TSTP Solution File: GRP595-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP595-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 11:48:12 EDT 2022
% Result : Unsatisfiable 0.46s 0.67s
% Output : Refutation 0.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of clauses : 30 ( 30 unt; 0 nHn; 30 RR)
% Number of literals : 30 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 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(double_divide(u,v),inverse(double_divide(u,inverse(double_divide(w,v)))))),w),
file('GRP595-1.p',unknown),
[] ).
cnf(2,axiom,
equal(inverse(double_divide(u,v)),multiply(v,u)),
file('GRP595-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))),
file('GRP595-1.p',unknown),
[] ).
cnf(4,plain,
equal(multiply(multiply(multiply(u,v),w),double_divide(w,u)),v),
inference(rew,[status(thm),theory(equality)],[2,1]),
[iquote('0:Rew:2.0,1.0,2.0,1.0,2.0,1.0')] ).
cnf(6,plain,
equal(multiply(multiply(u,v),double_divide(v,multiply(multiply(w,u),x))),double_divide(x,w)),
inference(spr,[status(thm),theory(equality)],[4]),
[iquote('0:SpR:4.0,4.0')] ).
cnf(7,plain,
equal(multiply(u,double_divide(double_divide(v,w),multiply(w,u))),v),
inference(spr,[status(thm),theory(equality)],[4]),
[iquote('0:SpR:4.0,4.0')] ).
cnf(18,plain,
equal(double_divide(multiply(u,double_divide(v,multiply(w,u))),w),v),
inference(spr,[status(thm),theory(equality)],[6,7]),
[iquote('0:SpR:6.0,7.0')] ).
cnf(32,plain,
equal(multiply(u,multiply(v,double_divide(w,multiply(u,v)))),inverse(w)),
inference(spr,[status(thm),theory(equality)],[18,2]),
[iquote('0:SpR:18.0,2.0')] ).
cnf(37,plain,
equal(multiply(u,double_divide(v,multiply(multiply(w,x),u))),double_divide(multiply(x,v),w)),
inference(spr,[status(thm),theory(equality)],[18]),
[iquote('0:SpR:18.0,18.0')] ).
cnf(42,plain,
equal(double_divide(double_divide(multiply(u,v),w),multiply(w,u)),v),
inference(spr,[status(thm),theory(equality)],[6,18]),
[iquote('0:SpR:6.0,18.0')] ).
cnf(55,plain,
equal(double_divide(double_divide(u,v),multiply(v,multiply(multiply(w,u),x))),double_divide(x,w)),
inference(spr,[status(thm),theory(equality)],[4,42]),
[iquote('0:SpR:4.0,42.0')] ).
cnf(67,plain,
equal(multiply(inverse(u),double_divide(multiply(v,double_divide(u,multiply(multiply(w,x),v))),w)),x),
inference(spr,[status(thm),theory(equality)],[32,4]),
[iquote('0:SpR:32.0,4.0')] ).
cnf(76,plain,
equal(multiply(inverse(u),double_divide(double_divide(multiply(v,u),w),w)),v),
inference(rew,[status(thm),theory(equality)],[37,67]),
[iquote('0:Rew:37.0,67.0')] ).
cnf(142,plain,
equal(double_divide(multiply(u,v),multiply(w,inverse(v))),double_divide(u,w)),
inference(spr,[status(thm),theory(equality)],[76,18]),
[iquote('0:SpR:76.0,18.0')] ).
cnf(143,plain,
equal(inverse(double_divide(multiply(u,v),multiply(w,inverse(v)))),multiply(w,u)),
inference(spr,[status(thm),theory(equality)],[76,32]),
[iquote('0:SpR:76.0,32.0')] ).
cnf(149,plain,
equal(multiply(inverse(double_divide(u,v)),double_divide(double_divide(w,x),x)),multiply(multiply(v,w),u)),
inference(spr,[status(thm),theory(equality)],[4,76]),
[iquote('0:SpR:4.0,76.0')] ).
cnf(154,plain,
equal(multiply(multiply(u,v),double_divide(double_divide(multiply(w,double_divide(v,u)),x),x)),w),
inference(spr,[status(thm),theory(equality)],[2,76]),
[iquote('0:SpR:2.0,76.0')] ).
