TSTP Solution File: NUN085+2 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUN085+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n017.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 16:34:57 EDT 2022
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 19
% Syntax : Number of formulae : 139 ( 52 unt; 0 def)
% Number of atoms : 315 ( 118 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 310 ( 134 ~; 95 |; 77 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 204 ( 11 sgn 96 !; 45 ?)
% 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_7a,axiom,
! [X7,Y10] :
( ! [Y20] :
( ~ r1(Y20)
| Y20 != Y10 )
| ~ r2(X7,Y10) ) ).
fof(zeroplusoneidzero,conjecture,
! [Y1] :
( ! [Y2] :
( ! [Y3] :
( ~ r1(Y3)
| ~ r3(Y3,Y2,Y1) )
| ! [Y4] :
( ~ r1(Y4)
| ~ r2(Y4,Y2) ) )
| ! [Y5] :
( Y1 != Y5
| ~ r1(Y5) ) ) ).
fof(subgoal_0,plain,
! [Y1] :
( ~ ! [Y2] :
( ! [Y3] :
( ~ r1(Y3)
| ~ r3(Y3,Y2,Y1) )
| ! [Y4] :
( ~ r1(Y4)
| ~ r2(Y4,Y2) ) )
=> ! [Y5] :
( ~ ( Y1 != Y5 )
=> ~ r1(Y5) ) ),
inference(strip,[],[zeroplusoneidzero]) ).
fof(negate_0_0,plain,
~ ! [Y1] :
( ~ ! [Y2] :
( ! [Y3] :
( ~ r1(Y3)
| ~ r3(Y3,Y2,Y1) )
| ! [Y4] :
( ~ r1(Y4)
| ~ r2(Y4,Y2) ) )
=> ! [Y5] :
( ~ ( Y1 != Y5 )
=> ~ r1(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,
! [X1,X8] :
? [Y5] :
( Y5 = skolemFOFtoCNF_Y4(X1,X8)
& ? [Y15] :
( r2(X8,Y15)
& r3(X1,Y15,Y5) ) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_10,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_9]) ).
fof(normalize_0_11,plain,
! [X1,X8] :
? [Y15] :
( r2(X8,Y15)
& r3(X1,Y15,skolemFOFtoCNF_Y5(X1,X8)) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [X1,X8] :
( r2(X8,skolemFOFtoCNF_Y15(X1,X8))
& r3(X1,skolemFOFtoCNF_Y15(X1,X8),skolemFOFtoCNF_Y5(X1,X8)) ),
inference(skolemize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [X1,X8] : r3(X1,skolemFOFtoCNF_Y15(X1,X8),skolemFOFtoCNF_Y5(X1,X8)),
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [X1,X8] : skolemFOFtoCNF_Y5(X1,X8) = skolemFOFtoCNF_Y4(X1,X8),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_15,plain,
! [X1,X8] : r2(X8,skolemFOFtoCNF_Y15(X1,X8)),
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_16,plain,
! [X11] :
? [Y21] :
! [X12] :
( ( X12 != Y21
& ~ r2(X11,X12) )
| ( X12 = Y21
& r2(X11,X12) ) ),
inference(canonicalize,[],[axiom_2]) ).
