TSTP Solution File: SYN359+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN359+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.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 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SYN359+1 : TPTP v8.1.0. Released v2.0.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n021.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 : Mon Sep 5 02:50:01 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(big_q_type, type, (
% 0.13/0.39 big_q: ( $i * $i ) > $o)).
% 0.13/0.39 tff(tptp_fun_X_0_type, type, (
% 0.13/0.39 tptp_fun_X_0: $i)).
% 0.13/0.39 tff(tptp_fun_Z_1_type, type, (
% 0.13/0.39 tptp_fun_Z_1: $i > $i)).
% 0.13/0.39 tff(big_r_type, type, (
% 0.13/0.39 big_r: $i > $o)).
% 0.13/0.39 tff(1,plain,
% 0.13/0.39 (^[Y: $i] : refl(((~big_r(Y)) | big_q(Y, tptp_fun_Z_1(Y))) <=> ((~big_r(Y)) | big_q(Y, tptp_fun_Z_1(Y))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 (![Y: $i] : ((~big_r(Y)) | big_q(Y, tptp_fun_Z_1(Y))) <=> ![Y: $i] : ((~big_r(Y)) | big_q(Y, tptp_fun_Z_1(Y)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.39 tff(3,plain,
% 0.13/0.39 (![Y: $i] : ((~big_r(Y)) | ?[Z: $i] : big_q(Y, Z)) <=> ![Y: $i] : ((~big_r(Y)) | ?[Z: $i] : big_q(Y, Z))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(4,plain,
% 0.13/0.39 ((~(((?[X: $i] : big_r(X) & ![Y: $i] : (big_r(Y) => ?[Z: $i] : big_q(Y, Z))) & ![X: $i, Y: $i] : (big_q(X, Y) => big_q(X, X))) => ?[X: $i, Y: $i] : (big_q(X, Y) & big_r(Y)))) <=> (~((~(?[X: $i] : big_r(X) & ![Y: $i] : ((~big_r(Y)) | ?[Z: $i] : big_q(Y, Z)) & ![X: $i, Y: $i] : ((~big_q(X, Y)) | big_q(X, X)))) | ?[X: $i, Y: $i] : (big_q(X, Y) & big_r(Y))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(5,axiom,(~(((?[X: $i] : big_r(X) & ![Y: $i] : (big_r(Y) => ?[Z: $i] : big_q(Y, Z))) & ![X: $i, Y: $i] : (big_q(X, Y) => big_q(X, X))) => ?[X: $i, Y: $i] : (big_q(X, Y) & big_r(Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','x2110')).
% 0.13/0.39 tff(6,plain,
% 0.13/0.39 (~((~(?[X: $i] : big_r(X) & ![Y: $i] : ((~big_r(Y)) | ?[Z: $i] : big_q(Y, Z)) & ![X: $i, Y: $i] : ((~big_q(X, Y)) | big_q(X, X)))) | ?[X: $i, Y: $i] : (big_q(X, Y) & big_r(Y)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.13/0.39 tff(7,plain,
% 0.13/0.39 (?[X: $i] : big_r(X) & ![Y: $i] : ((~big_r(Y)) | ?[Z: $i] : big_q(Y, Z)) & ![X: $i, Y: $i] : ((~big_q(X, Y)) | big_q(X, X))),
% 0.13/0.39 inference(or_elim,[status(thm)],[6])).
% 0.13/0.39 tff(8,plain,
% 0.13/0.39 (![Y: $i] : ((~big_r(Y)) | ?[Z: $i] : big_q(Y, Z))),
% 0.13/0.39 inference(and_elim,[status(thm)],[7])).
% 0.13/0.39 tff(9,plain,
% 0.13/0.39 (![Y: $i] : ((~big_r(Y)) | ?[Z: $i] : big_q(Y, Z))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[8, 3])).
% 0.13/0.39 tff(10,plain,(
% 0.13/0.39 ![Y: $i] : ((~big_r(Y)) | big_q(Y, tptp_fun_Z_1(Y)))),
% 0.13/0.39 inference(skolemize,[status(sab)],[9])).
% 0.13/0.39 tff(11,plain,
% 0.13/0.39 (![Y: $i] : ((~big_r(Y)) | big_q(Y, tptp_fun_Z_1(Y)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 (?[X: $i] : big_r(X) <=> ?[X: $i] : big_r(X)),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(13,plain,
% 0.13/0.39 (?[X: $i] : big_r(X)),
% 0.13/0.39 inference(and_elim,[status(thm)],[7])).
