%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET931+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 : n015.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 08:57:50 AM UTC 2026
% Result : Theorem 0.10s 0.44s
% 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(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
fof(l46_zfmisc_1,axiom,
! [A,B,C] :
( subset(A,unordered_pair(B,C))
<=> ~ ( A != unordered_pair(B,C)
& A != singleton(C)
& A != singleton(B)
& A != empty_set ) ),
file('theBenchmark.p',l46_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(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t37_xboole_1,axiom,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('theBenchmark.p',t37_xboole_1) ).
fof(t75_zfmisc_1,conjecture,
! [A,B,C] :
( set_difference(A,unordered_pair(B,C)) = empty_set
<=> ~ ( A != unordered_pair(B,C)
& A != singleton(C)
& A != singleton(B)
& A != empty_set ) ),
file('theBenchmark.p',t75_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,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_2_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_2_1]) ).
fof(f_3_1,plain,
! [A,B,C] :
( ( subset(A,unordered_pair(B,C))
| ( A != unordered_pair(B,C)
& A != singleton(C)
& A != singleton(B)
& A != empty_set ) )
& ( A = unordered_pair(B,C)
| A = singleton(C)
| A = singleton(B)
| A = empty_set
| ~ subset(A,unordered_pair(B,C)) ) ),
inference(fof_nnf,[status(thm)],[l46_zfmisc_1]) ).
fof(f_3_2,plain,
! [U_4,U_3,U_2] :
( ( subset(U_4,unordered_pair(U_3,U_2))
| ( U_4 != unordered_pair(U_3,U_2)
& U_4 != singleton(U_2)
& U_4 != singleton(U_3)
& U_4 != empty_set ) )
& ( U_4 = unordered_pair(U_3,U_2)
| U_4 = singleton(U_2)
| U_4 = singleton(U_3)
| U_4 = empty_set
| ~ subset(U_4,unordered_pair(U_3,U_2)) ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_10,U_8,U_6] :
( subset(U_10,unordered_pair(U_8,U_6))
| ( U_10 != unordered_pair(U_8,U_6)
& U_10 != singleton(U_6)
& U_10 != singleton(U_8)
& U_10 != empty_set ) )
& ! [U_9,U_7,U_5] :
( U_9 = unordered_pair(U_7,U_5)
| U_9 = singleton(U_5)
| U_9 = singleton(U_7)
| U_9 = empty_set
| ~ subset(U_9,unordered_pair(U_7,U_5)) ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
cnf(f_3_4,plain,
( U_9 = unordered_pair(U_7,U_5)
| U_9 = singleton(U_5)
| U_9 = singleton(U_7)
| U_9 = empty_set
| ~ subset(U_9,unordered_pair(U_7,U_5)) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_5,plain,
( U_10 != empty_set
| subset(U_10,unordered_pair(U_8,U_6)) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_6,plain,
( U_10 != singleton(U_8)
| subset(U_10,unordered_pair(U_8,U_6)) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_7,plain,
( U_10 != singleton(U_6)
| subset(U_10,unordered_pair(U_8,U_6)) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_8,plain,
( U_10 != unordered_pair(U_8,U_6)
| subset(U_10,unordered_pair(U_8,U_6)) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_4_2,plain,
? [U_11] : empty(U_11),
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_11,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_12] : ~ empty(U_12),
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_12,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] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_6_2,plain,
! [U_14,U_13] : subset(U_14,U_14),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_14] : subset(U_14,U_14),
inference(miniscope,[status(thm)],[f_6_2]) ).
cnf(f_6_4,plain,
subset(U_14,U_14),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
! [A,B] :
( ( set_difference(A,B) = empty_set
| ~ subset(A,B) )
& ( subset(A,B)
| set_difference(A,B) != empty_set ) ),
inference(fof_nnf,[status(thm)],[t37_xboole_1]) ).
fof(f_7_2,plain,
! [U_16,U_15] :
( ( set_difference(U_16,U_15) = empty_set
| ~ subset(U_16,U_15) )
& ( subset(U_16,U_15)
| set_difference(U_16,U_15) != empty_set ) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( ! [U_20,U_18] :
( set_difference(U_20,U_18) = empty_set
| ~ subset(U_20,U_18) )
& ! [U_19,U_17] :
( subset(U_19,U_17)
| set_difference(U_19,U_17) != empty_set ) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
cnf(f_7_4,plain,
( subset(U_19,U_17)
| set_difference(U_19,U_17) != empty_set ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_5,plain,
( set_difference(U_20,U_18) = empty_set
| ~ subset(U_20,U_18) ),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,negated_conjecture,
~ ! [A,B,C] :
( set_difference(A,unordered_pair(B,C)) = empty_set
<=> ~ ( A != unordered_pair(B,C)
& A != singleton(C)
& A != singleton(B)
& A != empty_set ) ),
inference(negate,[status(cth)],[t75_zfmisc_1]) ).
