TSTP Solution File: GRP012+5 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP012+5 : TPTP v8.1.0. Released v3.1.0.
% 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 : Sat Jul 16 11:44:45 EDT 2022
% Result : Theorem 0.91s 1.16s
% Output : Refutation 0.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of clauses : 21 ( 10 unt; 0 nHn; 21 RR)
% Number of literals : 40 ( 0 equ; 22 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 11 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
product(skc8,skc9,skc7),
file('GRP012+5.p',unknown),
[] ).
cnf(2,axiom,
product(u,skc5,u),
file('GRP012+5.p',unknown),
[] ).
cnf(3,axiom,
product(skc5,u,u),
file('GRP012+5.p',unknown),
[] ).
cnf(4,axiom,
product(u,inverse(u),skc5),
file('GRP012+5.p',unknown),
[] ).
cnf(6,axiom,
product(inverse(skc9),inverse(skc8),skc6),
file('GRP012+5.p',unknown),
[] ).
cnf(8,axiom,
~ product(inverse(skc6),inverse(skc7),skc5),
file('GRP012+5.p',unknown),
[] ).
cnf(9,axiom,
( ~ product(u,v,w)
| ~ product(x,w,y)
| ~ product(x,u,z)
| product(z,v,y) ),
file('GRP012+5.p',unknown),
[] ).
cnf(10,axiom,
( ~ product(u,v,w)
| ~ product(x,v,y)
| ~ product(z,x,u)
| product(z,y,w) ),
file('GRP012+5.p',unknown),
[] ).
cnf(12,plain,
( ~ product(u,v,w)
| ~ product(x,u,skc5)
| product(x,w,v) ),
inference(res,[status(thm),theory(equality)],[3,10]),
[iquote('0:Res:3.0,10.0')] ).
cnf(15,plain,
( ~ product(u,inverse(v),w)
| ~ product(x,u,v)
| product(x,w,skc5) ),
inference(res,[status(thm),theory(equality)],[4,10]),
[iquote('0:Res:4.0,10.0')] ).
cnf(19,plain,
( ~ product(u,v,w)
| ~ product(u,skc5,x)
| product(x,v,w) ),
inference(res,[status(thm),theory(equality)],[3,9]),
[iquote('0:Res:3.0,9.0')] ).
cnf(22,plain,
( ~ product(u,skc5,v)
| ~ product(u,w,x)
| product(x,inverse(w),v) ),
inference(res,[status(thm),theory(equality)],[4,9]),
[iquote('0:Res:4.0,9.0')] ).
cnf(50,plain,
( ~ product(u,v,skc5)
| product(u,skc5,inverse(v)) ),
inference(res,[status(thm),theory(equality)],[4,12]),
[iquote('0:Res:4.0,12.0')] ).
cnf(95,plain,
( ~ product(u,skc5,v)
| product(v,inverse(u),skc5) ),
inference(res,[status(thm),theory(equality)],[4,19]),
[iquote('0:Res:4.0,19.0')] ).
cnf(205,plain,
( ~ product(u,inverse(skc9),skc8)
| product(u,skc6,skc5) ),
inference(res,[status(thm),theory(equality)],[6,15]),
[iquote('0:Res:6.0,15.0')] ).
cnf(275,plain,
( ~ product(u,v,w)
| product(w,inverse(v),u) ),
inference(res,[status(thm),theory(equality)],[2,22]),
[iquote('0:Res:2.0,22.0')] ).
cnf(761,plain,
~ product(skc7,skc5,inverse(skc6)),
inference(res,[status(thm),theory(equality)],[95,8]),
[iquote('0:Res:95.1,8.0')] ).
cnf(774,plain,
~ product(skc7,skc6,skc5),
inference(res,[status(thm),theory(equality)],[50,761]),
[iquote('0:Res:50.1,761.0')] ).
cnf(1242,plain,
( ~ product(skc8,skc9,u)
| product(u,skc6,skc5) ),
inference(res,[status(thm),theory(equality)],[275,205]),
[iquote('0:Res:275.1,205.0')] ).
cnf(2260,plain,
product(skc7,skc6,skc5),
inference(res,[status(thm),theory(equality)],[1,1242]),
[iquote('0:Res:1.0,1242.0')] ).
cnf(2266,plain,
$false,
inference(mrr,[status(thm)],[2260,774]),
[iquote('0:MRR:2260.0,774.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP012+5 : TPTP v8.1.0. Released v3.1.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n017.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 : Tue Jun 14 13:09:24 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.91/1.16
% 0.91/1.16 SPASS V 3.9
% 0.91/1.16 SPASS beiseite: Proof found.
% 0.91/1.16 % SZS status Theorem
% 0.91/1.16 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.91/1.16 SPASS derived 2254 clauses, backtracked 0 clauses, performed 0 splits and kept 1664 clauses.
% 0.91/1.16 SPASS allocated 86703 KBytes.
% 0.91/1.16 SPASS spent 0:00:00.81 on the problem.
% 0.91/1.16 0:00:00.03 for the input.
% 0.91/1.16 0:00:00.03 for the FLOTTER CNF translation.
% 0.91/1.16 0:00:00.02 for inferences.
% 0.91/1.16 0:00:00.00 for the backtracking.
% 0.91/1.16 0:00:00.70 for the reduction.
% 0.91/1.16
% 0.91/1.16
% 0.91/1.16 Here is a proof with depth 4, length 21 :
% 0.91/1.16 % SZS output start Refutation
% See solution above
% 0.91/1.16 Formulae used in the proof : prove_distribution
% 0.91/1.16
%------------------------------------------------------------------------------