TSTP Solution File: BOO034-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : BOO034-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 23:49:30 EDT 2022
% Result : Unsatisfiable 0.20s 0.48s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of clauses : 35 ( 35 unt; 0 nHn; 35 RR)
% Number of literals : 35 ( 0 equ; 6 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(multiply(multiply(a,inverse(a),b),inverse(multiply(multiply(c,d,e),f,multiply(c,d,g))),multiply(d,multiply(g,f,e),c)),b),
file('BOO034-1.p',unknown),
[] ).
cnf(2,axiom,
equal(multiply(multiply(u,v,w),x,multiply(u,v,y)),multiply(u,v,multiply(w,x,y))),
file('BOO034-1.p',unknown),
[] ).
cnf(3,axiom,
equal(multiply(u,v,v),v),
file('BOO034-1.p',unknown),
[] ).
cnf(4,axiom,
equal(multiply(u,u,v),u),
file('BOO034-1.p',unknown),
[] ).
cnf(6,axiom,
equal(multiply(u,v,inverse(v)),u),
file('BOO034-1.p',unknown),
[] ).
cnf(7,plain,
~ equal(multiply(multiply(a,inverse(a),b),inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)),b),
inference(rew,[status(thm),theory(equality)],[2,1]),
[iquote('0:Rew:2.0,1.0')] ).
cnf(16,plain,
equal(multiply(u,v,multiply(w,multiply(u,v,w),x)),multiply(u,v,w)),
inference(spr,[status(thm),theory(equality)],[2,4]),
[iquote('0:SpR:2.0,4.0')] ).
cnf(17,plain,
equal(multiply(u,v,multiply(w,multiply(u,v,x),x)),multiply(u,v,x)),
inference(spr,[status(thm),theory(equality)],[2,3]),
[iquote('0:SpR:2.0,3.0')] ).
cnf(21,plain,
equal(multiply(multiply(u,u,v),w,u),multiply(u,u,multiply(v,w,x))),
inference(spr,[status(thm),theory(equality)],[4,2]),
[iquote('0:SpR:4.0,2.0')] ).
cnf(22,plain,
equal(multiply(multiply(u,v,w),x,v),multiply(u,v,multiply(w,x,v))),
inference(spr,[status(thm),theory(equality)],[3,2]),
[iquote('0:SpR:3.0,2.0')] ).
cnf(26,plain,
equal(multiply(u,v,multiply(w,u,x)),multiply(w,u,multiply(u,v,x))),
inference(spr,[status(thm),theory(equality)],[3,2]),
[iquote('0:SpR:3.0,2.0')] ).
cnf(29,plain,
equal(multiply(u,v,u),u),
inference(rew,[status(thm),theory(equality)],[4,21]),
[iquote('0:Rew:4.0,21.0,4.0,21.0')] ).
cnf(37,plain,
equal(multiply(multiply(u,v,w),x,u),multiply(u,v,multiply(w,x,u))),
inference(spr,[status(thm),theory(equality)],[29,2]),
[iquote('0:SpR:29.0,2.0')] ).
cnf(53,plain,
equal(multiply(u,v,multiply(inverse(v),u,w)),u),
inference(spr,[status(thm),theory(equality)],[6,16]),
[iquote('0:SpR:6.0,16.0')] ).
cnf(118,plain,
equal(multiply(u,v,multiply(w,u,inverse(v))),u),
inference(spr,[status(thm),theory(equality)],[6,17]),
[iquote('0:SpR:6.0,17.0')] ).
cnf(145,plain,
equal(multiply(u,v,multiply(w,x,multiply(y,u,inverse(v)))),multiply(multiply(u,v,w),x,u)),
inference(spr,[status(thm),theory(equality)],[118,2]),
[iquote('0:SpR:118.0,2.0')] ).
cnf(157,plain,
equal(multiply(u,v,multiply(w,x,multiply(y,u,inverse(v)))),multiply(u,v,multiply(w,x,u))),
inference(rew,[status(thm),theory(equality)],[37,145]),
[iquote('0:Rew:37.0,145.0')] ).
cnf(173,plain,
equal(multiply(u,v,multiply(w,inverse(v),multiply(x,u,inverse(v)))),u),
inference(spr,[status(thm),theory(equality)],[22,118]),
[iquote('0:SpR:22.0,118.0')] ).
cnf(177,plain,
equal(multiply(u,v,multiply(inverse(v),w,v)),multiply(u,w,v)),
inference(spr,[status(thm),theory(equality)],[6,22]),
[iquote('0:SpR:6.0,22.0')] ).
