TSTP Solution File: NUN065+2 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUN065+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n026.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 1.37s 1.56s
% Output : CNFRefutation 1.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 32
% Syntax : Number of formulae : 212 ( 53 unt; 0 def)
% Number of atoms : 505 ( 227 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 474 ( 181 ~; 220 |; 73 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 1 con; 0-2 aty)
% Number of variables : 348 ( 31 sgn 115 !; 41 ?)
% 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_3,axiom,
! [X13,X14] :
? [Y22] :
! [X15] :
( ( ~ r3(X13,X14,X15)
& X15 != Y22 )
| ( r3(X13,X14,X15)
& X15 = Y22 ) ) ).
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_4a,axiom,
! [X4] :
? [Y9] :
( ? [Y16] :
( r1(Y16)
& r3(X4,Y16,Y9) )
& Y9 = X4 ) ).
fof(axiom_7a,axiom,
! [X7,Y10] :
( ! [Y20] :
( ~ r1(Y20)
| Y20 != Y10 )
| ~ r2(X7,Y10) ) ).
fof(nononesexist,conjecture,
? [Y1] :
( ! [Y2] :
( ! [Y3] :
( ~ r1(Y3)
| ~ r2(Y3,Y2) )
| Y1 != Y2 )
& ! [Y4] :
( ~ r1(Y4)
| Y1 != Y4 ) ) ).
fof(subgoal_0,plain,
? [Y1] :
( ! [Y2] :
( ! [Y3] :
( ~ r1(Y3)
| ~ r2(Y3,Y2) )
| Y1 != Y2 )
& ! [Y4] :
( ~ r1(Y4)
| Y1 != Y4 ) ),
inference(strip,[],[nononesexist]) ).
fof(negate_0_0,plain,
~ ? [Y1] :
( ! [Y2] :
( ! [Y3] :
( ~ r1(Y3)
| ~ r2(Y3,Y2) )
| Y1 != Y2 )
& ! [Y4] :
( ~ r1(Y4)
| Y1 != Y4 ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X11] :
? [Y21] :
! [X12] :
( ( X12 != Y21
& ~ r2(X11,X12) )
| ( X12 = Y21
& r2(X11,X12) ) ),
inference(canonicalize,[],[axiom_2]) ).
fof(normalize_0_1,plain,
! [X11] :
? [Y21] :
! [X12] :
( ( X12 != Y21
& ~ r2(X11,X12) )
| ( X12 = Y21
& r2(X11,X12) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X11,X12] :
( ( X12 != skolemFOFtoCNF_Y21(X11)
& ~ r2(X11,X12) )
| ( X12 = skolemFOFtoCNF_Y21(X11)
& r2(X11,X12) ) ),
inference(skolemize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X11,X12] :
( ( X12 != skolemFOFtoCNF_Y21(X11)
& ~ r2(X11,X12) )
| ( X12 = skolemFOFtoCNF_Y21(X11)
& r2(X11,X12) ) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X11,X12] :
( ( X12 != skolemFOFtoCNF_Y21(X11)
| r2(X11,X12) )
& ( ~ r2(X11,X12)
| X12 = skolemFOFtoCNF_Y21(X11) ) ),
inference(clausify,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [X11,X12] :
( X12 != skolemFOFtoCNF_Y21(X11)
| r2(X11,X12) ),
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,
! [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_10,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_9]) ).
fof(normalize_0_11,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_10]) ).
fof(normalize_0_12,plain,
! [X1,X8] :
? [Y7] :
( r2(Y7,skolemFOFtoCNF_Y4(X1,X8))
& r3(X1,X8,Y7) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [X1,X8] :
( r2(skolemFOFtoCNF_Y7(X1,X8),skolemFOFtoCNF_Y4(X1,X8))
& r3(X1,X8,skolemFOFtoCNF_Y7(X1,X8)) ),
inference(skolemize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [X1,X8] : r2(skolemFOFtoCNF_Y7(X1,X8),skolemFOFtoCNF_Y4(X1,X8)),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [X11,X12] :
( ~ r2(X11,X12)
| X12 = skolemFOFtoCNF_Y21(X11) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_16,plain,
! [X1,X8] : r3(X1,X8,skolemFOFtoCNF_Y7(X1,X8)),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_17,plain,
! [X13,X14] :
? [Y22] :
! [X15] :
( ( X15 != Y22
& ~ r3(X13,X14,X15) )
| ( X15 = Y22
& r3(X13,X14,X15) ) ),
inference(canonicalize,[],[axiom_3]) ).
fof(normalize_0_18,plain,
! [X13,X14] :
? [Y22] :
! [X15] :
( ( X15 != Y22
& ~ r3(X13,X14,X15) )
| ( X15 = Y22
& r3(X13,X14,X15) ) ),
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [X13,X14,X15] :
( ( X15 != skolemFOFtoCNF_Y22(X13,X14)
& ~ r3(X13,X14,X15) )
| ( X15 = skolemFOFtoCNF_Y22(X13,X14)
& r3(X13,X14,X15) ) ),
inference(skolemize,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [X13,X14,X15] :
( ( X15 != skolemFOFtoCNF_Y22(X13,X14)
& ~ r3(X13,X14,X15) )
| ( X15 = skolemFOFtoCNF_Y22(X13,X14)
& r3(X13,X14,X15) ) ),
inference(specialize,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [X13,X14,X15] :
( ( X15 != skolemFOFtoCNF_Y22(X13,X14)
| r3(X13,X14,X15) )
& ( ~ r3(X13,X14,X15)
| X15 = skolemFOFtoCNF_Y22(X13,X14) ) ),
inference(clausify,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [X13,X14,X15] :
( ~ r3(X13,X14,X15)
| X15 = skolemFOFtoCNF_Y22(X13,X14) ),
inference(conjunct,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
! [X4] :
? [Y9] :
( Y9 = X4
& ? [Y16] :
( r1(Y16)
& r3(X4,Y16,Y9) ) ),
inference(canonicalize,[],[axiom_4a]) ).
fof(normalize_0_24,plain,
! [X4] :
? [Y9] :
( Y9 = X4
& ? [Y16] :
( r1(Y16)
& r3(X4,Y16,Y9) ) ),
inference(specialize,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
! [X4] :
( skolemFOFtoCNF_Y9(X4) = X4
& ? [Y16] :
( r1(Y16)
& r3(X4,Y16,skolemFOFtoCNF_Y9(X4)) ) ),
inference(skolemize,[],[normalize_0_24]) ).
fof(normalize_0_26,plain,
! [X4] :
? [Y16] :
( r1(Y16)
& r3(X4,Y16,skolemFOFtoCNF_Y9(X4)) ),
inference(conjunct,[],[normalize_0_25]) ).
fof(normalize_0_27,plain,
! [X4] :
( r1(skolemFOFtoCNF_Y16(X4))
& r3(X4,skolemFOFtoCNF_Y16(X4),skolemFOFtoCNF_Y9(X4)) ),
inference(skolemize,[],[normalize_0_26]) ).
