%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET971+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 : 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 : Thu Sep 24 08:57:53 AM UTC 2026
% Result : Theorem 1.65s 6.97s
% Output : Proof 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 53 ( 30 unt; 0 def)
% Number of atoms : 91 ( 51 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 67 ( 29 ~; 19 |; 16 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 64 ( 0 sgn 32 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('theBenchmark.p',commutativity_k3_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(t124_zfmisc_1,conjecture,
! [A,B,C,D] :
( ( subset(C,D)
& subset(A,B) )
=> set_intersection2(cartesian_product2(A,D),cartesian_product2(B,C)) = cartesian_product2(A,C) ),
file('theBenchmark.p',t124_zfmisc_1) ).
fof(t28_xboole_1,axiom,
! [A,B] :
( subset(A,B)
=> set_intersection2(A,B) = A ),
file('theBenchmark.p',t28_xboole_1) ).
fof(f_1_1,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(f_1_2,plain,
! [U_1,U_0] : set_intersection2(U_1,U_0) = set_intersection2(U_0,U_1),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
set_intersection2(U_1,U_0) = set_intersection2(U_0,U_1),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_6_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_6_2,plain,
! [U_11,U_10,U_9,U_8] : cartesian_product2(set_intersection2(U_11,U_10),set_intersection2(U_9,U_8)) = set_intersection2(cartesian_product2(U_11,U_9),cartesian_product2(U_10,U_8)),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
cartesian_product2(set_intersection2(U_11,U_10),set_intersection2(U_9,U_8)) = set_intersection2(cartesian_product2(U_11,U_9),cartesian_product2(U_10,U_8)),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,negated_conjecture,
~ ! [A,B,C,D] :
( ( subset(C,D)
& subset(A,B) )
=> set_intersection2(cartesian_product2(A,D),cartesian_product2(B,C)) = cartesian_product2(A,C) ),
inference(negate,[status(cth)],[t124_zfmisc_1]) ).
fof(f_7_2,negated_conjecture,
? [A,B,C,D] :
( set_intersection2(cartesian_product2(A,D),cartesian_product2(B,C)) != cartesian_product2(A,C)
& subset(C,D)
& subset(A,B) ),
inference(fof_nnf,[status(thm)],[f_7_1]) ).
fof(f_7_3,negated_conjecture,
? [U_15,U_14,U_13,U_12] :
( set_intersection2(cartesian_product2(U_15,U_12),cartesian_product2(U_14,U_13)) != cartesian_product2(U_15,U_13)
& subset(U_13,U_12)
& subset(U_15,U_14) ),
inference(variable_rename,[status(thm)],[f_7_2]) ).
fof(f_7_4,negated_conjecture,
? [U_14,U_13,U_12] :
( set_intersection2(cartesian_product2(sK3,U_12),cartesian_product2(U_14,U_13)) != cartesian_product2(sK3,U_13)
& subset(U_13,U_12)
& subset(sK3,U_14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_15,sK3)],[f_7_3]) ).
fof(f_7_5,negated_conjecture,
? [U_13,U_12] :
( set_intersection2(cartesian_product2(sK3,U_12),cartesian_product2(sK4,U_13)) != cartesian_product2(sK3,U_13)
& subset(U_13,U_12)
& subset(sK3,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_14,sK4)],[f_7_4]) ).
fof(f_7_6,negated_conjecture,
? [U_12] :
( set_intersection2(cartesian_product2(sK3,U_12),cartesian_product2(sK4,sK5)) != cartesian_product2(sK3,sK5)
& subset(sK5,U_12)
& subset(sK3,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_13,sK5)],[f_7_5]) ).
fof(f_7_7,negated_conjecture,
( set_intersection2(cartesian_product2(sK3,sK6),cartesian_product2(sK4,sK5)) != cartesian_product2(sK3,sK5)
& subset(sK5,sK6)
& subset(sK3,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_12,sK6)],[f_7_6]) ).
fof(f_7_8,negated_conjecture,
( set_intersection2(cartesian_product2(sK3,sK6),cartesian_product2(sK4,sK5)) != cartesian_product2(sK3,sK5)
& subset(sK5,sK6)
& subset(sK3,sK4) ),
inference(definitional_conversion,[status(esa)],[f_7_7]) ).
cnf(f_7_9,negated_conjecture,
subset(sK3,sK4),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_10,negated_conjecture,
subset(sK5,sK6),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_11,negated_conjecture,
set_intersection2(cartesian_product2(sK3,sK6),cartesian_product2(sK4,sK5)) != cartesian_product2(sK3,sK5),
inference(clausify,[status(thm)],[f_7_8]) ).
fof(f_8_1,plain,
! [A,B] :
( set_intersection2(A,B) = A
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t28_xboole_1]) ).
