TSTP Solution File: BOO015-2 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : BOO015-2 : TPTP v8.1.0. Bugfixed v1.0.1.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 23:49:27 EDT 2022
% Result : Unsatisfiable 0.73s 0.92s
% Output : Refutation 0.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 14
% Syntax : Number of clauses : 87 ( 87 unt; 0 nHn; 87 RR)
% Number of literals : 87 ( 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 : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(multiply(a,b),c),
file('BOO015-2.p',unknown),
[] ).
cnf(2,axiom,
equal(add(inverse(a),inverse(b)),d),
file('BOO015-2.p',unknown),
[] ).
cnf(3,axiom,
~ equal(inverse(c),d),
file('BOO015-2.p',unknown),
[] ).
cnf(4,axiom,
equal(add(u,v),add(v,u)),
file('BOO015-2.p',unknown),
[] ).
cnf(5,axiom,
equal(multiply(u,v),multiply(v,u)),
file('BOO015-2.p',unknown),
[] ).
cnf(6,axiom,
equal(multiply(add(u,v),add(w,v)),add(multiply(u,w),v)),
file('BOO015-2.p',unknown),
[] ).
cnf(7,axiom,
equal(multiply(add(u,v),add(u,w)),add(u,multiply(v,w))),
file('BOO015-2.p',unknown),
[] ).
cnf(8,axiom,
equal(add(multiply(u,v),multiply(w,v)),multiply(add(u,w),v)),
file('BOO015-2.p',unknown),
[] ).
cnf(9,axiom,
equal(add(multiply(u,v),multiply(u,w)),multiply(u,add(v,w))),
file('BOO015-2.p',unknown),
[] ).
cnf(10,axiom,
equal(add(u,inverse(u)),multiplicative_identity),
file('BOO015-2.p',unknown),
[] ).
cnf(12,axiom,
equal(multiply(u,inverse(u)),additive_identity),
file('BOO015-2.p',unknown),
[] ).
cnf(14,axiom,
equal(multiply(u,multiplicative_identity),u),
file('BOO015-2.p',unknown),
[] ).
cnf(15,axiom,
equal(multiply(multiplicative_identity,u),u),
file('BOO015-2.p',unknown),
[] ).
cnf(17,axiom,
equal(add(additive_identity,u),u),
file('BOO015-2.p',unknown),
[] ).
cnf(57,plain,
equal(add(multiply(u,b),c),multiply(add(u,a),b)),
inference(spr,[status(thm),theory(equality)],[1,8]),
[iquote('0:SpR:1.0,8.0')] ).
cnf(61,plain,
equal(add(multiply(u,inverse(v)),additive_identity),multiply(add(u,v),inverse(v))),
inference(spr,[status(thm),theory(equality)],[12,8]),
[iquote('0:SpR:12.0,8.0')] ).
cnf(67,plain,
equal(add(additive_identity,multiply(u,inverse(v))),multiply(add(v,u),inverse(v))),
inference(spr,[status(thm),theory(equality)],[12,8]),
[iquote('0:SpR:12.0,8.0')] ).
cnf(69,plain,
equal(add(c,multiply(u,b)),multiply(b,add(u,a))),
inference(rew,[status(thm),theory(equality)],[4,57,5]),
[iquote('0:Rew:4.0,57.0,5.0,57.0')] ).
cnf(78,plain,
equal(multiply(inverse(u),add(v,u)),multiply(v,inverse(u))),
inference(rew,[status(thm),theory(equality)],[17,61,4,5]),
[iquote('0:Rew:17.0,61.0,4.0,61.0,5.0,61.0')] ).
cnf(79,plain,
equal(multiply(inverse(u),add(u,v)),multiply(v,inverse(u))),
inference(rew,[status(thm),theory(equality)],[17,67,5]),
[iquote('0:Rew:17.0,67.0,5.0,67.0')] ).
cnf(85,plain,
equal(multiply(add(u,v),v),add(multiply(u,additive_identity),v)),
inference(spr,[status(thm),theory(equality)],[17,6]),
[iquote('0:SpR:17.0,6.0')] ).
