TSTP Solution File: BOO012-4 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : BOO012-4 : 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 23:49:25 EDT 2022
% Result : Unsatisfiable 0.21s 0.47s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of clauses : 37 ( 37 unt; 0 nHn; 37 RR)
% Number of literals : 37 ( 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(inverse(inverse(x__dfg)),x__dfg),
file('BOO012-4.p',unknown),
[] ).
cnf(2,axiom,
equal(add(u,v),add(v,u)),
file('BOO012-4.p',unknown),
[] ).
cnf(3,axiom,
equal(multiply(u,v),multiply(v,u)),
file('BOO012-4.p',unknown),
[] ).
cnf(4,axiom,
equal(multiply(add(u,v),add(u,w)),add(u,multiply(v,w))),
file('BOO012-4.p',unknown),
[] ).
cnf(5,axiom,
equal(add(multiply(u,v),multiply(u,w)),multiply(u,add(v,w))),
file('BOO012-4.p',unknown),
[] ).
cnf(6,axiom,
equal(add(u,additive_identity),u),
file('BOO012-4.p',unknown),
[] ).
cnf(7,axiom,
equal(multiply(u,multiplicative_identity),u),
file('BOO012-4.p',unknown),
[] ).
cnf(8,axiom,
equal(add(u,inverse(u)),multiplicative_identity),
file('BOO012-4.p',unknown),
[] ).
cnf(9,axiom,
equal(multiply(u,inverse(u)),additive_identity),
file('BOO012-4.p',unknown),
[] ).
cnf(14,plain,
equal(multiply(multiplicative_identity,u),u),
inference(spr,[status(thm),theory(equality)],[3,7]),
[iquote('0:SpR:3.0,7.0')] ).
cnf(28,plain,
equal(add(additive_identity,u),u),
inference(spr,[status(thm),theory(equality)],[2,6]),
[iquote('0:SpR:2.0,6.0')] ).
cnf(37,plain,
equal(add(multiply(u,v),u),multiply(u,add(v,multiplicative_identity))),
inference(spr,[status(thm),theory(equality)],[7,5]),
[iquote('0:SpR:7.0,5.0')] ).
cnf(38,plain,
equal(multiply(u,add(v,inverse(u))),add(multiply(u,v),additive_identity)),
inference(spr,[status(thm),theory(equality)],[9,5]),
[iquote('0:SpR:9.0,5.0')] ).
cnf(43,plain,
equal(multiply(u,add(inverse(u),v)),add(additive_identity,multiply(u,v))),
inference(spr,[status(thm),theory(equality)],[9,5]),
[iquote('0:SpR:9.0,5.0')] ).
cnf(47,plain,
equal(add(u,multiply(u,v)),multiply(u,add(v,multiplicative_identity))),
inference(rew,[status(thm),theory(equality)],[2,37]),
[iquote('0:Rew:2.0,37.0')] ).
cnf(51,plain,
equal(multiply(u,add(v,inverse(u))),add(additive_identity,multiply(u,v))),
inference(rew,[status(thm),theory(equality)],[2,38]),
[iquote('0:Rew:2.0,38.0')] ).
cnf(52,plain,
equal(multiply(u,add(v,inverse(u))),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[28,51]),
[iquote('0:Rew:28.0,51.0')] ).
cnf(53,plain,
equal(multiply(u,add(inverse(u),v)),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[28,43]),
[iquote('0:Rew:28.0,43.0')] ).
cnf(70,plain,
equal(multiply(u,multiplicative_identity),multiply(u,u)),
inference(spr,[status(thm),theory(equality)],[8,52]),
[iquote('0:SpR:8.0,52.0')] ).
cnf(73,plain,
equal(multiply(u,inverse(u)),multiply(u,additive_identity)),
inference(spr,[status(thm),theory(equality)],[28,52]),
[iquote('0:SpR:28.0,52.0')] ).
cnf(74,plain,
equal(multiply(u,u),u),
inference(rew,[status(thm),theory(equality)],[7,70]),
[iquote('0:Rew:7.0,70.0')] ).
cnf(76,plain,
equal(multiply(u,additive_identity),additive_identity),
inference(rew,[status(thm),theory(equality)],[9,73]),
[iquote('0:Rew:9.0,73.0')] ).
