TSTP Solution File: SYN361+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN361+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.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 23:54:58 EDT 2022
% Result : Theorem 0.13s 0.38s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SYN361+1 : TPTP v8.1.0. Released v2.0.0.
% 0.10/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n024.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Sep 5 02:56:33 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 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 * $i ) > $o)).
% 0.13/0.38 tff(tptp_fun_V_0_type, type, (
% 0.13/0.38 tptp_fun_V_0: $i)).
% 0.13/0.38 tff(tptp_fun_Y_1_type, type, (
% 0.13/0.38 tptp_fun_Y_1: $i > $i)).
% 0.13/0.38 tff(big_q_type, type, (
% 0.13/0.38 big_q: ( $i * $i ) > $o)).
% 0.13/0.38 tff(big_s_type, type, (
% 0.13/0.38 big_s: $i > $o)).
% 0.13/0.38 tff(1,plain,
% 0.13/0.38 (^[U: $i] : refl(big_s(U) <=> big_s(U))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(2,plain,
% 0.13/0.38 (![U: $i] : big_s(U) <=> ![U: $i] : big_s(U)),
% 0.13/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.38 tff(3,plain,
% 0.13/0.38 (^[U: $i] : rewrite((~(~big_s(U))) <=> big_s(U))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(4,plain,
% 0.13/0.38 (![U: $i] : (~(~big_s(U))) <=> ![U: $i] : big_s(U)),
% 0.13/0.38 inference(quant_intro,[status(thm)],[3])).
% 0.13/0.38 tff(5,plain,
% 0.13/0.38 ((~?[U: $i] : (~big_s(U))) <=> (~?[U: $i] : (~big_s(U)))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(6,plain,
% 0.13/0.38 ((~(((?[V: $i] : ![X: $i] : big_p(X, V) & ![X: $i] : (big_s(X) => ?[Y: $i] : big_q(Y, X))) & ![X: $i, Y: $i] : (big_p(X, Y) => (~big_q(X, Y)))) => ?[U: $i] : (~big_s(U)))) <=> (~((~(?[V: $i] : ![X: $i] : big_p(X, V) & ![X: $i] : ((~big_s(X)) | ?[Y: $i] : big_q(Y, X)) & ![X: $i, Y: $i] : ((~big_p(X, Y)) | (~big_q(X, Y))))) | ?[U: $i] : (~big_s(U))))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(7,axiom,(~(((?[V: $i] : ![X: $i] : big_p(X, V) & ![X: $i] : (big_s(X) => ?[Y: $i] : big_q(Y, X))) & ![X: $i, Y: $i] : (big_p(X, Y) => (~big_q(X, Y)))) => ?[U: $i] : (~big_s(U)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','x2112')).
% 0.13/0.38 tff(8,plain,
% 0.13/0.38 (~((~(?[V: $i] : ![X: $i] : big_p(X, V) & ![X: $i] : ((~big_s(X)) | ?[Y: $i] : big_q(Y, X)) & ![X: $i, Y: $i] : ((~big_p(X, Y)) | (~big_q(X, Y))))) | ?[U: $i] : (~big_s(U)))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.13/0.38 tff(9,plain,
% 0.13/0.38 (~?[U: $i] : (~big_s(U))),
% 0.13/0.38 inference(or_elim,[status(thm)],[8])).
% 0.13/0.38 tff(10,plain,
% 0.13/0.38 (~?[U: $i] : (~big_s(U))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.13/0.38 tff(11,plain,
% 0.13/0.38 (~?[U: $i] : (~big_s(U))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.13/0.38 tff(12,plain,
% 0.13/0.38 (~?[U: $i] : (~big_s(U))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[11, 5])).
% 0.13/0.38 tff(13,plain,
% 0.13/0.38 (~?[U: $i] : (~big_s(U))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.13/0.38 tff(14,plain,
% 0.13/0.38 (~?[U: $i] : (~big_s(U))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[13, 5])).
% 0.13/0.38 tff(15,plain,
% 0.13/0.38 (~?[U: $i] : (~big_s(U))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[14, 5])).
% 0.13/0.38 tff(16,plain,
% 0.13/0.38 (^[U: $i] : refl($oeq((~(~big_s(U))), (~(~big_s(U)))))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(17,plain,(
% 0.13/0.38 ![U: $i] : (~(~big_s(U)))),
% 0.13/0.38 inference(nnf-neg,[status(sab)],[15, 16])).
