%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN056+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 0.13s 0.38s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYN056+1 : TPTP v9.0.0. Released v2.0.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 12:28:31 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.38 % SZS status Theorem
% 0.13/0.38 % SZS output start Proof
% 0.13/0.38 tff(big_p_type, type, (
% 0.13/0.38 big_p: $i > $o)).
% 0.13/0.38 tff(tptp_fun_X_2_type, type, (
% 0.13/0.38 tptp_fun_X_2: $i)).
% 0.13/0.38 tff(big_r_type, type, (
% 0.13/0.38 big_r: $i > $o)).
% 0.13/0.38 tff(big_q_type, type, (
% 0.13/0.38 big_q: $i > $o)).
% 0.13/0.38 tff(tptp_fun_Y_3_type, type, (
% 0.13/0.38 tptp_fun_Y_3: $i)).
% 0.13/0.38 tff(big_s_type, type, (
% 0.13/0.38 big_s: $i > $o)).
% 0.13/0.38 tff(tptp_fun_X_0_type, type, (
% 0.13/0.38 tptp_fun_X_0: $i)).
% 0.13/0.38 tff(tptp_fun_Y_1_type, type, (
% 0.13/0.38 tptp_fun_Y_1: $i)).
% 0.13/0.38 tff(1,assumption,(~(big_s(Y!3) | (~big_q(Y!3)))), introduced(assumption)).
% 0.13/0.38 tff(2,plain,
% 0.13/0.38 ((big_s(Y!3) | (~big_q(Y!3))) | big_q(Y!3)),
% 0.13/0.38 inference(tautology,[status(thm)],[])).
% 0.13/0.38 tff(3,plain,
% 0.13/0.38 (big_q(Y!3)),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.13/0.38 tff(4,plain,
% 0.13/0.38 ((big_s(Y!3) | (~big_q(Y!3))) | (~big_s(Y!3))),
% 0.13/0.38 inference(tautology,[status(thm)],[])).
% 0.13/0.38 tff(5,plain,
% 0.13/0.38 (~big_s(Y!3)),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[4, 1])).
% 0.13/0.38 tff(6,assumption,(big_q(Y!3)), introduced(assumption)).
% 0.13/0.38 tff(7,assumption,(![Y: $i] : (~big_q(Y))), introduced(assumption)).
% 0.13/0.38 tff(8,plain,
% 0.13/0.38 ((~![Y: $i] : (~big_q(Y))) | (~big_q(Y!3))),
% 0.13/0.38 inference(quant_inst,[status(thm)],[])).
% 0.13/0.38 tff(9,plain,
% 0.13/0.38 ($false),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[8, 7, 6])).
% 0.13/0.38 tff(10,plain,((~![Y: $i] : (~big_q(Y))) | (~big_q(Y!3))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.38 tff(11,plain,
% 0.13/0.38 (~![Y: $i] : (~big_q(Y))),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[10, 3])).
% 0.13/0.38 tff(12,plain,
% 0.13/0.38 ((big_p(X!0) | ![Y: $i] : (~big_q(Y))) <=> (big_p(X!0) | ![Y: $i] : (~big_q(Y)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(13,plain,
% 0.13/0.38 (((![X: $i] : (~big_p(X)) | big_q(Y!1)) & (big_p(X!0) | ![Y: $i] : (~big_q(Y)))) <=> ((![X: $i] : (~big_p(X)) | big_q(Y!1)) & (big_p(X!0) | ![Y: $i] : (~big_q(Y))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(14,plain,
% 0.13/0.38 ((?[X: $i] : big_p(X) <=> ?[Y: $i] : big_q(Y)) <=> (?[X: $i] : big_p(X) <=> ?[Y: $i] : big_q(Y))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(15,axiom,(?[X: $i] : big_p(X) <=> ?[Y: $i] : big_q(Y)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel26_1')).
% 0.13/0.38 tff(16,plain,
% 0.13/0.38 (?[X: $i] : big_p(X) <=> ?[Y: $i] : big_q(Y)),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.13/0.38 tff(17,plain,
% 0.13/0.38 (?[X: $i] : big_p(X) <=> ?[Y: $i] : big_q(Y)),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[16, 14])).
