TSTP Solution File: BOO006-2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : BOO006-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 23:49:23 EDT 2022
% Result : Unsatisfiable 0.18s 0.39s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of clauses : 10 ( 10 unt; 0 nHn; 10 RR)
% Number of literals : 10 ( 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(multiply(a,additive_identity),additive_identity),
file('BOO006-2.p',unknown),
[] ).
cnf(2,axiom,
equal(add(u,v),add(v,u)),
file('BOO006-2.p',unknown),
[] ).
cnf(7,axiom,
equal(add(multiply(u,v),multiply(u,w)),multiply(u,add(v,w))),
file('BOO006-2.p',unknown),
[] ).
cnf(10,axiom,
equal(multiply(u,inverse(u)),additive_identity),
file('BOO006-2.p',unknown),
[] ).
cnf(15,axiom,
equal(add(additive_identity,u),u),
file('BOO006-2.p',unknown),
[] ).
cnf(204,plain,
equal(multiply(u,add(v,inverse(u))),add(multiply(u,v),additive_identity)),
inference(spr,[status(thm),theory(equality)],[10,7]),
[iquote('0:SpR:10.0,7.0')] ).
cnf(229,plain,
equal(multiply(u,add(v,inverse(u))),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[15,204,2]),
[iquote('0:Rew:15.0,204.0,2.0,204.0')] ).
cnf(256,plain,
equal(multiply(u,inverse(u)),multiply(u,additive_identity)),
inference(spr,[status(thm),theory(equality)],[15,229]),
[iquote('0:SpR:15.0,229.0')] ).
cnf(265,plain,
equal(multiply(u,additive_identity),additive_identity),
inference(rew,[status(thm),theory(equality)],[10,256]),
[iquote('0:Rew:10.0,256.0')] ).
cnf(266,plain,
$false,
inference(unc,[status(thm)],[265,1]),
[iquote('0:UnC:265.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : BOO006-2 : TPTP v8.1.0. Released v1.0.0.
% 0.02/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n020.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 20:41:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.39
% 0.18/0.39 SPASS V 3.9
% 0.18/0.39 SPASS beiseite: Proof found.
% 0.18/0.39 % SZS status Theorem
% 0.18/0.39 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.39 SPASS derived 177 clauses, backtracked 0 clauses, performed 0 splits and kept 87 clauses.
% 0.18/0.39 SPASS allocated 63425 KBytes.
% 0.18/0.39 SPASS spent 0:00:00.05 on the problem.
% 0.18/0.39 0:00:00.02 for the input.
% 0.18/0.39 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.39 0:00:00.00 for inferences.
% 0.18/0.39 0:00:00.00 for the backtracking.
% 0.18/0.39 0:00:00.01 for the reduction.
% 0.18/0.39
% 0.18/0.39
% 0.18/0.39 Here is a proof with depth 2, length 10 :
% 0.18/0.39 % SZS output start Refutation
% See solution above
% 0.18/0.39 Formulae used in the proof : prove_right_identity commutativity_of_add distributivity4 multiplicative_inverse1 additive_id2
% 0.18/0.39
%------------------------------------------------------------------------------