%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET978+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 : n004.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 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(rc1_xboole_0,axiom,
? [A] : empty(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ empty(A),
file('theBenchmark.p',rc2_xboole_0) ).
fof(symmetry_r1_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
=> disjoint(B,A) ),
file('theBenchmark.p',symmetry_r1_xboole_0) ).
fof(t127_zfmisc_1,axiom,
! [A,B,C,D] :
( ( disjoint(C,D)
| disjoint(A,B) )
=> disjoint(cartesian_product2(A,C),cartesian_product2(B,D)) ),
file('theBenchmark.p',t127_zfmisc_1) ).
fof(t131_zfmisc_1,conjecture,
! [A,B,C,D] :
( A != B
=> ( disjoint(cartesian_product2(C,singleton(A)),cartesian_product2(D,singleton(B)))
& disjoint(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),D)) ) ),
file('theBenchmark.p',t131_zfmisc_1) ).
fof(t17_zfmisc_1,axiom,
! [A,B] :
( A != B
=> disjoint(singleton(A),singleton(B)) ),
file('theBenchmark.p',t17_zfmisc_1) ).
fof(f_1_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_1_2,plain,
? [U_0] : empty(U_0),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
empty(sK1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_0,sK1)],[f_1_2]) ).
cnf(f_1_4,plain,
empty(sK1),
inference(clausify,[status(thm)],[f_1_3]) ).
fof(f_2_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_2_2,plain,
? [U_1] : ~ empty(U_1),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
~ empty(sK2),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_1,sK2)],[f_2_2]) ).
cnf(f_2_4,plain,
~ empty(sK2),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
! [A,B] :
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0]) ).
fof(f_3_2,plain,
! [U_3,U_2] :
( disjoint(U_2,U_3)
| ~ disjoint(U_3,U_2) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( disjoint(U_2,U_3)
| ~ disjoint(U_3,U_2) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [A,B,C,D] :
( disjoint(cartesian_product2(A,C),cartesian_product2(B,D))
| ( ~ disjoint(C,D)
& ~ disjoint(A,B) ) ),
inference(fof_nnf,[status(thm)],[t127_zfmisc_1]) ).
fof(f_4_2,plain,
! [U_7,U_6,U_5,U_4] :
( disjoint(cartesian_product2(U_7,U_5),cartesian_product2(U_6,U_4))
| ( ~ disjoint(U_5,U_4)
& ~ disjoint(U_7,U_6) ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( ~ disjoint(U_7,U_6)
| disjoint(cartesian_product2(U_7,U_5),cartesian_product2(U_6,U_4)) ),
inference(clausify,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
( ~ disjoint(U_5,U_4)
| disjoint(cartesian_product2(U_7,U_5),cartesian_product2(U_6,U_4)) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,negated_conjecture,
~ ! [A,B,C,D] :
( A != B
=> ( disjoint(cartesian_product2(C,singleton(A)),cartesian_product2(D,singleton(B)))
& disjoint(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),D)) ) ),
inference(negate,[status(cth)],[t131_zfmisc_1]) ).
fof(f_5_2,negated_conjecture,
? [A,B,C,D] :
( ( ~ disjoint(cartesian_product2(C,singleton(A)),cartesian_product2(D,singleton(B)))
| ~ disjoint(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),D)) )
& A != B ),
inference(fof_nnf,[status(thm)],[f_5_1]) ).
fof(f_5_3,negated_conjecture,
? [U_11,U_10,U_9,U_8] :
( ( ~ disjoint(cartesian_product2(U_9,singleton(U_11)),cartesian_product2(U_8,singleton(U_10)))
| ~ disjoint(cartesian_product2(singleton(U_11),U_9),cartesian_product2(singleton(U_10),U_8)) )
& U_11 != U_10 ),
inference(variable_rename,[status(thm)],[f_5_2]) ).
fof(f_5_4,negated_conjecture,
? [U_11,U_10] :
( ( ? [U_15,U_13] : ~ disjoint(cartesian_product2(U_15,singleton(U_11)),cartesian_product2(U_13,singleton(U_10)))
| ? [U_14,U_12] : ~ disjoint(cartesian_product2(singleton(U_11),U_14),cartesian_product2(singleton(U_10),U_12)) )
& U_11 != U_10 ),
inference(miniscope,[status(thm)],[f_5_3]) ).
