TSTP Solution File: SYN051+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN051+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.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 23:53:21 EDT 2022
% Result : Theorem 0.23s 0.42s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SYN051+1 : TPTP v8.1.0. Released v2.0.0.
% 0.08/0.15 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.15/0.37 % Computer : n023.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Mon Sep 5 01:43:32 EDT 2022
% 0.15/0.37 % CPUTime :
% 0.15/0.37 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.15/0.37 Usage: tptp [options] [-file:]file
% 0.15/0.37 -h, -? prints this message.
% 0.15/0.37 -smt2 print SMT-LIB2 benchmark.
% 0.15/0.37 -m, -model generate model.
% 0.15/0.37 -p, -proof generate proof.
% 0.15/0.37 -c, -core generate unsat core of named formulas.
% 0.15/0.37 -st, -statistics display statistics.
% 0.15/0.37 -t:timeout set timeout (in second).
% 0.15/0.37 -smt2status display status in smt2 format instead of SZS.
% 0.15/0.37 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.15/0.37 -<param>:<value> configuration parameter and value.
% 0.15/0.37 -o:<output-file> file to place output in.
% 0.23/0.42 % SZS status Theorem
% 0.23/0.42 % SZS output start Proof
% 0.23/0.42 tff(big_f_type, type, (
% 0.23/0.42 big_f: $i > $o)).
% 0.23/0.42 tff(tptp_fun_X_1_type, type, (
% 0.23/0.42 tptp_fun_X_1: $i)).
% 0.23/0.42 tff(p_type, type, (
% 0.23/0.42 p: $o)).
% 0.23/0.42 tff(tptp_fun_X_0_type, type, (
% 0.23/0.42 tptp_fun_X_0: $i)).
% 0.23/0.42 tff(1,assumption,(p), introduced(assumption)).
% 0.23/0.42 tff(2,plain,
% 0.23/0.42 (?[X: $i] : (big_f(X) | (~p)) <=> ?[X: $i] : (big_f(X) | (~p))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(3,plain,
% 0.23/0.42 (^[X: $i] : rewrite((p => big_f(X)) <=> (big_f(X) | (~p)))),
% 0.23/0.42 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(4,plain,
% 0.23/0.42 (?[X: $i] : (p => big_f(X)) <=> ?[X: $i] : (big_f(X) | (~p))),
% 0.23/0.42 inference(quant_intro,[status(thm)],[3])).
% 0.23/0.42 tff(5,axiom,(?[X: $i] : (p => big_f(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel21_1')).
% 0.23/0.42 tff(6,plain,
% 0.23/0.42 (?[X: $i] : (big_f(X) | (~p))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.23/0.42 tff(7,plain,
% 0.23/0.42 (?[X: $i] : (big_f(X) | (~p))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.23/0.42 tff(8,plain,(
% 0.23/0.42 big_f(X!0) | (~p)),
% 0.23/0.42 inference(skolemize,[status(sab)],[7])).
% 0.23/0.42 tff(9,plain,
% 0.23/0.42 (big_f(X!0)),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[8, 1])).
% 0.23/0.42 tff(10,assumption,(~((~p) <=> big_f(X!0))), introduced(assumption)).
% 0.23/0.42 tff(11,plain,
% 0.23/0.42 (^[X: $i] : refl(((~p) <=> big_f(X)) <=> ((~p) <=> big_f(X)))),
% 0.23/0.42 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(12,plain,
% 0.23/0.42 (![X: $i] : ((~p) <=> big_f(X)) <=> ![X: $i] : ((~p) <=> big_f(X))),
% 0.23/0.42 inference(quant_intro,[status(thm)],[11])).
% 0.23/0.42 tff(13,plain,
% 0.23/0.42 (^[X: $i] : rewrite((~(p <=> big_f(X))) <=> ((~p) <=> big_f(X)))),
% 0.23/0.42 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(14,plain,
% 0.23/0.42 (![X: $i] : (~(p <=> big_f(X))) <=> ![X: $i] : ((~p) <=> big_f(X))),
% 0.23/0.42 inference(quant_intro,[status(thm)],[13])).
% 0.23/0.42 tff(15,plain,
% 0.23/0.42 ((~?[X: $i] : (p <=> big_f(X))) <=> (~?[X: $i] : (p <=> big_f(X)))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(16,axiom,(~?[X: $i] : (p <=> big_f(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel21')).
% 0.23/0.42 tff(17,plain,
% 0.23/0.42 (~?[X: $i] : (p <=> big_f(X))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.23/0.42 tff(18,plain,
% 0.23/0.42 (~?[X: $i] : (p <=> big_f(X))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[17, 15])).