cnf(156,plain,
equal(multiply(multiply(u,inverse(v)),multiply(w,v)),multiply(u,w)),
inference(rew,[status(thm),theory(equality)],[2,143]),
[iquote('0:Rew:2.0,143.0')] ).
cnf(159,plain,
equal(multiply(multiply(u,v),double_divide(double_divide(w,x),x)),multiply(multiply(u,w),v)),
inference(rew,[status(thm),theory(equality)],[2,149]),
[iquote('0:Rew:2.0,149.0')] ).
cnf(161,plain,
equal(multiply(multiply(u,multiply(v,double_divide(w,u))),w),v),
inference(rew,[status(thm),theory(equality)],[159,154]),
[iquote('0:Rew:159.0,154.0')] ).
cnf(217,plain,
equal(double_divide(u,multiply(v,inverse(double_divide(w,x)))),double_divide(multiply(multiply(x,u),w),v)),
inference(spr,[status(thm),theory(equality)],[4,142]),
[iquote('0:SpR:4.0,142.0')] ).
cnf(225,plain,
equal(double_divide(multiply(multiply(u,v),w),x),double_divide(v,multiply(x,multiply(u,w)))),
inference(rew,[status(thm),theory(equality)],[2,217]),
[iquote('0:Rew:2.0,217.0')] ).
cnf(254,plain,
equal(multiply(multiply(u,inverse(double_divide(v,w))),x),multiply(u,multiply(multiply(w,x),v))),
inference(spr,[status(thm),theory(equality)],[4,156]),
[iquote('0:SpR:4.0,156.0')] ).
cnf(267,plain,
equal(multiply(multiply(u,multiply(v,w)),x),multiply(u,multiply(multiply(v,x),w))),
inference(rew,[status(thm),theory(equality)],[2,254]),
[iquote('0:Rew:2.0,254.0')] ).
cnf(268,plain,
equal(multiply(u,multiply(multiply(v,w),double_divide(w,u))),v),
inference(rew,[status(thm),theory(equality)],[267,161]),
[iquote('0:Rew:267.0,161.0')] ).
cnf(398,plain,
equal(double_divide(multiply(multiply(multiply(u,v),double_divide(v,w)),double_divide(x,u)),w),x),
inference(spr,[status(thm),theory(equality)],[268,18]),
[iquote('0:SpR:268.0,18.0')] ).
cnf(433,plain,
equal(double_divide(double_divide(u,v),v),u),
inference(rew,[status(thm),theory(equality)],[55,398,225]),
[iquote('0:Rew:55.0,398.0,225.0,398.0')] ).
cnf(674,plain,
equal(inverse(double_divide(u,multiply(v,w))),multiply(v,multiply(w,u))),
inference(spr,[status(thm),theory(equality)],[433,32]),
[iquote('0:SpR:433.0,32.0')] ).
cnf(754,plain,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
inference(rew,[status(thm),theory(equality)],[2,674]),
[iquote('0:Rew:2.0,674.0')] ).
cnf(755,plain,
$false,
inference(unc,[status(thm)],[754,3]),
[iquote('0:UnC:754.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP595-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.14 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 13 11:55:12 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.46/0.67
% 0.46/0.67 SPASS V 3.9
% 0.46/0.67 SPASS beiseite: Proof found.
% 0.46/0.67 % SZS status Theorem
% 0.46/0.67 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.46/0.67 SPASS derived 702 clauses, backtracked 0 clauses, performed 0 splits and kept 467 clauses.
% 0.46/0.67 SPASS allocated 64929 KBytes.
% 0.46/0.67 SPASS spent 0:00:00.29 on the problem.
% 0.46/0.67 0:00:00.04 for the input.
% 0.46/0.67 0:00:00.00 for the FLOTTER CNF translation.
% 0.46/0.67 0:00:00.00 for inferences.
% 0.46/0.67 0:00:00.00 for the backtracking.
% 0.46/0.67 0:00:00.23 for the reduction.
% 0.46/0.67
% 0.46/0.67
% 0.46/0.67 Here is a proof with depth 7, length 30 :
% 0.46/0.67 % SZS output start Refutation
% See solution above
% 0.46/0.67 Formulae used in the proof : single_axiom multiply prove_these_axioms_3
% 0.46/0.67
%------------------------------------------------------------------------------