cnf(88,plain,
equal(add(multiply(u,v),inverse(v)),multiply(add(u,inverse(v)),multiplicative_identity)),
inference(spr,[status(thm),theory(equality)],[10,6]),
[iquote('0:SpR:10.0,6.0')] ).
cnf(95,plain,
equal(add(multiply(u,v),inverse(u)),multiply(multiplicative_identity,add(v,inverse(u)))),
inference(spr,[status(thm),theory(equality)],[10,6]),
[iquote('0:SpR:10.0,6.0')] ).
cnf(97,plain,
equal(add(multiply(inverse(a),u),inverse(b)),multiply(d,add(u,inverse(b)))),
inference(spr,[status(thm),theory(equality)],[2,6]),
[iquote('0:SpR:2.0,6.0')] ).
cnf(99,plain,
equal(multiply(u,add(v,u)),add(multiply(v,additive_identity),u)),
inference(rew,[status(thm),theory(equality)],[5,85]),
[iquote('0:Rew:5.0,85.0')] ).
cnf(104,plain,
equal(add(inverse(u),multiply(v,u)),add(v,inverse(u))),
inference(rew,[status(thm),theory(equality)],[4,88,15,5]),
[iquote('0:Rew:4.0,88.0,15.0,88.0,5.0,88.0')] ).
cnf(105,plain,
equal(add(inverse(u),multiply(u,v)),add(v,inverse(u))),
inference(rew,[status(thm),theory(equality)],[4,95,15]),
[iquote('0:Rew:4.0,95.0,15.0,95.0')] ).
cnf(107,plain,
equal(add(inverse(b),multiply(inverse(a),u)),multiply(d,add(u,inverse(b)))),
inference(rew,[status(thm),theory(equality)],[4,97]),
[iquote('0:Rew:4.0,97.0')] ).
cnf(154,plain,
equal(add(multiply(a,u),c),multiply(a,add(u,b))),
inference(spr,[status(thm),theory(equality)],[1,9]),
[iquote('0:SpR:1.0,9.0')] ).
cnf(157,plain,
equal(add(multiply(u,v),u),multiply(u,add(v,multiplicative_identity))),
inference(spr,[status(thm),theory(equality)],[14,9]),
[iquote('0:SpR:14.0,9.0')] ).
cnf(158,plain,
equal(multiply(u,add(v,inverse(u))),add(multiply(u,v),additive_identity)),
inference(spr,[status(thm),theory(equality)],[12,9]),
[iquote('0:SpR:12.0,9.0')] ).
cnf(176,plain,
equal(add(c,multiply(a,u)),multiply(a,add(u,b))),
inference(rew,[status(thm),theory(equality)],[4,154]),
[iquote('0:Rew:4.0,154.0')] ).
cnf(178,plain,
equal(add(u,multiply(u,v)),multiply(u,add(v,multiplicative_identity))),
inference(rew,[status(thm),theory(equality)],[4,157]),
[iquote('0:Rew:4.0,157.0')] ).
cnf(182,plain,
equal(multiply(u,add(v,inverse(u))),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[17,158,4]),
[iquote('0:Rew:17.0,158.0,4.0,158.0')] ).
cnf(202,plain,
equal(multiply(u,inverse(u)),multiply(u,additive_identity)),
inference(spr,[status(thm),theory(equality)],[17,182]),
[iquote('0:SpR:17.0,182.0')] ).
cnf(204,plain,
equal(multiply(u,multiplicative_identity),multiply(u,u)),
inference(spr,[status(thm),theory(equality)],[10,182]),
[iquote('0:SpR:10.0,182.0')] ).
cnf(207,plain,
equal(multiply(u,u),u),
inference(rew,[status(thm),theory(equality)],[14,204]),
[iquote('0:Rew:14.0,204.0')] ).
cnf(209,plain,
equal(multiply(u,additive_identity),additive_identity),
inference(rew,[status(thm),theory(equality)],[12,202]),
[iquote('0:Rew:12.0,202.0')] ).
cnf(210,plain,
equal(multiply(u,add(v,u)),add(additive_identity,u)),
inference(rew,[status(thm),theory(equality)],[209,99]),
[iquote('0:Rew:209.0,99.0')] ).
