TSTP Solution File: GRP001-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP001-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n004.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 11:44:39 EDT 2022
% Result : Unsatisfiable 0.20s 0.49s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of clauses : 25 ( 12 unt; 0 nHn; 25 RR)
% Number of literals : 47 ( 0 equ; 27 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
product(u,u,identity),
file('GRP001-1.p',unknown),
[] ).
cnf(2,axiom,
product(a,b,c),
file('GRP001-1.p',unknown),
[] ).
cnf(3,axiom,
~ product(b,a,c),
file('GRP001-1.p',unknown),
[] ).
cnf(4,axiom,
product(identity,u,u),
file('GRP001-1.p',unknown),
[] ).
cnf(5,axiom,
product(u,identity,u),
file('GRP001-1.p',unknown),
[] ).
cnf(8,axiom,
product(u,v,multiply(u,v)),
file('GRP001-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ product(u,v,w)
| ~ product(u,v,x)
| equal(x,w) ),
file('GRP001-1.p',unknown),
[] ).
cnf(10,axiom,
( ~ product(u,v,w)
| ~ product(x,v,y)
| ~ product(z,x,u)
| product(z,y,w) ),
file('GRP001-1.p',unknown),
[] ).
cnf(11,axiom,
( ~ product(u,v,w)
| ~ product(x,y,v)
| ~ product(u,x,z)
| product(z,y,w) ),
file('GRP001-1.p',unknown),
[] ).
cnf(12,plain,
( ~ product(c,u,v)
| ~ product(b,u,w)
| product(a,w,v) ),
inference(res,[status(thm),theory(equality)],[2,10]),
[iquote('0:Res:2.0,10.0')] ).
cnf(13,plain,
( ~ product(a,u,v)
| ~ product(b,w,u)
| product(c,w,v) ),
inference(res,[status(thm),theory(equality)],[2,11]),
[iquote('0:Res:2.0,11.0')] ).
cnf(20,plain,
( ~ product(u,v,c)
| ~ product(w,v,a)
| ~ product(b,w,u) ),
inference(res,[status(thm),theory(equality)],[10,3]),
[iquote('0:Res:10.3,3.0')] ).
cnf(23,plain,
( ~ product(u,b,a)
| ~ product(b,u,a) ),
inference(res,[status(thm),theory(equality)],[2,20]),
[iquote('0:Res:2.0,20.2')] ).
cnf(33,plain,
( ~ product(u,identity,v)
| equal(v,u) ),
inference(res,[status(thm),theory(equality)],[5,9]),
[iquote('0:Res:5.0,9.0')] ).
cnf(74,plain,
( ~ product(u,v,w)
| ~ product(x,u,identity)
| product(x,w,v) ),
inference(res,[status(thm),theory(equality)],[4,10]),
[iquote('0:Res:4.0,10.0')] ).
cnf(119,plain,
( ~ product(b,u,identity)
| product(c,u,a) ),
inference(res,[status(thm),theory(equality)],[5,13]),
[iquote('0:Res:5.0,13.0')] ).
cnf(128,plain,
( ~ product(b,b,identity)
| ~ product(b,c,a) ),
inference(res,[status(thm),theory(equality)],[119,23]),
[iquote('0:Res:119.1,23.0')] ).
cnf(133,plain,
~ product(b,c,a),
inference(mrr,[status(thm)],[128,1]),
[iquote('0:MRR:128.0,1.0')] ).
cnf(136,plain,
( ~ product(b,c,u)
| product(a,u,identity) ),
inference(res,[status(thm),theory(equality)],[1,12]),
[iquote('0:Res:1.0,12.0')] ).
cnf(163,plain,
product(a,multiply(b,c),identity),
inference(res,[status(thm),theory(equality)],[8,136]),
[iquote('0:Res:8.0,136.0')] ).
cnf(330,plain,
( ~ product(u,v,identity)
| product(u,identity,v) ),
inference(res,[status(thm),theory(equality)],[1,74]),
[iquote('0:Res:1.0,74.0')] ).
cnf(472,plain,
product(a,identity,multiply(b,c)),
inference(res,[status(thm),theory(equality)],[163,330]),
[iquote('0:Res:163.0,330.0')] ).
cnf(557,plain,
equal(multiply(b,c),a),
inference(res,[status(thm),theory(equality)],[472,33]),
[iquote('0:Res:472.0,33.0')] ).
cnf(580,plain,
product(b,c,a),
inference(spr,[status(thm),theory(equality)],[557,8]),
[iquote('0:SpR:557.0,8.0')] ).
cnf(582,plain,
$false,
inference(mrr,[status(thm)],[580,133]),
[iquote('0:MRR:580.0,133.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP001-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n004.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 : Tue Jun 14 04:51:24 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.49
% 0.20/0.49 SPASS V 3.9
% 0.20/0.49 SPASS beiseite: Proof found.
% 0.20/0.49 % SZS status Theorem
% 0.20/0.49 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.49 SPASS derived 498 clauses, backtracked 0 clauses, performed 0 splits and kept 272 clauses.
% 0.20/0.49 SPASS allocated 63474 KBytes.
% 0.20/0.49 SPASS spent 0:00:00.13 on the problem.
% 0.20/0.49 0:00:00.03 for the input.
% 0.20/0.49 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.49 0:00:00.01 for inferences.
% 0.20/0.49 0:00:00.00 for the backtracking.
% 0.20/0.49 0:00:00.07 for the reduction.
% 0.20/0.49
% 0.20/0.49
% 0.20/0.49 Here is a proof with depth 6, length 25 :
% 0.20/0.49 % SZS output start Refutation
% See solution above
% 0.20/0.49 Formulae used in the proof : square_element a_times_b_is_c prove_b_times_a_is_c left_identity right_identity total_function1 total_function2 associativity1 associativity2
% 0.20/0.49
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