TSTP Solution File: SWW101+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWW101+1 : TPTP v8.1.0. Released v5.2.0.
% 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 : Thu Jul 21 00:59:09 EDT 2022
% Result : Theorem 1.28s 1.51s
% Output : CNFRefutation 1.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 35
% Syntax : Number of formulae : 175 ( 66 unt; 1 def)
% Number of atoms : 415 ( 255 equ)
% Maximal formula atoms : 37 ( 2 avg)
% Number of connectives : 419 ( 179 ~; 181 |; 44 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 94 ( 3 sgn 55 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(def_bool,axiom,
! [X] :
( bool(X)
<=> ( X = false
| X = true ) ) ).
fof(false_true_err_in_d,axiom,
( d(true)
& d(false)
& d(err) ) ).
fof(def_forallprefers,axiom,
! [X,Y] :
( forallprefers(X,Y)
<=> ( ( ~ d(X)
& d(Y) )
| ( d(X)
& d(Y)
& ~ bool(X)
& bool(Y) )
| ( X = false
& Y = true ) ) ) ).
fof(def_phi,axiom,
! [X] :
( ( d(X)
& phi(X) = X )
| ( ~ d(X)
& phi(X) = err ) ) ).
fof(prop_true,axiom,
! [X] :
( prop(X) = true
<=> bool(X) ) ).
fof(prop_false,axiom,
! [X] :
( prop(X) = false
<=> ~ bool(X) ) ).
fof(lazy_impl_axiom2,axiom,
! [B] : lazy_impl(false,B) = true ).
fof(lazy_impl_axiom3,axiom,
! [B] : lazy_impl(true,B) = phi(B) ).
fof(def_false1,axiom,
false1 = false ).
fof(def_f7,axiom,
! [P] : f7(P) = lazy_impl(prop(P),P) ).
fof(def_false2,axiom,
? [P] :
( false2 = phi(f7(P))
& ~ ? [P1] : forallprefers(f7(P1),f7(P)) ) ).
fof(false1_false2,conjecture,
false1 = false2 ).
fof(definition_0,definition,
! [X,Y] :
( definitionFOFtoCNF_0(X,Y)
<=> ( X != false
| Y != true ) ) ).
fof(subgoal_0,plain,
false1 = false2,
inference(strip,[],[false1_false2]) ).
fof(negate_0_0,plain,
false1 != false2,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [P] :
( false2 = phi(f7(P))
& ! [P1] : ~ forallprefers(f7(P1),f7(P)) ),
inference(canonicalize,[],[def_false2]) ).
fof(normalize_0_1,plain,
( false2 = phi(f7(skolemFOFtoCNF_P))
& ! [P1] : ~ forallprefers(f7(P1),f7(skolemFOFtoCNF_P)) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
false2 = phi(f7(skolemFOFtoCNF_P)),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
( d(err)
& d(false)
& d(true) ),
inference(canonicalize,[],[false_true_err_in_d]) ).
fof(normalize_0_4,plain,
d(false),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [X] :
( ( ~ d(X)
& phi(X) = err )
| ( phi(X) = X
& d(X) ) ),
inference(canonicalize,[],[def_phi]) ).
fof(normalize_0_6,plain,
! [X] :
( ( ~ d(X)
& phi(X) = err )
| ( phi(X) = X
& d(X) ) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [X] :
( ( ~ d(X)
| phi(X) = X )
& ( phi(X) = X
| phi(X) = err )
& ( phi(X) = err
| d(X) ) ),
inference(clausify,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X] :
( ~ d(X)
| phi(X) = X ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [P] : f7(P) = lazy_impl(prop(P),P),
inference(canonicalize,[],[def_f7]) ).
fof(normalize_0_10,plain,
! [P] : f7(P) = lazy_impl(prop(P),P),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [X] :
( ~ bool(X)
<=> ( X != false
& X != true ) ),
inference(canonicalize,[],[def_bool]) ).
fof(normalize_0_12,plain,
! [X] :
( ~ bool(X)
<=> ( X != false
& X != true ) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [X] :
( ( X != false
| bool(X) )
& ( X != true
| bool(X) )
& ( ~ bool(X)
| X = false
| X = true ) ),
inference(clausify,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [X] :
( X != false
| bool(X) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [X] :
( prop(X) != true
<=> ~ bool(X) ),
inference(canonicalize,[],[prop_true]) ).
