TSTP Solution File: NUN066+2 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUN066+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n020.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 16:34:54 EDT 2022
% Result : Theorem 10.57s 10.83s
% Output : CNFRefutation 10.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 24
% Syntax : Number of formulae : 175 ( 30 unt; 0 def)
% Number of atoms : 450 ( 204 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 426 ( 151 ~; 205 |; 70 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 1 con; 0-2 aty)
% Number of variables : 280 ( 19 sgn 96 !; 44 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_1,axiom,
? [Y24] :
! [X19] :
( ( ~ r1(X19)
& X19 != Y24 )
| ( r1(X19)
& X19 = Y24 ) ) ).
fof(axiom_2,axiom,
! [X11] :
? [Y21] :
! [X12] :
( ( ~ r2(X11,X12)
& X12 != Y21 )
| ( r2(X11,X12)
& X12 = Y21 ) ) ).
fof(axiom_1a,axiom,
! [X1,X8] :
? [Y4] :
( ? [Y5] :
( ? [Y15] :
( r2(X8,Y15)
& r3(X1,Y15,Y5) )
& Y5 = Y4 )
& ? [Y7] :
( r2(Y7,Y4)
& r3(X1,X8,Y7) ) ) ).
fof(axiom_3a,axiom,
! [X3,X10] :
( ! [Y12] :
( ! [Y13] :
( ~ r2(X3,Y13)
| Y13 != Y12 )
| ~ r2(X10,Y12) )
| X3 = X10 ) ).
fof(axiom_5a,axiom,
! [X5] :
? [Y8] :
( ? [Y17] :
( r1(Y17)
& r4(X5,Y17,Y8) )
& ? [Y18] :
( r1(Y18)
& Y8 = Y18 ) ) ).
fof(axiom_7a,axiom,
! [X7,Y10] :
( ! [Y20] :
( ~ r1(Y20)
| Y20 != Y10 )
| ~ r2(X7,Y10) ) ).
fof(nonzerononetwoexist,conjecture,
? [Y1] :
( ! [Y2] :
( ! [Y3] :
( ! [Y4] :
( ~ r1(Y4)
| ~ r2(Y4,Y3) )
| ~ r2(Y3,Y2) )
| Y1 != Y2 )
& ! [Y5] :
( ~ r1(Y5)
| Y1 != Y5 ) ) ).
fof(subgoal_0,plain,
? [Y1] :
( ! [Y2] :
( ! [Y3] :
( ! [Y4] :
( ~ r1(Y4)
| ~ r2(Y4,Y3) )
| ~ r2(Y3,Y2) )
| Y1 != Y2 )
& ! [Y5] :
( ~ r1(Y5)
| Y1 != Y5 ) ),
inference(strip,[],[nonzerononetwoexist]) ).
fof(negate_0_0,plain,
~ ? [Y1] :
( ! [Y2] :
( ! [Y3] :
( ! [Y4] :
( ~ r1(Y4)
| ~ r2(Y4,Y3) )
| ~ r2(Y3,Y2) )
| Y1 != Y2 )
& ! [Y5] :
( ~ r1(Y5)
| Y1 != Y5 ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X1,X8] :
? [Y4] :
( ? [Y5] :
( Y5 = Y4
& ? [Y15] :
( r2(X8,Y15)
& r3(X1,Y15,Y5) ) )
& ? [Y7] :
( r2(Y7,Y4)
& r3(X1,X8,Y7) ) ),
inference(canonicalize,[],[axiom_1a]) ).
fof(normalize_0_1,plain,
! [X1,X8] :
? [Y4] :
( ? [Y5] :
( Y5 = Y4
& ? [Y15] :
( r2(X8,Y15)
& r3(X1,Y15,Y5) ) )
& ? [Y7] :
( r2(Y7,Y4)
& r3(X1,X8,Y7) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X1,X8] :
( ? [Y5] :
( Y5 = skolemFOFtoCNF_Y4(X1,X8)
& ? [Y15] :
( r2(X8,Y15)
& r3(X1,Y15,Y5) ) )
& ? [Y7] :
( r2(Y7,skolemFOFtoCNF_Y4(X1,X8))
& r3(X1,X8,Y7) ) ),
inference(skolemize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X1,X8] :
? [Y7] :
( r2(Y7,skolemFOFtoCNF_Y4(X1,X8))
& r3(X1,X8,Y7) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X1,X8] :
( r2(skolemFOFtoCNF_Y7(X1,X8),skolemFOFtoCNF_Y4(X1,X8))
& r3(X1,X8,skolemFOFtoCNF_Y7(X1,X8)) ),
inference(skolemize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [X1,X8] : r2(skolemFOFtoCNF_Y7(X1,X8),skolemFOFtoCNF_Y4(X1,X8)),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X7,Y10] :
( ~ r2(X7,Y10)
| ! [Y20] :
( Y20 != Y10
| ~ r1(Y20) ) ),
inference(canonicalize,[],[axiom_7a]) ).
