TSTP Solution File: BOO014-2 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : BOO014-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 0.72s 0.91s
% Output : Refutation 0.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 15
% Syntax : Number of clauses : 90 ( 90 unt; 0 nHn; 90 RR)
% Number of literals : 90 ( 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(add(a,b),c),
file('BOO014-2.p',unknown),
[] ).
cnf(2,axiom,
equal(multiply(inverse(a),inverse(b)),d),
file('BOO014-2.p',unknown),
[] ).
cnf(3,axiom,
~ equal(inverse(c),d),
file('BOO014-2.p',unknown),
[] ).
cnf(4,axiom,
equal(add(u,v),add(v,u)),
file('BOO014-2.p',unknown),
[] ).
cnf(5,axiom,
equal(multiply(u,v),multiply(v,u)),
file('BOO014-2.p',unknown),
[] ).
cnf(6,axiom,
equal(multiply(add(u,v),add(w,v)),add(multiply(u,w),v)),
file('BOO014-2.p',unknown),
[] ).
cnf(7,axiom,
equal(multiply(add(u,v),add(u,w)),add(u,multiply(v,w))),
file('BOO014-2.p',unknown),
[] ).
cnf(8,axiom,
equal(add(multiply(u,v),multiply(w,v)),multiply(add(u,w),v)),
file('BOO014-2.p',unknown),
[] ).
cnf(9,axiom,
equal(add(multiply(u,v),multiply(u,w)),multiply(u,add(v,w))),
file('BOO014-2.p',unknown),
[] ).
cnf(10,axiom,
equal(add(u,inverse(u)),multiplicative_identity),
file('BOO014-2.p',unknown),
[] ).
cnf(12,axiom,
equal(multiply(u,inverse(u)),additive_identity),
file('BOO014-2.p',unknown),
[] ).
cnf(14,axiom,
equal(multiply(u,multiplicative_identity),u),
file('BOO014-2.p',unknown),
[] ).
cnf(15,axiom,
equal(multiply(multiplicative_identity,u),u),
file('BOO014-2.p',unknown),
[] ).
cnf(16,axiom,
equal(add(u,additive_identity),u),
file('BOO014-2.p',unknown),
[] ).
cnf(17,axiom,
equal(add(additive_identity,u),u),
file('BOO014-2.p',unknown),
[] ).
cnf(57,plain,
equal(add(multiply(u,v),v),multiply(add(u,multiplicative_identity),v)),
inference(spr,[status(thm),theory(equality)],[15,8]),
[iquote('0:SpR:15.0,8.0')] ).
cnf(60,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(66,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(68,plain,
equal(multiply(add(inverse(a),u),inverse(b)),add(d,multiply(u,inverse(b)))),
inference(spr,[status(thm),theory(equality)],[2,8]),
[iquote('0:SpR:2.0,8.0')] ).
cnf(69,plain,
equal(add(u,multiply(v,u)),multiply(add(v,multiplicative_identity),u)),
inference(rew,[status(thm),theory(equality)],[4,57]),
[iquote('0:Rew:4.0,57.0')] ).
cnf(75,plain,
equal(multiply(inverse(u),add(v,u)),multiply(v,inverse(u))),
inference(rew,[status(thm),theory(equality)],[17,60,4,5]),
[iquote('0:Rew:17.0,60.0,4.0,60.0,5.0,60.0')] ).
cnf(76,plain,
equal(multiply(inverse(u),add(u,v)),multiply(v,inverse(u))),
inference(rew,[status(thm),theory(equality)],[17,66,5]),
[iquote('0:Rew:17.0,66.0,5.0,66.0')] ).
cnf(78,plain,
equal(multiply(inverse(b),add(inverse(a),u)),add(d,multiply(u,inverse(b)))),
inference(rew,[status(thm),theory(equality)],[5,68]),
[iquote('0:Rew:5.0,68.0')] ).
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(91,plain,
equal(add(multiply(a,u),b),multiply(c,add(u,b))),
inference(spr,[status(thm),theory(equality)],[1,6]),
[iquote('0:SpR:1.0,6.0')] ).
