%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET985+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 : n026.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 3.25s 3.57s
% Output : Proof 3.41s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
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(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t113_zfmisc_1,axiom,
! [A,B] :
( cartesian_product2(A,B) = empty_set
<=> ( B = empty_set
| A = empty_set ) ),
file('theBenchmark.p',t113_zfmisc_1) ).
fof(t138_zfmisc_1,axiom,
! [A,B,C,D] :
( subset(cartesian_product2(A,B),cartesian_product2(C,D))
=> ( ( subset(B,D)
& subset(A,C) )
| cartesian_product2(A,B) = empty_set ) ),
file('theBenchmark.p',t138_zfmisc_1) ).
fof(t139_zfmisc_1,conjecture,
! [A] :
( ~ empty(A)
=> ! [B,C,D] :
( ( subset(cartesian_product2(B,A),cartesian_product2(D,C))
| subset(cartesian_product2(A,B),cartesian_product2(C,D)) )
=> subset(B,D) ) ),
file('theBenchmark.p',t139_zfmisc_1) ).
fof(t2_xboole_1,axiom,
! [A] : subset(empty_set,A),
file('theBenchmark.p',t2_xboole_1) ).
fof(f_1_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_1_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_1_1]) ).
fof(f_2_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_2_2,plain,
? [U_0] : empty(U_0),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
empty(sK1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_0,sK1)],[f_2_2]) ).
cnf(f_2_4,plain,
empty(sK1),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_3_2,plain,
? [U_1] : ~ empty(U_1),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
~ empty(sK2),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_1,sK2)],[f_3_2]) ).
cnf(f_3_4,plain,
~ empty(sK2),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_4_2,plain,
! [U_3,U_2] : subset(U_3,U_3),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_3] : subset(U_3,U_3),
inference(miniscope,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
subset(U_3,U_3),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
! [A,B] :
( ( cartesian_product2(A,B) = empty_set
| ( B != empty_set
& A != empty_set ) )
& ( B = empty_set
| A = empty_set
| cartesian_product2(A,B) != empty_set ) ),
inference(fof_nnf,[status(thm)],[t113_zfmisc_1]) ).
fof(f_5_2,plain,
! [U_5,U_4] :
( ( cartesian_product2(U_5,U_4) = empty_set
| ( U_4 != empty_set
& U_5 != empty_set ) )
& ( U_4 = empty_set
| U_5 = empty_set
| cartesian_product2(U_5,U_4) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_9,U_7] :
( cartesian_product2(U_9,U_7) = empty_set
| ( U_7 != empty_set
& U_9 != empty_set ) )
& ! [U_8,U_6] :
( U_6 = empty_set
| U_8 = empty_set
| cartesian_product2(U_8,U_6) != empty_set ) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
cnf(f_5_4,plain,
( U_6 = empty_set
| U_8 = empty_set
| cartesian_product2(U_8,U_6) != empty_set ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_5,plain,
( U_9 != empty_set
| cartesian_product2(U_9,U_7) = empty_set ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_6,plain,
( U_7 != empty_set
| cartesian_product2(U_9,U_7) = empty_set ),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
! [A,B,C,D] :
( ( subset(B,D)
& subset(A,C) )
| cartesian_product2(A,B) = empty_set
| ~ subset(cartesian_product2(A,B),cartesian_product2(C,D)) ),
inference(fof_nnf,[status(thm)],[t138_zfmisc_1]) ).
fof(f_6_2,plain,
! [U_13,U_12,U_11,U_10] :
( ( subset(U_12,U_10)
& subset(U_13,U_11) )
| cartesian_product2(U_13,U_12) = empty_set
| ~ subset(cartesian_product2(U_13,U_12),cartesian_product2(U_11,U_10)) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( subset(U_13,U_11)
| cartesian_product2(U_13,U_12) = empty_set
| ~ subset(cartesian_product2(U_13,U_12),cartesian_product2(U_11,U_10)) ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_4,plain,
( subset(U_12,U_10)
| cartesian_product2(U_13,U_12) = empty_set
| ~ subset(cartesian_product2(U_13,U_12),cartesian_product2(U_11,U_10)) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,negated_conjecture,
~ ! [A] :
( ~ empty(A)
=> ! [B,C,D] :
( ( subset(cartesian_product2(B,A),cartesian_product2(D,C))
| subset(cartesian_product2(A,B),cartesian_product2(C,D)) )
=> subset(B,D) ) ),
inference(negate,[status(cth)],[t139_zfmisc_1]) ).
