TSTP Solution File: GRP597-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP597-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 11:48:13 EDT 2022
% Result : Unsatisfiable 0.58s 0.74s
% Output : Refutation 0.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 3
% Syntax : Number of clauses : 36 ( 36 unt; 0 nHn; 36 RR)
% Number of literals : 36 ( 0 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(double_divide(double_divide(u,v),inverse(double_divide(u,inverse(double_divide(inverse(w),v))))),w),
file('GRP597-1.p',unknown),
[] ).
cnf(2,axiom,
equal(inverse(double_divide(u,v)),multiply(v,u)),
file('GRP597-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1)),
file('GRP597-1.p',unknown),
[] ).
cnf(4,plain,
equal(double_divide(double_divide(u,v),multiply(multiply(v,inverse(w)),u)),w),
inference(rew,[status(thm),theory(equality)],[2,1]),
[iquote('0:Rew:2.0,1.0,2.0,1.0')] ).
cnf(6,plain,
equal(multiply(multiply(multiply(u,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(u,multiply(multiply(multiply(multiply(v,inverse(u)),w),inverse(x)),double_divide(w,v))),x),
inference(spr,[status(thm),theory(equality)],[4]),
[iquote('0:SpR:4.0,4.0')] ).
cnf(13,plain,
equal(multiply(multiply(multiply(multiply(multiply(u,inverse(v)),w),inverse(x)),double_divide(w,u)),v),inverse(x)),
inference(spr,[status(thm),theory(equality)],[4,6]),
[iquote('0:SpR:4.0,6.0')] ).
cnf(145,plain,
equal(double_divide(u,multiply(inverse(u),double_divide(double_divide(v,w),multiply(multiply(w,inverse(inverse(x))),v)))),x),
inference(spr,[status(thm),theory(equality)],[13,7]),
[iquote('0:SpR:13.0,7.0')] ).
cnf(146,plain,
equal(multiply(multiply(inverse(u),double_divide(double_divide(v,w),multiply(multiply(w,inverse(inverse(x))),v))),u),inverse(x)),
inference(spr,[status(thm),theory(equality)],[13]),
[iquote('0:SpR:13.0,13.0')] ).
cnf(170,plain,
equal(double_divide(u,multiply(inverse(u),inverse(v))),v),
inference(rew,[status(thm),theory(equality)],[4,145]),
[iquote('0:Rew:4.0,145.0')] ).
cnf(171,plain,
equal(multiply(multiply(inverse(u),inverse(v)),u),inverse(v)),
inference(rew,[status(thm),theory(equality)],[4,146]),
[iquote('0:Rew:4.0,146.0')] ).
cnf(231,plain,
equal(double_divide(double_divide(u,v),multiply(multiply(v,u),inverse(w))),w),
inference(spr,[status(thm),theory(equality)],[2,170]),
[iquote('0:SpR:2.0,170.0')] ).
cnf(240,plain,
equal(double_divide(double_divide(u,inverse(u)),inverse(v)),v),
inference(spr,[status(thm),theory(equality)],[171,4]),
[iquote('0:SpR:171.0,4.0')] ).
cnf(242,plain,
equal(multiply(inverse(u),double_divide(v,inverse(v))),inverse(u)),
inference(spr,[status(thm),theory(equality)],[171,6]),
[iquote('0:SpR:171.0,6.0')] ).
cnf(273,plain,
equal(double_divide(double_divide(u,inverse(u)),multiply(v,w)),double_divide(w,v)),
inference(spr,[status(thm),theory(equality)],[2,240]),
[iquote('0:SpR:2.0,240.0')] ).
cnf(416,plain,
equal(double_divide(double_divide(inverse(u),inverse(inverse(v))),inverse(u)),v),
inference(spr,[status(thm),theory(equality)],[171,231]),
[iquote('0:SpR:171.0,231.0')] ).
cnf(464,plain,
equal(double_divide(double_divide(inverse(u),inverse(multiply(v,w))),inverse(u)),double_divide(w,v)),
inference(spr,[status(thm),theory(equality)],[2,416]),
[iquote('0:SpR:2.0,416.0')] ).
cnf(635,plain,
equal(double_divide(inverse(u),multiply(inverse(v),v)),u),
inference(spr,[status(thm),theory(equality)],[273,231]),
[iquote('0:SpR:273.0,231.0')] ).
cnf(694,plain,
equal(multiply(multiply(inverse(u),u),inverse(v)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[635,2]),
[iquote('0:SpR:635.0,2.0')] ).
cnf(695,plain,
equal(double_divide(u,multiply(multiply(multiply(inverse(v),v),inverse(w)),inverse(u))),w),
inference(spr,[status(thm),theory(equality)],[635,4]),
[iquote('0:SpR:635.0,4.0')] ).
