TSTP Solution File: REL046+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : REL046+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n018.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 : Mon Jul 18 19:46:10 EDT 2022
% Result : Theorem 2.65s 2.90s
% Output : CNFRefutation 2.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 28
% Syntax : Number of formulae : 142 ( 83 unt; 0 def)
% Number of atoms : 229 ( 227 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 170 ( 83 ~; 73 |; 9 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 228 ( 0 sgn 60 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(maddux1_join_commutativity,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0) ).
fof(maddux2_join_associativity,axiom,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2) ).
fof(maddux3_a_kind_of_de_Morgan,axiom,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) ).
fof(maddux4_definiton_of_meet,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))) ).
fof(goals,conjecture,
! [X0,X1,X2] :
( join(X0,meet(X1,X2)) = meet(X1,X2)
=> ( join(X0,X1) = X1
& join(X0,X2) = X2 ) ) ).
fof(subgoal_0,plain,
! [X0,X1,X2] :
( join(X0,meet(X1,X2)) = meet(X1,X2)
=> join(X0,X1) = X1 ),
inference(strip,[],[goals]) ).
fof(subgoal_1,plain,
! [X0,X1,X2] :
( ( join(X0,meet(X1,X2)) = meet(X1,X2)
& join(X0,X1) = X1 )
=> join(X0,X2) = X2 ),
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ! [X0,X1,X2] :
( join(X0,meet(X1,X2)) = meet(X1,X2)
=> join(X0,X1) = X1 ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(canonicalize,[],[maddux2_join_associativity]) ).
fof(normalize_0_1,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
? [X0,X1] :
( join(X0,X1) != X1
& ? [X2] : join(X0,meet(X1,X2)) = meet(X1,X2) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_3,plain,
( join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1) != skolemFOFtoCNF_X1
& ? [X2] : join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,X2)) = meet(skolemFOFtoCNF_X1,X2) ),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [X2] : join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,X2)) = meet(skolemFOFtoCNF_X1,X2),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)) = meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(canonicalize,[],[maddux3_a_kind_of_de_Morgan]) ).
fof(normalize_0_7,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(canonicalize,[],[maddux1_join_commutativity]) ).
fof(normalize_0_9,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(canonicalize,[],[maddux4_definiton_of_meet]) ).
fof(normalize_0_11,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1) != skolemFOFtoCNF_X1,
inference(conjunct,[],[normalize_0_3]) ).
cnf(refute_0_0,plain,
join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
join(skolemFOFtoCNF_X0,join(meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2),X_142)) = join(join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),X_142),
inference(subst,[],[refute_0_0:[bind(X0,$fot(skolemFOFtoCNF_X0)),bind(X1,$fot(meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2))),bind(X2,$fot(X_142))]]) ).
cnf(refute_0_2,plain,
join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)) = meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_3,plain,
( join(skolemFOFtoCNF_X0,join(meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2),X_142)) != join(join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),X_142)
| join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)) != meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)
| join(skolemFOFtoCNF_X0,join(meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2),X_142)) = join(meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2),X_142) ),
introduced(tautology,[equality,[$cnf( $equal(join(skolemFOFtoCNF_X0,join(meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2),X_142)),join(join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),X_142)) ),[1,0],$fot(meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2))]]) ).
cnf(refute_0_4,plain,
( join(skolemFOFtoCNF_X0,join(meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2),X_142)) != join(join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),X_142)
| join(skolemFOFtoCNF_X0,join(meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2),X_142)) = join(meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2),X_142) ),
inference(resolve,[$cnf( $equal(join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
join(skolemFOFtoCNF_X0,join(meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2),X_142)) = join(meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2),X_142),
inference(resolve,[$cnf( $equal(join(skolemFOFtoCNF_X0,join(meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2),X_142)),join(join(skolemFOFtoCNF_X0,meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),X_142)) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
join(skolemFOFtoCNF_X0,join(meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2),complement(join(complement(skolemFOFtoCNF_X1),skolemFOFtoCNF_X2)))) = join(meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2),complement(join(complement(skolemFOFtoCNF_X1),skolemFOFtoCNF_X2))),
inference(subst,[],[refute_0_5:[bind(X_142,$fot(complement(join(complement(skolemFOFtoCNF_X1),skolemFOFtoCNF_X2))))]]) ).
cnf(refute_0_7,plain,
X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_8,plain,
join(X0,X1) = join(X1,X0),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_9,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_10,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_11,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
( join(X0,X1) != join(X1,X0)
| join(X1,X0) = join(X0,X1) ),
inference(subst,[],[refute_0_11:[bind(X,$fot(join(X0,X1))),bind(Y,$fot(join(X1,X0)))]]) ).
