%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : FLD030-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 02:28:23 EDT 2022
% Result : Unsatisfiable 0.18s 0.41s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of clauses : 14 ( 6 unt; 0 nHn; 14 RR)
% Number of literals : 27 ( 0 equ; 19 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,
defined(a),
file('FLD030-3.p',unknown),
[] ).
cnf(2,axiom,
defined(b),
file('FLD030-3.p',unknown),
[] ).
cnf(4,axiom,
product(multiplicative_identity,a,d),
file('FLD030-3.p',unknown),
[] ).
cnf(5,axiom,
~ product(d,b,multiply(a,b)),
file('FLD030-3.p',unknown),
[] ).
cnf(12,axiom,
( ~ product(u,v,w)
| ~ product(x,y,v)
| ~ product(u,x,z)
| product(z,y,w) ),
file('FLD030-3.p',unknown),
[] ).
cnf(13,axiom,
( ~ defined(u)
| product(multiplicative_identity,u,u) ),
file('FLD030-3.p',unknown),
[] ).
cnf(21,axiom,
( ~ defined(u)
| ~ defined(v)
| defined(multiply(v,u)) ),
file('FLD030-3.p',unknown),
[] ).
cnf(25,axiom,
( ~ defined(u)
| ~ defined(v)
| product(v,u,multiply(v,u)) ),
file('FLD030-3.p',unknown),
[] ).
cnf(48,plain,
( ~ product(u,v,d)
| ~ product(u,w,multiply(a,b))
| ~ product(v,b,w) ),
inference(res,[status(thm),theory(equality)],[12,5]),
[iquote('0:Res:12.3,5.0')] ).
cnf(55,plain,
( ~ product(multiplicative_identity,u,multiply(a,b))
| ~ product(a,b,u) ),
inference(res,[status(thm),theory(equality)],[4,48]),
[iquote('0:Res:4.0,48.0')] ).
cnf(88,plain,
( ~ defined(multiply(a,b))
| ~ product(a,b,multiply(a,b)) ),
inference(res,[status(thm),theory(equality)],[13,55]),
[iquote('0:Res:13.1,55.0')] ).
cnf(89,plain,
~ product(a,b,multiply(a,b)),
inference(ssi,[status(thm)],[88,21,1,2]),
[iquote('0:SSi:88.0,21.0,1.0,2.2')] ).
cnf(97,plain,
( ~ defined(b)
| ~ defined(a) ),
inference(res,[status(thm),theory(equality)],[25,89]),
[iquote('0:Res:25.2,89.0')] ).
cnf(99,plain,
$false,
inference(ssi,[status(thm)],[97,1,2]),
[iquote('0:SSi:97.1,97.0,1.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : FLD030-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.32 % Computer : n023.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Tue Jun 7 03:32:53 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.41
% 0.18/0.41 SPASS V 3.9
% 0.18/0.41 SPASS beiseite: Proof found.
% 0.18/0.41 % SZS status Theorem
% 0.18/0.41 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.41 SPASS derived 55 clauses, backtracked 0 clauses, performed 0 splits and kept 68 clauses.
% 0.18/0.41 SPASS allocated 75698 KBytes.
% 0.18/0.41 SPASS spent 0:00:00.07 on the problem.
% 0.18/0.41 0:00:00.04 for the input.
% 0.18/0.41 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.41 0:00:00.00 for inferences.
% 0.18/0.41 0:00:00.00 for the backtracking.
% 0.18/0.41 0:00:00.00 for the reduction.
% 0.18/0.41
% 0.18/0.41
% 0.18/0.41 Here is a proof with depth 4, length 14 :
% 0.18/0.41 % SZS output start Refutation
% See solution above
% 0.18/0.41 Formulae used in the proof : a_is_defined b_is_defined product_4 not_product_5 associativity_multiplication_2 existence_of_identity_multiplication well_definedness_of_multiplication totality_of_multiplication
% 0.18/0.41
%------------------------------------------------------------------------------