TSTP Solution File: SYN967+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN967+1 : TPTP v8.1.0. Released v3.1.0.
% 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 : Fri Sep 30 00:01:26 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
% 0.06/0.11 % Problem : SYN967+1 : TPTP v8.1.0. Released v3.1.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n015.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 09:56:12 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.
% 0.20/0.38 % SZS status Theorem
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 tff(q_type, type, (
% 0.20/0.38 q: $i > $o)).
% 0.20/0.38 tff(tptp_fun_B_0_type, type, (
% 0.20/0.38 tptp_fun_B_0: $i)).
% 0.20/0.38 tff(p_type, type, (
% 0.20/0.38 p: $i > $o)).
% 0.20/0.38 tff(tptp_fun_A_1_type, type, (
% 0.20/0.38 tptp_fun_A_1: $i)).
% 0.20/0.38 tff(1,assumption,(p(B!0) | (~q(A!1))), introduced(assumption)).
% 0.20/0.38 tff(2,plain,
% 0.20/0.38 (^[X: $i] : refl(((~(p(A!1) | (~p(X)))) | (~(p(B!0) | (~q(X))))) <=> ((~(p(A!1) | (~p(X)))) | (~(p(B!0) | (~q(X))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(3,plain,
% 0.20/0.38 (![X: $i] : ((~(p(A!1) | (~p(X)))) | (~(p(B!0) | (~q(X))))) <=> ![X: $i] : ((~(p(A!1) | (~p(X)))) | (~(p(B!0) | (~q(X)))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.38 tff(4,plain,
% 0.20/0.38 (^[X: $i] : trans(monotonicity(rewrite(((p(A!1) | (~p(X))) & (p(B!0) | (~q(X)))) <=> (~((~(p(A!1) | (~p(X)))) | (~(p(B!0) | (~q(X))))))), ((~((p(A!1) | (~p(X))) & (p(B!0) | (~q(X))))) <=> (~(~((~(p(A!1) | (~p(X)))) | (~(p(B!0) | (~q(X))))))))), rewrite((~(~((~(p(A!1) | (~p(X)))) | (~(p(B!0) | (~q(X))))))) <=> ((~(p(A!1) | (~p(X)))) | (~(p(B!0) | (~q(X)))))), ((~((p(A!1) | (~p(X))) & (p(B!0) | (~q(X))))) <=> ((~(p(A!1) | (~p(X)))) | (~(p(B!0) | (~q(X)))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(5,plain,
% 0.20/0.38 (![X: $i] : (~((p(A!1) | (~p(X))) & (p(B!0) | (~q(X))))) <=> ![X: $i] : ((~(p(A!1) | (~p(X)))) | (~(p(B!0) | (~q(X)))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.38 tff(6,plain,
% 0.20/0.38 ((![Y: $i] : (p(Y) | (~q(Y))) & ![X: $i] : (~((p(A!1) | (~p(X))) & (p(B!0) | (~q(X)))))) <=> (![Y: $i] : (p(Y) | (~q(Y))) & ![X: $i] : (~((p(A!1) | (~p(X))) & (p(B!0) | (~q(X))))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(7,plain,
% 0.20/0.38 ((~![A: $i, B: $i] : ((~![Y: $i] : (p(Y) | (~q(Y)))) | ?[X: $i] : ((p(A) | (~p(X))) & (p(B) | (~q(X)))))) <=> (~![A: $i, B: $i] : ((~![Y: $i] : (p(Y) | (~q(Y)))) | ?[X: $i] : ((p(A) | (~p(X))) & (p(B) | (~q(X))))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(8,plain,
% 0.20/0.38 ((~![A: $i, B: $i] : (![Y: $i] : (q(Y) => p(Y)) => ?[X: $i] : ((p(X) => p(A)) & (q(X) => p(B))))) <=> (~![A: $i, B: $i] : ((~![Y: $i] : (p(Y) | (~q(Y)))) | ?[X: $i] : ((p(A) | (~p(X))) & (p(B) | (~q(X))))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(9,axiom,(~![A: $i, B: $i] : (![Y: $i] : (q(Y) => p(Y)) => ?[X: $i] : ((p(X) => p(A)) & (q(X) => p(B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.20/0.38 tff(10,plain,
% 0.20/0.38 (~![A: $i, B: $i] : ((~![Y: $i] : (p(Y) | (~q(Y)))) | ?[X: $i] : ((p(A) | (~p(X))) & (p(B) | (~q(X)))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.20/0.38 tff(11,plain,
% 0.20/0.38 (~![A: $i, B: $i] : ((~![Y: $i] : (p(Y) | (~q(Y)))) | ?[X: $i] : ((p(A) | (~p(X))) & (p(B) | (~q(X)))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[10, 7])).