cnf(refute_0_13,plain,
join(X1,X0) = join(X0,X1),
inference(resolve,[$cnf( $equal(join(X0,X1),join(X1,X0)) )],[refute_0_8,refute_0_12]) ).
cnf(refute_0_14,plain,
join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),
inference(subst,[],[refute_0_13:[bind(X0,$fot(complement(join(complement(X0),X1)))),bind(X1,$fot(complement(join(complement(X0),complement(X1)))))]]) ).
cnf(refute_0_15,plain,
( X0 != join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1)))
| join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) != join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))
| X0 = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X0,join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))) ),[0],$fot(join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))))]]) ).
cnf(refute_0_16,plain,
( X0 != join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1)))
| X0 = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) ),
inference(resolve,[$cnf( $equal(join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
X0 = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),
inference(resolve,[$cnf( $equal(X0,join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1)))) )],[refute_0_7,refute_0_16]) ).
cnf(refute_0_18,plain,
join(complement(join(complement(X0),X1)),meet(X0,X1)) = join(meet(X0,X1),complement(join(complement(X0),X1))),
inference(subst,[],[refute_0_13:[bind(X0,$fot(meet(X0,X1))),bind(X1,$fot(complement(join(complement(X0),X1))))]]) ).
cnf(refute_0_19,plain,
meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_20,plain,
( meet(X0,X1) != complement(join(complement(X0),complement(X1)))
| complement(join(complement(X0),complement(X1))) = meet(X0,X1) ),
inference(subst,[],[refute_0_11:[bind(X,$fot(meet(X0,X1))),bind(Y,$fot(complement(join(complement(X0),complement(X1)))))]]) ).
cnf(refute_0_21,plain,
complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(resolve,[$cnf( $equal(meet(X0,X1),complement(join(complement(X0),complement(X1)))) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),
introduced(tautology,[refl,[$fot(join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))))]]) ).
cnf(refute_0_23,plain,
( complement(join(complement(X0),complement(X1))) != meet(X0,X1)
| join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) != join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))
| join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(complement(join(complement(X0),X1)),meet(X0,X1)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))) ),[1,1],$fot(meet(X0,X1))]]) ).
cnf(refute_0_24,plain,
( complement(join(complement(X0),complement(X1))) != meet(X0,X1)
| join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(complement(join(complement(X0),X1)),meet(X0,X1)) ),
inference(resolve,[$cnf( $equal(join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(complement(join(complement(X0),X1)),meet(X0,X1)),
inference(resolve,[$cnf( $equal(complement(join(complement(X0),complement(X1))),meet(X0,X1)) )],[refute_0_21,refute_0_24]) ).
cnf(refute_0_26,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_27,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_11,refute_0_26]) ).
cnf(refute_0_28,plain,
( join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) != join(complement(join(complement(X0),X1)),meet(X0,X1))
| join(complement(join(complement(X0),X1)),meet(X0,X1)) != join(meet(X0,X1),complement(join(complement(X0),X1)))
| join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(meet(X0,X1),complement(join(complement(X0),X1))) ),
inference(subst,[],[refute_0_27:[bind(X,$fot(join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))))),bind(Y,$fot(join(complement(join(complement(X0),X1)),meet(X0,X1)))),bind(Z,$fot(join(meet(X0,X1),complement(join(complement(X0),X1)))))]]) ).
cnf(refute_0_29,plain,
( join(complement(join(complement(X0),X1)),meet(X0,X1)) != join(meet(X0,X1),complement(join(complement(X0),X1)))
| join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(meet(X0,X1),complement(join(complement(X0),X1))) ),
inference(resolve,[$cnf( $equal(join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),join(complement(join(complement(X0),X1)),meet(X0,X1))) )],[refute_0_25,refute_0_28]) ).
cnf(refute_0_30,plain,
join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(meet(X0,X1),complement(join(complement(X0),X1))),
inference(resolve,[$cnf( $equal(join(complement(join(complement(X0),X1)),meet(X0,X1)),join(meet(X0,X1),complement(join(complement(X0),X1)))) )],[refute_0_18,refute_0_29]) ).
cnf(refute_0_31,plain,
( X0 != join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))
| join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) != join(meet(X0,X1),complement(join(complement(X0),X1)))
| X0 = join(meet(X0,X1),complement(join(complement(X0),X1))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X0,join(meet(X0,X1),complement(join(complement(X0),X1)))) ),[0],$fot(join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))))]]) ).