cnf(212,plain,
equal(multiply(u,add(v,u)),u),
inference(rew,[status(thm),theory(equality)],[17,210]),
[iquote('0:Rew:17.0,210.0')] ).
cnf(255,plain,
equal(add(u,multiply(u,v)),multiply(u,add(u,v))),
inference(spr,[status(thm),theory(equality)],[207,9]),
[iquote('0:SpR:207.0,9.0')] ).
cnf(256,plain,
equal(add(multiply(u,v),u),multiply(u,add(v,u))),
inference(spr,[status(thm),theory(equality)],[207,9]),
[iquote('0:SpR:207.0,9.0')] ).
cnf(257,plain,
equal(multiply(b,add(b,a)),add(c,b)),
inference(spr,[status(thm),theory(equality)],[207,69]),
[iquote('0:SpR:207.0,69.0')] ).
cnf(262,plain,
equal(multiply(b,add(a,b)),add(b,c)),
inference(rew,[status(thm),theory(equality)],[4,257]),
[iquote('0:Rew:4.0,257.0,4.0,257.0')] ).
cnf(263,plain,
equal(add(b,c),b),
inference(rew,[status(thm),theory(equality)],[212,262]),
[iquote('0:Rew:212.0,262.0')] ).
cnf(271,plain,
equal(multiply(u,add(v,multiplicative_identity)),multiply(u,add(u,v))),
inference(rew,[status(thm),theory(equality)],[178,255]),
[iquote('0:Rew:178.0,255.0')] ).
cnf(272,plain,
equal(add(u,multiply(u,v)),multiply(u,add(v,u))),
inference(rew,[status(thm),theory(equality)],[4,256]),
[iquote('0:Rew:4.0,256.0')] ).
cnf(273,plain,
equal(multiply(u,add(v,multiplicative_identity)),u),
inference(rew,[status(thm),theory(equality)],[178,272,212]),
[iquote('0:Rew:178.0,272.0,212.0,272.0')] ).
cnf(274,plain,
equal(add(u,multiply(u,v)),u),
inference(rew,[status(thm),theory(equality)],[273,178]),
[iquote('0:Rew:273.0,178.0')] ).
cnf(275,plain,
equal(multiply(u,add(u,v)),u),
inference(rew,[status(thm),theory(equality)],[273,271]),
[iquote('0:Rew:273.0,271.0')] ).
cnf(299,plain,
equal(add(u,multiply(v,inverse(u))),multiply(add(u,v),multiplicative_identity)),
inference(spr,[status(thm),theory(equality)],[10,7]),
[iquote('0:SpR:10.0,7.0')] ).
cnf(320,plain,
equal(add(u,multiply(v,inverse(u))),add(u,v)),
inference(rew,[status(thm),theory(equality)],[15,299,5]),
[iquote('0:Rew:15.0,299.0,5.0,299.0')] ).
cnf(420,plain,
equal(multiply(inverse(b),d),inverse(b)),
inference(spr,[status(thm),theory(equality)],[2,212]),
[iquote('0:SpR:2.0,212.0')] ).
cnf(428,plain,
equal(multiply(d,inverse(b)),inverse(b)),
inference(rew,[status(thm),theory(equality)],[5,420]),
[iquote('0:Rew:5.0,420.0')] ).
cnf(502,plain,
equal(add(a,c),a),
inference(spr,[status(thm),theory(equality)],[1,274]),
[iquote('0:SpR:1.0,274.0')] ).
cnf(543,plain,
equal(multiply(c,a),c),
inference(spr,[status(thm),theory(equality)],[502,212]),
[iquote('0:SpR:502.0,212.0')] ).
cnf(549,plain,
equal(multiply(a,c),c),
inference(rew,[status(thm),theory(equality)],[5,543]),
[iquote('0:Rew:5.0,543.0')] ).
cnf(888,plain,
equal(multiply(inverse(a),d),inverse(a)),
inference(spr,[status(thm),theory(equality)],[2,275]),
[iquote('0:SpR:2.0,275.0')] ).