fof(f_8_2,negated_conjecture,
? [A,B,C] :
( ( set_difference(A,unordered_pair(B,C)) != empty_set
& ( A = unordered_pair(B,C)
| A = singleton(C)
| A = singleton(B)
| A = empty_set ) )
| ( A != unordered_pair(B,C)
& A != singleton(C)
& A != singleton(B)
& A != empty_set
& set_difference(A,unordered_pair(B,C)) = empty_set ) ),
inference(fof_nnf,[status(thm)],[f_8_1]) ).
fof(f_8_3,negated_conjecture,
? [U_23,U_22,U_21] :
( ( set_difference(U_23,unordered_pair(U_22,U_21)) != empty_set
& ( U_23 = unordered_pair(U_22,U_21)
| U_23 = singleton(U_21)
| U_23 = singleton(U_22)
| U_23 = empty_set ) )
| ( U_23 != unordered_pair(U_22,U_21)
& U_23 != singleton(U_21)
& U_23 != singleton(U_22)
& U_23 != empty_set
& set_difference(U_23,unordered_pair(U_22,U_21)) = empty_set ) ),
inference(variable_rename,[status(thm)],[f_8_2]) ).
fof(f_8_4,negated_conjecture,
( ? [U_29,U_27,U_25] :
( set_difference(U_29,unordered_pair(U_27,U_25)) != empty_set
& ( U_29 = unordered_pair(U_27,U_25)
| U_29 = singleton(U_25)
| U_29 = singleton(U_27)
| U_29 = empty_set ) )
| ? [U_28,U_26,U_24] :
( U_28 != unordered_pair(U_26,U_24)
& U_28 != singleton(U_24)
& U_28 != singleton(U_26)
& U_28 != empty_set
& set_difference(U_28,unordered_pair(U_26,U_24)) = empty_set ) ),
inference(miniscope,[status(thm)],[f_8_3]) ).
fof(f_8_5,negated_conjecture,
( ? [U_29,U_27,U_25] :
( set_difference(U_29,unordered_pair(U_27,U_25)) != empty_set
& ( U_29 = unordered_pair(U_27,U_25)
| U_29 = singleton(U_25)
| U_29 = singleton(U_27)
| U_29 = empty_set ) )
| ? [U_26,U_24] :
( sK3 != unordered_pair(U_26,U_24)
& sK3 != singleton(U_24)
& sK3 != singleton(U_26)
& sK3 != empty_set
& set_difference(sK3,unordered_pair(U_26,U_24)) = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_28,sK3)],[f_8_4]) ).
fof(f_8_6,negated_conjecture,
( ? [U_29,U_27,U_25] :
( set_difference(U_29,unordered_pair(U_27,U_25)) != empty_set
& ( U_29 = unordered_pair(U_27,U_25)
| U_29 = singleton(U_25)
| U_29 = singleton(U_27)
| U_29 = empty_set ) )
| ? [U_24] :
( sK3 != unordered_pair(sK4,U_24)
& sK3 != singleton(U_24)
& sK3 != singleton(sK4)
& sK3 != empty_set
& set_difference(sK3,unordered_pair(sK4,U_24)) = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_26,sK4)],[f_8_5]) ).
fof(f_8_7,negated_conjecture,
( ? [U_29,U_27,U_25] :
( set_difference(U_29,unordered_pair(U_27,U_25)) != empty_set
& ( U_29 = unordered_pair(U_27,U_25)
| U_29 = singleton(U_25)
| U_29 = singleton(U_27)
| U_29 = empty_set ) )
| ( sK3 != unordered_pair(sK4,sK5)
& sK3 != singleton(sK5)
& sK3 != singleton(sK4)
& sK3 != empty_set
& set_difference(sK3,unordered_pair(sK4,sK5)) = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_24,sK5)],[f_8_6]) ).