fof(normalize_0_7,plain,
! [X7,Y10] :
( ~ r2(X7,Y10)
| ! [Y20] :
( Y20 != Y10
| ~ r1(Y20) ) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X7,Y10,Y20] :
( Y20 != Y10
| ~ r1(Y20)
| ~ r2(X7,Y10) ),
inference(clausify,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [Y1] :
( ? [Y2] :
( Y1 = Y2
& ? [Y3] :
( r2(Y3,Y2)
& ? [Y4] :
( r1(Y4)
& r2(Y4,Y3) ) ) )
| ? [Y5] :
( Y1 = Y5
& r1(Y5) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_10,plain,
! [Y1] :
( ? [Y2] :
( Y1 = Y2
& ? [Y3] :
( r2(Y3,Y2)
& ? [Y4] :
( r1(Y4)
& r2(Y4,Y3) ) ) )
| ? [Y5] :
( Y1 = Y5
& r1(Y5) ) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [Y1] :
( ( Y1 = skolemFOFtoCNF_Y2_1(Y1)
| Y1 = skolemFOFtoCNF_Y5_1(Y1) )
& ( Y1 = skolemFOFtoCNF_Y2_1(Y1)
| r1(skolemFOFtoCNF_Y5_1(Y1)) )
& ( Y1 = skolemFOFtoCNF_Y5_1(Y1)
| r1(skolemFOFtoCNF_Y4_1(Y1)) )
& ( Y1 = skolemFOFtoCNF_Y5_1(Y1)
| r2(skolemFOFtoCNF_Y3_1(Y1),skolemFOFtoCNF_Y2_1(Y1)) )
& ( Y1 = skolemFOFtoCNF_Y5_1(Y1)
| r2(skolemFOFtoCNF_Y4_1(Y1),skolemFOFtoCNF_Y3_1(Y1)) )
& ( r1(skolemFOFtoCNF_Y4_1(Y1))
| r1(skolemFOFtoCNF_Y5_1(Y1)) )
& ( r1(skolemFOFtoCNF_Y5_1(Y1))
| r2(skolemFOFtoCNF_Y3_1(Y1),skolemFOFtoCNF_Y2_1(Y1)) )
& ( r1(skolemFOFtoCNF_Y5_1(Y1))
| r2(skolemFOFtoCNF_Y4_1(Y1),skolemFOFtoCNF_Y3_1(Y1)) ) ),
inference(clausify,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [Y1] :
( r1(skolemFOFtoCNF_Y5_1(Y1))
| r2(skolemFOFtoCNF_Y4_1(Y1),skolemFOFtoCNF_Y3_1(Y1)) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [X11] :
? [Y21] :
! [X12] :
( ( X12 != Y21
& ~ r2(X11,X12) )
| ( X12 = Y21
& r2(X11,X12) ) ),
inference(canonicalize,[],[axiom_2]) ).
fof(normalize_0_14,plain,
! [X11] :
? [Y21] :
! [X12] :
( ( X12 != Y21
& ~ r2(X11,X12) )
| ( X12 = Y21
& r2(X11,X12) ) ),
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [X11,X12] :
( ( X12 != skolemFOFtoCNF_Y21(X11)
& ~ r2(X11,X12) )
| ( X12 = skolemFOFtoCNF_Y21(X11)
& r2(X11,X12) ) ),
inference(skolemize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [X11,X12] :
( ( X12 != skolemFOFtoCNF_Y21(X11)
& ~ r2(X11,X12) )
| ( X12 = skolemFOFtoCNF_Y21(X11)
& r2(X11,X12) ) ),
inference(specialize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [X11,X12] :
( ( X12 != skolemFOFtoCNF_Y21(X11)
| r2(X11,X12) )
& ( ~ r2(X11,X12)
| X12 = skolemFOFtoCNF_Y21(X11) ) ),
inference(clausify,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [X11,X12] :
( ~ r2(X11,X12)
| X12 = skolemFOFtoCNF_Y21(X11) ),
inference(conjunct,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
? [Y24] :
! [X19] :
( ( X19 != Y24
& ~ r1(X19) )
| ( X19 = Y24
& r1(X19) ) ),
inference(canonicalize,[],[axiom_1]) ).
fof(normalize_0_20,plain,
! [X19] :
( ( X19 != skolemFOFtoCNF_Y24
& ~ r1(X19) )
| ( X19 = skolemFOFtoCNF_Y24
& r1(X19) ) ),
inference(skolemize,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [X19] :
( ( X19 != skolemFOFtoCNF_Y24
& ~ r1(X19) )
| ( X19 = skolemFOFtoCNF_Y24
& r1(X19) ) ),
inference(specialize,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [X19] :
( ( X19 != skolemFOFtoCNF_Y24
| r1(X19) )
& ( ~ r1(X19)
| X19 = skolemFOFtoCNF_Y24 ) ),
inference(clausify,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
! [X19] :
( ~ r1(X19)
| X19 = skolemFOFtoCNF_Y24 ),
inference(conjunct,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
! [Y1] :
( r1(skolemFOFtoCNF_Y4_1(Y1))
| r1(skolemFOFtoCNF_Y5_1(Y1)) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_25,plain,
! [Y1] :
( Y1 = skolemFOFtoCNF_Y5_1(Y1)
| r1(skolemFOFtoCNF_Y4_1(Y1)) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_26,plain,
! [Y1] :
( Y1 = skolemFOFtoCNF_Y5_1(Y1)
| r2(skolemFOFtoCNF_Y4_1(Y1),skolemFOFtoCNF_Y3_1(Y1)) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_27,plain,
! [Y1] :
( r1(skolemFOFtoCNF_Y5_1(Y1))
| r2(skolemFOFtoCNF_Y3_1(Y1),skolemFOFtoCNF_Y2_1(Y1)) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_28,plain,
! [Y1] :
( Y1 = skolemFOFtoCNF_Y2_1(Y1)
| r1(skolemFOFtoCNF_Y5_1(Y1)) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_29,plain,
! [Y1] :
( Y1 = skolemFOFtoCNF_Y2_1(Y1)
| Y1 = skolemFOFtoCNF_Y5_1(Y1) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_30,plain,
! [X11,X12] :
( X12 != skolemFOFtoCNF_Y21(X11)
| r2(X11,X12) ),
inference(conjunct,[],[normalize_0_17]) ).
fof(normalize_0_31,plain,
! [X10,X3] :
( X3 = X10
| ! [Y12] :
( ~ r2(X10,Y12)
| ! [Y13] :
( Y13 != Y12
| ~ r2(X3,Y13) ) ) ),
inference(canonicalize,[],[axiom_3a]) ).
fof(normalize_0_32,plain,
! [X10,X3] :
( X3 = X10
| ! [Y12] :
( ~ r2(X10,Y12)
| ! [Y13] :
( Y13 != Y12
| ~ r2(X3,Y13) ) ) ),
inference(specialize,[],[normalize_0_31]) ).
fof(normalize_0_33,plain,
! [X10,X3,Y12,Y13] :
( Y13 != Y12
| ~ r2(X10,Y12)
| ~ r2(X3,Y13)
| X3 = X10 ),
inference(clausify,[],[normalize_0_32]) ).
fof(normalize_0_34,plain,
! [Y1] :
( Y1 = skolemFOFtoCNF_Y5_1(Y1)
| r2(skolemFOFtoCNF_Y3_1(Y1),skolemFOFtoCNF_Y2_1(Y1)) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_35,plain,
! [X5] :
? [Y8] :
( ? [Y17] :
( r1(Y17)
& r4(X5,Y17,Y8) )
& ? [Y18] :
( Y8 = Y18
& r1(Y18) ) ),
inference(canonicalize,[],[axiom_5a]) ).
