%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU165+3 : 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 08:58:19 AM UTC 2026
% Result : Theorem 0.10s 0.40s
% Output : Proof 0.10s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
fof(fc1_zfmisc_1,axiom,
! [A,B] : ~ empty(ordered_pair(A,B)),
file('theBenchmark.p',fc1_zfmisc_1) ).
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(d5_tarski,axiom,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
file('theBenchmark.p',d5_tarski) ).
fof(t106_zfmisc_1,conjecture,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(B,D)
& in(A,C) ) ),
file('theBenchmark.p',t106_zfmisc_1) ).
fof(l55_zfmisc_1,axiom,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(B,D)
& in(A,C) ) ),
file('theBenchmark.p',l55_zfmisc_1) ).
fof(f_1_1,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_tarski]) ).
fof(f_1_2,plain,
! [U_1,U_0] : unordered_pair(U_1,U_0) = unordered_pair(U_0,U_1),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
unordered_pair(U_1,U_0) = unordered_pair(U_0,U_1),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_2_2,plain,
! [U_3,U_2] :
( ~ in(U_2,U_3)
| ~ in(U_3,U_2) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( ~ in(U_2,U_3)
| ~ in(U_3,U_2) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc1_zfmisc_1]) ).
fof(f_3_2,plain,
! [U_5,U_4] : ~ empty(ordered_pair(U_5,U_4)),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
~ empty(ordered_pair(U_5,U_4)),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_4_2,plain,
? [U_6] : empty(U_6),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
empty(sK1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_6,sK1)],[f_4_2]) ).
cnf(f_4_4,plain,
empty(sK1),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_5_2,plain,
? [U_7] : ~ empty(U_7),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
~ empty(sK2),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_7,sK2)],[f_5_2]) ).
cnf(f_5_4,plain,
~ empty(sK2),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
inference(fof_nnf,[status(thm)],[d5_tarski]) ).
fof(f_6_2,plain,
! [U_9,U_8] : ordered_pair(U_9,U_8) = unordered_pair(unordered_pair(U_9,U_8),singleton(U_9)),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
ordered_pair(U_9,U_8) = unordered_pair(unordered_pair(U_9,U_8),singleton(U_9)),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,negated_conjecture,
~ ! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(B,D)
& in(A,C) ) ),
inference(negate,[status(cth)],[t106_zfmisc_1]) ).
fof(f_7_2,negated_conjecture,
? [A,B,C,D] :
( ( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
& in(B,D)
& in(A,C) )
| ( ( ~ in(B,D)
| ~ in(A,C) )
& in(ordered_pair(A,B),cartesian_product2(C,D)) ) ),
inference(fof_nnf,[status(thm)],[f_7_1]) ).
fof(f_7_3,negated_conjecture,
? [U_13,U_12,U_11,U_10] :
( ( ~ in(ordered_pair(U_13,U_12),cartesian_product2(U_11,U_10))
& in(U_12,U_10)
& in(U_13,U_11) )
| ( ( ~ in(U_12,U_10)
| ~ in(U_13,U_11) )
& in(ordered_pair(U_13,U_12),cartesian_product2(U_11,U_10)) ) ),
inference(variable_rename,[status(thm)],[f_7_2]) ).
fof(f_7_4,negated_conjecture,
( ? [U_21,U_19,U_17,U_15] :
( ~ in(ordered_pair(U_21,U_19),cartesian_product2(U_17,U_15))
& in(U_19,U_15)
& in(U_21,U_17) )
| ? [U_20,U_18,U_16,U_14] :
( ( ~ in(U_18,U_14)
| ~ in(U_20,U_16) )
& in(ordered_pair(U_20,U_18),cartesian_product2(U_16,U_14)) ) ),
inference(miniscope,[status(thm)],[f_7_3]) ).
