%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP011-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n004.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 11:44:44 EDT 2022
% Result : Unsatisfiable 0.12s 0.41s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of clauses : 16 ( 16 unt; 0 nHn; 16 RR)
% Number of literals : 16 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
file('GRP011-4.p',unknown),
[] ).
cnf(2,axiom,
equal(multiply(identity,u),u),
file('GRP011-4.p',unknown),
[] ).
cnf(3,axiom,
equal(multiply(inverse(u),u),identity),
file('GRP011-4.p',unknown),
[] ).
cnf(4,axiom,
equal(multiply(d,c),multiply(b,c)),
file('GRP011-4.p',unknown),
[] ).
cnf(5,axiom,
~ equal(d,b),
file('GRP011-4.p',unknown),
[] ).
cnf(12,plain,
equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v)),
inference(spr,[status(thm),theory(equality)],[3,1]),
[iquote('0:SpR:3.0,1.0')] ).
cnf(13,plain,
equal(multiply(multiply(b,c),u),multiply(d,multiply(c,u))),
inference(spr,[status(thm),theory(equality)],[4,1]),
[iquote('0:SpR:4.0,1.0')] ).
cnf(14,plain,
equal(multiply(inverse(u),multiply(u,v)),v),
inference(rew,[status(thm),theory(equality)],[2,12]),
[iquote('0:Rew:2.0,12.0')] ).
cnf(15,plain,
equal(multiply(d,multiply(c,u)),multiply(b,multiply(c,u))),
inference(rew,[status(thm),theory(equality)],[1,13]),
[iquote('0:Rew:1.0,13.0')] ).
cnf(18,plain,
equal(multiply(inverse(inverse(u)),v),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[14]),
[iquote('0:SpR:14.0,14.0')] ).
cnf(21,plain,
equal(multiply(inverse(inverse(u)),identity),u),
inference(spr,[status(thm),theory(equality)],[3,14]),
[iquote('0:SpR:3.0,14.0')] ).
cnf(24,plain,
equal(multiply(u,identity),u),
inference(rew,[status(thm),theory(equality)],[18,21]),
[iquote('0:Rew:18.0,21.0')] ).
cnf(49,plain,
equal(multiply(u,inverse(u)),identity),
inference(spr,[status(thm),theory(equality)],[18,3]),
[iquote('0:SpR:18.0,3.0')] ).
cnf(68,plain,
equal(multiply(d,identity),multiply(b,identity)),
inference(spr,[status(thm),theory(equality)],[49,15]),
[iquote('0:SpR:49.0,15.0')] ).
cnf(75,plain,
equal(d,b),
inference(rew,[status(thm),theory(equality)],[24,68]),
[iquote('0:Rew:24.0,68.0,24.0,68.0')] ).
cnf(76,plain,
$false,
inference(mrr,[status(thm)],[75,5]),
[iquote('0:MRR:75.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP011-4 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 14 05:06:39 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.41
% 0.12/0.41 SPASS V 3.9
% 0.12/0.41 SPASS beiseite: Proof found.
% 0.12/0.41 % SZS status Theorem
% 0.12/0.41 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.41 SPASS derived 54 clauses, backtracked 0 clauses, performed 0 splits and kept 20 clauses.
% 0.12/0.41 SPASS allocated 63154 KBytes.
% 0.12/0.41 SPASS spent 0:00:00.06 on the problem.
% 0.12/0.41 0:00:00.03 for the input.
% 0.12/0.41 0:00:00.00 for the FLOTTER CNF translation.
% 0.12/0.41 0:00:00.00 for inferences.
% 0.12/0.41 0:00:00.00 for the backtracking.
% 0.12/0.41 0:00:00.00 for the reduction.
% 0.12/0.41
% 0.12/0.41
% 0.12/0.41 Here is a proof with depth 4, length 16 :
% 0.12/0.41 % SZS output start Refutation
% See solution above
% 0.12/0.41 Formulae used in the proof : associativity left_identity left_inverse product_equality prove_left_cancellation
% 0.12/0.41
%------------------------------------------------------------------------------