TSTP Solution File: SEU119+2 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU119+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 12:38:29 EDT 2022
% Result : Theorem 0.20s 0.42s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 15
% Syntax : Number of formulae : 111 ( 30 unt; 0 def)
% Number of atoms : 286 ( 99 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 319 ( 144 ~; 105 |; 46 &)
% ( 20 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-3 aty)
% Number of variables : 171 ( 5 sgn 88 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A) ).
fof(d1_xboole_0,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ) ).
fof(d3_xboole_0,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
& in(D,B) ) ) ) ).
fof(d7_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
<=> set_intersection2(A,B) = empty_set ) ).
fof(t3_xboole_0,conjecture,
! [A,B] :
( ~ ( ~ disjoint(A,B)
& ! [C] :
~ ( in(C,A)
& in(C,B) ) )
& ~ ( ? [C] :
( in(C,A)
& in(C,B) )
& disjoint(A,B) ) ) ).
fof(subgoal_0,plain,
! [A,B] :
( ~ disjoint(A,B)
=> ~ ! [C] :
~ ( in(C,A)
& in(C,B) ) ),
inference(strip,[],[t3_xboole_0]) ).
fof(subgoal_1,plain,
! [A,B] :
( ( ~ ( ~ disjoint(A,B)
& ! [C] :
~ ( in(C,A)
& in(C,B) ) )
& ? [C] :
( in(C,A)
& in(C,B) ) )
=> ~ disjoint(A,B) ),
inference(strip,[],[t3_xboole_0]) ).
fof(negate_0_0,plain,
~ ! [A,B] :
( ~ disjoint(A,B)
=> ~ ! [C] :
~ ( in(C,A)
& in(C,B) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B] :
( set_intersection2(A,B) != empty_set
<=> ~ disjoint(A,B) ),
inference(canonicalize,[],[d7_xboole_0]) ).
fof(normalize_0_1,plain,
! [A,B] :
( set_intersection2(A,B) != empty_set
<=> ~ disjoint(A,B) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B] :
( ( set_intersection2(A,B) != empty_set
| disjoint(A,B) )
& ( ~ disjoint(A,B)
| set_intersection2(A,B) = empty_set ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B] :
( set_intersection2(A,B) != empty_set
| disjoint(A,B) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A] :
( A != empty_set
<=> ? [B] : in(B,A) ),
inference(canonicalize,[],[d1_xboole_0]) ).
fof(normalize_0_5,plain,
! [A] :
( A != empty_set
<=> ? [B] : in(B,A) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B] :
( ( A != empty_set
| ~ in(B,A) )
& ( A = empty_set
| in(skolemFOFtoCNF_B(A),A) ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A] :
( A = empty_set
| in(skolemFOFtoCNF_B(A),A) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,B,C] :
( C != set_intersection2(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( in(D,A)
& in(D,B) ) ) ),
inference(canonicalize,[],[d3_xboole_0]) ).
fof(normalize_0_9,plain,
! [A,B,C] :
( C != set_intersection2(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( in(D,A)
& in(D,B) ) ) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A,B,C,D] :
( ( C != set_intersection2(A,B)
| ~ in(D,C)
| in(D,A) )
& ( C != set_intersection2(A,B)
| ~ in(D,C)
| in(D,B) )
& ( C = set_intersection2(A,B)
| in(skolemFOFtoCNF_D(A,B,C),A)
| in(skolemFOFtoCNF_D(A,B,C),C) )
& ( C = set_intersection2(A,B)
| in(skolemFOFtoCNF_D(A,B,C),B)
| in(skolemFOFtoCNF_D(A,B,C),C) )
& ( C != set_intersection2(A,B)
| ~ in(D,A)
| ~ in(D,B)
| in(D,C) )
& ( ~ in(skolemFOFtoCNF_D(A,B,C),A)
| ~ in(skolemFOFtoCNF_D(A,B,C),B)
| ~ in(skolemFOFtoCNF_D(A,B,C),C)
| C = set_intersection2(A,B) ) ),
inference(clausify,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [A,B,C,D] :
( C != set_intersection2(A,B)
| ~ in(D,C)
| in(D,A) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
? [A,B] :
( ~ disjoint(A,B)
& ! [C] :
( ~ in(C,A)
| ~ in(C,B) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_13,plain,
( ~ disjoint(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)
& ! [C] :
( ~ in(C,skolemFOFtoCNF_A_2)
| ~ in(C,skolemFOFtoCNF_B_1) ) ),
inference(skolemize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [C] :
( ~ in(C,skolemFOFtoCNF_A_2)
| ~ in(C,skolemFOFtoCNF_B_1) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [C] :
( ~ in(C,skolemFOFtoCNF_A_2)
| ~ in(C,skolemFOFtoCNF_B_1) ),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(canonicalize,[],[commutativity_k3_xboole_0]) ).