cnf(refute_0_32,plain,
( X0 != join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))
| X0 = join(meet(X0,X1),complement(join(complement(X0),X1))) ),
inference(resolve,[$cnf( $equal(join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),join(meet(X0,X1),complement(join(complement(X0),X1)))) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
X0 = join(meet(X0,X1),complement(join(complement(X0),X1))),
inference(resolve,[$cnf( $equal(X0,join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))) )],[refute_0_17,refute_0_32]) ).
cnf(refute_0_34,plain,
skolemFOFtoCNF_X1 = join(meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2),complement(join(complement(skolemFOFtoCNF_X1),skolemFOFtoCNF_X2))),
inference(subst,[],[refute_0_33:[bind(X0,$fot(skolemFOFtoCNF_X1)),bind(X1,$fot(skolemFOFtoCNF_X2))]]) ).
cnf(refute_0_35,plain,
( skolemFOFtoCNF_X1 != join(meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2),complement(join(complement(skolemFOFtoCNF_X1),skolemFOFtoCNF_X2)))
| join(meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2),complement(join(complement(skolemFOFtoCNF_X1),skolemFOFtoCNF_X2))) = skolemFOFtoCNF_X1 ),
inference(subst,[],[refute_0_11:[bind(X,$fot(skolemFOFtoCNF_X1)),bind(Y,$fot(join(meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2),complement(join(complement(skolemFOFtoCNF_X1),skolemFOFtoCNF_X2)))))]]) ).
cnf(refute_0_36,plain,
join(meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2),complement(join(complement(skolemFOFtoCNF_X1),skolemFOFtoCNF_X2))) = skolemFOFtoCNF_X1,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X1,join(meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2),complement(join(complement(skolemFOFtoCNF_X1),skolemFOFtoCNF_X2)))) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
( join(meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2),complement(join(complement(skolemFOFtoCNF_X1),skolemFOFtoCNF_X2))) != skolemFOFtoCNF_X1
| join(skolemFOFtoCNF_X0,join(meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2),complement(join(complement(skolemFOFtoCNF_X1),skolemFOFtoCNF_X2)))) != join(meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2),complement(join(complement(skolemFOFtoCNF_X1),skolemFOFtoCNF_X2)))
| join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1) = join(meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2),complement(join(complement(skolemFOFtoCNF_X1),skolemFOFtoCNF_X2))) ),
introduced(tautology,[equality,[$cnf( $equal(join(skolemFOFtoCNF_X0,join(meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2),complement(join(complement(skolemFOFtoCNF_X1),skolemFOFtoCNF_X2)))),join(meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2),complement(join(complement(skolemFOFtoCNF_X1),skolemFOFtoCNF_X2)))) ),[0,1],$fot(skolemFOFtoCNF_X1)]]) ).
cnf(refute_0_38,plain,
( join(skolemFOFtoCNF_X0,join(meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2),complement(join(complement(skolemFOFtoCNF_X1),skolemFOFtoCNF_X2)))) != join(meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2),complement(join(complement(skolemFOFtoCNF_X1),skolemFOFtoCNF_X2)))
| join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1) = join(meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2),complement(join(complement(skolemFOFtoCNF_X1),skolemFOFtoCNF_X2))) ),
inference(resolve,[$cnf( $equal(join(meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2),complement(join(complement(skolemFOFtoCNF_X1),skolemFOFtoCNF_X2))),skolemFOFtoCNF_X1) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1) = join(meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2),complement(join(complement(skolemFOFtoCNF_X1),skolemFOFtoCNF_X2))),
inference(resolve,[$cnf( $equal(join(skolemFOFtoCNF_X0,join(meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2),complement(join(complement(skolemFOFtoCNF_X1),skolemFOFtoCNF_X2)))),join(meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2),complement(join(complement(skolemFOFtoCNF_X1),skolemFOFtoCNF_X2)))) )],[refute_0_6,refute_0_38]) ).
cnf(refute_0_40,plain,
( join(meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2),complement(join(complement(skolemFOFtoCNF_X1),skolemFOFtoCNF_X2))) != skolemFOFtoCNF_X1
| join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1) != join(meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2),complement(join(complement(skolemFOFtoCNF_X1),skolemFOFtoCNF_X2)))
| join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1) = skolemFOFtoCNF_X1 ),
introduced(tautology,[equality,[$cnf( $equal(join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),join(meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2),complement(join(complement(skolemFOFtoCNF_X1),skolemFOFtoCNF_X2)))) ),[1],$fot(skolemFOFtoCNF_X1)]]) ).
