TSTP Solution File: BOO005-2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : BOO005-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 0.46s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of clauses : 29 ( 29 unt; 0 nHn; 29 RR)
% Number of literals : 29 ( 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,multiplicative_identity),multiplicative_identity),
file('BOO005-2.p',unknown),
[] ).
cnf(2,axiom,
equal(add(u,v),add(v,u)),
file('BOO005-2.p',unknown),
[] ).
cnf(3,axiom,
equal(multiply(u,v),multiply(v,u)),
file('BOO005-2.p',unknown),
[] ).
cnf(4,axiom,
equal(multiply(add(u,v),add(w,v)),add(multiply(u,w),v)),
file('BOO005-2.p',unknown),
[] ).
cnf(6,axiom,
equal(add(multiply(u,v),multiply(w,v)),multiply(add(u,w),v)),
file('BOO005-2.p',unknown),
[] ).
cnf(7,axiom,
equal(add(multiply(u,v),multiply(u,w)),multiply(u,add(v,w))),
file('BOO005-2.p',unknown),
[] ).
cnf(8,axiom,
equal(add(u,inverse(u)),multiplicative_identity),
file('BOO005-2.p',unknown),
[] ).
cnf(10,axiom,
equal(multiply(u,inverse(u)),additive_identity),
file('BOO005-2.p',unknown),
[] ).
cnf(12,axiom,
equal(multiply(u,multiplicative_identity),u),
file('BOO005-2.p',unknown),
[] ).
cnf(13,axiom,
equal(multiply(multiplicative_identity,u),u),
file('BOO005-2.p',unknown),
[] ).
cnf(15,axiom,
equal(add(additive_identity,u),u),
file('BOO005-2.p',unknown),
[] ).
cnf(53,plain,
equal(add(multiply(u,v),v),multiply(add(u,multiplicative_identity),v)),
inference(spr,[status(thm),theory(equality)],[13,6]),
[iquote('0:SpR:13.0,6.0')] ).
cnf(63,plain,
equal(add(u,multiply(v,u)),multiply(add(v,multiplicative_identity),u)),
inference(rew,[status(thm),theory(equality)],[2,53]),
[iquote('0:Rew:2.0,53.0')] ).
cnf(74,plain,
equal(add(u,multiply(u,v)),multiply(add(v,multiplicative_identity),u)),
inference(spr,[status(thm),theory(equality)],[3,63]),
[iquote('0:SpR:3.0,63.0')] ).
cnf(99,plain,
equal(multiply(add(u,v),v),add(multiply(u,additive_identity),v)),
inference(spr,[status(thm),theory(equality)],[15,4]),
[iquote('0:SpR:15.0,4.0')] ).
cnf(113,plain,
equal(multiply(u,add(v,u)),add(multiply(v,additive_identity),u)),
inference(rew,[status(thm),theory(equality)],[3,99]),
[iquote('0:Rew:3.0,99.0')] ).
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(258,plain,
equal(multiply(u,multiplicative_identity),multiply(u,u)),
inference(spr,[status(thm),theory(equality)],[8,229]),
[iquote('0:SpR:8.0,229.0')] ).
cnf(262,plain,
equal(multiply(u,u),u),
inference(rew,[status(thm),theory(equality)],[12,258]),
[iquote('0:Rew:12.0,258.0')] ).
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(268,plain,
equal(multiply(u,add(v,u)),add(additive_identity,u)),
inference(rew,[status(thm),theory(equality)],[265,113]),
[iquote('0:Rew:265.0,113.0')] ).
cnf(280,plain,
equal(multiply(u,add(v,u)),u),
inference(rew,[status(thm),theory(equality)],[15,268]),
[iquote('0:Rew:15.0,268.0')] ).
cnf(330,plain,
equal(add(multiply(u,v),u),multiply(u,add(v,u))),
inference(spr,[status(thm),theory(equality)],[262,7]),
[iquote('0:SpR:262.0,7.0')] ).
cnf(339,plain,
equal(add(u,multiply(u,v)),multiply(u,add(v,u))),
inference(rew,[status(thm),theory(equality)],[2,330]),
[iquote('0:Rew:2.0,330.0')] ).
cnf(340,plain,
equal(multiply(add(u,multiplicative_identity),v),v),
inference(rew,[status(thm),theory(equality)],[74,339,280]),
[iquote('0:Rew:74.0,339.0,280.0,339.0')] ).
cnf(471,plain,
equal(add(u,multiplicative_identity),multiplicative_identity),
inference(spr,[status(thm),theory(equality)],[340,12]),
[iquote('0:SpR:340.0,12.0')] ).
cnf(488,plain,
$false,
inference(unc,[status(thm)],[471,1]),
[iquote('0:UnC:471.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : BOO005-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.11/0.12 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n025.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 16:04:59 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.46
% 0.19/0.46 SPASS V 3.9
% 0.19/0.46 SPASS beiseite: Proof found.
% 0.19/0.46 % SZS status Theorem
% 0.19/0.46 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.46 SPASS derived 311 clauses, backtracked 0 clauses, performed 0 splits and kept 121 clauses.
% 0.19/0.46 SPASS allocated 63558 KBytes.
% 0.19/0.46 SPASS spent 0:00:00.10 on the problem.
% 0.19/0.46 0:00:00.03 for the input.
% 0.19/0.46 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.46 0:00:00.00 for inferences.
% 0.19/0.46 0:00:00.00 for the backtracking.
% 0.19/0.46 0:00:00.04 for the reduction.
% 0.19/0.46
% 0.19/0.46
% 0.19/0.46 Here is a proof with depth 4, length 29 :
% 0.19/0.46 % SZS output start Refutation
% See solution above
% 0.19/0.46 Formulae used in the proof : prove_a_plus_1_is_a commutativity_of_add commutativity_of_multiply distributivity1 distributivity3 distributivity4 additive_inverse1 multiplicative_inverse1 multiplicative_id1 multiplicative_id2 additive_id2
% 0.19/0.46
%------------------------------------------------------------------------------