TSTP Solution File: BOO010-2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : BOO010-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 23:49:24 EDT 2022
% Result : Unsatisfiable 0.19s 0.46s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of clauses : 40 ( 40 unt; 0 nHn; 40 RR)
% Number of literals : 40 ( 0 equ; 3 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 : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(add(a,multiply(a,b)),a),
file('BOO010-2.p',unknown),
[] ).
cnf(2,axiom,
equal(add(u,v),add(v,u)),
file('BOO010-2.p',unknown),
[] ).
cnf(3,axiom,
equal(multiply(u,v),multiply(v,u)),
file('BOO010-2.p',unknown),
[] ).
cnf(5,axiom,
equal(multiply(add(u,v),add(u,w)),add(u,multiply(v,w))),
file('BOO010-2.p',unknown),
[] ).
cnf(6,axiom,
equal(add(multiply(u,v),multiply(w,v)),multiply(add(u,w),v)),
file('BOO010-2.p',unknown),
[] ).
cnf(7,axiom,
equal(add(multiply(u,v),multiply(u,w)),multiply(u,add(v,w))),
file('BOO010-2.p',unknown),
[] ).
cnf(8,axiom,
equal(add(u,inverse(u)),multiplicative_identity),
file('BOO010-2.p',unknown),
[] ).
cnf(10,axiom,
equal(multiply(u,inverse(u)),additive_identity),
file('BOO010-2.p',unknown),
[] ).
cnf(12,axiom,
equal(multiply(u,multiplicative_identity),u),
file('BOO010-2.p',unknown),
[] ).
cnf(13,axiom,
equal(multiply(multiplicative_identity,u),u),
file('BOO010-2.p',unknown),
[] ).
cnf(14,axiom,
equal(add(u,additive_identity),u),
file('BOO010-2.p',unknown),
[] ).
cnf(15,axiom,
equal(add(additive_identity,u),u),
file('BOO010-2.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(73,plain,
equal(add(u,u),multiply(add(multiplicative_identity,multiplicative_identity),u)),
inference(spr,[status(thm),theory(equality)],[13,63]),
[iquote('0:SpR:13.0,63.0')] ).
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(80,plain,
~ equal(multiply(add(b,multiplicative_identity),a),a),
inference(rew,[status(thm),theory(equality)],[74,1]),
[iquote('0:Rew:74.0,1.0')] ).
cnf(81,plain,
~ equal(multiply(a,add(b,multiplicative_identity)),a),
inference(rew,[status(thm),theory(equality)],[3,80]),
[iquote('0:Rew:3.0,80.0')] ).
cnf(156,plain,
equal(multiply(u,add(multiplicative_identity,multiplicative_identity)),add(u,u)),
inference(spr,[status(thm),theory(equality)],[73,3]),
[iquote('0:SpR:73.0,3.0')] ).
cnf(181,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(204,plain,
equal(multiply(u,add(v,inverse(u))),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[15,181,2]),
[iquote('0:Rew:15.0,181.0,2.0,181.0')] ).
cnf(227,plain,
equal(add(multiply(u,v),add(u,u)),multiply(u,add(v,add(multiplicative_identity,multiplicative_identity)))),
inference(spr,[status(thm),theory(equality)],[156,7]),
[iquote('0:SpR:156.0,7.0')] ).
cnf(258,plain,
equal(multiply(u,inverse(u)),multiply(u,additive_identity)),
inference(spr,[status(thm),theory(equality)],[15,204]),
[iquote('0:SpR:15.0,204.0')] ).
cnf(260,plain,
equal(multiply(u,multiplicative_identity),multiply(u,u)),
inference(spr,[status(thm),theory(equality)],[8,204]),
[iquote('0:SpR:8.0,204.0')] ).
