TSTP Solution File: GRP492-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP492-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n013.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 11:47:43 EDT 2022
% Result : Unsatisfiable 0.19s 0.48s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 5
% Syntax : Number of clauses : 68 ( 68 unt; 0 nHn; 68 RR)
% Number of literals : 68 ( 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 : 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(identity,double_divide(double_divide(double_divide(u,v),identity),double_divide(w,v)))),w),
file('GRP492-1.p',unknown),
[] ).
cnf(2,axiom,
equal(double_divide(double_divide(u,v),identity),multiply(v,u)),
file('GRP492-1.p',unknown),
[] ).
cnf(3,axiom,
equal(double_divide(u,identity),inverse(u)),
file('GRP492-1.p',unknown),
[] ).
cnf(4,axiom,
equal(double_divide(u,inverse(u)),identity),
file('GRP492-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))),
file('GRP492-1.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(identity,double_divide(multiply(v,u),double_divide(w,v)))),w),
inference(rew,[status(thm),theory(equality)],[6,1,3]),
[iquote('0:Rew:6.0,1.0,3.0,1.0')] ).
cnf(10,plain,
equal(double_divide(double_divide(u,v),multiply(v,u)),identity),
inference(spr,[status(thm),theory(equality)],[6,4]),
[iquote('0:SpR:6.0,4.0')] ).
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(13,plain,
equal(multiply(identity,u),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[3,6]),
[iquote('0:SpR:3.0,6.0')] ).
cnf(49,plain,
equal(double_divide(double_divide(identity,u),double_divide(identity,double_divide(multiply(inverse(v),u),identity))),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(50,plain,
equal(double_divide(double_divide(identity,u),double_divide(identity,double_divide(multiply(identity,u),inverse(v)))),v),
inference(spr,[status(thm),theory(equality)],[3,7]),
[iquote('0:SpR:3.0,7.0')] ).
cnf(55,plain,
equal(double_divide(identity,double_divide(identity,double_divide(multiply(u,inverse(identity)),double_divide(v,u)))),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(57,plain,
equal(double_divide(double_divide(identity,u),double_divide(identity,inverse(multiply(inverse(v),u)))),v),
inference(rew,[status(thm),theory(equality)],[3,49]),
[iquote('0:Rew:3.0,49.0')] ).
cnf(58,plain,
equal(double_divide(double_divide(identity,u),double_divide(identity,double_divide(inverse(inverse(u)),inverse(v)))),v),
inference(rew,[status(thm),theory(equality)],[13,50]),
[iquote('0:Rew:13.0,50.0')] ).
cnf(66,plain,
equal(double_divide(double_divide(identity,u),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(multiply(inverse(v),w))),u),v))),double_divide(identity,w)),
inference(spr,[status(thm),theory(equality)],[57,7]),
[iquote('0:SpR:57.0,7.0')] ).
cnf(69,plain,
equal(double_divide(double_divide(identity,u),double_divide(identity,inverse(inverse(identity)))),u),
inference(spr,[status(thm),theory(equality)],[12,57]),
[iquote('0:SpR:12.0,57.0')] ).
cnf(77,plain,
equal(double_divide(double_divide(identity,u),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),u),v))),double_divide(identity,v)),
inference(spr,[status(thm),theory(equality)],[69,7]),
[iquote('0:SpR:69.0,7.0')] ).
cnf(79,plain,
equal(double_divide(identity,double_divide(identity,inverse(inverse(identity)))),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[4,69]),
[iquote('0:SpR:4.0,69.0')] ).
cnf(80,plain,
equal(double_divide(inverse(identity),double_divide(identity,inverse(inverse(identity)))),identity),
inference(spr,[status(thm),theory(equality)],[3,69]),
[iquote('0:SpR:3.0,69.0')] ).
cnf(88,plain,
equal(double_divide(inverse(identity),double_divide(identity,inverse(inverse(identity)))),double_divide(identity,inverse(inverse(identity)))),
inference(spr,[status(thm),theory(equality)],[79,69]),
[iquote('0:SpR:79.0,69.0')] ).