fof(normalize_0_17,plain,
! [X11] :
? [Y21] :
! [X12] :
( ( X12 != Y21
& ~ r2(X11,X12) )
| ( X12 = Y21
& r2(X11,X12) ) ),
inference(specialize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [X11,X12] :
( ( X12 != skolemFOFtoCNF_Y21(X11)
& ~ r2(X11,X12) )
| ( X12 = skolemFOFtoCNF_Y21(X11)
& r2(X11,X12) ) ),
inference(skolemize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [X11,X12] :
( ( X12 != skolemFOFtoCNF_Y21(X11)
& ~ r2(X11,X12) )
| ( X12 = skolemFOFtoCNF_Y21(X11)
& r2(X11,X12) ) ),
inference(specialize,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [X11,X12] :
( ( X12 != skolemFOFtoCNF_Y21(X11)
| r2(X11,X12) )
& ( ~ r2(X11,X12)
| X12 = skolemFOFtoCNF_Y21(X11) ) ),
inference(clausify,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [X11,X12] :
( ~ r2(X11,X12)
| X12 = skolemFOFtoCNF_Y21(X11) ),
inference(conjunct,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
? [Y1] :
( ? [Y2] :
( ? [Y3] :
( r1(Y3)
& r3(Y3,Y2,Y1) )
& ? [Y4] :
( r1(Y4)
& r2(Y4,Y2) ) )
& ? [Y5] :
( Y1 = Y5
& r1(Y5) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_23,plain,
( ? [Y2] :
( ? [Y3] :
( r1(Y3)
& r3(Y3,Y2,skolemFOFtoCNF_Y1_1) )
& ? [Y4] :
( r1(Y4)
& r2(Y4,Y2) ) )
& ? [Y5] :
( skolemFOFtoCNF_Y1_1 = Y5
& r1(Y5) ) ),
inference(skolemize,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
? [Y2] :
( ? [Y3] :
( r1(Y3)
& r3(Y3,Y2,skolemFOFtoCNF_Y1_1) )
& ? [Y4] :
( r1(Y4)
& r2(Y4,Y2) ) ),
inference(conjunct,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
( ? [Y3] :
( r1(Y3)
& r3(Y3,skolemFOFtoCNF_Y2_1,skolemFOFtoCNF_Y1_1) )
& ? [Y4] :
( r1(Y4)
& r2(Y4,skolemFOFtoCNF_Y2_1) ) ),
inference(skolemize,[],[normalize_0_24]) ).
fof(normalize_0_26,plain,
? [Y4] :
( r1(Y4)
& r2(Y4,skolemFOFtoCNF_Y2_1) ),
inference(conjunct,[],[normalize_0_25]) ).
fof(normalize_0_27,plain,
( r1(skolemFOFtoCNF_Y4_1)
& r2(skolemFOFtoCNF_Y4_1,skolemFOFtoCNF_Y2_1) ),
inference(skolemize,[],[normalize_0_26]) ).
fof(normalize_0_28,plain,
r2(skolemFOFtoCNF_Y4_1,skolemFOFtoCNF_Y2_1),
inference(conjunct,[],[normalize_0_27]) ).
fof(normalize_0_29,plain,
r1(skolemFOFtoCNF_Y4_1),
inference(conjunct,[],[normalize_0_27]) ).
fof(normalize_0_30,plain,
? [Y24] :
! [X19] :
( ( X19 != Y24
& ~ r1(X19) )
| ( X19 = Y24
& r1(X19) ) ),
inference(canonicalize,[],[axiom_1]) ).
fof(normalize_0_31,plain,
! [X19] :
( ( X19 != skolemFOFtoCNF_Y24
& ~ r1(X19) )
| ( X19 = skolemFOFtoCNF_Y24
& r1(X19) ) ),
inference(skolemize,[],[normalize_0_30]) ).
fof(normalize_0_32,plain,
! [X19] :
( ( X19 != skolemFOFtoCNF_Y24
& ~ r1(X19) )
| ( X19 = skolemFOFtoCNF_Y24
& r1(X19) ) ),
inference(specialize,[],[normalize_0_31]) ).
fof(normalize_0_33,plain,
! [X19] :
( ( X19 != skolemFOFtoCNF_Y24
| r1(X19) )
& ( ~ r1(X19)
| X19 = skolemFOFtoCNF_Y24 ) ),
inference(clausify,[],[normalize_0_32]) ).
fof(normalize_0_34,plain,
! [X19] :
( ~ r1(X19)
| X19 = skolemFOFtoCNF_Y24 ),
inference(conjunct,[],[normalize_0_33]) ).
fof(normalize_0_35,plain,
? [Y5] :
( skolemFOFtoCNF_Y1_1 = Y5
& r1(Y5) ),
inference(conjunct,[],[normalize_0_23]) ).
fof(normalize_0_36,plain,
( skolemFOFtoCNF_Y1_1 = skolemFOFtoCNF_Y5_1
& r1(skolemFOFtoCNF_Y5_1) ),
inference(skolemize,[],[normalize_0_35]) ).
fof(normalize_0_37,plain,
r1(skolemFOFtoCNF_Y5_1),
inference(conjunct,[],[normalize_0_36]) ).
fof(normalize_0_38,plain,
skolemFOFtoCNF_Y1_1 = skolemFOFtoCNF_Y5_1,
inference(conjunct,[],[normalize_0_36]) ).
