TSTP Solution File: NUN073+2 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUN073+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 16:34:55 EDT 2022
% Result : Theorem 1.24s 1.45s
% Output : CNFRefutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 16
% Syntax : Number of formulae : 99 ( 31 unt; 0 def)
% Number of atoms : 240 ( 92 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 266 ( 125 ~; 95 |; 42 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-1 aty)
% Number of variables : 116 ( 3 sgn 64 !; 22 ?)
% 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_3a,axiom,
! [X3,X10] :
( ! [Y12] :
( ! [Y13] :
( ~ r2(X3,Y13)
| Y13 != Y12 )
| ~ r2(X10,Y12) )
| X3 = X10 ) ).
fof(axiom_7a,axiom,
! [X7,Y10] :
( ! [Y20] :
( ~ r1(Y20)
| Y20 != Y10 )
| ~ r2(X7,Y10) ) ).
fof(oneuneqtwo,conjecture,
! [Y1] :
( ! [Y2] :
( ! [Y4] :
( ~ r1(Y4)
| ~ r2(Y4,Y2) )
| Y2 != Y1 )
| ! [Y3] :
( ! [Y5] :
( ~ r1(Y5)
| ~ r2(Y5,Y3) )
| ~ r2(Y3,Y1) ) ) ).
fof(subgoal_0,plain,
! [Y1] :
( ~ ! [Y2] :
( ! [Y4] :
( ~ r1(Y4)
| ~ r2(Y4,Y2) )
| Y2 != Y1 )
=> ! [Y3] :
( ~ ! [Y5] :
( ~ r1(Y5)
| ~ r2(Y5,Y3) )
=> ~ r2(Y3,Y1) ) ),
inference(strip,[],[oneuneqtwo]) ).
fof(negate_0_0,plain,
~ ! [Y1] :
( ~ ! [Y2] :
( ! [Y4] :
( ~ r1(Y4)
| ~ r2(Y4,Y2) )
| Y2 != Y1 )
=> ! [Y3] :
( ~ ! [Y5] :
( ~ r1(Y5)
| ~ r2(Y5,Y3) )
=> ~ r2(Y3,Y1) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [Y24] :
! [X19] :
( ( X19 != Y24
& ~ r1(X19) )
| ( X19 = Y24
& r1(X19) ) ),
inference(canonicalize,[],[axiom_1]) ).
fof(normalize_0_1,plain,
! [X19] :
( ( X19 != skolemFOFtoCNF_Y24
& ~ r1(X19) )
| ( X19 = skolemFOFtoCNF_Y24
& r1(X19) ) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X19] :
( ( X19 != skolemFOFtoCNF_Y24
& ~ r1(X19) )
| ( X19 = skolemFOFtoCNF_Y24
& r1(X19) ) ),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X19] :
( ( X19 != skolemFOFtoCNF_Y24
| r1(X19) )
& ( ~ r1(X19)
| X19 = skolemFOFtoCNF_Y24 ) ),
inference(clausify,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X19] :
( X19 != skolemFOFtoCNF_Y24
| r1(X19) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
? [Y1] :
( ? [Y2] :
( Y2 = Y1
& ? [Y4] :
( r1(Y4)
& r2(Y4,Y2) ) )
& ? [Y3] :
( r2(Y3,Y1)
& ? [Y5] :
( r1(Y5)
& r2(Y5,Y3) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_6,plain,
( ? [Y2] :
( Y2 = skolemFOFtoCNF_Y1_1
& ? [Y4] :
( r1(Y4)
& r2(Y4,Y2) ) )
& ? [Y3] :
( r2(Y3,skolemFOFtoCNF_Y1_1)
& ? [Y5] :
( r1(Y5)
& r2(Y5,Y3) ) ) ),
inference(skolemize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
? [Y2] :
( Y2 = skolemFOFtoCNF_Y1_1
& ? [Y4] :
( r1(Y4)
& r2(Y4,Y2) ) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
( skolemFOFtoCNF_Y2_1 = skolemFOFtoCNF_Y1_1
& ? [Y4] :
( r1(Y4)
