TSTP Solution File: BOO017-2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : BOO017-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 23:49:27 EDT 2022
% Result : Unsatisfiable 0.19s 0.47s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of clauses : 17 ( 17 unt; 0 nHn; 17 RR)
% Number of literals : 17 ( 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 : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(add(x__dfg,y__dfg),z__dfg),
file('BOO017-2.p',unknown),
[] ).
cnf(2,axiom,
~ equal(multiply(x__dfg,z__dfg),x__dfg),
file('BOO017-2.p',unknown),
[] ).
cnf(3,axiom,
equal(add(u,v),add(v,u)),
file('BOO017-2.p',unknown),
[] ).
cnf(4,axiom,
equal(multiply(u,v),multiply(v,u)),
file('BOO017-2.p',unknown),
[] ).
cnf(6,axiom,
equal(multiply(add(u,v),add(u,w)),add(u,multiply(v,w))),
file('BOO017-2.p',unknown),
[] ).
cnf(8,axiom,
equal(add(multiply(u,v),multiply(u,w)),multiply(u,add(v,w))),
file('BOO017-2.p',unknown),
[] ).
cnf(11,axiom,
equal(multiply(u,inverse(u)),additive_identity),
file('BOO017-2.p',unknown),
[] ).
cnf(15,axiom,
equal(add(u,additive_identity),u),
file('BOO017-2.p',unknown),
[] ).
cnf(16,axiom,
equal(add(additive_identity,u),u),
file('BOO017-2.p',unknown),
[] ).
cnf(185,plain,
equal(multiply(u,add(v,inverse(u))),add(multiply(u,v),additive_identity)),
inference(spr,[status(thm),theory(equality)],[11,8]),
[iquote('0:SpR:11.0,8.0')] ).
cnf(208,plain,
equal(multiply(u,add(v,inverse(u))),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[16,185,3]),
[iquote('0:Rew:16.0,185.0,3.0,185.0')] ).
cnf(262,plain,
equal(multiply(u,inverse(u)),multiply(u,additive_identity)),
inference(spr,[status(thm),theory(equality)],[16,208]),
[iquote('0:SpR:16.0,208.0')] ).
cnf(271,plain,
equal(multiply(u,additive_identity),additive_identity),
inference(rew,[status(thm),theory(equality)],[11,262]),
[iquote('0:Rew:11.0,262.0')] ).
cnf(341,plain,
equal(multiply(add(u,v),u),add(u,multiply(v,additive_identity))),
inference(spr,[status(thm),theory(equality)],[15,6]),
[iquote('0:SpR:15.0,6.0')] ).
cnf(363,plain,
equal(multiply(u,add(u,v)),u),
inference(rew,[status(thm),theory(equality)],[4,341,15,271]),
[iquote('0:Rew:4.0,341.0,15.0,341.0,271.0,341.0')] ).
cnf(659,plain,
equal(multiply(x__dfg,z__dfg),x__dfg),
inference(spr,[status(thm),theory(equality)],[1,363]),
[iquote('0:SpR:1.0,363.0')] ).
cnf(670,plain,
$false,
inference(mrr,[status(thm)],[659,2]),
[iquote('0:MRR:659.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : BOO017-2 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n017.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jun 1 19:51:57 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.47
% 0.19/0.47 SPASS V 3.9
% 0.19/0.47 SPASS beiseite: Proof found.
% 0.19/0.47 % SZS status Theorem
% 0.19/0.47 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.47 SPASS derived 423 clauses, backtracked 0 clauses, performed 0 splits and kept 153 clauses.
% 0.19/0.47 SPASS allocated 63704 KBytes.
% 0.19/0.47 SPASS spent 0:00:00.12 on the problem.
% 0.19/0.47 0:00:00.03 for the input.
% 0.19/0.47 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.47 0:00:00.00 for inferences.
% 0.19/0.47 0:00:00.00 for the backtracking.
% 0.19/0.47 0:00:00.06 for the reduction.
% 0.19/0.47
% 0.19/0.47
% 0.19/0.47 Here is a proof with depth 2, length 17 :
% 0.19/0.47 % SZS output start Refutation
% See solution above
% 0.19/0.47 Formulae used in the proof : x_times_y prove_sum commutativity_of_add commutativity_of_multiply distributivity2 distributivity4 multiplicative_inverse1 additive_id1 additive_id2
% 0.19/0.47
%------------------------------------------------------------------------------