%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET024+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 : n006.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 08:55:58 AM UTC 2026
% Result : Theorem 3.04s 13.31s
% Output : Proof 3.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 65 ( 24 unt; 0 def)
% Number of atoms : 190 ( 32 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 204 ( 79 ~; 75 |; 42 &)
% ( 5 <=>; 3 =>; 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; 2 con; 0-2 aty)
% Number of variables : 99 ( 2 sgn 74 !; 5 ?)
% 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(singleton_set_defn,axiom,
! [X] : singleton(X) = unordered_pair(X,X),
file('SET005+0.ax',singleton_set_defn) ).
fof(complement,axiom,
! [X,Z] :
( member(Z,complement(X))
<=> ( ~ member(Z,X)
& member(Z,universal_class) ) ),
file('SET005+0.ax',complement) ).
fof(union_defn,axiom,
! [X,Y,Z] :
( member(Z,union(X,Y))
<=> ( member(Z,Y)
| member(Z,X) ) ),
file('SET005+0.ax',union_defn) ).
fof(set_in_its_singleton,conjecture,
! [X] :
( member(X,universal_class)
=> member(X,singleton(X)) ),
file('theBenchmark.p',set_in_its_singleton) ).
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_6_1,plain,
! [X] : singleton(X) = unordered_pair(X,X),
inference(fof_nnf,[status(thm)],[singleton_set_defn]) ).
fof(f_6_2,plain,
! [U_26] : singleton(U_26) = unordered_pair(U_26,U_26),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
singleton(U_26) = unordered_pair(U_26,U_26),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_14_1,plain,
! [X,Z] :
( ( member(Z,complement(X))
| member(Z,X)
| ~ member(Z,universal_class) )
& ( ( ~ member(Z,X)
& member(Z,universal_class) )
| ~ member(Z,complement(X)) ) ),
inference(fof_nnf,[status(thm)],[complement]) ).
fof(f_14_2,plain,
! [U_62,U_61] :
( ( member(U_61,complement(U_62))
| member(U_61,U_62)
| ~ member(U_61,universal_class) )
& ( ( ~ member(U_61,U_62)
& member(U_61,universal_class) )
| ~ member(U_61,complement(U_62)) ) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
( ! [U_66,U_64] :
( member(U_64,complement(U_66))
| member(U_64,U_66)
| ~ member(U_64,universal_class) )
& ! [U_65,U_63] :
( ( ~ member(U_63,U_65)
& member(U_63,universal_class) )
| ~ member(U_63,complement(U_65)) ) ),
inference(miniscope,[status(thm)],[f_14_2]) ).
cnf(f_14_5,plain,
( ~ member(U_63,U_65)
| ~ member(U_63,complement(U_65)) ),
inference(clausify,[status(thm)],[f_14_3]) ).
cnf(f_14_6,plain,
( member(U_64,complement(U_66))
| member(U_64,U_66)
| ~ member(U_64,universal_class) ),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_22_1,plain,
! [X,Y,Z] :
( ( member(Z,union(X,Y))
| ( ~ member(Z,Y)
& ~ member(Z,X) ) )
& ( member(Z,Y)
| member(Z,X)
| ~ member(Z,union(X,Y)) ) ),
inference(fof_nnf,[status(thm)],[union_defn]) ).
fof(f_22_2,plain,
! [U_105,U_104,U_103] :
( ( member(U_103,union(U_105,U_104))
| ( ~ member(U_103,U_104)
& ~ member(U_103,U_105) ) )
& ( member(U_103,U_104)
| member(U_103,U_105)
| ~ member(U_103,union(U_105,U_104)) ) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
( ! [U_111,U_109,U_107] :
( member(U_107,union(U_111,U_109))
| ( ~ member(U_107,U_109)
& ~ member(U_107,U_111) ) )
& ! [U_110,U_108,U_106] :
( member(U_106,U_108)
| member(U_106,U_110)
| ~ member(U_106,union(U_110,U_108)) ) ),
inference(miniscope,[status(thm)],[f_22_2]) ).
cnf(f_22_4,plain,
( member(U_106,U_108)
| member(U_106,U_110)
| ~ member(U_106,union(U_110,U_108)) ),
inference(clausify,[status(thm)],[f_22_3]) ).
cnf(f_22_5,plain,
( ~ member(U_107,U_111)
| member(U_107,union(U_111,U_109)) ),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_44_1,negated_conjecture,
~ ! [X] :
( member(X,universal_class)
=> member(X,singleton(X)) ),
inference(negate,[status(cth)],[set_in_its_singleton]) ).
fof(f_44_2,negated_conjecture,
? [X] :
( ~ member(X,singleton(X))
& member(X,universal_class) ),
inference(fof_nnf,[status(thm)],[f_44_1]) ).
