%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN059+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 0.16s 0.34s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SYN059+1 : TPTP v9.0.0. Released v2.0.0.
% 0.11/0.11 % Command : run_E %s %d THM
% 0.11/0.30 % Computer : n008.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Fri Jun 20 12:27:18 EDT 2025
% 0.11/0.31 % CPUTime :
% 0.16/0.34 % SZS status Theorem
% 0.16/0.34 % SZS output start Proof
% 0.16/0.34 tff(big_j_type, type, (
% 0.16/0.34 big_j: $i > $o)).
% 0.16/0.34 tff(tptp_fun_U_3_type, type, (
% 0.16/0.34 tptp_fun_U_3: $i)).
% 0.16/0.34 tff(big_h_type, type, (
% 0.16/0.34 big_h: $i > $o)).
% 0.16/0.34 tff(tptp_fun_X_0_type, type, (
% 0.16/0.34 tptp_fun_X_0: $i)).
% 0.16/0.34 tff(big_g_type, type, (
% 0.16/0.34 big_g: $i > $o)).
% 0.16/0.34 tff(big_f_type, type, (
% 0.16/0.34 big_f: $i > $o)).
% 0.16/0.34 tff(tptp_fun_X_2_type, type, (
% 0.16/0.34 tptp_fun_X_2: $i)).
% 0.16/0.34 tff(tptp_fun_Y_1_type, type, (
% 0.16/0.34 tptp_fun_Y_1: $i)).
% 0.16/0.34 tff(tptp_fun_Y_4_type, type, (
% 0.16/0.34 tptp_fun_Y_4: $i)).
% 0.16/0.34 tff(tptp_fun_W_5_type, type, (
% 0.16/0.34 tptp_fun_W_5: $i)).
% 0.16/0.34 tff(1,assumption,(~(big_h(X!2) | (~big_f(X!2)))), introduced(assumption)).
% 0.16/0.34 tff(2,plain,
% 0.16/0.34 ((big_h(X!2) | (~big_f(X!2))) | (~big_h(X!2))),
% 0.16/0.34 inference(tautology,[status(thm)],[])).
% 0.16/0.34 tff(3,plain,
% 0.16/0.34 (~big_h(X!2)),
% 0.16/0.34 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.16/0.34 tff(4,plain,
% 0.16/0.34 (((~big_h(X!2)) | (~big_j(Y!1))) | big_h(X!2)),
% 0.16/0.34 inference(tautology,[status(thm)],[])).
% 0.16/0.34 tff(5,plain,
% 0.16/0.34 ((~big_h(X!2)) | (~big_j(Y!1))),
% 0.16/0.34 inference(unit_resolution,[status(thm)],[4, 3])).
% 0.16/0.34 tff(6,plain,
% 0.16/0.34 ((big_h(X!2) | (~big_f(X!2))) | big_f(X!2)),
% 0.16/0.34 inference(tautology,[status(thm)],[])).
% 0.16/0.34 tff(7,plain,
% 0.16/0.34 (big_f(X!2)),
% 0.16/0.34 inference(unit_resolution,[status(thm)],[6, 1])).
% 0.16/0.34 tff(8,assumption,(~((~![X: $i] : (big_h(X) | (~big_f(X)))) | (~![U: $i] : (big_j(U) | (~big_g(U)))))), introduced(assumption)).
% 0.16/0.34 tff(9,plain,
% 0.16/0.34 (((~![X: $i] : (big_h(X) | (~big_f(X)))) | (~![U: $i] : (big_j(U) | (~big_g(U))))) | ![U: $i] : (big_j(U) | (~big_g(U)))),
% 0.16/0.34 inference(tautology,[status(thm)],[])).
% 0.16/0.34 tff(10,plain,
% 0.16/0.34 (![U: $i] : (big_j(U) | (~big_g(U)))),
% 0.16/0.34 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.16/0.34 tff(11,plain,
% 0.16/0.34 (((~![X: $i] : (big_h(X) | (~big_f(X)))) | (~![U: $i] : (big_j(U) | (~big_g(U))))) | ![X: $i] : (big_h(X) | (~big_f(X)))),
% 0.16/0.34 inference(tautology,[status(thm)],[])).
% 0.16/0.34 tff(12,plain,
% 0.16/0.34 (![X: $i] : (big_h(X) | (~big_f(X)))),
% 0.16/0.34 inference(unit_resolution,[status(thm)],[11, 8])).
% 0.16/0.34 tff(13,assumption,(~((~big_f(W!5)) | (~big_g(Y!4)) | (~((~big_h(W!5)) | (~big_j(Y!4)))))), introduced(assumption)).