fof(normalize_0_16,plain,
! [X] :
( prop(X) != true
<=> ~ bool(X) ),
inference(specialize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [X] :
( ( prop(X) != true
| bool(X) )
& ( ~ bool(X)
| prop(X) = true ) ),
inference(clausify,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [X] :
( ~ bool(X)
| prop(X) = true ),
inference(conjunct,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [B] : lazy_impl(true,B) = phi(B),
inference(canonicalize,[],[lazy_impl_axiom3]) ).
fof(normalize_0_20,plain,
! [B] : lazy_impl(true,B) = phi(B),
inference(specialize,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [P1] : ~ forallprefers(f7(P1),f7(skolemFOFtoCNF_P)),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_22,plain,
! [P1] : ~ forallprefers(f7(P1),f7(skolemFOFtoCNF_P)),
inference(specialize,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
! [X,Y] :
( ~ forallprefers(X,Y)
<=> ( ( X != false
| Y != true )
& ( ~ d(Y)
| d(X) )
& ( ~ d(X)
| ~ d(Y)
| ~ bool(Y)
| bool(X) ) ) ),
inference(canonicalize,[],[def_forallprefers]) ).
fof(normalize_0_24,plain,
! [X,Y] :
( ~ forallprefers(X,Y)
<=> ( ( X != false
| Y != true )
& ( ~ d(Y)
| d(X) )
& ( ~ d(X)
| ~ d(Y)
| ~ bool(Y)
| bool(X) ) ) ),
inference(specialize,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
! [X,Y] :
( ~ definitionFOFtoCNF_0(X,Y)
<=> ( X = false
& Y = true ) ),
inference(canonicalize,[],[definition_0]) ).
fof(normalize_0_26,plain,
! [X,Y] :
( ~ forallprefers(X,Y)
<=> ( definitionFOFtoCNF_0(X,Y)
& ( ~ d(Y)
| d(X) )
& ( ~ d(X)
| ~ d(Y)
| ~ bool(Y)
| bool(X) ) ) ),
inference(simplify,[],[normalize_0_24,normalize_0_25]) ).
fof(normalize_0_27,plain,
! [X,Y] :
( ( definitionFOFtoCNF_0(X,Y)
| forallprefers(X,Y) )
& ( ~ d(Y)
| d(X)
| forallprefers(X,Y) )
& ( ~ definitionFOFtoCNF_0(X,Y)
| ~ forallprefers(X,Y)
| d(Y) )
& ( ~ d(X)
| ~ definitionFOFtoCNF_0(X,Y)
| ~ forallprefers(X,Y)
| ~ bool(X) )
& ( ~ d(X)
| ~ definitionFOFtoCNF_0(X,Y)
| ~ forallprefers(X,Y)
| d(Y) )
& ( ~ d(X)
| ~ definitionFOFtoCNF_0(X,Y)
| ~ forallprefers(X,Y)
| bool(Y) )
& ( ~ definitionFOFtoCNF_0(X,Y)
| ~ forallprefers(X,Y)
| ~ bool(X)
| d(Y) )
& ( ~ definitionFOFtoCNF_0(X,Y)
| ~ forallprefers(X,Y)
| d(X)
| d(Y) )
& ( ~ definitionFOFtoCNF_0(X,Y)
| ~ forallprefers(X,Y)
| d(Y)
| bool(Y) )
& ( ~ d(X)
| ~ d(Y)
| ~ bool(Y)
| forallprefers(X,Y)
| bool(X) ) ),
inference(clausify,[],[normalize_0_26]) ).
fof(normalize_0_28,plain,
! [X,Y] :
( definitionFOFtoCNF_0(X,Y)
| forallprefers(X,Y) ),
inference(conjunct,[],[normalize_0_27]) ).
fof(normalize_0_29,plain,
d(true),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_30,plain,
! [X] :
( X != true
| bool(X) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_31,plain,
! [X] :
( prop(X) != false
<=> bool(X) ),
inference(canonicalize,[],[prop_false]) ).
