TSTP Solution File: BOO070-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : BOO070-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 23:49:33 EDT 2022
% Result : Unsatisfiable 1.54s 1.70s
% Output : Refutation 1.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 2
% Syntax : Number of clauses : 53 ( 53 unt; 0 nHn; 53 RR)
% Number of literals : 53 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 17 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(multiply(multiply(u,inverse(u),v),inverse(multiply(multiply(w,x,y),z,multiply(w,x,x1))),multiply(x,multiply(x1,z,y),w)),v),
file('BOO070-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(multiply(a,a,b),a),
file('BOO070-1.p',unknown),
[] ).
cnf(3,plain,
equal(multiply(multiply(u,inverse(u),v),inverse(multiply(multiply(w,x,multiply(y,multiply(z,x1,x2),x3)),inverse(multiply(multiply(x3,y,x2),x1,multiply(x3,y,z))),multiply(w,x,multiply(x4,inverse(x4),x5)))),multiply(x,x5,w)),v),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(6,plain,
equal(multiply(multiply(u,v,w),inverse(multiply(multiply(x,y,z),x1,multiply(x,y,x2))),multiply(y,multiply(x2,x1,z),x)),multiply(v,multiply(w,inverse(multiply(u,v,x3)),x3),u)),
inference(spr,[status(thm),theory(equality)],[1]),
[iquote('0:SpR:1.0,1.0')] ).
cnf(13,plain,
equal(multiply(inverse(u),multiply(v,inverse(multiply(u,inverse(u),w)),w),u),v),
inference(spr,[status(thm),theory(equality)],[6,1]),
[iquote('0:SpR:6.0,1.0')] ).
cnf(28,plain,
equal(multiply(multiply(u,multiply(v,inverse(multiply(w,u,x)),x),y),inverse(multiply(multiply(z,x1,x2),x3,multiply(z,x1,x4))),multiply(x1,multiply(x4,x3,x2),z)),multiply(multiply(v,inverse(multiply(w,u,x)),x),multiply(y,inverse(multiply(multiply(w,u,v),inverse(multiply(multiply(x5,x6,x7),x8,multiply(x5,x6,x9))),multiply(x6,multiply(x9,x8,x7),x5))),w),u)),
inference(spr,[status(thm),theory(equality)],[6]),
[iquote('0:SpR:6.0,6.0')] ).
cnf(39,plain,
equal(multiply(multiply(u,inverse(u),v),inverse(multiply(multiply(w,x,y),multiply(z,inverse(multiply(y,inverse(y),x1)),x1),multiply(w,x,inverse(y)))),multiply(x,z,w)),v),
inference(spr,[status(thm),theory(equality)],[13,1]),
[iquote('0:SpR:13.0,1.0')] ).
cnf(48,plain,
equal(multiply(multiply(u,v,w),inverse(multiply(multiply(x,y,z),multiply(x1,inverse(multiply(z,inverse(z),x2)),x2),multiply(x,y,inverse(z)))),multiply(y,x1,x)),multiply(v,multiply(w,inverse(multiply(u,v,x3)),x3),u)),
inference(spr,[status(thm),theory(equality)],[13,6]),
[iquote('0:SpR:13.0,6.0')] ).
cnf(60,plain,
equal(multiply(multiply(u,inverse(u),v),inverse(multiply(w,multiply(multiply(x,inverse(x),inverse(w)),inverse(multiply(multiply(y,z,x1),x2,multiply(y,z,x3))),multiply(z,multiply(x3,x2,x1),y)),multiply(x4,inverse(x4),x5))),multiply(inverse(w),x5,w)),v),
inference(spr,[status(thm),theory(equality)],[3]),
[iquote('0:SpR:3.0,3.0')] ).
cnf(103,plain,
equal(multiply(multiply(u,inverse(u),v),inverse(multiply(w,inverse(w),multiply(x,inverse(x),y))),multiply(inverse(w),y,w)),v),
inference(rew,[status(thm),theory(equality)],[1,60]),
[iquote('0:Rew:1.0,60.0')] ).
cnf(112,plain,
equal(multiply(multiply(u,inverse(u),v),inverse(multiply(w,inverse(w),multiply(x,inverse(x),y))),multiply(inverse(w),y,w)),multiply(inverse(z),v,z)),
inference(spr,[status(thm),theory(equality)],[103]),
[iquote('0:SpR:103.0,103.0')] ).
