TSTP Solution File: GRP491-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP491-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 : Sat Jul 16 11:47:43 EDT 2022
% Result : Unsatisfiable 0.18s 0.42s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of clauses : 40 ( 40 unt; 0 nHn; 40 RR)
% Number of literals : 40 ( 0 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(double_divide(double_divide(identity,u),double_divide(identity,double_divide(double_divide(double_divide(u,v),identity),double_divide(w,v)))),w),
file('GRP491-1.p',unknown),
[] ).
cnf(2,axiom,
equal(double_divide(double_divide(u,v),identity),multiply(v,u)),
file('GRP491-1.p',unknown),
[] ).
cnf(3,axiom,
equal(double_divide(u,identity),inverse(u)),
file('GRP491-1.p',unknown),
[] ).
cnf(4,axiom,
equal(double_divide(u,inverse(u)),identity),
file('GRP491-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(multiply(identity,a2),a2),
file('GRP491-1.p',unknown),
[] ).
cnf(6,plain,
equal(inverse(double_divide(u,v)),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[3,2]),
[iquote('0:Rew:3.0,2.0')] ).
cnf(7,plain,
equal(double_divide(double_divide(identity,u),double_divide(identity,double_divide(multiply(v,u),double_divide(w,v)))),w),
inference(rew,[status(thm),theory(equality)],[6,1,3]),
[iquote('0:Rew:6.0,1.0,3.0,1.0')] ).
cnf(12,plain,
equal(multiply(inverse(u),u),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[4,6]),
[iquote('0:SpR:4.0,6.0')] ).
cnf(13,plain,
equal(multiply(identity,u),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[3,6]),
[iquote('0:SpR:3.0,6.0')] ).
cnf(14,plain,
~ equal(inverse(inverse(a2)),a2),
inference(rew,[status(thm),theory(equality)],[13,5]),
[iquote('0:Rew:13.0,5.0')] ).
cnf(50,plain,
equal(double_divide(double_divide(identity,u),double_divide(identity,double_divide(multiply(inverse(v),u),identity))),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(51,plain,
equal(double_divide(double_divide(identity,u),double_divide(identity,double_divide(multiply(identity,u),inverse(v)))),v),
inference(spr,[status(thm),theory(equality)],[3,7]),
[iquote('0:SpR:3.0,7.0')] ).
cnf(56,plain,
equal(double_divide(identity,double_divide(identity,double_divide(multiply(u,inverse(identity)),double_divide(v,u)))),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(58,plain,
equal(double_divide(double_divide(identity,u),double_divide(identity,inverse(multiply(inverse(v),u)))),v),
inference(rew,[status(thm),theory(equality)],[3,50]),
[iquote('0:Rew:3.0,50.0')] ).
cnf(59,plain,
equal(double_divide(double_divide(identity,u),double_divide(identity,double_divide(inverse(inverse(u)),inverse(v)))),v),
inference(rew,[status(thm),theory(equality)],[13,51]),
[iquote('0:Rew:13.0,51.0')] ).
cnf(70,plain,
equal(double_divide(double_divide(identity,u),double_divide(identity,inverse(inverse(identity)))),u),
inference(spr,[status(thm),theory(equality)],[12,58]),
[iquote('0:SpR:12.0,58.0')] ).
cnf(78,plain,
equal(double_divide(double_divide(identity,u),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(inverse(identity))),u),v))),double_divide(identity,v)),
inference(spr,[status(thm),theory(equality)],[70,7]),
[iquote('0:SpR:70.0,7.0')] ).
cnf(80,plain,
equal(double_divide(identity,double_divide(identity,inverse(inverse(identity)))),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[4,70]),
[iquote('0:SpR:4.0,70.0')] ).
cnf(81,plain,
equal(double_divide(inverse(identity),double_divide(identity,inverse(inverse(identity)))),identity),
inference(spr,[status(thm),theory(equality)],[3,70]),
[iquote('0:SpR:3.0,70.0')] ).
cnf(89,plain,
equal(double_divide(inverse(identity),double_divide(identity,inverse(inverse(identity)))),double_divide(identity,inverse(inverse(identity)))),
inference(spr,[status(thm),theory(equality)],[80,70]),
[iquote('0:SpR:80.0,70.0')] ).
cnf(94,plain,
equal(double_divide(identity,inverse(inverse(identity))),identity),
inference(rew,[status(thm),theory(equality)],[81,89]),
[iquote('0:Rew:81.0,89.0')] ).
cnf(95,plain,
equal(double_divide(double_divide(identity,u),identity),u),
inference(rew,[status(thm),theory(equality)],[94,70]),
[iquote('0:Rew:94.0,70.0')] ).
cnf(97,plain,
equal(double_divide(inverse(identity),identity),identity),
inference(rew,[status(thm),theory(equality)],[94,81]),
[iquote('0:Rew:94.0,81.0')] ).
