TSTP Solution File: SYN367+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN367+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.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 23:55:00 EDT 2022
% Result : Theorem 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN367+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.33 % Computer : n015.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Mon Sep 5 03:07:42 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34 Usage: tptp [options] [-file:]file
% 0.14/0.34 -h, -? prints this message.
% 0.14/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.34 -m, -model generate model.
% 0.14/0.34 -p, -proof generate proof.
% 0.14/0.34 -c, -core generate unsat core of named formulas.
% 0.14/0.34 -st, -statistics display statistics.
% 0.14/0.34 -t:timeout set timeout (in second).
% 0.14/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34 -<param>:<value> configuration parameter and value.
% 0.14/0.34 -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_q_type, type, (
% 0.20/0.38 big_q: $i > $o)).
% 0.20/0.38 tff(tptp_fun_X_1_type, type, (
% 0.20/0.38 tptp_fun_X_1: $i)).
% 0.20/0.38 tff(p_type, type, (
% 0.20/0.38 p: $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_r(X)) <=> (~![X: $i] : big_r(X))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(2,plain,
% 0.20/0.38 ((~(![X: $i] : ((p & big_q(X)) | ((~p) & big_r(X))) => (![X: $i] : big_q(X) | ![X: $i] : big_r(X)))) <=> (~(![X: $i] : big_q(X) | ![X: $i] : big_r(X) | (~![X: $i] : ((p & big_q(X)) | ((~p) & big_r(X))))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(3,axiom,(~(![X: $i] : ((p & big_q(X)) | ((~p) & big_r(X))) => (![X: $i] : big_q(X) | ![X: $i] : big_r(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','x2118')).
% 0.20/0.38 tff(4,plain,
% 0.20/0.38 (~(![X: $i] : big_q(X) | ![X: $i] : big_r(X) | (~![X: $i] : ((p & big_q(X)) | ((~p) & big_r(X)))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.20/0.38 tff(5,plain,
% 0.20/0.38 (~![X: $i] : big_r(X)),
% 0.20/0.38 inference(or_elim,[status(thm)],[4])).
% 0.20/0.38 tff(6,plain,
% 0.20/0.38 (~![X: $i] : big_r(X)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.20/0.38 tff(7,plain,
% 0.20/0.38 (~![X: $i] : big_r(X)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.20/0.38 tff(8,plain,
% 0.20/0.38 (~![X: $i] : big_r(X)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.20/0.38 tff(9,plain,
% 0.20/0.38 (~![X: $i] : big_r(X)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.20/0.38 tff(10,plain,
% 0.20/0.38 (~![X: $i] : big_r(X)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.20/0.38 tff(11,plain,
% 0.20/0.38 (~![X: $i] : big_r(X)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[10, 1])).
% 0.20/0.38 tff(12,plain,(
% 0.20/0.38 ~big_r(X!1)),
% 0.20/0.38 inference(skolemize,[status(sab)],[11])).
% 0.20/0.38 tff(13,plain,
% 0.20/0.38 ((p | (~big_r(X!1))) | big_r(X!1)),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(14,plain,
% 0.20/0.38 (p | (~big_r(X!1))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.20/0.38 tff(15,plain,
% 0.20/0.38 (^[X: $i] : refl(((~((~p) | (~big_q(X)))) | (~(p | (~big_r(X))))) <=> ((~((~p) | (~big_q(X)))) | (~(p | (~big_r(X))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(16,plain,
% 0.20/0.38 (![X: $i] : ((~((~p) | (~big_q(X)))) | (~(p | (~big_r(X))))) <=> ![X: $i] : ((~((~p) | (~big_q(X)))) | (~(p | (~big_r(X)))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[15])).
% 0.20/0.38 tff(17,plain,
% 0.20/0.38 (^[X: $i] : trans(monotonicity(rewrite((p & big_q(X)) <=> (~((~p) | (~big_q(X))))), rewrite(((~p) & big_r(X)) <=> (~(p | (~big_r(X))))), (((p & big_q(X)) | ((~p) & big_r(X))) <=> ((~((~p) | (~big_q(X)))) | (~(p | (~big_r(X))))))), rewrite(((~((~p) | (~big_q(X)))) | (~(p | (~big_r(X))))) <=> ((~((~p) | (~big_q(X)))) | (~(p | (~big_r(X)))))), (((p & big_q(X)) | ((~p) & big_r(X))) <=> ((~((~p) | (~big_q(X)))) | (~(p | (~big_r(X)))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(18,plain,
% 0.20/0.38 (![X: $i] : ((p & big_q(X)) | ((~p) & big_r(X))) <=> ![X: $i] : ((~((~p) | (~big_q(X)))) | (~(p | (~big_r(X)))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[17])).
% 0.20/0.38 tff(19,plain,
% 0.20/0.38 (![X: $i] : ((p & big_q(X)) | ((~p) & big_r(X))) <=> ![X: $i] : ((p & big_q(X)) | ((~p) & big_r(X)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(20,plain,
% 0.20/0.38 (![X: $i] : ((p & big_q(X)) | ((~p) & big_r(X)))),
% 0.20/0.38 inference(or_elim,[status(thm)],[4])).