fof(normalize_0_17,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(specialize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
~ disjoint(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),
inference(conjunct,[],[normalize_0_13]) ).
cnf(refute_0_0,plain,
( set_intersection2(A,B) != empty_set
| disjoint(A,B) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) != empty_set
| disjoint(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_2,plain,
( A = empty_set
| in(skolemFOFtoCNF_B(A),A) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_3,plain,
( set_intersection2(X_21,X_22) = empty_set
| in(skolemFOFtoCNF_B(set_intersection2(X_21,X_22)),set_intersection2(X_21,X_22)) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(set_intersection2(X_21,X_22)))]]) ).
cnf(refute_0_4,plain,
( C != set_intersection2(A,B)
| ~ in(D,C)
| in(D,A) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_5,plain,
( set_intersection2(A,B) != set_intersection2(A,B)
| ~ in(D,set_intersection2(A,B))
| in(D,A) ),
inference(subst,[],[refute_0_4:[bind(C,$fot(set_intersection2(A,B)))]]) ).
cnf(refute_0_6,plain,
set_intersection2(A,B) = set_intersection2(A,B),
introduced(tautology,[refl,[$fot(set_intersection2(A,B))]]) ).
cnf(refute_0_7,plain,
( ~ in(D,set_intersection2(A,B))
| in(D,A) ),
inference(resolve,[$cnf( $equal(set_intersection2(A,B),set_intersection2(A,B)) )],[refute_0_6,refute_0_5]) ).
cnf(refute_0_8,plain,
( ~ in(skolemFOFtoCNF_B(set_intersection2(X_21,X_22)),set_intersection2(X_21,X_22))
| in(skolemFOFtoCNF_B(set_intersection2(X_21,X_22)),X_21) ),
inference(subst,[],[refute_0_7:[bind(A,$fot(X_21)),bind(B,$fot(X_22)),bind(D,$fot(skolemFOFtoCNF_B(set_intersection2(X_21,X_22))))]]) ).
cnf(refute_0_9,plain,
( set_intersection2(X_21,X_22) = empty_set
| in(skolemFOFtoCNF_B(set_intersection2(X_21,X_22)),X_21) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_B(set_intersection2(X_21,X_22)),set_intersection2(X_21,X_22)) )],[refute_0_3,refute_0_8]) ).
cnf(refute_0_10,plain,
( set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = empty_set
| in(skolemFOFtoCNF_B(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)),skolemFOFtoCNF_A_2) ),
inference(subst,[],[refute_0_9:[bind(X_21,$fot(skolemFOFtoCNF_A_2)),bind(X_22,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_11,plain,
( ~ in(C,skolemFOFtoCNF_A_2)
| ~ in(C,skolemFOFtoCNF_B_1) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_12,plain,
( ~ in(skolemFOFtoCNF_B(set_intersection2(skolemFOFtoCNF_B_1,X_35)),skolemFOFtoCNF_A_2)
| ~ in(skolemFOFtoCNF_B(set_intersection2(skolemFOFtoCNF_B_1,X_35)),skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_11:[bind(C,$fot(skolemFOFtoCNF_B(set_intersection2(skolemFOFtoCNF_B_1,X_35))))]]) ).
