TSTP Solution File: SYN056+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN056+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.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 : Thu Sep 29 23:53:24 EDT 2022
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN056+1 : TPTP v8.1.0. Released v2.0.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n025.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 : Mon Sep 5 01:34:34 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(big_p_type, type, (
% 0.12/0.38 big_p: $i > $o)).
% 0.12/0.38 tff(tptp_fun_X_2_type, type, (
% 0.12/0.38 tptp_fun_X_2: $i)).
% 0.12/0.38 tff(big_r_type, type, (
% 0.12/0.38 big_r: $i > $o)).
% 0.12/0.38 tff(big_q_type, type, (
% 0.12/0.38 big_q: $i > $o)).
% 0.12/0.38 tff(tptp_fun_Y_3_type, type, (
% 0.12/0.38 tptp_fun_Y_3: $i)).
% 0.12/0.38 tff(big_s_type, type, (
% 0.12/0.38 big_s: $i > $o)).
% 0.12/0.38 tff(tptp_fun_X_0_type, type, (
% 0.12/0.38 tptp_fun_X_0: $i)).
% 0.12/0.38 tff(tptp_fun_Y_1_type, type, (
% 0.12/0.38 tptp_fun_Y_1: $i)).
% 0.12/0.38 tff(1,assumption,(~(big_s(Y!3) | (~big_q(Y!3)))), introduced(assumption)).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 ((big_s(Y!3) | (~big_q(Y!3))) | big_q(Y!3)),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (big_q(Y!3)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 ((big_s(Y!3) | (~big_q(Y!3))) | (~big_s(Y!3))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (~big_s(Y!3)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[4, 1])).
% 0.12/0.38 tff(6,assumption,(big_q(Y!3)), introduced(assumption)).
% 0.12/0.38 tff(7,assumption,(![Y: $i] : (~big_q(Y))), introduced(assumption)).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 ((~![Y: $i] : (~big_q(Y))) | (~big_q(Y!3))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[8, 7, 6])).
% 0.12/0.38 tff(10,plain,((~![Y: $i] : (~big_q(Y))) | (~big_q(Y!3))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 (~![Y: $i] : (~big_q(Y))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[10, 3])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 ((big_p(X!0) | ![Y: $i] : (~big_q(Y))) <=> (big_p(X!0) | ![Y: $i] : (~big_q(Y)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (((![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))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 ((?[X: $i] : big_p(X) <=> ?[Y: $i] : big_q(Y)) <=> (?[X: $i] : big_p(X) <=> ?[Y: $i] : big_q(Y))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(15,axiom,(?[X: $i] : big_p(X) <=> ?[Y: $i] : big_q(Y)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel26_1')).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (?[X: $i] : big_p(X) <=> ?[Y: $i] : big_q(Y)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (?[X: $i] : big_p(X) <=> ?[Y: $i] : big_q(Y)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[16, 14])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 (?[X: $i] : big_p(X) <=> ?[Y: $i] : big_q(Y)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (?[X: $i] : big_p(X) <=> ?[Y: $i] : big_q(Y)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 (?[X: $i] : big_p(X) <=> ?[Y: $i] : big_q(Y)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (?[X: $i] : big_p(X) <=> ?[Y: $i] : big_q(Y)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[20, 14])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 (?[X: $i] : big_p(X) <=> ?[Y: $i] : big_q(Y)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.12/0.38 tff(23,plain,(
% 0.12/0.38 (![X: $i] : (~big_p(X)) | big_q(Y!1)) & (big_p(X!0) | ![Y: $i] : (~big_q(Y)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[22])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 ((![X: $i] : (~big_p(X)) | big_q(Y!1)) & (big_p(X!0) | ![Y: $i] : (~big_q(Y)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[23, 13])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 (big_p(X!0) | ![Y: $i] : (~big_q(Y))),
% 0.12/0.38 inference(and_elim,[status(thm)],[24])).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 (big_p(X!0) | ![Y: $i] : (~big_q(Y))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[25, 12])).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (big_p(X!0)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[26, 11])).