fof(f_7_5,negated_conjecture,
( ? [U_21,U_19,U_17,U_15] :
( ~ in(ordered_pair(U_21,U_19),cartesian_product2(U_17,U_15))
& in(U_19,U_15)
& in(U_21,U_17) )
| ? [U_18,U_16,U_14] :
( ( ~ in(U_18,U_14)
| ~ in(sK3,U_16) )
& in(ordered_pair(sK3,U_18),cartesian_product2(U_16,U_14)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_20,sK3)],[f_7_4]) ).
fof(f_7_6,negated_conjecture,
( ? [U_21,U_19,U_17,U_15] :
( ~ in(ordered_pair(U_21,U_19),cartesian_product2(U_17,U_15))
& in(U_19,U_15)
& in(U_21,U_17) )
| ? [U_16,U_14] :
( ( ~ in(sK4,U_14)
| ~ in(sK3,U_16) )
& in(ordered_pair(sK3,sK4),cartesian_product2(U_16,U_14)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_18,sK4)],[f_7_5]) ).
fof(f_7_7,negated_conjecture,
( ? [U_21,U_19,U_17,U_15] :
( ~ in(ordered_pair(U_21,U_19),cartesian_product2(U_17,U_15))
& in(U_19,U_15)
& in(U_21,U_17) )
| ? [U_14] :
( ( ~ in(sK4,U_14)
| ~ in(sK3,sK5) )
& in(ordered_pair(sK3,sK4),cartesian_product2(sK5,U_14)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_16,sK5)],[f_7_6]) ).
fof(f_7_8,negated_conjecture,
( ? [U_21,U_19,U_17,U_15] :
( ~ in(ordered_pair(U_21,U_19),cartesian_product2(U_17,U_15))
& in(U_19,U_15)
& in(U_21,U_17) )
| ( ( ~ in(sK4,sK6)
| ~ in(sK3,sK5) )
& in(ordered_pair(sK3,sK4),cartesian_product2(sK5,sK6)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_14,sK6)],[f_7_7]) ).
fof(f_7_9,negated_conjecture,
( ? [U_19,U_17,U_15] :
( ~ in(ordered_pair(sK7,U_19),cartesian_product2(U_17,U_15))
& in(U_19,U_15)
& in(sK7,U_17) )
| ( ( ~ in(sK4,sK6)
| ~ in(sK3,sK5) )
& in(ordered_pair(sK3,sK4),cartesian_product2(sK5,sK6)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_21,sK7)],[f_7_8]) ).
fof(f_7_10,negated_conjecture,
( ? [U_17,U_15] :
( ~ in(ordered_pair(sK7,sK8),cartesian_product2(U_17,U_15))
& in(sK8,U_15)
& in(sK7,U_17) )
| ( ( ~ in(sK4,sK6)
| ~ in(sK3,sK5) )
& in(ordered_pair(sK3,sK4),cartesian_product2(sK5,sK6)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_19,sK8)],[f_7_9]) ).
fof(f_7_11,negated_conjecture,
( ? [U_15] :
( ~ in(ordered_pair(sK7,sK8),cartesian_product2(sK9,U_15))
& in(sK8,U_15)
& in(sK7,sK9) )
| ( ( ~ in(sK4,sK6)
| ~ in(sK3,sK5) )
& in(ordered_pair(sK3,sK4),cartesian_product2(sK5,sK6)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_17,sK9)],[f_7_10]) ).
fof(f_7_12,negated_conjecture,
( ( ~ in(ordered_pair(sK7,sK8),cartesian_product2(sK9,sK10))
& in(sK8,sK10)
& in(sK7,sK9) )
| ( ( ~ in(sK4,sK6)
| ~ in(sK3,sK5) )
& in(ordered_pair(sK3,sK4),cartesian_product2(sK5,sK6)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_15,sK10)],[f_7_11]) ).