cnf(89,plain,
equal(double_divide(double_divide(identity,u),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),u),inverse(identity)))),identity),
inference(spr,[status(thm),theory(equality)],[79,7]),
[iquote('0:SpR:79.0,7.0')] ).
cnf(93,plain,
equal(double_divide(identity,inverse(inverse(identity))),identity),
inference(rew,[status(thm),theory(equality)],[80,88]),
[iquote('0:Rew:80.0,88.0')] ).
cnf(94,plain,
equal(double_divide(double_divide(identity,u),identity),u),
inference(rew,[status(thm),theory(equality)],[93,69]),
[iquote('0:Rew:93.0,69.0')] ).
cnf(96,plain,
equal(double_divide(inverse(identity),identity),identity),
inference(rew,[status(thm),theory(equality)],[93,80]),
[iquote('0:Rew:93.0,80.0')] ).
cnf(98,plain,
equal(double_divide(double_divide(identity,u),double_divide(identity,double_divide(multiply(identity,u),v))),double_divide(identity,v)),
inference(rew,[status(thm),theory(equality)],[93,77]),
[iquote('0:Rew:93.0,77.0')] ).
cnf(100,plain,
equal(inverse(inverse(identity)),identity),
inference(rew,[status(thm),theory(equality)],[3,96]),
[iquote('0:Rew:3.0,96.0')] ).
cnf(101,plain,
equal(double_divide(identity,identity),identity),
inference(rew,[status(thm),theory(equality)],[100,93]),
[iquote('0:Rew:100.0,93.0')] ).
cnf(102,plain,
equal(inverse(identity),identity),
inference(rew,[status(thm),theory(equality)],[3,101]),
[iquote('0:Rew:3.0,101.0')] ).
cnf(105,plain,
equal(double_divide(identity,double_divide(identity,double_divide(multiply(u,identity),double_divide(v,u)))),v),
inference(rew,[status(thm),theory(equality)],[102,55]),
[iquote('0:Rew:102.0,55.0')] ).
cnf(112,plain,
equal(multiply(u,identity),u),
inference(rew,[status(thm),theory(equality)],[6,94,3]),
[iquote('0:Rew:6.0,94.0,3.0,94.0')] ).
cnf(117,plain,
equal(double_divide(identity,double_divide(identity,double_divide(u,double_divide(v,u)))),v),
inference(rew,[status(thm),theory(equality)],[112,105]),
[iquote('0:Rew:112.0,105.0')] ).
cnf(119,plain,
equal(double_divide(double_divide(identity,u),double_divide(identity,double_divide(inverse(inverse(u)),v))),double_divide(identity,v)),
inference(rew,[status(thm),theory(equality)],[13,98]),
[iquote('0:Rew:13.0,98.0')] ).
cnf(120,plain,
equal(double_divide(identity,inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[119,58]),
[iquote('0:Rew:119.0,58.0')] ).
cnf(123,plain,
equal(double_divide(double_divide(identity,u),double_divide(identity,double_divide(multiply(multiply(inverse(v),w),u),v))),double_divide(identity,w)),
inference(rew,[status(thm),theory(equality)],[120,66]),
[iquote('0:Rew:120.0,66.0')] ).
cnf(132,plain,
equal(double_divide(double_divide(identity,u),double_divide(identity,double_divide(multiply(double_divide(identity,identity),u),identity))),identity),
inference(rew,[status(thm),theory(equality)],[102,89]),
[iquote('0:Rew:102.0,89.0,102.0,89.0')] ).
cnf(133,plain,
equal(double_divide(double_divide(identity,u),double_divide(identity,inverse(multiply(inverse(identity),u)))),identity),
inference(rew,[status(thm),theory(equality)],[3,132]),
[iquote('0:Rew:3.0,132.0,3.0,132.0')] ).
cnf(134,plain,
equal(double_divide(double_divide(identity,u),multiply(identity,u)),identity),
inference(rew,[status(thm),theory(equality)],[120,133,102]),
[iquote('0:Rew:120.0,133.0,102.0,133.0')] ).