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(101,plain,
equal(add(b,multiply(a,u)),multiply(c,add(u,b))),
inference(rew,[status(thm),theory(equality)],[4,91]),
[iquote('0:Rew:4.0,91.0')] ).
cnf(105,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(106,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(147,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(148,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(157,plain,
equal(multiply(u,add(inverse(u),v)),add(additive_identity,multiply(u,v))),
inference(spr,[status(thm),theory(equality)],[12,9]),
[iquote('0:SpR:12.0,9.0')] ).
cnf(164,plain,
equal(add(u,multiply(u,v)),multiply(u,add(v,multiplicative_identity))),
inference(rew,[status(thm),theory(equality)],[4,147]),
[iquote('0:Rew:4.0,147.0')] ).
cnf(167,plain,
equal(multiply(u,add(v,inverse(u))),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[17,148,4]),
[iquote('0:Rew:17.0,148.0,4.0,148.0')] ).
cnf(168,plain,
equal(multiply(u,add(inverse(u),v)),multiply(u,v)),
inference(rew,[status(thm),theory(equality)],[17,157]),
[iquote('0:Rew:17.0,157.0')] ).
cnf(189,plain,
equal(multiply(u,inverse(u)),multiply(u,additive_identity)),
inference(spr,[status(thm),theory(equality)],[17,167]),
[iquote('0:SpR:17.0,167.0')] ).
cnf(191,plain,
equal(multiply(u,multiplicative_identity),multiply(u,u)),
inference(spr,[status(thm),theory(equality)],[10,167]),
[iquote('0:SpR:10.0,167.0')] ).
cnf(193,plain,
equal(multiply(u,u),u),
inference(rew,[status(thm),theory(equality)],[14,191]),
[iquote('0:Rew:14.0,191.0')] ).
cnf(195,plain,
equal(multiply(u,additive_identity),additive_identity),
inference(rew,[status(thm),theory(equality)],[12,189]),
[iquote('0:Rew:12.0,189.0')] ).
cnf(207,plain,
equal(multiply(c,add(additive_identity,b)),add(b,additive_identity)),
inference(spr,[status(thm),theory(equality)],[195,101]),
[iquote('0:SpR:195.0,101.0')] ).
cnf(216,plain,
equal(multiply(b,c),b),
inference(rew,[status(thm),theory(equality)],[5,207,16,4]),
[iquote('0:Rew:5.0,207.0,16.0,207.0,4.0,207.0,16.0,207.0')] ).
cnf(262,plain,
equal(multiply(add(u,v),u),add(u,multiply(v,additive_identity))),
inference(spr,[status(thm),theory(equality)],[16,7]),
[iquote('0:SpR:16.0,7.0')] ).
cnf(269,plain,
equal(add(a,multiply(b,u)),multiply(c,add(a,u))),
inference(spr,[status(thm),theory(equality)],[1,7]),
[iquote('0:SpR:1.0,7.0')] ).
cnf(282,plain,
equal(multiply(u,add(u,v)),u),
inference(rew,[status(thm),theory(equality)],[5,262,16,195]),
[iquote('0:Rew:5.0,262.0,16.0,262.0,195.0,262.0')] ).
cnf(303,plain,
equal(add(u,multiply(v,u)),multiply(add(u,v),u)),
inference(spr,[status(thm),theory(equality)],[193,8]),
[iquote('0:SpR:193.0,8.0')] ).
cnf(304,plain,
equal(add(u,multiply(u,v)),multiply(u,add(u,v))),
inference(spr,[status(thm),theory(equality)],[193,9]),
[iquote('0:SpR:193.0,9.0')] ).
cnf(316,plain,
equal(add(u,multiply(v,u)),multiply(u,add(u,v))),
inference(rew,[status(thm),theory(equality)],[5,303]),
[iquote('0:Rew:5.0,303.0')] ).
cnf(317,plain,
equal(multiply(add(u,multiplicative_identity),v),v),
inference(rew,[status(thm),theory(equality)],[69,316,282]),
[iquote('0:Rew:69.0,316.0,282.0,316.0')] ).
cnf(320,plain,
equal(add(u,multiply(v,u)),u),
inference(rew,[status(thm),theory(equality)],[317,69]),
[iquote('0:Rew:317.0,69.0')] ).
cnf(321,plain,
equal(multiply(u,add(v,multiplicative_identity)),u),
inference(rew,[status(thm),theory(equality)],[164,304,282]),
[iquote('0:Rew:164.0,304.0,282.0,304.0')] ).
cnf(322,plain,
equal(add(u,multiply(u,v)),u),
inference(rew,[status(thm),theory(equality)],[321,164]),
[iquote('0:Rew:321.0,164.0')] ).
cnf(473,plain,
equal(multiply(a,c),a),
inference(spr,[status(thm),theory(equality)],[1,282]),
[iquote('0:SpR:1.0,282.0')] ).
cnf(527,plain,
equal(add(inverse(b),d),inverse(b)),
inference(spr,[status(thm),theory(equality)],[2,320]),
[iquote('0:SpR:2.0,320.0')] ).
cnf(537,plain,
equal(add(c,a),c),
inference(spr,[status(thm),theory(equality)],[473,320]),
[iquote('0:SpR:473.0,320.0')] ).
