TSTP Solution File: GRP616-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP616-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 11:48:18 EDT 2022
% Result : Unsatisfiable 0.83s 1.04s
% Output : Refutation 0.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 3
% Syntax : Number of clauses : 47 ( 47 unt; 0 nHn; 47 RR)
% Number of literals : 47 ( 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(inverse(double_divide(inverse(double_divide(u,inverse(v))),w)),double_divide(u,w)),v),
file('GRP616-1.p',unknown),
[] ).
cnf(2,axiom,
equal(inverse(double_divide(u,v)),multiply(v,u)),
file('GRP616-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(multiply(b,a),multiply(a,b)),
file('GRP616-1.p',unknown),
[] ).
cnf(4,plain,
equal(double_divide(multiply(u,multiply(inverse(v),w)),double_divide(w,u)),v),
inference(rew,[status(thm),theory(equality)],[2,1]),
[iquote('0:Rew:2.0,1.0,2.0,1.0')] ).
cnf(6,plain,
equal(multiply(double_divide(u,v),multiply(v,multiply(inverse(w),u))),inverse(w)),
inference(spr,[status(thm),theory(equality)],[4,2]),
[iquote('0:SpR:4.0,2.0')] ).
cnf(7,plain,
equal(double_divide(multiply(double_divide(u,v),multiply(inverse(w),multiply(v,multiply(inverse(x),u)))),x),w),
inference(spr,[status(thm),theory(equality)],[4]),
[iquote('0:SpR:4.0,4.0')] ).
cnf(9,plain,
equal(double_divide(multiply(u,multiply(multiply(v,w),x)),double_divide(x,u)),double_divide(w,v)),
inference(spr,[status(thm),theory(equality)],[2,4]),
[iquote('0:SpR:2.0,4.0')] ).
cnf(14,plain,
equal(multiply(u,multiply(double_divide(v,w),multiply(inverse(x),multiply(w,multiply(inverse(u),v))))),inverse(x)),
inference(spr,[status(thm),theory(equality)],[4,6]),
[iquote('0:SpR:4.0,6.0')] ).
cnf(80,plain,
equal(double_divide(multiply(u,multiply(inverse(v),multiply(double_divide(w,x),multiply(inverse(y),multiply(x,multiply(inverse(u),w)))))),y),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(81,plain,
equal(double_divide(multiply(double_divide(u,v),multiply(inverse(w),multiply(double_divide(x,y),multiply(inverse(z),multiply(y,multiply(multiply(v,u),x)))))),z),w),
inference(spr,[status(thm),theory(equality)],[9,7]),
[iquote('0:SpR:9.0,7.0')] ).
cnf(147,plain,
equal(double_divide(multiply(double_divide(multiply(u,multiply(inverse(inverse(v)),w)),double_divide(w,u)),inverse(x)),x),v),
inference(spr,[status(thm),theory(equality)],[14,7]),
[iquote('0:SpR:14.0,7.0')] ).
cnf(148,plain,
equal(multiply(u,multiply(double_divide(multiply(v,multiply(inverse(inverse(w)),x)),double_divide(x,v)),inverse(u))),inverse(w)),
inference(spr,[status(thm),theory(equality)],[14]),
[iquote('0:SpR:14.0,14.0')] ).
cnf(170,plain,
equal(double_divide(multiply(inverse(u),inverse(v)),v),u),
inference(rew,[status(thm),theory(equality)],[4,147]),
[iquote('0:Rew:4.0,147.0')] ).
cnf(171,plain,
equal(multiply(u,multiply(inverse(v),inverse(u))),inverse(v)),
inference(rew,[status(thm),theory(equality)],[4,148]),
[iquote('0:Rew:4.0,148.0')] ).
cnf(230,plain,
equal(double_divide(multiply(inverse(u),multiply(v,w)),double_divide(w,v)),u),
inference(spr,[status(thm),theory(equality)],[2,170]),
[iquote('0:SpR:2.0,170.0')] ).
cnf(242,plain,
equal(double_divide(inverse(u),double_divide(inverse(v),v)),u),
inference(spr,[status(thm),theory(equality)],[171,4]),
[iquote('0:SpR:171.0,4.0')] ).
