%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU144+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 08:58:11 AM UTC 2026
% Result : Theorem 19.25s 19.56s
% Output : Proof 19.63s
% 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(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('theBenchmark.p',d1_tarski) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(dt_k1_tarski,axiom,
$true,
file('theBenchmark.p',dt_k1_tarski) ).
fof(l2_zfmisc_1,conjecture,
! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ),
file('theBenchmark.p',l2_zfmisc_1) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
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] :
( ( 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_2_2,plain,
! [U_5,U_4] :
( ( U_4 = singleton(U_5)
| ? [U_3] :
( ( ~ in(U_3,U_4)
& U_3 = U_5 )
| ( U_3 != U_5
& in(U_3,U_4) ) ) )
& ( ! [U_2] :
( ( in(U_2,U_4)
| U_2 != U_5 )
& ( U_2 = U_5
| ~ in(U_2,U_4) ) )
| U_4 != singleton(U_5) ) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( ! [U_13,U_11] :
( U_11 = singleton(U_13)
| ? [U_9] :
( ~ in(U_9,U_11)
& U_9 = U_13 )
| ? [U_8] :
( U_8 != U_13
& in(U_8,U_11) ) )
& ! [U_12,U_10] :
( ( ! [U_7] :
( in(U_7,U_10)
| U_7 != U_12 )
& ! [U_6] :
( U_6 = U_12
| ~ in(U_6,U_10) ) )
| U_10 != singleton(U_12) ) ),
inference(miniscope,[status(thm)],[f_2_2]) ).
fof(f_2_4,plain,
( ! [U_13,U_11] :
( U_11 = singleton(U_13)
| ? [U_9] :
( ~ in(U_9,U_11)
& U_9 = U_13 )
| ( sK1(U_13,U_11) != U_13
& in(sK1(U_13,U_11),U_11) ) )
& ! [U_12,U_10] :
( ( ! [U_7] :
( in(U_7,U_10)
| U_7 != U_12 )
& ! [U_6] :
( U_6 = U_12
| ~ in(U_6,U_10) ) )
| U_10 != singleton(U_12) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_8,sK1(U_13,U_11))],[f_2_3]) ).
fof(f_2_5,plain,
( ! [U_13,U_11] :
( U_11 = singleton(U_13)
| ( ~ in(sK2(U_13,U_11),U_11)
& sK2(U_13,U_11) = U_13 )
| ( sK1(U_13,U_11) != U_13
& in(sK1(U_13,U_11),U_11) ) )
& ! [U_12,U_10] :
( ( ! [U_7] :
( in(U_7,U_10)
| U_7 != U_12 )
& ! [U_6] :
( U_6 = U_12
| ~ in(U_6,U_10) ) )
| U_10 != singleton(U_12) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_9,sK2(U_13,U_11))],[f_2_4]) ).
cnf(f_2_6,plain,
( U_6 = U_12
| ~ in(U_6,U_10)
| U_10 != singleton(U_12) ),
inference(clausify,[status(thm)],[f_2_5]) ).
cnf(f_2_7,plain,
( in(U_7,U_10)
| U_7 != U_12
| U_10 != singleton(U_12) ),
inference(clausify,[status(thm)],[f_2_5]) ).
cnf(f_2_8,plain,
( sK2(U_13,U_11) = U_13
| in(sK1(U_13,U_11),U_11)
| U_11 = singleton(U_13) ),
inference(clausify,[status(thm)],[f_2_5]) ).
cnf(f_2_9,plain,
( ~ in(sK2(U_13,U_11),U_11)
| in(sK1(U_13,U_11),U_11)
| U_11 = singleton(U_13) ),
inference(clausify,[status(thm)],[f_2_5]) ).
cnf(f_2_10,plain,
( sK2(U_13,U_11) = U_13
| sK1(U_13,U_11) != U_13
| U_11 = singleton(U_13) ),
inference(clausify,[status(thm)],[f_2_5]) ).
cnf(f_2_11,plain,
( ~ in(sK2(U_13,U_11),U_11)
| sK1(U_13,U_11) != U_13
| U_11 = singleton(U_13) ),
inference(clausify,[status(thm)],[f_2_5]) ).
fof(f_3_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_3_2,plain,
! [U_17,U_16] :
( ( subset(U_17,U_16)
| ? [U_15] :
( ~ in(U_15,U_16)
& in(U_15,U_17) ) )
& ( ! [U_14] :
( in(U_14,U_16)
| ~ in(U_14,U_17) )
| ~ subset(U_17,U_16) ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_21,U_19] :
( subset(U_21,U_19)
| ? [U_15] :
( ~ in(U_15,U_19)
& in(U_15,U_21) ) )
& ! [U_20,U_18] :
( ! [U_14] :
( in(U_14,U_18)
| ~ in(U_14,U_20) )
| ~ subset(U_20,U_18) ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
fof(f_3_4,plain,
( ! [U_21,U_19] :
( subset(U_21,U_19)
| ( ~ in(sK3(U_21,U_19),U_19)
& in(sK3(U_21,U_19),U_21) ) )
& ! [U_20,U_18] :
( ! [U_14] :
( in(U_14,U_18)
| ~ in(U_14,U_20) )
| ~ subset(U_20,U_18) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_15,sK3(U_21,U_19))],[f_3_3]) ).
