%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU151+3 : TPTP v9.3.1. Released v3.2.0.
% 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 : n018.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 08:58:14 AM UTC 2026
% Result : Theorem 82.87s 83.18s
% Output : Proof 83.10s
% 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(d2_tarski,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = B
| D = A ) ) ),
file('theBenchmark.p',d2_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(t10_zfmisc_1,conjecture,
! [A,B,C,D] :
~ ( A != D
& A != C
& unordered_pair(A,B) = unordered_pair(C,D) ),
file('theBenchmark.p',t10_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,C] :
( ( C = unordered_pair(A,B)
| ? [D] :
( ( ~ in(D,C)
& ( D = B
| D = A ) )
| ( D != B
& D != A
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ( D != B
& D != A ) )
& ( D = B
| D = A
| ~ in(D,C) ) )
| C != unordered_pair(A,B) ) ),
inference(fof_nnf,[status(thm)],[d2_tarski]) ).
fof(f_3_2,plain,
! [U_8,U_7,U_6] :
( ( U_6 = unordered_pair(U_8,U_7)
| ? [U_5] :
( ( ~ in(U_5,U_6)
& ( U_5 = U_7
| U_5 = U_8 ) )
| ( U_5 != U_7
& U_5 != U_8
& in(U_5,U_6) ) ) )
& ( ! [U_4] :
( ( in(U_4,U_6)
| ( U_4 != U_7
& U_4 != U_8 ) )
& ( U_4 = U_7
| U_4 = U_8
| ~ in(U_4,U_6) ) )
| U_6 != unordered_pair(U_8,U_7) ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_18,U_16,U_14] :
( U_14 = unordered_pair(U_18,U_16)
| ? [U_12] :
( ~ in(U_12,U_14)
& ( U_12 = U_16
| U_12 = U_18 ) )
| ? [U_11] :
( U_11 != U_16
& U_11 != U_18
& in(U_11,U_14) ) )
& ! [U_17,U_15,U_13] :
( ( ! [U_10] :
( in(U_10,U_13)
| ( U_10 != U_15
& U_10 != U_17 ) )
& ! [U_9] :
( U_9 = U_15
| U_9 = U_17
| ~ in(U_9,U_13) ) )
| U_13 != unordered_pair(U_17,U_15) ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
fof(f_3_4,plain,
( ! [U_18,U_16,U_14] :
( U_14 = unordered_pair(U_18,U_16)
| ? [U_12] :
( ~ in(U_12,U_14)
& ( U_12 = U_16
| U_12 = U_18 ) )
| ( sK1(U_18,U_16,U_14) != U_16
& sK1(U_18,U_16,U_14) != U_18
& in(sK1(U_18,U_16,U_14),U_14) ) )
& ! [U_17,U_15,U_13] :
( ( ! [U_10] :
( in(U_10,U_13)
| ( U_10 != U_15
& U_10 != U_17 ) )
& ! [U_9] :
( U_9 = U_15
| U_9 = U_17
| ~ in(U_9,U_13) ) )
| U_13 != unordered_pair(U_17,U_15) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_11,sK1(U_18,U_16,U_14))],[f_3_3]) ).
fof(f_3_5,plain,
( ! [U_18,U_16,U_14] :
( U_14 = unordered_pair(U_18,U_16)
| ( ~ in(sK2(U_18,U_16,U_14),U_14)
& ( sK2(U_18,U_16,U_14) = U_16
| sK2(U_18,U_16,U_14) = U_18 ) )
| ( sK1(U_18,U_16,U_14) != U_16
& sK1(U_18,U_16,U_14) != U_18
& in(sK1(U_18,U_16,U_14),U_14) ) )
& ! [U_17,U_15,U_13] :
( ( ! [U_10] :
( in(U_10,U_13)
| ( U_10 != U_15
& U_10 != U_17 ) )
& ! [U_9] :
( U_9 = U_15
| U_9 = U_17
| ~ in(U_9,U_13) ) )
| U_13 != unordered_pair(U_17,U_15) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_12,sK2(U_18,U_16,U_14))],[f_3_4]) ).
