TSTP Solution File: GRP001-4 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP001-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.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 11:44:39 EDT 2022
% Result : Unsatisfiable 0.21s 0.43s
% Output : Refutation 0.21s
% 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; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 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('GRP001-4.p',unknown),
[] ).
cnf(2,axiom,
equal(multiply(identity,u),u),
file('GRP001-4.p',unknown),
[] ).
cnf(3,axiom,
equal(multiply(u,u),identity),
file('GRP001-4.p',unknown),
[] ).
cnf(4,axiom,
equal(multiply(a,b),c),
file('GRP001-4.p',unknown),
[] ).
cnf(5,axiom,
~ equal(multiply(b,a),c),
file('GRP001-4.p',unknown),
[] ).
cnf(10,plain,
equal(multiply(u,multiply(v,multiply(u,v))),identity),
inference(spr,[status(thm),theory(equality)],[1,3]),
[iquote('0:SpR:1.0,3.0')] ).
cnf(13,plain,
equal(multiply(a,multiply(b,u)),multiply(c,u)),
inference(spr,[status(thm),theory(equality)],[4,1]),
[iquote('0:SpR:4.0,1.0')] ).
cnf(15,plain,
equal(multiply(u,multiply(u,v)),multiply(identity,v)),
inference(spr,[status(thm),theory(equality)],[3,1]),
[iquote('0:SpR:3.0,1.0')] ).
cnf(16,plain,
equal(multiply(u,multiply(u,v)),v),
inference(rew,[status(thm),theory(equality)],[2,15]),
[iquote('0:Rew:2.0,15.0')] ).
cnf(25,plain,
equal(multiply(u,identity),u),
inference(spr,[status(thm),theory(equality)],[3,16]),
[iquote('0:SpR:3.0,16.0')] ).
cnf(44,plain,
equal(multiply(c,b),multiply(a,identity)),
inference(spr,[status(thm),theory(equality)],[3,13]),
[iquote('0:SpR:3.0,13.0')] ).
cnf(47,plain,
equal(multiply(c,b),a),
inference(rew,[status(thm),theory(equality)],[25,44]),
[iquote('0:Rew:25.0,44.0')] ).
cnf(57,plain,
equal(multiply(u,multiply(v,u)),multiply(v,identity)),
inference(spr,[status(thm),theory(equality)],[10,16]),
[iquote('0:SpR:10.0,16.0')] ).
cnf(77,plain,
equal(multiply(u,multiply(v,u)),v),
inference(rew,[status(thm),theory(equality)],[25,57]),
[iquote('0:Rew:25.0,57.0')] ).
cnf(113,plain,
equal(multiply(b,a),c),
inference(spr,[status(thm),theory(equality)],[47,77]),
[iquote('0:SpR:47.0,77.0')] ).
cnf(115,plain,
$false,
inference(mrr,[status(thm)],[113,5]),
[iquote('0:MRR:113.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP001-4 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n022.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Tue Jun 14 06:13:18 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.43
% 0.21/0.43 SPASS V 3.9
% 0.21/0.43 SPASS beiseite: Proof found.
% 0.21/0.43 % SZS status Theorem
% 0.21/0.43 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.43 SPASS derived 88 clauses, backtracked 0 clauses, performed 0 splits and kept 27 clauses.
% 0.21/0.43 SPASS allocated 63185 KBytes.
% 0.21/0.43 SPASS spent 0:00:00.07 on the problem.
% 0.21/0.43 0:00:00.04 for the input.
% 0.21/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.43 0:00:00.00 for inferences.
% 0.21/0.43 0:00:00.00 for the backtracking.
% 0.21/0.43 0:00:00.00 for the reduction.
% 0.21/0.43
% 0.21/0.43
% 0.21/0.43 Here is a proof with depth 3, length 16 :
% 0.21/0.43 % SZS output start Refutation
% See solution above
% 0.21/0.43 Formulae used in the proof : associativity left_identity squareness a_times_b_is_c prove_b_times_a_is_c
% 0.21/0.43
%------------------------------------------------------------------------------