TSTP Solution File: NUM844+2 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : NUM844+2 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n020.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 : Sun Sep 18 13:12:14 EDT 2022

% Result   : Theorem 0.20s 0.39s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : NUM844+2 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n020.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 : Fri Sep  2 15:23:44 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.
% 0.20/0.39  % SZS status Theorem
% 0.20/0.39  % SZS output start Proof
% 0.20/0.39  tff(vplus_type, type, (
% 0.20/0.39     vplus: ( $i * $i ) > $i)).
% 0.20/0.39  tff(vd413_type, type, (
% 0.20/0.39     vd413: $i)).
% 0.20/0.39  tff(vsucc_type, type, (
% 0.20/0.39     vsucc: $i > $i)).
% 0.20/0.39  tff(vd411_type, type, (
% 0.20/0.39     vd411: $i)).
% 0.20/0.39  tff(vmul_type, type, (
% 0.20/0.39     vmul: ( $i * $i ) > $i)).
% 0.20/0.39  tff(v1_type, type, (
% 0.20/0.39     v1: $i)).
% 0.20/0.39  tff(1,plain,
% 0.20/0.39      ((vsucc(vmul(vd411, v1)) = vplus(vmul(vd411, v1), v1)) <=> (vsucc(vd411) = vplus(vmul(vd411, v1), v1))),
% 0.20/0.39      inference(rewrite,[status(thm)],[])).
% 0.20/0.39  tff(2,plain,
% 0.20/0.39      ((vsucc(vmul(vd411, v1)) = vplus(vmul(vd411, v1), v1)) <=> (vsucc(vmul(vd411, v1)) = vplus(vmul(vd411, v1), v1))),
% 0.20/0.39      inference(rewrite,[status(thm)],[])).
% 0.20/0.39  tff(3,axiom,(vsucc(vmul(vd411, v1)) = vplus(vmul(vd411, v1), v1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''holds(264, 412, 2)'')).
% 0.20/0.39  tff(4,plain,
% 0.20/0.39      (vsucc(vmul(vd411, v1)) = vplus(vmul(vd411, v1), v1)),
% 0.20/0.39      inference(modus_ponens,[status(thm)],[3, 2])).
% 0.20/0.39  tff(5,plain,
% 0.20/0.39      (vsucc(vd411) = vplus(vmul(vd411, v1), v1)),
% 0.20/0.39      inference(modus_ponens,[status(thm)],[4, 1])).
% 0.20/0.39  tff(6,plain,
% 0.20/0.39      (vplus(vsucc(vd411), vd413) = vplus(vplus(vmul(vd411, v1), v1), vd413)),
% 0.20/0.39      inference(monotonicity,[status(thm)],[5])).
% 0.20/0.39  tff(7,plain,
% 0.20/0.39      (vplus(vmul(vd411, vd413), vplus(vsucc(vd411), vd413)) = vplus(vmul(vd411, vd413), vplus(vplus(vmul(vd411, v1), v1), vd413))),
% 0.20/0.39      inference(monotonicity,[status(thm)],[6])).
% 0.20/0.39  tff(8,plain,
% 0.20/0.39      (vplus(vmul(vd411, vd413), vplus(vplus(vmul(vd411, v1), v1), vd413)) = vplus(vmul(vd411, vd413), vplus(vsucc(vd411), vd413))),
% 0.20/0.39      inference(symmetry,[status(thm)],[7])).
% 0.20/0.39  tff(9,plain,
% 0.20/0.39      (vplus(vd413, vsucc(vd411)) = vplus(vd413, vplus(vmul(vd411, v1), v1))),
% 0.20/0.39      inference(monotonicity,[status(thm)],[5])).
% 0.20/0.39  tff(10,plain,
% 0.20/0.39      (vplus(vd413, vplus(vmul(vd411, v1), v1)) = vplus(vd413, vsucc(vd411))),
% 0.20/0.39      inference(symmetry,[status(thm)],[9])).
% 0.20/0.39  tff(11,plain,
% 0.20/0.39      (^[Vd78: $i, Vd79: $i] : refl((vplus(Vd79, Vd78) = vplus(Vd78, Vd79)) <=> (vplus(Vd79, Vd78) = vplus(Vd78, Vd79)))),
% 0.20/0.39      inference(bind,[status(th)],[])).
