TSTP Solution File: NUN071+2 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUN071+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 16:34:55 EDT 2022
% Result : Theorem 0.99s 1.20s
% Output : CNFRefutation 0.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 30
% Syntax : Number of formulae : 227 ( 94 unt; 0 def)
% Number of atoms : 499 ( 170 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 443 ( 171 ~; 141 |; 131 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 1 con; 0-2 aty)
% Number of variables : 440 ( 17 sgn 161 !; 87 ?)
% 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_4,axiom,
! [X16,X17] :
? [Y23] :
! [X18] :
( ( ~ r4(X16,X17,X18)
& X18 != Y23 )
| ( r4(X16,X17,X18)
& X18 = Y23 ) ) ).
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_2a,axiom,
! [X2,X9] :
? [Y2] :
( ? [Y3] :
( ? [Y14] :
( r2(X9,Y14)
& r4(X2,Y14,Y3) )
& Y3 = Y2 )
& ? [Y6] :
( r3(Y6,X2,Y2)
& r4(X2,X9,Y6) ) ) ).
fof(axiom_4a,axiom,
! [X4] :
? [Y9] :
( ? [Y16] :
( r1(Y16)
& r3(X4,Y16,Y9) )
& Y9 = X4 ) ).
fof(axiom_5a,axiom,
! [X5] :
? [Y8] :
( ? [Y17] :
( r1(Y17)
& r4(X5,Y17,Y8) )
& ? [Y18] :
( r1(Y18)
& Y8 = Y18 ) ) ).
fof(onetimesoneeqone,conjecture,
? [Y1] :
( ? [Y2] :
( r4(Y2,Y2,Y1)
& ? [Y4] :
( r1(Y4)
& r2(Y4,Y2) ) )
& ? [Y3] :
( Y1 = Y3
& ? [Y5] :
( r1(Y5)
& r2(Y5,Y3) ) ) ) ).
fof(subgoal_0,plain,
? [Y1] :
( ? [Y2] :
( r4(Y2,Y2,Y1)
& ? [Y4] :
( r1(Y4)
& r2(Y4,Y2) ) )
& ? [Y3] :
( Y1 = Y3
& ? [Y5] :
( r1(Y5)
& r2(Y5,Y3) ) ) ),
inference(strip,[],[onetimesoneeqone]) ).
fof(negate_0_0,plain,
~ ? [Y1] :
( ? [Y2] :
( r4(Y2,Y2,Y1)
& ? [Y4] :
( r1(Y4)
& r2(Y4,Y2) ) )
& ? [Y3] :
( Y1 = Y3
& ? [Y5] :
( r1(Y5)
& r2(Y5,Y3) ) ) ),
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,
! [X2,X9] :
? [Y2] :
( ? [Y3] :
( Y3 = Y2
& ? [Y14] :
( r2(X9,Y14)
& r4(X2,Y14,Y3) ) )
& ? [Y6] :
( r3(Y6,X2,Y2)
& r4(X2,X9,Y6) ) ),
inference(canonicalize,[],[axiom_2a]) ).
fof(normalize_0_7,plain,
! [X2,X9] :
? [Y2] :
( ? [Y3] :
( Y3 = Y2
& ? [Y14] :
( r2(X9,Y14)
& r4(X2,Y14,Y3) ) )
& ? [Y6] :
( r3(Y6,X2,Y2)
& r4(X2,X9,Y6) ) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X2,X9] :
( ? [Y3] :
( Y3 = skolemFOFtoCNF_Y2(X2,X9)
& ? [Y14] :
( r2(X9,Y14)
& r4(X2,Y14,Y3) ) )
& ? [Y6] :
( r3(Y6,X2,skolemFOFtoCNF_Y2(X2,X9))
& r4(X2,X9,Y6) ) ),
inference(skolemize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [X2,X9] :
? [Y3] :
( Y3 = skolemFOFtoCNF_Y2(X2,X9)
& ? [Y14] :
( r2(X9,Y14)
& r4(X2,Y14,Y3) ) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X2,X9] :
( skolemFOFtoCNF_Y3(X2,X9) = skolemFOFtoCNF_Y2(X2,X9)
& ? [Y14] :
( r2(X9,Y14)
& r4(X2,Y14,skolemFOFtoCNF_Y3(X2,X9)) ) ),
inference(skolemize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [X2,X9] :
? [Y14] :
( r2(X9,Y14)
& r4(X2,Y14,skolemFOFtoCNF_Y3(X2,X9)) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [X2,X9] :
( r2(X9,skolemFOFtoCNF_Y14(X2,X9))
& r4(X2,skolemFOFtoCNF_Y14(X2,X9),skolemFOFtoCNF_Y3(X2,X9)) ),
inference(skolemize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [X2,X9] : r4(X2,skolemFOFtoCNF_Y14(X2,X9),skolemFOFtoCNF_Y3(X2,X9)),
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [X2,X9] : skolemFOFtoCNF_Y3(X2,X9) = skolemFOFtoCNF_Y2(X2,X9),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_15,plain,
! [X2,X9] : r2(X9,skolemFOFtoCNF_Y14(X2,X9)),
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_16,plain,
! [X11,X12] :
( ~ r2(X11,X12)
| X12 = skolemFOFtoCNF_Y21(X11) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_17,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_18,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_17]) ).
fof(normalize_0_19,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_18]) ).
fof(normalize_0_20,plain,
! [X1,X8] :
? [Y7] :
( r2(Y7,skolemFOFtoCNF_Y4(X1,X8))
& r3(X1,X8,Y7) ),
inference(conjunct,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [X1,X8] :
( r2(skolemFOFtoCNF_Y7(X1,X8),skolemFOFtoCNF_Y4(X1,X8))
& r3(X1,X8,skolemFOFtoCNF_Y7(X1,X8)) ),
inference(skolemize,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [X1,X8] : r2(skolemFOFtoCNF_Y7(X1,X8),skolemFOFtoCNF_Y4(X1,X8)),
inference(conjunct,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
! [X1,X8] : r3(X1,X8,skolemFOFtoCNF_Y7(X1,X8)),
inference(conjunct,[],[normalize_0_21]) ).
fof(normalize_0_24,plain,
! [X13,X14] :
? [Y22] :
! [X15] :
( ( X15 != Y22
& ~ r3(X13,X14,X15) )
| ( X15 = Y22
& r3(X13,X14,X15) ) ),
inference(canonicalize,[],[axiom_3]) ).
fof(normalize_0_25,plain,
! [X13,X14] :
? [Y22] :
! [X15] :
( ( X15 != Y22
& ~ r3(X13,X14,X15) )
| ( X15 = Y22
& r3(X13,X14,X15) ) ),
inference(specialize,[],[normalize_0_24]) ).
fof(normalize_0_26,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_25]) ).
fof(normalize_0_27,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_26]) ).
fof(normalize_0_28,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_27]) ).
fof(normalize_0_29,plain,
! [X13,X14,X15] :
( ~ r3(X13,X14,X15)
| X15 = skolemFOFtoCNF_Y22(X13,X14) ),
inference(conjunct,[],[normalize_0_28]) ).
fof(normalize_0_30,plain,
! [X4] :
? [Y9] :
( Y9 = X4
& ? [Y16] :
( r1(Y16)
& r3(X4,Y16,Y9) ) ),
inference(canonicalize,[],[axiom_4a]) ).
fof(normalize_0_31,plain,
! [X4] :
? [Y9] :
( Y9 = X4
& ? [Y16] :
( r1(Y16)
& r3(X4,Y16,Y9) ) ),
inference(specialize,[],[normalize_0_30]) ).
fof(normalize_0_32,plain,
! [X4] :
( skolemFOFtoCNF_Y9(X4) = X4
& ? [Y16] :
( r1(Y16)
& r3(X4,Y16,skolemFOFtoCNF_Y9(X4)) ) ),
inference(skolemize,[],[normalize_0_31]) ).
