%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP534-1 : 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 11:47:55 EDT 2022
% Result : Unsatisfiable 0.17s 0.40s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of clauses : 16 ( 16 unt; 0 nHn; 16 RR)
% Number of literals : 16 ( 0 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 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,divide(divide(u,v),w)),v),w),
file('GRP534-1.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(u,divide(divide(v,v),w)),multiply(u,w)),
file('GRP534-1.p',unknown),
[] ).
cnf(3,axiom,
equal(divide(divide(u,u),v),inverse(v)),
file('GRP534-1.p',unknown),
[] ).
cnf(4,axiom,
equal(divide(u,u),identity),
file('GRP534-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(multiply(multiply(inverse(b2),b2),a2),a2),
file('GRP534-1.p',unknown),
[] ).
cnf(6,plain,
equal(divide(identity,u),inverse(u)),
inference(rew,[status(thm),theory(equality)],[4,3]),
[iquote('0:Rew:4.0,3.0')] ).
cnf(7,plain,
equal(divide(u,inverse(v)),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[6,2,4]),
[iquote('0:Rew:6.0,2.0,4.0,2.0')] ).
cnf(12,plain,
equal(multiply(inverse(u),u),identity),
inference(spr,[status(thm),theory(equality)],[7,4]),
[iquote('0:SpR:7.0,4.0')] ).
cnf(13,plain,
equal(multiply(identity,u),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[7,6]),
[iquote('0:SpR:7.0,6.0')] ).
cnf(16,plain,
~ equal(multiply(identity,a2),a2),
inference(rew,[status(thm),theory(equality)],[12,5]),
[iquote('0:Rew:12.0,5.0')] ).
cnf(17,plain,
~ equal(inverse(inverse(a2)),a2),
inference(rew,[status(thm),theory(equality)],[13,16]),
[iquote('0:Rew:13.0,16.0')] ).
cnf(33,plain,
equal(divide(divide(u,divide(identity,v)),u),v),
inference(spr,[status(thm),theory(equality)],[4,1]),
[iquote('0:SpR:4.0,1.0')] ).
cnf(41,plain,
equal(divide(multiply(u,v),u),v),
inference(rew,[status(thm),theory(equality)],[7,33,6]),
[iquote('0:Rew:7.0,33.0,6.0,33.0')] ).
cnf(56,plain,
equal(divide(identity,inverse(u)),u),
inference(spr,[status(thm),theory(equality)],[12,41]),
[iquote('0:SpR:12.0,41.0')] ).
cnf(58,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[13,56,7]),
[iquote('0:Rew:13.0,56.0,7.0,56.0')] ).
cnf(59,plain,
$false,
inference(unc,[status(thm)],[58,17]),
[iquote('0:UnC:58.0,17.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP534-1 : TPTP v8.1.0. Released v2.6.0.
% 0.12/0.12 % Command : run_spass %d %s
% 0.12/0.32 % Computer : n012.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Tue Jun 14 01:45:40 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.17/0.40
% 0.17/0.40 SPASS V 3.9
% 0.17/0.40 SPASS beiseite: Proof found.
% 0.17/0.40 % SZS status Theorem
% 0.17/0.40 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.40 SPASS derived 36 clauses, backtracked 0 clauses, performed 0 splits and kept 24 clauses.
% 0.17/0.40 SPASS allocated 63157 KBytes.
% 0.17/0.40 SPASS spent 0:00:00.06 on the problem.
% 0.17/0.40 0:00:00.04 for the input.
% 0.17/0.40 0:00:00.00 for the FLOTTER CNF translation.
% 0.17/0.40 0:00:00.00 for inferences.
% 0.17/0.40 0:00:00.00 for the backtracking.
% 0.17/0.40 0:00:00.00 for the reduction.
% 0.17/0.40
% 0.17/0.40
% 0.17/0.40 Here is a proof with depth 2, length 16 :
% 0.17/0.40 % SZS output start Refutation
% See solution above
% 0.17/0.40 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms_2
% 0.17/0.40
%------------------------------------------------------------------------------