cnf(refute_0_41,plain,
( join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1) != join(meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2),complement(join(complement(skolemFOFtoCNF_X1),skolemFOFtoCNF_X2)))
| join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1) = skolemFOFtoCNF_X1 ),
inference(resolve,[$cnf( $equal(join(meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2),complement(join(complement(skolemFOFtoCNF_X1),skolemFOFtoCNF_X2))),skolemFOFtoCNF_X1) )],[refute_0_36,refute_0_40]) ).
cnf(refute_0_42,plain,
join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1) = skolemFOFtoCNF_X1,
inference(resolve,[$cnf( $equal(join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),join(meet(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2),complement(join(complement(skolemFOFtoCNF_X1),skolemFOFtoCNF_X2)))) )],[refute_0_39,refute_0_41]) ).
cnf(refute_0_43,plain,
join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1) != skolemFOFtoCNF_X1,
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_44,plain,
$false,
inference(resolve,[$cnf( $equal(join(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X1) )],[refute_0_42,refute_0_43]) ).
fof(negate_1_0,plain,
~ ! [X0,X1,X2] :
( ( join(X0,meet(X1,X2)) = meet(X1,X2)
& join(X0,X1) = X1 )
=> join(X0,X2) = X2 ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(canonicalize,[],[maddux2_join_associativity]) ).
fof(normalize_1_1,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(specialize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
? [X0,X1,X2] :
( join(X0,X2) != X2
& join(X0,X1) = X1
& join(X0,meet(X1,X2)) = meet(X1,X2) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_3,plain,
( join(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X2_1) != skolemFOFtoCNF_X2_1
& join(skolemFOFtoCNF_X0_1,meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1)) = meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1)
& join(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_1) = skolemFOFtoCNF_X1_1 ),
inference(skolemize,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
join(skolemFOFtoCNF_X0_1,meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1)) = meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1),
inference(conjunct,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(canonicalize,[],[maddux3_a_kind_of_de_Morgan]) ).
fof(normalize_1_6,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(specialize,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(canonicalize,[],[maddux1_join_commutativity]) ).
fof(normalize_1_8,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(specialize,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(canonicalize,[],[maddux4_definiton_of_meet]) ).
fof(normalize_1_10,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(specialize,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
join(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X2_1) != skolemFOFtoCNF_X2_1,
inference(conjunct,[],[normalize_1_3]) ).
cnf(refute_1_0,plain,
join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(canonicalize,[],[normalize_1_1]) ).
cnf(refute_1_1,plain,
join(skolemFOFtoCNF_X0_1,join(meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1),X_256)) = join(join(skolemFOFtoCNF_X0_1,meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1)),X_256),
inference(subst,[],[refute_1_0:[bind(X0,$fot(skolemFOFtoCNF_X0_1)),bind(X1,$fot(meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1))),bind(X2,$fot(X_256))]]) ).
cnf(refute_1_2,plain,
join(skolemFOFtoCNF_X0_1,meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1)) = meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1),
inference(canonicalize,[],[normalize_1_4]) ).
cnf(refute_1_3,plain,
( join(skolemFOFtoCNF_X0_1,join(meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1),X_256)) != join(join(skolemFOFtoCNF_X0_1,meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1)),X_256)
| join(skolemFOFtoCNF_X0_1,meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1)) != meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1)
| join(skolemFOFtoCNF_X0_1,join(meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1),X_256)) = join(meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1),X_256) ),
introduced(tautology,[equality,[$cnf( $equal(join(skolemFOFtoCNF_X0_1,join(meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1),X_256)),join(join(skolemFOFtoCNF_X0_1,meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1)),X_256)) ),[1,0],$fot(meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1))]]) ).
cnf(refute_1_4,plain,
( join(skolemFOFtoCNF_X0_1,join(meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1),X_256)) != join(join(skolemFOFtoCNF_X0_1,meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1)),X_256)
| join(skolemFOFtoCNF_X0_1,join(meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1),X_256)) = join(meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1),X_256) ),
inference(resolve,[$cnf( $equal(join(skolemFOFtoCNF_X0_1,meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1)),meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1)) )],[refute_1_2,refute_1_3]) ).
cnf(refute_1_5,plain,
join(skolemFOFtoCNF_X0_1,join(meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1),X_256)) = join(meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1),X_256),
inference(resolve,[$cnf( $equal(join(skolemFOFtoCNF_X0_1,join(meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1),X_256)),join(join(skolemFOFtoCNF_X0_1,meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1)),X_256)) )],[refute_1_1,refute_1_4]) ).