fof(normalize_0_39,plain,
! [X13,X14] :
? [Y22] :
! [X15] :
( ( X15 != Y22
& ~ r3(X13,X14,X15) )
| ( X15 = Y22
& r3(X13,X14,X15) ) ),
inference(canonicalize,[],[axiom_3]) ).
fof(normalize_0_40,plain,
! [X13,X14] :
? [Y22] :
! [X15] :
( ( X15 != Y22
& ~ r3(X13,X14,X15) )
| ( X15 = Y22
& r3(X13,X14,X15) ) ),
inference(specialize,[],[normalize_0_39]) ).
fof(normalize_0_41,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_40]) ).
fof(normalize_0_42,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_41]) ).
fof(normalize_0_43,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_42]) ).
fof(normalize_0_44,plain,
! [X13,X14,X15] :
( ~ r3(X13,X14,X15)
| X15 = skolemFOFtoCNF_Y22(X13,X14) ),
inference(conjunct,[],[normalize_0_43]) ).
fof(normalize_0_45,plain,
? [Y3] :
( r1(Y3)
& r3(Y3,skolemFOFtoCNF_Y2_1,skolemFOFtoCNF_Y1_1) ),
inference(conjunct,[],[normalize_0_25]) ).
fof(normalize_0_46,plain,
( r1(skolemFOFtoCNF_Y3_1)
& r3(skolemFOFtoCNF_Y3_1,skolemFOFtoCNF_Y2_1,skolemFOFtoCNF_Y1_1) ),
inference(skolemize,[],[normalize_0_45]) ).
fof(normalize_0_47,plain,
r3(skolemFOFtoCNF_Y3_1,skolemFOFtoCNF_Y2_1,skolemFOFtoCNF_Y1_1),
inference(conjunct,[],[normalize_0_46]) ).
fof(normalize_0_48,plain,
r1(skolemFOFtoCNF_Y3_1),
inference(conjunct,[],[normalize_0_46]) ).
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_Y4(X1,skolemFOFtoCNF_Y1_1)),
inference(subst,[],[refute_0_6:[bind(X8,$fot(skolemFOFtoCNF_Y1_1))]]) ).
cnf(refute_0_8,plain,
r3(X1,skolemFOFtoCNF_Y15(X1,X8),skolemFOFtoCNF_Y5(X1,X8)),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_9,plain,
skolemFOFtoCNF_Y5(X1,X8) = skolemFOFtoCNF_Y4(X1,X8),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_10,plain,
( skolemFOFtoCNF_Y5(X1,X8) != skolemFOFtoCNF_Y4(X1,X8)
| ~ r3(X1,skolemFOFtoCNF_Y15(X1,X8),skolemFOFtoCNF_Y5(X1,X8))
| r3(X1,skolemFOFtoCNF_Y15(X1,X8),skolemFOFtoCNF_Y4(X1,X8)) ),
introduced(tautology,[equality,[$cnf( r3(X1,skolemFOFtoCNF_Y15(X1,X8),skolemFOFtoCNF_Y5(X1,X8)) ),[2],$fot(skolemFOFtoCNF_Y4(X1,X8))]]) ).
cnf(refute_0_11,plain,
( ~ r3(X1,skolemFOFtoCNF_Y15(X1,X8),skolemFOFtoCNF_Y5(X1,X8))
| r3(X1,skolemFOFtoCNF_Y15(X1,X8),skolemFOFtoCNF_Y4(X1,X8)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y5(X1,X8),skolemFOFtoCNF_Y4(X1,X8)) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
r3(X1,skolemFOFtoCNF_Y15(X1,X8),skolemFOFtoCNF_Y4(X1,X8)),
inference(resolve,[$cnf( r3(X1,skolemFOFtoCNF_Y15(X1,X8),skolemFOFtoCNF_Y5(X1,X8)) )],[refute_0_8,refute_0_11]) ).
cnf(refute_0_13,plain,
r2(X8,skolemFOFtoCNF_Y15(X1,X8)),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_14,plain,
r2(X_58,skolemFOFtoCNF_Y15(X1,X_58)),
inference(subst,[],[refute_0_13:[bind(X8,$fot(X_58))]]) ).
cnf(refute_0_15,plain,
( ~ r2(X11,X12)
| X12 = skolemFOFtoCNF_Y21(X11) ),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_16,plain,
( ~ r2(X_58,skolemFOFtoCNF_Y15(X1,X_58))
| skolemFOFtoCNF_Y15(X1,X_58) = skolemFOFtoCNF_Y21(X_58) ),
inference(subst,[],[refute_0_15:[bind(X11,$fot(X_58)),bind(X12,$fot(skolemFOFtoCNF_Y15(X1,X_58)))]]) ).