% 0.20/0.38 tff(12,plain,
% 0.20/0.38 (~![A: $i, B: $i] : ((~![Y: $i] : (p(Y) | (~q(Y)))) | ?[X: $i] : ((p(A) | (~p(X))) & (p(B) | (~q(X)))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.20/0.38 tff(13,plain,
% 0.20/0.38 (~![A: $i, B: $i] : ((~![Y: $i] : (p(Y) | (~q(Y)))) | ?[X: $i] : ((p(A) | (~p(X))) & (p(B) | (~q(X)))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[12, 7])).
% 0.20/0.38 tff(14,plain,
% 0.20/0.38 (~![A: $i, B: $i] : ((~![Y: $i] : (p(Y) | (~q(Y)))) | ?[X: $i] : ((p(A) | (~p(X))) & (p(B) | (~q(X)))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[13, 7])).
% 0.20/0.38 tff(15,plain,
% 0.20/0.38 (~![A: $i, B: $i] : ((~![Y: $i] : (p(Y) | (~q(Y)))) | ?[X: $i] : ((p(A) | (~p(X))) & (p(B) | (~q(X)))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.20/0.38 tff(16,plain,
% 0.20/0.38 (~![A: $i, B: $i] : ((~![Y: $i] : (p(Y) | (~q(Y)))) | ?[X: $i] : ((p(A) | (~p(X))) & (p(B) | (~q(X)))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[15, 7])).
% 0.20/0.38 tff(17,plain,
% 0.20/0.38 (![Y: $i] : (p(Y) | (~q(Y))) & ![X: $i] : (~((p(A!1) | (~p(X))) & (p(B!0) | (~q(X)))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[16, 6])).
% 0.20/0.38 tff(18,plain,
% 0.20/0.38 (![X: $i] : (~((p(A!1) | (~p(X))) & (p(B!0) | (~q(X)))))),
% 0.20/0.38 inference(and_elim,[status(thm)],[17])).
% 0.20/0.38 tff(19,plain,
% 0.20/0.38 (![X: $i] : ((~(p(A!1) | (~p(X)))) | (~(p(B!0) | (~q(X)))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[18, 5])).
% 0.20/0.38 tff(20,plain,
% 0.20/0.38 (![X: $i] : ((~(p(A!1) | (~p(X)))) | (~(p(B!0) | (~q(X)))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[19, 3])).
% 0.20/0.39 tff(21,plain,
% 0.20/0.39 (((~![X: $i] : ((~(p(A!1) | (~p(X)))) | (~(p(B!0) | (~q(X)))))) | (~(p(B!0) | (~q(A!1))))) <=> ((~![X: $i] : ((~(p(A!1) | (~p(X)))) | (~(p(B!0) | (~q(X)))))) | (~(p(B!0) | (~q(A!1)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(22,plain,
% 0.20/0.39 (($false | (~(p(B!0) | (~q(A!1))))) <=> (~(p(B!0) | (~q(A!1))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(23,plain,
% 0.20/0.39 ((~$true) <=> $false),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(24,plain,
% 0.20/0.39 ((p(A!1) | (~p(A!1))) <=> $true),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(25,plain,
% 0.20/0.39 ((~(p(A!1) | (~p(A!1)))) <=> (~$true)),
% 0.20/0.39 inference(monotonicity,[status(thm)],[24])).
% 0.20/0.39 tff(26,plain,
% 0.20/0.39 ((~(p(A!1) | (~p(A!1)))) <=> $false),
% 0.20/0.39 inference(transitivity,[status(thm)],[25, 23])).
% 0.20/0.39 tff(27,plain,
% 0.20/0.39 (((~(p(A!1) | (~p(A!1)))) | (~(p(B!0) | (~q(A!1))))) <=> ($false | (~(p(B!0) | (~q(A!1)))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[26])).
% 0.20/0.39 tff(28,plain,
% 0.20/0.39 (((~(p(A!1) | (~p(A!1)))) | (~(p(B!0) | (~q(A!1))))) <=> (~(p(B!0) | (~q(A!1))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[27, 22])).
% 0.20/0.39 tff(29,plain,
% 0.20/0.39 (((~![X: $i] : ((~(p(A!1) | (~p(X)))) | (~(p(B!0) | (~q(X)))))) | ((~(p(A!1) | (~p(A!1)))) | (~(p(B!0) | (~q(A!1)))))) <=> ((~![X: $i] : ((~(p(A!1) | (~p(X)))) | (~(p(B!0) | (~q(X)))))) | (~(p(B!0) | (~q(A!1)))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[28])).
% 0.20/0.39 tff(30,plain,
% 0.20/0.39 (((~![X: $i] : ((~(p(A!1) | (~p(X)))) | (~(p(B!0) | (~q(X)))))) | ((~(p(A!1) | (~p(A!1)))) | (~(p(B!0) | (~q(A!1)))))) <=> ((~![X: $i] : ((~(p(A!1) | (~p(X)))) | (~(p(B!0) | (~q(X)))))) | (~(p(B!0) | (~q(A!1)))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[29, 21])).
