%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU295+2 : TPTP v9.3.1. Released v3.3.0.
% 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 : n013.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 08:58:53 AM UTC 2026
% Result : Theorem 30.15s 30.49s
% Output : Proof 30.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 28 ( 13 unt; 0 def)
% Number of atoms : 50 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 43 ( 21 ~; 12 |; 7 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 33 ( 1 sgn 22 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t13_finset_1,lemma,
! [A,B] :
( ( finite(B)
& subset(A,B) )
=> finite(A) ),
file('theBenchmark.p',t13_finset_1) ).
fof(t15_finset_1,conjecture,
! [A,B] :
( finite(A)
=> finite(set_intersection2(A,B)) ),
file('theBenchmark.p',t15_finset_1) ).
fof(t17_xboole_1,lemma,
! [A,B] : subset(set_intersection2(A,B),A),
file('theBenchmark.p',t17_xboole_1) ).
fof(f_251_1,plain,
! [A,B] :
( finite(A)
| ~ finite(B)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t13_finset_1]) ).
fof(f_251_2,plain,
! [U_1166,U_1165] :
( finite(U_1166)
| ~ finite(U_1165)
| ~ subset(U_1166,U_1165) ),
inference(variable_rename,[status(thm)],[f_251_1]) ).
fof(f_251_3,plain,
! [U_1166] :
( ! [U_1165] :
( ~ finite(U_1165)
| ~ subset(U_1166,U_1165) )
| finite(U_1166) ),
inference(miniscope,[status(thm)],[f_251_2]) ).
fof(f_251_4,plain,
! [U_1166,U_1165] :
( ~ finite(U_1165)
| ~ subset(U_1166,U_1165)
| finite(U_1166) ),
inference(definitional_conversion,[status(esa)],[f_251_3]) ).
cnf(f_251_5,plain,
( ~ finite(U_1165)
| ~ subset(U_1166,U_1165)
| finite(U_1166) ),
inference(clausify,[status(thm)],[f_251_4]) ).
fof(f_261_1,negated_conjecture,
~ ! [A,B] :
( finite(A)
=> finite(set_intersection2(A,B)) ),
inference(negate,[status(cth)],[t15_finset_1]) ).
fof(f_261_2,negated_conjecture,
? [A,B] :
( ~ finite(set_intersection2(A,B))
& finite(A) ),
inference(fof_nnf,[status(thm)],[f_261_1]) ).
fof(f_261_3,negated_conjecture,
? [U_1191,U_1190] :
( ~ finite(set_intersection2(U_1191,U_1190))
& finite(U_1191) ),
inference(variable_rename,[status(thm)],[f_261_2]) ).
fof(f_261_4,negated_conjecture,
? [U_1191] :
( ? [U_1190] : ~ finite(set_intersection2(U_1191,U_1190))
& finite(U_1191) ),
inference(miniscope,[status(thm)],[f_261_3]) ).
fof(f_261_5,negated_conjecture,
( ? [U_1190] : ~ finite(set_intersection2(sK265,U_1190))
& finite(sK265) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK265]),skolemize(U_1191,sK265)],[f_261_4]) ).
fof(f_261_6,negated_conjecture,
( ~ finite(set_intersection2(sK265,sK266))
& finite(sK265) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK266]),skolemize(U_1190,sK266)],[f_261_5]) ).
fof(f_261_7,negated_conjecture,
( ~ finite(set_intersection2(sK265,sK266))
& finite(sK265) ),
inference(definitional_conversion,[status(esa)],[f_261_6]) ).
cnf(f_261_8,negated_conjecture,
finite(sK265),
inference(clausify,[status(thm)],[f_261_7]) ).
cnf(f_261_9,negated_conjecture,
~ finite(set_intersection2(sK265,sK266)),
inference(clausify,[status(thm)],[f_261_7]) ).
fof(f_270_1,plain,
! [A,B] : subset(set_intersection2(A,B),A),
inference(fof_nnf,[status(thm)],[t17_xboole_1]) ).
fof(f_270_2,plain,
! [U_1216,U_1215] : subset(set_intersection2(U_1216,U_1215),U_1216),
inference(variable_rename,[status(thm)],[f_270_1]) ).
fof(f_270_3,plain,
! [U_1215,U_1216] : subset(set_intersection2(U_1216,U_1215),U_1216),
inference(definitional_conversion,[status(esa)],[f_270_2]) ).
cnf(f_270_4,plain,
subset(set_intersection2(U_1216,U_1215),U_1216),
inference(clausify,[status(thm)],[f_270_3]) ).
cnf(t1,plain,
finite(sK265),
inference(start,[status(thm),parent(0:0)],[f_261_8]) ).
cnf(t2,plain,
( ~ subset(set_intersection2(sK265,sK266),sK265)
| finite(set_intersection2(sK265,sK266))
| ~ finite(sK265) ),
inference(extension,[status(thm),parent(t1:1)],[f_251_5]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
~ finite(set_intersection2(sK265,sK266)),
inference(extension,[status(thm),parent(t2:2)],[f_261_9]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
subset(set_intersection2(sK265,sK266),sK265),
inference(extension,[status(thm),parent(t2:3)],[f_270_4]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU295+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n013.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 19 23:48:50 UTC 2026
% 0.09/0.35 % CPUTime :
% 30.15/30.49 % SZS status Theorem for theBenchmark
% 30.15/30.49 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------