%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET959+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 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 08:57:52 AM UTC 2026
% Result : Theorem 9.55s 9.83s
% Output : Proof 10.27s
% 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(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(t112_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,B) )
& ! [C] :
~ ( ! [D,E] : C != ordered_pair(D,E)
& in(C,A) ) )
=> A = B ),
file('theBenchmark.p',t112_zfmisc_1) ).
fof(t2_tarski,axiom,
! [A,B] :
( ! [C] :
( in(C,A)
<=> in(C,B) )
=> A = B ),
file('theBenchmark.p',t2_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] : 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] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
inference(fof_nnf,[status(thm)],[d5_tarski]) ).
fof(f_3_2,plain,
! [U_5,U_4] : ordered_pair(U_5,U_4) = unordered_pair(unordered_pair(U_5,U_4),singleton(U_5)),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
ordered_pair(U_5,U_4) = unordered_pair(unordered_pair(U_5,U_4),singleton(U_5)),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc1_zfmisc_1]) ).
fof(f_4_2,plain,
! [U_7,U_6] : ~ empty(ordered_pair(U_7,U_6)),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
~ empty(ordered_pair(U_7,U_6)),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_5_2,plain,
? [U_8] : empty(U_8),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
empty(sK1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_8,sK1)],[f_5_2]) ).
cnf(f_5_4,plain,
empty(sK1),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_6_2,plain,
? [U_9] : ~ empty(U_9),
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_9,sK2)],[f_6_2]) ).
cnf(f_6_4,plain,
~ empty(sK2),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_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,B) )
& ! [C] :
~ ( ! [D,E] : C != ordered_pair(D,E)
& in(C,A) ) )
=> A = B ),
inference(negate,[status(cth)],[t112_zfmisc_1]) ).
fof(f_7_2,negated_conjecture,
? [A,B] :
( A != B
& ! [C,D] :
( ( in(ordered_pair(C,D),A)
| ~ in(ordered_pair(C,D),B) )
& ( in(ordered_pair(C,D),B)
| ~ in(ordered_pair(C,D),A) ) )
& ! [C] :
( ? [D,E] : C = ordered_pair(D,E)
| ~ in(C,B) )
& ! [C] :
( ? [D,E] : C = ordered_pair(D,E)
| ~ in(C,A) ) ),
inference(fof_nnf,[status(thm)],[f_7_1]) ).
fof(f_7_3,negated_conjecture,
? [U_19,U_18] :
( U_19 != U_18
& ! [U_17,U_16] :
( ( in(ordered_pair(U_17,U_16),U_19)
| ~ in(ordered_pair(U_17,U_16),U_18) )
& ( in(ordered_pair(U_17,U_16),U_18)
| ~ in(ordered_pair(U_17,U_16),U_19) ) )
& ! [U_15] :
( ? [U_14,U_13] : U_15 = ordered_pair(U_14,U_13)
| ~ in(U_15,U_18) )
& ! [U_12] :
( ? [U_11,U_10] : U_12 = ordered_pair(U_11,U_10)
| ~ in(U_12,U_19) ) ),
inference(variable_rename,[status(thm)],[f_7_2]) ).
fof(f_7_4,negated_conjecture,
? [U_19,U_18] :
( U_19 != U_18
& ! [U_23,U_21] :
( in(ordered_pair(U_23,U_21),U_19)
| ~ in(ordered_pair(U_23,U_21),U_18) )
& ! [U_22,U_20] :
( in(ordered_pair(U_22,U_20),U_18)
| ~ in(ordered_pair(U_22,U_20),U_19) )
& ! [U_15] :
( ? [U_14,U_13] : U_15 = ordered_pair(U_14,U_13)
| ~ in(U_15,U_18) )
& ! [U_12] :
( ? [U_11,U_10] : U_12 = ordered_pair(U_11,U_10)
| ~ in(U_12,U_19) ) ),
inference(miniscope,[status(thm)],[f_7_3]) ).
fof(f_7_5,negated_conjecture,
? [U_18] :
( sK3 != U_18
& ! [U_23,U_21] :
( in(ordered_pair(U_23,U_21),sK3)
| ~ in(ordered_pair(U_23,U_21),U_18) )
& ! [U_22,U_20] :
( in(ordered_pair(U_22,U_20),U_18)
| ~ in(ordered_pair(U_22,U_20),sK3) )
& ! [U_15] :
( ? [U_14,U_13] : U_15 = ordered_pair(U_14,U_13)
| ~ in(U_15,U_18) )
& ! [U_12] :
( ? [U_11,U_10] : U_12 = ordered_pair(U_11,U_10)
| ~ in(U_12,sK3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_19,sK3)],[f_7_4]) ).