fof(f_44_3,negated_conjecture,
? [U_182] :
( ~ member(U_182,singleton(U_182))
& member(U_182,universal_class) ),
inference(variable_rename,[status(thm)],[f_44_2]) ).
fof(f_44_4,negated_conjecture,
( ~ member(sK8,singleton(sK8))
& member(sK8,universal_class) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_182,sK8)],[f_44_3]) ).
fof(f_44_5,negated_conjecture,
( ~ member(sK8,singleton(sK8))
& member(sK8,universal_class) ),
inference(definitional_conversion,[status(esa)],[f_44_4]) ).
cnf(f_44_6,negated_conjecture,
member(sK8,universal_class),
inference(clausify,[status(thm)],[f_44_5]) ).
cnf(f_44_7,negated_conjecture,
~ member(sK8,singleton(sK8)),
inference(clausify,[status(thm)],[f_44_5]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(t1,plain,
( ~ member(sK8,singleton(sK8))
| ~ member(sK8,complement(singleton(sK8))) ),
inference(start,[status(thm),parent(0:0)],[f_14_5]) ).
cnf(t2,plain,
( member(sK8,universal_class)
| ~ member(sK8,union(universal_class,complement(singleton(sK8))))
| member(sK8,complement(singleton(sK8))) ),
inference(extension,[status(thm),parent(t1:1)],[f_22_4]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ member(sK8,universal_class)
| member(sK8,union(universal_class,complement(singleton(sK8)))) ),
inference(extension,[status(thm),parent(t2:2)],[f_22_5]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
member(sK8,universal_class),
inference(extension,[status(thm),parent(t4:2)],[f_44_6]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( member(sK8,singleton(sK8))
| member(sK8,complement(singleton(sK8)))
| ~ member(sK8,universal_class) ),
inference(extension,[status(thm),parent(t2:3)],[f_14_6]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:3]) ).
cnf(t10,plain,
$false,
inference(reduction,[status(thm),parent(t8:2)],[t8:2,t1:1]) ).
cnf(t11,plain,
~ member(sK8,singleton(sK8)),
inference(extension,[status(thm),parent(t8:3)],[f_44_7]) ).
cnf(t12,plain,
$false,
inference(connection,[status(thm),parent(t11:1)],[t11:1,t8:3]) ).
cnf(t13,plain,
( ~ member(sK8,unordered_pair(sK8,sK8))
| ~ subclass(unordered_pair(sK8,sK8),singleton(sK8))
| member(sK8,singleton(sK8)) ),
inference(extension,[status(thm),parent(t1:2)],[f_1_5]) ).
cnf(t14,plain,
$false,
inference(connection,[status(thm),parent(t13:1)],[t13:1,t1:2]) ).
cnf(t15,plain,
( singleton(sK8) != unordered_pair(sK8,sK8)
| subclass(unordered_pair(sK8,sK8),singleton(sK8)) ),
inference(extension,[status(thm),parent(t13:2)],[f_3_5]) ).
cnf(t16,plain,
$false,
inference(connection,[status(thm),parent(t15:1)],[t15:1,t13:2]) ).
cnf(t17,plain,
singleton(sK8) = unordered_pair(sK8,sK8),
inference(extension,[status(thm),parent(t15:2)],[f_6_3]) ).
cnf(t18,plain,
$false,
inference(connection,[status(thm),parent(t17:1)],[t17:1,t15:2]) ).
cnf(t19,plain,
( ~ member(sK8,universal_class)
| sK8 != sK8
| member(sK8,unordered_pair(sK8,sK8)) ),
inference(extension,[status(thm),parent(t13:3)],[f_4_7]) ).
cnf(t20,plain,
$false,
inference(connection,[status(thm),parent(t19:1)],[t19:1,t13:3]) ).
cnf(t21,plain,
sK8 = sK8,
inference(extension,[status(thm),parent(t19:2)],[equality_1]) ).
cnf(t22,plain,
$false,
inference(connection,[status(thm),parent(t21:1)],[t21:1,t19:2]) ).
cnf(t23,plain,
member(sK8,universal_class),
inference(extension,[status(thm),parent(t19:3)],[f_44_6]) ).
cnf(t24,plain,
$false,
inference(connection,[status(thm),parent(t23:1)],[t23:1,t19:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET024+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
% 0.12/10.39 % Computer : n006.cluster.edu
% 0.12/10.39 % Model : x86_64 x86_64
% 0.12/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/10.39 % Memory : 8046.5625MB
% 0.12/10.39 % OS : Linux 6.8.0-71-generic
% 0.12/10.39 % CPULimit : 300
% 0.12/10.39 % WCLimit : 300
% 0.12/10.39 % DateTime : Sat Sep 19 21:28:58 UTC 2026
% 0.12/10.39 % CPUTime :
% 3.04/13.31 % SZS status Theorem for theBenchmark
% 3.04/13.31 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------