TSTP Solution File: SYN058+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN058+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 23:53:25 EDT 2022
% Result : Theorem 0.20s 0.38s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN058+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n018.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 01:33:01 EDT 2022
% 0.13/0.34 % 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.
% 0.20/0.38 % SZS status Theorem
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 tff(big_f_type, type, (
% 0.20/0.38 big_f: $i > $o)).
% 0.20/0.38 tff(tptp_fun_X_2_type, type, (
% 0.20/0.38 tptp_fun_X_2: $i)).
% 0.20/0.38 tff(big_p_type, type, (
% 0.20/0.38 big_p: $i > $o)).
% 0.20/0.38 tff(big_g_type, type, (
% 0.20/0.38 big_g: $i > $o)).
% 0.20/0.38 tff(big_s_type, type, (
% 0.20/0.38 big_s: $i > $o)).
% 0.20/0.38 tff(tptp_fun_X1_1_type, type, (
% 0.20/0.38 tptp_fun_X1_1: $i)).
% 0.20/0.38 tff(big_q_type, type, (
% 0.20/0.38 big_q: $i > $o)).
% 0.20/0.38 tff(big_r_type, type, (
% 0.20/0.38 big_r: $i > $o)).
% 0.20/0.38 tff(tptp_fun_X_0_type, type, (
% 0.20/0.38 tptp_fun_X_0: $i)).
% 0.20/0.38 tff(1,plain,
% 0.20/0.38 ((~![X: $i] : (big_g(X) | (~(big_p(X) & big_f(X))))) <=> (~![X: $i] : (big_g(X) | (~(big_p(X) & big_f(X)))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(2,plain,
% 0.20/0.38 ((~![X: $i] : ((big_p(X) & big_f(X)) => big_g(X))) <=> (~![X: $i] : (big_g(X) | (~(big_p(X) & big_f(X)))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(3,axiom,(~![X: $i] : ((big_p(X) & big_f(X)) => big_g(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel28')).
% 0.20/0.38 tff(4,plain,
% 0.20/0.38 (~![X: $i] : (big_g(X) | (~(big_p(X) & big_f(X))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.20/0.39 tff(5,plain,
% 0.20/0.39 (~![X: $i] : (big_g(X) | (~(big_p(X) & big_f(X))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.20/0.39 tff(6,plain,
% 0.20/0.39 (~![X: $i] : (big_g(X) | (~(big_p(X) & big_f(X))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.20/0.39 tff(7,plain,
% 0.20/0.39 (~![X: $i] : (big_g(X) | (~(big_p(X) & big_f(X))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.20/0.39 tff(8,plain,
% 0.20/0.39 (~![X: $i] : (big_g(X) | (~(big_p(X) & big_f(X))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.20/0.39 tff(9,plain,
% 0.20/0.39 (~![X: $i] : (big_g(X) | (~(big_p(X) & big_f(X))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.20/0.39 tff(10,plain,
% 0.20/0.39 (~![X: $i] : (big_g(X) | (~(big_p(X) & big_f(X))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.20/0.39 tff(11,plain,(
% 0.20/0.39 ~(big_g(X!2) | (~(big_p(X!2) & big_f(X!2))))),
% 0.20/0.39 inference(skolemize,[status(sab)],[10])).
% 0.20/0.39 tff(12,plain,
% 0.20/0.39 (big_p(X!2) & big_f(X!2)),
% 0.20/0.39 inference(or_elim,[status(thm)],[11])).
% 0.20/0.39 tff(13,plain,
% 0.20/0.39 (big_f(X!2)),
% 0.20/0.39 inference(and_elim,[status(thm)],[12])).
% 0.20/0.39 tff(14,plain,
% 0.20/0.39 (~big_g(X!2)),
% 0.20/0.39 inference(or_elim,[status(thm)],[11])).
% 0.20/0.39 tff(15,plain,
% 0.20/0.39 (big_p(X!2)),
% 0.20/0.39 inference(and_elim,[status(thm)],[12])).
% 0.20/0.39 tff(16,plain,
% 0.20/0.39 (^[X: $i] : refl(((~big_p(X)) | ![Z: $i] : big_q(Z)) <=> ((~big_p(X)) | ![Z: $i] : big_q(Z)))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(17,plain,
% 0.20/0.39 (![X: $i] : ((~big_p(X)) | ![Z: $i] : big_q(Z)) <=> ![X: $i] : ((~big_p(X)) | ![Z: $i] : big_q(Z))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[16])).
% 0.20/0.39 tff(18,plain,
% 0.20/0.39 (^[X: $i] : rewrite(((~big_p(X)) | ![Z: $i] : big_q(Z)) <=> ((~big_p(X)) | ![Z: $i] : big_q(Z)))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(19,plain,
% 0.20/0.39 (![X: $i] : ((~big_p(X)) | ![Z: $i] : big_q(Z)) <=> ![X: $i] : ((~big_p(X)) | ![Z: $i] : big_q(Z))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[18])).
% 0.20/0.39 tff(20,plain,
% 0.20/0.39 (![X: $i] : ((~big_p(X)) | ![Z: $i] : big_q(Z)) <=> ![X: $i] : ((~big_p(X)) | ![Z: $i] : big_q(Z))),
% 0.20/0.39 inference(transitivity,[status(thm)],[19, 17])).
