TSTP Solution File: GRP483-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP483-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n016.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 : 600s
% DateTime : Sat Jul 16 11:47:41 EDT 2022
% Result : Unsatisfiable 0.19s 0.52s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 5
% Syntax : Number of clauses : 54 ( 54 unt; 0 nHn; 54 RR)
% Number of literals : 54 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(double_divide(double_divide(double_divide(u,double_divide(v,identity)),double_divide(double_divide(w,double_divide(x,double_divide(x,identity))),double_divide(u,identity))),v),w),
file('GRP483-1.p',unknown),
[] ).
cnf(2,axiom,
equal(double_divide(double_divide(u,v),identity),multiply(v,u)),
file('GRP483-1.p',unknown),
[] ).
cnf(3,axiom,
equal(double_divide(u,identity),inverse(u)),
file('GRP483-1.p',unknown),
[] ).
cnf(4,axiom,
equal(double_divide(u,inverse(u)),identity),
file('GRP483-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))),
file('GRP483-1.p',unknown),
[] ).
cnf(6,plain,
equal(inverse(double_divide(u,v)),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[3,2]),
[iquote('0:Rew:3.0,2.0')] ).
cnf(7,plain,
equal(double_divide(double_divide(double_divide(u,inverse(v)),double_divide(inverse(w),inverse(u))),v),w),
inference(rew,[status(thm),theory(equality)],[3,1,4]),
[iquote('0:Rew:3.0,1.0,3.0,1.0,4.0,1.0,3.0,1.0,3.0,1.0')] ).
cnf(12,plain,
equal(multiply(inverse(u),u),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[4,6]),
[iquote('0:SpR:4.0,6.0')] ).
cnf(15,plain,
equal(multiply(multiply(u,v),double_divide(v,u)),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[6,12]),
[iquote('0:SpR:6.0,12.0')] ).
cnf(44,plain,
equal(double_divide(double_divide(u,double_divide(inverse(v),inverse(double_divide(double_divide(w,inverse(inverse(x))),double_divide(inverse(u),inverse(w)))))),x),v),
inference(spr,[status(thm),theory(equality)],[7]),
[iquote('0:SpR:7.0,7.0')] ).
cnf(45,plain,
equal(inverse(double_divide(double_divide(u,inverse(identity)),double_divide(inverse(v),inverse(u)))),v),
inference(spr,[status(thm),theory(equality)],[7,3]),
[iquote('0:SpR:7.0,3.0')] ).
cnf(46,plain,
equal(multiply(u,double_divide(double_divide(v,inverse(u)),double_divide(inverse(w),inverse(v)))),inverse(w)),
inference(spr,[status(thm),theory(equality)],[7,6]),
[iquote('0:SpR:7.0,6.0')] ).
cnf(52,plain,
equal(double_divide(double_divide(double_divide(inverse(u),inverse(v)),identity),v),u),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(55,plain,
equal(double_divide(multiply(inverse(u),inverse(v)),u),v),
inference(rew,[status(thm),theory(equality)],[6,52,3]),
[iquote('0:Rew:6.0,52.0,3.0,52.0')] ).
cnf(56,plain,
equal(multiply(double_divide(inverse(u),inverse(v)),double_divide(v,inverse(identity))),u),
inference(rew,[status(thm),theory(equality)],[6,45]),
[iquote('0:Rew:6.0,45.0')] ).
cnf(59,plain,
equal(double_divide(double_divide(u,double_divide(inverse(v),multiply(double_divide(inverse(u),inverse(w)),double_divide(w,inverse(inverse(x)))))),x),v),
inference(rew,[status(thm),theory(equality)],[6,44]),
[iquote('0:Rew:6.0,44.0')] ).
cnf(68,plain,
equal(double_divide(inverse(identity),inverse(u)),u),
inference(spr,[status(thm),theory(equality)],[12,55]),
[iquote('0:SpR:12.0,55.0')] ).
cnf(71,plain,
equal(inverse(identity),identity),
inference(spr,[status(thm),theory(equality)],[68,4]),
[iquote('0:SpR:68.0,4.0')] ).
cnf(72,plain,
equal(double_divide(double_divide(u,double_divide(inverse(v),inverse(inverse(identity)))),u),v),
inference(spr,[status(thm),theory(equality)],[68,7]),
[iquote('0:SpR:68.0,7.0')] ).
cnf(73,plain,
equal(multiply(inverse(u),inverse(identity)),inverse(u)),
inference(spr,[status(thm),theory(equality)],[68,6]),
[iquote('0:SpR:68.0,6.0')] ).