% 0.20/0.38 tff(21,plain,
% 0.20/0.38 (![X: $i] : ((p & big_q(X)) | ((~p) & big_r(X)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.20/0.38 tff(22,plain,(
% 0.20/0.38 ![X: $i] : ((p & big_q(X)) | ((~p) & big_r(X)))),
% 0.20/0.38 inference(skolemize,[status(sab)],[21])).
% 0.20/0.38 tff(23,plain,
% 0.20/0.38 (![X: $i] : ((~((~p) | (~big_q(X)))) | (~(p | (~big_r(X)))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.20/0.38 tff(24,plain,
% 0.20/0.38 (![X: $i] : ((~((~p) | (~big_q(X)))) | (~(p | (~big_r(X)))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.20/0.38 tff(25,plain,
% 0.20/0.38 (((~![X: $i] : ((~((~p) | (~big_q(X)))) | (~(p | (~big_r(X)))))) | ((~((~p) | (~big_q(X!1)))) | (~(p | (~big_r(X!1)))))) <=> ((~![X: $i] : ((~((~p) | (~big_q(X)))) | (~(p | (~big_r(X)))))) | (~((~p) | (~big_q(X!1)))) | (~(p | (~big_r(X!1)))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(26,plain,
% 0.20/0.38 ((~![X: $i] : ((~((~p) | (~big_q(X)))) | (~(p | (~big_r(X)))))) | ((~((~p) | (~big_q(X!1)))) | (~(p | (~big_r(X!1)))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(27,plain,
% 0.20/0.39 ((~![X: $i] : ((~((~p) | (~big_q(X)))) | (~(p | (~big_r(X)))))) | (~((~p) | (~big_q(X!1)))) | (~(p | (~big_r(X!1))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.20/0.39 tff(28,plain,
% 0.20/0.39 (~((~p) | (~big_q(X!1)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[27, 24, 14])).
% 0.20/0.39 tff(29,plain,
% 0.20/0.39 ((~![X: $i] : big_q(X)) <=> (~![X: $i] : big_q(X))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(30,plain,
% 0.20/0.39 (~![X: $i] : big_q(X)),
% 0.20/0.39 inference(or_elim,[status(thm)],[4])).
% 0.20/0.39 tff(31,plain,
% 0.20/0.39 (~![X: $i] : big_q(X)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.20/0.39 tff(32,plain,
% 0.20/0.39 (~![X: $i] : big_q(X)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[31, 29])).
% 0.20/0.39 tff(33,plain,
% 0.20/0.39 (~![X: $i] : big_q(X)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[32, 29])).
% 0.20/0.39 tff(34,plain,
% 0.20/0.39 (~![X: $i] : big_q(X)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.20/0.39 tff(35,plain,
% 0.20/0.39 (~![X: $i] : big_q(X)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[34, 29])).
% 0.20/0.39 tff(36,plain,
% 0.20/0.39 (~![X: $i] : big_q(X)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[35, 29])).
% 0.20/0.39 tff(37,plain,(
% 0.20/0.39 ~big_q(X!0)),
% 0.20/0.39 inference(skolemize,[status(sab)],[36])).
% 0.20/0.39 tff(38,plain,
% 0.20/0.39 (((~p) | (~big_q(X!0))) | big_q(X!0)),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(39,plain,
% 0.20/0.39 ((~p) | (~big_q(X!0))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.20/0.39 tff(40,plain,
% 0.20/0.39 (((~![X: $i] : ((~((~p) | (~big_q(X)))) | (~(p | (~big_r(X)))))) | ((~((~p) | (~big_q(X!0)))) | (~(p | (~big_r(X!0)))))) <=> ((~![X: $i] : ((~((~p) | (~big_q(X)))) | (~(p | (~big_r(X)))))) | (~((~p) | (~big_q(X!0)))) | (~(p | (~big_r(X!0)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(41,plain,
% 0.20/0.39 ((~![X: $i] : ((~((~p) | (~big_q(X)))) | (~(p | (~big_r(X)))))) | ((~((~p) | (~big_q(X!0)))) | (~(p | (~big_r(X!0)))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(42,plain,
% 0.20/0.39 ((~![X: $i] : ((~((~p) | (~big_q(X)))) | (~(p | (~big_r(X)))))) | (~((~p) | (~big_q(X!0)))) | (~(p | (~big_r(X!0))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.20/0.39 tff(43,plain,
% 0.20/0.39 (~(p | (~big_r(X!0)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[42, 24, 39])).
% 0.20/0.39 tff(44,plain,
% 0.20/0.39 ((p | (~big_r(X!0))) | (~p)),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(45,plain,
% 0.20/0.39 (~p),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.20/0.39 tff(46,plain,
% 0.20/0.39 (((~p) | (~big_q(X!1))) | p),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(47,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[46, 45, 28])).
% 0.20/0.39 % SZS output end Proof
%------------------------------------------------------------------------------