cnf(717,plain,
equal(double_divide(u,multiply(inverse(v),inverse(u))),v),
inference(rew,[status(thm),theory(equality)],[694,695]),
[iquote('0:Rew:694.0,695.0')] ).
cnf(753,plain,
equal(inverse(inverse(u)),u),
inference(spr,[status(thm),theory(equality)],[717,635]),
[iquote('0:SpR:717.0,635.0')] ).
cnf(756,plain,
equal(double_divide(double_divide(inverse(u),v),inverse(u)),v),
inference(rew,[status(thm),theory(equality)],[753,416]),
[iquote('0:Rew:753.0,416.0')] ).
cnf(813,plain,
equal(inverse(multiply(u,v)),double_divide(v,u)),
inference(rew,[status(thm),theory(equality)],[756,464]),
[iquote('0:Rew:756.0,464.0')] ).
cnf(940,plain,
equal(multiply(multiply(inverse(u),v),u),v),
inference(spr,[status(thm),theory(equality)],[753,171]),
[iquote('0:SpR:753.0,171.0')] ).
cnf(955,plain,
equal(multiply(u,double_divide(v,inverse(v))),u),
inference(spr,[status(thm),theory(equality)],[753,242]),
[iquote('0:SpR:753.0,242.0')] ).
cnf(994,plain,
equal(multiply(multiply(u,v),inverse(u)),v),
inference(spr,[status(thm),theory(equality)],[753,940]),
[iquote('0:SpR:753.0,940.0')] ).
cnf(1001,plain,
equal(multiply(u,double_divide(inverse(v),v)),u),
inference(spr,[status(thm),theory(equality)],[753,955]),
[iquote('0:SpR:753.0,955.0')] ).
cnf(1040,plain,
equal(multiply(u,inverse(multiply(v,u))),inverse(v)),
inference(spr,[status(thm),theory(equality)],[994]),
[iquote('0:SpR:994.0,994.0')] ).
cnf(1049,plain,
equal(multiply(u,double_divide(u,v)),inverse(v)),
inference(rew,[status(thm),theory(equality)],[813,1040]),
[iquote('0:Rew:813.0,1040.0')] ).
cnf(1053,plain,
equal(multiply(inverse(u),u),double_divide(inverse(v),v)),
inference(spr,[status(thm),theory(equality)],[1001,940]),
[iquote('0:SpR:1001.0,940.0')] ).
cnf(1078,plain,
equal(multiply(inverse(u),v),double_divide(inverse(v),u)),
inference(spr,[status(thm),theory(equality)],[1049,940]),
[iquote('0:SpR:1049.0,940.0')] ).
cnf(1087,plain,
~ equal(multiply(inverse(a1),a1),double_divide(inverse(b1),b1)),
inference(rew,[status(thm),theory(equality)],[1078,3]),
[iquote('0:Rew:1078.0,3.0')] ).
cnf(1107,plain,
equal(double_divide(inverse(u),u),double_divide(inverse(v),v)),
inference(rew,[status(thm),theory(equality)],[1078,1053]),
[iquote('0:Rew:1078.0,1053.0')] ).
cnf(1204,plain,
~ equal(double_divide(inverse(b1),b1),double_divide(inverse(a1),a1)),
inference(rew,[status(thm),theory(equality)],[1078,1087]),
[iquote('0:Rew:1078.0,1087.0')] ).
cnf(1205,plain,
$false,
inference(unc,[status(thm)],[1204,1107]),
[iquote('0:UnC:1204.0,1107.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP597-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n028.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 04:22:22 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.58/0.74
% 0.58/0.74 SPASS V 3.9
% 0.58/0.74 SPASS beiseite: Proof found.
% 0.58/0.74 % SZS status Theorem
% 0.58/0.74 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.58/0.74 SPASS derived 970 clauses, backtracked 0 clauses, performed 0 splits and kept 503 clauses.
% 0.58/0.74 SPASS allocated 66258 KBytes.
% 0.58/0.74 SPASS spent 0:00:00.39 on the problem.
% 0.58/0.74 0:00:00.03 for the input.
% 0.58/0.74 0:00:00.00 for the FLOTTER CNF translation.
% 0.58/0.74 0:00:00.01 for inferences.
% 0.58/0.74 0:00:00.00 for the backtracking.
% 0.58/0.74 0:00:00.32 for the reduction.
% 0.58/0.74
% 0.58/0.74
% 0.58/0.74 Here is a proof with depth 12, length 36 :
% 0.58/0.74 % SZS output start Refutation
% See solution above
% 0.58/0.74 Formulae used in the proof : single_axiom multiply prove_these_axioms_1
% 0.58/0.74
%------------------------------------------------------------------------------