TSTP Solution File: BOO015-4 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : BOO015-4 : TPTP v8.1.0. Released v1.1.0.
% 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 9.33s 9.48s
% Output : Refutation 9.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 9
% Syntax : Number of clauses : 92 ( 92 unt; 0 nHn; 92 RR)
% Number of literals : 92 ( 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(add(inverse(a),inverse(b)),inverse(multiply(a,b))),
file('BOO015-4.p',unknown),
[] ).
cnf(2,axiom,
equal(add(u,v),add(v,u)),
file('BOO015-4.p',unknown),
[] ).
cnf(3,axiom,
equal(multiply(u,v),multiply(v,u)),
file('BOO015-4.p',unknown),
[] ).
cnf(4,axiom,
equal(multiply(add(u,v),add(u,w)),add(u,multiply(v,w))),
file('BOO015-4.p',unknown),
[] ).
cnf(5,axiom,
equal(add(multiply(u,v),multiply(u,w)),multiply(u,add(v,w))),
file('BOO015-4.p',unknown),
[] ).
cnf(6,axiom,
equal(add(u,additive_identity),u),
file('BOO015-4.p',unknown),
[] ).
cnf(7,axiom,
equal(multiply(u,multiplicative_identity),u),
file('BOO015-4.p',unknown),
[] ).
cnf(8,axiom,
equal(add(u,inverse(u)),multiplicative_identity),
file('BOO015-4.p',unknown),
[] ).
cnf(9,axiom,
equal(multiply(u,inverse(u)),additive_identity),
file('BOO015-4.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(299,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(319,plain,
equal(multiply(u,multiply(v,inverse(u))),additive_identity),
inference(rew,[status(thm),theory(equality)],[9,299]),
[iquote('0:Rew:9.0,299.0')] ).
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)],[512,319]),
[iquote('0:SpR:512.0,319.0')] ).
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(873,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(901,plain,
equal(add(u,inverse(add(v,inverse(u)))),u),
inference(rew,[status(thm),theory(equality)],[6,873]),
[iquote('0:Rew:6.0,873.0')] ).
cnf(1051,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(1089,plain,
equal(multiply(u,inverse(multiply(v,inverse(u)))),u),
inference(rew,[status(thm),theory(equality)],[7,1051]),
[iquote('0:Rew:7.0,1051.0')] ).
cnf(1165,plain,
equal(add(inverse(u),inverse(add(v,u))),inverse(u)),
inference(spr,[status(thm),theory(equality)],[512,901]),
[iquote('0:SpR:512.0,901.0')] ).
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(7965,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)],[6,7965]),
[iquote('0:Rew:6.0,7965.0')] ).
cnf(19531,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(19681,plain,
equal(add(u,add(add(v,u),w)),add(u,add(v,w))),
inference(rew,[status(thm),theory(equality)],[512,19531,111]),
[iquote('0:Rew:512.0,19531.0,111.0,19531.0')] ).
cnf(19682,plain,
equal(add(add(u,v),w),add(v,add(u,w))),
inference(rew,[status(thm),theory(equality)],[2224,19681]),
[iquote('0:Rew:2224.0,19681.0')] ).
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)],[3,24368,1089]),
[iquote('0:Rew:3.0,24368.0,1089.0,24368.0,3.0,24368.0')] ).
cnf(29409,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(29451,plain,
equal(add(u,add(v,inverse(add(w,inverse(u))))),add(v,u)),
inference(rew,[status(thm),theory(equality)],[19682,29409]),
[iquote('0:Rew:19682.0,29409.0')] ).
cnf(29656,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(29746,plain,
equal(add(u,add(v,inverse(add(v,inverse(u))))),add(v,inverse(add(v,inverse(u))))),
inference(rew,[status(thm),theory(equality)],[2,29656]),
[iquote('0:Rew:2.0,29656.0')] ).
cnf(29747,plain,
equal(add(u,inverse(add(u,inverse(v)))),add(u,v)),
inference(rew,[status(thm),theory(equality)],[29451,29746]),
[iquote('0:Rew:29451.0,29746.0')] ).
cnf(30448,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(30652,plain,
equal(add(inverse(add(u,v)),inverse(multiply(v,inverse(u)))),add(u,inverse(add(u,v)))),
inference(rew,[status(thm),theory(equality)],[2,30448]),
[iquote('0:Rew:2.0,30448.0')] ).
cnf(30653,plain,
equal(add(u,inverse(add(u,v))),inverse(multiply(v,inverse(u)))),
inference(rew,[status(thm),theory(equality)],[2994,30652]),
[iquote('0:Rew:2994.0,30652.0')] ).
cnf(30665,plain,
equal(inverse(multiply(inverse(u),inverse(v))),add(v,u)),
inference(rew,[status(thm),theory(equality)],[30653,29747]),
[iquote('0:Rew:30653.0,29747.0')] ).
cnf(30793,plain,
equal(inverse(multiply(inverse(u),v)),add(inverse(v),u)),
inference(spr,[status(thm),theory(equality)],[512,30665]),
[iquote('0:SpR:512.0,30665.0')] ).
cnf(32429,plain,
equal(add(inverse(u),inverse(v)),inverse(multiply(v,u))),
inference(spr,[status(thm),theory(equality)],[512,30793]),
[iquote('0:SpR:512.0,30793.0')] ).
cnf(32485,plain,
~ equal(inverse(multiply(b,a)),inverse(multiply(a,b))),
inference(rew,[status(thm),theory(equality)],[32429,1]),
[iquote('0:Rew:32429.0,1.0')] ).
cnf(32521,plain,
~ equal(inverse(multiply(a,b)),inverse(multiply(a,b))),
inference(rew,[status(thm),theory(equality)],[3,32485]),
[iquote('0:Rew:3.0,32485.0')] ).
cnf(32522,plain,
$false,
inference(obv,[status(thm),theory(equality)],[32521]),
[iquote('0:Obv:32521.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : BOO015-4 : TPTP v8.1.0. Released v1.1.0.
% 0.12/0.13 % 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 18:17:19 EDT 2022
% 0.13/0.34 % CPUTime :
% 9.33/9.48
% 9.33/9.48 SPASS V 3.9
% 9.33/9.48 SPASS beiseite: Proof found.
% 9.33/9.48 % SZS status Theorem
% 9.33/9.48 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.33/9.48 SPASS derived 21000 clauses, backtracked 0 clauses, performed 0 splits and kept 3027 clauses.
% 9.33/9.48 SPASS allocated 86828 KBytes.
% 9.33/9.48 SPASS spent 0:00:09.11 on the problem.
% 9.33/9.48 0:00:00.03 for the input.
% 9.33/9.48 0:00:00.00 for the FLOTTER CNF translation.
% 9.33/9.48 0:00:00.12 for inferences.
% 9.33/9.48 0:00:00.00 for the backtracking.
% 9.33/9.48 0:00:08.92 for the reduction.
% 9.33/9.48
% 9.33/9.48
% 9.33/9.48 Here is a proof with depth 8, length 92 :
% 9.33/9.48 % SZS output start Refutation
% See solution above
% 9.46/9.64 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
% 9.46/9.64
%------------------------------------------------------------------------------