fof(f_7_2,negated_conjecture,
? [A] :
( ? [B,C,D] :
( ~ subset(B,D)
& ( subset(cartesian_product2(B,A),cartesian_product2(D,C))
| subset(cartesian_product2(A,B),cartesian_product2(C,D)) ) )
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[f_7_1]) ).
fof(f_7_3,negated_conjecture,
? [U_17] :
( ? [U_16,U_15,U_14] :
( ~ subset(U_16,U_14)
& ( subset(cartesian_product2(U_16,U_17),cartesian_product2(U_14,U_15))
| subset(cartesian_product2(U_17,U_16),cartesian_product2(U_15,U_14)) ) )
& ~ empty(U_17) ),
inference(variable_rename,[status(thm)],[f_7_2]) ).
fof(f_7_4,negated_conjecture,
( ? [U_16,U_15,U_14] :
( ~ subset(U_16,U_14)
& ( subset(cartesian_product2(U_16,sK3),cartesian_product2(U_14,U_15))
| subset(cartesian_product2(sK3,U_16),cartesian_product2(U_15,U_14)) ) )
& ~ empty(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_17,sK3)],[f_7_3]) ).
fof(f_7_5,negated_conjecture,
( ? [U_15,U_14] :
( ~ subset(sK4,U_14)
& ( subset(cartesian_product2(sK4,sK3),cartesian_product2(U_14,U_15))
| subset(cartesian_product2(sK3,sK4),cartesian_product2(U_15,U_14)) ) )
& ~ empty(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_16,sK4)],[f_7_4]) ).
fof(f_7_6,negated_conjecture,
( ? [U_14] :
( ~ subset(sK4,U_14)
& ( subset(cartesian_product2(sK4,sK3),cartesian_product2(U_14,sK5))
| subset(cartesian_product2(sK3,sK4),cartesian_product2(sK5,U_14)) ) )
& ~ empty(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_15,sK5)],[f_7_5]) ).
fof(f_7_7,negated_conjecture,
( ~ subset(sK4,sK6)
& ( subset(cartesian_product2(sK4,sK3),cartesian_product2(sK6,sK5))
| subset(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK6)) )
& ~ empty(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_14,sK6)],[f_7_6]) ).
fof(f_7_8,negated_conjecture,
( ~ subset(sK4,sK6)
& ( subset(cartesian_product2(sK4,sK3),cartesian_product2(sK6,sK5))
| subset(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK6)) )
& ~ empty(sK3) ),
inference(definitional_conversion,[status(esa)],[f_7_7]) ).
cnf(f_7_9,negated_conjecture,
~ empty(sK3),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_10,negated_conjecture,
( subset(cartesian_product2(sK4,sK3),cartesian_product2(sK6,sK5))
| subset(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK6)) ),
inference(clausify,[status(thm)],[f_7_8]) ).
cnf(f_7_11,negated_conjecture,
~ subset(sK4,sK6),
inference(clausify,[status(thm)],[f_7_8]) ).
fof(f_8_1,plain,
! [A] : subset(empty_set,A),
inference(fof_nnf,[status(thm)],[t2_xboole_1]) ).
fof(f_8_2,plain,
! [U_18] : subset(empty_set,U_18),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
subset(empty_set,U_18),
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_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,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_6,axiom,
( subset(Eq_y_0,Eq_y_1)
| ~ subset(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 : SET985+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
% 0.09/0.36 % Computer : n026.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 23:12:50 UTC 2026
% 0.09/0.36 % CPUTime :
% 3.25/3.57 % SZS status Theorem for theBenchmark
% 3.25/3.57 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------