& r2(Y4,skolemFOFtoCNF_Y2_1) ) ),
inference(skolemize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
? [Y4] :
( r1(Y4)
& r2(Y4,skolemFOFtoCNF_Y2_1) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
( r1(skolemFOFtoCNF_Y4_1)
& r2(skolemFOFtoCNF_Y4_1,skolemFOFtoCNF_Y2_1) ),
inference(skolemize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
r2(skolemFOFtoCNF_Y4_1,skolemFOFtoCNF_Y2_1),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
skolemFOFtoCNF_Y2_1 = skolemFOFtoCNF_Y1_1,
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_13,plain,
r1(skolemFOFtoCNF_Y4_1),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_14,plain,
! [X19] :
( ~ r1(X19)
| X19 = skolemFOFtoCNF_Y24 ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_15,plain,
? [Y3] :
( r2(Y3,skolemFOFtoCNF_Y1_1)
& ? [Y5] :
( r1(Y5)
& r2(Y5,Y3) ) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_16,plain,
( r2(skolemFOFtoCNF_Y3_1,skolemFOFtoCNF_Y1_1)
& ? [Y5] :
( r1(Y5)
& r2(Y5,skolemFOFtoCNF_Y3_1) ) ),
inference(skolemize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
r2(skolemFOFtoCNF_Y3_1,skolemFOFtoCNF_Y1_1),
inference(conjunct,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
? [Y5] :
( r1(Y5)
& r2(Y5,skolemFOFtoCNF_Y3_1) ),
inference(conjunct,[],[normalize_0_16]) ).
fof(normalize_0_19,plain,
( r1(skolemFOFtoCNF_Y5_1)
& r2(skolemFOFtoCNF_Y5_1,skolemFOFtoCNF_Y3_1) ),
inference(skolemize,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
r2(skolemFOFtoCNF_Y5_1,skolemFOFtoCNF_Y3_1),
inference(conjunct,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
r1(skolemFOFtoCNF_Y5_1),
inference(conjunct,[],[normalize_0_19]) ).
fof(normalize_0_22,plain,
! [X11] :
? [Y21] :
! [X12] :
( ( X12 != Y21
& ~ r2(X11,X12) )
| ( X12 = Y21
& r2(X11,X12) ) ),
inference(canonicalize,[],[axiom_2]) ).
fof(normalize_0_23,plain,
! [X11] :
? [Y21] :
! [X12] :
( ( X12 != Y21
& ~ r2(X11,X12) )
| ( X12 = Y21
& r2(X11,X12) ) ),
inference(specialize,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
! [X11,X12] :
( ( X12 != skolemFOFtoCNF_Y21(X11)
& ~ r2(X11,X12) )
| ( X12 = skolemFOFtoCNF_Y21(X11)
& r2(X11,X12) ) ),
inference(skolemize,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
! [X11,X12] :
( ( X12 != skolemFOFtoCNF_Y21(X11)
& ~ r2(X11,X12) )
| ( X12 = skolemFOFtoCNF_Y21(X11)
& r2(X11,X12) ) ),
inference(specialize,[],[normalize_0_24]) ).
fof(normalize_0_26,plain,
! [X11,X12] :
( ( X12 != skolemFOFtoCNF_Y21(X11)
| r2(X11,X12) )
& ( ~ r2(X11,X12)
| X12 = skolemFOFtoCNF_Y21(X11) ) ),
inference(clausify,[],[normalize_0_25]) ).
fof(normalize_0_27,plain,
! [X11,X12] :
( ~ r2(X11,X12)
| X12 = skolemFOFtoCNF_Y21(X11) ),
inference(conjunct,[],[normalize_0_26]) ).
