TSTP Solution File: BOO013-4 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : BOO013-4 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 23:49:26 EDT 2022
% Result : Unsatisfiable 0.17s 0.45s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of clauses : 52 ( 52 unt; 0 nHn; 52 RR)
% Number of literals : 52 ( 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 : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(add(a,b),multiplicative_identity),
file('BOO013-4.p',unknown),
[] ).
cnf(2,axiom,
equal(multiply(a,b),additive_identity),
file('BOO013-4.p',unknown),
[] ).
cnf(3,axiom,
~ equal(inverse(a),b),
file('BOO013-4.p',unknown),
[] ).
cnf(4,axiom,
equal(add(u,v),add(v,u)),
file('BOO013-4.p',unknown),
[] ).
cnf(5,axiom,
equal(multiply(u,v),multiply(v,u)),
file('BOO013-4.p',unknown),
[] ).
cnf(6,axiom,
equal(multiply(add(u,v),add(u,w)),add(u,multiply(v,w))),
file('BOO013-4.p',unknown),
[] ).
cnf(7,axiom,
equal(add(multiply(u,v),multiply(u,w)),multiply(u,add(v,w))),
file('BOO013-4.p',unknown),
[] ).
cnf(8,axiom,
equal(add(u,additive_identity),u),
file('BOO013-4.p',unknown),
[] ).
cnf(9,axiom,
equal(multiply(u,multiplicative_identity),u),
file('BOO013-4.p',unknown),
[] ).
cnf(10,axiom,
equal(add(u,inverse(u)),multiplicative_identity),
file('BOO013-4.p',unknown),
[] ).
cnf(11,axiom,
equal(multiply(u,inverse(u)),additive_identity),
file('BOO013-4.p',unknown),
[] ).
cnf(18,plain,
equal(multiply(multiplicative_identity,u),u),
inference(spr,[status(thm),theory(equality)],[5,9]),
[iquote('0:SpR:5.0,9.0')] ).
cnf(29,plain,
equal(add(additive_identity,u),u),
inference(spr,[status(thm),theory(equality)],[4,8]),
[iquote('0:SpR:4.0,8.0')] ).
cnf(50,plain,
equal(add(multiply(u,v),u),multiply(u,add(v,multiplicative_identity))),
inference(spr,[status(thm),theory(equality)],[9,7]),
[iquote('0:SpR:9.0,7.0')] ).
cnf(51,plain,
equal(multiply(u,add(v,inverse(u))),add(multiply(u,v),additive_identity)),
inference(spr,[status(thm),theory(equality)],[11,7]),
[iquote('0:SpR:11.0,7.0')] ).
cnf(55,plain,
equal(add(additive_identity,multiply(a,u)),multiply(a,add(b,u))),
inference(spr,[status(thm),theory(equality)],[2,7]),
[iquote('0:SpR:2.0,7.0')] ).
cnf(57,plain,
equal(multiply(u,add(inverse(u),v)),add(additive_identity,multiply(u,v))),
inference(spr,[status(thm),theory(equality)],[11,7]),
[iquote('0:SpR:11.0,7.0')] ).
cnf(62,plain,
equal(add(u,multiply(u,v)),multiply(u,add(v,multiplicative_identity))),
inference(rew,[status(thm),theory(equality)],[4,50]),
[iquote('0:Rew:4.0,50.0')] ).
cnf(64,plain,
equal(multiply(a,add(b,u)),multiply(a,u)),
inference(rew,[status(thm),theory(equality)],[29,55]),
[iquote('0:Rew:29.0,55.0')] ).
cnf(67,plain,
equal(multiply(u,add(v,inverse(u))),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[29,51,4]),
[iquote('0:Rew:29.0,51.0,4.0,51.0')] ).
cnf(68,plain,
equal(multiply(u,add(inverse(u),v)),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[29,57]),
[iquote('0:Rew:29.0,57.0')] ).
