TSTP Solution File: SEU154+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU154+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n027.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 12:38:50 EDT 2022
% Result : Theorem 1.74s 1.97s
% Output : CNFRefutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 17
% Syntax : Number of formulae : 114 ( 26 unt; 0 def)
% Number of atoms : 282 ( 104 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 282 ( 114 ~; 122 |; 21 &)
% ( 21 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 234 ( 17 sgn 86 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A) ).
fof(d10_xboole_0,axiom,
! [A,B] :
( A = B
<=> ( subset(A,B)
& subset(B,A) ) ) ).
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ) ).
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(l28_zfmisc_1,conjecture,
! [A,B] :
( ~ in(A,B)
=> disjoint(singleton(A),B) ) ).
fof(t2_xboole_1,axiom,
! [A] : subset(empty_set,A) ).
fof(subgoal_0,plain,
! [A,B] :
( ~ in(A,B)
=> disjoint(singleton(A),B) ),
inference(strip,[],[l28_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B] :
( ~ in(A,B)
=> disjoint(singleton(A),B) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B] :
( ~ disjoint(singleton(A),B)
& ~ in(A,B) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ disjoint(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B)
& ~ in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
~ disjoint(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B] :
( set_intersection2(A,B) != empty_set
<=> ~ disjoint(A,B) ),
inference(canonicalize,[],[d7_xboole_0]) ).
fof(normalize_0_4,plain,
! [A,B] :
( set_intersection2(A,B) != empty_set
<=> ~ disjoint(A,B) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,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_4]) ).
fof(normalize_0_6,plain,
! [A,B] :
( set_intersection2(A,B) != empty_set
| disjoint(A,B) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,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_8,plain,
! [A,B,C] :
( C != set_intersection2(A,B)
<=> ? [D] :
( ~ in(D,C)
<=> ( in(D,A)
& in(D,B) ) ) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,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_8]) ).
fof(normalize_0_10,plain,
! [A,B,C,D] :
( C != set_intersection2(A,B)
| ~ in(D,C)
| in(D,A) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(canonicalize,[],[commutativity_k3_xboole_0]) ).
fof(normalize_0_12,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(canonicalize,[],[d3_tarski]) ).
fof(normalize_0_14,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [A,B,C] :
( ( ~ in(skolemFOFtoCNF_C_1(A,B),B)
| subset(A,B) )
& ( in(skolemFOFtoCNF_C_1(A,B),A)
| subset(A,B) )
& ( ~ in(C,A)
| ~ subset(A,B)
| in(C,B) ) ),
inference(clausify,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [A,B] :
( ~ in(skolemFOFtoCNF_C_1(A,B),B)
| subset(A,B) ),
inference(conjunct,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [A,B] :
( in(skolemFOFtoCNF_C_1(A,B),A)
| subset(A,B) ),
inference(conjunct,[],[normalize_0_15]) ).
fof(normalize_0_18,plain,
! [A] : subset(empty_set,A),
inference(canonicalize,[],[t2_xboole_1]) ).
fof(normalize_0_19,plain,
! [A] : subset(empty_set,A),
inference(specialize,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [A,B] :
( A != B
<=> ( ~ subset(A,B)
| ~ subset(B,A) ) ),
inference(canonicalize,[],[d10_xboole_0]) ).
fof(normalize_0_21,plain,
! [A,B] :
( A != B
<=> ( ~ subset(A,B)
| ~ subset(B,A) ) ),
inference(specialize,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [A,B] :
( ( A != B
| subset(A,B) )
& ( A != B
| subset(B,A) )
& ( ~ subset(A,B)
| ~ subset(B,A)
| A = B ) ),
inference(clausify,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
! [A,B] :
( ~ subset(A,B)
| ~ subset(B,A)
| A = B ),
inference(conjunct,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
! [A,B,C] :
( C = set_intersection2(A,B)
| in(skolemFOFtoCNF_D(A,B,C),B)
| in(skolemFOFtoCNF_D(A,B,C),C) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_25,plain,
! [A,B] :
( B != singleton(A)
<=> ? [C] :
( C != A
<=> in(C,B) ) ),
inference(canonicalize,[],[d1_tarski]) ).