% 0.12/0.38 tff(28,assumption,(![X: $i] : (big_r(X) | (~big_p(X)))), introduced(assumption)).
% 0.12/0.38 tff(29,assumption,(big_p(X!0)), introduced(assumption)).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 (((~![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)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 ((~![X: $i] : (big_r(X) | (~big_p(X)))) | (big_r(X!0) | (~big_p(X!0)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(32,plain,
% 0.12/0.38 ((~![X: $i] : (big_r(X) | (~big_p(X)))) | big_r(X!0) | (~big_p(X!0))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.12/0.39 tff(33,plain,
% 0.12/0.39 (big_r(X!0)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[32, 29, 28])).
% 0.12/0.39 tff(34,assumption,(~big_s(Y!3)), introduced(assumption)).
% 0.12/0.39 tff(35,plain,
% 0.12/0.39 ((~(big_r(X!0) <=> big_s(Y!3))) | (~big_r(X!0)) | big_s(Y!3)),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(36,plain,
% 0.12/0.39 (~(big_r(X!0) <=> big_s(Y!3))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[35, 34, 33])).
% 0.12/0.39 tff(37,plain,
% 0.12/0.39 (^[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))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(38,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[37])).
% 0.12/0.39 tff(39,plain,
% 0.12/0.39 (^[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)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(40,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[39])).
% 0.12/0.39 tff(41,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(42,plain,
% 0.12/0.39 (^[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))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(43,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[42])).
% 0.12/0.39 tff(44,axiom,(![X: $i, Y: $i] : ((big_p(X) & big_q(Y)) => (big_r(X) <=> big_s(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel26_2')).
% 0.12/0.39 tff(45,plain,
% 0.12/0.39 (![X: $i, Y: $i] : ((~(big_p(X) & big_q(Y))) | (big_r(X) <=> big_s(Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.12/0.39 tff(46,plain,
% 0.12/0.39 (![X: $i, Y: $i] : ((~(big_p(X) & big_q(Y))) | (big_r(X) <=> big_s(Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.12/0.39 tff(47,plain,(
% 0.12/0.39 ![X: $i, Y: $i] : ((~(big_p(X) & big_q(Y))) | (big_r(X) <=> big_s(Y)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[46])).
% 0.12/0.39 tff(48,plain,
% 0.12/0.39 (![X: $i, Y: $i] : ((big_r(X) <=> big_s(Y)) | (~big_q(Y)) | (~big_p(X)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.12/0.39 tff(49,plain,
% 0.12/0.39 (![X: $i, Y: $i] : ((big_r(X) <=> big_s(Y)) | (~big_q(Y)) | (~big_p(X)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[48, 38])).
% 0.12/0.39 tff(50,plain,
% 0.12/0.39 (((~![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)))) <=> ((~![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)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(51,plain,
% 0.12/0.39 (((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)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(52,plain,
% 0.12/0.39 (((~![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)))) <=> ((~![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))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[51])).
% 0.12/0.39 tff(53,plain,
% 0.12/0.39 (((~![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)))) <=> ((~![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)))),
% 0.12/0.39 inference(transitivity,[status(thm)],[52, 50])).
% 0.12/0.39 tff(54,plain,
% 0.12/0.39 ((~![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)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(55,plain,
% 0.12/0.39 ((~![X: $i, Y: $i] : ((big_r(X) <=> big_s(Y)) | (~big_q(Y)) | (~big_p(X)))) | (~big_q(Y!3)) | (~big_p(X!0)) | (big_r(X!0) <=> big_s(Y!3))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.12/0.39 tff(56,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[55, 29, 49, 6, 36])).
% 0.12/0.39 tff(57,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,[]))).
% 0.12/0.39 tff(58,plain,
% 0.12/0.39 (~![X: $i] : (big_r(X) | (~big_p(X)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[57, 27, 5, 3])).
