TSTP Solution File: SYN969+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN969+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYN969+1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n016.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Sep 5 10:07:55 EDT 2022
% 0.13/0.35 % 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.
% 0.20/0.39 % SZS status Theorem
% 0.20/0.39 % SZS output start Proof
% 0.20/0.39 tff(p_type, type, (
% 0.20/0.39 p: $i > $o)).
% 0.20/0.39 tff(tptp_fun_B_0_type, type, (
% 0.20/0.39 tptp_fun_B_0: $i)).
% 0.20/0.39 tff(r_type, type, (
% 0.20/0.39 r: $i > $o)).
% 0.20/0.39 tff(q_type, type, (
% 0.20/0.39 q: $i > $o)).
% 0.20/0.39 tff(1,plain,
% 0.20/0.39 (((~q(B!0)) & ![Y: $i] : (p(Y) | (~r(Y))) & (![X: $i] : (q(X) | (~p(X))) & r(B!0))) <=> ((~q(B!0)) & ![Y: $i] : (p(Y) | (~r(Y))) & ![X: $i] : (q(X) | (~p(X))) & r(B!0))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(2,plain,
% 0.20/0.39 ((![X: $i] : (q(X) | (~p(X))) & r(B!0)) <=> (![X: $i] : (q(X) | (~p(X))) & r(B!0))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(3,plain,
% 0.20/0.39 (((~q(B!0)) & ![Y: $i] : (p(Y) | (~r(Y))) & (![X: $i] : (q(X) | (~p(X))) & r(B!0))) <=> ((~q(B!0)) & ![Y: $i] : (p(Y) | (~r(Y))) & (![X: $i] : (q(X) | (~p(X))) & r(B!0)))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[2])).
% 0.20/0.39 tff(4,plain,
% 0.20/0.39 (((~q(B!0)) & ![Y: $i] : (p(Y) | (~r(Y))) & (![X: $i] : (q(X) | (~p(X))) & r(B!0))) <=> ((~q(B!0)) & ![Y: $i] : (p(Y) | (~r(Y))) & ![X: $i] : (q(X) | (~p(X))) & r(B!0))),
% 0.20/0.39 inference(transitivity,[status(thm)],[3, 1])).
% 0.20/0.39 tff(5,plain,
% 0.20/0.39 ((~![B: $i] : (q(B) | (~![Y: $i] : (p(Y) | (~r(Y)))) | (~(![X: $i] : (q(X) | (~p(X))) & r(B))))) <=> (~![B: $i] : (q(B) | (~![Y: $i] : (p(Y) | (~r(Y)))) | (~(![X: $i] : (q(X) | (~p(X))) & r(B)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(6,plain,
% 0.20/0.39 ((~![B: $i] : ((![X: $i] : (p(X) => q(X)) & r(B)) => (![Y: $i] : (r(Y) => p(Y)) => q(B)))) <=> (~![B: $i] : (q(B) | (~![Y: $i] : (p(Y) | (~r(Y)))) | (~(![X: $i] : (q(X) | (~p(X))) & r(B)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(7,axiom,(~![B: $i] : ((![X: $i] : (p(X) => q(X)) & r(B)) => (![Y: $i] : (r(Y) => p(Y)) => q(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.20/0.39 tff(8,plain,
% 0.20/0.39 (~![B: $i] : (q(B) | (~![Y: $i] : (p(Y) | (~r(Y)))) | (~(![X: $i] : (q(X) | (~p(X))) & r(B))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.20/0.39 tff(9,plain,
% 0.20/0.39 (~![B: $i] : (q(B) | (~![Y: $i] : (p(Y) | (~r(Y)))) | (~(![X: $i] : (q(X) | (~p(X))) & r(B))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.20/0.39 tff(10,plain,
% 0.20/0.39 (~![B: $i] : (q(B) | (~![Y: $i] : (p(Y) | (~r(Y)))) | (~(![X: $i] : (q(X) | (~p(X))) & r(B))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.20/0.39 tff(11,plain,
% 0.20/0.39 (~![B: $i] : (q(B) | (~![Y: $i] : (p(Y) | (~r(Y)))) | (~(![X: $i] : (q(X) | (~p(X))) & r(B))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.20/0.39 tff(12,plain,
% 0.20/0.39 (~![B: $i] : (q(B) | (~![Y: $i] : (p(Y) | (~r(Y)))) | (~(![X: $i] : (q(X) | (~p(X))) & r(B))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[11, 5])).
