%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET630+3 : TPTP v9.3.1. Released v2.2.0.
% 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 : 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 08:57:10 AM UTC 2026
% Result : Theorem 15.34s 15.69s
% Output : Proof 15.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 78 ( 48 unt; 0 def)
% Number of atoms : 137 ( 30 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 113 ( 54 ~; 47 |; 9 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 84 ( 0 sgn 53 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(symmetric_difference_defn,axiom,
! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)),
file('theBenchmark.p',symmetric_difference_defn) ).
fof(intersect_with_union,axiom,
! [B,C,D] :
( intersect(B,union(C,D))
<=> ( intersect(B,D)
| intersect(B,C) ) ),
file('theBenchmark.p',intersect_with_union) ).
fof(intersection_and_union_disjoint,axiom,
! [B,C] : disjoint(intersection(B,C),difference(B,C)),
file('theBenchmark.p',intersection_and_union_disjoint) ).
fof(disjoint_defn,axiom,
! [B,C] :
( disjoint(B,C)
<=> ~ intersect(B,C) ),
file('theBenchmark.p',disjoint_defn) ).
fof(commutativity_of_intersection,axiom,
! [B,C] : intersection(B,C) = intersection(C,B),
file('theBenchmark.p',commutativity_of_intersection) ).
fof(symmetry_of_intersect,axiom,
! [B,C] :
( intersect(B,C)
=> intersect(C,B) ),
file('theBenchmark.p',symmetry_of_intersect) ).
fof(prove_intersection_and_symmetric_difference_disjoint,conjecture,
! [B,C] : disjoint(intersection(B,C),symmetric_difference(B,C)),
file('theBenchmark.p',prove_intersection_and_symmetric_difference_disjoint) ).
fof(f_1_1,plain,
! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)),
inference(fof_nnf,[status(thm)],[symmetric_difference_defn]) ).
fof(f_1_2,plain,
! [U_1,U_0] : symmetric_difference(U_1,U_0) = union(difference(U_1,U_0),difference(U_0,U_1)),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
symmetric_difference(U_1,U_0) = union(difference(U_1,U_0),difference(U_0,U_1)),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [B,C,D] :
( ( intersect(B,union(C,D))
| ( ~ intersect(B,D)
& ~ intersect(B,C) ) )
& ( intersect(B,D)
| intersect(B,C)
| ~ intersect(B,union(C,D)) ) ),
inference(fof_nnf,[status(thm)],[intersect_with_union]) ).
fof(f_2_2,plain,
! [U_4,U_3,U_2] :
( ( intersect(U_4,union(U_3,U_2))
| ( ~ intersect(U_4,U_2)
& ~ intersect(U_4,U_3) ) )
& ( intersect(U_4,U_2)
| intersect(U_4,U_3)
| ~ intersect(U_4,union(U_3,U_2)) ) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( ! [U_10,U_8,U_6] :
( intersect(U_10,union(U_8,U_6))
| ( ~ intersect(U_10,U_6)
& ~ intersect(U_10,U_8) ) )
& ! [U_9,U_7,U_5] :
( intersect(U_9,U_5)
| intersect(U_9,U_7)
| ~ intersect(U_9,union(U_7,U_5)) ) ),
inference(miniscope,[status(thm)],[f_2_2]) ).
cnf(f_2_4,plain,
( intersect(U_9,U_5)
| intersect(U_9,U_7)
| ~ intersect(U_9,union(U_7,U_5)) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
! [B,C] : disjoint(intersection(B,C),difference(B,C)),
inference(fof_nnf,[status(thm)],[intersection_and_union_disjoint]) ).
fof(f_3_2,plain,
! [U_12,U_11] : disjoint(intersection(U_12,U_11),difference(U_12,U_11)),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
disjoint(intersection(U_12,U_11),difference(U_12,U_11)),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_6_1,plain,
! [B,C] :
( ( disjoint(B,C)
| intersect(B,C) )
& ( ~ intersect(B,C)
| ~ disjoint(B,C) ) ),
inference(fof_nnf,[status(thm)],[disjoint_defn]) ).