cnf(540,plain,
equal(add(a,c),c),
inference(rew,[status(thm),theory(equality)],[4,537]),
[iquote('0:Rew:4.0,537.0')] ).
cnf(543,plain,
equal(add(d,inverse(b)),inverse(b)),
inference(rew,[status(thm),theory(equality)],[4,527]),
[iquote('0:Rew:4.0,527.0')] ).
cnf(609,plain,
equal(add(d,multiply(u,inverse(b))),multiply(add(d,u),inverse(b))),
inference(spr,[status(thm),theory(equality)],[543,7]),
[iquote('0:SpR:543.0,7.0')] ).
cnf(611,plain,
equal(multiply(b,inverse(b)),multiply(b,d)),
inference(spr,[status(thm),theory(equality)],[543,167]),
[iquote('0:SpR:543.0,167.0')] ).
cnf(613,plain,
equal(multiply(b,d),additive_identity),
inference(rew,[status(thm),theory(equality)],[12,611]),
[iquote('0:Rew:12.0,611.0')] ).
cnf(614,plain,
equal(add(d,multiply(u,inverse(b))),multiply(inverse(b),add(d,u))),
inference(rew,[status(thm),theory(equality)],[5,609]),
[iquote('0:Rew:5.0,609.0')] ).
cnf(616,plain,
equal(multiply(inverse(b),add(inverse(a),u)),multiply(inverse(b),add(d,u))),
inference(rew,[status(thm),theory(equality)],[614,78]),
[iquote('0:Rew:614.0,78.0')] ).
cnf(640,plain,
equal(add(inverse(a),d),inverse(a)),
inference(spr,[status(thm),theory(equality)],[2,322]),
[iquote('0:SpR:2.0,322.0')] ).
cnf(653,plain,
equal(add(d,inverse(a)),inverse(a)),
inference(rew,[status(thm),theory(equality)],[4,640]),
[iquote('0:Rew:4.0,640.0')] ).
cnf(691,plain,
equal(multiply(a,inverse(a)),multiply(a,d)),
inference(spr,[status(thm),theory(equality)],[653,167]),
[iquote('0:SpR:653.0,167.0')] ).
cnf(693,plain,
equal(multiply(a,d),additive_identity),
inference(rew,[status(thm),theory(equality)],[12,691]),
[iquote('0:Rew:12.0,691.0')] ).
cnf(732,plain,
equal(multiply(u,multiply(v,inverse(u))),multiply(u,inverse(u))),
inference(spr,[status(thm),theory(equality)],[320,168]),
[iquote('0:SpR:320.0,168.0')] ).
cnf(741,plain,
equal(multiply(u,multiply(v,inverse(u))),additive_identity),
inference(rew,[status(thm),theory(equality)],[12,732]),
[iquote('0:Rew:12.0,732.0')] ).
cnf(1432,plain,
equal(multiply(inverse(c),c),multiply(a,inverse(c))),
inference(spr,[status(thm),theory(equality)],[540,75]),
[iquote('0:SpR:540.0,75.0')] ).
cnf(1465,plain,
equal(multiply(a,inverse(c)),additive_identity),
inference(rew,[status(thm),theory(equality)],[12,1432,5]),
[iquote('0:Rew:12.0,1432.0,5.0,1432.0')] ).
cnf(1803,plain,
equal(add(inverse(d),additive_identity),add(b,inverse(d))),
inference(spr,[status(thm),theory(equality)],[613,105]),
[iquote('0:SpR:613.0,105.0')] ).
cnf(1804,plain,
equal(add(inverse(d),additive_identity),add(a,inverse(d))),
inference(spr,[status(thm),theory(equality)],[693,105]),
[iquote('0:SpR:693.0,105.0')] ).
cnf(1814,plain,
equal(add(b,inverse(d)),inverse(d)),
inference(rew,[status(thm),theory(equality)],[17,1803,4]),
[iquote('0:Rew:17.0,1803.0,4.0,1803.0')] ).
cnf(1815,plain,
equal(add(a,inverse(d)),inverse(d)),
inference(rew,[status(thm),theory(equality)],[17,1804,4]),
[iquote('0:Rew:17.0,1804.0,4.0,1804.0')] ).
cnf(1846,plain,
equal(multiply(b,inverse(d)),b),
inference(spr,[status(thm),theory(equality)],[1814,282]),
[iquote('0:SpR:1814.0,282.0')] ).
cnf(1861,plain,
equal(multiply(c,add(a,inverse(d))),add(a,b)),
inference(spr,[status(thm),theory(equality)],[1846,269]),
[iquote('0:SpR:1846.0,269.0')] ).