cnf(refute_1_6,plain,
join(skolemFOFtoCNF_X0_1,join(meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1),complement(join(complement(skolemFOFtoCNF_X2_1),skolemFOFtoCNF_X1_1)))) = join(meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1),complement(join(complement(skolemFOFtoCNF_X2_1),skolemFOFtoCNF_X1_1))),
inference(subst,[],[refute_1_5:[bind(X_256,$fot(complement(join(complement(skolemFOFtoCNF_X2_1),skolemFOFtoCNF_X1_1))))]]) ).
cnf(refute_1_7,plain,
X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(canonicalize,[],[normalize_1_6]) ).
cnf(refute_1_8,plain,
join(X0,X1) = join(X1,X0),
inference(canonicalize,[],[normalize_1_8]) ).
cnf(refute_1_9,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_1_10,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_1_11,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_1_9,refute_1_10]) ).
cnf(refute_1_12,plain,
( join(X0,X1) != join(X1,X0)
| join(X1,X0) = join(X0,X1) ),
inference(subst,[],[refute_1_11:[bind(X,$fot(join(X0,X1))),bind(Y,$fot(join(X1,X0)))]]) ).
cnf(refute_1_13,plain,
join(X1,X0) = join(X0,X1),
inference(resolve,[$cnf( $equal(join(X0,X1),join(X1,X0)) )],[refute_1_8,refute_1_12]) ).
cnf(refute_1_14,plain,
join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),
inference(subst,[],[refute_1_13:[bind(X0,$fot(complement(join(complement(X0),X1)))),bind(X1,$fot(complement(join(complement(X0),complement(X1)))))]]) ).
cnf(refute_1_15,plain,
( X0 != join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1)))
| join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) != join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))
| X0 = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X0,join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))) ),[0],$fot(join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))))]]) ).
cnf(refute_1_16,plain,
( X0 != join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1)))
| X0 = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) ),
inference(resolve,[$cnf( $equal(join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))) )],[refute_1_14,refute_1_15]) ).
cnf(refute_1_17,plain,
X0 = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),
inference(resolve,[$cnf( $equal(X0,join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1)))) )],[refute_1_7,refute_1_16]) ).
cnf(refute_1_18,plain,
join(complement(join(complement(X0),X1)),meet(X0,X1)) = join(meet(X0,X1),complement(join(complement(X0),X1))),
inference(subst,[],[refute_1_13:[bind(X0,$fot(meet(X0,X1))),bind(X1,$fot(complement(join(complement(X0),X1))))]]) ).
cnf(refute_1_19,plain,
meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(canonicalize,[],[normalize_1_10]) ).
cnf(refute_1_20,plain,
( meet(X0,X1) != complement(join(complement(X0),complement(X1)))
| complement(join(complement(X0),complement(X1))) = meet(X0,X1) ),
inference(subst,[],[refute_1_11:[bind(X,$fot(meet(X0,X1))),bind(Y,$fot(complement(join(complement(X0),complement(X1)))))]]) ).
cnf(refute_1_21,plain,
complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(resolve,[$cnf( $equal(meet(X0,X1),complement(join(complement(X0),complement(X1)))) )],[refute_1_19,refute_1_20]) ).
cnf(refute_1_22,plain,
join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),
introduced(tautology,[refl,[$fot(join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))))]]) ).
cnf(refute_1_23,plain,
( complement(join(complement(X0),complement(X1))) != meet(X0,X1)
| join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) != join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))
| join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(complement(join(complement(X0),X1)),meet(X0,X1)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))) ),[1,1],$fot(meet(X0,X1))]]) ).
cnf(refute_1_24,plain,
( complement(join(complement(X0),complement(X1))) != meet(X0,X1)
| join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(complement(join(complement(X0),X1)),meet(X0,X1)) ),
inference(resolve,[$cnf( $equal(join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))) )],[refute_1_22,refute_1_23]) ).
cnf(refute_1_25,plain,
join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(complement(join(complement(X0),X1)),meet(X0,X1)),
inference(resolve,[$cnf( $equal(complement(join(complement(X0),complement(X1))),meet(X0,X1)) )],[refute_1_21,refute_1_24]) ).
cnf(refute_1_26,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_1_27,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_1_11,refute_1_26]) ).
cnf(refute_1_28,plain,
( join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) != join(complement(join(complement(X0),X1)),meet(X0,X1))
| join(complement(join(complement(X0),X1)),meet(X0,X1)) != join(meet(X0,X1),complement(join(complement(X0),X1)))
| join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(meet(X0,X1),complement(join(complement(X0),X1))) ),
inference(subst,[],[refute_1_27:[bind(X,$fot(join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))))),bind(Y,$fot(join(complement(join(complement(X0),X1)),meet(X0,X1)))),bind(Z,$fot(join(meet(X0,X1),complement(join(complement(X0),X1)))))]]) ).