% 0.12/0.39 tff(59,plain,
% 0.12/0.39 ((![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))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(60,plain,
% 0.12/0.39 ((![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))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(61,plain,
% 0.12/0.39 (((![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))))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[60])).
% 0.12/0.39 tff(62,plain,
% 0.12/0.39 (((~![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))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(63,plain,
% 0.12/0.39 ((~(![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))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(64,plain,
% 0.12/0.39 ((![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))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(65,plain,
% 0.12/0.39 ((~(![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)))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[64])).
% 0.12/0.39 tff(66,plain,
% 0.12/0.39 ((~(![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))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[65, 63])).
% 0.12/0.39 tff(67,axiom,(~(![X: $i] : (big_p(X) => big_r(X)) <=> ![Y: $i] : (big_q(Y) => big_s(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel26')).
% 0.12/0.39 tff(68,plain,
% 0.12/0.39 ((~![X: $i] : (big_r(X) | (~big_p(X)))) <=> ![Y: $i] : (big_s(Y) | (~big_q(Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.12/0.39 tff(69,plain,
% 0.12/0.39 ((~![X: $i] : (big_r(X) | (~big_p(X)))) <=> ![Y: $i] : (big_s(Y) | (~big_q(Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[68, 62])).
% 0.12/0.39 tff(70,plain,
% 0.12/0.39 ((~![X: $i] : (big_r(X) | (~big_p(X)))) <=> ![Y: $i] : (big_s(Y) | (~big_q(Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[69, 62])).
% 0.12/0.39 tff(71,plain,
% 0.12/0.39 ((~![X: $i] : (big_r(X) | (~big_p(X)))) <=> ![Y: $i] : (big_s(Y) | (~big_q(Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[70, 62])).
% 0.12/0.39 tff(72,plain,
% 0.12/0.39 ((~![X: $i] : (big_r(X) | (~big_p(X)))) <=> ![Y: $i] : (big_s(Y) | (~big_q(Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[71, 62])).
% 0.12/0.39 tff(73,plain,
% 0.12/0.39 ((~![X: $i] : (big_r(X) | (~big_p(X)))) <=> ![Y: $i] : (big_s(Y) | (~big_q(Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[72, 62])).
% 0.12/0.39 tff(74,plain,
% 0.12/0.39 ((~![X: $i] : (big_r(X) | (~big_p(X)))) <=> ![Y: $i] : (big_s(Y) | (~big_q(Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[73, 62])).
% 0.12/0.39 tff(75,plain,(
% 0.12/0.39 (![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)))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[74])).
% 0.12/0.39 tff(76,plain,
% 0.12/0.39 ((![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)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[75, 61])).
% 0.12/0.39 tff(77,plain,
% 0.12/0.39 (![X: $i] : (big_r(X) | (~big_p(X))) | ![Y: $i] : (big_s(Y) | (~big_q(Y)))),
% 0.12/0.39 inference(and_elim,[status(thm)],[76])).
% 0.12/0.39 tff(78,plain,
% 0.12/0.39 (![X: $i] : (big_r(X) | (~big_p(X))) | ![Y: $i] : (big_s(Y) | (~big_q(Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[77, 59])).
% 0.12/0.39 tff(79,plain,
% 0.12/0.39 (![Y: $i] : (big_s(Y) | (~big_q(Y)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[78, 58])).
% 0.12/0.39 tff(80,plain,
% 0.12/0.39 (((~![Y: $i] : (big_s(Y) | (~big_q(Y)))) | (big_s(Y!3) | (~big_q(Y!3)))) <=> ((~![Y: $i] : (big_s(Y) | (~big_q(Y)))) | big_s(Y!3) | (~big_q(Y!3)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(81,plain,
% 0.12/0.39 ((~![Y: $i] : (big_s(Y) | (~big_q(Y)))) | (big_s(Y!3) | (~big_q(Y!3)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(82,plain,
% 0.12/0.39 ((~![Y: $i] : (big_s(Y) | (~big_q(Y)))) | big_s(Y!3) | (~big_q(Y!3))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.12/0.39 tff(83,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[82, 79, 5, 3])).