% 0.16/0.34 tff(14,plain,
% 0.16/0.34 (((~big_f(W!5)) | (~big_g(Y!4)) | (~((~big_h(W!5)) | (~big_j(Y!4))))) | ((~big_h(W!5)) | (~big_j(Y!4)))),
% 0.16/0.34 inference(tautology,[status(thm)],[])).
% 0.16/0.34 tff(15,plain,
% 0.16/0.34 ((~big_h(W!5)) | (~big_j(Y!4))),
% 0.16/0.34 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.16/0.34 tff(16,plain,
% 0.16/0.34 (((~big_f(W!5)) | (~big_g(Y!4)) | (~((~big_h(W!5)) | (~big_j(Y!4))))) | big_g(Y!4)),
% 0.16/0.34 inference(tautology,[status(thm)],[])).
% 0.16/0.34 tff(17,plain,
% 0.16/0.34 (big_g(Y!4)),
% 0.16/0.34 inference(unit_resolution,[status(thm)],[16, 13])).
% 0.16/0.34 tff(18,assumption,(![U: $i] : (big_j(U) | (~big_g(U)))), introduced(assumption)).
% 0.16/0.34 tff(19,plain,
% 0.16/0.34 (((~![U: $i] : (big_j(U) | (~big_g(U)))) | (big_j(Y!4) | (~big_g(Y!4)))) <=> ((~![U: $i] : (big_j(U) | (~big_g(U)))) | big_j(Y!4) | (~big_g(Y!4)))),
% 0.16/0.34 inference(rewrite,[status(thm)],[])).
% 0.16/0.34 tff(20,plain,
% 0.16/0.34 ((~![U: $i] : (big_j(U) | (~big_g(U)))) | (big_j(Y!4) | (~big_g(Y!4)))),
% 0.16/0.34 inference(quant_inst,[status(thm)],[])).
% 0.16/0.34 tff(21,plain,
% 0.16/0.34 ((~![U: $i] : (big_j(U) | (~big_g(U)))) | big_j(Y!4) | (~big_g(Y!4))),
% 0.16/0.34 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.16/0.34 tff(22,plain,
% 0.16/0.34 (big_j(Y!4)),
% 0.16/0.34 inference(unit_resolution,[status(thm)],[21, 18, 17])).
% 0.16/0.34 tff(23,plain,
% 0.16/0.34 (((~big_f(W!5)) | (~big_g(Y!4)) | (~((~big_h(W!5)) | (~big_j(Y!4))))) | big_f(W!5)),
% 0.16/0.34 inference(tautology,[status(thm)],[])).
% 0.16/0.34 tff(24,plain,
% 0.16/0.34 (big_f(W!5)),
% 0.16/0.34 inference(unit_resolution,[status(thm)],[23, 13])).
% 0.16/0.34 tff(25,assumption,(![X: $i] : (big_h(X) | (~big_f(X)))), introduced(assumption)).
% 0.16/0.34 tff(26,plain,
% 0.16/0.34 (((~![X: $i] : (big_h(X) | (~big_f(X)))) | (big_h(W!5) | (~big_f(W!5)))) <=> ((~![X: $i] : (big_h(X) | (~big_f(X)))) | big_h(W!5) | (~big_f(W!5)))),
% 0.16/0.34 inference(rewrite,[status(thm)],[])).
% 0.16/0.34 tff(27,plain,
% 0.16/0.34 ((~![X: $i] : (big_h(X) | (~big_f(X)))) | (big_h(W!5) | (~big_f(W!5)))),
% 0.16/0.34 inference(quant_inst,[status(thm)],[])).
% 0.16/0.34 tff(28,plain,
% 0.16/0.34 ((~![X: $i] : (big_h(X) | (~big_f(X)))) | big_h(W!5) | (~big_f(W!5))),
% 0.16/0.34 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.16/0.34 tff(29,plain,
% 0.16/0.34 (big_h(W!5)),
% 0.16/0.34 inference(unit_resolution,[status(thm)],[28, 25, 24])).
% 0.16/0.35 tff(30,plain,
% 0.16/0.35 ((~((~big_h(W!5)) | (~big_j(Y!4)))) | (~big_h(W!5)) | (~big_j(Y!4))),
% 0.16/0.35 inference(tautology,[status(thm)],[])).
% 0.16/0.35 tff(31,plain,
% 0.16/0.35 ($false),
% 0.16/0.35 inference(unit_resolution,[status(thm)],[30, 29, 22, 15])).