cnf(refute_0_17,plain,
skolemFOFtoCNF_Y15(X1,X_58) = skolemFOFtoCNF_Y21(X_58),
inference(resolve,[$cnf( r2(X_58,skolemFOFtoCNF_Y15(X1,X_58)) )],[refute_0_14,refute_0_16]) ).
cnf(refute_0_18,plain,
skolemFOFtoCNF_Y15(X1,X8) = skolemFOFtoCNF_Y21(X8),
inference(subst,[],[refute_0_17:[bind(X_58,$fot(X8))]]) ).
cnf(refute_0_19,plain,
( skolemFOFtoCNF_Y15(X1,X8) != skolemFOFtoCNF_Y21(X8)
| ~ r3(X1,skolemFOFtoCNF_Y15(X1,X8),skolemFOFtoCNF_Y4(X1,X8))
| r3(X1,skolemFOFtoCNF_Y21(X8),skolemFOFtoCNF_Y4(X1,X8)) ),
introduced(tautology,[equality,[$cnf( r3(X1,skolemFOFtoCNF_Y15(X1,X8),skolemFOFtoCNF_Y4(X1,X8)) ),[1],$fot(skolemFOFtoCNF_Y21(X8))]]) ).
cnf(refute_0_20,plain,
( ~ r3(X1,skolemFOFtoCNF_Y15(X1,X8),skolemFOFtoCNF_Y4(X1,X8))
| r3(X1,skolemFOFtoCNF_Y21(X8),skolemFOFtoCNF_Y4(X1,X8)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y15(X1,X8),skolemFOFtoCNF_Y21(X8)) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
r3(X1,skolemFOFtoCNF_Y21(X8),skolemFOFtoCNF_Y4(X1,X8)),
inference(resolve,[$cnf( r3(X1,skolemFOFtoCNF_Y15(X1,X8),skolemFOFtoCNF_Y4(X1,X8)) )],[refute_0_12,refute_0_20]) ).
cnf(refute_0_22,plain,
r3(X_66,skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y1_1),skolemFOFtoCNF_Y4(X_66,skolemFOFtoCNF_Y1_1)),
inference(subst,[],[refute_0_21:[bind(X1,$fot(X_66)),bind(X8,$fot(skolemFOFtoCNF_Y1_1))]]) ).
cnf(refute_0_23,plain,
r2(skolemFOFtoCNF_Y4_1,skolemFOFtoCNF_Y2_1),
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_24,plain,
r1(skolemFOFtoCNF_Y4_1),
inference(canonicalize,[],[normalize_0_29]) ).
cnf(refute_0_25,plain,
( ~ r1(X19)
| X19 = skolemFOFtoCNF_Y24 ),
inference(canonicalize,[],[normalize_0_34]) ).
cnf(refute_0_26,plain,
( ~ r1(skolemFOFtoCNF_Y4_1)
| skolemFOFtoCNF_Y4_1 = skolemFOFtoCNF_Y24 ),
inference(subst,[],[refute_0_25:[bind(X19,$fot(skolemFOFtoCNF_Y4_1))]]) ).
cnf(refute_0_27,plain,
skolemFOFtoCNF_Y4_1 = skolemFOFtoCNF_Y24,
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y4_1) )],[refute_0_24,refute_0_26]) ).
cnf(refute_0_28,plain,
r1(skolemFOFtoCNF_Y5_1),
inference(canonicalize,[],[normalize_0_37]) ).
cnf(refute_0_29,plain,
skolemFOFtoCNF_Y1_1 = skolemFOFtoCNF_Y5_1,
inference(canonicalize,[],[normalize_0_38]) ).
cnf(refute_0_30,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_31,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_32,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
( skolemFOFtoCNF_Y1_1 != skolemFOFtoCNF_Y5_1
| skolemFOFtoCNF_Y5_1 = skolemFOFtoCNF_Y1_1 ),
inference(subst,[],[refute_0_32:[bind(X,$fot(skolemFOFtoCNF_Y1_1)),bind(Y,$fot(skolemFOFtoCNF_Y5_1))]]) ).
