%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : CAT018-1 : 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 : Fri Jul 15 00:07:32 EDT 2022
% Result : Unsatisfiable 0.20s 0.55s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of clauses : 20 ( 8 unt; 0 nHn; 20 RR)
% Number of literals : 43 ( 0 equ; 29 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
defined(a,b),
file('CAT018-1.p',unknown),
[] ).
cnf(2,axiom,
defined(b,c),
file('CAT018-1.p',unknown),
[] ).
cnf(3,axiom,
~ defined(a,compose(b,c)),
file('CAT018-1.p',unknown),
[] ).
cnf(4,axiom,
( ~ defined(u,v)
| product(u,v,compose(u,v)) ),
file('CAT018-1.p',unknown),
[] ).
cnf(6,axiom,
( ~ defined(u,v)
| ~ product(w,x,u)
| defined(x,v) ),
file('CAT018-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ defined(u,v)
| ~ product(w,v,x)
| ~ product(y,w,u)
| defined(y,x) ),
file('CAT018-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ defined(u,v)
| ~ product(w,x,v)
| defined(u,w) ),
file('CAT018-1.p',unknown),
[] ).
cnf(12,axiom,
( ~ identity_map(u)
| ~ defined(v,u)
| ~ defined(u,w)
| defined(v,w) ),
file('CAT018-1.p',unknown),
[] ).
cnf(14,axiom,
identity_map(codomain(u)),
file('CAT018-1.p',unknown),
[] ).
cnf(18,axiom,
product(codomain(u),u,u),
file('CAT018-1.p',unknown),
[] ).
cnf(26,plain,
( ~ identity_map(u)
| ~ defined(u,compose(b,c))
| ~ defined(a,u) ),
inference(res,[status(thm),theory(equality)],[12,3]),
[iquote('0:Res:12.3,3.0')] ).
cnf(42,plain,
( ~ defined(u,v)
| defined(u,codomain(v)) ),
inference(res,[status(thm),theory(equality)],[18,9]),
[iquote('0:Res:18.0,9.1')] ).
cnf(130,plain,
( ~ defined(u,v)
| ~ defined(w,v)
| ~ product(x,u,w)
| defined(x,compose(u,v)) ),
inference(res,[status(thm),theory(equality)],[4,7]),
[iquote('0:Res:4.1,7.1')] ).
cnf(134,plain,
( ~ defined(u,v)
| ~ product(w,x,u)
| defined(w,compose(x,v)) ),
inference(mrr,[status(thm)],[130,6]),
[iquote('0:MRR:130.0,6.2')] ).
cnf(1033,plain,
( ~ defined(u,v)
| defined(codomain(u),compose(u,v)) ),
inference(res,[status(thm),theory(equality)],[18,134]),
[iquote('0:Res:18.0,134.1')] ).
cnf(1112,plain,
( ~ identity_map(codomain(b))
| ~ defined(b,c)
| ~ defined(a,codomain(b)) ),
inference(res,[status(thm),theory(equality)],[1033,26]),
[iquote('0:Res:1033.1,26.1')] ).
cnf(1120,plain,
( ~ defined(b,c)
| ~ defined(a,codomain(b)) ),
inference(ssi,[status(thm)],[1112,14]),
[iquote('0:SSi:1112.0,14.0')] ).
cnf(1121,plain,
~ defined(a,codomain(b)),
inference(mrr,[status(thm)],[1120,2]),
[iquote('0:MRR:1120.0,2.0')] ).
cnf(1124,plain,
~ defined(a,b),
inference(res,[status(thm),theory(equality)],[42,1121]),
[iquote('0:Res:42.1,1121.0')] ).
cnf(1125,plain,
$false,
inference(mrr,[status(thm)],[1124,1]),
[iquote('0:MRR:1124.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : CAT018-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun May 29 16:37:13 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.55
% 0.20/0.55 SPASS V 3.9
% 0.20/0.55 SPASS beiseite: Proof found.
% 0.20/0.55 % SZS status Theorem
% 0.20/0.55 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.55 SPASS derived 900 clauses, backtracked 0 clauses, performed 0 splits and kept 407 clauses.
% 0.20/0.55 SPASS allocated 76436 KBytes.
% 0.20/0.55 SPASS spent 0:00:00.19 on the problem.
% 0.20/0.55 0:00:00.03 for the input.
% 0.20/0.55 0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.55 0:00:00.02 for inferences.
% 0.20/0.55 0:00:00.00 for the backtracking.
% 0.20/0.55 0:00:00.11 for the reduction.
% 0.20/0.55
% 0.20/0.55
% 0.20/0.55 Here is a proof with depth 4, length 20 :
% 0.20/0.55 % SZS output start Refutation
% See solution above
% 0.20/0.55 Formulae used in the proof : assume_ab_exists assume_bc_exists prove_a_bc_exists closure_of_composition associative_property2 category_theory_axiom1 category_theory_axiom3 category_theory_axiom6 codomain_is_an_identity_map product_on_codomain
% 0.20/0.55
%------------------------------------------------------------------------------