TSTP Solution File: SET902+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET902+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n019.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 03:38:13 EDT 2022
% Result : Theorem 0.12s 0.35s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 28
% Syntax : Number of formulae : 137 ( 65 unt; 0 def)
% Number of atoms : 294 ( 232 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 298 ( 141 ~; 102 |; 46 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 115 ( 6 sgn 60 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_xboole_0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A) ).
fof(idempotence_k2_xboole_0,axiom,
! [A,B] : set_union2(A,A) = A ).
fof(l1_zfmisc_1,axiom,
! [A] : singleton(A) != empty_set ).
fof(l4_zfmisc_1,axiom,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = empty_set
| A = singleton(B) ) ) ).
fof(t43_zfmisc_1,conjecture,
! [A,B,C] :
~ ( singleton(A) = set_union2(B,C)
& ~ ( B = singleton(A)
& C = singleton(A) )
& ~ ( B = empty_set
& C = singleton(A) )
& ~ ( B = singleton(A)
& C = empty_set ) ) ).
fof(t7_xboole_1,axiom,
! [A,B] : subset(A,set_union2(A,B)) ).
fof(subgoal_0,plain,
! [A,B,C] :
( ( singleton(A) = set_union2(B,C)
& ~ ( B = singleton(A)
& C = singleton(A) )
& ~ ( B = empty_set
& C = singleton(A) ) )
=> B = singleton(A) ),
inference(strip,[],[t43_zfmisc_1]) ).
fof(subgoal_1,plain,
! [A,B,C] :
( ( singleton(A) = set_union2(B,C)
& ~ ( B = singleton(A)
& C = singleton(A) )
& ~ ( B = empty_set
& C = singleton(A) )
& B = singleton(A) )
=> C = empty_set ),
inference(strip,[],[t43_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B,C] :
( ( singleton(A) = set_union2(B,C)
& ~ ( B = singleton(A)
& C = singleton(A) )
& ~ ( B = empty_set
& C = singleton(A) ) )
=> B = singleton(A) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B,C] :
( B != singleton(A)
& singleton(A) = set_union2(B,C)
& ( B != empty_set
| C != singleton(A) )
& ( B != singleton(A)
| C != singleton(A) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( skolemFOFtoCNF_B != singleton(skolemFOFtoCNF_A_2)
& singleton(skolemFOFtoCNF_A_2) = set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)
& ( skolemFOFtoCNF_B != empty_set
| skolemFOFtoCNF_C != singleton(skolemFOFtoCNF_A_2) )
& ( skolemFOFtoCNF_B != singleton(skolemFOFtoCNF_A_2)
| skolemFOFtoCNF_C != singleton(skolemFOFtoCNF_A_2) ) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
singleton(skolemFOFtoCNF_A_2) = set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B] : subset(A,set_union2(A,B)),
inference(canonicalize,[],[t7_xboole_1]) ).
fof(normalize_0_4,plain,
! [A,B] : subset(A,set_union2(A,B)),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A,B] :
( ~ subset(A,singleton(B))
<=> ( A != empty_set
& A != singleton(B) ) ),
inference(canonicalize,[],[l4_zfmisc_1]) ).
fof(normalize_0_6,plain,
! [A,B] :
( ~ subset(A,singleton(B))
<=> ( A != empty_set
& A != singleton(B) ) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B] :
( ( A != empty_set
| subset(A,singleton(B)) )
& ( A != singleton(B)
| subset(A,singleton(B)) )
& ( ~ subset(A,singleton(B))
| A = empty_set
| A = singleton(B) ) ),
inference(clausify,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,B] :
( ~ subset(A,singleton(B))
| A = empty_set
| A = singleton(B) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
skolemFOFtoCNF_B != singleton(skolemFOFtoCNF_A_2),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_10,plain,
! [A] : set_union2(A,A) = A,
inference(canonicalize,[],[idempotence_k2_xboole_0]) ).
fof(normalize_0_11,plain,
! [A] : set_union2(A,A) = A,
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(canonicalize,[],[commutativity_k2_xboole_0]) ).
fof(normalize_0_13,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
( skolemFOFtoCNF_B != empty_set
| skolemFOFtoCNF_C != singleton(skolemFOFtoCNF_A_2) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_15,plain,
! [A] : singleton(A) != empty_set,
inference(canonicalize,[],[l1_zfmisc_1]) ).