fof(f_6_2,plain,
! [U_31,U_30] :
( ( disjoint(U_31,U_30)
| intersect(U_31,U_30) )
& ( ~ intersect(U_31,U_30)
| ~ disjoint(U_31,U_30) ) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_35,U_33] :
( disjoint(U_35,U_33)
| intersect(U_35,U_33) )
& ! [U_34,U_32] :
( ~ intersect(U_34,U_32)
| ~ disjoint(U_34,U_32) ) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
cnf(f_6_4,plain,
( ~ intersect(U_34,U_32)
| ~ disjoint(U_34,U_32) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_5,plain,
( disjoint(U_35,U_33)
| intersect(U_35,U_33) ),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_8_1,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(fof_nnf,[status(thm)],[commutativity_of_intersection]) ).
fof(f_8_2,plain,
! [U_39,U_38] : intersection(U_39,U_38) = intersection(U_38,U_39),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
intersection(U_39,U_38) = intersection(U_38,U_39),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_10_1,plain,
! [B,C] :
( intersect(C,B)
| ~ intersect(B,C) ),
inference(fof_nnf,[status(thm)],[symmetry_of_intersect]) ).
fof(f_10_2,plain,
! [U_43,U_42] :
( intersect(U_42,U_43)
| ~ intersect(U_43,U_42) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
( intersect(U_42,U_43)
| ~ intersect(U_43,U_42) ),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_12_1,negated_conjecture,
~ ! [B,C] : disjoint(intersection(B,C),symmetric_difference(B,C)),
inference(negate,[status(cth)],[prove_intersection_and_symmetric_difference_disjoint]) ).
fof(f_12_2,negated_conjecture,
? [B,C] : ~ disjoint(intersection(B,C),symmetric_difference(B,C)),
inference(fof_nnf,[status(thm)],[f_12_1]) ).
fof(f_12_3,negated_conjecture,
? [U_57,U_56] : ~ disjoint(intersection(U_57,U_56),symmetric_difference(U_57,U_56)),
inference(variable_rename,[status(thm)],[f_12_2]) ).
fof(f_12_4,negated_conjecture,
? [U_56] : ~ disjoint(intersection(sK4,U_56),symmetric_difference(sK4,U_56)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_57,sK4)],[f_12_3]) ).
fof(f_12_5,negated_conjecture,
~ disjoint(intersection(sK4,sK5),symmetric_difference(sK4,sK5)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_56,sK5)],[f_12_4]) ).
fof(f_12_6,negated_conjecture,
~ disjoint(intersection(sK4,sK5),symmetric_difference(sK4,sK5)),
inference(definitional_conversion,[status(esa)],[f_12_5]) ).
cnf(f_12_7,negated_conjecture,
~ disjoint(intersection(sK4,sK5),symmetric_difference(sK4,sK5)),
inference(clausify,[status(thm)],[f_12_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_5,axiom,
( difference(Eq_x_0,Eq_x_1) = difference(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( disjoint(Eq_y_0,Eq_y_1)
| ~ disjoint(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,
( ~ intersect(difference(sK5,sK4),intersection(sK5,sK4))
| ~ disjoint(difference(sK5,sK4),intersection(sK5,sK4)) ),
inference(start,[status(thm),parent(0:0)],[f_6_4]) ).
cnf(t2,plain,
( intersect(difference(sK5,sK4),intersection(sK5,sK4))
| disjoint(difference(sK5,sK4),intersection(sK5,sK4)) ),
inference(extension,[status(thm),parent(t1:1)],[f_6_5]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( intersect(intersection(sK5,sK4),difference(sK5,sK4))
| ~ intersect(difference(sK5,sK4),intersection(sK5,sK4)) ),
inference(extension,[status(thm),parent(t2:2)],[f_10_3]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ disjoint(intersection(sK5,sK4),difference(sK5,sK4))
| ~ intersect(intersection(sK5,sK4),difference(sK5,sK4)) ),
inference(extension,[status(thm),parent(t4:2)],[f_6_4]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
disjoint(intersection(sK5,sK4),difference(sK5,sK4)),
inference(extension,[status(thm),parent(t6:2)],[f_3_3]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( ~ intersect(intersection(sK5,sK4),difference(sK5,sK4))
| intersect(difference(sK5,sK4),intersection(sK5,sK4)) ),
inference(extension,[status(thm),parent(t1:2)],[f_10_3]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t1:2]) ).
