TSTP Solution File: GRP003-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP003-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 11:44:41 EDT 2022
% Result : Unsatisfiable 0.19s 0.42s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of clauses : 15 ( 7 unt; 0 nHn; 15 RR)
% Number of literals : 30 ( 0 equ; 19 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
product(inverse(u),u,identity),
file('GRP003-1.p',unknown),
[] ).
cnf(2,axiom,
product(identity,u,u),
file('GRP003-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ product(u,v,w)
| ~ product(x,v,y)
| ~ product(z,x,u)
| product(z,y,w) ),
file('GRP003-1.p',unknown),
[] ).
cnf(4,axiom,
( ~ product(u,v,w)
| ~ product(x,y,v)
| ~ product(u,x,z)
| product(z,y,w) ),
file('GRP003-1.p',unknown),
[] ).
cnf(5,axiom,
~ product(a,identity,a),
file('GRP003-1.p',unknown),
[] ).
cnf(6,plain,
( ~ product(u,v,a)
| ~ product(w,v,identity)
| ~ product(a,w,u) ),
inference(res,[status(thm),theory(equality)],[3,5]),
[iquote('0:Res:3.3,5.0')] ).
cnf(8,plain,
( ~ product(u,a,identity)
| ~ product(a,u,identity) ),
inference(res,[status(thm),theory(equality)],[2,6]),
[iquote('0:Res:2.0,6.0')] ).
cnf(10,plain,
( ~ product(u,v,w)
| ~ product(inverse(w),u,x)
| product(x,v,identity) ),
inference(res,[status(thm),theory(equality)],[1,4]),
[iquote('0:Res:1.0,4.0')] ).
cnf(11,plain,
~ product(a,inverse(a),identity),
inference(res,[status(thm),theory(equality)],[1,8]),
[iquote('0:Res:1.0,8.0')] ).
cnf(15,plain,
( ~ product(u,v,w)
| ~ product(x,u,identity)
| product(x,w,v) ),
inference(res,[status(thm),theory(equality)],[2,3]),
[iquote('0:Res:2.0,3.0')] ).
cnf(19,plain,
( ~ product(u,inverse(v),identity)
| product(u,identity,v) ),
inference(res,[status(thm),theory(equality)],[1,15]),
[iquote('0:Res:1.0,15.0')] ).
cnf(31,plain,
product(inverse(inverse(u)),identity,u),
inference(res,[status(thm),theory(equality)],[1,19]),
[iquote('0:Res:1.0,19.0')] ).
cnf(48,plain,
( ~ product(identity,u,inverse(v))
| product(v,u,identity) ),
inference(res,[status(thm),theory(equality)],[31,10]),
[iquote('0:Res:31.0,10.1')] ).
cnf(128,plain,
product(u,inverse(u),identity),
inference(res,[status(thm),theory(equality)],[2,48]),
[iquote('0:Res:2.0,48.0')] ).
cnf(132,plain,
$false,
inference(unc,[status(thm)],[128,11]),
[iquote('0:UnC:128.0,11.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP003-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n026.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 03:41:21 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.42
% 0.19/0.42 SPASS V 3.9
% 0.19/0.42 SPASS beiseite: Proof found.
% 0.19/0.42 % SZS status Theorem
% 0.19/0.42 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.42 SPASS derived 126 clauses, backtracked 0 clauses, performed 0 splits and kept 82 clauses.
% 0.19/0.42 SPASS allocated 63180 KBytes.
% 0.19/0.42 SPASS spent 0:00:00.07 on the problem.
% 0.19/0.42 0:00:00.03 for the input.
% 0.19/0.42 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.42 0:00:00.00 for inferences.
% 0.19/0.42 0:00:00.00 for the backtracking.
% 0.19/0.42 0:00:00.01 for the reduction.
% 0.19/0.42
% 0.19/0.42
% 0.19/0.42 Here is a proof with depth 5, length 15 :
% 0.19/0.42 % SZS output start Refutation
% See solution above
% 0.19/0.42 Formulae used in the proof : left_inverse left_identity associativity1 associativity2 prove_there_is_a_right_identity
% 0.19/0.42
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