fof(normalize_0_33,plain,
! [X4] :
? [Y16] :
( r1(Y16)
& r3(X4,Y16,skolemFOFtoCNF_Y9(X4)) ),
inference(conjunct,[],[normalize_0_32]) ).
fof(normalize_0_34,plain,
! [X4] :
( r1(skolemFOFtoCNF_Y16(X4))
& r3(X4,skolemFOFtoCNF_Y16(X4),skolemFOFtoCNF_Y9(X4)) ),
inference(skolemize,[],[normalize_0_33]) ).
fof(normalize_0_35,plain,
! [X4] : r3(X4,skolemFOFtoCNF_Y16(X4),skolemFOFtoCNF_Y9(X4)),
inference(conjunct,[],[normalize_0_34]) ).
fof(normalize_0_36,plain,
! [X4] : skolemFOFtoCNF_Y9(X4) = X4,
inference(conjunct,[],[normalize_0_32]) ).
fof(normalize_0_37,plain,
! [X4] : r1(skolemFOFtoCNF_Y16(X4)),
inference(conjunct,[],[normalize_0_34]) ).
fof(normalize_0_38,plain,
? [Y24] :
! [X19] :
( ( X19 != Y24
& ~ r1(X19) )
| ( X19 = Y24
& r1(X19) ) ),
inference(canonicalize,[],[axiom_1]) ).
fof(normalize_0_39,plain,
! [X19] :
( ( X19 != skolemFOFtoCNF_Y24
& ~ r1(X19) )
| ( X19 = skolemFOFtoCNF_Y24
& r1(X19) ) ),
inference(skolemize,[],[normalize_0_38]) ).
fof(normalize_0_40,plain,
! [X19] :
( ( X19 != skolemFOFtoCNF_Y24
& ~ r1(X19) )
| ( X19 = skolemFOFtoCNF_Y24
& r1(X19) ) ),
inference(specialize,[],[normalize_0_39]) ).
fof(normalize_0_41,plain,
! [X19] :
( ( X19 != skolemFOFtoCNF_Y24
| r1(X19) )
& ( ~ r1(X19)
| X19 = skolemFOFtoCNF_Y24 ) ),
inference(clausify,[],[normalize_0_40]) ).
fof(normalize_0_42,plain,
! [X19] :
( ~ r1(X19)
| X19 = skolemFOFtoCNF_Y24 ),
inference(conjunct,[],[normalize_0_41]) ).
fof(normalize_0_43,plain,
! [X1,X8] :
? [Y5] :
( Y5 = skolemFOFtoCNF_Y4(X1,X8)
& ? [Y15] :
( r2(X8,Y15)
& r3(X1,Y15,Y5) ) ),
inference(conjunct,[],[normalize_0_19]) ).
fof(normalize_0_44,plain,
! [X1,X8] :
( skolemFOFtoCNF_Y5(X1,X8) = skolemFOFtoCNF_Y4(X1,X8)
& ? [Y15] :
( r2(X8,Y15)
& r3(X1,Y15,skolemFOFtoCNF_Y5(X1,X8)) ) ),
inference(skolemize,[],[normalize_0_43]) ).
fof(normalize_0_45,plain,
! [X1,X8] :
? [Y15] :
( r2(X8,Y15)
& r3(X1,Y15,skolemFOFtoCNF_Y5(X1,X8)) ),
inference(conjunct,[],[normalize_0_44]) ).
fof(normalize_0_46,plain,
! [X1,X8] :
( r2(X8,skolemFOFtoCNF_Y15(X1,X8))
& r3(X1,skolemFOFtoCNF_Y15(X1,X8),skolemFOFtoCNF_Y5(X1,X8)) ),
inference(skolemize,[],[normalize_0_45]) ).
fof(normalize_0_47,plain,
! [X1,X8] : r3(X1,skolemFOFtoCNF_Y15(X1,X8),skolemFOFtoCNF_Y5(X1,X8)),
inference(conjunct,[],[normalize_0_46]) ).
fof(normalize_0_48,plain,
! [X1,X8] : skolemFOFtoCNF_Y5(X1,X8) = skolemFOFtoCNF_Y4(X1,X8),
inference(conjunct,[],[normalize_0_44]) ).
fof(normalize_0_49,plain,
! [X1,X8] : r2(X8,skolemFOFtoCNF_Y15(X1,X8)),
inference(conjunct,[],[normalize_0_46]) ).
fof(normalize_0_50,plain,
! [X2,X9] :
? [Y6] :
( r3(Y6,X2,skolemFOFtoCNF_Y2(X2,X9))
& r4(X2,X9,Y6) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_51,plain,
! [X2,X9] :
( r3(skolemFOFtoCNF_Y6(X2,X9),X2,skolemFOFtoCNF_Y2(X2,X9))
& r4(X2,X9,skolemFOFtoCNF_Y6(X2,X9)) ),
inference(skolemize,[],[normalize_0_50]) ).
fof(normalize_0_52,plain,
! [X2,X9] : r3(skolemFOFtoCNF_Y6(X2,X9),X2,skolemFOFtoCNF_Y2(X2,X9)),
inference(conjunct,[],[normalize_0_51]) ).
fof(normalize_0_53,plain,
! [X2,X9] : r4(X2,X9,skolemFOFtoCNF_Y6(X2,X9)),
inference(conjunct,[],[normalize_0_51]) ).
fof(normalize_0_54,plain,
! [X16,X17] :
? [Y23] :
! [X18] :
( ( X18 != Y23
& ~ r4(X16,X17,X18) )
| ( X18 = Y23
& r4(X16,X17,X18) ) ),
inference(canonicalize,[],[axiom_4]) ).
fof(normalize_0_55,plain,
! [X16,X17] :
? [Y23] :
! [X18] :
( ( X18 != Y23
& ~ r4(X16,X17,X18) )
| ( X18 = Y23
& r4(X16,X17,X18) ) ),
inference(specialize,[],[normalize_0_54]) ).
fof(normalize_0_56,plain,
! [X16,X17,X18] :
( ( X18 != skolemFOFtoCNF_Y23(X16,X17)
& ~ r4(X16,X17,X18) )
| ( X18 = skolemFOFtoCNF_Y23(X16,X17)
& r4(X16,X17,X18) ) ),
inference(skolemize,[],[normalize_0_55]) ).
fof(normalize_0_57,plain,
! [X16,X17,X18] :
( ( X18 != skolemFOFtoCNF_Y23(X16,X17)
& ~ r4(X16,X17,X18) )
| ( X18 = skolemFOFtoCNF_Y23(X16,X17)
& r4(X16,X17,X18) ) ),
inference(specialize,[],[normalize_0_56]) ).
fof(normalize_0_58,plain,
! [X16,X17,X18] :
( ( X18 != skolemFOFtoCNF_Y23(X16,X17)
| r4(X16,X17,X18) )
& ( ~ r4(X16,X17,X18)
| X18 = skolemFOFtoCNF_Y23(X16,X17) ) ),
inference(clausify,[],[normalize_0_57]) ).
fof(normalize_0_59,plain,
! [X16,X17,X18] :
( ~ r4(X16,X17,X18)
| X18 = skolemFOFtoCNF_Y23(X16,X17) ),
inference(conjunct,[],[normalize_0_58]) ).
fof(normalize_0_60,plain,
! [X5] :
? [Y8] :
( ? [Y17] :
( r1(Y17)
& r4(X5,Y17,Y8) )
& ? [Y18] :
( Y8 = Y18
& r1(Y18) ) ),
inference(canonicalize,[],[axiom_5a]) ).
fof(normalize_0_61,plain,
! [X5] :
? [Y8] :
( ? [Y17] :
( r1(Y17)
& r4(X5,Y17,Y8) )
& ? [Y18] :
( Y8 = Y18
& r1(Y18) ) ),
inference(specialize,[],[normalize_0_60]) ).
