TSTP Solution File: GRP494-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP494-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 11:47:44 EDT 2022
% Result : Unsatisfiable 0.17s 0.42s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of clauses : 29 ( 29 unt; 0 nHn; 29 RR)
% Number of literals : 29 ( 0 equ; 2 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 : 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(double_divide(double_divide(v,w),double_divide(identity,identity)),double_divide(u,w))),v),
file('GRP494-1.p',unknown),
[] ).
cnf(2,axiom,
equal(double_divide(double_divide(u,v),identity),multiply(v,u)),
file('GRP494-1.p',unknown),
[] ).
cnf(3,axiom,
equal(double_divide(u,identity),inverse(u)),
file('GRP494-1.p',unknown),
[] ).
cnf(4,axiom,
equal(double_divide(u,inverse(u)),identity),
file('GRP494-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(multiply(identity,a2),a2),
file('GRP494-1.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(double_divide(double_divide(v,w),inverse(identity)),double_divide(u,w))),v),
inference(rew,[status(thm),theory(equality)],[3,1]),
[iquote('0:Rew:3.0,1.0')] ).
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(52,plain,
equal(double_divide(double_divide(identity,u),double_divide(double_divide(double_divide(v,identity),inverse(identity)),inverse(u))),v),
inference(spr,[status(thm),theory(equality)],[3,7]),
[iquote('0:SpR:3.0,7.0')] ).
cnf(54,plain,
equal(double_divide(double_divide(identity,u),double_divide(double_divide(identity,inverse(identity)),double_divide(u,inverse(v)))),v),
inference(spr,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpR:4.0,7.0')] ).
cnf(60,plain,
equal(double_divide(double_divide(identity,u),double_divide(double_divide(inverse(v),inverse(identity)),inverse(u))),v),
inference(rew,[status(thm),theory(equality)],[3,52]),
[iquote('0:Rew:3.0,52.0')] ).
cnf(61,plain,
equal(double_divide(double_divide(identity,u),double_divide(identity,double_divide(u,inverse(v)))),v),
inference(rew,[status(thm),theory(equality)],[4,54]),
[iquote('0:Rew:4.0,54.0')] ).
cnf(74,plain,
equal(double_divide(double_divide(identity,u),double_divide(identity,identity)),u),
inference(spr,[status(thm),theory(equality)],[4,61]),
[iquote('0:SpR:4.0,61.0')] ).
cnf(75,plain,
equal(double_divide(identity,double_divide(identity,double_divide(inverse(identity),inverse(u)))),u),
inference(spr,[status(thm),theory(equality)],[4,61]),
[iquote('0:SpR:4.0,61.0')] ).
cnf(77,plain,
equal(double_divide(double_divide(identity,u),inverse(identity)),u),
inference(rew,[status(thm),theory(equality)],[3,74]),
[iquote('0:Rew:3.0,74.0')] ).
cnf(87,plain,
equal(double_divide(double_divide(identity,u),double_divide(double_divide(v,inverse(identity)),double_divide(u,inverse(identity)))),double_divide(identity,v)),
inference(spr,[status(thm),theory(equality)],[77,7]),
[iquote('0:SpR:77.0,7.0')] ).
cnf(88,plain,
equal(double_divide(identity,inverse(identity)),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[4,77]),
[iquote('0:SpR:4.0,77.0')] ).
cnf(90,plain,
equal(inverse(identity),identity),
inference(rew,[status(thm),theory(equality)],[4,88]),
[iquote('0:Rew:4.0,88.0')] ).
cnf(96,plain,
equal(double_divide(double_divide(identity,u),double_divide(double_divide(inverse(v),identity),inverse(u))),v),
inference(rew,[status(thm),theory(equality)],[90,60]),
[iquote('0:Rew:90.0,60.0')] ).
cnf(104,plain,
equal(double_divide(identity,double_divide(identity,double_divide(identity,inverse(u)))),u),
inference(rew,[status(thm),theory(equality)],[90,75]),
[iquote('0:Rew:90.0,75.0')] ).
cnf(120,plain,
equal(double_divide(double_divide(identity,u),double_divide(inverse(inverse(v)),inverse(u))),v),
inference(rew,[status(thm),theory(equality)],[3,96]),
[iquote('0:Rew:3.0,96.0')] ).
cnf(128,plain,
equal(double_divide(double_divide(identity,u),double_divide(double_divide(v,identity),double_divide(u,identity))),double_divide(identity,v)),
inference(rew,[status(thm),theory(equality)],[90,87]),
[iquote('0:Rew:90.0,87.0')] ).
cnf(129,plain,
equal(double_divide(double_divide(identity,u),double_divide(inverse(v),inverse(u))),double_divide(identity,v)),
inference(rew,[status(thm),theory(equality)],[3,128]),
[iquote('0:Rew:3.0,128.0,3.0,128.0')] ).
cnf(130,plain,
equal(double_divide(identity,inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[129,120]),
[iquote('0:Rew:129.0,120.0')] ).
cnf(131,plain,
equal(double_divide(identity,double_divide(identity,u)),u),
inference(rew,[status(thm),theory(equality)],[130,104]),
[iquote('0:Rew:130.0,104.0')] ).
cnf(202,plain,
equal(double_divide(identity,u),inverse(u)),
inference(spr,[status(thm),theory(equality)],[130,131]),
[iquote('0:SpR:130.0,131.0')] ).
cnf(203,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[202,130]),
[iquote('0:Rew:202.0,130.0')] ).
cnf(223,plain,
$false,
inference(unc,[status(thm)],[203,14]),
[iquote('0:UnC:203.0,14.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP494-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.32 % Computer : n007.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Mon Jun 13 04:28:38 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.17/0.42
% 0.17/0.42 SPASS V 3.9
% 0.17/0.42 SPASS beiseite: Proof found.
% 0.17/0.42 % SZS status Theorem
% 0.17/0.42 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 SPASS derived 144 clauses, backtracked 0 clauses, performed 0 splits and kept 73 clauses.
% 0.17/0.42 SPASS allocated 63405 KBytes.
% 0.17/0.42 SPASS spent 0:00:00.08 on the problem.
% 0.17/0.42 0:00:00.04 for the input.
% 0.17/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.17/0.42 0:00:00.00 for inferences.
% 0.17/0.42 0:00:00.00 for the backtracking.
% 0.17/0.42 0:00:00.02 for the reduction.
% 0.17/0.42
% 0.17/0.42
% 0.17/0.42 Here is a proof with depth 3, length 29 :
% 0.17/0.42 % SZS output start Refutation
% See solution above
% 0.17/0.42 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms_2
% 0.17/0.42
%------------------------------------------------------------------------------