TSTP Solution File: CAT009-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : CAT009-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 00:07:29 EDT 2022
% Result : Unsatisfiable 0.60s 0.79s
% Output : Refutation 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of clauses : 22 ( 9 unt; 0 nHn; 22 RR)
% Number of literals : 42 ( 0 equ; 28 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
defined(b,a),
file('CAT009-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(domain__dfg(compose(b,a)),domain__dfg(a)),
file('CAT009-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ defined(u,v)
| product(u,v,compose(u,v)) ),
file('CAT009-1.p',unknown),
[] ).
cnf(4,axiom,
( ~ product(u,v,w)
| defined(u,v) ),
file('CAT009-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ defined(u,v)
| ~ product(w,x,u)
| defined(x,v) ),
file('CAT009-1.p',unknown),
[] ).
cnf(12,axiom,
identity_map(domain__dfg(u)),
file('CAT009-1.p',unknown),
[] ).
cnf(14,axiom,
defined(u,domain__dfg(u)),
file('CAT009-1.p',unknown),
[] ).
cnf(16,axiom,
product(u,domain__dfg(u),u),
file('CAT009-1.p',unknown),
[] ).
cnf(18,axiom,
( ~ identity_map(u)
| ~ defined(u,v)
| product(u,v,v) ),
file('CAT009-1.p',unknown),
[] ).
cnf(19,axiom,
( ~ identity_map(u)
| ~ defined(v,u)
| product(v,u,v) ),
file('CAT009-1.p',unknown),
[] ).
cnf(20,axiom,
( ~ product(u,v,w)
| ~ product(u,v,x)
| equal(x,w) ),
file('CAT009-1.p',unknown),
[] ).
cnf(21,plain,
( ~ product(u,v,domain__dfg(a))
| ~ product(u,v,domain__dfg(compose(b,a))) ),
inference(res,[status(thm),theory(equality)],[20,2]),
[iquote('0:Res:20.2,2.0')] ).
cnf(34,plain,
( ~ defined(u,v)
| defined(domain__dfg(u),v) ),
inference(res,[status(thm),theory(equality)],[16,5]),
[iquote('0:Res:16.0,5.1')] ).
cnf(35,plain,
( ~ defined(u,v)
| ~ defined(compose(u,v),w)
| defined(v,w) ),
inference(res,[status(thm),theory(equality)],[3,5]),
[iquote('0:Res:3.1,5.1')] ).
cnf(41,plain,
( ~ defined(u,v)
| defined(v,domain__dfg(compose(u,v))) ),
inference(res,[status(thm),theory(equality)],[14,35]),
[iquote('0:Res:14.0,35.1')] ).
cnf(618,plain,
( ~ identity_map(u)
| ~ defined(u,domain__dfg(compose(b,a)))
| ~ product(u,domain__dfg(compose(b,a)),domain__dfg(a)) ),
inference(res,[status(thm),theory(equality)],[18,21]),
[iquote('0:Res:18.2,21.1')] ).
cnf(621,plain,
( ~ identity_map(u)
| ~ product(u,domain__dfg(compose(b,a)),domain__dfg(a)) ),
inference(mrr,[status(thm)],[618,4]),
[iquote('0:MRR:618.1,4.1')] ).
cnf(2572,plain,
( ~ identity_map(domain__dfg(compose(b,a)))
| ~ identity_map(domain__dfg(a))
| ~ defined(domain__dfg(a),domain__dfg(compose(b,a))) ),
inference(res,[status(thm),theory(equality)],[19,621]),
[iquote('0:Res:19.2,621.1')] ).
cnf(2573,plain,
~ defined(domain__dfg(a),domain__dfg(compose(b,a))),
inference(ssi,[status(thm)],[2572,12]),
[iquote('0:SSi:2572.1,2572.0,12.0,12.0')] ).
cnf(2577,plain,
~ defined(a,domain__dfg(compose(b,a))),
inference(res,[status(thm),theory(equality)],[34,2573]),
[iquote('0:Res:34.1,2573.0')] ).
cnf(2579,plain,
~ defined(b,a),
inference(res,[status(thm),theory(equality)],[41,2577]),
[iquote('0:Res:41.1,2577.0')] ).
cnf(2580,plain,
$false,
inference(mrr,[status(thm)],[2579,1]),
[iquote('0:MRR:2579.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : CAT009-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n020.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 : Sun May 29 19:29:24 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.60/0.79
% 0.60/0.79 SPASS V 3.9
% 0.60/0.79 SPASS beiseite: Proof found.
% 0.60/0.79 % SZS status Theorem
% 0.60/0.79 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.60/0.79 SPASS derived 2170 clauses, backtracked 0 clauses, performed 0 splits and kept 805 clauses.
% 0.60/0.79 SPASS allocated 77404 KBytes.
% 0.60/0.79 SPASS spent 0:00:00.43 on the problem.
% 0.60/0.79 0:00:00.04 for the input.
% 0.60/0.79 0:00:00.00 for the FLOTTER CNF translation.
% 0.60/0.79 0:00:00.03 for inferences.
% 0.60/0.79 0:00:00.00 for the backtracking.
% 0.60/0.79 0:00:00.34 for the reduction.
% 0.60/0.79
% 0.60/0.79
% 0.60/0.79 Here is a proof with depth 5, length 22 :
% 0.60/0.79 % SZS output start Refutation
% See solution above
% 0.60/0.79 Formulae used in the proof : ba_defined prove_domain_of_ba_equals_domain_of_a closure_of_composition associative_property1 associative_property2 domain_is_an_identity_map mapping_from_x_to_its_domain product_on_domain identity1 identity2 composition_is_well_defined
% 0.60/0.79
%------------------------------------------------------------------------------