%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET024-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:41:33 PM UTC 2026
% Result : Unsatisfiable 25.96s 3.77s
% Output : Proof 25.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 14 unt; 0 def)
% Number of atoms : 28 ( 8 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 13 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 19 ( 4 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f8,axiom,
singleton_set(X) = non_ordered_pair(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set) ).
fof(f8_nnf,plain,
! [X] : singleton_set(X) = non_ordered_pair(X,X),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X] : singleton_set(X) = non_ordered_pair(X,X),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
singleton_set(X0) = non_ordered_pair(X0,X0),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(f5,axiom,
( U != X
| ~ little_set(U)
| member(U,non_ordered_pair(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',non_ordered_pair2) ).
fof(f5_nnf,plain,
! [U,X,Y] :
( U != X
| ~ little_set(U)
| member(U,non_ordered_pair(X,Y)) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [U,X,Y] :
( U != X
| ~ little_set(U)
| member(U,non_ordered_pair(X,Y)) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( X0 != X1
| ~ little_set(X0)
| member(X0,non_ordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p163,plain,
( ~ little_set(X0)
| member(X0,non_ordered_pair(X0,X1)) ),
inference(equality_resolution,[status(thm)],[c5]) ).
cnf(f141,hypothesis,
little_set(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_little_set) ).
fof(f141_nnf,plain,
little_set(a),
inference(nnf_transformation,[status(thm)],[f141]) ).
cnf(c141,plain,
little_set(a),
inference(cnf_transformation,[status(esa)],[f141_nnf]) ).
cnf(p8711,plain,
member(a,non_ordered_pair(a,X0)),
inference(resolution,[status(thm)],[p163,c141]) ).
cnf(p9017,plain,
member(a,singleton_set(a)),
inference(superposition,[status(thm)],[c8,p8711]) ).
cnf(f142,negated_conjecture,
~ member(a,singleton_set(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_membership_of_singleton_set) ).
fof(f142_nnf,plain,
~ member(a,singleton_set(a)),
inference(nnf_transformation,[status(thm)],[f142]) ).
fof(f142_sk,plain,
~ member(a,singleton_set(a)),
inference(skolemisation,[status(esa)],[f142_nnf]) ).
cnf(c142,plain,
~ member(a,singleton_set(a)),
inference(cnf_transformation,[status(esa)],[f142_sk]) ).
cnf(p9021,plain,
$false,
inference(resolution,[status(thm)],[p9017,c142]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET024-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.38 % Computer : n020.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Thu Sep 24 09:16:18 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 25.96/3.77 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.96/3.77 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------