TSTP Solution File: GRP562-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP562-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n032.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 11:48:03 EDT 2022
% Result : Unsatisfiable 0.13s 0.37s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of clauses : 12 ( 12 unt; 0 nHn; 12 RR)
% Number of literals : 12 ( 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 : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(divide(divide(divide(u,inverse(v)),w),divide(u,w)),v),
file('GRP562-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,inverse(v)),multiply(u,v)),
file('GRP562-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(multiply(multiply(inverse(b2),b2),a2),a2),
file('GRP562-1.p',unknown),
[] ).
cnf(4,plain,
equal(divide(divide(multiply(u,v),w),divide(u,w)),v),
inference(rew,[status(thm),theory(equality)],[2,1]),
[iquote('0:Rew:2.0,1.0')] ).
cnf(6,plain,
equal(divide(divide(multiply(divide(multiply(u,v),w),x),divide(u,w)),v),x),
inference(spr,[status(thm),theory(equality)],[4]),
[iquote('0:SpR:4.0,4.0')] ).
cnf(15,plain,
equal(multiply(divide(multiply(divide(multiply(u,inverse(v)),w),x),divide(u,w)),v),x),
inference(spr,[status(thm),theory(equality)],[6,2]),
[iquote('0:SpR:6.0,2.0')] ).
cnf(52,plain,
equal(divide(divide(u,divide(divide(multiply(v,inverse(w)),x),divide(v,x))),u),w),
inference(spr,[status(thm),theory(equality)],[15,6]),
[iquote('0:SpR:15.0,6.0')] ).
cnf(74,plain,
equal(divide(multiply(u,v),u),v),
inference(rew,[status(thm),theory(equality)],[2,52,4]),
[iquote('0:Rew:2.0,52.0,4.0,52.0')] ).
cnf(82,plain,
equal(divide(u,divide(v,v)),u),
inference(spr,[status(thm),theory(equality)],[74,4]),
[iquote('0:SpR:74.0,4.0')] ).
cnf(98,plain,
equal(multiply(divide(u,u),v),v),
inference(spr,[status(thm),theory(equality)],[82,74]),
[iquote('0:SpR:82.0,74.0')] ).
cnf(136,plain,
equal(multiply(multiply(inverse(u),u),v),v),
inference(spr,[status(thm),theory(equality)],[2,98]),
[iquote('0:SpR:2.0,98.0')] ).
cnf(138,plain,
$false,
inference(unc,[status(thm)],[136,3]),
[iquote('0:UnC:136.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : GRP562-1 : TPTP v8.1.0. Released v2.6.0.
% 0.00/0.09 % Command : run_spass %d %s
% 0.08/0.29 % Computer : n032.cluster.edu
% 0.08/0.29 % Model : x86_64 x86_64
% 0.08/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.29 % Memory : 8042.1875MB
% 0.08/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.29 % CPULimit : 300
% 0.08/0.29 % WCLimit : 600
% 0.08/0.29 % DateTime : Mon Jun 13 09:53:11 EDT 2022
% 0.08/0.29 % CPUTime :
% 0.13/0.37
% 0.13/0.37 SPASS V 3.9
% 0.13/0.37 SPASS beiseite: Proof found.
% 0.13/0.37 % SZS status Theorem
% 0.13/0.37 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.37 SPASS derived 115 clauses, backtracked 0 clauses, performed 0 splits and kept 72 clauses.
% 0.13/0.37 SPASS allocated 63472 KBytes.
% 0.13/0.37 SPASS spent 0:00:00.07 on the problem.
% 0.13/0.37 0:00:00.03 for the input.
% 0.13/0.37 0:00:00.00 for the FLOTTER CNF translation.
% 0.13/0.37 0:00:00.00 for inferences.
% 0.13/0.37 0:00:00.00 for the backtracking.
% 0.13/0.37 0:00:00.02 for the reduction.
% 0.13/0.37
% 0.13/0.37
% 0.13/0.37 Here is a proof with depth 6, length 12 :
% 0.13/0.37 % SZS output start Refutation
% See solution above
% 0.13/0.37 Formulae used in the proof : single_axiom multiply prove_these_axioms_2
% 0.13/0.37
%------------------------------------------------------------------------------