TSTP Solution File: SYN376+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN376+1 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 23:55:03 EDT 2022
% Result : Theorem 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SYN376+1 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Sep 5 03:08:01 EDT 2022
% 0.13/0.34 % 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.
% 0.21/0.39 % SZS status Theorem
% 0.21/0.39 % SZS output start Proof
% 0.21/0.39 tff(big_p_type, type, (
% 0.21/0.39 big_p: $i > $o)).
% 0.21/0.39 tff(tptp_fun_X_2_type, type, (
% 0.21/0.39 tptp_fun_X_2: $i)).
% 0.21/0.39 tff(tptp_fun_X_1_type, type, (
% 0.21/0.39 tptp_fun_X_1: $i)).
% 0.21/0.39 tff(tptp_fun_X_0_type, type, (
% 0.21/0.39 tptp_fun_X_0: $i)).
% 0.21/0.39 tff(1,plain,
% 0.21/0.39 (^[Y: $i] : refl((big_p(Y) <=> big_p(X!2)) <=> (big_p(Y) <=> big_p(X!2)))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(2,plain,
% 0.21/0.39 (![Y: $i] : (big_p(Y) <=> big_p(X!2)) <=> ![Y: $i] : (big_p(Y) <=> big_p(X!2))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.39 tff(3,plain,
% 0.21/0.39 (?[X: $i] : ![Y: $i] : (big_p(Y) <=> big_p(X)) <=> ?[X: $i] : ![Y: $i] : (big_p(Y) <=> big_p(X))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(4,plain,
% 0.21/0.39 ((~(?[X: $i] : ![Y: $i] : (big_p(Y) <=> big_p(X)) => (![X: $i] : big_p(X) | ![X: $i] : (~big_p(X))))) <=> (~(![X: $i] : big_p(X) | ![X: $i] : (~big_p(X)) | (~?[X: $i] : ![Y: $i] : (big_p(Y) <=> big_p(X)))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(5,axiom,(~(?[X: $i] : ![Y: $i] : (big_p(Y) <=> big_p(X)) => (![X: $i] : big_p(X) | ![X: $i] : (~big_p(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','x2127')).
% 0.21/0.39 tff(6,plain,
% 0.21/0.39 (~(![X: $i] : big_p(X) | ![X: $i] : (~big_p(X)) | (~?[X: $i] : ![Y: $i] : (big_p(Y) <=> big_p(X))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.21/0.39 tff(7,plain,
% 0.21/0.39 (?[X: $i] : ![Y: $i] : (big_p(Y) <=> big_p(X))),
% 0.21/0.39 inference(or_elim,[status(thm)],[6])).
% 0.21/0.39 tff(8,plain,
% 0.21/0.39 (?[X: $i] : ![Y: $i] : (big_p(Y) <=> big_p(X))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.21/0.39 tff(9,plain,(
% 0.21/0.39 $oeq(![Y: $i] : (big_p(Y) <=> big_p(X!2)), ![Y: $i] : (big_p(Y) <=> big_p(X!2)))),
% 0.21/0.39 inference(transitivity,[status(sab)],[8])).
% 0.21/0.39 tff(10,plain,
% 0.21/0.39 (![Y: $i] : (big_p(Y) <=> big_p(X!2))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.21/0.39 tff(11,plain,
% 0.21/0.39 ((~![Y: $i] : (big_p(Y) <=> big_p(X!2))) | (big_p(X!1) <=> big_p(X!2))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(12,plain,
% 0.21/0.39 (big_p(X!1) <=> big_p(X!2)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.21/0.39 tff(13,plain,
% 0.21/0.39 ((~![Y: $i] : (big_p(Y) <=> big_p(X!2))) | (big_p(X!0) <=> big_p(X!2))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(14,plain,
% 0.21/0.39 (big_p(X!0) <=> big_p(X!2)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[13, 10])).
% 0.21/0.39 tff(15,plain,
% 0.21/0.39 ((~![X: $i] : big_p(X)) <=> (~![X: $i] : big_p(X))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(16,plain,
% 0.21/0.39 (~![X: $i] : big_p(X)),
% 0.21/0.39 inference(or_elim,[status(thm)],[6])).
% 0.21/0.39 tff(17,plain,
% 0.21/0.39 (~![X: $i] : big_p(X)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.21/0.39 tff(18,plain,
% 0.21/0.39 (~![X: $i] : big_p(X)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[17, 15])).
% 0.21/0.39 tff(19,plain,
% 0.21/0.39 (~![X: $i] : big_p(X)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[18, 15])).
% 0.21/0.39 tff(20,plain,
% 0.21/0.39 (~![X: $i] : big_p(X)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.21/0.39 tff(21,plain,
% 0.21/0.39 (~![X: $i] : big_p(X)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[20, 15])).
% 0.21/0.39 tff(22,plain,
% 0.21/0.39 (~![X: $i] : big_p(X)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[21, 15])).
% 0.21/0.39 tff(23,plain,(
% 0.21/0.39 ~big_p(X!0)),
% 0.21/0.39 inference(skolemize,[status(sab)],[22])).
% 0.21/0.39 tff(24,plain,
% 0.21/0.39 ((~(big_p(X!0) <=> big_p(X!2))) | big_p(X!0) | (~big_p(X!2))),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(25,plain,
% 0.21/0.39 ((~(big_p(X!0) <=> big_p(X!2))) | (~big_p(X!2))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.21/0.39 tff(26,plain,
% 0.21/0.39 (~big_p(X!2)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[25, 14])).
% 0.21/0.39 tff(27,plain,
% 0.21/0.39 ((~(~big_p(X!1))) <=> big_p(X!1)),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(28,plain,
% 0.21/0.39 ((~![X: $i] : (~big_p(X))) <=> (~![X: $i] : (~big_p(X)))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(29,plain,
% 0.21/0.39 (~![X: $i] : (~big_p(X))),
% 0.21/0.39 inference(or_elim,[status(thm)],[6])).
% 0.21/0.39 tff(30,plain,
% 0.21/0.39 (~![X: $i] : (~big_p(X))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.21/0.39 tff(31,plain,
% 0.21/0.39 (~![X: $i] : (~big_p(X))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[30, 28])).
% 0.21/0.39 tff(32,plain,
% 0.21/0.39 (~![X: $i] : (~big_p(X))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[31, 28])).
% 0.21/0.39 tff(33,plain,
% 0.21/0.39 (~![X: $i] : (~big_p(X))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.21/0.39 tff(34,plain,
% 0.21/0.39 (~![X: $i] : (~big_p(X))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[33, 28])).
% 0.21/0.39 tff(35,plain,
% 0.21/0.39 (~![X: $i] : (~big_p(X))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[34, 28])).
% 0.21/0.39 tff(36,plain,(
% 0.21/0.39 ~(~big_p(X!1))),
% 0.21/0.39 inference(skolemize,[status(sab)],[35])).
% 0.21/0.39 tff(37,plain,
% 0.21/0.39 (big_p(X!1)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[36, 27])).
% 0.21/0.39 tff(38,plain,
% 0.21/0.39 ((~(big_p(X!1) <=> big_p(X!2))) | (~big_p(X!1)) | big_p(X!2)),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(39,plain,
% 0.21/0.39 ((~(big_p(X!1) <=> big_p(X!2))) | big_p(X!2)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.21/0.39 tff(40,plain,
% 0.21/0.39 ($false),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[39, 26, 12])).
% 0.21/0.39 % SZS output end Proof
%------------------------------------------------------------------------------