cnf(80,plain,
equal(multiply(multiply(u,v),double_divide(v,u)),identity),
inference(rew,[status(thm),theory(equality)],[71,15]),
[iquote('0:Rew:71.0,15.0')] ).
cnf(81,plain,
equal(double_divide(identity,inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[71,68]),
[iquote('0:Rew:71.0,68.0')] ).
cnf(82,plain,
equal(multiply(double_divide(inverse(u),inverse(v)),double_divide(v,identity)),u),
inference(rew,[status(thm),theory(equality)],[71,56]),
[iquote('0:Rew:71.0,56.0')] ).
cnf(85,plain,
equal(multiply(inverse(u),identity),inverse(u)),
inference(rew,[status(thm),theory(equality)],[71,73]),
[iquote('0:Rew:71.0,73.0')] ).
cnf(89,plain,
equal(multiply(double_divide(inverse(u),inverse(v)),inverse(v)),u),
inference(rew,[status(thm),theory(equality)],[3,82]),
[iquote('0:Rew:3.0,82.0')] ).
cnf(90,plain,
equal(double_divide(double_divide(u,double_divide(inverse(v),identity)),u),v),
inference(rew,[status(thm),theory(equality)],[71,72]),
[iquote('0:Rew:71.0,72.0,71.0,72.0')] ).
cnf(91,plain,
equal(double_divide(double_divide(u,inverse(inverse(v))),u),v),
inference(rew,[status(thm),theory(equality)],[3,90]),
[iquote('0:Rew:3.0,90.0')] ).
cnf(97,plain,
equal(double_divide(multiply(inverse(u),identity),u),identity),
inference(spr,[status(thm),theory(equality)],[71,55]),
[iquote('0:SpR:71.0,55.0')] ).
cnf(101,plain,
equal(double_divide(inverse(u),u),identity),
inference(rew,[status(thm),theory(equality)],[85,97]),
[iquote('0:Rew:85.0,97.0')] ).
cnf(126,plain,
equal(multiply(double_divide(inverse(u),identity),identity),u),
inference(spr,[status(thm),theory(equality)],[71,89]),
[iquote('0:SpR:71.0,89.0')] ).
cnf(133,plain,
equal(multiply(inverse(inverse(u)),identity),u),
inference(rew,[status(thm),theory(equality)],[3,126]),
[iquote('0:Rew:3.0,126.0')] ).
cnf(134,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[85,133]),
[iquote('0:Rew:85.0,133.0')] ).
cnf(136,plain,
equal(double_divide(double_divide(u,v),u),v),
inference(rew,[status(thm),theory(equality)],[134,91]),
[iquote('0:Rew:134.0,91.0')] ).
cnf(139,plain,
equal(double_divide(double_divide(u,double_divide(inverse(v),multiply(double_divide(inverse(u),inverse(w)),double_divide(w,x)))),x),v),
inference(rew,[status(thm),theory(equality)],[134,59]),
[iquote('0:Rew:134.0,59.0')] ).
cnf(148,plain,
equal(double_divide(identity,u),inverse(u)),
inference(spr,[status(thm),theory(equality)],[134,81]),
[iquote('0:SpR:134.0,81.0')] ).
cnf(156,plain,
equal(inverse(multiply(u,v)),double_divide(v,u)),
inference(spr,[status(thm),theory(equality)],[6,134]),
[iquote('0:SpR:6.0,134.0')] ).
cnf(190,plain,
equal(multiply(u,double_divide(double_divide(identity,inverse(u)),double_divide(inverse(v),identity))),inverse(v)),
inference(spr,[status(thm),theory(equality)],[71,46]),
[iquote('0:SpR:71.0,46.0')] ).
cnf(196,plain,
equal(multiply(u,double_divide(double_divide(v,inverse(u)),identity)),inverse(inverse(v))),
inference(spr,[status(thm),theory(equality)],[101,46]),
[iquote('0:SpR:101.0,46.0')] ).
cnf(203,plain,
equal(multiply(u,multiply(inverse(u),v)),v),
inference(rew,[status(thm),theory(equality)],[6,196,3,134]),
[iquote('0:Rew:6.0,196.0,3.0,196.0,134.0,196.0')] ).
cnf(211,plain,
equal(multiply(u,double_divide(double_divide(identity,inverse(u)),v)),inverse(v)),
inference(rew,[status(thm),theory(equality)],[134,190,3]),
[iquote('0:Rew:134.0,190.0,3.0,190.0')] ).
