TSTP Solution File: GRP495-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP495-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 11:47:45 EDT 2022
% Result : Unsatisfiable 0.21s 0.51s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 5
% Syntax : Number of clauses : 55 ( 55 unt; 0 nHn; 55 RR)
% Number of literals : 55 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(double_divide(double_divide(identity,u),double_divide(double_divide(double_divide(v,w),double_divide(identity,identity)),double_divide(u,w))),v),
file('GRP495-1.p',unknown),
[] ).
cnf(2,axiom,
equal(double_divide(double_divide(u,v),identity),multiply(v,u)),
file('GRP495-1.p',unknown),
[] ).
cnf(3,axiom,
equal(double_divide(u,identity),inverse(u)),
file('GRP495-1.p',unknown),
[] ).
cnf(4,axiom,
equal(double_divide(u,inverse(u)),identity),
file('GRP495-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))),
file('GRP495-1.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(identity,u),double_divide(double_divide(double_divide(v,w),inverse(identity)),double_divide(u,w))),v),
inference(rew,[status(thm),theory(equality)],[3,1]),
[iquote('0:Rew:3.0,1.0')] ).
cnf(51,plain,
equal(double_divide(double_divide(identity,u),double_divide(double_divide(double_divide(v,identity),inverse(identity)),inverse(u))),v),
inference(spr,[status(thm),theory(equality)],[3,7]),
[iquote('0:SpR:3.0,7.0')] ).
cnf(53,plain,
equal(double_divide(double_divide(identity,u),double_divide(double_divide(identity,inverse(identity)),double_divide(u,inverse(v)))),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(56,plain,
equal(double_divide(identity,double_divide(double_divide(double_divide(u,v),inverse(identity)),double_divide(inverse(identity),v))),u),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(59,plain,
equal(double_divide(double_divide(identity,u),double_divide(double_divide(inverse(v),inverse(identity)),inverse(u))),v),
inference(rew,[status(thm),theory(equality)],[3,51]),
[iquote('0:Rew:3.0,51.0')] ).
cnf(60,plain,
equal(double_divide(double_divide(identity,u),double_divide(identity,double_divide(u,inverse(v)))),v),
inference(rew,[status(thm),theory(equality)],[4,53]),
[iquote('0:Rew:4.0,53.0')] ).
cnf(73,plain,
equal(double_divide(double_divide(identity,u),double_divide(identity,identity)),u),
inference(spr,[status(thm),theory(equality)],[4,60]),
[iquote('0:SpR:4.0,60.0')] ).
cnf(74,plain,
equal(double_divide(identity,double_divide(identity,double_divide(inverse(identity),inverse(u)))),u),
inference(spr,[status(thm),theory(equality)],[4,60]),
[iquote('0:SpR:4.0,60.0')] ).
cnf(76,plain,
equal(double_divide(double_divide(identity,u),inverse(identity)),u),
inference(rew,[status(thm),theory(equality)],[3,73]),
[iquote('0:Rew:3.0,73.0')] ).
cnf(82,plain,
equal(double_divide(double_divide(identity,double_divide(identity,u)),double_divide(double_divide(double_divide(v,inverse(identity)),inverse(identity)),u)),v),
inference(spr,[status(thm),theory(equality)],[76,7]),
[iquote('0:SpR:76.0,7.0')] ).
cnf(86,plain,
equal(double_divide(double_divide(identity,u),double_divide(double_divide(v,inverse(identity)),double_divide(u,inverse(identity)))),double_divide(identity,v)),
inference(spr,[status(thm),theory(equality)],[76,7]),
[iquote('0:SpR:76.0,7.0')] ).
cnf(87,plain,
equal(double_divide(identity,inverse(identity)),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[4,76]),
[iquote('0:SpR:4.0,76.0')] ).
cnf(89,plain,
equal(inverse(identity),identity),
inference(rew,[status(thm),theory(equality)],[4,87]),
[iquote('0:Rew:4.0,87.0')] ).
cnf(92,plain,
equal(double_divide(double_divide(identity,u),double_divide(double_divide(double_divide(v,w),identity),double_divide(u,w))),v),
inference(rew,[status(thm),theory(equality)],[89,7]),
[iquote('0:Rew:89.0,7.0')] ).
cnf(95,plain,
equal(double_divide(double_divide(identity,u),double_divide(double_divide(inverse(v),identity),inverse(u))),v),
inference(rew,[status(thm),theory(equality)],[89,59]),
[iquote('0:Rew:89.0,59.0')] ).
