TSTP Solution File: GRP047-2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP047-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 11:44:59 EDT 2022
% Result : Unsatisfiable 0.19s 0.52s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of clauses : 33 ( 13 unt; 0 nHn; 33 RR)
% Number of literals : 63 ( 0 equ; 34 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 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,
equalish(a,b),
file('GRP047-2.p',unknown),
[] ).
cnf(2,axiom,
~ equalish(multiply(c,a),multiply(c,b)),
file('GRP047-2.p',unknown),
[] ).
cnf(3,axiom,
product(identity,u,u),
file('GRP047-2.p',unknown),
[] ).
cnf(4,axiom,
product(inverse(u),u,identity),
file('GRP047-2.p',unknown),
[] ).
cnf(5,axiom,
product(u,v,multiply(u,v)),
file('GRP047-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ product(u,v,w)
| ~ product(u,v,x)
| equalish(x,w) ),
file('GRP047-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ product(u,v,w)
| ~ product(x,v,y)
| ~ product(z,x,u)
| product(z,y,w) ),
file('GRP047-2.p',unknown),
[] ).
cnf(8,axiom,
( ~ product(u,v,w)
| ~ product(x,y,v)
| ~ product(u,x,z)
| product(z,y,w) ),
file('GRP047-2.p',unknown),
[] ).
cnf(9,axiom,
( ~ equalish(u,v)
| ~ product(w,x,u)
| product(w,x,v) ),
file('GRP047-2.p',unknown),
[] ).
cnf(10,plain,
( ~ product(u,v,multiply(c,b))
| ~ product(u,v,multiply(c,a)) ),
inference(res,[status(thm),theory(equality)],[6,2]),
[iquote('0:Res:6.2,2.0')] ).
cnf(11,plain,
( ~ equalish(u,v)
| product(identity,u,v) ),
inference(res,[status(thm),theory(equality)],[3,9]),
[iquote('0:Res:3.0,9.1')] ).
cnf(13,plain,
( ~ equalish(multiply(u,v),w)
| product(u,v,w) ),
inference(res,[status(thm),theory(equality)],[5,9]),
[iquote('0:Res:5.0,9.1')] ).
cnf(14,plain,
( ~ equalish(u,v)
| ~ equalish(v,w)
| product(identity,u,w) ),
inference(res,[status(thm),theory(equality)],[11,9]),
[iquote('0:Res:11.1,9.1')] ).
cnf(16,plain,
( ~ product(identity,u,v)
| equalish(v,u) ),
inference(res,[status(thm),theory(equality)],[3,6]),
[iquote('0:Res:3.0,6.0')] ).
cnf(22,plain,
( ~ equalish(u,v)
| equalish(v,u) ),
inference(res,[status(thm),theory(equality)],[11,16]),
[iquote('0:Res:11.1,16.0')] ).
cnf(23,plain,
equalish(multiply(identity,u),u),
inference(res,[status(thm),theory(equality)],[5,16]),
[iquote('0:Res:5.0,16.0')] ).
cnf(28,plain,
equalish(u,multiply(identity,u)),
inference(res,[status(thm),theory(equality)],[23,22]),
[iquote('0:Res:23.0,22.0')] ).
cnf(29,plain,
( ~ product(u,v,w)
| ~ product(identity,u,x)
| product(x,v,w) ),
inference(res,[status(thm),theory(equality)],[3,8]),
[iquote('0:Res:3.0,8.0')] ).
cnf(43,plain,
( ~ product(u,v,w)
| ~ product(x,u,identity)
| product(x,w,v) ),
inference(res,[status(thm),theory(equality)],[3,7]),
[iquote('0:Res:3.0,7.0')] ).
cnf(46,plain,
( ~ product(u,v,w)
| ~ product(x,u,y)
| product(x,w,multiply(y,v)) ),
inference(res,[status(thm),theory(equality)],[5,7]),
[iquote('0:Res:5.0,7.0')] ).
cnf(87,plain,
( ~ product(identity,inverse(u),v)
| product(v,u,identity) ),
inference(res,[status(thm),theory(equality)],[4,29]),
[iquote('0:Res:4.0,29.0')] ).
cnf(116,plain,
( ~ product(u,inverse(v),identity)
| product(u,identity,v) ),
inference(res,[status(thm),theory(equality)],[4,43]),
[iquote('0:Res:4.0,43.0')] ).
cnf(254,plain,
( ~ product(u,identity,v)
| product(u,w,multiply(v,w)) ),
inference(res,[status(thm),theory(equality)],[3,46]),
[iquote('0:Res:3.0,46.0')] ).
cnf(288,plain,
product(multiply(identity,inverse(u)),u,identity),
inference(res,[status(thm),theory(equality)],[5,87]),
[iquote('0:Res:5.0,87.0')] ).
cnf(342,plain,
product(multiply(identity,inverse(inverse(u))),identity,u),
inference(res,[status(thm),theory(equality)],[288,116]),
[iquote('0:Res:288.0,116.0')] ).
cnf(577,plain,
( ~ product(u,identity,c)
| ~ product(u,a,multiply(c,b)) ),
inference(res,[status(thm),theory(equality)],[254,10]),
[iquote('0:Res:254.1,10.1')] ).
cnf(613,plain,
( ~ equalish(b,u)
| product(identity,a,u) ),
inference(res,[status(thm),theory(equality)],[1,14]),
[iquote('0:Res:1.0,14.0')] ).
cnf(656,plain,
( ~ equalish(b,u)
| equalish(u,a) ),
inference(res,[status(thm),theory(equality)],[613,16]),
[iquote('0:Res:613.1,16.0')] ).
cnf(668,plain,
equalish(multiply(identity,b),a),
inference(res,[status(thm),theory(equality)],[28,656]),
[iquote('0:Res:28.0,656.0')] ).
cnf(700,plain,
product(identity,b,a),
inference(res,[status(thm),theory(equality)],[668,13]),
[iquote('0:Res:668.0,13.0')] ).
cnf(705,plain,
( ~ product(u,identity,v)
| product(u,a,multiply(v,b)) ),
inference(res,[status(thm),theory(equality)],[700,46]),
[iquote('0:Res:700.0,46.0')] ).
cnf(714,plain,
~ product(u,identity,c),
inference(mrr,[status(thm)],[577,705]),
[iquote('0:MRR:577.1,705.1')] ).
cnf(715,plain,
$false,
inference(unc,[status(thm)],[714,342]),
[iquote('0:UnC:714.0,342.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP047-2 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n021.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 12:00:57 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.52
% 0.19/0.52 SPASS V 3.9
% 0.19/0.52 SPASS beiseite: Proof found.
% 0.19/0.52 % SZS status Theorem
% 0.19/0.52 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.52 SPASS derived 705 clauses, backtracked 0 clauses, performed 0 splits and kept 527 clauses.
% 0.19/0.52 SPASS allocated 63619 KBytes.
% 0.19/0.52 SPASS spent 0:00:00.17 on the problem.
% 0.19/0.52 0:00:00.04 for the input.
% 0.19/0.52 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.52 0:00:00.01 for inferences.
% 0.19/0.52 0:00:00.00 for the backtracking.
% 0.19/0.52 0:00:00.10 for the reduction.
% 0.19/0.52
% 0.19/0.52
% 0.19/0.52 Here is a proof with depth 7, length 33 :
% 0.19/0.52 % SZS output start Refutation
% See solution above
% 0.19/0.52 Formulae used in the proof : a_equals_b prove_multiply_substitution2 left_identity left_inverse total_function1 total_function2 associativity1 associativity2 product_substitution3
% 0.19/0.52
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