cnf(f_3_5,plain,
( in(U_14,U_18)
| ~ in(U_14,U_20)
| ~ subset(U_20,U_18) ),
inference(clausify,[status(thm)],[f_3_4]) ).
cnf(f_3_6,plain,
( in(sK3(U_21,U_19),U_21)
| subset(U_21,U_19) ),
inference(clausify,[status(thm)],[f_3_4]) ).
cnf(f_3_7,plain,
( ~ in(sK3(U_21,U_19),U_19)
| subset(U_21,U_19) ),
inference(clausify,[status(thm)],[f_3_4]) ).
fof(f_4_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_tarski]) ).
cnf(f_4_2,plain,
$true,
inference(clausify,[status(thm)],[f_4_1]) ).
fof(f_5_1,negated_conjecture,
~ ! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ),
inference(negate,[status(cth)],[l2_zfmisc_1]) ).
fof(f_5_2,negated_conjecture,
? [A,B] :
( ( ~ subset(singleton(A),B)
& in(A,B) )
| ( ~ in(A,B)
& subset(singleton(A),B) ) ),
inference(fof_nnf,[status(thm)],[f_5_1]) ).
fof(f_5_3,negated_conjecture,
? [U_23,U_22] :
( ( ~ subset(singleton(U_23),U_22)
& in(U_23,U_22) )
| ( ~ in(U_23,U_22)
& subset(singleton(U_23),U_22) ) ),
inference(variable_rename,[status(thm)],[f_5_2]) ).
fof(f_5_4,negated_conjecture,
( ? [U_27,U_25] :
( ~ subset(singleton(U_27),U_25)
& in(U_27,U_25) )
| ? [U_26,U_24] :
( ~ in(U_26,U_24)
& subset(singleton(U_26),U_24) ) ),
inference(miniscope,[status(thm)],[f_5_3]) ).
fof(f_5_5,negated_conjecture,
( ? [U_27,U_25] :
( ~ subset(singleton(U_27),U_25)
& in(U_27,U_25) )
| ? [U_24] :
( ~ in(sK4,U_24)
& subset(singleton(sK4),U_24) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_26,sK4)],[f_5_4]) ).
fof(f_5_6,negated_conjecture,
( ? [U_27,U_25] :
( ~ subset(singleton(U_27),U_25)
& in(U_27,U_25) )
| ( ~ in(sK4,sK5)
& subset(singleton(sK4),sK5) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_24,sK5)],[f_5_5]) ).
fof(f_5_7,negated_conjecture,
( ? [U_25] :
( ~ subset(singleton(sK6),U_25)
& in(sK6,U_25) )
| ( ~ in(sK4,sK5)
& subset(singleton(sK4),sK5) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_27,sK6)],[f_5_6]) ).
fof(f_5_8,negated_conjecture,
( ( ~ subset(singleton(sK6),sK7)
& in(sK6,sK7) )
| ( ~ in(sK4,sK5)
& subset(singleton(sK4),sK5) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_25,sK7)],[f_5_7]) ).
fof(f_5_9,negated_conjecture,
( ( ~ subset(singleton(sK6),sK7)
| ~ sP1 )
& ( in(sK6,sK7)
| ~ sP1 )
& ( ~ in(sK4,sK5)
| ~ sP0 )
& ( subset(singleton(sK4),sK5)
| ~ sP0 )
& ( sP1
| sP0 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1])],[f_5_8]) ).
cnf(f_5_10,negated_conjecture,
( sP1
| sP0 ),
inference(clausify,[status(thm)],[f_5_9]) ).
cnf(f_5_11,negated_conjecture,
( subset(singleton(sK4),sK5)
| ~ sP0 ),
inference(clausify,[status(thm)],[f_5_9]) ).
cnf(f_5_12,negated_conjecture,
( ~ in(sK4,sK5)
| ~ sP0 ),
inference(clausify,[status(thm)],[f_5_9]) ).
cnf(f_5_13,negated_conjecture,
( in(sK6,sK7)
| ~ sP1 ),
inference(clausify,[status(thm)],[f_5_9]) ).
cnf(f_5_14,negated_conjecture,
( ~ subset(singleton(sK6),sK7)
| ~ sP1 ),
inference(clausify,[status(thm)],[f_5_9]) ).
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]) ).
cnf(f_4_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_4_2]) ).
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,
( singleton(Eq_x_0) = singleton(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) = 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_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,
( 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,
( 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
% 0.00/0.03 % Problem : SEU144+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n016.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % 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 23:26:51 UTC 2026
% 0.10/0.36 % CPUTime :
% 19.25/19.56 % SZS status Theorem for theBenchmark
% 19.25/19.56 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------