%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET081+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 : n015.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 08:56:15 AM UTC 2026
% Result : Theorem 11.65s 11.90s
% Output : Proof 11.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 17 unt; 0 def)
% Number of atoms : 73 ( 38 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 69 ( 28 ~; 23 |; 15 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 22 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
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(only_member_in_singleton,conjecture,
! [X,Y] :
( member(Y,singleton(X))
=> Y = X ),
file('theBenchmark.p',only_member_in_singleton) ).
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_5,plain,
( U_22 = U_18
| U_22 = U_20
| ~ member(U_22,unordered_pair(U_20,U_18)) ),
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_44_1,negated_conjecture,
~ ! [X,Y] :
( member(Y,singleton(X))
=> Y = X ),
inference(negate,[status(cth)],[only_member_in_singleton]) ).
fof(f_44_2,negated_conjecture,
? [X,Y] :
( Y != X
& member(Y,singleton(X)) ),
inference(fof_nnf,[status(thm)],[f_44_1]) ).
fof(f_44_3,negated_conjecture,
? [U_183,U_182] :
( U_182 != U_183
& member(U_182,singleton(U_183)) ),
inference(variable_rename,[status(thm)],[f_44_2]) ).
fof(f_44_4,negated_conjecture,
? [U_182] :
( U_182 != sK8
& member(U_182,singleton(sK8)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_183,sK8)],[f_44_3]) ).
fof(f_44_5,negated_conjecture,
( sK9 != sK8
& member(sK9,singleton(sK8)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_182,sK9)],[f_44_4]) ).
fof(f_44_6,negated_conjecture,
( sK9 != sK8
& member(sK9,singleton(sK8)) ),
inference(definitional_conversion,[status(esa)],[f_44_5]) ).
cnf(f_44_7,negated_conjecture,
member(sK9,singleton(sK8)),
inference(clausify,[status(thm)],[f_44_6]) ).
cnf(f_44_8,negated_conjecture,
sK9 != sK8,
inference(clausify,[status(thm)],[f_44_6]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_31,axiom,
( member(Eq_y_0,Eq_y_1)
| ~ member(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(t1,plain,
sK9 != sK8,
inference(start,[status(thm),parent(0:0)],[f_44_8]) ).
cnf(t2,plain,
( sK9 = sK8
| ~ member(sK9,unordered_pair(sK8,sK8))
| sK9 = sK8 ),
inference(extension,[status(thm),parent(t1:1)],[f_4_5]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( singleton(sK8) != unordered_pair(sK8,sK8)
| ~ member(sK9,singleton(sK8))
| sK9 != sK9
| member(sK9,unordered_pair(sK8,sK8)) ),
inference(extension,[status(thm),parent(t2:2)],[equality_31]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
sK9 = sK9,
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,
member(sK9,singleton(sK8)),
inference(extension,[status(thm),parent(t4:3)],[f_44_7]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
singleton(sK8) = unordered_pair(sK8,sK8),
inference(extension,[status(thm),parent(t4:4)],[f_6_3]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t4:4]) ).
cnf(t12,plain,
$false,
inference(reduction,[status(thm),parent(t2:3)],[t2:3,t1:1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET081+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
% 0.08/0.35 % Computer : n015.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 21:41:18 UTC 2026
% 0.08/0.36 % CPUTime :
% 11.65/11.90 % SZS status Theorem for theBenchmark
% 11.65/11.90 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------