fof(f_7_6,negated_conjecture,
( sK3 != sK4
& ! [U_23,U_21] :
( in(ordered_pair(U_23,U_21),sK3)
| ~ in(ordered_pair(U_23,U_21),sK4) )
& ! [U_22,U_20] :
( in(ordered_pair(U_22,U_20),sK4)
| ~ in(ordered_pair(U_22,U_20),sK3) )
& ! [U_15] :
( ? [U_14,U_13] : U_15 = ordered_pair(U_14,U_13)
| ~ in(U_15,sK4) )
& ! [U_12] :
( ? [U_11,U_10] : U_12 = ordered_pair(U_11,U_10)
| ~ in(U_12,sK3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_18,sK4)],[f_7_5]) ).
fof(f_7_7,negated_conjecture,
( sK3 != sK4
& ! [U_23,U_21] :
( in(ordered_pair(U_23,U_21),sK3)
| ~ in(ordered_pair(U_23,U_21),sK4) )
& ! [U_22,U_20] :
( in(ordered_pair(U_22,U_20),sK4)
| ~ in(ordered_pair(U_22,U_20),sK3) )
& ! [U_15] :
( ? [U_14,U_13] : U_15 = ordered_pair(U_14,U_13)
| ~ in(U_15,sK4) )
& ! [U_12] :
( ? [U_10] : U_12 = ordered_pair(sK5(U_12),U_10)
| ~ in(U_12,sK3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_11,sK5(U_12))],[f_7_6]) ).
fof(f_7_8,negated_conjecture,
( sK3 != sK4
& ! [U_23,U_21] :
( in(ordered_pair(U_23,U_21),sK3)
| ~ in(ordered_pair(U_23,U_21),sK4) )
& ! [U_22,U_20] :
( in(ordered_pair(U_22,U_20),sK4)
| ~ in(ordered_pair(U_22,U_20),sK3) )
& ! [U_15] :
( ? [U_14,U_13] : U_15 = ordered_pair(U_14,U_13)
| ~ in(U_15,sK4) )
& ! [U_12] :
( U_12 = ordered_pair(sK5(U_12),sK6(U_12))
| ~ in(U_12,sK3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_10,sK6(U_12))],[f_7_7]) ).
fof(f_7_9,negated_conjecture,
( sK3 != sK4
& ! [U_23,U_21] :
( in(ordered_pair(U_23,U_21),sK3)
| ~ in(ordered_pair(U_23,U_21),sK4) )
& ! [U_22,U_20] :
( in(ordered_pair(U_22,U_20),sK4)
| ~ in(ordered_pair(U_22,U_20),sK3) )
& ! [U_15] :
( ? [U_13] : U_15 = ordered_pair(sK7(U_15),U_13)
| ~ in(U_15,sK4) )
& ! [U_12] :
( U_12 = ordered_pair(sK5(U_12),sK6(U_12))
| ~ in(U_12,sK3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_14,sK7(U_15))],[f_7_8]) ).
fof(f_7_10,negated_conjecture,
( sK3 != sK4
& ! [U_23,U_21] :
( in(ordered_pair(U_23,U_21),sK3)
| ~ in(ordered_pair(U_23,U_21),sK4) )
& ! [U_22,U_20] :
( in(ordered_pair(U_22,U_20),sK4)
| ~ in(ordered_pair(U_22,U_20),sK3) )
& ! [U_15] :
( U_15 = ordered_pair(sK7(U_15),sK8(U_15))
| ~ in(U_15,sK4) )
& ! [U_12] :
( U_12 = ordered_pair(sK5(U_12),sK6(U_12))
| ~ in(U_12,sK3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_13,sK8(U_15))],[f_7_9]) ).
fof(f_7_11,negated_conjecture,
( sK3 != sK4
& ! [U_23,U_21] :
( in(ordered_pair(U_23,U_21),sK3)
| ~ in(ordered_pair(U_23,U_21),sK4) )
& ! [U_22,U_20] :
( in(ordered_pair(U_22,U_20),sK4)
| ~ in(ordered_pair(U_22,U_20),sK3) )
& ! [U_15] :
( U_15 = ordered_pair(sK7(U_15),sK8(U_15))
| ~ in(U_15,sK4) )
& ! [U_12] :
( U_12 = ordered_pair(sK5(U_12),sK6(U_12))
| ~ in(U_12,sK3) ) ),
inference(definitional_conversion,[status(esa)],[f_7_10]) ).
