] : (big_j(X) | (~(big_f(X) & big_k(X))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.11/0.36 tff(5,plain,
% 0.11/0.36 (~![X: $i] : (big_j(X) | (~(big_f(X) & big_k(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_j(X) | (~(big_f(X) & big_k(X))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.11/0.36 tff(7,plain,
% 0.11/0.36 (~![X: $i] : (big_j(X) | (~(big_f(X) & big_k(X))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.11/0.36 tff(8,plain,(
% 0.11/0.36 ~(big_j(X!0) | (~(big_f(X!0) & big_k(X!0))))),
% 0.11/0.36 inference(skolemize,[status(sab)],[7])).
% 0.11/0.36 tff(9,plain,
% 0.11/0.36 (big_f(X!0) & big_k(X!0)),
% 0.11/0.36 inference(or_elim,[status(thm)],[8])).
% 0.11/0.36 tff(10,plain,
% 0.11/0.36 (big_k(X!0)),
% 0.11/0.36 inference(and_elim,[status(thm)],[9])).
% 0.11/0.36 tff(11,plain,
% 0.11/0.36 (^[X: $i] : refl((big_h(X) | (~big_k(X))) <=> (big_h(X) | (~big_k(X))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(12,plain,
% 0.11/0.36 (![X: $i] : (big_h(X) | (~big_k(X))) <=> ![X: $i] : (big_h(X) | (~big_k(X)))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[11])).
% 0.11/0.36 tff(13,plain,
% 0.11/0.36 (![X: $i] : (big_h(X) | (~big_k(X))) <=> ![X: $i] : (big_h(X) | (~big_k(X)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(14,plain,
% 0.11/0.36 (^[X: $i] : rewrite((big_k(X) => big_h(X)) <=> (big_h(X) | (~big_k(X))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(15,plain,
% 0.11/0.36 (![X: $i] : (big_k(X) => big_h(X)) <=> ![X: $i] : (big_h(X) | (~big_k(X)))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[14])).
% 0.11/0.36 tff(16,axiom,(![X: $i] : (big_k(X) => big_h(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel32_3')).
% 0.11/0.36 tff(17,plain,
% 0.11/0.36 (![X: $i] : (big_h(X) | (~big_k(X)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.11/0.36 tff(18,plain,
% 0.11/0.36 (![X: $i] : (big_h(X) | (~big_k(X)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.11/0.36 tff(19,plain,(
% 0.11/0.36 ![X: $i] : (big_h(X) | (~big_k(X)))),
% 0.11/0.36 inference(skolemize,[status(sab)],[18])).
% 0.11/0.36 tff(20,plain,
% 0.11/0.36 (![X: $i] : (big_h(X) | (~big_k(X)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.11/0.36 tff(21,plain,
% 0.11/0.36 (((~![X: $i] : (big_h(X) | (~big_k(X)))) | (big_h(X!0) | (~big_k(X!0)))) <=> ((~![X: $i] : (big_h(X) | (~big_k(X)))) | big_h(X!0) | (~big_k(X!0)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(22,plain,
% 0.11/0.36 ((~![X: $i] : (big_h(X) | (~big_k(X)))) | (big_h(X!0) | (~big_k(X!0)))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(23,plain,
% 0.11/0.36 ((~![X: $i] : (big_h(X) | (~big_k(X)))) | big_h(X!0) | (~big_k(X!0))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.11/0.36 tff(24,plain,
% 0.11/0.36 (big_h(X!0)),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[23, 20, 10])).
% 0.11/0.36 tff(25,plain,
% 0.11/0.36 ((big_g(X!0) | big_h(X!0)) | (~big_h(X!0))),
% 0.11/0.36 inference(tautology,[status(thm)],[])).
% 0.11/0.36 tff(26,plain,
% 0.11/0.36 (big_g(X!0) | big_h(X!0)),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.11/0.36 tff(27,plain,
% 0.11/0.36 (~big_j(X!0)),
% 0.11/0.36 inference(or_elim,[status(thm)],[8])).
% 0.11/0.36 tff(28,plain,
% 0.11/0.36 (^[X: $i] : refl((big_j(X) | (~big_i(X)) | (~big_h(X))) <=> (big_j(X) | (~big_i(X)) | (~big_h(X))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(29,plain,
% 0.11/0.36 (![X: $i] : (big_j(X) | (~big_i(X)) | (~big_h(X))) <=> ![X: $i] : (big_j(X) | (~big_i(X)) | (~big_h(X)))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[28])).