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(336,plain,
equal(multiply(add(u,v),u),add(u,multiply(v,additive_identity))),
inference(spr,[status(thm),theory(equality)],[14,5]),
[iquote('0:SpR:14.0,5.0')] ).
cnf(356,plain,
equal(multiply(u,add(u,v)),u),
inference(rew,[status(thm),theory(equality)],[3,336,14,267]),
[iquote('0:Rew:3.0,336.0,14.0,336.0,267.0,336.0')] ).
cnf(380,plain,
equal(multiply(add(u,multiplicative_identity),u),add(u,u)),
inference(spr,[status(thm),theory(equality)],[264,63]),
[iquote('0:SpR:264.0,63.0')] ).
cnf(384,plain,
equal(add(u,multiply(v,u)),multiply(add(u,v),u)),
inference(spr,[status(thm),theory(equality)],[264,6]),
[iquote('0:SpR:264.0,6.0')] ).
cnf(392,plain,
equal(multiply(u,add(u,multiplicative_identity)),add(u,u)),
inference(rew,[status(thm),theory(equality)],[3,380]),
[iquote('0:Rew:3.0,380.0')] ).
cnf(393,plain,
equal(add(u,u),u),
inference(rew,[status(thm),theory(equality)],[356,392]),
[iquote('0:Rew:356.0,392.0')] ).
cnf(409,plain,
equal(add(multiply(u,v),add(u,u)),multiply(u,add(v,multiplicative_identity))),
inference(rew,[status(thm),theory(equality)],[393,227]),
[iquote('0:Rew:393.0,227.0')] ).
cnf(427,plain,
equal(multiply(add(u,multiplicative_identity),v),multiply(v,add(v,u))),
inference(rew,[status(thm),theory(equality)],[63,384,3]),
[iquote('0:Rew:63.0,384.0,3.0,384.0')] ).
cnf(428,plain,
equal(multiply(add(u,multiplicative_identity),v),v),
inference(rew,[status(thm),theory(equality)],[356,427]),
[iquote('0:Rew:356.0,427.0')] ).
cnf(432,plain,
equal(add(u,multiply(u,v)),u),
inference(rew,[status(thm),theory(equality)],[428,74]),
[iquote('0:Rew:428.0,74.0')] ).
cnf(466,plain,
equal(add(multiply(u,v),u),multiply(u,add(v,multiplicative_identity))),
inference(rew,[status(thm),theory(equality)],[393,409]),
[iquote('0:Rew:393.0,409.0')] ).
cnf(467,plain,
equal(add(u,multiply(u,v)),multiply(u,add(v,multiplicative_identity))),
inference(rew,[status(thm),theory(equality)],[2,466]),
[iquote('0:Rew:2.0,466.0')] ).
cnf(468,plain,
equal(multiply(u,add(v,multiplicative_identity)),u),
inference(rew,[status(thm),theory(equality)],[432,467]),
[iquote('0:Rew:432.0,467.0')] ).
cnf(469,plain,
$false,
inference(unc,[status(thm)],[468,81]),
[iquote('0:UnC:468.0,81.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : BOO010-2 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n023.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Wed Jun 1 18:38:41 EDT 2022
% 0.13/0.33 % 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 294 clauses, backtracked 0 clauses, performed 0 splits and kept 125 clauses.
% 0.19/0.46 SPASS allocated 63569 KBytes.
% 0.19/0.46 SPASS spent 0:00:00.11 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 0:00:00.05 for the reduction.
% 0.19/0.46
% 0.19/0.46
% 0.19/0.46 Here is a proof with depth 4, length 40 :
% 0.19/0.46 % SZS output start Refutation
% See solution above
% 0.19/0.46 Formulae used in the proof : prove_a_plus_ab_is_a commutativity_of_add commutativity_of_multiply distributivity2 distributivity3 distributivity4 additive_inverse1 multiplicative_inverse1 multiplicative_id1 multiplicative_id2 additive_id1 additive_id2
% 0.19/0.46
%------------------------------------------------------------------------------