fof(normalize_0_26,plain,
! [A,B] :
( B != singleton(A)
<=> ? [C] :
( C != A
<=> in(C,B) ) ),
inference(specialize,[],[normalize_0_25]) ).
fof(normalize_0_27,plain,
! [A,B,C] :
( ( B != singleton(A)
| C != A
| in(C,B) )
& ( B != singleton(A)
| ~ in(C,B)
| C = A )
& ( skolemFOFtoCNF_C(A,B) != A
| ~ in(skolemFOFtoCNF_C(A,B),B)
| B = singleton(A) )
& ( B = singleton(A)
| skolemFOFtoCNF_C(A,B) = A
| in(skolemFOFtoCNF_C(A,B),B) ) ),
inference(clausify,[],[normalize_0_26]) ).
fof(normalize_0_28,plain,
! [A,B,C] :
( B != singleton(A)
| ~ in(C,B)
| C = A ),
inference(conjunct,[],[normalize_0_27]) ).
fof(normalize_0_29,plain,
! [A,B,C] :
( C = set_intersection2(A,B)
| in(skolemFOFtoCNF_D(A,B,C),A)
| in(skolemFOFtoCNF_D(A,B,C),C) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_30,plain,
~ in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
inference(conjunct,[],[normalize_0_1]) ).
cnf(refute_0_0,plain,
~ disjoint(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( set_intersection2(A,B) != empty_set
| disjoint(A,B) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_2,plain,
( set_intersection2(singleton(X_431),B) != empty_set
| disjoint(singleton(X_431),B) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(singleton(X_431)))]]) ).
cnf(refute_0_3,plain,
( C != set_intersection2(A,B)
| ~ in(D,C)
| in(D,A) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_4,plain,
( set_intersection2(A,B) != set_intersection2(A,B)
| ~ in(D,set_intersection2(A,B))
| in(D,A) ),
inference(subst,[],[refute_0_3:[bind(C,$fot(set_intersection2(A,B)))]]) ).
cnf(refute_0_5,plain,
set_intersection2(A,B) = set_intersection2(A,B),
introduced(tautology,[refl,[$fot(set_intersection2(A,B))]]) ).
cnf(refute_0_6,plain,
( ~ in(D,set_intersection2(A,B))
| in(D,A) ),
inference(resolve,[$cnf( $equal(set_intersection2(A,B),set_intersection2(A,B)) )],[refute_0_5,refute_0_4]) ).
cnf(refute_0_7,plain,
( ~ in(X_29,set_intersection2(X_27,X_28))
| in(X_29,X_27) ),
inference(subst,[],[refute_0_6:[bind(A,$fot(X_27)),bind(B,$fot(X_28)),bind(D,$fot(X_29))]]) ).
cnf(refute_0_8,plain,
set_intersection2(A,B) = set_intersection2(B,A),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_9,plain,
set_intersection2(X_28,X_27) = set_intersection2(X_27,X_28),
inference(subst,[],[refute_0_8:[bind(A,$fot(X_28)),bind(B,$fot(X_27))]]) ).
cnf(refute_0_10,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_11,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_12,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( set_intersection2(X_28,X_27) != set_intersection2(X_27,X_28)
| set_intersection2(X_27,X_28) = set_intersection2(X_28,X_27) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(set_intersection2(X_28,X_27))),bind(Y,$fot(set_intersection2(X_27,X_28)))]]) ).
cnf(refute_0_14,plain,
set_intersection2(X_27,X_28) = set_intersection2(X_28,X_27),
inference(resolve,[$cnf( $equal(set_intersection2(X_28,X_27),set_intersection2(X_27,X_28)) )],[refute_0_9,refute_0_13]) ).