fof(normalize_0_32,plain,
! [X] :
( prop(X) != false
<=> bool(X) ),
inference(specialize,[],[normalize_0_31]) ).
fof(normalize_0_33,plain,
! [X] :
( ( prop(X) != false
| ~ bool(X) )
& ( prop(X) = false
| bool(X) ) ),
inference(clausify,[],[normalize_0_32]) ).
fof(normalize_0_34,plain,
! [X] :
( prop(X) = false
| bool(X) ),
inference(conjunct,[],[normalize_0_33]) ).
fof(normalize_0_35,plain,
! [X] :
( ~ bool(X)
| X = false
| X = true ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_36,plain,
! [B] : lazy_impl(false,B) = true,
inference(canonicalize,[],[lazy_impl_axiom2]) ).
fof(normalize_0_37,plain,
! [B] : lazy_impl(false,B) = true,
inference(specialize,[],[normalize_0_36]) ).
fof(normalize_0_38,plain,
! [X,Y] :
( ( X = false
| definitionFOFtoCNF_0(X,Y) )
& ( Y = true
| definitionFOFtoCNF_0(X,Y) )
& ( X != false
| Y != true
| ~ definitionFOFtoCNF_0(X,Y) ) ),
inference(clausify,[],[normalize_0_25]) ).
fof(normalize_0_39,plain,
! [X,Y] :
( X != false
| Y != true
| ~ definitionFOFtoCNF_0(X,Y) ),
inference(conjunct,[],[normalize_0_38]) ).
fof(normalize_0_40,plain,
false1 != false2,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_41,plain,
false1 = false,
inference(canonicalize,[],[def_false1]) ).
cnf(refute_0_0,plain,
false2 = phi(f7(skolemFOFtoCNF_P)),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
d(false),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
( ~ d(X)
| phi(X) = X ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_3,plain,
( ~ d(false)
| phi(false) = false ),
inference(subst,[],[refute_0_2:[bind(X,$fot(false))]]) ).
cnf(refute_0_4,plain,
phi(false) = false,
inference(resolve,[$cnf( d(false) )],[refute_0_1,refute_0_3]) ).
cnf(refute_0_5,plain,
f7(P) = lazy_impl(prop(P),P),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_6,plain,
f7(false) = lazy_impl(prop(false),false),
inference(subst,[],[refute_0_5:[bind(P,$fot(false))]]) ).
cnf(refute_0_7,plain,
( X != false
| bool(X) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_8,plain,
( false != false
| bool(false) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(false))]]) ).
cnf(refute_0_9,plain,
false = false,
introduced(tautology,[refl,[$fot(false)]]) ).
cnf(refute_0_10,plain,
bool(false),
inference(resolve,[$cnf( $equal(false,false) )],[refute_0_9,refute_0_8]) ).
cnf(refute_0_11,plain,
( ~ bool(X)
| prop(X) = true ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_12,plain,
( ~ bool(false)
| prop(false) = true ),
inference(subst,[],[refute_0_11:[bind(X,$fot(false))]]) ).
cnf(refute_0_13,plain,
prop(false) = true,
inference(resolve,[$cnf( bool(false) )],[refute_0_10,refute_0_12]) ).
cnf(refute_0_14,plain,
( f7(false) != lazy_impl(prop(false),false)
| prop(false) != true
| f7(false) = lazy_impl(true,false) ),
introduced(tautology,[equality,[$cnf( $equal(f7(false),lazy_impl(prop(false),false)) ),[1,0],$fot(true)]]) ).
cnf(refute_0_15,plain,
( f7(false) != lazy_impl(prop(false),false)
| f7(false) = lazy_impl(true,false) ),
inference(resolve,[$cnf( $equal(prop(false),true) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
f7(false) = lazy_impl(true,false),
inference(resolve,[$cnf( $equal(f7(false),lazy_impl(prop(false),false)) )],[refute_0_6,refute_0_15]) ).
cnf(refute_0_17,plain,
lazy_impl(true,B) = phi(B),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_18,plain,
lazy_impl(true,false) = phi(false),
inference(subst,[],[refute_0_17:[bind(B,$fot(false))]]) ).
