TSTP Solution File: GRP602-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP602-1 : 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 11:48:14 EDT 2022
% Result : Unsatisfiable 0.48s 0.66s
% Output : Refutation 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 3
% Syntax : Number of clauses : 38 ( 38 unt; 0 nHn; 38 RR)
% Number of literals : 38 ( 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 : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(inverse(double_divide(inverse(double_divide(u,inverse(double_divide(v,double_divide(u,w))))),w)),v),
file('GRP602-1.p',unknown),
[] ).
cnf(2,axiom,
equal(inverse(double_divide(u,v)),multiply(v,u)),
file('GRP602-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(multiply(multiply(inverse(b2),b2),a2),a2),
file('GRP602-1.p',unknown),
[] ).
cnf(4,plain,
equal(multiply(u,multiply(multiply(double_divide(v,u),w),v)),w),
inference(rew,[status(thm),theory(equality)],[2,1]),
[iquote('0:Rew:2.0,1.0,2.0,1.0,2.0,1.0')] ).
cnf(6,plain,
equal(multiply(multiply(double_divide(u,double_divide(v,w)),x),u),multiply(w,multiply(x,v))),
inference(spr,[status(thm),theory(equality)],[4]),
[iquote('0:SpR:4.0,4.0')] ).
cnf(8,plain,
equal(multiply(double_divide(u,v),multiply(v,multiply(w,u))),w),
inference(spr,[status(thm),theory(equality)],[6,4]),
[iquote('0:SpR:6.0,4.0')] ).
cnf(12,plain,
equal(multiply(double_divide(multiply(u,multiply(v,w)),x),multiply(x,v)),double_divide(w,u)),
inference(spr,[status(thm),theory(equality)],[8]),
[iquote('0:SpR:8.0,8.0')] ).
cnf(15,plain,
equal(multiply(double_divide(multiply(u,v),double_divide(v,w)),u),w),
inference(spr,[status(thm),theory(equality)],[8]),
[iquote('0:SpR:8.0,8.0')] ).
cnf(18,plain,
equal(multiply(double_divide(multiply(multiply(double_divide(u,v),w),u),x),multiply(x,w)),v),
inference(spr,[status(thm),theory(equality)],[4,8]),
[iquote('0:SpR:4.0,8.0')] ).
cnf(33,plain,
equal(double_divide(u,multiply(double_divide(multiply(v,u),w),v)),w),
inference(spr,[status(thm),theory(equality)],[12,15]),
[iquote('0:SpR:12.0,15.0')] ).
cnf(58,plain,
equal(multiply(multiply(double_divide(multiply(u,v),w),u),v),inverse(w)),
inference(spr,[status(thm),theory(equality)],[33,2]),
[iquote('0:SpR:33.0,2.0')] ).
cnf(65,plain,
equal(multiply(double_divide(multiply(u,multiply(v,w)),x),u),double_divide(w,multiply(x,v))),
inference(spr,[status(thm),theory(equality)],[33]),
[iquote('0:SpR:33.0,33.0')] ).
cnf(72,plain,
equal(double_divide(multiply(u,v),double_divide(v,multiply(w,u))),w),
inference(spr,[status(thm),theory(equality)],[12,33]),
[iquote('0:SpR:12.0,33.0')] ).
cnf(74,plain,
equal(multiply(double_divide(u,multiply(v,w)),multiply(w,u)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[72,2]),
[iquote('0:SpR:72.0,2.0')] ).
cnf(113,plain,
equal(multiply(double_divide(multiply(multiply(double_divide(u,v),w),u),double_divide(multiply(w,x),double_divide(x,y))),y),v),
inference(spr,[status(thm),theory(equality)],[15,18]),
[iquote('0:SpR:15.0,18.0')] ).
cnf(137,plain,
equal(multiply(double_divide(u,multiply(double_divide(multiply(v,multiply(w,u)),x),v)),inverse(x)),w),
inference(spr,[status(thm),theory(equality)],[58,8]),
[iquote('0:SpR:58.0,8.0')] ).
cnf(157,plain,
equal(multiply(double_divide(u,double_divide(u,multiply(v,w))),inverse(v)),w),
inference(rew,[status(thm),theory(equality)],[65,137]),
[iquote('0:Rew:65.0,137.0')] ).
cnf(176,plain,
equal(multiply(double_divide(u,inverse(v)),multiply(multiply(w,x),u)),inverse(double_divide(x,multiply(v,w)))),
inference(spr,[status(thm),theory(equality)],[74]),
[iquote('0:SpR:74.0,74.0')] ).
cnf(197,plain,
equal(multiply(double_divide(u,inverse(v)),multiply(multiply(w,x),u)),multiply(multiply(v,w),x)),
inference(rew,[status(thm),theory(equality)],[2,176]),
[iquote('0:Rew:2.0,176.0')] ).
cnf(213,plain,
equal(double_divide(multiply(inverse(u),v),multiply(u,w)),double_divide(v,w)),
inference(spr,[status(thm),theory(equality)],[157,33]),
[iquote('0:SpR:157.0,33.0')] ).
cnf(224,plain,
equal(multiply(double_divide(u,double_divide(u,v)),inverse(double_divide(w,x))),multiply(x,multiply(v,w))),
inference(spr,[status(thm),theory(equality)],[8,157]),
[iquote('0:SpR:8.0,157.0')] ).