cnf(114,plain,
equal(multiply(multiply(u,inverse(u),v),inverse(multiply(inverse(w),multiply(inverse(inverse(multiply(w,inverse(w),x))),inverse(multiply(w,inverse(w),x)),x),w)),multiply(inverse(inverse(multiply(w,inverse(w),x))),x,inverse(multiply(w,inverse(w),x)))),v),
inference(spr,[status(thm),theory(equality)],[103,3]),
[iquote('0:SpR:103.0,3.0')] ).
cnf(135,plain,
equal(multiply(multiply(u,multiply(multiply(v,w,x),inverse(multiply(multiply(v,w,y),u,z)),z),multiply(v,w,y)),inverse(multiply(x1,inverse(x1),multiply(x2,inverse(x2),x3))),multiply(inverse(x1),x3,x1)),multiply(w,multiply(x,u,y),v)),
inference(spr,[status(thm),theory(equality)],[6,103]),
[iquote('0:SpR:6.0,103.0')] ).
cnf(136,plain,
equal(multiply(inverse(u),v,u),v),
inference(rew,[status(thm),theory(equality)],[103,112]),
[iquote('0:Rew:103.0,112.0')] ).
cnf(138,plain,
equal(multiply(u,inverse(multiply(v,inverse(v),w)),w),u),
inference(rew,[status(thm),theory(equality)],[136,13]),
[iquote('0:Rew:136.0,13.0')] ).
cnf(155,plain,
equal(multiply(multiply(u,inverse(u),v),inverse(multiply(multiply(w,x,y),z,multiply(w,x,inverse(y)))),multiply(x,z,w)),v),
inference(rew,[status(thm),theory(equality)],[138,39]),
[iquote('0:Rew:138.0,39.0')] ).
cnf(158,plain,
equal(multiply(multiply(u,v,w),inverse(multiply(multiply(x,y,z),x1,multiply(x,y,inverse(z)))),multiply(y,x1,x)),multiply(v,multiply(w,inverse(multiply(u,v,x2)),x2),u)),
inference(rew,[status(thm),theory(equality)],[138,48]),
[iquote('0:Rew:138.0,48.0')] ).
cnf(169,plain,
equal(multiply(multiply(u,inverse(u),v),inverse(inverse(inverse(multiply(w,inverse(w),x)))),x),v),
inference(rew,[status(thm),theory(equality)],[136,114,138]),
[iquote('0:Rew:136.0,114.0,138.0,114.0,136.0,114.0')] ).
cnf(170,plain,
equal(multiply(multiply(u,multiply(multiply(v,w,x),inverse(multiply(multiply(v,w,y),u,z)),z),multiply(v,w,y)),inverse(multiply(x1,inverse(x1),multiply(x2,inverse(x2),x3))),x3),multiply(w,multiply(x,u,y),v)),
inference(rew,[status(thm),theory(equality)],[136,135]),
[iquote('0:Rew:136.0,135.0')] ).
cnf(189,plain,
equal(multiply(multiply(u,inverse(u),v),inverse(multiply(multiply(w,inverse(w),x),y,multiply(w,inverse(w),z))),multiply(z,y,x)),v),
inference(spr,[status(thm),theory(equality)],[136,1]),
[iquote('0:SpR:136.0,1.0')] ).
cnf(197,plain,
equal(multiply(inverse(inverse(u)),inverse(multiply(multiply(v,w,x),y,multiply(v,w,z))),multiply(w,multiply(z,y,x),v)),u),
inference(spr,[status(thm),theory(equality)],[136,1]),
[iquote('0:SpR:136.0,1.0')] ).
cnf(225,plain,
equal(multiply(multiply(u,inverse(multiply(v,inverse(v),w)),x),inverse(multiply(multiply(y,z,x1),x2,multiply(y,z,x3))),multiply(z,multiply(x3,x2,x1),y)),multiply(inverse(multiply(v,inverse(v),w)),multiply(x,inverse(u),w),u)),
inference(spr,[status(thm),theory(equality)],[138,6]),
[iquote('0:SpR:138.0,6.0')] ).
cnf(227,plain,
equal(inverse(multiply(u,inverse(u),v)),inverse(v)),
inference(spr,[status(thm),theory(equality)],[138,136]),
[iquote('0:SpR:138.0,136.0')] ).
cnf(239,plain,
equal(multiply(u,inverse(inverse(inverse(v))),v),u),
inference(spr,[status(thm),theory(equality)],[136,138]),
[iquote('0:SpR:136.0,138.0')] ).
