TSTP Solution File: BOO004-4 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : BOO004-4 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 23:49:22 EDT 2022
% Result : Unsatisfiable 0.19s 0.43s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of clauses : 26 ( 26 unt; 0 nHn; 26 RR)
% Number of literals : 26 ( 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; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(add(a,a),a),
file('BOO004-4.p',unknown),
[] ).
cnf(2,axiom,
equal(add(u,v),add(v,u)),
file('BOO004-4.p',unknown),
[] ).
cnf(3,axiom,
equal(multiply(u,v),multiply(v,u)),
file('BOO004-4.p',unknown),
[] ).
cnf(4,axiom,
equal(multiply(add(u,v),add(u,w)),add(u,multiply(v,w))),
file('BOO004-4.p',unknown),
[] ).
cnf(5,axiom,
equal(add(multiply(u,v),multiply(u,w)),multiply(u,add(v,w))),
file('BOO004-4.p',unknown),
[] ).
cnf(6,axiom,
equal(add(u,additive_identity),u),
file('BOO004-4.p',unknown),
[] ).
cnf(7,axiom,
equal(multiply(u,multiplicative_identity),u),
file('BOO004-4.p',unknown),
[] ).
cnf(8,axiom,
equal(add(u,inverse(u)),multiplicative_identity),
file('BOO004-4.p',unknown),
[] ).
cnf(9,axiom,
equal(multiply(u,inverse(u)),additive_identity),
file('BOO004-4.p',unknown),
[] ).
cnf(28,plain,
equal(add(additive_identity,u),u),
inference(spr,[status(thm),theory(equality)],[2,6]),
[iquote('0:SpR:2.0,6.0')] ).
cnf(39,plain,
equal(add(multiply(u,v),u),multiply(u,add(v,multiplicative_identity))),
inference(spr,[status(thm),theory(equality)],[7,5]),
[iquote('0:SpR:7.0,5.0')] ).
cnf(40,plain,
equal(multiply(u,add(v,inverse(u))),add(multiply(u,v),additive_identity)),
inference(spr,[status(thm),theory(equality)],[9,5]),
[iquote('0:SpR:9.0,5.0')] ).
cnf(49,plain,
equal(add(u,multiply(u,v)),multiply(u,add(v,multiplicative_identity))),
inference(rew,[status(thm),theory(equality)],[2,39]),
[iquote('0:Rew:2.0,39.0')] ).
cnf(53,plain,
equal(multiply(u,add(v,inverse(u))),add(additive_identity,multiply(u,v))),
inference(rew,[status(thm),theory(equality)],[2,40]),
[iquote('0:Rew:2.0,40.0')] ).
cnf(54,plain,
equal(multiply(u,add(v,inverse(u))),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[28,53]),
[iquote('0:Rew:28.0,53.0')] ).
cnf(72,plain,
equal(multiply(u,multiplicative_identity),multiply(u,u)),
inference(spr,[status(thm),theory(equality)],[8,54]),
[iquote('0:SpR:8.0,54.0')] ).
cnf(75,plain,
equal(multiply(u,inverse(u)),multiply(u,additive_identity)),
inference(spr,[status(thm),theory(equality)],[28,54]),
[iquote('0:SpR:28.0,54.0')] ).
cnf(76,plain,
equal(multiply(u,u),u),
inference(rew,[status(thm),theory(equality)],[7,72]),
[iquote('0:Rew:7.0,72.0')] ).
cnf(78,plain,
equal(multiply(u,additive_identity),additive_identity),
inference(rew,[status(thm),theory(equality)],[9,75]),
[iquote('0:Rew:9.0,75.0')] ).
cnf(97,plain,
equal(multiply(add(u,v),u),add(u,multiply(v,additive_identity))),
inference(spr,[status(thm),theory(equality)],[6,4]),
[iquote('0:SpR:6.0,4.0')] ).
cnf(109,plain,
equal(multiply(u,add(u,v)),u),
inference(rew,[status(thm),theory(equality)],[3,97,6,78]),
[iquote('0:Rew:3.0,97.0,6.0,97.0,78.0,97.0')] ).
cnf(132,plain,
equal(add(u,multiply(u,v)),multiply(u,add(u,v))),
inference(spr,[status(thm),theory(equality)],[76,5]),
[iquote('0:SpR:76.0,5.0')] ).
cnf(141,plain,
equal(multiply(u,add(v,multiplicative_identity)),u),
inference(rew,[status(thm),theory(equality)],[49,132,109]),
[iquote('0:Rew:49.0,132.0,109.0,132.0')] ).
cnf(142,plain,
equal(add(u,multiply(u,v)),u),
inference(rew,[status(thm),theory(equality)],[141,49]),
[iquote('0:Rew:141.0,49.0')] ).
cnf(207,plain,
equal(add(u,u),u),
inference(spr,[status(thm),theory(equality)],[7,142]),
[iquote('0:SpR:7.0,142.0')] ).
cnf(218,plain,
$false,
inference(unc,[status(thm)],[207,1]),
[iquote('0:UnC:207.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : BOO004-4 : TPTP v8.1.0. Released v1.1.0.
% 0.10/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jun 1 17:01:52 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.43
% 0.19/0.43 SPASS V 3.9
% 0.19/0.43 SPASS beiseite: Proof found.
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.43 SPASS derived 162 clauses, backtracked 0 clauses, performed 0 splits and kept 53 clauses.
% 0.19/0.43 SPASS allocated 63272 KBytes.
% 0.19/0.43 SPASS spent 0:00:00.07 on the problem.
% 0.19/0.43 0:00:00.04 for the input.
% 0.19/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.43 0:00:00.00 for inferences.
% 0.19/0.43 0:00:00.00 for the backtracking.
% 0.19/0.43 0:00:00.01 for the reduction.
% 0.19/0.43
% 0.19/0.43
% 0.19/0.43 Here is a proof with depth 3, length 26 :
% 0.19/0.43 % SZS output start Refutation
% See solution above
% 0.19/0.43 Formulae used in the proof : prove_a_plus_a_is_a commutativity_of_add commutativity_of_multiply distributivity1 distributivity2 additive_id1 multiplicative_id1 additive_inverse1 multiplicative_inverse1
% 0.19/0.43
%------------------------------------------------------------------------------