% 0.12/0.39 tff(84,plain,(big_s(Y!3) | (~big_q(Y!3))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.39 tff(85,plain,
% 0.12/0.39 ((~(big_r(X!2) | (~big_p(X!2)))) | (~(big_s(Y!3) | (~big_q(Y!3))))),
% 0.12/0.39 inference(and_elim,[status(thm)],[76])).
% 0.12/0.39 tff(86,plain,
% 0.12/0.39 (~(big_r(X!2) | (~big_p(X!2)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.12/0.39 tff(87,plain,
% 0.12/0.39 ((big_r(X!2) | (~big_p(X!2))) | big_p(X!2)),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(88,plain,
% 0.12/0.39 (big_p(X!2)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.12/0.39 tff(89,plain,
% 0.12/0.39 ((big_r(X!2) | (~big_p(X!2))) | (~big_r(X!2))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(90,plain,
% 0.12/0.39 (~big_r(X!2)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[89, 86])).
% 0.12/0.39 tff(91,plain,
% 0.12/0.39 (((~![X: $i] : (big_r(X) | (~big_p(X)))) | (big_r(X!2) | (~big_p(X!2)))) <=> ((~![X: $i] : (big_r(X) | (~big_p(X)))) | big_r(X!2) | (~big_p(X!2)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(92,plain,
% 0.12/0.39 ((~![X: $i] : (big_r(X) | (~big_p(X)))) | (big_r(X!2) | (~big_p(X!2)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(93,plain,
% 0.12/0.39 ((~![X: $i] : (big_r(X) | (~big_p(X)))) | big_r(X!2) | (~big_p(X!2))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.12/0.39 tff(94,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[93, 28, 90, 88])).
% 0.12/0.39 tff(95,plain,(~![X: $i] : (big_r(X) | (~big_p(X)))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.39 tff(96,plain,
% 0.12/0.39 (![Y: $i] : (big_s(Y) | (~big_q(Y)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[78, 95])).
% 0.12/0.39 tff(97,assumption,(![Y: $i] : (big_s(Y) | (~big_q(Y)))), introduced(assumption)).
% 0.12/0.39 tff(98,assumption,(big_q(Y!1)), introduced(assumption)).
% 0.12/0.39 tff(99,plain,
% 0.12/0.39 (((~![Y: $i] : (big_s(Y) | (~big_q(Y)))) | (big_s(Y!1) | (~big_q(Y!1)))) <=> ((~![Y: $i] : (big_s(Y) | (~big_q(Y)))) | big_s(Y!1) | (~big_q(Y!1)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(100,plain,
% 0.12/0.39 ((~![Y: $i] : (big_s(Y) | (~big_q(Y)))) | (big_s(Y!1) | (~big_q(Y!1)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(101,plain,
% 0.12/0.39 ((~![Y: $i] : (big_s(Y) | (~big_q(Y)))) | big_s(Y!1) | (~big_q(Y!1))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.12/0.39 tff(102,plain,
% 0.12/0.39 (big_s(Y!1)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[101, 98, 97])).
% 0.12/0.39 tff(103,plain,
% 0.12/0.39 ((~(big_r(X!2) <=> big_s(Y!1))) | big_r(X!2) | (~big_s(Y!1))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(104,plain,
% 0.12/0.39 (~(big_r(X!2) <=> big_s(Y!1))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[103, 90, 102])).