fof(normalize_0_28,plain,
! [X4] : r3(X4,skolemFOFtoCNF_Y16(X4),skolemFOFtoCNF_Y9(X4)),
inference(conjunct,[],[normalize_0_27]) ).
fof(normalize_0_29,plain,
! [X4] : skolemFOFtoCNF_Y9(X4) = X4,
inference(conjunct,[],[normalize_0_25]) ).
fof(normalize_0_30,plain,
! [X4] : r1(skolemFOFtoCNF_Y16(X4)),
inference(conjunct,[],[normalize_0_27]) ).
fof(normalize_0_31,plain,
? [Y24] :
! [X19] :
( ( X19 != Y24
& ~ r1(X19) )
| ( X19 = Y24
& r1(X19) ) ),
inference(canonicalize,[],[axiom_1]) ).
fof(normalize_0_32,plain,
! [X19] :
( ( X19 != skolemFOFtoCNF_Y24
& ~ r1(X19) )
| ( X19 = skolemFOFtoCNF_Y24
& r1(X19) ) ),
inference(skolemize,[],[normalize_0_31]) ).
fof(normalize_0_33,plain,
! [X19] :
( ( X19 != skolemFOFtoCNF_Y24
& ~ r1(X19) )
| ( X19 = skolemFOFtoCNF_Y24
& r1(X19) ) ),
inference(specialize,[],[normalize_0_32]) ).
fof(normalize_0_34,plain,
! [X19] :
( ( X19 != skolemFOFtoCNF_Y24
| r1(X19) )
& ( ~ r1(X19)
| X19 = skolemFOFtoCNF_Y24 ) ),
inference(clausify,[],[normalize_0_33]) ).
fof(normalize_0_35,plain,
! [X19] :
( ~ r1(X19)
| X19 = skolemFOFtoCNF_Y24 ),
inference(conjunct,[],[normalize_0_34]) ).
fof(normalize_0_36,plain,
! [Y1] :
( ? [Y2] :
( Y1 = Y2
& ? [Y3] :
( r1(Y3)
& r2(Y3,Y2) ) )
| ? [Y4] :
( Y1 = Y4
& r1(Y4) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_37,plain,
! [Y1] :
( ? [Y2] :
( Y1 = Y2
& ? [Y3] :
( r1(Y3)
& r2(Y3,Y2) ) )
| ? [Y4] :
( Y1 = Y4
& r1(Y4) ) ),
inference(specialize,[],[normalize_0_36]) ).
fof(normalize_0_38,plain,
! [Y1] :
( ( Y1 = skolemFOFtoCNF_Y2_1(Y1)
| Y1 = skolemFOFtoCNF_Y4_1(Y1) )
& ( Y1 = skolemFOFtoCNF_Y2_1(Y1)
| r1(skolemFOFtoCNF_Y4_1(Y1)) )
& ( Y1 = skolemFOFtoCNF_Y4_1(Y1)
| r1(skolemFOFtoCNF_Y3_1(Y1)) )
& ( Y1 = skolemFOFtoCNF_Y4_1(Y1)
| r2(skolemFOFtoCNF_Y3_1(Y1),skolemFOFtoCNF_Y2_1(Y1)) )
& ( r1(skolemFOFtoCNF_Y3_1(Y1))
| r1(skolemFOFtoCNF_Y4_1(Y1)) )
& ( r1(skolemFOFtoCNF_Y4_1(Y1))
| r2(skolemFOFtoCNF_Y3_1(Y1),skolemFOFtoCNF_Y2_1(Y1)) ) ),
inference(clausify,[],[normalize_0_37]) ).
fof(normalize_0_39,plain,
! [Y1] :
( r1(skolemFOFtoCNF_Y4_1(Y1))
| r2(skolemFOFtoCNF_Y3_1(Y1),skolemFOFtoCNF_Y2_1(Y1)) ),
inference(conjunct,[],[normalize_0_38]) ).
fof(normalize_0_40,plain,
! [Y1] :
( Y1 = skolemFOFtoCNF_Y2_1(Y1)
| r1(skolemFOFtoCNF_Y4_1(Y1)) ),
inference(conjunct,[],[normalize_0_38]) ).
fof(normalize_0_41,plain,
! [Y1] :
( Y1 = skolemFOFtoCNF_Y2_1(Y1)
| Y1 = skolemFOFtoCNF_Y4_1(Y1) ),
inference(conjunct,[],[normalize_0_38]) ).
fof(normalize_0_42,plain,
! [Y1] :
( r1(skolemFOFtoCNF_Y3_1(Y1))
| r1(skolemFOFtoCNF_Y4_1(Y1)) ),
inference(conjunct,[],[normalize_0_38]) ).
fof(normalize_0_43,plain,
! [Y1] :
( Y1 = skolemFOFtoCNF_Y4_1(Y1)
| r1(skolemFOFtoCNF_Y3_1(Y1)) ),
inference(conjunct,[],[normalize_0_38]) ).
fof(normalize_0_44,plain,
! [Y1] :
( Y1 = skolemFOFtoCNF_Y4_1(Y1)
| r2(skolemFOFtoCNF_Y3_1(Y1),skolemFOFtoCNF_Y2_1(Y1)) ),
inference(conjunct,[],[normalize_0_38]) ).
fof(normalize_0_45,plain,
! [X10,X3] :
( X3 = X10
| ! [Y12] :
( ~ r2(X10,Y12)
| ! [Y13] :
( Y13 != Y12
| ~ r2(X3,Y13) ) ) ),
inference(canonicalize,[],[axiom_3a]) ).
fof(normalize_0_46,plain,
! [X10,X3] :
( X3 = X10
| ! [Y12] :
( ~ r2(X10,Y12)
| ! [Y13] :
( Y13 != Y12
| ~ r2(X3,Y13) ) ) ),
inference(specialize,[],[normalize_0_45]) ).
fof(normalize_0_47,plain,
! [X10,X3,Y12,Y13] :
( Y13 != Y12
| ~ r2(X10,Y12)
| ~ r2(X3,Y13)
| X3 = X10 ),
inference(clausify,[],[normalize_0_46]) ).
fof(normalize_0_48,plain,
! [X19] :
( X19 != skolemFOFtoCNF_Y24
| r1(X19) ),
inference(conjunct,[],[normalize_0_34]) ).
cnf(refute_0_0,plain,
( X12 != skolemFOFtoCNF_Y21(X11)
| r2(X11,X12) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_1,plain,
( skolemFOFtoCNF_Y21(X11) != skolemFOFtoCNF_Y21(X11)
| r2(X11,skolemFOFtoCNF_Y21(X11)) ),
inference(subst,[],[refute_0_0:[bind(X12,$fot(skolemFOFtoCNF_Y21(X11)))]]) ).
cnf(refute_0_2,plain,
skolemFOFtoCNF_Y21(X11) = skolemFOFtoCNF_Y21(X11),
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_Y21(X11))]]) ).
