%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET977+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 08:57:53 AM UTC 2026
% Result : Theorem 1.16s 1.40s
% Output : Proof 1.16s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(d1_xboole_0,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('theBenchmark.p',d1_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(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
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(t128_zfmisc_1,axiom,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(singleton(C),D))
<=> ( in(B,D)
& A = C ) ),
file('theBenchmark.p',t128_zfmisc_1) ).
fof(t129_zfmisc_1,axiom,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,singleton(D)))
<=> ( B = D
& in(A,C) ) ),
file('theBenchmark.p',t129_zfmisc_1) ).
fof(t130_zfmisc_1,conjecture,
! [A,B] :
( A != empty_set
=> ( cartesian_product2(A,singleton(B)) != empty_set
& cartesian_product2(singleton(B),A) != empty_set ) ),
file('theBenchmark.p',t130_zfmisc_1) ).
fof(f_1_1,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_1_2,plain,
! [U_1,U_0] :
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_tarski]) ).
fof(f_2_2,plain,
! [U_3,U_2] : unordered_pair(U_3,U_2) = unordered_pair(U_2,U_3),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
unordered_pair(U_3,U_2) = unordered_pair(U_2,U_3),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [A] :
( ( A = empty_set
| ? [B] : in(B,A) )
& ( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(fof_nnf,[status(thm)],[d1_xboole_0]) ).
fof(f_3_2,plain,
! [U_6] :
( ( U_6 = empty_set
| ? [U_5] : in(U_5,U_6) )
& ( ! [U_4] : ~ in(U_4,U_6)
| U_6 != empty_set ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_8] :
( U_8 = empty_set
| ? [U_5] : in(U_5,U_8) )
& ! [U_7] :
( ! [U_4] : ~ in(U_4,U_7)
| U_7 != empty_set ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
fof(f_3_4,plain,
( ! [U_8] :
( U_8 = empty_set
| in(sK1(U_8),U_8) )
& ! [U_7] :
( ! [U_4] : ~ in(U_4,U_7)
| U_7 != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_5,sK1(U_8))],[f_3_3]) ).
cnf(f_3_5,plain,
( ~ in(U_4,U_7)
| U_7 != empty_set ),
inference(clausify,[status(thm)],[f_3_4]) ).
cnf(f_3_6,plain,
( U_8 = empty_set
| in(sK1(U_8),U_8) ),
inference(clausify,[status(thm)],[f_3_4]) ).
fof(f_4_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_4_2,plain,
! [U_10,U_9] : ordered_pair(U_10,U_9) = unordered_pair(unordered_pair(U_10,U_9),singleton(U_10)),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
ordered_pair(U_10,U_9) = unordered_pair(unordered_pair(U_10,U_9),singleton(U_10)),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_5_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_5_1]) ).
fof(f_6_1,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc1_zfmisc_1]) ).
fof(f_6_2,plain,
! [U_12,U_11] : ~ empty(ordered_pair(U_12,U_11)),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
~ empty(ordered_pair(U_12,U_11)),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_7_2,plain,
? [U_13] : empty(U_13),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
empty(sK2),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_13,sK2)],[f_7_2]) ).
cnf(f_7_4,plain,
empty(sK2),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_8_2,plain,
? [U_14] : ~ empty(U_14),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
~ empty(sK3),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_14,sK3)],[f_8_2]) ).
cnf(f_8_4,plain,
~ empty(sK3),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
! [A,B,C,D] :
( ( in(ordered_pair(A,B),cartesian_product2(singleton(C),D))
| ~ in(B,D)
| A != C )
& ( ( in(B,D)
& A = C )
| ~ in(ordered_pair(A,B),cartesian_product2(singleton(C),D)) ) ),
inference(fof_nnf,[status(thm)],[t128_zfmisc_1]) ).
fof(f_9_2,plain,
! [U_18,U_17,U_16,U_15] :
( ( in(ordered_pair(U_18,U_17),cartesian_product2(singleton(U_16),U_15))
| ~ in(U_17,U_15)
| U_18 != U_16 )
& ( ( in(U_17,U_15)
& U_18 = U_16 )
| ~ in(ordered_pair(U_18,U_17),cartesian_product2(singleton(U_16),U_15)) ) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
( ! [U_26,U_24,U_22,U_20] :
( in(ordered_pair(U_26,U_24),cartesian_product2(singleton(U_22),U_20))
| ~ in(U_24,U_20)
| U_26 != U_22 )
& ! [U_25,U_23,U_21,U_19] :
( ( in(U_23,U_19)
& U_25 = U_21 )
| ~ in(ordered_pair(U_25,U_23),cartesian_product2(singleton(U_21),U_19)) ) ),
inference(miniscope,[status(thm)],[f_9_2]) ).
cnf(f_9_4,plain,
( U_25 = U_21
| ~ in(ordered_pair(U_25,U_23),cartesian_product2(singleton(U_21),U_19)) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_5,plain,
( in(U_23,U_19)
| ~ in(ordered_pair(U_25,U_23),cartesian_product2(singleton(U_21),U_19)) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_6,plain,
( in(ordered_pair(U_26,U_24),cartesian_product2(singleton(U_22),U_20))
| ~ in(U_24,U_20)
| U_26 != U_22 ),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_1,plain,
! [A,B,C,D] :
( ( in(ordered_pair(A,B),cartesian_product2(C,singleton(D)))
| B != D
| ~ in(A,C) )
& ( ( B = D
& in(A,C) )
| ~ in(ordered_pair(A,B),cartesian_product2(C,singleton(D))) ) ),
inference(fof_nnf,[status(thm)],[t129_zfmisc_1]) ).