cnf(244,plain,
equal(multiply(double_divide(inverse(u),u),inverse(v)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[171,6]),
[iquote('0:SpR:171.0,6.0')] ).
cnf(274,plain,
equal(double_divide(multiply(u,v),double_divide(inverse(w),w)),double_divide(v,u)),
inference(spr,[status(thm),theory(equality)],[2,242]),
[iquote('0:SpR:2.0,242.0')] ).
cnf(427,plain,
equal(double_divide(inverse(u),double_divide(inverse(inverse(v)),inverse(u))),v),
inference(spr,[status(thm),theory(equality)],[171,230]),
[iquote('0:SpR:171.0,230.0')] ).
cnf(464,plain,
equal(double_divide(inverse(u),double_divide(inverse(multiply(v,w)),inverse(u))),double_divide(w,v)),
inference(spr,[status(thm),theory(equality)],[2,427]),
[iquote('0:SpR:2.0,427.0')] ).
cnf(720,plain,
equal(double_divide(multiply(u,inverse(u)),inverse(v)),v),
inference(spr,[status(thm),theory(equality)],[274,230]),
[iquote('0:SpR:274.0,230.0')] ).
cnf(769,plain,
equal(multiply(inverse(u),multiply(v,inverse(v))),inverse(u)),
inference(spr,[status(thm),theory(equality)],[720,2]),
[iquote('0:SpR:720.0,2.0')] ).
cnf(770,plain,
equal(multiply(u,multiply(inverse(u),multiply(inverse(v),multiply(w,inverse(w))))),inverse(v)),
inference(spr,[status(thm),theory(equality)],[720,6]),
[iquote('0:SpR:720.0,6.0')] ).
cnf(776,plain,
equal(double_divide(multiply(inverse(u),multiply(inverse(v),multiply(w,inverse(w)))),u),v),
inference(spr,[status(thm),theory(equality)],[720,4]),
[iquote('0:SpR:720.0,4.0')] ).
cnf(793,plain,
equal(double_divide(multiply(inverse(u),inverse(v)),u),v),
inference(rew,[status(thm),theory(equality)],[769,776]),
[iquote('0:Rew:769.0,776.0')] ).
cnf(797,plain,
equal(multiply(u,multiply(inverse(u),inverse(v))),inverse(v)),
inference(rew,[status(thm),theory(equality)],[769,770]),
[iquote('0:Rew:769.0,770.0')] ).
cnf(825,plain,
equal(double_divide(multiply(inverse(u),multiply(double_divide(v,w),multiply(inverse(double_divide(inverse(x),x)),multiply(w,multiply(inverse(y),v))))),y),u),
inference(spr,[status(thm),theory(equality)],[80,274]),
[iquote('0:SpR:80.0,274.0')] ).
cnf(857,plain,
equal(double_divide(multiply(inverse(u),multiply(double_divide(v,w),multiply(multiply(x,inverse(x)),multiply(w,multiply(inverse(y),v))))),y),u),
inference(rew,[status(thm),theory(equality)],[2,825]),
[iquote('0:Rew:2.0,825.0')] ).
cnf(891,plain,
equal(inverse(inverse(u)),u),
inference(spr,[status(thm),theory(equality)],[793,720]),
[iquote('0:SpR:793.0,720.0')] ).
cnf(897,plain,
equal(double_divide(inverse(u),double_divide(v,inverse(u))),v),
inference(rew,[status(thm),theory(equality)],[891,427]),
[iquote('0:Rew:891.0,427.0')] ).
cnf(961,plain,
equal(inverse(multiply(u,v)),double_divide(v,u)),
inference(rew,[status(thm),theory(equality)],[897,464]),
[iquote('0:Rew:897.0,464.0')] ).
cnf(1016,plain,
equal(double_divide(multiply(u,multiply(v,w)),double_divide(w,u)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[891,4]),
[iquote('0:SpR:891.0,4.0')] ).
cnf(1019,plain,
equal(multiply(u,multiply(v,inverse(u))),v),
inference(spr,[status(thm),theory(equality)],[891,171]),
[iquote('0:SpR:891.0,171.0')] ).
cnf(1021,plain,
equal(multiply(double_divide(inverse(u),u),v),v),
inference(spr,[status(thm),theory(equality)],[891,244]),
[iquote('0:SpR:891.0,244.0')] ).