% 0.13/0.39 tff(14,plain,
% 0.13/0.39 (?[X: $i] : big_r(X)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.13/0.39 tff(15,plain,(
% 0.13/0.39 big_r(X!0)),
% 0.13/0.39 inference(skolemize,[status(sab)],[14])).
% 0.13/0.39 tff(16,plain,
% 0.13/0.39 (((~![Y: $i] : ((~big_r(Y)) | big_q(Y, tptp_fun_Z_1(Y)))) | ((~big_r(X!0)) | big_q(X!0, tptp_fun_Z_1(X!0)))) <=> ((~![Y: $i] : ((~big_r(Y)) | big_q(Y, tptp_fun_Z_1(Y)))) | (~big_r(X!0)) | big_q(X!0, tptp_fun_Z_1(X!0)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(17,plain,
% 0.13/0.39 ((~![Y: $i] : ((~big_r(Y)) | big_q(Y, tptp_fun_Z_1(Y)))) | ((~big_r(X!0)) | big_q(X!0, tptp_fun_Z_1(X!0)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(18,plain,
% 0.13/0.39 ((~![Y: $i] : ((~big_r(Y)) | big_q(Y, tptp_fun_Z_1(Y)))) | (~big_r(X!0)) | big_q(X!0, tptp_fun_Z_1(X!0))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.13/0.39 tff(19,plain,
% 0.13/0.39 (big_q(X!0, tptp_fun_Z_1(X!0))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[18, 15, 11])).
% 0.13/0.39 tff(20,plain,
% 0.13/0.39 (^[X: $i, Y: $i] : refl(((~big_q(X, Y)) | big_q(X, X)) <=> ((~big_q(X, Y)) | big_q(X, X)))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(21,plain,
% 0.13/0.39 (![X: $i, Y: $i] : ((~big_q(X, Y)) | big_q(X, X)) <=> ![X: $i, Y: $i] : ((~big_q(X, Y)) | big_q(X, X))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[20])).
% 0.13/0.39 tff(22,plain,
% 0.13/0.39 (![X: $i, Y: $i] : ((~big_q(X, Y)) | big_q(X, X)) <=> ![X: $i, Y: $i] : ((~big_q(X, Y)) | big_q(X, X))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(23,plain,
% 0.13/0.39 (![X: $i, Y: $i] : ((~big_q(X, Y)) | big_q(X, X))),
% 0.13/0.39 inference(and_elim,[status(thm)],[7])).
% 0.13/0.39 tff(24,plain,
% 0.13/0.39 (![X: $i, Y: $i] : ((~big_q(X, Y)) | big_q(X, X))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.13/0.39 tff(25,plain,(
% 0.13/0.39 ![X: $i, Y: $i] : ((~big_q(X, Y)) | big_q(X, X))),
% 0.13/0.39 inference(skolemize,[status(sab)],[24])).
% 0.13/0.39 tff(26,plain,
% 0.13/0.39 (![X: $i, Y: $i] : ((~big_q(X, Y)) | big_q(X, X))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.13/0.39 tff(27,plain,
% 0.13/0.39 (((~![X: $i, Y: $i] : ((~big_q(X, Y)) | big_q(X, X))) | ((~big_q(X!0, tptp_fun_Z_1(X!0))) | big_q(X!0, X!0))) <=> ((~![X: $i, Y: $i] : ((~big_q(X, Y)) | big_q(X, X))) | (~big_q(X!0, tptp_fun_Z_1(X!0))) | big_q(X!0, X!0))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(28,plain,
% 0.13/0.39 ((~![X: $i, Y: $i] : ((~big_q(X, Y)) | big_q(X, X))) | ((~big_q(X!0, tptp_fun_Z_1(X!0))) | big_q(X!0, X!0))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(29,plain,
% 0.13/0.39 ((~![X: $i, Y: $i] : ((~big_q(X, Y)) | big_q(X, X))) | (~big_q(X!0, tptp_fun_Z_1(X!0))) | big_q(X!0, X!0)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.13/0.39 tff(30,plain,
% 0.13/0.39 (big_q(X!0, X!0)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[29, 26, 19])).