cnf(refute_1_29,plain,
( join(complement(join(complement(X0),X1)),meet(X0,X1)) != join(meet(X0,X1),complement(join(complement(X0),X1)))
| join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(meet(X0,X1),complement(join(complement(X0),X1))) ),
inference(resolve,[$cnf( $equal(join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),join(complement(join(complement(X0),X1)),meet(X0,X1))) )],[refute_1_25,refute_1_28]) ).
cnf(refute_1_30,plain,
join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(meet(X0,X1),complement(join(complement(X0),X1))),
inference(resolve,[$cnf( $equal(join(complement(join(complement(X0),X1)),meet(X0,X1)),join(meet(X0,X1),complement(join(complement(X0),X1)))) )],[refute_1_18,refute_1_29]) ).
cnf(refute_1_31,plain,
( X0 != join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))
| join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) != join(meet(X0,X1),complement(join(complement(X0),X1)))
| X0 = join(meet(X0,X1),complement(join(complement(X0),X1))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X0,join(meet(X0,X1),complement(join(complement(X0),X1)))) ),[0],$fot(join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))))]]) ).
cnf(refute_1_32,plain,
( X0 != join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))
| X0 = join(meet(X0,X1),complement(join(complement(X0),X1))) ),
inference(resolve,[$cnf( $equal(join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),join(meet(X0,X1),complement(join(complement(X0),X1)))) )],[refute_1_30,refute_1_31]) ).
cnf(refute_1_33,plain,
X0 = join(meet(X0,X1),complement(join(complement(X0),X1))),
inference(resolve,[$cnf( $equal(X0,join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))) )],[refute_1_17,refute_1_32]) ).
cnf(refute_1_34,plain,
X_199 = join(meet(X_199,X_200),complement(join(complement(X_199),X_200))),
inference(subst,[],[refute_1_33:[bind(X0,$fot(X_199)),bind(X1,$fot(X_200))]]) ).
cnf(refute_1_35,plain,
meet(X_194,X_195) = complement(join(complement(X_194),complement(X_195))),
inference(subst,[],[refute_1_19:[bind(X0,$fot(X_194)),bind(X1,$fot(X_195))]]) ).
cnf(refute_1_36,plain,
join(complement(X_195),complement(X_194)) = join(complement(X_194),complement(X_195)),
inference(subst,[],[refute_1_8:[bind(X0,$fot(complement(X_195))),bind(X1,$fot(complement(X_194)))]]) ).
cnf(refute_1_37,plain,
( join(complement(X_195),complement(X_194)) != join(complement(X_194),complement(X_195))
| join(complement(X_194),complement(X_195)) = join(complement(X_195),complement(X_194)) ),
inference(subst,[],[refute_1_11:[bind(X,$fot(join(complement(X_195),complement(X_194)))),bind(Y,$fot(join(complement(X_194),complement(X_195))))]]) ).
cnf(refute_1_38,plain,
join(complement(X_194),complement(X_195)) = join(complement(X_195),complement(X_194)),
inference(resolve,[$cnf( $equal(join(complement(X_195),complement(X_194)),join(complement(X_194),complement(X_195))) )],[refute_1_36,refute_1_37]) ).
cnf(refute_1_39,plain,
( join(complement(X_194),complement(X_195)) != join(complement(X_195),complement(X_194))
| meet(X_194,X_195) != complement(join(complement(X_194),complement(X_195)))
| meet(X_194,X_195) = complement(join(complement(X_195),complement(X_194))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_194,X_195),complement(join(complement(X_194),complement(X_195)))) ),[1,0],$fot(join(complement(X_195),complement(X_194)))]]) ).
cnf(refute_1_40,plain,
( meet(X_194,X_195) != complement(join(complement(X_194),complement(X_195)))
| meet(X_194,X_195) = complement(join(complement(X_195),complement(X_194))) ),
inference(resolve,[$cnf( $equal(join(complement(X_194),complement(X_195)),join(complement(X_195),complement(X_194))) )],[refute_1_38,refute_1_39]) ).
cnf(refute_1_41,plain,
meet(X_194,X_195) = complement(join(complement(X_195),complement(X_194))),
inference(resolve,[$cnf( $equal(meet(X_194,X_195),complement(join(complement(X_194),complement(X_195)))) )],[refute_1_35,refute_1_40]) ).
cnf(refute_1_42,plain,
complement(join(complement(X_195),complement(X_194))) = meet(X_195,X_194),
inference(subst,[],[refute_1_21:[bind(X0,$fot(X_195)),bind(X1,$fot(X_194))]]) ).