fof(f_7_13,negated_conjecture,
( ( ~ in(ordered_pair(sK7,sK8),cartesian_product2(sK9,sK10))
| ~ sP1 )
& ( in(sK8,sK10)
| ~ sP1 )
& ( in(sK7,sK9)
| ~ sP1 )
& ( ~ in(sK4,sK6)
| ~ in(sK3,sK5)
| ~ sP0 )
& ( in(ordered_pair(sK3,sK4),cartesian_product2(sK5,sK6))
| ~ sP0 )
& ( sP1
| sP0 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1])],[f_7_12]) ).
cnf(f_7_14,negated_conjecture,
( sP1
| sP0 ),
inference(clausify,[status(thm)],[f_7_13]) ).
cnf(f_7_15,negated_conjecture,
( in(ordered_pair(sK3,sK4),cartesian_product2(sK5,sK6))
| ~ sP0 ),
inference(clausify,[status(thm)],[f_7_13]) ).
cnf(f_7_16,negated_conjecture,
( ~ in(sK4,sK6)
| ~ in(sK3,sK5)
| ~ sP0 ),
inference(clausify,[status(thm)],[f_7_13]) ).
cnf(f_7_17,negated_conjecture,
( in(sK7,sK9)
| ~ sP1 ),
inference(clausify,[status(thm)],[f_7_13]) ).
cnf(f_7_18,negated_conjecture,
( in(sK8,sK10)
| ~ sP1 ),
inference(clausify,[status(thm)],[f_7_13]) ).
cnf(f_7_19,negated_conjecture,
( ~ in(ordered_pair(sK7,sK8),cartesian_product2(sK9,sK10))
| ~ sP1 ),
inference(clausify,[status(thm)],[f_7_13]) ).
fof(f_8_1,plain,
! [A,B,C,D] :
( ( in(ordered_pair(A,B),cartesian_product2(C,D))
| ~ in(B,D)
| ~ in(A,C) )
& ( ( in(B,D)
& in(A,C) )
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ) ),
inference(fof_nnf,[status(thm)],[l55_zfmisc_1]) ).
fof(f_8_2,plain,
! [U_25,U_24,U_23,U_22] :
( ( in(ordered_pair(U_25,U_24),cartesian_product2(U_23,U_22))
| ~ in(U_24,U_22)
| ~ in(U_25,U_23) )
& ( ( in(U_24,U_22)
& in(U_25,U_23) )
| ~ in(ordered_pair(U_25,U_24),cartesian_product2(U_23,U_22)) ) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_33,U_31,U_29,U_27] :
( in(ordered_pair(U_33,U_31),cartesian_product2(U_29,U_27))
| ~ in(U_31,U_27)
| ~ in(U_33,U_29) )
& ! [U_32,U_30,U_28,U_26] :
( ( in(U_30,U_26)
& in(U_32,U_28) )
| ~ in(ordered_pair(U_32,U_30),cartesian_product2(U_28,U_26)) ) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
cnf(f_8_4,plain,
( in(U_32,U_28)
| ~ in(ordered_pair(U_32,U_30),cartesian_product2(U_28,U_26)) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_5,plain,
( in(U_30,U_26)
| ~ in(ordered_pair(U_32,U_30),cartesian_product2(U_28,U_26)) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_6,plain,
( in(ordered_pair(U_33,U_31),cartesian_product2(U_29,U_27))
| ~ in(U_31,U_27)
| ~ in(U_33,U_29) ),
inference(clausify,[status(thm)],[f_8_3]) ).
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,
( unordered_pair(Eq_x_0,Eq_x_1) = unordered_pair(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,
( ordered_pair(Eq_x_0,Eq_x_1) = ordered_pair(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( singleton(Eq_x_0) = singleton(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,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_8,axiom,
( in(Eq_y_0,Eq_y_1)
| ~ in(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_9,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| 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 : SEU165+3 : 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
% 0.10/0.36 % Computer : n001.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 19 23:30:25 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.40 % SZS status Theorem for theBenchmark
% 0.10/0.40 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------