%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET983+1 : TPTP v9.3.1. Released v3.2.0.
% 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 : n001.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 08:57:54 AM UTC 2026
% Result : Theorem 0.14s 0.39s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 33 ( 15 unt; 0 def)
% Number of atoms : 127 ( 18 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 146 ( 52 ~; 41 |; 49 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 91 ( 0 sgn 58 !; 25 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d3_xboole_0,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
& in(D,A) ) ) ),
file('theBenchmark.p',d3_xboole_0) ).
fof(t123_zfmisc_1,axiom,
! [A,B,C,D] : cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)) = set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)),
file('theBenchmark.p',t123_zfmisc_1) ).
fof(t137_zfmisc_1,conjecture,
! [A,B,C,D,E] :
( ( in(A,cartesian_product2(D,E))
& in(A,cartesian_product2(B,C)) )
=> in(A,cartesian_product2(set_intersection2(B,D),set_intersection2(C,E))) ),
file('theBenchmark.p',t137_zfmisc_1) ).
fof(f_3_1,plain,
! [A,B,C] :
( ( C = set_intersection2(A,B)
| ? [D] :
( ( ~ in(D,C)
& in(D,B)
& in(D,A) )
| ( ( ~ in(D,B)
| ~ in(D,A) )
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ~ in(D,B)
| ~ in(D,A) )
& ( ( in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_intersection2(A,B) ) ),
inference(fof_nnf,[status(thm)],[d3_xboole_0]) ).
fof(f_3_2,plain,
! [U_8,U_7,U_6] :
( ( U_6 = set_intersection2(U_8,U_7)
| ? [U_5] :
( ( ~ in(U_5,U_6)
& in(U_5,U_7)
& in(U_5,U_8) )
| ( ( ~ in(U_5,U_7)
| ~ in(U_5,U_8) )
& in(U_5,U_6) ) ) )
& ( ! [U_4] :
( ( in(U_4,U_6)
| ~ in(U_4,U_7)
| ~ in(U_4,U_8) )
& ( ( in(U_4,U_7)
& in(U_4,U_8) )
| ~ in(U_4,U_6) ) )
| U_6 != set_intersection2(U_8,U_7) ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_18,U_16,U_14] :
( U_14 = set_intersection2(U_18,U_16)
| ? [U_12] :
( ~ in(U_12,U_14)
& in(U_12,U_16)
& in(U_12,U_18) )
| ? [U_11] :
( ( ~ in(U_11,U_16)
| ~ in(U_11,U_18) )
& in(U_11,U_14) ) )
& ! [U_17,U_15,U_13] :
( ( ! [U_10] :
( in(U_10,U_13)
| ~ in(U_10,U_15)
| ~ in(U_10,U_17) )
& ! [U_9] :
( ( in(U_9,U_15)
& in(U_9,U_17) )
| ~ in(U_9,U_13) ) )
| U_13 != set_intersection2(U_17,U_15) ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
fof(f_3_4,plain,
( ! [U_18,U_16,U_14] :
( U_14 = set_intersection2(U_18,U_16)
| ? [U_12] :
( ~ in(U_12,U_14)
& in(U_12,U_16)
& in(U_12,U_18) )
| ( ( ~ in(sK1(U_18,U_16,U_14),U_16)
| ~ in(sK1(U_18,U_16,U_14),U_18) )
& in(sK1(U_18,U_16,U_14),U_14) ) )
& ! [U_17,U_15,U_13] :
( ( ! [U_10] :
( in(U_10,U_13)
| ~ in(U_10,U_15)
| ~ in(U_10,U_17) )
& ! [U_9] :
( ( in(U_9,U_15)
& in(U_9,U_17) )
| ~ in(U_9,U_13) ) )
| U_13 != set_intersection2(U_17,U_15) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_11,sK1(U_18,U_16,U_14))],[f_3_3]) ).
fof(f_3_5,plain,
( ! [U_18,U_16,U_14] :
( U_14 = set_intersection2(U_18,U_16)
| ( ~ in(sK2(U_18,U_16,U_14),U_14)
& in(sK2(U_18,U_16,U_14),U_16)
& in(sK2(U_18,U_16,U_14),U_18) )
| ( ( ~ in(sK1(U_18,U_16,U_14),U_16)
| ~ in(sK1(U_18,U_16,U_14),U_18) )
& in(sK1(U_18,U_16,U_14),U_14) ) )
& ! [U_17,U_15,U_13] :
( ( ! [U_10] :
( in(U_10,U_13)
| ~ in(U_10,U_15)
| ~ in(U_10,U_17) )
& ! [U_9] :
( ( in(U_9,U_15)
& in(U_9,U_17) )
| ~ in(U_9,U_13) ) )
| U_13 != set_intersection2(U_17,U_15) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_12,sK2(U_18,U_16,U_14))],[f_3_4]) ).
cnf(f_3_8,plain,
( in(U_10,U_13)
| ~ in(U_10,U_15)
| ~ in(U_10,U_17)
| U_13 != set_intersection2(U_17,U_15) ),
inference(clausify,[status(thm)],[f_3_5]) ).
fof(f_7_1,plain,
! [A,B,C,D] : cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)) = set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)),
inference(fof_nnf,[status(thm)],[t123_zfmisc_1]) ).
