TSTP Solution File: GRP451-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP451-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 11:47:32 EDT 2022
% Result : Unsatisfiable 0.20s 0.43s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of clauses : 19 ( 19 unt; 0 nHn; 19 RR)
% Number of literals : 19 ( 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(divide(divide(divide(u,u),divide(u,divide(v,divide(divide(divide(u,u),u),w)))),w),v),
file('GRP451-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,divide(divide(v,v),w)),multiply(u,w)),
file('GRP451-1.p',unknown),
[] ).
cnf(3,axiom,
equal(divide(divide(u,u),v),inverse(v)),
file('GRP451-1.p',unknown),
[] ).
cnf(4,axiom,
~ equal(multiply(inverse(b1),b1),multiply(inverse(a1),a1)),
file('GRP451-1.p',unknown),
[] ).
cnf(5,plain,
equal(divide(u,inverse(v)),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[3,2]),
[iquote('0:Rew:3.0,2.0')] ).
cnf(6,plain,
equal(divide(inverse(divide(u,divide(v,divide(inverse(u),w)))),w),v),
inference(rew,[status(thm),theory(equality)],[3,1]),
[iquote('0:Rew:3.0,1.0,3.0,1.0')] ).
cnf(7,plain,
equal(divide(inverse(divide(u,u)),v),inverse(v)),
inference(spr,[status(thm),theory(equality)],[3]),
[iquote('0:SpR:3.0,3.0')] ).
cnf(9,plain,
equal(divide(multiply(inverse(u),u),v),inverse(v)),
inference(spr,[status(thm),theory(equality)],[5,3]),
[iquote('0:SpR:5.0,3.0')] ).
cnf(11,plain,
equal(multiply(divide(u,u),v),inverse(inverse(v))),
inference(spr,[status(thm),theory(equality)],[5,3]),
[iquote('0:SpR:5.0,3.0')] ).
cnf(20,plain,
equal(multiply(multiply(inverse(u),u),v),inverse(inverse(v))),
inference(spr,[status(thm),theory(equality)],[9,5]),
[iquote('0:SpR:9.0,5.0')] ).
cnf(57,plain,
equal(divide(inverse(divide(divide(u,u),divide(v,inverse(w)))),w),v),
inference(spr,[status(thm),theory(equality)],[7,6]),
[iquote('0:SpR:7.0,6.0')] ).
cnf(70,plain,
equal(divide(inverse(inverse(multiply(u,v))),v),u),
inference(rew,[status(thm),theory(equality)],[3,57,5]),
[iquote('0:Rew:3.0,57.0,5.0,57.0')] ).
cnf(87,plain,
equal(multiply(inverse(inverse(multiply(u,inverse(v)))),v),u),
inference(spr,[status(thm),theory(equality)],[70,5]),
[iquote('0:SpR:70.0,5.0')] ).
cnf(96,plain,
equal(inverse(inverse(multiply(u,inverse(v)))),divide(inverse(inverse(u)),v)),
inference(spr,[status(thm),theory(equality)],[87,70]),
[iquote('0:SpR:87.0,70.0')] ).
cnf(100,plain,
equal(multiply(inverse(inverse(inverse(inverse(inverse(u))))),u),multiply(inverse(v),v)),
inference(spr,[status(thm),theory(equality)],[20,87]),
[iquote('0:SpR:20.0,87.0')] ).
cnf(102,plain,
equal(multiply(divide(inverse(inverse(u)),v),v),u),
inference(rew,[status(thm),theory(equality)],[96,87]),
[iquote('0:Rew:96.0,87.0')] ).
cnf(105,plain,
equal(inverse(inverse(inverse(inverse(u)))),u),
inference(spr,[status(thm),theory(equality)],[102,11]),
[iquote('0:SpR:102.0,11.0')] ).
cnf(114,plain,
equal(multiply(inverse(u),u),multiply(inverse(v),v)),
inference(rew,[status(thm),theory(equality)],[105,100]),
[iquote('0:Rew:105.0,100.0')] ).
cnf(120,plain,
$false,
inference(unc,[status(thm)],[114,4]),
[iquote('0:UnC:114.0,4.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP451-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.14 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n029.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 22:42:10 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.43
% 0.20/0.43 SPASS V 3.9
% 0.20/0.43 SPASS beiseite: Proof found.
% 0.20/0.43 % SZS status Theorem
% 0.20/0.43 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.43 SPASS derived 95 clauses, backtracked 0 clauses, performed 0 splits and kept 50 clauses.
% 0.20/0.43 SPASS allocated 63256 KBytes.
% 0.20/0.43 SPASS spent 0:00:00.06 on the problem.
% 0.20/0.43 0:00:00.03 for the input.
% 0.20/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.43 0:00:00.00 for inferences.
% 0.20/0.43 0:00:00.00 for the backtracking.
% 0.20/0.43 0:00:00.01 for the reduction.
% 0.20/0.43
% 0.20/0.43
% 0.20/0.43 Here is a proof with depth 4, length 19 :
% 0.20/0.43 % SZS output start Refutation
% See solution above
% 0.20/0.43 Formulae used in the proof : single_axiom multiply inverse prove_these_axioms_1
% 0.20/0.43
%------------------------------------------------------------------------------