%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET102+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 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 : n017.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 08:56:20 AM UTC 2026
% Result : Theorem 13.66s 14.02s
% Output : Proof 13.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 46 ( 27 unt; 0 def)
% Number of atoms : 119 ( 32 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 124 ( 51 ~; 44 |; 25 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 81 ( 3 sgn 60 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subclass_defn,axiom,
! [X,Y] :
( subclass(X,Y)
<=> ! [U] :
( member(U,X)
=> member(U,Y) ) ),
file('SET005+0.ax',subclass_defn) ).
fof(extensionality,axiom,
! [X,Y] :
( X = Y
<=> ( subclass(Y,X)
& subclass(X,Y) ) ),
file('SET005+0.ax',extensionality) ).
fof(unordered_pair_defn,axiom,
! [U,X,Y] :
( member(U,unordered_pair(X,Y))
<=> ( ( U = Y
| U = X )
& member(U,universal_class) ) ),
file('SET005+0.ax',unordered_pair_defn) ).
fof(unordered_pair,axiom,
! [X,Y] : member(unordered_pair(X,Y),universal_class),
file('SET005+0.ax',unordered_pair) ).
fof(ordered_pair_defn,axiom,
! [X,Y] : ordered_pair(X,Y) = unordered_pair(singleton(X),unordered_pair(X,singleton(Y))),
file('SET005+0.ax',ordered_pair_defn) ).
fof(unordered_pair_member_of_ordered_pair,conjecture,
! [X,Y] : member(unordered_pair(X,singleton(Y)),ordered_pair(X,Y)),
file('theBenchmark.p',unordered_pair_member_of_ordered_pair) ).
fof(f_1_1,plain,
! [X,Y] :
( ( subclass(X,Y)
| ? [U] :
( ~ member(U,Y)
& member(U,X) ) )
& ( ! [U] :
( member(U,Y)
| ~ member(U,X) )
| ~ subclass(X,Y) ) ),
inference(fof_nnf,[status(thm)],[subclass_defn]) ).
fof(f_1_2,plain,
! [U_3,U_2] :
( ( subclass(U_3,U_2)
| ? [U_1] :
( ~ member(U_1,U_2)
& member(U_1,U_3) ) )
& ( ! [U_0] :
( member(U_0,U_2)
| ~ member(U_0,U_3) )
| ~ subclass(U_3,U_2) ) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
( ! [U_7,U_5] :
( subclass(U_7,U_5)
| ? [U_1] :
( ~ member(U_1,U_5)
& member(U_1,U_7) ) )
& ! [U_6,U_4] :
( ! [U_0] :
( member(U_0,U_4)
| ~ member(U_0,U_6) )
| ~ subclass(U_6,U_4) ) ),
inference(miniscope,[status(thm)],[f_1_2]) ).
fof(f_1_4,plain,
( ! [U_7,U_5] :
( subclass(U_7,U_5)
| ( ~ member(sK1(U_7,U_5),U_5)
& member(sK1(U_7,U_5),U_7) ) )
& ! [U_6,U_4] :
( ! [U_0] :
( member(U_0,U_4)
| ~ member(U_0,U_6) )
| ~ subclass(U_6,U_4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_1,sK1(U_7,U_5))],[f_1_3]) ).
cnf(f_1_5,plain,
( member(U_0,U_4)
| ~ member(U_0,U_6)
| ~ subclass(U_6,U_4) ),
inference(clausify,[status(thm)],[f_1_4]) ).
fof(f_3_1,plain,
! [X,Y] :
( ( X = Y
| ~ subclass(Y,X)
| ~ subclass(X,Y) )
& ( ( subclass(Y,X)
& subclass(X,Y) )
| X != Y ) ),
inference(fof_nnf,[status(thm)],[extensionality]) ).
fof(f_3_2,plain,
! [U_10,U_9] :
( ( U_10 = U_9
| ~ subclass(U_9,U_10)
| ~ subclass(U_10,U_9) )
& ( ( subclass(U_9,U_10)
& subclass(U_10,U_9) )
| U_10 != U_9 ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_14,U_12] :
( U_14 = U_12
| ~ subclass(U_12,U_14)
| ~ subclass(U_14,U_12) )
& ! [U_13,U_11] :
( ( subclass(U_11,U_13)
& subclass(U_13,U_11) )
| U_13 != U_11 ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
cnf(f_3_5,plain,
( subclass(U_11,U_13)
| U_13 != U_11 ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
! [U,X,Y] :
( ( member(U,unordered_pair(X,Y))
| ( U != Y
& U != X )
| ~ member(U,universal_class) )
& ( ( ( U = Y
| U = X )
& member(U,universal_class) )
| ~ member(U,unordered_pair(X,Y)) ) ),
inference(fof_nnf,[status(thm)],[unordered_pair_defn]) ).
