%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET060+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 : n019.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 08:56:07 AM UTC 2026
% Result : Theorem 1.77s 2.04s
% Output : Proof 1.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 44 ( 20 unt; 0 def)
% Number of atoms : 110 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 111 ( 45 ~; 43 |; 20 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 63 ( 3 sgn 44 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(intersection,axiom,
! [X,Y,Z] :
( member(Z,intersection(X,Y))
<=> ( member(Z,Y)
& member(Z,X) ) ),
file('SET005+0.ax',intersection) ).
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(special_classes_lemma,conjecture,
! [X,Y] : ~ member(Y,intersection(complement(X),X)),
file('theBenchmark.p',special_classes_lemma) ).
fof(f_13_1,plain,
! [X,Y,Z] :
( ( member(Z,intersection(X,Y))
| ~ member(Z,Y)
| ~ member(Z,X) )
& ( ( member(Z,Y)
& member(Z,X) )
| ~ member(Z,intersection(X,Y)) ) ),
inference(fof_nnf,[status(thm)],[intersection]) ).
fof(f_13_2,plain,
! [U_54,U_53,U_52] :
( ( member(U_52,intersection(U_54,U_53))
| ~ member(U_52,U_53)
| ~ member(U_52,U_54) )
& ( ( member(U_52,U_53)
& member(U_52,U_54) )
| ~ member(U_52,intersection(U_54,U_53)) ) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
( ! [U_60,U_58,U_56] :
( member(U_56,intersection(U_60,U_58))
| ~ member(U_56,U_58)
| ~ member(U_56,U_60) )
& ! [U_59,U_57,U_55] :
( ( member(U_55,U_57)
& member(U_55,U_59) )
| ~ member(U_55,intersection(U_59,U_57)) ) ),
inference(miniscope,[status(thm)],[f_13_2]) ).
cnf(f_13_4,plain,
( member(U_55,U_59)
| ~ member(U_55,intersection(U_59,U_57)) ),
inference(clausify,[status(thm)],[f_13_3]) ).
cnf(f_13_5,plain,
( member(U_55,U_57)
| ~ member(U_55,intersection(U_59,U_57)) ),
inference(clausify,[status(thm)],[f_13_3]) ).
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]) ).
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,Y] : ~ member(Y,intersection(complement(X),X)),
inference(negate,[status(cth)],[special_classes_lemma]) ).
fof(f_44_2,negated_conjecture,
? [X,Y] : member(Y,intersection(complement(X),X)),
inference(fof_nnf,[status(thm)],[f_44_1]) ).
fof(f_44_3,negated_conjecture,
? [U_183,U_182] : member(U_182,intersection(complement(U_183),U_183)),
inference(variable_rename,[status(thm)],[f_44_2]) ).
fof(f_44_4,negated_conjecture,
? [U_182] : member(U_182,intersection(complement(sK8),sK8)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_183,sK8)],[f_44_3]) ).
fof(f_44_5,negated_conjecture,
member(sK9,intersection(complement(sK8),sK8)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_182,sK9)],[f_44_4]) ).
fof(f_44_6,negated_conjecture,
member(sK9,intersection(complement(sK8),sK8)),
inference(definitional_conversion,[status(esa)],[f_44_5]) ).
cnf(f_44_7,negated_conjecture,
member(sK9,intersection(complement(sK8),sK8)),
inference(clausify,[status(thm)],[f_44_6]) ).
cnf(t1,plain,
( ~ member(sK9,sK8)
| ~ member(sK9,complement(sK8)) ),
inference(start,[status(thm),parent(0:0)],[f_14_5]) ).
cnf(t2,plain,
( member(sK9,intersection(complement(sK8),sK8))
| ~ member(sK9,union(intersection(complement(sK8),sK8),complement(sK8)))
| member(sK9,complement(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(sK9,intersection(complement(sK8),sK8))
| member(sK9,union(intersection(complement(sK8),sK8),complement(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(sK9,intersection(complement(sK8),sK8)),
inference(extension,[status(thm),parent(t4:2)],[f_44_7]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( member(sK9,complement(sK8))
| ~ member(sK9,intersection(complement(sK8),sK8)) ),
inference(extension,[status(thm),parent(t2:3)],[f_13_4]) ).
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(sK9,intersection(complement(sK8),sK8))
| ~ member(sK9,union(intersection(complement(sK8),sK8),sK8))
| member(sK9,sK8) ),
inference(extension,[status(thm),parent(t1:2)],[f_22_4]) ).
cnf(t12,plain,
$false,
inference(connection,[status(thm),parent(t11:1)],[t11:1,t1:2]) ).
cnf(t13,plain,
( ~ member(sK9,intersection(complement(sK8),sK8))
| member(sK9,union(intersection(complement(sK8),sK8),sK8)) ),
inference(extension,[status(thm),parent(t11:2)],[f_22_5]) ).
cnf(t14,plain,
$false,
inference(connection,[status(thm),parent(t13:1)],[t13:1,t11:2]) ).
cnf(t15,plain,
member(sK9,intersection(complement(sK8),sK8)),
inference(extension,[status(thm),parent(t13:2)],[f_44_7]) ).
cnf(t16,plain,
$false,
inference(connection,[status(thm),parent(t15:1)],[t15:1,t13:2]) ).
cnf(t17,plain,
( member(sK9,sK8)
| ~ member(sK9,intersection(complement(sK8),sK8)) ),
inference(extension,[status(thm),parent(t11:3)],[f_13_5]) ).
cnf(t18,plain,
$false,
inference(connection,[status(thm),parent(t17:1)],[t17:1,t11:3]) ).
cnf(t19,plain,
$false,
inference(reduction,[status(thm),parent(t17:2)],[t17:2,t1:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET060+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
% 0.09/0.37 % Computer : n019.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 19 21:35:52 UTC 2026
% 0.09/0.37 % CPUTime :
% 1.77/2.04 % SZS status Theorem for theBenchmark
% 1.77/2.04 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------