% 0.13/0.38 tff(18,plain,
% 0.13/0.38 (?[X: $i] : big_p(X) <=> ?[Y: $i] : big_q(Y)),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.13/0.38 tff(19,plain,
% 0.13/0.38 (?[X: $i] : big_p(X) <=> ?[Y: $i] : big_q(Y)),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.13/0.38 tff(20,plain,(
% 0.13/0.38 (![X: $i] : (~big_p(X)) | big_q(Y!1)) & (big_p(X!0) | ![Y: $i] : (~big_q(Y)))),
% 0.13/0.38 inference(skolemize,[status(sab)],[19])).
% 0.13/0.38 tff(21,plain,
% 0.13/0.38 ((![X: $i] : (~big_p(X)) | big_q(Y!1)) & (big_p(X!0) | ![Y: $i] : (~big_q(Y)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.13/0.38 tff(22,plain,
% 0.13/0.38 (big_p(X!0) | ![Y: $i] : (~big_q(Y))),
% 0.13/0.38 inference(and_elim,[status(thm)],[21])).
% 0.13/0.38 tff(23,plain,
% 0.13/0.38 (big_p(X!0) | ![Y: $i] : (~big_q(Y))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[22, 12])).
% 0.13/0.38 tff(24,plain,
% 0.13/0.38 (big_p(X!0)),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[23, 11])).
% 0.13/0.38 tff(25,assumption,(![X: $i] : (big_r(X) | (~big_p(X)))), introduced(assumption)).
% 0.13/0.38 tff(26,assumption,(big_p(X!0)), introduced(assumption)).
% 0.13/0.38 tff(27,plain,
% 0.13/0.38 (((~![X: $i] : (big_r(X) | (~big_p(X)))) | (big_r(X!0) | (~big_p(X!0)))) <=> ((~![X: $i] : (big_r(X) | (~big_p(X)))) | big_r(X!0) | (~big_p(X!0)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(28,plain,
% 0.13/0.38 ((~![X: $i] : (big_r(X) | (~big_p(X)))) | (big_r(X!0) | (~big_p(X!0)))),
% 0.13/0.38 inference(quant_inst,[status(thm)],[])).
% 0.13/0.38 tff(29,plain,
% 0.13/0.38 ((~![X: $i] : (big_r(X) | (~big_p(X)))) | big_r(X!0) | (~big_p(X!0))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.13/0.38 tff(30,plain,
% 0.13/0.38 (big_r(X!0)),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[29, 26, 25])).
% 0.13/0.38 tff(31,assumption,(~big_s(Y!3)), introduced(assumption)).
% 0.13/0.38 tff(32,plain,
% 0.13/0.38 ((~(big_r(X!0) <=> big_s(Y!3))) | (~big_r(X!0)) | big_s(Y!3)),
% 0.13/0.38 inference(tautology,[status(thm)],[])).
% 0.13/0.38 tff(33,plain,
% 0.13/0.38 (~(big_r(X!0) <=> big_s(Y!3))),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[32, 31, 30])).
% 0.13/0.38 tff(34,plain,
% 0.13/0.38 (^[X: $i, Y: $i] : refl(((big_r(X) <=> big_s(Y)) | (~big_q(Y)) | (~big_p(X))) <=> ((big_r(X) <=> big_s(Y)) | (~big_q(Y)) | (~big_p(X))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(35,plain,
% 0.13/0.38 (![X: $i, Y: $i] : ((big_r(X) <=> big_s(Y)) | (~big_q(Y)) | (~big_p(X))) <=> ![X: $i, Y: $i] : ((big_r(X) <=> big_s(Y)) | (~big_q(Y)) | (~big_p(X)))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[34])).
% 0.13/0.38 tff(36,plain,
% 0.13/0.38 (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((big_p(X) & big_q(Y)) <=> (~((~big_p(X)) | (~big_q(Y))))), ((~(big_p(X) & big_q(Y))) <=> (~(~((~big_p(X)) | (~big_q(Y))))))), rewrite((~(~((~big_p(X)) | (~big_q(Y))))) <=> ((~big_p(X)) | (~big_q(Y)))), ((~(big_p(X) & big_q(Y))) <=> ((~big_p(X)) | (~big_q(Y))))), (((~(big_p(X) & big_q(Y))) | (big_r(X) <=> big_s(Y))) <=> (((~big_p(X)) | (~big_q(Y))) | (big_r(X) <=> big_s(Y))))), rewrite((((~big_p(X)) | (~big_q(Y))) | (big_r(X) <=> big_s(Y))) <=> ((big_r(X) <=> big_s(Y)) | (~big_q(Y)) | (~big_p(X)))), (((~(big_p(X) & big_q(Y))) | (big_r(X) <=> big_s(Y))) <=> ((big_r(X) <=> big_s(Y)) | (~big_q(Y)) | (~big_p(X)))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(37,plain,
% 0.13/0.38 (![X: $i, Y: $i] : ((~(big_p(X) & big_q(Y))) | (big_r(X) <=> big_s(Y))) <=> ![X: $i, Y: $i] : ((big_r(X) <=> big_s(Y)) | (~big_q(Y)) | (~big_p(X)))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[36])).
