TSTP Solution File: RNG008-3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG008-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 : Mon Jul 18 20:41:11 EDT 2022
% Result : Unsatisfiable 0.20s 0.53s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of clauses : 38 ( 38 unt; 0 nHn; 38 RR)
% Number of literals : 38 ( 0 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 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(2,axiom,
equal(add(u,additive_inverse(u)),additive_identity),
file('RNG008-3.p',unknown),
[] ).
cnf(3,axiom,
equal(multiply(u,u),u),
file('RNG008-3.p',unknown),
[] ).
cnf(4,axiom,
equal(multiply(a,b),c),
file('RNG008-3.p',unknown),
[] ).
cnf(5,axiom,
~ equal(multiply(b,a),c),
file('RNG008-3.p',unknown),
[] ).
cnf(6,axiom,
equal(add(additive_identity,u),u),
file('RNG008-3.p',unknown),
[] ).
cnf(8,axiom,
equal(multiply(u,add(v,w)),add(multiply(u,v),multiply(u,w))),
file('RNG008-3.p',unknown),
[] ).
cnf(9,axiom,
equal(multiply(add(u,v),w),add(multiply(u,w),multiply(v,w))),
file('RNG008-3.p',unknown),
[] ).
cnf(11,axiom,
equal(additive_inverse(additive_inverse(u)),u),
file('RNG008-3.p',unknown),
[] ).
cnf(15,axiom,
equal(multiply(u,additive_inverse(v)),additive_inverse(multiply(u,v))),
file('RNG008-3.p',unknown),
[] ).
cnf(16,axiom,
equal(multiply(additive_inverse(u),v),additive_inverse(multiply(u,v))),
file('RNG008-3.p',unknown),
[] ).
cnf(17,axiom,
equal(add(add(u,v),w),add(u,add(v,w))),
file('RNG008-3.p',unknown),
[] ).
cnf(18,axiom,
equal(add(u,v),add(v,u)),
file('RNG008-3.p',unknown),
[] ).
cnf(19,axiom,
equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
file('RNG008-3.p',unknown),
[] ).
cnf(49,plain,
equal(additive_inverse(multiply(u,additive_inverse(u))),additive_inverse(u)),
inference(spr,[status(thm),theory(equality)],[16,3]),
[iquote('0:SpR:16.0,3.0')] ).
cnf(54,plain,
equal(additive_inverse(additive_inverse(multiply(u,u))),additive_inverse(u)),
inference(rew,[status(thm),theory(equality)],[15,49]),
[iquote('0:Rew:15.0,49.0')] ).
cnf(55,plain,
equal(additive_inverse(u),u),
inference(rew,[status(thm),theory(equality)],[11,54,3]),
[iquote('0:Rew:11.0,54.0,3.0,54.0')] ).
cnf(58,plain,
equal(add(u,u),additive_identity),
inference(rew,[status(thm),theory(equality)],[55,2]),
[iquote('0:Rew:55.0,2.0')] ).
cnf(71,plain,
equal(multiply(u,multiply(v,multiply(u,v))),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[19,3]),
[iquote('0:SpR:19.0,3.0')] ).
cnf(77,plain,
equal(multiply(u,multiply(u,v)),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[3,19]),
[iquote('0:SpR:3.0,19.0')] ).
cnf(120,plain,
equal(add(add(u,v),w),add(v,add(u,w))),
inference(spr,[status(thm),theory(equality)],[18,17]),
[iquote('0:SpR:18.0,17.0')] ).
cnf(123,plain,
equal(add(additive_identity,u),add(v,add(v,u))),
inference(spr,[status(thm),theory(equality)],[58,17]),
[iquote('0:SpR:58.0,17.0')] ).
cnf(126,plain,
equal(add(u,add(u,v)),v),
inference(rew,[status(thm),theory(equality)],[6,123]),
[iquote('0:Rew:6.0,123.0')] ).
cnf(127,plain,
equal(add(u,add(v,w)),add(v,add(u,w))),
inference(rew,[status(thm),theory(equality)],[17,120]),
[iquote('0:Rew:17.0,120.0')] ).
cnf(272,plain,
equal(add(multiply(u,add(u,v)),multiply(v,add(u,v))),add(u,v)),
inference(spr,[status(thm),theory(equality)],[9,3]),
[iquote('0:SpR:9.0,3.0')] ).
cnf(298,plain,
equal(add(add(multiply(u,u),multiply(u,v)),add(multiply(v,u),multiply(v,v))),add(u,v)),
inference(rew,[status(thm),theory(equality)],[8,272]),
[iquote('0:Rew:8.0,272.0,8.0,272.0')] ).