% 0.13/0.38 tff(18,plain,
% 0.13/0.38 (![U: $i] : big_s(U)),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[17, 4])).
% 0.13/0.38 tff(19,plain,
% 0.13/0.38 (![U: $i] : big_s(U)),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[18, 2])).
% 0.13/0.38 tff(20,plain,
% 0.13/0.38 ((~![U: $i] : big_s(U)) | big_s(V!0)),
% 0.13/0.38 inference(quant_inst,[status(thm)],[])).
% 0.13/0.38 tff(21,plain,
% 0.13/0.38 (big_s(V!0)),
% 0.13/0.38 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.13/0.38 tff(22,plain,
% 0.13/0.38 (^[X: $i] : refl(((~big_s(X)) | big_q(tptp_fun_Y_1(X), X)) <=> ((~big_s(X)) | big_q(tptp_fun_Y_1(X), X)))),
% 0.13/0.38 inference(bind,[status(th)],[])).
% 0.13/0.38 tff(23,plain,
% 0.13/0.38 (![X: $i] : ((~big_s(X)) | big_q(tptp_fun_Y_1(X), X)) <=> ![X: $i] : ((~big_s(X)) | big_q(tptp_fun_Y_1(X), X))),
% 0.13/0.38 inference(quant_intro,[status(thm)],[22])).
% 0.13/0.38 tff(24,plain,
% 0.13/0.38 (![X: $i] : ((~big_s(X)) | ?[Y: $i] : big_q(Y, X)) <=> ![X: $i] : ((~big_s(X)) | ?[Y: $i] : big_q(Y, X))),
% 0.13/0.38 inference(rewrite,[status(thm)],[])).
% 0.13/0.38 tff(25,plain,
% 0.13/0.38 (?[V: $i] : ![X: $i] : big_p(X, V) & ![X: $i] : ((~big_s(X)) | ?[Y: $i] : big_q(Y, X)) & ![X: $i, Y: $i] : ((~big_p(X, Y)) | (~big_q(X, Y)))),
% 0.13/0.38 inference(or_elim,[status(thm)],[8])).
% 0.13/0.38 tff(26,plain,
% 0.13/0.38 (![X: $i] : ((~big_s(X)) | ?[Y: $i] : big_q(Y, X))),
% 0.13/0.38 inference(and_elim,[status(thm)],[25])).
% 0.13/0.38 tff(27,plain,
% 0.13/0.38 (![X: $i] : ((~big_s(X)) | ?[Y: $i] : big_q(Y, X))),
% 0.13/0.38 inference(modus_ponens,[status(thm)],[26, 24])).
% 0.13/0.38 tff(28,plain,(
% 0.13/0.38 ![X: $i] : ((~big_s(X)) | big_q(tptp_fun_Y_1(X), X))),
% 0.13/0.38 inference(skolemize,[status(sab)],[27])).
% 0.13/0.39 tff(29,plain,
% 0.13/0.39 (![X: $i] : ((~big_s(X)) | big_q(tptp_fun_Y_1(X), X))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[28, 23])).
% 0.13/0.39 tff(30,plain,
% 0.13/0.39 (((~![X: $i] : ((~big_s(X)) | big_q(tptp_fun_Y_1(X), X))) | ((~big_s(V!0)) | big_q(tptp_fun_Y_1(V!0), V!0))) <=> ((~![X: $i] : ((~big_s(X)) | big_q(tptp_fun_Y_1(X), X))) | (~big_s(V!0)) | big_q(tptp_fun_Y_1(V!0), V!0))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(31,plain,
% 0.13/0.39 ((~![X: $i] : ((~big_s(X)) | big_q(tptp_fun_Y_1(X), X))) | ((~big_s(V!0)) | big_q(tptp_fun_Y_1(V!0), V!0))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(32,plain,
% 0.13/0.39 ((~![X: $i] : ((~big_s(X)) | big_q(tptp_fun_Y_1(X), X))) | (~big_s(V!0)) | big_q(tptp_fun_Y_1(V!0), V!0)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.13/0.39 tff(33,plain,
% 0.13/0.39 (big_q(tptp_fun_Y_1(V!0), V!0)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[32, 29, 21])).