cnf(refute_0_13,plain,
( set_intersection2(skolemFOFtoCNF_B_1,X_35) = empty_set
| in(skolemFOFtoCNF_B(set_intersection2(skolemFOFtoCNF_B_1,X_35)),skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_9:[bind(X_21,$fot(skolemFOFtoCNF_B_1)),bind(X_22,$fot(X_35))]]) ).
cnf(refute_0_14,plain,
( ~ in(skolemFOFtoCNF_B(set_intersection2(skolemFOFtoCNF_B_1,X_35)),skolemFOFtoCNF_A_2)
| set_intersection2(skolemFOFtoCNF_B_1,X_35) = empty_set ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_B(set_intersection2(skolemFOFtoCNF_B_1,X_35)),skolemFOFtoCNF_B_1) )],[refute_0_13,refute_0_12]) ).
cnf(refute_0_15,plain,
( ~ in(skolemFOFtoCNF_B(set_intersection2(skolemFOFtoCNF_B_1,X_36)),skolemFOFtoCNF_A_2)
| set_intersection2(skolemFOFtoCNF_B_1,X_36) = empty_set ),
inference(subst,[],[refute_0_14:[bind(X_35,$fot(X_36))]]) ).
cnf(refute_0_16,plain,
set_intersection2(A,B) = set_intersection2(B,A),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_17,plain,
set_intersection2(X_36,skolemFOFtoCNF_B_1) = set_intersection2(skolemFOFtoCNF_B_1,X_36),
inference(subst,[],[refute_0_16:[bind(A,$fot(X_36)),bind(B,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_18,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_19,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_20,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
( set_intersection2(X_36,skolemFOFtoCNF_B_1) != set_intersection2(skolemFOFtoCNF_B_1,X_36)
| set_intersection2(skolemFOFtoCNF_B_1,X_36) = set_intersection2(X_36,skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(set_intersection2(X_36,skolemFOFtoCNF_B_1))),bind(Y,$fot(set_intersection2(skolemFOFtoCNF_B_1,X_36)))]]) ).
cnf(refute_0_22,plain,
set_intersection2(skolemFOFtoCNF_B_1,X_36) = set_intersection2(X_36,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( $equal(set_intersection2(X_36,skolemFOFtoCNF_B_1),set_intersection2(skolemFOFtoCNF_B_1,X_36)) )],[refute_0_17,refute_0_21]) ).
cnf(refute_0_23,plain,
( set_intersection2(skolemFOFtoCNF_B_1,X_36) != set_intersection2(X_36,skolemFOFtoCNF_B_1)
| ~ in(skolemFOFtoCNF_B(set_intersection2(X_36,skolemFOFtoCNF_B_1)),skolemFOFtoCNF_A_2)
| in(skolemFOFtoCNF_B(set_intersection2(skolemFOFtoCNF_B_1,X_36)),skolemFOFtoCNF_A_2) ),
introduced(tautology,[equality,[$cnf( ~ in(skolemFOFtoCNF_B(set_intersection2(skolemFOFtoCNF_B_1,X_36)),skolemFOFtoCNF_A_2) ),[0,0],$fot(set_intersection2(X_36,skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_24,plain,
( ~ in(skolemFOFtoCNF_B(set_intersection2(X_36,skolemFOFtoCNF_B_1)),skolemFOFtoCNF_A_2)
| in(skolemFOFtoCNF_B(set_intersection2(skolemFOFtoCNF_B_1,X_36)),skolemFOFtoCNF_A_2) ),
inference(resolve,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_B_1,X_36),set_intersection2(X_36,skolemFOFtoCNF_B_1)) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ in(skolemFOFtoCNF_B(set_intersection2(X_36,skolemFOFtoCNF_B_1)),skolemFOFtoCNF_A_2)
| set_intersection2(skolemFOFtoCNF_B_1,X_36) = empty_set ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_B(set_intersection2(skolemFOFtoCNF_B_1,X_36)),skolemFOFtoCNF_A_2) )],[refute_0_24,refute_0_15]) ).
cnf(refute_0_26,plain,
( ~ in(skolemFOFtoCNF_B(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)),skolemFOFtoCNF_A_2)
| set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2) = empty_set ),
inference(subst,[],[refute_0_25:[bind(X_36,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_27,plain,
( set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = empty_set
| set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2) = empty_set ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_B(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)),skolemFOFtoCNF_A_2) )],[refute_0_10,refute_0_26]) ).