cnf(299,plain,
equal(add(u,add(multiply(u,v),add(v,multiply(v,u)))),add(u,v)),
inference(rew,[status(thm),theory(equality)],[17,298,3,18]),
[iquote('0:Rew:17.0,298.0,3.0,298.0,18.0,298.0,3.0,298.0')] ).
cnf(300,plain,
equal(add(u,add(v,add(multiply(u,v),multiply(v,u)))),add(u,v)),
inference(rew,[status(thm),theory(equality)],[127,299]),
[iquote('0:Rew:127.0,299.0')] ).
cnf(1040,plain,
equal(add(u,add(multiply(v,u),multiply(u,v))),add(v,add(v,u))),
inference(spr,[status(thm),theory(equality)],[300,126]),
[iquote('0:SpR:300.0,126.0')] ).
cnf(1109,plain,
equal(add(u,add(multiply(v,u),multiply(u,v))),u),
inference(rew,[status(thm),theory(equality)],[126,1040]),
[iquote('0:Rew:126.0,1040.0')] ).
cnf(1206,plain,
equal(add(multiply(u,multiply(v,u)),add(multiply(v,u),multiply(multiply(u,multiply(v,u)),v))),multiply(u,multiply(v,u))),
inference(spr,[status(thm),theory(equality)],[71,1109]),
[iquote('0:SpR:71.0,1109.0')] ).
cnf(1208,plain,
equal(add(multiply(u,v),add(multiply(u,v),multiply(multiply(u,v),u))),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[77,1109]),
[iquote('0:SpR:77.0,1109.0')] ).
cnf(1280,plain,
equal(multiply(u,multiply(v,u)),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[126,1208,19]),
[iquote('0:Rew:126.0,1208.0,19.0,1208.0')] ).
cnf(1296,plain,
equal(add(multiply(u,v),add(multiply(v,multiply(u,v)),multiply(v,multiply(u,multiply(v,u))))),multiply(v,multiply(u,v))),
inference(rew,[status(thm),theory(equality)],[127,1206,19]),
[iquote('0:Rew:127.0,1206.0,19.0,1206.0,19.0,1206.0')] ).
cnf(1297,plain,
equal(add(multiply(u,v),add(multiply(v,u),multiply(v,u))),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[1280,1296]),
[iquote('0:Rew:1280.0,1296.0,1280.0,1296.0,1280.0,1296.0')] ).
cnf(1298,plain,
equal(multiply(u,v),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[6,1297,18,58]),
[iquote('0:Rew:6.0,1297.0,18.0,1297.0,58.0,1297.0')] ).
cnf(1299,plain,
~ equal(multiply(a,b),c),
inference(rew,[status(thm),theory(equality)],[1298,5]),
[iquote('0:Rew:1298.0,5.0')] ).
cnf(1303,plain,
~ equal(c,c),
inference(rew,[status(thm),theory(equality)],[4,1299]),
[iquote('0:Rew:4.0,1299.0')] ).
cnf(1304,plain,
$false,
inference(obv,[status(thm),theory(equality)],[1303]),
[iquote('0:Obv:1303.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : RNG008-3 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n018.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon May 30 18:46:27 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.53
% 0.20/0.53 SPASS V 3.9
% 0.20/0.53 SPASS beiseite: Proof found.
% 0.20/0.53 % SZS status Theorem
% 0.20/0.53 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.53 SPASS derived 768 clauses, backtracked 0 clauses, performed 0 splits and kept 123 clauses.
% 0.20/0.53 SPASS allocated 64393 KBytes.
% 0.20/0.53 SPASS spent 0:00:00.17 on the problem.
% 0.20/0.53 0:00:00.03 for the input.
% 0.20/0.53 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.53 0:00:00.01 for inferences.
% 0.20/0.53 0:00:00.00 for the backtracking.
% 0.20/0.53 0:00:00.10 for the reduction.
% 0.20/0.53
% 0.20/0.53
% 0.20/0.53 Here is a proof with depth 3, length 38 :
% 0.20/0.53 % SZS output start Refutation
% See solution above
% 0.20/0.53 Formulae used in the proof : right_inverse boolean_ring a_times_b_is_c prove_commutativity left_identity distribute1 distribute2 additive_inverse_additive_inverse multiply_additive_inverse1 multiply_additive_inverse2 associative_addition commutative_addition associative_multiplication
% 0.20/0.53
%------------------------------------------------------------------------------