% 0.16/0.35 tff(32,plain,(((~big_f(W!5)) | (~big_g(Y!4)) | (~((~big_h(W!5)) | (~big_j(Y!4))))) | (~![X: $i] : (big_h(X) | (~big_f(X)))) | (~![U: $i] : (big_j(U) | (~big_g(U))))), inference(lemma,lemma(discharge,[]))).
% 0.16/0.35 tff(33,plain,
% 0.16/0.35 ((~big_f(W!5)) | (~big_g(Y!4)) | (~((~big_h(W!5)) | (~big_j(Y!4))))),
% 0.16/0.35 inference(unit_resolution,[status(thm)],[32, 12, 10])).
% 0.16/0.35 tff(34,plain,
% 0.16/0.35 (((~![X: $i] : (big_h(X) | (~big_f(X)))) | (big_h(X!2) | (~big_f(X!2)))) <=> ((~![X: $i] : (big_h(X) | (~big_f(X)))) | big_h(X!2) | (~big_f(X!2)))),
% 0.16/0.35 inference(rewrite,[status(thm)],[])).
% 0.16/0.35 tff(35,plain,
% 0.16/0.35 ((~![X: $i] : (big_h(X) | (~big_f(X)))) | (big_h(X!2) | (~big_f(X!2)))),
% 0.16/0.35 inference(quant_inst,[status(thm)],[])).
% 0.16/0.35 tff(36,plain,
% 0.16/0.35 ((~![X: $i] : (big_h(X) | (~big_f(X)))) | big_h(X!2) | (~big_f(X!2))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.16/0.35 tff(37,plain,
% 0.16/0.35 ($false),
% 0.16/0.35 inference(unit_resolution,[status(thm)],[36, 25, 3, 7])).
% 0.16/0.35 tff(38,plain,((big_h(X!2) | (~big_f(X!2))) | (~![X: $i] : (big_h(X) | (~big_f(X))))), inference(lemma,lemma(discharge,[]))).
% 0.16/0.35 tff(39,plain,
% 0.16/0.35 (big_h(X!2) | (~big_f(X!2))),
% 0.16/0.35 inference(unit_resolution,[status(thm)],[38, 12])).
% 0.16/0.35 tff(40,plain,
% 0.16/0.35 (((~(big_h(X!2) | (~big_f(X!2)))) | (~(big_j(U!3) | (~big_g(U!3)))) | (~((~(big_f(W!5) & big_g(Y!4))) | (big_h(W!5) & big_j(Y!4))))) <=> ((~(big_h(X!2) | (~big_f(X!2)))) | (~(big_j(U!3) | (~big_g(U!3)))) | (~((~big_f(W!5)) | (~big_g(Y!4)) | (~((~big_h(W!5)) | (~big_j(Y!4)))))))),
% 0.16/0.35 inference(rewrite,[status(thm)],[])).
% 0.16/0.35 tff(41,plain,
% 0.16/0.35 ((((![X: $i] : (big_h(X) | (~big_f(X))) & ![U: $i] : (big_j(U) | (~big_g(U)))) | ![W: $i, Y: $i] : ((~(big_f(W) & big_g(Y))) | (big_h(W) & big_j(Y)))) & (((~(big_h(X!2) | (~big_f(X!2)))) | (~(big_j(U!3) | (~big_g(U!3))))) | (~((~(big_f(W!5) & big_g(Y!4))) | (big_h(W!5) & big_j(Y!4)))))) <=> (((![X: $i] : (big_h(X) | (~big_f(X))) & ![U: $i] : (big_j(U) | (~big_g(U)))) | ![W: $i, Y: $i] : ((~(big_f(W) & big_g(Y))) | (big_h(W) & big_j(Y)))) & ((~(big_h(X!2) | (~big_f(X!2)))) | (~(big_j(U!3) | (~big_g(U!3)))) | (~((~(big_f(W!5) & big_g(Y!4))) | (big_h(W!5) & big_j(Y!4))))))),
% 0.16/0.35 inference(rewrite,[status(thm)],[])).
% 0.16/0.35 tff(42,plain,
% 0.16/0.35 ((~((![X: $i] : (big_h(X) | (~big_f(X))) & ![U: $i] : (big_j(U) | (~big_g(U)))) <=> ![W: $i, Y: $i] : ((~(big_f(W) & big_g(Y))) | (big_h(W) & big_j(Y))))) <=> (~((![X: $i] : (big_h(X) | (~big_f(X))) & ![U: $i] : (big_j(U) | (~big_g(U)))) <=> ![W: $i, Y: $i] : ((~(big_f(W) & big_g(Y))) | (big_h(W) & big_j(Y)))))),
% 0.16/0.35 inference(rewrite,[status(thm)],[])).
