%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET077+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 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 : n016.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 08:56:13 AM UTC 2026
% Result : Theorem 40.65s 46.00s
% Output : Proof 40.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 80 ( 50 unt; 0 def)
% Number of atoms : 186 ( 29 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 182 ( 76 ~; 72 |; 30 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 152 ( 10 sgn 99 !; 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(class_elements_are_sets,axiom,
! [X] : subclass(X,universal_class),
file('SET005+0.ax',class_elements_are_sets) ).
fof(extensionality,axiom,
! [X,Y] :
( X = Y
<=> ( subclass(Y,X)
& subclass(X,Y) ) ),
file('SET005+0.ax',extensionality) ).
fof(unordered_pair,axiom,
! [X,Y] : member(unordered_pair(X,Y),universal_class),
file('SET005+0.ax',unordered_pair) ).
fof(singleton_set_defn,axiom,
! [X] : singleton(X) = unordered_pair(X,X),
file('SET005+0.ax',singleton_set_defn) ).
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(apply_defn,axiom,
! [XF,Y] : apply(XF,Y) = sum_class(image(XF,singleton(Y))),
file('SET005+0.ax',apply_defn) ).
fof(singletons_are_sets,conjecture,
! [X] : member(singleton(X),universal_class),
file('theBenchmark.p',singletons_are_sets) ).
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]) ).
fof(f_1_5,plain,
( ! [U_7,U_5] :
( ~ member(sK1(U_7,U_5),U_5)
| ~ sP0(U_7,U_5) )
& ! [U_7,U_5] :
( member(sK1(U_7,U_5),U_7)
| ~ sP0(U_7,U_5) )
& ! [U_7,U_5] :
( subclass(U_7,U_5)
| sP0(U_7,U_5) )
& ! [U_6,U_4,U_0] :
( member(U_0,U_4)
| ~ member(U_0,U_6)
| ~ subclass(U_6,U_4) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_1_4]) ).
cnf(f_1_6,plain,
( member(U_0,U_4)
| ~ member(U_0,U_6)
| ~ subclass(U_6,U_4) ),
inference(clausify,[status(thm)],[f_1_5]) ).
fof(f_2_1,plain,
! [X] : subclass(X,universal_class),
inference(fof_nnf,[status(thm)],[class_elements_are_sets]) ).
fof(f_2_2,plain,
! [U_8] : subclass(U_8,universal_class),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
! [U_8] : subclass(U_8,universal_class),
inference(definitional_conversion,[status(esa)],[f_2_2]) ).
cnf(f_2_4,plain,
subclass(U_8,universal_class),
inference(clausify,[status(thm)],[f_2_3]) ).
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]) ).
fof(f_3_4,plain,
( ! [U_13,U_11] :
( subclass(U_11,U_13)
| ~ sP1(U_13,U_11) )
& ! [U_13,U_11] :
( subclass(U_13,U_11)
| ~ sP1(U_13,U_11) )
& ! [U_14,U_12] :
( U_14 = U_12
| ~ subclass(U_12,U_14)
| ~ subclass(U_14,U_12) )
& ! [U_13,U_11] :
( sP1(U_13,U_11)
| U_13 != U_11 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1])],[f_3_3]) ).
cnf(f_3_6,plain,
( U_14 = U_12
| ~ subclass(U_12,U_14)
| ~ subclass(U_14,U_12) ),
inference(clausify,[status(thm)],[f_3_4]) ).
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]) ).
fof(f_5_3,plain,
! [U_25,U_24] : member(unordered_pair(U_25,U_24),universal_class),
inference(definitional_conversion,[status(esa)],[f_5_2]) ).
cnf(f_5_4,plain,
member(unordered_pair(U_25,U_24),universal_class),
inference(clausify,[status(thm)],[f_5_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]) ).
fof(f_6_3,plain,
! [U_26] : singleton(U_26) = unordered_pair(U_26,U_26),
inference(definitional_conversion,[status(esa)],[f_6_2]) ).
cnf(f_6_4,plain,
singleton(U_26) = unordered_pair(U_26,U_26),
inference(clausify,[status(thm)],[f_6_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]) ).
fof(f_22_4,plain,
( ! [U_107,U_111,U_109] :
( ~ member(U_107,U_109)
| ~ sP12(U_107,U_111,U_109) )
& ! [U_107,U_111,U_109] :
( ~ member(U_107,U_111)
| ~ sP12(U_107,U_111,U_109) )
& ! [U_107,U_111,U_109] :
( member(U_107,union(U_111,U_109))
| sP12(U_107,U_111,U_109) )
& ! [U_106,U_108,U_110] :
( member(U_106,U_108)
| member(U_106,U_110)
| ~ member(U_106,union(U_110,U_108)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP12])],[f_22_3]) ).
cnf(f_22_5,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_4]) ).
cnf(f_22_6,plain,
( member(U_107,union(U_111,U_109))
| sP12(U_107,U_111,U_109) ),
inference(clausify,[status(thm)],[f_22_4]) ).
cnf(f_22_8,plain,
( ~ member(U_107,U_109)
| ~ sP12(U_107,U_111,U_109) ),
inference(clausify,[status(thm)],[f_22_4]) ).
fof(f_42_1,plain,
! [XF,Y] : apply(XF,Y) = sum_class(image(XF,singleton(Y))),
inference(fof_nnf,[status(thm)],[apply_defn]) ).
fof(f_42_2,plain,
! [U_179,U_178] : apply(U_179,U_178) = sum_class(image(U_179,singleton(U_178))),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
! [U_178,U_179] : apply(U_179,U_178) = sum_class(image(U_179,singleton(U_178))),
inference(definitional_conversion,[status(esa)],[f_42_2]) ).