cnf(135,plain,
equal(double_divide(double_divide(identity,u),inverse(inverse(u))),identity),
inference(rew,[status(thm),theory(equality)],[13,134]),
[iquote('0:Rew:13.0,134.0')] ).
cnf(139,plain,
equal(double_divide(double_divide(identity,u),u),identity),
inference(spr,[status(thm),theory(equality)],[112,10]),
[iquote('0:SpR:112.0,10.0')] ).
cnf(158,plain,
equal(double_divide(identity,multiply(u,v)),double_divide(v,u)),
inference(spr,[status(thm),theory(equality)],[6,120]),
[iquote('0:SpR:6.0,120.0')] ).
cnf(166,plain,
equal(double_divide(double_divide(identity,u),double_divide(identity,double_divide(multiply(v,u),identity))),double_divide(identity,v)),
inference(spr,[status(thm),theory(equality)],[139,7]),
[iquote('0:SpR:139.0,7.0')] ).
cnf(175,plain,
equal(double_divide(double_divide(identity,u),multiply(v,u)),double_divide(identity,v)),
inference(rew,[status(thm),theory(equality)],[120,166,3]),
[iquote('0:Rew:120.0,166.0,3.0,166.0')] ).
cnf(191,plain,
equal(double_divide(double_divide(identity,u),double_divide(identity,double_divide(multiply(inverse(inverse(v)),u),identity))),double_divide(identity,v)),
inference(spr,[status(thm),theory(equality)],[135,7]),
[iquote('0:SpR:135.0,7.0')] ).
cnf(202,plain,
equal(double_divide(double_divide(identity,u),multiply(inverse(inverse(v)),u)),double_divide(identity,v)),
inference(rew,[status(thm),theory(equality)],[120,191,3]),
[iquote('0:Rew:120.0,191.0,3.0,191.0')] ).
cnf(203,plain,
equal(double_divide(identity,inverse(inverse(u))),double_divide(identity,u)),
inference(rew,[status(thm),theory(equality)],[175,202]),
[iquote('0:Rew:175.0,202.0')] ).
cnf(204,plain,
equal(double_divide(identity,u),inverse(u)),
inference(rew,[status(thm),theory(equality)],[120,203]),
[iquote('0:Rew:120.0,203.0')] ).
cnf(205,plain,
equal(double_divide(double_divide(identity,u),inverse(double_divide(multiply(v,u),double_divide(w,v)))),w),
inference(rew,[status(thm),theory(equality)],[204,7]),
[iquote('0:Rew:204.0,7.0')] ).
cnf(213,plain,
equal(double_divide(double_divide(identity,u),inverse(double_divide(multiply(multiply(inverse(v),w),u),v))),double_divide(identity,w)),
inference(rew,[status(thm),theory(equality)],[204,123]),
[iquote('0:Rew:204.0,123.0')] ).
cnf(218,plain,
equal(inverse(double_divide(identity,double_divide(u,double_divide(v,u)))),v),
inference(rew,[status(thm),theory(equality)],[204,117]),
[iquote('0:Rew:204.0,117.0')] ).
cnf(221,plain,
equal(inverse(multiply(u,v)),double_divide(v,u)),
inference(rew,[status(thm),theory(equality)],[204,158]),
[iquote('0:Rew:204.0,158.0')] ).
cnf(227,plain,
equal(double_divide(u,double_divide(v,u)),v),
inference(rew,[status(thm),theory(equality)],[112,218,6]),
[iquote('0:Rew:112.0,218.0,6.0,218.0')] ).
cnf(235,plain,
equal(double_divide(double_divide(identity,u),multiply(double_divide(v,w),multiply(w,u))),v),
inference(rew,[status(thm),theory(equality)],[6,205]),
[iquote('0:Rew:6.0,205.0')] ).
cnf(236,plain,
equal(double_divide(inverse(u),multiply(double_divide(v,w),multiply(w,u))),v),
inference(rew,[status(thm),theory(equality)],[204,235]),
[iquote('0:Rew:204.0,235.0')] ).