fof(normalize_0_28,plain,
! [X10,X3] :
( X3 = X10
| ! [Y12] :
( ~ r2(X10,Y12)
| ! [Y13] :
( Y13 != Y12
| ~ r2(X3,Y13) ) ) ),
inference(canonicalize,[],[axiom_3a]) ).
fof(normalize_0_29,plain,
! [X10,X3] :
( X3 = X10
| ! [Y12] :
( ~ r2(X10,Y12)
| ! [Y13] :
( Y13 != Y12
| ~ r2(X3,Y13) ) ) ),
inference(specialize,[],[normalize_0_28]) ).
fof(normalize_0_30,plain,
! [X10,X3,Y12,Y13] :
( Y13 != Y12
| ~ r2(X10,Y12)
| ~ r2(X3,Y13)
| X3 = X10 ),
inference(clausify,[],[normalize_0_29]) ).
fof(normalize_0_31,plain,
! [X7,Y10] :
( ~ r2(X7,Y10)
| ! [Y20] :
( Y20 != Y10
| ~ r1(Y20) ) ),
inference(canonicalize,[],[axiom_7a]) ).
fof(normalize_0_32,plain,
! [X7,Y10] :
( ~ r2(X7,Y10)
| ! [Y20] :
( Y20 != Y10
| ~ r1(Y20) ) ),
inference(specialize,[],[normalize_0_31]) ).
fof(normalize_0_33,plain,
! [X7,Y10,Y20] :
( Y20 != Y10
| ~ r1(Y20)
| ~ r2(X7,Y10) ),
inference(clausify,[],[normalize_0_32]) ).
cnf(refute_0_0,plain,
( X19 != skolemFOFtoCNF_Y24
| r1(X19) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_1,plain,
( skolemFOFtoCNF_Y24 != skolemFOFtoCNF_Y24
| r1(skolemFOFtoCNF_Y24) ),
inference(subst,[],[refute_0_0:[bind(X19,$fot(skolemFOFtoCNF_Y24))]]) ).
cnf(refute_0_2,plain,
skolemFOFtoCNF_Y24 = skolemFOFtoCNF_Y24,
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_Y24)]]) ).
cnf(refute_0_3,plain,
r1(skolemFOFtoCNF_Y24),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y24) )],[refute_0_2,refute_0_1]) ).
cnf(refute_0_4,plain,
r2(skolemFOFtoCNF_Y4_1,skolemFOFtoCNF_Y2_1),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_5,plain,
skolemFOFtoCNF_Y2_1 = skolemFOFtoCNF_Y1_1,
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_6,plain,
( skolemFOFtoCNF_Y2_1 != skolemFOFtoCNF_Y1_1
| ~ r2(skolemFOFtoCNF_Y4_1,skolemFOFtoCNF_Y2_1)
| r2(skolemFOFtoCNF_Y4_1,skolemFOFtoCNF_Y1_1) ),
introduced(tautology,[equality,[$cnf( r2(skolemFOFtoCNF_Y4_1,skolemFOFtoCNF_Y2_1) ),[1],$fot(skolemFOFtoCNF_Y1_1)]]) ).
cnf(refute_0_7,plain,
( ~ r2(skolemFOFtoCNF_Y4_1,skolemFOFtoCNF_Y2_1)
| r2(skolemFOFtoCNF_Y4_1,skolemFOFtoCNF_Y1_1) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y2_1,skolemFOFtoCNF_Y1_1) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
r2(skolemFOFtoCNF_Y4_1,skolemFOFtoCNF_Y1_1),
inference(resolve,[$cnf( r2(skolemFOFtoCNF_Y4_1,skolemFOFtoCNF_Y2_1) )],[refute_0_4,refute_0_7]) ).
cnf(refute_0_9,plain,
r1(skolemFOFtoCNF_Y4_1),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_10,plain,
( ~ r1(X19)
| X19 = skolemFOFtoCNF_Y24 ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_11,plain,
( ~ r1(skolemFOFtoCNF_Y4_1)
| skolemFOFtoCNF_Y4_1 = skolemFOFtoCNF_Y24 ),
inference(subst,[],[refute_0_10:[bind(X19,$fot(skolemFOFtoCNF_Y4_1))]]) ).
