TSTP Solution File: GRP555-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP555-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n012.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 11:48:01 EDT 2022
% Result : Unsatisfiable 0.21s 0.48s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 3
% Syntax : Number of clauses : 35 ( 35 unt; 0 nHn; 35 RR)
% Number of literals : 35 ( 0 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 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(divide(divide(u,inverse(divide(v,divide(u,w)))),w),v),
file('GRP555-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,inverse(v)),multiply(u,v)),
file('GRP555-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3))),
file('GRP555-1.p',unknown),
[] ).
cnf(4,plain,
equal(divide(multiply(u,divide(v,divide(u,w))),w),v),
inference(rew,[status(thm),theory(equality)],[2,1]),
[iquote('0:Rew:2.0,1.0')] ).
cnf(6,plain,
equal(multiply(multiply(u,divide(v,divide(u,inverse(w)))),w),v),
inference(spr,[status(thm),theory(equality)],[4,2]),
[iquote('0:SpR:4.0,2.0')] ).
cnf(7,plain,
equal(divide(multiply(multiply(u,divide(v,divide(u,w))),divide(x,v)),w),x),
inference(spr,[status(thm),theory(equality)],[4]),
[iquote('0:SpR:4.0,4.0')] ).
cnf(8,plain,
equal(multiply(u,divide(v,divide(u,divide(w,x)))),divide(multiply(w,v),x)),
inference(spr,[status(thm),theory(equality)],[4]),
[iquote('0:SpR:4.0,4.0')] ).
cnf(11,plain,
equal(multiply(multiply(u,divide(v,multiply(u,w))),w),v),
inference(rew,[status(thm),theory(equality)],[2,6]),
[iquote('0:Rew:2.0,6.0')] ).
cnf(13,plain,
equal(multiply(multiply(multiply(u,divide(v,multiply(u,w))),divide(x,v)),w),x),
inference(spr,[status(thm),theory(equality)],[11]),
[iquote('0:SpR:11.0,11.0')] ).
cnf(15,plain,
equal(multiply(u,divide(v,divide(u,multiply(w,x)))),multiply(multiply(w,v),x)),
inference(spr,[status(thm),theory(equality)],[4,11]),
[iquote('0:SpR:4.0,11.0')] ).
cnf(35,plain,
equal(divide(divide(multiply(u,v),w),divide(u,w)),v),
inference(spr,[status(thm),theory(equality)],[8,4]),
[iquote('0:SpR:8.0,4.0')] ).
cnf(64,plain,
equal(divide(divide(multiply(u,v),inverse(w)),multiply(u,w)),v),
inference(spr,[status(thm),theory(equality)],[2,35]),
[iquote('0:SpR:2.0,35.0')] ).
cnf(72,plain,
equal(divide(multiply(multiply(u,v),w),multiply(u,w)),v),
inference(rew,[status(thm),theory(equality)],[2,64]),
[iquote('0:Rew:2.0,64.0')] ).
cnf(81,plain,
equal(divide(u,divide(v,multiply(v,divide(w,u)))),w),
inference(spr,[status(thm),theory(equality)],[72,7]),
[iquote('0:SpR:72.0,7.0')] ).
cnf(97,plain,
equal(divide(multiply(u,v),multiply(u,divide(w,x))),multiply(x,divide(v,w))),
inference(spr,[status(thm),theory(equality)],[81,8]),
[iquote('0:SpR:81.0,8.0')] ).
cnf(99,plain,
equal(divide(multiply(u,v),multiply(u,divide(v,w))),w),
inference(spr,[status(thm),theory(equality)],[81,4]),
[iquote('0:SpR:81.0,4.0')] ).
cnf(103,plain,
equal(multiply(u,divide(v,divide(u,w))),divide(multiply(x,v),divide(y,multiply(y,divide(w,x))))),
inference(spr,[status(thm),theory(equality)],[81,8]),
[iquote('0:SpR:81.0,8.0')] ).
cnf(105,plain,
equal(divide(inverse(u),divide(v,multiply(v,multiply(w,u)))),w),
inference(spr,[status(thm),theory(equality)],[2,81]),
[iquote('0:SpR:2.0,81.0')] ).
cnf(106,plain,
equal(divide(u,divide(v,multiply(v,w))),multiply(x,divide(w,divide(x,u)))),
inference(spr,[status(thm),theory(equality)],[4,81]),
[iquote('0:SpR:4.0,81.0')] ).