cnf(77,plain,
equal(multiply(add(u,v),u),add(u,multiply(v,additive_identity))),
inference(spr,[status(thm),theory(equality)],[8,6]),
[iquote('0:SpR:8.0,6.0')] ).
cnf(83,plain,
equal(add(a,multiply(b,u)),multiply(multiplicative_identity,add(a,u))),
inference(spr,[status(thm),theory(equality)],[1,6]),
[iquote('0:SpR:1.0,6.0')] ).
cnf(85,plain,
equal(add(u,multiply(inverse(u),v)),multiply(multiplicative_identity,add(u,v))),
inference(spr,[status(thm),theory(equality)],[10,6]),
[iquote('0:SpR:10.0,6.0')] ).
cnf(91,plain,
equal(multiply(u,add(u,v)),add(u,multiply(v,additive_identity))),
inference(rew,[status(thm),theory(equality)],[5,77]),
[iquote('0:Rew:5.0,77.0')] ).
cnf(93,plain,
equal(add(a,multiply(b,u)),add(a,u)),
inference(rew,[status(thm),theory(equality)],[18,83]),
[iquote('0:Rew:18.0,83.0')] ).
cnf(96,plain,
equal(add(u,multiply(inverse(u),v)),add(u,v)),
inference(rew,[status(thm),theory(equality)],[18,85]),
[iquote('0:Rew:18.0,85.0')] ).
cnf(129,plain,
equal(multiply(a,inverse(b)),multiply(a,multiplicative_identity)),
inference(spr,[status(thm),theory(equality)],[10,64]),
[iquote('0:SpR:10.0,64.0')] ).
cnf(133,plain,
equal(multiply(a,inverse(b)),a),
inference(rew,[status(thm),theory(equality)],[9,129]),
[iquote('0:Rew:9.0,129.0')] ).
cnf(186,plain,
equal(multiply(u,multiplicative_identity),multiply(u,u)),
inference(spr,[status(thm),theory(equality)],[10,67]),
[iquote('0:SpR:10.0,67.0')] ).
cnf(189,plain,
equal(multiply(u,inverse(u)),multiply(u,additive_identity)),
inference(spr,[status(thm),theory(equality)],[29,67]),
[iquote('0:SpR:29.0,67.0')] ).
cnf(190,plain,
equal(multiply(u,u),u),
inference(rew,[status(thm),theory(equality)],[9,186]),
[iquote('0:Rew:9.0,186.0')] ).
cnf(193,plain,
equal(multiply(u,additive_identity),additive_identity),
inference(rew,[status(thm),theory(equality)],[11,189]),
[iquote('0:Rew:11.0,189.0')] ).
cnf(194,plain,
equal(multiply(u,add(u,v)),add(u,additive_identity)),
inference(rew,[status(thm),theory(equality)],[193,91]),
[iquote('0:Rew:193.0,91.0')] ).
cnf(196,plain,
equal(multiply(u,add(u,v)),u),
inference(rew,[status(thm),theory(equality)],[8,194]),
[iquote('0:Rew:8.0,194.0')] ).
cnf(229,plain,
equal(add(u,multiply(u,v)),multiply(u,add(u,v))),
inference(spr,[status(thm),theory(equality)],[190,7]),
[iquote('0:SpR:190.0,7.0')] ).
cnf(240,plain,
equal(multiply(u,add(v,multiplicative_identity)),u),
inference(rew,[status(thm),theory(equality)],[62,229,196]),
[iquote('0:Rew:62.0,229.0,196.0,229.0')] ).
cnf(242,plain,
equal(add(u,multiply(u,v)),u),
inference(rew,[status(thm),theory(equality)],[240,62]),
[iquote('0:Rew:240.0,62.0')] ).
cnf(340,plain,
equal(add(u,multiply(v,u)),u),
inference(spr,[status(thm),theory(equality)],[5,242]),
[iquote('0:SpR:5.0,242.0')] ).