cnf(899,plain,
equal(multiply(d,inverse(a)),inverse(a)),
inference(rew,[status(thm),theory(equality)],[5,888]),
[iquote('0:Rew:5.0,888.0')] ).
cnf(932,plain,
equal(add(b,inverse(b)),add(b,d)),
inference(spr,[status(thm),theory(equality)],[428,320]),
[iquote('0:SpR:428.0,320.0')] ).
cnf(936,plain,
equal(add(b,d),multiplicative_identity),
inference(rew,[status(thm),theory(equality)],[10,932]),
[iquote('0:Rew:10.0,932.0')] ).
cnf(965,plain,
equal(add(a,inverse(a)),add(a,d)),
inference(spr,[status(thm),theory(equality)],[899,320]),
[iquote('0:SpR:899.0,320.0')] ).
cnf(966,plain,
equal(add(a,d),multiplicative_identity),
inference(rew,[status(thm),theory(equality)],[10,965]),
[iquote('0:Rew:10.0,965.0')] ).
cnf(1280,plain,
equal(multiply(inverse(d),multiplicative_identity),multiply(b,inverse(d))),
inference(spr,[status(thm),theory(equality)],[936,78]),
[iquote('0:SpR:936.0,78.0')] ).
cnf(1284,plain,
equal(multiply(inverse(d),multiplicative_identity),multiply(a,inverse(d))),
inference(spr,[status(thm),theory(equality)],[966,78]),
[iquote('0:SpR:966.0,78.0')] ).
cnf(1290,plain,
equal(multiply(b,inverse(d)),inverse(d)),
inference(rew,[status(thm),theory(equality)],[15,1280,5]),
[iquote('0:Rew:15.0,1280.0,5.0,1280.0')] ).
cnf(1291,plain,
equal(multiply(a,inverse(d)),inverse(d)),
inference(rew,[status(thm),theory(equality)],[15,1284,5]),
[iquote('0:Rew:15.0,1284.0,5.0,1284.0')] ).
cnf(1309,plain,
equal(add(b,inverse(d)),b),
inference(spr,[status(thm),theory(equality)],[1290,274]),
[iquote('0:SpR:1290.0,274.0')] ).
cnf(1337,plain,
equal(multiply(a,add(inverse(d),b)),add(c,inverse(d))),
inference(spr,[status(thm),theory(equality)],[1291,176]),
[iquote('0:SpR:1291.0,176.0')] ).
cnf(1346,plain,
equal(add(c,inverse(d)),c),
inference(rew,[status(thm),theory(equality)],[1,1337,1309,4]),
[iquote('0:Rew:1.0,1337.0,1309.0,1337.0,4.0,1337.0')] ).
cnf(1403,plain,
equal(multiply(inverse(b),b),multiply(c,inverse(b))),
inference(spr,[status(thm),theory(equality)],[263,79]),
[iquote('0:SpR:263.0,79.0')] ).
cnf(1418,plain,
equal(multiply(c,inverse(b)),additive_identity),
inference(rew,[status(thm),theory(equality)],[12,1403,5]),
[iquote('0:Rew:12.0,1403.0,5.0,1403.0')] ).
cnf(1453,plain,
equal(multiply(inverse(d),c),inverse(d)),
inference(spr,[status(thm),theory(equality)],[1346,212]),
[iquote('0:SpR:1346.0,212.0')] ).
cnf(1463,plain,
equal(multiply(c,inverse(d)),inverse(d)),
inference(rew,[status(thm),theory(equality)],[5,1453]),
[iquote('0:Rew:5.0,1453.0')] ).
cnf(1552,plain,
equal(add(inverse(c),c),add(a,inverse(c))),
inference(spr,[status(thm),theory(equality)],[549,104]),
[iquote('0:SpR:549.0,104.0')] ).
cnf(1576,plain,
equal(add(a,inverse(c)),multiplicative_identity),
inference(rew,[status(thm),theory(equality)],[10,1552,4]),
[iquote('0:Rew:10.0,1552.0,4.0,1552.0')] ).