cnf(refute_0_28,plain,
( set_intersection2(A,B) != set_intersection2(B,A)
| set_intersection2(B,A) = set_intersection2(A,B) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(set_intersection2(A,B))),bind(Y,$fot(set_intersection2(B,A)))]]) ).
cnf(refute_0_29,plain,
set_intersection2(B,A) = set_intersection2(A,B),
inference(resolve,[$cnf( $equal(set_intersection2(A,B),set_intersection2(B,A)) )],[refute_0_16,refute_0_28]) ).
cnf(refute_0_30,plain,
set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2) = set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),
inference(subst,[],[refute_0_29:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_31,plain,
( set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2) != empty_set
| set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2) != set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)
| set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = empty_set ),
introduced(tautology,[equality,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2),empty_set) ),[0],$fot(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_32,plain,
( set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2) != empty_set
| set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = empty_set ),
inference(resolve,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2),set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1)) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = empty_set,
inference(resolve,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_A_2),empty_set) )],[refute_0_27,refute_0_32]) ).
cnf(refute_0_34,plain,
( empty_set != empty_set
| set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) != empty_set
| set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = empty_set ),
introduced(tautology,[equality,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),empty_set) ),[1],$fot(empty_set)]]) ).
cnf(refute_0_35,plain,
( empty_set != empty_set
| set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) = empty_set ),
inference(resolve,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),empty_set) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
( empty_set != empty_set
| disjoint(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),empty_set) )],[refute_0_35,refute_0_1]) ).
cnf(refute_0_37,plain,
empty_set = empty_set,
introduced(tautology,[refl,[$fot(empty_set)]]) ).
cnf(refute_0_38,plain,
disjoint(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( $equal(empty_set,empty_set) )],[refute_0_37,refute_0_36]) ).
cnf(refute_0_39,plain,
~ disjoint(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_40,plain,
$false,
inference(resolve,[$cnf( disjoint(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1) )],[refute_0_38,refute_0_39]) ).
fof(negate_1_0,plain,
~ ! [A,B] :
( ( ~ ( ~ disjoint(A,B)
& ! [C] :
~ ( in(C,A)
& in(C,B) ) )
& ? [C] :
( in(C,A)
& in(C,B) ) )
=> ~ disjoint(A,B) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [A,B] :
( disjoint(A,B)
& ( disjoint(A,B)
| ? [C] :
( in(C,A)
& in(C,B) ) )
& ? [C] :
( in(C,A)
& in(C,B) ) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
( disjoint(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2)
& ( disjoint(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2)
| ? [C] :
( in(C,skolemFOFtoCNF_A_3)
& in(C,skolemFOFtoCNF_B_2) ) )
& ? [C] :
( in(C,skolemFOFtoCNF_A_3)
& in(C,skolemFOFtoCNF_B_2) ) ),
inference(skolemize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
? [C] :
( in(C,skolemFOFtoCNF_A_3)
& in(C,skolemFOFtoCNF_B_2) ),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
( in(skolemFOFtoCNF_C,skolemFOFtoCNF_A_3)
& in(skolemFOFtoCNF_C,skolemFOFtoCNF_B_2) ),
inference(skolemize,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
in(skolemFOFtoCNF_C,skolemFOFtoCNF_B_2),
inference(conjunct,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
in(skolemFOFtoCNF_C,skolemFOFtoCNF_A_3),
inference(conjunct,[],[normalize_1_3]) ).
fof(normalize_1_6,plain,
! [A,B,C] :
( C != set_intersection2(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( in(D,A)
& in(D,B) ) ) ),
inference(canonicalize,[],[d3_xboole_0]) ).