fof(normalize_0_62,plain,
! [X5] :
( ? [Y17] :
( r1(Y17)
& r4(X5,Y17,skolemFOFtoCNF_Y8(X5)) )
& ? [Y18] :
( skolemFOFtoCNF_Y8(X5) = Y18
& r1(Y18) ) ),
inference(skolemize,[],[normalize_0_61]) ).
fof(normalize_0_63,plain,
! [X5] :
? [Y17] :
( r1(Y17)
& r4(X5,Y17,skolemFOFtoCNF_Y8(X5)) ),
inference(conjunct,[],[normalize_0_62]) ).
fof(normalize_0_64,plain,
! [X5] :
( r1(skolemFOFtoCNF_Y17(X5))
& r4(X5,skolemFOFtoCNF_Y17(X5),skolemFOFtoCNF_Y8(X5)) ),
inference(skolemize,[],[normalize_0_63]) ).
fof(normalize_0_65,plain,
! [X5] : r4(X5,skolemFOFtoCNF_Y17(X5),skolemFOFtoCNF_Y8(X5)),
inference(conjunct,[],[normalize_0_64]) ).
fof(normalize_0_66,plain,
! [X5] :
? [Y18] :
( skolemFOFtoCNF_Y8(X5) = Y18
& r1(Y18) ),
inference(conjunct,[],[normalize_0_62]) ).
fof(normalize_0_67,plain,
! [X5] :
( skolemFOFtoCNF_Y8(X5) = skolemFOFtoCNF_Y18(X5)
& r1(skolemFOFtoCNF_Y18(X5)) ),
inference(skolemize,[],[normalize_0_66]) ).
fof(normalize_0_68,plain,
! [X5] : skolemFOFtoCNF_Y8(X5) = skolemFOFtoCNF_Y18(X5),
inference(conjunct,[],[normalize_0_67]) ).
fof(normalize_0_69,plain,
! [X5] : r1(skolemFOFtoCNF_Y17(X5)),
inference(conjunct,[],[normalize_0_64]) ).
fof(normalize_0_70,plain,
! [X5] : r1(skolemFOFtoCNF_Y18(X5)),
inference(conjunct,[],[normalize_0_67]) ).
fof(normalize_0_71,plain,
! [Y1] :
( ! [Y2] :
( ~ r4(Y2,Y2,Y1)
| ! [Y4] :
( ~ r1(Y4)
| ~ r2(Y4,Y2) ) )
| ! [Y3] :
( Y1 != Y3
| ! [Y5] :
( ~ r1(Y5)
| ~ r2(Y5,Y3) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_72,plain,
! [Y1] :
( ! [Y2] :
( ~ r4(Y2,Y2,Y1)
| ! [Y4] :
( ~ r1(Y4)
| ~ r2(Y4,Y2) ) )
| ! [Y3] :
( Y1 != Y3
| ! [Y5] :
( ~ r1(Y5)
| ~ r2(Y5,Y3) ) ) ),
inference(specialize,[],[normalize_0_71]) ).
fof(normalize_0_73,plain,
! [Y1,Y2,Y3,Y4,Y5] :
( Y1 != Y3
| ~ r1(Y4)
| ~ r1(Y5)
| ~ r2(Y4,Y2)
| ~ r2(Y5,Y3)
| ~ r4(Y2,Y2,Y1) ),
inference(clausify,[],[normalize_0_72]) ).
fof(normalize_0_74,plain,
! [X19] :
( X19 != skolemFOFtoCNF_Y24
| r1(X19) ),
inference(conjunct,[],[normalize_0_41]) ).
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( $equal(skolemFOFtoCNF_Y21(X11),skolemFOFtoCNF_Y21(X11)) )],[refute_0_2,refute_0_1]) ).
cnf(refute_0_4,plain,
r2(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)),
inference(subst,[],[refute_0_3:[bind(X11,$fot(skolemFOFtoCNF_Y24))]]) ).
cnf(refute_0_5,plain,
r4(X2,skolemFOFtoCNF_Y14(X2,X9),skolemFOFtoCNF_Y3(X2,X9)),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_6,plain,
skolemFOFtoCNF_Y3(X2,X9) = skolemFOFtoCNF_Y2(X2,X9),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_7,plain,
( skolemFOFtoCNF_Y3(X2,X9) != skolemFOFtoCNF_Y2(X2,X9)
| ~ r4(X2,skolemFOFtoCNF_Y14(X2,X9),skolemFOFtoCNF_Y3(X2,X9))
| r4(X2,skolemFOFtoCNF_Y14(X2,X9),skolemFOFtoCNF_Y2(X2,X9)) ),
introduced(tautology,[equality,[$cnf( r4(X2,skolemFOFtoCNF_Y14(X2,X9),skolemFOFtoCNF_Y3(X2,X9)) ),[2],$fot(skolemFOFtoCNF_Y2(X2,X9))]]) ).
cnf(refute_0_8,plain,
( ~ r4(X2,skolemFOFtoCNF_Y14(X2,X9),skolemFOFtoCNF_Y3(X2,X9))
| r4(X2,skolemFOFtoCNF_Y14(X2,X9),skolemFOFtoCNF_Y2(X2,X9)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y3(X2,X9),skolemFOFtoCNF_Y2(X2,X9)) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
r4(X2,skolemFOFtoCNF_Y14(X2,X9),skolemFOFtoCNF_Y2(X2,X9)),
inference(resolve,[$cnf( r4(X2,skolemFOFtoCNF_Y14(X2,X9),skolemFOFtoCNF_Y3(X2,X9)) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
r2(X9,skolemFOFtoCNF_Y14(X2,X9)),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_11,plain,
r2(X_57,skolemFOFtoCNF_Y14(X2,X_57)),
inference(subst,[],[refute_0_10:[bind(X9,$fot(X_57))]]) ).
cnf(refute_0_12,plain,
( ~ r2(X11,X12)
| X12 = skolemFOFtoCNF_Y21(X11) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_13,plain,
( ~ r2(X_57,skolemFOFtoCNF_Y14(X2,X_57))
| skolemFOFtoCNF_Y14(X2,X_57) = skolemFOFtoCNF_Y21(X_57) ),
inference(subst,[],[refute_0_12:[bind(X11,$fot(X_57)),bind(X12,$fot(skolemFOFtoCNF_Y14(X2,X_57)))]]) ).
cnf(refute_0_14,plain,
skolemFOFtoCNF_Y14(X2,X_57) = skolemFOFtoCNF_Y21(X_57),
inference(resolve,[$cnf( r2(X_57,skolemFOFtoCNF_Y14(X2,X_57)) )],[refute_0_11,refute_0_13]) ).
cnf(refute_0_15,plain,
skolemFOFtoCNF_Y14(X2,X9) = skolemFOFtoCNF_Y21(X9),
inference(subst,[],[refute_0_14:[bind(X_57,$fot(X9))]]) ).
cnf(refute_0_16,plain,
( skolemFOFtoCNF_Y14(X2,X9) != skolemFOFtoCNF_Y21(X9)
| ~ r4(X2,skolemFOFtoCNF_Y14(X2,X9),skolemFOFtoCNF_Y2(X2,X9))
| r4(X2,skolemFOFtoCNF_Y21(X9),skolemFOFtoCNF_Y2(X2,X9)) ),
introduced(tautology,[equality,[$cnf( r4(X2,skolemFOFtoCNF_Y14(X2,X9),skolemFOFtoCNF_Y2(X2,X9)) ),[1],$fot(skolemFOFtoCNF_Y21(X9))]]) ).
cnf(refute_0_17,plain,
( ~ r4(X2,skolemFOFtoCNF_Y14(X2,X9),skolemFOFtoCNF_Y2(X2,X9))
| r4(X2,skolemFOFtoCNF_Y21(X9),skolemFOFtoCNF_Y2(X2,X9)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y14(X2,X9),skolemFOFtoCNF_Y21(X9)) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
r4(X2,skolemFOFtoCNF_Y21(X9),skolemFOFtoCNF_Y2(X2,X9)),
inference(resolve,[$cnf( r4(X2,skolemFOFtoCNF_Y14(X2,X9),skolemFOFtoCNF_Y2(X2,X9)) )],[refute_0_9,refute_0_17]) ).