cnf(refute_0_3,plain,
r2(X11,skolemFOFtoCNF_Y21(X11)),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y21(X11),skolemFOFtoCNF_Y21(X11)) )],[refute_0_2,refute_0_1]) ).
cnf(refute_0_4,plain,
r2(X_52,skolemFOFtoCNF_Y21(X_52)),
inference(subst,[],[refute_0_3:[bind(X11,$fot(X_52))]]) ).
cnf(refute_0_5,plain,
( Y20 != Y10
| ~ r1(Y20)
| ~ r2(X7,Y10) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_6,plain,
( Y10 != Y10
| ~ r1(Y10)
| ~ r2(X7,Y10) ),
inference(subst,[],[refute_0_5:[bind(Y20,$fot(Y10))]]) ).
cnf(refute_0_7,plain,
Y10 = Y10,
introduced(tautology,[refl,[$fot(Y10)]]) ).
cnf(refute_0_8,plain,
( ~ r1(Y10)
| ~ r2(X7,Y10) ),
inference(resolve,[$cnf( $equal(Y10,Y10) )],[refute_0_7,refute_0_6]) ).
cnf(refute_0_9,plain,
( ~ r1(skolemFOFtoCNF_Y21(X_52))
| ~ r2(X_52,skolemFOFtoCNF_Y21(X_52)) ),
inference(subst,[],[refute_0_8:[bind(X7,$fot(X_52)),bind(Y10,$fot(skolemFOFtoCNF_Y21(X_52)))]]) ).
cnf(refute_0_10,plain,
~ r1(skolemFOFtoCNF_Y21(X_52)),
inference(resolve,[$cnf( r2(X_52,skolemFOFtoCNF_Y21(X_52)) )],[refute_0_4,refute_0_9]) ).
cnf(refute_0_11,plain,
r2(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)),
inference(subst,[],[refute_0_3:[bind(X11,$fot(skolemFOFtoCNF_Y24))]]) ).
cnf(refute_0_12,plain,
r2(skolemFOFtoCNF_Y7(X1,X8),skolemFOFtoCNF_Y4(X1,X8)),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_13,plain,
( ~ r2(X11,X12)
| X12 = skolemFOFtoCNF_Y21(X11) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_14,plain,
( ~ r2(skolemFOFtoCNF_Y7(X1,X8),skolemFOFtoCNF_Y4(X1,X8))
| skolemFOFtoCNF_Y4(X1,X8) = skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y7(X1,X8)) ),
inference(subst,[],[refute_0_13:[bind(X11,$fot(skolemFOFtoCNF_Y7(X1,X8))),bind(X12,$fot(skolemFOFtoCNF_Y4(X1,X8)))]]) ).
cnf(refute_0_15,plain,
skolemFOFtoCNF_Y4(X1,X8) = skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y7(X1,X8)),
inference(resolve,[$cnf( r2(skolemFOFtoCNF_Y7(X1,X8),skolemFOFtoCNF_Y4(X1,X8)) )],[refute_0_12,refute_0_14]) ).
cnf(refute_0_16,plain,
r3(X1,X8,skolemFOFtoCNF_Y7(X1,X8)),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_17,plain,
r3(X_102,X_103,skolemFOFtoCNF_Y7(X_102,X_103)),
inference(subst,[],[refute_0_16:[bind(X1,$fot(X_102)),bind(X8,$fot(X_103))]]) ).
cnf(refute_0_18,plain,
( ~ r3(X13,X14,X15)
| X15 = skolemFOFtoCNF_Y22(X13,X14) ),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_19,plain,
( ~ r3(X_102,X_103,skolemFOFtoCNF_Y7(X_102,X_103))
| skolemFOFtoCNF_Y7(X_102,X_103) = skolemFOFtoCNF_Y22(X_102,X_103) ),
inference(subst,[],[refute_0_18:[bind(X13,$fot(X_102)),bind(X14,$fot(X_103)),bind(X15,$fot(skolemFOFtoCNF_Y7(X_102,X_103)))]]) ).
cnf(refute_0_20,plain,
skolemFOFtoCNF_Y7(X_102,X_103) = skolemFOFtoCNF_Y22(X_102,X_103),
inference(resolve,[$cnf( r3(X_102,X_103,skolemFOFtoCNF_Y7(X_102,X_103)) )],[refute_0_17,refute_0_19]) ).
cnf(refute_0_21,plain,
skolemFOFtoCNF_Y7(X1,X8) = skolemFOFtoCNF_Y22(X1,X8),
inference(subst,[],[refute_0_20:[bind(X_102,$fot(X1)),bind(X_103,$fot(X8))]]) ).
cnf(refute_0_22,plain,
skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y7(X1,X8)) = skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y7(X1,X8)),
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y7(X1,X8)))]]) ).
cnf(refute_0_23,plain,
( skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y7(X1,X8)) != skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y7(X1,X8))
| skolemFOFtoCNF_Y7(X1,X8) != skolemFOFtoCNF_Y22(X1,X8)
| skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y7(X1,X8)) = skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y22(X1,X8)) ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y7(X1,X8)),skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y7(X1,X8))) ),[1,0],$fot(skolemFOFtoCNF_Y22(X1,X8))]]) ).
cnf(refute_0_24,plain,
( skolemFOFtoCNF_Y7(X1,X8) != skolemFOFtoCNF_Y22(X1,X8)
| skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y7(X1,X8)) = skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y22(X1,X8)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y7(X1,X8)),skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y7(X1,X8))) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y7(X1,X8)) = skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y22(X1,X8)),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y7(X1,X8),skolemFOFtoCNF_Y22(X1,X8)) )],[refute_0_21,refute_0_24]) ).
cnf(refute_0_26,plain,
( skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y7(X1,X8)) != skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y22(X1,X8))
| skolemFOFtoCNF_Y4(X1,X8) != skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y7(X1,X8))
| skolemFOFtoCNF_Y4(X1,X8) = skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y22(X1,X8)) ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_Y4(X1,X8),skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y7(X1,X8))) ),[1],$fot(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y22(X1,X8)))]]) ).
cnf(refute_0_27,plain,
( skolemFOFtoCNF_Y4(X1,X8) != skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y7(X1,X8))
| skolemFOFtoCNF_Y4(X1,X8) = skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y22(X1,X8)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y7(X1,X8)),skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y22(X1,X8))) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
skolemFOFtoCNF_Y4(X1,X8) = skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y22(X1,X8)),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y4(X1,X8),skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y7(X1,X8))) )],[refute_0_15,refute_0_27]) ).
cnf(refute_0_29,plain,
skolemFOFtoCNF_Y4(X_108,skolemFOFtoCNF_Y24) = skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y22(X_108,skolemFOFtoCNF_Y24)),
inference(subst,[],[refute_0_28:[bind(X1,$fot(X_108)),bind(X8,$fot(skolemFOFtoCNF_Y24))]]) ).
