TSTP Solution File: GRP105-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP105-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %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 : 600s
% DateTime : Sat Jul 16 11:45:19 EDT 2022
% Result : Unsatisfiable 0.80s 1.04s
% Output : Refutation 0.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 3
% Syntax : Number of clauses : 67 ( 57 unt; 0 nHn; 67 RR)
% Number of literals : 87 ( 0 equ; 31 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 14 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(double_divide(inverse(double_divide(double_divide(u,v),inverse(double_divide(u,inverse(w))))),v),w),
file('GRP105-1.p',unknown),
[] ).
cnf(2,axiom,
equal(inverse(double_divide(u,v)),multiply(v,u)),
file('GRP105-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)))
| ~ equal(multiply(multiply(inverse(b2),b2),a2),a2) ),
file('GRP105-1.p',unknown),
[] ).
cnf(4,plain,
equal(double_divide(multiply(multiply(inverse(u),v),double_divide(v,w)),w),u),
inference(rew,[status(thm),theory(equality)],[2,1]),
[iquote('0:Rew:2.0,1.0,2.0,1.0')] ).
cnf(6,plain,
equal(multiply(u,multiply(multiply(inverse(v),w),double_divide(w,u))),inverse(v)),
inference(spr,[status(thm),theory(equality)],[4,2]),
[iquote('0:SpR:4.0,2.0')] ).
cnf(7,plain,
equal(double_divide(multiply(multiply(inverse(u),multiply(multiply(inverse(v),w),double_divide(w,x))),v),x),u),
inference(spr,[status(thm),theory(equality)],[4]),
[iquote('0:SpR:4.0,4.0')] ).
cnf(9,plain,
equal(double_divide(multiply(multiply(multiply(u,v),w),double_divide(w,x)),x),double_divide(v,u)),
inference(spr,[status(thm),theory(equality)],[2,4]),
[iquote('0:SpR:2.0,4.0')] ).
cnf(44,plain,
equal(double_divide(multiply(multiply(inverse(u),multiply(multiply(inverse(v),multiply(multiply(inverse(w),x),double_divide(x,y))),w)),v),y),u),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(50,plain,
equal(double_divide(multiply(inverse(u),u),inverse(v)),v),
inference(spr,[status(thm),theory(equality)],[6,7]),
[iquote('0:SpR:6.0,7.0')] ).
cnf(51,plain,
equal(multiply(inverse(u),multiply(inverse(v),v)),inverse(u)),
inference(spr,[status(thm),theory(equality)],[50,2]),
[iquote('0:SpR:50.0,2.0')] ).
cnf(52,plain,
equal(double_divide(multiply(multiply(inverse(u),multiply(inverse(v),v)),w),inverse(w)),u),
inference(spr,[status(thm),theory(equality)],[50,4]),
[iquote('0:SpR:50.0,4.0')] ).
cnf(53,plain,
equal(multiply(inverse(u),multiply(multiply(inverse(v),multiply(inverse(w),w)),u)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[50,6]),
[iquote('0:SpR:50.0,6.0')] ).
cnf(60,plain,
equal(double_divide(multiply(inverse(u),v),inverse(v)),u),
inference(rew,[status(thm),theory(equality)],[51,52]),
[iquote('0:Rew:51.0,52.0')] ).
cnf(61,plain,
equal(multiply(inverse(u),multiply(inverse(v),u)),inverse(v)),
inference(rew,[status(thm),theory(equality)],[51,53]),
[iquote('0:Rew:51.0,53.0')] ).
cnf(98,plain,
equal(double_divide(inverse(u),inverse(multiply(inverse(v),v))),u),
inference(spr,[status(thm),theory(equality)],[51,60]),
[iquote('0:SpR:51.0,60.0')] ).
cnf(101,plain,
equal(double_divide(inverse(multiply(inverse(u),u)),inverse(v)),v),
inference(spr,[status(thm),theory(equality)],[51,50]),
[iquote('0:SpR:51.0,50.0')] ).
cnf(128,plain,
equal(double_divide(multiply(multiply(inverse(u),inverse(v)),v),inverse(multiply(inverse(w),w))),u),
inference(spr,[status(thm),theory(equality)],[98,4]),
[iquote('0:SpR:98.0,4.0')] ).