fof(normalize_1_7,plain,
! [A,B,C] :
( C != set_intersection2(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( in(D,A)
& in(D,B) ) ) ),
inference(specialize,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
! [A,B,C,D] :
( ( C != set_intersection2(A,B)
| ~ in(D,C)
| in(D,A) )
& ( C != set_intersection2(A,B)
| ~ in(D,C)
| in(D,B) )
& ( C = set_intersection2(A,B)
| in(skolemFOFtoCNF_D(A,B,C),A)
| in(skolemFOFtoCNF_D(A,B,C),C) )
& ( C = set_intersection2(A,B)
| in(skolemFOFtoCNF_D(A,B,C),B)
| in(skolemFOFtoCNF_D(A,B,C),C) )
& ( C != set_intersection2(A,B)
| ~ in(D,A)
| ~ in(D,B)
| in(D,C) )
& ( ~ in(skolemFOFtoCNF_D(A,B,C),A)
| ~ in(skolemFOFtoCNF_D(A,B,C),B)
| ~ in(skolemFOFtoCNF_D(A,B,C),C)
| C = set_intersection2(A,B) ) ),
inference(clausify,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
! [A,B,C,D] :
( C != set_intersection2(A,B)
| ~ in(D,A)
| ~ in(D,B)
| in(D,C) ),
inference(conjunct,[],[normalize_1_8]) ).
fof(normalize_1_10,plain,
disjoint(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_11,plain,
! [A,B] :
( set_intersection2(A,B) != empty_set
<=> ~ disjoint(A,B) ),
inference(canonicalize,[],[d7_xboole_0]) ).
fof(normalize_1_12,plain,
! [A,B] :
( set_intersection2(A,B) != empty_set
<=> ~ disjoint(A,B) ),
inference(specialize,[],[normalize_1_11]) ).
fof(normalize_1_13,plain,
! [A,B] :
( ( set_intersection2(A,B) != empty_set
| disjoint(A,B) )
& ( ~ disjoint(A,B)
| set_intersection2(A,B) = empty_set ) ),
inference(clausify,[],[normalize_1_12]) ).
fof(normalize_1_14,plain,
! [A,B] :
( ~ disjoint(A,B)
| set_intersection2(A,B) = empty_set ),
inference(conjunct,[],[normalize_1_13]) ).
fof(normalize_1_15,plain,
! [A] :
( A != empty_set
<=> ? [B] : in(B,A) ),
inference(canonicalize,[],[d1_xboole_0]) ).
fof(normalize_1_16,plain,
! [A] :
( A != empty_set
<=> ? [B] : in(B,A) ),
inference(specialize,[],[normalize_1_15]) ).
fof(normalize_1_17,plain,
! [A,B] :
( ( A != empty_set
| ~ in(B,A) )
& ( A = empty_set
| in(skolemFOFtoCNF_B(A),A) ) ),
inference(clausify,[],[normalize_1_16]) ).
fof(normalize_1_18,plain,
! [A,B] :
( A != empty_set
| ~ in(B,A) ),
inference(conjunct,[],[normalize_1_17]) ).
cnf(refute_1_0,plain,
in(skolemFOFtoCNF_C,skolemFOFtoCNF_B_2),
inference(canonicalize,[],[normalize_1_4]) ).
cnf(refute_1_1,plain,
in(skolemFOFtoCNF_C,skolemFOFtoCNF_A_3),
inference(canonicalize,[],[normalize_1_5]) ).
cnf(refute_1_2,plain,
( C != set_intersection2(A,B)
| ~ in(D,A)
| ~ in(D,B)
| in(D,C) ),
inference(canonicalize,[],[normalize_1_9]) ).
cnf(refute_1_3,plain,
( set_intersection2(A,B) != set_intersection2(A,B)
| ~ in(D,A)
| ~ in(D,B)
| in(D,set_intersection2(A,B)) ),
inference(subst,[],[refute_1_2:[bind(C,$fot(set_intersection2(A,B)))]]) ).
cnf(refute_1_4,plain,
set_intersection2(A,B) = set_intersection2(A,B),
introduced(tautology,[refl,[$fot(set_intersection2(A,B))]]) ).
cnf(refute_1_5,plain,
( ~ in(D,A)
| ~ in(D,B)
| in(D,set_intersection2(A,B)) ),
inference(resolve,[$cnf( $equal(set_intersection2(A,B),set_intersection2(A,B)) )],[refute_1_4,refute_1_3]) ).
