%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET020+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 : n009.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 08:55:57 AM UTC 2026
% Result : Theorem 14.06s 14.30s
% Output : Proof 14.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 45 ( 21 unt; 0 def)
% Number of atoms : 106 ( 58 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 100 ( 39 ~; 30 |; 28 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 12 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(first_second,axiom,
! [X,Y] :
( ( member(Y,universal_class)
& member(X,universal_class) )
=> ( second(ordered_pair(X,Y)) = Y
& first(ordered_pair(X,Y)) = X ) ),
file('SET005+0.ax',first_second) ).
fof(unique_1st_and_2nd_in_pair_of_sets1,conjecture,
! [U,V,X] :
( ( X = ordered_pair(U,V)
& member(V,universal_class)
& member(U,universal_class) )
=> ( second(X) = V
& first(X) = U ) ),
file('theBenchmark.p',unique_1st_and_2nd_in_pair_of_sets1) ).
fof(f_9_1,plain,
! [X,Y] :
( ( second(ordered_pair(X,Y)) = Y
& first(ordered_pair(X,Y)) = X )
| ~ member(Y,universal_class)
| ~ member(X,universal_class) ),
inference(fof_nnf,[status(thm)],[first_second]) ).
fof(f_9_2,plain,
! [U_42,U_41] :
( ( second(ordered_pair(U_42,U_41)) = U_41
& first(ordered_pair(U_42,U_41)) = U_42 )
| ~ member(U_41,universal_class)
| ~ member(U_42,universal_class) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
( first(ordered_pair(U_42,U_41)) = U_42
| ~ member(U_41,universal_class)
| ~ member(U_42,universal_class) ),
inference(clausify,[status(thm)],[f_9_2]) ).
cnf(f_9_4,plain,
( second(ordered_pair(U_42,U_41)) = U_41
| ~ member(U_41,universal_class)
| ~ member(U_42,universal_class) ),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_44_1,negated_conjecture,
~ ! [U,V,X] :
( ( X = ordered_pair(U,V)
& member(V,universal_class)
& member(U,universal_class) )
=> ( second(X) = V
& first(X) = U ) ),
inference(negate,[status(cth)],[unique_1st_and_2nd_in_pair_of_sets1]) ).
fof(f_44_2,negated_conjecture,
? [U,V,X] :
( ( second(X) != V
| first(X) != U )
& X = ordered_pair(U,V)
& member(V,universal_class)
& member(U,universal_class) ),
inference(fof_nnf,[status(thm)],[f_44_1]) ).
fof(f_44_3,negated_conjecture,
? [U_184,U_183,U_182] :
( ( second(U_182) != U_183
| first(U_182) != U_184 )
& U_182 = ordered_pair(U_184,U_183)
& member(U_183,universal_class)
& member(U_184,universal_class) ),
inference(variable_rename,[status(thm)],[f_44_2]) ).
fof(f_44_4,negated_conjecture,
? [U_183,U_182] :
( ( second(U_182) != U_183
| first(U_182) != sK8 )
& U_182 = ordered_pair(sK8,U_183)
& member(U_183,universal_class)
& member(sK8,universal_class) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_184,sK8)],[f_44_3]) ).
fof(f_44_5,negated_conjecture,
? [U_182] :
( ( second(U_182) != sK9
| first(U_182) != sK8 )
& U_182 = ordered_pair(sK8,sK9)
& member(sK9,universal_class)
& member(sK8,universal_class) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_183,sK9)],[f_44_4]) ).
fof(f_44_6,negated_conjecture,
( ( second(sK10) != sK9
| first(sK10) != sK8 )
& sK10 = ordered_pair(sK8,sK9)
& member(sK9,universal_class)
& member(sK8,universal_class) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_182,sK10)],[f_44_5]) ).
fof(f_44_7,negated_conjecture,
( ( second(sK10) != sK9
| first(sK10) != sK8 )
& sK10 = ordered_pair(sK8,sK9)
& member(sK9,universal_class)
& member(sK8,universal_class) ),
inference(definitional_conversion,[status(esa)],[f_44_6]) ).
cnf(f_44_8,negated_conjecture,
member(sK8,universal_class),
inference(clausify,[status(thm)],[f_44_7]) ).
cnf(f_44_9,negated_conjecture,
member(sK9,universal_class),
inference(clausify,[status(thm)],[f_44_7]) ).
cnf(f_44_10,negated_conjecture,
sK10 = ordered_pair(sK8,sK9),
inference(clausify,[status(thm)],[f_44_7]) ).
cnf(f_44_11,negated_conjecture,
( second(sK10) != sK9
| first(sK10) != sK8 ),
inference(clausify,[status(thm)],[f_44_7]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_8,axiom,
( first(Eq_x_0) = first(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( second(Eq_x_0) = second(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(t1,plain,
( second(sK10) != sK9
| first(sK10) != sK8 ),
inference(start,[status(thm),parent(0:0)],[f_44_11]) ).
cnf(t2,plain,
( first(ordered_pair(sK8,sK9)) != sK8
| first(sK10) != first(ordered_pair(sK8,sK9))
| first(sK10) = sK8 ),
inference(extension,[status(thm),parent(t1:1)],[equality_3]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( sK10 != ordered_pair(sK8,sK9)
| first(sK10) = first(ordered_pair(sK8,sK9)) ),
inference(extension,[status(thm),parent(t2:2)],[equality_8]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
sK10 = ordered_pair(sK8,sK9),
inference(extension,[status(thm),parent(t4:2)],[f_44_10]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( ~ member(sK9,universal_class)
| ~ member(sK8,universal_class)
| first(ordered_pair(sK8,sK9)) = sK8 ),
inference(extension,[status(thm),parent(t2:3)],[f_9_3]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:3]) ).
cnf(t10,plain,
member(sK8,universal_class),
inference(extension,[status(thm),parent(t8:2)],[f_44_8]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
member(sK9,universal_class),
inference(extension,[status(thm),parent(t8:3)],[f_44_9]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t8:3]) ).
cnf(t14,plain,
( second(ordered_pair(sK8,sK9)) != sK9
| second(sK10) != second(ordered_pair(sK8,sK9))
| second(sK10) = sK9 ),
inference(extension,[status(thm),parent(t1:2)],[equality_3]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t1:2]) ).
cnf(t16,plain,
( sK10 != ordered_pair(sK8,sK9)
| second(sK10) = second(ordered_pair(sK8,sK9)) ),
inference(extension,[status(thm),parent(t14:2)],[equality_9]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
sK10 = ordered_pair(sK8,sK9),
inference(extension,[status(thm),parent(t16:2)],[f_44_10]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
( ~ member(sK9,universal_class)
| ~ member(sK8,universal_class)
| second(ordered_pair(sK8,sK9)) = sK9 ),
inference(extension,[status(thm),parent(t14:3)],[f_9_4]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t14:3]) ).
cnf(t22,plain,
member(sK8,universal_class),
inference(extension,[status(thm),parent(t20:2)],[f_44_8]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
member(sK9,universal_class),
inference(extension,[status(thm),parent(t20:3)],[f_44_9]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t20:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET020+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 : n009.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 21:28:57 UTC 2026
% 0.08/0.36 % CPUTime :
% 14.06/14.30 % SZS status Theorem for theBenchmark
% 14.06/14.30 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------