cnf(refute_0_19,plain,
( f7(false) != lazy_impl(true,false)
| lazy_impl(true,false) != phi(false)
| f7(false) = phi(false) ),
introduced(tautology,[equality,[$cnf( ~ $equal(f7(false),phi(false)) ),[0],$fot(lazy_impl(true,false))]]) ).
cnf(refute_0_20,plain,
( f7(false) != lazy_impl(true,false)
| f7(false) = phi(false) ),
inference(resolve,[$cnf( $equal(lazy_impl(true,false),phi(false)) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
f7(false) = phi(false),
inference(resolve,[$cnf( $equal(f7(false),lazy_impl(true,false)) )],[refute_0_16,refute_0_20]) ).
cnf(refute_0_22,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_23,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_24,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( f7(false) != phi(false)
| phi(false) = f7(false) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(f7(false))),bind(Y0,$fot(phi(false)))]]) ).
cnf(refute_0_26,plain,
phi(false) = f7(false),
inference(resolve,[$cnf( $equal(f7(false),phi(false)) )],[refute_0_21,refute_0_25]) ).
cnf(refute_0_27,plain,
( phi(false) != f7(false)
| phi(false) != false
| f7(false) = false ),
introduced(tautology,[equality,[$cnf( $equal(phi(false),false) ),[0],$fot(f7(false))]]) ).
cnf(refute_0_28,plain,
( phi(false) != false
| f7(false) = false ),
inference(resolve,[$cnf( $equal(phi(false),f7(false)) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
f7(false) = false,
inference(resolve,[$cnf( $equal(phi(false),false) )],[refute_0_4,refute_0_28]) ).
cnf(refute_0_30,plain,
~ forallprefers(f7(P1),f7(skolemFOFtoCNF_P)),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_31,plain,
~ forallprefers(f7(false),f7(skolemFOFtoCNF_P)),
inference(subst,[],[refute_0_30:[bind(P1,$fot(false))]]) ).
cnf(refute_0_32,plain,
( f7(false) != false
| ~ forallprefers(false,f7(skolemFOFtoCNF_P))
| forallprefers(f7(false),f7(skolemFOFtoCNF_P)) ),
introduced(tautology,[equality,[$cnf( ~ forallprefers(f7(false),f7(skolemFOFtoCNF_P)) ),[0],$fot(false)]]) ).
cnf(refute_0_33,plain,
( ~ forallprefers(false,f7(skolemFOFtoCNF_P))
| forallprefers(f7(false),f7(skolemFOFtoCNF_P)) ),
inference(resolve,[$cnf( $equal(f7(false),false) )],[refute_0_29,refute_0_32]) ).
cnf(refute_0_34,plain,
~ forallprefers(false,f7(skolemFOFtoCNF_P)),
inference(resolve,[$cnf( forallprefers(f7(false),f7(skolemFOFtoCNF_P)) )],[refute_0_33,refute_0_31]) ).
cnf(refute_0_35,plain,
( definitionFOFtoCNF_0(X,Y)
| forallprefers(X,Y) ),
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_36,plain,
( definitionFOFtoCNF_0(false,f7(skolemFOFtoCNF_P))
| forallprefers(false,f7(skolemFOFtoCNF_P)) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(false)),bind(Y,$fot(f7(skolemFOFtoCNF_P)))]]) ).
cnf(refute_0_37,plain,
definitionFOFtoCNF_0(false,f7(skolemFOFtoCNF_P)),
inference(resolve,[$cnf( forallprefers(false,f7(skolemFOFtoCNF_P)) )],[refute_0_36,refute_0_34]) ).
cnf(refute_0_38,plain,
d(true),
inference(canonicalize,[],[normalize_0_29]) ).
cnf(refute_0_39,plain,
( ~ d(true)
| phi(true) = true ),
inference(subst,[],[refute_0_2:[bind(X,$fot(true))]]) ).
cnf(refute_0_40,plain,
phi(true) = true,
inference(resolve,[$cnf( d(true) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
f7(true) = lazy_impl(prop(true),true),
inference(subst,[],[refute_0_5:[bind(P,$fot(true))]]) ).
cnf(refute_0_42,plain,
( X != true
| bool(X) ),
inference(canonicalize,[],[normalize_0_30]) ).
cnf(refute_0_43,plain,
( true != true
| bool(true) ),
inference(subst,[],[refute_0_42:[bind(X,$fot(true))]]) ).