cnf(t12,plain,
( intersect(intersection(sK5,sK4),difference(sK4,sK5))
| ~ intersect(intersection(sK5,sK4),union(difference(sK4,sK5),difference(sK5,sK4)))
| intersect(intersection(sK5,sK4),difference(sK5,sK4)) ),
inference(extension,[status(thm),parent(t10:2)],[f_2_4]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
( disjoint(intersection(sK5,sK4),union(difference(sK4,sK5),difference(sK5,sK4)))
| intersect(intersection(sK5,sK4),union(difference(sK4,sK5),difference(sK5,sK4))) ),
inference(extension,[status(thm),parent(t12:2)],[f_6_5]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
( union(difference(sK4,sK5),difference(sK5,sK4)) != symmetric_difference(sK4,sK5)
| disjoint(intersection(sK4,sK5),symmetric_difference(sK4,sK5))
| intersection(sK5,sK4) != intersection(sK4,sK5)
| ~ disjoint(intersection(sK5,sK4),union(difference(sK4,sK5),difference(sK5,sK4))) ),
inference(extension,[status(thm),parent(t14:2)],[equality_12]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
intersection(sK5,sK4) = intersection(sK4,sK5),
inference(extension,[status(thm),parent(t16:2)],[f_8_3]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
~ disjoint(intersection(sK4,sK5),symmetric_difference(sK4,sK5)),
inference(extension,[status(thm),parent(t16:3)],[f_12_7]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t16:3]) ).
cnf(t22,plain,
( symmetric_difference(sK4,sK5) != union(difference(sK4,sK5),difference(sK5,sK4))
| union(difference(sK4,sK5),difference(sK5,sK4)) = symmetric_difference(sK4,sK5) ),
inference(extension,[status(thm),parent(t16:4)],[equality_2]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t16:4]) ).
cnf(t24,plain,
symmetric_difference(sK4,sK5) = union(difference(sK4,sK5),difference(sK5,sK4)),
inference(extension,[status(thm),parent(t22:2)],[f_1_3]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
( ~ disjoint(intersection(sK5,sK4),difference(sK4,sK5))
| ~ intersect(intersection(sK5,sK4),difference(sK4,sK5)) ),
inference(extension,[status(thm),parent(t12:3)],[f_6_4]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t12:3]) ).
cnf(t28,plain,
( difference(sK4,sK5) != difference(sK4,sK5)
| ~ disjoint(intersection(sK4,sK5),difference(sK4,sK5))
| intersection(sK4,sK5) != intersection(sK5,sK4)
| disjoint(intersection(sK5,sK4),difference(sK4,sK5)) ),
inference(extension,[status(thm),parent(t26:2)],[equality_12]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t26:2]) ).
cnf(t30,plain,
intersection(sK4,sK5) = intersection(sK5,sK4),
inference(extension,[status(thm),parent(t28:2)],[f_8_3]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t28:2]) ).
cnf(t32,plain,
disjoint(intersection(sK4,sK5),difference(sK4,sK5)),
inference(extension,[status(thm),parent(t28:3)],[f_3_3]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t28:3]) ).
cnf(t34,plain,
( sK5 != sK5
| sK4 != sK4
| difference(sK4,sK5) = difference(sK4,sK5) ),
inference(extension,[status(thm),parent(t28:4)],[equality_5]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t28:4]) ).
cnf(t36,plain,
sK4 = sK4,
inference(extension,[status(thm),parent(t34:2)],[equality_1]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t34:2]) ).
cnf(t38,plain,
sK5 = sK5,
inference(extension,[status(thm),parent(t34:3)],[equality_1]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t34:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET630+3 : TPTP v9.3.1. Released v2.2.0.
% 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
% 0.07/0.34 % Computer : n019.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sat Sep 19 22:44:20 UTC 2026
% 0.07/0.35 % CPUTime :
% 15.34/15.69 % SZS status Theorem for theBenchmark
% 15.34/15.69 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------