cnf(137,plain,
equal(double_divide(multiply(u,v),inverse(multiply(inverse(w),w))),double_divide(v,u)),
inference(spr,[status(thm),theory(equality)],[2,98]),
[iquote('0:SpR:2.0,98.0')] ).
cnf(138,plain,
equal(double_divide(u,multiply(inverse(v),inverse(u))),v),
inference(rew,[status(thm),theory(equality)],[137,128]),
[iquote('0:Rew:137.0,128.0')] ).
cnf(192,plain,
equal(multiply(inverse(u),u),multiply(inverse(v),v)),
inference(spr,[status(thm),theory(equality)],[101,98]),
[iquote('0:SpR:101.0,98.0')] ).
cnf(205,plain,
equal(double_divide(multiply(multiply(inverse(u),u),double_divide(v,w)),w),v),
inference(spr,[status(thm),theory(equality)],[192,4]),
[iquote('0:SpR:192.0,4.0')] ).
cnf(208,plain,
equal(double_divide(multiply(multiply(inverse(u),u),v),w),multiply(multiply(inverse(v),x),double_divide(x,w))),
inference(spr,[status(thm),theory(equality)],[192,7]),
[iquote('0:SpR:192.0,7.0')] ).
cnf(219,plain,
equal(double_divide(u,multiply(inverse(v),v)),inverse(u)),
inference(spr,[status(thm),theory(equality)],[192,138]),
[iquote('0:SpR:192.0,138.0')] ).
cnf(222,plain,
equal(double_divide(multiply(multiply(multiply(inverse(u),u),v),double_divide(v,w)),w),double_divide(x,inverse(x))),
inference(spr,[status(thm),theory(equality)],[192,9]),
[iquote('0:SpR:192.0,9.0')] ).
cnf(245,plain,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)))
| ~ equal(multiply(multiply(inverse(u),u),a2),a2) ),
inference(spl,[status(thm),theory(equality)],[192,3]),
[iquote('0:SpL:192.0,3.3')] ).
cnf(246,plain,
equal(double_divide(u,inverse(u)),double_divide(v,inverse(v))),
inference(rew,[status(thm),theory(equality)],[9,222]),
[iquote('0:Rew:9.0,222.0')] ).
cnf(248,plain,
equal(multiply(multiply(inverse(u),u),v),inverse(inverse(v))),
inference(spr,[status(thm),theory(equality)],[219,2]),
[iquote('0:SpR:219.0,2.0')] ).
cnf(263,plain,
equal(double_divide(u,inverse(multiply(inverse(v),v))),inverse(u)),
inference(spr,[status(thm),theory(equality)],[51,219]),
[iquote('0:SpR:51.0,219.0')] ).
cnf(268,plain,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)))
| ~ equal(inverse(inverse(a2)),a2) ),
inference(rew,[status(thm),theory(equality)],[248,245]),
[iquote('0:Rew:248.0,245.3')] ).
cnf(269,plain,
equal(multiply(multiply(inverse(u),v),double_divide(v,w)),double_divide(inverse(inverse(u)),w)),
inference(rew,[status(thm),theory(equality)],[248,208]),
[iquote('0:Rew:248.0,208.0')] ).
cnf(270,plain,
equal(double_divide(inverse(inverse(double_divide(u,v))),v),u),
inference(rew,[status(thm),theory(equality)],[248,205]),
[iquote('0:Rew:248.0,205.0')] ).
cnf(274,plain,
equal(double_divide(inverse(multiply(u,v)),u),v),
inference(rew,[status(thm),theory(equality)],[2,270]),
[iquote('0:Rew:2.0,270.0')] ).
cnf(275,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[263,98]),
[iquote('0:Rew:263.0,98.0')] ).
cnf(276,plain,
equal(inverse(multiply(u,v)),double_divide(v,u)),
inference(rew,[status(thm),theory(equality)],[263,137]),
[iquote('0:Rew:263.0,137.0')] ).
cnf(281,plain,
equal(double_divide(double_divide(u,v),v),u),
inference(rew,[status(thm),theory(equality)],[276,274]),
[iquote('0:Rew:276.0,274.0')] ).
cnf(307,plain,
equal(multiply(multiply(inverse(u),v),double_divide(v,w)),double_divide(u,w)),
inference(rew,[status(thm),theory(equality)],[275,269]),
[iquote('0:Rew:275.0,269.0')] ).