cnf(refute_0_44,plain,
true = true,
introduced(tautology,[refl,[$fot(true)]]) ).
cnf(refute_0_45,plain,
bool(true),
inference(resolve,[$cnf( $equal(true,true) )],[refute_0_44,refute_0_43]) ).
cnf(refute_0_46,plain,
( ~ bool(true)
| prop(true) = true ),
inference(subst,[],[refute_0_11:[bind(X,$fot(true))]]) ).
cnf(refute_0_47,plain,
prop(true) = true,
inference(resolve,[$cnf( bool(true) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
( f7(true) != lazy_impl(prop(true),true)
| prop(true) != true
| f7(true) = lazy_impl(true,true) ),
introduced(tautology,[equality,[$cnf( $equal(f7(true),lazy_impl(prop(true),true)) ),[1,0],$fot(true)]]) ).
cnf(refute_0_49,plain,
( f7(true) != lazy_impl(prop(true),true)
| f7(true) = lazy_impl(true,true) ),
inference(resolve,[$cnf( $equal(prop(true),true) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
f7(true) = lazy_impl(true,true),
inference(resolve,[$cnf( $equal(f7(true),lazy_impl(prop(true),true)) )],[refute_0_41,refute_0_49]) ).
cnf(refute_0_51,plain,
lazy_impl(true,true) = phi(true),
inference(subst,[],[refute_0_17:[bind(B,$fot(true))]]) ).
cnf(refute_0_52,plain,
( f7(true) != lazy_impl(true,true)
| lazy_impl(true,true) != phi(true)
| f7(true) = phi(true) ),
introduced(tautology,[equality,[$cnf( ~ $equal(f7(true),phi(true)) ),[0],$fot(lazy_impl(true,true))]]) ).
cnf(refute_0_53,plain,
( f7(true) != lazy_impl(true,true)
| f7(true) = phi(true) ),
inference(resolve,[$cnf( $equal(lazy_impl(true,true),phi(true)) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
f7(true) = phi(true),
inference(resolve,[$cnf( $equal(f7(true),lazy_impl(true,true)) )],[refute_0_50,refute_0_53]) ).
cnf(refute_0_55,plain,
( f7(true) != phi(true)
| phi(true) = f7(true) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(f7(true))),bind(Y0,$fot(phi(true)))]]) ).
cnf(refute_0_56,plain,
phi(true) = f7(true),
inference(resolve,[$cnf( $equal(f7(true),phi(true)) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
( phi(true) != f7(true)
| phi(true) != true
| f7(true) = true ),
introduced(tautology,[equality,[$cnf( $equal(phi(true),true) ),[0],$fot(f7(true))]]) ).
cnf(refute_0_58,plain,
( phi(true) != true
| f7(true) = true ),
inference(resolve,[$cnf( $equal(phi(true),f7(true)) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
f7(true) = true,
inference(resolve,[$cnf( $equal(phi(true),true) )],[refute_0_40,refute_0_58]) ).
cnf(refute_0_60,plain,
( prop(X) = false
| bool(X) ),
inference(canonicalize,[],[normalize_0_34]) ).
cnf(refute_0_61,plain,
( prop(X_49) = false
| bool(X_49) ),
inference(subst,[],[refute_0_60:[bind(X,$fot(X_49))]]) ).
cnf(refute_0_62,plain,
( ~ bool(X)
| X = false
| X = true ),
inference(canonicalize,[],[normalize_0_35]) ).
cnf(refute_0_63,plain,
( ~ bool(X_49)
| X_49 = false
| X_49 = true ),
inference(subst,[],[refute_0_62:[bind(X,$fot(X_49))]]) ).
cnf(refute_0_64,plain,
( X_49 = false
| X_49 = true
| prop(X_49) = false ),
inference(resolve,[$cnf( bool(X_49) )],[refute_0_61,refute_0_63]) ).
cnf(refute_0_65,plain,
( P = false
| P = true
| prop(P) = false ),
inference(subst,[],[refute_0_64:[bind(X_49,$fot(P))]]) ).