% 0.20/0.39  tff(12,plain,
% 0.20/0.39      (![Vd78: $i, Vd79: $i] : (vplus(Vd79, Vd78) = vplus(Vd78, Vd79)) <=> ![Vd78: $i, Vd79: $i] : (vplus(Vd79, Vd78) = vplus(Vd78, Vd79))),
% 0.20/0.39      inference(quant_intro,[status(thm)],[11])).
% 0.20/0.39  tff(13,plain,
% 0.20/0.39      (![Vd78: $i, Vd79: $i] : (vplus(Vd79, Vd78) = vplus(Vd78, Vd79)) <=> ![Vd78: $i, Vd79: $i] : (vplus(Vd79, Vd78) = vplus(Vd78, Vd79))),
% 0.20/0.39      inference(rewrite,[status(thm)],[])).
% 0.20/0.39  tff(14,axiom,(![Vd78: $i, Vd79: $i] : (vplus(Vd79, Vd78) = vplus(Vd78, Vd79))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''ass(cond(61, 0), 0)'')).
% 0.20/0.39  tff(15,plain,
% 0.20/0.39      (![Vd78: $i, Vd79: $i] : (vplus(Vd79, Vd78) = vplus(Vd78, Vd79))),
% 0.20/0.39      inference(modus_ponens,[status(thm)],[14, 13])).
% 0.20/0.39  tff(16,plain,(
% 0.20/0.39      ![Vd78: $i, Vd79: $i] : (vplus(Vd79, Vd78) = vplus(Vd78, Vd79))),
% 0.20/0.39      inference(skolemize,[status(sab)],[15])).
% 0.20/0.39  tff(17,plain,
% 0.20/0.39      (![Vd78: $i, Vd79: $i] : (vplus(Vd79, Vd78) = vplus(Vd78, Vd79))),
% 0.20/0.39      inference(modus_ponens,[status(thm)],[16, 12])).
% 0.20/0.39  tff(18,plain,
% 0.20/0.39      ((~![Vd78: $i, Vd79: $i] : (vplus(Vd79, Vd78) = vplus(Vd78, Vd79))) | (vplus(vd413, vplus(vmul(vd411, v1), v1)) = vplus(vplus(vmul(vd411, v1), v1), vd413))),
% 0.20/0.39      inference(quant_inst,[status(thm)],[])).
% 0.20/0.39  tff(19,plain,
% 0.20/0.39      (vplus(vd413, vplus(vmul(vd411, v1), v1)) = vplus(vplus(vmul(vd411, v1), v1), vd413)),
% 0.20/0.39      inference(unit_resolution,[status(thm)],[18, 17])).
% 0.20/0.39  tff(20,plain,
% 0.20/0.39      (vplus(vplus(vmul(vd411, v1), v1), vd413) = vplus(vd413, vplus(vmul(vd411, v1), v1))),
% 0.20/0.39      inference(symmetry,[status(thm)],[19])).
% 0.20/0.39  tff(21,plain,
% 0.20/0.39      (vplus(vplus(vmul(vd411, v1), v1), vd413) = vplus(vd413, vsucc(vd411))),
% 0.20/0.39      inference(transitivity,[status(thm)],[20, 10])).
% 0.20/0.39  tff(22,plain,
% 0.20/0.39      (vplus(vmul(vd411, vd413), vplus(vplus(vmul(vd411, v1), v1), vd413)) = vplus(vmul(vd411, vd413), vplus(vd413, vsucc(vd411)))),
% 0.20/0.39      inference(monotonicity,[status(thm)],[21])).
% 0.20/0.39  tff(23,plain,
% 0.20/0.39      (vplus(vmul(vd411, vd413), vplus(vd413, vsucc(vd411))) = vplus(vmul(vd411, vd413), vplus(vplus(vmul(vd411, v1), v1), vd413))),
% 0.20/0.39      inference(symmetry,[status(thm)],[22])).