cnf(246,plain,
equal(double_divide(double_divide(identity,u),multiply(v,multiply(multiply(inverse(v),w),u))),double_divide(identity,w)),
inference(rew,[status(thm),theory(equality)],[6,213]),
[iquote('0:Rew:6.0,213.0')] ).
cnf(247,plain,
equal(double_divide(inverse(u),multiply(v,multiply(multiply(inverse(v),w),u))),inverse(w)),
inference(rew,[status(thm),theory(equality)],[204,246]),
[iquote('0:Rew:204.0,246.0,204.0,246.0')] ).
cnf(311,plain,
equal(double_divide(double_divide(u,v),u),v),
inference(spr,[status(thm),theory(equality)],[227]),
[iquote('0:SpR:227.0,227.0')] ).
cnf(333,plain,
equal(multiply(u,double_divide(u,v)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[311,6]),
[iquote('0:SpR:311.0,6.0')] ).
cnf(336,plain,
equal(double_divide(inverse(u),multiply(v,multiply(w,u))),double_divide(w,v)),
inference(spr,[status(thm),theory(equality)],[311,236]),
[iquote('0:SpR:311.0,236.0')] ).
cnf(355,plain,
equal(double_divide(multiply(inverse(u),v),u),inverse(v)),
inference(rew,[status(thm),theory(equality)],[336,247]),
[iquote('0:Rew:336.0,247.0')] ).
cnf(546,plain,
equal(inverse(double_divide(inverse(u),v)),double_divide(inverse(v),u)),
inference(spr,[status(thm),theory(equality)],[333,355]),
[iquote('0:SpR:333.0,355.0')] ).
cnf(563,plain,
equal(double_divide(inverse(u),v),multiply(u,inverse(v))),
inference(rew,[status(thm),theory(equality)],[6,546]),
[iquote('0:Rew:6.0,546.0')] ).
cnf(566,plain,
equal(multiply(u,inverse(multiply(v,multiply(w,u)))),double_divide(w,v)),
inference(rew,[status(thm),theory(equality)],[563,336]),
[iquote('0:Rew:563.0,336.0')] ).
cnf(570,plain,
equal(multiply(u,double_divide(multiply(v,u),w)),double_divide(v,w)),
inference(rew,[status(thm),theory(equality)],[221,566]),
[iquote('0:Rew:221.0,566.0')] ).
cnf(942,plain,
equal(double_divide(u,double_divide(v,multiply(u,w))),multiply(w,v)),
inference(spr,[status(thm),theory(equality)],[227,570]),
[iquote('0:SpR:227.0,570.0')] ).
cnf(1445,plain,
equal(inverse(double_divide(u,multiply(v,w))),multiply(v,multiply(w,u))),
inference(spr,[status(thm),theory(equality)],[942,333]),
[iquote('0:SpR:942.0,333.0')] ).
cnf(1516,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(rew,[status(thm),theory(equality)],[6,1445]),
[iquote('0:Rew:6.0,1445.0')] ).
cnf(1517,plain,
$false,
inference(unc,[status(thm)],[1516,5]),
[iquote('0:UnC:1516.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP492-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n013.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 : 600
% 0.13/0.34 % DateTime : Tue Jun 14 04:25:58 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.48
% 0.19/0.48 SPASS V 3.9
% 0.19/0.48 SPASS beiseite: Proof found.
% 0.19/0.48 % SZS status Theorem
% 0.19/0.48 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.48 SPASS derived 868 clauses, backtracked 0 clauses, performed 0 splits and kept 146 clauses.
% 0.19/0.48 SPASS allocated 64452 KBytes.
% 0.19/0.48 SPASS spent 0:00:00.14 on the problem.
% 0.19/0.48 0:00:00.03 for the input.
% 0.19/0.48 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.48 0:00:00.01 for inferences.
% 0.19/0.48 0:00:00.00 for the backtracking.
% 0.19/0.48 0:00:00.07 for the reduction.
% 0.19/0.48
% 0.19/0.48
% 0.19/0.48 Here is a proof with depth 5, length 68 :
% 0.19/0.48 % SZS output start Refutation
% See solution above
% 0.19/0.49 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms_3
% 0.19/0.49
%------------------------------------------------------------------------------