TSTP Solution File: SYN976+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN976+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 00:01:27 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
% 0.04/0.12 % Problem : SYN976+1 : TPTP v8.1.0. Released v3.1.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n001.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 10:08:15 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(q_type, type, (
% 0.20/0.38 q: $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(p_type, type, (
% 0.20/0.38 p: $i > $o)).
% 0.20/0.38 tff(k!0_type, type, (
% 0.20/0.38 k!0: $o)).
% 0.20/0.38 tff(g_type, type, (
% 0.20/0.38 g: $o)).
% 0.20/0.38 tff(f_type, type, (
% 0.20/0.38 f: $o)).
% 0.20/0.38 tff(1,plain,
% 0.20/0.38 (((~q(A!1)) & (k!0 & ![X: $i] : (p(X) & q(X)))) <=> ((~q(A!1)) & k!0 & ![X: $i] : (p(X) & q(X)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(2,plain,
% 0.20/0.38 ((k!0 & ![X: $i] : (p(X) & q(X))) <=> (k!0 & ![X: $i] : (p(X) & q(X)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(3,plain,
% 0.20/0.38 (((~q(A!1)) & (k!0 & ![X: $i] : (p(X) & q(X)))) <=> ((~q(A!1)) & (k!0 & ![X: $i] : (p(X) & q(X))))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[2])).
% 0.20/0.38 tff(4,plain,
% 0.20/0.38 (((~q(A!1)) & (k!0 & ![X: $i] : (p(X) & q(X)))) <=> ((~q(A!1)) & k!0 & ![X: $i] : (p(X) & q(X)))),
% 0.20/0.38 inference(transitivity,[status(thm)],[3, 1])).
% 0.20/0.38 tff(5,plain,
% 0.20/0.38 ((~![A: $i] : (q(A) | (~(k!0 & ![X: $i] : (p(X) & q(X)))))) <=> (~![A: $i] : (q(A) | (~(k!0 & ![X: $i] : (p(X) & q(X))))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(6,plain,
% 0.20/0.38 ((~![A: $i] : (q(A) | (~((f | g) & ![X: $i] : (p(X) & q(X)))))) <=> (~![A: $i] : (q(A) | (~(k!0 & ![X: $i] : (p(X) & q(X))))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(7,plain,
% 0.20/0.38 ((~![A: $i] : (q(A) | (~((f | g) & ![X: $i] : (p(X) & q(X)))))) <=> (~![A: $i] : (q(A) | (~((f | g) & ![X: $i] : (p(X) & q(X))))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(8,plain,
% 0.20/0.38 ((~![A: $i] : (((f | g) & ![X: $i] : (p(X) & q(X))) => q(A))) <=> (~![A: $i] : (q(A) | (~((f | g) & ![X: $i] : (p(X) & q(X))))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(9,axiom,(~![A: $i] : (((f | g) & ![X: $i] : (p(X) & q(X))) => q(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 0.20/0.38 tff(10,plain,
% 0.20/0.38 (~![A: $i] : (q(A) | (~((f | g) & ![X: $i] : (p(X) & 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] : (q(A) | (~((f | g) & ![X: $i] : (p(X) & 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] : (q(A) | (~((f | g) & ![X: $i] : (p(X) & 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] : (q(A) | (~((f | g) & ![X: $i] : (p(X) & 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] : (q(A) | (~(k!0 & ![X: $i] : (p(X) & q(X)))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[13, 6])).
% 0.20/0.38 tff(15,plain,
% 0.20/0.38 (~![A: $i] : (q(A) | (~(k!0 & ![X: $i] : (p(X) & q(X)))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[14, 5])).
% 0.20/0.38 tff(16,plain,
% 0.20/0.38 (~![A: $i] : (q(A) | (~(k!0 & ![X: $i] : (p(X) & q(X)))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.20/0.38 tff(17,plain,
% 0.20/0.38 (~![A: $i] : (q(A) | (~(k!0 & ![X: $i] : (p(X) & q(X)))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[16, 5])).
% 0.20/0.38 tff(18,plain,
% 0.20/0.38 ((~q(A!1)) & k!0 & ![X: $i] : (p(X) & q(X))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[17, 4])).
% 0.20/0.38 tff(19,plain,
% 0.20/0.38 (~q(A!1)),
% 0.20/0.38 inference(and_elim,[status(thm)],[18])).
% 0.20/0.38 tff(20,plain,
% 0.20/0.38 (((~p(A!1)) | (~q(A!1))) | q(A!1)),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(21,plain,
% 0.20/0.38 ((~p(A!1)) | (~q(A!1))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.20/0.38 tff(22,plain,
% 0.20/0.38 (^[X: $i] : refl((~((~p(X)) | (~q(X)))) <=> (~((~p(X)) | (~q(X)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(23,plain,
% 0.20/0.38 (![X: $i] : (~((~p(X)) | (~q(X)))) <=> ![X: $i] : (~((~p(X)) | (~q(X))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[22])).
% 0.20/0.38 tff(24,plain,
% 0.20/0.38 (^[X: $i] : rewrite((p(X) & q(X)) <=> (~((~p(X)) | (~q(X)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(25,plain,
% 0.20/0.38 (![X: $i] : (p(X) & q(X)) <=> ![X: $i] : (~((~p(X)) | (~q(X))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[24])).
% 0.20/0.38 tff(26,plain,
% 0.20/0.38 (![X: $i] : (p(X) & q(X))),
% 0.20/0.38 inference(and_elim,[status(thm)],[18])).
% 0.20/0.38 tff(27,plain,
% 0.20/0.38 (![X: $i] : (~((~p(X)) | (~q(X))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.20/0.38 tff(28,plain,
% 0.20/0.38 (![X: $i] : (~((~p(X)) | (~q(X))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.20/0.38 tff(29,plain,
% 0.20/0.38 ((~![X: $i] : (~((~p(X)) | (~q(X))))) | (~((~p(A!1)) | (~q(A!1))))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(30,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[29, 28, 21])).
% 0.20/0.38 % SZS output end Proof
%------------------------------------------------------------------------------