cnf(refute_1_43,plain,
( complement(join(complement(X_195),complement(X_194))) != meet(X_195,X_194)
| meet(X_194,X_195) != complement(join(complement(X_195),complement(X_194)))
| meet(X_194,X_195) = meet(X_195,X_194) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_194,X_195),complement(join(complement(X_195),complement(X_194)))) ),[1],$fot(meet(X_195,X_194))]]) ).
cnf(refute_1_44,plain,
( meet(X_194,X_195) != complement(join(complement(X_195),complement(X_194)))
| meet(X_194,X_195) = meet(X_195,X_194) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_195),complement(X_194))),meet(X_195,X_194)) )],[refute_1_42,refute_1_43]) ).
cnf(refute_1_45,plain,
meet(X_194,X_195) = meet(X_195,X_194),
inference(resolve,[$cnf( $equal(meet(X_194,X_195),complement(join(complement(X_195),complement(X_194)))) )],[refute_1_41,refute_1_44]) ).
cnf(refute_1_46,plain,
meet(X_200,X_199) = meet(X_199,X_200),
inference(subst,[],[refute_1_45:[bind(X_194,$fot(X_200)),bind(X_195,$fot(X_199))]]) ).
cnf(refute_1_47,plain,
( meet(X_200,X_199) != meet(X_199,X_200)
| meet(X_199,X_200) = meet(X_200,X_199) ),
inference(subst,[],[refute_1_11:[bind(X,$fot(meet(X_200,X_199))),bind(Y,$fot(meet(X_199,X_200)))]]) ).
cnf(refute_1_48,plain,
meet(X_199,X_200) = meet(X_200,X_199),
inference(resolve,[$cnf( $equal(meet(X_200,X_199),meet(X_199,X_200)) )],[refute_1_46,refute_1_47]) ).
cnf(refute_1_49,plain,
( X_199 != join(meet(X_199,X_200),complement(join(complement(X_199),X_200)))
| meet(X_199,X_200) != meet(X_200,X_199)
| X_199 = join(meet(X_200,X_199),complement(join(complement(X_199),X_200))) ),
introduced(tautology,[equality,[$cnf( $equal(X_199,join(meet(X_199,X_200),complement(join(complement(X_199),X_200)))) ),[1,0],$fot(meet(X_200,X_199))]]) ).
cnf(refute_1_50,plain,
( X_199 != join(meet(X_199,X_200),complement(join(complement(X_199),X_200)))
| X_199 = join(meet(X_200,X_199),complement(join(complement(X_199),X_200))) ),
inference(resolve,[$cnf( $equal(meet(X_199,X_200),meet(X_200,X_199)) )],[refute_1_48,refute_1_49]) ).
cnf(refute_1_51,plain,
X_199 = join(meet(X_200,X_199),complement(join(complement(X_199),X_200))),
inference(resolve,[$cnf( $equal(X_199,join(meet(X_199,X_200),complement(join(complement(X_199),X_200)))) )],[refute_1_34,refute_1_50]) ).
cnf(refute_1_52,plain,
skolemFOFtoCNF_X2_1 = join(meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1),complement(join(complement(skolemFOFtoCNF_X2_1),skolemFOFtoCNF_X1_1))),
inference(subst,[],[refute_1_51:[bind(X_199,$fot(skolemFOFtoCNF_X2_1)),bind(X_200,$fot(skolemFOFtoCNF_X1_1))]]) ).
cnf(refute_1_53,plain,
( skolemFOFtoCNF_X2_1 != join(meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1),complement(join(complement(skolemFOFtoCNF_X2_1),skolemFOFtoCNF_X1_1)))
| join(meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1),complement(join(complement(skolemFOFtoCNF_X2_1),skolemFOFtoCNF_X1_1))) = skolemFOFtoCNF_X2_1 ),
inference(subst,[],[refute_1_11:[bind(X,$fot(skolemFOFtoCNF_X2_1)),bind(Y,$fot(join(meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1),complement(join(complement(skolemFOFtoCNF_X2_1),skolemFOFtoCNF_X1_1)))))]]) ).
cnf(refute_1_54,plain,
join(meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1),complement(join(complement(skolemFOFtoCNF_X2_1),skolemFOFtoCNF_X1_1))) = skolemFOFtoCNF_X2_1,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X2_1,join(meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1),complement(join(complement(skolemFOFtoCNF_X2_1),skolemFOFtoCNF_X1_1)))) )],[refute_1_52,refute_1_53]) ).