cnf(refute_0_19,plain,
r4(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y2(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y24)),
inference(subst,[],[refute_0_18:[bind(X2,$fot(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24))),bind(X9,$fot(skolemFOFtoCNF_Y24))]]) ).
cnf(refute_0_20,plain,
( ~ r2(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y2(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y24))
| skolemFOFtoCNF_Y2(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y24) = skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24) ),
inference(subst,[],[refute_0_12:[bind(X11,$fot(skolemFOFtoCNF_Y24)),bind(X12,$fot(skolemFOFtoCNF_Y2(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y24)))]]) ).
cnf(refute_0_21,plain,
r2(skolemFOFtoCNF_Y7(X1,X8),skolemFOFtoCNF_Y4(X1,X8)),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_22,plain,
r3(X1,X8,skolemFOFtoCNF_Y7(X1,X8)),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_23,plain,
r3(X_81,X_82,skolemFOFtoCNF_Y7(X_81,X_82)),
inference(subst,[],[refute_0_22:[bind(X1,$fot(X_81)),bind(X8,$fot(X_82))]]) ).
cnf(refute_0_24,plain,
( ~ r3(X13,X14,X15)
| X15 = skolemFOFtoCNF_Y22(X13,X14) ),
inference(canonicalize,[],[normalize_0_29]) ).
cnf(refute_0_25,plain,
( ~ r3(X_81,X_82,skolemFOFtoCNF_Y7(X_81,X_82))
| skolemFOFtoCNF_Y7(X_81,X_82) = skolemFOFtoCNF_Y22(X_81,X_82) ),
inference(subst,[],[refute_0_24:[bind(X13,$fot(X_81)),bind(X14,$fot(X_82)),bind(X15,$fot(skolemFOFtoCNF_Y7(X_81,X_82)))]]) ).
cnf(refute_0_26,plain,
skolemFOFtoCNF_Y7(X_81,X_82) = skolemFOFtoCNF_Y22(X_81,X_82),
inference(resolve,[$cnf( r3(X_81,X_82,skolemFOFtoCNF_Y7(X_81,X_82)) )],[refute_0_23,refute_0_25]) ).
cnf(refute_0_27,plain,
skolemFOFtoCNF_Y7(X1,X8) = skolemFOFtoCNF_Y22(X1,X8),
inference(subst,[],[refute_0_26:[bind(X_81,$fot(X1)),bind(X_82,$fot(X8))]]) ).
cnf(refute_0_28,plain,
( skolemFOFtoCNF_Y7(X1,X8) != skolemFOFtoCNF_Y22(X1,X8)
| ~ r2(skolemFOFtoCNF_Y7(X1,X8),skolemFOFtoCNF_Y4(X1,X8))
| r2(skolemFOFtoCNF_Y22(X1,X8),skolemFOFtoCNF_Y4(X1,X8)) ),
introduced(tautology,[equality,[$cnf( r2(skolemFOFtoCNF_Y7(X1,X8),skolemFOFtoCNF_Y4(X1,X8)) ),[0],$fot(skolemFOFtoCNF_Y22(X1,X8))]]) ).
cnf(refute_0_29,plain,
( ~ r2(skolemFOFtoCNF_Y7(X1,X8),skolemFOFtoCNF_Y4(X1,X8))
| r2(skolemFOFtoCNF_Y22(X1,X8),skolemFOFtoCNF_Y4(X1,X8)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y7(X1,X8),skolemFOFtoCNF_Y22(X1,X8)) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
r2(skolemFOFtoCNF_Y22(X1,X8),skolemFOFtoCNF_Y4(X1,X8)),
inference(resolve,[$cnf( r2(skolemFOFtoCNF_Y7(X1,X8),skolemFOFtoCNF_Y4(X1,X8)) )],[refute_0_21,refute_0_29]) ).
cnf(refute_0_31,plain,
r2(skolemFOFtoCNF_Y22(X_97,skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y4(X_97,skolemFOFtoCNF_Y24)),
inference(subst,[],[refute_0_30:[bind(X1,$fot(X_97)),bind(X8,$fot(skolemFOFtoCNF_Y24))]]) ).
cnf(refute_0_32,plain,
r3(X4,skolemFOFtoCNF_Y16(X4),skolemFOFtoCNF_Y9(X4)),
inference(canonicalize,[],[normalize_0_35]) ).
cnf(refute_0_33,plain,
skolemFOFtoCNF_Y9(X4) = X4,
inference(canonicalize,[],[normalize_0_36]) ).
cnf(refute_0_34,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_35,plain,
( ~ r3(X4,skolemFOFtoCNF_Y16(X4),skolemFOFtoCNF_Y9(X4))
| r3(X4,skolemFOFtoCNF_Y16(X4),X4) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y9(X4),X4) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
r3(X4,skolemFOFtoCNF_Y16(X4),X4),
inference(resolve,[$cnf( r3(X4,skolemFOFtoCNF_Y16(X4),skolemFOFtoCNF_Y9(X4)) )],[refute_0_32,refute_0_35]) ).
cnf(refute_0_37,plain,
r1(skolemFOFtoCNF_Y16(X4)),
inference(canonicalize,[],[normalize_0_37]) ).
cnf(refute_0_38,plain,
( ~ r1(X19)
| X19 = skolemFOFtoCNF_Y24 ),
inference(canonicalize,[],[normalize_0_42]) ).
cnf(refute_0_39,plain,
( ~ r1(skolemFOFtoCNF_Y16(X4))
| skolemFOFtoCNF_Y16(X4) = skolemFOFtoCNF_Y24 ),
inference(subst,[],[refute_0_38:[bind(X19,$fot(skolemFOFtoCNF_Y16(X4)))]]) ).
cnf(refute_0_40,plain,
skolemFOFtoCNF_Y16(X4) = skolemFOFtoCNF_Y24,
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y16(X4)) )],[refute_0_37,refute_0_39]) ).
cnf(refute_0_41,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_42,plain,
( ~ r3(X4,skolemFOFtoCNF_Y16(X4),X4)
| r3(X4,skolemFOFtoCNF_Y24,X4) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y16(X4),skolemFOFtoCNF_Y24) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
r3(X4,skolemFOFtoCNF_Y24,X4),
inference(resolve,[$cnf( r3(X4,skolemFOFtoCNF_Y16(X4),X4) )],[refute_0_36,refute_0_42]) ).
cnf(refute_0_44,plain,
r3(X_83,skolemFOFtoCNF_Y24,X_83),
inference(subst,[],[refute_0_43:[bind(X4,$fot(X_83))]]) ).
cnf(refute_0_45,plain,
( ~ r3(X_83,skolemFOFtoCNF_Y24,X_83)
| X_83 = skolemFOFtoCNF_Y22(X_83,skolemFOFtoCNF_Y24) ),
inference(subst,[],[refute_0_24:[bind(X13,$fot(X_83)),bind(X14,$fot(skolemFOFtoCNF_Y24)),bind(X15,$fot(X_83))]]) ).
cnf(refute_0_46,plain,
X_83 = skolemFOFtoCNF_Y22(X_83,skolemFOFtoCNF_Y24),
inference(resolve,[$cnf( r3(X_83,skolemFOFtoCNF_Y24,X_83) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
X_97 = skolemFOFtoCNF_Y22(X_97,skolemFOFtoCNF_Y24),
inference(subst,[],[refute_0_46:[bind(X_83,$fot(X_97))]]) ).