cnf(refute_1_6,plain,
( ~ in(skolemFOFtoCNF_C,X_105)
| ~ in(skolemFOFtoCNF_C,skolemFOFtoCNF_A_3)
| in(skolemFOFtoCNF_C,set_intersection2(skolemFOFtoCNF_A_3,X_105)) ),
inference(subst,[],[refute_1_5:[bind(A,$fot(skolemFOFtoCNF_A_3)),bind(B,$fot(X_105)),bind(D,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_1_7,plain,
( ~ in(skolemFOFtoCNF_C,X_105)
| in(skolemFOFtoCNF_C,set_intersection2(skolemFOFtoCNF_A_3,X_105)) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C,skolemFOFtoCNF_A_3) )],[refute_1_1,refute_1_6]) ).
cnf(refute_1_8,plain,
( ~ in(skolemFOFtoCNF_C,skolemFOFtoCNF_B_2)
| in(skolemFOFtoCNF_C,set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2)) ),
inference(subst,[],[refute_1_7:[bind(X_105,$fot(skolemFOFtoCNF_B_2))]]) ).
cnf(refute_1_9,plain,
in(skolemFOFtoCNF_C,set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2)),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C,skolemFOFtoCNF_B_2) )],[refute_1_0,refute_1_8]) ).
cnf(refute_1_10,plain,
disjoint(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2),
inference(canonicalize,[],[normalize_1_10]) ).
cnf(refute_1_11,plain,
( ~ disjoint(A,B)
| set_intersection2(A,B) = empty_set ),
inference(canonicalize,[],[normalize_1_14]) ).
cnf(refute_1_12,plain,
( ~ disjoint(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2)
| set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2) = empty_set ),
inference(subst,[],[refute_1_11:[bind(A,$fot(skolemFOFtoCNF_A_3)),bind(B,$fot(skolemFOFtoCNF_B_2))]]) ).
cnf(refute_1_13,plain,
set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2) = empty_set,
inference(resolve,[$cnf( disjoint(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2) )],[refute_1_10,refute_1_12]) ).
cnf(refute_1_14,plain,
( set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2) != empty_set
| ~ in(skolemFOFtoCNF_C,set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2))
| in(skolemFOFtoCNF_C,empty_set) ),
introduced(tautology,[equality,[$cnf( in(skolemFOFtoCNF_C,set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2)) ),[1],$fot(empty_set)]]) ).
cnf(refute_1_15,plain,
( ~ in(skolemFOFtoCNF_C,set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2))
| in(skolemFOFtoCNF_C,empty_set) ),
inference(resolve,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2),empty_set) )],[refute_1_13,refute_1_14]) ).
cnf(refute_1_16,plain,
in(skolemFOFtoCNF_C,empty_set),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C,set_intersection2(skolemFOFtoCNF_A_3,skolemFOFtoCNF_B_2)) )],[refute_1_9,refute_1_15]) ).
cnf(refute_1_17,plain,
( A != empty_set
| ~ in(B,A) ),
inference(canonicalize,[],[normalize_1_18]) ).
cnf(refute_1_18,plain,
( empty_set != empty_set
| ~ in(B,empty_set) ),
inference(subst,[],[refute_1_17:[bind(A,$fot(empty_set))]]) ).
cnf(refute_1_19,plain,
empty_set = empty_set,
introduced(tautology,[refl,[$fot(empty_set)]]) ).
cnf(refute_1_20,plain,
~ in(B,empty_set),
inference(resolve,[$cnf( $equal(empty_set,empty_set) )],[refute_1_19,refute_1_18]) ).
cnf(refute_1_21,plain,
~ in(skolemFOFtoCNF_C,empty_set),
inference(subst,[],[refute_1_20:[bind(B,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_1_22,plain,
$false,
inference(resolve,[$cnf( in(skolemFOFtoCNF_C,empty_set) )],[refute_1_16,refute_1_21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU119+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 20 12:26:59 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.42
% 0.20/0.42 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.20/0.43
%------------------------------------------------------------------------------