TSTP Solution File: BOO014-4 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : BOO014-4 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 9.09s 9.31s
% Output : Refutation 9.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 9
% Syntax : Number of clauses : 91 ( 91 unt; 0 nHn; 91 RR)
% Number of literals : 91 ( 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(1,axiom,
~ equal(multiply(inverse(a),inverse(b)),inverse(add(a,b))),
file('BOO014-4.p',unknown),
[] ).
cnf(2,axiom,
equal(add(u,v),add(v,u)),
file('BOO014-4.p',unknown),
[] ).
cnf(3,axiom,
equal(multiply(u,v),multiply(v,u)),
file('BOO014-4.p',unknown),
[] ).
cnf(4,axiom,
equal(multiply(add(u,v),add(u,w)),add(u,multiply(v,w))),
file('BOO014-4.p',unknown),
[] ).
cnf(5,axiom,
equal(add(multiply(u,v),multiply(u,w)),multiply(u,add(v,w))),
file('BOO014-4.p',unknown),
[] ).
cnf(6,axiom,
equal(add(u,additive_identity),u),
file('BOO014-4.p',unknown),
[] ).
cnf(7,axiom,
equal(multiply(u,multiplicative_identity),u),
file('BOO014-4.p',unknown),
[] ).
cnf(8,axiom,
equal(add(u,inverse(u)),multiplicative_identity),
file('BOO014-4.p',unknown),
[] ).
cnf(9,axiom,
equal(multiply(u,inverse(u)),additive_identity),
file('BOO014-4.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(45,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(46,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(51,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(55,plain,
equal(add(u,multiply(u,v)),multiply(u,add(v,multiplicative_identity))),
inference(rew,[status(thm),theory(equality)],[2,45]),
[iquote('0:Rew:2.0,45.0')] ).
cnf(59,plain,
equal(multiply(u,add(v,inverse(u))),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[28,46,2]),
[iquote('0:Rew:28.0,46.0,2.0,46.0')] ).
cnf(60,plain,
equal(multiply(u,add(inverse(u),v)),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[28,51]),
[iquote('0:Rew:28.0,51.0')] ).
cnf(63,plain,
equal(multiply(u,add(add(v,inverse(u)),w)),add(multiply(u,v),multiply(u,w))),
inference(spr,[status(thm),theory(equality)],[59,5]),
[iquote('0:SpR:59.0,5.0')] ).
cnf(69,plain,
equal(multiply(u,multiplicative_identity),multiply(u,u)),
inference(spr,[status(thm),theory(equality)],[8,59]),
[iquote('0:SpR:8.0,59.0')] ).
cnf(72,plain,
equal(multiply(u,inverse(u)),multiply(u,additive_identity)),
inference(spr,[status(thm),theory(equality)],[28,59]),
[iquote('0:SpR:28.0,59.0')] ).
cnf(73,plain,
equal(multiply(u,u),u),
inference(rew,[status(thm),theory(equality)],[7,69]),
[iquote('0:Rew:7.0,69.0')] ).
cnf(75,plain,
equal(multiply(u,additive_identity),additive_identity),
inference(rew,[status(thm),theory(equality)],[9,72]),
[iquote('0:Rew:9.0,72.0')] ).
cnf(77,plain,
equal(multiply(u,add(add(v,inverse(u)),w)),multiply(u,add(v,w))),
inference(rew,[status(thm),theory(equality)],[5,63]),
[iquote('0:Rew:5.0,63.0')] ).
cnf(94,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(95,plain,
equal(add(u,multiply(v,inverse(u))),multiply(add(u,v),multiplicative_identity)),
inference(spr,[status(thm),theory(equality)],[8,4]),
[iquote('0:SpR:8.0,4.0')] ).
cnf(101,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(106,plain,
equal(multiply(u,add(u,v)),u),
inference(rew,[status(thm),theory(equality)],[3,94,6,75]),
[iquote('0:Rew:3.0,94.0,6.0,94.0,75.0,94.0')] ).