% 0.13/0.38 tff(38,plain,
% 0.13/0.38 (![X: $i, Y: $i] : ((~(big_p(X) & big_q(Y))) | (big_r(X) <=> big_s(Y))) <=> ![X: $i, Y: $i] : ((~(big_p(X) & big_q(Y))) | (big_r(X) <=> big_s(Y)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(39,plain,
% 0.13/0.38 (^[X: $i, Y: $i] : rewrite(((big_p(X) & big_q(Y)) => (big_r(X) <=> big_s(Y))) <=> ((~(big_p(X) & big_q(Y))) | (big_r(X) <=> big_s(Y))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(40,plain,
% 0.13/0.38 (![X: $i, Y: $i] : ((big_p(X) & big_q(Y)) => (big_r(X) <=> big_s(Y))) <=> ![X: $i, Y: $i] : ((~(big_p(X) & big_q(Y))) | (big_r(X) <=> big_s(Y)))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[39])).
% 0.13/0.38 tff(41,axiom,(![X: $i, Y: $i] : ((big_p(X) & big_q(Y)) => (big_r(X) <=> big_s(Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel26_2')).
% 0.13/0.38 tff(42,plain,
% 0.13/0.38 (![X: $i, Y: $i] : ((~(big_p(X) & big_q(Y))) | (big_r(X) <=> big_s(Y)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.13/0.38 tff(43,plain,
% 0.13/0.38 (![X: $i, Y: $i] : ((~(big_p(X) & big_q(Y))) | (big_r(X) <=> big_s(Y)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.13/0.38 tff(44,plain,(
% 0.13/0.38 ![X: $i, Y: $i] : ((~(big_p(X) & big_q(Y))) | (big_r(X) <=> big_s(Y)))),
% 0.13/0.38 inference(skolemize,[status(sab)],[43])).
% 0.13/0.38 tff(45,plain,
% 0.13/0.38 (![X: $i, Y: $i] : ((big_r(X) <=> big_s(Y)) | (~big_q(Y)) | (~big_p(X)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.13/0.38 tff(46,plain,
% 0.13/0.38 (![X: $i, Y: $i] : ((big_r(X) <=> big_s(Y)) | (~big_q(Y)) | (~big_p(X)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[45, 35])).
% 0.13/0.38 tff(47,plain,
% 0.13/0.38 (((~![X: $i, Y: $i] : ((big_r(X) <=> big_s(Y)) | (~big_q(Y)) | (~big_p(X)))) | ((~big_q(Y!3)) | (~big_p(X!0)) | (big_r(X!0) <=> big_s(Y!3)))) <=> ((~![X: $i, Y: $i] : ((big_r(X) <=> big_s(Y)) | (~big_q(Y)) | (~big_p(X)))) | (~big_q(Y!3)) | (~big_p(X!0)) | (big_r(X!0) <=> big_s(Y!3)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(48,plain,
% 0.13/0.38 (((big_r(X!0) <=> big_s(Y!3)) | (~big_q(Y!3)) | (~big_p(X!0))) <=> ((~big_q(Y!3)) | (~big_p(X!0)) | (big_r(X!0) <=> big_s(Y!3)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(49,plain,
% 0.13/0.38 (((~![X: $i, Y: $i] : ((big_r(X) <=> big_s(Y)) | (~big_q(Y)) | (~big_p(X)))) | ((big_r(X!0) <=> big_s(Y!3)) | (~big_q(Y!3)) | (~big_p(X!0)))) <=> ((~![X: $i, Y: $i] : ((big_r(X) <=> big_s(Y)) | (~big_q(Y)) | (~big_p(X)))) | ((~big_q(Y!3)) | (~big_p(X!0)) | (big_r(X!0) <=> big_s(Y!3))))),
% 0.13/0.38 inference(monotonicity,[status(thm)],[48])).
