TSTP Solution File: GRP553-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP553-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 11:48:00 EDT 2022
% Result : Unsatisfiable 0.20s 0.45s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% 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 : 6 ( 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(divide(divide(u,inverse(divide(v,divide(u,w)))),w),v),
file('GRP553-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,inverse(v)),multiply(u,v)),
file('GRP553-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1)),
file('GRP553-1.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(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(96,plain,
equal(divide(divide(multiply(u,v),divide(w,multiply(w,divide(x,u)))),x),v),
inference(spr,[status(thm),theory(equality)],[81,35]),
[iquote('0:SpR:81.0,35.0')] ).
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(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(113,plain,
equal(divide(multiply(multiply(u,divide(v,u)),w),v),w),
inference(rew,[status(thm),theory(equality)],[108,96]),
[iquote('0:Rew:108.0,96.0')] ).
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(140,plain,
equal(divide(multiply(u,v),u),v),
inference(rew,[status(thm),theory(equality)],[139,113]),
[iquote('0:Rew:139.0,113.0')] ).
cnf(203,plain,
equal(multiply(u,multiply(inverse(v),v)),u),
inference(spr,[status(thm),theory(equality)],[2,112]),
[iquote('0:SpR:2.0,112.0')] ).
cnf(226,plain,
equal(multiply(multiply(inverse(u),v),u),v),
inference(spr,[status(thm),theory(equality)],[140,2]),
[iquote('0:SpR:140.0,2.0')] ).
cnf(276,plain,
equal(multiply(inverse(u),u),multiply(inverse(v),v)),
inference(spr,[status(thm),theory(equality)],[203,226]),
[iquote('0:SpR:203.0,226.0')] ).
cnf(278,plain,
$false,
inference(unc,[status(thm)],[276,3]),
[iquote('0:UnC:276.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP553-1 : TPTP v8.1.0. Released v2.6.0.
% 0.12/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n024.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 23:08:18 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.45
% 0.20/0.45 SPASS V 3.9
% 0.20/0.45 SPASS beiseite: Proof found.
% 0.20/0.45 % SZS status Theorem
% 0.20/0.45 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.45 SPASS derived 218 clauses, backtracked 0 clauses, performed 0 splits and kept 106 clauses.
% 0.20/0.45 SPASS allocated 63536 KBytes.
% 0.20/0.45 SPASS spent 0:00:00.09 on the problem.
% 0.20/0.45 0:00:00.03 for the input.
% 0.20/0.45 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.45 0:00:00.00 for inferences.
% 0.20/0.45 0:00:00.00 for the backtracking.
% 0.20/0.45 0:00:00.03 for the reduction.
% 0.20/0.45
% 0.20/0.45
% 0.20/0.45 Here is a proof with depth 7, length 25 :
% 0.20/0.45 % SZS output start Refutation
% See solution above
% 0.20/0.45 Formulae used in the proof : single_axiom multiply prove_these_axioms_1
% 0.20/0.45
%------------------------------------------------------------------------------