cnf(110,plain,
equal(add(u,multiply(v,inverse(u))),add(u,v)),
inference(rew,[status(thm),theory(equality)],[14,95,3]),
[iquote('0:Rew:14.0,95.0,3.0,95.0')] ).
cnf(111,plain,
equal(add(u,multiply(inverse(u),v)),add(u,v)),
inference(rew,[status(thm),theory(equality)],[14,101]),
[iquote('0:Rew:14.0,101.0')] ).
cnf(129,plain,
equal(add(u,multiply(u,v)),multiply(u,add(u,v))),
inference(spr,[status(thm),theory(equality)],[73,5]),
[iquote('0:SpR:73.0,5.0')] ).
cnf(130,plain,
equal(add(multiply(u,v),u),multiply(u,add(v,u))),
inference(spr,[status(thm),theory(equality)],[73,5]),
[iquote('0:SpR:73.0,5.0')] ).
cnf(138,plain,
equal(multiply(u,add(v,multiplicative_identity)),u),
inference(rew,[status(thm),theory(equality)],[55,129,106]),
[iquote('0:Rew:55.0,129.0,106.0,129.0')] ).
cnf(139,plain,
equal(add(u,multiply(u,v)),u),
inference(rew,[status(thm),theory(equality)],[138,55]),
[iquote('0:Rew:138.0,55.0')] ).
cnf(140,plain,
equal(add(u,multiply(u,v)),multiply(u,add(v,u))),
inference(rew,[status(thm),theory(equality)],[2,130]),
[iquote('0:Rew:2.0,130.0')] ).
cnf(141,plain,
equal(multiply(u,add(v,u)),u),
inference(rew,[status(thm),theory(equality)],[139,140]),
[iquote('0:Rew:139.0,140.0')] ).
cnf(206,plain,
equal(add(u,multiply(v,u)),u),
inference(spr,[status(thm),theory(equality)],[3,139]),
[iquote('0:SpR:3.0,139.0')] ).
cnf(232,plain,
equal(multiply(u,add(add(v,u),w)),add(u,multiply(u,w))),
inference(spr,[status(thm),theory(equality)],[141,5]),
[iquote('0:SpR:141.0,5.0')] ).
cnf(236,plain,
equal(multiply(u,add(v,add(w,u))),add(multiply(u,v),u)),
inference(spr,[status(thm),theory(equality)],[141,5]),
[iquote('0:SpR:141.0,5.0')] ).
cnf(252,plain,
equal(multiply(u,add(add(v,u),w)),u),
inference(rew,[status(thm),theory(equality)],[139,232]),
[iquote('0:Rew:139.0,232.0')] ).
cnf(253,plain,
equal(multiply(u,add(v,add(w,u))),u),
inference(rew,[status(thm),theory(equality)],[139,236,2]),
[iquote('0:Rew:139.0,236.0,2.0,236.0')] ).
cnf(265,plain,
equal(multiply(u,inverse(inverse(u))),multiply(u,multiplicative_identity)),
inference(spr,[status(thm),theory(equality)],[8,60]),
[iquote('0:SpR:8.0,60.0')] ).
cnf(275,plain,
equal(multiply(u,inverse(inverse(u))),u),
inference(rew,[status(thm),theory(equality)],[7,265]),
[iquote('0:Rew:7.0,265.0')] ).
cnf(300,plain,
equal(multiply(u,multiply(v,inverse(u))),multiply(u,inverse(u))),
inference(spr,[status(thm),theory(equality)],[206,60]),
[iquote('0:SpR:206.0,60.0')] ).
cnf(303,plain,
equal(add(inverse(inverse(u)),u),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[275,206]),
[iquote('0:SpR:275.0,206.0')] ).
cnf(316,plain,
equal(add(u,inverse(inverse(u))),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[2,303]),
[iquote('0:Rew:2.0,303.0')] ).
cnf(320,plain,
equal(multiply(u,multiply(v,inverse(u))),additive_identity),
inference(rew,[status(thm),theory(equality)],[9,300]),
[iquote('0:Rew:9.0,300.0')] ).