cnf(refute_0_15,plain,
( set_intersection2(X_27,X_28) != set_intersection2(X_28,X_27)
| ~ in(X_29,set_intersection2(X_28,X_27))
| in(X_29,set_intersection2(X_27,X_28)) ),
introduced(tautology,[equality,[$cnf( ~ in(X_29,set_intersection2(X_27,X_28)) ),[1],$fot(set_intersection2(X_28,X_27))]]) ).
cnf(refute_0_16,plain,
( ~ in(X_29,set_intersection2(X_28,X_27))
| in(X_29,set_intersection2(X_27,X_28)) ),
inference(resolve,[$cnf( $equal(set_intersection2(X_27,X_28),set_intersection2(X_28,X_27)) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ in(X_29,set_intersection2(X_28,X_27))
| in(X_29,X_27) ),
inference(resolve,[$cnf( in(X_29,set_intersection2(X_27,X_28)) )],[refute_0_16,refute_0_7]) ).
cnf(refute_0_18,plain,
( ~ in(X_29,set_intersection2(empty_set,X_27))
| in(X_29,X_27) ),
inference(subst,[],[refute_0_17:[bind(X_28,$fot(empty_set))]]) ).
cnf(refute_0_19,plain,
( ~ in(skolemFOFtoCNF_C_1(A,B),B)
| subset(A,B) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_20,plain,
( ~ in(skolemFOFtoCNF_C_1(set_intersection2(X_34,X_35),X_34),X_34)
| subset(set_intersection2(X_34,X_35),X_34) ),
inference(subst,[],[refute_0_19:[bind(A,$fot(set_intersection2(X_34,X_35))),bind(B,$fot(X_34))]]) ).
cnf(refute_0_21,plain,
( in(skolemFOFtoCNF_C_1(A,B),A)
| subset(A,B) ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_22,plain,
( in(skolemFOFtoCNF_C_1(set_intersection2(X_27,X_28),B),set_intersection2(X_27,X_28))
| subset(set_intersection2(X_27,X_28),B) ),
inference(subst,[],[refute_0_21:[bind(A,$fot(set_intersection2(X_27,X_28)))]]) ).
cnf(refute_0_23,plain,
( ~ in(skolemFOFtoCNF_C_1(set_intersection2(X_27,X_28),B),set_intersection2(X_27,X_28))
| in(skolemFOFtoCNF_C_1(set_intersection2(X_27,X_28),B),X_27) ),
inference(subst,[],[refute_0_6:[bind(A,$fot(X_27)),bind(B,$fot(X_28)),bind(D,$fot(skolemFOFtoCNF_C_1(set_intersection2(X_27,X_28),B)))]]) ).
cnf(refute_0_24,plain,
( in(skolemFOFtoCNF_C_1(set_intersection2(X_27,X_28),B),X_27)
| subset(set_intersection2(X_27,X_28),B) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_1(set_intersection2(X_27,X_28),B),set_intersection2(X_27,X_28)) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( in(skolemFOFtoCNF_C_1(set_intersection2(X_34,X_35),X_34),X_34)
| subset(set_intersection2(X_34,X_35),X_34) ),
inference(subst,[],[refute_0_24:[bind(B,$fot(X_34)),bind(X_27,$fot(X_34)),bind(X_28,$fot(X_35))]]) ).
cnf(refute_0_26,plain,
subset(set_intersection2(X_34,X_35),X_34),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_1(set_intersection2(X_34,X_35),X_34),X_34) )],[refute_0_25,refute_0_20]) ).
cnf(refute_0_27,plain,
subset(set_intersection2(empty_set,X_35),empty_set),
inference(subst,[],[refute_0_26:[bind(X_34,$fot(empty_set))]]) ).
cnf(refute_0_28,plain,
subset(empty_set,A),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_29,plain,
subset(empty_set,X_53),
inference(subst,[],[refute_0_28:[bind(A,$fot(X_53))]]) ).
