%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU097+1 : TPTP v9.3.1. Released v3.2.0.
% 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 : n018.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 08:58:02 AM UTC 2026
% Result : Theorem 237.44s 237.77s
% Output : Proof 237.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 50 ( 24 unt; 0 def)
% Number of atoms : 92 ( 15 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 75 ( 33 ~; 25 |; 13 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 46 ( 1 sgn 30 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d6_xboole_0,axiom,
! [A,B] : symmetric_difference(A,B) = set_union2(set_difference(A,B),set_difference(B,A)),
file('theBenchmark.p',d6_xboole_0) ).
fof(fc12_finset_1,axiom,
! [A,B] :
( finite(A)
=> finite(set_difference(A,B)) ),
file('theBenchmark.p',fc12_finset_1) ).
fof(l3_finset_1,axiom,
! [A,B] :
( ( finite(B)
& finite(A) )
=> finite(set_union2(A,B)) ),
file('theBenchmark.p',l3_finset_1) ).
fof(t28_finset_1,conjecture,
! [A,B] :
( ( finite(B)
& finite(A) )
=> finite(symmetric_difference(A,B)) ),
file('theBenchmark.p',t28_finset_1) ).
fof(f_15_1,plain,
! [A,B] : symmetric_difference(A,B) = set_union2(set_difference(A,B),set_difference(B,A)),
inference(fof_nnf,[status(thm)],[d6_xboole_0]) ).
fof(f_15_2,plain,
! [U_20,U_19] : symmetric_difference(U_20,U_19) = set_union2(set_difference(U_20,U_19),set_difference(U_19,U_20)),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
! [U_19,U_20] : symmetric_difference(U_20,U_19) = set_union2(set_difference(U_20,U_19),set_difference(U_19,U_20)),
inference(definitional_conversion,[status(esa)],[f_15_2]) ).
cnf(f_15_4,plain,
symmetric_difference(U_20,U_19) = set_union2(set_difference(U_20,U_19),set_difference(U_19,U_20)),
inference(clausify,[status(thm)],[f_15_3]) ).
fof(f_17_1,plain,
! [A,B] :
( finite(set_difference(A,B))
| ~ finite(A) ),
inference(fof_nnf,[status(thm)],[fc12_finset_1]) ).
fof(f_17_2,plain,
! [U_24,U_23] :
( finite(set_difference(U_24,U_23))
| ~ finite(U_24) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
! [U_24] :
( ! [U_23] : finite(set_difference(U_24,U_23))
| ~ finite(U_24) ),
inference(miniscope,[status(thm)],[f_17_2]) ).
fof(f_17_4,plain,
! [U_23,U_24] :
( finite(set_difference(U_24,U_23))
| ~ finite(U_24) ),
inference(definitional_conversion,[status(esa)],[f_17_3]) ).
cnf(f_17_5,plain,
( finite(set_difference(U_24,U_23))
| ~ finite(U_24) ),
inference(clausify,[status(thm)],[f_17_4]) ).
fof(f_30_1,plain,
! [A,B] :
( finite(set_union2(A,B))
| ~ finite(B)
| ~ finite(A) ),
inference(fof_nnf,[status(thm)],[l3_finset_1]) ).
fof(f_30_2,plain,
! [U_39,U_38] :
( finite(set_union2(U_39,U_38))
| ~ finite(U_38)
| ~ finite(U_39) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
! [U_38,U_39] :
( finite(set_union2(U_39,U_38))
| ~ finite(U_38)
| ~ finite(U_39) ),
inference(definitional_conversion,[status(esa)],[f_30_2]) ).
cnf(f_30_4,plain,
( finite(set_union2(U_39,U_38))
| ~ finite(U_38)
| ~ finite(U_39) ),
inference(clausify,[status(thm)],[f_30_3]) ).
fof(f_60_1,negated_conjecture,
~ ! [A,B] :
( ( finite(B)
& finite(A) )
=> finite(symmetric_difference(A,B)) ),
inference(negate,[status(cth)],[t28_finset_1]) ).
fof(f_60_2,negated_conjecture,
? [A,B] :
( ~ finite(symmetric_difference(A,B))
& finite(B)
& finite(A) ),
inference(fof_nnf,[status(thm)],[f_60_1]) ).