cnf(339,plain,
equal(double_divide(multiply(multiply(inverse(u),multiply(multiply(inverse(v),double_divide(w,x)),w)),v),x),u),
inference(rew,[status(thm),theory(equality)],[307,44]),
[iquote('0:Rew:307.0,44.0')] ).
cnf(366,plain,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)))
| ~ equal(a2,a2) ),
inference(rew,[status(thm),theory(equality)],[275,268]),
[iquote('0:Rew:275.0,268.3')] ).
cnf(367,plain,
( ~ equal(multiply(b4,a4),multiply(a4,b4))
| ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(obv,[status(thm),theory(equality)],[366]),
[iquote('0:Obv:366.3')] ).
cnf(380,plain,
equal(multiply(inverse(u),multiply(v,u)),v),
inference(spr,[status(thm),theory(equality)],[275,61]),
[iquote('0:SpR:275.0,61.0')] ).
cnf(505,plain,
equal(multiply(inverse(multiply(u,v)),u),inverse(v)),
inference(spr,[status(thm),theory(equality)],[380]),
[iquote('0:SpR:380.0,380.0')] ).
cnf(515,plain,
equal(multiply(u,multiply(v,inverse(u))),v),
inference(spr,[status(thm),theory(equality)],[275,380]),
[iquote('0:SpR:275.0,380.0')] ).
cnf(517,plain,
equal(multiply(double_divide(u,v),v),inverse(u)),
inference(rew,[status(thm),theory(equality)],[276,505]),
[iquote('0:Rew:276.0,505.0')] ).
cnf(661,plain,
equal(multiply(u,inverse(v)),double_divide(v,inverse(u))),
inference(spr,[status(thm),theory(equality)],[517,515]),
[iquote('0:SpR:517.0,515.0')] ).
cnf(669,plain,
equal(inverse(double_divide(u,v)),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[281,517]),
[iquote('0:SpR:281.0,517.0')] ).
cnf(670,plain,
equal(multiply(u,v),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[2,669]),
[iquote('0:Rew:2.0,669.0')] ).
cnf(676,plain,
( ~ equal(multiply(a4,b4),multiply(a4,b4))
| ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[670,367]),
[iquote('0:Rew:670.0,367.0')] ).
cnf(714,plain,
equal(double_divide(multiply(u,multiply(inverse(v),multiply(multiply(inverse(u),double_divide(w,x)),w))),x),v),
inference(rew,[status(thm),theory(equality)],[670,339]),
[iquote('0:Rew:670.0,339.0')] ).
cnf(761,plain,
equal(double_divide(multiply(u,multiply(inverse(v),multiply(w,multiply(inverse(u),double_divide(w,x))))),x),v),
inference(rew,[status(thm),theory(equality)],[670,714]),
[iquote('0:Rew:670.0,714.0')] ).
cnf(776,plain,
( ~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1))
| ~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))) ),
inference(obv,[status(thm),theory(equality)],[676]),
[iquote('0:Obv:676.0')] ).
cnf(777,plain,
( ~ equal(double_divide(b1,inverse(b1)),double_divide(a1,inverse(a1)))
| ~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[670,776,661]),
[iquote('0:Rew:670.0,776.1,661.0,776.0,670.0,776.0,661.0,776.0,670.0,776.0')] ).
cnf(793,plain,
equal(multiply(inverse(u),double_divide(v,w)),double_divide(multiply(u,v),w)),
inference(spr,[status(thm),theory(equality)],[380,761]),
[iquote('0:SpR:380.0,761.0')] ).
cnf(882,plain,
equal(inverse(multiply(u,v)),double_divide(u,v)),
inference(spr,[status(thm),theory(equality)],[670,276]),
[iquote('0:SpR:670.0,276.0')] ).
cnf(892,plain,
equal(double_divide(u,v),double_divide(v,u)),
inference(rew,[status(thm),theory(equality)],[276,882]),
[iquote('0:Rew:276.0,882.0')] ).
cnf(1247,plain,
equal(multiply(inverse(u),v),double_divide(u,inverse(v))),
inference(spr,[status(thm),theory(equality)],[661,670]),
[iquote('0:SpR:661.0,670.0')] ).