cnf(212,plain,
equal(multiply(u,double_divide(inverse(inverse(u)),v)),inverse(v)),
inference(rew,[status(thm),theory(equality)],[148,211]),
[iquote('0:Rew:148.0,211.0')] ).
cnf(213,plain,
equal(multiply(u,double_divide(u,v)),inverse(v)),
inference(rew,[status(thm),theory(equality)],[134,212]),
[iquote('0:Rew:134.0,212.0')] ).
cnf(236,plain,
equal(double_divide(u,double_divide(v,u)),v),
inference(spr,[status(thm),theory(equality)],[136]),
[iquote('0:SpR:136.0,136.0')] ).
cnf(356,plain,
equal(double_divide(inverse(u),v),multiply(u,inverse(v))),
inference(spr,[status(thm),theory(equality)],[213,203]),
[iquote('0:SpR:213.0,203.0')] ).
cnf(373,plain,
equal(double_divide(double_divide(u,multiply(v,inverse(multiply(double_divide(inverse(u),inverse(w)),double_divide(w,x))))),x),v),
inference(rew,[status(thm),theory(equality)],[356,139]),
[iquote('0:Rew:356.0,139.0')] ).
cnf(397,plain,
equal(double_divide(double_divide(u,multiply(v,double_divide(double_divide(w,x),double_divide(inverse(u),inverse(w))))),x),v),
inference(rew,[status(thm),theory(equality)],[156,373]),
[iquote('0:Rew:156.0,373.0')] ).
cnf(398,plain,
equal(double_divide(double_divide(u,multiply(v,double_divide(double_divide(w,x),multiply(u,inverse(inverse(w)))))),x),v),
inference(rew,[status(thm),theory(equality)],[356,397]),
[iquote('0:Rew:356.0,397.0')] ).
cnf(399,plain,
equal(double_divide(double_divide(u,multiply(v,double_divide(double_divide(w,x),multiply(u,w)))),x),v),
inference(rew,[status(thm),theory(equality)],[134,398]),
[iquote('0:Rew:134.0,398.0')] ).
cnf(659,plain,
equal(multiply(multiply(u,v),double_divide(v,w)),double_divide(double_divide(u,identity),w)),
inference(spr,[status(thm),theory(equality)],[80,399]),
[iquote('0:SpR:80.0,399.0')] ).
cnf(667,plain,
equal(multiply(multiply(u,v),double_divide(v,w)),double_divide(inverse(u),w)),
inference(rew,[status(thm),theory(equality)],[3,659]),
[iquote('0:Rew:3.0,659.0')] ).
cnf(668,plain,
equal(multiply(multiply(u,v),double_divide(v,w)),multiply(u,inverse(w))),
inference(rew,[status(thm),theory(equality)],[356,667]),
[iquote('0:Rew:356.0,667.0')] ).
cnf(1636,plain,
equal(multiply(u,inverse(double_divide(v,w))),multiply(multiply(u,w),v)),
inference(spr,[status(thm),theory(equality)],[236,668]),
[iquote('0:SpR:236.0,668.0')] ).
cnf(1666,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(rew,[status(thm),theory(equality)],[6,1636]),
[iquote('0:Rew:6.0,1636.0')] ).
cnf(1667,plain,
$false,
inference(unc,[status(thm)],[1666,5]),
[iquote('0:UnC:1666.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP483-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n016.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 : 600
% 0.12/0.34 % DateTime : Tue Jun 14 11:09:31 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.52
% 0.19/0.52 SPASS V 3.9
% 0.19/0.52 SPASS beiseite: Proof found.
% 0.19/0.52 % SZS status Theorem
% 0.19/0.52 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.52 SPASS derived 864 clauses, backtracked 0 clauses, performed 0 splits and kept 162 clauses.
% 0.19/0.52 SPASS allocated 64812 KBytes.
% 0.19/0.52 SPASS spent 0:00:00.17 on the problem.
% 0.19/0.52 0:00:00.03 for the input.
% 0.19/0.52 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.52 0:00:00.01 for inferences.
% 0.19/0.52 0:00:00.00 for the backtracking.
% 0.19/0.52 0:00:00.10 for the reduction.
% 0.19/0.52
% 0.19/0.52
% 0.19/0.52 Here is a proof with depth 6, length 54 :
% 0.19/0.52 % SZS output start Refutation
% See solution above
% 0.19/0.52 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms_3
% 0.19/0.52
%------------------------------------------------------------------------------