TSTP Solution File: SYN052+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN052+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.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 23:53:22 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
% 0.06/0.12 % Problem : SYN052+1 : TPTP v8.1.0. Released v2.0.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n005.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Sep 5 01:23:03 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_f_type, type, (
% 0.20/0.38 big_f: $i > $o)).
% 0.20/0.38 tff(tptp_fun_X1_0_type, type, (
% 0.20/0.38 tptp_fun_X1_0: $i)).
% 0.20/0.38 tff(p_type, type, (
% 0.20/0.38 p: $o)).
% 0.20/0.38 tff(1,assumption,(~big_f(X1!0)), introduced(assumption)).
% 0.20/0.38 tff(2,plain,
% 0.20/0.38 (^[X: $i] : refl((p <=> big_f(X)) <=> (p <=> big_f(X)))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(3,plain,
% 0.20/0.38 (![X: $i] : (p <=> big_f(X)) <=> ![X: $i] : (p <=> big_f(X))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.38 tff(4,plain,
% 0.20/0.38 (![X: $i] : (p <=> big_f(X)) <=> ![X: $i] : (p <=> big_f(X))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(5,plain,
% 0.20/0.38 ((~(![X: $i] : (p <=> big_f(X)) => (p <=> ![X1: $i] : big_f(X1)))) <=> (~((~![X: $i] : (p <=> big_f(X))) | (p <=> ![X1: $i] : big_f(X1))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(6,axiom,(~(![X: $i] : (p <=> big_f(X)) => (p <=> ![X1: $i] : big_f(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel22')).
% 0.20/0.38 tff(7,plain,
% 0.20/0.38 (~((~![X: $i] : (p <=> big_f(X))) | (p <=> ![X1: $i] : big_f(X1)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.20/0.38 tff(8,plain,
% 0.20/0.38 (![X: $i] : (p <=> big_f(X))),
% 0.20/0.38 inference(or_elim,[status(thm)],[7])).
% 0.20/0.38 tff(9,plain,
% 0.20/0.38 (![X: $i] : (p <=> big_f(X))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.20/0.38 tff(10,plain,(
% 0.20/0.38 ![X: $i] : (p <=> big_f(X))),
% 0.20/0.38 inference(skolemize,[status(sab)],[9])).
% 0.20/0.38 tff(11,plain,
% 0.20/0.38 (![X: $i] : (p <=> big_f(X))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.20/0.38 tff(12,plain,
% 0.20/0.38 ((~![X: $i] : (p <=> big_f(X))) | (p <=> big_f(X1!0))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(13,plain,
% 0.20/0.38 (p <=> big_f(X1!0)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.20/0.38 tff(14,plain,
% 0.20/0.38 ((~(p <=> big_f(X1!0))) | (~p) | big_f(X1!0)),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(15,plain,
% 0.20/0.38 ((~(p <=> big_f(X1!0))) | (~p)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[14, 1])).
% 0.20/0.38 tff(16,plain,
% 0.20/0.38 (~p),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[15, 13])).
% 0.20/0.38 tff(17,plain,
% 0.20/0.38 ((p | ![X1: $i] : big_f(X1)) <=> (p | ![X1: $i] : big_f(X1))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(18,plain,
% 0.20/0.38 ((((~(~p)) | ![X1: $i] : big_f(X1)) & ((~p) | (~big_f(X1!0)))) <=> ((p | ![X1: $i] : big_f(X1)) & ((~p) | (~big_f(X1!0))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(19,plain,
% 0.20/0.38 (((~p) <=> ![X1: $i] : big_f(X1)) <=> ((~p) <=> ![X1: $i] : big_f(X1))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(20,plain,
% 0.20/0.38 ((~(p <=> ![X1: $i] : big_f(X1))) <=> ((~p) <=> ![X1: $i] : big_f(X1))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(21,plain,
% 0.20/0.38 ((p <=> ![X1: $i] : big_f(X1)) <=> (p <=> ![X1: $i] : big_f(X1))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(22,plain,
% 0.20/0.38 ((~(p <=> ![X1: $i] : big_f(X1))) <=> (~(p <=> ![X1: $i] : big_f(X1)))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[21])).
% 0.20/0.38 tff(23,plain,
% 0.20/0.38 ((~(p <=> ![X1: $i] : big_f(X1))) <=> ((~p) <=> ![X1: $i] : big_f(X1))),
% 0.20/0.38 inference(transitivity,[status(thm)],[22, 20])).
% 0.20/0.38 tff(24,plain,
% 0.20/0.38 (~(p <=> ![X1: $i] : big_f(X1))),
% 0.20/0.38 inference(or_elim,[status(thm)],[7])).
% 0.20/0.38 tff(25,plain,
% 0.20/0.38 ((~p) <=> ![X1: $i] : big_f(X1)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.20/0.38 tff(26,plain,
% 0.20/0.38 ((~p) <=> ![X1: $i] : big_f(X1)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[25, 19])).
% 0.20/0.38 tff(27,plain,
% 0.20/0.38 ((~p) <=> ![X1: $i] : big_f(X1)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.20/0.38 tff(28,plain,
% 0.20/0.38 ((~p) <=> ![X1: $i] : big_f(X1)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[27, 19])).
% 0.20/0.38 tff(29,plain,
% 0.20/0.38 ((~p) <=> ![X1: $i] : big_f(X1)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[28, 19])).
% 0.20/0.38 tff(30,plain,
% 0.20/0.38 ((~p) <=> ![X1: $i] : big_f(X1)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[29, 19])).
% 0.20/0.38 tff(31,plain,(
% 0.20/0.38 ((~(~p)) | ![X1: $i] : big_f(X1)) & ((~p) | (~big_f(X1!0)))),
% 0.20/0.38 inference(skolemize,[status(sab)],[30])).
% 0.20/0.38 tff(32,plain,
% 0.20/0.38 ((p | ![X1: $i] : big_f(X1)) & ((~p) | (~big_f(X1!0)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[31, 18])).
% 0.20/0.38 tff(33,plain,
% 0.20/0.38 (p | ![X1: $i] : big_f(X1)),
% 0.20/0.38 inference(and_elim,[status(thm)],[32])).
% 0.20/0.38 tff(34,plain,
% 0.20/0.38 (p | ![X1: $i] : big_f(X1)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[33, 17])).
% 0.20/0.39 tff(35,plain,
% 0.20/0.39 (![X1: $i] : big_f(X1)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[34, 16])).
% 0.20/0.39 tff(36,plain,
% 0.20/0.39 ((~![X1: $i] : big_f(X1)) | big_f(X1!0)),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(37,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[36, 35, 1])).
% 0.20/0.39 tff(38,plain,(big_f(X1!0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(39,plain,
% 0.20/0.39 ((~p) | (~big_f(X1!0))),
% 0.20/0.39 inference(and_elim,[status(thm)],[32])).
% 0.20/0.39 tff(40,plain,
% 0.20/0.39 (~p),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.20/0.39 tff(41,plain,
% 0.20/0.39 ((~(p <=> big_f(X1!0))) | p | (~big_f(X1!0))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(42,plain,
% 0.20/0.39 (~(p <=> big_f(X1!0))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[41, 40, 38])).
% 0.20/0.39 tff(43,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[12, 11, 42])).
% 0.20/0.39 % SZS output end Proof
%------------------------------------------------------------------------------