cnf(refute_0_30,plain,
( ~ subset(A,B)
| ~ subset(B,A)
| A = B ),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_31,plain,
( ~ subset(X_53,empty_set)
| ~ subset(empty_set,X_53)
| empty_set = X_53 ),
inference(subst,[],[refute_0_30:[bind(A,$fot(empty_set)),bind(B,$fot(X_53))]]) ).
cnf(refute_0_32,plain,
( ~ subset(X_53,empty_set)
| empty_set = X_53 ),
inference(resolve,[$cnf( subset(empty_set,X_53) )],[refute_0_29,refute_0_31]) ).
cnf(refute_0_33,plain,
( ~ subset(set_intersection2(empty_set,X_35),empty_set)
| empty_set = set_intersection2(empty_set,X_35) ),
inference(subst,[],[refute_0_32:[bind(X_53,$fot(set_intersection2(empty_set,X_35)))]]) ).
cnf(refute_0_34,plain,
empty_set = set_intersection2(empty_set,X_35),
inference(resolve,[$cnf( subset(set_intersection2(empty_set,X_35),empty_set) )],[refute_0_27,refute_0_33]) ).
cnf(refute_0_35,plain,
empty_set = set_intersection2(empty_set,X_27),
inference(subst,[],[refute_0_34:[bind(X_35,$fot(X_27))]]) ).
cnf(refute_0_36,plain,
( empty_set != set_intersection2(empty_set,X_27)
| set_intersection2(empty_set,X_27) = empty_set ),
inference(subst,[],[refute_0_12:[bind(X,$fot(empty_set)),bind(Y,$fot(set_intersection2(empty_set,X_27)))]]) ).
cnf(refute_0_37,plain,
set_intersection2(empty_set,X_27) = empty_set,
inference(resolve,[$cnf( $equal(empty_set,set_intersection2(empty_set,X_27)) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
( set_intersection2(empty_set,X_27) != empty_set
| ~ in(X_29,empty_set)
| in(X_29,set_intersection2(empty_set,X_27)) ),
introduced(tautology,[equality,[$cnf( ~ in(X_29,set_intersection2(empty_set,X_27)) ),[1],$fot(empty_set)]]) ).
cnf(refute_0_39,plain,
( ~ in(X_29,empty_set)
| in(X_29,set_intersection2(empty_set,X_27)) ),
inference(resolve,[$cnf( $equal(set_intersection2(empty_set,X_27),empty_set) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
( ~ in(X_29,empty_set)
| in(X_29,X_27) ),
inference(resolve,[$cnf( in(X_29,set_intersection2(empty_set,X_27)) )],[refute_0_39,refute_0_18]) ).
cnf(refute_0_41,plain,
( ~ in(skolemFOFtoCNF_D(X_412,X_413,empty_set),empty_set)
| in(skolemFOFtoCNF_D(X_412,X_413,empty_set),X_27) ),
inference(subst,[],[refute_0_40:[bind(X_29,$fot(skolemFOFtoCNF_D(X_412,X_413,empty_set)))]]) ).
cnf(refute_0_42,plain,
( C = set_intersection2(A,B)
| in(skolemFOFtoCNF_D(A,B,C),B)
| in(skolemFOFtoCNF_D(A,B,C),C) ),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_43,plain,
( empty_set = set_intersection2(X_412,X_413)
| in(skolemFOFtoCNF_D(X_412,X_413,empty_set),X_413)
| in(skolemFOFtoCNF_D(X_412,X_413,empty_set),empty_set) ),
inference(subst,[],[refute_0_42:[bind(A,$fot(X_412)),bind(B,$fot(X_413)),bind(C,$fot(empty_set))]]) ).
