TSTP Solution File: CAT006-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : CAT006-1 : 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 00:07:28 EDT 2022
% Result : Unsatisfiable 0.19s 0.40s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of clauses : 18 ( 8 unt; 0 nHn; 18 RR)
% Number of literals : 34 ( 0 equ; 23 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
defined(h,a),
file('CAT006-1.p',unknown),
[] ).
cnf(2,axiom,
identity_map(h),
file('CAT006-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(codomain(a),h),
file('CAT006-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ product(u,v,w)
| defined(u,v) ),
file('CAT006-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ defined(u,v)
| ~ product(w,x,v)
| defined(u,w) ),
file('CAT006-1.p',unknown),
[] ).
cnf(14,axiom,
identity_map(codomain(u)),
file('CAT006-1.p',unknown),
[] ).
cnf(18,axiom,
product(codomain(u),u,u),
file('CAT006-1.p',unknown),
[] ).
cnf(19,axiom,
( ~ identity_map(u)
| ~ defined(u,v)
| product(u,v,v) ),
file('CAT006-1.p',unknown),
[] ).
cnf(20,axiom,
( ~ identity_map(u)
| ~ defined(v,u)
| product(v,u,v) ),
file('CAT006-1.p',unknown),
[] ).
cnf(21,axiom,
( ~ product(u,v,w)
| ~ product(u,v,x)
| equal(x,w) ),
file('CAT006-1.p',unknown),
[] ).
cnf(22,plain,
( ~ product(u,v,h)
| ~ product(u,v,codomain(a)) ),
inference(res,[status(thm),theory(equality)],[21,3]),
[iquote('0:Res:21.2,3.0')] ).
cnf(33,plain,
( ~ identity_map(u)
| ~ defined(u,codomain(a))
| ~ product(u,codomain(a),h) ),
inference(res,[status(thm),theory(equality)],[19,22]),
[iquote('0:Res:19.2,22.1')] ).
cnf(36,plain,
( ~ identity_map(u)
| ~ product(u,codomain(a),h) ),
inference(mrr,[status(thm)],[33,5]),
[iquote('0:MRR:33.1,5.1')] ).
cnf(37,plain,
( ~ identity_map(codomain(a))
| ~ identity_map(h)
| ~ defined(h,codomain(a)) ),
inference(res,[status(thm),theory(equality)],[20,36]),
[iquote('0:Res:20.2,36.1')] ).
cnf(38,plain,
~ defined(h,codomain(a)),
inference(ssi,[status(thm)],[37,2,14]),
[iquote('0:SSi:37.1,37.0,2.0,14.0')] ).
cnf(39,plain,
( ~ defined(u,v)
| defined(u,codomain(v)) ),
inference(res,[status(thm),theory(equality)],[18,9]),
[iquote('0:Res:18.0,9.1')] ).
cnf(44,plain,
~ defined(h,a),
inference(res,[status(thm),theory(equality)],[39,38]),
[iquote('0:Res:39.1,38.0')] ).
cnf(45,plain,
$false,
inference(mrr,[status(thm)],[44,1]),
[iquote('0:MRR:44.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : CAT006-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n023.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun May 29 19:18:12 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.19/0.40
% 0.19/0.40 SPASS V 3.9
% 0.19/0.40 SPASS beiseite: Proof found.
% 0.19/0.40 % SZS status Theorem
% 0.19/0.40 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.40 SPASS derived 19 clauses, backtracked 0 clauses, performed 0 splits and kept 32 clauses.
% 0.19/0.40 SPASS allocated 75624 KBytes.
% 0.19/0.40 SPASS spent 0:00:00.06 on the problem.
% 0.19/0.40 0:00:00.04 for the input.
% 0.19/0.40 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.40 0:00:00.00 for inferences.
% 0.19/0.40 0:00:00.00 for the backtracking.
% 0.19/0.40 0:00:00.00 for the reduction.
% 0.19/0.40
% 0.19/0.40
% 0.19/0.40 Here is a proof with depth 4, length 18 :
% 0.19/0.40 % SZS output start Refutation
% See solution above
% 0.19/0.40 Formulae used in the proof : ha_defined h_is_the_identity_map prove_codomain_of_a_is_h associative_property1 category_theory_axiom3 codomain_is_an_identity_map product_on_codomain identity1 identity2 composition_is_well_defined
% 0.19/0.40
%------------------------------------------------------------------------------