cnf(240,plain,
equal(multiply(u,inverse(v),v),u),
inference(rew,[status(thm),theory(equality)],[227,138]),
[iquote('0:Rew:227.0,138.0')] ).
cnf(242,plain,
equal(multiply(multiply(u,inverse(u),v),inverse(inverse(inverse(w))),w),v),
inference(rew,[status(thm),theory(equality)],[227,169]),
[iquote('0:Rew:227.0,169.0')] ).
cnf(249,plain,
equal(multiply(multiply(u,multiply(multiply(v,w,x),inverse(multiply(multiply(v,w,y),u,z)),z),multiply(v,w,y)),inverse(multiply(x1,inverse(x1),x2)),x2),multiply(w,multiply(x,u,y),v)),
inference(rew,[status(thm),theory(equality)],[227,170]),
[iquote('0:Rew:227.0,170.0')] ).
cnf(270,plain,
equal(multiply(u,inverse(u),v),v),
inference(rew,[status(thm),theory(equality)],[239,242]),
[iquote('0:Rew:239.0,242.0')] ).
cnf(272,plain,
equal(multiply(u,inverse(multiply(multiply(v,w,x),y,multiply(v,w,z))),multiply(w,multiply(z,y,x),v)),u),
inference(rew,[status(thm),theory(equality)],[270,1]),
[iquote('0:Rew:270.0,1.0')] ).
cnf(283,plain,
equal(multiply(multiply(u,inverse(u),v),inverse(multiply(multiply(w,inverse(w),x),y,z)),multiply(z,y,x)),v),
inference(rew,[status(thm),theory(equality)],[270,189]),
[iquote('0:Rew:270.0,189.0')] ).
cnf(334,plain,
equal(multiply(u,inverse(multiply(multiply(v,w,x),y,multiply(v,w,inverse(x)))),multiply(w,y,v)),u),
inference(rew,[status(thm),theory(equality)],[270,155]),
[iquote('0:Rew:270.0,155.0')] ).
cnf(341,plain,
equal(multiply(u,multiply(v,inverse(multiply(w,u,x)),x),w),multiply(w,u,v)),
inference(rew,[status(thm),theory(equality)],[334,158]),
[iquote('0:Rew:334.0,158.0')] ).
cnf(362,plain,
equal(multiply(u,inverse(multiply(v,w,x)),multiply(x,w,v)),u),
inference(rew,[status(thm),theory(equality)],[270,283]),
[iquote('0:Rew:270.0,283.0,270.0,283.0')] ).
cnf(365,plain,
equal(multiply(multiply(u,inverse(multiply(v,w,x)),x),multiply(y,inverse(multiply(multiply(v,w,u),inverse(multiply(multiply(z,x1,x2),x3,multiply(z,x1,x4))),multiply(x1,multiply(x4,x3,x2),z))),v),w),multiply(w,multiply(u,inverse(multiply(v,w,x)),x),y)),
inference(rew,[status(thm),theory(equality)],[272,28]),
[iquote('0:Rew:272.0,28.0')] ).
cnf(367,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[272,197]),
[iquote('0:Rew:272.0,197.0')] ).
cnf(387,plain,
equal(multiply(multiply(u,v,w),x,multiply(u,v,y)),multiply(v,multiply(y,x,w),u)),
inference(rew,[status(thm),theory(equality)],[240,249,341,270]),
[iquote('0:Rew:240.0,249.0,341.0,249.0,270.0,249.0')] ).
cnf(417,plain,
equal(multiply(inverse(u),multiply(v,inverse(w),u),w),multiply(w,inverse(u),v)),
inference(rew,[status(thm),theory(equality)],[240,225,387,270]),
[iquote('0:Rew:240.0,225.0,387.0,225.0,270.0,225.0')] ).
cnf(433,plain,
equal(multiply(multiply(u,inverse(multiply(v,w,x)),x),multiply(y,inverse(multiply(v,w,u)),v),w),multiply(w,multiply(u,inverse(multiply(v,w,x)),x),y)),
inference(rew,[status(thm),theory(equality)],[240,365,387]),
[iquote('0:Rew:240.0,365.0,387.0,365.0')] ).
cnf(502,plain,
equal(multiply(u,v,inverse(u)),v),
inference(spr,[status(thm),theory(equality)],[367,136]),
[iquote('0:SpR:367.0,136.0')] ).
cnf(507,plain,
equal(multiply(u,v,inverse(v)),u),
inference(spr,[status(thm),theory(equality)],[367,240]),
[iquote('0:SpR:367.0,240.0')] ).