cnf(96,plain,
equal(double_divide(identity,double_divide(double_divide(double_divide(u,v),identity),double_divide(identity,v))),u),
inference(rew,[status(thm),theory(equality)],[89,56]),
[iquote('0:Rew:89.0,56.0')] ).
cnf(103,plain,
equal(double_divide(identity,double_divide(identity,double_divide(identity,inverse(u)))),u),
inference(rew,[status(thm),theory(equality)],[89,74]),
[iquote('0:Rew:89.0,74.0')] ).
cnf(119,plain,
equal(double_divide(double_divide(identity,u),double_divide(inverse(inverse(v)),inverse(u))),v),
inference(rew,[status(thm),theory(equality)],[3,95]),
[iquote('0:Rew:3.0,95.0')] ).
cnf(120,plain,
equal(double_divide(identity,double_divide(multiply(u,v),double_divide(identity,u))),v),
inference(rew,[status(thm),theory(equality)],[6,96,3]),
[iquote('0:Rew:6.0,96.0,3.0,96.0')] ).
cnf(122,plain,
equal(double_divide(double_divide(identity,u),double_divide(multiply(v,w),double_divide(u,v))),w),
inference(rew,[status(thm),theory(equality)],[6,92,3]),
[iquote('0:Rew:6.0,92.0,3.0,92.0')] ).
cnf(125,plain,
equal(double_divide(double_divide(identity,double_divide(identity,u)),double_divide(double_divide(double_divide(v,identity),identity),u)),v),
inference(rew,[status(thm),theory(equality)],[89,82]),
[iquote('0:Rew:89.0,82.0')] ).
cnf(126,plain,
equal(double_divide(double_divide(identity,double_divide(identity,u)),double_divide(inverse(inverse(v)),u)),v),
inference(rew,[status(thm),theory(equality)],[3,125]),
[iquote('0:Rew:3.0,125.0,3.0,125.0')] ).
cnf(127,plain,
equal(double_divide(double_divide(identity,u),double_divide(double_divide(v,identity),double_divide(u,identity))),double_divide(identity,v)),
inference(rew,[status(thm),theory(equality)],[89,86]),
[iquote('0:Rew:89.0,86.0')] ).
cnf(128,plain,
equal(double_divide(double_divide(identity,u),double_divide(inverse(v),inverse(u))),double_divide(identity,v)),
inference(rew,[status(thm),theory(equality)],[3,127]),
[iquote('0:Rew:3.0,127.0,3.0,127.0')] ).
cnf(129,plain,
equal(double_divide(identity,inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[128,119]),
[iquote('0:Rew:128.0,119.0')] ).
cnf(130,plain,
equal(double_divide(identity,double_divide(identity,u)),u),
inference(rew,[status(thm),theory(equality)],[129,103]),
[iquote('0:Rew:129.0,103.0')] ).
cnf(132,plain,
equal(double_divide(u,double_divide(inverse(inverse(v)),u)),v),
inference(rew,[status(thm),theory(equality)],[130,126]),
[iquote('0:Rew:130.0,126.0')] ).
cnf(181,plain,
equal(double_divide(double_divide(identity,identity),double_divide(multiply(inverse(u),v),u)),v),
inference(spr,[status(thm),theory(equality)],[129,122]),
[iquote('0:SpR:129.0,122.0')] ).
cnf(185,plain,
equal(double_divide(identity,multiply(u,v)),double_divide(v,u)),
inference(spr,[status(thm),theory(equality)],[6,129]),
[iquote('0:SpR:6.0,129.0')] ).
cnf(190,plain,
equal(double_divide(identity,double_divide(multiply(inverse(u),v),u)),v),
inference(rew,[status(thm),theory(equality)],[89,181,3]),
[iquote('0:Rew:89.0,181.0,3.0,181.0')] ).
cnf(201,plain,
equal(double_divide(identity,u),inverse(u)),
inference(spr,[status(thm),theory(equality)],[129,130]),
[iquote('0:SpR:129.0,130.0')] ).
cnf(202,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[201,129]),
[iquote('0:Rew:201.0,129.0')] ).
cnf(205,plain,
equal(double_divide(inverse(u),double_divide(multiply(v,w),double_divide(u,v))),w),
inference(rew,[status(thm),theory(equality)],[201,122]),
[iquote('0:Rew:201.0,122.0')] ).