cnf(493,plain,
equal(add(u,inverse(inverse(u))),add(u,additive_identity)),
inference(spr,[status(thm),theory(equality)],[9,111]),
[iquote('0:SpR:9.0,111.0')] ).
cnf(499,plain,
equal(add(u,add(v,inverse(u))),add(u,inverse(u))),
inference(spr,[status(thm),theory(equality)],[141,111]),
[iquote('0:SpR:141.0,111.0')] ).
cnf(512,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[316,493,6]),
[iquote('0:Rew:316.0,493.0,6.0,493.0')] ).
cnf(539,plain,
equal(add(u,add(v,inverse(u))),multiplicative_identity),
inference(rew,[status(thm),theory(equality)],[8,499]),
[iquote('0:Rew:8.0,499.0')] ).
cnf(562,plain,
equal(multiply(inverse(u),add(v,u)),multiply(inverse(u),v)),
inference(spr,[status(thm),theory(equality)],[512,59]),
[iquote('0:SpR:512.0,59.0')] ).
cnf(565,plain,
equal(add(inverse(u),multiply(u,v)),add(inverse(u),v)),
inference(spr,[status(thm),theory(equality)],[512,111]),
[iquote('0:SpR:512.0,111.0')] ).
cnf(566,plain,
equal(multiply(inverse(u),multiply(v,u)),additive_identity),
inference(spr,[status(thm),theory(equality)],[512,320]),
[iquote('0:SpR:512.0,320.0')] ).
cnf(584,plain,
equal(add(inverse(u),add(v,u)),multiplicative_identity),
inference(spr,[status(thm),theory(equality)],[512,539]),
[iquote('0:SpR:512.0,539.0')] ).
cnf(755,plain,
equal(multiply(inverse(add(u,v)),v),additive_identity),
inference(spr,[status(thm),theory(equality)],[141,566]),
[iquote('0:SpR:141.0,566.0')] ).
cnf(775,plain,
equal(multiply(u,inverse(add(v,u))),additive_identity),
inference(rew,[status(thm),theory(equality)],[3,755]),
[iquote('0:Rew:3.0,755.0')] ).
cnf(795,plain,
equal(add(inverse(multiply(u,v)),v),multiplicative_identity),
inference(spr,[status(thm),theory(equality)],[206,584]),
[iquote('0:SpR:206.0,584.0')] ).
cnf(814,plain,
equal(add(u,inverse(multiply(v,u))),multiplicative_identity),
inference(rew,[status(thm),theory(equality)],[2,795]),
[iquote('0:Rew:2.0,795.0')] ).
cnf(871,plain,
equal(add(u,inverse(add(v,inverse(u)))),add(u,additive_identity)),
inference(spr,[status(thm),theory(equality)],[775,111]),
[iquote('0:SpR:775.0,111.0')] ).
cnf(900,plain,
equal(add(u,inverse(add(v,inverse(u)))),u),
inference(rew,[status(thm),theory(equality)],[6,871]),
[iquote('0:Rew:6.0,871.0')] ).
cnf(1053,plain,
equal(multiply(u,inverse(multiply(v,inverse(u)))),multiply(u,multiplicative_identity)),
inference(spr,[status(thm),theory(equality)],[814,60]),
[iquote('0:SpR:814.0,60.0')] ).
cnf(1090,plain,
equal(multiply(u,inverse(multiply(v,inverse(u)))),u),
inference(rew,[status(thm),theory(equality)],[7,1053]),
[iquote('0:Rew:7.0,1053.0')] ).
cnf(1165,plain,
equal(add(inverse(u),inverse(add(v,u))),inverse(u)),
inference(spr,[status(thm),theory(equality)],[512,900]),
[iquote('0:SpR:512.0,900.0')] ).
cnf(2156,plain,
equal(add(add(add(u,v),w),v),add(add(u,v),w)),
inference(spr,[status(thm),theory(equality)],[252,206]),
[iquote('0:SpR:252.0,206.0')] ).
cnf(2224,plain,
equal(add(u,add(add(v,u),w)),add(add(v,u),w)),
inference(rew,[status(thm),theory(equality)],[2,2156]),
[iquote('0:Rew:2.0,2156.0')] ).