cnf(refute_0_30,plain,
r3(X4,skolemFOFtoCNF_Y16(X4),skolemFOFtoCNF_Y9(X4)),
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_31,plain,
skolemFOFtoCNF_Y9(X4) = X4,
inference(canonicalize,[],[normalize_0_29]) ).
cnf(refute_0_32,plain,
( skolemFOFtoCNF_Y9(X4) != X4
| ~ r3(X4,skolemFOFtoCNF_Y16(X4),skolemFOFtoCNF_Y9(X4))
| r3(X4,skolemFOFtoCNF_Y16(X4),X4) ),
introduced(tautology,[equality,[$cnf( r3(X4,skolemFOFtoCNF_Y16(X4),skolemFOFtoCNF_Y9(X4)) ),[2],$fot(X4)]]) ).
cnf(refute_0_33,plain,
( ~ r3(X4,skolemFOFtoCNF_Y16(X4),skolemFOFtoCNF_Y9(X4))
| r3(X4,skolemFOFtoCNF_Y16(X4),X4) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y9(X4),X4) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
r3(X4,skolemFOFtoCNF_Y16(X4),X4),
inference(resolve,[$cnf( r3(X4,skolemFOFtoCNF_Y16(X4),skolemFOFtoCNF_Y9(X4)) )],[refute_0_30,refute_0_33]) ).
cnf(refute_0_35,plain,
r1(skolemFOFtoCNF_Y16(X4)),
inference(canonicalize,[],[normalize_0_30]) ).
cnf(refute_0_36,plain,
( ~ r1(X19)
| X19 = skolemFOFtoCNF_Y24 ),
inference(canonicalize,[],[normalize_0_35]) ).
cnf(refute_0_37,plain,
( ~ r1(skolemFOFtoCNF_Y16(X4))
| skolemFOFtoCNF_Y16(X4) = skolemFOFtoCNF_Y24 ),
inference(subst,[],[refute_0_36:[bind(X19,$fot(skolemFOFtoCNF_Y16(X4)))]]) ).
cnf(refute_0_38,plain,
skolemFOFtoCNF_Y16(X4) = skolemFOFtoCNF_Y24,
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y16(X4)) )],[refute_0_35,refute_0_37]) ).
cnf(refute_0_39,plain,
( skolemFOFtoCNF_Y16(X4) != skolemFOFtoCNF_Y24
| ~ r3(X4,skolemFOFtoCNF_Y16(X4),X4)
| r3(X4,skolemFOFtoCNF_Y24,X4) ),
introduced(tautology,[equality,[$cnf( r3(X4,skolemFOFtoCNF_Y16(X4),X4) ),[1],$fot(skolemFOFtoCNF_Y24)]]) ).
cnf(refute_0_40,plain,
( ~ r3(X4,skolemFOFtoCNF_Y16(X4),X4)
| r3(X4,skolemFOFtoCNF_Y24,X4) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y16(X4),skolemFOFtoCNF_Y24) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
r3(X4,skolemFOFtoCNF_Y24,X4),
inference(resolve,[$cnf( r3(X4,skolemFOFtoCNF_Y16(X4),X4) )],[refute_0_34,refute_0_40]) ).
cnf(refute_0_42,plain,
r3(X_104,skolemFOFtoCNF_Y24,X_104),
inference(subst,[],[refute_0_41:[bind(X4,$fot(X_104))]]) ).
cnf(refute_0_43,plain,
( ~ r3(X_104,skolemFOFtoCNF_Y24,X_104)
| X_104 = skolemFOFtoCNF_Y22(X_104,skolemFOFtoCNF_Y24) ),
inference(subst,[],[refute_0_18:[bind(X13,$fot(X_104)),bind(X14,$fot(skolemFOFtoCNF_Y24)),bind(X15,$fot(X_104))]]) ).
cnf(refute_0_44,plain,
X_104 = skolemFOFtoCNF_Y22(X_104,skolemFOFtoCNF_Y24),
inference(resolve,[$cnf( r3(X_104,skolemFOFtoCNF_Y24,X_104) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
X_108 = skolemFOFtoCNF_Y22(X_108,skolemFOFtoCNF_Y24),
inference(subst,[],[refute_0_44:[bind(X_104,$fot(X_108))]]) ).
cnf(refute_0_46,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_47,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_48,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
( X_108 != skolemFOFtoCNF_Y22(X_108,skolemFOFtoCNF_Y24)
| skolemFOFtoCNF_Y22(X_108,skolemFOFtoCNF_Y24) = X_108 ),
inference(subst,[],[refute_0_48:[bind(X,$fot(X_108)),bind(Y,$fot(skolemFOFtoCNF_Y22(X_108,skolemFOFtoCNF_Y24)))]]) ).
cnf(refute_0_50,plain,
skolemFOFtoCNF_Y22(X_108,skolemFOFtoCNF_Y24) = X_108,
inference(resolve,[$cnf( $equal(X_108,skolemFOFtoCNF_Y22(X_108,skolemFOFtoCNF_Y24)) )],[refute_0_45,refute_0_49]) ).
cnf(refute_0_51,plain,
( skolemFOFtoCNF_Y22(X_108,skolemFOFtoCNF_Y24) != X_108
| skolemFOFtoCNF_Y4(X_108,skolemFOFtoCNF_Y24) != skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y22(X_108,skolemFOFtoCNF_Y24))
| skolemFOFtoCNF_Y4(X_108,skolemFOFtoCNF_Y24) = skolemFOFtoCNF_Y21(X_108) ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_Y4(X_108,skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y22(X_108,skolemFOFtoCNF_Y24))) ),[1,0],$fot(X_108)]]) ).
cnf(refute_0_52,plain,
( skolemFOFtoCNF_Y4(X_108,skolemFOFtoCNF_Y24) != skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y22(X_108,skolemFOFtoCNF_Y24))
| skolemFOFtoCNF_Y4(X_108,skolemFOFtoCNF_Y24) = skolemFOFtoCNF_Y21(X_108) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y22(X_108,skolemFOFtoCNF_Y24),X_108) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
skolemFOFtoCNF_Y4(X_108,skolemFOFtoCNF_Y24) = skolemFOFtoCNF_Y21(X_108),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y4(X_108,skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y22(X_108,skolemFOFtoCNF_Y24))) )],[refute_0_29,refute_0_52]) ).
cnf(refute_0_54,plain,
( ~ r1(skolemFOFtoCNF_Y4(X1,X8))
| ~ r2(skolemFOFtoCNF_Y7(X1,X8),skolemFOFtoCNF_Y4(X1,X8)) ),
inference(subst,[],[refute_0_8:[bind(X7,$fot(skolemFOFtoCNF_Y7(X1,X8))),bind(Y10,$fot(skolemFOFtoCNF_Y4(X1,X8)))]]) ).
cnf(refute_0_55,plain,
~ r1(skolemFOFtoCNF_Y4(X1,X8)),
inference(resolve,[$cnf( r2(skolemFOFtoCNF_Y7(X1,X8),skolemFOFtoCNF_Y4(X1,X8)) )],[refute_0_12,refute_0_54]) ).