cnf(refute_0_44,plain,
( empty_set = set_intersection2(X_412,X_413)
| in(skolemFOFtoCNF_D(X_412,X_413,empty_set),X_27)
| in(skolemFOFtoCNF_D(X_412,X_413,empty_set),X_413) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_D(X_412,X_413,empty_set),empty_set) )],[refute_0_43,refute_0_41]) ).
cnf(refute_0_45,plain,
( empty_set = set_intersection2(singleton(A),X_426)
| in(skolemFOFtoCNF_D(singleton(A),X_426,empty_set),X_426) ),
inference(subst,[],[refute_0_44:[bind(X_27,$fot(X_426)),bind(X_412,$fot(singleton(A))),bind(X_413,$fot(X_426))]]) ).
cnf(refute_0_46,plain,
( B != singleton(A)
| ~ in(C,B)
| C = A ),
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_47,plain,
( singleton(A) != singleton(A)
| ~ in(C,singleton(A))
| C = A ),
inference(subst,[],[refute_0_46:[bind(B,$fot(singleton(A)))]]) ).
cnf(refute_0_48,plain,
singleton(A) = singleton(A),
introduced(tautology,[refl,[$fot(singleton(A))]]) ).
cnf(refute_0_49,plain,
( ~ in(C,singleton(A))
| C = A ),
inference(resolve,[$cnf( $equal(singleton(A),singleton(A)) )],[refute_0_48,refute_0_47]) ).
cnf(refute_0_50,plain,
( ~ in(skolemFOFtoCNF_D(singleton(A),X_352,empty_set),singleton(A))
| skolemFOFtoCNF_D(singleton(A),X_352,empty_set) = A ),
inference(subst,[],[refute_0_49:[bind(C,$fot(skolemFOFtoCNF_D(singleton(A),X_352,empty_set)))]]) ).
cnf(refute_0_51,plain,
( ~ in(skolemFOFtoCNF_D(X_338,X_339,empty_set),empty_set)
| in(skolemFOFtoCNF_D(X_338,X_339,empty_set),X_27) ),
inference(subst,[],[refute_0_40:[bind(X_29,$fot(skolemFOFtoCNF_D(X_338,X_339,empty_set)))]]) ).
cnf(refute_0_52,plain,
( C = set_intersection2(A,B)
| in(skolemFOFtoCNF_D(A,B,C),A)
| in(skolemFOFtoCNF_D(A,B,C),C) ),
inference(canonicalize,[],[normalize_0_29]) ).
cnf(refute_0_53,plain,
( empty_set = set_intersection2(X_338,X_339)
| in(skolemFOFtoCNF_D(X_338,X_339,empty_set),X_338)
| in(skolemFOFtoCNF_D(X_338,X_339,empty_set),empty_set) ),
inference(subst,[],[refute_0_52:[bind(A,$fot(X_338)),bind(B,$fot(X_339)),bind(C,$fot(empty_set))]]) ).
cnf(refute_0_54,plain,
( empty_set = set_intersection2(X_338,X_339)
| in(skolemFOFtoCNF_D(X_338,X_339,empty_set),X_27)
| in(skolemFOFtoCNF_D(X_338,X_339,empty_set),X_338) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_D(X_338,X_339,empty_set),empty_set) )],[refute_0_53,refute_0_51]) ).
cnf(refute_0_55,plain,
( empty_set = set_intersection2(singleton(A),X_352)
| in(skolemFOFtoCNF_D(singleton(A),X_352,empty_set),singleton(A)) ),
inference(subst,[],[refute_0_54:[bind(X_27,$fot(singleton(A))),bind(X_338,$fot(singleton(A))),bind(X_339,$fot(X_352))]]) ).
cnf(refute_0_56,plain,
( empty_set = set_intersection2(singleton(A),X_352)
| skolemFOFtoCNF_D(singleton(A),X_352,empty_set) = A ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_D(singleton(A),X_352,empty_set),singleton(A)) )],[refute_0_55,refute_0_50]) ).