% 0.11/0.36 tff(30,plain,
% 0.11/0.36 (^[X: $i] : trans(monotonicity(trans(monotonicity(rewrite((big_i(X) & big_h(X)) <=> (~((~big_i(X)) | (~big_h(X))))), ((~(big_i(X) & big_h(X))) <=> (~(~((~big_i(X)) | (~big_h(X))))))), rewrite((~(~((~big_i(X)) | (~big_h(X))))) <=> ((~big_i(X)) | (~big_h(X)))), ((~(big_i(X) & big_h(X))) <=> ((~big_i(X)) | (~big_h(X))))), ((big_j(X) | (~(big_i(X) & big_h(X)))) <=> (big_j(X) | ((~big_i(X)) | (~big_h(X)))))), rewrite((big_j(X) | ((~big_i(X)) | (~big_h(X)))) <=> (big_j(X) | (~big_i(X)) | (~big_h(X)))), ((big_j(X) | (~(big_i(X) & big_h(X)))) <=> (big_j(X) | (~big_i(X)) | (~big_h(X)))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(31,plain,
% 0.11/0.36 (![X: $i] : (big_j(X) | (~(big_i(X) & big_h(X)))) <=> ![X: $i] : (big_j(X) | (~big_i(X)) | (~big_h(X)))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[30])).
% 0.11/0.36 tff(32,plain,
% 0.11/0.36 (![X: $i] : (big_j(X) | (~(big_i(X) & big_h(X)))) <=> ![X: $i] : (big_j(X) | (~(big_i(X) & big_h(X))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(33,plain,
% 0.11/0.36 (^[X: $i] : rewrite(((big_i(X) & big_h(X)) => big_j(X)) <=> (big_j(X) | (~(big_i(X) & big_h(X)))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(34,plain,
% 0.11/0.36 (![X: $i] : ((big_i(X) & big_h(X)) => big_j(X)) <=> ![X: $i] : (big_j(X) | (~(big_i(X) & big_h(X))))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[33])).
% 0.11/0.36 tff(35,axiom,(![X: $i] : ((big_i(X) & big_h(X)) => big_j(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel32_2')).
% 0.11/0.36 tff(36,plain,
% 0.11/0.36 (![X: $i] : (big_j(X) | (~(big_i(X) & big_h(X))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.11/0.36 tff(37,plain,
% 0.11/0.36 (![X: $i] : (big_j(X) | (~(big_i(X) & big_h(X))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.11/0.36 tff(38,plain,(
% 0.11/0.36 ![X: $i] : (big_j(X) | (~(big_i(X) & big_h(X))))),
% 0.11/0.36 inference(skolemize,[status(sab)],[37])).
% 0.11/0.36 tff(39,plain,
% 0.11/0.36 (![X: $i] : (big_j(X) | (~big_i(X)) | (~big_h(X)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.11/0.36 tff(40,plain,
% 0.11/0.36 (![X: $i] : (big_j(X) | (~big_i(X)) | (~big_h(X)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[39, 29])).
% 0.11/0.36 tff(41,plain,
% 0.11/0.36 (((~![X: $i] : (big_j(X) | (~big_i(X)) | (~big_h(X)))) | (big_j(X!0) | (~big_i(X!0)) | (~big_h(X!0)))) <=> ((~![X: $i] : (big_j(X) | (~big_i(X)) | (~big_h(X)))) | big_j(X!0) | (~big_i(X!0)) | (~big_h(X!0)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(42,plain,
% 0.11/0.36 ((~![X: $i] : (big_j(X) | (~big_i(X)) | (~big_h(X)))) | (big_j(X!0) | (~big_i(X!0)) | (~big_h(X!0)))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(43,plain,
% 0.11/0.36 ((~![X: $i] : (big_j(X) | (~big_i(X)) | (~big_h(X)))) | big_j(X!0) | (~big_i(X!0)) | (~big_h(X!0))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.11/0.36 tff(44,plain,
% 0.11/0.36 ((~big_i(X!0)) | (~big_h(X!0))),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[43, 40, 27])).
% 0.11/0.36 tff(45,plain,
% 0.11/0.36 (~big_i(X!0)),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[44, 24])).
% 0.11/0.36 tff(46,plain,
% 0.11/0.36 (big_f(X!0)),
% 0.11/0.36 inference(and_elim,[status(thm)],[9])).
% 0.11/0.36 tff(47,plain,
% 0.11/0.36 (^[X: $i] : refl((big_i(X) | (~big_f(X)) | (~(big_g(X) | big_h(X)))) <=> (big_i(X) | (~big_f(X)) | (~(big_g(X) | big_h(X)))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(48,plain,
% 0.11/0.36 (![X: $i] : (big_i(X) | (~big_f(X)) | (~(big_g(X) | big_h(X)))) <=> ![X: $i] : (big_i(X) | (~big_f(X)) | (~(big_g(X) | big_h(X))))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[47])).
