TSTP Solution File: BOO003-2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : BOO003-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 23:49:21 EDT 2022
% Result : Unsatisfiable 0.21s 0.42s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of clauses : 12 ( 12 unt; 0 nHn; 12 RR)
% Number of literals : 12 ( 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(multiply(a,a),a),
file('BOO003-2.p',unknown),
[] ).
cnf(2,axiom,
equal(add(u,v),add(v,u)),
file('BOO003-2.p',unknown),
[] ).
cnf(7,axiom,
equal(add(multiply(u,v),multiply(u,w)),multiply(u,add(v,w))),
file('BOO003-2.p',unknown),
[] ).
cnf(8,axiom,
equal(add(u,inverse(u)),multiplicative_identity),
file('BOO003-2.p',unknown),
[] ).
cnf(10,axiom,
equal(multiply(u,inverse(u)),additive_identity),
file('BOO003-2.p',unknown),
[] ).
cnf(12,axiom,
equal(multiply(u,multiplicative_identity),u),
file('BOO003-2.p',unknown),
[] ).
cnf(15,axiom,
equal(add(additive_identity,u),u),
file('BOO003-2.p',unknown),
[] ).
cnf(206,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(231,plain,
equal(multiply(u,add(v,inverse(u))),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[15,206,2]),
[iquote('0:Rew:15.0,206.0,2.0,206.0')] ).
cnf(260,plain,
equal(multiply(u,multiplicative_identity),multiply(u,u)),
inference(spr,[status(thm),theory(equality)],[8,231]),
[iquote('0:SpR:8.0,231.0')] ).
cnf(264,plain,
equal(multiply(u,u),u),
inference(rew,[status(thm),theory(equality)],[12,260]),
[iquote('0:Rew:12.0,260.0')] ).
cnf(265,plain,
$false,
inference(unc,[status(thm)],[264,1]),
[iquote('0:UnC:264.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : BOO003-2 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n029.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
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Wed Jun 1 21:42:46 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.42
% 0.21/0.42 SPASS V 3.9
% 0.21/0.42 SPASS beiseite: Proof found.
% 0.21/0.42 % SZS status Theorem
% 0.21/0.42 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.42 SPASS derived 191 clauses, backtracked 0 clauses, performed 0 splits and kept 91 clauses.
% 0.21/0.42 SPASS allocated 63426 KBytes.
% 0.21/0.42 SPASS spent 0:00:00.06 on the problem.
% 0.21/0.42 0:00:00.03 for the input.
% 0.21/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.42 0:00:00.00 for inferences.
% 0.21/0.42 0:00:00.00 for the backtracking.
% 0.21/0.42 0:00:00.02 for the reduction.
% 0.21/0.42
% 0.21/0.42
% 0.21/0.42 Here is a proof with depth 2, length 12 :
% 0.21/0.42 % SZS output start Refutation
% See solution above
% 0.21/0.42 Formulae used in the proof : prove_a_times_a_is_a commutativity_of_add distributivity4 additive_inverse1 multiplicative_inverse1 multiplicative_id1 additive_id2
% 0.21/0.42
%------------------------------------------------------------------------------