cnf(refute_1_55,plain,
( join(meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1),complement(join(complement(skolemFOFtoCNF_X2_1),skolemFOFtoCNF_X1_1))) != skolemFOFtoCNF_X2_1
| join(skolemFOFtoCNF_X0_1,join(meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1),complement(join(complement(skolemFOFtoCNF_X2_1),skolemFOFtoCNF_X1_1)))) != join(meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1),complement(join(complement(skolemFOFtoCNF_X2_1),skolemFOFtoCNF_X1_1)))
| join(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X2_1) = join(meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1),complement(join(complement(skolemFOFtoCNF_X2_1),skolemFOFtoCNF_X1_1))) ),
introduced(tautology,[equality,[$cnf( $equal(join(skolemFOFtoCNF_X0_1,join(meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1),complement(join(complement(skolemFOFtoCNF_X2_1),skolemFOFtoCNF_X1_1)))),join(meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1),complement(join(complement(skolemFOFtoCNF_X2_1),skolemFOFtoCNF_X1_1)))) ),[0,1],$fot(skolemFOFtoCNF_X2_1)]]) ).
cnf(refute_1_56,plain,
( join(skolemFOFtoCNF_X0_1,join(meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1),complement(join(complement(skolemFOFtoCNF_X2_1),skolemFOFtoCNF_X1_1)))) != join(meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1),complement(join(complement(skolemFOFtoCNF_X2_1),skolemFOFtoCNF_X1_1)))
| join(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X2_1) = join(meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1),complement(join(complement(skolemFOFtoCNF_X2_1),skolemFOFtoCNF_X1_1))) ),
inference(resolve,[$cnf( $equal(join(meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1),complement(join(complement(skolemFOFtoCNF_X2_1),skolemFOFtoCNF_X1_1))),skolemFOFtoCNF_X2_1) )],[refute_1_54,refute_1_55]) ).
cnf(refute_1_57,plain,
join(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X2_1) = join(meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1),complement(join(complement(skolemFOFtoCNF_X2_1),skolemFOFtoCNF_X1_1))),
inference(resolve,[$cnf( $equal(join(skolemFOFtoCNF_X0_1,join(meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1),complement(join(complement(skolemFOFtoCNF_X2_1),skolemFOFtoCNF_X1_1)))),join(meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1),complement(join(complement(skolemFOFtoCNF_X2_1),skolemFOFtoCNF_X1_1)))) )],[refute_1_6,refute_1_56]) ).
cnf(refute_1_58,plain,
( join(meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1),complement(join(complement(skolemFOFtoCNF_X2_1),skolemFOFtoCNF_X1_1))) != skolemFOFtoCNF_X2_1
| join(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X2_1) != join(meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1),complement(join(complement(skolemFOFtoCNF_X2_1),skolemFOFtoCNF_X1_1)))
| join(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X2_1) = skolemFOFtoCNF_X2_1 ),
introduced(tautology,[equality,[$cnf( $equal(join(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X2_1),join(meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1),complement(join(complement(skolemFOFtoCNF_X2_1),skolemFOFtoCNF_X1_1)))) ),[1],$fot(skolemFOFtoCNF_X2_1)]]) ).
cnf(refute_1_59,plain,
( join(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X2_1) != join(meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1),complement(join(complement(skolemFOFtoCNF_X2_1),skolemFOFtoCNF_X1_1)))
| join(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X2_1) = skolemFOFtoCNF_X2_1 ),
inference(resolve,[$cnf( $equal(join(meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1),complement(join(complement(skolemFOFtoCNF_X2_1),skolemFOFtoCNF_X1_1))),skolemFOFtoCNF_X2_1) )],[refute_1_54,refute_1_58]) ).
cnf(refute_1_60,plain,
join(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X2_1) = skolemFOFtoCNF_X2_1,
inference(resolve,[$cnf( $equal(join(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X2_1),join(meet(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X2_1),complement(join(complement(skolemFOFtoCNF_X2_1),skolemFOFtoCNF_X1_1)))) )],[refute_1_57,refute_1_59]) ).
cnf(refute_1_61,plain,
join(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X2_1) != skolemFOFtoCNF_X2_1,
inference(canonicalize,[],[normalize_1_11]) ).
cnf(refute_1_62,plain,
$false,
inference(resolve,[$cnf( $equal(join(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X2_1),skolemFOFtoCNF_X2_1) )],[refute_1_60,refute_1_61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : REL046+1 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.35 % Computer : n018.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Fri Jul 8 10:39:55 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2.65/2.90 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.65/2.90
% 2.65/2.90 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.75/2.91
%------------------------------------------------------------------------------