fof(f_60_3,negated_conjecture,
? [U_77,U_76] :
( ~ finite(symmetric_difference(U_77,U_76))
& finite(U_76)
& finite(U_77) ),
inference(variable_rename,[status(thm)],[f_60_2]) ).
fof(f_60_4,negated_conjecture,
? [U_76] :
( ~ finite(symmetric_difference(sK27,U_76))
& finite(U_76)
& finite(sK27) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_77,sK27)],[f_60_3]) ).
fof(f_60_5,negated_conjecture,
( ~ finite(symmetric_difference(sK27,sK28))
& finite(sK28)
& finite(sK27) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_76,sK28)],[f_60_4]) ).
fof(f_60_6,negated_conjecture,
( ~ finite(symmetric_difference(sK27,sK28))
& finite(sK28)
& finite(sK27) ),
inference(definitional_conversion,[status(esa)],[f_60_5]) ).
cnf(f_60_7,negated_conjecture,
finite(sK27),
inference(clausify,[status(thm)],[f_60_6]) ).
cnf(f_60_8,negated_conjecture,
finite(sK28),
inference(clausify,[status(thm)],[f_60_6]) ).
cnf(f_60_9,negated_conjecture,
~ finite(symmetric_difference(sK27,sK28)),
inference(clausify,[status(thm)],[f_60_6]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_19,axiom,
( finite(Eq_y_0)
| ~ finite(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(t1,plain,
finite(sK27),
inference(start,[status(thm),parent(0:0)],[f_60_7]) ).
cnf(t2,plain,
( finite(set_difference(sK27,sK28))
| ~ finite(sK27) ),
inference(extension,[status(thm),parent(t1:1)],[f_17_5]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ finite(set_difference(sK28,sK27))
| finite(set_union2(set_difference(sK27,sK28),set_difference(sK28,sK27)))
| ~ finite(set_difference(sK27,sK28)) ),
inference(extension,[status(thm),parent(t2:2)],[f_30_4]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( set_union2(set_difference(sK27,sK28),set_difference(sK28,sK27)) != symmetric_difference(sK27,sK28)
| finite(symmetric_difference(sK27,sK28))
| ~ finite(set_union2(set_difference(sK27,sK28),set_difference(sK28,sK27))) ),
inference(extension,[status(thm),parent(t4:2)],[equality_19]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( symmetric_difference(sK27,sK28) != symmetric_difference(sK27,sK28)
| finite(symmetric_difference(sK27,sK28))
| ~ finite(symmetric_difference(sK27,sK28)) ),
inference(extension,[status(thm),parent(t6:2)],[equality_19]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
~ finite(symmetric_difference(sK27,sK28)),
inference(extension,[status(thm),parent(t8:2)],[f_60_9]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
symmetric_difference(sK27,sK28) = symmetric_difference(sK27,sK28),
inference(extension,[status(thm),parent(t8:3)],[equality_1]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t8:3]) ).
cnf(t14,plain,
( symmetric_difference(sK27,sK28) != set_union2(set_difference(sK27,sK28),set_difference(sK28,sK27))
| set_union2(set_difference(sK27,sK28),set_difference(sK28,sK27)) = symmetric_difference(sK27,sK28) ),
inference(extension,[status(thm),parent(t6:3)],[equality_2]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t6:3]) ).
cnf(t16,plain,
symmetric_difference(sK27,sK28) = set_union2(set_difference(sK27,sK28),set_difference(sK28,sK27)),
inference(extension,[status(thm),parent(t14:2)],[f_15_4]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
( ~ finite(sK28)
| finite(set_difference(sK28,sK27)) ),
inference(extension,[status(thm),parent(t4:3)],[f_17_5]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t4:3]) ).
cnf(t20,plain,
finite(sK28),
inference(extension,[status(thm),parent(t18:2)],[f_60_8]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU097+1 : TPTP v9.3.1. Released v3.2.0.
% 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
% 0.10/0.37 % Computer : n018.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 19 23:20:56 UTC 2026
% 0.10/0.37 % CPUTime :
% 237.44/237.77 % SZS status Theorem for theBenchmark
% 237.44/237.77 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------