%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP598-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n004.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 0.47s 0.69s
% Output : Refutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of clauses : 25 ( 25 unt; 0 nHn; 25 RR)
% Number of literals : 25 ( 0 equ; 1 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('GRP598-1.p',unknown),
[] ).
cnf(2,axiom,
equal(inverse(double_divide(u,v)),multiply(v,u)),
file('GRP598-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(multiply(multiply(inverse(b2),b2),a2),a2),
file('GRP598-1.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(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(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(996,plain,
equal(multiply(inverse(double_divide(u,inverse(u))),v),v),
inference(spr,[status(thm),theory(equality)],[955,940]),
[iquote('0:SpR:955.0,940.0')] ).
cnf(1003,plain,
equal(multiply(multiply(inverse(u),u),v),v),
inference(rew,[status(thm),theory(equality)],[2,996]),
[iquote('0:Rew:2.0,996.0')] ).
cnf(1004,plain,
$false,
inference(unc,[status(thm)],[1003,3]),
[iquote('0:UnC:1003.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP598-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n004.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Tue Jun 14 10:08:54 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.47/0.69
% 0.47/0.69 SPASS V 3.9
% 0.47/0.69 SPASS beiseite: Proof found.
% 0.47/0.69 % SZS status Theorem
% 0.47/0.69 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.47/0.69 SPASS derived 792 clauses, backtracked 0 clauses, performed 0 splits and kept 391 clauses.
% 0.47/0.69 SPASS allocated 65506 KBytes.
% 0.47/0.69 SPASS spent 0:00:00.31 on the problem.
% 0.47/0.69 0:00:00.03 for the input.
% 0.47/0.69 0:00:00.00 for the FLOTTER CNF translation.
% 0.47/0.69 0:00:00.01 for inferences.
% 0.47/0.69 0:00:00.00 for the backtracking.
% 0.47/0.69 0:00:00.25 for the reduction.
% 0.47/0.69
% 0.47/0.69
% 0.47/0.69 Here is a proof with depth 10, length 25 :
% 0.47/0.69 % SZS output start Refutation
% See solution above
% 0.47/0.69 Formulae used in the proof : single_axiom multiply prove_these_axioms_2
% 0.47/0.69
%------------------------------------------------------------------------------