% 0.11/0.36 tff(49,plain,
% 0.11/0.36 (^[X: $i] : trans(monotonicity(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)))))), ((big_i(X) | (~(big_f(X) & (big_g(X) | big_h(X))))) <=> (big_i(X) | ((~big_f(X)) | (~(big_g(X) | big_h(X))))))), rewrite((big_i(X) | ((~big_f(X)) | (~(big_g(X) | big_h(X))))) <=> (big_i(X) | (~big_f(X)) | (~(big_g(X) | big_h(X))))), ((big_i(X) | (~(big_f(X) & (big_g(X) | big_h(X))))) <=> (big_i(X) | (~big_f(X)) | (~(big_g(X) | big_h(X))))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(50,plain,
% 0.11/0.36 (![X: $i] : (big_i(X) | (~(big_f(X) & (big_g(X) | big_h(X))))) <=> ![X: $i] : (big_i(X) | (~big_f(X)) | (~(big_g(X) | big_h(X))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[49])).
% 0.11/0.37 tff(51,plain,
% 0.11/0.37 (![X: $i] : (big_i(X) | (~(big_f(X) & (big_g(X) | big_h(X))))) <=> ![X: $i] : (big_i(X) | (~(big_f(X) & (big_g(X) | big_h(X)))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(52,plain,
% 0.11/0.37 (^[X: $i] : rewrite(((big_f(X) & (big_g(X) | big_h(X))) => big_i(X)) <=> (big_i(X) | (~(big_f(X) & (big_g(X) | big_h(X))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(53,plain,
% 0.11/0.37 (![X: $i] : ((big_f(X) & (big_g(X) | big_h(X))) => big_i(X)) <=> ![X: $i] : (big_i(X) | (~(big_f(X) & (big_g(X) | big_h(X)))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[52])).
% 0.11/0.37 tff(54,axiom,(![X: $i] : ((big_f(X) & (big_g(X) | big_h(X))) => big_i(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel32_1')).
% 0.11/0.37 tff(55,plain,
% 0.11/0.37 (![X: $i] : (big_i(X) | (~(big_f(X) & (big_g(X) | big_h(X)))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.11/0.37 tff(56,plain,
% 0.11/0.37 (![X: $i] : (big_i(X) | (~(big_f(X) & (big_g(X) | big_h(X)))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.11/0.37 tff(57,plain,(
% 0.11/0.37 ![X: $i] : (big_i(X) | (~(big_f(X) & (big_g(X) | big_h(X)))))),
% 0.11/0.37 inference(skolemize,[status(sab)],[56])).
% 0.11/0.37 tff(58,plain,
% 0.11/0.37 (![X: $i] : (big_i(X) | (~big_f(X)) | (~(big_g(X) | big_h(X))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.11/0.37 tff(59,plain,
% 0.11/0.37 (![X: $i] : (big_i(X) | (~big_f(X)) | (~(big_g(X) | big_h(X))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[58, 48])).
% 0.11/0.37 tff(60,plain,
% 0.11/0.37 (((~![X: $i] : (big_i(X) | (~big_f(X)) | (~(big_g(X) | big_h(X))))) | (big_i(X!0) | (~big_f(X!0)) | (~(big_g(X!0) | big_h(X!0))))) <=> ((~![X: $i] : (big_i(X) | (~big_f(X)) | (~(big_g(X) | big_h(X))))) | big_i(X!0) | (~big_f(X!0)) | (~(big_g(X!0) | big_h(X!0))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(61,plain,
% 0.11/0.37 ((~![X: $i] : (big_i(X) | (~big_f(X)) | (~(big_g(X) | big_h(X))))) | (big_i(X!0) | (~big_f(X!0)) | (~(big_g(X!0) | big_h(X!0))))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(62,plain,
% 0.11/0.37 ((~![X: $i] : (big_i(X) | (~big_f(X)) | (~(big_g(X) | big_h(X))))) | big_i(X!0) | (~big_f(X!0)) | (~(big_g(X!0) | big_h(X!0)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.11/0.37 tff(63,plain,
% 0.11/0.37 (big_i(X!0) | (~(big_g(X!0) | big_h(X!0)))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[62, 59, 46])).
% 0.11/0.37 tff(64,plain,
% 0.11/0.37 ($false),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[63, 45, 26])).
% 0.11/0.37 % SZS output end Proof
% 0.20/0.37 % E exiting
%------------------------------------------------------------------------------