TSTP Solution File: BOO013-2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : BOO013-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 : Thu Jul 14 23:49:26 EDT 2022
% Result : Unsatisfiable 0.18s 0.43s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% 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 : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(add(a,b),multiplicative_identity),
file('BOO013-2.p',unknown),
[] ).
cnf(2,axiom,
equal(add(a,c),multiplicative_identity),
file('BOO013-2.p',unknown),
[] ).
cnf(3,axiom,
equal(multiply(a,b),additive_identity),
file('BOO013-2.p',unknown),
[] ).
cnf(4,axiom,
equal(multiply(a,c),additive_identity),
file('BOO013-2.p',unknown),
[] ).
cnf(5,axiom,
~ equal(c,b),
file('BOO013-2.p',unknown),
[] ).
cnf(7,axiom,
equal(multiply(u,v),multiply(v,u)),
file('BOO013-2.p',unknown),
[] ).
cnf(10,axiom,
equal(add(multiply(u,v),multiply(w,v)),multiply(add(u,w),v)),
file('BOO013-2.p',unknown),
[] ).
cnf(16,axiom,
equal(multiply(u,multiplicative_identity),u),
file('BOO013-2.p',unknown),
[] ).
cnf(17,axiom,
equal(multiply(multiplicative_identity,u),u),
file('BOO013-2.p',unknown),
[] ).
cnf(19,axiom,
equal(add(additive_identity,u),u),
file('BOO013-2.p',unknown),
[] ).
cnf(68,plain,
equal(add(additive_identity,multiply(u,c)),multiply(add(a,u),c)),
inference(spr,[status(thm),theory(equality)],[4,10]),
[iquote('0:SpR:4.0,10.0')] ).
cnf(69,plain,
equal(add(additive_identity,multiply(u,b)),multiply(add(a,u),b)),
inference(spr,[status(thm),theory(equality)],[3,10]),
[iquote('0:SpR:3.0,10.0')] ).
cnf(79,plain,
equal(multiply(c,add(a,u)),multiply(u,c)),
inference(rew,[status(thm),theory(equality)],[19,68,7]),
[iquote('0:Rew:19.0,68.0,7.0,68.0')] ).
cnf(80,plain,
equal(multiply(b,add(a,u)),multiply(u,b)),
inference(rew,[status(thm),theory(equality)],[19,69,7]),
[iquote('0:Rew:19.0,69.0,7.0,69.0')] ).
cnf(152,plain,
equal(multiply(c,multiplicative_identity),multiply(b,c)),
inference(spr,[status(thm),theory(equality)],[1,79]),
[iquote('0:SpR:1.0,79.0')] ).
cnf(158,plain,
equal(multiply(b,c),c),
inference(rew,[status(thm),theory(equality)],[17,152,7]),
[iquote('0:Rew:17.0,152.0,7.0,152.0')] ).
cnf(276,plain,
equal(multiply(c,b),multiply(b,multiplicative_identity)),
inference(spr,[status(thm),theory(equality)],[2,80]),
[iquote('0:SpR:2.0,80.0')] ).
cnf(282,plain,
equal(c,b),
inference(rew,[status(thm),theory(equality)],[158,276,7,16]),
[iquote('0:Rew:158.0,276.0,7.0,276.0,16.0,276.0')] ).
cnf(283,plain,
$false,
inference(mrr,[status(thm)],[282,5]),
[iquote('0:MRR:282.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : BOO013-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n023.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 : Wed Jun 1 15:32:41 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.43
% 0.18/0.43 SPASS V 3.9
% 0.18/0.43 SPASS beiseite: Proof found.
% 0.18/0.43 % SZS status Theorem
% 0.18/0.43 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.43 SPASS derived 168 clauses, backtracked 0 clauses, performed 0 splits and kept 97 clauses.
% 0.18/0.43 SPASS allocated 63420 KBytes.
% 0.18/0.43 SPASS spent 0:00:00.09 on the problem.
% 0.18/0.43 0:00:00.04 for the input.
% 0.18/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.43 0:00:00.00 for inferences.
% 0.18/0.43 0:00:00.00 for the backtracking.
% 0.18/0.43 0:00:00.03 for the reduction.
% 0.18/0.43
% 0.18/0.43
% 0.18/0.43 Here is a proof with depth 2, length 19 :
% 0.18/0.43 % SZS output start Refutation
% See solution above
% 0.18/0.43 Formulae used in the proof : b_and_multiplicative_identity c_and_multiplicative_identity b_a_additive_identity c_a_additive_identity prove_b_is_a commutativity_of_multiply distributivity3 multiplicative_id1 multiplicative_id2 additive_id2
% 0.18/0.43
%------------------------------------------------------------------------------