cnf(refute_0_34,plain,
skolemFOFtoCNF_Y5_1 = skolemFOFtoCNF_Y1_1,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y1_1,skolemFOFtoCNF_Y5_1) )],[refute_0_29,refute_0_33]) ).
cnf(refute_0_35,plain,
( skolemFOFtoCNF_Y5_1 != skolemFOFtoCNF_Y1_1
| ~ r1(skolemFOFtoCNF_Y5_1)
| r1(skolemFOFtoCNF_Y1_1) ),
introduced(tautology,[equality,[$cnf( r1(skolemFOFtoCNF_Y5_1) ),[0],$fot(skolemFOFtoCNF_Y1_1)]]) ).
cnf(refute_0_36,plain,
( ~ r1(skolemFOFtoCNF_Y5_1)
| r1(skolemFOFtoCNF_Y1_1) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y5_1,skolemFOFtoCNF_Y1_1) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
r1(skolemFOFtoCNF_Y1_1),
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y5_1) )],[refute_0_28,refute_0_36]) ).
cnf(refute_0_38,plain,
( ~ r1(skolemFOFtoCNF_Y1_1)
| skolemFOFtoCNF_Y1_1 = skolemFOFtoCNF_Y24 ),
inference(subst,[],[refute_0_25:[bind(X19,$fot(skolemFOFtoCNF_Y1_1))]]) ).
cnf(refute_0_39,plain,
skolemFOFtoCNF_Y1_1 = skolemFOFtoCNF_Y24,
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y1_1) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
( skolemFOFtoCNF_Y1_1 != skolemFOFtoCNF_Y24
| skolemFOFtoCNF_Y24 = skolemFOFtoCNF_Y1_1 ),
inference(subst,[],[refute_0_32:[bind(X,$fot(skolemFOFtoCNF_Y1_1)),bind(Y,$fot(skolemFOFtoCNF_Y24))]]) ).
cnf(refute_0_41,plain,
skolemFOFtoCNF_Y24 = skolemFOFtoCNF_Y1_1,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y1_1,skolemFOFtoCNF_Y24) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
( skolemFOFtoCNF_Y24 != skolemFOFtoCNF_Y1_1
| skolemFOFtoCNF_Y4_1 != skolemFOFtoCNF_Y24
| skolemFOFtoCNF_Y4_1 = skolemFOFtoCNF_Y1_1 ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_Y4_1,skolemFOFtoCNF_Y24) ),[1],$fot(skolemFOFtoCNF_Y1_1)]]) ).
cnf(refute_0_43,plain,
( skolemFOFtoCNF_Y4_1 != skolemFOFtoCNF_Y24
| skolemFOFtoCNF_Y4_1 = skolemFOFtoCNF_Y1_1 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y1_1) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
skolemFOFtoCNF_Y4_1 = skolemFOFtoCNF_Y1_1,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y4_1,skolemFOFtoCNF_Y24) )],[refute_0_27,refute_0_43]) ).
cnf(refute_0_45,plain,
( skolemFOFtoCNF_Y4_1 != skolemFOFtoCNF_Y1_1
| ~ r2(skolemFOFtoCNF_Y4_1,skolemFOFtoCNF_Y2_1)
| r2(skolemFOFtoCNF_Y1_1,skolemFOFtoCNF_Y2_1) ),
introduced(tautology,[equality,[$cnf( r2(skolemFOFtoCNF_Y4_1,skolemFOFtoCNF_Y2_1) ),[0],$fot(skolemFOFtoCNF_Y1_1)]]) ).
cnf(refute_0_46,plain,
( ~ r2(skolemFOFtoCNF_Y4_1,skolemFOFtoCNF_Y2_1)
| r2(skolemFOFtoCNF_Y1_1,skolemFOFtoCNF_Y2_1) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y4_1,skolemFOFtoCNF_Y1_1) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
r2(skolemFOFtoCNF_Y1_1,skolemFOFtoCNF_Y2_1),
inference(resolve,[$cnf( r2(skolemFOFtoCNF_Y4_1,skolemFOFtoCNF_Y2_1) )],[refute_0_23,refute_0_46]) ).
cnf(refute_0_48,plain,
( ~ r2(skolemFOFtoCNF_Y1_1,skolemFOFtoCNF_Y2_1)
| skolemFOFtoCNF_Y2_1 = skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y1_1) ),
inference(subst,[],[refute_0_15:[bind(X11,$fot(skolemFOFtoCNF_Y1_1)),bind(X12,$fot(skolemFOFtoCNF_Y2_1))]]) ).