cnf(refute_0_66,plain,
( f7(P) != lazy_impl(prop(P),P)
| prop(P) != false
| f7(P) = lazy_impl(false,P) ),
introduced(tautology,[equality,[$cnf( $equal(f7(P),lazy_impl(prop(P),P)) ),[1,0],$fot(false)]]) ).
cnf(refute_0_67,plain,
( f7(P) != lazy_impl(prop(P),P)
| P = false
| P = true
| f7(P) = lazy_impl(false,P) ),
inference(resolve,[$cnf( $equal(prop(P),false) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
( P = false
| P = true
| f7(P) = lazy_impl(false,P) ),
inference(resolve,[$cnf( $equal(f7(P),lazy_impl(prop(P),P)) )],[refute_0_5,refute_0_67]) ).
cnf(refute_0_69,plain,
lazy_impl(false,B) = true,
inference(canonicalize,[],[normalize_0_37]) ).
cnf(refute_0_70,plain,
lazy_impl(false,P) = true,
inference(subst,[],[refute_0_69:[bind(B,$fot(P))]]) ).
cnf(refute_0_71,plain,
( f7(P) != lazy_impl(false,P)
| lazy_impl(false,P) != true
| f7(P) = true ),
introduced(tautology,[equality,[$cnf( ~ $equal(f7(P),true) ),[0],$fot(lazy_impl(false,P))]]) ).
cnf(refute_0_72,plain,
( f7(P) != lazy_impl(false,P)
| f7(P) = true ),
inference(resolve,[$cnf( $equal(lazy_impl(false,P),true) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
( P = false
| P = true
| f7(P) = true ),
inference(resolve,[$cnf( $equal(f7(P),lazy_impl(false,P)) )],[refute_0_68,refute_0_72]) ).
cnf(refute_0_74,plain,
( f7(skolemFOFtoCNF_P) = true
| skolemFOFtoCNF_P = false
| skolemFOFtoCNF_P = true ),
inference(subst,[],[refute_0_73:[bind(P,$fot(skolemFOFtoCNF_P))]]) ).
cnf(refute_0_75,plain,
( f7(skolemFOFtoCNF_P) != true
| ~ definitionFOFtoCNF_0(false,f7(skolemFOFtoCNF_P))
| definitionFOFtoCNF_0(false,true) ),
introduced(tautology,[equality,[$cnf( definitionFOFtoCNF_0(false,f7(skolemFOFtoCNF_P)) ),[1],$fot(true)]]) ).
cnf(refute_0_76,plain,
( ~ definitionFOFtoCNF_0(false,f7(skolemFOFtoCNF_P))
| skolemFOFtoCNF_P = false
| skolemFOFtoCNF_P = true
| definitionFOFtoCNF_0(false,true) ),
inference(resolve,[$cnf( $equal(f7(skolemFOFtoCNF_P),true) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
( skolemFOFtoCNF_P = false
| skolemFOFtoCNF_P = true
| definitionFOFtoCNF_0(false,true) ),
inference(resolve,[$cnf( definitionFOFtoCNF_0(false,f7(skolemFOFtoCNF_P)) )],[refute_0_37,refute_0_76]) ).
cnf(refute_0_78,plain,
( X != false
| Y != true
| ~ definitionFOFtoCNF_0(X,Y) ),
inference(canonicalize,[],[normalize_0_39]) ).
cnf(refute_0_79,plain,
( false != false
| true != true
| ~ definitionFOFtoCNF_0(false,true) ),
inference(subst,[],[refute_0_78:[bind(X,$fot(false)),bind(Y,$fot(true))]]) ).
cnf(refute_0_80,plain,
( true != true
| ~ definitionFOFtoCNF_0(false,true) ),
inference(resolve,[$cnf( $equal(false,false) )],[refute_0_9,refute_0_79]) ).
cnf(refute_0_81,plain,
~ definitionFOFtoCNF_0(false,true),
inference(resolve,[$cnf( $equal(true,true) )],[refute_0_44,refute_0_80]) ).
cnf(refute_0_82,plain,
( skolemFOFtoCNF_P = false
| skolemFOFtoCNF_P = true ),
inference(resolve,[$cnf( definitionFOFtoCNF_0(false,true) )],[refute_0_77,refute_0_81]) ).
