TSTP Solution File: GRP001-5 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP001-5 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.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 : Unsatisfiable 0.13s 0.35s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of clauses : 18 ( 10 unt; 0 nHn; 18 RR)
% Number of literals : 33 ( 0 equ; 19 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 10 con; 0-0 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
product(identity,u,u),
file('GRP001-5.p',unknown),
[] ).
cnf(2,axiom,
product(u,identity,u),
file('GRP001-5.p',unknown),
[] ).
cnf(3,axiom,
( ~ product(u,v,w)
| ~ product(x,v,y)
| ~ product(z,x,u)
| product(z,y,w) ),
file('GRP001-5.p',unknown),
[] ).
cnf(4,axiom,
( ~ product(u,v,w)
| ~ product(x,y,v)
| ~ product(u,x,z)
| product(z,y,w) ),
file('GRP001-5.p',unknown),
[] ).
cnf(5,axiom,
product(u,u,identity),
file('GRP001-5.p',unknown),
[] ).
cnf(6,axiom,
product(a,b,c),
file('GRP001-5.p',unknown),
[] ).
cnf(7,axiom,
~ product(b,a,c),
file('GRP001-5.p',unknown),
[] ).
cnf(8,plain,
( ~ product(u,v,c)
| ~ product(w,v,a)
| ~ product(b,w,u) ),
inference(res,[status(thm),theory(equality)],[3,7]),
[iquote('0:Res:3.3,7.0')] ).
cnf(10,plain,
( ~ product(u,b,a)
| ~ product(b,u,a) ),
inference(res,[status(thm),theory(equality)],[6,8]),
[iquote('0:Res:6.0,8.0')] ).
cnf(16,plain,
( ~ product(u,v,identity)
| ~ product(w,u,x)
| product(x,v,w) ),
inference(res,[status(thm),theory(equality)],[2,4]),
[iquote('0:Res:2.0,4.0')] ).
cnf(27,plain,
( ~ product(u,v,w)
| ~ product(x,u,identity)
| product(x,w,v) ),
inference(res,[status(thm),theory(equality)],[1,3]),
[iquote('0:Res:1.0,3.0')] ).
cnf(47,plain,
( ~ product(u,v,w)
| product(w,v,u) ),
inference(res,[status(thm),theory(equality)],[5,16]),
[iquote('0:Res:5.0,16.0')] ).
cnf(58,plain,
product(c,b,a),
inference(res,[status(thm),theory(equality)],[6,47]),
[iquote('0:Res:6.0,47.0')] ).
cnf(62,plain,
( ~ product(u,a,identity)
| product(u,c,b) ),
inference(res,[status(thm),theory(equality)],[6,27]),
[iquote('0:Res:6.0,27.0')] ).
cnf(67,plain,
~ product(b,c,a),
inference(res,[status(thm),theory(equality)],[58,10]),
[iquote('0:Res:58.0,10.0')] ).
cnf(75,plain,
product(a,c,b),
inference(res,[status(thm),theory(equality)],[5,62]),
[iquote('0:Res:5.0,62.0')] ).
cnf(77,plain,
product(b,c,a),
inference(res,[status(thm),theory(equality)],[75,47]),
[iquote('0:Res:75.0,47.0')] ).
cnf(83,plain,
$false,
inference(mrr,[status(thm)],[77,67]),
[iquote('0:MRR:77.0,67.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : GRP001-5 : TPTP v8.1.0. Released v1.0.0.
% 0.09/0.09 % Command : run_spass %d %s
% 0.09/0.29 % Computer : n011.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 600
% 0.09/0.29 % DateTime : Mon Jun 13 12:17:33 EDT 2022
% 0.09/0.29 % CPUTime :
% 0.13/0.35
% 0.13/0.35 SPASS V 3.9
% 0.13/0.35 SPASS beiseite: Proof found.
% 0.13/0.35 % SZS status Theorem
% 0.13/0.35 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35 SPASS derived 75 clauses, backtracked 0 clauses, performed 0 splits and kept 53 clauses.
% 0.13/0.35 SPASS allocated 63139 KBytes.
% 0.13/0.35 SPASS spent 0:00:00.05 on the problem.
% 0.13/0.35 0:00:00.03 for the input.
% 0.13/0.35 0:00:00.00 for the FLOTTER CNF translation.
% 0.13/0.35 0:00:00.00 for inferences.
% 0.13/0.35 0:00:00.00 for the backtracking.
% 0.13/0.35 0:00:00.00 for the reduction.
% 0.13/0.35
% 0.13/0.35
% 0.13/0.35 Here is a proof with depth 4, length 18 :
% 0.13/0.35 % SZS output start Refutation
% See solution above
% 0.13/0.35 Formulae used in the proof : left_identity right_identity associativity1 associativity2 square_element a_times_b_is_c prove_b_times_a_is_c
% 0.13/0.35
%------------------------------------------------------------------------------