cnf(refute_0_49,plain,
skolemFOFtoCNF_Y2_1 = skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y1_1),
inference(resolve,[$cnf( r2(skolemFOFtoCNF_Y1_1,skolemFOFtoCNF_Y2_1) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
( skolemFOFtoCNF_Y2_1 != skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y1_1)
| skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y1_1) = skolemFOFtoCNF_Y2_1 ),
inference(subst,[],[refute_0_32:[bind(X,$fot(skolemFOFtoCNF_Y2_1)),bind(Y,$fot(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y1_1)))]]) ).
cnf(refute_0_51,plain,
skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y1_1) = skolemFOFtoCNF_Y2_1,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y2_1,skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y1_1)) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
( skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y1_1) != skolemFOFtoCNF_Y2_1
| ~ r3(X_66,skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y1_1),skolemFOFtoCNF_Y4(X_66,skolemFOFtoCNF_Y1_1))
| r3(X_66,skolemFOFtoCNF_Y2_1,skolemFOFtoCNF_Y4(X_66,skolemFOFtoCNF_Y1_1)) ),
introduced(tautology,[equality,[$cnf( r3(X_66,skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y1_1),skolemFOFtoCNF_Y4(X_66,skolemFOFtoCNF_Y1_1)) ),[1],$fot(skolemFOFtoCNF_Y2_1)]]) ).
cnf(refute_0_53,plain,
( ~ r3(X_66,skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y1_1),skolemFOFtoCNF_Y4(X_66,skolemFOFtoCNF_Y1_1))
| r3(X_66,skolemFOFtoCNF_Y2_1,skolemFOFtoCNF_Y4(X_66,skolemFOFtoCNF_Y1_1)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y1_1),skolemFOFtoCNF_Y2_1) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
r3(X_66,skolemFOFtoCNF_Y2_1,skolemFOFtoCNF_Y4(X_66,skolemFOFtoCNF_Y1_1)),
inference(resolve,[$cnf( r3(X_66,skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y1_1),skolemFOFtoCNF_Y4(X_66,skolemFOFtoCNF_Y1_1)) )],[refute_0_22,refute_0_53]) ).
cnf(refute_0_55,plain,
r3(X_81,skolemFOFtoCNF_Y2_1,skolemFOFtoCNF_Y4(X_81,skolemFOFtoCNF_Y1_1)),
inference(subst,[],[refute_0_54:[bind(X_66,$fot(X_81))]]) ).
cnf(refute_0_56,plain,
( ~ r3(X13,X14,X15)
| X15 = skolemFOFtoCNF_Y22(X13,X14) ),
inference(canonicalize,[],[normalize_0_44]) ).
cnf(refute_0_57,plain,
( ~ r3(X_81,skolemFOFtoCNF_Y2_1,skolemFOFtoCNF_Y4(X_81,skolemFOFtoCNF_Y1_1))
| skolemFOFtoCNF_Y4(X_81,skolemFOFtoCNF_Y1_1) = skolemFOFtoCNF_Y22(X_81,skolemFOFtoCNF_Y2_1) ),
inference(subst,[],[refute_0_56:[bind(X13,$fot(X_81)),bind(X14,$fot(skolemFOFtoCNF_Y2_1)),bind(X15,$fot(skolemFOFtoCNF_Y4(X_81,skolemFOFtoCNF_Y1_1)))]]) ).
cnf(refute_0_58,plain,
skolemFOFtoCNF_Y4(X_81,skolemFOFtoCNF_Y1_1) = skolemFOFtoCNF_Y22(X_81,skolemFOFtoCNF_Y2_1),
inference(resolve,[$cnf( r3(X_81,skolemFOFtoCNF_Y2_1,skolemFOFtoCNF_Y4(X_81,skolemFOFtoCNF_Y1_1)) )],[refute_0_55,refute_0_57]) ).
cnf(refute_0_59,plain,
skolemFOFtoCNF_Y4(X1,skolemFOFtoCNF_Y1_1) = skolemFOFtoCNF_Y22(X1,skolemFOFtoCNF_Y2_1),
inference(subst,[],[refute_0_58:[bind(X_81,$fot(X1))]]) ).