fof(f_10_2,plain,
! [U_30,U_29,U_28,U_27] :
( ( in(ordered_pair(U_30,U_29),cartesian_product2(U_28,singleton(U_27)))
| U_29 != U_27
| ~ in(U_30,U_28) )
& ( ( U_29 = U_27
& in(U_30,U_28) )
| ~ in(ordered_pair(U_30,U_29),cartesian_product2(U_28,singleton(U_27))) ) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
( ! [U_38,U_36,U_34,U_32] :
( in(ordered_pair(U_38,U_36),cartesian_product2(U_34,singleton(U_32)))
| U_36 != U_32
| ~ in(U_38,U_34) )
& ! [U_37,U_35,U_33,U_31] :
( ( U_35 = U_31
& in(U_37,U_33) )
| ~ in(ordered_pair(U_37,U_35),cartesian_product2(U_33,singleton(U_31))) ) ),
inference(miniscope,[status(thm)],[f_10_2]) ).
cnf(f_10_4,plain,
( in(U_37,U_33)
| ~ in(ordered_pair(U_37,U_35),cartesian_product2(U_33,singleton(U_31))) ),
inference(clausify,[status(thm)],[f_10_3]) ).
cnf(f_10_5,plain,
( U_35 = U_31
| ~ in(ordered_pair(U_37,U_35),cartesian_product2(U_33,singleton(U_31))) ),
inference(clausify,[status(thm)],[f_10_3]) ).
cnf(f_10_6,plain,
( in(ordered_pair(U_38,U_36),cartesian_product2(U_34,singleton(U_32)))
| U_36 != U_32
| ~ in(U_38,U_34) ),
inference(clausify,[status(thm)],[f_10_3]) ).
fof(f_11_1,negated_conjecture,
~ ! [A,B] :
( A != empty_set
=> ( cartesian_product2(A,singleton(B)) != empty_set
& cartesian_product2(singleton(B),A) != empty_set ) ),
inference(negate,[status(cth)],[t130_zfmisc_1]) ).
fof(f_11_2,negated_conjecture,
? [A,B] :
( ( cartesian_product2(A,singleton(B)) = empty_set
| cartesian_product2(singleton(B),A) = empty_set )
& A != empty_set ),
inference(fof_nnf,[status(thm)],[f_11_1]) ).
fof(f_11_3,negated_conjecture,
? [U_40,U_39] :
( ( cartesian_product2(U_40,singleton(U_39)) = empty_set
| cartesian_product2(singleton(U_39),U_40) = empty_set )
& U_40 != empty_set ),
inference(variable_rename,[status(thm)],[f_11_2]) ).
fof(f_11_4,negated_conjecture,
? [U_40] :
( ( ? [U_42] : cartesian_product2(U_40,singleton(U_42)) = empty_set
| ? [U_41] : cartesian_product2(singleton(U_41),U_40) = empty_set )
& U_40 != empty_set ),
inference(miniscope,[status(thm)],[f_11_3]) ).
fof(f_11_5,negated_conjecture,
( ( ? [U_42] : cartesian_product2(sK4,singleton(U_42)) = empty_set
| ? [U_41] : cartesian_product2(singleton(U_41),sK4) = empty_set )
& sK4 != empty_set ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_40,sK4)],[f_11_4]) ).
fof(f_11_6,negated_conjecture,
( ( ? [U_42] : cartesian_product2(sK4,singleton(U_42)) = empty_set
| cartesian_product2(singleton(sK5),sK4) = empty_set )
& sK4 != empty_set ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_41,sK5)],[f_11_5]) ).
fof(f_11_7,negated_conjecture,
( ( cartesian_product2(sK4,singleton(sK6)) = empty_set
| cartesian_product2(singleton(sK5),sK4) = empty_set )
& sK4 != empty_set ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_42,sK6)],[f_11_6]) ).
fof(f_11_8,negated_conjecture,
( ( cartesian_product2(sK4,singleton(sK6)) = empty_set
| cartesian_product2(singleton(sK5),sK4) = empty_set )
& sK4 != empty_set ),
inference(definitional_conversion,[status(esa)],[f_11_7]) ).
cnf(f_11_9,negated_conjecture,
sK4 != empty_set,
inference(clausify,[status(thm)],[f_11_8]) ).
cnf(f_11_10,negated_conjecture,
( cartesian_product2(sK4,singleton(sK6)) = empty_set
| cartesian_product2(singleton(sK5),sK4) = empty_set ),
inference(clausify,[status(thm)],[f_11_8]) ).
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,
( sK1(Eq_x_0) = sK1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,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_10,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 : SET977+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
% 0.11/0.36 % Computer : n001.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Sep 19 23:15:10 UTC 2026
% 0.11/0.37 % CPUTime :
% 1.16/1.40 % SZS status Theorem for theBenchmark
% 1.16/1.40 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------