cnf(refute_0_48,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_49,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_50,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
( X_97 != skolemFOFtoCNF_Y22(X_97,skolemFOFtoCNF_Y24)
| skolemFOFtoCNF_Y22(X_97,skolemFOFtoCNF_Y24) = X_97 ),
inference(subst,[],[refute_0_50:[bind(X,$fot(X_97)),bind(Y,$fot(skolemFOFtoCNF_Y22(X_97,skolemFOFtoCNF_Y24)))]]) ).
cnf(refute_0_52,plain,
skolemFOFtoCNF_Y22(X_97,skolemFOFtoCNF_Y24) = X_97,
inference(resolve,[$cnf( $equal(X_97,skolemFOFtoCNF_Y22(X_97,skolemFOFtoCNF_Y24)) )],[refute_0_47,refute_0_51]) ).
cnf(refute_0_53,plain,
( skolemFOFtoCNF_Y22(X_97,skolemFOFtoCNF_Y24) != X_97
| ~ r2(skolemFOFtoCNF_Y22(X_97,skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y4(X_97,skolemFOFtoCNF_Y24))
| r2(X_97,skolemFOFtoCNF_Y4(X_97,skolemFOFtoCNF_Y24)) ),
introduced(tautology,[equality,[$cnf( r2(skolemFOFtoCNF_Y22(X_97,skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y4(X_97,skolemFOFtoCNF_Y24)) ),[0],$fot(X_97)]]) ).
cnf(refute_0_54,plain,
( ~ r2(skolemFOFtoCNF_Y22(X_97,skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y4(X_97,skolemFOFtoCNF_Y24))
| r2(X_97,skolemFOFtoCNF_Y4(X_97,skolemFOFtoCNF_Y24)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y22(X_97,skolemFOFtoCNF_Y24),X_97) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
r2(X_97,skolemFOFtoCNF_Y4(X_97,skolemFOFtoCNF_Y24)),
inference(resolve,[$cnf( r2(skolemFOFtoCNF_Y22(X_97,skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y4(X_97,skolemFOFtoCNF_Y24)) )],[refute_0_31,refute_0_54]) ).
cnf(refute_0_56,plain,
r2(skolemFOFtoCNF_Y6(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),X_89),skolemFOFtoCNF_Y4(skolemFOFtoCNF_Y6(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),X_89),skolemFOFtoCNF_Y24)),
inference(subst,[],[refute_0_55:[bind(X_97,$fot(skolemFOFtoCNF_Y6(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),X_89)))]]) ).
cnf(refute_0_57,plain,
r3(X1,skolemFOFtoCNF_Y15(X1,X8),skolemFOFtoCNF_Y5(X1,X8)),
inference(canonicalize,[],[normalize_0_47]) ).
cnf(refute_0_58,plain,
skolemFOFtoCNF_Y5(X1,X8) = skolemFOFtoCNF_Y4(X1,X8),
inference(canonicalize,[],[normalize_0_48]) ).
cnf(refute_0_59,plain,
( skolemFOFtoCNF_Y5(X1,X8) != skolemFOFtoCNF_Y4(X1,X8)
| ~ r3(X1,skolemFOFtoCNF_Y15(X1,X8),skolemFOFtoCNF_Y5(X1,X8))
| r3(X1,skolemFOFtoCNF_Y15(X1,X8),skolemFOFtoCNF_Y4(X1,X8)) ),
introduced(tautology,[equality,[$cnf( r3(X1,skolemFOFtoCNF_Y15(X1,X8),skolemFOFtoCNF_Y5(X1,X8)) ),[2],$fot(skolemFOFtoCNF_Y4(X1,X8))]]) ).
cnf(refute_0_60,plain,
( ~ r3(X1,skolemFOFtoCNF_Y15(X1,X8),skolemFOFtoCNF_Y5(X1,X8))
| r3(X1,skolemFOFtoCNF_Y15(X1,X8),skolemFOFtoCNF_Y4(X1,X8)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y5(X1,X8),skolemFOFtoCNF_Y4(X1,X8)) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
r3(X1,skolemFOFtoCNF_Y15(X1,X8),skolemFOFtoCNF_Y4(X1,X8)),
inference(resolve,[$cnf( r3(X1,skolemFOFtoCNF_Y15(X1,X8),skolemFOFtoCNF_Y5(X1,X8)) )],[refute_0_57,refute_0_60]) ).
cnf(refute_0_62,plain,
r2(X8,skolemFOFtoCNF_Y15(X1,X8)),
inference(canonicalize,[],[normalize_0_49]) ).
cnf(refute_0_63,plain,
r2(X_57,skolemFOFtoCNF_Y15(X1,X_57)),
inference(subst,[],[refute_0_62:[bind(X8,$fot(X_57))]]) ).
cnf(refute_0_64,plain,
( ~ r2(X_57,skolemFOFtoCNF_Y15(X1,X_57))
| skolemFOFtoCNF_Y15(X1,X_57) = skolemFOFtoCNF_Y21(X_57) ),
inference(subst,[],[refute_0_12:[bind(X11,$fot(X_57)),bind(X12,$fot(skolemFOFtoCNF_Y15(X1,X_57)))]]) ).
cnf(refute_0_65,plain,
skolemFOFtoCNF_Y15(X1,X_57) = skolemFOFtoCNF_Y21(X_57),
inference(resolve,[$cnf( r2(X_57,skolemFOFtoCNF_Y15(X1,X_57)) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
skolemFOFtoCNF_Y15(X1,X8) = skolemFOFtoCNF_Y21(X8),
inference(subst,[],[refute_0_65:[bind(X_57,$fot(X8))]]) ).
cnf(refute_0_67,plain,
( skolemFOFtoCNF_Y15(X1,X8) != skolemFOFtoCNF_Y21(X8)
| ~ r3(X1,skolemFOFtoCNF_Y15(X1,X8),skolemFOFtoCNF_Y4(X1,X8))
| r3(X1,skolemFOFtoCNF_Y21(X8),skolemFOFtoCNF_Y4(X1,X8)) ),
introduced(tautology,[equality,[$cnf( r3(X1,skolemFOFtoCNF_Y15(X1,X8),skolemFOFtoCNF_Y4(X1,X8)) ),[1],$fot(skolemFOFtoCNF_Y21(X8))]]) ).
cnf(refute_0_68,plain,
( ~ r3(X1,skolemFOFtoCNF_Y15(X1,X8),skolemFOFtoCNF_Y4(X1,X8))
| r3(X1,skolemFOFtoCNF_Y21(X8),skolemFOFtoCNF_Y4(X1,X8)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y15(X1,X8),skolemFOFtoCNF_Y21(X8)) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
r3(X1,skolemFOFtoCNF_Y21(X8),skolemFOFtoCNF_Y4(X1,X8)),
inference(resolve,[$cnf( r3(X1,skolemFOFtoCNF_Y15(X1,X8),skolemFOFtoCNF_Y4(X1,X8)) )],[refute_0_61,refute_0_68]) ).
cnf(refute_0_70,plain,
r3(X_81,skolemFOFtoCNF_Y21(X8),skolemFOFtoCNF_Y4(X_81,X8)),
inference(subst,[],[refute_0_69:[bind(X1,$fot(X_81))]]) ).
cnf(refute_0_71,plain,
( ~ r3(X_81,skolemFOFtoCNF_Y21(X8),skolemFOFtoCNF_Y4(X_81,X8))
| skolemFOFtoCNF_Y4(X_81,X8) = skolemFOFtoCNF_Y22(X_81,skolemFOFtoCNF_Y21(X8)) ),
inference(subst,[],[refute_0_24:[bind(X13,$fot(X_81)),bind(X14,$fot(skolemFOFtoCNF_Y21(X8))),bind(X15,$fot(skolemFOFtoCNF_Y4(X_81,X8)))]]) ).
