TSTP Solution File: CAT005-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : CAT005-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 0.18s 0.40s
% Output : Refutation 0.18s
% 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(a,d),
file('CAT005-1.p',unknown),
[] ).
cnf(2,axiom,
identity_map(d),
file('CAT005-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(domain__dfg(a),d),
file('CAT005-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ product(u,v,w)
| defined(u,v) ),
file('CAT005-1.p',unknown),
[] ).
cnf(6,axiom,
( ~ defined(u,v)
| ~ product(w,x,u)
| defined(x,v) ),
file('CAT005-1.p',unknown),
[] ).
cnf(13,axiom,
identity_map(domain__dfg(u)),
file('CAT005-1.p',unknown),
[] ).
cnf(17,axiom,
product(u,domain__dfg(u),u),
file('CAT005-1.p',unknown),
[] ).
cnf(19,axiom,
( ~ identity_map(u)
| ~ defined(u,v)
| product(u,v,v) ),
file('CAT005-1.p',unknown),
[] ).
cnf(20,axiom,
( ~ identity_map(u)
| ~ defined(v,u)
| product(v,u,v) ),
file('CAT005-1.p',unknown),
[] ).
cnf(21,axiom,
( ~ product(u,v,w)
| ~ product(u,v,x)
| equal(x,w) ),
file('CAT005-1.p',unknown),
[] ).
cnf(22,plain,
( ~ product(u,v,d)
| ~ product(u,v,domain__dfg(a)) ),
inference(res,[status(thm),theory(equality)],[21,3]),
[iquote('0:Res:21.2,3.0')] ).
cnf(30,plain,
( ~ identity_map(u)
| ~ defined(domain__dfg(a),u)
| ~ product(domain__dfg(a),u,d) ),
inference(res,[status(thm),theory(equality)],[20,22]),
[iquote('0:Res:20.2,22.1')] ).
cnf(31,plain,
( ~ identity_map(u)
| ~ product(domain__dfg(a),u,d) ),
inference(mrr,[status(thm)],[30,5]),
[iquote('0:MRR:30.1,5.1')] ).
cnf(34,plain,
( ~ identity_map(domain__dfg(a))
| ~ identity_map(d)
| ~ defined(domain__dfg(a),d) ),
inference(res,[status(thm),theory(equality)],[19,31]),
[iquote('0:Res:19.2,31.1')] ).
cnf(35,plain,
~ defined(domain__dfg(a),d),
inference(ssi,[status(thm)],[34,2,13]),
[iquote('0:SSi:34.1,34.0,2.0,13.0')] ).
cnf(45,plain,
( ~ defined(u,v)
| defined(domain__dfg(u),v) ),
inference(res,[status(thm),theory(equality)],[17,6]),
[iquote('0:Res:17.0,6.1')] ).
cnf(49,plain,
~ defined(a,d),
inference(res,[status(thm),theory(equality)],[45,35]),
[iquote('0:Res:45.1,35.0')] ).
cnf(50,plain,
$false,
inference(mrr,[status(thm)],[49,1]),
[iquote('0:MRR:49.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : CAT005-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n026.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 16:20:24 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.40
% 0.18/0.40 SPASS V 3.9
% 0.18/0.40 SPASS beiseite: Proof found.
% 0.18/0.40 % SZS status Theorem
% 0.18/0.40 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.40 SPASS derived 24 clauses, backtracked 0 clauses, performed 0 splits and kept 35 clauses.
% 0.18/0.40 SPASS allocated 75628 KBytes.
% 0.18/0.40 SPASS spent 0:00:00.06 on the problem.
% 0.18/0.40 0:00:00.03 for the input.
% 0.18/0.40 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.40 0:00:00.00 for inferences.
% 0.18/0.40 0:00:00.00 for the backtracking.
% 0.18/0.40 0:00:00.00 for the reduction.
% 0.18/0.40
% 0.18/0.40
% 0.18/0.40 Here is a proof with depth 4, length 18 :
% 0.18/0.40 % SZS output start Refutation
% See solution above
% 0.18/0.41 Formulae used in the proof : ad_defined d_is_identity_map prove_domain_of_a_is_d associative_property1 associative_property2 domain_is_an_identity_map product_on_domain identity1 identity2 composition_is_well_defined
% 0.18/0.41
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