cnf(refute_0_56,plain,
( ~ r2(skolemFOFtoCNF_Y24,X_101)
| X_101 = skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24) ),
inference(subst,[],[refute_0_13:[bind(X11,$fot(skolemFOFtoCNF_Y24)),bind(X12,$fot(X_101))]]) ).
cnf(refute_0_57,plain,
( r1(skolemFOFtoCNF_Y4_1(Y1))
| r2(skolemFOFtoCNF_Y3_1(Y1),skolemFOFtoCNF_Y2_1(Y1)) ),
inference(canonicalize,[],[normalize_0_39]) ).
cnf(refute_0_58,plain,
( r1(skolemFOFtoCNF_Y4_1(X_61))
| r2(skolemFOFtoCNF_Y3_1(X_61),skolemFOFtoCNF_Y2_1(X_61)) ),
inference(subst,[],[refute_0_57:[bind(Y1,$fot(X_61))]]) ).
cnf(refute_0_59,plain,
( Y1 = skolemFOFtoCNF_Y2_1(Y1)
| r1(skolemFOFtoCNF_Y4_1(Y1)) ),
inference(canonicalize,[],[normalize_0_40]) ).
cnf(refute_0_60,plain,
( Y1 = skolemFOFtoCNF_Y2_1(Y1)
| Y1 = skolemFOFtoCNF_Y4_1(Y1) ),
inference(canonicalize,[],[normalize_0_41]) ).
cnf(refute_0_61,plain,
( Y1 != skolemFOFtoCNF_Y4_1(Y1)
| skolemFOFtoCNF_Y4_1(Y1) = Y1 ),
inference(subst,[],[refute_0_48:[bind(X,$fot(Y1)),bind(Y,$fot(skolemFOFtoCNF_Y4_1(Y1)))]]) ).
cnf(refute_0_62,plain,
( Y1 = skolemFOFtoCNF_Y2_1(Y1)
| skolemFOFtoCNF_Y4_1(Y1) = Y1 ),
inference(resolve,[$cnf( $equal(Y1,skolemFOFtoCNF_Y4_1(Y1)) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
( skolemFOFtoCNF_Y4_1(Y1) != Y1
| ~ r1(skolemFOFtoCNF_Y4_1(Y1))
| r1(Y1) ),
introduced(tautology,[equality,[$cnf( r1(skolemFOFtoCNF_Y4_1(Y1)) ),[0],$fot(Y1)]]) ).
cnf(refute_0_64,plain,
( ~ r1(skolemFOFtoCNF_Y4_1(Y1))
| Y1 = skolemFOFtoCNF_Y2_1(Y1)
| r1(Y1) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y4_1(Y1),Y1) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
( Y1 = skolemFOFtoCNF_Y2_1(Y1)
| r1(Y1) ),
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y4_1(Y1)) )],[refute_0_59,refute_0_64]) ).
cnf(refute_0_66,plain,
( X_61 = skolemFOFtoCNF_Y2_1(X_61)
| r1(X_61) ),
inference(subst,[],[refute_0_65:[bind(Y1,$fot(X_61))]]) ).
cnf(refute_0_67,plain,
( X_61 != skolemFOFtoCNF_Y2_1(X_61)
| skolemFOFtoCNF_Y2_1(X_61) = X_61 ),
inference(subst,[],[refute_0_48:[bind(X,$fot(X_61)),bind(Y,$fot(skolemFOFtoCNF_Y2_1(X_61)))]]) ).
cnf(refute_0_68,plain,
( skolemFOFtoCNF_Y2_1(X_61) = X_61
| r1(X_61) ),
inference(resolve,[$cnf( $equal(X_61,skolemFOFtoCNF_Y2_1(X_61)) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
( skolemFOFtoCNF_Y2_1(X_61) != X_61
| ~ r2(skolemFOFtoCNF_Y3_1(X_61),skolemFOFtoCNF_Y2_1(X_61))
| r2(skolemFOFtoCNF_Y3_1(X_61),X_61) ),
introduced(tautology,[equality,[$cnf( r2(skolemFOFtoCNF_Y3_1(X_61),skolemFOFtoCNF_Y2_1(X_61)) ),[1],$fot(X_61)]]) ).
cnf(refute_0_70,plain,
( ~ r2(skolemFOFtoCNF_Y3_1(X_61),skolemFOFtoCNF_Y2_1(X_61))
| r1(X_61)
| r2(skolemFOFtoCNF_Y3_1(X_61),X_61) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y2_1(X_61),X_61) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
( r1(X_61)
| r1(skolemFOFtoCNF_Y4_1(X_61))
| r2(skolemFOFtoCNF_Y3_1(X_61),X_61) ),
inference(resolve,[$cnf( r2(skolemFOFtoCNF_Y3_1(X_61),skolemFOFtoCNF_Y2_1(X_61)) )],[refute_0_58,refute_0_70]) ).
cnf(refute_0_72,plain,
( r1(X_100)
| r1(skolemFOFtoCNF_Y4_1(X_100))
| r2(skolemFOFtoCNF_Y3_1(X_100),X_100) ),
inference(subst,[],[refute_0_71:[bind(X_61,$fot(X_100))]]) ).
cnf(refute_0_73,plain,
( ~ r1(skolemFOFtoCNF_Y3_1(X_96))
| skolemFOFtoCNF_Y3_1(X_96) = skolemFOFtoCNF_Y24 ),
inference(subst,[],[refute_0_36:[bind(X19,$fot(skolemFOFtoCNF_Y3_1(X_96)))]]) ).
cnf(refute_0_74,plain,
( r1(skolemFOFtoCNF_Y3_1(Y1))
| r1(skolemFOFtoCNF_Y4_1(Y1)) ),
inference(canonicalize,[],[normalize_0_42]) ).
cnf(refute_0_75,plain,
( ~ r1(skolemFOFtoCNF_Y3_1(X_46))
| skolemFOFtoCNF_Y3_1(X_46) = skolemFOFtoCNF_Y24 ),
inference(subst,[],[refute_0_36:[bind(X19,$fot(skolemFOFtoCNF_Y3_1(X_46)))]]) ).
cnf(refute_0_76,plain,
( Y1 = skolemFOFtoCNF_Y4_1(Y1)
| r1(skolemFOFtoCNF_Y3_1(Y1)) ),
inference(canonicalize,[],[normalize_0_43]) ).
cnf(refute_0_77,plain,
( X_46 = skolemFOFtoCNF_Y4_1(X_46)
| r1(skolemFOFtoCNF_Y3_1(X_46)) ),
inference(subst,[],[refute_0_76:[bind(Y1,$fot(X_46))]]) ).
cnf(refute_0_78,plain,
( X_46 = skolemFOFtoCNF_Y4_1(X_46)
| skolemFOFtoCNF_Y3_1(X_46) = skolemFOFtoCNF_Y24 ),
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y3_1(X_46)) )],[refute_0_77,refute_0_75]) ).