cnf(refute_0_72,plain,
skolemFOFtoCNF_Y4(X_81,X8) = skolemFOFtoCNF_Y22(X_81,skolemFOFtoCNF_Y21(X8)),
inference(resolve,[$cnf( r3(X_81,skolemFOFtoCNF_Y21(X8),skolemFOFtoCNF_Y4(X_81,X8)) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
skolemFOFtoCNF_Y4(skolemFOFtoCNF_Y6(skolemFOFtoCNF_Y21(X8),X_89),X8) = skolemFOFtoCNF_Y22(skolemFOFtoCNF_Y6(skolemFOFtoCNF_Y21(X8),X_89),skolemFOFtoCNF_Y21(X8)),
inference(subst,[],[refute_0_72:[bind(X_81,$fot(skolemFOFtoCNF_Y6(skolemFOFtoCNF_Y21(X8),X_89)))]]) ).
cnf(refute_0_74,plain,
r3(skolemFOFtoCNF_Y6(X2,X9),X2,skolemFOFtoCNF_Y2(X2,X9)),
inference(canonicalize,[],[normalize_0_52]) ).
cnf(refute_0_75,plain,
r3(skolemFOFtoCNF_Y6(X_82,X9),X_82,skolemFOFtoCNF_Y2(X_82,X9)),
inference(subst,[],[refute_0_74:[bind(X2,$fot(X_82))]]) ).
cnf(refute_0_76,plain,
( ~ r3(skolemFOFtoCNF_Y6(X_82,X9),X_82,skolemFOFtoCNF_Y2(X_82,X9))
| skolemFOFtoCNF_Y2(X_82,X9) = skolemFOFtoCNF_Y22(skolemFOFtoCNF_Y6(X_82,X9),X_82) ),
inference(subst,[],[refute_0_24:[bind(X13,$fot(skolemFOFtoCNF_Y6(X_82,X9))),bind(X14,$fot(X_82)),bind(X15,$fot(skolemFOFtoCNF_Y2(X_82,X9)))]]) ).
cnf(refute_0_77,plain,
skolemFOFtoCNF_Y2(X_82,X9) = skolemFOFtoCNF_Y22(skolemFOFtoCNF_Y6(X_82,X9),X_82),
inference(resolve,[$cnf( r3(skolemFOFtoCNF_Y6(X_82,X9),X_82,skolemFOFtoCNF_Y2(X_82,X9)) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
skolemFOFtoCNF_Y2(skolemFOFtoCNF_Y21(X8),X_89) = skolemFOFtoCNF_Y22(skolemFOFtoCNF_Y6(skolemFOFtoCNF_Y21(X8),X_89),skolemFOFtoCNF_Y21(X8)),
inference(subst,[],[refute_0_77:[bind(X9,$fot(X_89)),bind(X_82,$fot(skolemFOFtoCNF_Y21(X8)))]]) ).
cnf(refute_0_79,plain,
( skolemFOFtoCNF_Y2(skolemFOFtoCNF_Y21(X8),X_89) != skolemFOFtoCNF_Y22(skolemFOFtoCNF_Y6(skolemFOFtoCNF_Y21(X8),X_89),skolemFOFtoCNF_Y21(X8))
| skolemFOFtoCNF_Y22(skolemFOFtoCNF_Y6(skolemFOFtoCNF_Y21(X8),X_89),skolemFOFtoCNF_Y21(X8)) = skolemFOFtoCNF_Y2(skolemFOFtoCNF_Y21(X8),X_89) ),
inference(subst,[],[refute_0_50:[bind(X,$fot(skolemFOFtoCNF_Y2(skolemFOFtoCNF_Y21(X8),X_89))),bind(Y,$fot(skolemFOFtoCNF_Y22(skolemFOFtoCNF_Y6(skolemFOFtoCNF_Y21(X8),X_89),skolemFOFtoCNF_Y21(X8))))]]) ).
cnf(refute_0_80,plain,
skolemFOFtoCNF_Y22(skolemFOFtoCNF_Y6(skolemFOFtoCNF_Y21(X8),X_89),skolemFOFtoCNF_Y21(X8)) = skolemFOFtoCNF_Y2(skolemFOFtoCNF_Y21(X8),X_89),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y2(skolemFOFtoCNF_Y21(X8),X_89),skolemFOFtoCNF_Y22(skolemFOFtoCNF_Y6(skolemFOFtoCNF_Y21(X8),X_89),skolemFOFtoCNF_Y21(X8))) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
( skolemFOFtoCNF_Y22(skolemFOFtoCNF_Y6(skolemFOFtoCNF_Y21(X8),X_89),skolemFOFtoCNF_Y21(X8)) != skolemFOFtoCNF_Y2(skolemFOFtoCNF_Y21(X8),X_89)
| skolemFOFtoCNF_Y4(skolemFOFtoCNF_Y6(skolemFOFtoCNF_Y21(X8),X_89),X8) != skolemFOFtoCNF_Y22(skolemFOFtoCNF_Y6(skolemFOFtoCNF_Y21(X8),X_89),skolemFOFtoCNF_Y21(X8))
| skolemFOFtoCNF_Y4(skolemFOFtoCNF_Y6(skolemFOFtoCNF_Y21(X8),X_89),X8) = skolemFOFtoCNF_Y2(skolemFOFtoCNF_Y21(X8),X_89) ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_Y4(skolemFOFtoCNF_Y6(skolemFOFtoCNF_Y21(X8),X_89),X8),skolemFOFtoCNF_Y22(skolemFOFtoCNF_Y6(skolemFOFtoCNF_Y21(X8),X_89),skolemFOFtoCNF_Y21(X8))) ),[1],$fot(skolemFOFtoCNF_Y2(skolemFOFtoCNF_Y21(X8),X_89))]]) ).
cnf(refute_0_82,plain,
( skolemFOFtoCNF_Y4(skolemFOFtoCNF_Y6(skolemFOFtoCNF_Y21(X8),X_89),X8) != skolemFOFtoCNF_Y22(skolemFOFtoCNF_Y6(skolemFOFtoCNF_Y21(X8),X_89),skolemFOFtoCNF_Y21(X8))
| skolemFOFtoCNF_Y4(skolemFOFtoCNF_Y6(skolemFOFtoCNF_Y21(X8),X_89),X8) = skolemFOFtoCNF_Y2(skolemFOFtoCNF_Y21(X8),X_89) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y22(skolemFOFtoCNF_Y6(skolemFOFtoCNF_Y21(X8),X_89),skolemFOFtoCNF_Y21(X8)),skolemFOFtoCNF_Y2(skolemFOFtoCNF_Y21(X8),X_89)) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
skolemFOFtoCNF_Y4(skolemFOFtoCNF_Y6(skolemFOFtoCNF_Y21(X8),X_89),X8) = skolemFOFtoCNF_Y2(skolemFOFtoCNF_Y21(X8),X_89),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y4(skolemFOFtoCNF_Y6(skolemFOFtoCNF_Y21(X8),X_89),X8),skolemFOFtoCNF_Y22(skolemFOFtoCNF_Y6(skolemFOFtoCNF_Y21(X8),X_89),skolemFOFtoCNF_Y21(X8))) )],[refute_0_73,refute_0_82]) ).
cnf(refute_0_84,plain,
skolemFOFtoCNF_Y4(skolemFOFtoCNF_Y6(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),X_89),skolemFOFtoCNF_Y24) = skolemFOFtoCNF_Y2(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),X_89),
inference(subst,[],[refute_0_83:[bind(X8,$fot(skolemFOFtoCNF_Y24))]]) ).
cnf(refute_0_85,plain,
( skolemFOFtoCNF_Y4(skolemFOFtoCNF_Y6(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),X_89),skolemFOFtoCNF_Y24) != skolemFOFtoCNF_Y2(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),X_89)
| ~ r2(skolemFOFtoCNF_Y6(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),X_89),skolemFOFtoCNF_Y4(skolemFOFtoCNF_Y6(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),X_89),skolemFOFtoCNF_Y24))
| r2(skolemFOFtoCNF_Y6(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),X_89),skolemFOFtoCNF_Y2(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),X_89)) ),
introduced(tautology,[equality,[$cnf( r2(skolemFOFtoCNF_Y6(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),X_89),skolemFOFtoCNF_Y4(skolemFOFtoCNF_Y6(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),X_89),skolemFOFtoCNF_Y24)) ),[1],$fot(skolemFOFtoCNF_Y2(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),X_89))]]) ).