fof(f_4_2,plain,
! [U_17,U_16,U_15] :
( ( member(U_17,unordered_pair(U_16,U_15))
| ( U_17 != U_15
& U_17 != U_16 )
| ~ member(U_17,universal_class) )
& ( ( ( U_17 = U_15
| U_17 = U_16 )
& member(U_17,universal_class) )
| ~ member(U_17,unordered_pair(U_16,U_15)) ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_23,U_21,U_19] :
( member(U_23,unordered_pair(U_21,U_19))
| ( U_23 != U_19
& U_23 != U_21 )
| ~ member(U_23,universal_class) )
& ! [U_22,U_20,U_18] :
( ( ( U_22 = U_18
| U_22 = U_20 )
& member(U_22,universal_class) )
| ~ member(U_22,unordered_pair(U_20,U_18)) ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
cnf(f_4_7,plain,
( U_23 != U_19
| ~ member(U_23,universal_class)
| member(U_23,unordered_pair(U_21,U_19)) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
! [X,Y] : member(unordered_pair(X,Y),universal_class),
inference(fof_nnf,[status(thm)],[unordered_pair]) ).
fof(f_5_2,plain,
! [U_25,U_24] : member(unordered_pair(U_25,U_24),universal_class),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
member(unordered_pair(U_25,U_24),universal_class),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_7_1,plain,
! [X,Y] : ordered_pair(X,Y) = unordered_pair(singleton(X),unordered_pair(X,singleton(Y))),
inference(fof_nnf,[status(thm)],[ordered_pair_defn]) ).
fof(f_7_2,plain,
! [U_28,U_27] : ordered_pair(U_28,U_27) = unordered_pair(singleton(U_28),unordered_pair(U_28,singleton(U_27))),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
ordered_pair(U_28,U_27) = unordered_pair(singleton(U_28),unordered_pair(U_28,singleton(U_27))),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_44_1,negated_conjecture,
~ ! [X,Y] : member(unordered_pair(X,singleton(Y)),ordered_pair(X,Y)),
inference(negate,[status(cth)],[unordered_pair_member_of_ordered_pair]) ).
fof(f_44_2,negated_conjecture,
? [X,Y] : ~ member(unordered_pair(X,singleton(Y)),ordered_pair(X,Y)),
inference(fof_nnf,[status(thm)],[f_44_1]) ).
fof(f_44_3,negated_conjecture,
? [U_183,U_182] : ~ member(unordered_pair(U_183,singleton(U_182)),ordered_pair(U_183,U_182)),
inference(variable_rename,[status(thm)],[f_44_2]) ).
fof(f_44_4,negated_conjecture,
? [U_182] : ~ member(unordered_pair(sK8,singleton(U_182)),ordered_pair(sK8,U_182)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_183,sK8)],[f_44_3]) ).
fof(f_44_5,negated_conjecture,
~ member(unordered_pair(sK8,singleton(sK9)),ordered_pair(sK8,sK9)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_182,sK9)],[f_44_4]) ).
fof(f_44_6,negated_conjecture,
~ member(unordered_pair(sK8,singleton(sK9)),ordered_pair(sK8,sK9)),
inference(definitional_conversion,[status(esa)],[f_44_5]) ).
cnf(f_44_7,negated_conjecture,
~ member(unordered_pair(sK8,singleton(sK9)),ordered_pair(sK8,sK9)),
inference(clausify,[status(thm)],[f_44_6]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(t1,plain,
~ member(unordered_pair(sK8,singleton(sK9)),ordered_pair(sK8,sK9)),
inference(start,[status(thm),parent(0:0)],[f_44_7]) ).
cnf(t2,plain,
( ~ member(unordered_pair(sK8,singleton(sK9)),unordered_pair(singleton(sK8),unordered_pair(sK8,singleton(sK9))))
| ~ subclass(unordered_pair(singleton(sK8),unordered_pair(sK8,singleton(sK9))),ordered_pair(sK8,sK9))
| member(unordered_pair(sK8,singleton(sK9)),ordered_pair(sK8,sK9)) ),
inference(extension,[status(thm),parent(t1:1)],[f_1_5]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ordered_pair(sK8,sK9) != unordered_pair(singleton(sK8),unordered_pair(sK8,singleton(sK9)))
| subclass(unordered_pair(singleton(sK8),unordered_pair(sK8,singleton(sK9))),ordered_pair(sK8,sK9)) ),
inference(extension,[status(thm),parent(t2:2)],[f_3_5]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
ordered_pair(sK8,sK9) = unordered_pair(singleton(sK8),unordered_pair(sK8,singleton(sK9))),
inference(extension,[status(thm),parent(t4:2)],[f_7_3]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( ~ member(unordered_pair(sK8,singleton(sK9)),universal_class)
| unordered_pair(sK8,singleton(sK9)) != unordered_pair(sK8,singleton(sK9))
| member(unordered_pair(sK8,singleton(sK9)),unordered_pair(singleton(sK8),unordered_pair(sK8,singleton(sK9)))) ),
inference(extension,[status(thm),parent(t2:3)],[f_4_7]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:3]) ).
cnf(t10,plain,
unordered_pair(sK8,singleton(sK9)) = unordered_pair(sK8,singleton(sK9)),
inference(extension,[status(thm),parent(t8:2)],[equality_1]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
member(unordered_pair(sK8,singleton(sK9)),universal_class),
inference(extension,[status(thm),parent(t8:3)],[f_5_3]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t8:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET102+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 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 : n017.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
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 19 21:37:40 UTC 2026
% 0.14/0.36 % CPUTime :
% 13.66/14.02 % SZS status Theorem for theBenchmark
% 13.66/14.02 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------