cnf(f_3_6,plain,
( U_9 = U_15
| U_9 = U_17
| ~ in(U_9,U_13)
| U_13 != unordered_pair(U_17,U_15) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_7,plain,
( U_10 != U_17
| in(U_10,U_13)
| U_13 != unordered_pair(U_17,U_15) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_8,plain,
( U_10 != U_15
| in(U_10,U_13)
| U_13 != unordered_pair(U_17,U_15) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_9,plain,
( sK2(U_18,U_16,U_14) = U_16
| sK2(U_18,U_16,U_14) = U_18
| in(sK1(U_18,U_16,U_14),U_14)
| U_14 = unordered_pair(U_18,U_16) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_10,plain,
( ~ in(sK2(U_18,U_16,U_14),U_14)
| in(sK1(U_18,U_16,U_14),U_14)
| U_14 = unordered_pair(U_18,U_16) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_11,plain,
( sK1(U_18,U_16,U_14) != U_18
| sK2(U_18,U_16,U_14) = U_16
| sK2(U_18,U_16,U_14) = U_18
| U_14 = unordered_pair(U_18,U_16) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_12,plain,
( sK1(U_18,U_16,U_14) != U_16
| sK2(U_18,U_16,U_14) = U_16
| sK2(U_18,U_16,U_14) = U_18
| U_14 = unordered_pair(U_18,U_16) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_13,plain,
( sK1(U_18,U_16,U_14) != U_18
| ~ in(sK2(U_18,U_16,U_14),U_14)
| U_14 = unordered_pair(U_18,U_16) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_14,plain,
( sK1(U_18,U_16,U_14) != U_16
| ~ in(sK2(U_18,U_16,U_14),U_14)
| U_14 = unordered_pair(U_18,U_16) ),
inference(clausify,[status(thm)],[f_3_5]) ).
fof(f_4_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_4_2,plain,
? [U_19] : empty(U_19),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
empty(sK3),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_19,sK3)],[f_4_2]) ).
cnf(f_4_4,plain,
empty(sK3),
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_20] : ~ empty(U_20),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
~ empty(sK4),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_20,sK4)],[f_5_2]) ).
cnf(f_5_4,plain,
~ empty(sK4),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,negated_conjecture,
~ ! [A,B,C,D] :
~ ( A != D
& A != C
& unordered_pair(A,B) = unordered_pair(C,D) ),
inference(negate,[status(cth)],[t10_zfmisc_1]) ).
fof(f_6_2,negated_conjecture,
? [A,B,C,D] :
( A != D
& A != C
& unordered_pair(A,B) = unordered_pair(C,D) ),
inference(fof_nnf,[status(thm)],[f_6_1]) ).
fof(f_6_3,negated_conjecture,
? [U_24,U_23,U_22,U_21] :
( U_24 != U_21
& U_24 != U_22
& unordered_pair(U_24,U_23) = unordered_pair(U_22,U_21) ),
inference(variable_rename,[status(thm)],[f_6_2]) ).
fof(f_6_4,negated_conjecture,
? [U_24,U_23,U_22] :
( ? [U_21] :
( U_24 != U_21
& unordered_pair(U_24,U_23) = unordered_pair(U_22,U_21) )
& U_24 != U_22 ),
inference(miniscope,[status(thm)],[f_6_3]) ).
fof(f_6_5,negated_conjecture,
? [U_23,U_22] :
( ? [U_21] :
( sK5 != U_21
& unordered_pair(sK5,U_23) = unordered_pair(U_22,U_21) )
& sK5 != U_22 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_24,sK5)],[f_6_4]) ).
fof(f_6_6,negated_conjecture,
? [U_22] :
( ? [U_21] :
( sK5 != U_21
& unordered_pair(sK5,sK6) = unordered_pair(U_22,U_21) )
& sK5 != U_22 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_23,sK6)],[f_6_5]) ).
fof(f_6_7,negated_conjecture,
( ? [U_21] :
( sK5 != U_21
& unordered_pair(sK5,sK6) = unordered_pair(sK7,U_21) )
& sK5 != sK7 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_22,sK7)],[f_6_6]) ).
fof(f_6_8,negated_conjecture,
( sK5 != sK8
& unordered_pair(sK5,sK6) = unordered_pair(sK7,sK8)
& sK5 != sK7 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_21,sK8)],[f_6_7]) ).
cnf(f_6_9,negated_conjecture,
sK5 != sK7,
inference(clausify,[status(thm)],[f_6_8]) ).
cnf(f_6_10,negated_conjecture,
unordered_pair(sK5,sK6) = unordered_pair(sK7,sK8),
inference(clausify,[status(thm)],[f_6_8]) ).
cnf(f_6_11,negated_conjecture,
sK5 != sK8,
inference(clausify,[status(thm)],[f_6_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,
( sK1(Eq_x_0,Eq_x_1,Eq_x_2) = sK1(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_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,
( 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_8,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
% 0.00/0.02 % Problem : SEU151+3 : 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/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.38 % Computer : n018.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sat Sep 19 23:25:12 UTC 2026
% 0.10/0.38 % CPUTime :
% 82.87/83.18 % SZS status Theorem for theBenchmark
% 82.87/83.18 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------