TSTP Solution File: SYN196-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SYN196-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n018.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 23:54:09 EDT 2022

% Result   : Unsatisfiable 0.19s 0.49s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem  : SYN196-1 : TPTP v8.1.0. Released v1.1.0.
% 0.07/0.12  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33  % Computer : n018.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Mon Sep  5 02:11:16 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.33  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33  Usage: tptp [options] [-file:]file
% 0.12/0.33    -h, -?       prints this message.
% 0.12/0.33    -smt2        print SMT-LIB2 benchmark.
% 0.12/0.33    -m, -model   generate model.
% 0.12/0.33    -p, -proof   generate proof.
% 0.12/0.33    -c, -core    generate unsat core of named formulas.
% 0.12/0.33    -st, -statistics display statistics.
% 0.12/0.33    -t:timeout   set timeout (in second).
% 0.12/0.33    -smt2status  display status in smt2 format instead of SZS.
% 0.12/0.33    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33    -<param>:<value> configuration parameter and value.
% 0.12/0.33    -o:<output-file> file to place output in.
% 0.19/0.49  % SZS status Unsatisfiable
% 0.19/0.49  % SZS output start Proof
% 0.19/0.49  tff(s1_type, type, (
% 0.19/0.49     s1: $i > $o)).
% 0.19/0.49  tff(b_type, type, (
% 0.19/0.49     b: $i)).
% 0.19/0.49  tff(p0_type, type, (
% 0.19/0.49     p0: ( $i * $i ) > $o)).
% 0.19/0.49  tff(a_type, type, (
% 0.19/0.49     a: $i)).
% 0.19/0.49  tff(q0_type, type, (
% 0.19/0.49     q0: ( $i * $i ) > $o)).
% 0.19/0.49  tff(1,assumption,(~p0(b, b)), introduced(assumption)).
% 0.19/0.49  tff(2,plain,
% 0.19/0.49      (^[X: $i] : refl(p0(b, X) <=> p0(b, X))),
% 0.19/0.49      inference(bind,[status(th)],[])).
% 0.19/0.49  tff(3,plain,
% 0.19/0.49      (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.19/0.49      inference(quant_intro,[status(thm)],[2])).
% 0.19/0.49  tff(4,plain,
% 0.19/0.49      (![X: $i] : p0(b, X) <=> ![X: $i] : p0(b, X)),
% 0.19/0.49      inference(rewrite,[status(thm)],[])).
% 0.19/0.49  tff(5,axiom,(![X: $i] : p0(b, X)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_14')).
% 0.19/0.49  tff(6,plain,
% 0.19/0.49      (![X: $i] : p0(b, X)),
% 0.19/0.49      inference(modus_ponens,[status(thm)],[5, 4])).
% 0.19/0.49  tff(7,plain,(
% 0.19/0.49      ![X: $i] : p0(b, X)),
% 0.19/0.49      inference(skolemize,[status(sab)],[6])).
% 0.19/0.49  tff(8,plain,
% 0.19/0.49      (![X: $i] : p0(b, X)),
% 0.19/0.49      inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.49  tff(9,plain,
% 0.19/0.49      ((~![X: $i] : p0(b, X)) | p0(b, b)),
% 0.19/0.49      inference(quant_inst,[status(thm)],[])).
% 0.19/0.49  tff(10,plain,
% 0.19/0.49      ($false),
% 0.19/0.49      inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.19/0.49  tff(11,plain,(p0(b, b)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49  tff(12,plain,
% 0.19/0.49      (^[I: $i] : refl((s1(I) | (~p0(I, I))) <=> (s1(I) | (~p0(I, I))))),
% 0.19/0.49      inference(bind,[status(th)],[])).
% 0.19/0.49  tff(13,plain,
% 0.19/0.49      (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.19/0.49      inference(quant_intro,[status(thm)],[12])).
% 0.19/0.49  tff(14,plain,
% 0.19/0.49      (![I: $i] : (s1(I) | (~p0(I, I))) <=> ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.19/0.49      inference(rewrite,[status(thm)],[])).
% 0.19/0.49  tff(15,axiom,(![I: $i] : (s1(I) | (~p0(I, I)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_125')).
% 0.19/0.49  tff(16,plain,
% 0.19/0.49      (![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.19/0.49      inference(modus_ponens,[status(thm)],[15, 14])).
% 0.19/0.49  tff(17,plain,(
% 0.19/0.49      ![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.19/0.49      inference(skolemize,[status(sab)],[16])).
% 0.19/0.49  tff(18,plain,
% 0.19/0.49      (![I: $i] : (s1(I) | (~p0(I, I)))),
% 0.19/0.49      inference(modus_ponens,[status(thm)],[17, 13])).
% 0.19/0.49  tff(19,plain,
% 0.19/0.49      (((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))) <=> ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b)))),
% 0.19/0.49      inference(rewrite,[status(thm)],[])).
% 0.19/0.49  tff(20,plain,
% 0.19/0.49      ((~![I: $i] : (s1(I) | (~p0(I, I)))) | (s1(b) | (~p0(b, b)))),
% 0.19/0.49      inference(quant_inst,[status(thm)],[])).
% 0.19/0.49  tff(21,plain,
% 0.19/0.49      ((~![I: $i] : (s1(I) | (~p0(I, I)))) | s1(b) | (~p0(b, b))),
% 0.19/0.49      inference(modus_ponens,[status(thm)],[20, 19])).