% 0.13/0.38 tff(50,plain,
% 0.13/0.38 (((~![X: $i, Y: $i] : ((big_r(X) <=> big_s(Y)) | (~big_q(Y)) | (~big_p(X)))) | ((big_r(X!0) <=> big_s(Y!3)) | (~big_q(Y!3)) | (~big_p(X!0)))) <=> ((~![X: $i, Y: $i] : ((big_r(X) <=> big_s(Y)) | (~big_q(Y)) | (~big_p(X)))) | (~big_q(Y!3)) | (~big_p(X!0)) | (big_r(X!0) <=> big_s(Y!3)))),
% 0.13/0.39 inference(transitivity,[status(thm)],[49, 47])).
% 0.13/0.39 tff(51,plain,
% 0.13/0.39 ((~![X: $i, Y: $i] : ((big_r(X) <=> big_s(Y)) | (~big_q(Y)) | (~big_p(X)))) | ((big_r(X!0) <=> big_s(Y!3)) | (~big_q(Y!3)) | (~big_p(X!0)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(52,plain,
% 0.13/0.39 ((~![X: $i, Y: $i] : ((big_r(X) <=> big_s(Y)) | (~big_q(Y)) | (~big_p(X)))) | (~big_q(Y!3)) | (~big_p(X!0)) | (big_r(X!0) <=> big_s(Y!3))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.13/0.39 tff(53,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[52, 26, 46, 6, 33])).
% 0.13/0.39 tff(54,plain,((~big_p(X!0)) | (~big_q(Y!3)) | big_s(Y!3) | (~![X: $i] : (big_r(X) | (~big_p(X))))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.39 tff(55,plain,
% 0.13/0.39 (~![X: $i] : (big_r(X) | (~big_p(X)))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[54, 24, 5, 3])).
% 0.13/0.39 tff(56,plain,
% 0.13/0.39 ((![X: $i] : (big_r(X) | (~big_p(X))) | ![Y: $i] : (big_s(Y) | (~big_q(Y)))) <=> (![X: $i] : (big_r(X) | (~big_p(X))) | ![Y: $i] : (big_s(Y) | (~big_q(Y))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(57,plain,
% 0.13/0.39 ((![X: $i] : (big_r(X) | (~big_p(X))) | ![Y: $i] : (big_s(Y) | (~big_q(Y)))) <=> (![X: $i] : (big_r(X) | (~big_p(X))) | ![Y: $i] : (big_s(Y) | (~big_q(Y))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(58,plain,
% 0.13/0.39 (((![X: $i] : (big_r(X) | (~big_p(X))) | ![Y: $i] : (big_s(Y) | (~big_q(Y)))) & ((~(big_r(X!2) | (~big_p(X!2)))) | (~(big_s(Y!3) | (~big_q(Y!3)))))) <=> ((![X: $i] : (big_r(X) | (~big_p(X))) | ![Y: $i] : (big_s(Y) | (~big_q(Y)))) & ((~(big_r(X!2) | (~big_p(X!2)))) | (~(big_s(Y!3) | (~big_q(Y!3))))))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[57])).
% 0.13/0.39 tff(59,plain,
% 0.13/0.39 ((~(![X: $i] : (big_r(X) | (~big_p(X))) <=> ![Y: $i] : (big_s(Y) | (~big_q(Y))))) <=> (~(![X: $i] : (big_r(X) | (~big_p(X))) <=> ![Y: $i] : (big_s(Y) | (~big_q(Y)))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(60,plain,
% 0.13/0.39 ((![X: $i] : (big_r(X) | (~big_p(X))) <=> ![Y: $i] : (big_s(Y) | (~big_q(Y)))) <=> (![X: $i] : (big_r(X) | (~big_p(X))) <=> ![Y: $i] : (big_s(Y) | (~big_q(Y))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(61,plain,
% 0.13/0.39 ((~(![X: $i] : (big_r(X) | (~big_p(X))) <=> ![Y: $i] : (big_s(Y) | (~big_q(Y))))) <=> (~(![X: $i] : (big_r(X) | (~big_p(X))) <=> ![Y: $i] : (big_s(Y) | (~big_q(Y)))))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[60])).