% 0.20/0.39  tff(24,plain,
% 0.20/0.39      ((vmul(vsucc(vd411), vsucc(vd413)) = vplus(vmul(vsucc(vd411), vd413), vsucc(vd411))) <=> (vmul(vsucc(vd411), vsucc(vd413)) = vplus(vmul(vd411, vd413), vplus(vd413, vsucc(vd411))))),
% 0.20/0.39      inference(rewrite,[status(thm)],[])).
% 0.20/0.39  tff(25,plain,
% 0.20/0.39      ((vmul(vsucc(vd411), vsucc(vd413)) = vplus(vmul(vsucc(vd411), vd413), vsucc(vd411))) <=> (vmul(vsucc(vd411), vsucc(vd413)) = vplus(vmul(vsucc(vd411), vd413), vsucc(vd411)))),
% 0.20/0.39      inference(rewrite,[status(thm)],[])).
% 0.20/0.39  tff(26,axiom,(vmul(vsucc(vd411), vsucc(vd413)) = vplus(vmul(vsucc(vd411), vd413), vsucc(vd411))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''holds(266, 415, 0)'')).
% 0.20/0.39  tff(27,plain,
% 0.20/0.39      (vmul(vsucc(vd411), vsucc(vd413)) = vplus(vmul(vsucc(vd411), vd413), vsucc(vd411))),
% 0.20/0.39      inference(modus_ponens,[status(thm)],[26, 25])).
% 0.20/0.39  tff(28,plain,
% 0.20/0.39      (vmul(vsucc(vd411), vsucc(vd413)) = vplus(vmul(vd411, vd413), vplus(vd413, vsucc(vd411)))),
% 0.20/0.39      inference(modus_ponens,[status(thm)],[27, 24])).
% 0.20/0.39  tff(29,plain,
% 0.20/0.39      (vmul(vsucc(vd411), vsucc(vd413)) = vplus(vmul(vd411, vd413), vplus(vsucc(vd411), vd413))),
% 0.20/0.39      inference(transitivity,[status(thm)],[28, 23, 8])).
% 0.20/0.39  tff(30,plain,
% 0.20/0.39      ((~(vplus(vmul(vd411, vd413), vplus(vd413, vsucc(vd411))) = vplus(vmul(vd411, vd413), vplus(vsucc(vd411), vd413)))) <=> (~(vmul(vsucc(vd411), vsucc(vd413)) = vplus(vmul(vd411, vd413), vplus(vsucc(vd411), vd413))))),
% 0.20/0.39      inference(rewrite,[status(thm)],[])).
% 0.20/0.39  tff(31,plain,
% 0.20/0.39      ((~(vplus(vmul(vd411, vd413), vplus(vd413, vsucc(vd411))) = vplus(vmul(vd411, vd413), vplus(vsucc(vd411), vd413)))) <=> (~(vplus(vmul(vd411, vd413), vplus(vd413, vsucc(vd411))) = vplus(vmul(vd411, vd413), vplus(vsucc(vd411), vd413))))),
% 0.20/0.39      inference(rewrite,[status(thm)],[])).
% 0.20/0.39  tff(32,axiom,(~(vplus(vmul(vd411, vd413), vplus(vd413, vsucc(vd411))) = vplus(vmul(vd411, vd413), vplus(vsucc(vd411), vd413)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''holds(266, 415, 3)'')).
% 0.20/0.39  tff(33,plain,
% 0.20/0.39      (~(vplus(vmul(vd411, vd413), vplus(vd413, vsucc(vd411))) = vplus(vmul(vd411, vd413), vplus(vsucc(vd411), vd413)))),
% 0.20/0.39      inference(modus_ponens,[status(thm)],[32, 31])).
% 0.20/0.39  tff(34,plain,
% 0.20/0.39      (~(vmul(vsucc(vd411), vsucc(vd413)) = vplus(vmul(vd411, vd413), vplus(vsucc(vd411), vd413)))),
% 0.20/0.39      inference(modus_ponens,[status(thm)],[33, 30])).
% 0.20/0.39  tff(35,plain,
% 0.20/0.39      ($false),
% 0.20/0.39      inference(unit_resolution,[status(thm)],[34, 29])).
% 0.20/0.39  % SZS output end Proof
%------------------------------------------------------------------------------