%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET086+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 : n011.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 08:56:16 AM UTC 2026
% Result : Theorem 5.45s 5.75s
% Output : Proof 5.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 26 ( 9 unt; 0 def)
% Number of atoms : 70 ( 34 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 78 ( 34 ~; 25 |; 19 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 26 ( 1 sgn 12 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(member_of_substitution,conjecture,
! [X] :
? [U] :
( ( U = X
& ~ ? [Y] :
( X = singleton(Y)
& member(Y,universal_class) ) )
| ( X = singleton(U)
& member(U,universal_class) ) ),
file('theBenchmark.p',member_of_substitution) ).
fof(f_44_1,negated_conjecture,
~ ! [X] :
? [U] :
( ( U = X
& ~ ? [Y] :
( X = singleton(Y)
& member(Y,universal_class) ) )
| ( X = singleton(U)
& member(U,universal_class) ) ),
inference(negate,[status(cth)],[member_of_substitution]) ).
fof(f_44_2,negated_conjecture,
? [X] :
! [U] :
( ( U != X
| ? [Y] :
( X = singleton(Y)
& member(Y,universal_class) ) )
& ( X != singleton(U)
| ~ member(U,universal_class) ) ),
inference(fof_nnf,[status(thm)],[f_44_1]) ).
fof(f_44_3,negated_conjecture,
? [U_184] :
! [U_183] :
( ( U_183 != U_184
| ? [U_182] :
( U_184 = singleton(U_182)
& member(U_182,universal_class) ) )
& ( U_184 != singleton(U_183)
| ~ member(U_183,universal_class) ) ),
inference(variable_rename,[status(thm)],[f_44_2]) ).
fof(f_44_4,negated_conjecture,
? [U_184] :
( ( ! [U_186] : U_186 != U_184
| ? [U_182] :
( U_184 = singleton(U_182)
& member(U_182,universal_class) ) )
& ! [U_185] :
( U_184 != singleton(U_185)
| ~ member(U_185,universal_class) ) ),
inference(miniscope,[status(thm)],[f_44_3]) ).
fof(f_44_5,negated_conjecture,
( ( ! [U_186] : U_186 != sK8
| ? [U_182] :
( sK8 = singleton(U_182)
& member(U_182,universal_class) ) )
& ! [U_185] :
( sK8 != singleton(U_185)
| ~ member(U_185,universal_class) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_184,sK8)],[f_44_4]) ).
fof(f_44_6,negated_conjecture,
( ( ! [U_186] : U_186 != sK8
| ( sK8 = singleton(sK9)
& member(sK9,universal_class) ) )
& ! [U_185] :
( sK8 != singleton(U_185)
| ~ member(U_185,universal_class) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_182,sK9)],[f_44_5]) ).
fof(f_44_7,negated_conjecture,
( ( sK8 = singleton(sK9)
| ~ sP0 )
& ( member(sK9,universal_class)
| ~ sP0 )
& ! [U_186] :
( U_186 != sK8
| sP0 )
& ! [U_185] :
( sK8 != singleton(U_185)
| ~ member(U_185,universal_class) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_44_6]) ).
cnf(f_44_8,negated_conjecture,
( sK8 != singleton(U_185)
| ~ member(U_185,universal_class) ),
inference(clausify,[status(thm)],[f_44_7]) ).
cnf(f_44_9,negated_conjecture,
( U_186 != sK8
| sP0 ),
inference(clausify,[status(thm)],[f_44_7]) ).
cnf(f_44_10,negated_conjecture,
( member(sK9,universal_class)
| ~ sP0 ),
inference(clausify,[status(thm)],[f_44_7]) ).
cnf(f_44_11,negated_conjecture,
( sK8 = singleton(sK9)
| ~ sP0 ),
inference(clausify,[status(thm)],[f_44_7]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(t1,plain,
( sK8 != singleton(sK9)
| ~ member(sK9,universal_class) ),
inference(start,[status(thm),parent(0:0)],[f_44_8]) ).
cnf(t2,plain,
( ~ sP0
| member(sK9,universal_class) ),
inference(extension,[status(thm),parent(t1:1)],[f_44_10]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( sK8 != sK8
| sP0 ),
inference(extension,[status(thm),parent(t2:2)],[f_44_9]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
sK8 = sK8,
inference(extension,[status(thm),parent(t4:2)],[equality_1]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( ~ sP0
| sK8 = singleton(sK9) ),
inference(extension,[status(thm),parent(t1:2)],[f_44_11]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t1:2]) ).
cnf(t10,plain,
( sK8 != sK8
| sP0 ),
inference(extension,[status(thm),parent(t8:2)],[f_44_9]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
sK8 = sK8,
inference(extension,[status(thm),parent(t10:2)],[equality_1]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET086+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
% 0.08/0.35 % Computer : n011.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 19 21:38:56 UTC 2026
% 0.08/0.35 % CPUTime :
% 5.45/5.75 % SZS status Theorem for theBenchmark
% 5.45/5.75 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------