% 0.16/0.35 tff(43,plain,
% 0.16/0.35 (((![X: $i] : (big_h(X) | (~big_f(X))) & ![U: $i] : (big_j(U) | (~big_g(U)))) <=> ![W: $i, Y: $i] : ((~(big_f(W) & big_g(Y))) | (big_h(W) & big_j(Y)))) <=> ((![X: $i] : (big_h(X) | (~big_f(X))) & ![U: $i] : (big_j(U) | (~big_g(U)))) <=> ![W: $i, Y: $i] : ((~(big_f(W) & big_g(Y))) | (big_h(W) & big_j(Y))))),
% 0.16/0.35 inference(rewrite,[status(thm)],[])).
% 0.16/0.35 tff(44,plain,
% 0.16/0.35 ((~((![X: $i] : (big_h(X) | (~big_f(X))) & ![U: $i] : (big_j(U) | (~big_g(U)))) <=> ![W: $i, Y: $i] : ((~(big_f(W) & big_g(Y))) | (big_h(W) & big_j(Y))))) <=> (~((![X: $i] : (big_h(X) | (~big_f(X))) & ![U: $i] : (big_j(U) | (~big_g(U)))) <=> ![W: $i, Y: $i] : ((~(big_f(W) & big_g(Y))) | (big_h(W) & big_j(Y)))))),
% 0.16/0.35 inference(monotonicity,[status(thm)],[43])).
% 0.16/0.35 tff(45,plain,
% 0.16/0.35 ((~((![X: $i] : (big_h(X) | (~big_f(X))) & ![U: $i] : (big_j(U) | (~big_g(U)))) <=> ![W: $i, Y: $i] : ((~(big_f(W) & big_g(Y))) | (big_h(W) & big_j(Y))))) <=> (~((![X: $i] : (big_h(X) | (~big_f(X))) & ![U: $i] : (big_j(U) | (~big_g(U)))) <=> ![W: $i, Y: $i] : ((~(big_f(W) & big_g(Y))) | (big_h(W) & big_j(Y)))))),
% 0.16/0.35 inference(transitivity,[status(thm)],[44, 42])).
% 0.16/0.35 tff(46,plain,
% 0.16/0.35 (((![X: $i] : (big_f(X) => big_h(X)) & ![U: $i] : (big_g(U) => big_j(U))) <=> ![W: $i, Y: $i] : ((big_f(W) & big_g(Y)) => (big_h(W) & big_j(Y)))) <=> ((![X: $i] : (big_h(X) | (~big_f(X))) & ![U: $i] : (big_j(U) | (~big_g(U)))) <=> ![W: $i, Y: $i] : ((~(big_f(W) & big_g(Y))) | (big_h(W) & big_j(Y))))),
% 0.16/0.35 inference(rewrite,[status(thm)],[])).
% 0.16/0.35 tff(47,plain,
% 0.16/0.35 ((~((![X: $i] : (big_f(X) => big_h(X)) & ![U: $i] : (big_g(U) => big_j(U))) <=> ![W: $i, Y: $i] : ((big_f(W) & big_g(Y)) => (big_h(W) & big_j(Y))))) <=> (~((![X: $i] : (big_h(X) | (~big_f(X))) & ![U: $i] : (big_j(U) | (~big_g(U)))) <=> ![W: $i, Y: $i] : ((~(big_f(W) & big_g(Y))) | (big_h(W) & big_j(Y)))))),
% 0.16/0.35 inference(monotonicity,[status(thm)],[46])).
% 0.16/0.35 tff(48,plain,
% 0.16/0.35 ((~((![X: $i] : (big_f(X) => big_h(X)) & ![U: $i] : (big_g(U) => big_j(U))) <=> ![W: $i, Y: $i] : ((big_f(W) & big_g(Y)) => (big_h(W) & big_j(Y))))) <=> (~((![X: $i] : (big_h(X) | (~big_f(X))) & ![U: $i] : (big_j(U) | (~big_g(U)))) <=> ![W: $i, Y: $i] : ((~(big_f(W) & big_g(Y))) | (big_h(W) & big_j(Y)))))),
% 0.16/0.35 inference(transitivity,[status(thm)],[47, 42])).