cnf(424,plain,
equal(multiply(u,inverse(inverse(u))),multiply(u,multiplicative_identity)),
inference(spr,[status(thm),theory(equality)],[10,68]),
[iquote('0:SpR:10.0,68.0')] ).
cnf(435,plain,
equal(multiply(u,inverse(inverse(u))),u),
inference(rew,[status(thm),theory(equality)],[9,424]),
[iquote('0:Rew:9.0,424.0')] ).
cnf(445,plain,
equal(add(a,inverse(inverse(b))),add(a,b)),
inference(spr,[status(thm),theory(equality)],[435,93]),
[iquote('0:SpR:435.0,93.0')] ).
cnf(452,plain,
equal(add(a,inverse(inverse(b))),multiplicative_identity),
inference(rew,[status(thm),theory(equality)],[1,445]),
[iquote('0:Rew:1.0,445.0')] ).
cnf(459,plain,
equal(multiply(inverse(b),multiplicative_identity),multiply(inverse(b),a)),
inference(spr,[status(thm),theory(equality)],[452,67]),
[iquote('0:SpR:452.0,67.0')] ).
cnf(460,plain,
equal(inverse(b),a),
inference(rew,[status(thm),theory(equality)],[18,459,5,133]),
[iquote('0:Rew:18.0,459.0,5.0,459.0,133.0,459.0,5.0,459.0')] ).
cnf(578,plain,
equal(add(inverse(inverse(u)),u),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[435,340]),
[iquote('0:SpR:435.0,340.0')] ).
cnf(596,plain,
equal(add(u,inverse(inverse(u))),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[4,578]),
[iquote('0:Rew:4.0,578.0')] ).
cnf(658,plain,
equal(add(u,inverse(inverse(u))),add(u,additive_identity)),
inference(spr,[status(thm),theory(equality)],[11,96]),
[iquote('0:SpR:11.0,96.0')] ).
cnf(673,plain,
equal(add(u,inverse(inverse(u))),u),
inference(rew,[status(thm),theory(equality)],[8,658]),
[iquote('0:Rew:8.0,658.0')] ).
cnf(674,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[596,673]),
[iquote('0:Rew:596.0,673.0')] ).
cnf(705,plain,
equal(inverse(a),b),
inference(spr,[status(thm),theory(equality)],[460,674]),
[iquote('0:SpR:460.0,674.0')] ).
cnf(706,plain,
$false,
inference(mrr,[status(thm)],[705,3]),
[iquote('0:MRR:705.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : BOO013-4 : TPTP v8.1.0. Released v1.1.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.32 % Computer : n021.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Wed Jun 1 15:55:01 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.17/0.45
% 0.17/0.45 SPASS V 3.9
% 0.17/0.45 SPASS beiseite: Proof found.
% 0.17/0.45 % SZS status Theorem
% 0.17/0.45 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.45 SPASS derived 517 clauses, backtracked 0 clauses, performed 0 splits and kept 159 clauses.
% 0.17/0.45 SPASS allocated 63655 KBytes.
% 0.17/0.45 SPASS spent 0:00:00.11 on the problem.
% 0.17/0.45 0:00:00.03 for the input.
% 0.17/0.45 0:00:00.00 for the FLOTTER CNF translation.
% 0.17/0.45 0:00:00.01 for inferences.
% 0.17/0.45 0:00:00.00 for the backtracking.
% 0.17/0.45 0:00:00.04 for the reduction.
% 0.17/0.45
% 0.17/0.45
% 0.17/0.45 Here is a proof with depth 5, length 52 :
% 0.17/0.45 % SZS output start Refutation
% See solution above
% 0.17/0.45 Formulae used in the proof : b_a_multiplicative_identity b_an_additive_identity prove_a_inverse_is_b commutativity_of_add commutativity_of_multiply distributivity1 distributivity2 additive_id1 multiplicative_id1 additive_inverse1 multiplicative_inverse1
% 0.17/0.45
%------------------------------------------------------------------------------