cnf(refute_0_12,plain,
skolemFOFtoCNF_Y4_1 = skolemFOFtoCNF_Y24,
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y4_1) )],[refute_0_9,refute_0_11]) ).
cnf(refute_0_13,plain,
( skolemFOFtoCNF_Y4_1 != skolemFOFtoCNF_Y24
| ~ r2(skolemFOFtoCNF_Y4_1,skolemFOFtoCNF_Y1_1)
| r2(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y1_1) ),
introduced(tautology,[equality,[$cnf( r2(skolemFOFtoCNF_Y4_1,skolemFOFtoCNF_Y1_1) ),[0],$fot(skolemFOFtoCNF_Y24)]]) ).
cnf(refute_0_14,plain,
( ~ r2(skolemFOFtoCNF_Y4_1,skolemFOFtoCNF_Y1_1)
| r2(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y1_1) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y4_1,skolemFOFtoCNF_Y24) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
r2(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y1_1),
inference(resolve,[$cnf( r2(skolemFOFtoCNF_Y4_1,skolemFOFtoCNF_Y1_1) )],[refute_0_8,refute_0_14]) ).
cnf(refute_0_16,plain,
r2(skolemFOFtoCNF_Y3_1,skolemFOFtoCNF_Y1_1),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_17,plain,
r2(skolemFOFtoCNF_Y5_1,skolemFOFtoCNF_Y3_1),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_18,plain,
r1(skolemFOFtoCNF_Y5_1),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_19,plain,
( ~ r1(skolemFOFtoCNF_Y5_1)
| skolemFOFtoCNF_Y5_1 = skolemFOFtoCNF_Y24 ),
inference(subst,[],[refute_0_10:[bind(X19,$fot(skolemFOFtoCNF_Y5_1))]]) ).
cnf(refute_0_20,plain,
skolemFOFtoCNF_Y5_1 = skolemFOFtoCNF_Y24,
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y5_1) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
( skolemFOFtoCNF_Y5_1 != skolemFOFtoCNF_Y24
| ~ r2(skolemFOFtoCNF_Y5_1,skolemFOFtoCNF_Y3_1)
| r2(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y3_1) ),
introduced(tautology,[equality,[$cnf( r2(skolemFOFtoCNF_Y5_1,skolemFOFtoCNF_Y3_1) ),[0],$fot(skolemFOFtoCNF_Y24)]]) ).
cnf(refute_0_22,plain,
( ~ r2(skolemFOFtoCNF_Y5_1,skolemFOFtoCNF_Y3_1)
| r2(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y3_1) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y5_1,skolemFOFtoCNF_Y24) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
r2(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y3_1),
inference(resolve,[$cnf( r2(skolemFOFtoCNF_Y5_1,skolemFOFtoCNF_Y3_1) )],[refute_0_17,refute_0_22]) ).
cnf(refute_0_24,plain,
( ~ r2(X11,X12)
| X12 = skolemFOFtoCNF_Y21(X11) ),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_25,plain,
( ~ r2(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y3_1)
| skolemFOFtoCNF_Y3_1 = skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24) ),
inference(subst,[],[refute_0_24:[bind(X11,$fot(skolemFOFtoCNF_Y24)),bind(X12,$fot(skolemFOFtoCNF_Y3_1))]]) ).
cnf(refute_0_26,plain,
skolemFOFtoCNF_Y3_1 = skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),
inference(resolve,[$cnf( r2(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y3_1) )],[refute_0_23,refute_0_25]) ).
cnf(refute_0_27,plain,
( ~ r2(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y1_1)
| skolemFOFtoCNF_Y1_1 = skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24) ),
inference(subst,[],[refute_0_24:[bind(X11,$fot(skolemFOFtoCNF_Y24)),bind(X12,$fot(skolemFOFtoCNF_Y1_1))]]) ).