fof(normalize_0_16,plain,
! [A] : singleton(A) != empty_set,
inference(specialize,[],[normalize_0_15]) ).
cnf(refute_0_0,plain,
singleton(skolemFOFtoCNF_A_2) = set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
subset(A,set_union2(A,B)),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
subset(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),
inference(subst,[],[refute_0_1:[bind(A,$fot(skolemFOFtoCNF_B)),bind(B,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_3,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_4,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_5,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
( singleton(skolemFOFtoCNF_A_2) != set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)
| set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C) = singleton(skolemFOFtoCNF_A_2) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(singleton(skolemFOFtoCNF_A_2))),bind(Y,$fot(set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)))]]) ).
cnf(refute_0_7,plain,
set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C) = singleton(skolemFOFtoCNF_A_2),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_A_2),set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) )],[refute_0_0,refute_0_6]) ).
cnf(refute_0_8,plain,
( set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C) != singleton(skolemFOFtoCNF_A_2)
| ~ subset(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C))
| subset(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_A_2)) ),
introduced(tautology,[equality,[$cnf( subset(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) ),[1],$fot(singleton(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_9,plain,
( ~ subset(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C))
| subset(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_A_2)) ),
inference(resolve,[$cnf( $equal(set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),singleton(skolemFOFtoCNF_A_2)) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
subset(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_A_2)),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_B,set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) )],[refute_0_2,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ subset(A,singleton(B))
| A = empty_set
| A = singleton(B) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_12,plain,
( ~ subset(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_A_2))
| skolemFOFtoCNF_B = empty_set
| skolemFOFtoCNF_B = singleton(skolemFOFtoCNF_A_2) ),
inference(subst,[],[refute_0_11:[bind(A,$fot(skolemFOFtoCNF_B)),bind(B,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_13,plain,
( skolemFOFtoCNF_B = empty_set
| skolemFOFtoCNF_B = singleton(skolemFOFtoCNF_A_2) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_A_2)) )],[refute_0_10,refute_0_12]) ).
cnf(refute_0_14,plain,
skolemFOFtoCNF_B != singleton(skolemFOFtoCNF_A_2),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_15,plain,
skolemFOFtoCNF_B = empty_set,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B,singleton(skolemFOFtoCNF_A_2)) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C) = set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),
introduced(tautology,[refl,[$fot(set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C))]]) ).
cnf(refute_0_17,plain,
( set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C) != set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)
| skolemFOFtoCNF_B != empty_set
| set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C) = set_union2(empty_set,skolemFOFtoCNF_C) ),
introduced(tautology,[equality,[$cnf( $equal(set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) ),[1,0],$fot(empty_set)]]) ).
cnf(refute_0_18,plain,
( skolemFOFtoCNF_B != empty_set
| set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C) = set_union2(empty_set,skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( $equal(set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C) = set_union2(empty_set,skolemFOFtoCNF_C),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B,empty_set) )],[refute_0_15,refute_0_18]) ).
cnf(refute_0_20,plain,
( set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C) != set_union2(empty_set,skolemFOFtoCNF_C)
| singleton(skolemFOFtoCNF_A_2) != set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)
| singleton(skolemFOFtoCNF_A_2) = set_union2(empty_set,skolemFOFtoCNF_C) ),
introduced(tautology,[equality,[$cnf( $equal(singleton(skolemFOFtoCNF_A_2),set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) ),[1],$fot(set_union2(empty_set,skolemFOFtoCNF_C))]]) ).
cnf(refute_0_21,plain,
( singleton(skolemFOFtoCNF_A_2) != set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)
| singleton(skolemFOFtoCNF_A_2) = set_union2(empty_set,skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( $equal(set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),set_union2(empty_set,skolemFOFtoCNF_C)) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
singleton(skolemFOFtoCNF_A_2) = set_union2(empty_set,skolemFOFtoCNF_C),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_A_2),set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) )],[refute_0_0,refute_0_21]) ).
cnf(refute_0_23,plain,
set_union2(A,A) = A,
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_24,plain,
set_union2(empty_set,empty_set) = empty_set,
inference(subst,[],[refute_0_23:[bind(A,$fot(empty_set))]]) ).