cnf(206,plain,
equal(inverse(multiply(u,v)),double_divide(v,u)),
inference(rew,[status(thm),theory(equality)],[201,185]),
[iquote('0:Rew:201.0,185.0')] ).
cnf(212,plain,
equal(inverse(double_divide(multiply(inverse(u),v),u)),v),
inference(rew,[status(thm),theory(equality)],[201,190]),
[iquote('0:Rew:201.0,190.0')] ).
cnf(213,plain,
equal(inverse(double_divide(multiply(u,v),double_divide(identity,u))),v),
inference(rew,[status(thm),theory(equality)],[201,120]),
[iquote('0:Rew:201.0,120.0')] ).
cnf(223,plain,
equal(double_divide(u,double_divide(v,u)),v),
inference(rew,[status(thm),theory(equality)],[202,132]),
[iquote('0:Rew:202.0,132.0')] ).
cnf(229,plain,
equal(multiply(u,multiply(inverse(u),v)),v),
inference(rew,[status(thm),theory(equality)],[6,212]),
[iquote('0:Rew:6.0,212.0')] ).
cnf(231,plain,
equal(multiply(double_divide(identity,u),multiply(u,v)),v),
inference(rew,[status(thm),theory(equality)],[6,213]),
[iquote('0:Rew:6.0,213.0')] ).
cnf(232,plain,
equal(multiply(inverse(u),multiply(u,v)),v),
inference(rew,[status(thm),theory(equality)],[201,231]),
[iquote('0:Rew:201.0,231.0')] ).
cnf(326,plain,
equal(double_divide(inverse(u),double_divide(multiply(double_divide(v,u),w),v)),w),
inference(spr,[status(thm),theory(equality)],[223,205]),
[iquote('0:SpR:223.0,205.0')] ).
cnf(329,plain,
equal(double_divide(double_divide(u,v),u),v),
inference(spr,[status(thm),theory(equality)],[223]),
[iquote('0:SpR:223.0,223.0')] ).
cnf(357,plain,
equal(multiply(u,double_divide(u,v)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[329,6]),
[iquote('0:SpR:329.0,6.0')] ).
cnf(394,plain,
equal(multiply(double_divide(u,v),multiply(multiply(v,u),w)),w),
inference(spr,[status(thm),theory(equality)],[206,232]),
[iquote('0:SpR:206.0,232.0')] ).
cnf(497,plain,
equal(double_divide(inverse(u),v),multiply(u,inverse(v))),
inference(spr,[status(thm),theory(equality)],[357,229]),
[iquote('0:SpR:357.0,229.0')] ).
cnf(510,plain,
equal(multiply(u,inverse(double_divide(multiply(double_divide(v,u),w),v))),w),
inference(rew,[status(thm),theory(equality)],[497,326]),
[iquote('0:Rew:497.0,326.0')] ).
cnf(515,plain,
equal(multiply(u,multiply(v,multiply(double_divide(v,u),w))),w),
inference(rew,[status(thm),theory(equality)],[6,510]),
[iquote('0:Rew:6.0,510.0')] ).
cnf(1316,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(spr,[status(thm),theory(equality)],[394,515]),
[iquote('0:SpR:394.0,515.0')] ).
cnf(1330,plain,
$false,
inference(unc,[status(thm)],[1316,5]),
[iquote('0:UnC:1316.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : GRP495-1 : TPTP v8.1.0. Released v2.6.0.
% 0.13/0.14 % Command : run_spass %d %s
% 0.14/0.36 % Computer : n024.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Tue Jun 14 13:51:18 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.21/0.51
% 0.21/0.51 SPASS V 3.9
% 0.21/0.51 SPASS beiseite: Proof found.
% 0.21/0.51 % SZS status Theorem
% 0.21/0.51 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.51 SPASS derived 735 clauses, backtracked 0 clauses, performed 0 splits and kept 132 clauses.
% 0.21/0.51 SPASS allocated 64317 KBytes.
% 0.21/0.51 SPASS spent 0:00:00.13 on the problem.
% 0.21/0.51 0:00:00.03 for the input.
% 0.21/0.51 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.51 0:00:00.01 for inferences.
% 0.21/0.51 0:00:00.00 for the backtracking.
% 0.21/0.51 0:00:00.07 for the reduction.
% 0.21/0.51
% 0.21/0.51
% 0.21/0.51 Here is a proof with depth 6, length 55 :
% 0.21/0.51 % SZS output start Refutation
% See solution above
% 0.21/0.51 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms_3
% 0.21/0.51
%------------------------------------------------------------------------------