fof(normalize_0_36,plain,
! [X5] :
? [Y8] :
( ? [Y17] :
( r1(Y17)
& r4(X5,Y17,Y8) )
& ? [Y18] :
( Y8 = Y18
& r1(Y18) ) ),
inference(specialize,[],[normalize_0_35]) ).
fof(normalize_0_37,plain,
! [X5] :
( ? [Y17] :
( r1(Y17)
& r4(X5,Y17,skolemFOFtoCNF_Y8(X5)) )
& ? [Y18] :
( skolemFOFtoCNF_Y8(X5) = Y18
& r1(Y18) ) ),
inference(skolemize,[],[normalize_0_36]) ).
fof(normalize_0_38,plain,
! [X5] :
? [Y18] :
( skolemFOFtoCNF_Y8(X5) = Y18
& r1(Y18) ),
inference(conjunct,[],[normalize_0_37]) ).
fof(normalize_0_39,plain,
! [X5] :
( skolemFOFtoCNF_Y8(X5) = skolemFOFtoCNF_Y18(X5)
& r1(skolemFOFtoCNF_Y18(X5)) ),
inference(skolemize,[],[normalize_0_38]) ).
fof(normalize_0_40,plain,
! [X5] : skolemFOFtoCNF_Y8(X5) = skolemFOFtoCNF_Y18(X5),
inference(conjunct,[],[normalize_0_39]) ).
fof(normalize_0_41,plain,
! [X5] : r1(skolemFOFtoCNF_Y18(X5)),
inference(conjunct,[],[normalize_0_39]) ).
fof(normalize_0_42,plain,
! [X19] :
( X19 != skolemFOFtoCNF_Y24
| r1(X19) ),
inference(conjunct,[],[normalize_0_22]) ).
cnf(refute_0_0,plain,
r2(skolemFOFtoCNF_Y7(X1,X8),skolemFOFtoCNF_Y4(X1,X8)),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_1,plain,
( Y20 != Y10
| ~ r1(Y20)
| ~ r2(X7,Y10) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_2,plain,
( Y10 != Y10
| ~ r1(Y10)
| ~ r2(X7,Y10) ),
inference(subst,[],[refute_0_1:[bind(Y20,$fot(Y10))]]) ).
cnf(refute_0_3,plain,
Y10 = Y10,
introduced(tautology,[refl,[$fot(Y10)]]) ).
cnf(refute_0_4,plain,
( ~ r1(Y10)
| ~ r2(X7,Y10) ),
inference(resolve,[$cnf( $equal(Y10,Y10) )],[refute_0_3,refute_0_2]) ).
cnf(refute_0_5,plain,
( ~ r1(skolemFOFtoCNF_Y4(X1,X8))
| ~ r2(skolemFOFtoCNF_Y7(X1,X8),skolemFOFtoCNF_Y4(X1,X8)) ),
inference(subst,[],[refute_0_4:[bind(X7,$fot(skolemFOFtoCNF_Y7(X1,X8))),bind(Y10,$fot(skolemFOFtoCNF_Y4(X1,X8)))]]) ).
cnf(refute_0_6,plain,
~ r1(skolemFOFtoCNF_Y4(X1,X8)),
inference(resolve,[$cnf( r2(skolemFOFtoCNF_Y7(X1,X8),skolemFOFtoCNF_Y4(X1,X8)) )],[refute_0_0,refute_0_5]) ).
cnf(refute_0_7,plain,
( r1(skolemFOFtoCNF_Y5_1(Y1))
| r2(skolemFOFtoCNF_Y4_1(Y1),skolemFOFtoCNF_Y3_1(Y1)) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_8,plain,
( ~ r2(X11,X12)
| X12 = skolemFOFtoCNF_Y21(X11) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_9,plain,
( ~ r2(skolemFOFtoCNF_Y4_1(Y1),skolemFOFtoCNF_Y3_1(Y1))
| skolemFOFtoCNF_Y3_1(Y1) = skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y4_1(Y1)) ),
inference(subst,[],[refute_0_8:[bind(X11,$fot(skolemFOFtoCNF_Y4_1(Y1))),bind(X12,$fot(skolemFOFtoCNF_Y3_1(Y1)))]]) ).
cnf(refute_0_10,plain,
( skolemFOFtoCNF_Y3_1(Y1) = skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y4_1(Y1))
| r1(skolemFOFtoCNF_Y5_1(Y1)) ),
inference(resolve,[$cnf( r2(skolemFOFtoCNF_Y4_1(Y1),skolemFOFtoCNF_Y3_1(Y1)) )],[refute_0_7,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ r1(X19)
| X19 = skolemFOFtoCNF_Y24 ),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_12,plain,
( ~ r1(skolemFOFtoCNF_Y4_1(X_92))
| skolemFOFtoCNF_Y4_1(X_92) = skolemFOFtoCNF_Y24 ),
inference(subst,[],[refute_0_11:[bind(X19,$fot(skolemFOFtoCNF_Y4_1(X_92)))]]) ).
cnf(refute_0_13,plain,
( r1(skolemFOFtoCNF_Y4_1(Y1))
| r1(skolemFOFtoCNF_Y5_1(Y1)) ),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_14,plain,
( ~ r1(skolemFOFtoCNF_Y4_1(X_38))
| skolemFOFtoCNF_Y4_1(X_38) = skolemFOFtoCNF_Y24 ),
inference(subst,[],[refute_0_11:[bind(X19,$fot(skolemFOFtoCNF_Y4_1(X_38)))]]) ).
cnf(refute_0_15,plain,
( Y1 = skolemFOFtoCNF_Y5_1(Y1)
| r1(skolemFOFtoCNF_Y4_1(Y1)) ),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_16,plain,
( X_38 = skolemFOFtoCNF_Y5_1(X_38)
| r1(skolemFOFtoCNF_Y4_1(X_38)) ),
inference(subst,[],[refute_0_15:[bind(Y1,$fot(X_38))]]) ).