cnf(1875,plain,
equal(multiply(c,add(a,inverse(d))),c),
inference(rew,[status(thm),theory(equality)],[1,1861]),
[iquote('0:Rew:1.0,1861.0')] ).
cnf(1876,plain,
equal(multiply(c,inverse(d)),c),
inference(rew,[status(thm),theory(equality)],[1815,1875]),
[iquote('0:Rew:1815.0,1875.0')] ).
cnf(1889,plain,
equal(multiply(d,c),additive_identity),
inference(spr,[status(thm),theory(equality)],[1876,741]),
[iquote('0:SpR:1876.0,741.0')] ).
cnf(1892,plain,
equal(multiply(c,d),additive_identity),
inference(rew,[status(thm),theory(equality)],[5,1889]),
[iquote('0:Rew:5.0,1889.0')] ).
cnf(1944,plain,
equal(add(inverse(c),inverse(a)),add(inverse(a),additive_identity)),
inference(spr,[status(thm),theory(equality)],[1465,106]),
[iquote('0:SpR:1465.0,106.0')] ).
cnf(1964,plain,
equal(add(inverse(b),b),add(c,inverse(b))),
inference(spr,[status(thm),theory(equality)],[216,106]),
[iquote('0:SpR:216.0,106.0')] ).
cnf(1968,plain,
equal(add(inverse(c),additive_identity),add(d,inverse(c))),
inference(spr,[status(thm),theory(equality)],[1892,106]),
[iquote('0:SpR:1892.0,106.0')] ).
cnf(1978,plain,
equal(add(c,inverse(b)),multiplicative_identity),
inference(rew,[status(thm),theory(equality)],[10,1964,4]),
[iquote('0:Rew:10.0,1964.0,4.0,1964.0')] ).
cnf(1982,plain,
equal(add(d,inverse(c)),inverse(c)),
inference(rew,[status(thm),theory(equality)],[17,1968,4]),
[iquote('0:Rew:17.0,1968.0,4.0,1968.0')] ).
cnf(1988,plain,
equal(add(inverse(a),inverse(c)),inverse(a)),
inference(rew,[status(thm),theory(equality)],[4,1944,17]),
[iquote('0:Rew:4.0,1944.0,17.0,1944.0,4.0,1944.0')] ).
cnf(2031,plain,
equal(multiply(inverse(b),inverse(c)),multiply(inverse(c),multiplicative_identity)),
inference(spr,[status(thm),theory(equality)],[1978,76]),
[iquote('0:SpR:1978.0,76.0')] ).
cnf(2038,plain,
equal(multiply(inverse(b),inverse(c)),inverse(c)),
inference(rew,[status(thm),theory(equality)],[15,2031,5]),
[iquote('0:Rew:15.0,2031.0,5.0,2031.0')] ).
cnf(5771,plain,
equal(multiply(inverse(b),add(d,inverse(c))),multiply(inverse(b),inverse(a))),
inference(spr,[status(thm),theory(equality)],[1988,616]),
[iquote('0:SpR:1988.0,616.0')] ).
cnf(5785,plain,
equal(inverse(c),d),
inference(rew,[status(thm),theory(equality)],[2038,5771,1982,2,5]),
[iquote('0:Rew:2038.0,5771.0,1982.0,5771.0,2.0,5771.0,5.0,5771.0')] ).
cnf(5786,plain,
$false,
inference(mrr,[status(thm)],[5785,3]),
[iquote('0:MRR:5785.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : BOO014-2 : TPTP v8.1.0. Released v1.0.0.
% 0.00/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 1 17:12:12 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.72/0.91
% 0.72/0.91 SPASS V 3.9
% 0.72/0.91 SPASS beiseite: Proof found.
% 0.72/0.91 % SZS status Theorem
% 0.72/0.91 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.72/0.91 SPASS derived 3672 clauses, backtracked 0 clauses, performed 0 splits and kept 870 clauses.
% 0.72/0.91 SPASS allocated 67799 KBytes.
% 0.72/0.91 SPASS spent 0:00:00.57 on the problem.
% 0.72/0.91 0:00:00.03 for the input.
% 0.72/0.91 0:00:00.00 for the FLOTTER CNF translation.
% 0.72/0.91 0:00:00.03 for inferences.
% 0.72/0.91 0:00:00.00 for the backtracking.
% 0.72/0.91 0:00:00.49 for the reduction.
% 0.72/0.91
% 0.72/0.91
% 0.72/0.91 Here is a proof with depth 8, length 90 :
% 0.72/0.91 % SZS output start Refutation
% See solution above
% 0.72/0.91 Formulae used in the proof : a_plus_b_is_c a_inverse_times_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_id1 additive_id2
% 0.76/0.93
%------------------------------------------------------------------------------