cnf(2256,plain,
equal(multiply(inverse(add(u,add(v,w))),w),additive_identity),
inference(spr,[status(thm),theory(equality)],[253,566]),
[iquote('0:SpR:253.0,566.0')] ).
cnf(2308,plain,
equal(multiply(u,inverse(add(v,add(w,u)))),additive_identity),
inference(rew,[status(thm),theory(equality)],[3,2256]),
[iquote('0:Rew:3.0,2256.0')] ).
cnf(2945,plain,
equal(add(inverse(multiply(u,inverse(v))),inverse(add(v,u))),inverse(multiply(u,inverse(v)))),
inference(spr,[status(thm),theory(equality)],[110,1165]),
[iquote('0:SpR:110.0,1165.0')] ).
cnf(2994,plain,
equal(add(inverse(add(u,v)),inverse(multiply(v,inverse(u)))),inverse(multiply(v,inverse(u)))),
inference(rew,[status(thm),theory(equality)],[2,2945]),
[iquote('0:Rew:2.0,2945.0')] ).
cnf(7956,plain,
equal(add(u,inverse(add(v,add(w,inverse(u))))),add(u,additive_identity)),
inference(spr,[status(thm),theory(equality)],[2308,111]),
[iquote('0:SpR:2308.0,111.0')] ).
cnf(8076,plain,
equal(add(u,inverse(add(v,add(w,inverse(u))))),u),
inference(rew,[status(thm),theory(equality)],[6,7956]),
[iquote('0:Rew:6.0,7956.0')] ).
cnf(19519,plain,
equal(add(u,add(add(v,inverse(inverse(u))),w)),add(u,multiply(inverse(u),add(v,w)))),
inference(spr,[status(thm),theory(equality)],[77,111]),
[iquote('0:SpR:77.0,111.0')] ).
cnf(19572,plain,
equal(multiply(u,add(v,inverse(add(v,inverse(u))))),multiply(u,multiplicative_identity)),
inference(spr,[status(thm),theory(equality)],[8,77]),
[iquote('0:SpR:8.0,77.0')] ).
cnf(19637,plain,
equal(multiply(u,add(v,inverse(add(v,inverse(u))))),u),
inference(rew,[status(thm),theory(equality)],[7,19572]),
[iquote('0:Rew:7.0,19572.0')] ).
cnf(19677,plain,
equal(add(u,add(add(v,u),w)),add(u,add(v,w))),
inference(rew,[status(thm),theory(equality)],[512,19519,111]),
[iquote('0:Rew:512.0,19519.0,111.0,19519.0')] ).
cnf(19678,plain,
equal(add(add(u,v),w),add(v,add(u,w))),
inference(rew,[status(thm),theory(equality)],[2224,19677]),
[iquote('0:Rew:2224.0,19677.0')] ).
cnf(24368,plain,
equal(multiply(inverse(multiply(u,inverse(v))),add(v,u)),multiply(inverse(multiply(u,inverse(v))),v)),
inference(spr,[status(thm),theory(equality)],[110,562]),
[iquote('0:SpR:110.0,562.0')] ).
cnf(24441,plain,
equal(multiply(add(u,v),inverse(multiply(v,inverse(u)))),u),
inference(rew,[status(thm),theory(equality)],[3,24368,1090]),
[iquote('0:Rew:3.0,24368.0,1090.0,24368.0,3.0,24368.0')] ).
cnf(29406,plain,
equal(add(add(u,v),inverse(add(w,inverse(v)))),add(u,v)),
inference(spr,[status(thm),theory(equality)],[1165,8076]),
[iquote('0:SpR:1165.0,8076.0')] ).
cnf(29447,plain,
equal(add(u,add(v,inverse(add(w,inverse(u))))),add(v,u)),
inference(rew,[status(thm),theory(equality)],[19678,29406]),
[iquote('0:Rew:19678.0,29406.0')] ).
cnf(29652,plain,
equal(add(add(u,inverse(add(u,inverse(v)))),v),add(u,inverse(add(u,inverse(v))))),
inference(spr,[status(thm),theory(equality)],[19637,206]),
[iquote('0:SpR:19637.0,206.0')] ).