cnf(refute_0_86,plain,
( ~ r2(skolemFOFtoCNF_Y6(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),X_89),skolemFOFtoCNF_Y4(skolemFOFtoCNF_Y6(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),X_89),skolemFOFtoCNF_Y24))
| r2(skolemFOFtoCNF_Y6(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),X_89),skolemFOFtoCNF_Y2(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),X_89)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y4(skolemFOFtoCNF_Y6(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),X_89),skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y2(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),X_89)) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
r2(skolemFOFtoCNF_Y6(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),X_89),skolemFOFtoCNF_Y2(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),X_89)),
inference(resolve,[$cnf( r2(skolemFOFtoCNF_Y6(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),X_89),skolemFOFtoCNF_Y4(skolemFOFtoCNF_Y6(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),X_89),skolemFOFtoCNF_Y24)) )],[refute_0_56,refute_0_86]) ).
cnf(refute_0_88,plain,
r4(X2,X9,skolemFOFtoCNF_Y6(X2,X9)),
inference(canonicalize,[],[normalize_0_53]) ).
cnf(refute_0_89,plain,
r4(X_175,X_176,skolemFOFtoCNF_Y6(X_175,X_176)),
inference(subst,[],[refute_0_88:[bind(X2,$fot(X_175)),bind(X9,$fot(X_176))]]) ).
cnf(refute_0_90,plain,
( ~ r4(X16,X17,X18)
| X18 = skolemFOFtoCNF_Y23(X16,X17) ),
inference(canonicalize,[],[normalize_0_59]) ).
cnf(refute_0_91,plain,
( ~ r4(X_175,X_176,skolemFOFtoCNF_Y6(X_175,X_176))
| skolemFOFtoCNF_Y6(X_175,X_176) = skolemFOFtoCNF_Y23(X_175,X_176) ),
inference(subst,[],[refute_0_90:[bind(X16,$fot(X_175)),bind(X17,$fot(X_176)),bind(X18,$fot(skolemFOFtoCNF_Y6(X_175,X_176)))]]) ).
cnf(refute_0_92,plain,
skolemFOFtoCNF_Y6(X_175,X_176) = skolemFOFtoCNF_Y23(X_175,X_176),
inference(resolve,[$cnf( r4(X_175,X_176,skolemFOFtoCNF_Y6(X_175,X_176)) )],[refute_0_89,refute_0_91]) ).
cnf(refute_0_93,plain,
skolemFOFtoCNF_Y6(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),X_89) = skolemFOFtoCNF_Y23(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),X_89),
inference(subst,[],[refute_0_92:[bind(X_175,$fot(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24))),bind(X_176,$fot(X_89))]]) ).
cnf(refute_0_94,plain,
( skolemFOFtoCNF_Y6(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),X_89) != skolemFOFtoCNF_Y23(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),X_89)
| ~ r2(skolemFOFtoCNF_Y6(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),X_89),skolemFOFtoCNF_Y2(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),X_89))
| r2(skolemFOFtoCNF_Y23(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),X_89),skolemFOFtoCNF_Y2(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),X_89)) ),
introduced(tautology,[equality,[$cnf( r2(skolemFOFtoCNF_Y6(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),X_89),skolemFOFtoCNF_Y2(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),X_89)) ),[0],$fot(skolemFOFtoCNF_Y23(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),X_89))]]) ).
cnf(refute_0_95,plain,
( ~ r2(skolemFOFtoCNF_Y6(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),X_89),skolemFOFtoCNF_Y2(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),X_89))
| r2(skolemFOFtoCNF_Y23(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),X_89),skolemFOFtoCNF_Y2(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),X_89)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y6(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),X_89),skolemFOFtoCNF_Y23(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),X_89)) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
r2(skolemFOFtoCNF_Y23(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),X_89),skolemFOFtoCNF_Y2(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),X_89)),
inference(resolve,[$cnf( r2(skolemFOFtoCNF_Y6(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),X_89),skolemFOFtoCNF_Y2(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),X_89)) )],[refute_0_87,refute_0_95]) ).
cnf(refute_0_97,plain,
r2(skolemFOFtoCNF_Y23(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y2(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y24)),
inference(subst,[],[refute_0_96:[bind(X_89,$fot(skolemFOFtoCNF_Y24))]]) ).
cnf(refute_0_98,plain,
r4(X5,skolemFOFtoCNF_Y17(X5),skolemFOFtoCNF_Y8(X5)),
inference(canonicalize,[],[normalize_0_65]) ).
cnf(refute_0_99,plain,
skolemFOFtoCNF_Y8(X5) = skolemFOFtoCNF_Y18(X5),
inference(canonicalize,[],[normalize_0_68]) ).
cnf(refute_0_100,plain,
( skolemFOFtoCNF_Y8(X5) != skolemFOFtoCNF_Y18(X5)
| ~ r4(X5,skolemFOFtoCNF_Y17(X5),skolemFOFtoCNF_Y8(X5))
| r4(X5,skolemFOFtoCNF_Y17(X5),skolemFOFtoCNF_Y18(X5)) ),
introduced(tautology,[equality,[$cnf( r4(X5,skolemFOFtoCNF_Y17(X5),skolemFOFtoCNF_Y8(X5)) ),[2],$fot(skolemFOFtoCNF_Y18(X5))]]) ).
cnf(refute_0_101,plain,
( ~ r4(X5,skolemFOFtoCNF_Y17(X5),skolemFOFtoCNF_Y8(X5))
| r4(X5,skolemFOFtoCNF_Y17(X5),skolemFOFtoCNF_Y18(X5)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y8(X5),skolemFOFtoCNF_Y18(X5)) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
r4(X5,skolemFOFtoCNF_Y17(X5),skolemFOFtoCNF_Y18(X5)),
inference(resolve,[$cnf( r4(X5,skolemFOFtoCNF_Y17(X5),skolemFOFtoCNF_Y8(X5)) )],[refute_0_98,refute_0_101]) ).
cnf(refute_0_103,plain,
r1(skolemFOFtoCNF_Y17(X5)),
inference(canonicalize,[],[normalize_0_69]) ).
cnf(refute_0_104,plain,
( ~ r1(skolemFOFtoCNF_Y17(X5))
| skolemFOFtoCNF_Y17(X5) = skolemFOFtoCNF_Y24 ),
inference(subst,[],[refute_0_38:[bind(X19,$fot(skolemFOFtoCNF_Y17(X5)))]]) ).
cnf(refute_0_105,plain,
skolemFOFtoCNF_Y17(X5) = skolemFOFtoCNF_Y24,
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y17(X5)) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
( skolemFOFtoCNF_Y17(X5) != skolemFOFtoCNF_Y24
| ~ r4(X5,skolemFOFtoCNF_Y17(X5),skolemFOFtoCNF_Y18(X5))
| r4(X5,skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y18(X5)) ),
introduced(tautology,[equality,[$cnf( r4(X5,skolemFOFtoCNF_Y17(X5),skolemFOFtoCNF_Y18(X5)) ),[1],$fot(skolemFOFtoCNF_Y24)]]) ).
cnf(refute_0_107,plain,
( ~ r4(X5,skolemFOFtoCNF_Y17(X5),skolemFOFtoCNF_Y18(X5))
| r4(X5,skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y18(X5)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y17(X5),skolemFOFtoCNF_Y24) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
r1(skolemFOFtoCNF_Y18(X5)),
inference(canonicalize,[],[normalize_0_70]) ).