cnf(refute_0_25,plain,
set_union2(A,B) = set_union2(B,A),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_26,plain,
( set_union2(A,B) != set_union2(B,A)
| ~ subset(A,set_union2(A,B))
| subset(A,set_union2(B,A)) ),
introduced(tautology,[equality,[$cnf( subset(A,set_union2(A,B)) ),[1],$fot(set_union2(B,A))]]) ).
cnf(refute_0_27,plain,
( ~ subset(A,set_union2(A,B))
| subset(A,set_union2(B,A)) ),
inference(resolve,[$cnf( $equal(set_union2(A,B),set_union2(B,A)) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
subset(A,set_union2(B,A)),
inference(resolve,[$cnf( subset(A,set_union2(A,B)) )],[refute_0_1,refute_0_27]) ).
cnf(refute_0_29,plain,
subset(skolemFOFtoCNF_C,set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),
inference(subst,[],[refute_0_28:[bind(A,$fot(skolemFOFtoCNF_C)),bind(B,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_30,plain,
( set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C) != singleton(skolemFOFtoCNF_A_2)
| ~ subset(skolemFOFtoCNF_C,set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C))
| subset(skolemFOFtoCNF_C,singleton(skolemFOFtoCNF_A_2)) ),
introduced(tautology,[equality,[$cnf( subset(skolemFOFtoCNF_C,set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) ),[1],$fot(singleton(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_31,plain,
( ~ subset(skolemFOFtoCNF_C,set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C))
| subset(skolemFOFtoCNF_C,singleton(skolemFOFtoCNF_A_2)) ),
inference(resolve,[$cnf( $equal(set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),singleton(skolemFOFtoCNF_A_2)) )],[refute_0_7,refute_0_30]) ).
cnf(refute_0_32,plain,
subset(skolemFOFtoCNF_C,singleton(skolemFOFtoCNF_A_2)),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_C,set_union2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) )],[refute_0_29,refute_0_31]) ).
cnf(refute_0_33,plain,
( ~ subset(skolemFOFtoCNF_C,singleton(skolemFOFtoCNF_A_2))
| skolemFOFtoCNF_C = empty_set
| skolemFOFtoCNF_C = singleton(skolemFOFtoCNF_A_2) ),
inference(subst,[],[refute_0_11:[bind(A,$fot(skolemFOFtoCNF_C)),bind(B,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_34,plain,
( skolemFOFtoCNF_C = empty_set
| skolemFOFtoCNF_C = singleton(skolemFOFtoCNF_A_2) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_C,singleton(skolemFOFtoCNF_A_2)) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
( skolemFOFtoCNF_B != empty_set
| skolemFOFtoCNF_C != singleton(skolemFOFtoCNF_A_2) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_36,plain,
( empty_set != empty_set
| skolemFOFtoCNF_B != empty_set
| skolemFOFtoCNF_B = empty_set ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_B,empty_set) ),[1],$fot(empty_set)]]) ).
cnf(refute_0_37,plain,
( empty_set != empty_set
| skolemFOFtoCNF_B = empty_set ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B,empty_set) )],[refute_0_15,refute_0_36]) ).
cnf(refute_0_38,plain,
( empty_set != empty_set
| skolemFOFtoCNF_C != singleton(skolemFOFtoCNF_A_2) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B,empty_set) )],[refute_0_37,refute_0_35]) ).
cnf(refute_0_39,plain,
empty_set = empty_set,
introduced(tautology,[refl,[$fot(empty_set)]]) ).
cnf(refute_0_40,plain,
skolemFOFtoCNF_C != singleton(skolemFOFtoCNF_A_2),
inference(resolve,[$cnf( $equal(empty_set,empty_set) )],[refute_0_39,refute_0_38]) ).
cnf(refute_0_41,plain,
skolemFOFtoCNF_C = empty_set,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C,singleton(skolemFOFtoCNF_A_2)) )],[refute_0_34,refute_0_40]) ).
cnf(refute_0_42,plain,
set_union2(empty_set,skolemFOFtoCNF_C) = set_union2(empty_set,skolemFOFtoCNF_C),
introduced(tautology,[refl,[$fot(set_union2(empty_set,skolemFOFtoCNF_C))]]) ).