% 0.20/0.39 tff(21,plain,
% 0.20/0.39 (![X: $i] : ((~big_p(X)) | ![Z: $i] : big_q(Z)) <=> ![X: $i] : ((~big_p(X)) | ![Z: $i] : big_q(Z))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(22,plain,
% 0.20/0.39 (^[X: $i] : rewrite((big_p(X) => ![Z: $i] : big_q(Z)) <=> ((~big_p(X)) | ![Z: $i] : big_q(Z)))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(23,plain,
% 0.20/0.39 (![X: $i] : (big_p(X) => ![Z: $i] : big_q(Z)) <=> ![X: $i] : ((~big_p(X)) | ![Z: $i] : big_q(Z))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[22])).
% 0.20/0.39 tff(24,axiom,(![X: $i] : (big_p(X) => ![Z: $i] : big_q(Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel28_1')).
% 0.20/0.39 tff(25,plain,
% 0.20/0.39 (![X: $i] : ((~big_p(X)) | ![Z: $i] : big_q(Z))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.20/0.39 tff(26,plain,
% 0.20/0.39 (![X: $i] : ((~big_p(X)) | ![Z: $i] : big_q(Z))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.20/0.39 tff(27,plain,(
% 0.20/0.39 ![X: $i] : ((~big_p(X)) | ![Z: $i] : big_q(Z))),
% 0.20/0.39 inference(skolemize,[status(sab)],[26])).
% 0.20/0.39 tff(28,plain,
% 0.20/0.39 (![X: $i] : ((~big_p(X)) | ![Z: $i] : big_q(Z))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.20/0.39 tff(29,plain,
% 0.20/0.39 (((~![X: $i] : ((~big_p(X)) | ![Z: $i] : big_q(Z))) | ((~big_p(X!2)) | ![Z: $i] : big_q(Z))) <=> ((~![X: $i] : ((~big_p(X)) | ![Z: $i] : big_q(Z))) | (~big_p(X!2)) | ![Z: $i] : big_q(Z))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(30,plain,
% 0.20/0.39 ((~![X: $i] : ((~big_p(X)) | ![Z: $i] : big_q(Z))) | ((~big_p(X!2)) | ![Z: $i] : big_q(Z))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(31,plain,
% 0.20/0.39 ((~![X: $i] : ((~big_p(X)) | ![Z: $i] : big_q(Z))) | (~big_p(X!2)) | ![Z: $i] : big_q(Z)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.20/0.39 tff(32,plain,
% 0.20/0.39 (![Z: $i] : big_q(Z)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[31, 28, 15])).
% 0.20/0.39 tff(33,assumption,(~big_q(X!0)), introduced(assumption)).
% 0.20/0.39 tff(34,plain,
% 0.20/0.39 ((~![Z: $i] : big_q(Z)) | big_q(X!0)),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(35,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[34, 33, 32])).
% 0.20/0.39 tff(36,plain,(big_q(X!0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(37,plain,
% 0.20/0.39 ((big_q(X!0) | big_r(X!0)) | (~big_q(X!0))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(38,plain,
% 0.20/0.39 (big_q(X!0) | big_r(X!0)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.20/0.39 tff(39,plain,
% 0.20/0.39 (((~(big_q(X!0) | big_r(X!0))) | (big_q(X1!1) & big_s(X1!1))) <=> ((~(big_q(X!0) | big_r(X!0))) | (~((~big_q(X1!1)) | (~big_s(X1!1)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(40,plain,
% 0.20/0.39 (((~![X: $i] : (big_q(X) | big_r(X))) | ?[X1: $i] : (big_q(X1) & big_s(X1))) <=> ((~![X: $i] : (big_q(X) | big_r(X))) | ?[X1: $i] : (big_q(X1) & big_s(X1)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(41,plain,
% 0.20/0.39 ((![X: $i] : (big_q(X) | big_r(X)) => ?[X1: $i] : (big_q(X1) & big_s(X1))) <=> ((~![X: $i] : (big_q(X) | big_r(X))) | ?[X1: $i] : (big_q(X1) & big_s(X1)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(42,axiom,(![X: $i] : (big_q(X) | big_r(X)) => ?[X1: $i] : (big_q(X1) & big_s(X1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel28_2')).
% 0.20/0.39 tff(43,plain,
% 0.20/0.39 ((~![X: $i] : (big_q(X) | big_r(X))) | ?[X1: $i] : (big_q(X1) & big_s(X1))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.39 tff(44,plain,
% 0.20/0.39 ((~![X: $i] : (big_q(X) | big_r(X))) | ?[X1: $i] : (big_q(X1) & big_s(X1))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[43, 40])).
% 0.20/0.39 tff(45,plain,
% 0.20/0.39 ((~![X: $i] : (big_q(X) | big_r(X))) | ?[X1: $i] : (big_q(X1) & big_s(X1))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.20/0.39 tff(46,plain,
% 0.20/0.39 ((~![X: $i] : (big_q(X) | big_r(X))) | ?[X1: $i] : (big_q(X1) & big_s(X1))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[45, 40])).
% 0.20/0.39 tff(47,plain,
% 0.20/0.39 ((~![X: $i] : (big_q(X) | big_r(X))) | ?[X1: $i] : (big_q(X1) & big_s(X1))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[46, 40])).
% 0.20/0.39 tff(48,plain,
% 0.20/0.39 ((~![X: $i] : (big_q(X) | big_r(X))) | ?[X1: $i] : (big_q(X1) & big_s(X1))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.20/0.39 tff(49,plain,
% 0.20/0.39 ((~![X: $i] : (big_q(X) | big_r(X))) | ?[X1: $i] : (big_q(X1) & big_s(X1))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[48, 40])).
% 0.20/0.39 Proof display could not be completed: monotonicity rule is not handled
%------------------------------------------------------------------------------