% 0.13/0.39 tff(62,plain,
% 0.13/0.39 ((~(![X: $i] : (big_r(X) | (~big_p(X))) <=> ![Y: $i] : (big_s(Y) | (~big_q(Y))))) <=> (~(![X: $i] : (big_r(X) | (~big_p(X))) <=> ![Y: $i] : (big_s(Y) | (~big_q(Y)))))),
% 0.13/0.39 inference(transitivity,[status(thm)],[61, 59])).
% 0.13/0.39 tff(63,plain,
% 0.13/0.39 ((![X: $i] : (big_p(X) => big_r(X)) <=> ![Y: $i] : (big_q(Y) => big_s(Y))) <=> (![X: $i] : (big_r(X) | (~big_p(X))) <=> ![Y: $i] : (big_s(Y) | (~big_q(Y))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(64,plain,
% 0.13/0.39 ((~(![X: $i] : (big_p(X) => big_r(X)) <=> ![Y: $i] : (big_q(Y) => big_s(Y)))) <=> (~(![X: $i] : (big_r(X) | (~big_p(X))) <=> ![Y: $i] : (big_s(Y) | (~big_q(Y)))))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[63])).
% 0.13/0.39 tff(65,plain,
% 0.13/0.39 ((~(![X: $i] : (big_p(X) => big_r(X)) <=> ![Y: $i] : (big_q(Y) => big_s(Y)))) <=> (~(![X: $i] : (big_r(X) | (~big_p(X))) <=> ![Y: $i] : (big_s(Y) | (~big_q(Y)))))),
% 0.13/0.39 inference(transitivity,[status(thm)],[64, 59])).
% 0.13/0.39 tff(66,axiom,(~(![X: $i] : (big_p(X) => big_r(X)) <=> ![Y: $i] : (big_q(Y) => big_s(Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel26')).
% 0.13/0.39 tff(67,plain,
% 0.13/0.39 (~(![X: $i] : (big_r(X) | (~big_p(X))) <=> ![Y: $i] : (big_s(Y) | (~big_q(Y))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.13/0.39 tff(68,plain,
% 0.13/0.39 (~(![X: $i] : (big_r(X) | (~big_p(X))) <=> ![Y: $i] : (big_s(Y) | (~big_q(Y))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[67, 62])).
% 0.13/0.39 tff(69,plain,
% 0.13/0.39 (~(![X: $i] : (big_r(X) | (~big_p(X))) <=> ![Y: $i] : (big_s(Y) | (~big_q(Y))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[68, 59])).
% 0.13/0.39 tff(70,plain,
% 0.13/0.39 (~(![X: $i] : (big_r(X) | (~big_p(X))) <=> ![Y: $i] : (big_s(Y) | (~big_q(Y))))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[69, 62])).
% 0.13/0.39 unexpected number of arguments: (let ((a!1 (forall ((X $i)) (or (big_r X) (not (big_p X)))))
% 0.13/0.39 (a!3 (not (or (big_r X!2) (not (big_p X!2)))))
% 0.13/0.39 (a!4 (forall ((Y $i)) (or (big_s Y) (not (big_q Y)))))
% 0.13/0.39 (a!6 (not (or (big_s Y!3) (not (big_q Y!3))))))
% 0.13/0.39 (let ((a!2 (nnf-pos (proof-bind (lambda ((X $i))
% 0.13/0.39 (let ((a!1 (~ (or (big_r X) (not (big_p X)))
% 0.13/0.39 (or (big_r X) (not (big_p X))))))
% 0.13/0.39 (refl a!1))))
% 0.13/0.39 (~ a!1 a!1)))
% 0.13/0.39 (a!5 (nnf-pos (proof-bind (lambda ((Y $i))
% 0.13/0.39 (let ((a!1 (~ (or (big_s Y) (not (big_q Y)))
% 0.13/0.39 (or (big_s Y) (not (big_q Y))))))
% 0.13/0.39 (refl a!1))))
% 0.13/0.39 (~ a!4 a!4))))
% 0.13/0.39 (nnf-neg a!2
% 0.13/0.39 (sk (~ (not a!1) a!3))
% 0.13/0.39 a!5
% 0.13/0.39 (sk (~ (not a!4) a!6))
% 0.13/0.39 (~ (not (= a!1 a!4)) (and (or a!1 a!4) (or a!3 a!6))))))
% 0.13/0.39 Proof display could not be completed: unexpected number of arguments
% 0.13/0.39 % E exiting
%------------------------------------------------------------------------------