cnf(refute_0_43,plain,
( set_union2(empty_set,skolemFOFtoCNF_C) != set_union2(empty_set,skolemFOFtoCNF_C)
| skolemFOFtoCNF_C != empty_set
| set_union2(empty_set,skolemFOFtoCNF_C) = set_union2(empty_set,empty_set) ),
introduced(tautology,[equality,[$cnf( $equal(set_union2(empty_set,skolemFOFtoCNF_C),set_union2(empty_set,skolemFOFtoCNF_C)) ),[1,1],$fot(empty_set)]]) ).
cnf(refute_0_44,plain,
( skolemFOFtoCNF_C != empty_set
| set_union2(empty_set,skolemFOFtoCNF_C) = set_union2(empty_set,empty_set) ),
inference(resolve,[$cnf( $equal(set_union2(empty_set,skolemFOFtoCNF_C),set_union2(empty_set,skolemFOFtoCNF_C)) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
set_union2(empty_set,skolemFOFtoCNF_C) = set_union2(empty_set,empty_set),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C,empty_set) )],[refute_0_41,refute_0_44]) ).
cnf(refute_0_46,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_47,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_5,refute_0_46]) ).
cnf(refute_0_48,plain,
( set_union2(empty_set,empty_set) != empty_set
| set_union2(empty_set,skolemFOFtoCNF_C) != set_union2(empty_set,empty_set)
| set_union2(empty_set,skolemFOFtoCNF_C) = empty_set ),
inference(subst,[],[refute_0_47:[bind(X,$fot(set_union2(empty_set,skolemFOFtoCNF_C))),bind(Y,$fot(set_union2(empty_set,empty_set))),bind(Z,$fot(empty_set))]]) ).
cnf(refute_0_49,plain,
( set_union2(empty_set,empty_set) != empty_set
| set_union2(empty_set,skolemFOFtoCNF_C) = empty_set ),
inference(resolve,[$cnf( $equal(set_union2(empty_set,skolemFOFtoCNF_C),set_union2(empty_set,empty_set)) )],[refute_0_45,refute_0_48]) ).
cnf(refute_0_50,plain,
set_union2(empty_set,skolemFOFtoCNF_C) = empty_set,
inference(resolve,[$cnf( $equal(set_union2(empty_set,empty_set),empty_set) )],[refute_0_24,refute_0_49]) ).
cnf(refute_0_51,plain,
( set_union2(empty_set,skolemFOFtoCNF_C) != empty_set
| singleton(skolemFOFtoCNF_A_2) != set_union2(empty_set,skolemFOFtoCNF_C)
| singleton(skolemFOFtoCNF_A_2) = empty_set ),
introduced(tautology,[equality,[$cnf( $equal(singleton(skolemFOFtoCNF_A_2),set_union2(empty_set,skolemFOFtoCNF_C)) ),[1],$fot(empty_set)]]) ).
cnf(refute_0_52,plain,
( singleton(skolemFOFtoCNF_A_2) != set_union2(empty_set,skolemFOFtoCNF_C)
| singleton(skolemFOFtoCNF_A_2) = empty_set ),
inference(resolve,[$cnf( $equal(set_union2(empty_set,skolemFOFtoCNF_C),empty_set) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
singleton(skolemFOFtoCNF_A_2) = empty_set,
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_A_2),set_union2(empty_set,skolemFOFtoCNF_C)) )],[refute_0_22,refute_0_52]) ).
cnf(refute_0_54,plain,
singleton(A) != empty_set,
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_55,plain,
singleton(skolemFOFtoCNF_A_2) != empty_set,
inference(subst,[],[refute_0_54:[bind(A,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_56,plain,
$false,
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_A_2),empty_set) )],[refute_0_53,refute_0_55]) ).
fof(negate_1_0,plain,
~ ! [A,B,C] :
( ( singleton(A) = set_union2(B,C)
& ~ ( B = singleton(A)
& C = singleton(A) )
& ~ ( B = empty_set
& C = singleton(A) )
& B = singleton(A) )
=> C = empty_set ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
! [A,B] : subset(A,set_union2(A,B)),
inference(canonicalize,[],[t7_xboole_1]) ).
