%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET622+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 : n006.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 08:57:08 AM UTC 2026
% Result : Theorem 134.32s 134.65s
% Output : Proof 134.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 61 ( 46 unt; 0 def)
% Number of atoms : 98 ( 61 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 75 ( 38 ~; 29 |; 7 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 77 ( 0 sgn 43 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(associativity_of_intersection,axiom,
! [B,C,D] : intersection(intersection(B,C),D) = intersection(B,intersection(C,D)),
file('theBenchmark.p',associativity_of_intersection) ).
fof(difference_difference_union2,axiom,
! [B,C,D] : difference(B,difference(C,D)) = union(difference(B,C),intersection(B,D)),
file('theBenchmark.p',difference_difference_union2) ).
fof(symmetric_difference_and_difference,axiom,
! [B,C] : symmetric_difference(B,C) = difference(union(B,C),intersection(B,C)),
file('theBenchmark.p',symmetric_difference_and_difference) ).
fof(equal_defn,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('theBenchmark.p',equal_defn) ).
fof(reflexivity_of_subset,axiom,
! [B] : subset(B,B),
file('theBenchmark.p',reflexivity_of_subset) ).
fof(prove_th98,conjecture,
! [B,C,D] : difference(B,symmetric_difference(C,D)) = union(difference(B,union(C,D)),intersection(intersection(B,C),D)),
file('theBenchmark.p',prove_th98) ).
fof(f_1_1,plain,
! [B,C,D] : intersection(intersection(B,C),D) = intersection(B,intersection(C,D)),
inference(fof_nnf,[status(thm)],[associativity_of_intersection]) ).
fof(f_1_2,plain,
! [U_2,U_1,U_0] : intersection(intersection(U_2,U_1),U_0) = intersection(U_2,intersection(U_1,U_0)),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
intersection(intersection(U_2,U_1),U_0) = intersection(U_2,intersection(U_1,U_0)),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [B,C,D] : difference(B,difference(C,D)) = union(difference(B,C),intersection(B,D)),
inference(fof_nnf,[status(thm)],[difference_difference_union2]) ).
fof(f_2_2,plain,
! [U_5,U_4,U_3] : difference(U_5,difference(U_4,U_3)) = union(difference(U_5,U_4),intersection(U_5,U_3)),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
difference(U_5,difference(U_4,U_3)) = union(difference(U_5,U_4),intersection(U_5,U_3)),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [B,C] : symmetric_difference(B,C) = difference(union(B,C),intersection(B,C)),
inference(fof_nnf,[status(thm)],[symmetric_difference_and_difference]) ).
fof(f_3_2,plain,
! [U_7,U_6] : symmetric_difference(U_7,U_6) = difference(union(U_7,U_6),intersection(U_7,U_6)),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
symmetric_difference(U_7,U_6) = difference(union(U_7,U_6),intersection(U_7,U_6)),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_8_1,plain,
! [B,C] :
( ( B = C
| ~ subset(C,B)
| ~ subset(B,C) )
& ( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(fof_nnf,[status(thm)],[equal_defn]) ).
fof(f_8_2,plain,
! [U_38,U_37] :
( ( U_38 = U_37
| ~ subset(U_37,U_38)
| ~ subset(U_38,U_37) )
& ( ( subset(U_37,U_38)
& subset(U_38,U_37) )
| U_38 != U_37 ) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_42,U_40] :
( U_42 = U_40
| ~ subset(U_40,U_42)
| ~ subset(U_42,U_40) )
& ! [U_41,U_39] :
( ( subset(U_39,U_41)
& subset(U_41,U_39) )
| U_41 != U_39 ) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
cnf(f_8_6,plain,
( U_42 = U_40
| ~ subset(U_40,U_42)
| ~ subset(U_42,U_40) ),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_14_1,plain,
! [B] : subset(B,B),
inference(fof_nnf,[status(thm)],[reflexivity_of_subset]) ).
fof(f_14_2,plain,
! [U_69] : subset(U_69,U_69),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
subset(U_69,U_69),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,negated_conjecture,
~ ! [B,C,D] : difference(B,symmetric_difference(C,D)) = union(difference(B,union(C,D)),intersection(intersection(B,C),D)),
inference(negate,[status(cth)],[prove_th98]) ).
fof(f_15_2,negated_conjecture,
? [B,C,D] : difference(B,symmetric_difference(C,D)) != union(difference(B,union(C,D)),intersection(intersection(B,C),D)),
inference(fof_nnf,[status(thm)],[f_15_1]) ).
fof(f_15_3,negated_conjecture,
? [U_72,U_71,U_70] : difference(U_72,symmetric_difference(U_71,U_70)) != union(difference(U_72,union(U_71,U_70)),intersection(intersection(U_72,U_71),U_70)),
inference(variable_rename,[status(thm)],[f_15_2]) ).
fof(f_15_4,negated_conjecture,
? [U_71,U_70] : difference(sK4,symmetric_difference(U_71,U_70)) != union(difference(sK4,union(U_71,U_70)),intersection(intersection(sK4,U_71),U_70)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_72,sK4)],[f_15_3]) ).
fof(f_15_5,negated_conjecture,
? [U_70] : difference(sK4,symmetric_difference(sK5,U_70)) != union(difference(sK4,union(sK5,U_70)),intersection(intersection(sK4,sK5),U_70)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_71,sK5)],[f_15_4]) ).
fof(f_15_6,negated_conjecture,
difference(sK4,symmetric_difference(sK5,sK6)) != union(difference(sK4,union(sK5,sK6)),intersection(intersection(sK4,sK5),sK6)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_70,sK6)],[f_15_5]) ).
fof(f_15_7,negated_conjecture,
difference(sK4,symmetric_difference(sK5,sK6)) != union(difference(sK4,union(sK5,sK6)),intersection(intersection(sK4,sK5),sK6)),
inference(definitional_conversion,[status(esa)],[f_15_6]) ).
cnf(f_15_8,negated_conjecture,
difference(sK4,symmetric_difference(sK5,sK6)) != union(difference(sK4,union(sK5,sK6)),intersection(intersection(sK4,sK5),sK6)),
inference(clausify,[status(thm)],[f_15_7]) ).