cnf(refute_0_60,plain,
( skolemFOFtoCNF_Y4(X1,skolemFOFtoCNF_Y1_1) != skolemFOFtoCNF_Y22(X1,skolemFOFtoCNF_Y2_1)
| ~ r1(skolemFOFtoCNF_Y22(X1,skolemFOFtoCNF_Y2_1))
| r1(skolemFOFtoCNF_Y4(X1,skolemFOFtoCNF_Y1_1)) ),
introduced(tautology,[equality,[$cnf( ~ r1(skolemFOFtoCNF_Y4(X1,skolemFOFtoCNF_Y1_1)) ),[0],$fot(skolemFOFtoCNF_Y22(X1,skolemFOFtoCNF_Y2_1))]]) ).
cnf(refute_0_61,plain,
( ~ r1(skolemFOFtoCNF_Y22(X1,skolemFOFtoCNF_Y2_1))
| r1(skolemFOFtoCNF_Y4(X1,skolemFOFtoCNF_Y1_1)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y4(X1,skolemFOFtoCNF_Y1_1),skolemFOFtoCNF_Y22(X1,skolemFOFtoCNF_Y2_1)) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
~ r1(skolemFOFtoCNF_Y22(X1,skolemFOFtoCNF_Y2_1)),
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y4(X1,skolemFOFtoCNF_Y1_1)) )],[refute_0_61,refute_0_7]) ).
cnf(refute_0_63,plain,
~ r1(skolemFOFtoCNF_Y22(skolemFOFtoCNF_Y1_1,skolemFOFtoCNF_Y2_1)),
inference(subst,[],[refute_0_62:[bind(X1,$fot(skolemFOFtoCNF_Y1_1))]]) ).
cnf(refute_0_64,plain,
r3(skolemFOFtoCNF_Y3_1,skolemFOFtoCNF_Y2_1,skolemFOFtoCNF_Y1_1),
inference(canonicalize,[],[normalize_0_47]) ).
cnf(refute_0_65,plain,
r1(skolemFOFtoCNF_Y3_1),
inference(canonicalize,[],[normalize_0_48]) ).
cnf(refute_0_66,plain,
( ~ r1(skolemFOFtoCNF_Y3_1)
| skolemFOFtoCNF_Y3_1 = skolemFOFtoCNF_Y24 ),
inference(subst,[],[refute_0_25:[bind(X19,$fot(skolemFOFtoCNF_Y3_1))]]) ).
cnf(refute_0_67,plain,
skolemFOFtoCNF_Y3_1 = skolemFOFtoCNF_Y24,
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y3_1) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
( skolemFOFtoCNF_Y24 != skolemFOFtoCNF_Y1_1
| skolemFOFtoCNF_Y3_1 != skolemFOFtoCNF_Y24
| skolemFOFtoCNF_Y3_1 = skolemFOFtoCNF_Y1_1 ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_Y3_1,skolemFOFtoCNF_Y24) ),[1],$fot(skolemFOFtoCNF_Y1_1)]]) ).
cnf(refute_0_69,plain,
( skolemFOFtoCNF_Y3_1 != skolemFOFtoCNF_Y24
| skolemFOFtoCNF_Y3_1 = skolemFOFtoCNF_Y1_1 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y1_1) )],[refute_0_41,refute_0_68]) ).
cnf(refute_0_70,plain,
skolemFOFtoCNF_Y3_1 = skolemFOFtoCNF_Y1_1,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y3_1,skolemFOFtoCNF_Y24) )],[refute_0_67,refute_0_69]) ).
cnf(refute_0_71,plain,
( skolemFOFtoCNF_Y3_1 != skolemFOFtoCNF_Y1_1
| ~ r3(skolemFOFtoCNF_Y3_1,skolemFOFtoCNF_Y2_1,skolemFOFtoCNF_Y1_1)
| r3(skolemFOFtoCNF_Y1_1,skolemFOFtoCNF_Y2_1,skolemFOFtoCNF_Y1_1) ),
introduced(tautology,[equality,[$cnf( r3(skolemFOFtoCNF_Y3_1,skolemFOFtoCNF_Y2_1,skolemFOFtoCNF_Y1_1) ),[0],$fot(skolemFOFtoCNF_Y1_1)]]) ).