cnf(188,plain,
equal(multiply(u,v,multiply(w,inverse(v),u)),u),
inference(rew,[status(thm),theory(equality)],[157,173]),
[iquote('0:Rew:157.0,173.0')] ).
cnf(226,plain,
equal(multiply(multiply(inverse(inverse(u)),v,w),u,v),multiply(inverse(inverse(u)),v,w)),
inference(spr,[status(thm),theory(equality)],[53,188]),
[iquote('0:SpR:53.0,188.0')] ).
cnf(233,plain,
equal(multiply(inverse(inverse(u)),v,multiply(w,u,v)),multiply(inverse(inverse(u)),v,w)),
inference(rew,[status(thm),theory(equality)],[22,226]),
[iquote('0:Rew:22.0,226.0')] ).
cnf(271,plain,
equal(multiply(u,inverse(u),multiply(v,u,v)),v),
inference(spr,[status(thm),theory(equality)],[26,188]),
[iquote('0:SpR:26.0,188.0')] ).
cnf(300,plain,
equal(multiply(u,v,multiply(w,u,v)),multiply(w,u,v)),
inference(spr,[status(thm),theory(equality)],[3,26]),
[iquote('0:SpR:3.0,26.0')] ).
cnf(316,plain,
equal(multiply(u,inverse(u),v),v),
inference(rew,[status(thm),theory(equality)],[29,271]),
[iquote('0:Rew:29.0,271.0')] ).
cnf(317,plain,
~ equal(multiply(b,inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)),b),
inference(rew,[status(thm),theory(equality)],[316,7]),
[iquote('0:Rew:316.0,7.0')] ).
cnf(360,plain,
equal(inverse(inverse(u)),u),
inference(spr,[status(thm),theory(equality)],[316,6]),
[iquote('0:SpR:316.0,6.0')] ).
cnf(384,plain,
equal(multiply(u,v,multiply(w,u,v)),multiply(u,v,w)),
inference(rew,[status(thm),theory(equality)],[360,233]),
[iquote('0:Rew:360.0,233.0')] ).
cnf(391,plain,
equal(multiply(u,v,w),multiply(v,w,u)),
inference(rew,[status(thm),theory(equality)],[300,384]),
[iquote('0:Rew:300.0,384.0')] ).
cnf(394,plain,
~ equal(multiply(b,inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(f,e,g),c)),b),
inference(rew,[status(thm),theory(equality)],[391,317]),
[iquote('0:Rew:391.0,317.0')] ).
cnf(397,plain,
equal(multiply(u,v,multiply(v,inverse(v),w)),multiply(u,w,v)),
inference(rew,[status(thm),theory(equality)],[391,177]),
[iquote('0:Rew:391.0,177.0')] ).
cnf(404,plain,
equal(multiply(u,v,w),multiply(u,w,v)),
inference(rew,[status(thm),theory(equality)],[316,397]),
[iquote('0:Rew:316.0,397.0')] ).
cnf(421,plain,
~ equal(multiply(b,multiply(c,d,multiply(e,f,g)),inverse(multiply(c,d,multiply(e,f,g)))),b),
inference(rew,[status(thm),theory(equality)],[404,394,391]),
[iquote('0:Rew:404.0,394.0,391.0,394.0,404.0,394.0,391.0,394.0')] ).
cnf(422,plain,
~ equal(b,b),
inference(rew,[status(thm),theory(equality)],[6,421]),
[iquote('0:Rew:6.0,421.0')] ).
cnf(423,plain,
$false,
inference(obv,[status(thm),theory(equality)],[422]),
[iquote('0:Obv:422.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : BOO034-1 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n029.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jun 1 18:56:46 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.20/0.48
% 0.20/0.48 SPASS V 3.9
% 0.20/0.48 SPASS beiseite: Proof found.
% 0.20/0.48 % SZS status Theorem
% 0.20/0.48 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.48 SPASS derived 296 clauses, backtracked 0 clauses, performed 0 splits and kept 104 clauses.
% 0.20/0.48 SPASS allocated 63631 KBytes.
% 0.20/0.48 SPASS spent 0:00:00.12 on the problem.
% 0.20/0.48 0:00:00.03 for the input.
% 0.20/0.48 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.48 0:00:00.00 for inferences.
% 0.20/0.48 0:00:00.00 for the backtracking.
% 0.20/0.48 0:00:00.06 for the reduction.
% 0.20/0.48
% 0.20/0.48
% 0.20/0.48 Here is a proof with depth 5, length 35 :
% 0.20/0.48 % SZS output start Refutation
% See solution above
% 0.20/0.48 Formulae used in the proof : prove_single_axiom associativity ternary_multiply_1 ternary_multiply_2 right_inverse
% 0.20/0.48
%------------------------------------------------------------------------------