cnf(refute_0_17,plain,
( X_38 = skolemFOFtoCNF_Y5_1(X_38)
| skolemFOFtoCNF_Y4_1(X_38) = skolemFOFtoCNF_Y24 ),
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y4_1(X_38)) )],[refute_0_16,refute_0_14]) ).
cnf(refute_0_18,plain,
( Y1 = skolemFOFtoCNF_Y5_1(Y1)
| skolemFOFtoCNF_Y4_1(Y1) = skolemFOFtoCNF_Y24 ),
inference(subst,[],[refute_0_17:[bind(X_38,$fot(Y1))]]) ).
cnf(refute_0_19,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_20,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_21,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
( Y1 != skolemFOFtoCNF_Y5_1(Y1)
| skolemFOFtoCNF_Y5_1(Y1) = Y1 ),
inference(subst,[],[refute_0_21:[bind(X,$fot(Y1)),bind(Y,$fot(skolemFOFtoCNF_Y5_1(Y1)))]]) ).
cnf(refute_0_23,plain,
( skolemFOFtoCNF_Y4_1(Y1) = skolemFOFtoCNF_Y24
| skolemFOFtoCNF_Y5_1(Y1) = Y1 ),
inference(resolve,[$cnf( $equal(Y1,skolemFOFtoCNF_Y5_1(Y1)) )],[refute_0_18,refute_0_22]) ).
cnf(refute_0_24,plain,
( skolemFOFtoCNF_Y5_1(Y1) != Y1
| ~ r1(skolemFOFtoCNF_Y5_1(Y1))
| r1(Y1) ),
introduced(tautology,[equality,[$cnf( r1(skolemFOFtoCNF_Y5_1(Y1)) ),[0],$fot(Y1)]]) ).
cnf(refute_0_25,plain,
( ~ r1(skolemFOFtoCNF_Y5_1(Y1))
| skolemFOFtoCNF_Y4_1(Y1) = skolemFOFtoCNF_Y24
| r1(Y1) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y5_1(Y1),Y1) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
( skolemFOFtoCNF_Y4_1(Y1) = skolemFOFtoCNF_Y24
| r1(Y1)
| r1(skolemFOFtoCNF_Y4_1(Y1)) ),
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y5_1(Y1)) )],[refute_0_13,refute_0_25]) ).
cnf(refute_0_27,plain,
( skolemFOFtoCNF_Y4_1(X_92) = skolemFOFtoCNF_Y24
| r1(X_92)
| r1(skolemFOFtoCNF_Y4_1(X_92)) ),
inference(subst,[],[refute_0_26:[bind(Y1,$fot(X_92))]]) ).
cnf(refute_0_28,plain,
( skolemFOFtoCNF_Y4_1(X_92) = skolemFOFtoCNF_Y24
| r1(X_92) ),
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y4_1(X_92)) )],[refute_0_27,refute_0_12]) ).
cnf(refute_0_29,plain,
( skolemFOFtoCNF_Y4_1(Y1) = skolemFOFtoCNF_Y24
| r1(Y1) ),
inference(subst,[],[refute_0_28:[bind(X_92,$fot(Y1))]]) ).
cnf(refute_0_30,plain,
( skolemFOFtoCNF_Y3_1(Y1) != skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y4_1(Y1))
| skolemFOFtoCNF_Y4_1(Y1) != skolemFOFtoCNF_Y24
| skolemFOFtoCNF_Y3_1(Y1) = skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24) ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_Y3_1(Y1),skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y4_1(Y1))) ),[1,0],$fot(skolemFOFtoCNF_Y24)]]) ).
cnf(refute_0_31,plain,
( skolemFOFtoCNF_Y3_1(Y1) != skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y4_1(Y1))
| skolemFOFtoCNF_Y3_1(Y1) = skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)
| r1(Y1) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y4_1(Y1),skolemFOFtoCNF_Y24) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
( skolemFOFtoCNF_Y3_1(Y1) = skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)
| r1(Y1)
| r1(skolemFOFtoCNF_Y5_1(Y1)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y3_1(Y1),skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y4_1(Y1))) )],[refute_0_10,refute_0_31]) ).
cnf(refute_0_33,plain,
( ~ r2(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y3_1(X_458))
| skolemFOFtoCNF_Y3_1(X_458) = skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24) ),
inference(subst,[],[refute_0_8:[bind(X11,$fot(skolemFOFtoCNF_Y24)),bind(X12,$fot(skolemFOFtoCNF_Y3_1(X_458)))]]) ).
cnf(refute_0_34,plain,
( Y1 = skolemFOFtoCNF_Y5_1(Y1)
| r2(skolemFOFtoCNF_Y4_1(Y1),skolemFOFtoCNF_Y3_1(Y1)) ),
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_35,plain,
( skolemFOFtoCNF_Y4_1(Y1) != skolemFOFtoCNF_Y24
| ~ r2(skolemFOFtoCNF_Y4_1(Y1),skolemFOFtoCNF_Y3_1(Y1))
| r2(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y3_1(Y1)) ),
introduced(tautology,[equality,[$cnf( r2(skolemFOFtoCNF_Y4_1(Y1),skolemFOFtoCNF_Y3_1(Y1)) ),[0],$fot(skolemFOFtoCNF_Y24)]]) ).
cnf(refute_0_36,plain,
( ~ r2(skolemFOFtoCNF_Y4_1(Y1),skolemFOFtoCNF_Y3_1(Y1))
| r1(Y1)
| r2(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y3_1(Y1)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y4_1(Y1),skolemFOFtoCNF_Y24) )],[refute_0_29,refute_0_35]) ).
cnf(refute_0_37,plain,
( Y1 = skolemFOFtoCNF_Y5_1(Y1)
| r1(Y1)
| r2(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y3_1(Y1)) ),
inference(resolve,[$cnf( r2(skolemFOFtoCNF_Y4_1(Y1),skolemFOFtoCNF_Y3_1(Y1)) )],[refute_0_34,refute_0_36]) ).
cnf(refute_0_38,plain,
( X_458 = skolemFOFtoCNF_Y5_1(X_458)
| r1(X_458)
| r2(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y3_1(X_458)) ),
inference(subst,[],[refute_0_37:[bind(Y1,$fot(X_458))]]) ).