fof(normalize_1_1,plain,
! [A,B] : subset(A,set_union2(A,B)),
inference(specialize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(canonicalize,[],[commutativity_k2_xboole_0]) ).
fof(normalize_1_3,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(specialize,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
? [A,B,C] :
( C != empty_set
& B = singleton(A)
& singleton(A) = set_union2(B,C)
& ( B != empty_set
| C != singleton(A) )
& ( B != singleton(A)
| C != singleton(A) ) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_5,plain,
( skolemFOFtoCNF_C_1 != empty_set
& singleton(skolemFOFtoCNF_A_3) = set_union2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
& skolemFOFtoCNF_B_1 = singleton(skolemFOFtoCNF_A_3)
& ( skolemFOFtoCNF_B_1 != empty_set
| skolemFOFtoCNF_C_1 != singleton(skolemFOFtoCNF_A_3) )
& ( skolemFOFtoCNF_B_1 != singleton(skolemFOFtoCNF_A_3)
| skolemFOFtoCNF_C_1 != singleton(skolemFOFtoCNF_A_3) ) ),
inference(skolemize,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
singleton(skolemFOFtoCNF_A_3) = set_union2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
skolemFOFtoCNF_B_1 = singleton(skolemFOFtoCNF_A_3),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_8,plain,
! [A,B] :
( ~ subset(A,singleton(B))
<=> ( A != empty_set
& A != singleton(B) ) ),
inference(canonicalize,[],[l4_zfmisc_1]) ).
fof(normalize_1_9,plain,
! [A,B] :
( ~ subset(A,singleton(B))
<=> ( A != empty_set
& A != singleton(B) ) ),
inference(specialize,[],[normalize_1_8]) ).
fof(normalize_1_10,plain,
! [A,B] :
( ( A != empty_set
| subset(A,singleton(B)) )
& ( A != singleton(B)
| subset(A,singleton(B)) )
& ( ~ subset(A,singleton(B))
| A = empty_set
| A = singleton(B) ) ),
inference(clausify,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
! [A,B] :
( ~ subset(A,singleton(B))
| A = empty_set
| A = singleton(B) ),
inference(conjunct,[],[normalize_1_10]) ).
fof(normalize_1_12,plain,
skolemFOFtoCNF_C_1 != empty_set,
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_13,plain,
( skolemFOFtoCNF_B_1 != singleton(skolemFOFtoCNF_A_3)
| skolemFOFtoCNF_C_1 != singleton(skolemFOFtoCNF_A_3) ),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_14,plain,
skolemFOFtoCNF_C_1 != singleton(skolemFOFtoCNF_A_3),
inference(simplify,[],[normalize_1_13,normalize_1_7]) ).
cnf(refute_1_0,plain,
subset(A,set_union2(A,B)),
inference(canonicalize,[],[normalize_1_1]) ).
cnf(refute_1_1,plain,
set_union2(A,B) = set_union2(B,A),
inference(canonicalize,[],[normalize_1_3]) ).
cnf(refute_1_2,plain,
( set_union2(A,B) != set_union2(B,A)
| ~ subset(A,set_union2(A,B))
| subset(A,set_union2(B,A)) ),
introduced(tautology,[equality,[$cnf( subset(A,set_union2(A,B)) ),[1],$fot(set_union2(B,A))]]) ).
cnf(refute_1_3,plain,
( ~ subset(A,set_union2(A,B))
| subset(A,set_union2(B,A)) ),
inference(resolve,[$cnf( $equal(set_union2(A,B),set_union2(B,A)) )],[refute_1_1,refute_1_2]) ).
cnf(refute_1_4,plain,
subset(A,set_union2(B,A)),
inference(resolve,[$cnf( subset(A,set_union2(A,B)) )],[refute_1_0,refute_1_3]) ).
cnf(refute_1_5,plain,
subset(skolemFOFtoCNF_C_1,set_union2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)),
inference(subst,[],[refute_1_4:[bind(A,$fot(skolemFOFtoCNF_C_1)),bind(B,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_1_6,plain,
singleton(skolemFOFtoCNF_A_3) = set_union2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),
inference(canonicalize,[],[normalize_1_6]) ).