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_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_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_6,axiom,
( union(Eq_x_0,Eq_x_1) = union(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(t1,plain,
difference(sK4,symmetric_difference(sK5,sK6)) != union(difference(sK4,union(sK5,sK6)),intersection(intersection(sK4,sK5),sK6)),
inference(start,[status(thm),parent(0:0)],[f_15_8]) ).
cnf(t2,plain,
( union(difference(sK4,union(sK5,sK6)),intersection(sK4,intersection(sK5,sK6))) != union(difference(sK4,union(sK5,sK6)),intersection(intersection(sK4,sK5),sK6))
| difference(sK4,symmetric_difference(sK5,sK6)) != union(difference(sK4,union(sK5,sK6)),intersection(sK4,intersection(sK5,sK6)))
| difference(sK4,symmetric_difference(sK5,sK6)) = union(difference(sK4,union(sK5,sK6)),intersection(intersection(sK4,sK5),sK6)) ),
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,
( difference(sK4,difference(union(sK5,sK6),intersection(sK5,sK6))) != union(difference(sK4,union(sK5,sK6)),intersection(sK4,intersection(sK5,sK6)))
| difference(sK4,symmetric_difference(sK5,sK6)) != difference(sK4,difference(union(sK5,sK6),intersection(sK5,sK6)))
| difference(sK4,symmetric_difference(sK5,sK6)) = union(difference(sK4,union(sK5,sK6)),intersection(sK4,intersection(sK5,sK6))) ),
inference(extension,[status(thm),parent(t2:2)],[equality_3]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( symmetric_difference(sK5,sK6) != difference(union(sK5,sK6),intersection(sK5,sK6))
| sK4 != sK4
| difference(sK4,symmetric_difference(sK5,sK6)) = difference(sK4,difference(union(sK5,sK6),intersection(sK5,sK6))) ),
inference(extension,[status(thm),parent(t4:2)],[equality_5]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
sK4 = sK4,
inference(extension,[status(thm),parent(t6:2)],[equality_1]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
symmetric_difference(sK5,sK6) = difference(union(sK5,sK6),intersection(sK5,sK6)),
inference(extension,[status(thm),parent(t6:3)],[f_3_3]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t6:3]) ).
cnf(t12,plain,
difference(sK4,difference(union(sK5,sK6),intersection(sK5,sK6))) = union(difference(sK4,union(sK5,sK6)),intersection(sK4,intersection(sK5,sK6))),
inference(extension,[status(thm),parent(t4:3)],[f_2_3]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t4:3]) ).
cnf(t14,plain,
( intersection(sK4,intersection(sK5,sK6)) != intersection(intersection(sK4,sK5),sK6)
| difference(sK4,union(sK5,sK6)) != difference(sK4,union(sK5,sK6))
| union(difference(sK4,union(sK5,sK6)),intersection(sK4,intersection(sK5,sK6))) = union(difference(sK4,union(sK5,sK6)),intersection(intersection(sK4,sK5),sK6)) ),
inference(extension,[status(thm),parent(t2:3)],[equality_6]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t2:3]) ).
cnf(t16,plain,
( ~ subset(difference(sK4,union(sK5,sK6)),difference(sK4,union(sK5,sK6)))
| ~ subset(difference(sK4,union(sK5,sK6)),difference(sK4,union(sK5,sK6)))
| difference(sK4,union(sK5,sK6)) = difference(sK4,union(sK5,sK6)) ),
inference(extension,[status(thm),parent(t14:2)],[f_8_6]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
subset(difference(sK4,union(sK5,sK6)),difference(sK4,union(sK5,sK6))),
inference(extension,[status(thm),parent(t16:2)],[f_14_3]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(l9,lemma,
subset(difference(sK4,union(sK5,sK6)),difference(sK4,union(sK5,sK6))),
inference(lemma,[status(cth),parent(t16:2),below(t14:2)],[t16:2]) ).
cnf(t20,plain,
subset(difference(sK4,union(sK5,sK6)),difference(sK4,union(sK5,sK6))),
inference(lemma_extension,[status(thm),parent(t16:3)],[l9:1]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t16:3]) ).
cnf(t22,plain,
( intersection(intersection(sK4,sK5),sK6) != intersection(sK4,intersection(sK5,sK6))
| intersection(sK4,intersection(sK5,sK6)) = intersection(intersection(sK4,sK5),sK6) ),
inference(extension,[status(thm),parent(t14:3)],[equality_2]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t14:3]) ).
cnf(t24,plain,
intersection(intersection(sK4,sK5),sK6) = intersection(sK4,intersection(sK5,sK6)),
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]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET622+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n006.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 19 22:43:27 UTC 2026
% 0.08/0.36 % CPUTime :
% 134.32/134.65 % SZS status Theorem for theBenchmark
% 134.32/134.65 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------