TSTP Solution File: GRP001+6 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP001+6 : TPTP v8.1.0. Released v3.1.0.
% 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 : Sat Jul 16 11:44:40 EDT 2022
% Result : Theorem 2.68s 2.93s
% Output : Refutation 2.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of clauses : 26 ( 14 unt; 0 nHn; 26 RR)
% Number of literals : 47 ( 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; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
product(skc5,skc6,skc7),
file('GRP001+6.p',unknown),
[] ).
cnf(2,axiom,
product(u,skc4,u),
file('GRP001+6.p',unknown),
[] ).
cnf(3,axiom,
product(skc4,u,u),
file('GRP001+6.p',unknown),
[] ).
cnf(4,axiom,
product(u,u,skc4),
file('GRP001+6.p',unknown),
[] ).
cnf(5,axiom,
product(u,inverse(u),skc4),
file('GRP001+6.p',unknown),
[] ).
cnf(6,axiom,
product(inverse(u),u,skc4),
file('GRP001+6.p',unknown),
[] ).
cnf(7,axiom,
~ product(skc6,skc5,skc7),
file('GRP001+6.p',unknown),
[] ).
cnf(8,axiom,
product(u,v,skf1(v,u)),
file('GRP001+6.p',unknown),
[] ).
cnf(9,axiom,
( ~ product(u,v,w)
| ~ product(x,w,y)
| ~ product(x,u,z)
| product(z,v,y) ),
file('GRP001+6.p',unknown),
[] ).
cnf(10,axiom,
( ~ product(u,v,w)
| ~ product(x,v,y)
| ~ product(z,x,u)
| product(z,y,w) ),
file('GRP001+6.p',unknown),
[] ).
cnf(12,plain,
( ~ product(u,v,w)
| ~ product(x,u,skc4)
| product(x,w,v) ),
inference(res,[status(thm),theory(equality)],[3,10]),
[iquote('0:Res:3.0,10.0')] ).
cnf(18,plain,
( ~ product(u,skc7,v)
| ~ product(u,skc5,w)
| product(w,skc6,v) ),
inference(res,[status(thm),theory(equality)],[1,9]),
[iquote('0:Res:1.0,9.0')] ).
cnf(21,plain,
( ~ product(u,skc4,v)
| ~ product(u,w,x)
| product(x,w,v) ),
inference(res,[status(thm),theory(equality)],[4,9]),
[iquote('0:Res:4.0,9.0')] ).
cnf(22,plain,
( ~ product(u,skc4,v)
| ~ product(u,inverse(w),x)
| product(x,w,v) ),
inference(res,[status(thm),theory(equality)],[6,9]),
[iquote('0:Res:6.0,9.0')] ).
cnf(24,plain,
( ~ product(u,skf1(v,w),x)
| ~ product(u,w,y)
| product(y,v,x) ),
inference(res,[status(thm),theory(equality)],[8,9]),
[iquote('0:Res:8.0,9.0')] ).
cnf(35,plain,
( ~ product(skc7,skc5,u)
| product(u,skc6,skc4) ),
inference(res,[status(thm),theory(equality)],[4,18]),
[iquote('0:Res:4.0,18.0')] ).
cnf(43,plain,
product(skf1(skc5,skc7),skc6,skc4),
inference(res,[status(thm),theory(equality)],[8,35]),
[iquote('0:Res:8.0,35.0')] ).
cnf(52,plain,
( ~ product(u,v,skc4)
| product(u,skc4,v) ),
inference(res,[status(thm),theory(equality)],[4,12]),
[iquote('0:Res:4.0,12.0')] ).
cnf(118,plain,
product(skf1(skc5,skc7),skc4,skc6),
inference(res,[status(thm),theory(equality)],[43,52]),
[iquote('0:Res:43.0,52.0')] ).
cnf(197,plain,
( ~ product(u,v,w)
| product(w,v,u) ),
inference(res,[status(thm),theory(equality)],[2,21]),
[iquote('0:Res:2.0,21.0')] ).
cnf(294,plain,
( ~ product(u,skc4,v)
| product(skc4,u,v) ),
inference(res,[status(thm),theory(equality)],[5,22]),
[iquote('0:Res:5.0,22.1')] ).
cnf(672,plain,
product(skc4,skf1(skc5,skc7),skc6),
inference(res,[status(thm),theory(equality)],[118,294]),
[iquote('0:Res:118.0,294.0')] ).
cnf(730,plain,
( ~ product(skc4,skc7,u)
| product(u,skc5,skc6) ),
inference(res,[status(thm),theory(equality)],[672,24]),
[iquote('0:Res:672.0,24.0')] ).
cnf(5759,plain,
product(skc7,skc5,skc6),
inference(res,[status(thm),theory(equality)],[3,730]),
[iquote('0:Res:3.0,730.0')] ).
cnf(5788,plain,
product(skc6,skc5,skc7),
inference(res,[status(thm),theory(equality)],[5759,197]),
[iquote('0:Res:5759.0,197.0')] ).
cnf(5797,plain,
$false,
inference(mrr,[status(thm)],[5788,7]),
[iquote('0:MRR:5788.0,7.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP001+6 : TPTP v8.1.0. Released v3.1.0.
% 0.12/0.13 % 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 : Mon Jun 13 14:45:33 EDT 2022
% 0.19/0.34 % CPUTime :
% 2.68/2.93
% 2.68/2.93 SPASS V 3.9
% 2.68/2.93 SPASS beiseite: Proof found.
% 2.68/2.93 % SZS status Theorem
% 2.68/2.93 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.68/2.93 SPASS derived 5786 clauses, backtracked 0 clauses, performed 0 splits and kept 3694 clauses.
% 2.68/2.93 SPASS allocated 88558 KBytes.
% 2.68/2.93 SPASS spent 0:00:02.55 on the problem.
% 2.68/2.93 0:00:00.03 for the input.
% 2.68/2.93 0:00:00.03 for the FLOTTER CNF translation.
% 2.68/2.93 0:00:00.04 for inferences.
% 2.68/2.93 0:00:00.00 for the backtracking.
% 2.68/2.93 0:00:02.41 for the reduction.
% 2.68/2.93
% 2.68/2.93
% 2.68/2.93 Here is a proof with depth 8, length 26 :
% 2.68/2.93 % SZS output start Refutation
% See solution above
% 2.68/2.93 Formulae used in the proof : commutativity
% 2.68/2.93
%------------------------------------------------------------------------------