cnf(refute_0_39,plain,
( X_458 = skolemFOFtoCNF_Y5_1(X_458)
| skolemFOFtoCNF_Y3_1(X_458) = skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)
| r1(X_458) ),
inference(resolve,[$cnf( r2(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y3_1(X_458)) )],[refute_0_38,refute_0_33]) ).
cnf(refute_0_40,plain,
( Y1 = skolemFOFtoCNF_Y5_1(Y1)
| skolemFOFtoCNF_Y3_1(Y1) = skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)
| r1(Y1) ),
inference(subst,[],[refute_0_39:[bind(X_458,$fot(Y1))]]) ).
cnf(refute_0_41,plain,
( skolemFOFtoCNF_Y3_1(Y1) = skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)
| skolemFOFtoCNF_Y5_1(Y1) = Y1
| r1(Y1) ),
inference(resolve,[$cnf( $equal(Y1,skolemFOFtoCNF_Y5_1(Y1)) )],[refute_0_40,refute_0_22]) ).
cnf(refute_0_42,plain,
( ~ r1(skolemFOFtoCNF_Y5_1(Y1))
| skolemFOFtoCNF_Y3_1(Y1) = skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)
| r1(Y1) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y5_1(Y1),Y1) )],[refute_0_41,refute_0_24]) ).
cnf(refute_0_43,plain,
( skolemFOFtoCNF_Y3_1(Y1) = skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)
| r1(Y1) ),
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y5_1(Y1)) )],[refute_0_32,refute_0_42]) ).
cnf(refute_0_44,plain,
( skolemFOFtoCNF_Y3_1(skolemFOFtoCNF_Y21(X_876)) = skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)
| r1(skolemFOFtoCNF_Y21(X_876)) ),
inference(subst,[],[refute_0_43:[bind(Y1,$fot(skolemFOFtoCNF_Y21(X_876)))]]) ).
cnf(refute_0_45,plain,
( r1(skolemFOFtoCNF_Y5_1(Y1))
| r2(skolemFOFtoCNF_Y3_1(Y1),skolemFOFtoCNF_Y2_1(Y1)) ),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_46,plain,
( r1(skolemFOFtoCNF_Y5_1(X_64))
| r2(skolemFOFtoCNF_Y3_1(X_64),skolemFOFtoCNF_Y2_1(X_64)) ),
inference(subst,[],[refute_0_45:[bind(Y1,$fot(X_64))]]) ).
cnf(refute_0_47,plain,
( Y1 = skolemFOFtoCNF_Y2_1(Y1)
| r1(skolemFOFtoCNF_Y5_1(Y1)) ),
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_48,plain,
( Y1 = skolemFOFtoCNF_Y2_1(Y1)
| Y1 = skolemFOFtoCNF_Y5_1(Y1) ),
inference(canonicalize,[],[normalize_0_29]) ).
cnf(refute_0_49,plain,
( Y1 = skolemFOFtoCNF_Y2_1(Y1)
| skolemFOFtoCNF_Y5_1(Y1) = Y1 ),
inference(resolve,[$cnf( $equal(Y1,skolemFOFtoCNF_Y5_1(Y1)) )],[refute_0_48,refute_0_22]) ).
cnf(refute_0_50,plain,
( ~ r1(skolemFOFtoCNF_Y5_1(Y1))
| Y1 = skolemFOFtoCNF_Y2_1(Y1)
| r1(Y1) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y5_1(Y1),Y1) )],[refute_0_49,refute_0_24]) ).
cnf(refute_0_51,plain,
( Y1 = skolemFOFtoCNF_Y2_1(Y1)
| r1(Y1) ),
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y5_1(Y1)) )],[refute_0_47,refute_0_50]) ).
cnf(refute_0_52,plain,
( X_64 = skolemFOFtoCNF_Y2_1(X_64)
| r1(X_64) ),
inference(subst,[],[refute_0_51:[bind(Y1,$fot(X_64))]]) ).
cnf(refute_0_53,plain,
( X_64 != skolemFOFtoCNF_Y2_1(X_64)
| skolemFOFtoCNF_Y2_1(X_64) = X_64 ),
inference(subst,[],[refute_0_21:[bind(X,$fot(X_64)),bind(Y,$fot(skolemFOFtoCNF_Y2_1(X_64)))]]) ).
cnf(refute_0_54,plain,
( skolemFOFtoCNF_Y2_1(X_64) = X_64
| r1(X_64) ),
inference(resolve,[$cnf( $equal(X_64,skolemFOFtoCNF_Y2_1(X_64)) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
( skolemFOFtoCNF_Y2_1(X_64) != X_64
| ~ r2(skolemFOFtoCNF_Y3_1(X_64),skolemFOFtoCNF_Y2_1(X_64))
| r2(skolemFOFtoCNF_Y3_1(X_64),X_64) ),
introduced(tautology,[equality,[$cnf( r2(skolemFOFtoCNF_Y3_1(X_64),skolemFOFtoCNF_Y2_1(X_64)) ),[1],$fot(X_64)]]) ).
cnf(refute_0_56,plain,
( ~ r2(skolemFOFtoCNF_Y3_1(X_64),skolemFOFtoCNF_Y2_1(X_64))
| r1(X_64)
| r2(skolemFOFtoCNF_Y3_1(X_64),X_64) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y2_1(X_64),X_64) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
( r1(X_64)
| r1(skolemFOFtoCNF_Y5_1(X_64))
| r2(skolemFOFtoCNF_Y3_1(X_64),X_64) ),
inference(resolve,[$cnf( r2(skolemFOFtoCNF_Y3_1(X_64),skolemFOFtoCNF_Y2_1(X_64)) )],[refute_0_46,refute_0_56]) ).
cnf(refute_0_58,plain,
( r1(skolemFOFtoCNF_Y21(X_797))
| r1(skolemFOFtoCNF_Y5_1(skolemFOFtoCNF_Y21(X_797)))
| r2(skolemFOFtoCNF_Y3_1(skolemFOFtoCNF_Y21(X_797)),skolemFOFtoCNF_Y21(X_797)) ),
inference(subst,[],[refute_0_57:[bind(X_64,$fot(skolemFOFtoCNF_Y21(X_797)))]]) ).
cnf(refute_0_59,plain,
( X12 != skolemFOFtoCNF_Y21(X11)
| r2(X11,X12) ),
inference(canonicalize,[],[normalize_0_30]) ).