cnf(refute_0_79,plain,
( Y1 = skolemFOFtoCNF_Y4_1(Y1)
| skolemFOFtoCNF_Y3_1(Y1) = skolemFOFtoCNF_Y24 ),
inference(subst,[],[refute_0_78:[bind(X_46,$fot(Y1))]]) ).
cnf(refute_0_80,plain,
( skolemFOFtoCNF_Y3_1(Y1) = skolemFOFtoCNF_Y24
| skolemFOFtoCNF_Y4_1(Y1) = Y1 ),
inference(resolve,[$cnf( $equal(Y1,skolemFOFtoCNF_Y4_1(Y1)) )],[refute_0_79,refute_0_61]) ).
cnf(refute_0_81,plain,
( ~ r1(skolemFOFtoCNF_Y4_1(Y1))
| skolemFOFtoCNF_Y3_1(Y1) = skolemFOFtoCNF_Y24
| r1(Y1) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y4_1(Y1),Y1) )],[refute_0_80,refute_0_63]) ).
cnf(refute_0_82,plain,
( skolemFOFtoCNF_Y3_1(Y1) = skolemFOFtoCNF_Y24
| r1(Y1)
| r1(skolemFOFtoCNF_Y3_1(Y1)) ),
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y4_1(Y1)) )],[refute_0_74,refute_0_81]) ).
cnf(refute_0_83,plain,
( skolemFOFtoCNF_Y3_1(X_96) = skolemFOFtoCNF_Y24
| r1(X_96)
| r1(skolemFOFtoCNF_Y3_1(X_96)) ),
inference(subst,[],[refute_0_82:[bind(Y1,$fot(X_96))]]) ).
cnf(refute_0_84,plain,
( skolemFOFtoCNF_Y3_1(X_96) = skolemFOFtoCNF_Y24
| r1(X_96) ),
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y3_1(X_96)) )],[refute_0_83,refute_0_73]) ).
cnf(refute_0_85,plain,
( skolemFOFtoCNF_Y3_1(X_100) = skolemFOFtoCNF_Y24
| r1(X_100) ),
inference(subst,[],[refute_0_84:[bind(X_96,$fot(X_100))]]) ).
cnf(refute_0_86,plain,
( skolemFOFtoCNF_Y3_1(X_100) != skolemFOFtoCNF_Y24
| ~ r2(skolemFOFtoCNF_Y3_1(X_100),X_100)
| r2(skolemFOFtoCNF_Y24,X_100) ),
introduced(tautology,[equality,[$cnf( r2(skolemFOFtoCNF_Y3_1(X_100),X_100) ),[0],$fot(skolemFOFtoCNF_Y24)]]) ).
cnf(refute_0_87,plain,
( ~ r2(skolemFOFtoCNF_Y3_1(X_100),X_100)
| r1(X_100)
| r2(skolemFOFtoCNF_Y24,X_100) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y3_1(X_100),skolemFOFtoCNF_Y24) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
( r1(X_100)
| r1(skolemFOFtoCNF_Y4_1(X_100))
| r2(skolemFOFtoCNF_Y24,X_100) ),
inference(resolve,[$cnf( r2(skolemFOFtoCNF_Y3_1(X_100),X_100) )],[refute_0_72,refute_0_87]) ).
cnf(refute_0_89,plain,
( r1(X_101)
| r1(skolemFOFtoCNF_Y4_1(X_101))
| r2(skolemFOFtoCNF_Y24,X_101) ),
inference(subst,[],[refute_0_88:[bind(X_100,$fot(X_101))]]) ).
cnf(refute_0_90,plain,
( X_101 = skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)
| r1(X_101)
| r1(skolemFOFtoCNF_Y4_1(X_101)) ),
inference(resolve,[$cnf( r2(skolemFOFtoCNF_Y24,X_101) )],[refute_0_89,refute_0_56]) ).
cnf(refute_0_91,plain,
( ~ r2(skolemFOFtoCNF_Y24,X_367)
| X_367 = skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24) ),
inference(subst,[],[refute_0_13:[bind(X11,$fot(skolemFOFtoCNF_Y24)),bind(X12,$fot(X_367))]]) ).
cnf(refute_0_92,plain,
( Y1 = skolemFOFtoCNF_Y4_1(Y1)
| r2(skolemFOFtoCNF_Y3_1(Y1),skolemFOFtoCNF_Y2_1(Y1)) ),
inference(canonicalize,[],[normalize_0_44]) ).
cnf(refute_0_93,plain,
( X_69 = skolemFOFtoCNF_Y4_1(X_69)
| r2(skolemFOFtoCNF_Y3_1(X_69),skolemFOFtoCNF_Y2_1(X_69)) ),
inference(subst,[],[refute_0_92:[bind(Y1,$fot(X_69))]]) ).
cnf(refute_0_94,plain,
( X_69 = skolemFOFtoCNF_Y2_1(X_69)
| r1(X_69) ),
inference(subst,[],[refute_0_65:[bind(Y1,$fot(X_69))]]) ).
cnf(refute_0_95,plain,
( X_69 != skolemFOFtoCNF_Y2_1(X_69)
| skolemFOFtoCNF_Y2_1(X_69) = X_69 ),
inference(subst,[],[refute_0_48:[bind(X,$fot(X_69)),bind(Y,$fot(skolemFOFtoCNF_Y2_1(X_69)))]]) ).
cnf(refute_0_96,plain,
( skolemFOFtoCNF_Y2_1(X_69) = X_69
| r1(X_69) ),
inference(resolve,[$cnf( $equal(X_69,skolemFOFtoCNF_Y2_1(X_69)) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
( skolemFOFtoCNF_Y2_1(X_69) != X_69
| ~ r2(skolemFOFtoCNF_Y3_1(X_69),skolemFOFtoCNF_Y2_1(X_69))
| r2(skolemFOFtoCNF_Y3_1(X_69),X_69) ),
introduced(tautology,[equality,[$cnf( r2(skolemFOFtoCNF_Y3_1(X_69),skolemFOFtoCNF_Y2_1(X_69)) ),[1],$fot(X_69)]]) ).
cnf(refute_0_98,plain,
( ~ r2(skolemFOFtoCNF_Y3_1(X_69),skolemFOFtoCNF_Y2_1(X_69))
| r1(X_69)
| r2(skolemFOFtoCNF_Y3_1(X_69),X_69) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y2_1(X_69),X_69) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
( X_69 = skolemFOFtoCNF_Y4_1(X_69)
| r1(X_69)
| r2(skolemFOFtoCNF_Y3_1(X_69),X_69) ),
inference(resolve,[$cnf( r2(skolemFOFtoCNF_Y3_1(X_69),skolemFOFtoCNF_Y2_1(X_69)) )],[refute_0_93,refute_0_98]) ).
cnf(refute_0_100,plain,
( X_341 = skolemFOFtoCNF_Y4_1(X_341)
| r1(X_341)
| r2(skolemFOFtoCNF_Y3_1(X_341),X_341) ),
inference(subst,[],[refute_0_99:[bind(X_69,$fot(X_341))]]) ).
