%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET976+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 : n012.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 0.66s 0.92s
% Output : Proof 0.66s
% 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_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('theBenchmark.p',d1_tarski) ).
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_zfmisc_1,axiom,
! [A,B] : ~ empty(ordered_pair(A,B)),
file('theBenchmark.p',fc1_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(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(t129_zfmisc_1,conjecture,
! [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(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,B] :
( ( B = singleton(A)
| ? [C] :
( ( ~ in(C,B)
& C = A )
| ( C != A
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| C != A )
& ( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(fof_nnf,[status(thm)],[d1_tarski]) ).
fof(f_3_2,plain,
! [U_7,U_6] :
( ( U_6 = singleton(U_7)
| ? [U_5] :
( ( ~ in(U_5,U_6)
& U_5 = U_7 )
| ( U_5 != U_7
& in(U_5,U_6) ) ) )
& ( ! [U_4] :
( ( in(U_4,U_6)
| U_4 != U_7 )
& ( U_4 = U_7
| ~ in(U_4,U_6) ) )
| U_6 != singleton(U_7) ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_15,U_13] :
( U_13 = singleton(U_15)
| ? [U_11] :
( ~ in(U_11,U_13)
& U_11 = U_15 )
| ? [U_10] :
( U_10 != U_15
& in(U_10,U_13) ) )
& ! [U_14,U_12] :
( ( ! [U_9] :
( in(U_9,U_12)
| U_9 != U_14 )
& ! [U_8] :
( U_8 = U_14
| ~ in(U_8,U_12) ) )
| U_12 != singleton(U_14) ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
fof(f_3_4,plain,
( ! [U_15,U_13] :
( U_13 = singleton(U_15)
| ? [U_11] :
( ~ in(U_11,U_13)
& U_11 = U_15 )
| ( sK1(U_15,U_13) != U_15
& in(sK1(U_15,U_13),U_13) ) )
& ! [U_14,U_12] :
( ( ! [U_9] :
( in(U_9,U_12)
| U_9 != U_14 )
& ! [U_8] :
( U_8 = U_14
| ~ in(U_8,U_12) ) )
| U_12 != singleton(U_14) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_10,sK1(U_15,U_13))],[f_3_3]) ).
fof(f_3_5,plain,
( ! [U_15,U_13] :
( U_13 = singleton(U_15)
| ( ~ in(sK2(U_15,U_13),U_13)
& sK2(U_15,U_13) = U_15 )
| ( sK1(U_15,U_13) != U_15
& in(sK1(U_15,U_13),U_13) ) )
& ! [U_14,U_12] :
( ( ! [U_9] :
( in(U_9,U_12)
| U_9 != U_14 )
& ! [U_8] :
( U_8 = U_14
| ~ in(U_8,U_12) ) )
| U_12 != singleton(U_14) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_11,sK2(U_15,U_13))],[f_3_4]) ).
cnf(f_3_6,plain,
( U_8 = U_14
| ~ in(U_8,U_12)
| U_12 != singleton(U_14) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_7,plain,
( in(U_9,U_12)
| U_9 != U_14
| U_12 != singleton(U_14) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_8,plain,
( sK2(U_15,U_13) = U_15
| in(sK1(U_15,U_13),U_13)
| U_13 = singleton(U_15) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_9,plain,
( ~ in(sK2(U_15,U_13),U_13)
| in(sK1(U_15,U_13),U_13)
| U_13 = singleton(U_15) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_10,plain,
( sK2(U_15,U_13) = U_15
| sK1(U_15,U_13) != U_15
| U_13 = singleton(U_15) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_11,plain,
( ~ in(sK2(U_15,U_13),U_13)
| sK1(U_15,U_13) != U_15
| U_13 = singleton(U_15) ),
inference(clausify,[status(thm)],[f_3_5]) ).
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_17,U_16] : ordered_pair(U_17,U_16) = unordered_pair(unordered_pair(U_17,U_16),singleton(U_17)),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
ordered_pair(U_17,U_16) = unordered_pair(unordered_pair(U_17,U_16),singleton(U_17)),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc1_zfmisc_1]) ).