% 0.23/0.42 tff(19,plain,
% 0.23/0.42 (~?[X: $i] : (p <=> big_f(X))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[18, 15])).
% 0.23/0.42 tff(20,plain,
% 0.23/0.42 (~?[X: $i] : (p <=> big_f(X))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.23/0.42 tff(21,plain,
% 0.23/0.42 (~?[X: $i] : (p <=> big_f(X))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[20, 15])).
% 0.23/0.42 tff(22,plain,
% 0.23/0.42 (~?[X: $i] : (p <=> big_f(X))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[21, 15])).
% 0.23/0.42 tff(23,plain,
% 0.23/0.42 (~?[X: $i] : (p <=> big_f(X))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.23/0.42 tff(24,plain,
% 0.23/0.42 (^[X: $i] : refl($oeq((~(p <=> big_f(X))), (~(p <=> big_f(X)))))),
% 0.23/0.42 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(25,plain,(
% 0.23/0.42 ![X: $i] : (~(p <=> big_f(X)))),
% 0.23/0.42 inference(nnf-neg,[status(sab)],[23, 24])).
% 0.23/0.42 tff(26,plain,
% 0.23/0.42 (![X: $i] : ((~p) <=> big_f(X))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[25, 14])).
% 0.23/0.42 tff(27,plain,
% 0.23/0.42 (![X: $i] : ((~p) <=> big_f(X))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[26, 12])).
% 0.23/0.42 tff(28,plain,
% 0.23/0.42 ((~![X: $i] : ((~p) <=> big_f(X))) | ((~p) <=> big_f(X!0))),
% 0.23/0.42 inference(quant_inst,[status(thm)],[])).
% 0.23/0.42 tff(29,plain,
% 0.23/0.42 ($false),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[28, 27, 10])).
% 0.23/0.42 tff(30,plain,((~p) <=> big_f(X!0)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.42 tff(31,plain,
% 0.23/0.42 ((~((~p) <=> big_f(X!0))) | (~p) | (~big_f(X!0))),
% 0.23/0.42 inference(tautology,[status(thm)],[])).
% 0.23/0.42 tff(32,plain,
% 0.23/0.42 ((~p) | (~big_f(X!0))),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.23/0.42 tff(33,plain,
% 0.23/0.42 ($false),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[32, 9, 1])).
% 0.23/0.42 tff(34,plain,(~p), inference(lemma,lemma(discharge,[]))).
% 0.23/0.42 tff(35,plain,
% 0.23/0.42 (?[X: $i] : (p | (~big_f(X))) <=> ?[X: $i] : (p | (~big_f(X)))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(36,plain,
% 0.23/0.42 (^[X: $i] : rewrite((big_f(X) => p) <=> (p | (~big_f(X))))),
% 0.23/0.42 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(37,plain,
% 0.23/0.42 (?[X: $i] : (big_f(X) => p) <=> ?[X: $i] : (p | (~big_f(X)))),
% 0.23/0.42 inference(quant_intro,[status(thm)],[36])).
% 0.23/0.42 tff(38,axiom,(?[X: $i] : (big_f(X) => p)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel21_2')).
% 0.23/0.42 tff(39,plain,
% 0.23/0.42 (?[X: $i] : (p | (~big_f(X)))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.23/0.42 tff(40,plain,
% 0.23/0.42 (?[X: $i] : (p | (~big_f(X)))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.23/0.42 tff(41,plain,(
% 0.23/0.42 p | (~big_f(X!1))),
% 0.23/0.42 inference(skolemize,[status(sab)],[40])).
% 0.23/0.42 tff(42,plain,
% 0.23/0.42 (~big_f(X!1)),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[41, 34])).
% 0.23/0.42 tff(43,plain,
% 0.23/0.42 ((~((~p) <=> big_f(X!1))) | p | big_f(X!1)),
% 0.23/0.42 inference(tautology,[status(thm)],[])).
% 0.23/0.42 tff(44,plain,
% 0.23/0.42 (~((~p) <=> big_f(X!1))),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[43, 34, 42])).
% 0.23/0.42 tff(45,plain,
% 0.23/0.42 ((~![X: $i] : ((~p) <=> big_f(X))) | ((~p) <=> big_f(X!1))),
% 0.23/0.42 inference(quant_inst,[status(thm)],[])).
% 0.23/0.42 tff(46,plain,
% 0.23/0.42 ($false),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[45, 27, 44])).
% 0.23/0.42 % SZS output end Proof
%------------------------------------------------------------------------------