% 0.20/0.39 tff(31,plain,
% 0.20/0.39 ((~![X: $i] : ((~(p(A!1) | (~p(X)))) | (~(p(B!0) | (~q(X)))))) | ((~(p(A!1) | (~p(A!1)))) | (~(p(B!0) | (~q(A!1)))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(32,plain,
% 0.20/0.39 ((~![X: $i] : ((~(p(A!1) | (~p(X)))) | (~(p(B!0) | (~q(X)))))) | (~(p(B!0) | (~q(A!1))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.20/0.39 tff(33,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[32, 20, 1])).
% 0.20/0.39 tff(34,plain,(~(p(B!0) | (~q(A!1)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(35,plain,
% 0.20/0.39 ((p(B!0) | (~q(A!1))) | (~p(B!0))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(36,plain,
% 0.20/0.39 (~p(B!0)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.20/0.39 tff(37,plain,
% 0.20/0.39 (^[Y: $i] : refl((p(Y) | (~q(Y))) <=> (p(Y) | (~q(Y))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(38,plain,
% 0.20/0.39 (![Y: $i] : (p(Y) | (~q(Y))) <=> ![Y: $i] : (p(Y) | (~q(Y)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[37])).
% 0.20/0.39 tff(39,plain,
% 0.20/0.39 (![Y: $i] : (p(Y) | (~q(Y)))),
% 0.20/0.39 inference(and_elim,[status(thm)],[17])).
% 0.20/0.39 tff(40,plain,
% 0.20/0.39 (![Y: $i] : (p(Y) | (~q(Y)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.20/0.39 tff(41,plain,
% 0.20/0.39 (((~![Y: $i] : (p(Y) | (~q(Y)))) | (p(B!0) | (~q(B!0)))) <=> ((~![Y: $i] : (p(Y) | (~q(Y)))) | p(B!0) | (~q(B!0)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(42,plain,
% 0.20/0.39 ((~![Y: $i] : (p(Y) | (~q(Y)))) | (p(B!0) | (~q(B!0)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(43,plain,
% 0.20/0.39 ((~![Y: $i] : (p(Y) | (~q(Y)))) | p(B!0) | (~q(B!0))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.39 tff(44,plain,
% 0.20/0.39 (~q(B!0)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[43, 40, 36])).
% 0.20/0.39 tff(45,plain,
% 0.20/0.39 ((p(B!0) | (~q(B!0))) | q(B!0)),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(46,plain,
% 0.20/0.39 (p(B!0) | (~q(B!0))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.20/0.39 tff(47,plain,
% 0.20/0.39 ((p(B!0) | (~q(A!1))) | q(A!1)),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(48,plain,
% 0.20/0.39 (q(A!1)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[47, 34])).
% 0.20/0.39 tff(49,assumption,(~p(A!1)), introduced(assumption)).
% 0.20/0.39 tff(50,plain,
% 0.20/0.39 (((~![Y: $i] : (p(Y) | (~q(Y)))) | (p(A!1) | (~q(A!1)))) <=> ((~![Y: $i] : (p(Y) | (~q(Y)))) | p(A!1) | (~q(A!1)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(51,plain,
% 0.20/0.39 ((~![Y: $i] : (p(Y) | (~q(Y)))) | (p(A!1) | (~q(A!1)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(52,plain,
% 0.20/0.39 ((~![Y: $i] : (p(Y) | (~q(Y)))) | p(A!1) | (~q(A!1))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.20/0.39 tff(53,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[52, 40, 49, 48])).
% 0.20/0.39 tff(54,plain,(p(A!1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(55,plain,
% 0.20/0.39 ((p(A!1) | (~p(B!0))) | (~p(A!1))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(56,plain,
% 0.20/0.39 (p(A!1) | (~p(B!0))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.20/0.39 tff(57,plain,
% 0.20/0.39 (((~![X: $i] : ((~(p(A!1) | (~p(X)))) | (~(p(B!0) | (~q(X)))))) | ((~(p(A!1) | (~p(B!0)))) | (~(p(B!0) | (~q(B!0)))))) <=> ((~![X: $i] : ((~(p(A!1) | (~p(X)))) | (~(p(B!0) | (~q(X)))))) | (~(p(A!1) | (~p(B!0)))) | (~(p(B!0) | (~q(B!0)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(58,plain,
% 0.20/0.39 ((~![X: $i] : ((~(p(A!1) | (~p(X)))) | (~(p(B!0) | (~q(X)))))) | ((~(p(A!1) | (~p(B!0)))) | (~(p(B!0) | (~q(B!0)))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(59,plain,
% 0.20/0.39 ((~![X: $i] : ((~(p(A!1) | (~p(X)))) | (~(p(B!0) | (~q(X)))))) | (~(p(A!1) | (~p(B!0)))) | (~(p(B!0) | (~q(B!0))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.20/0.39 tff(60,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[59, 20, 56, 46])).
% 0.20/0.39 % SZS output end Proof
%------------------------------------------------------------------------------