cnf(95,plain,
equal(multiply(add(u,v),u),add(u,multiply(v,additive_identity))),
inference(spr,[status(thm),theory(equality)],[6,4]),
[iquote('0:SpR:6.0,4.0')] ).
cnf(102,plain,
equal(add(u,multiply(inverse(u),v)),multiply(multiplicative_identity,add(u,v))),
inference(spr,[status(thm),theory(equality)],[8,4]),
[iquote('0:SpR:8.0,4.0')] ).
cnf(107,plain,
equal(multiply(u,add(u,v)),u),
inference(rew,[status(thm),theory(equality)],[3,95,6,76]),
[iquote('0:Rew:3.0,95.0,6.0,95.0,76.0,95.0')] ).
cnf(112,plain,
equal(add(u,multiply(inverse(u),v)),add(u,v)),
inference(rew,[status(thm),theory(equality)],[14,102]),
[iquote('0:Rew:14.0,102.0')] ).
cnf(130,plain,
equal(add(u,multiply(u,v)),multiply(u,add(u,v))),
inference(spr,[status(thm),theory(equality)],[74,5]),
[iquote('0:SpR:74.0,5.0')] ).
cnf(139,plain,
equal(multiply(u,add(v,multiplicative_identity)),u),
inference(rew,[status(thm),theory(equality)],[47,130,107]),
[iquote('0:Rew:47.0,130.0,107.0,130.0')] ).
cnf(140,plain,
equal(add(u,multiply(u,v)),u),
inference(rew,[status(thm),theory(equality)],[139,47]),
[iquote('0:Rew:139.0,47.0')] ).
cnf(207,plain,
equal(add(u,multiply(v,u)),u),
inference(spr,[status(thm),theory(equality)],[3,140]),
[iquote('0:SpR:3.0,140.0')] ).
cnf(266,plain,
equal(multiply(u,inverse(inverse(u))),multiply(u,multiplicative_identity)),
inference(spr,[status(thm),theory(equality)],[8,53]),
[iquote('0:SpR:8.0,53.0')] ).
cnf(276,plain,
equal(multiply(u,inverse(inverse(u))),u),
inference(rew,[status(thm),theory(equality)],[7,266]),
[iquote('0:Rew:7.0,266.0')] ).
cnf(304,plain,
equal(add(inverse(inverse(u)),u),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[276,207]),
[iquote('0:SpR:276.0,207.0')] ).
cnf(317,plain,
equal(add(u,inverse(inverse(u))),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[2,304]),
[iquote('0:Rew:2.0,304.0')] ).
cnf(494,plain,
equal(add(u,inverse(inverse(u))),add(u,additive_identity)),
inference(spr,[status(thm),theory(equality)],[9,112]),
[iquote('0:SpR:9.0,112.0')] ).
cnf(513,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[317,494,6]),
[iquote('0:Rew:317.0,494.0,6.0,494.0')] ).
cnf(514,plain,
$false,
inference(unc,[status(thm)],[513,1]),
[iquote('0:UnC:513.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : BOO012-4 : TPTP v8.1.0. Released v1.1.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n021.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 17:25:16 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.21/0.47
% 0.21/0.47 SPASS V 3.9
% 0.21/0.47 SPASS beiseite: Proof found.
% 0.21/0.47 % SZS status Theorem
% 0.21/0.47 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.47 SPASS derived 395 clauses, backtracked 0 clauses, performed 0 splits and kept 107 clauses.
% 0.21/0.47 SPASS allocated 63526 KBytes.
% 0.21/0.47 SPASS spent 0:00:00.11 on the problem.
% 0.21/0.47 0:00:00.04 for the input.
% 0.21/0.47 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.47 0:00:00.00 for inferences.
% 0.21/0.47 0:00:00.00 for the backtracking.
% 0.21/0.47 0:00:00.03 for the reduction.
% 0.21/0.47
% 0.21/0.47
% 0.21/0.47 Here is a proof with depth 3, length 37 :
% 0.21/0.47 % SZS output start Refutation
% See solution above
% 0.21/0.47 Formulae used in the proof : prove_inverse_is_an_involution commutativity_of_add commutativity_of_multiply distributivity1 distributivity2 additive_id1 multiplicative_id1 additive_inverse1 multiplicative_inverse1
% 0.21/0.47
%------------------------------------------------------------------------------