cnf(refute_0_28,plain,
skolemFOFtoCNF_Y1_1 = skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),
inference(resolve,[$cnf( r2(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y1_1) )],[refute_0_15,refute_0_27]) ).
cnf(refute_0_29,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_30,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_31,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
( skolemFOFtoCNF_Y1_1 != skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)
| skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24) = skolemFOFtoCNF_Y1_1 ),
inference(subst,[],[refute_0_31:[bind(X,$fot(skolemFOFtoCNF_Y1_1)),bind(Y,$fot(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)))]]) ).
cnf(refute_0_33,plain,
skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24) = skolemFOFtoCNF_Y1_1,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y1_1,skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)) )],[refute_0_28,refute_0_32]) ).
cnf(refute_0_34,plain,
( skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24) != skolemFOFtoCNF_Y1_1
| skolemFOFtoCNF_Y3_1 != skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)
| skolemFOFtoCNF_Y3_1 = skolemFOFtoCNF_Y1_1 ),
introduced(tautology,[equality,[$cnf( $equal(skolemFOFtoCNF_Y3_1,skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)) ),[1],$fot(skolemFOFtoCNF_Y1_1)]]) ).
cnf(refute_0_35,plain,
( skolemFOFtoCNF_Y3_1 != skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)
| skolemFOFtoCNF_Y3_1 = skolemFOFtoCNF_Y1_1 ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24),skolemFOFtoCNF_Y1_1) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
skolemFOFtoCNF_Y3_1 = skolemFOFtoCNF_Y1_1,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y3_1,skolemFOFtoCNF_Y21(skolemFOFtoCNF_Y24)) )],[refute_0_26,refute_0_35]) ).
cnf(refute_0_37,plain,
( skolemFOFtoCNF_Y3_1 != skolemFOFtoCNF_Y1_1
| ~ r2(skolemFOFtoCNF_Y3_1,skolemFOFtoCNF_Y1_1)
| r2(skolemFOFtoCNF_Y1_1,skolemFOFtoCNF_Y1_1) ),
introduced(tautology,[equality,[$cnf( r2(skolemFOFtoCNF_Y3_1,skolemFOFtoCNF_Y1_1) ),[0],$fot(skolemFOFtoCNF_Y1_1)]]) ).
cnf(refute_0_38,plain,
( ~ r2(skolemFOFtoCNF_Y3_1,skolemFOFtoCNF_Y1_1)
| r2(skolemFOFtoCNF_Y1_1,skolemFOFtoCNF_Y1_1) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y3_1,skolemFOFtoCNF_Y1_1) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
r2(skolemFOFtoCNF_Y1_1,skolemFOFtoCNF_Y1_1),
inference(resolve,[$cnf( r2(skolemFOFtoCNF_Y3_1,skolemFOFtoCNF_Y1_1) )],[refute_0_16,refute_0_38]) ).
cnf(refute_0_40,plain,
( Y13 != Y12
| ~ r2(X10,Y12)
| ~ r2(X3,Y13)
| X3 = X10 ),
inference(canonicalize,[],[normalize_0_30]) ).
cnf(refute_0_41,plain,
( Y12 != Y12
| ~ r2(X10,Y12)
| ~ r2(X3,Y12)
| X3 = X10 ),
inference(subst,[],[refute_0_40:[bind(Y13,$fot(Y12))]]) ).
cnf(refute_0_42,plain,
Y12 = Y12,
introduced(tautology,[refl,[$fot(Y12)]]) ).
cnf(refute_0_43,plain,
( ~ r2(X10,Y12)
| ~ r2(X3,Y12)
| X3 = X10 ),
inference(resolve,[$cnf( $equal(Y12,Y12) )],[refute_0_42,refute_0_41]) ).