fof(f_5_2,plain,
! [U_19,U_18] : ~ empty(ordered_pair(U_19,U_18)),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
~ empty(ordered_pair(U_19,U_18)),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_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_6_2,plain,
! [U_23,U_22,U_21,U_20] :
( ( in(ordered_pair(U_23,U_22),cartesian_product2(U_21,U_20))
| ~ in(U_22,U_20)
| ~ in(U_23,U_21) )
& ( ( in(U_22,U_20)
& in(U_23,U_21) )
| ~ in(ordered_pair(U_23,U_22),cartesian_product2(U_21,U_20)) ) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_31,U_29,U_27,U_25] :
( in(ordered_pair(U_31,U_29),cartesian_product2(U_27,U_25))
| ~ in(U_29,U_25)
| ~ in(U_31,U_27) )
& ! [U_30,U_28,U_26,U_24] :
( ( in(U_28,U_24)
& in(U_30,U_26) )
| ~ in(ordered_pair(U_30,U_28),cartesian_product2(U_26,U_24)) ) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
cnf(f_6_4,plain,
( in(U_30,U_26)
| ~ in(ordered_pair(U_30,U_28),cartesian_product2(U_26,U_24)) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_5,plain,
( in(U_28,U_24)
| ~ in(ordered_pair(U_30,U_28),cartesian_product2(U_26,U_24)) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_6,plain,
( in(ordered_pair(U_31,U_29),cartesian_product2(U_27,U_25))
| ~ in(U_29,U_25)
| ~ in(U_31,U_27) ),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_7_2,plain,
? [U_32] : empty(U_32),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
empty(sK3),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_32,sK3)],[f_7_2]) ).
cnf(f_7_4,plain,
empty(sK3),
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_33] : ~ empty(U_33),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
~ empty(sK4),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_33,sK4)],[f_8_2]) ).
cnf(f_8_4,plain,
~ empty(sK4),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,negated_conjecture,
~ ! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,singleton(D)))
<=> ( B = D
& in(A,C) ) ),
inference(negate,[status(cth)],[t129_zfmisc_1]) ).
fof(f_9_2,negated_conjecture,
? [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)],[f_9_1]) ).
fof(f_9_3,negated_conjecture,
? [U_37,U_36,U_35,U_34] :
( ( ~ in(ordered_pair(U_37,U_36),cartesian_product2(U_35,singleton(U_34)))
& U_36 = U_34
& in(U_37,U_35) )
| ( ( U_36 != U_34
| ~ in(U_37,U_35) )
& in(ordered_pair(U_37,U_36),cartesian_product2(U_35,singleton(U_34))) ) ),
inference(variable_rename,[status(thm)],[f_9_2]) ).
fof(f_9_4,negated_conjecture,
( ? [U_45,U_43,U_41,U_39] :
( ~ in(ordered_pair(U_45,U_43),cartesian_product2(U_41,singleton(U_39)))
& U_43 = U_39
& in(U_45,U_41) )
| ? [U_44,U_42,U_40,U_38] :
( ( U_42 != U_38
| ~ in(U_44,U_40) )
& in(ordered_pair(U_44,U_42),cartesian_product2(U_40,singleton(U_38))) ) ),
inference(miniscope,[status(thm)],[f_9_3]) ).
fof(f_9_5,negated_conjecture,
( ? [U_45,U_43,U_41,U_39] :
( ~ in(ordered_pair(U_45,U_43),cartesian_product2(U_41,singleton(U_39)))
& U_43 = U_39
& in(U_45,U_41) )
| ? [U_42,U_40,U_38] :
( ( U_42 != U_38
| ~ in(sK5,U_40) )
& in(ordered_pair(sK5,U_42),cartesian_product2(U_40,singleton(U_38))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_44,sK5)],[f_9_4]) ).
fof(f_9_6,negated_conjecture,
( ? [U_45,U_43,U_41,U_39] :
( ~ in(ordered_pair(U_45,U_43),cartesian_product2(U_41,singleton(U_39)))
& U_43 = U_39
& in(U_45,U_41) )
| ? [U_40,U_38] :
( ( sK6 != U_38
| ~ in(sK5,U_40) )
& in(ordered_pair(sK5,sK6),cartesian_product2(U_40,singleton(U_38))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_42,sK6)],[f_9_5]) ).
fof(f_9_7,negated_conjecture,
( ? [U_45,U_43,U_41,U_39] :
( ~ in(ordered_pair(U_45,U_43),cartesian_product2(U_41,singleton(U_39)))
& U_43 = U_39
& in(U_45,U_41) )
| ? [U_38] :
( ( sK6 != U_38
| ~ in(sK5,sK7) )
& in(ordered_pair(sK5,sK6),cartesian_product2(sK7,singleton(U_38))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_40,sK7)],[f_9_6]) ).