cnf(29742,plain,
equal(add(u,add(v,inverse(add(v,inverse(u))))),add(v,inverse(add(v,inverse(u))))),
inference(rew,[status(thm),theory(equality)],[2,29652]),
[iquote('0:Rew:2.0,29652.0')] ).
cnf(29743,plain,
equal(add(u,inverse(add(u,inverse(v)))),add(u,v)),
inference(rew,[status(thm),theory(equality)],[29447,29742]),
[iquote('0:Rew:29447.0,29742.0')] ).
cnf(30442,plain,
equal(add(inverse(add(u,v)),inverse(multiply(v,inverse(u)))),add(inverse(add(u,v)),u)),
inference(spr,[status(thm),theory(equality)],[24441,565]),
[iquote('0:SpR:24441.0,565.0')] ).
cnf(30646,plain,
equal(add(inverse(add(u,v)),inverse(multiply(v,inverse(u)))),add(u,inverse(add(u,v)))),
inference(rew,[status(thm),theory(equality)],[2,30442]),
[iquote('0:Rew:2.0,30442.0')] ).
cnf(30647,plain,
equal(add(u,inverse(add(u,v))),inverse(multiply(v,inverse(u)))),
inference(rew,[status(thm),theory(equality)],[2994,30646]),
[iquote('0:Rew:2994.0,30646.0')] ).
cnf(30659,plain,
equal(inverse(multiply(inverse(u),inverse(v))),add(v,u)),
inference(rew,[status(thm),theory(equality)],[30647,29743]),
[iquote('0:Rew:30647.0,29743.0')] ).
cnf(30740,plain,
equal(multiply(inverse(u),inverse(v)),inverse(add(v,u))),
inference(spr,[status(thm),theory(equality)],[30659,512]),
[iquote('0:SpR:30659.0,512.0')] ).
cnf(30822,plain,
~ equal(inverse(add(b,a)),inverse(add(a,b))),
inference(rew,[status(thm),theory(equality)],[30740,1]),
[iquote('0:Rew:30740.0,1.0')] ).
cnf(30971,plain,
~ equal(inverse(add(a,b)),inverse(add(a,b))),
inference(rew,[status(thm),theory(equality)],[2,30822]),
[iquote('0:Rew:2.0,30822.0')] ).
cnf(30972,plain,
$false,
inference(obv,[status(thm),theory(equality)],[30971]),
[iquote('0:Obv:30971.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : BOO014-4 : TPTP v8.1.0. Released v1.1.0.
% 0.08/0.14 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n019.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 : Wed Jun 1 22:03:40 EDT 2022
% 0.13/0.35 % CPUTime :
% 9.09/9.31
% 9.09/9.31 SPASS V 3.9
% 9.09/9.31 SPASS beiseite: Proof found.
% 9.09/9.31 % SZS status Theorem
% 9.09/9.31 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.09/9.31 SPASS derived 20127 clauses, backtracked 0 clauses, performed 0 splits and kept 2879 clauses.
% 9.09/9.31 SPASS allocated 85641 KBytes.
% 9.09/9.31 SPASS spent 0:00:08.92 on the problem.
% 9.09/9.31 0:00:00.03 for the input.
% 9.09/9.31 0:00:00.00 for the FLOTTER CNF translation.
% 9.09/9.31 0:00:00.13 for inferences.
% 9.09/9.31 0:00:00.00 for the backtracking.
% 9.09/9.31 0:00:08.73 for the reduction.
% 9.09/9.31
% 9.09/9.31
% 9.09/9.31 Here is a proof with depth 8, length 91 :
% 9.09/9.31 % SZS output start Refutation
% See solution above
% 9.23/9.47 Formulae used in the proof : prove_c_inverse_is_d commutativity_of_add commutativity_of_multiply distributivity1 distributivity2 additive_id1 multiplicative_id1 additive_inverse1 multiplicative_inverse1
% 9.23/9.47
%------------------------------------------------------------------------------