% 0.19/0.49  tff(22,plain,
% 0.19/0.49      (s1(b)),
% 0.19/0.49      inference(unit_resolution,[status(thm)],[21, 18, 11])).
% 0.19/0.49  tff(23,plain,
% 0.19/0.49      ((~s1(a)) <=> (~s1(a))),
% 0.19/0.49      inference(rewrite,[status(thm)],[])).
% 0.19/0.49  tff(24,axiom,(~s1(a)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 0.19/0.49  tff(25,plain,
% 0.19/0.49      (~s1(a)),
% 0.19/0.49      inference(modus_ponens,[status(thm)],[24, 23])).
% 0.19/0.49  tff(26,plain,
% 0.19/0.49      (^[H: $i, F: $i, G: $i] : refl(((~q0(F, G)) | (~s1(H)) | s1(F)) <=> ((~q0(F, G)) | (~s1(H)) | s1(F)))),
% 0.19/0.49      inference(bind,[status(th)],[])).
% 0.19/0.49  tff(27,plain,
% 0.19/0.49      (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F)) <=> ![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.19/0.49      inference(quant_intro,[status(thm)],[26])).
% 0.19/0.49  tff(28,plain,
% 0.19/0.49      (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F)) <=> ![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.19/0.49      inference(rewrite,[status(thm)],[])).
% 0.19/0.49  tff(29,plain,
% 0.19/0.49      (^[H: $i, F: $i, G: $i] : rewrite(((s1(F) | (~q0(F, G))) | (~s1(H))) <=> ((~q0(F, G)) | (~s1(H)) | s1(F)))),
% 0.19/0.49      inference(bind,[status(th)],[])).
% 0.19/0.49  tff(30,plain,
% 0.19/0.49      (![H: $i, F: $i, G: $i] : ((s1(F) | (~q0(F, G))) | (~s1(H))) <=> ![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.19/0.49      inference(quant_intro,[status(thm)],[29])).
% 0.19/0.49  tff(31,axiom,(![H: $i, F: $i, G: $i] : ((s1(F) | (~q0(F, G))) | (~s1(H)))), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','rule_126')).
% 0.19/0.49  tff(32,plain,
% 0.19/0.49      (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.19/0.49      inference(modus_ponens,[status(thm)],[31, 30])).
% 0.19/0.49  tff(33,plain,
% 0.19/0.49      (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.19/0.50      inference(modus_ponens,[status(thm)],[32, 28])).
% 0.19/0.50  tff(34,plain,(
% 0.19/0.50      ![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.19/0.50      inference(skolemize,[status(sab)],[33])).
% 0.19/0.50  tff(35,plain,
% 0.19/0.50      (![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))),
% 0.19/0.50      inference(modus_ponens,[status(thm)],[34, 27])).
% 0.19/0.50  tff(36,plain,
% 0.19/0.50      (q0(a, b) <=> q0(a, b)),
% 0.19/0.50      inference(rewrite,[status(thm)],[])).
% 0.19/0.50  tff(37,axiom,(q0(a, b)), file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax','axiom_36')).
% 0.19/0.50  tff(38,plain,
% 0.19/0.50      (q0(a, b)),
% 0.19/0.50      inference(modus_ponens,[status(thm)],[37, 36])).
% 0.19/0.50  tff(39,plain,
% 0.19/0.50      (((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | (s1(a) | (~s1(b)) | (~q0(a, b)))) <=> ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | s1(a) | (~s1(b)) | (~q0(a, b)))),
% 0.19/0.50      inference(rewrite,[status(thm)],[])).
% 0.19/0.50  tff(40,plain,
% 0.19/0.50      (((~q0(a, b)) | (~s1(b)) | s1(a)) <=> (s1(a) | (~s1(b)) | (~q0(a, b)))),
% 0.19/0.50      inference(rewrite,[status(thm)],[])).
% 0.19/0.50  tff(41,plain,
% 0.19/0.50      (((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | ((~q0(a, b)) | (~s1(b)) | s1(a))) <=> ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | (s1(a) | (~s1(b)) | (~q0(a, b))))),
% 0.19/0.50      inference(monotonicity,[status(thm)],[40])).
% 0.19/0.50  tff(42,plain,
% 0.19/0.50      (((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | ((~q0(a, b)) | (~s1(b)) | s1(a))) <=> ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | s1(a) | (~s1(b)) | (~q0(a, b)))),
% 0.19/0.50      inference(transitivity,[status(thm)],[41, 39])).
% 0.19/0.50  tff(43,plain,
% 0.19/0.50      ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | ((~q0(a, b)) | (~s1(b)) | s1(a))),
% 0.19/0.50      inference(quant_inst,[status(thm)],[])).
% 0.19/0.50  tff(44,plain,
% 0.19/0.50      ((~![H: $i, F: $i, G: $i] : ((~q0(F, G)) | (~s1(H)) | s1(F))) | s1(a) | (~s1(b)) | (~q0(a, b))),
% 0.19/0.50      inference(modus_ponens,[status(thm)],[43, 42])).
% 0.19/0.50  tff(45,plain,
% 0.19/0.50      ($false),
% 0.19/0.50      inference(unit_resolution,[status(thm)],[44, 38, 35, 25, 22])).
% 0.19/0.50  % SZS output end Proof
%------------------------------------------------------------------------------