cnf(refute_0_60,plain,
( skolemFOFtoCNF_Y21(X11) != skolemFOFtoCNF_Y21(X11)
| r2(X11,skolemFOFtoCNF_Y21(X11)) ),
inference(subst,[],[refute_0_59:[bind(X12,$fot(skolemFOFtoCNF_Y21(X11)))]]) ).
cnf(refute_0_61,plain,
skolemFOFtoCNF_Y21(X11) = skolemFOFtoCNF_Y21(X11),
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_Y21(X11))]]) ).
cnf(refute_0_62,plain,
r2(X11,skolemFOFtoCNF_Y21(X11)),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y21(X11),skolemFOFtoCNF_Y21(X11)) )],[refute_0_61,refute_0_60]) ).
cnf(refute_0_63,plain,
r2(X_792,skolemFOFtoCNF_Y21(X_792)),
inference(subst,[],[refute_0_62:[bind(X11,$fot(X_792))]]) ).
cnf(refute_0_64,plain,
( Y13 != Y12
| ~ r2(X10,Y12)
| ~ r2(X3,Y13)
| X3 = X10 ),
inference(canonicalize,[],[normalize_0_33]) ).
cnf(refute_0_65,plain,
( Y12 != Y12
| ~ r2(X10,Y12)
| ~ r2(X3,Y12)
| X3 = X10 ),
inference(subst,[],[refute_0_64:[bind(Y13,$fot(Y12))]]) ).
cnf(refute_0_66,plain,
Y12 = Y12,
introduced(tautology,[refl,[$fot(Y12)]]) ).
cnf(refute_0_67,plain,
( ~ r2(X10,Y12)
| ~ r2(X3,Y12)
| X3 = X10 ),
inference(resolve,[$cnf( $equal(Y12,Y12) )],[refute_0_66,refute_0_65]) ).
cnf(refute_0_68,plain,
( ~ r2(X_792,skolemFOFtoCNF_Y21(X_792))
| ~ r2(X_793,skolemFOFtoCNF_Y21(X_792))
| X_793 = X_792 ),
inference(subst,[],[refute_0_67:[bind(X10,$fot(X_792)),bind(X3,$fot(X_793)),bind(Y12,$fot(skolemFOFtoCNF_Y21(X_792)))]]) ).
cnf(refute_0_69,plain,
( ~ r2(X_793,skolemFOFtoCNF_Y21(X_792))
| X_793 = X_792 ),
inference(resolve,[$cnf( r2(X_792,skolemFOFtoCNF_Y21(X_792)) )],[refute_0_63,refute_0_68]) ).
cnf(refute_0_70,plain,
( ~ r2(skolemFOFtoCNF_Y3_1(skolemFOFtoCNF_Y21(X_797)),skolemFOFtoCNF_Y21(X_797))
| skolemFOFtoCNF_Y3_1(skolemFOFtoCNF_Y21(X_797)) = X_797 ),
inference(subst,[],[refute_0_69:[bind(X_792,$fot(X_797)),bind(X_793,$fot(skolemFOFtoCNF_Y3_1(skolemFOFtoCNF_Y21(X_797))))]]) ).
cnf(refute_0_71,plain,
( skolemFOFtoCNF_Y3_1(skolemFOFtoCNF_Y21(X_797)) = X_797
| r1(skolemFOFtoCNF_Y21(X_797))
| r1(skolemFOFtoCNF_Y5_1(skolemFOFtoCNF_Y21(X_797))) ),
inference(resolve,[$cnf( r2(skolemFOFtoCNF_Y3_1(skolemFOFtoCNF_Y21(X_797)),skolemFOFtoCNF_Y21(X_797)) )],[refute_0_58,refute_0_70]) ).
cnf(refute_0_72,plain,
r2(X_52,skolemFOFtoCNF_Y21(X_52)),
inference(subst,[],[refute_0_62:[bind(X11,$fot(X_52))]]) ).
cnf(refute_0_73,plain,
( ~ r1(skolemFOFtoCNF_Y21(X_52))
| ~ r2(X_52,skolemFOFtoCNF_Y21(X_52)) ),
inference(subst,[],[refute_0_4:[bind(X7,$fot(X_52)),bind(Y10,$fot(skolemFOFtoCNF_Y21(X_52)))]]) ).
cnf(refute_0_74,plain,
~ r1(skolemFOFtoCNF_Y21(X_52)),
inference(resolve,[$cnf( r2(X_52,skolemFOFtoCNF_Y21(X_52)) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
~ r1(skolemFOFtoCNF_Y21(X_797)),
inference(subst,[],[refute_0_74:[bind(X_52,$fot(X_797))]]) ).
cnf(refute_0_76,plain,
( skolemFOFtoCNF_Y3_1(skolemFOFtoCNF_Y21(X_797)) = X_797
| r1(skolemFOFtoCNF_Y5_1(skolemFOFtoCNF_Y21(X_797))) ),
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y21(X_797)) )],[refute_0_71,refute_0_75]) ).
cnf(refute_0_77,plain,
( Y1 = skolemFOFtoCNF_Y5_1(Y1)
| r2(skolemFOFtoCNF_Y3_1(Y1),skolemFOFtoCNF_Y2_1(Y1)) ),
inference(canonicalize,[],[normalize_0_34]) ).
cnf(refute_0_78,plain,
( X_74 = skolemFOFtoCNF_Y5_1(X_74)
| r2(skolemFOFtoCNF_Y3_1(X_74),skolemFOFtoCNF_Y2_1(X_74)) ),
inference(subst,[],[refute_0_77:[bind(Y1,$fot(X_74))]]) ).
cnf(refute_0_79,plain,
( X_74 = skolemFOFtoCNF_Y2_1(X_74)
| r1(X_74) ),
inference(subst,[],[refute_0_51:[bind(Y1,$fot(X_74))]]) ).
cnf(refute_0_80,plain,
( X_74 != skolemFOFtoCNF_Y2_1(X_74)
| skolemFOFtoCNF_Y2_1(X_74) = X_74 ),
inference(subst,[],[refute_0_21:[bind(X,$fot(X_74)),bind(Y,$fot(skolemFOFtoCNF_Y2_1(X_74)))]]) ).
