%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET941+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 : n007.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 08:57:51 AM UTC 2026
% Result : Theorem 0.14s 5.66s
% Output : Proof 0.14s
% 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(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(d4_tarski,axiom,
! [A,B] :
( B = union(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( in(D,A)
& in(C,D) ) ) ),
file('theBenchmark.p',d4_tarski) ).
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(t94_zfmisc_1,conjecture,
! [A,B] :
( ! [C] :
( in(C,A)
=> subset(C,B) )
=> subset(union(A),B) ),
file('theBenchmark.p',t94_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] :
( ( subset(A,B)
| ? [C] :
( ~ in(C,B)
& in(C,A) ) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(fof_nnf,[status(thm)],[d3_tarski]) ).
fof(f_2_2,plain,
! [U_5,U_4] :
( ( subset(U_5,U_4)
| ? [U_3] :
( ~ in(U_3,U_4)
& in(U_3,U_5) ) )
& ( ! [U_2] :
( in(U_2,U_4)
| ~ in(U_2,U_5) )
| ~ subset(U_5,U_4) ) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( ! [U_9,U_7] :
( subset(U_9,U_7)
| ? [U_3] :
( ~ in(U_3,U_7)
& in(U_3,U_9) ) )
& ! [U_8,U_6] :
( ! [U_2] :
( in(U_2,U_6)
| ~ in(U_2,U_8) )
| ~ subset(U_8,U_6) ) ),
inference(miniscope,[status(thm)],[f_2_2]) ).
fof(f_2_4,plain,
( ! [U_9,U_7] :
( subset(U_9,U_7)
| ( ~ in(sK1(U_9,U_7),U_7)
& in(sK1(U_9,U_7),U_9) ) )
& ! [U_8,U_6] :
( ! [U_2] :
( in(U_2,U_6)
| ~ in(U_2,U_8) )
| ~ subset(U_8,U_6) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_3,sK1(U_9,U_7))],[f_2_3]) ).
cnf(f_2_5,plain,
( in(U_2,U_6)
| ~ in(U_2,U_8)
| ~ subset(U_8,U_6) ),
inference(clausify,[status(thm)],[f_2_4]) ).
cnf(f_2_6,plain,
( in(sK1(U_9,U_7),U_9)
| subset(U_9,U_7) ),
inference(clausify,[status(thm)],[f_2_4]) ).
cnf(f_2_7,plain,
( ~ in(sK1(U_9,U_7),U_7)
| subset(U_9,U_7) ),
inference(clausify,[status(thm)],[f_2_4]) ).
fof(f_3_1,plain,
! [A,B] :
( ( B = union(A)
| ? [C] :
( ( ~ in(C,B)
& ? [D] :
( in(D,A)
& in(C,D) ) )
| ( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| ! [D] :
( ~ in(D,A)
| ~ in(C,D) ) )
& ( ? [D] :
( in(D,A)
& in(C,D) )
| ~ in(C,B) ) )
| B != union(A) ) ),
inference(fof_nnf,[status(thm)],[d4_tarski]) ).
fof(f_3_2,plain,
! [U_17,U_16] :
( ( U_16 = union(U_17)
| ? [U_15] :
( ( ~ in(U_15,U_16)
& ? [U_14] :
( in(U_14,U_17)
& in(U_15,U_14) ) )
| ( ! [U_13] :
( ~ in(U_13,U_17)
| ~ in(U_15,U_13) )
& in(U_15,U_16) ) ) )
& ( ! [U_12] :
( ( in(U_12,U_16)
| ! [U_11] :
( ~ in(U_11,U_17)
| ~ in(U_12,U_11) ) )
& ( ? [U_10] :
( in(U_10,U_17)
& in(U_12,U_10) )
| ~ in(U_12,U_16) ) )
| U_16 != union(U_17) ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_25,U_23] :
( U_23 = union(U_25)
| ? [U_21] :
( ~ in(U_21,U_23)
& ? [U_14] :
( in(U_14,U_25)
& in(U_21,U_14) ) )
| ? [U_20] :
( ! [U_13] :
( ~ in(U_13,U_25)
| ~ in(U_20,U_13) )
& in(U_20,U_23) ) )
& ! [U_24,U_22] :
( ( ! [U_19] :
( in(U_19,U_22)
| ! [U_11] :
( ~ in(U_11,U_24)
| ~ in(U_19,U_11) ) )
& ! [U_18] :
( ? [U_10] :
( in(U_10,U_24)
& in(U_18,U_10) )
| ~ in(U_18,U_22) ) )
| U_22 != union(U_24) ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
fof(f_3_4,plain,
( ! [U_25,U_23] :
( U_23 = union(U_25)
| ? [U_21] :
( ~ in(U_21,U_23)
& ? [U_14] :
( in(U_14,U_25)
& in(U_21,U_14) ) )
| ? [U_20] :
( ! [U_13] :
( ~ in(U_13,U_25)
| ~ in(U_20,U_13) )
& in(U_20,U_23) ) )
& ! [U_24,U_22] :
( ( ! [U_19] :
( in(U_19,U_22)
| ! [U_11] :
( ~ in(U_11,U_24)
| ~ in(U_19,U_11) ) )
& ! [U_18] :
( ( in(sK2(U_24,U_22,U_18),U_24)
& in(U_18,sK2(U_24,U_22,U_18)) )
| ~ in(U_18,U_22) ) )
| U_22 != union(U_24) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_10,sK2(U_24,U_22,U_18))],[f_3_3]) ).