cnf(refute_0_83,plain,
( skolemFOFtoCNF_P != true
| true = skolemFOFtoCNF_P ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(skolemFOFtoCNF_P)),bind(Y0,$fot(true))]]) ).
cnf(refute_0_84,plain,
( skolemFOFtoCNF_P = false
| true = skolemFOFtoCNF_P ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_P,true) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
( f7(true) != true
| true != skolemFOFtoCNF_P
| f7(skolemFOFtoCNF_P) = true ),
introduced(tautology,[equality,[$cnf( $equal(f7(true),true) ),[0,0],$fot(skolemFOFtoCNF_P)]]) ).
cnf(refute_0_86,plain,
( f7(true) != true
| f7(skolemFOFtoCNF_P) = true
| skolemFOFtoCNF_P = false ),
inference(resolve,[$cnf( $equal(true,skolemFOFtoCNF_P) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
( f7(skolemFOFtoCNF_P) = true
| skolemFOFtoCNF_P = false ),
inference(resolve,[$cnf( $equal(f7(true),true) )],[refute_0_59,refute_0_86]) ).
cnf(refute_0_88,plain,
( ~ definitionFOFtoCNF_0(false,f7(skolemFOFtoCNF_P))
| skolemFOFtoCNF_P = false
| definitionFOFtoCNF_0(false,true) ),
inference(resolve,[$cnf( $equal(f7(skolemFOFtoCNF_P),true) )],[refute_0_87,refute_0_75]) ).
cnf(refute_0_89,plain,
( skolemFOFtoCNF_P = false
| definitionFOFtoCNF_0(false,true) ),
inference(resolve,[$cnf( definitionFOFtoCNF_0(false,f7(skolemFOFtoCNF_P)) )],[refute_0_37,refute_0_88]) ).
cnf(refute_0_90,plain,
skolemFOFtoCNF_P = false,
inference(resolve,[$cnf( definitionFOFtoCNF_0(false,true) )],[refute_0_89,refute_0_81]) ).
cnf(refute_0_91,plain,
f7(skolemFOFtoCNF_P) = f7(skolemFOFtoCNF_P),
introduced(tautology,[refl,[$fot(f7(skolemFOFtoCNF_P))]]) ).
cnf(refute_0_92,plain,
( f7(skolemFOFtoCNF_P) != f7(skolemFOFtoCNF_P)
| skolemFOFtoCNF_P != false
| f7(skolemFOFtoCNF_P) = f7(false) ),
introduced(tautology,[equality,[$cnf( $equal(f7(skolemFOFtoCNF_P),f7(skolemFOFtoCNF_P)) ),[1,0],$fot(false)]]) ).
cnf(refute_0_93,plain,
( skolemFOFtoCNF_P != false
| f7(skolemFOFtoCNF_P) = f7(false) ),
inference(resolve,[$cnf( $equal(f7(skolemFOFtoCNF_P),f7(skolemFOFtoCNF_P)) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
f7(skolemFOFtoCNF_P) = f7(false),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_P,false) )],[refute_0_90,refute_0_93]) ).
cnf(refute_0_95,plain,
( Y0 != X0
| Y0 != Z
| X0 = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z) ),[0],$fot(X0)]]) ).
cnf(refute_0_96,plain,
( X0 != Y0
| Y0 != Z
| X0 = Z ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_24,refute_0_95]) ).
cnf(refute_0_97,plain,
( f7(false) != false
| f7(skolemFOFtoCNF_P) != f7(false)
| f7(skolemFOFtoCNF_P) = false ),
inference(subst,[],[refute_0_96:[bind(X0,$fot(f7(skolemFOFtoCNF_P))),bind(Y0,$fot(f7(false))),bind(Z,$fot(false))]]) ).
cnf(refute_0_98,plain,
( f7(false) != false
| f7(skolemFOFtoCNF_P) = false ),
inference(resolve,[$cnf( $equal(f7(skolemFOFtoCNF_P),f7(false)) )],[refute_0_94,refute_0_97]) ).
cnf(refute_0_99,plain,
f7(skolemFOFtoCNF_P) = false,
inference(resolve,[$cnf( $equal(f7(false),false) )],[refute_0_29,refute_0_98]) ).