cnf(refute_0_81,plain,
( skolemFOFtoCNF_Y2_1(X_74) = X_74
| r1(X_74) ),
inference(resolve,[$cnf( $equal(X_74,skolemFOFtoCNF_Y2_1(X_74)) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
( skolemFOFtoCNF_Y2_1(X_74) != X_74
| ~ r2(skolemFOFtoCNF_Y3_1(X_74),skolemFOFtoCNF_Y2_1(X_74))
| r2(skolemFOFtoCNF_Y3_1(X_74),X_74) ),
introduced(tautology,[equality,[$cnf( r2(skolemFOFtoCNF_Y3_1(X_74),skolemFOFtoCNF_Y2_1(X_74)) ),[1],$fot(X_74)]]) ).
cnf(refute_0_83,plain,
( ~ r2(skolemFOFtoCNF_Y3_1(X_74),skolemFOFtoCNF_Y2_1(X_74))
| r1(X_74)
| r2(skolemFOFtoCNF_Y3_1(X_74),X_74) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y2_1(X_74),X_74) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
( X_74 = skolemFOFtoCNF_Y5_1(X_74)
| r1(X_74)
| r2(skolemFOFtoCNF_Y3_1(X_74),X_74) ),
inference(resolve,[$cnf( r2(skolemFOFtoCNF_Y3_1(X_74),skolemFOFtoCNF_Y2_1(X_74)) )],[refute_0_78,refute_0_83]) ).
cnf(refute_0_85,plain,
( skolemFOFtoCNF_Y21(X_797) = skolemFOFtoCNF_Y5_1(skolemFOFtoCNF_Y21(X_797))
| r1(skolemFOFtoCNF_Y21(X_797))
| r2(skolemFOFtoCNF_Y3_1(skolemFOFtoCNF_Y21(X_797)),skolemFOFtoCNF_Y21(X_797)) ),
inference(subst,[],[refute_0_84:[bind(X_74,$fot(skolemFOFtoCNF_Y21(X_797)))]]) ).
cnf(refute_0_86,plain,
( skolemFOFtoCNF_Y21(X_797) = skolemFOFtoCNF_Y5_1(skolemFOFtoCNF_Y21(X_797))
| skolemFOFtoCNF_Y3_1(skolemFOFtoCNF_Y21(X_797)) = X_797
| r1(skolemFOFtoCNF_Y21(X_797)) ),
inference(resolve,[$cnf( r2(skolemFOFtoCNF_Y3_1(skolemFOFtoCNF_Y21(X_797)),skolemFOFtoCNF_Y21(X_797)) )],[refute_0_85,refute_0_70]) ).
cnf(refute_0_87,plain,
( skolemFOFtoCNF_Y21(X_797) = skolemFOFtoCNF_Y5_1(skolemFOFtoCNF_Y21(X_797))
| skolemFOFtoCNF_Y3_1(skolemFOFtoCNF_Y21(X_797)) = X_797 ),
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y21(X_797)) )],[refute_0_86,refute_0_75]) ).
cnf(refute_0_88,plain,
( skolemFOFtoCNF_Y21(X_797) != skolemFOFtoCNF_Y5_1(skolemFOFtoCNF_Y21(X_797))
| skolemFOFtoCNF_Y5_1(skolemFOFtoCNF_Y21(X_797)) = skolemFOFtoCNF_Y21(X_797) ),
inference(subst,[],[refute_0_21:[bind(X,$fot(skolemFOFtoCNF_Y21(X_797))),bind(Y,$fot(skolemFOFtoCNF_Y5_1(skolemFOFtoCNF_Y21(X_797))))]]) ).
cnf(refute_0_89,plain,
( skolemFOFtoCNF_Y3_1(skolemFOFtoCNF_Y21(X_797)) = X_797
| skolemFOFtoCNF_Y5_1(skolemFOFtoCNF_Y21(X_797)) = skolemFOFtoCNF_Y21(X_797) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y21(X_797),skolemFOFtoCNF_Y5_1(skolemFOFtoCNF_Y21(X_797))) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
( skolemFOFtoCNF_Y5_1(skolemFOFtoCNF_Y21(X_797)) != skolemFOFtoCNF_Y21(X_797)
| ~ r1(skolemFOFtoCNF_Y5_1(skolemFOFtoCNF_Y21(X_797)))
| r1(skolemFOFtoCNF_Y21(X_797)) ),
introduced(tautology,[equality,[$cnf( r1(skolemFOFtoCNF_Y5_1(skolemFOFtoCNF_Y21(X_797))) ),[0],$fot(skolemFOFtoCNF_Y21(X_797))]]) ).
cnf(refute_0_91,plain,
( ~ r1(skolemFOFtoCNF_Y5_1(skolemFOFtoCNF_Y21(X_797)))
| skolemFOFtoCNF_Y3_1(skolemFOFtoCNF_Y21(X_797)) = X_797
| r1(skolemFOFtoCNF_Y21(X_797)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y5_1(skolemFOFtoCNF_Y21(X_797)),skolemFOFtoCNF_Y21(X_797)) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
( skolemFOFtoCNF_Y3_1(skolemFOFtoCNF_Y21(X_797)) = X_797
| r1(skolemFOFtoCNF_Y21(X_797)) ),
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y5_1(skolemFOFtoCNF_Y21(X_797))) )],[refute_0_76,refute_0_91]) ).
cnf(refute_0_93,plain,
skolemFOFtoCNF_Y3_1(skolemFOFtoCNF_Y21(X_797)) = X_797,
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y21(X_797)) )],[refute_0_92,refute_0_75]) ).
cnf(refute_0_94,plain,
skolemFOFtoCNF_Y3_1(skolemFOFtoCNF_Y21(X_876)) = X_876,
inference(subst,[],[refute_0_93:[bind(X_797,$fot(X_876))]]) ).
cnf(refute_0_95,plain,
( skolemFOFtoCNF_Y3_1(skolemFOFtoCNF_Y21(X_876)) != X_876
| skolemFOFtoCNF_Y3_1(skolemFOFtoCNF_Y21(X_876)) != skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)
| X_876 = skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24) ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_Y3_1(skolemFOFtoCNF_Y21(X_876)),skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)) ),[0],$fot(X_876)]]) ).