cnf(refute_0_72,plain,
( ~ r3(skolemFOFtoCNF_Y3_1,skolemFOFtoCNF_Y2_1,skolemFOFtoCNF_Y1_1)
| r3(skolemFOFtoCNF_Y1_1,skolemFOFtoCNF_Y2_1,skolemFOFtoCNF_Y1_1) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y3_1,skolemFOFtoCNF_Y1_1) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
r3(skolemFOFtoCNF_Y1_1,skolemFOFtoCNF_Y2_1,skolemFOFtoCNF_Y1_1),
inference(resolve,[$cnf( r3(skolemFOFtoCNF_Y3_1,skolemFOFtoCNF_Y2_1,skolemFOFtoCNF_Y1_1) )],[refute_0_64,refute_0_72]) ).
cnf(refute_0_74,plain,
( ~ r3(skolemFOFtoCNF_Y1_1,skolemFOFtoCNF_Y2_1,skolemFOFtoCNF_Y1_1)
| skolemFOFtoCNF_Y1_1 = skolemFOFtoCNF_Y22(skolemFOFtoCNF_Y1_1,skolemFOFtoCNF_Y2_1) ),
inference(subst,[],[refute_0_56:[bind(X13,$fot(skolemFOFtoCNF_Y1_1)),bind(X14,$fot(skolemFOFtoCNF_Y2_1)),bind(X15,$fot(skolemFOFtoCNF_Y1_1))]]) ).
cnf(refute_0_75,plain,
skolemFOFtoCNF_Y1_1 = skolemFOFtoCNF_Y22(skolemFOFtoCNF_Y1_1,skolemFOFtoCNF_Y2_1),
inference(resolve,[$cnf( r3(skolemFOFtoCNF_Y1_1,skolemFOFtoCNF_Y2_1,skolemFOFtoCNF_Y1_1) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
( skolemFOFtoCNF_Y1_1 != skolemFOFtoCNF_Y22(skolemFOFtoCNF_Y1_1,skolemFOFtoCNF_Y2_1)
| skolemFOFtoCNF_Y22(skolemFOFtoCNF_Y1_1,skolemFOFtoCNF_Y2_1) = skolemFOFtoCNF_Y1_1 ),
inference(subst,[],[refute_0_32:[bind(X,$fot(skolemFOFtoCNF_Y1_1)),bind(Y,$fot(skolemFOFtoCNF_Y22(skolemFOFtoCNF_Y1_1,skolemFOFtoCNF_Y2_1)))]]) ).
cnf(refute_0_77,plain,
skolemFOFtoCNF_Y22(skolemFOFtoCNF_Y1_1,skolemFOFtoCNF_Y2_1) = skolemFOFtoCNF_Y1_1,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y1_1,skolemFOFtoCNF_Y22(skolemFOFtoCNF_Y1_1,skolemFOFtoCNF_Y2_1)) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
( skolemFOFtoCNF_Y22(skolemFOFtoCNF_Y1_1,skolemFOFtoCNF_Y2_1) != skolemFOFtoCNF_Y1_1
| ~ r1(skolemFOFtoCNF_Y1_1)
| r1(skolemFOFtoCNF_Y22(skolemFOFtoCNF_Y1_1,skolemFOFtoCNF_Y2_1)) ),
introduced(tautology,[equality,[$cnf( ~ r1(skolemFOFtoCNF_Y22(skolemFOFtoCNF_Y1_1,skolemFOFtoCNF_Y2_1)) ),[0],$fot(skolemFOFtoCNF_Y1_1)]]) ).
cnf(refute_0_79,plain,
( ~ r1(skolemFOFtoCNF_Y1_1)
| r1(skolemFOFtoCNF_Y22(skolemFOFtoCNF_Y1_1,skolemFOFtoCNF_Y2_1)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y22(skolemFOFtoCNF_Y1_1,skolemFOFtoCNF_Y2_1),skolemFOFtoCNF_Y1_1) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
~ r1(skolemFOFtoCNF_Y1_1),
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y22(skolemFOFtoCNF_Y1_1,skolemFOFtoCNF_Y2_1)) )],[refute_0_79,refute_0_63]) ).
cnf(refute_0_81,plain,
$false,
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y1_1) )],[refute_0_37,refute_0_80]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUN085+2 : TPTP v8.1.0. Released v7.3.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n017.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 06:43:27 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.40
%------------------------------------------------------------------------------