%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET958+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 08:57:52 AM UTC 2026
% Result : Theorem 0.14s 0.64s
% 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(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_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(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(t111_zfmisc_1,conjecture,
! [A,B] :
( ( ! [C,D] :
( in(ordered_pair(C,D),A)
=> in(ordered_pair(C,D),B) )
& ! [C] :
~ ( ! [D,E] : C != ordered_pair(D,E)
& in(C,A) ) )
=> subset(A,B) ),
file('theBenchmark.p',t111_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] :
( ( 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_7,U_6] :
( ( subset(U_7,U_6)
| ? [U_5] :
( ~ in(U_5,U_6)
& in(U_5,U_7) ) )
& ( ! [U_4] :
( in(U_4,U_6)
| ~ in(U_4,U_7) )
| ~ subset(U_7,U_6) ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_11,U_9] :
( subset(U_11,U_9)
| ? [U_5] :
( ~ in(U_5,U_9)
& in(U_5,U_11) ) )
& ! [U_10,U_8] :
( ! [U_4] :
( in(U_4,U_8)
| ~ in(U_4,U_10) )
| ~ subset(U_10,U_8) ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
fof(f_3_4,plain,
( ! [U_11,U_9] :
( subset(U_11,U_9)
| ( ~ in(sK1(U_11,U_9),U_9)
& in(sK1(U_11,U_9),U_11) ) )
& ! [U_10,U_8] :
( ! [U_4] :
( in(U_4,U_8)
| ~ in(U_4,U_10) )
| ~ subset(U_10,U_8) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_5,sK1(U_11,U_9))],[f_3_3]) ).
cnf(f_3_5,plain,
( in(U_4,U_8)
| ~ in(U_4,U_10)
| ~ subset(U_10,U_8) ),
inference(clausify,[status(thm)],[f_3_4]) ).
cnf(f_3_6,plain,
( in(sK1(U_11,U_9),U_11)
| subset(U_11,U_9) ),
inference(clausify,[status(thm)],[f_3_4]) ).
cnf(f_3_7,plain,
( ~ in(sK1(U_11,U_9),U_9)
| subset(U_11,U_9) ),
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_13,U_12] : ordered_pair(U_13,U_12) = unordered_pair(unordered_pair(U_13,U_12),singleton(U_13)),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
ordered_pair(U_13,U_12) = unordered_pair(unordered_pair(U_13,U_12),singleton(U_13)),
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_15,U_14] : ~ empty(ordered_pair(U_15,U_14)),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
~ empty(ordered_pair(U_15,U_14)),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_6_2,plain,
? [U_16] : empty(U_16),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
empty(sK2),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_16,sK2)],[f_6_2]) ).
cnf(f_6_4,plain,
empty(sK2),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_7_2,plain,
? [U_17] : ~ empty(U_17),
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_17,sK3)],[f_7_2]) ).
cnf(f_7_4,plain,
~ empty(sK3),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_8_2,plain,
! [U_19,U_18] : subset(U_19,U_19),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_19] : subset(U_19,U_19),
inference(miniscope,[status(thm)],[f_8_2]) ).
cnf(f_8_4,plain,
subset(U_19,U_19),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,negated_conjecture,
~ ! [A,B] :
( ( ! [C,D] :
( in(ordered_pair(C,D),A)
=> in(ordered_pair(C,D),B) )
& ! [C] :
~ ( ! [D,E] : C != ordered_pair(D,E)
& in(C,A) ) )
=> subset(A,B) ),
inference(negate,[status(cth)],[t111_zfmisc_1]) ).
fof(f_9_2,negated_conjecture,
? [A,B] :
( ~ subset(A,B)
& ! [C,D] :
( in(ordered_pair(C,D),B)
| ~ in(ordered_pair(C,D),A) )
& ! [C] :
( ? [D,E] : C = ordered_pair(D,E)
| ~ in(C,A) ) ),
inference(fof_nnf,[status(thm)],[f_9_1]) ).
