TSTP Solution File: BOO071-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : BOO071-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.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 0.60s 0.77s
% Output : Refutation 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 2
% Syntax : Number of clauses : 21 ( 21 unt; 0 nHn; 21 RR)
% Number of literals : 21 ( 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 : 15 ( 15 usr; 13 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('BOO071-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(multiply(inverse(b),b,a),a),
file('BOO071-1.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(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(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(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(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(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(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(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(367,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[272,197]),
[iquote('0:Rew:272.0,197.0')] ).
cnf(512,plain,
equal(multiply(inverse(u),u,v),v),
inference(spr,[status(thm),theory(equality)],[367,270]),
[iquote('0:SpR:367.0,270.0')] ).
cnf(513,plain,
$false,
inference(unc,[status(thm)],[512,2]),
[iquote('0:UnC:512.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : BOO071-1 : TPTP v8.1.0. Released v2.6.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n022.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 19:03:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.60/0.77
% 0.60/0.77 SPASS V 3.9
% 0.60/0.77 SPASS beiseite: Proof found.
% 0.60/0.77 % SZS status Theorem
% 0.60/0.77 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.60/0.77 SPASS derived 344 clauses, backtracked 0 clauses, performed 0 splits and kept 184 clauses.
% 0.60/0.77 SPASS allocated 66336 KBytes.
% 0.60/0.77 SPASS spent 0:00:00.41 on the problem.
% 0.60/0.77 0:00:00.03 for the input.
% 0.60/0.77 0:00:00.00 for the FLOTTER CNF translation.
% 0.60/0.77 0:00:00.01 for inferences.
% 0.60/0.77 0:00:00.00 for the backtracking.
% 0.60/0.77 0:00:00.34 for the reduction.
% 0.60/0.77
% 0.60/0.77
% 0.60/0.77 Here is a proof with depth 5, length 21 :
% 0.60/0.77 % SZS output start Refutation
% See solution above
% 0.60/0.77 Formulae used in the proof : single_axiom prove_tba_axioms_5
% 0.60/0.77
%------------------------------------------------------------------------------