cnf(99,plain,
equal(double_divide(double_divide(identity,u),double_divide(identity,double_divide(multiply(identity,u),v))),double_divide(identity,v)),
inference(rew,[status(thm),theory(equality)],[94,78]),
[iquote('0:Rew:94.0,78.0')] ).
cnf(101,plain,
equal(inverse(inverse(identity)),identity),
inference(rew,[status(thm),theory(equality)],[3,97]),
[iquote('0:Rew:3.0,97.0')] ).
cnf(102,plain,
equal(double_divide(identity,identity),identity),
inference(rew,[status(thm),theory(equality)],[101,94]),
[iquote('0:Rew:101.0,94.0')] ).
cnf(103,plain,
equal(inverse(identity),identity),
inference(rew,[status(thm),theory(equality)],[3,102]),
[iquote('0:Rew:3.0,102.0')] ).
cnf(106,plain,
equal(double_divide(identity,double_divide(identity,double_divide(multiply(u,identity),double_divide(v,u)))),v),
inference(rew,[status(thm),theory(equality)],[103,56]),
[iquote('0:Rew:103.0,56.0')] ).
cnf(113,plain,
equal(multiply(u,identity),u),
inference(rew,[status(thm),theory(equality)],[6,95,3]),
[iquote('0:Rew:6.0,95.0,3.0,95.0')] ).
cnf(118,plain,
equal(double_divide(identity,double_divide(identity,double_divide(u,double_divide(v,u)))),v),
inference(rew,[status(thm),theory(equality)],[113,106]),
[iquote('0:Rew:113.0,106.0')] ).
cnf(120,plain,
equal(double_divide(double_divide(identity,u),double_divide(identity,double_divide(inverse(inverse(u)),v))),double_divide(identity,v)),
inference(rew,[status(thm),theory(equality)],[13,99]),
[iquote('0:Rew:13.0,99.0')] ).
cnf(121,plain,
equal(double_divide(identity,inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[120,59]),
[iquote('0:Rew:120.0,59.0')] ).
cnf(189,plain,
equal(multiply(double_divide(identity,double_divide(u,double_divide(v,u))),identity),inverse(v)),
inference(spr,[status(thm),theory(equality)],[118,6]),
[iquote('0:SpR:118.0,6.0')] ).
cnf(198,plain,
equal(double_divide(identity,double_divide(identity,double_divide(identity,inverse(u)))),u),
inference(spr,[status(thm),theory(equality)],[3,118]),
[iquote('0:SpR:3.0,118.0')] ).
cnf(204,plain,
equal(double_divide(identity,double_divide(identity,u)),u),
inference(rew,[status(thm),theory(equality)],[121,198]),
[iquote('0:Rew:121.0,198.0')] ).
cnf(205,plain,
equal(double_divide(u,double_divide(v,u)),v),
inference(rew,[status(thm),theory(equality)],[204,118]),
[iquote('0:Rew:204.0,118.0')] ).
cnf(214,plain,
equal(double_divide(identity,double_divide(u,double_divide(v,u))),inverse(v)),
inference(rew,[status(thm),theory(equality)],[113,189]),
[iquote('0:Rew:113.0,189.0')] ).
cnf(215,plain,
equal(double_divide(identity,u),inverse(u)),
inference(rew,[status(thm),theory(equality)],[205,214]),
[iquote('0:Rew:205.0,214.0')] ).
cnf(217,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[215,121]),
[iquote('0:Rew:215.0,121.0')] ).
cnf(233,plain,
$false,
inference(unc,[status(thm)],[217,14]),
[iquote('0:UnC:217.0,14.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP491-1 : TPTP v8.1.0. Released v2.6.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n028.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 : Mon Jun 13 15:02:07 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.42
% 0.18/0.42 SPASS V 3.9
% 0.18/0.42 SPASS beiseite: Proof found.
% 0.18/0.42 % SZS status Theorem
% 0.18/0.42 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.42 SPASS derived 156 clauses, backtracked 0 clauses, performed 0 splits and kept 72 clauses.
% 0.18/0.42 SPASS allocated 63415 KBytes.
% 0.18/0.42 SPASS spent 0:00:00.07 on the problem.
% 0.18/0.42 0:00:00.03 for the input.
% 0.18/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.42 0:00:00.00 for inferences.
% 0.18/0.42 0:00:00.00 for the backtracking.
% 0.18/0.42 0:00:00.02 for the reduction.
% 0.18/0.42
% 0.18/0.42
% 0.18/0.42 Here is a proof with depth 4, length 40 :
% 0.18/0.42 % SZS output start Refutation
% See solution above
% 0.18/0.42 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms_2
% 0.18/0.42
%------------------------------------------------------------------------------