cnf(refute_1_7,plain,
skolemFOFtoCNF_B_1 = singleton(skolemFOFtoCNF_A_3),
inference(canonicalize,[],[normalize_1_7]) ).
cnf(refute_1_8,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_1_9,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_1_10,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_1_8,refute_1_9]) ).
cnf(refute_1_11,plain,
( skolemFOFtoCNF_B_1 != singleton(skolemFOFtoCNF_A_3)
| singleton(skolemFOFtoCNF_A_3) = skolemFOFtoCNF_B_1 ),
inference(subst,[],[refute_1_10:[bind(X,$fot(skolemFOFtoCNF_B_1)),bind(Y,$fot(singleton(skolemFOFtoCNF_A_3)))]]) ).
cnf(refute_1_12,plain,
singleton(skolemFOFtoCNF_A_3) = skolemFOFtoCNF_B_1,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B_1,singleton(skolemFOFtoCNF_A_3)) )],[refute_1_7,refute_1_11]) ).
cnf(refute_1_13,plain,
( singleton(skolemFOFtoCNF_A_3) != set_union2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
| singleton(skolemFOFtoCNF_A_3) != skolemFOFtoCNF_B_1
| skolemFOFtoCNF_B_1 = set_union2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) ),
introduced(tautology,[equality,[$cnf( $equal(singleton(skolemFOFtoCNF_A_3),set_union2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)) ),[0],$fot(skolemFOFtoCNF_B_1)]]) ).
cnf(refute_1_14,plain,
( singleton(skolemFOFtoCNF_A_3) != set_union2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
| skolemFOFtoCNF_B_1 = set_union2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) ),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_1) )],[refute_1_12,refute_1_13]) ).
cnf(refute_1_15,plain,
skolemFOFtoCNF_B_1 = set_union2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_A_3),set_union2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)) )],[refute_1_6,refute_1_14]) ).
cnf(refute_1_16,plain,
( skolemFOFtoCNF_B_1 != set_union2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)
| set_union2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) = skolemFOFtoCNF_B_1 ),
inference(subst,[],[refute_1_10:[bind(X,$fot(skolemFOFtoCNF_B_1)),bind(Y,$fot(set_union2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)))]]) ).
cnf(refute_1_17,plain,
set_union2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) = skolemFOFtoCNF_B_1,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B_1,set_union2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)) )],[refute_1_15,refute_1_16]) ).
cnf(refute_1_18,plain,
( set_union2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1) != skolemFOFtoCNF_B_1
| ~ subset(skolemFOFtoCNF_C_1,set_union2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1))
| subset(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1) ),
introduced(tautology,[equality,[$cnf( subset(skolemFOFtoCNF_C_1,set_union2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)) ),[1],$fot(skolemFOFtoCNF_B_1)]]) ).
cnf(refute_1_19,plain,
( ~ subset(skolemFOFtoCNF_C_1,set_union2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1))
| subset(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1) ),
inference(resolve,[$cnf( $equal(set_union2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1),skolemFOFtoCNF_B_1) )],[refute_1_17,refute_1_18]) ).
cnf(refute_1_20,plain,
subset(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_C_1,set_union2(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_1)) )],[refute_1_5,refute_1_19]) ).
cnf(refute_1_21,plain,
( ~ subset(A,singleton(B))
| A = empty_set
| A = singleton(B) ),
inference(canonicalize,[],[normalize_1_11]) ).
cnf(refute_1_22,plain,
( ~ subset(X_30,singleton(skolemFOFtoCNF_A_3))
| X_30 = empty_set
| X_30 = singleton(skolemFOFtoCNF_A_3) ),
inference(subst,[],[refute_1_21:[bind(A,$fot(X_30)),bind(B,$fot(skolemFOFtoCNF_A_3))]]) ).
cnf(refute_1_23,plain,
( singleton(skolemFOFtoCNF_A_3) != skolemFOFtoCNF_B_1
| ~ subset(X_30,skolemFOFtoCNF_B_1)
| subset(X_30,singleton(skolemFOFtoCNF_A_3)) ),
introduced(tautology,[equality,[$cnf( ~ subset(X_30,singleton(skolemFOFtoCNF_A_3)) ),[1],$fot(skolemFOFtoCNF_B_1)]]) ).