fof(f_3_5,plain,
( ! [U_25,U_23] :
( U_23 = union(U_25)
| ? [U_21] :
( ~ in(U_21,U_23)
& ? [U_14] :
( in(U_14,U_25)
& in(U_21,U_14) ) )
| ( ! [U_13] :
( ~ in(U_13,U_25)
| ~ in(sK3(U_25,U_23),U_13) )
& in(sK3(U_25,U_23),U_23) ) )
& ! [U_24,U_22] :
( ( ! [U_19] :
( in(U_19,U_22)
| ! [U_11] :
( ~ in(U_11,U_24)
| ~ in(U_19,U_11) ) )
& ! [U_18] :
( ( in(sK2(U_24,U_22,U_18),U_24)
& in(U_18,sK2(U_24,U_22,U_18)) )
| ~ in(U_18,U_22) ) )
| U_22 != union(U_24) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_20,sK3(U_25,U_23))],[f_3_4]) ).
fof(f_3_6,plain,
( ! [U_25,U_23] :
( U_23 = union(U_25)
| ( ~ in(sK4(U_25,U_23),U_23)
& ? [U_14] :
( in(U_14,U_25)
& in(sK4(U_25,U_23),U_14) ) )
| ( ! [U_13] :
( ~ in(U_13,U_25)
| ~ in(sK3(U_25,U_23),U_13) )
& in(sK3(U_25,U_23),U_23) ) )
& ! [U_24,U_22] :
( ( ! [U_19] :
( in(U_19,U_22)
| ! [U_11] :
( ~ in(U_11,U_24)
| ~ in(U_19,U_11) ) )
& ! [U_18] :
( ( in(sK2(U_24,U_22,U_18),U_24)
& in(U_18,sK2(U_24,U_22,U_18)) )
| ~ in(U_18,U_22) ) )
| U_22 != union(U_24) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_21,sK4(U_25,U_23))],[f_3_5]) ).
fof(f_3_7,plain,
( ! [U_25,U_23] :
( U_23 = union(U_25)
| ( ~ in(sK4(U_25,U_23),U_23)
& in(sK5(U_25,U_23),U_25)
& in(sK4(U_25,U_23),sK5(U_25,U_23)) )
| ( ! [U_13] :
( ~ in(U_13,U_25)
| ~ in(sK3(U_25,U_23),U_13) )
& in(sK3(U_25,U_23),U_23) ) )
& ! [U_24,U_22] :
( ( ! [U_19] :
( in(U_19,U_22)
| ! [U_11] :
( ~ in(U_11,U_24)
| ~ in(U_19,U_11) ) )
& ! [U_18] :
( ( in(sK2(U_24,U_22,U_18),U_24)
& in(U_18,sK2(U_24,U_22,U_18)) )
| ~ in(U_18,U_22) ) )
| U_22 != union(U_24) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_14,sK5(U_25,U_23))],[f_3_6]) ).
cnf(f_3_8,plain,
( in(U_18,sK2(U_24,U_22,U_18))
| ~ in(U_18,U_22)
| U_22 != union(U_24) ),
inference(clausify,[status(thm)],[f_3_7]) ).
cnf(f_3_9,plain,
( in(sK2(U_24,U_22,U_18),U_24)
| ~ in(U_18,U_22)
| U_22 != union(U_24) ),
inference(clausify,[status(thm)],[f_3_7]) ).
cnf(f_3_10,plain,
( in(U_19,U_22)
| ~ in(U_11,U_24)
| ~ in(U_19,U_11)
| U_22 != union(U_24) ),
inference(clausify,[status(thm)],[f_3_7]) ).
