%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET911+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 08:57:47 AM UTC 2026
% Result : Theorem 0.09s 10.39s
% Output : Proof 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 18 ( 6 unt; 0 def)
% Number of atoms : 30 ( 14 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 24 ( 12 ~; 4 |; 5 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 17 ( 0 sgn 10 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t52_zfmisc_1,conjecture,
! [A,B] :
( in(A,B)
=> set_intersection2(B,singleton(A)) = singleton(A) ),
file('theBenchmark.p',t52_zfmisc_1) ).
fof(l32_zfmisc_1,axiom,
! [A,B] :
( in(A,B)
=> set_intersection2(B,singleton(A)) = singleton(A) ),
file('theBenchmark.p',l32_zfmisc_1) ).
fof(f_6_1,negated_conjecture,
~ ! [A,B] :
( in(A,B)
=> set_intersection2(B,singleton(A)) = singleton(A) ),
inference(negate,[status(cth)],[t52_zfmisc_1]) ).
fof(f_6_2,negated_conjecture,
? [A,B] :
( set_intersection2(B,singleton(A)) != singleton(A)
& in(A,B) ),
inference(fof_nnf,[status(thm)],[f_6_1]) ).
fof(f_6_3,negated_conjecture,
? [U_9,U_8] :
( set_intersection2(U_8,singleton(U_9)) != singleton(U_9)
& in(U_9,U_8) ),
inference(variable_rename,[status(thm)],[f_6_2]) ).
fof(f_6_4,negated_conjecture,
? [U_8] :
( set_intersection2(U_8,singleton(sK3)) != singleton(sK3)
& in(sK3,U_8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_9,sK3)],[f_6_3]) ).
fof(f_6_5,negated_conjecture,
( set_intersection2(sK4,singleton(sK3)) != singleton(sK3)
& in(sK3,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_8,sK4)],[f_6_4]) ).
fof(f_6_6,negated_conjecture,
( set_intersection2(sK4,singleton(sK3)) != singleton(sK3)
& in(sK3,sK4) ),
inference(definitional_conversion,[status(esa)],[f_6_5]) ).
cnf(f_6_7,negated_conjecture,
in(sK3,sK4),
inference(clausify,[status(thm)],[f_6_6]) ).
cnf(f_6_8,negated_conjecture,
set_intersection2(sK4,singleton(sK3)) != singleton(sK3),
inference(clausify,[status(thm)],[f_6_6]) ).
fof(f_7_1,plain,
! [A,B] :
( set_intersection2(B,singleton(A)) = singleton(A)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[l32_zfmisc_1]) ).
fof(f_7_2,plain,
! [U_11,U_10] :
( set_intersection2(U_10,singleton(U_11)) = singleton(U_11)
| ~ in(U_11,U_10) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( set_intersection2(U_10,singleton(U_11)) = singleton(U_11)
| ~ in(U_11,U_10) ),
inference(clausify,[status(thm)],[f_7_2]) ).
cnf(t1,plain,
set_intersection2(sK4,singleton(sK3)) != singleton(sK3),
inference(start,[status(thm),parent(0:0)],[f_6_8]) ).
cnf(t2,plain,
( ~ in(sK3,sK4)
| set_intersection2(sK4,singleton(sK3)) = singleton(sK3) ),
inference(extension,[status(thm),parent(t1:1)],[f_7_3]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
in(sK3,sK4),
inference(extension,[status(thm),parent(t2:2)],[f_6_7]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET911+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/10.36 % Computer : n018.cluster.edu
% 0.09/10.36 % Model : x86_64 x86_64
% 0.09/10.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.36 % Memory : 8046.5625MB
% 0.09/10.36 % OS : Linux 6.8.0-71-generic
% 0.09/10.36 % CPULimit : 300
% 0.09/10.36 % WCLimit : 300
% 0.09/10.36 % DateTime : Sat Sep 19 23:09:23 UTC 2026
% 0.09/10.36 % CPUTime :
% 0.09/10.39 % SZS status Theorem for theBenchmark
% 0.09/10.39 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------