fof(f_9_3,negated_conjecture,
? [U_26,U_25] :
( ~ subset(U_26,U_25)
& ! [U_24,U_23] :
( in(ordered_pair(U_24,U_23),U_25)
| ~ in(ordered_pair(U_24,U_23),U_26) )
& ! [U_22] :
( ? [U_21,U_20] : U_22 = ordered_pair(U_21,U_20)
| ~ in(U_22,U_26) ) ),
inference(variable_rename,[status(thm)],[f_9_2]) ).
fof(f_9_4,negated_conjecture,
? [U_25] :
( ~ subset(sK4,U_25)
& ! [U_24,U_23] :
( in(ordered_pair(U_24,U_23),U_25)
| ~ in(ordered_pair(U_24,U_23),sK4) )
& ! [U_22] :
( ? [U_21,U_20] : U_22 = ordered_pair(U_21,U_20)
| ~ in(U_22,sK4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_26,sK4)],[f_9_3]) ).
fof(f_9_5,negated_conjecture,
( ~ subset(sK4,sK5)
& ! [U_24,U_23] :
( in(ordered_pair(U_24,U_23),sK5)
| ~ in(ordered_pair(U_24,U_23),sK4) )
& ! [U_22] :
( ? [U_21,U_20] : U_22 = ordered_pair(U_21,U_20)
| ~ in(U_22,sK4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_25,sK5)],[f_9_4]) ).
fof(f_9_6,negated_conjecture,
( ~ subset(sK4,sK5)
& ! [U_24,U_23] :
( in(ordered_pair(U_24,U_23),sK5)
| ~ in(ordered_pair(U_24,U_23),sK4) )
& ! [U_22] :
( ? [U_20] : U_22 = ordered_pair(sK6(U_22),U_20)
| ~ in(U_22,sK4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_21,sK6(U_22))],[f_9_5]) ).
fof(f_9_7,negated_conjecture,
( ~ subset(sK4,sK5)
& ! [U_24,U_23] :
( in(ordered_pair(U_24,U_23),sK5)
| ~ in(ordered_pair(U_24,U_23),sK4) )
& ! [U_22] :
( U_22 = ordered_pair(sK6(U_22),sK7(U_22))
| ~ in(U_22,sK4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_20,sK7(U_22))],[f_9_6]) ).
fof(f_9_8,negated_conjecture,
( ~ subset(sK4,sK5)
& ! [U_23,U_24] :
( in(ordered_pair(U_24,U_23),sK5)
| ~ in(ordered_pair(U_24,U_23),sK4) )
& ! [U_22] :
( U_22 = ordered_pair(sK6(U_22),sK7(U_22))
| ~ in(U_22,sK4) ) ),
inference(definitional_conversion,[status(esa)],[f_9_7]) ).
cnf(f_9_9,negated_conjecture,
( U_22 = ordered_pair(sK6(U_22),sK7(U_22))
| ~ in(U_22,sK4) ),
inference(clausify,[status(thm)],[f_9_8]) ).
cnf(f_9_10,negated_conjecture,
( in(ordered_pair(U_24,U_23),sK5)
| ~ in(ordered_pair(U_24,U_23),sK4) ),
inference(clausify,[status(thm)],[f_9_8]) ).
cnf(f_9_11,negated_conjecture,
~ subset(sK4,sK5),
inference(clausify,[status(thm)],[f_9_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,
( 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_8,axiom,
( sK6(Eq_x_0) = sK6(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( sK7(Eq_x_0) = sK7(Eq_y_0)
| 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 : SET958+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
% 0.09/0.57 % Computer : n007.cluster.edu
% 0.09/0.57 % Model : x86_64 x86_64
% 0.09/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.57 % Memory : 8046.5625MB
% 0.09/0.57 % OS : Linux 6.8.0-71-generic
% 0.09/0.57 % CPULimit : 300
% 0.09/0.57 % WCLimit : 300
% 0.09/0.57 % DateTime : Sat Sep 19 23:06:20 UTC 2026
% 0.09/0.57 % CPUTime :
% 0.14/0.64 % SZS status Theorem for theBenchmark
% 0.14/0.64 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------