fof(f_8_8,negated_conjecture,
( ? [U_27,U_25] :
( set_difference(sK6,unordered_pair(U_27,U_25)) != empty_set
& ( sK6 = unordered_pair(U_27,U_25)
| sK6 = singleton(U_25)
| sK6 = singleton(U_27)
| sK6 = empty_set ) )
| ( sK3 != unordered_pair(sK4,sK5)
& sK3 != singleton(sK5)
& sK3 != singleton(sK4)
& sK3 != empty_set
& set_difference(sK3,unordered_pair(sK4,sK5)) = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_29,sK6)],[f_8_7]) ).
fof(f_8_9,negated_conjecture,
( ? [U_25] :
( set_difference(sK6,unordered_pair(sK7,U_25)) != empty_set
& ( sK6 = unordered_pair(sK7,U_25)
| sK6 = singleton(U_25)
| sK6 = singleton(sK7)
| sK6 = empty_set ) )
| ( sK3 != unordered_pair(sK4,sK5)
& sK3 != singleton(sK5)
& sK3 != singleton(sK4)
& sK3 != empty_set
& set_difference(sK3,unordered_pair(sK4,sK5)) = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_27,sK7)],[f_8_8]) ).
fof(f_8_10,negated_conjecture,
( ( set_difference(sK6,unordered_pair(sK7,sK8)) != empty_set
& ( sK6 = unordered_pair(sK7,sK8)
| sK6 = singleton(sK8)
| sK6 = singleton(sK7)
| sK6 = empty_set ) )
| ( sK3 != unordered_pair(sK4,sK5)
& sK3 != singleton(sK5)
& sK3 != singleton(sK4)
& sK3 != empty_set
& set_difference(sK3,unordered_pair(sK4,sK5)) = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_25,sK8)],[f_8_9]) ).
fof(f_8_11,negated_conjecture,
( ( set_difference(sK6,unordered_pair(sK7,sK8)) != empty_set
| ~ sP1 )
& ( sK6 = unordered_pair(sK7,sK8)
| sK6 = singleton(sK8)
| sK6 = singleton(sK7)
| sK6 = empty_set
| ~ sP1 )
& ( sK3 != unordered_pair(sK4,sK5)
| ~ sP0 )
& ( sK3 != singleton(sK5)
| ~ sP0 )
& ( sK3 != singleton(sK4)
| ~ sP0 )
& ( sK3 != empty_set
| ~ sP0 )
& ( set_difference(sK3,unordered_pair(sK4,sK5)) = empty_set
| ~ sP0 )
& ( sP1
| sP0 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1])],[f_8_10]) ).
cnf(f_8_12,negated_conjecture,
( sP1
| sP0 ),
inference(clausify,[status(thm)],[f_8_11]) ).
cnf(f_8_13,negated_conjecture,
( set_difference(sK3,unordered_pair(sK4,sK5)) = empty_set
| ~ sP0 ),
inference(clausify,[status(thm)],[f_8_11]) ).
cnf(f_8_14,negated_conjecture,
( sK3 != empty_set
| ~ sP0 ),
inference(clausify,[status(thm)],[f_8_11]) ).
cnf(f_8_15,negated_conjecture,
( sK3 != singleton(sK4)
| ~ sP0 ),
inference(clausify,[status(thm)],[f_8_11]) ).
cnf(f_8_16,negated_conjecture,
( sK3 != singleton(sK5)
| ~ sP0 ),
inference(clausify,[status(thm)],[f_8_11]) ).
cnf(f_8_17,negated_conjecture,
( sK3 != unordered_pair(sK4,sK5)
| ~ sP0 ),
inference(clausify,[status(thm)],[f_8_11]) ).
cnf(f_8_18,negated_conjecture,
( sK6 = unordered_pair(sK7,sK8)
| sK6 = singleton(sK8)
| sK6 = singleton(sK7)
| sK6 = empty_set
| ~ sP1 ),
inference(clausify,[status(thm)],[f_8_11]) ).
cnf(f_8_19,negated_conjecture,
( set_difference(sK6,unordered_pair(sK7,sK8)) != empty_set
| ~ sP1 ),
inference(clausify,[status(thm)],[f_8_11]) ).
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,
( set_difference(Eq_x_0,Eq_x_1) = set_difference(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,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_8,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
% 0.00/0.02 % Problem : SET931+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % 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 : n015.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 23:11:04 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.44 % SZS status Theorem for theBenchmark
% 0.10/0.44 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------