cnf(565,plain,
equal(multiply(u,v,w),multiply(w,v,u)),
inference(spr,[status(thm),theory(equality)],[362,270]),
[iquote('0:SpR:362.0,270.0')] ).
cnf(585,plain,
equal(multiply(u,multiply(v,inverse(multiply(w,u,x)),w),multiply(x,inverse(multiply(w,u,y)),y)),multiply(u,multiply(x,inverse(multiply(w,u,y)),y),v)),
inference(rew,[status(thm),theory(equality)],[565,433]),
[iquote('0:Rew:565.0,433.0')] ).
cnf(754,plain,
equal(multiply(inverse(u),multiply(v,inverse(multiply(u,inverse(u),w)),u),multiply(w,inverse(x),x)),multiply(inverse(u),multiply(w,inverse(x),x),v)),
inference(spr,[status(thm),theory(equality)],[270,585]),
[iquote('0:SpR:270.0,585.0')] ).
cnf(788,plain,
equal(multiply(inverse(u),multiply(v,inverse(w),u),w),multiply(inverse(u),w,v)),
inference(rew,[status(thm),theory(equality)],[270,754,240]),
[iquote('0:Rew:270.0,754.0,240.0,754.0')] ).
cnf(789,plain,
equal(multiply(u,inverse(v),w),multiply(inverse(v),u,w)),
inference(rew,[status(thm),theory(equality)],[417,788]),
[iquote('0:Rew:417.0,788.0')] ).
cnf(845,plain,
equal(multiply(u,v,w),multiply(v,u,w)),
inference(spr,[status(thm),theory(equality)],[367,789]),
[iquote('0:SpR:367.0,789.0')] ).
cnf(863,plain,
equal(multiply(u,v,w),multiply(w,u,v)),
inference(spr,[status(thm),theory(equality)],[845,565]),
[iquote('0:SpR:845.0,565.0')] ).
cnf(909,plain,
equal(multiply(u,v,w),multiply(u,w,v)),
inference(spr,[status(thm),theory(equality)],[863,565]),
[iquote('0:SpR:863.0,565.0')] ).
cnf(997,plain,
equal(multiply(inverse(u),v,multiply(w,inverse(v),u)),multiply(v,inverse(u),w)),
inference(rew,[status(thm),theory(equality)],[909,417]),
[iquote('0:Rew:909.0,417.0')] ).
cnf(4164,plain,
equal(multiply(inverse(inverse(u)),v,inverse(v)),multiply(v,inverse(inverse(u)),u)),
inference(spr,[status(thm),theory(equality)],[502,997]),
[iquote('0:SpR:502.0,997.0')] ).
cnf(4192,plain,
equal(multiply(u,v,v),v),
inference(rew,[status(thm),theory(equality)],[507,4164,367]),
[iquote('0:Rew:507.0,4164.0,367.0,4164.0')] ).
cnf(4273,plain,
equal(multiply(u,u,v),u),
inference(spr,[status(thm),theory(equality)],[4192,565]),
[iquote('0:SpR:4192.0,565.0')] ).
cnf(4327,plain,
$false,
inference(unc,[status(thm)],[4273,2]),
[iquote('0:UnC:4273.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : BOO070-1 : TPTP v8.1.0. Released v2.6.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n017.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 20:57:57 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.54/1.70
% 1.54/1.70 SPASS V 3.9
% 1.54/1.70 SPASS beiseite: Proof found.
% 1.54/1.70 % SZS status Theorem
% 1.54/1.70 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.54/1.70 SPASS derived 2706 clauses, backtracked 0 clauses, performed 0 splits and kept 535 clauses.
% 1.54/1.70 SPASS allocated 71823 KBytes.
% 1.54/1.70 SPASS spent 0:00:01.35 on the problem.
% 1.54/1.70 0:00:00.03 for the input.
% 1.54/1.70 0:00:00.00 for the FLOTTER CNF translation.
% 1.54/1.70 0:00:00.03 for inferences.
% 1.54/1.70 0:00:00.00 for the backtracking.
% 1.54/1.70 0:00:01.26 for the reduction.
% 1.54/1.70
% 1.54/1.70
% 1.54/1.70 Here is a proof with depth 7, length 53 :
% 1.54/1.70 % SZS output start Refutation
% See solution above
% 1.54/1.74 Formulae used in the proof : single_axiom prove_tba_axioms_4
% 1.54/1.74
%------------------------------------------------------------------------------