cnf(refute_0_96,plain,
( skolemFOFtoCNF_Y3_1(skolemFOFtoCNF_Y21(X_876)) != skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)
| X_876 = skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y3_1(skolemFOFtoCNF_Y21(X_876)),X_876) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
( X_876 = skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)
| r1(skolemFOFtoCNF_Y21(X_876)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y3_1(skolemFOFtoCNF_Y21(X_876)),skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)) )],[refute_0_44,refute_0_96]) ).
cnf(refute_0_98,plain,
~ r1(skolemFOFtoCNF_Y21(X_876)),
inference(subst,[],[refute_0_74:[bind(X_52,$fot(X_876))]]) ).
cnf(refute_0_99,plain,
X_876 = skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y21(X_876)) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
skolemFOFtoCNF_Y8(X5) = skolemFOFtoCNF_Y18(X5),
inference(canonicalize,[],[normalize_0_40]) ).
cnf(refute_0_101,plain,
r1(skolemFOFtoCNF_Y18(X5)),
inference(canonicalize,[],[normalize_0_41]) ).
cnf(refute_0_102,plain,
( ~ r1(skolemFOFtoCNF_Y18(X5))
| skolemFOFtoCNF_Y18(X5) = skolemFOFtoCNF_Y24 ),
inference(subst,[],[refute_0_11:[bind(X19,$fot(skolemFOFtoCNF_Y18(X5)))]]) ).
cnf(refute_0_103,plain,
skolemFOFtoCNF_Y18(X5) = skolemFOFtoCNF_Y24,
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y18(X5)) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
( skolemFOFtoCNF_Y18(X5) != skolemFOFtoCNF_Y24
| skolemFOFtoCNF_Y8(X5) != skolemFOFtoCNF_Y18(X5)
| skolemFOFtoCNF_Y8(X5) = skolemFOFtoCNF_Y24 ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_Y8(X5),skolemFOFtoCNF_Y18(X5)) ),[1],$fot(skolemFOFtoCNF_Y24)]]) ).
cnf(refute_0_105,plain,
( skolemFOFtoCNF_Y8(X5) != skolemFOFtoCNF_Y18(X5)
| skolemFOFtoCNF_Y8(X5) = skolemFOFtoCNF_Y24 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y18(X5),skolemFOFtoCNF_Y24) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
skolemFOFtoCNF_Y8(X5) = skolemFOFtoCNF_Y24,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y8(X5),skolemFOFtoCNF_Y18(X5)) )],[refute_0_100,refute_0_105]) ).
cnf(refute_0_107,plain,
skolemFOFtoCNF_Y8(X5) = skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),
inference(subst,[],[refute_0_99:[bind(X_876,$fot(skolemFOFtoCNF_Y8(X5)))]]) ).
cnf(refute_0_108,plain,
( skolemFOFtoCNF_Y8(X5) != skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)
| skolemFOFtoCNF_Y8(X5) != skolemFOFtoCNF_Y24
| skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24) = skolemFOFtoCNF_Y24 ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_Y8(X5),skolemFOFtoCNF_Y24) ),[0],$fot(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24))]]) ).
cnf(refute_0_109,plain,
( skolemFOFtoCNF_Y8(X5) != skolemFOFtoCNF_Y24
| skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24) = skolemFOFtoCNF_Y24 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y8(X5),skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24) = skolemFOFtoCNF_Y24,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y8(X5),skolemFOFtoCNF_Y24) )],[refute_0_106,refute_0_109]) ).
cnf(refute_0_111,plain,
( X_876 != skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)
| skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24) != skolemFOFtoCNF_Y24
| X_876 = skolemFOFtoCNF_Y24 ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_876,skolemFOFtoCNF_Y24) ),[0],$fot(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24))]]) ).
cnf(refute_0_112,plain,
( X_876 != skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)
| X_876 = skolemFOFtoCNF_Y24 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y24) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
X_876 = skolemFOFtoCNF_Y24,
inference(resolve,[$cnf( $equal(X_876,skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)) )],[refute_0_99,refute_0_112]) ).
cnf(refute_0_114,plain,
skolemFOFtoCNF_Y4(X1,X8) = skolemFOFtoCNF_Y24,
inference(subst,[],[refute_0_113:[bind(X_876,$fot(skolemFOFtoCNF_Y4(X1,X8)))]]) ).
cnf(refute_0_115,plain,
( skolemFOFtoCNF_Y4(X1,X8) != skolemFOFtoCNF_Y24
| ~ r1(skolemFOFtoCNF_Y24)
| r1(skolemFOFtoCNF_Y4(X1,X8)) ),
introduced(tautology,[equality,[$cnf( ~ r1(skolemFOFtoCNF_Y4(X1,X8)) ),[0],$fot(skolemFOFtoCNF_Y24)]]) ).
cnf(refute_0_116,plain,
( ~ r1(skolemFOFtoCNF_Y24)
| r1(skolemFOFtoCNF_Y4(X1,X8)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y4(X1,X8),skolemFOFtoCNF_Y24) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
~ r1(skolemFOFtoCNF_Y24),
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y4(X1,X8)) )],[refute_0_116,refute_0_6]) ).
cnf(refute_0_118,plain,
( X19 != skolemFOFtoCNF_Y24
| r1(X19) ),
inference(canonicalize,[],[normalize_0_42]) ).
cnf(refute_0_119,plain,
( skolemFOFtoCNF_Y24 != skolemFOFtoCNF_Y24
| r1(skolemFOFtoCNF_Y24) ),
inference(subst,[],[refute_0_118:[bind(X19,$fot(skolemFOFtoCNF_Y24))]]) ).
cnf(refute_0_120,plain,
skolemFOFtoCNF_Y24 = skolemFOFtoCNF_Y24,
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_Y24)]]) ).
cnf(refute_0_121,plain,
r1(skolemFOFtoCNF_Y24),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y24) )],[refute_0_120,refute_0_119]) ).
cnf(refute_0_122,plain,
$false,
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y24) )],[refute_0_121,refute_0_117]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUN066+2 : TPTP v8.1.0. Released v7.3.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 2 10:46:08 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 10.57/10.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.57/10.83
% 10.57/10.83 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 10.67/10.84
%------------------------------------------------------------------------------