cnf(108,plain,
equal(divide(multiply(u,v),divide(w,multiply(w,x))),multiply(multiply(u,x),v)),
inference(spr,[status(thm),theory(equality)],[72,81]),
[iquote('0:SpR:72.0,81.0')] ).
cnf(112,plain,
equal(multiply(u,divide(v,v)),u),
inference(rew,[status(thm),theory(equality)],[97,99]),
[iquote('0:Rew:97.0,99.0')] ).
cnf(119,plain,
equal(multiply(u,divide(v,divide(u,w))),multiply(multiply(x,divide(w,x)),v)),
inference(rew,[status(thm),theory(equality)],[108,103]),
[iquote('0:Rew:108.0,103.0')] ).
cnf(139,plain,
equal(multiply(u,divide(v,u)),v),
inference(spr,[status(thm),theory(equality)],[11,13]),
[iquote('0:SpR:11.0,13.0')] ).
cnf(142,plain,
equal(multiply(u,divide(v,divide(u,w))),multiply(w,v)),
inference(rew,[status(thm),theory(equality)],[139,119]),
[iquote('0:Rew:139.0,119.0')] ).
cnf(146,plain,
equal(divide(u,divide(v,multiply(v,w))),multiply(u,w)),
inference(rew,[status(thm),theory(equality)],[142,106]),
[iquote('0:Rew:142.0,106.0')] ).
cnf(160,plain,
equal(multiply(multiply(u,v),w),multiply(multiply(u,w),v)),
inference(rew,[status(thm),theory(equality)],[142,15]),
[iquote('0:Rew:142.0,15.0')] ).
cnf(168,plain,
equal(multiply(inverse(u),multiply(v,u)),v),
inference(rew,[status(thm),theory(equality)],[146,105]),
[iquote('0:Rew:146.0,105.0')] ).
cnf(258,plain,
equal(multiply(inverse(divide(u,u)),v),v),
inference(spr,[status(thm),theory(equality)],[112,168]),
[iquote('0:SpR:112.0,168.0')] ).
cnf(345,plain,
equal(multiply(multiply(inverse(divide(u,u)),v),w),multiply(w,v)),
inference(spr,[status(thm),theory(equality)],[258,160]),
[iquote('0:SpR:258.0,160.0')] ).
cnf(362,plain,
equal(multiply(u,v),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[258,345]),
[iquote('0:Rew:258.0,345.0')] ).
cnf(366,plain,
~ equal(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(b3,c3))),
inference(rew,[status(thm),theory(equality)],[362,3]),
[iquote('0:Rew:362.0,3.0')] ).
cnf(394,plain,
equal(multiply(multiply(u,v),w),multiply(v,multiply(u,w))),
inference(spr,[status(thm),theory(equality)],[362,160]),
[iquote('0:SpR:362.0,160.0')] ).
cnf(397,plain,
equal(multiply(multiply(u,v),w),multiply(multiply(v,w),u)),
inference(spr,[status(thm),theory(equality)],[362,160]),
[iquote('0:SpR:362.0,160.0')] ).
cnf(441,plain,
equal(multiply(u,multiply(v,w)),multiply(w,multiply(u,v))),
inference(rew,[status(thm),theory(equality)],[394,397]),
[iquote('0:Rew:394.0,397.0,394.0,397.0')] ).
cnf(442,plain,
$false,
inference(unc,[status(thm)],[441,366]),
[iquote('0:UnC:441.0,366.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP555-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n012.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 07:23:40 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.48
% 0.21/0.48 SPASS V 3.9
% 0.21/0.48 SPASS beiseite: Proof found.
% 0.21/0.48 % SZS status Theorem
% 0.21/0.48 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.48 SPASS derived 356 clauses, backtracked 0 clauses, performed 0 splits and kept 162 clauses.
% 0.21/0.48 SPASS allocated 63745 KBytes.
% 0.21/0.48 SPASS spent 0:00:00.11 on the problem.
% 0.21/0.48 0:00:00.03 for the input.
% 0.21/0.48 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.48 0:00:00.00 for inferences.
% 0.21/0.48 0:00:00.00 for the backtracking.
% 0.21/0.48 0:00:00.05 for the reduction.
% 0.21/0.48
% 0.21/0.48
% 0.21/0.48 Here is a proof with depth 8, length 35 :
% 0.21/0.48 % SZS output start Refutation
% See solution above
% 0.21/0.48 Formulae used in the proof : single_axiom multiply prove_these_axioms_3
% 0.21/0.48
%------------------------------------------------------------------------------