% 0.20/0.39 tff(13,plain,
% 0.20/0.39 (~![B: $i] : (q(B) | (~![Y: $i] : (p(Y) | (~r(Y)))) | (~(![X: $i] : (q(X) | (~p(X))) & r(B))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.20/0.39 tff(14,plain,
% 0.20/0.39 (~![B: $i] : (q(B) | (~![Y: $i] : (p(Y) | (~r(Y)))) | (~(![X: $i] : (q(X) | (~p(X))) & r(B))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[13, 5])).
% 0.20/0.39 tff(15,plain,
% 0.20/0.39 ((~q(B!0)) & ![Y: $i] : (p(Y) | (~r(Y))) & ![X: $i] : (q(X) | (~p(X))) & r(B!0)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[14, 4])).
% 0.20/0.39 tff(16,plain,
% 0.20/0.39 (r(B!0)),
% 0.20/0.39 inference(and_elim,[status(thm)],[15])).
% 0.20/0.39 tff(17,plain,
% 0.20/0.39 (^[Y: $i] : refl((p(Y) | (~r(Y))) <=> (p(Y) | (~r(Y))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(18,plain,
% 0.20/0.39 (![Y: $i] : (p(Y) | (~r(Y))) <=> ![Y: $i] : (p(Y) | (~r(Y)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[17])).
% 0.20/0.39 tff(19,plain,
% 0.20/0.39 (![Y: $i] : (p(Y) | (~r(Y)))),
% 0.20/0.39 inference(and_elim,[status(thm)],[15])).
% 0.20/0.39 tff(20,plain,
% 0.20/0.39 (![Y: $i] : (p(Y) | (~r(Y)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.20/0.39 tff(21,plain,
% 0.20/0.39 (((~![Y: $i] : (p(Y) | (~r(Y)))) | (p(B!0) | (~r(B!0)))) <=> ((~![Y: $i] : (p(Y) | (~r(Y)))) | p(B!0) | (~r(B!0)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(22,plain,
% 0.20/0.39 ((~![Y: $i] : (p(Y) | (~r(Y)))) | (p(B!0) | (~r(B!0)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(23,plain,
% 0.20/0.39 ((~![Y: $i] : (p(Y) | (~r(Y)))) | p(B!0) | (~r(B!0))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.20/0.39 tff(24,plain,
% 0.20/0.39 (p(B!0)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[23, 20, 16])).
% 0.20/0.39 tff(25,plain,
% 0.20/0.40 (^[X: $i] : refl((q(X) | (~p(X))) <=> (q(X) | (~p(X))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(26,plain,
% 0.20/0.40 (![X: $i] : (q(X) | (~p(X))) <=> ![X: $i] : (q(X) | (~p(X)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[25])).
% 0.20/0.40 tff(27,plain,
% 0.20/0.40 (![X: $i] : (q(X) | (~p(X)))),
% 0.20/0.40 inference(and_elim,[status(thm)],[15])).
% 0.20/0.40 tff(28,plain,
% 0.20/0.40 (![X: $i] : (q(X) | (~p(X)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.20/0.40 tff(29,plain,
% 0.20/0.40 (~q(B!0)),
% 0.20/0.40 inference(and_elim,[status(thm)],[15])).
% 0.20/0.40 tff(30,plain,
% 0.20/0.40 (((~![X: $i] : (q(X) | (~p(X)))) | (q(B!0) | (~p(B!0)))) <=> ((~![X: $i] : (q(X) | (~p(X)))) | q(B!0) | (~p(B!0)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(31,plain,
% 0.20/0.40 ((~![X: $i] : (q(X) | (~p(X)))) | (q(B!0) | (~p(B!0)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(32,plain,
% 0.20/0.40 ((~![X: $i] : (q(X) | (~p(X)))) | q(B!0) | (~p(B!0))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.20/0.40 tff(33,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[32, 29, 28, 24])).
% 0.20/0.40 % SZS output end Proof
%------------------------------------------------------------------------------