cnf(refute_1_24,plain,
( ~ subset(X_30,skolemFOFtoCNF_B_1)
| subset(X_30,singleton(skolemFOFtoCNF_A_3)) ),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_1) )],[refute_1_12,refute_1_23]) ).
cnf(refute_1_25,plain,
( ~ subset(X_30,skolemFOFtoCNF_B_1)
| X_30 = empty_set
| X_30 = singleton(skolemFOFtoCNF_A_3) ),
inference(resolve,[$cnf( subset(X_30,singleton(skolemFOFtoCNF_A_3)) )],[refute_1_24,refute_1_22]) ).
cnf(refute_1_26,plain,
( X_30 != singleton(skolemFOFtoCNF_A_3)
| singleton(skolemFOFtoCNF_A_3) != skolemFOFtoCNF_B_1
| X_30 = skolemFOFtoCNF_B_1 ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_30,skolemFOFtoCNF_B_1) ),[0],$fot(singleton(skolemFOFtoCNF_A_3))]]) ).
cnf(refute_1_27,plain,
( X_30 != singleton(skolemFOFtoCNF_A_3)
| X_30 = skolemFOFtoCNF_B_1 ),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_1) )],[refute_1_12,refute_1_26]) ).
cnf(refute_1_28,plain,
( ~ subset(X_30,skolemFOFtoCNF_B_1)
| X_30 = empty_set
| X_30 = skolemFOFtoCNF_B_1 ),
inference(resolve,[$cnf( $equal(X_30,singleton(skolemFOFtoCNF_A_3)) )],[refute_1_25,refute_1_27]) ).
cnf(refute_1_29,plain,
( ~ subset(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1)
| skolemFOFtoCNF_C_1 = empty_set
| skolemFOFtoCNF_C_1 = skolemFOFtoCNF_B_1 ),
inference(subst,[],[refute_1_28:[bind(X_30,$fot(skolemFOFtoCNF_C_1))]]) ).
cnf(refute_1_30,plain,
( skolemFOFtoCNF_C_1 = empty_set
| skolemFOFtoCNF_C_1 = skolemFOFtoCNF_B_1 ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1) )],[refute_1_20,refute_1_29]) ).
cnf(refute_1_31,plain,
skolemFOFtoCNF_C_1 != empty_set,
inference(canonicalize,[],[normalize_1_12]) ).
cnf(refute_1_32,plain,
skolemFOFtoCNF_C_1 = skolemFOFtoCNF_B_1,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C_1,empty_set) )],[refute_1_30,refute_1_31]) ).
cnf(refute_1_33,plain,
skolemFOFtoCNF_C_1 != singleton(skolemFOFtoCNF_A_3),
inference(canonicalize,[],[normalize_1_14]) ).
cnf(refute_1_34,plain,
( singleton(skolemFOFtoCNF_A_3) != skolemFOFtoCNF_B_1
| skolemFOFtoCNF_C_1 != skolemFOFtoCNF_B_1
| skolemFOFtoCNF_C_1 = singleton(skolemFOFtoCNF_A_3) ),
introduced(tautology,[equality,[$cnf( ~ $equal(skolemFOFtoCNF_C_1,singleton(skolemFOFtoCNF_A_3)) ),[1],$fot(skolemFOFtoCNF_B_1)]]) ).
cnf(refute_1_35,plain,
( skolemFOFtoCNF_C_1 != skolemFOFtoCNF_B_1
| skolemFOFtoCNF_C_1 = singleton(skolemFOFtoCNF_A_3) ),
inference(resolve,[$cnf( $equal(singleton(skolemFOFtoCNF_A_3),skolemFOFtoCNF_B_1) )],[refute_1_12,refute_1_34]) ).
cnf(refute_1_36,plain,
skolemFOFtoCNF_C_1 != skolemFOFtoCNF_B_1,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C_1,singleton(skolemFOFtoCNF_A_3)) )],[refute_1_35,refute_1_33]) ).
cnf(refute_1_37,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C_1,skolemFOFtoCNF_B_1) )],[refute_1_32,refute_1_36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.11 % Problem : SET902+1 : TPTP v8.1.0. Released v3.2.0.
% 0.08/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n019.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 Jul 10 02:22:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.35
% 0.12/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.36
%------------------------------------------------------------------------------