cnf(1082,plain,
equal(multiply(inverse(u),multiply(v,u)),v),
inference(spr,[status(thm),theory(equality)],[891,1019]),
[iquote('0:SpR:891.0,1019.0')] ).
cnf(1131,plain,
equal(multiply(inverse(multiply(u,v)),u),inverse(v)),
inference(spr,[status(thm),theory(equality)],[1082]),
[iquote('0:SpR:1082.0,1082.0')] ).
cnf(1139,plain,
equal(multiply(double_divide(u,v),v),inverse(u)),
inference(rew,[status(thm),theory(equality)],[961,1131]),
[iquote('0:Rew:961.0,1131.0')] ).
cnf(1195,plain,
equal(multiply(inverse(u),multiply(v,multiply(multiply(w,x),y))),double_divide(multiply(double_divide(x,w),double_divide(y,v)),u)),
inference(spr,[status(thm),theory(equality)],[1082,81]),
[iquote('0:SpR:1082.0,81.0')] ).
cnf(1202,plain,
equal(double_divide(double_divide(multiply(double_divide(inverse(u),u),double_divide(multiply(v,multiply(inverse(w),x)),double_divide(x,v))),y),w),y),
inference(rew,[status(thm),theory(equality)],[1195,857]),
[iquote('0:Rew:1195.0,857.0')] ).
cnf(1244,plain,
equal(double_divide(double_divide(double_divide(multiply(u,multiply(inverse(v),w)),double_divide(w,u)),x),v),x),
inference(rew,[status(thm),theory(equality)],[1021,1202]),
[iquote('0:Rew:1021.0,1202.0')] ).
cnf(1245,plain,
equal(double_divide(double_divide(inverse(inverse(u)),v),u),v),
inference(rew,[status(thm),theory(equality)],[1016,1244]),
[iquote('0:Rew:1016.0,1244.0')] ).
cnf(1246,plain,
equal(double_divide(double_divide(u,v),u),v),
inference(rew,[status(thm),theory(equality)],[891,1245]),
[iquote('0:Rew:891.0,1245.0')] ).
cnf(1347,plain,
equal(multiply(inverse(u),inverse(v)),double_divide(v,u)),
inference(spr,[status(thm),theory(equality)],[1139,1082]),
[iquote('0:SpR:1139.0,1082.0')] ).
cnf(1375,plain,
equal(multiply(u,double_divide(v,u)),inverse(v)),
inference(rew,[status(thm),theory(equality)],[1347,797]),
[iquote('0:Rew:1347.0,797.0')] ).
cnf(1674,plain,
equal(inverse(double_divide(u,v)),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[1246,1375]),
[iquote('0:SpR:1246.0,1375.0')] ).
cnf(1675,plain,
equal(multiply(u,v),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[2,1674]),
[iquote('0:Rew:2.0,1674.0')] ).
cnf(1676,plain,
$false,
inference(unc,[status(thm)],[1675,3]),
[iquote('0:UnC:1675.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : GRP616-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.07/0.14 % Command : run_spass %d %s
% 0.14/0.36 % Computer : n027.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 06:26:03 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.83/1.04
% 0.83/1.04 SPASS V 3.9
% 0.83/1.04 SPASS beiseite: Proof found.
% 0.83/1.04 % SZS status Theorem
% 0.83/1.04 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.83/1.04 SPASS derived 1208 clauses, backtracked 0 clauses, performed 0 splits and kept 579 clauses.
% 0.83/1.04 SPASS allocated 67033 KBytes.
% 0.83/1.04 SPASS spent 0:00:00.65 on the problem.
% 0.83/1.04 0:00:00.03 for the input.
% 0.83/1.04 0:00:00.00 for the FLOTTER CNF translation.
% 0.83/1.04 0:00:00.01 for inferences.
% 0.83/1.04 0:00:00.00 for the backtracking.
% 0.83/1.04 0:00:00.57 for the reduction.
% 0.83/1.04
% 0.83/1.04
% 0.83/1.04 Here is a proof with depth 12, length 47 :
% 0.83/1.04 % SZS output start Refutation
% See solution above
% 0.83/1.04 Formulae used in the proof : single_axiom multiply prove_these_axioms_4
% 0.83/1.04
%------------------------------------------------------------------------------