cnf(refute_0_101,plain,
( skolemFOFtoCNF_Y3_1(X_341) = skolemFOFtoCNF_Y24
| r1(X_341) ),
inference(subst,[],[refute_0_84:[bind(X_96,$fot(X_341))]]) ).
cnf(refute_0_102,plain,
( skolemFOFtoCNF_Y3_1(X_341) != skolemFOFtoCNF_Y24
| ~ r2(skolemFOFtoCNF_Y3_1(X_341),X_341)
| r2(skolemFOFtoCNF_Y24,X_341) ),
introduced(tautology,[equality,[$cnf( r2(skolemFOFtoCNF_Y3_1(X_341),X_341) ),[0],$fot(skolemFOFtoCNF_Y24)]]) ).
cnf(refute_0_103,plain,
( ~ r2(skolemFOFtoCNF_Y3_1(X_341),X_341)
| r1(X_341)
| r2(skolemFOFtoCNF_Y24,X_341) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y3_1(X_341),skolemFOFtoCNF_Y24) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
( X_341 = skolemFOFtoCNF_Y4_1(X_341)
| r1(X_341)
| r2(skolemFOFtoCNF_Y24,X_341) ),
inference(resolve,[$cnf( r2(skolemFOFtoCNF_Y3_1(X_341),X_341) )],[refute_0_100,refute_0_103]) ).
cnf(refute_0_105,plain,
( X_367 = skolemFOFtoCNF_Y4_1(X_367)
| r1(X_367)
| r2(skolemFOFtoCNF_Y24,X_367) ),
inference(subst,[],[refute_0_104:[bind(X_341,$fot(X_367))]]) ).
cnf(refute_0_106,plain,
( X_367 = skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)
| X_367 = skolemFOFtoCNF_Y4_1(X_367)
| r1(X_367) ),
inference(resolve,[$cnf( r2(skolemFOFtoCNF_Y24,X_367) )],[refute_0_105,refute_0_91]) ).
cnf(refute_0_107,plain,
( X_101 = skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)
| X_101 = skolemFOFtoCNF_Y4_1(X_101)
| r1(X_101) ),
inference(subst,[],[refute_0_106:[bind(X_367,$fot(X_101))]]) ).
cnf(refute_0_108,plain,
( X_101 != skolemFOFtoCNF_Y4_1(X_101)
| skolemFOFtoCNF_Y4_1(X_101) = X_101 ),
inference(subst,[],[refute_0_48:[bind(X,$fot(X_101)),bind(Y,$fot(skolemFOFtoCNF_Y4_1(X_101)))]]) ).
cnf(refute_0_109,plain,
( X_101 = skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)
| skolemFOFtoCNF_Y4_1(X_101) = X_101
| r1(X_101) ),
inference(resolve,[$cnf( $equal(X_101,skolemFOFtoCNF_Y4_1(X_101)) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
( skolemFOFtoCNF_Y4_1(X_101) != X_101
| ~ r1(skolemFOFtoCNF_Y4_1(X_101))
| r1(X_101) ),
introduced(tautology,[equality,[$cnf( r1(skolemFOFtoCNF_Y4_1(X_101)) ),[0],$fot(X_101)]]) ).
cnf(refute_0_111,plain,
( ~ r1(skolemFOFtoCNF_Y4_1(X_101))
| X_101 = skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)
| r1(X_101) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y4_1(X_101),X_101) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
( X_101 = skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)
| r1(X_101) ),
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y4_1(X_101)) )],[refute_0_90,refute_0_111]) ).
cnf(refute_0_113,plain,
( skolemFOFtoCNF_Y4(X1,X8) = skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)
| r1(skolemFOFtoCNF_Y4(X1,X8)) ),
inference(subst,[],[refute_0_112:[bind(X_101,$fot(skolemFOFtoCNF_Y4(X1,X8)))]]) ).
cnf(refute_0_114,plain,
skolemFOFtoCNF_Y4(X1,X8) = skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y4(X1,X8)) )],[refute_0_113,refute_0_55]) ).
cnf(refute_0_115,plain,
skolemFOFtoCNF_Y4(X_108,skolemFOFtoCNF_Y24) = skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),
inference(subst,[],[refute_0_114:[bind(X1,$fot(X_108)),bind(X8,$fot(skolemFOFtoCNF_Y24))]]) ).
cnf(refute_0_116,plain,
( skolemFOFtoCNF_Y4(X_108,skolemFOFtoCNF_Y24) != skolemFOFtoCNF_Y21(X_108)
| skolemFOFtoCNF_Y4(X_108,skolemFOFtoCNF_Y24) != skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)
| skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24) = skolemFOFtoCNF_Y21(X_108) ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_Y4(X_108,skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y21(X_108)) ),[0],$fot(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24))]]) ).
cnf(refute_0_117,plain,
( skolemFOFtoCNF_Y4(X_108,skolemFOFtoCNF_Y24) != skolemFOFtoCNF_Y21(X_108)
| skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24) = skolemFOFtoCNF_Y21(X_108) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y4(X_108,skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24) = skolemFOFtoCNF_Y21(X_108),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y4(X_108,skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y21(X_108)) )],[refute_0_53,refute_0_117]) ).
cnf(refute_0_119,plain,
skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24) = skolemFOFtoCNF_Y21(X_370),
inference(subst,[],[refute_0_118:[bind(X_108,$fot(X_370))]]) ).
cnf(refute_0_120,plain,
( skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24) != skolemFOFtoCNF_Y21(X_370)
| ~ r2(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24))
| r2(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y21(X_370)) ),
introduced(tautology,[equality,[$cnf( r2(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)) ),[1],$fot(skolemFOFtoCNF_Y21(X_370))]]) ).
cnf(refute_0_121,plain,
( ~ r2(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24))
| r2(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y21(X_370)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y21(X_370)) )],[refute_0_119,refute_0_120]) ).
cnf(refute_0_122,plain,
r2(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y21(X_370)),
inference(resolve,[$cnf( r2(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)) )],[refute_0_11,refute_0_121]) ).
cnf(refute_0_123,plain,
( Y13 != Y12
| ~ r2(X10,Y12)
| ~ r2(X3,Y13)
| X3 = X10 ),
inference(canonicalize,[],[normalize_0_47]) ).
cnf(refute_0_124,plain,
( Y12 != Y12
| ~ r2(X10,Y12)
| ~ r2(X3,Y12)
| X3 = X10 ),
inference(subst,[],[refute_0_123:[bind(Y13,$fot(Y12))]]) ).
cnf(refute_0_125,plain,
Y12 = Y12,
introduced(tautology,[refl,[$fot(Y12)]]) ).
cnf(refute_0_126,plain,
( ~ r2(X10,Y12)
| ~ r2(X3,Y12)
| X3 = X10 ),
inference(resolve,[$cnf( $equal(Y12,Y12) )],[refute_0_125,refute_0_124]) ).