fof(f_5_5,negated_conjecture,
? [U_10] :
( ( ? [U_15,U_13] : ~ disjoint(cartesian_product2(U_15,singleton(sK3)),cartesian_product2(U_13,singleton(U_10)))
| ? [U_14,U_12] : ~ disjoint(cartesian_product2(singleton(sK3),U_14),cartesian_product2(singleton(U_10),U_12)) )
& sK3 != U_10 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_11,sK3)],[f_5_4]) ).
fof(f_5_6,negated_conjecture,
( ( ? [U_15,U_13] : ~ disjoint(cartesian_product2(U_15,singleton(sK3)),cartesian_product2(U_13,singleton(sK4)))
| ? [U_14,U_12] : ~ disjoint(cartesian_product2(singleton(sK3),U_14),cartesian_product2(singleton(sK4),U_12)) )
& sK3 != sK4 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_10,sK4)],[f_5_5]) ).
fof(f_5_7,negated_conjecture,
( ( ? [U_15,U_13] : ~ disjoint(cartesian_product2(U_15,singleton(sK3)),cartesian_product2(U_13,singleton(sK4)))
| ? [U_12] : ~ disjoint(cartesian_product2(singleton(sK3),sK5),cartesian_product2(singleton(sK4),U_12)) )
& sK3 != sK4 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_14,sK5)],[f_5_6]) ).
fof(f_5_8,negated_conjecture,
( ( ? [U_15,U_13] : ~ disjoint(cartesian_product2(U_15,singleton(sK3)),cartesian_product2(U_13,singleton(sK4)))
| ~ disjoint(cartesian_product2(singleton(sK3),sK5),cartesian_product2(singleton(sK4),sK6)) )
& sK3 != sK4 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_12,sK6)],[f_5_7]) ).
fof(f_5_9,negated_conjecture,
( ( ? [U_13] : ~ disjoint(cartesian_product2(sK7,singleton(sK3)),cartesian_product2(U_13,singleton(sK4)))
| ~ disjoint(cartesian_product2(singleton(sK3),sK5),cartesian_product2(singleton(sK4),sK6)) )
& sK3 != sK4 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_15,sK7)],[f_5_8]) ).
fof(f_5_10,negated_conjecture,
( ( ~ disjoint(cartesian_product2(sK7,singleton(sK3)),cartesian_product2(sK8,singleton(sK4)))
| ~ disjoint(cartesian_product2(singleton(sK3),sK5),cartesian_product2(singleton(sK4),sK6)) )
& sK3 != sK4 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_13,sK8)],[f_5_9]) ).
fof(f_5_11,negated_conjecture,
( ( ~ disjoint(cartesian_product2(sK7,singleton(sK3)),cartesian_product2(sK8,singleton(sK4)))
| ~ disjoint(cartesian_product2(singleton(sK3),sK5),cartesian_product2(singleton(sK4),sK6)) )
& sK3 != sK4 ),
inference(definitional_conversion,[status(esa)],[f_5_10]) ).
cnf(f_5_12,negated_conjecture,
sK3 != sK4,
inference(clausify,[status(thm)],[f_5_11]) ).
cnf(f_5_13,negated_conjecture,
( ~ disjoint(cartesian_product2(sK7,singleton(sK3)),cartesian_product2(sK8,singleton(sK4)))
| ~ disjoint(cartesian_product2(singleton(sK3),sK5),cartesian_product2(singleton(sK4),sK6)) ),
inference(clausify,[status(thm)],[f_5_11]) ).
fof(f_6_1,plain,
! [A,B] :
( disjoint(singleton(A),singleton(B))
| A = B ),
inference(fof_nnf,[status(thm)],[t17_zfmisc_1]) ).
fof(f_6_2,plain,
! [U_17,U_16] :
( disjoint(singleton(U_17),singleton(U_16))
| U_17 = U_16 ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( disjoint(singleton(U_17),singleton(U_16))
| U_17 = U_16 ),
inference(clausify,[status(thm)],[f_6_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_4,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(equality_5,axiom,
( singleton(Eq_x_0) = singleton(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_7,axiom,
( disjoint(Eq_y_0,Eq_y_1)
| ~ disjoint(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET978+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
% 0.09/0.36 % Computer : n004.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 23:09:34 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.39 % SZS status Theorem for theBenchmark
% 0.13/0.39 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------