TSTP Solution File: CAT010-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : CAT010-1 : TPTP v8.1.0. Released v1.0.0.
% 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 : Fri Jul 15 00:07:30 EDT 2022
% Result : Unsatisfiable 0.55s 0.72s
% Output : Refutation 0.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of clauses : 24 ( 8 unt; 0 nHn; 24 RR)
% Number of literals : 52 ( 0 equ; 36 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
defined(b,a),
file('CAT010-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(codomain(compose(b,a)),codomain(b)),
file('CAT010-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ defined(u,v)
| product(u,v,compose(u,v)) ),
file('CAT010-1.p',unknown),
[] ).
cnf(4,axiom,
( ~ product(u,v,w)
| defined(u,v) ),
file('CAT010-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ defined(u,v)
| ~ product(w,x,u)
| defined(x,v) ),
file('CAT010-1.p',unknown),
[] ).
cnf(6,axiom,
( ~ defined(u,v)
| ~ product(w,v,x)
| ~ product(y,w,u)
| defined(y,x) ),
file('CAT010-1.p',unknown),
[] ).
cnf(8,axiom,
( ~ defined(u,v)
| ~ product(w,x,v)
| defined(u,w) ),
file('CAT010-1.p',unknown),
[] ).
cnf(13,axiom,
identity_map(codomain(u)),
file('CAT010-1.p',unknown),
[] ).
cnf(17,axiom,
product(codomain(u),u,u),
file('CAT010-1.p',unknown),
[] ).
cnf(18,axiom,
( ~ identity_map(u)
| ~ defined(u,v)
| product(u,v,v) ),
file('CAT010-1.p',unknown),
[] ).
cnf(19,axiom,
( ~ identity_map(u)
| ~ defined(v,u)
| product(v,u,v) ),
file('CAT010-1.p',unknown),
[] ).
cnf(20,axiom,
( ~ product(u,v,w)
| ~ product(u,v,x)
| equal(x,w) ),
file('CAT010-1.p',unknown),
[] ).
cnf(21,plain,
( ~ product(u,v,codomain(b))
| ~ product(u,v,codomain(compose(b,a))) ),
inference(res,[status(thm),theory(equality)],[20,2]),
[iquote('0:Res:20.2,2.0')] ).
cnf(28,plain,
( ~ defined(u,v)
| defined(u,codomain(v)) ),
inference(res,[status(thm),theory(equality)],[17,8]),
[iquote('0:Res:17.0,8.1')] ).
cnf(127,plain,
( ~ defined(u,v)
| ~ defined(w,v)
| ~ product(x,u,w)
| defined(x,compose(u,v)) ),
inference(res,[status(thm),theory(equality)],[3,6]),
[iquote('0:Res:3.1,6.1')] ).
cnf(130,plain,
( ~ defined(u,v)
| ~ product(w,x,u)
| defined(w,compose(x,v)) ),
inference(mrr,[status(thm)],[127,5]),
[iquote('0:MRR:127.0,5.2')] ).
cnf(618,plain,
( ~ identity_map(u)
| ~ defined(u,codomain(compose(b,a)))
| ~ product(u,codomain(compose(b,a)),codomain(b)) ),
inference(res,[status(thm),theory(equality)],[18,21]),
[iquote('0:Res:18.2,21.1')] ).
cnf(621,plain,
( ~ identity_map(u)
| ~ product(u,codomain(compose(b,a)),codomain(b)) ),
inference(mrr,[status(thm)],[618,4]),
[iquote('0:MRR:618.1,4.1')] ).
cnf(1003,plain,
( ~ defined(u,v)
| defined(codomain(u),compose(u,v)) ),
inference(res,[status(thm),theory(equality)],[17,130]),
[iquote('0:Res:17.0,130.1')] ).
cnf(2572,plain,
( ~ identity_map(codomain(compose(b,a)))
| ~ identity_map(codomain(b))
| ~ defined(codomain(b),codomain(compose(b,a))) ),
inference(res,[status(thm),theory(equality)],[19,621]),
[iquote('0:Res:19.2,621.1')] ).
cnf(2573,plain,
~ defined(codomain(b),codomain(compose(b,a))),
inference(ssi,[status(thm)],[2572,13]),
[iquote('0:SSi:2572.1,2572.0,13.0,13.0')] ).
cnf(2576,plain,
~ defined(codomain(b),compose(b,a)),
inference(res,[status(thm),theory(equality)],[28,2573]),
[iquote('0:Res:28.1,2573.0')] ).
cnf(2578,plain,
~ defined(b,a),
inference(res,[status(thm),theory(equality)],[1003,2576]),
[iquote('0:Res:1003.1,2576.0')] ).
cnf(2579,plain,
$false,
inference(mrr,[status(thm)],[2578,1]),
[iquote('0:MRR:2578.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : CAT010-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n023.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 : Sun May 29 17:06:12 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.55/0.72
% 0.55/0.72 SPASS V 3.9
% 0.55/0.72 SPASS beiseite: Proof found.
% 0.55/0.72 % SZS status Theorem
% 0.55/0.72 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.55/0.72 SPASS derived 2169 clauses, backtracked 0 clauses, performed 0 splits and kept 804 clauses.
% 0.55/0.72 SPASS allocated 77404 KBytes.
% 0.55/0.72 SPASS spent 0:00:00.37 on the problem.
% 0.55/0.72 0:00:00.03 for the input.
% 0.55/0.72 0:00:00.00 for the FLOTTER CNF translation.
% 0.55/0.72 0:00:00.03 for inferences.
% 0.55/0.72 0:00:00.00 for the backtracking.
% 0.55/0.72 0:00:00.29 for the reduction.
% 0.55/0.72
% 0.55/0.72
% 0.55/0.72 Here is a proof with depth 5, length 24 :
% 0.55/0.72 % SZS output start Refutation
% See solution above
% 0.55/0.72 Formulae used in the proof : ba_defined prove_codomain_of_ba_equals_codomain_of_b closure_of_composition associative_property1 associative_property2 category_theory_axiom1 category_theory_axiom3 codomain_is_an_identity_map product_on_codomain identity1 identity2 composition_is_well_defined
% 0.55/0.72
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