cnf(227,plain,
equal(multiply(double_divide(u,double_divide(u,inverse(v))),inverse(multiply(double_divide(multiply(w,x),v),w))),x),
inference(spr,[status(thm),theory(equality)],[58,157]),
[iquote('0:SpR:58.0,157.0')] ).
cnf(232,plain,
equal(multiply(double_divide(u,double_divide(u,v)),multiply(w,x)),multiply(w,multiply(v,x))),
inference(rew,[status(thm),theory(equality)],[2,224]),
[iquote('0:Rew:2.0,224.0')] ).
cnf(415,plain,
equal(double_divide(multiply(inverse(double_divide(u,v)),w),x),double_divide(w,multiply(v,multiply(x,u)))),
inference(spr,[status(thm),theory(equality)],[8,213]),
[iquote('0:SpR:8.0,213.0')] ).
cnf(428,plain,
equal(double_divide(multiply(multiply(u,v),w),x),double_divide(w,multiply(u,multiply(x,v)))),
inference(rew,[status(thm),theory(equality)],[2,415]),
[iquote('0:Rew:2.0,415.0')] ).
cnf(431,plain,
equal(multiply(double_divide(u,multiply(double_divide(u,v),multiply(double_divide(multiply(w,x),double_divide(x,y)),w))),y),v),
inference(rew,[status(thm),theory(equality)],[428,113]),
[iquote('0:Rew:428.0,113.0')] ).
cnf(467,plain,
equal(multiply(double_divide(u,multiply(double_divide(u,v),w)),w),v),
inference(rew,[status(thm),theory(equality)],[15,431]),
[iquote('0:Rew:15.0,431.0')] ).
cnf(506,plain,
equal(multiply(double_divide(multiply(u,v),w),u),double_divide(v,w)),
inference(spr,[status(thm),theory(equality)],[467,33]),
[iquote('0:SpR:467.0,33.0')] ).
cnf(522,plain,
equal(multiply(double_divide(u,inverse(v)),multiply(w,u)),multiply(v,w)),
inference(spr,[status(thm),theory(equality)],[74,467]),
[iquote('0:SpR:74.0,467.0')] ).
cnf(524,plain,
equal(double_divide(u,double_divide(u,v)),v),
inference(rew,[status(thm),theory(equality)],[506,33]),
[iquote('0:Rew:506.0,33.0')] ).
cnf(540,plain,
equal(multiply(double_divide(u,double_divide(u,inverse(v))),inverse(double_divide(w,v))),w),
inference(rew,[status(thm),theory(equality)],[506,227]),
[iquote('0:Rew:506.0,227.0')] ).
cnf(557,plain,
equal(multiply(u,multiply(v,w)),multiply(v,multiply(u,w))),
inference(rew,[status(thm),theory(equality)],[524,232]),
[iquote('0:Rew:524.0,232.0')] ).
cnf(685,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(rew,[status(thm),theory(equality)],[522,197]),
[iquote('0:Rew:522.0,197.0')] ).
cnf(688,plain,
~ equal(multiply(inverse(b2),multiply(b2,a2)),a2),
inference(rew,[status(thm),theory(equality)],[685,3]),
[iquote('0:Rew:685.0,3.0')] ).
cnf(711,plain,
~ equal(multiply(b2,multiply(inverse(b2),a2)),a2),
inference(rew,[status(thm),theory(equality)],[557,688]),
[iquote('0:Rew:557.0,688.0')] ).
cnf(735,plain,
equal(multiply(double_divide(u,double_divide(u,inverse(v))),multiply(v,w)),w),
inference(rew,[status(thm),theory(equality)],[2,540]),
[iquote('0:Rew:2.0,540.0')] ).
cnf(736,plain,
equal(multiply(u,multiply(inverse(u),v)),v),
inference(rew,[status(thm),theory(equality)],[557,735,524]),
[iquote('0:Rew:557.0,735.0,524.0,735.0')] ).
cnf(737,plain,
$false,
inference(unc,[status(thm)],[736,711]),
[iquote('0:UnC:736.0,711.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP602-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n028.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 : Mon Jun 13 23:07:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.48/0.66
% 0.48/0.66 SPASS V 3.9
% 0.48/0.66 SPASS beiseite: Proof found.
% 0.48/0.66 % SZS status Theorem
% 0.48/0.66 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.48/0.66 SPASS derived 632 clauses, backtracked 0 clauses, performed 0 splits and kept 420 clauses.
% 0.48/0.66 SPASS allocated 65151 KBytes.
% 0.48/0.66 SPASS spent 0:00:00.30 on the problem.
% 0.48/0.66 0:00:00.04 for the input.
% 0.48/0.66 0:00:00.00 for the FLOTTER CNF translation.
% 0.48/0.66 0:00:00.00 for inferences.
% 0.48/0.66 0:00:00.00 for the backtracking.
% 0.48/0.66 0:00:00.24 for the reduction.
% 0.48/0.66
% 0.48/0.66
% 0.48/0.66 Here is a proof with depth 8, length 38 :
% 0.48/0.66 % SZS output start Refutation
% See solution above
% 0.48/0.66 Formulae used in the proof : single_axiom multiply prove_these_axioms_2
% 0.48/0.66
%------------------------------------------------------------------------------