%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET045+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 : Thu Sep 24 08:56:04 AM UTC 2026
% Result : Theorem 0.09s 0.38s
% Output : Proof 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 22 ( 13 unt; 0 def)
% Number of atoms : 50 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 48 ( 20 ~; 18 |; 9 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 29 ( 2 sgn 17 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel41_1,axiom,
! [Z] :
? [Y] :
! [X] :
( element(X,Y)
<=> ( ~ element(X,X)
& element(X,Z) ) ),
file('theBenchmark.p',pel41_1) ).
fof(pel41,conjecture,
~ ? [Z] :
! [X] : element(X,Z),
file('theBenchmark.p',pel41) ).
fof(f_1_1,plain,
! [Z] :
? [Y] :
! [X] :
( ( element(X,Y)
| element(X,X)
| ~ element(X,Z) )
& ( ( ~ element(X,X)
& element(X,Z) )
| ~ element(X,Y) ) ),
inference(fof_nnf,[status(thm)],[pel41_1]) ).
fof(f_1_2,plain,
! [U_2] :
? [U_1] :
! [U_0] :
( ( element(U_0,U_1)
| element(U_0,U_0)
| ~ element(U_0,U_2) )
& ( ( ~ element(U_0,U_0)
& element(U_0,U_2) )
| ~ element(U_0,U_1) ) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
! [U_2] :
? [U_1] :
( ! [U_4] :
( element(U_4,U_1)
| element(U_4,U_4)
| ~ element(U_4,U_2) )
& ! [U_3] :
( ( ~ element(U_3,U_3)
& element(U_3,U_2) )
| ~ element(U_3,U_1) ) ),
inference(miniscope,[status(thm)],[f_1_2]) ).
fof(f_1_4,plain,
! [U_2] :
( ! [U_4] :
( element(U_4,sK1(U_2))
| element(U_4,U_4)
| ~ element(U_4,U_2) )
& ! [U_3] :
( ( ~ element(U_3,U_3)
& element(U_3,U_2) )
| ~ element(U_3,sK1(U_2)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_1,sK1(U_2))],[f_1_3]) ).
cnf(f_1_6,plain,
( ~ element(U_3,U_3)
| ~ element(U_3,sK1(U_2)) ),
inference(clausify,[status(thm)],[f_1_4]) ).
cnf(f_1_7,plain,
( element(U_4,sK1(U_2))
| element(U_4,U_4)
| ~ element(U_4,U_2) ),
inference(clausify,[status(thm)],[f_1_4]) ).
fof(f_2_1,negated_conjecture,
? [Z] :
! [X] : element(X,Z),
inference(negate,[status(cth)],[pel41]) ).
fof(f_2_2,negated_conjecture,
? [U_6] :
! [U_5] : element(U_5,U_6),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,negated_conjecture,
! [U_5] : element(U_5,sK2),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_6,sK2)],[f_2_2]) ).
fof(f_2_4,negated_conjecture,
! [U_5] : element(U_5,sK2),
inference(definitional_conversion,[status(esa)],[f_2_3]) ).
cnf(f_2_5,negated_conjecture,
element(U_5,sK2),
inference(clausify,[status(thm)],[f_2_4]) ).
cnf(t1,plain,
( ~ element(sK1(sK2),sK1(sK2))
| ~ element(sK1(sK2),sK1(sK2)) ),
inference(start,[status(thm),parent(0:0)],[f_1_6]) ).
cnf(t2,plain,
( element(sK1(sK2),sK1(sK2))
| ~ element(sK1(sK2),sK2)
| element(sK1(sK2),sK1(sK2)) ),
inference(extension,[status(thm),parent(t1:1)],[f_1_7]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
element(sK1(sK2),sK2),
inference(extension,[status(thm),parent(t2:2)],[f_2_5]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
$false,
inference(reduction,[status(thm),parent(t2:3)],[t2:3,t1:1]) ).
cnf(l1,lemma,
element(sK1(sK2),sK1(sK2)),
inference(lemma,[status(cth),parent(t1:1),below(0:0)],[t1:1]) ).
cnf(t7,plain,
element(sK1(sK2),sK1(sK2)),
inference(lemma_extension,[status(thm),parent(t1:2)],[l1:1]) ).
cnf(t8,plain,
$false,
inference(connection,[status(thm),parent(t7:1)],[t7:1,t1:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET045+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 This is a FOF_THM_RFO_NEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 19 21:30:21 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.38 % SZS status Theorem for theBenchmark
% 0.09/0.38 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------