cnf(f_3_11,plain,
( in(sK4(U_25,U_23),sK5(U_25,U_23))
| in(sK3(U_25,U_23),U_23)
| U_23 = union(U_25) ),
inference(clausify,[status(thm)],[f_3_7]) ).
cnf(f_3_12,plain,
( in(sK5(U_25,U_23),U_25)
| in(sK3(U_25,U_23),U_23)
| U_23 = union(U_25) ),
inference(clausify,[status(thm)],[f_3_7]) ).
cnf(f_3_13,plain,
( ~ in(sK4(U_25,U_23),U_23)
| in(sK3(U_25,U_23),U_23)
| U_23 = union(U_25) ),
inference(clausify,[status(thm)],[f_3_7]) ).
cnf(f_3_14,plain,
( in(sK4(U_25,U_23),sK5(U_25,U_23))
| ~ in(U_13,U_25)
| ~ in(sK3(U_25,U_23),U_13)
| U_23 = union(U_25) ),
inference(clausify,[status(thm)],[f_3_7]) ).
cnf(f_3_15,plain,
( in(sK5(U_25,U_23),U_25)
| ~ in(U_13,U_25)
| ~ in(sK3(U_25,U_23),U_13)
| U_23 = union(U_25) ),
inference(clausify,[status(thm)],[f_3_7]) ).
cnf(f_3_16,plain,
( ~ in(sK4(U_25,U_23),U_23)
| ~ in(U_13,U_25)
| ~ in(sK3(U_25,U_23),U_13)
| U_23 = union(U_25) ),
inference(clausify,[status(thm)],[f_3_7]) ).
fof(f_4_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_4_2,plain,
? [U_26] : empty(U_26),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
empty(sK6),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_26,sK6)],[f_4_2]) ).
cnf(f_4_4,plain,
empty(sK6),
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_27] : ~ empty(U_27),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
~ empty(sK7),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_27,sK7)],[f_5_2]) ).
cnf(f_5_4,plain,
~ empty(sK7),
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_29,U_28] : subset(U_29,U_29),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_29] : subset(U_29,U_29),
inference(miniscope,[status(thm)],[f_6_2]) ).
cnf(f_6_4,plain,
subset(U_29,U_29),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,negated_conjecture,
~ ! [A,B] :
( ! [C] :
( in(C,A)
=> subset(C,B) )
=> subset(union(A),B) ),
inference(negate,[status(cth)],[t94_zfmisc_1]) ).
fof(f_7_2,negated_conjecture,
? [A,B] :
( ~ subset(union(A),B)
& ! [C] :
( subset(C,B)
| ~ in(C,A) ) ),
inference(fof_nnf,[status(thm)],[f_7_1]) ).
fof(f_7_3,negated_conjecture,
? [U_32,U_31] :
( ~ subset(union(U_32),U_31)
& ! [U_30] :
( subset(U_30,U_31)
| ~ in(U_30,U_32) ) ),
inference(variable_rename,[status(thm)],[f_7_2]) ).
fof(f_7_4,negated_conjecture,
? [U_31] :
( ~ subset(union(sK8),U_31)
& ! [U_30] :
( subset(U_30,U_31)
| ~ in(U_30,sK8) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_32,sK8)],[f_7_3]) ).
fof(f_7_5,negated_conjecture,
( ~ subset(union(sK8),sK9)
& ! [U_30] :
( subset(U_30,sK9)
| ~ in(U_30,sK8) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_31,sK9)],[f_7_4]) ).
fof(f_7_6,negated_conjecture,
( ~ subset(union(sK8),sK9)
& ! [U_30] :
( subset(U_30,sK9)
| ~ in(U_30,sK8) ) ),
inference(definitional_conversion,[status(esa)],[f_7_5]) ).
cnf(f_7_7,negated_conjecture,
( subset(U_30,sK9)
| ~ in(U_30,sK8) ),
inference(clausify,[status(thm)],[f_7_6]) ).
cnf(f_7_8,negated_conjecture,
~ subset(union(sK8),sK9),
inference(clausify,[status(thm)],[f_7_6]) ).
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,
( union(Eq_x_0) = union(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,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_6,axiom,
( sK2(Eq_x_0,Eq_x_1,Eq_x_2) = sK2(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( sK3(Eq_x_0,Eq_x_1) = sK3(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,
( sK4(Eq_x_0,Eq_x_1) = sK4(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,
( sK5(Eq_x_0,Eq_x_1) = sK5(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,
( 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(equality_12,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 : SET941+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
% 0.11/5.38 % Computer : n007.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Sat Sep 19 23:05:54 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.14/5.66 % SZS status Theorem for theBenchmark
% 0.14/5.66 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------