fof(f_7_2,plain,
! [U_26,U_25,U_24,U_23] : cartesian_product2(set_intersection2(U_26,U_25),set_intersection2(U_24,U_23)) = set_intersection2(cartesian_product2(U_26,U_24),cartesian_product2(U_25,U_23)),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
cartesian_product2(set_intersection2(U_26,U_25),set_intersection2(U_24,U_23)) = set_intersection2(cartesian_product2(U_26,U_24),cartesian_product2(U_25,U_23)),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,negated_conjecture,
~ ! [A,B,C,D,E] :
( ( in(A,cartesian_product2(D,E))
& in(A,cartesian_product2(B,C)) )
=> in(A,cartesian_product2(set_intersection2(B,D),set_intersection2(C,E))) ),
inference(negate,[status(cth)],[t137_zfmisc_1]) ).
fof(f_8_2,negated_conjecture,
? [A,B,C,D,E] :
( ~ in(A,cartesian_product2(set_intersection2(B,D),set_intersection2(C,E)))
& in(A,cartesian_product2(D,E))
& in(A,cartesian_product2(B,C)) ),
inference(fof_nnf,[status(thm)],[f_8_1]) ).
fof(f_8_3,negated_conjecture,
? [U_31,U_30,U_29,U_28,U_27] :
( ~ in(U_31,cartesian_product2(set_intersection2(U_30,U_28),set_intersection2(U_29,U_27)))
& in(U_31,cartesian_product2(U_28,U_27))
& in(U_31,cartesian_product2(U_30,U_29)) ),
inference(variable_rename,[status(thm)],[f_8_2]) ).
fof(f_8_4,negated_conjecture,
? [U_30,U_29,U_28,U_27] :
( ~ in(sK5,cartesian_product2(set_intersection2(U_30,U_28),set_intersection2(U_29,U_27)))
& in(sK5,cartesian_product2(U_28,U_27))
& in(sK5,cartesian_product2(U_30,U_29)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_31,sK5)],[f_8_3]) ).
fof(f_8_5,negated_conjecture,
? [U_29,U_28,U_27] :
( ~ in(sK5,cartesian_product2(set_intersection2(sK6,U_28),set_intersection2(U_29,U_27)))
& in(sK5,cartesian_product2(U_28,U_27))
& in(sK5,cartesian_product2(sK6,U_29)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_30,sK6)],[f_8_4]) ).
fof(f_8_6,negated_conjecture,
? [U_28,U_27] :
( ~ in(sK5,cartesian_product2(set_intersection2(sK6,U_28),set_intersection2(sK7,U_27)))
& in(sK5,cartesian_product2(U_28,U_27))
& in(sK5,cartesian_product2(sK6,sK7)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_29,sK7)],[f_8_5]) ).
fof(f_8_7,negated_conjecture,
? [U_27] :
( ~ in(sK5,cartesian_product2(set_intersection2(sK6,sK8),set_intersection2(sK7,U_27)))
& in(sK5,cartesian_product2(sK8,U_27))
& in(sK5,cartesian_product2(sK6,sK7)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_28,sK8)],[f_8_6]) ).
fof(f_8_8,negated_conjecture,
( ~ in(sK5,cartesian_product2(set_intersection2(sK6,sK8),set_intersection2(sK7,sK9)))
& in(sK5,cartesian_product2(sK8,sK9))
& in(sK5,cartesian_product2(sK6,sK7)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_27,sK9)],[f_8_7]) ).
fof(f_8_9,negated_conjecture,
( ~ in(sK5,cartesian_product2(set_intersection2(sK6,sK8),set_intersection2(sK7,sK9)))
& in(sK5,cartesian_product2(sK8,sK9))
& in(sK5,cartesian_product2(sK6,sK7)) ),
inference(definitional_conversion,[status(esa)],[f_8_8]) ).
cnf(f_8_10,negated_conjecture,
in(sK5,cartesian_product2(sK6,sK7)),
inference(clausify,[status(thm)],[f_8_9]) ).
cnf(f_8_11,negated_conjecture,
in(sK5,cartesian_product2(sK8,sK9)),
inference(clausify,[status(thm)],[f_8_9]) ).
cnf(f_8_12,negated_conjecture,
~ in(sK5,cartesian_product2(set_intersection2(sK6,sK8),set_intersection2(sK7,sK9))),
inference(clausify,[status(thm)],[f_8_9]) ).
cnf(t1,plain,
~ in(sK5,cartesian_product2(set_intersection2(sK6,sK8),set_intersection2(sK7,sK9))),
inference(start,[status(thm),parent(0:0)],[f_8_12]) ).
cnf(t2,plain,
( ~ in(sK5,cartesian_product2(sK6,sK7))
| ~ in(sK5,cartesian_product2(sK8,sK9))
| cartesian_product2(set_intersection2(sK6,sK8),set_intersection2(sK7,sK9)) != set_intersection2(cartesian_product2(sK6,sK7),cartesian_product2(sK8,sK9))
| in(sK5,cartesian_product2(set_intersection2(sK6,sK8),set_intersection2(sK7,sK9))) ),
inference(extension,[status(thm),parent(t1:1)],[f_3_8]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
cartesian_product2(set_intersection2(sK6,sK8),set_intersection2(sK7,sK9)) = set_intersection2(cartesian_product2(sK6,sK7),cartesian_product2(sK8,sK9)),
inference(extension,[status(thm),parent(t2:2)],[f_7_3]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
in(sK5,cartesian_product2(sK8,sK9)),
inference(extension,[status(thm),parent(t2:3)],[f_8_11]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
in(sK5,cartesian_product2(sK6,sK7)),
inference(extension,[status(thm),parent(t2:4)],[f_8_10]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET983+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/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n001.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 19 23:15:40 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.14/0.39 % SZS status Theorem for theBenchmark
% 0.14/0.39 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------