cnf(refute_0_109,plain,
( ~ r1(skolemFOFtoCNF_Y18(X5))
| skolemFOFtoCNF_Y18(X5) = skolemFOFtoCNF_Y24 ),
inference(subst,[],[refute_0_38:[bind(X19,$fot(skolemFOFtoCNF_Y18(X5)))]]) ).
cnf(refute_0_110,plain,
skolemFOFtoCNF_Y18(X5) = skolemFOFtoCNF_Y24,
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y18(X5)) )],[refute_0_108,refute_0_109]) ).
cnf(refute_0_111,plain,
( skolemFOFtoCNF_Y18(X5) != skolemFOFtoCNF_Y24
| ~ r4(X5,skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y18(X5))
| r4(X5,skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y24) ),
introduced(tautology,[equality,[$cnf( r4(X5,skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y18(X5)) ),[2],$fot(skolemFOFtoCNF_Y24)]]) ).
cnf(refute_0_112,plain,
( ~ r4(X5,skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y18(X5))
| r4(X5,skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y24) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y18(X5),skolemFOFtoCNF_Y24) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
( ~ r4(X5,skolemFOFtoCNF_Y17(X5),skolemFOFtoCNF_Y18(X5))
| r4(X5,skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y24) ),
inference(resolve,[$cnf( r4(X5,skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y18(X5)) )],[refute_0_107,refute_0_112]) ).
cnf(refute_0_114,plain,
r4(X5,skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y24),
inference(resolve,[$cnf( r4(X5,skolemFOFtoCNF_Y17(X5),skolemFOFtoCNF_Y18(X5)) )],[refute_0_102,refute_0_113]) ).
cnf(refute_0_115,plain,
r4(X_175,skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y24),
inference(subst,[],[refute_0_114:[bind(X5,$fot(X_175))]]) ).
cnf(refute_0_116,plain,
( ~ r4(X_175,skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y24)
| skolemFOFtoCNF_Y24 = skolemFOFtoCNF_Y23(X_175,skolemFOFtoCNF_Y24) ),
inference(subst,[],[refute_0_90:[bind(X16,$fot(X_175)),bind(X17,$fot(skolemFOFtoCNF_Y24)),bind(X18,$fot(skolemFOFtoCNF_Y24))]]) ).
cnf(refute_0_117,plain,
skolemFOFtoCNF_Y24 = skolemFOFtoCNF_Y23(X_175,skolemFOFtoCNF_Y24),
inference(resolve,[$cnf( r4(X_175,skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y24) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
skolemFOFtoCNF_Y24 = skolemFOFtoCNF_Y23(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y24),
inference(subst,[],[refute_0_117:[bind(X_175,$fot(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)))]]) ).
cnf(refute_0_119,plain,
( skolemFOFtoCNF_Y24 != skolemFOFtoCNF_Y23(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y24)
| skolemFOFtoCNF_Y23(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y24) = skolemFOFtoCNF_Y24 ),
inference(subst,[],[refute_0_50:[bind(X,$fot(skolemFOFtoCNF_Y24)),bind(Y,$fot(skolemFOFtoCNF_Y23(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y24)))]]) ).
cnf(refute_0_120,plain,
skolemFOFtoCNF_Y23(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y24) = skolemFOFtoCNF_Y24,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y23(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y24)) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
( skolemFOFtoCNF_Y23(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y24) != skolemFOFtoCNF_Y24
| ~ r2(skolemFOFtoCNF_Y23(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y2(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y24))
| r2(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y2(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y24)) ),
introduced(tautology,[equality,[$cnf( r2(skolemFOFtoCNF_Y23(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y2(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y24)) ),[0],$fot(skolemFOFtoCNF_Y24)]]) ).
cnf(refute_0_122,plain,
( ~ r2(skolemFOFtoCNF_Y23(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y2(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y24))
| r2(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y2(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y24)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y23(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y24) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
r2(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y2(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y24)),
inference(resolve,[$cnf( r2(skolemFOFtoCNF_Y23(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y2(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y24)) )],[refute_0_97,refute_0_122]) ).
cnf(refute_0_124,plain,
skolemFOFtoCNF_Y2(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y24) = skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),
inference(resolve,[$cnf( r2(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y2(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y24)) )],[refute_0_123,refute_0_20]) ).
cnf(refute_0_125,plain,
( skolemFOFtoCNF_Y2(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y24) != skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)
| ~ r4(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y2(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y24))
| r4(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)) ),
introduced(tautology,[equality,[$cnf( r4(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y2(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y24)) ),[2],$fot(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24))]]) ).
cnf(refute_0_126,plain,
( ~ r4(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y2(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y24))
| r4(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y2(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
r4(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)),
inference(resolve,[$cnf( r4(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y2(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y24)) )],[refute_0_19,refute_0_126]) ).
cnf(refute_0_128,plain,
( Y1 != Y3
| ~ r1(Y4)
| ~ r1(Y5)
| ~ r2(Y4,Y2)
| ~ r2(Y5,Y3)
| ~ r4(Y2,Y2,Y1) ),
inference(canonicalize,[],[normalize_0_73]) ).
cnf(refute_0_129,plain,
( Y3 != Y3
| ~ r1(Y4)
| ~ r1(Y5)
| ~ r2(Y4,Y2)
| ~ r2(Y5,Y3)
| ~ r4(Y2,Y2,Y3) ),
inference(subst,[],[refute_0_128:[bind(Y1,$fot(Y3))]]) ).
cnf(refute_0_130,plain,
Y3 = Y3,
introduced(tautology,[refl,[$fot(Y3)]]) ).
cnf(refute_0_131,plain,
( ~ r1(Y4)
| ~ r1(Y5)
| ~ r2(Y4,Y2)
| ~ r2(Y5,Y3)
| ~ r4(Y2,Y2,Y3) ),
inference(resolve,[$cnf( $equal(Y3,Y3) )],[refute_0_130,refute_0_129]) ).
cnf(refute_0_132,plain,
( ~ r1(X_384)
| ~ r2(X_384,skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24))
| ~ r4(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)) ),
inference(subst,[],[refute_0_131:[bind(Y2,$fot(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24))),bind(Y3,$fot(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24))),bind(Y4,$fot(X_384)),bind(Y5,$fot(X_384))]]) ).
cnf(refute_0_133,plain,
( ~ r1(X_384)
| ~ r2(X_384,skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)) ),
inference(resolve,[$cnf( r4(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)) )],[refute_0_127,refute_0_132]) ).
cnf(refute_0_134,plain,
( ~ r1(skolemFOFtoCNF_Y24)
| ~ r2(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)) ),
inference(subst,[],[refute_0_133:[bind(X_384,$fot(skolemFOFtoCNF_Y24))]]) ).
cnf(refute_0_135,plain,
~ r1(skolemFOFtoCNF_Y24),
inference(resolve,[$cnf( r2(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)) )],[refute_0_4,refute_0_134]) ).
cnf(refute_0_136,plain,
( X19 != skolemFOFtoCNF_Y24
| r1(X19) ),
inference(canonicalize,[],[normalize_0_74]) ).
cnf(refute_0_137,plain,
( skolemFOFtoCNF_Y24 != skolemFOFtoCNF_Y24
| r1(skolemFOFtoCNF_Y24) ),
inference(subst,[],[refute_0_136:[bind(X19,$fot(skolemFOFtoCNF_Y24))]]) ).
cnf(refute_0_138,plain,
skolemFOFtoCNF_Y24 = skolemFOFtoCNF_Y24,
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_Y24)]]) ).
cnf(refute_0_139,plain,
r1(skolemFOFtoCNF_Y24),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y24) )],[refute_0_138,refute_0_137]) ).
cnf(refute_0_140,plain,
$false,
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y24) )],[refute_0_139,refute_0_135]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUN071+2 : TPTP v8.1.0. Released v7.3.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 2 04:24:45 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.99/1.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.99/1.20
% 0.99/1.20 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.99/1.22
%------------------------------------------------------------------------------