% 0.16/0.35 tff(49,axiom,(~((![X: $i] : (big_f(X) => big_h(X)) & ![U: $i] : (big_g(U) => big_j(U))) <=> ![W: $i, Y: $i] : ((big_f(W) & big_g(Y)) => (big_h(W) & big_j(Y))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel29')).
% 0.16/0.35 tff(50,plain,
% 0.16/0.35 (~((![X: $i] : (big_h(X) | (~big_f(X))) & ![U: $i] : (big_j(U) | (~big_g(U)))) <=> ![W: $i, Y: $i] : ((~(big_f(W) & big_g(Y))) | (big_h(W) & big_j(Y))))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.16/0.35 tff(51,plain,
% 0.16/0.35 (~((![X: $i] : (big_h(X) | (~big_f(X))) & ![U: $i] : (big_j(U) | (~big_g(U)))) <=> ![W: $i, Y: $i] : ((~(big_f(W) & big_g(Y))) | (big_h(W) & big_j(Y))))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[50, 45])).
% 0.16/0.35 tff(52,plain,
% 0.16/0.35 (~((![X: $i] : (big_h(X) | (~big_f(X))) & ![U: $i] : (big_j(U) | (~big_g(U)))) <=> ![W: $i, Y: $i] : ((~(big_f(W) & big_g(Y))) | (big_h(W) & big_j(Y))))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[51, 42])).
% 0.16/0.35 tff(53,plain,
% 0.16/0.35 (~((![X: $i] : (big_h(X) | (~big_f(X))) & ![U: $i] : (big_j(U) | (~big_g(U)))) <=> ![W: $i, Y: $i] : ((~(big_f(W) & big_g(Y))) | (big_h(W) & big_j(Y))))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.16/0.35 unexpected number of arguments: (let ((a!1 (forall ((X $i)) (or (big_h X) (not (big_f X)))))
% 0.16/0.35 (a!3 (forall ((U $i)) (or (big_j U) (not (big_g U)))))
% 0.16/0.35 (a!5 (not (or (big_h X!2) (not (big_f X!2)))))
% 0.16/0.35 (a!6 (not (or (big_j U!3) (not (big_g U!3)))))
% 0.16/0.35 (a!8 (proof-bind (lambda ((W $i) (Y $i))
% 0.16/0.35 (let ((a!1 (or (not (and (big_f W) (big_g Y)))
% 0.16/0.35 (and (big_h W) (big_j Y)))))
% 0.16/0.35 (refl (~ a!1 a!1))))))
% 0.16/0.35 (a!9 (forall ((W $i) (Y $i))
% 0.16/0.35 (or (not (and (big_f W) (big_g Y))) (and (big_h W) (big_j Y)))))
% 0.16/0.35 (a!10 (or (not (and (big_f W!5) (big_g Y!4)))
% 0.16/0.35 (and (big_h W!5) (big_j Y!4)))))
% 0.16/0.35 (let ((a!2 (nnf-pos (proof-bind (lambda ((X $i))
% 0.16/0.35 (let ((a!1 (~ (or (big_h X) (not (big_f X)))
% 0.16/0.35 (or (big_h X) (not (big_f X))))))
% 0.16/0.35 (refl a!1))))
% 0.16/0.35 (~ a!1 a!1)))
% 0.16/0.35 (a!4 (nnf-pos (proof-bind (lambda ((U $i))
% 0.16/0.35 (let ((a!1 (~ (or (big_j U) (not (big_g U)))
% 0.16/0.35 (or (big_j U) (not (big_g U))))))
% 0.16/0.35 (refl a!1))))
% 0.16/0.35 (~ a!3 a!3)))
% 0.16/0.35 (a!7 (nnf-neg (sk (~ (not a!1) a!5))
% 0.16/0.35 (sk (~ (not a!3) a!6))
% 0.16/0.35 (~ (not (and a!1 a!3)) (or a!5 a!6))))
% 0.16/0.35 (a!11 (~ (not (= (and a!1 a!3) a!9))
% 0.16/0.35 (and (or (and a!1 a!3) a!9) (or (or a!5 a!6) (not a!10))))))
% 0.16/0.35 (nnf-neg (monotonicity a!2 a!4 (~ (and a!1 a!3) (and a!1 a!3)))
% 0.16/0.35 a!7
% 0.16/0.35 (nnf-pos a!8 (~ a!9 a!9))
% 0.16/0.35 (sk (~ (not a!9) (not a!10)))
% 0.16/0.35 a!11)))
% 0.16/0.35 Proof display could not be completed: unexpected number of arguments
% 0.16/0.36 % E exiting
%------------------------------------------------------------------------------