cnf(1634,plain,
equal(multiply(inverse(c),inverse(a)),multiply(inverse(a),multiplicative_identity)),
inference(spr,[status(thm),theory(equality)],[1576,79]),
[iquote('0:SpR:1576.0,79.0')] ).
cnf(1641,plain,
equal(multiply(inverse(a),inverse(c)),inverse(a)),
inference(rew,[status(thm),theory(equality)],[5,1634,15]),
[iquote('0:Rew:5.0,1634.0,15.0,1634.0,5.0,1634.0')] ).
cnf(1674,plain,
equal(add(d,inverse(d)),add(d,c)),
inference(spr,[status(thm),theory(equality)],[1463,320]),
[iquote('0:SpR:1463.0,320.0')] ).
cnf(1676,plain,
equal(add(c,d),multiplicative_identity),
inference(rew,[status(thm),theory(equality)],[10,1674,4]),
[iquote('0:Rew:10.0,1674.0,4.0,1674.0')] ).
cnf(1723,plain,
equal(add(inverse(b),inverse(c)),add(inverse(c),additive_identity)),
inference(spr,[status(thm),theory(equality)],[1418,105]),
[iquote('0:SpR:1418.0,105.0')] ).
cnf(1738,plain,
equal(add(inverse(b),inverse(c)),inverse(c)),
inference(rew,[status(thm),theory(equality)],[17,1723,4]),
[iquote('0:Rew:17.0,1723.0,4.0,1723.0')] ).
cnf(1769,plain,
equal(multiply(inverse(c),multiplicative_identity),multiply(d,inverse(c))),
inference(spr,[status(thm),theory(equality)],[1676,79]),
[iquote('0:SpR:1676.0,79.0')] ).
cnf(1774,plain,
equal(multiply(d,inverse(c)),inverse(c)),
inference(rew,[status(thm),theory(equality)],[15,1769,5]),
[iquote('0:Rew:15.0,1769.0,5.0,1769.0')] ).
cnf(5282,plain,
equal(multiply(d,add(inverse(c),inverse(b))),add(inverse(b),inverse(a))),
inference(spr,[status(thm),theory(equality)],[1641,107]),
[iquote('0:SpR:1641.0,107.0')] ).
cnf(5296,plain,
equal(inverse(c),d),
inference(rew,[status(thm),theory(equality)],[1774,5282,1738,4,2]),
[iquote('0:Rew:1774.0,5282.0,1738.0,5282.0,4.0,5282.0,2.0,5282.0,4.0,5282.0')] ).
cnf(5297,plain,
$false,
inference(mrr,[status(thm)],[5296,3]),
[iquote('0:MRR:5296.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : BOO015-2 : TPTP v8.1.0. Bugfixed v1.0.1.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n027.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 23:58:04 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.73/0.92
% 0.73/0.92 SPASS V 3.9
% 0.73/0.92 SPASS beiseite: Proof found.
% 0.73/0.92 % SZS status Theorem
% 0.73/0.92 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.73/0.92 SPASS derived 3361 clauses, backtracked 0 clauses, performed 0 splits and kept 793 clauses.
% 0.73/0.92 SPASS allocated 67475 KBytes.
% 0.73/0.92 SPASS spent 0:00:00.55 on the problem.
% 0.73/0.92 0:00:00.04 for the input.
% 0.73/0.92 0:00:00.00 for the FLOTTER CNF translation.
% 0.73/0.92 0:00:00.03 for inferences.
% 0.73/0.92 0:00:00.00 for the backtracking.
% 0.73/0.92 0:00:00.46 for the reduction.
% 0.73/0.92
% 0.73/0.92
% 0.73/0.92 Here is a proof with depth 10, length 87 :
% 0.73/0.92 % SZS output start Refutation
% See solution above
% 0.73/0.92 Formulae used in the proof : a_times_b_is_c a_inverse_plus_b_inverse_is_d prove_c_inverse_is_d commutativity_of_add commutativity_of_multiply distributivity1 distributivity2 distributivity3 distributivity4 additive_inverse1 multiplicative_inverse1 multiplicative_id1 multiplicative_id2 additive_id2
% 0.73/0.92
%------------------------------------------------------------------------------