cnf(refute_0_44,plain,
( ~ r2(X_663,skolemFOFtoCNF_Y1_1)
| ~ r2(skolemFOFtoCNF_Y1_1,skolemFOFtoCNF_Y1_1)
| X_663 = skolemFOFtoCNF_Y1_1 ),
inference(subst,[],[refute_0_43:[bind(X10,$fot(skolemFOFtoCNF_Y1_1)),bind(X3,$fot(X_663)),bind(Y12,$fot(skolemFOFtoCNF_Y1_1))]]) ).
cnf(refute_0_45,plain,
( ~ r2(X_663,skolemFOFtoCNF_Y1_1)
| X_663 = skolemFOFtoCNF_Y1_1 ),
inference(resolve,[$cnf( r2(skolemFOFtoCNF_Y1_1,skolemFOFtoCNF_Y1_1) )],[refute_0_39,refute_0_44]) ).
cnf(refute_0_46,plain,
( ~ r2(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y1_1)
| skolemFOFtoCNF_Y24 = skolemFOFtoCNF_Y1_1 ),
inference(subst,[],[refute_0_45:[bind(X_663,$fot(skolemFOFtoCNF_Y24))]]) ).
cnf(refute_0_47,plain,
skolemFOFtoCNF_Y24 = skolemFOFtoCNF_Y1_1,
inference(resolve,[$cnf( r2(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y1_1) )],[refute_0_15,refute_0_46]) ).
cnf(refute_0_48,plain,
( skolemFOFtoCNF_Y24 != skolemFOFtoCNF_Y1_1
| ~ r1(skolemFOFtoCNF_Y24)
| r1(skolemFOFtoCNF_Y1_1) ),
introduced(tautology,[equality,[$cnf( r1(skolemFOFtoCNF_Y24) ),[0],$fot(skolemFOFtoCNF_Y1_1)]]) ).
cnf(refute_0_49,plain,
( ~ r1(skolemFOFtoCNF_Y24)
| r1(skolemFOFtoCNF_Y1_1) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y1_1) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
r1(skolemFOFtoCNF_Y1_1),
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y24) )],[refute_0_3,refute_0_49]) ).
cnf(refute_0_51,plain,
( Y20 != Y10
| ~ r1(Y20)
| ~ r2(X7,Y10) ),
inference(canonicalize,[],[normalize_0_33]) ).
cnf(refute_0_52,plain,
( Y10 != Y10
| ~ r1(Y10)
| ~ r2(X7,Y10) ),
inference(subst,[],[refute_0_51:[bind(Y20,$fot(Y10))]]) ).
cnf(refute_0_53,plain,
Y10 = Y10,
introduced(tautology,[refl,[$fot(Y10)]]) ).
cnf(refute_0_54,plain,
( ~ r1(Y10)
| ~ r2(X7,Y10) ),
inference(resolve,[$cnf( $equal(Y10,Y10) )],[refute_0_53,refute_0_52]) ).
cnf(refute_0_55,plain,
( ~ r1(skolemFOFtoCNF_Y1_1)
| ~ r2(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y1_1) ),
inference(subst,[],[refute_0_54:[bind(X7,$fot(skolemFOFtoCNF_Y24)),bind(Y10,$fot(skolemFOFtoCNF_Y1_1))]]) ).
cnf(refute_0_56,plain,
~ r1(skolemFOFtoCNF_Y1_1),
inference(resolve,[$cnf( r2(skolemFOFtoCNF_Y24,skolemFOFtoCNF_Y1_1) )],[refute_0_15,refute_0_55]) ).
cnf(refute_0_57,plain,
$false,
inference(resolve,[$cnf( r1(skolemFOFtoCNF_Y1_1) )],[refute_0_50,refute_0_56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUN073+2 : TPTP v8.1.0. Released v7.3.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n027.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Thu Jun 2 06:46:49 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.24/1.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.24/1.45
% 1.24/1.45 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.31/1.46
%------------------------------------------------------------------------------