% 0.13/0.39 tff(34,plain,
% 0.13/0.39 (^[X: $i, Y: $i] : refl(((~big_p(X, Y)) | (~big_q(X, Y))) <=> ((~big_p(X, Y)) | (~big_q(X, Y))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(35,plain,
% 0.13/0.39 (![X: $i, Y: $i] : ((~big_p(X, Y)) | (~big_q(X, Y))) <=> ![X: $i, Y: $i] : ((~big_p(X, Y)) | (~big_q(X, Y)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[34])).
% 0.13/0.39 tff(36,plain,
% 0.13/0.39 (![X: $i, Y: $i] : ((~big_p(X, Y)) | (~big_q(X, Y))) <=> ![X: $i, Y: $i] : ((~big_p(X, Y)) | (~big_q(X, Y)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(37,plain,
% 0.13/0.39 (![X: $i, Y: $i] : ((~big_p(X, Y)) | (~big_q(X, Y)))),
% 0.13/0.39 inference(and_elim,[status(thm)],[25])).
% 0.13/0.39 tff(38,plain,
% 0.13/0.39 (![X: $i, Y: $i] : ((~big_p(X, Y)) | (~big_q(X, Y)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.13/0.39 tff(39,plain,(
% 0.13/0.39 ![X: $i, Y: $i] : ((~big_p(X, Y)) | (~big_q(X, Y)))),
% 0.13/0.39 inference(skolemize,[status(sab)],[38])).
% 0.13/0.39 tff(40,plain,
% 0.13/0.39 (![X: $i, Y: $i] : ((~big_p(X, Y)) | (~big_q(X, Y)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.13/0.39 tff(41,plain,
% 0.13/0.39 (((~![X: $i, Y: $i] : ((~big_p(X, Y)) | (~big_q(X, Y)))) | ((~big_p(tptp_fun_Y_1(V!0), V!0)) | (~big_q(tptp_fun_Y_1(V!0), V!0)))) <=> ((~![X: $i, Y: $i] : ((~big_p(X, Y)) | (~big_q(X, Y)))) | (~big_p(tptp_fun_Y_1(V!0), V!0)) | (~big_q(tptp_fun_Y_1(V!0), V!0)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(42,plain,
% 0.13/0.39 ((~![X: $i, Y: $i] : ((~big_p(X, Y)) | (~big_q(X, Y)))) | ((~big_p(tptp_fun_Y_1(V!0), V!0)) | (~big_q(tptp_fun_Y_1(V!0), V!0)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(43,plain,
% 0.13/0.39 ((~![X: $i, Y: $i] : ((~big_p(X, Y)) | (~big_q(X, Y)))) | (~big_p(tptp_fun_Y_1(V!0), V!0)) | (~big_q(tptp_fun_Y_1(V!0), V!0))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.13/0.39 tff(44,plain,
% 0.13/0.39 (~big_p(tptp_fun_Y_1(V!0), V!0)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[43, 40, 33])).
% 0.13/0.39 tff(45,plain,
% 0.13/0.39 (^[X: $i] : refl(big_p(X, V!0) <=> big_p(X, V!0))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(46,plain,
% 0.13/0.39 (![X: $i] : big_p(X, V!0) <=> ![X: $i] : big_p(X, V!0)),
% 0.13/0.39 inference(quant_intro,[status(thm)],[45])).
% 0.13/0.39 tff(47,plain,
% 0.13/0.39 (?[V: $i] : ![X: $i] : big_p(X, V) <=> ?[V: $i] : ![X: $i] : big_p(X, V)),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(48,plain,
% 0.13/0.39 (?[V: $i] : ![X: $i] : big_p(X, V)),
% 0.13/0.39 inference(and_elim,[status(thm)],[25])).
% 0.13/0.39 tff(49,plain,
% 0.13/0.39 (?[V: $i] : ![X: $i] : big_p(X, V)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.13/0.39 tff(50,plain,(
% 0.13/0.39 $oeq(![X: $i] : big_p(X, V!0), ![X: $i] : big_p(X, V!0))),
% 0.13/0.39 inference(transitivity,[status(sab)],[49])).
% 0.13/0.39 tff(51,plain,
% 0.13/0.39 (![X: $i] : big_p(X, V!0)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.13/0.39 tff(52,plain,
% 0.13/0.39 ((~![X: $i] : big_p(X, V!0)) | big_p(tptp_fun_Y_1(V!0), V!0)),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(53,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[52, 51, 44])).
% 0.13/0.39 % SZS output end Proof
%------------------------------------------------------------------------------