TSTP Solution File: SET025-3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET025-3 : 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 : Tue Jul 19 05:22:47 EDT 2022
% Result : Unsatisfiable 0.18s 0.48s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of clauses : 9 ( 7 unt; 0 nHn; 9 RR)
% Number of literals : 11 ( 0 equ; 5 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(10,axiom,
~ little_set(ordered_pair(a,b)),
file('SET025-3.p',unknown),
[] ).
cnf(11,axiom,
( ~ member(u,v)
| little_set(u) ),
file('SET025-3.p',unknown),
[] ).
cnf(18,axiom,
little_set(non_ordered_pair(u,v)),
file('SET025-3.p',unknown),
[] ).
cnf(20,axiom,
equal(non_ordered_pair(singleton_set(u),non_ordered_pair(u,v)),ordered_pair(u,v)),
file('SET025-3.p',unknown),
[] ).
cnf(69,axiom,
( ~ little_set(u)
| member(u,universal_set) ),
file('SET025-3.p',unknown),
[] ).
cnf(153,plain,
~ member(ordered_pair(a,b),u),
inference(res,[status(thm),theory(equality)],[11,10]),
[iquote('0:Res:11.1,10.0')] ).
cnf(155,plain,
~ little_set(ordered_pair(a,b)),
inference(res,[status(thm),theory(equality)],[69,153]),
[iquote('0:Res:69.1,153.0')] ).
cnf(441,plain,
little_set(ordered_pair(u,v)),
inference(spr,[status(thm),theory(equality)],[20,18]),
[iquote('0:SpR:20.0,18.0')] ).
cnf(445,plain,
$false,
inference(unc,[status(thm)],[441,155]),
[iquote('0:UnC:441.0,155.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SET025-3 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % 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 Jul 10 13:04:25 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.48
% 0.18/0.48 SPASS V 3.9
% 0.18/0.48 SPASS beiseite: Proof found.
% 0.18/0.48 % SZS status Theorem
% 0.18/0.48 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.48 SPASS derived 278 clauses, backtracked 8 clauses, performed 3 splits and kept 393 clauses.
% 0.18/0.48 SPASS allocated 76183 KBytes.
% 0.18/0.48 SPASS spent 0:00:00.14 on the problem.
% 0.18/0.48 0:00:00.04 for the input.
% 0.18/0.48 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.48 0:00:00.01 for inferences.
% 0.18/0.48 0:00:00.00 for the backtracking.
% 0.18/0.48 0:00:00.06 for the reduction.
% 0.18/0.48
% 0.18/0.48
% 0.18/0.48 Here is a proof with depth 2, length 9 :
% 0.18/0.48 % SZS output start Refutation
% See solution above
% 0.18/0.48 Formulae used in the proof : prove_ordered_pairs_are_small a2 non_ordered_pair4 ordered_pair universal_set
% 0.18/0.48
%------------------------------------------------------------------------------