cnf(refute_0_127,plain,
( ~ r2(X_515,skolemFOFtoCNF_Y21(X_370))
| ~ r2(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y21(X_370))
| X_515 = skolemFOFtoCNF_Y24 ),
inference(subst,[],[refute_0_126:[bind(X10,$fot(skolemFOFtoCNF_Y24)),bind(X3,$fot(X_515)),bind(Y12,$fot(skolemFOFtoCNF_Y21(X_370)))]]) ).
cnf(refute_0_128,plain,
( ~ r2(X_515,skolemFOFtoCNF_Y21(X_370))
| X_515 = skolemFOFtoCNF_Y24 ),
inference(resolve,[$cnf( r2(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y21(X_370)) )],[refute_0_122,refute_0_127]) ).
cnf(refute_0_129,plain,
skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24) = skolemFOFtoCNF_Y21(X11),
inference(subst,[],[refute_0_118:[bind(X_108,$fot(X11))]]) ).
cnf(refute_0_130,plain,
( skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24) != skolemFOFtoCNF_Y21(X11)
| skolemFOFtoCNF_Y21(X11) = skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24) ),
inference(subst,[],[refute_0_48:[bind(X,$fot(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24))),bind(Y,$fot(skolemFOFtoCNF_Y21(X11)))]]) ).
cnf(refute_0_131,plain,
skolemFOFtoCNF_Y21(X11) = skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y21(X11)) )],[refute_0_129,refute_0_130]) ).
cnf(refute_0_132,plain,
( skolemFOFtoCNF_Y21(X11) != skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)
| ~ r2(X11,skolemFOFtoCNF_Y21(X11))
| r2(X11,skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)) ),
introduced(tautology,[equality,[$cnf( r2(X11,skolemFOFtoCNF_Y21(X11)) ),[1],$fot(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24))]]) ).
cnf(refute_0_133,plain,
( ~ r2(X11,skolemFOFtoCNF_Y21(X11))
| r2(X11,skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y21(X11),skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)) )],[refute_0_131,refute_0_132]) ).
cnf(refute_0_134,plain,
r2(X11,skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)),
inference(resolve,[$cnf( r2(X11,skolemFOFtoCNF_Y21(X11)) )],[refute_0_3,refute_0_133]) ).
cnf(refute_0_135,plain,
( skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24) != skolemFOFtoCNF_Y21(X_108)
| skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24) != skolemFOFtoCNF_Y21(X_370)
| skolemFOFtoCNF_Y21(X_370) = skolemFOFtoCNF_Y21(X_108) ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y21(X_108)) ),[0],$fot(skolemFOFtoCNF_Y21(X_370))]]) ).
cnf(refute_0_136,plain,
( skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24) != skolemFOFtoCNF_Y21(X_108)
| skolemFOFtoCNF_Y21(X_370) = skolemFOFtoCNF_Y21(X_108) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y21(X_370)) )],[refute_0_119,refute_0_135]) ).
cnf(refute_0_137,plain,
skolemFOFtoCNF_Y21(X_370) = skolemFOFtoCNF_Y21(X_108),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y21(X_108)) )],[refute_0_118,refute_0_136]) ).
cnf(refute_0_138,plain,
skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24) = skolemFOFtoCNF_Y21(X_380),
inference(subst,[],[refute_0_137:[bind(X_108,$fot(X_380)),bind(X_370,$fot(skolemFOFtoCNF_Y24))]]) ).
cnf(refute_0_139,plain,
( skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24) != skolemFOFtoCNF_Y21(X_380)
| ~ r2(X11,skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24))
| r2(X11,skolemFOFtoCNF_Y21(X_380)) ),
introduced(tautology,[equality,[$cnf( r2(X11,skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)) ),[1],$fot(skolemFOFtoCNF_Y21(X_380))]]) ).
cnf(refute_0_140,plain,
( ~ r2(X11,skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24))
| r2(X11,skolemFOFtoCNF_Y21(X_380)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y21(X_380)) )],[refute_0_138,refute_0_139]) ).
cnf(refute_0_141,plain,
r2(X11,skolemFOFtoCNF_Y21(X_380)),
inference(resolve,[$cnf( r2(X11,skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)) )],[refute_0_134,refute_0_140]) ).
cnf(refute_0_142,plain,
r2(X_515,skolemFOFtoCNF_Y21(X_370)),
inference(subst,[],[refute_0_141:[bind(X11,$fot(X_515)),bind(X_380,$fot(X_370))]]) ).
cnf(refute_0_143,plain,
X_515 = skolemFOFtoCNF_Y24,
inference(resolve,[$cnf( r2(X_515,skolemFOFtoCNF_Y21(X_370)) )],[refute_0_142,refute_0_128]) ).
cnf(refute_0_144,plain,
skolemFOFtoCNF_Y21(X_52) = skolemFOFtoCNF_Y24,
inference(subst,[],[refute_0_143:[bind(X_515,$fot(skolemFOFtoCNF_Y21(X_52)))]]) ).
cnf(refute_0_145,plain,
( skolemFOFtoCNF_Y21(X_52) != skolemFOFtoCNF_Y24
| ~ r1(skolemFOFtoCNF_Y24)
| r1(skolemFOFtoCNF_Y21(X_52)) ),
introduced(tautology,[equality,[$cnf( ~ r1(skolemFOFtoCNF_Y21(X_52)) ),[0],$fot(skolemFOFtoCNF_Y24)]]) ).
cnf(refute_0_146,plain,
( ~ r1(skolemFOFtoCNF_Y24)
| r1(skolemFOFtoCNF_Y21(X_52)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y21(X_52),skolemFOFtoCNF_Y24) )],[refute_0_144,refute_0_145]) ).
cnf(refute_0_147,plain,
~ r1(skolemFOFtoCNF_Y24),
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y21(X_52)) )],[refute_0_146,refute_0_10]) ).
cnf(refute_0_148,plain,
( X19 != skolemFOFtoCNF_Y24
| r1(X19) ),
inference(canonicalize,[],[normalize_0_48]) ).
cnf(refute_0_149,plain,
( skolemFOFtoCNF_Y24 != skolemFOFtoCNF_Y24
| r1(skolemFOFtoCNF_Y24) ),
inference(subst,[],[refute_0_148:[bind(X19,$fot(skolemFOFtoCNF_Y24))]]) ).
cnf(refute_0_150,plain,
skolemFOFtoCNF_Y24 = skolemFOFtoCNF_Y24,
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_Y24)]]) ).
cnf(refute_0_151,plain,
r1(skolemFOFtoCNF_Y24),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y24) )],[refute_0_150,refute_0_149]) ).
cnf(refute_0_152,plain,
$false,
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y24) )],[refute_0_151,refute_0_147]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUN065+2 : TPTP v8.1.0. Released v7.3.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n026.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 : Thu Jun 2 09:27:12 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.37/1.56 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.37/1.56
% 1.37/1.56 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.37/1.57
%------------------------------------------------------------------------------