cnf(refute_0_100,plain,
phi(f7(skolemFOFtoCNF_P)) = phi(f7(skolemFOFtoCNF_P)),
introduced(tautology,[refl,[$fot(phi(f7(skolemFOFtoCNF_P)))]]) ).
cnf(refute_0_101,plain,
( f7(skolemFOFtoCNF_P) != false
| phi(f7(skolemFOFtoCNF_P)) != phi(f7(skolemFOFtoCNF_P))
| phi(f7(skolemFOFtoCNF_P)) = phi(false) ),
introduced(tautology,[equality,[$cnf( $equal(phi(f7(skolemFOFtoCNF_P)),phi(f7(skolemFOFtoCNF_P))) ),[1,0],$fot(false)]]) ).
cnf(refute_0_102,plain,
( f7(skolemFOFtoCNF_P) != false
| phi(f7(skolemFOFtoCNF_P)) = phi(false) ),
inference(resolve,[$cnf( $equal(phi(f7(skolemFOFtoCNF_P)),phi(f7(skolemFOFtoCNF_P))) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
phi(f7(skolemFOFtoCNF_P)) = phi(false),
inference(resolve,[$cnf( $equal(f7(skolemFOFtoCNF_P),false) )],[refute_0_99,refute_0_102]) ).
cnf(refute_0_104,plain,
( phi(f7(skolemFOFtoCNF_P)) != phi(false)
| phi(false) != false
| phi(f7(skolemFOFtoCNF_P)) = false ),
inference(subst,[],[refute_0_96:[bind(X0,$fot(phi(f7(skolemFOFtoCNF_P)))),bind(Y0,$fot(phi(false))),bind(Z,$fot(false))]]) ).
cnf(refute_0_105,plain,
( phi(false) != false
| phi(f7(skolemFOFtoCNF_P)) = false ),
inference(resolve,[$cnf( $equal(phi(f7(skolemFOFtoCNF_P)),phi(false)) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
phi(f7(skolemFOFtoCNF_P)) = false,
inference(resolve,[$cnf( $equal(phi(false),false) )],[refute_0_4,refute_0_105]) ).
cnf(refute_0_107,plain,
( false2 != phi(f7(skolemFOFtoCNF_P))
| phi(f7(skolemFOFtoCNF_P)) != false
| false2 = false ),
introduced(tautology,[equality,[$cnf( ~ $equal(false2,false) ),[0],$fot(phi(f7(skolemFOFtoCNF_P)))]]) ).
cnf(refute_0_108,plain,
( false2 != phi(f7(skolemFOFtoCNF_P))
| false2 = false ),
inference(resolve,[$cnf( $equal(phi(f7(skolemFOFtoCNF_P)),false) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
false2 = false,
inference(resolve,[$cnf( $equal(false2,phi(f7(skolemFOFtoCNF_P))) )],[refute_0_0,refute_0_108]) ).
cnf(refute_0_110,plain,
false1 != false2,
inference(canonicalize,[],[normalize_0_40]) ).
cnf(refute_0_111,plain,
false1 = false,
inference(canonicalize,[],[normalize_0_41]) ).
cnf(refute_0_112,plain,
( false != false2
| false1 != false
| false1 = false2 ),
introduced(tautology,[equality,[$cnf( $equal(false1,false) ),[1],$fot(false2)]]) ).
cnf(refute_0_113,plain,
( false != false2
| false1 = false2 ),
inference(resolve,[$cnf( $equal(false1,false) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
false != false2,
inference(resolve,[$cnf( $equal(false1,false2) )],[refute_0_113,refute_0_110]) ).
cnf(refute_0_115,plain,
( false2 != false
| false = false2 ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(false2)),bind(Y0,$fot(false))]]) ).
cnf(refute_0_116,plain,
false2 != false,
inference(resolve,[$cnf( $equal(false,false2) )],[refute_0_115,refute_0_114]) ).
cnf(refute_0_117,plain,
$false,
inference(resolve,[$cnf( $equal(false2,false) )],[refute_0_109,refute_0_116]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWW101+1 : TPTP v8.1.0. Released v5.2.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n027.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sun Jun 5 03:18:07 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.28/1.51 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.28/1.51
% 1.28/1.51 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.36/1.52
%------------------------------------------------------------------------------