% 0.13/0.39 tff(31,plain,
% 0.13/0.39 (^[X: $i, Y: $i] : refl(((~big_r(Y)) | (~big_q(X, Y))) <=> ((~big_r(Y)) | (~big_q(X, Y))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(32,plain,
% 0.13/0.39 (![X: $i, Y: $i] : ((~big_r(Y)) | (~big_q(X, Y))) <=> ![X: $i, Y: $i] : ((~big_r(Y)) | (~big_q(X, Y)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[31])).
% 0.13/0.39 tff(33,plain,
% 0.13/0.39 (^[X: $i, Y: $i] : trans(monotonicity(rewrite((big_q(X, Y) & big_r(Y)) <=> (~((~big_r(Y)) | (~big_q(X, Y))))), ((~(big_q(X, Y) & big_r(Y))) <=> (~(~((~big_r(Y)) | (~big_q(X, Y))))))), rewrite((~(~((~big_r(Y)) | (~big_q(X, Y))))) <=> ((~big_r(Y)) | (~big_q(X, Y)))), ((~(big_q(X, Y) & big_r(Y))) <=> ((~big_r(Y)) | (~big_q(X, Y)))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(34,plain,
% 0.13/0.39 (![X: $i, Y: $i] : (~(big_q(X, Y) & big_r(Y))) <=> ![X: $i, Y: $i] : ((~big_r(Y)) | (~big_q(X, Y)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[33])).
% 0.13/0.39 tff(35,plain,
% 0.13/0.39 ((~?[X: $i, Y: $i] : (big_q(X, Y) & big_r(Y))) <=> (~?[X: $i, Y: $i] : (big_q(X, Y) & big_r(Y)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(36,plain,
% 0.13/0.39 (~?[X: $i, Y: $i] : (big_q(X, Y) & big_r(Y))),
% 0.13/0.39 inference(or_elim,[status(thm)],[6])).
% 0.13/0.39 tff(37,plain,
% 0.13/0.39 (~?[X: $i, Y: $i] : (big_q(X, Y) & big_r(Y))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.13/0.39 tff(38,plain,
% 0.13/0.39 (~?[X: $i, Y: $i] : (big_q(X, Y) & big_r(Y))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[37, 35])).
% 0.13/0.39 tff(39,plain,
% 0.13/0.39 (~?[X: $i, Y: $i] : (big_q(X, Y) & big_r(Y))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[38, 35])).
% 0.13/0.39 tff(40,plain,
% 0.13/0.39 (~?[X: $i, Y: $i] : (big_q(X, Y) & big_r(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_q(X, Y) & big_r(Y))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[40, 35])).
% 0.13/0.39 tff(42,plain,
% 0.13/0.39 (~?[X: $i, Y: $i] : (big_q(X, Y) & big_r(Y))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[41, 35])).
% 0.13/0.39 tff(43,plain,
% 0.13/0.39 (^[X: $i, Y: $i] : refl($oeq((~(big_q(X, Y) & big_r(Y))), (~(big_q(X, Y) & big_r(Y)))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(44,plain,(
% 0.13/0.39 ![X: $i, Y: $i] : (~(big_q(X, Y) & big_r(Y)))),
% 0.13/0.39 inference(nnf-neg,[status(sab)],[42, 43])).
% 0.13/0.39 tff(45,plain,
% 0.13/0.39 (![X: $i, Y: $i] : ((~big_r(Y)) | (~big_q(X, Y)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[44, 34])).
% 0.13/0.39 tff(46,plain,
% 0.13/0.39 (![X: $i, Y: $i] : ((~big_r(Y)) | (~big_q(X, Y)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[45, 32])).
% 0.13/0.39 tff(47,plain,
% 0.13/0.39 (((~![X: $i, Y: $i] : ((~big_r(Y)) | (~big_q(X, Y)))) | ((~big_r(X!0)) | (~big_q(X!0, X!0)))) <=> ((~![X: $i, Y: $i] : ((~big_r(Y)) | (~big_q(X, Y)))) | (~big_r(X!0)) | (~big_q(X!0, X!0)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(48,plain,
% 0.13/0.39 ((~![X: $i, Y: $i] : ((~big_r(Y)) | (~big_q(X, Y)))) | ((~big_r(X!0)) | (~big_q(X!0, X!0)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(49,plain,
% 0.13/0.39 ((~![X: $i, Y: $i] : ((~big_r(Y)) | (~big_q(X, Y)))) | (~big_r(X!0)) | (~big_q(X!0, X!0))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.13/0.39 tff(50,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[49, 15, 46, 30])).
% 0.13/0.39 % SZS output end Proof
%------------------------------------------------------------------------------