cnf(f_42_4,plain,
apply(U_179,U_178) = sum_class(image(U_179,singleton(U_178))),
inference(clausify,[status(thm)],[f_42_3]) ).
fof(f_44_1,negated_conjecture,
~ ! [X] : member(singleton(X),universal_class),
inference(negate,[status(cth)],[singletons_are_sets]) ).
fof(f_44_2,negated_conjecture,
? [X] : ~ member(singleton(X),universal_class),
inference(fof_nnf,[status(thm)],[f_44_1]) ).
fof(f_44_3,negated_conjecture,
? [U_182] : ~ member(singleton(U_182),universal_class),
inference(variable_rename,[status(thm)],[f_44_2]) ).
fof(f_44_4,negated_conjecture,
~ member(singleton(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(singleton(sK8),universal_class),
inference(definitional_conversion,[status(esa)],[f_44_4]) ).
cnf(f_44_6,negated_conjecture,
~ member(singleton(sK8),universal_class),
inference(clausify,[status(thm)],[f_44_5]) ).
cnf(equality_47,axiom,
( sP12(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP12(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(t1,plain,
~ member(singleton(sK8),universal_class),
inference(start,[status(thm),parent(0:0)],[f_44_6]) ).
cnf(t2,plain,
( member(singleton(sK8),apply(U_2404,U_2405))
| ~ member(singleton(sK8),union(apply(U_2404,U_2405),universal_class))
| member(singleton(sK8),universal_class) ),
inference(extension,[status(thm),parent(t1:1)],[f_22_5]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( sP12(singleton(sK8),apply(U_2404,U_2405),universal_class)
| member(singleton(sK8),union(apply(U_2404,U_2405),universal_class)) ),
inference(extension,[status(thm),parent(t2:2)],[f_22_6]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( apply(U_2404,U_2405) != sum_class(image(U_2404,singleton(U_2405)))
| universal_class != universal_class
| sP12(unordered_pair(sK8,sK8),sum_class(image(U_2404,singleton(U_2405))),universal_class)
| singleton(sK8) != unordered_pair(sK8,sK8)
| ~ sP12(singleton(sK8),apply(U_2404,U_2405),universal_class) ),
inference(extension,[status(thm),parent(t4:2)],[equality_47]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
singleton(sK8) = unordered_pair(sK8,sK8),
inference(extension,[status(thm),parent(t6:2)],[f_6_4]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( ~ member(unordered_pair(sK8,sK8),universal_class)
| ~ sP12(unordered_pair(sK8,sK8),sum_class(image(U_2404,singleton(U_2405))),universal_class) ),
inference(extension,[status(thm),parent(t6:3)],[f_22_8]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t6:3]) ).
cnf(t12,plain,
member(unordered_pair(sK8,sK8),universal_class),
inference(extension,[status(thm),parent(t10:2)],[f_5_4]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
( ~ subclass(universal_class,universal_class)
| ~ subclass(universal_class,universal_class)
| universal_class = universal_class ),
inference(extension,[status(thm),parent(t6:4)],[f_3_6]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t6:4]) ).
cnf(t16,plain,
subclass(universal_class,universal_class),
inference(extension,[status(thm),parent(t14:2)],[f_2_4]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(l8,lemma,
subclass(universal_class,universal_class),
inference(lemma,[status(cth),parent(t14:2),below(t6:4)],[t14:2]) ).
cnf(t18,plain,
subclass(universal_class,universal_class),
inference(lemma_extension,[status(thm),parent(t14:3)],[l8:1]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t14:3]) ).
cnf(t20,plain,
apply(U_2404,U_2405) = sum_class(image(U_2404,singleton(U_2405))),
inference(extension,[status(thm),parent(t6:5)],[f_42_4]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t6:5]) ).
cnf(t22,plain,
( ~ sP12(singleton(sK8),U_2410,apply(U_2404,U_2405))
| ~ member(singleton(sK8),apply(U_2404,U_2405)) ),
inference(extension,[status(thm),parent(t2:3)],[f_22_8]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t2:3]) ).
cnf(t24,plain,
( member(singleton(sK8),union(U_2410,apply(U_2404,U_2405)))
| sP12(singleton(sK8),U_2410,apply(U_2404,U_2405)) ),
inference(extension,[status(thm),parent(t22:2)],[f_22_6]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
( member(singleton(sK8),universal_class)
| ~ subclass(union(U_2410,apply(U_2404,U_2405)),universal_class)
| ~ member(singleton(sK8),union(U_2410,apply(U_2404,U_2405))) ),
inference(extension,[status(thm),parent(t24:2)],[f_1_6]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t24:2]) ).
cnf(t28,plain,
subclass(union(U_2410,apply(U_2404,U_2405)),universal_class),
inference(extension,[status(thm),parent(t26:2)],[f_2_4]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t26:2]) ).
cnf(t30,plain,
$false,
inference(reduction,[status(thm),parent(t26:3)],[t26:3,t1:1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET077+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/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/5.37 % Computer : n016.cluster.edu
% 0.08/5.37 % Model : x86_64 x86_64
% 0.08/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.37 % Memory : 8046.5625MB
% 0.08/5.37 % OS : Linux 6.8.0-71-generic
% 0.08/5.37 % CPULimit : 300
% 0.08/5.37 % WCLimit : 300
% 0.08/5.37 % DateTime : Sat Sep 19 21:42:28 UTC 2026
% 0.08/5.37 % CPUTime :
% 40.65/46.00 % SZS status Theorem for theBenchmark
% 40.65/46.00 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------