cnf(1283,plain,
equal(double_divide(u,inverse(double_divide(v,w))),double_divide(multiply(u,v),w)),
inference(rew,[status(thm),theory(equality)],[1247,793]),
[iquote('0:Rew:1247.0,793.0')] ).
cnf(1314,plain,
equal(double_divide(multiply(u,v),w),double_divide(u,multiply(w,v))),
inference(rew,[status(thm),theory(equality)],[2,1283]),
[iquote('0:Rew:2.0,1283.0')] ).
cnf(2897,plain,
equal(inverse(double_divide(u,multiply(v,w))),multiply(v,multiply(u,w))),
inference(spr,[status(thm),theory(equality)],[1314,2]),
[iquote('0:SpR:1314.0,2.0')] ).
cnf(2898,plain,
equal(double_divide(u,multiply(v,w)),double_divide(v,multiply(u,w))),
inference(spr,[status(thm),theory(equality)],[1314,892]),
[iquote('0:SpR:1314.0,892.0')] ).
cnf(2974,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(w,v))),
inference(rew,[status(thm),theory(equality)],[2,2897]),
[iquote('0:Rew:2.0,2897.0')] ).
cnf(3568,plain,
equal(inverse(double_divide(u,multiply(v,w))),multiply(multiply(u,w),v)),
inference(spr,[status(thm),theory(equality)],[2898,2]),
[iquote('0:SpR:2898.0,2.0')] ).
cnf(3628,plain,
equal(multiply(multiply(u,v),w),multiply(multiply(w,v),u)),
inference(rew,[status(thm),theory(equality)],[2,3568]),
[iquote('0:Rew:2.0,3568.0')] ).
cnf(3629,plain,
equal(multiply(u,multiply(v,w)),multiply(v,multiply(u,w))),
inference(rew,[status(thm),theory(equality)],[2974,3628]),
[iquote('0:Rew:2974.0,3628.0,2974.0,3628.0')] ).
cnf(3642,plain,
( ~ equal(double_divide(b1,inverse(b1)),double_divide(a1,inverse(a1)))
| ~ equal(multiply(a3,multiply(c3,b3)),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[3629,777]),
[iquote('0:Rew:3629.0,777.1')] ).
cnf(3716,plain,
( ~ equal(double_divide(b1,inverse(b1)),double_divide(a1,inverse(a1)))
| ~ equal(multiply(a3,multiply(b3,c3)),multiply(a3,multiply(b3,c3))) ),
inference(rew,[status(thm),theory(equality)],[670,3642]),
[iquote('0:Rew:670.0,3642.1')] ).
cnf(3717,plain,
~ equal(double_divide(b1,inverse(b1)),double_divide(a1,inverse(a1))),
inference(obv,[status(thm),theory(equality)],[3716]),
[iquote('0:Obv:3716.1')] ).
cnf(3718,plain,
$false,
inference(unc,[status(thm)],[3717,246]),
[iquote('0:UnC:3717.0,246.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP105-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.06/0.12 % Command : run_spass %d %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 : 600
% 0.12/0.33 % DateTime : Mon Jun 13 11:56:57 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.80/1.04
% 0.80/1.04 SPASS V 3.9
% 0.80/1.04 SPASS beiseite: Proof found.
% 0.80/1.04 % SZS status Theorem
% 0.80/1.04 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.80/1.04 SPASS derived 2005 clauses, backtracked 0 clauses, performed 0 splits and kept 621 clauses.
% 0.80/1.04 SPASS allocated 67810 KBytes.
% 0.80/1.04 SPASS spent 0:00:00.69 on the problem.
% 0.80/1.04 0:00:00.03 for the input.
% 0.80/1.04 0:00:00.00 for the FLOTTER CNF translation.
% 0.80/1.04 0:00:00.02 for inferences.
% 0.80/1.04 0:00:00.00 for the backtracking.
% 0.80/1.04 0:00:00.62 for the reduction.
% 0.80/1.04
% 0.80/1.04
% 0.80/1.04 Here is a proof with depth 10, length 67 :
% 0.80/1.04 % SZS output start Refutation
% See solution above
% 0.88/1.06 Formulae used in the proof : single_axiom multiply prove_these_axioms
% 0.88/1.06
%------------------------------------------------------------------------------