cnf(f_7_12,negated_conjecture,
( U_12 = ordered_pair(sK5(U_12),sK6(U_12))
| ~ in(U_12,sK3) ),
inference(clausify,[status(thm)],[f_7_11]) ).
cnf(f_7_13,negated_conjecture,
( U_15 = ordered_pair(sK7(U_15),sK8(U_15))
| ~ in(U_15,sK4) ),
inference(clausify,[status(thm)],[f_7_11]) ).
cnf(f_7_14,negated_conjecture,
( in(ordered_pair(U_22,U_20),sK4)
| ~ in(ordered_pair(U_22,U_20),sK3) ),
inference(clausify,[status(thm)],[f_7_11]) ).
cnf(f_7_15,negated_conjecture,
( in(ordered_pair(U_23,U_21),sK3)
| ~ in(ordered_pair(U_23,U_21),sK4) ),
inference(clausify,[status(thm)],[f_7_11]) ).
cnf(f_7_16,negated_conjecture,
sK3 != sK4,
inference(clausify,[status(thm)],[f_7_11]) ).
fof(f_8_1,plain,
! [A,B] :
( A = B
| ? [C] :
( ( ~ in(C,A)
& in(C,B) )
| ( ~ in(C,B)
& in(C,A) ) ) ),
inference(fof_nnf,[status(thm)],[t2_tarski]) ).
fof(f_8_2,plain,
! [U_26,U_25] :
( U_26 = U_25
| ? [U_24] :
( ( ~ in(U_24,U_26)
& in(U_24,U_25) )
| ( ~ in(U_24,U_25)
& in(U_24,U_26) ) ) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_26,U_25] :
( U_26 = U_25
| ? [U_28] :
( ~ in(U_28,U_26)
& in(U_28,U_25) )
| ? [U_27] :
( ~ in(U_27,U_25)
& in(U_27,U_26) ) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
fof(f_8_4,plain,
! [U_26,U_25] :
( U_26 = U_25
| ? [U_28] :
( ~ in(U_28,U_26)
& in(U_28,U_25) )
| ( ~ in(sK9(U_26,U_25),U_25)
& in(sK9(U_26,U_25),U_26) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_27,sK9(U_26,U_25))],[f_8_3]) ).
fof(f_8_5,plain,
! [U_26,U_25] :
( U_26 = U_25
| ( ~ in(sK10(U_26,U_25),U_26)
& in(sK10(U_26,U_25),U_25) )
| ( ~ in(sK9(U_26,U_25),U_25)
& in(sK9(U_26,U_25),U_26) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_28,sK10(U_26,U_25))],[f_8_4]) ).
cnf(f_8_6,plain,
( in(sK10(U_26,U_25),U_25)
| in(sK9(U_26,U_25),U_26)
| U_26 = U_25 ),
inference(clausify,[status(thm)],[f_8_5]) ).
cnf(f_8_7,plain,
( ~ in(sK10(U_26,U_25),U_26)
| in(sK9(U_26,U_25),U_26)
| U_26 = U_25 ),
inference(clausify,[status(thm)],[f_8_5]) ).
cnf(f_8_8,plain,
( in(sK10(U_26,U_25),U_25)
| ~ in(sK9(U_26,U_25),U_25)
| U_26 = U_25 ),
inference(clausify,[status(thm)],[f_8_5]) ).
cnf(f_8_9,plain,
( ~ in(sK10(U_26,U_25),U_26)
| ~ in(sK9(U_26,U_25),U_25)
| U_26 = U_25 ),
inference(clausify,[status(thm)],[f_8_5]) ).
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,
( sK5(Eq_x_0) = sK5(Eq_y_0)
| 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,
( sK8(Eq_x_0) = sK8(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( sK9(Eq_x_0,Eq_x_1) = sK9(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( sK10(Eq_x_0,Eq_x_1) = sK10(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,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_14,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 : SET959+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 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
% 0.02/0.30 % Computer : n012.cluster.edu
% 0.02/0.30 % Model : x86_64 x86_64
% 0.02/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.30 % Memory : 8046.5625MB
% 0.02/0.30 % OS : Linux 6.8.0-71-generic
% 0.02/0.30 % CPULimit : 300
% 0.02/0.30 % WCLimit : 300
% 0.02/0.30 % DateTime : Sat Sep 19 23:08:17 UTC 2026
% 0.02/0.31 % CPUTime :
% 9.55/9.83 % SZS status Theorem for theBenchmark
% 9.55/9.83 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------