TSTP Solution File: BOO004-2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : BOO004-2 : TPTP v8.1.0. Released v1.0.0.
% 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 0.22s 0.46s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of clauses : 30 ( 30 unt; 0 nHn; 30 RR)
% Number of literals : 30 ( 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('BOO004-2.p',unknown),
[] ).
cnf(2,axiom,
equal(add(u,v),add(v,u)),
file('BOO004-2.p',unknown),
[] ).
cnf(3,axiom,
equal(multiply(u,v),multiply(v,u)),
file('BOO004-2.p',unknown),
[] ).
cnf(4,axiom,
equal(multiply(add(u,v),add(w,v)),add(multiply(u,w),v)),
file('BOO004-2.p',unknown),
[] ).
cnf(6,axiom,
equal(add(multiply(u,v),multiply(w,v)),multiply(add(u,w),v)),
file('BOO004-2.p',unknown),
[] ).
cnf(7,axiom,
equal(add(multiply(u,v),multiply(u,w)),multiply(u,add(v,w))),
file('BOO004-2.p',unknown),
[] ).
cnf(8,axiom,
equal(add(u,inverse(u)),multiplicative_identity),
file('BOO004-2.p',unknown),
[] ).
cnf(10,axiom,
equal(multiply(u,inverse(u)),additive_identity),
file('BOO004-2.p',unknown),
[] ).
cnf(12,axiom,
equal(multiply(u,multiplicative_identity),u),
file('BOO004-2.p',unknown),
[] ).
cnf(13,axiom,
equal(multiply(multiplicative_identity,u),u),
file('BOO004-2.p',unknown),
[] ).
cnf(15,axiom,
equal(add(additive_identity,u),u),
file('BOO004-2.p',unknown),
[] ).
cnf(55,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(65,plain,
equal(add(u,multiply(v,u)),multiply(add(v,multiplicative_identity),u)),
inference(rew,[status(thm),theory(equality)],[2,55]),
[iquote('0:Rew:2.0,55.0')] ).
cnf(75,plain,
equal(add(u,u),multiply(add(multiplicative_identity,multiplicative_identity),u)),
inference(spr,[status(thm),theory(equality)],[13,65]),
[iquote('0:SpR:13.0,65.0')] ).
cnf(76,plain,
equal(add(u,multiply(u,v)),multiply(add(v,multiplicative_identity),u)),
inference(spr,[status(thm),theory(equality)],[3,65]),
[iquote('0:SpR:3.0,65.0')] ).
cnf(101,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(115,plain,
equal(multiply(u,add(v,u)),add(multiply(v,additive_identity),u)),
inference(rew,[status(thm),theory(equality)],[3,101]),
[iquote('0:Rew:3.0,101.0')] ).
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(258,plain,
equal(multiply(u,inverse(u)),multiply(u,additive_identity)),
inference(spr,[status(thm),theory(equality)],[15,231]),
[iquote('0:SpR:15.0,231.0')] ).
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(267,plain,
equal(multiply(u,additive_identity),additive_identity),
inference(rew,[status(thm),theory(equality)],[10,258]),
[iquote('0:Rew:10.0,258.0')] ).
cnf(270,plain,
equal(multiply(u,add(v,u)),add(additive_identity,u)),
inference(rew,[status(thm),theory(equality)],[267,115]),
[iquote('0:Rew:267.0,115.0')] ).
cnf(282,plain,
equal(multiply(u,add(v,u)),u),
inference(rew,[status(thm),theory(equality)],[15,270]),
[iquote('0:Rew:15.0,270.0')] ).
cnf(332,plain,
equal(add(multiply(u,v),u),multiply(u,add(v,u))),
inference(spr,[status(thm),theory(equality)],[264,7]),
[iquote('0:SpR:264.0,7.0')] ).
cnf(341,plain,
equal(add(u,multiply(u,v)),multiply(u,add(v,u))),
inference(rew,[status(thm),theory(equality)],[2,332]),
[iquote('0:Rew:2.0,332.0')] ).
cnf(342,plain,
equal(multiply(add(u,multiplicative_identity),v),v),
inference(rew,[status(thm),theory(equality)],[76,341,282]),
[iquote('0:Rew:76.0,341.0,282.0,341.0')] ).
cnf(343,plain,
equal(add(u,u),u),
inference(rew,[status(thm),theory(equality)],[342,75]),
[iquote('0:Rew:342.0,75.0')] ).
cnf(360,plain,
$false,
inference(unc,[status(thm)],[343,1]),
[iquote('0:UnC:343.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : BOO004-2 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n025.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Wed Jun 1 22:24:59 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.22/0.46
% 0.22/0.46 SPASS V 3.9
% 0.22/0.46 SPASS beiseite: Proof found.
% 0.22/0.46 % SZS status Theorem
% 0.22/0.46 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.46 SPASS derived 259 clauses, backtracked 0 clauses, performed 0 splits and kept 110 clauses.
% 0.22/0.46 SPASS allocated 63478 KBytes.
% 0.22/0.46 SPASS spent 0:00:00.09 on the problem.
% 0.22/0.46 0:00:00.03 for the input.
% 0.22/0.46 0:00:00.00 for the FLOTTER CNF translation.
% 0.22/0.46 0:00:00.00 for inferences.
% 0.22/0.46 0:00:00.00 for the backtracking.
% 0.22/0.46 0:00:00.03 for the reduction.
% 0.22/0.46
% 0.22/0.46
% 0.22/0.46 Here is a proof with depth 3, length 30 :
% 0.22/0.46 % SZS output start Refutation
% See solution above
% 0.22/0.47 Formulae used in the proof : prove_a_plus_a_is_a commutativity_of_add commutativity_of_multiply distributivity1 distributivity3 distributivity4 additive_inverse1 multiplicative_inverse1 multiplicative_id1 multiplicative_id2 additive_id2
% 0.22/0.47
%------------------------------------------------------------------------------