fof(f_8_2,plain,
! [U_17,U_16] :
( set_intersection2(U_17,U_16) = U_17
| ~ subset(U_17,U_16) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
( set_intersection2(U_17,U_16) = U_17
| ~ subset(U_17,U_16) ),
inference(clausify,[status(thm)],[f_8_2]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_5,axiom,
( cartesian_product2(Eq_x_0,Eq_x_1) = cartesian_product2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(t1,plain,
set_intersection2(cartesian_product2(sK3,sK6),cartesian_product2(sK4,sK5)) != cartesian_product2(sK3,sK5),
inference(start,[status(thm),parent(0:0)],[f_7_11]) ).
cnf(t2,plain,
( cartesian_product2(set_intersection2(sK3,sK4),set_intersection2(sK5,sK6)) != cartesian_product2(sK3,sK5)
| set_intersection2(cartesian_product2(sK3,sK6),cartesian_product2(sK4,sK5)) != cartesian_product2(set_intersection2(sK3,sK4),set_intersection2(sK5,sK6))
| set_intersection2(cartesian_product2(sK3,sK6),cartesian_product2(sK4,sK5)) = cartesian_product2(sK3,sK5) ),
inference(extension,[status(thm),parent(t1:1)],[equality_3]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( cartesian_product2(set_intersection2(sK3,sK4),set_intersection2(sK6,sK5)) != cartesian_product2(set_intersection2(sK3,sK4),set_intersection2(sK5,sK6))
| set_intersection2(cartesian_product2(sK3,sK6),cartesian_product2(sK4,sK5)) != cartesian_product2(set_intersection2(sK3,sK4),set_intersection2(sK6,sK5))
| set_intersection2(cartesian_product2(sK3,sK6),cartesian_product2(sK4,sK5)) = cartesian_product2(set_intersection2(sK3,sK4),set_intersection2(sK5,sK6)) ),
inference(extension,[status(thm),parent(t2:2)],[equality_3]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( cartesian_product2(set_intersection2(sK3,sK4),set_intersection2(sK6,sK5)) != set_intersection2(cartesian_product2(sK3,sK6),cartesian_product2(sK4,sK5))
| set_intersection2(cartesian_product2(sK3,sK6),cartesian_product2(sK4,sK5)) = cartesian_product2(set_intersection2(sK3,sK4),set_intersection2(sK6,sK5)) ),
inference(extension,[status(thm),parent(t4:2)],[equality_2]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
cartesian_product2(set_intersection2(sK3,sK4),set_intersection2(sK6,sK5)) = set_intersection2(cartesian_product2(sK3,sK6),cartesian_product2(sK4,sK5)),
inference(extension,[status(thm),parent(t6:2)],[f_6_3]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( set_intersection2(sK6,sK5) != set_intersection2(sK5,sK6)
| set_intersection2(sK3,sK4) != set_intersection2(sK3,sK4)
| cartesian_product2(set_intersection2(sK3,sK4),set_intersection2(sK6,sK5)) = cartesian_product2(set_intersection2(sK3,sK4),set_intersection2(sK5,sK6)) ),
inference(extension,[status(thm),parent(t4:3)],[equality_5]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t4:3]) ).
cnf(t12,plain,
set_intersection2(sK3,sK4) = set_intersection2(sK3,sK4),
inference(extension,[status(thm),parent(t10:2)],[equality_1]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
set_intersection2(sK6,sK5) = set_intersection2(sK5,sK6),
inference(extension,[status(thm),parent(t10:3)],[f_1_3]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t10:3]) ).
cnf(t16,plain,
( set_intersection2(sK5,sK6) != sK5
| set_intersection2(sK3,sK4) != sK3
| cartesian_product2(set_intersection2(sK3,sK4),set_intersection2(sK5,sK6)) = cartesian_product2(sK3,sK5) ),
inference(extension,[status(thm),parent(t2:3)],[equality_5]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t2:3]) ).
cnf(t18,plain,
( ~ subset(sK3,sK4)
| set_intersection2(sK3,sK4) = sK3 ),
inference(extension,[status(thm),parent(t16:2)],[f_8_3]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
subset(sK3,sK4),
inference(extension,[status(thm),parent(t18:2)],[f_7_9]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
( ~ subset(sK5,sK6)
| set_intersection2(sK5,sK6) = sK5 ),
inference(extension,[status(thm),parent(t16:3)],[f_8_3]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t16:3]) ).
cnf(t24,plain,
subset(sK5,sK6),
inference(extension,[status(thm),parent(t22:2)],[f_7_10]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET971+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
% 0.11/5.39 % Computer : n020.cluster.edu
% 0.11/5.39 % Model : x86_64 x86_64
% 0.11/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.39 % Memory : 8046.5625MB
% 0.11/5.39 % OS : Linux 6.8.0-71-generic
% 0.11/5.39 % CPULimit : 300
% 0.11/5.39 % WCLimit : 300
% 0.11/5.39 % DateTime : Sat Sep 19 23:09:53 UTC 2026
% 0.11/5.39 % CPUTime :
% 1.65/6.97 % SZS status Theorem for theBenchmark
% 1.65/6.97 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------