fof(f_9_8,negated_conjecture,
( ? [U_45,U_43,U_41,U_39] :
( ~ in(ordered_pair(U_45,U_43),cartesian_product2(U_41,singleton(U_39)))
& U_43 = U_39
& in(U_45,U_41) )
| ( ( sK6 != sK8
| ~ in(sK5,sK7) )
& in(ordered_pair(sK5,sK6),cartesian_product2(sK7,singleton(sK8))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_38,sK8)],[f_9_7]) ).
fof(f_9_9,negated_conjecture,
( ? [U_43,U_41,U_39] :
( ~ in(ordered_pair(sK9,U_43),cartesian_product2(U_41,singleton(U_39)))
& U_43 = U_39
& in(sK9,U_41) )
| ( ( sK6 != sK8
| ~ in(sK5,sK7) )
& in(ordered_pair(sK5,sK6),cartesian_product2(sK7,singleton(sK8))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_45,sK9)],[f_9_8]) ).
fof(f_9_10,negated_conjecture,
( ? [U_41,U_39] :
( ~ in(ordered_pair(sK9,sK10),cartesian_product2(U_41,singleton(U_39)))
& sK10 = U_39
& in(sK9,U_41) )
| ( ( sK6 != sK8
| ~ in(sK5,sK7) )
& in(ordered_pair(sK5,sK6),cartesian_product2(sK7,singleton(sK8))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_43,sK10)],[f_9_9]) ).
fof(f_9_11,negated_conjecture,
( ? [U_39] :
( ~ in(ordered_pair(sK9,sK10),cartesian_product2(sK11,singleton(U_39)))
& sK10 = U_39
& in(sK9,sK11) )
| ( ( sK6 != sK8
| ~ in(sK5,sK7) )
& in(ordered_pair(sK5,sK6),cartesian_product2(sK7,singleton(sK8))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_41,sK11)],[f_9_10]) ).
fof(f_9_12,negated_conjecture,
( ( ~ in(ordered_pair(sK9,sK10),cartesian_product2(sK11,singleton(sK12)))
& sK10 = sK12
& in(sK9,sK11) )
| ( ( sK6 != sK8
| ~ in(sK5,sK7) )
& in(ordered_pair(sK5,sK6),cartesian_product2(sK7,singleton(sK8))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_39,sK12)],[f_9_11]) ).
fof(f_9_13,negated_conjecture,
( ( ~ in(ordered_pair(sK9,sK10),cartesian_product2(sK11,singleton(sK12)))
| ~ sP1 )
& ( sK10 = sK12
| ~ sP1 )
& ( in(sK9,sK11)
| ~ sP1 )
& ( sK6 != sK8
| ~ in(sK5,sK7)
| ~ sP0 )
& ( in(ordered_pair(sK5,sK6),cartesian_product2(sK7,singleton(sK8)))
| ~ sP0 )
& ( sP1
| sP0 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1])],[f_9_12]) ).
cnf(f_9_14,negated_conjecture,
( sP1
| sP0 ),
inference(clausify,[status(thm)],[f_9_13]) ).
cnf(f_9_15,negated_conjecture,
( in(ordered_pair(sK5,sK6),cartesian_product2(sK7,singleton(sK8)))
| ~ sP0 ),
inference(clausify,[status(thm)],[f_9_13]) ).
cnf(f_9_16,negated_conjecture,
( sK6 != sK8
| ~ in(sK5,sK7)
| ~ sP0 ),
inference(clausify,[status(thm)],[f_9_13]) ).
cnf(f_9_17,negated_conjecture,
( in(sK9,sK11)
| ~ sP1 ),
inference(clausify,[status(thm)],[f_9_13]) ).
cnf(f_9_18,negated_conjecture,
( sK10 = sK12
| ~ sP1 ),
inference(clausify,[status(thm)],[f_9_13]) ).
cnf(f_9_19,negated_conjecture,
( ~ in(ordered_pair(sK9,sK10),cartesian_product2(sK11,singleton(sK12)))
| ~ sP1 ),
inference(clausify,[status(thm)],[f_9_13]) ).
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,
( singleton(Eq_x_0) = singleton(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,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_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,Eq_x_1) = sK1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( sK2(Eq_x_0,Eq_x_1) = sK2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,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_11,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
% 0.00/0.01 % Problem : SET976+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.01 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.02 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Sat Sep 19 23:09:07 UTC 2026
% 0.02/0.29 % CPUTime :
% 0.66/0.92 % SZS status Theorem for theBenchmark
% 0.66/0.92 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------