% 0.12/0.39 tff(105,plain,
% 0.12/0.39 (((~![X: $i, Y: $i] : ((big_r(X) <=> big_s(Y)) | (~big_q(Y)) | (~big_p(X)))) | ((~big_p(X!2)) | (~big_q(Y!1)) | (big_r(X!2) <=> big_s(Y!1)))) <=> ((~![X: $i, Y: $i] : ((big_r(X) <=> big_s(Y)) | (~big_q(Y)) | (~big_p(X)))) | (~big_p(X!2)) | (~big_q(Y!1)) | (big_r(X!2) <=> big_s(Y!1)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(106,plain,
% 0.12/0.39 (((big_r(X!2) <=> big_s(Y!1)) | (~big_q(Y!1)) | (~big_p(X!2))) <=> ((~big_p(X!2)) | (~big_q(Y!1)) | (big_r(X!2) <=> big_s(Y!1)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(107,plain,
% 0.12/0.39 (((~![X: $i, Y: $i] : ((big_r(X) <=> big_s(Y)) | (~big_q(Y)) | (~big_p(X)))) | ((big_r(X!2) <=> big_s(Y!1)) | (~big_q(Y!1)) | (~big_p(X!2)))) <=> ((~![X: $i, Y: $i] : ((big_r(X) <=> big_s(Y)) | (~big_q(Y)) | (~big_p(X)))) | ((~big_p(X!2)) | (~big_q(Y!1)) | (big_r(X!2) <=> big_s(Y!1))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[106])).
% 0.12/0.39 tff(108,plain,
% 0.12/0.39 (((~![X: $i, Y: $i] : ((big_r(X) <=> big_s(Y)) | (~big_q(Y)) | (~big_p(X)))) | ((big_r(X!2) <=> big_s(Y!1)) | (~big_q(Y!1)) | (~big_p(X!2)))) <=> ((~![X: $i, Y: $i] : ((big_r(X) <=> big_s(Y)) | (~big_q(Y)) | (~big_p(X)))) | (~big_p(X!2)) | (~big_q(Y!1)) | (big_r(X!2) <=> big_s(Y!1)))),
% 0.12/0.39 inference(transitivity,[status(thm)],[107, 105])).
% 0.12/0.39 tff(109,plain,
% 0.12/0.39 ((~![X: $i, Y: $i] : ((big_r(X) <=> big_s(Y)) | (~big_q(Y)) | (~big_p(X)))) | ((big_r(X!2) <=> big_s(Y!1)) | (~big_q(Y!1)) | (~big_p(X!2)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(110,plain,
% 0.12/0.39 ((~![X: $i, Y: $i] : ((big_r(X) <=> big_s(Y)) | (~big_q(Y)) | (~big_p(X)))) | (~big_p(X!2)) | (~big_q(Y!1)) | (big_r(X!2) <=> big_s(Y!1))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.12/0.39 tff(111,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[110, 98, 49, 88, 104])).
% 0.12/0.39 tff(112,plain,((~big_q(Y!1)) | (~![Y: $i] : (big_s(Y) | (~big_q(Y))))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.39 tff(113,plain,
% 0.12/0.39 (~big_q(Y!1)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[112, 96])).
% 0.12/0.39 tff(114,plain,
% 0.12/0.39 ((![X: $i] : (~big_p(X)) | big_q(Y!1)) <=> (big_q(Y!1) | ![X: $i] : (~big_p(X)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(115,plain,
% 0.12/0.39 ((![X: $i] : (~big_p(X)) | big_q(Y!1)) <=> (![X: $i] : (~big_p(X)) | big_q(Y!1))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(116,plain,
% 0.12/0.39 (![X: $i] : (~big_p(X)) | big_q(Y!1)),
% 0.12/0.39 inference(and_elim,[status(thm)],[24])).
% 0.12/0.39 tff(117,plain,
% 0.12/0.39 (![X: $i] : (~big_p(X)) | big_q(Y!1)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.12/0.39 tff(118,plain,
% 0.12/0.39 (big_q(Y!1) | ![X: $i] : (~big_p(X))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[117, 114])).
% 0.12/0.39 tff(119,plain,
% 0.12/0.39 (![X: $i] : (~big_p(X))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[118, 113])).
% 0.12/0.39 tff(120,plain,
% 0.12/0.39 ((~![X: $i] : (~big_p(X))) | (~big_p(X!2))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(121,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[120, 119, 88])).
% 0.12/0.39 % SZS output end Proof
%------------------------------------------------------------------------------