cnf(refute_0_57,plain,
( empty_set = set_intersection2(singleton(A),X_426)
| skolemFOFtoCNF_D(singleton(A),X_426,empty_set) = A ),
inference(subst,[],[refute_0_56:[bind(X_352,$fot(X_426))]]) ).
cnf(refute_0_58,plain,
( skolemFOFtoCNF_D(singleton(A),X_426,empty_set) != A
| ~ in(skolemFOFtoCNF_D(singleton(A),X_426,empty_set),X_426)
| in(A,X_426) ),
introduced(tautology,[equality,[$cnf( in(skolemFOFtoCNF_D(singleton(A),X_426,empty_set),X_426) ),[0],$fot(A)]]) ).
cnf(refute_0_59,plain,
( ~ in(skolemFOFtoCNF_D(singleton(A),X_426,empty_set),X_426)
| empty_set = set_intersection2(singleton(A),X_426)
| in(A,X_426) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_D(singleton(A),X_426,empty_set),A) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
( empty_set = set_intersection2(singleton(A),X_426)
| in(A,X_426) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_D(singleton(A),X_426,empty_set),X_426) )],[refute_0_45,refute_0_59]) ).
cnf(refute_0_61,plain,
( empty_set = set_intersection2(singleton(X_431),B)
| in(X_431,B) ),
inference(subst,[],[refute_0_60:[bind(A,$fot(X_431)),bind(X_426,$fot(B))]]) ).
cnf(refute_0_62,plain,
( empty_set != set_intersection2(singleton(X_431),B)
| set_intersection2(singleton(X_431),B) = empty_set ),
inference(subst,[],[refute_0_12:[bind(X,$fot(empty_set)),bind(Y,$fot(set_intersection2(singleton(X_431),B)))]]) ).
cnf(refute_0_63,plain,
( set_intersection2(singleton(X_431),B) = empty_set
| in(X_431,B) ),
inference(resolve,[$cnf( $equal(empty_set,set_intersection2(singleton(X_431),B)) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
( empty_set != empty_set
| set_intersection2(singleton(X_431),B) != empty_set
| set_intersection2(singleton(X_431),B) = empty_set ),
introduced(tautology,[equality,[$cnf( $equal(set_intersection2(singleton(X_431),B),empty_set) ),[1],$fot(empty_set)]]) ).
cnf(refute_0_65,plain,
( empty_set != empty_set
| set_intersection2(singleton(X_431),B) = empty_set
| in(X_431,B) ),
inference(resolve,[$cnf( $equal(set_intersection2(singleton(X_431),B),empty_set) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
( empty_set != empty_set
| disjoint(singleton(X_431),B)
| in(X_431,B) ),
inference(resolve,[$cnf( $equal(set_intersection2(singleton(X_431),B),empty_set) )],[refute_0_65,refute_0_2]) ).
cnf(refute_0_67,plain,
empty_set = empty_set,
introduced(tautology,[refl,[$fot(empty_set)]]) ).
cnf(refute_0_68,plain,
( disjoint(singleton(X_431),B)
| in(X_431,B) ),
inference(resolve,[$cnf( $equal(empty_set,empty_set) )],[refute_0_67,refute_0_66]) ).
cnf(refute_0_69,plain,
( disjoint(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B)
| in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_68:[bind(B,$fot(skolemFOFtoCNF_B)),bind(X_431,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_70,plain,
in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
inference(resolve,[$cnf( disjoint(singleton(skolemFOFtoCNF_A_2),skolemFOFtoCNF_B) )],[refute_0_69,refute_0_0]) ).
cnf(refute_0_71,plain,
~ in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
inference(canonicalize,[],[normalize_0_30]) ).
cnf(refute_0_72,plain,
$false,
inference(resolve,[$cnf( in(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) )],[refute_0_70,refute_0_71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU154+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 19 12:11:54 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.74/1.97 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.74/1.97
% 1.74/1.97 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.74/1.98
%------------------------------------------------------------------------------